chap_3-structural_bolts .pdf

7/28/2019 chap_3-structural_bolts .pdf

1/45

30

CHAPTER III

STRUCTURAL BOLTS

This chapter provides an in depth discussion of structural bolts including the

materials from which they are made, manufacturing processes, design require-

ments, strength, stiffness and ductility considerations and behavior of instru-

mented bolts. Since the scope of the research was limited to high-strength

structural bolts, discussion of bolt types other than A325 and A490 will be limited

to providing background information.

First, a background of standard bolt grades and material properties for high

strength structural bolts will be presented, including a brief discussion of foreign

bolt specifications. Next, the dimensions and manufacturing techniques of bolts

will be discussed. This will be followed a discussion of common installation and

fabrication techniques. An evaluation of current models for predicting the strength

and stiffness characteristics of bolts is given next, followed by a brief discussion of

ductility. Finally, the results of a comprehensive testing program will be presented

followed by a discussion and conclusions.

3.1 Standard Bolt Grades

Bolts typically used for structural joining applications can be classified based

on three ASTM specifications: A307, A325, and A490. A307 bolts, or black bolts,

are available in diameters ranging from 1/4 to 4 and in Grades A, B, and C.

Grade A bolts are intended for general applications and have a specified minimum


2/45

31

tensile strength of 60 ksi. Grade B bolts are intended for flange joints in piping

systems and have a tensile strength of 60 - 100 ksi. Grade C bolts are available

as anchor bolts or studs manufactured from A36 steel with a tensile strength of 58

- 80 ksi (ASTM A307-94).

A325 bolts are available standard diameters ranging from 1/2 to 1-1/2.

Bolts with diameters up to and including 1 have a minimum tensile strength of

120 ksi and bolts with larger diameters have a minimum tensile strength of 105

ksi. A325 are available in two types. Type 1 bolts are manufactured from medium

carbon, carbon boron, or medium carbon alloy steel. A325 Type 3 bolts are made

from corrosion resistant steel with weathering characteristics comparable to A588

steel. The A325 Type 2 bolt specification was withdrawn in November of 1991,

but consisted of bolts made from low carbon martensite steel (ASTM A325-97;

Kulak et al., 1987).

A490 bolts have a specified minimum tensile strength of 150 ksi and are

available in three types. A490 Type 1 bolts are available in diameters from 1/2 to

1-1/2 and are manufactured from alloy steel. A490 Type 2 bolts are available in

diameters of 1/2 to 1 and made from low carbon martensite steel. A490 Type 3

bolts are available in diameters from 1/2 to 1-1/2 and are made from corrosion

resistant steel with weathering characteristics comparable to A588 steel (ASTM

A490-97).

3.1.1 Other Bolt Types

Structural bolts other than those described above are also available. Both

the A325 and A490 specifications have metric companions designated A325M

and A490M, respectively. The bolts are designated M16, M20, M22, M24, M27,


3/45

32

M30, and M36. The M indicates that bolt is metric and the following number is

the nominal diameter in millimeters (CISC, 1997; ISO 7411).

The International for Organization Standards (ISO) has introduced a set of

specifications for bolts, nuts and washers that is very similar to the ASTM stan-

dards. ISO 7411 governs high strength structural bolts with large widths across

the flats and ISO 7412 govern high strength structural bolts with short thread

lengths. ISO 898 governs the properties of the material from which bolts are man-

ufactured. Property classes 8.8 and 10.9 correspond closely to ASTM material

specifications for A325 and A490 bolts, respectively. In addition to defining mini-

mum tensile strengths for the materials, the ISO specifies minimum elongations

after fracture that the bolt material must be able to sustain, thus providing mini-

mum ductilities in the specification. Designations for ISO bolts consist of the

specification number followed by the bolt size and property class. An ISO 7411 -

M16 x 80 - 8.8 bolt, for example, is a high strength structural bolt with a diameter

of 16 mm and a length of 80 mm made from material conforming to the 8.8 prop-

erty class. The ISO bolts are available in the same sizes as the A325M and

A490M bolts. A 12 mm diameter bolt is also available but is not recommended for

use (ISO 7411).

The Deutsches Institut fr Normung, or the German Specification, has a bolt

specification very similar to the ISO specification. DIN 6914 is the specification

that governs structural bolts. Like the ISO bolts, they are available in grades 8.8

and 10.9 which are similar to ASTM A325 and A490 bolts, respectively (Steurer,

1996).


4/45

33

3.2 Bolt Materials

The behavior of any structural component is highly dependent on the proper-

ties of material from which it is produced; bolts are no exception. The variations in

the characteristics of different grades and types of bolts is almost entirely due to

the variation of material properties.

3.2.1 Steel Composition

Because steel is invariably the material from which structural bolts are

made, a discussion of its composition is warranted. Typical carbon steel is made

up of iron, carbon, manganese, silicon, copper, phosphorus, sulfur, and other

residual elements. The properties of a heat of steel are largely dependent on the

amount of carbon present. Low carbon steel is typically classified as steel con-

taining between 0.02% and 0.30% carbon, medium carbon steel is typically classi-

fied as steel with carbon levels from 0.30% to 0.70%, and steel with carbon levels

greater than 0.70% is classified as high carbon steel (Pollack, 1988). Carbon is

the principal hardening element in steel. Increasing the level of carbon increases

the steels strength and hardness but at the cost of reduced ductility (AISI, 1986).

A steel is classified as an alloy if certain elements are present in levels

greater than specified limits. Typical alloying elements include manganese, phos-

phorous, sulfur, silicon, nickel, chromium, molybdenum, vanadium, copper, and

boron (AISI, 1986). More desirable hardening and ductility characteristics can be

achieved by using an alloy steel instead of standard carbon steel. Table 3-1 lists

chemical requirements for A325 Type 1, A490 Type 1 and A490 Type 2 bolts

(ASTM A325-97; ASTM A490-97).


5/45

34

* 1-1/2 diameter A490 Type 1 bolts require a carbon content of 0.35-0.53%. Boron shall not be added intentionally. Sufficient elements must be present so as to classify the steel as an alloy by the AISI.

3.2.2 Heat Treatment and Hardness Characteristics

To help increase strength and hardness while maintaining acceptable ductil-

ity levels, high-strength structural bolts must be quenched and tempered. A325

and A490 bolts are heated to a temperature above their transformation tempera-

ture, quenched, and then tempered to a temperature of at least F except for

A490 Type 2 bolts which are tempered at a temperature of at least F (ASTM

A325-97; ASTM A490-97). A325 bolts are typically tempered at F and A490

bolts are typically tempered at F (Baumsta, 1998). The range of hard-

nesses for structural bolts is shown Table 3-2.

