Structural Design Calculation For Pergola


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1 Structural Design Calculation For Pergola Revision :5 Prepared by :EC Date : 8/10/009
2 CONTENTS 1. Introduction... Design Code and Reference 3. Design Synopsis 4. Design Parameters 4.1 Design Load. 4. Design Wind Pressure. 4.3 Loading Combination. 5. Material Properties 6. Pergola at Area C: Loading assessment and design. 7. Pergola 3 at Area D : Loading assessment and design. 8. Pergola 4 at Area H1 : Loading assessment and design. 9. Pergola 5 at Area H : Loading assessment and design. 10. Loading schedule and Anchor Bolt Design. 11. Appendix A  Wind Topography Analysis Appendix B  Reference Design Intent Drawing Appendix C  Recycled Plastic Wood Test Report 1
3 1. Introduction This calculation is to design pergola s structure for four numbers proprietary pergola located at area C, D, H1 and H.. Design Code and Reference Code of Practice for the Structural Use of Steel 005 Code of Practice on Wind Effects Hong Kong Hong Kong Building (Construction) Regulations Design Synopsis The largest loaded span and loading area will be used for design. 4. Design Parameters For simplified analysis, Pergolas structure will be designed for weak direction. (i.e. largest wind projection area). 4.1 Design Load live load  recycle plastic wood (slat) = 0.75 kpa dead load  recycle plastic wood (slat) = 1197 kg/m 3 dead laod pergola steel structure = 7850 kg/m 3 4. Design Wind Pressure Design Wind Pressure (H<5m), q z = 1.8 kpa Topography Factor for Area D, H1, H S a = ( e *s) = (1 + 1.*0.3*1) = 1.85 Topography Factor for Area C S a = ( e *s) = (1 + 1.*0.3*0.) = Loading Combination 1) 1.4DL + 1.6LL ) 1.DL + 1.LL + 1.WL dn 3) 1.4DL + 1.4WL dn 4) 1.DL + 1.LL + 1.WL lat 5) 1.4DL + 1.4WL lat 6) 1.0DL 1.4WL dn Where DL = Dead load, LL = Live load, WL dn = downward wind load, WL lat = Lateral wind load
4 5. Material Properties Structural Steel Steel Grade = S75JR unless stated otherwise to BS EN 1005 Part 16 : 004 for Hot Rolled Sections and BS EN 1010 Part 1 : 006 for Hot finished hollow sections. = S75J0H for cold formed steel hollow, Strength reduced 5% to 0 N/mm to BS EN 1019 Part 1 : 006 Weld Strength = 0 N/mm Welding work shall be complicance with BS EN 1011 Part 1:1998 Electrodes to welding shall be complicance with BS EN ISO 560:005. Recycled Plastic Wood Tensile Strength = 11.9N/mm Bending Strength = 3.7 N/mm 3
5 6. Pergola at Area C : Loading assessment and design 4
6 Design for Steel Pergola at Ma Hang Headland Park Calculation is provided following load transfer path from roof deck to steel post and anchor bolt/steel base plate. Largest span, Loaded area, wind topography factor and loading combination will be used for structural member design. Pergola : Area : C Dead Load Slat Self Weight, q ds = Structural Steel Sefl weight, q dst = 1197 kg/m 7850 kg/m 3 3 Wind Load Basic wind pressure, q z = (H < 5m) 1.8 kpa Wind pressure coefficient, C p = Topography factor for Area A, S a = 1.15 Design wind pressure, q w =1.15*S a *C p *q z = (Additional 15% wind load is adopted for design) 4.81 kpa Live Load Maintenance Live load on roof deck, q l = 0.75 kpa Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood Design This Slat Plan From First Principle, 4 I sx = 1/1*60*90^3= mm Z sx = I sx / (D/) = /(90/)= mm A s = B*D = 60*90= 5400 mm 3
7 Maximum span, L = Load width for wind load, b w = Load width for live load, b l =80+60 = 1900 mm 60 mm 159 mm Dead Load self weight of slat, w ds = 1197*9.81/1000*60/1000*90/1000= kn/m Live load Maintenance live load, w ls = 0.75*159/1000= 0.1 kn/m Wind load Downward wind load, w ws = 4.81*60/1000= 0.9 kn/m Case 1 : 1.4 DL LL Factored UDL on slat, w f1 = 1.4*w ds +1.6*w ls = 0.8 kn/m Case : 1. DL + 1.LL + 1.WL (download) Factored UDL on slat, w f = 1.*w ds +1.*w ls +1.*w ws = 0.57 kn/m (Controlled case) Case 3 : 1.4 DL + 1.4WL (download) Factored UDL on slat, w f3 = 1.4*w ds +1.4*w ws = Use maximum factored UDL for Design, w fd = 0.49 kn/m 0.57 kn/m Bending design M f = 1/8*0.57*(1900/1000)^= 0.6 knm f b = M f / Z s = 0.6*10^6/81000= 3.1 N/mm < 11.9 N/mm Shear Design V f = 1/*0.8*1900/1000= 0.7 kn f v = V f / A s = 0.7*1000/5400= 0.05 N/mm < 0.6*11.9 = 7.14 N/mm
8 Connection design between 60x90mm slat and 80x50x4mm steel plate Design this steel plate connection Section Design this steel plate connection Section Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Bolt design M10 Grade 8.8 Bolt, A b = No. of bolt, n = 58 mm Factored Shear from slat, V f = 0.4 kn Bolt Shear stress, f vb = V f / (n*a b ) = 3.6 N/mm < 375 N/mm 80 mm (D) x 50 mm (B) x 4 mm steel plate Moment of inertia, I=1/1*4*80^3= mm 4 Elastic modulus, Z = /(80/)= 467 mm 3 Shear Area, A = 80*4= 30 mm v Factored Shear from slat, V f = 0.4 kn No. of plate provided per slat, n = Plate shear stress, f vp = V f / A v / n = 0.66 N/mm < 0.6*0 N/mm = 13 N/mm Eccentricity, e = Factored eccentric moment, M e = V f *e = 0.4*5/1000= 5 mm 0.01 knm Plate bending stress, f bp = M e / Z / n = 0.01*10^6//467= 1.17 N/mm < 0 N/mm Weld design for 80x50x4mm steel plate and 00x100x.6kg/m GMS RHS Weld length provided, L w = 80*= 160 mm Weld Moment of inertia, I = 1/1*80^3= 4667 mm 3 w Weld Elastic modulus, Zw = 4667/(80/)= 1067 mm Factored Shear from slat, V f = Factored Eccentric moment, M e = 0.4 kn 0.01 knm
