Structural Design Calculation For Pergola

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Structural Design Calculation

For Pergola

Revision :5 Prepared by :EC Date : 8/10/2009

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1

CONTENTS

1. Introduction ………..………

2. Design Code and Reference………

3. Design Synopsis

4. Design Parameters

4.1 Design Load……….

4.2 Design Wind Pressure……….

4.3 Loading Combination ……….

5. Material Properties

6. Pergola 2 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 H2 : Loading assessment and design…….

10. Loading schedule and Anchor Bolt Design ……….

11. Appendix A

-

Wind Topography Analysis

Appendix B

-

Reference Design Intent Drawing

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2

1.

Introduction

This calculation is to design pergola’s structure for four numbers proprietary

pergola located at area C , D , H1 and H2.

2.

Design Code and Reference

Code of Practice for the Structural Use of Steel 2005

Code of Practice on Wind Effects Hong Kong - 2004

Hong Kong Building (Construction) Regulations 1990

3.

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

4.2 Design Wind Pressure

Design Wind Pressure (H<5m) , q

z

=

1.82 kPa

Topography Factor for Area D, H1, H2

S

a

= (1 + 1.2

e

*s)

2

= (1 + 1.2*0.3*1)

2

=

1.85

Topography Factor for Area C

S

a

= (1 + 1.2

e

*s)

2

= (1 + 1.2*0.3*0.2)

2

=

1.15

4.3 Loading Combination

1) 1.4DL + 1.6LL

2) 1.2DL + 1.2LL + 1.2WL

dn

3) 1.4DL + 1.4WL

dn

4) 1.2DL + 1.2LL + 1.2WL

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,

(4)

3

5.

Material Properties

Structural Steel

Steel Grade

=

S275JR unless stated otherwise

to BS EN 10025 Part 1-6 : 2004 for Hot

Rolled Sections and BS EN 10210 Part 1 : 2006 for Hot

finished hollow sections.

=

S275J0H for cold formed steel hollow,

Strength reduced 25% to 220 N/mm

2

to BS EN 10219 Part 1 : 2006

Weld Strength =

220 N/mm

2

Welding work shall be complicance with BS EN 1011

Part 1:1998

Electrodes to welding shall be complicance with BS EN ISO 2560:2005.

Recycled Plastic Wood

Tensile Strength

=

11.9N/mm

2

(5)

4

6. Pergola 2 at Area C : Loading assessment and design

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3 2 3 3

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 : 2

Area : C

Dead Load

Slat Self Weight, qds = 1197 kg/m

Structural Steel Sefl weight, qdst = 7850 kg/m

Wind Load

Basic wind pressure , qz = 1.82 kPa

(H < 5m)

Wind pressure coefficient, Cp = 2

Topography factor for Area A, Sa = 1.15

Design wind pressure, qw =1.15*Sa*Cp *qz = 4.81 kPa

(Additional 15% wind load is adopted for design)

Live Load

Maintenance Live load on roof deck, ql = 0.75 kPa

Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood

Design This Slat

Plan

From First Principle,

4

Isx = 1/12*60*90^3= 3645000 mm

Zsx = Isx / (D/2) = 3645000/(90/2)= 81000 mm

(7)

2

Maximum span, L = 1900 mm Load width for wind load, bw = 60 mm

Load width for live load, bl =280+60 = 159 mm

Dead Load

self weight of slat, wds = 1197*9.81/1000*60/1000*90/1000= 0.063 kN/m

Live load

Maintenance live load, wls = 0.75*159/1000= 0.12 kN/m

Wind load

Downward wind load, wws = 4.81*60/1000= 0.29 kN/m

Case 1 : 1.4 DL + 1.6 LL

Factored UDL on slat , wf1 = 1.4*wds+1.6*wls= 0.28 kN/m

Case 2 : 1.2 DL + 1.2LL + 1.2WL(download)

Factored UDL on slat , wf2 = 1.2*wds+1.2*wls+1.2*wws= 0.57 kN/m (Controlled case)

Case 3 : 1.4 DL + 1.4WL(download)

