roof our prject

7/30/2019 Roof Our Prject

1/33

ROOF DESIGN

1. ROOF LOADING

1.1 LIVE LOAD

ROOF CATEGORY (EBCS-1, 1995 TABLE 2.13)

Roof not accessible except for normal maintenance, repair, painting

&minor repairs are under category H.

Imposed load on roof for slope category H

Roof is qk=0.25 KN/m2

Qk= 1KN

1.2 WIND LOAD

A. DETERMINATION OF EXTERNAL WIND PRESSURE (We)

The wind pressure acting on external surface of a structure.

We, shall be obtained from

( ) peeeref CzCqWe = ---------------------EBCS-1, 1995 Eqn 3.1

Where qref = reference mean wind velocity pressure derived from

reference wind velocity.

Ce = exposure coefficient accounting for the terrain & height above

the ground up to a height z.

(Ze) = reference height for the relevant pressure coefficient.

B. DETERMINATION OF REFERENCE WIND PRESSURE (qref)

refref vq2

2

= EBCS-1, 1995 sec. 3.7.1

Where:

1. r=air density (kg/m3) considering altitude of the place above

mean sea level

Addis Ababa is found above sea level of 2000m

r = 0.94 kg/m3 EBCS-1,1995 table 3.1

2. refv = reference wind velocity

refv = CDIRCTEMCALT refv , 0 ..EBCS-1, 1995 sec. 3.7.2(2)

Mean return period 50 years..EBCS-1,1995 sec. 3.7.2(1)


2/33

Where

CDIR =is the direction factor taken as 1

CTEM = is the temporary (seasonal) factor to be taken as 1

CALT = is the altitude factor to be taken as 1

refv , 0 = is the basic value of reference wind velocity to be

taken as 22m/s.

refv = CDIRCTEMCALT refv ,0 EBCS-1,1995- eqn. 3.7

=1*1*1*22m/se

=22m/se

Reference wind pressure ( refq )

refref vq2

2

=

22*2

94.0=refq 2 =227.48

C. DETERMINATION OF EXPOSSURE COEFFICIENT, Ce (z).

The exposure coefficient taken in to account, (Ce, z). The effect of

Terrain roughness

Topography and

Height above ground on the mean wind speed and turbulence

..EBCS-1, 1995 sec.3.8.5 (1)

For codification purpose it has been assumed that the quasi-static

gust load is determined from. EBCS-1, 1995 sec. 3.8.5(2)

( ) ( ) ( )( ) ( )

+=

zCzC

kzCzCzC

tr

Ttre

71

22

.EBCS-1, 1995 eqn.3.15

Where:

kT = is the terrain factor defined as (for terrain category IV) urban areasin which at least 15% of the surface is covered with building & their

average height exceeds 15m.

kT =0.24 ...EBCS-1, 1995 tab.3.2

Cr (z) = the roughness coefficient account for the variability of mean

wind velocity at the site of the structure due to


3/33

The height above the ground level (z)

The roughness of the terrain depending on the wind direction

...EBCS-1, 1995 sec.3.8.2

Cr (z), at height z is defined by logarithmic profileOne of the two cases must satisfy

Case-1 ( )

=

0

lnz

zKzC Tr forzmin


4/33

D. DETERMINATION OF EXTERNAL PRESSURE COEFFICIENT (Cpe

(z))

External pressure coefficient for hipped roofs.

For wind direction = 0

0

For wind direction =

90

0

o ..

e=b=23.90 or e=2h=2*16.50=33 e=23.90

2.39 7.96

18.

38

5.

52

0.

74

9.

24

9.24

10.35

0

1.50

15

20.70

= 0

0

Wind

= 90

0

H=16.5

0

90

1.50

10.4515.00

23.90

h=160

o= tan-1(1.5*2/20.7)=8.250 90= tan-1(1.5*2/10.45)=8.170

Reference height: ze=h=16.50m Reference height:

