Posco e&c - Manual of Seismic Steel Connections v1.1

POSCO E&C CO., LTD

MANUAL OF SEISMIC STEEL

CONNECTIONS

By:

Hernán Santa María O., Ph.D.

Associate Professor

Department of Structural and Geotechnical Engineering

Pontificia Universidad Católica de Chile

Camilo De la Barra B.

Civil Engineer, Pontificia Universidad Católica de Chile

Juan José Uribe M., MS.

Civil Engineer, Pontificia Universidad Católica de Chile

April 2012

MANUAL OF SEISMIC STEEL CONNECTIONS

ii

ACKNOWLEDGMENTS

The publication of this Manual was made possible by the financial support of

POSCO E&C. The authors greatly appreciate all the advice by Mr. Jae-Heung

Kim, Mr. Jang Ho Choi and Mr. Rodrigo García, all of them from POSCO E&C.

We wish to thank Javiera De la Barra for her valuable collaboration in

improving the quality of the drawings.

DISCLAIMER

The information presented in this Manual is based in design codes from Chile

and United States, engineering principles, and current construction and design

practice, and is for general information only. Under no circumstances does

DICTUC S.A. warrant or certify that the information contained here is free of

errors or deficiencies of any kind.

All the examples solved in this Manual refer to specific codes and standards.

Codes are often modified, so the users of this material have to be aware of the

codes that are in force at the time the Manual is used. Any reader of this

Manual assumes all the responsibility that comes from its use.

This manual may be changed at any time. Staff is encouraged to review this

manual periodically and suggest changes to keep the manual current and to

minimize differences between the manual and actual practices.

The origin of all the specific information, figures, and tables is properly

referenced inside this Manual. Before publishing a hard copy of this Manual, it

shall be verified that the use of the referenced information does not infringe

copyright.

Manual of Seismic Steel Connections Vs. 1.0

April 2012


iii

CONTENTS

1. Introduction

2. General information

2.1. Design Codes.

2.2. Material Properties.

2.3. Comments on the performance of steel structures during the

February 27th Chile Earthquake.

2.4. Bolted Connections.

2.5. Welded Connections.

2.6. Notation used on the manual.

2.7. Units used on the manual.

3. Base Plate Connections

3.1. Design Requirements.

3.2. Recommendations from AISC Manual of Steel Construction (13th Ed.).

3.3. Example.

3.4. References.

4. Brace Connections

4.1. General Description of Seismic Braced Frames.

4.2. Code Requirements for Braced Frames Connections, Design Forces

and Recommendations.

4.3. Discussion of some typical bracing connection cases.

4.4. References

4.5. Example: Brace to Beam-Column Connection.

4.6. V-brace to Beam Connection (at Beam Midspan).


iv

5. Shear Connections

5.1. Shear tab beam-to-column connection (single plate connection).

5.2. Shear single angle beam-to-column connection.

5.3. Shear double angle beam-to-column connection.

5.4. Shear single angle beam-to-beam connection.

5.5. Shear double angle beam-to-beam connection.

5.6. Shear Stiffened Seated beam-to-column connection.

5.7. Shear Unstiffened Seated beam-to-column connection.

6. Moment Connections

6.1. Bolted Extended End-Plate Moment Connection (unstiffened case).

6.2. Bolted Extended End-Plate Moment Connection (stiffened case).

6.3. Reduced Beam Section (RBS) Moment Connection.

6.4. Bolted Flange Plate Moment Connection.

6.5. Welded Unreinforced Flange-Welded Moment Connection.

6.6. Welded Connection Commentary for Continuity Plates and Doubler

Plates.

7.Columns Splices

7.1. Bolted Column Splice for SBCF.

7.2. Bolted Column Splice for SMF.

7.3. Welded Column Splice for SCBF.

7.4. Welded Column Splice for SMF.

8. Beam Splices

8.1. Beam Parallel Splice – All Bolted Splice Plates.

8.2. Beam Parallel Splice – Bolted End Plate.


v

9. Stoppers

9.1. Up-lift Clamps.

9.2. Lateral Stoppers.

10. Support of Equipment

10.1. Calculation of Seismic Forces on Equipment.

10.2. Skid-Mounted Equipment.

10.3. Post-Installed Anchor Bolts.

11. Expansion Joints

12. Cranes


vi

THIS PAGE INTENTIONALLY LEFT BLANK

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 1: INTRODUCTION

1-1

1. INTRODUCTION

The response of steel structures subjected to loads and deformations produced

by earthquakes is strongly dependant on the behavior of the connections. The

ductility of the structure, the total strength of the system, the deformation

capacity, the easiness of identifying damage and later repairing, the level of

inelastic incursions (or having a completely elastic response) are

characteristics highly dependent of the solution given to the connections of the

steel members.

The intention of this manual is to present the current design procedures for

connections for different members of steel buildings and to show the minimum

design checks that must be done for a correct design of those connections.

The currently available design methods are the Allowable Stress Design (ASD)

method and the Load and Resistance Factor Design (LRFD) method. The LRFD

method has been used in Europe, Canada and United States for a number of

years. Also, the American Institute of Steel Construction (AISC), the

organization that prepares the specifications for structural design of steel

buildings, has decided to favor LRFD over ASD. Therefore, in this Manual all

examples are developed using LRFD.

It was preferred to use the International System of Units (SI) because it is

mandatory in the current Chilean standards.

1.1 Contents

The manual is organized into 12 chapters. The first two chapters present a

general description of the design standards and the materials used. Chapters 3

through 8 show the description of different types of connections and design

procedures. Examples are developed for each case, using the international or

the Chilean standards. In Chapters 9 to 12 special cases are discussed, but no

examples are solved.

All the chapters with solved examples of connections have a similar structure:

first, the requirements from international and Chilean design codes are

discussed; then, the design of a connection is proposed and solved; the design

is performed using an international design code, but the effects of the Chilean

code in the final design are always included for discussion; finally, the resulting

design is summarized. In some examples the design forces are taken from the

most stringent conditions between Chilean and international design provisions.

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 1: INTRODUCTION

1-2

The chapters are as follows:

Chapter 1 – Introduction.

Chapter 2 – General information.

Chapter 3 – Base plates.

Chapter 4 – Brace connections.

Chapter 5 – Shear connections.

Chapter 6 – Moment connections.

Chapter 7 – Column splices.

Chapter 8 – Beam splices.

Chapter 9 – Stoppers, which includes up-lift clamps and lateral stoppers.

Chapter 10 – Support of equipments.

Chapter 11 – Expansion Joints.

Chapter 12 – Cranes.

In Chapter 2, general information about current international and Chilean

design standards, properties of typical steels used in construction, and a

description of the performance of steel structures during the February 27th,

2010 Chile earthquake, using available public information, are provided.

In Chapter 4, besides examples of brace connections, a discussion of the load

paths through the connection is made and is pointed out the attention that

have to be paid on several topics when designing these connections.

In Chapter 6, five moment beam-to-column connections are described and

examples are solved using international standards. Also, the discussion for a

typical moment beam-to-column connection (Bolted Flange Plate) is shown,

based in the requirements of the Chilean standard.

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 2: GENERAL INFORMATION

2-1

2. GENERAL INFORMATION

In this chapter is summarized general information needed to design

connections in steel structures. The information corresponds to a brief

description of the structural design codes that are used along this manual, a

description of the Chilean and international standards that are used to

characterize the main types of steels used for structural steel construction, and

a summary of the observed performance of steel structures during the 2010

Chile earthquake. Also, brief sections containing information of bolts and welds

for connections, as well as two sections for the general notation and units used

in this manual, are included.

The international codes refer to the standards used in the United States. Those

were chosen because important parts of the Chilean codes are based in the

specifications written by the American Institute of Steel Construction (AISC).

2.1 Design codes

2.1.a. International codes

The main specifications used for steel design in the United States, and that are

widely used in many countries, are the following:

ANSI/AISC 360-05 Specification for Structural Steel Buildings

This standard sets criteria for the design of structural steel buildings and other

structures, which are designed, fabricated, and erected with vertical and

horizontal members that are typical of buildings. It combines the Allowable

Stress Design (ASD) and Load and Resistance Factor Design (LRFD) methods

by defining the way in which the strength is calculated for a given limit state,

and the corresponding values of the safety factor and the resistance factor .

ANSI/AISC 341-05 Seismic Provisions for Structural Steel Buildings

This standard addresses the design and construction of structural steel

buildings located in high risk seismic zones.


2-2

ANSI/AISC 358-05 Prequalified Connections for Special and Intermediate Steel

Moment Frames for Seismic Applications

This Standard specifies design and detailing criteria for connections in

accordance with the AISC Seismic Provisions for Structural Steel Buildings for

use with special moment frames (SMF) and intermediate moment frames

(IMF). All these connections are prequalified, meaning that the connections

can provide the required inter-story drifts that SMF and IMF systems may

sustain. Other connections can be used if satisfactory evidence of adequate

performance is provided, in accordance with Appendix S of the AISC Seismic

Provisions.

2.1.b. Chilean codes

The Chilean codes related to seismic design of steel constructions are the

following:

NCh427.cR1977 Construction – Specifications for the design of steel structures

for building

This standard specifies the procedures for the design of steel structures for

buildings and also specifies the minimum resistance that the members and

connections must meet. Being a very old standard, is in a review process, and

it is not currently used in building design.

NCh433.Of1996 Modified in 2009 – Earthquake resistant design of buildings

This standard defines the requirements for the design of earthquake-resistant

buildings, equipments and other secondary buildings. It is not applied to

industrial.

Appendix B specifies that, while there is no official version for the design and

construction of steel buildings, the following standards must be used:

a) Specification for Structural Steel Buildings, American Institute of Steel

Construction 2005 (ANSI/AISC 360-05), for the design of the steel

members.

b) Regarding seismic design, the Seismic Provisions for Structural Steel

Buildings, American Institute of Steel Construction 2005 (ANSI/AISC

341-05), must be used. To apply this standard, the R and Ro values

taken from Table 5.1 of NCh433 should be the ones corresponding to


2-3

Special Moment Frames (SMF) or Special Concentric Brace Frames

(SCBF). Those R and Ro values can be used only in steel structures

designed according to ANSI/AISC 341-05 and ANSI/AISC 341-05.

In 2011, as a result of modifications due to the effects of the 2010 Chile

earthquake in buildings, new regulations for earthquake-design were adopted.

The new regulations introduced modifications in the definition of the

geotechnical parameters, the design spectra and the calculation of seismic

deformations. For all other requirements NCh433.Of1996 Modified in 2009

must be used.

NCh2369.Of2003 – Earthquake-resistant design of industrial structures and

facilities

This standard defines the requirements for the earthquake-resistant design of

industrial structures and facilities. It must be applied to the structures as well

as ducts and pipes and mechanical and electrical equipment, including their

anchors. It also applies to buildings structured by columns fixed to the base.

The basic objectives of the code are:

a) Life must be protected: protect life by avoiding the collapse of the

structure during earthquakes more severe than the design

earthquake; by preventing fires, explosions, or gas leaks; by

protecting the environment; and by guaranteeing the safe operation

of escape routes.

b) Maintain the continuity of operation of the industry: keep the

essential processes and services; minimize the stoppage time of the

industry; facilitate the inspection and repair of the damaged members

and connections.

To avoid collapse, the structures should have large strength and/or large

capacity to absorb energy, beyond the elastic limit of the material. To achieve

the former the structural system should be able to:

a) Ensure ductile behavior of elements and connections, and avoid

failures due to instability or brittle behavior, or ensure elastic

response of the structure.

b) Provide redundancy to the earthquake resistant system.


2-4

c) Avoid asymmetry and unneeded complexity of the structure.

To avoid stoppage of operation of the industry, the structure must also meet

the following requirements during an earthquake more severe than the design

earthquake.

d) Limit incursions in non-elastic behavior, if those are going to stop

operation of the industry.

e) All damage must occur at places that are visible and accessible.

f) Emergency and control equipment shall be properly qualified

according to international standards, with the approval of the process

engineers and specialists.

Chapter 8 of the standard defines special requirements for steel structures.

While there is no official version of a standard for the design and construction

of steel buildings, the following standards must be used in addition with

NCh23609.Of2003 design provisions:

a) Load and Resistance Factor Design Specifications for Structural Steel

Buildings, American Institute of Steel Construction 1999 (AISC 360-

99), for the design of the steel members.

b) Regarding seismic design, the Seismic Provisions for Structural Steel

Buildings, Part 1: Structural Steel Buildings, American Institute of

Steel Construction 1999 (AISC 341-99), must be used. Alternatively,

all provisions from chapter 8 and Annex B of NCh2369.Of2003 can be

used.

NCh3171.Of2010 – Structural design - General dispositions and combinations

of load

This standard defines the load combinations that must used for calculating the

required resistances of structural members. This standard has to be used

together with NCh433.Of1996 Modified in 2009. The load combinations for

designing industrial facilities are defined in NCh2369.Of2003.


2-5

2.2 Material properties

Steel is an alloy composed mostly of iron and small quantities of carbon.

Changes in the amount of carbon produce changes in strength, ductility and

hardness of steel. Properties of steel can also be changed by including copper,

chromium, manganese, nickel, silicon, vanadium, among others. Carbon steels

contain no more than 1.7% of carbon, and copper, manganese and silicon in

limited quantities. Structural steels for buildings are of the mild carbon type,

which is defined as carbon steel with a carbon content of 0.30 to 0.59%.

Other types of steels used for construction are high-strength low-alloy steels

and alloy-steels. These steels have larger amounts of additional chemical

elements such as chromium, molybdenum, nickel, titanium, vanadium, in

order to, for example, obtain better corrosion resistance, higher strength and

higher toughness.

The chemical composition of the steel, as well as mechanical properties such

as yield strength, ultimate strength, deformation capacity, are defined in

various standards. The American Society for Testing Materials (ASTM) has

defined several types of steel for use in buildings:

A36 Standard Specification for Carbon Structural Steel

A242 Standard Specification for High-Strength Low-Alloy Structural Steel

A529 Standard Specification for High-Strength Carbon-Manganese Steel of

Structural Quality

A572 Standard Specification for High-Strength Low-Alloy Columbium-

Vanadium Structural Steel

A514 Standard Specification for High-Yield-Strength, Quenched and

Tempered Alloy Steel Plate, Suitable for Welding

A588 Standard Specification for High-Strength Low-Alloy Structural Steel,

up to 50 ksi [345 MPa] Minimum Yield Point, with Atmospheric

Corrosion Resistance

A992 Standard Specification for Structural Steel Shapes

A1043 Standard Specification for Structural Steel with Low Yield to Tensile

Ratio for Use in Buildings

A1077 Standard Specification for Structural Steel with Improved Yield

Strength at High Temperature for Use in Buildings

The most commonly used steel is A36. The yield and tensile strengths of some

of the steels mentioned above are shown in Table 2.2-1.

http://www.astm.org/Standards/A36.htm

















2-6

Designation

Minimum yield

strength (Fy) (ksi)

Tensile strength (Fu)

(ksi) Steel type

A36 32 58 to 80

Carbon steel 36 58 to 80

A529 Gr42 42 60 to 85 Carbon steel

A529 Gr50 50 70 to 100

A572 Gr42 42 60

High-strength low-alloy steel

A572 Gr50 50 65

A572 Gr60 60 75

A572 Gr65 65 80

A242 42 63 High-strength low-alloy steel

A588 42 63 High-strength low-alloy steel

A992 50 to 65 65 High-strength low-alloy steel

Table 2.2-1: Structural steels defined by ASTM.

In Chile only one standard defines the steel for building construction,

NCh203.Of2006 Structural steel - Requirements. This standard defines the

requirements that the different types of steels for building (carbon steel, alloy-

steels, or high-strength low-alloy steels) must meet. Two general types of

steels are defined: structural steel for general construction and structural steel

for constructions subjected to dynamic loads. A dynamic load refers to seismic

loading or any other type of dynamic loads. The yield and tensile strengths of

steels defined in Chile are shown in Table 2.2-2.


2-7

Designation

Minimum yield

strength (Fy) (MPa)

Tensile strength (Fu)

(MPa) Steel type

A240ES 240 360 to 460 Carbon steel



M345ES 345 510 to 610 Alloy-steel

Y345ES 345 480 High-strength

low-alloy steel

A250ESP 250 to 350 400 to 550 Carbon steel

A345ESP 345 to 450 450 Carbon steel

Table 2.2-2: Structural steels defined in NCh203.Of2006.

Additional requirements for steel are defined in NCh2369.Of2003, Section

8.2.1.

Only A250ESP and A345ESP steels can be used for seismic design. These

steels must meet some special requirements:

- The maximum allowable value of the ratio Fy/Fu is 0.85.

- Yield strength less than 450 MPa.

- A minimum elongation in 50 mm of 20%.

- Minimum toughness of 27 J at 21°C, with the Charpy test, ASTM6.

- Guaranteed weldability.

ASTM A36 and ASTM A572 Gr 50 are steels similar to A250ESP and A345ESP,

respectively. This does not mean that are equivalent. Equivalency must be

checked, taking into account the requirements listed above. Table C.1 of

NCh203.Of2006 presents a list of verifications that must be performed to

verify equivalency. ASTM A992 (Gr50) complies with the requirements from

the Chilean standards.


2-8

2.3 Comments on the performance of steel structures during the

February 27th Chile Earthquake

On February 27th, 2010, the large Maule earthquake (Mw = 8.8) that affected

Chile was strongly felt at least from Temuco to La Ligua (USGS, 2010), in a

length of about 700 km. The area subjected to large ground shaking is

occupied by 75% of the total country population and three of the largest

population and industrial centers: Santiago, Concepción-Talcahuano, and

Valparaíso-Viña del Mar. About 370.000 houses were damaged or destroyed;

25 bridges collapsed (Hube et al. 2010); ports were damaged due to

liquefaction and lateral spreading (EERI, 2010).

Most of the steel structures in Chile are industrial facilities. Steel buildings for

other uses, like office space or parking garages, which must be designed using

NCh433, are rare. Therefore, most of the structures designed after 2003 were

designed using the seismic design code for industrial facilities, NCh2369,

rather than using NCh433.

Even though access to industrial facilities was limited, the observations by

Cruz and Valdivia (2011) and by Herrera et al. (2012) allow drawing

conclusions regarding the performance of steel industrial structures during the

2010 Chile earthquake.

A significant number of different types of industrial structures were located in

the affected area. The damage described by Cruz and Valdivia (2011) shows

that in power plants fragile components of electrical substation equipment

failed, but were promptly replaced; damage in under-designed or poorly

detailed connections; damage in older structures, like large deformations of

the stoppers; some rotation of shallow foundations of equipment.

Most of the large steel structures that support heavy equipment, like a steam

generating boiler or a large diameter pipe, showed very little damage.

Evidence was found of large displacements at seismic stoppers of large heavy

equipment.

Some mechanical or electrical equipment, with anchors with no adequate

seismic design, suffered of a bad performance. Also, an often found damage

occurred at concrete pedestals with poor design and detailing.

It is very important to notice that, in general, engineered steel structures

designed according to the latest design codes, and constructed using standard


2-9

construction practices, performed well. Damage was limited mostly to older

structures or to structures that did not comply with the current seismic codes.

Also, it is proposed that the adequate performance of steel structures was the

result of over strength rather than ductility, which is a consequence of the

application of the seismic code provisions used to design those structures.

References

Cruz, E. F., and Valdivia, D., (2011). Performance of industrial

facilities in the Chilean earthquake of 27 February 2010, Structural

Design Tall Special Buildings, 20, pg. 83–101.

Earthquake Engineering Research Institute (EERI), (2010). EERI

Special Earthquake Report—June 2010. EERI Newsletter Suppl.

Herrera, R. A., Beltran, J.F., Aguirre, C., and Verdugo, A., (2012).

Seismic performance of steel structures during the 2010 Maule

earthquake, STESSA 2012, Edited by Federico Mazzolani and Ricardo

Herrera, CRC Press 2011, Pages 37–43.

Hube M., Santa María H., Villalobos F., (2010) Preliminary analisys of the seismic response of bridges during the Chilean 27 February earthquake. Obras y Proyectos,Nº8, p. 48-57.

USGS. Magnitude 8.8 – Offshore Bio-Bio, Chile. Retrieved April 15th,

2012, from:

http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010tf

an/

http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010tfan/

http://earthquake.usgs.gov/earthquakes/eqinthenews/2010/us2010tfan/


2-10



2-11

2.4. Bolted connections

In bolted connections, the transmission of forces is made by the action of the

bolts, through shear action of the shank, bearing of the bolt against the

connected steel plates, or by friction induced by pretension of the bolts. The

typical configuration of a bolt is shown in Figure 2.4-1.

Figure 2.4-1: Bolt parts.

2.4.a. Commonly used bolts

AISC360-05 authorizes the use of ASTM A325 or ASTM A490 high-strength

bolts.

1. Bolt sizes

AISC360-05 gives the size of bolts in United States and S.I. units.

AISC Bolts: North American and metric bolts

North American bolts Metric bolts

Dimension

(in)

Approx.

Diameter (mm)

Approx.

Gross Area (mm2)

Dimension Diameter

(mm)

Approx.

Gross Area (mm2)

½ 13 127 -

5/8 16 198 M16 16 201

¾ 19 285 M20 20 314

7/8 22 388 M22 22 380

1 25 507 M24 24 452

1 1/8 29 641 M27 27 573

1 ¼ 32 792 M30 30 707

1 3/8 35 958 M36 36 1018

1 ½ 38 1140 -

Table 2.4-1: Gross section area for commonly used bolts.

United States and S.I. units.


2-12

2. Holes

The following table for Nominal Hole Dimensions in mm for various bolt

diameters is taken from AISC 360-05 Specification, table J3.3M.

Nominal Hole Dimensions (mm) - Table J3.3M of AISC 360-05 Specification

Bolt diameter

Hole Dimensions

Standard

(Dia.)

Oversize

(Dia.)

Short-Slot

(Width x Length)

Long-Slot

(Width x Length)

M16 18 20 18 x 22 18 x 40

M20 22 24 22 x 26 22 x 50

M22 24 28 24 x 30 24 x 55

M24 27(a) 30 27 x 32 27 x 60

M27 30 35 30 x 37 30 x 67

M30 33 38 33 x 40 33 x 75

>= M36 d + 3 d + 8 (d + 3) x (d + 10) (d+3) x 2.5d

(a) Clearance provided allows the use of a 1-in. bolt if desirable

Table 2.4-2: Nominal Hole Dimensions (mm) for several bolt diameters (mm).

Re. AISC360-05 Specification, table J3.3M

These standard hole-diameters are used for all hole related limit states, except

tear out.

For the use of standard holes, oversized holes, short-slotted holes and long-

slotted holes; see AISC360-05 Specification, chapter J, section J.3. “Bolts and

threaded parts”, sub-section 2. “Size and Use of Holes”.


2-13

3. Minimum Bolt Pretension:

According to AISC360-05 Specification, table J3.1M:

Minimum Bolt Pretension (kN) - Table J3.1M of AISC 360-05 Specification

Bolt size (mm) A325M Bolts A490M Bolts

M16 91 114

M20 142 179

M22 176 221

M24 205 257

M27 267 334

M30 326 408

M36 475 595

Table 2.4-3: Minimum Bolt Pretension (kN) for several bolt diameters (mm).

Re. AISC360-05 Specification, table J3.1M.

Note: this pretension is equal to 70% of the minimum tensile strength of bolts, rounded off to nearest kN, as specified in ASTM specification for A325M and

A490M bolts with UNC.

4. Nominal Strength of bolts:

According to AISC360-05 , table J3.2, for bearing and slip-critical connections:

A325-High-Strength Bolts:

Nominal Tensile Stress: 𝐹𝑛𝑡 = 620 𝑀𝑃𝑎

Nominal Shear Stress in Bearing-Type Connections (threads not excluded from

shear planes): 𝐹𝑛𝑣 = 330 𝑀𝑃𝑎

Nominal Shear Stress in Bearing-Type Connections (threads excluded from



2-14

A490-High-Strength Bolts:

Nominal Tensile Stress: 𝐹𝑛𝑡 = 780 𝑀𝑃𝑎

Nominal Shear Stress in Bearing-Type Connections (threads not excluded from


Nominal Shear Stress in Bearing-Type Connections (threads excluded from


Tip

It is always conservative to consider for bearing type connections threads not

excluded from shear planes.

2.4.b. Bolt detailing

1. Minimum Spacing

According to AISC360-05 Specification, J.3.3,the distance between centers of

standard, oversized or slotted holes, shall not be less than 8

3𝑑 ,𝑑 = nominal

diameter of the fastener. It is preferred to use a distance of 3𝑑.

2. Minimum Edge Distance

According to AISC360-05 Specification, J.3.4, the distance from the center of a

standard hole to an edge of a connected part in any direction shall not be less

than, either the applicable value from table J3.4M or, as required in Section

J3.10.


2-15

Minimum Edge Distance(a), mm, from center of standard hole(b) to edge of

connected part. Table J3.4 M of AISC 360-05 Specification

Bolt Diameter (mm) At sheared edges

At rolled edges of plates,

shapes or bars,

or thermally cut edges(c)

16 28 22

20 34 26

22 38(d) 28

24 42(d) 30

27 48 34

30 52 38

36 64 46

Over 36 1.75d 1.25

Notes: (a) Smaller edge distances are permitted to be used provided section J3.10 of AISC 360-05, as

appropriate, is satisfied. (b) For oversized or slotted holes, see table J3.5M of AISC 360-05. (c) All edge

distances are permitted to be reduced by 3 mm when the hole is at a point where required strength does

not exceed 25 percent of the maximum strength in the element. (d) It is permitted to have 32 mm at the

ends of the beam connection angles and shear end plates.

Table 2.4-4: Minimum edge distance (mm) from center of standard hole to edge of connected part, for several bolt diameters (mm). Re. AISC360-05

Specification, table J3.4M.

3. Maximum Spacing and Edge Distance

According to AISC360-05, J.3.5, the maximum distance from the center of any

bolt or rivet to the nearest edge of parts in contact shall be 12 times the

thickness of the connected part under consideration, but shall not exceed 150

mm. The longitudinal spacing of fasteners between elements that are in

continuous contact consisting of a plate and a shape or two plates shall be as

follows:

a) For painted members or unpainted members not subject to corrosion,

the spacing shall not exceed 24 times of the thickness of the thinner

plate or 305 mm

b) For unpainted members of weathering steel subject to atmospheric

corrosion, the spacing shall not exceed 14 times the thickness of the

thinner plate or 180 mm.


2-16

4. Usual Minimum Free Distances

Taking into account the previous information and Chilean practice, the

following table shows the minimum spacing between bolts centers and

minimum edge distances:

Typical minimum bolt spacing and edge distances (Chilean

Practice)

e1 e2

e3 e4

a b c a b c

3d 3d 1,75d 1,5d 1,25d 1,5d 1,25d 1,25d

Table 2.4-5: Usual minimum distances between bolts and plates edges

(Re. ICHA Manual for the Design of Steel Structures, Table 3-1)

Where

a = edges cutted with scissors or torch,

b = parts with edged plates mill and with brushed edges,

c = parts with edged plates mill.

A scheme to be used with the table above is presented:

Ru


2-17

Usual gage and other recommended dimensions:

(Re. ICHA Manual for the Design of Steel Structures):

Flanges Cold Formed Angles Rolled Angles

H or B

(mm)

Thickness Gages Diameters Gage Diameter

emáx

(mm)

g

(mm)

g1

(mm)

g2

(mm)

dmáx

(mm)

d1máx

(mm)

g

(mm)

dmáx

(mm)

25 3 15 - - 6 - 15 6

30 3 19 - - 6 - 19 8

35 3 22 - - 6 - - -

40 3,5 25 - - 8 - 25 10

45 4,5 30 - - 8 - - -

50 5 30 - - 10 - 30 10

55 6 35 - - 10 - - -

60 6 35 - - 12 - - -

65 6 40 - - 14 - 35 16

70 6 40 - - 16 - - -

75 8 50 - - 16 - - -

80 8 50 - - 16 - 45 22

90 8 55 - - 20 - - -

100 10 60 - - 24 - 55 27

125 12 70 60 40 24 14 - -

150 14 80 70 50 27 18 - -

175 16 90 80 60 27 20 - -

200 18 100 90 70 30 24 - -

Table 2.4-6: Gages: Angle cross sections – Cold formed and Rolled Shapes. (Re. ICHA Manual for the Design of Steel Structures, Table 3-1-a)


2-18

The following figures show the terms used in Table 2.4-6 (cold formed and

rolled angles respectively):

Cold formed sections, stiffened flanges:

Gage type Recommended gages Maximum diameter of bolt

Simple (1 hole) g >= 3e + 1,5d.

Preferably use g = B/2 B/3 -2e

Double (2 holes) g1>= 3e + 1,5d. g2 >= 2,67d.

Preferably use g2 >= 3d

(B-6e)/5,67

Multiple (n holes) 3(B-6e)/(8n +1)

Table 2.4-7: Recommended gages for folded shapes with stiffened flanges. (Re. ICHA Manual for the Design of Steel Structures, Table 3-1-b)

Following figures show the terms used in Table 2.4-7:


2-19

5. Entering and tightening clearance (in) for conventional bolts

(Re. AISC Manual of Steel Construction, 13th Ed. Table 7-16)

When an impact wrench is used, the following minimum clearances are

required:

Aligned bolts:

Entering and tightening Clearance (in.) - Aligned ASTM A325 and A490 Bolts

Nominal Bolt

Dia. Socket Dia. H1 H2 C1 C2

C3

Circular Clipped

5/8 1 3/4 25/64 1 1/4 1 1 11/16 11/16 9/16

3/4 2 1/4 15/32 1 3/8 1 1/4 3/4 3/4 11/16

7/8 2 1/2 35/64 1 1/2 1 3/8 7/8 7/8 13/16

1 2 5/8 39/64 1 5/8 1 7/16 15/16 1 7/8

1 1/8 2 7/8 11/16 1 7/8 1 9/16 1 1/6 1 1/8 1

1 1/4 3 1/8 25/32 2 1 11/16 1 1/8 1 1/4 1 1/8

1 3/8 3 1/4 27/32 2 1/8 1 3/4 1 1/4 1 3/8 1 1/4

1 1/2 3 1/2 15/16 2 1/4 1 7/8 1 5/16 1 1/2 1 5/16

Table 2.4-8: Entering and tightening clearance for aligned ASTM A325 and

A490 Bolts. The following figure shows the terms of Table 2.4-8:

C2

H2

C1

H2

H1

C1

C2

C3

fillet


2-20

Staggered bolts:

F

Stagger P (in.)

Nominal Bolt Diameter (in.)

5/8 3/4 7/8 1 1 1/8 1 1/4 1 3/8 1 1/2

1 1 5/8

1 1/8 1 1/2

1 1/4 1 1/2 1 15/16

1 3/8 1 7/16 1 7/8 2 3/16

1 1/2 1 1/4 1 13/16 2 1/8 2 5/16

1 5/8 1 1/4 1 3/4 2 1/16 2 5/16 2 9/16

1 3/4 1 3/16 1 11/16 2 2 1/4 2 9/16 2 13/16 3

1 7/8 1 1/8 1 9/16 1 15/16 2 3/16 2 1/2 2 3/4 3 3 3/4

2 1 1 1/2 1 13/16 2 1/8 2 7/16 2 3/4 2 15/16 3 1/4

2 1/8 13/16 1 3/8 1 11/16 2 2 3/8 2 11/16 2 15/16 3 3/16

2 1/4

1 1/4 1 9/16 1 7/8 2 1/4 2 5/8 2 7/8 3 3/16

2 3/8

1 1/8 1 1/2 1 3/4 2 1/8 2 1/2 2 13/16 3 1/8

2 1/2

7/8 1 3/8 1 5/8 2 2 7/16 2 3/4 3 1/16

2 5/8

1 3/16 1 1/2 1 15/16 2 5/16 2 7/8 3

2 3/4

15/16 1 3/8 1 7/8 2 1/8 2 1/2 2 7/8

2 7/8

1 3/16 1 3/4 2 1/16 2 3/8 2 13/16

3

7/8 1 5/8 2 2 1/4 2 11/16

3 1/8

1 1/2 1 7/8 2 1/8 2 1/2

3 1/4

1 1/4 1 3/4 2 2 3/8

3 3/8

15/16 1 5/8 1 15/16 2 1/4

3 1/2

1 3/8 1 3/4 2 1/8

3 5/8

1 1/16 1 9/16 2

3 3/4

1 5/16 1 7/8

3 7/8

1 11/16

4

1 3/8

Table 2.4-9: Entering and tightening clearance for staggered ASTM A325 and A490 Bolts.


2-21

Where

H1: height of the head.

H2: maximum shank extension (based on the use of one ASTM F436 washer).

C1: clearance for tightening.

C2: clearance for entering.

C3: clearance for fillet (based on the use of one ASTM F436 washer).

P: bolt stagger.

F: clearance for tightening staggered bolts.

The following figure defines the terms of Table 2.4-9:

2.4.c. Limit States in Bolted Joints

1. Shear and Tensile Strength

See AISC360-05 Specification, J3.6.

2. Combined Shear and Tension

a) In Bearing Type Connections: see AISC360-05 Specification, J3.7.

b) In Slip-Critical Connections: see AISC360-05 Specification, J3.9.

C1

P

F

Cf = tightening

clearance

standard

socket


2-22

3. Bearing


4. Slip Resistance


5. Connected elements (or plates)

For affected elements of members and connecting elements, see J.4 of

AISC360-05 Specification. In that case the limit states are:

- Strength of Elements in Tension (J.4.1)

- Strength of Elements in Shear (J.4.2)

- Block Shear Strength (J.4.3)

- Strength of Elements in Compression (J.4.4)

2.4.d. Seismic Requirements for Bolted Joints:

1. AISC341-05 Seismic Provision Requirements

For bolted joints, see section 7.2:

All bolts shall be high-strength bolts.

All bolts shall meet the requirements for slip-critical faying surfaces

(class A).

Standard or slotted-short holes perpendicular to the force action shall

be used.

See section 7.2 for special provisions for braces and prequalified

moment connections

The available shear strength of bolted joints using standard holes,

shall be calculated according to AISC360-05 J.3.7 and J.3.10 (bearing

type), except that the nominal bearing strength at bolt holes shall not

be taken greater than 2.4𝑑𝑡𝐹𝑢.

Important: Bolts and welds shall not be designed to share force in a joint or

the same force component in a connection.


2-23

2. NCh2369.Of2003 Code Requirements

For bolted joints, according to section 8.5.1, bolts for seismic constructions

shall be type ASTM A325 or ASTM A490 (or equivalent).

According to section 8.5.6, bolts for seismic constructions shall have the

adequate pretension for slip-critical type union. However, the strength of

bolted connections can be calculated as the strength corresponding to bearing

type unions.

2.4.e. References

Arze, Reciné y Asociados, Ingenieros Consultores, 2000. “Manual de

Diseño para Estructuras de Acero” (ICHA Manual for the Design of

Steel Structures). Instituto Chileno del Acero (ICHA), Santiago, Chile.


2-24



2-25

2.5. Welded Connections

2.5.a. Fillet welds

Fillet welds are used for joining parallel plates or T shapes. Fillet welds are

always PJP type.

Figure 2.5-1: Commonly used fillet welds.

1. Effective Area

(Re. AISC 360-05, J2.2a)

The effective area of a fillet weld shall be the effective length multiplied by the

effective throat. The effective throat of a fillet weld shall be the shortest

distance from the root to the face of the weld.

𝐴𝑤 = 𝑡𝑒𝑓𝑓 𝑙𝑤

the effective throat in a fillet weld (for FCAW, GMAW, SMAW processes) is

shown in the following figure:

Figure 2.5-2: Effective width in the fillet weld for FCAW, GMAW, SMAW

processes. 𝑡=leg dimension (named also 𝑡𝑤), 𝑡𝑒𝑓𝑓= effective throat of a fillet

weld.

Note: in SAW process for < 3/8" → 𝑡𝑒𝑓𝑓 = 𝑡 , and for 𝑡 ≥ 3/8" → 𝑡𝑒𝑓𝑓 = 𝑡 + 0.11"

T jointTraslaped joint

t

tteff

= 0,707 t


2-26

For fillet welds in holes and slots, the effective length shall be the length of the

centerline of the weld along the center of the plane through the throat.

In case of overlapping fillets, the effective area shall not exceed the nominal

cross-sectional area of the hole or slot, in the plane of the faying surface.

2. Limitations

(Re. AISC 360-05, J2.2b)

Minimum fillet weld size:

The minimum size of the fillet welds shall not be less than the size required to transmit calculated forces, nor the size shown in table J2.4 (see

Table 2.5-). These provisions do not apply to fillet weld reinforcements of PJP

or CJP groove welds.

Minimum Size of Fillet Welds - Table J2.4 AISC 360-05 Specification

Material of the Thinner Part Joined (mm) Minimum Size of Fillet Weld a (mm)

To 6 inclusive 3

Over 6 to 13 5

Over 13 to 19 6

Over 19 8

(a) Leg dimension of fillet welds. Single pass welds must be used

Table 2.5-1: Minimum size of Fillet Welds. (Re. AISC 360-05, Table J2.4).

Maximum fillet weld size:

According to the following figure for fillet welds along edges (Re. AISC 360-05,

J2.2b):

Figure 2.5-3: Maximum fillet weld size. 𝑡𝑝=thickness of the plate,

𝑡𝑤=fillet weld size.

tp tw


2-27

If 𝑡𝑝 < 6 𝑚𝑚 → 𝑡𝑤𝑀𝐴𝑋 = 𝑡𝑝

If 𝑡𝑝 ≥ 6 𝑚𝑚 → 𝑡𝑤𝑀𝐴𝑋 = 𝑡𝑝 − 2 𝑚𝑚 (See exception in AISC 360-05, Section J2-2b)

Minimum length of fillet welds:

The minimum effective length of fillet welds designed on the basis of strength

must meet:

𝑙𝑤 ≥ 𝑙𝑤𝑀𝐼𝑁 = 4𝑡𝑤

If longitudinal fillet welds are used alone in end connections of flat-plate

tension members, the length of each fillet weld shall be not less than the

perpendicular distance between them. For the effective area in this case, see

AISC 360-05, Table D3.1.

Figure 2.5-4: Longitudinal fillet welds. It is required that L>w.

(Re. AISC 360-05 Commentary, Fig. C-J2.2)

For end-loaded fillet welds:

If L= length of the weld<100𝑡𝑤 : it is permitted to take 𝑙𝑤 = 𝐿

If L= length of the weld >100𝑡𝑤 take 𝑙𝑤 = 𝛽𝐿, 𝛽 = 1.2 − 0.002 𝐿

𝑡𝑤 ≤ 1.0 .

When the length L of the weld exceeds 30 times the leg size 𝑡𝑤 , use

𝛽 = 0.6.

Lap joints:

The lap shall be five times the thickness of the thinner part (plate) joined, but

not less than 25 mm.

For lap joints joining plates or bars subjected to axial stress that use

transverse fillet welds only, see AISC 360-05, section J2.2b.


2-28

Fillet welds terminations:

Fillet welds are permitted to be stopped short or extend to the ends or sides of

parts or be boxed except as limited by the following:

1. For lap joints in which one connected part extends beyond an edge of

another connected part that is subject to calculated tensile stress,

fillet weld shall terminate not less than the size of the weld from that

edge.

Figure 2.5-5: Fillet welds near tension edges. (Re. AISC 360-05 Commentary, Fig. C-J2.5)

According to AISC 360-05 Commentary, where framing angles extend beyond

the end of the beam web to which they are welded, the free end of the beam

is subject to zero stress; thus, it is permissible for the fillet weld to extend

continuously across the top end, along the side and along the bottom end of

the angle to the extreme end of the beam.

Figure 2.5-6: Fillet welds details on framing angles.

(Re. AISC 360-05 Commentary, Fig. C-J2.7)


2-29

2. For connections where flexibility of the outstanding elements is

required, when end returns are used, the length of the return shall

exceed neither 4 times the nominal size of the weld nor half the width

of the part.

Figure 2.5-7: Flexible connection returns optimal unless subject to fatigue.

(Re. AISC 360-05 Commentary, Fig. C-J2.8) Note: W = weld size. The use of returns is optional.

3. Fillet welds joining transverse stiffeners to plate girder webs 19 mm

thick or less shall end not less than four times nor more than six

times the thickness of the web from the web toe of the web-to-flange

welds, except where the end of stiffeners are welded to the flange.

4. Fillet welds that occur on opposite sides of a common plane, shall be

interrupted at the corner common to both welds.

Figure 2.5-8: Details for fillet welds that occur on opposite sides of a common

plane.(Re. AISC 360-05 Commentary, Fig. C-J2.9)

Note: According to AISC 360-05 Commentary, End returns are not essential

for developing the capacity of fillet welded connections and have a negligible

effect on their strength.


2-30

2.5.b. Groove welds

Groove welds are used for attach top plates. They can be CJP (complete joint

penetration groove welds) or PJP (partial joint penetration groove welds). See

the following figure:

Figure 2.5-9: Commonly used groove welds.

1. Effective Area

(Re. AISC260-05, J2.1a)

The effective area of groove welds shall be considered as the length of the

weld times the effective throat thickness.

The effective throat of PJP Groove welds is shown on the following table:

Effective Throat of PJP Groove Welds - Table J2.1 of AISC 360-05 Specification

Welding

Process

Welding Position F(flat),

H(horiz.), V(vert.), OH(overhead)

Groove Type

(AWS D1.1, Figure 3.3)

Effective Throat

Shielded Metal

Arc (SMAW) All

J or U Groove

60° V Depth of Groove

Gas Metal Arc

(GMAW) All

J or U Groove


Flux Cored Arc

(FCAW) All

J or U Groove


Submerged Arc

(SAW) F

J or U Groove

60° Bevel or V Depth of Groove

Gas Metal Arc

(GMAW) F,H 45° Bevel Depth of Groove

Flux Cored Arc

(FCAW) F,H 45° Bevel Depth of Groove

Shielded Metal

Arc (SMAW) All 45° Bevel Depth of Groove Minus 3 mm

Gas Metal Arc

(GMAW) V,OH 45° Bevel Depth of Groove Minus 3 mm

Flux Cored Arc

(FCAW) V,OH 45° Bevel Depth of Groove Minus 3 mm

Table 2.5-2: Effective throat of PJP groove welds.

(Re. AISC 360-05, Table J2.1)

CJP PJP


2-31

For flare groove welds, see AISC 360-05, section J2-1a.

2. Limitations

(Re. AISC260-05, J2.1b)

Minimum effective throat thickness for PJP groove weld shall not be less than

the size required to transmit calculated forces, nor the size shown in the

following table. Minimum weld size is determined by the thinner of the two

parts joined.

Minimum Effective Throat Thickness of PJP Groove Welds- Table J2.3 AISC

360-05 Specification

Material of the Thinner Part Joined (mm) Minimum Effective Throat

Thickness (mm) - See table J2.1

To 6 inclusive 3

Over 6 to 13 5

Over 13 to 19 6

Over 19 to 38 8

Over 38 to 57 10

Over 57 to 150 13

Over 150 16

Table 2.5-3: Minimum effective throat thickness of PJP groove welds.


2.5.c. Plug and slot welds

See AISC 360-05, section J2-3.

2.5.d. Strength of weld

(Re. AISC 360-05, J2.4)

The design strength 𝜙𝑅𝑛 of welds shall be the lower value of the base material

and the weld metal strength, determined according to the limit states of

tensile rupture, shear rupture or yielding as follows:


2-32

Base metal:

𝑅𝑛 = 𝐹𝐵𝑀𝐴𝐵𝑀

𝐹𝐵𝑀= nominal strength of the base metal, per unit area (MPa)

𝐴𝐵𝑀= cross-sectional area of the base metal (mm2)

Weld metal:

𝑅𝑛 = 𝐹𝑤𝐴𝑤

𝐹𝑤= nominal strength of the weld metal, per unit area (MPa)

𝐴𝑤=effective area of the weld (mm2)

For fillet welds loaded in longitudinal shear, for example, we have the following

shear planes:

Figure 2.5-10: Shear planes for fillet welds loaded in longitudinal shear.

(Re. AISC 360-05, Fig. C-J2.10).

Values of 𝝓 ,𝛀 ,𝑭𝑩𝑴 ,𝑭𝒘 and limitations:

(Re.Table J2.5, AISC 360-05)

CJP Groove Welds:

For these welds, the strength of a joint made by CJP groove welds, whether

loaded in tension or compression, is dependent upon the strength of the base

metal, and no computation of the strength of the CJP groove weld is required.

See Table J2.5.

Note that for CJP welds, the limit state of weld metal strength will never

control since both the welds and the base metal have the same effective area,

and the filler metal is constrained to be stronger than the base metal.

Therefore, only the capacity of the base metal is of concern.


2-33

For tension applications, matching strength filler metal is required, as

defined in AWS D1.1 Table 3.1. For compression applications, up to 70 MPa

decrease in filler metal strength is permitted, which is equivalent to one

strength level.

CJP groove welds loaded in tension or compression parallel to the weld axis,

such as for the groove welded corners of box columns, do not transfer primary

load across the joint. In such cases, no computation of the strength of the CJP

groove weld strength is required.

PJP Groove Welds:

For PJP groove welds, the effective areas for the weld and base metal differ,

with the weld effective area being less than the base metal. If the weld’s

effective throat is small enough, then the weld will control over the base metal

strength. Refer to table J2.5.

Fillet Welds:

Refer to table J2.5, the shear strength of fillet welds is equal to 0.60FEXX and

the resistance factor is 0.75. The strength of the base metal is governed by

J4 and has to be checked.

As an alternative, for fillet welds loaded in plane:

𝜙𝑅𝑛 is permitted to be determined as follows:

(Re. AISC 360-05, J2.4)

𝜙 = 0.75

a) For a linear weld group loaded in-plane through its center of gravity:

𝑅𝑛 = 𝐹𝑤𝐴𝑤

𝐹𝑤 = 0.60𝐹𝐸𝑋𝑋(1.0 + 0.50 sin1.5 𝜃)

𝐹𝐸𝑋𝑋=electrode tensile strength (MPa)

𝜃= angle of loading measured from the weld longitudinal axis,

degrees.

𝐴𝑤=effective area of the weld (mm2)


2-34

Note: a linear weld group is one in which all elements are in a line or are

parallel

Figure 2.5-11: Angle of loading for a linear weld group loaded in plane through

the center of gravity.

b) For weld elements within a weld group that are loaded in-plane and

analyzed using and instantaneous center of rotation method, see

J2.4.

c) For fillet weld groups concentrically loaded and consisting of elements

that are oriented both longitudinally and transversely to the direction

of the applied load, the combined strength 𝑅𝑛 of the fillet weld group

shall be determined as the greater of:

𝑅𝑛 = 𝑅𝑤𝑙 + 𝑅𝑤𝑡 and 𝑅𝑛 = 0.85𝑅𝑤𝑙 + 1.5𝑅𝑤𝑡

Where:

𝑅𝑤𝑙 = the total nominal strength of longitudinally loaded fillet welds, as

determined in accordance with Table J2.5 (N).

𝑅𝑤𝑡 = the total nominal strength of transversely loaded fillet welds, as

determined in accordance with Table J2.5 (N).

2.5.e. Combination of welds

(Re. AISC 360-05,J2.5)

If two or more of the general types of welds (groove, fillet, plug, slot) are

combined in a single joint, the strength of each shall be separately computed

with reference to the axis of the group in order to determine the strength of

the combination.


2-35

2.5.f. Filler metal requirements:

(Re. AISC 360-05, J2.6)

For CJP subject to tension normal to the effective area shall comply with the

requirements for matching filler metal given in AWS D1.1. See Table 2.5-1.

Table 2.5-1: User note Table for filler metal requirements.

(Re. AISC 360-05, J2.6).

Filler metal with a specified Charpy V-Notch (CVN) toughness of 27 J at 4°C

shall be used in the following joints:

1. CJP groove welded T and corner joints with steel backing left in place,

subject to tension normal to the effective area, unless the joints are

designed using the nominal strength and resistance factor or safety

factor as applicable for PJP weld.

2. CJP welded splices subject to tension normal to the effective area in

heavy sections, as defined in A3.1c and A3.1d of the Specification.

2.5.g. Electrodes (AWS):

Commonly used electrodes are E60 and E70. EXX means that 𝑭𝑬𝑿𝑿 = XX

ksi.(electrode tensile strength).

2.5.h. Symbology and common used welds:

Typically the use of prequalified welded joints is recommended because with

this type of weld, there is no need of doing the prequalification tests as


2-36

required by AWS codes. The regular nomenclature and the characteristics of

prequalified welds are shown in the following summary table:

Figure 2.5-12: Common prequalified used welds: symbology and typology.

(Re. Table 4-53 AWS D1.1 code).


2-37

2.5.i. Detailing and Chilean Practice:

Geometry of weld access hole and cope:

Figure 2.5-13: Geometry of access holes and beam copes.

(Re. FEMA 350 ―Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings).

Notes for the figure above:

1. Bevel as required for selected groove weld.

2. Larger of 𝑡𝑏𝑓 or 13 mm (plus 1

2𝑡𝑏𝑓 or minus

1

4𝑡𝑏𝑓).

3. 3

4𝑡𝑏𝑓 to 𝑡𝑏𝑓 , ¾” minimum (± 6 mm).

4. 10 mm minimum radius (plus not limited, minus 0).

5. 3𝑡𝑏𝑓(± 13 mm).

6. See FEMA 353.

Also see section J1.6 of AISC 360-05: “Beam copes and weld access holes”

5

4

36

1

2

5

4

31

2

tbf

tbf

3/4 MIN.


2-38

2.5.j. Seismic Requirements for Welded Joints:

1. NCh2369.Of2003 Code Requirements:

The electrodes and solder flux for SMAW process, must meet with AWS A5.1,

A5.5, A5.17, A5.18, A5.23 and A5.29.

(Re. NCh2369.0f2003, 8.5.1)

The electrodes must have a minimum tenacity of 27 J at -29°C on Charpy

essay, according to ASTM A-6.

(Re. NCh2369.Of2003, 8.5.1)

Groove welds in seismic-resistant unions must be CJP type. (Re.

NCh2369.Of2003, 8.5.5).

Important:

Bolts and welds shall not be designed to share force in a joint or the same

force component in a connection.

2. AISC 341-05 Seismic Provisions Requirements:

Demand critical welds are generally CJP welds, or are those welds where the

failure would result in significant degradation in strength and stiffness of the

SRLS. See AISC 341-05 Code, section 7.3 “Welded Connections” and the user

table for examples of welds designated as demand critical.

AISC 341-05 Commentary:

For desirable details that avoid shared forces between welds and joints see

Fig. C-I-7-1a on the commentary and for problematic bolted/welded

connections see Fig. C-I-7-1b on the commentary.


2-39

2.6. Notation used in the manual

The following terms listed below are the most commonly used on the examples

of this Manual. Other terms not described in here will be properly defined on

each specific example.

2.6.a. Loads

𝑃𝐷 ,𝑉𝐷 ,𝑀𝐷: Dead (permanent) axial, shear and moment loads.

𝑃𝐿 ,𝑉𝐿 ,𝑀𝐿: Live axial, shear and moment loads.

𝑃𝐸 ,𝑉𝐸 ,𝑀𝐸: Seismic axial, shear and moment loads.

𝑃𝑆𝑂 ,𝑉𝑆𝑂 ,𝑀𝑆𝑂: Special operation axial, shear and moment overloads;

defined on NCh2369.0f2003, section 3.1.15.

𝑃𝑆𝐴 ,𝑉𝑆𝐴 ,𝑀𝑆𝐴: Accidental operation axial, shear and moment overloads;

defined on NCh2369.0f2003, section 3.1.16.

𝑃𝑢 ,𝑉𝑢 ,𝑀𝑢: Factored axial, shear and moment loads; according to the

applicable building code (unless otherwise stated).

𝑃𝑅𝐸𝑄 ,𝑉𝑅𝐸𝑄 ,𝑀𝑅𝐸𝑄: Required axial, shear and moment forces to be transferred

by the connection (unless otherwise stated.)

𝑃𝑛 ,𝑉𝑛 ,𝑀𝑛: Nominal axial, shear and moment strength.

𝑀𝑝: Plastic moment.

𝑅𝑛: Nominal strength.

𝑅𝑢: Factored required strength.

Note:

Sometimes, 𝑁 or 𝑇 are also used to define axial loads.

2.6.b. Dimensions and others

𝑑𝑐: Gap between structural elements.


2-40

𝑒: Eccentricity, unless otherwise stated.

𝑒: Distances for bolt positions, unless otherwise stated.

𝑓: Stress, unless otherwise stated

𝐹𝑐𝑟: Buckling or critical stress.

𝐹𝑒: Elastic buckling stress.

𝐻 : Story height.

𝑘 : Coefficient of buckling length.

𝐿𝑏: Distance between braces.

𝐿𝑛 : Clear distance of a structural element, as a column or beam.

R: Modification factor of the structural response.

Ω0: Horizontal seismic over strength factor.

𝜆𝑝: Compact slenderness. See AISC 360-05 Specification.

𝜆𝑟: Non-compact slenderness. See AISC 360-05 Specification.

2.6.c. H built-up Chilean steel shape sections

Figure 2.6-1: Chilean H-Shape section.

bf

tfy

x x

y

s

dh

tw


2-41

Notation: 𝐻 𝐴 × 𝐵 × 𝐶, where 𝐴 = 𝑑 ; 𝐵 = 𝑏𝑓; 𝐶 =weigth in 𝑘𝑔𝑓

𝑚

1. Dimensions of the steel shape

𝑏𝑓: Flange width.

𝑡𝑓: Flange thickness.

𝑕: Free distance between flanges.

𝑕0: Distance between flange centroids.

𝑑: Section depth.

𝑡𝑤: Web thickness.

𝑠: Weld fillet used for building the shape.

Note:

In many examples these terms have subscripts to indicate the structural

element such as beam, column, brace, etc.

2. Geometric properties of the steel shape

𝐴: Section gross area.

𝐼𝑥: Inertia moment about X axis.

𝐼𝑦 : Inertia moment about y-axis.

𝐽: Torsional constant.

𝐶𝑤: Warping constant.

𝑟: Radius of gyration.

𝑡: Thickness of the element.

𝜆𝑤 =𝑕

𝑡𝑤: Web slenderness.

𝜆𝑓 =𝑏𝑓

2𝑡𝑓: Flange slenderness.

𝑍: Plastic modulus.

𝐴𝑓 = 𝑏𝑓𝑡𝑓: Area of one flange.

𝐴𝑤 = 𝑑𝑡𝑤: Web area.

𝑆: Bending elastic modulus.

Note:

In many examples there are subscripts joining this terms to indicate the

element (beam, column, brace, plate, etc.) property.

2.6.d. Material notation

𝐸: Young modulus of the material.

𝐹𝑦: Yield strength of the material.


2-42

𝐹𝑢: Tensile rupture stress of the material (tensile strength).

𝐶𝑝𝑟 : Factor to account for increase in stress due to strain hardening.

𝑅𝑦𝐹𝑦: Expected yield stress of the material (𝑅𝑦 ≥ 1.0).

2.6.e. Bolted connections

𝐴𝑔: Gross area of a connector element.

𝐴𝑛: Nominal area of a connector element.

𝐴𝑒: Effective area of a connector element.

𝐴𝑏: Bolt area.

𝑑𝐶𝐴𝐿𝐶: Diameter for calculating 𝐴𝑒.

𝑑𝑏: Bolt diameter.

𝑑𝑕: Nominal hole diameter.

𝑑𝑕𝑜𝑙𝑒: Nominal hole diameter.

𝐹𝑛𝑡: Nominal tensile stress from table J3.2.

𝐹𝑛𝑣: Nominal shear stress from table J3.2.

𝑁𝐵: Number of bolts in a connection, unless otherwise stated.

𝑁𝑅: Number of bolts rows (for bolted connections aligned), unless

otherwise stated.

𝑁𝑠: Number of slip planes.

𝑛 =𝑁𝐵

𝑁𝑅: Number of bolts per rows (for bolted connections aligned), unless

otherwise stated.

𝑛: Number of bolts, unless otherwise stated.

2.6.f. Welded connections

𝐹𝐸𝑋𝑋: Electrode classification number (electrode strength).

𝐴𝐵𝑀: Cross sectional area of the base metal.

𝐹𝐵𝑀: Nominal stress strength of the base metal.

𝐴𝑤: Effective area of the weld.

𝐹𝑤: Nominal stress strength of the weld metal.

1. Fillet welds

𝑡𝑤: Fillet weld size.

𝑡𝑒𝑓𝑓 : Effective fillet weld throat size.

𝑙𝑤: Fillet weld length.

𝐿 or 𝐿𝑤 : Length of the weld, unless otherwise stated.


2-43

2. Groove welds

CJP: Complete joint penetration groove weld.

PJP: Partial joint penetration groove weld.

2.6.g. LRFD Design

𝜙: Resistance factor. In LRFD design it is required that 𝑅𝑢 ≤ 𝜙𝑅𝑛


2-44

2.7. Units used on the manual

Posco E&C. uses principally the SI system, using Newton (N) or Kilo-Newton

(kN) for forces and millimeters (mm) for distances. For helping in calculations,

a conversion table between the SI unit system and customary United States

unit system is given.

Dimension United States Units SI Units

Distance 1 in (1”) 25.4 mm

Force 1 kip 4.448 kN

Stress 1 ksi (1kip/in2) 6.894 N/mm2

Distance 1 ft (1’) 12 in (12”) = 317.5 mm

Force 1 lb. 0.00444 kN

Stress 1 MPa 1 N/mm2

Table 2.7-1: Units conversion table.

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 3: BASE PLATE CONNECTIONS

3-1

3. BASE PLATE CONNECTIONS

3.1. Design requirements

3.1.a. NCh2369.Of2003

Comply material specifications for steel and anchor bolts.

(Re. NCh2369.Of2003, 8.2.1 and 8.2.2)

Anchor bolts subjected to tension shall have chair (double base plate)

and must be visible to allow for inspection and repair, and the thread

shall have sufficient length to enable retightening of the nuts.

Therefore, anchors shall have a projection of at least 8 diameters and

no less than 250 mm measured from the base plate. The length of

the thread under the nut must be greater than 75 mm. See Figure

3-1.

(Re. NCh2369.Of2003, 8.6.2)

Note that careful inspection and reparation of these anchoring

systems should be performed after the occurrence of a major

earthquake. Also, anchor bolt deformation during strong seismic

events shall be allowed. These requirements imply that the use of

double base plates in columns is mandatory.

Figure 3-1: Typical detail for the double base plate connection. Adapted from

NCh2369.Of2003; Figure A.1.

Shear key

8d o

r 350 m

m

75 m

m (

thre

ad)

d


3-2

The exception to the previous requirement can be made when the bolts have

enough capacity to resist load combinations in which the seismic forces have

been amplified by 0.5R (but no more than 1.5 times) with respect to the value

indicated on sections 5 and 7 of the Chilean code.

(Re. NCh2369.Of2003, 8.6.2)

Base plates of columns and equipment in general must be provided

with shear keys or seismic stoppers designed to transmit the 100% of

the base shear.

(Re. NC23609.Of2003, 8.6.3)

According to subsection a) of section 8.6.3, supports with shear force

less than 50 kN can resist this force with the anchor bolts but

considering that only two of the anchor bolts are active and using the

corresponding tension-shear interaction equations with the maximum

tension and shear calculated.

Grout resistance (and also thickness) must not be considered in the

design of the base plate.

(Re. NCh2369.Of2003, 8.6.4)

The design of the shear anchor systems shall not take into account

the friction between the base plate and the foundation.

(Re. NCh2369.Of2003, 8.6.5)

The strengths of the shear keys and the anchor bolts cannot be

added.

(Re. NCh2369.Of2003, 8.6.6)

Ductile design: the concrete of the foundation must be designed to

resist the vertical and horizontal forces transmitted by the steel

anchor elements. The strength of the concrete and its reinforcements

must be such that the eventual failure occurs on the steel anchor

elements and not on the concrete.

(Re. NCh2369.Of2003, 8.6.8)


3-3

3.1.b. AISC 341-05

(Re. AISC 341-05, 8.5: Column Bases section)

1. Required strength of the column bases and their attachments to the

foundation

Required Axial Strength:

𝑃𝑢 (compression axial strength) and 𝑇𝑢 (tension axial strength) should be the

summation of the vertical components of the required strengths of the steel

elements that are connected to the column base (i.e. the column axial required

resistance according to section 8.3 of AISC341-05, depending on the type of

system, and the vertical components of the required strengths of the arriving

braces).

Required Shear Strength:

𝑉𝑢 (required shear strength) shall be the summation of the horizontal

component of the required strengths of the steel elements that are connected

to the column base:

For a single column, 8.5b(2) applies:

𝑉𝑢 ≥ min(2𝑅𝑦𝐹𝑦𝑍𝑥/𝐻,𝑉𝑢∗ )

Where 𝐻 is the story height and 𝑉𝑢∗ is the shear load calculated using the

combinations of the applicable building code, including the amplified seismic

load.

Required Flexural Strength:

𝑀𝑢 (required flexural strength) shall be the summation of the required

strengths of the steel elements that are connected to the column base:

For a single column, 8.5c(2) applies:

𝑀𝑢 ≥ min(1.1𝑅𝑦𝐹𝑦𝑍𝑥 ,𝑀𝑢∗ )

Where 𝑀𝑢∗ is the moment calculated using the combinations of the applicable

building code, including the amplified seismic load.


3-4

Note:

To understand the hypotheses and origin of these design forces, and how do

the base plate connections work, it is important to read the commentary of

section 8.5 of AISC341-05.

2. Available strength of the anchor bolts

According to AISC 341-05, this strength shall be determined from AISC 360-

05 J3 section, for bolt and threaded parts in connections. Appendix D of

AIC318 code also shows expressions for the tensile and shear strength of the

anchor bolts.

3. Available strength of the concrete elements (including anchor rod

embedment and reinforcing steel)

Refer to Appendix D of ACI 318 Code. This is not presented on this example.

3.1.c. AISC 360-05

Column Bases and Bearing on Concrete

(Re. AISC 360-05, J8)

There are formulas to be used (in absence of code regulations) for calculating

the design bearing strength of the concrete for the limit state of concrete

crushing (with 𝜙 = 0.6). The nominal bearing strength is determined as follows:

a) On the full area of a concrete support:

𝑃𝑝 = 0.85𝑓𝑐′𝐴1

b) On less than the full area of a concrete support:

𝑃𝑝 = 0.85𝑓𝑐′𝐴1 𝐴2/𝐴1 ≤ 1.7𝑓𝑐

′𝐴1

Where 𝐴1 = are of steel concentrically bearing on a concrete support, and 𝐴2=

maximum area of the portion of the supporting surface that is geometrically

similar to and concentric with the loaded area.

Anchor rods and embedments (Re. AISC 360-05, J9)

-Anchor rods shall be designed to provide the required resistance to loads on

the completed structure at the base of columns including the net tensile

components of any bending moments that may result from load combinations.


3-5

-Anchor rods shall be designed in accordance with the requirement for

threaded parts in table J3.2.

Note: In the case of the following numerical example, the design of the anchor

bolts will be made according to ACI 318, Appendix D.

- Hole sizes and washer dimensions for anchor rods: from the AISC Manual of

Steel Construction.

3.2. Recommendations from AISC Manual of Steel Construction (13th Edition)

(Re. Part 14 of the AISC Manual of Steel Construction)

Holes for anchor rods and grouting:

-An adequate washer plate should be provided for each anchor rod.

-When large base plates are used (and also when shear keys are used), there

should be grout holes to prevent air pockets (except when the grout is dry-

packed). These grout holes must be placed near the center of the plate.

-Recommended anchor rod holes are presented on table 14-2 of the Manual:

Recommended Maximum Sizes for Anchor-Rod Holes in Base Plates

Anchor Rod diameter (in)

Max. Hole Diameter (in)

Min. Washer Size (in)

Min. Washer Thickness (in)

¾ 1 5/16 2 ¼

7/8 1 9/16 2 1/2 5/16

1 1 13/16 3 3/8

1 ¼ 2 1/16 3 ½

1 ½ 2 5/16 3 1/2 ½

1 ¾ 2 3/4 4 5/8

2 3 1/4 5 3/4

2 ½ 3 3/4 5 1/2 7/8

Table 3-1: Recommended Maximum Sizes for Anchor-Rod Holes in Base Plates. Adapted from Table 14-2 of AISC Manual of Steel Construction, 13th Ed.


3-6

Notes for Table 3-1:

1. Circular or square washers meeting the washer size are acceptable

2. Clearance must be considered when choosing an appropriate anchor rod

hole location, noting effects such as the position of the rod in the hole with

respect to the column, weld size and other interferences.

3. When base plates are less than 1 ¼ in thick, punching of holes may be an

economical option. In this case, 3/4 in anchor rods and 1 1/16 in diameter

punched holes may be used with ASTM F844 (USS Standard) washers.

Anchor rods:

-Cast-in place anchor rods are generally made from unheaded rod material or

headed bolt material. There are three common types of cast-in-place anchor

rods as seen on Figure 14-8 of the Manual (hooked, headed and headed with

nut).

-Minimum edge distances, embedment length and the design of the anchorage

into the concrete are covered on ACI 318 code.

-When anchor rods are required for a calculated tensile force T (probably due

to large seismic forces), a better anchorage is made with headed anchor rods

(see Figure 14-8b of the Manual).

Washer plates:

-Because base plates typically have holes larger than the oversized holes to

allow for tolerances on the location of the anchor rod, washers are usually

made from ASTM A36 steel plate. They may be round, square or rectangular

and they have holes that generally are 1/16 in larger than the anchor rod

diameter. The thickness must be suitable for the forces to be transferred. See

Table 14-2 of the manual for minimum washer sizes.

3.3. Example: fixed column double base plate subjected to various types of loads.

Design a base plate connection for the connection shown in Figure 3-2.

Suppose that bending is about the strong axis for the wide flange column

shown. The column is a H 350 x 350 x 165.6 Chilean shape.

Use A345 ESP steel, required for constructions subjected to dynamical loading,

according to NCh203.Of2006 code, Table 3. Anchor rods are ASTM F1554 Gr

36. Concrete of the foundation is H30.


3-7

The column is located such that no “free edges” of concrete foundation are

near its position. Story height is 𝐻 = 5 𝑚.

Suppose that the column has been properly designed for resisting the forces

given by the load combinations of the applicable building code including the

amplified seismic load (in this case, the NCh2369.Of2003 Load Combinations

unless otherwise noted). These loads, at the base of the column and about the

major axis of the column are (convention is that compression loads are

positive sign):

Combination 1 (uplift):

𝑀𝑢 = 0 , 𝑁𝑢 = −1000 𝑘𝑁

Note for combination 1:

The uplift combination will typically control de design of anchor bolts since

they take the total of the tensile force and transmit it to the concrete

foundation. The design of the anchor bolts includes the anchorage to concrete.

The reference for that design is Appendix D of ACI 318 Code. Then, the

combinations for determining the uplift force should be taken from ACI 318

Code (or similar). In order to determine the maximum uplift force, typically

the combination 0.9D – 1.4(EH + EV) controls. EH is the horizontal earthquake

action and EV the vertical earthquake action.

Combination 2:

𝑀𝑢 = 500000 𝑘𝑁 −𝑚𝑚, 𝑁𝑢 = 1000 𝑘𝑁

Check immediately the AISC 341 requirements for determine the design forces

for combination 2:

𝑅𝑦 = 1.1 for A345 steel, similar to ASTM A572 Gr50 steel:

(Re. AISC 341-05, Table I-6-1)

1.1𝑅𝑦𝐹𝑦𝑍𝑥 = 1299939 𝑘𝑁 −𝑚𝑚

Therefore the design loads for combination 2 are:

𝑀𝑢2 ≥ min 1.1𝑅𝑦𝐹𝑦𝑍𝑥 ,𝑀𝑢 = 500000 𝑘𝑁 −𝑚𝑚 𝑁𝑢

2 = 1000 𝑘𝑁

Combination 3:

𝑀𝑢 = 200000 𝑘𝑁 −𝑚𝑚, 𝑁𝑢 = 2000 𝑘𝑁


3-8

Check immediately the AISC 341 requirements for determine the design forces

for combination 3:

1.1𝑅𝑦𝐹𝑦𝑍𝑥 = 1299939 𝑘𝑁 −𝑚𝑚

Therefore the design loads for combination 3 are:

𝑀𝑢3 ≥ min 1.1𝑅𝑦𝐹𝑦𝑍𝑥 ,𝑀𝑢 = 200000 𝑘𝑁 −𝑚𝑚 𝑁𝑢

3 = 2000 𝑘𝑁

Shear force:

𝑉𝑢 = 150 𝑘𝑁

Check immediately the AISC 341 requirements for determine the shear design

force (the story height is 5000 mm):

2𝑅𝑦𝐹𝑦𝑍𝑥

𝐻= 473 𝑘𝑁

Therefore:

𝑉𝑢 ≥ min 2𝑅𝑦𝐹𝑦𝑍𝑥/𝐻,𝑉𝑢 = 150 𝑘𝑁

Notes:

1. For this example, the design of the anchorage to the concrete foundation

(regarding to anchor bolts) will not be taken into account For that topic

refer to Appendix D of ACI 318-05 and ACI 318-11 codes, and make a

ductile design.

2. This example will consider the detailing requirements of NCh2369.Of2003

and the design forces will be taken from the provisions of AISC 341-05

code, as shown above. Note that when NCh2369.Of2003 is used for the

determination of the design forces, appropriate load combinations from

that code shall be used.


3-9

3.3.a. General view of the connection

Figure 3-2: Connection to be designed.

3.3.b. Section and materials properties

H 350 x 350 x 165.6

𝑑 = 350 𝑚𝑚, 𝑏𝑓 = 350 𝑚𝑚, 𝑡𝑓 = 25 𝑚𝑚, 𝑡𝑤 = 12 𝑚𝑚, 𝑠 = 6 𝑚𝑚

𝐴 = 21100 𝑚𝑚2 , 𝑍𝑥 = 3114000 𝑚𝑚3 , 𝑟𝑥 = 152 𝑚𝑚, 𝑟𝑦 = 92 𝑚𝑚, 𝐽 = 3830000 𝑚𝑚4

(Re. ICHA Manual for the Design of Steel Structures, Table 2.1.1)

A345 ESP:

(Re. Table 3, NCh203.Of.2003)

𝐹𝑦 = 345 𝑀𝑃𝑎 ,𝐹𝑢 = 450 𝑀𝑃𝑎

ASTM F1554 Gr36 (anchor bolts):

𝐹𝑦 = 250 𝑀𝑃𝑎 ,𝐹𝑢 = 400 𝑀𝑃𝑎

Note: To provide ductility, the anchor bolts must be made from a ductile

material. ASTM F1554 Gr36 bolts have a minimum ultimate elongation of 23%.

Mu

Pu

Vu

A-A section B-B section

BB

A

A


3-10

3.3.c. Design procedure

1. Uplift forces

𝑇𝑢 = 1000 𝑘𝑁

Determine the number of bolts and bolt area needed. From ACI 318-08 the

anchor bolt tensile strength is:

𝑁𝑠𝑎 = 𝑛𝐴𝑠𝑒 ,𝑁𝑓𝑢𝑡𝑎 (Re. ACI 318-08 Code, Eq.D-3).

Where:

𝑛 = number of bolts, 𝐴𝑠𝑒 ,𝑁 = effective cross-sectional area of an anchor bolt in

tension.

𝑓𝑢𝑡𝑎 = 400 𝑀𝑃𝑎 ≤ min 1.9𝑓𝑦𝑎 , 860 𝑀𝑃𝑎 = 475 𝑀𝑃𝑎 (Re. ACI 318-08 Code, D.5.1.2)

Use a reduction strength factor 𝜙 = 0.75 (anchorage supposed to be controlled

by the resistance of a ductile element, ACI 318-08, section D4.4). 𝑓𝑦𝑎 =

250 𝑀𝑃𝑎 is the specified tensile yield stress of the anchor steel. The 𝐴𝑠𝑒 ,𝑁 term

can be obtained from table 7-18 of AISC Manual of Steel Construction :

Threading Dimension for High Strength and Non-High Strength Bolts. For more

information, seeAISC Design Guide N°1.

Try anchor rods of 1 ½ in (38 mm). Therefore, 𝐴𝑠𝑒 ,𝑁 = 1.405 𝑖𝑛2 = 906 𝑚𝑚2. The

required number of bolts is:

𝑛 =𝑇𝑢

𝜙𝐴𝑠𝑒 ,𝑁𝑓𝑢𝑡𝑎= 3.7 → 𝑢𝑠𝑒 𝑛 = 4 𝑏𝑜𝑙𝑡𝑠

Notes:

According to the AISC Manual of Steel Construction 13th Ed., use at

least 4 bolts.

The design of the upper base plate and vertical stiffeners (see Figure

3-2) shall be carried out for the anchor bolt tension capacity

computed according to ACI 318 – Appendix D. Note that the ductile

behavior requirement implies that the anchor bolt shall be the first

element to reach the nominal strength. Also, ACI 318 code considers

and additional 0.75 factor for reducing the nominal anchor tensile

strength associated with concrete brittle failure modes (not developed

on this example).


3-11

For 1 ½ in (38 mm) anchor rods, the corresponding hole size is 2

5/16 in (59 mm) according to Table 3-1 of this chapter. Also, the

corresponding washer plate size is 3 ½ in (89 mm).

Consider the following figure to place the anchor bolts:

Figure 3-3: Base plate configuration.

Place the anchor bolts complying with the minimum distances as said on ACI

318 Code, App. D:

-Center to center distance between anchor bolts: 𝑠 ≥ 4𝑑𝑎 = 152 𝑚𝑚, with 𝑑𝑎 =

anchor bolt diameter (suppose untorqued cast-in anchor rods).

Use 𝒔 = 𝟏𝟕𝟓 𝒎𝒎. Also:

𝒃𝒆𝒅𝒈𝒆 = 𝟕𝟎 𝒎𝒎

𝒈 = 𝟏𝟐𝟎 𝒎𝒎

𝒔𝒆𝒅𝒈𝒆 = 𝟏𝟎𝟎 𝒎𝒎

Therefore, base plate dimensions are:

𝑵 = 𝒅 + 𝟐 𝒃𝒆𝒅𝒈𝒆 + 𝒈 = 𝟕𝟑𝟎 𝒎𝒎

𝑩 = 𝒔 + 𝟐𝒔𝒆𝒅𝒈𝒆 = 𝟑𝟕𝟓 𝒎𝒎

Note:

No minimum edge distance is considered, because in this example the column

is supposed to be away from pedestal edges.

sedge ss

b

g

d N

bf

B

edge

edge


3-12

Design of upper plate:

It is designed as a continuous beam. Consider the following model:

(𝑋 =𝑏𝑓

2= 175 𝑚𝑚 ,𝑌 = 𝑠 = 175 𝑚𝑚):

Figure 3-4: (a) Model for the design of the upper plate and vertical stiffener,

(b) Moment diagram due to anchor rods capacity on the upper plate.

From the previous figure, the reactions are (𝑇 = 𝐴𝑠𝑒 ,𝑁𝑓𝑢𝑡𝑎 = 363 𝑘𝑁 ):

𝑅 =11𝑇

8= 499 𝑘𝑁

𝐴 =5𝑇

16= 113 𝑘𝑁

Maximum moment values are:

𝑀1 =5𝑇𝑋

32= 9914 𝑘𝑁 −𝑚𝑚 and 𝑀2 = −

3𝑇𝑋

16= −11897 𝑘𝑁 −𝑚𝑚

Dimensions of the upper plate are:

Use thickness: 𝒕𝒖 = 𝟑𝟎 𝒎𝒎 and width: 𝒃𝒖 = 𝒈 + 𝒃𝒆𝒅𝒈𝒆 = 𝟏𝟗𝟎 𝒎𝒎

Check the flexural yielding limit:

𝜙𝐹𝑦𝑍 = 0.9𝐹𝑦 𝑏𝑢 𝑡𝑢

2

4 = 13274 𝑘𝑁 −𝑚𝑚 > 𝑀𝑀𝐴𝑋 = 11897 𝑘𝑁 −𝑚𝑚 OK

Design of vertical stiffeners:

Design the vertical stiffeners as columns. Use an effective length factor k=1.0

(conservative):

The maximum reaction is 𝑅 = 499 𝑘𝑁

Try height, thickness and width (comply with NCh2369.Of2003 code

requirements):

𝑯𝒔 = 𝟑𝟎𝟓 𝒎𝒎 ≥ max 8𝑑𝑎 , 250 𝑚𝑚 = 304 𝑚𝑚 OK

Y

T T

X X

A R A

M2

M1 M1


3-13

𝒕𝒔 = 𝟐𝟓𝒎𝒎

𝒃𝒔 = 𝒈 + 𝒃𝒆𝒅𝒈𝒆 = 𝟏𝟗𝟎 𝒎𝒎

Therefore (refer to Chapter E of AISC 360-05):

𝑟 = 𝐼/𝐴 = 𝑡𝑠

3𝑏𝑠12

𝑡𝑠𝑏𝑠=

𝑡𝑠

12= 7.22 𝑚𝑚 . Then,

𝑘𝐿

𝑟=

𝑘𝐻𝑠

𝑟= 42.3 < 4.71 𝐸/𝐹𝑦 = 113.4

𝐹𝑐𝑟 = 𝐹𝑦 0.658𝐹𝑦

𝐹𝑒 = 303 𝑀𝑃𝑎 → 𝜙𝑃𝑛 = 0.9𝐹𝑐𝑟𝑏𝑠𝑡𝑠 = 1294 𝑘𝑁 > 𝑅 = 499 𝑘𝑁 OK

Notes:

Note that vertical stiffeners shall also be checked for the compression

on the base plate for (M,P) combinations (see following sections in

this chapter), therefore the 𝑡𝑠 value shall be checked after again.

The welded connections of the vertical stiffeners and upper plates

shall be designed considering the anchor bolt capacity. The design of

these welds will not be made on this example.


3-14

2. M,N combinations

The anchor bolts shall be designed for resisting also the tensile forces coming

from the moment on the base and, if present, the uplift force T (see previous

section). For the calculation of the bearing stress distribution under the base

plate and the forces acting on the anchor bolts, refer to the following figure:

Figure 3-5: Definition of variables for M,N action on a base plate.

Adapted from AISC Design Guide # 1. Figure B.3. Notes:

There are many different ways of assuming the distribution of bearing

stresses under the base plate (e.g. uniform, linear, parabolic). In this

example it has been assumed a linear distribution as on AISC Design

Guide # 1. For more information see the AISC Design Guide # 1 (2nd

Ed), sections 3.3, 3.4 and Appendix B.

The triangular (linear) distribution does not in and of itself represent

an elastic design.

Static equilibrium gives:

𝐹𝑉: 𝑃 + 𝑇 =𝑓𝑝𝐴𝐵

2

𝑀: 𝑃𝐴′ + 𝑀 =𝑓𝑝𝐴𝐵

2 𝑁 ′ −

𝐴

3

𝐴′ =𝑁

2− 𝑏𝑒𝑑𝑔𝑒 (distance between the tension force and the column center).

B

d

N

P

M

N'AT

(N/2 - A/3)

bedge

bf

fp

(N/2 - )bedge


3-15

Solve both equations to obtain a quadratic expression for the bearing distance:

𝐴 =𝑓 ′ ± 𝑓′2−4

𝑓𝑝𝐵

6 (𝑃𝐴′ +𝑀)

𝑓𝑝𝐵

3

(minimum of the positive real roots).

Where:

𝑓 ′ =𝑓𝑝𝐵𝑁

′

2 (as a supposition of the design method, to calculate 𝑓𝑝 use the

expression for the available bearing strength 𝜙𝑃𝑝 of AISC 360-05, section J8).

The resulting tensile load on the anchor bolts is 𝑇 =𝑓𝑝𝐴𝐵

2− 𝑃. Check it against

the tensile capacity of the bolts. Note that if the distance 𝐴 is equal or greater

than 𝑁′, the bolts are not subjected to tension and mostly all the base plate is

under compression. In that case, it is possible to neglect the action of the

bolts.

For the cases when there is mainly compression between the base plate and

the foundation, the Guide proposes a different method of analysis:

If 𝑒 =𝑀𝑢

𝑃𝑢<

𝑁

6 the base plate is a small base plate and no tension exists. For that

case, the base pressures can be evaluated as:

𝑓𝑝𝑀𝐴𝑋 = 𝑃

𝐵𝑁 1 +

6𝑒

𝑁 ≤ 𝜙0.85𝑓𝑐

′ = 0.6 × 0.85𝑓𝑐′

(Full area of a concrete support. AISC 360-05, Eq. J8-1)

After evaluating the compression over the base plate and the tension

on the bolts, check the bending behavior on the base plate (i.e. check

the thickness of the base plate) considering an appropriate critical

section. Also, tension on the bolts shall be checked.

Combination 2:

𝑀𝑢2 = 500000 𝑘𝑁 −𝑚𝑚 ,𝑃𝑢

2 = 𝑁𝑢2 = 1000 𝑘𝑁

Base plate dimensions from previous section (bending about the strong axis of

the column):

𝑁 = 730 𝑚𝑚 ,𝐵 = 375 𝑚𝑚


3-16

First, determine the available bearing strength:

𝜙𝑃𝑝 = 0.60 × 0.85𝑓𝑐′𝐴1

𝐴2

𝐴1≤ 0.60 × 1.7𝑓𝑐

′𝐴1 (Re. AISC 360-05, Eq. J8-2)

𝐴1= area of steel concentrically bearing on a concrete support.

𝐴2=maximum area of the (concrete) portion of the supporting surface that is

geometrically similar and concentric with the loaded area. Assume 𝐴2

𝐴1= 4

Therefore, 𝑓𝑝 =𝜙𝑃𝑝

𝐴1= 0.60 × 0.85𝑓𝑐

′ 𝐴2

𝐴1= 25.5 𝑀𝑃𝑎 ≤ 0.60 × 1.7𝑓𝑐

′ = 25.5 𝑀𝑃𝑎

The eccentricity of the loads is:

𝑒 =𝑀𝑢

𝑃𝑢= 500 𝑚𝑚 >

𝑁

6= 122 𝑚𝑚 → 𝐿𝑎𝑟𝑔𝑒 𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 → 𝑎𝑛𝑐𝑕𝑜𝑟 𝑟𝑜𝑑𝑠 𝑎𝑐𝑡 𝑖𝑛 𝑡𝑒𝑛𝑠𝑖𝑜𝑛

𝐴′ =𝑁

2− 𝑏𝑒𝑑𝑔𝑒 = 295 𝑚𝑚

𝑓 ′ =𝑓𝑝𝐵𝑁

′

2= 3156 𝑘𝑁

𝑁 ′ = 𝑁 − 𝑏𝑒𝑑𝑔𝑒 = 660 𝑚𝑚

The bearing distance is then 𝐴 = 296 𝑚𝑚

The resulting tensile load on the anchor bolts is then (only 2 bolts are

working):

𝑇𝑟𝑜𝑑 =1

2 𝑓𝑝𝐴𝐵

2− 𝑃𝑢

2 = 208 ≤ 𝜙𝐴𝑠𝑒 ,𝑁𝑓𝑢𝑡𝑎 = 272 𝑘𝑁, 𝜙 = 0.75 OK

Check the base plate at an appropriate critical section:

Figure 3-6: (a) Section for bending analysis of the base plate (vertical

stiffeners shown), (b) Slab Model (three fixed and one free edges)

Use any reasonable method to solve the maximum moments on the Slab

Model.

ly

lx


3-17

Using tables for calculating the slab moments per mm of width (Stiglat &

Wippel book) for the case shown in the figure above.

𝑙𝑦 = 𝑔 + 𝑏𝑒𝑑𝑔𝑒 = 190 𝑚𝑚 , 𝑙𝑥 =𝑏𝑓

2= 175 𝑚𝑚 ,

𝑙𝑦𝑙𝑥

= 1.09 → 𝑐𝑜𝑒𝑓 = 12.7

𝐾 = 𝑓𝑝 𝑙𝑥 𝑙𝑦 = 848 𝑘𝑁 → 𝑀𝑀𝐴𝑋 =𝐾

𝑐𝑜𝑒𝑓= 67 𝑘𝑁 −𝑚𝑚

(Assume conservatively that the critical value of 𝑓𝑝 is constant all over the

slab).

The design condition is that: 𝜙𝐹𝑦𝑍𝐵𝐴𝑆𝐸𝑃𝐿𝐴𝑇𝐸 = 0.9 × 𝐹𝑦(

𝑏𝑡2

4) > 𝑀𝑀𝐴𝑋 .

𝑡𝑀𝐼𝑁 = 4𝑀

0.9 ∗ 𝐹𝑦= 29.3 𝑚𝑚 → 𝒖𝒔𝒆 𝒕𝒃𝒑 = 𝟑𝟎 𝒎𝒎

Check the vertical stiffeners with the force produced by the concrete pressure:

Assume conservatively that 𝑓𝑝 is uniform in all the length of the upper plate

projection on the base plate. The model is the following:

Figure 3-7: Determination for the concrete pressure reaction on the vertical

stiffeners.

𝑓 = 𝑓𝑝 𝑔 + 𝑏𝑒𝑑𝑔𝑒 = 4.85𝑘𝑁

𝑚𝑚,𝑋 =

𝑏𝑓

2= 175 𝑚𝑚

The reactions are:

𝑅 = 1.25𝑓𝑋 = 1060 𝑘𝑁 ,𝐴 = 2𝑓𝑋 − 𝑅 = 636 𝑘𝑁.

Then:

max 𝑅,𝐴 = 1060 𝑘𝑁 < 𝜙𝑃𝑛 = 1294 𝑘𝑁 OK

A R A

f

X X


3-18

Combination 3:

𝑀𝑢3 = 200000 𝑘𝑁 −𝑚𝑚 , 𝑃𝑢

3 = 𝑁𝑢3 = 2000 𝑘𝑁

Base plate dimensions from previous section (bending about the strong axis of

the column):

𝑁 = 730 𝑚𝑚,𝐵 = 375 𝑚𝑚

The eccentricity of the loads is:

𝑒 =𝑀𝑢

𝑃𝑢

= 100 𝑚𝑚 <𝑁

6= 122 𝑚𝑚 → 𝑆𝑚𝑎𝑙𝑙 𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 → 𝑎𝑛𝑐𝑕𝑜𝑟 𝑟𝑜𝑑𝑠 𝑛𝑜𝑡 𝑖𝑛 𝑡𝑒𝑛𝑠𝑖𝑜𝑛

𝑓𝑝𝑀𝐴𝑋 =𝑃

𝐵𝑁 1 +

6𝑒

𝑁 = 13.31 𝑀𝑃𝑎 > 𝑓𝑝

𝐴𝑉𝐴𝐼𝐿 = 0.60 × 0.85𝑓𝑐′ = 12.8 𝑀𝑃𝑎

Increase the width of the base plate: use 𝒔𝒆𝒅𝒈𝒆 = 𝟏𝟏𝟎 𝒎𝒎 → 𝑩 = 𝒔 + 𝟐𝒔𝒆𝒅𝒈𝒆 =

𝟑𝟗𝟓 𝒎𝒎. With this new width, all the verifications for combination 2 are OK.

Now:

𝑓𝑝𝑀𝐴𝑋 =𝑃

𝐵𝑁 1 +

6𝑒

𝑁 = 12.64 𝑀𝑃𝑎 < 𝑓𝑝

𝐴𝑉𝐴𝐼𝐿 = 12.8 𝑀𝑃𝑎

Check the base plate at an appropriate critical section. See Figure 3-6.

Using tables for the determination of this slab moments (Stiglat & Wippel

book):

𝑙𝑦 = 𝑔 + 𝑏𝑒𝑑𝑔𝑒 = 190 𝑚𝑚 , 𝑙𝑥 = 175 𝑚𝑚 ,𝑙𝑦𝑙𝑥

= 1.09 → 𝑐𝑜𝑒𝑓 = 12.7

𝐾 = 𝑓𝑝𝑀𝐴𝑋 𝑙𝑥 𝑙𝑦 = 420 𝑘𝑁 → 𝑀𝑀𝐴𝑋 =𝐾

𝑐𝑜𝑒𝑓= 33 𝑘𝑁 −𝑚𝑚

(Assume conservatively that the critical value of 𝑓𝑝𝑀𝐴𝑋 is constant all over the

slab).

The design condition is that: 𝑀𝑛 = 𝜙𝐹𝑦𝑍𝐵𝐴𝑆𝐸𝑃𝐿𝐴𝑇𝐸 = 0.9 × 𝐹𝑦(

𝑏𝑡2

4) > 𝑀𝑀𝐴𝑋 .

𝑡𝑀𝐼𝑁 = 4𝑀

0.9 × 𝐹𝑦= 21 𝑚𝑚 → 𝒖𝒔𝒆 𝒕𝒃𝒑 = 𝟑𝟎 𝒎𝒎

Check the vertical stiffeners with the force produced by the concrete pressure:

Assume conservatively that 𝑓𝑝𝑀𝐴𝑋 is uniform in all the length of the upper plate

projection on the base plate. The model is the same shown in Figure 3-7.

𝑓 = 𝑓𝑝𝑀𝐴𝑋 𝑔 + 𝑏𝑒𝑑𝑔𝑒 = 2.40 𝑘𝑁/𝑚𝑚,𝑋 =

𝑏𝑓

2= 175 𝑚𝑚


3-19

The reactions are: 𝑅 = 1.25𝑓𝑋 = 525 𝑘𝑁 ,𝐴 = 2𝑓𝑋 − 𝑅 = 315 𝑘𝑁

Then:

max 𝑅,𝐴 = 525 𝑘𝑁 < 𝜙𝑃𝑛 = 1294 𝑘𝑁 OK

3. Shear

𝑉𝑢 = 150 𝑘𝑁

Discussion:

When shear keys are used (see limit of 50 kN on the NCh2369.Of2003 code),

the anchor rods are supposed not to resist in shear. The shear is only carried

out by the shear key; and therefore it is necessary to separate the axial-

moment design from the shear design.

The shear key design shall be made considering a uniform stress due to

bearing with concrete (for transferring 𝑉𝑢 from the column to the concrete

foundation). For ductile behavior, the shear key must yield before the concrete

crushes in bearing.

If designing a shear key corresponding to a single plate (fixed to the base

plate), the plastic flexural behavior (if the plate has the adequate slenderness)

will be concentrated near the fixed en (plastic hinge region). Then, the

strength of the shear key corresponds to the plastic strength of the single

plate.

When large earthquakes are expected; the direction of the shear loading is not

known. Therefore, there is the need for a shear key which resists in two

perpendicular directions, and its capacity should be verified in this both

directions.

An example of one of those shear keys is the cruciform shape. In this case it is

not so clear that the plastic behavior under a uniform load will occur near the

fixed edge. The reason is that, there is a very stiff element at the middle of the

face of the plate. Although at both sides of the middle stiff element it can

occur yielding of the plates (ductile behavior), the stiff element can carry more

much load leading to a non-ductile global behavior.

For this case, the capacity of the shear keys shall be determined considering

appropriate boundary conditions and considering the minimum load being able

to be transferred, according to the failure mechanism.


3-20

For example, the capacity of the shear key can be estimated

assuming various yield lines paths:

Figure 3-8: Assumed yield lines for shear key cruciform shape.

Elevation view.

It is known that 𝑀𝑛 = 𝐹𝑦 𝑏𝑡2

4 = 𝐹𝑦(

𝑌𝑙𝑒𝑛𝑔𝑡 𝑕 𝑡22

4). It is possible to determine

on an assumed yield line its length 𝑌𝑙𝑒𝑛𝑔𝑡 𝑕 . With this nominal moment,

it is possible to determine the required total shear 𝑉𝑛 to produce a

hinge on the corresponding yield line assuming that this

“concentrated” force is applied at the gravity center of the geometric

shape that is located within the yield line; the stiff perpendicular

element and the grout line (the distance 𝑑 between the yield line and

the gravity center of this shape could be easily estimated, and

therefore 𝑉𝑛 =𝑀𝑛

𝑑).

Another alternative is to assume that the behavior of the shear key

will not be ductile, and assume that the connection has been designed

in general for forces reduced by an R factor (response modification

factor); for the shear key case, those design forces could be amplified

by a factor 𝛀𝒔𝒌 that reflects the assumption of non-ductile behavior

(this is similar to using an R* response modification factor so that

R*<R. Therefore it is possible to use 𝛀𝒔𝒌 =𝑹

𝑹∗). This alternative is

going to be used on this example.

For example, assume that 𝑉𝑢 presented on the example has not been already

amplified by this Ω𝑠𝑘 factor.

Therefore use a new 𝑉𝑢 = Ω𝑠𝑘 × 150 𝑘𝑁 = 3

2 × 150 𝑘𝑁 = 225 𝑘𝑁. (Suppose that 𝑉𝑢

came from a shear force reduced by R=3, and for the shear key it has been

considered R*=2<3). The use of an amplification factor like this shall be

discussed within project specifications.

Hsk

Bsk

G (grout)t2

1

23

4

5

t1


3-21

Trial sizes of the shear key:

The shear key will be located at the center of the base plate. Consider the

following figures:

Figure 3-9: Shear key dimensions. Plan and elevation view.

