I I I I I I I I I I I I I I I I I I 'D I I I

--~ I. \'101 I

I STRESS, STRAI NAND FORC E I DISTRIBUTIONS IN CUSSET I PLATE CONNECTIONS I

Prepared for I American Institute of Steel ConstructIon 400 North Michigan Avenue I Chicago, Illinois 60611 I I by Donald A. Rabern George C. Williams I and Ralph M. Richard ___ I I I of The Department 01 Civil Engineering and Englneerrng Mechanics I THE UNIVERSITY OF ARIZONA Tucson , ArIzona 85721 I RRHOl March, 1983

I 15~5 I 't-, .. mft/li i<~m~ ~c AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC. \ • •i The Wrigley BUilding 1400 North Michigan Avenue 1 Chicago. IllIOOIS 60611-4185 / 312 . 670-2400 rDu"DlD~

February 28, 1983

Dear Employee ~

Enclosed is a draft of the Swrnary Plan Description for the AISC Employees Pension Plan. You will receive the same infornBtion in a printed booklet frem Massachusetts Mutual next m::mth . At the same time you will receive a statement fran Massachusetts Mutual for the year ended December 31, 1982. This statement will reflect not only the trensfer of funds frun your account in the old de fined benefit plan, but also all contributions in your name in the new account during 1982.

If you have any questions after you have reviewed the SUIITT1aty Plan Description please feel free to contact me . l id suggest you wait until you receive your 1982 statement and ask any questions you may have at one time.

Sincerely, ~~~~~~ Richard F. Fox Plan Administrator

Steel STANDS for the future AMERICAN INSTITUTE OF STEEL CONSTRUCTION, INC.

The Wroglev BUilding / 400 Nonh Michigan Avenue / Chicago. illinoIs 60611-4185 /312 • 67()'2400

Steel STANDS for the future 4 I I I I I I I I I I I I I I I I I I 'D I I I

I ACKNOWLEDGMENTS

I This research was funded by a grant from The American I Institute of Steel Construction, and the authors wish to express their gratitude for this financial support . Additionally the I authors wish to express their appreciation to the members of the AISC Committee on Large Framing Connections for their advice I and guidance. I I I I I I I I iii I I I i I I I I I I I I I I I I I I I I I tv I I m I I I I LIST OF ILLUSTRATIONS Figure I Pa~e 1. University of Alberta Test Specimen 2 I 2. Gusset Plate Geometries ...... 5 3. Typical Failure Pattern University of I Alberta Testing . . " ...... 8 4. Framing Angle Behavior in Tension and Compression . . . . " . . .. I 9 5 . Single Shear Bolt-Plate Deformation Curve 12 6. I Weld Force Deformation Cur ve 15 7. I Double Framing Angles . . . . 16 8. Force Defor mation of Framing Angles, I Richar d Curve versus Test Results 17 9. Orthotropic Element Yield Surface 19 10. Tensile Fo r ce-Deformation Curve for I 5 x 5 x 3/8" Framing Angles, 3/4" Diameter Bolt and 1/2" Plate 20 I 11. Compressive Force-Deformation Curve for 5 x 5 x 3/8" Framing Angles , 3/4" Bolt I and 1/2" Plate 21 12. Plotted Yield Surface 22 I 13. Framing Angle Bar Material Property Formulation 24 14. Angle Performance for Stiffness . 25

I 15 . Cantilever Beam Analytical versus Test Results 27 I 16. Diagonal Bracing Connection ...... 29 v I I 0 I

I vi I LIST OF ILLUSTRATIONS (Cont . ) I Figure Page 17 . INELAS Finite Element I-Iodel of Diagonal I Bracing Connection . 30 18. Connection Locations for the 30 0 Gusset and Beam 33 I 0 19. 45 , l/S" Gusset Undistorted and Distorted Geometry 36

0 20. 45 • l/S" Gusset, Effective von Mises Stress Contour I and Surface Plots, 75 kip load...... 37

0 21- 45 , l/S" Gusset, Effective von ~lises Stress Contour I and Surface Plots, 150 kip load 3S 0 22 . 45 , l/S" Gusset, Maximum Shear St ress Contour and I Surface Plots, 150 kip load ...... 40 0 23. 45 , l/S" Beanr-Gusset Undistorted and Distorted I Geometry ...... 41 24. 45°, l/S" Beam-Gusset Effective von Mises Stress I Contour and Surface Plots, 150 kip load .... 42 0 25. 45 , 3/8" Beanr-Gusset Undistorted and Distorted Geometry ...... 44

I 26. 60°, l/S" Gusset Undistorted and Distorted Geometry 45

0 27. 60 , l/S" Gusset Effective von Mises Stress Contour I Plot, 140 kip load ...... 46 o 28. 60 , l/S" Gusset Force and Deflection Distributions, I 140 kip load • . 47 29. 60 °, l/S" Gusset Splice Plate Connection Force and I Deflection Distributions ...... 49 o 30 . 60 , l/S" Gusset Splice Plate Connection Force and I Deflection Resultants Plotted Vertically 50 I I I I vii I LIST OF ILLUSTRATIONS (Cont.) I Figure Page 0 31. 60 , 1/8" Gusset Total Force Distribution ... 51 I 0 32 . 60 , 1/8" Beam-Gusset Undistorted and Dis torted Geometry ...... 52 0 I 33. 60 , 1/8" Beam-Gusset Force Distribution, 140 kip load 53 0 I 34 . 30 , 1/8" Gusset Undistorted and Distorted Geometries ...... 54 o I 35 . 30 , 1/8" Beam-Gusset Undistorted and Distorted Geometries ...... 55 0 I 36 . 45 Gusset , Analytical versus Test Results 57 0 37. 45 Beam-Gusset, Analytical versus Test Results 58 I 38. 60° Gusset, Analytical versus Test Results 59 0 39. 60 Beam-Gusset Analytical versus Test Results 60 I 0 40. 30 Gusset , Analytical versus Test Results 61 0 I 41. 30 Beam-Gusset, Analytical versus Test Results 62 42 . {~hitmore Gusset Plate and Stress Distributions 64

I 43. Whitmore Criterion for Effective Area . . 65

44 . Block Shear Failure Mode for Coped Beams 68 I 45 . Constant and Linear Stress Distributions in Block Shear ...... 70

I 46 . Gusset Plate Block Shear Failure 72 I I I I I I I LIST OF TABLES I Table Page 1. University of Alberta Test Summary ...... 7 I 2. Single Bolt Single Shear Force Deformation Curve Parameter Sununary ...... 13 I 3. Beam End Moments in the Bracing Connection with Uniform Loading 31

I 4. Schedule of Finite Element Models 35 I I I I I I I I viii I I I ~ I.- I I I Results of physical testing and analytical studies are

I presented for typical column beam gusset connections. Force and I displacement distributions are reported for 45 0 , 600 and JOO dia~onal bracing connections. A comparison of analytical versus test results I from the connections are found to be similar verifying the methodology in developing the finite element models .

I Connector simulation for the finite element models is discussed I noting the material property formulation for the orthotropic behavior of double framing angle bolted connections. Weldment, single and I double shear connector formulation is also discussed. Review of previous work and design concepts for gusseted

I connections are included. The block shear concept is reviewed for I .possible application in the analysis and design of gusset plate connections. I It is concluded that nonlinear finite element software with orthotropic connector capability can realistically simulate the

I structural action of gusset connections. Additionally, the block I shear criteria may have application as an analysis and design aid. I I ix I I I I I CHAPTER I I INTRODUCTION The design of steel connections that are adequate for strength I and economical to fabricate is one of the most challenging prob lems for structural engineers. The large number of variables, including

I configurations, types of connectors, load intensities, and load com I binations involved makes it difficult to establish standard connection designs . This paper addresses analysis methods developed to better I understand the structural action of these connections. Full scale

res in~ of gusseted connections at the University of lberta (8)

I provided a basis to compare analytical predictions with test results. I Tests at the University of Alberta involved full scale testing of typical beam, column, gusset bolted connections. Figure I I illustrates the 45 0 configuration tested. Six tests were conducted 0 0 0 with 1/8" and 3/8" gussets in 45 , 30 , and 60 connections. Each

I connection tested was modeled with the nonlinear finite element routine I r.'ELAS (1) . The program was utili.ed to simulate nonlinear behavior in material and connectors. Properties for connectors were obtained

I from tests conducted at the University of Ari:ona (4) and the University of Illinois (3) on double framing angles, single and double shear.

I Properties for connectors were input from force deformation CUT\'es I plotted from physical test data. When this procedure is used, it is possible to include both geometric and material nonlinearity in the

I I I It>

Iv)· I 2 I I

I W 12 x 65

5 I W 24x 100 I I ..I I +-- Clip Angles F~=e=F====:!.... Welded 8 Gusset Plate I -:--+- Splice Plates I Bracing Member I W IO x 49 I I

I Figure 1. University of Alberta Test Specimen. I I I I I I 3 I analysis in an accurate and numerically efficient way. This methodology was used to assess the moment generated by double angle framed connec- I tions (2, 3) and also was used to develop the design procedure for single plate framing connections currently being used by the design

I profession (4). Additionally, the strength of eccentrically loaded I bolt and weldment groups in the current American Institute of Steel Construction Manual is based upon force deformation curves derived I from physical tests (5, 6, 7). This method of analysis produced results that compared well with results from full scale testing leading to a

I clearer understanding of the structural action of the connections. I The following discusses the methodology and results of the research efforts and their significance in the structural integrity I of bolted connections. I I I I I I I I I I· 1 1 1 CHAPTER 2 1 TESTING 1 University of Alberta Six full scale tests were conducted at the University of 1 Alberta. These six connections were designed for 450 , 300 and 600 1 diagonal bracing systems. Each connection was tested with both 1/8" and 3/8" gusset plates . Figure 1 illustrates the 45 0 connection. 1 The gusset plate was welded to a five foot W24xlOO beam with a 1/8" fillet on both sides of the plate using E70l8 electrodes. The

1 beam to column and gusset to column connection utilized two ~" x ~" 1 x 3/8" framing angles. Three-quarter A325 bolts were used in the connection, seven in the beam and six in gusset . All bolts were three 1 inches on center with a 21,;" edge distance. The column was a standard eight foot W12x65 section with a WlOx49 braCing member. Two 7~" x

I 3/8" splice plates were welded to the bracing member and bolted to 1 the gusset plate with 18 A325 3/4" diameter bolts on 21,;" centers. The steel grade in the specimens were CSA 44W, Fy - 42 . 7 ks! actual. I Physical dimensions of the gusset plates are shown in Figure 2. Load was applied in tension to the braCing member with load

I actuators and strain recorded at several locations on the gussets I for all load increments . Strain was monitored on both Sides of the plate. Due to slight eccentricities, strains on opposite sides of

I 4 I C) I ~ I 5 . I • I r~ I I I ., ...... ~ I o o Qj ('\") u Qj I u.. - .-<.. --% u Qj I / .- / . . - ; .,.. U" . / %_ ~N ;::; .- .- - ,/ . / So ,. l I / '" . : -/: . ~ / v '"N -/ - I -/- . -. / . .-'~ ·.. ... J I -/-:-/~ 8f [) - ~ ~ J I "'0 :: ~ ·... • N I • • I I •••••• I I I I 6 I the plates were not equal, indicating bending in the plates. \~en comparing analytical results to the test results, gages were averaged I to eliminate out of plane bending effects. Table 1 summarizes the tests performed . Figure 3 shows a typical failure that occured during

I the testing.