Table 3-1: Chemical Requirements for A325 and A490 Bolts.

Element

A325 Type 1 A490

Carbon C Boron C Alloy Type 1* Type 2

C 0.30-0.52% 0.30-0.52% 0.30-0.52% 0.30-0.48% 0.15-0.34%

Mn, min 0.60% 0.60% 0.60% --- 0.70%

P, max 0.040% 0.040% 0.035% 0.040% 0.040%

S 0.050% 0.050% 0.040% 0.040% 0.050%

Si 0.15-0.30% 0.10-0.30% 0.15-0.35% ---

B 0.0005-0.003% 0.0005% min

800

650

800

1200


6/45

35

3.3 Dimensions of High-Strength Fasteners

Figure 3-1 shows standard dimensioning nomenclature for high-strength fas-

teners. Heavy-hex, high-strength bolts are specially sized so that the same size

wrench will fit both the nut and the head of the bolt. Additionally, the thread

length, Lt, of high-strength bolts is shorter than for conventional bolts to allow the

threads to be easily excluded from the shear plane when used in shear. Because

of this, connection designers must take care when specifying the lengths of bolts

to provide enough threads to avoid jamming the nut into the thread runout when

pretensioning the bolt.

Table 3-2: Hardness Requirements for Structural Bolts.

Type Diameter, dB Length

Brinell Rockwell

Min Max Min Max

A307

Grade A1/2 to 4

< 3dB 121 241 69 RB 100 RB

> 3dB --- 241 --- 100 RB

A325

1/2 to 1< 3dB 253 319 25 RC 34 RC

> 3dB --- 319 --- 34 RC

1-1/8 to 1-1/2< 3dB 223 286 19 RC 30 RC

> 3dB --- 286 --- 30 RC

A490 1/2 to 1-1/2< 3dB 311 352 33 RC 38 RC

> 3dB --- 352 --- 38 RC


7/45

36

Figure 3-1: Nomenclature for Heavy-Hex Fastener Dimensions

3.4 Manufacturing Techniques

Bolts are manufactured in one of two basic ways; by forming or threading.

Each of these two manufacturing techniques can be broken down further into sub-

categories. Forming methods include cold heading, warm heading, hot forging or

forming, and turning or screw machining. Threading methods include roll thread-

ing, cut threading, and ground threading (Phebus et al., 1998). ASTM specifica-

tions require that A325 and A490 bolts be either rolled or cut while A307 bolts may

either cold or hot forged, or machined from bar stock (ASTM A307-94; ASTM

A325-97; ASTM A490-97).

Hb

F

Ls

Lb

Lth

ID

OD WT Hn

A325


8/45

37

3.5 Nuts and Washers

Nuts conforming to the A194/A194M or A563 specifications must be used

with A325 and A490 bolts. When washers are used with A325 bolts, they must

conform to either the F436 or F959 specification. When washers are used with

A490 bolts, they must conform to the F436 specification. The use of washers is

discussed further in Section 3.6.2 (ASTM A325-97; ASTM A490-97).

3.6 Bolt Installation

The installation of high-strength fasteners in structural systems must be

closely monitored to ensure that the proper pretension is applied to each bolt.

Variables that influence the installation of bolts include the type of tension control

system used, the type and size of bolts used, and the amount of lubrication

present on the bolts. Although they are permitted to be used as snug tight fasten-

ers, high-strength bolts are usually fully tensioned. To provide adequate preten-

sion, the bolt is tightened until the tension in the bolt approaches or slightly

exceeds the yield point of the bolt, typically 70% of the tensile strength. Table 3-3

shows the required pretensions by bolt type and size (AISC, 1994). The required

pretensions for bolts above 1 in diameter can be difficult to attain. For this rea-

son, fully tensioned bolts larger than 1 in diameter are not often used.


9/45

38

3.6.1 Pretensioning Methods

Several methods of pretensioning are available. They include the turn-of-

the-nut method, calibrated wrench method, and use of direct tension indicators or

tension control bolts.

The turn-of-the-nut method consists of calculating the amount of nut rotation,

past the snug tight condition, that is necessary to induce the required tension in

the bolt. Rotations of to are typical. The calibrated wrench method

consists of using a torque wrench, either manual, electric, or pneumatic, that is

calibrated with a torque-tension tester.

The Skidmoore-Wilhelm torque-tension tester, shown in Figure 3-2, provides

an accurate measure of the bolt tension relative to the torque applied by the

wrench. The tester is a doughnut shaped hydraulic load cell that has been cali-

brated in some unit of force, usually kips. A cross section of the tester is shown in

Figure 3-3. It is made up of an inner piston that slides inside an outer housing.

interchangeable bushings and face plates allow a wide range of bolt sizes to be

tested. As the a bolt is tightened in the tester, forces are exerted on the face plate

Table 3-3: Required Pretension for High-Strength Bolts (kips) (AISC, 1994)

Diameter A325 A490

1/2 12 15

5/8 19 24

3/4 28 35

7/8 39 49

1 51 64

1-1/8 56 80

1-1/4 71 102

1-3/8 85 121

1-1/2 103 148

120 240


10/45

39

and bushing which, in turn, create a hydraulic pressure that can be measured and

converted back into a force. The full stroke of the piston is approximately 0.25.

Figure 3-2: Skidmoore-Wilhelm Type Torque-Tension Tester

Direct tension indicators or load indicator washers, shown in Figure 3-4(a),

are washers that have raised dimples on their face that flatten out against thebase material as the nut is tightened. When the gap between the flat part of the

washer and the base material reaches a set limit, the bolt has reached its full pre-

tension. Different washers are required for A325 and A490 of the same diameter

because of the different pretensioning requirements.


11/45

40

Figure 3-3: Cross section of Skidemoore-Wilhelm Torque-Tension Tester

Tension control or twist-off bolts, shown in Figure 3-4(b), are bolts that have

a spine attached to the threaded end. A special wrench holds the spine and the

nut and turns them relative to each other until the spine shears off. The bolt man-

ufacturer calibrates the bolts so that the spines twist off when the bolt pretension

has reached the specified level.

