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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, vb, 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 qb is the wind pressure
corresponding to the reference value of the wind velocity
vb
where:
is the air density, which depends on altitude,
temperature, latitude and season. The recommended
value for design is 1.25 kg/m3
For design purposes, reference wind pressure are
obtained from maps and tables given in codes (CR 1-1-4 /
2012).
21
2b bq v
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
Mean wind velocity: terrain categories
Terrain roughness is described aerodynamically by the
roughness length, z0, 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:
where:
cr(z) is a roughness factor
z - height above ground
z0 – roughness length
m r bv z c z v
0 min max0
min
min
lnr
r
r
zk z for z z z
zc zz z
c z z
Mean wind velocity: variation with height
The terrain factor kr(z0) is given by the relationship:
0,07
00 0,189
0,05r
zk z
Mean wind pressure: variation with height
The roughness factor cr(z) is
used to describe the variation of
wind pressure with height 2
m r bq z c z q
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.
The turbulence intensity I(z) at height z can be expressed
as:
v
v
m
I zv z
min max
0
minmin
200
2.5lnv
v
for z z z mz
I zz
for z zI z z
Wind turbulence
Wind turbulence decreases with height above ground
Wind turbulence: gust factor
The gust factor cpq(z) is the ratio between the peak
pressure (due to wind turbulence) and mean pressure
(due to mean wind velocity)
The gust factor cpq(z) can be determined as:
where:
g = 3.5 is the amplitude factor
Iv(z) is the turbulence intensity at height z
1 2 1 7pq v vc z g I z I 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 qb
(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 cr(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 cpq(z)
– Isolated hills and other local topographical accidents can affect
the mean wind velocity. In design this effect is accounted through
the orography factor co. It need not be considered when the slope
is less than 5% (co=1.0).
Wind pressure at height z
Effect of topography
Wind pressure at height z can be obtained as:
The product between the gust factor, the roughness
factor and the topographical factor is called the exposure
factor, and is denoted by ce(z):
p e bq z c z q
2 2e o r pqc z c c z c z
Wind pressure at height z
2 2e o r pqc z c c z c z
Wind pressure at height z
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
FD = CD 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:
where:
Iw – the importance factor
qp(ze) – peak wind pressure at level ze
ze – reference height for external pressure.
cp – aerodynamic pressure coefficient (cpe for exterior
surfaces; cpi for internal surfaces)
Pressures are considered positive (+)
Suction is considered negative (-)
The total pressure on a structural element is obtained as
the algebraic sum of pressures on one side and suction
on the other side
e Iw pe p ew c q z i Iw pi p iw c q z
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:
e Iw pe p ew c q z i Iw pi p iw c q z
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 cpe 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 cpe,1 are intended for the design of small elements and
fixings with an area per element of 1 m2 or less such as cladding
elements and roofing elements. Values for cpe,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, ze, 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 ce(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 hstrip (max hstrip = 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 cp
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 cp
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
where:
Iw – the importance factor
qp(ze) – peak wind pressure at level ze
ze – reference height for external pressure.
cf - wind force coefficient
cd - dynamic response coefficient
Aref - reference area perpendicular on wind direction
w Iw d f p e refF c c q z A
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.
