Stiffener Design forBeam-to-Column Connections

Michelle L. Holland

Thesis submitted to the Faculty of theVirginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of Sciencein

Civil Engineering

Dr. Thomas M. Murray, chairDr. W. Samuel EasterlingDr. Siegfried M. Holzer

September 1999Blacksburg, Virginia

Keywords: Moment Connections, Stiffener Design, Column Stiffeners

Copyright 1999, Michelle L. Holland

Stiffener Design forBeam-to-Column Connections

Michelle L. Holland

(ABSTRACT)

Stiffeners are used as a means of providing additional support to columns at beam

connection locations. They are added when the strength of the column is exceeded but

full moment strength of the beam section is desired. In determining the design of column

stiffeners, there are no specifications for determining the distribution of load between the

column web and stiffeners. The AISC Load and Resistance Factor Design Specifications

provides guidelines for determining the stiffener area but no specifications are given.

The actual loads taken by the stiffener and web are therefore not truly known.

In this study, experiments were done to determine the load supported by the stiffeners

and web when tensile forces are applied to the specimen. The initial stiffener design for

the test specimens was based on LRFD guidelines. The actual load distribution between

the column web and stiffeners is determined from strain data obtained during testing.

This distribution is compared with the assumed loads obtained from the initial LRFD

calculations. Finite element analysis is also utilized to confirm the consistency of the

results obtained from the experiments. Using this information, a new method is

developed which better predicts the distribution of load between the column web and the

stiffener.

iii

ACKNOWLEDGMENTS

I owe a great deal of thanks to my family and friends who have always offered

their support and belief in me. I could not have made all the accomplishments throughout

my life without them. Dr. Thomas M. Murray has also provided guidance and has

challenged me during my graduate studies. For this, and for his patience, I extend my

greatest thanks. I also extend my thanks to Dr. W. Samuel Easterling and Dr. Siegfried

M. Holzer for their help, knowledge, and participation as members of my committee. To

Dennis Huffman and Brett Farmer, I also offer my appreciation for their help the

Structures Laboratory and for the hours of enjoyment.

iv

TABLE OF CONTENTS

Page

ABSTRACT ii

ACKNOWLEDGMENTS iii

TABLE OF CONTENTS iv

LIST OF FIGURES vi

LIST OF TABLES viii

CHAPTER I. INTRODUCTION 1

1.1 Overview of Design Problem 1

1.1.1 Background 11.1.2 Current Design Model 11.1.3 Objective of Study 4

1.2 AISC Column Side Limit State Design Strength 4

1.3 Force Distribution Prediction 10

1.4 Scope of Research 11

CHAPTER II. EXPERIMENTAL INVESTIGATION 12

2.1 Scope of Test 12

2.2 Test Details 12

2.2.1 Test 1 Geometry and Design 122.2.2 Test 2 Geometry and Design 14

2.3 Instrumentation 14

2.4 Test Procedure 17

2.5 Test Results 17

2.5.1 General 172.5.2 Test 1 172.5.3 Test 2 21

2.6 Summary of Experimental Results 26

CHAPTER III. DEVELOPMENT OF FINITE ELEMENT MODEL AND COMPARISON WITH TEST RESULTS 28

3.1 Development of Finite Element Model 28

v

3.1.1 Description of Finite Element Analysis 283.1.2 Shell Elements 28

3.2 Finite Element Results 29

3.2.1 Test 1 293.2.2 Test 2 293.2.3 Additional Finite Element Models 323.2.4 Parametric Study of Stiffener Sizes 34

3.3 Comparison of Experimental and Analytical Data 36

CHAPTER IV. DEVELOPMENT OF A DESIGN MODEL 38

4.1 Development of Effective Length 38

4.2 Load Distribution Between Column and Stiffener 42

CHAPTER V. SUMMARY AND RECOMMENDATIONS 45

5.1 Summary 45

5.2 Area Method Design Recommendations 46

5.3 Example Calculations 47

5.4 Recommendations for Further Research 49

REFERENCES 50

APPENDIX A. NOMENCLATURE 51

APPENDIX B. TEST 1 Results 54

B.1 Experimental Data 55B.2 ABAQUS Input Data File 61

APPENDIX C. TEST 2 Results 66

C.1 Experimental Data 67C.2 ABAQUS Input Data File 71

VITA 76

vi

LIST OF FIGURES

Figure Page

1.1 Moment Transfer Couple 2

1.2 Stiffener Force Based on AISC Manual Procedure 3

1.3 Local Flange Bending Stiffener Requirements 6

1.4 Local Web Yielding Stiffener Requirements 7

1.5 Effective Column Length and Load Distribution 11

2.1 Test 1 Specimen Geometry 13

2.2 Test 2 Specimen Geometry 15

2.3 Strain Gage Locations, Tests 1 and 2 16

2.4 Test 1 (W16x45) - Load vs. Micro-strain Results for Stiffeners R and L 18

2.5 Test 1 (W16x45) - Strain vs. Distance Results for Stiffener R 20

2.6 Test 1 (W16x45) - Strain vs. Distance Results for Stiffener L 20

2.7 Test 2 (W8x48) - Load vs. Micro-strain Results for Stiffeners R and L 22

2.8 Test 2 (W8x48) - Load vs. Micro-strain Results for Web R and L 23

2.9 Test 2 (W8x48) - Strain vs. Distance Results for Stiffener R 24

2.10 Test 2 (W8x48) - Strain vs. Distance Results for Stiffener L 24

2.11 Test 2 (W8x48) - Strain vs. Distance Results for Web R and L 25

2.12 Comparison of Stiffener Force Ratios 27

3.1 FE Model for Test Specimens 30

3.2 Finite Element Results for Stiffeners Stress vs. Distance - Test 1 and 2 31

3.3 Finite Element Results for Web - Test 2 32

3.4 W14x311 Finite Element Results 33

vii

3.5 W12x120 and W14x500 Finite Element Results 35

3.6 Comparison of Stiffener Force 37

4.1 Equivalent Load Distribution 39

4.2 Plot of Element Stresses W14x311 Specimen 40

4.3 Equivalent Column Web Load Distribution 41

viii

LIST OF TABLES

Table Page

2.1 Force Distribution - Test 1 (W16x45) 19

2.2 Force Distribution - Test 2 (W8x48) 26

3.1 Stiffener Force from FE Models 32

3.2 FEA Results for Additional Column Sections 34

3.3 FEA Results for W14x90 Stiffeners 36

3.4 Predicted versus Test Results 37

4.1 Effective Lengths 42

4.2 Effective Area Values 43

4.3 Comparison of Results 43

1

CHAPTER I

INTRODUCTION

1.1 OVERVIEW OF DESIGN PROBLEM

1.1.1 Background

In a rigid steel moment connection most of the moment is transferred through the

beam flanges to the column in the form of a couple. The couple is formed from this

moment and acts at a moment arm equal to the depth of the beam (center-to-center of the

flanges if directly welded). The beam is therefore exerting a tensile force through one

flange and a compressive force through the other as shown in Figure 1.1.

The forces resulting from the transfer of moment from the beam to the column are

relatively large concentrated forces. At the beam tension flange of the connection, the

pull created on the column flange may be great enough to cause slight deformation of the

flange. The strength of the column will therefore be impaired. Similarly, the

compressive force entering through the other flange may be large enough to cause

instability in the column web (Salmon and Johnson 1995). The connection can be

improved by providing additional strength to the column connection where the load is

being transferred in the form of stiffeners, Figure 1.1. Stiffeners are placed on the

column at the locations of the beam flange forces to prevent distortion of the column

flange where the beam exerts the tensile loading and web yielding and crippling at the

compression loading. Stiffeners are therefore designed to prevent local column failure

created by large beam forces at the moment connection (Segui 1994).

1.1.2 Current Design Model

Column stiffeners can be designed to prevent local flange bending, local web

yielding, local web crippling, and compression buckling of the column. The AISC Load

and Resistance Factor Design Specification for Structural Steel Buildings (1993)

contains design strengths for these limit states at the column in Chapter K. If the applied

factored force transmitted by the beam flange exceeds the column design strength, φRn,

for any limit state condition, stiffeners must be used for the full strength of the moment

2

Stiffener

Figure 1.1 Moment Transfer Couple

3

connection to be developed.

The AISC LRFD Specification (Load 1993) gives rules for sizing stiffeners based

on the applied loading and the controlling column side-limit state but does not provide

rules for assigning force values to the stiffeners. In Volume II of the AISC LRFD

Manual of Steel Construction (Manual 1993) a method is suggested for assigning

stiffener forces. It is noted that in this model, the column is assumed to support the total

applied moment until the limit state with the lowest design strength is exceeded. It is at

this moment that the force begins to be distributed to the stiffeners. This method

therefore assumes that the stiffeners do not receive any load applied at the connection

until the lowest column limit state design strength is exceeded. Figure 1.2 shows the

force resisted by the stiffeners compared to the total applied load if the AISC procedure is

used.

Stiffener Load Distibution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200 250 300

Applied Flange Force, kips

Figure 1.2 Stiffener Force Based on AISC Manual Procedure

4

This model can not be correct because it does not follow the behavior of the

connection. Moment connections are designed to transfer moments applied to the

column in the form of tensile and compressive forces. Stiffeners are therefore added to

the column at the application of the loads to provide support and stability. Welds are

used to provide a physical connection between the stiffeners and the column flanges and

web. These welds therefore provide a continuous load path between the column and

stiffeners allowing the stiffener to resist force as soon as loading is applied.

1.1.3 Objective of Study

To prove that the current model assumptions for assigning stiffener loads are

inadequate, testing was performed on two W-shaped column sections subjected to tensile

loading acting through a plate representing the beam flange. Stiffeners were added to the

column at the point of application of the load (at the plate location). Strain gages were

attached to the column stiffeners and web. During loading, strain readings were obtained

to monitor the distribution of load between the column and the stiffeners. Finite element

modeling was also performed to ensure the validity of the test and test procedure. Finite

element modeling was also done on a larger column section to support the accuracy of

the model for W-shaped sections of different geometry.

1.2 AISC COLUMN SIDE LIMIT STATE DESIGN STRENGTH

The current design procedures used for column stiffener design are found in the

LRFD Specification for Structural Steel Buildings, Chapter K (Specifications 1993).

Chapter K of the Specifications includes the column strength requirements that must be

considered in beam-to-column connection design. Each of the applicable column limit

states are analyzed to determine if additional reinforcement is needed to support the load

on the connection.

The LRFD Specifications consider the flange and web strengths of the column

separately. The flange limit state is local flange bending while the web section includes

the following limit states because most of the compressive force is transmitted through

the web:

• Local web yielding (tensile or compressive)

5

• Web crippling

• Compression buckling of the web

• Panel zone web shear

The size of stiffener required depends on which limit state is exceeded.

Local flange bending can occur when concentrated tensile forces are applied to

the column. The design strength of the flange from Section K1.2 of the Specifications is

φRn, where:

φ = 0.90

Rn = 6.25tf2Fyf

and tf = flange thickness, Fyf = yield stress of the flange material.

Stiffeners that extend to at least half the depth of the column web are required

when this limit state is exceeded and should be located at the application of the tensile

force, Figure 1.3. These stiffeners must be welded to the loaded flange and the weld

between the stiffener(s) and the web must be large enough to allow the unbalanced force

in the stiffener to be transmitted to the web (Specifications 1993).

When a force is being transmitted through the web, local web yielding may occur.

The strength of the member depends upon the location of the concentrated force(s)

relative to the top of the column when considering this limit state, Figure 1.4. The design

strength of the web from Section K1.3 of the Specifications is as follows:

• When the concentrated force is located at a distance greater than the depth

of the member away from the member end,

φ = 1.0

Rn = (5k + N) Fyw tw

where k = distance from outer face of flange to web toe of fillet, N = length of

bearing, Fyw = yield stress of web material, tw = web thickness.

• When the concentrated force is acting at a distance less than or equal to the

depth of the member d from the member end,

6

Stiffener

Column Web

P

≥ d/2

Stiffener

P

Typ Typ

Figure 1.3 Local Flange Bending Stiffener Requirements

7

Stiffener

Column Web

P

d/2

P

d

d

column end

Typ

Typ

Figure 1.4 Local Web Yielding Stiffener Requirements

8

φ = 1.0

Rn = (2.5k + N) Fyw tw

When tensile forces acting normal to the flange exceed this requirement, stiffeners must

be used and welded to the loaded flange. Similarly, for an excessive compressive force

acting normal to the flange, stiffeners are added and may either bear on or are welded to

the loaded flange. These stiffeners again must be at least one-half the depth of the web.

The stiffeners, in both cases, must be connected to allow the force to be transmitted to the

stiffener. The weld connecting the stiffener to the web is therefore designed to be large

enough to transmit this unbalanced force in the stiffener to the web (Specifications 1994).

