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Basis of Structural Design Course 10 Actions on structures: Wind loads Other loads Course notes are available for download at http://www.ct.upt.ro/users/aurelstratan/

Wind loading: normative references Normative references EN 1991-1-4: Eurocode 1: Actions on structures - Part 1-4: General actions - Wind actions CR 1-1-4/2012: Cod de proiectare. Evaluarea acţiunii vântului asupra construcţiilor. Wind action is classified as variable fixed actions according to EN 1990

Nature of wind loading Wind represents masses of air moving mainly horizontally (parallel to the ground) from areas of high pressure to ones of low pressure Wind generates pressures on external (and also internal) surfaces of structures The main effect of wind is a horizontal loading on buildings (especially high-rise) 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.

Basic value of mean wind velocity The reference value of the wind velocity, v b, is the characteristic 10 minutes mean wind velocity, irrespective of wind direction and time of year, at 10 m above ground level in open country terrain with low vegetation such as grass and isolated obstacles with separations of at least 20 obstacle heights. Reference values of wind velocity are determined for annual probabilities of exceedence of 0.02, which is equivalent to a mean return period of 50 years. For design purposes, basic values of wind velocity are obtained from maps and tables given in codes (CR 1-1- 4/2012).

Reference wind pressure Reference wind pressure q b is the wind pressure corresponding to the reference value of the wind velocity v b q b 1 v 2 2 b where: is the air density, which depends on altitude, temperature, latitude and season. The recommended value for design is 1.25 kg/m 3 For design purposes, reference wind pressure are obtained from maps and tables given in codes (CR 1-1-4 / 2012).

Reference wind pressure

Mean wind velocity: gradient height The mean wind velocity at great heights above the ground is constant and it is called the gradient wind speed. Near the ground the mean wind velocity is decreasing much due to frictional forces caused by the terrain, being equal with zero at the ground level. There is a boundary layer within which the wind speed varies from zero to the gradient wind speed (mean wind velocity increases with height).

Mean wind velocity: gradient height The thickness of the boundary layer (gradient height) depends on the ground roughness. Larger the roughness, larger the gradient height.

Mean wind velocity: terrain categories

Mean wind velocity: terrain categories Terrain roughness is described aerodynamically by the roughness length, z 0, expressed in meters. It represents a measure of the dimensions of eddies of turbulent wind at the ground surface.

Mean wind velocity: variation with height The mean wind velocity profile within the atmospheric boundary layer can be described by a logarithmic law: v z c z v m r b c r z z k r z ln for z z z z c r z z 0 min max 0 z z min min where: c r (z) is a roughness factor z - height above ground z 0 roughness length

Mean wind velocity: variation with height The terrain factor k r (z 0 ) is given by the relationship: k r 0,07 z0 z 0 0,189 0,05

Mean wind pressure: variation with height The roughness factor c r (z) is used to describe the variation of wind pressure with height q z c z q 2 m r b

Wind turbulence Wind velocity varies with time as shown in the figure below. This variation with respect to the mean wind velocity is called turbulence and is generated by the eddies caused by the wind blowing over obstacles

Wind turbulence The turbulence intensity I(z) at height z is defined as the standard deviation of the turbulence divided by the mean wind velocity. I v z v v z m The turbulence intensity I(z) at height z can be expressed as: I v z z 2.5ln z I v z z 0 min for z z z 200m min max for z z min

Wind turbulence Wind turbulence decreases with height above ground

Wind turbulence: gust factor The gust factor c pq (z) is the ratio between the peak pressure (due to wind turbulence) and mean pressure (due to mean wind velocity) The gust factor c pq (z) can be determined as: c z 1 2g I z 1 7 I z pq v v where: g = 3.5 is the amplitude factor I v (z) is the turbulence intensity at height z

Wind turbulence: gust factor

Wind pressure at height z Wind pressure at height z above ground can be obtained by considering the effects of mean wind velocity, wind turbulence, and topography on the reference pressure q b (at the ground level) Mean wind velocity increases with height above ground. The effect of mean wind velocity on wind pressure profile is accounted through the roughness factor c r (z) Wind turbulence decreases with height above ground. The effect of wind turbulence on wind pressure at height z is accounted through the gust factor c pq (z) Isolated hills and other local topographical accidents can affect the mean wind velocity. In design this effect is accounted through the orography factor c o. It need not be considered when the slope is less than 5% (c o =1.0).

