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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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