Crawford Kulak 1968

STUDIES IN STRUCTURAL ENGINEERING

A SERIES OF PAPERS AND REPORTS PRODUCED IN CONNECTION WITH RESEARCH AND TEACHING

AT THE DEPARTMENT OF CIVIL ENGINEERING NOVA SCOTIA TECHNICAL COLLEGE

HALIFAX, N. S.

NO. 4

BEHAVIOR OF ECCENTRICALLY LOADED

BOLTED CONNECTIONS

By

S. F. CRAWFORD

G. L. KULAK

BEHAVIOR OF ECCENTRICALLY LOADED

BOLTED CONNECTIONS

by

S. F. Crawford

G. L. Kulak

September, 1968

Department of Civil EngineeringNova Scotia Technical College

Halifax, Nova Scotia

ii

T A B L E O F C O N T E N T S

Page

Abstract vii

1 INTRODUCTION

1.1 General 1

1.2 Objectives 3

1.3 Scope 3

2 REVIEW OF PREVIOUS RESEARCH 5

3 ANALYTICAL STUDY

3.1 Introduction 11

3.2 Load - Deformation Response of 11Individual Fasteners

3.3 Prediction of Ultimate Connection 13Strength

4 EXPERIMENTAL STUDY

4.1 DESCRIPTION OF TEST SPECIMENS

4.1.1 Single Bolt Shear Specimens 18

4.1.2 Bolted Connection Specimens 18

4.2 METHOD OF TESTING

4.2.1 Single Bolt Shear Tests 21

4.2.2 Bolted Connection Tests 22

4.2.3 Single Bolt Tension Tests 24

iii

T A B L E O F C O N T E N T S (Continued)

Page

4.3 TEST RESULTS

4.3.1 Single Bolt Shear Tests 25

4.3.2 Bolted Connection Tests 26

4.3.3 Single Bolt Tension Tests 27

5 DISCUSSION OF RESULTS

5.1 SINGLE BOLT SHEAR TESTS 28

5.2 BOLTED CONNECTION TESTS

5.2.1 Load - Rotation Behavior 29

5.2.2 Load - Vertical Displacement 30Behavior

5.2.3 Prediction of Ultimate Loads 32

5.2.4 Comparison of Ultimate Loads 36and Current Allowable Loads

5.3 ULTIMATE LOAD TABLES 38

6 CONCLUSIONS 41

TABLES AND FIGURES 42

REFERENCES 60

APPENDICES 63

iv

L I S T O F T A B L E S

Table Page

1 Details of Test Specimens 43

2 Test Results 44

3 Tension Test Results 45

4 Details of Test Specimens by Others 46

5 Results and Predictions of Tests by Others 47

v

L I S T O F F I G U R E S

Figure Page

1 Typical Eccentrically Loaded Connections 48

2 Eccentrically Loaded Bolt Group 48

3 Single Bolt Shear Specimen 49

4 Bolted Connection Specimen 49

5 Single Bolt Shear Specimens Before Testing 50

6 Failed Single Bolt Shear Specimen 50

7 Bolted Specimen with Gages 51

8 Bolted Specimen in Test Machine 51

9 Typical Failed Bolted Specimens 52

10 Load - Deformation Curves for Single Bolt 53Shear Specimens

11 Load - Rotation Curve for Specimen B1 54








19 Moment - Rotation Curves for Specimens 58B4 and B5

20 Moment - Rotation Curves for Specimens 58B6 and B7

21 Typical Load - Vertical Displacement 59Curves for Bolted Specimens

v i

A C K N O W L E D G E M E N T S

The authors wish to express their thanks to

the following persons and organizations for their

assistance in this investigation:-

Canadian Steel Industries Construction Council

under whose sponsorship this investigation was

carried out.

Canada Iron Foundries Limited, Dartmouth, for

providing the test specimens.

Mr. N. P. Maycock of Steel Company of Canada,

Limited, for supplying the minimum strength

bolts.

Mr. D. Yeadon and other technicians of the

Civil Engineering Laboratories who helped

during the testing program.

v i i

A B S T R A C T

Although the present methods of investigating

eccentrically loaded fastener groups have produced safe

designs, the factor of safety is, in general, unknown.

These methods commonly assume that the fastener response

is perfectly elastic although some investigators have

used an elastic - perfectly plastic response. It is

clear that very l i t t l e experimental work has been per-

formed on this type of fastener group and the analytical

methods of design currently in use have not been subjected

to any significant amount of testing.

A rational theoretical method of predicting the

ultimate load on eccentrically loaded fastener groups has

been developed, The method is based on a recognition of

the true load - deformation response of the fasteners.

The validity of the theoretical approach has

been verified by an extensive testing program. A series

of single bolt tests on A325, 3/4" diameter bolts were

conducted to obtain the load - deformation relationship

of individual bolts for use in the theoretical prediction

of ultimate load. Eight full-size bolted connection

specimens which were designed to carry eccentric loads

were tested. The test results agreed favorably with the

theoretical predictions of the ultimate loads.

viii

The factor of safety against ultimate load

provided by the current allowable loads is shown to be

high and inconsistent. By making use of the more

accurate predictions presented herein, the factor of

safety can be brought in line with that of other

structural components and can be established at a con-

stant value for all connections of this type.

BEHAVIOR OF ECCENTRICALLY LOADED BOLTED CONNECTIONS

1 . I N T R O D U C T I O N

1.1 GENERAL

Ideally the line of action of a force acting on a

connection should pass through the centroid of the connecting

elements. This is not always practical, however, and

eccentric forces must often be accomodated. This thesis

reports the results of a study into the behavior of fastener

groups subjected to a combination of direct shear and moment.

The investigation has been limited to the case

where the eccentric load is in the same plane as the fastener

group. This type of connection occurs quite frequently in

practice. Some examples of this type of connection are:

1. Beams or girders which cannot be located on or

near the centre line of the columns, for example,

crane girders. Fig. 1(a).

2. Plate girder web splices. Fig. 1(b).

3. Connections supporting the ends of beams and

girders that constitute part of a wind bracing

system. Fig. 1(c).

In the past, theoretical approaches to this problem

have generally been based on the assumption that the load -

2

deformation response of the fasteners is elastic and that

the yield point (proportional limit) is not exceeded.1,2,3

However, it has been shown that the load - deformation

relationship of an individual fastener is not elastic and

that individual fasteners do not have a well-defined shear

yield stress.4,5

The method commonly used for the design of

eccentrically loaded fastener groups6,7 is based on the

assumption that the fasteners do behave elastically, that

is, the resistance of each fastener is assumed to be

proportional to its distance from the centre of rotation.

An empirical aspect is introduced in that the actual

eccentricity of the fastener group may be replaced with an

"effective eccentricity".8 This reduced value is used

to provide a less conservative and more realistic allowable

load on the connection in the absence of a more rational

approach.