𝑩𝒔𝒌 = 𝟐𝟓𝟎 𝒎𝒎 ,𝑵𝒔𝒌 = 𝟐𝟓𝟎 𝒎𝒎 , 𝒕𝟏 = 𝟐𝟒 𝒎𝒎 , 𝒕𝟐 = 𝟐𝟒 𝒎𝒎 ,𝑯𝒔𝒌 = 𝟐𝟐𝟎 𝒎𝒎

𝑮 = 𝒈𝒓𝒐𝒖𝒕 𝒕𝒉𝒊𝒄𝒌𝒏𝒆𝒔𝒔 = 𝟓𝟎 𝒎𝒎

𝑩 = 𝒃𝒂𝒔𝒆 𝒑𝒍𝒂𝒕𝒆 𝒘𝒊𝒅𝒕𝒉 = 𝟑𝟗𝟓 𝒎𝒎 ,𝑵 = 𝒃𝒂𝒔𝒆 𝒑𝒍𝒂𝒕𝒆 𝒉𝒆𝒊𝒈𝒉𝒕 = 𝟕𝟑𝟎 𝒎𝒎

The uniform load acting on the face perpendicular to 𝑉𝑢 is 𝑤 =𝑉𝑢

𝐵𝑠𝑘−𝑡2 𝐻𝑠𝑘−𝐺

(grout thickness is discounted).

Using only one side of the shear key face, the corresponding model is the

following:

Figure 3-10: Slab model for one side of the shear key face. Two embedded

sides and two free sides.

𝐿𝑥 =𝐵𝑠𝑘

2= 125 𝑚𝑚, 𝐿𝑦 = 𝐻𝑠𝑘 = 220 𝑚𝑚

Nsk

Bsk

t1

t2

Vu

N

B

Hsk

G


3-22

Note:

If the grout thickness is discounted, then the correct slab model is with a

loaded area in the height 𝐿𝑦 − 𝐺 on the above figure, and not loaded near the

upper fixed edge. In this case, a conservative model has been used

considering all the loaded area in all the height 𝐿𝑦.

From tables (Stiglat & Wippel book), use 𝐿𝑦/𝐿𝑥 = 1.76 → 𝑐𝑜𝑒𝑓 = 3.81

Therefore the relation between the slab moment and the shear 𝑉𝑢 is:

𝑀 =𝑤𝐿𝑥𝐿𝑦𝑐𝑜𝑒𝑓

=

𝑉𝑢

𝐵𝑠𝑘−𝑡2 𝐻𝑠𝑘−𝐺 𝐿𝑥𝐿𝑦

𝑐𝑜𝑒𝑓

Assuming a plastic behavior in bending (𝑁𝑠𝑘

2

𝑡1= 5.21 < 0.38

𝐸

𝐹𝑦= 9.15),

𝑀𝑛 = 𝑍𝐹𝑦 =𝑡2

4𝐹𝑦 = 50 𝑘𝑁 −𝑚𝑚

It is expected that 𝑀𝑛 > 𝑀. In the critical case: 𝑀𝑛 = 𝑀 and then solving for 𝑉𝑢:

𝑉𝑢 = 𝑀𝑛 × 𝑐𝑜𝑒𝑓 × 𝑁𝑠𝑘 − 𝑡2 𝐻𝑠𝑘 − 𝐺

𝐿𝑥𝐿𝑦= 264 𝑘𝑁

And therefore, the previous 𝑉𝑢 is the estimated capacity of the shear key.

Check that 𝑉𝑢 = 264 > 225 𝑘𝑁 OK

Check the concrete strength:

For ductile behavior, the capacity of the shear key must be lesser than the

concrete bearing strength.

Note: The concrete bearing strength shall be calculated discarding the grout

thickness.

𝜙𝑃𝑝 = 0.60 × 0.85𝑓𝑐′𝐴1

𝐴2

𝐴1

≤ 0.60 × 1.7𝑓𝑐′𝐴1

(Re. ACI 318-05, 10.14.1 Section)

Assume conservatively that 𝐴2 = 𝐴1, therefore:


3-23

𝐴1 = 𝐵𝑠𝑘 − 𝑡1 𝐻𝑠𝑘 − 𝐺 = 38420 𝑚𝑚2

𝜙𝑃𝑝 = 490 𝑘𝑁 > 264 𝑘𝑁 OK

Weld of the shear Key to base plate

Consider the shear key capacity to design this connection. Assume that the

shear is carried out principally by the portion of the cruciform shape that it is

parallel to the action 𝑉𝑢. Use fillet welds.

Determine the minimum required welding size. Assume that at each side of

the cruciform shape portion, there is a length 𝐿 of fillet weld (refer to Figure

3-11):

𝜙𝑅𝑛 = ϕ𝐹𝑤𝐴𝑤 = 0.75 × 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤 × 2𝐿 > 𝑉𝑢 = 264 𝑘𝑁

Use E70 electrode (0.6𝐹𝐸𝑋𝑋 = 289.5 𝑁/𝑚𝑚2) and L=150 mm to obtain:

𝑡𝑤 >𝑉𝑢

0.75 × 0.6𝐹𝐸𝑋𝑋 0.707 × 2𝐿 = 5.74 𝑚𝑚 → 𝑡𝑤 = 6 𝑚𝑚

Check with the minimum fillet weld size: Minimum thickness of the parts

joined=𝑚𝑖𝑛 𝑡1 , 𝑡2 , 𝑡𝑏𝑝 = 24 𝑚𝑚 → 𝑡𝑤𝑚𝑖𝑛 = 8 𝑚𝑚 → 𝒖𝒔𝒆 𝒕𝒘 = 𝟖 𝒎𝒎.


Because 𝑉𝑢 can act in any direction, repeat the same fillet weld on the

perpendicular plate of the cruciform shape.


3-24

Figure 3-11: Fillet welds scheme on the cruciform shape for a vertical 𝑉𝑢.

Check rupture of the base metal to develop weld strength for the shear key to

base plate weld

For shear keys:

𝜙𝐹𝐵𝑀𝐴𝐵𝑀 = 0.75 × 0.6𝐹𝑢𝐴𝑛𝑣

= 0.75 × 0.6 × 𝐹𝑢 × 𝑡1 × 𝑁𝑠𝑘 = 1215 𝑘𝑁 > 𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤 × 2𝐿 = 491 𝑘𝑁

With 𝐿 = 150 𝑚𝑚.

For base plate:

𝜙𝐹𝐵𝑀𝐴𝐵𝑀 = 0.75 × 0.6𝐹𝑢𝐴𝑛𝑣 = 0.75 × 0.6 × 𝐹𝑢 × 2𝑡𝑏𝑝𝑁𝑠𝑘

Base plate is thicker than the shear key, therefore this verification is OK.

Base plate to column weld

The connection of the column to the base plate is a bearing type one. As one

alternative, double sided fillet welds are used on a portion of the column web,

and single side fillet welds on the column flanges. Consider the following

figure:


3-25

Figure 3-12: Column to base plate fillet welds.

The uplift force acting on the first combination is supposed to be resisted by

the flange welds. Each fillet weld on the flanges shall be capable to resist:

𝑅1 =𝑇𝑈𝑃𝐿𝐼𝐹𝑇

2= 500 𝑘𝑁

Assume as an initial trial that the length of the flange fillet welds is 𝐿 = 𝑏𝑓 =

350 𝑚𝑚. The angle between weld axis and load is 𝜃 = 90°.

𝜙𝑅𝑛 = 0.75 × 𝐹𝑤𝐴𝑤 = 0.75 × 1.5 × 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤𝐿 > 𝑅1

→ 𝑡𝑤 ≥ 6.2 𝑚𝑚 → 𝒕𝒘 = 𝟖 𝒎𝒎

For the load combinations with moment (2 and 3), the fillet welds on the

flanges shall be capable of transfer:

𝑅2 =max(𝑀𝑢)

𝑑 − 𝑡𝑓= 1538 𝑘𝑁

With max(𝑀𝑢) equal to the maximum moment from combinations 2 and 3.

The angle between weld axis and load is 𝜃 = 90°.

𝜙𝑅𝑛 = 0.75 × 𝐹𝑤𝐴𝑤 = 0.75 × 1.5 × 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤𝐿 > 𝑅2

→ 𝑡𝑤 ≥ 19.1 𝑚𝑚 → 𝒕𝒘 = 𝟐𝟎 𝒎𝒎

Because of the shear force acting on the column (assumed to be resisted by

the web welds), the fillet welds on the column web shall be capable to transfer

the capacity of the shear key:

𝑉𝑢 = 264 𝑘𝑁


3-26

Assume as an initial trial that 2𝑇 = 200 𝑚𝑚. The angle between weld axis and

load is 𝜃 = 0°. 𝜙𝑅𝑛 = 0.75 × 𝐹𝑤𝐴𝑤 = 0.75 × 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤2𝑇 > 𝑉𝑢

→ 𝑡𝑤 ≥ 8.6 𝑚𝑚 → 𝒕𝒘 = 𝟏𝟎 𝒎𝒎

Check the minimum fillet weld size: min 𝑡𝑐𝑤 , 𝑡𝑏𝑝 = 12 → 𝑡𝑤𝑀𝐼𝑁 = 5 𝑚𝑚 OK.

Check also that the fillet welds on the column flange are capable to transfer

the shear capacity of the shear key:

𝜙𝑅𝑛 = 0.75 × 𝐹𝑤𝐴𝑤 = 0.75 × 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤2𝐿 = 2149 kN > 𝑉𝑢 = 264 𝑘𝑁

Check rupture of the base metal to develop weld strength:

Base plate to column welds (flanges)

For base plate:


= 0.75 × 0.6 × 𝐹𝑢 × 𝑡𝑏𝑝 2𝑏𝑓 = 4253 𝑘𝑁 > 𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤 × 2𝑏𝑓 = 2865 𝑘𝑁

For column:


= 0.75 × 0.6 × 𝐹𝑢 × 𝑡𝑓𝑏𝑓 = 1771 𝑘𝑁 > 𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤 × 2𝑏𝑓 = 2865 𝑘𝑁

Base plate to column welds (web)

For base plate:


= 0.75 ∗ 0.6 × 𝐹𝑢 × 𝑡𝑏𝑝 2𝑇 = 1215 𝑘𝑁 > 𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤 × 2𝑇 = 409 𝑘𝑁

For column:


= 0.75 × 0.6 × 𝐹𝑢 × 𝑡𝑤(𝑑 − 2𝑡𝑓) = 729 𝑘𝑁 > 𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 0.6𝐹𝐸𝑋𝑋 0.707𝑡𝑤 × 2𝑇 = 409 𝑘𝑁


3-27

3.3.d. Designed connection

Notes:

1) Anchorage to concrete has not been designed.

2) Anchor Bolts: 4 bolts ASTMF 1154 Gr. 36 Ø 38 mm.

3) Connections for vertical stiffeners and upper plate

are not designed.

grout

(typ)

A

B

C C

A - A plan

Upper plate

PL 350x190x30 (typ).

Column

H350x350x165.6.

Stiffener plate

PL 305x190x25 (typ).

B

A

B - B plan

Base plate

PL 730x395x30

C - C plan

(Shear key)

(typ)

10

10

Shear key to

base plate

L=150 mm

20Exterior of

flange

20Exterior of

flange

Column web

to base plate

L=100 mm

10

10

10

10

Shear key to

base plate

L=150 mm


3-28

3.3.e. Additional Discussion

Design forces when a concentric brace is connected to the base plate

This is a special case that is only mentioned for general purposes and is not

included in the numerical example.

If a brace is coming to a base plate connection, the design verifications of the

elements of the base plate and their attachments do not change with respect

to a connection without a brace. However the forces from the brace must be

considered.

Special and Ordinary Concentrically Braced Frames systems are discussed:

a) Special Concentrically Braced Frames (SCBF)

Axial Force

The required strength for the brace connection in SCBF systems is given by

section 13.3 of AISC 341-05, which says that:

Tensile forces

For tensile forces, the required strength shall be the lesser of the following:

- The expected yield strength of the brace in tension, determined as

𝑅𝑦𝐹𝑦𝐴𝑔.

- The maximum load effect, according by the analysis of the forces that

can be transferred to the brace by the overall system.

Then,

𝑇𝑢 𝑏𝑟𝑎 𝑐𝑒 = min(RyFyAg , Tu analysis )

According to the commentary C13.3a of the AISC 341-05 specification, there

are several ways to compute the maximum loads effect that can be transferred

to the bracing, for example a Pushover analysis; a determination of how much

force can be resisted before causing uplift of the foundation and an inelastic

time history analysis; between many others. However is not a common

practice on design projects to do these detailed analysis. In most cases there

is the need to provide a capacity large enough to ensure yielding of the brace.


3-29

Furthermore, according to the commentary C13.3a the upper limit of the

expected yield strength is included for elements where the limit of the system

strength is not given by the bracing, which is the case of foundations that are

designed in system base on the application of load combinations using the

amplified seismic load Ω0.

Considering the latter discussion, it is recommended to consider in a

conservative way that the tensile required strength of the brace for the base

plate design is:

𝑇𝑢 𝑏𝑟𝑎𝑐𝑒 = 𝑅𝑦𝐹𝑦𝐴𝑔

Then, if the angle of the brace with respect the horizontal line at the level of

the base plate is 𝜃 (see Figure 3-13), the tensile force acting over the base

plate is:

𝑇𝑢 = 𝑃𝑢 𝑐𝑜𝑙 − 𝑅𝑦𝐹𝑦𝐴𝑔 𝑏𝑟𝑎𝑐𝑒 sin(𝜃)

Where, as has seen before in this manual, the axial solicitation for the column

is determined according to the load combination that gives the greater axial

tension, generally this combination is 0.9D – 1.4(EH + EV). Note that the

connection for the axial loads is positive on compression.

Figure 3-13: Angle between brace and base plate.

Compressive forces

For compressive forces, the required strength shall be at least equal or greater

than 1.1𝑅𝑦𝑃𝑛, where 𝑃𝑛 is the compressive nominal strength of the brace. Then,

for the base plate the compression force is:

𝑃𝑢 = 𝑃𝑢 𝑐𝑜𝑙 + 1.1𝑅𝑦𝑃𝑛sin 𝜃

Base Plate

Brace


3-30

Where in this case, 𝑃𝑢 𝑐𝑜𝑙 is determined according to the load combination that

gives the greatest compressive force for the column.

Shear Force

According to section 8.5b of AISC 341-05, the required shear strength for the

base plate connection is given by the summation of the required strength of

the steel elements at the base plate connection.

For the case of the column at the base plate, the required strength is already

known from the above example. For the braces, the axial tensile required

strength of the brace is:


Then:

𝑉𝑢 = 𝑉𝑢 𝑐𝑜𝑙 + 𝑅𝑦𝐹𝑦𝐴𝑔 𝑏𝑟𝑎𝑐𝑒 cos(𝜃)

Notes:

It is possible to also consider the compression force in order to

project it and obtain shear force, but since the compression force will

always be less or equal than the tensile required strength of the

brace, generally it is only needed to consider the tensile case.

It is important to also consider the direction of the forces on the brace

and on the base of the column for the proper signs.

Flexural Strength

According to section 8.5 of AISC 341-05, the required flexural strength for

column bases is given by the summation of the required strengths of the steel

elements at the connection.

According to section 13.3b, the required flexural strength of the brace is:

𝑀𝑢 𝑏𝑟𝑎𝑐𝑒 = 1.1𝑅𝑦𝑀𝑝

Then, the required strength for the connection is:

𝑀𝑢 = 𝑀𝑢 𝑐𝑜𝑙 + 1.1𝑅𝑦𝑀𝑝 𝑏𝑟𝑎𝑐𝑒

The required flexural strength for braces may be neglected if the brace is

detailed in order that it can accommodate the inelastic rotations associated to

the post buckling deformations (braces will develop buckling that eventually

will generate plastic hinges at the ends of the brace). The accommodation of


3-31

the inelastic rotations is accomplished using single gusset plate with the brace

terminating before the line of restraint. For more information see Chapter 4 of

this Manual.

b) Ordinary Concentrically Braced Frames (OCBF)

Axial Force

The required strength for the brace connection in OCBF systems is given by

section 14.4 of AISC 341-05, which says that:

- For the limit state of bolt slip, the required strength of the bracing

connection shall be determined according to the load combinations

stipulated by the building code, not including the use of the amplified

seismic load. This is because the bolt slip failure does not constitute

a connection failure, and the dissipation of energy that occurs product

of the bolt slip reduces the seismic response.

- For all the other limit states, the required strength is the expected

yield tensile strength of the brace 𝑅𝑦𝐹𝑦𝐴𝑔. The required strength needs

not exceed either of the following:

- The maximum force that the structural system can develop.

- A load effect that considers the effect of the amplified seismic load.

Therefoe the axial uplift design force for the base plate connection, considering

the brace is:

𝑇𝑢 = 𝑃𝑢 𝑐𝑜𝑙 − 𝑅𝑦𝐹𝑦𝐴𝑔 𝑏𝑟𝑎𝑐𝑒 sin(𝜃)

Where 𝑃𝑢 𝑐𝑜𝑙 is given by the combination for the column that produces the

maximum uplift effect on the base plate and 𝜃 is the angle between the brace

and the horizontal line on the base plate.

Shear Force

According to section 8.5b of AISC 341-05, the required shear strength for the

base plate connection is given by the summation of the required strength of

the steel elements at the base plate connection.


3-32

For the case of the column that arrives to the base plate, the required strength

is already known from the above example. For the braces, the axial required

strength of the brace is:


Then:

𝑉𝑢 = 𝑉𝑢 𝑐𝑜𝑙 + 𝑅𝑦𝐹𝑦𝐴𝑔 𝑏𝑟𝑎𝑐𝑒 cos(𝜃)

Note:

It is important to consider the direction of the forces acting on the brace and

on the base of the column.

Flexural Strength

According to section 8.5 of AISC 341-05, the required flexural strength for

base plates is given by the summation of the required strengths of the steel

elements at the connection. However, for OCBF it is expected that the brace

will develop limited inelastic deformations. For this reason, it is not necessary

to consider the flexural strength of the brace that arrives to the base plate

connection.

3.4. References

Plates and slabs:

Stiglat & Wippel,1968, “Placas”. Instituto Eduardo Torroja de la

Construcción y el Cemento. Madrid.

References for base plate connections design:

William Honeck and Derek Westphal, Forell Elsesser Engineers Inc,

1999, “Steel tips: Practical Design and Detailing of Steel Column Base

Plates”. Structural Steel Educational Council.

James Fisher and Lawrence Kloiber, 2006, “AISC Steel Design Guide

# 1: Base Plate and Anchor Rod Design” 2nd Ed. American Institute of

Steel Construction, USA.




American Institute of Steel Construction, 2005, “AISC Manual of Steel

Construction”. 13th Edition. AISC, USA.

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 4: BRACE CONNECTIONS

4-1

4. BRACE CONNECTIONS

4.1. General Description of Seismic Braced Frames

Steel systems that contain braced frames are very efficient and economical

systems, because they resist lateral forces and displacements trough the axial

strength and stiffness of the brace members, with little or no bending until the

compression braces buckle.

Concentrically braced frames:

In concentrically braced frames, the centerlines of braces, beams and columns

intersect, or nearly intersect, minimizing flexural behavior. They are almost

similar to vertical trusses. According to AISC 341-05 Code, there are two

principal systems: Ordinary Concentrically Braced Frames (OCBF) and Special

Concentrically Braced Frames SCBF.

These structures tend to be more economical than moment frames and

eccentrically braced frames in terms of material, fabrication and erection costs.

Nevertheless, they have reduced flexibility in architectural and functional

issues due to the presence of braces that obstruct the spaces.

There are several types of braced concentrically systems. Some examples are

graphically presented below:

Figure 4.1-1: Examples of Concentric Bracing Configurations. Adapted from AISC 341-05, Fig. C-I-13.1

4.1.a. Ordinary Concentrically Braced Frames (OCBF)

In the case of Ordinary Concentrically Braced Frames (OCBF), as defined on

Section 14 of AISC 341-05 Code, it is expected that these systems will have

V-BracingInverted

V-BracingV-Bracing

Diagonal

Bracing


4-2

limited inelastic deformations. Therefore, they are designed for higher seismic

forces (higher than for SCBF systems) in order to take into account this limited

ductility. The design and construction procedure of OCBF systems is simpler

than in SCBF systems.

4.1.b. Special Concentrically Braced Frames (SCBF)

Special Concentrically Braced Frames (SCBF), as defined on section 13 of AISC

341-05 Code, are designed for a lower force level than OCBF systems (larger R

factor). Therefore, in contrast with OCBF frames, these systems require

numerous detailing and design requirements to ensure the required ductility

(for example, they need to have a post-buckling ductile behavior).

For SCBF systems, the use of tension only-bracing is not permitted according

to AISC 341-05 Code. Also, the Seismic Code requires that these systems

balance compression and tension braces. Along any line of bracing, braces

must be oriented so to engage at least 30%, but no more than 70% of the

total lateral force resisted by braces in tension.

Other requirements on the Seismic Code, in order to ensure ductility and

hysteretic damping, refer to limitations to member slenderness, compressive

strength, width-to-thickness ratios and special detailing for gusset plates.

Referring to connections on SCBF systems, there are two approaches used in

their design. The first one creates enough strength and rigidity in the

connections in order to force the formation of plastic hinges at the ends and

middle of the brace under compressive forces (when buckling occurs in the

plane of the gusset plates). The second approach ensures that plastic hinges

form in the gusset plate at the brace ends when out of plane buckling of the

gusset plate occurs, with a hinge still occurring at the midpoint of the brace.

The following requirement is for the last approach:


4-3

Figure 4.1-2: Brace-to-gusset plate requirement for buckling out-of-plane bracing system. Adapted from AISC 341-05, Fig. C-I-13.2.

Note:

It is recommended to detail a slightly longer distance than the 2𝑡 minimum.

Typically, values from 2𝑡 to 4𝑡 are used due to practical dimensioning

requirements of the gusset plate. The distance shall be measured from a line

perpendicular to the end of the brace member, in order to ensure buckling

perpendicular to the plane of the frame.

4.2. Code requirements for Brace Frame Connections, Design Forces and Recommendations:

4.2.a. NCh2369.0f2003:

Connections of the seismic braces shall be designed to resist 100% of the

tensile capacity of the braces, considering their gross area.

(Re. NCh2369.Of2003, 8.5.2)

There are also specific provisions for braced frames in section 8.3 of

the NCh2369.Of2003 Code. Some of them will be discussed later.

For horizontal braces apply section 8.7 of NCh2369.Of2003.

Slenderness of brace members shall be lesser than 1.5𝜋 𝐸

𝐹𝑦 . This limit

is slightly greater than the limit of AISC 341-05.

Gusset Plate

t= thickness of gusset plate

2t


4-4

4.2.b. AISC 341-05

1. SCBF Systems (Section 13)

Slenderness of the brace members: 𝑘𝐿

𝑟≤ 4.0 𝐸/𝐹𝑦 (Re. AISC 341-

05, Section 13.2a). See the exception on the code for braces with

some specific requirements.

Required strength for braces: see section 13.2b. Note that this

section mentions that when the effective area of the bracing members

is less than the gross area, for example in slotted HSS braces at the

gusset plate, there are tensile strength requirements based upon the

limit state of fracture in the net section.

Lateral force distribution (alternate braces in tension and compression

for redundancy): see section 13.2c.

Column and braces must comply with width-thickness limitations

given in section 8.2b (Seismically Compact Sections, according to

Table I-8-1).

Bracing connections in SCBF systems

(Re. AISC 341-05, section 13.3)

Required tensile strength: 𝑇𝑟𝑒𝑞 = min(𝑅𝑦𝐹𝑦𝐴𝑔 ,𝑇𝑢𝑀𝐴𝑋 ) , with 𝑇𝑢

𝑀𝐴𝑋 equal to

the maximum load effect (from analysis) that can be transferred to

the brace by the system.

Notes:

1. 𝑇𝑟𝑒𝑞 includes beam to column connection if it is contained on the

bracing system.

2. According to AISC 341-05 Commentary, 𝑇𝑢𝑀𝐴𝑋 can be calulated in

several ways (depending on specific situations). For example,

calculate the capacity from a pushover analysis (see other options in

the commentary). From a conceptual basis, since the character of

ground motions is not really well known, it is unrealistic to have an

accurate calculation of 𝑇𝑢𝑀𝐴𝑋 .

3. Therefore, generally it is only used the value of the brace yielding for

designing the connection.

Required flexural resistance (about the critical buckling axis):

𝑀𝑟𝑒𝑞 = 1.1𝑅𝑦𝑀𝑝. The exception is for brace connections that are

designed for 𝑇𝑟𝑒𝑞 and can accommodate the inelastic rotations

associated to brace post-buckling deformations. This is accomplished


4-5

using a gusset plate, with the brace finishing before the line of

restraint (see detailing requirements in Figure 4.1-2)

Required compressive strength: 𝐶𝑟𝑒𝑞 ≥ 1.1𝑅𝑦𝑃𝑛, with 𝑃𝑛 equal to the

nominal compressive strength of the brace. Note that it is necessary

to consider the true effective length of the brace, the connection fixity

(in order to calulate k), and the material overstrength. Brace buckling

capacity stress 𝐹𝑐𝑟 should be based on the actual brace length in lieu

of the traditional work-point to work-point length commonly used in

analysis. Therefore, braces for this analysis are “shorter” and 𝐹𝑐𝑟 is

increased:

Figure 4.2-1: Brace effective length – Adapted from Steel Tips : Design of Special Concentrically Braced Frames. Cochran & Honeck.

Some authors suggest always including 𝑅𝑦 factor in calulating 𝐹𝑐𝑟 as a

conservative measure. Note that the design of gusset plates shall include

consideration of buckling.

V-inverted and inverted V type bracing:

The required strength of beams intersected by braces, their

connections and supporting members shall be calulated based on the

load combinations of the applicable building code, assuming that

braces provide no support for dead and live loads. For load

combinations that include the earthquake effect, this effect (E) on the

beams shall be calulated as follows:

Force in tension braces: 𝑇 = 𝑅𝑦𝐹𝑦𝐴𝑔

Force in braces in compression: 𝐶 = 0.3𝑃𝑛

For additional required conditions of beams and their lateral bracing,

see section 13.4a(2).

Work - point to work point

Brace length to use for gusset

plate design


4-6

As said on the AISC 341-05 code, as a minimum one set of lateral braces is

required at the point of intersection of the V (or inverted V) braces; unless the

beam has enough out-of-plane strength and stiffness to ensure stability

between adjacent brace points (prevention of lateral torsional buckling).

K type bracing is not permitted on SCBF systems by the code. This is because

it is not desirable to have columns subjected to unbalanced lateral forces from

the braces, as these forces may contribute to column failures.

Figure 4.2-2: K type bracing.

For protected zones of bracing members in SCBF systems, consult the

section 13.6 of AISC 341-05.

2. OCBF Systems (Section 14)

Slenderness of the brace members:

Comply with the requirements of section 8.2b (seismically compact

sections, in order to limit local buckling and fracture).

For K, V or inverted-V systems: 𝑘𝐿

𝑟≤ 4.0 𝐸/𝐹𝑦 (Re. AISC 341-05,

Section 14.2). There is a exception in the code for HSS braces filled

with concrete.

According to the code user note, braces that are designed for tension only are

not adequate for K ,V and inverted V configurations.

Special systems (beams in V and V-inverted systems and columns in K

systems):


4-7

Beams and columns must be continuous at bracing connections away

from beam to column connection and shall meet the following for the

required strength:

Calculated from load combinations of the applicable building code,

assuming that braces provide no support for dead and live loads. For

the load combinations that include the earthquake effect, this effect

(E) on the beams shall be calulated as follows:

- Force in tension braces: 𝑇 = 𝑅𝑦𝐹𝑦𝐴𝑔. In V and V-inverted

systems, 𝑇 < 𝑇𝑢𝑀𝐴𝑋 , with 𝑇𝑢

𝑀𝐴𝑋 = maximum tensile force that

can be developed by the system.

- Force in all adjoining braces in compression: 𝐶 = 0.3𝑃𝑛

For conditions of beams and their lateral bracing , see section

14.3(2).

Bracing connections in OCBF systems


For bolt slip limit state: the required strength of the connection shall

be obtained using the load combinations of the applicable building

code, not using the amplified seismic load.

For any other limit state, the required strength is the expected yield

strength in tension: 𝑇𝑟𝑒𝑞 = 𝑅𝑦𝐹𝑦𝐴𝑔.

Notes:

1. The required strength of the connection does not require to exceed

either the maximum force that can be developed by the system nor a

load effect based upon using the amplified seismic load.

2. The bolt slip limit state does not constitute a connection failure and

the associated energy dissipation can serve to reduce seismic

response. This fact is reflected in that this limit state is designed for a

lower force level than other limit states.

Note that the design of gusset plates shall include consideration of buckling.

Tip:

Limits states of OCBF systems are the same as for the SCBF systems. However

in OCBF systems there are no requirements for ductility at the hinge zone, on

the gusset plates. It is possible to design a connection for “OCBF forces” and

add some ductility requirements from SBCF systems.


4-8

4.2.c. AISC Manual of Steel Construction 13th Ed. recommendations

1. Force transfer in bracing connections

(Re. AISC Manual of Steel Construction 13th Ed., Part 13)

There are many methods for calulating the force transfer on bracing

connections, and there is controversy on which one of those methods provide

safer and more economical connections. According to Thornton (1991), the

Uniform Force Method (recommended by the manual) best predicts both the

available strength and critical limit state of the connection; it also leads to

more economical and simpler designs.

Uniform Force Method (UFM):

1. Select the connection geometry such that moments do not exist on

the 3 planes of load transfer of the connection (gusset to beam,

gusset to column, and beam to column). Therefore, those 3

connections are designed for tension and shear only.

Figure 4.2-3: Diagonal Bracing Connection and External Forces. Adapted from AISC Manual of Steel Construction 13th Ed. Fig. 13-2(a) Note

that the working point in this case coincides with the beam and column centerlines.

From the figure above, the terms are:

𝑒𝑏 =𝑑𝑏

2, 𝑒𝑐 =

𝑑𝑐

2 (half of the beam and column depth). For a column web

support 𝑒𝑐~0.


4-9

𝛼 : distance from the external face of column flange (or web) to the centroid of

the gusset-beam connection.

𝛽 : distance from the external face of beam flange to the centroid of the

gusset-column connection.

Figure 4.2-4: Gusset free body diagram. Adapted from AISC Manual of Steel Construction 13th Ed. Fig. 13-2(b)

Figure 4.2-5: Column free body diagram and beam free body diagram. Adapted from AISC Manual of Steel Construction 13th Ed.

Fig. 13-2(c) and Fig. 13-2(d)

From the figures above:

𝑅 = 𝑅𝑢 = required strength at the end reaction of the beam.

𝐴𝑏 = required transverse force from adjacent bay (girder drag force).

𝐻 = horizontal component of 𝑃 (P is the axial force of the brace).


4-10

𝑉 = vertical component of 𝑃.

𝐻𝑏 = required shear force on gusset to beam connection.

𝐻𝑐 = required axial force on gusset to column connection.

𝑉𝑏 = required axial force on gusset to beam connection.

𝑉𝑐 = required shear force on gusset to column connection.

2. To obtain zero moment at the planes of the connections , try values

of 𝛼 and 𝛽 (locate the gusset to beam and gusset to column

connections centroids) such that:

𝛼 − 𝛽𝑡𝑎𝑛 𝜃 = 𝑒𝑏𝑡𝑎𝑛 𝜃 − 𝑒𝑐

3. Calulate the forces on the planes of load transfer:

𝑟 = 𝛼 + 𝑒𝑐 2 + 𝛽 + 𝑒𝑏

2

𝑉𝑐 =𝛽

𝑟𝑃 , 𝑉𝑏 =

𝑒𝑏

𝑟𝑃 , 𝐻𝑐 =

𝑒𝑐

𝑟𝑃 ,𝐻𝑏 =

𝛼

𝑟𝑃

Note: Axial force 𝑃 could be a tensile or compressive force (corresponding

signs will change).

4. Design the connections. Note that the beam to column connection

shall be designed for a required shear equal to 𝑅 − 𝑉𝑏 and a required

axial force equal to 𝐴𝑏 ± (𝐻 − 𝐻𝑏)

Note:

There are special cases listed on the AISC Manual of Steel Construction for

force transmission on bracing connections:

Modified working point location: for eccentric working point

connections. This situation will generate flexural forces in the framing

members and generally will lead to smaller gusset plates. Also it is

used for column web connections.

Minimizing the shear in beam to column connection

No gusset-to-column connection.


4-11

Note:

Make sure that when using the UFM method for designing the connections

between gusset and column or beam framing members, these connections

shall be centered or nearly centered on the corresponding gusset edge. Note

that it is not necessary to use all the gusset edge length for performing the

connection (for example a welded one); in practice welders generally weld all

the gusset edge length.

2. Available strength in bracing connections

(Re. AISC Manual of Steel Construction 13th Ed., Part 13)

For diagonal bracing connections, the available strength is calulated from the

applicable limit states of the bolts, welds and connecting elements; depending

on the specific case that we are analyzing.

3. Desirable details that avoid sharing forces between bolts and welds

Consult the welds general information chapter of this Manual.

4.2.d. Gusset plates design issues

Reference:

Steel Tips: Seismic Design and Behavior of Gusset Plates. Abolhassan Astaneh.

1998.

According to Astaneh (1998), gusset plates, in general, have performed

satisfactorily during past earthquakes. However, a few cases of failure of

gusset plates have been reported. The observed common failure modes are:

Fracture of the welds.

Buckling of the gusset plates.

Fracture of the net section of the gusset plate or the bracing member.

Most of these failures can be related to a non-ductile design and poor detailing

of the gusset plate connections. Therefore, design and detailing of gusset

plates must be made to prevent brittle modes of failure, and to ensure a

desirable ductile behavior.


4-12

Whitmore section:

As a recommendation, in order to obtain rational values for direct stresses in a

gusset plate on the areas at the end of the bracing members, the concept of

distribution of the force along 30° lines (made from the first part of the

connection), which is used to define width of the Whitmore section. The

following figures illustrate the concept:

Figure 4.2-6: Width of the Whitmore Section for Bolted or Welded Connections. Re. AISC Manual of Steel Construction, 13th Ed. Figure 9-1.

Out of plane buckling:

As said before, when a bracing member buckles out-of the plane of the braced

frame, the plastic hinge forms in the gusset plate. These plastic hinges need to

be free to rotate, because otherwise the gusset plates could fracture in a small

number of cycles. To ensure free rotation, the recommended detail is that the

bracing member should finish at a distance at least 2𝑡 away from the re-

entrant corner of the gusset plate.

Free Edge buckling:

To prevent the free edge buckling of the gusset plate prior to the gusset plates

reaching their maximum compression capacity, it is recommended to comply

with 𝐿𝑓𝑔

𝑡< 0.75

𝐸

𝐹𝑦. 𝐿𝑓𝑔 is the length of the free edge of the gusset plate and 𝑡 is

the gusset plate thickness.

Ductility of gusset plate connections:

Some tips and requirements with regard to ductility issues are given by

Astaneh:

w

Gusset or other

Connection elements

b) Welded Joint

30° 30° 30° 30°

l wl


4-13

Bolted gusset plates, if net section fracture is prevented, have more

ductility than welded plates. Additional ductility comes from slippage

of bolts.

Consider the 2𝑡 distance for out of plane buckling.

Buckling of gusset not only results in reduced compressive capacity,

but if buckling is elastic, it can lead to brittle behavior. It is

recommended that when buckling capacity of the gusset is less than

50% of its tensile capacity, the gusset plate shall be stiffened or

thickened to develop larger compressive capacity.

Prevent free edge buckling of the gusset. For this purpose, the edge

of the gusset plate can be stiffened by adding a relatively small angle

or plate. Also it is possible to increase the gusset thickness or reduce

𝐿𝑓𝑔 .

Seismic design of connection of a gusset plate to the bracing members:

According to Astaneh, the desirable order for failure modes in a typical

connection of a bracing member to the gusset plate:

Slippage of bolts (bolted connections).

Yielding of gross area of plates or angles used in the connections.

Bearing failure of bolt holes.

Local buckling of angles and plates used in the connections.

Edge distance fracture and bolt spacing failure in bolted connections

Fracture of effective net area of angles and plates in the connections /

Block shear failure.

Fracture of bolts and welds.

Note that in the case of braces connected with bolts, they may require that the

end of the braces be reinforced to keep the failure out of the reduced section

created by the bolt holes (in the effective area). Also, if hollow structural

sections are used for braces, there is a discount in the net area when they

reach the gusset plates (called knife plates) and may require net section

reinforcement plates. In general, welded connections eliminate the “effective

area” problem.

For the connection between the gusset plate and the beam or column, note

that if flange welds are used, weld access holes shall be discounted.

If welds are used to join gusset plates to the framing members (column or

beam), according to the AISC Manual of Steel Construction 13th Ed., the

connection should be designed for the larger of the peak stress and 1.25 (weld


4-14

ductility factor) times the average stress. The weld size needs no to be larger

than to develop the strength of the gusset.

Seismic design recommendations for gusset plates:

According to Astaneh, the desirable order of failure modes is:

Yielding in the Whitmore’s area of the gusset plate.

It can occur due to direct tension or compression. The yield capacity of a

gusset plate due to a direct axial load can be computed as:

𝑃𝑦 = 𝐴𝑔𝑤𝐹𝑦 , with 𝐴𝑔𝑤 = gross area of the gusset plate at the Whitmore’s

effective area.

Yielding of critical sections of the gusset plate under combined

stresses.

These critical sections can yield under a combination of axial load, bending and

shear. The following interaction equation can be used:

𝑁

𝜙𝑁𝑦

2

+ 𝑀

𝜙𝑀𝑝

+ 𝑉

𝜙𝑉𝑦

4

≤ 1.0

𝑁,𝑉,𝑀 : Axial load, shear load, and bending moment on the critical section.

𝑁𝑦=yield axial capacity of the cross section (𝐴𝐹𝑦), 𝑉𝑦 = yield shear capacity of

the cross section (0.6𝐴𝐹𝑦), 𝑀𝑝= plastic moment capacity, 𝑀𝑝 = 𝑍𝐹𝑦.

There are some other options like the Von Mises yield criterion, which can be

used for gusset connected edges stresses:

𝑁

𝜙𝐹𝑦𝐴

2

+ 3 𝑉

𝜙𝐹𝑦𝐴

2

≤ 1.0, with 𝐴 = area of the edge section.

Buckling of the gusset plate

The gusset plate can buckle due to compression just beyond the end of the

bracing member. To compute the buckling capacity is permitted to use

Whitmore’s width.


4-15

The buckling capacity is: 𝑃𝑐𝑟 = 𝐴𝑔𝑤𝐹𝑐𝑟 , where 𝐹𝑐𝑟 is the critical stress acting on a

unitary width gusset strip parallel to the axis of the brace within the

Whitmore’s effective width (typically the longest strip is used, nevertheless it

is also possible to use an average value of 3 different lengths, the central and

the two extreme strips from the Whitmore section). These strips are treated as

columns. See the following figures:

Figure 4.2-7: Buckling of gusset plate and model to calculate buckling capacity. Adapted from Steel Tips # 42: Seismic Behavior and Design of

Gusset Plates. Figure 4.7.

The typical check is on Whitmore’s area, using an effective length factor of

k=0.5 (Gross, 1990) or k=0.65 (Thorntorn, 1984) if the gusset is supported by

two edges; or 1.2 if the gusset is supported by one edge (in this case, the

gusset can readily move out of plane and a sidesway mode of buckling can

occur on it).

As recommendations for gusset detailing, at the brace end of the gusset plate,

a minimum of 1” (25 mm) offset from the brace to the gusset sloped edge

should be provided. The sloped angle measured from the brace axis, starting

from this edge, should be greater than 30° in order to maximize the Whitmore

section width for gusset plate compression strength, resulting in thinner gusset

plates.

Buckling of the edges of the gusset plate.

Meet the limit for 𝐿𝑔𝑓

𝑡 as discussed above. Horizontal or vertical stiffeners could

be added to reduce 𝐿𝑓𝑔 . The location of the stiffener must be verified to ensure

that it does not cross the yield line of the gusset plate.

Block shear failure / Fracture of the gusset plate net area


4-16

For block shear failure:

For ductile behavior, the capacity of the gusset in block shear failure should be

greater than 𝜙(1.1𝑅𝑦) times its yielding capacity at the Whitmore’s area.

For fracture of the net area:

For ductile behavior, make sure that the tensile capacity of the gusset fracture

on the Whitmore’s net area (𝑃𝑛 = 𝐹𝑢𝐴𝑛𝑤 ) should be greater than 𝜙(1.1𝑅𝑦) times

its yielding capacity at the Whitmore’s area.

Some Additional considerations on gusset plates:

Excessively thick gusset plates should be avoided.

For preventing web crippling of the beam attached to the gusset, it is

recommended to use a beam web thickness greater than 75% of the

gusset plate thickness (especially if large axial forces act on the

beam). In any case, beam web crippling must be checked and

stiffeners must be added if needed.

4.3. Discussion of some typical bracing connections cases

4.3.a. Brace to beam column connections

1. Forces to take into account and force transfer

According to the Chilean code, the connections of the seismic braces shall be

designed to resist 100% of the tensile capacity of the braces, considering their

gross area. The Chilean code does not include the 𝑅𝑦 factor (that accounts for

material over strength) in this calulation (unlike the AISC 341-05 code). This

aspect could be discussed and stipulated on project specifications.

Note that there are some exceptions on AISC 341-05 Code for the

determination of the required strength of the connection relating to “the

maximum force that can be developed by the system”. It is important to check

that this force (and any other possible design force) is larger than the 100%

tensile capacity of the brace (Chilean code requirement) because otherwise the

design would not meet the NCh2369.Of2003 requirements.


4-17

For force transfer, the most used method is the Uniform Force Method (UFM)

described in the AISC Manual of Steel Construction 13th Ed. With the design

force of the brace connection and the application of UFM, it is possible to

obtain the forces on the gusset edges in order to design the respective

connections (bolted or welded) to the beam or column.

When more than one brace arrive to the beam-column connection, all the

forces of those braces must be taken into account, considering the possibility

of braces in tension and compression, and also the different directions of the

forces.

2. Limit States to take into account

The following limit states are related to a general case (SCBF or OCBF

systems). For a particular system, only the corresponding limit states apply.

At brace ends and at gusset to beam or column connections:

Brace net section fracture (effective area).

Brace block shear fracture.

Brace to gusset weld fracture (if connection is welded).

Bearing on the gusset plate (if the connection is bolted).

Bearing on the brace (if the connection is bolted).

Tear out on the gusset plate (if the connection is bolted).

Tear out on the brace (if the connection is bolted).

Check the bolts on the brace-gusset connection (if the connection is

bolted).

Gusset block shear fracture.

Gusset tension yield or fracture.

Gusset or weld failure at column (if connection is welded).

Gusset or weld failure at beam (if connection is welded).

Check bolted connections of the gusset to the beam or column (if

connections are bolted).

Gusset buckling (out of plane).

Gusset free edge buckling.

Failure of critical section of a gusset plate due to a combination of

axial load, bending and shear load.

At beam or column elements, and beam-to-column connection:

Column or beam web yielding.

Column or beam web crippling.


4-18

Column or beam web shear.

Beam-to-column connection: design for the transfer of shear and

axial loads.

Note that column or beam web local buckling could be prevented choosing an

adequate thickness of their webs or adding stiffener plates.

3. Possible connections and discussion of some cases

There is a large number of different possible bracing connections. Some

examples of them are shown on the following figures:

Figure 4.3-1: Pipe bracing connection with out of plane hinging details. Steel Tips: Design of Special Concentric Braced Frames. Cochran & Honeck.

Fig. 6-1b.


4-19

Figure 4.3-2: H bracing connection with out of plane hinging details, and without out of plane hinging details. Steel Tips: Design of Special Concentric

Braced Frames. Cochran & Honeck. Fig. 6-1c and 6-1d.

Typically, the difference is located at the connection of the brace with the

gusset plate. If HSS sections are used, the connection is commonly made

reducing the section of the brace and developing a welded connection with the

gusset plate (knife plate). When other sections are used, for example H

sections or L sections, the connection between the brace and the gusset plate

is generally made from a bolted and welded combination.

As noted from the figures above, the “ductility details” include the 2t offset on

the gusset plate.

Brace to Gusset connections:

- Hollow structural sections (HSS) to gusset plates

Typically, when HSS brace sections (for example pipes, square or rectangular

hollow sections) arrive to gusset plates (called knife plate on this cases), a

reduction on the brace section is developed in order to “slot it” into the knife

plate. If this section is left unreinforced, net section fracture will be the

governing limit state and brace ductility may be significantly reduced (see

requirements on section 13.2b of AISC 341-05 for SCBF systems).

A typical detail of the reduced section for HSS sections is shown in the figure

below (from Rafael Sabelli: AISC Seismic Braced Frames):


4-20

Figure 4.3-3: Typical Detailing of the reduced section at Knife Plate. Adapted from AISC Seismic Braced Frames: Design Concepts and Connections. Rafael

Sabelli.

According to section 13.2b of AISC 341-05 Code, the expected tensile strength

of the reduced section needs to be greater than the required tensile strength

of the brace. In other words:

𝜙𝑅𝑡𝐹𝑢𝑈𝐴𝑛𝑒𝑡 ≥ 𝑅𝑦𝐹𝑦𝐴𝑔 →𝐴𝑛𝑒𝑡𝐴𝑔

≥𝑅𝑦𝐹𝑦

𝜙𝑅𝑡𝐹𝑢𝑈

If the inequality shown above is not satisfied, reinforcement is required.

According to AISC 341-05 Commentary, reinforcement may be provided in the

form of steel plates welded to the tube, increasing the effective area at the

reduced brace section. It is recommended that the connection (welds) of the

reinforcement to the brace to be designed for the strength of the

reinforcement on either side of the reduced section.

- H sections to gusset plates

Typically, they are bolted connections, using flange splice plates bolted to the

H section and welded to the gusset plate. Also, it is possible to use web plates

attached to the brace member and to the gusset plate.

Note that in this case there is also a reduction on the gross area of the brace

members due to the bolt holes, but unlike the previous case, splice plates are

being added immediately, increasing the net area of the cross section.

For bolted connections, bolts shall be high strength, pretensioned, with class A

faying surface. It is recommended (but not an obligation) to design these

connections as slip critical (class A faying surface) checking also bearing

failure.


4-21

Note that in the same connection, it is not allowed to share the design forces

between bolts and welds since slip critical bolts may slip under earthquake

loading.

There are also many other possibilities of brace members to gusset

connections, for example an angle brace member bolted to a gusset.

Gusset to beam and columns connections:

-For gusset welding to beam or column flanges:

For calculating the average stress on the weld; for example if Uniform Force

Method is used, the weld is subjected to a combination of shear (𝑉) and axial

force (𝑁). If double fillet welds are used (typical case), each one of length 𝐿;

the average shear force on the welded union can be conservatively evaluated

as:

𝑅 = 𝑁

2𝐿

2

+ 𝑉

2𝐿

2

For LRFD design, the requirement is that the design strength of the fillet weld

of unitary length be greater than 𝑅 (it is optional to take into account the angle

𝜃 of the loading with respect to the weld axis). Also, the ductility factor

discussed in 4.2.d (1.25) shall be included for the design. Note also that,

according to the AISC Manual of Steel Construction, the weld size needs not be

larger than to develop the strength of the gusset (this is optional).

Note that the same approach shown before can be used on stresses or forces

format. If there is a bending moment acting on the gusset edge, the stress can

be obtained easily with the 𝑀𝑦

𝐼 formula for slender elements (“elastic

stresses”); and also 𝑁

𝐴 for axial stress and

𝑉

𝐴 for shear stress. As a commentary,

these formulas are not 100% correct for gusset plates, but they are used only

because there is seemingly no other alternative. Note that when there is no

moment on the interface; the peak stress is equal to the average stress.

-Prying action on clip angles (bolted connections only)

Double clip angles (L sections) are generally used in bolted gusset to column

(or beam) connections. Prying action occurs on the bolts when they are

subject to tensile forces. Forces within a connection which result from the


4-22

deformation of the connected parts are known as prying forces. In bolted-tee

connections, these forces can cause an increase in the tensile load on the

bolts. According to AISC360-05 Specification, section J3.6, the required tensile

strength (for bolts and threaded parts) shall include any tension resulting from

prying action produced by deformation of the connected parts.

As a recommendation, the AISC Manual of Steel Construction 13th Ed. provides

simplified expressions for computing this effect. As said on the Manual, proper

design for prying action includes the selection of bolt diameter and fitting

thickness such that there is sufficient stiffness and strength in the connecting

element and strength in the bolt.

Beam to column connections

These connections shall be designed to transfer the forces on the beam (N, V,

M) obtained from analysis.

4.3.b. Brace to beam column connections with a small offset from the

working point

This case is a variation from the previous case, in which the work-point

location is on the intersection of the center of gravity of brace, beam, and

column members.

But, in order to get smaller gusset plates, sometimes the line of the center of

gravity of the brace does not coincide with the framing members lines,

creating an eccentric working point. Typically, the work-point is located at the

corner of the gusset and therefore this eccentricity will result in a moment that

shall need to be transferred by the column and/or the beam (this extra

moment shall be considered in the design of the framing members and their

connections).

For this case, see the Uniform Force Method, special case 1, as described on

the AISC Manual of Steel Construction, 13th Ed.

4.3.c. X Braces

There are several possible configurations for developing X-braces connections.

Usually, one of the diagonal members is discontinuous at the midspan

intersection, and a gusset plate is used to connect the braces. This situation is

illustrated in the following figure:


4-23

Figure 4.3-4: X-Brace connections for discontinuous typical cases.

1. Forces to take into account

Generally, both braces that arrive to an X-brace connection have the same

length and they have similar sectional and material properties. The design

forces are assumed to be the same obtained for bracing connections (as

described above for OCBF or SCBF systems) and it is supposed that one

diagonal is in compression and the other one in tension. Note that the UFM is

not used on this case, because there are only concentrically axial loads.

The problem is that the assumption of one tension diagonal and other

compression diagonal may be unconservative and not realistic for some cases.

According to section 8.3 of NCh2369.Of2003 Code (Braced Frames), the

diagonal elements in an X brace shall be connected at the point of intersection.

This point can be considered fixed in the out-of-plane direction, to calulate the

members out-of-plane buckling lengths when one of the diagonals is

continuous. The assumption made on the Chilean Code, limits the effective

length of the compression diagonal to 0.5 times the diagonal length for simply

supported boundary conditions (recommendations of Picard and Beaulieu).

This may be unconservative in some situations, when the assumption of one

diagonal in tension and the other in compression is not realistic.

For example, when there is a seismic load perpendicular to the plane of the

diagonals, there is the possibility that both braces may fall under compression,

and in that case, the transverse bracing provided by one diagonal to the other

is significantly reduced, and the buckling length should be considered to be

equal to total length of the diagonal. This situation must be considered in the

design of the X brace connection.

Some general recommendations made by authors that have studied this

theme are:


4-24

Consider if the diagonals are simply or rigidly attached to their ends

(i.e. correct boundary conditions).

Take into account the length and sectional and material properties of

the bracing members.

Brace effective length is a function of the axial loading and the

stiffness of both diagonals.

The assumption that the connections at the ends of the diagonals are

perfect hinges is on the conservative side.

The midspan connection can affect the effective length factor for the

compression diagonals (and therefore the buckling load). In order to

increase the load carrying capacity of the X-brace system, the

rotational stiffness of this connection should be increased via suitable

detailing. The knowledge of the rotational stiffness of the center

connection can be obtained with analytical or experimental studies.

Tension diagonal does not always brace the compression diagonal;

and therefore, the out of plane displacement of the mid-point

connection is a potential buckling mode that should be taken into

account.

Some selected references that contain recommendations for choosing a more

realistic effective length factor for X-brace design and some other important

aspects are presented at the Selected references section of this chapter

(section 4.4).

2. Limit states to take into account

Limit states for this case are practically the same as the described for beam-

to-column bracing connections, but applicable to this specific case. The

following limit states are related to a general case (SCBF and OCBF systems).

For a particular system, only the corresponding limit states apply.

At brace unions with gusset and in the gusset:

Brace net section fracture (effective area).

Brace block shear fracture.

Brace to gusset weld fracture (if connection is welded).

Bearing on the gusset plate (if the connection is bolted).

Bearing on the brace (if the connection is bolted).

Tear out on the gusset plate (if the connection is bolted).

Tear out on the brace (if the connection is bolted).

Check the bolts on the brace-gusset connection (if the connection is

bolted).


4-25

Gusset block shear fracture.

Gusset tension yield or fracture.

Check bolted connections of the gusset to the beam or column (if

connections are bolted).

Gusset buckling (out of plane).

Gusset free edge buckling.

3. Special Case: X-brace with a horizontal girder

A special case of X Bracing Connection occurs when a continuous horizontal in-

plane beam element, that crosses trough the connecting point, has been

added. This connection could be designed in a same way as the V-inverted

(below the beam) and V (above the beam) brace to beam connections,

considering all the braces and forces present at the crossing point.

Figure 4.3-5: X-brace with a horizontal girder connection, retrofitted with vertical stiffeners on beam web and a T-shape stiffener. Source: Posco E&C.

Angamos Seismic Retrofit.

A problem that occurred on these connections is that the girders are only used

to restrict the buckling effective length of adjacent columns, and have thin

web thickness, as compared to gusset thicknesses at the crossing point.

Therefore, the webs of the girders had to be retrofitted in order to transfer the

loads coming from bracing elements.

The other problem that occurs is related to the overall stability of the complete

brace-gusset-girder system (similar to the problems described above on this

section). For retrofitting, stiffeners are added to the girder web in order to

increase the torsion strength of the system, and also a T shape stiffener is

added for constraining the complete system to work together, to provide

additional torsional stiffness and increase the critical buckling load.


4-26

The recommendation is the same that on the typical X brace connections:

It is important to note that the out of plane buckling is a potential failure mode

(especially when braces are both under compression), and therefore, the

midspan connection should be analyzed and detailed properly to increase the

rotational stiffness.

Use girder webs with thicknesses similar to the gusset thickness (because they

also transfer the brace loads) and vertical stiffeners, if needed, to avoid more

retrofitting. Additionally, if the girders are used for restricting the buckling

effective length of columns, if they are rotated 90° (or they have bigger

sections) they continue to accomplish their mission, and the rotational stiffness

of the connection at midspan increases.

A software finite element analysis could help a lot in a design stage.

4.3.d. V-Brace to beam connection (connected at beam midspan)

1. Specific provisions and transfer of forces to the connection

As described on the previous general discussion section, V braces must comply

with several requirements of AISC 341-05 provisions, which will be

summarized here:

SCBF

The required strength for beams, their connections and supporting

members, shall be calculated considering no support of the braces to

the beam for dead and live loads, using the applicable load

combinations.

(Re AISC 341-05 13.4a)

Loads produced by earthquake effect shall be considered in beams as

𝑅𝑦𝐹𝑦𝐴𝑔 for all the braces that are in tension, and 0.3𝑃𝑛 for all the

braces subjected to compression.

(Re AISC 341-05 13.4a)

Where the effective net area of the brace is less than the gross area,

the required tensile rupture strength for braces shall be greater than

the lesser of 𝑅𝑦𝐹𝑦𝐴𝑔 and the maximum load effect that can be

transferred by the system.

(Re. AISC 341-05 13.2b)


4-27

Additionally, lateral bracing requirements for the beam flanges at the

connection shall follow Appendix A of the AISC 360-05. Beams shall be

continuous between columns.

(Re AISC 341-05 13.4a(2))

For the required strength of the connection of the braces, consider the

provisions of the section 13.3 of the AISC 341-05, which have been described

above.

Braces in SCBF shall meet the requirements of section 8.2b of AISC 341-05,

which refer to the seismically compact shapes requirements.

OCBF

The required strength for beams shall be calculated considering no

support of the braces to the beam for dead and live loads, considering

applicable load combinations.

(Re AISC 341-05 14.3(1))

Loads produced by earthquake effects shall be considered in beams

as 𝑅𝑦𝐹𝑦𝐴𝑔 for all the braces that are in tension and 0.3𝑃𝑛 for all the

braces subjected to compression. For braces in tension the forces not

need to exceed the maximum forces that the system can develop.

(Re AISC 341-05 14.3(1))

Lateral bracing requirements for both flanges of the beam at the connection

shall follow provisions of Appendix A of the AISC 360-05.

(Re AISC 341-05 14.3(2))

Beams must be continuous at bracing connections away from the beam-

column connection.

(Re. AISC 341-05 14.5c)

For the brace connection, consider the following:


4-28

For the limit state of bolt slip, the required strength of the

connections shall be taken as the force calulated with the load

combinations stipulated by applicable the building code, not including

the amplified seismic load. On the other hand, for other limit states,

the required strength is the expected yield strength in tension of the

brace: 𝑅𝑦𝐹𝑦𝐴𝑔. However the required strength for the connection does

not need to exceed the maximum force that the system can develop,

or a load effect that is based in the use of the amplified seismic load.

(Re. AISC 341-05 14.4)

Note: For V braces and inverted V braces, it is not recommended for the

braces to be designed as tension only members. (Re. AISC 341-05 14.2)

Braces in OCBF systems shall meet the requirements of section 8.2b of AISC

341-05, which refers to seismically compact shape requirements.

NCh2369.Of2003 Provisions:

Beams shall be continuous at the intersection point with the V braces,

and they have to be designed for the vertical loads considering no

support from the braces.

(Re NCh2369.Of2003 8.3.5)

Braces shall be capable of supporting dead and live loads induced by

the beam and the seismic forces from the analysis, but amplified by a

1.5 factor.

(Re NCh2369.Of2003 8.3.5)

Both bottom and top flanges of the beam shall be provided with

lateral support in order to resist a lateral load of 2% of the nominal

strength of the flange (0.02𝐹𝑦𝑏𝑓𝑡).

(Re NCh2369.Of2003 8.3.5)

Brace connections shall be designed for 100% of the tensile capacity

of the element.

(Re NCh2369.Of2003 8.5.2)

2. Force transfer Mechanism

Force transfer mechanism for V brace connections is simpler than the case of

beam-column brace connection, in which the gusset plate of the connection is


4-29

adjacent to the beam and column. A reasonable method for transferring forces

shall be used.

For V braces and inverted V braces, the gusset plate has only one edge of

connection, so the force transfer is direct. Consider the following connection:

Figure 4.3-6: V Brace connection.

This arrangement generates a shear force, a vertical force and a moment at

the gusset-to-beam conncection.

𝑉 = 𝑃𝑢cos 𝜃1 + 𝑇𝑢 cos 𝜃2

𝑇 = 𝑇𝑢 sin 𝜃1 − 𝑃𝑢 sin 𝜃2

𝑀 = 𝑑𝑏2 𝑉

Where 𝜃1 and 𝜃2 are the respective angles of the arriving braces with respect

to the beam center line, and 𝑑𝑏 is the depth of the beam. It is important to

notice that the calulation of these forces is totally independent of the

assumptions that are made in order to obtain 𝑃𝑢 and 𝑇𝑢.

3. Limit States verifications

For a general case, the following limit states verifications shall be done:

Brace – Gusset Connection:

Brace to gusset welded or bolted connection design.

Base metal failure (only for welded connection).

Bearing of the gusset plate (only for bolted connection).

Bearing of the brace (only for bolted connection).

Tear out of the brace (only for bolted connection).

Tear out of the gusset plate (only for bolted connection).

P Tuu

w.p.

1 2


4-30

Gusset to beam connection:

Beam–gusset welded connection (considering at the same time

stresses produced by shear force, vertical force, and moment from

the beam-gusset interface).

Applicable limit states from section J10 of AISC360-05 Specification:

Beam web local yielding.

Beam web Crippling.

Gusset Verifications:

Tensile yielding of the Whitmore area.

Tensile fracture of the Whitmore area.

Compression buckling of the Whitmore area.

Free edge buckling.

Gusset edge stresses.

4.3.e. Horizontal braces and strut connections

1. Introduction

Horizontal braces have the function of transfering forces between the frames

that are part of the horizontal forces resisting system, and/or to provide

structural redundancy. Struts are elements that resist only axial loads, and

they have the function of reducing the buckling length of columns, giving

lateral support to beams, and to transfer forces between frames.

2. Horizontal Braces

For horizontal bracing systems, the provisions developed for connections

between braces and beam and columns do not change. Regarding elements

and connections, the AISC 341-05 seismic provisions do not distinguish

between horizontal or vertical brace systems, so the design of horizontal

braces must be done considering the provisions of chapter 13 or 14 of AISC

341-05.

The NCh2369.Of2003 Chilean code establishes special provisions in the design

of horizontal braces (refer to section 8.7 of the NCh2369.Of2003), but these

differences are specified for the brace design and not for the connection

design. Regarding the connections:


4-31

Like all seismic diagonals, they shall be designed for 100% of their

gross section tensile capacity.

(Re. NCh2369.Of2003 8.5.2)

As the case of vertical braces, X diagonals in horizontal braces shall

be connected at the intersection of the diagonals. That point can be

considered fixed in the out of plane direction of braces in order to

calulate the buckling length of the members, only if one of the braces

is continuous.

(Re. NCh2369.Of2003 8.7.3.2)

Limit states used for the case of vertical braces also apply for the case of

horizontal braces.

3. Struts

As the case of horizontal braces, the design of connections for struts does not

introduce any new limit state or provision, however, it is very important to

discuss what a strut is.

What is a strut?

The elements that are part of a floor system have different functions,

according to the structure of the system. There are elements that primarily

behave in a flexural, axial, or combined way. However there are elements that

were intended to work as a beam, but the analysis shows a combined flexural

and axial behavior. A problem may occur if the design is done focusing in the

flexural behavior, not considering the axial force to which the element is

subject to.


4-32

Figure 4.3-7: Plan view of a floor system with diagonal bracing. (Adapted from POSCO E&C Coal handing System. Angamos Thermoelectric

Power Plant – Design Drawing Transfer Tower TT2).

From analysis, it is possible to deduct that beam A of the plan view shown in Figure 4.3-8 can be subjected to axial loads if the diagonal horizontal braces arriving at beam A have an asymmetric geometry or if the pair of braces work at different levels of strength. In Figure 4.3-8 another case of elements considered as beams and that can result having axial forces is shown.

Figure 4.3-8: Model view of a floor system. Taken from POSCO E&C Coal handing System Angamos Thermoelectric Power

Plant – Seismic Report Transfer Tower TT2.

In Figure 4.3-9 there are several elements that are beams, for example beam

B (enclosed in a circle) is clearly subject to transverse loads, which generate

bending moments in the weak axis of the beam. However this beam can also

provide lateral support to the main beams of the system (which are


4-33

perpendicular to beam B), and therefore, it can develop important axial forces,

so it shall be considered as a strut while designing.

If the beam has an axial force, it is important to design the element both as a

strut and as beam. If the beam is designed as hinged at the ends (simply

supported condition), the end connections would be designed as shear

connections. But, for example, the shear connections showed in Figure 4.3-10

are not intended for axial loads.

a) b)

Figure 4.3-9: Double Angle Shear Connection: a) Column to beam connection, b) Beam to beam connection.

Therefore, it is very important to verify the effect of the axial load of the beam

into the connection. Furthermore, the axial resistance of the bolts in this type

of connections, which are subjected to tensile load, is reduced due to the

prying effect in the angle, which generates an increment of the stresses

produced by the tensile forces in the bolts. AISC Manual of Steel Construction

13th Ed. contains several expressions for evaluating the prying effect.

The ICHA Manual for the Design of Steel Structures states that double and

single angle connections are not adequate to resist axial forces, and

recommends the shear tab connection.


4-34

4.4. References





Construction”. 13th Edition. AISC, USA.

Posco E&C. documents:

Posco E&C., 2011/03/04, “Angamos Seismic Retrofit Report (for

Boiler Steel Structure)”.

Posco E&C., 2011/03/29,”Transfer Tower (TT02) Seismic Report of

Coal Handling System for Thermoelectric Power Plant”

Steel Tips:

Albohassan Astaneh-Asl, 1998, “Seismic Behavior and Design of

Gusset Plates”. Structural Steel Educational Council, USA.

Michael L. Cochran and William C. Honeck, 2004, “Design of Special

Concentrically Braced Frames (With Comments on Ordinary

Concentric Braced Frames). Structural Steel Educational Council, USA.

Roy Becker, 1995, “Seismic Design of Special Concentrically Braced

Steel Frames”. Structural Steel Educational Council, USA.

X-braces information:

A. Picard and D. Beaulieu, 3rd quarter of 1987 and 4th quarter of 1988,

“Design of diagonal cross bracings (Discussion by Sayed Stoman)”.

Engineering Journal, AISC.

S. Stoman, 1989,“Effective length spectra for cross bracings”. Journal

of Structural Engineering, ASCE.

Ali Davaran, 2001, “Effective Length Factor for Discontinuous X-

Bracing Systems”. Journal of Engineering Mechanics.

R. Shankar Nair, 1997 4th quarter, “Practical Application of Energy

Methods to Structural Stability Problems”. Engineering Journal, AISC.

Jiho Moon, Ki-Yong Yoon, Tong-Seok Han, Hak-Eun Lee , 2007, “Out

of Plane Buckling and Design of X-Bracing Systems with

Discontinuous Diagonals”. Journal of Constructional Steel Research.

Rafael Sabelli and Douglas Hohbach, 1999, “Design of Cross Braced

Frames for Predictable Buckling Behavior”. Journal of Structural

Engineering, ASCE.


4-35

4.5. Example: Brace to Beam-Column Connection

4.5.a. Design requirements

1. NCh2369.Of2003

Use high strength bolts (ASTM A325 or ASTM A490). All welding

electrodes shall comply with the requirements shown in the code.

(Re.NCh2369.Of2003, 8.5.1)

Bolts must be prestressed to 70% of the nominal tensile strength.

Always the nominal strength shall be verified as a bearing type

connection.

(Re. NCh2369 8.5.6.Of2003, 8.5.6)

For field joints, refer to section 8.5.88 of the code.

2. AISC 341-05 & NCh2369.Of2003

This connection is supposed to be designed for an OCBF system. Therefore,

the design must follow the requirements shown in the General Discussion

Sections for Brace Connections (4.1 to 4.4 of this Manual) adopted from codes

and practical recommendations for the design of these connections.

The decision of using OCBF or SCBF design must be done considering the

seismic force strength level required and a discussion with the seismic

reviewer. According to common design practice, the OCBF system was chosen

for this example.

4.5.b. Design of the connection

Design a brace to beam-column connection for the connection shown in

Figures 4.5-1 and 4.5-2Figure 4.5-1. Design the connection between brace,

beam, and column. Use a bolted connection for the brace to the gusset plate

connection. For the gusset-to-beam connection, use a welded connection (E70

electrode). For the gusset-to-column and the beam-to-column connections,

use double clip-angle connections.

Use NCh2369.Of2003 for the calculation of loads. Suppose that the unfactored

loads on the brace are:


4-36

Compression case:

𝑃𝐷 = 190 𝑘𝑁,𝑃𝐿 = 400 𝑘𝑁,𝑃𝐸 = 680 𝑘𝑁,𝑃𝑆𝑂 = 0 𝑘𝑁,𝑃𝑆𝐴 = 0 𝑘𝑁

Tension case:

𝑇𝐷 = 250 𝑘𝑁,𝑇𝐿 = 460 𝑘𝑁,𝑇𝐸 = 750 𝑘𝑁,𝑇𝑆𝑂 = 0 𝑘𝑁,𝑇𝑆𝐴 = 0 𝑘𝑁

Suppose that brace, column, and beam sections are adequate to resist and

transfer the factored forces obtained from the structural analysis.

Figure 4.5-1: Connection to be designed. Frontal and plan view of column and

clip angles.

Figure 4.5-2: Connection to be designed. Brace to gusset plate connection detail.

Beam

Column

Braceclip angle

gusset plate

Flange splice plate

Gusset

Brace

Gusset splice plate


4-37

1. Sections and Material Properties

Brace section:

H 350 x 350 x 144.9


𝐴 = 18460 𝑚𝑚2 , 𝑍𝑥 = 2760000 𝑚𝑚3 , 𝑟𝑥 = 154 𝑚𝑚, 𝑟𝑦 = 92.3 𝑚𝑚, 𝐽 = 2590000 𝑚𝑚4

Column section:

H 450 x 450 x 193.7



Beam section:

H 600 x 300 x 229.2



Material properties:

Use for members, gusset, clip angles and splice plates A250 ESP

𝐹𝑦 = 250 𝑀𝑃𝑎 ,𝐹𝑢 = 400 𝑀𝑃𝑎.

BOLTS: ASTM A490, threads included in the shear planes, STD holes

𝐹𝑛𝑡 = 780 𝑀𝑃𝑎, 𝐹𝑛𝑣 = 414 𝑀𝑃𝑎

WELDS: E70 electrode.

Width-thicknesses limitations:

According to AISC 341-05 requirements for OCBF systems, bracing members

shall meet the requirements of section 8.2b. According to this section, the

brace section must be seismically compact.


4-38

Refer to table I-8-1 of AISC 341-05 code. For braces:

𝜆𝑓 =𝑏𝑓

2𝑡𝑓= 7.95 ≤ 0.30

𝐸

𝐹𝑦= 8.5

𝜆𝑤 =𝑑 − 2𝑡𝑓

𝑡𝑤= 30.6 ≤ 1.49

𝐸

𝐹𝑦= 42.1

In the Chilean NCh2369.Of2003 Code, there are similar requirements at

section 8.3, Braced Frames:

Seismic resistant elements that work under compression must have

width/thickness ratios lesser than 𝜆𝑟 (see table 8.1 of NCh2369.Of2003 code).

Braces (built-up sections):

𝜆𝑓 =𝑏𝑓

2𝑡𝑓= 7.95 ≤ 0.64

𝐸𝑘𝑐

𝐹𝑦= 15.4 with 0.35 ≤ 𝑘𝑐 =

4

𝑕

𝑡𝑤

= 0.72 ≤ 0.763


𝑡𝑤= 30.6 ≤ 1.49

𝐸

𝐹𝑦= 42.1

Column (built-up sections):

𝜆𝑓 =𝑏𝑓

2𝑡𝑓= 10.2 ≤ 0.64

𝐸𝑘𝑐

𝐹𝑦= 15.4 with 0.35 ≤ 𝑘𝑐 =

4

𝑕

𝑡𝑤

= 0.68 ≤ 0.763


𝑡𝑤= 33.8 ≤ 1.49

𝐸

𝐹𝑦= 42.1

Both column and brace sections meet the most stringent requirements of both

codes.

According to the Chilean code the slenderness of the bracing elements must be

less than 1.5𝜋 𝐸/𝐹𝑦~4.71 𝐸/𝐹𝑦.

Therefore, using 𝐿𝑏𝑟𝑎𝑐𝑒 = 6800 𝑚𝑚, and remembering that is more accurate to

use the actual brace length in lieu of the traditional work-point to work-point

length:

𝑘𝑥 = 1.0 (in – plane buckling)

𝑘𝑦 = 1.0 (out-of-plane buckling)

Then: 𝑘𝐿𝑏𝑟𝑎𝑐𝑒

𝑟𝑚 í𝑛=

𝑘𝐿𝑏𝑟𝑎𝑐𝑒

𝑟𝑦= 73.7 < 4.71 𝐸/𝐹𝑦 = 133.2 OK


4-39

Calculate the compressive strength of the brace: 𝜙𝑃𝑛 = 0.9𝐹𝑐𝑟𝐴𝑔 = 3115 𝑘𝑁, with

𝐹𝑐𝑟 = 0.658𝐹𝑦

𝐹𝑒 × 𝐹𝑦 = 188 𝑀𝑃𝑎.

2. Design forces

According to NCh2369.Of2003, all the connections for seismic braces shall be

designed for 100% of the tensile capacity considering the gross section of the

braces.

As stated on AISC 341-05, section 14.4:

For bolt slip limit state in OCBF systems: the required strength of the

connection shall be obtained using the load combinations of the

applicable building code, not using the amplified seismic load (Ω0

factor).

The design will be conservative, so the seismic amplification factor is going to

be used (Ω0 = 2.0 for NCh2369.Of2003 load combinations).

As commented before, the Chilean code does not impose the slip critical limit

state check for bolts (only requires for bolts to be prestressed to 70% of the

tensile nominal strength of the bolts).

Continuing with AISC 341-05:

For any other limit state, check only in tension for the expected yield

strength of the brace: 𝑇𝑟𝑒𝑞 = 𝑅𝑦𝐹𝑦𝐴𝑔. Note that this requirement is a

little more stringent than the NCh2369.2003 requirement.

The required strength of the connection does not require exceeding either the

maximum force that can be developed by the system, nor the load calculated

using the amplified seismic load on load combinations.

The design done here will be conservative, so the required strength of the

connection will be taken as the larger value between the required tensile and

compressive forces (except for slip-critical limit state). For the design forces,

the most stringent conditions between NCh2369.Of2003 and AISC 341-05 will

be chosen.

Note that the design of gusset plates shall include consideration of buckling

(the compressive force must be considered).


4-40

According to the previous comments, divide the design forces for tension and

compression cases on the brace.

Tensile design force:

As discussed above, for a conservative design:

𝑇𝑢 = max(𝑅𝑦𝐹𝑦𝐴𝑔 ,𝑇𝑢𝐶𝑂𝑀𝐵𝑂𝑆 )

𝑅𝑦𝐹𝑦𝐴𝑔 = 4615 𝑘𝑁

Note:

Use 𝑅𝑦 = 1.0 instead of 𝑅𝑦 = 1.5 for A250 ESP steel (similar to ASTM A36),

according to AISC 341 table I-6-1. With this, the design is unconservative

respect to AISC 341-05 requirements but still meets the NCh2369.Of2003

code.

𝑇𝑢𝐶𝑂𝑀𝐵𝑂𝑆 refers to the tensile factored load from analysis, conservatively

calculated with the seismic amplification Ω0 = 2.0 (instead of using 𝑏 = 1.1) on

the seismic terms of the NCh2369.Of2003 load combinations:

𝑇𝑢𝐶𝑂𝑀𝐵𝑂𝑆 = 1.2𝑇𝐷 + 1.0𝑇𝐿 + 𝑏𝑇𝐸 → 1.2𝑇𝐷 + 1.0𝑇𝐿 + Ω0𝑇𝐸 = 2260 𝑘𝑁

(Re. NCh2369.Of2003, 4.5)

Note:

If using a design force as 𝑇1equal to the maximum force that can be developed

by the system or load effect based upon using the amplified seismic load, in

order to comply with NCh2369.Of2003 requirements, check that 𝑇1 to be

greater than 𝑇2 which is the 100% of the brace tensile capacity. Always

discuss, in a previous design stage, with the seismic reviewer about the design

forces for brace connections.

Compressive design force:

Although there are no requirements for compressive force in OCBF braces,

conservatively use 𝑃𝑢 = max(𝜙𝑃𝑛𝐵𝑅𝐴𝐶𝐸 ,𝑃𝑢

𝐶𝑂𝑀𝐵𝑂𝑆)

𝑃𝑢𝐶𝑂𝑀𝐵𝑂𝑆 = 1.2𝑃𝐷 + 1.0𝑃𝐿 + 𝑏𝑃𝐸 → 1.2𝑃𝐷 + 1.0𝑃𝐿 + Ω0𝑃𝐸 = 1988 𝑘𝑁


4-41

(Re. NCh2369.Of2003, 4.5)

The design forces are (except for slip critical limit state):

𝑻𝒖 = 𝟒𝟔𝟏𝟓 𝒌𝑵

𝑷𝒖 = 𝟑𝟏𝟏𝟓 𝒌𝑵

3. Brace to gusset connection

The connection is going to be a bolted one. First, distribute the brace force

proportionally to web and flange areas:

Force on the web: 𝑇𝑢𝑤 =𝑇𝑢𝐴𝑤

𝐴𝑏𝑟𝑎𝑐𝑒=

𝑇𝑢𝑕𝑡𝑤

𝐴𝑏𝑟𝑎𝑐𝑒= 765 𝑘𝑁. Similarly: 𝑃𝑢𝑤 = 516 𝑘𝑁

Force on each flange: 𝑇𝑢𝑓 =𝑇𝑢𝑏𝑓𝑡𝑓

𝐴𝑏𝑟𝑎𝑐𝑒= 1925 𝑘𝑁. Similarly: 𝑃𝑢𝑓 = 1299 𝑘𝑁

The bolted connection is going to be controlled by 𝑇𝑢.

Bolts limit states:

Try ASTM A490 M22 bolts.

Flanges:

𝑇𝑢𝑓 = 1925 𝑘𝑁, and for slip-critical limit state: 𝑇𝑢𝑓𝑆𝐶 = 𝑇𝑢

𝐶𝑂𝑀𝐵𝑂𝑆 ×𝑏𝑓𝑡𝑓

𝐴𝑏𝑟𝑎𝑐𝑒 = 943 𝑘𝑁.

Slip critical failure:

This check is not required in NCh2369.Of2003, but it will be done as an

example.

𝑅𝑛 = 𝜇𝐷𝑢𝑕𝑠𝑐𝑇𝑏𝑁𝑠 (Per bolt)

(Re. AISC 360-05, Eq.J3-4)

Use 𝜙=0.85 (LRFD, connection designed to prevent slip at required strength-

level), 𝜇=0.35 (class A surface), 𝐷𝑢=1.13, 𝑕𝑠𝑐=1.0 (standard holes), 𝑇𝑏 =

221 𝑘𝑁 (AISC 360-05, Table J3.1M for M22, ASTM A490 bolts), 𝑁𝑠 = Number of

slip planes = 2.0 (2 plates, one on the exterior of the brace flange and another

on the interior).


4-42

𝜙𝑅𝑛 = 149𝑘𝑁

𝑏𝑜𝑙𝑡→ 𝑁𝐵 =

𝑇𝑢𝑓𝑠𝑐

𝜙𝑅𝑛= 6.3. Use 𝑵𝑩=10 bolts in the flange, distributed on 2

rows of 5 bolts each one.

Shear check:

For single shear on bolts, use 𝑇𝑢𝑓

2 (two shear planes). Therefore:

Tuf

2= 963 𝑘𝑁 ≤ 𝜙𝐹𝑛𝑣𝐴𝑏𝑁𝐵 ,𝜙 = 0.75 (Re. AISC 360-05, J3.6)

With 𝑁𝐵 = 10 bolts, 𝐴𝑏 = 380 𝑚𝑚2, corresponding to M22 bolts to obtain:

𝜙𝐹𝑛𝑣𝐴𝑏𝑁𝐵 = 1180 𝑘𝑁 > 963 𝑘𝑁 OK

Bearing strength check:

𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢 (Re. AISC 360-05, Eq. J3-6a)

Use 𝜙=0.75 (LRFD), 𝐿𝑐= clear distance in the direction of the force between

the edge of the hole and the edge of the adjacent hole or edge of the material,

try 𝒕 = 𝟐𝟐 𝒎𝒎 (flange plate thickness), 𝐹𝑢 = 400 𝑀𝑃𝑎, 𝑑=nominal bolt diameter

= 22 mm. Place the bolts on the flange plate (see Figure 4.5-3).

Figure 4.5-3: Bolts positions scheme on flange plate.

Note: 𝑁𝑏 means the number of bolts per row.

The values of the distances 𝑒1 , 𝑒3 ,𝑔 (bolts gage) ,𝑕 , and 𝑖 are shown in the

following table:

Gusset splice plate (flange)

(N -1)*e e

b/2

b/2

b Gusset

g

b b

gap

A

Brace

h

i

f

3b 1e3e3(N -1)*eb 1e3

g


4-43

e1 (mm) 70

e3 (mm) 40

g (mm) 182

h (mm) 34

i (mm) 30

Table 4.5-1

Note: in order to comply with the requirements of AISC 360-05 code for bolt

spacing between bolts and distance to the edges, use 𝑒1 >8

3𝑑 (preferably 3d).

Also note that the “i” dimension is measured from the fillet toe of the brace

web.

Bolts shall have a gage so that perforations do not enter into the zone of the

fillet toe of the brace web.

Assume trial values for plates dimensions (Figure 4.5-3).

𝒃 = 𝟏𝟎𝟎 𝒎𝒎 𝒕 = 𝟐𝟐 𝒎𝒎

Note that this plate thickness is the same as the brace flange thickness.

Additional geometry checks:

𝑔 +𝑏

2+𝑏

2+ 2𝑕 = 350 𝑚𝑚 = 𝑏𝑓

𝑖 +𝑡𝑤2

+ 𝑏 + 𝑕 + 𝑠 = 175 𝑚𝑚 =𝑏𝑓

2

OK

With the above values:

2.4𝑑𝑡𝐹𝑢 = 465 𝑘𝑁

Interior bolts:

1.2𝐿𝑐𝑡𝐹𝑢 = 486 𝑘𝑁 → 465 𝑘𝑁 , with 𝐿𝑐 = 𝑒1 − 𝑑𝑕𝑜𝑙𝑒 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter, of

the standard hole for M22 bolts (Re. AISC 360-05, Table J3.3M).

Exterior bolts:


4-44

1.2𝐿𝑐𝑡𝐹𝑢 = 296 𝑘𝑁 , with 𝐿𝑐 = 𝑒3 −𝑑𝑕𝑜𝑙𝑒

2 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter, of the

standard hole for M22 bolts (Re. AISC 360-05, Table J3.3M).

Considering all the bolts for the flange brace side (N° of exterior bolts =2, N°

of interior bolts =10-2=8):

𝜙𝑅𝑛 = 3231 𝑘𝑁 >𝑇𝑢𝑓

2= 963 𝑘𝑁 OK

Remember that the number of slip planes is 2 and the inner flange plates and

outer flange plates are the same thickness.

Web side:

𝑇𝑢𝑤 = 765 𝑘𝑁 and for slip-critical limit state: 𝑇𝑢𝑤𝑆𝐶 = 𝑇𝑢

𝐶𝑂𝑀𝐵𝑂𝑆 ×𝑕𝑡𝑤

𝐴𝑏𝑟𝑎𝑐𝑒= 375 𝑘𝑁


This check is not required by NCh2369.Of2003 code, but is done as an

example.

𝑅𝑛 = 𝜇𝐷𝑢𝑕𝑠𝑐𝑇𝑏𝑁𝑠

(Per bolt)

(Re. AISC 360-05, Eq.J3-4)


level), 𝜇=0.35 (class A surface), 𝐷𝑢=1.13, 𝑕𝑠𝑐=1.0 (standard holes), 𝑇𝑏 =

221 𝑘𝑁 (AISC 360-05, Table J3.1M for M22, ASTM A490 bolts) 𝑁𝑠 = Number of

slip planes = 2.0 (2 plates, one at each side of the brace web).

Then:



𝑇𝑢𝑤𝑠𝑐

𝜙𝑅𝑛= 2.5 Use 𝑵𝑩=4 bolts in the web, distributed in 2 rows

of 2 bolts each one.

Shear check:

For single shear in bolts, use 𝑇𝑢𝑤

2 (two shear planes):

Tuw

2= 383 𝑘𝑁 ≤ 𝜙𝐹𝑛𝑣𝐴𝑏𝑁𝐵 ,𝜙 = 0.75 (Re. AISC 360-05, J3.6)

For ASTM A490 Bolts with threads included in the shear plane:


4-45

𝐹𝑛𝑡 = 780 𝑀𝑃𝑎,𝐹𝑛𝑣 = 414 𝑀𝑃𝑎

Use 𝑁𝐵 = 4 𝑏𝑜𝑙𝑡𝑠, 𝐴𝑏 = 380 𝑚𝑚2 (M22 bolts) to obtain:



𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢 (Re. AISC 360-05, Eq. J3-6a)

Use 𝜙=0.75 (LRFD), 𝐿𝑐 = clear distance in the direction of the force, between


try 𝑡 = 10 𝑚𝑚 (web plate thickness; note that this is equal to brace web

thickness), 𝐹𝑢 = 400 𝑀𝑝𝑎 , 𝑑 = nominal bolt diameter = 22 mm.

Place the bolts on the web plate (see Figure 4.5-4Figure 4.5-4):

Figure 4.5-4: Bolts positions scheme on web plate. Note: 𝑁𝑏 means the

number of bolts per row.

The values of the distances 𝑒1 , 𝑒3 ,𝑔 (gage), and 𝑒4 are shown:

e1 (mm) 80

e3 (mm) 50

g (mm) 90

e4 (mm) 60

Table 4.5-2

Assume trial values for plate dimensions (see Figure 4.5-4Figure 4.5-4):

web plate

Gusset plate gap

e *(N -1)

b g

e *(N -1)

Brace

e3 e3

e3 e3

e4

e4

1 b

1 b


4-46

The dimensions of each web plate must fit in the brace web height.

𝒃 = 𝟐𝟏𝟎 𝒎𝒎 𝒕 = 𝟏𝟎 𝒎𝒎

With the above values:

2.4𝑑𝑡𝐹𝑢 = 211 𝑘𝑁

Interior bolts:

1.2𝐿𝑐𝑡𝐹𝑢 = 269 𝑘𝑁 → 211 𝑘𝑁 , with 𝐿𝑐 = 𝑒1 − 𝑑𝑕𝑜𝑙𝑒 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter,

from the standard hole for M22 bolts (Re. AISC 360-05, Table J3.3M).

Exterior bolts:


2 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter, from the

standard hole for M22 bolts. (Re. AISC 360-05, Table J3.3M)



𝜙𝑅𝑛 = 590 𝑘𝑁 >𝑇𝑢𝑤

2= 383 𝑘𝑁 OK

The number of slip planes is 2 and both left and right web plates are the same

size.

Steel connecting plates:

Brace side:

Flange splice plates:

Dimensions: 𝑏 = 100 𝑚𝑚, 𝑡 = 22 𝑚𝑚

Compression

See Figure 4.5-3Figure 4.5-3 to calculate the maximum unfixed length:

𝐿 = 2𝑒3 + 𝑔𝑎𝑝 5 𝑚𝑚 = 85 𝑚𝑚


4-47

Check one of the two flange plates per side (i.e. take 1 of a total of 4 flange

plates on the flange). Therefore the design force is 𝑃𝑢𝑓

4= 325 𝑘𝑁. Use 𝑟 =

𝑡

12=

6.35 𝑚𝑚 and 𝑘 = 1.0 to obtain 𝑘𝐿

𝑟= 13.4 < 25 → Ch. J applies.

(Re. AISC 360-05, J4.4)

Therefore,

𝑃𝑛 = 𝐹𝑦𝐴𝑔 → 𝜙𝑃𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏𝑡 = 495 𝑘𝑁 >𝑃𝑢𝑓

4= 325 𝑘𝑁 OK

Tension yielding on the gross area

(Re. AISC 360-05, J4.1a)

𝜙𝑇𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏𝑡 = 495 𝑘𝑁 >𝑇𝑢𝑓

4= 481 𝑘𝑁 OK

Tension rupture on the effective area

(Re. AISC 360-05, J4.1b)

𝑇𝑛 = 𝐹𝑢𝐴𝑒 → 𝜙𝑇𝑛 = 0.75𝐹𝑢𝐴𝑒

Where 𝐴𝑒 = 𝐴𝑛 ≤ 0.85𝐴𝑔 for bolted splice plates. In this case, 𝐴𝑛 = 𝐴𝑔 − 𝑑𝑐𝑎𝑙𝑐 𝑡 ,

with 𝑑𝑐𝑎𝑙𝑐 = 𝑑𝑕𝑜𝑙𝑒 + 2 𝑚𝑚 𝑑𝑎𝑚𝑎𝑔𝑒 = 26 𝑚𝑚. Therefore 𝐴𝑛 = 1628 𝑚𝑚2 ≤ 0.85𝐴𝑔 =

1870 𝑚𝑚2. Then:

𝜙𝑇𝑛 = 488 𝑘𝑁 >𝑇𝑢𝑓

4= 481 𝑘𝑁 OK

Block shear

(Re. AISC 360-05, J4.3)

𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 ≤ 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡

𝜙 = 0.75,𝑈𝑏𝑠 = 1.0

See the following figure:


4-48

Figure 4.5-5: Block shear scheme for 1 flange plate.

For this connection, the number of bolts per side is 𝑁𝑏 =𝑁𝑏𝑜𝑙𝑡𝑠

2=

10

2= 5

Then:

𝐴𝑔𝑣 = 𝑡 𝑒3 + 𝑁𝑏 − 1 𝑒1 = 7040 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 𝑑𝑐𝑎𝑙𝑐 𝑡 𝑁𝑏 − 0,5 = 4466 𝑚𝑚2

𝐴𝑛𝑡 = 𝑏

2− 0,5𝑑𝑐𝑎𝑙𝑐 𝑡 = 814 𝑚𝑚2

0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 = 1397 𝑘𝑁 > 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 = 1382 𝑘𝑁

→ 𝜙𝑅𝑛 = 1036 𝑘𝑁 >𝑇𝑢𝑓

4= 481 𝑘𝑁 OK

Web splice plates

Dimensions: 𝑏 = 210 𝑚𝑚, 𝑡 = 10 𝑚𝑚

Compression

See Figure 4.5-4Figure 4.5-4 to calculate the maximum unfixed length is

𝐿 = 2𝑒3 + 𝑔𝑎𝑝 5 𝑚𝑚 = 105 𝑚𝑚

Check one of the two web plates. Therefore the design force is 𝑃𝑢𝑤

2= 258 𝑘𝑁.

Use 𝑟 =𝑡

12= 2.9 𝑚𝑚 and 𝑘 = 1.0 to obtain

𝑘𝐿

𝑟= 36.4 > 25 →Ch. E applies.

(Re. AISC 360-05, J4.4)

Using the provisions of chapter E of AISC 360-05, calculate the compressive

strength of the plate:


4-49

𝑘𝐿

𝑟= 36.4 < 4.71 𝐸/𝐹𝑦 = 133.2 → 𝐹𝑐𝑟 = 𝐹𝑦(0.658

𝐹𝑦

𝐹𝑒 ) = 233 𝑀𝑃𝑎

𝐹𝑒 =𝜋2𝐸

𝑘𝐿

𝑟

2 = 1492𝑀𝑃𝑎 . Then 𝜙𝑃𝑛 = 0.9𝐹𝑐𝑟𝐴𝑔 = 0.9𝐹𝑐𝑟𝑏𝑡 = 440 𝑘𝑁 >𝑃𝑢𝑤

2= 258 𝑘𝑁 OK


(Re. AISC 360-05, J4.1a)

𝜙𝑇𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏𝑡 = 473 𝑘𝑁 >𝑇𝑢𝑤

2= 383 𝑘𝑁 OK


(Re. AISC 360-05, J4.1b)


Where 𝐴𝑒 = 𝐴𝑛 ≤ 0.85𝐴𝑔 for bolted splice plates. On this case, 𝐴𝑛 = 𝐴𝑔 − 2𝑑𝑐𝑎𝑙𝑐 𝑡 ,

with 𝑑𝑐𝑎𝑙𝑐 = 𝑑𝑕𝑜𝑙𝑒 + 2 𝑚𝑚 𝑑𝑎𝑚𝑎𝑔𝑒 = 26 𝑚𝑚. Therefore 𝐴𝑛 = 1580𝑚𝑚2 ≤ 0.85𝐴𝑔 =

1785 𝑚𝑚2. Then:

𝜙𝑇𝑛 = 474 𝑘𝑁 >𝑇𝑢𝑤

2= 383 𝑘𝑁 OK

Block shear

(Re. AISC 360-05, J4.3)


𝜙 = 0.75,𝑈𝑏𝑠 = 1.0

See the following figure:


4-50

Figure 4.5-6: Block shear scheme for a typical web plate.


2=

4

2= 2

Then:

𝐴𝑔𝑣 = 2𝑡 𝑒3 + 𝑁𝑏 − 1 𝑒1 = 2600 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 2𝑑𝑐𝑎𝑙𝑐 𝑡 𝑁𝑏 − 0,5 = 1820 𝑚𝑚2

𝐴𝑛𝑡 = 𝑔 − 𝑑𝑐𝑎𝑙𝑐 𝑡 = 640 𝑚𝑚2


𝜙𝑅𝑛 = 485 𝑘𝑁 >𝑇𝑢𝑤

2= 383 𝑘𝑁 OK

Gusset side:

Gusset splice plates (for union with flange splice plates)

Determine the dimension for this splice plates (Figure 4.5-3Figure 4.5-3):

𝒃𝒈 = 𝟒𝟎𝟎 𝒎𝒎 (width of the both flange plates) > 𝑏𝑓𝐵𝑅𝐴𝐶𝐸 = 350 𝑚𝑚

𝒕𝒈 = 𝟐𝟐 𝒎𝒎 (thickness of the gusset flange plates, first try to equal the brace

flange thickness so not adding filler plates)

Bearing check (bolts)

The positions of the bolts are already known from the previous design on the

brace side.


4-51

𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢

(Re. AISC 360-05, Eq. J3-6a)

2.4𝑑𝑡𝐹𝑢 = 465 𝑘𝑁

Interior bolts:

1.2𝐿𝑐𝑡𝐹𝑢 = 486 𝑘𝑁 , with 𝐿𝑐 = 𝑒1 − 𝑑𝑕𝑜𝑙𝑒 and 𝑑𝑕𝑜𝑙𝑒 is the 24 mm diameter of the


Exterior bolts:


2 and 𝑑𝑕𝑜𝑙𝑒 is the 24 mm diameter of the




𝜙𝑅𝑛 = 3231 𝑘𝑁 > 𝑇𝑢𝑓 = 1925 𝑘𝑁 OK

Now use the complete tension to verify.

Compression

Suppose that the setback of the plate is 𝐴 = 110 𝑚𝑚

See Figure 4.5-3Figure 4.5-3 to determine that the maximum unfixed length is

𝐿 = 𝐴 + 𝑒3 = 150 𝑚𝑚

The design force is 𝑃𝑢𝑓 = 1299 𝑘𝑁.

