Structural Design Calculation For Pergola -...

Structural Design Calculation

For Pergola

Revision :5

Prepared by :EC

Date : 8/10/2009

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

Appendix C - Recycled Plastic Wood Test Report

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/m3

dead laod –pergola steel structure = 7850 kg/m3

4.2 Design Wind Pressure

Design Wind Pressure (H<5m) , qz = 1.82 kPa

Topography Factor for Area D, H1, H2

Sa = (1 + 1.2 e*s)2

= (1 + 1.2*0.3*1)2

= 1.85

Topography Factor for Area C

Sa = (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 + 1.2WLdn

3) 1.4DL + 1.4WLdn

4) 1.2DL + 1.2LL + 1.2WLlat

5) 1.4DL + 1.4WLlat

6) 1.0DL – 1.4WLdn

Where DL = Dead load, LL = Live load, WLdn = downward wind load,

WLlat = Lateral wind load

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/mm2

to BS EN 10219 Part 1 : 2006

Weld Strength = 220 N/mm2

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/mm2

Bending Strength = 23.7 N/mm2

4

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

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

As = B*D = 60*90= 5400 mm

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

v

w

2

Connection design between 60x90mm slat and 80x50x4mm steel plate

Design this steel plate connection

Section


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


Factored Eccentric moment, Me = 0.01 kNm

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

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

Distance of bolt group centroid to one bol (50

2+50

2)

1/2 = 71 mm

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

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



CHECK OK

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)


1.9 m


Load area per SHS post, A = 1.9*2.5=


Height of SHS post, H =

2.5 m

4.75 m2

14

2.75 m




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


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 Projected Wind shear, S Level 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

3.95 7.39

w

w

2

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


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

fa = Pfd / A /n= 4.21*1000/2870/2= 0.73 N/mm

w

w



> 0.73 N/mm2

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

1.4DL = 1.4*3.01= 4.214 kN

Downward wind load :

Nos. of slat, n = 14

design wind pressure, qw = 4.81 kPa

load width per slat, B = 60 mm

(Section)

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



> 2.37 N/mm2

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)









3.01 kN


1.0DL = 1.0*3.01= 3.01 kN

w

w

2





(Section)


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

1.0DL - 1.4 * WLdownward = 11.9 kN


Axial deisgn

Pfd = 11.9 kN

fa = Pfd / A /n= 11.894*1000//2= 2.07 N/mm



> 2.07 N/mm2

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 = 11.894*1000/660 /2= 9.01 N/mm Bending weld stress, fbw = Mf / Zw /n =


10.402*10^6/13013/2 = 399.68 N/mm




CHECK OK

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.

Provide 8 nos. HIT-RE500/HAS-E M16x125 bolt

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

H1

3.01

3.56

6.57

3.95

7.39

7.68

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

5

3

2

3

3




design.

Pergola : 3

Area : D

Dead Load



Wind Load


(H < 5m)





Live Load



Design

This

Slat

Plan


4

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

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

As = B*D = 60*90= 5400 mm

v f s

Maximum span, L =2963-100 = 2863 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/mm

2 < 0.6*11.9

= 7.14 N/mm2

CHECK OK



Section


Section

v

w

2


Bolt design


No. of bolt, n = 2


2 2


CHECK OK


Moment of inertia, I 1/12*4*80^3= 170667 mm4





2 2


= 132 N/mm2

CHECK OK



2 2


CHECK OK












CHECK OK



Design this RHS

Section Plan



I = 14950000 mm4

Z = 149000 mm3

A = 2870 mm2





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

2

2

2

2




Loaded Unloaded

Section Section


Bolt design



For the bolt group,

Ixx = 10000 mm

Iyy = 10000 mm




Distance of bolt group centroid to one bolt(=50

2+50

2)