9 Shear Weld stress, f vw = V f / L w = 0.4*1000/160=.63 N/mm Bending weld stress, f bw = M e / Z w = 0.01*10^6/1067= 9.37 N/mm Combined weld stress, f ew = (f bw^+f vw^)^1/ = 9.73 N/mm Provide 4 mm fillet weld Provided weld strength, p w = 0.7*0*4= 616 N/mm > 9.73 N/mm Design for 00x100x.6kg/m GMS RHS supporting slat Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this RHS Section Plan Design 00x100x.6kg/m RHS as cantilever beam 00x100x.6kg/m GMS RHS I = Z = A = mm mm3 870 mm Length of RHS = 000 mm No. of Point load from slat, n = 14 Factored Self weight of RHS = 1.*.6*9.81/1000= 0.7 kn/m Equivalent Factored UDL on RHS, w = 0.4**14/(000/1000)= 5.88 kn/m 6.15 kn/m Cantilever span, L = Factored moment, M f = Factored Shear, V f = 1/*6.15*(1764/1000)^= 6.15*1764/1000= 1764 mm 9.57 knm kn
10 Bending design f b = M f / Z = 9.57*10^6/149000= 64.3 N/mm < 0 N/mm Shear design f v = V f / A v = 10.85*1000/870= 3.78 N/mm < 0.6*0 N/mm = 13 N/mm Deflection design UDL on RHS, wu = 5.88/1.= 4.9 kn/m E = N/mm d = wl^4 / 8EI = 3. mm < L / 180 = mm Design of Bolt joint at 00x100x.6kg/m vertical RHS post supporting RHS cantilever beam Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this bolt joint Loaded Unloaded Section Section Consider only larger projection is loaded and small projection unload for worst case design. Bolt design Area per bolt, A b = No. of bolt provided, n = mm For the bolt group, I xx = I yy = I p = I xx + I yy = mm mm 0000 mm Factored Direct Shear for bolt group, V f = Factored Moment for bolt group, M f = Distance of bolt group centroid to one bol ( ) 1/ = kn 9.57 knm 71 mm
11 Factored shear from bending, V fb = 9.57*10^6*71/0000/1000= kn For conservative design Factored design shear for bolt, V fd = V fb + V f = = 44.8 kn Bolt shear stress, f vb = V fd / A b = 44.8*1000/157= N/mm < 375 N/mm Design of 00x100x.6kg/m RHS Vertical post Design this steel post Each 00x100x.6kg/m RHS Vertical Post I = mm 4 Z = mm 3 A = 870 mm r = 7 mm Effective Height of RHS post, H = 750 mm No of post provided, n = Case 1 : 1.4DL+1.6LL Load widith per RHS post bay, b = Load length per RHS post bay, L = Load area per RHS post, A = 1.9*.5= No. of slat at roof deck, n = Height of RHS post, H = Dead load: self weight of slat = self weight of 00x100x.6kg/m RHS = Self weight of 160x80x14.4kg/m SHS = 1.9 m.5 m 4.75 m m 0.063*1.9*14=.6*9.81/1000*.5= 14.4*9.81/1000*.75*= 1.68 kn 0.55 kn 0.78 kn 3.01 kn
12 Live load : Maintenance live load = 0.75*4.75= 3.56 kn DL eccentric moment, M de = (1.33/3*3.01*1.33/0.441/3*3.01*0.441/)= 0.78 knm LL eccentric moment, M le = (1.33/3*3.56*1.33/0.441/3*3.56*0.441/)= 0.9 knm w = 1.4DL LL = 9.91 kn Axial deisgn P fd = 9.91 kn f a = P fd / A /n= 9.91*1000/870/= 1.73 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, p a = 195 N/mm > 1.73 N/mm Bending design Eccentric moment, M fe = (1.33/3*9.91*1.33/0.441/3*9.91*0.441/)/= 1.8 knm f b = M f e / Z = 1.8*10^6/149000= 8.59 N/mm < 0 N/mm Case : 1.DL+1.LL+1.WL (downward) 1.DL+1.LL+1.WL (downward) Section Factored Self weight of nos. RHS post = 1.*.6*9.81/1000*750/1000*= 0.95 kn Factored Axial compression from RHS beam, P f = kn Factored axial compression, P fd = 11.8 kn Factored moment, M f = 9.57 knm Axial deisgn P fd = 11.8 kn f a = P fd / A/n = 11.8*1000/870/=.06 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, p a = 195 N/mm >.06 N/mm
13 Bending design M f = 9.57 knm f b = M f / Z/ n = 9.57*10^6/149000/= 3.11 N/mm < 0 N/mm Case 3 : 1.DL + 1.LL + 1.WL (lateral) Load widith per RHS post bay, b = Load length per RHS post bay, L = Load area per SHS post, A = 1.9*.5= No. of slat at roof deck, n = Height of SHS post, H = Dead load: self weight of slat = self weight of 00x100x.6kg/m RHS = Self weight of 160x180x14.4kg/m SHS = 1.9 m.5 m 4.75 m m 0.063*1.9*14=.6*9.81/1000*.5= 14.4*9.81/1000*.75*= 1.68 kn 0.55 kn 0.78 kn 3.01 kn Live load : Maintenance live load = 0.75*4.75= 3.56 kn Lateral wind load assessment: Area I 500 Area II 00 Area III 750 Lateral wind load Section (Lateral wind load) Design wind pressure, q w =S a *C p *q z = 4.81 kpa I Roof Deck II 00x100x.3kg/m RHS postnos. Of 0.7m long III 00x100x.3kg/m SHS post nos. Of.75m long (1) () (3)=(1)*()*qw (4) (5)=(3)*(4) Area Project area, A (m) Nos of Projected Wind shear, S Level arm, L Moment, M b x d Area, n (kn) (m) (knm) I 0.09 x II 0.5 x III 0.1 x
14 Design factored Axial compression, P f = 1.DL + 1.LL= 1.* *3.56= 7.88 kn Design factored lateral wind shear, V f = 1.*S = 1.*3.95= 4.74 kn Design factored bending moment, M f = 1.*M = 1.*7.39= 8.87 knm Axial deisgn P fd = 7.88 kn f a = P fd / A /n= 7.88*1000/870/= 1.37 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 1.37 N/mm Shear design V f = 4.74 kn f v = V f / A /n= 4.74*1000/870/= 0.83 N/mm > 0.6*0 N/mm Bending design M f = 8.87 knm = 13 N/mm f b = M f / Z /n= 8.87*10^6/149000/= 9.77 N/mm < 0 N/mm Weld Design Consider one post Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored Shear, V f = Factored moment, M f = 7.88 kn 4.74 kn 8.87 knm Axial Weld stress, f aw = P f / L w /n = 7.88*1000/660/= 5.97 N/mm Shear Weld stress, f vw = V f / L w /n = 4.74*1000/660/= 3.59 N/mm Bending weld stress, f bw = M f / Z w /n = 8.87*10^6/13013/= N/mm For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 350 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 350 N/mm Case 4 : 1.4DL+1.4WL (lateral) Design factored Axial compression, P f = 1.4DL 1.4*3.01= 4.1 kn Design factored lateral wind shear, V f = 1.4*S = 1.4*3.95= 5.53 kn Design factored bending moment, M f = 1.4*M = 1.4*7.39= knm Axial deisgn P fd = 4.1 kn f a = P fd / A /n= 4.1*1000/870/= 0.73 N/mm