ze=h=16.50m

e=b or 2h whichever is smaller

b=cross wind dimension


5/33

FOR WIND DIRECTION =900

Imposed areas

F = 2.07*3.175=6.75 =2*(6.75+2.12)=17.74m2

o.5*2.07*2.05=2.12

G = 2.07*10.25=21.22 m2

H = 0.5*16.60*8.38=69.55 m2

I = 0.5*16.56*8.33=68.97 m2

e=b=20.70 or e=2h=33 e=20.70

5.975=

10.25

5.975=

10.35

2.07= 8.28

23.90

20.70

300

3.10

10.35

13.55

10.45


6/33

J = (0.5*20.70*10.45)-68.97=39.19 m2

L = 2.07*10.35=21.42 m2

M=0.5*8.28*8.28=34.28 m2*2=68.56 m2

N=0.5*(21.83+3.10)*10.35-34.28=94.73 m2*2 =189.466 m2

FOR WIND DIRECTION =00

F=3.562*2.39=8.51

=0.5*2.413*2.39=2.88 =2(8.51+2.88)=22.78 m2

G=11.95*2.39=28.56 m2

H=0.5(18.38+3)*7.96=85.01 m2

I=0.5(0.74+19.12)*7.96=79.04 m2

J=2.39*7.96=19.02*2=38.05 m2

K=0.5(3+5.52)*2.39=10.18 m2

L=0.5(10.45*20.70)-84.49=23.67*2=47.34 m2

M=0.5(9.24*18.31)=84.59*2=168.18 m2

Roof0 = 8.27o

Region F G H I J K M

Cpe,10 5 -1.7 -1.2 -0.6 -0.3 -0.6 0.6 -0.6

Cpe,1 5 -2.5 -2.0 -1.2 -0.3 -0.6 0.6 -1.2

5 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Cpe,10 15 -0.9 -0.8 -0.3 -0.5 -1.0 -1.2 -0.6

Cpe,1 15 -2.0 -1.5 -0.3 -0.5 -1.5 -2.0 1.2

15 0.2 0.2 0.2 0.0 0.0 0.0 0.0

Cpe,10 0 -1. 440 -1.070 -0. 503 -0. 365 -0. 730 0. 015 -0. 600

Cpe,1 0 -2.338 -1.838 -0.908 -0.365 -0.893 -0.245 -0.420

Cpe,10 0 0.065 0.065 0.065 0.000 0.000 0.000 0.000

Cpe,1

0

0.065 0.065 0.065 0.000 0.000 0.000 0.000

Roof0 = 8.17o


7/33

Region F G H I J L N

Cpe,10 5 -1.7 -1.2 -0.6 -0.3 -0.6 -1.2 -0.4

Cpe,1 5 -2.5 -2.0 -1.2 -0.3 -0.6 -2.0 -0.4

5 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Cpe,10 15 -0.9 -0.8 -0.3 -0.5 -1.0 -1.4 -0.3

Cpe,1 15 -2.0 -1.5 -0.3 -0.5 -1.5 -2.0 -0.3

15 0.2 0.2 0.2 0.0 0.0 0.0 0.0

Cpe,10 90 -1.446 -1.073 -0.505 -0.363 -0.727 -1.263 -0.368

Cpe,1 90 -2.342 -1.842 -0.915 -0.363 -0.885 -2.000 -0.368

Cpe,10 90 0.063 0.063 0.063 0.000 0.000 0.000 0.000

Cpe,1 90 0.063 0.063 0.063 0.000 0.000 0.000 0.000

External Wind Pressure calculation at = 0o

Qref Ce(z) Cpe W e(KN/m2)F 227.5 1.584 -1.440 -0.519

227.5 1.584 0.065 0.023

G 227.5 1.584 -1.070 -0.386

227.5 1.584 0.065 0.023

H 227.5 1.584 -0.503 -0.181

227.5 1.584 0.065 0.023

I 227.5 1.584 -0.365 -0.132

J 227.5 1.584 -0.730 -0.263

K 227.5 1.584 0.015 0.005

L 227.5 1.584 -1.265 -0.456

M 227.5 1.584 -0.600 -0.216

External Wind Pressure calculation at = 90o

Qref Ce(z) Cpe We(KN/m2)

F 227.5 1.584 -1.446 -0.521

227.5 1.584 0.063 0.023

G 227.5 1.584 -1.073 -0.387

227.5 1.584 0.063 0.023

H 227.5 1.584 -0.505 -0.182

227.5 1.584 0.063 0.023

I 227.5 1.584 -0.363 -0.131

J 227.5 1.584 -0.727 -0.262

K 227.5 1.584 -1.263 -0.455L 227.5 1.584 -0.600 -0.216

M 227.5 1.584 -0.368 -0.133

1.3 DESIGN OF ROOF COVER (DESIGN OF EGA)

Maximum wind load (critical wind load) is


8/33

WL=-0.521 KN/m2from computation

Live load from ..EBCS-1, 1995

Distributed live load qk=0.25 KN/m2

Concentrated live load Qk=1KN

Purlin spacing=1.5m

Take EGA-300 from KMPF manual

Thickness t=0.5mm, section modulus Sx=1970

Load W=3.92kg/m

Uniform load carrying capacity =1.36KPa=ULC

Load computation for roof cover

EGA width is 0.90m

EGA load in KN/m2

DLEGA=(3.92Kn/m)/(0.90m)