Web crippling only applies to compressive concentrated forces. The strength of

the member required to prevent web crippling again depends of the location of the

applied force relative to the column end. From Section K1.4 of the Specifications:

• If the compressive force is applied at a distance greater than or equal to one half

the depth of the member from the member end,

φ = 0.75 _______

Rn = 135tw2{ 1 + 3(N/d)(tw/tf)

1.5} √(Fywtf)/tw

where d = the depth of the column section

• If the compressive force is applied at a distance less then d/2 from the member

end,

For N/d ≤ 0.2, _______

Rn = 68tw2{ 1 + 3(N/d)(tw/tf)

1.5}√(Fywtf)/tw

For N/d > 0.2, ________

Rn = 68tw2{ 1 + (4N/d - 0.2)(tw/tf)

1.5}√(Fywtf)/tw

If this limit state is exceeded, transverse stiffeners at least one-half the depth of the web

are required at the application of the load and should either bear on or be welded to the

loaded flange. Again, the weld should be designed to allow the unbalanced force in the

stiffener to be transmitted to the web (Specifications 1993).

9

Compression buckling of the web occurs when compressive forces are applied at

both flanges of a member in the same location. From Section K1.6 in the Specifications,

the required strength for this limit state is:

φ = 0.90 ___

Rn = (1/h) 4,100 tw3 √Fyw

where h is the clear distance between flanges less the fillet or corner radius. If the

concentrated force near the end of the column, however, is applied (less than d/2 from the

member end), the nominal strength Rn is reduced by 50 percent. Stiffeners must be used

if the limit state is exceeded and can either bear on or be welded to the loaded flange so

the force can be adequately transmitted to the stiffener. In this case, the stiffeners must

be designed as axially compressed members and therefore must extend the full depth of

the web. The weld is designed the same.

Panel-zone web shear and sidesway web buckling, when applicable, are also limit

states to be considered in determining the need for stiffeners. These limit states will not

be discussed in detail here since they are not part of the study. Design provisions are

provided in Sections K1.5 and K1.7 of the Specifications.

If stiffeners are required because a column limit state has been exceeded, AISC

provides some design guidelines. The following rules are found in AISC K1.9 of the

Specifications:

1. The width of each stiffener plus one-half the thickness of the column web should notbe less than 1/3 the width of the flange or moment connection plate delivering theconcentrated force.

2. The thickness of the stiffeners should not be less than tb/2, where tb = thickness ofbeam flange or connection plate delivering the concentrated force.

3. When the concentrated force is only at one column flange, the stiffener length doesnot need to exceed one-half the column depth.

Full depth stiffeners are required for cases where applied compressive forces exceed the

applicable column limit states. Half depth stiffeners may be used for the other cases.

10

1.3 FORCE DISTRIBUTION PREDICTION

The current design model in the AISC Manual of Steel Construction Vol. II

(Manual Vol. II 1993) assigns only the magnitude of the force that cannot be carried by

the column flange or web to the stiffener. The stiffeners are therefore designed to support

the difference in load between the applied force and the limiting state of the column. The

Specifications are silent regarding the distribution of load between the column and

stiffener. It has therefore been assumed that the stiffener does not support any of the

applied load until the column has exceeded its limit state, see Figure 1.2. As stated

previously, this can not follow the behavior of the connection. It is therefore

advantageous to determine the distribution of force between the stiffener and column web

under loaded conditions. Once this distribution is determined, an effective design

approach can be developed.

The force distribution can be predicted based on the theory that at yield, the

applied load is distributed over a certain distance along the column, Figure 1.5. At

failure, yield lines form in a pattern extending a prescribed distance from the application

of load. The column will therefore resist the applied load over the total distance, (c),

along its length. This distance is then used to determine the effective column area. The

distance, (c), is determined in this study through experimental testing and finite element

analyses.

The distribution of load resisted by the column web and the stiffener is estimated

by using the ratio of the stiffener area to the effective column web area. This ratio

provides force values for the stiffener for any given applied force and assumes the

stiffener resists force before the column reaches a limit state. The resisting force in the

stiffener is then:

Pstiff = (Astiff/Atot)Papplied (1.1)

where Astiff = area of the stiffener cross section, Atot = total equivalent column/stiffener

area resisting the applied load, Papplied = applied load.

11

P

c

effective load distribution

Figure 1.5 Effective Column Length and Load Distribution

1.4 SCOPE OF RESEARCH

The current design model for assigning stiffener force does not follow the actual

behavior of the beam-to-column connection. It assumes that the stiffener is receiving no

force until the controlling limit state has been reached in the column. This assumption is

inaccurate because the stiffener is a force-resisting member in the moment connection

and will resist a portion of the force the instant it is applied. Research is therefore needed

to determine a method for predicting the distribution of force between the column and the

stiffeners. When this distribution is found, an accurate method for stiffener design can be

developed. Beam and column W-shaped sections are the focus in the moment

connections requiring the use of stiffeners for this research.

12

CHAPTER II

EXPERIMENTAL INVESTIGATION

2.1 SCOPE OF TESTING

The objective of this research is to determine the force distribution between the

column web and stiffener when the column flanges are subjected to tension loading as

caused by a welded beam-to-column moment connection. To this end, tests to simulate a

beam-to-column connection with column stiffening were conducted. Two separate

specimens with different limit states were tested to determine the percentage of load

resisted by the stiffener. Only W-shape column sections were considered in this

investigation. Each specimen was subjected to tensile forces simulating beam flange

loading.

Two W-sections with different limit states controlling the stiffener design were

chosen as test specimens. The material used for both column sections and the stiffener

plates was A36 steel. Both specimens were tested in tension only to simulate a gravity

type loading from the top flange of the beam. Test 1 was performed using a W16x45

column section with two full depth stiffeners. The controlling limit state for this column

section alone was local flange bending. Test 2 used a W8x48 column section also with

two full depth stiffeners. Web yielding was the controlling limit state for this test. The

limit states were calculated using the design criteria in the 1994 AISC LRFD

Specifications, Chapter K (Specifications 1994).

2.2 TEST DETAILS

2.2.1 Test 1 Geometry and Design

A W16x45 column section was used in Test 1. The geometry of the specimen is

shown in Figure 2.1. The column length was chosen to be adequate enough to avoid

bending of the section. A transition piece, simulating the beam tensile flange, was used

to allow the test specimen to fit into the testing machine. The universal testing machine

was then used to apply load to the system at the stiffener location.

13

PL 3/4 x 3 x 15"

W 16 x 45

Stiffener

6.0

16.0

3

0.57

ts=0.75

5/16

7/16

ws=3.0

7.0

1.5

TransitionPiece

Note: All dimensions are in inches, No Scale

Figure 2.1 Test 1 Specimen Geometry

14

Coupon tests were performed on both the flange and web material of the W16x45

section. From these tests, the flange yield stress was determined to be 47.2 ksi and the

web yield stress to be 50.7 ksi. These yield values were used in the LRFD calculations to

accurately represent the strength of the section. Local flange bending was determined to

be the controlling column side limit state with a resistance of Rn = 94.1 kips. The local

web yielding resistance was Rn = 130.5 kips.

The two stiffeners used were 3/4x3x15 in. plates and extended the full depth of

the column. The stiffeners were welded to the column flanges (7/16 in. fillet welds) and

web (5/16 in. fillet welds) to allow for full transfer of the load from the column to the

stiffener. The tension yield stress of the stiffeners was determined to be 38.6 ksi (yield

strength of 86.7 k).

2.2.2 Test 2 Geometry and Design

Test 2 used a W8x48 column section. The geometry of this specimen is shown in

Figure 2.2. The length of the column is sufficient in preventing bending of the column

section.

Coupon tests were performed on both the flange and web material to determine

the accurate strength of the section. From these tests, the flange yield stress was

determined to be 45.2 ksi and the web yield stress to be 46.8 ksi. These yield values were

used in the LRFD calculations. The controlling column side limit state was found to be

column web yielding with a resistance Rn = 125.1 kips. The local flange bending

resistance was Rn = 132.9 kips.

Two 3/8x3x7-1/8 in. plates extending the full depth of the column were used. The

stiffeners in this case were also welded to the column flanges (1/4 in. fillet welds) and

web (3/16 in. fillet welds) to allow for full transfer of the load from the column to the

stiffener. The tensile yield stress of the stiffener plates was determined to be 54.0 ksi

(yield strength of 60.75 k per stiffener).

2.3 INSTRUMENTATION

Three strain gages were placed on both sides of each stiffener to determine the

strain distribution along the width (from the column web to the stiffener edge) for both

15

PL 3/8 x 3 x 7-1/8”

W 8 x 48

Stiffener

6.0

16.0

3

0.69

ts=0.375

3/16

1/4

ws=3.0

8.0

1.5

Note: All dimensions are in inches, No Scale

Figure 2.2 Test 2 Specimen Geometry

16

Column

Stiffener R

Strain Gage(Typ)

0.75” (Typ) 0.75” (Typ)

Section

1.0” (Typ)

1.0”(Typ)

Web - R

Stiffener L

(a) Section

(b) Elevation

W eb - L

Notes: 1. Strain gages were used only at one end of the stiffeners in Test 1 2. Web strain gages were used only in Test 2

3. All dimensions are inches

Figure 2.3 Strain Gage Locations, Tests 1 and 2

17

tests. In the subsequent discussion of test results the locations are referred to as “Inner”,

“Middle” and “Outer.” For Test 1, the gages were located on both ends of the stiffener

(near the column flanges) to assure the load was consistent through the depth of the

stiffener. Once this was shown, only one end of the stiffener was gauged for Test 2. The

strain gage locations are shown in Figure 2.3. Test Specimen 2 also had strain gages on

the column web to verify that the full load was being distributed between the column web

and the two stiffeners. Gages on the web were placed at 1-in. increments starting at the

stiffener and extend 5 in. in each direction from the stiffener.

2.4 TESTING PROCEDURE

The test specimen was loaded in tension using a Satec Universal Testing machine.

Each specimen was loaded from 0 to 260 kips of tension in 5 kip increments (at 2

kips/min). Load and strain values were recorded at each increment. The specimens in

both tests were loaded to 260 kips but not to failure due to the limitations of the testing

machine. Using the strain data obtained from the tests, the load supported by the stiffener

and web was determined.

2.5 TEST RESULTS

2.5.1 General

The strain gage readings at the same locations on the stiffener (one on each side)

were averaged to eliminate possible local bending effects. Each stiffener was considered

separately to account for unequal distribution of load (one stiffener supporting a greater

load than the other). Averages were taken in a similar manner for the strain gage

readings on the column web of Test 2. Again, the web readings on each side of the

stiffener were considered separately. The linear load/strain relationships of the

experimental data provided in the following subsections shows that only minor yielding

of the test specimens occurred starting at about 250 kips.

2.5.2 Test 1

Figure 2.4 graphically shows the measured load verses strain relationship on the

stiffeners in Test 1. The relationships were determined from the average strain readings

18

Figure 2.4 Test 1 (W16x45) – Load vs. Micro-strainResults for Stiffeners R and L

Load vs. StrainTest 1: Stiffener R

0

50

100

150

200

250

300

0 200 400 600 800 1000 1200 1400

Micro-strain

Lo

ad (

k)

InnerMiddleOuter

Load vs. StrainTest 1, Stiffener L

0

50

100

150

200

250

300

0 200 400 600 800 1000 1200 1400

Micro-strain

Lo

ad (

k)

InnerMiddleOuter

19

obtained during testing. The graphs show that the strain gages provided consistent

measurements with no irregularities or inconsistent readings. The inner strain data was

that obtained from the gage closest to the column web. Similarly, the outer strain data

represents the strain from the gage furthest from the column web and the middle strain

data is from the gage between the two. It can be seen from Figure 2.4 that the stiffeners

take load as soon as it is applied to the test specimen. As stated previously, this is in

contrast with the AISC assumptions made about the behavior of the column/stiffener

system.

Figures 2.5 and 2.6 show the strain distribution of each stiffener at loads of 95 and

170 kips. The strain at each load is plotted as it varies with distance across the width of

the stiffener, from the column web to the free edge of the stiffener. Using the area under

the curve, the thickness of the stiffener, and a modulus of elasticity of 29,000 ksi, the

force resisted by each stiffener is:

Ps = E A ts (2.1)

where Ps is the force in the stiffener, A is the area under the curve and ts is the stiffener

thickness.

Table 2.1 gives force resisted by the stiffeners and column web for applied loads

of 95 kips and 170 kips. The stiffener forces were obtained using Equation 2.1. The web

force is the difference between the applied load and the calculated stiffener force. For

Test 1, the stiffener forces were 64% of the applied load with the web resisting the

remaining 36%. Strain gages were not applied to the column web for Test 1. The total

web force was therefore calculated by subtracting the stiffener load determined from the

experiment from the applied load.

