simplified method for design of moment end ......simplified method for design of moment end-plate...
TRANSCRIPT
SIMPLIFIED METHOD FOR DESIGN OF
MOMENT END-PLATE CONNECTIONS
by
Jeffrey T. Borgsmiller
Thesis submitted to the faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
in
CIVIL ENGINEERING
APPROVED:
Thomas M. Murray, Chai
W. Samuel Easterling Richard M. Barker
March, 1995
Blacksburg, Virginia
SIMPLIFIED METHOD FOR DESIGN OF
MOMENT END-PLATE CONNECTIONS
by Jeffrey T. Borgsmiller
Thomas M. Murray, Chairman
Civil Engineering
(ABSTRACT)
Bolted moment end-plate connections are extremely popular in the metal building
industry due to economics and construction ease, yet have proven to be quite complicated
from the analysis and design standpoint. Past research has shown that the design of these
connections is controlled by either the strength of the end-plate, determined by yield-line
analysis, or the strength of the bolts, determined by the semi-empirical Kennedy method.
The calculations involved in the Kennedy bolt analysis incorporate prying action, yet are
complex and extensive.
This study presents a simplified method for determining the ultimate strength of
moment end-plate connections. Classic yield-line analysis is used to determine the
connection capacity based on end-plate strength, and a simplified version of the Kennedy
method is used to predict the connection capacity based on bolt strength with prying
action. Assumptions are made that substantially reduce the calculations involved in the
bolt analysis. The simplified design procedure is verified by comparison with the results of
52 previously conducted full-scale connection tests. Design recommendations are made
and examples presented.
ACKNOWLEDGMENTS
The author wishes to express his sincere gratitude to his advisor, Dr. Thomas M.
Murray, for his guidance and support throughout the development of this thesis. His
effort and generosity will not be forgotten. Thanks also to Dr. W. Samuel Easterling and
Dr. Richard M. Barker for their advice and influence as committee members.
Emmett Sumner, Pete Allen, Dennis Huffman, and Brett Farmer all helped
tremendously in building and running the laboratory tests. The author wishes to thank
them and his other fellow lab workers for their kindness and assistance: Brad Davis,
David Gibbings, Karl Larson, Ron Meng, Bruce Shue, Rod Simon, and Budi Widjaja. The
laboratory test specimens were provided by Steelox Systems Inc. under the sponsorship of
Kawada Industries; great thanks goes to Hiro Matsuzaki from Kawada Industries.
Finally, the author wishes to give warm regards to his family. It has been their
love, support, and encouragement throughout the years that have made everything
possible.
TABLE OF CONTENTS
Page
ABSTRACT 00 cccccccsssesssnscceeecccececcevecsussesssessensseeneceeeeceeeeceeseseeesesesensesseeeseensnaeeres i
ACKNOWLEDGMENTS ...0....cccccccccccccccccssssssessssssncnecseeeceeeeceeseeeeseseceseeseesseseseteeensneaaeeees ili
TABLE OF CONTENTS .............cccccccccccssesccsccccccessnseceececessessneeeececcesesnessseeeeeseeessennsenees iv
LIST OF FIGURES. ..000..... 00 coccccccccccccccccsssscsssensnsnnsceececseccesececessesseseesesseseseeseessasssseaeeees vii
LIST OF TABLES... oo... cceeccccccccccccccccscceccsecssescescssssscessscessasessuesasececesessesssieeeeeecesenaes x
CHAPTER I. INTRODUCTION.......0.0.0000cccccccccccccccceseessceceeccecssssenseceeeeseeesseessseeeeees 1
LL Background ..............cccccceccccssccccscccsccceececessesesssscnesscessseseccececececeeeesecesesseseesnaaseess ]
1.2 Literature Review............ccccccccccccesssssccccseesssceseesesssscseesssuesesseesssasaeeeeeseeeeeeseeeees 7
1.3 Scope of Research. .............ccccccccccccccccccceseesesssssneaceceeecesceceeeeceeesceeeessseeeseseeesenaas 18
CHAPTER I. CONNECTION STRENGTH USING YIELD-LINE THEORY.......... 29
ZL Gomera 0.0.00... ccccceccssssseseeseecesceeeeeeeeceececeececceccescceesecseceeeesueassaaaaasaeusesseesseess 29
2.2 Application to Flush Moment End-Plates.........0....0..ccccccceeccccccesseseesesececeeeeeeeaees 34
2.2.1 Two-Bolt Flush Unstiffened Moment End-Plates .............0.......000ccccccee 34
2.2.2 Four-Bolt Flush Unstiffened Moment End-Plates..................0......0066 36
2.2.3 Four-Bolt Flush Stiffened Moment End-Plates ......0..............cccccccccceeeees 38
2.2.4 Six-Bolt Flush Unstiffened Moment End-Plates ..........0......0ccccccccceeeeees 4]
2.3 Application to Extended Moment End-Plates ...............ccccccccccssesseceeesesteeeesseees 44
2.3.1 Four-Bolt Extended Unstiffened Moment End-Plates........................... 44
2.3.2 Four-Bolt Extended Stiffened Moment End-Plates.....................cccccccee 47
2.3.3 Multiple Row Extended Unstiffened 1/2 Moment End-Plates............... 49 2.3.4 Multiple Row Extended Unstiffened 1/3 Moment End-Plates............... 52
2.3.5 Multiple Row Extended Stiffened 1/3 Moment End-Plates................... 55
CHAPTER III. CONNECTION STRENGTH USING SIMPLIFIED
BOLT ANALYSIS 00.occcccccccccccccccccecccceeseeseeseeusaseeessseseeeseeseseneees 61
BL Gomera oo... eccccceccsscescescseesececeeeeeeeeeeeeeeeeeeeeeeeceeeseeeeeeeesssasesessaeseseeeneeeseess 61
3.2 Application to Flush Moment End-Plates.................ccccceeeeeceeeteeeeeeneeentteeeeeenes 71
3.2.1 Two-Bolt Flush Unstiffened Moment End-Plates ..................::::::ceeeeeee 72
3.2.2 Four-Bolt Flush Unstiffened Moment End-Plates.....................:::c001eeee 72
3.2.3. Four-Bolt Flush Stiffened Moment End-Plates.....................cccccceeeeeeeees 74
3.2.4 Six-Bolt Flush Unstiffened Moment End-Plates .....................cccceeeeeeeeee 75
3.3 Application to Extended Moment End-Plates ...................cceceeeeeeeeeeeeneneeeneeeeees 77
3.3.1 Four-Bolt Extended Unstiffened Moment End-Plates........................4- 77
3.3.2 Four-Bolt Extended Stiffened Moment End-Plates.......................cc008 79
3.3.3 Multiple Row Extended Unstiffened 1/2 Moment End-Plates............... 80
3.3.4 Multiple Row Extended Unstiffened 1/3 Moment End-Plates............... 82 3.3.5 Multiple Row Extended Stiffened 1/3 Moment End-Plates................... 84
CHAPTER ITV. COMPARISON OF EXPERIMENTAL RESULTS
AND PREDICTIONS .000.oo.c ccc cececcsecccccsccueseeeecececessaeesseeeeseeeenaaeees 86
4.1 Previous Experimental Results...............0.ccccccccccccsssccecessseececeessseeeeceenseeseeeeaees 86
4.2 Determination of the Predicted Connection Strength .................:eecceeeeeeeeeee 92
4.3 Flush Moment End-Plate Comparisons. .............0....cccccccsesscecenceeeeeenneeteenteeeeeees 95
4.4 Extended Moment End-Plate Comparisons. ................c:ccccsccccecsseeeneeeeseeeeeneenees 98
CHAPTER V. SUMMARY, CONCLUSIONS AND RECOMMENDATIONG........ 102
S.1 0 SUMMary..0.. ec cccccceesccvecceccceseeevsssesecceccsscessuuussceecccessaeaeeeeesesseeesanssees 102
5.2 ComcliSIonS............0..0..cccccccessessssessesssssesscssessssesseceeeeeseecececcecececesceeeesueessaeaaaaas 120
5.3 Design Recommendations ..............c.cccccccceeeccseeeseeceeeeeeececescecccccceceeseeeeeaaeeaaaaas 12]
5.4 Design Examples. .............ccc cc ccccccsscccccccesesscceecceeessnsacaeeeceessesesseceeeecesesensnaees 124
5.4.1 Two-Bolt Flush Unstiffened Moment End-Plate Connection .............. 124
5.4.2 Multiple Row Extended Unstiffened 1/3 Moment End-Plate
COMMECHION 20000... occ eee ecccceeeeeeesssceccescceceeeeseseesensesenssasaesesecseceeeseeeeseeeeey 130
REFERENCES. ...0000....ccccccccccccccscsessesseecesecceecccecceceeceeceeeeseeeccccccccesseeseeeesuaasgaasaseeeseseeses 141
APPENDIX A. NOMENCLATURE ..0000......ccccccecccccccccccecccccccscessessseeeesecseseteeeesersstenees 143
APPENDIX B. TWO-BOLT FLUSH UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS 0.0.0.0... ccceeeecsessncceeneeeeeeeeeees 149
APPENDIX C. FOUR-BOLT FLUSH UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS 0000... eeeenecceeeseseeeeeeeeees 155
APPENDIX D. FOUR-BOLT FLUSH STIFFENED MOMENT
END-PLATE TEST CALCULATIONS ............... cee eee etter 160
Vv
APPENDIX E. SIX-BOLT FLUSH UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS ............. cc ceceeeeeeseeseettseseeeeeeees 166
APPENDIX F. FOUR-BOLT EXTENDED UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS ......... 0. cccccccccceeeeeenceeeeseerens 171
APPENDIX G. FOUR-BOLT EXTENDED STIFFENED MOMENT
END-PLATE TEST CALCULATIONS ...........0..occcceeeeseeseeeetteeeeeees 176
APPENDIX H. MULTIPLE ROW EXTENDED UNSTIFFENED 1/2
MOMENT END-PLATE TEST CALCULATIONS... 18]
APPENDIX I MULTIPLE ROW EXTENDED UNSTIFFENED 1/3
MOMENT END-PLATE TEST CALCULATIONS .....................24. 185
APPENDIX J. MULTIPLE ROW EXTENDED STIFFENED 1/3
MOMENT END-PLATE TEST CALCULATIONS ................00006 193
VITA Looe eecccceseessneeseneeeeneeeeaeescaeeecsaeecaneecsaeesaeeesaesensceseneseeaeeceaueeseaaeereaeesenaeeseaees 198
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
* LIST OF FIGURES
Page
Typical Uses of Moment End-Plate Conmections ..................ccccceececececeeeteesennneeters 2
Example of a Flush End-Plate Configuration ..................:ceecscceceeessseeeeeseesseeeseeeees 3
Example of an Extended End-Plate Configuration ...................:::cesessseseseeeeteseeeees 3
Flush End-Plate Configurations in Unification Study..................:cccsececceseeneeeererees 5
Extended End-Plate Configurations in Unification Study ..........0.....:ceeeeeeee 6
Kennedy Split-Tee Analogy. ..............cccccsccccccsessssseceeeeeesscnsnnececeeseseeeeessnaeeessoesessaes 8
Kennedy Split-Tee Behaviol..............cccccccccccccccscesssssssnnaccececeeeeeececeeceeeeeeseeeeenenaas 10
Extended End-Plate Configurations with Large
Inner Pitch Distances Used in this Study................cccccccccesssceceeseseteceeeesseeeeeeeseaes 17
Limits of Geometric Parameters for the Two-Bolt Flush Unstiffened
Moment End-Plate Connection Tests in the Unification Study............0........068 20
Limits of Geometric Parameters for the Four-Bolt Flush Unstiffened
Moment End-Plate Connection Tests in the Unification Study ......................044. 21
Limits of Geometric Parameters for the Four-Bolt Flush Stiffened
Moment End-Plate Connection Tests in the Unification Study...................008 22
Limits of Geometric Parameters for the Six-Bolt Flush Unstiffened
Moment End-Plate Connection Tests in the Unification Study ................000..20 23
Limits of Geometric Parameters for the Four-Bolt Extended Unstiffened
Moment End-Plate Connection Tests in the Unification Study.................0...00 24
Limits of Geometric Parameters for the Four-Bolt Extended Stiffened
Moment End-Plate Connection Tests in the Unification Study......................008 25
1.15
1.16
1.17
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
3.1
3.2
Limits of Geometric Parameters for the Multiple Row Extended Unstiffened
1/2 Moment End-Plate Connection Tests in the Unification Study .................0..
Limits of Geometric Parameters for the Multiple Row Extended Unstiffened 1/3 Moment End-Plate Connection Tests in the Unification Study................0.....
Limits of Geometric Parameters for the Multiple Row Extended Stiffened 1/3 Moment End-Plate Connection Tests in the Unification Study .....................
Virtual Displacements in a Two-Bolt Flush Unstiffened
End-Plate Comfiguration..............0.:ccccccccessscssccccessssseceeecessessesecaeeeeeeesesseeeaaaeeeeseeees
Yield-Line Mechanism for Two-Bolt Flush
Unstiffened Moment End-Plate. .................c..cccscecccccssccccecccccucesecsecccnsseccesececeauesess
Yield-Line Mechanism for Four-Bolt Flush
Unstiffened Moment End-Plate. ........0......ccccccccccccccsecccccccccccccececceccecstccecceeceecnseeens
Yield-Lme Mechanisms for Four-Bolt Flush
Stiffened Moment End-Plate ................cccccccccceccccccecccccecccccacscccesecectecccaececeeeesecens
Yield-Line Mechanisms for Six-Bolt Flush
Unstiffened Moment End-Plate. .................c.ccccccceeeeccccccssececccacccececccvececcecaeececseees
Yield-Line Mechanism for Four-Bolt Extended
Unstiffened Moment End-Plate................cc.ccccccccececccccccccccccccececcecccuececcececaecenaecs
Yield-Line Mechanisms for Four-Bolt Extended
Stiffened Moment End-Plate .....0...........ccccccccsescccceecccccececcnccccesecccaecccstsceecaseees
Yield-Line Mechanisms for Multiple Row Extended
Unstiffened 1/2 Moment End-Plate.......00.....ccccccccscccceesssssnneeeeeeceseesensnaeeeeeeesenenaes
Yield-Line Mechanisms for Multiple Row Extended
Unstiffened 1/3 Moment End-Plate...................ccccccceecccceeccceeccceccnsceenerecueces ececenee
Yield-Line Mechanism I for Multiple Row Extended
Stiffened 1/3 Moment End-Plate.......00.0...ccccccccccccscesseesesececccsaueuseseseecesssseenssseseeess
Yield-Line Mechanism II for Multiple Row Extended
Stiffened 1/3 Moment End-Plate.................ccccccccsssscceesssececesesneeeeeseseeeescessnseeres
Prying Forces as a Result of Plate Bending ................0..cccccccsccceecccceesseessseeteeeeees
Sample Applied Moment vs. Bolt Force Plots...............0..cccccccseseccseeceeseeseeenteeeeees
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
4.1
4.2
4.3
4.4
5.1
5.2
Bolt Analysis for Two-Bolt Flush Unstiffened Moment End-Plates..................... 67
Simplified Bolt Force Model for Two-Bolt Flush
Unstiffened Moment End-Plates ...............:c:::ccccccccceeeceeeeeeeeecnensaneeseeeeeseaeeusaceeeeees 67
Effects of Bolt Pretension..................ccccccccceesssscccceeeeeesesceeeceeceneeessaaeeeeeseneessenness 69
Simplified Bolt Force Model for Four-Bolt Flush Unstiffened and Stiffened Moment End-Plates. ...............c:ccccccccccceeeeeeceeseeeeeeenaeeuaaeeeeeeeeeeeseeees 73
Simplified Bolt Force Model for Six-Bolt Flush Unstiffened Moment End-Plates ..................ccccccessssssncceceeeeecceeceeeereeeeeseeeesesseenanens 76
Deformed Shape of Multiple Row End-Plates..................:::cccccccceseeeerseceeeeeeeeeenaaes 76
Simplified Bolt Force Model for Four-Bolt Extended
Unstiffened and Stiffened Moment End-Plates.................cccccscccceeesseeeeeeseneeeereees 78
Simplified Bolt Force Model for Multiple Row Extended Unstiffened 1/2 Moment End-Plates ................cccccccesescceceesecneeeeeeeeseeeeeeesnntesoneaaes 81
Simplified Bolt Force Model for Multiple Row Extended Unstiffened and Stiffened 1/3 Moment End-Plates. ..................ccccssccccccceesesssnsaceeeeceeseeseneeeeeeees 83
Longitudinal Elevation of Laboratory Test Setup..............:cccccccsssseceeeeeeeeeeessneeees 88
Cross-section of Laboratory Test Setup...............:.c:cccsssecccesneceeeeneeceeseeeeseneeeesseeey 89
Sample of Applied Moment vs. End-Plate Separation Plots ..................::..:::e 91
Determination of Experimental Yield Moment..................::ccccccccceeeeeeenneeeeereetetees 91
Design Example--Two-Bolt Flush Unstiffened Moment End-Plate Commection..............ccccccccccccsssscceceeeseeaneeecesssseesnaneeeeecseesssaeeneeeesennas 125
Design Example--Multiple Row Extended Unstiffened 1/3 Moment End-Plate Conmection............00...:ccceescsecceceeeeestneeeeeceeesesesssneuseseeeteesaees 131
Table
4.1
4.2
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
LIST OF TABLES
Page
Flush Moment End-Plate Predicted and Experimental Results.................0..08 96
Extended Moment End-Plate Predicted and Experimental Results ...................... 99
Summary of Bolt Equations. ........0.....ccccccccsseeceessnneeeeeesaneeeseesssceeeesoessnaeeeseeeenes 104
Summary of Two-Bolt Flush Unstiffened Moment End-Plate Analysis.............. 105
Summary of Four-Bolt Flush Unstiffened Moment End-Plate Analysis.............. 106
Summary of Four-Bolt Flush Stiffened Moment End-Plate Analysis--
Stiffened Between the Tension Bolt ROWS. ...............::c::cccsesceceestcceeetsneeeeseneeeaes 107
Summary of Four-Bolt Flush Stiffened Moment End-Plate Analysis--
Stiffened Outside the Tension Bolt ROWS ............::.ccccscccsssseeeeeeneeeeeeseeeeeesaesensaes 108
Summary of Six-Bolt Flush Unstiffened Moment End-Plate Analysis................ 109
Summary of Four-Bolt Extended Unstiffened Moment End-Plate Analysis ....... 11]
Summary of Four-Bolt Extended Stiffened Moment End-Plate Analysis ........... 112
Summary of Multiple Row Extended Unstiffened 1/2 Moment
End-Plate Amalysis .........00.....cccccccccccceeesssssccecceeeesscacecceeescesseeeeeeeeeeeeecnaneneeeeess 114
Summary of Multiple Row Extended Unstiffened 1/3 Moment
End-Plate Analysis ..............c.ccccccccccssssecceecssseeecesseeeccseesseeceeseseeeessseeseeeeesseneeeeees 116
Summary of Multiple Row Extended Stiffened 1/3 Moment End-Plate AmalySis ..................:::ccccsesesseeeeeeseeesseneceecseeeeeeeccecceeeeeeeseeeeseeeneaqqaqaqaas 118
CHAPTER I
INTRODUCTION
1.1 BACKGROUND
Bolted moment end-plate connections are extensively used aS moment-resistant
connections m metal buildings and steel portal frame construction. These connections are
primarily used to either splice two beams together, commonly called a “splice-plate
connection”, Figure 1.1(a), or to connect a beam to a column, Figure 1.1(b). Because of
their exceptional moment resistance and ease of erection, moment end-plate connections
have become predominant in the metal building industry.
There are two general types of moment end-plate connections: flush end-plates,
Figure 1.2, and extended end-plates, Figure 1.3. A flush end-plate is one in which the
end-plate does not extend beyond the flanges of the beam section and all rows of bolts are
contained within the beam flanges. Flush end-plates may be used with or without
stiffeners, which consist of gusset plates welded to both the end-plate and the beam web,
as shown in Figure 1.2(b). An extended end-plate connection is one in which the end-
plate protrudes beyond the flanges of the beam section to allow for the placement of
exterior bolts. Extended end-plates may also be used with or without stiffeners which
usually consist of a triangular gusset plate welded to both the end-plate extension and the
~ — oN
Tension Zone
(a) Beam-to-Beam Splice Connection
/ Tension Zone
wv
(b) Beam-to-Column Connection
Figure 1.1 Typical Uses of Moment End-Plate Connections
(a) Unstiffened (b) Stiffened
Figure 1.2 Example of a Flush End-Plate Configuration
L
(a) Unstiffened (b) Stiffened
Figure 1.3 Example of an Extended End-Plate Configuration
beam tension flange in the plane of the beam web, as shown in Figure 1.3(b). The use of
either the flush or extended end-plate connection in a design typically depends on the
magnitude of the loads and the desired stiffness of the connection.