15 slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 0.73 N/mm Shear design V f = 5.53 kn f v = V f / A/n = 5.53*1000/870/= 0.96 N/mm < 0.6*0 N/mm Bending design M f = knm = 13 N/mm f b = M f / Z/n = 10.35*10^6/149000/ = N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored Shear, V f = Factored moment, M f = 4.1 kn 5.53 kn knm Axial Weld stress, f aw = P f / L w /n = 4.1*1000/660/= 3.19 N/mm Shear Weld stress, f vw = V f / L w /n = 5.53*1000/660/= 4.19 N/mm Bending weld stress, f bw = M f / Z w /n = 10.35*10^6/13013/= N/mm For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 405 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 405 N/mm Case 5 : 1.4DL+1.4WL (downward) Load widith per SHS post bay, b = 1.9 m Load length per SHS post bay, L =.5 m Load area per SHS post, A = 1.9*.5= 4.75 m No. of slat at roof deck, n = 14 Height of SHS post, H =.75 m Dead load: self weight of slat = 0.063*1.9*14= 1.68 kn self weight of 00x100x.6kg/m RHS =.6*9.81/1000*.5= 0.55 kn Self weight of nos.160 x80x14.4kg/m SHS = 14.4*9.81/1000*.75*= 0.78 kn 3.01 kn 1.4DL = 1.4*3.01= 4.14 kn
16 Downward wind load : Nos. of slat, n = 14 design wind pressure, qw = 4.81 kpa load width per slat, B = 60 mm (Section)
17 Downward wind load, WL downward = 60/1000*1.9*14*4.81= 7.68 kn Eccentric moment, M e,downward = 7.68*1.935/= 7.43 knm 1.4DL * WL downward = 1.4*M e,downward = 13.6 kn knm Axial deisgn P fd = 13.6 kn f a = P fd / A /n= *1000/870/=.37 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm >.37 N/mm Bending design M f = knm f b = M f / Z /n= 10.40*10^6/149000/ = N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored moment, M f = 13.6 kn knm Axial Weld stress, f aw = P f / L w /n = *1000/660 /= 10.9 N/mm Bending weld stress, f bw = M f / Z w /n = 10.40*10^6/13013/ = N/mm For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 410 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 410 N/mm Case 6 : 1.0DL1.4WL (downward) Load widith per SHS post bay, b = 1.9 m Load length per SHS post bay, L =.5 m Load area per SHS post, A = 1.9*.5= 4.75 m No. of slat at roof deck, n = 14 Height of SHS post, H =.75 m Dead load: self weight of slat = 0.063*1.9*14= 1.68 kn self weight of 00x100x.6kg/m RHS =.6*9.81/1000*.5= 0.55 kn Self weight of nos.160 x80x14.4kg/m SHS = 14.4*9.81/1000*.75*= 0.78 kn 3.01 kn Live load : Maintenance live load = 0.75*4.75= 3.56 kn 1.0DL = 1.0*3.01= 3.01 kn
18 Downward wind load : Nos. of slat, n = 14 design wind pressure, qw = 4.81 kpa load width per slat, B = 60 mm (Section) Downward wind load, WL downward = 60/1000*1.9*14*4.81= 7.68 kn Eccentric moment, M e,downward = 7.68*1.935/= 7.43 knm 1.0DL * WL downward = 1.4*M e,downward = 11.9 kn knm Axial deisgn P fd = 11.9 kn f a = P fd / A /n= *1000//=.07 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm >.07 N/mm Bending design M f = knm f b = M f / Z /n= 10.40*10^6/149000/ = N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored moment, M f = 11.9 kn knm Axial Weld stress, f aw = P f / L w /n = *1000/660 /= 9.01 N/mm Bending weld stress, f bw = M f / Z w /n = 10.40*10^6/13013/ = N/mm For conservative design,
19 Combined weld stress, f ew = f bw +f aw +f vw = = 409 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 409 N/mm
20 Design of anchor bolt Plan Consider Case 1 and Case 5 for steel post, Factored Axial compression, P f = 13.6 kn (Case 5 control) Factored Shear, V f = 5.5 kn (Case 4 control) Factored moment, Mf = knm (Case 5 control) Anchor bolt design is performed by Hilti's computer program. Please refer next page. Provide 8 nos. HITRE500/HASE M16x15 bolt
21 Loading schedule (unfactored load) Item DL LL DL+LL Lateral wind Upward/downward wind Axial (kn) Axial (kn) Axial (kn) Shear (kn) Moment (knm) Axial (kn) Pergola 4 at Area H
22 7. Pergola 3 at Area D : Loading assessment and design 5
23 Design for Steel Pergola at Ma Hang Headland Park Calculation is provided following load transfer path from roof deck to steel post and anchor bolt/steel base plate. Largest span, Loaded area, wind topography factor and loading combination will be used for structural member design. Pergola : 3 Area : D Dead Load Slat Self Weight, q ds = Structural Steel Sefl weight, q dst = 1197 kg/m 7850 kg/m 3 3 Wind Load Basic wind pressure, q z = (H < 5m) 1.8 kpa Wind pressure coefficient, C p = Topography factor for Area A, S a = 1.8 Design wind pressure, q w =1.15*S a *C p *q z = (Additional 15% wind load is adopted for design) 7.6 kpa Live Load Maintenance Live load on roof deck, q l = 0.75 kpa Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood Design This Slat Plan From First Principle, 4 I sx = 1/1*60*90^3= mm Z sx = I sx / (D/) = /(90/)= mm A s = B*D = 60*90= 5400 mm 3
24 Maximum span, L = = Load width for wind load, b w = Load width for live load, b l =80+60 = 863 mm 60 mm 153 mm Dead Load self weight of slat, w ds = 1197*9.81/1000*60/1000*90/1000= kn/m Live load Maintenance live load, w ls = 0.75*153/1000= 0.11 kn/m Wind load Downward wind load, w ws = 7.6*60/1000= 0.46 kn/m Case 1 : 1.4 DL LL Factored UDL on slat, w f1 = 1.4*w ds +1.6*w ls = 0.6 kn/m Case : 1. DL + 1.LL + 1.WL (download) Factored UDL on slat, w f = 1.*w ds +1.*w ls +1.*w ws = 0.76 kn/m (Controlled case) Case 3 : 1.4 DL + 1.4WL (download) Factored UDL on slat, w f3 = 1.4*w ds +1.4*w ws = Use maximum factored UDL for Design, w fd = 0.73 kn/m 0.76 kn/m Bending design M f = 1/8*0.76*(863/1000)^= 0.78 knm f b = M f / Z s = 0.78*10^6/81000= 9.63 N/mm < 11.9 N/mm Shear Design V f = 1/*0.6*863/1000= 0.37 kn f = V / A = 0.37*1000/5400= N/mm < 0.6*11.9 v f s = 7.14 N/mm Connection design between 60x90mm slat and 80x50x4mm steel plate Design this steel plate connection Section Design this steel plate connection Section