Factored UDL on slat , wf3 = 1.4*wds+1.4*wws= 0.49 kN/m

Use maximum factored UDL for Design, wfd = 0.57 kN/m

Bending design Mf = 1/8*0.57*(1900/1000)^2= 0.26 kNm 2 2 fb = Mf / Zs = 0.26*10^6/81000= 3.21 N/mm < 11.9 N/mm CHECK OK Shear Design Vf = 1/2*0.28*1900/1000= 0.27 kN fv = Vf / As = 0.27*1000/5400= 0.05 N/mm < 0.6*11.9 = 7.14 N/mm2 CHECK OK

(8)

v

w

2

Connection design between 60x90mm slat and 80x50x4mm steel plate

Design this steel plate connection

Section

Load combination : 1.2 DL + 1.2LL + 1.2WL(download) control and is used for design

Bolt design

M10 Grade 8.8 Bolt, Ab = 58 mm

No. of bolt, n = 2

Factored Shear from slat, Vf = 0.42 kN

2 2

Bolt Shear stress, fvb = Vf / (n*Ab) = 3.62 N/mm < 375 N/mm

CHECK OK

80 mm (D) x 50 mm (B) x 4 mm steel plate Moment of inertia, I=1/12*4*80^3= 170667 mm4 Elastic modulus, Z = 170667/(80/2)= 4267 mm3 Shear Area, A = 80*4= 320 mm2

No. of plate provided per slat, n = 2

2 2

Plate shear stress, fvp = Vf / Av / n = 0.66 N/mm < 0.6*220 N/mm

= 132 N/mm2

CHECK OK

Eccentricity, e = 25 mm

Factored eccentric moment, Me = Vf *e = 0.42*25/1000= 0.01 kNm

2 2

Plate bending stress, fbp = Me / Z / n = 0.01*10^6/2/4267= 1.17 N/mm < 220 N/mm

CHECK OK

Weld design for 80x50x4mm steel plate and 200x100x22.6kg/m GMS RHS

Weld length provided, Lw = 80*2= 160 mm

Weld Moment of inertia, I = 1/12*80^3= 42667 mm3 Weld Elastic modulus, Zw = 42667/(80/2)= 1067 mm2

(9)

Shear Weld stress, fvw = Vf / Lw = 0.42*1000/160= 2.63 N/mm

Bending weld stress, fbw = Me / Zw = 0.01*10^6/1067= 9.37 N/mm

Combined weld stress, few = (fbw^2+fvw^2)^1/2 = 9.73 N/mm

Provide 4 mm fillet weld

Provided weld strength, pw = 0.7*220*4= 616 N/mm > 9.73 N/mm

CHECK OK

Design for 200x100x22.6kg/m GMS RHS supporting slat

Design this RHS

Section Plan

Design 200x100x22.6kg/m RHS as cantilever beam

200x100x22.6kg/m GMS RHS

I = 14950000 mm4

Z = 149000 mm3

A = 2870 mm2

Length of RHS = 2000 mm

No. of Point load from slat, n = 14

Factored Self weight of RHS = 1.2*22.6*9.81/1000= 0.27 kN/m Equivalent Factored UDL on RHS, w = 0.42*2*14/(2000/1000)= 5.88 kN/m 6.15 kN/m Cantilever span, L = 1764 mm Factored moment, Mf = Factored Shear, Vf = 1/2*6.15*(1764/1000)^2= 6.15*1764/1000= 9.57 kNm 10.85 kN

(10)

2 2 2 2 Bending design 2 2 fb = Mf / Z = 9.57*10^6/149000= 64.23 N/mm < 220 N/mm CHECK OK Shear design 2 2 fv = Vf / Av = 10.85*1000/2870= 3.78 N/mm < 0.6*220 N/mm = 132 N/mm2 CHECK OK Deflection design UDL on RHS, wu = 5.88/1.2= 4.9 kN/m E = 205000 N/mm2 d = wL^4 / 8EI = 3.2 mm < L / 180 = 11.11 mm

Design of Bolt joint at 200x100x22.6kg/m vertical RHS post supporting RHS cantilever beam