Use 𝑟 =𝑡

12= 6.35 𝑚𝑚 and 𝑘 = 1.0 to obtain

𝑘𝐿

𝑟= 23.6 < 25 →Ch. J applies

(Re. AISC 360-05, J4.4)

𝜙𝑃𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏𝑡 = 1980 𝑘𝑁 > 1299 𝑘𝑁 OK


(Re. AISC 360-05, J4.1a)

𝜙𝑇𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏𝑡 = 1980 𝑘𝑁 > 𝑇𝑢𝑓 = 1925 𝑘𝑁 OK


4-52


(Re. AISC 360-05, J4.1b)


Where 𝐴𝑒 = 𝐴𝑛 ≤ 0.85𝐴𝑔 for bolted splice plates. On this case, 𝐴𝑛 = 𝐴𝑔 − 2𝑑𝑐𝑎𝑙𝑐 𝑡 ,

with 𝑑𝑐𝑎𝑙𝑐 = 𝑑𝑕𝑜𝑙𝑒 + 2 𝑚𝑚 𝑑𝑎𝑚𝑎𝑔𝑒 = 26 𝑚𝑚. Therefore 𝐴𝑛 = 7656 𝑚𝑚2 > 0.85𝐴𝑔 =

7480 𝑚𝑚2 and then:

𝜙𝑇𝑛 = 2244𝑘𝑁 > 𝑇𝑢𝑓 = 1925 𝑘𝑁 OK

Block shear

(Re. AISC 360-05, J4.3)


𝜙 = 0.75,𝑈𝑏𝑠 = 1.0

Refer to following figure:

Figure 4.5-7: Block shear conservative scheme for gusset flange plate.


2=

10

2= 5

Then, being conservative:

𝐴𝑔𝑣 ≈ 2𝑡 𝑒3 + 𝑁𝑏 − 1 𝑒1 = 14080 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 2𝑑𝑐𝑎𝑙𝑐 𝑡 𝑁𝑏 − 0.5 = 8932 𝑚𝑚2

𝐴𝑛𝑡 ≈ 2 𝑏/2 − 0.5𝑑𝑐𝑎𝑙𝑐 𝑡 = 1628 𝑚𝑚2


𝜙𝑅𝑛 = 2072𝑘𝑁 > 𝑇𝑢𝑓 = 1925 𝑘𝑁 OK


4-53

Gusset plate (in union with web splice plates)

Assume a gusset plate thickness:

𝒕𝒈 = 𝟐𝟐 𝒎𝒎 > 𝒕𝒘𝑩𝑹𝑨𝑪𝑬 = 𝟏𝟎 𝒎𝒎

Therefore, filler plates will be required to perform the union between the web

of the brace and the gusset plate. The thickness of the filler plates will be

𝒕𝒇 = 𝟔 𝒎𝒎 → 𝒕𝒘𝑩𝑹𝑨𝑪𝑬 + 𝟐𝒕𝒇 = 𝒕𝒈. According to section J5 of AISC 360-05

Specification, there is a reduction on the shear strength of the bolts only if the

fillers have 𝑡𝑓 > 6 𝑚𝑚.

Bearing (bolts limit state)

Bolts are already placed from the previous design (web splice plate).

Note that the gusset thickness is more than twice the thickness of the web

plates. The web plates were designed to resist 𝑇𝑢𝑤 /2 ; so the gusset can resist

𝑇𝑢𝑤 .OK

Block shear

(Re. AISC 360-05, J4.3)

Consider the following figure:

Figure 4.5-8: Block shear conservative scheme for the gusset plate.

From the figure above:


4-54

The number of bolts per side is 𝑁𝑏 =𝑁𝑏𝑜𝑙𝑡𝑠

2=

4

2= 2

Then:

𝐴𝑔𝑣 = 2𝑡 𝑒3 + 𝑁𝑏 − 1 𝑒1 = 5720 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 2𝑑𝑐𝑎𝑙𝑐 𝑡 𝑁𝑏 − 0,5 = 4004 𝑚𝑚2

𝐴𝑛𝑡 = 𝑔 − 𝑑𝑐𝑎𝑙𝑐 𝑡 = 1408 𝑚𝑚2


𝜙𝑅𝑛 = 1066 𝑘𝑁 > 𝑇𝑢𝑤 = 765 𝑘𝑁 OK

Limit states of tension (yielding and rupture on the Whitmore’s section) and

buckling on the Whitmore’s section will be shown next.

4. Shear lag of the brace

For OCBF systems, there are no specific requirements for checking the shear

lag of the brace bolted section, so there is no need to check this requirement.

Plus, there are splice plates that can act as “reinforcement” of the net area.

5. Gusset plate

Flange gusset splice plate to gusset connection

These plates are going to be welded to the gusset (one at each side of the

gusset). First, calculate the length along the gusset for these plates. Refer to

Figure 4.5-3Figure 4.5-3.

𝐿𝑔𝑠 = 2𝑒3 + 𝑁𝑏 − 1 𝑒1 + 𝐴 = 470 𝑚𝑚

Use double fillet welds for each one of the 2 plates, E70 electrode (𝐹𝐸𝑋𝑋 =

482 𝑀𝑃𝑎 ) and assume that all of the 𝐿𝑔𝑠 length will be welded; so 𝑳𝒘 = 𝑳𝒈𝒔 =

𝟒𝟕𝟎 𝒎𝒎. Use 𝒕𝒘 = 𝟏𝟎 𝒎𝒎 to obtain:

𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 0.75 × 2 × 0.6𝐹𝐸𝑋𝑋 × 0.707𝑡𝑤 × 𝐿𝑤 = 1443 𝑘𝑁 >

𝑇𝑢𝑓

2= 963 𝑘𝑁 OK

Check the gusset and the flange plate rupture for the weld strength

The base metal of the gusset is on shear due to the development of the

strength of the welds for the connection designed above.

Rupture:


4-55

𝜙𝑅𝑛 = 0.75𝐹𝑏𝑚𝐴𝑏𝑚 = 0.75 × 𝐴𝑛𝑣

𝜙𝑅𝑛 = 0.75 ∗ 0.6𝐹𝑢𝐴𝑛𝑣 = 0.75 × 0.6 × 𝐹𝑢(2𝐿𝑤)𝑡𝑔𝑢𝑠𝑠𝑒𝑡 = 3722 𝑘𝑁 > 𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 1443 𝑘𝑁

OK

Also check the same flange splice plate on shear rupture:

𝜙𝑅𝑛 = 0.75 × 0.6𝐹𝑢𝐴𝑛𝑣 = 0.75 × 0.6 × 𝐹𝑢𝐿𝑤 𝑡𝑝𝑙𝑎𝑡𝑒 = 1861 𝑘𝑁 > 𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 1443 𝑘𝑁

OK

Check the gusset at Whitmore’s Area

First, calculate the gusset dimensions and place the brace connections within

the gusset:

Figure 4.5-9: Parameters for the definition of the gusset plate’s geometry.

The brace has an angle 𝜶 = 𝟒𝟔° with respect to the horizontal. Knowing that

the working point of the brace is located at the intersection of the working

lines of beam and column, the distance 𝐿𝑥1, measured from the column flange

to the line of action of the brace, is known a priori:

𝐿𝑥1 =1

tan 𝛼 𝑑𝑏2−𝑑𝑐2

tan 𝛼 = 64.7 𝑚𝑚

The distance 𝐿𝑔𝑠 on Figure 4.5-9Figure 4.5-9, corresponds to the length of the

flange plate to the gusset connection.

𝐿𝑔𝑠 = 470 𝑚𝑚

d

A

Brace CL

L

L

L B

y

Lx

Lx1

c/2

db/2

gs

1


4-56

Assume the following parameters for the distances 𝐿1 (from the end of the

brace to gusset connection to the beam flange), 𝐿𝑥 (horizontal distance for the

gusset dimension) and 𝐿𝑦 (vertical distance for the gusset dimension):

𝑳𝟏 = 𝟒𝟑𝟎 𝒎𝒎

𝑳𝒙 = 𝟏𝟎𝟎𝟎 𝒎𝒎

𝑳𝒚 = 𝟖𝟓𝟎 𝒎𝒎

Note that the distances mentioned above must be defined in order to comply

with basic geometry relations:

𝐿𝑦 ≥ 𝐿1 + 𝐿𝑔𝑠 sin 𝛼 + 𝑑𝑏𝑟𝑎𝑐𝑒

2+ 𝑡𝑔𝑠 cos 𝛼

𝐿𝑥 ≥ 𝐿1 + 𝐿𝑔𝑠 cos 𝛼 + 𝑑𝑏𝑟𝑎𝑐𝑒

2+ 𝑡𝑔𝑠 sin 𝛼

With 𝑡𝑔𝑠 equal to the thickness of the flange splice plates.

Once the basic geometry of the gusset is defined, it is possible to calculate the

coordinates of all the important points and also the Whitmore’s area. For this

task, it is useful to use an calculation sheet that shows these points in one

plot. The Whitmore’s area is measured from the beginning of the flange plate

to gusset connection, using the 30° angle:

Figure 4.5-10: Whitmore’s section on gusset’s geometry.

d

A

Brace CL

L

L

L

B

y

Lx

Lx1

c/2

db/2

gs

30°

30°

Lwhit

1


4-57

Whitmore’s length is:

𝐿𝑤𝑕𝑖𝑡 = 𝑑𝑏𝑟𝑎𝑐𝑒 + 2𝑡𝑔𝑠 + 2𝐿𝑔𝑠𝑡𝑎𝑛 30 = 937 𝑚𝑚

With 𝑡𝑔𝑠 equal to the gusset flange plate thickness, 𝑡𝑔𝑠 = 22 𝑚𝑚.

The values of gusset free edges distances (𝐴 and 𝐵 on the figures above) are

calculated using simple geometry relations: 𝐴 = 217 𝑚𝑚, 𝐵 = 545 𝑚𝑚

Plotting the several points defined by the variables already shown, it is noted

that a small portion of the Withmore’s width falls within the beam (mainly

within the flange). In the design process it is preferably that the Whitmore’s

width be located within the gusset plate. In this case, as the beam flange is

very thick (40 mm) compared to the gusset thickness, and a very small part of

the beam web is affected, the properties of the gusset plate will be used for

the entire Whitmore’s width (it simplifies calculations).

Yielding at the Whitmore’s area:

𝐴𝑔𝑤 = 𝐿𝑤𝑕𝑖𝑡𝑡𝑔 = 20608 𝑚𝑚2, with 𝑡𝑔 = 22 𝑚𝑚 (gusset plate thickness).

Then:

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔𝑤 = 4637 𝑘𝑁 > 𝑇𝑢 = 4615 𝑘𝑁 OK

Rupture at the Whitmore’s area:

As the connection at the end of the flange gusset splice plates is a welded one,

there is no need to do this check because it will not control.

Compression at the Whitmore’s area:

Use as buckling length the distance 𝐿1 = 430 𝑚𝑚 (note that this is not the

longest line from the end of the brace-gusset connection to the gusset edge;

but it is near to the average distance of the “three lines” option).

Use 𝑘 = 0.65 and 𝑟 =𝑡𝑔

12= 6.35 𝑚𝑚 to obtain

𝑘𝐿

𝑟= 44 > 25 → Ch. E applies. Then:

𝐹𝑒 =𝜋2𝐸

𝑘𝐿

𝑟

2 = 1019 𝑀𝑃𝑎 → 𝐹𝑐𝑟 = 0.658𝐹𝑦

𝐹𝑒𝐹𝑦 = 225 𝑀𝑃𝑎


4-58

𝜙𝑃𝑛 = 0.9𝐹𝑐𝑟𝐿𝑤𝑕𝑖𝑡𝑡𝑔 = 4184 𝑘𝑁 > 𝑃𝑢 = 3115 𝑘𝑁 OK

6. Gusset to beam and gusset to column connections

Uniform Force Method (UFM) forces

For all the limit states, except for bolt slip critical, the design forces are:

𝑇𝑢 = 4615 𝑘𝑁

𝑃𝑢 = 3115 𝑘𝑁

Parameters for UFM:

𝑒𝑏 =𝑑𝑏2

= 300 𝑚𝑚, 𝑒𝑐 =𝑑𝑐2

= 225 𝑚𝑚

𝜃 = 90° − 𝛼° = 90° − 46° = 44° (angle of the brace with respect to the vertical

line).

Choose trial values for connections centroids:

𝛼 = 530 𝑚𝑚

𝛽 = 480 𝑚𝑚

𝛼 − 𝛽𝑡𝑎𝑛 𝜃 = 66.5 𝑚𝑚

𝑒𝑏𝑡𝑎𝑛 𝜃 − 𝑒𝑐 = 64.7 𝑚𝑚

Both terms are quite similar, negligible moment is introduced.

Calculate the forces on the interphases:

𝑟 = 𝛼 + 𝑒𝑐 2 + 𝛽 + 𝑒𝑏

2 = 1086 𝑚𝑚

𝑉𝑐 =𝛽

𝑟𝑃 , 𝑉𝑏 =

𝑒𝑏𝑟𝑃 , 𝐻𝑐 =

𝑒𝑐𝑟𝑃 ,𝐻𝑏 =

𝛼

𝑟𝑃

For the compression case:

𝑃 = 𝑃𝑢 = 3115 𝑘𝑁

𝑉𝑢𝑐 = 1377 𝑘𝑁, 𝑉𝑢𝑏 = 861 𝑘𝑁

𝐻𝑢𝑐 = 646 𝑘𝑁, 𝐻𝑢𝑏 = 1521 𝑘𝑁


4-59

And the directions of the forces over the gusset plate are shown in the

following figure:

Figure 4.5-11: Forces on the gusset edges for the UFM.

A) Tension case. B) Compression case.

Tension case:

𝑃 = 𝑇𝑢 = 4615 𝑘𝑁

𝑉𝑢𝑐 = 2041 𝑘𝑁, 𝑉𝑢𝑏 = 1275 𝑘𝑁

𝐻𝑢𝑐 = 957 𝑘𝑁, 𝐻𝑢𝑏 = 2253 𝑘𝑁

Gusset edge stresses:

Use Von Misses criteria for both 𝐿𝑥 and 𝐿𝑦 edges:

𝜓 = 𝑁

𝜙𝐹𝑦𝐴

2

+ 3 𝑉

𝜙𝐹𝑦𝐴

2

≤ 1.0

𝐴 = 𝐿𝑥𝑡𝑔 or 𝐿𝑦𝑡𝑔 (Edge area)

𝜙𝑎𝑥𝑖𝑎𝑙 = 0.9 ,𝜙𝑠𝑕𝑒𝑎𝑟 = 1.0 (strength reduction factors)

𝐿𝑥 edge:

Tension case: 𝜓 = 0.75 < 1.0

Compression case:𝜓 = 0.51 < 1.0

𝐿𝑦 edge:

Tension case: 𝜓 = 0.79 < 1.0

Compression case: 𝜓 = 0.53 < 1.0

Huc

Huc

Vuc

Vuc

Vub

VubH

ub

Hub


4-60

Gusset free edges stability:

Noting that this check is not mandatory by code provisions:

𝐴 edge:

𝐿𝑔𝑓

𝑡=

𝐴

𝑡𝑔= 9.8 ≤ 0.75

𝐸

𝐹𝑦= 21.1 → no need for stiffener

𝐵 edge: 𝐿𝑔𝑓

𝑡=

𝐵

𝑡𝑔= 24.8 > 0.75 𝐸/𝐹𝑦 = 21.1 → stiffener needed

There are several possibilities for improving this edge stability, refer to the

general discussions of braces. A special design (stiffener, increasing the gusset

thickness or changing gusset dimensions) will not be made on this example,

but it is recommended to add a stiffener at the edge.

Gusset to beam connection

Welded connection design:

This connection is going to be fillet welded (double sided, E70 electrodes). Use

as effective length of the welds 𝐿𝑤 = 930 𝑚𝑚. Check that this connection is

within the 𝐿𝑥 distance and that there is an offset on the gusset corner:

𝛼 +𝐿𝑤

2= 995 𝑚𝑚 ≤ 𝐿𝑥 = 1000 𝑚𝑚 OK

𝑂𝑓𝑓𝑠𝑒𝑡𝑥 = 𝑂𝑥 = 𝛼 −𝐿𝑤2

= 65 𝑚𝑚

The tension case controls the design of the welds.

Then 𝑅𝑇𝐸𝑁𝑆𝐼𝑂𝑁 = 𝐻𝑢𝑏2 + 𝑉𝑢𝑏

2 = 2589 𝑘𝑁

Suppose that 𝑡𝑤 = 12 𝑚𝑚 (fillet weld size) to obtain:

𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 0.75 × 0.6𝐹𝐸𝑋𝑋 × 0.707𝑡𝑤 × 𝐿𝑤 × 2 = 3427 𝑘𝑁 > 1.25𝑅𝑇𝐸𝑁𝑆𝐼𝑂𝑁 = 3236 𝑘𝑁

OK

The 1.25 ductility factor for this welded edge connection has been used,

following the recommendations of AISC Manual of Steel Construction 13th Ed.


4-61

It is important to also check the gusset rupture and the beam flange rupture

(base metals) due to the development of the welds strength:

Gusset rupture:

𝜙𝑅𝑛 = 0.75𝐹𝑏𝑚𝐴𝑏𝑚 = 0.75 ∗ 0.6𝐹𝑢𝐴𝑛𝑣

𝜙𝑅𝑛 = 0.75 × 0.6𝐹𝑢 𝐿𝑤𝑡𝑔 = 3683 𝑘𝑁 > 𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 3427 𝑘𝑁 OK

Beam flange rupture:

𝜙𝑅𝑛 = 0.75𝐹𝑏𝑚𝐴𝑏𝑚 = 0.75 × 0.6𝐹𝑢𝐴𝑛𝑣

𝜙𝑅𝑛 = 0.75 × 0.6𝐹𝑢 2𝐿𝑤𝑡𝑏𝑓 = 13392 𝑘𝑁 > 𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 3427 𝑘𝑁 OK

Check of the beam web due to the action of a concentrated force:

Beam web yielding: (Re. AISC 360-05, J10)

This limit state must be checked for tension and compression forces. The

tension case controls. It is noted that the concentrated force to be resisted is

not applied at a distance from the beam end that is greater to the depth of the

beam (𝛼 = 580 𝑚𝑚 < 𝑑 = 600 𝑚𝑚).

Use 𝑡𝑏𝑤 = 10 𝑚𝑚, 𝑘 = 𝑡𝑏𝑓 + 𝑠 = 40 + 6 = 46 𝑚𝑚 and 𝑁 = max 𝑡𝑏𝑓 ,𝑘 = 46 𝑚𝑚 to

obtain:

𝜙𝑅𝑛 = 1.0 × { 2.5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑏𝑤 = 403 𝑘𝑁 < max 𝑉𝑢𝑏𝑇𝐸𝑁𝑆𝐼𝑂𝑁 ,𝑉𝑢𝑏

𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁 = 1275 𝑘𝑁

So, there is the need of adding stiffeners (or increasing the beam web

thickness). That design will not be done on this example (refer to Chapter 6 of

Moment Connections and section J10 of AISC 360-05 Specification for more

information about the design of stiffeners for concentrated forces).

Beam web Crippling

(Re. AISC 360-05, J10)

This limit state only applies for compression forces. The concentrated

compressive force to be resisted is applied at a distance from the beam end

that is greater than its half depth (𝛼 = 580 𝑚𝑚 >𝑑

2= 300 𝑚𝑚).

𝜙𝑅𝑛 = 0.75 × 0.80𝑡𝑏𝑤2 1 + 3

𝑁

𝑑𝑏

𝑡𝑏𝑤𝑡𝑏𝑓

1.5

𝐸𝐹𝑦𝑤 𝑡𝑏𝑓

𝑡𝑏𝑤 →


4-62

𝜙𝑅𝑛 = 873 𝑘𝑁 > 𝑉𝑢𝑏𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁 = 861 𝑘𝑁 OK

Gusset to column connection

This connection consists of 2 clip angles welded to the gusset plate, and

bolted to the column flange (one clip angle each side of the gusset plate).

Determine trial dimensions for the angle shape:

Figure 4.5-12: General Scheme of the clip angle connection.

Note that the number of bolts and rows in the final design is not necessarily the same as shown in this Figure.

Choose angles with 𝑩 = 𝟖𝟎 𝒎𝒎 and 𝒕 = 𝒕𝒂𝒏𝒈𝒍𝒆 = 𝟏𝟒 𝒎𝒎. The thickness of the

column flange is 𝒕𝒄𝒇 = 𝟐𝟐 𝒎𝒎. The centroid of this connection was assumed to

be located at 𝜷 = 𝟒𝟖𝟎 𝒎𝒎.

Properties for bolts used:

ASTM A490 M22 bolts, and according to the table J3.3M of AISC 360-05 code,

the hole diameter is 24 mm.

Initial try of:

(N -1)

e

A-A

B

B

t

Bolted side

B-B

t

L

g

BA

B

A

3

e3

e3

e3

bolt side


4-63

𝑵𝒃𝒐𝒍𝒕𝒔𝑻𝑶𝑻𝑨𝑳 = 𝟐𝟐 (total number of bolts, considering 2 clip angles)

𝑵𝒓 = 𝟏 (number of rows in each clip angle)

𝑵𝒃𝒐𝒍𝒕𝒔𝑺𝑰𝑫𝑬 =

𝟏

𝟐

𝑵𝒃𝒐𝒍𝒕𝒔𝑻𝑶𝑻𝑨𝑳

𝑵𝒓= 𝟏𝟏 (number of bolts on each row of each clip angle)

Bolted side of the connection design:

The tension case controls (𝐻𝑢𝑐𝑇𝐸𝑁𝑆𝐼𝑂𝑁 = 957 𝑘𝑁 and 𝑉𝑢𝑐

𝑇𝐸𝑁𝑆𝐼𝑂𝑁 = 2041 𝑘𝑁). Forces in

each bolt are:

𝑇𝑢𝐵𝑂𝐿𝑇 =

𝐻𝑢𝑐𝑇𝐸𝑁𝑆𝐼𝑂𝑁

𝑁𝑏𝑜𝑙𝑡𝑠𝑇𝑂𝑇𝐴𝐿 = 43 𝑘𝑁

𝑉𝑢𝐵𝑂𝐿𝑇 =

𝑉𝑢𝑐𝑇𝐸𝑁𝑆𝐼𝑂𝑁


Check direct shear in the bolts (𝐴𝑏 = 380 𝑚𝑚2 for M22 bolts):

𝜙𝑅𝑛 = 0.75 × 𝐹𝑛𝑣𝐴𝑏 = 118 𝑘𝑁 > 𝑉𝑢𝐵𝑂𝐿𝑇 = 93 𝑘𝑁 OK

Place the bolts at the connection and calculate other required distances:

Refer to Figure 4.5-12Figure 4.5-12. Use 𝒆𝟏 = 𝟔𝟎 𝒎𝒎 >𝟖

𝟑𝒅𝒃𝒐𝒍𝒕 ,𝒆𝟑 = 𝟓𝟎 𝒎𝒎,𝒆𝟒 =

𝟒𝟎 𝒎𝒎 > 𝒕𝒂𝒏𝒈𝒍𝒆

𝒈 = 𝟎 𝒎𝒎

Calculate the length of the angle (or length of the connection)

𝐿 = 2𝑒3 + 𝑒1(𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸 − 1) = 700 𝑚𝑚 → 𝛽 + 𝐿/2 = 830 𝑚𝑚 ≤ 𝐿𝑦 = 850 𝑚𝑚 OK

Calculate the offset at the gusset corner for this side:

𝑂𝑓𝑓𝑠𝑒𝑡𝑦 = 𝑂𝑦 = 𝛽 −𝐿

2= 130 𝑚𝑚

It is also noted that both clip angles fall within the column flange width and

that no interruption is made on the column fillet web toe area.

Interaction V-T for bolts (slip critical limit state):

(Re. AISC 360-05, J3.9)


4-64

Bolts are subjected to shear and tension components for the tension case,

which controls the design.

For the slip critical limit state, as said on AISC 341-05 for OCBF systems, the

required strength of the connection is obtained using the load combinations of

the applicable building code, not considering the amplified seismic load (Ω0

factor). Nevertheless, in this case, the design for all the slip critical limit states

has been made conservatively using a Ω0 = 2.0 factor. Therefore, the procedure

done with the UFM for the design forces, must be done equally with the design

forces for the slip-critical limit state (tensile case controls, 𝑇𝑢𝐶𝑂𝑀𝐵𝑂𝑆 = 2260 𝑘𝑁)

Applying the UFM to this force, the design forces for slip critical limit state on

the gusset to column connection are:

𝑉𝑢𝑐𝑠𝑐 = 999 𝑘𝑁

𝐻𝑢𝑐𝑠𝑐 = 468 𝑘𝑁

And the strength of one bolt is:

𝑅𝑛 = 𝜇𝐷𝑢𝑕𝑠𝑐𝑇𝑏𝑁𝑠 (Re. AISC 360-05, Eq. J3-4)

Use 𝜇 = 0.35 (class A faying surface), 𝐷𝑢 = 1.13 , 𝑕𝑠𝑐 = 1.0 (standard holes),

𝑇𝑏 = 221 𝑘𝑁 (table J3.1M on AISC 360-05), and 𝑁𝑠 = 1.0 (number of slip planes

on each angle). Then:

𝑅𝑛 = 87.4 𝑘𝑁

According to section J3.9 of AISC 360-05, when combined tension and shear

slip critical connections are performed, the previous available strength per bolt

must be reduced by the factor 𝑘𝑠.

𝑘𝑠 = 1 −𝑇𝑢

𝐷𝑢𝑇𝑏𝑁𝑏= 0.91, with 𝑁𝑏 = 11 (number of bolts carrying the applied tensile

force 𝑇𝑢 =𝐻𝑢𝑐𝑠𝑐

2; the check will be for one angle).

Using 𝜙 = 0.85 → 𝜙𝑘𝑠𝑅𝑛 × 𝑁𝑏 = 748 𝑘𝑁 >𝑉𝑢𝑐𝑠𝑐

2= 500 𝑘𝑁 OK

Interaction V-T for bearing type connections:

(Re. AISC 360-05, J3.7)

Now return using the design forces for all the other limit states.


4-65

𝑅𝑛 = 𝐹𝑛𝑡′ 𝐴𝑏, 𝐹𝑛𝑡

′ = 1.3𝐹𝑛𝑡 −𝐹𝑛𝑡

𝜙𝐹𝑛𝑣𝑓𝑣 ≤ 𝐹𝑛𝑡 . Use 𝜙 = 0.75 and 𝑓𝑣 =

𝑉𝑢𝐵𝑂𝐿𝑇

𝐴𝑏= 244 𝑀𝑃𝑎

(required shear stress on each bolt).

𝑅𝑛 = 152𝑘𝑁

𝑏𝑜𝑙𝑡→ 𝜙𝑅𝑛 = 114 𝑘𝑁 > 𝑉𝑢

𝐵𝑂𝐿𝑇 = 93 𝑘𝑁 OK

Bearing check for bolts in shear

Use 𝑡 = 𝑡𝑎𝑛𝑔𝑙𝑒 = 14 𝑚𝑚

𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢 = 296 𝑘𝑁

Interior bolts

1.2𝐿𝑐𝑡𝐹𝑢 = 242 𝑘𝑁, with 𝐿𝑐 = 𝑒1 − 𝑑𝑕𝑜𝑙𝑒 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter, from

standard hole for M22 bolts (Re. AISC 360-05, Table J3.3M). Then 𝜙𝑅𝑛 =

0.75𝑅𝑛 = 182 𝑘𝑁 > 𝑉𝑢𝐵𝑂𝐿𝑇 = 93 𝑘𝑁.

Exterior bolts:

1.2𝐿𝑐𝑡𝐹𝑢 = 255 𝑘𝑁, with 𝐿𝑐 = 𝑒3 −𝑑𝑕𝑜𝑙𝑒

2 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter, from standard

hole for M22 bolts (Re. AISC 360-05, Table J3.3M). Then 𝜙𝑅𝑛 = 0.75𝑅𝑛 =

191 𝑘𝑁 > 𝑉𝑢𝐵𝑂𝐿𝑇 = 93 𝑘𝑁

Check prying action

(Re. AISC Manual of Steel Construction 13th Ed.)

First calculate some parameters to be used:

𝑇 = 𝑇𝑢𝐵𝑂𝐿𝑇 =

𝐻𝑢𝑐

𝑁𝐵= 43 𝑘𝑁 (required tensile strength per bolt)

𝑑𝑏 = 22 𝑚𝑚 (bolt diameter)

𝑑′ = 24 𝑚𝑚 (hole diameter, use standard hole)

𝑝 = 𝑚𝑖𝑛 𝑒1 , 𝑒4 = 40 𝑚𝑚

𝐹𝑢 = 400 𝑀𝑃𝑎

𝐹𝑛𝑡 = 780 𝑀𝑃𝑎

𝐵 = 𝜙𝑇𝑛𝐵𝑂𝐿𝑇 = 0.75𝑇𝑛

𝐵𝑂𝐿𝑇 = 0.75𝐹𝑛𝑡𝐴𝑏 = 222 𝑘𝑁

𝛿 = 1 −𝑑′

𝑝= 0.4

The number of bolt rows is 𝑵𝒓 = 𝟏 on each angle. Refer to the following figure:


4-66

Figure 4.5-13: Prying force parameters definition.

Taken from AISC Manual of Steel Construction 13th Ed. Figure 9-4b.

From the figure above:

𝑔 = 𝑒4 = 40 𝑚𝑚

𝑏 = 𝑒4 −𝑡𝑎𝑛𝑔𝑙𝑒

2= 33 𝑚𝑚

𝑎 = 54 𝑚𝑚

𝑏′ = 𝑏 −𝑑𝑏2

= 22 𝑚𝑚

𝑎′ = min 𝑎 +𝑑𝑏2

; 1.25𝑏 +𝑑𝑏2 = 52.25 𝑚𝑚

Then calculate:

𝜌 =𝑏′

𝑎′= 0.42

𝛽 =1

𝜌 𝐵

𝑇− 1 = 9.8 > 1 → 𝛼′ = 1

Therefore, the required thickness for the angle in order to have adequate

fitting strength and stiffness and bolt strength is:

𝑡𝑚 í𝑛 = 4.44𝑇𝑏′

𝑝𝐹𝑢 (1+𝛿𝛼 ′ )= 13.76 𝑚𝑚 < 𝑡𝑎𝑛𝑔𝑙𝑒 = 14 𝑚𝑚 OK

Welded side of the connection design (E70 electrode):

The design will be made for each of the 2 angles. Therefore, the design force

is: 𝑅 =1

2 𝑉𝑢𝑐

2 + 𝐻𝑢𝑐2 = 1127 𝑘𝑁. Use 𝐿𝑤 = 𝐿 = 700 𝑚𝑚 and 𝑡𝑤 = 12 𝑚𝑚 (maximum

permitted) to obtain:

gq

b' a'

T + q

ab

T

b) prying forces in angle


4-67

𝜙𝑅𝑛WELDS = 0.75 × 0.6𝐹𝐸𝑋𝑋 × 0.707𝑡𝑤 × 𝐿𝑤 = 1290 𝑘𝑁 > 𝑅 = 1127 𝑘𝑁 OK

Check the gusset rupture so to develop the weld strength:

𝜙𝑅𝑛 = 0.75𝐹𝑏𝑚𝐴𝑏𝑚 = 0.75 ∗ 0.6𝐹𝑢𝐴𝑛𝑣

𝜙𝑅𝑛 = 0.75 × 0.6𝐹𝑢 𝐿𝑤𝑡𝑔 = 2772 𝑘𝑁 > 𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 1290 𝑘𝑁 OK

Clip angles strength

Check one of the two angles:

Shear Yielding

(Re. AISC 360-05, J4.2)

𝜙𝑅𝑛 = 1.0 × 0.6𝐹𝑦𝐴𝑔 = 1.0 × 0.6𝐹𝑦 𝐿𝑡𝑎𝑛𝑔𝑙𝑒 = 1470 𝑘𝑁 >𝑉𝑢𝑐

2= 1020 𝑘𝑁 OK

Shear Rupture

(Re. AISC 360-05, J4.2)

𝜙𝑅𝑛 = 0.75 ∗ 0.6𝐹𝑢𝐴𝑒

0.75 × 0.6𝐹𝑢 𝐴𝑔 − 𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸𝑑𝑐𝑎𝑙𝑐 𝑡𝑎𝑛𝑔𝑙𝑒 = 1043 𝑘𝑁 >

𝑉𝑢𝑐

2= 1020 𝑘𝑁 OK

𝑑𝑐𝑎𝑙𝑐 = 𝑑𝑕𝑜𝑙𝑒 + 2 𝑚𝑚 𝑑𝑎𝑚𝑎𝑔𝑒 = 26 𝑚𝑚

Block Shear

(Re. AISC 360-05, J4.3)

Refer to the following figure:

Figure 4.5-14: Block shear scheme for 1 clip angle.

𝐴𝑔𝑣 = 𝑡𝑎𝑛𝑔𝑙𝑒 𝑒3 + 𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸 − 1 𝑒1 = 9100 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸 − 0,5 𝑑𝑐𝑎𝑙𝑐 𝑡𝑎𝑛𝑔𝑙𝑒 = 5278 𝑚𝑚2

𝐴𝑛𝑡 = 54𝑡𝑎𝑛𝑔𝑙𝑒 − 0,5𝑑𝑐𝑎𝑙𝑐 𝑡𝑎𝑛𝑔𝑙𝑒 = 574 𝑚𝑚2

𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 = 1496 𝑘𝑁 < 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 = 1594 𝑘𝑁


4-68

𝜙𝑅𝑛 = 0.75𝑅𝑛 = 1122 𝑘𝑁 >𝑽𝒖𝒄

𝟐= 1020 𝑘𝑁 OK

Column flange strength

As the column flange is thicker than the clip angle, it is OK.

Column web strength due to concentrated loads:

Column web yielding:

(Re. AISC 360-05, J10)

This limit state must be checked for tension and compression forces. The

tension case controls. It is noted that the concentrated force to be resisted is

applied at a distance from the column end that is greater to the depth of the

column.

Use 𝑡𝑐𝑤 = 12 𝑚𝑚, 𝑘 = 𝑡𝑐𝑓 + 𝑠 = 22 + 6 = 28 𝑚𝑚, and 𝑁 = max 𝑡𝑐𝑓 , 𝑘 = 28 𝑚𝑚 to

obtain

𝜙𝑅𝑛 = 1.0 × { 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑐𝑤 = 504 𝑘𝑁 < max 𝐻𝑢𝑐𝑇𝐸𝑁𝑆𝐼𝑂𝑁 ,𝐻𝑢𝑐

𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁 = 957 𝑘𝑁

So, there is the need of adding stiffeners (or increasing the column web

thickness). That design will not be done in this example (refer to Chapter 6 of

Moment Connections and section J10 of AISC 360-05 Specification for more

information about the design of stiffeners for concentrated forces).

Column web Crippling:

(Re. AISC 360-05, J10)

This limit state only applies for compression forces. It is noted that the

concentrated compressive force to be resisted is applied at a distance from the

column end that is greater than its half depth.

𝜙𝑅𝑛 = 0.75 × 0.80𝑡𝑐𝑤2 1 + 3

𝑁

𝑑𝑐

𝑡𝑏𝑤𝑡𝑐𝑓

1.5

𝐸𝐹𝑦𝑤 𝑡𝑐𝑓

𝑡𝑐𝑤

𝜙𝑅𝑛 = 889 𝑘𝑁 > 𝐻𝑢𝑐𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁 = 646 𝑘𝑁 OK


4-69

7. Beam-to-column connection

The controlling combination is when the brace is in tension; suppose that the

required end reaction on the beam is 𝑅 = 50 𝑘𝑁 and the drag force on the beam

is 𝐴𝑏 = 0 𝑘𝑁. Therefore, forces present in the connection are the following

Slip critical limit state

Axial force:

𝐻𝑠𝑐 = 𝑇𝑢𝑠𝑐 cos 46° = 1570 𝑘𝑁 (Horizontal component of the brace force)

𝐴𝑥𝑖𝑎𝑙𝑠𝑐 = 𝑅𝑕𝑠𝑐 = 𝐴𝑏 ± 𝐻𝑢𝑏

𝑠𝑐 −𝐻𝑠𝑐 = 0 ± 1103 − 1570 = 467𝑘𝑁

Shear force:

𝑆𝑕𝑒𝑎𝑟𝑠𝑐 = 𝑅𝑣𝑠𝑐 = 𝑅 − 𝑉𝑢𝑏

𝑠𝑐 = 50 − 861 = 811 𝑘𝑁

Bearing limit state

Axial force:

𝐻 = 𝑇𝑢 cos 46° = 3206 𝑘𝑁 (Horizontal component of the brace force)

𝐴𝑥𝑖𝑎𝑙 = 𝑅𝑕 = 𝐴𝑏 ± 𝐻𝑢𝑏 − 𝐻 = 953 𝑘𝑁

Shear force:

𝑆𝑕𝑒𝑎𝑟 = 𝑅𝑣 = 𝑅 − 𝑉𝑢𝑏 = 1225 𝑘𝑁

Design of the connection

This connection consists of 2 clip angles welded to the beam web and bolted

to the column flange (one clip angle each side of the beam web).

Calculate trial dimensions for the angle shape (Figure 4.5-12Figure 4.5-12):

Choose angles with 𝑩 = 𝟏𝟎𝟎 𝒎𝒎 and 𝒕 = 𝒕𝒂𝒏𝒈𝒍𝒆 = 𝟏𝟖 𝒎𝒎. The thickness of the

column flange is 𝒕𝒄𝒇 = 𝟐𝟐 𝒎𝒎.

Properties for bolts used:

ASTM A490 M22 bolts, STD hole diameter is 24 mm according to table J3.3M

of AISC 360-05 code.


4-70

Initial try:

𝑵𝒃𝒐𝒍𝒕𝒔𝑻𝑶𝑻𝑨𝑳 = 𝟏𝟒 (Total number of bolts, considering the 2 clip angles)

𝑵𝒓 = 𝟏 (Number of rows on each clip angle)

𝑵𝒃𝒐𝒍𝒕𝒔𝑺𝑰𝑫𝑬 =

𝟏

𝟐

𝑵𝒃𝒐𝒍𝒕𝒔𝑻𝑶𝑻𝑨𝑳

𝑵𝒓= 𝟕 (Number of bolts on each row of each clip angle)

Bolted side of the connection design:

The tension case controls. The forces on each bolt are:

𝑇𝑢𝐵𝑂𝐿𝑇 =

𝑅𝑕


𝑉𝑢𝐵𝑂𝐿𝑇 =

𝑅𝑣


Check direct shear on the bolts (𝐴𝑏 = 380 𝑚𝑚2 for M22 bolts):

𝜙𝑅𝑛 = 0.75 × 𝐹𝑛𝑣𝐴𝑏 = 118𝑘𝑁 > 𝑉𝑢𝐵𝑂𝐿𝑇 = 88 𝑘𝑁 OK.

Place the bolts and determine other distances

Refer to Figure 4.5-12. Use 𝒆𝟏 = 𝟔𝟎 𝒎𝒎 >𝟖

𝟑𝒅𝒃𝒐𝒍𝒕 ,𝒆𝟑 = 𝟓𝟎 𝒎𝒎,𝒆𝟒 = 𝟓𝟎 𝒎𝒎 > 𝒕𝒂𝒏𝒈𝒍𝒆

𝒈 = 𝟎 𝒎𝒎

Calculate the length of the angle (or length of the connection):

𝐿 = 2𝑒3 + 𝑒1(𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸 − 1) = 460 𝑚𝑚

Check that the clip angle falls within the beam height:

𝐿 = 460 𝑚𝑚 < 𝑑𝑏 − 2𝑡𝑏𝑓 − 2𝑠 = 508 𝑚𝑚 OK

It is also noted that both clip angles fall within the column flange width and

that no interruption is made on the column fillet web toe area.

Interaction V-T for bolts (slip critical limit state):

(Re. AISC 360-05, J3.9)

Use the forces for slip critical limit state check.

𝑅𝑕𝑠𝑐 = 467𝑘𝑁 (axial force)


4-71

𝑅𝑣𝑠𝑐 = 811 𝑘𝑁 (shear force)

𝑅𝑛 = 𝜇𝐷𝑢𝑕𝑠𝑐𝑇𝑏𝑁𝑠 (Re. AISC 360-05, Eq. J3-4).

Use 𝜇 = 0.35 (class A faying surface), 𝐷𝑢 = 1.13, 𝑕𝑠𝑐 = 1.0 (standard holes),

𝑇𝑏 = 221 𝑘𝑁 (table J3.1M on AISC 360-05) and 𝑁𝑠 = 1.0 (number of slip planes

on each angle). Then:

𝑅𝑛 = 87.4 𝑘𝑁

According to section J3.9 of AISC 360-05, when there is combined tension and

shear in slip critical connections, the previous available strength must be

reduced by a factor 𝑘𝑠.


𝐷𝑢𝑇𝑏𝑁𝑏= 0.86, with 𝑁𝑏 = 7 (number of bolts carrying the applied tension

𝑇𝑢 =𝑅𝑕𝑠𝑐

2; the check will be performed for 1 angle).

Then, using 𝜙 = 0.85 → 𝜙𝑘𝑠𝑅𝑛 × 𝑁𝑏 = 451 𝑘𝑁 >𝑅𝑣𝑠𝑐

2= 405 𝑘𝑁 OK

Interaction V-T for bearing type connections

(Re. AISC 360-05, J3.7)

Use the design forces for all the other limit states.

𝑅𝑛 = 𝐹𝑛𝑡′ 𝐴𝑏, 𝐹𝑛𝑡

′ = 1.3𝐹𝑛𝑡 −𝐹𝑛𝑡

𝜙𝐹𝑛𝑣𝑓𝑣 ≤ 𝐹𝑛𝑡 . Use 𝜙 = 0.75 and 𝑓𝑣 =

𝑉𝑢𝐵𝑂𝐿𝑇

𝐴𝑏= 230 𝑀𝑃𝑎

(required shear stress on each bolt). Therefore:

𝑅𝑛 = 166𝑘𝑁

𝑏𝑜𝑙𝑡→ 𝜙𝑅𝑛 = 124 𝑘𝑁 > 𝑉𝑢

𝐵𝑂𝐿𝑇 = 88 𝑘𝑁 OK

Bearing check for bolts in shear (use 𝑡 = 𝑡𝑎𝑛𝑔𝑙𝑒 = 18 𝑚𝑚)

𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢 = 380 𝑘𝑁

Interior bolts:

1.2𝐿𝑐𝑡𝐹𝑢 = 311 𝑘𝑁 , with 𝐿𝑐 = 𝑒1 − 𝑑𝑕𝑜𝑙𝑒 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter, from


0.75𝑅𝑛 = 233 𝑘𝑁 > 𝑉𝑢𝐵𝑂𝐿𝑇 = 88 𝑘𝑁.

Exterior bolts:


4-72


2 and 𝑑𝑕𝑜𝑙𝑒 is 24 mm diameter from the


0.75𝑅𝑛 = 246 𝑘𝑁 > 𝑉𝑢𝐵𝑂𝐿𝑇 = 88 𝑘𝑁.

Check prying action

(Re. AISC Manual of Steel Construction 13th Ed.)

First, calculate some parameters to be used:

𝑇 = 𝑇𝑢𝐵𝑂𝐿𝑇 = 68 𝑘𝑁 (required tensile strength per bolt)

𝑑𝑏 = 22 𝑚𝑚 (bolt diameter)

𝑑′ = 24 𝑚𝑚 (hole diameter, use standard hole)

𝑝 = 𝑚𝑖𝑛 𝑒1 , 𝑒4 = 50 𝑚𝑚


𝐹𝑛𝑡 = 780 𝑀𝑃𝑎

𝐵 = 𝜙𝑇𝑛𝐵𝑂𝐿𝑇 = 0.75𝑇𝑛

𝐵𝑂𝐿𝑇 = 0.75𝐹𝑛𝑡𝐴𝑏 = 222 𝑘𝑁

𝛿 = 1 −𝑑′

𝑝= 0.52

Now, the number of bolt rows is 𝑵𝒓 = 𝟏 on each angle. Refer to Figure 4.5-13.

Then:

𝑔 = 𝑒4 = 50 𝑚𝑚

𝑏 = 𝑒4 −𝑡𝑎𝑛𝑔𝑙𝑒

2= 41 𝑚𝑚

𝑎 = 68 𝑚𝑚

𝑏′ = 𝑏 −𝑑𝑏2

= 30 𝑚𝑚

𝑎′ = min 𝑎 +𝑑𝑏2

; 1.25𝑏 +𝑑𝑏2 = 62.25 𝑚𝑚

And calculate:

𝜌 =𝑏′

𝑎′= 0.48

𝛽 =1

𝜌 𝐵

𝑇− 1 = 7 > 1 → 𝛼′ = 1

Therefore, the required thickness for the angle, so to have adequate fitting

strength and stiffness and bolt strength is:

𝑡𝑚 í𝑛 = 4.44𝑇𝑏′

𝑝𝐹𝑢 (1+𝛿𝛼 ′ )= 17.26 𝑚𝑚 < 𝑡𝑎𝑛𝑔𝑙𝑒 = 18 𝑚𝑚 OK


4-73

Welded side of the connection design (E70 electrode):

The design will be made for each angle. Therefore, the design force is 𝑅 =1

2 𝑅𝑣

2 + 𝑅𝑕2 = 776 𝑘𝑁. Use 𝐿𝑤 = 𝐿 = 460 𝑚𝑚 and 𝑡𝑤 = 11 𝑚𝑚 to obtain:

𝜙𝑅𝑛WELDS = 0.75 × 0.6𝐹𝐸𝑋𝑋 × 0.707𝑡𝑤 × 𝐿𝑤 = 777 𝑘𝑁 > 𝑅 = 776 𝑘𝑁 OK

Check the beam web rupture so to develop the weld strength:

𝜙𝑅𝑛 = 0.75𝐹𝑏𝑚𝐴𝑏𝑚 = 0.75 × 0.6𝐹𝑢𝐴𝑛𝑣

𝜙𝑅𝑛 = 0.75 × 0.6𝐹𝑢 𝐿𝑤 𝑡𝑏𝑤 = 828 𝑘𝑁 > 𝜙𝑅𝑛𝑊𝐸𝐿𝐷𝑆 = 777 𝑘𝑁 OK

Clip angles strength

Shear Yielding

(Re. AISC 360-05, J4.2)

𝜙𝑅𝑛 = 1.0 × 0.6𝐹𝑦𝐴𝑔 = 1.0 × 0.6𝐹𝑦 𝐿𝑡𝑎𝑛𝑔𝑙𝑒 = 1242 𝑘𝑁 >𝑅𝑣

2= 613 𝑘𝑁 OK

Shear Rupture

(Re. AISC 360-05, J4.2)

𝜙𝑅𝑛 = 0.75 × 0.6𝐹𝑢𝐴𝑒

0.75 × 0.6𝐹𝑢 𝐴𝑔 − 𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸𝑑𝑐𝑎𝑙𝑐 𝑡𝑎𝑛𝑔𝑙𝑒 = 901 𝑘𝑁 >

𝑅𝑣

2= 613 𝑘𝑁 OK

Use 𝑑𝑐𝑎𝑙𝑐 = 𝑑𝑕𝑜𝑙𝑒 + 2 𝑚𝑚 𝑑𝑎𝑚𝑎𝑔𝑒 = 26 𝑚𝑚

Block Shear

(Re. AISC 360-05, J4.3)

Refer to Figure 4.5-14. Then:

𝐴𝑔𝑣 = 𝑡𝑎𝑛𝑔𝑙𝑒 𝑒3 + 𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸 − 1 𝑒1 = 7380 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 𝑁𝑏𝑜𝑙𝑡𝑠𝑆𝐼𝐷𝐸 − 0.5 𝑑𝑐𝑎𝑙𝑐 𝑡𝑎𝑛𝑔𝑙𝑒 = 4338 𝑚𝑚2

𝐴𝑛𝑡 = 68𝑡𝑎𝑛𝑔𝑙𝑒 − 0.5𝑑𝑐𝑎𝑙𝑐 𝑡𝑎𝑛𝑔𝑙𝑒 = 990 𝑚𝑚2

𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 = 1437 𝑘𝑁 < 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 = 1503 𝑘𝑁

𝜙𝑅𝑛 = 0.75𝑅𝑛 = 1078 𝑘𝑁 >𝑅𝑣

2= 613 𝑘𝑁 OK

Column web shear:


4-74

The check is performed for 𝐻𝑢𝑐 = 957 𝑘𝑁.

𝜙𝑅𝑛 = 1.0 × 0,6𝐹𝑦𝐴𝑔 = 1.0 × 0.6𝐹𝑦𝑑𝑐𝑡𝑐𝑤 = 810 𝑘𝑁 < 953 𝑘𝑁

Therefore stiffeners for the column are needed. The design of them is not done

on this example. For major information refer to section J10 of AISC 360-05

Specification and Chapter 6 of Moment Connections on this Manual.

4.5.c. Designed connection

Detail 1

Detail 2

Detail 3

Detail 4

10

10

12

12

10

10

Gusset plate: t = 22 mm

Notes:

- Stiffener and doubler plates for column and beam

are not designed

-Welds: E70 electrodes

46°


4-75

Detail 1

PL 725X100X22

Gusset

PL t=22 mm

Brace

20 M22 ASTM A490

Detail 2

2 PL 365x210x10 (one each side)

8 M22 ASTM A490

Note:

Add 2 Filler plates (PL 365x210x6)

11 M22 ASTM A490 (Total = 22 M22)

filled weld to gusset

A - A:A A

Detail 3 : Clip angle for gusset to column


4-76

7 M22 ASTM A490 (Total = 14 M22)

fillet welded to beam web

A - A:A A

Detail 4 : Clip angle for beam to column


4-77

4.6. Example: V – Brace to Beam Connection (at Beam Midspan)


For a general discussion concerning brace connections design requirements,

see the previous General Discussion section on this chapter. In that section is

given an overview of the AISC and Chilean provisions regarding braces, for

SCBF and OCBF systems.

In this example design is going to be done according to the provision for OCBF

systems.


Design the V-brace to beam connection, at beam midspan, shown in Figure

4.6-1.

The acting forces on the brace for the design are obtained from loads

combinations that consider earthquake but not including the amplified seismic

load.

𝑇𝑢 = 4500 𝑘𝑁

𝑃𝑢 = 4000 𝑘𝑁

4.6-1: General view of the connection to be designed.

1. Section and Material properties

Brace section

H300x300x135.8 (Re. Table 2.1.1 ICHA)


4-78

𝑑 = 300 𝑚𝑚, 𝑏 = 300 𝑚𝑚, 𝑡𝑤 = 16 𝑚𝑚, 𝑡𝑓 = 22 𝑚𝑚, 𝐴 = 17296 𝑚𝑚2

𝐼𝑥 = 278000000 𝑚𝑚4 , 𝐼𝑦 = 99100000 𝑚𝑚4 , 𝑟𝑥 = 127 𝑚𝑚, 𝑟𝑦 = 76 𝑚𝑚

Beam section

H400x400x219.0 (Re. Table 2.1.1 ICHA)

𝑑 = 400 𝑚𝑚, 𝑏 = 400 𝑚𝑚, 𝑡𝑤 = 16 𝑚𝑚, 𝑡𝑓 = 28 𝑚𝑚, 𝐴 = 27904 𝑚𝑚2

Beam, columns and plates material properties

A345ESP (Re. Table 3, NCh203.Of2006)

𝐹𝑦 = 345 𝑀𝑃𝑎, 𝐹𝑢 = 450 𝑀𝑃𝑎, 𝐸 = 200000 𝑀𝑃𝑎

Weld properties

70 ksi electrode, 𝐹𝐸𝑋𝑋 = 480 𝑀𝑃𝑎

2. Verification of width – thickness ratios for braces

According to section 8.2b of AISC 341, braces shall comply with the following:

𝜆 < 𝜆𝑝𝑠

Where 𝜆𝑝𝑠 is obtained from table I-8-1 of the seismic provisions.

For brace flanges (A345ESP):

𝜆 =𝑏

2𝑡< 𝜆𝑝𝑠 = 0.30

𝐸

𝐹𝑦= 7.22

For the brace web (A345ESP):

𝜆 =𝑕

𝑡𝑤< 𝜆𝑝𝑠 = 1.12

𝐸

𝐹𝑦 2.33 −

𝑃𝑢0.9𝑃𝑦

≥ 1.49 𝐸

𝐹𝑦= 35.87


4-79

If the brace is working only under compression load, with no flexural

solicitation, it can be used 1.49 𝐸

𝐹𝑦 limit.

In this example,

Brace web:

𝝀 = 𝟔.𝟖 < 𝝀𝒑𝒔 OK

Brace flange:

𝝀 = 𝟏𝟔 < 𝝀𝒑𝒔 OK

3. Design forces

For OCBF use the following design forces on braces:

Tensile Force:

𝑇𝑢 = 𝑅𝑦𝐹𝑦𝐴𝑔 (Re. AISC 341-05 14.4).

Where 𝑅𝑦 is taken from the table I-6-1 of AISC 341-05 (similar to ASTM

A572Gr50 steel), which in the case of A345 ESP, is 𝑅𝑦 = 1.1:

𝑇𝑢 = 6564 𝑘𝑁

Compression force

𝐶𝑢 = 𝐴𝑔𝐹𝑐𝑟

Where 𝐹𝑐𝑟 is calculated according to the provisions of chapter E of the AISC

360-05 specification:

The element slenderness is (𝑘 = 1):

𝑘𝐿

𝑟𝑦= 56 < 4.0

𝐸

𝐹𝑦= 96.3 (Re. Section 14.2 AISC 341-05)

If 𝑘𝐿

𝑟< 4.71

𝐸

𝐹𝑦= 113.4:


4-80

𝐹𝑐𝑟 = 0.658𝐹𝑦

𝐹𝑒 𝐹𝑦

𝐹𝑒 =𝜋2𝐸

𝑘𝐿

𝑟𝑦

2 = 629 𝑀𝑃𝑎

Therefore:

𝐹𝑐𝑟 = 274 𝑀𝑃𝑎

And:

𝐶𝑢 = 4738 𝑘𝑁

And for the slip critical failure, the design forces on braces shall be considered

as (from load combinations, since it is allowed for the slip critical limit state):

𝑇𝑢𝑠𝑐 = 4500 𝑘𝑁

𝐶𝑢𝑠𝑐 = 4000 𝑘𝑁

Forces acting on the edge of the gusset plate

The forces on the beam to gusset plate connection are:

𝑉 = 𝐶𝑢cos 𝜃 + 𝑇𝑢 cos 𝜃

𝑇 = 𝑇𝑢 sin 𝜃 − 𝐶𝑢 sin 𝜃

𝑀 = 𝑑𝑏2 𝑉

Then,

𝑉 = 7992 𝑘𝑁

𝑇 = 1291 𝑘𝑁

𝑀 = 1598344 𝑘𝑁 ⋅ 𝑚𝑚

4. Gusset plate general Dimensions

Try with a gusset plate with the following dimensions:

𝑯𝟏𝒈 = 𝟒𝟓𝟎 𝒎𝒎

𝑯𝟐𝒈 = 𝟑𝟓𝟎 𝒎𝒎

𝑳𝑩𝒂𝒔𝒆 = 𝟏𝟕𝟔𝟎 𝒎𝒎

𝑩𝒈 = 𝟏𝟑𝟎𝟏 𝒎𝒎


4-81

𝒕𝒈𝒑 = 𝟑𝟎 𝒎𝒎 (Thickness of Gusset plate)

𝒘𝒈 = 𝟒𝟗𝟓 𝒎𝒎

4.6-2: General Dimensions of gusset plate

5. Connection of the brace to the gusset plate

The web and the flanges of the brace have to be connected to the gusset

plate. The calculation of the force distribution in the brace between the web

and flanges of the brace is:

𝑇𝑢 = 𝑇𝑢𝑤 + 2𝑇𝑢𝑓

𝐴𝑤 = 4096 𝑚𝑚2

𝐴𝑓 = 6600 𝑚𝑚2

𝑇𝑢𝑤 =𝐴𝑤𝐴𝑇𝑢 = 1554 𝑘𝑁

𝑇𝑢𝑓 =𝐴𝑓

𝐴𝑇𝑢 = 2505 𝑘𝑁

For the slip critical type of failure, the distribution of forces is:

𝑇𝑢𝑤𝑠𝑐 =𝐴𝑤𝐴𝑇𝑢 = 1066 𝑘𝑁

𝑇𝑢𝑓𝑠𝑐 =𝐴𝑓

𝐴𝑇𝑢 = 1717 𝑘𝑁

6. Connection of the brace flanges

For the flange connection of the brace, we use a cover plates per each flange,

bolted to the brace and welded to the gusset.


4-82

Check of the bolts

Use bolts M24 (24 mm of diameter, standard holes of 27 mm), ASTM A490

bolts, threads included in the shear plane. Even though NCh2369.Of2003 does

not require to verify the slip critical type of failure, in some project

specifications is common to verify this type of failure anyway.

Slip Critical failure

The nominal strength is:

𝜙𝑅𝑛 = 𝜙𝜇𝐷𝑢𝑕𝑠𝑐𝑇𝑏𝑁𝑠 (Re. AISC 360-05, J3-4)

𝜙 = 0.85 (Re. AISC358 2.4.1)

Consider Class A connection surfaces (conservative), and standard size holes

(Re. AISC 360-05, J3.8):

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13

Also, the tensile nominal strength for M24 ASTM 490 bolts is:

𝑇𝑏 = 257 𝑘𝑁 (Re. AISC 360-05, Table J3.1)

Since there is one slip plane, 𝑁𝑆 = 1.0.

Therefore, the nominal shear strength for one bolt is:

𝜙𝑅𝑛 = 86 𝑘𝑁

Then, the number of bolts required for the connection considering slip critical

failure is: 𝑁𝐵 ≥19.88. Use 𝑁𝐵 = 20.

Shear bolt nominal strength

The nominal shear strength is:

𝜙𝑅𝑛 = 𝜙𝐹𝑛𝑣𝐴𝑏 (Re. AISC360-05, J3-1)

𝜙 = 0.75 (Re. AISC358 2.4.1)


4-83

Where 𝐴𝑏 is the nominal gross area of the bolt, therefore:

𝐴𝑏 = 452 𝑚𝑚2

𝐹𝑛𝑣 = 414 𝑀𝑃𝑎 (Re. AISC360-05, Table J3.2)

Then:


Then, the number of bolts required for the connection is: 𝑁𝐵 > 17.83.

Then, 𝑵𝑩 = 𝟐𝟎 is OK.

Use two rows of ten bolts each one.

Tensile yielding of the plate

Consider that the flange is connected to the gusset plate with two plates (at

each side of the gusset plate). It is reasonable that cover plates do not have a

width greater than the width flange. The following relation shall be

accomplished:

2𝑡𝑓𝑝 + 𝑡𝑔𝑝 < 𝑏𝑓 = 300 𝑚𝑚

Where 𝑡𝑔𝑝 is the thickness of the gusset plate.

The nominal strength for tensile yielding limit state is:

𝑅𝑛 = 𝐹𝑦𝐴𝑔 (Re. AISC360-05 J4-1)

𝜙 = 0.9

Try with a plate of length 𝑳𝒑𝒇 = 𝟏𝟏𝟎𝟎 𝒎𝒎, 𝒃𝒑𝒇 = 𝟏𝟑𝟓 𝒎𝒎 wide (in order to cover

the entire flange) and a thickness 𝒕𝒑𝒇 = 𝟑𝟒 𝒎𝒎.


4-84

20 M24 A490

4.6-3: Bolt spacing and plate dimensions.

Then:

𝐴𝑔 = 𝑏𝑝𝑓 × 𝑡𝑝𝑓 = 4590 𝑚𝑚2

Then, for each plate

𝝓𝑹𝒏 = 𝟏𝟒𝟐𝟓 𝒌𝑵

And for the whole connection:

𝝓𝑹𝒏 = 𝟐𝟖𝟓𝟎 𝒌𝑵 > 2505 𝑘𝑁 OK

Tensile Rupture of the flange plate

The nominal strength for tensile rupture limit state is:

𝑅𝑛 = 𝐹𝑢𝐴𝑒 (Re. AISC360-05 J4-1)

𝜙 = 0.75

The effective area subject to tensile rupture is:

𝐴𝑒 = 𝐴𝑔 − 𝑑𝑕 × 𝑡𝑝𝑓 = 3604 𝑚𝑚2

Then, for the whole connection

𝝓𝑹𝒏 = 𝟐 × 𝟏𝟐𝟏𝟔 𝒌𝑵 = 𝟐𝟒𝟑𝟐 𝒌𝑵 < 2505 𝑘𝑁

Then, the plate is not strong enough. Try changing the thickness of the plate,

use 𝒕𝒑𝒇 = 𝟑𝟔 𝒎𝒎, then


4-85

𝝓𝑹𝒏 = 𝟐 × 𝟏𝟐𝟖𝟖 𝒌𝑵 = 𝟐𝟓𝟕𝟔 𝒌𝑵 > 2505 𝑘𝑁 OK

Bearing and tear out of the flange plate

For each plate:

Interior bolts

According to chapter J3.10 of the AISC 360-05, the bearing strength of the

plate is:

𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢 = 985 𝑘𝑁 (Re. AISC 360-05, J3-6a)

𝜙 = 0.75

Considering that 𝐿𝑐 for the internal bolts is:

𝐿𝑐 = 64 𝑚𝑚− 27 𝑚𝑚 = 37𝑚𝑚

Then,

𝑹𝒏 = 𝟕𝟏𝟗 𝒌𝑵 < 𝟗𝟑𝟑 𝒌𝑵 → 𝑹𝒏 = 𝟕𝟏𝟗 𝒌𝑵

Exterior bolts

Considering that 𝐿𝑐 for the exterior bolts is:

𝐿𝑐 = 46 𝑚𝑚−27

2= 32.5 𝑚𝑚

Then,

𝑹𝒏 = 𝟔𝟑𝟐 < 933 𝑘𝑁 → 𝑹𝒏 = 𝟔𝟑𝟐 𝒌𝑵

Then, the nominal strength of the connection is:

𝝓𝑹𝒏 = 𝝓 𝟗 × 𝟕𝟓𝟗 𝒌𝑵 + 𝟏 × 𝟓𝟖𝟓 𝒌𝑵 = 𝟓𝟑𝟐𝟗 𝒌𝑵 >2505

2 𝑘𝑁 OK

Bearing of the brace

The nominal strength for the bearing limit state in the brace is:

𝑅𝑛 = 2.4𝑑𝑡𝑓𝑏𝑟𝑎𝑐𝑒 𝐹𝑢 = 570 𝑘𝑁 (Re. AISC 360-05, J3-6a)


4-86

𝜙 = 0.75

Then, the nominal resistance of the connection is:

𝝓𝑹𝒏 = 𝟐𝟎 × 𝝓 × 𝟓𝟕𝟎 = 𝟖𝟓𝟓𝟒 𝒌𝑵 > 2505 𝑘𝑁 OK

Block shear rupture of the flange plate

The nominal strength for the block shear rupture limit state is given by:

(Re. AISC360-05, J4-5)


𝜙 = 0.75

Where 𝑈𝑏𝑠 = 1.0 in this case, according to the commentary of the AISC 360-05

specification (AISC 360-05 C-J4.2). The values of 𝐴𝑛𝑣 , 𝐴𝑛𝑡 and𝐴𝑔𝑣 are obtained

from the following figure:

4.6-4: Block Shear failure path for one flange plate.

Therefore,

𝐴𝑔𝑣 = 64 × 9 + 46 𝑡 = 22392 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 𝑁𝑏𝑜𝑙𝑡𝑠side − 0.5 × 27 × 𝑡 = 13158 𝑚𝑚2

𝐴𝑛𝑡 = 135

2 𝑚𝑚− 0.5 × 27 𝑡 = 1944 𝑚𝑚2

Then:

𝑹𝒏 = 𝟒𝟒𝟐𝟕 𝒌𝑵 < 5510 𝒌𝑵 → 𝝓𝑹𝒏 = 𝟑𝟑𝟐𝟏 𝒌𝑵 >𝟐𝟓𝟎𝟓

𝟐𝒌𝑵 OK

Welding of the flange plate

Use a two fillet weld between the gusset plate and the flange plate. Consider

t𝑤 = 12 𝑚𝑚. The nominal strength of the weld is:


4-87

𝑅𝑛 = 0.60𝐹𝑒𝑥𝑥𝐴𝑤

𝜙 = 0.75

Then

𝐴𝑤 = 𝐿𝑤 𝑡𝑒𝑓𝑓

𝑡𝑒𝑓𝑓 = 2 × 0.707 × 𝑡𝑤 = 17 𝑚𝑚

𝐿𝑤 = 438 𝑚𝑚

𝐴𝑤 = 7432 𝑚𝑚2

Therefore:

𝝓𝑹𝒏 = 𝟏𝟔𝟎𝟓 𝒌𝑵 >

𝟐𝟓𝟎𝟓

𝟐𝒌𝑵 OK

Base metal failure


𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛 𝑏𝑝

𝜙 = 0.75

For each flange plate:

𝐴𝑛 𝑏𝑝 = 𝐴𝑔 𝑓𝑝 = 𝑡𝑝𝑓𝐿𝑤 = 15768 𝑚𝑚2

Therefore:

𝝓𝑹𝒏 = 𝟑𝟏𝟗𝟑 𝒌𝑵 >𝟐𝟓𝟎𝟓

𝟐𝒌𝑵 OK

For the gusset plate:

𝐴𝑛 𝑔𝑝 = 𝐴𝑔 𝑔𝑝 = 2𝑡𝑔𝑝𝐿𝑤 = 26280 𝑚𝑚2

Therefore:

𝝓𝑹𝒏 = 𝟓𝟑𝟐𝟏 𝒌𝑵 >𝟐𝟓𝟎𝟓

𝟐𝒌𝑵 OK


4-88

7. Connection of the web

For the web connection of the brace, use two cover plates bolted to the brace

and to the gusset. Since the thickness of the gusset plate is greater than the

thickness of the web of the brace, we have to use fillers in order of

accommodate the plates of the connection. The reduction factor for the use of

fillers is,

(Re. section J.5 AISC 360-05)

𝑓𝑓𝑖𝑙𝑙 = 1 − 0.0154 𝑡 − 6

Where 𝑡 is the total thickness of the fillers. Considering two fillers 7 mm thick

each one:

𝑓𝑓𝑖𝑙𝑙 = 0.877

Check the bolts

Use M24 bolts (24 mm diameter, standard holes of 27 mm), ASTM A490

bolts, threads included in the shear plane. Even though NCh2369.Of2003 do

not require to verify the slip critical type of failure, in some projects

specifications require verification of this type of failure.


The nominal strength for slip critical failure is:


𝜙 = 0.85 (Re. AISC358 2.4.1)

Consider Class A connection surfaces (conservative), and standard size holes.

(Re. AISC 360-05, J3.8):

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13

Also, the tensile nominal strength for the M24 ASTM 490 bolts is:


There are two slip planes, 𝑁𝑆 = 2.0.


4-89

Therefore, the nominal strength in shear for one bolt is:

𝜙𝑅𝑛 = 178 × ϕ × 𝑓𝑓𝑖𝑙𝑙 = 133 𝑘𝑁


failure is: 𝑁𝐵 ≥7.03. Use 𝑁𝐵 = 8.




𝜙 = 0.75 (Re. AISC358 2.4.1)

Where 𝐴𝑏 is the nominal gross area of the bolt, therefore:

𝐴𝑏 = 452 𝑚𝑚2


Then:

𝜙𝑅𝑛 = 𝜙𝑓𝑓𝑖𝑙𝑙𝑅𝑛 = 123 𝑘𝑁

There are two shear planes:


Then, the number of bolts required for the connection is: 𝑁𝐵 > 6.31. Use 𝑁𝐵 =

8.

Use two rows of four bolts each one.

Tensile yielding of the plate



𝜙 = 0.9

Try plates 𝑳𝒑𝒘 = 𝟓𝟒𝟎 𝒎𝒎 long, 𝒃𝒑𝒘 = 𝟐𝟒𝟎 𝒎𝒎 wide, 𝒕𝒑𝒘 = 𝟏𝟒 𝒎𝒎 thick.


4-90

4.6-5: Bolt spacing and plate dimensions.

𝐴𝑔 = 𝑏𝑝𝑤 × 𝑡𝑝𝑤 = 3360 𝑚𝑚2

Then,

𝝓𝑹𝒏 = 𝟏𝟎𝟒𝟑 𝒌𝑵 >1554

2 𝑘𝑁 OK

Tensile Rupture of the web plate


𝑅𝑛 = 𝐹𝑢𝐴𝑒 (Re. AISC360-05 J4-1)

𝜙 = 0.75

The effective area subject to tensile rupture is:

𝐴𝑒 = 𝐴𝑔 − 2 × 𝑑𝑕 × 𝑡𝑝𝑓 = 2548 𝑚𝑚2

Then,

𝝓𝑹𝒏 = 𝟖𝟔𝟎 𝒌𝑵 >1554

2 𝑘𝑁 OK

Bearing and tear out of the web plate

Interior bolts


𝜙 = 0.75

16 M24 A490


4-91

Considering that 𝐿𝑐 for the interior bolts is:

𝐿𝑐 = 64 𝑚𝑚− 27 𝑚𝑚 = 37 𝑚𝑚

Then,

𝑹𝒏 = 𝟐𝟖𝟎 𝒌𝑵 < 𝟑𝟔𝟑 𝒌𝑵 → 𝑹𝒏 = 𝟐𝟖𝟎 𝒌𝑵

Exterior bolts


𝐿𝑐 = 46 𝑚𝑚−27

2= 32.5𝑚𝑚

Then,

𝑹𝒏 = 𝟐𝟒𝟔 < 363 𝑘𝑁 → 𝝓𝑹𝒏 = 𝟐𝟒𝟔 𝒌𝑵


𝝓𝑹𝒏 = 𝝓 𝟔 × 𝟐𝟖𝟎 𝒌𝑵 + 𝟐 × 𝟐𝟒𝟔 𝒌𝑵 = 𝟏𝟔𝟐𝟕 𝒌𝑵 >1554

2 𝑘𝑁 OK

Bearing of the brace

The nominal strength for the bearing limit state in the brace is:

𝑅𝑛 = 2.4𝑑𝑡𝑤𝑏𝑟𝑎𝑐𝑒 𝐹𝑢 = 415 𝑘𝑁 (Re. AISC 360-05, J3-6a)

𝜙 = 0.75

Then, the nominal resistance of the connection is:

𝝓𝑹𝒏 = 𝟖 × 𝝓 × 𝟒𝟏𝟓 = 𝟐𝟒𝟖𝟖 𝒌𝑵 >𝟏𝟔𝟗𝟔

𝟐 𝒌𝑵 OK

Block shear rupture of the web plate


(Re. AISC360-05, J4-5)


𝜙 = 0.75


4-92

𝑈𝑏𝑠 = 1.0, according to the commentary of the AISC 360-05 specification (AISC

360-05 C-J4.2). The values of 𝐴𝑛𝑣 , 𝐴𝑛𝑡 , and 𝐴𝑔𝑣 are obtained from the following

figure.

4.6-6: Shear block failure path.

𝐴𝑔𝑣 = 2 × 64 × 3 + 64 𝑡 = 6664 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 𝑁𝑏𝑜𝑙𝑡𝑠 − 1 × 27 × 𝑡 = 4018 𝑚𝑚2

𝐴𝑛𝑡 = 64 𝑚𝑚− 27 𝑡 = 518 𝑚𝑚2

Then:

𝑹𝒏 = 𝟏𝟑𝟏𝟖 𝒌𝑵 < 1613 𝒌𝑵 → 𝝓𝑹𝒏 = 𝟗𝟖𝟖 𝒌𝑵 >1554

2𝒌𝑵 OK

The connection to the gusset plate is exactly the same, but for the limit state

of bearing, it has to be considered the thickness of the gusset plate. Since the

gusset plate is thicker than the brace web, by inspection that limit state does

not control the design.

8. Connection between the gusset plate and the beam

Weld between gusset plate and the beam

According to the force transfer mechanism, the design forces for the weld are:

𝑉 = 7992 𝑘𝑁

𝑇 = 1291 𝑘𝑁

𝑀 = 1598344 𝑘𝑁 ⋅ 𝑚𝑚

Use the elastic method for the calculation of the maximum stress in the weld.

(Re. Chapter 8 AISC Manual of Steel Construction)


4-93

𝑓𝑥 =𝑀

𝐼𝑥

𝑕𝑤𝑒2

+𝑇

𝐴𝑒𝑓𝑓

𝑓𝑦 =𝑉𝑢𝐴𝑒𝑓𝑓

𝐹𝑢 = 𝑓𝑥2 + 𝑓𝑦

2

where 𝐼𝑥 is the inertia of the weld and 𝐴𝑒𝑓𝑓 is the effective area of the weld.

Use 26 mm fillet weld size; the height of the weld 𝑕𝑤𝑒 is equal to the length

of the base of the gusset on the beam. Then,

𝑕𝑤𝑒 = 𝐿𝑏𝑎𝑠𝑒 = 1760 𝑚𝑚

𝑡𝑒𝑓𝑓 = 2 × 26 × 0.707 𝑚𝑚 = 37 𝑚𝑚

𝐼𝑥 =𝑕𝑤𝑒

3 𝑡𝑒𝑓𝑓

12= 16702424405 𝑚𝑚4

𝐴𝑒𝑓𝑓 = 𝑡𝑒𝑓𝑓 𝑕𝑤𝑒 = 64705 𝑚𝑚2

𝑓𝑥 = 104 𝑀𝑃𝑎

𝑓𝑦 = 124 𝑀𝑃𝑎


the nominal strength for a weld is:

(Re. Table J2.5 AISC 360-05)

𝐹𝑤 = 0.60𝐹𝑒𝑥𝑥

𝜙 = 0.75

Then,

𝝓𝑭𝒘 = 𝟐𝟏𝟔 𝑴𝑷𝒂 > 162 𝑀𝑃𝑎 OK

Also we have to verify the average tension in the weld:

𝑓𝑎𝑣𝑔 =1

2

𝑇

𝐴𝑒𝑓𝑓+𝑀

𝐼𝑥

𝑕𝑤𝑒2

2

+ 𝑉

𝐴𝑒𝑓𝑓

2

+ 𝑇

𝐴𝑒𝑓𝑓−𝑀

𝐼𝑥

𝑕𝑤𝑒2

2

+ 𝑉

𝐴𝑒𝑓𝑓

2

𝑓𝑎𝑣𝑔 = 150 𝑀𝑃𝑎

And we have to verify for 1.25𝑓𝑎𝑣𝑔 , then:

𝝓𝑭𝒘 = 𝟐𝟏𝟔 𝑴𝑷𝒂 > 1.25𝑓𝑎𝑣𝑔 = 188 𝑀𝑃𝑎 OK


4-94

Base metal failure


𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛 𝑏𝑝

𝜙 = 0.75

Then, for the gusset plate:

𝐴𝑛 𝑔𝑝 = 𝐴𝑔 𝑔𝑝 = 𝑡𝑔𝑝𝐿𝑏𝑎𝑠𝑒 = 52800 𝑚𝑚2

Therefore:

𝝓𝑹𝒏 = 𝟏𝟎𝟔𝟗𝟐 𝒌𝑵 > 𝑉 = 𝟕𝟗𝟗𝟐 𝒌𝑵 OK

Also, for the beam flange

𝐴𝑛 = 2𝑡𝑏𝑓𝐿𝑏𝑎𝑠𝑒 = 98560 𝑘𝑁

Then,

𝝓𝑹𝒏 = 𝟏𝟗𝟗𝟓𝟖 𝒌𝑵 > 𝑉 = 𝟕𝟗𝟗𝟐 𝒌𝑵 OK

Beam web local yielding

The maximum distributed tensile force for the interface between beam and

gusset plate is given by:

𝑝𝑡𝑥 = 𝑡𝑒𝑓𝑓 𝑇


𝐼𝑥

𝑕𝑤𝑒2

And the length of the gusset base that is subject to tensile loads is given by:

𝐿𝑡 = 𝐿𝑏𝑎𝑠𝑒 𝑓𝑡

𝑓𝑡 + 𝑓𝑐

𝑓𝑡 = 𝑇


𝐼𝑝

𝑕𝑤𝑒2 = 104 𝑀𝑃𝑎

𝑓𝑐 = 𝑇


𝐼𝑝

𝑕𝑤𝑒2 = 64 𝑀𝑃𝑎


4-95

Then,

𝐿𝑡 = 1088 𝑚𝑚

𝑝𝑡𝑥 = 3.829 𝑘𝑁/𝑚𝑚

Then, the tensile force is:

𝑅𝑢 =1

2𝐿𝑡𝑝𝑥 = 2084 𝑘𝑁

And the nominal strength for web local yielding is (considering that the load is

applied at a distance greater than 𝑑/2 from the end of the member)

𝑅𝑛 = 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑤 (Re. J10-2 AISC 360-05)

𝜙 = 1.00

Where 𝑘 is the distance between the face of the flange and the toe of the fillet

weld of the beam. 𝑁 is the distance in which the load is applied, then:

𝑘 = 36 𝑚𝑚

𝑁 = 𝐿𝑡 = 1088 𝑚𝑚

𝝓𝑹𝒏 = 𝟕𝟎𝟎𝟐 𝒌𝑵 > 2418 𝑘𝑁 OK

Beam web Crippling

The maximum compressive force for unit of length in the interface beam-

gusset is given by:

𝑝𝑐𝑥 = 𝑡𝑒𝑓𝑓 𝑇


𝐼𝑥

𝑕𝑤𝑒2 = 2.362

𝑘𝑁

𝑚𝑚

And the length that is subject to compression is:

𝐿𝑐 = 𝐿𝑏𝑎𝑠𝑒 − 𝐿𝑡 = 672 𝑚𝑚

The force is:

𝑅𝑢 =1

2𝑝𝑐𝑥𝐿𝑐 = 793 𝑘𝑁

The nominal strength for web crippling, (considering that the load is applied at

a distance greater than 𝑑/2 from the end of the member) is:


4-96

𝑅𝑛 = 0.80𝑡𝑤2 1 + 3

𝑁

𝑑

𝑡𝑤

𝑡𝑓

1.5

𝐸𝐹𝑦𝑤 𝑡𝑓

𝑡𝑤 (Re. J10-4 AISC 360-05)

𝜙 = 0.75

𝑁 = 𝐿𝑐

Therefore,

𝝓𝑹𝒏 = 𝟓𝟑𝟔𝟎 𝒌𝑵 > 793 𝑘𝑁 OK

Since the last two verifications have considered the beam, it has to be verified

a load combination that considers 𝑃𝑢 = 0.3𝑃𝑛(Re AISC 341 14.3(1)), then, the

forces on the connection between the beam and the gusset are

𝑉 = 5646 𝑘𝑁

𝑇 = 3636 𝑘𝑁

𝑀 = 1129289 𝑘𝑁 ⋅ 𝑚𝑚

And the stresses are:

𝑓𝑡 = 𝑇


𝐼𝑥

𝑕𝑤𝑒2 = 116 𝑀𝑃𝑎

𝑓𝑐 = 𝑇


𝐼𝑝

𝑕𝑤𝑒2 = −3 𝑀𝑃𝑎

Then, the tensile and compressive forces are

𝑅𝑢𝑐 = 2.96 𝑘𝑁

𝑅𝑢𝑡 = 3633 𝑘𝑁

As it can be seen, both are lesser than the nominal resistances, but it is

important to verify this because the tensile force will increase if a smaller

compressive force is considered and web local yielding can occur.

Tensile Yielding of the Whitmore area

Considering that the Whitmore area is the result of projecting the width of the

connection between the brace and the gusset plate in 30 degrees until the end

of the connection, then:

𝐵𝑊 = 𝐵𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 + 2𝐿𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 tan 30°


4-97

Consider

𝐵𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = 300 + 2𝑡𝑝𝑓 = 376 𝑚𝑚

𝐿𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = 438 𝑚𝑚

𝐵𝑊 = 881 𝑚𝑚2

Then:

𝐴𝑤 = 𝐵𝑤 𝑡𝑔𝑝 = 26453 𝑚𝑚2

And the nominal resistance is:

𝑅𝑛 = 𝐹𝑦𝐴𝑤 (Re. J4-1 AISC 360-05)

𝜙 = 0.90

Then,

𝝓𝑹𝒏 = 𝟖𝟐𝟏𝟒 𝒌𝑵 > 6564 𝑘𝑁 OK

Compression buckling of the Whitmore Area

The average buckling length of the gusset plate is given by:

𝐿𝑔𝑏 = 𝐿𝑏𝑎𝑠𝑒 −𝑑

2 cos𝜃 +

𝐻1𝑔 cos 30°

𝑠𝑒𝑛 (𝜃 + 30°)− 𝐿𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = 446 𝑚𝑚

Furthermore,

𝑟 =𝑡𝑔𝑝

12= 8.66 𝑚𝑚

Considering 𝐾 = 1.2, because is only one edge of the gusset restrained, the

slenderness is

𝑘𝐿

𝑟= 61.8 > 25

Then, use the provisions of chapter E of AISC 360-05:

As 𝑘𝐿

𝑟< 4.71

𝐸

𝐹𝑦= 113.4:


4-98

𝐹𝑐𝑟 = 0.658𝐹𝑦

𝐹𝑒 𝐹𝑦

𝐹𝑒 =𝜋2𝐸

𝑘𝐿

𝑟

2 = 517 𝑀𝑝𝑎


The nominal resistance is:

𝑃𝑛 = 𝐴𝑤𝐹𝑐𝑟 (Re. E3-1 AISC 360-05)

𝜙 = 0.9

Then,

𝝓𝑷𝒏 = 𝟔𝟐𝟎𝟗 𝒌𝑵 > 4738 𝑘𝑁 OK

Free edge buckling

According to the geometry of the gusset connection, there are two free edges:

4.6-7: Free edge buckling lengths

𝐿𝑓𝑔1 =𝐻1𝑔

𝑠𝑒𝑛 𝜃 + 30° = 466 𝑚𝑚

𝐿𝑓𝑔2 =1

2

𝐵𝑔

𝑠𝑒𝑛(𝜃 − 30°)= 674 𝑚𝑚

Then, according to Astaneh, the maximum free edge length that does not

generates buckling is:

𝐿𝑓𝑔𝑚𝑎𝑥 = 0.75𝑡𝑔𝑝 𝐸

𝐹𝑦= 542 𝑚𝑚


4-99

Then, the first free edge complies with the requirements. The second one

does not comply, so stiffeners have to be provided as shown in Figure 4.6-8.

4.6-8: Stiffeners for free buckling

Designed Connection

4.6-9: General view of the designed connection.

STIFFENERS

(NOT DESIGNED)

H300X300X135.8

H400X400X219.0

TYP12

TYP26

M24

M24

M24

PL1100X135X38

2 PL540X240X14

t = 30 mm12

26

STIFFENERS

(NOT DESIGNED)


4-100


MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 5: SHEAR CONNECTIONS

5-1

5. SHEAR CONNECTIONS

5.1. Shear tab beam-to-column connection (single plate connection)


1. NCh2369.Of2003:

Use high strength bolts (ASTM A325 or ASTM A490). Arc welding


(Re. NCh2369. Of 2003, 8.5.1)

Bolts must be prestressed to 70% of the nominal tensile strength. Always

the nominal strength shall be verified as a bearing type connection.

(Re. NCh2369. Of 2003, 8.5.6)

For field joints, see requirements of section 8.5.8.

(Re. NCh2369. Of 2003, 8.5.8)

5.1.b. General recommendations

1. AISC Manual of Steel Construction 13th edition

Part 10 of the AISC Manual of Steel Construction requires the following

verifications for shear tab connections (or single plate connections):

Check applicable limit states for bolts (part 7 of the AISC Construction

Manual).

Check applicable limit states for welds (part 8 of the AISC Construction

Manual).

Check applicable limit states for the connecting elements (part 9 of the

AISC Construction Manual).

Furthermore, in this example, the conventional configuration for a shear tab

connection is used, which according to the AISC Construction Manual must

meet the following requirements (See Figure 5.1-1):

A single vertical line of bolts is permitted. The number of bolts is limited

from two to twelve.

The distance “a” (see Figure 5.1-1) has to be less or equal to 88 mm.

STD or SSL holes are permitted.


5-2

The horizontal edge distance, 𝐿𝑒𝑕, must be equal to or greater than 2𝑑𝑏 for

both the plate and the beam web.

The vertical edge distance, Lev, must satisfy requirements from table J3.4

of AISC 360-05 specification. (Minimum edge distances from center of

STD hole to edge of connected part, for more information, see AISC

Manual of Steel Construction)

The thickness of the plate and the beam web must satisfy 𝑡 ≤𝑑𝑏

2+ 1.6 𝑚𝑚

Furthermore, in the conventional configuration, the connection plate must be

welded on both sides for the connection with the column flange. It is

recommended that the length of the connecting plate must be greater than

one half of the depth of the beam.

Following the requirements described above, the connection must be verified

for bolt shear, block shear rupture, bearing, shear yielding and shear rupture.

The advantage of the conventional configuration is that neither buckling of the

plate nor the eccentricity of the bolts has to be verified. If STD holes are used

and the number of bolts is less than 10, plate buckling limit state will not

control for the conventional configuration.

Figure 5.1-1: General provisions for the shear tab connection conventional configuration. From AISC Manual of Steel Construction, 13th Ed, figure 10-1

5.1.c. Example

Design a shear tab bolted connection (single plate connection) between a

column flange and a beam as shown in Figure 5.1-2. Use A250 ESP steel

required for constructions subjected to dynamic loads, according

NCh203.Of2006 , Table 3. Use 70 ksi electrode for welds.

a Leh

Lev

L

n -

1 @

3"

Lev


5-3

The column and the beam are a Chilean H300x300x87.3 and a

H400x300x83.5 built-up sections. Assume that the connection transfers only

shear forces and the elements have been designed to support those forces.

The shear forces for the design are:

𝑉𝐷 = 90 𝑘𝑁 𝑉𝐿 = 120 𝑘𝑁

Figure 5.1-2: General view of the connection.

1. Materials and section properties

H300x300x87.3

(Re. Table 2.1.1 ICHA Manual for the Design of Steel Structures)

𝑑 = 300 𝑚𝑚, 𝑏 = 300 𝑚𝑚

𝑡𝑤 = 10 𝑚𝑚, 𝑡𝑓 = 14 𝑚𝑚

H400x300x83.5


𝑑 = 400 𝑚𝑚, 𝑏 = 300 𝑚𝑚

𝑡𝑤 = 6 𝑚𝑚, 𝑡𝑓 = 14 𝑚𝑚

A250ESP (Re. Table 3, NCh203.Of2006)

𝐹𝑦 = 250 𝑀𝑃𝑎, 𝐹𝑢 = 400 𝑀𝑃𝑎

PL HxBxt

H400X300X83.5

H300X300X87.3


5-4

BOLTS: ASTM A490, threads included in the shear planes, STD holes.

WELDS: 70 ksi electrode, 𝐹𝐸𝑋𝑋 = 480 MPa

2. Design Forces

𝑉𝑈 = 1.2𝑉𝐷 + 1.6𝑉𝐿 = 300 𝑘𝑁

3. Bolts

Use M20 bolts (20 mm of diameter, standard holes of 22 mm), ASTM A490

threads included in the shear plane. Even though NCh2369.Of2003 does not

require to verify the connection as slip critical, sometimes project

specifications do require it.

Tip:

It is important to notice that following the requirements for conventional shear

tab configurations, as defined on AISC Manual of Steel Construction 13th

edition, the thicknesses of the connecting plate and beam web are controlled

by the size of the bolt.

Slip Critical Connection


𝜙𝑅𝑛 = 𝜙𝜇𝐷𝑢𝑕𝑠𝑐𝑇𝑏𝑁𝑠 𝜙 = 0.85 (Re. AISC 360-05, J3-4)

Consider Class A connection surfaces, and standard size holes.

(Re. AISC 360-05, J3.8)

𝜇 = 0.35 𝑕𝑠𝑐 = 1.00 𝐷𝑢 = 1.13

Also, the tensile nominal strength for M20 ASTM 490 bolts is


Since there is one slip plane, then 𝑁𝑠 = 1.0.

For one bolt, the design slip strength is:



5-5


strength is: 𝑁𝐵 ≥ 4.98. Use 𝑁𝐵 = 5 bolts.



𝜙𝑅𝑛 = 𝜙𝐹𝑛𝑣𝐴𝑏 𝜙 = 0.75 (Re. AISC360-05, J3-1)

Where 𝐴𝑏 is the nominal gross area of the bolt, and in this example the

threads are supposed to be not excluded from the shear plane, then:

𝐴𝑏 = 314 𝑚𝑚2



The number of bolts required for the connection is: 𝑁𝐵 > 3.1.

Then, the slip critical strength controls the design, use 𝑵𝑩 = 𝟓.

Bolt spacing and plate dimensions

Consider a minimum bolt spacing of 60 mm and a minimum distance to the

edge of 34 mm (refer to Bolted Connections section 2.4 on this Manual). The

minimum length and width of the shear plate are:

𝐿𝑀𝐼𝑁 = 4 × 60 𝑚𝑚 + 2 × 34 𝑚𝑚 = 308 𝑚𝑚 𝐵𝑀𝐼𝑁 = 2 × 34 𝑚𝑚 + 𝑑𝑐

With 𝑑𝑐 the gap between the column and the beam, use 𝑑𝑐 = 12 mm, then:

𝐵𝑀𝐼𝑁 = 2 × 34 𝑚𝑚 + 12𝑚𝑚 = 80 𝑚𝑚

In order to satisfy the conventional configuration requirements, use 𝑩 = 𝟗𝟎 𝒎𝒎

and 𝑳 = 𝟑𝟐𝟎 𝒎𝒎. These values satisfy the requirements for the conventional

configuration for shear tab connections:

𝐿𝑒𝑕 = 40 𝑚𝑚 ≥ 2𝑑𝑏 = 40 𝑚𝑚 OK

𝑎 = 50 𝑚𝑚 < 88 𝑚𝑚 OK

Use a plate PL320 x 90 x 8.


5-6

Figure 5.1-3: Dimensions of the shear plate and bolt spacing.

4. Bearing strength at bolt holes

Interior bolts


𝐿𝑐 for the interior bolts is:

𝐿𝑐 = 60𝑚𝑚− 22𝑚𝑚 = 38 𝑚𝑚

Where the standard hole dimension for M20 bolts is 22 mm.

(Re. Table J3.3M AISC 360-05)

𝑹𝒏 = 𝟏𝟒𝟔𝒌𝑵 < 𝟏𝟓𝟒𝒌𝑵 → 𝝓𝑹𝒏 = 𝟏𝟎𝟗𝒌𝑵

Exterior bolts

𝐿𝑐 for the exterior bolts is:

𝐿𝑐 = 40 𝑚𝑚−22

2= 29 𝑚𝑚

𝑹𝒏 = 𝟏𝟏𝟏 𝒌𝑵 < 154 𝑘𝑁 → 𝝓𝑹𝒏 = 𝟖𝟑 𝒌𝑵

The bearing strength of the connection is:


5-7

𝝓𝑹𝒏 = 𝟒 × 𝟏𝟎𝟗 𝒌𝑵+ 𝟏 × 𝟖𝟑 𝒌𝑵 = 𝟓𝟏𝟗 𝒌𝑵 > 300 𝑘𝑁 OK

Check the conventional configuration requirements:

𝑡 = 8𝑚𝑚 <𝑑𝑏

2+ 1.6 𝑚𝑚 = 11.6 𝑚𝑚 OK

5. Shear yielding of the plate

The nominal strength for the shear yielding limit state is:

𝑅𝑛 = 0.6𝐹𝑦𝐴𝑔 (Re. AISC360-05 J4-3)

𝜙 = 1.00

𝐴𝑔 = 𝐿 ⋅ 𝑡 = 320 × 8 = 2560 𝑚𝑚2, therefore:

𝝓𝑹𝒏 = 𝟑𝟖𝟒 𝒌𝑵 > 300 𝑘𝑁 OK

6. Shear rupture of the plate

The nominal strength for the shear rupture limit state is:

𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 (Re. AISC360-05 J4-4)

𝜙 = 0.75

Where 𝐴𝑛𝑣 is the net area of the plate, which considers the reduction of the

section due to bolt holes, the calculation diameter for M20 holes is:

𝑑𝑕 = 22 𝑚𝑚 (Nominal hole for M20 bolts)

𝑑𝐶𝐴𝐿𝐶 = 22 𝑚𝑚 + 2 𝑚𝑚 = 24 𝑚𝑚

𝐴𝑛𝑣 = 𝐿 − 𝑁𝐵𝑑𝐶𝐴𝐿𝐶 𝑡 = 1600 𝑚𝑚2

𝝓𝑹𝒏 = 𝟐𝟖𝟖 𝒌𝑵 < 300 𝑘𝑁

Try changing the length of the plate to 340 mm:

𝐴𝑛𝑣 = 𝐿 − 𝑁𝐵𝑑𝐶𝐴𝐿𝐶 𝑡 = 1760 𝑚𝑚2 𝝓𝑹𝒏 = 𝟑𝟏𝟔 𝒌𝑵 > 300 𝑘𝑁 OK

7. Block shear rupture


𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 ≤ 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 (Re. AISC360-05, J4-5)


5-8

𝜙 = 0.75

Where Ubs = 1.0 in this case, according to the commentary in AISC 360-05

specification (AISC 360-05 C-J4.2). The values of 𝐴𝑛𝑣 , 𝐴𝑛𝑡 and 𝐴𝑔𝑣 are obtained


Figure 5.1-4: Block shear path.

Then:

𝐴𝑛𝑣 = 𝐿 − 50 𝑚𝑚− 4.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 1456 𝑚𝑚2 𝐴𝑔𝑣 = 𝐿 − 50 𝑚𝑚 𝑡 = 2320 𝑚𝑚2 𝐴𝑛𝑡 = 40 𝑚𝑚− 0.5𝑑𝐶𝐴𝐿𝐶 𝑡 = 224 𝑚𝑚2

𝑅𝑛 = 439 𝑘𝑁 > 438 𝑘𝑁 → 𝜙𝑅𝑛 = 328 𝑘𝑁 > 300 𝑘𝑁 OK

8. Bolt bearing of the beam web

The bearing nominal strength is given by the following expression:

𝑅𝑛 = 2.4𝑑𝑡𝑤𝐹𝑢 𝜙 = 0.75

Considering that 𝒕𝒘 = 𝟔 𝒎𝒎, for each bolt:

𝝓𝑹𝒏 = 𝟖𝟔 𝒌𝑵

Then for the whole connection:

𝝓𝑹𝒏 = 𝟓 × 𝟖𝟔 𝒌𝑵 = 𝟒𝟑𝟎 𝒌𝑵 > 300 𝑘𝑁 OK


5-9

Tip:

In this case it only has to be verified the bearing strength of the beam web

because there is no cope in the end of the beam; however if the beam is coped

in the end it has to be verified the tear out limit state.