The program outlined in this thesis is an attempt

to determine a rational method of predicting the ultimate

strength of eccentrically loaded fasteners. A recognition

of the true load - deformation response of the individual

fasteners4 is essential to the derivation of a solution.

3

1.2 OBJECTIVES

The objectives of this investigation were as follows:

1. To attempt to provide a theoretical basis for

the prediction of the ultimate strength of

eccentrically loaded fastener groups. (The

load is assumed to be applied in the same plane

as the fastener group.)

2. To check the validity of the theoretical

approach by means of a suitable testing program.

3. To evaluate the present design rules governing

the design of eccentrically loaded fasteners and,

if necessary, to suggest improvements.

1.3 SCOPE

The analytical study of the behavior of eccentrically

loaded fasteners included a study of existing methods of

evaluating the allowable strength of eccentric fasteners.

A new approach which recognizes the true load - deformation

response of the individual fasteners was developed and was

used to predict the ultimate load that an eccentric fastener

group could sustain. The results of the method currently

used in practice and the new approach were compared to the

experimental results.

4

A series of six tests were conducted on single bolt

specimens acting in double shear to determine the load -

deformation response of the individual fasteners. The

fasteners that were tested were 3/4 inch diameter high

strength bolts meeting ASTM A325 specifications9. The

results obtained were used in the prediction of the ultimate

strength of the test fastener groups.

A series of eight tests were conducted on multiple

fastener groups under eccentric load conditions. Each test

specimen was designed to provide two identical test groups.

The fastener groups consisted of one or two vertical lines

of 3/4 inch diameter A325 bolts under eccentricities of

load ranging from eight to 15 inches.

Ultimate load tables were compiled for eccentrically

loaded connections of one and of two vertical rows of

fasteners. The tables are based on minimum strength

ASTM A325 bolts. Since the ASTM specifications do not provide

requirements for shear strength of high strength bolts, a

series of five tension tests were conducted on A325 bolts

as an indirect method of determining the minimum shear

strength.

2 . R E V I E W O F P R E V I O U S R E S E A R C H

Until 1963 very little research had been conducted

on the behavior of eccentrically loaded fasteners where

the load was applied in the plane of the fasteners. It

appears that designers and researchers were more interested

in the effect of loads on the overall structural connection

rather than on the individual fasteners. As a result,

fasteners in sufficient numbers to preclude failure of

the fasteners themselves were provided.

Several researchers have conducted tests on

connections which were comparable to the present series of

tests. In 1936, J.C. Rathburn10 reported on a series of 18

connection specimens, seven of which were comparable to the

present tests. These were designed to evaluate various end

conditions and to evaluate the load - deformation

characteristics of the entire connection. In 1947 Hechtman

and Johnston11 tested 47 connections, which included all

practical fastener connections, for use in their proposed

method of semi-rigid design. Four of the test specimens

compare to the arrangement of the specimens of this program

but the results of those tests were not reported because the

web angle connection was considered not efficient as a semi-

rigid connection. In 1959 Munse, Bell, and Chesson12

5

6

studied four rigid beam-to-column angle connections

similar in several aspects to those in this program. Again

the entire connections rather than just the fasteners were

being tested.

As noted, the main difference between the present

program and those described above is that in all of the above

tests the entire connection was being examined whereas the

present test program has been designed specifically to

test the fasteners. Therefore their results, such as load -

deformation curves for the connection, have no direct

application to the action of the web bolts themselves.

The American Institute of Steel Construction6 and

Canadian Institute of Steel Construction7 design loads for

eccentric fastener groups make use of an elastic coefficient

C. This coefficient C is based on the assumption that the

load - deformation response of the fasteners is elastic.

It was recognized, however, that the elastic assumption was

unduly conservative and the AISC sponsored a series of ten

tests on eccentrically loaded riveted connections at Lehigh

University's Fritz Engineering Laboratory in 196313. These

tests were also reported by T.R. Higgins8.

From the results of these tests formulas for

evaluating an "effective eccentricity" evolved. The

7

"effective eccentricity" was intended to provide a

smooth transition from the case where there is little or

no effect due to the eccentricity of load (pure shear) to

the case where eccentricity produces a more significant

change in the reaction on the fastener (shear-moment).

It was also intended that the load factor of the

fasteners would be brought more in line with the load

factors of other parts of the connection.

The ten tests included one and two lines of

3/4 inch rivets with eccentricities of load ranging

from 2-1/2 to 6-1/2 inches. All other portions of the

test specimens were made sufficiently strong so that

any failure had to occur in the fasteners themselves.

The rotation of the web angles was measured and load versus

rotation curves were plotted for each specimen. From the

load - rotation curves the empirical formula for reducing

the actual eccentricity to a reasonable effective

eccentricity was selected. Thus, by reducing the

eccentricity, the elastic coefficient C is, in effect,

increased and the load factor (ultimate load/allowable

load) was decreased from approximately 4.5 to 3.25 (on the

average) for the specimens tested.

8

The prediction of the ultimate load capacity of

each specimen was based on:

1. Rotation of the connection about an instantaneous

centre of rotation computed on the assumption

that the rivets remain elastic.

2. Actual load - deformation response of individual

rivets.

It is noted that the calculation of the location of

the instantaneous centre of rotation assumes perfectly

elastic action in the fastener. This assumption is invalid

as was proven by the actual load - deformation response

of single rivet tests and as discussed below. The load -

deformation curves of the individual rivets were the result

of a series of six tests on single rivets in double shear

conducted as a part of the program. The predicted results

which combined the assumption of elastic fastener behavior

when locating the instantaneous centre of rotation with a

recognition of the true load - deformation response when

calculating the ultimate load of the group compared

favorably with the test results.

The tests conducted by Yarimci and Slutter and

consequently the design method as set forth in the sixth

edition of the AISC Steel Construction Manual6 can be

9

criticized on a number of points:

1. The number of tests upon which the method

is based was limited.

2. The range of eccentricities covered by the

tests was limited.

3. The lack of a rational basis for the method of

determining the effective eccentricity means

that extrapolation beyond the range investigated

is undesirable.

4. Power driven rivets were tested whereas high

strength bolts are used almost exclusively

in present construction methods.

Recently, several attempts have been made to use

an ultimate strength approach to provide a theoretical

basis for the design of eccentrically loaded fastener

groups 1 4 , 1 5. In each case the attempts have been based on

the assumption that under stress each fastener of the

connection will exert its maximum possible resistance,

irrespective of its location in the fastener group. That

this is an erroneous concept has been shown for one limit of

the problem, that of direct shear16.

As indicated, the number of research and experimental

programs designed to explore the behavior of eccentrically

10

loaded fasteners is limited. Recent editions of design

codes7, textbooks17 and literature surveys18 indicate

that no new acceptable theories have been advanced which

provide a more rational approach to this problem than

that presented by Higgins8. However, the increasing cost

of labour and material make it desirable to achieve a

connection design which will have a reasonable factor of

safety and which is also economical.

