Romanian Wind Code CR1-1-4

GOVERNMENT OF ROMANIA

MINISTRY OF REGIONAL DEVELOPMENT AND TOURISM

www.mdrt.ro

1. ------IND- 2012 0249 RO- EN- ------ 20120430 --- --- PROJET

ORDER

No…………of……………for approval of the technical regulation

"Design code. Assessment of wind action on structures”, code CR 1-1-4/2012

In accordance with the provisions of Article 10 and Article 38(2) of Law No 10/1995 regarding quality in constructions, with its subsequent modifications, the provisions of Article 2(3) and (4) of the Rules regarding the types of technical regulations and costs for regulatory activity in the field of constructions, town planning, landscaping, and habitat, approved by Government Decision No 203/2003, with its subsequent modifications and supplementation, and the provisions of Government Decision No 1016/2004 regarding measures for organising and carrying out the exchange of information in the field of technical standards and regulations, as well as the rules regarding information society services between Romania and the EU Member States, as well as the European Commission, with the subsequent modifications,

in light of Approval Report No 43/2011 of the Specialist Technical Committee No 4 “Actions on structures”,

on the grounds of Article 5(II)(e) and Article 13(6) of Government Decision No 1631/2009 concerning the organisation and operation of the Ministry of Regional Development and Tourism, with its subsequent modifications and supplementation,

the Ministry of Regional Development and Tourism hereby issues the following

ORDER:

Article 1. - Technical regulation “Design code. Assessment of wind action on structures”, code CR 1-1-4/2012, drawn up by the Technical University of Bucharest, stipulated in the annex*)*) that is an integrated part of this order, is hereby approved.

Article 2. - The present order shall be published in the Official Journal of Romania, Part I and shall come into force 30 days after its date of publication.

Article 3. - On the date the present order comes into force, technical regulation “Design code. Design basis and actions on structures. Wind action”, code NP 082-04, approved by Order No 165/15.02.2005 of the Ministry of Transport, Constructions, and Tourism, with its subsequent modifications and supplementation, shall be repealed.

This technical regulation was adopted in accordance with the notification procedure No RO/ ...... of ............... stipulated by Directive 98/34/EC of the European Parliament and of the Council of 22 June 1998, laying down a procedure for the provision of information in the field of technical standards and regulations, published in the Official Journal of the European Communities L 204 of 21 July 1998, amended by Directive 98/48/EC of the European Parliament and of the Council of 20 July 1998, published in the Official Journal of the European Communities L 217 of 5 August 1998.

MINISTER

CRISTIAN PETRESCU

*) The Order and its annex shall also be published in the Constructions Journal edited by the “URBAN-INCERC” National Institute for Research and Development in the field of Constructions, Town Planning, and Sustainable Territorial Development, which is coordinated by the Ministry of Regional Development and Tourism.

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Annex

to Order No……………./2012 of the Ministry of Regional Development and Tourism

DRAFT

DESIGN CODE

ASSESSMENT OF WIND ACTION ON STRUCTURES

Code CR 1-1-4/2012

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CONTENTS

1 GENERAL ASPECTS........................................................................................................................................6

1.1 Purpose and scope............................................................................................................61.2 Normative references.......................................................................................................71.3 Hypotheses..................................................................................................................71.4 Design assisted by testing................................................................................................81.5 Definitions and symbols..................................................................................................81.6 Combination of wind action with other actions.............................................................13

2 WIND VELOCITY. DYNAMIC WIND PRESSURE.............................................................................14

2.1 General aspects...............................................................................................................142.2 Reference values of the wind velocity and dynamic pressure......................................142.3 Ground roughness. Mean wind velocity and dynamic pressure....................................172.4 Wind turbulence. Peak wind velocity and dynamic pressure....................................19

3 WIND ACTION ON BUILDINGS AND OTHER STRUCTURES......................................................22

3.1 General aspects...............................................................................................................223.2 Wind pressure on surfaces.............................................................................................253.3 Wind forces...................................................................................................................263.4 Dynamic response coefficient of a structure.................................................................28

3.4.1 General information................................................................................................283.4.2 Assessment of the dynamic response coefficient...................................................28

4 AERODYNAMIC PRESSURE/SUCTION AND FORCE COEFFICIENTS............................................31

4.1 General information......................................................................................................314.2 Buildings....................................................................................................................33

4.2.1 General information...........................................................................................334.2.2 Vertical walls of rectangular plane buildings..........................................................344.2.3 Flat roofs.................................................................................................................374.2.4 Single pitch roofs...............................................................................................394.2.5 Double-pitched roofs...............................................................................................424.2.6 Quad pitched roofs..................................................................................................444.2.7 Multispan roofs.....................................................................................................454.2.8 Cylindrical roofs and domes...................................................................................474.2.9 Internal pressure.................................................................................................494.2.10 Pressure on exterior walls or roofs with several skins.......................................51

4.3 Canopies....................................................................................................................534.4 Free-standing walls, parapets, fences, and advertising boards..................................60

4.4.1 Free-standing vertical walls and parapets..........................................................604.4.2 Shelter factors for walls and fences........................................................................614.4.3 Advertising boards.............................................................................................62

4.5 Friction coefficients...................................................................................................634.6 Structural elements with a rectangular cross-section................................................644.7 Structural elements with cross-sections that have sharp edges.................................664.8 Structural elements with a regular polygonal cross-section......................................67

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4.9 Circular cylinders......................................................................................................684.9.1 Aerodynamic external pressure/suction coefficients.........................................684.9.2 Aerodynamic force coefficients.........................................................................704.9.3 Aerodynamic force coefficients for vertical cylinders arranged in line.............72

4.10 Spheres.........................................................................................................................734.11 Lattice structures and scaffolding................................................................................754.12 Flags.............................................................................................................................784.13 Effective slenderness and end-effect factor ..................................................79

5 PROCEDURES FOR DETERMINING THE DYNAMIC RESPONSE COEFFICIENT........................82

5.1 Wind turbulence........................................................................................................825.2 Detailed procedure for determining the dynamic response coefficient.....................835.3 Simplified procedure for determining the dynamic response coefficient for buildings

...................................................................................................................................855.4 Displacements and accelerations corresponding to the service limit state of a structure................................................................................................................................875.5 Comfort criteria.........................................................................................................88

6 AEROELASTIC INSTABILITY PHENOMENA GENERATED BY VORTICES.................................90

6.1 General information......................................................................................................906.2 Consideration of the effects of vortex shedding........................................................906.3 Main vortex shedding parameters.............................................................................90

6.3.1 The critical wind velocity vcrit,i................................................................................906.3.2 Strouhal number, St.................................................................................................916.3.3 Scruton number, Sc.................................................................................................936.3.4 Reynolds number, Re..............................................................................................93

6.4 Action caused by vortex shedding.............................................................................946.5 Calculation of the cross-wind displacement amplitude.............................................946.6 Vortex effects on vertical cylinders arranged in line or grouped..............................99

ANNEX A (NORMATIVE) ZONING OF WIND ACTION IN ROMANIA...........................................102

ANNEX B ( (NORMATIVE) EFFECTS OF THE TERRAIN..................................................................114

B.1 Transition between roughness categories 0, I, II, III, and IV..................................114B.2 Numerical calculation of the orography factor........................................................114B.3 Neighbouring buildings and/or structures...............................................................117B.4 Displacement height of the zero-elevation plane....................................................118

ANNEX C (INFORMATIVE) DYNAMIC CHARACTERISTICS OF STRUCTURES........................119

C.1 General aspects........................................................................................................119C.2 Fundamental natural frequency...............................................................................119C.3 Fundamental natural vector.....................................................................................121C.4 Equivalent mass.......................................................................................................122C.5 Logarithmic decrement of damping........................................................................123C.6 Dynamic characteristics of bridge structures..........................................................125

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ANNEX D (NORMATIVE) WIND ACTION ON BRIDGES....................................................................129

D.1 General elements.....................................................................................................129D.2 Choosing the procedure for calculating the wind action response..........................131D.3 Aerodynamic force coefficients..............................................................................131

D.3.1 Aerodynamic force coefficients in direction x (general method)....................131D.3.2 Wind forces on bridge decks in direction x – Simplified method....................134D.3.3 Wind forces on bridge decks in direction z......................................................135D.3.4 Wind forces on bridge decks in direction y.....................................................136

D.4 Bridge piles..............................................................................................................137D.4.1 Wind directions and design situations..............................................................137D.4.2 The effect of wind on bridge piles...................................................................137

1 GENERAL ASPECTS

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1.1 Purpose and scope

(1) The code contains the principles, application rules, and databases needed for the wind design of structures in Romania, harmonised with standard SR EN 1991-1-4, by taking into consideration the meteorological information concerning the annual maximum values of the mean wind velocity.

(2) The code regulates the way in which wind action and the structural response to this action are determined in order to design buildings and other structures. The provisions of the code refer to the entire structure of the building, as well as to its structural or non-structural elements (e.g. curtain walls, parapets, fixings, etc.).

The code presents practical methods and procedures for assessing the pressures/suction forces and/or wind forces applied to buildings and other usual structures, which are based on wind action representations in accordance with SR EN 1991-1-4.

(3) The code shall apply to the design and inspection of:

- buildings and other structures with heights up to 200 m (also see (4));

- bridges with a span of no more than 200 m (also see (4)), which comply with the dynamic response requirements stipulated in (D.2).

(4) The code does not contain provisions regarding the following aspects:

- assessment of wind action on lattice towers with non-parallel chords (for this situation, see SR EN 1993-3-1);

- assessment of wind action on guyed masts and guyed chimneys;

- assessment of combined wind-rain, wind-frost and wind-ice action (for these situations, see SR EN 1993-3-1);

- assessment of wind action during execution (see SR EN 1-1-4, Article 2(3) and SR EN 199-1-6);

- calculation of torsional vibrations, e.g. tall buildings with a central core;

- calculation of bridge deck vibration generated by transverse wind turbulence;

- assessment of wind action on cable supported bridges;

- considering the influence of upper vibration modes in the assessment of the dynamic structural response.

(5) The code does not include provisions regarding assessment of the effects of tornadoes on buildings and their structural or non-structural elements.

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(6) The provisions of the code are aimed at investors, design engineers, contractors as well as inspection and control bodies (inspection and/or surveying of the designs, inspection, control, and/or surveying of the construction works, as applicable).

1.2 Normative references

(1) The following normative references contain provisions which, by means of references made in the present text, constitute provisions of this code:

Item No

Legislative documents Publication

1.Design code. Basis of structural design, Code CR 0-2012

Notified draft technical regulation

Item No

Standards Name

1 SR EN 1990:2004/A1:2006 Eurocode: Basis of structural design - Bridges

2SR EN 1990:2004/A1:2006/NA:2009

Eurocode: Basis of structural design. Annex A2: Application for bridges. National Annex

3 SR EN 1991-1-4:2006Eurocode 1: Actions on structures. Part 1-4: General actions. Wind actions

4 SR EN 1991-1-4:2006/NB:2007Eurocode 1: Actions on structures. Part 1-4: General actions – Wind actions. National Annex

5 SR EN 1991-1-4:2006 /AC:2010Eurocode 1: Actions on structures. Part 1-4: General actions – Wind actions

6 SR EN 1991-1-6:2005Eurocode 1: Actions on structures. Part 1-6: General actions - Actions during execution

7 SR EN 1991-1-6:2005/NB:2008Eurocode 1: Actions on structures. Part 1-6: General actions. Actions during execution. National Annex

8 SR EN 1991-2:2004Eurocode 1: Actions on structures. Part 2: Traffic loads on bridges

9 SR EN 1991-2:2004/NB:2006Eurocode 1: Actions on structures. Part 2: Traffic loads on bridges. National Annex

10 SR EN 1993-3-1:2007Eurocode 3: Design of steel structures. Part 3-1: Towers, masts and chimneys. Towers and masts

11 SR EN 1993-3-1:2007/NB:2009Eurocode 3: Design of steel structures. Part 3-1: Towers, masts and chimneys. Towers and masts. National Annex

(2) This code includes text adopted from national standards SR EN 1991-1-4:2006 and SR EN 1991-1-4:2006/NB:2007, identified by means of a vertical line at the side and/or reference [3] given in the table above.

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1.3 Hypotheses

(1) The general hypotheses presented in CR 0 shall also be valid for the present code.

1.4 Design assisted by testing

(1) The wind action on structures and their response can also be assessed using the results of wind tunnel tests and/or digital methods, using suitable models of the structure and wind action.

(2) In order to carry out wind tunnel experimental tests, the wind action must be modelled so that (i) the mean wind velocity profile and (ii) the turbulence characteristics on site are complied with.

1.5 Definitions and symbols

(1) The following definitions are given to enable use of the design code:

- reference wind velocity - the characteristic wind speed averaged over a period of 10 minutes, with a 2 % annual exceedance probability (mean recurrence interval, MRI = 50 years), regardless of the direction of the wind, determined at a height of 10 m in open terrain;

- mean wind velocity - wind velocity averaged over a period of 10 minutes, with a 2 % annual exceedance probability regardless of the direction of the wind, determined at a height z above ground, by taking into consideration the effects of the ground roughness and site orography;

- peak wind velocity - maximum expected wind velocity over a period of 10 minutes, regardless of the direction of the wind, determined at a height z above ground, by taking into consideration the effects of the ground roughness, site orography, and wind turbulence;

- aerodynamic pressure/suction coefficient - the aerodynamic external pressure/suction coefficient characterises the effect of the wind on the exterior surfaces of buildings; the aerodynamic internal pressure/suction coefficient characterises the effect of the wind on the interior surfaces of buildings. Aerodynamic external pressure/suction coefficients can be divided into global coefficients and local coefficients. Local coefficients are aerodynamic pressure/suction coefficients for upwind surfaces less than or equal to 1 m 2, which are used, for example, to design small elements and fixings. Global coefficients are aerodynamic pressure/suction

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coefficients for upwind surfaces larger than 10 m2. The resultant (total) aerodynamic pressure coefficients characterise the resultant effect of the wind on a structure, a structural element or a component, expressed per surface unit;

- aerodynamic force coefficient - the aerodynamic force coefficient characterises the global effect of the wind on a structure or its elements (considered as a whole), including air friction on the surfaces (unless specified otherwise);

- quasi-static response factor - factor used to assess the correlation of wind pressures on the surface of the structure;

- resonant response factor - factor used to assess the effects of the dynamic amplification of the structural response, caused by the frequency content of the wind turbulence in quasi-resonance with the fundamental vibration frequency of the structure;

- characteristic (pressure / force) value – also see CR 0.

(2) The code uses the following symbols:

Latin upper-case letters

- A area (surface)

- Afr area (surface) exposed to wind

- Aref reference area

- B2 quasi-static response factor

- C wind load factor for bridges

- E Young’s modulus

- Ffr resultant frictional force

- Fj vortex exciting force applied to a point j of the structure

- Fw resultant wind force

- H height of an orographic element

- Iv turbulence intensity

- K mode shape factor; shape parameter

- Kiv interference factor for vortex shedding

- Krd reduction factor for parapets

- Kw correlation length factor

- L length of the span of a bridge deck; turbulence scale length

- Ld actual length of a downwind slope

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- Le effective length of an upwind slope

- Lj correlation length

- Lu actual length of an upwind slope

- N number of cycles caused by vortex shedding

- Ng number of load cycles for gust response

- R2 resonant response factor

- Re Reynolds number

- Rh, Rb aerodynamic admittance

- Sc Scruton number

- SL unilateral and normalised power spectral density

- St Strouhal number

- Ws weight of the structural elements which contribute to the stiffness of a chimney

- Wt total weight of a chimney.

Latin lower-case letters

- b width of the structure (cross-wind dimension, unless specified otherwise)

- cz > 1000m altitude factor

- cd dynamic response coefficient of the structure

- cdir directional factor

- ce exposure factor

- cf aerodynamic force coefficient

- cf,0 aerodynamic force coefficient for structures or structural elements without free-end air flow

- cf,l lift force coefficient

- cfr friction coefficient

- clat aerodynamic force coefficient in a direction transversal to the wind

- cM aerodynamic moment coefficient

- cp aerodynamic pressure/suction coefficient

- cp,net aerodynamic resultant (total) pressure coefficient

- cr roughness factor for wind velocity

- cr2 roughness factor for dynamic wind pressure

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- cpv gust factor for wind velocity

- cpq gust factor for dynamic wind pressure

- co orography factor

- cs size factor

- d length of the structure (dimension parallel to the wind direction, unless specified otherwise)

- e force eccentricity or distance to the edge

- fL non-dimensional frequency

- h height of the structure

- hmed height of the obstacle

- hdepl displacement height of the plane with zero elevation

- k equivalent roughness

- kp peak factor

- l length of a horizontal structure

- me equivalent mass per unit length

- ni natural frequency of the structure in vibration mode i

- n1,x fundamental frequency of along-wind vibration

- nl,y fundamental frequency of cross-wind vibration

- no ovalling frequency

- p annual probability of exceedance

- qb reference value of dynamic wind pressure

- qm mean value of dynamic wind pressure

- qp peak value of dynamic wind pressure

- r radius

- s factor; coordinate

- t averaged time of the reference wind velocity; plate thickness

- vb reference wind velocity

- vcrit critical wind velocity for vortex shedding

- vm mean wind velocity

- vp peak wind velocity

- w wind pressure

- x horizontal distance from the site to the top of a crest

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- ymax maximum cross-wind amplitude at critical wind velocity

- z height above ground

- zmedaverage height

- z0 roughness length

- ze, zi reference height for external/internal wind action

- zmaxmaximum height

- zmin minimum height

- zs reference height for determining the dynamic response factor of the structure.

Greek upper-case letters

- upwind slope

- 1,xfundamental along-wind mode shape

Greek lower-case letters

- Iw factor of importance – exposure to wind action

- logarithmic decrement of damping

- a logarithmic decrement of aerodynamic damping

- d logarithmic decrement of damping caused by special devices

- s logarithmic decrement of structural damping

- solidity ratio; blockage coefficient

- slenderness coefficient

- opening ratio; permeability of an envelope (skin)

- kinematic viscosity

- torsional rotation angle

- air density

- v standard deviation of the fluctuation of instantaneous wind velocity in the

region of mean velocity

- a,x standard deviation of along-wind acceleration of the structure

- mcreduction factor for multi-bay canopies

- r reduction factor of force coefficient for square sections with rounded corners

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- reduction factor of force coefficient for structural elements with end-effects

- end-effect factor for circular cylinders

- s shelter factor for walls and fences

- exponent of mode shape.

Indices

- b reference

- 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

- x along-wind direction

- y cross-wind direction

- z vertical direction.

1.6 Combination of wind action with other actions

(1) Characteristic values of wind action on buildings and other structures shall be obtained by applying the provisions of this code.

(2) The effects that wind actions can have on a building structure shall be grouped together with the structural effects of permanent and variable actions with design relevance, in accordance with CR 0.

(3) The fatigue phenomenon caused by the effects of wind action on fatigue-sensitive structures shall be taken into consideration.

2 WIND VELOCITY. DYNAMIC WIND PRESSURE

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2.1 General aspects

(1) The instantaneous values of wind velocity and dynamic wind pressure shall contain a mean component and a fluctuating component.

(2) Both wind speed and dynamic wind pressure shall be modelled as random values. Their mean component shall be modelled as a random variable; the fluctuating component shall be modelled as a stationary random process, normal and of zero mean value.

(3) The mean values of the dynamic wind pressure and velocity shall be determined on the basis of their reference values (described in Point 2.2) and of the ground roughness and orography (described in Point 2.3).

(4) The fluctuating component of the wind velocity shall be represented by the turbulence intensity defined in Point 2.4, which is used to define the peak wind velocity and dynamic pressure.

2.2 Reference values of the wind velocity and dynamic pressure

(1) The reference value of wind velocity (reference wind velocity), vb is the characteristic wind velocity averaged over a period of 10 minutes, calculated at a height of 10 m, regardless of the wind direction, in open country terrain (terrain of category II with a conventional roughness length, z0 = 0.05 m), which has an annual exceedance probability of 0.02 (which corresponds to a value with the mean recurrence interval MRI = 50 years).

(2) The wind action shall be considered to be horizontal and directional. If expressed directionally, the reference value of the wind velocity, vb shall be multiplied by a directional factor, cdir which takes into account the wind speed distribution in different horizontal directions. In the absence of directional wind speed measurements, the directional factor shall be considered equal to 1.0.

