WRAP-AROUND GUSSET PLATES

WRAP-AROUND GUSSET PLATES Where a horizontal brae is loated at a beam-to-olumn intersetion, the gusset plate must be ut out around the olumn as shown in Figure. These are alled wrap-around gusset plates. At loations with large olumns and heavy beam onnetion angles, a large area of the gusset plate is ut out as shown in Figure. In addition to the limit states presented in this hapter, the designer should also investigate the limit states that would normally be heked for standard gusset plates, suh as bolt strength, weld strength, shear frature and blok shear. Figure. Horizontal brae onnetion at beam-to-olumn intersetion. Figure. Horizontal brae onnetion at beam-to-olumn intersetion. Connetion Design for Steel Strutures Chapter 7e, Page of 5 Copyright 0 by Bo Dowswell

FORCE DISTRIBUTION The assumed fore distribution in wrap-around gusset plate onnetions is shown in Figure 3. The legs of wrap-around gusset plates are subjet to limit states ommon to flexural members; therefore, eah leg of the gusset plate is modeled as a antilever beam. For design purposes, the legs are assumed independent of one another. Figure 3. Fore system for wrap-around gusset plates. SHEAR STRENGTH The nominal shear strength of eah leg is, V V = 0.6F y dt (a) n = 0.6F y d t (b) n where t is the gusset plate thikness, d and d are the depths of the gusset plate legs, and F y is the yield strength. For the design to be adequate, the following must be satisfied, φv P (a) n φv P (b) n where P and P are the fatored omponents of P. For shear yielding, φ =.0. Connetion Design for Steel Strutures Chapter 7e, Page of 5 Copyright 0 by Bo Dowswell

FLEXURAL STRENGTH Eah leg of the gusset plate must resist the flexural stresses generated by the fore system in Figure 3. This fore system results in maximum bending moments at the reentrant orner in eah leg as shown in Figure 4. Figure 5 shows the stress ontour plots for a finite element model loaded in tension. In Figure 5a, it an be seen that the highest von Mises stresses are onentrated at the reentrant orner where the two legs meet. Figure 5b shows the normal stresses in the x-diretion and Figure 5 shows the normal stresses in the y-diretion. The stresses are largest at the edges of the gusset plate legs. The stresses in the y-diretion are higher than the stresses in the x-diretion beause of the larger utout dimension in the y-diretion. These stress patterns verify the auray of the proposed design model in determining the loation of the maximum flexural stresses. Figure 4. Bending stresses in eah leg. σ T (max) Reentrant orner σ C(max) y x σ C(max) a. von Mises stresses b. x-x normal stresses. y-y normal stresses Figure 5. Elasti Stress ontours for a typial model loaded in tension. y σ T (max) x From strain gage data and finite element models, it was determined that the flexural stresses in the gusset plates exeeded the yield stress throughout muh of the gusset plate. Although most of the plates had a substantial amount of the material above the proportional limit, none of the Connetion Design for Steel Strutures Chapter 7e, Page 3 of 5 Copyright 0 by Bo Dowswell

plates reahed full plastiity before bukling. A typial plot of the elasti and inelasti stresses is shown in Figure 6 for a finite element model loaded to its failure load. The theoretial stresses, whih were alulated using simple beam theory, are also shown in the figure. The proposed design method is based on an elasti bending stress distribution. The in-plane flexural deformation of Speimen T is shown in Figure 7. 0 Depth of Leg () 5.5 Elasti Plasti Theory -80-60 -40-0 0 0 40 60 80 Flexural Stress (ksi) Figure 6. Typial flexural stresses in gusset plate legs. Figure 7. In-plane deformation of Speimen T. The bending moments at the ritial setions of the plate are M M = Pe (3a) u = Pe (3b) u where P and P are the omponents of the fatored brae load, P. e and e are the utout dimensions at eah leg, as shown in Figure. The nominal moment apaity of eah leg is Connetion Design for Steel Strutures Chapter 7e, Page 4 of 5 Copyright 0 by Bo Dowswell

