SHEAR CONNECTION: DESIGN OF W-SHAPE BEAM TO RECTANGULAR/SQUARE HSS COLUMN SHEAR PLATE CONNECTION CALCULATION FOR SHEAR CONNECTION 8.xmcd 1 of 30
I. DESIGN DATA AND LOAD ( LRFD - AISC 14th Edition ) COLUMN PROPERTIES (col): HSS8X8X5/8 - A500-B Fy col = 46 ksi H col = 8 in tw col = 0.581 in E:= 29000ksi Fu col = 58 ksi B col = 8 in Ag col = 16.4 in 2 BEAM PROPERTIES (bm): W18X35 - A992 Fy bm = 50 ksi d bm = 17.7 in tw bm = 0.3 in k1 bm = 0.75 in Fu bm = 65 ksi bf bm = 6 in tf bm = 0.425 in k bm = 1.125 in Ag bm = 10.3 in 2 Sx bm = 57.6 in 3 Length of Beam, L bm := 10ft + 0in SHEAR PLATE (pl): A36 Fy pl = 36 ksi Fu pl = 58 ksi tpl := 3 8 in BOLTS: For Shear Plate to Beam Connection: Bolt Diameter, Bolt Shear Strength, Bolt Tensile Strength, Beam Edge Distance, db = 0.75 in Bolt_Type = "A325-N" Λrv = 17.892 kips Conn_type = "Bearing-type" Λrn = 29.821 kips Leh bm = 1.5 in Hole diameter: Plate Vertical Edge Distance, Plate Horizontal Edge Distance, Bolt Vertical Spacing, Bolt Horizontal Spacing (For Multiple bolt lines), Lev = 1.5 in Leh = 1.5 in s = 3 in sv = 3 in Shear Plate, hd plv = 0.875 in hd plh = 1.063 in Beam, hd bm = 0.875 in CALCULATION FOR SHEAR CONNECTION 8.xmcd 2 of 30
Bolt First Down from Top of beam, D = 3 in Gap between edge of beam to edge of support, gap := 1 2 in number of bolt rows: nr:= 5 number of vertical bolt lines: nv:= 2 total number of bolts: n:= nr nv n = 10 WELDS: E70xx LH Fu w = 70 ksi Preferred Weld Size Shear Plate to Column, w 1 := Ceil 5 8 tpl 1, 16 in 1 = 4 in SAFETY AND RESISTANCE FACTORS: Safety Factor, Ω (ASD) Resistance Factor, φ (LRFD) Modification Factor, 1 Λ= (IF ASD) Λ= ϕ (IF LRFD) Ω safety factor resistance factor modification factor For member/bolt in bearing, Ω brg = 2.00 ϕ brg = 0.75 Λ brg = 0.75 For block shear, Ω bs = 2.00 ϕ bs = 0.75 Λ bs = 0.75 For flexural local buckling / flexural strength, Ω b = 1.67 ϕ b = 0.9 Λ b = 0.90 For flexural rupture, Ω fr = 2.00 ϕ fr = 0.75 Λ fr = 0.75 For member shear (C, WT, L) For shear on N-type bolts, For fillet weld (shear), Ω v = 1.67 ϕ v = 0.90 Λ v = 0.90 Ω vtn = 2.00 ϕ vtn = 0.75 Λ vtn = 0.75 Ω vw = 2.00 ϕ vw = 0.75 Λ vw = 0.75 For shear rupture, Ω vr = 2.00 ϕ vr = 0.75 Λ vr = 0.75 For shear yielding, Ω vy = 1.50 ϕ vy = 1.00 Λ vy = 1.00 CALCULATION FOR SHEAR CONNECTION 8.xmcd 3 of 30
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APPLIED LOAD: % UDL, UDL:= 0.5 Given Load if any, Beam Shear Load, V giv := 0kips V = 99.8 kips 50% UDL II. CALCULATIONS: A. BEAM CHECK 1. Bolt Bearing Capacity on Beam (AISC 14th Ed. Specifications Chapter J, Section J3.10, pages 16.1-127 to 16.1-128) Bearing Area, Abrg bm := db tw bm Abrg bm = 0.225 in 2 Bolt centerline distance from face of support, a b := gap + Leh bm + 0.5( nv 1) sv a b = 3.5 in Eccentric Load Coefficient, (Table 7-7, AISC 14th Ed.) C = 7.292 Allowable Bearing Strength using edge distance,(j3-6a,j3-6c) Fbe:= Λ brg Fu bm Fbe = 18.647 kips min min ( ) ( ) 1.0 D 0.5 hd bm 1.0 Leh bm 0.5 hd bm 2.0 Abrg bm ( ) ( ) 1.2 D 0.5 hd bm 1.2 Leh bm 0.5 hd bm 2.4 Abrg bm tw bm tw bm tw bm tw bm if hd bm hd ls otherwise CALCULATION FOR SHEAR CONNECTION 8.xmcd 5 of 30