Table 2.1 Force Distribution - Test 1 (W16x45)

Applied Load(kips)

Total Stiffener Force(Ps)

Total Web Force(Pw)

% StiffenerLoad

95 60.8 34.2 64

170 109.15 60.85 64

20

Figure 2.5 Test 1 (W16x45) – Strain vs. DistanceResults for Stiffener R

Figure 2.6 Test 1 (W16x45) – Strain vs. DistanceResults for Stiffener L

Strain vs. DistanceStiffener R

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3

Distance (in.)

95 kips

170 kips

Strain vs. DistanceStiffener L

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5 3

Distance (in.)

95 kips

170 kips

21

2.5.3 Test 2

The loads vs. strain relationships for the stiffeners in Test 2 are shown graphically

in Figure 2.7. These relationships were again determined from the averages in the strain

gage readings at the same locations. The strain gages provided linear measurements to

260 kips except for the outer gage location on Stiffener R where yielding started at about

250 kips. Figure 2.7 shows that the strain gages for stiffener L provided consistent

measurements with no irregularities or inconsistent readings for the full range of the

loading. As seen from Figure 2.7, it is again apparent that the stiffeners take load as soon

as it is applied to the test specimen.

Strain gages were attached to the column web for Test 2 to show the assumption

that the web receives the remainder of the load not supported by the stiffeners. Figure 2.8

graphically shows the load vs. strain relationships for the column web on each side of the

stiffener. It can be seen from the graph that the strain readings obtained on the column

web were also consistent with no irregular readings and that the web takes load as soon as

it is applied to the test specimen. The 1-in. line represents the strain 1-in. away from the

stiffener. The additional lines represent similar values for the strain at 2, 3, 4, and 5 in.

away from the stiffener along the column web.

The force resisted by the stiffeners was also determined at applied loads of 95 and

170 kips for Test 2. The strain values at these loads are plotted in Figures 2.9 and 2.10

and vary with the distance along the width of the stiffener, from the column web to the

free edge of the stiffener. The force supported by each stiffener is calculated using

Equation 2.1 and the area under these curves.

Figure 2.11 shows the strain values along the web starting at the stiffener location

(at 0.0 inches) and extending 5 inches from the stiffener in each direction (Web R and

Web L reading). The strain values decrease as the distance from the stiffener increases as

expected. The force resisted by the column web is determined in the same manner as the

stiffener force (using Equation 2.1 for the column values). The column web forces were

also determined for loads of 95 and 170 kips to confirm that the full load was being

22

Figure 2.7 Test 2 (W18x48) – Load vs. Micro-strainResults for Stiffeners R and L

Load vs. StrainTest 2: Stiffener R

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500 3000

Micro-strain

Lo

ad (

k)

InnerMiddleOuter

Load vs. StrainTest 2: Stiffener L

0

50

100

150

200

250

300

0 500 1000 1500 2000 2500

Micro-strain

Lo

ad (

k)

InnerMiddleOuter

23

Figure 2.8 Test 2 (W8x48) – Load vs. Micro-strainResults for Web R and L

Load vs. StrainTest 2: Web R

0

50

100

150

200

250

300

0 200 400 600 800 1000 1200 1400 1600

Micro-strain

Lo

ad (

k) 1 in.2 in3 in.4 in.5 in.

Load vs. StrainTest 2: Web L

0

50

100

150

200

250

300

0 200 400 600 800 1000 1200 1400 1600 1800

Micro-strain

Lo

ad (

k) 1 in.2 in,3 in.4 in.5 in.

24

Figure 2.9 Test 2 (W8x48) – Strain vs. DistanceResults for Stiffener R

Figure 2.10 Test 2 (W8x48) – Strain vs. DistanceResults for Stiffener L

Strain vs. DistanceStiffener R

0

500

1000

1500

2000

0 0.5 1 1.5 2 2.5 3

Distance (in.)

95 kips

170 kips

Strain vs. DistanceStiffener L

0

500

1000

1500

2000

0 0.5 1 1.5 2 2.5 3

Distance (in.)

95 kips

170 kips

25

Figure 2.11 Test 2 (W8x48) – Strain vs. DistanceResults for Web R and L

Strain vs. DistanceWeb R: Load = 95k

0

200

400

600

800

1000

0 1 2 3 4 5 6

Distance (in.)

Mic

ro-s

trai

n

Strain vs. DistanceWeb L: Load = 95k

0

200

400

600

800

1000

0 1 2 3 4 5 6

Distance (in.)

Mic

ro-s

trai

n

26

accounted for in the measurements. When added, the forces obtained from the web and

stiffener measurements should equal the total load that is being applied.

Table 2.2 shows values for the force supported by the column web and stiffeners

for the specific applied loads. It can be seen, however, that the total stiffener force and

total web force do not add up to the applied load. These differences occur due to

assumptions and experimental variations. Because a strain gage could not be placed at

the web-stiffener connection, the web strain value at the connection was estimated from

the stiffener and web gage readings nearest to the weld, which introduces possible error.

The strain values in the stiffener vary linearly along the width allowing the readings at

web to be more accurately estimated. It is noted that the web strains, however, decrease

in a parabolic shape along the length of the web and the values could not be estimated as

easily.

Table 2.2 Force Distribution - Test 2 (W8x48)

Applied Load(kips)

Total Stiffener Force(Ps)

Total Web Force(Pw)

% TotalLoad

% StiffenerLoad

95 49.9 38.8 93.4 53.0

170 90.5 63.5 90.5 53.0

It was therefore assumed that the stiffeners receive the force values calculated

from the experiment and the web receives the remaining applied load because of the error

that occurs from the estimation of strain in the web. For this test, the stiffeners resist

about 53% of the load for each of the load levels with the web resisting the remaining

47%.

2.6 SUMMARY OF EXPERIMENTAL RESULTS

It is evident from the test results that force is distributed to the column stiffeners

as well as the column web at the instant that force is applied at the connection. If AISC

assumptions were accurate, yielding of the column would have occurred during the test

and the stiffener would not have taken any forces until the column limit state had been

27

exceeded as shown in Figure 2.12. Yielding of the column section, however, did not

occur during the experimental investigation due to the fact that the stiffeners received

load from the beginning of the test, before column failure.

Figure 2.12 Comparison of Stiffener Force Ratios

Stiffener Load Distribution

0.05

0.15

0.25

0.35

0.45

0.55

0.65

0.75

0 50 100 150 200 250 300

Applied Flange Force

Stif

fene

r F

orce

/App

lied

Fla

nge

For

ce

Test 2

AISC

28

CHAPTER III

DEVELOPMENT OF FINITE ELEMENT MODELAND COMPARISON WITH TEST RESULTS

3.1 DEVELPOMENT OF FINITE ELEMENT MODEL

3.1.1 Description of Finite Element Analysis

Finite element (FE) models were used in this research to analytically study

the behavior of the test specimens. A series of elements and nodes were used to represent

the geometry of the column/stiffener connection. The material and cross-section

definitions applicable to the steel sections were defined within the model. Constraints

and boundary conditions were also applied to applicable nodes throughout the analysis.

Since the section was loaded equally on both ends of the specimen during testing, the

bottom flange of the column was restrained in the FE model at the equivalent line load

location while the load is applied across the top flange. Constraints were therefore placed

on the nodes representing the bottom flange of the column section. The behavior of the

specimen is simulated through these boundary conditions which restricted linear and

rotational movements of the applicable nodes in the model. The computer software

ABAQUS (ABAQUS/Standard 1994) was used for this study to analyze the specimens in

Test 1, Test 2 and additional column sections.

The tensile load was modeled as a distributed load acting across the flange width

of the column at the stiffener location. This simulates the load acting on the column by

the top beam flange in gravity type loading. The specimens in Test 1 and Test 2 were

subjected to this type of loading in the experimental investigation. The FE models were

considered elastic because only minor yielding occurred in the connections during the

experimental investigation. A modulus of elasticity of 29,000 ksi and a Poisson’s Ratio

of 0.3 were used. The files containing the ABAQUS input data and the analysis results

are contained in Appendices A and B for Test 1 and Test 2.

3.1.2 Shell Elements

Shell elements are provided in ABAQUS and allow for six degrees of freedom at

all nodes. The cross sectional properties of the shell including the thickness of the

29

material are required input to define the behavior (ABAQUS/Standard Vol. II, 1994).

S8R type shell elements were used in the models. These elements were 8-node doubly

curved thick shells and utilized reduced integration to minimize ABAQUS run time while

providing accurate results. This element type contains 4-sides with nodes at the 4 corners

and at the middle of each side. Triangular, or 3-sided, elements were not used because

they have a tendency to introduce a false stiffness in the model. S8R’s are thick elements

(when the thickness is more than about 1/15 of the surface length of the shell) and also

account for transverse shear flexibility.

The finite element model used in the Test 1 analysis is represented in Figure 3.1.

When Test 2 geometry is applied, the FE model is the same. The width of each stiffener

is represented by two elements (see Figure 3.1) and the stress values obtained at the

nodes of these elements were used to compute the stiffener force.

3.2 FINITE ELEMENT RESULTS

3.2.1 Test 1

The finite element model was run in ABAQUS for a load case of 170 kips. The

stresses in the stiffener and web elements were obtained for this load in order to calculate

the load distributed between the web and stiffener. The variation of stress along the

width of the stiffener is shown in Figure 3.2 for the stiffener elements closest to the

column flange. Because the stress vs. distance relationship is linear, the load can be

easily and accurately calculated using the area under the curve. The FE results used as a

comparison with the experimental results are provided in Table 3.1 for a load of 170k and

can be determined for any load variation because it is an elastic analysis.

3.2.2 Test 2

The finite element model for Test 2 is similar to that used in Test 1. The

geometry of the model was modified to match the W section and stiffener dimensions

used in the Test 2 experiment. The stresses in the stiffener and web were again obtained

for a load of 170 kips. The variation of stress along the width of the stiffener is provided

in Figure 3.2 for the stiffener elements closest to the column flange at a load of 170 k.

30

Column Web -4 Elements deep

Column Flange –4 Elements wide

Stiffener Elements –2 wide per stiffener

Figure 3.1 FE Model for Test Specimens

31

Figure 3.2 Finite Element Results for StiffenersStress vs. Distance - Test 1 and 2

Stress vs. DistanceTest 2, Load = 170 k

0

10

20

30

40

50

60

0 0.5 1 1.5 2 2.5 3

Distance (in.) from Face of Column Web

Stre

ss (

ksi)

FEA

EXP.

Stress vs. DistanceTest 1, Load = 170 k

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3

Distance (in.) from Face of Column Web

Stre

ss (

ksi)

FEA

EXP.

32

Figure 3.3 shows the variation of force along the length of the web at a load of 170 k.

The ratio of stiffener force to the applied load is shown in Table 3.1 for Test 1 and Test 2.

Table 3.1 Stiffener Force from FE Models

Test Applied Load(kips)

Stiffener Force(Ps)

% StiffenerLoad

Test 1 – W16x45 170 111.4 65.5

Test 2 – W8x48 170 94.9 55.8

These values were obtained to confirm that the experimental data was consistent with the

results obtained from analytical methods. Because the results are consistent, an accurate

design procedure can be developed.

Figure 3.3 Finite Element Results for Web - Test 2

Additional FE models were performed on W-shaped column sections to show that

the results also apply to larger column section.

3.2.3 Additional Finite Element Models

Additional finite element model analyses were performed to confirm that the

results were consistent and could be applied to larger W-shaped sections. ABAQUS was

Finite Ele ment Res ults for W e b

0

5

10

15

20

25

0 2 4 6 8

Dis tanc e (in.) from S tiffe ner

Web

For

ce (

kips

)

FEA

T es t 2

33

used to analyze a W14x311 designed for a factored load of 1196 kips using 7/8 in. by 7

in. full depth stiffeners on each side of the column web. As with Test 1 and 2 column

sections, the LRFD method was used for designing the W14x311 column stiffeners. The

same element type, boundary conditions, and load distribution used for the previous

analyses was applied to this section. A572, Grade 50 material properties (yield stress of

50 ksi) were used for the column and stiffeners. The stresses in the stiffeners were

obtained for this load case. The variation of stress along the width of the stiffener is

similar to that obtained from the ABAQUS output for Tests 1 and 2. The load can be

easily calculated using the area under the stress/distance curve. The distribution of

stiffener load along its length is shown in Figure 3.4 for an applied load of 1196 k.

Figure 3.4 W14x311 Finite Element Results

The results are as follows:

Applied Load = 1196 kipsStiffener Force = 2(266.30) = 532.60 kips% Stiffener Load (Ps/P)(100) = 0.45(100) or 45%

Thus, the ABAQUS results for the W14x311 column section are consistent with that

obtained from the smaller sections used in Tests 1 and 2.