M td = (4a) n Fy 6 M td = (4b) n Fy 6 For the design to be adequate, the following must be satisfied: φm M (5a) n u φm M (5b) n u where φ = 0.9 for flexural yielding. Sometimes wrap-around gusset plates have the interior orner ut on a diagonal as shown in Figure 8b in an effort to inrease their apaity. The test Speimens 8 and 0, shown in Figure 8, were idential exept for the diagonal ut on Speimen 0. The tests and finite element models showed that the average apaity for Speimen 0 was perent higher than the average apaity for Speimen 8. Figure 9 shows the stress ontour plots for Speimen 0. Figure 9a shows the normal stresses in the x-diretion and Figure 9b shows the normal stresses in the y- diretion. The moment apaity at ross setions a-a and b-b should be heked at eah leg using Equations 3, 4, and 5. Calulations show that the flexural stresses in the x-diretion at Setion b-b are.40 times the stresses at Setion a-a. The finite element stresses in Figure 8a onfirm this. Similarly, Figure 8b onfirms that Setion a-a ontrols the design for the stresses in the y-diretion. The alulated flexural stresses in the y-diretion are 89% higher at Setion a-a than they are at Setion b-b. a. Speimen 8 b. Speimen 0 Figure 8. Details of Speimens 8 and 0. Connetion Design for Steel Strutures Chapter 7e, Page 5 of 5 Copyright 0 by Bo Dowswell

a b σ T (max) a y σ C(max) x b a. x-diretion normal stresses b a b a y σ C(max) x σ T (max) b. y-diretion normal stresses Figure 9. Elasti Stress ontours for a typial model loaded in tension. Connetion Design for Steel Strutures Chapter 7e, Page 6 of 5 Copyright 0 by Bo Dowswell

LATERAL-TORSIONAL BUCKLING Due to the flexural stresses in the gusset plate legs, they are subjet to lateral-torsional bukling. Tests showed that the flexural stresses in the legs an ause lateral-torsional bukling, even if the brae is loaded in tension. The permanent deformation in tension and ompression speimens an be seen in Figures 0 and respetively. All of the speimens had a permanent out-ofplane deformation at the plate edges with flexural ompression stresses. The out-of-plane deformation was aompanied by twisting of the gusset plate legs, indiating a lateral-torsional bukling failure. The finite element models are shown in Figures and 3 for tension and ompression loads respetively. a. top view. b. side view of longer edge. Figure 0. Tension Speimen T after test. a. Speimen 4C b. Speimen 7C Figure. Compression Speimens 4C and 7C after test. Connetion Design for Steel Strutures Chapter 7e, Page 7 of 5 Copyright 0 by Bo Dowswell

Maximum out-of-plane defletion a. Top view. Maximum out-of-plane defletion b. Side View. Figure. Typial bukled shape for the models loaded in tension. Maximum out-of-plane defletion Figure 3. Typial bukled shape for the models loaded in ompression. Eah leg of the gusset plate an be modeled as a antilever beam to determine the bukling load. Using the equations developed by Dowswell (004) for wide flange antilever beams, the ritial moment is, M r 3 dt i = 0.94 EG (9) L i Connetion Design for Steel Strutures Chapter 7e, Page 8 of 5 Copyright 0 by Bo Dowswell

Where E is the modulus of elastiity and G is the shear modulus. The design bukling apaity must be greater than the internal moment at eah gusset plate leg. φm M (0a) r u φm M (0b) r u where M u and M u are determined with Equations 3a and 3b respetively, and φ = 0.9 for lateral-torsional bukling. To determine the bukling length, L i to be used in Equation 9, the bukled shape of the speimens and finite element models was observed. For the speimens loaded in tension, the inside edges bukled farther than the outside edges. This behavior was expeted beause the maximum ompressive flexural stresses are on the inside edges, at the reentrant orner. The speimens loaded in ompression bukled farther on the outside edges. Figure 4 shows how this behavior affets the bukling length of the legs. The plate in Figure 4a was loaded in tension. The bukling of eah leg is restrained at the reentrant orner and the bukling length, L i is the length of the utout. The following bukling lengths an be used when the plate is loaded in tension: L= e for Leg, and L = e for Leg. For plates loaded in ompression, as shown in Figure 4b, the bukling length ends approximately at the enter of the adjaent leg. For design purposes, the following bukling lengths an be used when the plate is loaded in ompression: L = e + d for Leg, and L = e + d for Leg. Connetion Design for Steel Strutures Chapter 7e, Page 9 of 5 Copyright 0 by Bo Dowswell