9. Weld shear

According to the recommendations of the AISC Manual of Steel Construction,

the weld of the connection between the plate and the column flange has to be

verified considering eccentricity of the weld, even though the eccentricity for

the design of the bolts can be neglected.

The weld used for the connection between the plate and column flange are two

lines of welds parallel to the shear for both sides of the plate of connection,

(see Figure 5.1-53), then the eccentricity between the weld and the bolts line

is:

𝑒 = 50 𝑚𝑚

The weld is subject to a shear force and a moment given by:

𝑉𝑢 = 300 𝑘𝑁 → 𝑀𝑢 = 𝑒𝑉𝑢 = 15000 𝑘𝑁 −𝑚𝑚

Since there are shear and moment acting on the connection, it is used an

elastic method for the calculation of the maximum stress for the weld.

𝑓𝑥 =𝑀

𝐼𝑥

𝑕𝑤𝑒

2 (Re. AISC Manual of Steel Construction, Chapter 8)

𝑓𝑦 =𝑉𝑢𝐴𝑒𝑓𝑓

𝑓𝑢 = 𝑓𝑥2 + 𝑓𝑦

2

Where 𝐼𝑥 is the inertia of the weld and 𝐴𝑒𝑓𝑓 is the effective area of the weld.

Use 6 mm fillet welds , and the length of the weld, 𝑕𝑤𝑒 , is equal to the

length of the plate minus two times the thickness of the plate, 𝑕𝑤𝑒 = 324 𝑚𝑚 ,

therefore:

𝑡𝑒𝑓𝑓 = 6 × 0.707 𝑚𝑚 = 4.24 𝑚𝑚

𝐼𝑥 = 2 ×𝑕𝑤𝑒

3 𝑡𝑒𝑓𝑓

12= 24035304 𝑚𝑚4

𝐴𝑒𝑓𝑓 = 2 × 𝑡𝑒𝑓𝑓 𝑕𝑤𝑒 = 2747 𝑚𝑚2 𝑓𝑥 = 101 𝑀𝑃𝑎 𝑓𝑦 = 109 𝑀𝑃𝑎 𝑓𝑢 = 149 𝑀𝑃𝑎


5-10

The nominal strength of the weld is:

𝐹𝑤 = 0.60𝐹𝑒𝑥𝑥 (Re. Table J2.5 AISC 360-05) 𝜙 = 0.75

Then,


Figure 5.1-5: Weld distribution.

10. Designed connection

Figure 5-6: Designed connection.

66

PL 340x90x8

H400X300X83.5

H300X300X87.3


5-11

5.1.d. References

AISC Manual of Steel Construction, 13th Edition.

Arze, Reciné y Asociados, Ingenieros Consultores, 2000. “Manual

de Diseño para Estructuras de Acero” (ICHA Manual for the

Design of Steel Structures). Instituto Chileno del Acero (ICHA),

Santiago, Chile.


5-12

5.2. Shear single angle beam-to-column connection

5.2.a. Design requirements:

1. NCh2369. Of2003


electrodes shall comply with the requirements of the code.

(Re. NCh2369. Of 2003 8.5.1)

Bolts must be prestressed to a 70% of the nominal tensile strength.


connection.

(Re. NCh2369. Of 2003 8.5.6)


1. ICHA: Manual de Diseño para Estructuras de Acero

In shear connections for beams the angle recommended is L80x80, which

has been standardized for this application.

(Re. Section 3.2.3 ICHA Manual for the Design of Steel Structures)


Part 10 of the AISC construction manual requires the following verifications for

shear single angle connections:

Check applicable limit states for bolts, part 7 of the AISC Construction

Manual.

Check applicable limit states for the connecting elements, part 9 of the

AISC Construction Manual.

Furthermore, the AISC Construction Manual has the following verifications for

single angle connections:

Always consider the eccentricity for the bolts in the angle leg attached to

the support. For the calculation of the nominal resistance of bolts subject

to eccentric loads, use the provisions of part 7 of AISC manual of Steel

Construction.

Consider eccentricity when there are two rows of bolts or when the

eccentricity is greater than 3 in (76 mm).


5-13

The length of the angle connection is recommended to be at least equal to

one half of the T dimension of the beam to be supported.

The recommended minimum thickness of the angle is t = 10 mm for M20

or M22 bolts and 12 mm for M25 bolts.

5.2.c. Example

Design a shear single angle all bolted connection between a column flange and

a beam as shown in Figure 5.2-1. Use A250ESP steel, required for

constructions subject to dynamics loads, according to NCh203.Of2006 code,

Table 3.

The column and the beam are a Chilean H300x300x87.3 and an

H450x250x111.8 built-up section. Assume that the connection only transfers

shear forces and that the sections have been designed to resist those shear

actions.

The shear forces are

𝑉𝐷 = 110 𝑘𝑁

𝑉𝐿 = 150 𝑘𝑁


H450X250X111.8

H300X300X87.3


5-14

1. Section and material properties

H300x300x87.3


𝑑 = 300 𝑚𝑚, 𝑏 = 300 𝑚𝑚

𝑡𝑤 = 10 𝑚𝑚, 𝑡𝑓 = 14 𝑚𝑚

H450x250x111.8


𝑑 = 450 𝑚𝑚, 𝑏 = 250 𝑚𝑚

𝑡𝑤 = 8 𝑚𝑚, 𝑡𝑓 = 22 𝑚𝑚

A250ESP (Re. Table 3, NCh203. Of2006)

𝐹𝑦 = 250 𝑀𝑃𝑎, 𝐹𝑢 = 400 𝑀𝑃𝑎

BOLTS: ASTM A490 bolts, threads included in the shear plane, STD holes.

2. Design Forces

𝑉𝑈 = 1.2𝑉𝐷 + 1.6𝑉𝐿 = 372 𝑘𝑁

3. Bolts

For the angle leg attached to the beam the verifications to be done will be bolt

shear, bolt bearing and the solicitation will be the design shear established on

the previous section, but for bolts attached to the column it is important to

consider the eccentricity of the connection and the design force will be

different.

Try M24 bolts (24 mm of diameter, standard holes of 27 mm, refer to Bolted

Connections section on this manual).

Slip Critical connection



𝜙 = 0.85


5-15

Considering class A connection surfaces, and standard size holes:

(Re. AISC 360-05 J3.8)

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13

Pretension of the bolts equals 70% of the tensile nominal strength:


Since there is one slip plane, 𝑁𝑠 = 1.0.

The nominal strength for one bolt in shear is:


The number of bolts required for the connection considering slip critical failure

is: 𝑁𝐵 > 4.32. Use 𝑁𝐵 = 5.




𝜙 = 0.75

Where 𝐴𝑏 is the nominal gross area of the bolt. Threads are not excluded from

shear plane:

𝐴𝑏 = 452 𝑚𝑚2

𝐹𝑛𝑣 = 414 𝑀𝑃𝑎

𝝓𝑹𝒏 = 𝟏𝟒𝟎 𝒌𝑵 (Re. AISC360-05, Table J3.2)

The number of bolts required for the connection considering shear nominal

strength is: 𝑁𝐵 > 2.67.

The slip critical type of failure controls the design, use 𝑵𝑩 = 𝟓.


5-16

Bolts spacing and angle dimensions

Considering a minimum space between bolts of 64 mm and a minimum

distance to the edge of 32 mm, we have:

𝐻𝑚𝑖𝑛 = 4 × 64 𝑚𝑚 + 2 × 32 𝑚𝑚 = 320 𝑚𝑚

𝐵𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 𝑑𝑐

With 𝑑𝑐 the spacing between the column and the beam, use 𝑑𝑐 = 12 𝑚𝑚, then:

𝐵𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 12𝑚𝑚 = 76 𝑚𝑚

Use a L80 x 80 x t x 320 angle, with “t” the thickness of the angle leg.

Angle leg attached to the column:

Corresponds to the distance between the shear plane of the bolts attached to

the beam and the line of bolts attached to the column (see Figure 5.2-2),

then:

𝑒1 = 48 𝑚𝑚

Angle leg attached to the beam:

Correspond to the distance between the line of bolts attached to the beam and

the face of column flange.

𝑒2 = 36 𝑚𝑚 + 𝑑𝑐 = 48 𝑚𝑚 < 3" = 76 𝑚𝑚 (Re. Part 10 Manual of Steel Construction)

Figure 5.2-2: Dimensions of bolts (equal to the connection of the leg attached

to the column).

A A

A-A


5-17

Then, there is no need of consider the eccentricity of the bolts attached to the

beam.

4. Bearing and tear out of the angle leg

Interior bolt

Considering a angle thickness 𝒕 = 𝟖 𝒎𝒎, then the bearing strength of the plate

is:


𝜙 = 0.75

Considering that 𝐿𝐶 for the interior bolts is:

𝐿𝑐 = 64 𝑚𝑚− 27 𝑚𝑚 = 37 𝑚𝑚

𝝓𝑹𝒏 = 𝟏𝟎𝟔 𝒌𝑵 < 138 𝑘𝑁

Exterior bolt


𝐿𝑐 = 32 𝑚𝑚−27

2= 18.5 𝑚𝑚


(Table J3.3M, AISC 360-05)

Then,

𝝓𝑹𝒏 = 𝟓𝟑 𝒌𝑵 ≤ 𝟏𝟑𝟖 𝒌𝑵

Hence, the bearing strength of the connection is:

𝝓𝑹𝒏 = 𝟒 × 𝟏𝟎𝟔 𝒌𝑵+ 𝟓𝟑 𝒌𝑵 = 𝟒𝟕𝟕 𝒌𝑵 > 372 𝑘𝑁 OK

Therefore use an angle L80 x 80 x 8 x 320.


5-18

5. Nominal strength in bolts with eccentricity, for bolts attached to the

column

According to the AISC Construction Manual, part 7, there are two methods for

the calculation of the force in bolts with eccentricity, the instantaneous center

of rotation method and the elastic method. We use the elastic method, which

is more conservative than the instantaneous center of rotation since the first

does not consider the ductility of the bolts and the redistribution of stresses.

The elastic method is simpler.

Then,

𝑟𝑢 = 𝑟𝑝𝑥 + 𝑟𝑚𝑥 2

+ 𝑟𝑝𝑦 + 𝑟𝑚𝑦 2 (Re. AISC Manual of Steel Construction, part 7)

Where 𝑟𝑢 is the bolt maximum force at the connection.

𝑟𝑝𝑦 =𝑉𝑢𝑁𝐵

𝑟𝑚𝑥 =𝑉𝑢𝑒𝑐𝑦𝐼𝑝

𝑟𝑚𝑦 = 𝑟𝑝𝑥 = 0 (There are only shear forces and there is no axial force in the

beam)

Where 𝐼𝑝 and 𝑐𝑦 are the polar moment of inertia with respect to the center of

gravity of the bolts and 𝑐𝑦 is the maximum distance of a bolt of the connection

with respect to the center of gravity of the system. Considering the disposition

shown in the Figure 5.2-3, we have:

𝐼𝑃 = (𝑥𝑖2 + 𝑦𝑖

2)

𝑁𝐵

𝑖=1

= 40960 𝑚𝑚2

𝑐𝑦 = 128 𝑚𝑚

𝑁𝐵 = 5

𝑒1 = 48 𝑚𝑚


5-19

Figure 5.2-3: Distribution of bolts for the calculation of 𝐼𝑝

Then:

𝑟𝑝𝑦 = 75 𝑘𝑁

𝑟𝑚𝑥 = 56 𝑘𝑁

𝑟𝑢 = 94 𝑘𝑁

The strength of the bolts is the minimum between the bearing of the holes and

the shear strength for bolts, then:

𝜙𝑟𝑛 𝑠𝑕𝑒𝑎𝑟 = 𝜙𝐹𝑛𝑣𝐴𝑏 = 140 𝑘𝑁

𝜙𝑟𝑛 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 = 0.75 × 2.4𝑑𝑡𝐹𝑢 = 138 𝑘𝑁

𝝓𝒓𝒏 = 𝒎𝒊𝒏(𝝓𝒓𝒏 𝒔𝒉𝒆𝒂𝒓,𝝓𝒓𝒏 𝒃𝒆𝒂𝒓𝒊𝒏𝒈) = 𝟏𝟑𝟖 𝒌𝑵 > 𝟗𝟒 𝒌𝑵 OK

6. Shear yielding of the angle

The nominal strength for shear yielding limit state is:

𝑅𝑛 = 0.6𝐹𝑦𝐴𝑔 (Re. AISC 360-05, J4-3)

𝜙 = 1.00

Then,

𝐴𝑔 = 𝐻𝑡 = 320 × 8 = 2560 𝑚𝑚2, we have:

𝝓𝑹𝒏 = 𝟑𝟖𝟒 𝒌𝑵 > 372 𝑘𝑁 OK

7. Shear rupture of the angle

The nominal strength for shear rupture limit state is:

x

y


5-20

𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 (Re. AISC360-05, J4-4)

𝜙 = 0.75

Where 𝐴𝑛𝑣 is calculated considering

𝑑𝐶𝐴𝐿𝐶 = 27 𝑚𝑚 + 2 𝑚𝑚 = 29 𝑚𝑚

Then,

𝐴𝑛𝑣 = 𝐻 −𝑁𝐵𝑑𝐶𝐴𝐿𝐶 𝑡 = 1400 𝑚𝑚2

𝝓𝑹𝒏 = 𝟐𝟓𝟐 𝒌𝑵 < 372 𝑘𝑁

Change the thickness of the angle to 12 mm:


𝝓𝑹𝒏 = 𝟑𝟕𝟖 𝒌𝑵 > 372 𝑘𝑁 OK

8. Block shear rupture of the angle


𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 ≤ 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 (Re. Section J4-5 AISC 360-05)

𝜙 = 0.75


specification (AISC 360-05, C-J4.2). The values of 𝐴𝑛𝑣 , 𝐴𝑛𝑡 and 𝐴𝑔𝑣 are

obtained from the following figure:

Figure 5.2-4: Block shear failure path.


5-21

Then,

𝐴𝑛𝑣 = 𝐻 − 32𝑚𝑚− 4.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 1890 𝑚𝑚2

𝐴𝑔𝑣 = 𝐻 − 32𝑚𝑚 𝑡 = 3456 𝑚𝑚2

𝐴𝑛𝑡 = 32 𝑚𝑚− 0.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 210 𝑚𝑚2

Then:

𝝓𝑹𝒏 = 𝟒𝟎𝟑 𝒌𝑵 < 452 𝑘𝑁

𝝓𝑹𝒏 = 𝟒𝟎𝟑 𝒌𝑵 > 372 𝑘𝑁 OK



𝑅𝑛 = 2.4𝑑𝑡𝑤𝐹𝑢

𝜙 = 0.75

Considering that 𝒕𝒘 = 𝟖 𝒎𝒎, we have that for each bolt:

𝝓𝑹𝒏 = 𝟏𝟑𝟖 𝒌𝑵


𝝓𝑹𝒏 = 𝟓 × 𝟏𝟑𝟖 𝒌𝑵 = 𝟔𝟗𝟎 𝒌𝑵 > 372 𝑘𝑁 OK

Tip

In this case it has to be verified only the bearing strength of the beam web

because there is no cope in the end of the beam; however if the beam would

be coped in the ends then the tear out and the block shear limit states shall

also be verified.

10. Flexure of the support leg of the angle

The leg of the angle that is attached to the column is subjected to bending

with respect to the axis of the beam; therefore, the leg of the angle is subject

to a flexural solicitation given by:

𝑀𝑢 = 𝑒1 × 𝑉𝑢 = 48 × 372 = 17856 𝑘𝑁 −𝑚𝑚

Flexural yielding

For the flexural yielding, the nominal strength is given by:


5-22

𝑀𝑛 = 𝜙𝐹𝑦𝑍𝑥 (Re. Part 15 AISC Manual of Steel Construction)

𝜙 = 0.9

Where 𝑍𝑥 is calculated with the next expression:

𝑍𝑥 =𝐻2𝑡

4= 307200 𝑚𝑚3

𝝓𝑴𝒏 = 𝟔𝟐𝟏𝟐𝟎 𝒌𝑵−𝒎𝒎 OK

Flexural rupture

For the flexural yielding, we have that the nominal strength is given by:

𝑀𝑛 = 𝜙𝐹𝑢𝑍𝑥 𝑛𝑒𝑡 (Re. Part 15 AISC Manual of Steel Construction)

𝜙 = 0.75

Then,

𝑍𝑥 𝑛𝑒𝑡 =𝐻2𝑡

4− 𝑡 𝑦𝑖𝑑𝑕

𝑁𝐵

𝑖=1

= 173568 𝑚𝑚3

Where 𝑦𝑖 is the position of the center of the bolt’s holes and 𝑑𝑕 is the hole

diameter. Then,

𝝓𝑴𝒏 = 𝟓𝟐𝟎𝟕𝟎 𝒌𝑵−𝒎𝒎 OK

Connection Designed:

Figure 5.2-5: Single angle connection.

L80X80X12X320

H450X250X111.8

H300X300X87.3

10 M24 A490

A A

A-A

L80X80X12X320

H300X300X87.3


5-23

5.2.d. References


Arze, Reciné y Asociados, Ingenieros Consultores, 2000. “Manual

de Diseño para Estructuras de Acero” (ICHA Manual for the

Design of Steel Structures). Instituto Chileno del Acero (ICHA),

Santiago, Chile.


5-24

5.3. Shear double angle beam-to-column connection


1. NCh2369. Of2003



(Re. NCh2369. Of 2003 8.5.1)



(Re. NCh2369. Of 2003 8.5.6)





(Re. Section 3.2.3, ICHA Manual for the Design of Steel Structures)



verifications for shear double angle bolted connections:

Check applicable limit states for bolts.

(Part 7 of the AISC Manual of Steel Construction)

Check applicable limit states for the connecting elements

(Part 9 of the AISC Manual of Steel Construction)

Furthermore, the AISC Manual of Steel Construction has the following

recommendations for double angle connections:

For double angle connections where the bolts are in one row through the

web of the supported beam, it is not necessary to consider the eccentricity

effects on the bolts; however, in welded connections, eccentricity shall be

always considered.

To provide for flexibility, the maximum angle thickness for use with

workable gages should be limited to 15 mm.

It is recommended that the minimum angle length must be greater than

one half of the beam T- dimension.


5-25

5.3.c. Example

Design a shear double angle all bolted connection between a column flange

and a beam shown in Figure 5.3-1. Use A250 ESP steel, required for


Table 3.

The column and the beam are Chilean H300x300x87.3 and an

H450x250x111.8 built-up sections. Suppose that the connection only transfers

shear forces and that the sections have been designed to resist those forces.


𝑉𝐷 = 110 𝑘𝑁

𝑉𝐿 = 150 𝑘𝑁



H300x300x87.3


𝑑 = 300 𝑚𝑚, 𝑏 = 300 𝑚𝑚

𝑡𝑤 = 10 𝑚𝑚, 𝑡𝑓 = 14 𝑚𝑚

H450x250x111.8


𝑑 = 450 𝑚𝑚, 𝑏 = 250 𝑚𝑚

H450X250X111.8

H300X300X87.3A-A

H300X300X87.3

A A


5-26

𝑡𝑤 = 8 𝑚𝑚, 𝑡𝑓 = 22 𝑚𝑚


𝐹𝑦 = 250 𝑀𝑃𝑎, 𝐹𝑢 = 400 𝑀𝑃𝑎

BOLTS: ASTM A490, threads included in the shear plane, STD holes.

2. Design Forces

𝑉𝑈 = 1.2𝑉𝐷 + 1.6𝑉𝐿 = 372 𝑘𝑁

3. Bolts

For the angle legs attached to the column there will be twice the number of

bolts than in the angle legs attached to the beam. However for the bolts

attached to the beam there are two slip planes so whatever of both cases that

we will verify, the final design will lead to the same number of required bolts.

The verifications to be done will be bolt shear, bolt slip critical failure, bolt

bearing and the solicitation will be the design shear established in the previous

section.

Try M24 bolts (24 mm of diameter, standard holes of 27 mm).




Consider Class A surfaces connection, and standard size holes; then:

(Re. AISC 360-05 J3.8)

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13




5-27

Since there is a double angle connection between the column flange and the

beam, we have two slips planes (and also the number of bolts in the

connection to the column is twice than the connection to the beam, so the

resistance for both connections will be the same), then 𝑁𝑆 = 2.0.

Therefore, the design slip strength for one bolt is:

𝝓𝑹𝒏 = 𝟏𝟕𝟐 𝒌𝑵


is: 𝑁𝐵 > 2.16. Use 𝑁𝐵 = 3 bolts for the legs attached to the beam and 𝑁𝐵 = 6 for

the legs attached at the column.




Where 𝐴𝑏 is the nominal gross area of the bolt:

𝐴𝑏 = 452 𝑚𝑚2


𝝓𝑹𝒏 = 𝟏𝟒𝟎 𝒌𝑵

But it has to be considered that there are two bearing points between the

connecting angle and the bolts, therefore for one bolt:

𝝓𝑹𝒏 = 𝟐𝟒𝟎 𝒌𝑵

Then, the number of bolts required for the connection considering shear

nominal strength is: 𝑁𝐵 > 1.55.

The slip critical limit state controls the design, therefore use 𝑵𝒃 = 𝟑 bolts for

the legs attached to the beam and 𝑵𝑩 = 𝟔 bolts for the legs attached at the

column.


5-28

4. Bolt spacing and angle dimensions

Consider a minimum space between bolts of 64 mm and a minimum distance

to the edge of 32 mm (Refer to Bolted Connections section 2.4 on this

Manual):

𝐻𝑚𝑖𝑛 = 2 × 64 𝑚𝑚 + 2 × 32 𝑚𝑚 = 192 𝑚𝑚

𝐵𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 𝑑𝑐

With 𝑑𝑐 the spacing between the column and the beam, use 𝑑𝑐 = 12 𝑚𝑚, then:

𝐵𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 12𝑚𝑚 = 76 𝑚𝑚

Then considering the AISC Construction manual recommendations, it has to be

used a angle length equal or greater than one half of the beam T - dimension,

so we try with an angle L80 x 80 x 8 x 230.

Figure 5.3-2: Dimensions between bolts.


Interior bolts

Considering that the plate thickness is 𝒕 = 𝟖𝒎𝒎, then:


𝜙 = 0.75



5-29

𝐿𝑐 = 64 𝑚𝑚− 27 𝑚𝑚 = 37 𝑚𝑚


(Table J3.3M AISC 360-05)

Then,

𝝓𝑹𝒏 = 𝟏𝟎𝟔 𝒌𝑵 < 138 𝑘𝑁 OK

Exterior bolts


𝐿𝑐 = 51 𝑚𝑚−27

2= 37.5 𝑚𝑚

Then,

𝝓𝑹𝒏 = 𝟏𝟎𝟖 𝒌𝑵 ≤ 𝟏𝟑𝟖 𝒌𝑵 OK

Hence, the nominal strength of the connection is:

𝝓𝑹𝒏 = 𝟐 × 𝟏𝟎𝟔 𝒌𝑵 + 𝟏𝟎𝟖 𝒌𝑵 = 𝟑𝟐𝟎 𝒌𝑵

Given that there are two angles at the connection, the total capacity of the

connection is:

𝝓𝑹𝒏 = 𝟐 × 𝟑𝟐𝟎 𝒌𝑵 = 𝟔𝟒𝟎 𝒌𝑵 > 𝟑𝟕𝟐 𝒌𝑵 OK



𝑅𝑛 = 0.6𝐹𝑦𝐴𝑔 (Re. AISC360-05, J4-3)

𝜙 = 1.00

𝐴𝑔 = 𝐻𝑡 = 230 × 8 = 1840 𝑚𝑚2, therefore:

𝝓𝑹𝒏 = 𝟐𝟕𝟔 𝒌𝑵

Given that there are two angles at the connection, the total capacity of the

connection is:

𝝓𝑹𝒏 = 𝟐 × 𝟐𝟕𝟔 𝒌𝑵 = 𝟓𝟓𝟐 𝒌𝑵 > 372 𝑘𝑁 OK


5-30



𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 (Re. AISC360-05, J4-4)

𝜙 = 0.75

Where 𝐴𝑛𝑣 is the net area of the angle, then considering:

𝑑𝐶𝐴𝐿𝐶 = 27 𝑚𝑚 + 2 𝑚𝑚


𝝓𝑹𝒏 = 𝟐𝟎𝟓 𝒌𝑵

The total strength is:

𝝓𝑹𝒏 = 𝟐 × 𝟐𝟎𝟓 𝒌𝑵 = 𝟒𝟏𝟎 𝒌𝑵 > 372 𝑘𝑁 OK



𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 ≤ 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 (Re. J4-5 AISC 360-05)

𝜙 = 0.75

Where 𝑈𝑏𝑠 = 1.0 in this case, according to the commentary in AISC 360-05





5-31

𝐴𝑛𝑣 = 𝐻 − 51𝑚𝑚− 2.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 852 𝑚𝑚2

𝐴𝑔𝑣 = 𝐻 − 51𝑚𝑚 𝑡 = 1432 𝑚𝑚2

𝐴𝑛𝑡 = 32 𝑚𝑚− 0.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 210 𝑚𝑚2

Then:

𝝓𝑹𝒏 = 𝟐𝟏𝟔 𝒌𝑵 < 224 𝑘𝑁

𝝓𝑹𝒏 = 𝟐𝟏𝟔 𝒌𝑵

The total capacity of the connection is:

𝝓𝑹𝒏 = 𝟐 × 𝟐𝟏𝟔 𝒌𝑵 = 𝟒𝟑𝟐 𝒌𝑵 > 𝟑𝟕𝟐 𝒌𝑵 OK



𝑅𝑛 = 2.4𝑑𝑡𝑤𝐹𝑢

𝜙 = 0.75

Considering that 𝒕𝒘 = 𝟖 𝒎𝒎, then for each bolt:

𝝓𝑹𝒏 = 𝟏𝟑𝟖 𝒌𝑵

For the whole connection:

𝝓𝑹𝒏 = 𝟑 × 𝟏𝟑𝟖 𝒌𝑵 = 𝟒𝟏𝟒 𝒌𝑵 OK

Tip

In this case it only has to be verified the bearing strength of the beam web

because there is no cope in the end of the beam; however if the beam is coped

in the end it has to be verified the tear out limit state.


5-32

Designed connection

Figure 5.3-4: Single angle connection.

References

AISC Manual of Steel Construction, 13th Edition. Arze, Reciné y Asociados, Ingenieros Consultores, 2000. “Manual de



2 L80X80X8X230

H450X250X111.8

H300X300X87.3

9 M24 A490

A-A

H300X300X87.3

A A


5-33

5.4. Shear single angle beam-to-beam connection


1. NCh2369. Of2003:


electrodes shall comply with the requirements show in the code.

(Re. NCh2369. Of 2003 8.5.1)



connection.

(Re. NCh2369. Of 2003 8.5.6)





(Re. Section 3.2.3, ICHA Manual for the Design of Steel Structures)



verifications for shear single angle bolted connections:

Check applicable limit states for bolts (part 7 of the AISC Manual of Steel

Construction).


AISC Manual of Steel Construction).


verifications for single angle connections:

Always consider the eccentricity for the bolts in the angle leg attached to

the support. For the calculation of the nominal resistance of bolts subject

to eccentrically loads, use the dispositions of part 7 of AISC Manual of

Steel Construction, 13th edition.

Consider eccentricity when there are two rows of bolts or when the

eccentricity, e, is greater than 3 in. (76 mm)


5-34

The length of the angle connection is recommended to be at least equal to

one half of the T dimension of the beam to be supported.

Additionally, the recommended minimum thickness of the angle is t = 10

mm for M20 or M22 bolts and 12 mm for M25 bolts.

5.4.c. Example

Design a shear single angle all bolted connection between a beam web and a

girder shown in the Figure 5.4-1. Use A250ESP steel, required for


Table 3.

The beam and the girder are respectively Chilean H300 x 150 x54.8 and

H250x150x52.5 built-up sections. Suppose that the connection only transfers

shear forces and assume that the sections have been designed to resist those

forces.

The shear acting forces on the girder are:

𝑉𝐷 = 40 𝑘𝑁

𝑉𝐿 = 60 𝑘𝑁


1. Section and Materials properties

H300x150x54.8


𝑑 = 300 𝑚𝑚, 𝑏 = 150 𝑚𝑚

𝑡𝑤 = 6 𝑚𝑚, 𝑡𝑓 = 18 𝑚𝑚

H250X150X52.5

H300X150X54.8

Girder


5-35

H250x150x52.5


𝑑 = 250 𝑚𝑚, 𝑏 = 150 𝑚𝑚

𝑡𝑤 = 6 𝑚𝑚, 𝑡𝑓 = 18 𝑚𝑚


𝐹𝑦 = 250 𝑀𝑃𝑎, 𝐹𝑢 = 400 𝑀𝑃𝑎

BOLTS: ASTM A490, threads include in the shear plane, STD holes.

2. Design Forces

𝑉𝑈 = 1.2𝑉𝐷 + 1.6𝑉𝐿 = 144 𝑘𝑁

3. Bolts

For the angle leg attached to the girder the verifications must include bolt

shear, bolt bearing; the solicitation will be the design shear, but for bolts

attached to the beam we have to consider the eccentricity of the connection

and the design force will be different.





𝜙 = 0.85

Consider Class A surfaces (conservative), and standard size holes:

(Re. AISC 360-05 J3.8)

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13




5-36

Since there is one slip plane, then 𝑁𝑆 = 1.0.

The nominal strength for one bolt in shear.

𝝓𝑹𝒏 = 𝟔𝟎 𝒌𝑵


failure is: 𝑁𝐵 > 2.4. Use 𝑁𝐵 = 3.




Where 𝐴𝐵 is the nominal gross area of the bolt, then:

𝐴𝑏 = 314 𝑚𝑚2


Then, for one bolt:

𝝓𝑹𝒏 = 𝟗𝟕 𝒌𝑵



The slip critical failure controls the design, use 𝑵𝑩 = 𝟑.

Bolts spacing and angle dimensions


distance to the edge of 34 mm, we have:

𝐻𝑚𝑖𝑛 = 2 × 60 𝑚𝑚 + 2 × 34 𝑚𝑚 = 188 𝑚𝑚

𝐵𝑚𝑖𝑛 = 2 × 34 𝑚𝑚 + 𝑑𝑐

With 𝑑𝑐 the spacing between the girder and the beam, we use 𝑑𝑐 = 12 𝑚𝑚:

𝐵𝑚𝑖𝑛 = 2 × 34 𝑚𝑚 + 12𝑚𝑚 = 80 𝑚𝑚


5-37

Then we try an angle L 80 x 80 x 8 x 200.

Now that we have the dimensions of the angles we can determine the

eccentricity of the connection:

Angle leg attached to the beam:

Considering the distance between the shear plane of the bolts attached to the

girder and the centerline of the bolts attached to the beam, the eccentricity is:

𝑒1 = 46 𝑚𝑚

Angle leg attached to the girder:

Considering the distance between the shear plane of the bolts attached to the

beam and the centerline of the bolts attached to the girder, the eccentricity is:

𝑒2 = 34 𝑚𝑚 + 𝑑𝑐 = 46 𝑚𝑚 < 3" = 76 𝑚𝑚

(Re. Part 10 Manual of Steel Construction)

Then there is no need to consider the eccentricity of the bolts attached to the

beam.

Figure 5.4-2: Dimensions of the angle and spacing between bolts.

A-A

Beam web

A A


5-38


Interior bolt

Considering that the angle thickness is 𝑡 = 8 𝑚𝑚, the bearing strength of the

angle leg is:


𝜙 = 0.75


𝐿𝑐 = 60 𝑚𝑚− 22 𝑚𝑚 = 38 𝑚𝑚


(Re. J3.3M, AISC360-05)

Then, we have:

𝝓𝑹𝒏 = 𝟏𝟎𝟗 𝒌𝑵 < 115 𝑘𝑁

Exterior bolt


𝐿𝑐 = 40 𝑚𝑚−22

2𝑚𝑚 = 29 𝑚𝑚

Then,

𝝓𝑹𝒏 = 𝟖𝟑 𝒌𝑵 ≤ 𝟏𝟏𝟓 𝒌𝑵


𝝓𝑹𝒏 = 𝟐 × 𝟏𝟎𝟗 𝒌𝑵+ 𝟖𝟑 𝒌𝑵 = 𝟑𝟎𝟏 𝒌𝑵 > 144 𝑘𝑁 OK

Therefore the angle L 80 x 80 x 8 x 200 comply with the requirements.

5. Nominal strength of bolts with eccentricity (bolts attached to the beam):

According to the AISC Manual of Steel Construction, part 7, there are two

methods for the calculation of the force in bolts with eccentricity: the


5-39

instantaneous center of rotation method and the elastic method. Here it is

used the elastic method, which is more conservative than the instantaneous

center of rotation since the first does not consider the ductility of the bolts and

the redistribution of stresses. The elastic method is simpler.

Then,

𝑟𝑢 = 𝑟𝑝𝑥 + 𝑟𝑚𝑥 2

+ 𝑟𝑝𝑦 + 𝑟𝑚𝑦 2 (Re. AISC Construction manual, chapter 7)

Where 𝑟𝑢 is the bolt maximum force at the connection.

𝑟𝑝𝑦 =𝑉𝑢𝑁𝐵

𝑟𝑚𝑥 =𝑉𝑢𝑒𝑐𝑦𝐼𝑝

𝑟𝑚𝑦 = 𝑟𝑝𝑥 = 0

(There are only shear forces and no axial force is present on the girder)

Where 𝐼𝑝 and 𝑐𝑦 are the polar moment of inertia with respect to the center of

gravity of the bolts and the maximum distance of a bolt of the connection with

respect to the center of gravity of the system. Then, with the disposition

shown in Figure 5.4-3:

𝐼𝑃 = (𝑥𝑖2 + 𝑦𝑖

2)

𝑁𝐵

𝑖=1

= 7200 𝑚𝑚2

𝑐𝑦 = 60 𝑚𝑚

𝑁𝐵 = 3

𝑒 = 46 𝑚𝑚

Figure 5.4-3: Distribution of bolts for the calculation of 𝐼𝑝

x

y


5-40

Then:

𝑟𝑝𝑦 = 48 𝑘𝑁

𝑟𝑚𝑥 = 55 𝑘𝑁

𝑟𝑢 = 73 𝑘𝑁

The strength of the bolts is the minimum between the bearing of the holes and

the shear strength for bolts, then:

𝜙𝑟𝑛 𝑠𝑕𝑒𝑎𝑟 = 𝜙𝐹𝑛𝑣𝐴𝑏 = 97 𝑘𝑁

𝜙𝑟𝑛 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 = 0.75 × 2.4𝑑𝑡𝐹𝑢 = 115 𝑘𝑁

𝝓𝒓𝒏 = 𝐦𝐢𝐧(𝝓𝒓𝒏 𝒔𝒉𝒆𝒂𝒓,𝝓𝒓𝒏 𝒃𝒆𝒂𝒓𝒊𝒏𝒈) = 𝟗𝟕 𝒌𝑵 > 73 𝑘𝑁 OK


The nominal strength for the shear yielding limit state is:

𝑅𝑛 = 0.6𝐹𝑦𝐴𝑔 (Re. AISC360-05, J4-3)

𝜙 = 1.00

Then,

𝐴𝑔 = 𝐻𝑡 = 200 × 8 = 1600 𝑚𝑚2

𝝓𝑹𝒏 = 𝟐𝟒𝟎 𝒌𝑵 > 144 𝑘𝑁 OK



𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 (Re. AISC360-05, J4-4)

𝜙 = 0.75

Where 𝐴𝑛𝑣 is the net area of the angle. Considering:

𝑑𝐶𝐴𝐿𝐶 = 22 𝑚𝑚 + 2 𝑚𝑚

Then,


𝝓𝑹𝒏 = 𝟏𝟖𝟒 𝒌𝑵 > 𝟏𝟒𝟒 𝒌𝑵 OK


5-41




𝜙 = 0.75





𝐴𝑛𝑣 = 𝐻 − 40 𝑚𝑚− 2.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 800 𝑚𝑚2

𝐴𝑔𝑣 = 𝐻 − 40 𝑚𝑚 𝑡 = 1280 𝑚𝑚2

𝐴𝑛𝑡 = 34 𝑚𝑚− 0.5𝑑𝐶𝐴𝐿𝐶 𝑡 = 176 𝑚𝑚2

Then:

𝝓𝑹𝒏 = 𝟏𝟗𝟔 𝒌𝑵 ≥ 196 𝑘𝑁

𝝓𝑹𝒏 = 𝟏𝟗𝟔 𝒌𝑵 > 𝟏𝟒𝟒 𝒌𝑵 OK

9. Bolt bearing and tear out of the girder web

In this example it is necessary to cope the top flange of the girder. First define

the dimensions of the cope:


5-42

Figure 5.4-5: Dimensions of coped beams From AISC Manual of Steel Construction, 13thEd, Figure 9-2.

The dimensions of the cope are given by the section properties of the beam,

then:

𝑑𝑐 = 𝑡𝑓 𝑏𝑒𝑎𝑚 + 2 𝑚𝑚 = 20 𝑚𝑚

𝑐 =𝑏𝑓 𝑏𝑒𝑎𝑚

2−𝑡𝑤 𝑏𝑒𝑎𝑚

2+ 2 𝑚𝑚 = 74 𝑚𝑚

The 2 mm added is an arbitrary value for tolerance issues. According to Figure 5.4-5:

𝑒 = 𝑐 + 12 𝑚𝑚 = 86 𝑚𝑚

With the dimensions of the cope, proceed with the calculation of the tear out

and bearing nominal strengths.

The nominal strength of the tear out and bolt bearing limit states is:

𝑅𝑛 = 1.2𝐿𝑐𝑡𝑤𝐹𝑢 ≤ 2.4𝑑𝑡𝑤𝐹𝑢 = 115 𝑘𝑁 (Re. AISC 360-05, J3-6a)

𝜙 = 0.75

For interior bolts we have:

𝐿𝑐 = 60 𝑚𝑚− 22 𝑚𝑚 = 38 𝑚𝑚

𝝓𝑹𝒏 = 𝟖𝟐 𝒌𝑵 < 86 𝑘𝑁

For exterior bolts

𝐿𝑐 =𝑑𝑔𝑖𝑟𝑑𝑒𝑟

2 – 𝑑𝑐 − 60 𝑚𝑚−

22

2 𝑚𝑚 = 34 𝑚𝑚


5-43

𝝓𝑹𝒏 = 𝟕𝟑 𝒌𝑵 < 86 𝑘𝑁

Then, for the whole connection:

𝝓𝑹𝒏 = 𝟐 × 𝟖𝟐 𝒌𝑵+ 𝟕𝟑 𝒌𝑵 = 𝟐𝟑𝟕 𝒌𝑵 > 144 𝑘𝑁 OK

10. Flexure of leg of the angle attached to the beam

We have that for the angle leg attached to the beam, the flexural solicitation

is:

𝑀𝑢 = 𝑒1 × 𝑉𝑢 = 46 × 144 = 6624 𝑘𝑁 −𝑚𝑚

Flexural yielding

For the flexural yielding, the nominal strength is given by:

(Re. Part 15 AISC Manual of Steel Construction)

𝑀𝑛 = 𝜙𝐹𝑦𝑍𝑥

𝜙 = 0.9

Where 𝑍𝑥 is calculated with the next expression:

𝑍𝑥 =𝐻2𝑡

4= 80000 𝑚𝑚3

𝝓𝑴𝒏 = 𝟏𝟖𝟎𝟎𝟎 𝒌𝑵−𝒎𝒎 OK

Flexural rupture

For the flexural rupture, the nominal strength is given by the expression

obtained from the chapter 15 of the AISC construction manual:

𝑀𝑛 = 𝜙𝐹𝑢𝑍𝑥 𝑛𝑒𝑡

𝜙 = 0.75

Where 𝑍𝑥 𝑛𝑒𝑡 is calculated with the next expression:

𝑍𝑥 𝑛𝑒𝑡 =𝐻2𝑡

4− 𝑡 𝑦𝑖𝑑𝑕

𝑁𝐵

𝑖=1

= 58880 𝑚𝑚3

𝝓𝑴𝒏 = 𝟏𝟕𝟔𝟔𝟒 𝒌𝑵−𝒎𝒎 OK


5-44

Where 𝑦𝑖 is the distance to the center of the connection to the center of the

bolt hole, and 𝑑𝑕 is the dimension of the bolt hole.

11. Flexural strength of coped girder

According to Figure 5.4-5, the flexural required strength for the coped girder is:

𝑀𝑢 = e × 𝑉𝑢 = 12384 𝑘𝑁 −𝑚𝑚

According to part 9 of the AISC Manual of Steel Construction, the nominal

flexural resistance for coped beams is given by:

The rupture strength

𝑀𝑛 = 𝐹𝑢𝑆𝑛𝑒𝑡

𝜙 = 0.75

The buckling strength

𝑀𝑐𝑟 = 𝐹𝑐𝑟𝑆𝑛𝑒𝑡

𝜙 = 0.9

Where for the beam coped at the top end only:

𝐹𝑐𝑟 =𝜋2𝐸

12 1 − 𝜈2 𝑡𝑤𝑕𝑜

2

𝑓𝑘, 𝜈 = 0.3

𝑓 =2𝑐

𝑑 if

𝑐

𝑑≤ 1.0

𝑘 = 2.2 𝑕𝑜

𝑐

1.65

if 𝑐

𝑕𝑜≤ 1.0

This expression is valid when 𝑐 ≤ 2𝑑,𝑑𝑐 ≤ 0.2𝑑. In this example:

𝒄 = 𝟕𝟒 𝒎𝒎 < 𝟐𝒅 = 𝟓𝟎𝟎 𝒎𝒎 OK

𝒅𝒄 = 𝟐𝟎 𝒎𝒎 < 𝟎.𝟐𝒅 = 𝟓𝟎 𝒎𝒎 OK

Additionally, 𝑆𝑛𝑒𝑡 :

𝑕𝑜 = 𝑑 − 𝑑𝑐 = 230 𝑚𝑚

𝑥 =

𝑡𝑤 𝑕𝑜

2−𝑡𝑓2

2+

𝑡𝑓2𝑏𝑓

2

𝑡𝑤 𝑕𝑜 − 𝑡𝑓 + 𝑡𝑓𝑏𝑓 = 45.82 𝑚𝑚

𝐼𝑥 =𝑡𝑤 𝑕𝑜 − 𝑡𝑓

3

12+ 𝑕𝑜 − 𝑡𝑓 𝑡𝑤 𝑥 −

𝑕𝑜 + 𝑡𝑓

2

2

+ 𝑡𝑓𝑏𝑓 𝑥 −𝑡𝑓

2

2

= 16199094 𝑚𝑚4


5-45

𝑆𝑛𝑒𝑡 =𝐼𝑥

𝑕𝑜 − 𝑥 = 87952 𝑚𝑚3

Proceed to calculate the value of 𝐹𝑐𝑟:

𝒄

𝒅=

𝟕𝟒 𝒎𝒎

𝟐𝟓𝟎 𝒎𝒎= 𝟎.𝟐𝟗𝟔 OK

𝒄

𝒉𝒐=

𝟕𝟒 𝒎𝒎

𝟐𝟑𝟎 𝒎𝒎= 𝟎.𝟑𝟐 OK

𝑘 = 14.29

𝑓 = 0.592 𝑭𝒄𝒓 = 𝟏𝟎𝟒𝟎 𝑴𝑷𝒂

Flexural rupture:

𝝓𝑴𝒏 = 𝟐𝟔𝟑𝟖𝟓 𝒌𝑵−𝒎𝒎 > 12384 𝑘𝑁 −𝑚𝑚 OK

Flexural buckling:

𝝓𝑴𝒏 = 𝟖𝟐𝟑𝟐𝟑 𝒌𝑵−𝒎𝒎 > 𝟏𝟐𝟑𝟖𝟒 𝒌𝑵−𝒎𝒎 OK

12. Block shear rupture of the girder web

Since the girder is coped at the top end, in this example we have to also verify

the block shear nominal strength of the girder web.



𝜙 = 0.75





5-46

Figure 5.4-6: Block shear failure path of the girder.(ARREGLAR)

Then,

𝐴𝑛𝑣 = 165 𝑚𝑚− 2.5𝑑𝐶𝐴𝐿𝐶 𝑡𝑤 = 630 𝑚𝑚2

𝐴𝑔𝑣 = 165 𝑚𝑚 𝑡𝑤 = 990 𝑚𝑚2

𝐴𝑛𝑡 = 34 𝑚𝑚− 0.5𝑑𝐶𝐴𝐿𝐶 𝑡𝑤 = 132 𝑚𝑚2

𝝓𝑹𝒏 = 𝟏𝟓𝟑 𝒌𝑵 > 150 𝑘𝑁

𝝓𝑹𝒏 = 𝟏𝟓𝟎 𝒌𝑵 > 𝟏𝟒𝟒 𝒌𝑵 OK

Tip

In this example the girder was coped at only the top end, but if the beam was

coped at both ends it shall be also verified the shear rupture and shear

yielding of the beam web.

Designed Connection

Figure 5.4-7: Single angle connection. Connection to the beam is the same.

H250X150X52.5

H300X150X54.8

6 M20 A490

L80X80X8X200


5-47

References






5-48

5.5. Shear double angle beam-to-beam connection


1. NCh2369. Of2003

Use high strength bolts (ASTM A325 or ASTM A490). Arc welding shall

comply with the requirements shown in the code.

(Re. NCh2369. Of 2003 8.5.1)



(Re. NCh2369. Of 2003 8.5.6)





(Re. Section 3.2.3 ICHA Manual for the Design of Steel Structures)



verifications for shear single angle connections:

Check applicable limit states for bolts.

(Part 7 of the AISC construction manual)

Check applicable limit states for the connecting elements.

(Part 9 of the AISC construction manual)


recommendations for double angle connections:

For double angle connections where the bolts are in one row it is not

necessary to consider the eccentricity effects on the bolts; however, in

welded connections, eccentricity shall be always considered.

To provide for flexibility, the maximum angle thickness for use with

workable gages should be limited to 15 mm.

It is recommended that the minimum angle length must be greater than

one half of the beam T-dimension.


5-49

5.5.c. Example

Design a shear double angle all bolted connection between a beam web and a

girder shown in the Figure 5.5-1. Use A250 ESP steel, required for


Table 3.

The beam and the girder are a Chilean H300 x 150 x 54.8 and a H 250 x 150 x

52.5 built-up sections. Suppose that the connection only transfers shear forces

and assume that the sections have been designed to resist those forces.





1. Section and materials properties

H 300 x 150 x 54.8


𝑑 = 300 𝑚𝑚, 𝑏 = 150 𝑚𝑚

𝑡𝑤 = 6 𝑚𝑚, 𝑡𝑓 = 18 𝑚𝑚

H250X150X52.5

H300X150X54.8


5-50

H 250 x 150 x 52.5


𝑑 = 250 𝑚𝑚, 𝑏 = 150 𝑚𝑚

𝑡𝑤 = 6 𝑚𝑚, 𝑡𝑓 = 18 𝑚𝑚


𝐹𝑦 = 250 𝑀𝑃𝑎, 𝐹𝑢 = 400 𝑀𝑃𝑎


2. Design Forces

𝑉𝑈 = 1.2𝑉𝐷 + 1.6𝑉𝐿 = 144 𝑘𝑁

3. Bolts

For the angle legs attached to the girder web there will be twice the number of

bolts than in the angle legs attached to the beam. However for the bolts

attached to the beam there are slip planes so whatever of both cases that we

will verify, the final design will lead to the same number of required bolts. The

verifications to be done will be bolt shear, bolt slip critical failure, bolt bearing

and the solicitation will be the design shear established in the previous section.

Try M20 bolts (20 mm of diameter, standard holes of 22 mm, refer to Bolted

Connections section 2.4 on this Manual)




Considering Class A connection surfaces, and standard size holes:

(Re. AISC 360-05 J3.8):

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13

Also the tensile nominal strength for M20 ASTM 490 bolts is:


5-51


Since there are two slips planes, 𝑁𝑆 = 2.0.

Therefore, the designs slip strength for one bolt is:

𝝓𝑹𝒏 = 𝟏𝟐𝟎 𝒌𝑵

The number of bolts required for the connection considering slip critical

resistance is: 𝑁𝑏 > 1.2. Therefore use 𝑁𝐵 = 2 bolts for the legs attached to the

girder and 𝑁𝐵 = 4 bolts for the legs attached at the beam.





𝐴𝑏 = 314 𝑚𝑚2


𝝓𝑹𝒏 = 𝟗𝟕 𝒌𝑵

Consider two shear planes. Therefore, for one bolt:

𝝓𝑹𝒏 = 𝟏𝟗𝟒 𝒌𝑵



The slip critical resistance controls the design; use 𝑵𝒃 = 𝟐 bolts for the legs

attached to the girder and 𝑵𝒃 = 𝟒 bolts for the legs attached to the beam.

4. Bolt spacing and angle dimensions


distance to the edge of 34 mm:

𝐻𝑚𝑖𝑛 = 1 × 60 𝑚𝑚 + 2 × 34 𝑚𝑚 = 128 𝑚𝑚

𝐵𝑚𝑖𝑛 = 2 × 34 𝑚𝑚 + 𝑑𝑐


5-52

With 𝑑𝑐 the spacing between the column and the beam; use 𝑑𝑐 = 12 𝑚𝑚:

𝐵𝑚𝑖𝑛 = 2 × 34 𝑚𝑚 + 12𝑚𝑚 = 80 𝑚𝑚

Try with an L 80 x 80 x 6 x 130 angle.

Figure 5.5-2: Dimensions between bolts.


Interior bolts

Considering that the plate thickness is 𝒕 = 𝟔 𝒎𝒎, we have that the bearing

strength of the angle is:


𝜙 = 0.75


𝐿𝑐 = 60 𝑚𝑚− 22 = 38 𝑚𝑚

Then:

𝝓𝑹𝒏 = 𝟖𝟏 𝒌𝑵 < 85 𝑘𝑁

External bolts


𝐿𝑐 = 35 𝑚𝑚−22

2= 24 𝑚𝑚


5-53

Then:

𝝓𝑹𝒏 = 𝟓𝟏 𝒌𝑵 ≤ 𝟖𝟓 𝒌𝑵


𝝓𝑹𝒏 = 𝟖𝟏 𝒌𝑵+ 𝟓𝟏 𝒌𝑵 = 𝟏𝟑𝟐 𝒌𝑵

Given that the shear force is resisted by the two angles of the connection, the

total capacity of the connection is:

𝝓𝑹𝒏 = 𝟐 × 𝟏𝟑𝟐 𝒌𝑵 = 𝟐𝟔𝟒 𝒌𝑵 > 𝟏𝟒𝟒 𝒌𝑵 OK



𝑅𝑛 = 0.6𝐹𝑦𝐴𝑔 (Re. AISC360-05, J4-3)

𝜙 = 1.00

𝐴𝑔 = 𝐻𝑡 = 130 × 6 = 780 𝑚𝑚2

𝝓𝑹𝒏 = 𝟏𝟏𝟕 𝒌𝑵

Given that the shear force is resisted by the two angles of the connection, the

total capacity of the connection is:

𝝓𝑹𝒏 = 𝟐 × 𝟏𝟏𝟕 𝒌𝑵 = 𝟐𝟑𝟒 𝒌𝑵 > 144 𝑘𝑁 OK



𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 (Re. AISC360-05, J4-4)

𝜙 = 0.75

Where 𝐴𝑛𝑣 is the net area of the angle. Considering:

𝑑𝐶𝐴𝐿𝐶 = 22 𝑚𝑚 + 2 𝑚𝑚 = 24 𝑚𝑚

Then,

𝐴𝑛𝑣 = 𝐻 − 𝑁𝐵𝑑𝐶𝐴𝐿𝐶 𝑡 = 492 𝑚𝑚2

𝝓𝑹𝒏 = 𝟖𝟖 𝒌𝑵


5-54

The total capacity is:

𝝓𝑹𝒏 = 𝟐 × 𝟖𝟖 𝒌𝑵 = 𝟏𝟕𝟔 𝒌𝑵 > 𝟏𝟒𝟒 𝒌𝑵 OK




𝜙 = 0.75



specification (AISC 360-05, C-J4.2). The values of Anv, Ant and Agv are obtained


𝐴𝑛𝑣 = 𝐻 − 35 𝑚𝑚− 1.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 354 𝑚𝑚2

𝐴𝑔𝑣 = 𝐻 − 35 𝑚𝑚 𝑡 = 570 𝑚𝑚2

𝐴𝑛𝑡 = 34 𝑚𝑚− 0.5𝑑𝐶𝐴𝐿𝐶 𝑡 = 132 𝑚𝑚2

𝝓𝑹𝒏 = 𝟏𝟎𝟐 𝒌𝑵 < 104 𝑘𝑁

𝝓𝑹𝒏 = 𝟏𝟎𝟐 𝒌𝑵

The total capacity is:

𝝓𝑹𝒏 = 𝟐 × 𝟏𝟎𝟐 𝒌𝑵 = 𝟐𝟎𝟒 𝒌𝑵 > 𝟏𝟒𝟒 𝒌𝑵 OK

9. Bolt bearing an tear out of the girder web

In this it is necessary to cope the top flange of the girder. First define the

dimensions of the cope:


5-55

Figure 5.5-4: Dimensions of coped beams

From AISC Manual of Steel Construction, 13thEd, Figure 9-2.

The dimensions of the cope are given by the section properties of the beam,

then:

𝑑𝑐 = 𝑡𝑓 𝑏𝑒𝑎𝑚 + 2 𝑚𝑚 = 20 𝑚𝑚

𝑐 =𝑏𝑓 𝑏𝑒𝑎𝑚

2−𝑡𝑤 𝑏𝑒𝑎𝑚

2+ 2 𝑚𝑚 = 74 𝑚𝑚

The 2 mm added is an arbitrary value for tolerance issues. According to the

Figure 5.5-4:

𝑒 = 𝑐 + 12 𝑚𝑚 = 86 𝑚𝑚

With the dimensions of the cope, proceed with the calculation of the tear out

and bearing nominal strengths.

The nominal strength of the tear out and bolt bearing limit states is:

𝑅𝑛 = 1.2𝐿𝑐𝑡𝑤𝐹𝑢 ≤ 2.4𝑑𝑡𝑤𝐹𝑢 = 115 𝑘𝑁 (Re. AISC 360-05, J3-6a)

𝜙 = 0.75

For interior bolts:

𝐿𝑐 = 60 𝑚𝑚− 22 𝑚𝑚 = 38 𝑚𝑚

𝝓𝑹𝒏 = 𝟖𝟐 𝒌𝑵 < 86 𝑘𝑁

For exterior bolts:

𝐿𝑐 =𝑑𝑔𝑖𝑟𝑑𝑒𝑟

2 – 𝑑𝑐 − 30 𝑚𝑚−

22

2 𝑚𝑚 = 64 𝑚𝑚

𝝓𝑹𝒏 = 𝟏𝟑𝟖 𝒌𝑵 > 86 𝑘𝑁


5-56


Then we have that for the whole connection:

𝝓𝑹𝒏 = 𝟖𝟐 𝒌𝑵+ 𝟖𝟔 𝒌𝑵 = 𝟏𝟔𝟖 𝒌𝑵 > 𝟏𝟒𝟒 𝒌𝑵 OK

10. Flexural strength for coped girder check

According to Figure 5.5-4, the flexural moment that it has to be used for

verifying the resistance of the coped beam is:

𝑀𝑢 = 𝑒𝑉𝑢 = 12384 𝑘𝑁 −𝑚𝑚

The nominal flexural resistance for coped beams is:

(Re. Part 9 of AISC Manual of Steel Construction)

Rupture strength

𝑀𝑛 = 𝐹𝑢𝑆𝑛𝑒𝑡

𝜙 = 0.75

Buckling strength

𝑀𝑐𝑟 = 𝐹𝑐𝑟𝑆𝑛𝑒𝑡

𝜙 = 0.9

Where for the beam coped at the top end only:

𝐹𝑐𝑟 =𝜋2𝐸

12 1 − 𝜈2 𝑡𝑤𝑕𝑜

2

𝑓𝑘, 𝜈 = 0.3

𝑓 =2𝑐

𝑑 if

𝑐

𝑑≤ 1.0

𝑘 = 2.2 𝑕𝑜

𝑐

1.65

if 𝑐

𝑕𝑜≤ 1.0

This expression is valid when 𝑐 ≤ 2𝑑,𝑑𝑐 ≤ 0.2𝑑. In this example:

𝒄 = 𝟕𝟒 𝒎𝒎 < 2𝒅 = 𝟓𝟎𝟎 𝒎𝒎 OK

𝒅𝒄 = 𝟐𝟎 𝒎𝒎 < 𝟎.𝟐𝒅 = 𝟓𝟎 𝒎𝒎 OK

Now proceed to calculate the value of 𝑆𝑛𝑒𝑡 :

𝑕𝑜 = 𝑑 − 𝑑𝑐 = 230 𝑚𝑚


5-57

𝑥 =

𝑡𝑤 𝑕𝑜

2−𝑡𝑓2

2+

𝑡𝑓2𝑏𝑓

2

𝑡𝑤 𝑕𝑜 − 𝑡𝑓 + 𝑡𝑓𝑏𝑓 = 45.82 𝑚𝑚

𝐼𝑥 =𝑡𝑤 𝑕𝑜 − 𝑡𝑓

3

12+ 𝑕𝑜 − 𝑡𝑓 𝑡𝑤 𝑥 −

𝑕𝑜 + 𝑡𝑓

2

2

+ 𝑡𝑓𝑏𝑓 𝑥 −𝑡𝑓

2

2

= 16199094 𝑚𝑚4

𝑆𝑛𝑒𝑡 =𝐼𝑥

𝑕𝑜 − 𝑥 = 87952 𝑚𝑚3

Calculate the value of 𝐹𝑐𝑟:

𝒄

𝒅=

𝟕𝟒 𝒎𝒎

𝟐𝟓𝟎 𝒎𝒎= 𝟎.𝟐𝟗𝟔 OK

𝒄

𝒉𝒐=

𝟕𝟒 𝒎𝒎

𝟐𝟑𝟎 𝒎𝒎= 𝟎.𝟑𝟐 OK

𝑘 = 14.29

𝑓 = 0.592

𝑭𝒄𝒓 = 𝟏𝟎𝟒𝟎 𝑴𝑷𝒂

Then:

Flexural rupture:

𝝓𝑴𝒏 = 𝟐𝟔𝟑𝟖𝟓 𝒌𝑵−𝒎𝒎 OK

Flexural buckling:

𝝓𝑴𝒏 = 𝟖𝟐𝟑𝟐𝟑 𝒌𝑵−𝒎𝒎 OK

11. Block shear rupture of the girder web

Since the girder is coped at the top end, in this example it is necessary to

verify the block shear nominal strength of the girder web.



𝜙 = 0.75





5-58

Figure 5.5-5: Block shear failure path of the girder.


𝐴𝑔𝑣 = 135 𝑚𝑚 𝑡𝑤 = 810 𝑚𝑚2


Then:

𝝓𝑹𝒏 = 𝟏𝟒𝟔 𝒌𝑵 > 𝟏𝟑𝟏 𝒌𝑵

𝝓𝑹𝒏 = 𝟏𝟑𝟏 𝒌𝑵 < 144 𝑘𝑁

Then, the connection does not comply with the requirements. If the angle is

placed 30 mm below the actual position, as is shown in the next figure:

5.5-6: New Block Shear failure path for the new position of the angle.


𝐴𝑔𝑣 = 165 𝑚𝑚 𝑡𝑤 = 990 𝑚𝑚2


5-59


𝝓𝑹𝒏 = 𝟏𝟕𝟖 𝒌𝑵 > 𝟏𝟓𝟏 𝒌𝑵

𝝓𝑹𝒏 = 𝟏𝟓𝟏 𝒌𝑵 > 144 𝒌𝑵 OK

Tip

In this example the girder was coped at only the top end, but if the beam was

coped at both ends it should be also verified the shear rupture and shear

yielding of the girder web.

Designed Connection

Figure 5.5-7: Double angle connection.

References





H250X150X52.5

H300X150X54.8

6 M20 A490A-A

Beam web

A A


5-60

5.6. Shear Stiffened Seated beam-to-column connection


1. NCh2369. Of 2003:



(Re. NCh2369. Of 2003 8.5.1)



connection.

(Re. NCh2369. Of 2003 8.5.6)




verifications for shear stiffened seated connections:

Check applicable limit states for bolts (part 7 of the AISC Construction

Manual).


AISC Construction Manual)


recommendations for stiffened seated connections:

Stiffened seated connections consist in a seat angle that supports the

beam with a stiffening element, which could be a plate, a pair of angles or

a structural tee. Also a top angle is provided for stability issues (see

Figure 5.6-1). The stiffening element is assumed to carry the entire end

reaction of the supported beam applied at a distance 0.8W.

The top angle is not designed for any calculated strength requirements. It

is recommended that the thickness of the top angle to be 6 mm and the

leg attached to the column flange (or column web) to be greater than 4”.

The top angle can be bolted to the column and the beam with two bolts.

Verify the limit states of web yielding and web crippling of the beam

supported.


5-61

2. Steel Structures Design and behavior, Salmon, Johnson and Malhos

According to section 13.4 of the “Steel Structures Design and Behavior”, is

has to be considered the local buckling of the stiffener and the bearing at

the contact area of the stiffener have to be considered.

It is not necessary to consider that the bolts attached to the beam are

simultaneously subject to tensile and shear stresses, it is only necessary

to consider the shear stress for the design, since only for welded stiffened

seated connections is necessary the consideration of tensile and shear

stresses.

Figure 5.6-1: Typical Unstiffened connection From AISC Manual of Steel Construction, 13thEd, figure 10-10.

5.6.c. Example

Design a shear stiffened seated all bolted connection between a column flange

and a beam shown in the Figure 5.6-2. Use A250ESP steel, required for


Table 3.


H450x250x111.8 built-up section. Suppose that the connection only transfers

shear forces and assume that the sections have been designed to support

those forces.


𝑉𝐷 = 110 𝑘𝑁


5-62

𝑉𝐿 = 150 𝑘𝑁


1. Section and materials properties

H300x300x87.3


𝑑 = 300 𝑚𝑚, 𝑏 = 300 𝑚𝑚

𝑡𝑤 = 10 𝑚𝑚, 𝑡𝑓 = 14 𝑚𝑚

H450x250x111.8


𝑑 = 450 𝑚𝑚, 𝑏 = 250 𝑚𝑚

𝑡𝑤 = 8 𝑚𝑚, 𝑡𝑓 = 22 𝑚𝑚


𝐹𝑦 = 250 𝑀𝑃𝑎, 𝐹𝑢 = 400 𝑀𝑃𝑎


H450X250X108.7H300X300X87.5


5-63

WELD: 70 ksi electrode, 𝐹𝐸𝑋𝑋 = 480 MPa

2. Design Force

𝑉𝑈 = 1.2𝑉𝐷 + 1.6𝑉𝐿 = 372 𝑘𝑁

3. Bolts

The verifications to be done will be bolt shear and bolt slip critical failure. The

solicitation will be the design shear.





Considering class A connection surfaces, and standard size holes:

(Re. AISC 360-05 J3.8):

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13

Also the tensile nominal strength for M22 ASTM A490 bolts is:


The number of slip planes is 𝑁𝑆 = 1.0.

For one bolt, the nominal strength for the slip critical limit state is:

𝝓𝑹𝒏 = 𝟕𝟒 𝒌𝑵


failure is: 𝑁𝑏 > 5.02. Use 𝑁𝐵 = 6.




5-64


Where 𝐴𝑏 is the nominal gross area of the bolt, and threads are supposed to be

not excluded from the shear planes:

𝐴𝑏 = 380 𝑚𝑚2


Then, we have that:

𝝓𝑹𝒏 = 𝟏𝟏𝟕𝒌𝑵

𝒃𝒐𝒍𝒕



The slip critical failure controls the design, 𝑵𝒃 = 𝟔.

4. Bolt spacing and dimensions of angles


distance to the edge of 32 mm (refer to Bolted Connections section on this

manual):

For the leg attached to the column:

𝐻𝑚𝑖𝑛 = 2 × 66 𝑚𝑚 + 2 × 32 𝑚𝑚 = 196 𝑚𝑚

𝐵𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 = 64 𝑚𝑚

Figure 5.6-3: General dimensions of the stiffener angles


5-65

But it is convenient that the angles support all the base of the beam, so try

with an L 125 x 80 x 10 x 200 angle.

The stiffener width is W = 80 mm.

5. Seat plate design

For the seat plate we follow the recommendations of Section 13.9 from “Steel

Structures” of Vinnakota. The thickness of the plate generally is between the

9.5 and 12.7 mm. Then use a thickness 𝒕𝒑 = 𝟏𝟎 𝒎𝒎. For the length of the plate

use the width of the beam’s flange (250 mm); finally, for the width of the

plate use the same width of the angles, 80 mm, so consider a plate PL 250 x

80 x 10. Latter it will be necessary to verify if the width of the plate satisfies

the requirements for supporting the beam, since if the support is not large

enough failure of the connection due web crippling or local yielding of the

beam web can occur. For the connection between the plate and the angles

use the maximum fillet weld size permitted, which is the smaller thickness of

the elements connected minus 2 mm (Re. AISC 360-05, J2.2b). In this case

the thickness of the angles and the plate is 8 and 10 mm respectively, so use

𝒘 = 𝟖 𝒎𝒎 for the fillet weld. Welds are not permitted for the connection of the

plate and the flange of the beam (part 10 AISC Manual of Steel Construction).

Use two M22 bolts. See the following figure:

Figure 5.6-4: Seat plate

6. Web Local Yielding of the beam

When the force that is applied is concentrated at a distance that is no greater

than the depth of the beam, which is our case, we have that the resistance to

the web local yielding is given by:

𝑅𝑛 = 2.5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑤 (Re. AISC 360-05, J10-3)

PL 250X80X10

8 8


5-66

𝜙 = 1.00

Where 𝑘 is the distance from the edge of the beam flange to the toe of the

fillet, and 𝑁 is the length of bearing that support the beam. The value of 𝑁

must be greater than 𝑘 for end beam reactions.

𝑘 = 𝑡𝑓 + 5 𝑚𝑚

𝑘 = 27 𝑚𝑚

𝑁 = 80 𝑚𝑚− 𝑑𝑐 = 68 𝑚𝑚

𝑡𝑤 = 8 𝑚𝑚

Then:

𝝓𝑹𝒏 = 𝟐𝟕𝟏 𝒌𝑵 < 372 𝑘𝑁

Then, the connection does not comply with the requirements, so change the

plate to PL 250 x 135 x10 and change the angles to L 125 x 135 x 10 x

200. Then,

𝑁 = 135 𝑚𝑚− 𝑑𝑐 = 123 𝑚𝑚

𝝓𝑹𝒏 = 𝟑𝟖𝟏 𝒌𝑵 > 372 𝑘𝑁 OK

7. Local Buckling of the stiffener

Following the recommendations given in “Steel Structures Design and

Behavior” book by Salmon, the local buckling failure can be avoided following

the provisions of the AISC 360-05 B4. If the stiffener is compact, then local

buckling is avoided, then using the slenderness ratios of table B4.1, we have

the following:

𝜆𝑝 = 0.56 𝐸

𝐹𝑦= 15.83 (Re. AISC 360-05, table B4.1 case 3)

𝝀 =𝑾

𝒕=

𝟏𝟑𝟓

𝟏𝟎= 𝟏𝟑.𝟓 < 𝝀𝒑 OK

8. Bearing on the contact area of the stiffener

The bearing strength is provided by the following expression:

(Re. Section J7 AISC 360-05)

𝑅𝑛 = 1.8𝐹𝑦𝐴𝑝𝑏

𝜙 = 0.75


5-67

Where 𝐴𝑝𝑏 is the bearing projected area. Salmon recommendation is that the

bearing area must be taken equal to:

𝐴𝑝𝑏 = 2𝑡 𝑊 − 12.7 𝑚𝑚 = 2446 𝑚𝑚2

The bearing strength is:

𝝓𝑹𝒏 = 𝟖𝟐𝟓 𝒌𝑵 OK

Tip:

If a welded plate was used as stiffener it should also considered the effect of

the eccentricity of the load into the calculation of the bearing strength. The

eccentricity generates additional stresses on the stiffener.

9. Web Crippling of the beam:

When the concentrated force is applied at a distance that is no greater than

half the depth of the beam, and 𝑁

𝑑> 0.2, the available strength of the web

Crippling is given by:

𝑅𝑛 = 0.40𝑡𝑤2 1 +

4𝑁

𝑑− 0.2

𝑡𝑤𝑡𝑓

1.5


𝑡𝑤

𝜙 = 0.75 (Re. AISC 360-05, J10-5b)

𝑑 = 450 𝑚𝑚


𝑡𝑓 = 22

𝑁 = 135 𝑚𝑚− 𝑑𝑐 = 123 𝑚𝑚

Therefore:

𝝓𝑹𝒏 = 𝟐𝟔𝟗 𝒌𝑵 < 372 𝑘𝑁

Then, the nominal strength does not comply with the requirements, so use a

pair of stiffeners

Stiffeners for the beam web

Stiffeners shall be designed for the following force:

𝑅𝑢 = 𝑉𝑢 −𝜙𝑅𝑛 = 372 𝑘𝑁 − 269 𝑘𝑁 = 110 𝑘𝑁

Try a pair of stiffeners PL 406 x 110 x 10, then:


5-68

𝐼𝑠𝑡𝑖𝑓𝑓 =110 × 103

12= 9166 𝑚𝑚3

𝐴𝑠𝑡𝑖𝑓𝑓 = 110 × 10 = 1100 𝑚𝑚2

𝑟 = 𝐼𝑠𝑡𝑖𝑓𝑓

𝐴𝑠𝑡𝑖𝑓𝑓= 2.88 𝑚𝑚

Then, considering 𝑘 = 1.0 and 𝐿 = 406 𝑚𝑚:

𝑘𝐿

𝑟= 140 > 25 (Section J4.4 AISC 360-05)

Then, the design shall be done according the dispositions of the chapter E of

the AISC 360-05:

𝑘𝐿

𝑟= 140 > 4.71

𝐸

𝐹𝑦= 133, then:

𝐹𝑐𝑟 = 0.877𝐹𝑒

𝐹𝑒 =𝜋2𝐸

𝑘𝐿

𝑟

2 = 101 𝑀𝑃𝑎


The nominal strength of each stiffener is:

𝑅𝑛 = 𝐹𝑐𝑟𝐴𝑠𝑡𝑖𝑓𝑓

𝜙 = 0.9

Then,


Then, the nominal strength of the two stiffener of the beam is:

𝝓𝑹𝒏 = 𝟐 × 𝟖𝟖 𝒌𝑵 = 𝟏𝟕𝟔 𝒌𝑵 > 110 𝑘𝑁 OK

The weld of the stiffeners shall be designed to develop 𝑅𝑢.


5-69


Interior bolt

Consider that the plate thickness is 𝒕 = 𝟏𝟎 𝒎𝒎, the bearing strength of the

angle leg is:


𝜙 = 0.75


𝐿𝑐 = 66 𝑚𝑚− 24 = 42 𝑚𝑚

Then,

𝝓𝑹𝒏 = 𝟏𝟓𝟏 𝒌𝑵 < 158 𝑘𝑁

Exterior bolt


𝐿𝑐 = 34 𝑚𝑚−24

2= 22 𝑚𝑚

Then,

𝝓𝑹𝒏 = 𝟕𝟗 𝒌𝑵 ≤ 𝟏𝟓𝟖 𝒌𝑵


𝝓𝑹𝒏 = 𝟐 × 𝟕𝟗 𝒌𝑵+ 𝟒 × 𝟏𝟓𝟏 𝒌𝑵 = 𝟕𝟔𝟐 𝒌𝑵 > 𝟑𝟕𝟐 𝒌𝑵 OK

11. Bolt bearing of the column flange


𝑅𝑛 = 2.4𝑑𝑡𝑓𝐹𝑢

𝜙 = 0.75

Considering 𝒕𝒇 = 𝟏𝟒 𝒎𝒎, then for each bolt:


5-70

𝝓𝑹𝒏 = 𝟐𝟐𝟏 𝒌𝑵


𝝓𝑹𝒏 = 𝟔 × 𝟐𝟐𝟏 𝒌𝑵 = 𝟏𝟑𝟐𝟔 𝒌𝑵 > 372 𝑘𝑁 OK

Tip:

By inspection it can be seen that tear out limit state does not control the

design.

12. Selection of the top angle

For the top angle selection use the recommendations of chapter 10 of the AISC

Manual of Steel Construction. Use an L 100 X 100 X 6 X 250 angle. This

angle is connected to the beam by two bolts M20. This requires a minimum

space between bolts of 60 mm and a minimum distance to the edge of 34 mm,

requirements that are accomplished with the angle selected.

Designed connection

Figure 5.6-5: Stiffened seated connection

H450X250X108.7H300X300X87.5

6 M22 A490

4 M20 A490 L 100X100X6X250

2 L125x135X20X200

PL 250X135X10

2 STIFFENERS

PL 406X110X10

8


5-71

References


Salmon, Johnson and Malhos, 2009, “Steel Structures. Design and

Behavior”. Fifth Edition, Pearson Prentice Hall, Upper Saddle River NJ.

Vinnakota, 2006, “Steel Structures: Behavior and LRFD”. First Edition,

Mc Graw Hill company.





5-72

5.7. Shear Unstiffened Seated beam-to-column Connection


1. NCh2369. Of2003:



(Re. NCh2369. Of 2003 8.5.1)



connection.

(Re. NCh2369. Of 2003 8.5.6)




verifications for shear unstiffened seated connections:

Check applicable limit states for bolts (part 7 of the AISC Manual of Steel

Construction).


AISC Manual of Steel Construction).

Furthermore, the AISC Manual of Steel construction has the following

recommendations for this type of connection:

Unstiffened seated connections consist of a bottom seat angle that

supports the beam and a top angle for stability issues. The seat angle is

assumed to carry the entire end reaction of the beam (see Figure 5.7-1).

The top angle is not designed for any calculated strength requirements. It

is recommended that the thickness of the top angle be 6 mm and the leg

attached to the column flange (or to the column web) to be greater than

101 mm. The top angle can be bolted to the column and the beam with

two bolts.

The limit states of web yielding and web crippling of the beam supported

must be verified. The leg of the seat angle that is attached to the beam

must be verified for shear yielding and flexural yielding.


5-73

2. “Steel Structures, Design and Behavior”, Salmon

According to section 13.3 of this book, bolts of the seat angle are

subject to shear and tension simultaneously, so their design shall be

made according to the provisions of the AISC 360 J3.7.

Figure 5.7-1: Typical Unstiffened connection

From AISC Manual of Steel Construction, 13thEd, Figure 10-7

5.7.c. Example

Design a shear Unstiffened seated all bolted connection between the column

flange and the beam shown in the Figure 5.7-2. Use A250ESP steel, required

for constructions subject to dynamics loads, according NCh203.Of2006 code,

Table 3.


H450x250x111.8 built-up section. Suppose that the connection only transfers

shear forces and that the sections have been designed to resist those forces.

The shear forces are:

𝑉𝐷 = 100 𝑘𝑁

𝑉𝐿 = 150 𝑘𝑁


5-74



H300x300x87.3


𝑑 = 300 𝑚𝑚, 𝑏 = 300 𝑚𝑚

𝑡𝑤 = 10 𝑚𝑚, 𝑡𝑓 = 14 𝑚𝑚

H450x250x111.8


𝑑 = 450 𝑚𝑚, 𝑏 = 250 𝑚𝑚

𝑡𝑤 = 8 𝑚𝑚, 𝑡𝑓 = 22 𝑚𝑚


𝐹𝑦 = 250 𝑀𝑃𝑎, 𝐹𝑢 = 400 𝑀𝑃𝑎

BOLTS: ASTM A490, threads include in the shear plane, STD holes.

2. Design Forces

𝑉𝑈 = 1.2𝑉𝐷 + 1.6𝑉𝐿 = 360 𝑘𝑁

H450X250X111.8H300X300X87.3


5-75

3. Bolts

The verifications to be done will be bolt shear and slip critical failure. Try M22

bolts (22 mm of diameter, standard holes of 24 mm).

Slip Critical



Considering class A connection surfaces (conservative), and standard size

holes:

(Re. AISC 360-05 J3.8):

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13

Also the tensile nominal strength for M22 ASTM 490 bolts is:


Since there is one slip plane, 𝑁𝑆 = 1.0.

Therefore, the nominal strength of one bolt is:

𝝓𝑹𝒏 = 𝟕𝟒 𝒌𝑵


is: 𝑁𝑏 > 4.86. Use for this type of failure 𝑁𝐵 = 6.





𝐴𝑏 = 380 𝑚𝑚2



5-76

Then, we have that:

𝝓𝑹𝒏 = 𝟏𝟏𝟕 𝒌𝑵



The slip critical type of failure controls the design, use 𝑵𝒃 = 𝟔.

4. Bolt spacing and dimension of angles


distance to the edge of 32 mm (refer to Bolted Connection section on this

manual):

For the leg attached to the column:

𝐻𝑚𝑖𝑛 = 2 × 66 𝑚𝑚 + 2 × 32 𝑚𝑚 = 196 𝑚𝑚

𝐵𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 66 𝑚𝑚 = 130 𝑚𝑚

For the leg attached to the beam we have to consider only two bolts for

stability issues. The minimum dimensions of the leg are:

𝐻𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 𝑑𝑐

𝐵𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 66 𝑚𝑚 = 130 𝑚𝑚

With 𝑑𝑐 the spacing between the column and the beam. Use 𝑑𝑐 = 12 𝑚𝑚:

𝐻𝑚𝑖𝑛 = 2 × 32 𝑚𝑚 + 12 𝑚𝑚 = 76 𝑚𝑚

However, it is convenient that the seat angle cover all the flange of the beam

so try with an angle L200 x 80 x 10 x 250.

Figure 5.7-3: General dimensions of the seat angle.


5-77

5. Tension and shear interaction

Even though the design of the shear connection was done with a slip critical

failure approach, for the interaction of shear and tension in the bolts, produced

by the eccentricity of the shear force, it will be used the bearing type of failure

instead of slip critical.

For the calculation of the eccentricity, suppose that the shear force is

distributed uniformly in the seat angle in which is supported.

𝑀𝑢 = 𝑉𝑢𝑒1

𝑒1 = 12 𝑚𝑚 +80 − 12

2 𝑚𝑚 = 46 𝑚𝑚

𝑀𝑢 = 16560 𝑘𝑁 −𝑚𝑚

Then the inertia of the connection is calculated in order to establish the

maximum bolt tensile stress of the connection and then verify the resistance of

that bolt (see Figure 5.7-4):

Figure 5.7-4: Determination of inertia of the leg angle

𝐵𝑥2

2= 2𝐴𝑏 𝑑𝑝𝑖 − 𝑥

2

𝑖=1

𝐵 = 250 𝑚𝑚

𝐴𝑏 = 380 𝑚𝑚2

𝑑𝑝1= 200 𝑚𝑚− 34 𝑚𝑚 = 166 𝑚𝑚

𝑑𝑝2 = 200 𝑚𝑚− 34 𝑚𝑚− 66 𝑚𝑚 = 100 𝑚𝑚

𝑑3 = 200 𝑚𝑚− 34 𝑚𝑚− 2 × 66 𝑚𝑚 = 34 𝑚𝑚

Where the summation considers that there are two rows of bolts in tension.

Then,

T

dd

x

p2

T

p1

1

2


5-78

𝑥 = 34.6 𝑚𝑚

Then the inertia is:

𝐼 = 𝑑𝑝1 − 𝑥 2

2𝐴𝑏 + 𝑑𝑝2 − 𝑥 2

2𝐴𝑏 +𝑥3𝐵

12+𝑥2

4𝑥𝐵 = 19824582 𝑚𝑚4

𝑦𝑚𝑎𝑥 = 𝑑𝑝1 − 𝑥 = 131.4 𝑚𝑚

Then, the maximum tensile stress is:

𝐹𝑢 =𝑀𝑢𝑦𝑚𝑎𝑥

𝐼= 109 𝑀𝑃𝑎

The maximum tensile force for bolt is:

𝑇𝑢 = 𝐴𝑏𝐹𝑢 = 42 𝑘𝑁

Now, using the provisions of the AISC 360-05, we calculate 𝑘𝑠, factor that

modifies the slip strength of the bolt:


𝐷𝑢𝑇𝑏𝑁𝑏 (Re. AISC 360-05, J3-5a)

Where 𝑁𝑏 is the number of bolts that stands the tensile force, which in this

case corresponds to 1, since we calculate the tensile strength for one bolt.

𝑘𝑠 = 0.831

And the shear solicitation for one bolt corresponds to:

𝑅𝑢 𝑏𝑜𝑙𝑡 =𝑉𝑢6

= 60 𝑘𝑁


𝝓𝑹𝒏 = 𝝓𝒌𝒔𝝁𝑫𝒖𝒉𝒔𝒄𝑻𝒃𝑵𝒔 = 𝟔𝟐 𝒌𝑵 > 60 𝑘𝑁 OK

Also, we can verify the interaction for a bearing type connection:

The nominal tensile stress modified to include the effects of shearing stress is:


5-79

𝐹𝑛𝑡′ = 1.3𝐹𝑛𝑡 −

𝐹𝑛𝑡

𝜙𝐹𝑛𝑣𝑓𝑣 ≤ 𝐹𝑛𝑡 (Re. AISC 360-05, J3.7)

𝜙 = 0.75

Where:

𝑓𝑣 =𝑉𝑢

𝐴𝑏𝑁𝐵

= 163 𝑀𝑃𝑎

𝐹𝑛𝑡 = 780 𝑀𝑃𝑎 (Re. AISC 360-05, Table J3.2)

𝐹𝑛𝑣 = 414 𝑀𝑃𝑎 (Re. AISC 360-05, Table J3.2)

Therefore:

𝑭𝒏𝒕′ = 𝟔𝟎𝟒 𝑴𝑷𝒂 > 109 𝑀𝑃𝑎 OK

6. Web Local Yielding of the beam

When the force that is applied is concentrated at a distance that is no greater

than the depth of the beam, the available strength of web local yielding is

given by:

𝑅𝑛 = 2.5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑤 (Re. AISC 360-05, J10-3)

𝜙 = 1.00

Where 𝑘 is the distance from the edge of the beam flange to the toe of the

fillet weld, and 𝑁 is the length of bearing that supports the beam. The value of

𝑁 must be greater than 𝑘.

𝑘 = 𝑡𝑓 + 5 𝑚𝑚 (Re. ICHA-ARA Manual)

𝑘 = 27 𝑚𝑚

𝑁 = 80 𝑚𝑚− 𝑑𝑐 = 68 𝑚𝑚


Then:

𝝓𝑹𝒏 = 𝟐𝟕𝟏 𝒌𝑵 < 360 𝑘𝑁

Then, the nominal strength does not accomplish with the requirements, so use

a pair of stiffeners that will be designed later.


5-80

7. Web Crippling of the beam:

When the concentrated force that is applied at a distance that is no greater

than half the depth of the beam, and 𝑁

𝑑> 0.2, the available strength is given

by:

𝑅𝑛 = 0.40𝑡𝑤2 1 +

4𝑁

𝑑− 0.2

𝑡𝑤𝑡𝑓

1.5


𝑡𝑤

𝜙 = 0.75 (Re. AISC 360-05, J10-5b)

𝑑 = 450 𝑚𝑚


𝑡𝑓 = 22

𝑁 = 80 𝑚𝑚− 𝑑𝑐 = 68 𝑚𝑚

Therefore:

𝝓𝑹𝒏 = 𝟐𝟒𝟓 𝒌𝑵

Then, the nominal strength does not accomplish with the requirements, then

we require the use of stiffeners

Stiffeners for the beam web:

Stiffeners shall be designed for a compression force which is the difference

between the shear design force and the minimum nominal strength between

the limit states of web local yielding and web crippling.

𝑃𝑢 = max(𝑉𝑢 −𝜙𝑅𝑛 𝑤𝑒𝑏 𝑐𝑟𝑖𝑝𝑝𝑙𝑖𝑛𝑔 ,𝑉𝑢 –𝜙𝑅𝑛 𝑤𝑒𝑏 𝑙𝑜𝑐𝑎𝑙 𝑦𝑖𝑒𝑙𝑑𝑖𝑛𝑔 ) = 360 𝑘𝑁 − 269 𝑘𝑁 = 91 𝑘𝑁

Try a pair of stiffeners PL 406 x 110 x 10, then:

𝐼𝑠𝑡𝑖𝑓𝑓 =110 × 103

12= 9166 𝑚𝑚3

𝐴𝑠𝑡𝑖𝑓𝑓 = 110 × 10 = 1100 𝑚𝑚2

𝑟 = 𝐼𝑠𝑡𝑖𝑓𝑓

𝐴𝑠𝑡𝑖𝑓𝑓= 2.88 𝑚𝑚

Then, considering 𝑘 = 1.0 and 𝐿 = 406 𝑚𝑚:

𝑘𝐿

𝑟= 140 > 25 (Section J4.4 AISC 360-05)


5-81

The design shall be done according to the provisions of the chapter E of the

AISC 360-05:

𝑘𝐿

𝑟= 140 > 4.71

𝐸

𝐹𝑦= 133, then:

𝐹𝑐𝑟 = 0.877𝐹𝑒

𝐹𝑒 =𝜋2𝐸

𝑘𝐿

𝑟

2 = 101 𝑀𝑃𝑎


The nominal strength of each stiffener is:

𝑅𝑛 = 𝐹𝑐𝑟𝐴𝑠𝑡𝑖𝑓𝑓

𝜙 = 0.9

Then,


Then, the nominal strength of the two stiffeners of the beam is:

𝜙𝑅𝑛 = 2 × 88 𝑘𝑁 = 176 𝑘𝑁 > 91 𝑘𝑁 OK

The weld of the stiffeners shall be designed to develop 𝑃𝑢 and 𝑇𝑢.

8. Bearing of the angle leg

Considering that the plate thickness is 𝒕 = 𝟏𝟎 𝒎𝒎, the bearing strength of the

angle is:

𝑅𝑛 = 2.4𝑑𝑡𝐹𝑢 (Re. AISC 360-05, J3-6a)

𝜙 = 0.75

Then, for one bolt:

𝝓𝑹𝒏 = 𝟏𝟓𝟖 𝒌𝑵


𝝓𝑹𝒏 = 𝟔 × 𝟏𝟓𝟖 = 𝟗𝟒𝟖 𝒌𝑵 > 360 𝑘𝑁 OK

Tear out does not control the design.


5-82

9. Bolt bearing of the column flange


𝑅𝑛 = 2.4𝑑𝑡𝑓𝐹𝑢

𝜙 = 0.75

Considering that 𝒕𝒇 = 𝟏𝟒 𝒎𝒎, for each bolt:

𝝓𝑹𝒏 = 𝟐𝟐𝟏 𝒌𝑵


𝝓𝑹𝒏 = 𝟔 × 𝟐𝟐𝟏 𝒌𝑵 = 𝟏𝟑𝟐𝟔 𝒌𝑵 > 360 𝒌𝑵 OK

Tear out does not control the design.

10. Shear yielding of the angle leg attached to the beam


𝑅𝑛 = 0.6𝐹𝑦𝐴𝑔 (Re. AISC360-05, J4-3)

𝜙 = 1.00

Then, considering that the gross shear area of the angle is:𝐴𝑔 = 𝐵𝑡 = 250 × 10 =

2500 𝑚𝑚2:

𝝓𝑹𝒏 = 𝟑𝟕𝟓 𝒌𝑵 > 372 𝑘𝑁 OK

11. Flexural yielding of the leg attached to the beam of the angle

The design moment corresponds to the design shear multiplied by the distance

between the point of application of the force and the critical section that is

going to be verified. AISC does not give any recommendation for the

determination of the point of application of the shear force and the critical

section.

For the critical section it is going to be used the recommendations of Salmon

(“Steel Structures, Design and Behavior” 5th edition), that indicate that the

critical section is located at 3/8” (9.52 mm) of the face of the angle (see

Figure 5.7-5).


5-83

Tip

The 3/8” distance is a conservative assumption for the measure of the fillet toe

of the angle.

Figure 5.7-5: Recommendation for critical section

From Salmon Steel Structures, 5th Ed, Figure 13.3.3

On the other hand, the point of application of the force is given by considering

the reaction at the center of the bearing distance 𝑁 required according to the

solicitation (it can also be considered the force applied at the center of the

bearing distance that it is effectively being use in the design, but this leads to

thicker angles). This means that we have to calculate from the web crippling

and the local yielding of web of the beam the required 𝑁 and with that value

calculate the eccentricity 𝑒.

Local yielding of the web:

𝑁𝑟𝑒𝑞 =𝑉𝑢

𝐹𝑦𝑤 𝑡𝑤− 2.5𝑘 = 112 𝑚𝑚

Web Crippling

𝑁𝑟𝑒𝑞 =

𝑉𝑢

𝜙0.4𝑡𝑤2


𝑡𝑤

− 1

1

𝑡𝑤

𝑡𝑓

1.5 + 0.2

𝑑

4

𝑁𝑟𝑒𝑞 = 329 𝑚𝑚

Then the maximum 𝑁𝑟𝑒𝑞 is 329 mm.

Critical section


5-84

In this case, the effective bearing distance used in the design is less than 𝑁𝑟𝑒𝑞

(This is because the use of stiffeners), do it is used 𝑁𝑟𝑒𝑞 = 80. Then, the

eccentricity is:

𝑒 = 𝑑𝑐 +𝑁𝑟𝑒𝑞

2− 𝑡 + 9.51 𝑚𝑚 = 32.5 𝑚𝑚

Then:

𝑀𝑢 = 𝑉𝑢𝑒 = 11700 𝑘𝑁 −𝑚𝑚

The nominal flexural resistance is:

𝑀𝑛 = 𝑍𝐹𝑦

𝜙 = 0.9

For the leg of the angle 𝑆 is:

𝑍 =𝑡2𝐵

4= 6250 𝑚𝑚3

And:

𝜙𝑀𝑛 = 1406 𝑘𝑁 −𝑚𝑚

Then we have to change the thickness of the angle. If 𝒕 = 𝟐𝟓 𝒎𝒎 is used:

𝑒 = 𝑑𝑐 +𝑁𝑟𝑒𝑞

2− 𝑡 + 9.51 𝑚𝑚 = 17.5 𝑚𝑚

Then:

𝑀𝑢 = 𝑉𝑢𝑒 = 6300 𝑘𝑁 −𝑚𝑚

For the leg of the angle 𝑍 is:

𝑍 =𝑡2𝐵

4= 39062 𝑚𝑚3

Then:

𝝓𝑴𝒏 = 𝟖𝟕𝟖𝟖 𝒌𝑵−𝒎𝒎 OK

Then we use an angle L200 X 80 X 25 X 250.

Tip

The use of unstiffened seated connections leads to thick angle connections for

some beams, due to of the flexural failure of the seat. The AISC dispositions

does not recommend any limit for the use of this type of connections but if the

thickness of the angles become a problem, the alternative is to switch from a


5-85

unstiffened to stiffened connection, in which the shear force applied is taken

almost completely by the stiffener element.

12. Selection of the top angle

For the top angle selection use the recommendations of Part 10 of the AISC

Manual of Steel Construction We use an L 100 X 100 X 6 X 250 angle. This

angle is connected to the beam by two M20 bolts. This requires a minimum

space between bolts of 60 mm and a minimum distance to the edge of 34 mm,

requirements that we accomplish with the angle selected.

Designed Connection

Figure 5.7-6: Unstiffened seated connection

References


Salmon, Johnson and Malhos, 2009, “Steel Structures. Design and

Behavior”. Fifth Edition, Pearson Prentice Hall, Upper Saddle River NJ.




H450X250X111.8H300X300X87.3

L200X80X25X250

2 M20 A490L100X100X6X250

6 M22 A490 2 M20 A490

2 STIFFENERS

PL 406X110X10


5-86


MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 6: MOMENT CONNECTIONS

6-1

6. MOMENT CONNECTIONS

This chapter is devoted to the design of moment connections for Special

Moment Frames (SMF). Five examples of moment connections are developed,

which correspond to prequalified connections according to the AISC 358 and

its supplement n°1. The examples developed are: Bolted extended end-plate

moment connection (unstiffened and stiffened); Reduce beam section (RBS);

bolted flange plate moment connection (BFP); welded unreinforced flange-

welded web connection. Also, a commentary for welding in moment

connections is added. The BFP connection is the most used in the Chilean

practice, and for that reason, in the corresponding example is included a

discussion section evaluating the main differences between the Chilean

practice and the AISC provisions.

6.1. Bolted Extended End-Plate Moment Connection (unstiffened case)


1. NCh2369.Of2003

Use high strength bolts (ASTM A325 or ASTMA490).

(Re. NCh2369.Of2003, 8.5.1)

Bolts must be prestressed to 70% of its nominal tensile strength. Always


(Re. NCh2369.Of2003, 8.5.6)

Moment connections between beams and columns of seismic rigid frames

must have, at least, a resistance equal to the connected elements.

(Re. NCh2369.Of2003, 8.5.3)

In beam-to-column connections of rigid frames, the upper and lower

flanges should have lateral braces or supports designed for a force equal

to 0.02𝐹𝑦𝑏𝑓𝑡𝑓.

