DUCTILITY AND STRENGTH OF SINGLE PLATE ......12. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/4-Inch A36 Plates 97 13. Load-Deformation Data for a 3/4-Inch

DUCTILITY AND STRENGTH OFSINGLE PLATE CONNECTIONS

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GILLETT# PAUL EDWARD DUCTILITY AND STRENGTH OF SINGLE PLATE CONNECTIONS,

THE UNIVERSITY OF ARIZONA, PH,D t , 1978

University Mcrdfilrns

International 300 N. ZtED ROAD, ANN ARBOH, Ml 48106

DUCTILITY AND STRENGTH OF SINGLE

PLATE CONNECTIONS

by

Paul Edward Gillett

A Dissertation Submitted to the Faculty of the

DEPARTMENT OF CIVIL ENGINEERING AiND ENGINEERING MECHANICS

In Partial Fulfillment of the Requirements For the Degree of

DOCTOR OF PHILOSOPHY WITH A MAJOR IN CIVIL ENGINEERING

In the Graduate College

THE UNIVERSITY OF ARIZONA

19 7 8

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

I hereby recommend that this dissertation prepared under my

direction by Paul Edward Gillett

entitled DUCTILITY AND STRENGTH OF SINGLE PLATE CONNECTIONS

be accepted as fulfilling the dissertation requirement for the

degree of Doctor of Philosophy

Dissertation Director

As members of the Final Examination Committee, we certify

that we have read this dissertation and agree that it may be

presented for final defense.

./?n

.) C\/Wi •/>- is

V a 90^- 0 YVU$.t±

Final approval and acceptance of this dissertation is contingent on the candidate's adequate performance and defense thereof at the final oral examination.

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

ACKNOWLEDGMENTS

Appreciation is gratefully acknowledged to the many people who

made contributions to this study. A prompt and successful completion

must be attributed in large part to their efforts.

Robert Crooks deserves a special word of thanks. He partici

pated in all seventy-five single bolt, single shear tests, wrote a mesh

generator for framing plate finite element models, and provided assis

tance in numerous other ways. Lou Gemson and Bill Lichtenwalter fabri

cated the test fixture and deformation measuring device, and helped

prepare the test plates for testing. Thanks are extended to Lou for

his advice and comments with regard to this project and otherwise.

The American Iron and Steel Institute (AISI) provided the

grant for this research. The strong interest and support of the

members of Joint Task Force of AISI and the American Institute of Steel

Construction for Project 302 meant valuable guidance during all phases

of the study.

Appreciation is extended to the members of the graduate com

mittee, Professors James D. Kriegh, Richmond C. Neff, Allan J. Malvik,

Hussein A. Kamel and Ralph M. Richard for their efforts. Dr. Richard,

as the academic and dissertation advisor is entitled to special thanks

for providing the initial involvement and continued support throughout

the study. Many, many hours of his time were spent in discussions,

review and guidance.

iii

Special appreciation is expressed to David Daigle and

Manoucher Homayoun, long time friends, for their support and encour

agement .

Finally, Sharon and my parents deserve a special word for

their support, which made this work possible.

TABLE OF CONTENTS

Page

LIST OF TABLES vii

LIST OF ILLUSTRATIONS x

ABSTRACT xiv

1. INTRODUCTION 1

Objective 1 Procedure 5

2. SINGLE BOLT, SINGLE SHEAR TESTS 5

Testing Program 6 Test Fixture 10 Test Procedure 12 Load-Deformation Curves 12

Control of Load-Deformation Relationship by the Thinner Plate 15

Failure Deformations, Loads and Modes 15

3. FINITE ELEMENT MODEL 21

Program INELAS ..... 21 Definition of Eccentricity . 22 Definition of Rotation 22 Full Beam and Connection Models 24

Comparison with Lipson's Tests 24 Behavior of the Connection 24

Equivalence to Rigid Plate Action 27 Bolt Loads in the Connection ......... 29 Effect of Load Eccentricity 29

Simplified Model 32 Comparison with Full Beam and Connection Model . . 59

4. MOMENT-ROTATION CURVES 45

Scope of Calculations 45 Source of Ductility 47 Limiting Deformation .... 54 Analytic Expressions 56

v

vi

TABLE OF CONTENTS--Continued

Page

5. FRAMING PLATE AND WELD LOADS 65

6. DESIGN PROCEDURES 69

Beam Line Method 69 Theory 69

Use of Table X 73 Use of Analytic Expressions 79

7. FACTORS OF SAFETY IN THE DESIGN METHODS 80

Table X Design Procedure 80 Alternate Procedure .... 81 Design Examples 85

8. SUMMARY AND CONCLUSION 91

Summary 91 Conclusions 92 Apparent Success of Existing Connections . 92

APPENDIX A: TEST RESULTS 94

APPENDIX B: EFFECTIVE SPRING RATES IN SINGLE SHEAR JOINTS CCHANCE VOUGHT) 148

APPENDIX C: DESIGN EXAiMPLE USING THE ALTERNATE PROCEDURE. . . 150

REFERENCES 135

LIST OF TABLES

Table Page

1. Test Program for Single Bolt, Single Shear Tests 7

2. Curve Parameters 14

3. Failure Modes, Average Maximum Loads and Failure Deformations for the Test Specimens 19

4. Comparison of Moment-Rotation Curves for Seven-Bolt Connection for Full Beam and Connection Model with a Rigid Plate Model CPure Moment) 28

5. Comparison of Shear Loads for Seven-Bolt Connection for Full Beam and Connection Model with a Rigid Plate Model (Pure Shear) 28

6. Minimum Framing Plate Thicknesses and the Beams on Which the Thicknesses Were Based 48

7. $re£ f°r Use in the Nondimensional Moment-Rotation Equation 63

8. M f Values in Inch-Kips Based on Test Results for Use r in the Mondimensional Moment-Rotation Equation 63

9. Limiting Deformations (A^m) in Inches 64

10. Summary of Example Problems ..... 86

11. Results of Tests on Tensile Test Coupons 95

12. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/4-Inch A36 Plates 97

13. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 5/16-Inch A36 Plates. 99




vii

viii

LIST OF TABLES--Continued

Table Page

17. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 1/4-inch and 3/8-Inch A36 Plates 107

18. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 1/4-Inch and 1/2-Inch A36 Plates 109

19. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 3/8-Inch and 1/2-Inch A36 Plates Ill



22. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 7/16-Inch A36 Plates ..... 117



25. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 1/4-Inch and 1/2-Inch A36 Plates . 123


27. Load-Deformation Data for a 1-inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates 127

28. Load-Deformation Data for a 1-inch Diameter A325 Bolt Connecting Two 5/8-Inch A36 Plates 129

29. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A572, Grade 50, Plates .... 131

30. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A572, Grade 50, Plates 133

31. Load-Deformation Data for a 3/4-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates. 135

ix

LIST OF TABLES--Continued

Table Page




35. Load Deformation Data for a 1-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates 143

36. Load-Deformation Data for a 1-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates 145

37. Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A572, Grade 50, Plates 147

LIST OF ILLUSTRATIONS

Figure Page

1. Single Plate Framing Connection Connecting Beam to Web of Supporting Beam 2

2. Single Plate Framing Connection Connecting Beam to Flange of Supporting Column 2

3. Dimensions of Test Plates 9

4. Test Fixture 11

5. Deformation Measuring Device 11

6. Combined Plot of Analytical Expressions for 3/4-Inch Diameter A325 Bolt Specimen 16

7. Shear Failure of the Bolt IS

8. Bearing Failure of the Plate 18

9. Transverse Tension Tearing of the Plate 18

10. Definition of Eccentricity 23

11. Deformed Shape of Cross Section of Beam with Corresponding Centerline Rotation Superimposed 25

12. Finite Element Grid for Full Beam and Connection Model ... 26

13. Load Vectors Acting on Bolts from Supported Beam under Pure Moment 30

14. Load Paths from the Beam Flanges to Connection Bolts .... 31

15. Moment-Rotation Relationships with Varying Eccentricities for a Seven-Bolt Connection 35

16. Finite Element Grid for the Two-Bolt Connection 34

17. Finite Element Grid for the Three-Bolt Connection 35

18. Finite Element Grid for the Five-Bolt Connection 36

19. Finite Element Grid for the Seven-Bolt Connection 37

x

xi

LIST OF I ILLUSTRATIONS- - Continued

Figure Page

20. Finite Element Grid for the Nine-Bolt Connection 38

21. Comparison of Moment-Rotation Curves with Connection under Pure Moment 40

22. Comparison of Magnitudes of Bolt Loads with Connection under Pure Moment 41

23. Comparison of Load-Centerline Rotation Curves with Connection under Pure Shear 42

24. Comparison of Magnitudes of Bolt Loads with Connection under Pure Shear 43

25. Dimensions of Typical Single Plate Framing Connection ... 46

26. Moment-Rotation Relationship for Two-Bolt Connection .... 49

27. Moment-Rotation Relationship for Three-Bolt Connection ... 50

28. Moment-Rotation Relationship for Five-Bolt Connection ... 51

29. Moment-Rotation Relationship for Seven-Bolt Connection ... 52

30. Moment-Rotation Relationship for Nine-Bolt Connection ... 53

31. Transverse Tension Tear in Test Specimen 55

32. Bearing Failure in Test Specimen 55

33. Nondimensional Equation with Ten Percent Bounds Superimposed on Reduced Moment-Rotation Curve Data Points 57

34. Lipson's Test Results with Predictions by Nondimensional Equation Superimposed 58

35. uimiting Rotation Equations Superimposed on Typical Moment-Rotation Curves 60

36. Finite Element Model of Framing Plate ..... 66

37. Horizontal Normal Stress in Ksi near Weld in Framing Plate . 67

38. Simply Supported Beam with Superimposed End Moments 70

39. Moment-Rotation Relationship for Beam Shown in Figure 38 . . 70

xii

LIST OF ILLUSTRATIONS--Continued

Figure Page

40. Moment-Rotation Relationship for Connection 72

41. Moment-Rotation Relationships for Beam and Connection Superimposed 72

42. Typical Beam Line with Vertical Approximation 74

43. Bilinear Approximation of the Moment-Rotation Curves for the Five-Bolt Connection 77

44. Beam with iMoment Diagrams 78

45. Rotation of a Connection with Deformation of the Bolt ... 83

46. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/4-Inch A36 Plates 96





51. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 1/4-Inch and 3/8-Inch A36 Plates 106





xiii

LIST OF ILLUSTRATIONS--Continued

Figure Page


57, Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates 118

58. Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 1/4-Inch and 3/8-Inch A36 Plates . . 120

59. Plot of Load-Deformation Data for a 7/8-Inch Diameter A32S Bolt Connecting 1/4-Inch and 1/2-Inch A36 Plates . . 122

60. Plot of Load-Deformation Data for a 7/8-Inch Diameter A32S Bolt Connecting 3/8-Inch and 1/2-Inch A36 Plates . . 124

61. Plot of Load-Deformation Data for a 1-Inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates 126

62. Plot of Load-Deformation Data for a 1-Inch Diameter A325 3olt Connecting Two 5/8-Inch A36 Plates 128

63. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A572, Grade 50, Plates 130

64. Plot of Load-Deformation Data for a 7/8-Inch Diameter A32S Bolt Connecting Two 3/8-Inch A572, Grade 50, Plates 132



67. Plot of Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates . 138




71. Plot of Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A572, Grade 50, Plates ... 146

ABSTRACT

A study of the strength and ductility of single plate framing

connections was made by a combination of experimental work and finite

element analysis. The experimental work consisted of a series of load-

deformation measurements on two plates connected by a single bolt loaded

in single shear. These load-deformation relationships were used as

the properties of a shear fastener element representing one bolt in

finite element models of single plate framing connections. Moment-

rotation curves were obtained through use of the finite element models

for a variety of loading patterns in order to establish patterns of

behavior for the connections. A nondimensional moment-rotation

equation was developed from the moment-rotation curves, along with an

equation for limiting rotations to prevent bolt or plate failure, or

excessive deformations.

Two design procedures were investigated: use of Table X of the

present AXSC manual, and application of a factor of safety to the equa

tions developed in the study. A series of designs were made using

both procedures.

The primary conclusion that resulted from this study is that,

in general, the single plate framing connection does not exhibit the

strength and ductility generally desired in bolted connections.

Application of Table X will prevent the use of single plate framing

connections in almost all cases; application of the design criteria

developed in this study will prevent their use in a significant number

xiv

of cases, especially those requiring five or more bolts and those

connections in which the framing plate and beam web thicknesses are

relatively large.

CHAPTER 1

INTRODUCTION

The single plate framing connection has been considered by-

designers to be a simple support connection that is economical in both

material requirements and in fabrication and erection of steel buildings.

Two typical single plate framing connections are shown in Figures 1

and 2. In both cases, the connection consists of a single plate pre

punched with bolt holes and shopwelded to the supporting member.

During erection, the supported beam, also prepunched with holes, is

brought into position and field bolted to the framing plate.

Objective

The current design procedure for the single plate framing con

nection is to assume each bolt carries an equal portion of the total

shear load, and in agreement with the simple support assumption, to give

no recognition for any moment capacity of the connection. In fact, the

single plate framing connection is often called the shear tab connection

because of this assumption. Investigations into the strength and ductil

ity of the single plate framing connections have been extremely limited

(Caccavale, 1975; Lipson, 1968) and have neither satisfactorily estab

lished or disproved the validity of the design procedure. Before the

single plate framing connection can be generally accepted by the steel

industry, however, the behavior of the connection must be investigated.

The objective of this study was to establish the strength and ductility

1

c

Figure 1. Single Plate Framing Connection Connecting Beam to Web of Supporting Beam

Figure 2. Single Plate Framing Connection Connecting Beam to Flange of Supporting Column

3 of the single plate framing connection and to investigate design pro

cedures capable of providing a suitable factor of safety.

Procedure

The procedure followed in establishing the strength and ductility

of the single plate framing connection was based on a nonlinear finite

element analysis developed by Professor R. M. Richard at the University

of Arizona and demonstrated by Caccavale (Caccavale, 1975). The method

consisted of basically two parts:

1. Determining experimentally the load-deformation relationship

for a single bolt connecting two plates in single shear. These single

bolt, single shear load-deformation relationships lump together all

linear and nonlinear deformation occurring in the bolt and the connected

plates.

2. Analyzing the connection with a mathematical model composed

of nonlinear finite elements. The nonlinear behavior of each bolt and

the connected plates were modeled as shear connectors with their load-

deformation properties obtained from (1) above.

The significance of this procedure is that the behavior of a

single plate framing connection consisting of any pattern of bolts under

an arbitrary loading can be analyzed quickly and economically by computer

rather than by expensive full scale tests.

In order to achieve the objectives of this study, the following

steps were followed:

1. A series of single bolt, single shear tests were performed

for the range of bolt diameters and plate thicknesses expected in single

plate framing connections.

4

2. Finite element models were developed for a sufficient number

of single plate framing connection combinations in order that trends

in behavior could be determined.

3. Moment-rotation curves were obtained through the finite

element models. This included developing a nondimensional analytical

expression capable of representing most framing plate designs.

4. The stresses of the framing plate and the weld of the

framing plate to its support were investigated.

5. Design procedures were studied,

6. A method for inclusion of a factor of safety for strength

and ductility in a design procedure was determined.