(3) The reference value of the dynamic wind pressure (reference wind pressure), qb is the characteristic value of the dynamic wind pressure, calculated using the reference value of the wind velocity:

qb=12

ρ⋅vb2

(2.1)

where ρ is the air density, which varies with altitude, temperature, latitude, and season. For standard air (ρ=1.25 kg/m3), the reference pressure (expressed in Pascals) shall be determined with the relationship:

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qb [Pa ]=0 ,625⋅vb2 [m/s ]

(2.2)

(4) The reference values of the dynamic wind pressure in Romania are shown on the zoning map given in Figure 2.1. Table A.1 of Annex A contains the reference values of the dynamic wind pressure for 337 towns and cities in Romania.

(5) The zoning map with the reference values of the dynamic wind pressure given in Figure 2.1 shall be valid for altitudes of up to 1 000 m. The reference value of the dynamic wind pressure for a site located at an altitude z higher than 1 000 m can be determined with relationship (A.1) given in Annex A.

(6) For the south-western areas of Banat region (where the reference values of the dynamic wind pressure are higher than or equal to 0.7 kPa – see Figure 2.1) and the mountain areas located at an altitude higher than 1 000 m, recent primary data recorded by the National Meteorological Administration, ANM, should be used. Also, if the directional factor cdir needs to be determined, recent primary data supplied by ANM should be used.

(7) The reference wind velocity for a site shall be obtained from the reference value of the dynamic wind pressure corresponding to the respective site (taken from the zoning map shown in Figure 2.1 or directly from Table A.1), using relationship (A.3) given in Annex 3.

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Figure 2.1 Zoning of the reference values of dynamic wind pressure, qb in kPa, where MRI = 50 years

NOTE. For altitudes higher than 1 000 m, the values of the dynamic wind pressure shall be corrected using relationship (A.1) given in Annex A

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SCALE

2.3 Ground roughness. Mean wind velocity and dynamic pressure

(1) The roughness of the ground surface shall be aerodynamically modelled by the roughness length, z0, expressed in metres. This represents a conventional measurement of the turbulent wind vortices on the ground surface. Table 2.1 presents the classification of the terrain categories as a function of the roughness length, z0.

Table 2.1. Roughness length, z0, in metres, for various terrain categories [3] 1), 2), 3)

Terrain category

Terrain descriptionz0,m

zmin,m

0 Sea or coastal areas exposed to winds blowing from the sea 0.003 1

ILakes or flat and horizontal areas with negligible vegetation and without obstacles

0.01 1

IIOpen terrain - areas with grass and/or isolated obstacles (trees, buildings) located at distances of at least 20 times the height of the obstacle

0.05 2

IIIAreas with uniform cover of vegetation, buildings, or isolated obstacles located at distances of no more than 20 times the height of the obstacle (e.g. villages, suburban terrain, forests)

0.3 5

IVAreas where at least 15 of the surface is covered with buildings more than 10 m high (e.g. urban areas)

1.0 101) Lower values of the roughness length z0 shall lead to higher values of the mean wind velocity2) To be included in terrain categories III and IV, the respective terrain must cover a distance of at least 500 m and 800 m, respectively, in the vicinity of the structure.

(2) The variation of mean wind velocity with the height above ground level caused by the roughness of the surface shall be represented by a logarithmic profile. The mean wind velocity, vm(z) at a height z above ground level depends on the ground roughness and the reference wind speed, vb (without taking into consideration the site orography):

vm ( z )=cr ( z )⋅vb(2.3)

where cr(z) is the roughness factor for wind velocity.

(3) The roughness factor for wind velocity, cr(z) models the variation of the mean wind velocity with the height z above ground level for various terrain categories (with a roughness length z0), as a function of the reference wind velocity:

cr ( z)={kr ( z0)⋅ln( zz 0

) pentru zmin< z ≤zmax= 200 m

cr (z=zmin ) pentru z≤z min

(2.4)

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where the ground factor kr is given by relationship

k r (z0 )=0 ,189⋅( z0

0 , 05 )0 , 07

(2.5).

The values z0 and zmin are given in Table 2.1. The values kr(z0) are given in Table 2.2.

Table 2.2. The kr(z0) and kr2(z0) factors for different terrain categories

Terrain category

0 I II III IV

kr(z0) 0.155 0.169 0.189 0.214 0.233kr

2(z0) 0.024 0.028 0.036 0.046 0.054

(4) The logarithmic velocity profile shall be valid for moderate and strong winds (mean velocity > 10 m/s) in a neutral atmosphere (where the vertical thermal convection of the air can be ignored).

Although the logarithmic profile is valid for the entire height of the limit atmospheric stratum, its use is especially recommended for the first 200 m from the ground surface (representing approximately 10 % of the height of the limit atmospheric stratum).

(5) If the terrain orography (isolated hills, cliffs) increases the wind velocity by more than 5 % of the value calculated without taking into consideration the orographic effects (the orography factor co is higher than 1.05), the mean velocity calculated with relationship (2.3) shall be multiplied by the orography factor co (see relationship 2.6). Annex B presents a procedure for calculating the orography factor c0.

The effects of orography may be neglected when the average slope of the upwind terrain (compared to the direction of air flow) is less than 3°. The upwind terrain may be considered up to a distance equal to 10 times the height of the isolated orographic element.

If the orographic effects cannot be neglected, the mean wind velocity, vm(z) at a height z above ground level shall be determined with relationship:

vm ( z )=co⋅cr ( z )⋅vb(2.6)

(6) If the building/structure being analysed is/will be located in the vicinity of another structure that is at least twice as high as the average height of the neighbouring structures, then it can be exposed (depending on the geometry of the structure) to increased wind velocities for certain wind directions. Annex B presents a method for considering this effect.

(7) The effect of neighbouring buildings (located at small distances away) may also be taken into account when assessing the mean wind velocity. Annex B presents an approximate method for considering this effect.

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(8) The mean dynamic wind pressure, qm(z) at a height z above ground level (without taking into consideration the orography of the site) shall depend on the ground roughness and the reference value of the dynamic wind pressure, qb and shall be determined with relationship:

qm ( z )=cr2 ( z)⋅qb

(2.7)

where cr2(z) is the roughness factor for dynamic wind pressure.

If the orographic effects cannot be neglected, the mean dynamic wind pressure, qm(z) at a height z above ground level shall be determined with relationship:

qm ( z )=co2⋅cr

2 ( z)⋅qb(2.8)

(9) The roughness factor for dynamic wind pressure, cr2(z) models the variation of the mean

wind pressure with the height z above ground level for various terrain categories (with a roughness length z0), as a function of the reference value of the dynamic wind pressure:

cr2 ( z )={k r

2( z0)⋅[ ln( zz 0

) ]2

pentru zmin< z ≤z max= 200 m

cr2 ( z=zmin ) pentru z≤zmin (2.9)

The values kr2(z0) for the five terrain categories are given in Table 2.2.

2.4 Wind turbulence. Peak wind velocity and dynamic pressure

(1) The wind turbulence intensity, Iv shall characterise the fluctuation of the instantaneous wind velocity in the region of the mean velocity. The turbulence intensity at a height z above ground level shall be defined as the ratio between the standard deviation σv of the fluctuation of the instantaneous wind velocity, v(z,t) and the mean wind velocity at a height z, vm(z):

I v ( z )=σ v

vm ( z )(2.10)

(2) The turbulence intensity at a height z shall be determined with relationship:

I v ( z )={√ β

2,5⋅ln( zz0)

pentru zmin< z ≤zmax= 200 m

I v (z=z min ) pentru z≤zmin(2.11)

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(3) The values of the factor of proportionality shall vary with the ground roughness (z0, m) and can be considered, in a simplified way, to be independent of the height z above ground level:

4,5≤β=4,5−0 ,856 ln ( z0)≤7,5(2.12)

The values √ β are given in Table 2.3, so that they can be used in relationship (2.11).

Table 2.3. √ β values, depending on the terrain categoryTerrain category 0 I II III IV

√ β 2.74 2.74 2.66 2.35 2.12

(4) The peak wind velocity, vp(z) at a height z above ground level, caused by gusts of wind, shall be determined with relationship:

v p ( z )=cpv ( z )⋅vm ( z )(2.13)

where cpv(z) is the gust factor for the mean wind velocity.

(5) The gust factor for the mean wind velocity, cpv(z) at a height z above ground level shall be defined as the ratio between the peak wind velocity (caused by gusts of turbulent wind) and the mean value (averaged over 10 minutes) at a height z of the wind velocity:

cpv ( z )=1+g⋅I v ( z )=1+3,5⋅I v ( z )(2.14)

where g is the peak factor whose recommended value is g=3.5

(6) The peak dynamic wind pressure, qp(z) at a height z above ground level, caused by gusts of wind, shall be determined with relationship:

q p ( z )=cpq ( z )⋅qm ( z )(2.15)

(7) The gust factor for the mean dynamic wind pressure, cpq(z) at a height z above ground level shall be defined as the ratio between the peak dynamic wind pressure (caused by gusts of wind) and the mean dynamic wind pressure (caused by the mean wind velocity) at a height z, namely:

cpq ( z )=1+2 g⋅I v ( z )=1+7⋅I v ( z )(2.16)

(8) The peak dynamic wind pressure, qp(z) at a height z above ground level can be expressed as a function of the reference value of the dynamic wind pressure, qb (at 10 m, in open country terrain – terrain category II):

q p ( z )=cpq ( z )⋅qm ( z )=cpq ( z )⋅cr2 ( z )⋅qb

(2.17)

21

(9) The exposure (or combined) factor, ce(z) shall be defined as the product between the gust factor, cpq(z) and the roughness factor, cr

2(z):

ce ( z )=cpq ( z )⋅cr2 ( z )

(2.18)

The exposure factor variation for various terrain categories is shown in Figure 2.2.

(10) If the orographic effect cannot be neglected, the exposure factor, ce(z) shall also take into consideration the factor c0

2 (see relationship 2.8) as follows:

ce ( z )=c02⋅cr

2 ( z )⋅cpq ( z )(2.19)

(11) Using relationships (2.17) and (2.18), the peak dynamic wind pressure at a height z above ground level, qp(z) can be expressed in summary as a function of the exposure factor, ce(z) and the reference value of the dynamic wind pressure, qb:

q p ( z )=ce ( z )⋅qb(2.20)

0

20

40

60

80

100

120

140

160

180

200

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Inal

tim

ea d

easu

pra

tere

nulu

i

z, m

Factorul de expunere, ce(z)

Teren categoria 0

Teren categoria I

Teren categoria II

Teren categoria III

Teren categoria IV

Fig. 2.2 Exposure factor, ce(z)

3 WIND ACTION ON BUILDINGS AND OTHER STRUCTURES

22

Terrain of category IV

Terrain of category III

Terrain of category IITerrain of category I

Terrain of category 0

Exposure factor, ce(z)

Hei

ght a

bove

gro

und

leve

l z, m

3.1 General aspects

(1) Chapter 3 presents the main elements and methods used to assess the action and effects of wind on buildings and other common structures.

(2) The equivalent static wind action shall be defined as an action which, when applied statically to the structure or its elements, causes the expected maximum values of the displacement and effort induced by the actual wind action.

(3) The wind action shall be represented by the pressures applied by the wind to the surfaces of buildings and structures, or by the forces applied by the wind on buildings and other structures. Wind actions are variable over time and act both directly, as pressure/suction on the exterior surfaces of enclosed structures and buildings, as well as indirectly, on the interior surfaces of enclosed structures and buildings, due to the porosity of the exterior surfaces. The pressure/suction can also act directly on the interior surfaces of open structures and buildings. The pressure/suction shall act on the surface of the structures, creating normal forces on their surfaces. In addition, when large structural surfaces are exposed to the wind, the horizontal frictional forces that act tangentially to the respective surfaces can have significant effects.

(4) Wind action shall be classified as a fixed variable action; wind actions assessed in the form of pressure/suction or forces shall be represented by their characteristic values.

(5) Wind actions on structures with a dynamic along-wind response shall be represented, in a simplified way, by a set of pressures/suctions or equivalent static forces which shall be obtained by multiplying the peak values of the pressure/suction or forces that act on the structure with the dynamic response coefficient.

(6) The total response in the direction of turbulent wind shall be determined as the sum between:

i. the component which displays a static action, and

ii. the fluctuating resonant component, caused by those fluctuations of turbulent excitation whose frequency is close to the vibration frequencies of the structure.

The provisions stipulated in this code shall enable assessment of the dynamic along-wind response caused by the frequency content of the turbulent wind in resonance with the fundamental frequency of along-wind vibration.

(7) The assessment of the effects of the wind on buildings/structures that are unusual in terms of type, complexity and dimensions, structures with a height (buildings, antennas) or spans (bridges) above 200 m, anchored antennas, and suspension bridges shall require special wind engineering studies.

(8) for very flexible structures, such as cables, antennas, towers, chimneys, and bridges, the wind-structure interaction can lead to their aeroelastic response. Chapter 6 includes simplified rules for assessing the aeroelastic response.

23

(9) In accordance with the provisions of CR 0, structures can be divided into importance-exposure classes depending on the human and economic consequences that can be caused by a major natural and/or anthropic hazard, as well as their role in the post-hazard response activities carried out by the community (Table 3.1).

(10) To enable assessment of the wind action on structures, each importance-exposure class (I-IV) shall be associated with an importance - exposure factor, Iw applied to its characteristic value. The values of the importance - exposure factor, Iw for wind actions are:

- Iw =1.15 for structures belonging to importance-exposure classes I and II;- Iw =1.00 for structures belonging to importance-exposure classes III and IV.

Table 3.1 Importance-exposure classes for structures

Importance-exposure

classBuildings Engineering structures

Class I

Structures that are essential for the community

(a) Hospitals and other health buildings equipped with emergency services and operating theatres

(b) Fire-fighting stations, police stations, and garages for the vehicles used by various types of emergency services

(c) Stations for the production and distribution of power and/or which provide essential services to the other categories of structures

(d) Buildings which contain toxic gases, explosives, and other dangerous substances

(e) Centres for communication and coordination of emergency situations

(f) Emergency shelters(g) Buildings with functions that are

essential for public administration(h) Buildings with functions that are

essential for public order and national defence and security

(i) Very tall buildings, regardless of their function (buildings with a total above-ground height of 45 m or higher)

and other buildings of the same type

(a) Water tanks, water treatment, purification, and pumping stations

(b) Power transformer substations(c) Structures which contain

radioactive materials(d) Structures with functions that are

essential for public order and national defence and security

(e) Telecommunication towers (f) Air and sea traffic control towers(g) Pillars for electric power

transmission and distribution lines

and other structures of the same type

Class II Structures which, in the event of an emergency, may pose a major threat to

human life

24

(a) Hospitals and other health buildings, other than those belonging to class I, which have a capacity of over 100 persons in the total exposed area

(b) Schools, high-schools, universities, or other education buildings, which have a capacity of over 250 persons in the total exposed area

(c) elderly care homes, creches, nurseries, and other care facilities, which have a capacity of over 150 persons in the total exposed area

(d) Residential, office or commercial buildings, which have a capacity of over300 persons in the total exposed area

(e) Conference, theatre and exhibition halls, with a capacity of over 200 persons in the total exposed area

(f) Buildings belonging to the national cultural patrimony, museums, etc.

(g) Mall-type buildings, with a capacity of over 3 000 persons in the total exposed area

(h) Prisons(i) Buildings which directly serve the

following facilities: electrical substations, water treatment, purification and pumping stations, power production and distribution stations, telecommunication centres

(j) Tall buildings, regardless of their function (buildings with a total above-ground height between 28 m and 45 m)

and other buildings of the same type

(a) Stadium stands or sports halls(b) Structures which are used to store

explosives, toxic gas, and other dangerous substances

(c) Underground and above-ground tanks used to store flammable materials (gas, liquids)

(d) Water towers(e) Cooling towers for thermal power

stations, industrial parks

and other structures of the same type

Class III All other structures, except for those belonging to classes I, II and IV

Class IVTemporary structures, agricultural structures, warehouse buildings, etc. which are

characterised by a low risk of human life loss

3.2 Wind pressure on surfaces

(1) The wind pressure/suction which acts on the exterior rigid surfaces of a building/structure shall be determined with the relationship:

25

we=γ Iw⋅cpe⋅qp ( ze )(3.1)

where:

qp(ze) is the peak dynamic wind pressure determined at a height ze;

ze is the reference height for external pressure (see Chapter 4);

cpe is the aerodynamic pressure/suction coefficient for exterior surfaces (see Chapter 4);

Iw is the importance – exposure factor.

(2) The wind pressure/suction which acts on the interior rigid surfaces of a building/structure shall be determined with the relationship:

w i=γIw⋅cpi⋅qp (zi )(3.2)

where:

qp(zi) is the peak dynamic wind pressure determined at a height zi;

zi is the reference height for internal pressure (see Chapter 4);

cpi is the aerodynamic pressure/suction coefficient for interior surfaces (see Chapter 4);


(3) The resultant (total) wind pressure on a structural element shall be the difference between the pressure (towards the surface) and suction (away from the surface) on the two faces of the element; the pressure and suction shall be considered with their sign. The pressure shall be considered with the (+) sign and the suction shall be considered with the sign (-) (see Figure 3.1).

26

Positive internal pressure

Negative internal pressure

pos pos

pos pos

neg neg

neg

neg neg

neg

neg neg

Wind

Wind

Wind

Wind

Figure 3.1 Pressure/suction on surfaces [3]

3.3 Wind forces

(1) The wind force that acts on a building/structure or structural element can be determined in two ways:

i. as a global force, using the aerodynamic force coefficients, or

ii. by adding up the pressures/suctions which act on the (rigid) surfaces of the building/structure, using the aerodynamic pressure/suction coefficients.

(2) The wind force shall be assessed for the most unfavourable wind direction for the building/structure.

(3) The global along-wind force Fw, which acts on a structure or structural element with a reference area Aref positioned perpendicular to the wind direction, shall be determined with the general relationship:

Fw=γ Iw⋅cd⋅c f⋅qp (ze )⋅A ref(3.3)

or by vectorial composition of the forces for the individual structural elements, using relationship:

Fw=γ Iw⋅cd⋅ ∑elemente

c f⋅qp (ze )⋅A ref

(3.4)

In relationships (3.3) and (3.4):

qp(ze) is the peak dynamic wind pressure determined at a height ze;

cd is the dynamic response coefficient of the structure (see Chapter 5);

cf is the aerodynamic force coefficient for the building/structure or the structural element, which shall include the frictional effects (see Chapter 4);

Aref is the reference area, positioned perpendicular to the wind direction, for buildings/structures (relationship (3.3)) or their elements (relationship (3.4));


(4) The global along-wind force, Fw which acts on a building/structure or structural element can be determined by vectorial composition of the forces Fw,e, Fw,i, calculated based on the external and internal pressure/suction with relationships (3.5) and (3.6)

- forces due to pressure/suction being applied to exterior surfaces

Fw ,e=cd⋅ ∑suprafete

we (ze )⋅A ref

(3.5)

- forces due to pressure/suction being applied to interior surfaces

27

Fw ,i= ∑suprafete

wi ( zi )⋅Aref

(3.6)

with the frictional forces, Ffr created by the friction of the air parallel to the exterior surfaces and calculated with relationship (3.7):

F fr=γ Iw⋅c fr⋅q p ( ze )⋅A fr(3.7)

In relationships (3.5), (3.6) and (3.7):

cd is the dynamic response coefficient of the structure (see Chapter 5);

we(ze) is the wind pressure which acts on an individual exterior surface at a height ze;

wi(zi) is the wind pressure which acts on an individual interior surface at a height zi;

Aref is the reference area of the individual surface;

cfr is the friction coefficient (see Point 4.5);

Afr is the area of the exterior surface, parallel to the wind direction (see Point 4.5);


(5) The effects generated by air friction on the surfaces can be neglected when the total area of the surfaces parallel to the wind direction (or slightly inclined from the wind direction) shall represent less than 1/4 of the total area of all exterior cross-wind surfaces. The effects generated by air friction on the surfaces shall not be neglected when performing a test at the limit state of static equilibrium, ECH (see CR 0).

(6) The general torsional effects caused by oblique wind action or non-correlated wind gusts on quasi-parallelepipedal buildings/structures can be estimated, in a simplified way, by taking into consideration the force Fw applied with an eccentricity e = b /10, where b is the dimension of the side of the cross-section of the structure, positioned (quasi)-perpendicular to the wind direction (also see Point 4.1.8).

3.4 Dynamic response coefficient of a structure

3.4.1 General information

(1) The dynamic response coefficient of a structure, cd takes into consideration the amplification of the wind action effects due to structural vibrations that are quasi-resonant with the frequency content of atmospheric turbulence, as well as the reduction of the wind action effects due to the non-simulated occurrence of peak wind pressure on the surface of the structure.