(Re. NCh2369.Of2003, 8.5.4)

Moment connections of rigid frames for seismic applications shall be of FR

type (fully restricted). The connections shall be designed in a way such

that the plastic hinge is developed at a safe distance from the column,


6-2

which can be obtained by strengthening the connection or weakening the

beam in the desired position for the plastic hinge.

(Re. NCh2369.Of2003, 8.4.1)

Transverse sections of columns and beams in rigid earthquake-resistant

frames shall qualify as compact, that is, their width to thickness ratios

shall be lesser than 𝜆𝑝 given on Table 8.1 of the code.

(Re. NCh2369.Of2003, 8.4.2)

Appendix B (normative appendix) of the NCh2369.Of2003 refers to the

design of beam-column connection on rigid frames.

(Re. NCh2369.Of2003, App. B)

2. AISC 341-05

For the design of beam-to-column connections on special moment frames

(SMF) it is recommended to see Chapter 9 of this code. Some important

aspects are listed below:

Beam-to-column connections requirements: see section 9.2a.The required

shear strength should be calculated taking into account the flexural plastic

hinges produced by the earthquake (E) load.

Unless otherwise designated by AISC 358, CJP groove welds of beam

flanges, shear plates, and beam webs to column shall be demand critical

welds as defined in section 7.3b (Section 9.2c).

The protected zone is defined in AISC 358. In general, for unreinforced

connections, the protected zone will extend from the face of the column to

one half of the beam depth beyond the plastic hinge point (Section 9.2d).

Panel zone of beam to column connections: see section 9.3.

For beam and column limitations (for SMF systems in general), see section

9.4.

Continuity plates shall be consistent with the connection designed

according to AISC 358 (Section 9.5).

In beam-to-column connections, check the column-beam moment ratio

(section 9.6) and the lateral bracing (section 9.7 and 9.8).

3. AISC 358 General Requirements (summary of important aspects)

Rolled Wide-Flange Members and Built-up Members:

Some limitations shall be considered for the member shapes, see sections

2.3.1 and 2.3.2 of AISC 358.


6-3

LRFD Reduction Factors:

When available strengths are calculated according to AISC 358, use for ductile

limit states 𝜙𝑑 = 1.0 , and for non-ductile limit states 𝜙𝑛 = 0.9. If AISC 360 is

used for calculating available strengths, use the reduction factors stipulated

there.

Plastic Hinge Location and Probable Maximum Moment at Plastic Hinge (𝑀𝑝𝑟 )

This location is shown for each individual connection. For the 𝑀𝑝𝑟 calculation

see Eq. 2.4.3-1.

Panel and Protected Zones:

SMF (Special Moment Frames) systems shall conform to the minimum

requirements of section 9.3 of AISC 341-05. The protected zone shall be as

defined for each prequalified connection and it shall meet the requirements of

section 7.4 of AISC 341-05.

Welding Requirements:

Filler metals and welding procedures shall meet the requirements of

section 7.3 and Appendix W of the AISC 341-05 code.

For backing at beam to column and continuity plate to column joint, see

AISC 358-05, section 3.3.

Bolt Requirements:

Use only ASTM A325 or ASTM A490 bolts. They shall be pretensioned high

strength bolts.

(Re. AISC 358-05, 4.1)

6.1.b. Example

Design a bolted extended and unstiffened end plate moment connection for

the beam to column border connection shown in Figure 6.1-1 and 6.1-2. Use

A250 ESP steel, required for constructions subjected to dynamical loading,

according to NCh203.Of2006 code, Table 3.

The sections used are H 450 X 150 X 68.4 for the beam and H 450 x 250 x

149.8 for the column (both sections are Chilean Shapes). Use standard holes


6-4

for bolts. Suppose that the beams and columns have been properly designed

for resisting the forces given by the load combinations of the applicable

building code (including seismic load).

Follow the instructions given on “AISC 358-05 Prequalified Connections (SMF

and IMF systems) for Seismic Applications” document.

Figure 6.1-1: Connection to be designed. Frontal and Lateral View.

Figure 6.1-2: Connection to be designed. Plan view

1. Sections and materials properties

H450 X 150 X 68.4


𝑑 = 450 𝑚𝑚 , 𝑏𝑓 = 150 𝑚𝑚, 𝑡𝑓 = 18 𝑚𝑚, 𝑡𝑤 = 8 𝑚𝑚, 𝑠 = 5 𝑚𝑚


H 450 X 250 X 149.8




beam

end - plate

continuity

plates

column


6-5

A250ESP (Re. Table 3, NCh203.Of.2003)

𝐹𝑦 = 250 𝑀𝑃𝑎 , 𝐹𝑢 = 400 𝑀𝑃𝑎


6.1.c. Design procedure according to AISC 358

Base on the steps listed on Chapter 6 of AISC 358-05, also considering

supplement N° 1.

Try a 4 bolt, unstiffened extended end plate for the beam-to-column

connection, shown in Figures 6-1-1 and 5.1-2.

1. Prequalification limits

(Re. AISC 358, Supplement N°1 (2009); Table 6.1)

The minimum and maximum values of the several parameters for the design

of these connections are shown now (the notation of AISC 358 is presented,

see Figure Figure 6.1-3):

13 𝑚𝑚 ≤ 𝑡𝑝 = 𝑡𝑕𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑒𝑛𝑑 𝑝𝑙𝑎𝑡𝑒 ≤ 57 𝑚𝑚

178 𝑚𝑚 ≤ 𝑏𝑝 = 𝑤𝑖𝑑𝑡𝑕 𝑜𝑓 𝑒𝑛𝑑 𝑝𝑙𝑎𝑡𝑒 ≤ 273 𝑚𝑚

102 𝑚𝑚 ≤ 𝑔 = 𝑕𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑏𝑜𝑙𝑡𝑠 ≤ 152 𝑚𝑚

38 𝑚𝑚 ≤ 𝑝𝑓𝑖 ,𝑝𝑓𝑜 ≤ 114 𝑚𝑚

𝑝𝑓𝑖 = 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑏𝑒𝑎𝑚 𝑓𝑙𝑎𝑛𝑔𝑒 𝑎𝑛𝑑 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑖𝑛𝑛𝑒𝑟 𝑟𝑜𝑤 𝑜𝑓 𝑏𝑜𝑙𝑡𝑠

𝑝𝑓𝑜 = 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑏𝑒𝑎𝑚 𝑓𝑙𝑎𝑛𝑔𝑒 𝑎𝑛𝑑 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑜𝑢𝑡𝑒𝑟 𝑟𝑜𝑤 𝑜𝑓 𝑏𝑜𝑙𝑡𝑠

349 𝑚𝑚 ≤ 𝑑 = 𝑑𝑒𝑝𝑡𝑕 𝑜𝑓 𝑡𝑕𝑒 𝑏𝑒𝑎𝑚 ≤ 1400 𝑚𝑚

10 𝑚𝑚 ≤ 𝑡𝑏𝑓 = 𝑡𝑕𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑏𝑒𝑎𝑚 𝑓𝑙𝑎𝑛𝑔𝑒 ≤ 19 𝑚𝑚

152 𝑚𝑚 ≤ 𝑏𝑏𝑓 = 𝑤𝑖𝑑𝑡𝑕 𝑜𝑓 𝑏𝑒𝑎𝑚 𝑓𝑙𝑎𝑛𝑔𝑒 ≤ 235 𝑚𝑚

Note: the beam flange thickness is 150 mm, which is little lesser than the

minimum value of 152 mm. The difference of 2 mm is accepted.


6-6

Figure 6.1-3: Notation (used on AISC 358-05) for the extended end plate beam-to-column moment connection. Adapted from AISC 358-05, Fig. 6.2

2. Beam Limitations


Beams shall be rolled or welded built-up sections. For built-up sections, at

moment connected ends, within at least the lesser of 𝑑 and 3𝑏𝑏𝑓 , the beam

web and flanges shall be connected using either CJP groove welds or a pair of

fillet welds each one having a size of ¾ times the beam web thickness but not

less than 6 mm. For the remainder of the beam, the welds size shall not be

less than the required to accomplish shear transfer from web to flanges.

See also:

Section 6.4.5: Clear span to depth ratio for SMF systems is required to be 𝐿𝑛

𝑑> 7.0 (suppose this is OK).

Section 6.4.6: Width-thickness ratios for the flanges and web of the beam

shall conform to the limits on AISC 341. On this case, on AISC 341 section

bcf

dc

twc bbftwb

gbp

de pfo

t fb

pfi

tpt fc

c

d


6-7

9.4 requires that the beam must be seismically compact (flanges and

web) according to table I-8-1. The beam selected is seismically compact.

Note that abrupt changes of beam flange areas in plastic hinge regions are

not allowed.

Section 6.4.7 (Lateral Bracing): for SMF it should be provided lateral

bracing according to AISC 341 section 9.8

Section 6.4.8 (Protected Zone): for unstiffened case, the protected zone is

determined as the portion of the beam between the face of the column

and a distance equal to the depth of the beam or 3 times the width of

flange from the face of the column, whichever is less.

3. Column Limitations

(Re. AISC 358-05, Section 6.5)

The end plate shall be connected to the flange of the column. The column

depth must be equal or lesser than the beam depth. The width-thickness

ratio for flanges and web of the column shall conform to the limits in table

I-8-1 of AISC 341. Assume that the column used is seismically compact.

4. Beam-Column Relationship Limitations


Panel zones shall conform to the requirements of section 9.3 (SMF) of

AISC 341-05 and the column-beam moment ratio shall conform the

requirements for SMF systems on AISC 341-05.

5. Continuity Plates

See section 6.7 of AISC 358 for the requirements of continuity plates for

this type of connections.

6. Gage and Pitch Distances

(Re. AISC 358-05, Sections 6.9.1 and 6.9.2)

The gage 𝑔 is limited to the width of the connected beam flange.

For bolts up to 25 mm of diameter, the minimum pitch distance is:

𝒅𝒃 + 𝟏𝟐 𝒎𝒎

For bolts larger than 25 mm of diameter, the minimum pitch distance is:

𝒅𝒃 + 𝟏𝟗 𝒎𝒎


6-8

Pitch distances are 𝑝𝑓𝑖 and 𝑝𝑓𝑜 as already shown on Figure Figure 6.1-3.

7. End Plate Width

(Re. AISC 358-05, Section 6.9.3)

It shall be greater or equal than the connected beam flange width.

The effective end plate width shall not be taken as greater than the beam

flange width plus 25 mm.

8. Welding Details


Weld access holes shall not be used.

Beam web to end-plate joint shall be made using fillet welds or CJP groove

welds. When fillet welds are used, they shall be designed to develop the

full strength of the web in tension from the inside face of the flange to 150

mm beyond the bolt row farthest from the beam flange.

The beam flange to end-plate joint shall be made using a CJP groove weld

without backing. The CJP groove weld shall be made such that the root of

the weld is on the beam web side of the flange. The inside face of the

flange shall have a 8-mm fillet weld. These welds shall be demand critical.

Back gouging of the root is not required in the flange directly above and

below the beam web for a length equal to 1.5𝑘1. A full-depth PJP groove

weld shall be permitted at this location.

The following design steps are taken from section 6.10 of AISC 358-05.

9. Compute the moment at the face of the column

𝑀𝑓 = 𝑀𝑝𝑒 + 𝑉𝑢𝑆𝑕 (Re. AISC 358-05, Eq. 6.9-2)

Where: 𝑀𝑝𝑒 = 𝐶𝑝𝑟𝑅𝑦𝐹𝑦𝑍𝑥 = beam plastic hinge moment (Re. AISC 358-05, Eq.

6.9-3) and 𝑉𝑢 =2𝑀𝑝𝑒

𝐿′+ 𝑉𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = shear at plastic hinge location.

𝑆𝑕 = distance from the face of the column to the plastic hinge = min(𝑑

2+ 3𝑏𝑏𝑓 )

(for 4 bolt extended unstiffened connection type, 𝑑 is the depth of the beam)

(Re. AISC 358-05, Eq. 6.9-4). 𝐿′=𝐿𝑛 − 2𝑆𝑕 = distance between plastic hinges,

with 𝐿𝑛 = clear length of the beam.


6-9

Note: for the full explanation of the different terms, see section 6.10 of AISC

358-05.

In this case:

𝐶𝑝𝑟 =𝐹𝑦+𝐹𝑢

2𝐹𝑦= 1.3 > 1.2 → 𝐶𝑝𝑟 = 1.2 (Re. AISC 358-05, Eq. 2.4.3-2)

𝑅𝑦 = 1.5 for A250 ESP steel (similar to ASTM A36), according to AISC 341 table

I-6-1.

Assume 𝐿𝑛 = 4000 𝑚𝑚 →𝐿𝑛

𝑑> 7.0. The value of 𝑆𝑕 = 225 𝑚𝑚. Therefore 𝐿′ =

3550 𝑚𝑚

Assume the following gravitational loads:

𝑞𝐷 = 0.025 𝑘𝑁/𝑚𝑚 (Dead load, includes the beam self weight)

𝑞𝐿 = 0.016 𝑘𝑁/𝑚𝑚 (Live load)

Therefore: 𝑉𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 1.2𝑞𝐷+1.0𝑞𝐿 𝐿

′

2= 82 𝑘𝑁 and

2𝑀𝑝𝑒

𝐿′= 383 𝑘𝑁. Then, 𝑉𝑢 = 464 𝑘𝑁

and 𝑀𝑓 = 783498 𝑘𝑁 −𝑚𝑚.

Note: when using the NCh2369.Of2003 code, the moment connection shall

have at least a strength equal to the strength of the connected elements. It is

possible to use as design moment the value 𝑀𝑝 = 𝐹𝑦𝑍𝑥 and it is possible to

include also the effect of the shear 𝑉𝑔𝑟𝑎𝑣𝑖𝑡𝑦 .

10. Define preliminary values for the connection geometry and bolt grade

Use a 4 bolt unstiffened extended end plate moment connection. Try the

following dimensions (and meet also the prequalification limits already shown):

Parameter Value (mm)

𝒕𝒑 43

𝒃𝒑 210

𝒈 130

𝒑𝒇𝒊 60

𝒑𝒇𝒐 60

𝒅𝒆 60

Note: for calculations use the effective value: 𝒃𝒑 = 𝒃𝒑

𝑬𝑭𝑭 = 𝒃𝒇𝒃 + 𝟐𝟓 = 𝟏𝟕𝟓 𝒎𝒎


6-10

11. Calculate the required bolt diameter using the corresponding equation

𝑑𝑏𝑅𝐸𝑄 =

2𝑀𝑓

𝜋𝜙𝑛𝐹𝑛𝑡 𝑕1+𝑕0 (Re. AISC 358-05, Eq. 6.9-6)

Where: 𝐹𝑛𝑡 = 780 𝑀𝑃𝑎 for ASTM A490 bolts, 𝜙𝑛 = 0.9, 𝑕𝑖=distance from the

centerline of beam compression flange to the ith tension bolt row (see Figure

Figure 6.1-4). In this case, the connection is symmetric (because 𝑀𝑓 could be

positive or negative, according to the seismic loading). Therefore:

𝑕1 = 𝑑 − 1.5𝑡𝑓𝑏 − 𝑝𝑓𝑖 = 363 𝑚𝑚

𝑕0 = 𝑑 + 𝑝𝑓𝑜 −𝑡𝑓𝑏

2= 501 𝑚𝑚

Then: 𝑑𝑏𝑅𝐸𝑄 = 28.7 𝑚𝑚

Figure 6.1-4: Bolts in tension and distances 𝑕0 and 𝑕1.

Adapted from AISC 358-05, table 6.2.

12. Select a bolt diameter

Try M30 bolts.

13. Calculate the required end plate-thickness

𝑡𝑝𝑅𝐸𝑄 =

1.11𝑀𝑓

𝜙𝑑𝐹𝑦𝑝 𝑌𝑝 (Re. AISC 358, Eq. 6.9-8)

Where: 𝐹𝑦𝑝 = 250 𝑀𝑃𝑎 (minimum yield stress for the end plate), 𝜙𝑑 = 1.0.

For the determination of 𝑌𝑝 = end-plate yield mechanism parameter, see table

6.2 on AISC 358-05, corresponding to 4 bolt unstiffened end-plate

connections.

2P t

M np

h 0

h 1

2P t


6-11

Figure 6.1-5: Yield Line Pattern Model. Adapted from AISC 358-05, Table 6.2.

𝑌𝑝 =𝑏𝑝2 𝑕1

1

𝑝𝑓𝑖+

1

𝑠 + 𝑕0

1

𝑝𝑓𝑜 −

1

2 +

2

𝑔 𝑕1(𝑝𝑓𝑖 + 𝑠)

𝑠 =1

2 𝑏𝑝𝑔 = 75.5 𝑚𝑚 (Note that if 𝑝𝑓𝑖 > 𝑠 → 𝑢𝑠𝑒 𝑝𝑓𝑖 = 𝑠)

Therefore, 𝑌𝑝 = 2393 𝑚𝑚𝑡𝑝𝑅𝐸𝑄 = 38 𝑚𝑚

Tip

It is prudent to check also the condition of “prying” effect. According to the

AISC Design Guide # 4, if the applied force is less than 90% of the end-plate

strength (determined using the yield line analysis), the end-plate is considered

to be “thick” and no prying forces are considered; when the applied load is

greater than ninety percent of the end plate strength, the end plate is

considered to be „thin‟ and the prying forces are assumed to be at a maximum.

For conservative plate thicknesses, assume that no prying force occurs,

therefore:


1.11𝑀𝑛𝑝

𝜙𝑑𝐹𝑦𝑝𝑌𝑝

bp

g

de

pfotbf

pfi

s

tbw

h1

h0


6-12

𝑀𝑛𝑝 = “no prying moment” = 2𝑃𝑡(𝑕0 + 𝑕1)

𝑃𝑡= bolt tensile strength = 𝐹𝑡 𝜋𝑑𝑏

2

4 , 𝐹𝑡 = 𝐹𝑛𝑡 = 780 𝑀𝑃𝑎 for ASTM A490 bolts.

Calculations give:

𝑃𝑡 = 551 𝑘𝑁 → 𝑀𝑛𝑝 = 952732 𝑘𝑁 −𝑚𝑚

𝑡𝑝𝑅𝐸𝑄

= 42.03 𝑚𝑚 (no prying action effect controls).

14. Select the end plate-thickness

The assumed plate thickness 𝒕𝒑 = 𝟒𝟑 𝒎𝒎 > 𝒕𝒑𝑹𝑬𝑸

is OK.

15. Calculate the factored beam flange force:

𝐹𝑓𝑢 =𝑀𝑓

𝑑−𝑡𝑏𝑓= 1813 𝑘𝑁 (Re. AISC 358, Eq. 6.9-9)

16. Check shear yielding resistance of the extended portion of the four-bolt

extended unstiffened end-plate (4E)

𝐹𝑓𝑢

2< 𝜙𝑑𝑅𝑛 = 𝜙𝑑0.6𝐹𝑦𝑝𝑏𝑝𝑡𝑝 (Re. AISC 358, Eq. 6.9-10)

𝜙𝑑0.6𝐹𝑦𝑝𝑏𝑝𝑡𝑝 = 1129 𝑘𝑁 >𝐹𝑓𝑢

2= 907 𝑘𝑁 OK

If the previous equation is not satisfied, increase the end plate thickness until

it is satisfied. In this case there is no need to increase 𝑡𝑝. OK.

17. Check shear rupture resistance of the extended portion of the four-bolt

extended unstiffened end-plate (4E)

𝐹𝑓𝑢

2< 𝜙𝑛𝑅𝑛 = 𝜙𝑛0.6𝐹𝑢𝑝𝐴𝑛 (Re. AISC 358-05, Eq.6.9-11)

Where: 𝐹𝑢𝑝 = 400 MPa (minimum tensile strength of the end-plate).

𝐴𝑛 = 𝑏𝑝 − 2 𝑑𝑏 +1

8∗ 25.4 𝑚𝑚 𝑡𝑝 = 4672 𝑚𝑚2 = net area of the end-plate.

Calculations give:

𝜙𝑛0.6𝐹𝑢𝑝𝐴𝑛 = 1009 𝑘𝑁 >𝐹𝑓𝑢

2= 907 𝑘𝑁 OK


6-13


it is satisfied. In this case there is no need of increasing 𝑡𝑝. OK

18. The bolt shear rupture strength of the connection is provided by the bolts

at one (compression) flange

𝑉𝑢 = 𝑉𝑅𝐸𝑄 < 𝜙𝑛𝑅𝑛 = 𝜙𝑛 𝑛𝑏 𝐹𝑣𝐴𝑏 (Re. AISC 358-05, Eq. 6.9-15)

𝐴𝑏 = 707 𝑚𝑚2 = bolt nominal area, for M30 bolts.

𝐹𝑣 = 𝐹𝑛𝑣 = 414 𝑀𝑃𝑎 for ASTM A490 Bolts, threads included.

𝑛𝑏 = 4 (number of bolts at compression side)

Calculations give:

𝜙𝑛 𝑛𝑏 𝐹𝑣𝐴𝑏 = 1054 𝑘𝑁 > 𝑉𝑢 = 464 𝑘𝑁 OK

19. Check the bolt-bearing/tear out of the end plate and column flange

𝑉𝑢 < 𝜙𝑛𝑅𝑛 = 𝜙𝑛 𝑛𝑖 𝑟𝑛𝑖 + 𝜙𝑛(𝑛𝑜)𝑟𝑛𝑜 (Re. AISC 358-05, Eq. 6.9-17)

Where: 𝑛𝑖= Number of inner bolts = 2, 𝑛𝑜=Number of outer bolts = 2. In

general (for inner bolts and outer bolts), 𝑟𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑏𝑡𝐹𝑢.

End-plate side:

The upper limit is

2.4𝑑𝑏𝑡𝐹𝑢 = 1238 𝑘𝑁

Use 𝑑𝑏 = 30 𝑚𝑚, 𝐹𝑢 = 400 𝑀𝑃𝑎, 𝑡 = 𝑡𝑝 = 43 𝑚𝑚, and:

- Inner bolts:

𝐿𝑐 = 𝑝𝑓𝑖 + 𝑝𝑓𝑜 + 𝑡𝑏𝑓 − 33 = 105 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 = 2167 𝑘𝑁 → 𝑅𝑛 = 1238 𝑘𝑁

- Outer bolts:

𝐿𝑐 = 𝑑𝑒 −33

2= 43.5 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 = 897 𝑘𝑁

Therefore the strength is:

𝜙𝑛𝑅𝑛 = 3845 𝑘𝑁 > 𝑉𝑢 = 464 𝑘𝑁 OK


6-14

Note: The diameter of the standard hole for the bolt M30 is 33 mm. See AISC

360-05, table J3.3M.

Column flange side:

The upper limit is

2.4𝑑𝑏𝑡𝐹𝑢 = 922 𝑘𝑁

Use 𝑑𝑏 = 30 𝑚𝑚, 𝐹𝑢 = 400 𝑀𝑃𝑎, 𝑡 = 𝑡𝑐𝑓 = 32 𝑚𝑚 , and:

- Inner bolts:


- Outer bolts:

𝐿𝑐 = 𝑑𝑒 −33

2= 43.5 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 = 668 𝑘𝑁

Therefore the strength is:

𝜙𝑛𝑅𝑛 = 2862 𝑘𝑁 > 𝑉𝑢 = 464 𝑘𝑁 OK

Note: The diameter of the standard hole for the bolt M30 is 33 mm. See AISC

360-05, table J3.3M.

20. Design the flange to end plate and web to end plate welds, using the

requirements of the section 6.9.7 of AISC 358-05 code

Beam flanges to end-plate weld:

Use CJP groove welds. The inside face of the flange shall have an 8-mm fillet

weld.

Beam web to end-plate weld:

Use fillet welds, E70 electrode. For 8 mm (material thickness of the thinner

part joined) thickness, the minimum weld size is 5 mm according to AISC 360-

05, table J2.4.


6-15

The required weld to develop the bending stress on the beam web near the

tension bolts is (according to AISC Design Guide # 4):

(For E70 electrodes, 𝐹𝑊 = 0.6𝐹𝐸𝑋𝑋 = 289.5 𝑁/𝑚𝑚2):

𝑡𝑤 ≥0.6𝐹𝑦𝑏 𝑡𝑤𝑏

2 × 0.707𝐹𝑤= 2.9 𝑚𝑚

With 𝐹𝑦𝑏 = 250 MPa (beam yield stress), 𝑡𝑤𝑏 = 8 mm (beam web thickness)

The required weld size for resisting the shear 𝑉𝑢 between the beam and the

end-plate is:

𝑡𝑤 ≥𝑉𝑢

2 × 0.707𝐹𝑤𝐿𝑣= 5.5 𝑚𝑚

With 𝐿𝑣 the following effective length:

𝐿𝑣 = min 𝑑

2− 𝑡𝑓𝑏 , 𝑑 − 2𝑡𝑓𝑏 − 𝑝𝑓𝑖 + 2𝑑𝑏 = 207 𝑚𝑚

Note: The applied shear is to be resisted by weld between the minimum of the

following distances: the distance between the mid-depth of the beam and the

compression flange or the distance between the inner row of tension bolts plus

two bolt diameters and the compression flange. (Re. AISC Design Guide # 4

and AISC Manual of Steel of Construction 13th Ed.).

Use a pair of fillet welds, with 𝒕𝒘 = 𝟏𝟎 𝒎𝒎.

21. Check the column flange for flexural yielding

𝑡𝑐𝑓𝑅𝐸𝑄 =

1.11𝑀𝑓

𝜙𝑑𝐹𝑦𝑐 𝑌𝑐≤ 𝑡𝑐𝑓 (Re. AISC 358-05, Eq. 6.9-20)

Where 𝑌𝑐 = unstiffened column flange yield line mechanism parameter from

table 6.5 of AISC 358-05 (for four bolt extended end plate connection) and 𝑡𝑐𝑓

= column flange thickness. See Figure Figure 6.1-6:


6-16

Figure 6.1-6: Column flange yield line mechanism parameter for four bolt

extended connection type. Adapted from AISC 358-05, table 6.5.

𝑌𝑐 =𝑏𝑐𝑓

2 𝑕1

1

𝑠 + 𝑕0

1

𝑠 +

2

𝑔 𝑕1 𝑠 +

3𝑐

4 + 𝑕0 𝑠 +

𝑐

4 +

𝑐2

2 +

𝑔

2= 3452 𝑚𝑚

With: 𝑠 =1

2 𝑏𝑐𝑓𝑔 = 90 𝑚𝑚 and 𝑐 = 𝑕0 − 𝑕1 = 138 𝑚𝑚

Therefore, 𝑡𝑐𝑓𝑅𝐸𝑄 = 31.7 𝑚𝑚 < 𝑡𝑐𝑓 . So far, there is no need for continuity plates

(web stiffeners).

Note: If the previous equation is not satisfied, increase the column size or add

web stiffeners (continuity plates). If stiffeners are added, previous equation

must be checked using 𝑌𝑐 for the stiffened column flange from table 6.5 of

AISC 358-05 (for four bolt extended end plate connection).

22. If stiffeners are required for column flange flexural yielding, determine the

required stiffener force

The column flange flexural design strength is:

𝜙𝑑𝑀𝑐𝑓 = 𝜙𝑑𝐹𝑦𝑐𝑌𝑐𝑡𝑐𝑓2

(Re. AISC 358-05, Eq. 6.9-21)

bcf

s

c

s

tbw

g

h1

h0

tp


6-17

According to AISC 358, use unstiffened 𝑌𝑐 for the previous calculus.

Therefore, the equivalent column flange design force is 𝜙𝑑𝑅𝑛 = 𝜙𝑑𝑀𝑐𝑓/(𝑑 − 𝑡𝑏𝑓 )

and it shall be used for the design of web stiffeners. In this case, there was

not needing of stiffeners for column flexural yielding.

23. Check the local column web yielding strength of the unstiffened column

web at the beam flanges

The strength requirement is:

𝜙𝑑𝑅𝑛 ≥ 𝐹𝑓𝑢

𝑅𝑛 = 𝐶𝑡 6𝑘𝑐 + 𝑡𝑏𝑓 + 2𝑡𝑝 𝐹𝑦𝑐 𝑡𝑐𝑤

(Re. AISC 358-05, Eq. 6.9-23 and 6.9-24)

Use:

𝑡𝑏𝑓 , 𝑡𝑝 , 𝑡𝑐𝑤 : beam flange thickness, end-plate thickness and column web

thickness (already known).

𝐹𝑦𝑐 = 250 𝑀𝑃𝑎

𝐶𝑡 = 1.0 (supposing that the distance from the column top to the top face of the

beam flange is greater than the depth of the column. 𝑘𝑐 = 𝑡𝑐𝑓 + 𝑠 = 37 𝑚𝑚.

If the strength requirement is not satisfied, column web continuity plates are

required.

Therefore:

𝜙𝑑𝑅𝑛 = 652 𝑘𝑁 < 𝐹𝑓𝑢 → Continuity web plates are required

24. Check the unstiffened column web buckling strength at the beam

compression flange

This section applies for forces applied at both flanges of a member at the same

location. On this case, the connection to be designed is an exterior one, so this

limit state does not apply.

25. Check the unstiffened column web crippling strength at the beam

compression flange

The strength requirement is 𝜙𝑅𝑛 ≥ 𝐹𝑓𝑢 , with 𝜙 = 0.75. If this equation is not

satisfied, column web continuity plates are required. In this case, assume that

𝐹𝑓𝑢 is applied a distance greater than 𝑑𝑐

2 from the end of the column. Therefore:


6-18

𝑅𝑛 = 0.80𝑡𝑐𝑤2 1 + 3

𝑁

𝑑𝑐

𝑡𝑐𝑤

𝑡𝑐𝑓

1.5

𝐸𝐹𝑦𝑐 𝑡𝑐𝑓

𝑡𝑐𝑤 (Re. AISC 358-05, Eq. 6.9-29)

With 𝑁 = thickness of beam flange plus 2 times the groove weld reinforcement

leg size (in this case, 𝑁 = 𝑡𝑏𝑓). All the other terms have been already

explained.

Doing the calculations, the strength is:

𝑅𝑛 = 735 𝑘𝑁 → 𝜙𝑅𝑛 = 551 𝑘𝑁 < 𝐹𝑓𝑢 → Continuity web plates are required

26. If stiffener plates are required for any of the column side limit states, the

required strength is

𝐹𝑠𝑢 = 𝐹𝑓𝑢 −𝑚𝑖𝑛𝜙𝑅𝑛 = 1262 𝑘𝑁 (𝐹𝑠𝑢 is a compression force because column web

crippling controls).

6.1.d. Panel Zone / Continuity Plates / Column-Beam Moment Ratio /

Lateral Bracing

1. According to AISC Code

Check the panel zone:

As said on AISC 358-05, check the panel zone in accordance with Section

6.6.1 of AISC 358-05. This section refers to AISC 341-05, Section 9.3 (SMF

systems).

2. Shear strength of the panel zone

(Re. AISC 341-05, Section 9.3a)

Consider the following figure (for an interior connection):


6-19

Figure 6.1-7: Typical panel zones forces. Figure adapted from AISC Design

Guide N°13, Fig. 2-3.

The total panel zone shear 𝑉𝑢 can be determined with the beam flange forces

(𝑃𝑢𝑓𝑖 = 𝑀𝑢𝑖 /(𝑑𝑖 − 𝑡𝑏𝑓𝑖 )) and the story shear 𝑉𝑢𝑠 . According to Figure 6.1-7,

𝑉𝑢 = 𝑃𝑢𝑓1 + 𝑃𝑢𝑓2 − 𝑉𝑢𝑠 . On this case, neglect the story shear and compute:

𝑉𝑢 = 𝑃𝑢𝑓 =𝑀𝑓

𝑑−𝑡𝑏𝑓= 1813 𝑘𝑁 (exterior connection).

The shear strength is

𝜙𝑅𝑛 = 1.0 × 0.6𝐹𝑦𝑑𝑐𝑡𝑤(1 +3𝑏𝑐𝑓 𝑡𝑐𝑓

2

𝑑𝑏𝑑𝑐𝑡𝑤) = 796 𝑘𝑁 (Re. AISC 360-05, Eq. J10-11).

Note: suppose that frame stability is considered in the analysis and that

𝑃𝑢 < 0.75𝑃𝑦.

Therefore, 𝜙𝑅𝑛 < 𝑉𝑢 , web doubler plates are required.

Tip

Generally, a better solution than using web doubler plates is to choose a

column with a thicker web, eliminating the need for the doubler plates which

have details that are expensive and difficult to fabricate.

3. Panel zone thickness

(Re. AISC 341-05, Section 9.3b)

For the column web and each doubler plate:

V us

V us

P uf 1

M u 1

V u

P uf 1

P uf 2

P uf 2

M u 2


6-20

𝑡 ≥𝑑𝑧 + 𝑤𝑧

90

Suppose that the continuity plate dimensions are 𝑒𝑠 = 35 𝑚𝑚 (thickness) and 𝑏𝑠

(width, which is going to be defined later).

The panel zone dimension between continuity plates is 𝑑𝑧 = 𝑑𝑏 − 𝑡𝑓𝑏 − 𝑒𝑠 =

397 𝑚𝑚 (𝑑𝑏 = depth of the beam). The panel zone dimension between column

flanges is 𝑤𝑧 = 𝑕𝑐𝑜𝑙𝑢𝑚𝑛 = 386 𝑚𝑚. Then: 𝑡 ≥ 8.7 𝑚𝑚.

The column web thickness is not ok. AISC 341 makes an exception when using

plug welds for the attachment of the doubler plates to the column web. In

that case, the total panel zone thickness must be greater than 8.7 𝑚𝑚. Use

plug welds for doubler plates to column web connection.

4. Panel zone doubler plates

(Re. AISC 341-05, Section 9.3c)

Welds to column flanges: use CJP or fillet welds that develop the available

shear strength of the full doubler plate thickness

When placed against column web: doubler plates shall be welded top and

bottom edge to develop the proportion of the total force that is transmitted to

the doubler plate.

When placed away from column web: doubler plates must be placed

symmetrically in pairs and welded to continuity plates to develop the

proportion of the total force that is transmitted to the doubler plate.

In this example, doubler plates are placed against the column web (with plug

welds).

Size the doubler plates:

Use A250 ESP for the doubler plates, for determining the thickness of the

doubler plates considering them acting on shear yielding and developing the

proportion of the total force transmitted to them:

2𝑡𝑑𝑝 ≥𝑉𝑢−𝜙𝑣𝑅𝑣

𝜙0.6𝐹𝑦𝑤𝑧= 17.6 𝑚𝑚.


6-21

With 𝜙 = 1.0 according to section J4 of AISC 360-05 Specification.

Use 𝟐𝒕𝒅𝒑 = 𝟏𝟖 𝒎𝒎 → 𝒕𝒅𝒑 = 𝟗 𝒎𝒎 (OK with minimum requirements for panel zone

thickness)

If considering the doubler plates to be CJP groove welded to the column

flanges, use for the doubler plates width: 𝑩𝒅𝒑 = 𝒅𝒄 − 𝟐 𝒕𝒇𝒄 + 𝒔𝒄 = 𝟑𝟕𝟔 𝒎𝒎. For

the depth of the doubler plates, consider the distance between continuity

plates: 𝑫𝒅𝒑 = 𝒅𝒃 − 𝒕𝒃𝒇 − 𝒆𝒔 = 𝟑𝟗𝟕 𝒎𝒎.

Figure 6.1-8: Doubler plate dimensions.

5. Welded unions of the doubler plates

See Welded Connection Commentary for Continuity Plates and Doubler Plates

for Chapter 6 on this Manual.

6. Design of the continuity plates (web stiffeners)

In this case, continuity plates are needed. As said on AISC 358-05, Continuity

plates shall also conform to section J10.8 of AISC 360-05 Specification and the

welds shall be in accordance with section 6.7.3 of AISC 358-05.

A

Section A - A

Ddp

tfc

Bdp

s c

d c

A

tdp

tdp


6-22

From the limit states mentioned on the steps above calculate the

difference between the applied force and the minimum available strength

𝑅𝑠𝑢𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁 = 𝐹𝑠𝑢 = 𝐹𝑓𝑢 −𝑚𝑖𝑛𝜙𝑅𝑛 = 1262 𝑘𝑁

Size the continuity plates: Use A250 ESP for continuity plates. Try

𝒆𝒔 = 𝟑𝟓 𝒎𝒎 (continuity plate thickness), 𝒃𝒔 = 𝟏𝟎𝟓 𝒎𝒎 (continuity plate

width) and 𝑳𝒔 = 𝒉𝒄 = 𝟑𝟖𝟔 𝒎𝒎 (continuity plate depth, use the column

height between flanges).

Figure 6.1-9: Continuity plates dimensions.

Check additional stiffener requirements from AISC 360-05

(Re. AISC 360-05, Section J10.8)

𝑏𝑠 +1

2𝑡𝑐𝑤 = 109 𝑚𝑚 ≥

1

3𝑏𝑏𝑓 = 50 𝑚𝑚 OK

𝑒𝑠 = 35 𝑚𝑚 ≥ 𝑚𝑎𝑥 1

2𝑡𝑏𝑓 ,

𝑏𝑠

15 = 9 𝑚𝑚 OK

Compression check for the continuity plates:

As said on AISC 360-05 J10.8 Section, use an effective length of 0.75𝑕

(289.5 mm) and a cross section composed of 2 stiffeners and a portion of the

web having a width of 12𝑡𝑤 (exterior stiffener)

A A

e s

L s

b s

b bftcw

Section A - A


6-23

Figure 6.1-10: Section of continuity plates plus web fraction resisting

compression force.

According to the previous figure, the properties of the section to resist

compression are:

𝐴 = 2𝑏𝑠𝑒𝑠 + 12𝑡𝑐𝑤2 , 𝐼 =

2𝑏𝑠𝑒𝑠3

12+

𝑡𝑐𝑤 12𝑡𝑐𝑤 3

12 , 𝑟 =

𝐼

𝐴= 12.8 𝑚𝑚. Use 𝑘 = 1.0.

According to AISC 360 J4.4 Section: 𝑘𝐿

𝑟= 22.53 < 25 → Use Ch. J

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴 = 1827 𝑘𝑁 > 𝐹𝑓𝑢 = 1813 𝑘𝑁 OK

Notes:

For the compression check, it has been used 𝐹𝑓𝑢 instead of 𝑅𝑠𝑢𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁

because the section considered for resisting the compression takes into

account a portion of the column web. 𝑅𝑠𝑢𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁 will be used for the welds for

continuity plates to column flanges unions.

No tension check is done, because the applicable limit states analyzed

(according to AISC 358-05) were all compression limit states.

For welded unions of the continuity plates, see Welded Connection

Commentary for Continuity Plates and Doubler Plates of Chapter 6 on this

Manual.

7. Check the beam-column moment ratio

Check the column beam moment ratio according to AISC 341-05 code.

(Assume that the factored axial force on the column is 𝑃𝑢𝑐 = 500 𝑘𝑁) :

𝑀𝑝𝑐

∗

𝑀𝑝𝑏∗ > 1.0 (Re. AISC 341-05, Eq. 9-3)

With:

bs

es

bs

es

tw

12tw


6-24

𝑀𝑝𝑐∗ = 𝑍𝑐 𝐹𝑦𝑐 −

𝑃𝑢𝑐𝐴𝑔

= 2𝑍𝑐 𝐹𝑦𝑐 −𝑃𝑢𝑐𝐴𝑔

= 1580067 𝑘𝑁 −𝑚𝑚

And

𝑀𝑝𝑏∗ = 𝑀𝑝𝑒 + 𝑉𝑢 𝑆𝑕 +

𝑑𝑐

2 = 887946 𝑘𝑁 −𝑚𝑚.

Therefore:

𝑀𝑝𝑐

∗

𝑀𝑝𝑏∗ = 1.8 > 1.0 OK

8. Lateral bracing

Beam lateral bracing:

According to section 9.8 of AISC 341-05, both beam flanges shall be laterally

braced, with a maximum spacing of 𝐿𝑏 =0.086𝑟𝑦𝐸

𝐹𝑦= 2346 𝑚𝑚. (Use 𝑳𝒃 = 𝟐𝟎𝟎𝟎 𝒎𝒎).

Assume that with this lateral spacing, the beam can properly support the

loads.

Meet the provisions of Appendix 6 of AISC 360-05:

Required brace strength:

𝑃𝑏𝑟 =0.02𝑀𝑟𝐶𝑑

𝑕𝑜= 26 𝑘𝑁. (Re. AISC 360-05, Eq. A-6-7)

Use:

𝑀𝑟 = 𝑅𝑦𝐹𝑦𝑍𝑏 , 𝐶𝑑 = 1.0, 𝑕𝑜 = (𝑑𝑏 − 𝑡𝑏𝑓 ) .

Required brace stiffness (𝜙 = 0.75):

𝛽𝑏𝑟 = 1

𝜙

10𝑀𝑟𝐶𝑑

𝐿𝑏𝑕𝑜 = 8.7 𝑘𝑁/𝑚𝑚 (Re. AISC 360-05, Eq. A-6-8)

Supplemental beam lateral bracing (at hinge location):

Assume that the connection between the beam and the slab is done with shear

welded connectors provided by 300 mm. Therefore, according to AISC 358-05,

supplemental top and bottom flange lateral bracing at hinge location is not

required.


6-25

Column lateral bracing:

Considering the user note in the 9.7 Section of AISC 341-05; column lateral

bracing can be achieved by the use of braces, decks, slabs, and also with

indirect lateral bracing. On this case, the ratio of beam-column moments is

lesser than 2.0, therefore the column does not remains elastic outside the

panel zone.

In this case there is no specific design for column lateral brace (at beam flange

levels). Suppose that the bracing is achieved with a slab and by indirect

bracing. If needed, an specific bracing system design shall be made.

6.1.e. Panel Zone/ Continuity Plates / Column-Beam Moment Ratio /

Lateral Bracing

1. Check the previous design according to NCh2369.Of2003 Code

Refer to Chapter 8 and Appendix B (Beam-to-Column unions on rigid steel

frames) of NCh2369.Of2003 Code.

Note: According to Appendix B, the provisions of NCh2369.Of2003 code for

rigid unbraced frames are normative, and the designer does not have to take

account the additional obligatory requirements of AISC 341-1999 (SMF

systems and IMF systems). On this example, a design using AISC 341 and

AISC 358 codes has been done; nevertheless it is going to be checked with the

NCh2369.Of2003 code. The sections used comply with the limits of Table 8.1

on Chilean code.

2. Panel zone

(Re. NCh2369.Of2003, B.2)

As said on B.2.1, the analysis can be done with elastic or plastic methods. The

panel zone shall be retrofitted with doubler plates and/or diagonal stiffeners

(see Figures B.1 and B.2 of the code) if 𝑅𝑢 > 𝜙𝑅𝑣 = 0.75𝑅𝑣.

(Re. NCh2369.Of2003, B.2.2)

The determination of 𝑅𝑢 and 𝑅𝑣 is quite similar to AISC 341 code. Considering

an interior connection:

𝑅𝑢 =𝑀𝑢1

𝑑𝑚1+

𝑀𝑢2

𝑑𝑚2− 𝑉𝑢 (Re. NCh2369.Of2003, Eq. B-1)


6-26

With 𝑀𝑢𝑖=beam moments (not greater than plastic beam moments, on this

case use 𝑀𝑢 = 𝐹𝑦𝑍𝑥 = 377250 𝑘𝑁 −𝑚𝑚 ) determined using the load combinations

of the code and the amplification of the earthquake term by 2; 𝑑𝑚𝑖 = 0.95𝑑𝑖 ,

𝑉𝑢=shear force in the column at the level of the union (neglect it as on the

previous design).

Assume that 𝑃𝑢 ≤ 0.75𝑃𝑦, therefore the calculation of:

𝜙𝑅𝑣 = 0.75 × 0.6𝐹𝑦𝑑𝑐𝑡𝑝(1 +3𝑏𝑐𝑓 𝑡𝑐𝑓

2

𝑑𝑏𝑑𝑐 𝑡𝑝) is quite similar to the AISC 341 code, but

using a 𝜙 = 0.75 and 𝑡𝑝 = 𝑡𝑐𝑤 + 2𝑡𝑑𝑝 instead of only 𝑡𝑐𝑤 .

Considering then the doubler plates designed on the previous stage (2 plates,

𝑡𝑑𝑝 = 9 𝑚𝑚 ) , calculations give:

𝜙𝑅𝑣 = 1508 𝑘𝑁 < 𝑅𝑢 = 883 𝑘𝑁 Doubler plate thickness is OK.

According to section B.2.5 of the Chilean code, the minimum thickness of the

column web and doubler plates must be the same as AISC 341.

3. Some welding requirements of doubler plates

(Re. NCh2369-Of2003, B.2.4 and B.8)

Doubler plates shall be welded to the column flanges with fillet or CJP groove

welds designed to resist the shear required strength (on seismic frames, the

welds shall resist the total shear strength of the doubler plate). If they are

against the column web, they shall be welded on their bottom and top ends

(and the welds must resist the proportion of the force transmitted to the

doubler plates). If they are away from the column web, doubler plates shall be

placed symmetrically and welded to the continuity plates (and the welds must

resist the proportion of the force transmitted to the each one of the doubler

plates).

Note: As seen, the previous dispositions are quite similar to AISC dispositions.

Refer to Welded Connection Commentary for Continuity Plates and Doubler

Plates of Chapter 6 on this Manual.

4. Continuity plates

(Re. NCh2369.Of2003, B.3 to B.6)

Limit states check list:


6-27

1.- Flange local bending

Equal to AISC code, 𝜙𝑅𝑛 = 0.9 × 6.25𝑡𝑐𝑓2 𝐹𝑦𝑓 = 1440 𝑘𝑁 > 𝑅𝑢 =

𝑀𝑢

𝑑𝑚= 883 𝑘𝑁. See the

additional requirements on B.3.2 to B.3.3

2.- Web local yielding

Similar to AISC code, except that if 𝑁 < 𝑘 → take 𝑁 = 𝑘 = 37 𝑚𝑚. Therefore:

𝜙𝑅𝑛 = 1.0 ∗ 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑐𝑤 = 444 𝑘𝑁 < 𝑅𝑢 = 883 𝑘𝑁.

Note: 𝑘 = 𝑡𝑐𝑓 + 𝑠 = 37 𝑚𝑚 ,𝑁 = 𝑡𝑏𝑓 = 18 𝑚𝑚 → 𝑁 = 37

3.-Web crippling

Equal to AISC code: 𝑅𝑛 = 0.8𝑡𝑐𝑤2 [1 + 3

𝑁

𝑑𝑐

𝑡𝑐𝑤

𝑡𝑐𝑓

1.5

] 𝐸𝐹𝑦𝑤 𝑡𝑐𝑓

𝑡𝑐𝑤

Use 𝜙 = 0.75 to obtain: 𝜙𝑅𝑛 = 551 𝑘𝑁 < 𝑅𝑢 = 883 𝑘𝑁

4.- Web compression buckling:

This limit state does not apply for exterior connections.

5. Force for the design of weld connections of the continuity plates

According to B.3.4. (and note (1)), continuity plates shall be welded to the

web and the loaded flange so to transfer to the web the proportion of the force

carried by the stiffeners:

𝑅𝑛 ,𝑠𝑡 = 𝑅𝑢 − 𝜙𝑅𝑛 ,𝑚𝑖𝑛 = 438 𝑘𝑁

And the minimum total stiffener area shall be 𝐴𝑠𝑡 =𝑅𝑛 ,𝑠𝑡

𝜙𝐹𝑦 ,𝑠𝑡= 1948 𝑚𝑚2

6. Additional criteria for continuity plates

(Re. NCh2369.Of2003, B.7 Section)

𝑏𝑠 +1

2𝑡𝑐𝑤 = 109 ≥

1

3𝑏𝑐𝑓 = 83.3 OK


6-28

𝑒𝑠 = 35 𝑚𝑚 > max 𝑡𝑏𝑓 ,𝑏𝑠 𝐹𝑦

250 = 18 𝑚𝑚 OK

Compression check:

According to B.7.2, the section resisting the compression is the same as the

previous design (external stiffeners), therefore:

𝜙𝑃𝑛 = 1827 𝑘𝑁 > 𝑅𝑢 = 883 𝑘𝑁 OK

7. Some welding requirements of the continuity plates

According to NCh2369.Of2003 (B3.4, B4.2 and B5.2) the continuity plate to

loaded flange welds shall transfer the proportion of the load corresponding to

the stiffener and the continuity plate to web welding shall be dimensioned to

transmit the proportion of the load carried by the stiffeners.

Note: As seen, the previous dispositions are quite similar to AISC dispositions.


Plates of Chapter 6 on this Manual.

8. Column-beam moment ratio:

According to NCh2369.Of2003, section 8.4.4 (R>3 systems): 𝑀𝑝𝑐/ 𝑀𝑝𝑣 > 1.2

for the columns and beams at the union analyzed. (See exceptions when is not

needed to meet the previous inequality at 8.4.4).

The code does not specify the calculation of the moments, so use the plastic

moments of the gross sections. Using this, 𝑀𝑝𝑐/ 𝑀𝑝𝑣 = 4.7 > 1.2 OK.

9. Lateral bracing:

According to NCh2369.Of2003, section 8.5.4, on beam-to-column connections

for rigid frames both beam flanges shall count with lateral bracing designed for

0.02𝐹𝑦𝑏𝑓𝑡. On this case, this is similar to AISC dispositions so the previous

design is OK, considering that a slab braces the superior flange of the beam.


6-29

Designed connection:

Figure 6.1-11: Connection Designed.

Notes:

Some of the following assumptions are inherent to the design procedure

presented on this example (See AISC Design Guide # 4). A summary of those

assumptions (not explicit on the document) follows:

All bolts are tightened to a pretension not less than AISC requirement.

However, slip critical connections requirements are not needed in this

case.

Only are permitted ASTM A325 or ASTM A490 bolts.

All of the shear force is assumed to be resisted by the compression side

bolts.

Beam web to end plate welds in the vicinity of the tension bolts are

designed to develop the yield stress of the beam web. This weld strength

is recommended even if the full moment capacity of the beam is not

required for frame strength.

Only the web to end plate weld between the mid-depth of the beam and

the inside face of the beam compression flange may be used to resist the

beam shear (based on judgment).

Yield-line analysis is used for end-plate strength determination

Bolt prying forces are not a consideration, since the required end plate

thickness prevents their development.

4 M30 ASTM A490

4 M30 ASTM A490

PL 210x740x43 mm

Beam: H 450 x 150 x 68.4

Column: H 450 x 250 x 149.8

2PL 386 x 85 x 35 mm

2PL 397 x 376 x 9 mm

Bolts positions

pfo= 60 mm

pfi = 60 mm

de = 60 mm

g= 140 mm

Note:

Connections for doubler and web plates

are not designed

10

10Typ

g

pfi

de

pfoCJP

CJP


6-30

6.1.f. References

Murray and Summer, 2004, “AISC Design Guide 4: Extended

End-Plate Moment Connections; Seismic and Wind Applications”

2nd Edition. American Institute of Steel Construction, USA.

Carter, 1999, “AISC Design Guide 13: Stiffening of Wide Flange

Columns at Moment Connections: Wind and Seismic

Applications”. American Institute of Steel Construction, Chicago

IL.

American Institute of Steel Construction, 2005, “AISC Manual of

Steel Construction”. 13th Edition. AISC, USA.


6-31

6.2. Bolted Extended End-Plate Moment Connection (stiffened

case)


1. NCh2369.Of2003

Same as example 6.1.

2. AISC 341-05:




6.2.b. Example

Design a bolted extended and stiffened end plate moment connection for the

beam to column border connection shown in Figure 6.2-1. Sections used are H

450 x 150 x 68.4 for the beam and H 450 x 250 x 149.8 for the column (both

sections are Chilean Shapes). Use standard holes for bolts and A250 ESP steel,

required for constructions subjected to dynamical loading, according to

NCh203.Of2006 code, Table 3. Suppose that beams and columns have been

properly designed for resisting the forces given by the load combinations of

the applicable building code (including seismic load).


and IMF systems) for Seismic Applications” document.

Note that this connection has been already designed for the unstiffened case

on example 6.1. Therefore, the input data for this example is the same and

many steps of the design will be resumed. Assume the same gravitational

loads applied to the beam from example 6.1.


6-32

Figure 6.2-1: Connection to be designed. Frontal View.

Tip

The 4 bolt unstiffened extended end-plate connection is commonly more used

than the connection to be designed. Nevertheless, the fact of adding a

stiffeners leads to thinner end-plates. The 8 bolt stiffened configuration is

another possibility which stands larger moments than the 4 bolt configuration.

1. Sections and material properties

H450 x 150 x 68.4




H 450 x 250 x 149.8




A250ESP (Re. Table 3, NCh203.Of.2003)

𝐹𝑦 = 250 𝑀𝑃𝑎 , 𝐹𝑢 = 400 𝑀𝑃𝑎


6.1.d. Design procedure according to AISC 358

Base on the steps listed on Chapter 6 of AISC 358-05, and consider

supplement N° 1.


6-33

Try a 4 bolt, stiffened extended end plate for the beam-to-column

connection, shown in figure Figure 6.2-1.


(Re. AISC 358, Supplement N°1 (2009); Table 6.1)


of these connections are shown now (the notation of AISC 358 is presented,

see Figure 6.2-2):




44 𝑚𝑚 ≤ 𝑝𝑓𝑖 ,𝑝𝑓𝑜 ≤ 140 𝑚𝑚






Note: the beam flange thickness is 150 mm, which is little lesser than the

minimum value of 152 mm. The difference of 2 mm is accepted


6-34

6.2-2: Notation (used on AISC 358-05) for the extended end plate beam-to-

column moment connection. Adapted from AISC 358-05, Fig. 6.3.

2. Beam Limitations


Same as example 6.1, except that for the protected zone (6.4.8), for the

stiffened case shall be calculated as the portion of the beam between the face

of the column and a distance equal to the location of the end of the stiffener

plus one-half the depth of the beam or 3 times the width of the beam flange,

whichever is less.

3. Column Limitations



4. Beam-Column Relationship Limitations



bpb

bf

t wb

t wc

g

bcf

dc

d

de

pfo t fb

p fi

c

tfc tp

t s

Lst

hst


6-35

5. Continuity Plates


6. Gage and Pitch Distances

(Re. AISC 358-05, Sections 6.9.1 and 6.9.2)


7. End Plate Width



8. End Plate Stiffener


The minimum end plate stiffener (gusset plate welded between the connected

beam flange and the end-plate) length shall be:

𝐿𝑠𝑡 =𝑕𝑠𝑡

tan 30°

With 𝑕𝑠𝑡 = height of the end-plate from the outside of the beam flange to the

end of the end-plate.

The stiffeners shall be terminated at beam flange at the end of the end-plate

with landings of approximately 25 mm long. The stiffener shall be clipped

where it meets the beam flange and end-plate to provide clearance between

the stiffener and the beam flange weld.

When the beam and end-plate stiffeners have the same material strengths,

the thickness of the stiffeners shall be greater than or equal to the beam web

thickness. If not, the thickness of the stiffeners shall be greater than or equal

to the beam web thickness multiplied by the ratio of beam-to-stiffener plate

material yield stress.


6-36

9. Welding Details



Additionally, when used, all end-plate stiffener joints shall be made using CJP

groove welds. The exception is when the thickness of the stiffeners is 10 mm

or less, then fillet welds that develop the strength of the stiffener can be used.


10. Compute the moment at the face of the column

Same as example 6.1, except that 𝑆𝑕 changes to 𝑆𝑕 = 𝐿𝑠𝑡 + 𝑡𝑝 and therefore

some derived values also change. On this case, for the stiffeners assume:

𝑳𝒔𝒕 = 𝟐𝟏𝟎 𝒎𝒎 ,𝒉𝒔𝒕 = 𝒑𝒇𝒐 + 𝒅𝒆 = 𝟏𝟐𝟎 𝒎𝒎.

For the values of 𝑡𝑝 , 𝑝𝑓𝑜 and 𝑑𝑒 refer to the following step.

Note that:

𝐿𝑠𝑡 >𝑕𝑠𝑡

tan 30

Then, 𝑆𝑕 = 245 𝑚𝑚 and then:

𝑉𝑢 = 468 𝑘𝑁 and 𝑀𝑓 = 793625 𝑘𝑁 −𝑚𝑚.

11. Define preliminary values for the connection geometry and bolt grade

Use a 4 bolt stiffened extended end plate moment connection.

Try the following dimensions (and meet also the prequalification limits already

shown):


𝒕𝒑 35

𝒃𝒑 210

𝒈 130

𝒑𝒇𝒊 60

𝒑𝒇𝒐 60

𝒅𝒆 60


6-37

Notes:

For calculations use the effective value : 𝒃𝒑 = 𝒃𝒑𝑬𝑭𝑭 = 𝒃𝒃𝒇 + 𝟐𝟓 = 𝟏𝟕𝟓 𝒎𝒎

The only different value of the connection geometry respect to example

6.1 is the end-plate thickness 𝒕𝒑.

12. Calculate the required bolt diameter using the corresponding equation

Procedure is same as the one on example 6.1, using:

𝑕1 = 𝑑 − 1.5𝑡𝑓𝑏 − 𝑝𝑓𝑖 = 363 𝑚𝑚


2= 501 𝑚𝑚

Then:

𝑑𝑏𝑅𝐸𝑄 = 28.8 𝑚𝑚

13. Select a bolt diameter

Same as example 6.1, use M30 bolts.

14. Calculate the required end plate-thickness

For the stiffened case, the 𝑌𝑝 term changes. From table 6.3 of AISC 358-05:

𝑠 =1

2 𝑏𝑝𝑔 = 75.4 𝑚𝑚 (Note that if 𝑝𝑓𝑖 > 𝑠 → 𝑢𝑠𝑒 𝑝𝑓𝑖 = 𝑠)

Case 1 of table 6.3: 𝑑𝑒 ≤ 𝑠. Therefore:

𝑌𝑝 =𝑏𝑝2 𝑕1

1

𝑝𝑓𝑖+

1

𝑠 + 𝑕0

1

𝑝𝑓𝑜+

1

2𝑠 +

2

𝑔 𝑕1 𝑝𝑓𝑖 + 𝑠 + 𝑕0 𝑑𝑒 + 𝑝𝑓𝑜

Then, 𝑌𝑝 = 3653 𝑚𝑚𝑡𝑝𝑅𝐸𝑄 = 30.9 𝑚𝑚 (note that 𝐹𝑦𝑝 = 250 𝑀𝑃𝑎)

Tip

It is prudent to check also the condition of “prying” effect. According to the

AISC Design Guide # 4, if the applied force is less than 90% of the end-plate

strength (calculated using the yield line analysis), the end-plate is considered

to be “thick” and no prying forces are considered; when the applied load is

greater than ninety percent of the end plate strength, the end plate is

considered to be “thin” and the prying forces are assumed to be at a


6-38

maximum. For conservative plate thicknesses, assume that no prying force

occurs, therefore:


1.11𝑀𝑛𝑝


𝑀𝑛𝑝 = “no prying moment” = 2𝑃𝑡(𝑕0 + 𝑕1)


2

4 ,

𝐹𝑡 = 𝐹𝑛𝑡 = 780 𝑀𝑃𝑎 for ASTM A490 bolts.

Calculations give:

𝑃𝑡 = 551 𝑘𝑁 → 𝑀𝑛𝑝 = 952732 𝑘𝑁 −𝑚𝑚

Therefore, 𝑡𝑝𝑅𝐸𝑄

= 34.03 𝑚𝑚 (no prying action effect controls).

15. Select the end plate-thickness

The assumed plate thickness 𝒕𝒑 = 𝟑𝟓 𝒎𝒎 > 𝒕𝒑𝑹𝑬𝑸

is OK.

16. Calculate the factored beam flange force

Same procedure as example 6.1:

𝐹𝑓𝑢 =𝑀𝑓

𝑑−𝑡𝑏𝑓= 1837 𝑘𝑁 (Re. AISC 358, Eq. 6.9-9)

17. For the 4 bolt extended stiffened end-plate, select the end plate stiffener

thickness and design the stiffener-to-beam flange and stiffener to-end-

plate welds

𝑡𝑠,𝑚𝑖𝑛 = 𝑡𝑏𝑤 𝐹𝑦𝑏

𝐹𝑦𝑠 (Re. AISC 358-05, Eq. 6.9-13).

The stiffener material is assumed to be A250 ESP. Therefore:

𝑡𝑠,𝑚𝑖𝑛 = 8 𝑚𝑚

The stiffener geometry shall conform to the requirements of section 6.9.4 of

AISC 358-05. In addition, to prevent local buckling of the stiffener plate, the

following width-to-thickness criterion shall be satisfied:


6-39

𝑕𝑠𝑡

𝑡𝑠≤ 0.56

𝐸

𝐹𝑦𝑠 (Re. AISC 358-05, Eq. 6.9-14).

In this case, with the following geometry for the stiffener, all the checks are

OK:

𝐿𝑠𝑡 = 210 𝑚𝑚, 𝑕𝑠𝑡 = 120 𝑚𝑚, 𝑡𝑠 = 10 𝑚𝑚

The stiffener-to beam flange and stiffener-to-end-plate welds shall be designed

to develop the stiffener plate in shear at the beam flange and in tension at the

end-plate. For the weld to beam flange, CJP groove or fillet welds can be

used. If the stiffener plate thickness is greater than 10 mm, CJP groove welds

shall be used for the stiffener-to-end-plate weld. Otherwise, double-sided fillet

welds are permitted to be used.

On this case, use CJP groove welds for both connections (stiffener-to-end-

plate and stiffener-to-beam-flange) since the stiffeners thickness is equal

to the critical value of 10 mm.

18. The bolt shear rupture strength of the connection is provided by the bolts

at one (compression) flange

The procedure is the same as the one on example 6.1, calculations give:

𝜙𝑛 𝑛𝑏 𝐹𝑣𝐴𝑏 = 1054 𝑘𝑁 > 𝑉𝑢 = 468 𝑘𝑁 OK

19. Check the bolt-bearing/tear out of the end plate and column flange

The procedure is the same as on example 6.1, calculations give:

End-plate side:

𝜙𝑛𝑅𝑛 = 3130 𝑘𝑁 > 𝑉𝑢 = 468 𝑘𝑁 OK

Column flange side:

𝜙𝑛𝑅𝑛 = 2862 𝑘𝑁 > 𝑉𝑢 = 468 𝑘𝑁 OK

20. Design the flange to end plate and web to end plate welds, using the

requirements of the section 6.9.7 of AISC 358-05 code

The procedure is the same as in example 6.1.


6-40

Beam flanges to end-plate weld:


weld.

Beam web to end-plate weld:

Use a pair of fillet welds, with 𝒕𝒘 = 𝟏𝟎 𝒎𝒎, E70 electrodes.

21. Check the column flange for flexural yielding

The procedure is the same as on example 6.1. Doing the calculations first for

the unstiffened column flange, 𝑡𝑐𝑓𝑅𝐸𝑄 = 31.9 𝑚𝑚 < 𝑡𝑐𝑓 . So far, there is no needing

of continuity plates (web stiffeners).

22. If stiffeners are required for column flange flexural yielding, calculate the

required stiffener force

In this case, there was no need for stiffening the column web.

23. Check the local column web yielding strength of the unstiffened column

web at the beam flanges

The strength requirement is:

𝜙𝑑𝑅𝑛 ≥ 𝐹𝑓𝑢

With 𝑅𝑛 = 𝐶𝑡 6𝑘𝑐 + 𝑡𝑏𝑓 + 2𝑡𝑝 𝐹𝑦𝑐 𝑡𝑐𝑤 . Same as example 6.1, calculations give

𝜙𝑑𝑅𝑛 = 620 𝑘𝑁 < 𝐹𝑓𝑢 = 1837 𝑘𝑁 → Continuity web plates are required

24. Check the unstiffened column web buckling strength at the beam

compression flange





6-41

25. Check the unstiffened column web crippling strength at the beam

compression flange

Procedure is the same as example 6.1, calculations give:

𝜙𝑅𝑛 = 551 𝑘𝑁 < 𝐹𝑓𝑢 = 1837 𝑘𝑁 → Continuity web plates are required

26. If stiffener plates are required for any of the column side limit states, the

required strength is

𝐹𝑠𝑢 = 𝐹𝑓𝑢 −𝑚𝑖𝑛𝜙𝑅𝑛 = 1337 𝑘𝑁

(Compression force due column web crippling controls)

27. Continuity Plate / Panel Zone / Column-Beam Moment Ratio / Lateral

Bracing

Note that the section used on this example are the same as example 6.1 The

forces obtained (𝐹𝑓𝑢and 𝐹𝑠𝑢) and the end-plate thickness 𝑡𝑝 on this example are

different than on the example 6.1; nevertheless, the procedure for the design

of the panel zone (doubler plates and transverse web stiffeners) and lateral

bracing is the same. No specific design or calculations will be done on this

example.

6.2-3: Designed Connection.

4 M30 ASTM A490

4 M30 ASTM A490

PL 210x740x35 mm

Beam: H 450 x 150 x 68.4

CJP

Column: H 450 x 250 x 149.8

Note:

Doubler and web plates and their

connections are not designed

10

10Typ

Stiffener details

hst = 120 mm

Lst = 210 mm

Bolts positions

pfo= 60 mm

pfi = 60 mm

de = 60 mm

g= 140 mm

g

pfi

de

pfo

CJP


6-42

Notes

There are some assumptions inherent to the design procedure presented on

this example (See AISC Design Guide # 4). A summary of those assumptions

(not explicit in the document) follows:

All bolts are tightened to a pretension not less than AISC requirement.

However, slip critical connections requirements are not needed in this

case.

Only ASTM A325 or ASTM A490 bolts are permitted.

It is assumed that all the shear force is resisted by the compression side

bolts.

Beam web to end plate welds in the vicinity of the tension bolts are

designed to develop the yield stress of the beam web. This weld strength

is recommended even if the full moment capacity of the beam is not

required for frame strength.

Only the web to end plate weld between the mid-depth of the beam and

the inside face of the beam compression flange may be used to resist the

beam shear (based on judgment).

Yield-line analysis is used for end-plate strength calculation.

Bolt prying forces are not a consideration, since the required end plate

thickness prevents their development.


6-43

6.3. Reduced Beam Section (RBS) Moment Connection.


1. NCh2369.Of2003

Use high strength bolts (ASTM A325 or ASTMA490).

(Re. NCh2369.Of2003, 8.5.1)



connection.

(Re. NCh2369.Of2003, 8.5.6)

Beam-to-column connections of seismic frames must have, at least, a

resistance equal to the resistance of connected elements.

(Re. NCh2369.Of2003, 8.5.3)

In beam – to - column connections of rigid frames, the upper and

lower flanges of the beam should have lateral braces or supports

designed for a force equal to 0.02𝐹𝑦𝑏𝑓𝑡𝑓.

(Re. NCh2369.Of2003, 8.5.4)

Moment connections of rigid frames for seismic applications shall be

of FR type (fully restricted). The connections shall be designed in a

way such that the plastic hinge is developed at a safe distance from

the column, which can be obtained by strengthening the connection

or weakening the beam in the desired position for the plastic hinge.

(Re. NCh2369.Of2003, 8.4.1)

Transverse sections of columns and beams in rigid earthquake-

resistant frames shall qualify as compact, that is, their width to

thickness ratios shall be lesser than 𝜆𝑝 given on Table 8.1 of the code.

(Re. NCh2369.Of2003, 8.4.2)

Appendix B (normative appendix) of the NCh2369.Of2003 refers to

the design of beam-column connection on rigid frames.

(Re. NCh2369.Of2003, App. B)


6-44

2. AISC 341-05


(SMF) it is recommended to see Chapter 9 of AISC 341-05. Some important


The required shear strength should be calculated taking into account the

flexural plastic hinges produced by the earthquake (E) load. For more

beam-to-column connections requirements, see section 9.2a

Unless otherwise defined by AISC 358, CJP groove welds of beam flanges,

shear plates, and beam webs to column shall be demand critical welds as

defined in section 7.3b (section 9.2c).

The protected zone is defined in AISC 358. In general, for unreinforced


one half of the beam depth beyond the plastic hinge point (section 9.2d).

For the design requirements of panel zone of beam – to - column

connections: see section 9.3.

For beam and column limitations, see section 9.4.


according to AISC 358 (section 9.5).




Rolled Wide-Flange Members and Built-up Members

Some limitations shall be considered for the member shapes, see sections

2.3.1 and 2.3.2 of AISC 358.

LRFD Reduction Factors

When available strengths are calculated according to AISC 358, use for ductile

limit states 𝜙𝑑 = 1.0, and for non-ductile limit states 𝜙𝑛 = 0.9. If AISC 360 is

used for calculating available strengths, use the reduction factors stipulated

there.

Plastic Hinge Location and Probable Maximum Moment at Plastic Hinge (𝑀𝑝𝑟 )

This location is shown for each type of connection. For the 𝑀𝑝𝑟 calculation, see

Eq. 2.4.3-1.


6-45

Continuity plates, panel and protected Zones

For continuity plates, refer to 2.4.4 section of AISC 358-05.

Panel and protected zones: for SMF systems, panel zones shall conform to the

minimum requirements of section 9.3 of AISC 341-05. The protected zone

shall be as defined for each prequalified connection and it shall meet the

requirements of section 7.4 of AISC 341-05.

Welding Requirements

Filler metals and welding procedures shall meet the requirements of section

7.3 and Appendix W of the AISC 341-05 code.

For backing at beam to column and continuity plate to column joint, see AISC

358-05, section 3.3.

Bolt Requirements

Use only ASTM A325 or ASTM A490 bolts. They shall be pretensioned high

strength bolts.

(Re. AISC 358-05, 4.1)

6.3.b. Example

Design a reduced beam section (RBS) moment connection for the beam to

column exterior connection shown in Figure Figure 6.3-1. Use A345 ESP steel,

required for constructions subjected to dynamical loading, according to

NCh203.Of2006 code, Table 3.

The sections used are H 600 x 300 x 229.2 for the beam and H 450 x 450 x

355.2 for the column (both are Chilean Shapes). Suppose that beams and

columns have been properly designed for resisting the forces produced by the

load combinations of the applicable building code (including seismic loads).


and IMF systems) for Seismic Applications”.


6-46

Figure 6.3-1: Connection to be designed. Frontal and plan view.


H 600 x 300 x 229.2




H 450 x 450 x 355.2




A345 ESP


𝐹𝑦 = 345 𝑀𝑃𝑎 , 𝐹𝑢 = 450 𝑀𝑃𝑎

reduced beam section

column

continuity plates

(if required)

doubler plates

(if required)

Reduced Beam Section


6-47

Both sections have seismically compact web and flanges, according to AISC

341-05 Table I-8-1.

6.3.c. Restrictions for prequalification according to AISC 358

Base on the steps listed on Chapter 5 of AISC 358-05, consider supplement

N°1.

Tip

The intention of designing a reduced beam section is to move the plastic hinge

location away from the column face. This is achieved by removing a portion of

the beam flanges and, thus, weakening the beam so as to force the plastic

hinge to occur at a specified location.



Beam limitations:

Beam section must comply with the limitations of section 2.3 of AISC 358-

05. Beams shall be rolled wide-flange or built-up I members.

Depth of the beam is limited to W36 for rolled shapes. For built-up

shapes, use the maximum depth for wide flange rolled shapes. (OK)

Weight limited to 447 kg/m: Beam weight is 229.2 kgf/m < 447 kgf/m

(OK).

Flange thickness < 44.5 mm (OK)

Clear span to depth ratio: greater or equal to 7 for SMF systems.

Suppose the clear span to be OK with this.

Width thickness ratios for flanges and web of the beam shall conform to

the limits on AISC 341-05.(OK)

Lateral bracing: according to section 9.8 of AISC 341-05 (SMF systems).

For supplemental lateral bracing at the reduced section, also refer to the

same section. The location of this supplemental lateral bracing shall be

located no longer than d/2 beyond the end of the RBS farthest from the

face of the column (d=beam depth). No attachment shall be made to the

beam in the region extending from the face of the column to end of the

RBS farthest from the face of the column. (See also exception where the

beam supports an structural slab).

Protected zone: from the face of the column to the end of the RBS section

farthest from the column face


6-48

Column limitations:

Note: See also AISC 358-05, Supplement N°1 corresponding section.

Column sections can be rolled or built-up. Comply with AISC 358-05,

section 2.3.

Depth of the column is limited to W36 for rolled shapes. For built-up

shapes, use the maximum depth for rolled shapes. (OK)

Width thickness ratios for flanges and web of the beam shall conform to

the limits of section 9.4 of AISC 341-05. (OK)

Lateral bracing: according to section 9.7 of AISC 341-05 (SMF systems).

2. Beam-to-column relationship limitations


Panel zones: comply with the requirement of section 9.3 (SMF systems) of

AISC 341-05.

See 5.4.2a for column-beam moment ratio calculation at this RBS

connection.

3. Beam flange to column flange weld limitations


Beam flanges to column flange: use of CJP groove welds and conform to

the requirements for demand critical weld in section 7.3 and appendix W

of AISC 341-05.

Weld access holes: according to AISC 360-05 Specification, section J1.6

4. Beam web to column connection limitations

(Re. AISC 358-05, Section 5.6.)

Required shear strength of the beam web connection: according to Eq.

5.8-9 of AISC 358-05.

Detailing of web connection (SMF systems):

Beam web shall be connected to the column flange using a CJP groove weld

extending between weld access holes. The single plate shear connection shall

be permitted to be used as backing for the CJP groove weld. Plate thickness


6-49

must be at least 10 mm. Weld tabs are not required at the end of the CJP

groove weld at the beam web. Bolt holes in the beam web for the purpose of

erection are permitted.

5. Fabrication of flange cuts

Refer to section 5.7 of AISC 358-05.

6.3.d. Design procedure according to AISC 358


Note:

The AISC 358-05 notation has been adopted for the design procedure.

1. Chose trial values for RBS dimensions 𝑎,𝑏 and 𝑐 (see Figure Figure 6.3-2):

0.5𝑏𝑏𝑓 ≤ 𝑎 ≤ 0.75𝑏𝑏𝑓

0.65𝑑 ≤ 𝑏 ≤ 0.85𝑑

0.1𝑏𝑏𝑓 ≤ 𝑐 ≤ 0.25𝑏𝑏𝑓

With 𝑏𝑏𝑓 = 300 𝑚𝑚 and 𝑑 = 600 𝑚𝑚.

Try: 𝑎 = 190 𝑚𝑚, 𝑏 = 450 𝑚𝑚, 𝑐 = 60 𝑚𝑚

Figure 6.3-2: Notation (used on AISC 358-05) for reduced beam section

moment connection. Adapted from AISC 358-05, Fig. 5.1.

R = Radius of Cut = (4c + b)/8c2

a b

Reduced Beam

Section

c

c

Protected Zone


6-50

2. Compute the plastic section modulus at the center of the reduced beam

section

𝑍𝑒 = 𝑍𝑥 − 2𝑐𝑡𝑏𝑓 𝑑 − 𝑡𝑏𝑓 = 4708000 𝑚𝑚3 (Re. AISC 358-05, Eq. 5.8-4)

3. Compute the probable maximum moment at the center of the reduced

beam section

𝑀𝑝𝑟 = 𝐶𝑝𝑟𝑅𝑦𝐹𝑦𝑍𝑒 (Re. AISC 358-05, Eq. 5.8-4).

Use 𝐶𝑝𝑟 =𝐹𝑦+𝐹𝑢

2𝐹𝑢= 1.15 and 𝑅𝑦 = 1.1 for A345 ESP steel (similar to ASTM A572 Gr.

50) according to table I-6-1 of AISC 341-05. Then:

𝑀𝑝𝑟 = 2058573 𝑘𝑁 −𝑚𝑚

4. Compute the shear force at the center of the RBS‟s at each end of the

beam

Use a free body diagram of the portion of the beam between the centers of the

RBS sections. Consider the 𝑀𝑝𝑟 moments acting at the center of each RBS

section and include gravity loads (use combination 1.2D+1.0L):

Figure 6.3-3: Example of calculation of shear at center of RBS cuts. The lower image is the free body diagram of the portion of the beam between the RBS’s.

Adapted from AISC 358-05 (Commentary), Fig.C-5.1.

From Figure 6.3-3:


6-51

𝑉𝑅𝐵𝑆 =2𝑀𝑝𝑟

𝐿′+𝑤𝐿′

2

And

𝑉𝑅𝐵𝑆′ =

2𝑀𝑝𝑟

𝐿′−𝑤𝐿′

2

Note: Consider 𝑤 = 𝑤𝑢= factored uniform beam gravity load.

Assume that 𝐿𝑛=distance between column flanges (nearest to beam ends)

equal to 6000 mm. and:

𝑆𝑕 = 𝑎 +𝑏

2= 415 𝑚𝑚

Then: 𝐿′ = 𝐿𝑛 − 2𝑆𝑕 = 5170 𝑚𝑚.

Assume as gravity loads:

𝑤𝐷 = 0.03𝑘𝑁

𝑚𝑚,𝑤𝐿 = 0.016

𝑘𝑁

𝑚𝑚→ 𝑤𝑢 = 1.2𝑤𝐷 + 1.0𝑤𝐿 = 0.052

𝑘𝑁

𝑚𝑚

Therefore: 𝑉𝑅𝐵𝑆 = 931 𝑘𝑁 ,𝑉𝑅𝐵𝑆′ = 662 𝑘𝑁

5. Compute the probable maximum moment at the face of the column

Use a free body diagram of the segment of the beam between the center of

the RBS and the face of the column (see the following figure). Therefore:

𝑀𝑓 = 𝑀𝑝𝑟 + 𝑉𝑅𝐵𝑆𝑆𝑕 = 2444843 𝑘𝑁 −𝑚𝑚 (Re. AISC 358-05, Eq. 5.8-6)

Use 𝑉𝑅𝐵𝑆 = max(𝑉𝑅𝐵𝑆 ,𝑉𝑅𝐵𝑆′ ) in Eq. 5.8-6 of AISC 358-05, the gravity load of the

mentioned segment was neglected (optionally this effect could be included).

Figure 6.3-4: Free body diagram between center of RBS and face of the

column. Adapted from AISC 358-05, Fig. 5.2.


6-52

6. Compute the plastic moment of the beam based on the expected yield

stress

𝑀𝑝𝑒 = 𝑍𝑏𝑅𝑦𝐹𝑦 = 2806782 𝑘𝑁 −𝑚𝑚 (Re. AISC 358-05, Eq. 5.8-7).

Use 𝑍𝑏 = 𝑍𝑥 of the beam.

7. Check the strength of the beam at the face of the column

𝑀𝑓 ≤ 𝜙𝑑𝑀𝑝𝑒

(Re. AISC 358-05, Eq. 5.8-8)

If the previous equation is not satisfied, increase the value of 𝑐 and/or

decrease the values of 𝑎 and 𝑏 and repeat previous steps. On this case

(𝜙𝑑 = 1.0): 𝑀𝑓 ≤ 𝜙𝑑𝑀𝑝𝑒 . OK.

8. Calculate the required shear strength of beam and beam web-to-column

connection from

𝑉𝑢 =2𝑀𝑝𝑟

𝐿′+ 𝑉𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 𝑉𝑅𝐵𝑆 + 𝑤𝑢 𝑎 +

𝑏

2 = 952 𝑘𝑁

Check the shear strength of the beam according to Chapter G of AISC 360-05

Specification. According to this chapter, for I members with:

𝑕

𝑡𝑤= 52 ≤ 2.24

𝐸

𝐹𝑦= 53.93 → 𝜙𝑉𝑛 = 1.0 × 0.6𝐹𝑦𝐴𝑤 = 1242 𝑘𝑁 > 𝑉𝑢

9. Design the beam flange to column and beam web-to-column connections

according to AISC 358-05, sections 5.5 and 5.6

Beam flange to column connection:

Meeting with AISC 358-05 requirements, section 5.5, use CJP groove welds

(demand critical). Weld access holes geometry must comply with AISC 360-05,

Section J1.6. For weld access holes geometry, select a depth of 40 mm and a

height equal to 25 mm.


6-53

Beam web to column connection:

Meeting with AISC 358-05 requirements, section 5.6; the required force to be

transmitted is 𝑉𝑢 = 952 𝑘𝑁. Then:

Use CJP groove weld for the beam web to column flange connection. Select a

10 mm thick single plate (to support erection loads) that can be used as

backing for the CJP groove weld.

Check the beam web shear strength:

𝑉𝑛 = 𝜙 0.6𝐹𝑦𝐴𝑔 , 𝜙 = 1.0 (Re. AISC 360-05, Eq. J4-3)

Use for 𝐴𝑔 the beam web area, discounting the weld access holes height:

𝐴𝑔 = 𝑡𝑤 𝑕 − 2 × 25 𝑚𝑚 = 4700 𝑚𝑚2 → 𝜙𝑉𝑛 = 973 𝑘𝑁 > 𝑉𝑢 = 952 𝑘𝑁 OK

6.3.e. Panel Zone / Continuity Plate / Column-Beam Moment Ratio /

Lateral Bracing according to AISC Code

1. Panel zone

Check the column panel zone according to AISC 358-05, Section 5.4. This

section refers to AISC 341-05, Section 9.3 (SMF Systems):

2. Shear strength of the panel zone

(Re. AISC 341-05, Section 9.3a)

Consider the following figure (for a general interior connection):


6-54

Figure 6.3-5: Typical panel zones forces.

Figure adapted from AISC Design Guide N°13, Fig. 2-3.

The total panel zone shear 𝑉𝑢 can be calculated with the beam flange forces

(𝑃𝑢𝑓𝑖 = 𝑀𝑢𝑖 /(𝑑𝑖 − 𝑡𝑏𝑓𝑖 )) and the story shear 𝑉𝑢𝑠 . According to figure above,

𝑉𝑢 = 𝑃𝑢𝑓1 + 𝑃𝑢𝑓2 − 𝑉𝑢𝑠 . On this case, neglect the story shear and compute

𝑉𝑢 = 𝑃𝑢𝑓 =𝑀𝑓

𝑑−𝑡𝑏𝑓= 4366 𝑘𝑁 (exterior connection).

The shear strength is:

𝜙𝑅𝑣 = 1.0 × 0.6𝐹𝑦𝑑𝑐𝑡𝑤(1 +3𝑏𝑐𝑓 𝑡𝑐𝑓

2

𝑑𝑏𝑑𝑐 𝑡𝑤) = 3074 𝑘𝑁 (Re. AISC 360-05, Eq. J10-11).

Note: suppose that frame stability is considered in the analysis and that

𝑃𝑢 < 0.75𝑃𝑦.

Therefore, 𝜙𝑅𝑣 < 𝑉𝑢 , so web doubler plates are required.

Tip

Generally, a better solution than using web doubler plates is to choose a

column with a thicker web, eliminating the need for the doubler plates which

have details that are expensive and difficult to fabricate.

3. Panel zone thickness

(Re. AISC 341-05, Section 9.3b)

For the column web and each doubler plate:

V us

V us

P uf 1

M u 1

V u

P uf 1

P uf 2

P uf 2

M u 2


6-55

𝑡 ≥𝑑𝑧 + 𝑤𝑧

90

Suppose that the continuity plate dimensions are 𝑒𝑠 = 30 𝑚𝑚 (thickness) and 𝑏𝑠

(width, which is going to be defined later).

The panel zone dimension between continuity plates is 𝑑𝑧 = 𝑑𝑏 − 𝑡𝑓𝑏 − 𝑒𝑠 =

530 𝑚𝑚 (𝑑𝑏 = depth of the beam). The panel zone dimension between column

flanges is 𝑤𝑧 = 𝑕𝑐𝑜𝑙𝑢𝑚𝑛 = 370 𝑚𝑚. Then 𝑡 ≥ 10 𝑚𝑚 (column web thickness is OK).

4. Panel zone doubler plates

(Re. AISC 341-05, Section 9.3c)

Welds to column flanges:

Use CJP or fillet welds that develop the available shear strength of the full

doubler plate thickness.

When placed against column web:

Doubler plates shall be welded top and bottom edge to develop the proportion

of the total force that is transmitted to the doubler plate.

When placed away from column web:

Doubler plates must be placed symmetrically in pairs and welded to continuity

plates to develop the proportion of the total force that is transmitted to the

doubler plate.

Size the doubler plates:

Use A345 ESP for the doubler plates and for calculating the thickness of

the doubler plates, consider them acting on shear yielding and developing the

proportion of the total force transmitted to them (𝜙 = 1.0):

2𝑡𝑑𝑝 ≥𝑉𝑢 − 𝜙𝑣𝑅𝑣

𝜙0.6𝐹𝑦𝑤𝑧

= 16.9 𝑚𝑚

Use 𝟐𝒕𝒅𝒑 = 𝟐𝟎 𝒎𝒎 → 𝒕𝒅𝒑 = 𝟏𝟎 𝒎𝒎 ≥ 𝒕𝒅𝒑𝒎𝒊𝒏 = 𝟏𝟎 𝒎𝒎 OK.


6-56

If considering the doubler plates to be CJP groove welded to the column

flanges, use for the doubler plates width 𝑩𝒅𝒑 = 𝒅𝒄 − 𝟐 𝒕𝒇𝒄 + 𝒔𝒄 = 𝟑𝟒𝟐 𝒎𝒎. For

the depth of the doubler plates, consider the distance between continuity

plates: 𝑫𝒅𝒑 = 𝒅𝒃 − 𝒕𝒃𝒇 − 𝒆𝒔 = 𝟓𝟑𝟎 𝒎𝒎.

Figure 6.3-6: Doubler plate dimensions.

Welded unions of the doubler plates:


for Chapter 6 on this Manual.


Check continuity plate requirements according to AISC 358-05, Chapter 2

The need for continuity plate is checked according to Section 2.4.4. of AISC

358-05 Code:

𝑡𝑐𝑓 = 40 𝑚𝑚 < 0.4 1.8𝑏𝑏𝑓 𝑡𝑏𝑓 𝐹𝑦𝑏 𝑅𝑦𝑏

𝐹𝑦𝑐 𝑅𝑦𝑐= 58.8 𝑚𝑚 → Continuity plates are required.

𝑡𝑐𝑓 = 40 <𝑏𝑏𝑓

6= 50 𝑚𝑚 → Continuity plates are required.

A

Section A - A

Ddp

tfc

Bdp

s c

d c

A

tdp

tdp


6-57

6. Thickness of the continuity plates

(Re. AISC 358-05, Section 2.4.4a)

For this exterior connection: 𝑒𝑠 ≥1

2𝑡𝑏𝑓 = 20 𝑚𝑚.

7. Requirements of AISC 360-05 Specification, J10 Section

Calculate the concentrated force(s) acting on the beam flange, using the

moment projected at the column flange side (𝑀𝑓):

𝑅𝑢 =𝑀𝑓

𝑑−𝑡𝑓𝑏= 4366 𝑘𝑁 (Tension and compression)

Calculate the available strengths, according to the following limit states:

Flange Local Bending (caused by the tension 𝑅𝑢):

𝜙𝑅𝑛 = 0.9 × 6.25𝑡𝑐𝑓2 𝐹𝑦𝑓 = 3105 𝑘𝑁 < 𝑅𝑢

Web local yielding:

Suppose that the concentrated force to be resisted is applied at a distance

from the column end, greater than 𝑑𝑐. Therefore:

𝑅𝑛 = 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑐𝑤 , 𝜙 = 1.0

Use: 𝑘 = 𝑡𝑐𝑓 + 𝑠𝑐 = 54 𝑚𝑚 , 𝑁 = 𝑡𝑏𝑓 = 40 𝑚𝑚 to obtain:

𝜙𝑅𝑛 = 2674 𝑘𝑁 < 𝑅𝑢

Web crippling:

Suppose that the concentrated force to be resisted is applied at a distance

from the column end greater than 𝑑𝑐/2. Therefore:

𝑅𝑛 = 0.8𝑡𝑐𝑤2 1 + 3

𝑁

𝑑𝑐

𝑡𝑐𝑤

𝑡𝑐𝑓

1.5

𝐸𝐹𝑦𝑤 𝑡𝑐𝑓

𝑡𝑐𝑤 .

Use 𝜙 = 0.75 to obtain:

𝜙𝑅𝑛 = 4459 𝑘𝑁 > 𝑅𝑢


6-58

Web sidesway buckling:

According to AISC 360-05 Commentary this limit state does not apply for

moment connections.

Web compression buckling:




From last limit states, calculate the difference between the applied force and

the minimum available strength (web local yielding on this case)

𝑅𝑠𝑢𝐶𝑂𝑀𝑃𝑅𝐸𝑆𝑆𝐼𝑂𝑁 = 𝑅𝑢 − min 𝜙𝑅𝑛 = 1692 𝑘𝑁

From the first limit state, calculate the difference between the applied force

and the available strength (flange local bending on this case):

𝑅𝑠𝑢𝑇𝐸𝑁𝑆𝐼𝑂𝑁 = 𝑅𝑢 − 𝜙𝑅𝑛 = 1261 𝑘𝑁

Size the continuity plates:

Use A345 ESP for continuity plates. Try 𝒆𝒔 = 𝟑𝟎 𝒎𝒎 (continuity plate

thickness), 𝒃𝒔 =𝟏

𝟐 𝒃𝒃𝒇 − 𝒕𝒄𝒘 = 𝟏𝟑𝟕.𝟓 𝒎𝒎 (continuity plate width, first trial to

match the beam flanges) and 𝑳𝒔 = 𝒉𝒄 = 𝟑𝟕𝟎 𝒎𝒎 (continuity plate depth, use the

column height between flanges).


6-59

Figure 6.3-7: Continuity plates dimensions.

Check additional stiffener requirements from AISC 360-05

(Re. AISC 360-05, Section J10.8)

𝑏𝑠 +1

2𝑡𝑐𝑤 = 150 𝑚𝑚 ≥

1

3𝑏𝑏𝑓 = 100 𝑚𝑚 OK

𝑒𝑠 ≥ 𝑚𝑎𝑥 1

2𝑡𝑏𝑓 ,

𝑏𝑠

15 = 20 𝑚𝑚 OK

Check also from AISC 358-05, 2.4.4a (exterior connection):

𝑒𝑠 ≥1

2𝑡𝑏𝑓 = 20 𝑚𝑚. OK

Compression check for the continuity plates:

As said on AISC 360-05, section J10.8, use an effective length of 0.75𝑕 (277.5

mm) and a cross section composed of 2 stiffeners and a portion of the web

having a width of 12𝑡𝑤 (exterior stiffener)

Figure 6.3-8: Section of continuity plates plus web fraction resisting

compression force.

A A

e s

L s

b s

b bftcw

Section A - A

bs

es

bs

es

tw

12tw


6-60

According to the previous figure, the properties of the section to resist

compression are:

𝐴 = 2𝑏𝑠𝑒𝑠 + 12𝑡𝑐𝑤2 , 𝐼 =

2𝑏𝑠𝑒𝑠3

12+𝑡𝑐𝑤 12𝑡𝑐𝑤

3

12, 𝑟 =

𝐼

𝐴= 60 𝑚𝑚

Use 𝑘 = 1.0.

According to AISC 360 J4.4 Section 𝑘𝐿

𝑟= 4.618 < 25 → Use Chapter J.

𝜙𝑃𝑛 = 0.9𝐹𝑦𝐴 = 4890 𝑘𝑁 > 𝑅𝑢 OK

Tension check of the continuity plates:

According to Chapter D of AISC 360-05, for each stiffener the tension strength

is:

𝜙𝑅𝑛 = 0.9𝐹𝑦𝑏𝑠𝑒𝑠 = 1280 𝑘𝑁 >𝑅𝑠𝑢𝑇𝐸𝑁𝑆𝐼𝑂𝑁

2= 630 𝑘𝑁 OK

Note:

As it can be seen, the section for compression check is a “cross” (including a

portion of the column web) and it is checked for 𝑅𝑢 while the section for

tension check are the two separated stiffeners (no web portion) and they are

checked for 𝑅𝑠𝑢𝑇𝐸𝑁𝑆𝐼𝑂𝑁 .

Welded unions of the continuity plates:


of Chapter 6 on this Manual.

8. Column-beam moment ratio

According to AISC 358-05, Section 5.4; for SMF systems the column-beam

moment ratio shall comply with (assume that the factored axial force on the

column is 𝑃𝑢𝑐 = 1000 𝑘𝑁):

𝑀𝑝𝑐

∗

𝑀𝑝𝑏∗ > 1.0 (Re. AISC 341-05, Eq. 9-3)

With:

𝑀𝑝𝑐∗ = 𝑍𝑐 𝐹𝑦𝑐 −

𝑃𝑢𝑐𝐴𝑔

= 2𝑍𝑐 𝐹𝑦𝑐 −𝑃𝑢𝑐𝐴𝑔

= 5318817 𝑘𝑁 −𝑚𝑚


6-61

And:

𝑀𝑝𝑏∗ = 𝑀𝑝𝑟 + 𝑀𝑣 = 𝑀𝑝𝑟 + 𝑉𝑅𝐵𝑆(𝑎 +

𝑏

2+𝑑𝑐

2) = 2654268 𝑘𝑁 −𝑚𝑚.

Therefore:

𝑀𝑝𝑐

∗

𝑀𝑝𝑏∗ = 2.003 > 1.0 OK

9. Lateral bracing

Beam lateral bracing:

According to section 9.8 of AISC 341-05, both beam flanges shall be laterally

braced, with a maximum spacing of 𝐿𝑏 =0.086𝑟𝑦𝐸

𝐹𝑦= 3914 𝑚𝑚. (Use 𝑳𝒃 =

𝟑𝟎𝟎𝟎 𝒎𝒎). Assume that with this lateral spacing, the beam can properly

support the loads.