CHAPTER 2

SINGLE BOLT, SINGLE SHEAR TESTS

The load-deformation relationship for a single bolt connecting

two plates in single shear lumps together all the linear and nonlinear

deformations occurring in the bolt, the bolt holes, and the connected

plates. This relationship can be used as the property of a shear

fastener element to model one bolt in a finite element model of a

single plate framing connection consisting of any number of bolts.

To be used in this manner, however, the single bolt, single shear load-

deformation relationship should model as closely as possible the actual

behavior of a bolt in a single plate framing connection.

Most load-deformation information for bolts loaded in single

shear have been obtained by loading the bolts in double shear and

reducing the results. Double shear tests reduced to single shear

results do not adequately model the behavior of a bolt in a single

plate framing connection because the usual purpose of such tests was

to test only the bolt. The double shear test fixtures were designed

for a minimum amount of distortion in the fixture, with any failure

occurring in the bolt. However, distortion of the bolt hole and

out-of-plane bending of the plates can be a significant portion of the

total ductility of the single shear connection. Also, failure can

occur in the plates as well as in the bolts.

5

6

The extent of single bolt, single shear load-deformation tests

consists of a limited series of tests performed by Caccavale (Caccavale,

1975J. Because the double shear tests did not satisfy the modeling

requirements and because Caccavale's tests were limited in range, a

total of seventy-five single bolt, single shear load-deformation tests

were performed as part of this study.

Testing Program

Single plate framing connections may be made up from a large

range of bolt materials and diameters, plate materials and thicknesses,

edge distances, methods of cutting the plate, and methods of producing

the bolt holes. In order to have a manageable program to obtain results

useful to the industry, the testing program included the bolt and plate

combinations shown in Table 1. In setting up the testing program the

following limitations and considerations were made:

1. Only ASTM A525 and ASTM A490 bolts were used. Other bolt

materials are not sufficiently widespread in use to warrant their con

sideration in this study.

2. Bolt diameters were 3/4 inches, 7/8 inches, and one inch.

These were considered to be the sizes most likely to be used in single

plate framing connections.

3. Plate materials were ASTM A36 or ASTM AS72, Grade 50, steel.

Although A36 steel was considered as the only steel generally to be used

for the single plate framing connection, the usefulness of information

for the Grade 50 material warranted its inclusion in the test program.

Table 1. Test Program for Single Bolt, Single Shear Tests. --(X denotes at least one test)

A325 Bolts A490 Bolts

Plate Combinations 3/4-Inch 7/8-Inch 1-Inch 3/4-Inch 7/8-Inch 1-Inch

vO to <

1/4, 1/4 X

vO to <

1/4, 3/S X X

vO to <

1/4, 1/2 X X

vO to <

5/16, 5/16 X X

vO to < 3/8, 3/8 X X vO to <

3/8, 1/2 X X

vO to <

7/16, 7/16 X X

vO to <

1/2, 1/2 X X X X X X

vO to <

5/8, 5/8 X X X X

A572

Gr 50

3/8, 3/8 X X

A572

Gr 50

1/2, 1/2 X

8

4. Plate thicknesses were varied by 1/16 inch from 1/4-inch

plates to 5/8-inch plates.

5. Edge distances were 1-1/4 inches for 3/4-inch diameter bolts,

1-1/2 inches for 7/8-inch diameter bolts, and 1-5/4 inches for one-inch

diameter bolts. These edge distances are those listed in the AISC

Specification ("Specification for the Design, Fabrication and Erection

of Structural Steel Buildings, 1969) for plates with sheared edges.

6. Plate edges were sheared. Microcracks and fissures caused

by shearing were considered to cause a more critical edge condition.

7. Bolt holes were punched.

Dimensions of the test plates are shown in Figure 3. The

dimensions of the plates were chosen to provide conditions similar to

the conditions around one bolt in a single plate framing connection.

The test plates were taken from the stock of and prepared by

a local steel fabricator. All specimens were without any loose rust

with the mill scale left undisturbed. Tensile test coupons from the

same stock as the test plates were ordered along with the test plates.

The results of the tensile tests on the coupons are shown in

Appendix A.

The A325 and A490 bolts were also ordered from a local steel

fabricator. No tests were run on the bolts; however, the bolts were

taken from the fabricator's regular stock,

l/l U1 1/1 r-1 +J O O h ,a o jo r :

00 T : w

—I fN K)

fH pH f-l o o o 4-< 4H

Centerline of Punched Hole

•=r cm t \S,N H H

i i r

tn i—» i = i O LO

Punched Hole

1-1/16" for 1" bolt

15/16" for 7/8" bolt

13/16" for 3/4" bolt

Drilled Holes for

3/4" bolts

© (VI

1-3/16" 1-5/8" 1-3/16"

Figure 3. Dimensions of Test Plates

10

Test Fixture

A test fixture was designed for use in the 200,000 pound

Tinius-Olsen testing machine located in the Structures Laboratory at

the University of Arizona. Primary considerations in design of the

fixture included a load capacity sufficient to test 7/8-inch diameter

A325 bolts connecting 5/S-inch A56 steel plates. The fixture was

designed for easy installation and removal of both the test specimens

from the fixture and the entire test fixture from the testing machine.

Design of the deformation measuring apparatus eliminated the effects

of any deformations in the test fixture.

A picture of the test fixture is shown in Figure 4. The fix

ture consisted of identical brackets, one bolted to the outside of

the moving head and one to the fixed head. One-inch diameter hardened

steel pins attached 1-3/8-inch by three-inch connecting bars to the

brackets. Two grips each were in turn pinned to each connecting bar

by one-inch pins. The test specimens were clamped into the grips by

two 5/4-inch diameter A525 bolts. Shims were inserted between the test

plate and the grips to obtain the proper positioning of the specimens.

Deformations were measured by the two dial gages as shown in

the picture of Figure 5. The dial gages were mounted to an aluminum

bracket which in turn was clamped to one of the test plates. A second

bracket was clamped to the other test plate to provide benches for the

probes of the dial gages. The use of two dial gages compensated for

any out-of-plane bending that occurred in the test specimens.

Figure 4. Test Fixture

Figure 5. Deformation Measuring Device

12

Test Procedure

The test procedure consisted of first bolting the test plates

together and hand-tightening the bolt. The entire test specimen was

then aligned in the test fixture and the bolts connecting the grips,

shims and test specimen were hand tightened. A preload of 5000 pounds

was then applied to the specimen to bring the bolt into bearing and to

eliminate all slip from the connection. The connecting bolt was then

tightened by the turn-of-the-nut method with the preload maintained.

The preload was then removed and the dial gages were mounted. A load

was then applied at a slow rate, with load and deformation readings

taken at appropriate intervals.

Load-Deformation Curves

Tabulated results of the single bolt, single shear tests are

given in Appendix A. These data points were obtained by averaging the

dial gage readings and subtracting the elastic response of the connected

plates. Point plots of the data are also included in Appendix A.

Superimposed on the point plots are curves representing a

weighted least squares fit of the Richard formula CRichard, 1975),

R =

1 + 1

Kx A n^l/n i 1 + 1 R

0

n^l/n i

+ K A P

where: R - bolt load

A - bolt-plate deformation

R - bolt reference load o

13

n - bolt load-deformation curve shape parameter

and with K, and K defined as follows: 1 P

K - slope of the load-deformation curve in the extreme P yielding range

- 1C - K , where K is the initial slope of the load-

deformation curve

Table 2 gives the curve parameters for the single bolt, single

shear tests. The plots show that excellent agreement is obtained between

actual test results and the analytical expression. Of special interest

is that even strain softening of the connection can be described with

the analytical expression.

Test results obtained by Caccavale indicated that the initial

slope, K, of the load-deformation curve can be determined by the formula,

V2 K = 2E 1

h + h

where: E - Modulus of elasticity (29,000 ksi for steel)

t^, t^ - plate thicknesses

This equation was developed by Professor R. M. Richard at the University

of Arizona through studies of unpublished Chance Vought tests for single

fastener lap joint stiffnesses (see Appendix B). Results of the single

bolt, single shear tests obtained in this study indicate that this

formula is in excellent agreement with the actual tests.

Table 2. Curve Parameters

3olt Plates X K R n 0 0

5/4"iA325 1/4 * 1/4 A36 7230. 0. 20. .3

M 3/io - 3/16 A 36 9063. 0. 24. • 9

It 3/3 - 3/8 A36 10375. 0. 40. .5

H 7/16 - 7/16 A36 12700. 10. 40. . 5

<1 1/2 - 1/2 A 36 14500. 20. 30. _ -

M 1/4 - 3/3 A36 3700. -30. 30. . 6

r( 1/4 - 1/2 A36 966 7. -50. 30. .6

'f 3/3 - 1/2 A 36 1 J

o

o

0. 40. . 5

it 3/3 - 3/3 A3 72 Gr 30 10875. 20. 30. .7

7/3"tA325 3/ 16 - 5/16 A36 9063. 0. 30. 7

11 5/3 - 3/3 A36 10373. 20. 40. . 5

• J 7/16 - 7/16 A36 12700. 0. 50. .5

II 1/2 • 1/2 A3 6 14500, 10. 40. . 7

M 1/4 - 3/3 A 36 3700. 20. 30. .3

rf 1/4 - 1/2 A3o 9667. 20. 30. 1.1

rt 3/3 - 1/2 A36 12400. 10. 40. .6

i r 3/3 - 3/3 AS 72 ur 30 10373. 10. 40. . 6

l"-SAo23 1/2 - 1/2 A36 14500. 20. 50. . 5

'1 5/3 - 3/3 13125 . 40. 50. . 6

3/4"-JA490 1/2 - 1/2 A36 14500. 10, 40. .5

i t 5/3 - 5/3 A 36 13125. 10. 50. ,4

7/3<iA490 1/2 - 1/2 A 36 14500. 0. 50. .5

If 5/3 - 3/3 A36 13125. 40. 50. .5

1 1 1/2 - 1/2 A572 'jf 30 14500. 40. ill. . 6

L":A490 1/2 - r /-> W -» A 36 14500 . 30. 40. . 7

1 • 5/3 - 3/3 A36 13125 :o. 50. .6

15

Control of Load-Deformation Relationship by the Thinner Plate

Figure 6 is the combined plot of the analytical expression for

3/4-inch diameter A325 bolts connecting one 1/4-inch thick plate with

second plate thicknesses of 1/4 inches, 3/8 inches, and 1/2 inches.

Similar plots can be obtained for other plate thicknesses as well as

with varying bolt diameters. The important feature of this figure is

that the loads do not vary significantly at any given deformation, and

at larger deformations the loads are very close. This indicates that

the thinner plate in the combination will govern the load-deformation

relationship.

This observation is significant in that the framing plate and

beam web thicknesses in single plate framing connections will generally

not be the same; however, the strength and ductility of the connection

will depend upon the characteristics of the thinner plate.

Failure Deformations, Loads and Modes

With the behavior of one bolt in a finite element model of a

single plate framing connection being described by the load-deformation

relationship obtained through single bolt, single shear tests, infor

mation concerning the modes of failure, failure deformations and

failure loads are also required in order that strength in the connec

tion can be predicted through the finite element model.

Gaylord and Gaylord (Gaylord and Gaylord, 1972) list several

possible modes of failure that can occur in lapped plate connections;

that is, type of connection encountered in the single plate framing

connection. A description of three of these failure modes that were

encountered in the single bolt, single shear tests follows:

16

O ZD O

PL's 1/4 and 1/2

PL's 1/4 and

PL's 1/4 and 1/4

/ z1

;.r:rOR.^r r INCH55

] y ~j • P i r r n>v|p r .\jr - - r< \-c;

Figure 6. Combined Plot of Analytical Expressions for 5/4-Inch Diameter A325 Bolt Specimen

17

1. Shear failure of the bolt in which a rupture of the bolt

on the shear plane between the two overlapping plates occurs as shown in

Figure 7. This case was the most critical encountered since the connec

tion is no longer capable of carrying any load.

2. Bearing failure of the plates in which yielding of the

plate material takes place behind the bolt. This produces bulging

behind the bolt as shown in Figure 8. This case is not as critical

because the connection does not generally lose any load-carrying capac

ity; however, the deformations can become excessive.

3. Transverse tension tearing of the plate which is similar

to bearing failure of the plate, but instead of simply bulging behind

the bolt, a crack develops on the free edge and progresses toward the

bolt (see Figure 9). This failure mode results in "strain softening"

since the connection still has load-carrying capability, although at a

reduced level. The presence of the crack, however, is undesirable.

Table 3 lists the failure modes for the complete series of

single bolt, single shear tests. Dual listings indicate that where

two or more tests of a given bolt and plate combination were run, there

was at least one occurrence of each failure mode listed.

Also shown in Table 3 are average maximum loads for each bolt

and plate combination. These are based on the maximum load for each

test; they are not necessarily the load at bolt shear failure or the

end of the test.

An important index for predicting failure of a single-bolt

connection is the deformation at failure. Its importance is emphasized

when the load-deformation curve is expressed with the Richard formula.

->

Figure 7. Shear Failure of the Bolt

Figure 8. Bearing Failure of the Plate

Figure 9. Transverse Tension Tearing of the

Table 3. Failure Modes, Average Maximum Loads and Failure Deformations for the Test Specimens

Bole Places Failure

Mode Average Max. Load (Kins)

Failure Deformation (Inches)

3/4<pA32S 1/4 - 1/4 A36 TT 19.9 0.30

> 1 3/16 - 5/16 A36 TT 24.3 0.30

I I 3/8 - 3/3 A36 BR-TT 33,3 0.3C

I t 7/16 - 7/16 A36 3S 34.9 0 .23

r t 1/2 - 1/2 A36 3S 33,0 0.13

i t 1/4 - 3/3 A36 TT 21.9 0.30

i t 1/4 - 1/2 A36 3R-TT 22.0 0.30

r r 3/3 - 1/2 A36 3S 32.4 0.23

i r 3/8 - 3/8 A572 Gr 30 as 36.6 0.30

7/34A32S 5/16 - 5/16 A36 rr 23.1 0.30

r r 3/8 - 3/8 A36 3R 39.0 0.30

r r 7/16 - 7/16 A36 BS 39.9 0.24

i r 1/2 - 1/2 A36 3S 38.3 0.20

r r 1/4 - 3/8 A36 3R 26.1 0.30

r r 1/4 - 1/2 A36 3R 23.4 0.30

t t 3/3 - 1/2 A36 35 33.7 0.30

r r 3/8 - 3/8 AS 72 Gr SO 3S 38.2 0.30

1 •> A32S 1/2 - 1/2 A36 TT 46.2 0.24

t r 3/3 - 5/3 A36 3R-3S 60.3 0.30

3/4"$A490 1/2 - 1/2 A36 TT 33.6 0.30

5/3 - 5/8 A56 3S 44.9 0.30

7/3<SA490 1/2 - 1/2 A36 TT 40.9 0.30

> i 3/3 - 3/3 A36 BS 48.3 0.13

M 1/2 - 1/2 A572 Gr 30 TT-3S 32.9 0.17

1 J A490 1/2 - 1/2 A36 TT 48.2 0.27

t r 3/3 - 3/3 A36 3R 61.3 0.30

Legend: TT

3R

35

Transverse Tension Tear

Bearing

3olt Shear

Examination of the plot of the analytical expression for the 1/4-inch

and 1/4-inch plate combination of Figure 6 shows that for deformations

greater than 0.05 inches, yielding at constant load occurred. How

ever, in tests where bolt shear failure occurred, failure for a given

combination occurred within a rather small range of deformations.