3 . A N A L Y T I C A L S T U D I E S

3.1 INTRODUCTION

A theoretical approach has been developed to

predict the behavior of fasteners subjected to a

combination of direct shear and moment. This approach,

presented in this chapter, uses the true load - deformation

response of fasteners to predict the ultimate strength of

eccentrically loaded fastener groups. The prediction of the

ultimate load rather than a yield load will enable designers

to apply a suitable load factor to the connection as is

done with other connection components of a structure. Since

the method involves an iterative procedure, a digital

computer is used in its development.

3.2 LOAD - DEFORMATION RESPONSE OF INDIVIDUAL FASTENERS

The relationship for load - deformation of a

single fastener in double shear4 has been expressed as

in which:

R = fastener load at any given deformation.

11

12

R u l t = ultimate load attainable by fastener.

= shearing, bending and bearing deformation

of fastener and local bearing deformation of

the connecting plates.

= regression coefficients.

e = base of natural logarithms.

In order to use this expression the constants

R u l t, and must be evaluated for the material under

consideration. For the purpose of this investigation six

single fasteners were tested in a compression jig, shown

in Fig. 3. (These tests are described more fully in

Section 4.2.1.) The bolt specimens were 3/4 inch diameter

A325 bolts connecting ASTM A36 steel plates. The values

for the ultimate shear strength of the fastener, R u l t, and

the maximum deformation of the fastener and material,

, were obtained directly from the test results, A

trial and error curve fitting procedure was used to

determine values of the coefficients and , which, when

substituted in the load - deformation expression, best

fitted the experimental data. With this information the

ultimate strength of connections can be predicted as des-

cribed in the following section.

13

3.3 PREDICTION OF ULTIMATE CONNECTION STRENGTH

This theoretical approach is based on three

assumptions:

1. The connection, under an eccentric load, rotates

about an instantaneous centre of rotation.

2. The deformation which occurs at each fastener

varies linearly with its distance from the

centre of rotation and in a direction per-

pendicular to the radius of rotation of the

fastener.

3. The ultimate strength of the group is reached

when the ultimate strength of the fastener

furthest from the centre of rotation is

reached.

It is further assumed that the connected plates

remain rigid during rotation and that constraints on the

members or the connection do not force rotation about

some point other than the theoretical one. Most practical

connections comply with these conditions.

For a given fastener configuration of m fasteners

with given eccentricity of load, e, (see Fig. 2) a trial

location of the instantaneous centre of rotation is chosen.

This will be a point on the straight line drawn through the

14

centre of gravity of the connection, perpendicular to the

line of action of the applied load and on the opposite side

of the centre of gravity from the applied load. The

distance from the instantaneous centre of rotation of the

connection to the centre of gravity of the fastener group

is called ro.

The distance from the centre of rotation of the

connection to each fastener is calculated. For orientation

purposes the x-axis of the connection is taken as being

perpendicular to the line of action of the externally

applied load with the origin located at the instantaneous

centre. The radius of rotation of the nth fastener becomes

(1)

The maximum fastener deformation occurs at the

fastener which is farthest removed from the instantaneous

centre. The maximum deformation of this fastener is assumed

to be the equal to the maximum deformation as obtained from

the single bolt shear tests. Therefore, the deformation of

the nth fastener is

(2)

15

in which rmax is the radius of rotation of the fastener

which is furthest from the instantaneous centre of rotation,

From the load - deformation relationship of

individual fasteners (Sect. 3.2) the resisting force of

each fastener acting perpendicular to the radius of

rotation of the fastener is calculated as

(3)

The component of the fastener force acting in the

direction opposite to that of the applied external load is

called the vertical force, Rv. From the geometry of the

connection, the vertical force of each fastener is

(4)

In order that the connection be in equilibrium

the equations of statics must be satisfied.

(5)

(6)

(7)

The first condition (5) is automatically satisfied

since there are no external forces acting on the connection

16

in the x-direction. From the third condition, (7),

the externally applied force, P, can be found. Taking

the sum of the moments about the instantaneous centre:

(8)

The second condition of equilibrium (6) must also be

satisfied:

(9)

If this condition (9) is not satisfied a new location of

the instantaneous centre must be chosen and the procedure

repeated. When a value of ro is chosen such that the

connection is in equilibrium, the value of P which satisfies

this condition is the ultimate load which the connection can

sustain.

Since an iterative procedure is used to determine

the ultimate load on a connection, a program for a digital

computer has been written. (See Appendix A for the flow

chart of the program and Appendix B for the program

printout.) The program increments the value of the

instantaneous radius of rotation, ro. The first trial

17

value of ro is taken as 0.10 inch and is increased in

.02 inch increments until a value of P is calculated such

that Eqn. 9 is satisfied within ± 2 kips. This allowance

is made since in an interative procedure "exact" equality of

Eqn. 9 will not be obtained except by coincidence.

The procedure outlined in this section has been

used to predict the ultimate loads of a series of full

size test connections and, having thus verified its use,

to predict the ultimate loads of a full range of typical

bolted connections. These topics are discussed in Chapters

4 and 5.

4 . E X P E R I M E N T A L S T U D Y

4.1 DESCRIPTION OF TEST SPECIMENS

4.1.1 Single Bolt Shear Specimens

Six single bolt specimens were tested in double

shear in order to establish the load - deformation response

of the individual fasteners in test material. The test bolts

were 3/4 inch diameter A325 bolts, all from the same lot and

specially manufactured to minimum strength properties of

ASTM A3259. The bolts were installed in ASTM A36 steel

plates, 4" x 4" in size, which were cut from the same

material as was used to manufacture the bolted connection

specimens described in Section 4.1.2. The two outside

plates (Fig. 3) were cut from the 1/2 inch plate which was

used to make the test web angles while the centre 3/4 inch

plate was cut from the web of the 24I100 which constituted

the centre beam of the test specimen. The holes in all

single bolt specimen plates were 13/16 inch diameter drilled

holes.

4.1.2 Bolted Connection Specimens

The bolted connection specimens were designed so that

18

19

the test bolts in the web angles were the critical com-

ponents. The end conditions of the specimen preclude

distortion of the web angles at the 90° corners as there

is no moment created at the reaction.

Eight specimens, which included four different

bolt groupings with varying eccentricities, were tested.

The arrangement of each test specimen gave an identical

connection at either end, thus providing two duplicate

tests in one operation. A diagram of a bolted connection

specimen is shown in Fig. 4.

The test specimen consisted of a central beam

connected by two web angles at each end to support arms.

The fasteners being tested were those connecting the web

angles to the beam. The central beam was a two foot long

section cut from a 24I100 steel shape. Web stiffeners were

welded at the centre under the load point. The leg of the

angles containing the test bolts was manufactured from

1/2 inch thick plate and the leg connected to the support

arm from 3/4 inch thick plate. All bolt holes were match-

drilled. The complete specimen, including the support arms,

was manufactured from A36 steel using standard shop practice.

