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EUROPEAN STANDARD
NORME EUROPÉENNE
EUROPÄISCHE NORM
EN199114:2005+A1
April 2010
ICS 91.010.30
Supersedes ENV 199124:1995
Incorporating corrigendum January 2010
English version
Eurocode 1 :  Actions sur les structures  Partie 14: Actions générales  Actions du vent  Eurocode 1: Einwirkungen auf Tragwerke  Teil 14: Allgemeine Einwirkungen  Windlasten 
This European Standard was approved by CEN on 4 June 2004.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Uptodate lists and bibliographical references concerning such national standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
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Ref. No. EN 199114:2005: E
1Page  
Section 1 General  9  
1.1  Scope  9  
1.2  Normative references  10  
1.3  Assumptions  10  
1.4  Distinction between Principles and Application Rules  10  
1.5  Design assisted by testing and measurements  10  
1.6  Definitions  10  
1.7  Symbols  11  
Section 2 Design situations  16  
Section 3 Modelling of wind actions  17  
3.1  Nature  17  
3.2  Representations of wind actions  17  
3.3  Classification of wind actions  17  
3.4  Characteristic values  17  
3.5  Models  17  
Section 4 Wind velocity and velocity pressure  18  
4.1  Basis for calculation  18  
4.2  Basic values  18  
4.3  Mean wind  19  
4.3.1  Variation with height  19  
4.3.2  Terrain roughness  19  
4.3.3  Terrain orography  21  
4.3.4  Large and considerably higher neighbouring structures  21  
4.3.5  Closely spaced buildings and obstacles  22  
4.4  Wind turbulence  22  
4.5  Peak velocity pressure  22  
Section 5 Wind actions  24  
5.1  General  24  
5.2  Wind pressure on surfaces  24  
5.3  Wind forces  25  
Section 6 Structural factor c_{s}c_{d}  28  
6.1  General  28  
6.2  Determination of c_{s}c_{d}  28  
6.3  Detailed procedure  28  
6.3.1  Structural factor c_{s}c_{d}  28  
6.3.2  Serviceability assessments  30  
6.3.3  Wake buffeting  30  
Section 7 Pressure and force coefficients  31  
7.1  General  31  
7.1.1  Choice of aerodynamic coefficient  31  
7.1.2  Asymmetric and counteracting pressures and forces  32  
7.1.3  Effects of ice and snow  32  
7.2  Pressure coefficients for buildings  33  
7.2.1  General  33  
7.2.2  Vertical walls of rectangular plan buildings  34  
7.2.3  Flat roofs  37  
7.2.4  Monopitch roofs  40  
7.2.5  Duopitch roofs  43  
7.2.6  Hipped roofs  47  
7.2.7  Multispan roofs  48  
7.2.8  Vaulted roofs and domes  50 2  
7.2.9  Internal pressure  51  
7.2.10  Pressure on walls or roofs with more than one skin  53  
7.3  Canopy roofs  54  
7.4  Freestanding walls, parapets, fences and signboards  61  
7.4.1  Freestanding walls and parapets  61  
7.4.2  Shelter factors for walls and fences  63  
7.4.3  Signboards  63  
7.5  Friction coefficients  64  
7.6  Structural elements with rectangular sections  65  
7.7  Structural elements with sharp edged section  67  
7.8  Structural elements with regular polygonal section  67  
7.9  Circular cylinders  69  
7.9.1  External pressure coefficients  69  
7.9.2  Force coefficients  71  
7.9.3  Force coefficients for vertical cylinders in a row arrangement  74  
7.10  Spheres  74  
7.11  Lattice structures and scaffoldings  76  
7.12  Flags  78  
7.13  Effective slenderness λ and endeffect factor Ψ_{λ}  80  
Section 8 Wind actions on bridges  82  
8.1  General  82  
8.2  Choice of the response calculation procedure  85  
8.3  Force coefficients  85  
8.3.1  Force coefficients in xdirection (general method)  85  
8.3.2  Force in xdirection  Simplified Method  88  
8.3.3  Wind forces on bridge decks in zdirection  89  
8.3.4  Wind forces on bridge decks in ydirection  90  
8.4  Bridge piers  91  
8.4.1  Wind directions and design situations  91  
8.4.2  Wind effects on piers  91  
Annex A (informative) Terrain effects  92  
A.1  Illustrations of the upper roughness of each terrain category  92  
A.2  Transition between roughness categories 0,1, II, III and IV  93  
A.3  Numerical calculation of orography coefficients  95  
A.4  Neighbouring structures  100  
A.5  Displacement height  101  
Annex B (informative) Procedure 1 for determining the structural factor c_{s}c_{d}  102  
B.1  Wind turbulence  102  
B.2  Structural factor  103  
B.3  Number of loads for dynamic response  105  
B.4  Service displacement and accelerations for serviceability assessments of a vertical structure  105  
Annex C (informative) Procedure 2 for determining the structural factor c_{s}c_{d}  108  
C.1  Wind turbulence  108  
C.2  Structural factor  108  
C.3  Number of loads for dynamic response  109  
C.4  Service displacement and accelerations for serviceability assessments  109  
Annex D (informative) c_{s}c_{d} values for different types of structures  111  
Annex E (informative) Vortex shedding and aeroelastic instabilities  114  
E.1  Vortex shedding  114  
E.1.1  General  114  
E.1.2  Criteria for vortex shedding  114  
E.1.3  Basic parameters for vortex shedding  115  
E.1.4  Vortex shedding action  118  
E.1.5  Calculation of the cross wind amplitude  118  
E.1.6  Measures against vortex induced vibrations  128  
E.2  Galloping  129  
E.2.1  General  129 3  
E.2.2  Onset wind velocity  129  
E.2.3  Classical galloping of coupled cylinders  131  
E.3  Interference galloping of two or more free standing cylinders  133  
E.4  Divergence and Flutter  134  
E.4.1  General  134  
E.4.2  Criteria for platelike structures  134  
E.4.3  Divergency velocity  134  
Annex F (informative) Dynamic characteristics of structures  136  
F.1  General  136  
F.2  Fundamental frequency  136  
F.3  Fundamental mode shape  141  
F.4  Equivalent mass  143  
F.5  Logarithmic decrement of damping  143  
Bibliography  146 
This document EN 199114:2005 has been prepared by Technical Committee CEN/TC250 “Structural Eurocode”, the secretariat of which is held by BSI.
This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by October 2005, and conflicting national standards shall be withdrawn at the latest by March 2010.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard : Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
This European Standard supersedes ENV 199124: 1995.
CEN/TC 250 is responsible for all Structural Eurocodes.
In 1975, the Commission of the European Community decided on an action programme in the field of construction, based on article 95 of the Treaty. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications.
Within this action programme, the Commission took the initiative to establish a set of harmonised technical rules for the design of construction works which, in a first stage, would serve as an alternative to the national rules in force in the Member States and, ultimately, would replace them.
For fifteen years, the Commission, with the help of a Steering Committee with Representatives of Member States, conducted the development of the Eurocodes programme, which led to the first generation of European codes in the 1980s.
In 1989, the Commission and the Member States of the EU and EFTA decided, on the basis of an agreement^{1} between the Commission and CEN, to transfer the preparation and the publication of the Eurocodes to the CEN through a series of Mandates, in order to provide them with a future status of European Standard (EN). This links de facto the Eurocodes with the provisions of all the Council’s Directives and/or Commission’s Decisions dealing with European standards (e.g. the Council Directive 89/106/EEC on construction products  CPD  and Council Directives 93/37/EEC, 92/50/EEC and 89/440/EEC on public works and services and equivalent EFTA Directives initiated in pursuit of setting up the internal market).
The Structural Eurocode programme comprises the following standards generally consisting of a number of Parts :
EN 1990  Eurocode :  Basis of Structural Design 
EN 1991  Eurocode 1:  Actions on structures 
EN 1992  Eurocode 2:  Design of concrete structures 
EN 1993  Eurocode 3:  Design of steel structures 
^{1} Agreement between the Commission of the European Communities and the European Committee for Standardisation (CEN) concerning the work on EUROCODES for the design of building and civil engineering works (BC/CEN/03/89).
5EN 1994  Eurocode 4:  Design of composite steel and concrete structures 
EN 1995  Eurocode 5:  Design of timber structures 
EN 1996  Eurocode 6:  Design of masonry structures 
EN 1997  Eurocode 7:  Geotechnical design 
EN 1998  Eurocode 8:  Design of structures for earthquake resistance 
EN 1999  Eurocode 9:  Design of aluminium structures 
Eurocode standards recognise the responsibility of regulatory authorities in each Member State and have safeguarded their right to determine values related to regulatory safety matters at national level where these continue to vary from State to State.
The Member States of the EU and EFTA recognise that Eurocodes serve as reference documents for the following purposes :
The Eurocodes, as far as they concern the construction works themselves, have a direct relationship with the Interpretative Documents^{2} referred to in Article 12 of the CPD, although they are of a different nature from harmonised product standards^{3}. Therefore, technical aspects arising from the Eurocodes work need to be adequately considered by CEN Technical Committees and/or EOTA Working Groups working on product standards with a view to achieving full compatibility of these technical specifications with the Eurocodes.
The Eurocode standards provide common structural design rules for everyday use for the design of whole structures and component products of both a traditional and an innovative nature. Unusual forms of construction or design conditions are not specifically covered and additional expert consideration will be required by the designer in such cases.
^{2} According to Art. 3.3 of the CPD, the essential requirements (ERs) shall be given concrete form in interpretative documents for the creation of the necessary links between the essential requirements and the mandates for harmonised ENs and ETAGs/ETAs.
^{3} According to Art. 12 of the CPD the interpretative documents shall:
The Eurocodes, de facto, play a similar role in the field of the ER 1 and a part of ER 2.
6The National Standards implementing Eurocodes will comprise the full text of the Eurocode (including any annexes), as published by CEN, which may be preceded by a National title page and National foreword, and may be followed by a National annex.
The National annex may only contain information on those parameters which are left open in the Eurocode for national choice, known as Nationally Determined Parameters, to be used for the design of buildings and civil engineering works to be constructed in the country concerned, i.e. :
It may also contain
There is a need for consistency between the harmonised technical specifications for construction products and the technical rules for works^{4}. Furthermore, all the information accompanying the CE Marking of the construction products which refer to Eurocodes should clearly mention which Nationally Determined Parameters have been taken into account.
EN 199114 gives design guidance and actions for the structural design of buildings and civil engineering works for wind.
EN 199114 is intended for the use by clients, designers, contractors and relevant authorities.
EN 199114 is intended to be used with EN 1990, the other Parts of EN 1991 and EN 19921999 for the design of structures.
This standard gives alternative procedures, values and recommendations for classes with notes indicating where National choice may be made. Therefore the National Standard implementing EN 199114 should have a National Annex containing Nationally Determined Parameters to be used for the design of buildings and civil engineering works to be constructed in the relevant country.
National choice is allowed for EN 199114 through clauses:
1.5(2)
4.1 (1)
4.2 (1)P Note 2
4.2 (2)P Notes 1,2, 3 and 5
4.3.1 (1) Notes 1 and 2
4.3.2(1)
4.3.2 (2)
4.3.3 (1)
4.3.4(1)
4.3.5(1)
4.4(1) Note 2
4.5(1) Notes 1 and 2
^{4} see Art.3.3 and Art.12 of the CPD, as well as clauses 4.2, 4.3.1, 4.3.2 and 5.2 of ID 1.
75.3 (5)
6.1 (1)
6.3.1 (1) Note 3
6.3.2(1)
7.1.2 (2)
7.1.3 (1)
7.2.1 (1) Note 2
7.2.2 (1)
7.2.2 (2) Note 1
7.2.3 (2)
7.2.3 (4)
7.2.4 (1)
7.2.4 (3)
7.2.5(1)
7.2.5 (3)
7.2.6 (1)
7.2.6 (3)
7.2.7
7.2.8 (1)
7.2.9 (2)
7.2.10 (3) Notes 1 and 2
7.3 (6)
7.4.1 (1)
7.4.3 (2)
7.6 (1) Note 1
7.7 (1) Note 1
7.8(1)
7.9.2 (2)
7.10(1) Note 1
7.11 (1) Note 2
7.13(1)
7.13(2)
Table 7.14
8.1 (1) Notes 1 and 2
8.1 (4)
8.1 (5)
8.2 (1) Note 1
8.3 (1)
8.3.1 (2)
8.3.2 (1)
8.3.3 (1) Note 1
8.3.4 (1)
8.4.2 (1)
A.2 (1)
E.1.3.3 (1)
E.1.5.1 (1) Notes 1 and 2
E.1.5.1 (3)
E.1.5.2.6 (1) Note 1
E.1.5.3 (2) Note l
E.1.5.3 (4)
E.1.5.3 (6)
E.3 (2)
The following normative documents contain provisions which, through references in this text, constitute provisions of this European standard. For dated references, subsequent amendments to, or revisions of any of these publications do not apply. However, parties to agreements based on this European standard are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. For undated references the latest edition of the normative document referred to applies.
EN 1990  Eurocode:  Basis of structural design 
EN 199113  Eurocode 1:  Actions on structures: Part 13: Snow loads 
EN 199116  Eurocode 1:  Actions on structures: Part 16: Actions during execution 
EN 1991 2  Eurocode 1:  Actions on structures: Part 2: Traffic loads on bridges 
EN 199331  Eurocode 3:  Design of steel structures: Part 31: Masts and towers 
NOTE: The National Annex may give guidance on design assisted by testing and measurements.
For the purposes of this European Standard, the definitions given in ISO 2394, ISO 3898 and ISO 8930 and the following apply. Additionally for the purposes of this Standard a basic list of definitions is provided in EN 1990,1.5.
the 10 minute mean wind velocity with an annual risk of being exceeded of 0, 02, irrespective of wind direction, at a height of 10 m above flat open country terrain and accounting for altitude effects (if required)
the fundamental basic wind velocity modified to account for the direction of the wind being considered and the season (if required)
10the basic wind velocity modified to account for the effect of terrain roughness and orography
external pressure coefficients give the effect of the wind on the external surfaces of buildings; internal pressure coefficients give the effect of the wind on the internal surfaces of buildings.
The external pressure coefficients are divided into overall coefficients and local coefficients. Local coefficients give the pressure coefficients for loaded areas of 1 m^{2} or less e.g. for the design of small elements and fixings; overall coefficients give the pressure coefficients for loaded areas larger than 10 m^{2}.
Net pressure coefficients give the resulting effect of the wind on a structure, structural element or component per unit area.
force coefficients give the overall effect of the wind on a structure, structural element or component as a whole, including friction, if not specifically excluded
the background factor allowing for the lack of full correlation of the pressure on the structure surface
the resonance response factor allowing for turbulence in resonance with the vibration mode
NOTE The notation used is based on ISO 3898:1999. In this Part the symbol dot in expressions indicates the multiplication sign. This notation has been employed to avoid confusion with functional expressions.
Latin upper case letters
A  area 
A_{fr}  area swept by the wind 
A_{ref}  reference area 
B^{2}  background response part 
C  wind load factor for bridges 
E  Young’s modulus 
F_{fr}  resultant friction force 
F_{j}  vortex exciting force at point j of the structure 
F_{w}  resultant wind force 
H  height of a topographic feature 
I_{v}  turbulence intensity 
K  mode shape factor; shape parameter 
K_{a}  aerodynamic damping parameter 11 
K_{iv}  interference factor for vortex shedding 
K_{rd}  reduction factor for parapets 
K_{w}  correlation length factor 
K_{x}  non dimensional coefficient 
L  length of the span of a bridge deck; turbulent length scale 
L_{d}  actual length of a downwind slope 
L_{e}  effective length of an upwind slope 
L_{j}  correlation length 
L_{u}  actual length of an upwind slope 
N  number of cycles caused by vortex shedding 
N_{g}  number of loads for gust response 
R^{2}  resonant response part 
Re  Reynolds number 
R_{h}, R_{b}  aerodynamic admittance 
S  wind action 
Sc  Scruton number 
S_{L}  non dimensional power spectral density function 
St  Strouhal number 
W_{s}  weight of the structural parts contributing to the stiffness of a chimney 
W_{t}  total weight of a chimney 
Latin lower case letters
a_{G}  factor of galloping instability 
a_{IG}  combined stability parameter for interference galloping 
b  width of the structure (the length of the surface perpendicular to the wind direction if not otherwise specified) 
c_{alt}  altitude factor 
c_{d}  dynamic factor 
c_{dir}  directional factor 
c_{e}(Z)  exposure factor 
c_{f}  force coefficient 
c_{f,0}  force coefficient of structures or structural elements without freeend flow 
c_{f,I}  lift force coefficient 
c_{fr}  friction coefficient 
c_{Iat}  aerodynamic exciting coefficient 
c_{M}  moment coefficient 
c_{p}  pressure coefficient 
c_{pe}  external pressure coefficient 
c_{pi}  internal pressure coefficient 
c_{p,net}  net pressure coefficient 
C_{prob}  probability factor 
c_{r}  roughness factor 
c_{o}  orography factor 12 
c_{s}  size factor 
c_{season}  seasonal factor 
d  depth of the structure (the length of the surface parallel to the wind direction if not otherwise specified) 
e  eccentricity of a force or edge distance 
f_{L}  non dimensional frequency 
h  height of the structure 
h_{ave}  obstruction height 
h_{dis}  displacement height 
k  equivalent roughness 
k_{l}  turbulence factor 
k_{p}  peak factor 
k_{r}  terrain factor 
k_{Θ}  torsional stiffness 
I  length of a horizontal structure 
m  mass per unit length 
m_{1}  equivalent mass per unit length 
n_{i}  natural frequency of the structure of the mode i 
n_{1,x}  fundamental frequency of along wind vibration 
n_{1,y}  fundamental frequency of crosswind vibration 
n_{0}  ovalling frequency 
P  annual probability of exceedence 
q_{b}  reference mean (basic) velocity pressure 
q_{p}  peak velocity pressure 
r  radius 
s  factor; coordinate 
t  averaging time of the reference wind speed, plate thickness 
V_{CG}  onset wind velocity for galloping 
V_{CIG}  critical wind velocity for interference galloping 
V_{crit}  critical wind velocity of vortex shedding 
V_{div}  divergence wind velocity 
V_{m}  mean wind velocity 
V_{b,0}  fundamental value of the basic wind velocity 
v_{b}  basic wind velocity 
w  wind pressure 
X  horizontal distance of the site from the top of a crest 
xdirection  horizontal direction, perpendicular to the span 
ydirection  horizontal direction along the span 
Y_{max}  maximum crosswind amplitude at critical wind speed 
Z  height above ground 
Z_{ave}  average height 
zdirection  vertical direction 13 
z_{0}  roughness length 
z_{e}, Z_{i}  reference height for external wind action, internal pressure 
z_{g}  distance from the ground to the considered component 
z_{max}  maximum height 
z_{min}  minimum height 
z_{s}  reference height for determining the structural factor 
Greek upper case letters
Φ  upwind slope 
Φ_{1,X}  fundamental alongwind modal shape 
Greek lower case letters
α_{G}  galloping instability parameter 
α_{IG}  combined stability parameter of interference galloping 
δ  logarithmic decrement of damping 
δ_{a}  logarithmic decrement of aerodynamic damping 
δ_{d}  logarithmic decrement of damping due to special devices 
δ_{s}  logarithmic decrement of structural damping 
ε  coefficient 
ε_{0}  bandwidth factor 
ε_{1}  frequency factor 
η  variable 
φ  solidity ratio, blockage of canopy 
λ  slenderness ratio 
μ  opening ratio, permeability of a skin 
ν  upcrossing frequency; Poisson ratio; kinematic viscosity 
θ  torsional angle; wind direction 
ρ  air density 
σ_{v}  standard deviation of the turbulence 
σ_{a,x}  standard deviation of alongwind acceleration 
Ψ_{mc}  reduction factor for multibay canopies 
Ψ_{r}  reduction factor of force coefficient for square sections with rounded corners 
Ψ_{λ}  reduction factor of force coefficient for structural elements with endeffects 
Ψ_{λα}  endeffect factor for circular cylinders 
Ψ_{s}  shelter factor for walls and fences 
ξ  exponent of mode shape 
Indices
crit  critical 
e  external ; exposure 
fr  friction 
i  internal ; mode number 
j  current number of incremental area or point of a structure 
m  mean 
p  peak; parapet 
ref  reference 
v  wind velocity 
x  alongwind direction 
y  crosswind direction 
z  vertical direction 
NOTE See also EN 199113, EN 19912 and ISO 12494
NOTE See also EN 199116
NOTE See also EN 1990, 3.2 (2) (P)
NOTE The number of load cycles may be obtained from Annex B, C and E.
NOTE All coefficients or models, to derive wind actions from basic values, are chosen so that the probability of the calculated wind actions does not exceed the probability of these basic values.
The response of structures should be calculated according to Section 5 from the peak velocity pressure, q_{p}, at the reference height in the undisturbed wind field, the force and pressure coefficients and the structural factor c_{s}c_{d} (see Section 6). q_{p} depends on the wind climate, the terrain roughness and orography, and the reference height. q_{p} is equal to the mean velocity pressure plus a contribution from shortterm pressure fluctuations.
NOTE Simplified guidance on aeroelastic response is given in Annex E.
The mean wind velocity v_{m} should be determined from the basic wind velocity v_{b} which depends on the wind climate as described in 4.2, and the height variation of the wind determined from the terrain roughness and orography as described in 4.3. The peak velocity pressure is determined in 4.5.
The fluctuating component of the wind is represented by the turbulence intensity defined in 4.4.
NOTE The National Annex may provide National climatic information from which the mean wind velocity v_{m} the peak velocity pressure q_{p} and additional values may be directly obtained for the terrain categories considered.
NOTE 1  This terrain corresponds to terrain category II in Table 4.1. 
NOTE 2  The fundamental value of the basic wind velocity, v_{b,0}, may be given in the National Annex. 
v_{b} = C_{dir} · C_{season} · V_{b,0} (4.1)
where:
v_{b}  is the basic wind velocity, defined as a function of wind direction and time of year at 10 m above ground of terrain category II 
v_{b,0}  is the fundamental value of the basic wind velocity, see (1)P 
C_{dir}  is the directional factor, see Note 2. 
C_{season}  is the season factor, see Note 3. 
18NOTE 1 Where the influence of altitude on the basic wind velocity v_{b} is not included in the specified fundamental value v_{b,0} the National Annex may give a procedure to take it into account.
NOTE 2 The value of the directional factor, c_{dir}, for various wind directions may be found in the National Annex. The recommended value is 1,0.
NOTE 3 The value of the season factor, c_{season}, may be given in the National Annex. The recommended value is 1,0.
NOTE 4 The 10 minutes mean wind velocity having the probability p for an annual exceedence is determined by multiplying the basic wind velocity v_{b} in 4.2 (2)P by the probability factor, c_{prob} given by Expression (4.2). See also EN 199116.
where:
k  is the shape parameter depending on the coefficient of variation of the extremevalue distribution. 
n  is the exponent. 
NOTE 5 The values for K and n may be given in the National Annex. The recommended values are 0,2 for K and 0,5 for n.
NOTE See also EN 199116.
v_{m}(z) = c_{r}(z) · c_{o}(z) · v_{b} (4.3)
where:
c_{r}(z)  is the roughness factor, given in 4.3.2 
c_{o}(z)  is the orography factor, taken as 1,0 unless otherwise specified in 4.3.3 
NOTE 1 Information on c_{o} may be given in the National Annex. If the orography is accounted for in the basic wind velocity, the recommended value is 1,0.
NOTE 2 Design charts or tables for v_{m}(z) may be given in the National Annex.
The influence of neighbouring structures on the wind velocity should be considered (see 4.3.4).
the height above ground level
the ground roughness of the terrain upwind of the structure in the wind direction considered
19NOTE The procedure for determining c_{r}(z) may be given in the National Annex. The recommended procedure for the determination of the roughness factor at height z is given by Expression (4.4) and is based on a logarithmic velocity profile.
where:
z_{0}  is the roughness length 
k_{r}  terrain factor depending on the roughness length zo calculated using 
where:
Z_{o,II}  = 0,05 m (terrain category II, Table 4.1) 
Z_{min}  is the minimum height defined in Table 4.1 
Z_{max}  is to be taken as 200 m 
z_{0}, Z_{min} depend on the terrain category. Recommended values are given in Table 4.1 depending on five representative terrain categories.
Expression (4.4) is valid when the upstream distance with uniform terrain roughness is long enough to stabilise the profile sufficiently, see (2).
Terrain category  z_{0} m  z_{min} m  

