Wind Loading for a Hipped Roof example, In accordance with EN1991-1-4

1. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
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GEODOMISI Ltd. - Dr. Costas Sachpazis
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Engineering & Retaining Structures.
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WIND LOADING FOR A HIPPED ROOF (EN1991-1-4)
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2. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30)
6936425722 & (+44) 7585939944, costas@sachpazis.info
Civil & Geotechnical Engineering
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Dr. C. Sachpazis
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Building data
Type of roof;
Hipped
Length of building;
L = 32000 mm
Width of building;
W = 10000 mm
Height to eaves;
H = 15000 mm
Pitch of main slope;
α0 = 20.0 deg
Pitch of gable slope;
α90 = 20.0 deg
Total height;
h = 16820 mm
Basic values
Fundamental basic wind velocity;
vb,0 = 21.8 m/s
Season factor;
cseason = 1.00
Direction factor;
cdir = 1.00
Shape parameter K;
K = 0.2
Exponent n;
n = 0.5
Probability factor;
cprob = [(1 - K × ln(-ln(1-p)))/(1 - K × ln(-ln(0.98)))] = 1.00
n
Basic wind velocity (Exp. 4.1);
vb = cdir × cseason × vb,0 × cprob = 21.8 m/s
Reference mean velocity pressure;
qb = 0.5 × ρ × vb = 0.298 kN/m
2
Orography
Orography factor not significant;
co = 1.0
Terrain category;
Average height of surrounding buildings;
IV
have = 15000 mm
Distance to nearest building;
xdis = 30000 mm
2
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3. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30)
6936425722 & (+44) 7585939944, costas@sachpazis.info
Civil & Geotechnical Engineering
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Dr. C. Sachpazis
08/02/2014
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The velocity pressure for the windward face of the building with a 0 degree wind is to be considered as 1 part as the height h is less than b
(cl.7.2.2)
The velocity pressure for the windward face of the building with a 90 degree wind is to be considered as 2 parts as the height h is greater than b
but less than 2b (cl.7.2.2)
Peak velocity pressure - windward wall - Wind 0 deg
Reference height (at which q is sought);
z = 15000mm
Displacement height (Annex A.2);
hdis = min(0.8 × have, 0.6 × z) = 9000 mm
Roughness length (Table 4.1);
z0 = 1000 mm
Roughness length (Category II);
z0,II = 50 mm
Minimum height (Table 4.1);
zmin = 10000 mm
Maximum height;
zmax = 200000 mm
Terrain factor;
kr = 0.19 × (z0 / z0,II)
Roughness factor;
cr = kr × ln(zmin / z0) = 0.54
Mean wind;
vm = cr × co × vb = 11.8 m/s
0.07
= 0.23
Turbulence factor;
kI = 1.0
Turbulence intensity;
Iv = kI / (co × ln(zmin / z0)) = 0.434
Peak velocity pressure;
qp = (1 + 7 × Iv) × 0.5 × ρ × vm = 0.35 kN/m
2
Structural factor
Building type;
Structural factor (Annex D);
Concrete
csCd = 0.79
Peak velocity pressure - windward wall (lower part) - Wind 90 deg
Reference height (at which q is sought);
z = 10000mm
Displacement height (Annex A.2);
hdis = min(0.8 × have, 0.6 × z) = 6000 mm
Terrain factor;
kr = 0.19 × (z0 / z0,II)
Roughness factor;
cr = kr × ln(zmin / z0) = 0.54
0.07
= 0.23
2

4. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30)
6936425722 & (+44) 7585939944, costas@sachpazis.info
Civil & Geotechnical Engineering
Calc. by
Date
Dr. C. Sachpazis
08/02/2014
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Mean wind;
vm = cr × co × vb = 11.8 m/s
Turbulence factor;
kI = 1.0
Turbulence intensity;
Iv = kI / (co × ln(zmin / z0)) = 0.434
Peak velocity pressure;
qp = (1 + 7 × Iv) × 0.5 × ρ × vm = 0.35 kN/m
2
2
Peak velocity pressure - windward wall (upper part) - Wind 90 deg
Reference height (at which q is sought);
z = 15000mm
Displacement height (Annex A.2);
hdis = min(0.8 × have, 0.6 × z) = 9000 mm
Terrain factor;
kr = 0.19 × (z0 / z0,II)
Roughness factor;
cr = kr × ln(zmin / z0) = 0.54
0.07
= 0.23
Mean wind;
vm = cr × co × vb = 11.8 m/s
Turbulence factor;
kI = 1.0
Turbulence intensity;
Iv = kI / (co × ln(zmin / z0)) = 0.434
Peak velocity pressure;
qp = (1 + 7 × Iv) × 0.5 × ρ × vm = 0.35 kN/m
2
2
Peak velocity pressure - roof
Reference height (at which q is sought);
z = 16820mm
Displacement height (Annex A.2);
hdis = min(0.8 × have, 0.6 × z) = 10092 mm
Terrain factor;
kr = 0.19 × (z0 / z0,II)
Roughness factor;
cr = kr × ln(zmin / z0) = 0.54
0.07
= 0.23
Mean wind;
vm = cr × co × vb = 11.8 m/s
Turbulence factor;
kI = 1.0
Turbulence intensity;
Iv = kI / (co × ln(zmin / z0)) = 0.434
Peak velocity pressure;
qp = (1 + 7 × Iv) × 0.5 × ρ × vm = 0.35 kN/m
2
Peak velocity pressure for internal pressure
Peak velocity pressure – internal (as roof press.);
qp,i = 0.35 kN/m
2
2
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5. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30)
6936425722 & (+44) 7585939944, costas@sachpazis.info
Civil & Geotechnical Engineering
Calc. by
Date
Dr. C. Sachpazis
08/02/2014
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Pressures and forces
Net pressure;
p = csCd × qp × cpe - qp,i × cpi;
Net force;
Fw = pw × Aref;
Roof load case 1 - Wind 0, cpi -0.30, - cpe
Zone
Ext pressure
coefficient
cpe
Peak velocity
pressure
2
qp, (kN/m )
Net pressure
2
p (kN/m )
Area
2
Aref (m )
Net force
Fw (kN)
F (-ve)
-0.77
0.35
-0.11
43.59
-4.67
G (-ve)
-0.70
0.35
-0.09
54.49
-4.83
H (-ve)
-0.27
0.35
0.03
45.59
1.43
I (-ve)
-0.47
0.35
-0.02
80.32
-1.93
J (-ve)
-0.90
0.35
-0.14
23.16
-3.33
K (-ve)
-0.97
0.35
-0.16
40.18
-6.52
L (-ve)
-1.40
0.35
-0.28
28.61
-8.07
M (-ve)
-0.67
0.35
-0.08
24.60
-1.95
Total vertical net force;
Fw,v = -28.08 kN
Total horizontal net force;
Fw,h = 1.27 kN
Walls load case 1 - Wind 0, cpi -0.30, - cpe
Zone
Ext pressure
coefficient
cpe
Peak velocity
pressure
2
qp, (kN/m )
Net pressure
2
p (kN/m )
Area
2
Aref (m )
Net force
Fw (kN)
A
-1.20
0.35
-0.23
96.00
-21.71
B
-0.80
0.35
-0.12
54.00
-6.25
Date

6. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30)
6936425722 & (+44) 7585939944, costas@sachpazis.info
Civil & Geotechnical Engineering
Calc. by
Date
Dr. C. Sachpazis
08/02/2014
Chk'd by
Date
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D
0.80
0.35
0.33
480.00
156.42
E
-0.53
0.35
-0.04
480.00
-20.32
Overall loading
Equiv leeward net force for overall section;
Fl = Fw,wE = -20.3 kN
Net windward force for overall section;
Fw = Fw,wD = 156.4 kN
Lack of correlation (cl.7.2.2(3) – Note);
fcorr = 0.88; as h/W is 1.682
Overall loading overall section;
Fw,D = fcorr × (Fw - Fl) + Fw,h = 156.0 kN
Roof load case 2 - Wind 90, cpi -0.30, - cpe
Zone
Ext pressure
coefficient
cpe
Peak velocity
pressure
2
qp, (kN/m )
Net pressure
2
p (kN/m )
Area
2
Aref (m )
Net force
Fw (kN)
F (-ve)
-0.77
0.35
-0.12
4.26
-0.53
G (-ve)
-0.70
0.35
-0.10
5.32
-0.56
H (-ve)
-0.27
0.35
0.03
17.03
0.43
I (-ve)
-0.47
0.35
-0.03
17.03
-0.59
J (-ve)
-0.90
0.35
-0.16
9.58
-1.58
L (-ve)
-1.40
0.35
-0.31
10.64
-3.35
M (-ve)
-0.67
0.35
-0.09
17.03
-1.61
N (-ve)
-0.27
0.35
0.03
259.66
6.53
Total vertical net force;
Fw,v = -1.19 kN
Total horizontal net force;
Fw,h = 0.52 kN
Walls load case 2 - Wind 90, cpi -0.30, - cpe
Date

7. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Civil & Geotechnical Engineering
Calc. by
Date
Dr. C. Sachpazis
08/02/2014
Zone
Ext pressure
coefficient
cpe
Peak velocity
pressure
2
qp, (kN/m )
Net pressure
2
p (kN/m )
Area
2
Aref (m )
Net force
Fw (kN)
A
-1.20
0.35
-0.25
30.00
-7.64
B
-0.80
0.35
-0.13
120.00
-16.17
C
-0.50
0.35
-0.04
330.00
-14.78
Db
0.74
0.35
0.33
100.00
32.99
Du
0.74
0.35
0.34
50.00
16.76
E
-0.37
0.35
-0.01
150.00
-1.03
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Overall loading
Equiv leeward net force for upper section;
Fl = Fw,wE / Aref,wE × Aref,wu = -0.3 kN
Net windward force for upper section;
Fw = Fw,wu = 16.8 kN
Lack of correlation (cl.7.2.2(3) – Note);
fcorr = 0.85; as h/L is 0.526
Overall loading upper section;
Fw,u = fcorr × (Fw - Fl) + Fw,h = 15.1 kN
Equiv leeward net force for bottom section;
Fl = Fw,wE / Aref,wE × Aref,wb = -0.7 kN
Net windward force for bottom section;
Fw = Fw,wb = 33.0 kN
Lack of correlation (cl.7.2.2(3) – Note);
fcorr = 0.85; as h/L is 0.526
Overall loading bottom section;
Fw,b = fcorr × (Fw - Fl) = 28.6 kN
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8. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30)
6936425722 & (+44) 7585939944, costas@sachpazis.info
Civil & Geotechnical Engineering
Calc. by
Date
Dr. C. Sachpazis
08/02/2014
Chk'd by
Date
App'd by
Date

9. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Tel.: (+30) 210 5238127, 210 5711263 - Fax.:+30 210 5711461 - Mobile: (+30)
6936425722 & (+44) 7585939944, costas@sachpazis.info
Civil & Geotechnical Engineering
Calc. by
Date
Dr. C. Sachpazis
08/02/2014
Chk'd by
Date
App'd by
Date

10. Wind Loading for a Hipped Roof example, In accordance with
EN1991-1-4
Job Ref.
Section
Sheet no./rev. 1
Project:
GEODOMISI Ltd. - Dr. Costas Sachpazis
Civil & Geotechnical Engineering Consulting Company for
Structural Engineering, Soil Mechanics, Rock Mechanics, Foundation
Engineering & Retaining Structures.
Date
Dr. C. Sachpazis
08/02/2014
Chk'd by
Date
App'd by
Date
L
J
Calc. by
L
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J