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Allowable Bearing Strength using bolt spacing,(j3-6a,j3-6c) Fbs:= Λ brg Fu bm Fbs = 26.325 kips ( ) ( ) min 1.0 s hd bm tw bm, 2.0 Abrg bm if hd bm hd ls min 1.2 s hd bm tw bm, 2.4 Abrg bm otherwise Bolt Bearing Capacity, Rbrg bm := C min( Fbe, Fbs, Λrv) Rbrg bm = 130.478 kips V = 99.8 kips RESULT = Bearing Capacity > Force Applied,OK 2. Shear Capacity of Beam (AISC 14th Ed. Specifications Chapter G, Section G2.1, pages 16.1-67 to 16.1-69) Clear distance between flanges of beam, less the fillet or corner radii, h:= d bm 2 kdes bm h = 16.046 in Limiting depth-thickness ratio, h tw := h tw bm h tw = 53.487 Clear distance between transverse stiffeners, a:= 0in if h tw < 260 min 3 h, 260 h tw 2 h otherwise a = 0 in CALCULATION FOR SHEAR CONNECTION 8.xmcd 7 of 30
Web plate buckling coefficient, kv:= 5 if h tw < 260 5 + 5 otherwise a h 2 (G2-6) kv = 5 Web shear coefficient, Cv:= 1 if h tw 1.1 kv E Fy bm (G2-3) kv E 1.1 Fy bm if 1.1 h tw kv E Fy bm < h tw 1.37 kv E Fy bm (G2-4) 1.51 E kv if 1.37 2 h tw Fybm kv E Fy bm < h tw (G2-5) Cv = 1 Shear Capacity of Section, Rv bm := Λ vbm 0.6 Fy bm d bm tw bm Cv (G2-1) Rv bm = 159.3 kips V = 99.8 kips RESULT = Shear Capacity of Section > Force Applied, OK B. BEAM TO SHEAR PLATE CHECK 1. Eccentric Bolt Shear Capacity (AISC 14th Ed. Manual Part 7, pages 7-6 to 7-12) Shear Capacity per bolt, Λrv = 17.892 kips CALCULATION FOR SHEAR CONNECTION 8.xmcd 8 of 30
Eccentric Bolt Capacity, Reb:= C Λrv Reb = 130.478 kips V = 99.8 kips RESULT = Bolt Shear Capacity > Force Applied, OK 2. Check for Spacing (AISC 14th Ed. Specifications Chapter J, Section J3.3 and J3.5, pages 16.1-122 to 16.1-124) Vertical Spacing, s = 3 in s min := 2 2 db 3 s min = 2 in ( ( )) s max := min 12in, 24 min tw bm, tpl s max = 7.200 in RESULT = s > s.min & s < s.max, OK Horizontal Spacing, sv = 3 in sv min := 2 2 db 3 sv min = 2 in ( ( )) sv max := min 12in, 24 min tw bm, tpl sv max = 7.200 in RESULT = sv > sv.min & sv < sv.max, OK 3. Check for Edge Distance (AISC 14th Ed. Specifications Chapter J, Section J3.4 and J3.5, pages 16.1-122 to 16.1-124) Vertical Edge Distance, Lev = 1.5 in CALCULATION FOR SHEAR CONNECTION 8.xmcd 9 of 30
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Le min = 1 in C 2 = 0 in Lev min := Le min + C 2 Lev min = 1 in Lev max := min( 6in, 12 tpl) Lev max = 4.500 in RESULT = Lev > Lev.min & Lev < Lev.max, OK Horizontal Edge Distance, Leh = 1.5 in Leh bm = 1.5 in Le min = 1 in Leh minpl = 1.125 in Leh minbm = 1 in Leh maxpl := min( 6in, 12 tpl) Leh maxpl = 4.500 in ( ) Leh maxbm := min 6in, 12 tw bm Leh maxbm = 3.600 in RESULT = Leh > Leh.min & Leh < Leh.max, OK C. SHEAR PLATE CHECK 1. Check for Maximum Shear Plate Thickness (AISC 14th Ed. Manual Part 10, page 10-104) Exceptions for nv = 1 and nv = 2 tpl db 2 + 1 16 db tw bm 2 + 1 16 Leh pl 2 db pl Leh bmw 2 db pl CALCULATION FOR SHEAR CONNECTION 8.xmcd 11 of 30