28

(2) The more flexible and lighter the structure, and the lower its level of damping, the higher the structural response amplification shall be. The larger the structural surface exposed to wind action, the more accentuated the structural response reduction due to the non-simultaneous occurrence of peak wind pressures shall be.

3.4.2 Assessment of the dynamic response coefficient

3.4.2.1 Simplified assessment procedure

(1) The dynamic response coefficient, cd can be determined in a simplified way, as follows:

- in accordance with the provisions stipulated in Sub-chapter 5.3, for parallelepipedal buildings with a height of up to 30 m and planar dimensions of up to 50 m;

- cd =1 for facades and roof elements with a natural vibration frequency higher than 5 Hz; the natural vibration frequencies of facades and roof elements can be determined using the provisions stipulated in Annex C; normally, glass-covered openings smaller than 3 m shall have natural frequencies higher than 5 Hz;

- cd = 1 for chimneys with a circular cross-section and a height h < 60 m, which comply with the condition h < 6.5d, where d is the chimney diameter.

(2) If the situation does not match the conditions specified in 3.4.2.1(1), the assessment procedure detailed in 3.4.2.2 shall be used.

3.4.2.2 Detailed assessment procedure

(1) In general, the dynamic response coefficient, cd shall be determined with the following relationship:

cd=1+2⋅k p⋅I v (zs )⋅√B2+R2

1+7⋅I v (z s)(3.8)

where:

zs is the reference height for determining the dynamic response coefficient; this height shall be determined in accordance with Figure 3.2; for situations that are not shown in Figure 3.2, zs can be considered equal to h, the height of the structure;

kp is the peak factor for the maximum extreme response of the structure; the calculation for the peak factor, kp is given in Chapter 5;

Iv is the wind turbulence intensity, as defined in Sub-chapter 2.4;

B2 is the non-resonant (quasi-static) response factor, which determines the correlation of the wind pressure on the surface of the structure (determines the non-resonant response component); the detailed calculation for the non-resonant response factor, B2

is given in Chapter 5;

29

R2 is the resonant response factor, which determines that dynamic amplification effects of the structural response, caused by the frequency content of the turbulence in quasi-resonance with the fundamental natural vibration frequency of the structure (determines the resonant response component); the detailed calculation for the resonant response factor, R2 is given in Chapter 5.

(2) Relationship (3.8) is based on the hypothesis that only the along-wind vibrations of the structure, which corresponds to its fundamental natural vibration mode, are important.

zS = 0.6 . h zmin zs=h1+h2≥zmin zs=h1+

h2≥zmin

a) vertical structures, buildings.

b) structures which vibrate in the horizontal plane, girders

c) (advertising) board type structures

Figure 3.2. Reference height zs for the dynamic wind calculation of parallelepipedal structures [3]

(3) For tall or flexible buildings (height h ≥ 30 m or natural vibration frequency n1 ≤ 1 Hz) the maximum along-wind displacement and acceleration of the building must be checked, the former assessed at a height z = zs and the latter assessed at a height z = h. A method for determining these response values is given in Chapter 5.

(4) For slender buildings (h/d > 4) and chimneys (h/d > 6.5) positioned in pairs or groups, the increase of the wind effects due to turbulent backwater shall be considered (see Chapter 6).

(5) The effects of turbulent backwater on a building or chimney can, in a simplified way, be considered negligible if at least one of the following requirements is complied with:

- the distance between two buildings or chimneys is 25 times longer than the size of the structure or chimney located upwind from the direction of the air flow, measured perpendicular to the wind direction;

- the fundamental natural vibration frequency of the building or chimney (for which the effects of backwater turbulence are assessed) is higher than 1 Hz.

30

(6) If the requirements stipulated in 3.4.2.2(5) are not met, wind tunnel tests must be carried out.

4 AERODYNAMIC PRESSURE/SUCTION AND FORCE COEFFICIENTS

31

4.1 General information

(1) The wind effects on the rigid surfaces of buildings and structures can be assessed in two ways: (i) using aerodynamic pressure/suction coefficients, and (ii) using aerodynamic force coefficients.

(2) In general, aerodynamic coefficients shall depend on: the geometry and dimensions of the structure, the wind approach angle, the roughness category of the ground within the site where the structure is located; the Reynolds number, etc.

(3) The provisions of this chapter refer to determining the aerodynamic coefficients required in order to assess wind action on the rigid surfaces of buildings and structures. Depending on the element or building/structure for which the wind action needs to be assessed, the aerodynamic coefficients used can be:

- aerodynamic external and internal pressure/suction coefficients, cpe(i), see 4.1 (4);

- aerodynamic external (total) pressure coefficients, cp, net, see 4.1 (5);

- friction coefficients, cfr, see 4.1 (6);

- aerodynamic force coefficients, cf, see 4.1 (7).

(4) The aerodynamic external pressure/suction coefficients shall be used to determine the wind pressure/suction on the exterior rigid surfaces of buildings and structures; the aerodynamic internal pressure/suction coefficients shall be used to determine the wind pressure/suction on the interior rigid surfaces of buildings and structures.

Aerodynamic external pressure/suction coefficients can be divided into global coefficients and local coefficients. Local coefficients are aerodynamic pressure/suction coefficients for exposed areas of 1 m2 and shall be used to design small elements and fixings. Global coefficients are aerodynamic pressure/suction coefficients for exposed areas larger than 10 m2

and shall be used to design buildings/structures or their elements with exposed areas larger than 10 m2.

The aerodynamic internal and external pressure/suction coefficients shall be determined for:

- buildings, using the provisions stipulated in 4.2, both for internal pressure/suction and for external pressure/suction,

- circular cylinders, using the provisions stipulated in 4.2.9, for internal pressure/suction, and the provisions stipulated in 4.9.1, for external pressure/suction.

(5) The resultant (total) pressure coefficients shall be used to determine the resultant wind pressure/suction on the rigid surfaces of buildings/structures or their components.

The resultant pressure/suction coefficients shall be determined for:

- canopies, using the provisions stipulated in 4.3;

32

- free-standing walls, parapets, advertising boards and fences, using the provisions stipulated in 4.4.

(6) The friction coefficients shall be determined for walls and the surfaces defined in 3.3 (4) and (5), using the provisions stipulated in 4.5.

(7) The aerodynamic force coefficients shall be used to determine the global wind force applied to the structure, structural element or component, which shall also include friction, unless this is explicitly excluded.

The aerodynamic force coefficients shall be determined for:

- boards, using the provisions stipulated in 4.3;

- structural elements with a rectangular cross-section, using the provisions stipulated in 4.6;

- structural elements with a sharp edge cross-section, using the provisions stipulated in 4.7;

- structural elements with a regular polygonal cross-section, using the provisions stipulated in 4.8;

- circular cylinders, using the provisions stipulated in 4.9.2 and 4.9.3;

- spheres, using the provisions stipulated in 4.10;

- lattice structures and scaffolding, using the provisions stipulated in 4.11;

- flags, using the provisions stipulated in 4.12.

(8) If instantaneous wind fluctuations on the rigid surfaces of a structure can lead to significant asymmetric loads and the shape of the structure is sensitive to such loads (e.g. symmetric buildings with a single central core subjected to torsion), then their effect must be taken into consideration. Therefore, the pressure/suction distribution shown in Figure 4.1 shall be used for torsionally sensitive rectangular structures, in order to represent the torsional effects caused by a non-perpendicular incident wind or a lack of correlation between the peak wind pressures which act on different points of the structure.

(9) If ice or snow alters the geometry of the structure and changes its shape and/or reference area, the latter shall be those corresponding to the surface of the snow or ice layer.

33

Figure 4.1 Wind pressure/suction distribution for considering torsional effects [3]

NOTE: The areas and values for cpe are given in Table 4.1 and Figure 4.5

4.2 Buildings

4.2.1 General information

(1) The aerodynamic external pressure/suction coefficients, cpe, for buildings and individual parts of buildings shall depend on the size of the exposed area - A. These are given in tables, for exposed areas, A of 1 m2 and 10 m2, for typical building configurations, with the notations cpe,1 for local coefficients and cpe,10 for global coefficients.

NOTE 1: The exposed area is the area of a structure through which the wind action is transmitted to the section taken into consideration in the calculations.

NOTE 2: For other values of the exposed area, the variation of aerodynamic coefficients can be obtained from Figure 4.2.

(2) The values cpe,1 shall be used to design small elements and fixings with an area per element of up to 1 m2 (e.g. facade or roof elements). The values cpe,10 shall be used to design elements with an area per element of up to 10 m2 or the supporting structure of a building.

(3) The values cpe,10 and cpe,1 given in Tables 4.1 4.5 are given for the orthogonal wind directions of 00, 900 and 1800.

NOTE: The values given in Tables 4.1 4.5 shall only apply to buildings.

34

cpe – area E

cpe – area D

V

NOTE:cpe = cpe,1 A 1m2

cpe = c pe,1 + (c pe,10 - c pe,1) log10A 1m2 < A < 10m2

cpe = cpe,10 A 10m2

Figure 4.2 Variation of the aerodynamic external pressure/suction coefficient with the dimensions of the area exposed to wind A [3]

(4) For cornices, the pressure on the underside of the cornice shall be equal to the pressure corresponding to the wall area adjacent to the cornice; the pressure on the back of the cornice shall be equal to the pressure corresponding to the adjacent roof area (see Figure 4.3).

Figure 4.3 - Pressures on the roof cornice [3]

4.2.2 Vertical walls of rectangular plane buildings

(1) The reference heights, ze, used to determine the profile of the wind pressure applied to the along-wind vertical walls of rectangular plane buildings (area D, Figure 4.5), shall depend on the h/b ratio and are given in Figure 4.4 for the following three situations:

- for buildings where height h is lower than b, only one area shall be considered;

35

pressure on the back of the cornice

pressure on the underside of the cornice

cornice

- for buildings where height h is higher than b, but lower than 2b, two areas shall be considered: a lower area which extends from ground level to a height equal to b and an upper area;

- for buildings where height h is higher than 2b, several areas shall be considered as follows: a lower area which extends from ground level to a height equal to b; an upper area which extends from the top of the building downwards, for a height b; a middle area, located between the previous two areas, which is divided into horizontal strips with a height hstrip, as shown in Figure 4.4.

To determine the profile of the wind pressure/suction on the side walls and the back wall (areas A, B, C, and E, see Figure 4.5), the reference height, ze, shall be equal to the height of the building.

Facade Reference height

Shape of the wind pressure profile on the surface

36

qp(z)=qp(ze)

qp(z)=qp(h)

qp(z)=qp(b)

Figure 4.4 Reference heights ze and the corresponding wind pressure profile as a function of h and b

NOTE: The wind action direction shall be perpendicular to the plane delimited by h and b [3]

(2) Areas A, B, C, D, and E for which the aerodynamic external pressure/suction coefficients cpe,10 and cpe,1 are defined are given in Figure 4.5. The values of the aerodynamic external pressure/suction coefficients cpe,10 and cpe,1 are given in Table 4.1, as a function of the h/d ratio. The intermediary values can be obtained by linear interpolation. The values given in Table 4.1 can also be used for the walls of buildings with single- or double-pitched roofs.

Table 4.1 Values of the aerodynamic external pressure/suction coefficients for the vertical walls of rectangular plane buildings [3]

Area A B C D E

h/d cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

5 -1.2 -1.4 -0.8 -1.1 -0.5 +0.8 +1.0 -0.71 -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: For buildings with h/d > 5, the total wind force shall be directly assessed, based on the rules given in 4.6–4.8 and 4.9.2 for aerodynamic force coefficients.

37

qp(z)=qp(b)

qp(z)=qp(h)

qp(z)=qp(zstrip)ze=zstriphstrip

Figure 4.5 Notations for vertical walls [3]

(3) When the wind force applied to building structures is determined by simultaneously applying the aerodynamic pressure/suction coefficients cpe to the (exposed) front area and the (non-exposed) back area (areas D and E) of the building, the lack of correlation of the wind pressures between the two areas can be considered as follows: for buildings where h/d ≥ 5, the resultant force shall be multiplied by 1; for buildings where h/d ≤ 1, the resultant force shall be multiplied by 0.85; for intermediary h/d values, linear interpolation shall be used.

4.2.3 Flat roofs

(1) Roofs shall be considered to be flat if the slope α is within the range -50< α <50.

(2) Roofs shall be divided into exposure areas in accordance with Figure 4.6.

38

Winddirection

Winddirection

Winddirection

Winddirection

Winddirection

Winddirection

Winddirection

Elevation

Elevation for e ≥ d Elevation for e ≥ 5d

Elevation for e < d

e = b or 2h, whichever is smaller

b: dimension of the side perpendicular to the wind direction

(3) The reference height for flat roofs and roofs with curved eaves shall be considered to be h. The reference height for flat roofs that have an attic (with parapets) shall be considered to be h + hp, see Figure 4.6

(4) The aerodynamic pressure/suction coefficients for each area are given in Table 4.2.

(5) The resultant aerodynamic pressure coefficient on the attic/parapet shall be determined using the provisions stipulated in 4.4.

Figure 4.6 - Notations for flat roofs [3]

39

Wind directio

n

e=b or 2hwhichever is smaller

b - dimension of the side perpendicular to the wind direction

reference height:ze = h

attic (parapet) curved or mansard eaves

Eaves limit

ze = hze = h + hp

Table 4.2 Values of the aerodynamic external pressure / suction coefficients for flat roofs [3]

Type of roof

AreaF G H I

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

Straight edges -1.8 -2.5 -1.2 -2.0 -0.7 -1.2+0.2-0.2

With parapets

hp/h = 0.025 -1.6 -2.2 -1.1 -1.8 -0.7 -1.2+0.2-0.2

hp/h = 0.05 -1.4 -2.0 -0,9 -1.6 -0.7 -1.2+0.2-0.2

hp/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 can be used for the intermediary values of hp/h and r/h.

NOTE 2. For roofs with mansard eaves, linear interpolation between α = 30°, 45° and α = 60° can be used. For α > 60°, linear interpolation can be used, between the values for α = 60° and the values for flat roofs with straight edges. NOTE 3. The values with both signs shall be taken into consideration for area I.NOTE 4. For mansard eaves, the aerodynamic external pressure coefficients are given in Table 4.4a “Aerodynamic external pressure/suction coefficients for double-pitched roofs (wind direction = 0°)”, Areas F and G, by taking into consideration the angle of the mansard eaves.NOTE 5. The aerodynamic external pressure coefficients for curved eaves shall be obtained by linear interpolation along the curve between the values for the walls and the values for the roof.NOTE 6. For mansard eaves with a horizontal dimension less than e/10, the values corresponding to straight edges shall be used.

(6) For long roofs, the air friction forces along the building shall be taken into consideration.

4.2.4 Single pitch roofs

(1) The roof shall be divided into exposure areas in accordance with Figure 4.7.

40

(2) The reference height, ze shall be considered equal to h.


(4) For long roofs, the air friction forces shall be taken into consideration.

Figure 4.7 Notations for single pitch roofs [3]

41

(b) wind direction = 00 and = 1800


Winddirection

Wind directio

n

wind wind

e=b or 2hwhichever is smaller

b - side dimensionperpendicular to wind direction

(c) wind direction = 900

upper eaves

lower eaves

upper eaves

lower eaves

upper eaves

lower eaves

(a) general case

F

upper

F

lower

Table 4.30a Values of the aerodynamic external pressure/suction coefficients for single pitch roofs [3]

Slope angle

α

Areas for wind direction = 0° Areas of wind direction = 180°F G H F G H

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

5°-1.7 -2.5 -1.2 -2.0 -0.6 -1.2

-2.3 -2.5 -1.3 -2.0 -0.8 -1.20 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

-0.6 -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 -0.575° +0.8 +0.8 +0.8 -0.5 -1.0 -0.5 -0.5

NOTE 1. For = 0° (see Table 4.3a), the pressure shall vary rapidly between the positive values and the negative values on the upwind slope, for a slope angle α from +5° to +45°, so that both the positive values and the negative values are given. Two situations must be taken into consideration for these roofs: one with all positive values and the other with all negative values. Negative and positive values cannot be considered simultaneously for the same face.

NOTE 2. For intermediary slope angles, linear interpolation between values with the same sign can be used. Values equal to 0.0 are given in order to enable interpolation.

Table 4.30b Values of the aerodynamic external pressure/suction coefficients for single pitch roofs [3]

Slope angle α

Areas for wind direction = 90°Fupper Flower G H I

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

5° -2.1 -2.6 -2.1 -2.4 -1.8 -2.0 -0.6 -1.2 -0.515° -2.4 -2.9 -1.6 -2.4 -1.9 -2.5 -0.8 -1.2 -0.7 -1.230° -2.1 -2.9 -1.3 -2.0 -1.5 -2.0 -1.0 -1.3 -0.8 -1.245° -1.5 -2.4 -1.3 -2.0 -1.4 -2.0 -1.0 -1.3 -0.9 -1.260° -1.2 -2.0 -1.2 -2.0 -1.2 -2.0 -1.0 -1.3 -0.7 -1.275° -1.2 -2.0 -1.2 -2.0 -1.2 -2.0 -1.0 -1.3 -0.5

4.2.5 Double-pitched roofs

42

(1) The roof shall be divided into exposure areas in accordance with Figure 4.8.



(4) For long roofs, the air friction forces shall be taken into consideration.

Figure 4.8 Notations for double-pitched roofs [3]

43

(b) wind direction = 00

Winddirection

e = b or 2hwhichever is smaller

b - side dimensionperpendicular to wind direction

upwind slope

Winddirection

(c) wind direction = 900

downwind slopewind

upwind slope

upwind slope

Negative slope anglePositive slope angle

downwind slope

winddownwind slope

Cre

st o

r ea

ves

crest

or eaves

(a) general case

Table 4.40a Values of the aerodynamic external pressure/suction coefficients for double-pitched roofs [3]

Slope angle α

Areas for wind direction = 0°F G H I J

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,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 -0.6

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

30°-0.5 -1.5 -0.5 -1.5 -0.2 -0.4 -0.5

+0.7 +0.7 +0.4 0 0

45°0 0 0 -0.2 -0.3

+0.7 +0.7 +0.6 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. For = 0° the pressure shall vary rapidly between the positive values and the negative values on the upwind slope, for a slope angle α from +5° to +45°, so that both the positive values and the negative values are given. For these roofs, four exposure situations shall be considered, where the highest or the lowest values for areas F, G, and H are combined with the highest or the lowest values for areas I and J. Negative and positive values cannot be considered simultaneous ly

for the same exposed face.

NOTE 2. For intermediary slope angles, linear interpolation between values with the same sign can be used. (For slope angles between α = +5° and α = -5°, the values shall not be interpolated, and the slope roof data given in 4.2.3 shall be used instead). Values equal to 0.0 are given in order to enable interpolation.

Table 4.40b Values of the aerodynamic external pressure/suction coefficients for double-pitched roofs [3]

Slope angle αAreas for wind direction = 90°

F G H Icpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,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

44

Slope angle αAreas for wind direction = 90°

F G H Icpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1

5° -1.6 -2.2 -1.3 -2.0 -0.7 -1.2 -0.615° -1.3 -2.0 -1.3 -2.0 -0.6 -1.2 -0.530° -1.1 -1.5 -1.4 -2.0 -0.8 -1.2 -0.545° -1.1 -1.5 -1.4 -2.0 -0.9 -1.2 -0.560° -1.1 -1.5 -1.2 -2.0 -0.8 -1.0 -0.575° -1.1 -1.5 -1.2 -2.0 -0.8 -1.0 -0.5

4.2.6 Quad pitched roofs

(1) The roof shall be divided into areas in accordance with Figure 4.9.



(4) For long roofs, the frictional forces shall be taken into consideration.

Figure 4.9 Notations for quad pitched roofs [3]

45

(a) wind direction = 00


e = b or 2hwhichever is smaller

b - dimension of the side perpendicular to the wind direction

(b) wind direction = 900

Wind direction

Wind direction

Wind Wind

Table 4.5 Values of the aerodynamic external pressure/suction coefficients for quad pitched roofs [3]

Slope angle α0 for = 0° α90for = 90°

Areas for wind direction = 0° and = 90°

F G H I J K L M N

cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,1 cpe,10 cpe,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 -0.40 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

-0.3 -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. For = 0°, the pressure shall vary rapidly between the positive values and the negative values on the upwind slope, for a slope angle α from +5° to +45°, so that both the positive values and the negative values are given. Two situations must be taken into consideration for these roofs: one with all positive values and the other with all negative values. Negative and positive values cannot be considered simultaneously for the same face.

