CALCULATION SHEET
Document Ref:
SX016a-EN-EU
Document Ref:
SX016a-EN-EU
Title
Example: Determination of loads on a building envelope
Title
Example: Determination of loads on a building envelope
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Made by
Matthias Oppe
Date
June 2005
Made by
Matthias Oppe
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Sheet
1
of
Example: Determination of loads on a building
envelope
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.
8
CALCULATION SHEET
7,30
5,988
of
Basic values
vb
= cdir × cseason × vb,0
Where: vb
basic wind velocity
cdir
directional factor
cseason
seasonal factor
vb,0
fundamental value of the basic wind velocity
vb,0
= 26 m/s (for Aachen - Germany)
Terrain category II
⇒
z0 = 0,05 m
z > zmin
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:
EN 1991-1-4
§ 4.2
Fundamental value of the basic wind velocity (see European windmap):
[m]
•
8
Determination of basic wind velocity:
0
7,2
30,00
2
1 Wind loads
α
,00
72
Sheet
⇒
EN 1991-1-4
§ 4.3.2
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
qb =
1
2
× ρ air × v b
2
where:
ρ air = 1,25 kg/m³ (air density)
⇒
qb =
EN 1991-1-4
§ 4.5
eq. 4.10
1
× 1,25 × 26 2 = 422,5 N/m²
2
Peak pressure
h´ = 7,30 – 15 tan 5° = 5,988 m
1
q p (z) = [1 + 7l v (z)]× × ρ × v m (z) 2
2
Calculation of vm(z)
vm(z)
mean wind velocity
vm(z) = cr(z) × co(z) × vb
EN 1991-1-4
§ 4.5, eq. 4.8
CALCULATION SHEET
Document Ref:
SX016a-EN-EU
Document Ref:
SX016a-EN-EU
Title
Example: Determination of loads on a building envelope
Title
Example: Determination of loads on a building envelope
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Made by
Matthias Oppe
Date
June 2005
Made by
Matthias Oppe
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Where: co(z)
is the orography factor
cr(z)
is the roughness factor
⎛ z ⎞
c r (z) = k T × ln⎜⎜ ⎟⎟
⎝ z0 ⎠
kT
3
of
8
0 ,07
⎞
⎛
⎛ 0 ,05 ⎞
× ⎜ 0,19 × ⎜
× ln (7 ,30 / 0,05) ⎟
⎟
⎟
⎜
⎝ 0 ,05 ⎠
⎠
⎝
is the terrain factor, depending on the roughness length z0
calculated using
z0,II = 0,05 (terrain category II)
is the minimum height
zmax
is to be taken as 200 m
EN 1991-1-4
§4.3.2
Table 4.1
Where: kI
z
so:
EN 1991-1-4
§ 7.2
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
§5.2 eq. 5.1
we = qp(ze) × cpe
turbulence intensity
l v = l v ( z min )
8
2
(pressure coefficients for internal frame)
Calculation of lv(z)
kI
lv =
co ( z ) × ln( z / z 0 )
of
Wind pressure on surfaces
0 , 07
zmin
4
⎡
⎤
7
2
−3
= ⎢1 +
⎥ × 422,5 × 0,947 ×10 = 0,911 kN/m²
,
/
,
ln
(
7
30
0
05
)
⎣
⎦
is the roughness length
Where:
Sheet
⎡
⎤ 1
7
2
qp (7 ,30) = ⎢1 +
⎥ × 2 × 1,25 × 26
ln
(
7
30
0
05
)
,
/
,
⎣
⎦
for z ≤ z min
⎛ z ⎞
k T = 0,19 × ⎜⎜ 0 ⎟⎟
⎝ z 0,II ⎠
lv(z)
CALCULATION SHEET
for z min ≤ z ≤ z max
c r (z) = c r ( z min )
Where: z0
Sheet
where: ze
for z min ≤ z ≤ z max
EN 1991-1-4
§4.4 eq. 4.7
cpe
for z < z min
is the reference height for the external pressure
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
is the turbulence factor recommended value for kI is 1,0
= 7,30 m
zmin < z < zmax
⎡
⎤ 1
7k I
2
q p (z) = ⎢1 +
k T × ln( z / z 0 ) )
⎥ × × ρ × v b × (1
44244
3
2 4243
o ( z ) × ln( z / z 0 ) ⎦
⎣14c4
1
wind profile
424443 basic pressure
squared gust factor
a) vertical walls
h 7,30
for =
= 0,24 ≤ 0,25
d 30,00
D:
cpe = 0,7
E:
cpe = - 0,3
EN 1991-1-4
§ 7.2
Table 7.1
CALCULATION SHEET
Document Ref:
SX016a-EN-EU
Document Ref:
SX016a-EN-EU
Title
Example: Determination of loads on a building envelope
Title
Example: Determination of loads on a building envelope
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Made by
Matthias Oppe
Date
June 2005
Made by
Matthias Oppe
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Sheet
5
of
8
EN 1991-1-4
§ 7.2
Table 7.4a
b) duopitch roofs
with α = 5,0°,
θ = 0° (wind direction)
e = min (b; 2h)
= min (72,00; 14,60)
= 14,60 m
cpe = - 1,2
H:
cpe = - 0,6
I:
cpe = - 0,6
J:
cpe = 0,2 / - 0,6
6
Sheet
of
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
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:
2) downwind face
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.
