wind effects on buildings

Wind Effects on BuildingsWind Effects on Buildings

Lecture 1

Matthew Trussoni, PhD, AIA, PE

[email protected]

Milwaukee School of Engineering

Risks Produced by WindRisks Produced by Wind

• Structural Failure

•Wind Load

•Redistribution of Snow

•Cladding Failure

•Wind Load•Wind Load

•Projectile Impact

•Aerodynamic Instability

•Serviceability Problems

•Air Quality

Hurricane AndrewHurricane Andrew

Hurricane KatrinaHurricane Katrina

Image: mceer.buffalo.edu/.../default.asp

Tacoma Narrows BridgeTacoma Narrows Bridge

http://www.youtube.com/watch?v=P0Fi1VcbpAI

Relationship Between Wind and HeightRelationship Between Wind and Height

Image: www.omafra.gov.on.ca/.../facts/03-047.htm

MultiMulti--disciplinary Engineeringdisciplinary Engineering

• Meteorology

•Aerodynamics

•Structural Engineering

•Structural Dynamics

•Statistics•Statistics

•Architecture

•Wind Tunnel Testing

•Computational Fluid Dynamics

Books on Wind EngineeringBooks on Wind Engineering

• Wind Effects on Structures: Fundamentals and Applications to Design By Simiu & Scanlan

•Wind Loading on Structures by JD Holmes

•The Designers Guide to Wind Loading of Building Structures. Part 1 & Part 2 by NJ Cook

•Wind Effects on Buildings, Volume 1 & 2 by TV Lawson•Wind Effects on Buildings, Volume 1 & 2 by TV Lawson

•Wind Forces in Engineering by Peter Sachs

•Wind Engineering: A Handbook for Structural Engineers by Henry Liu

•Design of Buildings and Bridges for Wind: A Practical Guide for ASCE 7 Standard Users and Designers of Special Structures by Emil Simiu and Toshio Miyata

The Origin and Nature of WindThe Origin and Nature of Wind

•Composition of Standard Atmosphere

•Properties of Standard Atmosphere

•Ideal Gas Law

•Energy Balance of Unit Mass of Air

•Adiabatic Relationships•Adiabatic Relationships

•Coriolis Effect

•Geostrophic Wind

Composition of Standard AtmosphereComposition of Standard Atmosphere

Gas Volume (%)

Nitrogen 78.09

Oxygen 20.95

Argon 0.93

Carbon Dioxide 0.03

Other 0.01

Properties of Standard AtmosphereProperties of Standard Atmosphere

Temperature 15 ˚ C 59 ˚ F

Absolute Temp 288.15 ˚ K 518.69 ˚ R

Pressure 101.3 KPa 14.69 lb/in2

Density 1.225 Kg/M3 0.0765 lb/ft3

Viscosity 1.793x10-5 Kg/(m s) 3.745x10-7 Slug/ (Ft s)

KinematicViscosity

1.464x10-5 M2/s 1.576x10-4 Ft2/s

Gravity 9.807 M/s 32.17 Ft/s

Gas Constant 287 M2/(s2˚K) 1716 Ft2/(s2˚R)

Spec. Heat Constant Pressure

1005 J/(Kg ˚K) 6013 Ft lb/(Slug ˚R)

Spec. HeatConstant Volume

718 J/(Kg ˚K) 4297Ft lb/(Slug ˚R)

Ratio of Spec. Heats 1.4 1.4

Speed of Sound 340 M/s 1116 Ft/s

Ideal Gas LawIdeal Gas Law

TheThe aabsolute bsolute temperature (T), pressure (p) and density (temperature (T), pressure (p) and density (TheThe aabsolute bsolute temperature (T), pressure (p) and density (temperature (T), pressure (p) and density (ρρ) ) are are rrelated to a close approximation by the ideal gas lawelated to a close approximation by the ideal gas law

Gas Constant = Gas Constant = RRgg = C= Cpp –– CCvv

Energy Balance of Unit Mass of AirEnergy Balance of Unit Mass of Air

ddq = Energy increment inputq = Energy increment inputddq = Energy increment inputq = Energy increment inputCCvv = Specific Heat Constant Volume= Specific Heat Constant VolumedTdT = Increase in Internal Energy= Increase in Internal Energypdvpdv = Work Done by Volume Expansion= Work Done by Volume Expansion