NOTE 2. For intermediary slope angles, linear interpolation between values with the same sign can be used. Values equal to 0.0 are given in order to enable interpolation.

NOTE 3. The values of the aerodynamic pressure/suction coefficients shall be determined as a function of the upwind slope angle.

4.2.7 Multispan roofs

(1) The aerodynamic pressure/suction coefficients for wind directions 0°, 90°, and 180° on each span of a multispan roof can be calculated as a function of the aerodynamic pressure/suction coefficient for each individual span.

The modifying factors for (local or global) pressures for wind directions 0°, 90°, and 180° on each span shall be calculated:

- from the provisions of Point 4.2.4 for single pitch roofs, modified for their position in accordance with Figure 4.10a and b;

46

- from the provisions of Point 4.2.5 for double-pitched roofs for < 0, modified for their position in accordance with Figure 4.10c and d.

(2) Areas F/G/J shall only be taken into consideration for the upwind slope. Areas H and I shall be taken into consideration for each span of a multiple roof.

(3) The reference height, ze shall be considered to be the height of the structure, h. see Figure 4.10.

(4) If no resultant horizontal force applied to the roof is determined, each span shall be

designed for a minimum horizontal force equal to 0 ,05⋅qp ( ze )⋅Ades

, where Ades is the planar area of each span of the roof.

47

NOTE 1. In configuration b) two cases should be considered, depending on the sign of the aerodynamic pressure/suction coefficient cpe on the first roof.

NOTE 2. In configuration c, the first and the last cpe shall correspond to cpe a single pitch roof, whilst the second and all the other cpe shall correspond to cpe a double-pitched roof.

Figure 4.10 Notations for multispan roofs [3]

4.2.8 Cylindrical roofs and domes

(1) The roof shall be divided into areas in accordance with Figure 4.11 and Figure 4.12.

48

wal

l

wal

l

wal

lw

all

wal

l

wal

lw

all

wal

l

wal

l

wal

l

(2) The reference height, ze shall be considered to be: ze = h + f.

(3) The values cpe,10 and cpe,1 for different areas are given in Figures 4.11 and 4.12.

NOTE: In area A, for 0 < h/d < 0.5, cpe,10 shall be obtained by linear interpolation.In area A, for 0.2 f/d 0.3 and h/d 0.5, two values shall be considered for c

pe,10; the diagram does not apply to flat roofs.

Figure 4.11 Aerodynamic external pressure/suction coefficients cpe,10

for cylindrical roofs with a rectangular plane shape [3]

49

NOTE. cpe,10 shall be constant along circular arcs, sphere intersections, and planes perpendicular to the wind direction; as a first approximation, cpe,10 can be determined by linear interpolation between the values in areas A, B, and C along the circular arcs that are parallel with the wind. In the same way, the values cpe,10 in area A can be obtained, by linear interpolation in Figure 4.12, if 0 < h/d < 1 and the values in area B or C can be obtained if 0 < h/d < 0.5.

Figure 4.12 Aerodynamic external pressure/suction coefficients cpe,10

for dome roofs with a planar circular shape [3]

(2) The aerodynamic pressure/suction coefficients for the walls of rectangular plane buildings and cylindrical roofs can be determined in accordance with Point 4.2.2.

4.2.9 Internal pressure

(1) Internal and external pressure shall be considered to act at the same time (simultaneously). The most unfavourable combination of external and internal pressures shall be considered for every possible combination of openings and air leakage paths.

50

cpe,10 shall be constant along each plane

(2) The aerodynamic internal pressure/suction coefficient, cpi, shall depend on the size and distribution of the openings in the building envelope. When on at least two sides of the building (facades or roof) the total area of the openings on each side is more than 30 % of the area of that side, the actions on the structure shall not be calculated using the rules given in this sub-chapter, but using the rules stipulated in Sub-chapters 4.3 and 4.4.

Note. The openings of a building include small openings (such as: open windows, ventilators, chimneys, etc.) as well as background permeability (which includes air leakage around doors, windows, technical equipment and the building envelope). The background permeability is typically between 0.01 % and 0.1 % of the area of the respective face.

(4) A face of a building can be considered dominant when the area of all openings on that face is at least twice the area of the gaps and openings on all of the other faces of the respective building.

(5) For a building with a dominant face, the internal pressure shall be taken as a percentage of the external pressure which acts on the openings on the dominant face. The values given by relationships (4.1) and (4.2) shall be used.

When the area of the openings on a dominant face is twice the area of the openings and gaps on the other faces of the building, then

cpi = 0.75 . cpe (4.1)

When the area of the openings on a dominant face is at least three times the area of the openings and gaps on the other faces of the building, then

cpi = 0.90 . cpe (4.2)

where cpe is the aerodynamic external pressure/suction coefficient at the openings in the

dominant face. When these openings are located in areas with different values of external pressure, an area-weighted average coefficient cpe shall be used.

When the area of the openings on a dominant face is between 2 and 3 times the area of the openings in the remaining faces of the building, linear interpolation can be used to calculate cpi.

(6) For buildings without a dominant face, the aerodynamic internal pressure/suction coefficient cpi is given in Figure 4.13 and shall be determined as a function of the ratio between the height and the width of the building h/d, as well as the opening ratio for each wind direction , which shall be determined with relationship (4.3):

μ=∑ ariilor golurilor unde c pe este negativ sau zero

∑ ariilor tuturor golurilor (4.3)

NOTE 1. This relationship shall apply to the facades and roofs of buildings with or without internal partitions.

51

NOTE 2 When it is not possible, or not considered justified to estimate the value for particular cases, then cpi shall be taken as +0.2 sau –0.3 (the value that leads to the most unfavourable effects shall be taken into consideration).

Figure 4.13 Aerodynamic internal pressure/suction coefficients, cpi for uniformly distributed openings [3]

NOTE. Linear interpolation can be used for values between h/d = 0.25 and h/d = 1.0

(7) The reference height, zi, for internal pressures shall be considered equal to the reference height, ze for external pressure/suction on the facades which, through their openings, contribute to the creation of internal pressure. If there are several openings, the highest value of ze shall be used to determine zi.

(8) The aerodynamic internal pressure/suction coefficient for open silos and chimneys shall be:

cpi = -0.60 (4.4)

The aerodynamic internal pressure/suction coefficient for a vented tank with small openings shall be:

cpi = -0.40 (4.5)

The reference height zi shall be equal to the height of the structure.

4.2.10 Pressure on exterior walls or roofs with several skins

(1) For exterior walls or roofs with more than one skin, the wind force shall be calculated separately for each skin.

(2) The permeability of the skin shall be defined as the ratio between the total area of the openings and the total area of the envelope. An envelope shall be defined as impermeable if the value is lower than 0.1 %.

52

(3) If a skin is permeable, then the wind force on the impermeable skin shall be calculated as the difference between the external pressure and the internal pressure, as described in Point 3.2(3). If several skins are permeable, then the wind force on each skin shall depend on:

- the relative rigidity of the skins;

- the external and internal pressures;

- the distance between the skins.

The wind pressure on the most rigid skin shall be calculated as the difference between the external pressure and the internal pressure.

In cases where the airflow between the layers of the envelope is blocked (Figure 7.14(a)) and the free distance between the skins is less than 100 mm (the thermal insulation material is included in one of the skins and there is no airflow through the insulation), the following rules should be applied:

- for walls and roofs with uniformly distributed openings, which have an impermeable skin on the inside and a permeable skin on the outside, the wind force on the outside skin can be calculated with cp,net = (2/3)∙cpe for pressure and cp,net = (1/3)∙cpe for suction. The wind force on the inside skin can be calculated with cp,net = cpe - cpi;

- for walls and roofs with an impermeable skin on the inside and a more rigid, impermeable skin on the outside, the wind force on the outside skin can be calculated with cp,net = cpe - cpi;

- for walls and roofs with a permeable skin on the inside and with uniformly distributed openings and an impermeable skin on the outside, the wind force on the outside skin can be calculated with cp,net = cpe - cpi. The wind force on the inside skin can be calculated with cp,net = 1/3∙cpi;

- for walls and roofs with an impermeable skin on the outside and an impermeable more rigid skin on the inside, the wind force on the outside skin can be calculated with cp,net

= cpe. The wind force on the inside skin can be calculated with cp,net = cpe - cpi.

These rules shall not apply if the air inlets allow the air layer to pass through to faces of the building other than the face on which the wall is located (Figure 4.14(b)).

(a) the extremity of the air layer is closed

53

(b) the extremity of the air layer is open

Figure 4.14 Corner detail for exterior walls with several skins [3]

4.3 Canopies

(1) Canopies are roofs of structures which do not have permanent vertical enclosures, such as petrol stations, agricultural barns, etc.

(2) The degree of air blockage under a canopy is shown in Figure 4.15. It depends on the blockage coefficient , which shall be defined as the ratio between the area of possible obstructions under the canopy and the area under the canopy, both areas being normal to the wind direction ( = 0 corresponds to a canopy which covers an empty space, and = 1 corresponds to a canopy which covers a fully blocked space (but is not a closed building)).

(3) The global aerodynamic force coefficients, cf, and the resultant aerodynamic pressure coefficients cp,net, are given in Tables 4.6, 4.7 and 4.8 for = 0 and = 1; these values take into consideration the combined effect of the wind acting both on the back and on the underside of the canopy, for all wind directions. The intermediary values shall be obtained by linear interpolation.

(4) Behind the position of maximum blockage (from the wind direction), the values cp,net shall be used for = 0.

(5) The global aerodynamic force coefficients shall be used to determine the resultant force. The aerodynamic resultant pressure coefficients shall be used to determine the maximum local pressure for all wind directions and to design the roof elements and fixings.

54

Canopy which covers an empty space ( = 0)

Canopy blocked by the goods stored in its area ( = 1)

Figure 4.15 Airflow in the area of a canopy [3]

(6) Canopies shall be designed for the following test situations, as follows:

- for single pitch canopies (Table 4.6), the load shall be applied to the centre of pressure located at d/4 (d = dimension corresponding to the wind direction, Figure 4.16);

- for double-pitched canopies (Table 4.7), the load shall be applied to the centre of pressure located in the centre of each pitch (Figure 4.17); in addition, a double-pitched canopy must be able to take over a load situation in which one of the pitches takes over the maximum load and the other pitch is unloaded;

- for multi-bay double-pitched canopies, each opening shall be calculated by applying the reduction factors mc given in Table 4.8, to the aerodynamic resultant pressure coefficients cp,net given in Table 4.7.

For canopies with two skins, the load on the impermeable skin and its fixings shall be calculated with cp,net and the load on the permeable skin and its fixing shall be calculated with

1/3 cp,net.

(7) The air friction forces shall also be taken into consideration (see 4.5).

(8) The reference height, ze shall be considered equal to h, as shown in Figures 4.16 and 4.17.

55

Table 4.6 - Global aerodynamic force coefficients, cf and aerodynamic resultant pressure

coefficients, cp,net for single pitch canopies [3]

Resultant pressure coefficients, cp,net

Canopy slope α

Blockage coefficient,

Global force

coefficients, cf

Area A Area B Area C

Maximum, for any + 0.2 + 0.5 + 1.8 + 1.10° Minimum, for = 0 - 0.5 - 0.6 - 1.3 - 1.4

Minimum, for = 1 - 1.3 - 1.5 - 1.8 - 2.2Maximum, for any + 0.4 + 0.8 + 2.1 + 1.3

5° Minimum, for = 0 - 0.7 - 1.1 - 1.7 - 1.8Minimum, for = 1 - 1.4 - 1.6 - 2.2 - 2.5Maximum, for any + 0.5 + 1.2 + 2.4 + 1.6





30° Minimum, for = 0 - 1.8 - 3.0 - 3.8 - 3.6Minimum, for = 1 - 1.4 - 1.5 - 2.2 - 2.7

NOTE. The sign + indicates a downward resultant wind action The sign - indicates an upward resultant wind action.

56

wind

Figure 04.16 Position of the centre of pressure for a single pitch canopy [3]

57

Table 04.7 - Global aerodynamic force coefficients, cf and aerodynamic resultant pressure

coefficients, cp,net for single pitch canopies [3]


Canopy slope α


Global force coefficients, cf

Area A Area B Area C Area D

Maximum, for any + 0.7 + 0.8 + 1.6 + 0.6 + 1.7- 20° Minimum, for = 0 - 0.7 - 0.9 - 1.3 - 1.6 - 0.6

Minimum, for = 1 - 1.3 - 1.5 - 2.4 - 2.4 - 0.6Maximum, for any + 0.5 + 0.6 + 1.5 + 0.7 + 1.4

- 15° Minimum, for = 0 - 0.6 - 0.8 - 1.3 - 1.6 - 0.6Minimum, for = 1 - 1.4 - 1.6 - 2.7 - 2.6 - 0.6Maximum, for any + 0.4 + 0.6 + 1.4 + 0.8 + 1.1



+ 5° Minimum, for = 0 - 0.6 - 0.6 - 1.4 - 1.4 - 1.1Minimum, for = 1 - 1.3 - 1.3 - 2.0 - 1.8 - 1.5Maximum, for any + 0.4 + 0.7 + 1.8 + 1.4 + 0.4





58


Canopy slope α


Global force coefficients, cf

Area A Area B Area C Area D

+ 30° Minimum, for = 0 - 1.0 - 1.4 - 1.9 - 1.4 - 2.0Minimum, for = 1 - 1.3 - 1.4 - 1.8 - 1.4 - 2.0

NOTE. The sign + indicates a downward resultant wind action The sign - indicates an upward resultant wind action.

(9) The loads on each slope of multispan canopies (see Figure 4.18) shall be determined by applying the reduction factors ψmc, given in Table 4.8, to the global force coefficients and the resultant pressure coefficients corresponding to isolated double-pitched canopies.

59

Figure 04.17 Position of the centre of pressure for double-pitched canopies [3]

Table 04.8 Values of the reduction factors, ψmc for multispan canopies [3]

Number of spans

Position Factors ψmc for any blockage coefficient for force coefficients

(applied to a downward action) and pressure

coefficients

for force coefficients (applied to an upward action) and pressure

coefficients1 End span 1.0 0.82 Second span 0.9 0.73 Third and subsequent

spans0.7 0.7

60

Figure 4.18 Multispan canopies [3]

4.4 Free-standing walls, parapets, fences, and advertising boards

(1) The aerodynamic resultant pressure coefficients cp, net for free-standing walls and parapets shall depend on the blockage coefficient, . For solid walls, = 1; for walls which are 80 % solid (walls which have 20 % openings), = 0.8. Walls and fences with a blockage coefficient ≤ 0.8 should be considered to be plane lattices, in accordance with 4.11.

In both cases, the reference area shall be considered to be the total area. For the parapets and noise barriers of bridges, the provisions stipulated in Annex D shall apply.

4.4.1 Free-standing vertical walls and parapets

(1) For free-standing vertical walls and parapets, the aerodynamic resultant pressure coefficients cp,net, are given for areas A, B, C, and D, in accordance with Figure 4.19.

The aerodynamic resultant pressure coefficients, cp,net for free-standing vertical walls and parapets are given in Table 4.9 for two values of the blockage coefficient (see 4.4(1)). These values shall correspond to an oblique wind action on a wall without a corner (see Figure 4.19) and, in the case of a wall with a corner, shall correspond to the two opposite directions shown in Figure 4.19. In both cases, the reference area shall be the total area. Linear interpolation can be used for blockage coefficients between 0.8 and 1.

Table 4.9 Aerodynamic resultant pressure coefficients, cp,net for free-standing vertical walls and parapets [3]

Blockage coefficient

Area A B C D

= 1

without corners

l/h ≤ 3 2.3 1.4 1.2 1.2l/h = 5 2.9 1.8 1.4 1.2l/h ≥ 10 3.4 2.1 1.7 1.2

with corners with a length ≥ ha

2.1 1.8 1.4 1.2

= 0.8 1.2 1.2 1.2 1.2a If the length of the corner is between 0.0 and h, linear interpolation can be used

(2) The reference height for vertical walls shall be equal to ze = h, see Figure 4.19. The reference height for parapets in buildings shall be equal to ze = h + hp, see Figure 4.6.

61

θ θWithout a corner With a corner

Wind approach angle

for l > 4h

for l ≤ 4h

for l ≤ 2h

Figure 4.19 Notations for free-standing vertical walls and parapets [3]

4.4.2 Shelter factors for walls and fences

(1) If there are along-wind walls or fences with a height equal to or higher than a wall or fence with the height h, an additional shelter factor shall be used in order to obtain the aerodynamic resultant pressure coefficient. The value of the shelter factor, s shall depend on the distance between the walls, x and the value of the blockage coefficient, of the wall or panel located upwind compared to the direction of airflow. The s values are represented in Figure 4.20.

62

The aerodynamic resultant pressure coefficient for the sheltered wall cp,net,s shall be given by relationship:

cp,net,s = s cp,net (4.6)

(2) The shelter factor shall not be applied in the end areas, for a distance equal to h measured from the free extremity of the wall.

Figure 4.20 Shelter factor, s for free-standing walls and fences for between 0.8 and 1.0 [3]

4.4.3 Advertising boards

(1) For advertising boards installed at a height zg (measured from ground level) higher than h/4 (see Figure 4.21), the aerodynamic force coefficient shall have the following value:

cf = 1.80 (4.7)

The value obtained with relationship (4.7) shall also be used if zg is lower than h/4 and b/h ≤

1.

(2) The resultant force which is normal to the board shall apply at the height of the board centre, with a horizontal eccentricity e. The horizontal eccentricity e shall have the following value:

e = 0.25 b (4.8)

(3) Advertising boards installed at a height zg (measured from ground level) which is lower than h/4 and b/h > 1 shall be considered to be edge walls (see 4.4.1).

63

x/ h

She

lter

fac

tor

s

The possibility of occurrence of aeroelastic phenomena of divergence and flutter shall be checked.

NOTE 1.Reference height: ze = zg + h/2NOTE 2. Reference area: Aref = b · h

Figure 4.21 Notations for advertising boards [3]

4.5 Friction coefficients

(1) For the situations defined in 3.3(4), the air friction on the exposed surface shall be taken into consideration.

(2) The friction coefficients, cfr for the surfaces of walls and roofs are given in Table 4.10.

(3) The reference area Afr is shown in Figure 4.22. The frictional forces shall be applied to the exterior surface parallel to the wind direction, located at a distance equal to 2·b or 4·h, whichever is lower, from the eaves or corner.

(4) The reference height, ze shall be equal to the height of the building h, see Figure 4.22.

Table 04.10 Friction coefficients, cfr for the surfaces of walls, parapets and roofs [3]

Type of surface Friction coefficient cfr

Smooth (e.g. steel, smooth concrete) 0.01

Rough (e.g. unfinished concrete, bitumen boards) 0.02

Very rough (e.g. ribs, ripples, folds) 0.04

64

Figure 4.22 Reference area for determining the frictional force [3]

4.6 Structural elements with a rectangular cross-section

(1) The aerodynamic force coefficient, cf for structural elements with a rectangular cross-section on which the wind acts perpendicular to one face shall be determined with relationship:

cf = cf,0 ∙ r ∙ (4.9)

where:

cf,0 is the aerodynamic force coefficient for rectangular cross-sections with sharp corners and no free-end airflow (element with infinite length), Figure 4.23;

r is the reduction factor for square cross-sections with rounded corners, which depends on the Reynolds number, see NOTE 1;

- the reduction factor for elements with free-end airflow (the reduction occurs due to additional air leakage paths being provided around an element with finite length), defined in 4.13.

NOTE 1. The approximated upper limits of r (obtained in conditions of reduced turbulence) are given in Figure 4.24. These values shall be considered to be covering values.

NOTE 2. Figure 4.24 can also be used for buildings with h/d > 5.0.

65

wind

Reference area

wind

wind

wind

Figure 04.23 Aerodynamic force coefficients, cf,0 for rectangular cross-sections with sharp

corners and without free-end airflow [3]

Figure 4.24. Reduction factor, r for square cross-sections with rounded corners [3]

(2) The reference area Aref shall be determined with relationship:

Aref = . b (4.10)

where is the length of the structural element being considered.

66

(3) The reference height, ze shall be equal to the maximum height above ground level of the element being considered.

(4) For thin cross-sections (d/b < 0.2), the forces can, at certain wind approach angles, increase to 25 %.