The two limit states controlling the design of moment end-plate connections are
end-plate yielding and bolt failure. Extensive studies have been conducted in the past on
the analysis and design of these connections. From these studies came several different
design procedures for determining the end-plate thickness and bolt diameter based on
results from the finite-element method, yield-line theory, or experimental test data. Srouji
et al. (1983b) reported that there is a great deal of variation in the predictions from the
different procedures, especially in the case of bolt forces, as some methods assume bolt
prying action to be significant, while others assume it to be negligible. Because of this, an
extended study was conducted which unified the design procedures for the moment end-
plate configurations shown in Figures 1.4 and 1.5 (Srouji et a/., 1983a, 1983b; SEI, 1984;
Hendrick et a/., 1985; Morrison ef al., 1985, 1986; Bond and Murray, 1989; Abel and
Murray, 1992b). This unified design procedure provides a rational and consistent means
of calculating end-plate thickness and bolt forces, yet, requires long and tedious
calculations.
The purpose of the current study is to mtroduce a simplified and less tedious
approach to the design of moment end-plate connections. In the proposed approach,
rational assumptions are made allowing the bolt force equations to be minimized, resulting
in a simple and straight-forward design procedure. Current literature regarding the design
elie ele eje
e @ ee
(a) Two-Bolt Unstiffened (b) Four-Bolt Unstiffened
ele ele ele ele
@ 1} @ e e
(c) Four-Bolt Stiffened (d) Four-Bolt Stiffened
between tension bolt rows outside tension bolt rows
@ e @t ®
eo} @
@ } @
(e) Six-Bolt Unstiffened
Figure 1.4 Flush End-Plate Configurations in Unification Study
e ele
ee ee
ele ele
(a) Four-Bolt Unstiffened (b) Four-Bolt Stiffened
e © e ©
ele ele ej} e e}e
eje
ee ele
(c) Multiple Row Unstiffened 1/2 (d) Multiple Row Unstiffened 1/3
@ | e
ele ele ee
ele
(e) Multiple Row Stiffened 1/3
Figure 1.5 Extended End-Plate Configurations in Unification Study
of moment end-plate connections is first reviewed, followed by the development of yield-
line and simplified bolt force design procedures for various flush and extended end-plate
configurations. Comparisons between the predictions and extensive experimental results
are made, after which conclusions and design recommendations are presented.
1.2 LITERATURE REVIEW
An extensive review of end-plate connection literature prior to 1983 was reported
by Srouji et a/. (1983b). The design procedures and equations for determiming end-plate
strength and bolt force predictions from several authors were presented, as well as a
comparison of the various results. It was found that there was quite a variation in the
results of the different prediction methods. The review concluded that yield-line analysis
- can be used for the design of end-plate strength, and the capacity of the bolts can be
predicted from a method proposed by Kennedy eft al. (1981). Srouji’s review spawned an
extensive investigation under the guidance of Dr. Thomas M. Murray, who sought to unify
the design procedures of moment end-plate connections using yield-line theory and the
modified Kennedy method. A review of the reports and findings from this investigation
follow an overview of the Kennedy method for bolt predictions.
Kennedy ef al. (1981) introduced a method for predicting bolt forces with prying
action im split-tee connections. The Kennedy split-tee analogy, shown m Figure 1.6,
consists of a plate bolted to a rigid support with four bolts and welded to a flange through
which a tension load is applied. In Figure 1.6, 2F is the applied tension force to the flange,
Q is the prying force, and B is the total resulting bolt force.
00
Hy
Valitse
Figure 1.6 Kennedy Split-Tee Analogy
(after Kennedy ef al. , 1981)
The basic assumption in the Kennedy method is that the plate goes through three
stages of behavior as the applied load increases. At the lower levels of applied load,
plastic hinges have not developed in the split-tee plate and its behavior is termed thick
plate behavior, Figure 1.7(a). The prying force, Q, at this stage is assumed to be zero. As
the applied load increases, two plastic hinges form at the intersections of the plate
centerlme and each web face, Figure 1.7(b). This yielding marks the “thick plate limit”
and indicates the initiation of the second stage of plate behavior, termed intermediate
plate behavior. The prying force at this stage is somewhere between zero and the
maximum value. Aa a greater level of load is applied, two additional plastic hinges form
at the centerline of the plate and each bolt, Figure 1.7(c). The formation of this second set
of plastic hinges marks the “thin plate limit” and indicates the initiation of the third stage
of plate behavior, termed thin plate behavior. The prying force at this stage is at a
maximum, constant value. Once the status of the plate behavior has been determined, the
bolt force is calculated by summing the portion of the applied flange force designated to
the bolt with the appropriate prying force, B =F + Q.
Kennedy e¢ al. (1981) establishes the stage of plate behavior by comparing the
plate thickness, t,, with a thick plate limit, t,, and a thin plate limit, t;,. The thick plate
limit is found by iteration using:
2pr(2F) (1) tj = 5
F 2 by BS
(a) First Stage -- Thick Plate Behavior
| 2F
Indicates plastic hinge
wt
t a | | a
Q B BQ
(b) Second Stage -- Intermediate Plate Behavior
| &F
Indicates plastic hinge
(c) Third Stage -- Thin Plate Behavior
Figure 1.7 Kennedy Split-Tee Behavior
(after Morrison ef al. , 1985, 1986)
10
and the thin plate limit is found by iteration using:
pr(2F)- 2dpFy/8 i= 5 5
br rB-{ F +w 3-45] 2 Py brtyy 2w't))
where 2F = applied flange force, bs = beam flange width, F,, = plate yield stress, d, = bolt
(1.2)
diameter, Fy, = nominal strength of the bolts, designated in Table J3.1 of AISC (1986), w
= width of plate per bolt at a bolt line minus the bolt hole diameter, and p;= pitch distance
from the flange face to the center of the bolt line. If t, > t:, the plate behaves as a thick
plate and the prying force is zero. Hence, the bolt force, B, for thick plate behavior is
simply the applied flange force, 2F, divided by the number of bolts, 4, or:
B=F/2; if tp > ti (thick plate behavior) (1.3)
If t; > tp > ti, the plate is in the intermediate stage and some prying force is included in
the bolt force. The prying force, Q, is calculated by:
Q= pr(F) 7 a
(1.4)
where the distance, a, has been suggested to be between 2d, and 3d). The bolt force for
mtermediate plate behavior is therefore:
B=F/2+Q; if t; >t, >t, (intermediate plate behavior) (1.5)
If tp < ti, the plate behaves as a thin plate and the prying force in the bolts is at a
maximum and constant value, Qmax, calculated by:
11
(1.6) Q max =
where F' is:
2 3 Pe tp Foy (0.85 be / 2 +0.80w) + 7dpFyp/ 8 (1.7)
Ape
The bolt force for thin plate behavior is therefore:
B = F/2 + Qhax ; if tp <ti (thin plate behavior) (1.8)
It was noted that the quantities under the radicals in Equations 1.4 and 1.6 can be
negative. A negative value for these terms indicates that the plate has yielded locally m
shear before the bolt prying action force could be developed, making the connection
inadequate for the applied loads.
Srouji e¢ a/. (1983b) used yield-line analysis and the Kennedy method of bolt force
predictions in the first of many studies aimed at moment end-plate design unification. He
presented yield-line design methodology for four end-plate configurations: two-bolt flush
unstiffened (Figure 1.4(a)), four-bolt flush unstiffened (Figure 1.4(b)), four-bolt extended
unstiffened (Figure 1.5(a)), and four-bolt extended stiffened (Figure 1.5(b)). Bolt force
predictions including prying action were produced for the two-bolt and four-bolt flush
unstiffened configurations. These predictions were based on a modified version of the
Kennedy method, which assumes the far interior bolts in the four-bolt flush unstiffened
configuration carry 1/6 of the total applied flange force. An experimental investigation
was conducted to verify the end-plate and bolt force predictions. Eight two-bolt flush
12
unstiffened moment end-plate connection tests were conducted and reported in Srouji et
al. (1983a). In addition, six four-bolt flush unstiffened moment end-plate connection tests
were conducted, the results of which are reported in Srouji ef al. (1984). It was
concluded that yield-line analysis and the modified Kennedy method are accurate means of
predicting end-plate strength and the bolt forces. In addition, the moment-rotation plots
of the experimental tests indicate that the two configurations tested can be classified as
Type I connections, AISC (1989).
Hendrick et al. (1984) continued Srouji’s work by analyzing and testing two four-
bolt flush stiffened end-plate configurations: those with the stiffener between the tension
bolt rows (Figure 1.4(c)), and those with the stiffener outside the tension bolt rows
(Figure 1.4(d)). Analysis included the use of yield-line theory for end-plate strength
predictions and Srouji’s modified Kennedy approach for bolt force predictions. Eight full
scale tests were conducted to verify the prediction methods for the four-bolt stiffened
configuration. It was concluded that additional modifications to the Kennedy method of
bolt force predictions were necessary in regards to the distance “a” in Figure 1.6. An
empirical equation for a was derived from regression analysis:
a = 3.682(t,/d,)° - 0.085 (1.9)
In addition, Hendrick et al. changed the assumption regarding the fraction of applied
flange force carried by the far inner bolts from 1/6 to 1/8. These modifications were
carried into the analyses of the tests previously conducted by Srouji et a/., and reported in
Hendrick et a/. (1985), which contained a unification of the design procedures for the four
13
end-plate configurations tested thus far by Srouji and Hendrick: two-bolt flush
unstiffened, four bolt flush unstiffened, four-bolt flush stiffened between the tension bolt
rows, and four-bolt flush stiffened outside the tension bolt rows. Analytical predictions
for end-plate strength using yield-line theory and bolt forces using Hendrick’s modified
Kennedy approach correlated well with all of the test data. In addition, it was concluded
that the four end-plate configurations exhibit adequate moment-rotation stiffness to be
classified as Type I connections, AISC (1989).
Three tests were analyzed and conducted by SEI (1984) which imcluded two
multiple row extended unstiffened 1/3 configurations (Figure 1.5(d)), and one multiple
row extended stiffened 1/3 configuration (Figure 1.5(e)). Note that the designation “1/3”
in the multiple row extended configuration reflects the number of bolt rows outside and
imside, respectively, of the beam tension flange. The tests were analyzed using yield-line
analysis for end-plate predictions and the modified Kennedy method for bolt force
predictions. Modifications to the Kennedy method were necessary for determining how
much of the applied flange force was carried by the outer and inner bolts in these extended
end-plate configurations. Factors, designated as “a” and “B,” were incorporated into the
Kennedy procedure for this purpose, and were calculated based on the results of the yield-
line analysis. The results correlated well with the experimental results.
Four-bolt extended stiffened (Figure 1.5(b)) and multiple row extended unstiffened
1/3 (Figure 1.5(d)) configurations were analyzed and tested by Morrison et a/. (1985) and
Morrison et a/. (1986), respectively. Analysis procedures included the use of yield-line
14
theory and modified Kennedy bolt force predictions. Once again, modifications to the
Kennedy method were necessary for determining how much of the applied flange force
was carried by the outer and inner bolts in the extended end-plate configurations. Unlike
SEI (1984), which used the yield-line results to determine the modification factors,
Morrison’s modification factors came directly from the experimental results of six four-
bolt extended stiffened tests and six multiple row extended unstiffened 1/3 tests. It was
concluded from these tests that the outer bolts do not exhibit prying action, and therefore
carry the majority of the applied flange force. The factors incorporated into the modified
Kennedy analysis, « and B, account for this phenomenon. It was additionally concluded
that the four-bolt extended stiffened and multiple row extended unstiffened 1/3
configurations contain adequate stiffness to be classified as Type I connections, AISC
(1989).
Five full-scale flush unstiffened end-plate configurations with six bolts at the
tension flange (Figure 1.4(e)) were analyzed and tested by Bond and Murray (1989). The
analysis procedures set forth previously in the unification studies were adopted for end-
plate strength and bolt force calculations. Modifications to the Kennedy bolt prediction
method were made with regards to the disbursement of the applied flange force among the
bolts. New factors, different from those proposed by Morrison et al. (1986), were
introduced which proportioned the applied flange force to each of the three lines of bolts.
These factors were extrapolated from the test results. Once the modifications were
implemented, predictions correlated well with the test data. In addition, it was concluded
15
that the six-bolt flush unstiffened end-plate connection can be classified as a Type I
connection, AISC (1989).
Abel and Murray (1992b) added a ninth configuration to the unification of moment
end-plate design: the four-bolt extended unstiffened configuration (Figure 1.5(a)).
Analysis was conducted using the previously set forth yield-line analysis and modified
Kennedy method. Four full scale tests were conducted to verify the predictions. It was
concluded that the outer and inner rows of bolts each carry half of the applied flange
force, however, when the bolt force prediction controls in the analysis, no prying action
exists in the outer bolts. As with the other configurations, the four-bolt extended
unstiffened moment end-plate connection contains adequate moment-rotation stiffness to
be classified as a Type I connection, AISC (1989).
Additional end-plate configurations have also been tested but not fully analyzed by
the unified methods. Two tests on a multiple row extended unstiffened 1/2 configuration
(Figure 1.5(c)) were conducted by Abel and Murray (1992a). Two four-bolt extended
unstiffened configurations with large pitch distances between the face of the beam tension
flange and the first interior row of bolts, Figure 1.8(a), were tested and reported by
Borgsmiller et al. (1995). And lastly, two multiple row extended unstiffened 1/3
configurations with large inner pitch distances, Figure 1.8(b), were conducted, one by
Rodkey and Murray (1993) and one by Borgsmiller et a/. (1995).
16
be tares inner pitch distance
eo; @
(a) Four-Bolt Unstiffened
@ @
i taree inner pitch distance
@; ®@ @ @ @ @
® e
(b) Multiple Row Unstiffened 1/3
Figure 1.8 Extended End-Plate Configurations with Large Inner Pitch Distances Used in this Study
17
1.3 SCOPE OF RESEARCH
As previously mentioned, the purpose of this research is to develop a simplified
design procedure for moment end-plate connections, stemming from the existing unified
design procedure. The simplified approach is based on rational assumptions made with
regards to the bolt behavior. These assumptions decrease the amount of bolt force
calculations in the Kennedy method. The proposed design procedure will provide criteria
for:
e Determination of end-plate thickness by yield-lme theory given
end-plate geometry, beam geometry, and material yield stress,
e.g., strength criterion.
e Determination of bolt forces including prying effects by a
simplified Kennedy method given end-plate geometry, end-plate
thickness, bolt diameter, and bolt proof load, e.g., bolt force
criterion.
The objectives of this study were accomplished by developing end-plate strength
prediction and simplified bolt force prediction equations for the five flush end-plate
configurations in Figure 1.4 and the five extended end-plate configurations in Figure 1.5.
In addition, the new approach was adapted to include extended end-plate configurations
having large pitch distances between the inner face of the beam tension flange and the first
row of interior bolts. Two such configurations were included and are shown in Figure
1.8. Note that the designations “1/2” and “1/3” in the descriptions of the multiple row
extended configurations reflect on the number of bolt rows outside and iside,
respectively, of the beam tension flange. The predictions were then compared to the
18
experimental results of the previously conducted full-scale tests in the unification study to
verify the accuracy of the proposed simplified approach. Figures 1.9 through 1.17 present
the various parameters that define the end-plate geometry for each of the nine
configurations tested in the unification study. These geometric parameters varied within
the limits shown in the table accompanying each figure. All bolts in the tests were type
A325. Nomenclature is defined in Appendix A.
19
Py Pr
@ ®
et h
t P
@ e
ae
te
Parameter Low (in.) High (in.) d, 5/8 3/4
tp 3/8 1/2
Pr 1 5/16 1 7/8
g 2 1/4 3 3/4
h 10 24
be 5 6
te 3/16 1/4
Figure 1.9 Limits of Geometric Parameters for the Two-Bolt
Flush Unstiffened Moment End-Plate Connection
Tests in the Unification Study (after Srouji et al. , 1983a)
20
-— PS _
P Pre ‘ e @ Pe
Py
@ e
ty h
t + P
@ ®
Lem | ——b t =
f
Parameter Low (in.) High (in.) d, 5/8 3/4
tp 3/8 1/2 Pr 1 3/8 17/8 Po 3 3
2 2 3/4 31/2 h 16 24
be 6 6
tr 1/4 1/4
Figure 1.10 Limits of Geometric Parameters for the Four-Bolt
Flush Unstiffened Moment End-Plate Connection
Tests in the Unification Study
(after Srouji et al. , 1983b, 1984)
21
- _— P Py ml Py
Pre Py @ e@ Pre @ @
Py P, P a ei}; e ee ;
h
tL 4 t
t > t 5 Pp P
@ @ @ ®
| La be Le
Parameter Low (in.) High (in.)
d, 5/8 3/4
tp 3/8 1/2
Dr 1 3/8 17/8 Po 1 7/8 3
g 2 3/4 3 1/2
h 16 24
be 6 6
te 1/4 3/8
Figure 1.11 Limits of Geometric Parameters for the Four-Bolt
Flush Stiffened Moment End-Plate Connection
22
Tests in the Unification Study
(after Hendrick ef al. , 1984)
-— Poe | C~dSS
Py Py
ro} 7] @ F ® Th,
Pyis @ e Py
e e@
h
tt
t p
@ @
te
Parameter Low (in.) High (in.)
d, 3/4 1
tp 3/8 1/2 Dr 11/2 2 Do 21/2 2 1/2 g 3 4
h 28 36
be 6 10
tr 3/8 3/8
Figure 1.12 Limits of Geometric Parameters for the Six-Bolt
Flush Unstiffened Moment End-Plate Connection
Tests in the Unification Study (after Bond and Murray, 1989)
23
@ @ FF Pext
Pro
Py Pri
® e —-
et h
t +s p
@ @
mellem} —b i =
f
Parameter Low (in.) High (in.)
d, 1/2 1 1/4
tp 3/8 7/8
Pri 1 1/4 4
Peo 1 1/4 2 1/2
Pext 2 1/2 4
g 2 1/2 7
h 16.2 64
bs 5 10 1/4
te 1/4 ]
Figure 1.13 Limits of Geometric Parameters for the Four-Bolt
Extended Unstiffened Moment End-Plate Connection Tests
in the Unification Study (after Abel and Murray, 1992b;
24
Borgsmiller e¢ al. , 1995)
|
- Poy
Py e al Py ‘
P, ° {Pe
ft
to Pp
@
ao Ly
Parameter Low (in.) High (im.)
dy 5/8 1
tp 3/8 5/8
Dr 1 13/4 Dext 2 1/2 3 1/2
g 2 3/4 41/2
h 15 3/4 24
be 6 8
te 3/8 1/2
Figure 1.14 Limits of Geometric Parameters for the Four-Bolt
Extended Stiffened Moment End-Plate Connection
Tests in the Unification Study
(after Morrison ef al. , 1985)
25
Pio
+ ty
tt,
ele
1 —
Parameter Low (in.) High (in.)
d, 3/4 3/4
tp 3/8 3/4 Pr 11/4 11/4 Pe 2 1/4 21/4 Pext 2 1/2 2 1/2
g 3 3
h 26 26
be 6 6
te 7/16 7/16
Figure 1.15 Limits of Geometric Parameters for the Multiple Row Extended Unstiffened 1/2 Moment End-Plate Connection
Tests in the Unification Study (after Abel and Murray, 1992a)
26
&
@ e —T Pr
Pri
e e PB
@ @ |—| Pos P,
—| @ e
® @
ORLTIETEIILE —
Lt,
Parameter Low (in.) High (in.)
d, 3/4 11/2
tp 3/8 3/4
Pri 1 1/8 4
Pro 11/8 2 9/16
Po 2 1/4 4 1/2
Pext 2 3/8 5 1/8
g 2 3/4 5 9/16
h 30 64
be 8 10
te 3/8 1
Figure 1.16 Limits of Geometric Parameters for the Multiple Row
Extended Unstiffened 1/3 Moment End-Plate Connection Tests
in the Unification Study (after SEI, 1984; Morrison ef al. , 1986;
Rodkey and Murray, 1993; Borgsmiller et al. , 1995)
27
g
[1 a.
oy | © | © Tp, ve a Py
@ ee - PL Pas
Pais ® ee |- . 2, e}e
h
— ty
t —*
e @
|
Parameter Low (in.) High (in.)
d, ] 1
ty 3/4 3/4 Pr 1 5/8 1 5/8
Po 3 3
Pext 3 3/8 3 3/8
g 3 1/2 3 1/2
h 62 62
by 10 10
te 1 1 Figure 1.17 Limits of Geometric Parameters for the Multiple Row
Extended Stiffened 1/3 Moment End-Plate Connection
Tests in the Unification Study
(after SEI, 1984)
28
CHAPTER I
CONNECTION STRENGTH USING YIELD-LINE THEORY
2.1 GENERAL
A yield line is a continuous formation of plastic hinges along a straight or curved
line in a plate or slab structure. A failure mechanism is assumed to exist when the yield
lines form a kinematically valid collapse mechanism. /Yield-line theory is therefore
analogous to plastic design theory in which elastic deformations are negligible compared
to the plastic deformations resulting from the yield lines. Because of this, it can be
assumed that the yield lines divide the plate or slab into rigid plane regions allowing its
deformed shape to be geometrically defined. Much of the yield-line theory development is
related to remforced concrete slabs; however, the principles and findings are applicable to
steel plates.