I University of Illinois I Research conducted at the University of Illinois was done to determine moment rotation characteristics of beam to column double I angle connections. One of the major points of the research was center- ed around the properties of framing angles in tension and compression

I and determining what percent of the fixed end beam moment was trans- I mit ted by the double angle framing connection. Results from these tests were used to simulate the nonlinear behavior of the framing angles in I program lNELAS. The testing resulted in load-displacement curves for double

I angles in tension and compression. Figure 4 shows how the angles I deflect in compression and tension and their corresponding load deformation curves . It can be seen that the angle allows considerable deforma- I tion when loaded in tension. The deformation in the angle legs is similar to the structural action of a fixed beam with one end displaced

I relative to the other. In compression the angles bear on the bolted I surface and what deformation that is seen is due to hole elongation, bolt shear and flexure. It is apparent that the angles are considerably I more flexible in tension in compression . How the properties were I I ------

Table 1. UnIversi ty of Alberta Test Summary .

H.,x l.o .• ~ (~Ir·) ..• .. 11 ur.: I.oeall oln III Cuasel COlnll~lll8 r · t /811 45" 150 At taat two bult huteAl! In .pUce I) A [ear oc-currell at [lie RU!i8e l plat~ lI!llt pdLCern Iip 'Icc 1)1 o h .' connc," t Illn d' lhe end of t he blollt p.lllcllI II) Sll ghl hu t e \t l on~"ll,m In fra.lng ang l e \..unncl.: lion.

1/S" 1.5" ).14 Old not fall I) Slid I 1 lI.. u •• l of 'Jk IJl n~ at sa~ I,\utllon .I~ the I/~" l~tOl fa II nrc.

1/8" bO" l td At hol~8 connecl l u" 10 co It"*, I) C\UUhH pi Ilc Cl) l u.1I I ,IIU .... Lion tn.tll" 4nn1tl8 ho J..:II ~lo .. ~.ll~J fJndl v l...tll JnK with ~e,·olhl.A r'l Ku:.tllO; 1 1'1 .l l~ roA (lute at hC.J1II welli . II) S light !lule o.! I uul-t.1 I f ,'11 ,,, ",p ll ... c allate bult 1'.lllfo!l"n

u JIg" 60 .!.!II Old 1I0t faJ 1 I) S ll ~h l y' .... .JlnK ami lu, I.- ..dlll,~.H Ion I" S1JllloI' 1.11 Cd" uf "... t .... I'i l .

JOn lId" 1 ~8 At l .tn L\l1I bolt hul ulII I" up l i ~c f) 'rc.Jr lilt! of lh ~ gu:.o toi.:l I' loll..: 1III UU~1i pllll~ h"ll poIUetll Lh .. hUll "liI nnot 1,)1 1,..011 :.0. II) SIIt;111 ... hm.· .. t hm UI "., I l-ln,I,,·:. hl..- 1.:",1,.,1 ,"IIIlIIC .. tl on .

-- J/tj" 10" 1'J~ IUd nul (;,Ill I) S 11 t:lll ylddluK .W·, hulc ~lunK"lJIUI In ...1 1k: .Ire". .1 I /ij" l.:bL •• I. - (!) I ; .D 1 8 1 1 1 1 1 I

I o Tested 60 Gusset I .. 1 I 1 I ..... I

I o 60 Gusset Fracture Pattern I

1 Figure 3. Typical Failure Pattern University of Alberta Testing. I I 9 I I I I I Tension Compression I

I 32 I I I Compression I 28 24 I Tension I I ~ 20 I '"c. I ~ 16 I ~ I '0 I 12 '"0 I ..J 8 I 4

I .1 .2 .3 .4 .5 .6 .7 .8 .9 Deformation (Inches)

I Figure 4. Framing Angle Behavior in Tension and CompresSion. I I I I?. ~

I 10

I developed for the analytical studies will be discussed later in this I report. Similar testing is being done at the University of Arizona (20) to investigate framing angle properties of several other configura- I tions. I I I I I I I I I I I I I I I I I Cl!APTER 3 I CONNECTOR SIMULATION The analysis of bolted and welded fasteners utilizing the I finite element method requires the properties of the fasteners be I adequately described. Stiffness, strength and orthotropic behavior should be taken into account to simulate the s~ructural action of I the connector. As shown in Figure 4, the douhle angle connector behaves. differently in compression than in tension. Capabilities

I to simulate the fastener behavior is available in program INELAS (1). I This program was written to analyze plates stressed into the inelastic range. The nonlinear structural response is calculated by a numerical I algorithm that uses the von Mises yield criteria and the associated flow rule.

I Properties of fastener elements are derived from force deforma- I tion curves obtained from physical tests. Experimentally determined force deformation curves for high strength bolts are presented in Reference (4). I These tests were made to develop design procedure for the single plate framing connection. Figure 5 Ulustrates a typical plot for two 3/8"

I (A36) plates connected b.y a 3/4" A325 high s~rength bolt along with the I analytical formula (9). Tab.le 2 summarizes the force deformation curve parameters for the single bolt single shear tes~s made for this study. I Similar force deformation curves for bolts in double shear may be found in Re fe rence 6.

I 11 I I 12 I I I I I I I I I I I I ~ *---~----~--~----~--~--~ I 0-0.000 o.oeo O.l2O O.lllO 0.240 O.D! 0.3110 OEFORf1RTlQN (INCHES) I 3/4 R325 BOLTS - A36 PLATES 3/8 AND 3/8 I Figure 5. Single Shear Bolt-Plate Deformation Curve. I I ID ID I ID ~ I 13

Table 2. I Single Bolt-Single Shear Fa ree-Deformation Curve Parameter Summary . I

=!olr Plltes , , R I " ) j/J"~";Z5 I/J I/J A50 ·:so. J. I 3/16 5116 \;6 9063, ,) .. .J 51' - l/8 A36 :Og-5. 0 JO. •• :/16 ;/16 \36 l:!;OO. 10 J,) ;

I In 1/~ 0\36 lJ500. 10. 30. l/J 3/8 \:36 -liOO. -30 lO " 11 J 1/2 A36 I ~6oi -lJ , 30. 0 " lIS 1/2 A36 I:JOO. ~ JO. .l I 3/S 5/8 \Sn Gr SO 10875. ~O. 30. ., i/S"Ml25 3116 3/16 U6 ~06J. 0 30. I l/8 5/8 .-\36 1~8j; . 10. JO. J " 1116 7/16 "36 t:!;OO. O. ;~ .J

l/~ 1/~ A36 1'500. 10. 10.

I 111 3/S -\36 3~00. :0. 3Q. l II" It: 436 lob;. :0. :;0 I 3/8 1/2 A36 . :..100. :0 . .0 • 3/S 3/'3 .\S;~ Cr .0 t'.JS:":; "0 I 1" )A32S 1/: 1/: 0\36 !.!SIJO. :Q. 31 S 3/8 3/l 131:5. JO 3J. .6 I ,j/J"~.\J90 In ~I : 0130 ~J:;"O. 10 .J. .3 i/:J ii' .\30 .::it:S. ,.)

- /'j¢"4~O t/: II: \,jn :':300 .J iJ. :;

I 5/S ilS \';0 Ul':S. .0. jO. ,J

1/: \; i: :;., J ~~ln 1/: ';r :11 ;'" , I :"~AJ·.lO 11: 1/ : .\3';' .J5,lO 3n or. • 3d 5, s \36 .j~ ;S " ,Q • I I I I ~ '" I 14 I The force deformation curves for (E60, 1/4") weldments were presented in Reference 5. Figure 6 is a typical plot of the test

I data along with its analytical formula. The parameters of this I formula for other electrode strengths, weld sizes, and tributary lengths may be computed by direct ratios. I Force deformation (compression and tension) curves for double framing angles were presented in Reference 3. It is apparent from

I these tests that the double framing angles are orthotropic in both I strength and stiffness. To extend these force deformation relationships to the more general case, shear tests were made to determine the shear

I force deformation curves (~'s versus A's). Figure 7 shows the double framing angles.

I In all cases the force deformation characteristics of the I fasteners are described analytically by the Richard Equation (9). The equation describes curve shapes from input quantities of elastic stiff- I ness, plastic stiffness, reference load. and the Richard parameter. Figure 8 illustrates possible curve shapes the equation describes and a

I comparison of a Richard curve fit to a double angle tension test. I Describing the orthotropic behavior of double framing angles requires a yield surface which accounts for the response of anRles in I tension, compression and shear. This surface can be generated with a combination of a bar and an isotropic fastener element. The bar

I element increases the shear component of force with the isotropic I I I I 15 I I 14 I

12 I 0 0 0 p 0 0 Richard o 0 0 Curve o c 0 0 o v - _ cr--"O - 0 0 , I \ 0 0 "\ o~~ 0 10 0 0 ~\ 0 0 of' \ 0 I 0 , 0 00 But ler-Kul ~k Curve I 00 P 4-73 AIS Manual 1 F 0:f I 8 Load kip/in. °i! R = (K' KQlll + K;l ll II I n " + I(K-Kolllrt 6 \ R. I I I 4 I 1/4" fi Ilet welds 2 9: 0 degrees I K = 5000.11,., R.,=II.I Kp=O, n=1.