2/044.0

1000

10*

92.0

/92.3mKN

m

mKNDL

EGA==

Case -1

Pd=LLq+DL

=1.6 qk+1.3 Gk

=1.6*0.25+1.3(0.044)

=1.6*0.25*cos(8.25)+1.3(0.044)

=0.453KN/m2


9/33

Moment calculation

Because of in case 3 the value is greater than 1.36KN/m2 we shall compute

the section modulus for case 3

mKNm

WlPL

M /609.08

5.1*0572.0

4

5.1*58.1

84

22

=+=+=

Section modulus, SX

Allowable carrying capacity of roof is 250N/mm2

3

2

6

4.2434/250

/10*609.0mm

mmN

mNmmMS

all

x ===

From table of KMPF manual selec EGA sheet having section of modulus

Sx

>2434

Take section of modulus Sx =2749mm

3

Section property

Thikness t=0.7mm

Weight w=5.49kg\m

Capacity=1.90kpa

Dead Load of EGA= 2/061.00.9*1000

10*5.49mkn=

Perpendicular dead load of EGA Ro0f is

DL EGA =O.O61 cos8.25

=0.0604

Load computation at 0=8.25

Case 1Pd=LLq+DL

=1.6qk+1.3Gk

=1.6*0.25COS8.25+1.3(0.0604)

=0.474KN/m2

Case 2


10/33

Pd=WL+DL

=1.6WL+0.9GK

=1.6*O.521+0.9(0.0604)

=0.834KN/m2

Case 3

Pd=LLQK+DL

=1.6QK+1.3GK

=1.6*1*cos8.25+1.3(0.0604)

=1.583KN+0.0785KN/m2

Moment Computation

Case1

M=Pd L2/8=0.474*1.52/8=0.133KNm/m

Case 2

M=PdL2/8=0.834*1.52/8=0.235kNm/m

Case 3

M=Pd*L/4+PdL2/8

=1.583*1.5/4+0.0785*1.52/8

=0.594+0.0221

=0.616kNm/mSection modulus computation

SX=M/rall=0.616*106Nmm/m/250N/mm2

2464.31mm3


11/33

Thickness t=0.7mm=0.0007m

2;ZIGBA PURLIN

Unit weight =6KN/m3

Allowable stress, ball=6.9Mpa.

C/C purlin spacing=0.9m

Cross sectional area=50x70mm

Truss spacing=1.5m

A/ INTERIOR PURLIN

Dead load computation

DL EGA=0.055KN/m

DL Purlin=0.05*0.07*6=0.021KN/m

Total dead load, DL=0.076KN/m

LOAD COMPUTATION

Note:

1.Wind pressure is acts on the areas of the surface producing force

normal to the surface of the structure (EBCS-1-1995 SEC.3.4.1(1))

2.The characteristics values Qk&qk are related to the projected area of

the roof under consideration(EBCS-1-1995 sec.2.6.3.4.2(1))

WIND LOADSWL+=0.023KN/m2

WL-=0.521KN/m2

X-Components

DLGK=0.076sin8.25=0.0109KN/m

LLqk=0.25*0.9sin8.25=0.0323KN/m

LLQK=1*sin8.25=0.1435KN/m

Y-components

DLGK=0.076cos8.25=0.0752KN/m

LLqk=0.25*0.9cos8.25=0.2227KN/m

LLQK=1*cos8.25=0.9897KN/m

WL=0.023*0.9=0.0207KN/m


12/33

COMBINATION

X-direction

Case1: Pdx=dead load distributed live load

=1.3Gk+1.6qL

=1.3*0.0109+1.6*0.0323

=0.0659KN/m

Case 2:Pdx=Dead load +Concentrated live load

=1.3Gk+1.6qk

=1.3*0.0109 +1.6*0.1435

=0.244KN/m

Y-directionCase1:Pdy=dead load +distributed live load

=1.3Gk+1.6qk

=1.3(0.0752) +1.6(0.2227)