In determining the location of a yield line in a steel plate, the following guidelines
have been established by Srouji et al. (1983b):
e Axes of rotation generally lie along lines of support.
e Yield lines pass through the intersection of the axes of
rotation of adjacent plate segments.
e Along a yield line, the bending moment is assumed to be
constant and equal to the plastic moment of the plate.
29
Yield-line mechanisms can be analyzed using two methods: the equilibrium
method and the virtual work method. The latter method is more suitable for application to
steel end-plates and is used herein. In this method, the external work done by the applied
loads in moving through a small arbitrary virtual deflection is set equal to the internal
work done by the plate as it rotates along the yield lines to accommodate this virtual
deflection. For a selected yield-line pattern and loading, a specific plastic moment 1s
required of the plate along these hinge lines. It is important to note that this method is an
upper bound approach to the strength of the plate, meaning that all of the possible yield-
line patterns must be investigated to ensure that the least upper bound to the strength has
been found. The failure mechanism for a plate with a given plastic moment capacity
consists of the yield-line pattern which produces the smallest failure load. Conversely, for
a given loading, the appropriate mechanism is that which produces the /argest required
plastic moment capacity of the plate.
To determine the controlling failure load or the required plate moment capacity, an
arbitrary succession of all possible yield-line patterns must be selected using the three
previously mentioned guidelines. By equating the internal and external work, the relation
between the applied loads and the ultimate resisting moment is obtained. The resulting
equation is then solved for either the unknown failure load or unknown plate moment
capacity. By comparing the different values obtained from the various mechanisms, the
controlling minimum load or maximum required plate capacity is identified.
30
The internal work stored in a yield-line mechanism is the sum of the internal work
stored in each yield line forming the mechanism. The internal work per unit length stored
in a single yield line is obtained by multiplying the normal moment on the yield line with
the normal rotation of the yield line. Thus, the work stored in the n™ yield line of length
L, is (Srouji et al., 1983b):
Wi= [m,0,ds=m,0,L, (2.1)
Lh
where m, is the plastic moment capacity of the plate, 6, is the relative normal rotation of
line n, and ds is the elemental length of line n. The internal work stored by an entire yield-
line mechanism can be written as (Srouji et a/., 1983b):
W; = Sm, 6,La (2.2) n=]
where N is the number of yield lines in the mechanism.
For complicated yield-line patterns, the expressions for the relative plate rotation
are somewhat tedious to obtain. It is therefore more convenient to resolve the internal
work components in the x- and y- directions. This results in the following form of
Equation 2.2 (Srouji et al., 1983b):
N
W; = 2 (mp Px Lax + Mpy Iny Ly) (2.3) n=
where m,x and m,, are the x- and y- components of the plate moment capacity per unit
length, 0,, and 6,y are the x- and y- components of the relative normal rotation of the plate
31
segments, and L,, and L,, are the x- and y- components of the n'" yield line length. For
steel plates:
2
— _ _ Py Pp = Mpy = Mp = (2.4)
where F,, is the yield stress of the end-plate material and t, is the plate thickness. The
values of 8, and 0,, are obtained by drawing convenient straight les, parallel to the x-
and y- axes, on the two plate segments intersecting at the yield line. The relative rotation
of the plate segments can then be visualized by “looking down” the axes of these straight
lines at the deformed shape of the plate in the x-z and y-z planes. The values of the
relative rotations from each viewpoint can then be calculated by selecting straight lines
with known displacements at the ends.
Each moment end-plate configuration has a different expression for internal work,
W;, due to unique yield-line mechanisms. However, the external work, W., is the same for
all end-plate configurations. The external work done due to a unit displacement at the
outside of the beam tension flange, resulting in a rotation of the beam cross-section about
the outside of the beam compression flange, is given by (Srouji et a/., 1983b).:
1 W. = M, @= M,(-] (2.5)
where M, is the ultimate beam moment at the end-plate, and 6 is the virtual rotation at the
connection, equal to 1/h, where h is the total depth of the beam section. Figure 2.1 shows
32
o
SS
“s.,
~—
Assumed Deformed Shape ——~
4
LLL ML
Figure 2.1 Virtual Displacements in a Two-Bolt Flush
Unstiffened End-Plate Configuration
33
8 in the plastic deformed shape of a two-bolt flush unstiffened moment end-plate
configuration.
2.2 APPLICATION TO FLUSH MOMENT END-PLATES
Yield-line analysis was performed on the five flush end-plate configurations shown
m Figure 1.4. The five configurations are: two-bolt unstiffened, four-bolt unstiffened,
four-bolt stiffened between the tension bolt rows, four-bolt stiffened outside the bolt rows,
and six bolt unstiffened. Studies have been done on all five of these configurations in the
past; hence, the equations and procedures herein are based on these studies.
2.2.1 Two-Bolt Flush Unstiffened Moment End-Plates
A study was done by Srouji, et a/. (1983b) to determine the behavior of two-bolt
flush unstiffened moment end-plate connections. The following discussion is based on that
study.
The yield-line mechanism in Figure 2.2 is the controlling yield-line pattern for the
two-bolt flush unstiffened moment end-plate connection. The geometric parameters are
also defined in the figure. The external work, W., is calculated for all end-plate
configurations using Equation 2.5. The internal work in this yield-line mechanism is given
by:
W;= —* (h- ro (244 +=(pe+ ) (2.6)
34
-— P, é P,
@ i ® \ Ss
fe t h H WwW
t 5 p
@ @
Ly
Figure 2.2 Yield-Line Mechanism for Two-Bolt Flush Unstiffened Moment End-Plate
(after Srouji et al. , 1983b)
35
where m, is given by Equation 2.4.. The moment capacity of the end-plate, M,, is found
by equating the external and internal work expressions, resulting in:
b 1 ] 2 - _ -f)_* ,f} 44 2.7 MI 4m, (h ro} 5 at) «2(pp4s) (2.7)
Implementing m, and rearranging M,,) results in an expression for the required end-plate
thickness, t,, in terms of the desired ultimate load, M.:
1/2
tp = Mu! Foy _ (2.8)
be({ 1 1) 2 (h— ett te 1 + a (Prt *)
The unknown dimension, s, in Figure 2.2 is found by differentiating the internal work
expression, Equation 2.6, with respect to s and equating to zero. The resulting expression
for s is:
s = > vb (2.9)
2.2.2 Four-Bolt Flush Unstiffened Moment End-Plates
A study was performed by Srouji et a/. (1983b) on the behavior of four-bolt flush
unstiffened moment end-plate connections. The following discussion is based on that
study.
The controlling yield-line mechanism and geometric parameters for the four-bolt
flush unstiffened moment end-plate are shown in Figure 2.3. The imternal work for the
mechanism, W,, and resulting capacity of the end-plate, M,i, are:
36
g i
Ans é U .
, Y % Pp / \ t ‘ \ p / . f
@ x
ay /}
; \ i t Py s ‘ ? '
1 ! t i ‘ }
4 a: é * a7
Sime ss NATE? u stata fe ai ie i} a
vs
He t h
é
Figure 2.3 Yield-Line Mechanism for Four-Bolt Flush
Unstiffened Moment End-Plate
(after Srouji et al. , 1983b)
37
4mp| be ( h—- h- h-
w, = “Mee (PL AP) satprmye[ P) (2.10)
h 2 pf
br (HP Pe) h—py M, =4m ——— + +2(prt+pptu (2.11) P 2X Pe u ) g
By rearranging the equation for M,1, the required end-plate thickness for a given loading is
expressed as:
1/2
t= My/ Foy (2.12) Pp
be ( ho Pa [b | ——+ + ——*£ | + A pe+ ppt 9 PF u Pet Pp u) 2
The unknown dimension, u, in Figure 2.3 is found by differentiating the internal work
expression with respect to u and equating to zero. The resulting expression for u is:
1 be Pea) =-— |p 2.13 u ay ral h- p, (2.13)
2.2.3 Four-Bolt Flush Stiffened Moment End-Plates
A study on the behavior of four-bolt flush stiffened moment end-plate connections
was done by Hendrick e¢ al. (1985). The following discussion is based on that study.
Two configurations of four-bolt flush stiffened end-plates were investigated: those
stiffened with a gusset plate between the tension bolt rows, Figure 1.4(c), and those
stiffened with a gusset plate on the outside of the tension bolt rows, Figure 1.4 (d). The
controllmg yield-line mechanism for the configuration with the stiffener between the
38
tension bolt rows is shown in Figure 2.4(a). Included in the figure are the geometric
parameters. The internal work stored in this yield-line mechanism 1s:
W; =e we) torn) eben} (2 2). (2.14) h 2\Pp Ps 5
On equating the internal and external work expressions, the following expression 1s
obtained for the end-plate strength:
My ~tn-n)* (+ Hy) torn) /eo-Pal2(2 + oh (2.15) Pe Ps’ 8 s
where m, is calculated from Equation 2.4. This expression for the plate capacity can be
solved for the plate thickness, t,, in terms of a desired ultimate moment of the connection,
M.:
1/2
a My/ Foy (2.16) - _pyor(1,1),2 _ eft , 2
The unknown quantity, s, is found by differentiating the internal work expression,
Equation 2.14, with respect to s and equating to zero. The resulting expression for s is:
s= = Vb (2.17)
The controlling yield-line mechanism and geometric parameters for the four-bolt
flush stiffened end-plate with the stiffener on the outside of the tension bolt rows is shown
in Figure 2.4(b). The imternal work and resulting end-plate capacity of this mechanism
are:
39
wt Seco Tio
, .
i ‘. Pp ; . t , ‘
’ x vA rT LY
. 1 *
Pp “AY a s Se a
p a“ ‘A
- @ ‘@ . f 4 a . ‘ . ; + a
x 4 % - . ’ * a
w
(a) Stiffener Between the
Tension Bolt Rows
Figure 2.4 Yield-Line Mechanisms for Four-Bolt Flush
Lt f
f
vies Pp / Ny
t f ‘, p ‘ . f p ’ ‘
t2 © ® nm iY wy ue ay
HEX eh
PME AFG Py XY ffs
ey | sty fos 1 ?
+ ‘MOY s \ ; ‘
* SH, ! SRB Pp “A ‘ foe s
7
4
7
‘
iu
He ¢ h Ww t
Pp y , ‘
7 5
f
(b) Stiffener Outside the
Tension Bolt Rows
Stiffened Moment End-Plate
(after Hendrick ef al. , 1985)
40
_4mp be 2 be {4 3] g 2(m (2.18) WwW; = “SP on] 2 ~2torem) “1246-n.) 5. Th, Top, +2 5 -»)}
2.19 Mai - ‘ig bo] 3 +2(o¢+00)} +E +124b-aa} (2 | + Op, +2[% *n)) ( )
Rearranging M,, and inserting m, gives the expression for the required plate thickness:
V2
My/ Fpy (2.20)
(| lorem) +t s12%h-pa (2 | ‘on « (Pe “*)
to=
where p, is the distance from the furthermost interior bolt centerline to the face of the
stiffener plate on the outside of the tension bolt rows.
2.2.4 Six-Bolt Flush Unstiffened Moment End-Plates
A study was conducted by Bond and Murray (1989) on the behavior of six-bolt
flush unstiffened moment end-plate connections. The following discussion is based on that
study.
The two controlling yield-line mechanisms and geometric parameters for the six-
bolt flush unstiffened end-plate configuration are shown in Figure 2.5. One of these two
yield-line patterns will govern the analysis based on the variable geometric parameters of
the specific end-plate. The yield-lme patterns of these mechanisms differ in the location of
a single pair of yield lines within the depth of the beam near the beam tension flange. In
the first mechanism, Mechanism I, this particular yield line begins at the first bolt from the
41
- Pte
eee
- —_
we, 7 Meee,
~ ~
4 a
et
of
-
way *
-
—
aoe”
oe
oreo
(b) Mechanism I (a) Mechanism I
(after Bond and Murray, 1989)
Figure 2.5 Yield-Line Mechanisms for Six-Bolt Flush
Unstiffened Moment End-Plate
42
inside of the beam tension flange and ends at the face of the beam web a distance u to the
inside of the furthermost interior tension bolt, as shown in Figure 2.5{a). In the second
mechanism, Mechanism II, the distinguishing yield line begins at the intersection of the
inside face of the beam tension flange and the face of the beam web, and ends at the
furthermost interior bolt, as shown in Figure 2.5(b). Both patterns are symmetric about
the beam web. The equations for Wi, M,i, and t, for each mechanism are as follows:
Mechanism I:
4mp| be {h—-p,; h-p h-p WwW =—— be RP, — F131 4%p-+pp, +0 t (2.21) i h | 2\ pe a (pr Pb1,3 ) g
Mp =4mp (He Ps) s2lpr+peia¢a) 21) (2.22) 2\ p u g
1/2
t.= M u/ Foy (2.23) P
bef he Pt, h- Bsa + 2(p5+ Pbi3t (2 Pe)
2\ Pr u , 8
where the unknown parameter, u, is found by taking the derivative of the internal work
expression, Equation 2.21, with respect to u and setting equal to zero:
b 1 foes{ AE Bs] (2.24) h- py
Mechanism IT:
4m, bef BoPe Pe) g W. = _t +=(pe+ h-t,) +—(h-p,3) += (2.25) i-FZ * Pe a =(04 Poiak f) = Pt3) 5
43
be (AP Ps) 2 2u g =4 —}| —— +—— |+- h—te}+— (h- = 2.26
Moi ny] 2 \ be + +7 (pr+Pai3l f)+ ¢ (b—p43)+ | (2.26)
V2
_ My/ Fy (2.27) be { h- h- 2 2u be( hoe + hess) + a (Prt Pbi,3)(h- te)+ = Pt3)+
2\ pr u
where the unknown parameter, u, is found as described earlier:
1 u= 5 vbes (2.28)
2.3 APPLICATION TO EXTENDED MOMENT END-PLATES
Yield-line analysis was performed on the five extended end-plate configurations
shown in Figure 1.5. The five configurations are: four-bolt unstiffened, four-bolt
stiffened, multiple row unstiffened 1/2, multiple row unstiffened 1/3, and multiple row
stiffened 1/3. Analytical studies on all of these configurations except for the multiple row
unstiffened 1/2 have been performed in the past. Thus, the equations and procedures that
follow are based on these studies.
2.3.1 Four-Bolt Extended Unstiffened Moment End-Plates
A study was conducted by Srouji ef ail. (1983b) on the behavior of four-bolt
extended unstiffened moment end-plate connections. The following discussion is based on
that study, however, the equations have been generalized to include end-plate
configurations with large inner pitch distances, Figure 1.8(a).
44
The yield-line mechanism in Figure 2.6 is the controlling yield-line pattern for the
four-bolt extended unstiffened moment end-plate. The geometric parameters are also
shown in the figure. The external work, W., for all end-plate configurations is given by
Equation 2.4. The internal work stored in this mechanism, W;, is expressed as:
ime be{ 4 +3(2)]- be{ W;= h 5 ors +(prits) (h Pit Pre 2 (2.29)
where pg; is the inner pitch distance, pe, is the outer pitch distance, and s is the distance
between parallel yield lines, to be determined. The ultimate capacity of the end-plate, M,,,
is found by equating the external and internal work expressions, resulting in:
Mp = amy] (2 4 +(prit 2)Jo- Pt) +Be{o | (2.30)
Rearranging this expression for M,) results in the required end-plate thickness for a desired
ultimate moment, M,:
1/2
tp = Me! Foy (2.31) be | (2) te h ) — +—|+(preits} —| |(h- + — + —
f 2\pri § ( ts g (h- Pr) 2\Pfo 2
The unknown dimension, s, in Figure 2.6 is found by differentiatmg the internal work
expression, Equation 2.29, with respect to s and equating to zero. The resulting
expression for s is:
s = — ,/b,g (2.32)
45
f
EF 4
-—-@-——--@ Pext Pro
AHR AWS
Pp, ; ‘ Pri } ‘
“—}+-@ | @ \ / s
Ht h w
t -—S p
e e
_|
Lt
Figure 2.6 Yield-Lie Mechanism for Four-Bolt Extended Unstiffened Moment End-Plate
(after Srouji e¢ al. , 1983b)
46
2.3.2 Four-Bolt Extended Stiffened Moment End-Plates
A study was conducted by Srouji ef al. (1983b) on the behavior of four-bolt
extended stiffened moment end-plate connections. The following discussion is based on
that study.
Figure 2.7 shows the two controlling yield-line mechanisms and geometric
parameters for the four-bolt extended stiffened end-plate configuration. The two
mechanisms depend on the length of the end-plate extension beyond the exterior bolt line,
d., and the dimension s. These two parameters determine whether or not a hinge line
forms at the extreme edge of the end-plate. The first case, Figure 2.7(a), m which a hinge
line does form near the outside edge of the end-plate, is denoted as Case 1. The second
case, Figure 2.7(b), in which no hinge line forms above the outside bolt line, is denoted as
Case 2. The dimension, s, is found by differentiating the mternal work expression with
respect to s and equating to zero. The resulting expression for s is:
s = — /b-g (2.33)
The equations for the imternal work, W;, end-plate capacity, M,, and required plate
thickness for a given loading, t,, for each case are as follows:
Case I, whens < d.:
Wi =— (42) (ors 9(2) flo 0.) ++ Pr) (2.34) Pf
M 1 = tmp] (4 1 +(pet (2) le Pt) + (b+ pr) (2.35) Pf &
47
f b
+ -— Ss Fa \ d e i \ d e
© Pext pana : e Pp ext
Py ae -» P, P, eo a Pe
P; f , a mA p t p |) a ae Py
|e eile Ss ‘, H fe ‘ /
‘ / s \ /
h h
t he t Ww w
tT t_ 45 p p
@ @ @ @
LL 1
L t L t f f
(a) Case 1, when s< d, (b) Case 2, when s > d,
Figure 2.7 Yield-Line Mechanisms for Four-Bolt Extended Stiffened Moment End-Plate
(after Srouji et al. , 1983b)
48
1/2
M u/ Foy
" ae(t. 1) + (pe (3) fe" pr) * (n+ Pr) Pf
Case 2, when s > d,:
w= an ears +(pr+ 102) 0-0) ++)
Pr 28 g
Myi= Amp) “(+ L) «(nr+4,) 2) f(@-v.)++P0) 1/2
M y/ Foy
- eft +) + (prt &) 2) [(@- Pr)+(h+ Pr)|
Pf s
2.3.3 Multiple Row Extended Unstiffened 1/2 Moment End-Plates
(2.36)
(2.37)
(2.38)
(2.39)
Two yield-line mechanisms, shown in Figure 2.8, are appropriate for the multiple
row extended unstiffened 1/2 moment end-plate connection. These patterns differ in the
location of a single pair of yield lines within the depth of the beam near the beam tension
flange, much like the patterns for the six-bolt flush unstiffened configuration previously
described. In the first mechanism, or Mechanism I, this particular yield le begins at the
first bolt from the inside of the beam tension flange and ends at the face of the beam web a
distance u to the inside of the innermost bolt line, as shown in Figure 2.8(a). In the second
mechanism, Mechanism II, the distinguishing yield line begins at the intersection of the
mside face of the beam flange and the face of the beam web, and ends at the furthermost
49
Lt
}-----------@---} Poxt Te
Lt
p---@------ -@ omen Poxt
1
(b) Mechanism II (a) Mechanism I
Figure 2.8 Yield-Line Mechanisms for Multiple Row Extended
Unstiffened 1/2 Moment End-Plate
50
bolt to the inside of the beam tension flange, as shown in Figure 2.8(b). Both yield-line
patterns are symmetrical about the beam web. The equations for internal work, Wj, end-
plate moment capacity, M,), and required plate thickness, t,, for each mechanism are as
follows:
Mechanism I:
4m h- h- h- W; — _P b(t, yioPt Pea) Aoe+Pot ul H) (2.40)
h | 2\2 pr pr U g
_ _ h- MoI =4m) Bef, RPP BPA) oforepy eu rs] (2.41)
2\2 pr Pf u z
1/2
t= Mu/ Foy (2.42) p 7 _ _ _ eft yb php Po P2) soles pytul P|
2\2 pe pr u &
The dimension, u, is found by taking the derivative of the internal work expression,
Equation 2.40, with respect to u, and setting equal to zero. The resulting expression is:
u=t bea Pea) (2.43) 2 h- py
Mechanism IT:
4my{be(1 h h-p, h- 2 2u wee BGP FB) 2p ts) 24a) 8 (2.44)
br ] h h—p; h— pr 2 2u _ & 2.45
pndny (LB gee BeBe +7 (ert PeXh-te) +h Pra)t5| (2.49)
51
1/2
t= Mu/ Foy (2.46) p= be) h h-p; Pr 2 2u g —| —+— +—— + ——~ | + — (prt pp Xh- te )+ —(h- py2 J+ = 2\2 pp Pr u a Xo te) a ) 2
The unknown dimension, u, is found as described earlier, resulting m:
1 U= 5 Voss (2.47)
2.3.4 Multiple Row Extended Unstiffened 1/3 Moment End-Plates
A study of the behavior of multiple row extended unstiffened 1/3 moment end-
plate connections was performed by SEI (1984) and Morrison ef al. (1986). The
following discussion is based on those studies, however, the equations have been
generalized to include end-plate configurations with large mner pitch distances, Figure
1.8(b).