4.7 Structural elements with cross-sections that have sharp edges

(1) The aerodynamic force coefficient, cf of structural elements with cross-sections that have sharp edges (e.g. elements with the cross-sections shown in Figure 4.25) shall be determined with relationship:

cf = cf,0 ∙ (4.11)

where:

cf,0 is the aerodynamic force coefficient for rectangular cross-sections with sharp edges and no free-end airflow;

- the reduction factor for elements with free-end airflow, defined in 4.13.

The recommended value for elements without free-end airflow cf,0 = 2.0. This value shall be obtained in conditions of reduced turbulence and shall be considered to be a covering value.

Figure 4.25 Cross-sections with sharp edges [3]

NOTE. Relationship (4.11) and Figure 4.25 can also be used for buildings with h/d > 5.0.

(2) The reference areas shall be determined as follows (see Figure 4.25):

in direction x: Aref,x = . b

(4.12)in direction y: Aref,y = . d


67

→wind

direction

(3) The reference height, ze shall be equal to the maximum height above ground level of the cross-section being considered.

4.8 Structural elements with a regular polygonal cross-section

(1) The aerodynamic force coefficient, cf for elements with a regular polygonal cross-section with 5 or more faces shall be determined with relationship:

cf = cf,0 ∙ (4.13)

where:

cf,0 is the aerodynamic force coefficient of structural elements without free-end air flow;

- the reduction factor for elements with free-end airflow, defined in 4.13.

The values of the aerodynamic force coefficient, cf,0, obtained in conditions of reduced turbulence, are given in Table 4.11.

Table 4.11 Aerodynamic force coefficient, cf,0 for regular polygonal cross-sections [3]

Number of faces

Section Surface and corner finishing Reynolds number, Re(1) cf,0

5 pentagon all types all values 1.806 hexagon all types all values 1.60

8 octagon

smooth surfacer/b < 0.075 (2)

Re 2.4 105 1.45

Re 3 105 1.30smooth surfacer/b 0.075 (2)

Re 2 105 1.30Re 7 105 1.10

10 decagon all types all values 1.30

12 dodecagon

smooth surface (3)

rounded corners2 105 < Re < 1.2

106 0.90

all other types Re < 4 105 1.30Re > 4 105 1.10

16–18Hexadecagonoctadecagon

smooth surface (3)

rounded corners

Re < 2 105

similar to circular

cylinders, see (4.9)

2 105 Re < 1.2 106

0.70

68

1)The Reynolds number Re is defined in Sub-chapter 4.9 and shall be determined for vm( ze);

2) r = corner radius, b = diameter of the circle circumscribed to the cross-section (see Figure 4.26)

3) In accordance with wind tunnel tests carried out for galvanised steel elements with a cross-section where b=0.3 m and r=0.06 b

Figure 4.26 Regular polygonal cross-section [3]

(2) For buildings where h / d > 5, cf can be determined using relationship (4.13), as well as from the data given in Table 4.11 and Figure 4.25.

(3) The reference area Aref shall be obtained with relationship:

Aref = . b (4.14)

where:

is the length of the structural element being considered;

b is the diameter of the circle circumscribed to the cross-section (see Figure 4.26).

(4) The reference height, ze shall be equal to the maximum height above ground level of the cross-section of the element being considered.

4.9 Circular cylinders

4.9.1 Aerodynamic external pressure/suction coefficients

(1) The aerodynamic external pressure / suction coefficients for structures with circular cross-sections shall depend on the Reynolds number, Re defined with relationship:

Re=b⋅v p (ze )

ν(4.15)

69

where:

b is the diameter of the circular cross-section;

is the kinematic viscosity of air ( = 1510-6 m2/s);

vp (ze) is the peak wind velocity defined at a height ze (see 2.4 (5) and NOTE 2 for Figure 4.27).

(2) The aerodynamic external pressure / suction coefficients, cpe for circular cylinders shall be determined with relationship:

cpe = cp,0 . ψ (4.16)

where:

cp,0 is the aerodynamic external pressure / suction coefficient for elements without free-end airflow (see (3));

is the end-effect factor (see (4)).

(3) The values of the aerodynamic external pressure / suction coefficient, cp,0 are given in Figure 4.27 as a function of the angle at various values of the Reynolds number.

(4) The end-effect factor, shall be given by relationship (4.17):

= 1 for 0° min

(4.17)for min < < A

= for A 180°

where:

A defines the airflow separation point (see Figure 4.27);

- the reduction factor for elements with free-end airflow (end-effect factor) (see 4.13).

70

Figure 4.27 Value distribution of the aerodynamic external pressure / suction coefficients for circular cylinders, at different values of the Reynolds number and without considering the

end-effect [3]

NOTE 1. The intermediary values can be obtained by linear interpolation.

NOTE 2. The characteristic values shown in Figure 4.27 are given in Table 4.12. The data given in the figure and table are obtained using the Reynolds number, calculated using the peak wind velocity, vp(ze).

NOTE 3. The data shown in Figure 4.27 are based on an equivalent roughness of the cylinder, k/b smaller than 510-4. Typical roughness values k are given in Table 4.13.

Table 4.12 Typical values for the pressure distribution in circular cylinders without an end-effect, at different values of the Reynolds number [3]

Re min. cp0,min A cp0,h

5 · 105 85 -2.2 135 -0.4

2 · 106 80 -1.9 120 -0.7

107 75 -1.5 105 -0.8

wheremin characterises the position where the minimum pressure is achieved

on the cylinder surface, in [°]cp0,min is the minimum value of the aerodynamic pressure/suction

coefficientA is the position of the airflow separation point

cp0,h is the reference aerodynamic pressure/ suction coefficient

(5) The reference area, Aref shall be determined with relationship:

Aref = . b (4.18)

71

where is the length of the element being considered.


4.9.2 Aerodynamic force coefficients

(1) The aerodynamic force coefficient cf, for a circular cylinder with a finite height shall be given by relationship:

cf = cf,0 . (4.19)

where:

cf,0 is the aerodynamic force coefficient for cylinders without free-end air flow (see Figure 4.28);

- the end-effect factor (see 4.13).

Figure 4.28 Aerodynamic force coefficient cf,0 for circular cylinders without free-end airflow and for various values of the equivalent roughness k/b [3]

NOTE 1. Figure 4.28 can also be used for buildings with h/d > 5.0.

NOTE 2. Figure 4.28 is based on the Reynolds number calculated using the peak wind velocity, vp(ze).

(2) Table 4.13 gives values of the equivalent roughness k.

72

(3) For braided cables (wire strands), cf,0 shall be equal to 1.2 for any values of the Reynolds number, Re.

Table 4.13 Equivalent roughness, k [3]

Type of surfaceEquivalent

roughness, k Type of surfaceEquivalent

roughness, k[mm] [mm]

Glass 0.0015 Smooth concrete 0.2

Polished metal 0.002 Board 0.5

Fine paint 0.006 Rough concrete 1.0

Sprayed paint 0.02 Raw timber 2.0

Shiny steel 0.05 Rust 2.0

Cast iron 0.2 Masonry 3.0

Galvanised steel 0.2

(4) The reference area, Aref shall be determined with relationship:

Aref = . b (4.20)



(6) The assessment of wind action on cylinders located in the vicinity of a flat surface, for which the ratio between the distances zg/b < 1.5 (see Figure 4.29), requires specialist advice.

Figure 4.29 Cylinder located in the vicinity of a flat surface [3]

4.9.3 Aerodynamic force coefficients for vertical cylinders arranged in line

(1) For vertical cylinders arranged in line, the aerodynamic force coefficient cf,0 shall depend on the direction of the wind action compared to the cylinder line and the ratio between the distance a and the diameter b (see Table 4.14). The aerodynamic force coefficient cf, for any circular cylinder can be obtained with relationship:

cf = cf,0 . . κ (4.21)

73

where:

cf,0 is the aerodynamic force coefficient for cylinders without free-end air flow (see Figure 4.9.2);

is the end-effect factor (see 4.13);

κ is the factor given in Table 4.14 (for the most unfavourable wind direction).

Table 4.14 Factor κ for vertical cylinders arranged in line [3]

a/b κ

2.5 < a/b < 3.5 1.15

3.5 < a/b < 30

a/b > 30 1.00

a - distance; b - diameter

4.10 Spheres

(1) The along-wind aerodynamic force coefficient cf,x for spheres shall be determined as a function of the Reynolds number Re (see 4.9.1) and the equivalent roughness k/b (see Table 4.13).

NOTE 1. The values cf,x obtained by carrying out measurements in conditions of reduced turbulence are given in Figure 4.30. The values shown in Figure 4.30 are based on the Reynolds number calculated using the peak wind velocity, vp(ze).

NOTE 2. The values shown in Figure 4.30 shall be valid for the ratio zg > b/2, where zg is the distance from the sphere to the flat surface and b is the diameter of the sphere (see Figure 4.31). For zg ≤ b/2, the force coefficient cf,x shall be multiplied by 1.6.

74

Figure 4.30 Along-wind aerodynamic force coefficient for spheres [3]

Figure 4.31 Sphere near a flat surface [3]

(2) The aerodynamic force coefficient in a vertical direction, cf,z for spheres shall be determined with relationship:

cf,z = 0for

zg > b2

(4.22)cf,z = +0.60

for zg < b

2

(3) To determine the force along-wind and in vertical direction, the reference area, Aref shall be given by relationship:

A ref = π⋅b2

4 (4.23)

(4) The reference height shall be:

75

smooth surface

ze=z g+b2

(4.24)

4.11 Lattice structures and scaffolding

(1) The aerodynamic force coefficient, cf, for lattice structures and scaffolding with parallel chords shall be obtained with relationship:

cf = cf,0 . (4.25)

where:

cf,0 is the aerodynamic force coefficient for lattice structures and scaffolding without free-end airflow; this coefficient is given in Figures 4.33–4.35 as a function of the blockage coefficient, (4.11 (2)) and the Reynolds number, Re;

Re is the Reynolds number which uses the mean diameter bi of the elements (see Figure 4.32); for non-circular cross-sections, the mean value of the dimensions of the upwind cross-section shall be used;

is the end-effect factor (see 4.13), which depends on the slenderness of the structure, , calculated with length and width b = d, see Figure 4.32;

NOTE. The values shown in Figures 4.33 to 4.35 are based on the Reynolds number calculated using the peak wind velocity, vp(ze).

Figure 4.32 - Lattice structures or scaffolding [3]

76

Figure 4.33 Aerodynamic force coefficient, cf,0 for planar lattice structures which contain elements with sharp edges (e.g. angle plates), as a function of the blockage coefficient [3]

Figure 4.34 Aerodynamic force coefficient, cf,0 for spatial lattice structures which contain elements with sharp edges (e.g. angle plates), as a function of the blockage coefficient [3]

77

Figure 4.35 Aerodynamic force coefficient, cf,0 for planar or spatial lattice structures which contain elements with a circular cross-section [3]

(2) The blockage coefficient, shall be determined with relationship:

ϕ= AAc

(4.26)

where:

A is the sum of the projected areas of the structural elements (bars, gusset plates) on a

cross-wind plane,

A=∑i

bi⋅ℓ i+∑k

Agk

;

Ac is the total area of the structure projected in a cross-wind plane, Ac=d ;

is the length of the lattice structure;

d is the width of the lattice structure;

78

bi, i is the width and length of the elements i of the structure (see Figure 4.32), projected

normal to the exposed face;

Agk - area of the gusset plate k.

(3) The reference area Aref shall be determined with relationship:

Aref = A (4.27)

(4) The reference height, ze shall be equal to the maximum height of the element above ground level.

4.12 Flags

(1) The aerodynamic force coefficients, cf and the reference areas, Aref for flags are given in Table 4.15.

(2) The reference height, ze shall be equal to the height of the flag above ground level.

Table 4.15 - Aerodynamic force coefficients, cf for flags [3]

Flags Aref cfFixed flags

h . 1.8

Force normal to the planeFree flags

h.

0 ,02+0,7⋅mf

ρ⋅h⋅( A ref

h2 )−1, 25

a)

b) 0.5.h.

79

Planar forcewhere:

mf is the mass of the area unit of the flag ρ is the air density (equal to 1.25 kg/m3)ze is the height of the flag above ground level

NOTE. The calculation relationship given for flags that are not fixed (free) shall include the dynamic forces caused by the flag fluttering.

4.13 Effective slenderness and end-effect factor

(1) The reduction factor for elements with free-end airflow (end-effect factor), can be determined as a function of the effective slenderness, .

NOTE. The values of the aerodynamic force coefficients, cf,0 given in points 4.6–4.12 are based on the results of measurements carried out on structures without free-end airflow. The end-effect factor shall take into consideration the reduction of wind action on structures due to airflow around their free end. The values given in Figure 4.36 and Table 4.16 are based on the results of measurements carried out in conditions of reduced turbulence.

(2) The effective slenderness, shall be defined as a function of the position and dimensions of the structure. The values are given in Table 4.16, and the values are given in Figure 4.36 for different blockage coefficients, .

(3) The blockage coefficient, (see Figure 4.37) shall be given by relationship:

ϕ= AAc

(4.28)

where:

A is the sum of the projected areas of the elements;

Ac is the total area of the structure, Ac = . b.

80

Table 4.16 Effective slenderness, for cylinders, polygonal cross-sections, rectangular cross-sections, structural elements with sharp edges, and lattice structures [3]

No Position of the structure,wind perpendicular to the plane of the page

Effective slenderness,

1

For polygonal cross-sections, rectangular cross-sections, structural elements with cross-sections with sharp edges, and lattice structures:for 50 m, the lowest value between the following shall be chosen: =1.4 · /b or =70 for <15 m, the lowest value between the following shall be chosen: =2 · /b or =70

2

For circular cylinders:for 50 m, the lowest value between the following shall be chosen: =0.7 · /b or =70for <15 m, the lowest value between the following shall be chosen: = /b or =70

3 For intermediary values of , linear interpolation can be used

4

for 50 m, the highest value between the following shall be chosen: =0.7 · /b or =70for <15 m, the highest value between the following shall be chosen: = /b or =70

For intermediary values of , linear interpolation can be used

81

Figure 4.36 End-effect factor, as a function of the blockage coefficient,

and the slenderness, [3]

Figure 4.37 Areas used to define the blockage coefficient, [3]

5 PROCEDURES FOR DETERMINING THE DYNAMIC RESPONSE COEFFICIENT

82

5.1 Wind turbulence

(1) The integral turbulence scale length, L(z) represents the mean value of the wind vortices caused by along-wind air turbulence. For heights z lower than 200 m, the integral turbulence scale length can be determined with relationship:

L ( z)={Lt⋅( zzt)α

, pentru z min≤z≤zmax=200 m

L (zmin ) , pentru z< zmin

(5.1)

where the reference height zt = 200 m, the reference length of the scale Lt = 300 m and

α = 0.67 + 0.05 ln(z0). The roughness length, z0 and the minimum height, zmin are given in

Table 2.1.

(2) The along-wind turbulence, characterised by a power distribution of wind gusts as a function of their frequency, shall be expressed by the power spectral density of turbulent wind gusts, Sv(z,n). The unilateral (defined only for positive frequencies) and normalised (for unit area) form of the power spectral density (SL(z, n) shall be:

SL( z , n )=n⋅Sv( z , n)

σv2

=6,8⋅f L( z , n )

(1+10 ,2⋅f L( z ,n ))5 /3(5.2)

where

Sv(z,n) is the unilateral power spectral density (defined only for positive frequencies) of wind gusts in their direction;

n is the wind gust frequency;

σ v2

is the dispersion of the wind velocity variation with the mean velocity;

f L( z , n)=n⋅L( z )vm( z )

is the non-dimensional frequency calculated as a function of the frequency, n, the mean wind velocity at a height z, vm(z) (see relationship 2.3) and the integral turbulence scale length, L(z) defined in (5.1). The function of the unilateral and normalised power spectral density is shown in Figure 5.1.

83

0.00

0.05

0.10

0.15

0.20

0.25

1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02

SL (fL)

fL

Figure 05.1 Normalised and unilateral power spectral density of along-wind gusts, SL(fL)

5.2 Detailed procedure for determining the dynamic response coefficient

(1) The dynamic response coefficient, cd is presented in Sub-chapter 3.4.2.2 and shall be determined with relationship (3.8):

cd=1+2⋅k p⋅I v (zs )⋅√B2+R2

1+7⋅I v (z s)

(2) The non-resonant (quasi-static) response factor, B2, which takes into consideration the effective correlation of the values of the peak pressure on the exposed face of the building/structure, shall be determined with relationship:

B2= 1

1+0,9⋅( b+hL ( zs) )

0 ,63

(5.3)

where:

b, h are the width and height of the structure, see Figure 3.2;

84

L(zs) is the integral turbulence scale length given by relationship (5.1) at the reference height, zs defined in Figure 3.2.

(3) The peak factor for determining the maximum extreme response of the structure, kp, defined as the ratio between the maximum extreme value of the fluctuating component of the structural response and its standard deviation, shall be obtained with relationship:

k p=√2⋅ln (ν⋅T )+ γ

√2⋅ln (ν⋅T )≥3

(5.4)

where:

ν is the average vibration frequency in the direction and under the action of turbulent wind;

T is the averaged time for the reference wind velocity, T = 600 s (the same as for the mean wind velocity);

γ = 0.5772, is Euler’s constant.

(4) The average frequency ν of the vibrations in the direction and under the action of turbulent wind shall be obtained with relationship:

ν=n1 , x⋅√ R2

B2+R2≥0 ,08 Hz

(5.5)

where n1,x is the fundamental natural vibration frequency of the structure in the direction of turbulent wind. The limit value of 0.08 Hz in relationship (5.5) corresponds to a peak factor kp=3.0 in relationship (5.4).

(5) The resonant response factor, R2, which takes into consideration the frequency content of the wind turbulence in quasi-resonance with the fundamental natural vibration frequency of the structure, shall be determined with relationship:

R2= π2

2⋅δ⋅SL( zs ,n1,x )⋅Rh (ηh )⋅Rb(ηb )

(5.6)

where:

δ is the logarithmic decrement of damping given in Annex C, in C.5;

SL is the unilateral and normalised power spectral density given by relationship (5.2), assessed at height zs for the frequency n1,x;

Rh, Rb are the aerodynamic admittance functions given by relationships (5.7) and (5.8).

(6) The aerodynamic admittance functions Rh and Rb, for the fundamental natural vector, shall be determined with the relationships:

85

Rh (ηh )={ 1 pentru ηh=01ηh

−1

2⋅ηh2(1−e

−2⋅ηh) pentru ηh¿0

(5.7)

Rb (ηb )={ 1 pentru ηb=01ηb

−1

2⋅ηb2(1−e

−2⋅ηb) pentru ηb ¿0

(5.8)

The values ηh

and ηb

shall be determined as follows:

ηh=4,6⋅h⋅n1, x

vm ( zs)(5.9)

ηb=4,6⋅b⋅n1 , x

vm (zs ) (5.10)

5.3 Simplified procedure for determining the dynamic response coefficient for buildings

(1) Using the detailed procedure for calculating the dynamic response coefficient (described in Point 5.2), covering values of this coefficient were obtained for buildings with a rectangular parallelepipedal shape and a regular mass and rigidity distribution. The values are based on the approximated estimation of the fundamental natural vibration frequency and the logarithmic decrement of structural damping using the simplified relationships given in Annex C.

(2) The values of the dynamic response coefficient are given in Table 5.1 for buildings made of reinforced concrete and Table 5.2 for buildings with a metallic structure. The values shall be valid for buildings with the horizontal dimensions measured perpendicular to the wind direction, b ≤ 50 m and the height, h ≤ 30 m (see Figure 3.2a).

(3) For all other situations of buildings where the simplified procedure cannot be applied using the values given in Tables 5.1 and 5.2, the dynamic response coefficient shall be determined in accordance with the method presented in detail in 5.2.