=0454KN/m

Case 2:Pdy=Dead Load +Wind Load

=0.9Gk+1.3WkESCP1.1983 Sec3.3.2.1(4)

=0.9(0.0752) +1.3(0.0207)

=0.0946KN/m

Case 3:Pdy=dead Load +Concentrated live load=1.3Gk+1.6Qk----------ESCP 1.1983Sec.3.3.2.1(1)

=1.3(0.0752)+1.6(0.9897)

=1.679KN/m

Case 4:Pdy=Dead Load +Live Load +Wind Load

=0.8(1.3Gk +1.6qk +1.6 Wk)--------ESCP 1.1983 Sec.3.3.2.1(2)

=0.8(1.3(0.0752)+1.6(0.2227)+1.6(0.0207))

=0.390KN/m

Maximum Loads

X-direction. Pdx=0.0659KN/m

Y-direction. Pdy=0.454KN/m

Mx=WxL2/8=(0.0659*1.52)/8=0.1853KN-m

My=WyL2/8=(0.454*1.52)/8=0.1277KN-m


13/33

Section Modulus

Zy=b2h/6=(0.052*0.07)/6=2.917*10-5

Zx=bh2/6=(0.05*0.072)/6=4.0833*10-5

Check Bending Stress

x=Mx/Zx=0.01853/4.0833*10-5=453.80KN/m2

x=(453.80*103/106)N/mm2

x=0.454N/mm2

x=0.454Mpa

y=My/Zy=0.1277/2.917*10-5=4377.785KN/m2

y=(43775.785*103/106)N/mm2

y=4.378N/mm2

y=4.378Mpa

220 yxtalt +=

22378.4454.0 +=total

!...........96.6401.4 OkMpaMpaallbtotal

==

Deflection Check

Allowable deflection

mmmmL

5.7200

1500

200max ===

EI

WL

384

54

=

Where:

E=12KN/mm2

=12*106/m2

X-direction

Dead Load DLy=0.0752KN/m

Dead LoadLLy=0.2227KN/m

Ix=bd3/12=(0.05*0.073)/12=1.429*10-6

mmmmKN

x 14.100114.010*429.1*10*12*384

5.1*/)2227.00752.0(*566

4

==+

=


14/33

y-direction

Dead Load DLx=0.0109KN/m

Live Load LLx=0.0323KN/m

Iy=b3*d/12=(0.053*0.07)/12=0.729*10 -6

mmmmKN

y 325.0000325.010*729.0*10*12*384

5.1*/)0323.00109.0(*566

4

==+

=

mmyxtotal

85.1325.014.1 2222 =+=+=

1.185mm vdd f where: rsterssdesignshead = e

Vd=the design value for end shear force

A

vdd

2

3=

2

wlvd= ;W=factererd load combination

=1.3(0.076)+1.6(0.25)=0.4988KN/m

A=cross sectional area

=0.05*0.07=0.0035m

2

KNvd 3741.02

5.1*4988.0==

22 /1603.0/33.16007.0*05.0*2

3741.0*3

2

3mmNmKN

KN

A

vdd ====

Design shear strength; fvd

m

fvkkfvd

*mod= ;Where:-kmod=0.8,modification factor for medium

forwoodm3.1

=2

/5.2 mmNrengthticshearstcharactersfvk ==

2/54.1

3.1

5.2*8.0mmNfvd ==

!/54.1/1603.022 OkmmNfvdmmNd =


15/33

Design Bearing stress

dccdc fk 909090 *

where:-

lbb

vdcd

*90 = ;Assume that 125.15.1*75.075.0 === llb

22

90 /00651.0/651.6125.1*05.0

3741.0mmNmKNcd ===

m

kccsysdm

dc

fkkkf

90900

90

***=

Where:-

Ksys=load shearing factor=1

Kc90=bearing factor=1

2

90 /5.2 mmNthticsstrengcharactersf kc ==

==> hingstrengtDesignbearf dc =90

2

90/54.1

3.1

5.2*1*1*8.0mmNf dc ==

==> dccdc ff 909090 *

0.06511*1.54

0.06511.54------------------OK!