Retaining Ring

Hydraulic Piston

InterchangableBushing

Outer Housing

InterchangableFace Plate

Hydraulic Oil


12/45

41

Figure 3-4: DTI Washers (a) and Tension Control Bolts (b)

When using the calibrated wrench method or tension control bolts, great

care must be taken to prevent the nut from running up onto the thread runout por-

tion of the bolt. If this happens, either the torque measurements will be errone-

ous, or the spine will twist-off of the tension control bolt without inducing the

desired pretension. Bolts designed for shear in the threads excluded configura-

tion are particularly susceptible to this problem. The problem can be avoided by

using additional washers.1

3.6.2 Bolt Friction

When a high-strength bolt is tensioned by torquing, approximately 40 to 50%

of the applied torque is lost in friction between the bearing faces of the bolt and

the base material and 30 to 40% is lost due to friction between the nut and bolt

threads. This leaves only 10 to 30% of the applied torque to induce the axial pre-

1. The 1994 LRFD, on page 8-8, states that additional washers are permitted to be used

under the nut or under the head when circumstances permit. It is recommended by theauthor, however, that shim plates be used when more than four washers are required.

(a) (b)


13/45

42

tension (Barron et al., 1998a). Reducing the amount of friction in the bolt system

allows the same pretension to be applied with a lower torque.

The torque-tension relationship of bolts can be expressed in its simplest

form as (Novak et al., 1998)

. EQ 3-1

where:

T = the applied torque (k-in)

K = the nut factor

db = the bolt diameter (in)

F = the bolt pretension (kip)

The nut factor is a measure of the friction present in the bolt, nut, and washer sys-

tem. The average nut factor for a 1 diameter A490 bolt as received from the sup-

plier is 0.179, the average nut factor for the same bolt preserved with Johnson

stick wax is 0.275, and the average nut factor for a rusty 1 diameter A490 bolt is

0.389 (Novak et al., 1998). Two of the easiest ways to reduce bolt friction are to

use washers and lubricants.

Washers help to reduce the friction between the bearing surfaces of the nut

face and base material by providing a clean, smooth surface, free of mill scale andrust. The use of washers under the turned element is required by the RCSC

specification when high-strength bolts in standards holes are tensioned by the cal-

ibrated wrench method, or when the yield strength of the base metal is less than

40 ksi (RCSC, 1996). When tension control bolts are used, the nut and washer

T KdbF


14/45

43

that are supplied with the bolt must be used. ASTM F436 hardened washers are

typically used with high-strength bolts.

By using commercially available lubricants, the nut factor can be reduced to

values of 0.050 to 0.100 (Novak et al., 1998). When using lubricants, it is impor-

tant to lubricate both the threads and the bearing faces of the bolt head, nut face,

washers and base material.

3.7 Strength

Of the many characteristics of bolts, strength is the most important. The

possible failure modes of bolts are tensile failure, shear failure, and combined ten-

sile and shear failure.

3.7.1 Tensile Strength

Tensile loading is the most fundamental mode of loading of bolts. The possi-

ble failure mechanisms under axial loading are tension failure of the bolt, stripping

of the bolt threads, and stripping of the nut threads. High-strength fasteners are

designed so that tension failure of the bolt will occur before stripping of the

threads. As a result, the design engineer need only be concerned with tensile

strength of the bolt.

The axial strength of a bolt can be calculated as the ultimate strength of the

bolt material multiplied by the cross sectional area of the bolt. Considering a fail-

ure in the shank of the bolt, the cross sectional area is calculated as shown in

Equation 3-2 (Barron et al., 1998a).

EQ 3-2Ab4db

2


15/45

44

where

Ab = cross sectional area of the bolt shank (in2)

db = nominal diameter of the bolt (in)

Bolts subjected to tension rarely fracture through the shank, though, and

using the area of the shank in capacity calculations can result in an overestimate

of the bolts actual strength. Another alternative is to use the root area of the

threads in capacity calculations, as shown in Equation 3-3 (Barron et al., 1998a).

EQ 3-3

where

Abr = cross sectional area of the bolts root (in2)

nth = number of threads per inch of the bolt

Tests conducted on fasteners show that using the root area for strength cal-

culations yields conservative results. Equation 3-4 is an empirical equation that

returns an area that is midway between the root and shank area (ASTM A490-97;

Barron et al., 1998a).

EQ 3-4

Abr4 db

1.3

nth

2

Abe 4 db

0.9743nth

2


16/45

45

where

Abe = effective cross sectional area of the bolt

It should be noted that Equations 3-3 and 3-4 are not valid for metric bolts.

Equations 3-5 and 3-6 should be used for metric bolts (Barron et al., 1998a).

EQ 3-5

EQ 3-6

where

pb = thread pitch of a bolt (mm)

The number of threads included in the grip of the bolt has an effect on the

bolts capacity. ASTM F606 requires that heavy hex bolts be tensile tested with

four complete threads exposed within the grip. This is in contrast to the six

exposed threads required for standard bolts (ASTM A490-97).

It has been noted in the literature that the tensile strength of a bolt is, to a

small degree, a dependent on the length of threads present in the bolts grip, Ltg.

Testing has demonstrated that the ultimate capacity of bolts with fewer threads in

the grip is slightly larger than the capacity of bolts with many threads present in

the grip. The increase in capacity is not generally regarded as being sufficient to

require a certain number of threads be included or excluded from the grip. The

only requirement is that the end of the bolt be at least flush with the face of the nut

so that all of the threads within the nut are engaged. A general rule of thumb that

Abr4 db 1.3pb( )

2

Abe4 db 0.9382pb( )

2


17/45

46

is often used is to require that two threads of the bolt stick out beyond the face of

the nut.

3.7.1.1 LRFD

An alternative method for the determination of the tensile strength of bolts is

used by the LRFD (AISC, 1994). The capacity is computed as

EQ 3-7

where

Bn = the nominal tensile resistance of the bolt

Ft = the effective tensile strength of the bolt material,

Ab = the nominal area of the bolts shank

Ft is taken as 90 ksi for A325 bolts and 113 ksi for A490 bolts. Table 3-4

shows the ratios of the effective tensile area of a bolt to its gross area. Since Abe

/ Ab is approximately equal to 0.75, Equation 3-7 provides a reasonable estimate

of the bolt strength for the range of bolt sizes typically used for bolted connections.

For design, the nominal tensile resistance of the bolt, Bn, is multiplied by a resis-

tance factor, bf, of 0.75.