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, Ab = 157 mm

No. of bolt provided, n = 4

For the bolt group,

Ixx = 10000 mm

Iyy = 10000 mm

Ip = Ixx + Iyy = 20000 mm

Factored Direct Shear for bolt group, Vf = 10.85 kN

Factored Moment for bolt group, Mf = 9.57 kNm

(11)

Factored shear from bending, Vfb = 9.57*10^6*71/20000/1000= 33.97 kN

For conservative design

Factored design shear for bolt, Vfd = Vfb + Vf = 33.97+10.85= 44.82 kN

2 2

Bolt shear stress, fvb = Vfd / Ab = 44.82*1000/157= 285.48 N/mm < 375 N/mm

CHECK OK

Design of 200x100x22.6kg/m RHS Vertical post

Design this steel post

Each 200x100x22.6kg/m RHS Vertical Post

I = 14950000 mm4

Z = 149000 mm3

A = 2870 mm2

r = 72 mm

Effective Height of RHS post, H = 2750 mm

No of post provided, n = 2

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*2.5= No. of slat at roof deck, n =

Height of RHS post, H = 1.9 m 2.5 m 4.75 m2 14 2.75 m

Dead load: self weight of slat =

self weight of 200x100x22.6kg/m RHS = Self weight of 160x80x14.4kg/m SHS = 0.063*1.9*14= 22.6*9.81/1000*2.5= 14.4*9.81/1000*2.75*2= 1.68 kN 0.55 kN 0.78 kN 3.01 kN

(12)

2

Live load : Maintenance live load = 0.75*4.75= 3.56 kN

DL eccentric moment, Mde= (1.323/3*3.01*1.323/2-0.441/3*3.01*0.441/2)= 0.78 kNm LL eccentric moment, Mle= (1.323/3*3.56*1.323/2-0.441/3*3.56*0.441/2)= 0.92 kNm w = 1.4DL + 1.6 LL = 9.91 kN Axial deisgn Pfd = 9.91 kN fa = Pfd / A /n= 9.91*1000/2870/2= 1.73 N/mm slendereness ratio, = L/r 2750/72= 38.19 <180 2 2

From table of HK2005, reduced axial stress, pa = 195 N/mm > 1.73 N/mm

CHECK OK Bending design Eccentric moment, Mfe = (1.323/3*9.91*1.323/2-0.441/3*9.91*0.441/2)/2= 1.28 kNm 2 2 fb = Mf e/ Z = 1.28*10^6/149000= 8.59 N/mm < 220 N/mm CHECK OK Case 2 : 1.2DL+1.2LL+1.2WL(downward) 1.2DL+1.2LL+1.2WL(downward) Section

Factored Self weight of 2nos. RHS post = 1.2*22.6*9.81/1000*2750/1000*2= 0.95 kN Factored Axial compression from RHS beam, Pf = 10.85 kN

Factored axial compression, Pfd = 11.8 kN

Factored moment, Mf = 9.57 kNm Axial deisgn Pfd = 11.8 kN fa = Pfd / A/n = 11.8*1000/2870/2= 2.06 N/mm2 slendereness ratio, = L/r 2750/72= 38.19 <180 2 2

(13)

Bending design Mf = 9.57 kNm 2 2 fb = Mf / Z/ n = 9.57*10^6/149000/2= 32.11 N/mm < 220 N/mm CHECK OK Case 3 : 1.2DL + 1.2LL + 1.2WL (lateral)

Load widith per RHS post bay, b = 1.9 m Load length per RHS post bay, L =

Load area per SHS post, A = 1.9*2.5= No. of slat at roof deck, n =

Height of SHS post, H =

2.5 m 4.75 m2

14 2.75 m

Lateral wind load assessment:

Area I 500 Area II 200

Area III 2750

Lateral wind load

Section

(Lateral wind load)

Design wind pressure, qw =Sa*Cp *qz = 4.81 kPa

I- Roof Deck

II- 200x100x22.3kg/m RHS post-2nos. Of 0.7m long III- 200x100x22.3kg/m SHS post 2nos. Of 2.75m long

(1) (2) (3)=(1)*(2)*qw (4) (5)=(3)*(4)

Area Project area, A (m) Nos of ProjectedWind shear, SLevel arm, L Moment, M

b x d Area, n (kN) (m) (kNm)