L a. Plates loaded in tension. L b. Plates loaded in ompression. Figure 4. Effetive length of gusset legs. For plates with a diagonal ut as shown in Figure 7b, whih are loaded in tension, the bukling length an be taken as the portion of the leg with parallel edges, measured to the start of the diagonal ut. For plates with a diagonal ut loaded in ompression, the bukling length is determined the same as for standard gusset plates. VAILIDATION OF DESIGN METHOD The nominal apaity of the plate, P min is the minimum of the bending, shear, and bukling limit states. The apaities for eah speimen were alulated using the proposed design method, and summarized in Table. All of the loads are expressed as the maximum nominal load parallel to the brae based on the minimum apaity of the two legs. P e is the bending apaity, P v is the shear apaity, P b is the lateral-torsional bukling apaity, and P min is the minimum of P e, P v and P b. The speimen numbers are suffixed with T if the plate was loaded in tension, and C if it was loaded in ompression. Connetion Design for Steel Strutures Chapter 7e, Page 0 of 5 Copyright 0 by Bo Dowswell

Table. Calulated apaities. Spe. No. P e P v P b P min Pred. Failure Mode T 33. 45.7 05.94 33. Y 6T 3.79 0.7 43.48 3.79 Y 8T 46.00 55.8 4.9 46.00 Y 9T 35.77 5.6 84.90 35.77 Y 0T 68.00 04.0 45.7 68.00 Y C 39.5 5.9 56.80 39.5 Y C 3.87 44.6 73.46 3.87 Y 3C 36.4 5.6 96.08 36.4 Y 4C 3. 0.7 6.3 6.3 B 5C 5.84 8.70.43.43 B 6C 3.79 0.7 7.83 7.83 B 7C 45.07 44. 4.9 45.07 Y 8C 46.48 57.4 94.73 46.48 Y 9C 36.7 8.6 69.46 36.7 Y 0C 67.47 0.4 9.83 67.47 Y P e alulated elasti bending apaity P v alulated shear apaity P b alulated lateral-torsional bukling apaity P min minimum of P e, P v and P b (proposed nominal apaity) Y: yielding B: bukling The experimental results are summarized in Table. P ey is the experimental yield load, the yield load from the finite element models, and P avg is the average of P ey and P fy. P fy is Connetion Design for Steel Strutures Chapter 7e, Page of 5 Copyright 0 by Bo Dowswell