⇒ cpe = - 0,6
(see Table 7.4a , Note 1)
Characteristic values for wind loading in [kN/m] for an internal frame:
- zones D, E, G, H, I and J
I: w = 5,25
D: w = 4,59
External pressure coefficients cpe (for zone D, E, G, H, I and J):
H: c pe = -0,6
J: w = 5,25
H: w = 5,25
E: w = 3,28
J: c pe = -0,6
I: c pe = -0,6
e/10 = 1,46
1,46
30,00
D: c pe = 0,7
E: c pe = -0,3
Internal pressure coefficient
The wind pressure acting on the internal surfaces of a structure, wi should be
obtained from the following expression
wi = qp(zi) × cpi
where: zi
cpi
7,30
G: w = 9,18
G: c pe = -1,2
8
Wind loads
1) upwind face
G:
CALCULATION SHEET
is the reference height for the internal pressure
is the pressure coefficient for the internal pressure
EN 1991-1-4
§5.2 eq.5.2
[m]
EN 1991-1-4
§ 7.2.9
CALCULATION SHEET
Document Ref:
SX016a-EN-EU
Document Ref:
SX016a-EN-EU
Title
Example: Determination of loads on a building envelope
Title
Example: Determination of loads on a building envelope
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Eurocode Ref
EN 1991-1-3, EN 1991-1-4
Made by
Matthias Oppe
Date
June 2005
Made by
Matthias Oppe
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Checked by
Christian Müller
Date
June 2005
Sheet
7
of
8
2 Snow loads
CALCULATION SHEET
Sheet
8
of
Snow load on the roof
s = 0,8 × 1,0 × 1,0 × 0,772 = 0,618 kN/m²
General
spacing = 7,20 m
Snow loads on the roof should be determined as follows:
s = μi × ce × cz × sk
where: μi
EN 1991-1-3
§5.2.2 eq.5.1
is the roof shape coefficient
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
for an internal frame:
s = 0,618 × 7,20 = 4,45 kN/m
s = 4,45 kN/m
α
7,30
ce
⇒
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.
The roof shape coefficient depends on the roof angle.
0° ≤ α ≤ 30°
⇒
μ1 = 0,8
EN 1991-1-3
§5.3
Table 5.1
Snow load on the ground
The characteristic value depends on the climatic region.
For a site in Aachen (Germany) the following expression is relevant:
⎡ ⎛ A ⎞2 ⎤
s k = (0,264 × 2 − 0,002) × ⎢1 + ⎜
⎟ ⎥ kN/m²
⎢⎣ ⎝ 256 ⎠ ⎥⎦
Where: z
A
is the zone number (depending on the snow load on sea
level), here: z = 2
is the altitude above sea level, here A = 175 m
⎡ ⎛ 175 ⎞ 2 ⎤
s k = (0,264 × 2 − 0,002) × ⎢1 + ⎜
⎟ ⎥ = 0,772 kN/m²
⎣⎢ ⎝ 256 ⎠ ⎥⎦
EN 1991-1-3
Annex C
Table C1
30,00
[m]
8