0  Sea or coastal area exposed to the open sea  0,003  1 
I  Lakes or flat and horizontal area with negligible vegetation and without obstacles  0,01  1 
II  Area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights  0,05  2 
III  Area with regular cover of vegetation or buildings or with isolated obstacles with separations of maximum 20 obstacle heights (such as villages, suburban terrain, permanent forest)  0,3  5 
IV  Area in which at least 15 % of the surface is covered with buildings and their average height exceeds 15 m  1,0  10 
NOTE: The terrain categories are illustrated in A.1. 
Figure 4.1 —Assessment of terrain roughness
NOTE The National Annex may give definitions of the angular sector and of the upstream distance. The recommended value of the angular sector may be taken as the 30° angular sector within ±15° from the wind direction. The recommended value for the upstream distance may be obtained from A.2.
NOTE The procedure to be used for determining c_{o} may be given in the National Annex. The recommended procedure is given in A.3.
NOTE The National Annex may give a procedure to take account of this effect. A recommended conservative first approximation is given in A.4.
NOTE The National Annex may give a procedure. A recommended first approximation is given in A.5. In rough terrain closely spaced buildings modify the mean wind flow near the ground, as if the ground level was raised to a height called displacement height h_{dis}.
NOTE 1 The turbulent component of wind velocity has a mean value of 0 and a standard deviation σ_{v}. The standard deviation of the turbulence σ_{v} may be determined using Expression (4.6).
σ_{v} = K_{r} · V_{b} · k_{l} (4.6)
For the terrain factor k_{r} see Expression (4.5), for the basic wind velocity v_{b} see Expression (4.1) and for turbulence factor k_{l} see Note 2.
NOTE 2 The recommended rules for the determination of I_{v}(z) are given in Expression (4.7)
where:
k_{l} is the turbulence factor. The value of k_{l} may be given in the National Annex. The recommended value for k_{l} is 1,0. c_{0} is the orography factor as described in 4.3.3 z_{0} is the roughness length, given in Table 4.1
NOTE 1 The National Annex may give rules for the determination of q_{p}(z). The recommended rule is given in Expression (4.8).
where:
22
ρ is the air density, which depends on the altitude, temperature and barometric pressure to be expected in the region during wind storms c_{c}(z) is the exposure factor given in Expression (4.9) q_{b} is the basic velocity pressure given in Expression (4.10) NOTE 2 The values for ρ may be given in the National Annex. The recommended value is 1,25 kg/m .
NOTE 3 The value 7 in Expression (4.8) is based on a peak factor equal to 3,5 and is consistent with the values of the pressure and force coefficients in Section 7.
For flat terrain where c_{0}(z) = 1,0 (see 4.3.3), the exposure factor c_{e}(z) is illustrated in Figure 4.2 as a function of height above terrain and a function of terrain category as defined in Table 4.1.
Figure 4.2 — Illustrations of the exposure factor c_{e}(z) for c_{0} = 1,0, k_{l} = 1,0
NOTE A summary of calculation procedures for the determination of wind actions is given in Table 5.1.
Parameter  Subject Reference 