The finite element program provided by I-DEAS Master Series 6 was used to

analyze a W12x120 and W14x500 column section. All finite element definitions,

W 1 4 x 3 1 1 S tiffen er F o rce D istr ib u tio n

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 1 2 3 4 5 6 7

D ista n ce (in .) fro m F ac e o f C o lu m n W eb

34

methodology, and procedure used for these models is the same as those used previously

for the ABAQUS analyses. The W12x120 was designed for a factored load of 400 kips

using 1/2 in. by 5 in. full depth stiffeners on each side of the column web (yield stress for

all material was 50 ksi). A factored load of 2500 kips was applied to a W14x500 column

section with 1-3/4 in. by 7 in. full depth stiffeners on each side of the column web. The

LRFD method was used for designing these column stiffeners. The forces in the stiffener

elements were recovered for the load cases in each column section. The element forces

along the stiffener width were then added together to determine the total stiffener force.

The variation of forces along the stiffener width is shown in Figure 3.5 and is similar to

the results obtained from the ABAQUS output for the W14x311 column section. The

results are summarized in Table 3.2.

Table 3.2 FEA Results for Additional Column Sections

Column Section Stiffeners – 2 Plates Ptot (kips) Pstiff (kips) Pstiff/Ptot

W14x311 7/8x7 1196 532.6 0.45

W12x120 1/2x5 400 196.4 0.49

W14x500 1-3/4x7 2500 1086.8 0.43

3.2.4 Parametric Study of Stiffener Sizes

Finite Element Analysis was used to examine the effects of stiffener size on load

distribution between the column web and stiffener. I-DEAS Master Series 6 was again

used to analyze the column section and stiffener as described in the previous section. A

factored load of 200 kips was applied to a W14x90 column section and analyzed three

times using a different stiffener size for each run. The forces in the stiffener elements

were recovered from each analysis for the load case. The element forces along the

stiffener width were then added together to determine the total stiffener force. The

variation of force along the width of the stiffener for these FEA runs was consistent with

the analysis results provided in the previous subsections. The results are provided in

Table 3.3.

35

Figure 3.5 W12x120 and W14x500 Finite Element Results

W14x500 Stiffener Force DistributionTotal Applied Load = 2500 k

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7

Distance (in.) from Face of Column Web

W12x120 Stiffener Force DistributionTotal Applied Load = 400 k

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5

Distance (in.) from Face of Column Web

36

Table 3.3 FEA Results for W14x90 Stiffeners

StiffenersColumn Section

2 Plates Area (in.2)

Ptot (kips) Pstiff (kips) Pstiff/Ptot

W14x90 (a) 3/8x5 3.75 200 106.52 0.53

W14x90 (b) 1/4x6 3.00 200 105.54 0.53

W14x90 (c) 3/8x4-1/4 3.38 200 100.88 0.50

3.3 COMPARISON OF EXPERIMENTAL AND ANALYTICAL DATA

The results obtained from the finite element analysis and experimental tests

provided consistent data. The distribution of load between the stiffeners and column web

was similar in both types of investigations. The main difference between the results

obtained from the two methods of investigation was in the determination of load.

Stiffener load was calculated from strain values in the experimental method while the

finite element method used stress values.

The method for predicting the column and stiffener design load based on Load

and Resistance Factor Design (LRFD) requirements was discussed in Chapter I. LRFD

requirements assign stiffener load based on limit state strengths of the column section.

The results of the predicted, experimental and analytical investigation are compared in

Table 3.4. These results are calculated in the same manner as discussed in Chapter II

(using the area under either the strain vs. distance curve for experimental data or stress

vs. distance curve for analytical data). The ratio of the stiffener load to the total load

(Ps/P) is given for the LRFD method, as determined experimentally, and from the finite

element results where P is the total load applied to the test specimen and Ps is the load

carried by both stiffeners. It can be seen from Table 3.4 that the differences between the

experimental and finite element results are small (less than 5%).

The Ps/P ratios are consistent between the experimental and finite element tests

and exhibit the same linear behavior. In all cases, the ratio of stiffener load to the applied

load remains constant for all load cases. The LRFD method for determining stiffener

37

Table 3.4 Predicted versus Test Results

TestLoad(kips)

Ps/P:LRFD

Ps/P:Experiment

Ps/P:Finite Element

Test 1-W16x45 170 0.44 0.64 0.65Test 2-W8x48 170 0.43 0.53 0.56

W14x311 1196 0.16 N/A 0.45W12x120 400 0.38 N/A 0.49W14x500 2500 0.31 N/A 0.43W14x90 200 0.47 N/A 0.53

load, however, does not demonstrate a linear relationship and therefore does not

correspond to the behavior of the connection. Figure 3.6 shows the difference between

the experimental results and the LRFD method for assigning the distribution of load to

the column stiffener. The results of the analyses provide a basis for accurately predicting

the load distribution between the stiffener and column that will follow the behavior of the

connection. The distribution of load between the stiffener and column web will be

dependent upon an effective column area and the area of its associated stiffener.

Figure 3.6 Comparison of Stiffener Force

Stiffener Load Distribution

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200 250 300

Applied Flange Force, kips

Stif

fene

r F

orce

/App

lied

Fla

nge

For

ce

Testing

LRFD

38

CHAPTER IV

DEVELOPMENT OF A DESIGN MODEL

4.1 DEVELOPMENT OF EFFECTIVE LENGTH

In the experimental and analytical investigations, there was a difference in the

proportion of load distributed to the stiffeners due to the differences in geometry between

the three column sections. The load distribution was therefore determined to be

dependent upon the geometry of the column sections and their respective stiffeners. The

column area that supports the loading, or the area affected by the applied load, was

determined from the data obtained from experimental and analytical results.

From the experimental and analytical results, an effective length (the distance

along the length of the column web that the applied load was distributed) was determined

for each test specimen. Figure 4.1 graphically shows how the applied load is distributed

along the column length. The effective column length from the ABAQUS analysis for

the W14x311 section is shown in Figure 4.2 and displays the element forces for each

element. It can be seen that the load is distributed a prescribed distance across the flange

width at the application of the load and along the length of the web in a definite pattern.

As shown in Figure 4.3 for the W12x120 and W14x90 sections, the load is distributed at

a 45-degree angle along the length of the web from the point of load application. The

effective length (le) includes all elements that contain reaction force values. Using this

total distance (le), the column area affected by the loading was determined. The total area

affected will therefore include this column area and the area of the two stiffeners. Based

on a ratio of the stiffener area to the total calculated area, the percentage of load received

by the stiffener can be calculated.

Based on experimental and finite element results, the effective length was

determined to be 8.2k1 where k1 is the distance from the center of the web to the end of

the fillet radius connecting the column web to the flange. From on the plot in Figure 4.2

for the W14x311 column section, le was determined by finding the length across the

elements containing element forces and found to be 11.78 inches. Using the equation

39

Stiffener

Column Web

P

le

1/2 le

equivalent load distribution

ts

tw

1/2 le

Figure 4.1 Equivalent Load Distribution

40

Figure 4.2 Plot of Element StressesW14x311 Specimen

Distribution of Stressesalong the Column Web

41

Figure 4.3 Equivalent Column Web Load Distribution

(b) W14x90 - Element Forces Along WebAll Elements are 1/2” - Square

le by equation

450

Column Web

(a) W12x120 - Element Forces Along WebAll Elements are 1/2” - Square

450

le by equationColumn Web

42

le = 8.2(k1), the value for the effective length is 10.76 inches. The value obtained from

the contour plot is larger because of the element sizes. If the elements were smaller, the

effective length would approach this value of 10.76 inches. The same is true for the

W12x120 and W14x90 sections shown in Figure 3.3. Values for effective length were

calculated for all sections included in this research and are summarized in Table 4.1.

Table 4.1 Effective Lengths

Test k1 (in.) Calculated le (in.)le = 8.2(k1)

Test 1 – W16x45 13/16 6.66Test 2 – W8x48 5/8 5.13

W14x311 1-5/16 10.76W12x120 1 8.20W14x500 1-3/4 14.35W14x90 7/8 7.18

The column area affected by the applied load can now be calculated and the distribution

of load between columns and stiffeners can be determined for all W-shaped column

sections.

4.2 LOAD DISTRIBUTION BETWEEN COLUMN AND STIFFENER

Load will be distributed along the column web and radiate a distance, le, from the

location where the load is applied. The column is then assumed to be affected through an

area of the effective length times the thickness (tw) of column web. The total area,

including the area of the stiffeners, can be calculated as follows:

Atot = Acol + Astiff

Atot = le(tw) + 2(ts)(ws)

Atot = 8.2(k1)(tw) + 2(ts)(ws) (4.1)

where ts is the thickness of the stiffener and ws is the stiffener width. Table 4.2

summarizes these values for each column section.

The distribution of load between the column and stiffener can be estimated by

using the ratio of the stiffener area to the effective column area. This ratio will provide

load values for the stiffener for any given applied force. It assumes, therefore, that the

43

Table 4.2 Effective Area Values

Section Stiffeners2 Plates

Astiff

(in.2)8.2k1

(in.)tw

(in.)Aeffect

(in.2)Atot

(in.2)Astiff/Atot

W16x45 3/4x3 4.50 6.66 0.345 2.30 6.80 0.66W8x48 3/8x3 2.26 5.13 0.400 2.05 4.31 0.52

W14x311 7/8x7 12.25 1.41 1.410 15.18 27.43 0.45W12x120 1/2x5 5.00 8.20 0.710 5.82 10.82 0.46W14x500 1-3/4x7 24.50 14.35 2.190 31.43 55.93 0.44

W14x90 (a) 3/8x5 3.75 7.18 0.440 3.16 6.91 0.54W14x90 (b) 1/4x6 3.00 7.18 0.440 3.16 6.16 0.49W14x90 (c) 3/8x4-1/2 3.38 7.18 0.440 3.16 6.54 0.52

stiffener does receive load before the column reaches a limit state. This equation is

consistent with the data obtained from testing and is contrary to the assumption made in

the LRFD Manual that the stiffener does not support any load until the column has

reached its limit state. The equation can be written as follows:

Ps = (Astiff/Atot)(Papplied) (4.2)

This equation provides stiffener loads that follow the behavior of the connection and

therefore allows for the development of a more accurate design procedure. The ratios of

Ps/Papplied are compared in Table 4.3 for the experimental investigation, finite element

analysis, and the calculated values based on equations 4.1 and 4.2 for each section.

Table 4.3 Comparison of Results

Ps/PappliedSection Astiff/Atot

Equation 4.1 Experimental Finite ElementW16x45 0.66 0.64 0.65W8x48 0.52 0.53 0.56

W14x311 0.45 N/A 0.45W12x120 0.46 N/A 0.49W14x500 0.44 N/A 0.43

W14x90 (a) 0.54 N/A 0.53W14x90 (b) 0.49 N/A 0.53W14x90 (c) 0.52 N/A 0.50

44

Based on the consistency of the results obtained in the experimental and analytical

investigations, the new stiffener design procedure can be used to accurately predict load

distribution between the stiffener and column web. The Area Design Method is based on

the effective areas of the column and the stiffeners as calculated from Equation 4.1.

Using Equation 4.2, the load distributed to the stiffeners can be determined for any

applied load. The steps necessary for stiffener design using the Area Method will be

develop and provided in Chapter 5.

45

CHAPTER V

SUMMARY AND RECOMMENDATIONS

5.1 SUMMARY

The current AISC design model for predicting stiffener load does not follow the

true behavior of the beam-to-column connection. This design procedure is based on

LRFD recommendations, which assume that the stiffener does not receive any of the load

applied to the connection until the controlling limit state load of the column section has

been reached. Once this load is reached, it is assumed that the stiffener supports load in a

nonlinear manner when compared to the total applied load. Results obtained from

experimental and analytical investigations differ from the current design assumptions.

It was therefore found necessary to develop a more accurate procedure for

predicting the distribution of load between the stiffeners and column web. Experimental

and analytical tests were performed to develop a new procedure for predicting load

distribution based on the behavior of the connection. Analytical investigations were

performed to insure the accuracy of the results obtained from the experimental tests.

From experimentation, a ratio of the stiffener load to the applied load was

obtained to determine the amount of load the stiffener was receiving. It was found that

the stiffener received the same percentage of the applied load throughout the entire test

period (starting from load = 0.0 pounds). This load percentage (or ratio) was therefore

determined to be dependent upon the geometry of the column section and its

corresponding stiffener.