1/2 = 71 mm




2 2


CHECK OK




I = 14950000 mm

4

Z = 149000 mm3

A = 2870 mm2

r = 72 mm

Effective Height of RHS post, H = 2750 mm




2

2.772 m





2.131 m

5.91 m2

14

2.75 m




0.063*2.772*14=

22.6*9.81/1000*2.131=

14.4*9.81/1000*2.75*2=

2.44 kN

0.47 kN

0.78 kN

3.69 kN




w = 1.4DL + 1.6 LL = 12.254 kN

2

Axial deisgn

Pfd = 12.254 kN

fa = Pfd / A /n= 12.254*1000/2870/2= 2.13 N/mm



CHECK OK

Bending design


2 2

fb = Mf e/ Z = 1.59*10^6/149000= 10.67 N/mm < 220 N/mm

CHECK OK



Section





Axial deisgn

Pfd = 11.16 kN

fa = Pfd / A/n = 11.16*1000/2870/2= 1.94 N/mm2



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



2.772 m





2.131 m

5.91 m2

14

2.75 m




0.063*2.772*14=

22.6*9.81/1000*2.131=

14.4*9.81/1000*2.75*2=

2.44 kN

0.47 kN

0.78 kN

3.69 kN



Area I 500

Area II 200

Area III 2750


(Lateral wind load)


I- Roof Deck


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



6.85 13.35




w

w

Axial deisgn

Pfd = 9.74 kN

2

fa = Pfd / A /n= 9.74*1000/2870/2= 1.7 N/mm



> 1.7 N/mm2

CHECK OK

Shear design

Vf = 8.22 kN

2 2

fv = Vf / A /n= 8.22*1000/2870/2= 1.43 N/mm > 0.6*220 N/mm

= 132 N/mm2

CHECK OK

Bending design

Mf = 16.02 kNm

2 2

fb = Mf / Z /n= 16.02*10^6/149000/2= 53.76 N/mm < 220 N/mm

CHECK OK

Weld Design

Consider one post














CHECK OK





Axial deisgn

Pfd = 5.17 kN 2

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



> 0.9 N/mm2

CHECK OK

Shear design

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




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




3.69 kN

1.4DL = 1.4*3.69= 5.166 kN

w

w

2





(Section)



1.4DL + 1.4 * WLdownward = 32.1 kN


Axial deisgn

Pfd = 32.1 kN

fa = Pfd / A /n= 32.0684*1000/2870/2= 5.59 N/mm



> 5.59 N/mm2

CHECK OK

Bending design

Mf = 24.024 kNm

2 2

fb = Mf / Z /n= 24.024*10^6/149000/ 2= 80.62 N/mm < 220 N/mm

CHECK OK

Weld Design








2 2 1/2

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



CHECK OK










3.69 kN


1.0DL = 1.0*3.69= 3.69 kN





(Section)





Axial deisgn

w

w

2

Pfd = 22.9 kN

fa = Pfd / A /n= 22.906*1000//2= 3.99 N/mm



> 3.99 N/mm2

CHECK OK

Bending design

Mf = 24.024 kNm

2 2

fb = Mf / Z /n= 24.024*10^6/149000/ 2= 80.62 N/mm < 220 N/mm

CHECK OK

Weld Design








For conservative design, 2 2 1/2




CHECK OK


Plan




(Case 5 control)




Item

DL

LL

DL+LL

Lateral wind

Upward/downward


at Area

H1

3.69

4.43

8.12

6.85

13.35

17.74

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

6

3

2

3

3




design.

Pergola : 4

Area : H1

Dead Load



Wind Load


(H < 5m)





Live Load



Design

This

Slat

Plan


4

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

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

As = B*D = 60*90= 5400 mm

v f s




Dead Load


Live load


Wind load


Case 1 : 1.4 DL + 1.6 LL







Bending design

Mf = 1/8*0.77*(2100/1000)^2= 0.42 kNm

2 2

fb = Mf / Zs = 0.42*10^6/81000= 5.19 N/mm < 11.9 N/mm

CHECK OK

Shear Design

Vf = 1/2*0.28*2100/1000= 0.29 kN

f = V / A = 0.29*1000/5400= 0.054 N/mm

2 < 0.6*11.9

= 7.14 N/mm2

CHECK OK



Section


Section

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












CHECK OK



Design this RHS

Section Plan



I = 6120000 mm4

Z = 76500 mm3

A = 1840 mm2





5.72 kN/m




Bending design 2 2

fb = Mf / Z = 6.23*10^6/76500= 81.44 N/mm < 220 N/mm

CHECK OK

Shear design 2 2

fv = Vf / Av = 8.44*1000/1840= 4.59 N/mm < 0.6*220 N/mm

= 132 N/mm2

CHECK OK

Deflection design

UDL on RHS, wu = 5.45/1.2= 4.54 kN/m

E = 205000 N/mm2

d = wL^4 / 8EI = 7.3 mm < L / 180

= 11.13 mm

2

2

2

2




Loaded Unloaded

Section Section


Bolt design



For the bolt group,

Ixx = 10000 mm

Iyy = 10000 mm





2+50

2)