RESULT = No need to check maximum thickness of plate CALCULATION FOR SHEAR CONNECTION 8.xmcd 12 of 30
Coefficient for Eccentrically Loaded Bolts (AISC 14th Ed. Manual Part 7, page 7-19) C' = 38.669 in Area of Bolts Ab:= π db 2 4 Ab = 0.442 in 2 Length of Plate Lpl:= ( nr 1) s + Lpl = 15 in 2 Lev Maximum Thickness F nv1 6 0.9 Ab C' tpl max := (10-3) Fy pl Lpl 2 tpl max = 0.759 in tpl = 0.375 in RESULT = Max Thickness need not be checked Governing Shear Plate Thickness, tpl g := if Case pl = 1 tpl tpl if if tpl < tpl max tpl= tpl max 1 Floor tpl max, 16 in tpl otherwise 3 tpl g = 8 in otherwise CALCULATION FOR SHEAR CONNECTION 8.xmcd 13 of 30
2. Bolt Bearing Capacity of Shear Plate (AISC 14th Ed.Specifications Chapter J, Section J3.10, pages 16.1-127 to 16.1-128) Bearing Area, Abrg pl := db tpl g Abrg pl = 0.281 in 2 Allowable Bearing Strength using edge distance, (J3-6a,J3-6c) Fbe:= Λ brg Fu pl Fbe = 18.963 kips min min ( ) ( ) 1.0 Lev 0.5hd plv 1.0 Leh 0.5hd plh 2.0 Abrg pl ( ) ( ) 1.2 Lev 0.5hd plv 1.2 Leh 0.5hd plh 2.4 Abrg pl tpl g tpl g tpl g tpl g if hd plh hd ls otherwise Allowable Bearing Strength using bolt spacing, (J3-6a,J3-6c) Fbs:= Λ brg Fu pl Fbs = 29.362 kips ( ) ( ) min 1.0 s hd plv tpl g, 2.0 Abrg pl if hd plh hd ls min 1.2 s hd plv tpl g, 2.4 Abrg pl otherwise Bolt Bearing Capacity, Rbrg pl := C min( Fbe, Fbs, Λrv) Rbrg pl = 130.478 kips V = 99.8 kips RESULT = Bearing Capacity > Force Applied, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 14 of 30
3. Shear Yielding Capacity of Shear Plate (AISC 14th Ed. Specifications Chapter J, Section J4.2, page 16.1-129) Length of Plate, Lpl:= ( nr 1)s + 2Lev Lpl = 15 in Check if Length of Plate is acceptable, (AISC 14th Ed, Manual Part 10, page 10-106) ( ) Length := "Plate Length is OK per AISC Requirements" if Lpl 0.5 d bm 2k bm "Increase Plate Length per AISC Requirements" otherwise Length = "Plate Length is OK per AISC Requirements" Gross Shear Capacity, Rvy pl := Λ vy 0.6 Fy pl tpl g Lpl (J4-3) Rvy pl = 121.5 kips V = 99.8 kips RESULT = Shear Yielding Capacity > Force Applied, OK 4. Shear Rupture Capacity of Shear Plate (AISC 14th Ed, Specifications Chapter J, Section J4.2, page 16.1-129) Net Area, Anv:= ( Lpl nr hd plv ) tpl g Anv = 3.984 in 2 Shear Rupture Capacity, Rvr pl := Λ vr 0.6 Fu pl Anv (J4-4) Rvr pl = 103.992 kips V = 99.8 kips RESULT = Shear Rupture Capacity > Force Applied, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 15 of 30
5. Block Shear Capacity of Shear Plate (AISC 14th Ed. Specifications Chapter J, Section J4.3, page 16.1-129) Reduction Factor, U bs := 1.0 if nv= 1 (tension stress is uniform) Gross Shear Area U bs = 0.5 Agv:= [( nr 1) s + Lev] tpl g Agv = 5.062 in 2 Net Tension Area 0.5 if nv > 1 Ant:= Leh + ( nv 1) sv ( nv 0.5) hd plh Ant = 1.09 in 2 Net Shear Area Anv:= ( nr 1) s + Lev ( nr 0.5) hd plv Anv = 3.586 in 2 tpl g tpl g (tension stress is non-uniform) Block Shear Capacity of Plate, (J4-5) ( ) Rbs pl := Λ bs min 0.6Fu pl Anv + U bs Fu pl Ant, 0.6 Fy pl Agv + U bs Fu pl Ant Rbs pl = 105.717 kips V = 99.8 kips RESULT = Block Shear Capacity > Force Applied, OK 6. Local Buckling Capacity of Shear Plate (AISC 14th Ed., Manual Part 9, page 9-9) Distance of bolt line to support, a b := gap + Leh bm a b = 2 in CALCULATION FOR SHEAR CONNECTION 8.xmcd 16 of 30