Two yield-line mechanisms, shown in Figure 2.9, are appropriate for the multiple
row extended unstiffened 1/3 moment end-plate configuration. The yield-line patterns of
these mechanisms differ in the location of a single pair of yield lines within the depth of the
beam near the beam tension flange, similar to those for the multiple row extended
unstiffened 1/2 configuration just described. Mechanism I is shown in Figure 2.9(a) and
Mechanism II is shown in Figure 2.9(b). The geometric parameters are also shown in the
figure. The equations for W;, M,i, tp, and u for each mechanism are as follows:
Mechanism I:
52
Pext
Lt
Lt
(b) Mechanism IT (a) Mechanism I
(after SEI, 1984)
Figure 2.9 Yield-Line Mechanisms for Multiple Row Extended Unstiffened 1/3 Moment End-Plate
53
4m - _ h- W,=— Melt ho jpop Pe) + Apri+puiste Pe (2.48)
2\2 Peo Pri u g
_ _ h-
My = Amy] ( hoy bope h Pa) aout poise ul 2)| (2.49)
2\2 Peo = Pi
1/2
Pl ee. nk h-p a h-p eo”)
“(5+ " Pri " Bes) «aossePoiar Wl 8 7
w= bea( EP) (2.51)
Mechanism IT:
4mp|/be{/1 h h-py h-p 2 2u 2 Ww, =— (1. + ty 13) 4“(p ‘+pp) 3Kh—-te} +— (h-pi3) +=
| 2 Peo Pe OU s| citPoia)b-ts) g (Ps) +5
(2.52)
bef 1 oh h- h- 2 2 My =n +t y 2) «2oesepanal-te)* 22 O-na)oS
2 Peo P£i u 2
(2.53)
1/2
My/ Foy t, = P be) h h-p, MPa) 2 2u g
>| 5st + + +—(PfitPb13hh- te) +—(h- pi3) +> 2 Pho PF£i u 3 X 3 | ) 2
(2.54)
1 u= > b-g (2.55)
54
2.3.5 Multiple Row Extended Stiffened 1/3 Moment End-Plates
A study was conducted by SEI (1984) on the behavior of multiple row extended
stiffened 1/3 moment end-plate connections. The equations and discussion herein are
based on that study.
The two yield-line mechanisms shown in Figure 2.10 and Figure 2.11 control the
analysis of multiple row extended stiffened 1/3 end-plate configurations. The two
mechanisms differ by the location of a single pair of yield lines--the same distinguishing
pair of yield lines just described for the multiple row extended unstiffened 1/3
configuration. Mechanism I is shown in Figure 2.10, and Mechanism II is shown in Figure
2.11. For each mechanism, there are two cases, which depend on the length of the end-
plate extension beyond the exterior bolt line, d., and the dimension s. These parameters
determine whether or not a yield line forms at the extreme edge of the end-plate. The first
case for each mechanism, in which a hinge line does form near the outside edge of the end-
plate, is denoted as Case 1, Figures 2.10(a) and 2.11(a). The second case for each
mechanism, in which no yield line forms above the outside bolt line is denoted as Case 2,
Figures 2.10(b) and 2.11(b). The dimension, s, is found by differentiating the mternal
work expressions with respect to s and equating to zero. The resulting expression for
both mechanisms is:
S = svbes (2.56)
55
ay Nee
watSe
be a, °
~ -
““~.
me 6UGNT)0 geet”
”— Oa
*
Le
ba
(b) Case 2, when s > d,
56
(after SEI, 1984)
Le
Stiffened 1/3 Moment End-Plate
aA A
es a
QO
di ® o
a.
3 a
v ~
wey
oO +
a 4
{ i
4 4
iN @=-@-@_
a
aS o
rte
— aNe
SeneaSeeeSEeye “A
v cope et”
oN 9-0-9
n a”
on
3
Figure 2.10 Yield-Line Mechanism I for Multiple Row Extended
(a) Case 1, when s < d,
Pext
ay
-
-?
Lo
- ~ mee,
~~ ~m ~ 7.
>.
-" o
- -
-o °
Cy
oO ar
at 2
s oO
A 42 al wo
Ay
o _
on
a HH
»” <u
A, |
Ay
IN @--@--@.
roe
X
/
ae
ws
2” x
tae?
~,
[peoeees ——
“se, /
Ne See,
rat *. <
a
Ne awn
> a
“ oa
nan a
a
(b) Case 2, when s > d. (a) Case 1, whens<d,
Figure 2.11 Yield-Line Mechanism II for Multiple Row Extended Stiffened 1/3 Moment End-Plate
(after SEI, 1984)
57
The equations for the internal work, W;, end-plate capacity, M,i, and required end-plate
thickness, t,, for a desired ultimate load are as follows for each mechanism and case:
Mechanism T:
Case 1, whens < d,:
4 b h = h- h- h+ h-p wi-fi Pt pA Pts 5 Pr s2oreparsty| g h
+) Zenon) 2\ Pr PF u
(2.57)
b h h- h—- h+ h- 2 My 4m {1+ Pe, AO Pt3 5 PE) +2for+ pars ul 21) 2 emo)
Pr = Pf u
(2.58) - 2
ne My/ Foy
Pel + + vee + “Pes + a +pe+Pb1 seu") + (s+p¢)(h+pr)
(2.59)
The unknown parameter, u, in Figure 2.10 is found from differentiating the internal work
expression, Equation 2.57, with respect to u, and setting equal to zero, resulting in:
b 1 foes S22 | (2.60) h- py
Case 2, when s > d,:
h hep, h-py3 + h-p Pee bop hopes | ‘Br +Ape+Poi3 +f
4 wi 5 Pe) “ avoaieen) 2\ pe Pr u 2
(2.61)
58
| h bepp be pes | ht “Pr (3 M, =4m,|—]| 1+—+ +2 pe+ +u
i. 2 Pr Pf u 2 pr Pols
a ) +24 niko)
(2.62)
1/2
t.= Mu/ Foy p=
| h hope hopes he “Pe (" P) 2 —|1+—+ +2 pe+pp 3tu +—(d.tp, Kh+pe > Pr Pr u 2 2 f 13 g a e \ )
(2.63)
where u is the same as for Case 1, Equation 2.60.
Mechanism IT:
Case 1, whens < d,:
4 h bp b-py b+ 2 Wi= Te ea AIP O, mr) .2 =(6r+Pera)rts)+ (o-Ps) -2orntove |
(2.64)
h b-p eps , ttPr Mama (+ +t BBB FePo IPE) ppt} 2H(r-ps)+2ore oes)
(2.65)
1/2
My/ Foy p>
b h hk h- ht pr 2u 2 gZ Melis Bs = t —Pe : mr) 2 *(pe+Poia(b-ty) )+5 (bps) a(t Pr Xht Pe) +
t
(2.66)
The unknown dimension, u, in Figure 2.11 is found as described earlier resulting m:
59
_ . bre (2.67)
Case 2, whens > d.:
4
w= efi toe a A mmr) ,2 = (er+uia) 4) +" (b-P)+ (demon)
(2.68)
Hp, SHR bp 2
(2.69)
1/2
Mu/ Foy
b= b h-py Ps _ beer 2u 2 Sela 4 Ft or ; 3 x mer)? «ler+Po1a)(h-te) + (b-Pr3)+ (de ot Prt pr) +e
(2.70)
where the unknown parameter, u, is the same as for Case 1, Equation 2.67.
60
CHAPTER Il
CONNECTION STRENGTH USING SIMPLIFIED BOLT ANALYSIS
3.1 GENERAL
Yield-line theory predicts a moment capacity for end-plate connections which is
controlled by yielding of the plate. It does not predict the connection capacity based on
bolt failure. Because both the plate and the bolts are essential to the connection
performance, it is necessary to analyze the capacity of the connection based on bolt forces
mcluding prying action. Experimental tests have shown that prying action in the bolts
arises when the end-plate deforms out of its original flat state, as shown in Figure 3.1
(Srouji et al, 1983a, 1983b, 1984; Hendrick et al., 1984; SEI, 1984, Morrison ef ai.,
1985, 1986; Bond and Murray, 1989; Abel and Murray, 1992b). As the plate deforms,
contact points are made between the plates, giving rise to the points of application of
prying forces. A simplified form of a method introduced by Kennedy ef a/. (1981) has
been adopted for predicting the connection moment capacity for the limit state of bolt
rupture which includes prying action.
As described in Chapter I, the primary assumption im the Kennedy method is that,
as the end-plate deforms out of its original state, it displays one of three stages of behavior
depending on the thickness of the plate and the magnitude of the applied load. The three
61
Zan
KZ
de ) rb Contact points for
prying forces
M M
samen ewes: Original state
Deformed state
Figure 3.1 Prying Forces as a Result of Plate Bending
62
stages of plate behavior are thick, intermediate, and thin (Figure 1.7). Each stage of plate
behavior has a corresponding equation for calculating a prying force which is mcorporated
into the bolt force calculation. Once the stage of plate behavior is determined, the prying
force, and hence, the bolt force can be calculated. The moment at which bolt failure
occurs, Mu ton, is designated as the moment at which one of the bolts first reaches its proof
load, as shown in the sample applied moment versus bolt force plot in Figure 3.2(a). The
bolt proof load, P,, is calculated by multiplying the bolt cross-sectional area, Ap, with the
nominal strength of the bolt, Fy, defined in Table J3.2, AISC (1986):
P, = ApFy, (3.1)
The modified Kennedy method has been proven to be quite accurate for predicting
bolt forces with prying action in end-plate connections at any stage of loading (Srouji e¢
al., 1983a, 1983b, 1984; Hendrick et a/., 1984; SEI, 1984, Morrison et ai/., 1985, 1986;
Bond and Murray, 1989; Abel and Murray, 1992b). The correlation between the modified
Kennedy method and experimental bolt force is shown in the sample plot in Figure 3.2(a).
As discussed in Chapter I, extensive calculations and iterations are involved in the
modified Kennedy method. However, when considering the ultimate moment capacity of
the connection, these calculations can be reduced considerably.
After reviewing the results of previously conducted connection tests, two rational
assumptions were devised in order to minimize the bolt force calculations in the Kennedy
method. The first assumption considers bolt yielding. It was evident that, in most of the
tests, the connection continued carrying load beyond the point at which the first bolt
63
Bolt
Fo
rce
(kip
s)
Bolt Fo
rce
(kips)
50
40
30
20
10 -F—
80
300
| Bolt Proofload
o——_e-__0___o— :
te iz ly wi
—O@— Expermantal ; a
——Kemedyaal | pu | | - _| :
0 50 100 150 200 250
Applied Moment (k-ft)
(a) Kennedy et al. Prediction
(after Abel and Murray, 1992a)
P, = 70.7 kips |
20
—@— Bi=load-carrymg
—— B2=load-carryng
—O— B3=nct load-carrymng
—O— B4=load-carryng
, |
a |
500 1000 1500
Applied Moment (k-ft)
(b) Determination of Load-Carrying Bolts
(after Borgsmiller et al. , 1995)
Figure 3.2 Sample Applied Moment vs. Bolt Force Plots
64
2000
reached its proof load, Mupon (Figure 3.2(a) and (b)). Because the proof load of a bolt
designates the point at which yielding commences, and because of the ductile nature of
steel, it can be assumed that bolts that have reached their proof load can continue yielding
without rupture until the other bolts reach their proof load as well. This assumption is
justified by the notable yield plateau on bolt stress-strain graphs obtained by Abel and
Murray (1992b). The second assumption is a conservative one, and states that when a
bolt reaches its proof load, the plate behaves as a “thin” plate and the maximum possible
prymg force, Qnax, can be incorporated into the bolt analysis. It is important to note that,
because of the second assumption, this simplified method is only applicable when
predicting the ultimate capacity of the connection. In other words, this simplified
approach is geared towards calculating the maximum possible applied moment when the
bolts have reached their proof load, P,.
When calculating the connection strength using the simplified approach, all load-
carrying bolt forces are set equal to their proof load, P,, the maximum possible prying
force for a given end-plate configuration, Qnax, is calculated, and the two are incorporated
into the analysis of the connection moment capacity for the limit state of bolt rupture. Ifa
bolt does not carry any load, its force is always equal to the minimum pretension force, T),
specified in Table J3.1, AISC (1986). A “load-carrying bolt” is one that has been
experimentally proven to carry load in an end-plate connection. For instance bolts By, Bz,
and B, in Figure 3.2(b) show an increase in bolt load as the applied moment increases,
65
whereas B; stays at approximately the pretension force, 51 kips, throughout the entire
test. The load-carrying bolts in this hypothetical test are therefore B,, B2, and Bu.
To illustrate the simplified approach, consider the schematic of a two-bolt flush
unstiffened end-plate configuration shown in Figure 3.3. In the figure, M, = ultimate
moment capacity of the connection as controlled by bolt rupture with prying action, F; =
the total applied flange force resulting from the applied moment, B = the bolt force m one
bolt, equal to the bolt proof load, P,, and Quax = the maximum possible prying force in one
bolt resulting from the plate deformation. Summing the moments results in:
Mg =2Pidy— 2 Q max (dy— a) 6.2)
= 2(P,- Qmnax) 4) + Qmax (@)]
The term, Qmax(a), in this equation only constitutes approximately 2% of M,. Hence, in
the spirit of simplification and in keeping things conservative, it can be assumed that the
Qmax(a) term is negligible, resulting in the following expression for M,:
Mg = 2(0- Qmax ) dy (3.3)
Based on this simplified equation of equilibrium, a simpler model of the connection
indicates that the bolt force can be taken as (P; - Quax) rather than having two sets of
forces, P, and Qmax. This further simplified model is shown in Figure 3.4.
If the bolt force is considered to be (P; - Qmax), care must be taken to ensure that it
is not less than the minimum pretension of the bolt, T,. If this is the case, the value for T,
is used instead of (Pi - Qmax) in Equation 3.3 The calculation of M, is therefore expressed
as:
66
|—
Figure 3.3 Bolt Analysis for Two-Bolt Flush
Unstiffened Moment End-Plates
: 2(P, ~Q inex?
Figure 3.4 Simplified Bolt Force Model for Two-Bolt Flush
Unstiffened Moment End-Plates
67
| 2(Pk- Qmax ) dy 4 vex 2(T, ) dy C. )
The pretension phenomenon is depicted in Figure 3.5. By pretensioning the bolts, the
plates are compressed an equivalent amount as the bolt pretension. As load is applied to
the connection, no load is applied into the bolt until the precompression of the plates is
diminished. Once this happens, the bolt load increases beyond the pretension force until it
reaches its proof load.
The procedure used in calculating M, for the two-bolt flush unstiffened
configuration can be generalized to include any configuration. The predicted ultimate
moment capacity of the connection for the limit state of bolt rupture including prying
action in any end-plate configuration is calculated by:
Ni Nj
> 2(Pt- Qmax); d+ D7 2(To) Mg= |") Je (3.5)
> 2(T) d max! n=1
where Nj = the number of load-carrying bolt rows, N; = the number of non-load-carrying
bolt rows, N = the total number of bolt rows, d = the distance from the respective bolt
row to the compression flange centerline, and “q” signifies that prying action is included.
It is noted, and will be demonstrated later, that the general expression for M, is not always
algebraically correct for all end-plate configurations when summing the moments. Much
depends on the assumed placement of the prying force, Qmax, and the distance “a”.
Because of the fact that it is impossible to pinpoint the exact location of the prying force,
68
= Th Ty, /2
PR “ 5 “
——F* ff
(a) Zero Applied Load (b) Applied Load Equivalent
to T,/2
LW —- Ty
— Mz>M1
—l (c) Applied Load Equivalent to T,
Figure 3.5 Effects of Bolt Pretension
69
and in keeping the design of all end-plate configurations unified, Equation 3.5 has been
adopted to predict the ultimate moment of the connection when controlled by bolt force.
The maximum possible prying force for an end-plate configuration, Qmax, is calculated
using Equation 1.6:
(1.6) Q max =
and F' is:
2 3 toFy/(0.85b¢/2+0.80w)+ 2 dpFy/ 8 pa /P py (0.85 be )+adpF yp (1.7) 4pe
Kennedy e¢ al. (1981) cautioned that, if the quantity under the radical in Equation 1.6 is
negative, the end-plate will fail locally in shear before prying forces can be developed, and
the connection is inadequate for the applied load. Also, the distance “a” is dependent on
whether Qmax is being calculated for an interior bolt or an exterior bolt. For interior bolt
calculation and all of those in flush end-plate configurations, a is calculated by Equation
1.9:
a; = 3.682(t,/d,)* - 0.085 (1.9)
When calculating Q,,.. for an outer bolt, a is the minimum of:
3.682(tp/ dy)’ — 0.085 oF min Pext~ Pf,o
(3.6)
70
where pex = the distance from the outer face of the beam tension flange to the edge of the
end-plate extension, and p¢, = the outer pitch distance between the outer face of the beam
tension flange and the centerline of the exterior bolt line (Figure 2.5).
The calculations involved in the simplified bolt force analysis are a substantial
decrease from those involved in the modified Kennedy analysis used in the previous
studies (Srouji et a/., 1983a, 1983b; SEI, 1984; Hendrick e¢ a/, 1984, 1985; Morrison ef
al., 1985, 1986; Bond and Murray, 1989; Abel and Murray, 1992b). The need to
determine the stage of plate behavior, and hence the need for the complex Equations 1.1,
1.2, and 1.4, is eliminated. Also, the simplified approach eliminates the use of the
inconsistent « and 6 factors which were used to determine the amount of flange force
carried by different lines of bolts. The studies of the past, especially those dealing with
extended end-plate connections, incorporated a and B factors into the bolt analysis to
determine the amount of flange force carried by the outer and inner bolts, respectively
(SEL 1984; Morrison et al., 1985, 1986; Abel and Murray, 1992b). These factors were
usually extrapolated from the test results and were inconsistent from one configuration to
the next. Because of the assumption that all of the load-carrying bolts can yield, the need
for a and B factors in the simplified analysis is eliminated, making it consistent and
determinant among all end-plate configurations.
3.2 APPLICATION TO FLUSH MOMENT END-PLATES
Simplified bolt force analysis was performed on the five flush end-plate
configurations shown in Figure 1.4. The five configurations are: two-bolt unstiffened,
71
four-bolt unstiffened, four-bolt stiffened between the tension bolt rows, four-bolt stiffened
outside the bolt rows, and six bolt unstiffened. Experimental investigations have been
conducted on all five of these configurations. The equations and procedures that follow
are supported by the results from these past studies.
3.2.1 Two-Bolt Flush Unstiffened Moment End-Plates
Srouji et al. (1983a) performed eight full-scale tests on two-bolt flush unstiffened
moment end-plate connections. The model used for the simplified bolt analysis of this
configuration was described earlier and is depicted in Figure 3.4. The bolt force versus
applied moment plots from Srouji’s study indicate that the two tension bolts can both be
considered load-carrying bolts. The ultimate moment capacity as controlled by bolt failure
was given in Equation 3.4:
_ 2(Pi- Qinax ) dy = 2(Ts) 4, (3.4)
where Qnax is calculated from Equation 1.6., and the distance “a” is calculated from
Equation 1.9.