I 0.09 x 1.9 1 0.82 2.75 2.26

II 0.5 x 0.1 2 0.48 3.1 1.49

III 0.1 x 2.75 2 2.65 1.375 3.64

(14)

w w

2

Design factored Axial compression, Pf = 1.2DL + 1.2LL= 1.2*3.01+1.2*3.56= 7.88 kN

Design factored lateral wind shear, Vf = 1.2*S = 1.2*3.95= 4.74 kN

Design factored bending moment, Mf = 1.2*M = 1.2*7.39= 8.87 kNm

Axial deisgn

Pfd = 7.88 kN

fa = Pfd / A /n= 7.88*1000/2870/2= 1.37 N/mm

slendereness ratio, = L/r 2750/72= 38.19 <180

From table of HK2005, reduced axial stress, pa = 195 N/mm2 > 1.37 N/mm2

CHECK OK Shear design Vf = 4.74 kN 2 2 fv = Vf / A /n= 4.74*1000/2870/2= 0.83 N/mm > 0.6*220 N/mm = 132 N/mm2 CHECK OK Bending design Mf = 8.87 kNm 2 2 fb = Mf / Z /n= 8.87*10^6/149000/2= 29.77 N/mm < 220 N/mm CHECK OK Weld Design Consider one post

Weld length provided, Lw = 2*10+2*80+4*120= 660 mm

Weld Moment of inertia, I = 2*10*80^2+2*1/12*80^3+4*1/12*120^3+4*80*40^2= 1301333 mm3 Weld Elastic modulus, Z = 1301333/(200)= 13013 mm2

Factored Axial compression, Pf = 7.88 kN

Factored Shear, Vf = 4.74 kN

Factored moment, Mf = 8.87 kNm

Axial Weld stress, faw = Pf / Lw /n = 7.88*1000/660/2= 5.97 N/mm

Shear Weld stress, fvw = Vf / Lw /n = 4.74*1000/660/2= 3.59 N/mm

Bending weld stress, fbw = Mf / Zw /n = 8.87*10^6/13013/2= 340.81 N/mm

For conservative design,

Combined weld stress, few = fbw+faw+fvw = 340.81+3.59+5.97= 350 N/mm

Provided weld strength, pw = 0.7*220*6= 924 N/mm > 350 N/mm

CHECK OK Case 4 : 1.4DL+1.4WL(lateral)

Design factored Axial compression, Pf = 1.4DL 1.4*3.01= 4.21 kN

Axial deisgn

Pfd = 4.21 kN

(15)

w w

CHECK OK Shear design Vf = 5.53 kN 2 2 fv = Vf / A/n = 5.53*1000/2870/2= 0.96 N/mm < 0.6*220 N/mm = 132 N/mm2 CHECK OK Bending design Mf = 10.35 kNm 2 2 fb = Mf / Z/n = 10.35*10^6/149000/2 = 34.73 N/mm < 220 N/mm CHECK OK Weld Design

CHECK OK Case 5 : 1.4DL+1.4WL(downward)

Load widith per SHS post bay, b = 1.9 m Load length per SHS post bay, L = 2.5 m Load area per SHS post, A = 1.9*2.5= 4.75 m2 No. of slat at roof deck, n = 14 Height of SHS post, H = 2.75 m

Dead load:

self weight of slat = 0.063*1.9*14= 1.68 kN self weight of 200x100x22.6kg/m RHS = 22.6*9.81/1000*2.5= 0.55 kN Self weight of 2nos.160 x80x14.4kg/m SHS = 14.4*9.81/1000*2.75*2= 0.78 kN

3.01 kN

(16)

Downward wind load :

Nos. of slat, n = 14

design wind pressure, qw = 4.81 kPa load width per slat, B = 60 mm

(17)

w w

2

Downward wind load, WLdownward = 60/1000*1.9*14*4.81= 7.68 kN

Eccentric moment, Me,downward = 7.68*1.935/2= 7.43 kNm

1.4DL + 1.4 * WLdownward = 13.6 kN 1.4*Me,downward = 10.402 kNm Axial deisgn Pfd = 13.6 kN fa = Pfd / A /n= 13.5796*1000/2870/2= 2.37 N/mm slendereness ratio, = L/r 2750/72= 38.19 <180