Thus the deformation is an important indicator of the connection

capacity. Failure deformations from the single bolt, single shear

tests are given in Table 3. When there was more than one test of a o •

particular bolt-plate combination, the smallest deformation is given.

Additionally, deformations greater than 0.30 inches were considered as

failure due to excessive deformation.

CHAPTER 3

FINITE ELEMENT MODEL

The procedure used for creating an appropriate finite element

model capable of predicting the behavior of the single plate framing

connection consisted of first creating a model that included the entire

framing plate, bolts, and supported beam. Loads corresponding to those

used by Lipson in his tests were then applied to this model and results

obtained were then compared to actual test results for verification.

With the full beam and connection model thus verified, results were

then obtained for a variety of loading conditions to determine patterns

in the behavior of the connection. Based on these studies, simplified

finite element models were then created which adequately predicted the

connection behavior, but at a significant savings of computer time.

Program INELAS

Program INELAS was the finite element program used for the

computer analysis (Richard, 1968). The INELAS program is capable of

static analysis of three-dimensional structural systems which consist

of two-dimensional elements. Material behavior may be either linear

or nonlinear, with the nonlinear differential equations that describe

the nonlinear structural response solved by either the first order

Euler method or the fourth order Runge-Kutta method. The nonlinear

structural response is based on a numerical algorithm that gives results

essentially identical to the Von Mises criterion and the Prandtl-Reuss

21

22

flow rule (Richard and Blacklock, 1969). Nonlinear uniaxial stress-

strain relationships are represented in the INELAS program by use of

the Richard equation (Richard, 1975).

Definition of Eccentricity

The dimension in the single plate framing connection from the

bolts to the weldment at the supporting members is usually three inches.

This distance can be of the same order of magnitude as the eccentricities

of loading expected in these connections. Thus a specific point had to

be chosen to define the eccentricity of the connection. In this study

eccentricities of loading were measured from the bolt as shown in

Figure 10.

Definition of Rotation

Significant distortion of the cross section of the beam can

take place because of shear loading and due to the transition from a

normal beam stress distribution to the stress distribution at the con

necting bolts. Definition of rotation then is actually a compromise

between various possible measures as well as convenience in calculation.

The rotation used in this study was based upon the horizontal centerline

rotation in the finite element model. It was determined by finding the

relative vertical displacement between the node point at the inter

section of the bolt line and the centerline of the beam, and the closest

node point that is also on the beam centerline. This relative displace

ment was then divided by the distance between the two nodes to obtain

the rotation.

23

Moment

Figure 10. Definition of Eccentricity

24

Figure 11 is a plot of the deformed shape of the cross section

at increasing load increments for a seven-bolt connection loaded at an

eccentricity of one-half the bolt pattern depth. Superimposed on the

cross section is the line corresponding to the rotation determined by

the above method. As shown on the plot, the horizontal rotation is a

good measure of the connection rotation.

Full Beam and Connection Models

Comparison with Lipson's Tests

Caccavale modeled the actual test arrangements used by Lipson

and showed that the analytical procedure was a valid method for predict

ing the behavior of single plate framing connections. The excellent

correlation between the analytical procedure and the experimental

results is documented in Caccavale's thesis (Caccavale, 1975).

Behavior of the Connection

With establishment of correlation between the finite element

model results and actual test results for a specific loading on the

connection, prediction of local behavior within the connection can also

be expected with the analytical procedure. Using a full beam and con

nection finite element model, the behavior of a connection consisting

of a one-half inch framing plate with seven 5/4-inch diameter A325

bolts supporting a IV 30 x 99 beam was investigated for a variety of

loading conditions. The finite element grid, which is shown in

Figure 12, was based on the grid used by Caccavale. From the results

of these analyses, several important observations were made.

25

Percent of Total Applied Load

50% 80% 90% 100%

Top Flange

a.

0

Deflection (inches)

Bottom Flange

Figure 11. Deformed Shape of Cross Section of Beam with Corresponding Centerline Rotation Superimposed

< Figure 12. Finite lilement Grid for Full Beam and Connection Model

av

27

Equivalence to Rigid Plate Action. A comparison was also made

between the moment-rotation relationships of the full beam and connec

tion finite element model, and a second model consisting of a rigid

plate connected to the bolt elements, which in turn were fixed to a

rigid support. Table 4 lists data points for the moment-rotation curves

for a connection loaded under pure moment as obtained through use of the

full beam and connection model and by the rigid plate model. Table 5

lists data points obtained in the same manner for the deformation at

the middle bolt plotted against the total shear for the connection loaded

in pure shear. In both cases, agreement is very good, especially con

sidering the extent of simplifications made for the rigid plate model.

One important conclusion from this comparison is that virtually

all the ductility available in the single plate framing connection is

due to the deformation of the bolt and bolt hole; very little ductility

results from other deformations of the plates. This ductility results

from the plastic deformation of the plate material in the proximity of

the bolt hole, bending and shear deformation of the bolt, and out-of-

plane bending of the framing plate and beam web.

A second important conclusion from the comparison is that the

moment-rotation relationships may be described in terms of the depth of

the bolt pattern rather than the depth of the beam. When both the

framing plate and the beam are idealized as rigid plates, the only

variable remaining which describes the effect of geometry is the depth

of the bolt pattern.

The eccentricity of the connection loading may then be

described in terms of the depth of the bolt pattern. This is shown in

28

Table 4. Comparison of for Full Beam (Pure Moment)

Moment-Rotation Curves for and Connection Model with

Seven-Bolt Connection a Rigid Plate Model

Moment (Kip-inches)

Rotation CRadians) Full Model Rigid Plate Model

.00065 473 454

.00215 710 676

.00795 947 909

.02506 1183 1143

Table 5. Comparison of Shear Loads for Seven-Bolt Connection for Full Beam and Connection Model with a Rigid Plate Model (Pure Shear)

Shear Load [Kips)

Deformation (Inches) Full Model Rigid Plate Model

.004 92 86

.014 138 131

.055 184 177

.173 230 223

29

Chapter 4, where moment-rotation curves are nondimensionalized using the

depth of the bolt pattern used as a parameter.

Bolt Loads in the Connection. One of the more interesting

aspects of the behavior of the single plate framing connection is the

angle of bearing of the bolts. Figure 13 is a graphical illustration

of the load vectors when the seven-bolt connection is loaded by pure

moment. In contrast to the normal assumption with pure moment that

the bolts carry horizontal loads only, the load vectors on all seven

bolts also have vertical components.

The vertical bolt load components can be explained by consider

ing the load paths in the supported beam. When a beam is subjected to

a moment, a large part of that moment is carried as forces in the beam

flanges. At the connection, however, the moment is carried by the bolts

only and those forces must get from the beam flanges to the bolts.

Figure 14 illustrates with arrows the directions of the force vectors

at various points along the beam. As shown in Figure 14, the outer

bolts are subjected to vertical components, both in the same direction.

Equilibrium is then maintained by the inner bolts with vertical force

components in the opposite direction.

Although the vertical force components for this pure moment case

are small and do not represent a significant difference from normal

force direction assumptions, they do illustrate the capability of the

INELAS program to predict the internal behavior of a single plate

framing connection.

Effect of Load Eccentricity. An important observation made of

the behavior of the single plate framing connection was the variation

30

Horizontal Vertical Component Component Resultant

-43750 4808 43994

O -37848 1704 37886

•30714 -2850 30846

9 0 -7324 7324

30714 -2850 30846

G- 1>_. 37848 1704 37886

43730 4808 43994

Z = 0 Z = 0

Figure 13. Load Vectors Acting on Bolts from Supported Beam under Pure Moment

o

o

o

o

o

o

o

Figure 14. Load Paths from the Beam Flanges to Connection Bolts

32

of the moment-rotation relationship with eccentricity of loading.

Figure 15 is a plot of the moment-rotation relationships for the seven-

bolt connection, with load eccentricities of infinity (pure moment),

l,61h, 0.81h, and 0,22h, where h is the depth of the bolt pattern.

This plot illustrates that there will be little variation in the

moment-rotation relationships for eccentricities greater than the

depth of the bolt pattern, and those moment-rotation relationships can

be represented by a single curve. For eccentricities less than the

depth of the bolt pattern, however, the moment-rotation relationships

become sensitive to variations with eccentricity and must be repre

sented by individual curves.

Simplified Model

Simplified finite element models were created based on findings

obtained through use of the full beam and connection model. The sim

plified models presented the advantage of very significant reductions

in computer time, computer cost, turn-around time and volume of output.

The simplified finite element models consisted of a short seg

ment of the beam, with the bolt elements attached at one edge. The

other ends of the bolt elements were attached directly to a fixed

support. Loads were applied to the beam as though the beam consisted

of the web plate only; that is, beam flanges were provided on the model

but were not included in distributing loads. The actual finite

element grids used are shown in Figures 16 through 20.

1200

e = infinity (pure moment)

1050

900

750

600

450

300

ISO

0

0 .025 .030 .005 . 0 1 0 .015 Rotation (Radians)

Figure 15. Moment-Rotation Relationships with Varying Eccentricities for a Seven-Bolt Connection

Figure 16. Finite Element Grid for the Two-Bolt Connection

Fig. 17. Finite Element Grid for the Three-Bolt Connection

36

-Q

O

-Q

Figure 18. Finite Element Grid for the Five-Bolt Connection

Figure 19. Finite Element Grid for the Seven-Bolt Connection

38

-6)

-O

-Q

Figure 20, Finite Element Grid for the Nine-Bolt Connection

39

Comparison with Full Beam and Connection Model

Verification of the full beam and connection model was accom

plished by direct comparison with results obtained from full scale

experimental tests. Verification of the simplified model was accom

plished by comparing results for a seven-bolt connection obtained

through use of a simplified model with similar results obtained

through the full beam and connection model.

Several items were compared in the verification. These were

the moment-rotation curve and individual bolt loads under pure moment,

and load-centerline rotation curve and individual bolt loads under

pure shear.

Figure 21 is the comparison of the moment-rotation curves

for the connection loaded under pure moment. As shown, the two

moment-rotation curves are essentially identical. Figure 22 is a bar

graph comparing the magnitudes of bolt loads. The forces in the bolts

compare favorably.

Figure 23 is the comparison of the load-centerline rotation

curves for the seven-bolt connection loaded under pure shear. Once

again, the two curves are virtually identical. Figure 24 is a bar

graph comparing the magnitudes of bolt loads. In this case, bolt loads

from both models are almost identical to each other.

With the excellent agreement obtained between the simplified

model and the full beam and connection model for the seven-bolt con

nection combined with the observation that the connection is almost

equivalent to bolts connecting two rigid plates, the simplified model

40

1200

1050

900

iH

Jj£ \ /

750

600

simplified model 450

full beam and connection model

300

150

.010 .015 .020 0 .005 .025

Rotation (radians)

Figure 21. Coronarison of Moment-Rotation Curves with Connection under Pure Moment

41

4

5

6

7

/ / >

ZZT

h

1/ / } —I— 20 40

Ca)

40% of applied load

3

4

5

6

7

/ / / y

' y / / •

zizr

rT̂ 7TJ

/ / / I

1/ / / a 20

Cb)

60% of applied load

40

1

2

/ / / /

4

5

6

7

2 / / / A

/ / /

7ZZ.

/ / /

y y y y

V > / / / A

20 CcJ

80% of applied load

40

1

2

4

5

6

/ / / / / 2

/ / / / A

/ / / / 1 "Z

/ / / /

/ / / / 3 / / / / / - y

20 Cd)

100% of applied load

40

Figure 22. Comparison of Magnitudes of Bolt Loads with Connection under Pure Moment. -- (Loads are in kips)

42

300

250

200

150

100

simplified model


U .0020 .0015 .0005 .0010

Rotation (Radians)

Figure 25. Comparison of Load-Centerline Rotation Curves with Connection under Pure Shear

43

7-7-1

r~7~7

6

7

"̂77

t ~~7a

7 T

7-̂ 1 1

20 (a)

40% of applied load

40

1

2

4

5

6

7

/ / / X

3 / / /

/ / /

V~T 3 z: 2:

/ / /

20

CbJ

60% of applied load

40

1

2

3

4

5

6

7

/ / / /

' / / / /

/ / / /

/ / / / 3 / / / A

/ / / /

/ / / / 20

Cc)

80% of applied load

40

1

2 \ / / / / A

4

5

6

7

/ / / /

/ / / / /

/ / / ; s 3 ' / / / /iz

/ / / / / :

/ / / / / -

20

Cd)

100% of applied load

40

Figure 24. Comparison of Magnitudes of Bolt Loads with Connection under Pure Shear. -- (Loads are in kips)

44

was considered to be sufficiently accurate to provide the analytical

results used in the study.

CHAPTER 4

MOMENT-ROTATION CURVES

Moment-rotation curves provide the primary source of informa

tion about structural action of the single plate framing connection.

If a connection is to support a beam, it must be capable of carrying

the beam end reaction and at the same time allow the end of the beam

to rotate to its equilibrium position without causing excessive loads

or deformations in either the beam or the connection. The necessary

information to determine the capabilities of the connection is con

tained in its moment-rotation relationship.

Scope of Calculations

With the capabilities of the INELAS program used in conjunction

with the single bolt, single shear load-deformation curves, virtually

any pattern of bolts and dimensions of single plate framing connections

can be analyzed. However, to reduce the number of cases to a manage

able number, the following limitations were applied:

1. The dimensions of the single plate framing connections

were those shown in Figure 25. The distance from the top bolt to the

top of the plate was taken as half the bolt spacing (one and one-half

inches).

2. The two and three rows of bolts had 3/4 inch-diameter

A325 bolts and the five, seven and nine rows of bolts had 7/8-inch-

diameter A525 bolts.

45

1-1/4" for 3/4" < p bolts

1-1/2" for 7/8" $ bolts

. ^

1 - 1 / 2 "

< t

i

3" between bolts

r

- i

3" between bolts

j I

1 - 1 / 2 "

Figure 25. Dimensions of Typical Single Plate Framing Connection

47

3. The framing plate thicknesses matched the web thickness

of the lightest beam of the series capable of accommodating the

particular bolt pattern. This resulted in the thicknesses shown in

Table 6. The W S x 13 and the W 12 x 16.5 were not the lightest beams

in their series, but were used because they came closest to the 1/4-inch

minimum plate thickness for which load-deformation curves were available.

Moment-rotation curves for the above program are shown in

Figures 26 through 30. These plots consist of a set of curves each for

the two-, three-, five-, seven-, and nine-bolt connections. Each plot

has moment-rotation curves for eccentricities of 0, O.lh, 0.5h, and

l.Oh, where h is the depth of the bolt pattern. Also shown in the plots

is a curve showing the maximum allowable rotations based upon limiting

the deformation in the bolts to 0.2 inches for the nine-bolt connection

and 0.3 inches for the two-, three-, five-, and seven-bolt connections.

Source of Ductility

The moment-rotation curves illustrate that the single plate

framing connection is sensitive to the eccentricity of the load. This

is in contrast to other "simple" beam connections in which only one

moment-rotation curve is generally required to describe all values of

eccentricity. The reason for this can be explained by comparing the

sources of ductility of various types of connections.