Table. Experimental and finite element loads. Spe. No. P ey P fy P avg P avg Pmin Exp. Failure Mode T 69.0 50.7 59.85.8 Y/B 6T 4.3 39.9 4.0.9 Y/B 8T 85.3 73.8 79.55.73 Y/B 9T 5.5 46.9 49.0.38 Y/B 0T 96. 84.8 90.50.33 Y/B C 33.3 5.6 4.45.07 Y/B C 47.3 44.7 46.00.40 Y 3C 46.6 45.0 45.80.7 Y/B 4C 3.0 30. 3.0.9 B 5C 8.7 36.3 3.50.45 Y/B 6C 5.3 34.5 9.90.07 B 7C 46.4 5.3 48.85.08 Y/B 8C 38.4 67.6 53.00.4 Y 9C 44.4 38.7 4.55.3 Y/B 0C 57.0 76.6 66.80 0.99 Y/B P ey experimental yield load determined using a /64 offset P finite element yield load determined using a /64 offset fy P avg average of ey P and P fy The P avg to P min ratios are in the fifth olumn of Table. Pavg Pmin varied from 0.99 to.9 with an average of.34 and a standard deviation of 0.8. Dowswell and Barber (004) summarized the test results for ompat orner gusset plates in ompression, and found the urrent design equations to be onservative by an average of 47 perent with a standard deviation of 0.3. Based on this data, the auray of the proposed design proedure for wrap-around gusset plates is similar to the auray of the urrent design proedure for standard gusset plates. The experimental failure modes are summarized in the sixth olumn of Table. All of the speimens failed by a ombination of bukling and yielding; therefore it was diffiult to determine whether the orret failure mode was predited with the proposed design method. Two of the speimens, Speimens C and 8C, were almost fully yielded before bukling ourred due to a loss of stiffness. Both of these speimens also had a predited failure mode of yielding as shown in Table. Speimens 4C and 6C bukled while most of the plate material was in the elasti range. The predited failure mode for both of these plates was also bukling. For these four tests with definite failure modes, the design model predited the orret failure mode. Connetion Design for Steel Strutures Chapter 7e, Page of 5 Copyright 0 by Bo Dowswell

EXAMPLES Example The strength of the wrap around gusset plate onnetion in Figure 5 will be heked using LRFD. The bottom of the brae is down 4¼ from the top of steel. Axial fore in brae: 35 kips tension or ompression Gusset plate thikness: a Gusset plate material: A57 Grade 50 Clip angle material: A36 W and WT material: A99 Bolts: ¾- diameter A35N Weld: 70 ksi AWS Edge Distane: ¼ unless shown otherwise Holes: Standard m- diameter Figure. E-. Connetion for Example. Brae-to-Gusset Plate Bolt shear frature From Manual Table 7-, the design shear strength for eah bolt, φ = 5.9 kips bolt. r n Connetion Design for Steel Strutures Chapter 7e, Page 3 of 5 Copyright 0 by Bo Dowswell

φ = 6 bolts 5.9 kips bolt = 95.4 kips > 35 kips o.k. v Bolt bearing at gusset plate The smallest edge distane is for the bolt losest to the W8. The distane in the diretion of load, from the enter of the bolt to the plate edge, is.64 L =.64 3 6 =.3 Figure E-. ( 0.75)(.)(.3 )( 3 8 )( 65 ksi) ( 0.75)(.4)( 3 4 )( 3 8 )( 65 ksi) φ = φ = 48.9 kips / bolt > 3.9 kips / bolt. Use φ = 3.9 kips / bolt Between the bolts, L = 3 3 6 =.9 ( 0.75)(.)(.9 )( 3 8 )( 65 ksi) ( 0.75)(.4)( 3 4 )( 3 8 )( 65 ksi) φ = φ = 48.0 kips / bolt > 3.9 kips / bolt. Use φ = 3.9 kips / bolt φ = 3.9 kips / bolt 6 bolts = 97 kips >3 5 kips o.k. Bolt bearing at brae flange Holes at end of brae: 4 L = 3 6 = 0.844 ( 0.75)(.)( 0.844 )( 0.530 )( 65 ksi) ( 0.75) (.4) ( 3 4 ) ( 0.530 )( 65 ksi) φ = Connetion Design for Steel Strutures Chapter 7e, Page 4 of 5 Copyright 0 by Bo Dowswell