peak velocity pressure q_{p}  
basic wind velocity v_{b}  4.2 (2)P 
reference height z_{e}  Section 7 
terrain category  Table 4.1 
characteristic peak velocity pressure q_{p}  4.5(1) 
turbulence intensity I_{v}  4.4 
mean wind velocity v_{m}  4.3.1 
orography coefficient c_{0}(z)  4.3.3 
roughness coefficient c_{r}(z)  4.3.2 
Wind pressures, e.g. for cladding, fixings and structural parts  
external pressure coefficient c_{pe}  Section 7 
internal pressure coefficient c_{pi}  Section 7 
net pressure coefficient c_{P,net}  Section 7 
external wind pressure: w_{e} = q_{p} c_{pe}  5.2 (1) 
internal wind pressure: w_{i} = q_{p} c_{pi}  5.2 (2) 
Wind forces on structures, e.g. for overall wind effects  
structural factor: c_{s}c_{d}  6 
wind force F_{w} calculated from force coefficients  5.3 (2) 
wind force F_{w} calculated from pressure coefficients  5.3 (3) 
W_{e} = q_{p}(z_{e}) · C_{pe} (5.1)
where:
q_{p}(z_{e})  is the peak velocity pressure 
z_{e}  is the reference height for the external pressure given in Section 7 
C_{pe}  is the pressure coefficient for the external pressure, see Section 7. 
NOTE q_{p}(z) is defined in 4.5
W_{i} = q_{p}(z_{i}) · c_{pi} (5.2)
where:
q_{p}(Z_{i})  is the peak velocity pressure 
Z_{i}  is the reference height for the internal pressure given in Section 7 
c_{pi}  is the pressure coefficient for the internal pressure given in Section 7 
NOTE q_{p}(z) is defined in 4.5
Figure 5.1 — Pressure on surfaces
by calculating forces using force coefficients (see (2)) or
by calculating forces from surface pressures (see (3))
F_{w} = c_{s}c_{d} · c_{f} · q_{p}(z_{e}) · A_{ref} (5.3)
or by vectorial summation over the individual structural elements (as shown in 7.2.2) by using Expression (5.4)
25where:
c_{s}c_{d}  is the structural factor as defined in Section 6 
c_{f}  is the force coefficient for the structure or structural element, given in Section 7 or Section 8 
q_{p}(z_{e})  is the peak velocity pressure (defined in 4.5) at reference height z_{e} (defined in Section 7 or Section 8) 
A_{ref}  is the reference area of the structure or structural element, given in Section 7 or Section 8 
NOTE Section 7 gives C_{f} values for structures or structural elements such as prisms, cylinders, roofs, signboards, plates and lattice structures etc. These values include friction effects. Section 8 gives C_{f}, values for bridges.
external forces:
internal forces:
friction forces:
F_{fr} = C_{fr} · q_{p}(Z_{e}) · A_{fr} (5.7)
where:
c_{s}c_{d}  is the structural factor as defined in Section 6 
w_{e}  is the external pressure on the individual surface at height z_{e}, given in Expression (5.1) 
W_{i}  is the internal pressure on the individual surface at height z_{i}, given in Expression (5.2) 
A_{ref}  is the reference area of the individual surface 
c_{fr}  is the friction coefficient derived from 7.5 
A_{fr}  is the area of external surface parallel to the wind, given in 7.5. 
NOTE 1 For elements (e.g. walls, roofs), the wind force becomes equal to the difference between the external and internal resulting forces.
NOTE 2 Friction forces F_{fr} act in the direction of the wind components parallel to external surfaces.
NOTE The National Annex may determine whether this lack of correlation may be applied generally or be restricted to walls as applied in 7.2.2 (3). It is recommended to consider the lack of correlation only for walls (see 7.2.2 (3)).
NOTE The structural factor c_{s}c_{d} may be separated into a size factor c_{s} and a dynamic factor based on 6.3. Information on whether the structural factor c_{s}c_{d} should be separated or not may be given in the National Annex.
NOTE 1 Natural frequencies of facade and roof elements may be calculated using Annex F (glazing spans smaller than 3 m usually lead to natural frequencies greater than 5 Hz)
NOTE 2 The figures in Annex D give values of C_{s}C_{d} for various types of structures. The figures give envelopes of safe values calculated from models complying with the requirements in 6.3.1.
where:
z_{s}  is the reference height for determining the structural factor, see Figure 6.1. For structures where Figure 6.1 does not apply z_{s} may be set equal to h, the height of the structure. 
k_{p}  is the peak factor defined as the ratio of the maximum value of the fluctuating part of the response to its standard deviation28 
I_{v}  is the turbulence intensity defined in 4.4 
B^{2}  is the background factor, allowing for the lack of full correlation of the pressure on the structure surface 
R^{2}  is the resonance response factor, allowing for turbulence in resonance with the vibration mode 
NOTE 1 The size factor c_{s} takes into account the reduction effect on the wind action due to the nonsimultaneity of occurrence of the peak wind pressures on the surface and may be obtained from Expression (6.2):
NOTE 2 The dynamic factor c_{d} takes into account the increasing effect from vibrations due to turbulence in resonance with the structure and may be obtained from Expression (6.3):
NOTE 3 The procedure to be used to determine k_{p}, B and R may be given in the National Annex. A recommended procedure is given in Annex B. An alternative procedure is given in Annex C. As an indication to the users the differences in c_{s}C_{d} using Annex C compared to Annex B does not exceed approximately 5%.
NOTE The contribution to the response from the second or higher alongwind vibration modes is negligible.
Figure 6.1 — General shapes of structures covered by the design procedure. The structural dimensions and the reference height used are also shown.
NOTE The National Annex may give a method for determining the alongwind displacement and the standard deviation of the alongwind acceleration. The recommended method is given in Annex B. An alternative method is given in Annex C.
NOTE If none of the conditions in 6.3.3 (2) is fulfilled wind tunnel tests or specialist advice is recommended.
NOTE 1 External pressure coefficients give the effect of the wind on the external surfaces of buildings; internal pressure coefficients give the effect of the wind on the internal surfaces of buildings.
NOTE 2 The external pressure coefficients are divided into overall coefficients and local coefficients. Local coefficients give the pressure coefficients for loaded areas of 1 m^{2}. They may be used for the design of small elements and fixings. Overall coefficients give the pressure coefficients for loaded areas of 10 m^{2}. They may be used for loaded areas larger than 10 m^{2}.
NOTE Net pressure coefficients give the resulting effect of the wind on a structure, structural element or component per unit area.
A reduction factor depending on the effective slenderness of the structure may be applied, using 7.13.
NOTE Force coefficients give the overall effect of the wind on a structure, structural element or component as a whole, including friction, if not specifically excluded.
NOTE The National Annex may give procedures for other structures. The recommended procedures are:
Figure 7.1 — Pressure distribution used to take torsional effects into account. The zones and values for c_{pe} are given in Table 7.1 and Figure 7.5.
NOTE Further information may be given in the National Annex.
32
NOTE 1 Values for c_{pe,1} are intended for the design of small elements and fixings with an area per element of 1 m^{2} or less such as cladding elements and roofing elements. Values for c_{pe,10} may be used for the design of the overall load bearing structure of buildings.
NOTE 2 The National Annex may give a procedure for calculating external pressure coefficients for loaded areas above 1 m^{2} based on external pressure coefficients c_{pe,1}, and c_{pe,10}. The recommended procedure for loaded areas up to 10 m^{2} is given in Figure 7.2.
Figure 7.2 — Recommended procedure for determining the external pressure coefficient c_{pe} for buildings with a loaded area A between 1 m^{2} and 10 m^{2}
Figure 7.3 — Illustration of relevant pressures for protruding roofs
34NOTE The rules for the velocity pressure distribution for leeward wall and sidewalls (zones A, B, C and E, see Figure 7.5) may be given in the National Annex or be defined for the individual project. The recommended procedure is to take the reference height as the height of the building.
Figure 7.4 — Reference height, z_{e}, depending on h and b, and corresponding velocity pressure profile
Figure 7.5 — Key for vertical walls
36NOTE 1 The values of c_{pe,10} and C_{pe,1} may be given in the National Annex. The recommended values are given in Table 7.1, depending on the ratio h/d. For intermediate values of h/d, linear interpolation may be applied. The values of Table 7.1 also apply to walls of buildings with inclined roofs, such as duopitch and monopitch roofs.
Zone  A  B  C  D  E  

h/d  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1} 
5  1,2  −1,4  −0,8  “1,1  −0,5  +0,8  +1,0  −0,7  
1  −1,2  −1,4  −0,8  “1,1  −0,5  +0,8  +1,0  −0,5  
≤0,25  −1,2  −1,4  −0,8  −1,1  −0,5  +0,7  +1,0  −0,3 
NOTE 2 For buildings with h/d > 5, the total wind loading may be based on the provisions given in 7.6 to 7.8 and 7.9.2.
NOTE The lack of correlation of wind pressures between the windward and leeward side may be considered as follows. For buildings with h/d ≥ 5 the resulting force is multiplied by 1. For buildings with h/d ≤ 1, the resulting force is multiplied by 0,85. For intermediate values of h/d, linear interpolation may be applied.
NOTE The zones may be defined by the National Annex. The recommended zones are given in Figure 7.6.
NOTE 1 The pressure coefficients may be set by the National Annex. The recommended values are given in Table 7.2
NOTE 2 The resulting pressure coefficient on the parapet should be determined using 7.4.
Figure 7.6 — Key for flat roofs
38Roof type  Zone  

F  G  H  I  
C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  
Sharp eaves  –1,8  –2,5  –1,2  –2,0  –0,7  –1,2  +0,2  
–0,2  
With Parapets  h_{p}/h=0,025  –1,6  –2,2  –1,1  –1,8  –0,7  –1,2  +0,2  
–0,2  
h_{p}/h=0,05  –1,4  –2,0  –0,9  –1,6  –0,7  –1,2  +0,2  
–0,2  
h_{p}/h=0,10  –1,2  –1,8  –0,8  –1,4  –0,7  –1,2  +0,2  
–0,2  
Curved Eaves  r/h = 0,05  –1,0  –1,5  –1,2  –1,8  –0,4  +0,2  
–0,2  
r/h = 0,10  –0,7  –1,2  –0,8  –1,4  –0,3  +0,2  
–0,2  
r/h = 0,20  –0,5  –0,8  –0,5  –0,8  –0,3  +0,2  
–0,2  
Mansard Eaves  α = 30°  –1,0  –1,5  –1,0  –1,5  –0,3  +0,2  
–0,2  
α = 45°  –1,2  –1,8  –1,3  –1,9  –0,4  +0,2  
–0,2  
α = 60°  –1,3  –1,9  –1,3  –1,9  –0,5  +0,2  
–0,2  
NOTE 1 For roofs with parapets or curved eaves, linear interpolation may be used for intermediate values of h_{p}/h and r/h. NOTE 2 For roofs with mansard eaves, linear interpolation between α = 30°, 45° and α = 60° may be used. For α > 60° linear interpolation between the values for α = 60° and the values for flat roofs with sharp eaves may be used. NOTE 3 In Zone I, where positive and negative values are given, both values should be considered. NOTE 4 For the mansard eave itself, the external pressure coefficients are given in Table 7.4a “External pressure coefficients for duopitch roofs: wind direction 0° “, Zone F and G, depending on the pitch angle of the mansard eave. NOTE 5 For the curved eave itself, the external pressure coefficients are given by linear interpolation along the curve, between values on the wall and on the roof. NOTE 6 For mansard eaves with horizontal dimension less than e/10, the values for sharp eaves should be used. For the definition of e see Figure 7.6. 
NOTE The zones may be defined by the National Annex. The recommended zones are given in Figure 7.7.
NOTE The pressure coefficients may be set by the National Annex. The recommended values are given in Table 7.3a and Table 7.3b.
Figure 7.7 — Key for monopitch roofs
41Pitch Angle α  Zone for wind direction θ = 90°  Zone for wind direction θ = 180 °  