25 Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Bolt design M10 Grade 8.8 Bolt, A b = No. of bolt, n = 58 mm Factored Shear from slat, V f = 0.4 kn Bolt Shear stress, f vb = V f / (n*a b ) = 3.6 N/mm < 375 N/mm 80 mm (D) x 50 mm (B) x 4 mm steel plate Moment of inertia, I 1/1*4*80^3= mm 4 Elastic modulus, Z = /(80/)= 467 mm 3 Shear Area, A = 80*4= 30 mm v Factored Shear from slat, V f = 0.4 kn No. of plate provided per slat, n = Plate shear stress, f vp = V f / A v / n = 0.66 N/mm < 0.6*0 N/mm = 13 N/mm Eccentricity, e = Factored eccentric moment, M e = V f *e = 0.4*5/1000= 5 mm 0.01 knm Plate bending stress, f bp = M e / Z / n = 0.01*10^6//467= 1.17 N/mm < 0 N/mm Weld design for 80x50x4mm steel plate and 00x100x.6kg/m GMS RHS Weld length provided, L w = 80*= 160 mm Weld Moment of inertia, I = 1/1*80^3= 4667 mm 3 w Weld Elastic modulus, Zw = 4667/(80/)= 1067 mm Factored Shear from slat, V f = Factored Eccentric moment, M e = 0.4 kn 0.01 knm Shear Weld stress, f vw = V f / L w = 0.4*1000/160=.63 N/mm Bending weld stress, f bw = M e / Z w = 0.01*10^6/1067= 9.37 N/mm Combined weld stress, f ew = (f bw^+f vw^)^1/ = 9.73 N/mm Provide 4 mm fillet weld Provided weld strength, p w = 0.7*0*4= 616 N/mm > 9.73 N/mm
26 Design for 00x100x.6kg/m GMS RHS supporting slat Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this RHS Section Plan Design 00x100x.6kg/m RHS as cantilever beam 00x100x.6kg/m GMS RHS I = Z = A = mm mm3 870 mm Length of RHS = 131 mm No. of Point load from slat, n = 14 Factored Self weight of RHS = 1.*.6*9.81/1000= 0.7 kn/m Equivalent Factored UDL on RHS, w = 0.4**14/(131/1000)= 5.5 kn/m 5.79 kn/m Cantilever span, L = 1764 mm Factored moment, M f = 1/*5.79*(1764/1000)^= 9.01 knm Factored Shear, V f = 5.79*1764/1000= 10.1 kn Bending design f b = M f / Z = 9.01*10^6/149000= N/mm < 0 N/mm Shear design f v = V f / A v = 10.1*1000/870= 3.56 N/mm < 0.6*0 N/mm = 13 N/mm Deflection design UDL on RHS, wu = 5.5/1.= 4.6 kn/m E = N/mm d = wl^4 / 8EI = 3.87 mm < L / 180 = mm
27 Design of Bolt joint at 00x100x.6kg/m vertical RHS post supporting RHS cantilever beam Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this bolt joint Loaded Unloaded Section Section Consider only larger projection is loaded and small projection unload for worst case design. Bolt design Area per bolt, A b = No. of bolt provided, n = mm For the bolt group, I xx = I yy = I p = I xx + I yy = mm mm 0000 mm Factored Direct Shear for bolt group, V f = Factored Moment for bolt group, M f = 10.1 kn 9.01 knm Distance of bolt group centroid to one bolt(= ) 1/ = 71 mm Factored shear from bending, V fb = 9.01*10^6*71/0000/1000= kn For conservative design Factored design shear for bolt, V fd = V fb + V f = = 4. kn Bolt shear stress, f vb = V fd / A b = 4.*1000/157= N/mm < 375 N/mm
28 Design of 00x100x.6kg/m RHS Vertical post Design this steel post Each 00x100x.6kg/m RHS Vertical Post I = mm 4 Z = mm 3 A = 870 mm r = 7 mm Effective Height of RHS post, H = No of post provided, n = 750 mm Case 1 : 1.4DL+1.6LL Load widith per RHS post bay, b = Load length per RHS post bay, L = Load area per RHS post, A =.77*.131= No. of slat at roof deck, n = Height of RHS post, H = Dead load: self weight of slat = self weight of 00x100x.6kg/m RHS = Self weight of 160x80x14.4kg/m SHS =.77 m.131 m 5.91 m m 0.063*.77*14=.6*9.81/1000*.131= 14.4*9.81/1000*.75*=.44 kn 0.47 kn 0.78 kn 3.69 kn Live load : Maintenance live load = 0.75*5.91= 4.43 kn DL eccentric moment, M de = (1.33/3*3.69*1.33/0.441/3*3.69*0.441/)= 0.96 knm LL eccentric moment, M le = (1.33/3*4.43*1.33/0.441/3*4.43*0.441/)= 1.15 knm w = 1.4DL LL = 1.54 kn
29 Axial deisgn P fd = 1.54 kn f a = P fd / A /n= 1.54*1000/870/=.13 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, p a = 195 N/mm >.13 N/mm Bending design Eccentric moment, M fe = (1.33/3*1.54*1.33/0.441/3*1.54*0.441/)/= 1.59 knm f b = M f e / Z = 1.59*10^6/149000= N/mm < 0 N/mm Case : 1.DL+1.LL+1.WL (downward) 1.DL+1.LL+1.WL (downward) Section Factored Self weight of nos. RHS post = 1.*.6*9.81/1000*750/1000*= 0.95 kn Factored Axial compression from RHS beam, P f = 10.1 kn Factored axial compression, P fd = kn Factored moment, M f = 9.01 knm Axial deisgn P fd = kn f a = P fd / A/n = 11.16*1000/870/= 1.94 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, p a = 195 N/mm > 1.94 N/mm Bending design M f = 9.01 knm f b = M f / Z/ n = 9.01*10^6/149000/= 30.3 N/mm < 0 N/mm
30 Case 3 : 1.DL + 1.LL + 1.WL (lateral) Load widith per RHS post bay, b = Load length per RHS post bay, L = Load area per SHS post, A =.77*.131= No. of slat at roof deck, n = Height of SHS post, H = Dead load: self weight of slat = self weight of 00x100x.6kg/m RHS = Self weight of 160x180x14.4kg/m SHS =.77 m.131 m 5.91 m m 0.063*.77*14=.6*9.81/1000*.131= 14.4*9.81/1000*.75*=.44 kn 0.47 kn 0.78 kn 3.69 kn Live load : Maintenance live load = 0.75*5.91= 4.43 kn Lateral wind load assessment: Area I 500 Area II 00 Area III 750 Lateral wind load Section (Lateral wind load) Design wind pressure, q w =S a *C p *q z = 7.6 kpa I Roof Deck II 00x100x.3kg/m RHS postnos. Of 0.7m long III 00x100x.3kg/m SHS post nos. Of.75m long (1) () (3)=(1)*()*qw (4) (5)=(3)*(4) Area Project area, A (m) Nos of Projected Wind shear, S Level arm, L Moment, M b x d Area, n (kn) (m) (knm) I 0.09 x II 0.5 x III 0.1 x Design factored Axial compression, P f = 1.DL + 1.LL= 1.* *4.43= 9.74 kn Design factored lateral wind shear, V f = 1.*S = 1.*6.85= 8. kn Design factored bending moment, M f = 1.*M = 1.*13.35= 16.0 knm