Bn FtAb

Ft 0.75Fu


18/45

47

Table 3-4: Nominal and Effective Bolt Areas

3.7.1.2 Eurocode

The Eurocode (1993) predicts the tensile strength of a bolt as

EQ 3-8

where

Bn = the nominal tensile resistance of the bolt

Fu = the tensile strength of the bolt material

Abe = the effective tensile area of the bolt

The ultimate strength of the bolt material is taken as 800 N/mm2 (116 ksi) for

grade 8.8 bolts and 1000 N/mm2 (145 ksi) for grade 10.9 bolts. For design, the

nominal resistance of the bolt is divided by a partial safety factor, Mb, of 1.25.

This results in a design resistance, Bn, of 0.72AbeFu.3.7.2 Shear Strength

In its simplest form, the shear strength of a bolt is calculated by multiplying

the bolt materials ultimate strength, reduced by 40% for shear stress instead of

tensile stress, by the bolts cross sectional area. The cross sectional area

Dia. nth Ab Abe Abr Abe/ Ab Abr / Ab

1/2" 13 0.1963 0.1419 0.1257 0.7227 0.64005/8" 11 0.3068 0.2260 0.2017 0.7367 0.6576

3/4" 10 0.4418 0.3345 0.3019 0.7571 0.6834

7/8" 9 0.6013 0.4617 0.4192 0.7679 0.6971

1" 8 0.7854 0.6057 0.5509 0.7713 0.7014

1-1/8" 7 0.9940 0.7633 0.6929 0.7679 0.6971

1-1/4" 7 1.2272 0.9691 0.8896 0.7897 0.7249

1-3/8" 6 1.4849 1.1549 1.0538 0.7778 0.7097

1-1/2" 6 1.7671 1.4052 1.2935 0.7952 0.7320

Bn 0.9FuAbe


19/45

48

depends on whether the shear plane passes through the shank of the bolt or

through its threads. When the shear plane passes through the bolts shank, Ag

should be used and when it passes through the threaded portion, Ar should be

used. The advantage of designing a connection with the threads excluded from

the shear plane becomes obvious upon examination of Equations 3-2 and 3-3.

Bolts subjected to shear through their threads have strengths ranging from 64% to

73% of the same bolts subjected to shear through their shanks. The reduced

thread length of heavy hex bolts allows the threads to be more easily excluded

from the shear plane than for standard bolts.

3.7.2.1 LRFD

The LRFD (AISC, 1994) uses a design approach for the shear resistance of

a bolt that is similar to the approach used for the tensile strength. The nominal

shear resistance is calculated as

EQ 3-9

where

Bv = the nominal shear resistance of the bolt

Fv = the effective shear strength of the bolt material

Ab = the gross area of the bolts shankWhen the threads of the bolt are excluded from the shear plane, Fv is calcu-

lated as (AISC, 1994)

Bv FvAb


20/45


21/45

50

and for grade 10.9 bolts with the threads not excluded from the shear plane,

EQ 3-14

where

Bv = the nominal shear resistance of the bolt

Fu = the ultimate strength of the bolt material

Ab = the gross area of the bolts shank

Abe = the effective tensile area of the bolt

As with the tensile strength, the nominal shear strength is divided by a partial

safety factor, Mb, of 1.25 to obtain the design resistance.

3.7.3 Torsional Strength

The shear stress of a bolt subjected to torsion is described by Equation 3-15

below.

EQ 3-15

where:

= shear stress (ksi)

T = applied torque (k-in)

= radius of the point of stress (in)

J = polar moment of inertia (in4)

Bv 0.5FuAbe

TJ


22/45

51

Substituting the bolts polar moment of inertia and the outer radius into Equation

3-15 yields the maximum shear stress in the bolt (Barron et al., 1998a).

EQ 3-16

where:

dr = the diameter of the root of the threads (in)

The importance of the torsional strength of fasteners becomes obvious when

using fully tensioned, high-strength bolts. A typical 7/8 diameter A490 bolt

requires 600 to 640 ft-lbs of torque to provide adequate pretension. Assuming

that 50% of that torque is applied directly to the bolt (the other 50% being attrib-

uted to friction and axial tension) shear stresses of up 50 ksi can be generated.

3.7.4 BendingAlthough bolts arent typically designed for bending, bending stresses are

often present due to misalignment, non-perpendicular holes, joint prying and other

causes. The stress in a bolt due to bending is the same as for any other typical

member and is written as

. EQ 3-17

max16T

dr

McI


23/45

52

where:

= bending stress (ksi)

M = applied bending moment (k-in)

c = distance from the neutral axis of the point of stress (in)

I = the moment of inertia of the bolt (in4)

Coupled with the pretension and tension due to loading, the bending stresses can

be critical. The commentary to the LRFD addresses the bending of fasteners by

using a relatively low resistance factor of 0.75 for strength calculations (AISC,

1994).

3.7.5 Combined Loading

So far, four individual modes of loading have been discussed. In connec-

tions, though, fasteners are often subjected to a combination of loadings. A com-

bination of shear and tension, for example, is often present in connections

between diagonal bracing and beam and columns. The simple act of pretension-

ing a bolt induces both shear stress from the applied torque and axial stress from

the resulting pretension. In fact, tests show that the tensile capacity of a bolt is

reduced by as much as 15-20% during pretensioning (Barron et al., 1998a). For

these reasons, it is clear that combined loading conditions deserve special atten-

tion.

Tests conducted at the University of Illinois indicate that the interaction

between shear and tension in bolts can be accurately predicted by using the ellip-

tical relationship (Kulak et al., 1987)

. EQ 3-18x

2

0.62( )2 y

2 1.0


24/45

53

where:

x = ratio of shear stress to tensile strength

y = ratio of tensile stress to tensile strength

This relationship can be reduced to a circular one if the ratio of shear stress to

shear strength that is shown in Equation 3-19 is used.

EQ 3-19

where:

RT = ratio of tensile stress to tensile strength

RV = ratio of shear stress of shear strength

The LRFD recommends a simplified, tri-linear version of the circular relationship.

Both relationships are shown in Figure 3-5.

The relationship between torsion and tension in bolts is critical because

high-strength bolts are nearly always fully tensioned by torquing. Figure 3-6

shows the load-elongation curves for two bolts. The upper curve represents a bolt

that was loaded from the snug tight condition until failure and the lower curve rep-

resents a bolt that was fully tensioned before being loaded to failure. The fully ten-

sioned bolt yields at a lower tension than the snug tight bolt because of the

interaction between the axial and torsional stresses. After being fully tensioned,

though, the torsion is relieved and the bolt is able to reach the full tensile strength

of the snug tight bolt. The dashed portion of the lower curve represents the

behavior of a bolt that is loaded to failure by torquing.