The steel for all web angles was cut from the same plate and

all central beam sections were cut from the same beam. All

20

dimensions of the test specimens were checked against the

shop drawing dimensions prior to assembly of the specimens.

The connections tested in this program consisted of

one or of two vertical lines of bolts. The number of bolts

per line varied from four to six and the load eccentricity

ranged from eight inches to 15 inches. A complete description

of the test connection geometry and eccentricity is provided

in Table 1. The test bolts in the web angles of all

specimens were 3/4 inch diameter A325 bolts manufactured to

minimum strength properties of ASTM A3259. The holes for

the test bolts in the web angles and beam were 3/4 inch

diameter and were match-drilled. Because the bolts and

holes were nominally 3/4 inch diameter, the bolts had to

be lightly driven into the holes with a hammer. This

minimum clearance between the bolt and hole caused the

external force on the connection to be taken by direct

bearing on the bolts with minimum initial slippage and each

fastener carried its portion of the load immediately. Thus

the deformation of each fastener immediately varies

linearly with its distance from the centre of rotation

(Sect. 3.3) and the load - deformation relationship of each

fastener follows the same pattern as that of the single bolt

shear tests. This idealized condition probably does not

occur under working loads. It was felt however, that as

21

the practical connection does approach its ultimate

capacity, this situation would be approximated, that is,

the relatively large shearing deformations which occur in

some bolts would mean that eventually all bolts would be in

bearing. In any event, rather than introduce another

variable (slippage), this experimental procedure was used.

The web angles were connected to the support arms with

7/8 inch diameter A325 bolts in sufficient numbers to

prevent any slip at the support during the tests.

The bases of the support arms had a 10 inch radius

to maintain the eccentricity of load on the specimen during

the loading sequence. Two five inch diameter hardened

steel rollers were used under each support to permit free

lateral movement of the bases.

4.2 METHOD OF TESTING

4.2.1 Single Bolt Shear Tests

Each test specimen was assembled as shown in Fig. 3.

The test bolt was tightened to a snug position and the nut

was given an additional one-half turn as per standard

installation procedure19.

22

The assemblies were loaded in compression in a

440,000 lb. electro-mechanical testing machine. A .0001 inch

dial gage was used to measure the movement of the loading

head. This movement was assumed to be the same as the sum

of the shearing deformation of bolt and the bearing

deformations of the bolt and adjacent plates. Readings were

taken at 5 kip increments up to a load of 40 kips and at

approximately 2.5 kip increments from that point to the

ultimate load. The load rate for each test was .025 inches

per minute. All test bolts failed in shear at the thread

run-out portion of the bolt. Fig. 5 shows the six specimens

prior to testing and Fig. 6 shows a specimen after testing.

4.2.2 Bolted Connection Tests

Each test specimen was assembled as shown in Fig.4.

One pair of support arms was used for all tests. The

3/4 inch diameter test bolts and the 7/8 inch diameter

support arm bolts were tightened to a snug position and the

nuts then given an additional one-half turn. The central

beam and web angles of each specimen were whitewashed prior

to the test so that the yielding pattern of the material

could be observed.

The location of the .0001 inch dial gages on the

23

specimen is shown in Fig. 4. Gages number 1,2,3 and 4 on

one side and corresponding gages 6,7,8 and 9 on the other

side were used to measure the horizontal movement of the

web angles with respect to the centre beam. The vertical

distances between gage pairs 1-2, 3-4, 6-7, and 8-9 were

set at known values and these were used to calculate the

rotation of the web angles. Gages 5 and 10 measured the

vertical movement of the web angle with respect to the top

flange of the beam.

These tests were also conducted in the 440,000 lb.

electro-mechanical testing machine. A loading rate of

.025 inches per minute was used for lower loads and

.05 inches per minute was used when deflections increased.

Deformation readings were taken at load intervals of

approximately 1/15 of the predicted ultimate load while

within the elastic range. The load increment was decreased

as the ultimate load was approached. The gages were removed

after the ultimate load had been reached and before failure

occurred. Failure in all cases occurred by the shearing of

the bolt furthest from the centre of rotation of the angles.

A typical instrumented specimen is shown in Fig. 7

and Fig. 8 shows the same specimen in the testing machine.

Fig. 9 shows two typical specimens after failure has occurred.

24

4.2.3 Single Bolt Tension Tests

The ASTM specifications do not provide shear

strength requirements of high strength bolts and the minimum

shear strength, in particular, is required in order that any

design load tables for eccentrically loaded connections will

refer to minimum strength bolts. It is commonly assumed

that the ratio of the minimum shear strength to the ultimate

shear strength is equal to the ratio of the minimum

tensile strength to the ultimate tensile strength20.

Based on this assumption the minimum shear strength of a

single fastener , can be expressed as

in which = Minimum tensile strength as specified inASTM A325

= Ultimate tensile strength as determinedfrom tension tests on full-size specimens

= Double shear strength as determined by sheartests (Sect. 4.2.2)

To obtain the ultimate tensile strength, five

individual 3/4 inch diameter A325 bolts were tested in

tension in a 100,000 lb. mechanical testing machine. The

tension jig used for the tests consisted of a rigid plate

25

with a 13/16 inch diameter hole in the centre attached to the

immovable (upper) head of the testing machine and a 3/4 inch

inside diameter nut attached to the movable head. The bolt

passed downward through the hole with the shoulders of the

head resting on the top side of the rigid plate. The bolt

was turned into the nut until six threads remained exposed

between the nut and the thread run-out. The loading rate

used for each test was 0.025 inches per minute.

In all specimens the section of the bolt in the

region of the six exposed threads was noticeably elongated

when failure occurred.

4.3 TEST RESULTS

4.3.1 Single Bolt Shear Tests

The results of the single bolt shear tests are pre-

sented in Fig. 10 in the form of a load versus deformation

graph. The theoretical load - deformation relationship,

, which best fits the experimental data

is shown as the solid line. The ultimate load and

deformation of each specimen are also listed on Fig. 10.

26

4.3.2 Bolted Connection Tests

The results of these tests are presented in Figs. 11

through 21 and in Table 2. Figs. 11 through 18 show the

load on the specimen versus the rotation of the bolted

connection. The specimens were orientated in a North-

South direction and curves are shown for each of the North

and South connections. The rotation of the connection

was calculated using the deformations recorded by the dial

gages located on the vertical faces of the specimen

(see Fig. 4) and the actual distance between the axes of

each pair of dial gages. The rotation of each connection as

shown is the average of the rotations of both sides

(East and West). For example, the rotation of the South

connection is the average of the rotations calculated from

the readings of Gages 1 and 2 and Gages 6 and 7. Similarly,

for the North end, Gages 3 and 4 and Gages 8 and 9 were

used. The ultimate load for each specimen is also shown on

the figures.

