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Document Ref: SX016a-EN-EU Sheet 1 of 8 Title

Example: Determination of loads on a building envelope

Eurocode Ref EN 1991-1-3, EN 1991-1-4 Made by Matthias Oppe Date June 2005

CALCULATION SHEET

Checked by Christian Müller Date June 2005


This worked example explains the procedure of determination of loads on a portal frame building. Two types of actions are considered: wind actions and snow actions.

30,00

5,98

8

α

[m]

7,20

7,30 72,00

Basic data

• Total length : b = 72,00 m

• Spacing: s = 7,20 m

• Bay width : d = 30,00 m

• Height (max): h = 7,30 m

• Roof slope: α = 5,0°

Height above ground:

h = 7,30 m

α = 5°

leads to:

h´ = 7,30 – 15 tan 5° = 5,988 m

Example: Determination of loads on a building envelopeC

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CALCULATION SHEET


1 Wind loads

Basic values Determination of basic wind velocity: EN 1991-1-4 vb = cdir × cseason × vb,0 § 4.2

Where: vb basic wind velocity cdir directional factor cseason seasonal factor vb,0 fundamental value of the basic wind velocity

Fundamental value of the basic wind velocity (see European windmap):

vb,0 = 26 m/s (for Aachen - Germany)

EN 1991-1-4 Terrain category II ⇒ z0 = 0,05 m § 4.3.2 z > zmin

Table 4.1

⇒ vb = cdir × cseason × vb,0 = 26 m/s

For simplification the directional factor cdir and the seasonal factor cseason are in general equal to 1,0.

Basic velocity pressure

EN 1991-1-4 2bairb 2

1 vq ××= ρ § 4.5 eq. 4.10

25,1air =ρwhere: kg/m³ (air density)

5,4222625,121 2

b =××=q⇒ N/m²

Peak pressure

[ ] 2mvp (z)

21(z)71(z) vlq ×××+= ρ EN 1991-1-4

§ 4.5, eq. 4.8Calculation of vm(z)

vm(z) mean wind velocity

vm(z) = cr(z) × co(z) × vb


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Where: co(z) is the orography factor

cr(z) is the roughness factor

maxmin0

rr forln(z) zzzzzkc ≤≤⎟⎟

⎠

⎞⎜⎜⎝

⎛×=

minminrr for)((z) zzzcc ≤=

Where: z0 is the roughness length

kr is the terrain factor, depending on the roughness length z0 calculated using

07,0

II0,

0r 19,0 ⎟

⎟⎠

⎞⎜⎜⎝

⎛×=

zz

k

EN 1991-1-4 Where: z0,II = 0,05 (terrain category II) §4.3.2

zmin is the minimum height

Table 4.1 zmax is to be taken as 200 m

Calculation of Iv(z)

Iv(z) turbulence intensity

EN 1991-1-4

minminvv

maxmin0o

Iv

for)(

for)/ln()(

zzzII

zzzzzzc

kI

<=

≤≤×

= §4.4 eq. 4.7

Where: kI is the turbulence factor recommended value for kI is 1,0 z = 7,30 m so: zmin < z < zmax

( 20r

2b

0o

Ip )/ln(

21

)/ln()(71(z)

profilewindpressurebasicfactorgustsquared

zzkvzzzc

kq ×××××⎥⎦

⎤⎢⎣

⎡×

+= ρ )

Corrigendum


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2070

2p

)05,0/307(ln050050190

2625121

)050307(ln71)307(

⎟⎟⎠

⎞⎜⎜⎝

⎛×⎟

⎠⎞

⎜⎝⎛××

×××⎥⎦

⎤⎢⎣

⎡+=

,,,,

,,/,

,q

,

911,010947,05,422)050307(ln

71 32 =×××⎥⎦

⎤⎢⎣

⎡+= −

,/, kN/m²

Wind pressure on surfaces EN 1991-1-4 § 7.2(pressure coefficients for internal frame)

A positive wind load 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.