φ = 6. kips / bolt 46.5 kips / bolt. Use φ = 6. kips / bolt Remaining holes: L = 3 36=.9 ( 0.75)(.)(.9 )( 0.530 )( 65 ksi) ( 0.75)(.4)( 3 4 )( 0.530 )( 65 ksi) φ = φ = 67.9 kips / bolt > 46.5 kips / bolt. Use φ = 46.5 kips / bolt φ = 6. kips / bolt bolts + 46.5 kips / bolt 4 bolts = 38 kips >35 kips o.k. Whitmore yielding ( ) L = 5 + 6 tan 30 =.4 w A = 3 8.4 = 4.65 w P = 4.65in 50 ksi = 3 kips n φ = 0.9 3 kips = 09 kips > 35 kips o.k. P n Blok shear of brae flange gv ( 7.5 )( 0.530 ) 3.84 in A = = ( ) A nv = 7.5.5 holes 7 8 0.530 =.68 in 8.00-5 A gt = =.5 in ( ) A nt = hole 7 8 0.530 = 0.43 in 4 U =.0 φ= 0.75 bs ( )( 0.6 0.6 ) R = FA + U FA FA + U FA n u nv bs u nt y gv bs u nt 0.6 FA + U FA = (0.6)(65 ksi )(.68 ) + (.0)(65 ksi)(0.43 ) = 3 kips u nv bs u nt 0.6 FA + U FA = (0.6)(50 ksi)(3.84 ) + (.0)(65 ksi)(0.43 ) = 43 kips y gv bs u nt Connetion Design for Steel Strutures Chapter 7e, Page 5 of 5 Copyright 0 by Bo Dowswell

( ) φ = 0.75 3 kips = 98 kips > 35 kips o.k. Blok shear of gusset plate Due to the geometry of the gusset plate, blok shear an our in ompression, where the shear planes extend into the utout. For ompression loads, the edge distanes in the diretion of load are 6.44 and.64, and for tension loads, the edge distanes are 3. and 4.4 The sum of edge distanes is smaller for tension loads; therefore, this will result in the lowest blok shear apaity. ( )( 6 ) 3. +4.4 ( 3 8 ) 7.3 in A gv = + = A = 7.3.5 holes 7 8 3 8 = 5.68 in nv ( ) ( ) A nt = 5.5 hole 7 8 3 8 =.73 in U =.0 φ= 0.75 bs R = 0.6FA + U FA 0.6FA + U FA n u nv bs u nt y gv bs u nt 0.6 FA + U FA = (0.6)(65 ksi )(5.68 ) + (.0)(65 ksi)(.73 ) = 334 kips u nv bs u nt 0.6 FA + U FA = (0.6)(50 ksi)(7.3 ) + (.0)(65 ksi)(.73 ) = 33 kips y gv bs u nt φ = 0.75 33 kips = 49 kips > 35 kips o.k. Leg Conneting to W4 Shear yielding of gusset plate Fydt ( ) φ V =.0 0.6 =.0 0.6 50 ksi 0 3 8 = kips n kips >.5 kips o.k. Flexural yielding of gusset plate td ( 38 )( 0 ) ( ) Fy φ Mn = 0.9 = 0.9 50 ksi = 8 kip 6 6 Mu= Pe =.5 kips = 70 kip Connetion Design for Steel Strutures Chapter 7e, Page 6 of 5 Copyright 0 by Bo Dowswell

8 kip- > 70 kip- o.k. Lateral-torsional bukling of gusset plate leg L=7 for ompression loads and for tension loads. Use L=7 3 dt ( 0 )( 3 8 )3 φ M r = 0.9 6,848 = 0.9 6,848 = 470 k L 7 470 k- > 70 k- o.k. Bolt shear frature The work point is loated at the enter of the W4; therefore, the bolts are subjet to an eentriity of w From Manual Table 7-, the available shear strength for eah bolt, φ = 5.9 kips bolt. r n Interpolating from Manual Table 7-7 with Angle = 0, S = 3, n = 3, and e x = w : C =.33. φ =.33 bolts 5.9 kips bolt = 37.0 kips >.5 kips o.k. v Bolt bearing at gusset plate For bolt bearing, the effet of eentriity must be aounted for; therefore, the effetive number of bolts, C =.33, will be used from Manual Table 7-7. The smallest edge distane is 4, whih is at the edge parallel to the beam axis. Although the load is parallel to this edge, the bolt group is loaded eentrially, and eah bolt has a skewed resultant load, with at least a small omponent perpendiular to the smallest edge. It is onservative to assume the 4 edge distane applies to all bolts in the bearing alulation. 4 L = 3 6 = 0.844 Between the bolts, L = 3 3 6 =.9 0.844 <.9 ; use L = 0.844 ( 0.75)(.)( 0.844 )( 3 8 )( 58 ksi) ( 0.75)(.4)( 3 4 )( 3 8 )( 58 ksi) φ = φ = 6.5 kips / bolt 9.4 kips / bolt. Use φ = 6.5 kips / bolt Connetion Design for Steel Strutures Chapter 7e, Page 7 of 5 Copyright 0 by Bo Dowswell