Vibration

The fundamental frequency of vibration of rectangular supported on four

edges

( )

m

lEI

lf *

221

=

Where:-

m=mass equal to self-weight and other permanent action per unit

area(KN/m2)

l =span length=1.5m

( EI) l =in l direction

(EI)b=in b direction

632

10*875.4212

07.0*5.1

12

* ===dl

Il

b L

d


16/33

6

3

10*429.112

07.0*05.0 ==bI

( ) mNmKNlEI /514500/5.54110*875.42*10*12 66 ===

( ) mNmKNbEI /17148/148.1710*429.1*10*12 66 ===

Mass;M=factored combined load

M=0.4988KN/m/m

2288.49

10

1000*4988.0

m

kg

m

KgM ==

Htzf 90.7088.49

514500*

5.1*221

==

==>Since fundamental frequency greater than8Htz;

The following condition should be satisfied.

/F1.5mm/KN and100( 1f -1)

Where:-

=damping coefficient=0.01

=maximum vertical deflection caused by concentrated vertical force

F=1KN

mmmEI

pL

x

1.40041.0429.1*12*48

5.1*1

48

33

====

633

10*429.112

07.0*05.0

12

===bd

Ix

610*12=E

ylsevelocitisunitimpe=

( )

200

6.04.0440

++

=mbl

Where:-

b=width(m)

40=number of first-order model with natural frequency below 40Htz

( )

( )

25.042

1

40 140

=

bEI

lEI

l

b

f


17/33

( )( )

25.042

40

17148

514500

5.1

05.01

9.70

40

=

=((-0.682)(0.000001234)(30))

=(-2.525*10

-5

)

1/4

=0.07089

M =04988KN/m

( )00885.0

037441.200

770136.1

2005.1*05.0*4988.0

07089.0*6.04.04==

++

=

( )11100

f

Where:-

( ) 291.0101.0*90.7011 ==f

V0.262OK!

/F1.5mm/KN

4.1mm/1KN=4.1KN>1.5mm/KNNot OK!

CHECK FOR LATERAL BUCKLING

1.5 TRUSS DESIGN

The truss is constructed of eucalyptus since the purilnes are at 0.9m

spaced. The rafter and the horizontal member are assumed to be

continuous throughout the length. The truss is designed for the maximum

reaction force from the purline .

291.0100


18/33

Load from purilne to truss.

( ) mKNW /459.0459.00659.0 22 =+=

Reaction force KNWL

R 344.02

5.1*459.0

2===

Exterior reaction force Re=0.344KN at 0.9m spacing,

Interior reaction force Ri=0.344KN at 0.9m spacing on rafter of the truss.

LOAD FROM TRUSS

Material property:-property of equliptus.

TRUSS TOTAL LENGTH COMPUTITION

Truss 1

Major horizontal =10.45m

>> vertical =1.50m

Unit wt.

(KN/m3)

diamet

er(m)

area(m2) wt.

(KN/m)

remark

10 8.5 0.10 0.0079 0.067 V&D members

12 8.5 0.12 0.0113 0.096 major V,H&rafter

W(KN/m)

R

R

Wx=0.0659 KN/m It includes self

Wy=0.459 KN/m weight of purline.


19/33

>> diagonal (rafter) =10.56m

Total length =22.51m

Vertical & diagonal members

Spacing of vertical i=1.20m

Slope of roof in (%)=14.36%

No of verticals =9

No of diagonals =8

No of joints =10

Total length of vertical and diagonal members =17.35

TOTAL LOAD COMPUTATION

Factor loads: wt(10)=16.6m*0.087 KN/m=1.44 KN

wt(12)=22.62m*0.125 KN/m=2.83 KN

total load of truss =4.27 KN

No of joints =10

Internal joints =8

External joints =2

Loads on truss joints

KNsofvertical

totalloadsernaljo 474.0927.4

#intint ===

KNloadsernaljo

sexternaljo 237.02

474.0

2

intintint ===

DEAD LOAD OF CHIP WOOD CEILING (CHIP BOARD).

Properties of chip board

Unit wt., =8KN/m3

Thickness, t=8mm=0.008m

Truss spacing =1.5m

Length =10.45m

Wt=*t*l*c/c spacing

=8KN/m3*0.008m*10.45m*1.5m

=1.0032KN


20/33

Factored load=1.3*1.0032KN =1.30416 KN

DEAD LOAD OF CEILING BATTENS (30mmx40mm)

Spacing c/c=60mm

In the truss direction # of ceiling battens=10.45/0.6=17.4

Use 18 battens

Other direction # of ceiling battens=1.5/0.6=2.5,use 3 battens

Length of ceiling battens is =18*1.5+3*10.45=58.35m

Unit wt, = 6kN/m3

Wt of battens=6*0.03*0.04*38.35=0.42012KN

Factored battens load =0.546156kN

T0tal load at the bottom of the truss Joints

Load =1.30416+0.546156=1.850kN

# Of Joints=10

Exterior =2

Interior =2

Joint load Int = kN206.09

850.1=

Joint load ext = kN103.02

206.0

=

Total load at the top of the truss joints.

