Wind Actions to en 1991-1-4(2005)

Design of wind actions on a portal frame building according to EN 1991 -1-4(2005) B a s i c i n fo fo r m a t i o n

1 Total length

b=70 m

2 bay width

3 spacing

4 height (max)

5 roof slope

H. above ground

d=25 m

s= 7 m

h= 7.5 m

slope α=5°

h’=7.5 -12.5 -12.5 tan5°=6.41m

6.4 m

7.5 m

70.0 70.0 m       

25.0 25.0 m

Fig1: one storey building frame

5°

6.4m

7.5m

25 m

Fig 2 : transversal transversal

Basic values D e te r m in a t io n o f b a s i c w i n d v e l o c i ty

Fig 3 : Actions of wind o n surfaces

vb  cdir cseasonvb,0 vb

EN 1991-1-4(2005) 4.2

is the basic wind velocity

cdir  is the directional factor c season  is the seasonal factor

vb ,0 is the fundamental value of the basic wind velocity (obtained from meteo center national annex) take

vb ,0

=30m /s 

terrain category III → z 0 =0.3 m and

z=7.5 m

we have

z min=5 m

EN 1991-1-4(2005) 4.3.2 (table 4.1)

z≥ z min

vb  cdir cseasonvb,0  30m / s we take

cdir  = c  season =1.0 for the unfavorable case because

as reduction factors

B a s i c v el o c i t y p r es s u r e

c dir  and c season are used generally

q p

1 

2

2

  air vb

EN 1991-1-4(2005) 4.5 eq 4.10 3

Where recommended value   air  =1.25kg/m (air density)

q p 

1 2

*1.25*30 2  562.5 N / m2

Peak pressure

q p  z   1  7 I v  z  

1 2

  vm

z

2

 

EN 1991-1-4(2005) 4.5 eq 4.8

Calculation of vm  z 

vm  z   cr  z  c0  z  vb c0  z  is the orography factor cr   z   is the roughness factor

  z      case  z   0

cr  z   k r  log 

where  zmin

 z  z max → 5m  7.5m  200m

k r  Is the terrain factor depending on the roughness length z 0 calculated using   z 0  k r   0.19    z    0, II  

0.07

Calculation of the turbulence intensity  I v  z   I v 

k  I 

  z   c0  z  log     z 0 

 I v  I v  z min 

for z min ≤ z≤z max

EN 1991-1-4(2005) 4.4 eq 4.7 

for z≤ z min

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

Z=7.5 m then

  2       7 k  1 z  2 r  *   vb q p  z   1  *  k r  log         2  z 0     z     c0  z  log      basic  pressure   wind profile  z   0    

   squared  gust  factor 

  2   7 *1 1 7.5     * *1.25*302 *  0.19 log  q p  7.5   1   2  0.3    1*log  7.5             basic  pressure  wind  profile 0.3        squared  gust  factor 

=667.94 N/m 2 2

=0.668KN/m  Wind pressure on su rfaces

EN 1991-1-4(2005) 7.2

 A positive wind loads stands for pressure whereas a negative wind load indicates suction on the surface.this definition applies for the external wind action as well as for the internal wind action.

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

1 / n i g h t s i t u a t i o n → all the building is closed  E x t e r n a l p r e s s u r e c o e ff i c i e n t s

Wind 1 θ=0°  The wind pressure acting on the external surface,w e Should be obtained from the following expression

we  q p  ze  .c pe

EN 1991-1-4(2005) 5.2 eq 5.1

 z e  is the reference height for the external pressure c pe is the pressure coefficient for the external pressure depending on the si ze of the loaded

area A

Fig 5: euro curve for c  pe

c pe,10

EN 1991-1-4(2005) 7.2.1

= 

if 1m2  A  10m2  then c pe  c pe,1   c pe,1  c pe,10  log10 A a)Vertical walls

For

h d 



7.5 25

 0.3  0.25  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 have m 

  f  0.25  

  f  x  

2 15

2 15

 y B  yA  x B  xA

*0.25  p  0.7  p 

x

2 3

 then   f   0.3 

2 15



0.8  0.7 1  0.25



2 15

2 3

0.3 

2 3

 0.71

This value will be neglected to the table value D

c  pe=0.7

and

E

EN 1991-1-4(2005) table 7.4a

c   pe=-0.3

fig 6: euro fig top ve w + zone actions b ) D u o p it c h r o o f s

α=5.0°

;

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

Fig 7: euro fig transverversal ve w zon e c  p e 

J:

F

G

H

I

J

-1.7

-1.2

-0.6

-0.6

-0.6

t wo cases are considered c   pe =+ 0.2 /-0.6 but

c   pe=-0.6

EN 1991-1-4(2005) table 7.4a note1

Fig 8 : top vew and zone details I n t e r n a l pr e s s u r e c o e f f i c i e n t s

The wind pressure acting on the internal surfaces of the structure w  i  is obtained from the EN 1991-1-4(2005) (5.2) eq 5.2 expression

wi  q p  zi  c pi  z i is the reference height for thr internal pressure

c pi 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 EN 1991-1-4(2005) (7.2.9 (6))

We calculate it from the

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)

c pi  0.2

In this case W i n d l o a ds

w   c pe  c pi  q p s





S= 7 m (spacing)





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

w



c

 pe





c pi *0.668 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)

-6.55

-4.68

-3.28

+2.34

-2.34

-8.88

-6.55

-3.74

-3.74

-3.74

-0.935

0.534

0.534

0.534

70*11 =

70*1.5

Port.frame 

W (K N/m )

0.935 0.668 0.468

Surfaces

0.334 0.334 -1.269

75*6.4

75*6.4

=480

2 

(m   )

=480

Value

160.32

2

1515 4 10

62.5*1.5 70*11 = =93.75 770

770

87.66

411.18

=11.25

160.32 14.28

411.18

KN

The A,B,or C zone is not considered because of the symetric actions -3.74 ( J ) -6.55 (G)

-3.74 (H ) -3.74 (I )

-8.88(F)

w1

-2.34 (E )

+2.34(D)

1.5

11

1.5

11

Fig 9: wind distribution actions on duopitch roofs

=105 56.07

d=25m

EN 1991(2005)7.2.2 fig 7.4

→+0.7 →wind

b=70m E →-0.3

D

 A

B

C

 A=e/5 B=4e/5 =3m

=12m

C=d-e

EN 1991-1-4:2005 7.2.2 (2)

=10m

Fig 10 wind distributions on vertical walls

D e te r m i n a ti o n o f w i n d ac t i o n s f o rc e s



 Fw  cs cd .

c f q p  ze  . Aref

 

EN 1991-1-4(2005) 5.2.2( eq5.3)

 

éléments

c s cd 



1.0

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

The decomposition is V =zone*cos α=zone*0.996

and

H=zone*sinα=zone*0.087 

Point application of forces

 T  x T 

 X  H  

i

i

i



160.32* 0 160.32* 25  2*1.25  7.66 *0.75 35.77* 7 35.77*19.5  4.88*13.25

 14.33m

315.36

Y  H  

T  y T  i

i

 35.0m

i

 T z  T 

 Z  H  

i

i



2*160.32*3.2   2*1.25  7.66  *6.06  35.77*7.02  35.77* 6.89  4.88*7.44 315.36

i

 3.29m

 T  x T 

 X V  

i

i

i



14.23*0.75* 2  87.31*0.75  409.54*7  409.54*19.5  55.85*13.25 990.7

 11.79m

Y V  

  T  y  T  i

i

i

 35.0m

 Z 

V 



 T z  T  i

i

i



14.23*6.06* 2  87.31*6.06  409.54*7.02  409.54*6.89  55.85* 7.44 990.7

 6.88m y z

F2

w1

J G

H

I E

D F1

x

Fig 11 application forces

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

Horizontal

vertical

H (KN)

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

 X  H   14.33

Y  H 

 35.0  Z  H   3.29









R z

990.7

 X 

V 

 11.79 Y V   35.0

Z R z

11.79 m

12.5m

W

6.88 m

R x B

A 25.0 m 14.33 m

Fig 12 force positions

f o r ce s a c t io n s

3.29 m

 Z V   6.88

O v er t u r n in g m o m e n t

M ov =R   x *3.29+R z *(25-11.79) =315.36*3.29+990.7*13.21 =14125 KNm s t ab i li z in g m o m e n t

take 0.6 KN/m 2  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 Stability

:

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 t wo cases are similar e90 =e180 =min(b;2h) =min(25;15) =15m

EN 1991-1-4:2005 (7.2.5 Figure 7.8) x

z E

I

I

H

H G

G F

F

D

y w2

Fig 13 application forces

F

e/4

H

I

G faite ou noue

G

H

b=25m

I

F

e/4

e/10

e/2

Fig 12 euro zone decompositions for duopitch roofs( θ =90°) E x t e r n a l p r e s s u r e c o e f fi c i e n t s  

EN 1991-1-4(2005) table 7.1

a)Vertical w alls  zo n e

A

B

C

D

E

C p e

-1.2

-0.8

-0.5

+0.7

-0.3

 A is limited to e/5=15*0.2=3m B is limited to 4e/5

=12m

C is limited to d-e=70-15 =55 m

b=25 m

b=25 m and d=70 m(in accordance to θ=90°)

e/5(A)

e4/5(B)

d-e (C)