31 Axial deisgn P fd = 9.74 kn f a = P fd / A /n= 9.74*1000/870/= 1.7 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 1.7 N/mm Shear design V f = 8. kn f v = V f / A /n= 8.*1000/870/= 1.43 N/mm > 0.6*0 N/mm Bending design M f = 16.0 knm = 13 N/mm f b = M f / Z /n= 16.0*10^6/149000/= N/mm < 0 N/mm Weld Design Consider one post Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored Shear, V f = Factored moment, M f = 9.74 kn 8. kn 16.0 knm Axial Weld stress, f aw = P f / L w /n = 9.74*1000/660/= 7.38 N/mm Shear Weld stress, f vw = V f / L w /n = 8.*1000/660/= 6.3 N/mm Bending weld stress, f bw = M f / Z w /n = 16.0*10^6/13013/= N/mm For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 69 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 69 N/mm Case 4 : 1.4DL+1.4WL (lateral) Design factored Axial compression, P f = 1.4DL 1.4*3.69= 5.17 kn Design factored lateral wind shear, V f = 1.4*S = 1.4*6.85= 9.59 kn Design factored bending moment, M f = 1.4*M = 1.4*13.35= knm Axial deisgn P fd = 5.17 kn f a = P fd / A /n= 5.17*1000/870/= 0.9 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 0.9 N/mm Shear design
32 V f = 9.59 kn f v = V f / A/n = 9.59*1000/870/= 1.67 N/mm < 0.6*0 N/mm Bending design M f = knm = 13 N/mm f b = M f / Z/n = 18.69*10^6/149000/ = 6.7 N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored Shear, V f = Factored moment, M f = 5.17 kn 9.59 kn knm Axial Weld stress, f aw = P f / L w /n = 5.17*1000/660/= 3.9 N/mm Shear Weld stress, f vw = V f / L w /n = 9.59*1000/660/= 7.7 N/mm Bending weld stress, f bw = M f / Z w /n = 18.69*10^6/13013/= N/mm For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 79 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 79 N/mm Case 5 : 1.4DL+1.4WL (downward) Load widith per SHS post bay, b =.77 m Load length per SHS post bay, L =.131 m Load area per SHS post, A =.77*.131= 5.91 m No. of slat at roof deck, n = 14 Height of SHS post, H =.75 m Dead load: self weight of slat = 0.063*.77*14=.44 kn self weight of 00x100x.6kg/m RHS =.6*9.81/1000*.131= 0.47 kn Self weight of nos.160 x80x14.4kg/m SHS = 14.4*9.81/1000*.75*= 0.78 kn 3.69 kn 1.4DL = 1.4*3.69= kn
33 Downward wind load : Nos. of slat, n = 14 design wind pressure, qw = 7.6 kpa load width per slat, B = 60 mm (Section) Downward wind load, WL downward = 60/1000*.77*14*7.6= kn Eccentric moment, M e,downward = 17.74*1.935/= knm 1.4DL * WL downward = 1.4*M e,downward = 3.1 kn 4.04 knm Axial deisgn P fd = 3.1 kn f a = P fd / A /n= *1000/870/= 5.59 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 5.59 N/mm Bending design M f = 4.04 knm f b = M f / Z /n= 4.04*10^6/149000/ = 80.6 N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored moment, M f = 3.1 kn 4.04 knm Axial Weld stress, f aw = P f / L w /n = *1000/660 /= 4.9 N/mm Bending weld stress, f bw = M f / Z w /n = 4.04*10^6/13013/ = N/mm
34 1/ Combined weld stress, f ew = (f bw +f aw ) = (93.08^+4.9^)^0.5= 93 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 93 N/mm Case 6 : 1.0DL1.4WL (downward) Load widith per SHS post bay, b =.77 m Load length per SHS post bay, L =.131 m Load area per SHS post, A =.77*.131= 5.91 m No. of slat at roof deck, n = 14 Height of SHS post, H =.75 m Dead load: self weight of slat = 0.063*.77*14=.44 kn self weight of 00x100x.6kg/m RHS =.6*9.81/1000*.131= 0.47 kn Self weight of nos.160 x80x14.4kg/m SHS = 14.4*9.81/1000*.75*= 0.78 kn 3.69 kn Live load : Maintenance live load = 0.75*5.91= 4.43 kn 1.0DL = 1.0*3.69= 3.69 kn Downward wind load : Nos. of slat, n = 14 design wind pressure, qw = 7.6 kpa load width per slat, B = 60 mm (Section) Downward wind load, WL downward = 60/1000*.77*14*7.6= kn Eccentric moment, M e,downward = 17.74*1.935/= knm 1.0DL * WL downward = 1.4*M e,downward =.9 kn 4.04 knm Axial deisgn
35 P fd =.9 kn f a = P fd / A /n=.906*1000//= 3.99 N/mm slendereness ratio, = L/r 750/7= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 3.99 N/mm Bending design M f = 4.04 knm f b = M f / Z /n= 4.04*10^6/149000/ = 80.6 N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored moment, M f =.9 kn 4.04 knm Axial Weld stress, f aw = P f / L w /n =.906*1000/660 /= N/mm Bending weld stress, f bw = M f / Z w /n = 4.04*10^6/13013/ = N/mm For conservative design, 1/ Combined weld stress, f ew = (f bw +f aw ) = (93.08^+.906^)^0.5= 93 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 93 N/mm Design of anchor bolt Plan Consider Case 1 and Case 5 for steel post, Factored Axial compression, P f = 3.1 kn (Case 5 control) Factored Shear, V f = Factored moment, Mf = 9.6 kn 4.04 knm Anchor bolt design is performed by Hilti's computer program. Please refer next page. Provide 8 nos. HITRE500/HASE M16x15 bolt (Case 4 control) (Case 5 control)
36 Loading schedule (unfactored load) Item DL LL DL+LL Lateral wind Upward/downward wind Axial (kn) Axial (kn) Axial (kn) Shear (kn) Moment (knm) Axial (kn) Pergola 4 at Area H
37 8. Pergola 4 at Area H1 : Loading assessment and design 6
38 Design for Steel Pergola at Ma Hang Headland Park Calculation is provided following load transfer path from roof deck to steel post and anchor bolt/steel base plate. Largest span, Loaded area, wind topography factor and loading combination will be used for structural member design. Pergola : 4 Area : H1 Dead Load Slat Self Weight, q ds = Structural Steel Sefl weight, q dst = 1197 kg/m 7850 kg/m 3 3 Wind Load Basic wind pressure, q z = (H < 5m) 1.8 kpa Wind pressure coefficient, C p = Topography factor for Area A, S a = 1.8 Design wind pressure, q w =1.15*S a *C p *q z = (Additional 15% wind load is adopted for design) 7.6 kpa Live Load Maintenance Live load on roof deck, q l = 0.75 kpa Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood Design This Slat Plan From First Principle, 4 I sx = 1/1*60*90^3= mm Z sx = I sx / (D/) = /(90/)= mm A s = B*D = 60*90= 5400 mm 3