F  G  H  F  G  H  
C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  
5°  −1,7  −2,5  −1,2  −2,0  −0,6  −1,2  −2,3  −2,5  −1,3  −2,0  −0,8  −1,2 
+0,0  +0,0  +0,0  
15°  −0,9  −2,0  −0,8  −1,5  −0,3  −2,5  −2,8  −1,3  −2,0  −0,9  −1,2  
+0,2  +0,2  +0,2  
30°  −0,5  −1,5  −0,5  −1,5  −0,2  −1,1  −2,3  −0,8  −1,5  −0,8  
+0,7  +0,7  +0,4  
45°  −0,0  −0,0  −0,0  −0,6  −1,3  −0,5  −0,7  
+0,7  +0,7  +0,6  
60°  +0,7  +0,7  +0,7  −0,5  −1,0  −0,5  −0,5  
75°  +0,8  +0,8  +0,8  −0,5  −1,0  −0,5  −0,5 
Pitch Angle α  Zone for wind direction θ = 90°  

F_{UP}  F_{low}  G  H  1  
C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  
5°  −2,1  −2,6  −2,1  −2,4  −1,8  −2,0  −0,6  −1,2  −0,5  
15°  −2,4  −2,9  −1,6  −2,4  −1,9  −2,5  −0,8  −1,2  −0,7  −1,2 
30°  −2,1  −2,9  −1,3  −2,0  −1,5  −2,0  −1,0  −1,3  −0,8  −1,2 
45°  −1,5  −2,4  −1,3  −2,0  −1,4  −2,0  −1,0  −1,3  −0,9  −1,2 
60°  −1,2  −2,0  −1,2  −2,0  −1,2  −2,0  −1,0  −1,3  −0,7  −1,2 
75°  −1,2  −2,0  −1,2  −2,0  −1,2  −2,0  −1,0  −1,3  −0,5  
NOTE 1 At θ = 0° (see table a)) the pressure changes rapidly between positive and negative values around a pitch angle of α = +5° to +45°, so both positive and negative values are given. For those roofs, two cases should be considered: one with all positive values, and one with all negative values. No mixing of positive and negative values is allowed on the same face. NOTE 2 Linear interpolation for intermediate pitch angles may be used between values of the same sign. The values equal to 0.0 are given for interpolation purposes 
NOTE The zones may be defined by the National Annex. The recommended zones are given in Figure 7.8.
NOTE The pressure coefficients may be set by the National Annex. The recommended values are given in Table 7.4a and Table 7.4b.
Figure 7.8 — Key for duopitch roofs
44Pitch Angle α  Zone for wind direction θ = 0 °  

F  G  H  I  J  
C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  
−45°  −0,6  −0,6  −0,8  −0,7  −1,0  −1,5  
−30°  −1,1  −2,0  −0,8  −1,5  −0,8  −0,6  −0,8  −1,4  
−15°  −2,5  −2,8  −1,3  −2,0  −0,9  −1,2  −0,5  −0,7  −1,2  
−5°  −2,3  −2,5  −1,2  −2,0  −0,8  −1,2  +0,2  +0,2  
−0,6  −0,6  
5°  −1,7  −2,5  −1,2  −2,0  −0,6  −1,2  −0,6  +0,2  
+0,0  +0,0  +0,0  −0,6  
15°  −0,9  −2,0  −0,8  −1,5  −0,3  −0,4  −1,0  −1,5  
+0,2  +0,2  +0,2  +0,0  +0,0  +0,0  
30°  −0,5  −1,5  −0,5  −1,5  −0,2  −0,4  −0,5  
+0,7  +0,7  +0,4  +0,0  +0,0  
45°  −0,0  −0,0  −0,0  −0,2  −0,3  
+0,7  +0,7  +0,6  +0,0  +0,0  
60°  +0,7  +0,7  +0,7  −0,2  −0,3  
75°  +0,8  +0,8  +0,8  −0,2  −0,3  
NOTE 1 At θ = 0° the pressure changes rapidly between positive and negative values on the windward face around a pitch angle of α = −5° to +45°, so both positive and negative values are given. For those roofs, four cases should be considered where the largest or smallest values of all areas F, G and H are combined with the largest or smallest values in areas I and J. No mixing of positive and negative values is allowed on the same face. NOTE 2 Linear interpolation for intermediate pitch angles of the same sign may be used between values of the same sign. (Do not interpolate between α = +5° and α = −5°, but use the data for flat roofs in 7.2.3). The values equal to 0,0 are given for interpolation purposes 
Pitch Angle α  Zone for wind direction θ = 0 °  

F  G  H  I  
C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  
−45°  −1,4  −2,0  −1,2  −2,0  −1,0  −1,3  −0,9  −1,2  
−30°  −1,5  −2,1  −1,2  −2,0  −1,0  −1,3  −0,9  −1,2  
−15°  −1,9  −2,5  −1,2  −2,0  −0,8  −1,2  −0,8  −1,2  
−5°  −1,8  −2,5  −1,2  −2,0  −0,7  −1,2  −0,6  −1,2  
5°  −1,6  −2,2  −1,3  −2,0  −0,7  −1,2  −0,6  
15°  −1,3  −2,0  −1,3  −2,0  −0,6  −1,2  −0,5  
30°  −1,1  −1,5  −1,4  −2,0  −0,8  −1,2  −0,5  
45°  −1,1  −1,5  −1,4  −2,0  −0,9  −1,2  −0,5  
60°  −1,1  −1,5  −1,2  −2,0  −0,8  −1,0  −0,5  
75°  −1,1  −1,5  −1,2  −2,0  −0,8  −1,0  −0,5 
NOTE The zones may be defined by the National Annex. The recommended zones are given in Figure 7.9.
NOTE The pressure coefficients may be set by the National Annex. The recommended values are given in Table 7.5.
Figure 7.9 — Key for hipped roofs
47Pitch angle  Zone for wind direction θ = 0° and θ = 90°  

α_{0} for θ = 0°  F  G  H  I  J  K  L  M  N  
α_{90} for θ = 90°  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  C_{pe,10}  C_{pe,1}  
5°  −1,7  −2,5  −1,2  −2,0  −0,6  −1,2  −0,3  −0,6  −0,6  −1,2  −2,0  −0,6  −1,2  −0,4  
+0,0  +0,0  +0,0  
15°  −0,9  −2,0  −0,8  −1,5  −0,3  −0,5  −1,0  −1,5  −1,2  −2,0  −1,4  −2,0  −0,6  −1,2  −0,3  
+0,2  +0,2  +0,2  
30°  −0,5  −1,5  −0,5  −1,5  −0,2  −0,4  −0,7  −1,2  −0,5  −1,4  −2,0  −0,8  −1,2  −0,2  
+0,5  +0,7  +0,4  
45°  −0,0  −0,0  −0,0  −0,3  −0,6  −0,3  −1,3  −2,0  −0,8  −1,2  −0,2  
+0,7  +0,7  +0,6  
60°  +0,7  +0,7  +0,7  −0,3  −0,6  −0,3  −1,2  −2,0  −0,4  −0,2  
75°  +0,8  +0,8  +0,8  −0,3  −0,6  −0,3  −1,2  −2,0  −0,4  −0,2  
NOTE 1 At θ = 0° the pressures changes rapidly between positive and negative values on the windward face at pitch angle of α = +5° to +45°, so both positive and negative values are given. For those roofs, two cases should be considered: one with all positive values, and one with all negative values. No mixing of positive and negative values are allowed. NOTE 2 Linear interpolation for intermediate pitch angles of the same sign may be used between values of the same sign. The values equal to 0,0 are given for interpolation purposes NOTE 3 The pitch angle of the windward face always will govern the pressure coefficients. 
Modifying factors for the pressures (local and global) for wind directions 0° and 180° on each span should be derived:
0,05 · q_{p,ze} · A_{Shed}  
where  A_{Shed} is the bae area of each multispan roof. 
Figure 7.10 — Key to multispan roofs
49NOTE The values of c_{pe,10} and c_{pe,1} to be used for circular cylindrical roofs and domes may be given in the National Annex. The recommended values of c_{pe,10} are given in Figures 7.11 and 7.12 for different zones. The reference height should be taken as z_{e} = h + f.
Figure 7.11 — Recommended values of external pressure coefficients c_{pe,10} for vaulted roofs with rectangular base
50Figure 7.12 — Recommended values of external pressure coefficients c_{pe,10} for domes with circular base
51NOTE The openings of a building include small openings such as: open windows, ventilators, chimneys, etc. as well as background permeability such as air leakage around doors, windows, services and through the building envelope. The background permeability is typically in the range 0,01% to 0, 1% of the face area. Additional information may be given in a National Annex.
NOTE Checking of the accidental design situation is important for tall internal walls (with high risk of hazard) when the wall has to carry the full external wind action because of openings in the building envelope.
NOTE This can also be applied to individual internal volumes within the building.
When the area of the openings at the dominant face is twice the area of the openings in the remaining faces,
C_{pi} = 0,75 · C_{pe} (7.1)
When the area of the openings at the dominant face is at least 3 times the area of the openings in the remaining faces,
C_{pi} = 0,90 · C_{pe} (7.2)
where C_{pe} is the value for the external pressure coefficient at the openings in the dominant face. When these openings are located in zones with different values of external pressures an area weighted average value of C_{pe} should be used.
When the area of the openings at the dominant face is between 2 and 3 times the area of the openings in the remaining faces linear interpolation for calculating C_{pi} may be used.
Figure 7.13 — Internal pressure coefficients for uniformly distributed openings
52NOTE 1 This applies to façades and roof of buildings with and without internal partitions.
NOTE 2 Where it is not possible, or not considered justified, to estimate μ for a particular case then C_{pi} should be taken as the more onerous of +0,2 and −0,3.
C_{pi} = −0,60 (7.4)
The internal pressure coefficient of vented tanks with small openings should be based on Expression (7.5):
C_{pi} = −0,40 (7.5)
The reference height z_{i} is equal to the height of the structure.
NOTE 1 The National Annex may give values for the wind effects on external walls and roofs with more than one skin. As a first approximation it is recommended that the wind pressure on the most rigid skin may be taken as the difference between the internal and the external pressures.
NOTE 2 The National Annex may give rules for cases where the extremities of the layer between the skins are air tight (Figure 7.14(a)) and where the free distance between the skins is less than 100 mm (the thermal insulation material being included in one skin, when there is no airflow within the insulation). As a first approximation the following recommended rules may be applied:
If entries of air put the layer of air into communication with faces of the building other than the face on which the wall is situated (Figure 7.14(b)), these rules are not applicable.
Figure 7.14 — Corner details for external walls with more than one skin.
NOTE: φ = 0 represents an empty canopy, and φ = 1 represents the canopy fully blocked with contents to the down wind eaves only (this is not a closed building).
NOTE The location may be given in the National Annex. The recommended location is in Figure 7.16.
For canopies with double skins, the impermeable skin and its fixings should be calculated with C_{p,net} and the permeable skin and its fixings with 1/3 C_{p,net}.
Figure 7.15 — Airflow over canopy roofs
55Roof angle α  Blockage φ  Overall Force Coefficients C_{f}  Zone A  Zone B  Zone C 

0°  Maximum all φ Maximum φ = 0 Maximum φ = 1 
+ 0,2 − 0,5 − 1,3 
+ 0,5 − 0,6 − 1,5 
+ 1,8 − 1,3 − 1,8 
+ 1,1 − 1,4 − 2,2 
5°  Maximum all φ Maximum φ = 0 Maximum φ = 1 
+ 0,4 − 0,7 − 1,4 
− 0,8 − 1,1 − 1,6 
+ 2,1 − 1,7 − 2,2 
− 1,3 − 1,8 − 2,5 
10°  Maximum all φ Maximum φ = 0 Maximum φ = 1 
+ 0,5 − 0,9 − 1,4 
+ 1,2 − 1,5 − 1,6 
+ 2,4 − 2,0 − 2,6 
+ 1,6 − 2,1 − 2,7 
15°  Maximum all φ Maximum φ = 0 Maximum φ = 1 
+ 0,7 − 1,1 − 1,4 
+ 1,4 − 1,8 − 1,6 
+ 2,7 − 2,4 − 2,9 
+ 1,8 − 2,5 − 3,0 
20°  Maximum all φ Maximum φ = 0 Maximum φ = 1 
+ 0,8 − 1,3 − 1,4 
+ 1,7 − 2,2 − 1,6 
+ 2,9 − 2,8 − 2,9 
+ 2,1 − 2,9 − 3,0 
25°  Maximum all φ Maximum φ = 0 Maximum φ = 1 
+ 1,0 − 1,6 − 1,4 
+ 2,0 − 2,6 − 1,5 
+ 3,1 − 3,2 − 2,5 
+ 2,3 − 3,2 − 2,8 
30°  Maximum all φ Maximum φ = 0 Maximum φ = 1 
+ 1,2 − 1,8 − 1,4 
+ 2,2 − 3,0 − 1,5 
+ 3,2 − 3,8 − 2,2 
+ 2,4 − 3,6 − 2,7 
NOTE + values indicate a net downward acting wind action − values represent a net upward acting wind action 
Figure 7.16 — Location of the centre of force for monopitch canopies
57Roof angle α [°]  Blockage φ  Overall Force Coefficients C_{f}  Zone A  Zone B  Zone C  Zone D 