RT2

RV2

1.0


25/45

54

Figure 3-5: Tension-Shear Interaction Relationship for Bolts

Figure 3-6: Fully Tension vs. Snug Tight P- Curves for Bolts

RV

RT

0

1

0 1

RT2

RV2

1.0

RT RV 1.3

Elongation

BoltLoad

Fully Tensioned

Snug Tight


26/45

55

It should be noted that well lubricated twist-off or tension control bolts dont

exhibit the behavior shown in Figure 3-6 because torsion only exists in the portion

of the bolt between the twist-off spine and the nut. When a standard bolt is tight-

ened, a torque is applied to the shank of the bolt. It is this torsion that, combined

the applied tension, affects the behavior of the bolt. When a tension control bolt is

tightened, the torque is applied to the portion of the bolt between the twist of

spline and the nut. Any residual torsion present in the shank of a tension control

bolt is left as a result of friction between the nut or bolt head and the washers.

Because of this, the tension control bolts will tend to follow the path of the snug

tight bolts in Figure 3-6, even when they are fully tensioned.

3.8 Stiffness

The stiffness of structural joints using bolts in tension depends greatly on the

stiffness of the individual bolts. Because of this, accurate predictions of the stiff-

ness of the individual bolts are essential to accurate models of the overall connec-

tion stiffness.

The stiffness of an axially loaded member can be expressed in the familiar

form shown in Equation 3-20.

EQ 3-20kAE

L


27/45

56

where:

k = local axial stiffness (kip/in)

A = the cross sectional area of the member (in2)

E = the modulus of elasticity (ksi)

L = the member length (in)

The stiffness of a bolt is complicated, though, by the fact that it has a changing

cross section. As shown in Figure 3-1 and Section 3.7.1, the cross sectional area

of the bolts shank is larger than that of its threaded portion. This difference in

area can be represented by considering a component spring with different stiff-

nesses in series. The stiffnesses are calculated by using Equation 3-20 for each

section separately. The overall stiffness is then calculated as shown in Equations

3-21(a) and 3-21(b) (Barron et al., 1998b).

EQ 3-21(a)

EQ 3-21(b)

where:

Kb = the overall stiffness of the bolt (kip/in)

ks = the stiffness of the bolt shank (kip/in)

kt = the stiffness of the bolts threaded portion (kip/in)

Ls = the length of the shank (in)

1

Kb

1

ks

1

kt

1

Kb

LsAbE

LtgAbeE


28/45

57

Ltg = the length of threads included in the bolts grip (in)

Ab = the cross sectional area of the bolts shank (in2)

Abe = the effective area of the bolts threaded portion (in2)

Tests indicate that Equation 3-21(b) overestimates the stiffness of bolts. To

slightly reduce the predicted stiffness, it has been proposed by Barron and Bick-

ford (1998b) that part of the bolt head stiffness and part of the nut stiffness be

included in the overall stiffness calculation. This adjustment is included as shown

in Equation 3-22.

EQ 3-22

where:

f = a correlation factor

db = the nominal diameter of the bolt (in)

Recommendations for the value of the factor, f, in Equation 3-22 range from 0.3 to

0.6 (Barron et al., 1998b).

3.9 Ductility

The ductility of fasteners is important because fasteners are often the weak-

est link in a bolted connection. Generally, steel loses ductility as it is hardened.

Consequently, A490 bolts are generally considered to possess less ductility than

A325 bolts because they are harder.

1

Kb

fdbAbE

LsAbE

LtgAbeE

fdbAbeE


29/45

58

The length of the threaded portion of the bolt that is present in its grip, L tg, is

significant when considering ductility. This is true because nearly all of the yield-

ing in the bolt takes place in its threaded portion. When more threads are

included within the grip, more material is available for yielding and the overall

elongation capacity, or ductility, of the bolt is greater.

3.10 Individual Bolt Testing Program

The objectives of the individual bolt testing were to 1) determine the preload

of the bolts when the spline of the bolts twisted off, 2) verify the manufactures cer-

tification for strength, 3) provide information about the stiffness and ductility of the

bolts as a function of the length, and 4) provide benchmark strain-bolt force rela-

tionships for the instrumented bolts.

Several bolts were selected for testing from the lots of bolts used in the com-

ponent and full scale tests. Because the strength, stiffness, and ductility of bolts is

dependent on the diameter, grade, and length, two lengths of bolts were selected

from the 7/8 in and 1 in diameter A325 and A490 lots.

Several types of individual bolt tests were performed. The first type of tests

conducted were calibration tests to determine the preload in the tension control

bolts when the spline twisted off. The second type of tests conducted were direct

tension tests to determine the bolts initial stiffness, yield point, ultimate strength

and ductility. The Skidmore-Wilhelm torque tension tester was used for both

types of tests. The third type of test conducted was an in-situ test to determine

the relationship between the bolt force and externally applied load. Finally, bench-

mark tests of instrumented bolts were performed to provide a relationship

between the strain in a bolts shank and the bolt force.


30/45

59

It should be noted that the results of the tests documented here can only be

rigorously applied to button head bolts. Although the behavior of hex head bolts

will, in most respects, be nearly identical, differences in stiffness and strength may

arise due to the different configuration. A comprehensive investigation of hex

head bolt characteristics that is very similar to that documented here for button

head bolts was conducted by Steurer (1996).

3.10.1 Pretension Calibration Tests

For the first type of test, the pretension calibration test, the Skidmore-Wil-

helm torque tension tester was used alone as shown in Figure 3-2. The torque

tension tester is essentially a hydraulic load cell with a hole in the center to allow a

bolt to pass through. It consists of an inner piston with a 0.25 in stroke operating

inside of an outer housing. The force of the bolt being tightened causes an

increase in the internal hydraulic pressure which is then converted to force using a

calibrated pressure transducer. An analog pressure gage calibrated to read bolt

force in kips was supplied with the tester but an electronic pressure transducer

was later added to facilitate automatic data acquisition. After adding the pressure

transducer, the tester was recalibrated to its full scale capacity in a universal test-

ing machine.