39 Maximum span, L = Load width for wind load, b w = Load width for live load, b l =80+60 = 100 mm 60 mm 158 mm Dead Load self weight of slat, w ds = 1197*9.81/1000*60/1000*90/1000= kn/m Live load Maintenance live load, w ls = 0.75*158/1000= 0.1 kn/m Wind load Downward wind load, w ws = 7.6*60/1000= 0.46 kn/m Case 1 : 1.4 DL LL Factored UDL on slat, w f1 = 1.4*w ds +1.6*w ls = 0.8 kn/m Case : 1. DL + 1.LL + 1.WL (download) Factored UDL on slat, w f = 1.*w ds +1.*w ls +1.*w ws = 0.77 kn/m (Controlled case) Case 3 : 1.4 DL + 1.4WL (download) Factored UDL on slat, w f3 = 1.4*w ds +1.4*w ws = Use maximum factored UDL for Design, w fd = 0.73 kn/m 0.77 kn/m Bending design M f = 1/8*0.77*(100/1000)^= 0.4 knm f b = M f / Z s = 0.4*10^6/81000= 5.19 N/mm < 11.9 N/mm Shear Design V f = 1/*0.8*100/1000= 0.9 kn f = V / A = 0.9*1000/5400= N/mm < 0.6*11.9 v f s = 7.14 N/mm Connection design between 60x90mm slat and 80x50x4mm steel plate Design this steel plate connection Section Design this steel plate connection Section
40 Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Bolt design M10 Grade 8.8 Bolt, A b = No. of bolt, n = 58 mm Factored Shear from slat, V f = 0.4 kn Bolt Shear stress, f vb = V f / (n*a b ) = 3.6 N/mm < 375 N/mm 80 mm (D) x 50 mm (B) x 4 mm steel plate Moment of inertia, I 1/1*4*80^3= mm 4 Elastic modulus, Z = /(80/)= 467 mm 3 Shear Area, A = 80*4= 30 mm v Factored Shear from slat, V f = 0.4 kn No. of plate provided per slat, n = Plate shear stress, f vp = V f / A v / n = 0.66 N/mm < 0.6*0 N/mm = 13 N/mm Eccentricity, e = Factored eccentric moment, M e = V f *e = 0.4*5/1000= 5 mm 0.01 knm Plate bending stress, f bp = M e / Z / n = 0.01*10^6//467= 1.17 N/mm < 0 N/mm Weld design for 80x50x4mm steel plate and 160x80x17.5kg/m GMS RHS Weld length provided, L w = 80*= 160 mm Weld Moment of inertia, I = 1/1*80^3= 4667 mm 3 w Weld Elastic modulus, Zw = 4667/(80/)= 1067 mm Factored Shear from slat, V f = Factored Eccentric moment, M e = 0.4 kn 0.01 knm Shear Weld stress, f vw = V f / L w = 0.4*1000/160=.63 N/mm Bending weld stress, f bw = M e / Z w = 0.01*10^6/1067= 9.37 N/mm Combined weld stress, f ew = (f bw^+f vw^)^1/ = 9.73 N/mm Provide 4 mm fillet weld Provided weld strength, p w = 0.7*0*4= 616 N/mm > 9.73 N/mm
41 Design for 160x80x17.5kg/m GMS RHS supporting slat Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this RHS Section Plan Design 160x80x17.5kg/m RHS as cantilever beam 160x80x14.4kg/m GMS RHS I = Z = A = mm mm mm Length of RHS = 004 mm No. of Point load from slat, n = 13 Factored Self weight of RHS = 1.*.6*9.81/1000= 0.7 kn/m Equivalent Factored UDL on RHS, w = 0.4**13/(004/1000)= 5.45 kn/m 5.7 kn/m Cantilever span, L = 1476 mm Factored moment, M f = 1/*5.7*(1476/1000)^= 6.3 knm Factored Shear, V f = 5.7*1476/1000= 8.44 kn Bending design f b = M f / Z = 6.3*10^6/76500= N/mm < 0 N/mm Shear design f v = V f / A v = 8.44*1000/1840= 4.59 N/mm < 0.6*0 N/mm = 13 N/mm Deflection design UDL on RHS, wu = 5.45/1.= 4.54 kn/m E = N/mm d = wl^4 / 8EI = 7.3 mm < L / 180 = mm
42 Design of Bolt joint at 160x80x17.5kg/m vertical RHS post supporting RHS cantilever beam Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this bolt joint Loaded Unloaded Section Section Consider only larger projection is loaded and small projection unload for worst case design. Bolt design Area per bolt, A b = No. of bolt provided, n = mm For the bolt group, I xx = I yy = I p = I xx + I yy = mm mm 0000 mm Factored Direct Shear for bolt group, V f = Factored Moment for bolt group, M f = 8.44 kn 6.3 knm Distance of bolt group centroid to one bol ( ) 1/ = 71 mm Factored shear from bending, V fb = 6.3*10^6*71/0000/1000=.1 kn For conservative design Factored design shear for bolt, V fd = V fb + V f = = kn Bolt shear stress, f vb = V fd / A b = 30.56*1000/157= N/mm < 375 N/mm
43 Design of 160x80x17.5kg/m RHS Vertical post Design this steel post Each 160x80x17.5kg/m RHS Vertical Post I = mm 4 Z = mm 3 A = 1840 mm r = 58 mm Effective Height of RHS post, H = 750 mm No of post provided, n = Case 1 : 1.4DL+1.6LL Load widith per RHS post bay, b = Load length per RHS post bay, L = Load area per RHS post, A =.1*.005= No. of slat at roof deck, n = Height of RHS post, H = Dead load: self weight of slat = self weight of 00x100x.6kg/m RHS = Self weight of 160x80x14.4kg/m SHS =.1 m.005 m 4.1 m m 0.063*.1*13=.6*9.81/1000*.005= 14.4*9.81/1000*.75*= 1.7 kn 0.44 kn 0.78 kn.94 kn Live load : Maintenance live load = 0.75*4.1= 3.16 kn DL eccentric moment, M de = (1.33/3*.94*1.33/0.441/3*.94*0.441/)= 0.76 knm LL eccentric moment, M le = (1.33/3*3.16*1.33/0.441/3*3.16*0.441/)= 0.8 knm w = 1.4DL LL = 9.17 kn
44 Axial deisgn P fd = 9.17 kn f a = P fd / A /n= 9.17*1000/1840/=.49 N/mm slendereness ratio, = L/r 750/58= <180 From table of HK005, reduced axial stress, p a = 195 N/mm >.49 N/mm Bending design Eccentric moment, M fe = (1.33/3*9.17*1.33/0.441/3*9.17*0.441/)/= 1.19 knm f b = M f e / Z = 1.19*10^6/76500= N/mm < 0 N/mm Case : 1.DL+1.LL+1.WL (downward) 1.DL+1.LL+1.WL (downward) Section Factored Self weight of nos. RHS post = 1.*.6*9.81/1000*750/1000*= 0.95 kn Factored Axial compression from RHS beam, P f = 8.44 kn Factored axial compression, P fd = 9.39 kn Factored moment, M f = 6.3 knm Axial deisgn P fd = 9.39 kn f a = P fd / A/n = 9.39*1000/1840/=.55 N/mm slendereness ratio, = L/r 750/58= <180 From table of HK005, reduced axial stress, p a = 195 N/mm >.55 N/mm Bending design M f = 6.3 knm f b = M f / Z/ n = 6.3*10^6/76500/= 40.7 N/mm < 0 N/mm
45 Case 3 : 1.DL + 1.LL + 1.WL (lateral) Load widith per RHS post bay, b = Load length per RHS post bay, L = Load area per SHS post, A =.1*.005= No. of slat at roof deck, n = Height of SHS post, H = Dead load: self weight of slat = self weight of 00x100x.6kg/m RHS = Self weight of 160x180x14.4kg/m SHS =.1 m.005 m 4.1 m m 0.063*.1*13=.6*9.81/1000*.005= 14.4*9.81/1000*.75*= 1.7 kn 0.44 kn 0.78 kn.94 kn Live load : Maintenance live load = 0.75*4.1= 3.16 kn Lateral wind load assessment: Area I 500 Area II 160 Area III 750 Lateral wind load Section (Lateral wind load) Design wind pressure, q w =S a *C p *q z = 7.6 kpa I Roof Deck II 160x80x14.4kg/m RHS postnos. Of 0.7m long III 160x80x14.4kg/m SHS post .75m long (1) () (3)=(1)*()*qw (4) (5)=(3)*(4) Area Project area, A (m) Nos of Projected Wind shear, S Level arm, L Moment, M b x d Area, n (kn) (m) (knm) I 0.09 x II 0.5 x III 0.08 x Design factored Axial compression, P f = 1.DL + 1.LL= 1.*.94+1.*3.16= 7.3 kn Design factored lateral wind shear, V f = 1.*S = 1.*5.55= 6.66 kn Design factored bending moment, M f = 1.*M = 1.*10.93= 13.1 knm