Meet the provisions of Appendix 6 of AISC 360-05:

Required brace strength:

𝑃𝑏𝑟 =0.02𝑀𝑟𝐶𝑑

𝑕𝑜= 100.2 𝑘𝑁. (Re. AISC 360-05, Eq. A-6-7)

Use 𝑀𝑟 = 𝑅𝑦𝐹𝑦𝑍𝑏 , 𝐶𝑑 = 1.0, 𝑕𝑜 = (𝑑𝑏 − 𝑡𝑏𝑓 )

Required brace stiffness (𝜙 = 0.75):

𝛽𝑏𝑟 = 1

𝜙

10𝑀𝑟𝐶𝑑

𝐿𝑏𝑕𝑜 = 22.3 𝑘𝑁/𝑚𝑚 (Re. AISC 360-05, Eq. A-6-8)

Supplemental beam lateral bracing (at hinge location):

Assume that the connection between the beam and the slab is made with

shear welded connectors provided by 300 mm. Therefore, according to AISC

358-05, supplemental top and bottom flange lateral bracing at RBS section is

not required.


6-62

Tip

The reduction of the beam flange can significantly reduce the stiffness (and

stability) of the beam cross section, creating a greater propensity for LTB

lateral torsional buckling of the beam in the reduced section. The addition of

lateral bracing near the RBS may be required if a structural slab is not present

or if above minimum acceptable performance is desired.

Column lateral bracing:

According to section 9.7 of AISC 341-05, column flanges require lateral

bracing only at the beam top flange level if it is shown that the column

remains elastic outside the panel zone. Then: 𝑀𝑝𝑐

∗

𝑀𝑝𝑏∗ = 2.003 > 2.0 . And,

considering the user note in the same section; column lateral bracing can be

achieved by the use of braces, decks, slabs, and also with indirect lateral

bracing. Therefore, there is no need for designing a specific brace for column.

6.3.f. Panel Zone / Continuity Plate /Column-Beam Moment Ratio /

Lateral Bracing according to NCh2369.Of2003 Code

Refer to Chapter 8 and Appendix B (Beam-to-Column unions on rigid steel

frames) of NCh2369.Of2003 Code.

Note: According to Appendix B, the provisions of NCh2369.Of2003 code for

rigid unbraced frames are normative, and the designer does not have to take

account the additional obligatory requirements of AISC 341-1999 (SMF

systems and IMF systems). On this example, it has been made a design using

AISC 341 and AISC 358 codes, but it is going to be checked with the

NCh2369.Of2003 code.

1. Panel zone

(Re. NCh2369.Of2003, B.2)

As said on B.2.1, the analysis can be done with elastic or plastic methods. The

panel zone shall be retrofitted with doubler plates and/or diagonal stiffeners

(see Figures B.1 and B.2 of the code) if 𝑅𝑢 > 𝜙𝑅𝑣 = 0.75𝑅𝑣

(Re. NCh2369.Of2003, B.2.2).

The calculation of 𝑅𝑢 and 𝑅𝑣 is quite similar to AISC 341 code. Considering an

internal connection:


6-63

𝑅𝑢 =𝑀𝑢1

𝑑𝑚1+

𝑀𝑢2

𝑑𝑚2− 𝑉𝑢 (Re. NCh2369.Of2003, Eq. B-1)

With 𝑀𝑢𝑖=beam moments (not greater than plastic beam moments, on this

case use 𝑀𝑢 = 𝐹𝑦𝑍𝑒 = 1624260 𝑘𝑁 −𝑚𝑚 assuming that the plastic hinge is going

to be developed on the RBS section) calculated using the load combinations of

the code and the amplification of the earthquake term by 2; 𝑑𝑚𝑖 = 0.95𝑑𝑖 ,

𝑉𝑢=shear force in the column at the level of the union (neglect it as on the

previous design).

Assume that 𝑃𝑢 ≤ 0.75𝑃𝑦, therefore the calculation of:

𝜙𝑅𝑣 = 0.75 × 0.6𝐹𝑦𝑑𝑐𝑡𝑝 1 +3𝑏𝑐𝑓 𝑡𝑐𝑓

2

𝑑𝑏𝑑𝑐 𝑡𝑝 is quite similar to the AISC 341 code, but

using a 𝜙 = 0.75 and 𝑡𝑝 = 𝑡𝑐𝑤 + 2𝑡𝑑𝑝 instead of only 𝑡𝑐𝑤 .

Considering then the doubler plates designed on the previous stage (2 plates,

𝑡𝑑𝑝 = 10 𝑚𝑚 ), calculations give: 𝜙𝑅𝑣 = 3702 𝑘𝑁 > 𝑅𝑢 = 2850 𝑘𝑁 doubler plate

thickness is OK.

According to section B.2.5, the minimum thickness of the column web and

doubler plates must be the same as AISC 341 code.

2. Some welding requirements of doubler plates:

(Re. NCh2369-Of2003, B.2.4 and B.8)

Doubler plates shall be welded to the column flanges with fillet or CJP groove

welds designed to resist the shear required strength (on seismic frames, the

welds shall resist the total shear strength of the doubler plate). If they are

against the column web, they shall be welded on their bottom and top ends

(and the welds must resist the proportion of the force transmitted to the

doubler plates). If they are away from the column web, doubler plates shall be

placed symmetrically and welded to the continuity plates (and the welds must

resist the proportion of the force transmitted to the each one of the doubler

plates).

Note:

As seen, the previous provisions are quite similar to AISC provisions. Refer to

Welded Connection Commentary for Continuity Plates and Doubler Plates of

Chapter 6 on this Manual.


6-64


(Re. NCh2369.Of2003, B.3 to B.6)

Limit states check list:

Flange local bending

Equal to AISC code

𝜙𝑅𝑛 = 0.9 × 6.25𝑡𝑐𝑓2 𝐹𝑦𝑓 = 3105 𝑘𝑁 > 𝑅𝑢 =

𝑀𝑢

𝑑𝑏 − 𝑡𝑏𝑓= 2900 𝑘𝑁

See the additional requirements on B.3.2 to B.3.3

Web local yielding

Similar to AISC code, except that if 𝑁 < 𝑘 → take 𝑁 = 𝑘 = 54 𝑚𝑚. Therefore:

𝜙𝑅𝑛 = 1.0 × 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑐𝑤 = 2795 𝑘𝑁 < 𝑅𝑢 = 2900 𝑘𝑁

Web crippling

Equal to AISC code:

𝑅𝑛 = 0.8𝑡𝑐𝑤2 [1 + 3

𝑁

𝑑𝑐

𝑡𝑐𝑤𝑡𝑐𝑓

1.5

] 𝐸𝐹𝑦𝑤 𝑡𝑐𝑓

𝑡𝑐𝑤

Use 𝜙 = 0.75 to obtain:

𝜙𝑅𝑛 = 4459 𝑘𝑁 > 𝑅𝑢 = 2900 𝑘𝑁

Web compression buckling:

This limit state does not apply for exterior connections.

Force for the design of weld connections of the continuity plates:

According to B.3.4. (and note (1)), the continuity plates shall be welded to the

web and the loaded flange so to transfer to the web the proportion of the force

carried by the stiffeners:

𝑅𝑛 ,𝑠𝑡 = 𝑅𝑢 − 𝜙𝑅𝑛 ,𝑚𝑖𝑛 = 106 𝑘𝑁


6-65

And the minimum stiffener total area shall be 𝐴𝑠𝑡 =𝑅𝑛 ,𝑠𝑡

𝜙𝐹𝑦 ,𝑠𝑡= 341 𝑚𝑚2.

Additional criteria for continuity plates:

(Re. NCh2369.Of2003, B.7 Section)

𝑏𝑠 +1

2𝑡𝑐𝑤 = 150 ≥

1

3𝑏𝑐𝑓 = 150 OK

𝑒𝑠 = 30 𝑚𝑚 < max 𝑡𝑏𝑓 ,𝑏𝑠 𝐹𝑦

250 = 40 𝑚𝑚 NOT OK

Use 𝒆𝒔 = 𝟒𝟎 𝒎𝒎 and keep from the previous design 𝒃𝒔 and 𝑳𝒔. The stiffener

area is 𝑨𝒔𝒕 = 𝟓𝟓𝟎𝟎 𝒎𝒎𝟐 > 𝑨𝒔𝒕,𝒎𝒊𝒏/𝟐

Compression check:

According to B.7.2, the section resisting the compression is the same as the

previous design (external stiffeners), therefore:

𝜙𝑃𝑛 = 5744 𝑘𝑁 > 𝑅𝑢 = 2900 𝑘𝑁 OK

Some welding requirements of the continuity plates:

According to NCh2369.Of2003 (B3.4, B4.2 and B5.2) the continuity plate to

loaded flange welding shall transfer the proportion of the load corresponding to



Note:

As seen, the previous provisions are quite similar to AISC provisions. Refer to

Welded Connection Commentary for Continuity Plates and Doubler Plates of

Chapter 6 on this Manual.

4. Column-beam moment ratio

According to NCh2369.Of2003, section 8.4.4 (R>3 systems): 𝑀𝑝𝑐/ 𝑀𝑝𝑣 > 1.2

for the columns and beams at the union analyzed. (See exceptions of not

meeting the previous inequality at 8.4.4).

The code does not specify the calculation of the moments, so use the plastic

moments of the gross sections. Then:

𝑀𝑝𝑐/ 𝑀𝑝𝑣 = 2.22 > 1.2 OK


6-66

5. Lateral bracing

According to NCh2369.Of2003, section 8.5.4, on beam-to-column connections

for rigid frames both beam flanges shall count with lateral bracing designed for

0.02𝐹𝑦𝑏𝑓𝑡. On this case, this is similar to AISC provisions, so the previous

design is OK, considering that the slab braces the superior flange of the beam.

Note:

According to the previous checks, the Chilean code is more stringent than the

AISC code only with the minimum thickness requirement of the continuity

plate. AISC is more stringent with the strength requirements for stiffeners.


Figure 6.3-9: Designed Connection.

CJP

CJP

CJP

Notes:

1.- Weld access holes must comply with AISC360 requirements

2.- The connections for continuity plates and doubler plates are not designed

2PL 370 x 137.5 x 40 mm

2PL 530 x 342 x 10 mm

R = (4c + b)/8c = 30.9 mm2

a=190mm b=450mm

c

c=60mm

Beam : H 600 X 300 X 229.2

Column : H 450 X 450 X 355.2


6-67

6.4. Bolted Flange Plate Moment Connection


1. NCh2369.Of2003



(Re. NCh2369. Of 2003, 8.5.1)


Always the nominal strength must be verified as a baring type connection.

(Re. NCh2369. Of 2003, 8.5.6)

Moment connections between columns and beams must have, at least, a

resistance equal to the strength of the connected elements.

(Re. NCh2369. Of 2003, 8.5.3)

In beam-to-column connections of rigid frames, the upper and lower

flanges should have lateral braces or supports designed for a force equal

to 0.02𝐹𝑦𝑏𝑓𝑡𝑓.

(Re. NCh2369.Of2003, 8.5.4)

Groove welds joints in seismic connections shall be complete joint

penetration type (CJP).

(Re. NCh2369. Of 2003, 8.5.5)

Moment connections of rigid frames for seismic applications shall be of FR

type (fully restricted). The connections shall be designed in a way such

that the plastic hinge is developed at a safe distance from the column,

which can be obtained by strengthening the connection or weakening the

beam in the desired position for the plastic hinge.

(Re. NCh2369.Of2003, 8.4.1)

Transverse sections of columns and beams in rigid earthquake-resistant

frames shall qualify as compact, that is, their width to thickness ratios

shall be lesser than 𝜆𝑝 given on Table 8.1 of the code.

(Re. NCh2369.Of2003, 8.4.2)

Appendix B (normative appendix) of the NCh2369.Of2003 refers to the

design of beam-column connection on rigid frames.


6-68

(Re. NCh2369.Of2003, App. B)

2. AISC 341-05


(SMF) it is recommended to see the Chapter 9 of this code. Some important


Beam-to-column connections requirements: see section 9.2a. The

required shear strength should be calculated taking into account the

flexural plastic hinges produced by the earthquake (E) load.

Unless otherwise designated by AISC358, CJP groove welds of beam


welds as defined in section 7.3b.(Section 9.2c)

The protected zone is defined in AISC358. In general, for unreinforced


one half of the beam depth beyond the plastic hinge point (Section 9.2d).



9.4.


according to AISC 358 (Section 9.5).


(section 9.6) and the lateral bracing (sections 9.7 and 9.8).


From chapter 7 of the supplement N°1 for AISC 358-05, following

recommendations for prequalified BFP connections are listed:

The beam web is connected to the columns using a bolted single plate

with bolts in short slotted holes.

The flange plates of the connection are welded to the flange of the column

with complete joint penetration groove welds and bolted to the beam

flanges with high strength bolts.

Top and bottom plates shall be identical.

Beam Limitations:

- Beams shall be rolled wide flange or welded built-up I shaped

members conforming to the requirements of section 2.3 of AISC

358.


6-69

- Width – thickness ratios for the flanges and web of the beam

shall conform to the limits of section 9.4 of AISC 341-05.

- Beam depth is limited to W36 for rolled shapes. Depth of built up

sections shall not exceed the depth permitted for rolled wide-

flange shapes.

- The weight of the beam shall not exceed 224 kg/m.

- Beam flange thickness is limited to 25 mm.

- The clear span to depth ratio of the beam is limited to be greater

than 9 in SMF.

- Lateral bracing shall be provided at the end of the protected zone

(See Figure 6.4-1) in both inferior and superior flanges of the

beam. The location of the lateral bracing can vary between 𝑑 and

1.5𝑑 (with 𝑑 the depth of the beam) from the farthest bolt with

respect to the face of the column. There is no need to provide

lateral bracing if the beam supports a concrete slab with welded

shear connectors spaced at a maximum of 300 mm. Lateral

bracing shall conform section 9.8 of AISC 341 Seismic Provisions.

6.4-1: Protected zone in beam to column connections.

Adapted from AISC 358-05, Figure 7.1.

Column Limitations:

- Columns shall be any rolled shapes or welded built-up sections

permitted in section 2.3 of the AISC 358.

- Rolled shape column depth shall be limited to W36 maximum when

concrete structural slab is provided. In the absence of a concrete

structural slab, rolled shape columns depth is limited to W14.


6-70

- Width – thickness ratios for the flanges and web of the column shall

conform to the limits of section 9.4 or 10.4 of the AISC seismic

provisions.

- The beam shall be connected to the flange of the column.

- Lateral bracing of columns shall conform to section 9.7 of the AISC

Seismic Provisions.

Single plate connection can be made with groove weld CJP or two sided

fillets welds or two sided PJP welds.

Flange plates shall conform to the ASTM A36/A36M or A572/A572M Grade

50 specification. Flange plates shall be connected to column flange using

CJP groove welds and these welds shall be considered as demand critical.

If backing is used, it shall be removed.

Bolts must be arranged symmetrically with respect to the axes of the

beam and only two bolts per row are permitted. The length of the bolt

group cannot be greater than the depth of the beam. The bolt diameter is

limited by 28 mm. STD holes shall be used in beam flanges and bolts in

the flange plate shall be ASTM A490 or A490M or ASTMF2280 with threads

excluded from the shear plane.

6.4.b. Example

Design a bolted flange plate moment connection (BFP) for the beam-to-column

connection shown in Figure 6.4-22. Use A345 ESP steel, required for

constructions subject to dynamic loads, according to NCh203.Of2006 , Table 3.

Use 70 ksi electrodes for welds.

The column and the beam are Chilean H 500 x 350 x 165.6 and H 500 x 300 x

132.3 built-up sections. The connection transfers shear and moment. The clear

span of the beam is 8000 mm.

The forces for the design are:

Beam:



Column:

𝑃𝑢 = 426 𝑘𝑁


6-71

Suppose that the beams and columns have been properly designed for

resisting the forces given by the load combinations of the applicable building

code (including seismic load).


and IMF systems) for Seismic Applications” document and its supplement N°1.

6.4-2: General view of the connection.


H500x350x165.6


𝑑 = 500 𝑚𝑚, 𝑏 = 350 𝑚𝑚, 𝑡𝑤 = 8 𝑚𝑚

𝑡𝑓 = 25 𝑚𝑚, 𝑍𝑥 = 4561000 𝑚𝑚3

H500x300x132.3


𝑑 = 500 𝑚𝑚, 𝑏 = 300 𝑚𝑚, 𝑡𝑤 = 8 𝑚𝑚

𝑡𝑓 = 22 𝑚𝑚, 𝑍𝑥 = 3571000 𝑚𝑚3

A345 ESP

(Re. Table 3, NCh203.Of2006)

𝐹𝑦 = 345 𝑀𝑃𝑎, 𝐹𝑢 = 450 𝑀𝑃𝑎


WELDS: 70 ksi electrodes, 𝐹𝐸𝑋𝑋 = 480 𝑀𝑃𝑎

H 500X300X132.3

H 500X350X165.6


6-72

Width–thickness ratio limits

Limits are given on Table I-8-1 of the AISC 341-05.

For beam and column flanges (A345 ESP):

𝜆 =𝑕

tw

< 𝜆𝑝𝑠 = 0.30 𝐸

𝐹𝑦= 7.22

For beam and column webs (A345 ESP):

𝜆 =𝑏

2𝑡< 𝜆𝑝𝑠 = 2.45

𝐸

𝐹𝑦= 58.98

In this case, both column and beam comply with the maximum limits.

4. Design Forces

Design forces according to the NCh2369.Of 2003 must be calculated

considering that the connection must stand at least the strength of the

connected elements; however this code does not consider any criterion for the

calculation of those forces.

Using the requirements of AISC 358-05 (more stringent than

NCh2369.Of2003):

𝑀𝑢 = 𝑀𝑝𝑟 = 𝐶𝑝𝑟𝑅𝑦𝐹𝑦𝑍𝑒 (Re. AISC 358, 2.4.3-1)

Where 𝑅𝑦 is the ratio of expected yield strength to the minimum specified yield

stress. 𝑍𝑒 is the effective plastic modulus of the section and 𝐶𝑝𝑟 is a factor to

take account for the peak connection strength:

𝐶𝑝𝑟 =𝐹𝑦 + 𝐹𝑢

2𝐹𝑦< 1.2

𝐶𝑝𝑟 = 1.15 < 1.2 → 𝐶𝑝𝑟 = 1.15

A345 ESP is similar to ASTM A572 Gr 50, according to the table I-6-1 of the

AISC 341 seismic specification, then 𝑅𝑦 = 1.1. Furthermore, considering that

the plastic modulus section is the corresponding to the beam, 𝑍𝑒 = 𝑍𝑥

Therefore:


6-73

𝑀𝑝𝑟 = 1558473 𝑘𝑁−𝑚𝑚

For the shear design force, consider the plastic hinges at the ends of the

beam:

𝑉𝑢 = 1.2𝑉𝐷 + 1.0𝑉𝐿 +2𝑀𝑝𝑟

𝐿= 458 𝑘𝑁

For further discussion regarding the calculation of the design forces according

to the Chilean provisions and practice, see the section of additional comments

at the end of this example.

5. Design of the flange plates

Design the flange plates as plates subjected to tensile force. The force that

each plate shall resist is given by:

𝐹𝑝 =1.25𝑀𝑝𝑟

𝑑+𝑡𝑝 (Re. Section 7, step 4, AISC 358-05)

The additional 1.25 factor is due to the fact that the plastic hinge will not be

located in the face of the column, but at a distance that depends of the length

of the connection that will cause an increment of the plastic moment for the

contribution of the shear force. This factor shall be verified after the design

procedure of the bolted flange plates. Note that 𝑡𝑝 is the thickness of the

flange plates.

Try PL 500 x 300 x 20, therefore:

𝐹𝑝 = 1.251558473

500 + 20= 3746 𝑘𝑁

6. Bolts

Use M27 bolts (27 mm of diameter, standard holes of 30 mm). Even though

the NCh2369.Of2003 does not require to verify the connection as a slip critical

type, sometimes project specifications do require it.



𝜙𝑛𝑅𝑛 = 𝜙𝑛𝜇𝐷𝑢𝑕𝑠𝑐𝑇𝑏𝑁𝑠 (Re. AISC 360-05, J3-4)


6-74

𝜙𝑛 = 0.9 (Re. AISC 358 2.4.1)

Considering Class A connection surfaces, and standard size holes:

(Re. AISC 360-05, J3.8):

𝜇 = 0.35

𝑕𝑠𝑐 = 1.00

𝐷𝑢 = 1.13

Also the nominal tensile strength for M27 ASTM A490 bolts is:


Since there is one slip plane, then 𝑁𝑆 = 1.0.

For one bolt, the design slip critical strength is:

𝜙𝑛𝑅𝑛 = 132 𝑘𝑁


strength is: 𝑁𝐵 ≥28.37. Use 𝑁𝐵 = 30.



𝜙𝑛𝑅𝑛 = 𝜙𝑛𝐹𝑛𝑣𝐴𝑏 (Re. AISC360-05, J3-1)

𝜙𝑛 = 0.9 (Re. AISC358 2.4.1)


𝐴𝑏 = 573 𝑚𝑚2 𝐹𝑛𝑣 = 414 𝑀𝑃𝑎 (Re. AISC360-05, Table J3.2)

Then:

𝜙𝑛𝑅𝑛 = 214 𝑘𝑁

Then, the number of bolts required for the connection is: 𝑁𝐵 > 17.5.

Use 𝑁𝐵 = 18.

Even though the slip critical limit state controls the design, in this case, due

the excessively large amount of bolts required, it is decided to use the shear


6-75

nominal strength of the bolts. Furthermore, slip critical check is not needed by

AISC 358 or NCh2369.Of2003.

Then, use 𝑵𝑩 = 18 for each flange plate. Use rows of two bolts each one.

Considering the size of the bolts that are going to be used, the length of the

connection will be greater than the depth of the beam. This does not

accomplish the requirements of AISC 358 for the prequalified connection, but

it is preferred the use of rows of two bolts instead of limiting the length of the

connection.

7. Verification of ductile behavior of the plates

For the ductile behavior of the flange plates, following check shall be done:

(Re. Section 7.6, step 2, AISC 358-05)

𝐴𝑒𝑓𝑓𝑅𝑡𝐹𝑢 > 𝐴𝑔𝑅𝑦𝐹𝑦

With 𝑅𝑦 = 1.1 , 𝑅𝑡 = 1.1 according to the table I-6-1 of the AISC 341 (ASTM

A572 grade 50 for flange plates). Considering two rows of bolts, the effective

area is (𝑑𝑕 = 30 𝑚𝑚):

𝐴𝑒𝑓𝑓 = 300 × 20 − 2 × 𝑑𝑕 × 20 = 4800 𝑚𝑚2

Then:

𝑨𝒆𝒇𝒇𝑹𝒕𝑭𝒖 = 𝟐𝟑𝟕𝟔 𝒌𝑵 > 𝑨𝒈𝑹𝒚𝑭𝒚 = 𝟐𝟐𝟕𝟕 𝒌𝑵 OK

Tip:

Since the effective area is controlled by the diameter and number of the bolts,

it is important that the bolts shall have reasonable diameters in order to

ensure a ductile behavior of the flange plates.

8. Bolts spacing and plate dimensions

Considering a minimum bolt spacing of 72 mm and a minimum distance to the

edge of 48 mm (refer to Bolted Connections section 2.4 on this manual), the

minimum length and width of the flange plates are:

𝐿𝑀𝐼𝑁 = 8 × 72 𝑚𝑚 + 2 × 48 𝑚𝑚 + 𝑑𝑐

With 𝑑𝑐 = 12 𝑚𝑚 the assumed spacing between the column and the beam,

then:

𝐿𝑀𝐼𝑁 = 684 𝑚𝑚


6-76

The minimum width of the plate is given by:

𝐵𝑀𝐼𝑁 = 1 × 72𝑚𝑚 + 2 × 48 𝑚𝑚 = 168 𝑚𝑚 OK

Then the plate PL 500 x 300 x 20 does not accomplish with the required

spacing. Try a PL 690 X 300 X 20 plate.

The length of the bolt group is:

𝐿𝑏𝑜𝑙𝑡 𝑔𝑟𝑜𝑢𝑝 = 72 × 8 = 576 𝑚𝑚 > 𝑑 = 500 𝑚𝑚

Then the connection does not accomplish with the maximum length

requirement from AISC 358-05, but as discussed above, this fact will not be

considered in the design.

6.4-3: Bolts disposition and flange plate dimensions.

9. Bearing strength on the flange plate holes

Interior bolts

The bearing strength of each plate is:


𝜙𝑛 = 0.9 (Re. AISC358 2.4.1)


𝐿𝑐 = 72 𝑚𝑚− 30 𝑚𝑚 = 42 𝑚𝑚


6-77

The flange plate thickness is 𝑡 = 20 𝑚𝑚, then:

𝜙𝑛𝑅𝑛 = 408 𝑘𝑁 < 524 𝑘𝑁 → 𝜙𝑛𝑅𝑛 = 408 𝑘𝑁

Exterior bolts


𝐿𝑐 = 54 𝑚𝑚−30

2= 39 𝑚𝑚

𝜙𝑛𝑅𝑛 = 379 𝑘𝑁 < 524 𝑘𝑁 → 𝜙𝑛𝑅𝑛 = 379 𝑘𝑁


𝜙𝑛𝑅𝑛 = 16 × 408 𝑘𝑁 + 2 × 379 𝑘𝑁 = 7286 𝑘𝑁 > 𝐹𝑝 = 3746 𝑘𝑁 OK

10. Bearing strength on the beam flange holes

Since the beam flange is thicker than each flange plate, this limit state does

not control the design:

𝑡𝑏𝑓 = 22 𝑚𝑚 > 𝑡𝑝 = 20 𝑚𝑚

11. Tensile yielding of flange plates

Now that the dimensions of the flange plate connections are known, the tensile

force in the plates can be estimated accurately. The shear force is estimated,

considering a free body diagram of the beam between the two hinges, which

are located at the ends of the flange plate connections on the ends of the

beam.

𝑉𝑕 = 1.2𝑉𝐷 + 1.0𝑉𝐿 +2𝑀𝑝𝑟

𝐿𝑕

𝐿𝑕 = 8000 𝑚𝑚− 2 × 𝐿𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = 8000 𝑚𝑚− 2 × 636 𝑚𝑚 = 6728 𝑚𝑚 𝑉𝑕 = 531 𝑘𝑁

Then the moment expected at the face of the column flange is:

𝑀𝑓 = 𝑀𝑝𝑟 + 𝑉𝑕 × 𝐿𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = 1896189 𝑘𝑁 −𝑚𝑚

Then the force of the plates is:

𝐹𝑝𝑓 =𝑀𝑓

𝑑 + 𝑡𝑝= 3646 𝑘𝑁


6-78

Then the 1.25 factor used before was conservative, and the number of bolts

calculated on the previous steps is conservative.



𝜙𝑑 = 1.00 (Re. AISC358 2.4.1)

The gross tensile area of each flange plate is: 𝐴𝑔 = 𝐵𝑡 = 300 × 20 = 6000 𝑚𝑚2:

𝜙𝑑𝑅𝑛 = 2070 𝑘𝑁 < 3646 𝑘𝑁

Try PL 690 X 300 X 40 flange plates, then:

𝐹𝑝𝑓 =𝑀𝑓

𝑑 + 𝑡𝑝= 3511 𝑘𝑁

𝜙𝑑𝑅𝑛 = 4140 𝑘𝑁 > 3511 𝑘𝑁

12. Tensile rupture of flange plates


𝑅𝑛 = 𝐹𝑢𝐴𝑛 (Re. AISC360-05 J4-2)

𝜙𝑛 = 0.9 (Re. AISC358 2.4.1)

Where 𝐴𝑛 is the net area of the plate, which considers the reduction of the

section because of bolt holes, the nominal dimension for the holes for a M27

bolt is 𝑑𝑕 = 30 𝑚𝑚 , and taking into account the damage:

𝑑𝐶𝐴𝐿𝐶 = 30 𝑚𝑚 + 2 𝑚𝑚 = 32 𝑚𝑚

𝐴𝑛 = 𝐵 − 2 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 9440 𝑚𝑚2 < 0.85𝐴𝑔 = 10200 𝑚𝑚2

𝜙𝑛𝑅𝑛 = 3823 𝑘𝑁 > 3511 𝑘𝑁 OK

13. Block shear rupture on the flange plates


𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 ≤ 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 (Re. AISC360-05, J4-5)

𝜙𝑛 = 0.9 (Re. AISC358 2.4.1)


6-79

Where 𝑈𝑏𝑠 = 1.0 in this case, according to the commentary in the AISC 360-05

specification (AISC 360-05 C-J4.2). The values of 𝐴𝑛𝑣 , 𝐴𝑛𝑡 and 𝐴𝑔𝑣 are obtained


6.4-4: Block shear path.

𝐴𝑛𝑣 = 2 × 630 − 8.5 × 𝑑𝐶𝐴𝐿𝐶 𝑡 = 28640 𝑚𝑚2

𝐴𝑔𝑣 = 2 × 630 𝑡 = 50400 𝑚𝑚2

𝐴𝑛𝑡 = 150 𝑚𝑚− 𝑑𝐶𝐴𝐿𝐶 𝑡 = 4720 𝑚𝑚2

Then:

𝑅𝑛 = 8871 𝑘𝑁 < 11301 𝑘𝑁 → 𝜙𝑛𝑅𝑛 = 8772 𝑘𝑁 > 3511 𝑘𝑁 OK

14. Compression buckling of the plate

According to the provisions of the section J4.4 of the AISC 360-05, the

compressive strength depends of the slenderness of the plate 𝐾𝐿/𝑟 :

According to the recommendations of the chapter 7 in supplement N°1 for

AISC 358-05, 𝐾𝐿 may be taken as 0.65𝑆1, where 𝑆1 is the distance from the

face of the column to the nearest row of bolts, then:

𝑆1 = 60 𝑚𝑚

𝑟 = 𝐼

𝐴

𝐼 =𝑡3𝐵

12= 1600000 𝑚𝑚4

𝐴 = 12000 𝑚𝑚2

𝑟 = 11.54 𝑚𝑚


6-80

𝐾𝐿

𝑟=

0.65𝑆1

𝑟= 3.37

Since 𝐾𝑙

𝑟< 25, the nominal strength is given by:

𝑃𝑛 = 𝐹𝑦𝐴𝑔

𝜙𝑑 = 1.00

𝜙𝑑𝑃𝑛 = 4140 𝑘𝑁 > 3511 𝑘𝑁 OK

15. Shear tab design force

The shear design force is:

𝑉𝑢 = 𝑉𝑕 = 531 𝑘𝑁

For the detail of the design of the shear tab, see section 3.1, Shear Tab

Connection, of this manual. The result of this design is:

Use a PL 450 X 100 X 10 plate, welded to the column flange with 6 mm two

fillet weld size.

6.4-5: Shear tab dimensions and bolt configuration.

16. Panel Zone

The panel zone shall be verified according to section 7.4 of AISC 358-05

supplement N°1, which refers to 9.3 of AISC 341-05. According to section 9.3

of AISC 341-05 Seismic Provisions.


6-81

According to section 9.3 of AISC 341-05, the required minimum shear strength

of the panel zone shall be calculated from the summation of the shear

produced by the expected plastic hinge moments at the columns faces.

The shear strength (according to the limit state of shear yielding) is given by

the following:

(Re. Section J10.6 AISC 360-05)

If it is considered frame stability including plastic panel zone deformation, the

nominal strength is:

If 𝑃𝑢 ≤ 0.75𝑃𝑦:

𝑅𝑛 = 0.60𝐹𝑦𝑑𝑐𝑡𝑤 1 +3𝑏𝑐𝑓 𝑡𝑐𝑓

2

𝑑𝑏𝑑𝑐𝑡𝑤 (Re. AISC 360-05, J10-11)

If 𝑃𝑢 > 0.75𝑃𝑦:


2

𝑑𝑏𝑑𝑐𝑡𝑤 1.9 − 1.2

𝑃𝑢

𝑃 𝑐 (Re. AISC 360-05, J10-12)

Where,

𝑃𝑢 :𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑓𝑜𝑟𝑐𝑒 𝑖𝑛 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛

𝑏𝑐𝑓 :𝑤𝑖𝑑𝑡𝑕 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛 𝑓𝑙𝑎𝑛𝑔𝑒

𝑑𝑏 :𝐵𝑒𝑎𝑚 𝑑𝑒𝑝𝑡𝑕

𝑃𝑦 :𝐴𝑥𝑖𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡𝑕 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛

𝑑𝑐 :𝐶𝑜𝑙𝑢𝑚𝑛 𝑑𝑒𝑝𝑡𝑕

𝑡𝑐𝑓 :𝑇𝑕𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛 𝑓𝑙𝑎𝑛𝑔𝑒

𝑡𝑤 :𝐶𝑜𝑙𝑢𝑚𝑛 𝑤𝑒𝑏 𝑡𝑕𝑖𝑐𝑘𝑛𝑒𝑠𝑠

The nominal strength is 𝜙𝑣𝑅𝑛, with 𝜙𝑣 = 1.0 according to the AISC 341-05,

section 9.3a.

If the panel zone cannot comply with the above requirements, strength shall

be provided with doubler plates, that must be designed according to the

provisions of AISC 360-05, J10-9. Doubler plates must resist 𝑅𝑢 −𝜙𝑣𝑅𝑛.

Calculation of 𝑅𝑢:

For the calculation of the shear solicitation in the panel zone, consider the

following figure (for a general interior connection):


6-82

6.4-6: Typical panel zones forces.

Figure adapted from AISC Design Guide N°13, Fig. 2-3.

The shear demand for the panel zone is:

𝑉𝑢 = 𝑃𝑢𝑓1 + 𝑃𝑢𝑓2 − 𝑉𝑢𝑠

𝑉𝑢𝑠 = 0 (Assumption)

𝑃𝑢𝑓𝑖 =𝑀𝑢𝑖

𝑑𝑏𝑖 − 𝑡𝑏𝑓𝑖

𝑀𝑢𝑖 is the plastic moment of the beam. Then, for this example, in which there

is only one beam arriving to the column (exterior connection):

𝑉𝑢 =𝑀𝑓

𝑑𝑏 − 𝑡𝑏𝑓=

1909865

500 − 22= 3995 𝑘𝑁

Assuming that 𝑃𝑢 < 0.75𝑃𝑦, the strength of the panel zone is:


2

𝑑𝑏𝑑𝑐𝑡𝑤 = 1099 𝑘𝑁 < 𝑉𝑢 NOT OK

Doubler plates are required. Their design will follow provisions of AISC 360-05,

chapter G:

𝑅𝑛 = 0.6𝐹𝑦𝐴𝑤

𝜙 = 0.9

𝐴𝑤 = 2𝑤𝑧𝑡𝑑𝑝

𝑤𝑧 = 500 − 2 × 25 = 450 𝑚𝑚

With 𝑤𝑧 the width of the panel zone of the column between column flanges.

V us

V us

P uf 1

M u 1

V u

P uf 1

P uf 2

P uf 2

M u 2


6-83

Then:

2𝑡𝑑𝑝 ≥𝑉𝑢 − 𝜙𝑣𝑅𝑛

0.6𝐹𝑦𝑤𝑧

= 31.08 𝑚𝑚

𝑡𝑑𝑝 > 15.54 𝑚𝑚

Use doubler plates with thickness 𝑡𝑑𝑝 = 16 𝑚𝑚.

Welding of the doubler plates


for Chapter 6.

Thickness of the web of the column verification

Finally, verify the thickness of the web of the column:

𝑡 ≥ (𝑑𝑧 + 𝑤𝑧)/90 (Re. AISC 341-05, 9-2)

Where 𝑑𝑧 is the depth of the panel zone between continuity plates, then:

𝑑𝑧 = 500 − 2 × 22 = 456 𝑚𝑚

𝑡 ≥456 + 450

90= 10𝑚𝑚

Then the column web is not ok, but using doubler plates that are plug welded

to the column web, the thickness considered is the summation of the doubler

plates and the web of the column, so the panel zone thickness is OK.


Continuity plates must be designed considering the provisions of chapter 2 of

AISC 358-05, which refers to section J10 of the AISC360-05. Continuity plates

are not required if the following criterions are met:

𝑡𝑐𝑓 ≥ 0.4 1.8𝑏𝑏𝑓 𝑡𝑏𝑓𝐹𝑦𝑏 𝑅𝑦𝑏

𝐹𝑦𝑐 𝑅𝑦𝑐 (Re. AISC 358-05, 2.4.4-1)

𝑡𝑐𝑓 ≥𝑏𝑏𝑓

6 (Re. AISC 358-05, 2.4.4-2)

Where 𝑡𝑐𝑓 is the minimum required thickness of the column flange. Then, we

have:


6-84

𝑡𝑐𝑓 ≥ 43.6 𝑚𝑚 (Re. AISC 358-05, 2.4.4-1)

𝑡𝑐𝑓 ≥ 50 𝑚𝑚 (Re. AISC 358-05, 2.4.4-2)

Therefore, continuity plates are needed.

Continuity plates have to be designed for a force equal to 𝑅𝑢 − 𝜙𝑅𝑛, where 𝜙𝑅𝑛

is the nominal strength of the column flange or the column web according to

the following limit states:

Flange local bending of the column flange

The nominal resistance is given by:

𝑅𝑛 = 6.25𝑡𝑐𝑓2 𝐹𝑦𝑓 (Re. AISC 360-05. J10-1)

𝜙 = 0.90

Then,

𝜙𝑅𝑛 = 1347 𝑘𝑁

Web local yielding

Consider that the concentrated force is applied at a distance to the end of the

column greater than the depth of the element, the nominal resistance is given

by:

𝑅𝑛 = 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑤 (Re. AISC 360-05. J10-2)

𝜙 = 1.00

Considering that the column web is reinforced by the doubler plates, the

thickness 𝑡𝑤 is:

𝑡𝑤 = 𝑡𝑐𝑤 + 2𝑡𝑑𝑝 = 40 𝑚𝑚

Additionally, 𝑘 is the distance from the face of the flange to the web toe of the

fillet weld. Then, considering that for the column the value of 𝑘 is 30 mm, and

the value of N is the length of bearing, that in this case corresponds to the

thickness of the flange of the beam, 𝑁 = 22 𝑚𝑚. However, the value of N

cannot be less than k for beam end reactions, so use 𝑁 = 𝑘 = 30 𝑚𝑚, then:

𝜙𝑅𝑛 = 2484 𝑘𝑁


6-85

Web Crippling

Considering that the concentrated compressive force is located at a distance

from the end of the member greater than half of the depth of the column:

𝑅𝑛 = 0.80𝑡𝑤2 1 + 3

𝑁

𝑑

𝑡𝑤

𝑡𝑓

1.5


𝑡𝑤 (Re. AISC 360-05. J10-4)

𝜙 = 0.75

Them considering 𝑁 = 30 𝑚𝑚, and 𝑡𝑤 the thickness of the column web including

doubler plates, we have:

𝜙𝑅𝑛 = 8600 𝑘𝑁

Web Compresion Buckling

This section only applies when the member is subjected to a pair of

compressive concentrated forces that are applied at both flanges of the

member, so in this case (an exterior connection), this limit state does not

apply.

Considering all the limit states:

min𝜙𝑅𝑛 = 1347 𝑘𝑁

Then,

𝑅𝑠𝑢 = 𝑃𝑢𝑓 − 𝜙𝑅𝑛

𝑃𝑢𝑓 =𝑀𝑓


𝑅𝑠𝑢 = 2619 𝑘𝑁

According to the AISC 358-05, thickness of the continuity plates must comply

with the following provisions:

For exterior connections:

𝑡𝑐𝑝 ≥1

2𝑡𝑏𝑓 (Re. AISC 358-05, 2.4.4a)

For two side (interior) connections:

𝑡𝑐𝑝 ≥ max 𝑡𝑏𝑓𝑖 (Re. AISC 358-05, 2.4.4b)


6-86

This example is an interior connection. Therefore, the minimum thickness of

the continuity plate must be 11 mm.

According to the AISC 358 provisions of the section 2.4.4, continuity plates

must comply with the provisions of section J10 of the AISC 360-05. Therefore,

the continuity plate shall be designed as a stiffener, which is designed as an

element subjected to tensile forces, according to chapter D, and as element

subjected to compressive forces, according to the chapter E and section J4.4 of

AISC 360-05.

Design for tensile forces

Tensile yielding:

𝑅𝑛 = 𝐹𝑦𝐴𝑔 (Re. AISC 360-05, D2-1)

𝜙 = 0.9

Then, the required thickness, considering that the width of both continuity

plates is 𝑏𝑐𝑝 = 342 𝑚𝑚, then:

𝑡𝑐𝑝 ≥𝑅𝑠𝑢

𝜙𝐹𝑦𝑏𝑐𝑝= 24.66 𝑚𝑚

Use 𝒕𝒄𝒑 = 𝟐𝟓 𝒎𝒎.

Tensile fracture:

𝑅𝑛 = 𝐹𝑢𝐴𝑒 (Re. AISC 360-05, D2-2)

𝜙 = 0.75

Where 𝐴𝑒 correspond to the effective area, which in this case is equal to 𝐴𝑔.

Then we have:

𝜙𝑅𝑛 = 2885 𝑘𝑁 > 2619 𝑘𝑁 OK

Design for compressive forces

According to section E6.2 and J4.4 of AISC 360-05, the nominal strength is:


6-87

If 𝑘𝐿

𝑟≤ 25:

𝑅𝑛 = 𝐹𝑦𝐴𝑔 (Re. AISC 360-05, J4-6)

If 𝑘𝐿

𝑟> 25: the design must be made according to chapter E of the AISC 360-05.

Section J10.8 of AISC 360-05 establishes that the effective length for the

buckling verification is 0.75𝑕, where 𝑕 is the length of the stiffener; the area of

the stiffener must be considered as a cross section, with the two continuity

plates and an orthogonal section corresponding to 25𝑡𝑤 for exterior stiffeners or

12𝑡𝑤 for interior stiffeners (see Figure 6.4-7).

6.4-7: Design area for the stiffeners.

For the exterior connection analyzed (considering that 𝑡𝑤 includes the

thickness of the doubler plates):

𝐴𝑠𝑡𝑖𝑓𝑓 = 𝑏𝑐𝑝 𝑡𝑐𝑝 + 12𝑡𝑤2 = 27750 𝑚𝑚2

𝐼𝑥𝑥 = 12𝑡𝑤

3𝑡𝑤12

+𝑡𝑐𝑝

3 𝑏𝑐𝑝12

= 369085312 𝑚𝑚4

𝐼𝑦𝑦 =𝑏𝑐𝑝

3 𝑡𝑐𝑝12

+ 𝑡𝑤4 = 85896850 𝑚𝑚4

𝑕 = 𝑑𝑐 − 2𝑡𝑐𝑓 = 450 𝑚𝑚

𝑘𝐿 = 0.75𝑕 = 337 𝑚𝑚

Verify only the weak axis, which corresponds to 𝐼𝑦𝑦 :

𝑟 = 𝐼𝑦𝑦𝐴

= 55.63

Stiffener Stiffener

12tw or 25tw

x

y


6-88

𝑘𝐿

𝑟= 6.05

Then, design according to J4.4 of the AISC 360-05.

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔 , 𝐴𝑔 = 𝐴𝑠𝑡𝑖𝑓𝑓

𝜙𝑅𝑛 = 8616 𝑘𝑁 > 𝑃𝑢𝑓 =𝑀𝑓

𝑑𝑏−𝑡𝑏𝑓= 3966 𝑘𝑁 OK

AISC 360 J10-8 additional criteria:

The width of the continuity plate plus one half of the thickness of the column

shall be not less than one third of the width of the flange of the beam or

moment connection plate that delivers the force:

𝑏𝑐𝑝

2+

𝑡𝑤

2= 175 𝑚𝑚 >

𝑏𝑏𝑓

3= 100 𝑚𝑚 OK

𝑏𝑐𝑝

2+

𝑡𝑤

2= 175 𝑚𝑚 >

𝑏𝑝

3= 100 𝑚𝑚 OK

The thickness of the continuity plate shall not be less than one half the

thickness of the flange or moment connection that transmits the force and

greater or equal than the width of the continuity plate divided by 15:

𝑡𝑐𝑝 = 25 𝑚𝑚 >𝑡𝑏𝑓

2= 11 𝑚𝑚 OK

𝑡𝑐𝑝 = 25 𝑚𝑚 >𝑡𝑝

2= 20 𝑚𝑚 OK

𝑡𝑐𝑝 = 25 𝑚𝑚 >𝑏𝑐𝑝 /2

15= 11.4 𝑚𝑚 OK

Finally the continuity plate shall extend at least one half of the column depth.

18. Lateral Bracing

Following section 7.3.1 of the AISC 358 supplement, lateral bracing must be

provided according to 9.8 for SMF of the AISC 341 Seismic Provisions. Thus,

lateral bracing must be provided at spacing not greater than 𝐿𝑏 = 0.086𝑟𝑦𝐸/𝐹𝑦

and braces must meet the provisions of Appendix 6 of the AISC 360-05,

considering 𝑀𝑟 = 𝑅𝑦𝑍𝐹𝑦 and 𝐶𝑑 = 1.0:

Resistance required by the brace (nodal bracing):

𝑃𝑟 = 0.02𝑀𝑟𝐶𝑑/𝑕𝑜 (Re. AISC 360-05, A-6-7)


6-89

Stiffness required by the brace:

𝛽𝑏𝑟 =1

𝜙

10𝑀𝑟𝐶𝑑

𝐿𝑏𝑕𝑜 (Re. AISC 360-05, A-6-8)

𝜙 = 0.75

Where 𝑕𝑜 is the distance between flange centroids.

Provide lateral bracing only in the inferior flange of the beam, because it is

supposed that the beam stand a slab that provides lateral bracing for the

superior flange. Furthermore, suppose that the inferior flange has lateral

bracing at both sides of the beam, so design the braces only for tensile force

solicitations.

𝑀𝑟 = 1355194 𝑘𝑁 −𝑚𝑚

𝑕𝑜 = 500 − 22 = 478 𝑚𝑚

𝑃𝑟 = 56.7 𝑘𝑁

Suppose that 𝐿𝑏 is the maximum value permitted, which is:

𝐿𝑏 =0.086𝑟𝑦𝐸

𝐹𝑦, 𝑟𝑦 = 76.7 𝑚𝑚

𝐿𝑏 = 3823 𝑚𝑚

Then:

𝛽𝑏𝑟 = 9.88𝑘𝑁

𝑚𝑚

And the resistance to tensile forces is given by:

Tensile yielding:

𝑅𝑛 = 𝐹𝑦𝐴𝑔 (Re. AISC 360-05, D2-1)

𝜙 = 0.9

Then, the required area is:

𝐴𝑔 ≥ max 𝑃𝑏𝑟

0.9𝐹𝑦,𝛽𝑏𝑟

𝐸𝐿𝑏𝑟

Considering a distance between adjacent beams of 𝐿𝑏𝑟 = 4000 𝑚𝑚:


6-90

𝐴𝑔 ≥ 189 𝑚𝑚2

Try a tubular section D1 7/8, with a thickness of 1.5 mm. The area of this

section is 217 mm2.

NCh2369.Of2003 establishes that the lateral bracing must be designed to

withstand a force equal 0.02𝐹𝑦𝑏𝑏𝑓 𝑡𝑏𝑓 , which in this example results 45.5 𝑘𝑁, that

is less than the requirements of AISC. OK.

19. Beam – column relationship limitations

According to the section 7.4 of the AISC 358 supplement N°1, we have that

the column- beam ratio shall conform to the requirements of the section 9.6 of

the AISC 341 Seismic Provisions for SMF. The code establishes the following:

𝑀𝑝𝑐

𝑀𝑝𝑏

≥ 1.0

Then, we have:

𝑀𝑝𝑐

𝑀𝑝𝑏

=2𝑍𝑐𝑥𝐹𝑦𝑐 − 2𝑍𝑐𝑥𝑃𝑢𝑐 /𝐴𝑔

1.1𝑅𝑦𝐹𝑦𝑏𝑍𝑏𝑥 + 𝑀𝑢𝑣

Where 𝑀𝑢𝑣 = 𝑉𝑕𝐿𝑐𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑜𝑛 = 351392 𝑘𝑁 −𝑚𝑚, then:

𝑀𝑝𝑐

𝑀𝑝𝑏= 1.61 > 1.0 OK

On the other hand, the provisions of section 8.4.4 of NCh2369.Of2003

establish that the ratio between the sum of the resistance moments of the

columns to the resistance of the beams that arrive to the connection must be

equal or greater than 1.2. The code does not specify how the resistance

moments should be calculated, therefore, we use the same moments of the

AISC specification, so this ratio is OK.


6-91


6.4-8: Designed connection.

6.4.c. Panel zone and continuity plates according to NCh2369. Of

2003

1. Panel Zone

According to the NCh2369. Of 2003, section B2.2:

𝑅𝑢 =𝑀𝑢1

𝑑𝑚1+

𝑀𝑢2

𝑑𝑚2− 𝑉𝑢 (Re. NCh2369. Of 2003, B-1)

Where 𝑑𝑚𝑖 correspond to 0.95𝑑𝑖, where 𝑑𝑖 is the height of the beam 𝑖. Consider

only for this example that 𝑉𝑢 = 0 and that 𝑀𝑢 is 𝑀𝑓 (For the use of 𝑀𝑢 according

to the Chilean practice see the discussion at the end of this example):

𝑅𝑢 = 3460 𝑘𝑁

According to section B2.2, the available strength of the panel zone is:

𝑅𝑛 = 0.60𝐹𝑦𝑑𝑐𝑡𝑝 1 +3𝑏𝑐𝑓 𝑡𝑐𝑓

2

𝑑𝑏𝑑𝑐𝑡𝑝 if 𝑃𝑢 ≤ 0.75𝑃𝑦 (Re. NCh2369. Of 2003, B-2)

𝜙 = 0.75

Where 𝑡𝑝 is the total thickness of the panel zone, including doubler plates,

then:

𝑡𝑝 = 2 × 16 𝑚𝑚 + 𝑡𝑐𝑤 = 40 𝑚𝑚

𝜙𝑅𝑛 = 3308 𝑘𝑁 < 3460 𝑘𝑁

H 500X350X165.6

H 500X300X132.3

Continuity plate t = 25 mm

Doubler plate t = 16 mm

PL 690X300X4018 M27 A490

5 M27 A490PL 450X110X10

6

6


6-92

Then, considering the provisions of the NCh2369.Of2003, the thickness of the

doubler plates shall be increased. Use 𝒕𝒅𝒑 = 𝟐𝟎 𝒎𝒎, then:

𝑡𝑝 = 2 × 20 𝑚𝑚 + 𝑡𝑐𝑤 = 48 𝑚𝑚

𝜙𝑅𝑛 = 3925 𝑘𝑁 > 3460 𝑘𝑁 OK


According to the provisions of section B.3, B.4, B.5, B6 and B.7 of

NCh2369.Of2003, Continuity Plates must be designed considering:


The nominal strength is given by:

𝑅𝑛 = 6.25𝑡𝑐𝑓2 𝐹𝑦𝑓 (Re. NCh2369. Of 2003, B3.1)

𝜙 = 0.90

Then,

𝜙𝑅𝑛 = 1347 𝑘𝑁

Web local yielding

Considering that the concentrated force is applied at a distance to the end of

the element greater than the depth of the element, the nominal resistance is

given by:

𝑅𝑛 = 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑤 (Re. NCh2369. Of 2003, B-5)

𝜙 = 1.00

Considering that 𝑡𝑤 includes the thickness of the doubler plates.

Where 𝑘 is the distance from the face of the flange to the web toe of the fillet.

Then considering that for the column the value of 𝑘 is 30 mm, and the value of

N is the length of bearing that in this case corresponds to the thickness of the

flange of the beam, 𝑁 = 22 𝑚𝑚. However the value of 𝑁 cannot be less than 𝑘

for beam end reactions, so we take 𝑁 = 𝑘 = 30 𝑚𝑚, then:

𝜙𝑅𝑛 = 2980 𝑘𝑁


6-93

Web Crippling


from the end of the member greater than half of the depth of the column, the

nominal resistance is:

𝑅𝑛 = 0.80𝑡𝑤2 1 + 3

𝑁

𝑑

𝑡𝑤

𝑡𝑓

1.5


𝑡𝑤 (Re. NCh2369. Of 2003, B-7)

𝜙 = 0.75

Them considering 𝑁 = 22 𝑚𝑚 (Thickness of the beam flange):

𝜙𝑅𝑛 = 12255 𝑘𝑁

Web Compression Buckling



member, so in this case (a exterior connection), this limit state does not apply.

Then, the force of design for the continuity plates is given by:

𝑅𝑠𝑢 = 3460 − 1347 𝑘𝑁 = 2113 𝑘𝑁

Then, the design force is lesser than the calculated with the AISC

requirements; however the doubler plates of the connections have to be

increased.

Welding of the continuity plates:

According to NCh2369.Of2003 (B3.4,B4.2 and B5.2) the continuity plate to




Note: As seen, the previous provisions are quite similar to AISC provisions.


Plates of Chapter 6.

Additional requirements from appendix B of NCh2369. Of 2003

According to section B7.1 of NCh2369.Of 003:


6-94

The width of each continuity plate plus one half of the column web shall be

greater than one third of the width of the flange of the column or plate of

moment connection that delivers the concentrated load:

𝑏𝑐𝑝

2+

𝑡𝑤

2= 175 𝑚𝑚 >

𝑏𝑐𝑓

3= 116 𝑚𝑚 OK

The thickness of the continuity plate shall be greater than the thickness of the

flange of the beam or the flange that transmit the concentrated force and

greater than its own width multiplied by 𝐹𝑦/250, with 𝐹𝑦 in MPa:

𝑡𝑐𝑝 = 25 𝑚𝑚 > 𝑡𝑏𝑓 = 22 𝑚𝑚 OK

𝑡𝑐𝑝 = 25 𝑚𝑚 >𝑏𝑐𝑝

2

𝐹𝑦

250= 12.7 𝑚𝑚 OK

Additionally, the thickness of the continuity plate shall be no lesser than the

thickness of the element of the moment connection that transmits the

concentrated force to the column:

𝑡𝑐𝑝 = 25 𝑚𝑚 < 𝑡𝑝 = 40 𝑚𝑚 NOT OK.

Then, the thickness of the continuity plate has to be increased to 𝑡𝑐𝑝 = 40 𝑚𝑚.

The design according to the additional provisions of NCh2369of.2003 is the

following:

6.4-9 Designed connection, with additional criteria from NCh2369Of.2003.

H 500X350X165.6

H 500X300X132.3

Continuity plate t = 40 mm


PL 690X300X4018 M27 A490

5 M27 A490PL 450X110X10

6

6


6-95

6.4.d. Additional comments: Chilean practice and provisions

The BFP moment connection is the most typical connection in the Chilean

practice; because of that, it is important to give some additional comments

regarding this connection.

The BFP connections present advantages for the Chilean construction practice.

Since the number of qualified professionals on steel construction is limited on

Chile, the most favorable connections are the ones that are simple and require

less constructive details to be executed at the construction site. The BFP

connection has the advantage of requiring that the welded parts, such as the

shear tab plate or the connection of the flange plates to the column, can be

done a the shop, which significantly reduces the amount of qualified

professionals required on site, to obtain a connection that has good behavior

under cyclic loads.

1. Design Forces

NCh2369Of.2003 establishes that the design forces that have to be considered

in the design of moment connections between beam and columns shall be, at

least, equal to the strength of the connected elements (Re. Section 8.5.4).

This is equivalent to say that the design forces for the moment connections are

obtained considering the plastic moment that can be developed at the beam.

The latter does not considers effects such as strain hardening and the actual

expected yield stress of the available steel plates. These effects are considered

by the AISC seismic provisions by amplifying the plastic moment developed at

the beam by the coefficients 𝐶𝑝𝑟 and 𝑅𝑦.

Therefore, the design moment to design the connection, according to the

Chilean provisions, is at least:

𝑀𝑝 = 𝑍𝑥𝐹𝑦

In the example developed in this section, the design moment according to the

AISC provisions was:

𝑀𝑝 = 1558473 𝑘𝑁 −𝑚𝑚

Whereas the design moment according to the Chilean provision is:

𝑀𝑝 = 1231994 𝑘𝑁 −𝑚𝑚


6-96

which is approximately 25% smaller than the design moment obtained with

the AISC provisions.

The shear design force has to be calculated from the plastic moment that can

be developed at the ends of the beam (it is a capacity design), assuming that

plastic hinges develop at certain sections. Also, gravity loads are applied

simultaneously with the seismic loads.

NCh2369.Of2003 does not give any indication regarding the position where the

plastic hinges (neither establishes any criterion for designing a protected zone,

as the AISC provisions does). The only requirement is that the plastic hinge

must be located at a prudent distance from the face of the column (Re.

Section 8.4.1). Since there are no provisions regarding the exact location of

the plastic hinge, the use of the recommendations of the AISC 358-05 seems a

valid alternative. The indication for BFP connections is that the plastic hinge is

located at the end of the bolt group of the connection. Then, the shear design

force would be:

𝑉𝑕 = 𝑉𝑢 𝑠𝑡𝑎𝑡𝑖𝑐 +2𝑀𝑝

𝐿𝑕

𝐿𝑕 = 𝐿𝑏𝑒𝑎𝑚 − 2𝐿𝑝𝑕

Where 𝐿𝑝𝑕 is the distance from the plastic hinge to the face of the column, and

𝐿𝑏𝑒𝑎𝑚 is the length of the beam between column faces. The force 𝑉𝑢 𝑠𝑡𝑎𝑡𝑖𝑐

corresponds to the shear load calculated from load combinations that does not

include the seismic effect, such as self weight and live loads.

The location of the plastic hinge at a section far from the end of the beam will

induce a larger moment at the face of the column, which corresponds to the

shear design force multiplied by the distance from the face to the plastic

hinge.

Since the design moment according to the Chilean provisions is smaller than

the AISC moment, the required length of the connection will be smaller, and

then the design shear load will be smaller. Therefore, the amplification of the

required moment strength due to the distance between the plastic hinge and

the column will be lesser than the required moment strength obtained in the

case of the AISC provisions.

The use of the Chilean design provisions will result in smallest BFP

connections, mostly because these connections do not take into account the


6-97

possibility of strain hardening and larger expected yield strength. It means

that it is implied in the design standard that it is expected that the

displacement demands of the steel structures due to a Chilean earthquake are

not large. This is supported by observation from the performance of steel

structures during previous earthquakes in Chile.

Anyway, it is important that at the stage of the project, when the basis of

design are established, to have a discussion in order to decide the use of

Chilean practice and provisions or the use of the AISC codes.

2. Detailing requirements

For the BFP connections, AISC 358-05 establishes some detailing requirements

such as:

Two bolts per row.

Length of the connections limited by the depth of the beam.

Flange plates shall be CJP welded.

Limitations for flange and web width-thickness ratios.

The first two requirements are not established in the Chilean code. The CJP

welding requirement is established in section 8.5.5 of NCh2369.Of2003, and

the limitations for width-thickness ratios are established in section 8.4.3 of

NCh2369.Of2003, which are slightly less demanding than AISC.

3. Design verifications

General verifications

The Chilean provisions do not establish additional design verifications

compared to the verifications for this type of connection according to the AISC

provisions. The limit states that should be verified according to the Chilean

provisions are:

Flange plates:

Slip critical for bolts (this limit state is not mandatory).

Shear resistance for bolts.

Bearing and tear out of the plate.

Tensile yielding of the plate.

Tensile rupture of the plate.

Block shear rupture of the plate.


6-98

Compression buckling of the plate.

Shear tab:

Slip critical for bolts (this limit state is not mandatory).

Shear resistance for bolts.

Bearing and tear out of the plate.

Tensile yielding of the plate.

Tensile rupture of the plate.

Block shear rupture of the plate.

Welding of the plate.

The main difference between the Chilean and AISC provisions is that the latter

considers, for prequalified BFP moment connections, an additional requirement

in order to ensure the ductile behavior of the connection. The additional

requirement is given by forcing that the tensile rupture limit state has to be

greater than the tensile yielding limit state, considering the factors 𝑅𝑡 and 𝑅𝑦

for each limit state respectively, as seen on the solved example previously.

Panel Zone

For the design of the panel zone, the required verifications have to be done

according to the provisions of Appendix B of NCh2369Of.2003. These

provisions are, in general, the same as established in the AISC 341-05 Seismic

Provisions, and in AISC 358-05 Supplement N°1.

However, some differences arise from the calculation of the design force that

the panel zone must resist. The design force according, to Appendix B of the

NCh2369Of.2003 is given by:

𝑅𝑢 =𝑀𝑢1

𝑑𝑚1+

𝑀𝑢2

𝑑𝑚2− 𝑉𝑢 (Re. B-1, NCh2369.Of2003)

This design force is obtained from equilibrium of the free body diagram of the

beam-to–column connection. 𝑀𝑢1 and 𝑀𝑢2 correspond to the moments of the

beams that arrive to the connection, calculated from the load combinations

established in NCh2369Of.2003, considering that the seismic load is amplified

by 2.0, but the moments need not exceed the plastic moments of the beams.

The force 𝑉𝑢 corresponds to the shear force in the column.

Although AISC 341-05 considers the same free body diagram than the Chilean

provisions, AISC 341-05 establishes that this free body diagram must be done


6-99

considering the projected moments from the plastic hinges, whereas the

Chilean provisions use the moments provided by the load combinations.

The other difference in the calculation of the design force for the panel zone,

are the values of 𝑑𝑚1 and 𝑑𝑚2, which are recommended to be 0.95 times the

depth of the beams arriving to the connection, whereas the AISC provisions

consider the distance between centers of the flange plates of the beams.

If the panel zone resistance 𝑅𝑣 is smaller than the design force 𝑅𝑢, continuity

plates shall be provided. The value of 𝑅𝑣 is calculated from the same equations

for both Chilean and AISC provisions (see section 6.4.c and 6.4.d of this

chapter), but the reduction factor considered in the Chilean provision is:

𝜙𝑣 = 0.75

Whereas the AISC provisions establish that 𝜙𝑣 = 1.00. Then, the Chilean

provisions use smaller design forces, but considers also a lesser panel zone

resistance.

For the continuity plate design, the limit states considered are the same for

both Chilean and AISC provisions:


Web local yielding

Web crippling

Web compression buckling

Finally, NCh2369.Of2003 and AISC provisions establish additional

requirements for the dimensions of the continuity plates. Both provisions are

quite similar and for more detail see 6.4.c and 6.4.d of this chapter.

Nevertheless, the Chilean code establishes that the thickness of the continuity

plates shall not be lesser than the thickness of the flange plate that transmits

the moment from the beam to the column, whereas the AISC provisions only

require that the thickness of the continuity plates shall not be lesser than half

of the thickness of the plate that transmit the forces to the column. This can

lead to bigger continuity plates, but the Chilean provision considers smaller

design forces for the connection and therefore, the flange plates that transmit

the forces to the column have smaller thicknesses.


6-100

4. Additional requirements

Lateral bracing

NCh2369Of.2003 requires that the beam at the connection shall be provided

with lateral support on the beam flanges. The lateral support shall be capable

to resist 0.02𝐹𝑦𝑏𝑓𝑡𝑓. Whereas the AISC provisions establish that the lateral

bracing for the beam shall be designed according to the Appendix 6 of the

AISC 360 (see 6.4.b of this chapter). Both requirements are very similar and

will lead to similar designs.

Column-beam ratios

NCh2369.Of2003 establishes in section 8.4.4 that the summation of the

moment capacities of the columns that arrive to the column-to-beam

connection shall be 1.2 times greater or equal than the summation of the

capacities of the beams arriving to the connection. However, the code does not

give indications for the calculation of these capacities. On the other hand, AISC

358-05 Supplement N°1 establishes that the ratio between the capacities of

the columns and beams shall be greater or equal to 1.0, and gives an

expression to calculate those moment capacities (see 6.4.b.19 of this chapter).


6-101

6.5. Welded Unreinforced Flange-Welded Web Moment Connection


1. NCh2369.Of2003



(Re. NCh2369, 8.5.1)

Bolts must be prestressed to a 70% of the nominal strength for slip

critical; however the nominal strength could be calculated as the

corresponding for bearing type connections.

(Re. NCh2369, 8.5.6)

For field joints, see requirements of 8.5.8 section.

(Re. NCh2369, 8.5.8)

The moment connections between columns and beams must have as

minimum, the resistance equal to the connected elements.

(Re. NCh2369, 8.5.3)

In column – beams joints, both inferior and superior flange must have

lateral bracing designed for a force equal to 0.02𝐹𝑦𝑏𝑓𝑡.

(Re. NCh2369, 8.5.4)

The groove welds joints in seismic connections must be of complete joint

penetration (CJP).

(Re. NCh2369, 8.5.5)

The design of the panel zone must be according to the provisions of the

appendix B of the NCh2369.Of2003 (Beam-column connection design on

rigid steel frames).


6-102

2. AISC 341-05

For the design of beam-to-column connections of special moment frames

(SMF) it is recommended to see Chapter 9. Some important aspects are:

Requirements of beam-to-column connections: see section 9.2a. The

required shear strength should take into account the plastic hinge flexural

capacity for the earthquake (E) load effect.

Unless otherwise designated by AISC358, CJP groove welds of beam


welds as defined in section 7.3b. (Section 9.2c).

The extent of the protected zone shall be defined on AISC358. For

unreinforced connections, the protected zone will extend from the face of

the column to one half of the beam depth beyond the plastic hinge point

(Section 9.2d).



9.4.


according to AISC358 (Section 9.5)



3. AISC 358-05: Prequalified Connections for Special and Intermediate Steel

Moment Frames for Seismic Application and Supplement No1 to AISC

358-05

From chapter 8 of the supplement of the AISC 358-05:

Beam Limitations:

- Beams shall be rolled wide flange or welded built-up I shaped

members conforming to the requirements of section 2.3 of the AISC

358.

- Beam depth is limited to a maximum of W36 for rolled shapes. Depth

of built up sections shall no exceed the depth permitted for rolled

wide-flange shapes.

- Width – thickness ratios for the flanges and web of the beam shall

conform to the limits of section 9.4 of the AISC seismic provisions.

- The weight of the beam shall not exceed 224 kg/m.

- Beam flange thickness is limited to 25 mm.


6-103

- The clear span to depth ratio of the beam is limited to be greater than

7 in SMF.

- Lateral bracing shall be provided at the end of the protected zone

(see Figure 6.5-1) in both inferior and superior flanges of the beam.

The location of the lateral bracing can be vary between d and 1.5d

(with d the depth of the beam) from the face of the column. There is

no need to provided lateral bracing if the beam support a concrete

slab with welded shear connectors spaced at a maximum of 300 mm.

Lateral bracing shall conform section 9.8 of AISC 341 Seismic

Provisions.

6.5-1: Protected zone for WUF-W moment connections.

Column Limitations:

- Columns shall be any rolled shapes or welded built-up sections

permitted in section 2.3 of the AISC 358.

- Rolled shape column depth shall be limited to a maximum of W36.

The depth of the built up wide-flange columns shall not exceed that

for rolled shapes.

- Width – thickness ratios for the flanges and web of the beam shall

conform to the limits of section 9.4 or 10.4 of the AISC seismic

provisions.

- The beam shall be connected to the flange of the column.

- Lateral bracing of columns shall conform to section 9.7 of the AISC

Seismic Provisions.

Panel zones shall conform to the requirements of section 9.3 for SMF of

the AISC 341 Seismic Provisions.


6-104

The column – beam ratios are limited by the requirements of section 9.6

of the AISC 341 Seismic Provisions. The summation 𝑀𝑝𝑏∗ shall be taken

equal to (𝑀𝑝𝑟 + 𝑀𝑣), where 𝑀𝑝𝑟 is computed according to the provisions of

section 8.7 of the AISC 358 supplement and 𝑀𝑣 is the additional moment

product of the shear amplification at the plastic hinge to the centerline of

the column.

Beam flanges shall be connected to the column flange using complete

joint penetration groove welds (CJP). Beam flange welds shall conform to

the provisions of the section 7.3 and appendix W of the AISC Seismic

Provisions.

Weld access hole geometry shall conform to the requirements of AWS

D1.8 section 6.9.1.2. Weld access hole quality requirements shall conform

to the requirements of AWS D1.8 Section 6.92.

The single plate connection shall be provided with a thickness equal or

greater than the thickness of the beam web. The height of the single plate

shall allow a 6 mm minimum and 13 mm maximum overlap with the weld

access hole at the top and bottom. The single plate width beyond the end

of the weld access hole must be 50 mm minimum.

The single plate shear connection shall be welded to the column flange

and the welds must stand a shear strength of at least 𝑕𝑝𝑡𝑝 0.6𝑅𝑦𝐹𝑦𝑝 , where

𝑕𝑝 is the height of the plate and 𝑡𝑝 is the thickness of the plate.

The single plate must be connected to the beam web with fillet welds. The

size of the fillet weld shall be the thickness of the single plate minus 2

mm. The fillets must extend along the sloped top and bottom portions of

the plate and along the full single plate heigth. The fillets must end at a

distance no greater than 25 mm but not less than 13 mm from the edge

of the access hole.

The beam web must be connected with the column flange with a CJP

groove weld. This welds shall be provided over the full length of the web

between the access holes and must comply with the requirements of the

section 7.3 and the appendix W of the AISC Seismic Provisions. Weld tabs

are not required.


6-105

6.5-2: Details of the connection.

Adapted from AISC358 Supplement n°1, Figure 8.2.

6.5.b. Example

Design a Welded Unreinforced Flange-Welded (WUF-W) Web Moment

Connection between a column and a beam, shown in Figure 6.5-3. Use

A345ESP steel. Use 70 ksi electrode for welds.

The column and beam are Chilean H500x350x165.6 and H500x300x132.3

built-up sections. The connection transfers shear and moment. The clear span

of the beam is 8000 mm.

The design forces are:

Beam:



Column:

𝑃𝑢 = 500 𝑘𝑁

CJP beam web to column

flange web

single plate to column

flange web

Erection bolts in standard holes or horizontal

short slots are permitted as needed for erection

loads and safety

single plate to

beam web weld


6-106

6.5-3: General view of the connection.

3. Section properties

H500x350x165.6


𝑑 = 500 𝑚𝑚, 𝑏 = 350 𝑚𝑚, 𝑡𝑤 = 8

𝑡𝑓 = 25 𝑚𝑚, 𝑍𝑥 = 4561000 𝑚𝑚3

H500x300x132.3


𝑑 = 500 𝑚𝑚, 𝑏 = 300 𝑚𝑚, 𝑡𝑤 = 8

𝑡𝑓 = 22 𝑚𝑚, 𝑍𝑥 = 3571000 𝑚𝑚3

Width –Thickness ratio limitations

The limitations of the width – thickness ratios are given in table I-8-1 of AISC

341-05.

For beam and column flanges:

𝜆 =𝑏

2𝑡< 𝜆𝑝𝑠 = 0.30

𝐸

𝐹𝑦= 7.22

H500X350X165.6

H500X300X132.3


6-107

For beam and column webs:

𝜆 =𝑕

𝑡𝑤< 𝜆𝑝𝑠 = 2.45

𝐸

𝐹𝑦= 58.98

Column flange:

𝜆 = 7.0 < 𝜆𝑝𝑠 OK

Column web:

𝜆 = 56.3 < 𝜆𝑝𝑠 OK

Beam flange:

𝜆 = 6.8 < 𝜆𝑝𝑠 OK

Beam web:

𝜆 = 57 < 𝜆𝑝𝑠 OK

4. Design forces

Calculation of the maximum probable moment and shear force

The maximum probable moment is calculated according to section 2.4.3 of

AISC 358-05:

𝑀𝑝𝑟 = 𝐶𝑝𝑟𝑅𝑦𝐹𝑦𝑍𝑒

In this case, according to section 8.7 of AISC 358 supplement, 𝐶𝑝𝑟 shall be

taken equal to 1.4. For A345ESP according to the table I-6-1 of the AISC 341

Seismic Provisions, considering that the A345ESP is similar to an ASTM A572

grade 50, then 𝑅𝑦 = 1.1. Finally 𝑍𝑒 = 𝑍𝑥, so the probable moment is:

𝑀𝑝𝑟 = 1897271 𝑘𝑁 −𝑚𝑚

Since the plastic hinge is located at the face of the column, the effective

moment will be:


6-108

𝑀𝑓 = 𝑀𝑝𝑟

Considering that the plastic hinge is immediately adjacent to the face of the

column, the shear force is:

𝑉𝑕 =2𝑀𝑝𝑟

𝐿+ 𝑉𝑔𝑟𝑎𝑣𝑖𝑡𝑦

𝑉𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 1.2𝑉𝐷 + 1.0𝑉𝐿 = 68

𝑉𝑕 = 542 𝑘𝑁

5. Beam to column moment ratio verification

According to section 8.4 of the AISC 358 supplement n°1, the column - beam

ratio shall conform to the requirements of the section 9.6 of the AISC 341

Seismic Provision for SMF. The code establishes the following:

𝑀𝑝𝑐

𝑀𝑝𝑏∗ ≥ 1.0

𝑀𝑝𝑏 = (𝑀𝑝𝑟 + 𝑀𝑣)

𝑀𝑣 is permitted to be calculated according to section 8.4 of the AISC 358

supplement as 𝑉𝑕𝑑𝑐/2, where 𝑑𝑐 is the depth of the column. Then:

𝑀𝑝𝑐

𝑀𝑝𝑏=

2𝑍𝑐𝑥 𝐹𝑦𝑐−2𝑍𝑐𝑥 𝑃𝑢𝑐 /𝐴𝑔

1.4𝑅𝑦𝐹𝑦𝑏 𝑍𝑏𝑥 +𝑉𝑕𝑑𝑐/2= 1.44 > 1.0 OK

6.5.c. Single plate shear connection design

1. Design Force

According to the provisions of the section 8.6 of the AISC 358 supplement, the

shear strength of the single plate shear connection has to be greater than

𝑕𝑝𝑡𝑝(0.6𝑅𝑦𝐹𝑦𝑝 ). To calculate the value of 𝑕𝑝 (the height of the plate that resist

shear), we fix the dimension of the access holes.

According to section J1.6 of the Commentary of the AISC 360-05 Specification,

the dimensions of the access hole are given by:

Width: Greater than 1.5𝑡𝑏𝑤 or 38 mm.

Height: Greater than 1.5𝑡𝑏𝑤 or 25 mm, but less than 50 mm.


6-109

Then, the dimensions for the access holes are:

𝐿𝑎𝑕 = 38 𝑚𝑚

𝐻𝑎𝑕 = 25 𝑚𝑚

𝑕𝑝 = 𝑑𝑏 − 2𝑡𝑏𝑓 − 2𝐻𝑎𝑕 = 406 𝑚𝑚

𝑡𝑝 = 𝑡𝑐𝑤 = 8 𝑚𝑚

Note: For the dimensions of the access holes, conservatively it was not

considered for the design the minimum overlap of 6 mm in access holes.

Therefore:

𝑕𝑝𝑡𝑝 0.6𝑅𝑦𝐹𝑦𝑝 = 739 𝑘𝑁

Which is greater than 𝑉𝑕 = 585 𝑘𝑁, so we design for 𝑉𝑢 = 739 𝑘𝑁.

2. Shear yielding of the plate


𝑅𝑛 = 0.6𝐹𝑦𝐴𝑔 (Re. AISC360-05 J4-3)

𝜙 = 1.00

Consider a plate with a height equal to 𝑕𝑝 and a thickness 𝒕 = 𝟏𝟐 𝒎𝒎. The

width of the plate is given by the minimum established by section 8.6 of the

AISC 358 supplement n°1:

𝑏𝑝 = 𝐿𝑎𝑕 + 50 𝑚𝑚 + 12 𝑚𝑚 = 100 𝑚𝑚

The 50 mm come from the AISC 358 supplement n°1 provisions and the 12

mm are for tolerance issues.

Then, considering that the gross shear area of the plate is: 𝐴𝑔 = 𝑕𝑝𝑡 = 406 ×

12 = 4872 𝑚𝑚2, we have:

𝝓𝑹𝒏 = 𝟏𝟎𝟎𝟖 𝒌𝑵 > 739 𝑘𝑁 OK


6-110

3. Shear rupture of the plate


𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 (Re. AISC360-05 J4-4)

𝜙 = 0.75

Then, considering 𝐴𝑛𝑣 = 𝐴𝑔, we have:

𝜙𝑅𝑛 = 986 𝑘𝑁 > 739 𝑘𝑁 OK

4. Weld shear

The weld used for the connection between the plate and the column flange

consist one weld at each side of the plate connection. The eccentricity between

the weld and the line of application of the shear, is taken as a half of the width

of the single plate connection:

𝑒 = 50 𝑚𝑚

Then, the weld is subject to a shear force and a moment given by:

𝑉𝑢 = 739 𝑘𝑁, 𝑀𝑢 = 𝑒𝑉𝑢 = 38950 𝑘𝑁 −𝑚𝑚

Since there are shear and moment acting on the connection, use the elastic

method for the calculation of the maximum stress for the weld:

(Re. Part 8 AISC Manual of Steel Construction)

𝑓𝑥 =𝑀

𝐼𝑥

𝑕𝑤𝑒

2

𝑓𝑦 =𝑉𝑢

𝐴𝑒𝑓𝑓

𝐹𝑢 = 𝑓𝑥2 + 𝑓𝑦

2

Where 𝐼𝑥 and 𝐴𝑒𝑓𝑓 are the inertia and the effective area of the weld. Use 10

mm fillet weld size, which complies with maximum fillet weld size; the

height of the weld 𝑕𝑤𝑒 is equal to the length of the plate minus two times the

thickness of the plate, 𝑕𝑤𝑒 = 382 mm.

𝑡𝑒𝑓𝑓 = 2 × 8 × 0.707 𝑚𝑚 = 14.14 𝑚𝑚


6-111

𝐼𝑥 =𝑕𝑤𝑒

3 𝑡𝑒𝑓𝑓

12= 65683797 𝑚𝑚4

𝐴𝑒𝑓𝑓 = 𝑡𝑒𝑓𝑓 𝑕𝑤𝑒 = 5401 𝑚𝑚2

𝑓𝑥 = 113 𝑀𝑃𝑎

𝑓𝑦 = 144 𝑀𝑃𝑎


According to the AISC 360-05, table J2.5, the nominal strength for a weld is:

𝐹𝑤 = 0.60𝐹𝑒𝑥𝑥

𝜙 = 0.75

Then,


5. Panel Zone

The panel zone must be verified according to section 8.4 of AISC 358-05

Supplement N°1, which refers to sections 9.3 or 10.3 of the AISC 341 Seismic

Provisions.

According to section 9.3 of AISC 341, the required shear strength of the panel

zone shall be calculated from the summation of the projected expected plastic

hinge moments at the column faces.

The shear strength (according to the limit state of shear yielding) is given by

the following:

(Re. Section J10.6 AISC 360-05)

If it is considered frame stability including plastic panel zone deformation, the

nominal strength is:

If 𝑃𝑢 ≤ 0.75𝑃𝑦:


2

𝑑𝑏𝑑𝑐𝑡𝑤 (Re. AISC 360-05, J10-11)

If 𝑃𝑢 > 0.75𝑃𝑦:


2

𝑑𝑏𝑑𝑐𝑡𝑤 1.9 − 1.2

𝑃𝑢

𝑃 𝑐 (Re. AISC 360-05, J10-12)


6-112

Where,

𝑃𝑢 : 𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑖𝑛 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛

𝑏𝑐𝑓 : 𝑤𝑖𝑑𝑡𝑕 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛 𝑓𝑙𝑎𝑛𝑔𝑒

𝑑𝑏 : 𝐵𝑒𝑎𝑚 𝑑𝑒𝑝𝑡𝑕

𝑃𝑦 : 𝐴𝑥𝑖𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 𝑠𝑡𝑟𝑒𝑛𝑔𝑡𝑕 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛

𝑑𝑐 : 𝐶𝑜𝑙𝑢𝑚𝑛 𝑑𝑒𝑝𝑡𝑕

𝑡𝑐𝑓 : 𝑇𝑕𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡𝑕𝑒 𝑐𝑜𝑙𝑢𝑚𝑛 𝑓𝑙𝑎𝑛𝑔𝑒

𝑡𝑤 : 𝐶𝑜𝑙𝑢𝑚𝑛 𝑤𝑒𝑏 𝑡𝑕𝑖𝑐𝑘𝑛𝑒𝑠𝑠

Finally, the nominal resistance is 𝜙𝑣𝑅𝑛, with 𝜙𝑣 = 1.0 according to the AISC

341, section 9.3a.

If the shear strength is not enough, doubler plates shall be provided, which

must be designed according to AISC 360-05, J10-9, which refers to the

requirements of the chapter G of the AISC 360-05. The doubler plates must

resist 𝑅𝑢 − 𝜙𝑣𝑅𝑛.

6. Calculation of 𝑅𝑢

For the calculation of the shear forces in the panel zone, consider the following

figure.

6.5-4: Typical panel zones forces. Figure adapted from AISC Design Guide

N°13, Fig. 2-3.

The shear forces in the columns can be estimated assuming that the inflection

point is located at the middle of the story height of the column. However, the

effect of the column shear is neglected, which is a conservative assumption.

The shear design force for the panel zone is:

V us

V us

(P ) uf 2 (P ) uf 1

(P ) uf 2 (P ) uf 1

(M ) u 1(M ) u 2

V u


6-113

𝑉𝑢 = 𝑃𝑢𝑓1 + 𝑃𝑢𝑓2 − 𝑉𝑢𝑠

𝑉𝑢𝑠 = 0 (Assumption)

𝑃𝑢𝑓𝑖 =𝑀𝑢𝑖

𝑑𝑏𝑖 − 𝑡𝑏𝑓𝑖

𝑀𝑢𝑖 is the plastic moment of the beam. For this example, there is only one

beam at the column (exterior connection):

𝑉𝑢 =𝑀𝑓

𝑑𝑏 − 𝑡𝑏𝑓=

1897271

500 − 22= 3969 𝑘𝑁

Assuming that 𝑃𝑢 < 0.75𝑃𝑐, the resistance of the panel zone is:


2

𝑑𝑏𝑑𝑐𝑡𝑤 = 1099 𝑘𝑁 < 𝑉𝑢

Doubler plates are required; their design will follow the provisions of chapter G

of AISC 360-05:

𝑅𝑛 = 0.6𝐹𝑦𝐴𝑤

𝜙 = 0.9

𝐴𝑤 = 2𝑤𝑧𝑡𝑑𝑝

𝑤𝑧 = 500 − 2 × 25 = 450 𝑚𝑚

Where 𝑤𝑧 is the width of the panel zone of the column between column

flanges.

Then,

2𝑡𝑑𝑝 ≥𝑉𝑢 − 𝜙𝑣𝑅𝑛

0.6𝐹𝑦𝑤𝑧

= 30.81 𝑚𝑚

𝑡𝑑𝑝 > 15.4 𝑚𝑚

We use doubler plates with a thickness 𝑡𝑑𝑝 = 16 𝑚𝑚.

7. Welding of the doubler plates


for Chapter 6.

8. Thickness of the web of the column

Verify the thickness of the web of the column:


6-114

𝑡 ≥ (𝑑𝑧 + 𝑤𝑧)/90

Where 𝑑𝑧 is the depth of the panel zone between continuity plates, then:

𝑑𝑧 = 500 − 2 × 22 = 456 𝑚𝑚

𝑡 ≥456 + 450

90= 10𝑚𝑚

Then the column web is not ok. But using doubler plates that are plug welded

to the column web, the thickness considered is the summation of the doubler

plates and the web of the column:

𝑡 = 2 × 𝑡𝑑𝑝 + 𝑡𝑐𝑤 = 40 𝑚𝑚 > 10 𝑚𝑚 OK


Continuity plates must be designed considering chapter 2 of AISC 358-05,

which refers to section J10 of AISC360-05. The continuity plate is not required

complying with the following criterion:

𝑡𝑐𝑓 ≥ 0.4 1.8𝑏𝑏𝑓 𝑡𝑏𝑓𝐹𝑦𝑏 𝑅𝑦𝑏

𝐹𝑦𝑐 𝑅𝑦𝑐 (Re. AISC 358-05, 2.4.4-1)

𝑡𝑐𝑓 ≥𝑏𝑏𝑓

6 (Re. AISC 358-05, 2.4.4-2)

Where 𝑡𝑐𝑓 is the minimum thickness of the column flange. Then, we have:

𝑡𝑐𝑓 ≥ 43.6 𝑚𝑚 (Re. AISC 358-05, 2.4.4-1)

𝑡𝑐𝑓 ≥ 50 𝑚𝑚 (Re. AISC 358-05, 2.4.4-2)

Therefore, continuity plates are needed.

The continuity plates have to be designed to a force that is 𝑅𝑢 −𝜙𝑅𝑛, where

𝜙𝑅𝑛 is the nominal strength of the column flange or the column web to the

following limit states:



𝑅𝑛 = 6.25𝑡𝑐𝑓2 𝐹𝑦𝑓 (Re. AISC 360-05. J10-1)

𝜙 = 0.90


6-115

Then:

𝜙𝑅𝑛 = 1347 𝑘𝑁

Web local yielding

Consider that the concentrated force is applied at a distance to the end of the

element greater than the depth of the element; the nominal resistance is given

by:

𝑅𝑛 = 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑤 (Re. AISC 360-05. J10-2)

𝜙 = 1.00

The value of 𝑡𝑤 considers the thickness of the doubler plates.



N is the length of bearing that in our case corresponds to the thickness of the

flange of the beam, 𝑁 = 22 𝑚𝑚. However the value of 𝑁 cannot be less than 𝑘

for beam end reactions, so we take 𝑁 = 𝑘 = 30 𝑚𝑚, then we have:

𝜙𝑅𝑛 = 2484 𝑘𝑁

Web Crippling


from the end of the member greater than half of the depth of the column:

𝑅𝑛 = 0.80𝑡𝑤2 1 + 3

𝑁

𝑑

𝑡𝑤

𝑡𝑓

1.5


𝑡𝑤 (Re. AISC 360-05. J10-4)

𝜙 = 0.9

Then, considering 𝑁 = 30 𝑚𝑚:

𝜙𝑅𝑛 = 10321 𝑘𝑁




member, so in this case (a exterior connection), this limit state does not apply.


6-116

Considering all the limit states:

min𝜙𝑅𝑛 = 1347 𝑘𝑁

Then,

𝑅𝑠𝑢 = 𝑃𝑢𝑓 − 𝜙𝑅𝑛

𝑃𝑢𝑓 =𝑀𝑓


𝑅𝑠𝑢 = 2622 𝑘𝑁

According to the AISC 358-05, the thickness of the continuity plates must

accomplish with the following provisions:

For exterior connections:

𝑡𝑐𝑝 ≥1

2𝑡𝑏𝑓 (Re. AISC 358-05, 2.4.4a)

For two side (interior) connections:

𝑡𝑐𝑝 ≥ max 𝑡𝑏𝑓𝑖 (Re. AISC 358-05, 2.4.4b)

This example is an exterior connection. Therefore, the minimum thickness of

the continuity plate must be 11 mm.

According to the AISC 358 provisions, section 2.4.4, continuity plates must

comply with the provisions of section J10 of AISC 360-05. Therefore, the

continuity plate shall be designed as a stiffener, which is designed as an

element subjected to tensile forces according to chapter D of AISC 360-05,

and as an element subjected to compressive forces, according to chapter E

and section J4.4 of AISC 360-05.

10. Design for tensile forces

Tensile yielding:

𝑅𝑛 = 𝐹𝑦𝐴𝑔 (Re. AISC 360-05, D2-1)

𝜙 = 0.9

Then, the required thickness, considering that the width of both continuity

plates is 𝑏𝑐𝑝 = 342 𝑚𝑚, then:

𝑡𝑐𝑝 ≥𝑅𝑠𝑢

𝜙𝐹𝑦𝑏𝑐𝑝= 24.69 𝑚𝑚


6-117

Use 𝒕𝒄𝒑 = 𝟐𝟓 𝒎𝒎.

Tensile fracture:

𝑅𝑛 = 𝐹𝑢𝐴𝑒 (Re. AISC 360-05, D2-2)

𝜙 = 0.75

Where 𝐴𝑒 corresponds to the effective area, which in this case is equal to 𝐴𝑔.

The result is:

𝜙𝑅𝑛 = 2885 𝑘𝑁 > 2622 𝑘𝑁 OK

11. Design for compressive forces

According to the provisions of the section E6.2 and J4.4 of the AISC 360-05,

we have that the nominal strength is:

If 𝑘𝐿

𝑟≤ 25 then 𝑅𝑛 = 𝐹𝑦𝐴𝑔 (Re. AISC 360-05, J4-6)

If 𝑘𝐿

𝑟> 25 then the design must be made according to the provisions of chapter

E of AISC 360-05.

Before proceeding with the verification for compressive forces, it has to be

considered that the section J10.8 of AISC 360-05 establish that the effective

length for the buckling verification is 0.75𝑕, where 𝑕 is the length of the

stiffener, and the area of the stiffener must be consider as a cross section,

with the two continuity plates and a orthogonal section corresponding to 25𝑡𝑤

for exterior stiffeners or 12𝑡𝑤 for interior stiffeners, of the section of the

column web, including doubler plates (see Figure 6.5-5).

6.5-5: Design area for the stiffeners.

Stiffener Stiffener

12tw or 25tw

x

y


6-118

For the exterior connection analyzed:

𝐴𝑠𝑡𝑖𝑓𝑓 = 𝑏𝑐𝑝 𝑡𝑐𝑝 + 12𝑡𝑤2 = 27750 𝑚𝑚2

𝐼𝑥𝑥 = 12𝑡𝑤

3𝑡𝑤12

+𝑡𝑐𝑝

3 𝑏𝑐𝑝12

= 369085312 𝑚𝑚4

𝐼𝑦𝑦 =𝑏𝑐𝑝

3 𝑡𝑐𝑝12

+ 𝑡𝑤4 = 85896850 𝑚𝑚4

𝑕 = 𝑑𝑐 − 2𝑡𝑐𝑓 = 450 𝑚𝑚

𝑘𝐿 = 0.75𝑕 = 337 𝑚𝑚

Only the weak axis is verified, which corresponds to:

𝑟 = 𝐼𝑦𝑦𝐴

= 55.63

𝑘𝐿

𝑟= 6.05

Then, design according to the provisions of the section J4 of the AISC 360-05

results in:

𝑅𝑛 = 𝐴𝑠𝑡𝑖𝑓𝑓 𝐹𝑦 = 9573 𝑘𝑁

𝜙𝑅𝑛 = 8616 𝑘𝑁 > 𝑃𝑢𝑓 =𝑀𝑓

𝑑𝑏−𝑡𝑏𝑓= 3969 𝑘𝑁 OK

12. AISC 360 J10-8 additional criteria

The width of the continuity plate plus one half of the thickness of the column

shall be not less than one third of the width of the flange of the beam or

moment connection plate that delivers the force:

𝑏𝑐𝑝

2+

𝑡𝑤

2= 175 𝑚𝑚 >

𝑏𝑏𝑓

3= 100 𝑚𝑚 OK

The thickness of the continuity plate shall not be less than one half the

thickness of the flange or moment connection that transmits the force and

greater or equal than the width of the continuity plate divided by 15:

𝑡𝑐𝑝 = 25 𝑚𝑚 >𝑡𝑏𝑓

2= 11 𝑚𝑚 OK

𝑡𝑐𝑝 = 25 𝑚𝑚 >𝑏𝑐𝑝 /2

15= 11.4 𝑚𝑚 OK

Finally the continuity plate shall extend at least one half of the column depth,

which in this case is accomplished because the continuity plate extends in all

the depth of the column.


6-119

13. Lateral Bracing

Following the provisions of section 8.3.1 of the AISC 358 supplement, lateral

bracing must be provided according to 9.8 for SMF of the AISC 341 Seismic

Provision. Thus, lateral bracing must be provided at a spacing not greater than

𝐿𝑏 = 0.086𝑟𝑦𝐸/𝐹𝑦, and the braces must meet the provisions of Appendix 6 of

AISC 360-05, considering a design moment equal to 𝑀𝑟 = 𝑅𝑦𝑍𝐹𝑦 , and 𝐶𝑑 = 1.0:

Resistance required by the brace (nodal bracing):

𝑃𝑟 = 0.02𝑀𝑟𝐶𝑑/𝑕𝑜 (Re. AISC 360-05, A-6-7)

Stiffness required by the brace:

𝛽𝑏𝑟 =1

𝜙

10𝑀𝑟𝐶𝑑

𝐿𝑏𝑕𝑜 (Re. AISC 360-05, A-6-8)

𝜙 = 0.75

Where 𝑕𝑜 is the distance between flange centroids.

Provide lateral bracing only at the bottom flange of the beam. Furthermore,

suppose that the inferior flange has lateral bracing at both sides of the beam,

so design the braces only for tensile forces.

𝑀𝑟 = 1355194 𝑘𝑁 −𝑚𝑚

𝑕𝑜 = 500 − 22 = 478 𝑚𝑚

𝑃𝑟 = 56.7 𝑘𝑁

Assume that 𝐿𝑏 is the maximum value permitted, which is:

𝐿𝑏 =0.086𝑟𝑦𝐸

𝐹𝑦, 𝑟𝑦 = 76.7 𝑚𝑚

𝐿𝑏 = 3823 𝑚𝑚

Then:

𝛽𝑏𝑟 = 9.88 𝑘𝑁

𝑚𝑚

The resistance to tensile forces is given by tensile yielding:

𝑅𝑛 = 𝐹𝑦𝐴𝑔 (Re. AISC 360-05, D2-1)

𝜙 = 0.9


6-120

Then, the required area for the cross section of the brace in tension is (from

strength and stiffness requirements):

𝐴𝑔 ≥ max 𝑃𝑏𝑟

0.9𝐹𝑦,𝛽𝑏𝑟

𝐸𝐿𝑏𝑟

Considering a distance between adjacent beams of 𝐿𝑏𝑟 = 4000 𝑚𝑚:

𝐴𝑔 ≥ 189 𝑚𝑚2

Then a tubular section D1 7/8, with a thickness of 1.5 mm, may be used. The

area of this section is 217 mm2.

