wind actions to en 1991-1-4(2005)

8/9/2019 Wind Actions to en 1991-1-4(2005)

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Design of wind actions on a portal frame building

according to EN 1991 -1-4(2005)

Basic in format ion

1 Total length 2 bay width 3 spacing 4 height(max)

5 roof slope H. aboveground

b=70 m d=25 m s= 7 m h= 7.5 m slope α=5° h’=7.5 -12.5

tan5°=6.41m

Fig1: one storey building frame

Fig 2 : transversal

6.4m

5°

25 m

7.5m

70.0 m

25.0 m

7.5 m

6.4 m


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Basic values

Determinat ion of b asic wind ve lo c i ty

Fig 3 : Actions of wind on surfaces

,0b dir season bv c c v

EN 1991-1-4(2005) 4.2

bv is the basic wind velocity

dir c is the directional factor

seasonc is the seasonal factor

,0bv

is the fundamental value of the basic wind velocity

(obtained from meteo center national annex)

take ,0bv =30m /s

terrain category III → z 0 =0.3 m and z min=5 m EN 1991-1-4(2005) 4.3.2 (table 4.1)

z=7.5 m we have z≥ z min

,0 30 /b dir season bv c c v m s

we take dir c = seasonc =1.0 for the unfavorable case because c dir and c season are used generallyas reduction factors

Basic v eloci ty pr essure


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21

2 p air b

q v EN 1991-1-4(2005) 4.5 eq 4.10

Where recommended valueair =1.25kg/m

3 (air density)

2 21 *1.25*30 562.5 /2

pq N m

Peak pressure

21

1 72

p v mq z I z v z EN 1991-1-4(2005) 4.5 eq 4.8

Calculation of mv z

0m r bv z c z c z v

0c z is the orography factor

r c z is the roughness factor

0

logr r

z c z k

z

case where min max z z z → 5 7.5 200m m m

r k Is the terrain factor depending on the roughness length z 0 calculated using

0.07

0

0,

0.19r II

z k

z

Calculation of the turbulence intensity v I z

00

log

I v

k I

z c z

z

for z min ≤ z≤z max EN 1991-1-4(2005) 4.4 eq 4.7

minv v I I z for z≤ z min

where I k is the turbulence factor (recommended value is I k =1.0)


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Fig 4: description of (+) and(-) wind

1/ nigh t si tuat ion → all the building is closed

External pressu re coeff ic ients

Wind 1 θ=0°

The wind pressure acting on the external surface,w e

Should be obtained from the following expression

.e p e pew q z c EN 1991-1-4(2005) 5.2 eq 5.1


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e z is the reference height for the external pressure

pec is the pressure coefficient for the external pressure depending on the size of the loaded

area A

Fig 5: euro curve for c pe

= ,10 pec EN 1991-1-4(2005) 7.2.1 2 21 10if m A m then ,1 ,1 ,10 10log pe pe pe pec c c c A

a)Vert ical walls

For7.5

0.3 0.2525

h

d then a linear interpolation is needed

1st point A(0.25;0.7) and 2 nd point B(1;0.8)

f x mx p we have0.8 0.7 2

1 0.25 15

B A

B A

y ym

x x

2 2

0.25 *0.25 0.715 3

f p p

2 2

15 3 f x x then

2 20.3 0.3 0.71

15 3 f

This value will be neglected to the table value EN 1991-1-4(2005) table 7.4a

D c pe=0.7 and E c pe=-0.3


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fig 6: euro fig top vew + zone actions

b)Duo pitch roofs

α=5.0° ; θ=0°(wind direction) ; e=min(b;2h) =min(75;15) =15m

Fig 7: euro fig transverversal vew

zon e F G H I J

c pe -1.7 -1.2 -0.6 -0.6 -0.6

J: two cases are considered c pe=+ 0.2 /-0.6

but c pe=-0.6 EN 1991-1-4(2005) table 7.4a note1


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Fig 8 : top vew and zone details

Internal pressure coeff ic ients

The wind pressure acting on the internal surfaces of the structure w i is obtained from the

expression EN 1991-1-4(2005) (5.2) eq 5.2

i p i piw q z c

i z is the reference height for thr internal pressure

pic is the pressure coefficient for the internal pressure

The internal pressure coefficient depends on the size and distribution of the opening in the

structure envelope

We calculate it from the EN 1991-1-4(2005) (7.2.9 (6))

h/d=7.5/25=0.3 →assimilation to h/d=0.25 (see section above)

when we haven’t information about opening we take the more unfavorable

of (+0.2) and (-0.3) EN 1991-1-4(2005) (7.2.9 (6)note 2)