46 Axial deisgn P fd = 7.3 kn f a = P fd / A /n= 7.3*1000/1840/= 1.99 N/mm slendereness ratio, = L/r 750/58= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 1.99 N/mm Shear design V f = 6.66 kn f v = V f / A /n= 6.66*1000/1840/= 1.81 N/mm > 0.6*0 N/mm Bending design M f = 13.1 knm = 13 N/mm f b = M f / Z /n= 13.1*10^6/76500/= N/mm < 0 N/mm Weld Design Consider one post Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored Shear, V f = Factored moment, M f = 7.3 kn 6.66 kn 13.1 knm Axial Weld stress, f aw = P f / L w /n = 7.3*1000/660/= 5.55 N/mm Shear Weld stress, f vw = V f / L w /n = 6.66*1000/660/= 5.05 N/mm Bending weld stress, f bw = M f / Z w /n = 13.1*10^6/13013/= N/mm For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 515 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 515 N/mm Case 4 : 1.4DL+1.4WL (lateral) Design factored Axial compression, P f = 1.4DL 1.4*.94= 4.1 kn Design factored lateral wind shear, V f = 1.4*S = 1.4*5.55= 7.77 kn Design factored bending moment, M f = 1.4*M = 1.4*10.93= 15.3 knm Axial deisgn P fd = 4.1 kn f a = P fd / A /n= 4.1*1000/1840/= 1.1 N/mm slendereness ratio, = L/r 750/58= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 1.1 N/mm
47 Shear design V f = 7.77 kn f v = V f / A/n = 7.77*1000/1840/=.11 N/mm < 0.6*0 N/mm Bending design M f = 15.3 knm = 13 N/mm f b = M f / Z/n = 15.3*10^6/76500/ = 100 N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored Shear, V f = Factored moment, M f = 4.1 kn 7.77 kn 15.3 knm Axial Weld stress, f aw = P f / L w /n = 4.1*1000/660/= 3.1 N/mm Shear Weld stress, f vw = V f / L w /n = 7.77*1000/660/= 5.89 N/mm Bending weld stress, f bw = M f / Z w /n = 15.3*10^6/13013/= N/mm For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 597 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 597 N/mm Case 5 : 1.4DL+1.4WL (downward) Load widith per SHS post bay, b =.1 m Load length per SHS post bay, L =.005 m Load area per SHS post, A =.1*.005= 4.1 m No. of slat at roof deck, n = 13 Height of SHS post, H =.75 m Dead load: self weight of slat = 0.063*.1*13= 1.7 kn self weight of 00x100x.6kg/m RHS =.6*9.81/1000*.005= 0.44 kn Self weight of nos.160 x80x14.4kg/m SHS = 14.4*9.81/1000*.75*= 0.78 kn.94 kn 1.4DL = 1.4*.94= kn
48 Downward wind load : Nos. of slat, n = 13 design wind pressure, qw = 7.6 kpa load width per slat, B = 60 mm (Section) Downward wind load, WL downward = 60/1000*.1*13*7.6= 1.48 kn Eccentric moment, M e,downward = 1.48*1.935/= 1.07 knm 1.4DL * WL downward = 1.4*M e,downward = 3. kn knm Axial deisgn P fd = 3. kn f a = P fd / A /n= 3.344*1000/1840/= 6.31 N/mm slendereness ratio, = L/r 750/58= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 6.31 N/mm Bending design M f = knm f b = M f / Z /n= *10^6/76500/ = N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored moment, M f = 3. kn knm Axial Weld stress, f aw = P f / L w /n = 3.344*1000/660 /= 17.6 N/mm Bending weld stress, f bw = M f / Z w /n = *10^6/13013/ = N/mm
49 For conservative design, Combined weld stress, f ew = f bw +f aw +f vw = = 667 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 667 N/mm Case 6 : 1.0DL1.4WL (downward) Load widith per SHS post bay, b =.1 m Load length per SHS post bay, L =.005 m Load area per SHS post, A =.1*.005= 4.1 m No. of slat at roof deck, n = 13 Height of SHS post, H =.75 m Dead load: self weight of slat = 0.063*.1*13= 1.7 kn self weight of 00x100x.6kg/m RHS =.6*9.81/1000*.005= 0.44 kn Self weight of nos.160 x80x14.4kg/m SHS = 14.4*9.81/1000*.75*= 0.78 kn.94 kn Live load : Maintenance live load = 0.75*4.1= 3.16 kn 1.0DL = 1.0*.94=.94 kn Downward wind load : Nos. of slat, n = 13 design wind pressure, qw = 7.6 kpa load width per slat, B = 60 mm (Section) Downward wind load, WL downward = 60/1000*.1*13*7.6= 1.48 kn Eccentric moment, M e,downward = 1.48*1.935/= 1.07 knm 1.0DL * WL downward = 1.4*M e,downward = 16.6 kn knm
50 Axial deisgn P fd = 16.6 kn f a = P fd / A /n= *1000//= 4.51 N/mm slendereness ratio, = L/r 750/58= <180 From table of HK005, reduced axial stress, pa = 195 N/mm > 4.51 N/mm Bending design M f = knm f b = M f / Z /n= *10^6/76500/ = N/mm < 0 N/mm Weld Design Weld length provided, L w = *10+*80+4*10= 660 mm Weld Moment of inertia, I = *10*80^+*1/1*80^3+4*1/1*10^3+4*80*40^= mm 3 w w Weld Elastic modulus, Z = /(00)= mm Factored Axial compression, P f = Factored moment, M f = 16.6 kn knm Axial Weld stress, f aw = P f / L w /n = *1000/660 /= 1.57 N/mm Bending weld stress, f bw = M f / Z w /n = *10^6/13013/ = N/mm For conservative design, 1/ Combined weld stress, f ew = (f bw +f aw ) = (649.7^ ^)^0.5= 649 N/mm Provide 6 mm fillet weld Provided weld strength, p w = 0.7*0*6= 94 N/mm > 649 N/mm Design of anchor bolt Plan Consider Case 1 and Case 5 for steel post, Factored Axial compression, P f = 3. kn (Case 5 control) Factored Shear, V f = Factored moment, Mf = 7.8 kn knm Anchor bolt design is performed by Hilti's computer program. Please refer next page. Provide 8 nos. HITRE500/HASE M16x15 bolt (Case 4 control) (Case 5 control)
51 Loading schedule (unfactored load) Item DL LL DL+LL Lateral wind Upward/downward wind Axial (kn) Axial (kn) Axial (kn) Shear (kn) Moment (knm) Axial (kn) Pergola 4 at Area H