The results obtained from the experimental and analytical investigations were

compared to develop the necessary information to determine the effective areas of the

column/stiffener connection. It was found that the applied load affected the column over

a distance of le along its length. The total area affected by the applied load (Acolumn +

Astiffeners) was calculated and the relationship between the affected areas and the load

distribution could then be determined. A new procedure can now developed, the Area

Method, to accurately predict the load distribution between the column and stiffeners in a

beam-to-column connection.

46

5.2 AREA METHOD DESIGN RECOMMENDATIONS

The design procedure for the area method is developed in accordance with

information obtained from experimentation as discussed in Chapter IV. The area method

procedure incorporates LRFD guidelines for determining minimum stiffener size. The

recommended area method design procedure is as follows:

1. Assume the applied load and column section are given.

2. Determine the column side limit states as described in Chapter K of the LRFDSpecifications. If the given applied load exceeds any limit state stiffeners must beadded and the following steps for its design should be utilized.

3. Determine the effective column length and area (k1 and tw are provided in the LRFDfor the section being analyzed).

le = 8.2(k1)Acolumn = le(tw)

4. Determine the minimum stiffener size requirements based on the suggested followingrules for stiffener design (LRDF):

a. The width of each stiffener plus one-half the thickness of the column web shouldnot be less than one-third the width of the flange or moment connection platedelivering the concentrated force.

b. The thickness of the stiffeners should not be less than tb/2 (where tb = thickness ofthe beam flange or connection plate).

c. The stiffener length does not need to exceed one-half the column depth if theconcentrated force only acts on one column flange.

d. The weld joining the stiffeners to the column web should be sized to carry theforce in the stiffener caused by unbalanced moments on opposite sides of thecolumn.

5. Calculate the total stiffener area (Astiff) and it’s load capacity (Ps)allow.

Astiff = Σws(ts) where ws is the stiffener width, ts is the stiffener thickness(Ps)allow = Astiff(Fys) where Fys is the yield strength of the stiffener

6. Calculate the total area affected by the applied load.

Atot = Astiff + Acolumn

7. Calculate the percentage of load distributed to column and stiffener.

47

Pstiff/Ptot = Astiff/Atot orPstiff = (Astiff/Atot)Ptot

Pcolumn = Ptot - Pstiff

8. Compare these loads (Pcolumn and Pstiff) with the limiting values for the column andstiffener.

9. If these loads exceed the limiting values, increase the stiffener size and repeat theprocedure. If these loads do not exceed the limiting values, then the stiffener size isadequate.

10. Design the welds between the stiffener and the column web and flange.

5.3 EXAMPLE CALCULATIONS

The following example uses the procedure described above for a W10x88 column

connection. It will be necessary to design column stiffeners given the following loading

and material information:

Given:

1. Column: W10x88 tw = 0.625 in. d = 10.875 in. bf = 10.25 in. k = 1.625 in. tf = 1.0 in. k1 = 13/16 in. Fyf = Fyw = 36 ksi Connector plate width bf = 9.5 in. Connector plate thickness, N = 1.0 in. Fys = yield stress of stiffener material = 36 ksi

Design Load: Papplied = 300 kips in tension The load is applied at a distance greater than d/2 from the member end and acts all column flanges.

Solution:

2. Calculate column side limit states.

• Local Flange Bending:

Rn = 6.25(tf)2(Fyf)

= 6.25(1.0)2(36)

48

= 225 k < 300 k

• Local Web Yielding:

Rn = (5k + N)(Fyw)(tw)

= [5(1.625) + 1.0](36)(0.625)

= 205 k < 300 k

• Web Crippling:

Rn = 135tw2[1 + 3(N/d)(tw/tf)

1.5]√(Fywtf)/tw

= 135(0.625)2[1 + 3(1/10.875)(0.625/1) 1.5]√(36x1)/0.625

= 455 k

• Web Buckling:

Rn = [4,100tw3√Fyw]/h

h = d - 2(tf) = 8.875

Rn = [4,100(0.625)3√36]/8.875

= 677 k

Web yielding controls: Rn = 205 k < 450 k, therefore stiffeners are required.

3. le = 8.2(k1) = 8.2(13/16) = 6.66 in.Acolumn = le(tw) = 6.66(0.625) = 4.16 in.2

4. (a). ws + 1/2(tw) > 1/3(bf) ws > 1/3(9.5) - 1/2(0.625) ws > 2.85 in.

Use ws = 3.5 in.

(b). ts > N/2 ts > 1/2

Use ts = 5/8 in.

(c). Use 2 full depth stiffener (concentrated force is acting on all column flanges).

5. Astiff = Σws(ts) = 2(3.5)(0.625) = 4.375 in.2

(Ps)allow = Fys(Astiff) = 36(4.375) = 157.5 kips

49

6. Atot = Astiff + Acolumn

= 4.375 + 4.16 = 8.535 in.2

7. Pstiff = (Astiff/Atot)Ptot

= (4.375/8.535)300 = 153.8 kips

Pcolumn = Ptot - Pstiff

= 300 - 153.8 = 146.2 kips

8. Pcolumn = 146.2 < 205 kipsPstiff = 153.8 < 157.5 kips

9. Stiffener and column section are adequate since the limiting values were notexceeded.

10. From the LRFD Specifications, Section J2, Table J2.4, the weld size should bea minimum of 1/4” in length.

From the Area Method, two 5/8 in. x 3.5 in. full depth stiffeners were used. If the LRFD

design procedure were used, two 1/2 in. x 2.85 in. stiffeners would have been sufficient.

5.4 RECOMMENDATIONS FOR FURTHER RESEARCH

The current design procedure for assigning stiffener force does not follow the

behavior of a beam-to-column connection. This research was therefore performed to

develop a method that would accurately predict the distribution of force between a

column and its associated stiffeners. Column W-shaped sections were the focus for

moment connections requiring the use of stiffeners for this research. Experimentation

was limited to one section type subjected to tensile loading only. Laboratory testing was

only performed on two of the W-shaped specimens. Additional experimentation would

be necessary in order to validate the use of the Area Method over the current LRFD

procedure for the design of column stiffeners. It is also recommended that further

research be done to incorporate different column-shaped sections such as angles or

channels. Compressive forces could also be introduced into the experiment separately or

in combination with the tensile force. Future research is needed to extend the

applicability of the Area Method Design Procedure to other column sections subjected to

compressive and tensile loads.

50

REFERENCES:

ABAQUS/Standard User’s Manual, Vol. I & II (ver. 5.4), (1994). Hibbit, Karlsson &Sorensen, Inc., Pawtucket, Rhode Island.

Load and Resistance Factor Design Specification for Structural Steel Buildings, (1993).American Institute of Steel Construction, Inc., Chicago, Illinois.

Manual of Steel Construction: Load & Resistance Factor Design, 2nd ed., (1994).American Institute of Steel Construction, Inc., Chicago, Illinois.

Salmon, C. G., and Johnson, J. E. (1995). Steel Structures, Design and Behavior (4thed.). HarperCollinsPublishers Inc., New York, New York.

Segui, William T. (1994). LRFD Steel Design. PWS Publishing Company, Boston,Massachusetts.

51

APPENDIX ANomenclature

52

General Nomenclature

A Area under a strain/distance curve, in.2

Acolumn Area of column web affected by an applied load, in.2

Astiff Area of a stiffener cross section, in.2

Astiffeners Total area of all stiffener cross sections used in a column connection, in.2

Atot Total column/stiffener area affected by an applied load, in.2

E Modulus of elasticity, ksi

Fyf Yield stress of flange material, ksi

Fys Yield stress of stiffener material, ksi

Fyw Yield stress of web material, ksi

N Length of bearing, in.

P Total applied load, kips

Papplied Applied load, kips

Pcolumn Force in column, kips

Ps Force in stiffener, kips

(Ps)allow Allowable stiffener load based on yield of material, kips

Pstiff Force in stiffener, kips

Ptot Total applied load, kips

Pw Force in column web, kips

Rn Nominal resistance, kips

bf Flange width, in.

c Length of the effective load distribution along the column web, in.

d Depth of column section, in.

h Clear distance between flanges less the fillet or corner radius, in.

k Distance from outer face of flange to web toe of fillet, in.

k1 Distance from the web center line to flange toe of fillet, in.

le Distance along the length of column affected by the applied load, in.

tb Thickness of beam flange or connection plate delivering the concentratedforce, in.

53

tf Flange thickness, in.

ts Stiffener thickness, in.

tw Web thickness, in.

ws Stiffener width, in.

φ Resistance factor

54

APPENDIX BTEST 1 Result

55

B.1 Experimental Data

AVERAGE STRAIN GAGE READINGSBOTTOM FLANGE - LEFT STIFF. (micro-strain)

LOAD Inner Middle Outer at 0.25" at 2.75"0 1E+30 1E+30 1E+30 0.001 0.0010 -9.61538 -12.499999 -8.65384 1.923077 2.884615

5.2 12.98077 4.326925 19.71154 5.769231 -40.384610.2 34.61539 24.999995 41.34618 13.46154 -62.515.2 53.84614 44.23076 59.13462 25.96154 -71.153820.1 76.92306 67.307695 82.69228 44.23077 -66.346225.2 100.9615 91.826925 105.7692 62.5 -60.576930.2 120.6731 112.98076 128.3654 82.6923 -52.884635.2 143.75 138.46153 152.8846 101.9231 -42.307740.2 167.3077 162.49998 176.9231 124.0385 -29.8077

45.18 188.9423 185.09612 200 145.1923 -17.307750.1 212.0192 210.09614 222.5961 167.3077 -2.88462

55.13 235.0962 235.09613 245.6731 189.4231 10.5769260.05 255.7693 259.1346 270.1923 211.5384 27.88461

65.1 282.6923 287.0192 298.0769 236.5384 49.0384670.06 307.2116 313.46155 325 260.5769 65.3846175.03 333.1731 340.3846 351.4423 285.5769 84.6153880.16 360.577 368.74995 377.8846 310.5769 103.846185.14 386.0577 395.1923 404.3269 336.5384 12590.15 408.1731 418.74995 427.8846 360.5769 141.346295.16 437.0192 448.0769 456.7308 386.5384 164.4231

99.9 460.0961 471.63455 479.8077 410.5769 180.7692105.11 485.5769 499.03845 507.2115 438.4615 204.8077110.01 511.5385 525.48075 533.6538 464.4231 226.9231115.22 537.5 551.4423 559.6153 491.3461 245.1923120.12 561.5385 576.92305 585.0961 518.2692 268.2692125.09 587.9808 603.36535 611.5384 546.1538 291.3461130.07 615.8654 631.24995 637.0192 574.0384 311.5384135.04 640.3846 656.24995 662.0192 602.8846 334.6154140.02 669.2308 684.61535 688.9423 630.7692 357.6923154.94 744.2307 759.1345 758.6538 712.5 424.0384155.17 750.4808 763.94225 762.0192 722.1153 429.8077160.07 775 788.46145 787.5 750 451.9231165.05 803.3653 816.3461 814.423 779.8076 475.9615170.02 827.4038 840.3846 838.4615 807.6923 499.0384175.23 853.3653 865.8653 864.9038 725 525.9615180.05 876.4423 893.26915 880.2884 764.4231 557.6923185.18 900.9615 919.2307 908.6538 799.0384 588.4615190.11 923.5577 944.7115 941.3459 848.0768 620.1923195.05 947.5961 972.1153 969.7117 884.6153 648.0768

56

199.9 970.1922 999.03815 996.6345 913.4614 675.9615205 997.5961 1030.2885 1025.961 949.9999 708.6538

210.05 1021.634 1056.25 1052.404 985.5768 730.7692215.18 1048.077 1085.577 1081.731 999.9999 753.8461220.42 1074.039 1112.019 1108.654 1039.423 775.9615225.36 1080.289 1117.3075 1113.462 1047.115 782.6923229.13 1119.231 1160.096 1158.654 1084.615 831.7307

235 1152.885 1195.673 1149.039 1129.808 854.8076240.17 1177.885 1223.077 1171.154 1162.5 882.6922245.08 1194.712 1241.827 1193.269 1225 902.8845250.2 1228.365 1277.404 1226.443 1280.769 939.423

255.02 1252.885 1303.3655 1243.269 1327.885 965.3845268 1318.27 1370.673 1296.635 1411.538 1033.654

AVERAGE STRAIN GAGE READINGSBOTTOM FLANGE - RIGHT STIFF. (micro-strain)

LOAD Inner Middle Outer at 0.25" at 2.75"0 1E+30 1E+30 5E+29 0.001 0.0010 -5.28846 -6.73077 -6.25 0.961538 1.923077