φ = 6.5 kips / bolt.33 bolts = 38.4 kips >.5 kips o.k. Bolt bearing at beam flange For bolt bearing, the effet of eentriity must be aounted for; therefore, the effetive number of bolts, C =.33, will be used from Manual Table 7-7. The edge distane perpendiular to the beam axis is 3 L = 6.73 =.6 4 L =.6 3 6 =. Between the bolts, L = 3 3 6 =.9. <.9 ; use L =. ( 0.75)(.)(. )( 0.385 )( 65 ksi) ( 0.75)(.4)( 3 4 )( 0.385 )( 65 ksi) φ = φ = 7. kips / bolt 33.8 kips / bolt. Use φ = 7. kips / bolt φ = 7. kips / bolt.33 bolts = 63.4 kips >.5 kips o.k. Shear frature of gusset plate ( )[ ]( ) φ R = 0.75 0.6 3 8 0 (3)(7 / 8 ) 65 ksi = 80.9 kips >.5 kips o.k. n Flexural frature of gusset plate at W4 bolts 3 ( ) (.50 )(. )( 3 8 ) ( 4. )(.56 )( 3 8 ) 7.3 Ζ net = + = 3 φ M = F Z = 65 ksi 7.3 = 476 kip- n u net 3 M =.5 kips = 39.4 kip- < 476 kip- o.k. u 4 Blok shear of gusset plate Connetion Design for Steel Strutures Chapter 7e, Page 8 of 5 Copyright 0 by Bo Dowswell

gv ( 8 )( 3 8 ) 3.00 in A = = ( ) A nv = 8.5 holes 7 8 3 8 =.8 in ( ) A nt = hole 7 8 3 8 = 0.305 in 4 U =.0 φ= 0.75 bs R = 0.6FA + U FA 0.6FA + U FA n u nv bs u nt y gv bs u nt 0.6 FA + U FA = (0.6)(65 ksi )(.8 ) + (.0)(65 ksi)(0.305 ) = 05 kips u nv bs u nt 0.6 FA + U FA = (0.6)(50 ksi)(3.00 ) + (.0)(65 ksi)(0.305 ) = 0 kips y gv bs u nt φ = 0.75 05 kips = 78.8 kips >.5 kips o.k. Leg Conneting to W8 Shear yielding of gusset plate Fyd t ( ) φ V =.0 0.6 =.0 0.6 50 ksi 0 3 8 = kips n kips > 6.8 kips o.k. Flexural yielding of gusset plate td ( 38 )( 0 ) ( ) Fy φ Mn = 0.9 = 0.9 50 ksi = 8 kip 6 6 Mu = Pe = 6.8 kips 8.5 = kip 8 kip- > kip- o.k. Lateral-torsional bukling of gusset plate leg L=3.5 for ompression loads and 8.5 for tension loads. Use L=3.5 3 dt ( 0 )( 3 8 )3 φ M r = 0.9 6,848 = 0.9 6,848 = 603 kip L 3.5 Connetion Design for Steel Strutures Chapter 7e, Page 9 of 5 Copyright 0 by Bo Dowswell