The web-angle, the top-and-seat angle, and the T-stub top-and-

seat connections all obtain their primary ductility through the bending

of the angle leg or the flange of the T-stub. The single plate framing

connection, however, gets most of its ductility from the deformation of

the bolts and bolt holes. For the single plate framing connection, the

48

Table 6. Minimum Framing Plate Thicknesses and the Beams on Which the Thicknesses Were Based

Number of Bolts per Column Framing Plate Thickness From Beam

2 1/4 inches W 8 x 13

3 1/4 inches W 12 x 16.5

5 5/16 inches W 18 x 35

7 5/8 inches W 24 x 55

9 1/2 inches W 30 x 99

49

Q O O

o en

Limiting Rotation

-z. UJ n o

C2 a o

Framing Plate Thickness 1/4' Bolt 3/4" <p A325

O o

J UU sJ •J

"'ON • =-C^N3 :

Figure 26, Moment-Rotation Relationship for Two-Bolt Connection

50

o a

si

I J i

c a

2 § X * — a

tn UJ

! ^ a. Limiting

Rotation

2: LU

o 2Z Framing Plate Thickness 1/4

O O

n --s r> r> r' 1 n \j * : i- J

ROTR'iGM ER-OLRNSl

Figure 27. Moment-Rotation Relationship for Three-Bolt Connection

51

o a a

a (Ti

a

X Limiting Rotation

>• .i

f— z: LU v

a a

O

Beam W IS x 35 Framing Plate Thickness 5/16 Bolt 7/8" $ A525

a o

""-a .a. 0 r*i J 3 vC'o' C --3S1

RC"PTI ON CRSDISNSl

Figure 28. Moment-Rotation Relationship for Five-Bolt Connection

52

Limiting Rotation

Beam W 24 x 55

Framing Plato Thickness 5/8 Bolt 7/3" $ A325

Figure 29. Moment-Rotation Relationships for Seven-Bolt Connection

c 5

Limiting Rotation

•IC 1 ; T

o •5* I

Q_ C-J

a

'Tl

Beam W 50 x 99 Framing Plate Thickness 1/2 Bolt 7/8" ( p A525

«— r*»£ Ci ^ 1 r. ••u ' £. P r*

^QThMGN ERPQfSNS!

Figure 30. Moment-Rotation Relationship for Nine-Bolt Connection

54

value of the eccentricity has a very strong influence on the angle of

bearing on the extreme bolts. That is, for very small eccentricities,

the extreme bolts are used primarily in carrying shear. With larger

eccentricities, the extreme bolts are used for carrying moment.

Limiting Deformation

The mathematical basis for the finite element analysis of the

single plate framing connection provides no limit to the amount of

rotation a connection can undergo. As a practical matter, however,

the rotation of the connection must be limited so that actual rupture

of the bolt, framing plate or beam web will not occur, nor will the

deformations in the connection exceed tolerable limits.

The limiting rotation curves reflect these limits. For those

cases in which rupture of the bolt is expected, the maximum deformation

of any bolt in the connection was not allowed to exceed the deformation

at rupture based on the single bolt, single shear tests (see Table 5).

The remainder of the cases were limited to a maximum bolt deformation

of 0.3 inches. Visual examination of specimens during the single bolt,

single shear tests led to the conclusion that a deformation greater

than 0.3 inches was excessive as shown in Figures 31 and 32.

It is noted, however, that many specimens began transverse

tension tearing at just beyond 0.1 inches of deformation. There was

little reduction in strength for most cases; however, this tearing

would be undesirable in a connection.

Figure 31. Transverse Tension Tear in Test Specimen

ik'4̂ ; '-.Vf-iV • ?:• '&• \,'/

Figure 32. Bearing Failure in Test Specimen

56

Analytic Expressions

The number of moment-rotation curves required to describe the

behavior of the single plate framing connections considering various

combinations of bolt sizes, number of bolts, and minimum plate thick

nesses, as well as varying effective eccentricities of loading, is

quite large. A reduction in the number of curves is required before

these can be used as a practical design and analysis tool.

The results of a procedure to reduce all curves to a single

nondimensional equation are shown in Figure 33. In this figure, the

data points used to generate the original moment-rotation curves

(Figures 26 through 30) are shown as symbols. The middle line is the

plot of the nondimensional equation. The upper and lower curves rep

resent the range in which data falls within ten percent of the

nondimensional equation.

Figure 33 illustrates that most data points do fall within

ten percent of the analytic equation. The equation appears to describe

the moment-rotation curves for the single plate framing connection

parameters and effective eccentricities covered.

The strongest confirmation of the nondimensional procedure

occurs when the curves are used to predict the results obtained by

Lipson in his experimental work (Lipson, 1968). Figure 34 shows pre

dictions obtained through the nondimensional procedure superimposed

on a plot of the moment-rotation curves obtained by Lipson. Excellent

correlation is obtained.

Lower values obtained from the nondimensional procedure when

compared to Lipson's results can be attributed to at least two reasons:

57

Figure 33. Mondimensional Equation with Ten Percent Bounds Superimposed on Reduced Moment-Rotation Curve Data Points.

58

700 Lipson's tests (.2 ea.)

Nondimensional Equation

Limiting Rotation

600 _

6 bolts

500 _ i '-j

o ^ 400 _

5 bolts

300

4 bolts >*

200

3 bolts

LOO ^

2 bolts

0 . 1 0 . 2 0.5 Rotation (radians)

.04 0.5

Figure 54. Lipson's Test Results with Predictions by Non-dimensional Equation Superimposed

59

1. Boit-plate combinations loaded in compression will have

higher load capacities and stiffnesses than the same combinations loaded

in tension. Lipson (Lipson, 1968) reported this feature on tests of

bolts loaded in double shear; similar results can be expected in single

shear tests. The effect of the two different load capacities and stiff

nesses in the single plate framing connection is to shift the neutral

axis as load is applied, resulting in moment capacities higher than

those predicted by the nondimensional procedure.

2. The single bolt, single shear tests used in this study

corresponding to the framing plate and beam web thicknesses of Lipson's

tests had sheared edges, with transverse tension tearing as the failure

mechanism. Since this tearing reduces the possible capacity of the

bolt-plate combination, lower moment capacities can be expected through

the nondimensional procedure.

A second aspect to be considered with the nondimensional moment-

rotation curves is the limiting rotation. Figure 35 shows a bilinear

equation superimposed on the moment-rotation curve plot for the seven-

bolt connection. Figure 35, which is typical of the other cases,

illustrates that the bilinear equation models the original limiting

rotation curve quite well, with slightly conservative results throughout.

The nondimensional moment-rotation equation used is the Richard

nonlinear equation (Richard, 1975) which describes the shape of the

curve, combined with a second expression to account for the effect of

the load eccentricity. Written separately, the two parts are

60

(N o 1—1 X w

0 V 0

cn 0 :u

CO CJ z: HH

( C-

2 0 •w"

vO

0 w

Bilinear limiting rotation equation

Actual limiting rotation curve

0 .000 0 .006 0.012 0.018 0.024

ROTATION (RADIANS)

0.030 0.036

Figure 55. Limiting Rotation Equations Superimposed on Typical Moment-Rotation Curves,

61

and

where

M * _ 60 <j>*

1 + 60<fi

*' 2/3 ; 3/2

I 1 . 1 ,

M M* fl " 11 - e/h' 3' ;Mref

ref -

M*

<p*

moment in the connection

reference moment based on a pure moment being applied to a connection and all bolts being loaded to their maximum capacities

intermediate nondimensional moment value

free end rotation of the beam divided by a reference rotation value, The reference rotation value is determined by the equation

<$> 0.3 in

ref (n - 1) C3 in)

n

e

h

number of bolts

eccentricity of the load

depth of the bolt pattern

The equation for the two-part limiting rotation expression is

given by

0.. for M - 0.93 M _ lim ref

<P lim

'i- in nA 1 for M < 0.93 M -lim : 0.9j Mref | ref

where

-r _ ^ lim Uiro ~ " (n - 1) [3 in) |

L 2 J

and ^lim " limiting rotation for the particular bolt-plate combination

Tables 7 through 9 summarize the data required for use of the

above equations based on data obtained through use of the unreduced

results of the single bolt, single shear tests with an average plate

yield point stress of 44.0 ksi.

Table 7. ^re£ f°r Use in the Nondimensional Moment-Rotation Equation

Number of Bolts ^ref

(Radians)

3 0 .1

5 0 .05

7 0 .0333

9 0 .025

Table 8. M - Values ret in Inch-kips Based on Test Results for Use in

the Nondimensional Moment-Rotation Equation

3/4 <$> A325 Bolts

Minimum N u m b e r o £ Bo 1 t s Plate Thickness 3 5 7 9

1/4 12 0 358 716 1194

5/16 146 437 875 1458

3/8 200 600 1200 1998

7/16 210 628 1256 2094

1/2 200 594 1188 1980

7/8 A325 Bolts

1/4 138 420 836 1393

5/16 169 506 1012 1686

3/8 234 702 1404 2340

7/16 239 718 1436 2394

1/2 233 698 1397 2323

64

Table 9. Limiting Deformations (A,. ) in Inches s lim

Minimum Bolt Diameter Plate Thickness 3/4j> 7/80

1/4 0.3 in 0.3 in

5/16 0.3 0.3

3/8 0.3 0.3

7/16 0.3 0.25

1/2 0.15 0.2

CHAPTER 5

FRAMING PLATE AND WELD LOADS

A preliminary study of the stresses in the framing plate and

the weld connecting the framing plate to its support was performed for

a seven-bolt single plate framing connection for pure moment loading.

The results of the study showed that a print-through of the bolt loads

through the plate directly back to the weld can be expected for this

loading condition. The stresses in the plate and the connecting weld

can then be calculated fairly closely by dividing the maximum bolt load

by the tributary area of the plate and connecting weld, respectively.

These results were obtained by creating a finite element

model of the framing plate and applying loads obtained from the full

beam and connection model. Accuracy of the finite element mesh was

established by preparing three different models of the connection, with

each succeeding model having a finer element mesh. The finite element

model with the medium mesh is shown in Figure 36. The coarse mesh

results were taken directly from the full beam and connection model.

Figure 37 is a plot of the normal stress versus the position in the

plate near the weld as obtained from the three finite element models.

The second and third finite element models yielded results

that were nearly the same, indicating that the second mesh yielded

excellent results, with further mesh divisions not yielding a signif

icant increase in accuracy. In fact, the results of the first mesh

65

66

c ;

Figure 56. Finite Element Model of Framing Plate. --(Model is symmetrical about the centerline)

67


• - medium mesh

Jnlabeled - fine mesh

Figure 37. Horizontal Normal Stress in Ksi near Weld in Framing Plate

68

indicated the general trends of the stresses quite well, with only the

local variations missing.

The print-through effect can be shown by comparing the finite

element results with a hand calculation. The ultimate load for a

3/4~inch diameter A325 bolt connecting two 1/2-inch A36 plates is

33 kips. The tributary area for this connection was the three-inch

bolt spacing times the 1/2 inch plate thickness. The stress obtained

by this procedure is 22 ksi. This is only 20 percent lower than the

peak normal stress obtained by the finite element analysis.

CHAPTER 6

DESIGN PROCEDURES

Two procedures appear suitable for the design of single plate

framing connections. These are, first, the use of existing Table X

of the AISC manual (Manual of Steel Construction, 1970) and, second,

use of the analytic expressions given in Chapter 4. Both methods

account for the effective eccentricity of the end reaction. The best

method for obtaining the effective eccentricity appears to be the beam

line method (Batho, 1954).

determining the effective eccentricity of the end reaction of a

single plate framing connection. This procedure utilizes directly

the nonlinear moment-rotation curves for the connection and assumes

linear action for the beam.

Theory

The basic theory behind the beam line method can be illustrated

by considering a simply supported, uniformly loaded beam with super

imposed moments applied at its ends (Figure 58). The end rotation, <$>,

for the beam can be shown to be

Beam Line Method

The beam line method is a theoretically sound procedure for

M L s

24EI 2EI

69

w

~n \\\\

Figure 38. Simply Supported Beam with Superimposed End Moments

M

mm

o 5

Rotation

Figure 39. Moment-Rotation Relationship for Beam Shown in Figure 38

71

From this equation, <f> is a linear function of the superimposed end

moments.

Two aspects of this equation are of special interest. First,

if the superimposed end moments are zero, then the end rotations are

those for a "simply supported" beam. Second, i£ the end rotations are

zero, then the applied end moment is the "fixed end" moment.

A plot of moment versus rotation shows the importance of these

two values as shown in Figure 39. These two points represent the end

points of a straight line defining the moment-rotation relationship

for the uniformly loaded beam with a superimposed end moment somewhere

between that of a fixed end support and a simple support.

Consider a connection that has a given moment-rotation relation

ship such as shown in Figure 40, and is used to support the beam. The

only combination of moments and rotations which is mutually acceptable

to both the beam and the connection is the one in which the moment in

the beam and the connection is the same. This combination can be found

by superimposing the moment-rotation relationships for the beam on that

for the connection (Figure 41). The point at which both moments and

rotations match is, of course, the intersection of the two curves.

It should be noted that when using the beam line method with

the single plate framing connection that the ultimate moment of the

connection is significantly less than the fixed end moment of the

supported beam. Thus the beam line may be approximated by a vertical

line for most connections. This approximation is used throughout

this study.

0

o

Rotation

Figure 40. Moment-Rotation Relationship for Connection

M s

(Moment, Rotation) for Supported Beam

o

Rotation

Figure 41. Moment-Rotation Relationships for Beam and Connection Superimposed

73

Figure 42 shows the beam line for a uniformly loaded W 18 x 35

beam with a span of 30 feet superimposed on the moment-rotation curve

for a single plate framing connection consisting of two 3/4-inch

diameter A325 bolts. The eccentricity for this connection is 1.0

times the depth of the bolt pattern. As shown, the vertical approxi

mation for the beam line is valid.

With the end moments thus determined, the effective eccentricity

can then be found by dividing the moment by the end reaction.

The use of the beam line method for single plate framing connec

tions is complicated, however, by the variation of the moment-rotation

relationship with eccentricity. Because of this, the beam line method

for this connection becomes an iterative process in which an eccentric

ity is assumed and the moment is determined from the appropriate moment-

rotation curve. The resulting eccentricity is then calculated from the

moment and the end reaction, and is compared to the assumed eccentricity.

If agreement is satisfactory, calculations are completed; otherwise, the

calculations are carried through another iteration.

Use of Table X

Table X of the AISC manual tabularizes the coefficients required

to determine the capacity of a bolted connection supporting a load

applied at a known eccentricity, and can be directly applied to the

design of a single plate framing connection once the effective eccentric

ity of the end reaction has been determined through the beam line method.

A special interpretation, however, must be made between the single

plate framing connection and Table X with regard to the effective eccen

tricity. The effective eccentricity in Table X is assumed to be constant,

74

80

70

60 Beam Line for W 18 x 35, Uniformly

Loaded, Span of 30 Feet

50

40

30 Vertical Line Approximation

20

Moment-rotation curve for two-bolt connection with 3/4-inch diameter A325 bolts

10

0

.025 .020 .015 .010 .005 0

Rotat ion (radians)

Figure 42. Typical Beam Line with Vertical Approximation

with only the load being able to vary. With the single plate framing

connection, however, the eccentricity is a function of the load.