3.2.2. Four-Bolt Flush Unstiffened Moment End-Plates
Srouji et al. (1983b, 1984) performed six full-scale tests on four-bolt flush
unstiffened moment end-plate connections. The model used for the simplified bolt analysis
is shown in Figure 3.6. The bolt force versus applied moment plots resulting from Srouji’s
study indicate that all four of the tension bolts act as load-carrying bolts. The ultimate
72
a Possible stiffener locations
Figure 3.6 Simplified Bolt Force Model for Four-Bolt Flush
Unstiffened and Stiffened Moment End-Plates
73
capacity of the connection for the limit state of bolt rupture is calculated from expanding
Equation 3.5:
2(P,- Qinax (di + 42) M.= (3.7) q max 2(Ty (d+ d>)
where Qmax is calculated from Equation 1.6., and the distance “a” from Equation 1.9. It
was noted earlier that the equation for M, may not demonstrate equilibrium based on the
forces in the model of the connection. This is the case when summing the moments of the
forces in Figure 3.6. However, as previously discussed, Equation 3.7 accurately predicts
the connection capacity and keeps it consistent with other end-plate configurations.
3.2.3 Four-Bolt Flush Stiffened Moment End-Plates
Eight full-scale tests were performed on four-bolt flush stiffened moment end-plate
connections by Hendrick et al. (1984). Four of the tests conducted had the stiffener
between the tension bolt rows, and four of the tests had the stiffener outside of the tension
bolt rows. The simplified bolt analysis model for the four-bolt flush stiffened
configuration is the same as that for the four-bolt flush unstiffened configuration depicted
in Figure 3.6. In seven of the eight tests in Hendrick’s study, the bolt force versus applied
moment plot indicates that all four bolts carry load. The one test in which this is not
indicated, instrumentation problems arose in the outer bolts during the test procedure. It
is therefore assumed that all four of the tension bolts are load-carrying bolts. Calculation
of the ultimate moment is the same as for the four-bolt flush unstiffened configuration:
74
_ | 2CPe- Qmax )(di + 42) Mam |2(t)(di+ da) C7)
where Qnax and a are calculated as described above.
3.2.4 Six-Bolt Flush Unstiffened Moment End-Plates
Five full-scale tests were conducted by Bond and Murray (1989) on six-bolt flush
unstiffened moment end-plate connections. The analytical bolt model for the six-bolt flush
unstiffened configuration is shown in Figure 3.7. There are inconsistencies in the 1989
report regarding whether the middle line of bolts carries any of the applied flange force.
Originally, it was stated that, due to the deformed shape of the plate, no prymg action in
the middle bolt line occurs, as shown in Figure 3.8. Further on, however, prying force in
the middle bolts was explained and included in the bolt force calculations. The bolt force
versus applied moment plots in the appendices indicate that prying action does exist in the
middle line of bolts, and that they carry a slight portion of the applied load. However, to
be consistent with the bolt analysis procedures for the multiple row extended 1/3
configurations, yet to be described, it is assumed that the middle line of bolts does not
carry any of the applied flange force. This assumption is also justified by earlier
statements regarding uncertainty in the placement of prying forces. It is therefore assumed
that the two bolts adjacent the beam tension flange and the furthermost interior two bolts
are load-carrying bolts, and the force in the middle line of bolts is always equal to the
minimum pretension. The ultimate moment of the connection controlled by bolt proof
load, M,, is calculated by expanding Equation 3.5 as follows:
75
2 a(P, —Q nax)
oT;
2(P, ~Q inax?
Figure 3.7 Simplified Bolt Force Model for Six-Bolt Flush
Unstiffened Moment End-Plates
No added ————_
Bolt Force
MOO
Ww
aewne-- Original state
Deformed state
Figure 3.8 Deformed Shape of Multiple Row End-Plates
76
_ 2(P,- Qmax (d+ 43) + 2(T,)d2 5
a 2(T, (d+ d2+d3) ( 8)
where Qrax is calculated from equation 1.6, and the distance “a” from Equation 1.9.
3.3 APPLICATION TO EXTENDED MOMENT END-PLATES
Ultimate moment predictions based on the simplified bolt analysis of the five
extended end-plate connections shown in Figure 1.5 were performed. The five
configurations are: four-bolt unstiffened, four-bolt stiffened, multiple row unstiffened 1/2,
multiple row unstiffened 1/3, and multiple row stiffened 1/3. Experimental investigations
on all five configurations have been conducted in the past. The procedures that follow are
supported by the results from these investigations.
3.3.1 Four-Bolt Extended Unstiffened Moment End-Plates
Six tests were conducted on four-bolt extended unstiffened moment end-plate
connections. Four of the tests were conducted by Abel and Murray (1992b) and two were
conducted by Borgsmiller et a/. (1995). The two tests conducted by Borgsmiller et al.
(1995) had large pitch distances between the inner face of the beam tension flange and the
first row of interior tension bolts (Figure 1.8(a)). The procedure described hereim has
been generalized to include such configurations. The simplified bolt force model including
prying action is shown in Figure 3.9. It was concluded that all four bolts on the tension
side of the connection contribute in carrying the applied load, as observed im the bolt force
77
Possible stiffener location
M q SS s
Figure 3.9 Simplified Bolt Force Model for Four-Bolt Extended Unstiffened and Stiffened Moment End-Plates
78
versus applied moment plots of all six tests. Expanding Equation 3.5 results in the
expression for the ultimate connection moment capacity controlled by bolt proof load:
2(P,- Qmnax,o) do+ 2(Pt—- Qmax,i) di
2(P,- Qmax,o)do+ 2(Tp di) (3.9) ( (P.- Qmmax,i)di+ 2(Tp (do)
2(T, (do+d;)
bo
where Qmaxo and Qmax; indicate the maximum prying force in the outside and mside bolts,
respectively, calculated from Equation 1.6. There are two different F' terms, F'; and F',, in
the calculation of the maximum prying force because of the different pitch distances on the
inner and outer portions of the end-plate. The expression for computing F' is given in
Equation 1.7. The inner pitch distance, p¢i, is used in calculating F';, and the outer pitch
distance, pro, is used im calculating F',. When computing Qmao, the distance “a” is
calculated from Equation 3.6. When computing Qyaxi, the distance “a” is calculated from
Equation 1.9.
3.3.2 Four-Bolt Extended Stiffened Moment End-Plates
Six full-scale experimental tests were performed by Morrison et a/. (1985) on the
four-bolt extended stiffened moment end-plate configuration. The analytical model for
this configuration is the same as that for the four-bolt extended unstiffened configuration
just described, and is shown in Figure 3.9. As with the four-bolt extended unstiffened
configuration, all four bolts on the tension side of the connection contribute in carrying the
79
applied load, and the ultimate moment capacity controlled by bolt failure including prying
action is:
2(P, — Qmax 0) do + 2(P, ~ Qmax,i) di
P- Q max 0) dg + 2(Tp (d; i) (3.9) ( (Pi- Qinax,i) di + 2(Tp do)
2(T, do+ di)
Ww WN
The values for Qmax,o and Qmaxi, Computed from Equation 1.6, are dependent on the values
a, and a;, calculated from Equations 3.6 and 1.9, respectively.
3.3.3 Multiple Row Extended Unstiffened 1/2 Moment End-Plates
Abel and Murray (1992a) conducted two full-scale tests on the multiple row
extended unstiffened 1/2 moment end-plate connection. The analytical model for the
simplified bolt analysis is shown in Figure 3.10. The bolt force versus applied moment
plot of one of these tests indicates that the far interior line of bolts maintained a bolt force
equal to the pretension force throughout the test. The bolt force of this line of bolts was
not plotted against the applied moment for the other test. Therefore, it can be concluded
that the far mterior line of bolts does not carry any of the applied load, and the exterior
bolts and the first interior row of bolts are considered load-carrying bolts. The expression
for the ultimate capacity of the connection controlled by the limit state of bolt rupture is:
2(P:- Qmax,o) di + 2(P}—- Qmax,i) 42+ 2(Ty) d3 ( Mo csateyace) 20
(
N
2 Py- Qmax,i)d2+ 2(Tp d+ d3)
2 Th \dy+ d5+ d3)
80
2(P, —Q max.o) N |
2(P, — Q ax. )
+ 27,
_N
N
Figure 3.10 Simplified Bolt Force Model for Multiple Row
Extended Unstiffened 1/2 Moment End-Plates
$1
where Qmaxo 2nd Qmax are calculated from Equation 1.6. The values a, and a; in Figure
3.10 are calculated from Equations 3.6 and 1.9, respectively.
3.3.4 Multiple Row Extended Unstiffened 1/3 Moment End-Plates
A total of ten full-scale tests were performed on multiple row extended unstiffened
1/3 moment end-plate connections. One test was conducted by Borgsmiller et a/. (1995),
one test conducted by Rodkey and Murray (1993), six tests conducted by Morrison ef al.
(1986), and two tests conducted by SEI (1984). The tests which were conducted by
Borgsmiller et al. (1995) and Rodkey and Murray (1993) had large distances between the
inner face of the beam tension flange and the first row of mterior tension bolts (Figure
1.8(b)). The procedure herein has been generalized to include such configurations. The
simplified analytical bolt model is shown in Figure 3.11. The bolt force versus applied
moment plots of six of the ten tests indicate that all of the bolts carry a portion of the
applied load except for the middle row of interior bolts. In one test, the bolt force of the
middle row of interior bolts was not plotted against the applied moment, as the
appropriate data was “not available” (Morrison et a/., 1986). The deformed shape of the
miner portion of the end-plate is similar to that of the six-bolt flush unstiffened
configuration shown in Figure 3.8. It was therefore concluded that the load-carrying bolt
rows are the exterior, first interior, and far interior lines of bolts. The moment capacity of
the connection controlled by bolt rupture is obtained from expanding Equation 3.5:
82
Possible stiffener location
x XN
~ x
s. x
2(P, —@ max.o)
- 2(Py —~@ maxi )
oO _——_—_——_ ZL — oT,
Wa 2(P, — Q naxx. ) — o
Figure 3.11 Simplified Bolt Force Model for Multiple Row Extended Unstiffened and Stiffened 1/3 Moment End-Plates
83
2(P,- Qmax,o di) + 2(Pr- Qmax,i(d2+ 44) + (Ty) d3
2(P,— Qmax,o (di) + 2(Tp Kd2+d3+ d4) (3.11) ( (P.- Qmax.i)(d2+d4) + 2(Ty )(di+ 43)
2(Ty (d+ d2+d3+d4) N
where Qmaxo and Qmax; are calculated from Equation 1.6. Two different values of F' are
used in the prying force calculations. F'; is used in calculating Qnax; with the large mner
pitch distance, pr;, and F', is used in calculating Qnax,. with the outer pitch distance, peo.
Both Fj and F’, are calculated from Equation 1.7. The values a, and a; m Figure 3.11 are
calculated from Equations 3.6 and 1.9, respectively.
3.3.5 Multiple Row Extended Stiffened 1/3 Moment End-Plates
One test was performed by SEI (1984) on a multiple row extended stiffened 1/3
moment end-plate connection. The simplified analytical bolt model is the same as for the
multiple row extended unstiffened 1/3 configuration just described, and is shown in Figure
3.11. The bolt force versus applied moment plots for this test were limited, so it was
assumed that the load-carrying bolts for this configuration are the same as those for the
multiple row extended unstiffened 1/3 configuration: exterior line, first interior line, and
far interior lme. The maximum possible applied moment before the load-carrying bolt
forces reach their proof load is calculated the same as for the previous configuration:
2(P,— Qmax,o (di) + 2(Pt- Qmax,i (d2+ 44) + 2(Tp) d3 | ( M.< a Qmax,o (41) + 2(Tp )(d2+d3+ da) (3.11)
(
tw
2 P- Q max i)(dy+ dq) +2(T (dit d3)
2 Ty (dy + d5+ d3+ d4)
84
Qmaxo ANd Qmax, are calculated from Equation 1.6, and the values a, and a; in Figure 3.11
are obtained as described above.
85
COMPARISON OF EXPERIMENTAL RESULTS AND
CHAPTER IV
PREDICTIONS
4.1 PREVIOUS EXPERIMENTAL RESULTS
Appendices B through J contain the geometric parameters and calculations for the
52 end-plate connections tested in the past (Srouji e¢ al, 1983a, 1983b, 1984; SEI, 1984;
Hendrick et al, 1984, 1985; Morrison eft al., 1985, 1986; Bond and Murray, 1989; Abel
and Murray, 1992a, 1992b; Rodkey and Murray, 1993; Borgsmiller et a/., 1995). The test
designations in the appendices follow the following format:
where d, = nominal bolt diameter, t, = end-plate thickness, h = beam depth, and the “XX”
XX - dy-tp-h
is the configuration identification, defined for each as:
two-bolt flush unstiffened (one row of tension
bolts)
four-bolt flush unstiffened (two rows of
tension bolts)
four-bolt flush stiffened between the two
tension bolt rows
four-bolt flush stiffened outside the two
tension bolt rows
six-bolt, multiple row flush unstiffened (three
rows of tension bolts)
four-bolt extended unstiffened, F, refers to nominal plate yield stress
86
ES = four-bolt extended stiffened
MRE1/2 = multiple row extended unstiffened, 1 exterior
tension bolt row, 2 interior tension bolt rows
MRE1/3 = multiple row extended unstiffened, 1 exterior tension bolt row, 3 interior tension bolt rows
MRES1/3 = multiple row extended stiffened, 1 exterior tension bolt row, 3 interior tension bolt rows
The yield strength of the connection end-plate material, F,,, shown in the appendices was
determined by standard ASTM coupon tests. All bolts were A325 with a nominal tensile
strength, Fy, equal to 90 ksi, as specified in Table J3.2, AISC (1986). In the tests
conducted by Abel and Murray (1992b), the strength of the A325 bolts was measured by
tensile tests conducted in a universal testing machine. Also shown in Appendices B
through J are the appropriate yield-line mechanisms and simplified bolt force models for
each end-plate configuration.
All tests were splice moment connections under pure moment, as shown in Figure
4.1. The test beam was simply supported and loaded with two equal concentrated loads
symmetrically placed. Load was applied by a hydraulic ram via a load cell and spreader
beam, as shown in Figure 4.2. Lateral support for both the test specimen and the spreader
beam was provided by lateral brace mechanisms bolted to steel wide flange frames
anchored to the laboratory reaction floor.
To compare the experimental results to the predicted strength of the connections,
it was necessary to determine the experimental failure load of each test. Depending on the
shape of the applied moment versus end-plate separation plot from the experimental tests,
87
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88
Test Frame aN
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Hydraulic Ram ——7—
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Roller
Test Specimen
Lateral Brace Mechanisms yi
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TTA OOO
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Figure 4.2 Cross-section of Laboratory Test Setup
89
one of two different failure loads was identified, M, or M,. Applied moment versus end-
plate separation plots came as a result of placing measuring devices on the end-plates at or
near the beam tension flange during the test procedure. These plots are an indication as to
whether or not the end-plate yields. If the plot has a nearly horizontal yield plateau, such
as Plot A in Figure 4.3, the failure load of the specimen is taken as the maximum applied
load in the test, M,. From a design standpoint, this is acceptable since the maximum
applied load in the test closely correlates to the point at which the connection yields. A
connection displaying this behavior is in relatively little danger of experiencing excessive
deformations under service loads. Plot B in Figure 4.3 shows a curve with no distinct
yield point and a sloped yield plateau. Connections displaying this type of applied moment
versus end-plate separation behavior would experience large deformations under working
loads if the design failure load were assumed to be the maximum applied moment in the
test. Therefore, the failure load is determined to be near the point at which the connection
yields, M,. This experimental yield moment is established by dividing the applied moment
versus end-plate separation plot into two linear segments which intersect at the yield
moment, as shown in Figure 4.4.
The maximum applied moment, M,, and experimental yield moment, M,, for each
of the 52 tests were determined and can be found in Appendices B through J. It was
necessary to establish a numerical threshold for distinguishing which value, M, or My, to
use for the experimental failure load, Mg. In some cases, it was difficult to determine
whether some of the applied moment versus plate separation plots displayed the behavior
90
Appl
ied
Moment
e e
Plot A *
soo ove ee eo © © OF ® ao 0 © 20°? e
° e
End-Plate Separation
Figure 4.3 Sample of Applied Moment vs.
End-Plate Separation Plots
e
¢ Experimental Data Applied
Moment
— Bilinear Approximation
My = Experimental] Yield Moment
End—-Plate Separation
Figure 4.4 Determination of Experimental Yield Moment
91
of Plot A or Plot B in Figure 4.3. This threshold was empirically established through the
ratio of M, to M,, and is expressed as follows:
Maii=M, if M,/M, < 0.75 (4.1)
Mai=M, if M,/M, > 0.75 (4.2)
It should be noted that this threshold is an approximate one, and that if the M,/M, ratio is
approximately equal to 0.75, +/- 0.02, either value, M, or My, can be taken as the
experimental failure load. The values corresponding to the appropriate experimental
failure load of each test are shown shaded in the appendices.
4.2 DETERMINATION OF THE PREDICTED CONNECTION STRENGTH
Prediction of the ultimate strength of moment end-plate connections was presented
for two limit states. Chapter II described the prediction of the ultimate strength for the
limit state of plate yielding, M,), using yield-line theory. Chapter I described the
prediction of the connection strength for the limit state of bolt fracture including prymg
action, M,, using a simplified version of the Kennedy method. Appendices B through J
show the calculations of M,; and M, for each of the connections tested. Notice that the
asterisk (*) next to Qmax in the appendices indicates that (P; - Qmax) < T,, which plays a
crucial role in the calculation of M,.
Once the connection strength predictions for the end-plate yield and bolt rupture
limit states have been calculated, a final, controlling connection strength prediction, Morea,
must be chosen. To do so, an important assumption is necessary: the end-plate must
sufficiently yield in order for prying action to occur in the bolts. Ifthe end-plate does not
92
substantially deform out of its original state, there can be no points of application for
prying forces (Figure 3.1). This concept was originally introduced by Kennedy ef al.
(1981), as they presented the three stages of plate behavior caused by increasing load.
The circumstance initiating the different stages of plate behavior is the formation of plastic
hinges, or end-plate yielding.
The outcome of this assumption is the concept of a “prymg action threshold.”
Until this threshold is reached, the plate behaves as a thick plate, and no prying action
takes place in the bolts. Beyond the threshold, maximum prying action occurs in the bolts
due to the sufficient deformation of the plate. The prying action threshold is taken as 90%
of the full strength of the plate as determined by yield-line analysis, or 0.90M,). Thorough
review of the past experimental data lead to the conclusion that the plate begins deformmg
out of its original state at approximately 80% of the full strength of the plate, or 0.80M,1.
However, to assume maximum prying action in the bolts at the point at which yielding in
the plates commences would be unreasonably conservative. Therefore, it was assumed
that the plate has deformed sufficiently at 90% of the plate strength to warrant the use of
maximum prying action in the bolts. The predicted strength of the connection is
controlled by the following guidelines:
If applied moment < 0.90M,, thick plate behavior (4.3)
If applied moment > 0.90M,; thin plate behavior (4.4)
If the plate behaves as a thick plate, no prying action is considered in the bolts.
Calculation of the connection strength for the limit state of bolt rupture with no prying
93
action, My», follows the same philosophy outlined in Chapter III, except Qmax is set equal
to zero and all of the bolts in the connection are assumed to carry load. The connection
strength for the limit state of bolt rupture with no prying action is therefore calculated
from a revised version of Equation 3.5:
N
Map = >, 2(P,); di (4.5) i=]
where N = the number of bolt rows, d, = the distance from the respective bolt row to the
compression flange centerline, and “np” signifies that no prying action is included.
Once M,,, M,, and M,) are known, the controlling prediction of the connection
strength, M,,-a4, can be determined. As mentioned earlier, the prying action threshold has
been identified as 90% of the plate strength, or 0.90M,). Ifthe strength for the limit state
of bolt rupture with no prying action, M,», is less than the prying action threshold, the
connection will fail by bolt rupture before the plate can yield and before prying action can
take place in the bolts, a “thick” plate failure. If the strength for the limit state of bolt
rupture with no prying action, Mpp, is greater than the prying action threshold, prying
action takes place in the bolts, because the plate yields before the bolts rupture. If the
strength for the limit state of bolt rupture with prying action, M,, is less than the strength
of the plate, M,;, the connection will fail by means of bolt rupture with prying action
before the plate can fully yield. However, if M, is greater than M,y, the connection will fail
by plate yielding. In summary:
Mored = Map if Map, < 0.90M,, (4.6)
Morea = M, if 0.90M,; < Mnap and M, < Mp (4.7)
94
Mopred = Msg. if Moi < M, (4.8)
The final predicted strength of each of the 52 tests is shown in Appendices B
through J. Comparison of the experimental results to the predictions is necessary to verify
the simplified approach.