603 kip- > kip- o.k. Bolt shear frature The gage in the outstanding leg of the lip angle is ; therefore, the bolts are subjet to an eentriity of From Manual Table 7-, the available shear strength for eah bolt, φ = 5.9 kips bolt. r n From Manual Table 7-7 with Angle = 0, S = 3, n = 3, and e x = : C =.3. φ =.3 bolts 5.9 kips bolt = 35.5 kips > 6.8 kips o.k. v Shear yielding at lip angle ( ) φ =.0 0.6 3 8 9 36 ksi = 7.9 kips > 6.8 kips o.k. Shear frature at lip angle ( )[ ]( ) φ = 0.75 0.6 3 8 9 (3)(7 / 8 ) 58 ksi = 6.4 kips > 6.8 kips o.k. Weld lip angle to gusset plate Manual Table 8-8 with the load angle equal zero kl = 3 = 3.00 l = 9 kl 3.00 k = = = 0.333 l 9 x = 0.0670 Interpolated from Table 8-8 xl = ( 0.0670)( 9 ) = 0.603 al = 3 0.603 =.90 al.90 a = = = 0.3 l 9 Connetion Design for Steel Strutures Chapter 7e, Page 0 of 5 Copyright 0 by Bo Dowswell

Interpolating from Table 8-8 k 0.3 0.333 0.4 a 0.300.79.94 3.3 0.3.86 0.400.45.58.84 D req, d Pu 6.8 kips = = =.39 sixteenths <3 φcc l (0.75)(.86)(.0)(9 ) o.k. Blok shear of gusset plate around perimeter of weld t req, d Dreq, d.39 = 3.09 = ( 3.09) = 0.066<38 F 65 u o.k. Bolt bearing at lip angle For bolt bearing, the effet of eentriity must be aounted for; therefore, the effetive number of bolts, C =.3, will be used from Manual Table 7-7. The edge distane is The bolt group is loaded eentrially, and eah bolt has a skewed resultant load, with at least a small omponent perpendiular to the edge. It is onservative to assume the edge distane applies to all bolts in the bearing alulation. L = 3 6 =.09 Between the bolts, L = 3 3 6 =.9.09 <.9 ; use L =.09 ( 0.75)(.)(.09 )( 3 8 )( 58 ksi) ( 0.75)(.4)( 3 4 )( 3 8 )( 58 ksi) φ = φ =.3 kips / bolt 9.4 kips / bolt. Use φ =.4 kips / bolt φ =.4 kips / bolt.3 bolts = 47.7 kips > 6.8 kips o.k. Bolt bearing at beam web For bolt bearing, the effet of eentriity must be aounted for; therefore, the effetive number of bolts, C =.3, will be used from Manual Table 7-7. Connetion Design for Steel Strutures Chapter 7e, Page of 5 Copyright 0 by Bo Dowswell

( ) φ = 0.75.4 3 4 0.300 65 ksi = 6.3 kips φ = 6.3 kips / bolt.3 bolts = 58.6 kips > 6.8 kips o.k. Flexural yielding of lip angle at outstanding leg ( 38 )( 9 ) 3 Ζ= = 7.59 4 3 φ M = F Z = 50 ksi 7.59 = 380 kip- n y M = 6.8 kips = 53.6 kip- < 380 kip- o.k. u Flexural frature of lip angle at outstanding leg 3 ( ) (.50 )(. )( 3 8 ) ( 3.97 )(.06 )( 3 8 ) 5.54 Ζ net = + = 3 φ M = F Z = 65 ksi 5.54 = 360 kip- n u net M = 6.8 kips = 53.6 kip- < 360 kip- o.k. u Blok shear of lip angle gv ( 7 )( 3 8 ).8in A = = ( ) A nv = 7.5 holes 7 8 3 8 =.99 in ( ) A nt = hole 7 8 3 8 = 0.398 in U =.0 φ= 0.75 bs R = 0.6FA + U FA 0.6FA + U FA n u nv bs u nt y gv bs u nt 0.6 FA + U FA = (0.6)(58 ksi )(.99 ) + (.0)(58 ksi)(0.398 ) = 9.3 kips u nv bs u nt 0.6 FA + U FA = (0.6)(36 ksi)(.8 ) + (.0)(58 ksi)(0.398 ) = 83.8 kips y gv bs u nt Connetion Design for Steel Strutures Chapter 7e, Page of 5 Copyright 0 by Bo Dowswell

