The Part 1.4 of EN 1991 [9] deals with the effects of wind on structures. The scope of this part covers up to 200 m height buildings for the common effects on all parts of the building: components, claddings and fixings, etc. Other effects, as thermal effects on winds, vibrations where more than a relevant fundamental mode needs to be considered, the torsional vibrations due to transverse winds, etc. are not covered. Three models of response are given:
the quasi-static response, the dynamic and the aeroelastic.
The effect of the wind on the structure (i.e. the response of the structure) depends on the size, shape and dynamic properties of the structure. Wind fluctuates with time and this fluctuation can originate different effects depending on the building characteristics. For most buildings, only a quasi-static response structure needs to be considered. Dynamic structural responses are needed to be considered only in the cases with very low natural frequency (lower than 1 Hz) and low damping. Aeroelastic response should be considered for flexible structures such as cables, masts, chimneys and bridges. Therefore, the quasi-static response is treated here only.
The wind acts directly as a pressure on the external surfaces of enclosed structures and, because of the porosity of the external surface it also acts indirectly on the internal surfaces. It may also act directly on the internal surface of open structures.
Pressures act on areas of the surface resulting in forces normal to the surface of the structure or of individual cladding components. Additionally, when large areas of structures are swept by the wind, friction forces acting tangentially to the surface may be significant.
The quasi-static action of the wind is represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of the turbulent wind.
The fundamental value of the basic wind velocity, vb,0, is the main variable used to define the wind in a site. It is defined as the characteristic 10 minutes mean wind velocity at 10 m height on a terrain category II. The terrain category II is defined as an area with low vegetation such as grass and isolated obstacles (trees, buildings) with separations of at least 20 obstacle heights.
The Part [6] does not provide maps of fundamental wind velocity; they shall be given in the National Annexes of CEN Member States to be operative in design procedure.
From the fundamental wind velocity the basic wind velocity is derived, vb as:
vb = cdir·cseason· vb,0 (10
where cdir and cseason are the directional and seasonal factors, taking into account that the wind in some directions could be reduced and that temporary structures spanning a few months might have a lower probability of high winds. These two factors are usually taken as the unity.
The basic wind pressure, qb is derived from the basic wind velocity as:
qb = ρ/2 · vb2 (11)
where ρ is the density of the air (it can be set to 1,25 kg/m3).
The basic wind pressure represents the mean value of the pressure on a building placed at a site in a terrain category II and with a reference height of 10 m. The transformation of this value to the pressure at a building at the actual terrain category in reference height is carried out by the mean wind velocity at the relevant height by:
vm (z) = cr(z)· c0(z)· vb (12)
where: vm (z) is the mean wind velocity at z reference height cr(z) is the roughness factor, and
c0(z) is the orography factor
The orography factor takes into account the fact that for buildings placed on elevations, valleys, etc. the wind could be increased. Usually, it is considered as the unity.
The roughness factor is derived as:
cr(z) = kr ln (z/z0) for z ≥ zmin ; (13) kr = 0,19 (z0/z0,II)0,07 ; (14) where: kr the terrain factor,
z0 the roughness length given for every terrain category, zmin the minimum height given for relevant terrain category.
There are five different terrain categories defined in Annex A of [6]: from category 0, corresponding to sea or coastal areas exposed to open sea to category IV, where areas with buildings of average height exceeding 15 m should be considered.
Figure 4.4 The peak and mean velocities
The value of peak velocity represents the effect of the average velocity in 10 minutes plus the effect of the gust, see Figure 4.4, it is obtained from the mean wind velocity by multiplication by the gust factor G:
vp (z) = G ·vm (z); (15)
where: G = for z ≥ zmin , andkI is the turbulence factor
The peak velocity pressure in the relevant height is finally:
(16) In common cases it may be taken c0(z ) = kI = 1.0, then it can be simplified to:
(17)
It can also be expressed in the form:
(18)
where is the exposure factor
(19)
This exposure factor then gives the relationship between the peak velocity pressure for the building reference height and the basic velocity pressure of the site, depending on the different terrain categories. See Figure 4.5.
Figure 4.5 Exposure factor for the reference height and terrain categories
Quasi-static wind response: pressure and wind forces
The wind forces can be determined with the help of pressure or force coefficients:
a) Pressure coefficients
The force on the whole structure is determined by the vectorial summation of the external, internal and friction forces on all the surfaces of the building:
(20)
(21)
(22)
where: Fw,e, Fw,i andAfr are the external, internal and friction forces and
where
is the structural factor
and are the pressure coefficients for external or internal pressure is the friction coefficient
and are the external and internal pressure on the individual surface is the peak velocity pressure at the reference height
is the reference area for an individual surface
is the area of the external surface parallel to the wind
b) Force coefficients
The force on the whole structure or on one member can be calculated by the expression:
(23) where: is the force coefficient for the member or the whole structure given for
different shapes in section 7 of [8]
Section 7 of [6] indicates the way to obtain all these coefficients for common types of buildings or members.
Programs
The supplementary spreadsheet wind.xls to this Guidebook facilitates to obtain the wind loads on common buildings.
Example 1:
Consider the case of the industrial hall shown in the figure to be built in Alicante (Spain) by the seashore.
From the wind map of Spain we obtain:
The basic wind velocity, vb = cdir ·cseason· vb,0 = 1 × 1 × 27 = 27 m/s.
Considering a terrain roughness of category 0 (faced to open sea) z0 = 0,003 m, zmin = 1 m
The basic wind pressure, qb
qb = ρ/2 · vb2 = 1,25 kg/m3 × (27 m/s )2/2 = 0,455 kN/m2 z = 10 m
z0 = 0,003 zmin = 1 m Roughness factor, cr(z)
cr(z) = 0,19 (z0/z0,II)0,07 ln (z/z0) = 1,26572 the mean wind velocity
vm (z) = cr(z)· c0(z)· vb = 34.1744 m/s c0(z) =1.
the peak velocity
vp (z) = G ·vm (z) = 46,65 m/s
where G= = 1,3649
The peak velocity pressure for c0(z ) = kI = 1.0;
= 1,360 kN/m2
where = 2,98453
Quasi-static wind response: pressure and wind forces
The wind forces can be determined with the help of pressure or force coefficients. The pressure coefficients are used in this case.
Pressure coefficients:
The force on the whole structure is determined by the vectorial summation of the external, internal and friction forces on all the surfaces of the building:
The friction forces can be disregarded due to the small area on which they are applied.
There is no dominant face in this building and, besides, no special characteristics are given to the calculation of the μ coefficient, so two hypotheses have to be analysed for the internal force coefficients: cpi = +0,2 and cpi = -0,3.
Taking account of the dimensions of the building:
e = min[ b, 2 h]= min[30, 2×10] = 20 m
the pressures on the faces and roof can be taken from Figure 7.8 and Table 7.4a of [5].
One central frame is considered here. The influence area for each frame is 5 m wide.
Surface D E F G H I J
The signs of the internal forces are changed with respect to the internal coefficients to be added algebraically to the external forces; therefore, the sign of the total forces has to be considered from the point of view of the external surfaces. From the two hypotheses ((cpi= 0,2 or cpi= -0,3) the one most critical for the frame has to be chosen.