Interior joint load =0.688+0.51=1.188 KN

exterior joint load =0.344+0.26=0.604 KN

REACTION FORCES OF THE TRUSS

4.80

0.6

A B C D E F G H I

I

I

II

I

I

I

J

1.5

0.65

0.20.20.20.1

R3=1.40

0.20.2

0.2 0.2 0.20.2

R1=0.02 R2=1.27

5.00

0.61.2

1.2

1.21.2

1.2

1.2

1.21.2

1

2

34

56

7

8

91.

32

1.

14

0.

96

0.

78

0.

61

0.

44

0.

27

1.82 1.69 1.581.47

1.35 1.28 1.231.20

1.5

0

0.

12


21/33

R1=0.02

R2=11.18+1.40+0.02=12.60

R3=1.40

Joint-J

Fy=0 ==>JI sin8.17-0.6-0.1=0

0.142JI =0.7JI=0.7/ 0.142=4.93 KN..tension

Fx=0 ==>JS-JIcos8.17=0

JS=4.93 cos 8.170=4.88 KN.. compression

Joint-S

=8.170

0.1

JI

JS

0.6

0.14

RS

0.21

IS

SJ


22/33

Fy=0 ==> -IS-0.21+1.4=0

IS=-0.21+1.4=1.19.tension

Fx=0 ==> -RS+SJ=0

RS=SJ = 4.88 KN.compression

Joint-I

Fy=0 ==>HI sin8.170+RI sin4.430+IS-1.2-JI sin8.170=0

0.142HI +0.077RI=-1.19+1.2+4.93*0.142

0.142HI +0.077RI= 0.71 KN.*

Fx=0 ==>-HI cos8.170+RI cos4.430+JI cos8.170=0

-0.99HI +0.997RI=-4.93*0.99

-0.99HI +0.997RI=-4.88 KN.**

Solving for the two equations simultaneously:

HI= 4.975 KNTENSION

RI= 0.0456KN.COMPRESION

Joint-R

Fy=0 ==> RH+RI sin4.43-0.21=0

RH=0.0456*0.077+0.21=0.214 KN.tension

Fx=0 ==>QR-RS+RI cos4.430=0

JI

=tan -1(.093/1.2)= 4.430

IS

HI

RI

1.2

RH

=tan -1(0.093/1.2)=4.430

0.21

RI

QR RS


23/33

QR=4.88-0.0456 *0.997=4.835 KN compression

Joint-H

Fy=0 ==> +HQ sin12.680+HG sin8.170-HI sin8.170-RH -1.2= 0

0.22HQ+HG sin8.170=4.975*0.142+1.2+0.214

0.22HQ +0.142HG= 2.12.*

Fx=0 ==> HQ cos12.680-HG cos8.170+HI cos8.170=0

0.976HQ-0.99HG =-4.975*0.99

0.976HQ -0.99HG= -4.925.**


HQ= 3.927 KNCOMPRESION

HG= 8.846KN.TENSION

Joint-Q

Fy=0 ==> QG-QHsin12.68-0.21=0

QG=3.927*0.22+0.21=1.074 KN.TENSION

Fx=0 ==> QP-QR-QHcos12.680=0

QP= 4.835 +3.927*0.976=8.615KN......COMPRESSION

Joint-G

HI=4.96

=tan -1(0.27/1.2)= 12.680

RH

HG

HQ

1.2

QG

0.21

QP

QH

QR =tan-1(0.27/1.2)= 12.680

GH= 5.87

=tan -1(0.44/1.2)= 20.1360

GQ

GF

GP

1.2


24/33

Fy=0 ==> GP sin20.1360+GF sin8.170-GH sin8.170-GQ-1.2 =0

0.344GP+0.142GF=8.81*0.142+1.07+1.2

0.344GP +0.142GF= 3.52.*

Fx=0 ==> GP cos20.1360-GF cos8.170+HG cos8.170=0

0.94GP-0.99GF =-8.81*0.99

0.94GP -0.99GF= -8.72.**


GP= 4.74 KNCOMPRESION

GF= 13.30 KN.TENSION

Joint-P

Fy=0 ==> PF-PGsin20.136-0.21=0

PF=4.74*0.344+0.21=1.84 KN.TENSION

Fx=0 ==> PO-PQ-PGcos20.1360=0

PO= 8.64 +4.74*0.94=13.10KN......COMPRESSION

Joint-F

PF

0.21

PO

PG

PQ =tan-1(0.44/1.2)= 20.1360

FG= 13.30

=tan -1(0.61/1.2)= 26.950

FP

FE

OF

1.2


25/33

Fy=0 ==> OF sin26.950+FE sin8.170-FG sin8.170-FP-1.2 =0

0.453OF+0.142FE=13.30*0.142+1.84+1.2

0.453OF +0.142FE= 4.93.*

Fx=0 ==> OF cos26.950-FE cos8.170+FG cos8.170=0

0.89OF-0.99FE =-13.30*0.99

0.89OF -0.99FE= -13.167.**


OF= 5.23 KNCOMPRESION

EF= 18.01 KN.TENSION

Joint-O

Fy=0 ==> OE-OF sin26.95-0.21+12.60=0

OE=5.23*0.453+0.21-12.60=-10.02

KN.COMPRESION

Fx=0 ==> NO-OP-OF cos26.950=0

NO= 13.10 +5.23*0.89=17.76

KN......COMPRESSION

Joint-E

OE

0.21NO

OF

OP =tan-1(0.61/1.2)= 26.950

12.60

EF= 18.01

=tan -1(0.78/1.25)= 31.960

EO

ED

EN

1.2


26/33

Fy=0 ==> -EN sin31.960+ED sin8.170-EF sin8.170-EO-1.2 =0

-0.529EN+0.142ED=18.01*0.142-10.02+1.2

-0.592EN +0.142ED= -6.26.*

Fx=0 ==> -EN cos31.960-ED cos8.170+EF cos8.170=0

-0.848EN-0.99ED =18.01*0.99

-0.848EN -0.99ED= 17.83.**


EN= 5.19 KNCOMPRESION

ED= -22.46 KN.TENSION

Joint-N

Fy=0 ==> ND+NE sin31.96-0.21=0

ND=-5.19*0.529+0.21=-2.54 KN.COMPRESION

Fx=0 ==> NM-NO+NE cos31.960=0

NM= 17.76-5.19*0.848=13.38

KN......COMPRESSION

Joint-D

Fy=0 ==> -MD sin37.520+CD sin8.170-ED sin8.170-DN-1.2 =0

-0.609MD+0.142CD=-22.46*0.142+-2.54+1.2

-0.609MD +0.142CD= -4.53.*

Fx=0 ==> -MD cos37.520-CD cos8.170+ED cos8.170=0

-0.793MD-0.99CD =22.46*0.99

ED= -22.46

=tan -1(0.96/1.25)= 37.520

DN

CD

MD

1.2

ND

0.21

NM

NE

NO=tan -1(0.78/1.25)= 31.960


27/33

-0.793MD -0.99CD= 22.24.**


MD= 1.855 KNTENSION

CD= -23.95 KNCOMPRESION

Joint-M

Fy=0 ==> MC+MD sin37.52-0.21=0

MC=-1.855*0.609+0.21=-0.92

KN..COMPRESSION

Fx=0 ==> ML-MN+MD cos26.950=0

ML= 13.38 -1.855*0.793=11.89

KN..COMPRESSION

Joint-C

Fy=0 ==> CL sin42.360+CB sin8.170-CD sin8.170+CM-1.2 =0

0.674CL+0.142CB=-23.95*0.142+0.92+1.2

0.674CL +0.142CB= 1.28.*

Fx= 0 ==> CL cos42.360-CB cos8.170+CD cos8.170=0

0.739CL-0.99CB =23.95*0.99

MC

0.21

ML

MD