NCh2369.Of2003 establishes that the lateral bracing must be designed to

resist a force equal 0.02𝐹𝑦𝑏𝑏𝑓 𝑡𝑏𝑓 , which in this example is equal to 45.5 𝑘𝑁, which

is 20% less than the requirements from AISC.

14. Verification of shear strength of the beam

The beam is subjected to a shear force 𝑉𝑕 = 542 𝑘𝑁; then, according to the

provisions of chapter G of AISC 360-05:

𝑉𝑛 = 0.6𝐹𝑦𝐴𝑤𝐶𝑣 (Re. AISC 360-05, G2-1)

𝜙 = 1.0

𝐶𝑣 = 1.0

𝐴𝑤 = 500 × 8 = 4000 𝑚𝑚2

𝜙𝑉𝑛 = 828 𝑘𝑁 > 542 𝑘𝑁 OK

Designed Connection

6.5-6: General view of the designed connection.

H500X350X165,6

H500X300X132,3

Contuinity plate t = 25 mm


PL t = 12 mm10

10

CJP


6-121

6.5.d. Panel zone and continuity plates according to NCh2369.Of2003

1. Panel Zone

According to the NCh2369.Of2003, section B2.2:

𝑅𝑢 =𝑀𝑢1

𝑑𝑚1+

𝑀𝑢2

𝑑𝑚2− 𝑉𝑢 (Re. NCh2369.Of2003, B-1)

Where 𝑑𝑚𝑖 corresponds to 0.95𝑑𝑖, and 𝑑𝑖 is the height of the beam i. Consider

for this example that 𝑉𝑢 = 0 and that 𝑀𝑢 is 𝑀𝑓:

𝑅𝑢 = 3994 𝑘𝑁

According to section B2.2, the resistance of the panel zone is:

𝑅𝑛 = 0.60𝐹𝑦𝑑𝑐𝑡𝑝 1 +3𝑏𝑐𝑓 𝑡𝑐𝑓

2

𝑑𝑏𝑑𝑐𝑡𝑝 𝑖𝑓 𝑃𝑢 ≤ 0.75𝑃𝑦 (Re. NCh2369.Of2003, B-2)

𝜙 = 0.75

Where 𝑡𝑝 is the total thickness of the panel zone, including doubler plates,

then:

𝑡𝑝 = 2 × 16 𝑚𝑚 + 𝑡𝑐𝑤 = 40 𝑚𝑚

𝜙𝑅𝑛 = 3308 𝑘𝑁 < 3994

Then considering the provisions of the NCh2369.Of2003, the thickness of the

doubler plates shall be increased. Use 𝒕𝒅𝒑 = 𝟐𝟒 𝒎𝒎, wich results in the

following verification:

𝜙𝑅𝑛 = 4550 𝑘𝑁 > 3994 𝑘𝑁 OK


According to section B.3, B.4, B.5, B6 and B.7 of NCh2369.Of2003, Continuity

Plates must be designed considering:



𝑅𝑛 = 6.25𝑡𝑐𝑓2 𝐹𝑦𝑓 (Re. NCh2369.Of2003, B3.1)


6-122

𝜙 = 0.90

Then,

𝜙𝑅𝑛 = 1347 𝑘𝑁

Web local yielding

Considering that the concentrated force is applied at a distance to the end of

the element greater than the depth of the element, the nominal resistance is

given by:

𝑅𝑛 = 5𝑘 + 𝑁 𝐹𝑦𝑤 𝑡𝑤 (Re. NCh2369.Of2003, B-5)

𝜙 = 1.00

Also considering that 𝑡𝑤 includes the thickness of the doubler plates.



N is the length of bearing that in our case corresponds to the thickness of the

flange of the beam, 𝑁 = 22 𝑚𝑚. However, the value of N cannot be less than 𝑘

for beam end reactions, so it is used 𝑁 = 𝑘 = 30 𝑚𝑚. Resulting in:

𝜙𝑅𝑛 = 3477 𝑘𝑁

Web Crippling


from the end of the member greater than half of the depth of the column, the

nominal resistance is:

𝑅𝑛 = 0.80𝑡𝑤2 1 + 3

𝑁

𝑑

𝑡𝑤

𝑡𝑓

1.5


𝑡𝑤 (Re. NCh2369.Of2003, B-7)

𝜙 = 0.75

Then, considering 𝑁 = 22 𝑚𝑚,

𝜙𝑅𝑛 = 15064 𝑘𝑁


6-123




member, so in this case (a exterior connection), this limit does not apply.

Then, the force of design for the continuity plates is given by:

𝑅𝑠𝑢 = 3994 − 1347 𝑘𝑁 = 2647 𝑘𝑁

Then, the design force increases but does not control the design.

3. Welding of the continuity plate

According to NCh2369.Of2003 (B3.4, B4.2 and B5.2), the continuity plate to


the stiffener. The continuity plate-to-web welding shall be dimensioned to


Note: As seen, the previous provisions are quite similar to AISC provisions.


Plates of Chapter 6.

Additional requirements of appendix B of NCh2369.Of2003:

According to the provisions of section B7.1 of NCh2369.Of2003:

The width of each continuity plate plus one half of the column web shall be

greater than one third of the width of the flange of the column or plate of

moment connection that delivers the concentrated load:

𝑏𝑐𝑝

2+

𝑡𝑤

2= 200𝑚𝑚 >

𝑏𝑐𝑓

3= 166 𝑚𝑚 OK

The thickness of the continuity plate shall be greater than the thickness of the

flange of the beam or the flange that transmit the concentrated force and

greater than its own width multiplied by 𝐹𝑦/250, with 𝐹𝑦 in MPa:

𝑡𝑐𝑝 = 25 𝑚𝑚 > 𝑡𝑏𝑓 = 22 𝑚𝑚 OK

𝑡𝑐𝑝 = 25 𝑚𝑚 >𝑏𝑐𝑝

2

𝐹𝑦

250= 12.7 𝑚𝑚 OK


6-124

Then, the only change is the thickness of the doubler plates.

6.5-7 Designed connection considering additional criteria of NCh2369Of.2003.

H500X350X165,6

H500X300X132,3

Contuinity plate t = 25 mm


PL t = 12 mm10

10

CJP


6-125

6.6. Welded Connection Commentary for Continuity Plates and

Doubler Plates

6.6.a. Welded unions of the continuity plates

There are many solutions for the detailing of continuity plates welding. No

specific design will be shown; but some requirements and information tips are

listed down.

1. Tension stiffeners

According to AISC360-05, Section J10.9; the welds of the continuity plates to

the flanges shall be sized for the difference between the required strength and

the applicable limit state strength (𝑅𝑠𝑢). The stiffener to web welds shall be

sized to transfer to the web the algebraic difference in tensile force at the ends

of the stiffener.

2. Compression stiffeners

According to AISC360-05, Section J10.9; the welds of the continuity plates to

the flange shall be sized for the difference between the required strength and

the applicable limit state strength (𝑅𝑠𝑢). The weld to the web shall be sized to

transfer to the web the algebraic difference in compression force at the ends of

the stiffener.

As said on AISC341-05, Section 7.5; corners of continuity plates placed in the

webs of rolled shapes shall be clipped according to the following figure (for

avoid welding into k-area of rolled shapes):


6-126

Figure 6.6-1: Configuration of Continuity Plates.

Taken from AISC341-05 Commentary, Figure C-I-7.2

At the end of weld adjacent to the column web/flange juncture, weld tabs for

continuity plates shall not be used, except when permitted by the engineer of

record. Unless specified by the engineer of record that they be removed, weld

tabs shall not be removed when used in this location.

As said on AISC358-05, Section 2.4.4b; continuity plates shall be CJP groove

welded to column flanges. The weld between the continuity plate and the

column web shall be CJP groove weld or fillet weld. The required strength of

the sum of the welded joints of the continuity plates to the column web shall

be the smallest of:


6-127

a) The sum of the design strengths in tension of the contact areas of the

continuity plates to the column flanges that have attached beam

flanges.

b) The design strength in shear of the contact area of the plate with the

column web

c) The design strength in shear of the column panel zone

d) The sum of the expected yield strengths of the beam flanges

transmitting force to the continuity plates.

For seeing examples of different welding configurations for the continuity

plates (to column flanges and at their ends), refer to Section 4.3 of AISC

Design Guide # 13. Also see Ch. 6 (Design Examples).

6.6.b. Welded unions of the doubler plates

There are many solutions for the detailing of doubler plates welding. No

specific design will be shown; but some requirements and information tips are

listed down.

As said on the commentary of AISC341-05, when web doubler plates extend

between the continuity plates, they may be welded directly to the column

flanges and continuity plates. The welded joint between the doubler-plate and

the column web is required to be configured to transmit the proportionated

load from the continuity plate to each element of the panel zone.

For the doubler-plate to column flange connection, the commentary of

AISC341-05 says that it is anticipated that the panel zone will yield in a

seismic event, and the webs connecting the web doubler plate to the column

flanges are required to be sized to develop the shear strength of the full web

doubler plate thickness. The possible configurations (CJP groove welds of fillet

welds) are shown on the next figure. Note that the column fillet radius and the

plate thickness should be considered before selecting the fillet-welded joint.


6-128

Figure 6.6-2: Web doubler plates.

Taken from AISC341-05 Commentary, Figure C-I-9.3

For seeing examples of different welding configurations for the doubler plates

(to column flanges and at their ends), refer to Section 4.4 of AISC Design

Guide # 13. Also consult Ch.6 (Design Examples).

References:

Carter, 1999, “AISC Design Guide 13: Stiffening of Wide Flange

Columns at Moment Connections: Wind and Seismic

Applications”. American Institute of Steel Construction, Chicago

IL.

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 7: COLUMN SPLICES

7-1

7. COLUMN SPLICES

7.1. Bolted Column Splice for SCBF

7.1.a. Connection design requirements

1. NCh2369.Of2003

Use high strength bolts (ASTM A325 or ASTM A490)

(Re.NCh2369.Of2003, 8.5.1)



connection.

(Re. NCh2369.Of2003, 8.5.6)

For column splices, meet the following:

(Re.NCh2369.Of2003, 8.5.9)

- In buildings, the minimum distance between the splice of the

columns and the top flange of the lower beam must be equal or larger

than the lesser value between 900 mm and half of the clear height

(𝐿𝑛) of the column.

- Splices must be dimensioned for the design forces obtained from the

load combinations (NCh2369.Of2003, 4.5) in which the earthquake

must be amplified by 2.0.

2. AISC 341-05

General requirements:

(Re.8.4, AISC 341-05)

The required strength of a column splice in the seismic load resisting

system (SLRS) shall be equal to the required strength of the columns,

including those calculated from sections 8.3, 9.9, 10.9, 11.9, 13.5 and

16.5b.


7-2

In column bolted splices of SMF, plates or channels shall be used on

both sides of the web.

Location of column splices: the center line of the splice for column

splices made with fillet welds of PJP groove welds shall be located

1200 mm or more away from the beam-to-column connection. When

column clear height between beam-to-column connections is less than

2400 mm, splices shall be located at half the clear height.

Specific requirements (SCBF systems):

(Re.13.5, AISC 341-05)

For SCBF systems: In addition to meeting the requirements of section 8.4,

column splices in SCBF shall be designed to develop 50% of the lesser

available flexural strength of the connected members. The required shear

strength of column web splices shall be at least equal to 𝑀𝑝𝑐/𝐻(LRFD)

or 𝑀𝑝𝑐/1.5𝐻 (ASD), as appropriate, where 𝑀𝑝𝑐 is the sum of nominal plastic

flexural strengths of the column above and below the splice.

Most stringent conditions between these two codes will be used for the

determination of the design forces (M, V and N).

7.1.b. Example

Design an all bolted column splice for a special concentrically braced frame for

the connection shown in Figure 7.1-1 and Figure 7.1-2. Use A250 ESP steel,

required for constructions subjected to dynamic loading, according to

NCh203.Of2006 code, Table 3.

The upper and the lower columns are Chilean H350X350X175.1 built-up

sections. Assume that the column clear height is 𝐿𝑛=3700 mm. The columns

have been designed for resisting the forces given by the load combinations of

the applicable building code (including the seismic load) and the ends are not

prepared for full contact in bearing. Suppose that the loads on the columns

are:

𝑃𝐷 = 290 𝑘𝑁,𝑃𝐿 = 45 𝑘𝑁,𝑃𝐸 = 200 𝑘𝑁

𝑉𝐷 = 50 𝑘𝑁,𝑉𝐿 = 20 𝑘𝑁,𝑉𝐸 = 60 𝑘𝑁

𝑀𝐷 = 50000 𝑘𝑁 −𝑚𝑚,𝑀𝐿 = 30000 𝑘𝑁 −𝑚𝑚 𝑘𝑁,𝑀𝐸 = 60000 𝑘𝑁 −𝑚𝑚


7-3

d

Inner

flange

plate

Outter

flange

plate

gap

web plate

tf

t w

g

General view of the connection:

Figure 7.1-1: Connection to be designed. Frontal and lateral view.

Figure 7.1-2: Connection to be designed. Column section.

Column Section

t1

t2

tf

t3 b2

bf

b 3

b 1


7-4

1. Sections and Materials properties

H350X350X175.1



A250 ESP:


𝐹𝑦 = 250 𝑀𝑃𝑎 ,𝐹𝑢 = 400 𝑀𝑃𝑎,𝐸 = 200000 𝑀𝑃𝑎

BOLTS: ASTM A490, threads included in the shear planes, STD holes


2. Design forces

Required axial strength:

Use the combinations of NCh2369.Of2003 code, section 4.5b):

i. 1.2D+1.0L ±1.1E, but the E term must be amplified by 2.0, according

to NCh2369.Of 2003, 8.5.9; therefore the combination used is: 1.2D

+1.0L±2.2E.

ii. 0.9D±1.1E, but the E term must be amplified by 2.0, according to

NCh2369.Of2003, 8.5.9; therefore the combination used is:

0.9D±2.2E.

Therefore, calculate the maximum compressive force (when E term is being

added) for the first load combination and the maximum tensile force (when E

is being subtracted) for these load combinations.

𝑃𝑢 𝑖 = 833 𝑘𝑁 (Compression).

𝑃𝑢 𝑖𝑖 = −179 𝑘𝑁 (Tension).

According to AISC 341-05, section 8.3, if

𝑃𝑢

𝜙𝑐𝑃𝑛> 0.4, without the consideration

of the amplified seismic load, the required axial and tensile strength should

take into account the Ω0 factor on the load combinations given by the

applicable building code. In this case, the NCh2369.Of2003, has mandatorily


7-5

amplified the earthquake E term by a 2.0 factor, so it is not necessary to do

this check for determine the most stringent condition between these two codes.

Then:

𝑃𝑅𝐸𝑄 𝑖 = 833 𝑘𝑁 (Compression)

𝑃𝑅𝐸𝑄 𝑖𝑖 = −179 𝑘𝑁 (Tension)

Required flexural strength

From NCh2369.Of2003 load combinations (using absolute values):

M1 = max 1.2𝑀𝐷 + 1.0𝑀𝐿 + 2.2𝑀𝐸; 0.9𝑀𝐷 + 2.2𝑀𝐸 = 222000 𝑘𝑁 −𝑚𝑚

In order to comply with AISC 341-05, section 13.5; use 50% of the column

nominal strength 𝑀𝑛. Suppose that the column reaches its plastic capacity

(𝑀𝑛 = 𝑀𝑝 = 𝐹𝑦𝑍𝑥 = 801000 𝑘𝑁 −𝑚𝑚).

Then

𝑀2 = 0.5𝑀𝑛 = 0.5𝑀𝑝 = 400500 𝑘𝑁 −𝑚𝑚

Using as the required moment, the most stringent between NCh2369.Of2003

and AISC 341-05 conditions:

𝑀𝑅𝐸𝑄 = max 𝑀1 ,𝑀2 = 400500 𝑘𝑁 −𝑚𝑚

Tips:

i. Note that 𝑀𝑅𝐸𝑄 = 50% 𝑀𝑛 > 𝑀𝑢 = 𝑀1 at the splice location and this

condition meets the requirements of AISC 341-05 (see 8.4 comments

of the code). 𝑀𝑢 = 𝑀1 is obtained according to NCh2369.Of2003.

ii. The 100% of 𝑀𝑛 (the column strength capacity is always larger than

𝑀𝑢) could be used for the design of this splice. This is recommendable

for a quick design in a design stage where splice locations are not

defined and the loads are not well known.

Required shear strength


𝑉1 = max 1.2𝑉𝐷 + 1.0𝑉𝐿 + 2.2𝑉𝐸; 0.9𝑉𝐷 + 2.2𝑉𝐸 = 212 𝑘𝑁


7-6

Using AISC 341-05, the lower and the upper column are the same, hence:

V2 =2𝑀𝑝𝑐

𝐻=

2𝑀𝑝𝑐

𝐿𝑛

𝑀𝑝𝑐 = 𝐹𝑦𝑍𝑥 = 801000 𝑘𝑁 −𝑚𝑚

Therefore, using the most stringent condition between NCh2369.Of2003 and

AISC 341-05:

𝑉𝑅𝐸𝑄 = max V1, V2 = 433 𝑘𝑁

Tips:

i. Note that 𝑉𝑅𝐸𝑄 =2𝑀𝑝𝑐

𝐿𝑛> 𝑉𝑢 = 𝑉1 at the splice location and this condition

meets the requirements of AISC 341-05 (see 8.4 comments of the

code). 𝑉𝑢 = 𝑉1 is obtained according to NCh2369.Of2003.

ii. It is possible to do a more conservative design using 𝑉𝑛 > 𝑉𝑢 but

checking always that 𝑉𝑛 > 𝑉𝑅𝐸𝑄 =2𝑀𝑝𝑐

𝐿𝑛.

3. Forces transferred by the splice

All the forces, including the axial forces 𝑃𝑅𝐸𝑄 (compression) or 𝑇𝑅𝐸𝑄 (tension),

are transferred from the upper shaft to the lower shaft via the bolted splice

plates.

Figure 7.1-3: Forces transferred by the splice.

Compression case and tension case.

M

V

P

M

V

T

P1 P2

P3T1 T2

T3

Compresion Case Tension Case


7-7

Suppose that the required shear force (𝑉𝑅𝐸𝑄) will be transferred entirely by the

web splice plate.

Compressive axial force case:

It is assumed that the moment is resisted entirely by the flange splices, and

that the axial load is distributed among the web and flange splices

proportionately to the relative areas.

𝑃1,2 𝑅𝐸𝑄 =𝑃𝑅𝐸𝑄 𝐴𝑓

𝐴±

𝑀𝑅𝐸𝑄

𝑑−𝑡𝑓 (Axial forces transferred through the flanges).

𝑃3 𝑅𝐸𝑄 =𝑃𝑅𝐸𝑄 𝑑−2𝑡𝑓 𝑡𝑤

𝐴 (Axial force transferred through the web).

Tensile axial force case:

Same as above:

𝑇1,2 𝑅𝐸𝑄 =𝑇𝑅𝐸𝑄 𝐴𝑓

𝐴±

𝑀𝑅𝐸𝑄

𝑑−𝑡𝑓 (Axial forces transferred through the flanges).

𝑇3 𝑅𝐸𝑄 =𝑇𝑅𝐸𝑄 𝑑−2𝑡𝑓 𝑡𝑤

𝐴 (Axial force transferred through the web).

With 𝐴𝑓 = 𝑏𝑓𝑡𝑓 the area of one flange of the column shape and 𝐴 the total area

of the column shape.

Tips:

i. There are other ways of distributing forces. You can use any

reasonable way.

ii. The maximum compression and tension cases on flanges and the

compression and tension cases on the web shall be checked.


7-8

Calculations give the following results (convention is positive for compression

and negative for tension):

5.a.-Compression case

P1 REQ (kN) 1559

P2 REQ (kN) -905

P3 REQ (kN) 179

5.b.-Tension case

T1 REQ (kN) 1162

T2 REQ (kN) -1303

T3 REQ (Kn) -39

Table 7.1-1: Forces transferred by the splices. Refer to Figure 7.1-3

Therefore, the maximum forces to be transferred are:

Through flanges:

𝑃𝑓 = 1559 𝑘𝑁 ,𝑇𝑓 = 1303 𝑘𝑁

Through web:

𝑃𝑤 = 179 𝑘𝑁 ,𝑇𝑤 = 39 𝑘𝑁,𝑉𝑤 = 433 𝑘𝑁

On each flange, these flange forces will be transferred by an inner flange splice

plate (total area of the two plates is 𝐴𝑖𝑓 = 2𝑏2𝑡2) and by an outer splice flange

plate (total area of 𝐴𝑜𝑓 = 𝑏1𝑡1). Hence, divide the flange forces using the same

concept of relative areas as shown before.

On the web, there is a symmetrical distribution of web plates at each side

(each plate with area 𝐴𝑤𝑝 = 𝑏3𝑡3), so the forces in the web will be simply

divided by 2.

Tip:

Note that as the connection to be designed is a “not-bearing” type, axial

compression forces need to be transferred by the splice plates, leading to a

larger amount of bolts and dimensions of plates that if the connection is

designed as a “bearing” type one (for bearing strength between surfaces in

contact, see AISC 360-05 Specification, J7).


7-9

4. Design of web splice

𝑃𝑤 = 179 𝑘𝑁 ,𝑇𝑤 = 39 𝑘𝑁,𝑉𝑤 = 433 𝑘𝑁

Web bolts:

Calculate the maximum force on a bolt for eccentric shear and axial force (see

Figure 7.1-4). 𝑉𝑤 = 433 𝑘𝑁, max 𝑃𝑤 ,𝑇𝑤 = 179 𝑘𝑁

Try M24 bolts, 𝑵𝑩=8 bolts and 𝑵𝑹= 2 rows. Number of bolts per row 𝒏=4.

Place the bolts at 𝒆𝟏 = 𝟕𝟎𝒎𝒎, 𝒆𝟐 = 𝟏𝟎𝟎𝒎𝒎,𝒆𝟑 = 𝟒𝟓𝒎𝒎,𝒆𝟒 = 𝟓𝟎𝒎𝒎 the web

plate section dimensions (both plates are equal) are:

𝑏3 = 2𝑒4 + 𝑒2 = 200 𝑚𝑚, use 𝑡3 = 10 𝑚𝑚

Figure 7.1-4: Bolts positions on web splice plate. Bolt A has the larger load.

Use a gap 𝒈 = 𝟓 𝒎𝒎. Therefore, using the midline of the gap, the distance from

the line of action of 𝑉𝑤 to the gravity center of the bolts arrangement is

𝑒𝑥 =𝑔

2+ 𝑒3 + 1.5𝑒1 = 152.5 𝑚𝑚. Use the classical elastic method for the analysis of

the eccentric shear bolted connection.

A

x

y

P

P

g

b3

e1

e1

e1

y

x

e3

e3

e4

e2 e

4


7-10

𝑁𝐵= number of bolts = 8.

𝑃𝑥 =𝑃𝑤2

= 90 𝑘𝑁

𝑃𝑦 =𝑉𝑤2

= 217 𝑘𝑁

The eccentric shear is analyzed on one of the web plates.

Figure 7.1-5: Forces scheme on the web splice. Frontal and lateral view.

𝑀𝑂 = 𝑃𝑦𝑒𝑥 = 33014 𝑘𝑁 −𝑚𝑚

𝑟𝑖2 = 𝑥𝑖

2 + 𝑦𝑖2 = 69000 𝑚𝑚2

Considering the critical bolt:

𝑦𝑖 =𝑒2

2

𝑥𝑖 = 1.5𝑒1

The required 𝑅𝑖 𝑅𝐸𝑄 force to be transferred by bolt A is:

𝑅𝑥𝑖𝑅𝐸𝑄 =𝑃𝑥𝑁𝐵

+𝑀0𝑦𝑖 𝑟𝑖

2 = 35 𝑘𝑁

𝑅𝑦𝑖𝑅𝐸𝑄 =𝑃𝑦𝑁𝐵

+𝑀0𝑥𝑖 𝑟𝑖

2 = 77 𝑘𝑁

𝑅𝑖𝑅𝐸𝑄 = 𝑅𝑥𝑖𝑅𝐸𝑄2 + 𝑅𝑦𝑖𝑅𝐸𝑄

2 = 85 𝑘𝑁

VF

F

V

F

F/2 F/2


7-11

Bolts check:

Slip critical failure

For conservative calculations, use for slip-critical connection type check, class

A surface (𝜇 = 0.35), and for bearing type connections, consider threads

included on the shear plane.


(Re. AISC 360-05, Eq. J3-4)


level), 𝜇=0.35 (class A surface), 𝐷𝑢=1.13, 𝑕𝑠𝑐=1.0 (standard holes), 𝑇𝑏=257

kN (AISC 360-05, Table J3.1M for M24, ASTM A490 bolts) 𝑁𝑠 = Number of

slip planes = 1.0.

Therefore:


𝑏𝑜𝑙𝑡> 𝑅𝑖𝑅𝐸𝑄 = 85 𝑘𝑁 OK

Note:

It is not an obligation to do the slip critical connection check in bolted connections.

If it is desired to have a rigid connection, slip critical check is recommended. In

this example, we will follow the design with the number of bolts obtained from the

slip critical check.


𝑅𝑛 = 2.4𝑑𝑡𝐹𝑢 = 230𝑘𝑁

𝑏𝑜𝑙𝑡

(Re. AISC 360-05, Eq. J3-6a)

Use 𝜙=0.75 (LRFD), = 𝑚𝑖𝑛 (𝑡𝑤 , 𝑡3) = 10 𝑚𝑚 , 𝐹𝑢 = 400 𝑀𝑃𝑎, 𝑑=nominal bolt

diameter = 24 mm.

𝑅𝑖𝑅𝐸𝑄 = 85 𝑘𝑁 < 𝜙𝑅𝑛 = 173 𝑘𝑁 OK

Single shear on bolts:

For single shear on the most loaded bolt, check the following:


7-12

𝑅𝑖𝑅𝐸𝑄 ≤ 𝜙𝐹𝑛𝑣𝐴𝑏 ,𝜙 = 0.75

(Re. AISC 360-05, J3.6)

Use 𝐴𝑏 = 452 𝑚𝑚2 corresponding to M24 bolts to obtain:

𝑅𝑖𝑅𝐸𝑄 = 85 𝑘𝑁 ≤ 𝜙𝐹𝑛𝑣𝐴𝑏 = 140 𝑘𝑁 OK

Web splice plate:

Dimensions from above:

Width 𝒃𝟑 = 𝟐𝟎𝟎 𝒎𝒎, Thickness 𝒕𝟑 = 𝟏𝟎 𝒎𝒎, Length 𝑳𝟑 = 𝑔 + 2 3𝑒1 + 2𝑒3 =

𝟔𝟎𝟓𝒎𝒎

Compressive force:

𝑃𝑤 = 179 𝑘𝑁

The maximum free length is: 2𝑒3 + 𝑔 = 95 𝑚𝑚 𝑘𝐿 = 95 𝑚𝑚

Using AISC 360-05, section J4.4:

𝑟𝑀𝐼𝑁 = 𝐼

𝐴=

𝑡3

3𝑏312

𝑡3𝑏3= 2.89 𝑚𝑚 →

𝑘𝐿

𝑟𝑀𝐼𝑁= 32.91 > 25 → Use Ch. E.

𝑘𝐿

𝑟𝑀𝐼𝑁= 32.91 < 4.71

𝐸

𝐹𝑦= 133 , therefore with 𝐹𝑒 =

𝜋2𝐸

𝑘𝐿

𝑟

2 = 1823 𝑀𝑃𝑎:

𝐹𝑐𝑟 = 0.658𝐹𝑦

𝐹𝑒 𝐹𝑦 = 236 𝑀𝑃𝑎

(Re. AISC 360-05, Eq. E7-2)

𝜙𝑃𝑛 = 0.9𝐹𝑐𝑟𝐴𝑔 = 0.9𝐹𝑐𝑟𝑏3𝑡3 = 425 𝑘𝑁 >𝑃𝑤

2= 90 𝑘𝑁 OK

Tensile Yielding on splice plate:

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏3𝑡3 = 450 𝑘𝑁 > 𝑇𝑤 =

39

2= 20 𝑘𝑁 OK

(Re. AISC 360-05, Eq. J4-1)


7-13

Tensile rupture on splice plate:

𝜙𝑅𝑛 = 0.75𝐹𝑢𝐴𝑒

(Re. AISC 360-05, Eq. J4-2)

For bolted splice plates, 𝐴𝑒 = 𝐴𝑛 ≤ 0.85𝐴𝑔

(Re. AISC 360-05, D3.2)

𝐴𝑛 = 𝐴𝑔 − 2𝑡3𝑑𝐶𝐴𝐿𝐶

𝑑𝐶𝐴𝐿𝐶 = 27 𝑚𝑚 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑕𝑜𝑙𝑒 + 2 𝑚𝑚 𝑑𝑎𝑚𝑎𝑔𝑒 = 29 𝑚𝑚

𝐴𝑛 = 1420 𝑚𝑚2 ≤ 0.85𝐴𝑔 = 1700 𝑚𝑚2

𝜙𝑅𝑛 = 426 𝑘𝑁 >𝑇𝑤

2= 20 𝑘𝑁 OK

Block Shear Strength on splice plate:

(Re. AISC 360-05, Eq. J4-5)


𝜙 = 0.75,𝑈𝑏𝑠 = 1.0

Figure 7.1-6: Block shear for web splice plate.

𝐴𝑔𝑣 = 2𝑡3 3𝑒1 + 𝑒3 = 5600 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 7𝑑𝐶𝐴𝐿𝐶 𝑡3 = 3070 𝑚𝑚2

𝐴𝑛𝑡 = 𝑒2𝑡3 − 𝑑𝐶𝐴𝐿𝐶 𝑡3 = 710 𝑚𝑚2

𝑅𝑛 = 1020 𝑘𝑁 ≤ 1049 𝑘𝑁 → 𝜙𝑅𝑛 = 766 𝑘𝑁 >𝑇𝑤

2= 20 𝑘𝑁 OK

Shear yielding of the splice plate:

𝜙𝑅𝑛 = 1.0 × 0.6𝐹𝑦𝐴𝑔 = 300 𝑘𝑁 >𝑉𝑤

2= 217 𝑘𝑁 OK

e3

e2

e1

e1

e1

T


7-14

(Re. AISC 360-05, Eq. J4-3)

Shear rupture of the splice plate:

𝜙𝑅𝑛 = 0.75 × 0.6𝐹𝑢𝐴𝑛𝑣

(Re. AISC 360-05, Eq. J4-4)

𝐴𝑛𝑣 = 𝑏3𝑡3 − 2𝑑𝐶𝐴𝐿𝐶 𝑡3 = 1420 𝑚𝑚2 (Net area subject to shear)

𝜙𝑅𝑛 = 256 𝑘𝑁 >𝑉𝑤

2= 217 𝑘𝑁 OK

Combined shear-tension interaction

The required condition is:

𝑃𝑊/2

𝜙𝑃𝑦

2

+ 𝑉𝑊/2

𝜙𝑉𝑦

4

≤ 1.0

With

𝑃𝑤 = 179 𝑘𝑁,𝑉𝑤 = 433 𝑘𝑁

𝜙𝑃𝑦 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏3𝑡3 = 450 𝑘𝑁

𝜙𝑉𝑦 = 0.6𝐹𝑦𝐴𝑔 = 300 𝑘𝑁

Then:

𝑃𝑊

𝜙𝑃𝑦

2

+ 𝑉𝑊

𝜙𝑉𝑦

4

= 0.31 ≤ 1.0 OK

5. Design of flange splice

𝑃𝑓 = 1559 𝑘𝑁,𝑇𝑓 = 1303 𝑘𝑁

Flange bolts:

Split the forces according to the areas of inner and outer plates:

Try the following dimensions:

Outer Plate (1PL): 𝑏1 = 340𝑚𝑚, 𝑡1 = 12 𝑚𝑚. Therefore 𝑨𝒈𝟏 = 𝒃𝟏𝒕𝟏 = 𝟒𝟎𝟖𝟎 𝒎𝒎𝟐

Inner Plates (2PL): 𝑏2 = 150𝑚𝑚, 𝑡2 = 12 𝑚𝑚. Therefore 𝑨𝒈𝟐 = 𝒃𝟐𝒕𝟐 = 𝟏𝟖𝟎𝟎 𝒎𝒎𝟐


7-15

Forces on outer plate:

𝑃𝑓𝑜 =𝑃𝑓𝐴𝑔1

𝐴𝑔1 + 2𝐴𝑔2

= 828 𝑘𝑁

𝑇𝑓𝑜 =𝑇𝑓𝐴𝑔1


= 692 𝑘𝑁

Forces on the inner plates (for the plates):

𝑃𝑓𝑖 =𝑃𝑓2𝐴𝑔2


= 731 𝑘𝑁

𝑇𝑓𝑖 =𝑇𝑓2𝐴𝑔2


= 611 𝑘𝑁

Bolts design:

Verify the shear on connection for friction type and bearing type failure. Try

M20, ASTM A490 bolts.

Slip critical failure


(Re. AISC 360-05, Eq. J3-4)


level), 𝜇=0.35 (class A surface), 𝐷𝑢=1.13, 𝑕𝑠𝑐=1.0 (standard holes), 𝑇𝑏=179kN

(AISC 360-05, Table J3.1M for M20, ASTM A490 bolts) 𝑁𝑠 = Number of slip

planes = 1.0.

Therefore:



max 𝑃𝑓𝑜 ,𝑇𝑓𝑜

𝜙𝑅𝑛= 13.75. Use 𝑵𝑩 = 𝟏𝟔 bolts in 𝑵𝑹 = 𝟒 rows.

(Number of bolts per row, 𝒏 = 𝟒).

Note:






7-16

Single shear on bolts

For single shear on bolts, use max 𝑃𝑓𝑜 ,𝑇𝑓𝑜 . Therefore:

max 𝑃𝑓𝑜 ,𝑇𝑓𝑜 = 828 𝑘𝑁 ≤ 𝜙𝐹𝑛𝑣𝐴𝑏𝑁𝐵 ,𝜙 = 0.75

(Re. AISC 360-05, J3.6)

Use 𝑁𝐵=16 bolts, 𝐴𝑏 = 314 𝑚𝑚2 corresponding to M20 bolts to obtain:



𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢 = 230𝑘𝑁

𝑏𝑜𝑙𝑡

(Re. AISC 360-05, Eq. J3-6a)

Use 𝜙 = 0.75 (LRFD), 𝐿𝑐 = clear distance in the direction of the force, between


𝑡 = 𝑚𝑖𝑛(𝑡1, 𝑡2 , 𝑡𝑓) = 12 𝑚𝑚 ,𝐹𝑢 = 400 𝑀𝑃𝑎, 𝑑=nominal bolt diameter = 20 mm.

Place the bolts:

Try:

𝑒1 = 65 𝑚𝑚, 𝑒2 = 60 𝑚𝑚, 𝑒3 = 40 𝑚𝑚, 𝑒4 = 45 𝑚𝑚,

𝑒5 = 𝑏1 − 2𝑒2 − 2𝑒4 = 130 𝑚𝑚.


7-17

tw

e3

b1

e3

e1

e1

e1

e4 e4e5e2 e2

b2 b2

bf

e4e4

Figure 7.1-7: Bolt positions for flange splice.

Edge bolts: 𝐿𝑐 = 𝑒3 −22

2= 29 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 = 167

𝑘𝑁

𝑏𝑜𝑙𝑡

Interior bolts: 𝐿𝑐 = 𝑒1 − 22 = 43 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 = 247𝑘𝑁

𝑏𝑜𝑙𝑡→ 𝑅𝑛 = 230

𝑘𝑁

𝑏𝑜𝑙𝑡

Note: The diameter of the standard hole for the bolt M20 is 22mm. See AISC

360-05, table J3.3M.

Considering all the bolts:

𝜙𝑅𝑛 = 0.75 4 × 167 + 12 × 230 = 2575 𝑘𝑁 > max 𝑃𝑓𝑜 ,𝑇𝑓𝑜 OK


7-18

Flange plates:

Flange inner plate


Inner Plates (2PL): 𝒃𝟐 = 𝟏𝟓𝟎 𝒎𝒎, 𝒕𝟐 = 𝟏𝟐 𝒎𝒎. Therefore 𝑨𝒈𝟐 = 𝒃𝟐𝒕𝟐 =

𝟏𝟖𝟎𝟎 𝒎𝒎𝟐, 𝑳𝟐 𝒎𝒎 = 𝒈 + 𝟐 𝟐𝒆𝟑 + 𝟐𝒆𝟏 = 𝟒𝟐𝟓 𝒎𝒎.

Compressive force:

Per each one of the inner plates: 𝑃𝑓𝑖

2= 365 𝑘𝑁




𝐴= 𝑡2

3𝑏212

𝑡2𝑏2

= 3.46 𝑚𝑚 →𝑘𝐿

𝑟𝑀𝐼𝑁= 24.54 < 25 → use Ch. J

𝜙𝑃𝑛 = 0.9𝐹𝑦𝐴𝑔 = 405 𝑘𝑁 >𝑃𝑓𝑖

2 OK

Tensile force:

Per each one of the inner plates: 𝑇𝑓𝑖

2= 305 𝑘𝑁

Tensile Yielding on splice plate:

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏2𝑡2 = 405 𝑘𝑁 >𝑇𝑓𝑖

2= 305 𝑘𝑁 OK

(Re. AISC 360-05, Eq. J4-1)



(Re. AISC 360-05, Eq. J4-2)


(Re. AISC 360-05, D3.2)




7-19

𝐴𝑛 = 1224 𝑚𝑚2 ≤ 0.85𝐴𝑔 = 1530 𝑚𝑚2

𝜙𝑅𝑛 = 367 𝑘𝑁 >𝑇𝑓𝑖

2= 305 𝑘𝑁 OK

Block Shear Strength on splice plate:

(Re. AISC 360-05, Eq. J4-5)

𝑅𝑛 = 0.6𝐹𝑢𝐴𝑛𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 ≤ 0.6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡 ,

𝜙 = 0.75,𝑈𝑏𝑠 = 1.0

Figure 7.1-8: Block shear for inner flange plates.

𝐴𝑔𝑣 = 2𝑡2 3𝑒1 + 𝑒3 = 5640 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 7𝑑𝐶𝐴𝐿𝐶𝑡2 = 3624 𝑚𝑚2

𝐴𝑛𝑡 = 𝑒2𝑡2 − 𝑑𝐶𝐴𝐿𝐶𝑡2 = 432 𝑚𝑚2

𝑅𝑛 = 1043 𝑘𝑁 > 1019 𝑘𝑁 → 𝜙𝑅𝑛 = 764 𝑘𝑁 >𝑇𝑓𝑖

2= 305 𝑘𝑁

Flange outer plate


Outer Plate (1PL): 𝒃𝟏 = 𝟑𝟒𝟎 𝒎𝒎, 𝒕𝟏 = 𝟏𝟐 𝒎𝒎. Therefore 𝑨𝒈𝟏 = 𝒃𝟏𝒕𝟏 =

𝟒𝟎𝟖𝟎 𝒎𝒎𝟐, 𝑳𝟏 𝒎𝒎 = 𝑳𝟐 = 𝟒𝟐𝟓 𝒎𝒎.

- Compressive force:

𝑃𝑓𝑜 = 828 𝑘𝑁


e3

e2

e1

e1

e1

T


7-20



𝐴=

𝑡1

3𝑏112

𝑡1𝑏1= 3.46 𝑚𝑚 →

𝑘𝐿

𝑟𝑀𝐼𝑁= 24.54 < 25 → use Ch. J

𝜙𝑃𝑛 = 0.9𝐹𝑦𝐴𝑔 = 918 𝑘𝑁 > 𝑃𝑓𝑜 = 828 𝑘𝑁 OK

- Tensile force:

𝑇𝑓𝑜 = 692 𝑘𝑁

- Tensile Yielding on splice plate:

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏1𝑡1 = 918 𝑘𝑁 > 𝑇𝑓𝑜 = 692 𝑘𝑁 OK

(Re. AISC 360-05, Eq. J4-1)

- Tensile rupture on splice plate:


(Re. AISC 360-05, Eq. J4-2)


(Re. AISC 360-05, D3.2)



𝐴𝑛 = 2928 𝑚𝑚2 ≤ 0.85𝐴𝑔 = 3468 𝑚𝑚2

𝜙𝑅𝑛 = 878 𝑘𝑁 > 𝑇𝑓𝑜 = 692 𝑘𝑁 OK

- Block Shear Strength on splice plate:

(Re. AISC 360-05, Eq. J4-5)


𝜙 = 0.75,𝑈𝑏𝑠 = 1.0


7-21

Figure 7.1-9: Block shear for outer flange plate.

𝐴𝑔𝑣 = 2𝑡1 3𝑒1 + 𝑒3 = 5640 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 7𝑑𝐶𝐴𝐿𝐶𝑡1 = 3624 𝑚𝑚2

𝐴𝑛𝑡 = 2𝑒2 + 𝑒5 𝑡1 − 3𝑑𝐶𝐴𝐿𝐶𝑡1 = 2136 𝑚𝑚2

𝑅𝑛 = 1724 𝑘𝑁 > 1700 𝑘𝑁 → 𝜙𝑅𝑛 = 1275 𝑘𝑁 > 𝑇𝑓𝑜 = 692 𝑘𝑁 OK

T

e1

2e + e2 5

e1

e1

e3


7-22


Locate the center of the splice at 1.5 m from the top flange of the bottom

beam.

Final tips:

i. If the upper column and the lower column of the splice were of

different sizes (specially different heights), filler plates would be

needed for the correct positioning of the flange cover plates.

ii. The approximation done in this example, for considering that the

bending moment is completely transferred through the flanges of the

column, is not far away from reality. Note that also it has been made

an approximation for the distribution of axial forces, according to

their relative areas principle. Any other reasonable principle or model

for the distribution of forces could be used.

2PL 150x425x12mm

PL 340x425x12mm

(gap)

H 350x350x175.1

32 M20 ASTM A490PL 200x605x8mm

A

A

A-A Section

16 M24 ASTM A490


7-23

7.2. Bolted Column Splice for SMF


1. NCh2369.Of2003:

Use high strength bolts (ASTM A325 or ASTM A490)

(Re. NCh2369.Of 2003, 8.5.1)



connection.

(Re. NCh2369.Of2003, 8.5.6)

For column splices, accomplish the following instructions:

(Re. NCh2369.Of 2003, 8.5.9)


columns and the top flange of the lower beam must be equal or

larger than the lesser value between 900 mm and half of the clear

height (𝐿𝑛) of the column.

- Splices must be dimensioned for the design forces obtained from

the load combinations (NCh2369.Of2003, 4.5) in which the

earthquake must be amplified by 2.0.

2. AISC 341-05:


(Re. 8.4, AISC 341-05)




16.5b.

In column bolted splices of SMF, plates or channels shall be used on

both sides of the web.


7-24

Location of column splices: the centerline of the splice for column

splices made with fillet welds of PJP groove welds shall be located

1200 mm or more away from the beam-to-column connection. When

column clear height between beam-to-column connections is less than

2400 mm, splices shall be located at half the clear height.

Specific requirements (SMF systems):

(Re. 9.9, AISC 341-05)

For SMF systems: When column splices are not made with groove welds, they

shall have a required flexural strength that is at least equal to RyFyZx (LRFD) or

RyFyZx/1.5 (ASD), as appropriate, of the smaller column. The required shear

strength of column web splices shall be at least equal to 𝑀𝑝𝑐/𝐻 (LRFD) or

𝑀𝑝𝑐/1.5𝐻 (ASD), as appropriate, where 𝑀𝑝𝑐 is the sum of nominal plastic

flexural strengths of the column above and below the splice.

7.2.b. Example

The design procedure for this column splice is the same shown in example 7.1.

In this example, the difference is only in the design forces between SMF

systems (more stringent design moments in AISC 341-05) in comparison with

SCBF systems, because in SMF systems the columns resist bigger moments

especially due to earthquake action. Refer to example 7.1 for the design

procedure of a general column splice.


7-25

7.3. Welded Column Splice for SCBF


1. NCh2369.Of2003

See NCh2369.Of2003, section 8.5.1 for electrode requirements.

Groove welds in seismic-resistant unions must be of CJP type.

(Re. NCh2369.Of2003, 8.5.5)

For column splices, meet the following:

(Re. NCh2369.Of 2003, 8.5.9)





- Splices must be dimensioned for the design forces obtained from the

load combinations (NCh2369.Of2003, point 4.5), in which the

earthquake load must be amplified by 2.0.

2. AISC 341-05


(Re. 8.4, AISC 341-05)




16.5b.

In addition to the previous point, welded column splices that are

subjected to a calculated net tensile load effect, calculated using the

load combinations stipulated by the applicable building code

(including the amplified seismic load), shall meet the following

requirements:

- For PJP groove welds, the available strength shall at least equal to

200% the required strength.


7-26

- The available strength of each flange splice shall be at least

0.5𝑅𝑦𝐴𝑓𝐹𝑦(LRFD) or 0.5𝑅𝑦𝐴𝑓𝐹𝑦/1.5 (ASD).

Note that according to AISC 341 Commentary, a CJP groove weld may

be considered as satisfying this previous requirement.

The centerline of the splice for column splices made with fillet welds

or PJP groove welds shall be located 1200 mm or more away from the

beam-to-column connection. When the column clear height between

beam-to-column connections is less than 2400 mm, splices shall be

located at half the clear height.

Specific requirements (SCBF systems):

For SCBF systems: “In addition to meeting the requirements of

section 8.4, column splices in SBCF shall be designed to develop 50%

of the lesser available flexural strength of the connected members.

The required shear strength of column web splices , shall be at least

equal to 𝑀𝑝𝑐/𝐻 (LRFD) or 𝑀𝑝𝑐/1.5𝐻 (ASD), as appropriate, where

𝑀𝑝𝑐 is the sum of nominal plastic flexural strengths of the column

above and below the splice”.

Most stringent conditions between these two codes will be used for the

determination of the design forces (M, V and N).

7.3.b. Example

Design a fully welded column splice for a special concentrically braced frame

for the connection shown in Figure 7.3-1. Use A250 ESP steel, required for

constructions subjected to dynamic loading, according to NCh203.Of2006

code, Table 3. Use E70 electrodes for welded connections.

The upper and the lower columns are Chilean H 350 X 350 X 175.1 built-up

sections. Assume that the clear height of the column is 𝐿𝑛=3700 mm. The

columns have been designed for resisting the forces given by the load

combinations of the applicable building code (including the seismic load).

Suppose that the loads on the columns are:

𝑃𝐷 = 290 𝑘𝑁,𝑃𝐿 = 45 𝑘𝑁,𝑃𝐸 = 200 𝑘𝑁

𝑉𝐷 = 50 𝑘𝑁,𝑉𝐿 = 20 𝑘𝑁,𝑉𝐸 = 60 𝑘𝑁


7-27

𝑀𝐷 = 50000 𝑘𝑁 −𝑚𝑚,𝑀𝐿 = 30000 𝑘𝑁 −𝑚𝑚 𝑘𝑁,𝑀𝐸 = 60000 𝑘𝑁 −𝑚𝑚

Figure 7.3-1: Connection to be designed. Frontal and lateral view.

1. Sections and materials properties

H350 X 350 X 175.1



A250 ESP:

(Re. Table 3, NCh203Of.2003)

𝐹𝑦 = 250 𝑀𝑃𝑎 ,𝐹𝑢 = 400 𝑀𝑃𝑎,𝐸 = 200000 𝑀𝑃𝑎

WELDS: 70 ksi electrode, 𝐹𝐸𝑋𝑋 = 480 MPa

2. Design forces

Required axial strength:

Use the combinations of NCh2369 code, section 4.5b):

Design a welded splice

t f

d


7-28

i. 1.2D + 1.0L ± 1.1E, but the E term shall be amplified by 2.0,

according to NCh2369.Of 2003, 8.5.9; therefore the combination used

is: 1.2D + 1.0L ± 2.2E.

ii. 0.9D ± 1.1E, but the E term shall be amplified by 2.0, according to

NCh2369.Of 2003, 8.5.9; therefore the combination used is: 0.9D ±

2.2E.

Therefore, calculate the maximum compressive force (when E term is being

added) for the first load combination and the maximum tensile force (when E

is being subtracted) for the second load combination.

𝑃𝑢 𝑖 = 833 𝑘𝑁 (Compression).

𝑃𝑢 𝑖𝑖 = −179 𝑘𝑁 (Tension).

According to AISC 341-05, section 8.3, if 𝑃𝑢

𝜙𝑐𝑃𝑛> 0.4, without the consideration

of the amplified seismic load, the required axial and tensile strength should

take into account the Ω0 factor on the load combinations given by the

applicable building code. In this case, the NCh2369.Of2003, has mandatorily

amplified the earthquake E term by a 2.0 factor, so it is not necessary to do

this check for determine the most stringent condition between these two codes.

Then:

𝑃𝑅𝐸𝑄 𝑖 = 833 𝑘𝑁 (Compression)

𝑃𝑅𝐸𝑄 𝑖𝑖 = −179 𝑘𝑁 (Tension)

Note that an axial net tensile load of one combination has been obtained,

considering the amplified seismic load. According to AISC 341-05 code, if

groove welds are used for the splice, the condition of having an available

strength of each flange splice at least of 0.5𝑅𝑦𝐹𝑦𝐴𝑓 (LRFD) is immediately OK.

Required flexural strength


M1 = max 1.2𝑀𝐷 + 1.0𝑀𝐿 + 2.2𝑀𝐸; 0.9𝑀𝐷 + 2.2𝑀𝐸 = 222000 𝑘𝑁 −𝑚𝑚

In order to accomplish AISC 341-05, section 13.5; use 50% of the column

nominal strength 𝑀𝑛. Suppose that the column reaches its plastic capacity

(𝑀𝑛 = 𝑀𝑝 = 𝐹𝑦𝑍𝑥 = 801000 𝑘𝑁 −𝑚𝑚).


7-29

Then

𝑀2 = 0.5𝑀𝑛 = 0.5𝑀𝑝 = 400500 𝑘𝑁 −𝑚𝑚

Using as the required moment, the most stringent between NCh2369.Of2003

and AISC 341-05 conditions:

𝑀𝑅𝐸𝑄 = max 𝑀1 ,𝑀2 = 400500 𝑘𝑁 −𝑚𝑚

Tips:

iii. Note that 𝑀𝑅𝐸𝑄 = 50% 𝑀𝑛 > 𝑀𝑢 = 𝑀1 at the splice location and this

condition meets the requirements of AISC 341-05 (see 8.4 comments

of the code). 𝑀𝑢 = 𝑀1 is obtained according to NCh2369.Of2003.

iv. The 100% of 𝑀𝑛 (the column strength capacity is always larger than

𝑀𝑢) could be used for the design of this splice. This is recommendable

for a quick design in a design stage where splice locations are not

defined and the loads are not well known.

Required shear strength


𝑉1 = max 1.2𝑉𝐷 + 1.0𝑉𝐿 + 2.2𝑉𝐸; 0.9𝑉𝐷 + 2.2𝑉𝐸 = 212 𝑘𝑁

Using AISC 341-05, the lower and the upper column are the same, hence:

V2 =2𝑀𝑝𝑐

𝐻=

2𝑀𝑝𝑐

𝐿𝑛

𝑀𝑝𝑐 = 𝐹𝑦𝑍𝑥 = 801000 𝑘𝑁 −𝑚𝑚

Therefore, using the most stringent condition between NCh2369.Of2003 and

AISC 341-05:

𝑉𝑅𝐸𝑄 = max V1, V2 = 433 𝑘𝑁

Tips:

i. Note that 𝑉𝑅𝐸𝑄 =2𝑀𝑝𝑐

𝐿𝑛> 𝑉𝑢 = 𝑉1 at the splice location and this condition

meets the requirements of AISC 341-05 (see 8.4 comments of the

code). 𝑉𝑢 = 𝑉1 is obtained according to NCh2369.Of2003.

ii. It is possible to do a more conservative design using 𝑉𝑛 > 𝑉𝑢 but

checking always that 𝑉𝑛 > 𝑉𝑅𝐸𝑄 =2𝑀𝑝𝑐

𝐿𝑛.


7-30

3. Welds used

As said before, try CJP groove welds for splice webs and flanges.

4. Check the shear strength for the splice

Assume that the shear force is transferred completely by the web CJP weld

splice. Use weld access holes with a height of 2.0𝒕𝒘=32 mm (comply with

recommendations of AISC 360-05, Section J1.6 and Chilean practice) and

depth equal to 25 mm.

For CJP groove welds subjected to shear force, according to AISC 360-05

Table J2.5, the strength of the joint is controlled by the base metal (web

metal). Therefore, according to AISC 360-05 section J4:

Shear yielding:

(Re. AISC 360-05, Eq. J4-3)

𝜙𝑅𝑛 = 1.0 0.6𝐹𝑦𝐴𝑤 = 0.6𝐹𝑦𝑡𝑤(𝑑 − 2𝑡𝑓 − 64 𝑚𝑚) = 566 𝑘𝑁 > 𝑉𝑅𝐸𝑄 = 433 𝑘𝑁 OK

Shear rupture:

(Re. AISC 360-05, Eq. J4-4)

𝜙𝑅𝑛 = 0.75 0.6𝐹𝑢𝐴𝑛𝑣 = 0.6𝐹𝑢𝑡𝑤 𝑑 − 2𝑡𝑓 − 64 𝑚𝑚 = 680 𝑘𝑁 > 𝑉𝑅𝐸𝑄 = 433 𝑘𝑁 OK

5. Check the axial strength of the splice

It has been assumed that the column sections are designed for the loads given

by NCh2369.Of2003 load combinations. Therefore the sections can resist

𝑃𝑅𝐸𝑄 𝑖 = −179 𝑘𝑁 (tension) and also 𝑃𝑅𝐸𝑄 𝑖 = 833 𝑘𝑁 (compression). CJP

groove welds are capable of developing 𝑃𝑅𝐸𝑄 𝑖 𝑎𝑛𝑑 𝑃𝑅𝐸𝑄(𝑖𝑖). OK

6. Check the flexural strength of the splice

Assume that the moment is taken entirely by the flanges of the columns,

therefore the required force on each one will be:

𝑅𝑅𝐸𝑄 =𝑀𝑅𝐸𝑄

𝑑 − 𝑡𝑓= 1232 𝑘𝑁

For CJP groove welds subjected to tension force normal to weld axis, according

to AISC 360-05 Table J2.5, the strength of the joint is controlled by the base

metal (flange metal). Therefore, according to AISC 360-05 section J4:


7-31

Tensile yielding:

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝐴𝑓 = 1969 𝑘𝑁 > 𝑅𝑅𝐸𝑄 OK

Tensile rupture:

𝜙𝑅𝑛 = 0.75𝐹𝑢𝐴𝑒 = 0.75𝐹𝑢𝐴𝑓 = 2625 𝑘𝑁 > 𝑅𝑅𝐸𝑄 OK

7. Filler metal requirements

From AISC 360-05 J2.6 section, for A250 ESP steel (similar to ASTM A36) a 70

ksi electrode can be used. The complete information for matching filler metals

for CJP groove welds subjected to tension normal to weld axis is given in AWS

D1.1. The filler metal must also comply with AISC 341-05 Seismic Provisions,

section 7.3.


Locate the center of the splice at 1.5 m from the top flange of the bottom

beam. The geometry of the access holes is shown on the following figure:

Figure 7.3-1: Connection Designed. E70 electrodes are used.

Upper Column

Lower Column

Note: The radius must give a soft transition. Use R > 10mm

CJP

25mm

2,0 tw


7-32

Notes and final tips:

i. There are other (welded) solutions instead the one presented in this

example (CJP groove welds for web and flanges). For example, it is

possible to use a welded web plate for transferring the required

shear. Note that according to NCh2369.Of2003, if groove welds are

used; they shall be CJP type.

ii. Note that this type of solution for the column splice is not very

popular in seismic areas because it is a field welded connection. It is

preferable to use a bolted connection or a shop welded connection.


7-33

7.4. Welded Column Splice for SMF


1. NCh2369.Of2003

See NCh2369.Of2003, section 8.5.1 for electrode requirements.

Groove welds in seismic-resistant unions must be of CJP type.

(Re. NCh2369.Of2003, 8.5.5)

For column splices, comply the following instructions:

(Re. NCh2369.Of 2003, 8.5.9)





- The splices must be dimensioned for the design forces obtained from

load combinations of the Code (NCh2369.Of2003, point 4.5), in which

the earthquake load must be amplified by 2.0.

2. AISC 341-05


(Re. 8.4, AISC 341-05)

The required strength of the column splice in the seismic load

resisting system (SLRS) shall equal the required strength of the

columns, including those calculated from sections 8.3, 9.9, 10.9,

11.9, 13.5 and 16.5b.

In addition to the previous point, welded column splices that are

subjected to a calculated net tensile load effect, calculated using the

load combinations stipulated by the applicable building code including

the amplified seismic load, shall meet the following requirements:

- For PJP groove welds, the available strength shall at least equal to

200% the required strength.


7-34

- The available strength of each flange splice shall be at least of

0.5𝑅𝑦𝐴𝑓𝐹𝑦 (LRFD) or 0.5𝑅𝑦𝐴𝑓𝐹𝑦/1.5 (ASD).

Note that according to AISC 341 Commentary, a CJP groove weld may

be considered as satisfying this previous requirement.

The centerline of the splice for column splices made with fillet welds

or PJP groove welds shall be located 1200 mm or more away from the

beam-to-column connection. When the column clear height between

beam-to-column connections is less than 2400 Mm, splices shall be

located at half the clear height.

Specific requirements (SMF systems):

For SMF systems: “Column splices must comply with the requirements

of section 8.4a. Where groove welds are used to make the splice,

they shall be CJP type and must comply with the requirements of

section 7.3b. Weld tabs shall be removed. When column splices are

not made with CJP welds, they shall have a required flexural strength

of 𝑅𝑦𝐹𝑦𝑍𝑥 (LRFD) or 𝑅𝑦𝐹𝑦𝑍𝑥/1.5 (ASD), as appropriate, of the smaller

column. The required shear strength of column web splices, shall be

at least equal to 𝑀𝑝𝑐/𝐻 (LRFD) or 𝑀𝑝𝑐/1.5𝐻 (ASD), as appropriate,

where 𝑀𝑝𝑐 is the sum of nominal plastic flexural strengths of the

column above and below the splice”.


The design procedure for this column splice is the same shown in example 7.3.

In this example, the difference is only in the design forces between SMF

systems (more stringent design moments from AISC 341-05) in comparison

with SCBF systems, because in SMF systems the columns resist bigger

moments especially due to earthquake action. Refer to example 7.3 for the

design procedure of a general welded column splice.

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 8: BEAM SPLICES

8-1

8. BEAM SPLICES

8.1. Beam Parallel Splice – All Bolted Splice Plates


1. NCh2369.Of2003

Use high strength bolts (ASTM A325 or ASTM A490).

(Re. NCh2369.Of2003, 8.5.1)



connection.

(Re. NCh2369.Of2003, 8.5.6)

2. AISC 341

There are no specific provisions for the design of beam splices.

3. AISC 360

(Re. AISC360-05, J6)

For beam splices:

Groove welded splices: shall develop the nominal strength of the

smaller spliced section.

Other type of splices: shall develop the strength required by forces at

the point of the splice (on the center of gravity of the bolts).

Tip:

(Re. AISC Manual of Steel Construction, chapter 12).

It is convenient to design for a minimum value of the available strength of the

beam section. This is because, since load application and frequency of

application can change during the lifetime of the structure, it is prudent for the

designer to specify some minimum strength requirement at the splice. This

previous statement is also based on the fact that the inflection points (many

splices are located at or near inflection points, zero moment) can change

during an earthquake, and therefore, actual forces could differ significantly

from those assumed.


8-2

Some authors recommend design for at least 50% of the member capacity

(0.5𝜙𝑀𝑝 and 0.5𝜙𝑉𝑝), but always check that the design forces are larger than

𝑀𝑢 and 𝑉𝑢 from load combinations.

8.1.b. Example

Design the connection of the all bolted beam splice shown in Figures 8.1-1 and

8.1-2. Use A345 ESP steel, required for constructions subjected to dynamical

loading, according to NCh203.Of2006 code, Table 3.

Both beams are Chilean H450 x 200 x 112.7 built-up sections. Use standard

holes for bolts. Suppose that the beams have been properly designed for


code (including seismic load). These loads, at the location of the splice, are:

𝑀𝑢 = 523000 𝑘𝑁 − 𝑚𝑚 , 𝑉𝑢 = 265 𝑘𝑁, 𝑁𝑢 = 0 𝑘𝑁

Suppose that the splice location has been defined previously (many factors

affect the location of beam splices, such as the length of the members limited

by the transportation, or by the capacity of the assembly equipment).

Figure 8.1-1: Connection to be designed. Frontal and Lateral View.


8-3

Figure 8.1-2: Connection to be designed. Beam Section.

1. Section and Material Properties

H450 x 200 x 112.7



A345 ESP:


𝐹𝑦 = 345 𝑀𝑃𝑎 , 𝐹𝑢 = 450 𝑀𝑃𝑎



2. Design Forces

Use conservatively the total capacity of the beam for the shear force and

moment. Assume that the section reaches the plastic capacity. Therefore:

𝑉𝑅𝐸𝑄 = 𝜙𝑉𝑝 = 1.0 0.6𝐹𝑦𝐴𝑤 = 1.0 0.6𝐹𝑦𝑑𝑡𝑤 = 745 𝑘𝑁 > 𝑉𝑢

𝑀𝑅𝐸𝑄 = 𝜙𝑀𝑝 = 0.9 𝐹𝑦𝑍𝑥 = 830277 𝑘𝑁 − 𝑚𝑚 > 𝑀𝑢

Tip:

Note that these design forces are meeting the requirements of AISC360-05

code, J6 section. This is because always 𝜙𝑉𝑝 > 𝑉𝑢 and 𝜙𝑀𝑝 > 𝑀𝑢. 𝑉𝑢 and 𝑀𝑢 are

t1

t2

b1

b2b2

b3

t3


8-4

obtained from the applicable building code load combination; in this case,

NCh2369.Of2003.

The choice of the percentage of the member’s capacity, in order to calculate

𝑉𝑅𝐸𝑄 and 𝑀𝑅𝐸𝑄 could be discussed with a seismic reviewer. In a previous design

stage, where the final location of the splice is not well known, it is conservative

to use 100% of the member capacity for the design forces.

Forces transferred by the splice:

Assume that the shear is completely transferred by the web plates, and that

the moment is completely transferred by the flanges, with a couple of tension

and compression forces.

Then, the design forces for the splice are:

𝑉𝑅𝐸𝑄 = 745 𝑘𝑁 (Web splice)


𝑑−𝑡𝑓= 1967 𝑘𝑁 (Flange splices)

Tip:

If there is also axial force acting on the beam (neglected in this example), it

should be divided, according to a relative areas principle, among the flanges

and web. A common assumption is that flanges also carry the entire axial load.

3. Design of the web splice

Tip:

It is always preferable the use of 2 identical web plates at each side of the

beam’s web, because with this, a symmetrical distribution of shear force in the

plane of the beam web is obtained, the bolts are subjected to double shear

and therefore it is possible to reduce the number of bolts in the connection and

the inherent eccentricity out of the plane.

𝑉𝑅𝐸𝑄 = 745 𝑘𝑁

Web bolts:

Try M24 bolts. Try 𝑵𝑩 = 9 bolts, and 𝑵𝑹 = 3 rows. Number of bolts per row:

𝒏 = 3.Place the bolts:𝑒1 = 80 𝑚𝑚, 𝑒2 = 120 𝑚𝑚, 𝑒3 = 45 𝑚𝑚, 𝑒4 = 50 𝑚𝑚. Then, the

web plate dimensions are:

𝑏3 = 2𝑒2 + 2𝑒4 = 340 𝑚𝑚, use 𝑡3 = 8 𝑚𝑚.


8-5

Figure 8.1-3: Bolts positions on the web plate. Bolt A has the larger load.

Suppose a gap between the two parts of the connected beam 𝒈 = 𝟓 𝒎𝒎. Using

the midline of the gap, the distance from the line of action of 𝑉𝑅𝐸𝑄 to the center

of gravity of the arrangement of bolts is 𝑒𝑥 =𝑔

2+ 𝑒3 + 𝑒1 = 127.5 𝑚𝑚. Use the

classical method (elastic) for the analysis of the eccentric shear bolted

connection.

𝑃𝑥 = 0 𝑘𝑁

𝑃𝑦 =𝑉𝑅𝐸𝑄

2= 373 𝑘𝑁

Shear is analyzed in one of the web plates.

𝑀0 = 𝑃𝑦𝑒𝑥 = 47507 𝑘𝑁 − 𝑚𝑚

𝑟𝑖2 = 𝑥𝑖

2 + 𝑦𝑖2 = 124800 𝑚𝑚2

Considering the critical bolt (𝑥𝑖 = 𝑒1 , 𝑦𝑖 = 𝑒2), the required force 𝑅𝑖𝑅𝐸𝑄 to be

transferred by bolt A is:

𝑅𝑥𝑖𝑅𝐸𝑄 =𝑃𝑥

𝑁𝐵

+𝑀0𝑦𝑖

𝑟𝑖2 = 46 𝑘𝑁

𝑅𝑦𝑖𝑅𝐸𝑄 =𝑃𝑦

𝑁𝐵

+𝑀0𝑥𝑖

𝑟𝑖2 = 72 𝑘𝑁

𝑅𝑖𝑅𝐸𝑄 = 𝑅𝑥𝑖𝑅𝐸𝑄2 + 𝑅𝑦𝑖𝑅𝐸𝑄

2 = 85 𝑘𝑁

x

yV

Ae4

e2

e2

e4

e3 e1 e1 e3

b3 req


8-6

Bolts check:


For conservative calculations, use for slip-critical connection type check, class

A surface (𝜇 = 0.35), and for bearing type connections, consider threads

included in the shear plane.


(Re. AISC360-05, Eq. J3.4)

Use 𝜙=0.85 (connection designed to prevent slip at required strength level),

𝜇=0.35 (class A surface), 𝐷𝑢=1.13, 𝑕𝑠𝑐=1.0 (standard holes), 𝑇𝑏=257kN (AISC

360-05, Table J3.1M for M24, ASTM A490 bolts), 𝑁𝑠= number of slip planes =

1.0.

Therefore:


𝑏𝑜𝑙𝑡> 𝑅𝑖𝑅𝐸𝑄 = 84

𝑘𝑁

𝑏𝑜𝑙𝑡 OK

Note:






Check the total shear, with the total number of bolts.

𝑅𝑛 = 2.4𝑑𝑡𝐹𝑢 = 207𝑘𝑁

𝑏𝑜𝑙𝑡

(Re. AISC360-05, Eq. J3-6a)

Use 𝜙 = 0.75, 𝑡 = 𝑚𝑖𝑛 𝑡𝑤 , 𝑡3 = 8 𝑚𝑚, 𝐹𝑢 = 450 𝑀𝑃𝑎, 𝑑=nominal bolt diameter =

24 mm.


𝑏𝑜𝑙𝑡> 84

𝑘𝑁

𝑏𝑜𝑙𝑡 OK


8-7

Single shear resistance check:

For single shear on the most loaded bolt, check the following:

𝑅𝑖𝑅𝐸𝑄 ≤ 𝜙𝐹𝑛𝑣𝐴𝑏 , 𝜙 = 0.75

(Re. AISC360-05, J3.6)

Use 𝑨𝒃 = 𝟒𝟓𝟐 𝒎𝒎𝟐 for M24 bolts to obtain:

𝜙𝐹𝑛𝑣𝐴𝑏 = 140 𝑘𝑁 > 𝑅𝑖𝑅𝐸𝑄 = 85 𝑘𝑁 OK

Web splice plates:

Dimensions taken from above:

Width 𝒃𝟑 = 𝟑𝟒𝟎 𝒎𝒎, Thickness 𝒕𝟑 = 𝟖 𝒎𝒎, Length 𝑳𝟑 = 𝑔 + 2(2𝑒1 + 2𝑒3) =

𝟓𝟎𝟓 𝒎𝒎.

Check the shear force acting on each plate:

𝑉𝑅𝐸𝑄

2= 373 𝑘𝑁

Shear yielding of the splice plate:

𝜙𝑅𝑛 = 1.0 0.6𝐹𝑦𝐴𝑔 = 563𝑘𝑁 > 373 𝑘𝑁 OK

(Re. AISC360-05, Eq. J4-3)

Shear rupture of the splice plate:

𝑑𝐶𝐴𝐿𝐶 = 27 𝑚𝑚 (𝑆𝑇𝐷 𝑕𝑜𝑙𝑒) + 2 𝑚𝑚 𝑑𝑎𝑚𝑎𝑔𝑒 = 29 𝑚𝑚 𝜙𝑅𝑛 = 0.75(0.6𝐹𝑢𝐴𝑛𝑣 )

(Re. AISC360-05, Eq. J4-4)

𝐴𝑛𝑣 = 𝑏3𝑡3 − 3𝑑𝐶𝐴𝐿𝐶 𝑡3 = 2024 𝑚𝑚2 (Net area subjected to shear)

𝜙𝑅𝑛 = 410 𝑘𝑁 > 373 𝑘𝑁 OK


8-8

4. Design of the flange splices

Use inner and outer flange plates. The force 𝑅𝑅𝐸𝑄 will be divided according

to a relative area principle.

Try the following dimensions for the flange cover plates:

Outer plate: (1PL) 𝑏1 = 200 𝑚𝑚 𝑡1 = 27 𝑚𝑚 𝐴𝑔1 = 5400 𝑚𝑚2

Inner plates: (2PL) 𝑏2 = 80 𝑚𝑚 𝑡2 = 24 𝑚𝑚 𝐴𝑔2 = 1920 𝑚𝑚2

Tip:

In small beam sections, typically with one flange (outer) plate, it is possible to

transfer the required flexural strength. In this case, it has been decided to use

100% of the element capacity, leading to the use of two flange plates (outer

and inner plates). With this configuration, the number of bolts is reduced

because they are subjected to double shear.

Forces on the inner plates (for both plates): 𝑅𝑅𝐸𝑄𝑖𝑛𝑛𝑒𝑟 = 𝑅𝑅𝐸𝑄

2𝐴𝑔2

𝐴𝑔1+2𝐴𝑔2 = 818 𝑘𝑁

Force on the outer plate: 𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟 = 𝑅𝑅𝐸𝑄

𝐴𝑔1

𝐴𝑔1+2𝐴𝑔2 = 1150 𝑘𝑁

Note that the forces on the outer plate are greater than the forces on the inner

plate (therefore, use the force on the outer plate for the different checks).

Flange bolts

Check the shear on the connections as friction type and also bearing type

connections. Try M24, ASTM A490 bolts.



(Re. AISC360-05, Eq. J3.4)

Use 𝜙=0.85 (connection designed to prevent slip critical at required strength

level), 𝜇=0.35 (class A surface), 𝐷𝑢=1.13, 𝑕𝑠𝑐 = 1.0 (standard holes), 𝑇𝑏 =

257 𝑘𝑁 (AISC 360-05, Table J3.1M for M24, ASTM A490 bolts), 𝑁𝑠= Number of

slip planes = 1.0.


8-9

Therefore:



𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟

𝜙𝑅𝑛= 13.37 .Use 𝑵𝑩 = 𝟏𝟒 bolts in 𝑵𝑹 = 2 rows. (Number of

bolts per row 𝑛 = 7 bolts).

Note:





Bearing type connection check:

For single shear on bolts, use the maximum shear force (between inner or

outer flange plates):𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟

Check the following:

𝜙𝐹𝑛𝑣𝐴𝑏𝑁𝐵 ≥ 𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟 , 𝜙 = 0.75 (LRFD) (Re. AISC360-05, J3.6)

Use 𝑵𝑩 = 14 bolts, 𝐴𝑏 = 452 𝑚𝑚2 corresponding to M24 bolts to obtain:

𝐹𝑛𝑣𝐴𝑏𝑁𝐵 = 1967 𝑘𝑁 ≥ 𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟 = 1150 𝑘𝑁 OK


𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑡𝐹𝑢 = 622𝑘𝑁

𝑏𝑜𝑙𝑡

(Re. AISC360-05, Eq. J3-6a)

Use 𝝓=0.75, 𝑳𝒄=clear distance in the direction of the applied force, between

the edge of the hole and the edge of the adjacent hole or edge of the plate,

𝑡 = 𝑚𝑖𝑛(𝑡𝑓 , 𝑡1 , 𝑡2) = 24 𝑚𝑚, 𝑭𝒖 = 450 𝑀𝑃𝑎, 𝒅=nominal bolt diameter = 24 mm.

Place the bolts:

Try:

𝑒1 = 75 𝑚𝑚, 𝑒2 = 120 𝑚𝑚, 𝑒3 = 40 𝑚𝑚, 𝑒4 = 40 𝑚𝑚


8-10

Figure 8.1-4: Bolts positions for flange splice.

Check: 𝑏2 = 𝑒2 + 2𝑒4 = 200 𝑚𝑚. OK

Edge bolts:

𝐿𝑐 = 𝑒3 −27

2= 31.5 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡 𝐹𝑢 = 408

𝑘𝑁

𝑏𝑜𝑙𝑡

Interior bolts:

𝐿𝑐 = 𝑒1 − 27 = 48 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡 𝐹𝑢 = 622𝑘𝑁

𝑏𝑜𝑙𝑡

Note: The diameter of the standard hole for the bolt M24 is 27 mm. See

AISC360-05, table J3.3M.

Considering all bolts:

𝜙𝑅𝑛 = 0.75 2 × 408 + 12 × 622 = 6211 𝑘𝑁 > 𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟 = 1150 𝑘𝑁 OK

Flange splice plates:

Flange inner plates:


Inner plates: (2PL) 𝑏2 = 80 𝑚𝑚, 𝑡2 = 24 𝑚𝑚, 𝐴𝑔2 = 1920 𝑚𝑚2 , 𝐿2 = 𝑔 + 2(6𝑒1 + 2𝑒3) =

1085 𝑚𝑚

e3

6 @ e1

e3g

e2

b1

e4e4

b2b2

tw


8-11

Tensile force:

𝑅𝑅𝐸𝑄𝑖𝑛𝑛𝑒𝑟 /2 = 408 𝑘𝑁 (Per each one of the inner plates)

Tensile yielding on splice plate

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏2𝑡2 = 596 𝑘𝑁 > 408 𝑘𝑁 OK

(Re. AISC360-05, Eq. J4-1)



(Re. AISC360-05, Eq. J4-2)

For bolted splice plates: 𝐴𝑒 = 𝐴𝑛 ≥ 0.85𝐴𝑔

(Re. AISC360-05, D3.2)

𝐴𝑛 = 𝐴𝑔 − 𝑡2𝑑𝐶𝐴𝐿𝐶


(Re. AISC360-05, D3.2)

𝐴𝑛 = 1224 𝑚𝑚2 ≤ 0.85𝐴𝑔 = 1632 𝑚𝑚2

𝜙𝑅𝑛 = 413 𝑘𝑁 ≥ 408 𝑘𝑁 OK

Block shear strength on splice plate:

(Re. AISC360-05, Eq. J4-5)


𝜙 = 0.75, 𝑈𝑏𝑠 = 1.0

Figure 8.1-5: Block shear for inner flange plates.

6 @ e1

e3

T


8-12

𝐴𝑔𝑣 = 𝑡2 6𝑒1 + 𝑒3 = 11760 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 6.5𝑡2𝑑𝐶𝐴𝐿𝐶 = 7236 𝑚𝑚2

𝐴𝑛𝑡 = 𝑒4𝑡2 − 0.5𝑡2𝑑𝐶𝐴𝐿𝐶 = 612 𝑚𝑚2

𝑅𝑛 = 2229 𝑘𝑁 < 2710 𝑘𝑁 → 𝜙𝑅𝑛 = 1672 𝑘𝑁 > 408 𝑘𝑁 OK

Compressive force

𝑅𝑅𝐸𝑄

𝑖𝑛𝑛𝑒𝑟 /2 = 408 𝑘𝑁 (Per each one of the inner plates)

The maximum unfixed length is: 2𝑒3 + 𝑔 = 85 𝑚𝑚 𝑘𝐿 = 85 𝑚𝑚

Using AISC360-05, section J4.4 “Strength of elements in compression”:


𝐴=

𝑏2𝑡2

3

12

𝑏2𝑡2

= 6.93 𝑚𝑚 →𝑘𝐿

𝑟𝑀𝐼𝑁

= 12.26 < 25 → 𝑢𝑠𝑒 𝐶𝑕. 𝐽

𝜙𝑃𝑛 = 0.9𝐹𝑦𝐴𝑔 = 596 𝑘𝑁 > 408 𝑘𝑁 OK

Flange outer plate:


Outer plate: (1PL) 𝑏1 = 200 𝑚𝑚, 𝑡1 = 27 𝑚𝑚, 𝐴𝑔1 = 5400 𝑚𝑚2

Tensile force:

𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟 = 1150 𝑘𝑁 (On the outer plate)

Tensile yielding on splice plate:

𝜙𝑅𝑛 = 0.9𝐹𝑦𝐴𝑔 = 0.9𝐹𝑦𝑏1𝑡1 = 1677 𝑘𝑁 > 1150 𝑘𝑁 OK

(Re. AISC360-05, Eq. J4-1)



(Re. AISC360-05, Eq. J4-2)

For bolted splice plates: 𝐴𝑒 = 𝐴𝑛 ≤ 0.85𝐴𝑔

(Re. AISC360-05, D3.2)



8-13


(Re. AISC360-05, D3.2)

𝐴𝑛 = 3834 𝑚𝑚2 ≤ 0.85𝐴𝑔 = 4590 𝑚𝑚2

𝜙𝑅𝑛 = 1294 𝑘𝑁 ≥ 1150 𝑘𝑁 OK

Block shear strength on splice plate:

(Re. AISC360-05, Eq. J4-5)


𝜙 = 0.75, 𝑈𝑏𝑠 = 1.0

Figure 8.1-6: Block shear for outer flange plates.

𝐴𝑔𝑣 = 𝑡12 6𝑒1 + 𝑒3 = 26460 𝑚𝑚2

𝐴𝑛𝑣 = 𝐴𝑔𝑣 − 13𝑡1𝑑𝐶𝐴𝐿𝐶 = 16281 𝑚𝑚2

𝐴𝑛𝑡 = 𝑒2𝑡1 − 𝑡1𝑑𝐶𝐴𝐿𝐶 = 2457 𝑚𝑚2

𝑅𝑛 = 5502 𝑘𝑁 < 6583 𝑘𝑁 → 𝜙𝑅𝑛 = 4127 𝑘𝑁 > 1150 𝑘𝑁 OK

Compressive force

𝑅𝑅𝐸𝑄𝑜𝑢𝑡𝑒𝑟 = 1150 𝑘𝑁 (On the outer plate)

The maximum unfixed length is: 2𝑒3 + 𝑔 = 85 𝑚𝑚 𝑘𝐿 = 85 𝑚𝑚

Using AISC360-05, section J4.4 “Strength of elements in compression”:


𝐴=

𝑏1𝑡1

3

12

𝑏1𝑡1

= 7.79 𝑚𝑚 →𝑘𝐿

𝑟𝑀𝐼𝑁

= 10.9 < 25 → 𝑢𝑠𝑒 𝐶𝑕. 𝐽

𝜙𝑃𝑛 = 0.9𝐹𝑦𝐴𝑔 = 1677 𝑘𝑁 > 1150 𝑘𝑁 OK

T

e2

e3

6 @ e1


8-14

8.1.c. Designed Connection

Figure 8.1-7: Designed beam splice.

Note:

The designer should note that bolt holes in flanges (and web) may prohibit the

development of a full strength connection at that point. In the example done,

it has been assumed that the forces are obtained from the beam full capacity

(conservative assumption).

From AISC360-05 Manual, Section F13: Proportions of Beam and Girders:

F13.1: Holes Reductions:

In addition to the limit states specified on other sections of Chapter F, the

nominal flexural strength, 𝑀𝑛, shall be limited according to limit state of tensile

rupture of the tension flange (and therefore it is possible to obtain an 𝑀𝑛 <

𝑀𝐶𝐻𝐴𝑃𝑇𝐸𝑅 𝐹 obtained from the gross section of the beam).

On AISC360-05 Manual, Section G8: Beam and Girders with web openings:

The effect of web openings on the nominal shear strength of steel and

composite beams shall be calculated (there is a reduction on web area 𝐴𝑤).

Adequate reinforcement shall be provided when the required strength exceeds

the available strength of the member at the opening.

1PL 200x1085x27

2PL 80x1085x24 28 M24A

A

2 PL 340x505x8

18 M24

Same connection

on the top flange

A - A section

BOLTS: ASTM A490

Symmetrical connection


8-15

8.2. Beam Parallel Splice – Bolted End Plate.


1. NCh2369.Of2003

Use high strength bolts (ASTM A325 or ASTM A490).

(Re. NCh2369.Of2003, 8.5.1)



connection.

(Re. NCh2369.Of2003, 8.5.6)

2. AISC 341

There are no specific provisions for the design of beam splices.

3. AISC 360

(Re. AISC360-05, J6)

For beam splices:

Groove welded splices: shall develop the nominal strength of the

smaller spliced section.

Other type of splices: shall develop the strength required by forces at

the point of the splice (on the center of gravity of the bolts).

Tip:

(Re. AISC Manual of Steel Construction, chapter 12).

It is convenient to design for a minimum value of the available strength of the

beam section. This is because, since load application and frequency of

application can change during the lifetime of the structure, it is prudent for the

designer to specify some minimum strength requirement at the splice. This

previous statement is also based on the fact that the inflection points (many

splices are located at or near inflection points, zero moment) can change

during an earthquake, and therefore, actual forces could differ significantly

from those assumed.

Some authors recommend design for at least 50% of the member capacity

(0.5𝜙𝑀𝑝 and 0.5𝜙𝑉𝑝), but always check that the design forces are larger than

𝑀𝑢 and 𝑉𝑢 from load combinations.


8-16

Notes:

For Extended End Plate Moment Connection (similar to beam-to-

column moment connections, but without concerns about the “column

part”), it has been decided to follow the design procedure presented

on AISC358-05 code: Prequalified Connections for Special and

Intermediate Steel Moment Frames for Seismic Applications (and its

supplement AISC358-05s1-09: Supplement No.1 to ANSI/AISC350-

05). This connection is presented on Chapter 6 of AISC358-05 code.

This beam splice is intended to be at a high seismic demand area,

then the requirements for special moment frames (SMF) will be

followed.

4. AISC 358 General Requirements (summary)

LRFD Reduction Factors:

For ductile limit states, 𝜙𝑑 = 1.0. For non-ductile limit states, 𝜙𝑛 = 0.9.

Welding Requirements:

Filler metals and welding procedures shall meet the requirements of section

7.3 and Appendix W of the AISC341-05 code.

For “Backing at beam to column and Continuity plate to column joint”, see

AISC358-05, section 3.3.

Bolts Requirements:

Use only ASTM A325 or ASTM A490 bolts, and they shall be pretensioned high

strength type. (Re. AISC 358-05, 4.1)

8.2.b. Example

Design a bolted extended and unstiffened end plate moment splice for the

beam connection shown in Figure 8.2-1. Use A345 ESP steel, required for

constructions subjected to dynamical loading, according to NCh203.Of2006

code, Table 3.

Both beams are Chilean H500 x 200 x 85.7 built-up sections. Use standard

holes for bolts. Suppose that the beams have been properly designed for



8-17

code (including seismic load) and that the sections are compatible with

AISC341 requirements. These loads, at the location of the splice, are:

𝑀𝑢 = 513000 𝑘𝑁 − 𝑚𝑚 , 𝑉𝑢 = 550 𝑘𝑁, 𝑁𝑢 = 0 𝑘𝑁

Suppose that the splice location has been previously defined. Many factors

affect the location of beam splices, such as the length of the members, limited

by transportation issues; or by the capacity of the assembly equipment).

Figure 8.2-1: Connection to be designed. (a) Frontal and Lateral View,

(b) Beam Section.

Tip:

According to various authors, this connection is economical for light

constructions (there is less material and bolts than the connection designed on

example 8.1). For bigger beams, the shear force is increased and the end-

plate splices are more expensive, therefore the connections are replaced for

the all bolted cover plate types.

If the bolts are properly designed, this connection can develop a satisfactory

behavior up to the beam plastic capacity.

1. Section and Material Properties

H500 x 200 x 85.7




8-18

A345 ESP:


𝐹𝑦 = 345 𝑀𝑃𝑎 , 𝐹𝑢 = 450 𝑀𝑃𝑎

BOLTS: ASTM A490 Bolts, threads included in the shear planes, STD holes.


2. Design Forces

Conservatively, use the total capacity of the beam for the shear force and

moment. Assume that the section can reach the plastic capacity.

𝑉𝑅𝐸𝑄 = 𝜙𝑉𝑝 = 1.0 0.6𝐹𝑦𝐴𝑤 = 1.0 0.6𝐹𝑦𝑑𝑡𝑤 = 828 𝑘𝑁 > 𝑉𝑢

𝑀𝑅𝐸𝑄 = 𝜙𝑀𝑝 = 0.9 𝐹𝑦𝑍𝑥 = 672543 𝑘𝑁 − 𝑚𝑚 > 𝑀𝑢

Tip:

Note that these design forces meet the requirements of AISC360-05 code, J6

section. This is because always 𝜙𝑉𝑝 > 𝑉𝑢and 𝜙𝑀𝑝 > 𝑀𝑢. 𝑉𝑢 and 𝑀𝑢 are obtained

from the applicable building code load combination; in this case,

NCh2369.Of2003. Even though both of the limit states for calculating the

design forces are ductile, the strength reduction factors 𝜙 are not related with

𝜙𝑑 and 𝜙𝑛 shown above; they are related with the factors of AISC 360-05

Specification.

The choice of the percentage of the member’s capacity, in order to calculate

𝑉𝑅𝐸𝑄 and 𝑀𝑅𝐸𝑄 could be discussed with the seismic reviewer. In an early design

stage, where the exact location of the splice is not well known, it is very

conservative to use 100% of the member capacity for the calculation of design

forces.

Forces transferred by the splice:

Assume that the shear is completely transferred by the bolts of the end plates,

and that the moment is completely transferred by the flanges, with a couple of

tension and compression forces.

Then, the design forces for the splice are:



8-19


𝑑 − 𝑡𝑓= 1395 𝑘𝑁

Tip:

If there is also axial force acting on the beam (neglected in this example), it

should be divided according a relative areas principle, among the flanges and

the web. A common assumption is that the flanges also carry the entire axial

load.

3. Design procedure

Base on the steps listed on Chapter 6 of AISC358-05, also considering

supplement N° 1. Although these documents show the design for beam-to-

column connections, the design of this beam splice is similar to those

connections.

Try a 4 bolt, unstiffened extended end plate for splicing the two parallel

beams, shown in Figure 8.2-1.

Prequalification limits:

(Re. AISC358, Supplement N°1 (2009); Table 6.1)


of these connections are shown now (the notation of AISC358 is presented):




38 𝑚𝑚 ≤ 𝑝𝑓𝑖 , 𝑝𝑓𝑜 ≤ 114 𝑚𝑚







8-20

Figure 8.2-2: Notation (used on AISC 358-05) for the extended end plate

beam moment splice. Adapted from AISC358-05, Fig. 6.2.

Beam Limitations:

(Re. AISC358-05, section 6.4)

Beams shall be rolled or welded built-up sections. For built-up sections, at

moment connected ends, within at least the lesser of 𝑑 and 3𝑏𝑏𝑓 , the beam

web and flanges shall be connected using either CJP groove welds or a pair of

fillet welds, each one having a size of ¾ times the beam web thickness, but

not less than 6 mm. For the rest of the beam, the welds size shall not be less

than the size required to accomplish shear transfer from web to flanges.

See also 6.4.5 (Clear span to depth ratio), 6.4.7 (Lateral Bracing) and 6.4.8

(Protected Zone) on AISC358-05.

Pitch Distances:

(Re. AISC358-05, Section 6.9.2)

For the 4 Bolt Extended End Plate Moment Connection:

For bolts up to 25 mm of diameter, the minimum pitch distance is: 𝒅𝒃 + 𝟏𝟐 𝒎𝒎

For bolts larger than 25 mm of diameter, the minimum pitch distance

is: 𝒅𝒃 + 𝟏𝟗 𝒎𝒎.

Pitch distances are 𝑝𝑓𝑖 and 𝑝𝑓𝑜 as shown on Figure 8.2-2.

dePfo

t fb

Pfi

tpd

bp

bbf

twb

g


8-21

End Plate Width:


It shall be greater or equal than the connected beam flange width.

The effective end plate width shall not be taken as greater than the beam

flange width plus 25 mm.

Welding Details:


Weld access holes shall not be used.

Beam web to end-plate joint shall be made using fillet welds or CJP groove

welds. When fillet welds are used, they shall be designed to develop the full

strength of the web in tension, from the inside face of the flange to 150 mm

beyond the bolt row farthest from the beam flange.

The beam flange to end-plate joint shall be made using a CJP groove weld

without backing. The CJP groove weld shall be made such that the root of the

weld is on the beam web side of the flange. The inside face of the flange shall

have a 8-mm fillet weld. These welds shall be demand critical.

Backgouging of the root is not required in the flange directly above and below

the beam web for a length equal to 1.5𝑘1. A full-depth PJP groove weld shall be

permitted at this location.

4. Design steps

(Re. AISC358-05 and supplement No.1, Section 6.10)

Calculate the forces for the connection design:

For this connection, do not follow the step (1) presented on AISC358 code.

Use the values calculated above.


𝑀𝑅𝐸𝑄 = 672543 𝑘𝑁 − 𝑚𝑚

Select the option for the extended end plate moment connection and

establish preliminary values for the connection geometry and bolt

grade.

Use a 4 bolt unstiffened extended end plate moment connection.


8-22

Try the following dimensions:


𝒕𝒑 30

𝒃𝒑 225

𝒈 140

𝒑𝒇𝒊 60

𝒑𝒇𝒐 60

𝒅𝒆 60

Calculate the required bolt diameter using the corresponding

equation:

𝑑𝑏𝑅𝐸𝑄 =

2𝑀𝑓

𝜋𝜙𝑛 𝐹𝑛𝑡 𝑕1+𝑕0 (Re. AISC358-05, Eq. 6.9-6)

Where: 𝑀𝑓 = 𝑀𝑅𝐸𝑄, 𝐹𝑛𝑡 = 780 𝑀𝑃𝑎 for ASTM A490 bolts, 𝜙𝑛 = 0.9, 𝑕𝑖=distance

from the centerline of the compression flange to the ith tension bolt row. In

this case, the connection is symmetric (because 𝑀𝑓 could be positive or

negative, according to the seismic loading). Therefore:

𝑕1 = 𝑑 − 1.5𝑡𝑓𝑏 − 𝑝𝑓𝑖 = 413 𝑚𝑚


2= 551 𝑚𝑚

Then: 𝑑𝑏𝑅𝐸𝑄 = 25.1 𝑚𝑚

Figure 8.2-3: Bolts in tension and distances 𝑕0 & 𝑕1.

Adapted from AISC 358-05, table 6.2.

Select a bolt diameter:

Try M27 bolts.

2P t

M nph 0

h 1

2P t


8-23

Calculate the required end plate-thickness:


1.11𝑀𝑓


(Re. AISC358, Eq. 6.9-8)

Where: 𝑀𝑓 = 𝑀𝑅𝐸𝑄 , 𝐹𝑦𝑝 = 345 𝑀𝑃𝑎 (minimum yield stress for the end plate),

𝜙𝑑 = 1.0.

For the calculation of 𝑌𝑝 = end-plate yield mechanism parameter, see tables

6.2 of the AISC358-05 code, corresponding to 4 bolt unstiffened end-plate

connections.

Figure 8.2-4: Yield Line Pattern Model. Adapted from AISC 358-05, Table 6.2.

𝑌𝑝 =𝑏𝑝

2 𝑕1

1

𝑝𝑓𝑖

+1

𝑠 + 𝑕0

1

𝑝𝑓𝑜

−1

2 +

2

𝑔 𝑕1(𝑝𝑓𝑖 + 𝑠)

𝑠 =1

2 𝑏𝑝𝑔 = 89 𝑚𝑚 (Note that if 𝑝𝑓𝑖 > 𝑠 → 𝑢𝑠𝑒 𝑝𝑓𝑖 = 𝑠)

Therefore, 𝑌𝑝 = 3152 𝑚𝑚 𝑡𝑝𝑅𝐸𝑄 = 26.1 𝑚𝑚

bp

g

de

pfo

tbfp

fi

s

tbw

h1

h0


8-24

Tip:

It is prudent to check also the “prying” effect. According to the AISC Design

Guide N°4, if the applied force is less than 90% of the end-plate strength

(calculated using the yield line analysis), the end-plate is considered to be

“thick”, and no prying forces are considered. When the applied load is greater

than ninety percent of the end plate strength, the end plate is considered to be

“thin”, and the prying forces are assumed to be at a maximum. For

conservative plate thickness design, assume that no prying force occurs,

therefore:


1.11𝑀𝑛𝑝


𝑀𝑛𝑝 = “no prying moment” = 2𝑃𝑡(𝑕0 + 𝑕1) (see Figure 8.2-3).


2

4 , 𝐹𝑡 = 𝐹𝑛𝑡 = 780 MPa for ASTM A490 bolts.

Calculations give:

𝑃𝑡 = 447 𝑘𝑁 → 𝑀𝑛𝑝 = 861032 𝑘𝑁 − 𝑚𝑚

Therefore, 𝑡𝑝𝑅𝐸𝑄

=29.6 mm (no prying action effect controls).

Select the end plate-thickness:

The assumed plate thickness 𝒕𝒑 = 𝟑𝟎 𝒎𝒎 is OK.