Coefficient, λ:= 10 tpl g λ = 0.188 Lpl Fy pl 475 + 280 Lpl a b 2 1 ksi Q:= 1 if λ 0.7 1.34 0.486 λ 1.30 λ 2 otherwise if 0.7 < λ 1.41 Q = 1 Allowable Buckling Stress, Fcr:= Fy pl Q Fcr = 36 ksi Gross Plastic Section Modulus, tpl g Lpl 2 Zx pl := 4 Zx pl = 21.094 in 3 Eccentricity, e pl := a b e pl = 2 in Buckling Capacity, Fcr Zx pl Rbc pl := Λ b e pl Rbc pl = 341.719 kips V = 99.8 kips RESULT = Local Buckling Capacity will not Control! CALCULATION FOR SHEAR CONNECTION 8.xmcd 17 of 30
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7. Flexural Yielding Capacity with von-mises shear reduction (AISC 14th Ed., Manual Part 10, page 10-103/Muir, Larry and Hewitt,Christopher, "Design of Unstiffened Extended Single-Plate Shear Connections", Engineering Journal, 2nd Quarter 2009, page 69.) Flexural Capacity, Rfc pl := Λ b Fy pl 2.25+ 16 Lpl tpl g e pl Lpl 2 Rfc pl = 114.479 kips V = 99.8 kips RESULT = Flexural Yielding Capacity > Applied Force, OK 8. Flexural Rupture Capacity (AISC 14th Ed., Steel Construction Manual Design Examples page IIA-104) Net Plastic Section Modulus, tpl Lpl 2 Znet pl := 4 tpl Lpl 2 4 Znet pl = 15.116 in 3 ( ) hd plv s tpl nr 2 1 4 ( ) 2 tpl hd plv 4 hd plv nr 2 s tpl 4 if mod( nr, 2) = 0 if mod( nr, 2) > 0 Flexural Rupture Capacity, (AISC 14th Ed., Manual Part 15, page 15-4) Λ fr Fu pl Znet pl Rfr pl := e pl Rfr pl = 328.767 kips V = 99.8 kips RESULT = Flexural Rupture Capacity > Applied Force, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 19 of 30
9. Interaction of Shear Yielding, Shear Buckling, and Flexural Yielding of Plate (AISC 14th Ed. Manual Part 10, page 10-104 to 10-105) From AISC Manual Equation 10-5, V r V c 2 V r := V M r + 1.0 M c 2 V r = 99.8 kips M r := V r gap + Leh bm + 0.5( nv 1) sv M r = 349.3 kips in Shear yielding, V c := Λ vy 0.6 Fy pl tpl g Lpl V c = 121.5 kips Flexural yielding, M c := Λ b Fy pl Zx pl M c = 683.437 kips in Interaction, V r V c 2 M r + = 0.936 M c 2 RESULT = Interaction < 1.0, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 20 of 30
D. COLUMN CHECKS Connecting Face of HSS, B HSS := H col if ConnectingFace = "Longer Side" B HSS = 8 in B col otherwise H HSS := B col if ConnectingFace = "Longer Side" H HSS = 8 in H col otherwise CALCULATION FOR SHEAR CONNECTION 8.xmcd 21 of 30
1. Limits of Applicability (AISC Steel Design Guide 24, Chapter 7, Table 7.2A, page 82) a. HSS wall slenderness: B HSS 40 tw col B HSS = 13.769 tw col RESULT = Connection is applicable. b. HSS wall slenderness( for branch plate shear loading): Width to Thickness Ratio of HSS, WTR:= B HSS 3 tw col tw col WTR = 10.769 Limiting Width to Thickness Ratio, L WTR := 1.40 E Fy col L WTR = 35.152 RESULT = Connection is applicable. c. Material strength: Fy col 52ksi Fy col = 46 ksi RESULT = Connection is applicable. d. Ductility: Fy col = 0.793 Fu col Fy col 0.8 Fu col RESULT = Connection is applicable. CALCULATION FOR SHEAR CONNECTION 8.xmcd 22 of 30