I 0.02 0.04 0.06 0.08 0.10 0.12 I Deformation, inches I Figure 6. Weld Force Deformation Curve. I I I 16 I I I I I I I I I I I I Figure 7. Double-Framing Angles. I I I I I 17 I :J ; I . J - I S I J I K = Elastic Stiffness ~ :I Kp= Plastic Stiffness Ro= Reference Load , A = Deformation I R = Load · n = Richard Parameter I •· I ....- I" 1_ ,_ .- ._ .- aa.,..rllJll I R I C~O CURVE SM;t·~S I I I I I I I

. 1 .2 .3 .4 .5 .6 .7 .8 .9 I Deformation (Inches) I Figure 8. Force Deformation of Framing Angles, Richard Curve I versus Test Results . I I I 18 I fastener element simulating the structural action of tension loads. These two elements acting together produce the yield surface illus- I trated in Figure 9. The elliptical portion of the surface simulates I the combination of shear and tension on the angles. The lower part of the surface simulates the action of the double angle in compr~ssion I and shear. An example of this concept can be illustrated from physical tests of the angles . Figure 10 shows the force deformation curve

I generated by pulling two 5 x 5 x 3/8" framing angles with 3/4" diameter bolts and 1/2" plate. Figure 11 is the force deformation curve for the

I same size angle i n compression. Plot ting the data from the two tests I in t he form of an e l lipse pr oduces the s urface in Figure 12 . To obtain input properties for the bar and discrete fastener I elements in program INELAS, the following procedure is followed. The I bar element in the orthotropic system has an area set equal to 1.0. This is to facilitate the use of a post processing program that plots I forces and displacements of the connectors. Input properties for the element are defined below: I EM , K - Young's Modulus or elastic stiffness for I fastener element . EMF , K s Plastic Modulus or plastic stiffness for p I fastener element. SY, R - Reference stress or reference load for 0 I fastener element. I PNL - Richard parameter. I I I 19 I I I I I I I I I I Rno - I I

I Figure 9. Orthotropic Element Yield Surface. I I I I I I I ...-~ § I -.. I ~ I ~ ~ I -0 rn 0... I -:.:: 0 .,~ cr 0 I ...J ~ I '" I I I ' ~----~----~--~----~---.--~ 0-0.000 0.0'10 0.140 0.210 0.2110 0 .420 I DEFORMATION (INCHES) I Figure 10. Tensile Force-Deformation Curve for 5 x 5 x 3/8" I Framing Angles, 3/4" Diameter Bolt and 1/2" Plate. I I I 21 I ~ I ~

I ~ .....0 I ~ 0 I CD ~ I Ii ~ IJ) Q.. I -x: 0~ a:CJ .... 0 I -J I!I ~ I!I I ~ I!I

~ I!I I ..0

I ~ 0- I ~*---~--~--~--~--~--~ I 0-0.000 0.060 0.120 0 . 1110 0.240 0.300 0.360 DEFORMRTION (INCHES) I

F!gure 11. Compressive Force-Deformation Curve for 5 x 5 x 3/8" I Framing Angles, 3/4" Diameter Bolt and 1/2" Plate. I I I 22 I I I I I I I I (0 . Rno ) i-_.::.:( 5~. .::8_7.5) I C714 . .750) I CRso .0) I I I Figure 12. Plotted Yield Surface. I I I I I 23

I If A - 1.0 for the bar, then strength for the bar B is I cry * Aa a SY * 1. ~ SY where: cry s actual yield (or reference) stress I Aa = area of the two framing angles Stiffness must also be determined for the formulation of the properties. I AE stiffness s_ L

I and since the area of the bar is unity I I * EM + Aa * EMactual = EMinput l*EMP-Aa*EMP -EM!' I actual input The properties must be modified further to develop the proper I yield surface and stiffness. Figure 13 illustrates this point from the strength and stiffness considerations. Noting the slopes from the force

I deformation curves of the same figure, the following may be noted:

EM input I ~ar = L I where L is the distance between bolts .

EM input I L - Kshear - K tension I so Einput - L (Kshear - Ktension) I where: Kshear = is the same for a bolt in double shear

Ktension • computed from flexural conSiderations I (see Figure 14) I I I 24 I I I STRENGTH Elliptical

I '" "- \ I R I --f-----t-- t --+,.. S::::yo;--- --r" input \ / I ' ...... '" I

I Circular

I STIFFNESS I I

I Force I I I Deformation I Figure 13. Framing Angle Bar Material Property Formulation. I I I

I ~

1 Ir 1-I I I I

I t plate

/ I I I ..\--- Def lected Shape I I

I tangle I --" I I I _, I K . K + K I t ens Ion plate 2 angles

4 E(tplate )tanale I Kplate = tplate + tangle I K2 angles = I I Figure 14. Angle Performance for Stiffness. I I I 26 I To illustrate the calculations to obtain K for two three-inch angle segments with leg length equal to 3" and thickness of 3/8", an example I is given below:

I 1 1 + 1 K - -K K I tension 2angles plate

1 1 K -K I compression - plate I where: K - 2 l2EI - 491.4 2angles L3

I which represents the bar element. I and: 4Et t angle plate K = 25,714 KI inch plate t t - I angle + plate which represents the discrete fastener element. I Thus: Ktension - 482 K/in.

I K compression - 25,714 K/in.

I These numbers agree well with physical tests documented in Reference 20 and Figure 10 .

I The methodology discussed above was used to model a cantilever I beam connected by framing angles (10). The model depicts a test done at the University of Illinois. A comparison of the experimental and I finite element results is presented in Figure 15. The analytical results I agree well with the test results . I ------iH€ee

500

~ oo

300 ~.. , -!£ ;; ~ --- - - til" .., IMEl AS 0 100 ;5" 7

• W16 I 50 - 4 ' O· 100 •

o 10 10 JO ~ o 50 70 80 3 ""Ii... "~ i .., I .0

Figure 15. Cantilever Beam Analytical versus Test Results. ....N I I CHAPTER 4 I ANALYSES OF DIAGONAL BRACING CONNECTIONS I A study by Hormby (10) of the connection shown in Figure 16 I was made using the finite element model shown in Figure 17. In this connection the 9/16" gusset plate was welded to the top flange of the

I W24 x 68 beam. The 4 x 3-1/2 x 1/2" framing angles were welded to the I gusset plate and bolted to the web of the W36 x 280 column. In practice this type of connection would be considered flexible since only web angles I are used to join the beam to the column. However, this study showed that the gusset plate provided sufficient stiffness; that the beam when loaded

I with its uniform service load, developed end moments approximately equal I to the fixed end moments. Thus the addition of the gusset plate, which is generally designed on the basis of the bracing load only, actually I results in a haunched fLxed-end beam. These studies are summarized in Table 3 for three different uniform load intensities. In addition to

I the Hormby study, the six diagonal bracing connections built and tested I at the University of Alberta were modeled. Four separate pieces of software were used in the connection I studies. Three of the programs were post processing tools for plotting force and displacement fields and contours and stress surfaces. The

I major tool was a program called lllELAS (1). The program is used for I static analysis of structural systems which exhibits linear and/or nonlinear, isotropic and/or anisotropic material behavior. I 28 I I 29 I I r"" :-I I

I -t-- I- I I I 2'· 8"z' I = I I H , ',I'\ I _1__ ,QM5 , 3It< ' ~ I .. I

I Figur e 16, Diagonal Bracin2 Connection. I I I I I 30 I

I c .....o u ..U I C oC U CI: I .....c: u E I -'" g,'"c

~ I Q'" .... I o I I I I ../' / I I I \ I r\ ""\ I I \ I T I ITT'" I I I I I ------t'tJi3i:l

Table 3. Beam End Moments 1n the Bracing Connection with Uniform Loading.

MOMENTS (Kj o.in)

Actual as Percent Fixed-End of Fixed-End Loads AclOual Uniform Ilaunched Uniform Ilaunched

Working 2757 2520 2814 109\ 98\ Yield 4063 3780 4221 107\ 96\ 2 . 25 x Yield 5855 5670 6331 103\ 92\ I 32 I There were several components to consider in designing a I reliable finite element of the connection. Since the column was supported along its outer flange during the test, it was not included

I in the model . The gusset plate and beam web were simulated by quadri- I lateral and triangular plates, whereas the beam flanges were simulated by bar elements. Bolts, welds and framing angles were simulated as I discussed in Chapter 3. The combination of these elements produced a two-dimensional model resulting in an efficient and manageable numerical

I analysis. I In the beginning of these studies it was not clear if the gusset plate alone would be enough to adequately simulate the structural action I occurring in the connection. So two models were generated for each test conducted. One model consisted of the gusset and its connectors. The

I second included the beam and its connectors. An example of the 30 0 I beam-gusset and support conditions is shown in Figure 18. Neither model depicts the connection as it would occur in the I field, but instead establish limits of maximum and minimum rotation the joint will experience. An actual connection would behave somewhere

I between the two extremes. The gusset model without the beam demon- I strates the condition when the beam is very stiff and does not permit the gusset to rotate. The beam-gusset model demonstrates the maximum I rotation and connection flexibility by letting the end of the beam rotate freely. The two limiting conditions were modeled to simulate

I the University of Alberta tests which permitted the free end of the I I I 33 I I '-Double Angle Element I -- -Beam I

I Weld Element I I - -Gusset

I - Splice Plates I - Double Shear I Bolt Element I I Loads

I Figure 18. Connection Locations fo r the 0 I 30 Gusset and Beam. I I I ,,,,

I 34 I beam to deflect without restraint and to simulate the beam with no rotation. I Table 4 describes the twelve major models generated. Several· other models or variations of those models were run to verify the

I behavior of the connections. Each of the twelve represent correspond- I ing physical tests. Loads were taken from the test conducted at the University of Alberta . Results from all the models were consistent with I all twelve test configurations. To reduce the volume and redundancy of information in this report, each model will only be discussed briefly

I with the exception of the sixty degree, one eighth inch gusset and beam I model . This model is probably a more general condition and will be looked at in depth. I The 45 0 1/8" gusset model was loaded to 150 kips with increments of load of 0.5, 0 . 35, and 0.15. The distorted shape is plotted

I over the original shape in Figure 19 . This distorted shape is exag- I gerated to show the plate behavior more clearly. The rotation of the gusset, the splice plates interaction with the gusset, and the overall I deflection pattern is clearly illustrated. A surface and contour plot of effective (von Mises) stress at 75 kips is shown in Figure 20. This

I corresponds to the first increment of load. For the last increment I of load, a similar plot is shown in Figure 21. It is noted that at 150 kips, the peaks of the surface in the stress plots have become much I smoother, indicating a significant redistribution of stress as the material yields. At the end of the splice plates the contour pattern

I matches the tear pattern at failure in the actual physical test. I I I 35 I Table 4. Schedule of Finite Element Models. I I Gusset Gusset or Thickness Load I Angle Beam Gusset (in) (kips)