5.2 23.07692 23.55769 24.03846 22.11538 5.76923110.2 52.40384 53.84615 53.36538 38.46154 3.84615415.2 79.32694 81.73078 80.76925 55.76923 8.65384620.1 106.25 109.1346 107.6923 76.92308 23.0769225.2 133.1731 137.5 135.5769 98.07691 35.5769230.2 157.2115 161.5384 159.1346 117.3077 49.0384635.2 183.1731 187.5 184.1346 138.4615 63.4615440.2 209.1346 213.9423 209.1346 159.6154 78.84615

45.18 233.6539 238.9423 232.2115 179.8077 95.192350.1 258.6539 263.9423 257.6923 201.9231 112.5

55.13 283.6539 288.4615 281.7308 223.0769 129.807760.05 307.2115 313.4615 307.2116 244.2308 150

65.1 333.1731 338.4615 332.6923 266.3461 173.076970.06 359.1346 365.3846 359.1346 289.4231 192.307775.03 384.6154 390.8654 383.1731 311.5384 214.423180.16 411.5385 417.7885 409.6154 335.5769 234.615485.14 436.0577 442.3077 432.6923 358.6538 256.730890.15 460.5769 467.3077 455.7693 381.7308 275.961595.16 486.5385 493.2692 480.2885 405.7692 298.0769

99.9 511.0577 517.3077 501.9231 427.8846 316.3461105.11 536.5385 541.8269 525 452.8846 339.423110.01 561.5384 565.8654 547.5961 476.9231 361.5384115.22 587.5 590.8654 569.7115 501.9231 382.6923120.12 611.5385 613.4616 590.3846 525.9615 405.7692

57

125.09 637.0192 637.9808 611.0577 550.9615 428.8461130.07 662.9808 662.5 633.6538 575.9615 450135.04 686.5384 685.0961 653.3653 600.9615 473.0769140.02 712.0192 709.1346 675.4808 625.9615 497.1154154.94 782.6923 775.4808 736.0576 698.0768 567.3076155.17 789.423 781.2499 739.9038 707.6923 575.3076160.07 812.5 802.8846 760.5769 731.7307 600165.05 837.9807 826.4423 781.25 757.6923 625170.02 864.423 851.4422 804.8076 785.5768 655.7692175.23 889.4231 874.0384 824.5192 813.4615 680.7692180.05 908.6538 892.3077 840.3845 838.4615 703.8461185.18 931.25 913.4613 860.0961 864.423 728.8461190.11 951.923 933.173 882.6924 887.4999 753.8461195.05 975.9613 956.25 904.8077 913.4614 778.8461199.9 996.1538 974.519 921.1539 937.4999 797.1153

205 1017.308 995.6728 936.0576 963.4614 821.1538210.05 1037.981 1014.904 956.2499 986.5384 842.3076215.18 1058.173 1033.654 975.0002 1009.615 832.6923220.42 1079.808 1053.846 999.5192 1034.615 830.7692225.36 1082.212 1055.288 1006.731 1043.269 835.5768229.13 1109.616 1083.173 1036.538 1072.115 979.8076

235 1129.808 1102.885 1063.461 1094.231 1100.961240.17 1141.827 1122.116 1077.885 1107.692 1305.769245.08 1147.115 1130.288 1084.135 1115.385 1425.961250.2 1167.789 1155.289 1112.019 1137.5 1538.461

255.02 1183.173 1184.135 1140.866 1151.923 1544.231268 1231.25 1241.827 1175.481 1192.308 1600.961

AVERAGE STRAIN GAGE READINGSTOP FLANGE - LEFT STIFF. (micro-strain)

LOAD Inner Middle Outer at 0.25" at 2.75"0 1E+30 1E+30 1E+30 0.001 0.0010 -16.3462 -12.980767 -15.8654 0.961538 0.961538

5.2 2.40385 6.25 2.884615 13.46154 -6.7307710.2 24.51923 26.92308 22.59616 22.11538 -24.038515.2 43.75 47.596127 42.30771 34.61538 -28.846220.1 65.86539 71.153854 66.34616 51.92308 -20.192325.2 89.90385 94.71152 90.38462 70.1923 -8.6538530.2 110.0961 115.86537 111.5385 87.49999 2.88461535.2 132.2116 139.42308 136.0577 107.6923 16.3461540.2 155.7692 162.98077 160.0962 127.8846 32.69231

45.18 176.9231 186.05765 183.1731 148.0769 5050.1 199.5193 209.1346 205.2885 169.2308 68.26923

58

55.13 223.0769 233.6538 228.8461 190.3846 88.4615360.05 244.2308 255.7692 250.9616 211.5384 108.6538

65.1 268.2692 281.24995 276.9231 234.6154 131.730870.06 294.2307 307.21155 302.4038 257.6923 155.769275.03 318.75 335.5769 330.2885 278.8461 179.807780.16 344.2308 361.05765 356.7307 302.8846 202.884685.14 367.7885 386.05765 381.25 326.923 228.846190.15 390.3846 410.5769 406.25 349.0384 251.923195.16 417.7885 438.94225 434.6154 373.0769 277.8846

99.9 439.4231 462.0192 458.1731 394.2308 300.9615105.11 463.4615 487.0192 481.7308 420.1923 328.8461110.01 488.4615 513.46155 509.1346 443.2692 355.7692115.22 512.0193 538.46155 533.6539 467.3077 380.7692120.12 535.0961 562.98075 558.6538 491.3461 408.6538125.09 562.9808 592.7884 587.9808 517.3077 435.5769130.07 587.5 619.2307 614.4231 542.3076 462.5135.04 610.5769 642.7884 638.9423 566.3461 490.3846140.02 636.5385 670.19225 663.4615 592.3076 518.2692154.94 706.7307 743.26915 735.5769 661.5384 595.1923155.17 712.0192 746.15375 737.4999 670.1923 604.8076160.07 735.0962 769.71145 761.0576 696.1538 632.6923165.05 762.5 798.55765 787.4999 723.0768 663.4615170.02 786.5384 822.1153 808.6538 750 692.3076175.23 811.5384 846.63455 831.25 777.8845 777.8845180.05 834.6154 872.59605 854.8076 806.7307 806.7307185.18 859.1345 898.5576 882.2115 832.6923 832.6923190.11 886.0577 930.28835 912.9807 859.6153 859.6153195.05 911.5384 958.6536 937.0192 886.5384 886.5384199.9 938.4615 990.8654 970.673 917.3076 917.3076

205 966.3459 1021.1536 999.5192 944.2307 944.2307210.05 994.7115 1053.846 942.3076 975.9614 975.9614215.18 1023.077 1084.615 958.1733 1005.769 1005.769220.42 1050.962 1113.4615 892.7886 1036.538 1036.538225.36 1057.693 1120.673 884.1343 1046.154 1046.154229.13 1092.308 1160.096 916.8269 1077.885 1077.885

235 1114.904 1189.9035 938.4614 1103.846 1103.846240.17 1133.173 1219.2305 1216.346 1124.038 1124.038245.08 1153.366 1247.596 1275.481 1139.423 1139.423250.2 1187.981 1274.519 1339.423 1173.077 1173.077

255.02 1210.096 1299.519 1404.327 1192.308 1192.308268 1263.942 1367.7885 1497.596 1243.269 1243.269

59

AVERAGE STRAIN GAGE READINGSTOP FLANGE - RIGHT STIFF. (micro-strain)

LOAD Inner Middle Outer at 0.25" at 2.75"0 1E+30 1E+30 1E+30 0.001 0.0010 -14.9038 -7.21154 -5.28846 0.961538 0.961538

5.2 11.0577 22.11539 24.51923 12.5 -28.846210.2 39.90384 52.40387 56.24998 26.92308 -32.692315.2 65.86539 80.28844 84.6154 45.19231 -2520.1 92.78846 108.6539 113.4615 66.34615 -7.6923125.2 120.1923 137.0192 142.3077 88.46153 12.530.2 142.3077 162.0192 167.3077 110.5769 30.7692335.2 167.7885 187.9807 192.7885 131.7308 50.9615440.2 192.7885 214.4231 219.2308 154.8077 72.11538

45.18 215.3846 239.4231 242.7885 177.8846 93.2692250.1 239.4231 264.4231 268.2692 200.9615 116.3462

55.13 263.4616 290.3846 292.3077 224.0384 139.423160.05 286.0577 315.3846 316.3461 247.1154 162.5

65.1 312.0192 340.3846 341.3462 271.1538 187.570.06 338.4616 366.8269 366.3462 296.1538 212.575.03 364.9039 392.3077 390.8654 319.2308 237.580.16 390.8654 420.1923 416.8269 345.1923 264.423185.14 414.9038 443.2692 438.9423 369.2308 289.423190.15 438.9423 467.7885 462.0192 394.2308 315.384695.16 465.8654 493.75 486.0577 419.2308 341.3461

99.9 488.4615 517.3077 507.6923 443.2692 366.3461105.11 511.5384 540.8654 530.2885 469.2307 392.3077110.01 535.5769 564.9038 552.4038 493.2692 418.2692115.22 558.6538 589.4231 578.3654 520.1923 450120.12 581.7308 611.5385 598.5576 545.1923 475.9615125.09 607.6923 635.5769 620.1923 571.1538 501.9231130.07 632.2115 659.6154 642.7884 597.1154 528.8461135.04 654.8076 681.7308 662.5 623.0768 554.8076140.02 680.2884 706.25 686.0577 649.0384 583.6538154.94 749.5192 773.0768 748.0768 722.1153 660.5768155.17 755.2885 777.4038 751.4423 731.7307 671.1538160.07 777.8846 799.0384 771.1538 757.6923 697.1153165.05 801.4423 821.1538 791.3461 783.6538 726.9231170.02 829.3269 849.0384 817.3077 813.4615 764.4231175.23 851.923 869.7115 837.0192 840.3845 792.3076180.05 867.3076 887.0192 850 866.3461 821.1538185.18 888.4615 908.6538 872.5961 889.423 850.9615190.11 907.2115 929.8076 897.5961 911.5384 890.3845195.05 930.7692 952.4038 921.1538 935.5768 920.1922199.9 949.5192 969.7115 937.9807 959.6153 960.5768

60

205 970.1923 988.9422 953.8461 983.6538 985.5768210.05 987.0192 1006.731 972.1153 1005.769 1025215.18 1007.212 1022.597 988.4615 1030.769 1054.808220.42 1027.885 1040.866 1007.212 1055.769 1086.538225.36 1031.731 1042.308 1009.615 1065.385 1102.885229.13 1060.577 1069.231 1035.577 1096.154 1124.038

235 1083.173 1088.943 1057.693 1125 1116.346240.17 1101.923 1104.327 1074.519 1149.038 1137.5245.08 1111.539 1112.019 1082.212 1162.5 1133.654250.2 1128.366 1150.481 1085.577 1225.961 1166.346

255.02 1166.347 1176.923 1112.02 1247.115 1192.308268 1247.116 1219.712 1148.077 1324.038 1211.538

61

B.2 ABAQUS Input Data File

*HEADINGW16X45 COLUMN WITH 2 3/4X3X14-7/8" STIFFENERSS8R ELEMENTS 6/19/96LOAD = 150 kips Test 1

*NODE**BOTTOM FLANGE NODES1,1.0,0.5,0.282525,17.0,0.5,0.282526,1.0,2.2588,0.282550,17.0,2.2588,0.282551,1.0,4.0175,0.282575,17.0,4.0175,0.282576,1.0,5.7763,0.2825100,17.0,5.7763,0.2825101,1.0,7.535,0.2825125,17.0,7.535,0.2825**WEB NODES126,1.0,4.0175,4.315150,17.0,4.0175,4.315151,1.0,4.0175,8.3475175,17.0,4.0175,8.3475176,1.0,4.0175,12.38200,17.0,4.0175,12.38201,1.0,4.0175,16.413225,17.0,4.0175,16.413**TOP FLANGE NODES226,1.0,0.5,16.413250,17.0,0.5,16.413251,1.0,2.2588,16.413275,17.0,2.2588,16.413276,1.0,5.7763,16.413300,17.0,5.7763,16.413301,1.0,7.535,16.413325,17.0,7.535,16.413**STIFFENER NODES401,9.0,7.0175,0.2825425,9.0,7.0175,16.413426,9.0,5.5175,0.2825450,9.0,5.5175,16.413451,9.0,4.0175,0.2825475,9.0,4.0175,16.413476,9.0,2.5175,0.2825500,9.0,2.5175,16.413501,9.0,1.0175,0.2825525,9.0,1.0175,16.413**FLANGE INTERMEDIATE NODES13,9.0,0.5,0.282538,9.0,2.2588,0.282563,9.0,4.0175,0.282588,9.0,5.7763,0.2825113,9.0,7.535,0.2825238,9.0,0.5,16.4125