CHECK OK Bending design Mf = 10.402 kNm 2 2 fb = Mf / Z /n= 10.402*10^6/149000/ 2= 34.91 N/mm < 220 N/mm CHECK OK Weld Design

Axial Weld stress, faw = Pf / Lw /n = 13.5796*1000/660 /2= 10.29 N/mm

Bending weld stress, fbw = Mf / Zw /n = 10.402*10^6/13013/2 = 399.68 N/mm

Combined weld stress, few = fbw+faw+fvw = 399.68+10.29= 410 N/mm

CHECK OK

Case 6 : 1.0DL-1.4WL(downward)

Dead load:

3.01 kN

(18)

w w

2

(Section)

1.0DL - 1.4 * WLdownward = 11.9 kN 1.4*Me,downward = 10.402 kNm Axial deisgn Pfd = 11.9 kN fa = Pfd / A /n= 11.894*1000//2= 2.07 N/mm slendereness ratio, = L/r 2750/72= 38.19 <180

Bending weld stress, fbw = Mf / Zw /n =

(19)

(20)

Design of anchor bolt

Plan

Consider Case 1 and Case 5 for steel post,

Factored Axial compression, Pf = 13.6 kN (Case 5 control)

Factored Shear, Vf = Factored moment, Mf = 5.5 kN 10.402 kNm (Case 4 control) (Case 5 control)

Anchor bolt design is performed by Hilti's computer program. Please refer next page.

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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

(22)

7. Pergola 3 at Area D : Loading assessment and design

(23)

3 2 3 3

Design for Steel Pergola at Ma Hang Headland Park

Pergola : 3

Area : D

Dead Load

Wind Load

(H < 5m)

Live Load

Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood

Design This Slat

Plan

4

Isx = 1/12*60*90^3= 3645000 mm

Zsx = Isx / (D/2) = 3645000/(90/2)= 81000 mm

(24)

v f s

Maximum span, L =2963-100 = 2863 mm Load width for wind load, bw = 60 mm

Dead Load

Live load

Wind load

Case 1 : 1.4 DL + 1.6 LL

Bending design Mf = 1/8*0.76*(2863/1000)^2= 0.78 kNm 2 2 fb = Mf / Zs = 0.78*10^6/81000= 9.63 N/mm < 11.9 N/mm CHECK OK Shear Design Vf = 1/2*0.26*2863/1000= 0.37 kN f = V / A = 0.37*1000/5400= 0.069 N/mm2 < 0.6*11.9 = 7.14 N/mm2 CHECK OK

Connection design between 60x90mm slat and 80x50x4mm steel plate

Section

(25)

v

w

2

Bolt design

No. of bolt, n = 2

2 2

CHECK OK

80 mm (D) x 50 mm (B) x 4 mm steel plate Moment of inertia, I 1/12*4*80^3= 170667 mm4 Elastic modulus, Z = 170667/(80/2)= 4267 mm3 Shear Area, A = 80*4= 320 mm2

2 2

= 132 N/mm2

CHECK OK

2 2

CHECK OK

Factored Eccentric moment, Me = 0.01 kNm

(26)

Design for 200x100x22.6kg/m GMS RHS supporting slat

Design this RHS

Section Plan

I = 14950000 mm4

Z = 149000 mm3

A = 2870 mm2

Factored Self weight of RHS = 1.2*22.6*9.81/1000= 0.27 kN/m Equivalent Factored UDL on RHS, w = 0.42*2*14/(2131/1000)= 5.52 kN/m 5.79 kN/m Cantilever span, L = 1764 mm Factored moment, Mf = 1/2*5.79*(1764/1000)^2= 9.01 kNm Factored Shear, Vf = 5.79*1764/1000= 10.21 kN Bending design 2 2 fb = Mf / Z = 9.01*10^6/149000= 60.47 N/mm < 220 N/mm CHECK OK Shear design 2 2 fv = Vf / Av = 10.21*1000/2870= 3.56 N/mm < 0.6*220 N/mm = 132 N/mm2 CHECK OK Deflection design UDL on RHS, wu = 5.52/1.2= 4.6 kN/m E = 205000 N/mm2 d = wL^4 / 8EI = 3.87 mm < L / 180 = 11.84 mm