Energy Balance with Ideal Gas SubstitutionEnergy Balance with Ideal Gas Substitution

Specific Volume = v = 1/Specific Volume = v = 1/ρρ

Ideal GasIdeal Gas

Adiabatic RelationshipsAdiabatic Relationships

If there is no input or output of heat then If there is no input or output of heat then dqdq = 0 and:= 0 and:

Therefore:Therefore:

Since Since RRgg = C= Cpp –– CCvv and and γγ == CCpp // CCvv

Adiabatic RelationshipsAdiabatic Relationships

Taking the Taking the lnln of both sides & where C = constantof both sides & where C = constant

Therefore:Therefore:

&&

Using the Perfect Gas Law implies also thatUsing the Perfect Gas Law implies also that

&&

&&

Adiabatic Lapse RateAdiabatic Lapse Rate

If we consider the static condition of air, then focus on a If we consider the static condition of air, then focus on a horizontal slice of that air (horizontal slice of that air (δδzz). The pressure at the bottom of ). The pressure at the bottom of

the slice will be greater than at the top by and amount (the slice will be greater than at the top by and amount (δδpp) ) equal to weight per unit area of the air slice. The height is equal to weight per unit area of the air slice. The height is

measured as positive direction up.measured as positive direction up.

The limit of the infinitesimal slice thickness, the hydrostatic The limit of the infinitesimal slice thickness, the hydrostatic pressure gradient is’pressure gradient is’


Substituting equations in for p and Substituting equations in for p and ρρ..

It follows thatIt follows thatIt follows thatIt follows that


If we substitute in the values for g and Cp we find the lapse If we substitute in the values for g and Cp we find the lapse rate in static dry air to be.rate in static dry air to be.

Which translates into about 10 ˚C per 1000 meters in Which translates into about 10 ˚C per 1000 meters in height (5.5˚F per 1000 Ft).height (5.5˚F per 1000 Ft).

The air density ratio to that at see level is given by.The air density ratio to that at see level is given by.


Take the example of Denver Colorado altitude of 1637 M.Take the example of Denver Colorado altitude of 1637 M.

In wind engineering the dynamic pressure, q, of the wind is In wind engineering the dynamic pressure, q, of the wind is given by:given by:given by:given by:

With this equation it can be found that the reduced air With this equation it can be found that the reduced air density at Denver results in about a 13% reduction in the density at Denver results in about a 13% reduction in the wind load as compared to the wind load at sea level.wind load as compared to the wind load at sea level.

CoriolisCoriolis EffectEffect

TheThe corioliscoriolis effect is the deflection of an object that is effect is the deflection of an object that is affected by a rotating frame of referenceaffected by a rotating frame of reference

Images: www.indiana.edu/.../coriolis.html

GeostrophicGeostrophic WindWind

When there is no friction the wind will flow parallel to When there is no friction the wind will flow parallel to couture lines of pressurecouture lines of pressure

Images: www.newmediastudio.org/.../Spiral_Winds.html

GeostrophicGeostrophic WindWindThis diagram represents the northern hemisphere where This diagram represents the northern hemisphere where the the corioliscoriolis forces acts outward from low pressure and forces acts outward from low pressure and inward toward high pressure. This configuration shows inward toward high pressure. This configuration shows how winds flow counterclockwise around lows and how winds flow counterclockwise around lows and clockwise around highs. In the southern hemisphere the clockwise around highs. In the southern hemisphere the corioliscoriolis force acts in the opposite direction reversing the force acts in the opposite direction reversing the flowsflows


GeostrophicGeostrophic WindWindAs you get closer to the ground the friction with the earth As you get closer to the ground the friction with the earth slows the wind down and causes the wind to deflect. This slows the wind down and causes the wind to deflect. This also reduces the also reduces the corioliscoriolis effect, hence increasing the effect effect, hence increasing the effect of the pressure gradient. This causes the wind to cross the of the pressure gradient. This causes the wind to cross the gradient bars instead of following them.gradient bars instead of following them.


Cyclones & AnticyclonesCyclones & AnticyclonesIn the northern hemisphere, this causes the wind to spiral In the northern hemisphere, this causes the wind to spiral clockwise out of high pressure (A. anticlockwise out of high pressure (A. anti--cyclone). And wind cyclone). And wind to spiral counterclockwise into a low.to spiral counterclockwise into a low.