− 20  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,7 − 0,7 − 1,3 
+ 0,8 − 0,9 − 1,5 
+ 1,6 − 1,3 − 2,4 
+ 0,6 − 1,6 − 2,4 
+ 1,7 − 0,6 − 0,6 
− 15  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,5 − 0,6 − 1,4 
+ 0,6 − 0,8 − 1.6 
+ 1,5 − 1,3 − 2,7 
+ 0,7 − 1,6 − 2,6 
+ 1,4 − 0,6 − 0,6 
−10  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,4 − 0,6 − 1,4 
+ 0,6 − 0,8 − 1,6 
+ 1,4 − 1,3 − 2,7 
+ 0,8 − 1,5 − 2,6 
+ 1,1 − 0,6 − 0,6 
− 5  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,3 − 0,5 − 1,3 
+ 0,5 − 0,7 − 1,5 
+ 1,5 − 1,3 − 2,4 
+ 0,8 − 1,6 − 2,4 
+ 0,8 − 0,6 − 0,6 
− 5  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,3 − 0,6 − 1,3 
+ 0,6 − 0,6 − 1,3 
+ 1,8 − 1,4 − 2,0 
+ 1,3 − 1,4 − 1,8 
+ 0,4 − 1,1 − 1,5 
+ 10  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,4 − 0,7 − 1,3 
+ 0,7 − 0,7 − 1,3 
+ 1,8 − 1,5 − 2,0 
+ 1,4 − 1,4 − 1,8 
+ 0,4 − 1,4 − 1,8 
+15  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,4 − 0,8 − 1,3 
+ 0,9 − 0,9 − 1,3 
+ 1,9 − 1,7 − 2,2 
+ 1,4 − 1,4 − 1,6 
+ 0,4 − 1,8 − 2,1 
+ 20  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,6 − 0,9 − 1,3 
+ 1,1 − 1,2 − 1,4 
+ 1,9 − 1,8 − 2,2 
+ 1,5 − 1,4 − 1,6 
+ 0,4 − 2,0 − 2,1 58 
+25  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,7 − 1,0 − 1,3 
+ 1,2 − 1,4 − 1,4 
+ 1,9 − 1,9 − 2,0 
+ 1,6 − 1,4 − 1,5 
+ 0,5 − 2,0 − 2,0 
+ 30  Maximum all φ Minimum φ = 0 Minimum φ = 1 
+ 0,9 − 1,0 − 1,3 
+ 1,3 − 1,4 − 1,4 
+ 1,9 − 1,9 − 1,8 
+ 1,6 − 1,4 − 1,4 
+ 0,7 − 2,0 − 2,0 
NOTE + values indicate a net downward acting wind action − values represent a net upward acting wind action 
Figure 7.17 — Arrangements of loads obtained from force coefficients for duopitch canopies
Bay  Location  ψ_{mc} factors for all φ  

on maximum (downward) force and pressure coefficients  on minimum (upward) force and pressure coefficients  
1  End bay  1,0  0,8 
2  second bay  0,9  0,7 
3  third and subsequent bays  0,7  0,7 
Figure 7.18 — Multibay canopies
NOTE For parapets and noise barriers of bridges see Section 8.
NOTE Values of the resulting pressure coefficients c_{p,net} for freestanding walls and parapets may be given in the National Annex. Recommended values are given in Table 7.9 for two different solidity ratio, see 7.4 (1). These recommended values correspond to a direction of oblique wind compared to the wall without return corner (see Figure 7.19) and, in the case of the wall with return corner, to the two opposite directions indicated in Figure 7.19. The reference area in both cases is the gross area. Linear interpolation may be used for solidity ratio between 0,8 and 1.
Solidity  Zone  A  B  C  D  

φ = 1  Without return corners  ℓ/h ≤ 3  2,3  1,4  1,2  1,2 
ℓ/h = 5  2,9  1,8  1,4  1,2  
ℓ/h ≥ 10  3,4  2,1  1,7  1,2  
with return corners of length ≥ h ^{a}  2,1  1,8  1,4  1,2  
φ = 0,8  1,2  1,2  1,2  1,2  
^{a} Linear interpolation may be used for return corner lengths between 0,0 and h 
Figure 7.19 — Key to zones of freestanding walls and parapets
62The resulting net pressure coefficient on the sheltered wall, c_{p,net,s,} is given by Expression (7.6):
c_{p,net,s} = ψ_{s} · c_{p,net} (7.6)
Figure 7.20 — Shelter factor ψ_{s} for walls and fences for φvalues between 0,8 and 1,0
c_{f} = 1,80 (7.7)
Expression (7.7) is also applicable where z_{g} is less than h/4 and b/h ≤ 1.
NOTE The value of the horizontal eccentricity e may be given in the National Annex. The recommended value is
e = ± 0,25b (7.8)
Figure 7.21 — Key for signboards
Divergence or stall flutter instabilities should be checked.
Surface  Friction coefficient c_{fr} 

Smooth (i.e. steel, smooth concrete) 
0,01 
Rough (i.e. rough concrete, tarboards) 
0,02 
very rough (i.e. ripples, ribs, folds) 
0,04 
Figure 7.22 — Reference area for friction
c_{f} = c_{f,0} · ψ_{r} · ψ_{λ} (7.9)
where:
c_{f,0}  is the force coefficient of rectangular sections with sharp corners and without freeend flow as given by Figure 7.23. 
ψ_{r}  is the reduction factor for square sections with rounded corners. ψ_{r} depends on Reynolds number, see Note 1. 
ψ_{λ}  is the endeffect factor for elements with freeend flow as defined in 7.13. 
Figure 7.23 — Force coefficients c_{f,0} of rectangular sections with sharp corners and without free end flow
NOTE 1 The values of ψ_{r} may be given in the National Annex. Recommended approximate upper bound values of ψ_{r} are given in Figure 7.24. Figure 7.24 are obtained under lowturbulent conditions. These coefficients are assumed to be safe.
NOTE 2 Figure 7.24 may also be used for buildings with h/d > 5.0
Figure 7.24 — Reduction factor ψ_{r} for a square crosssection with rounded corners
A_{ref} = ℓ · b (7.10)
where:
ℓ is the length of the structural element being considered.
66The reference height z_{e} is equal to the maximum height above ground of the section being considered.
c_{f} = c_{f,0} · ψ_{λ} (7.11)
ψ_{λ} is the endeffect factor (see 7.13)
Figure 7.25 — Sharp edged structural sections
NOTE 1 The National Annex may specify c_{f,0}. For all elements without freeend flow the recommended value is 2,0. This value is based on measurements under lowturbulent conditions. It is assumed to be a safe value.
NOTE 2 Expression (7.11) and Figure 7.25 may also be used for buildings with h/d > 5,0
in x  direction :  A_{ref,x} = ℓ · b  (7.12) 
in y  direction :  A_{ref,y} = ℓ · b 
where:
ℓ is the length of the structural element being considered.
c_{f} = c_{f,0} · ψ_{λ} (7.13)
where:
ψ_{λ}  is the endeffect factor as defined in 7.13. 
c_{f,0}  is the force coefficient of structural elements without freeend flow. 
NOTE The values of c_{f,0} may be given in the National Annex. Recommended conservative values based on measurements under lowturbulent conditions are given in Table 7.11.
Number of sides 
Sections  Finish of surface and of corners  Reynolds number Re^{(a)}  C_{f,0} 

5  Pentagon  all  All  1,80 
6  Hexagon  all  All  1,60 
8  Octagon  surface smooth ^{(b)} r/b < 0,075  Re ≤ 2,4 · 10^{5}  1,45 
Re ≥3 · 10^{5}  1,30  
surface smooth ^{(b)} r/b ≥ 0,075  Re ≤ 2 · 10^{5}  1,30  
Re ≥ 7 · 10^{5}  1,10  
10  Decagon  all  All  1,30 
12  Dodecagon  surface smooth ^{(c)} corners rounded  2 · 10^{5} < Re < 1,2 · 10^{6}  0,90 
all others  Re < 4 · 10^{5}  1,30  
Re > 4 · 10^{5}  1,10  
1618  Hexdecagon to Octadecagon  surface smooth ^{(c)} corners rounded  Re < 2 · 10^{5}  treat as a circular cylinder, see (7.9) 
2 · 10^{5}≤ Re < 1,210^{6}  0,70  
^{(a)} Reynolds number with v = v_{m} and v_{m} given in 4.3, Re, is defined in 7.9 ^{(b)} r = corner radius, b = diameter of circumscribed circumference, see Figure 7.26 ^{(c)} From wind tunnel tests on sectional models with galvanised steel surface and a section with b = 0,3 m and corner radius of 0,06 b 
NOTE See also Table 7.11 and Figure 7.26.
Figure 7.26 — Regular polygonal section
68A_{ref} = ℓ · b (7.14)
where:
ℓ  is the length of the structural element being considered. 
b  is the diameter of circumscribed circumference, see Figure 7.26. 
where:
b  is the diameter 
v  is the kinematic viscosity of the air (v = 15 · 10 ^{6} m^{2}/s) 
v(z_{e})  is the peak wind velocity defined in Note 2 of Figure 7.27at height z_{e} 
c_{pe} = c_{p,0} · ψ_{λα} (7.16)
where:
c_{p,0}  is the external pressure coefficient without freeend flow (see (3)) 
ψ_{λα}  is the endeffect factor (see (4)) 
where:
α_{A}  is the position of the flow separation (see Figure 7.27) 69 
ψ_{λ}  is the endeffect factor (see 7.13) 
Figure 7.27 —Pressure distribution for circular cylinders for different Reynolds number ranges and without endeffects
70Re  α_{min}  c_{p0,min}  α_{A}  c_{p0,h} 

5·10^{5}  85  −2,2  135  −0,4 
2·10^{6}  80  −1,9  120  −0,7 
10_{7}  75  −1,5  105  −0,8 
where: α_{min} is the position of the minimum pressure in [°] c_{p0,min} is the value of the minimum pressure coefficient α_{A} is the position of the flow separation in [°] c_{p0,h} is the base pressure coefficient 
A_{ref} = ℓ · b (7.18)
c_{f} = c_{f,0} · ψ_{λ} (7.19)
where:
c_{f,0}  is the force coefficient of cylinders without freeend flow (see Figure 7.28) 
ψ_{λ}  is the endeffect factor (see 7.13) 
Figure 7.28 — Force coefficient c_{f,0} for circular cylinders without freeend flow and for different equivalent roughness k/b
NOTE 1 Figure 7.28 may also be used for building with h/d > 5.0
NOTE 2 Figure 7.28 is based on the Reynolds number with and q_{p} given in 4.5
NOTE For aged surfaces the values of the equivalent surface roughness k may be given in the National Annex.
Type of surface  Equivalent roughness k mm  Type of surface  Equivalent roughness k mm 

glass  0,0015  smooth concrete  0,2 
polished metal  0,002  planed wood  0,5 
fine paint  0,006  rough concrete  1,0 
spray paint  0,02  rough sawn wood  2,0 
bright steel  0,05  rust  2,0 
cast iron  0,2  brickwork  3,0 
galvanised steel  0,2 
A_{ref} = ℓ · b (7.20)
where:
ℓ  is the length of the structural element being considered. 
Figure 7.29 — Cylinder near a plane surface
For vertical circular cylinders in a row arrangement, the force coefficient c_{f,0} depends on the wind direction related to the row axis and the ratio of distance a and the diameter b as defined in Table 7.14. The force coefficient, c_{f,} for each cylinder may be obtained by Expression (7.21):
c_{f} = c_{f,0} · ψ_{λ} · k (7.21)
where:
c_{f,0}  is the force coefficient of cylinders without freeend flow, (see 7.9.2) 
ψ_{λ}  is the endeffect factor (see 7.13) 
k  is the factor given in Table 7.14 (for the most unfavourable wind direction) 
a/b  k  
2,5 < a/b < 3,5  1,15  
3,5 < a/b < 30  
a/b > 30  1,00  
a: distance b: diameter NOTE For a/b < 2,5 the values of k may be given in the National Annex 
74NOTE 1 The values of c_{f,x} may be given in the National Annex. Recommended values based on measurements in low turbulent flow are given in Figure 7.30. Figure 7.30 is based on the Reynolds number with and q_{p} given in 4.5
NOTE 2 The values in Figure 7.30 are limited to values z_{g} > b/2, where z_{g} is the distance of the sphere from a plain surface, b is the diameter (see Figure 7.31). For z_{g} < b/2 the force coefficient c_{f,x} is be multiplied by the factor 1,6.
Figure 7.30 — Alongwind force coefficient of a sphere
Figure 7.31 — Sphere near a plain surface
75c_{f} = c_{f,0} · Ψ_{λ} (7.25)
where:
c_{f,0}  is the force coefficient of lattice structures and scaffoldings without endeffects. It is given by Figures 7.33 to 7.35 as a function of solidity ratio φ (7.11 (2)) and Reynolds number Re. 
Re  is the Reynolds number using the average member diameter b_{i} see Note 1 
Ψ_{λ}  is the endeffect factor (see 7.13) as a function of the slenderness of the structure, λ, calculated with ℓ and width b = d, see Figure 7.32. 
NOTE 1 Figure 7.35 is based on the Reynolds number with and q_{p} given in 4.5.
NOTE 2 The National Annex may give a reduction factor for scaffolding without air tightness devices and affected by solid building obstruction. A recommended value is given in EN 12811.
Figure 7.32 — Lattice structure or scaffolding
Figure 7.33 — Force coefficient c_{f},_{0} for a plane lattice structure with angle members as a function of solidity ratio φ
76Figure 7.34 —Force coefficient c_{f,0} for a spatial lattice structure with angle members as a function of solidity ratio φ
Figure 7.35 — Force coefficient c_{f,0} for plane and spatial lattice structure with members of circular crosssection
77where:
A  is the sum of the projected area of the members and gusset plates of the face projected normal to the face: 
A_{c}  is the the area enclosed by the boundaries of the face projected normal to the face = d ℓ 
ℓ  is the length of the lattice 
d  is the width of the lattice 
b_{i}, ℓ_{i}  is the width and length of the individual member i (see Figure 7.32), projected normal to the face 
A_{gk}  is the area of the gusset plate k 
A_{ref} = A (7.27)
Flags  A_{ref}  c_{f}  