3.10.1.1 Test Method

For the pretension calibration tests, the bolt being tested was inserted

though the center of the tester from behind and the spacer plates, washers, and

nuts were installed on the bolt from the front. No more than four washers were

used together on either side of the bolt (i.e. under the head or nut). When more

washers were required for longer bolts, 1/2 in shim plates were used. After ensur-

ing that enough washers and spacer plates were used to avoid running the nut


31/45

60

onto the shank of the bolt during tightening, the nut was tightened finger tight, and

the data acquisition system was balanced. Next the bolt was tightened using one

of two LeJeune wrenches until the spine of the bolt twisted off and the bolts pre-

tension was recorded.

The load reading from the pressure transducer dropped slightly (~3-5%)

after the spine of the bolt twisted off but reached a constant value within 30 to 45

seconds. This constant value was the value recorded as the pretension in the

bolt.

3.10.1.2 Results

The results of 109 tests of LeJeune tension control bolts were used to verify

the pretension induced when tightening. A significant difference in pretension

was noticed between the bolts tightened using an electric wrench and the bolts

tightened using a manual ratcheting wrench. On average, the pretension in bolts

tightened with the manual wrench was 81.5% of the pretension required by the

LRFD while electric wrench induced an average of 96.1% of the required preten-

sion. Table 3-5 shows the results grouped by type and size of bolt.

The pretension achieved was highly dependent on the condition of threads

of the bolts. After sitting the kegs for several months, the bolts tended to dry out

and lose the lubrication that was applied by the manufacturer. Informal tests of

bolts in this condition resulted in very low pretensions. As a result, all bolts tested

individually and in the component and full scale tests were well lubricated. This is

a violation of ASTM F1852-98 which states that no lubrication shall be permitted

other than that applied by the manufacturer. The author views this requirement

as impractical. The bolts used in this investigation were kept in a well controlled

environment, presumably in a much more desirable environment than would be


32/45

61

experienced on a typical job site, and the threads of the bolts still dried out result-

ing in increased thread friction, larger nut factors, and lower induced pretensions.

The potential drawbacks of adding additional lubrication are more than overshad-

owed by the consequences of not adding lubrication.

Table 3-5: Pretension Calibration Test Results

3.10.1.3 DTI Washer Tests

A small number of direct tension indicator washers were obtained and an

informal investigation was conducted using standard hex head bolts. Five, 7/8

diameter and two, 1 diameter A325 bolts were calibrated using the washers. The

average preloads achieved were 44.6 kip and 58.3 kip, respectively. All of the

pretensions exceeded the required pretensions of the LRFD (AISC, 1994).

3.10.2 Direct Tension Testing

Direct tension testing was conducted to obtain reliable load-elongation datafor the bolt which included the elastic stiffness, plastic stiffness, yield point, ulti-

mate strength and ultimate elongation.

Wrench: Elect Man Elect Man Elect Man Elect Man

Average: 38.3 kip 37.5 kip 53.8 kip 42.0 kip 44.3 kip 36.2 kip 57.8 kip 47.1 kipSt Dev: 6.5 kip 12.3 kip 4.6 kip 2.2 kip 7.1 kip 8.5 kip 5.2 kip 4.2 kip

Samples: 18 6 12 4 28 16 15 10

Required: 39.0 kip 39.0 kip 51.0 kip 51.0 kip 49.0 kip 49.0 kip 64.0 kip 64.0 kip

Ratio: 98.1% 96.2% 105.6% 82.4% 90.3% 73.9% 90.2% 73.7%

7/8" A325 1" A325 7/8" A490 1" A490


33/45

62


The Skidmore-Wilhelm torque tension tester was again used for the tension

testing but was attached to a hydraulic pump and placed into the test apparatus

as shown in Figure 3-7. Attaching the tester to the hydraulic pump allowed a load

to be applied to the bolt in pure tension instead of as a torqued tension. The

tester was recalibrated after attaching the pump. The test apparatus allowed the

elongation of the bolt to be measured as the force was applied to provide a force-

elongation relationship for the bolt. LVDTs measured the displacement of the bolt

head and the end of the bolt. The difference in the readings from the measured

displacements provided the elongation. To avoid damaging the LVDTs with the

bolts as they fractured, the LVDTs were attached to the bolts with fishing line that

was strung over rods as shown in the figure. This allowed the LVDTs to be placed

vertically and behind plexiglass, out of harms way.

Two different procedures were used for the tension testing. Test method #1

was used for tests 1-20 while method #2 was used for tests 21-73.

3.10.2.1.1 Tension Test Method #1: The piston of the torque-tension tester

was positioned very close to its fully contracted position. The bolt was then

inserted, the spacer plates and washers were added and the nut was snugged

tight. The LVDTs were then attached to the ends of the bolt, the data acquisition

system was balanced and the bolt was loaded using the hydraulic pump to a point

slightly above its expected pretension level. This provided data points for the

elastic portion of the bolts force-elongation relationship. Next, the load was

released from the bolt, the LVDT was detached from the nut end of the bolt, the

bolt was pretensioned using one of the LeJeune wrenches and the pretension


34/45

63

was recorded. Finally, the LVDT was reattached to the nut end of the bolt and the

bolt was loaded to failure with the hydraulic pump.

Figure 3-7: Direct Bolt Tension Test Setup

Using this method created several problems. First, positioning the piston of

the tester near its fully contracted position was a problem because if the piston

actually bottomed out while the bolt was being tightened with the wrench, the load

readings obtained were erroneous. This happened a few times. The second


35/45

64

problem with this method is that the full range of the tester couldnt be used for the

actual tension test and many of the bolts tested didnt actually fracture. Finally,

the data reduction was difficult because the force-elongation relationship was

obtained in two separate parts that had to be reconnected. This test method was

abandoned in favor of method #2 after bolt test #20.

3.10.2.1.2 Tension Test Method #2: For method #2, the piston of the tester

was position at its fully extended position, the bolt was inserted, the washers and

spacer plates were installed and the nut was snugged tight. The acquisition sys-

tem was then balanced and the bolt was pretensioned with one of the LeJeune

wrenches. After recording the pretension, the load was released and the piston

was repositioned at its fully contracted position. Additional plates and washers

were added to the same bolt as needed and the nut was again snugged tight.

Finally, the LVDTs were attached to the ends of the bolt, the data acquisition was

balanced and the bolt was loaded to failure using the hydraulic pump.

