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EC1 Wind EN 1991-1-4
calculation example for
a duopitch canopy roof
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EC1 Wind EN 1991-1-4 calculation example for a duopitch canopy roof
Assumptions:
Load area
Point1
Point2
Point3
Point4
Identifier X(m) Y(m) Z(m) X(m) Y(m) Z(m) X(m) Y(m) Z(m) X(m) Y(m) Z(m)
1 5.000 14.800 7.628 5.000 -4.800 7.628 15.400 -4.800 5.736 15.400 14.800 5.736
2 5.000 -4.800 7.628 5.000 14.800 7.628 -5.400 14.800 5.736 -5.400 -4.800 5.736
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h = 7.6284831 m andkg/m3 (recommended value in EC1).
For X+ wind θ = 00, b = 19.600 m and d = 20.800 m.
For Y+ wind direction θ = 900, b = 20.800 m and d = 19.600 m.
For terrain category II => z0 = 0.05 m, zmin = 2 m and z0II = 0.05 m.
φ = 0 (option in the wind family property list).
The results of the automatic calculation and creation of the loads:
z = 7.6285 m; due to zmin < z => z = 7.6285 m
vb = cdir • cSeason • vb,0 = 1 • 1 • 22 m/s = 22 m/s
kr = 0.19 • z0 / z0,II 0.07 = 0.19
cr (z) = kr • ln(z/z0 ) = 0.95525
KL = 1.0
vm (z) = cr (z) • co (z) • vb = 21.0155 m/s
Iv (z) = v / vm (z) = kl / [co (z) • ln(z/z0 ] = 0.1989
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ce (z) = qp (z) / qb = 2.18298
qb = 0.5 • • vb 2
= 302.5
qp (z) = [1 + 7 • Iv (z)] • 0.5 • • vb 2
= 660.351 N/m2
CsCd calculation for X+ direction:
h = 7.6285 m
z = h ∙ 0.6 = 4.577 m and zmin < z =>
reevaluate Iv(z) used in CsCd at z = 4.577 m
cr (z) = kr • ln(z/z0 ) = 0.8582
KL = 1.0
vm (z) = cr (z) • co (z) • vb = 18.88 m/s
Iv (z) = v / vm (z) = kl / [co (z) • ln(z/z0 ] = 0.2214
natural frequency n = n1,x = 46
h [Hz] = 6.03003 Hz
= 0.67 + 0.05 • ln(z0 ) = 0.5202
turbulent length scale L(z) = Lt • z
zt = 42.0477
non-dimensional frequency fL (z, n) = n • L ( )z
vm ( )z = 13.4294
SL (z, n) = n • Sv (z, n)
v 2 =
6.8 • fL(z, n)
( )1 + 10.2 • fL(z, n) 5/3 = 0.024786
background factor B2
= 1
1 + 0.9 •
b+h
L ( )zs
0.63
= 0.59366
nh = 11.2075
nb = 28.7956
aerodynamic admittance functions Rh and Rb
R h = 1
h -
1
2 • h2 (1 - e
-2 h
) = 0.08525
R b = 1
b -
1
2 • b2 (1 - e
-2 b
) = 0.03412
R2 =
2
2 • • SL(zs, n1, x) • Rh(h) • Rb(b) = 0.01779
up-crossing frequency = n1, x •
= 1.02856
peak factor kp = +
= 3.752
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cscd = 1 + 2 • kp • lv(zs) • B
2 + R
2
1 + 7 • lv(zs) = 0.902 (>CsCd min(0.85)) for X+.
The pitch angle of each slope is 10.31 ° so the cp,net values are extracted from Table 7.7
for X+ wind direction. Linear interpolation is used for the intermediate values of α and φ. For
user option φ = 0 there are generated cp,net loads for φ = 0 and the maximum φ.
X+:
φ max cp,net cf
[A] 0.7125 0.4
[B] 1.8063
[C] 1.4
[D] 0.4
φ 0 cp,net cf
[A] -0.7125 -0.7063
[B] -1.5125
[C] -1.4
[D] -1.4251
w = cp,net ∙ qp (ze) ∙ cscd
CsCd is considered the same for the entire building per wind direction. The value for X+ is
calculated above.
For the A zones:
w A φ max = cscd ∙ qp (ze) ∙ 0.71253 = 0.71253N/m2 (in WX+S load case)
w A φ 0 = cscd ∙ qp (ze) ∙ 0.71253 = 0.71253 N/m2 (in WX+S load case)
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Like all above the position and the geometry of the loads based on the zones provided
by the Table 7.7, on the roof, are calculated automatically. All the loads and the load cases are
automatically generated.
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Fw = cscd • cf • qp (ze) • Aref (5.3)
Knowing len, the length of the linear load, the above formula translated for our linear loads
becomes:
Fw linear = cscd • cf • qp (ze) • Aref / len
Note: In Advance Design, for canopy cf loads, cscd is considered to be equal to 1.
Fw = 1 • cf • qp (ze) • 207.1874 m2 / 19.6 m
Fw A φ max = 2792.1713 N/m
Fw A φ 0 = -4930.0309N/m
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The position and the geometry of the cf loads are based on the Figure 7.17.
All the loads and the load cases are automatically generated:
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Y+:
For θ = 900 the Table 7.6 from monopitch canopies is used, and α is considered to be equal to
00 for the both slopes (1 & 2).
φ max cp,net cf
[A] 0.5 0.2
[B] 1.8
[C] 1.1
φ 0 cp,net cf
[A] -0.6 -0.5
[B] -1.3
[C] -1.4
w = cp,net ∙ qp (ze) ∙ cscd
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For the A zones:
w A φ max = cscd ∙ qp (ze) ∙ 0.5 = 297.8183 N/m2 (in WX+S load case)
w A φ 0 = cscd ∙ qp (ze) ∙ -0.6. = -357.3819 N/m2 (in WX+S load case)
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Like all above the position and the geometry of the loads based on the zones provided
by the Table 7.6, on the roof, are calculated automatically. The results are:
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The linear load length len = 10.57 m for Y direction for each slope.
Fw linear = cscd • cf • qp (ze) • Aref / len
Note: In Advance Design, for canopy cf loads, cscd is considered to be equal to 1.
Fw linear = 1 • cf • qp (ze) • 207.1874 m2 / 10.5708 m
Fw A φ max = 2588.58 N/m
Fw A φ 0 = -6471.45 N/m
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The position and the geometry of the cf loads are based on the Figure 7.16 for each slope.
The results are:
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