Fig 13 zone distributions b ) D u o p it c h r o o f s

α=5.0°

;

See fig above

θ=90°=180°(wind direction) EN 1991-1-4(2005) table 7.4b

zone

F

G

H

I

c   pe

-1.6

-1.3

-0.7

-0.6

Internal pressure coefficients

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

wi  q p  zi  c pi

 z i

is the reference height for thr internal pressure

c pi  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) In this case

EN 1991-1-4(2005) (7.2.9 (6)note 2)

c pi  0.2

Wind loads

w   c pe  c pi  * q p =  c pe  c pi  *0.668

EN 1991-1-4(2005) (7.2.9 (6)note 2)

Table 3 details in zone zo n e

A

B

C

D

E

F

G

H

I

c  p e 

-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/ 

-0.935

-0.668

+0.334

-0.334

-1.202

-1.0

-0.601

-0.534

2 

m   )

-0.468

1.202 (F )

0.534 (I)

0.534 (I)

0.601 (H)

0.601 (H)

1.0 (G)

C  0.668 (B) 0.47

0.935

1.0 (G)

1.202 (F

)

C  0.668 (B) 0.47

wind

A

0.935 (A) 1.5

22

Fig 14

1.5

distribution actions

Determination of fric 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° 

 F  fr  cFr q p  ze  Aref   c Fr  is the friction coefficient

q p  z e 

 Aref  

see above

 Aref     =

EN 1991-1-4(2005) (7.5 table 7.10)

q p  z 

is the area of external surface parallel to the wind

C fr =0.04

EN 1991-1-4(2005) (5.3 eq 5.7   )

EN 1991-1-4(2005) 7.5

(ripples,ribs,folds..)

width*lenght

Lenght L=min(2b ;4h) =min(2*25,4*7.5) =30m 

EN 1991-1-4(2005) 7.5(3)

Width a) v e r t i c al w a l ls     6504*2=13 m  b ) d u o p i t ch r o o f s  2*( 12.5/cos(5°))=25.1 m 

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

 F  fr   0.04* 0.668* 30*13  10.42KN 

Vertical w alls 

D u o p i t c h r o o f s    F fr 

KN   0.04*0.668*30* 25.1 20.12

F Fr   roofs F Fr  walls//wind

d=70m

h=7.5m 6.4m

b=25m wind

Fig 15 friction forces

Determination o f

forc es

See procedure for θ=0°

wind 2

(θ=90° or θ=180° )

table 4: global forces by zone Zone

Surface

Vertical

2 

(m   )

R Z

R x   ( K N )

1.1 

  173.75 2 

0

0.334*173.75  58.033

 

1.1 

0

0.334*173.75  58.033

1.202*11.25  13.522

0

25*  6.4 

E

25*  6.4 

2*

(KN)

 

D

F

Horizontal

  173.75 2 

15 15 *  11.25 10 4

G

H

15  15   25    26.25 2  10 

26.25*1.0  26.25

0

 15 15     150  2 10 

150* 0.601  90.15

0

 

1562.5*0.534  834.375

0

25 

I

25  70 

15 

  1562.5 2

10.42  20.12  30.54

F  fr R z =964.297

Z

R  x=+146.606  

R z

12.5 m

12.5 m

7.5 m

R x B

A

3.2 m

25.0 m

Fig16 force point f o r ce s a c t io n s O v er t u r n in g m o m e n t

M ov =R   x *3.2+R z *35 =146.606*3.2+964.297*35 =43219.5 KNm s t ab i li z in g m o m e n t

take 0.6 KN/m 2  as an approximative value of self-weight then(but not final)

  W=0.6*70*25=1050 KN M w=   1050*35=36750 KNm Stability

:

43219.5-36750=6469.5 KNm

Olso in this case the structure is not stable

Z

Rz 35.0m

35.0m

Rx 3.2m X

W

Fig 17 long span

2/ Day situatio n → the building is o p e n e d In this case rhe internal coeffi cient must be calculated from En 19 91-1-4 (2005)7.2.9 Take a 5*4.5 m 2  3*(2*1.5)m2 

one door in front ( θ =90°) three doors in long spans and hasard disribution( θ =0°)

Dominant face :22.5m2 Other faces: 3m2 

22.5 9

 2.5 then

c p ,i  0.75c p, e  En

1991 -1-4 (2005)7.2.9(  eq7.1   )

So we re turn to the d e p a r t c a s e   and recalculate the a l l w i n d a c t i o n s   http://www.arab-eng.org/vb/users/355867.html

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