SHEAR CONNECTION: DESIGN OF W-SHAPE BEAM TO RECTANGULAR/SQUARE HSS COLUMN SHEAR PLATE CONNECTION

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1 SHEAR CONNECTION: DESIGN OF W-SHAPE BEAM TO RECTANGULAR/SQUARE HSS COLUMN SHEAR PLATE CONNECTION CALCULATION FOR SHEAR CONNECTION 8.xmcd 1 of 30

2 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 = 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 = in k bm = 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 = kips Conn_type = "Bearing-type" Λrn = 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 = in hd plh = in Beam, hd bm = in CALCULATION FOR SHEAR CONNECTION 8.xmcd 2 of 30

3 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

4 CALCULATION FOR SHEAR CONNECTION 8.xmcd 4 of 30

5 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 to ) Bearing Area, Abrg bm := db tw bm Abrg bm = 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 = Allowable Bearing Strength using edge distance,(j3-6a,j3-6c) Fbe:= Λ brg Fu bm Fbe = 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

6 CALCULATION FOR SHEAR CONNECTION 8.xmcd 6 of 30

7 Allowable Bearing Strength using bolt spacing,(j3-6a,j3-6c) Fbs:= Λ brg Fu bm Fbs = 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 = 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 to ) Clear distance between flanges of beam, less the fillet or corner radii, h:= d bm 2 kdes bm h = in Limiting depth-thickness ratio, h tw := h tw bm h tw = 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

8 Web plate buckling coefficient, kv:= 5 if h tw < 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 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 = 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 = kips CALCULATION FOR SHEAR CONNECTION 8.xmcd 8 of 30

9 Eccentric Bolt Capacity, Reb:= C Λrv Reb = 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 to ) 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 = 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 = 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 to ) Vertical Edge Distance, Lev = 1.5 in CALCULATION FOR SHEAR CONNECTION 8.xmcd 9 of 30

10 CALCULATION FOR SHEAR CONNECTION 8.xmcd 10 of 30

11 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 = 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 = in Leh minbm = 1 in Leh maxpl := min( 6in, 12 tpl) Leh maxpl = in ( ) Leh maxbm := min 6in, 12 tw bm Leh maxbm = 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 ) Exceptions for nv = 1 and nv = 2 tpl db db tw bm Leh pl 2 db pl Leh bmw 2 db pl CALCULATION FOR SHEAR CONNECTION 8.xmcd 11 of 30

12 RESULT = No need to check maximum thickness of plate CALCULATION FOR SHEAR CONNECTION 8.xmcd 12 of 30

13 Coefficient for Eccentrically Loaded Bolts (AISC 14th Ed. Manual Part 7, page 7-19) C' = in Area of Bolts Ab:= π db 2 4 Ab = in 2 Length of Plate Lpl:= ( nr 1) s + Lpl = 15 in 2 Lev Maximum Thickness F nv Ab C' tpl max := (10-3) Fy pl Lpl 2 tpl max = in tpl = 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

14 2. Bolt Bearing Capacity of Shear Plate (AISC 14th Ed.Specifications Chapter J, Section J3.10, pages to ) Bearing Area, Abrg pl := db tpl g Abrg pl = in 2 Allowable Bearing Strength using edge distance, (J3-6a,J3-6c) Fbe:= Λ brg Fu pl Fbe = 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 = 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 = kips V = 99.8 kips RESULT = Bearing Capacity > Force Applied, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 14 of 30

15 3. Shear Yielding Capacity of Shear Plate (AISC 14th Ed. Specifications Chapter J, Section J4.2, page ) 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 ) ( ) 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 = 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 ) Net Area, Anv:= ( Lpl nr hd plv ) tpl g Anv = in 2 Shear Rupture Capacity, Rvr pl := Λ vr 0.6 Fu pl Anv (J4-4) Rvr pl = kips V = 99.8 kips RESULT = Shear Rupture Capacity > Force Applied, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 15 of 30