The change of eccentricity with load can be shown by the use

of the nondimensional moment-rotation curve shown in Figure 33. Since

most single plate framing connections function at the knee or beyond

the linear range of the moment-rotation curve, an increase in rotation

from a specified value yields a relatively small increase in the moment

value. Mow the end rotation, $, for a uniformly loaded beam, for

example, is given by the equation

3 2 wL _ RL

^ " 24EI " 12EI '

where the end reaction, R, is given by

R = ilt • K 2

Hence R is directly proportional to the end rotation, <f>, as long as

the beam behaves linearly.

Since the eccentricity is determined by dividing the moment by

the end reaction, an increase in the end reaction which is accompanied

by only a small increase in moment will result in a reduction in the

eccentricity.

Further reduction in the eccentricity can be expected since the

moment capacity of a single plate framing connection also decreases

with reduction in eccentricity (see Figures 26 through 30),

To demonstrate this, an approximate solution can be found

by a bilinear idealization of a typical moment-rotation relationship.

76

Figure 43 is the moment-rotation relationship for the five-bolt connec

tion (see Figure 28) with a bilinear curve superimposed. This bilinear

curve is intended to approximate a range of eccentricities from 0.4

to 1.0 times the depth of the bolt pattern since most eccentricities

lie in this range. It is further noted that most single plate framing

connections will be at their ultimate moment capacity according to this

simplified moment-rotation relationship.

Since the beam has little additional capacity beyond first

yield (about 12 percent), the end reaction does not increase signif

icantly. With both the connection moment and the end reaction essen

tially constant, the eccentricity will remain the same regardless of the

rotation. This means a plastic hinge could form in the beam, and analy

sis by Table X would still be valid.

An alternative way to demonstrate the variation of eccentricity

with load is through an analogy with the plastic analysis method.

Figure 44 (a) shows a beam supported by single plate framing connections

and carrying a concentrated load. Figure 44 (b) shows the moment dia

gram for the beam at working load level. The effective eccentricity at

working load, e also shown in Figure 44 (b), is the distance from the

connection to the point where the moment is zero. At working load the

moment in the beam is M even though the single plate framing connec

tions have reached their full plastic capacities, MpC-

Increasing the load on the beam from the working load level to

the full plastic level changes the moment diagram as shown in

Figure 44 (c). The moment in the beam increases from the working

level, Mwp to its full plastic level, M . The single plate framing

77

560_

490-

420

350.

280

210.

140

70.

.054 .045 .036 .027 .01S .009 0

Rotation (Radians)

Fig. 43. Bilinear Approximation of the Moment-Rotation Curves for the Five-Bolt Connection. — (Heavy solid line is the approximation. The area represented is shaded.)

78

1

p

r 1/

f (a)

V C L M pc

r

Ae Ae e

V IZbs,

n A H M pc

Cc)

Figure 44. Beam with Moment Diagrams

connections, however, reached their full plastic capacity, ^pcJ at

working load level and remain unchanged with the increase in load.

As shown in Figure 44 (c), the eccentricity is reduced by the amount

Ae to the eccentricity at the plastic hinge mechanism, e .

Once the plastic hinge mechanism has formed, the beam can carry

no further load and the moment diagram will remain unchanged. Thus the

eccentricity of the end reaction will also remain unchanged after the

plastic hinge mechanism is reached.

This concept is important because the eccentricity used in

Table X should be that obtained at ultimate load of the beam, or

approximately, at the first yield of the beam. Chapter 7 illustrates

the use of Table X in single plate framing connection design.

Use of Analytic Expressions

The second method, use of the analytic expressions of Chapter 4

for the moment-rotation relationship and the limiting rotations, as a

design procedure is also closely interrelated with the beam line method.

The beam line method is used to determine the moment and rotation of

the connection and the effective eccentricity of the end reaction.

These values are then used in limiting rotation expressions as illus

trated in Chapter 7. In this procedure, if the actual end rotation is

less than a limiting rotation, then the connection is considered satis

factory. A method for inclusion of a factor of safety is also discussed

in Chapter 7.

CHAPTER 7

FACTORS OF SAFETY IN THE DESIGN METHODS

Obtaining a suitable factor of safety for the single plate

framing connection is a difficult problem because the connection is

extremely nonlinear even in the working load range of the supported

beam.

Table X Design Procedure

Design by Table X would appear to be the simplest procedure

since a factor of safety is already incorporated into the procedure.

A study by Crawford and Kulak (Crawford and Kulak, 1971) indicated a

range in factor of safety from about 2.5 to 3.5 for eccentrically

loaded connections designed using Table X. However, these factors of

safety, when applied to the design of single plate framing connections,

prevent the use of these connections in almost all cases.

For example, consider a W 18 x 35 beam with a length of

30 feet (L/d = 20) and carrying a uniformly distributed load of 1.0

kip per foot. Based on the pure shear assumption, two 3/4-inch

diameter A325 bolts with a total capacity of 19.4 kips should carry

the 15 kip end reactions. However, an eccentricity of 3.3 inches

is determined through an analysis by the beam line method. Then the

allowable end reaction as determined by Table X is S kips, which is

less than the 15 kip end reaction, so the two-bolt connection is not

adequate.

80

81

Another interesting aspect of this example can be observed by

increasing the number of bolts to three. This increase in the number

of bolts reduces the allowable capacity to 7.2 kips because of a signif

icant increase in the eccentricity. Five bolts, the maximum possible

in the beam, also have a capacity of 7.2 kips. In fact, a one-bolt

connection, which would allow essentially free rotation, has the capac

ity of 9.72 kips which is greater than any other bolt pattern compatible

with the geometry of the beam as determined from Table X.

This example illustrates the statement previously made that

design by use of Table X will prevent the use of most single plate

framing connections.

Alternate Procedure

Because of the resulting limitations imposed by Table X, an

alternate procedure using the moment-rotation curves and the limiting

rotation curves is suggested.

The beam line method, which is based on linear behavior of the

beam, can (on a rational basis) provide approximately a 1.5 factor of

safety, which is the ratio of the load at first yield to the working

stress load. This value, however, is significantly below the 2.5 to

3.5 range for the factor of safety generally desired for bolted

connections.

With the problems encountered in trying to increase the factor

of safety above 1.5, the alternate method is suggested which limits

connection deformation in addition to applying a factor of safety to

the loads. This method consists of first determining the rotation,

moment, and eccentricity on the connection with the 1,5 factor of

82

safety mentioned previously. Then a factor of safety is applied to

the limiting rotation. Limiting the rotation is intended to assure

that no failure will occur in the connection, nor will deformations

of the bolts and framing plate be excessive.

It should be noted that the normal philosophy and design speci

fications for simple beam connection design include factors of safety,

such that the connection has sufficient strength and ductility so that

the supported member will fail first. The suggested procedure, how

ever, reduces the factor of safety of the connection to that of the

beam.

An immediate effect of this design procedure will be to limit

the number and spacing of bolts permitted in a connection. For a

simply supported beam with a uniformly distributed load, the end

rotation at theoretical first yield of the beam (see Figure 45) can

be shown to be approximately

a 2 Fy L * = J F d

where

Fy - yield stress of the beam

E - modulus of elasticity

L - length of the beam

d - nominal depth of the beam

If the allowable deformation of a bolt and/or plate is limited

to one-third (1/3) the failure deformation, the allowable end rotation

can then be shown td be

83

A bolt

Figure 45, Rotation of a Connection with Deformation of the Bolt

^allow

o A 2 max

where

A - failure deformation of a bolt and/or plate max r

h - depth of the bolt pattern

The ratio of the allowable rotation to the rotation at first

yield can then be shown to be

<f> ,, EdA •allow max

tj) F Lh y y

Now consider a beam with a 36 ksi yield strength and an L/d

ratio of 20, and an allowable deformation of 0,1 inches for a bolt.

Setting the ratio, equal to one then results in a maximum

bolt pattern depth of 12.5 inches. This limits the connection to five

bolts for a three-inch bolt spacing.

Another consideration that may further reduce the size of

the bolt pattern is the effect of heavier framing plate and web thick

nesses since this reduces the allowable deformation in bolts.

A factor of 3.0 applied to the limiting deformation value is

suggested for two reasons. First, for those single bolt, single shear

tests in which transverse tension tearing was the controlling factor,

this tearing started in several specimens at deformations as low as

0.10 inches. The 0.10 inches of deformation is one-third the 0.3

inches of deformation at which deformations were considered too

excessive to continue the test. Second, for those single bolt, single

85

shear tests in which bolt failure was the controlling factor, some

scattering of data was observed when measuring the deformation at

bolt failure. However, a factor of 3.0 should supply a sufficient

factor of safety to include almost every case of bolt shear.

Design Examples

Basing calculations on a 1.5 factor applied to the working load

and a 3.0 factor applied to the limiting rotation, a series of design

examples were made. The results of the examples are summarized in

Table 10, with one problem worked out in detail in Appendix C,

Calculations were made using the nondimensional moment-rotation equa

tion and the limiting rotation equations. Tables 7, 8 and 9 were used to

obtain the various parameters required for the calculations. A com

parison of these results was then made to results obtained through use

of Table X of the AISC manual by dividing the end reaction from the

single plate framing connection by the allowable load determined through

use of Table X (R/P ratio).

Several important observations can be made from these comparisons.

1. The values of the R/P ratio always greater than one illus

trates that the factors of safety of the connections are less than than

that normally specified for bolted connections. This indicates that the

single plate framing connection in general does not have the strength

and ductility desired for bolted connections.

2. A range in R/P ratio values from 1.05 to 2.14 indicates that

a constant factor of safety is not obtained through the alternate proce

dure. This variation in actual factor of safety occurs because the

procedure only requires that the connection rotation does not exceed a

86

Table 10. Summary of Example Problems

Value*

IV

L

L'd

Beam

# 1 n #3 #4

w. L.

f.v.

ref

ref

h

e/h

M

lim

*1 lm

^lim

pall

R/P all

Meet Criteria

18.9

7.0

4.7

W 18 x 35

66.15

99.2

5

.00392

.05

506.0

1 2 . 0

.084

100.0

1 . 0 1

.3

.025

.00531

63.0

1.05

Yes

6.4

1 2 . 0

8 . 0

1 . 6

24.0

1 6 . 0

1 8 . 0

1 0 . 0

5.0

W 18 x 35 W 18 x 35 W 24 x 55

38.4

57.6

3

.00669

0 . 1

169.0

6 . 0

.148

51.2

.889

.3

.050

.0164

36.4

1.05

No

19.2

2 8 . 8

3

.0134

. 1

169.0

6 . 0

.755

130.5

4.53

. 3

.050

.0415

1 6 . 1

1.19

Mo

90.0

135.0

7

.00417

.0333

1404.0

1 8 . 0

.367

893.0

6 . 6 2

. 3

.0167

.0114

48.1

1.87

Mo

#5

9.3

14.0

7.0

W 24 x 55

65.1

97.7

5

.00591

.05

702.0

1 2 . 0

.384

450.0

4.61

<T . J

.025

.0172

36.3

1.79

Mo

87

Table 10. Summary of Example Problems (cont'd.)

Value*

W

L

L'd

Beam

R r w. L.

ft 6 #7 # 8 #9 #10

f.y.

ref

ref

h

e/h

M

e

V lim

0 • lim

^lim

Pall

R/Pall

Meet Criteria

3.4

23.0

11.5

W 24 x 55

39.1

58.65

3.0

.00958

. 1

234.0

6 . 0

.421

148.0

2.53

. 3

.05

.034

24.7

1.58

Yes

13.0

1 8 . 0

7.2

W 30 x 99

117.0

175.5

9.0

.00588

.025

2328.0

24.0

.416

1753.0

9.99

. 2

.00833

.00674

53.47

2.19

No

8 . 1

23.0

9.2

W 30 x 99

93.15

139.7

7.0

.00765

.0333

1397.0

1 8 . 0

.417

1049.0

7.51

_ 2

.0111

.00897

43.77

2.13

No

4.1

32.5

13.0

W 30 x 99

66.63

99.9

5.0

.01092

.05

698.0

1 2 . 0

.444

532.0

5.32

. 2

.01667

.0137

32.67

2.04

No

1.5

54.0

2 1 . 6

IV 30 x 99

40.5

60.75

3.0

.01833

. 1

233.0

6 . 0

.488

178.0

2.93

. 2

.0333

.0274

22.5

1 . 8 0

Yes

Table 10. Summary of Example Problems Ccont'd.)

Value* #11 ir 12 #13 #14

W 1.75 1.75 2.76 2.76

L 30.0 30.0 40.0 40.0

L / d 20 .0 20 .0 20 .0 20 .0

Beam W 18 x 55 W 18 x 55 IV 24 x 110 W 24 x 110

R . 26.25 26.25 55.2 55.2 W . L.

R- 59.4 39.4 32.8 82.8 f.y.

n 3.0 5.0 5.0 7.0

({> .0165 .0165 .0165 .0165

<!> _ 0.1 0.05 .05 .0333 ref

M r 234.0 702.0 698.0 1397.0 ref

h 6.0 12.0 12.0 18.0

e/h .798 1.0 .617 .882

M 189.0 632.0 613.0 1315.0

e 4.79 16.0 7.40 15.88

A,. .3 .3 .2 .2 lim

.05 .025 .0167 .0111 lim

<K. .043 .0242 .0157 .0111 lim

P .. 15.37 12.26 25.0 22.79 all

R/P n 1.71 2.14 2.21 2.43

Meet Criteria Yes Yes No No

Table 10. Summary of Example Problems (cont'd.)

89

*Legend:

W - distributed load in kips per foot

L - span of beam in feet

L/j - span to depth ratio for the beam

Beam - AISC designation for beam

R . - end reaction in kips at working load level of the beam w.L. r •a'

R„ - end reaction in kips at first yield load level of the beam

n - number of bolts

<}) - free end rotation in radians at first yield load level of the beam

<J>re£ - reference rotation in radians for the connection

Mre£ - reference moment in kip-inches for the connection

h - depth of bolt pattern in inches

e/h - ratio of eccentricity to depth of bolt pattern

M - moment at the connection in kip-inches

e - eccentricity in inches

- limiting deformation in the bolt-plate combination

^lim ~ interme<Aiate limiting rotation value in radians

^lim - limiting rotation in radians

P n - allowable end reaction obtained through Table X of a AISC manual

R/P^^ - ratio of end reaction at working load to allowable end reaction obtained through Table X

90

maximum allowable value. Rotations in actual connections can range

from near to substantially under the allowable value.

3. Increasing the number of bolts beyond the minimum required

for the connection generally increases rather than decreases the R/P

ratio. A particular connection with a required three bolts had a

1.71 R/P ratio. Arbitrarily increasing the number of bolts to five

resulted in a 2.14 R/P ratio. This contradiction of the "more is

better" philosophy results from the extra bolts attracting a larger

end moment coupled with a reduced rotation which results in a larger

eccentricity.

The primary difference between the eccentrically loaded con

nection procedure of Table X and the single plate framing connection

criteria presented here lies in the philosophy for determining the factor

of safety. A design made using Table X includes a factor of safety of

2.5 to 3.5 times the working load, whereas a design by the alternate

method includes a factor of safety on the load and limits excessive

deformation of the connection elements.