h · ℓ  1,8  
h · ℓ
0,5 · h · ℓ 

where:
NOTE The equation for free flags includes dynamic forces from the flag flutter effect 
NOTE The force coefficients, c_{f,0}, given in 7.6 to 7.12 are based on measurements on structures without freeend flow away from the ground. The endeffect factor takes into account the reduced resistance of the structure due to the wind flow around the end (endeffect). Figure 7.36 and Table 7.16 are based on measurements in low turbulent flow. Values, taking the effect of turbulence into account may be specified in the National Annex.
NOTE The National Annex may give values for λ and Ψ_{λ}. Recommended values for λ are given in Table 7.16 and indicative values for Ψ_{λ} are given in Figure 7.36 for different solidity ratio φ.
No.  Position of the structure, wind normal to the plane of the page 
Effective slenderness λ 

1  For polygonal, rectangular and sharp edged sections and lattice structures: for ℓ ≥ 50 m,λ =1,4 ℓ/b or λ= 70, whichever is smaller for ℓ <15 m,λ=2 ℓ/b or λ= 70, whichever is smaller For circular cylinders: for ℓ ≥ 50, λ =0,7 ℓ/b or λ =70, whichever is smaller for ℓ <15 m, λ=ℓ/b or λ=70, whichever is smaller For intermediate values of ℓ, linear interpolation should be used 

2  
3  
4  for ℓ ≥ 50 m, λ =0,7 ℓ/b or λ = 70, whichever is larger for ℓ <15 m, λ=ℓ/b or ℓ= 70, whichever is larger For intermediate values of ℓ, linear interpolation should be used 
Figure 7.36 — Indicative values of the endeffect factor Ψ_{λ} as a function of solidity ratio φ versus slenderness λ
where:
A  is the sum of the projected areas of the members 
A_{c}  is the overall envelope area A_{c} = ℓ · b 
Figure 7.37 — Definition of solidity ratio φ
8182NOTE 1 Wind actions for other types of bridges (e.g. arch bridges, bridges with suspension cables or cable stayed, roofed bridges, moving bridges and bridges with multiple or significantly curved decks) may be defined in the National Annex.
NOTE 2 The angle of the wind direction to the deck axis in the vertical and horisontal planes may be defined in the National Annex.
Figure 8.1  Crosssections of normal construction decks
where:
xdirection  is the direction parallel to the deck width, perpendicular to the span 
ydirection  is the direction along the span 
zdirection  is the direction perpendicular to the deck 
The forces produced in the x and ydirections are due to wind blowing in different directions and normally are not simultaneous. The forces produced in the zdirection can result from the wind blowing in a wide range of directions; if they are unfavourable and significant, they should be taken into account as simultaneous with the forces produced in any other direction.
NOTE The notation used for bridges differs from that in 1.7. The following notations (see Figure 8.2) are used for bridges:
L length in ydirection b width in xdirection d depth in zdirection The values to be given to L, b and d in various cases are, where relevant, more precisely defined in various clauses. When Sections 5 to 7 are referred to, the notations for b and d need to be readjusted.
Figure 8.2 — Directions of wind actions on bridges
NOTE The National Annex may give a value for . The recommended value is 23 m/s.
NOTE The value of may be defined in the National Annex. The recommended value of is 25 m/s.
NOTE 1 The National Annex may give criteria and procedures.
NOTE 2 If a dynamic response procedure is not needed, c_{s}c_{d} may be taken equal to 1,0.
NOTE 3 For normal road and railway bridge decks of less than 40 m span a dynamic response procedure is generally not needed. For the purpose of this categorization, normal bridges may be considered to include bridges constructed in steel, concrete, aluminium or timber, including composite construction, and whose shape of cross sections is generally covered by Figure 8.1.
NOTE The National Annex may give force coefficients for parapets and gantries on bridges. It is recommended to use 7.4.
c_{f,x} = c_{fx,0} (8.1)
where:
c_{fx,0}  is the force coefficient without freeend flow (see 7.13). 
NOTE 1 A bridge has usually no freeend flow because the flow is deviated only along two sides (over and under the bridge deck).
NOTE 2 For normal bridges c_{fx,0} may be taken equal to 1,3. Alternatively, c_{fx,0} may be taken from Figure 8.3 , where some typical cases for determining A_{ref,x} (as defined in 8.3.1(4)) and d_{tot} are shown .
85Figure 8.3 — Force coefficient for bridges, c_{fx,0}
NOTE 3 Where the angle of inclination of the wind exceeds 10°, the drag coefficient may be derived from special studies. This angle of inclination may be due to the slope of the terrain in the oncoming wind direction.
NOTE 4 Where two generally similar decks are at the same level and separated transversely by a gap not significantly exceeding 1 m , the wind force on the windward structure may be calculated as if it were a single structure. In other cases special consideration may have to be given to windstructure interaction.
Figure 8.4 — Bridge with inclined windward face
86NOTE This reduction is not applicable to F_{w}, defined in 8.3.2, unless otherwise specified in the National Annex.
However, the total reference area should not exceed that obtained from considering an equivalent plain (web) beam of the same overall depth, including all projecting parts.
Figure 8.5 — Depth to be used for A_{ref,x}
87Road restraint system  on one side  on both sides 

Open parapet or open safety barrier  d + 0,3 m  d + 0,6 m 
Solid parapet or solid safety barrier  d + d_{1}  d + 2d_{1} 
Open parapet and open safety barrier  d + 0,6 m  d + 1,2 m 
where :
v_{b}  is the basic wind speed (see 4.2 (2)) 
C  is the wind load factor. C = c_{e} · c_{f,x}, where c_{e} is the exposure factor given in 4.5 and c_{f,x} is given in 8.3.1(1) 
A_{ref,x}  is the reference area given in 8.3.1 
ρ  is the density of air (see 4.5) 
88NOTE Cvalues may be defined in the National Annex. Recommended values are given in Table 8.2.
b/d_{tot}  z_{e} ≤ 20 m  z_{e} = 50 m 

≤0,5  6,7  8,3 
≥4,0  3,6  4,5 
This table is based on the following assumptions :
For intermediate values of b/d_{tot}, and of z_{e} linear interpolation may be used 
89NOTE 1 The National Annex may give values for c_{f,z}. In the absence of wind tunnel tests the recommended value may be taken equal to ±0,9. This value takes globally into account the influence of a possible transverse slope of the deck, of the slope of terrain and of fluctuations of the angle of the wind direction with the deck due to turbulence.
As an alternative c_{f,z} may be taken from Figure 8.6. In using it:
the depth d_{tot} may be limited to the depth of the deck structure, disregarding the traffic and any bridge equipment
for flat, horizontal terrain the angle α of the wind with the horizontal may be taken as ± 5° due to turbulence. This is also valid for hilly terrain when the bridge deck is at least 30 m above ground.
NOTE 2 This force may have significant effects only if the force is of the same order as the dead load.
Figure 8.6 — Force coefficient c_{f,z} for bridges with transversal slope and wind inclination
A_{ref,z} = b · L (8.3)
NOTE The National Annex may give the values. The recommended values are:
NOTE Execution transient situations are usually more critical for piers and for some types of decks subject to particular execution methods than the persistent ones. For characteristic values during transient design situations see EN 199116. For scaffoldings, see 7.11.
NOTE 1 Simplified rules may be given in the National Annex.
NOTE 2 The National Annex may give procedures for the treatment of asymmetric loading. The recommended procedure is to completely remove the design wind load from those parts of the structure where its action will produce a beneficial effect (see 7.1.2 (1)).
(informative)
Terrain category 0 Sea, coastal area exposed to the open sea 

Terrain category I Lakes or area with negligible vegetation and without obstacles 

Terrain category II Area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights 

Terrain category III Area with regular cover of vegetation or buildings or with isolated obstacles with separations of maximum 20 obstacle heights (such as villages, suburban terrain, permanent forest) 

Terrain category IV Area in which at least 15% of the surface is covered with buildings and their average height exceeds 15 m 
NOTE The procedure to be used may be given in the National Annex. Two recommended procedures, Procedure 1 and Procedure 2, are given below.
Procedure 1
If the structure is situated near a change of terrain roughness at a distance:
 – less than 2 km from the smoother category 0
 – less than 1 km from the smoother categories I to III
the smoother terrain category in the upwind direction should be used.
Small areas (less than 10% of the area under consideration) with deviating roughness may be ignored.
Procedure 2
 Determine the roughness categories for the upstream terrain in the angular sectors to be considered.
 For every angular sector, determine the distance x from the building to the upstream roughness changes
 If the distance x from the building to a terrain with lower roughness length is smaller than the values given in Table A.1, then the lower value for the roughness length should be used for the angular sector considered. If this distance x is larger than the value in Table A.1, the higher value for the roughness length should be used.
Small areas (less than 10% of the area under consideration) with deviating roughness may be ignored.
Where no distance x is given in Table A.1 or for heights exceeding 50 m, the smaller roughness length should be used.
For intermediate values of height z, linear interpolation may be used.
A building in a certain terrain category may be calculated in a lower terrain category if it is situated within the distance limits defined in Table A.1.
Height z  I to II  I to III 
5 m  0,50 km  5,00 km 
7 m  1,00 km  10,00 km 
10 m  2,00 km  20,00 km 
15 m  5,00 km  
20 m  12,00 km  
30 m  20,00 km  
50 m  50,00 km 
Height z  Il to III  Il to IV 
5 m  0,30 km  2,00 km 
7 m  0,50 km  3,50 km 
10 m  1,00 km  7,00 km 
15 m  3,00 km  20,00 km 
20 m  7,00 km  
30 m  10,00 km  
50 m  30,00 km 
Height z  III to IV 
5 m  0,20 km 
7 m  0,35 km 
10 m  0,70 km 
15 m  2,00 km 
20 m  4,50 km 
30 m  7,00 km 
50 m  20,00 km 
Figure A.1 — Illustration of increase of wind velocities over orography
NOTE The turbulence intensity will decrease with increasing wind velocity and equal value for the standard deviation
It is defined by:
c_{o} = l for Φ < 0,05 (A.1)
c_{o} = 1+2 · s · Φ for 0,05 < Φ < 0,3 (A.2)
c_{o} = 1+0,6 · s for Φ > 0,3 (A.3)
where:
s  is the orographic location factor, to be obtained from Figure A.2 or Figure A.3 scaled to the length of the effective upwind slope length, L_{e} 
Φ  is the upwind slope H/L_{u} in the wind direction (see Figure A.2 and Figure A.3) 
L_{e}  is the effective length of the upwind slope, defined in Table A.2 
L_{u}  is the actual length of the upwind slope in the wind direction 
L_{d}  is the actual length of the downwind slope in the wind direction 
H  is the effective height of the feature 
x  is the horizontal distance of the site from the top of the crest 
z  is the vertical distance from the ground level of the site 
Type of slope (Φ= H/L_{u})  