Effect of topography Wind pressure at height z

Wind pressure at height z can be obtained as: q z c z q p e b The product between the gust factor, the roughness factor and the topographical factor is called the exposure factor, and is denoted by c e (z): c z c c z c z 2 2 e o r pq Wind pressure at height z

Wind pressure at height z c z c c z c z 2 2 e o r pq

Nature of wind loading Wind actions act directly as pressures on the external surfaces of enclosed structures and, because of porosity of the external surface, also act indirectly on the internal surfaces. They 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 wind action is represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of the turbulent wind.

Wind effects on structures Wind effects on structures can be classified as follows: static or quasistatic response turbulence induced vibrations vortex induced vibrations galloping flutter response due to interference of nearby structures

Wind effects on structures Most buildings are not streamlined, and are called bluff bodies in aerodynamics. drag force, in the direction of the flow F D = C D q lift force, perpendicular to flow direction torsion moment For bluff bodies, wind flow separates and causes the formation of the so-called "wake" pressure on the windward side suction on the leeward side suction/pressure on lateral surfaces

Wind pressure on surfaces Wind pressure w(z) on rigid exterior and interior surfaces of the structure at height z above ground are obtained as: w c q z w c q z e Iw pe p e where: Iw the importance factor q p (z e ) peak wind pressure at level z e z e reference height for external pressure. c p aerodynamic pressure coefficient (c pe for exterior surfaces; c pi for internal surfaces) Pressures are considered positive (+) Suction is considered negative (-) i Iw pi p i The total pressure on a structural element is obtained as the algebraic sum of pressures on one side and suction on the other side

Wind pressure on surfaces Wind pressure w(z) on rigid exterior and interior surfaces of the structure at height z above ground are obtained as: w e Iw cpe qp z e w c q z i Iw pi p i

Aerodynamic pressure coefficients Aerodynamic pressure coefficients depend on: geometry of the structure/element size of the structure/element terrain roughness wind direction with respect to the structure Reynolds number etc.

Pressure coefficients: loaded area Aerodynamic pressure coefficients c pe for buildings and parts of buildings depend on the size of the loaded area A, which is the area of the structure, that produces the wind action in the section to be calculated Values for c pe,1 are intended for the design of small elements and fixings with an area per element of 1 m 2 or less such as cladding elements and roofing elements. Values for c pe,10 may be used for the design of the overall load bearing structure of buildings. Due to non-uniform action of wind, peak pressure on a small area is higher than the peak overall pressure on a large area (for which some portions are loaded less)

Press. coeff.: vertical walls of rect. plan buildings The reference heights, z e, for rectangular plan buildings depend on the aspect ratio h/b and are always the upper heights of the different parts of the walls Reference heights are used to compute the exposure factor c e (z) Three cases: A building, whose height h is less than b should be considered to be one part.

Press. coeff.: vertical walls of rect. plan buildings A building, whose height h is greater than b, but less than 2b, may be considered to be two parts, comprising: a lower part extending upwards from the ground by a height equal to b and an upper part consisting of the remainder.

Press. coeff.: vertical walls of rect. plan buildings A building, whose height h is greater than 2b may be considered to be in multiple parts, comprising: a lower part extending upwards from the ground by a height equal to b; an upper part extending downwards from the top by a height equal to b and a middle region, between the upper and lower parts, which may be divided into horizontal strips with a height h strip (max h strip = b)

Press. coeff.: vertical walls of rect. plan buildings Depending on geometry and position with respect to wind direction, different regions of vertical walls are assigned different names, with corresponding values of pressure coefficients c p

Pressure coefficients Similar procedure are specified in the code for roofs of buildings (of different geometry), canopies, isolated vertical walls, fences etc.