62

263,9.0,2.2588,16.413288,9.0,5.7763,16.413313,9.0,7.535,16.413**WEB INTERMEDIATE NODES138,9.0,4.0175,4.315163,9.0,4.0175,8.3475188,9.0,4.0175,12.38213,9.0,4.0175,16.413**SUPPLEMENTAL NODES1001,1.0,1.0175,0.28251025,17.0,1.0175,0.28251026,1.0,2.5175,0.28251050,17.0,2.5175,0.28251051,1.0,5.5175,0.28251075,17.0,5.5175,0.28251076,1.0,7.0175,0.28251100,17.0,7.0175,0.2825**2001,1.0,1.0175,16.4132025,17.0,1.0175,16.4132026,1.0,2.5175,16.4132050,17.0,2.5175,16.4132051,1.0,5.5175,16.4132075,17.0,5.5175,16.4132076,1.0,7.0175,16.4132100,17.0,7.0175,16.413**INTERMEDIATE NODES1013,9.0,1.0175,0.28251038,9.0,2.5175,0.28251063,9.0,5.5175,0.28251088,9.0,7.0175,0.28252013,9.0,1.0175,16.4132038,9.0,2.5175,16.4132063,9.0,5.5175,16.4132088,9.0,7.0175,16.413*NGEN,NSET=BOTFLG1,1326,3851,6376,88101,1131001,10131026,10381051,10631076,1088*NGEN,NSET=NBOTFLG13,2538,5063,7588,100113,1251013,10251038,10501063,1075

63

1088,1100**WEB INTERMEDIATE NODES*NGEN,NSET=NWEB138,150163,175188,200213,225*NGEN,NSET=WEB126,138151,163176,188201,213**TOP FLANGE INTERMEDIATE NODES*NGEN,NSET=TOPFLG226,238251,263276,288301,3132001,20132026,20382051,20632076,2088*NGEN,NSET=NTOPFLG238,250263,275288,300313,3252013,20252038,20502063,20752088,2100**NODES FOR STIFFENER 1*NGEN,NSET=LSTIFF401,425426,450451,475**NODES FOR STIFFENER 2*NGEN,NSET=RSTIFF451,475476,500501,525**NODES TO BE LOADED*NSET,NSET=NLOAD425,525*NSET,NSET=SLOAD450,475,500**NODES FIXED AT WALL*NSET,NSET=NFIXEDNBOTFLG,BOTFLG,401,426,451,476,501**GENERATE ELEMENTS*ELEMENT, TYPE=S8R1,1,3,28,26,2,1003,27,100113,26,28,53,51,27,1028,52,102625,51,53,78,76,52,1053,77,1051

64

37,76,78,103,101,77,1078,102,107649,51,53,153,151,52,128,152,12661,151,153,203,201,152,178,202,17673,226,228,253,251,227,2003,252,200185,251,253,203,201,252,2028,202,202697,201,203,278,276,202,2053,277,2051109,276,278,303,301,277,2078,302,2076121,401,403,453,451,402,428,452,426133,451,453,503,501,452,478,502,476*ELGEN,ELSET=EBOTFLG1,12,2,1,113,12,2,1,125,12,2,1,137,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=EBOTFLG0.565*ELGEN,ELSET=EWEB49,12,2,1,161,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=EWEB0.345*ELGEN,ELSET=ETOPFLG73,12,2,1,185,12,2,1,197,12,2,1,1109,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=ETOPFLG0.565*ELGEN,ELSET=ESTIFF121,12,2,1,1133,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=ESTIFF0.75*ELSET,ELSET=EOUTPUT,GENERATE121,145,1*NSET,NSET=DEFLECTLSTIFF,RSTIFF**TIE STIFFENER NODES TO FLANGE NODES*MPCTIE,1088,401TIE,1063,426TIE,63,451TIE,1038,476TIE,1013,501TIE,2088,425TIE,2063,450TIE,213,475TIE,2038,500TIE,2013,525*MATERIAL,NAME=STEEL*ELASTIC29000.0,0.3*BOUNDARYNFIXED,1,3

65

*STEP*STATIC*CLOADNLOAD,3,18.75SLOAD,3,37.5*EL PRINT,ELSET=EOUTPUT,SUMMARY=NO,POSITION=NODESS11*END STEP

66

APPENDIX CTEST 2 Results

67

C.1 Experimental Data

Load Micro-strain: Stiffener R Load Micro-strain: Stiffener L(kips) 0.75 in. 1.5 in. 2.25 in. (kips) 0.75 in. 1.5 in. 2.25 in.

0 3.5 3.5 3.5 0 8.5 9.5 10.55.35 41.34616 45.19231 49.51923 5.35 37.5 38.46154 39.4230810.5 80.76923 86.05769 93.26922 10.5 77.40385 81.73077 84.61538

15.18 112.9808 119.7115 128.3654 15.18 112.9808 120.6731 126.442320.5 152.4039 161.0577 171.6346 20.5 155.7692 166.3462 174.519225.2 187.9808 198.5577 211.5385 25.2 190.8654 203.8461 213.942330.2 225.9616 238.9423 255.2885 30.2 228.8461 243.75 254.326935.1 262.9808 278.8461 298.5577 35.1 265.3846 282.6923 295.192340 300.4808 319.7115 341.3462 40 302.8846 322.1154 335.5769

45.1 338.9423 360.0961 385.0961 45.1 341.3461 362.0192 376.923150 376.4423 400.4808 428.3654 50 378.3654 401.4423 416.826955 413.9423 441.3461 472.1154 55 416.3462 440.3846 457.211560 452.4038 481.7308 515.3846 60 454.3269 480.2884 497.5962

64.95 490.8654 523.5577 559.6154 64.95 491.8269 519.7116 538.461670.1 531.25 566.8269 606.7307 70.1 532.2115 562.0192 581.7307

75.13 570.1923 608.6539 650.4808 75.13 570.673 602.4038 623.076980 607.6922 649.0384 693.75 80 608.6538 641.8269 663.4615

85.1 647.1154 690.8654 737.9808 85.1 646.6346 681.7308 704.807790 684.6154 731.25 781.25 90 684.6154 721.6346 745.1923

95.1 723.0769 772.5961 825.9615 95.1 723.0769 762.0192 787.0192100 762.0192 813.4615 869.2307 100 760.5769 801.4423 826.923105 800 854.3269 913.4615 105 798.5576 841.3461 868.2692110 838.9422 897.1153 958.6538 110 837.5 881.7307 909.1346

115.16 879.3269 939.423 1004.807 115.16 876.923 923.0769 950.9615122.8 938.4615 1003.365 1073.077 122.8 935.0961 983.6538 1013.461125 956.2499 1022.596 1093.269 125 952.4038 1001.442 1031.731130 995.1923 1064.423 1138.462 130 990.8653 1042.308 1072.596135 1034.135 1106.731 1183.654 135 1028.846 1081.731 1113.462

140.1 1074.52 1148.558 1229.808 140.1 1068.269 1122.596 1155.289145 1112.981 1191.346 1275.481 145 1104.808 1161.058 1193.75

150.2 1155.288 1237.019 1325.962 150.2 1144.231 1200.961 1232.212155.2 1195.192 1281.25 1373.077 155.2 1181.731 1239.423 1271.635165.5 1276.443 1368.269 1467.308 165.5 1259.616 1319.712 1353.366170.1 1312.981 1408.173 1510.577 170.1 1294.231 1355.288 1389.423175 1347.116 1444.712 1549.519 175 1326.923 1389.423 1423.077180 1390.866 1492.308 1600.481 180 1369.712 1433.654 1468.269

186.3 1440.385 1544.712 1657.212 186.3 1418.269 1484.135 1520.192190.3 1472.596 1578.846 1693.27 190.3 1449.039 1515.866 1552.404195 1510.096 1619.231 1737.019 195 1485.577 1553.366 1589.423201 1557.211 1669.712 1790.866 201 1531.731 1601.442 1638.462

68

204.5 1584.135 1699.039 1822.596 204.5 1557.693 1628.366 1665.385210.06 1627.885 1746.635 1873.558 210.06 1600.481 1672.116 1709.135215.42 1670.673 1792.308 1922.596 215.42 1641.827 1715.865 1753.366220.1 1707.693 1832.212 1965.866 220.1 1678.365 1752.885 1791.827225.05 1747.116 1874.52 2012.019 225.05 1716.827 1792.788 1831.25230.12 1787.019 1918.269 2060.096 230.12 1756.25 1833.654 1873.077235.2 1827.404 1961.539 2107.692 235.2 1796.154 1875 1916.827240 1866.346 2004.808 2159.135 240 1834.616 1915.385 1957.693245 1907.692 2051.442 2212.981 245 1875.962 1959.615 2003.846

250.5 1952.885 2100.962 2270.192 250.5 1920.673 2007.212 2053.846255.1 2011.539 2130.769 2460.096 255.1 1958.173 2041.346 2085.096260 1991.346 2169.712 2723.558 260 1982.212 2048.558 2110.5770 -72.5962 -3.36538 359.1346 0 -26.4423 -59.6154 -70.6731

Load Micro-strain: Web R(kips) 1 in. 2 in. 3 in. 4 in. 5 in. 6 in. 7in.

0 28 29 30 31 32 33 345.35 11.53846 3.846156 -0.48077 -1.92308 -1.92308 -1.92308 -1.9230810.5 27.88462 11.53846 2.403845 -1.44231 -3.36538 -2.88462 -3.84616

15.18 45.19231 19.71154 4.80769 -0.96154 -4.32692 -4.8077 -5.7692320.5 68.75 31.73077 10.09616 0.961535 -4.32693 -5.28846 -7.6923125.2 89.90384 42.78846 15.38462 2.403845 -3.84616 -5.76923 -8.6538530.2 112.9808 54.80769 20.67308 4.32692 -3.84616 -6.73077 -11.057735.1 136.0577 67.30769 25.96153 6.25 -3.84616 -8.17308 -12.980840 160.577 80.76925 32.69231 9.615385 -3.36539 -8.65385 -14.4231

45.1 185.577 94.23075 38.46154 11.53847 -3.36539 -9.61539 -16.346250 211.0577 108.6539 45.19231 15.38461 -2.40385 -9.61538 -17.788555 236.5384 122.5962 51.4423 17.30769 -1.92308 -11.5385 -20.192360 262.9808 137.0193 58.65384 20.67308 -0.96154 -11.5385 -21.6346

64.95 288.9423 151.9231 65.8654 23.55769 -0.48077 -12.5 -23.076970.1 317.3077 167.7885 73.07691 26.92308 0.48077 -12.5 -25

75.13 343.75 182.2115 80.28845 29.8077 0.48077 -13.9423 -26.923180 370.6731 197.1154 87.50001 33.17308 1.923075 -13.9423 -28.3654

85.1 397.1154 212.0192 94.71155 36.05769 2.403845 -14.9038 -30.288590 423.5577 226.9231 101.4423 39.42308 2.88461 -14.4231 -31.7308

95.1 449.5193 240.8654 108.1731 42.30769 3.84615 -15.8654 -34.1346100 476.4423 255.7692 115.3846 45.1923 4.80769 -16.3462 -35.5769105 502.8846 270.6731 122.1154 48.55768 5.28846 -16.8269 -37.0192110 530.2885 286.0577 129.8077 51.44232 6.25 -17.3077 -38.4615

115.16 557.6923 300.9616 137.5 54.32691 6.730765 -17.7885 -40.8654122.8 598.5577 324.0385 148.5577 60.09614 8.653845 -18.75 -42.7885125 611.0577 330.7692 151.4423 61.05771 8.17308 -19.2308 -44.2307130 637.9807 346.6346 159.6154 64.90387 9.61538 -19.7115 -45.6731135 665.3846 361.5384 166.3462 67.30768 9.615385 -20.6731 -47.5962

140.1 693.2692 377.4038 174.0385 71.15384 11.05769 -21.1538 -49.0385

69

145 719.7116 392.3077 181.25 74.03848 12.01923 -21.6346 -50.4808150.2 748.5577 408.6539 188.9423 77.88462 12.5 -22.1154 -52.4039155.2 775.4807 423.5577 196.1539 80.76921 12.98077 -22.5962 -54.3269165.5 831.25 454.8077 211.5385 87.98076 15.38462 -24.0385 -57.6923170.1 857.2115 470.1923 218.75 90.86539 15.86538 -24.5192 -59.6154175 880.7692 483.6539 225.4808 94.71155 17.78846 -25 -60.5769180 912.4999 500.9615 233.6539 98.07691 18.26923 -25.4808 -62.9808

186.3 947.5961 521.1538 243.75 102.8846 19.71153 -25.4808 -64.9039190.3 970.1922 533.6538 250 105.2885 20.19231 -26.4423 -65.8654195 997.596 550 258.1731 109.1346 21.15384 -26.4423 -67.3077201 1031.731 569.2308 267.3077 113.9423 22.59615 -26.9231 -69.7115

204.5 1051.923 580.7692 273.0769 116.3461 23.55769 -27.4038 -71.1538210.06 1084.615 599.5192 282.6923 121.1538 25 -27.8846 -72.5962215.42 1116.346 617.7884 291.3462 125 26.44229 -28.8462 -74.5192220.1 1144.231 634.1346 300 128.8462 27.88461 -28.8462 -75.9616225.05 1174.039 651.4422 308.1731 133.1731 28.36536 -29.3269 -77.8846230.12 1204.808 669.7115 317.7885 137.9808 29.80768 -29.3269 -79.3269235.2 1236.058 687.5 326.4423 142.3077 31.73077 -29.8077 -81.25240 1266.827 705.2884 335.5769 146.6346 33.17307 -29.8077 -82.2115245 1298.558 723.5577 344.7116 150.9615 34.61539 -30.2885 -84.1346

250.5 1333.654 744.7115 355.2885 155.7692 37.01922 -30.7692 -86.0577255.1 1370.673 765.8653 365.8654 161.0577 38.46153 -31.25 -88.4615260 1423.077 795.673 380.2885 167.7885 39.90384 -31.25 -90.86540 66.82692 37.98077 18.26923 8.653846 2.884615 0 -3.36538

Load Micro-strain: Web L(kips) 1 in. 2 in. 3 in. 4 in. 5 in. 6 in. 7 in.