Shallow (0,05 < Φ < 0,3)  Steep (Φ > 0,3) 
L_{e} = L_{u}  L_{e} = H/0,3 
NOTE The calculated graphs in Figures A.2 and A.3 exceed the area of application as defined above. The consideration of orographic effects beyond these boundaries is optional.
Figure A.2 — Factor s for cliffs and escarpments
Figure A.3 — Factor s for hills and ridges
For the ranges
take:
where
and
when
take:
s = 0
For the ranges
take:
where
and
98For the range
interpolate between values for
For the ranges
take:
where:
and
when
take:
s = 0
NOTE Expressions A.5 and A.12 are identical.
x ≤ r:
r < x < 2 · r :
x ≥ 2 · r: z_{n} = h_{low}
in which the radius r is:
r = h_{high} if h_{high}≤ 2·d_{large}
r = 2·d_{large} if h_{high} > 2·d_{large}
The structural height h_{low}, the radius r, the distance x and the dimensions d_{small} and d_{large} are illustrated in Figure A.4 Increased wind velocities can be disregarded when h_{low} is more than half the height h_{high} of the high building, i.e. z_{n} = h_{low}.
Figure A.4 — Influence of a high rise building, on two different nearby structures (1 and 2)
100Figure A.5 — Obstruction height and upwind spacing
x ≤ 2 · h_{ave} h_{dis} is the lesser of 0,8 · h_{ave} or 0,6 · h
2 · h_{ave} < x < 6 · h_{ave} h_{dis} is the lesser of 1,2 · h_{ave} − 0,2 · x or 0,6 · h (A. 15)
x ≥ 6 · h_{ave} h_{dis} = 0
In the absence of more accurate information the obstruction height may be taken as h_{ave} = 15 m for terrain category IV. These rules are direction dependent, the values of h_{ave} and x should be established for each 30° sector as described in 4.3.2.
(informative)
with a reference height of z_{t} = 200 m, a reference length scale of L_{t} = 300 m, and with α = 0,67 + 0,05 ln(z_{0}), where the roughness length z_{0} is in m. The minimum height z_{min} is given in Table 4.1.
where S_{v}(z,n) is the onesided variance spectrum, and
is a nondimensional frequency determined by the frequency n = n_{1,x}, the natural frequency of the structure in Hz, by the mean velocity v_{m}(z) and the turbulence length scale L(z) defined in (B. 1). The power spectral density function is illustrated in Figure B.1.
Figure B.1 —Power spectral density function S_{L}(f_{L})
where:
b, h  is the width and height of the structure, see Figure 6.1. 
L(z_{s})  is the turbulent length scale given in B. 1 (1) at reference height z_{s} defined in Figure 6.1. It is on the safe side to use B^{2} = 1. 
Figure B.2 —Peak factor
where:
v  is the upcrossing frequency given in (4) 
T  is the averaging time for the mean wind velocity, T = 600 seconds. 
where n_{1,x} is the natural frequency of the structure, which may be determined using Annex F. The limit of v ≥ 0,08 Hz corresponds to a peak factor of 3,0.
where:
δ  is the total logarithmic decrement of damping given in F.5 
S_{L}  is the nondimensional power spectral density function given in B. 1 (2) 
Rh, Rb  is the aerodynamic admittance functions given in (6). 
with:
NOTE For mode shapes with internal node points more detailed calculations should be used.
Figure B.3 — Number of gust loads N_{g} for an effect ΔS/S_{k} during a 50 years period
The relationship between ΔS/S_{k} and N_{g} is given by Expression B.9.
where:
c_{f}  is the force coefficient, see Section 7 
ρ  is the air density, see 4.5 (1) 
b  is the width of the structure, defined in Figure 6.1 
I_{v}(z_{s})  is the turbulence intensity at the height z = z_{s} above ground, see 4.4 (1) 
v_{m}(z_{s})  is the mean wind velocity for z = z_{s}, see 4.3.1 (1) 
z_{s}  is the reference height, see Figure 6.1 
R  is the square root of resonant response, see B. 2 (5) 
K_{x}  is the nondimensional coefficient, given by Expression (B. 11) 
m_{1,x}  is the along wind fundamental equivalent mass, see F.4 (1) 
n_{1,x}  is the fundamental frequency of along wind vibration of the structure; approximations are given in Annex F 
Φ_{1,x}(z)  is the fundamental along wind modal shape, as a first approximation the expressions given in Annex F may be used 
where:
h  is the height of the structure (see Figure 6.1). 
106NOTE Assuming Φ_{1,x}(z) = (z/h)^{ζ} (see Annex F) and c_{o}(z) = 1 (flat terrain, see 4.3.3), Expression (B.11) can be approximated by Expression (B.12). This approximation is shown in Figure B.4
where:
z_{0} is the roughness length (Table 4.1) ζ is the exponent of the mode shape (see Annex F)
Figure B.4 — Approximation of the non dimensional coefficient, K_{x} according to Expression (B.12)
(informative)
where:
b,h  is the width and height of the structure, see Figure 6.1 
L(z_{s})  is the turbulent length scale given in B.1 (1) at reference height z_{s} defined in Figure 6.1. 
It is on the safe side to use B^{2} = 1.
where:
δ  is the total logarithmic decrement of damping given in Annex F 
S_{L}  is the wind power spectral density function given in B. 1 (2) 
n_{1,x}  is the natural frequency of the structure, which may be determined using Annex F 
K_{s}  is the size reduction function given in (5). 
The constants G_{y} and G_{z} depend on the mode shape variation along the horizontal yaxis and vertical zaxis, respectively. The decay constants c_{y} and c_{z} are both equal to 11,5.
Mode shape  Uniform  Linear  Parabolic  Sinusoidal  

G:  1/2  3/8  5/18  4/π^{2}  
K:  1  3/2  5/3  4/π  

where:
c_{f}  is the force coefficient, see Section 7 
ρ  is the air density, see 4.5 
I_{v}(Z_{s})  is the turbulence intensity at height z_{s} above ground, see 4.4 (1) 
v_{m}(z_{s})  is the characteristic mean wind velocity at height z_{s}, see 4.3.1 (1) 
z_{s}  is the reference height, see Figure 6.1 
R  is the square root of the resonant response, see C.2 (4) 109 
K_{y},K_{z}  is the constants given in C.2 (6) 
μ_{ref}  is the reference mass per unit area, see F.5 (3) 
Φ(y,z)  is the mode shape 
Φ_{max}  is the mode shape value at the point with maximum amplitude 
(informative)
Figure D.1 — c_{s}c_{d} for multistorey steel buildings with rectangular ground plan and vertical external walls, with regular distribution of stiffness and mass (frequency according to Expression (F.2)).
111Figure D.2 — c_{s}c_{d} for multistorey concrete buildings with rectangular ground plan and vertical external walls, with regular distribution of stiffness and mass (frequency according to Expression (F.2)).
Figure D.3 — c_{s}c_{d} for steel chimneys without liners (frequency according to Expression (F.3), with ε_{1}=1000 and W_{s}/W_{t}=1,0).
112Figure D.4 — c_{s}c_{d} for concrete chimneys without liners (frequency according to Expression (F.3), with ε_{1}=700 and W_{s}/W_{t}=1,0).
Figure D.5 — c_{s}c_{d} for steel chimneys with liners and different values of δ_{s} according to Table F.2 (frequency according to Expression (F.3), with ε_{1}=1000 and W_{s}W_{t}=0,5).
113(informative)
NOTE 1 Broadbanded response is normally most important for reinforced concrete structures and heavy steel structures.
NOTE 2 Narrowbanded response is normally most important for light steel structures.
V_{crit,i} > 1.25 · V_{m} (E.1)
where:
V_{crit,i}  is the critical wind velocity for mode i, as defined in E.1.3.1 
V_{m}  is the characteristic 10 minutes mean wind velocity specified in 4.3.1 (1) at the cross section where vortex shedding occurs (see Figure E.3). 
where:
b  is the reference width of the crosssection at which resonant vortex shedding occurs and where the modal deflection is maximum for the structure or structural part considered; for circular cylinders the reference width is the outer diameter 
n_{i,y}  is the natural frequency of the considered flexural mode i of crosswind vibration; approximations for n_{1,y} are given in F.2 
St  Strouhal number as defined in E.1.3.2. 
where:
b  is the outer shell diameter 
St  is the Strouhal number as defined in E.1.3.2 
n_{i,o}  is the natural frequency of the ovalling mode i of the shell 
NOTE 1 For shells without stiffening rings no is given in F.2 (3)
NOTE 2 Procedures to calculate ovalling vibrations are not covered in Annex E.
The Strouhal number St for different crosssections may be taken from Table E.1.
115Crosssection  St 

0,18  
from Figure E.1  
0,11 0,10 0,14 

0,13 



0,11 

NOTE Extrapolations for Strouhal numbers as function of d/b are not allowed. 
Figure E.1 — Strouhal number (St) for rectangular crosssections with sharp corners
where:
δ_{s}  is the structural damping expressed by the logarithmic decrement. 
ρ  is the air density under vortex shedding conditions. 
m_{i,e}  is the equivalent mass m_{e} per unit length for mode i as defined in F.4 (1) 
b  is the reference width of the crosssection at which resonant vortex shedding occurs 
NOTE The value of the air density ρ may be given in the National Annex. The recommended value is 1,25 kg/m^{3}.
where:
b  is the outer diameter of the circular cylinder 
v  is the kinematic viscosity of the air (v ≈ 15 · 10^{−6} m^{2}/s) 
v_{crit,i}  is the critical wind velocity, see E.1.3.1 
F_{w} (s) = m(s) · (2 · π · n_{i,y})^{2} · Φ_{i,y}(s) · y_{F,max} (E.6)
where:
m(s)  is the vibrating mass of the structure per unit length [kg/m] 
n_{i,y}  is the natural frequency of the structure 
Φ_{i,y}(s)  is the mode shape of the structure normalised to 1 at the point with the maximum displacement 
y_{F,max}  is the maximum displacement over time of the point with Φ_{i,y}(s) equal to 1, see E.1.5 
NOTE 1 The choice of calculation approach or alternative calculation procedures may be specified in the National Annex.
NOTE 2 A direct comparison of the approaches proposed in E.1.5.2 and E.1.5.3 is not possible because some of the input parameters are chosen for different environmental conditions. The National Annex may define the range of application for each of the approaches proposed.
NOTE 3 Mixing of the approaches E.1.5.2 and E.1.5.3 is not allowed, except if it is specifically stated in the text.
NOTE The National Annex may give the regions where very cold and stratified flow conditions may occur. For these regions the approach 2 in E.1.5.3 is more appropriate, and the National Annex may define appropriate input parameters (like K_{a} or turbulence intensity) which should be used in this approach.
The largest displacement y_{F,max} can be calculated using Expression (E.7).
where:
St  is the Strouhal number given in Table E.1 
Sc  is the Scruton number given in E.1.3.3 
K_{w}  is the effective correlation length factor given in E.1.5.2.4 
K  is the mode shape factor given in E.1.5.2.5 
c_{lat}  is the lateral force coefficient given in Table E.2 
NOTE The aeroelastic forces are taken into account by the effective correlation length factor K_{w}.
Crosssection  c_{lat,0} 

from Figure E.2  
1,1  
0,8 1,2 0,3 

2,3 



0,8


NOTE Extrapolations for lateral force coefficients as function of d/b are not allowed. 
Figure E.2 — Basic value of the lateral force coefficient c_{lat,0} versus Reynolds number Re(v_{crit,i}) for circular cylinders, see E.1.3.4
Critical wind velocity ratio  c_{lat} 

c_{lat} = c_{lat,0}  
c_{lat} = 0  
where: c_{lat,0} is the basic value of c_{lat} as given in Table E.2 and, for circular cylinders, in Figure E.2 v_{crit,i} is the critical wind velocity (see E. 1.3.1) v_{m,Lj} is the mean wind velocity (see 4.3.1) in the centre of the effective correlation length as defined in Figure E.3 
Figure E.3 — Examples for application of the correlation length L_{j} (j= 1, 2, 3)
y_{F}(S_{j})/b  L_{j}/b 

< 0,1  6 
0,1 to 0,6  
>0,6  12 
where:
Φ_{i,y}  is the mode shape i (see F.3). 
L_{j}  is the correlation length 
ℓ_{j}  is the length of the structure between two nodes (see Figure E.3); for cantilevered structures it is equal to the height of the structure 
n  is the number of regions where vortex excitation occurs at the same time (see Figure E.3) 
m  is the number of antinodes of the vibrating structure in the considered mode shape Φ_{i,y} 
s  is the coordinate defined in Table E.5. 
Structure  mode shape Φ_{i,y}(s) 
K_{w}  K 