Calculate the factored beam flange force:

𝐹𝑓𝑢 = 𝑅𝑅𝐸𝑄 =𝑀𝑓

𝑑 − 𝑡𝑏𝑓= 1395 𝑘𝑁

(Re. AISC 358, Eq. 6.9-9)

Check shear yielding resistance of the extended portion of the four-

bolt extended unstiffened end-plate (4E):

𝐹𝑓𝑢

2< 𝜙𝑑𝑅𝑛 = 𝜙𝑑0.6𝐹𝑦𝑝𝑏𝑝𝑡𝑝

(Re. AISC 358, Eq. 6.9-10)

𝜙𝑑0.6𝐹𝑦𝑝𝑏𝑝𝑡𝑝 = 1397 𝑘𝑁 >𝐹𝑓𝑢

2= 698 𝑘𝑁 OK


8-25


it is satisfied. In this case, there is no need of increasing 𝑡𝑝. OK

Check shear rupture resistance of the extended portion of the four-

bolt extended unstiffened end-plate (4E):

𝐹𝑓𝑢

2< 𝜙𝑛𝑅𝑛 = 𝜙𝑛0.6𝐹𝑢𝑝𝐴𝑛

(Re. AISC358-05, Eq.6.9-11)

Where: 𝐹𝑢𝑝 = 450 MPa (minimum tensile strength of the end-plate).

𝐴𝑛 = 𝑏𝑝 − 2 𝑑𝑏 +1

8× 25.4 𝑚𝑚 𝑡𝑝 = 4940 𝑚𝑚2 = net area of the end-plate.

Calculations give:

𝜙𝑛0.6𝐹𝑢𝑝𝐴𝑛 = 1200 𝑘𝑁 >𝐹𝑓𝑢

2= 698 𝑘𝑁 OK


it is satisfied. In this case there is no need of increasing 𝑡𝑝. OK

The bolt shear rupture strength of the connection is provided by the

bolts at one compression flange:

𝑉𝑢 = 𝑉𝑅𝐸𝑄 < 𝜙𝑛𝑅𝑛 = 𝜙𝑛 𝑛𝑏 𝐹𝑣𝐴𝑏

(Re. AISC358-05, Eq. 6.9-15)

𝐴𝑏 = 573 𝑚𝑚2 = bolt nominal area, for M27 bolts.

𝐹𝑣 = 𝐹𝑛𝑣 = 414 𝑀𝑃𝑎 for ASTM A490 Bolts, threads included.

𝑛𝑏 = 4 (number of bolts at compression side).

Calculations give: 𝜙𝑛 𝑛𝑏 𝐹𝑣𝐴𝑏 = 853 𝑘𝑁 > 𝑉𝑅𝐸𝑄 = 828 𝑘𝑁 OK

Check the bolt-bearing/tear out of the end plate:

𝑉𝑢 = 𝑉𝑅𝐸𝑄 < 𝜙𝑛𝑅𝑛 = 𝜙𝑛 𝑛𝑖 𝑟𝑛𝑖 + 𝜙𝑛(𝑛𝑜)𝑟𝑛𝑜

(Re. AISC358-05, Eq. 6.9-17)

Where: 𝑛𝑖= Number of inner bolts = 2, 𝑛𝑜=Number of outer bolts = 2


8-26

𝑟𝑛𝑖 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2. 4𝑑𝑏𝑡𝐹𝑢 for each inner bolt and 𝑟𝑛𝑜 = 1.2𝐿𝑐𝑡𝐹𝑢 ≤ 2.4𝑑𝑏𝑡𝐹𝑢 for each

outer bolt. The upper limit is 2.4𝑑𝑏𝑡𝐹𝑢 = 875 𝑘𝑁

Use 𝑑𝑏 = 27 𝑚𝑚, 𝐹𝑢 = 450 𝑀𝑃𝑎 , 𝑡 = 𝑡𝑝 = 30 𝑚𝑚 , and:

Inner bolts:


Outer bolts:

𝐿𝑐 = 𝑑𝑒 −30

2= 45 𝑚𝑚 → 𝑅𝑛 = 1.2𝐿𝑐𝑡𝐹𝑢 = 729 𝑘𝑁

Therefore the resistance is: 𝜙𝑛𝑅𝑛 = 2887 𝑘𝑁 > 𝑉𝑅𝐸𝑄 = 828 𝑘𝑁 OK

Note: The diameter of the standard hole for the bolt M27 is 30 mm. See

AISC360-05, table J3.3M.

Design the flange to end-plate and web to end-plate welds, using the

requirements of section 6.9.7 of the AISC358-05 code.

i) Beam flanges to end-plate weld:


weld.

ii) Beam web to end-plate weld:

Use fillet welds, E70 electrode. For a 30 mm thick end-plate, the minimum

weld size is 8 mm according to AISC360-05, table J2.4.

The weld required to develop the bending stress on the beam web, near the

tension bolts, is (according to AISC Design Guide # 4):

(For E70 electrodes, 𝐹𝑊 = 0.6𝐹𝐸𝑋𝑋 = 289.5 𝑁/𝑚𝑚2):

𝑡𝑤 ≥0.6𝐹𝑦𝑏 𝑡𝑤𝑏

2 × 0.707𝐹𝑤= 4.04 𝑚𝑚

With 𝐹𝑦𝑏 = 345 MPa (beam yield stress), 𝑡𝑤𝑏 = 8 mm (beam web thickness).


8-27

The weld size required for resisting the shear 𝑉𝑅𝐸𝑄 between the beam and the

end-plate is:

𝑡𝑤 ≥𝑉𝑅𝐸𝑄

2 × 0.707𝐹𝑤𝐿𝑣

= 8.72

Where 𝐿𝑣 is the following effective length:

𝐿𝑣 = min 𝑑

2− 𝑡𝑓𝑏 , 𝑑 − 2𝑡𝑓𝑏 − 𝑝𝑓𝑖 + 2𝑑𝑏 = 232 𝑚𝑚.

Note: The applied shear is to be resisted by welding between the minimum of

the following distances: the distance between the mid-depth of the beam and

the compression flange or the distance between the inner row of tension bolts

plus two bolt diameters and the compression flange.

(Re. AISC Design Guide # 4 and AISC Manual of Steel of Construction 13th

Ed.).

Use a pair of fillet welds, with 𝒕𝒘 = 𝟏𝟎 𝒎𝒎.

8.2.c. Designed Connection

Notes:

The following assumptions are inherent to the design procedure presented in

this example (see AISC Design Guide # 4). A summary of those assumptions

(not explicit on the document) are presented:

Web

CJP

CJP

Web

A

A

2PL 740x225x30

Bolts: M24 ASTM A490

A - A section


8-28

All bolts are tightened to a pretension not less than AISC

requirement. However, slip critical connections requirements are not

needed to be checked.

Only permitted bolts are ASTM A325 or ASTM A490.

All the shear force is resisted by the compression side bolts.

Beam web-to-end-plate welds in the vicinity of the tension bolts are

designed to develop the yield stress of the beam web. This weld

strength is recommended, even if the full moment capacity of the

beam is not used to design the beam.

Only the web-to-end-plate weld, between the mid-depth of the beam

and the inside face of the beam compression flange, may be used to

resist the beam shear.

Yield-line analysis is used to calculate end-plate strength.

Bolt prying forces are not a consideration, since the required end-

plate thickness prevents their development.

8.2.d. References

Murray and Summer, 2004, “AISC Design Guide 4: Extended

End-Plate Moment Connections; Seismic and Wind Applications”

2nd Edition. American Institute of Steel Construction, USA.

MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 9: STOPPERS

9-1

9. STOPPERS

9.1. Up-lift Clamps

9.1.a. General Description

Up-lift clamps are intended for systems of mobile equipment over rails with wheels (for example cranes), as in Figure 9.1-1. The objective of the up-lift clamps is to prevent falling of the equipment produced by the lifting of it due to the action of vertical seismic forces. The design of the up-lift clamp is done only to stand the vertical seismic forces of the equipment or by the use of minimum up-lift forces, which are provided by the project specifications. Either case considered, there is no need to consider loads in any other direction.

Figure 9.1-1: Schematic view of an up-lift clamp for a crane.

9.1.b. Design Forces

For the design of the up-lift clamps there are no specific provisions in the

Chilean code nor in international codes, but, since up-lift clamps are intended

to avoid up-lift of equipment with wheels over rails, the design of these

devices shall be done according to the seismic vertical forces obtained for the

design of support of equipment (Refer to chapter 10, section 10.1 of this

Manual for the calculation of seismic forces on equipment).

According to the mentioned section, we have to distinguish between

equipment mounted on the structure and equipment attached directly to the

ground. For both cases, a seismic coefficient 𝐶𝑣 has to be considered to

calculate vertical seismic forces. The design force 𝐹𝑣 is:

𝐹𝑣 = 𝐶𝑣𝑊𝑒


9-2

Where 𝑊𝑒 is the weight of the equipment over the rail, including overloads. If

there are mobile loads acting over the equipment (the case of cranes), it is

important to consider the most adverse position of this load for the location of

the up-lift clamp in consideration. However, the probability of having an

earthquake at the maximum operation loads are acting is minimum, and

therefore a minimum operation load, provided by the project specifications

should be considered.

An elastic design of the up-lift clamp should be considered, not taking into

account the possible ductile behavior of the element. Therefore, for the

calculation of the vertical seismic coefficient, 𝐶𝑣, the response modification

factor to obtain 𝐶𝑣 must be equal to 1.0.

It is also possible to use alternative analysis procedures to obtain the design

forces, (depending on the project requirements and specifications). One

alternative is to use a given value of 𝐶𝑣, regardless of the peak ground

acceleration the structure location, and the structural properties of the

equipment and its attachments.

9.1.c. General considerations for the design

As was said above, up-lift clamps must be designed only for vertical forces. To

consider this, it is required to take into account the general disposition of the

up-lift clamp. An example is shown in Figure 9.1-2:

Figure 9.1-2: General schematic disposition of an up-lift clamp, lateral and frontal view.

Lifting forces acting on the equipment can induce collision between the bottom

part of the up-lift clamp (the hook) and the element of the substructure of the


9-3

equipment to which the rail is attached. Thus, the hook of the up-lift clamp is

subjected to a force equal to the lifting force of the equipment.

For the design, the interaction between the stresses produced by the axial load (corresponding to the vertical seismic load) and the bending moment on section A-A (see Figure 9.1-3) must be verified. The bending moment is produced by the vertical seismic load that it is applied at a distance 𝑑 from the

center of the section A-A.

Figure 9.1-3: Specifications to obtain moment and axial force on the up-lift clamp.

Then, if 𝑛𝑢𝑐 as the number of up-lift clamps used:

𝐹 =𝐶𝑣𝑊𝑒

𝑛𝑢𝑐 (axial force on A-A section)

𝑀 =𝐶𝑣𝑊𝑒

𝑛𝑢𝑐𝑑 (bending moment on A-A section)

If 𝐴 is the area of the section A-A and 𝑆 the elastic modulus, the stresses are:

Bending Stress

𝜎𝑏 =𝑀

𝑆

Axial Stress

𝜎𝑎 =𝐹

𝐴

The calculated stresses have to be checked using allowable design stresses,

and also we have to verify that the interaction is accomplished, which for

example could be a condition like this:


9-4

𝜎𝑏 ≤ 𝜎𝑏𝑎𝑑𝑚

𝜎𝑎 ≤ 𝜎𝑎𝑎𝑑𝑚

𝜎𝑎𝜎𝑎𝑎𝑑𝑚

+𝜎𝑏

𝜎𝑏𝑎𝑑𝑚

≤ 1.0

It is important to verify the possibility of buckling in bending of the uplift

clamp, if it is too slender. In order to avoid this, the slenderness of the uplift

clamp section has to be verified and if does not accomplish with the

slenderness requirements, stiffeners must be provided.

Finally, it is important to consider the only provision of NCh2369.Of2003

related to up-lift clamps, which recommends for cranes distance of 20 mm

between the hook of the up-lift clamp and the rail support (Re. Section 11.1.5

NCh2369.Of2003):

Figure 9.1-4: Recommended separation between up-lift clamp and rail support. Adapted from NCh2369.Of2003, Figure A.3.

Also, for up-lift clamps that touch stoppers connected to concrete (see Figure

9.1-1), it is important to leave enough space to properly install the adhesive

anchor bolts and develop the ultimate force on concrete, the prying action on

the stoppers as needed and the interference between the head of the anchor

bolts and the up-lift clamp.


9-5

9.2. Lateral Stoppers

9.2.a. General description of stopper systems

Stoppers are resistant mechanisms used for controlling displacements of

equipment and piping in certain directions. They allow displacements on the

non-restricted directions for thermal expansion of the equipment. Stoppers are

commonly used on high temperature devices, such as boilers, deareators,

pipes, etc. The idea is to control certain displacements for operation continuity

of the equipment or pipe, and avoid their damage (generally very expensive to

repair or replace) in case of an earthquake. Therefore, stoppers transfer the

inertial forces of the nonstructural component to the support structure.

Unfortunately, there are no clear provisions on Chilean codes for the support

of equipment and, additionally, stopper systems differ from one equipment to

the others, so engineers must take special care in the design process and

adapt to each particular situation. One problem found on the February 27th

Chile earthquake was the damage of several nonstructural components (for

example, mechanical equipment) due to the poor design of their supports and

the lack of specific requirements for this design (some provisions are found on

NCh2369.Of2003 and NCh433.Of2009).

Currently, a new normative for earthquake-resistance design of nonstructural

components is proposed (MINVU NTM 001-2010) with new recommendations

(mainly based on ASCE 7-10 provisions) oriented to accomplish that the

nonstructural components have a seismic performance compatible with the

support structure. Some recommendations and general provisions are

discussed in this chapter.

9.2.b. Chilean code related requirements

There are no clear provisions in NCh2369.Of2003 to design stoppers for

equipment. There are only some general provisions that are mentioned now:

9.2.b.1. Anchorage

When seismic stoppers that are anchored to concrete are needed, refer to

dispositions of section 8.6 of the NCh2369.Of2003 code.


9-6

9.2.b.2. Large suspended equipment

(Re. NCh2369.Of2003, 11.4)

Boilers, metallurgical furnace reactors, and other large suspended equipment

shall be attached to the structure with connectors that transmit the seismic

forces without restraining the free vertical and/or horizontal thermal dilatation.

This is explained graphically with Figure A.7 of Appendix A shown below:

Figure 9.2-1: Typical details of large suspended equipment, seismic connectors and anchor bolts. The detail shown corresponds to stopper joints. Taken from

NCh2369.Of2003, Figure A.7 (b).


9-7

9.2.b.3. Piping and ducts

(Re. NCh2369.Of2003, 11.5)

Section 11.5.1: Pipe systems and ducts of large dimensions shall be equipped

with expansion joints and supports that warrant their seismic stability and that

simultaneously allow for thermal deformations.

9.2.b.4. Rotatory kilns and dryers

(Re. NCh2369.Of2003, 11.9)

Section 11.9.1: Longitudinal earthquake must be resisted by rims and thrust

rollers installed at both sides of the rims, and placed in only one support to

allow for longitudinal expansions.

Between the thrust rollers and the rims, a free space shall be left in order to

facilitate the operation. The design of the rim and the rollers must consider the

possibility of longitudinal impact when this free space is closed. It is allowed to

design the rollers and their mechanisms as sacrifice elements that can fail

during an earthquake; in this case the manufacturer must provide detailed

repair instructions in a reduced time to prevent damages of the kiln in the

cooling process.

Section 11.9.2: Transverse earthquake must be resisted by rims and lateral

rollers placed in several supports. The width of the rollers shall be greater than

the width of the rims, to prevent them from falling due to thrust roller failure.


9-8

Figure 9.2-2: Typical details of kilns and rotatory dryers. Taken from NCh2369.Of2003, Figure A.11.


9-9

9.2.c. Other recommendations and discussion of some examples

According to ASCE7-10 code, the transfer of the seismic inertial forces shall be

such that a continuous load path of sufficient strength and stiffness between

the component and the supporting structure shall be provided. Local elements

of the structure, including connections, shall be designed and constructed for

the component forces that control the design of the elements or their

connections.

The idea is that if damage due to the control of large seismic displacements is

expected at the stoppers, then they shall be easily replaceable elements

(stoppers are “seismic fuses”). For example, for the February 27th earthquake,

some boiler stoppers were subjected to inelastic behavior and they dissipated

a large amount of energy, which is very good according to the seismic design

philosophy. If stoppers were not reparable or inspectable, their design should

be done considering larger seismic forces (for example using a smaller R

reduction factor than the value used for the design of steel members).

ASCE 7-10, summary of requirements:

It is important to note that requirements of MINVU NTM 001-2010 are

principally based on ASCE 7-10 provisions. According to section 13.4 of ASCE

7-10 (Nonstructural Component Anchorage), the nonstructural components

and their supports shall be attached or anchored to the supporting structure

using bolted connections, welded connections, or otherwise positively fastened

without consideration of frictional resistance produced by the effects of gravity.

The attachment of nonstructural components shall resist the design forces of

that code (or another design forces, for example, the loads indicated on

Section 10.1 of this Manual) and anchors in concrete must satisfy the

requirements of Appendix D of ACI318.

For multiple attachments, the calculation of force distribution at one location

shall take into account the stiffness and ductility of the component, component

supports, attachments and structure, and the ability to redistribute loads to

other attachments in a group. Also, supports shall be designed for seismic

relative displacements shown on that code, and, if talking about seismic

stoppers, they shall control those seismic displacements and accommodate

thermal displacements of the equipment. Seismic supports shall be

constructed so that support engagement is maintained during a seismic event.


9-10

Other general requirements for support of equipment are listed on section 13.6

of ASCE 7-10 (Mechanical and Electrical Components).

FEMA E-74 document (2011):

This document has some examples of typical causes of damage and the

corresponding seismic protective measures for nonstructural components

(mechanical, electrical and plumbing components) on chapter 6, section 6.4. It

may be in the reader’s interest to study those examples of risk mitigation for

different equipment or piping.

9.2.c.1. Piping supports

In FEMA E-74 document, in the Pressure Piping Section (6.4.3), Floor Mounted

Supports Subsection (6.4.3.5), there are several examples of damage of

piping and adjacent supports due to poor seismic restraint. A picture is

presented below:

Figure 9.2-3: Damage to piping, stud wall and finishes due to movement of

poorly restrained floor-mounted piping in the 1994 magnitude-6.7 Northridge Earthquake. Taken from FEMA E-74, Figure 6.4.3.5-2.

As seismic mitigation consideration, the document states that horizontal or

vertical pipe runs need vertical, lateral and longitudinal restraints (it is

important to have in mind the thermal expansion if it is present on the pipe).

For example, floor-mounted supports can be used to provide restraint for any

combination of vertical, lateral and longitudinal loads; and they can be used

with or without vibration isolation. Longitudinal supports require positive

support to the pipe with a pipe clamp or welded lug.


9-11

Figure 9.2-4: Floor-mounted supports for industrial piping in Chile; piping undamaged in the 2010 Chile Earthquake. Taken from FEMA E-74, Figure 6.4.3.5-5.

Another example is the use of guide plates as part of the supporting structure

for pipes. These guide plates slide in one direction and hold the pipe on the

perpendicular direction. As pipes may be subjected to thermal expansion,

principally on the longitudinal direction due to their length, stoppers and

support structures must accommodate these movements, but limit the seismic

movements of the pipe in order to avoid damage.


9-12

Figure 9.2-5: Pipe support structure. Guide plate is item 8. Taken from Posco E&C. information of Campiche Thermoelectrial Power Plant

DWG N°: WD380-EP146-HRS04.


9-13

It is a good practice to do a detailed model of the pipe supports for the

analysis. They typically include: support conditions, element type used and

material properties, loads and their point of application.

9.2.c.2. Boiler lateral stoppers

Boiler can be roughly described as a large suspended mass hanging from the

“roof” of the boiler supporting structure. Stoppers connect the boiler with

lateral resisting frames in order to restrain seismic displacements in the

horizontal plane (lateral motion of the boiler). They are designed to provide

energy dissipation through nonlinear behavior when large seismic events

occur. Therefore, stoppers transmit those inertia lateral forces to the structure

and they are expected to be “seismic fuses”, in a way that they can easily

reach plastic behavior and therefore they should be easy replaceable

elements.

The complete system that restrains the lateral movement between the boiler

and the support structure is composed of guideposts (supporting columns),

buckstays (beams pararallel to boiler casing) and the stoppers. Stoppers are

fixed to buckstays and they have a restraint with the guideposts on the

corresponding lateral direction.

Boiler stoppers are beam-type elements that restraint displacements in only

one direction. They do not take axial forces; their behavior is purely flexural so

they are an excellent source of energy dissipation. Because boilers are

equipment that work under high temperature ranges, they exhibit thermal

expansion. Stoppers must therefore, control or limit relative horizontal

displacements between the equipment and the structure, without inhibiting the

relative displacements due to temperature changes.

Special careful must be taken when modeling these devices: it is of special

interest to evaluate the internal forces acting on the stoppers between the

boiler and the supporting structure. The common modeling practice is to

assume the restricted directions as connected points in that direction and

without friction. Sometimes stoppers are composed of two or more elements

(for example, one element for restraining movement in one direction and

another element for the movement in the opposite direction); in that case

sometimes a mistake is made: both elements are modeled and both are

restrained, so in the analysis they take approximately half of the load that

corresponds them in the reality.


9-14

Figure 9.2-6: Seismic stoppers damage details. (a) General view, 2 levels. (b)

Detail of Damage at buckstay connection. Taken from EQCO Report: NVTS Boiler System – Damage Report.

Figure 9.2-7: Retrofitted stopper at Angamos Thermoelectric Power Plant.

Taken from Posco E&C Seismic Retrofit Report. 2011/03/04. Complete BQ307L.

If ductile behavior is expected on the load path of the seismic loads due to the

inertial forces coming from the boiler, stoppers are the appropriate elements

to dissipate energy. The recommended design procedure of the stoppers, their

connections and surrounding elements should be the following:

a) Design the stopper with the loads obtained from analysis (integrated

model). If the stopper cannot be easily replaced, use R=1.

b) Compute capacity of the stopper.

c) Use the capacity of the stopper as the forces to design the guide post, the

buckstays and all the connections between the different elements. Therefore,


9-15

all the other elements connected to the stoppers shall be at least capable to

transfer this load.

9.2.d. References

Cruz, E. F., and Valdivia, D., (2011). Performance of industrial

facilities in the Chilean earthquake of 27 February 2010, Structural

Design Tall Special Buildings, 20, pg. 83–101.

FEMA E-74, 2011, “Reducing the Risk of Nonstructural Earthquake

Damage. A Practical Guide”, 4th Edition. FEMA, Washington D.C.

http://www.fema.gov/plan/prevent/earthquake/fema74/

FEMA 412, 2002,”Installing Seismic Restraints for Mechanical

Equipment”. VISCMA, FEMA & ASCE.

FEMA 413, 2004, “Installing Seismic Restraints for Electrical

Equipment”. VISCMA, FEMA & ASCE.

FEMA P-414, 2004, “Installing Seismic Restraints for Duct and Pipe”.

VISCMA, FEMA & ASCE.

Ministerio de Vivienda y Urbanismo (MINVU), 2010, “Estructuras:

Diseño Sísmico de Componentes y Sistemas No Estructurales”

(Anteproyecto de norma NTM 001-2010).

EQCO Earthquake Engineering Consultants, NVTS Boiler System-

Damage Report.

Posco E&C, Campiche Thermoelectrical Power Plant, DWG N°:

WD380-EP146-HRS04 (Figure 9.2-5).

Posco E&C, Angamos Seismic Retrofit Report, 2011-03-04.

American Society of Civil Engineers, 2010, “Minimum Design Loads

for Buildings and Other Structures” (ASCE 7-2010). ASCE, Virginia.


9-16


MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 10: SUPPORT OF EQUIPMENT

10-1

10. SUPPORT OF EQUIPMENT

10.1. Calculation of seismic forces on equipment

In this section we will discuss the provisions for calculation of seismic forces

acting on equipment as defined in the Chilean Seismic Code for Industrial

Structures, NCh2369.Of2003.

The provisions for calculation of seismic forces on equipment can be found on

section 7 of NCh2369.Of2003. For additional provisions regarding seismic

forces and support requirements on equipment also see sections 5 and 11 of

the code. An overview of this provisions and a guide for their use is provided

as follows.

It is important to remark that the seismic analysis must be done in at least

two approximately perpendicular directions (Re. NCh2369.Of2003 section

5.1.1).

Additionally, it is important to consider that the design of the equipment must

be made considering the total horizontal seismic force in a given direction and

the simultaneous total vertical seismic force. The combination of horizontal

and vertical seismic effects must be done directly, and no modal superposition

method can be used (for example CQC).

10.1.a. Equipment mounted on the structure

Mounted equipment must comply with section 11.3.2 of NCh2369.Of2003,

which indicates that equipment on buildings extending more than one story

high, shall have a support system that does not increase the seismic stiffness

of the building. If this is not possible, equipment must be included in the

model of the seismic-resistant system.

For the calculation of the design force, the code establishes several

alternatives, according to the mathematical model of the structure.

If the equipment or its secondary structure is included in the structural

model, the horizontal seismic force for the equipment is: (Re.

NCh2369.Of2003 section 7.2.1)

𝐹𝑝 = 1.2

𝑄𝑝𝑅1

𝑅𝑝< 𝑃𝑝 (Re. NCh2369.Of2003 7-1)


10-2

Where:

𝑄𝑝: Shear force in the base of the equipment or secondary structure,

according to the structural analysis of the building, including seismic

forces reduced by the R factor defined in NCh2369.Of2003.

𝑅1: Response modification factor defined in the section 6.1 of the

disposition. It corresponds to:

𝑅1 = 𝑅𝑄𝑜

𝑄𝑚𝑖𝑛 if

𝑄𝑜

𝑄𝑚𝑖𝑛< 1

𝑅1 = 𝑅 if 𝑄𝑜

𝑄𝑚𝑖𝑛> 1

𝑅1 = 0.5𝑅 if 𝑄𝑜

𝑄𝑚𝑖𝑛< 0.5

𝑄𝑜 is the shear force on the base of the structure and 𝑄𝑚𝑖𝑛 is the minimum

value for the base shear force, established in section 5.4.5 of the code.

𝑃𝑝 : Corresponds to the weight of the equipment.

𝑅𝑝: Response modification factor taken from table 7.1 of the code:

Secondary Element or equipment 𝑹𝒑

- Equipment or elements, flexible or stiff, with non-ductile materials or

appendages. 1.5

- Precast secondary elements or equipment, cantilever elements,

partitions.

- Electrical and mechanical equipment in general

- Chimneys, tanks, steel towers.

- Other cases not specified in this table

3

- Storage Racks

- Secondary structures 4

Table 10.1.a-1: Value of 𝑅𝑝 according to the type of structure.

Taken from the NCh2369.Of2003, table 7-1.

This value of the seismic force corresponds to an equivalent static analysis of

the equipment for the seismic effects, independent of the structure of its

support. Nevertheless, this considers that the equipment was included in an

appropriate way in the building model, i.e. the stiffness and mass of the

equipment are well considered in the structural model of the whole building.


10-3

For the case of elastic behavior, 𝑅𝑝 can be used as 1.0. The values of the table

7-1 of the NCh2369.Of2003 Chilean code are maximum values; some cases

may require lower values.

Also, the reason for including the factor 𝑅1/𝑅𝑝 is to change the response

modification factor for the design of the equipment from 𝑅 to 𝑅𝑝.

The decision of considering or not the effect of the equipment on the structure

depends of the influence that the equipment produces on the response of the

building. There is influence of the equipment on the response if the stiffness or

the inertia of the equipment is determinant for the behavior of the whole

structure or for a local part of it. So, even if the stiffness and inertia of the

equipment are small in comparison with the whole structure, if they influence

locally in the structure, then they have to be included in the building model.

(Re. NCh2369.Of2003 section C5.3.1.5).

Unfortunately, the code does not give any guidance for this purpose and only

establishes the fact that it must be considered (Re. NCh2369.Of2003 section

5.3.1.5).

It is important to notice that the horizontal force acting on the equipment is

located at the center of gravity of the element, so accurate calculation of this

property must be done.

If the equipment does not have to be considered in the structural model of

the building, the horizontal seismic forces must be calculated according to

the following provisions (Re. NCh2369.Of2003 section 7.2.2):

a) When the acceleration at the base level of the equipment, 𝑎𝑝, is known,

obtained from a modal dynamic analysis of the building, including the response

modification factor 𝑅 of the structure, then:

𝐹𝑝 = 3.0𝑎𝑝𝐾𝑝

𝑅𝑝𝑃𝑝 < 𝑃𝑝 (Re. NCh2369.Of2003 7-2)

Where 𝑅𝑝 and 𝑃𝑝 were defined in the previous section. Note that values for this

equation are different for each direction of analysis.

The value of 𝐾𝑝 can be calculated by two ways, depending if the information of

the fundamental periods of the equipment/secondary structure (𝑇𝑝) and the

main structure (𝑇∗) are available or not.


10-4

- If 𝑇𝑝 and 𝑇∗ are known, (𝑇∗ corresponds to the period that has the highest

equivalent translational mass in the direction of analysis) in which the

secondary element may enter in resonance. 𝑇∗ cannot be less than 0.06

seconds for the calculations shown:

𝐾𝑝 = 0.5 +0.5

1−𝛽2 + 0.3𝛽2 2 (Re. NCh2369.Of2003 7-4)

Where:

𝛽 = 1 if 0.8𝑇∗ ≤ 𝑇𝑝 ≤ 1.1𝑇∗

𝛽 = 1.25𝑇𝑃

𝑇∗ if 𝑇𝑝 < 0.8𝑇∗

𝛽 = 0.91𝑇𝑝

𝑇∗ if 𝑇𝑝 > 1.1𝑇∗

- If you do not know the fundamental period of the equipment/secondary

structure and the period of the structure, use:

𝐾𝑝 = 2.2 (Re. NCh2369.Of2003 7-3)

b) When a modal dynamic analysis of the building has not been done, the

horizontal seismic force can be calculated as:

𝐹𝑝 = 0.7𝑎𝑘𝐾𝑝

𝑅𝑝𝑃𝑝 < 𝑃𝑝 (Re. NCh2369.Of2003 7-5)

The value of 𝐾𝑝 is calculated in the same way as the previous section.

Finally, for the calculation of the horizontal force, the value of 𝑎𝑘 is needed,

which, in this case, has not being obtained from a modal dynamic analysis of

the structure without considering the equipment mass on the main structure,

so use the following expression that the Chilean code recommends:

- If the level height 𝑘 (location of the equipment) is known (Re.

NCh2369.Of2003 section 7.2.4):

𝑎𝑘 =𝐴0

𝑔 1 + 3

𝑍𝑘

𝐻 (Re. NCh2369.Of2003 7-6)

Where 𝐴0 is the maximum effective acceleration defined in the section 5.3.3 of

NCh2369.Of2003; 𝑍𝑘 is the height of the level 𝑘 with respect to the base level;

and 𝐻 is the total height of the building with respect to the base level.


10-5

- If the level height (location of the equipment) is unknown (Re.

NCh2369.Of2003 section 7.2.3), use:

𝑎𝑘 = 4𝐴0

𝑔

The expressions of ASCE 7 could also be used to define the horizontal seismic

force for equipments.

The horizontal seismic force is given by:

𝐹𝑝 =0.4 𝑎𝑝𝑆𝐷𝑆𝑊𝑝

𝑅𝑝

𝐼𝑝

1 + 2𝑧

ℎ (Re. ASCE 7 Equation 13.3-1)

Where 𝑎𝑝 is the component amplification factor, which varies from 1.0 to 2.5

(for the selection of this value, see tables 13.5-1 or 13.6-1 of ASCE 7); 𝑆𝐷𝑆 is

the short period spectral response acceleration, which is defined in section

11.4 of ASCE 7; 𝐼𝑝 is the importance factor, which varies from 1.0 to 1.5; 𝑊𝑝 is

the operating weight of the equipment; 𝑅𝑝 is the response modification factor

for the equipment, which varies from 1 to 12; 𝑧 is the height of the point of

attachment between the equipment and the structure; and ℎ is the height of

the structure with respect the base.

ASCE 7 considers the height of the structure ℎ as the average roof height with

respect to the base level.

The determination of the height of the structure is an important issue, which

seems obvious at first sight but it is not always simple, as the example shown

at the left of Figure 10.1.a-1. For example, if the equipment is located in a

substructure attached to the ground inside the main building (see right of the

Figure 10.1.a-1), the height ℎ for the calculation of the horizontal seismic force

is the height of the substructure and not the height of the main building.


10-6

Figure 10.1.a-1: Examples of height determination for horizontal seismic

forces.

For both cases of including or not the equipment/secondary structure in

the main structural model of the building, which are described above and

correspond to sections 7.2.1 and 7.2.2 of NCh2369.Of2003, the horizontal

seismic force calculated must be greater than:

𝐹𝑝𝑚𝑖𝑛 =0.8𝐴0𝑃𝑝

𝑔 (Re. NCh2369.Of2003 section 7.2.5)

If the structure and the equipment have been integrated in the same model,

which considers satisfactorily the interaction between the building and the

equipment and the dynamical properties of the equipment, there is no need of

using sections 7.2.1 and 7.2.2 of the NCh2369. Of2003.

10.1.b. Vertical Seismic Forces

According to the provisions of section 5.1.1 of NCh2369.Of2003, vertical

seismic accelerations must be considered in hanging bars of suspended

equipment (section 5.1.1a of the disposition) and in the case of foundations

and anchorage elements and support of structures and equipment (section

5.1.1c of the disposition). In section 5.5 it can be found provisions for the

calculation of the vertical seismic force.

According to the 5.5.1 of NCh2369.Of2003 the seismic vertical acceleration

can be considered as static, considering a seismic coefficient which depends of

the type of element to be designed. In the case of the elements that fall on the

category of section 5.1.1c, which is the case of interest, the seismic coefficient

is:

𝐶𝑣 =2

3

𝐴0

𝑔 (Re. NCh2369.Of2003 section 5.5.1b)


10-7

Then, the vertical seismic force for the support of the equipment is:

𝐹𝑣𝑝 = 𝐶𝑣𝑃𝑝

The seismic coefficient for the cases that fall on the category of the section

5.1.1a of the code is also of our interest since in those cases the suspension

bars and support elements for equipment (in the case of hanged equipment)

can be included. In those cases the seismic coefficient can be obtained from:

𝐶𝑣 =𝐴0

𝑃 (Re. NCh2369.Of2003 section 5.5.1a)

And the vertical seismic force must be calculated according to the following

expression:

𝐹𝑣 = ±𝐶𝑣𝐼𝑃

Where 𝑃 is the sum of the permanent loads and live loads on the support and 𝐼

is the importance coefficient which is defined according to the 4.3.1 and 4.3.2

of the NCh2369.Of2003.

As an alternative for the previous analysis, it is possible to use the same

procedure used for horizontal forces applied to the vertical direction. This is

more precise since considers the dynamical properties of the equipment for the

vertical direction.

Finally, the provisions of section 5.5 establish an alternative calculation

method for the vertical seismic loads, which consist in the development of a

vertical dynamic analysis using spectral accelerations obtained from expression

5-5 of the code, considering 𝑅 = 3 and 𝜉 = 0.03. The spectral acceleration does

not have to be greater than 𝐼𝐴0. The problem with this option is that the code

does not consider how to use the accelerations or the forces obtained from this

type of analysis in order to obtain design forces for equipment.

10.1.c. Stiff and robust equipment directly supported to the ground

In the case of equipment directly supported to the ground, and also if the

equipment is sufficiently stiff and robust (this considers a fundamental period

for the equipment less than 0.06 seconds, including the effects of the

connection to the respective foundation), it is possible to design using a static

analysis, with forces obtained from the following seismic coefficients:


10-8

Horizontal Seismic Coefficient:

𝐶ℎ = 0.7𝐴0

𝑔 (Re. NCh2369.Of2003 section 5.6)

Vertical Seismic Coefficient:

𝐶𝑣 = 0.5𝐴0

𝑔 (Re. NCh2369.Of2003 section 5.6)

Then, the seismic forces for the equipment are:

𝐹𝑝ℎ = 𝐶ℎ𝑃𝑝

𝐹𝑝𝑣 = 𝐶𝑣𝑃𝑝

Also, it can be possible to calculate seismic forces with the same input as if the

equipment/secondary structure were a main structure on the ground.

10.1.d. Additional comments

Future provisions that will be used in Chile, (based on ASCE 7 code) are the

MINVU NTM 001-2010 for the seismic design of nonstructural components. It

has other expressions (but similar) than those presented on this section for

the calculation of seismic forces on equipment, and with detail in the

calculation procedure.

10.1.e. References







10-9

10.2. Skid-mounted equipment

10.2.a. General description and recommendations

Sometimes, for cleaning or easiness of transportation, equipment is resting

over skid beams (typically on Channel or H sections). These skids are

connected to a concrete foundation (by anchor bolts) or to the steel structure

(by standard bolts). A scheme of a skid mounted equipment is shown on the

following figure:

Figure 10.2.a-1: Skid-mounted equipment.

For designing the anchorage of the skids it is important to take note of the

following tips:

The skid to foundation connection must be designed in order to

minimize sliding, tilting or overturning of the equipment. In many

situations, the equipment operability could be compromised, and the

intention of the seismic design philosophy is to guarantee continuous

operation.

The design loads for the equipment can be calculated using section

10.1 of this Manual (or similar reasonable provisions). Note that it is

important to do a review of the equipment drawing (from vendor) and

define values of some important parameters like: plan dimension of

the equipment base frame; height of the equipment; location, size,

and embedment length of the anchor bolts; weight of the equipment

(distinguish between operating and non-operating conditions); and

location of the center of gravity of the equipment (where design

forces are applied). It is also important to take into account any other

forces due to the interaction with other components (for example,

with pipes attached to the equipment).

A recommendation of FEMA E-74 Document is to place two or more

anchors on each side of the equipment. Another recommendation is


10-10

to use shims or grout to level the equipment. If grout is used, it

should be continuous with the contact surface.

If anchoring skids to steel framing members, it is important to take

into account the integrity of these structural members when drilling

them. When anchoring to concrete (slab or foundation) it is important

to check that the height of the concrete pedestal or thickness of the

concrete slab is greater than the required embedment length for the

anchor rods.

Design forces from load combinations shall be used to check the skid

beams, the anchorage of these skids and the supporting structural

element. Note that the skids for the equipment must have enough

strength and stiffness to resist those forces and minimize

deformations that could be dangerous for the mounted equipment. If

needed, stiffeners may be added to transfer large loads.

10.2.b. Some important skid and anchor bolts related aspects

When there is an overturning moment due to a lateral force and/or an uplift

force acting on the equipment, the anchor bolts generally will be subjected to

tension and shear. The corresponding interaction must be checked for

calculating the required strength of the anchors. All other limit states present

on the bolts and the attaching members must be included in the verification,

depending if the anchorage is made with concrete or steel.

Note that if bolts are under tension, then the prying effect usually needs to be

considered to calculate the required thickness of the skid flange and the bolt

diameter, so there is sufficient stiffness and strength in the connecting

elements and in the bolts. A reference for this topic is the AISC Manual of

Steel Construction (13th Ed.), Chapter 9: “Design of Connecting Elements”.

Prying action calculations have been made for other examples of this Manual.

If ductility is needed on the anchor bolts (when there are large seismic forces),

it may be necessary to provide an exposed length for the bolts (same as the

column base plate requirement when large seismic effects are expected) and

add a stiffener on the skid member to resist the tension force that is being

developed on the anchors. Note that skid steel members must resist the

seismic design forces due to the presence of the equipment. If anchorage is

made on concrete, the design must be made according to ACI code (ACI358

and/or ACI349) and it must provide a ductile behavior, avoiding brittle


10-11

(concrete related) controlling failure modes. Remember that the concrete

foundation must also be dimensioned and designed.

Figure 10.2.b-2: Prying action in angle scheme.

Adapted from AISC Manual of Steel Construction 13th Ed.

Figure 10.2.b-3: Example of exposed length for anchor bolt when ductility is

required.

When none of the details from Figure 10.2-3 (exposed length for the anchor

bolts or stiffeners on the channel skid beam) are present, the head of the

anchor is tightened to the top surface of the bottom flange of the skid beam.

When this occurs, force amplification has to be considered on the design

verification of flanges and anchor bolts due to prying effect and the lack of

exposed length required by section 8.6.2 of NCh2369.Of2003. These


10-12

amplifications of forces will directly affect the diameter of the bolts and the

detailing and anchoring of them, even more if ductile behavior is necessary.

For transferring the seismic shear, typically the friction force shall not be

considered to help the shear base resistance. If needed, shear keys (for

concrete foundation) must be designed, or seismic stoppers could be included.

Grout thickness shall not be considered on the bearing lateral resistance of a

concrete foundation.

10.2.c. References





Construction”. 13th Edition. Chapter 9: “Design of Connecting

Elements”, AISC, USA.


10-13

10.3. Post-Installed Anchor Bolts

This section refers to post-installed anchor bolts for equipment or other

elements anchored to concrete. Anchors are the most important part to

transfer the load from the superstructure or the equipment to the supporting

structure. There must be a continuous load path with enough strength and

stiffness between the superstructure and the supporting structure.

It is important to pay attention to the design of these elements as a load

transfer mechanism. Otherwise, super structure and sub-structure, designed

separately, will not behave as a single structure and this situation will lead to a

non desired failure.

10.3.a. General description of post-Installed anchor bolts

When an anchor rod is installed after placing concrete, making a hole in the

hardened concrete with a drill-bit, it is called "Post installed anchor". Some

types of post-installed anchor bolts are presented in the following figure:

Figure 10.3.a-1: Different Types of Post-Installed Anchor Bolts: (a) Adhesive Anchor; (b) Undercut Anchor; (c) Torque-Controlled Expansion Anchor: (c1) Sleeve type and (c2) Stud type; (d) Drop-in Type Displacement-Controlled

Expansion Anchor. Taken from ACI318-11 Code, Figure RD.1.1.

The most widely used anchors for seismic restraints are the undercut and the

adhesive anchors.

Basic working principles of anchor bolts.

According to HILTI Manual (2009), there are 3 basic principles which make an

anchor rod hold in a base material when subjected to a tensile force:

Friction (when expansion forces are present, friction between anchor and hole

wall is provided), keying (anchors rely on the interlock of the anchor with

deformations in the hole wall to resist the applied tension), and bonding (when

adhesive bonding is provided between the anchor and the hole wall). These

principles are generally combined in real situations.


10-14

Figure 10.3.a-2: Friction, keying, and bonding principles on anchor bolts.

Taken from HILTI Manual (2009).

When anchor bolts are subjected to shear forces, most of them develop their

shear resistance due to bearing against the hole wall near the surface of the

base material.

Other important definitions

(Re. ACI318-11, D.1)

Attachments: are structural assemblies (external to the base material and

embedment surface) that transmit loads to or receive loads from the anchor.

An example of attachment is a base plate.

Ductile Steel Element: is an element with a tensile test elongation of at least

14% and reduction in area of at least 30% (when the element does not meet

any or both of the previous conditions, it is considered a brittle element). A

steel element that meets the requirements of ASTM A307 (and ASTM F1554)

shall be considered ductile.

10.3.b. Failure modes of anchorages in concrete and general requirements for strength of anchors

In this section the different possible failure modes will be presented but not

specific code requirements will be shown.

This chapter is not meant to explain in detail the different failure modes (and

their corresponding equations) of the anchor bolts and the concrete. The

reader is encouraged to study them with attention. According to ACI318-11,

Appendix D, the following failure modes (where applicable) shall be

considered:

(Re. ACI318-11, D.4.1)


10-15

a) Steel strength of the anchor in tension.

b) Concrete breakout strength of the anchor in tension (applicable to all

anchor types).

c) Pullout strength cast-in, post-installed expansion or undercut anchor

in tension.

d) Concrete side-face blowout strength of headed anchor in tension.

e) Bond strength of adhesive anchor in tension.

f) Steel strength of anchor in shear.

g) Concrete breakout of anchor in shear (applicable to all anchor types).

h) Concrete pryout of anchor in shear (applicable to all anchor types).

ACI318-11 references on commentary RD.4.1 discuss in more detail the

different anchor failure modes. It is important to note that anchors shall satisfy

the required edge distances, spacing, and thicknesses to preclude splitting

failure, as required in section D.8 of ACI318-11.

Figure 10.3.b-3: Failure modes for anchors in tension.

Taken from ACI 318-11, Figure RD.4.1a.

Figure 10.3.b-4: Failure modes for anchors in shear.

Taken from ACI 318-11, Figure RD.4.1b.


10-16

The design of the anchors shall meet table D.4.1.1 of ACI318-11 and, for

earthquake loading, the design shall satisfy D.3.3. Note that when both tensile

and shear forces are present, proper tension-shear interaction must be

considered according to D.7. For more general provisions and strength

reduction factors for the different limit states, see section D.4 of the code.

For calculating the design tensile and shear strengths (considering the various

applicable limits states), see section D.5 and D.6 of Appendix D.

An additional reference that contains a summary of the limit states according

to the 2008 version of ACI318 code, properties for different types of HILTI

anchors and worked examples is the HILTI Manual (2011). Also HILTI Manual

(2009) has a brief description of some failure modes. See the references of

this chapter.

10.3.c. Seismic design philosophy for anchorages

The underlying seismic design philosophy in the design of anchors in concrete

is to ensure ductile failure modes of the anchor. If damage occurs, it should be

in an easily replaceable element. Note that any concrete failure is a brittle

mode of failure.

As said on NEHRP 2009 Recommended Seismic Provisions, anchors must be

designed to have ductile behavior (or to have a specified degree of over

strength). Depending on the specifics of the design condition, ductile design of

anchors in concrete may satisfy one or more of the following objectives:

1. Adequate load redistribution among anchors in a group (to adjacent

anchors).

2. Allowance for anchor overload without brittle failure.

3. Energy dissipation.

NEHRP 2009 Recommended Seismic Provisions state the following:

“Achieving deformable, energy-absorbing behavior in the anchor itself is often

difficult. Unless the design specifically addresses the conditions influencing

desirable hysteretic response (adequate gauge length, anchor spacing, edge

distance, steel properties, etc.), anchors cannot be relied upon for energy

dissipation. Simple geometric rules, such as restrictions on the ratio of anchor

embedment length to depth, are not adequate to produce reliable ductile

behavior. For example, a single anchor with sufficient embedment to force

ductile tension failure in the steel body of the anchor bolt may still experience


10-17

concrete fracture (a non-ductile failure mode) if the edge distance is small, the

anchor is placed in a group of tension-loaded anchors with reduced spacing, or

the anchor is loaded in shear instead of tension. In the common case where

anchors are subject primarily to shear, response governed by the steel

element may be non-ductile if the deformation of the anchor is constrained by

rigid elements on either side of the joint. Designing the attachment so that its

response is governed by a deformable link in the load path to the anchor is

encouraged. This approach provides ductility and over strength in the

connection while protecting the anchor from overload. Ductile bolts should only

be relied upon as the primary ductile mechanism of a system if the bolts are

designed to have adequate gauge length (unbonded strained length of the

bolt) to accommodate the anticipated nonlinear displacements of the system

at the design earthquake”.

10.3.d. NCh2369.Of2003 code requirements for anchorage on concrete

Refer to section 8.6 of NCh2369.Of2003 code for anchorages (of steel

structures). A summary of the basic requirements is presented:

Section 8.6.2: When anchor bolts are subjected to tension, they must

meet some minimum lengths in order to make easier their inspection

and reparation, and the thread must have enough length to be able to

tighten the nuts. See the following figure:

Figure 10.3.d-5: Definition of minimum lengths for anchor bolts according to

Chilean Code. Adapted from NCh2369.Of2003 code, Figure A.1: Column Bases.

When anchor bolts do not meet the previous requirement, they must

be designed to stand load combinations in which the seismic forces

have been amplified by the maximum value between 0.5R and 1.5


10-18

times with respect to the value indicated on sections 5 and 7. (See

also sections 7.3.2 and 7.3.3 of the code). In section 7.3.2 it is also

mentioned that when the anchor rods are superficial (length < 8

diameters), seismic forces must be increased.

Note that the value of R mentioned above is the same value used for

the analysis and design of the structure or the design of an

equipment anchored by bolts. Also note that only seismic forces must

be amplified, not all the loads in the load combination. The mode of

failure of the each system must be of ductile type; if not, the R value

shall be reduced.

For important equipment and in the structure of large suspended

equipment, ductile, easily fixable and eventually replaceable bolts

shall be used. An example of this type of anchors is the hummer head

bolt, as shown in Figure A.7 of NCh2369.Of2003.

Section 8.6.3: Column and equipment base plates must be provided

of shear plates or seismic stoppers designed to transmit 100% of the

base shear. See 8.6.4 to 8.6.6 for additional requirements related

with shear force.

Section 8.6.8: The concrete of the foundations must be designed to

resist the vertical and horizontal forces transmitted by the steel

anchoring elements. The concrete and the reinforcement strength

shall be such that the failure is produced on the steel anchoring

elements and not on the concrete (ductile design concept).

10.3.e. ACI318 code requirements for anchorage on concrete

Refer to Appendix D of ACI318-11 and ACI318-08 Code.

Basic requirements for post-installed anchor bolts

In order to use the requirements of Appendix D, post-installed, undercut, and

expansion anchors must meet the assessment criteria of ACI355.2 code

“Qualification of Post-Installed Mechanical Anchors in Concrete”. When high

seismic forces are present, post-installed anchor bolts must show a capacity to

resist large deformations. Provisions for adhesive anchors were added in the

2011 code; they shall meet the assessment criteria of ACI355.4 code

“Qualification of Post-Installed Adhesive Anchors in Concrete”.


10-19

Force calculation

D.3.1: Anchors and anchor groups shall be designed for critical effects of

factored loads obtained from an elastic analysis. Plastic analysis approaches

are permitted where nominal strength is controlled by ductile steel elements,

provided that deformational compatibility is taken into account.

Note that if the strength of the anchorage is governed by breakage of the

concrete, the behavior is brittle and there is little ductility. In that case, the

code recommends use the theory of elasticity, and assume that the

attachment that distributes the loads to the anchors is very stiff.

On the other hand, if the anchor strength is governed by ductile yielding of the

anchor steel, the analysis based on the theory of elasticity is conservative.

Some references for plastic analysis approaches are shown in the Commentary

of the code.

See D.3 provisions for other general requirements.

Requirements for anchor bolts in seismic zones

(Re. ACI318-08 and ACI318-11, D.3.3)

Note that provisions of Appendix D do not apply at plastic hinge zones of

concrete structures (D.3.3.1).

One main objective of this chapter is to focus on the ductile design of the

anchorage to concrete. There were some changes between the 2008 and 2011

ACI 318 provisions. The most important provisions will be summarized. The

reader is encouraged to carefully study the provisions of Appendix D and its

commentary.

ACI318-08

Section D.3.3.3:

Anchor design strength related to concrete failure modes must take into

account an additional reduction factor of 0.75 (therefore, tensile resistance is

𝟎.𝟕𝟓𝜙𝑁𝑛 and shear resistance is 𝟎.𝟕𝟓𝜙𝑉𝑛). The resistance must be calculated

assuming cracked concrete (unless proven otherwise).


10-20

Sections D.3.3.4, D.3.3.5 and D.3.3.6: In these provisions, the ductile failure

behavior is achieved designing in two ways:

Section D.3.3.4: Anchors shall be designed to be governed by the steel

strength of a ductile steel element (of the anchor itself) in accordance with

D.5.1 (tensile loading design requirements) and D.6.1 (shear loading design

requirements). Therefore, anchor rods must be ductile steel elements as

defined previously.

Section D.3.3.5: Instead of D.3.3.4, the attachment that the anchor is

connecting to the structure shall be designed so that the attachment will

undergo ductile yielding at a force level corresponding to anchor forces no

greater than the design strength of the anchors, as specified in D.3.3.3

Also, the code provides a third option when ductile behavior could not be

achieved (for example due to geometrical or material restrictions):

Section D.3.3.6: As an alternative to D.3.3.4 and D.3.3.5, it shall be permitted

to take the design strength of the anchors as 0.4 times the design strength

determined with D.3.3.3 (this reduced strength is made for minimize the

possibility of brittle failure).

ACI318-11

In this version of the code, the requirements are separated between tensile

and shear loading. The code requirements for ductile behavior are now clearly

specified and these provisions are more explicit than the ones presented on

2008 version. According to the seismic design philosophy, it is advisable to use

those provisions, because it is expected that they will lead to ductile behavior

of the connection.

D.3.3.4.-Requirements for Tensile Loading (summary):

ACI318-11, section D.3.3.4.2:

Where the tensile component of the strength-level earthquake force applied to

anchors exceeds 20% of the total factored anchor tensile force associated with

the same load combination (i.e. the earthquake seismic force is significant),

anchors and their attachments shall be designed in accordance with D.3.3.4.3

and the anchor design tensile strength shall be calculated in accordance with

D.3.3.4.4. When the previous condition is not met, see D.3.3.4.1 on the code.


10-21

ACI318-11, section D.3.3.4.3:

Anchors and their attachments shall satisfy one option from (a) trough (d).

a) For single anchors, the concrete-governed strength shall be greater

than the steel strength of the anchor. For anchor groups, the ratio of

the tension load of the most highly stressed anchor to the steel

strength of the same anchor shall be equal or greater than the ratio

of the tensile load on tension loaded anchors to the concrete

governed strength of those anchors. There are several additional

provisions for increasing ductility and energy dissipation that are

listed on the code (points 1 to 6 of D.3.3.4.3(a)). Note that according

to the commentary on RD3.3, if these ductility requirements are not

satisfied, then the attachment to the anchors should be designed for

yielding.

b) The anchor or group of anchors shall be designed for the maximum

tension that can be transmitted to the anchor or to the group, based

on the development of a ductile yield mechanism in the attachment,

in flexure, shear or bearing (or a combination of those conditions),

considering both material over strength and strain hardening effects

for the attachment. The anchor design tensile strength shall be

calculated with D.3.3.4.4 (discussed below).

In option (a), the ductile failure mechanism of the anchor is controlled by

requiring yielding of the anchor prior to a brittle concrete failure. On option

(b), the ductile behavior is achieved by designing the attachment (secondary

element) to yield before the failure of the anchors. For example, if the strength

of a base plate is less than the anchor bolts strength, it means that the failure

mode will occur at the base plate and, because it yields, the controlling limit

state is ductile.

c) The anchor or group of anchors shall be designed for the maximum

tension that can be transmitted by a non-yielding attachment. Anchor

tensile design strength shall be calculated with D.3.3.4.4 (discussed

below).

d) The anchor or group of anchors shall be designed for the maximum

tension obtained from the design load combinations that include the

earthquake load E, with E increased by 𝛀𝟎 (over strength factor


10-22

defined on ASCE 7 code). The anchor tensile design strength shall

satisfy the tensile strength requirements of D.4.1.1.

When to use each option of the above?

According to the commentary in RD.3.3.4.3 of ACI318-11:

Option (a) should be used only when the anchor yield behavior is well

defined and where the interaction of the yielding anchor with other

elements in the load path has been adequately addressed.

In option (b), the force associated with the steel attachment (for

example an angle, base plate or web tab), should be the expected

strength rather than the specified yield strength of the steel.

Option (c) shall apply to a variety of cases, particularly when AISC

341 provisions are used, which specify the use of loads based on

member strengths.

ACI318-11, section D.3.3.4.4:

This section refers to the calculation of the anchor tensile design strength for

resisting earthquake forces, for the limit states listed in table D.4.1.1

including concrete (brittle) limit states. It shall be assumed for the calculations

that the concrete is cracked, unless it can be demonstrated that the concrete

remains uncracked (see RD.3.3.4.4 commentary).

ACI318-11, section D.3.3.4.5:

This section refers to anchor reinforcement.

D.3.3.5.- Requirements for Shear Loading (summary):

ACI318-11, section D.3.3.5.2:

Where the shear component of the strength-level earthquake force applied to

anchors exceeds 20% of the total factored anchor shear force associated with

the same load combination (i.e. the earthquake seismic force is significant),

anchors and their attachments shall be designed in accordance with

D.3.3.5.3. The anchor design shear strength shall be calculated in accordance

with D.6. When the previous condition is not met, see D.3.3.5.1 at the code.


10-23

ACI318-11, section D.3.3.5.3:

Anchors and their attachments shall satisfy one option from (a) trough (d). A

summary is presented:

Note: There is no corresponding option to option (a) of D.3.3.4.3, because the

cross section of the steel element of the anchor cannot be configured so that

steel failure in shear provides any meaningful degree of ductility.

a) The anchor or group of anchors shall be designed for the maximum

shear that can be transmitted to the anchor or to the group, based on

the development of a ductile yield mechanism in the attachment in

flexure, shear, or bearing (or a combination of those conditions)

considering both material over strength and strain hardening effects

for the attachment.

b) The anchor or group of anchors shall be designed for the maximum

shear that can be transmitted to the anchors by a non-yielding

attachment.

c) The anchor or group of anchors shall be designed for the maximum

shear obtained from the design load combinations that include E, with

E increased by 𝛀𝟎 (over strength factor defined on ASCE 7 code). The

anchor design shear strength shall satisfy the tensile strength

requirements of D.4.1.1.

ACI318-11, section D.3.3.5.4:

This section refers to anchor reinforcement.

D.3.3.6.- Requirements for tension-shear forces:

When anchor bolts are subjected to both tension and shear forces, they shall

be designed to satisfy the requirements of D.7 (tension-shear interaction),

with the anchor design tensile strength calculated from D.3.3.4.4.

10.3.f. Additional Tips and Warnings

It is recommended to do the design verifications taking into account

bolt supplier recommendations (for example, checking HILTI Manuals

if using that type of bolts). Sometimes, those recommendations are

not conservative compared to code requirements, so it is


10-24

recommended to also check code requirements. The commonly used

and selected reference for the design of anchor bolts in concrete is

the Appendix D of the ACI318 Code.

HILTI’s PROFIS Anchor software could be helpful for analyzing and

designing anchor bolts according to ACI318 provisions. This software

performs a simplified finite element analysis to establish anchor load

distribution on an elastic basis. It is recommended to use good

engineering judgment when introducing input data and when

analyzing the results given by the software. The final design made by

the software may not be 100% accurate and, if needed, it must be

modified.

Field inspection during the installation of post-installed anchor bolts is

of high importance, especially for chemical anchors. Provisions of ACI

318-2011 code are listed on section D.9, and for adhesive anchors

there are additional requirements included on D.9.2.1 through

D.9.2.4.

In construction drawings, it is important to leave “hold” marks in

order to wait for the drilling of the anchor holes until the supporting

structure of the equipment is mounted, so as to not cause

interferences between the anchors and the concrete reinforcement.

10.3.g. References

Cook and Klingner, 1992, “Ductile Multiple Anchor Steel-to-Concrete

Connections”. ASCE Journal of Structural Engineering, Vol. 118, N°6,

June, 1992.

HILTI, 2009, “Anchor Fastening Technology Manual”. Edition February

2009.

HILTI, 2011, “North American Product Technical guide. Vol.2: Anchor

Fastening Technical Guide 2011”.

American Concrete Institute, 2011, “Building Code Requirement for

Structural Concrete (ACI318-11) and Commentary”, Appendix D. ACI,

USA.

American Concrete Institute, 2008, “Building Code Requirement for

Structural Concrete (ACI318-08) and Commentary”, Appendix D. ACI,

Farmington Hills, USA.

FEMA, 2009 “FEMA P-750: NEHRP Recommended Seismic Provisions

for New Buildings and Other Structures”, C13.4: Nonstructural

Component Anchorage. Building Seismic Safety Council, Washington

D.C.



MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 11: EXPANSION JOINTS

11-1

11. EXPANSION JOINTS

In this chapter we discuss the general provisions regarding expansion joints

according to the Chilean code NCh2369.Of2003, and some other general

recommendations.

11.1. Seismic Displacements

One of the most common mistakes in seismic design is to consider that the

seismic displacements are produced by seismic forces modified by the

response modification factor R. This common mistake leads to

underestimations of the actual displacements that the structure will undertake,

thus, when the expansion joint design is made, this design is for an smaller

level of displacement. It is important that the calculation of displacements

shall be done according to the provisions of the applicable code, in this case

the Chilean code.

According to the NCh2369.Of2003, displacements shall be calculated in the

following way when the analysis considers R-factor reduced seismic loads (Re.

Section 6.1 of the NCh2369.Of2003):

𝑑 = 𝑑0 + 𝑅1𝑑𝑑 (Re. 6-1 on NCh2369.Of2003)

Where 𝑑 is the seismic displacement, 𝑑0 corresponds to the displacement

produced by non-seismic service loads. 𝑅1 is:

𝑅1 =

𝑅

𝑄𝑜

𝑄𝑚𝑖𝑛

0.5 <𝑄𝑜

𝑄𝑚𝑖𝑛

< 1.0

0.5 𝑅 𝑄𝑜

𝑄𝑚𝑖𝑛

≤ 0.5

𝑅 𝑄𝑜

𝑄𝑚𝑖𝑛

≥ 1.0

Finally, 𝑑𝑑 is the seismic displacement calculated in the structural analysis

considering the response modification factor 𝑅. Note that it is always

conservative to use 𝑅1 = 𝑅. In some codes and specifications 𝑅1 is called 𝐶𝑑.

This provision takes into account the fact that the reduction of the seismic

forces because of the ductile behavior of the structure, which is expressed with

the factor 𝑅, is not applicable to deformations, which are calculated

considering the elastic response of the structure, but without the use of a


11-2

reduction factor. Also, if anelastic methods are used, deformation 𝑑 shall be

obtained directly from the analysis.

Consider the following situation:

Figure 11-1: Schematic disposition of two separated structures.

Two structures separated by a gap 𝑆. To avoid the impact between the two

frames produced by the seismic displacements, the minimum gap that has to

be provided is given by the greater of the following values (Re. Section 6.2.1

of the NCh2369.Of2003):

𝑆 = 𝑅1𝑖𝑑𝑑𝑖 2 + 𝑅1𝑗𝑑𝑑𝑗

2+ 𝑑0𝑖 + 𝑑0𝑗 (Re. 6-2 NCh2369.Of2003)

𝑆 = 0.002 ℎ𝑖 + ℎ𝑗 (Re. 6-3 NCh2369.Of2003)

𝑆 = 30 𝑚𝑚

Where 𝑑𝑑𝑖 and 𝑑𝑑𝑗 are the seismic displacements of each structure calculated

considering the response modification factor 𝑅 (which can be different for each

structure); 𝑅1𝑖 and 𝑅1𝑗 are the response modification factors for each structure

as defined in section 6.1 (explained above); 𝑑0𝑖 and 𝑑0𝑗 are the non-seismic

deformations for service loads; and ℎ𝑖 and ℎ𝑗 are the heights of the considered

level for each structure, measured from their respective base levels.

The first expression takes into account the fact that the maximum seismic

displacements for each building will not generally occur at the same time, so

that expression is a less conservative alternative than using:

𝑆 = 𝑅1𝑖𝑑𝑑𝑖 + 𝑅1𝑖𝑑𝑑𝑖 + 𝑑0𝑖 + 𝑑0𝑗

i j

s


11-3

This above expression is considered in some codes like the New Zealand code.

The application of the rule 𝑅1𝑖𝑑𝑑𝑖 2 + 𝑅1𝑗𝑑𝑑𝑗

2 is of common practice in Chile

and is a better estimate of probable relative displacements between structures

than the summation of the maximums values of the seismic displacements.

(Re. C6.2 of the NCh2369.Of2003).

For rigid or fragile nonstructural components, their separation with respect to

the structure (to avoid impacts) must be larger than the relative deformation

between the levels where the element is located. It has to be calculated with

the corresponding 𝑑 values, but not less than 0.005 times of the element

height (Re. NCh2369.Of2003, section 6.2.2).

Note that when the relative displacement between two points of a system is

needed (e.g. story drifts, allowable deformation between boiler and the

structure of the boiler support) and dynamic analysis is used, that relative

displacement cannot be estimated as the difference of the maximum

displacement at each point; it has to be calculated using the combination of

the relative deformation for each mode or, if it is not possible to do the latter,

as the addition of the maximum displacement of each point, which is a

conservative alternative.

11.2. Expansion Joint

If the two structures are connected, an expansion has to be considered for the

connection, which must be capable to withstand demand of seismic

deformations, but also the thermal expansion effects (and also deformations

from other sources, different from seismic origins).

Figure 11-2: Scheme of a connection between two structures and location of

an expansion joint.

In this case is important to notice the difference between a stiff connection

and a flexible connection between the structures.

i j

Expansion jointConnection


11-4

11.2.a. Flexible connection

In the case of a flexible connection there is no need to consider the connecting

element in the structural analysis, the expansion joint must stand

displacements according to section 6.1 of the Chilean code (meeting the

minimum separation of 6.2), calculated from the analysis of each structure

separately, without considering the structural properties of the connection.

11.2.b. Stiff connection

If the connection has a significant stiffness with respect to the structures which

it is attached to, the response of the buildings, and therefore, the relative

displacement between them, will depend of the properties of the connection.

Therefore, the connection and thus, the two structures connected with the

proper stiffness and inertia of the connection, have to be part of the structural

analysis. In this case, it is not possible to use directly the expressions of

section 6.1 of the Chilean code without considering the connection; the

displacement and the design force in the expansion joint must be obtained

directly from the structural analysis (use section 6.1 of the Chilean code).

Figure 11-3: Schematic representation of the location of the stiffness of a

connection between two structures.

Unfortunately, the Chilean code does not give any criterion to establish the

flexibility or stiffness of the connection. In the case of pipes, the code only

says that if the weight of the pipes is small in comparison with the structures

that they connect, it is not necessary to consider the pipe in the analysis;

otherwise, it must be done an analysis that includes the properties of the pipe

(Re. section 11.5.2 of the NCh2369.Of2003).

Summarizing:

If the connection is flexible, it is not necessary to consider it in the

structural analysis and the design of the expansion joint is done

according to the displacements calculated according to section 6.1 of

the Chilean code.

i jKej


11-5

If the connection is stiff, it shall be included in the structural analysis,

and the design of the expansion joint must be done according to the

displacements that result from the analysis considering section 6.1 of

the Chilean code.

Tip:

The design of the expansion joint must be done for all seismic displacements

simultaneously; this is longitudinal, vertical and transverse displacement.

Also, consider that the calculated seismic displacement that is used for the

design does not have sign, so it has to be considered as positive or negative

(in all possible combinations between the calculated displacements). If it is

possible, more accurate analysis, like time-history analysis, is encouraged to

use in order to calculate more realistic displacements between the structures.

11.3. Design of the expansion joint

Once the displacements are known, the design of the expansion joint will

depend on the properties of it. If the expansion joint is only a sliding support

between the structures, the design must be concentrated in calculating the

required dimensions of the support. If, for example, in a pipe that connects

two structures, the design will depend of the requirements established by the

pipe supplier.

For example, if a metallic bellow is used, EJMA (Expansion Joint Manufacturers

Association) use a design criterion of allowable expansion for the bellow.

Figure 11-4: Metallic bellow. Taken from Introduction to Metallic Expansion Joints, EJMA.


11-6

11.3.a. Allowable expansion amount according to EJMA document:

Allowable axial displacement:

Single system: 𝑋 = 𝑒 ⋅ 𝑛

Double system: 𝑋 = 2 ⋅ 𝑒 ⋅ 𝑛

Allowable lateral displacement:

Single system: 𝑌 = 𝑛 ⋅ 𝐶 ⋅𝑒

3⋅ 𝐷𝑝

Double system (universal type): 𝑌 = 2 ⋅ 𝑛 ⋅ 𝐿1 − 𝑐 ⋅𝑒

𝛼⋅ 𝐷𝑝

Double system (hinged, gimbal type): 𝑌 = 2 ⋅ 𝑛 ⋅ 𝐿2 ⋅𝑒

𝐷𝑝

Allowable bending angle

𝜃 = 2 ⋅ 180 ⋅𝑒

𝜋⋅ 𝐷𝑝

Allowable bending radius

𝑅 = 𝐷𝑝 ⋅𝑊

𝑒

Where the difference between a single system and a double system is given by

the number of bellows used. 𝐷𝑝 is the diameter of the bellow, 𝑒 is the allowable

expansion amount per one corrugation of bellows; 𝑛 is the number of

corrugations of the bellow; 𝐶 is the length of the bellow; 𝑊 is the distance

between corrugations; 𝐿1 is the total length of bellows containing intermediate

pipe of double system; 𝐿2 is the distance between hinge pins of hinged type

and 𝛼 is the factor depending on the ratio of bellows length of double system

bellows to total on.

The expressions shown above correspond to allowable displacements in the

case of independent displacements, but if we have combined displacements

the design methodology that EJMA uses is:

𝑒 ≥ 𝑒𝑥 + 𝑒𝑦 + 𝑒𝜃


11-7

Single system:

𝑒𝑥 =𝑋

𝑛

𝑒𝑦 = 3 ⋅ 𝐷𝑝 ⋅𝑌

𝑛⋅ 𝐶

𝑒𝜃 = 𝐷𝑝 ⋅ 𝜋 ⋅𝜃

2⋅ 𝑛 ⋅ 180

Double system:

𝑒𝑥 =𝑋

2𝑛

𝑒𝑦 = 𝛼 ⋅ 𝐷𝑝 ⋅𝑌

2⋅ 𝑛 𝐿1 − 𝐶

𝛼 =3𝐿2 − 3𝐶𝐿

3𝐿2 − 6𝐶𝐿 + 4𝐶2

Figure 11-5: Displacements on the bellow. Taken from Introduction to Metallic Expansion Joints, EJMA.


11-8

11.4. References

Expansion Joint manufacturers Association, EJMA, Introduction to

metallic Expansion Joints. Mega Flexon. Expansion Joint & Flexible

Products.

The document that presents the future provisions that will be used in Chile,

(based on the ASCE 7 code) is MINVU NTM 001-2010 for the seismic design of

nonstructural components. Additional tips for expansion joints and seismic

damage mitigation can be found on the FEMA E-74 document.







MANUAL OF SEISMIC STEEL CONNECTIONS. CHAPTER 12: CRANES

12-1

12. CRANES

12.1. General description of bridge cranes

“A Bridge Crane consists of an assembled structure which spans between

parallel rails or runway tracks, and is adapted to carry a suspended load

horizontally along the runway. Bridge cranes can be top running or under-hung

with single or double girder configurations. They also incorporate hoists on

trolleys to move the load laterally as well as vertically. Bridge cranes can be

mobilized via push trucks, geared or motorized end trucks” (Re. J. Herbert

Corporation webpage). In crane supporting structures, the geometry of the

building is commonly defined by the dimensional characteristics of the crane.

A bridge crane consists of three principal components:

The bridge crane which traverses across the runway.

Trolley and hoist, which traverse across the bridge crane and lift or

lower the load.

The runway girder (crane girder), which is supported to the building

structure (attached to the columns).

Figure 12-1: Bridge crane scheme.

Taken from Dearborn Overhead Crane.

The objective of this chapter is to briefly explain the most important aspects

on the design of the supporting structures for crane bridges (classification of

the systems, design loads, design process, etc.), introducing some code

provisions and references, and also some tips that could be helpful for the

designer. It is expected that the reader closely examine the various references

that are presented, when looking for more detail in the subject.


12-2

12.2. Systems Classification

As indicated on AISC Design Guide N° 7, the main difference between crane

buildings and other industrial buildings is the frequency of loading produced by

cranes. Therefore, crane buildings should be classified according to the

frequency of loading. Note that there is a crane building classification (AISE

Technical Report N°13) and a crane classification (CMAA 70).

The crane building classification, as indicated on AISE Technical Report N°13

(based on ASD), is based primarily on the number of cycles or repetitions of a

specific loading case anticipated for portions of the structure. Based on the

expected service life (generally 50 years is recommended) and the rate of load

repetitions, the owner shall specify the classification for all or any portion of

the industrial building. Classes groups go from A to D.

Once classified, the report shows the loading conditions and the approximate

number of loading cycles for each class (see table 5.1 of the report). Then the

document refers to the allowable stress range for repeated loads, as specified

on AISC Specification for Structural Steel Buildings (ASD) – 1989.

The crane classification as stated on CMAA 70 document “is based on the load

spectrum reflecting the actual service conditions as closely as possible”. For

the definition of the load spectrum, it is encouraged to read the document. In

simple words, cranes classification is made according to the service conditions

of the most severely loaded part of the crane. The individual parts which are

clearly separated from the rest or forming a self-contained structural unit, can

be classified into different loading groups if the service conditions are fully

known.

Crane classes go from A (standby or infrequent service) to F (continuous

severe service). It is important to note that when the crane service is higher,

more severe fatigue conditions will be presented. As indicated on AISC Design

Guide 7, the fatigue associated with crane class is especially critical for the

design of crane runways and connections of crane runway beams to columns.

Tables 11.2.1 and 11.2.2 on the Design Guide, help to relate the CMAA 70 with

the AISC Specification for Structural Steel Buildings (1989) Loading Conditions

and thus, with the approximate range of number of loading cycles. On later

editions of AISC Specifications, there are no longer references to loading

conditions. For example, on AISC360-05 (LRFD), Appendix 3 – Design for

Fatigue, equations are used for determining the design stress range for a

given number of stress range fluctuation in the design life (𝑁), properly

defined by the designer. LRFD fatigue provisions are the most up to date AISC


12-3

provision and they are recommended for use by the authors of the Design

Guide. A more detailed discussion about fatigue damage and crane runway

fatigue considerations is written on sections 12.1 and 12.2 of AISC Design

Guide 7.

12.3. Chilean code provisions

There are not specific requirements in Chilean codes for the design of crane

supporting structures. There are only some few related references on chapter

11 “Specific Structures” of NCh2369.Of2003.

12.3.a. Industrial Mill Buildings (summary of important aspects)

(Re. NCh2369.Of2003, 11.1)

The provisions presented on this section shall apply to industrial

buildings with or without travelling cranes.

(Re. NCh2369.Of2003, 11.1.1)

When travelling cranes are present on buildings with transverse

frames (namely, permanent loads do not result only from self-

weight), buildings shall have a continuous brace system on the roof.

When there are roof trusses, the continuous bracing system shall be

placed on the plane of the lower chord of the truss. See the following

figure:

(Re. NCh2369.Of2003, 11.1.2)

Figure 12-2: Roof bracing. Taken from NCh2369.Of2003, Figure A.2.

In buildings with travelling cranes, the seismic analysis must be made

for the most probable magnitude and height of the suspended load

present during the design earthquake. For these effects, the


12-4

frequency of the design earthquake and the operation conditions of

the cranes must be considered.

(Re. NCh2369.Of2003, 11.1.3)

Note that according to commentary C.11.1.3, some recommendations that can

be considered safe are:

In cranes of maintenance, fabrication and similar operation, in which

on rare occasions the maximum load is lifted and the operation is not

continuous, the lifted load can be neglected for the seismic analysis.

For cranes of heavy and continuous operation with maximum load, it

is recommended to use this load at the highest level on the seismic

analysis. See figures corresponding to C.11.1.3.

If various cranes are present, either in a bay or in parallel bays, a

seismic load combination with all the cranes unloaded and parked on

the worst position must be considered.

(Re. NCh2369.Of2003, 11.1.4)

The lateral connection between the crane girders (runway girders)

and the columns must be flexible in the vertical direction.

Additionally, safety devices (uplift clamps) to prevent bogie falling in

case the wheels run out of the rails must be considered. See the

following figure:

(Re. NCh2369.Of2003, 11.1.5)

Figure 12-3: Detail of crane girders and columns.

Taken from NCh2369.Of2003, Figure A.3.


12-5

12.3.b. Light steel bays

(Re. NCh2369.Of2003, 11.2)

No specific provisions for cranes are mentioned in this section. The only

requirement is that travelling cranes must have a nominal capacity lesser or

equal than 100 kN (cranes without operator cabin), or 50 kN (cranes with

operator cabin).

12.3.c. Large mobile equipment

(Re. NCh2369.Of2003, 11.6)

Large mobile equipment (for example, travelling portal cranes) must

be subjected to a dynamic analysis, considering the magnitude and

the most unfavorable positions of the loads. The analysis can be

performed assuming that the wheels are pivoted on rails or the

ground; but if significant uplifting is involved, counterweights must be

placed in order to avoid it. See Figure A.8 of Appendix A.

To avoid the possibility of impact between the rail flanges and the

wheels, the system shall be self-centering. See Figure A.9 of

Appendix A.

Special attention shall be laid to the eccentricity effects that occur on

these systems for seismic loads.

12.4. Loads and load combinations

In service, cranes supporting structures are subjected to repeated loads that

vary over time and generate stresses on all the members and connections

present on the load path of the crane.

Crane loading conditions generally are not well defined in building codes.

There are some code provisions that specify the manner of calculating different

crane induced loads and load combinations. It has to be noted that different

results when using different design codes, so the designer should use

judgment, and project specifications must provide the specific code provisions

to be used in a given project. In this section, some general and common

provisions are shown.

Some common international provisions for crane loads are specified on ASCE 7

code and AISE Technical Report N°13. The first document can be used with the

Strength Design and the Allowable Stress Design methods, and the second

recommendations are based on ASD.


12-6

According to ASCE 7 C4.9 Commentary, all support components of the moving

bridge cranes and monorail cranes, including runway beams, brackets, if

present, bracings and connections, shall be designed to withstand the

maximum wheel load of the crane and the vertical impact, the lateral and

longitudinal forces induced by the crane . The runway beam shall be designed

for crane stop forces.

12.5. Crane Induced Loads

12.5.a. Vertical Impact

Because of the motion of the crane and the lifting and lowering of the

suspended load, additional vertical inertia forces shall be included. Two

different provisions of common crane design related documents are presented:

ASCE 7

(Re. ASCE 7-2010, 4.9)

Increase the maximum wheel load by the following percentages to obtain the

vertical impact force:

Crane type

Percentage

Monorail cranes (powered) 25

Cab-operated or remotely operated bridge cranes (powered) 25

Pendant-operated bridge cranes (powered) 10

Bridge cranes or cranes with hand-geared bridge, trolley, and hoist 0

Table 12-1: Increase applied to the maximum wheel loads to obtain the

vertical impact force, according to ASCE 7-2010.

As defined on ASCE 7, maximum wheel loads shall be the ones produced by

the weight of the bridge crane, plus the sum of the rated capacity (or crane

live load as indicated on ASCE 7) and the weight of the trolley, with the trolley

positioned on its runway at the location where the resulting load results in

maximum effect.

AISE Technical Report N° 13

(Re. AISE Technical Report N°13, 3.4.2)

Vertical impact increase, according to table 3.2 of AISE Technical Report N°13,

is 25% for all types of cranes; excluding motor room maintenance cranes,

etc.; with a 20% percentage.


12-7

12.5.b. Side Thrust (Lateral Force)

As indicated on AISC Design Guide N° 7 horizontal forces exist due to various

factors such as runway misalignment, crane skew, trolley acceleration, trolley

braking and crane steering.

ASCE 7

(Re. ASCE 7-2010, 4.9)

“The lateral force on crane runway beams with electrically powered trolleys

shall be calculated as 20% of the sum of the rated capacity of the crane and

the weight of the hoist and trolley. The lateral force shall be assumed to act

horizontally at the traction surface on a runway beam, and shall be distributed

with due regard to the lateral stiffness of the runway beam and supporting

structure”.



The total side thrust shall be distributed among the resisting members with

according to the lateral stiffnesses of the structures supporting the rails. These

forces shall be the greatest among the following options: the load specified in

table 3.2 of the report; 20% of the combined weight of the lifted load and

trolley; and 10% of the combined weight of the lifted load and the crane

weight (see the report for stacker cranes exception).

According to this report, the lifted load is the total weight lifted by the hoist,

including working loads, all the hooks, the lifting beams, magnets and other

appurtenances required for service, but excluding the weight of the column,

ram or other material handling device which is rigidly guided in the vertical

direction during hoisting action. For pendant operated cranes, side thrust is

taken as 20% of the maximum wheel load on the driving wheels (typically half

of the total wheels). Also, radio-operated cranes shall be considered the same

as cab-operated cranes for vertical impact, side thrust and traction

determination.


12-8

12.5.c. Longitudinal or Tractive Force

ASCE 7

(Re. ASCE 7-2010, 4.9)

The longitudinal force on the crane runway beam (except for bridge crane with

hand-geared bridges) is calculated as 10% of the maximum wheel loads of the

crane. This force shall be assumed to act horizontally at the traction surface of

the runway beam in either direction parallel to the beam.



The traction shall be taken as 20% of the maximum load on the driving wheels

for all type of cranes, according to table 3.2 of this report.

12.5.d. Crane Stop Forces

According to section 3.4.3 of AISE Technical Report N° 13, the load applied to

the crane stop shall be included in the design of the runway girders, their

connections and the supporting framework. The bumper force is dependent on

the energy-absorbing device used in the crane bumper. Generally, the crane

supplier provides the bumper force.

12.5.e. Seismic Loads

According to section 3.9 of AISE Technical Report N°13, the seismic mass of

cranes and trolleys that lift a suspended load need to be considered in the

calculation of the seismic load, including only the empty weight of the

equipment. This is different from the requirements of NCh2369.Of2003 shown

above in this document. It is important to take into account the interaction

between the equipment and the crane building, and that there are vertical

accelerations present on large seismic events, so special attention must be

considered to avoid the uplifting of the cranes. Other considerations with

respect to seismic loads must be discussed within each project specifications.


12-9

12.6. Cranes Load Combinations

In general, building codes do not indicate how to combine different crane

loads, and how many cranes should be considered simultaneously loaded at a

given time. The engineer must use his judgment for these cases or proper

discussion shall be previously had to define the project specifications.

As indicated on AISC Design Guide N°7, when one crane is being analyzed,

each span must be designed for the most severe loading with the crane in the

worst position for each element that is affected.

Chilean code NCh2369.Of2003, for example, only indicates that if various

cranes are present, they must be analyzed unloaded and parked for the worst

effects. If considering the crane loads as service live loads (SC) or special

operating live loads (SO), the combinations with other effects (wind,

earthquake, live loads, etc.) are addressed on section 4.5 of the Chilean code.

When various cranes are present, and where it is desired to make a

differentiation between the different crane induced loads (also including other

loads such as dead, live, and earthquake loads), a recommendation is to take

a view at AISE Technical Report N°13, section 3.10 (based on ASD). It must

be noted that on this report, building classifications were based upon the most

frequently encountered situations, so they should be used with engineering

judgment. Some other loads combinations that have been commonly used by

engineers are shown on AISC Design Guide N°7, section 13.7. Note that the

critical case for a specific element may occur when one or more loads are not

acting. Additionally, special loads combinations could be discussed on project

specifications.

Other references for cranes induced loads and load combinations are the CMAA

Specification N°70 and N°74, and the MBMA Low Rise Building Systems

Manual.

As examples indicated showed in the AISC Design Guide N°7, other load

combinations (not shown on AISE Technical Report N°13) that have been used

by engineers include:

1. A maximum of two cranes coupled together with maximum wheel

loads, 50 percent of the specified side thrust from each crane, and 90

percent of the specified traction. No vertical impact.

2. One crane in the aisle and the other one in an adjacent aisle with

maximum wheel loads, specified vertical impact, and with 50 percent

combined specified side thrust and specified traction for each crane.


12-10

3. A maximum of two cranes in one aisle and one or two cranes in an

adjacent aisle with maximum wheel loads, and 50 percent of the

specified thrust of the cranes in the aisle producing the maximum

side thrust, with no side thrust from the cranes in the adjacent aisle.

No vertical impact or traction.

12.7. Previous considerations for the design process

Some basic information that has to be taken into account for the design

process is listed below:

Type of crane to be used.

Operating conditions.

Building type and the dimensions of the place where the bridge crane

is going to be installed in order to size the length of the principal

beam (bridge crane) and have some other required dimensions (for

example, the head-room clearance available above the specified

crane level).

Consider properties and location of safety and maintenance devices

for the service condition of the crane: railings, access routes and

stairs, adequate walkways, etc.

Crane required characteristics: number of cranes required, lifting

height, maximum rated load, self-weight, length of the bridge crane,

estimated number of lifts in time period , hoisting speed, travelling

speed, method of crane control (for example cabin on crane, pendant

control unit, remote control, etc.), system of power supply, support

conditions and details, details of the clearances required between the

crane and the structure, runway length, runaway girder spans, etc.

Vendors should give the specific information required by the project

engineer. For example, maximum wheel loads, wheel spacing, trolley

weight, etc.

12.8. Design aspects

12.8.a. Crane Runway Girders

Crane runway girders will be subjected to the following internal forces and

moments that must be considered on the design:

Biaxial bending due to vertical actions and transverse horizontal

actions.

Axial compression or tension due to longitudinal horizontal actions.


12-11

Torsion due to eccentricities of vertical actions and transverse

horizontal actions, relative to the shear center of the cross section of

the beam.

Vertical and horizontal shear due to vertical actions and transverse

horizontal actions.

Note that when fatigue is critical on any limit state (especially on higher

service levels for the crane, according to CMAA 70 classification), it must be

considered because this type of elements and their connections are subjected

to repeated cycles of loading during their life time. There are also serviceability

limit states, used to control relative and absolute lateral movements of the

runways that will be discussed later on this section.

Generally, crane runway girders are made from rolled or welded H sections (W

sections), and when required, a channel cap is added on the top flange to

increase the strength of the section. There are other options also for the cross

section of the runway girder, for example a plate or triangulated box girder.

Note that fatigue restrictions are more severe for built-up shapes. As indicated

on AISC Design Guide N°7, the difference between a rolled shape vs. a built-

up member using continuous fillet welds is a reduction in the allowable fatigue

stress.

Runway beam design procedure:

(Re. AISC Design Guide N°7)

The basic steps will be shown according to the AISC Design Guide N°7 but with

some additional information included. Internal forces and moments which

affect the crane runway girders must be taken into account. For additional

guidance and solved examples, see section 18.1 of the Design Guide.

1. - Serviceability limit states: calculate the required moments of inertia 𝐼𝑥 and

𝐼𝑦 to satisfy deflection control criteria. Vertical deflection (due to wheel loads

without impact) is limited to L/600 to L/1000 , depending on the CMAA 70

crane class and the type of crane. Horizontal deflections are limited up to

L/400 for all cranes.

Other recommendations from other documents that limit vertical and

horizontal deflections on the runway beam can be found in ICHA Manual for

the Design of Steel Structures, table 15.3.1; and in Eurocode 3, Part 6 (ENV

1993-6), tables 7.1 and 7.2. It is recommended to discuss before the design,

all the limits that are going to be controlled.


12-12

2. - Obtain the worst load conditions (moving the crane to various positions)

for the runway beams and their connections.

3. - Calculate the bending moments (𝑀𝑥 and 𝑀𝑦) considering the effects of

impact. Note that the moment 𝑀𝑦 can be calculated applying the lateral cranes

forces on the top flange, but increased due to the fact that the force is applied

at the top of the rail, as indicated on AISE Technical Report N° 13.

4. - Check bending about the x-x axis ignoring 𝑀𝑦, considering appropriate

support and bracing conditions. If needed, channel caps could be added to the

top flange. If desired, bending about the y-y axis ignoring 𝑀𝑥 could be also

evaluated. Note that chapter F of AISC 360-05 Specification can be used for

these verifications.

5.- Check the bi-axial-bending interaction on the top flange. Typically, axial

forces on the beam girder due to longitudinal force generate stress levels that

can be neglected (if desired, an additional check could be done for the

longitudinal stress, considering the full cross sectional area of the beam).

Chapter H of AISC 360-05 can be used to verify interaction. A typical design

assumption is that only the top flange resists the lateral crane loads.

6.- Check web sidesway buckling (see AISC 360-05, section J10.4) in order to

prevent buckling in the tension flange of a beam where the flanges are not

restrained by bracings or stiffeners and are subjected to concentrated loads.

This failure mode can be prevented by an adequate design of the lateral

bracing or stiffeners located at the load point.

7.- Additional checks (not specified in the Design Guide, but that could be

performed)

Applicable limit states of section J10 of AISC360-05 Specification.

Verify shear stress on the runway beam check.

Crane uplift: design of uplift clamps (required by NCh2369.Of2003 as

indicated above on this document) for vertical uplift forces (especially

when earthquake effects are considered, modeled for example, as

static forces on the crane).

Geometry of the top flange and its reinforcements should be chosen

from those alternatives that offer the best torsional resistance

(torsion can also be checked) and the best lateral stiffness.


12-13

According to the Design Guide, if the fatigue is a consideration, the above

procedure should be altered so the live load stress range for the critical case

does not exceed the fatigue limit stresses.

Other design tips for runway beams are included in the AISC Design Guide

N°7. See sections 18.2 (Plate Girders), 18.3 (Simple Span vs. Continuous

Runways), 18.4 (Channel Caps), 18.5 (Runway Bracing Concepts), 18.6

(Crane Stops), 18.7 (Crane Rail Attachments) and 18.8 (Crane Rails and Crane

Joints); in the AISE Technical Report N°13, section 5.8 (Crane Runway

Girders); and in CMAA Specification N° 70, section 3.5 (Design Limitations).

There are additional recommendations for the design of these elements, their

bracings, welding, stiffeners, etc.

12.8.b. Column Design

There are different options for the type of column that supports a runway

girder. They can be bracketed, stepped, laced or battened as shown in the

following figure:

Figure 12-4: Bridge Crane Columns Types.

Taken from AISC Design Guide N°7, Figure 20.1.1.

Overhead travelling crane runway girders are typically supported by stepped

columns. According to AISE Technical Report N°13, built-up step columns

made of two or more segments tied together by solid web plates, lacing, or

intermittent vertical diaphragms, shall have the connecting segments and

their connections designed to provide integral behavior of the combined

column section. When intermittent vertical diaphragms or diagonal lacing are

used, column shafts between panel points and the intermediate web member

shall be designed for all the forces derived from analysis. By recommendation,


12-14

brackets shall not be used to support runway girders with total reactions at the

column larger than 50 kips (222 kN).

As said on AISC Design Guide N° 7, the eccentric crane loads (the critical

bending case occurs generally when the crane is not centered over the column

but located just to one side) and lateral loads produce moments in the column.

The calculation of the moments in the columns requires a complete frame

analysis in order to obtain reliable results. Two parameters that have marked

effect on column moments are the base fixity and the amount of load sharing

with adjacent bents (discussed and exampled on the Design Guide).

According to Design Guide, a frame analysis to obtain an “exact” solution will

contain the following:

It accounts for sidesway.

It properly handles the restraint at the top (generally, 2 supports due

to the intersection of the column with the truss chords of the roof)

and at the base of the column.

It accounts for non-prismatic member geometry (for example, on

stepped columns).

Some preliminary design methods and final design procedures for this type of

columns, including solved examples, are shown on sections 20.2 and 20.3 of

the AISC Design Guide N°7.


12-15

According to Chilean practice, the following column shapes are recommended

in a predesign stage:

Bridge crane type Column shape recommended

Small: Lifts up to 10 ton. Use IP ore even IN shapes with global slenderness about the strong axis

not greater than 100.

Medium: Lifts up to 30 ton.

Two options are recommended:

1- Use an IP shape with slenderness lesser than 80 if a bracket system

which receives the crane bridge beam is used.

2- If a column which changes of section after supporting the crane

bridge beam is used, study the dimensions so that the column is an H

shape with enough depth for placing the crane bridge beam and giving

free space for operation. Besides, at least 250 mm must stay free so to

continue the column upward.

Big: Lifts more than 80 ton Normally special sections are used, or a section composed by two H

shapes.

Table 12-2: Recommended column shapes according to Chilean practice, for

different types of bridge cranes.

12.9. Additional information

On chapter 15 of the AISC Manual of Steel Construction 13th Edition, titled

“Design of Hanger Connections, Bracket Plates and Crane-Rail Connections”,

there are some recommendations for the design of:

-Bracket plates connections (sometimes used for supporting the crane runway

girder), including simplified equations for the limitation of the load on the

bracket, flexural yielding, rupture and local buckling recommendations.

-Crane rail connections: includes a general description of bolted and welded

splices on rail connections. Also, this chapter contains a description a various

recommendations related to different rail fastenings (hook bolt fastenings, rail

clip fastenings, rail clamp fastenings and patented rail clip fastenings).


12-16

12.10. References

J. Herbert Corporation webpage:

http://www.jherbertcorp.com/crane-bridge.htm

Dearborn Overhead Crane webpage:

http://www.dearborncrane.com

Association of Iron and Steel Engineers, 2003, Technical Report N°

13, “Guide for the Design and Construction of Mill Buildings” (AISE

Technical Report N° 13). AISE, Pittsburgh, PA.

Metal Building Manufacturers Association, 2022, “Low Rise Building

Systems Manual”. MBMA, Cleveland, OH.

American Institute of Steel Construction, 2004, Steel Design Guide

N°7, “Industrial Buildings. Roofs to Anchor Rods”, 2nd Ed. (AISC

Design Guide N°7). James Fisher, AISC, USA.

Crane Manufacturers Association of America, 2000, “CMAA

Specification N°70 , Revised 2000”, CMAA, Charlotte, NC.

Crane Manufacturers Association of America, 2000, “CMAA

Specification N°74 For Electric Overhead Travelling Cranes”, CMAA,

Charlotte, NC.

Instituto Chileno del Acero, 2000, “Manual de Diseño para Estructuras

de Acero, Método de Factores de Carga y Resistencia, Tomo I” (ICHA

ARA Manual), ICHA, Santiago, Chile.



European Committee for Standardization (CEN), 1999, “Eurocode 3:

Design of Steel Structures – Part 6: Crane Supporting Structures”

(ENV 1993-6). CEN, Brussels.

Posco e&c - Manual of Seismic Steel Connections v1.1

Documents

Transcript of Posco e&c - Manual of Seismic Steel Connections v1.1