1/2 = 71 mm




2 2


CHECK OK

I = 6120000 mm4

Z = 76500 mm3

A = 1840 mm2

r = 58 mm

Effective Height of RHS post, H =

2750 mm


2



2.1 m




4.21 m2

13

2.75 m




0.063*2.1*13=

22.6*9.81/1000*2.005=

14.4*9.81/1000*2.75*2=

1.72 kN

0.44 kN

0.78 kN

2.94 kN




Load length per RHS post bay, L = 2.005 m




w = 1.4DL + 1.6 LL = 9.172 kN

2

Axial deisgn

Pfd = 9.172 kN

fa = Pfd / A /n= 9.172*1000/1840/2= 2.49 N/mm



CHECK OK

Bending design


2 2

fb = Mf e/ Z = 1.19*10^6/76500= 15.56 N/mm < 220 N/mm

CHECK OK



Section





Axial deisgn

Pfd = 9.39 kN

fa = Pfd / A/n = 9.39*1000/1840/2= 2.55 N/mm2



CHECK OK

Bending design

Mf = 6.23 kNm 2 2

fb = Mf / Z/ n = 6.23*10^6/76500/2= 40.72 N/mm < 220 N/mm

CHECK OK



2.1 m





2.005 m

4.21 m2

13

2.75 m




0.063*2.1*13=

22.6*9.81/1000*2.005=

14.4*9.81/1000*2.75*2=

1.72 kN

0.44 kN

0.78 kN

2.94 kN



Area I 500

Area II 160

Area III 2750


(Lateral wind load)


I- Roof Deck


III- 160x80x14.4kg/m SHS post -2.75m long



5.55 10.93




w

w

2

2

Axial deisgn

Pfd = 7.32 kN

fa = Pfd / A /n= 7.32*1000/1840/2= 1.99 N/mm



> 1.99 N/mm2

CHECK OK

Shear design

Vf = 6.66 kN

2 2

fv = Vf / A /n= 6.66*1000/1840/2= 1.81 N/mm > 0.6*220 N/mm

= 132 N/mm2

CHECK OK

Bending design

Mf = 13.12 kNm

2 2

fb = Mf / Z /n= 13.12*10^6/76500/2= 85.75 N/mm < 220 N/mm

CHECK OK

Weld Design

Consider one post














CHECK OK





Axial deisgn

Pfd = 4.12 kN

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



> 1.12 N/mm2

CHECK OK

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








2.94 kN

1.4DL = 1.4*2.94= 4.116 kN

w

w

2





(Section)





Axial deisgn

Pfd = 23.2 kN

fa = Pfd / A /n= 23.2344*1000/1840/2= 6.31 N/mm



> 6.31 N/mm2

CHECK OK

Bending design

Mf = 16.898 kNm

2 2

fb = Mf / Z /n= 16.898*10^6/76500/ 2= 110.44 N/mm < 220 N/mm

CHECK OK

Weld Design












CHECK OK










2.94 kN


1.0DL = 1.0*2.94= 2.94 kN





(Section)





w

w

2

Axial deisgn

Pfd = 16.6 kN

fa = Pfd / A /n= 16.596*1000//2= 4.51 N/mm



> 4.51 N/mm2

CHECK OK

Bending design

Mf = 16.898 kNm

2 2

fb = Mf / Z /n= 16.898*10^6/76500/ 2= 110.44 N/mm < 220 N/mm

CHECK OK

Weld Design












CHECK OK


Plan




(Case 5 control)




Item

DL

LL

DL+LL

Lateral wind

Upward/downward


at Area

H1

2.94

3.16

6.1

5.55

10.93

12.48

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

7

3

2

3

3




design.