External pressure coefficients

The wind pressure acting on the external surfaces, we should be obtained from the following expression: EN 1991-1-4 we = qp(ze) × cpe §5.2 eq. 5.1

where: ze is the reference height for the external pressure

cpe is the pressure coefficient for the external pressure depending on the size of the loaded area A. = cpe,10 because the loaded area A for the structure is larger than 10 m²

a) vertical walls EN 1991-1-4 § 7.2

for 25,024,000,3030,7

≤==dh

Table 7.1

D: cpe = 0,7

E: cpe = - 0,3


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b) duopitch roofs EN 1991-1-4 § 7.2with α = 5,0°, Table 7.4a

θ = 0° (wind direction)

e = min (b; 2h) = min (72,00; 14,60) = 14,60 m

1) upwind face G: cpe = - 1,2 2) downwind face

H: cpe = - 0,6

I: cpe = - 0,6

J: cpe = 0,2 / - 0,6

⇒ cpe = - 0,6

(see Table 7.4a , Note 1)

External pressure coefficients cpe (for zone D, E, G, H, I and J):

I: = -0,6J: = -0,6H: = -0,6G: = -1,2

E: = -0,3D: = 0,7

cccc

cc

pe

pepepe

pepe

Internal pressure coefficient EN 1991-1-4 §5.2The wind pressure acting on the internal surfaces of a structure, wi should be

obtained from the following expression

eq.5.2

wi = qp(zi) × cpi

where: zi is the reference height for the internal pressure

cpi is the pressure coefficient for the internal pressure


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The internal pressure coefficient depends on the size and distribution of the openings in the building envelope.

Within this example it is not possible to estimate the permeability and opening ratio of the building. So cpi should be taken as the more onerous of + 0,2 and – 0,3. In this case cpi is unfavorable when cpi is taken to + 0,2.

EN 1991-1-4 § 7.2.9 (6) Note 2

Wind loads

The wind loadings per unit length w (in kN/m) for an internal frame are calculated using the influence width (spacing) s = 7,20 m:

w = (cpe + cpi) × qp × s Internal and external pressures are considered to act at the same time. The worst combination of external and internal pressures are to be considered for every combination of possible openings and other leakage paths.

EN 1991-1-4 § 7.2.9

Characteristic values for wind loading in [kN/m] for an internal frame:

- zones D, E, G, H, I and J

D: = 4,59 E: = 3,28

I: = 5,25J: = 5,25H: = 5,25G: = 9,18

w w

wwww

30,00e/10 = 1,46 1,46

7,30

[m]


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CALCULATION SHEET


2 Snow loads

General Snow loads on the roof should be determined as follows: EN 1991-1-3 s = μi × ce × cz × sk §5.2.2 eq.5.1

where: μi is the roof shape coefficient

ce is the exposure coefficient, usually taken as 1,0

ct is the thermal coefficient, set to 1,0 for normal situations

sk is the characteristic value of ground snow load for the relevant altitude

Roof shape coefficient

Shape coefficients are needed for an adjustment of the ground snow load to a snow load on the roof taking into account effects caused by non-drifted and drifted snow load arrangements.

EN 1991-1-3 The roof shape coefficient depends on the roof angle. §5.3 Table 5.1 °≤≤° 300 α ⇒ μ1 = 0,8

Snow load on the ground

The characteristic value depends on the climatic region.

For a site in Aachen (Germany) the following expression is relevant:

EN 1991-1-3 ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+×−×=

2

k 2561002,0264,0 Azs kN/ m² Annex C

Table C1

Where: z is the zone number (depending on the snow load on sea level), here: z = 2

A is the altitude above sea level, here A = 175 m

( ) 772,02561751002,02264,0

2

k =⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛+×−×=s kN/m²


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CALCULATION SHEET


Snow load on the roof

s = 0,8 × 1,0 × 1,0 × 0,772 = 0,618 kN/m²

spacing = 7,20 m

⇒ for an internal frame:

s = 0,618 × 7,20 = 4,45 kN/m

α

7,30

30,00

s = 4,45 kN/m

[m]


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