Moment - rotation curves are plotted in Figs. 19 and

20. These curves show the moments carried by identical

fastener groups which have different eccentricities.

Fig. 21 illustrates load versus vertical deformation

curves for three representative test specimens. The data for

27

these curves were obtained from Gages 5 and 10, located on

the top flange of the centre beam over the centre line

of the bolt group.

Table 2 lists predicted and actual ultimate loads,

the current allowable load6 and the factor of safety

against ultimate based on this current allowable value.

Also listed in Table 2 are the theoretical and experimental

radii of rotation of each test connection.

4.3.3 Single Bolt Tension Tests

The results of the five single bolt tension tests

are tabulated in Table 3. Also shown is the minimum

specified tensile strength of A325 bolts and the percentage

by which the actual strength is greater than the specified

strength. The strength of the bolts is (on the average)

less than 1% above the minimum strength.

5 . D I S C U S S I O N O F R E S U L T S

5.1 SINGLE BOLT SHEAR TESTS

The load - deformation behavior of the fasteners

used in these tests (Fig. 10) is very similar to that

presented by Fisher4. For small values of deformation

the relationship between load and deformation is approx-

imately linear and as the deformation approaches ultimate

the bolt force increases at a decreasing rate. The

mathematical expression for the load - deformation

relationship, , (see Sect. 3.2) best

fits the data when values = 10.0 and = 0.55 are used

as the two empirical coefficients.

No appreciable slippage between the connecting

plates occurred and as can be seen from the load -

deformation curve none of the test bolts have a well-defined

yield point.

The mean maximum bolt force was 74.0 kips with a

standard deviation of 2.4 kips and the mean maximum

deformation was 0.34 inches with a standard deviation of

0.03 inches. The mean values were used to predict the

ultimate loads of the test connections.

28

29

5.2 BOLTED CONNECTION TESTS

5.2.1 Load - Rotation Behavior

The load - rotation response of the connections of

the eight test specimens is shown in Figs. 11 through 18.

The curves show that a linear (elastic) relationship

between the applied load and the connection rotation exists

at low loads. For higher loads the relationship becomes non-

linear (plastic), as expected. Failure of each specimen

occurred at the connection which had the larger rotation at

ultimate load in all cases except one. Specimen B8 failed

at the connection with the smaller rotation but there was

only 3.5% difference in the angles of rotation of the North

and South connections.

At low loads the bolts behave elastically and the

elastic rotation of identical bolt groups should be the same

for equal applied moments regardless of the direct shear

force. The moment - rotation curves in Fig. 19 and Fig. 20

show that this is true. Also, within the plastic range of

two identical fastener groups with different eccentricities,

the connection with the smaller eccentricity carries the

smaller moment and larger shear force. The curves of

Specimens B4 and B5 (Fig. 19) confirm this while the curves

of Specimens B6 and B7 (Fig. 20) appear to be reversed.

30

At higher strains the curves of B6 and B7 resume their

proper order. The yield marks as observed on the test angles

of B7 are more prominent than those on B6 leading to the con-

clusion that these elements of B7 were less rigid than those

of B6. This can account for the greater rotation of B7.

The tests performed in this investigation reflect

the conditions of loading on the bolts which exist in a

"statically determinate" connection such as cantilever

brackets and members with negligible resistance to moment.

Since these restraint (end) conditions do not represent

many practical cases, the moment - rotation relationships

have little direct use.

5.2.2 Load - Vertical Displacement Behavior

The load versus vertical displacement curves,

Fig. 21, show the same trends as seen in the load -

rotation curves. The curves indicate a linear relation-

ship at low loads and a curvilinear relationship as the

load approaches its ultimate value. They show no specific

yield point for the fasteners.

As discussed in Chapter 3, the ultimate load pre-

dictions are made by determining the instantaneous radius

31

of rotation by an iteration method. An experimental

radius of rotation can be calculated from the test data

making use of the angle of rotation of the connection and

the vertical displacement of the bolt group. The

theoretical and experimental radii of rotation are listed

in Table 2 and the experimental values do not agree closely

with the theoretical ones. However, the radius of the

connection which failed on each specimen was, in all except

two cases, the smaller of the experimental radii for that

specimen. This confirms the observation made with regard

to the load - rotation curves, that failure occurred at

the connection with the greatest angle of rotation and

therefore the smallest radius of rotation since the maximum

bolt deformation of each is considered to be the same.

The radius of rotation is calculated by dividing

the vertical displacement of the bolt group by the tangent

of the angle of rotation. The vertical displacement and

the angle of rotation are both small so that a small error

in the measurement of either would significantly affect

the calculation of the experimental radius of rotation.

However, since the angle of rotation of the connection is

the result of readings taken from four gages while the

vertical displacement was measured with one gage, the most

probable source of error is in the measurement of the

32

vertical displacement.

In several instances one connection of a specimen

tended to have an upward or negative movement during the

first few load increments. It is presumed that the negative

movement occurred as a result of redistribution of the

forces on the test fasteners and support arms. When the

internal equilibrium of the connections was reached, both

ends resumed positive movements. As a result of this

negative movement, the net vertical displacement at

ultimate load of one connection may be greater than the

other. This is reflected in the radius of rotation cal-

culation. For example, the South end of Specimen B1

and the North end of Specimen B7 had upward movement

at the initial loads and the radius of rotation of the

failed connection appears to be greater than the unfailed

one. Because of these discrepancies in the calculation

of the experimental radius of rotation, the theoretical

value has been used in any calculation of predicted loads.

5.2.3 Prediction of Ultimate Loads

The predicted ultimate loads for the test specimens

ranged between 5% and 14% higher than the ultimate test

loads (Table 2). Several factors which influence this trend

33

towards lower test loads can be cited.

First, the analytical solution presented in this

report determines the ultimate strength of a single

connection. Since the test specimens consist of two

identical connections each, the ultimate load prediction

for the specimen is obtained by doubling the prediction for

a single connection. In the ideal situation, both

connections would fail simultaneously. However, due to

material discrepancies, manufacturing tolerances, etc., the

ultimate load of the specimen was reached when one only

connection had failed. It is probable that the ultimate

load on the specimen is not 2.0 P but rather some lesser

value, say 1.9 P, where P is the predicted ultimate load

per connection.

Secondly, the theoretical load - deformation

relationship for individual fasteners does not exactly

follow the mean curve for the experimental data. As can

be seen in Fig. 10, the load - deformation relationship

that has been selected as the curve which most closely

fits the data is above the mean value of the test points

for deformations of approximately 0.06 inches to 0.22 inches

and below the mean value for deformations which are greater

than 0.22 inches. In the connections investigated, the

34

most significant vertical forces were attributed to the

bolts whose deformations came within the 0.06 inches to

0.22 inches range. This would tend to make the predictions

on the high side and unconservative.

