DUCTILITY AND STRENGTH OF SINGLE PLATE ......12. Load-Deformation Data for a 3/4-Inch Diameter A325...
Transcript of DUCTILITY AND STRENGTH OF SINGLE PLATE ......12. Load-Deformation Data for a 3/4-Inch Diameter A325...
DUCTILITY AND STRENGTH OFSINGLE PLATE CONNECTIONS
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Authors Gillett, Paul Edward
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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
14. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A36 Plates 101
15. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 7/16-Inch A36 Plates 103
16. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates 105
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
20. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 5/16-Inch A36 Plates 113
21. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A36 Plates 115
22. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 7/16-Inch A36 Plates ..... 117
23. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates 119
24. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 1/4-Inch and 3/8-Inch A36 Plates 121
25. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 1/4-Inch and 1/2-Inch A36 Plates . 123
26. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 3/8-Inch and 1/2-Inch A36 Plates 125
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
32. Load-Deformation Data for a 3/4-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates 137
33. Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates 139
34. Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates 141
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
47. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 5/16-Inch A36 Plates 98
48. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A36 Plates 100
49. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 7/16-Inch A36 Plates 102
50. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates 104
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
52. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 1/4-Inch and 1/2-Inch A36 Plates 108
53. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting 3/8-Inch and 1/2-Inch A36 Plates 110
54. Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 5/16-Inch A36 Plates 112
55. Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A36 Plates 114
xiii
LIST OF ILLUSTRATIONS--Continued
Figure Page
56. Plot of Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 7/16-Inch A36 Plates 116
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
65. Plot of Load-Deformation Data for a 3/4-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates 134
66. Plot of Load-Deformation Data for a 3/4-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates 136
67. Plot of Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates . 138
68. Plot of Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates 140
69. Plot of Load-Deformation Data for a 1-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates 142
70. Plot of Load-Deformation Data for a 1-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates 144
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
full beam and connection 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
full beam and connection model
• - 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
Table 13. 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
Figure 43. Plot of Load-Deformation Data for a 5/4-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A36 Plates
101
Table 14. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A36 Plates
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
Figure 49. Plot of Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 7/16-Inch A36 Plates
103
Table 15. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 7/16-Inch A36 Plates
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
Table 16. Load-Deformation Data for a 3/4-Inch Diameter A325 Bolt Connecting Two 1/2-Inch A36 Plates
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
Table 20. Load-Deformation Data for a 7/8-Inch Diameter A525 Bolt Connecting Two 5/16-Inch A36 Plates
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
Table 21. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting Two 3/8-Inch A36 Plates
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
Figure 57. Plot of Load-Deformation Data for a 7/8-Inch Diameter A525 Bolt Connecting Two 1/2-Inch A36 Plates
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
Table 24. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 1/4-Inch and 3/8-Inch A36 Plates
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
Table 25. Load-Deformation Data for a 7/8-Inch Diameter A325 Bolt Connecting 1/4-Inch and 1/2-Inch A36 Plates
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
Table 31. Load-Deformation Data for a 3/4-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates
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
Figure 66. Plot of Load-Deformation Data for a 3/4-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A56 Plates
137
Table 32. Load-Deformation Data for a 3/4-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates
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
Figure 67. Plot of Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 1/2-Inch A36 Plates
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
Table 34. Load-Deformation Data for a 7/8-Inch Diameter A490 Bolt Connecting Two 5/8-Inch A36 Plates
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
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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.
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