Pergola : 4

Area : H2

Dead Load



Wind Load


(H < 5m)





Live Load



Design

This

Slat

Plan


4

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

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

As = B*D = 60*90= 5400 mm

v f s




Dead Load


Live load


Wind load


Case 1 : 1.4 DL + 1.6 LL







Bending design

Mf = 1/8*0.76*(1759/1000)^2= 0.29 kNm

2 2

fb = Mf / Zs = 0.29*10^6/81000= 3.58 N/mm < 11.9 N/mm

CHECK OK

Shear Design

Vf = 1/2*0.26*1759/1000= 0.23 kN

f = V / A = 0.23*1000/5400= 0.043 N/mm

2 < 0.6*11.9

= 7.14 N/mm2

CHECK OK



Section


Section

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












CHECK OK



Design this RHS

Section Plan



I = 6120000 mm4

Z = 76500 mm3

A = 1840 mm2





5.87 kN/m




Bending design 2 2

fb = Mf / Z = 9.13*10^6/76500= 119.35 N/mm < 220 N/mm

CHECK OK

Shear design 2 2

fv = Vf / Av = 10.35*1000/1840= 5.63 N/mm < 0.6*220 N/mm

= 132 N/mm2

CHECK OK

Deflection design

UDL on RHS, wu = 5.6/1.2= 4.67 kN/m

E = 205000 N/mm2

d = wL^4 / 8EI = 9.05 mm < L / 180

= 11.67 mm

2

2

2

2




Loaded Unloaded

Section Section


Bolt design



For the bolt group,

Ixx = 10000 mm

Iyy = 10000 mm





2+50

2)

1/2 = 71 mm




2 2


CHECK OK




I = 6120000 mm

4

Z = 76500 mm3

A = 1840 mm2

r = 58 mm

Effective Height of RHS post, H = 2750 mm




2

1.758 m





2.1 m

3.69 m2

8

2.75 m




0.063*1.758*8=

22.6*9.81/1000*2.1=

14.4*9.81/1000*2.75*2=

1.55 kN

0.47 kN

0.78 kN

2.8 kN




w = 1.4DL + 1.6 LL = 8.352 kN

2

Axial deisgn

Pfd = 8.352 kN

fa = Pfd / A /n= 8.352*1000/1840/2= 2.27 N/mm



CHECK OK

Bending design


2 2

fb = Mf e/ Z = 1.08*10^6/76500= 14.12 N/mm < 220 N/mm

CHECK OK



Section





Axial deisgn

Pfd = 11.3 kN

fa = Pfd / A/n = 11.3*1000/1840/2= 3.07 N/mm2



CHECK OK

Bending design

Mf = 9.13 kNm 2 2

fb = Mf / Z/ n = 9.13*10^6/76500/2= 59.67 N/mm < 220 N/mm

CHECK OK



1.759 m





2.1 m

3.69 m2

14

2.75 m




0.063*1.759*14=

22.6*9.81/1000*2.1=

14.4*9.81/1000*2.75*2=

1.55 kN

0.47 kN

0.78 kN

2.8 kN



Area I 500

Area II 160

Area III 2750


(Lateral wind load)


I- Roof Deck


III- 160x80x14.4kg/m SHS post -2.75m long



5.32 10.3




w

w

2

2

Axial deisgn

Pfd = 6.68 kN

fa = Pfd / A /n= 6.68*1000/1840/2= 1.82 N/mm



> 1.82 N/mm2

CHECK OK

Shear design

Vf = 6.38 kN

2 2

fv = Vf / A /n= 6.38*1000/1840/2= 1.73 N/mm > 0.6*220 N/mm

= 132 N/mm2

CHECK OK

Bending design

Mf = 12.36 kNm

2 2

fb = Mf / Z /n= 12.36*10^6/76500/2= 80.78 N/mm < 220 N/mm

CHECK OK

Weld Design

Consider one post














CHECK OK





Axial deisgn

Pfd = 3.92 kN

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



> 1.07 N/mm2

CHECK OK

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








2.8 kN

1.4DL = 1.4*2.8= 3.92 kN

w

w

2





(Section)





Axial deisgn

Pfd = 21.3 kN

fa = Pfd / A /n= 21.252*1000/1840/2= 5.78 N/mm



> 5.78 N/mm2

CHECK OK

Bending design

Mf = 15.246 kNm

2 2

fb = Mf / Z /n= 15.246*10^6/76500/ 2= 99.65 N/mm < 220 N/mm

CHECK OK

Weld Design












CHECK OK










2.8 kN


1.0DL = 1.0*2.8= 2.8 kN





(Section)





w

w

2

Axial deisgn

Pfd = 15.2 kN

fa = Pfd / A /n= 15.18*1000//2= 4.13 N/mm



> 4.13 N/mm2

CHECK OK

Bending design

Mf = 15.246 kNm

2 2

fb = Mf / Z /n= 15.246*10^6/76500/ 2= 99.65 N/mm < 220 N/mm

CHECK OK

Weld Design












CHECK OK


Plan




(Case 5 control)