(27)

2

2 2 2

Design of Bolt joint at 200x100x22.6kg/m vertical RHS post supporting RHS cantilever beam

Loaded Unloaded

Section Section

Bolt design

For the bolt group,

Ixx = 10000 mm

Iyy = 10000 mm

Distance of bolt group centroid to one bolt(=502+502)1/2 = 71 mm Factored shear from bending, Vfb = 9.01*10^6*71/20000/1000= 31.99 kN

2 2

(28)

Design of 200x100x22.6kg/m RHS Vertical post

I = 14950000 mm4

Z = 149000 mm3

A = 2870 mm2

r = 72 mm

No of post provided, n =

Case 1 : 1.4DL+1.6LL

Load widith per RHS post bay, b =

2

2.772 m Load length per RHS post bay, L =

Load area per RHS post, A = 2.772*2.131= No. of slat at roof deck, n =

Height of RHS post, H =

2.131 m 5.91 m2

14 2.75 m

DL eccentric moment, Mde= (1.323/3*3.69*1.323/2-0.441/3*3.69*0.441/2)= 0.96 kNm

LL eccentric moment, Mle= (1.323/3*4.43*1.323/2-0.441/3*4.43*0.441/2)= 1.15 kNm

(29)

2 Axial deisgn Pfd = 12.254 kN fa = Pfd / A /n= 12.254*1000/2870/2= 2.13 N/mm slendereness ratio, = L/r 2750/72= 38.19 <180 2 2

CHECK OK Bending design Mf = 9.01 kNm 2 2 fb = Mf / Z/ n = 9.01*10^6/149000/2= 30.23 N/mm < 220 N/mm CHECK OK

(30)

Case 3 : 1.2DL + 1.2LL + 1.2WL (lateral)

2.131 m 5.91 m2

14 2.75 m

Area III 2750

Lateral wind load

Section

(Lateral wind load)

I- Roof Deck

II- 200x100x22.3kg/m RHS post-2nos. Of 0.7m long III- 200x100x22.3kg/m SHS post 2nos. Of 2.75m long

(1) (2) (3)=(1)*(2)*qw (4) (5)=(3)*(4)

I 0.09 x 2.772 1 1.9 2.75 5.23

II 0.5 x 0.1 2 0.76 3.1 2.36

III 0.1 x 2.75 2 4.19 1.375 5.76

6.85 13.35

(31)

w w Axial deisgn Pfd = 9.74 kN 2 fa = Pfd / A /n= 9.74*1000/2870/2= 1.7 N/mm slendereness ratio, = L/r 2750/72= 38.19 <180

CHECK OK Case 4 : 1.4DL+1.4WL(lateral)

Axial deisgn

Pfd = 5.17 kN

2

fa = Pfd / A /n= 5.17*1000/2870/2= 0.9 N/mm

CHECK OK

(32)

w w Vf = 9.59 kN 2 2 fv = Vf / A/n = 9.59*1000/2870/2= 1.67 N/mm < 0.6*220 N/mm = 132 N/mm2 CHECK OK Bending design Mf = 18.69 kNm 2 2 fb = Mf / Z/n = 18.69*10^6/149000/2 = 62.72 N/mm < 220 N/mm CHECK OK Weld Design

CHECK OK Case 5 : 1.4DL+1.4WL(downward)

Load widith per SHS post bay, b = 2.772 m Load length per SHS post bay, L = 2.131 m Load area per SHS post, A = 2.772*2.131= 5.91 m2 No. of slat at roof deck, n =

14 Height of SHS post, H = 2.75 m

Dead load:

3.69 kN

(33)

w w

2

(Section)

(34)

2 2 1/2

Combined weld stress, few = (fbw +faw ) = (923.08^2+24.29^2)^0.5= 923 N/mm

CHECK OK

Case 6 : 1.0DL-1.4WL(downward)

Dead load:

3.69 kN

1.0DL = 1.0*3.69= 3.69 kN

(Section)