I Gusset .125 150 .375 300 I 45 0 .125 150 Beam/ Gusset I .375 300

.125 140 I Gusset .375 320 60 0

I Beam/ .125 140 Gusset I .375 320 .125 158 Gusset I .375 320 300 Beam/ .125 158 I Gusset .375 320 I I I I I Q) I!) ID I to. "-l I 36 I I I I I I I I I I I I

I o Figure 19. 45 , 1/8" Gusset Undistorted and Distorted Geometry. I I I I I 37 I I I I I I I I I I I I

I 0 Figure 20. 45 , l/S" Gusset, Effective (von Mises) Stress Contour I and Surface Plots, 75 Kip Load. I I I m

I II),D P- It) I 38 I I I

I A;5 I I I I I I I I I

I o Figure 21. 45 , 1/8" Gusset. Effective (von Mises) Stress Contour I and Surface Plots, 150 kip load. I I II)

,,n~ I I:!J I 39 I The 3/8" model was loaded to 300 kips and produced the same behavioral pattern as the 1/8" gusset model as did all of the models in the study. I In addition to the von Mises stress, maximum shear surface and contour I plots were generated. Figure 22 illustrates a similar surface pattern as developed for the von ~1ises stress . Note the shape typifies the I structural action which occurs in the block shear concept . The gusset plate modeled above was restrained with framing

I angles on the column side and fixed on the beam side. In actuality, I the beam would deflect with the gusset plate as load was applied. To investigate how this effected the model, an expanded model was generated I with the beam included to determine its influence. Figure 23 is a plot of this model with the distorted shaped overlayed. As seen in the

I figure, the beam moves along with the gusset almost as a rigid body I pivoting about the lower portion of the gusset . The deflection pattern is similar to the previous model . The reorientation did not I significantly alter the force and stress fields in the connections, but deflections were somewhat different due to the reorientation of the

I gusset and beam . Figure 24 indicates the same effective stress pat- I tern and magnitudes as the gusset model with low stresses in the beam, along with a sharp gradient in the stress field at the gusset to beam I connection. As shown previously, the same high stress pattern occurs at the end of the splice plate where the effective stresses 3re in the

I 4S ksi range which is well beyond the elastic limit of the material. I The 3/8" model of the same configuration performed in a similar manner I I ~ I .!)I!> ..n -

I 40 I I I

I 20 I I I I I I I I I o Figure 22. 45 , 1/8" Gusset, Maximum Shear Stress Contour I and Surface Plots, 150 kip load. I I I I 41 I I I I I I I I I I I I I I

0 I Figure 23. 45 • 1/8" Bearn-Gusset Undistorted and Distorted Geometry. I I I 42 I I I I I I I I I I I I I a Figure 24 . 45 , 1/8" Beam-Gusset Effective (von Mises) I Stress Contour and Surface Plots, 150 kip load. I I I I 43 I with the exception of greater rotation since the load was increased to 300 kips as illustrated in Figure 25. Again, stress patterns were I essentially the same with displacements being changed somewhat by the rigid body rotation of the beam.

I The 600 gusset was modeled in a similar fashion. Shown in I Figure 26 is the 1/8" gusset with the exaggerated distorted shape plotted over it. This model had a total applied load of 140 kips. I In Figure 27 the effective stress contour plot shows the same pattern as in the 45 0 models. The maximum effective stress contour again is

I 45 ksi at the base, resulting in excessive yielding or failure of the I splice plate as before. Force and displacement distributions in the column and beam I connectors were significant findings in the study. Physical tests of the gusset plates were not instrumented to determine loads and displace-

I ments at the individual connectors, whereas these analytical methods I determine the orientation and magnitude of forces and respective displacements. Traditionally, connectors in gusset plates have been I designed by assuming vertical loads were resisted in vertical shear forces by the column connectors, and horizontal loads were resisted in

I horizontal shear by the beam connectors. If this were the case, framing I angles would always take load in the direction of the column in which the angles are very stiff. Figure 28 shows resultant connector loads I and displacements from the 140 kip load. From these analysis, it is seen that both the weldments and bolts have significant loads normal

I to the connection line. The forces and displacements in the splice I I IT.> It>'"

I 44 I I I I I I I I I I I I I I

o I Figure 25. 45 • 3/8" Beam-Gusset Undistorted and Distorted Geometry. I I I 45 I I . C;' I '"' 5 '"o !lI t.:: I .".. '"' o u" I ....OJ C ." C

I ."'" '"''" o" I ....'"'!J) ." C I ;:0 I

o I o '" I I I I I I I I 46 I I 1

I ...... o Cl- .... I ::J o u oC I u

I ...... _ ~I c , - , . o ' . o > ~.. I ....> u ,... CJ "I , - ....GI I . , - , ....

'"u ..en I ~." -'" ....'"o , , Co I ,, ...... Q. ' -. , ...... -...... o 0"" I "'0-< ... .' , :o~

I ZJ '\ ~ JL__ ~ __ ~ ______~ ______~-M~,

- 16 - I 1 -10 -7 - ~ -I I inc.he I I I I 47 I I I I 0.0015 I 0.0019 0.0023 I O.con I Def lection in. 12.05 9.11 ~.SBS.~.23 I 1.50 ... " 3.38 -/ 4.05- S.tB t 64.66 Normal I 82 .84 Shear B.19 6.40 - 15.89 Shear 7.25 I 3B.08 Nonna 1 I ---.n 7.99 I I Forces ki DS I

0 Figure 2S. 60 , l/S" Gusset Force and Deflection I Distributions, 140 kip load . I I I I 4S plate to gusset connection are shown in Figure 29, where it is seen

I that the center bolts have about half the load of the outer bolts. I Illustrated in Figure 30 are resultant bolt forces and displacements plotted in the vertical direction to indicate the variation of the I magnitude of displacements and forces in the bolt pa ttern. All of the models studied had yielding in the gusset at maximum load. however

I the load never redistributed in an even manner to all the bolts. The I entire connection distribution of forces in the gusset is given in Figure 31 . At the corner of the gusset compression occurs due to the I near rigid body rotation of the plate. I The beam-gusset model gave similar results. Figure 32 shows the model with its distorted shape. Force and displacement fields I vary somewhat from the gusset model . Figure 33 shows the magnitude and orientation of resultants from the 140 kip load which may be compared I to Figure 31 . It is noted that the line of action for all the reactions I are essentially in line with the direction of applied load for all cases. The 300 gusset model was generated to complete the span of I geometry commonly found in gusset connections. Results from the l/S" and 3/S" gussets were similar to corresponding results of the 45 0 and I 60 0 configurations. Shown in Figure 34 is the model and its distorted I shape. This gusset was loaded to 158 kips. In the 30° beam-gusset model rotation was not as significant due to the angle of loading and I location of the bolts. The distorted shape and model is shown in Figure 35. I I I I 49 I

I '.lUI :.ca:::s 0.:'::1\1 ~.""" ~..... -1.011'. - I I I I I I 1%.11 ... ~ ,.. ---...~ ----. I ...... ---I.'. I ,. .,., I ....• J.,;;,t ...... -!) ••• a • • I ' .D I

o Figure 29. 60 • 1/8" Gusset Splice Plate Connection Force and I Deflection Distributions. I I I 50 I

I 1%. 7% ' .4Z ••• I I ..- s.. '.41 I 1 1 1 1

,e.", II ... I ... t I 1 ...... on ...... I I I o ~I 1 I I I I . ..- 0..211' • ..211' ._ I ~ ! ! 1 I ...... c.= I . I • .:cos I I • .;zn. :J. ~, I I, I I I " " " '" I I 0 Figure 30. 60 , 1/8" Gusset Splice Plate Connection Force and I Deflection Resultants Plotted Vertically . I ------c,aei:l

14 .51 12.46 12 .06 9.11 3.56 5.23 6.23 1 .95

3.38 4.06

5.18 8.19 6.40 -- 7.25 -- 7.99 -- 8.'/1

10 ...... 8.34

0 Figure 31. 60 , 1/8" r.usset TotAL Force Distribution. I ~

I S2 I I I I I I I I I I I I I I

0 I Figure 32 . 60 • l/S" Beam-Gusset Undistorted and Distorted Geometry . I I ------· qaei:l

1I . Z9

15.33 _t 47 87

__ 147 87 .... I

1·11

121 ~ ~140 70

Figure 33. 60° , l/S" Beam- Cusset Fo r ce Distribution , 140 Kip load. I:') l .~i~ IT> ./1

I 54 I I I I I I I I I I I I I I I I Figure 34 . 30°, l/S" Gusset Undistorted and Distorted Geometries. I I 55 I , , I I I I , I I I , I Ii I I I I I , I I , I I I I I I .j I I I i ,I I I 11 I I I I I, I I I I, I , \ I I I \ 1 1, I I I I I v,,1 I '\\ I ,I I I , I v; ¥~'" , I :X- I I ~y ~ Ii ~ I I ,"'- L ~ , I I , h . ~, f I ~ , ,. ~ I o Fig ur e 35 . 30 , 1/8" Beam- Gusset Undis torted I and Distorted Geometries . I I I I CHAPTER 5 I ANALYTICAL VERSUS TEST RESULTS The combined results of the physical tests and analytical I studies make it possible to evaluate the validity of the analytical I techniques used for connection stress and strain predictions. Three major items were compared to ascertain the validity of the models. I i) Similarity in deflected shape, yield patterns and failure locations.