CHAPTER 8

SUMMARY AND CONCLUSION

Summary

The results of an investigation of the strength and ductility

of single plate framing connections have been presented. The study

was made by a combination of experimental work and finite element

analysis. The experimental work consisted of a series of load-

deformation measurements on two plates connected by a single bolt

loaded in single shear. These load-deformation relationships were

then used as the properties of a shear fastener element representing

one bolt in finite element models of single plate framing connections.

Moment-rotation curves were obtained using these models for a large

variety of loading patterns in order to establish patterns of behavior

for the connections.

From the moment-rotation curves, a single nondimensional

moment-rotation curve was developed. Also developed was an equation

for predicting limiting rotations due to bolt or plate failure, or

excessive deformations. A method for including a factor of safety

with these equations was presented, and particular values for the

factor of safety were recommended.

A series of single plate framing connection designs were made

using the nondimensional moment-rotation curve and the recommended

safety factors.

91

92

Conclusions

The primary conclusion that resulted from this study is that,

in general, the single plate framing connection does not exhibit the

strength and ductility generally desired in bolted connections.

Application of the design criteria presented here would prevent the use

of single plate framing connections in a significant number of cases,

especially those requiring five or more bolts and those connections in

which the framing plate and beam web thicknesses are relatively large.

If the single plate framing connections are to be used, a

factor of safety below that generally desired for bolted connections

must be accepted. A design procedure incorporating a factor of safety

approximately equal to that of the supported beam has been presented

as an alternate design procedure.

Due regard should be given to the limited ductility and signif

icantly reduced factor of safety of the single plate framing connection,

regardless of the design procedure chosen. Serious consideration should

always be given toward using an alternate type of connection.

Apparent Success of Existing Connections

It has been noted that single plate framing connections have

been used with apparent success for a number of years. This apparent

success may be attributed primarily to the following reasons:

1. The connections may have sufficient strength to carry the

design load, but at a significantly lower factor of safety than the

designer had intended.

93

2. Some free end rotation occurs. Bolt holes are normally

oversized, allowing a potential for some slip between the beam and the

framing plate before the bolts come into bearing. The recommendations

of this study were based on no free end rotation occurring.

3. Many structures have not realized their full design load.

Thus the connections may have never been loaded to their design

capacity.

4. Some rotation of the supporting structure may occur. This

is especially true when the framing plate is welded to the web of a

second beam.

5. Materials often exceed the design specifications. For

example, the A36 steel plates used in the single bolt, single shear

tests had an average yield strength of 44 kips per square inch.

APPENDIX A

TEST RESULTS

94

Table 11. Results of Tests on Tensile Test Coupons

95

Nominal Plate Yield Ultimate Rupture Thickness Strength Strength Strength Cinches) Cksi) (ksi) (ksi)

1/4 41.0 49.5 32.9

1/4 41.7 49.6 32.4

1/4 44.0 59.7 48.4

5/16 41.1 61.9 58.3

5/16 41.6 61.5 56.1

3/8 45.8 72.6 61.8

3/8 47.1 71.7 61.7

A36 3/8

7/16

52.0

41.2

77.5

68.3

60.5

48.2

1/2 46.0 64.9 48.4

1/2 46.9 65.5 50.9

1/2 40.7 59.9 40.7

1/2 40.1 63.8 46.6

1/2 40.1 64.4 47.2

5/8 Coupons not available

A572

Gr 50

3/8

1/2

54.0

57.0

76.2

83.3

52.9

57.0

Figure 46. Plot of Load-Deformation Data for a 5/4-Inch Diameter A32S Bolt Connecting Two 1/4-Inch A 56 Plates

97

Table 12. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/4-Inch A36 Plates

FIRST TEST SECOND TEST THIRD TEST

LOAD (KIPS)

DEF. (INCHES)

LOAD (KIPS)

DEF. (INCHES)

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000 0. 0 0-0000 0.0 0-0000

2.0 .0009 2. 0 -0004 2. 0 - 0016

a. o .00 11 4. 0 .0009 4.0 . 0024

6.0 . 0022 6.0 .00 15 6. 0 - 0030

3.0 .0035 3.0 .0 022 8.0 . 0035

10.0 .0043 10. 0 .0031 l 0.0 .0046

12.0 .0053 12. 0 .0043 12.0 .0071

la. o .0039 14.0 .0067 14.0 .0124

16. 0 . 0294 16. 0 .0104 1b.0 . 0219

17.0 .0762 17. 0 .0147 17.0 . 0302

17.3 . 1051 13. 0 .0105 18.0 . 0415

17.0 . 1 562 19. 0 .0252 19.0 . 0747

16.9 . 2057 20. 0 .0420 20.0 . 1530

16.7 . 2563 21. 0 .0903 20. 2 . 1975

16.2 . 3079 21.4 . 1487 20.2 .2580

21.5 . 2087 20.2 .3065

21.5 .2587

20- 4 .3119

i

I I

98

o C3 o T1

O

a

i?1

o

a: o

T

a

o *^ •s n ^ c, T =;n

DcrGF^'iGM f INCHES)

2 / 4 R 3 2 b S O L i 5 - — ^ L h ' E S 5 / 1 5 P M C z / l S

Figure 47. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 5/16-Inch A56 Plates


SINGLE TESi

LOAD (KIPS)

DEF. (INCHES

0. 0 0.0000

2. 0 .0001

4. 0 .0008

6- 0 .00 14

3. 0 . 0018

10. 0 .0021

12. 0 .003 1

14. 0 .0042

16. 0 .0053

13. 0 .0081

20. 0 .0166

21. 0 . 0251

22. 0 . 0399

23. 0 .0635

2 3. 9 .0970

23.5 . 1496

23.7 .2006

23. 5 .251b

23. 1 .3057

100


101


F1HST TEST SECOND TEST THIRD TEST

LOAD DEF. LOAD DEF. LOAD DEF. (KIPS) (INCHES) (KIPS) (INCHES) (KIPS) (INCHES)

0.0 0.0000 0. 0 0.0000 0.0 0.0000

2.0 . 0003 2. 0 .0002 2. 0 .0002

1.0 . 0009 4. 0 .0 009 4.0 .0007

6.0 .00 14 6. 0 .0014 6.0 .0012

a. o .0018 8. 0 .0021 3. 0 .0018

10.0 .0024 10- 0 .0027 10.0 .0024

12,0 .0034 12. 0 .0031 12.0 .0031

14.0 .0093 14. 0 .0043 14.0 .0043

16.0 .0 130 16. 0 .0058 16.0 . 0068

18.0 .0207 18. 0 -0092 18-0 .0130

20.0 .03 19 20. 0 .0 164 20.0 .01 94

21.0 .0385 22. 0 . 0251 22. 0 .0291

22. 0 .0439 24. 0 .0423 24.0 .0453

23.0 . 0499 26. 0 .0725 26.0 . 0770

24.0 .0578 28. 0 .1212 28. 0 . 1 197

25.0 . 066 1 30. 0 . 1788 30. 0 . 1 958

26.0 . 0775 31.0 .2132 3 1.0 .2462

27. 0 .0908 32. 0 .2570 32-0 .3150

20.0 . 1057 33. 0 - 3 1 0 4 31.8 .3586

29.0 . 1230 34. 0 .3822

30.0 . 1443

31.0 . 1697

32.0 . 2055

33-0 . 24 9 4

34.0 . 3207

102


103


FIRST TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0-0000

2.0 .0005

4.0 .0008

6.0 .0007

3.0 .0019

10.0 .0025

12-0 .0032

14.0 .0039

16.0 .0049

13.0 .0059

20.0 .0073

22.0 .0 106

24.0 .0231

26.0 . 0370

28.0 .0573

30.0 .0835

32.0 .118 7

34.0 .1800

35.0 . 2338

35. 3 .2818

SECOND TEST

LOAD (KIPS)

DEF. (INCHES

0. 0 0.0000

2. 0 .0002

4. 0 .0008

6. 0 .0012

8.0 .0017

10. 0 .0021

12- 0 .0025

14.0 •V -0031

16. 0 .0042

13. 0 .0051

NJ 0

1 o

.0068

22. 0 .0154

24. 0 .0253

26. 0 .0425

23. 0 .0688

o t o . 1 005

32. 0 . 1457

34. 0 .2.330

34.8 .3 114

THIRD TEST

LCAD (KIPS)

DEF. (INCHES)

0-0 0.0000

2. 0 .0005

4.0 .0013

6. 0 . 0017

8. 0 . 0024

10. 0 .0032

12. 0 . 0037

1 4. 0 -0049

16. 0 .0069

18.0 .01 16

20. 0 .0183

22. 0 .0281

24. 0 .0403

26. 0 .0570

28. 0 . 0773

30.0 . 1065

32. 0 .1612

34-0 .2435

34. 6 .29 89

104

Figure 50. Plot of Load-Deformation Data for a 3/4-Inch Diameter A32S Bolt Connecting Two 1/2-Inch A36 Plates

105


FIRST TEST

LOAD (KIPS) (INCHES)

0.0 0.0000

2.0 .0006

4.0 .0009

6.0 .0013

8.0 .0019

10.0 .00 28

12. 0 .0034

14.0 .00 39

1 b. 0 .0051

18.0 .0064

20.0 .0087

22.0 .0204

25.0 .0454

26.0 .0555

28.0 . 0757

30.0 .1085

31.6 . 1448

SECOND TEST

LOAD (KIPS)

DEF. (1t1C fi tl 3

0. 0 0.0000

2. 0 .0003

4. 0 .0005

6. 0 .0013

8. 0 .0014

10. 0 .0023

12.0 . 0031

14. 0 .0039

16. 0 .0051

18. 0 .0087

20. 0 .0 165

22. 0 .0284

24. 0 .0442

26. 0 - 0685

2 8. 0 .0997

30.0 .1515

31.3 .2034

THIHD TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

2. 0 -0006

4.0 .0010

6 . 0 . 00 1 1

S. 0 . 0019

10.0 . 0023

12.0 . 0026

14.0 -0034

16. 0 .0039

18.0 . 0049

20.0 .0052

22.0 . 0079

24.0 .0135

26. 0 . 0200

28.0 . 0322

30.0 -0520

32.0 .0733

33.0 . 0947

3 4,0 . 1460

34. 1 . 1565

106

Figure 51. Plot of Load-Deforraation Data for a 5/4-Inch Diameter A525 Bolt Connecting 1/4-Inch and 5/S-inch A36 Plates

107

Table 17. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 1/4-Inch-and 3/8-Inch A36 Plates-

FIRSI TEST

LOAD (KIPS)

D3F. (INCHES)

0. 0 0.0000 2. 0 .0006

4.0 .00 1 1

6-0 .00 14

3.0 .0020

10.0 .0029

12.0 .0048

14.0 .0074

16.0 .0135

17.0 .0 163

18.0 .021 1

19.0 .0270

20-0 .0393

21-0 .0586

22.0 .0979

22. 2 . 1369

21.9 . 1854

20.7 . 2336

19.6 .2823

SECOND TEST

LOAD (KIPS)

DEF. (IHCHZS)

0. 0 0.0000

2. 0 .0006

4. 0 .0013

6. 0 .0024

8. 0 .0030

10. 0 .0041

12- 0 - 0058

1 4. 0 .0089

16.0 .0140

18. 0 .0236

19. 0 .0335

20. 0 .0623

21.0 . 1126

21. 1 . 1681

20.2 .2162

19.2 .2654

18.6 .3 140

THIBD TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

2.0 . 0006

4.0 . 00 16

6.0 . 0022

8.0 .0030

10.0 .0041

12.0 . 0073

14.0 .0124

16.0 .0235

18.0 • 049 b

19.0 .0710

20.0 .1118

20. 2 .1347

20. 3 . 1737

18.8 .2255

1 d. 1 -2796

Figure 52, Plot of Load-Deformation Data for a 5/4-Inch Diameter A525 Bolt Connecting 1/4-Inch and 1/2-Inch A36 Plates

109

Table 18. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 1/4-rInch and. 1/2-Inch A36 Plates

FIRST TEST SECOND TEST THIRD TEST

LOAD DEF. LOAD DEF. LOAD DEF. (KIPS) (INCHES) (KIPS) (INCHES) (KIPS) (INCHES)

o

o 0.0000 0- 0 0.0000 0.0 0.0000

2-0 . 0005 2- 0 .0005 2-0 . 0005

4.0 .0013 4- 0 .0013 4.0 - 00 13

6.0 .00 15 6. 0 .0015 6.0 . 00 18

8.0 .0027 a. o .0022 S- 0 .0022

o i

o .0038 10. 0 .0036 10.0 .0031

12. 0 . 0053 12- 0 .0050 12. 0 . 0043

« o

.0074 14. 0 .0076 14.0 . 0061

16.0 -0 111 16. 0 .0108 16.0 .0106

CD

• o

.0170 18. 0 .0 160 18. 0 .0175

19.0 .0268 19. 0 .0218 19.0 .0233

i a - 6 -0819 20. 0 .0346 20. 0 . 0366

IB. 1 .1310 21.0 .0520 21.0 .0620

1 7.6 - 1805 21.3 , 0748 21.5 .0819

17.4 .2296 22. 1 . 1 108 21.7 .1199

17.2 . 2796 21-5 . 1749 21.6 .1784

19.9 .2247 21-1 .2275

18.8 .2743 19-9 . 2782

110

Figure 53. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 3/8-Inch and 1/2-Inch A36 Plates

Ill

Table 19. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 3/8-Inch and 1/2-Inch A36 Plates

SINGLE TEST

LOAD (KIPS)

DEC. (INCHES

0. 0 0.0000

2. 0 .0002

4. 0 .0008

6. 0 .0015

3. 0 .0019

10. 0 . 0024

1 2. 0 .0029

14. 0 .0041

1 6. 0 .0078

13. 0 .0136

20. 0 .0198

2 2 . 0 .0295

24. 0 . 0392

26. 0 .0650

28. 0 .0947

30. 0 .1419

32. 0 .2237

3 2. 4 .2706

112

Figure 54. Plot of Load-Deformation Data Diameter A325 Bolt Connecting Plates

for a 7/S-Inch Two 5/16-Inch A36

113


FIRST TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

2, 0 - 0006

4. 0 .0013

6. 0 .0018

8. 0 .0021

10.0 . 0028

12. 0 . 0034

14. 0 . 0044

16.0 . 0050

18- 0 . 0064

20. 0 . 0081

21.0 . 0099

22. 0 . 01 27

23.0 .0180

24.0 .0414

25. 0 . 0627

26. 0 .0805

27.0 . 1008

28.0 . 1302

2b. 2 . 1431

28.7 . 1921

29. 3 . 2409

29.8 .2904

SECOND TEST

LCAD (KIPS)

DEF. (INCHES)

o

* o

0.0000

2.0 . 0007

4.0 . 0008

6.0 .00 15

8.0 .0016

10.0 .0023

12.0 .0029

14.0 .0036

16.0 . 0047

18.0 .0059 o

• o

.0079

21.0 .0092

22.0 .0 1 10

23.0 .0 150

24. 0 . 0404

25.0 . 0657

26.0 .0835

27.0 • 1 158

27-6 . 1982

to

-J

* c.