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Applicability of Connection: RESULT = Connection Applicable, Proceed to HSS Local Checks 2. HSS Local Check a. HSS Punching Shear (AISC Steel Design Guide 24, Table 7-2, page 81) Maximum Shear Plate thickness to avoid Shear Tab Punching thru column wall, Fu col tpl PSmax := tw Fy col pl tpl PSmax = 0.936 in tpl = 0.375 in RESULT = Plate thickness = Maximum Plate Thickness, OK E. SHEAR PLATE TO COLUMN CHECK WITH THROUGH PLATE AS REQUIRED 1. Weld Check for Shear Plate to Column (AISC 14th Ed. Manual Part 8, pages 8-9 to 8-15) No. of Weld side, n ws := 2 Minimum weld size, 1 w min1 = 4 in w 1 = 1 4 in RESULT = Preferred Weld Size = Minimum Weld Size,OK (AISC 14th Ed. Specifications Chapter J, pages 16.1-111) Maximum Weld Size, w max := 1 tpl 16 in if tpl 1 4 in tpl otherwise 5 w max = 16 in w 1 = 1 4 in RESULT = Maximum Weld > Preferred Weld, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 24 of 30
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2. Weld Check for Shear Plate to Column if Through Plate is Required Bolt centerline distance from face of support, e w := gap + Leh bm + 0.5( nv 1) sv e w = 3.5 in Force Acting on the Connection ( ) V e w + H HSS V tp := H HSS V tp = 143.463 kips Shear Strength, For Column: Rv col := Λ vr 0.6 Fu col tw col n ws Rv col = 30.328 kips in For Shear Plate: Rv pl := Λ vr 0.6 Fu pl tpl g Rv pl = 9.787 kips in For Weld: Rv w := Λ vw 0.6 Fu w sin( 45deg) n ws Rv w = 44.548 ksi Maximum effective weld size, ( ) min Rv col, Rv pl w eff := Rv w w eff = 0.22 in Length of Weld, Lw:= ( nr 1) s + 2Lev Lw = 15 in CALCULATION FOR SHEAR CONNECTION 8.xmcd 26 of 30
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Weld Capacity, ( ) Rw pl := Λ vw 0.6 Fu w sin( 45deg) n ws min w 1, w eff Lw Rw pl = 146.812 kips V tp = 143.463 kips RESULT = Limit State Not Applicable, Through Plate Not Required CALCULATION FOR SHEAR CONNECTION 8.xmcd 28 of 30
III. DETAILS: A. SKETCH SHEAR CONNECTION: DETAIL OF W-SHAPE BEAM TO RECTANGULAR/SQUARE HSS COLUMN SHEAR PLATE CONNECTION CALCULATION FOR SHEAR CONNECTION 8.xmcd 29 of 30
B. TABLE: SHEAR CONNECTION SCHEDULE Column D Shear Plate Bolts at Shear Plate Bolt Spacing Edge Distance (in) Size Grade tpl (in) Grade db (in) Type nr nv HSS8X8X5/8 A500-B 3 3/8 A36 3/4 A325-N 5 2 3 3 1 1/2 1 1/2 s (in) sv (in) Lev (in) Leh (in) Size Beam Grade Edge Distance Leh bm (in) gap (in) Weld Size w 1 (in) Beam Shear Load (kips) Rcap (kips) W18X35 A992 1 1/2 1/2 1/4 99.80 103.99 Governing Capacity Shear Rupture of Plate Remarks Through Plate Not Required IV. REFERENCES Steel Construction Manual ( 14th )- LRFD American Institute of Steel Construction, Inc. 2010 CALCULATION FOR SHEAR CONNECTION 8.xmcd 30 of 30