0 35 36 37 38 39 40 415.35 51.44231 32.21154 17.78846 8.653845 3.84615 0 -2.4038510.5 95.67306 60.09616 33.17308 15.86539 7.21154 0.480765 -3.84616

15.18 130.2885 80.76923 44.23077 21.15384 8.653845 0 -6.7307720.5 168.2693 103.3654 56.73077 26.44231 10.57693 0.48077 -8.1730825.2 200.4808 122.5962 66.82692 31.73077 12.98077 0 -9.1346230.2 234.6154 142.3077 77.40384 36.05769 14.90385 0 -10.576935.1 266.8269 161.0577 87.5 40.38462 16.34615 -0.48077 -12.980840 298.5577 179.3269 96.63461 44.71154 17.78846 -0.48077 -14.4231

45.1 330.2884 197.1154 106.25 49.03846 19.23077 -0.48077 -16.346250 361.0577 214.9038 115.3846 53.36538 20.67308 -0.96154 -17.788555 391.3462 231.25 124.0385 56.25 21.63462 -1.44231 -20.673160 421.6346 249.0385 133.1731 60.57692 23.07692 -1.92308 -22.5962

64.95 451.9231 266.3462 142.3077 63.9423 24.03846 -2.40385 -23.557770.1 483.6539 284.6154 151.4424 68.26923 25.96154 -2.88462 -25.9615

75.13 514.4231 300.9615 160.0962 72.11538 26.44231 -2.88462 -27.884680 543.75 318.2692 169.2308 75.96153 28.36538 -3.36538 -29.3269

85.1 574.0385 335.0962 177.4038 79.32693 29.80769 -3.84615 -30.2885

70

90 603.8462 352.4039 186.5385 83.65383 30.76923 -3.84616 -32.211595.1 635.0961 369.7115 195.1923 87.50001 31.73077 -4.32693 -34.6154100 664.4231 386.5385 204.3269 91.34615 33.17307 -4.80769 -36.0577105 694.7115 403.3654 212.9808 94.71153 34.13461 -5.28847 -37.9808110 724.9999 420.6731 221.6346 99.03848 36.05769 -5.28847 -39.4231

115.16 755.7692 438.4615 230.7692 102.8846 37.01923 -5.76923 -41.3462122.8 801.923 463.9423 244.2308 108.6538 38.94231 -6.25 -43.75125 814.9038 471.1539 248.0769 109.6154 39.42307 -6.25 -44.7115130 844.7115 488.4615 257.2115 113.4616 40.86538 -6.25 -46.1538135 874.5192 504.8077 265.3846 116.8269 41.82692 -7.21154 -48.0769

140.1 904.8076 522.1154 273.5577 120.6731 43.26923 -7.21154 -50145 933.173 538.4616 281.7308 124.0385 44.23077 -8.17308 -51.9231

150.2 964.423 555.7692 290.8654 128.3654 45.67307 -8.17308 -53.3654155.2 994.2309 573.0769 300 131.7308 46.15384 -9.13462 -55.2885165.5 1055.289 606.7307 317.3077 139.4231 49.03846 -9.13462 -58.6539170.1 1082.212 622.1154 324.5192 142.7885 50 -10.0962 -60.0961175 1106.731 635.5768 331.7308 145.1923 50.96154 -10.0962 -61.0577180 1139.423 653.8462 340.8654 149.5193 52.40384 -10.5769 -63.9423

186.3 1175.962 674.5192 351.9231 153.8462 53.84615 -11.0577 -65.8654190.3 1199.039 687.5 357.6923 156.25 54.32692 -11.5385 -67.3077195 1225.481 701.923 365.8654 159.6154 55.28846 -11.5385 -68.2692201 1260.096 721.1538 375 163.4616 56.25 -12.0192 -70.6731

204.5 1278.366 730.7692 379.8077 165.3847 57.21154 -12.9808 -71.6346210.06 1309.135 748.0769 388.4616 169.2308 58.17307 -13.4615 -73.5577215.42 1338.462 764.423 396.6346 172.1154 58.65385 -13.9423 -75.4808220.1 1364.423 778.3653 403.3654 175 59.61538 -14.4231 -77.4039225.05 1390.865 793.2692 410.0962 177.8846 60.09615 -14.9039 -78.8462230.12 1417.788 807.6923 417.3077 180.2885 60.57692 -15.8654 -80.7692235.2 1444.231 822.1153 424.5192 183.1731 61.05769 -16.3462 -82.6923240 1471.635 836.5384 431.25 186.0577 62.01923 -16.8269 -84.1346245 1499.038 850.9615 438.4615 188.9423 62.5 -18.2692 -86.5385

250.5 1528.846 867.3077 446.6346 191.3462 63.46153 -18.75 -87.9808255.1 1562.5 885.0961 455.2885 195.1923 64.42308 -19.2308 -90.3846260 1614.423 912.9809 469.2308 200.4808 65.86538 -20.1923 -93.26930 83.17308 44.23077 23.55769 11.05769 5.28846 0 -2.40385

71

C.2 ABAQUS Input Data File

*NODEW8X48 COLUMN WITH 2 3/8X3X7-1/8" STIFFENERSS8R ELEMENTS 6/19/96LOAD = 150 kips Test 2

**BOTTOM FLANGE NODES1,1.0,0.5,0.342525,19.0,0.5,0.342526,1.0,2.5275,0.342550,19.0,2.5275,0.342551,1.0,4.555,0.342575,19.0,4.555,0.342576,1.0,6.5825,0.3425100,19.0,6.5825,0.3425101,1.0,8.61,0.3425125,19.0,8.61,0.3425**WEB NODES126,1.0,4.555,2.4675150,19.0,4.555,2.4675151,1.0,4.555,4.5825175,19.0,4.555,4.5825176,1.0,4.555,6.7175200,19.0,4.555,6.7175201,1.0,4.555,8.8425225,19.0,4.555,8.8425**TOP FLANGE NODES226,1.0,0.5,8.8425250,19.0,0.5,8.8425251,1.0,2.5275,8.8425275,19.0,2.5275,8.8425276,1.0,6.5875,8.8425300,19.0,6.5875,8.8425301,1.0,8.61,8.8425325,19.0,8.61,8.8425**STIFFENER NODES401,10.0,7.555,0.3425425,10.0,7.555,8.8425426,10.0,6.055,0.3425450,10.0,6.055,8.8425451,10.0,4.555,0.3425475,10.0,4.555,8.8425476,10.0,3.055,0.3425500,10.0,3.055,8.8425501,10.0,1.555,0.3425525,10.0,1.555,8.8425**FLANGE INTERMEDIATE NODES13,10.0,0.5,0.342538,10.0,2.5275,0.342563,10.0,4.555,0.342588,10.0,6.5825,0.3425113,10.0,8.61,0.3425238,10.0,0.5,8.8425263,10.0,2.5275,8.8425

72

288,10.0,6.5825,8.8425313,10.0,8.61,8.8425**WEB INTERMEDIATE NODES138,10.0,4.555,2.4675163,10.0,4.555,4.5925188,10.0,4.555,6.7175213,10.0,4.555,8.8425**SUPPLEMENTAL NODES1001,1.0,1.555,0.34251025,19.0,1.555,0.34251026,1.0,3.055,0.34251050,19.0,3.055,0.34251051,1.0,6.055,0.34251075,19.0,6.055,0.34251076,1.0,7.555,0.34251100,19.0,7.555,0.3425**2001,1.0,1.555,8.84252025,19.0,1.555,8.84252026,1.0,3.055,8.84252050,19.0,3.055,8.84252051,1.0,6.055,8.84252075,19.0,6.055,8.84252076,1.0,7.555,8.84252100,19.0,7.555,8.8425**INTERMEDIATE NODES1013,10.0,1.555,0.34251038,10.0,3.055,0.34251063,10.0,6.055,0.34251088,10.0,7.555,0.34252013,10.0,1.555,8.84252038,10.0,3.055,8.84252063,10.0,6.055,8.84252088,10.0,7.555,8.8425*NGEN,NSET=BOTFLG1,1326,3851,6376,88101,1131001,10131026,10381051,10631076,1088*NGEN,NSET=NBOTFLG13,2538,5063,7588,100113,1251013,10251038,10501063,10751088,1100

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**WEB INTERMEDIATE NODES*NGEN,NSET=NWEB138,150163,175188,200213,225*NGEN,NSET=WEB126,138151,163176,188201,213**TOP FLANGE INTERMEDIATE NODES*NGEN,NSET=TOPFLG226,238251,263276,288301,3132001,20132026,20382051,20632076,2088*NGEN,NSET=NTOPFLG238,250263,275288,300313,3252013,20252038,20502063,20752088,2100**NODES FOR STIFFENER 1*NGEN,NSET=LSTIFF401,425426,450451,475**NODES FOR STIFFENER 2*NGEN,NSET=RSTIFF451,475476,500501,525**NODES TO BE LOADED*NSET,NSET=NLOAD425,525*NSET,NSET=SLOAD450,475,500**NODES FIXED*NSET,NSET=NFIXEDNBOTFLG,BOTFLG,401,426,451,476,501**GENERATE ELEMENTS*ELEMENT,TYPE=S8R1,1,3,28,26,2,1003,27,100113,26,28,53,51,27,1028,52,102625,51,53,78,76,52,1053,77,105137,76,78,103,101,77,1078,102,1076

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49,51,53,153,151,52,128,152,12661,151,153,203,201,152,178,202,17673,226,228,253,251,227,2003,252,200185,251,253,203,201,252,2028,202,202697,201,203,278,276,202,2053,277,2051109,276,278,303,301,277,2078,302,2076121,401,403,453,451,402,428,452,426133,451,453,503,501,452,478,502,476*ELGEN,ELSET=EBOTFLG1,12,2,1,113,12,2,1,125,12,2,1,137,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=EBOTFLG0.685*ELGEN,ELSET=EWEB49,12,2,1,161,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=EWEB0.4*ELGEN,ELSET=ETOPFLG73,12,2,1,185,12,2,1,197,12,2,1,1109,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=ETOPFLG0.685*ELGEN,ELSET=ESTIFF121,12,2,1,1133,12,2,1,1*SHELL SECTION,MATERIAL=STEEL,ELSET=ESTIFF0.375*ELSET,ELSET=EOUTPUT,GENERATE121,145,1*NSET,NSET=DEFLECTLSTIFF,RSTIFF**TIE NODES*MPCTIE,1088,401TIE,1063,426TIE,63,451TIE,1038,476TIE,1013,501TIE,2088,425TIE,2063,450TIE,213,475TIE,2038,500TIE,2013,525*MATERIAL,NAME=STEEL*ELASTIC29000.0,0.3*BOUNDARYNFIXED,1,3*STEP

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*STATIC*CLOADNLOAD,3,18.75SLOAD,3,37.5*EL PRINT,ELSET=EOUTPUT,SUMMARY=NO,POSITION=NODESS11*END STEP

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VITA

Michelle L. Holland

Michelle L. Floyd was born on January 23, 1972 in Norfolk, VA. After graduating from

high school in Newport News, she enrolled at Virginia Tech in 1990. She obtained a Bachelor of

Science in Civil Engineering in December of 1994. In January 1995, she enrolled in Civil

Engineering graduate program, Structures Division, at Virginia Tech in pursuit of a Master of

Science Degree. In July of 1996 she began working as an Associate Engineer for Newport News

Shipbuilding, Submarine Division and was married to R. Cameron Holland IV in September of that

year.