52 9. Pergola 5 at Area H : Loading assessment and design 7
53 Design for Steel Pergola at Ma Hang Headland Park Calculation is provided following load transfer path from roof deck to steel post and anchor bolt/steel base plate. Largest span, Loaded area, wind topography factor and loading combination will be used for structural member design. Pergola : 4 Area : H Dead Load Slat Self Weight, q ds = Structural Steel Sefl weight, q dst = 1197 kg/m 7850 kg/m 3 3 Wind Load Basic wind pressure, q z = (H < 5m) 1.8 kpa Wind pressure coefficient, C p = Topography factor for Area A, S a = 1.8 Design wind pressure, q w =1.15*S a *C p *q z = (Additional 15% wind load is adopted for design) 7.6 kpa Live Load Maintenance Live load on roof deck, q l = 0.75 kpa Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood Design This Slat Plan From First Principle, 4 I sx = 1/1*60*90^3= mm Z sx = I sx / (D/) = /(90/)= mm A s = B*D = 60*90= 5400 mm 3
54 Maximum span, L = Load width for wind load, b w = Load width for live load, b l =90+60 = 1759 mm 60 mm 150 mm Dead Load self weight of slat, w ds = 1197*9.81/1000*60/1000*90/1000= kn/m Live load Maintenance live load, w ls = 0.75*150/1000= 0.11 kn/m Wind load Downward wind load, w ws = 7.6*60/1000= 0.46 kn/m Case 1 : 1.4 DL LL Factored UDL on slat, w f1 = 1.4*w ds +1.6*w ls = 0.6 kn/m Case : 1. DL + 1.LL + 1.WL (download) Factored UDL on slat, w f = 1.*w ds +1.*w ls +1.*w ws = 0.76 kn/m (Controlled case) Case 3 : 1.4 DL + 1.4WL (download) Factored UDL on slat, w f3 = 1.4*w ds +1.4*w ws = Use maximum factored UDL for Design, w fd = 0.73 kn/m 0.76 kn/m Bending design M f = 1/8*0.76*(1759/1000)^= 0.9 knm f b = M f / Z s = 0.9*10^6/81000= 3.58 N/mm < 11.9 N/mm Shear Design V f = 1/*0.6*1759/1000= 0.3 kn f = V / A = 0.3*1000/5400= N/mm < 0.6*11.9 v f s = 7.14 N/mm Connection design between 60x90mm slat and 80x50x4mm steel plate Design this steel plate connection Section Design this steel plate connection Section
55 Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Bolt design M10 Grade 8.8 Bolt, A b = No. of bolt, n = 58 mm Factored Shear from slat, V f = 0.4 kn Bolt Shear stress, f vb = V f / (n*a b ) = 3.6 N/mm < 375 N/mm 80 mm (D) x 50 mm (B) x 4 mm steel plate Moment of inertia, I 1/1*4*80^3= mm 4 Elastic modulus, Z = /(80/)= 467 mm 3 Shear Area, A = 80*4= 30 mm v Factored Shear from slat, V f = 0.4 kn No. of plate provided per slat, n = Plate shear stress, f vp = V f / A v / n = 0.66 N/mm < 0.6*0 N/mm = 13 N/mm Eccentricity, e = Factored eccentric moment, M e = V f *e = 0.4*5/1000= 5 mm 0.01 knm Plate bending stress, f bp = M e / Z / n = 0.01*10^6//467= 1.17 N/mm < 0 N/mm Weld design for 80x50x4mm steel plate and 160x80x17.5kg/m GMS RHS Weld length provided, L w = 80*= 160 mm Weld Moment of inertia, I = 1/1*80^3= 4667 mm 3 w Weld Elastic modulus, Zw = 4667/(80/)= 1067 mm Factored Shear from slat, V f = Factored Eccentric moment, M e = 0.4 kn 0.01 knm Shear Weld stress, f vw = V f / L w = 0.4*1000/160=.63 N/mm Bending weld stress, f bw = M e / Z w = 0.01*10^6/1067= 9.37 N/mm Combined weld stress, f ew = (f bw^+f vw^)^1/ = 9.73 N/mm Provide 4 mm fillet weld Provided weld strength, p w = 0.7*0*4= 616 N/mm > 9.73 N/mm
56 Design for 160x80x17.5kg/m GMS RHS supporting slat Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this RHS Section Plan Design 160x80x17.5kg/m RHS as cantilever beam 160x80x17.5kg/m GMS RHS I = Z = A = mm mm mm Length of RHS = 100 mm No. of Point load from slat, n = 14 Factored Self weight of RHS = 1.*.6*9.81/1000= 0.7 kn/m Equivalent Factored UDL on RHS, w = 0.4**14/(100/1000)= 5.6 kn/m 5.87 kn/m Cantilever span, L = 1764 mm Factored moment, M f = 1/*5.87*(1764/1000)^= 9.13 knm Factored Shear, V f = 5.87*1764/1000= kn Bending design f b = M f / Z = 9.13*10^6/76500= N/mm < 0 N/mm Shear design f v = V f / A v = 10.35*1000/1840= 5.63 N/mm < 0.6*0 N/mm = 13 N/mm Deflection design UDL on RHS, wu = 5.6/1.= 4.67 kn/m E = N/mm d = wl^4 / 8EI = 9.05 mm < L / 180 = mm
57 Design of Bolt joint at 160x80x17.5kg/m vertical RHS post supporting RHS cantilever beam Load combination : 1. DL + 1.LL + 1.WL (download) control and is used for design Design this bolt joint Loaded Unloaded Section Section Consider only larger projection is loaded and small projection unload for worst case design. Bolt design Area per bolt, A b = No. of bolt provided, n = mm For the bolt group, I xx = I yy = I p = I xx + I yy = mm mm 0000 mm Factored Direct Shear for bolt group, V f = Factored Moment for bolt group, M f = kn 9.13 knm Distance of bolt group centroid to one bol ( ) 1/ = 71 mm Factored shear from bending, V fb = 9.13*10^6*71/0000/1000= 3.41 kn For conservative design Factored design shear for bolt, V fd = V fb + V f = = 4.76 kn Bolt shear stress, f vb = V fd / A b = 4.76*1000/157= 7.36 N/mm < 375 N/mm
58 Design of 160x80x17.5kg/m RHS Vertical post Design this steel post Each 160x80x14.4kg/m RHS Vertical Post I = mm 4 Z = mm 3 A = 1840 mm r = 58 mm Effective Height of RHS post, H = No of post provided, n = 750 mm Case 1 : 1.4DL+1.6LL Load widith per RHS post bay, b = Load length per RHS post bay, L = Load area per RHS post, A = 1.758*.1= No. of slat at roof deck, n = Height of RHS post, H = Dead load: self weight of slat = self weight of 00x100x.6kg/m RHS = Self weight of 160x80x14.4kg/m SHS = m.1 m 3.69 m 8.75 m 0.063*1.758*8=.6*9.81/1000*.1= 14.4*9.81/1000*.75*= 1.55 kn 0.47 kn 0.78 kn.8 kn Live load : Maintenance live load = 0.75*3.69=.77 kn DL eccentric moment, M de = (1.33/3*.8*1.33/0.441/3*.8*0.441/)= 0.73 knm LL eccentric moment, M le = (1.33/3*.77*1.33/0.441/3*.77*0.441/)= 0.7 knm w = 1.4DL LL = 8.35 kn
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