MN =tan-1(0.96/1.25)= 37.520

CD= -23.95

=tan -1(1.14/1.25)= 42.360

CM

CB

CL

1.2


28/33

0.739CL -0.99CB= 23.71.**


CL= 3.73 KNCOMPRESION

CB= 21.17 KN.TENSION

Joint-L

Fy=0 ==> BL-LC sin42.36-0.21=0

BL=3.73*0.674+0.21=2.72 KN.TENSION

Fx=0 ==> LK-ML-LC cos42.360=0

LK= 11.89+3.73*0.739=14.65

KN.COMPRESSION

Joint-B

Fy=0 ==> BK sin46.560+BA sin8.170-BC sin8.170-BL-1.2 =0

0.726BK+0.142BA=21.17*0.142+2.72+1.20.726BK +0.142BA= 6.93.*

Fx=0 ==> BK cos46.560-BA cos8.170+BC cos8.170=0

0.688BK-0.99BA =-21.17*0.99

0.688BK -0.99BA= -20.96.**


BL

0.21

LK

LC

LM =tan-1(1.14/1.25)= 42.360

BC= 21.17

=tan -1(1.32/1.25)= 46.560

BL

BA

BK

1.2


29/33

BK= 4.75KNCOMPRESION

BA=24.47KN.TENSION

Joint-K

Fy=0 ==> -AK+KB sin46.56-0. 1+0.02=0

AK=4.75*0.726-0. 1+0.02=3.37.TENSION

Fx=0 ==> -KL+KB cos46. 560+0.53=0

-14.64+4.75 *0.688+0.53=0. OK!

Joint-A

Fy=0 ==> AK-0.6-ABsin8.17=0

3.37+0.6-24.47sin8.17=0. OK!

Wall load

Moment Due To External Wind Pressure, We.

We=qref*Ceze*Cpe

From the previous computition

qref=227.48

Ce=1.5836

External pressure coefficient, (Cpe)

For wall

==

==

mh

mbe

3350.16*22

10.23min

The minimum value is e=b=23.10m

0. 02

AK

0. 1

0.53

KBB

EKL =tan-1

(1.32/1.25)=46.560

AK

0.6

AB


30/33

Since d=19.90


31/33

A We=227.48*1.5836*-1.0=-360.24 N/m2=-

0.36024 KN/m2

B* We=227.48*1.5836*-0.8=-288.19 N/m2=-

0.28819 KN/m2

D We=227.48*1.5836*0.787=283.51N/m2=0.28351 KN/m2

E We=227.48*1.5836*-0.3=-108.07 N/m2=-

0.10807 KN/m2

Internal Wind Pressure

Wi ==qref*ce(zi)*cpi

in our case ce(zi)=ce(ze)=1.5836

Taking the most critical cases ,cpi =+0.8 or -0.5

qref =227.48 N/m2

Wi =227.48*1.5836*0.8=288.19N/m2=288.19KN/m2

=242*1.983*-0.5 =-108.07N/m2=-0.10808 KN/m2

The net wind pressure,

Wnet =We-Wi

The critical wind pressure occurs on zone A of the building.

Wnet ,max =-0.36024-0.10808 = -0.46832 KN/m

2

,suction pressure.

Approximate wind force calculation on the wall at each level

The approximate wind force on the wall at each level is obtained by

multiplying the wind

Pressure by the area of the building contributing force at that level.

Area contributed force

Roof

5th fl

4th fl

3th fl

2th fl

1th fl

Gr fl

23,10m

3m

2m

3m

3m

3m

3m1.5m


32/33

level Height(m) Area(m2) F(KN)Roof 18.5 23.10*1.5=34.6

5

0.46832*34.65=16.2

35th floor 17 23.10*3=69.30 0.46832*69.30=32.4

54th floor 14 23.10*3=69.30 0.46832*69.30=32.4

53th floor 11 23.10*3=69.30 0.46832*69.30=32.4

52th floor 8 23.10*3=69.30 0.46832*69.30=32.4

51th floor 5 23.10*3=69.30 0.46832*69.30=32.4

5

Ground floor 2 - 0

Design Of Rafter

LL=0.5KN/m2*1.20m=0.6 KN/m

ed WDLLLW 35.135.13.1 +=

ed WDLW *35.1*35.16.0*3.11 ++=

mKNWd /71.146832.0*35.1076.0*35.175.0*3.11 =++=

46832.0*35.1*35.16.0*3.12

+= DLWd

mKNWd /45.046832.0*35.1076.0*35.175.0*3.12 =+=


33/33

mKNLWd

M /17.08

9.0*71.1

8

* 22===

Check the stress

MPaI

CMall

9.6*

==

634

10*908.464

1.0*

64

*

===

d

I

!........................9.6559.110*908.4

045.0*17.0

6OKMPaMPa all ===

Check deflection

mmLe

allowable 5.4200

900

200===

!.............5.425.010*908.4*10*12*384

9.0*1710*5

384

569

44

OKmmallmmEI

Wl====

1.71 KN/m

9m

d=100mmd

roof our prject

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