Hurricanes are example of extreme low pressure systems. Hurricanes are example of extreme low pressure systems. This explains why a hurricane flow is counterclockwise in This explains why a hurricane flow is counterclockwise in the northern hemisphere and clockwise in the southern the northern hemisphere and clockwise in the southern hemisphere.hemisphere.

Cyclones & AnticyclonesCyclones & Anticyclones

••Cyclones, rotating winds around low pressures, can Cyclones, rotating winds around low pressures, can generate very high winds. In the northern hemisphere the generate very high winds. In the northern hemisphere the rotation is counterclockwise.rotation is counterclockwise.

••Anticyclones, rotating winds around high pressure, are Anticyclones, rotating winds around high pressure, are associated with generally lighter winds and the rotation is associated with generally lighter winds and the rotation is associated with generally lighter winds and the rotation is associated with generally lighter winds and the rotation is clockwise in the northern hemisphere.clockwise in the northern hemisphere.

••Rotation directions are switched in the southern Rotation directions are switched in the southern hemispherehemisphere

Hurricane Hurricane -- Scale Scale

Source: http://scienceprep.org/images/hurricanescale.jpg

Tornado WindsTornado Winds

http://esminfo.prenhall.com/science/geoanimations/animations/Tornadoes.html

••Winds speeds can vary from 72mph to 300mphWinds speeds can vary from 72mph to 300mph

••Only the most critical structures are designed to resist Only the most critical structures are designed to resist these forcesthese forcesthese forcesthese forces

••Only 2 percent of tornados produce wind speeds over Only 2 percent of tornados produce wind speeds over 200mph200mph

••Conditions are most favorable over flat plains during the Conditions are most favorable over flat plains during the summer months summer months

Tornado Winds Tornado Winds –– Fujita ScaleFujita Scale

F-# Intensity Phrase Wind Speed Type of Damage Done

F0 Gale tornado 40-72 mphSome damage to chimneys; breaks branches off trees; pushes over shallow-rooted trees; damages sign boards.

F1 Moderate tornado 73-112 mphThe lower limit is the beginning of hurricane wind speed; peels surface off roofs; mobile homes pushed off foundations or overturned; moving autos pushed off the roads; attached garages may be destroyed.

F2 Significant tornado 113-157 mphConsiderable damage. Roofs torn off frame houses; mobile homes demolished; boxcars pushed over; large trees snapped or uprooted; light object missiles generated.

F3 Severe tornado 158-206 mphRoof and some walls torn off well constructed houses; trains overturned; most trees in forces uprooted

Source: //www.tornadoproject.com/fscale/fscale.htm

F3 Severe tornado 158-206 mphin forces uprooted

F4Devastating

tornado207-260 mph

Well-constructed houses leveled; structures with weak foundations blown off some distance; cars thrown and large missiles generated.

F5 Incredible tornado 261-318 mphStrong frame houses lifted off foundations and carried considerable distances to disintegrate; automobile sized missiles fly through the air in excess of 100 meters; trees debarked; steel reinforced concrete structures badly damaged.

F6Inconceivable

tornado319-379 mph

These winds are very unlikely. The small area of damage they might produce would probably not be recognizable along with the mess produced by F4 and F5 wind that would surround the F6 winds. Missiles, such as cars and refrigerators would do serious secondary damage that could not be directly identified as F6 damage. If this level is ever achieved, evidence for it might only be found in some manner of ground swirl pattern, for it may never be identifiable through engineering studies

Wind Effects on BuildingsWind Effects on Buildings

Lecture 2

TurbulenceTurbulence

••Wind is rarely free of turbulenceWind is rarely free of turbulence

••Caused by friction with earths surface as well as Caused by friction with earths surface as well as thermal effectsthermal effects

••At very high speeds the friction effect dominatesAt very high speeds the friction effect dominates

••Need to examine how the presence of turbulence Need to examine how the presence of turbulence ••Need to examine how the presence of turbulence Need to examine how the presence of turbulence enters into the equations of motionenters into the equations of motion

••We also need to understand the how to handle We also need to understand the how to handle the highly unsteady nature of wind loading that is the highly unsteady nature of wind loading that is the result of turbulent windthe result of turbulent wind

Equations for the Motion of AirEquations for the Motion of Air

••ConservationConservation of Massof Mass••MomentumMomentum EquationsEquations••CoriolisCoriolis TermsTerms••Shear Stress TermsShear Stress Terms