Wind forces method For structures like signboards, lattice structures and scaffoldings, flags, etc. wind actions is modelled as a resultant force F c c q z A w Iw d f p e ref where: Iw the importance factor q p (z e ) peak wind pressure at level z e z e reference height for external pressure. c f - wind force coefficient c d - dynamic response coefficient A ref - reference area perpendicular on wind direction

Other loads: traffic loads on bridges In practice a highway bridge is loaded in a very complex way by vehicles of varying sizes and groupings. In order to simplify the design process this real loading is typically simulated by two basic imposed loads - a uniformly distributed load and a knife edge load - representing an extreme condition of normal usage. The design is then checked for a further load arrangement representing the passage of an abnormal load. The magnitudes of all these loads are generally related to the road classification, the highway authority's requirements and the loaded length of the bridge.

Other loads: traffic loads on bridges Railway bridge design must take account of static loading and forces associated with the movement of vehicles. As for highway bridges, two models of loading are specified for consideration as separate load cases. They represent ordinary traffic on mainline railways and, where appropriate, abnormal heavy loads. They are expressed as static loads due to stationary vehicles and are factored to allow for dynamic effects associated with train speeds up to 300km/h. Eurocode 1 also gives guidance on the distribution of loads and their effects and specifies horizontal forces due to vehicle motion. Centrifugal forces associated with the movement around curves, lateral forces due to oscillation of vehicles (nosing) and longitudinal forces due to traction and braking are included. Other aspects of bridge loading which need to be considered include accidental loads and the possibility of premature failure due to fatigue under traffic loading.

Other loads: crane loads For buildings fitted with travelling overhead cranes, the loads due to the crane itself and the lifted load are considered separately. The self weight of the crane installation is generally readily available from the manufacturer, and the load lifted corresponds to the maximum lifting capacity of the crane. When a load is lifted from rest, there is an associated acceleration in the vertical direction, which causes an additional force. This force is in addition to the normal force due to gravity, and is generally allowed for by factoring the normal static crane loads. Movements of the crane, both along the length and across the width of the building, are also associated with accelerations and retardations, this time in the horizontal plane. The associated horizontal forces must be taken into account in the design of the supporting structure.

Other loads: wave loading For offshore structures in deep waters, wave loads can be particularly severe. The loads arise due to movement of water associated with wave action. These movements can be described mathematically to relate forces to physical wave characteristics such as height and wavelength. The treatment is therefore similar to wind loads in that these physical characteristics are predicted and corresponding forces on the particular structural arrangement then calculated. These calculation procedures are, however, very complicated and must realistically be performed on a computer.

Other loads: temperature effects Exposed structures such as bridges may be subject to significant temperature variation which must be taken into account in the design. If it is not provided for in terms of allowing for expansion, significant forces may develop and must be included in the design calculations. In addition, differential temperatures, e.g. between the concrete deck and steel girders of a composite bridge, can induce a stress distribution which must be considered by the designer.

Other loads: retained material Structures for retaining and containing material (granular or liquid) will be subject to a lateral pressure. For liquids it is simply the hydrostatic pressure. For granular material a similar approach can be adopted, but with a reduction in pressure depending on the ability of the material to maintain a stable slope - this is the Rankine approach. Ponding of water on flat roofs should be avoided by ensuring adequate falls (1:60 or more) to gutters.

Other loads: seismic loads Seismic actions on structures are due to strong ground motion. They are a function of the ground motion itself and of the dynamic characteristics of the structure. Strong ground motion can be measured by one of its parameters, the peak ground acceleration being the parameter most usually adopted for engineering purposes.

Other loads: accidental loads Accidental actions may occur as a result of accidental situations. The situations include fire, impact or explosion. It is very difficult to quantify these effects. In many cases it may be preferable to avoid the problem, for instance by providing crash barriers to avoid collision from vehicles or roof vents to dissipate pressures from explosions. Where structures such as crash barriers for vehicles and crowds must be designed for 'impact' the loading is treated as an equivalent static load.