φ = 0.75 83.8 kips = 6.8 kips > 6.8 kips o.k. Disussion The method of setions was used to alulate the stresses at ritial loations in the gusset plate. The seletion of the ritial setions is at the disretion of the engineer and is based on judgment and experiene, and in many ases, the ritial ross setion will not be at the same loation as for this example. One example of this ours when the outside orner of the gusset plate is ut on a diagonal. In this ase, the bending apaity of the gusset must be heked along the diagonal. The inside orner an be ut as required to provide adequate bending resistane. Example The strength of the gusset plate in Figure 6 will be heked. The onnetion is idential to the one in Example, exept the utout has a diagonal ut and the load has been inreased to 50 kips. Only the limit states assoiated with the strength of the gusset plate legs will be heked. Axial fore in brae: 50 kips tension or ompression Gusset plate thikness: a Plate material: A57 Grade 50 Figure. E-. Connetion for Example. Shear in Leg Fydt ( ) φ V =.0 0.6 =.0 0.6 50ksi 0 0.375 = 3 kips n Connetion Design for Steel Strutures Chapter 7e, Page 3 of 5 Copyright 0 by Bo Dowswell

3 kips > 3. kips o.k. Shear in Leg Shear apaity will be analyzed at a plane immediately beyond the lip angle leg. The leg width at this loation is, d = 0 + 4 3.5 8.5 =.7in. Fyd t ( ) φ V =.0 0.6 =.0 0.6 50ksi.7 0.375 = 3 kips n 3 kips > 38.3 kips o.k. Bending in Leg td ( 0.375 )( 0 ) ( ) Fy φ Mn = 0.9 = 0.9 50ksi = 8 kip 6 6 Mu= Pe = 3.kips 8 = 57 kip 8 kip > 57 kip o.k. Bending in Leg (Case : Immediately beyond the lip angle leg) d = 0 + 4 3.5 8.5 =.7in. td ( 0.375 )(.7 ) ( ) Fy φ Mn = 0.9 = 0.9 50ksi = 385 kip 6 6 Mu = Pe = 38.3kips 3.5 = 34 kip 385 kip > 34 kip o.k. Bending in Leg (Case : End of diagonal ut) td ( 0.375 )( 4 ) ( ) Fy φ Mn = 0.9 = 0.9 50ksi = 55 kip 6 6 Mu = Pe = 38.3kips 8.5 = 36 kip Connetion Design for Steel Strutures Chapter 7e, Page 4 of 5 Copyright 0 by Bo Dowswell

55 kip > 36 kip o.k. Bukling at Leg L=7 for ompression loads and 8 for tension loads. Use L=7 3 dt ( 0 )( 0.375 )3 φ M r = 0.9 6,848 = 0.9 6,848 = 470 kip L 7 470 kip > 57 kip o.k. Bukling at Leg L=3.5 for ompression loads and 0 for tension loads. Use L=3.5 3 dt ( 0 )( 0.375 )3 φ M r = 0.9 6,848 = 0.9 6,848 = 604 kip L 3.5 604 kip > 34 kip o.k. REFERENCES Dowswell, B. (005), Design of Wrap-Around Steel Gusset Plates, Ph.D. Dissertation, The University of Alabama at Birmingham. Dowswell, B. (004), Lateral-Torsional Bukling of Wide Flange Cantilever Beams, Engineering Journal, AISC, Third Quarter, pp. 35-47. Dowswell, B. and Barber, S. (004), Bukling of Gusset Plates: A Comparison of Design Equations to Test Data, Proeedings of the Annual Stability Conferene, Strutural Stability Researh Counil, Rolla, MO. Connetion Design for Steel Strutures Chapter 7e, Page 5 of 5 Copyright 0 by Bo Dowswell