In this case 0.2 pic

Wind loads

pe pi pw c c q s S= 7 m (spacing)

7 * 0.668 4.676 pe pi pe piw c c c c applied to a portal frame (KN/m)


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*0.668 pe piw c c applied to surfaces(KN/m2 )

Table 1 θ=0°

zone A B C D E F G H I J

c p e -1.2 -0.8 -0.5 0.7 -0.3 -1.7 -1.2 -0.6 -0.6 -0.6

c p i +0.2 +0.2 +0.2 +0.2 +0.2 +0.2 +0.2 +0.2 +0.2 +0.2

c p e -c p i -1.4 -1.0 -0.7 +0.5 -0.5 -1.9 -1.4 -0.8 -0.8 -0.8

W(KN/m)

Port.frame

-6.55 -4.68 -3.28 +2.34 -2.34 -8.88 -6.55 -3.74 -3.74 -3.74

W(KN/m ) 0.935

0.668

0.468 0.334

0.334

-1.269 -0.935 0.534 0.534 0.534

Surfaces

(m 2 )

75*6.4

=48075*6.4

=480

15152

4 10

=11.25

62.5*1.5

=93.75

70*11=

770

70*11=

770

70*1.5

=105

Value

KN

160.32

160.32

14.28 87.66 411.18 411.18 56.07

The A,B,or C zone is not considered because of the symetric actions

Fig 9: wind distribution actions on duopitch roofs

1.5

w1

-6.55 (G)

-8.88(F)

11111.5

-2.34 (E )

-3.74 (I )

-3.74 (H )

+2.34(D)

-3.74 ( J )


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d=25m

EN 1991(2005)7.2.2 fig 7.4

→+0.7

→wind D b=70m E →-0.3

A B C

A=e/5 B=4e/5 C=d-e

=3m =12m =10m EN 1991-1-4:2005 7.2.2 (2)

Fig 10 wind distributions on vertical walls

Determination of wind act ions forces

. .w s d f p e ref éléments

F c c c q z A EN 1991-1-4(2005) 5.2.2( eq5.3)

1.0 s d

c c EN 1991-1-4(2005) (6.2 note 1.c)

The decomposition is V =zone*cosα=zone*0.996 and H=zone*sinα=zone*0.087

Point appl ication of forces

i i

H

i

xT X

T

160.32* 0 160.32* 25 2*1.25 7.66 *0.75 35.77* 7 35.77*19.5 4.88*13.25315.36

14.33m


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35.0i i

H

i

m yT

Y T

i i

H

i

T z Z

T

2*160.32*3.2 2*1.25 7.66 *6.06 35.77*7.02 35.77* 6.89 4.88*7.44315.36

3.29m

i i

V

i

xT X

T

14.23*0.75* 2 87.31*0.75 409.54*7 409.54*19.5 55.85*13.25

990.7

11.79m

i i

V

i

yT Y

T

35.0m

i i

V

i

T z Z

T

14.23*6.06* 2 87.31*6.06 409.54*7.02 409.54*6.89 55.85* 7.44990.7

6.88m

Fig 11 application forces

x

yz

ED

I

J

H

F2

F1

G

w1


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Table 2 wind 1( θ=0°) horizontal and vertical forces to Aref

Zone Horizontal

H (KN)

vertical

V (KN)

Coordinates (m)

X Y Z

D 160.32 0 0 35 3.20

E 160.32 0 25.0 35 3.20

F 1 14.28sin5 1.25 14.28cos5 14.23 0.75 1.875 6.06

F 2 14.28sin5 1.25 14.28cos5 14.23 0.75 68.125 6.06

G 87.66*0.087 7.66 87.66*0.996 87.31 0.75 35 6.06

H 411.18*0.087 35.77 411.18*0.996 409.54 7.0 35 7.02

I 411.18*0.087 35.77 411.18*0.996 409.54 19.5 35 6.89

J 56.07*0.087 4.88 56.07* 0.996 55.85 13.25 35 7.44

R x 315.36 14.33

H X 35.0

H Y 3.29 H Z

R z

990.7 11.79V X 35.0V Y 6.88V Z

12.5m

W

Fig 12 force positions

fo rces act ion s

14.33 m

6.88 mR x

3.29 m

R z

Z

25.0 m

BA

11.79 m


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Overturn in g mom ent

M ov =R x *3.29+R z *(25-11.79)

=315.36*3.29+990.7*13.21

=14125 KNm

stab i liz ing mom ent

take 0.6 KN/m2 as an approximative value of self-weight then(but not final)