Thirdly, it is recognized that the deformation of

the connection bolts do not reach the maximum value

indicated by the single bolt shear tests. In the single bolt

tests the load and deformation direction remains constant

whereas, in the bolted connection tests, the load and

deformation of each bolt changes direction continually as

the instantaneous centre of rotation changes with increase

in applied load. At low loads the force on the connection

bolts acts, in effect, parallel to the direction of the

applied load, but as the load is increased to the ultimate

load, the line of action of the force on each bolt rotates

to a position which is perpendicular to the radius of

rotation of that bolt. It was observed from the test

specimens after testing that the bolt holes were deformed

and scored by the circular movement of the bolts. Because

of this "effective rotation" of the bolts and the deformation

of the connecting plates, it is unlikely that the bolt

which is furthest from the final centre of rotation will be

deformed as much as an individual fastener loaded with a

unidirectional force. Thus, the deformation and consequently

35

the forces on the remaining bolts in the connection will

be reduced. Calculations show that a 10-15% decrease in

maximum deformation results in a 2% decrease in the

theoretical ultimate load of the specimens that were

tested.

On the basis of these three points the ultimate

load predictions appear to be reasonable and should, in

fact, be slightly higher than the test loads. Since the

amount by which the predictions are on the conservative

side is small, this can be taken into consideration when

selecting a factor of safety for the fasteners.

The validity of the theoretical approach presented

in this thesis has also been substantiated by using the

results of the test series on riveted connections con-

ducted by Yarimci and Slutter13. The details of the test

specimens are shown on Table 4 and the results of those

tests and the prediction for the ultimate load using the

method described herein are listed in Table 5. The

actual test load and the predicted load closely agree.

The predictions were calculated using the actual maximum

rivet force and maximum rivet deformation as set forth by

the single rivet curves of that report. A maximum bolt

force (Rult) of 55.0 kips and a maximum deformation ( )

of 0.30 inches were used.

36

The test program reported in this thesis and the test

program reported by Yarimci and Slutter cover a reasonably

representative sample of eccentrically loaded connections.

The tested connections include fastener groups with one

and two vertical lines of fasteners. The number of

fasteners per line range from two to six, and the load

eccentricities range from 2-1/2 inches to 15 inches. The

test results agree satisfactorily with the predictions made

using the analytical approach presented in this report.

It is felt that on the basis of these studies this method

of predicting the ultimate load capacity of connections is

acceptable and accurate predictions of ultimate loads can be

made.

5.2.4 Comparison of Ultimate Loads and Current Allowable Loads

The allowable loads for the tested specimens as

permitted by the AISC and CISC Manuals6,7 are tabulated in

Table 2. These values are based on the assumption that

each fastener of the group carries an equal share of the

direct load and that each carries an additional load due

to moment which is proportional to its distance from the

centre of gravity of the group and which acts at right angles

to the line connecting the fastener to the centre of gravity

37

of the group. The actual eccentricity of the connection

is replaced by a reduced "effective eccentricity"8 for use

in calculating the moment on the connection. The factor of

safety for the test specimens, calculated on the basis of

these allowable loads, is obtained by dividing the ultimate

test load by the allowable load. This factor of safety is

tabulated for each specimen in Table 2. It ranges in value

from 2.68 to 3.42.

Although it is not the purpose of this thesis to

recommend allowable loads, it is felt that the present

factor of safety is unnecessarily high. Studies on bearing-

type bolted connections in tension members21 have

indicated that a factor of safety against fastener shear

failure as low as 2.1 is adequate. This value is higher

than the factor of safety of the connected material and

other structural components. It was recommended that a

desirable design criterion for bearing-type fasteners be

that the factor of safety of the fasteners be somewhat

higher than that of the connecting plate. The suggested21

value is 2.0 to 2.2 which is the same order of magnitude

as for fasteners in tension. It would be desirable to have

a single factor of safety common to all types of connections

for the sake of consistency and uniformity.

38

5.3 ULTIMATE LOAD TABLES

Ultimate load tables have been prepared for

eccentrically loaded fastener groups which use A325 bolts

and structural carbon steel elements. These are enclosed

in Appendix C. The fastener groups which are included

are composed of one or of two vertical lines of up to 12

fasteners per line. The maximum eccentricity considered

is 24 inches. The analytical method presented in Chapter 3

of this report has been used as the basis of the load

tables. The tables apply to ASTM A325 bolts only. The

load tables are presented in a different form as charts in

Appendix D. The charts show the ultimate loads of the

fastener groups with respect to the load eccentricity of

the connection.

It would be desirable to have a simple formula for

computing ultimate loads. However, it has not been found

possible to formulate a rational equation which takes

into account the independent variables such as load

eccentricity, number of lines and rows of fasteners, and

fastener group geometry. It is felt that the load tables

provide an adequate presentation of the ultimate loads of

common fastener configurations.

Load tables which are to be useful to designers and

39

engineers must be applicable to any type of connecting plates

and to all bolt diameters. It has been shown20 that, although

the type of connecting material affects the amount of total

deformation, it has no effect on the shear strength of the

bolts. For example, the shear strength of the A325 bolt

will be the same in A36 steel plates as it will be in

G40.12 steel. The total deformation capacity will be less

in G40.12 steel. However, this difference is offset some-

what by the more favorable distribution of the joint load

in the higher strength steels. Also, as mentioned previously

(Sect. 5.2.3) a considerable decrease in deformation

produces only a small change in the ultimate load of the

bolt group. It has also been shown20 that, within the range

of common structural sizes, bolt diameter is an independent

variable. It is considered justifiable then to use the

results of shear tests on 3/4 inch diameter A325 bolts

in ASTM A36 steel connecting plates to predict ultimate

loads which can be applied to A325 bolts of all diameters

in various types of steel plates.

The ultimate load tables are to be used by select-

ing from the table the tabulated value for the fastener

group and eccentricity which applies to the connection

being investigated. This value is to be multiplied by the

double shear area of the bolts being used to obtain the

40

ultimate load which the connection can carry.

It should be noted that the tables should be pre-

pared on the basis of minimum strength properties as des-

cribed in Sect. 4.2.3. However, since the theoretical

minimum strength of the test bolts were less than 1%

below their actual strength, the actual strength of the

bolts was used.

It would seem unadvisable to use these tables for

bolts in single shear since variables such as the prying

action of the plates and eccentric action of the forces on

the bolt itself have not been considered in these tests.

It is felt that the tables could not be applied to

ASTM A490 bolts. Although the bolt strength and ultimate

deformations of single bolt tests increase proportionally,

the empirical parameters for the load - deformation curve

(Sect. 3.2) are significantly different than those for

A325 bolts4. The analytical method could be used to produce

tables for A490 bolts by using the load - deformation

relationship of A490 single bolt tests.

41

6 . C O N C L U S I O N S

The following conclusions have been reached as a

result of this investigation:

1. A theoretical method for predicting the ultimate

load - bearing capacity of eccentrically loaded

bolted connections has been developed. The

method uses the actual load - deformation response

of individual fasteners as its basis.