86

Table 5.1 Values of the dynamic response coefficient, cd for buildings with a reinforced concrete structure

(δs = 0.10)

z0, mb→,

h↓, m10 20 30 40 50

0.003

10 0.95 0.92 0.90 0.89 0.88

20 0.95 0.93 0.91 0.90 0.88

30 0.96 0.93 0.91 0.90 0.89

0.01

10 0.94 0.91 0.89 0.87 0.86

20 0.94 0.91 0.90 0.88 0.87

30 0.95 0.92 0.90 0.89 0.88

0.05

10 0.92 0.88 0.85 0.85 0.85

20 0.92 0.89 0.87 0.85 0.85

30 0.93 0.90 0.88 0.86 0.85

0.30

10 0.87 0.85 0.85 0.85 0.85

20 0.88 0.85 0.85 0.85 0.85

30 0.89 0.86 0.85 0.85 0.85

1.00

10 0.85 0.85 0.85 0.85 0.85

20 0.85 0.85 0.85 0.85 0.85

30 0.85 0.85 0.85 0.85 0.85

Table 5.2 Values of the dynamic response coefficient, cd for buildings with a metallic structure (δs = 0.05)

z0, mb→,

h↓, m10 20 30 40 50

0.003

10 1.00 0.95 0.93 0.91 0.90

20 1.03 0.98 0.95 0.93 0.92

30 1.06 1.01 0.98 0.95 0.94

0.01

10 0.98 0.94 0.91 0.89 0.88

20 1.02 0.97 0.94 0.92 0.90

30 1.05 1.00 0.96 0.94 0.92

0.05

10 0.96 0.91 0.88 0.86 0.85

20 1.00 0.94 0.91 0.89 0.87

30 1.03 0.97 0.94 0.92 0.90

0.30

10 0.90 0.86 0.85 0.85 0.85

20 0.95 0.89 0.86 0.85 0.85

30 0.98 0.92 0.89 0.87 0.85

1.00

10 0.85 0.85 0.85 0.85 0.85

20 0.89 0.85 0.85 0.85 0.85

30 0.92 0.87 0.85 0.85 0.85

87

5.4 Displacements and accelerations corresponding to the service limit state of a structure

88

(1) For tall or flexible buildings (height h ≥ 30 m or the natural vibration frequency n1 ≤ 1 Hz), a service limit state verification shall use the maximum values of the along-wind displacement and acceleration of the building, the former assessed at a height z = zs and the latter assessed at a height z = h. The maximum along-wind displacement of the structure at the height zs shall be determined using the global along-wind force Fw defined in Sub-chapter 3.3.

(2) The standard deviation, σa,x of the characteristic along-wind acceleration of the structure

at height z shall be obtained with relationship:

σ a , x=c f⋅ρ⋅b⋅I v (zs)⋅v m

2 (zs )m1, x

⋅R⋅K x⋅Φ1 , x ( z )

(5.11)

where:

cf is the aerodynamic force coefficient, see Chapter 4;

- for buildings, it can be considered simplified

c f ={ 0,9+0,4⋅hd

, pentru 0 ,25≤ hd<1,0

1, 25+0 ,05⋅hd

, pentru 1 ,0≤hd≤5,0

vezi subcapitolele 4 . 6, 4 . 8 sau 4 . 9 .2 pentru hd>5,0

ρ is the air density, equal to 1.25 kg/m3;

b is the width of the structure, defined in Figure 3.2;

d is the length of the structure, defined in Figure 3.2;

h is the height of the structure, defined in Figure 3.2;

Iv(zs) is the turbulence intensity at height z = zs above ground level; see Point 2.4(2) and Figure 3.2;

vm(zs) is the mean wind velocity for z = zs for a reference wind velocity with MRI = 10 years (to determine the wind velocity with MRI = 10 years, see Annex A); (also see Points 2.3(2) and 5.5(2));

zs is the reference height; see Figure 3.2;

R is the square root of the resonant response factor; see Point 5.2(5);

Kx is the non-dimensional coefficient given by relationship (5.12);

m1,x is the equivalent mass for the fundamental along-wind vibration mode; see Point C.4 (1);

n1,x is the fundamental natural along-wind vibration frequency of the structure;

89

Φ1,x (z)is the y-coordinate of the fundamental natural along-wind vibration vector at a

height z.

(3) The non-dimensional coefficient Kx shall be determined with the general relationship:

K x=∫0

h

vm2 ( z )⋅Φ1 , x ( z ) dz

vm2 (z s)⋅∫

0

h

Φ1 , x2 ( z )dz

(5.12)

where h is the height of the structure (see Figure 4.1).

NOTE. If Φ1,x(z)= (z/h) (see Annex C) and co(z) = 1 (level ground, see Point 2.3(5)),

relationship (5.12) can be approximated using the following relationship:

K x=

(2⋅ζ+1 )⋅{(ζ+1 )⋅[ ln( zs

z0)+0,5 ]−1}

(ζ+1 )2⋅ln( zs

z0)

(5.13)

where

z0 is the roughness length (see Table 2.1);

is the exponent of the approximated along-wind mode shape (see Annex C).

(4) The peak characteristic accelerations of structures, amax,x shall be obtained by multiplying the standard deviation given in Point 5.3(2) by the peak factor given in Point 5.2(3), calculated using the frequency = n1,x:

amax, x=(√2⋅ln (n1, x⋅T )+ γ

√2⋅ln (n1 , x⋅T ) )⋅σ a , x

(5.14)

5.5 Comfort criteria

(1) The effects of the wind on buildings should not cause discomfort to its occupants. The discomfort experienced by the occupants shall depend on the amplitude and frequency of oscillation of the building and various other physiological and psychological factors associated with the characteristics of each person.

(2) To make sure that the building is used appropriately, the following requirement shall be complied with:

90

amax, x≤alim (5.15)

where

amax,x is the peak along-wind acceleration on the top level of the building (z=h), assessed with relationship (5.14), for a reference wind velocity with MRI = 10 years (to determine the wind velocity with MRI = 10 years, see Annex A);

alim is the upper limit comfort acceleration calculated with relationship:

a lim={a0

n1 , x0 , 56

pentru n1,x<1 Hz

a0 pentru 1 Hz ≤ n1,x ≤ 2 Hz0,5⋅a0⋅n1 , x pentru n1,x ≥ 2 Hz

(5.16)

where:

a0 = 6 cm/s2 for office buildings;

a0 = 4 cm/s2 for residential buildings;

n1,x is the natural frequency of the building corresponding to the first mode of along-wind bending vibration.

6 AEROELASTIC INSTABILITY PHENOMENA GENERATED BY VORTICES

91

6.1 General information

(1) For slender structures (chimneys, towers, cables, etc.) the dynamic effect caused by alternating vortex shedding must be taken into consideration. The vortex shedding phenomenon causes a fluctuating cross-wind action whose frequency depends on the mean wind velocity, as well as the shape and dimensions of the planar cross-section of the structure. If the vortex shedding frequency is close to a natural vibration frequency of the structure, quasi-resonance conditions which lead to amplification of the oscillation amplitude of the structure shall be ensured; these shall be higher as the damping and mass of the structure or element are lower. The resonance requirement shall be considered met when the wind velocity is theoretically equal to the critical wind velocity which causes the vortex shedding (defined in 6.3.1).

6.2 Consideration of the effects of vortex shedding

(1) The effects of vortex shedding shall be considered if the following requirement is met

vcrit ,i≤1 ,25⋅vm(6.1)

where:

vcrit,i is the critical wind velocity for the vibration mode i (see 6.3.1);

vm is the mean wind velocity in the section where the vortex shedding occurs.

6.3 Main vortex shedding parameters

6.3.1 The critical wind velocity vcrit,i

(1) The critical wind velocity for the vibration mode i can be defined as the wind speed for which the vortex shedding frequency is equal to a natural cross-wind vibration frequency of the structure, and is given by relationship:

92

vcrit ,i=b⋅ni , y

St (6.2)

where

b is the width of the cross-section where the resonant vortex shedding occurs; for circular cylinders, the reference width shall be the outer diameter;

ni,y is the natural frequency of the cross-wind vibration mode i;

St is the Strouhal number, defined in 6.3.2.

(2) The critical wind velocity for the ovalling vibration mode i of the cylinder wall shall be defined as the wind velocity at which double the vortex shedding frequency is equal to the natural frequency of the ovalling vibration mode i of the cylinder wall and is given by relationship:

vcrit ,i=b⋅n i,o

2⋅St(6.3)

where

b is the outer diameter of the cylinder;

St is the Strouhal number, defined in 6.3.2;

ni,o is the natural frequency of the ovalling vibration mode i of the cylinder wall.

6.3.2 Strouhal number, St

(1) The Strouhal number, St, is a non-dimensional parameter which depends on the shape of the cross-section, the turbulence characteristics, the Reynolds number calculated for vcrit,i, and the surface roughness. For cross-sections with sharp edges/corners, the Strouhal number can be assessed in a simplified way as a function of the shape of the cross-section only.

Table 6.1 and Figure 6.1 (for rectangular cross-sections) give guidance average values for the Strouhal number, St.

93

Table 6.01 The Strouhal number, St for different cross-sectional shapes [3]

Cross-section St

0.18

For all values of the Reynolds number, Re

from Figure 6.1

0.5 ≤ d/b ≤ 10d/b = 1 0,11d/b = 1.5 0.10

d/b = 2 0.14

Linear interpolationd/b = 1 0.13

d/b = 2 0.08


d/b = 2 0.12

Linear interpolationd/b = 1.3 0.11

d/b = 2.0 0.07

Linear interpolationNOTE. Extrapolations of the Strouhal number as a function of the ratio d/b are not permitted.

94

Figure 6.01 Strouhal number St for rectangular cross-sections with sharp corners [3]

6.3.3 Scruton number, Sc

(1) The Scruton number, Sc is a non-dimensional parameter which depends on the equivalent mass, the critical damping fraction, and the reference dimension of the cross-section. The vibration sensitivity depends on the structural damping and the ratio between the mass of the structure and the mass of the air. The Scruton number, Sc, shall be given by relationship:

Sc=2⋅mie⋅δ s

ρ⋅b2

(6.4)

where:

mie is the equivalent mass per unit length for the cross-wind vibration mode i, as defined in C.4 (1);

δs is the logarithmic decrement of structural damping;

ρ is the air density, whose value is equal to 1.25 kg/m3)

b is the size of the cross-section, assessed in the cross-section where the critical resonant vortex shedding phenomenon occurs.

6.3.4 Reynolds number, Re

(1) The vortex shedding of a circular cylinder shall depend on the Reynolds number, Re corresponding to the critical wind velocity vcrit,i. The Reynolds number corresponding to the critical wind speed shall be given by relationship:

95

Re (vcrit,i )=b⋅vcrit,i

μ (6.5)

where

b is the outer diameter of the circular cylinder;

μ is the kinematic air viscosity (μ 15.10-6 m2/s);

vcrit,i is the critical wind velocity (see 6.3.1).

6.4 Action caused by vortex shedding

(1) The effects of the vibrations caused by vortex shedding shall be assessed using the force of inertia per unit length, Fw(s) which acts across-wind at the height s of the structure

(measured from the base) and shall be given by relationship:

Fw ( s)=m ( s)⋅(2⋅π⋅ni , y )2⋅Φi , y (s )⋅yF ,max (6.6)

where

m(s) is the structural mass per unit length [kg/m];

ni,y is the natural vibration frequency of the structure in a plane perpendicular to

wind direction;

Φi,y (s) is the natural vibration shape of the structure in a plane perpendicular to the

wind direction, normalised at value 1 when the displacement is maximum;

yF,max is the maximum displacement of the structure at a height s (where Φi,y (s) =

1), see 6.5.

6.5 Calculation of the cross-wind displacement amplitude

(1) The maximum cross-wind displacement, yF,max shall be calculated with relationship:

yF ,max

b= 1

St2⋅ 1

Sc⋅K⋅Kw⋅c lat

(6.7)

where:

St is the Strouhal number, Table 6.1;

96

Sc is the Scruton number, relationship (6.4);

Kw is the correlation length factor, Lj;

K is the vibration mode shape factor;

clat is the aerodynamic force coefficient in a cross-wind direction;

b is the size of the cross-section, assessed in the cross-section where the critical resonant vortex shedding phenomenon occurs.

(2) The values clat,0 of the aerodynamic force coefficient in a cross-wind direction are given in

Figure 6.2 and Table 6.2, depending on the Reynolds number and for values

vcrit,i

vm,Lj

≤0 , 83

. For

other values of the ratio

vcrit,i

vm,Lj

, the values given in Table 6.3 should be used.

Figure 6.02 Main values of the aerodynamic lateral force coefficient, clat,0 depending on the Reynolds number, Re(vcrit,i) for circular cylinders [3]

97

Table 6.02 Main values of the aerodynamic lateral force coefficient, clat,0 for different cross-sections [3]

Cross-section clat,0

from Figure 6.2

For all Reynolds numbers (Re)

0.5 ≤ d/b ≤ 10 1.1

d/b = 1 0.8d/b = 1.5 1.2

d/b = 2 0.3


d/b = 2 2.3


d/b = 2 1.1

Linear interpolationd/b = 1.3 0.8

d/b = 2.0 1.0

Linear interpolationNOTE. The extrapolation of the lateral force coefficients as a function of the ratio d/b is not permitted.

98

Table 6.03 Aerodynamic lateral force coefficient, clat as a function of the critical wind velocity

ratio,

vcrit,i

vm,Lj [3]

clat

vcrit,i

vm,Lj

≤0 , 83 clat = clat,0

0 ,83≤vcrit,i

vm,Lj

≤1 ,25 c lat=(3−2,4⋅vcrit,i

vm ,Lj)⋅c lat , 0

1 , 25≤vcrit,i

v m,Lj

clat = 0

where:clat,0 is the main value from Table 6.2 and, for circular cylinders, from

Figure 6.2;vcrit,i is the critical wind velocity (see relationship (6.1));vm,

Lj is the mean wind velocity (see 2.3(2)) at the centre of the effective correlation length, as defined in Figure 6.3.

(3) The correlation length factor and the vibration mode shape factor for certain simple structures are given in Table 6.5, as a function of the correlation length, Lj given in Table 6.4.

(4) The correlation length can be considered to be the distance between the nodes of the mode shape (for exemplification, see Table 6.4 and Figure 6.3).

Table 6.04 The correlation length, Lj as a function of the vibration amplitude, yF(sj) [3]

yF(sj) / b Lj / b< 0.1 6

Between 0.1 and 0.6

4,8+12⋅yF (s j )

b> 0.6 12

99

NOTE 1. If at least two correlation lengths are given, it is recommended that both are used for calculation and the maximum value of clat is chosen.

NOTE 2. n is the number of areas where vortex shedding occurs simultaneously.

NOTE 3. m is the number of loops of the natural vibration mode shape Φi,y.

Figure 6.03 Examples of application of the correlation length, Lj (j = 1, 2, 3) [3]

Table 6.05 Correlation length factor, Kw and vibration mode shape factor, K for certain simple structures (λ = / b) [3]

Structure Kw K

0.13

100

vibration mode 1 vibration mode 2

loop

vm,L1

vm,L1

vm,L2

vm,L1

vm,L1

vm,L2

vm,L1

vm,L2

Structure Kw K

0.10

0.11

0.10

6.6 Vortex effects on vertical cylinders arranged in line or grouped

(1) For circular cylinders arranged in line or grouped (whether coupled or not) (Figure 6.4), vibrations can occur which are excited by alternative vortex shedding.

Figure 6.04 Fitting of cylinders in line or grouped [3]

(2) The oscillation amplitude can be calculated using relationship (6.7), with the amendments brought by relationships (6.8) and (6.9), respectively:

101

- For circular cylinders arranged in line and not coupled:

clat = 1.5 . clat (individual)for

1≤ab≤10

(6.8)clat = clat (individual)for

10< ab≤15

linear interpolationfor

10≤ab≤15

where clat (individual) = clat shall have the values given in Table 6.3 and the Strouhal number shall be determined with relationships:

for 1≤a

b≤9

St = 0.18for

ab>9

- For coupled cylinders:

clat = Kiv . clat (individual) for 1.0 a/b 3.0 (6.9)

where Kiv is the interference factor for the vortex shedding (indicated in Table 6.6) as a function of the Strouhal number and the Scruton number.

102

Table 6.06 Data for estimating the cross-wind response of coupled cylinders arranged in line or grouped [3]

Coupled cylinders Scruton number,

Sc=2⋅δ s∑ m i , y

ρ⋅b2

a/b = 1 a/b ≥ 2

Kiv = 1.5 Kiv = 1.5

Kiv = 4.8 Kiv = 3.0

Kiv = 4.8 Kiv = 3.0

Linear interpolation

Inverse values of the Strouhal number for coupled cylinders arranged in line or grouped

ANNEX A (normative) ZONING OF WIND ACTION IN ROMANIA

103

The statistical analysis carried out in order to obtain the zoning of natural wind hazards in Romania used, as entry data, the maximum annual values of the wind velocity at a height of 10 m above ground level, measured in more than 140 weather stations belonging to the National Meteorological Administration up until 2005. The results of the statistical analysis are the characteristic (reference) values of the wind velocity with IMR=50 years, calculated using the Gumbel extreme value distribution.

The reference values of the dynamic wind pressure were obtained by processing the reference values of the wind velocity at the sites of the weather stations where records were made.

The data included in the zoning map of the reference values of the dynamic wind pressure for altitudes of up to 1 000 m (Figure 2.1) represent dynamic pressures averaged over 10 minutes and with a mean recurrence interval of 50 years, in accordance with the provisions of SR EN 1991-1-4.

Table A.1 gives the reference values of the dynamic wind pressure for 337 towns and cities in Romania, located at altitudes of up to 1 000 m.

The reference value of the dynamic wind pressure for a site located at an altitude z higher than 1 000 m can be determined with relationship:

qb,z>1000m=c z>1000m⋅qb(A.1)

where:

qb,z>1000m- is the reference value of the dynamic wind pressure for a site located at an altitude z higher than 1 000 m;

qb - is the reference value of the dynamic wind pressure on site, given in the zoning map shown in Figure 2.1;

cz>1000m - is the altitude factor, approximated with relationship:

c z>1000m=1+1,6⋅( z1000

−1)(A.2)

For sites located at altitudes higher than 1 000 m and in areas with special wind exposure (south-west of the Banat area), it is recommended that primary data are obtained from ANM and specialist institutions operating in the field of civil engineering are consulted in order to analyse this data.

For a site located at an altitude of up to 1 000 m, the reference value of the wind velocity with a mean recurrence interval of 50 years shall be determined on the basis of the reference value of the dynamic wind pressure corresponding to the respective site (see the zoning map shown in Figure 2.1 and the data given in Table A.1) and shall be calculated with relationship:

104

vb=√ 2⋅qb

ρ=√1,6⋅qb

(A.3)

where ρ is the air density, equal to 1.25 kg/m3, and qb is the reference value of the dynamic wind pressure measured in Pa (1 kPa=1 000 Pa).