. 2453

25.7 .2916

114

Figurs 55. Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A56 Plates

lis


FIRST TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

2.0 .0002

4. 0 .0009

6.0 .0011

3. 0 .00 17

10.0 .002 1

12.0 .0028

14.0 .0035

16.0 .0047

18.0 .0089

20.0 .0161

22. 0 . .0238

24.0 .0346

26.0 .0468

23. 0 . 0610

30.0 .0327

32.0 . 1 099

34.0 .1511

35.0 . 1770

36.0 .2013

37.0 . 2 2 a 1

38.0 .2600

39.0 . 3019

SECOND TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

2. 0 .0005

4. 0 .0007

6. 0 .0011

8. 0 .0017

1 0. 0 .0021

12. 0 .0028

14.0 .0033

1 6. 0 .0052

18. 0 .0 104

•20. 0 .0 161

22. 0 .0278

24. 0 -0386

26. 0 . 0538

28. 0 -0725

30. 0 .0947

32. 0 .1234

34. 0 . 1576

36. 0 .2038

37. 0 .2277

38. 0 .2620

39. 0 .3014

THIRD TEST

LOAD (KIPS)

DEI'. (INCHES)

0.0 0.0000

2.0 0-0000

4.0 .0007

6.0 -001 1

8.0 .0019

10. 0 .0021

12. 0 .0028

14.0 • 0040

16.0 .0060

18.0 .0144

20. 0 . 0241

22. 0 .0353

24. 0 .0501

26.0 .0638

28. 0 .0780

30.0 .0982

32.0 . 1194

34.0 .1636

35-0 . 1 865

36.0 .2128

37. 0 .2437

38.0 . 2790

39.0 . 3239

116

CO CO -3 CD

/ ' D H j Z D D ! t C U'JL S VJ

no .-» {c- — ~ -n̂ .*• ""C,̂ \j sj j • ; <t J - i-J J w i- J J

rrORf*^-10M ( iMCHESJ

C _ 31 QTLC "7 / 1 R Q\! i L_ ! 1 1 L_ -j ; : 1 U • i' \

:. ic:

1 / ! '

Figure 56. Plot of Load-Deformation Data for a 7/8-Inch Diameter AS2S Bolt Connecting Two 7/16-Inch A36 Plates

117

Table 22. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two .7/16-Inch A36 Plates

FIRST TEST

LOAD (KIPS)

DEF. (ItiCHZS

0.0 0.0000

2.0 .0003

4.0 . 0008

6.0 .0011

8.0 .00 15

10.0 .002 1

12.0 .0025

14.0 .0033

16.0 .0043

13.0 .0083

20.0 .0120

22. 0 .0 163

24.0 .0220

26.0 .03 13

28. 0 .0476

30. 0 . 0 63 3

32.0 .0846

34.0 . 1 103

36.0 .1441

37.0 . 1 b 74

38. 0 . 1 940

39.0 . 2322

39.9 . 3061

SBCOU D TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

2. 0 .0003

4. 0 .0008

6- 0 .0013

8. 0 ,0020

10. 0 .0023

12. 0 .0025

14.0 .0031

16. 0 . 0038

18. 0 .0046

20. 0 .0058

22. 0 .0073

2 4. 0 .0 115

26. 0 .0 103

28. 0 .0276

30.0 .0413

32. 0 .063 1

34.0 .0893

36. 0 .1261

37. 0 . 1424

38. 0 .1673

3 9. 0 . 1922

40. 0 . 2416

THIRD T£ST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

2.0 .0003

4.0 .0010

6.0 .0013

8.0 .0015

10- 0 .0023

12.0 .0028

14.0 . 0048

16.0 -0050

18.0 . 0068

20.0 .0135

22-0 .0193

24. 0 . 0270

26. 0 . 03 83

28.0 . 053 1

30.0 .0708

32.0 .0906

34.0 .1158

36.0 - 1516

37.0 . 1749

38.0 .2128

39.0 . 2782

3 9.1 .3027

118


119

Table 23, Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates

FIRST TES11

LOAD (KIPS)

DEF. (I HCHiiS)

0.0 0.0000

2- 0 .0003

4- 0 .0009

6.0 .0012

8. 0 .0014

10.0 .0019

12. 0 . 0025

14.0 .0030

16.0 . 0033

18- 0 .0041

20. 0 . 00 48

22-0 . 005o

24. 0 -0069

26.0 . 0037

to

00

1 o

.0120

30. 0 .0173

32.5 .0345

34. 0 .0633

36- 0 -094 1

U*

• O

-1170

38.0 . 1469

39-0 . 1843

40.0 . 2027

SECOND TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0-0000

2.0 .0006

4.0 .0009

6.0 .00 17

8.0 . 00 1b

10-0 . 0022

12.0 . 0027

14,0 .0030

16.0 . 0041

18-0 .0044

20-0 .0053

22.0 . 0061

24. 0 . 0072

2 6.0 . 0087

28-0 .0110

30-0 .0213

32,0 - 04d1

34.0 .0598

36-0 .0781

37.0 - 0925

38.0 .1114

39.0 . 1503

39.3 . 2033

120

Figure 58. Plot of Load-Deformation Data for a 7/3-Inch Diameter A325 Bolt Connecting l/4-[nch and 3/8-Inch A36 Plates

121


SINGLE TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

2. 0 .0006

4. 0 .0013

o. 0 .0014

8. 0 .0021

10.0 .0027

12. 0 .0031

14. 0 .0035

16. 0 .0046

18.0 .0063

20. 0 .0 104

22.5 .0215

24. 0 .0332

26- 0 . 0613

25. 5 .0949

24. 9 .1260

23. 9 .1777

23. 0 .2289

22. 4 .2800

122

Figure 59. Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 1/4-Inch and. 1/2-Inch. A36 Plates

123


SINGLE TEST

LOAD (KIPS)

DEE. (INCHES

0. 0 0.0000

2. 0 .0005

4. 0 . 0012

6. 0 .0013

a. o .0017

10. 0 - 0024

12. 0 .0029

14. 0 .0035

16. 0 .0 0.39

18. 0 . 0048

20. 0 .0058

22. 0 .0074

24, 0 .0111

26. 0 .0181

28. 0 .0440

28.4 .0629

26. 9 .1037

25. 8 . 1596

25. 3 .2094

24. 9 . 2605

24. 5 .3 105

124

Figure 60. Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 5/8-Inch and 1/2-Inch A56 Plates

125

Table 26. Load-Deformation Data for 7/8-Inch Diameter A325 Bolt Connecting 3/8-Inch and 1/2-Inch A36 Plates

SINGLE TEST

LOAD (KIPS)

DEf . (INCHES)

0. 0 0.0000

2. 0 .0005

4. 0 -0010

6. 0 .0017

a. 0 .0020

1 0. 0 .0025

12. 0 .0033

14. 0 .0035

16. 0 .0045

13. 0 .0055

20. 0 -0135

22. 0 . 0202

24. 0 . 0 285

26. 0 .0337

28. 0 .0525

30. 0 .0697

32. 0 .0955

3 4. 0 . 1 282

35. 0 .1481

36. 0 . 1720

37. 0 .2003

33. 0 .2347

3d. 7 .2^76

126

Figure 61. Plot of toad-Deformation Data for a 1-Inch Diameter A525 Bolt Connecting Two 1/2-Inch A36 Plates

127

Table 27. Load-Deformation Data for a 1-Inch Diameter A32S Bolt Connecting Two 1/2-Inch A36 Plates

FIRST TEST

LOAD (XIPS)

DEF. (INCHES)

0.0 0.0000

3.0 .0007

6.0 . 0009

9.0 .00 16

12.0 .0023

15.0 .0039

18.0 .006 1

21.0 .0103

24.0 .0170

27.0 .0252

30.0 .0379

33.0 .0576

36.0 .0883

39.0 .1300

42.0 . 1842

45.0 . 2543

46.2 . 2752

SECOND TEST

LOAD (KIPS)

PFF (INCHES)

0. 0 0.0000

3. 0 . 0005

6. 0 .0007

9. 0 . 0014

12. 0 .0016

15. 0 .0022

18. 0 .0031

21- 0 . 004 1

24. 0 .0 110

27. 0 .0212

30. 0 .0349

33. 0 .0551

36. 0 .0868

39.0 .1270

42. 0 .1817

45. 0 .2553

4 6.2 . 2952

THIRD TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3.0 -0005

6. 0 . 001 4

9.0 .0019

12.0 ,002b

15.0 .0039

13.0 .0061

21-0 . 0096

24- 0 .0165

27-0 . 0272

30-0 .0394

33. 0 . 05b6

3b. 0 .0868

39. 0 .1310

42-0 - 1972

43. 7 . 2405

128

Figure 62. Plot of Load-Deformation Data for a 1-Inch Diameter A325 Bolt Connecting Two 5/8-Inch A56 Plates

129

Table 28. Load-Deformation Data for a 1-Inch Diameter A325 Bolt Connecting Two 5/8-Inch A36 Plates

FIEST TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3. 0 .0003

6.0 .0005

9.0 .0011

12.0 .00 15

15.0 .0023

18.0 .0030

21.0 .0041

24.0 .0 105

27.0 .0 161

30.0 .0225

33. 0 .0303

36.0 .0405

39.0 .0543

42.0 .0755

45.0 . 1123

43. 0 . 1635

50.9 . 2483

SECOND TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3. 0 .0003

6. 0 .0010

9. 0 .0013

12- 0 .0018

15. 0 .0026

18.0 .00 33

21.0 .0043

24. 0 .0050

27. 0 .007 1

o •

o .0088

33. 0 .0288

36. 0 .0395

39. 0 .0533

42. 0 .0725

45. 0 .0933

4 3.0 .1200

51.0 . 1548

54. 0 .2050

57. 0 .2803

58.4 .3262

THIRD TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3. 0 .0001

6.0 . 0013

9.0 . 0016

12.0 . 0023

15.0 . 0031

18.0 .0038

2 1.0 . 0051

24.0 . 0060

27. 0 . 0076

30.0 .0100

33.0 .0141

36.0 .0295

39.0 .0458

42. 0 . 0640

45.0 . 0863

48 .0 . 1 165

51.0 . 1553

54.0 .2045

57.0 .2713

58.7 .3186

130

Figure 63, Plot of Load-Deformation Data for a 3/4-Inch Diameter A525 Bolt Connecting Two 3/8-Inch A572, Grade 50, Plates

131

Table 29. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A572,-Grade-50, Plates

FIRST TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3.0 .0001

6.0 .0007

9.0 .00 18

12.0 .0033

15.0 .0059

18.0 .00 80

21.0 .0 196

24.0 .03 12

27.0 .0553

30.0 .1024

32. 4 . 1675

33.4 .2174

34.2 .2673

34. 7 .3177

SECOND TES'I

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3. 0 .0006

6. 0 .0012

9. 0 .0023

12. 0 .0038

1 5. 0 .0064

18. 0 .0105

21. 0 .0191

24. 0 .0317

27. 0 .0633

30. 0 .1119

32. 1 .1626

33. 4 .2129

34.2 .2623

34.9 .3 127

THIBD TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3.0 . 0004

6.0 . 00 17

9.0 .0028

12.0 . 0041

15.0 . 0064

la.o .0110

21.0 . 0206

24.0 .0352

27.0 .0738

30.0 .1409

31.6 . 1996

32.6 .2500

33. 2 .2989

132

Q ~> O

o CT a uo m

23'

o CO a 3 rn

p"

CD o ;•

C4

CO Q_

a a; o

0 /

G4n

99

i ni" i ~ ̂ I i ' -Uw> J i JU

DtirOR^'iCM

l .Zb"d

LNOxS 1

Figure 64, Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A572, Grade 30, Plates

133

Table 30. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 3/8-Inch AS72, Grade 50, Plates

FIH5T TEST

LOAD (XIPS)

DEF. (INCHES)

0.0 0.00 00

3.0 .000 1

6.0 .0010

9.0 .0021

12.0 .0031

15.0 .0044

13.0 .0090

21.0 .0176

24.0 .0292

27.0 .0498

30.0 .0709

33.0 . 1049

J5. 3 .16 56

36. 1 .2150

36.9 .2654

37.2 .3049

SECOND TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3. 0 .0011

6. 0 .0017

9. 0 . 0 026

12. 0 . 0038

15. 0 .0052

18. 0 .0075

21-0 -0111

24. 0 .0182

27. 0 .0313

30. 0 .0514

33. 0 -0874

35.3 - 1351

36. 3 . 1844

37.5 - 2333

38.9 .2821

39.2 .3076

THIRD TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3-0 -.000 1

6-0 . 0007

9- 0 .0018

12.0 -0028

15.0 .0044

18- 0 -0070

21.0 - 0141

24.0 . 0252

27. 0 . 0428

30.0 .0664

33. 0 .1119

34. 5 . 1647

35.5 .2136

36. 4 -2635

37.0 -3124

154

Figure 65, Plot of Load-Deformation Data for a 5/4-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A56 Plates

135


FIRST TEST S E CO N D TEST THIRD TEST

LOAD DEF. LOAD DEF. LOAD DEF. (SIPS) (INCHES) (KIPS) (INCHES) (KIPS) (INCHES)

0. 0 0.0000 0. 0 0.0000 0.0 0.0000

3.0 .00 10 3- 0 .0007 3.0 . 0007

6.0 .0019 6. 0 .0014 6. 0 . 0014

9.0 .0029 9. 0 .0024 9.0 .0019

12.0 .0043 12. 0 .0033 12.0 . 0063

15.0 .0059 15.0 .0054 15.0 .0 114

18.0 .0 106 18. 0 .0066 18.0 .0176

21.0 .0203 21-0 .0218 21.0 . 0263

24.0 .03 20 24. 0 .0335 24.0 .0385

27. 0 .0 487 27. 0 .0487 27.0 .0552

30.0 .0719 30. 0 .0729 30. 0 . 0829

33.0 . 1 136 33. 0 .1241 32.6 . 1451

35.0 . 1 364 34. 3 .1570 33.3 . 1966

35.8 . 2398 36. 0 .2293 33.6 . 2470

36.0 .26 53 36. 6 .2832 33.7 .2980

36. 7 .3097


137


FIRST TEST

LOAD (KIPS)

D2F. (INCHES)

0.0 0.0000

3.0 .0006

6.0 . 0008

9.0 .0016

12.0 .00 13

15.0 .0023

13.0 .0058

21.0 .0096

24.0 .0 145

27.0 .0233

30.0 .0335

33.0 .0508

36.0 .0305

39.0 . 1328

39.9 . 1547

4 1.7 .2030

42.9 .2519

43.9 . 3009

SECOND TEST

LOAD (KIPS)

DEE. (INCHES)

0. 0 0.0000

3. 0 -0006

6. 0 .0008

9 . 0 .001b

12. 0 .0025

15. 0 .0078

18. 0 .0125

21-0 .0193

24. 0 .0275

2 7 . 0 -0373

3 0.0 .0505

33. 0 .0703

3 6, 0 . 1025

39.0 .1513

41.3 -2071

42.8 .2565

44.5 .3053

THIRD TEST

LOAD (KIPS)

Dh,F. (INCHES)

0.0 0.0000

3. 0 . 0006

6.0 .0013

9-0 .0021

12.0 . 0030

15.0 .0043

13.0 . 0060

21.0 - 0 108

to

-p: • O

.0195

27.0 .0323

30- 0 .0465

33.0 .0653

36-0 .0945

39.0 . 1343

42.0 . 1 940

43. 6 -2479

44.7 . 2973

138


139

Table 33, Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates

F i a s r TEST

LOAD (SIPS)