Method #2 offered several advantages over method #1. First there was no

danger of bottoming out the piston of the tester while pretensioning the bolt. Sec-

ond, the full range of the tester was available for the tension testing. Finally, the

reduction of data obtained using method number #2 was much easier than that

obtained from method #1.

3.10.2.2 Data Reduction

The methods used to reduce the data varied depending on the type of test

conducted and the method used. Some aspects of the data reduction were com-

mon to all of the tests. These will be discussed here while those aspects specific

to individual methods will be discussed under separate headings.


36/45

65

Because of the limited stroke of the tester, all of the bolts didnt actually frac-

ture. All bolts which are included in this dissertation did at least reach a peak load

level and were relaxing before the limit of the tester was reached. The force-elon-

gation data presented for those that didnt fracture include a portion of apparent

hardening at the end of the curves. This is due to the piston reaching the end of

its stroke which caused an increase in internal hydraulic pressure without actually

increasing the load on the bolt.

The hydraulic pump that was used to load the bolts was a manual pump. As

a result, the unrefined force-elongation curves contain divots that are due to a

relaxation in the system when the handle of the pump is being raised between

strokes. Although these divots may provide useful information, they have been

removed from the data. Figure 3-8 shows a plot of the unrefined data with the

smoothed data superimposed.

3.10.2.2.1 Tension Test Method #1: The reduction of the data obtained from

tension test method #1 required several steps. The elastic portion of the curve

was obtained separately from the inelastic portion. As a result, an offset was

present in the raw data. This offset was removed by examining points of common

force between both data sets. Next, the initial portion of the elastic data was

examined for linearity. Some data showed a lack of linearity in the first 5 to 10

kips, apparently due to slack in the system. This nonlinear region, if present, was

removed to avoid skewing the stiffness values obtained from the elastic portion of

the curve. After eliminating any erroneous data points, an apparent yield point

was identified and a best linear fit was made through the data up to this point.

The slope of this linear fit was recorded as the elastic stiffness of the bolt. Next,

the entire force-elongation curve was shifted to ensure that the linear fit passed


37/45

66

though the point of zero force and elongation. Finally, the data was smoothed by

removing any divots from the inelastic region.

Figure 3-8: Divots Caused by the Manual Hydraulic Pump

3.10.2.2.2 Tension Test Method #2: The reduction of data obtained from

tension test method #2 was the same as that for data obtained from tension test

method #1 with the exception that the was no offset between the elastic andinelastic parts of the force-elongation curve to be removed.

0

10

20

30

40

50

60

70

80

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Elongation (in)

BoltForce(kip

)


38/45

67

3.10.2.3 Results

The complete results of the individual bolt testing are presented along with

the bolt certifications in Appendix C. A discussion of the results and selected data

are presented in this section.

Fifty-five bolts were tested to failure under direct tension as described ear-

lier. Several different quantities were examined. These include elastic stiffness,

elastic limit, ultimate strength, and ductility.

3.10.2.3.1 Elastic Stiffness: The elastic stiffness prediction shown in Equa-

tion 3-22 includes a factor for the contribution of the bolt head and nut to the bolts

overall stiffness. If the elastic stiffness of the bolt, Kb is known, the correlation fac-

tor, f, can be determined explicitly as shown in Equation 3-23 (Barron et al.,

1998b).

EQ 3-23

The average value of f found from the tension tests is 0.73 with a standard

deviation of 0.54. Several of the tests exhibited stiffnesses that were substantially

lower than expected. Values of f obtained from these tests are as large as 2.86.

The reason for the lack of stiffness in these tests is unknown. These tests are

undoubtedly the source of the large standard deviation in the factor, f. When the

results of seven tests which yielded values for f above 1.00 are discarded, the

f

E

Kb

LsAb

LtgAbe

db1

Ab

1

Abe


39/45

68

average of the remaining tests was found to be 0.55 with a standard deviation of

0.16.

3.10.2.3.2 Elastic Limit: When considering the nonlinear behavior of bolts or

bolted connections, it is necessary to know when the elastic limit has been

reached. Manufacturer certifications and standard codes do specify an elastic

limit. They simply report or specify a minimum ultimate strength which leads to an

elastic-perfectly plastic material model. Depending on the level of accuracy

required, this may or may not suffice. By dividing the measured elastic limit by the

bolts ultimate strength, a ratio can be defined and used to predict the onset of

inelastic behavior.

For the purposes of this dissertation, the elastic limit is defined as the load at

the last data point lying with a strain less than a 0.5% offset. The average ratio

obtained from the tension tests was 0.83 with a standard deviation of 0.04. For

the sake of simplicity, a ratio of 0.85 is recommended.1

3.10.2.3.3 Ultimate Strength: Ultimate strength is the single most important

characteristic of a bolt. A goal of the tension testing was to verify the manufac-

turers certified values of ultimate strength. The ultimate strength is defined as the

largest load achieved during a tension test, divided by the effective area of the

bolt. Two variations of the tests performed as part of this research from the ASTM

standard are noted. First, ASTM F606 section 3.4.1 states that 4 threads shall be

exposed between the fixture and thread runout portion of the bolt. The number

threads included in the bolts grip was a variable in our test series. Therefore, this

requirement was waived. Second, the manufacturers certification for the bolts

1. The Eurocode (1993) recommends ratios of 0.80 for grade 8.8 bolts and 0.90 for grade10.9 bolts for Fy / Fu.


40/45

69

used in the test series indicate that a wedge tension test was used to determine

the ultimate strength. ASTM F606 section 3.5.1 states that in a wedge tension

test, a wedge shall be used under the head of the bolt. No such wedge was

used in the tests. ASTM F606 section 3.4.1 permits the used of a suitable fixture

for tensile testing.

On average, the ultimate strength determined from the tension tests was 8%

higher than that reported on the manufacturers certification with a standard devi-

ation of 4%. An examination of the manufacturers certifications for the bolts

showed that the average ultimate strength of the A325 bolts was 140.0 ksi with a

standard deviation of 3.4 ksi and the average ultimate strength of the A490 bolts

was 162.7 ksi with a standard deviation of 2.7 ksi. These values represent an

average strength that is 16.7% higher than that specified for the A325 bolts and

8.5% higher for that specified the A490 bolts.

3.10.2.3.4 Elongation: The elongation at failure of a bolt is a direct indicator

of the bolts ductility. Of the fifty-five bolts tested under direct tension, thirteen

A325 and twenty-four A490 bolts actually fractured. The other tests were stopped

because the stroke of the Skidmore-Wilhelm tester was exhausted. The percent

elongation of the fractured bolts was calculated as shown in Equation 3-24.