The characteristic values of the wind velocities defined with a mean recurrence interval of 100 years and 10 years can be calculated, in a simplified way, as a function of the characteristic value of the wind velocity with a mean recurrence interval of 50 years, using the following relationships:

vb ,IMR=100 ani

v b,IMR=50 ani

≃1 ,10

(A.4)

v b,IMR=10 ani

v b,IMR=50 ani

≃0 ,75

(A.5)

The characteristic values of the dynamic wind pressures defined with a mean recurrence interval of 100 years and 10 years can be calculated, in a simplified way, as a function of the characteristic value of the dynamic wind pressure with a mean recurrence interval of 50 years, using the following relationships:

qb,IMR=100 ani

qb,IMR=50 ani

≃1 ,15

(A.6)

qb,IMR=10 ani

qb,IMR=50 ani

≃0 , 65

(A.7)

Table A.1 Reference values of the dynamic wind pressure for 337 towns and cities in Romania

105

No Town/City Countyqb, kPa

(MRI=50 years)

1 Abrud ALBA 0.4

2 Adamclisi CONSTANTA 0.5

3 Adjud VRANCEA 0.6

4 Agnita SIBIU 0.4

5 Aiud ALBA 0.4

6 ALBA IULIA ALBA 0.4

7 Alesd BIHOR 0.5

8 ALEXANDRIA TELEORMAN 0.7

9 Amara IALOMITA 0.6

10 Anina CARAS-SEVERIN 0.7

11 Aninoasa HUNEDOARA 0.4

12 ARAD ARAD 0.5

13 Ardud SATU MARE 0.4

14 Avrameni BOTOSANI 0.7

15 Avrig SIBIU 0.6

16 Azuga PRAHOVA 0.6

17 Babadag TULCEA 0.6

18 BACAU BACAU 0.6

19 Baia de Arama MEHEDINTI 0.4

20 Baia de Aries ALBA 0.4

21 BAIA MARE MARAMURES 0.6

22 Baia Sprie MARAMURES 0.6

23 Bals DOLJ 0.5

24 Banloc TIMIS 0.7

25 Baraolt COVASNA 0.6

26 Basarabi CONSTANTA 0.5

27 Baicoi PRAHOVA 0.4

28 Babeni VALCEA 0.4

29 Baile Govora VALCEA 0.4

30 Baile Herculane CARAS-SEVERIN 0.6

31 Baile Olanesti VALCEA 0.4

32 Baile Tusnad HARGHITA 0.6

33 Bailesti DOLJ 0.4

34 Balan HARGHITA 0.6

35 Balcesti VALCEA 0.5

106


(MRI=50 years)

36 Baneasa CONSTANTA 0.6

37 Barlad VASLUI 0.6

38 Bechet DOLJ 0.4

39 Beclean BISTRITA NASAUD 0.4

40 Beius BIHOR 0.5

41 Berbesti VALCEA 0.4

42 Beresti GALATI 0.6

43 Bicaz NEAMT 0.4

44 BISTRITA BISTRITA NASAUD 0.4

45 Blaj ALBA 0.6

46 Bocsa CARAS-SEVERIN 0.7

47 Boldesti-Scaeni PRAHOVA 0.4

48 Bolintin-Vale GIURGIU 0.5

49 Borod BIHOR 0.5

50 Borsec HARGHITA 0.4

51 Borsa MARAMURES 0.4

52 BOTOSANI BOTOSANI 0.7

53 Brad HUNEDOARA 0.4

54 Bragadiru ILFOV 0.5

55 BRASOV BRASOV 0.6

56 BRAILA BRAILA 0.6

57 Breaza PRAHOVA 0.4

58 Brezoi VALCEA 0.4

59 Brosteni SUCEAVA 0.4

60 Bucecea BOTOSANI 0.7

61 BUCHAREST BUCHAREST 0.5

62 Budesti CALARASI 0.4

63 Buftea ILFOV 0.5

64 Buhusi BACAU 0.6

65 Bumbesti-Jiu GORJ 0.4

66 Busteni PRAHOVA 0.6

67 BUZAU BUZAU 0.7

68 Buzias TIMIS 0.6

69 Cajvana SUCEAVA 0.6

70 Calafat DOLJ 0.4

107


(MRI=50 years)

71 Caracal OLT 0.7

72 Caransebes CARAS-SEVERIN 0.6

73 Carei SATU MARE 0.4

74 Cavnic MARAMURES 0.6

75 Calan HUNEDOARA 0.4

76 CALARASI CALARASI 0.6

77 Calimanesti VALCEA 0.4

78 Cazanesti IALOMITA 0.6

79 Campia Turzii CLUJ 0.4

80 Campeni ALBA 0.4

81 Campina PRAHOVA 0.4

82 Campulung ARGES 0.4

83 Campulung Mold. SUCEAVA 0.6

84 Ceahlau NEAMT 0.4

85 Cehu Silvaniei SALAJ 0.4

86 Cernavoda CONSTANTA 0.5

87 Chisineu-Cris ARAD 0.6

88 Chitila ILFOV 0.5

89 Ciacova TIMIS 0.7

90 Cisnadie SIBIU 0.6

91 CLUJ-NAPOCA CLUJ 0.5

92 Codlea BRASOV 0.6

93 Colibasi ARGES 0.5

94 Comarnic PRAHOVA 0.4

95 Comanesti BACAU 0.6

96 CONSTANTA CONSTANTA 0.5

97 Copsa Mica SIBIU 0.4

98 Corabia OLT 0.5

99 Corugea TULCEA 0.5

100 Costesti ARGES 0.5

101 Cotnari IASI 0.7

102 Covasna COVASNA 0.7

103 CRAIOVA DOLJ 0.5

104 Cristuru Secuiesc HARGHITA 0.4

105 Cugir ALBA 0.4

108


(MRI=50 years)

106 Curtea de Arges ARGES 0.4

107 Curtici ARAD 0.6

108 Darabani BOTOSANI 0.7

109 Dabuleni DOLJ 0.5

110 Darmanesti BACAU 0.6

111 Dej CLUJ 0.4

112 Deta TIMIS 0.7

113 DEVA HUNEDOARA 0.4

114 Dolhasca SUCEAVA 0.6

115 Dorohoi BOTOSANI 0.7

116 Dragomiresti MARAMURES 0.4

117 Dragasani VALCEA 0.5

118 Draganesti-Olt OLT 0.7

119 DROBETA TURNU SEVERIN MEHEDINTI 0.6

120 Dumbraveni SIBIU 0.4

121 Eforie Nord CONSTANTA 0.5

122 Eforie Sud CONSTANTA 0.5

123 Fagaras BRASOV 0.4

124 Faget TIMIS 0.4

125 Falticeni SUCEAVA 0.6

126 Faurei BRAILA 0.6

127 Fetesti IALOMITA 0.6

128 Fieni DAMBOVITA 0.4

129 Fierbinti-Targ IALOMITA 0.4

130 Filiasi DOLJ 0.4

131 Flamanzi BOTOSANI 0.7

132 FOCSANI VRANCEA 0.6

133 Fundulea CALARASI 0.4

134 Frasin SUCEAVA 0.6

135 GALATI GALATI 0.6

136 Gaesti DAMBOVITA 0.5

137 Gataia TIMIS 0.7

138 Geoagiu HUNEDOARA 0.4

139 Gheorgheni HARGHITA 0.4

140 Gherla CLUJ 0.4

109


(MRI=50 years)

141 Ghimbav BRASOV 0.6

142 GIURGIU GIURGIU 0.5

143 Grivita IALOMITA 0.6

144 Gurahont ARAD 0.4

145 Gura Humorului SUCEAVA 0.6

146 Hateg HUNEDOARA 0.4

147 Harlau IASI 0.7

148 Harsova CONSTANTA 0.6

149 Holod BIHOR 0.6

150 Horezu GORJ 0.4

151 Huedin CLUJ 0.5

152 Hunedoara HUNEDOARA 0.4

153 Husi VASLUI 0.7

154 Ianca BRAILA 0.6

155 IASI IASI 0.7

156 Iernut MURES 0.4

157 Ineu ARAD 0.5

158 Isaccea TULCEA 0.6

159 Insuratei BRAILA 0.6

160 Intorsura Buzaului COVASNA 0.6

161 Jimbolia TIMIS 0.4

162 Jibou SALAJ 0.4

163 Jurilovca TULCEA 0.6

164 Lehliu Gara CALARASI 0.6

165 Lipova ARAD 0.4

166 Liteni SUCEAVA 0.6

167 Livada SATU MARE 0.6

168 Ludus MURES 0.4

169 Lugoj TIMIS 0.4

170 Lupeni HUNEDOARA 0.4

171 Mangalia CONSTANTA 0.5

172 Marghita BIHOR 0.5

173 Macin TULCEA 0.6

174 Magurele ILFOV 0.5

175 Marasesti VRANCEA 0.6

110


(MRI=50 years)

176 Medgidia CONSTANTA 0.5

177 Medias SIBIU 0.4

178 MIERCUREA CIUC HARGHITA 0.6

179 Miercurea Nirajului MURES 0.4

180 Miercurea Sibiului SIBIU 0.6

181 Mihailesti GIURGIU 0.5

182 Milisauti SUCEAVA 0.6

183 Mizil PRAHOVA 0.6

184 Moinesti BACAU 0.6

185 Moldova Noua CARAS-SEVERIN 0.7

186 Moneasa ARAD 0.4

187 Moreni DAMBOVITA 0.4

188 Motru GORJ 0.4

189 Murgeni VASLUI 0.6

190 Nadlac ARAD 0.4

191 Nasaud BISTRITA NASAUD 0.4

192 Navodari CONSTANTA 0.5

193 Negresti VASLUI 0.7

194 Negresti Oas SATU MARE 0.6

195 Negru Voda CONSTANTA 0.5

196 Nehoiu BUZAU 0.6

197 Novaci GORJ 0.4

198 Nucet BIHOR 0.4

199 Ocna Mures ALBA 0.4

200 Ocna Sibiului SIBIU 0.6

201 Ocnele Mari VALCEA 0.4

202 Odobesti VRANCEA 0.6

203 Odorheiul Secuiesc HARGHITA 0.4

204 Oltenita CALARASI 0.4

205 Onesti BACAU 0.6

206 ORADEA BIHOR 0.5

207 Oravita CARAS-SEVERIN 0.7

208 Orastie HUNEDOARA 0.4

209 Orsova MEHEDINTI 0.6

210 Otopeni ILFOV 0.5

111


(MRI=50 years)

211 Otelu Rosu CARAS-SEVERIN 0.4

212 Ovidiu CONSTANTA 0.5

213 Panciu VRANCEA 0.6

214 Pantelimon ILFOV 0.5

215 Pascani IASI 0.7

216 Patarlagele BUZAU 0.6

217 Pancota ARAD 0.5

218 Pecica ARAD 0.5

219 Petrila HUNEDOARA 0.4

220 Petrosani HUNEDOARA 0.4

221 PIATRA NEAMT NEAMT 0.6

222 Piatra Olt DOLJ 0.7

223 PITESTI ARGES 0.5

224 PLOIESTI PRAHOVA 0.4

225 Plopeni PRAHOVA 0.6

226 Podu Iloaiei IASI 0.7

227 Pogoanele BUZAU 0.7

228 Popesti Leordeni ILFOV 0.5

229 Potcoava OLT 0.5

230 Predeal BRASOV 0.6

231 Pucioasa DAMBOVITA 0.4

232 Racari DAMBOVITA 0.5

233 Radauti SUCEAVA 0.6

234 Rauseni BOTOSANI 0.7

235 Ramnicu Sarat BUZAU 0.6

236 RAMNICU VALCEA VALCEA 0.4

237 Rasnov BRASOV 0.6

238 Recas TIMIS 0.4

239 Reghin MURES 0.4

240 Resita CARAS-SEVERIN 0.7

241 Roman NEAMT 0.7

242 Rosiori de Vede TELEORMAN 0.7

243 Rovinari GORJ 0.4

244 Roznov NEAMT 0.6

245 Rupea BRASOV 0.4

112


(MRI=50 years)

246 Salcea SUCEAVA 0.6

247 Salonta BIHOR 0.6

248 Santana ARAD 0.6

249 SATU MARE SATU MARE 0.4

250 Sacele BRASOV 0.6

251 Sacuieni BIHOR 0.5

252 Saliste SIBIU 0.6

253 Salistea de Sus MARAMURES 0.4

254 Sarmasu MURES 0.4

255 Savarsin ARAD 0.4

256 Saveni BOTOSANI 0.7

257 Sangeorz Bai BISTRITA NASAUD 0.4

258 Sangeorgiu de Padure MURES 0.4

259 Sannicolau Mare TIMIS 0.4

260 Scornicesti OLT 0.5

261 Sebes ALBA 0.4

262 Sebis ARAD 0.4

263 Seini MARAMURES 0.6

264 Segarcea DOLJ 0.5

265 SFANTU GHEORGHE COVASNA 0.6

266 Sf. Gheorghe TULCEA 0.6

267 SIBIU SIBIU 0.6

268 Sighetul Marmatiei MARAMURES 0.6

269 Sighisoara MURES 0.4

270 Simeria HUNEDOARA 0.4

271 Sinaia PRAHOVA 0.4

272 Siret SUCEAVA 0.6

273 SLATINA OLT 0.5

274 Slanic Moldova BACAU 0.7

275 Slanic Prahova PRAHOVA 0.6

276 SLOBOZIA IALOMITA 0.6

277 Solca SUCEAVA 0.6

278 Sovata MURES 0.4

279 Stei BIHOR 0.5

280 Strehaia MEHEDINTI 0.4

113


(MRI=50 years)

281 SUCEAVA SUCEAVA 0.6

282 Sulina TULCEA 0.6

283 Simleul Silvaniei SALAJ 0.4

284 Somcuta Mare MARAMURES 0.4

285 Stefanesti ARGES 0.5

286 Stefanesti BOTOSANI 0.7

287 Talmaciu SIBIU 0.6

288 Tasnad SATU MARE 0.4

289 Tautii Magheraus MARAMURES 0.6

290 TARGOVISTE DAMBOVITA 0.4

291 Targu Bujor GALATI 0.6

292 Targu Carbunesti GORJ 0.4

293 Targu Frumos IASI 0.7

294 TARGU JIU GORJ 0.4

295 Targu Lapus MARAMURES 0.4

296 TARGU MURES MURES 0.4

297 Targu Ocna BACAU 0.6

298 Targu Neamt NEAMT 0.6

299 Targu Secuiesc COVASNA 0.7

300 Tarnaveni MURES 0.4

301 Techirghiol CONSTANTA 0.5

302 Tecuci GALATI 0.6

303 Teius ALBA 0.4

304 Tismana GORJ 0.4

305 Titu DAMBOVITA 0.5

306 TIMISOARA TIMIS 0.6

307 Toplita HARGHITA 0.4

308 Topoloveni ARGES 0.5

309 Turceni GORJ 0.4

310 Turnu Magurele TELEORMAN 0.5

311 TULCEA TULCEA 0.6

312 Turda CLUJ 0.4

313 Tusnad HARGHITA 0.6

314 Tandarei IALOMITA 0.6

315 Ticleni GORJ 0.4

114


(MRI=50 years)

316 Ulmeni MARAMURES 0.4

317 Ungheni MURES 0.4

318 Uricani GORJ 0.4

319 Urlati PRAHOVA 0.6

320 Urziceni IALOMITA 0.6

321 Valea lui Mihai BIHOR 0.4

322 VASLUI VASLUI 0.7

323 Vascau BIHOR 0.4

324 Vatra Dornei SUCEAVA 0.4

325 Valenii de Munte PRAHOVA 0.6

326 Vanju Mare MEHEDINTI 0.6

327 Vicovu de Sus SUCEAVA 0.6

328 Victoria BRASOV 0.4

329 Videle TELEORMAN 0.5

330 Viseu de Sus MARAMURES 0.4

331 Vlahita Harghita 0.4

332 Voluntari ILFOV 0.5

333 Vulcani HUNEDOARA 0.4

334 ZALAU SALAJ 0.4

335 Zarnesti BRASOV 0.4

336 Zimnicea TELEORMAN 0.7

337 Zlatna ALBA 0.4

ANNEX B (normative) EFFECTS OF THE TERRAIN

115

B.1 Transition between roughness categories 0, I, II, III, and IV

(1) The determination of the design wind velocity must take into consideration the transition between the terrain categories corresponding to different degrees of roughness (see Table 2.1).

(2) If the site of the building or structure is located in the vicinity of an area where the terrain roughness changes at a distance of less than:

- 2 km from terrain belonging to category 0

- 1 km from terrain belonging to categories I, II, and III,

then the least rough terrain category located in the vicinity of the site shall be used.

(3) If the requirements stipulated in (2) are not met, or if the roughness changing areas represent less than 10 % of the surface being considered by applying the distances mentioned in Point (2), the terrain roughness category shall be that present on the site of the structure.

B.2 Numerical calculation of the orography factor

(1) For isolated hills and cliffs, the wind velocity shall change as a function of the gradient, Φ

of the cross-wind slope (

Φ= HLu

, where the height H and the length Lu are defined in Figure B.1).

Figure B.1. The increase in wind velocity due to orography [3]

116

vm ( z ) - mean velocity at a height z above ground levelvm,plat ( z )

- mean velocity at a height z above flat ground

co=vm ( z )

v m,plat ( z ) - orography factor

vm,plat ( z )

vm ( z )

vm,plat ( z )

(2) The orography factor shall be determined as a function of the wind velocity at the base of the slope and shall be calculated with relationship:

c0={ 1, pentru Φ≤0 ,051+2⋅s⋅Φ , pentru 0,05<Φ≤0,3

1+0,6⋅s , pentru Φ>0,3(B.1)

where:

s is the location factor obtained from Figure B.2 or Figure B.3;

Φ is the gradient of the upwind slope, H/Lu (see Figure B.2 and Figure B.3).

(3) The highest increase in wind velocity shall take place near the top of the slope.

(4) The orographic effects shall be taken into consideration in the following situations:

a) for sites located on the upwind slope of hills, ridges and cliffs, where 0.05 < Φ 0.3 and │x│ Lu/2;

b) for sites located on the downwind slope of hills and ridges, where

Φ < 0.3 and x < Ld / 2, or where Φ 0.3 and x < 1.6 H;

c) for sites located on the downwind slope of steep cliffs and gradients Φ < 0.3 and x < Le / 2, or where Φ 0.3 and x < 5 H;

where (see Figures B.2 and B.3):

Le is the effective length of the upwind slope, given in Table B.1;

Lu is the actual length of the upwind slope;

Ld is the actual length of the downwind slope;

H is the effective height of the hill, ridge, cliff, etc.;

x is the horizontal distance from the site to the top of a ridge;

z is the vertical distance from ground level to the site.

Table 0B.1 Values of the effective length, Le [3]

Type of slope (Φ = H / Lu)

Moderate slope (0.05 < Φ 0.3) Steep slope (Φ > 0.3)

Le = Lu Le = H / 0.3

117

Figure B.2 Factor s for steep cliffs and slopes [3]

Figure B.3 - Factor s for hills and ridges [3]

(4) In valleys, if the velocity is not expected to increase, co(z) can be considered equal to 1.0.

118

downwind slope < 0.05

downwind slope < 0.05

ridge

wind site

wind site

ridge

B.3 Neighbouring buildings and/or structures

(1) If a building/structure is twice the average height, hmed of the neighbouring buildings/structures, then the peak wind velocity and dynamic wind pressure, vp and qp, for any neighbouring structure shall be considered at a height zn (assuming that ze = zn) above ground level, determined with the relationship:

zn={12

r , daca x≤r

12 [r−(1−2⋅h jmare

r )⋅( x−r )] , daca r<x<2r

hmic , daca x≥2r(B.2)

where the radius r is:

r={ hmare , daca hmare≤2⋅dmare

2⋅dmare , daca himare>2⋅dmare(B.3)

The neighbouring structure with a lower height hlow, the radius r, the distance x and the dimensions dlow and dhigh is shown in Figure B.4. The increase in wind velocity and dynamic pressure can be ignored when hlow exceeds half the height hhigh of the tall building. In this situation, zn=hlow.

Figure B.4 The influence of a tall building on two neighbouring buildings (1 and 2) [3]

119

hhigh

hlow,1

hmed

zn

dhigh

dhigh

dlow

dlow

B.4 Displacement height of the zero-elevation plane

(1) For buildings located on terrain of category IV, the vicinity of other buildings and obstacles modifies the wind velocity and pressure profile. This modification behaves as if the ground level (zero-elevation plane) rises to a height, hdepl, called displacement height of the zero-elevation plane, which can be determined with relationship (B.4) (see Figure B.5).:

hdepl={min [0,8⋅hmed , 0,6⋅h ] , daca x≤2⋅hmed

min [ (1,2⋅hmed−0,2⋅x ) , 0,6⋅h ] , daca 2⋅hmed<x<6⋅hmed

0 , daca x≥6⋅hmed

(B.4)

The height z given by the relationships for calculating the mean wind velocity (2.3) and the dynamic wind pressure (2.7) shall be replaced with an effective height, (z - hdepl). In this situation, the profile of the exposure factor (see Figure 2.1) shall be displaced upwards with the height hdepl.

(2) In the absence of more accurate information, for a terrain of category IV, hmed = 15 m.

Figure B.5 Obstacle height and upwind distance [3]

ANNEX C (informative) DYNAMIC CHARACTERISTICS OF STRUCTURES

120

6hmed

2hmed

hmed

hdepl

hdepl

C.1 General aspects

(1) The calculation methods recommended in this annex are based on the hypothesis that the behaviour of structures belongs to the linear elastic range.

(2) The dynamic properties of structures shall be assessed on a theoretical and/or experimental basis by applying the methods used in structural dynamics.

(3) In a first approximation, the dynamic properties of structures (natural frequencies, natural vectors, equivalent masses, and logarithmic decrement of damping) can be assessed, in a simplified way, using the relationships given in C.2–C.6.

C.2 Fundamental natural frequency

(1) For structures with embedded foundations or overhangs which have a mass attached to their free end, relationship (C.1) can be used to calculate their fundamental natural frequency, n1:

n1=1

2⋅π⋅√ g

x1(C.1)

where

g is the gravity acceleration, equal to 9.81 m/s2;

x1 is the maximum displacement due to the dead load applied in the direction of vibration, in [m].

(2) The fundamental natural frequency n1 for multi-storey buildings exposed to wind action can be estimated with the relationship:

n1=55h

[Hz] for buildings made of reinforced concrete(C.2a)

and

n1=40h

[Hz] for buildings with a metallic structure(C.2b)

where h is the height of the building, in [m].

121

(3) The fundamental bending frequency, n1 for chimneys can be estimated with the relationship:

n1=ε1⋅b

hef2⋅√W s

W t [Hz] (C.3)

with

hef=h1+h2

3 (C.4)

where

b is the diameter of the chimney at the top, [m];

hef is the effective height of the chimney, [m]; h1 and h2 are given in Figure C.1;

Ws is the weight of the structural elements which contribute to the stiffness of a chimney;

Wt is the total weight of a chimney;

ε1 is equal to 1000 for metallic chimneys, and 700 for reinforced concrete and masonry chimneys.