DEF. (INCHES)

0.0 0.0000

3.0 .0007

6.0 .00 17

9.0 .0024

12.0 .0036

15.0 .0049

18.0 .0071

21,0 .0 113

24.0 .0 180

27.0 .0257

30.0 .0384

33.0 .0606

35.b .0903

33.5 . 1395

'+0. 4 .1873

SECOND TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3. 0 .0005

6. 0 .0014

9. 0 .0021

12.0 .0033

15. 0 .0069

18. 0 .0101

21.0 ,0143

24. 0 .0195

27. 0 .0267

30. 0 .0404

33. 0 .071 1

36. 0 . 1 128

33, 2 . 1480

39.7 . 1934

40. 0 .2449

40. 4 .2953

THIRD TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0-0000

3.0 . 0005

b. 0 .0012

9.0 .0019

12. 0 . 0028

15.0 .0037

1 d. 0 .0066

21.0 .0113

24.0 .0175

27,0 . 0262

30.0 .0419

33.0 . 071 1

36.0 .1113

37.6 . 1396

39. 6 , 1 87 9

4 1.2 . 2357

4 1.7 . 2842

4 1.7 . 3072

o o a CD uo

a o o CT

3 O a

o o a

a CD ra d Cvj

a o o

CM

o a a

C3 a

o o

-0.300 0-050

QtFGRHrir [GN ( INCHES J

7/S R^90 BOLTS - 5/8 PNQ 5/8 R36 PLfl

Figure 68. Plot of Load-Deformation Data for a 7/8-Inch Diamete A490 Bolt Connecting Two 5/8-Inch A36 Plates

141


FIRST TEST

LOAD (KIPS)

DEF. (INCHES

0.0 0.0000

3.0 .00 05

6. J .0010

9.0 .00 18

12.0 .0025

15.0 .0033

13.0 .0045

2 1.0 . 0063

24. 0 .0095

27.0 .0 138

JO.O .0210

33.0 .03 23

36.0 .0480

39.0 .0708

42.0 . 1015

45.0 . 1423

43.0 .1550

50,6 . 25 1 3

52.2 . 3007

SECOND TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3. 0 .0006

6. 0 . 0008

9. 0 .0013

12. 0 .0018

15. 0 .0038

18. 0 . 0080

2 1.0 .0113

24. 0 .0165

27. 0 .0233

30. 0 .0325

33. 0 .0443

36. 0 .0650

39. 0 .0918

42. 0 . 1300

43.5 . 1784

THIKD TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3.0 . 0003

6.0 .0010

S.O .0018

12.0 . 0020

15.0 . 0029

18.0 . 0 03 3

21.0 .0058

24.0 . 0085

27.0 .0143

30.0 .0215

33.0 .031 8

36.0 .0435

39. 0 .0728

42.0 . 1065

45.0 . 1753

45.0 . 1838

142

Figure 69. Plot of Load-Deformation Data for A490 Bolt Connecting Two 1/2-Inch

a 1-Inch Diameter Aoo Plates

143

Table 35. Load-Deformation Data for a 1-Inch Diameter A490 Bolt Connecting Two 1/2-Inch a.36 Plates

FIRST TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3.0 .0005

6.0 .0012

9.0 .00 16

12.0 .0023

15.0 .0032

18.0 . J036

21.0 . 0053

24.0 .0070

27.0 .0152

30.0 . 0239

33.0 .0421

36.0 .0708

39.0 . 1075

42.0 . 1552

45.0 .2 173

46. 7 .2727

3ECCNB TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3. 0 .0005

6. 0 .0009

9. 0 . 0014

12. 0 .0018

o i

in

. 0024

o »

CO

. 0036

21.0 .0073

24. 0 .0135

27. 0 . 0227

30. 0 .0349

33. 0 .0561

36. 0 .0938

39.0 . 1375

42. 0 . 18U7

45.0 . 24 13

47. 1 .3011

THIRD TEST

LOAD (XIPS)

DEF. (INCHES)

0. 0 0.0000

3.0 . 0002

6.0 .0012

9.0 .00 14

12. 0 . 002 1

15. 0 . 0024

18.0 . 0036

21-0 .0063

24.0 . 0 100

27. 0 .0167

30.0 . 0269

33. 0 . 0426

36.0 . 0678

39.0 . 1005

42.0 .1452

45-0 .2078

47. 6 .2981

144

Figure 70. Plot of Load-Deformation Data for A490 Bolt Connecting Two 5/3-Inch

a 1-Inch Diameter A36 Plates

145

Table 36. Load-Deformation Data for a 1-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates

FIRST TEST

LOAD (KIPS)

npp (INCHES)

0.0 0.0000

3.0 .0 003

6.0 .000b

9.0 .0013

12.0 .0020

15.0 .0026

13.0 .0035

21.0 .0043

24. 0 .0055

27. 0 .0063

30.0 . 0 09 0

33.0 .0 113

36.0 .0 155

39.0 .02 13

42.0 .0305

45.0 .0433

48.0 .0730

51.0 . 10 13

54.0 . 1 370

57.0 . 1763

60.0 . 2360

SECOND TEST

LOAD (KIPS)

DEF. (INCHES)

0. 0 0.0000

3.0 .0008

6. 0 .0013

9. 0 .0013

12. 0 .0023

15. 0 .0028

13. 0 .0035

21.0 .0043

24.0 .0053

27. 0 . 006o

30. 0 .0033

33. 0 .0 108

36. 0 .0135

39. 0 .0198

42. 0 . 0370

45. 0 . 0548

4 3. 0 . 0755

51. 0 . 1033

54. 0 . 1405

57. 0 . 1S03

60. 0 . 2565

6 1.8 . 3054

THIRD TEST

LOAD (KIPS)

DEP. (INCHES)

0.0 0.0000

3. 0 .0003

6.0 .0013

5.0 . 002 1

12.0 .0025

15.0 .0033

18.0 .0040

21.0 . 0051

24.0 . 0058

27.0 . 0073

30.0 . 0093

33.0 -0123

36.0 .0170

39.0 .0263

42. 0 . 0455

45.0 . 0693

48. 0 . 0930

5 1.0 .12 56

54.0 . 1625

57. 0 . 2068

60.0 -2675

6 2.0 . 3189

146

Figure 71. Plot of Load-Deformation Data for a 7/S-lnch Diameter A490 Bolt Connecting Two 1/2-Inch A572, Grade 50, Plates

147

Table 37. Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch-A572, Grade 50, Plates

FIRST TSST

LOAD (KIPS)

DEF. (INCHES

0. 0 0.0000

3. 0 . 0007

6.0 .0009

9-0 .00 16

12.0 .0023

15.0 .0034

13.0 . 0051

21.0 .0073

24.0 .0 100

27 . 0 . 0 132

30.0 .U 174

33.0 .0231

36. 0 .0308

39.0 .0435

42. 0 .0632

o I .0903

48. 0 .1210

49. 5 .1429

52.4 .1931

54.2 .24 19

55.4 .2913

SSCOiN'D TEST

LOAD (KIPS)

DEF. (INCHES)

0.0 0.0000

3. 0 .0007

6. 0 .0017

9. 0 .0021

12. 0 .0031

1 5. 0 .0039

1 ii. 0 . 0049

21.0 . 005o • 24. 0 .0075

27. 0 .0092

30. 0 .0 132

33. 0 . 0 1 Bo

36.0 .0 278

39. 0 .0395

42. 0 .0567

45. 0 .0873

48. 0 . 1 280

51.0 .1917

52. 0 .2346

THIRD TEST

LOAD (KIPS)

DEF. (INCHES)

0 . 0 0.0000

3. 0 . 0005

D . 0 .0014

9.0 .0019

12.0 . 003 1

15.0 . 0044

18. 0 . 0069

21.0 .0 103

24.0 .0140

27. 0 .0192

30.0 . 0259

33. 0 . 033 1

36.0 .0443

39 .0 .0580

42. 0 . 0787

45.0 .1083

48. 0 .1595

48.0 .1715

APPENDIX B

EFFECTIVE SPRING RATES IN SINGLE SHEAR JOINTS (CHANCE VOUGHT)

148

149

SR

1.4i

SR

JOINT SPRING RATE:

SR. SR

where S R, tabulated

.8 .9 1.0 7 3 .5 . 6 2 4 t/D

(sheet thickness/fastner diameter)

attachment diameter and SR x' CT&

sheet 1/8 | 5/32 3/16 1/4 | 5/16 3/8 7/16 1/2 7/16 | 5/8

ALUM .163 | .203 .244 .325 | .40 6 .487 .563 .650 .732 | .813

STEEL 3.62 | 4.53 5.44 7.2 5 | 9.06 10.9 12.6 14.5 16.3 | 18.1

OTHER •same as for steel x ' Eother ! Est )3 OTHER •same as for steel x ' Eother ! Est eel1

To Determine SRj0 jn1. :

1. Calculate t/D for each sheet 2. Determine K for each sheet from curve 3. Determine SR for each sheet from table

4. Calculate SFi- -• f using above formula

tfrom Caccavale, 1975)

APPENDIX C

DESIGN EXAMPLE USING THE ALTERNATE PROCEDURE

150

151

Design a single plate framing connection to support a W 24 x 76

beam of A36 steel carrying a 3-kip-per-foot load on a 30-foot span

(L/^ = 15). Use 7/8-inch diameter A325 bolts.

1. Determine end reactions at working load and first yield of the beam:

_ wL _ (3k/ft) C30 ft) _ ,iek wL = T = 2 = 45

Rfy = 1,5R«1 ' 1'5 C4sk) " 67';k

2. Determine the number of bolts required based on pure shear assumption:

R . ._k n = —r-j , . w , . . = r = 3.4 Use 4 bolts

allowable per bolt -,-k.. .. r lo.2o /bolt

3. Determine free end rotation of the beam at first yield:

= 1,5 C3 k/ft)(30 ft)3(144 inW) = rad

fy " bl 24(29000 k/in ) (2100 in )

alternately,

* * r - ' ££ • - - 0 1 2 4 3 j Ed j(290Q0 ksi) (24 mj

4. Determine £ref. (see definition):

=t °.;i. •'•ri = j;n.—— = .0667 radians ref "(n-lj(3 in J") C4-l)

. 2 J 2

152

5. Calculate $*:

4>* = <f> _ /d) -v vfy ret

.0120 radians

.0667 radians = 0 . 1 8 0

6. Calculate M*

M* = 60p 60 ( . 180 )

1 + 60<J)* 1 . 1

2/3 13/2 i + f e o ( . i s o )

1 . 1

2/3 * 3/2 = 0 . S 1 8

7. Determine M ^ (see definition):

M . = iL4.5 in (39.9k) + (1.5 in)(39.9k)' 2 = 479 k-in rer L

(Maximum capacity per bolt is from Table 3, based on the beam web thickness of 0.44 in = 7/16 in)

8. Determine the depth of the bolt pattern:

h = (n-l)(3 in) = (4-1) (3 in) = 9 in

9. Iterate to find the moment and eccentricity:

Try e/h = 1.0

M = M* | 1- (1-e/h)"5'9 !M .= (0.818 1- (1-1) °-9] (489 k-in) =392 ^ * ret

e = M/R. 392 k-in vfy 67.5 k

e/h = 5.81 in/9 in = 0 . 6 4 6

Try e/h = 0.6

= 5.81 in

M (0.818) 1- (1-.6)-3'9 (479 k-in) = 381 k-in

155

e = M/R fy

381 k-in 67.5 k

= 5.64 in

e/h = 5.64 in/9 in = 0.627 h

Try e/h = 0.65

M = (0.818) 1- (1-.65)°'9 (479 k-in) = 584 k-in

e = M/R 584 k-in = 5.69 in £X = 67.5 k

e/h = 5.69 in/9 in = 0.652 O.K.

10. Determine (from Table 9):

A,. = 0 .25 in lim

11. Calculate . lim

• = —f— = -rt i?)-5- -i - : -M = 0.0185 radians lim (n-1) (o m) < •. o . (4-1) (.> m) : ; j|

2 2 J

12. Determine (4).. : lim

Since - = ,—r- = 0.802 is less than 0.9j, M j. 479 k-m ref

t M * n mor j ' 384 k-in 1 I

'ref/ ~ /

= 0.0.59 radians

^lim ^lim 0.95 M ~ °*0185 rad ;0.93(479 k-in)

15. Check:

< d), . . so connection satisfies criteria fy lim

1S4

14. Size framing plate:

k _ Maximum Load per Bolt _ 39.9

allowable stress x (3 inches) ~ (^ k/in2!(3 in)

= 0.605 in use 5/8-inch plate

15. Size weld (use Table XIV of Steel Manual):

I = 9 in + 2(1.5 in.) = 12 in.

a = e/2, = 5.69/12 in. = 0.474

c = 0.62

= 1.0 (assume E70XX electrodes)

P 45^ D = ir = n tin nwn •—7 ~ 6.05 Use 3/8 in in fillet

c c, % 0.62(1.0) (12 in) ' , ... . , 1 ^ v. ; weld, both sides

16. Compare with Table X

n 4

- /f 6 , = /(6(5.69 in) C / ' (n+l) bj /1(4+1) (5 in)

+ 1 = 1 . 6 1

^allow = 1.61 (13.23 k/bolt) = 21.3k

REFERENCES

Batho, Cyril, Second Report, Steel Structures Research Commi-ttee, Department of Scientific and Industrial Research of Great Britain, H. M. Stationery Office, London, 1934.

Caccavale, Salvatore E., "Ductility of Single Plate Framing Connections," thesis presented to the University of Arizona, at Tucson, Arizona, in partial fulfillment of the requirements for the degree of Master of Science, 1975.

Crawford, Sherwood F., and Kulak, Geoffrey L., "Eccentrically Loaded Bolted Connections," Journal of the Structural Division, American Society of Civil Engineers, Vol. 105, No. ST5, Proc. Paper 7956, March, 1971.

Gaylord, Edwin H., Jr., and Gaylord, Charles N., Design of Steel Structures, Second Edition, McGraw-Hill, Inc., New York, New York, 1972.

Lipson, Samuel L., "Single-Angle and Single-Plate Beam Framing Connections," Proceedings, Canadian Structural Engineering Conference, Toronto, Ontario, Canada, February, 1968.

Manual of Steel Construction, Seventh Edition, American Institute of Steel Construction, New York, New York, 1970.

Richard, Ralph M., "User's Manual for Nonlinear Finite Element Analysis Program INELAS," Department of Civil Engineering, The University of Arizona, Tucson, Arizona, 1968.

Richard, Ralph M., "Versatile Elastic-Plastic Stress-Strain Formula," Journal of the Engineering Mechanics Division, American Society of Civil Engineers, Vol. 101, No. EM4, Proc. Paper 11474, August, 1975.

Richard, Ralph M., and Blacklock, James R., "Finite Element Analysis of Inelastic Structures," AIM Journal, Vol. 7, No. 5, March, 1969.

"Specification for the Design, Fabrication and Erection of Structural Steel Buildings," .American Institute of Steel Construction, New York, New York, February, 1969.

155

Documents

DUCTILITY AND STRENGTH OF SINGLE PLATE ......12. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/4-Inch A36 Plates 97 13. Load-Deformation Data for a 3/4-Inch