1.0DL - 1.4 * WLdownward = 22.9 kN

1.4*Me,downward = 24.024 kNm

(35)

w w 2 Pfd = 22.9 kN fa = Pfd / A /n= 22.906*1000//2= 3.99 N/mm slendereness ratio, = L/r 2750/72= 38.19 <180

2 2 1/2

CHECK OK

Design of anchor bolt

Plan

(36)

Pergola 4 at Area

(37)

8. Pergola 4 at Area H1 : Loading assessment and design

(38)

3 2 3 3

Design for Steel Pergola at Ma Hang Headland Park

Pergola : 4

Area : H1

Dead Load

Wind Load

(H < 5m)

Live Load

Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood

Design This Slat

Plan

4

Isx = 1/12*60*90^3= 3645000 mm

Zsx = Isx / (D/2) = 3645000/(90/2)= 81000 mm

(39)

v f s

Dead Load

Live load

Wind load

Case 1 : 1.4 DL + 1.6 LL

Connection design between 60x90mm slat and 80x50x4mm steel plate

Section

(40)

v

w

2

Bolt design

No. of bolt, n = 2

2 2

CHECK OK

2 2

= 132 N/mm2

CHECK OK

2 2

CHECK OK

(41)

Design for 160x80x17.5kg/m GMS RHS supporting slat

Design this RHS

Section Plan

I = 6120000 mm4

Z = 76500 mm3

A = 1840 mm2

(42)

2

2 2 2

Design of Bolt joint at 160x80x17.5kg/m vertical RHS post supporting RHS cantilever beam

Loaded Unloaded

Section Section

Bolt design

For the bolt group,

Ixx = 10000 mm

Iyy = 10000 mm

Distance of bolt group centroid to one bol (502+502)1/2 = 71 mm Factored shear from bending, Vfb = 6.23*10^6*71/20000/1000= 22.12 kN

2 2

(43)

I = 6120000 mm4

Z = 76500 mm3

A = 1840 mm2

r = 58 mm

No of post provided, n = 2

Case 1 : 1.4DL+1.6LL

Load widith per RHS post bay, b = 2.1 m

4.21 m2 13 2.75 m

Design of 160x80x17.5kg/m RHS Vertical post

Load length per RHS post bay, L = 2.005 m

(44)

(45)

Case 3 : 1.2DL + 1.2LL + 1.2WL (lateral)

2.005 m 4.21 m2

13 2.75 m

Area III 2750

Lateral wind load

Section

(Lateral wind load)

I- Roof Deck

II- 160x80x14.4kg/m RHS post-2nos. Of 0.7m long III- 160x80x14.4kg/m SHS post -2.75m long

(1) (2) (3)=(1)*(2)*qw (4) (5)=(3)*(4)

I 0.09 x 2.1 1 1.44 2.75 3.96

II 0.5 x 0.1 2 0.76 3.1 2.36

III 0.08 x 2.75 2 3.35 1.375 4.61

5.55 10.93

(46)

w w 2 2 Axial deisgn Pfd = 7.32 kN fa = Pfd / A /n= 7.32*1000/1840/2= 1.99 N/mm slendereness ratio, = L/r 2750/58= 47.41 <180

CHECK OK Case 4 : 1.4DL+1.4WL(lateral)

Axial deisgn

Pfd = 4.12 kN

fa = Pfd / A /n= 4.12*1000/1840/2= 1.12 N/mm

(47)

w w Shear design Vf = 7.77 kN 2 2 fv = Vf / A/n = 7.77*1000/1840/2= 2.11 N/mm < 0.6*220 N/mm = 132 N/mm2 CHECK OK Bending design Mf = 15.3 kNm 2 2 fb = Mf / Z/n = 15.3*10^6/76500/2 = 100 N/mm < 220 N/mm CHECK OK Weld Design

CHECK OK Case 5 : 1.4DL+1.4WL(downward)

Dead load:

2.94 kN

(48)

w w

2

(Section)

(49)

CHECK OK

Case 6 : 1.0DL-1.4WL(downward)

Dead load:

2.94 kN

1.0DL = 1.0*2.94= 2.94 kN

(Section)