Item

DL

LL

DL+LL

Lateral wind

Upward/downward


at Area

H2

2.8

2.77

5.57

5.32

10.3

11.26

10. Loading Schedule and Anchor Bolt Design

8


Item

DL

LL

DL+LL

Lateral wind

Upward/downward

wind

Axial (kN) Axial (kN) Axial (kN) Shear (kN) Moment (kNm) Axial (kN)

Pergola 1 at

Area C

3.01

3.56

6.57

3.95

7.39

7.68

Item

DL

LL

DL+LL

Lateral wind

Upward/downward

wind


Pergola 2 at

Area D

3.69

4.43

8.12

6.85

13.35

17.74

Item

DL

LL

DL+LL

Lateral wind

Upward/downward

wind


Pergola 3 at

Area H1

2.94

3.16

6.1

5.55

10.93

12.48

Item

DL

LL

DL+LL

Lateral wind

Upward/downward

wind


Pergola 4 at

Area H2

2.8

2.77

5.57

5.32

10.3

11.26

Pergola Area Axial (kN) Shear (kN) Moment (kNm)

2 C 13.6 5.53 10.402

3 D 32.1 9.59 24.02

4 H1 23.2 7.77 16.90

5 H2 21.3 7.45 15.25

Factored Anchor bolt design load

Control case

User application

PROFIS Anchor 1.8.0

http://www.hilti.com/

Specifier's comments:

Company:

Specifier:

Address:

Phone/Fax: - / -

E-Mail:

Page 1 of 5

Project:

Contract No.:

Responsible:

Location/Date: - / 23/9/2009

Anchor type and size: HIT-RE 500 + HAS-E (5.8)-M16

Effective embedment depth: hef

= 125 mm

Material: 5.8

Approval No.:

Issued/Valid: - / -

Proof: Engineering judgement SOFA - after ETAG testing

Stand-off installation: eb

= 0 mm (no stand-off) ; t = 12 mm

Anchor plate: S235 (ST37) ; ; lx x ly x t = 400 x 400 x 12 mm

Base material: uncracked concrete C25/30, fcc = 30.00 N/mm ; h = 350 mm

Reinforcement: reinforcement spacing >= 150 mm

no longitudinal edge reinforcement

Anchor

Geometry [mm]

plan view y

section A z

x

t=12

hef

=125

lx

= 400 x

section B z

y

h = 350

>10h

ef 300

section A

>10h ef

ly

= 400

Loading

Resulting loads [kN, kNm] Design loads [kN, kNm]

N 32.10

Vx 0.00

Vy 9.59

Mx -24.02

My 0.00

Mz 0.00

Eccentricity (structural section) [mm]

ex = 0 ; ey = 0

Input data and results must be checked for agreement with the existing conditions and for plausibility!

PROFIS Anchor ( c ) 2003 Hilti AG, FL-9494 Schaan Hilti is a registered Trademark of Hilti AG, Schaan


NRk,s

[kN ] M,s

h [kN ] N

h [kN ]

72.15 1.500 48.10 26.00

Rd,p Sd

Rk,c

User application

PROFIS Anchor 1.8.0


Company: Page 2 of 5 Specifier: Project: Address:

Phone/Fax: - / -

E-Mail:

Contract No.:

Responsible:


Load case (Design loads):

Anchor reactions [kN]

Tension force: (+Tension -Pressure)

Anchor

1 Tension force

26.00 Shear force

1.20 2 26.00 1.20 3 26.00 1.20

4 11.98 1.20 5 11.98 1.20

6 0.00 1.20 7 0.00 1.20

8 0.00 1.20

max. concrete compressive strain [ : 0.18

max. concrete compressive stress [N/mm : 4.86

resulting tension force [kN]: 102.00

resulting compression force [kN]: 69.87

Tension load

Design values [kN] Proof Load Capacity Utilisation

N [%] Status

Steel failure 26.00 48.10 54 OK Pull-out failure 26.00 37.99 68 OK

Concrete cone failure 101.97 121.65 84 OK

Steel failure N

Rd,s Sd

Pull-out failure

NRk,p

[kN ]

62.42

c

1.095

M,p

1.800

N

h [kN ]