I ii) Response of framing angles, welds and bolts. I iii) Strain magnitudes. All three items, when compared between analytical and physical tests, I compared favorably. The comparisons verify the validity of the techniques used to simulate the gusset plate connections. I The tests done at the University of Alberta had extensive I instrumentation, however, only certain strain readings at critical loca tions were selected as shown in Figures 36 through 41. These values I were compared with results from the analytical predictions. Areas of low strain gradients as shown in Figures 22 and 24 agreed quite well

I with the test results . In areas of high strain gradients, results I differed significantly as may be expected. These high gradient areas had strains changing an order of magnitude in less than one half inch. I A finer mesh in these areas would possibly provide better results. I 56 I ;t> l 'P':..>

.00110 Analytical 3/8" I .00090 Test .00120 Analytical I .00130 Test 1/8" .0009 Analytical I .0005 Test 3/8" r-. 0010 Analytical 1/8" I .0009 Test , I 0 ~ 0 J 0 I 0 ,0 0 0 o , 0 0 0 0 0 I 0 0 i' ,0 0 0 0 0 0 "' I 0 ,0 I .00047 Analytical 3/8" I L.00094 Test .00060 Analytical 1/8" I .00070 Test I

I Figure 36 . 45° Gusset, Analytical versus Test Results . I I I I 58 I I

I 0 I .00160 Analytical 0 .00090 Test 3/8" I 0 .00 180 Analytical .00130 Test 1/8" 0 I .00120 Analytical 0 .00050 Test 3/8" 0 ~.00150 Analytical I .00090 Test 1/8" 0 \ I I , o 1 1\ \ I 0 of' 0 0 , 0 0 I 0 0 0 o 0 " 0 0 0 , 0 0 I ~ 0 0 0 0 0' 0 I , 0

I .00060 Analytical 3/8" .00046 Test .00080 Analytical 1/8" I .00070 Test

o I Figure 37. 45 Beam-Gusset, Analytical versus Test Results. I I I I 59 I

.00457 Analytical 3/8" I .00353 Test .00127 Analytical I .00087 Test 1/8" .00210 Analytical .00331 Test 3/8" I .00090 Analytical .00181 Test I 7 0 1 ,.J- ..... 0 I o 0 ..g/ 0 0 o 0 ...... 0 0 0 I o 0 0 ....0 0 ..... 0 0 o 0 I 0 0 1 / 7> 0 ...0 I ""yt1,., ~~6Not Available Test 3/8" I .00089 Analytical .00091 Test 1/8" I I o I Figure 38 . 60 Gusset, Analytical versus Test Results. I I I I I 60 I I I o .00504 Analytical 3/8" .00353 Test I o .00241 Analytical 1/8" o .00087 Test I o .00286 Analytical 3/8" o .00331 Test I ~00104 Analytical 1/8" o .00181 Test I o \ I 0 1 o o o I ... 0 o o o o o o ...... o o I o o 00 0 1 I ....o

. 00194 Analytical 3/8" I Not Available Test .00104 Analytical 1/8" I .00091 Test

I o Figure 39. 60 Beam-Gusset, Analytical versus Test Results. I I I I 61 I

I .00042 Analytical 3/8" .0002 Analytical .00069 Test .0001 Test 3/8" .00262 Analytical .0058 Analytica l I .00140 Test 1/8"7r .0054 Test 1/8" I I II o~ I 0 1 0 0 0 0 0 0 0 ' I 0 0 , 0 0 0 0 0 I 0 0 0 0 0 ' 0 0 1 I \0 \ I .00117 Analytical ~00134 Analytical .00140 Test 3/8" .00170 Test 3/8" ~ .00304 Analytical .00693 Analytical I .00132 Test 1/8" .00477 Test 1/8" I

o I Figure 40 . 30 Gusset , Analytical ve r s us Test Results . I I I I ,t> I :: "" I 62 1 I 10 .00074 Analytical 3/8" .00023 ~nalytical I .00069 Tes t .00011 Test 3/8" .00408 Analytical 1/8" .00757 ~nalytical I .00140 Test .00531 Test 1/8"

I o 1 o I 1 o ~ 1 0 1 o o o o o o 0 ' 1 o o o o o 1 o o 0 ' I 0 1 \ .00144 Analytical 3/8" \ .00136 Analytical 3/8" 1 .00140 Test l.00170 Test .00549 Analytical 1/8" .00772 Analytical I .00132 Test .00477 Test 1/8" o 1 Figure 41. 30 Beam-Gusset, Analytical versus Test Results. I I .., .~ (D I -.1 P I I I CHAPTER 6 I CURRENT DESIGN CONCEPTS Gusset plate analysis and design procedures have not been fully

I established. Experimental work done prior to the University of Alberta I testing was done by \

I The model was made of aluminum and had extensive instrumentation. I Whitmore observed that the high strains occurred at the ends of tension and compression diagonals. Beam formulas were found to be inaccurate I for stress analysis, particularly at the edge of the plate. The "\

I maximum normal stress in the gusset was established from this research. I This criterion assumes that the member force is distributed evenly over an effective area of the plate which is obtained by multiplying I the thickness of the plate by an effective length. The effective length is determined by constructing 30 0 line segments from the begin-

I ning of the bolt pattern to the end of the bolt pattern as shown in I Figure 43. The finite element results obtained from this study support the 14hitmore criterion. As seen in previous figures, maximum effective I stress patterns are similar to the 30 0 Whitmore pattern. Although a I 63 I ,Z> ,'Z> .. ..) I ",

I 64

I Double Plate Gusset I , / , / @ "" "<3' ' 0' @ I I I @~"'" "'" l /@@ @ Critical " © @ @ ) I <.. @ @ / "/ I " / Section ',@ / 1 @ @ I ,,© / I 'v,/ . ___ .L ___ J . ",1. +--f------+--..., Truss I Chord I I Warren Truss Connection I

I Experimental I Beam Theory

Normal 0 I Stress +------~~~~------~ '-':: I I

I Distanc;;e along critical sect ion I

I Figure 42. l.Thitmore Gusset Plate and Stress Dist ributions. I I ;;.~ '"

1 65 1 I I 45 deg. I 1 ~ Effect ive Length ..... 1 I ./ .... .// I 1 ( ...... '\ .\J .... , \ \ ', 30 deg . 1 ...... 30'-' ! " ...... ,,\ '"I

1 1\ / \ 1 ,. \ . ~ I I ' ••.. 60 deg. LI ____• ~ I I

I Figure 43. Whi~more Criterion for Effec~ive Area . I I 1 I 66 I good design aid, the Whitmore criterion seems to be supported in concept but analyses may show that the angle could be modified to more accurately I depict normal stresses under loadings other than observed in the Whitmore testing.

I Extensive analytical studies have not been made for gusset plates. I Prior to the development of the finite element method and lar~e comput- ing capability, analysis of gusset plate connections were too complex I to adequately describe the influence of material behavior, connectors and boundary conditions. Finite element work was performed by several

I researchers as this analytical tool became available. Elastic analyses I were performed by Vasarhelyi (13), Davis (14), and Desai (15). Non- linear applications were introduced by Struik (16) in 1972. Struik I used a nonlinear finite element program to predict effects beyond the elastic range and to estimate the effects of bolt holes in the gusset.

I Although the analyses were quite thorough, they did not include the I nonlinearity of the fasteners. Results presented by Struik were con- sis tent with results gained from studies performed for this paper although I displacement field and forces on the connectors were not available. The gusset investigated by Struik was geometrically the same as the

I specimen Whitmore used in his experimental work in 1952. I I I I I I I I CHAPTER 7 I BLOCK SHEAR I A possible method for the design of gusset plates may exist in the block shear concept. The concept is discussed in the 8th edition I of the AISC commentary section 1. 5. 1. 2 (7) . Briefly, the AISC code applies block shear to coped beams as illustrated in Figure 44 . The

I accep tance of these results by the AISC committee came from tests at

the University of Alberta and the University of Texas. These tests

II demonstrated that the failure load may be predicted by combining ulti- I mate s hear strength over the net section subject to shear s t ress with the ultimate tensile strength of the net section subject to tensile I stress . Thus , t he formula:

RS - 0.30 A F + 0 . 50 A F I - ~ v u t u where : I ~S ~ Resistance to block shear, kips A Net shear area, in. 2 v = 2 I At - Net tension area, in . F - Specified minimum tensile strength, ksi u I Initial work leading up to this formula was done by Birkemoe and I Gilmore (17). Their work included physical testing of connections subject to block shear failure.

I 67 I I I 68 I I I I I

I Fai lure by Tearing Net Shear Area. Av ---...... - ou t of Shaded I Portion

Net Tensi Ie Area. I At I I I I Figure 44 . Block Shear Failure Mode for Coped Beams . I I I I I I ~

I 69 I Yura, Birkemoe and Ricles (18) did additional work extending tests to include two rows of bolts, as well as additional single bolt I testing. Their results indicated that the block shear formula with two rows of bolts overestimated the capacit y of the connection. Ricles

I and Yura (19) made additional studies with a linear finite element I analysis to predict failure patterns in the two row bolted connections . These prompted a modified block shear formula which assumes a linear I distribution along the tensile failure area of the specimen. Previously tensile stress was assumed constant. Figure 45 illustrates both the

I linear and constant distributions for a typical specimen . To support I this concept they purposed the follOWing formulas: Block shear capacity - tensile strength + shear yielding; I g + R - F (g + e )0.5t - __-,,-2 t '1, + 0.6F (e + Es)t f u n w w y g w I g + e n I or for design purposes: Block shear capacity - 0.5 F A + 0.6F A I u net y v gross'

I where: I At z net area of web in tensile stress plane of connection; A = net area of web in shear stress plane of connection; v I ~ = diameter of bolt; '1, - the effective diameter of the bolt hole (~ + 1/8); I I I 70 I I I, • 0 .6 Fu l I • J Av I Rupture surface.(. 10. II At V ! ~ l I Fu I Constant Stress Distribution

I g I , " e!lj I 06 Fy l Elg 4 • • l s I • • s « Rupture -<. l -... surface ~ - I I , j l I Fu I Linearly Varying Stress Distribution I I I Figure 45. Constant and Linear Stress Distributions in Block Shear. I I .D I ~

I 71

e ~ edge distance from center line of the bolt hole to free edge; I g e = end distance from center line of the bolt hole to free end; n

F ~ static ultimate tensile stress of material; I u F - static yield stress of material; y I g = gage length of bolt line; I s = center-to-center spacing of bolts. These formulas gave results which compared favorably with physical tests. I As seen in contour plots of the gusseted connections studied in this paper, the diagonal brace connection to gusset plate fails in a

I similar manner to the coped beams tested. Figure 46 illustrates this I point . The similarity in the two problems has prompted the idea of modifying the block shear formula from the AISC specification to a design I tool for designing the bracing connection. Thus, a modified block shear criterion may be applicable to determining the gusset plate size and

I thickness. This modified procedure would use the gross section along the I bolt lines in large connections. An argument for using the gross section may be based on the fact that the interior bolts may never slip into bear- I ing as illustrated in Figure 30. For the gusset test, specimens there are two rows with nine bolts each at 2-1/4" on center, spaced five inches apart

I as illustrated in Figure 2. Thus, using the block shear concept with I shear forces along the bolt lines and tension along the end of the splice plate,

r - A F + A F I ultimate vg vu tg tu I I I I 72 I I I I • I • • I • Rupture Surface I • • I

I Load I I I Figure 46. Gusset Plate Block Shear Failure. I I I I I I 73 I where: Avg - gross shear area;