1.0DL - 1.4 * WLdownward = 16.6 kN

(50)

w w 2 Axial deisgn Pfd = 16.6 kN fa = Pfd / A /n= 16.596*1000//2= 4.51 N/mm slendereness ratio, = L/r 2750/58= 47.41 <180

2 2 1/2

CHECK OK

Design of anchor bolt

Plan

(51)

Pergola 4 at Area

(52)

9. Pergola 5 at Area H2 : Loading assessment and design

(53)

3 2 3 3

Design for Steel Pergola at Ma Hang Headland Park

Pergola : 4

Area : H2

Dead Load

Wind Load

(H < 5m)

Live Load

Design for 60 (B) mm x 90 mm (D) Slat, Recycled Plastic Wood

Design This Slat

Plan

4

Isx = 1/12*60*90^3= 3645000 mm

Zsx = Isx / (D/2) = 3645000/(90/2)= 81000 mm

(54)

v f s

Dead Load

Live load

Wind load

Case 1 : 1.4 DL + 1.6 LL

Connection design between 60x90mm slat and 80x50x4mm steel plate

Section

(55)

v

w

2

Bolt design

No. of bolt, n = 2

2 2

CHECK OK

2 2

= 132 N/mm2

CHECK OK

2 2

CHECK OK

(56)

Design for 160x80x17.5kg/m GMS RHS supporting slat

Design this RHS

Section Plan

I = 6120000 mm4

Z = 76500 mm3

A = 1840 mm2

(57)

2

2 2 2

Design of Bolt joint at 160x80x17.5kg/m vertical RHS post supporting RHS cantilever beam

Loaded Unloaded

Section Section

Bolt design

For the bolt group,

Ixx = 10000 mm

Iyy = 10000 mm

Distance of bolt group centroid to one bol (502+502)1/2 = 71 mm Factored shear from bending, Vfb = 9.13*10^6*71/20000/1000= 32.41 kN

2 2

(58)

Design of 160x80x17.5kg/m RHS Vertical post

I = 6120000 mm4

Z = 76500 mm3

A = 1840 mm2

r = 58 mm

No of post provided, n =

Case 1 : 1.4DL+1.6LL

Load widith per RHS post bay, b =

2

1.758 m Load length per RHS post bay, L =

2.1 m 3.69 m2

8 2.75 m

(59)

(60)

Case 3 : 1.2DL + 1.2LL + 1.2WL (lateral)

2.1 m 3.69 m2

14 2.75 m

Area III 2750

Lateral wind load

Section

(Lateral wind load)

I- Roof Deck

II- 160x80x14.4kg/m RHS post-2nos. Of 0.7m long III- 160x80x14.4kg/m SHS post -2.75m long

(1) (2) (3)=(1)*(2)*qw (4) (5)=(3)*(4)

I 0.09 x 1.759 1 1.21 2.75 3.33

II 0.5 x 0.1 2 0.76 3.1 2.36

III 0.08 x 2.75 2 3.35 1.375 4.61

5.32 10.3

(61)

w w 2 2 Axial deisgn Pfd = 6.68 kN fa = Pfd / A /n= 6.68*1000/1840/2= 1.82 N/mm slendereness ratio, = L/r 2750/58= 47.41 <180

CHECK OK Case 4 : 1.4DL+1.4WL(lateral)

Axial deisgn

Pfd = 3.92 kN

fa = Pfd / A /n= 3.92*1000/1840/2= 1.07 N/mm

(62)

w w Shear design Vf = 7.45 kN 2 2 fv = Vf / A/n = 7.45*1000/1840/2= 2.02 N/mm < 0.6*220 N/mm = 132 N/mm2 CHECK OK Bending design Mf = 14.42 kNm 2 2 fb = Mf / Z/n = 14.42*10^6/76500/2 = 94.25 N/mm < 220 N/mm CHECK OK Weld Design

CHECK OK Case 5 : 1.4DL+1.4WL(downward)

Dead load:

2.8 kN

(63)

w w

2

(Section)

Weld Moment of inertia, I = 2*10*80^2+2*1/12*80^3+4*1/12*120^3+4*80*40^2= 1301333