4.3 FLUSH MOMENT END-PLATE COMPARISONS
The predicted and experimental results for the flush moment end-plate connection
tests are listed in Table 4.1. Twenty-seven tests, comprising four different configurations,
were examined. Included in the table are M,, Mi, 0.90Myi, Map, Morea, My, and My. Note
that in the cases where M,) < M,, it was not necessary to calculate either 0.90M,; or Map
as the connection strength was controlled by M,, thus the dashes m the columns
contaming 0.90M,; and M,,. Also in the table are design ratios, comparing Morea to M,
and M,. A design ratio smaller than 1.0 is conservative, and one larger than 1.0 is
unconservative. The shaded values are the ratios corresponding to the applicable failure
load, determined by the My, to M, ratio as described above. If M,/M, < 0.75, the
applicable design ratio is Mprea/My; if M,/M, > 0.75, the applicable design ratio is
Mprea/Mu. The appropriate design ratios are shown shaded in the appendices as well. In
all but five of the flush end-plate tests, the experimental failure load was designated as the
maximum applied load in the test, and the applicable design ratio is Mprea/Mu. This
indicates that the applied moment versus end-plate separation curve for most flush
configurations resembles Plot A in Figure 4.3.
95
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Eight tests were conducted by Srouji ef a/. (1983a) on the two-bolt unstiffened
configuration. Design ratios varied from 0.81 to 1.03 and were, with one exception,
calculated by Mprea/My. It can be concluded that the predictions are conservative, but
correspond well with the experimental results for two-bolt flush unstiffened end-plate
configurations.
Six tests were conducted by Srouji ef a/. (1983b, 1984) on four-bolt unstiffened
end-plate configurations. Design ratios varied from 0.94 to 1.04, mdicating that the
simplified approach adequately predicts the behavior of this configuration.
Four-bolt flush stiffened tests were performed by Hendrick et al. (1984, 1985).
Four tests were stiffened between the tension bolt rows and four tests were stiffened
outside the tension bolt rows. Design ratios varied from 0.83 to 1.04, indicating that, even
though slightly conservative, the predictions correlate well with the experimental results of
this configuration.
Finally, five tests were conducted by Bond and Murray (1989) on six-bolt flush
unstiffened end-plate configurations. In four of the tests, the failure load was designated
as the yield moment, M,, due to a small M,/M, ratio. The other test had a designated
failure load equal to the maximum applied moment. Design ratios varied from 0.94 to
1.11 mdicating that the predictions are slightly unconservative, but still correlate well with
the experimental results.
97
4.4 EXTENDED MOMENT END-PLATE COMPARISONS
The predicted and experimental results for the extended moment end-plate
comnection tests are listed in Table 4.2. Twenty-five tests, comprising five extended end-
plate configurations, were studied. As with the flush end-plate tests, design ratios were
computed. The appropriate design ratios, based on the value of M,/M,, are shown shaded
in the table. In fourteen of the tests, the design ratio was controlled by M,, and in eleven
tests, the design ratio was controlled by M,. This indicates that, unlike flush end-plate
configurations, extended end-plates have a tendency to display either type of behavior
shown in Figure 4.3.
Six Four-bolt unstiffened tests were performed by Abel and Murray (1992b) and
Borgsmiller et al. (1995). The design ratios for five of the six tests varied from 0.80 to
1.07; one test had a design ratio of 1.37. The predicted failure moment for the latter test
was controlled by the plate, M,:. Such was the case when Abel and Murray (1992b)
analyzed the connection using the unification procedures of past studies. In other words,
for this particular test, the simplified approach results in an identical prediction to that of
the unified approach. It is also noted that the design ratio comparing M,,.q to M, for this
test is equal to 0.93. Aside from the one test, the results are somewhat conservative, but
compare well with the experimental results.
Six tests were conducted by Morrison et a/. (1985) on the four-bolt stiffened
configuration. Design ratios varied from 0.85 to 1.35, indicating some scatter in the
results. However, as was just noted with Abel and Murray (1992b), the prediction of the
98
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test having a design ratio equal to 1.35 was controlled by M,i, meaning the result of this
study was identical to that in Morrison ef al. (1985). It is also noted that the design ratio
Of Mprea/M, for this test was 0.94. Aside from the one test, the predictions from the
simplified approach compare well with the experimental results.
Two tests were performed by Abel and Murray (1992a) on the multiple row
extended unstiffened 1/2 end-plate configuration. The design ratios from these tests were
0.85 and 1.29, indicating that there is some scatter in the results. Due to the limited
testing done on this configuration, it is difficult to determine a conclusion as to the
accuracy of the simplified prediction method.
Ten multiple row unstiffened 1/3 connections were tested: one by Borgsmiller et
al. (1995), six by Morrison e¢ al. (1986), one by Rodkey and Murray (1993), and two by
SEI (1984). Design ratios from these ten tests ranged from 0.87 to 1.39, indicating scatter
m these results. However, aside from the value equal to 1.39, the other nine test design
ratios vary from 0.87 to 1.10. The test that produced a design ratio of 1.39 was
conducted by SEI (1984), who said, “the yield-line prediction of the failure load [is] not
close since the failure was due to large bolt forces and the full strength of the plate was
not reached.” This confusing statement would lead to the conclusion that bolt prying
action can occur prior to plate bending. However, due to the overwhelming evidence
against this statement, it can be concluded that, with the exception of the one test, the
simplified procedure accurately predicts the failure load of multiple row extended 1/3 end-
plate configurations.
100
One test was conducted by SEI (1984) on a multiple row extended stiffened 1/3
end-plate connection. The design ratio is 1.12, indicating slightly unconservative results
for the limited experimental data.
101
CHAPTER V
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
5.1 SUMMARY
This study has introduced a simplified method for the design of moment end-plate
connections. The new method calculates the ultimate strength of the connection based on
two limit states: end-plate yielding and bolt rupture. Yield-line theory was used for
determining the connection strength based on end-plate yielding, and a simplified version
of the Kennedy method was used for determining the connection strength as controlled by
the bolts with or without prying action. The bolt calculations were reduced substantially
from those in the modified Kennedy method, for only the computation of a maximum
prying force, Qmax, is involved. A primary assumption in this approach is that the end-
plate must substantially yield in order to produce prying forces in the bolts; if the plate is
strong enough, no prying action occurs and the bolts are loaded in direct tension.
The simplified approach was used to predict the failure moments of 52
connections, comprising nine different configurations. The predictions were compared to
the experimental results from past tests for verification. The nine configurations are:
102
Flush Configurations Extended Configurations
- two-bolt unstiffened - four-bolt unstiffened
- four-bolt unstiffened - four-bolt stiffened
- four-bolt stiffened - multiple row unstiffened 1/2
- six-bolt unstiffened - multiple row unstiffened 1/3
- multiple row stiffened 1/3
Tables 5.1 through 5.11 summarize the proposed analysis procedures for these moment
end-plate configurations. Table 5.1 lists the equations for bolt prying action, Qmax, bolt
proof load, P,, and bolt pretension, T,, which are common for every end-plate
configuration. Tables 5.2 through 5.11 show diagrams of the end-plate geometry, yield-
line mechanisms, and simplified bolt force models, as well as equations for calculating the
design strength of the connection, ¢M,. The connection design strength is calculated for
the limit states of end-plate yield, M,1, and bolt rupture with or without prying action, Mg,
M,p. The resistance factors 6, and o, have been incorporated into the equations to make
them applicable to Load and Resistance Factor Design. It is recognized that an m-depth
probabilistic study on the proposed analytical models is necessary in order to determine
accurate and dependable resistance factors. Such a study is beyond the scope of this
research, hence the common resistance factors for yielding and bolt rupture are used. The
resistance factor for bolt rupture, @,, is 0.75, and the resistance factor for end-plate yield,
dy, 1s 0.90, AISC (1986). It should be noted that the expression for the plastic moment
capacity per unit length, m, = (Fpytp’)/4, has been substituted into the equations for ¢,M,1
in Tables 5.2 through 5.11.
103
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119
5.2 CONCLUSIONS
The major conclusions drawn from this study are:
1.) The threshold for determining whether to use the experimental yield moment,
M,, or the maximum applied moment, M,, as the experimental failure moment can be
designated by the ratio of M, to My. If M,/M, < 0.75, My is designated as the
experimental failure moment; if M,/M, > 0.75, M, is designated as the experimental failure
moment.
2.) The threshold when prying action begins to take place in the bolts is at 90%
of the full strength of the plate, or 0.90M,). If the applied load is less than this value, the
end-plate behaves as a thick plate and prying action can be neglected in the bolts. Once
the applied moment crosses the threshold of 0.90M,i, the plate can be approximated as a
thin plate and maximum prying action is incorporated in the bolt analysis.
3.) Of the 52 tests examined in this study, 34 were governed by yielding of the
end-plate. The yield-line mechanisms described in Chapter II adequately predict the
strength of these end-plate connections. The mean value of the predicted to applied
moment ratios for the 34 tests is 1.02, and the standard deviation equal to 12.6%.
However, three of the 34 tests had unconservative ratios of predicted to applied moment
equal to 1.35, 1.37, and 1.39. The ratio of predicted to applied moment for the other 31
tests varied from 0.85 to 1.11, yielding a mean value equal to 0.99 and a 6.2% standard
deviation.
120
4.) Of the 52 tests examined in this study, 18 were governed by bolt rupture. In
eleven tests, the prediction including prying action, M,, controlled, and in seven tests, the
prediction with no prying action, My», controlled. The simplified Kennedy bolt analysis
method described in Chapter [II adequately predicted the strength of the end-plate
connections examined in this study. The ratio of predicted to applied moment for the
cases when prying action was included ranged from 0.80 to 1.12, with an average value
equal to 0.91 and a 10.1% standard deviation. The same ratio for the cases when prying
action was not included ranged from 0.84 to 1.29, yielding an average equal to 1.01 and a
13.9% standard deviation.
5.3 DESIGN RECOMMENDATIONS
The proposed analytical procedure is appropriate for the design of moment end-
plate connections having one of the nie configurations examined in this study. Two
LRFD design procedures have been devised depending on the limiting provisions in the
design. If it is necessary to limit bolt diameter, Design Procedure 1 is recommended. If it
is necessary to limit the thickness of the end-plate, Design Procedure 2 is recommended.
Because none of the experimental tests examined in this study used A490 bolts, the two
proposed design procedures only allow for the use of A325 bolts.
Design Procedure 1: The following procedure results im a design with a relatively thick
end-plate and smaller diameter bolts. The design is governed by bolt rupture when no
prying action is included, requiring “thick” plate behavior. The design steps are:
121
1.)
2.)
3.)
4.)
Compute the ultimate factored moment, Mu, using the load factors specified
in Chapter A, AISC (1986). Set the connection design strength, ¢M,, equal
to the ultimate moment for the most efficient design:
oM, = My (5.1)
Choose one of the nine configurations, and establish values to define the
end-plate geometry: bg g, ps ts tu, h, ps, ps, etc. In addition, choose the
type of end-plate material.
Divide 6M, by 0.90 and set it equal to the appropriate equation for the
resistance based on end-plate yield, 6,M,1, from the summary tables:
gMy =o,M 5.2 0.90 Py pl ( )
This is to ensure that the plate will be strong enough to cause the connection
to fail by bolt rupture with no prying action, thick plate behavior. Solve for
the required end-plate thickness, t,.
Set OM, equal to the appropriate expression for the resistance based on bolt
rupture with no prying action, ¢,M,p), from the summary tables:
6M, = $;Mnp (5.3)
Solve for the required bolt proof load, P,.
Solve for the required bolt diameter, d,, from the expression:
2
P, = (a8) Foy (5.4)
where F,y = 90 ksi, the nominal bolt tensile strength as specified i Table
J3.2, AISC (1986).
122
5.) Check that My) < 0.90 M,: for the chosen values of tp and d,. If the
inequality is true, the design is completed. Otherwise, increase the plate
thickness until the inequality stands.
Design Procedure 2: The following procedure results in a design with a relatively thin
end-plate and larger diameter bolts. The design is governed by either the yielding of
the end-plate or bolt rupture when prying action is included, “thin” plate behavior.
The design steps are:
1.) Compute the ultimate factored moment, M,, using the load factors specified
in Chapter A, AISC (1986). Set the connection resistance, 6M,, equal to the
ultimate moment for the most efficient design:
6M, = M, (5.5)
Choose one of the nine configurations, and establish values to define the
end-plate geometry: by g, ps ts tw, b, ps, ps, etc. In addition, choose the
type of end-plate material.
2.) Set oM, equal to the appropriate equation for the resistance based on end-
plate yield, ¢,M,i, from the summary tables:
oM,, = dyMp1 (5.6)
Solve for the required end-plate thickness, t,.
3.) Select a trial bolt diameter, d,, and calculate the connection resistance for the
limit state of bolt rupture with prying action, $,M,, using the appropriate
equation in the summary tables.
4.) Make sure ¢,M, > M,. If necessary, adjust the bolt diameter until @M, is
slightly larger than M,.
123
5.4 DESIGN EXAMPLES
5.4.1 Two-Bolt Flush Unstiffened Moment End-Plate Connection
Determine the required end-plate thickness and bolt diameter for an end-plate
connection with the geometry shown in Figure 5.1 and an ultimate factored moment of
540 k-in. The end-plate material is A572 Gr 50 and the bolts are A325.
Design Procedure 1:
1.) M, was given as 540 k-in. Therefore:
oM, = M, = 540 k-in
2.) Divide 6M, by 0.90 and set it equal to 6M, from Table 5.2:
9M, = 240 = 600 k—in 0.90 0.90
b - 2th-p VL} all 2 - - 0,M = 9, Fyt.@ re +1} -2tepe0 |e o01 m
g, = 0.90
Solve for the required end-plate thickness, t,:
1/2
600/(¢y F..,) t= y "py P be { 1 2 (h- eyee{ ts 1 + 249)
where s and p; are:
1 1 sS=—,/breg = —,/6(2.75) = 2.03 in. 1 fore = + (6273)
Pt = pet te= 1.375 + 0.25 = 1.625 in.
124
|
Pr Py
@ @
fe t h
t }—5 Pp
e @
Lemme mm} —— +
Ly f
Parameter Value (in.)
h 16
be 6
tr 1/4
ty 1/4
Pr 1 3/8
g 2 3/4 Figure 5.1 Design Example--Two-Bolt Flush Unstiffened
Moment End-Plate Connection
125
1/2
600/(0.90(50))
(16 - 1.625) $( 1+ 1) 4 2 (1.375 +203) 2\1.375 2.03/ 2.75
Try t, = 7/16 in.
t= = 0.389 in.
3.) Compute the required bolt proof load, P,, by equating oM, to 6,M,, using
Table 5.2:
6M, = 6/Map = 6,[2(P,)di] = 540 k-in o, = 0.75
where
d; = h-p,- f 16- 1.625 0.25 _ 14.25 in. 2 2
Solving for P, results in:
P = 540 540 = 253k
@.(2Xd,) 0.75(2)(14.25)
4.) Solve for the required bolt diameter, d,:
_ dy _ , P= | Fw) = 25.3 k Fy, = 90 ksi (AISC, 1986)
dy = [Ate = 925) _ 0598 in mF, m(90)
Try di, = 5/8 in.
5.) Check that M,, < 0.90M,, with t, = 7/16 im. and d, = 5/8 m.:
M,, = 2(P,)d, = | HOO) | 14.25 = 786 k-in
126
b =F Y fy) 1 i1),2 Mo “rycen ft j + Prt ‘|
f
> 6f ] 1 2 = 50(0.4375)* (16 —1.625)| — + + (1.375 + 2.03)
2\1.375 2.03/ 2.75
= 844 k-in
0.90M,,, = 0.90(844) = 759 k—in < M,, = 786 k-in NG
It is therefore necessary to increase the plate thickness until 0.90My > Map.
Try t, = 1/2 in.
M_, =F. t?(h- Pe t,! +2 +s)
6( 1 1 2 = 500.5) (16— 1.625 ( + + 1.375 +2.03
0(05)'( 1 1375 2.03 375 | )
=1102 k—in :
0.90M.,, = 0.90(1102) = 992 k-in > M,, = 786 k—in OK
Summary For the given loading, materials and geometry, use 1/2 im. thick
A572 Gr. 50 end-plate material, and 5/8 in. diameter A325 bolts.
Design Procedure 2:
1.) M, was given as 540 k-in. Therefore:
oM, = M, = 540 k-in
2.) Set OM, equal to o,M,) from Table 5.2:
b = - (pp VfL) 14! =( })= 3 OM, =, M.) =, Fryta(h P, | , eee pets} |=540 k-in
¢, = 0.90
127
Solve for the required end-plate thickness, t,:
1/2
540/(g, F.)
where s and p, are:
s= > vbe8 = + ¥6(2.75) = 2.03 in.
Pt = pet te= 1.375 + 0.25 = 1.625 mm.
1/2
t= 540/(0.90(50)) ~ 0369 in.
P (16 — 1.625) S( 4 | 4 2 (1.375 + 2.03) 2\1.375 2.03/ 2.75
Try t, = 3/8 in.
3.) Try d, = 3/4 im. Calculate 6,M, from Table 5.2:
$,[2(P,~ Qin) i] nor #rMq= ¢,[2(Te) 44 |
q=
max
where T,, is the pretension load, specified in Table J3.1, AISC (1986), as 28
kips for 3/4 in. diameter A325 bolts. P, is:
2 2
P, = ms (F,,) = 20>" (00) = 39.76 k
and Qmax from Table 5.1 is:
128
where
3 3 t
a= 3.680{ ©] — 0.085 = 3.682( 2375) — 0.085 = 0.375in.
b
0.375
w = b/2 - (dy + 1/16) = 6.0/2 - (3/4 + 1/16) = 2.1875 in.
2 3 Pe tp Foy (0.85 be/ 2+ 0.80 w) + 7dpFypy/8
Apr
_ (0.375)7(50)(0.85(6.0 / 2) + 0.80(2. 1875)) + 7(0.75)°(90)/8
- 4(1.375) = 821k
Therefore,
Qo. = (2.1875)(0.375)° | (50)? - { 8.21 962k 4(0.375) (2.1875)(0.375)
(P: - Qmax) = 39.76 - 9.62 = 30.14 k > T, = 28k
resulting in:
o,M, = 0.75[2(39.76 - 9.62)(14.25)] = 644 k-in
4.) Compare o,M, with M,:
o,M, = 644 k-in > M, = 540 k-in OK
Summary For the given loading, materials and geometry, use 3/8 in. thick
A572 Gr. 50 end-plate material, and 3/4 in. diameter A325 bolts.
The final design example summary is as follows:
129
Final Design Summary
Design Procedure J
End Plate: A572 Gr 50 tp = 1/2 in.
Bolts: A325 d, = 5/8 in.
Design Procedure 2
End Plate: A572 Gr 50 tp = 3/8 in.
Bolts: A325 d, = 3/4 in.
5.4.2 Multiple Row Extended Unstiffened 1/3 Moment End-Plate Connection
Determine the required end-plate thickness and bolt diameter for an end-plate
connection with the geometry shown in Figure 5.2 and an ultimate factored moment of
12,000 k-in. The end-plate material is A572 Gr 50 and the bolts are A325.
Design Procedure 1:
1.) M, was given as 12,000 k-in. Therefore:
6M, = M, = 12,000 k-in
2.) Divide @M, by 0.90 and set it equal to 6yM,: from Table 5.10 for
Mechanisms I and I m the yield-line analysis:
gM, _ 12000 = 13,333 k—in
0.90 0.90
Mechanism I:
130
& |
® ® | Pext Pry
Ps ele Py
ef @ |—/ Pus P,
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h
—- t
‘_——
ele
ez ai?
Parameter Value (in.)
h 62
be 10
tr 1
ty 3/8
Pei 4 P£o 2 3/8
Pext 4 1/4
g 41/2
Figure 5.2 Design Example--Multiple Row Extended Unstiffened 1/3 Moment End-Plate Connection
13]
be} 1 bh | bp; | bps h-P; dy My = $y Foyt? Meh, B top BoP +ApPeit+Pp13+U = 13,333 k~m yeh Py PP D2” eo Pej u Apri+Pois 2
Solve for the required end-plate thickness, t,:
1/2
13333/(¢,(50) - oy) | tft, h + h— py + bP) +2(peit Poi 3t uf =P)
2\2 Pro P£i u g
where
Pt=pe+te=4+1=5 m.
Pb1,3 = 2Pb = 2(3.5) = 7 in.
Pa =pPrt+ por3=5+7= 12 m.
bea( MPa | -i 10(45) - 2) = 3141 in.
Substituting into the plate thickness expression:
1/2
lias i aay) = 0679in (2. +—— + )+2(44 7+ 344i) 25) 2\2 2375 4 3141 45
Mechanism IT:
dy Mp = by Foal (3 tee Pa +2 (P43 + Pora}ih- te)+ 2 (h- pa) 13,333 k—in
$y = 0.90
Solve for the required end-plate thickness, t,:
132
3.)