I Atg - gross tensile area; I F vu a ultimate shear strength; F tu = ultimate tensile strength. I Applying this to the 1/8" gusset configuration yields the following: 2 Avg * t (iv) - (.125) (8 x 2~) 2 - 4.5 in. 2 I Atg - t (i t ) - (.125) (5) - .625 in. I Fvu - . 6 Fy - 25.6 kSi F tu - 55.5 ksi

I (4.5) 25.6 + (.625) (55.5) a 150 kips. The loads at which tearing occurred at the ends of the splice

I plates in the 60 000,45 and 3D gussets were 140, 150 and 158 kips I respectively . In the case of small connections where there are five or less bolts in a row, it may be appropriate that the net section alon ~ the I bolt line be used to compute the strength of this connection. Additional I tests are needed to establish this design concept for small connections. I I I I I I I I I CHAPTER 8 I SUMMARY The analytical models of gusset connections which include the

I plate and the connectors have been shown to predict the strain distri- I butions in gusset plates in an adequate manner. Comparing the results of these models with physical tests have verified the analytical techni- I ques used in the study. Findings from the finite element models showed that significant normal load is transmitted to welds and double angle

I connections. In general, the reaction of the connections were oriented I closely to the applied load. These studies also support the Whitmore criterion for gusset plate design. I A recommended alternate procedure was introduced utilizing block shear theory. Previous work in beam connections provide a founda-

I tion to support the use of the block shear failure theory and should be I investigated in further studies for the design of gusset plates. Pre- liminary findings show positive results predicting failure loads in the I gusset plates with good accuracy. Work done in this study has provided inSight into the structural

I action of this connection which may lead to efficient design guides and I procedures. Further research may provide the structural design profession with needed design tools that ultimately minimize assumptions and I produce a more reliable and economical gusset connection. I 74 I I I I APPENDIX I Page 45° 1/8" Gusset ~fodel 76 I 45° 3/8" Gusset ~del 87 45° 1/8" Beam-Gusset Hodel 95

I 45° 3/8" Beam-Gusset Model 100 I 60° 1/8" Gusset Hodel 104 60° 3/8" Gusset Model 108 I 60° 1/8" Beam-Gusset Model 113 60° 3/8" Beam-Gusset Model 119

I 30° 1/8" Gusset Model 123 I 30° 3/8" Gusset Model 129 30° 1/8" Beam-Gusset Model 134 I 30° 3/8" Beam-Gusset Model 139 I I I I I

I 75 I I 76 I I I I I I I I I I I I

I Figure A. i. Undistorted 45 0 Gusset Grid. I I I I .!:' ,D ,!j I ,:.0 1:.0 I 77 I I I I I I I I I I I I I

0 I Figure A. 2 . 1/8" 45 Gusset Grid and Distorted Geometry . I I I ;:0 I:':> I:;:) I llo ,D

I 78 I I

I Inches -25 -22 -19 -16 -- 13 - 10 - 7 -4- -1 2 I '" . , I •, ,, I , , ;0' , , . ,, . . - • . I ,, • I 0;' , •, , , , I wI - ,, ., :l I ., , , I n <5 ' W :r ~O ~ (1) '0 0 (J) , , I ., , I .., , , , , , , , ~ -- ... • I - I i" , , I I , , - , , , .,- , , , , , I , , , I

a I Figure A.3. Effective Stress Contour Plot 1/8" 45 Gusset, P = 150K. I I II I g<.!l I .D I 79 I I I 20 I I I I I I I I I I Figure A.4 . Maximum Shear Surface and Contour Plot, I 1/8" 45 0 Gusset, P = l50K . I I I I 80 I I

I Inches -25 -u - 19 - 16 - 13 - 10 -7 - I 2 I • N N , ,, I , " -I '" , , I ,, I • .. • • •, I I • -. ,, '" ,, , -::s I , • I n - , , :,-0 • 1'0 til ""oS' ' 0 I I " , , , , " ...I •, " . I • , ,, " I .!. -r-___~ " I N · I I Figure A. 5. Maximum Shear Contour Plot, 1/8" 450 Gusset, P ~ 150K. I I I I I

I 81 I I In h es -~5 -22 -19 - 16 - 10 -7 -·1 - 1 I I IV'" , , , , /,. rc:' . ~) 10 , , , I , , , ,o ' , . r . I :0 __ "' , , I , ' , , 0 ~ , ' y' • I -- o \ ...... ' 0 '" ·c \ c.i' ; '0 I\J C , I C , (..) , " -- , " , , " "'s , ' , \ '"," . '0 , " / .> ~\:" . , , ," , ' ::J I "'0 ' , I - , , (') " \~ ::,-0- - ,, , , , , \ (1) , , , " 0 rJ> , " , , I I _ , , -I • <-;- , ----' ' 0 /. \ , , o I I , ~ ... , "'0' ' 0 1 15 .0/' .." -' '0 , , I • , I :;; " O~ "" I~~,; •. I I Figure A.6. Effective Stress Contour Plot, 1/8" 450 Gusset , P : 75K . I I I I ------roe {oj

100.

40.3 c::::::::J=

11.150 r 1.29// R 1.tto 6.4 I IJ.281 r ~. 90S H 10. )20 I 1.) .155 r 1.:r.!5 65. 7 R 10.810 C::::J:F===~ 1 12.105 Y 0. 891 R 12 .11,0 I 12.11/, Y .1 .81,8 ---- R 12 . I.UO X 1...' .8J.l Y 1.)85 II 12.920 =C::> 10sk

1S0 riPS

106 k

00 I"

0 Figure A. 7. Resultant Bol t Forces. l/S" 45 Gusset. P - l50K. 83 I I

I 7 . )~O I ! 1 .294 R 7.IWJ I 10. 2S1 r 0. 905 R 10.)20 I I 10 .7S5 ! 1.~5 R 1O .!10 I 12.1OS ! 0. 3.1 I R 12 . 11J I l2.17~ ! J.Sh! i\ 12 . ~OO I 12. ~Ll I r 1.)35 R 12 . 920 I I I I I .;)JS1 I r . :lJ14 !\ .:)05) If I . 0075 I r . 0010 J .0)76 I .:109S ! . :>.)12 ! . lOO6 I I .:lIlO t . OOU R ."no I .mo r . 0'J10 I 1I .0l20 I .J129 ! .;)J18 I R .01)1 I I Figure A. 8. Resultant Forces and Dis~lacements. I 1/8" 45 0 Gusset. P ~ 150K. I ------:l6aBe

50.3

24.1 c:::::::J-

X ).216 t 0.608 R ). )50 2.7 r ~ . 682 t 0.)96 R ~. 700 r ~. 7)1 ~ t ~ .LL5 28.9 c::::::J1=== R ~ . 752 x 5.S65 r 0.021 R 5. 57J X 5.20~ t n .l . 2~ R 5.2) r SSM. I o. 77~ R S. 6JO

7S liP'

53! k

0 Flgllrc A. 9 . Resul tant Bolt Fo r ces, l/B" 45 Gusset . P = 75K. I S5 I

I ).216 I ! a.5Oa R ) . )50 I L.6aZ r 0.)96 I R ~ . 700 I L. 7)1 ! J .~; ~ L. 752 I S.56S I ! 0.n1 R 5.570 I S.2JL ! 1.!J211 ~ S.2)J I I 5.sL~ ! O. 77~ I 11 5.600 I I I I I . :l(2) ! .:)007 R .ont l' I .:lO)l -i) T .0001. I I R .00))

I .;);)~1 I I .000!1 H~ .oou I iT I .;;'l!.6 ! .~JOa I n R .:>0:.7 I I

Figure A.lO. Resultant Bolt Forces and Displacements. l/S" 450 Gusset, I P = 75K. I I 86 I I

8 .03 9.68 I E!) - 52 10 .i5 I 11.19 8 82 ~33 5.54 I ~~ ~ ~---El~ ~ ~ . 7.09 -a .04 n5 rT~. "'78""-:-=-- I I I I 0 .0018 C. 0023 0.00351 .0055 --'!) -2J -'" ~ ~ ~ --el~ I ~oa19 a:1JlJ16 ....-",,16 I 0.0045 0.0020 . 0.0016 ~ ~ I o-:"j!\:s 0~1 8 O~~ O.~.~ I I Figur e A .11. Result ant Forces a nd Displacements, 1/8" 45° I Gusset Splice Plate, P - 150K. I I I!) ,1) 'D .D I .)0 I 87 I I I I I I I I I I I

I Figur e A. 12 . 3/8" 45° Gusset Grid and Distorted Geometry. I I I I I 88 I I I I I I c I I I I I I

a I Figure A.13. 3/8" 45 Gusset Effective Stress Surface Contour Plot, P = 300K . I I I I I ~

I 89 I

Ill c h e~ I -

: l\j • . Vl ' I I • , , , • ~ . - • '0 ' 0 l\; '" , c;) ~ I '0 _I . I '"' ::l I (") - -, ::r o (1) I VI ...I '0' I '0 1.. - I I I - 10 ' • ' 0 I \. I

o I Figure A.14. 3/8" 45 Gusset Effective Stress Contour Plot, P - 300K. I I I I I 90 I I I I I I I I , / \ l~ " I - ' I I I

o Figure A. IS. J/8" 4S Gusset Maximum Shear Stress Surface I Contour Plot, P : JOOK. I I I I I .;)

1 91 1 I \1\ h cs -25 - 22 - 19 - IG - 1:\ - 10 - 7 "·1 - I 2 I N 1 I ~ , ,

.., , , ... I , , .- , , 0 , , '0 ~ . 1 .,....u" , , '" '0 • , , , "0' , , '0 • • 1 • • t.> , • .C) · • ~ " • , , -:::l , .. 1 () , 0 ::l" •, til IJ) , , , 1 ... . , • '0' '0 /.- , V. O , , 1 I - , .. •, , , I 0'<;

I , N - , 1

o Figure A. 16 . 3/8" 45 Gusset ~laximum Shear Stress Contour Plot , 1 P s 300K . 1 1 1 1 ------t -rr

198.7

123.5 c:::::::J=

I 10.79 Y 2. 31. R n .oS 13.4 I 1l.L7 T 2.U6 B 1l.63 X lI..61 Y 2. 16 -- ft !I• • 76 I 16.12 886 ~ Y 2. 02 ft 16. 2L I 16 .57 Y 2. L3 =_,,=_,d...-th a 16.70 I 17.:lIS I 2.)6 ft 17.22 21 2.1 k

300 UPS

Figure A.17. Resultant Bolt Forces, 3/8" 450 Gusset, 212.1 k P = 300K. I 93 I I 110. 7' r 2.)4 • n .05 I 1).!.7 I Y 2.:l6 R 1).6) I I 16. 12 r 2.02 I ! t~ . 2u I 17 . :l6 ! 2. )6 I R 17 .22 I I