Based on lecture by Peter Erwin, 2008

••Shear Stress TermsShear Stress Terms••ViscosityViscosity

Conservation of MassConservation of MassMass Flow into Elemental Volume

Rate of increase of mass in the elemental volume =

Mass flow into face abcd =

Mass flow out of face efgh =

Net mass flow into volume through faces abcd and efgh =

Conservation of MassConservation of MassMass Flow into Elemental Volume

Net mass flow into volume through faces bfgc and aehd=

Net mass flow into volume through faces aefb and hgcd =

Total mass flow into volume through all faces =

Conservation of MassConservation of MassContinuity Equation for incompressible flow

The continuity of mass implies that

Canceling and using the fact that in wind engineering we may take that the density, ρ, as constant we obtain the continuity equation.

Momentum BalanceMomentum BalanceX-Direction

Force = Rate of Change of Momentum

Momentum in the x-direction of air in the elemental volume =

Therefore the rate of change of momentum =


There is also momentum flowing into the volume through its faces.

The new flow of x-momentum into the volume through both faces abcd and efgh =


Switch stations. Now,

The new flow of x-momentum into the volume through both faces bfgc and aehd =


In a similar fashion we also evaluate the net flow of x-momentum into the volume through faces dcgh and hgfe =

Collecting all the flows of x-momentum into the volume we get:


We have so far ignored the pressure acting on the volume. At station 1 we have pressure, p1. Then the force on face abcd is =

Similarly the force action on face efgh is =

Therfore the net force in the x-direction is =


Since the force in the x-direction will increase the x-momentum we must add the increase in momentum due to the pressure gradient to that of the inflows. Yielding:

Canceling and using a constant density the equation can be written=

Momentum BalanceMomentum Balance

If we look at the 2nd, 3rd and 4th terms of the left side in the previous equation, they can be written as:

X-Direction

From the continuity equation:

Hence x-momentum =

Momentum BalanceMomentum Balance

Similar equations follow for the momentum in the other 2 directions:

Y & Z-Directions

Y-direction =

Z-direction =

Inclusion of Inclusion of CoriolisCoriolis TermsTerms

X-direction =

Y-direction =

Z-direction =

Shear stress terms importanceShear stress terms importance

••AirAir is viscous and its viscosity results in shear stresses.is viscous and its viscosity results in shear stresses.••These are generally small but can influence flows over These are generally small but can influence flows over curved bodies, through small cracks and openingscurved bodies, through small cracks and openings••Viscous effects put limits on how small wind tunnel models Viscous effects put limits on how small wind tunnel models can becan be••In turbulent flow the turbulence creates substantial effective In turbulent flow the turbulence creates substantial effective shear stresses that resemble the stresses resulting from shear stresses that resemble the stresses resulting from shear stresses that resemble the stresses resulting from shear stresses that resemble the stresses resulting from much higher viscositymuch higher viscosity••Turbulence and wind shear are very significant in the Turbulence and wind shear are very significant in the planetary boundary layerplanetary boundary layer

Shear force due to shear stressesShear force due to shear stresses

Viscosity and kinematic viscosityViscosity and kinematic viscosity

Where µ = viscosity

Where V = kinematic viscosity

NavierNavier Stokes EquationsStokes Equations

X-momentum equation:

General equations for the motion of air

Y-momentum equation:

Z-momentum equation:

Computational Fluid DynamicsComputational Fluid Dynamics

••Uses equations of motion to solve specificUses equations of motion to solve specific problemsproblems••The flow is broken down into a finite number of gridded The flow is broken down into a finite number of gridded elements and the equations of motion are elements and the equations of motion are discretizeddiscretized••For most practical problems the flow becomes turbulentFor most practical problems the flow becomes turbulent••Turbulence causes great difficulty since it requires Turbulence causes great difficulty since it requires extremely small grid system and it must be solved on a very extremely small grid system and it must be solved on a very small time stepssmall time stepssmall time stepssmall time steps••Can be Can be used as an approximate guide during preliminary used as an approximate guide during preliminary designdesign••It is currently mainly used for internal applicationIt is currently mainly used for internal application

Computational Fluid DynamicsComputational Fluid Dynamics

wind effects on buildings

Documents

wind engineering wind

wind engineeringbooks

ideal gas lawgas constant

density temperature

pressure p

standard users

volume expansionenergy

energy increment inputq