1/2
13333/(¢y Foy)
p te! h bp, hPa 2 2u g | = + + 2 + 8 + = (pei + ppi3)(b- te) + —(b- Pi3)+ 5 2\2 Pro Péi u z . ) g 2
where
p:=5 mn. Pvi3 = 7 mM. Ps = 12 wn.
calculated earlier, and u is:
1 1 . u= a vbr = 3 10(4.5) = 3.354 in.
Substituting into the plate thickness expression:
1/2
_ 13333/(0.90(50))
- 19(2 62 62-5 62-12 —| = + —— + ——
2 2375 4 3354
= 0.629 in.
2 _ 2(3354) | 4.5 }+ Larner 1+ (62 -12)+ ,
Choose the larger required end-plate thickness calculated from Mechanism I
and Mechanism II:
t t, Mechanism!
P t, Mechanism II
0.679 in. . . t_= _ =0.679 in. (MechanismI governs) Fax | 0-629 in.
Try tp, = 11/16 m.
Compute the required bolt proof load, P,, by equating ¢M, to 6,M,, using
Table 5.10:
OM, = O;Mop = 0,[2(P:)(di + dz + d3 + dg)} = 12,000 k-in ob, = 0.75
where
133
d, = h+Pfo = 62+2.375 = 64.375 in.
tr 1 . d, =h-p,—-— = 62-—5-—— = 56.5 in. 2 Pr 7 7
d3 = do—-Ppp = 56.5-—3.5 = 53.0 in.
d, = d3-Pp = 53-3.5 = 49.5 in.
Solving for P, results in:
Pp = 12000 _ 12000 358K * $,2Xd}+do+d3+d4) 0.75(2)(64.375+ 56545304495)
4.) Solve for the required bolt diameter, d,, by:
2
P= = (Fe) = 358k Fy, = 90 ksi (AISC, 1986)
dy = jth = [4G°8) - 0712 in. mF yp (90)
Try dy = 3/4 in.
5.) Check that M,, < 0.90M,; with tp = 11/16 in. and d, = 3/4 in.:
M np = 2(P, Kd, + d5+ d3+d,)
where
2 2
P, = 7% (F,) = 20>” (00) = 398 k
M np = 2(39.8)64.375 + 56.5 + 53.0 + 49.5) = 17,780 k- in
134
be(1 h h-p, a) h-p M, = F t2 M(t + + +apritppi3t+u P Py | a\2 P£o Pri u 2 fi g
_ - 62-5 = sxose5?| | p02, 0279, 2 2) +24+7 sais 25) —+ +
2 2375 4 3141 45
= 15,175 k-in (Mechanism 1)
0.90M 0.90(15,175) = 13,658 k—- in < Mppy = 17,780 k-in NG pl ~
It is therefore necessary to increase the plate thickness until 0.90M,) > Map.
Try t, = 13/16 in.
befl oh hp, he h-p Migs (L + Pty P| sHonitpuist 2)
2 Pfo P£i u
-5 62- 62-5 ~swos125?| (5+ 62,2? , 8 2) (44743141 2 )
2\2°2375° #4 ~~ 3141
=21195k-in (Mechanism I)
0.90 M yj = 0.90(21195) = 19,076 k—in > Myy = 17,780 k- in OK
Summary For the given loading, materials and geometry, use 13/16 im. thick
A572 Gr. 50 end-plate material, and 3/4 in. diameter A325 bolts.
Design Procedure 2:
1.) My was given as 12,000 k-ft. Therefore:
oM, = M, = 12,000 k-in
2.) Set @M, equal to o,M,: from Table 5.10 for Mechanisms I and II in the yield-
line analysis:
Mechanism I:
135
bef 1 bh bp, bp 3 h-pr dy Mpi =y Foyt M(t, m boPe trPe +APei+Po1st¥ = 12,000 kin y pl = fy “py'P 2 Pty Pei u 2 a g
Solve for the required end-plate thickness, t,:
1/2
12000/(¢,(50)
Pl be(1, bh bp mae , h- Pr belt Pre + Pri + 7 }+2(eci4 Pbi3+ a 3
where p;, Pvi3, and py are the same as for Design Procedure I:
P=pett=4+1=5in.
Poi3 = 2pp = 2(3.5) = 7 m.
Po =Prt+ po3=5+7= 12m.
and u is:
u= ; bre BPD) = 4 rocas( 2=22) = 3141 in.
1/2
7 12000/(0.90(50)) - 0644 in
2
t.= Pp _ _ _
o(d 62 + 62 5 62 12) ofa 7+ 3141) 2 *) 2 2375 4 3141 45
Mechanism IT:
b, (1 h h-p, h-p 2 2u zg . M, =¢,F,t?) ©] — + — +—<t + 22 4+ -{p,.+ h-t,)+ —(h- + =] =12,000 k- in ¢, My = ¢,F, | 2 (3 P,. Pai a 5 (Pas Pris ‘) Z (h- p.s} 2
$, = 0.90
Solve for the required end-plate thickness, t,:
136
1/2
12000/(¢, Foy ) (3 h hp, pa 2 2u g bef By BoP PP | 2G para hte)+ 2B (b- pis)+®
2 Pro PEi u a ° X g 2
where u is:
u= 2b; =5 10(4.5) = 3.354 in.
/2
12000/(0.90(50
tp = 10/1 62 62-5 62-12 A ey) 2(3354 4.5 = 0.598 in. 10(2 a4 A ) +2 (447962 ~1) + 2G359) (62-12) +48 2\2 2375 4 3.354 4.5 45 2
Choose the larger required end-plate thickness calculated from Mechanism I
and Mechanism II:
t, Mechanism I
t_=
P xl tp Mechanism II
0.644 in. ; = . =0.644in. (Mechanism] governs) Px | 0-998 in.
Try tp = 11/16 in,
3.) Try d,=7/8 in. Calculate 6,M, from Table 5.10:
é,[2(P- Qmax,o (41) + 2(Pr- Qmax,iXd2+ 44) + 2(Tp )43|
é,[2(P- Qmax,o (41) + 2(Tp )(d2 + 43+ d,)]
b;[2(P- Qmax,i (42+ d4)+ 2(Tp \(dy+ d3)|
,[2(Tp )(di+ d2+ 3+ d4)|
o, = 0.75
where T, is the pretension load, specified in Table J3.1, AISC (1986), as 39
kips for 7/8 inch diameter A325 bolts, and P, is calculated as:
137
2 2
P, = = (Fy) = Fn” (00) = 541k
The inner prying force, Qmaxi, is calculated from Table 5.10:
where
3 t
aj = 3682{ 2) — 0.085 = 3.682 287° b
3
— 0.085 = L701in.
W = by2 - (dy + 1/16) = 10/2 - (7/8 + 1/16) = 4.0625 in.
2 _ thE py(0.85b¢/2+0.80w) +2 dpFyp/ 8 1 —_
Apri
_ (0.6875)*(50)(0.85(10 /2)+ 0.80(4.0625)) + (0.875)? (90)/8
4(4) = 12.56 k
Therefore,
2 2 Ono = (4.0625) 0.6875) (50)? - { 12.56 1394 k
, 4(1701) (4.0625) 0.6875)
(P, - Qmaxi) = (54.1 - 13.94) = 40.18 k > T, = 39 k
The outer prying force, Qmax,o, is calculated from Table 5.10:
where
138
3 3 t
.
s602{ 2 — 0.085 = 3 682( 29875 ) — 0.085 =1.701in.| _ 199) in dp 0.875 =] .
mnin| POxt™ Pho = 4.25 ~ 2.375 = 1.875 in.
ag=
2 3 _ tpFpy(0.85bs/2+0.80w) + 7 dpFyp/ 8
° 4Pro
_ (0.6875)*(50)(0.85(10 / 2) + 0.80(4.0625)) + 2(0.875)°(90)/ 8 - 4(2.375)
=2115k
Therefore,
2 2 One o = (4.0625)(0.6875) (50)? - 2115 ) 1362 k
4(1701) (4.0625) 0.6875)
(P, - Qmaxo) = (54.1 - 13.62) = 40.50 k > T, = 39k
The calculation of ,M, is therefore:
?, M, = o,{2(P, ~~ Qinax,o)(41) + 2(P, ~ Qinax,i (42+ d4) + 2(Tp)ds|
= 0.75[2 541 -13.62)( 64375) + 2(54.1—13.94)(565+49.5) + 2 39)(53.0)|
= 13,400 k-in
4.) Compare $,M, with M,:
6,M, = 13,400 k-in > My = 12,000 k-in OK
Summary For the given loading, materials and geometry, use 11/16 in. thick
A572 Gr. 50 end-plate material, and 7/8 in. diameter A325 bolts.
The final design example summary is as follows:
139
Final Design Summary
Design Procedure 1
End Plate: A572 Gr 50 tp = 13/16 in.
Bolts: A325 d, = 3/4 in.
Design Procedure 2
End Plate: A572 Gr 50 tp = 11/16 m.
Bolts: A325 d, = 7/8 in.
140
REFERENCES
Abel, M. S. and T. M. Murray (1992a), “Multiple Row, Extended Unstiffened End-Plate Connection Tests,” Research Report CE/VPI-ST-92/04, Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA,
August 1992.
Abel, M. S. and T. M. Murray (1992b), “Analytical and Experimental Investigation of the Extended Unstiffened Moment End-Plate Connection with Four Bolts at the Beam
Tension Flange,” Research Report CE/VPI-ST-93/08, Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, December 1992, Revised October 1994.
AISC (1986), “Load and Resistance Factor Design Specification for Structural Steel Buildings,” First Edition, American Institute of Steel Construction, Chicago, IL,
1986.
AISC (1989), “Specification for Structural Steel Buildings,” Ninth Edition, American
Institute of Steel Construction, Chicago, IL, 1989.
Bond, D. E. and T. M. Murray (1989), “Analytical and Experimental Investigation of a
Flush Moment End-Plate Connection with Six Bolts at the Tension Flange,”
Research Report CE/VPI-ST-89/10, Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, December 1989.
Borgsmiller, J. T., E. A. Sumner and T. M. Murray (1995), “Tests of Extended Moment
End-Plate Connections Having Large Inner Pitch Distances,” Research Report
CE/VPI-ST-95/01, Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, March 1995.
Hendrick, D., A. R. Kukreti and T. M. Murray (1984), “Analytical and Experimental
Investigation of Stiffened Flush End-Plate Connections with Four Boits at the
Tension Flange,” Research Report FSEL/MBMA 84-02, Fears Structural Engineermg Laboratory, University of Oklahoma, Norman, OK, September 1984.
Hendrick, D., A. R. Kukreti and T. M. Murray (1985), “Unification of Flush End-Plate
Design Procedures,” Research Report FSEL/MBMA 85-01, Fears Structural
Engineering Laboratory, University of Oklahoma, Norman, OK, March 1985.
14]
Kennedy, N. A., S. Vinnakota and A. N. Sherbourne (1981), “The Split-Tee Analogy in
Bolted Splices and Beam-Column Connections,” Joints in Structural Steelwork,
John Wiley & Sons, London-Toronto, 1981, pp. 2.138-2.157.
Morrison, S. J., A. Astaneh-Asl and T. M. Murray (1985), “Analytical and Experimental
Investigation of the Extended Stiffened Moment End-Plate Connection with Four
Bolts at the Beam Tension Flange,” Research Report FSEL/MBMA 85-05, Fears
Structural Engineering Laboratory, University of Oklahoma, Norman, OK,
December 1985.
Morrison, S. J., A. Astaneh-Asl and T. M. Murray (1986), “Analytical and Experimental
Investigation of the Multiple Row Extended Moment End-Plate Connection with
Eight Bolts at the Beam Tension Flange,” Research Report FS<EL/MBMA 86-01,
Fears Structural Engineering Laboratory, University of Oklahoma, Norman, OK,
May 1986.
Rodkey, R. W. and T. M. Murray (1993), “Eight-Bolt Extended Unstiffened End-Plate Connection Test,” Research Report CE/VPI-ST-93/10, Department of Crvil
Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA,
December 1993.
SEI (1984), “Multiple Row, Extended End-Plate Connection Tests,” Research Report,
Structural Engineers, Inc., Norman, OK, December 1984.
Srouji, R., A. R. Kukreti and T. M. Murray (1983a), “Strength of Two Tension Bolt Flush
End-Plate Connections,” Research Report FSEL/MBMA 83-03, Fears Structural Engineering Laboratory, University of Oklahoma, Norman, OK, July 1983.
Srouji, R., A. R. Kukreti and T. M. Murray (1983b), “Yield-Line Analysis of End-Plate Connections with Bolt Force Predictions,” Research Report FSEL/MBMA 83-05,
Fears Structural Engineering Laboratory, University of Oklahoma, Norman, OK,
December 1983.
Srouji, R., A. R. Kukreti and T. M. Murray (1984), “Yield-Line Analysis of End-Plate
Connections with Bolt Force Predictions -- Addendum,” Research Report
FSEL/MBMA 83-05A, Fears Structural Engineering Laboratory, University of
Oklahoma, Norman, OK, August 1984.
142
APPENDIX A
NOMENCLATURE
143
aj
Ao
B;
B2
By
br
di
qd,
dz
NOMENCLATURE
nominal bolt area
distance from the bolt centerline to the prying force
distance from the interior bolt centerline to the inner prying force
distance from the outer bolt centerline to the outer prying force
bolt force
exterior bolt force in multiple row extended end-plate configurations
first interior bolt force in multiple row extended end-plate configurations
second interior bolt force m multiple row extended end-plate
configurations
third interior bolt force in multiple row extended end-plate configurations
beam flange width
distance from a bolt line to the center of the beam compression flange
nominal bolt diameter
end-plate extension beyond the exterior bolt centerline
Pext - P£o
distance from the interior bolt centerline to the center of the beam
compression flange in four-bolt extended end-plate configurations
distance from the outer bolt centerline to the center of the beam
compression flange in four-bolt extended end-plate configurations
distance from the center of the beam compression flange to the farthest
load-carrying bolt line
distance from the center of the beam compression flange to the second
farthest load-carrying bolt line
144
ds
F'
F;
F,
hy
distance from the center of the beam compression flange to the third
farthest load-carrying bolt line
distance from the center of the beam compression flange to the fourth
farthest load-carrying bolt line
applied force
beam flange force
end-plate material yield stress
nominal tensile strength for A325 bolts (Table J3.2; AISC, 1986)
90 ksi
flange force per bolt at the thin plate limit
flange force per bolt at the thin plate limit when calculating Q,,x, for end-
plate configurations with large mner pitch distances
flange force per bolt at the thin plate limit when calculating Qnax.. for end-
plate configurations with large inner pitch distances
bolt gage
total beam depth
distance from the inner edge of the stiffener to outer edge of the
compression flange in four-bolt flush configurations stiffened outside the
tension bolt rows
h - pr - Ps
length of yield line n
x-component of the length of yield line n
y-component of the length of yield line n
applied moment
bolt moment capacity
connection failure moment
M, or M,
nominal connection resistance
145
Mu bot =
M
Mi
M2
Tpy
Po
Pb1,3
connection strength for the limit state of bolt fracture with no prying action
connection strength for the limit state of end-plate yielding
predicted strength of the connection
connection strength for the limit state of bolt fracture with prying action
maximum applied moment in laboratory test
required strength of the connection, AISC (1986)
moment at which bolt force reaches its proof load, P,
working moment
experimental yield moment, obtained from the plot of end-plate separation
vs. applied moment via two intersecting lmes
plastic moment at the first plate hinge line
plastic moment at the second plate hinge line
plastic moment capacity per unit length of the end-plate
(Fpytp’/4 x-component of the plastic moment capacity per unit length of the end-
plate
y-component of the plastic moment capacity per unit length of the end-
plate
total number of yield lines in a mechanism
total number of bolt rows in the connection
number of load-carrying bolt rows in the connection
number of non-load-carrying bolt rows in the connection
bolt material ultimate tensile load capacity, proof load
ApF yp
distance from bolt centerline to bolt centerline
distance from the first interior bolt centerline to the mnermost interior bolt
centerline in configurations with three interior bolt rows
2Po
146
Pext
Pr
Pei
P£o
Ps
Pr2
Ps
Qrax
Qinax.i
Qinax.o —
Tp
tr
tw
ty
end-plate extension beyond the exterior face of the beam tension flange
distance from the bolt centerline adjacent the beam tension flange to the
near face of the beam tension flange
distance from the first interior bolt centerline to the inner face of the beam
tension flange
distance from the outer bolt centerline to the outer face of the beam tension
flange
distance from the bolt centerline to the near face of the stiffener in four-bolt
flush stiffened configurations
distance from the first interior bolt centerline to the far face of the beam
tension flange
te + Pei
distance from the second interior bolt centerline to the far face of the beam
tension flange
Pit Po
distance from the innermost interior bolt centerline to the far face of the
beam tension flange
Pt + poi3
prying force
maximum possible prying force
maximum possible prying force for mterior bolts
maximum possible prying force for outer bolts
distance from the innermost bolt centerline to the innermost yield line
specified pretension load in high strength bolts, Table J3.1, AISC (1986)
beam flange thickness
end-plate thickness
beam web thickness
Kennedy thick plate limit
147
‘1
uy
U2
RQ c¢-
&:-
WD
“i
= cD
2
Dm aA
Kennedy thin plate limit
distance from the innermost bolt centerline to the innermost yield line
distance from the innermost bolt centerline to the innermost yield line for
Mechanism I
distance from the innermost bolt centerline to the innermost yield line for
Mechanism II
external work
M.,(1/h)
total internal energy stored in a yield-line mechanism
internal energy stored in a single yield line
width of end-plate per bolt minus the bolt hole diameter
b/2 - (d, + 1/16)
outer end-plate factor used in past studies
inner end-plate factor used in past studies
resistance factor
resistance factor for bolt rupture
0.75
resistance factor for end-plate yield
0.90
pi
relative normal plate rotation on yield-line n
x-component of the relative normal plate rotation on yield-lne n
y-component of the relative normal plate rotation on yield-line n
148
APPENDIX B
TWO-BOLT FLUSH UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS
149
-— Py : / ‘ P,
«|»
oH t h WwW
|S
@ @
L
Lt
Yield-Line Mechanism for Two-Bolt Flush
Unstiffened Moment End-Plates
(after Srouji ef al. , 1983b)
150
ZZ nn 2(P, —Q ax)
Simplified Bolt Force Model for Two-Bolt Flush
Unstiffened Moment End-Plates
151
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154
APPENDIX C
FOUR-BOLT FLUSH UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS
155
Yield-Line Mechanism for Four-Bolt Flush
Unstiffened Moment End-Plates
(after Srouji et al. , 1983b)
156
{— Possible stiffener locations
i | ; i
2(P, ~Q inax)
> 2(P, -Q max?