I I .J057 r . :102S ~ .0062 I .JOS8 ! . 002) I R .0:l90 I.oU O Y . :).)26 R . JU) I x . J127 ! . ~25 R .J129 I .Jl ;9 r . :lO25 I R . JlLl x . J1L8 r .JJ'2 I l . J1St I )00 0 I

Figure A.1B. Resultant Force and Displacements, 3/B" 45 a Gusset, I P = 300K. I I 94 I I 0 .0030 0.0035 0 .0044 0.0062 ri31 ~ ~ ~ --t:l I 0 .0141

I 0.0142 I I ~ I I I

12.26 13.25 15.28 18.27 I ~~ .3.00~ lZ.;xfJ ---it!) --~- ~--.:::; I 27 .08 I I I I Figure A. 19. Resultant Forces and Displacements 3/8" 4S o Gusset Splice I Plate. P • 300K. I I I ~ I 95 I I I I I I I I I I I I I I

o I Figure A. 20 . 45 Beam-Gussec Undistorted Grid. I I I I I I I I I I I I I I I

I --. I Figure A.21. 1/8" 450 Beam-Gusset Grid and I Distorted Geometry. I I I 97 I I I I

I \ 2';' I \ I I I I I I 0'"--, 0- - I I

o I Figure A. 22. 1/8" 45 Beam-Gusset Effective Stress Surface Contour Plot. P = lSOK _ I I I 98

I Inche5 - 2 ~ - 2 2 · 19 -16 - l oS - 10 -/ ..I I U' I t. - ,-' I v. '" ,,,I I a> I --. , V. '" • I ~ . - I o I N 10 " I I ., -. <0'-- --;: '" - .. • I t - '" - ..." .. ..., :J '" ~c;. ~ () I - '.- - I ::y' ,.r () ------. , (1) , VI I ", ~ \ o '" I , , -I - , , U\ • ' ~,, " -I - , I '" I _ I '" - -- .. I I I

Figure A. 23. Effective Stress Contour Plot , 1/8" 450 Beam-Gusset, I P = lSOK. I I I I .·· 1 '19 I I 12.09 I 7.02 8.00 9.01 .....-a 67 I 10.52 11 .::5 I 8 ;7 .. !) I 6.51 I I I

" "~S: I 0.0015 ).0018 O .ooo_~_ O.CO~Y·~~ ~ iC) ~ -.D ~ ~ . 019 .- 6 I .~027

I J.J047 ·21:28 J .OC20 I :;.0016 I I Figure A. 24 . Resultant Forces and Displacements 1/8" 4So Beam-Gusset. I P - lS0K. I I .-~ I 100 I I I I I I I I I I I I I - I

o I Figure A. 2S . 3/8" 4S Beam-Gusset Grid and Distorted Shape. I I I 101 I

I (II I I I I II I I I I I I , -- en -- I '" "'

a I Figure A. 26 . Effective Stress Contour Plot, 3/8" 45 Seam-Gusset, P = 3001<. I I :; I . ~ I 10Z I I I I ..:, 141 I I I 22 . 10 22 .00 I I I I I I .. :1' .;: I I Figure A. Z7. Resultant Forces 3/8" 450 Beam-Gusset, P - 300K. I I I lU3 I I I

g . Q!'~ I ... 4 , I I I I

I t5.~ .. la .... 1:. &1' 13.Si • 0 -., ..., --e ...., I ~:I!I

5.23

I ~~~ ., ,/) .,/) ~ -"J 1:'.6-4 13.:7 ii".32 :,-:'"., - I I I Figure A.28. Resultant Forces and Displacements 3/8" "5 o Beam-Gusset I Splice Plate, P - 300K . I I I!) { .-t> '/1 I 104 I I - - I

...>. I u ..E ..0 I <.:> ""...... 0 u I ....In ~ ""c: I '" ..... ""l- <.:> I u.. In :>'" <.:> I 0 0 '" Co I ...... -.

a- N I ..: ..... :> I ....00 '"" I I I I I ------• Hie

14.51 12.06 9.11 3.S8 5.2J 6.23

3.3U 4 .06

5. I H 6.19

,,!jIl62 ~~02 ~.91 '1.25 61 .... ~3 1 - - ) 38- 6 .1 5

- -- J

II. 'II 10 . 44

0 Figure A.30 . Resultsnt Forces, 60 1/8" Gusset, P - 140K...... a <.n I 106

I 0'1 0,., ~c '"s::! I ;:? Po ~c r- I r. ?J "'T:,\ r I 0 = c- ~~c ~ . .f! -= §' ~c ,'-: :: crt" ~e,<= I N -'" ? 8 ..,F= ~~ [R @ ~' 0 'If:' I 0 ~-" .1 0 Jo0 !5 '" If!. I 0~ ':::;; r- g I I 0 C N 7 I ~ I u C 0'1 u.. I ~ , ..... o ..en" I '"

..: I ...... co" -< I "- I , I ,

_0 '01 ;:: I ~ '"'~ 0: ~ = :: :: " I = :: I 107 I I 7.55 9.65 ~ ~ d9 ~~"'--I1) - I 8.34 6. 5 6 .03 5.68 .75 · I I I I I I 0.0025 I I 0 .0039 ~6 I I

o I Figure A.32. Resultant Forces and Displacements 60 1/8" Cusset Splice Plate, P - 140K. I I I . I .: -~ .1) I 108 I I I . I ..'".... ~ 0 <.:l'" I -a '"...'" 0 I ....'"co -a'" c co I -a ...... I <.:l.. co co'" ::l <.:l I 0 0 '" Co ...... I M

M M I « ... ::l'" I ...... CI) I I I I I ------u

N WW W W W W N Ul 00 0 Ul Ul o Ul

20 t--- 20 IS 15

10 ti

~ ~ - N NW W WW o 0 -0 UlO Ul O Ul UlO

Figuru A.34 . EffeClive Stress Contour Plot 3/8" 60 o Gusse t, P - 320K.

....o '" I 110

I . • I •I

I : / ' - ~ .; I V :' >c: I o ..,N • • I , /' i' 0. I /! . ! o o I 0J '" .~/ ~ I I / .,. ./ / ~ QJ U &'" I u C ; :l CO u • • .... I . ' :l ~" I . /~) ./ /1/ C / I • I I col I N N • ,I ..,. .. I I • .I • • .: • I . I I I . I ~

I 111 I I ., ··". . / · I , 0 N'" i e '~ M I r • • • f• '. o.. •. ' • . i,. ,. ~ I! ... I M III'" t ~ I-• t; t 0 0 I ).t. ",

.~ I '" -- - "til I •• I I I

• "" -11.. - r.- t . .", .- "'n - - • • • I , .. - - - -- , "' .... I - ' ,!!If) .- • • - ..... , -,,,,, -tJiI, ,."",,, I ~ "" • I

Figure A. 37. Resultant Forces and Displacements , 3/8" 600 Guss et Splice I Plate , P - 320K . I I I I I 113 I I I I ~~---~---+--~~ .--+- I I I I I I I I I

o I Figure A. 38 . Undistorted 60 Beam-Gusset Grid . I I I I I!) I!).- I ',.1...,

I 114 I I I I _.------I ------I I I I I I I o I Figure A. 39. 1/8" 60 Beam-Gusset Grid and Distorted Geometry. I I I I :~ •m I 115 I I I I I

• c '. I I I I . ....".

" I : I

0 I Figure A.40. 1/8" 60 Beam-Gusset Effective Stress Surface and Contour Plot P ~ 140K. I I I .- I ..., I 116 I I

I 0"" '! ""..... • I I ~.. 0..

~ .,Qj 'I!~ '" ~ . I <.>" ~ co I '" 0 '" 0 JP -0 I -...co

"'Qj I ...

0.0111

0 .0102

O.OOI!S

0 .1Im

0.0014

0 . ...,

0.0D5I

4 0.ooao.0QDID .0014 0.0011 O·oatS

0.000t

0 .0001

~ ...... o Figure A.42. Resultant Displacements, 1/8" 60 Beam-Gusset, P = 140K. I 113 I ,. .. I -----,. .. I ....

I ,. ..

--'" --" --" -.-:;;-" ~~i.•""S -"'''~--~ I 1.01 S.;:')' I .. '.37 . I I I

I •. = ~ .OCII • I I ~"''' -1. ...". I I

0 I Figure A.43. Resultant Forces and Displacements, 60 1/8" Beam-Gusset Splice Plate, P = 140K. I I I I 119 I I I -- 1 --. I -- . I I I I I I I I I I o I Figure A. 44 . 3/8" 60 Beam-Gusset Grid and Distorted Geometry. I I I I 120 I I (II (II (II I I I I I I I I I I

I Figure A. 4S . Effective Stress Con tour Plot , 3/8" Bea~- "usset, P - 320K. I I I I I 121 I I o N'" I M

'"CJ I

I 122 I

O. CDtO O.o:m a.DIm I -eo.oa:s ..., -.. O.otll - I

a.om I a.om 1 .a.,11 I I I I

I.", 1' ..1 , •.• _____ I . ---"" ---..... --....., I I lZ, "1 _----<0 e I • • a I I I o Figure A. 47 . Resultant Forces and Di spl acements 60 3/8" Beam-Gusset I Splice Place, P R 320K . I I I 123 I I I I I I I I I I I I I ' I I o Figure A.48. 30 Gusset Undistorred Geometry. I I I I 124 I I I I I I I I I I I I r, I I ~~------.' I I 0 Figure A. 49. J/8" 30 Gusset Grid and Distorted Geometry. I I I 125

I ~ b ~ ~ I / ( I I ''\ I I '30 40 ./ I 40 ~----I "----1 35

I 35 \ ( _//~ '--. I gg:=J l/ \ I 35~ J /-\\ 40 I I C~ JJ I I

I 45 I I () \J~~~ : J \ \ \l -; '\ \'v 30 I ~ r~TIfI\ ( ~- I I

Figure A.50. Effective Stress Contour Plot l/S" 300 Gusset. I P - 15SK. I I I :.,'" -..j

I 126

I 17.611 I I t I I I I I ZIl.311 I ~ I 14.19 IO-S3 I ~~ I 09 I \ ~ 1 8

I \ 3.u I ! 1 .Sl o I Figure A.51. Resultant Forces, 1/8" 30 Gusset, P - 158K. I I ... 1):1