Note. h3 = h1/3, see Point C.4(2).

Figure C.01 Geometric parameters for chimneys [3]

(4) The fundamental natural ovalling frequency, n1,o of the walls of long cylinders (chimneys), without circular stiffeners, can be calculated with relationship:

122

n1,o=0 , 492⋅√ t3⋅E

μs⋅(1−ν2 )⋅b4

(C.5)

where

E is Young’s modulus, in [N/m2];

t is the thickness of the cylinder wall, in [m];

is Poisson’s coefficient;

s is the cylinder wall mass per unit area [kg/m2];

b is the diameter of the cylinder, in [m].

The circular stiffeners shall increase the ovalling frequency.

C.3 Fundamental natural vector

(1) For buildings, towers, and chimneys, which are modelled as overhangs with embedded foundations, the fundamental natural bending vector, Φ1(z) (see Figure C.2) can be approximated with a relationship with the following form:

Φ1 (z )=( zh )

ζ

(C.6)

where

ζ = 0.6 for slender structures built on frames with non-load bearing walls;

ζ = 1.0 for buildings with a central core and perimetral columns or buildings with vertical columns and wind protections;

ζ = 1.5 for buildings with a central core made of reinforced concrete;

ζ = 2.0 for chimneys and towers;

ζ = 2.5 for metallic lattice towers.

(2) The fundamental natural bending vector in the vertical plane, Φ1(s) for simply supported and embedded structures and structural elements can be approximated as shown in Table C.1.

123

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

z/h

F1(z)

Figure C.02 Fundamental natural bending vector for buildings, towers, and chimneys

Table C.01 Fundamental natural bending vector in the vertical plane for simply supported and embedded structures and structural elements [3]

Static diagram Natural vector Φ1(s)

C.4 Equivalent mass

(1) The equivalent mass per unit length, me for the fundamental vibration mode shall be given by the relationship:

124

ζ = 0.6

ζ = 1.0

ζ = 1.5

ζ = 2.0

ζ = 2.5

me=∫0

l

m (s )⋅Φ12 (s ) ds

∫0

l

Φ12 (s ) ds

(C.7)

where

m is the mass of the structure per unit length;

is the height or span of the structure or structural element.

(2) For overhangs with a variable mass distribution, me can be approximated using the average value of m in the upper third of the structure, h3 (see Figure C.1).

(3) For structures supported at both ends, which have a span , and variable mass distribution, me can be approximated using the average value of m for a length /3 centred in relation to the point on the structure where Φ(s) is maximum (see Table C.1).

C.5 Logarithmic decrement of damping

(1) The logarithmic decrement of damping, δ for the fundamental vibration mode shall be estimated with the relationship:

δ=δ s+δa+δd (C.8)

where

δs 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 masses, liquid

dampers, etc.), if applicable.

(2) Table C.2 contains approximated values for the logarithmic decrement of structural damping, δ s.

(3) The logarithmic decrement of aerodynamic damping, δ a for the fundamental bending

mode caused by along-wind vibrations shall be estimated with the relationship:

δa=cf⋅ρ⋅b⋅v m (z s)

2⋅n1⋅me (C.9)

where:

cf is the aerodynamic force coefficient for a longitudinal wind action

125

ρ is the air density, equal to 1.25 kg/m3;

b is the width of the structure;

vm(zs) is the mean wind velocity for z = zs (see Point 2.3(2));

zs is the reference height;

n1 is the fundamental natural along-wind vibration frequency of the structure;

me is the equivalent mass per unit length of the structure, determined with relationship (C.7).

Tab0le C.2 Approximated values for the logarithmic decrement of structural damping, δs for the fundamental natural vibration mode [3]

Type of structure

Logarithmic decrement of

structural damping, δs

Reinforced concrete buildings 0.10Steel buildings 0.05Mixed concrete + steel buildings 0.08Reinforced concrete towers and chimneys 0.03Unlined welded metal chimneys without exterior thermal insulation 0.012Unlined welded metal chimneys with exterior thermal insulation 0.020

Metal chimneys with a lining layer and external thermal insulation a

h/b < 18 0.02020 ≤ h/b < 24 0.040h/b ≥ 26 0.014

Metal chimneys with several lining layers and external thermal insulation a

h/b < 18 0.02020 ≤ h/b < 24 0.040h/b ≥ 26 0.025

Metal chimneys with masonry lining 0.070Metal chimneys with gunite lining 0.030Unlined coupled chimneys 0.015Cable-stayed unlined metal chimneys 0.04Metallic bridges Welded 0.02+ metallic lattice towers

With high-strength bolts 0.03

With ordinary bolts 0.05Mixed bridges 0.04

Concrete bridgesPrestressed, without cracks 0.04with cracks 0.10

Wooden bridges 0.06–0.12Aluminium alloy bridges 0.02Fibreglass and plastic (composite) bridges 0.04–0.08

126

CablesWith parallel cables 0.006With wire strands 0.020

a For intermediary values of h/b, linear interpolation can be used.

(5) If the structure is equipped with special dissipative devices, adequate theoretical or experimental methods shall be used to determine the value δd.

C.6 Dynamic characteristics of bridge structures

(1) The fundamental bending frequency in a vertical direction, n1,B of a bridge with solid core decks or caisson decks can be approximated using the relationship:

n1 , B=K 2

2⋅π⋅L2⋅√ E⋅I b

m(C.10)

where

L is the length of the main span, in [m];

E is Young’s modulus, in [N/m2];

Ib is the moment of inertia of the cross-sectional area for vertical bending, calculated

at mid-span, in [m4];

m is the mass per unit length of the cross-section at mid-span (assessed for permanent loads), in [kg/m];

K is a non-dimensional factor which depends on the spans, as follow:

- For single-span bridges:

K = π if it is simply supported; or

K = 3.9 if it is encased at one end and free at the other end; or

K = 4.7 if it is encased at both ends;

- For two-span continuous bridges:

K shall be obtained from Figure C.3, using the curve applicable to two-span bridges; L1 is the length of the lateral span and L ≥ L1;

- For three-span continuous bridges:

K shall be obtained from Figure C.3, using the curve applicable to three-span bridges; where

L1 is the length of the largest lateral span;

L2 is the length of the other lateral span and L ≥ L1 ≥ L2;

127

This shall also apply to three-span bridges where the central span is overhanging/suspended.

If L1 > L, then K can be obtained using the curve for two-span bridges, by neglecting the

shortest lateral span and taking into consideration the longest lateral span as the main span of an equivalent two-span bridge.

- For symmetrical four-span continuous bridges (bridges that are symmetrical in relation to the central support), K can be obtained using the curve for two-span bridges shown in Figure C.3, considering each half of the bridge to be an equivalent two-span bridge.

- For asymmetrical four-span continuous bridges or bridges with more than four continuous spans, K can be obtained using the curve for three-span bridges shown in Figure C.3, considering the largest interior span to be the main span.

NOTE. If the value at the supports is higher than twice the value at mid-span, or if it is lower than 80 % of the value at mid-span, then relationship (C.10) shall only be used to obtain very approximate values.

(2) The fundamental torsional frequency of bridges with solid core decks shall be equal to the fundamental bending frequency calculated with relationship (C.10), providing that the average value of the longitudinal moment of inertia upon bending per unit width is at least 100 times the average value of the transversal moment of inertia upon bending per unit length.

(3) The fundamental torsional frequency of bridges with caisson decks can be approximated with the relationship:

n1 , T=n1, B⋅√P1⋅(P2+P3 ) (C.11)

with

P1=m⋅b2

I p(C.12)

P2=∑ r j

2⋅I j

b2⋅I p(C.13)

P3=L2⋅∑ J j

2⋅K⋅b2⋅I p⋅(1+ν ) (C.14)

where

n1,B is the fundamental bending frequency, in Hz;

128

b is the total width of the bridge;

m is the mass per unit length, defined in C.4;

is Poisson’s coefficient for the decking material;

rj is the distance from the axis of the caisson element j to the axis of the bridge;

Ij is the mass moment of inertia per unit length of the caisson element j for vertical

bending at mid-span, which takes into consideration the effective width of the deck;

Ip is the mass moment of inertia per unit length of the cross-section at mid-span. It

shall be obtained with the relationship:

I p=md⋅b2

12+∑ ( I pj+m j⋅r j

2 ) (C.15)

where

md is the mass per unit length of the deck (without caissons) only, at mid-span;

Ipj is the mass moment of inertia of the caisson j at mid-span;

mj is the mass per unit length of the caisson j at mid-span, without taking into

consideration the part attached to the deck;

Jj is the torsion constant of the caisson j at mid-span, which shall be obtained with relationship:

J j=4⋅A j

2

∮ dst

(C.16)

where

Aj is the area of the opening delimited by the caisson at mid-span;

∮ dst

is the integral along the perimeter of the caisson of the length/thickness ratio for each side of the caisson at mid-span.

NOTE. If relationship (C.16) is applied for bridges with several caissons whose planar shape ratio (= span / width) is higher than 6 shall lead to a negligible drop in the torsion constant assessment accuracy.

(4) The fundamental natural bending vector in the vertical plane, Φ1(s) for bridges can be approximated as shown in Table C.1.

(5) Approximated values of the logarithmic decrement of structural damping, δS for bridges are given in Table C.2.

129

(6) The logarithmic decrement of aerodynamic damping, δa for the fundamental bending mode caused by along-wind vibrations shall be estimated with relationship (C.9).

(7) If the structure of the bridge is equipped with special dissipative devices, adequate theoretical, or experimental methods shall be used to determine the value δd.

Figure C.03 Factor K used to calculate the fundamental bending frequency [3]

130

Two-span bridges

Three-span bridges

ANNEX D (normative) WIND ACTION ON BRIDGES

D.1 General elements

(1) The provisions stipulated in this annex shall only apply to bridges with constant height and cross-sections similar to those shown in Figure D.1, which are made up of a single or multispan deck.

Figure D.1 Examples of cross-sections of common decks [3]

131

open or closed

Lattice orslab Lattice or

slab

(2) The wind forces applied to bridge decks are detailed in D.2 and D.3. The wind forces applied to piles are dealt with in D.4. The forces applied by wind action separately to different parts of a bridge shall be considered simultaneously if their effect is more unfavourable.

(3) Wind action on bridges shall produce forces in directions x, y and z as shown in Figure D.2, where:

direction x is the direction parallel with the deck width, perpendicular to the span

direction y is the direction along the span

direction z is the direction perpendicular to the deck

The forces applied in directions x and y are caused by wind action in different directions and shall not normally occur simultaneously. The forces applied in direction z can be caused by wind action in several directions; if they are unfavourable and significant, they shall be taken into consideration concomitant with the forces applied in any other direction.

NOTE. The following notations shall be used for bridges (see Figure D.2):

L length in direction y

b width in direction x

d height in direction z

For some of the provisions included in this annex, the values attributed to L, b and d are defined more accurately. When references are made to Chapters 3 and 5, the notations applicable to b and d shall be readapted.

Figure D.2 Directions of wind action on bridges [3]

(4) When road traffic is considered to be simultaneous with the wind (see A2.2.1 and A2.2.2 in Annex A2 of SR EN 1990:2004/A1:2006), the combined value Fwk of the wind action

132

Winddirection

on the bridge and vehicles shall be limited to a value Fw

¿

determined by replacing the value vb

with the value vb*. The value shall be vb

*= 23 m/s.

(5) When railway traffic is considered to be simultaneous with the wind (see A2.2.1 and A2.2.4 in Annex A2 of SR EN 1990:2004/A1:2006), the combined value Fwk of the wind

action on the bridge and trains shall be limited to a value Fw

**

determined by replacing the value vb with the value vb

*. The value shall be vb**= 25 m/s.

D.2 Choosing the procedure for calculating the wind action response

(1) The need to use a method for calculating the dynamic response for bridges shall be assessed. The dynamic calculation method is generally not necessary for the decks of normal road and railway bridges with a span of up to 40 m. For this classification, normal bridges can be considered to be steel, concrete, aluminium, or wooden bridges, including composite (mixed) bridges whose usual cross-sectional shape is described in Figure D.1.

(2) If a dynamic response calculation method is not necessary, the value of the dynamic response coefficient, cd can be considered equal to 1.

D.3 Aerodynamic force coefficients

(1) When necessary, the aerodynamic force coefficients for the parapets and signalling supports of bridges shall be determined. In this situation, the provisions stipulated in 4.4 should be used.

D.3.1 Aerodynamic force coefficients in direction x (general method)

(1) The aerodynamic force coefficients for wind action on bridge decks in direction x shall be determined with relationship:

cf,x = cfx,0 (D.1)

where:

cfx,0 is the aerodynamic force coefficient if there is no free-end airflow (see 4.13).

(2) For normal bridges (defined in D.2.1), cfx,0 can be considered equal to 1.3. Alternatively, cfx,0

can be taken in accordance with Figure D.3, which shows a few common cases for determining the values Aref,x and dtot.

133

(3) When the slope angle of the wind action exceeds 10°, the aerodynamic force coefficient can be obtained by carrying out special studies. This slope angle can be due to the along-wind gradient of the terrain.

(4) If two bridge decks which are generally similar are located at the same level and are separated transversally by a gap of up to 1 m, the force on the structure exposed to wind action can be calculated similar to an individual structure. In other situations, special attention shall be paid to the wind-structure interaction.

Figure D.3 Aerodynamic force coefficient for bridges, cfx,0 [3]

(5) Where the face exposed to wind action is inclined (see Figure D.4), the aerodynamic force coefficient cfx,0 can be reduced by 0.5 % for each degree of sloping, 1 from the vertical, but this reduction shall be limited to a maximum of 30 %. This reduction shall not apply to the value Fw, defined in D.3.2.

134

a) the construction phase, open face parapets more than 50 % and open face

safety barriersb) Solid face parapets, noise barriers, safety

barriers, and traffic barriers

Separate lattice girders

Types of bridges

Figure D.4 Bridge deck with a sloping face exposed to wind action [3]

(6) When the bridge deck is sloping in a transversal direction, cfx,0 can increase by 3 % for each degree of sloping, but no more than 25 %.

(7) The reference areas, Aref,x for the combinations of loads without the traffic load shall be defined as follows:

a) for solid core girder decks, Aref,x shall be the sum of (see Figure D.5 and Table D.1):

1) the areas of the exposed surfaces of the main girder

2) the surface areas of those parts of the main girders which are below the level of the first girder

3) the surface areas of the cornice, pavement, or rail track on a crushed stone prism located above the level of the main girder

4) the exposed areas of the solid face safety devices or noise barriers, where relevant, located above the level of the surface described in 3) or, in the absence of such equipment, 0.3 m for each open face parapet or barrier.

b) for lattice girder desk, Aref,x shall be the sum of:

1) the front areas of a cornice, pavement, or rail track on a crushed stone prism

2) the areas of the solid faces of the main lattice girders, located above, or underneath the surfaces described in 1).

3) the front areas of the solid face safety devices, where relevant, located above the level of the surface described in 1) or, in the absence of such equipment, 0.3 m for each open face parapet or barrier.

However, the total reference area shall not exceed the area obtained by considering an equivalent plane solid core girder with the same total height, including all its designed parts.

c) for bridge decks consisting of several girders, during execution, before installing the rolling track slab, Aref,x shall be the exposed surface of two main girders.

135

Solid face parapet, noise barrier, or solid

safety barrier

Figure D.5 Height that must be used to determine Aref,x [3]

Table D.1 – Height dtot that must be used to determine Aref,x [3]

Road protection devices on one side on two sidesOpen face parapet or safety barrier d + 0.3 m d + 0.6 mSolid face parapet or safety barrier d + d1 d + 2 d1Open face parapet and safety barrier d + 0.6 m d + 1.2 m

(8) The reference areas, Aref,x for the combinations of loads that include the traffic load shall be considered as stipulated in (4), with the following modifications. If the surfaces are larger than those described in Paragraphs a)(3) and (4) and b)(3), the following shall be taken into consideration:

a) for road bridges, the surface area obtained by considering a height of 2 m above the road, for the most unfavourable length, regardless of the position of the vertical traffic loads;

b) for railway bridges, the surface area obtained by considering a height of 4 m above the upper level of the tracks, for the entire length of the bridge.

(9) The reference height, ze, can be considered the distance at the lowest ground level to the centre of gravity of the bridge deck, without taking into consideration the other parts (e.g. parapets) of the reference surfaces.

(10) The effects of wind pressure due to moving vehicles are not covered by this code. For the wind effects due to passing trains, see SR EN 1991-2.

D.3.2 Wind forces on bridge decks in direction x – Simplified method

(1) When it is not necessary to use a dynamic response calculation method, the force applied by wind action in direction x can be obtained using the relationship:

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Open face safety barrier

Open face parapet

Fw=12⋅ρ⋅vb

2⋅C⋅A ref,x

(D.2)

where:

vb is the reference wind velocity

C is the wind load factor. C = ce · cf,x, where ce is the exposure factor and cf,x is given in

D.3.1(1); the values for C are given in Table D.2

Aref,x is the reference area specified in D.3.1

is the air density

Table 0D.2 — Values of the load factor, C [3]

b/dtot ze ≤ 20 m ze = 50 m

0.5 6.7 8.3 4.0 3.6 4.5

The values given in the table were determined on the basis of the following hypotheses:

- Terrain of category II;- Aerodynamic force coefficient cfx,0 in accordance with 4.3.1 (1) ;- co = 1.0 ;

- kl = 1.0.

For intermediary values of b/dtot, and ze, linear interpolation can be used.

D.3.3 Wind forces on bridge decks in direction z

(1) For wind action on bridge decks in direction z, the aerodynamic force coefficients cf,z must be defined both in an ascending and a descending direction (lift force coefficients). cf,z must not be used to analyse the vertical vibrations of bridge decks.

(2) In the absence of wind tunnel tests, the recommended value cf,z can be considered equal to ± 0.9. This value shall take into consideration, overall, the influence of a potential transversal slope of the deck, the ground gradient and the fluctuations of the wind incidence angle with the bridge deck due to turbulence.

(3) Alternatively, cf,z can be assessed using Figure D.6. In this situation:

- the height dtot can be limited to the height of the bridge deck, not taking into account the

traffic or the equipment installed on the bridge;

- for horizontal flat terrain, the angle of the wind with the horizontal axis can be considered equal to 5° due to turbulence. This recommendation shall also apply to uneven terrain, where the bridge deck is located at least 30 m above ground level.

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Figure D.6 Aerodynamic force coefficient, cf,z for bridges with a transversal slope [3]

(4) Wind forces on the bridge decks in direction z can only have significant effects if they have the same size grade as the vertical forces due to permanent actions.

(5) The reference area Aref,z shall be equal to (see Figure D.2):

Aref,z = b . L (D.3)

(6) The end-effect factor shall not be taken into consideration (see Chapter 4).

(7) The reference height shall be the same as for cf,x (see D.3.1(6)).

(8) The force eccentricity in direction x can be considered to be e = b/5.

D.3.4 Wind forces on bridge decks in direction y

(1) If necessary, the longitudinal wind forces in direction y shall be considered.

The values for the longitudinal wind actions in direction y shall be:

- for bridges with solid core girders, 25 % of the wind forces in direction x;

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deck slope with the horizontal axis (superelevation)wind action angle with the horizontal axis

- for bridges with lattice girders, 50 % of the wind forces in direction x.

D.4 Bridge piles

D.4.1 Wind directions and design situations

(1) To assess the wind action on bridge decks and their supporting piles, the most unfavourable wind direction for the entire structure must be identified, for the effects considered.

(2) The wind action shall be calculated separately for transient design situations during the construction stages, when the wind action on the bridge deck cannot be transmitted horizontally or redistributed. If, during such situations, the piles support overhanging parts of bridge deck or scaffolding, a possible asymmetry of the wind action on these elements must be taken into consideration. For the characteristic values obtained during transient design situations see SR EN 1991-1-6, and for scaffolding see 4.11.

D.4.2 The effect of wind on bridge piles

(1) The effects of the wind on bridge piles shall be assessed using the general format defined in the code. For global loads, the provisions stipulated in Points 4.6, 4.8, or 4.9.2 shall be taken into consideration.

(2) For asymmetrical loads, the design load due to wind action on those parts of the structure where it causes favourable effects should not be taken into consideration.

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Romanian Wind Code CR1-1-4

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Transcript of Romanian Wind Code CR1-1-4