16 5. Block Shear Capacity of Shear Plate (AISC 14th Ed. Specifications Chapter J, Section J4.3, page ) 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 = 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 = 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 = 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

17 Coefficient, λ:= 10 tpl g λ = Lpl Fy pl Lpl a b 2 1 ksi Q:= 1 if λ 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 = in 3 Eccentricity, e pl := a b e pl = 2 in Buckling Capacity, Fcr Zx pl Rbc pl := Λ b e pl Rbc pl = kips V = 99.8 kips RESULT = Local Buckling Capacity will not Control! CALCULATION FOR SHEAR CONNECTION 8.xmcd 17 of 30

18 CALCULATION FOR SHEAR CONNECTION 8.xmcd 18 of 30

19 7. Flexural Yielding Capacity with von-mises shear reduction (AISC 14th Ed., Manual Part 10, page /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 Lpl tpl g e pl Lpl 2 Rfc pl = 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 = in 3 ( ) hd plv s tpl nr ( ) 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 = kips V = 99.8 kips RESULT = Flexural Rupture Capacity > Applied Force, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 19 of 30

20 9. Interaction of Shear Yielding, Shear Buckling, and Flexural Yielding of Plate (AISC 14th Ed. Manual Part 10, page to ) From AISC Manual Equation 10-5, V r V c 2 V r := V M r M c 2 V r = 99.8 kips M r := V r gap + Leh bm + 0.5( nv 1) sv M r = kips in Shear yielding, V c := Λ vy 0.6 Fy pl tpl g Lpl V c = kips Flexural yielding, M c := Λ b Fy pl Zx pl M c = kips in Interaction, V r V c 2 M r + = M c 2 RESULT = Interaction < 1.0, OK CALCULATION FOR SHEAR CONNECTION 8.xmcd 20 of 30

21 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

22 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 = 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 = Limiting Width to Thickness Ratio, L WTR := 1.40 E Fy col L WTR = RESULT = Connection is applicable. c. Material strength: Fy col 52ksi Fy col = 46 ksi RESULT = Connection is applicable. d. Ductility: Fy col = Fu col Fy col 0.8 Fu col RESULT = Connection is applicable. CALCULATION FOR SHEAR CONNECTION 8.xmcd 22 of 30

23 CALCULATION FOR SHEAR CONNECTION 8.xmcd 23 of 30

24 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 = in tpl = 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 ) 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

25 CALCULATION FOR SHEAR CONNECTION 8.xmcd 25 of 30

26 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 = kips Shear Strength, For Column: Rv col := Λ vr 0.6 Fu col tw col n ws Rv col = kips in For Shear Plate: Rv pl := Λ vr 0.6 Fu pl tpl g Rv pl = kips in For Weld: Rv w := Λ vw 0.6 Fu w sin( 45deg) n ws Rv w = 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

27 CALCULATION FOR SHEAR CONNECTION 8.xmcd 27 of 30

28 Weld Capacity, ( ) Rw pl := Λ vw 0.6 Fu w sin( 45deg) n ws min w 1, w eff Lw Rw pl = kips V tp = kips RESULT = Limit State Not Applicable, Through Plate Not Required CALCULATION FOR SHEAR CONNECTION 8.xmcd 28 of 30

29 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

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 /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 A /2 1/2 1/ Governing Capacity Shear Rupture of Plate Remarks Through Plate Not Required IV. REFERENCES Steel Construction Manual ( 14th )- LRFD American Institute of Steel Construction, Inc CALCULATION FOR SHEAR CONNECTION 8.xmcd 30 of 30

SHEAR CONNECTION: W BEAM WITH SHEAR PLATE ONE-WAY SHEAR CONNECTION TO W COLUMN WEB

1 of 18 SHEAR CONNECTION: W BEAM WITH SHEAR PLATE ONE-WAY SHEAR CONNECTION TO W COLUMN WEB Description:Detailed Report 17 2 of 18 I. DESIGN DATA AND LOADS (ASD-14th Edition) COLUMN PROPERTIES: W14X90 -