2. The results of an extensive testing program have

verified the ultimate load predictions made for

the test specimens using the new theoretical

approach.

3. The factor of safety which the current allowable

loads provide for eccentrically loaded connections

is both high and inconsistent. By making use of

the more accurate predictions of ultimate loads as

its basis, the factor of safety can be brought more

in line with that of other structural components and

can be established at a constant value for all

connections of this type.

42

TABLES AND FIGURES

Table 1 - DETAILS OF TEST SPECIMENS

43

SpecimenNumber

B1

B2

B3

B4

B5

B6

B7

B8

Bolt Group Eccentricitye (ins.)

8

10

12

13

15

12

15

15

P(ins.)

2-1/2

3

3

3

3

3

3

2-1/2

s(ins.)

-

-

-

-

2-1/2

2-1/2

2-1/2

NOTES: - All central beams-24 I 100, A36 steelAll angle test legs-1/2 inch thick, A36 steelAll test bolts-ASTM A325, 3/4 inch diameterAll test bolt holes-3/4 inch diameter, match-drilled

Table 2 - TEST RESULTS

SpecimenNumber

B1

B2

B3

B4

B5

B6

B7

B8

Pred.

P u l t

(kips)

252

244

206

274

239

293

239

309

Test

P u l t

(kips)

225

230

190

251

221

264

212

266

TestPred.

0.894

0.945

0.924

0.916

0.925

0.901

0.885

0.860

Theor.Radius ofRotation(ins.)

0.98

1.12

0.88

1.32

1.12

0.98

0.80

0.92

Exp. Radiusof Rotation (in.)FailedEnd

1.13(N)

1.01(S)

0.47(S)

0.66(N)

0.66(S)

0.39(N)

0.67(S)

0.62(S)

UnfailedEnd

0.44

1.25

0.64

0.80

-

0.72

0.52

0.82

CurrentAllowableLoad (kip)(AISC,CISC)

84

75

60

79

67

82

63

76

CurrentFactorof

Safety

2.68

3.09

3.17

3.18

3.28

3.10

3.36

3.42

44

45

Table 3 - TENSION TEST RESULTS

Bolt No.

1

2

3

4

5

Actual TensileStrength (lb.)

40,200

40,240

40,320

40,600

40,240

Specified TensileStrength (lb.) 9

40,100

40,100

40,100

40,100

40,100

% AboveMin. Strength

0.25

0.35

0.55

1.25

0.35

9

46

Table 4 - DETAILS OF TEST SPECIMENS BY OTHERS

SpecimenNumber

TP-1

TP-2

TP-3

TP-4

TP-5

TP-6

TP-7

TP-8

TP-9

TP-10

RivetGroup

Eccentricitye (in.)

2-1/2

3-1/2

6-1/2

2-1/2

4-1/2

6-1/2

3-1/2

6-1/2

3-1/2

6-1/2

P(in.)

3

3

3

3

3

3

3

3

3

3

s(in.)

-

-

-

-

-

-

2-1/2

2-1/2

2-1/2

2-1/2

NOTES: - Central beams-15 I 50 or 24 I 120, A7 steelTest angles-7/16" or 1/2" thick, A7 steelTest rivets-ASTM A141, 3/4" diameterTest rivet holes-13/16" diameter, punched

47

Table 5 - RESULTS AND PREDICTIONS OF TESTS BY OTHERS

SpecimenNumber

TP-1

TP-2

TP-3

TP-4

TP-5

TP-6

TP-7

TP-8

TP-9

TP-10

PredictedLoad(Others)(kips)

208

165.6

98

561

428

335

195

122.5

534

358

PredictedLoad(new)(kips)

210

166

96

566

454

358

190

115

561

367

TestLoad(kips)

216.5

160.75

100

550

440

362

221.75

120

568

354

TestPred.(Others)

1.04

0.97

1.02

0.98

1.03

1.08

1.14

0.98

1.06

0.99

TestPred.(new)

1.03

0.97

1.04

0.97

0.97

1.03

1.17

1.04

1.01

0.96

48

Fig. 1 TYPICAL ECCENTRICALLYLOADED CONNECTIONS

Fig. 2 ECCENTRICALLY LOADED BOLT GROUP

49

Fig. 3 SINGLE BOLT SHEAR SPECIMEN

Fig. 4 BOLTED CONNECTION SPECIMEN

50

Fig. 5 SINGLE BOLT SPECIMENS

Fig. 6 FAILED SINGLE BOLT SPECIMEN

51

Fig. 7 BOLTED SPECIMEN WITH GAGES

Fig. 8 BOLTED SPECIMEN IN TEST MACHINE

52

Fig. 9 TYPICAL FAILED BOLTED SPECIMENS

53

Fig. 10 LOAD - DEFORMATION CURVES FOR SINGLE BOLT TESTS

54

Fig. 11 LOAD - ROTATION CURVE FOR SPECIMEN B1


55



56



57



58

Fig. 19 MOMENT - ROTATION CURVES FOR SPECIMENS B4 AND B5

Fig. 20 MOMENT - ROTATION CURVES FOR SPECIMENS B6 AND B7

Fig. 21 TYPICAL LOAD - VERTICAL DISPLACEMENT CURVES FOR BOLTED SPECIMENS

59

60

R E F E R E N C E S

1. Grinter, L.E.DESIGN OF MODERN STEEL STRUCTURES, The MacMillanCompany, New York, 2nd edition, 1960, pp. 32-48

2. Bresler, B., and Lin, T.Y.DESIGN OF STEEL STRUCTURES, John Wiley and Sons,Inc., New York, 1960, pp. 86-100

3. Gaylord, E.H., and Gaylord, C.N.DESIGN OF STEEL STRUCTURES, McGraw-Hill BookCompany, Inc., 1957, pp. 246-254

4. Fisher, J.W.BEHAVIOR OF FASTENERS AND PLATES WITH HOLES, Journalof the Structural Division, Proceedings of theAmerican Society of Civil Engineers, Proc. Paper4587, Vol. 91, ST 6, December, 1965

5. Fisher, J.W., Kulak, G.L., and Beedle, L.S.BEHAVIOR OF LARGE BOLTED JOINTS, Highway ResearchRecord, Highway Research Board, Washington, D.C.,NO. 147, 1966

6. MANUAL OF STEEL CONSTRUCTION, 6th edition, AmericanInstitute of Steel Construction, New York, 1963

7. HANDBOOK OF STEEL CONSTRUCTION, 1st edition, CanadianInstitute of Steel Construction, Toronto, Ontario,1967

8. Higgins, T.R.NEW FORMULA FOR FASTENERS LOADED OFF CENTRE,Engineering-News Record, May 21, 1964, pp. 102

9. SPECIFICATION FOR HIGH-STRENGTH STEEL BOLTS A325-66a,American Society for Testing and Materials, 1967

61

10. Rathburn, J.C.ELASTIC PROPERTIES OF RIVETED CONNECTIONS, ASCEProceedings, Vol. 101, p. 524, 1936

11. Hechtman, R.A., and Johnston, B.G.RIVETED SEMI-RIGID BEAM-TO-COLUMN BUILDINGCONNECTIONS, Progress Report No, 1, Committee onSteel Structures Research, AISC, November, 1947