I 127 I I 0.C1l2Z 0 .0031 0.0025 0.0CZ3 O.ccn C.::tl2O O.ceca 1 I I I 0.a:!41 I

I O. ot a.llc29 o. 40 ~ I 0.00'78 ot 0.C022 o.bcze 0.t19

I 0.at'117 ~ O.COI7• 0.0018

I 0.0C54 1 I I

Figure A. 52. Resultant Displacements. 1/S")0o Gusset . I P • l5SK. I I 128 I 7 .49 7.16 ____7.09 7 .57 _ 8.86 • ~ ---t) ~ ~ .. !f0.53 :e t) I ~ 13.02 - 11.81 I 6.91 6.88 7 .20 7.75 9.44 .55 I ~ ~ ~ ~ ;;:O;-~0 . 70 2 13.57 I I I I 0.0020 0.0019 0.0018 0.0021 0.D028 ~ ----'" --l1l I ~ ~ ~ ~ ~O.OOty. 0066- ~ - 0.0052 I

0.0032 0.0021 0.0018 0.0017 0.0019 0.0022 I ~ ~ ~ ~ O·~O.~~~ 0 .0074 I I

Figure A. 53. Resultant Forces and Displacements 1/8" 300 Gusset Splice I Plate, P ~ 158K. I I I .~ I ;

I 129 I I I I I I 1 I I 1 I I I I I I I - --- . I o Figure A. S4. 3/8" 30 Gusset Grid and Distorted Geometry. I I I I ~ I 130 I I I 30 I I I I I I I

I 25 :0 -- I IS ""l i I

I Figure A. SS . Effective Stress Contour Plot. 3/8" 30 0 Gusset . P = 320K I I I I 131 I

Z7.l2 ::!.l1 .:5.C'Z \ \ \ \ I \ , , , I , 152 I 90J I I

Z4 •• I 15.11 I 1~1 ~'''7 75 C!J2 .SI "... , I I

\ ~ . SB I , !I.SO

o I Figure A. 56. Resultant Forces , 3/8" 30 Gusset, P - 320K I I I I lD I 'l>,..

I 132 I ".0195 I \ I I I I •• t\X7

I • • /ISS'T I ..- I I •. 01~ 0.4112 I I

I o Figure A.S7. Resultant Displacements, 3/8" 30 Gusset, P = 320K. I I I I I" ".

I 133 I I I It.811 13.511 IS.o.c 11S .55 ~ • -e - ~- ~ I 31.60 I

I 11 .03 !)'----~ 20 . ~ I I I

0.cc:!3 o. 0D:3I5 0.00.3 O.OOSI I ~ ~ ~ -o!l -e -e ~ --e I 0 .0%11 -t O.~

I O·aaso O.oo.S 0.00.\ 0.CG40 0.0044 ~ ~ ~ ~ ~ ~ O.mO.~ ~ I

I Figure A. S8. Resultant Forces and Displacements, 3/8" 30 o Gusset Splice Plate, P - 320K. I I I I .-r.:> .n

I 134 I I I I I I I I I I I I

I I I I I I I \ \ I I I I I I I I I I

I 0 Figure A. 59. 1/8" 30 Beam-Cusset Grid and Distorted Geometry. I I I It> I ~

I 135 I

5 I 10 I I 15 I

5 I 10 15 I j~ 35 I '-----' 40

15 I <5 50 I 50 I I I

I Figure A.60. Effective Stress Contour Plot, l/S" 30 0 Beam-Gusset, I P - 15SK. I I I IP . ~ I ...,! I 136 I I

I 27~ f I 15.91 I I l.CS I I I 19.15 I IS'~

I 13.~ I I 12a ~ 5 ~1 12.15 ~ I I \Q.as I .. v'--~ ----~ .~~.S2~.C5 I

Figure A. 61. o I Resultant Forces, 1/8" 30 Beam-Gusset, p a lS8R. I I" I ~ I 137 I 0.0087 I

I O.OOS· ':j I 0.0051 I

I '-10.CO~9 ~ I ~oon

I 0.OO2p·0IW0.002S0.0023 0·0023 0.0015 O. I I

I 0.0229 I O.OOIIG

I O.DOeS I 0.0054 I 0.0050 I I I Figure A. 62 . Resultan t Displacements l/B" 30° Beam-Gusset. P = 15BK. I I ;: I I 138 I I I I 12.05 6.94 6.56 7.37 7 .80 .66 ___ I -"1!) ~ ~ ~-;;'~ .;I ~...------A> I i: 13. <36 I I

0.0020 0 .0019 0.0021 0 .0027 I ~ ~ ~ ~ --elO . ~~ I 0.0054

I O.C033 0 .0018 0.0018 0 .0020 --el ~ ~ I I I Figure A.63. Resultant Forces and Displacements 1/8" 30 o Beam-Gusset I Splice Plate, P • l58K. I I I 139 I I 1 I • ! _ .- I I I I \ I \ I I I I I I

I o Figure A. 64 . 3/8" 30 Beam-Gusset Grid and Distorted Geometry. I I I ~ I 140 I ., I I :0 ---. I 25 \ I 30 5 10 I 15 30 :0 25 I ~a ~ 30 I 35 I I

__....--, "0 I 35 33 r---., I \. I

o I Figure A. 6S . Effective Stress Contour Plot. 3/8" 30 Beam-Gusset. p - 320K. I I I 'I> I ~ • I 141 I 19.42 19.79 ~ I 20." ~

Z2.lS ~\I 134 1 I Z4.11 I I Z6 .80

1 26 .8026. 9 .34 25 fi7 I , "\ . 24.53 I I I I

I 26.87 I I I I I

o I Figure A.66 . Result ant Forces 3/8" 30 Beam Gusset, P 2 320K. I :=:D 1 ...on

I 14 2 I 0.0301 - I I

I O.Cl22O 0.OZ3Q I 1 1 I O.~ I 0.Q3IU I I I O'O~ I O.~ I I

o I Figure A. 67. Resultant Displacements 3/8" 30 Beam-Gusset. P • 320K. I I 143 I I I

I 31 .56 I I I I I

0.0It!S o.~ 0.004-4 I ~ ~ ~ ~ ~ o.~ --el o.cz\% ~-d

I 0.0%2:9

o.tx:ss 0.00-45 0.0041 O.OO.a 0·0043 I ~ ---e ~ ~ ~ ~ O.Ci'$ 0.00:;: ~ I I Figure A.68. Resultant Forces and Displacements 3/8" 300 Beam-Gusset. I P s 320K . I I I I I REFERENCES

1 . Richard, R. M., User ' s Manual for Nonlinear Finite Element Analysis I Program INELAS Dept. of Civil Engineering, The University of Arizona, Tucson, Arizona, 1968 (Updated 1982).

2. Beaufoy, L. A. and Hoharram, "Derived Homent-Angle Curves for Web I Cleat Connections," Preliminary Publication, Third Congress, International Association for Bridge and Structural Engineer I ing, 1948. 3. Lewitt, C. W., Chesson, E., and Hunse, W. B. , "Restraint Character istics of Flexible Riveted and Bolted Beam-to-Column Connections," I Structural Research Series Report No. 296, University of Illinois, Urbana , Illinois, March, 1966.

4 . Richard, R. M. , Gillett, P. E., Kreigh, J . D., and Lewis, B. A., "The I Analysis and Design of Single Plate Framing Connections," AISC Engineering Journal, No.2, 1980 .

I 5. Butler, L. J . and Kulak, G. L . , "St rength of Fillet Welds as a Function of Load," Welding Journal Research Supplement," May, 1971. I 6. Crawford, S. F. and Kulak, G. L., "Eccentrically Loaded Bolted Connec tions," Journal of the Structural Division, ASCE, ~1arch, 1971.

7. Manual of Steel Construction, 8th edition, by the American Institute of I Steel Construction, Chicago, Illinois, 1980.

8. Bjorhovde, R. and Chakrabarti, S . K., "Tests of Full Size Gusset Plate I Connections, " Research Report, In Preparation, University of Arizona, Tucson, Arizona, 1983. I 9. Richard, R. M. and Abbott, B. J., "A Versatile Elastic-Plastic Stress Strain Formula , " Journal of the Engineering Hechanics Division, ASCE , August, 1975.

I 10 . Richard R. H. , Bormby, D. E., "Force Distribution in Framing Connec tions Progress Report - May 1981 to March 1982," Department of I Civil Engineering and Engineering ~Iechanics, February, 1982. 11. Whitmore, R. E. , "Experimental Investigation of Stresses in Gusset Plates," University of Tennessee Engineering Experiment Station I Bulletin, No . 16, May, 1952. I 144 I I ."

1 145

12. Birkemoe, P. C., Eubanks, R. A., and Munse, W. H., "Distribution of 1 Stresses and Partition of Loads in Gusseted Connections," Structural Research Series Report No. 343, Department of Civil 1 Engineering, University of Illinois, Urbana, March, 1969. 13. Vasarhelyi, D. D., "Tests of Gusset Plate ~lodels," Journal of the Structural Division, ASCE, Vol. 97 , ST2, February, 1971.

1 14. Davis, C. S., "Computer Analysis of the Stresses in a Gusset Plate," M.S . thesis, Department of Civil Engineering, University of I Washington, Seattle, 1967. 15. Desai, S., "Application of the Finite Element Method to the Problem of Gusseted Connections," Fritz Engineering Laboratory Report I (Internal), January, 1970. 16. Struik, J . H. A., "Applications of Finite Element Analysis to Non Linear Plane Stress Problems," Ph . D. Dissertation, Department I of Civil Engineering, Lehigh University, Lehigh, Pennsylvania, 1972.

I 17. Birkemoe , P. C. and Gilmor, M. I., " Behavior of Bearing Critical Double Angle Beam Connections ," Engineering Journal, Am rican Institute of Steel Construction, Vol. 15, No.4, 1978, pp. 109- I 115 . 18. Yura, J. A., Birkmoe, P. C., and Ricles, J . M., "Beam-Web Shear Connections - An Experimental StudY," Journal of the Structural I Division, ASCE, Vol . 108, No. ST2, February, 1982, pp. 311-326 .

19. Ricles, J . M. and Yura, J. A., "Strength of Double-Row Bolted-Web I Connections," Journal of the Structural Division, ASCE, Vol. 109, No.1, January, 1983, pp. 126-142.

I 20 . Irish, D. J., "Strength and Behavior of Connection Elements," Masters ThesiS, Department of Civil Engineering and Engineering Mechanics, I University of Arizona, Tucson, Arizona, 1983. I I I I I Ii) .-r.:> I ." I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I