see F.3 with ζ = 2,0 n = 1 ;m = 1 
0,13  
see Table F.1 n = 1;m = 1 
0,10  
see Table F.1 n =1;m = 1 
0,11  
modal analysis n = 3 m = 3 
0,10  
NOTE 1 The mode shape, Φ,_{i,y}(s), is taken from F.3. The parameters n and m are defined in Expression (E.8) and in Figure E.3 NOTE 2 λ = ℓ/b 
where:
m  is defined in E.1.5.2.4 (1) 
Φ_{i,y}(s)  is the crosswind mode shape i (see F.3) 
ℓ_{j}  is the length of the structure between two nodes (see Figure E.3) 
where:
n_{y}  is the natural frequency of crosswind mode [Hz]. Approximations for n_{y} are given in Annex F 
v_{crit}  is the critical wind velocity [m/s] given in E.1.3.1 
v_{0}  is times the modal value of the Weibull probability distribution assumed for the wind velocity [m/s], see Note 2 
T  is the life time in seconds, which is equal to 3,2 10^{7} multiplied by the expected lifetime in years 
ε_{0}  is the bandwidth factor describing the band of wind velocities with vortexinduced vibrations, see Note 3 
NOTE 1 The National Annex may specify the minimum value of N. The recommended value is N ≥ 10^{4}.
NOTE 2 The value v_{0} can be taken as 20 % of the characteristic mean wind velocity as specified in 4.3.1 (1) at the height of the cross section where vortex shedding occurs.
NOTE 3 The bandwidth factor ε_{0} is in the range 0,1 − 0,3. It may be taken as ε_{0} = 0,3.
Figure E.4 — Inline and grouped arrangements of cylinders
For inline, free standing circular cylinders without coupling:
where:
c_{lat (single)} = c_{lat} as given in Table E.3
For coupled cylinders:
c_{lat} = K_{iv} · c_{lat(single)} for 1,0 ≤ a/b ≤ 3,0 (E.12)
where:
K_{iv}  is the interference factor for vortex shedding (Table E.8) 
St  is the Strouhal number, given in Table E.8 
Sc  is the Scruton number, given in Table E.8 
For coupled cylinders with a/b > 3,0 specialist advice is recommended.
126NOTE The factor 1,5 · c_{lat} for circular cylinders without coupling is a rough approximation. It is expected to be conservative.
y_{max} = σ_{y} · k_{p} (E.13)
where:
σ_{y}  is the standard deviation of the displacement, see (2) 
k_{p}  is the peak factor, see (6) 
where:
C_{c}  is the aerodynamic constant dependent on the crosssectional shape, and for a circular cylinder also dependent on the Reynolds number Re as defined in E.1.3.4 (1); given in Table E.6. 
K_{a}  is the aerodynamic damping parameter as given in E.1.5.3 (4) 
a_{L}  is the normalised limiting amplitude giving the deflection of structures with very low damping; given in Table E.6 
Sc  is the Scruton number given in E.1.3.3 
St  is the Strouhal number given in Table E.1 
ρ  is the air density under vortex shedding conditions, see Note 1 
m_{e}  is the effective mass per unit length; given in F.4 (1) 
h,b  is the height and width of structure. For structures with varying width, the width at the point with largest displacements is used. 
NOTE 1 The value of the air density ρ may be given in the National Annex. The recommended value is 1,25 kg/m^{3}.
NOTE 2 The aerodynamic constant C_{c} depends on the lift force acting on a nonmoving structure.
NOTE 3 The motioninduced wind loads are taken into account by K_{a} and a_{L}.
where the constants c_{1} and c_{2} are given by:
NOTE Using K_{a,max} for turbulence intensities larger 0 % gives conservative predictions of displacements. More detailed information on the influence of the turbulence intensity on K_{a} may be specified in the National Annex.
Constant  Circular cylinder Re ≤ 10^{5} 
Circular cylinder Re = 5 · 10^{5} 
Circular cylinder Re ≥ 10^{6} 
Square crosssection 

c_{c}  0,02  0,005  0,01  0,04 
K_{a,max}  2  0,5  1  6 
a_{L}  0,4  0,4  0,4  0,4 
NOTE: For circular cylinders the constants c_{c} and K_{a,max} are assumed to vary linearly with the logarithm of the Reynolds number for 10^{5} < Re <5·10^{5} and for 5·10^{5} < Re < 10^{6} Text deleted 
NOTE The National Annex may specify the peak factor. Expression (E. 17) gives the recommended value.
where:
Sc  is the Scruton number as defined in E.1.3.3 (1) 
n_{1,y}  is the crosswind fundamental frequency of the structure; approximations of n_{1,y} are given in F.2 
b  is the width as defined in Table E.7 
a_{G}  is the factor of galloping instability (Table E.7); if no factor of galloping instability is known, a_{G} = 10 may be used. 
v_{CG} > 1,25 · v_{m} (E.19)
where:
v_{m}  is the mean wind velocity as defined in Expression (4.3) and calculated at the height, where galloping process is expected, likely to be the point of maximum amplitude of oscillation. 
interaction effects between vortex shedding and galloping are likely to occur. In this case specialist advice is recommended.
Crosssection  Factor of galloping instability a_{G} 
Crosssection  Factor of galloping instability a_{G} 


1,0  1,0  
4  
d/b=2  2  d/b=2  0,7  
d/b=1,5  1,7  d/b=2,7  5  
d/b=1  1,2  d/b=5  7  
d/b=2/3  1  d/b=3  7,5  
d/b=1/2  0,7  d/b=3/4  3,2  
d/b=1/3  0,4  d/b=2  1  
NOTE Extrapolations for the factor aG as function of d/b are not allowed. 
where Sc, a_{G} and b are given in Table E.8 and n_{1,y} is the natural frequency of the bending mode (see F.2).
v_{CG} > 1,25 · v_{m}(z) (E.22)
where:
v_{m}(z)  is the mean wind velocity as defined in Expression (4.3), calculated at the height z, where the galloping excitation is expected, that is likely to be the point of maximum amplitude of oscillation 
Coupled cylinders  Scruton number (compare with Expression (E.4))  

a/b = 1  a/b ≥ 2  a/b ≤ 1,5  a/b ≥ 2,5  
K_{iv} = 1,5  K_{iv} = 1,5  a_{G} = 1,5  a_{G} = 3,0  
K_{iv} = 4,8  K_{iv} = 3,0  a_{G} = 6,0  a_{G} = 3,0  
K_{iv} = 4,8  K_{iv} = 3,0  a_{G} = 1,0  a_{G} = 2,0  
linear interpolation  
where:
Sc  is the Scruton number as defined in E.1.3.3 (1) 
a_{IG}  is the combined stability parameter a_{lG} = 3,0 
n_{1,y}  is the fundamental frequency of crosswind mode. Approximations are given in F.2 
a  is the spacing 
b  is the diameter 
NOTE The National Annex may give additional guidance on a_{IG}.
Figure E.5 — Geometric parameters for interference galloping
where:
k_{Θ}  is the torsional stiffness 
c_{M}  is the aerodynamic moment coefficient, given in Expression (E.25): 
dc_{M}/dΘ  is the rate of change of aerodynamic moment coefficient with respect to rotation about the torsional centre, Θ is expressed in radians. 
M  is the aerodynamic moment of a unit length of the structure 
ρ  is the density of air given in 4.5 134 
d  is the in wind depth (chord) of the structure (see Figure E.6) 
b  is the width as defined in Figure E.6 
v_{div} > 2 · v_{m}(z_{s})
where:
v_{m}(z_{s})  is the mean wind velocity as defined in Expression (4.3) at height z_{s} (defined in Figure 6.1) 
Figure E.6 — Rate of change of aerodynamic moment coefficient, dc_{M}/dΘ, with respect to geometric centre “GC” for rectangular section
(informative)
where:
g  is the acceleration of gravity = 9,81 m/s^{2} 
x_{1}  is the maximum displacement due to self weight applied in the vibration direction in m 
where:
h  is the height of the structure in m 
The same expression may give some guidance for singlestorey buildings and towers.
with:
where:
b  is the top diameter of the chimney [m], 
h_{eff}  is the effective height of the chimney [m], h_{1} and h_{2} are given in Figure F.1, 
W_{s}  is the weight of structural parts contributing to the stiffness of the chimney, 
W_{t}  is the total weight of the chimney, 
ε_{1}  is equal to 1000 for steel chimneys, and 700 for concrete and masonry chimneys. 
Figure F.1 — Geometric parameters for chimneys
where:
E  is Young’s modulus in [N/m^{2}] 
t  is the shell thickness in [m] 
v  is Poisson ratio 
μ_{s}  is the mass of the shell per unit area in [kg/m^{2}] 
b  is the diameter of the shell in [m] 
Expression (F.5) gives the lowest natural frequency of the shell. Stiffness rings increase n_{0}.
where:
L  is the length of the main span in m 
E  is Youngs Modulus in N/m^{2} 
l_{b}  is the second moment of area of crosssection for vertical bending at midspan in m^{4} 
m  is the mass per unit length of the full crosssection ad midspan (for dead and superimposed dead loads) in kg/m 
K  is a dimensionless factor depending on span arrangement defined below. 
K = π if simply supported or
K = 3,9 if propped cantilevered or
K = 4,7 if fixed end supports
K is obtained from Figure F.2, using the curve for twospan bridges, where
L_{1} is the length of the side span and L ≥ L_{1}
K is obtained from Figure F.2, using the appropriate curve for threespan bridges, where
L_{1} is the length of the longest side span
L_{2} is the length of the other side span and L ≥ L_{1} ≥ L_{2}
This also applies to threespan bridges with a cantilevered/suspended main span.
If L_{1} > L then K may be obtained from the curve for two span bridges, neglecting the shortest side span and treating the largest side span as the main span of an equivalent twospan bridge.
K may be obtained from the curve for twospan bridges in Figure F.2 treating each half of the bridge as an equivalent twospan bridge.
K may be obtained from Figure F.2 using the appropriate curve for threespan bridges, choosing the main span as the greatest internal span.
NOTE 1 If the value of at the support exceeds twice the value at midspan, or is less than 80 % of the midspan value, then the Expression (F.6) should not be used unless very approximate values are sufficient.
NOTE 2 A consistent set should be used to give n_{1,B} in cycles per second.
with:
where:
n_{1,B}  is the fundamental bending frequency in Hz 
b  is the total width of the bridge 
m  is the mass per unit length defined in F.2 (5) 
v  is Poisson’s ratio of girder material 
r_{j}  is the distance of individual box centreline from centreline of bridge 
I_{j}  is the second moment of mass per unit length of individual box for vertical bending at midspan, including an associated effective width of deck 
I_{p}  is the second moment of mass per unit length of crosssection at midspan. It is described by Expression (F. 11). 
where:
m_{d}  is the mass per unit length of the deck only, at midspan 
I_{pj}  is the mass moment of inertia of individual box at midspan 
m_{j}  is the mass per unit length of individual box only, at midspan, without associated portion of deck 139 
J_{j}  is the torsion constant of individual box at midspan. It is described by Expression (F.12). 
where:
A_{j}  is the enclosed cell area at midspan 
is the integral around box perimeter of the ratio length/thickness for each portion of box wall at midspan 
140NOTE Slight loss of accuracy may occur if the proposed Expression (F.12) is applied to multibox bridges whose plan aspect ratio (=span/width) exceeds 6.
Figure F.2 — Factor K used for the derivation of fundamental bending frequency
where:
ζ = 0,6  for slender frame structures with non loadsharing walling or cladding 141 
ζ = 1,0  for buildings with a central core plus peripheral columns or larger columns plus shear bracings 
ζ = 1,5  for slender cantilever buildings and buildings supported by central reinforced concrete cores 
ζ = 2,0  for towers and chimneys 
ζ = 2,5  for lattice steel towers 
Figure F.3— Fundamental flexural mode shape for buildings, towers and chimneys cantilevered from the ground
Scheme  Mode shape  Φ_{1}(s) 

where:
m  is the mass per unit length 
ℓ  is the height or span of the structure or the structural element 
i = 1  is the mode number 
δ = δ_{s} + δ_{a} + δ_{d} (F.15)
where:
δ_{s}  is the logarithmic decrement of structural damping 
δ_{a}  is the logarithmic decrement of aerodynamic damping for the fundamental mode 
δ_{d}  is the logarithmic decrement of damping due to special devices (tuned mass dampers, sloshing tanks etc.) 
where:
c_{f}  is the force coefficient for wind action in the wind direction stated in Section 7. 
μ_{e}  is the equivalent mass per unit area of the structure which for rectangular areas given by Expression (F.17). 
where
μ(y,z)  is the mass per unit area of the structure 
Φ_{1}(y,z)  is the mode shape. 
The mass per unit area of the structure at the point of the largest amplitude of the mode shape is normally a good approximation to μ_{e}.
Structural type  structural damping, δ_{s} 


reinforced concrete buildings  0,10  
steel buildings  0,05  
mixed structures concrete + steel  0,08  
reinforced concrete towers and chimneys  0,03  
unlined welded steel stacks without external thermal insulation  0,012  
unlined welded steel stack with external thermal insulation  0,020  
steel stack with one liner with external thermal insulation^{a}  h/b < 18  0,020  
20 ≤ h/b < 24  0,040  
h/b ≥ 26  0,014  
steel stack with two or more liners with external thermal insulation ^{a}  h/b < 18  0,020  
20 ≤ h/b < 24  0,040  
h/b > 26  0,025  
steel stack with internal brick liner  0,070  
steel stack with internal gunite  0,030  
coupled stacks without liner  0,015  
guyed steel stack without liner  0,04  
steel bridges + lattice steel towers  welded  0,02  
high resistance bolts  0,03  
ordinary bolts  0,05  
composite bridges  0,04  
concrete bridges  prestressed without cracks  0,04  
with cracks  0,10  
Timber bridges  0,06 − 0,12  
Bridges, aluminium alloys  0,02  
Bridges, glass or fibre reinforced plastic  0,04 − 0,08  
cables  parallel cables  0,006  
spiral cables  0,020  
NOTE The values for timber and plastic composites are indicative only. In cases where aerodynamic effects are found to be significant in the design, more refinded figures are needed through specialist advice (agreed if appropriate with the competent Authority. Note deleted 

^{a} For intermediate values of h/b, linear interpolation may be used 
ISO 2394  General principles on reliability for structures 
ISO 3898  Bases for design of structures — Notations — General symbols 
ISO 8930  General principles on reliability for structures  List of equivalent terms 
EN 128111  Temporary works equipment  Part 1: Scaffolds  Performance requirements and general design 
ISO 12494  Atmospheric icing of structures 