12. Munse, W.H., Bell, W.G., and Chesson, E., Jr.BEHAVIOR OF RIVETED AND BOLTED BEAM-TO-COLUMNCONNECTIONS, ASCE Proceedings, Vol. 85, p.29,March, 1959

13. Yarimci, E., and Slutter, R.G.RESULTS OF TESTS ON RIVETED CONNECTIONS, FritzEngineering Laboratory, Lehigh University,Bethlehem, Pennsylvania, Report No. 200.63.403.1,April, 1963

14. Shermer, C.L.ULTIMATE STRENGTH ANALYSIS AND DESIGN OFECCENTRICALLY LOADED BOLTED OR RIVETED FASTENERS,Preprint for ASCE Structural Engineering Conference,October, 1964

15. Abolitz, A.L.PLASTIC DESIGN OF ECCENTRICALLY LOADED FASTENERSEngineering Journal, AISC, Vol. 3, No. 3, July, 1966

16. Kulak, G.L., and Fisher, J.W.Discussion of PLASTIC DESIGN OF ECCENTRICALLYLOADED FASTENERS by Abolitz, A.L., EngineeringJournal, American Institute of Steel Construction,July, 1967

17. McGuire, WilliamSTEEL STRUCTURES, Prentice-Hall, Inc., EnglewoodCliffs, N.J., 1968, pp. 812-820

62

18. BIBLIOGRAPHY ON BOLTED AND RIVETED JOINTS, ASCE Manualsand Reports on Engineering Practice, No. 48, NewYork, 1967

19. SPECIFICATION FOR STRUCTURAL JOINTS USING ASTM A325 orA490 BOLTS, Research Council on Riveted and BoltedStructural Joints, March, 1964

20. Fisher, J.W., and Wallaert, J.J.SHEAR STRENGTH OF HIGH STRENGTH BOLTS, Journal ofthe Structural Division, Proceedings of theAmerican Society of Civil Engineers, Proc. Paper4368, Vol. 91, ST 3, June, 1965

21. Fisher, J.W., and Beedle, L.S.CRITERIA FOR DESIGNING BEARING-TYPE BOLTED JOINTS,Journal of the Structural Division, Proceeding ofthe American Society of Civil Engineers, Proc.Paper 4511, Vol. 91, ST 5, October, 1965

63

L I S T O F A P P E N D I C E S

Appendix Page

A Flow Chart of Computer Program for 64Calculating Ultimate Loads

B Computer Program for Calculating 65Ultimate Loads

C Ultimate Load Tables 67

D Ultimate Load Charts 69

64

APPENDIX A

FLOW CHART OF COMPUTER PROGRAM FOR CALCULATING ULTIMATE LOADS

65

APPENDIX B

COMPUTER PROGRAM FOR CALCULATING ULTIMATE LOADS

This program, to calculate the ultimate load of

eccentrically loaded fastener groups is written in

Fortran IV for the IBM 1130 computer.

67

APPENDIX C. ULTIMATE LOAD TABLES

ULTIMATE ECCENTRIC LOADS ON FASTENER GROUPS - ONE LINE

e = Actual eccentricity ofapplied load

n = Total number of fastenersper vertical line

K = Value tabulated belowPult = Ultimate load on the

connection in kipsPult = K x Double shear area of bolt

(This table is valid for ASTM A325 bolts only)

ein.

3

4

5

6

7

8

9

10

11

12

14

16

18

20

22

24

n

2

72

55

46

38

32

28

26

24

22

19

15

13

12

11

10

9

3

143

114

94

78

67

60

54

49

44

41

35

28

25

22

18

15

4

230

194

164

141

124

109

99

89

82

75

64

55

51

46

41

36

5

320

278

242

211

187

166

150

135

125

114

99

87

76

70

63

58

6

410

367

326

290

260

234

212

193

177

163

141

125

112

102

91

84

7

499

457

414

374

338

308

281

257

237

219

190

169

150

135

122

113

8

587

546

504

461

420

386

355

328

302

282

246

217

196

177

161

149

9

670

636

594

550

509

470

435

403

375

349

307

272

244

221

203

186

10

765

724

683

640

597

556

518

482

450

422

372

333

299

273

248

230

11

858

816

772

730

687

644

604

566

531

498

443

396

358

327

299

276

12

959

909

863

820

777

734

692

652

614

579

517

466

422

384

352

326

68

APPENDIX C. ULTIMATE LOAD TABLES

ULTIMATE ECCENTRIC LOADS ON FASTENER GROUPS - TWO LINES

e = Actual eccentricity ofapplied load

n = Total number of fastenersper vertical line

K = Value tabulated belowP u l t= Ultimate load on the

connection in kipsP u l t= K x Double shear area of bolt

(This table is valid for ASTM A325 bolts only)

ein.

3

4

5

6

7

8

9

10

11

12

14

16

18

20

22

24

n

2

166

137

116

99

88

78

70

64

58

54

45

40

36

32

29

27

3

302

252

212

184

163

145

131

120

110

100

89

77

68

62

57

53

4

465

399

345

304

268

242

218

199

184

168

147

128

116

104

95

86

5

639

562

493

438

390

351

316

290

266

247

213

189

169

156

139

130

6

815

734

657

589

530

482

438

403

372

343

299

267

238

216

198

180

7

992

911

829

753

683

623

573

526

488

451

396

351

317

286

263

238

8

1168

1088

1005

925

849

780

718

665

616

574

507

448

403

366

336

309

9

1360

1266

1183

1100

1019

944

875

814

758

708

624

557

503

456

417

383

10

1530

1443

1361

1277

1194

1113

1038

970

907

852

756

676

610

555

510

470

11

1719

1635

1551

1467

1381

1297

1217

1143

1073

1009

899

807

729

666

612

565

12

1924

1838

1742

1656

1571

1484

1401

1321

1245

1176

1050

946

859

783

722

667

APPENDIX D. ULTIMATE LOAD CHARTS

ULTIMATE ECCENTRIC LOADS ON FASTENER GROUPS - ONE LINE(Valid for A325 Bolts only)

n = number of fasteners per line

Ultimate Load (kips) = K x Double Shear Area of bolt

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APPENDIX D. ULTIMATE LOAD CHARTS

ULTIMATE ECCENTRIC LOADS ON FASTENER GROUPS - TWO LINES(Valid for A325 Bolts only)

n = number of fasteners per line

Ultimate Load (kips) = K x Double Shear Area of bolt

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Crawford Kulak 1968

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Transcript of Crawford Kulak 1968