37.99

N

h [kN ]

26.00

Concrete cone failure

2

Ac,N [mm ] 0 2

Ac,N [mm ] ccr,N [mm ] scr,N [mm ]

212500.0 62500.0 125 250

ec1,N

ec2,N

re,N

s,N

ucr,N 1.000 0.835 1.000 1.000 1.400

N0

[kN] M,c

NRd,c

[kN ]

NSd

[kN ]

55.11 1.800 121.65 101.97






Rk,c V [kN ]

Sd

Rk,c

User application

PROFIS Anchor 1.8.0



Phone/Fax: - / -

E-Mail:

Contract No.:

Responsible:


Shear load

Design values [kN] Proof Load Capacity Utilisation

V [%] Status

Steel failure (without lever

arm)

Pryout failure

1.20

1.20

34.60

61.73

3

2

OK

OK Concrete edge failure in

direction y+

9.59 134.07 7 OK

Steel failure (without lever arm) h

[kN ]

V

h [kN ]

VRk,s [kN ]

43.25

M,s

1.250

VRd,s

34.60

Sd

1.20

Pryout failure

2

Ac,N

[mm ]

300000.0

0 2

Ac,N

[mm ]

62500.0 c

cr,N [mm ]

125 s

cr,N [mm ] k-factor

250 2.000

s,N

ec1,N ec2,N

re,N ucr,N

1.000 1.000 1.000 1.000 1.400

N0

[kN ]

55.11

M,c,p

1.500

h

Rd,c1

61.73

Vh

[kN ]

1.20

Concrete edge failure in direction y+

lf [mm ] d

nom [mm ] c

1 [mm ] A [mm

2] A

0 [mm

2] c,V c,V

125 16 650 787500.0 1901250.0

s,V

h,V ,V

ec,V ucr,V

1.000 1.407 1.000 1.000 1.400

V0

[kN ] M,c

V

Rd,c

[kN ] V

Sd

[kN ]

246.47 1.500 134.07 9.59

Combined tension and shear loads

N V Utilisation

N,V [%] Status

0.838 0.072 - 76 OK

N + V <= 1

( N + V) / 1.2 <= 1

Edge reinforcement

Edge reinforcement is not required to avoid splitting failure

No edge reinforcement is required to assure characteristic shear resistance against concrete edge failure




Sk

Sk

User application

PROFIS Anchor 1.8.0



Phone/Fax: - / -

E-Mail:

Contract No.:

Responsible:


Displacements

The displacement of the highest loaded anchor should be calculated according to the relevant approval. The displacement due to

hole tolerances can be neglected, because this method assumes filled holes (Hilti Dynamic Set). The characteristic loads of the

highest loaded anchor are

Nh

= 20.19 [kN]

Vh

= 2.37 [kN]

The acceptable anchor displacements depend on the fastened construction and must be defined by the designer!

Proof of the transmission of the anchor loads to the supports

Transmission of the anchor loads into the concrete

Checking the transfer of loads into the base is required in accordance with ETAG Section 7.1!

Shear resistance of base material

Shear resistance of the base material must be checked according to relevant approval or Eurocode 2/ BS8110 etc.

Warnings

An even load distribution of the shear load is assumed, e.g. by using the Hilti Dynamic Set.

The compliance with current standards (e.g. EC3) is the responsibility of the user

Dry hole and standard cleaning are assumed! Temperature influence is neglected!

Fastening meets the design criteria!




-200 200

200

200 200

-200

-200 -200

1

2 -150 -150 4 -150 0 7 0

0 -150 5 150 0 8 150 150

150

3 150 -150 6 -150 150

User application

PROFIS Anchor 1.8.0



Phone/Fax: - / -

E-Mail:

Contract No.:

Responsible:


Anchorplate, steel: S235 (ST37)

Section type: Square hollow section - 150 x 150 x 10,0 (150 x 150 x 10)

Hole diameter d f = 18 mm

Recommended plate thickness: not calculated

y

6 7 8

x

4 5

1 2 3

50.0 50.0

200.0 200.0

Coordinates Anchor [mm]

Anchor x y

Anchor x y

Anchor x y

Anchorplate [mm]

x y


Appendix A - Wind Topography Analysis

9

Appendix B - Reference Design Intent Drawing

10

Appendix C - Recycled Plastic Wood Test Report

1

Structural Design Calculation For Pergola -...

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