W=0.6*70*25=1050 KN

M w =1050*12.5=13125 KNm

Stabil i ty : 14125-13125=1000 KNm

The structure is not stable then the difference will be taken by anchors

Wind 2 a/ θ=90°

b/ θ=180°

we consider that the two cases are similar

e90 =e180 =min(b;2h) =min(25;15) =15m EN 1991-1-4:2005 (7.2.5 Figure 7.8)

Fig 13 application forces

G

H

y

xz

E

D

II

H

F F

G

w2


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15/19

zone F G H I

c pe -1.6 -1.3 -0.7 -0.6

Internal pressure coeff ic ients

The wind pressure acting on the internal surfaces of the structure w i is obtained from the

expression

i p i piw q z c

i z is the reference height for thr internal pressure

pic is the pressure coefficient for the internal pressure

The internal pressure coefficient depends on the size and distribution of the opening in the

structure envelope

h/d=7.5/70=0.1≤0.25

when we haven’t information about opening we take the more unfavorable

of (+0.2) and (-0.3) EN 1991-1-4(2005) (7.2.9 (6)note 2)

In this case 0.2 pic

Wind loads

* pe pi pw c c q = *0.668 pe pic c EN 1991-1-4(2005) (7.2.9 (6)note 2)

Table 3 details in zone

zon e A B C D E F G H I

c pe -1.2 -0.8 -0.5 +0.7 -0.3 -1.6 -1.3 -0.7 -0.6

c p i +0.2 +0.2 +0.2 +0.2 +0.2 +0.2 +0.2 +0.2 +0.2

Cpe-cpi -1.4 -1.0 -0.7 +0.5 -0.5 -1.8 -1.5 -0.9 -0.8

W(KN/

m 2 )

-0.935 -0.668 -0.468 +0.334 -0.334 -1.202 -1.0 -0.601 -0.534


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Fig 14 distribution actions

Determinat ion of fr ic tion forces EN 1991-1-4(2005) (5.3 note 4)

The effects of wind friction on the surface can be disregarded when the total area of all surfaces parallel

With the wind is equal or less than 4 times the total area of all external surfaces perpendicular to the wind

Considered only wind θ=90°

fr Fr p e ref F c q z A EN 1991-1-4(2005) (5.3 eq 5.7 )

Fr c is the friction coefficient EN 1991-1-4(2005) (7.5 table 7.10)

p eq z see above pq z

ref A

is the area of external surface parallel to the wind EN 1991-1-4(2005) 7.5

C fr =0.04 (ripples,ribs,folds..)

ref A

= width*lenght

Lenght L=min(2b ;4h) =min(2*25,4*7.5) =30m EN 1991-1-4(2005) 7.5(3)

Width

a) vert ical w al ls 6504*2=13 m

b) duop i tch roo fs 2*( 12.5/cos(5°))=25.1 m

take only a lineair distribution forces to all faces(apply only for q p(7.5))

1.0 (G)

0.601 (H)

0.534 (I)

1.202 (F )

1.5

0.935 A

0.668 (B)

0.47 C

1.202 (F )

0.668 (B)

0.47 C

1.0 (G)

0.601 (H)

0.534 (I)

221.5

0.935 (A)

wind


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G 15 1525 26.25

2 10

26.25*1.0 26.25 0

H 15 1525 150

2 10

150* 0.601 90.15 0

I 1525 70 1562.5

2

1562.5*0.534 834.375 0

F fr 10.42 20.12 30.54

R z =964.297 R x =+146.606

Fig16 force point

fo rces act ion s

Overturn in g moment

M ov =R x *3.2+R z *35

=146.606*3.2+964.297*35

=43219.5 KNm

stab i liz ing mom ent

take 0.6 KN/m2 as an approximative value of self-weight then(but not final)

7.5 m R x3.2 m

R zZ

25.0 m

BA

12.5 m

12.5 m


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W=0.6*70*25=1050 KN

M w =1050*35=36750 KNm

Stabil i ty : 43219.5-36750=6469.5 KNm

Olso in this case the structure is not stable

Fig 17 long span

2/ Day situat io n → the building is opened

In this case rhe internal coefficient must be calculated from En 1991-1-4 (2005)7.2.9

Take a 5*4.5 m2 one door in front ( θ =90°)

3*(2*1.5)m2 three doors in long spans and hasard disribution( θ =0°)

Dominant face :22.5m2

Other faces: 3m2 22.5

2.59

then , ,0.75 p i p ec c En 1991 -1-4 (2005)7.2.9( eq7.1 )

So we return to the depart case and recalculate the al l w ind act ions

http://www.arab-eng.org/vb/users/355867.html Ibnmessaoud10

W

Z

X3.2m

35.0m

Rx

Rz

35.0m
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wind actions to en 1991-1-4(2005)

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