EQ 3-24

10

Lg

Lg


41/45

70

where:

Lg = the grip length of the bolt

= the elongation at fracture measured by the acquisition system

The elongation at failure determined from the tests was 5.2% with a stan-

dard deviation of 1.6% for the A325 bolts and was 3.6% with a standard deviation

1.1% for the A490 bolts.

3.10.3 in-situ Tension Testing

A third type of test was performed on two bolts, bolts #9A and 44A. This test

was designed to obtain a relationship between the applied force and bolt force for

pretensioned bolts. It is generally accepted that the force present in bolts remains

relatively constant at the pretension load until the clamping force of the bolts is

overcome by the external loads. At that point, the force in the bolts increases at a

rate that is at least proportional to the applied load, depending on the level of pry-

ing present.


To replicate the in-situ condition, the valve restricting oil flow from the tester

into the reservoir of the hydraulic pump was opened to allow free flow. The bolt

was then inserted into the tester, the washers and spacer plates were added and

the nut was fully tensioned using one of the LeJeune wrenches. By allowing the

oil to flow freely from the tester into the reservoir of the hydraulic pump, the piston

of the tester bottomed out as the bolt was fully tensioned. After the bolt was ten-

sioned, the LVDTs were attached to the ends of the bolt, the acquisition system

was balanced, the valve on the hydraulic pump was closed and the bolt was

loaded to failure.


42/45

71

3.10.3.2 Data Reduction

When subjecting bolts to direct tension, there is no way to measure the force

in the bolt directly; only the force applied to the bolt can be measured. The very

nature of the in-situ test is to find a relationship between the applied load and the

bolt force. Therefore, it is recognized that the two are not equal and an indirect

method of determining the bolt force must be employed.

Two approximations must be made concerning the actual bolt force in these

tests. First, because the valve controlling the flow oil between the tester and the

reservoir of the hydraulic pump was left open while the bolt was tightened, no

direct measure of the bolts preload was possible. As a result, the average pre-

load of six other bolts from the same lots were used as the preload of the bolts

tested. Second, the force-elongation relationship of the bolts tested in the in-situ

condition were approximated as the multi-linear representation of an identical bolt

tested under the standard tension test method. The multi-linear force-elongation

relation of bolt #9 was used for #9A and #44 was used for #44A.

The data reduction for each bolt consisted of two steps. First, the bolts esti-

mated preload was used to calculate the initial elongation. Second, the initial

elongation was added to the actual elongation from the in-situ test. This sum was

then used to calculate the bolt force based on the approximated multi-linear load-

elongation relation for each of the data points recorded.

3.10.3.3 Results

The relationship between the bolt force and the external applied load for bolt

#44A is shown in Figure 3-9. The dashed line represents the one-to-one relation-

ship expected from a bolt with no preload. If the material clamped by a bolt is con-

sidered rigid, then there should be no increase in the bolt force until the externally


43/45

72

applied load reaches and exceeds the bolts preload. If it recognized however,

that the material clamped by a bolt is elastic, then a small increase in bolt force is

expected before the externally applied load overcomes the bolts preload1. An

examination of Figure 3-9 shows that a portion of the line representing the bolt

force actually lies below the idealized dashed line. It is recognized that this is the-

oretically impossible and violates equilibrium. The problem is attributed to experi-

mental error arising from the aforementioned approximations.

Figure 3-9: Bolt Force and External Load Relationship for Test 44A

1. A complete treatment of the problem is given by Kulak, Fisher, and Struik (1987).

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Applied Load (kip)

Bo

ltForce

(kip)


44/45

73

3.10.3.4 Instrumented Bolt Tension Testing

Bolts instrumented with strain gages were used in the component tests.

Each of these bolts was calibrated in the elastic range to obtain a relationship

between the strain in the bolt and load present in the bolt. Because they were

only calibrated in the elastic range, these relationships are not representative of

the entire force range of the bolts. For this reason, five instrumented bolts were

tested to failure in the tension test setup shown in Figure 3-7.

The method used in testing the instrumented bolts was very similar to ten-

sion test method #2. The piston of the tester was positioned in the fully extended

position, the bolt was inserted, the spacer plates and washers were added and

the nut was snugged tight. Next the data acquisition system was balanced and

the nut was tightened using a spud wrench to a level near the expected preten-

sion of the bolt while the acquisition system recorded the internal strain and

applied load. This was the method used to calibrate the instrumented bolts used

in the component tests. Next, the load was released and the bolt was tensioned

using one of the LeJeune wrenches. The load was then released again, the pis-

ton of tester positioned at its fully contracted position, and additional spacer plates

and washers were added as needed. Finally, the LVDTs were attached to the

ends of the bolt, the acquisition system was balanced and the bolt was loaded to

failure while recording the internal strain, applied load, and bolt elongation.

3.11 Discussion

Several observations can be made from the examination of the design

codes and experimental results presented in the chapter.


45/45

The models employed by the LRFD for bolt strengths result in values that are

approximately equal to those based on more rigorous models but require less

computation.

The conservative resistance factors used by the LRFD and Eurocode com-

bined with the overstrength of the bolt material properties yield conservative

design values for the tensile resistance, as Table 3-6 shows.

Table 3-6: Design vs Actual Tensile Capacities for the 7/8 and 1 Bolts Used

The model proposed by Barron and Bickford (1998b) provides reasonable esti-

mates of the axial stiffness of the bolts tested.

Under tensile loading, A325 bolts demonstrated 44% higher elongation at fail-

ure than A490 bolts.

The levels of pretension achieved were somewhat lower than LRFD require-

ments when an electric wrench was used for tightening and were significantly

lower than code requirements when a manual wrench was used for tightening.

The level of pretension achieved is largely dependent on the condition of the

threads of the bolt and nut.

Actual Eurocode LRFD

Bolt Strength Bn Bn / Bactual Bn Bn / Bactual7/8" A325 64.6 kip 38.6 kip 0.60 40.6 kip 0.63

1" A325 84.8 kip 50.6 kip 0.60 53.0 kip 0.63

7/8" A490 75.1 kip 48.2 kip 0.64 51.0 kip 0.68

1" A490 98.6 kip 63.3 kip 0.64 66.6 kip 0.68

chap_3-structural_bolts .pdf

Documents

Transcript of chap_3-structural_bolts .pdf