Simplified Bolt Force Model for Four-Bolt Flush
Unstiffened and Stiffened Moment End-Plates
157
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wMo9gOT =n
mM ¢
= qd W
SE =3
‘WH |
=jd mSsLe0
8 =h
‘mM $70
=f m9
=jq WL
Of =
91-8/E-b/E-7A
(861 “IE861)
72 12 NOUS
£60" ze"
AS
SU YL
$8
-W/paldy VA
TTT
bw >
vi
PA
WATT
UA O8ET
sdry 96'9
sdry O€ TI
WH 9001
MH SL8T%
STE
LI
WH ST
bl
(21481) SY
0'06
sary 8°6€
sdry 37
mw ¢oL0
(pamseaul)
sy g'7¢
WH 9€07
we
mse
ws
moO
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m9
wWol
= [4060
91-U/ l-b/e-Ca
(861 “G€861)
72 32
ITNOUS
GL
> (xB)
- 1g) ~ »
P60" PELE
°° eT
r7'l WA
OL = AW
-WyPardyy WA
p9€l = poldy]
ey —
= vi
= 14060
bw >
WA Pel
= 1d
WA LE61
=bw
* sdry
pb'Z1 = xeul)
sdr] 91°6
=
“W SLE‘
=e W
SL817 =,
Ul $761
=P
UW SU
=1P (2148)
ISy 0°06
=q4q sary
8°6€ =
sdry 87
= UW
$10 =
(pamseoul) sy
['p9 = Ady
"WH 068'1
=n We
¢ = qd
UW CL Z
=3 TH
CLE =jd
WH SLEO
=h ‘WM
S70 =f
m9
=jq WH
PZ =q
bO-S/E-b/E-TA
(p86l “IE861)
“7 72 NOUS
159
APPENDIX D
FOUR-BOLT FLUSH STIFFENED MOMENT
END-PLATE TEST CALCULATIONS
160
f
he ~~ T , y ‘
Pp t é \. Pp f p t é ‘ Pp f
Pra] p eo } ©& Pre @ ® s - . o wh at
= Ps NE AY Pp Ps | re i BHU?
e e @ SHE? » ‘ ‘ / sy Send” BP, \ Hi i S “A H hd
\ ie
h h
_H t A t h Ww 1 Ww t
t H—5 t. —+— p Pp
® ® ® | ®@
_L _|_L
LL. t L t f f
Stiffener Between the Stiffener Outside the
Tension Bolt Rows Tension Bolt Rows
Yield-Line Mechanisms for Four-Bolt Flush
Stiffened Moment End-Plate
(after Hendrick ef al. , 1985)
16]
{ Possible stiffener locations
t-Z 2(P, —Qinax)
Zy—+—— 2(P, ~Q
max?
pr----------4
Lone. +4
Simplified Bolt Force Model for Four-Bolt Flush
Unstiffened and Stiffened Moment End-Plates
162
FA TL
WA PL
UA 6'6ET
QI > (XPD
- 1d) — »
bW
>
oe
WA
WA G6EL
UA 1961
sdry 3301
sdry gr'9
WH EPpe 0
MH SL8T%
64881
TH SL8'1Z
(21421) ISX
0°06
sdry 36
sdry 37
‘W SL0
(pemseant) Is}
73°7S
“UW 8077
we
UW Sve
WoL
UW oZe'l
“ul 99€'0
wWSz0
mg
“Hl pz
= [4060
bo-8/E-b/e- TE
($861) “2
14 YOAGNAH
‘FOr PRP
PL
= ny
1o'l WA
PL = AW
“W/peldy UA
6 PL = paidy]
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= du
ey —
= 14060 by
> WA
6 PL = dn
UA ZI
= byw
sdry €9'01
= XeUd) sdry
078 =
"H 06€'0
=B WCL8LZ
= (MN M
STL IL
= 7p
WoZlrl
=IP (21981)
Sq 0°06
= qs
sdry 8°6€
= sdry
87 =
WE ¢L°0
= (pamseout)
sy gpc¢
= Ady WH
1677 =sd
WH €
= qd um
¢'€ =
S| =jd
MW 6568
=
WH 6LE0
=
TH S70
=f m9
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9] =q
91-8/€-b/t-7OA
(861) 72
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POT
WPT BUS
= ny
rll WA
$8 = AW
“Wyperdy UI
696 = poldyy
wy —
= day]
wy —
= 14060
bw >
WA 6°96
= [dw WA
YZ
= bw
sdy ¢9'01
= XE)
sdry 078
=
“Ul 06€'0
=e wWoLglt
= Mh
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=e
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(2198) Sq
0°06 = qq
sdry 8'6€
= sdry
87 =QL
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= (pemseoul)
sy gP'os
= Ady
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= Ww
¢ =qd
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=h W
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91-8/t-b/€-THA
(861) 72
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163
98°0 98°0
WA 80!
UA 801
= TE
= AW
QL > (
XBWIQ)
- 1d) — «
L6'0 wigs
SA
£60 WA
$8 = AW
“Wypaidyy VA
778 = poidyy
tS =
vA = 141060
bw >
WA U7
= 1d WA
6°56 = by
sdry 109
= sdry
90°8 =a
"Cl 6bL'0
=e WStTIET
=m McLetL
= WH
S@rl =
IP (21981) IS
0°06 = 444
sdry 9°47
= sdry
61 =
WH $79'0
= (pemseaut)
sy 6'¢¢
= Ady W
1€07 =sd
Hl S181
= qd HSL
= Wl
SLE =jd
Ww é6sr0l
=
UW 18€0
= h MH
$70 =f
"at 9
=Jq WH
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91-8/£-8/S-TOA
(861)
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LT
= peidyy
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br
<
VA Sstl
UA TIOL
VAETIL
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sdry 10°9
sd 90'8
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Well
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(214®1) IST
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mH Stl
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wg
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=14~W06'0
91°8/€-8/S-7EA
(6861) ‘72
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= =—- = AW
860 WA
OL = sW
-W/perdyy WA
OLOL = par
wey —
= day
eI = 14060
by >
WA OLOL
= dy VA
1961 = bw
sdry 8301
= sdr
gp°9 =
"Wl €PE0
=8 Welt
= M
‘WCL88l =P
McLgI%
=IP (219421)
IS¥ 0°06
= qaj sdr]
8°6€ =
sdry gz
=Q1 ‘mM
$L0 =
(pamsvout) sy
78°77 = Ad
‘WH 3077
=sd ‘WE
=qd UW
CTE =
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=jd WO6L9I
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S70 =f)
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PT-8/€-b/E-TOF (p861)
“7? 12 YOMYGNAH
164
GI. > (xBMD
- 1d)
— »
80 0
$80 —
WA bse
WA Ost
“Stpy
ET-UIl-b/E-TOF (86D)
72 1? YORIGNAH
680 PA
LOZ =n
w6°0 UA
007 = AW
“W/poidyy WA
ZEST = pordyy
eA —
= ve
—
= 14(~06'0 bw
> UA
TEI = [dw
WA OTIZ
= by
sdry OP'9
= XEUI) sdry
L€°6 =
W ZS0'1
= WsLgle
=m WSZISLL
= wWSz79S 0%
== IP
(219481) ISX 0°06
= qq sdry
8°6€ =
sdry 37
= H
SL'0 =
(pomsvout) sy
L0°0¢ = Adj
“Wt 8077
=sd WE
=qd Ul
SUE =
WH C181
=jd WMewsst
=
mW L060
=h Ul
LEO =f
m9
=jq
‘Wl €Z
=q
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OTT
= pod]
IFIN06'0 <
byw <
WA VS
VA L9IZ
VA 8 0b7
WA OT
sdry Or'9
sdry 1£°6
TH 701
TH CL8L%
UW SZ9S LI
“Ul $795
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sy 0'06
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sdry 87
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(pamseaut) sx
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8077
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WSTe
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“uw 20S'0
WH SLE0
‘ua 9
‘HH £2
€t-U/l-b/E- THA (p861)
“7? 72 YORIGNAH
= duyj
= [4N06'0 = 1d =
byw
165
APPENDIX E
SIX-BOLT FLUSH UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS
166
h
we QO
QQ Fu
on |
A, ~
2--@:@ :
”
wore
° wsa
~
oh =
=< =<
oro
<< =
aN ee
“
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oe oO
| Ou
a
a
~
o ~
on
&
HH Q
a
on
l QP.
on
a
T ' ‘ 4 4
oo
uo ee
mse +
Rwy Seeeees eee
SSS
SS
oe
ee ee
SS
SS
st =
So
“s ~
eee
et
+
A,
Mechanism II
Yield-Line Mechanisms for Six-Bolt Flush
Mechanism I
Unstiffened Moment End-Plate
(after Bond and Murray, 1989)
167
“| Li 2(P —Qinax)
7 ZZ oly
ZA — 2(P, —Qinax?
Mg S ;
WZ.
Simplified Bolt Force Model for Six-Bolt Flush
Unstiffened Moment End-Plates
168
QJ.
> (XBWID
- 1d) —
+
850 WA
S9E = ny
960 BA
Ove. AWE
“W/Peidyy WA
TZ
= pal
vA —
= day
vA = 14/060
bw >
UA TLZ
= 1d
WA 6 ler
= bw
k sdry
3°71 = Xen)
sdry 67'9
=
"Wt LS€0
=e WM
SLEIT =
WELEST
= wmESsOg
= wWEeceee
=IP (91981)
ISX 0°06
= qhy sdry
8°6€ =i
sdry 82
=q1 HI
$10 = qp
(pamsveut) sy
1°79 = Ady
WH LIT
=7n W
8r6'l =[n
WH 862
= eid
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=qd W167
=8 WI
90% = jd
‘mt 1€0
=h W
8L€°0 =f
ag
=Jq "Hl
96'SE =4
9£€-8/€-b/€-N (6861)
AVWANAW GNV
GNOd
80
WA 66€
=n
TRL.
Wt 08%
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-Wypaidyy WI
COE = pod
vA =
vA —
= 14060
bw > UA
EOE = [dW
UA E88
= by
* sdry
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sdry 15°07
=f
‘W 1860
=e WCLE6E
8 8==
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= Wl
L0°€Z =
Wh LS°SZ
= Ip
(91921) IS
0°06 = qty
sary 2°0L
= sdry
1¢ =
‘uw |
= (pemsvout)
sy p9
= Ady ‘Wl
PSl'¢ =7
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= jn
Wl OTL
= gid
WM ¢%
=qd ‘W
86'€ =
“Ul 88'l
=jd W
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WH 8€0
=f ‘Wt
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=q
82-2/I-1-daN (6861)
AVUUNA UNV
GNOd
8r'0 WH
SIE =n
oO. ff
3 WASsl
. = AW
“WP WA
UPL = por
vA —
= doy eA
—
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WA LPL!
= Id WA
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* sdry
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sdry ger
=
M0070 =e
WoLLOb ==
mM 90607
=€P ‘mM
90pEu =
= @P mM
906S% =
= IP
(21981) ISX
0:06 = hy
sdry ips
=1d sdry
6£ =4QL
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(pemsvsut) sy
¢°9¢ = Adj
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=
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[0 Wl
9189 =
gid mW
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ppl =jd
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=h Ml
9LE0 =f
‘m@ £00!
=J4 WH
16LZ =q
87-8/€-8/L-TAN
(686 AVAANW
AGNV GNOd
169
GL
> (XBUY
- 1g) — »
660.27. WH
OLE = ny
10'l UA
SSE = AI
-W/poldy] UA
O'BSE = pod
we =
wa —
= 14060 bW
> UA
O'BSE = 1d
VA O1P9
=byw
sdry 877]
= sdry
O€'rl =A
"Ml 865°0
=e Ww
Sfp0% =
WM CISssz
=EP MW
SISel€e =
‘Mm SISsee
=IP (21981)
IS¥ 0°06
= q4q
sdry [ps
= sdry
6¢ =
‘Wt £480
= (pemsvaut)
sy ¢°79
= Adj W
6LTT =7
‘Wt SOlz
=n
Wl 6769
= ¢1d
‘Ww SZ
=qd WH
8P'€ =
WS
= jd Wl
66b'0 =
‘Wl 6LE0
=f We
L6¢ =3jq
Wl L6'SE
=q
G9E-2/1-8/L- TaN
(6861) AVAYNW
AGNV CNOd
6L0 UA
6S = ny
wt
“A
SSE / om
AYT
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O79E = pel
wy —
= day]
eA —
= 14060
bw >
UA OIE
= [dQ
WA €6r9
= bw
sdry go ll
= sdry
99'r 1 =
“Wt 9€9'0
=e ms79m07
3
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‘MH $868'8%
= EP
WH Ss6el€
=7P mw
cg6see =IP
(2191) ISX
0°06 = qa
sary Ips
=Id sdr
6€ =4qL
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= (pamseaut)
sy p'09
= Ady
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=m
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1069 =
gid
WH SZ
= qd ‘Wh
SPE =
Ww Z'l
=jd ‘tt
8090 =
‘WH L8€0
= ‘m9
=jq ‘Wl
66°SE =q
9€-27/1-8/L- TaN
(6861) AVAUNIN GNV GNOd
170
APPENDIX F
FOUR-BOLT EXTENDED UNSTIFFENED MOMENT
END-PLATE TEST CALCULATIONS
17]
+
Pr 0
i % i 4
Faia i \
Py fw Pri / ‘
/ \
ele ‘ i
‘ / s ry , /
% i
t h WwW
t -—S P
|
Yield-Line Mechanism for Four-Bolt Extended
Unstiffened Moment End-Plates
(after Srouji et al. , 1983b)
172
ext
Possible stiffener location TT a
2(P, —Q max.o)
ZZ a 2(Pr —@ maxi )
Simplified Bolt Force Model for Four-Bolt Extended
Unstiffened and Stiffened Moment End-Plates
173
GL
> (Xemd)
- 1d) — »
=n fe
WREESLE 0°}
Cpe AAR
UA SLZ
LO'l WALPIE
=pudy
EANLIZ
=—- = perdyy “WPI
UA 9197
= pordy]
eI =
IGIN106'0 >
UAVL
= 14A06'0
> UA
9197 =
ey —
= 141060 PASI
=I4N060 WA
CBSE = 141060
bw >
UALrIE
=n
bw < wAre7s
= =1dW
bw < WA
C'86E =1dy
WwAsEr
=bw VASs6l
=bW WA
O'E6I = bw
shy %p7%Z
=
= Oxeu)
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9681 =O'xeUd
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say ¢9'61
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sdry 99°¢
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768 = FxXeulg)
say 46%E
2 =O.
sdyog'sp =
= Ou sdry
pe'se =04
say 467
=
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9gsp = hd
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6717 =e
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(pemseou) sdry
6's =
sdry 9¢
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37 =
sdry 87
=qL WSZLI
8 =4P
‘Wl $40
== MH
SLO = qP
(pamsvaut) Isy
Cop = Adq
(pomseour) sy
p'L¢ = Ady
(poemseeul) Isy_
6°99 = Ady
HL
=3 M667
= "Wl
9867 =3
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= ojd ‘CUT
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S71 =ojd
WHS %
= yd W
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WoT
= yd Wb
= pod mM
OZ = xed
WM Serv
= ixed Mogg0
0 =—-=
WS8gzo0 =
‘TH €€9°0
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m™mLs990 8==f
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gl =q
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91-8/L-8/I 1-9€4
8 I-b/E-b/€-0SA 81-8/S-b/£-0SA
(47661) AVANIN CNV THAV
(97661) AVIRINW UNV TSHEV
(47661) AVANT ANV THEV
174
03°" Fl
trl Ca
A
$80 UA
OSEL = AW
“Wy/pes WACWIL
=pady
IGA06'0 <
VAP Osrl
= day
WAL PII
==14WO6'0 bw <
WASP!
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=bN
sd] ge]
= = o'xemgd) sdy
og 9, = Fxemg
say o¢%p
2 =O
sdy ¢gpl
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=f W
SL896% = M
mM 99¢8¢
=IP Wl
£pL'>9 =Op
(21981) ISX
0'06 = hq
sdry £04
=i sdry
1¢ =qL
Wr |
=qp (pomseaut)
Sy €°6¢
= Ady WS
=3
Mosel
=ojd ‘Wy
=yd Wsz7LE
= Wad mM
910 =h
wW9001 =f
‘mM s7908
=J4 mM
cLge9 =4
b9-b/€-[-SSA
(S661) ‘12 19
WA TINSOYOd
BBO
PO PSP
= BN
LOT VA
OL = SW
“W/perdyy WA
SL = poldyy
IF06'0 <
WA 88
= day
WA TW!
= 141060 bw
< WA
£08 = 1d
UWA ZSL
= bw
sdr] 79%
= O'XBUIL) sdry
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sdry 92'9
=O.) sdry
L€°7 =
Tl MOOS 1
=08 mo9OST
8 =r
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= =M
WM UETL
=~ UW
S989LI =OPp
(2198) ISX
0°06 = Qsy
sary LL1
=
sdry ZI
=41 WI
sO = qp
(pomseaut) sy
7'6¢ =
Ady WS
% =3
WSZIET
=ojd Wl
SLE =yd
WM C790
= 1Ked wWgeo
=h W700
2«0=f Wl
¢ =jq
SOL =q
U/l 9L-8/E-*/1-S
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19 WaT
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> (xemMd)
- id) — +
SL0 WI
Cos = ny
Lot ..
UR
OSE = AI
“W/poldyy WA
O'SLE = paldyy
wy —
= day]
ey = 14
060
bw >
WA O'SLE
= 1d WA
69S =bw
sary 68'pZ
= O'XEUIY) sdry
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sdry €¢'€r
= 0] sdry
€S ep =
hd W
OLCOTT
=08 Wl
97Z'[ =e
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= \M TM
Cpz7ZEl =
8==—P WH
SI8s'4l =op
Is¥ S101
= qsq
(pemseaut) sdry
9°pZ1 = id
sdry IL
=qL UW
STL = qp
(pemseout) sy
¢'9p =
Ady m9
=3
mz
=ojd WZ
= yd
“Ul SLE'E
= yxod "Wl
9880 =
‘Wl 169°0
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SZ 01 =Jjq
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=Y
9I-8/L-b/1 1-9€0
(42661) AVN
UNV TadV
175
APPENDIX G
FOUR-BOLT EXTENDED STIFFENED MOMENT
END-PLATE TEST CALCULATIONS
176
Case 1, when s < d,
f
-— f MN
Ss y ‘\ d e
/ . @ ® Poxt
Pp f s, ” ° Py
== Z P; . - ” — Py
@ }; © 3S ‘\ f
\ /
h i
t Ww
—+—
@ @
LL
Ly
Yield-Line Mechanisms for Four-Bolt Extended
Stiffened Moment End-Plates
(after Srouji et al. , 1983b)
177
by
[-— / \ d
Pel P eo Pad Pp,
Pe a“ sN PE ee 5 \ i
h
Ht w
+S
@ e
LL
Ly
Case 2, when s > d,
ext
Possible stiffener location ’ ’ ‘ ‘ , ‘ CL, ——ee 7 ’ ’
ac , ‘
‘
2(P, —Q max.o)
ZA ———- 2(P, —Q ax. )
Simplified Bolt Force Model for Four-Bolt Extended Unstiffened and Stiffened Moment End-Plates
178
QL > (XB8MQ)
- 1d) — +
$80 WL
TSE2 SR
Wd V7
O81 = AW
-W/Pridyy WA
9661 = paidyy
14060
< WA
OLSZ =
day UA
BL81 = 14060
bw <
WA L807
= 1dy WA
9661 =bw
sdry 668
= O'XEWY) sdr]
668 = FxXenIg)
sdry 79°C 1
=O
sdry 79'S]
=
‘WH 8790
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180
APPENDIX H
MULTIPLE ROW EXTENDED UNSTIFFENED 1/2 MOMENT
END-PLATE TEST CALCULATIONS
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Yield-Line Mechanisms for Multiple Row Extended
Unstiffened 1/2 Moment End-Plate
182
Simplified Bolt Force Model for Multiple Row Extended
Unstiffened 1/2 Moment End-Plates
183
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184
APPENDIX I
MULTIPLE ROW EXTENDED UNSTIFFENED 1/3 MOMENT
END-PLATE TEST CALCULATIONS
185
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Yield-Line Mechanisms for Multiple Row Extended
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186
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AN
(6861) IHS
192
APPENDIX J
MULTIPLE ROW EXTENDED STIFFENED 1/3 MOMENT
END-PLATE TEST CALCULATIONS
193
Pex:
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Case 2, when s > d, Case 1, when s< d,
Yield-Line Mechanism I for Multiple Row Extended Stiffened 1/3 Moment End-Plate
(after SEI, 1984)
194
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é || o-e--6
oo"
\
/
-@::
wey
~
®
ae" SUN
oecr? “ss
| =
ee
—
tes oO
“a Oo
gf 2
° a,
A, —
Case 2, when s > d, Case 1, when s < d,
Yield-Line Mechanism II for Multiple Row Extended
Stiffened 1/3 Moment End-Plate
(after SEI, 1984)
195
Possible stiffener location |
| o Ye 2(Py —Q max.o?
| Zs 2(P, —Q max.i )
7—— GH ——> 27»
Li 2(Py —Q ax )
“a Ss S os no
oC t+
os
ae Yi
Simplified Bolt Force Model for Multiple Row Extended Unstiffened and Stiffened 1/3 Moment End-Plates
196
SEI (1984)
MRES 1/3-1-3/4-62
= 62 in.
= 10 in.
= 1 in. tp= 0.75 in.
pext = 3.375 in. pfi = 1.625 in. pb= 3 in.
pfo = 1.625 in. pt3 = 8.625 in.
= 3.5 in.
Fpy = 49.1 ksi (measured) = 1 in.
= 51 kips
= 70.7 kips
Fyb = 90.0 ksi (table) dl = 63.125 in. d= 55.875 in.
= 58.875 in. d4= 52.875 in.
= 3.9375 in.
ai= 1.468 in.
ao = 1.468 in.
Fi= 36.88 kips
F'o= 36.88 kips Qmax,i = 16.62 kips
Qmax,o = 16.62 kips
Mq= 2050.7 k-ft Mpl = 2311.0 k-ft > Mq
0.90Mpl = 2079.9 k-ft Mnp= 2718.5 k-ft > 0.90Mpl
Mpred = 2050.7 k-ft Mpred/M- My = 1600 k-ft 1.28
ee Mu= 1834 kf fe
* — (Pt- Qmax) <Tb
197
VITA
Jeffrey Thomas Borgsmiller was born in Albuquerque, New Mexico on August 8,
1971. He was raised in Denver, Colorado where he graduated from Northglenn High
School. In May of 1993, he received his Bachelor of Science degree in Civil Engineering
from the University of Colorado at Boulder. He entered the structures graduate program
at Virginia Polytechnic Institute and State University in the Fall of 1993 to pursue a
Master of Science degree in Civil Engineering.
De By
198