Lecture 1 - BTES

Wind Effects on Buildings Lecture 1

Matthew Trussoni, PhD, AIA, PE [email protected] Milwaukee School of Engineering

Risks Produced by Wind Structural Failure •Wind Load •Redistribution of Snow •Cladding Failure •Wind Load •Projectile Impact •Aerodynamic Instability •Serviceability Problems •Air Quality •

Hurricane Andrew

Hurricane Katrina

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

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

Relationship Between Wind and Height

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

Multi Multi--disciplinary Engineering Meteorology •Aerodynamics •Structural Engineering •Structural Dynamics •Statistics •Architecture •Wind Tunnel Testing •Computational Fluid Dynamics •

Books 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 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 Wind •Composition

of Standard Atmosphere •Properties of Standard Atmosphere •Ideal Gas Law •Energy Balance of Unit Mass of Air •Adiabatic Relationships •Coriolis Effect •Geostrophic Wind

Composition of Standard Atmosphere

Gas

Volume (%)

Nitrogen

78.09

Oxygen

20.95

Argon

0.93

Carbon Dioxide

0.03

Other

0.01

Properties 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)

Kinematic Viscosity

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. Heat Constant Volume

718 J/(Kg ˚K)

4297Ft lb/(Slug ˚R)

Ratio of Spec. Heats 1.4

1.4

Speed of Sound

1116 Ft/s

340 M/s

Ideal Gas Law

The absolute temperature (T), pressure (p) and density (ρ) are related to a close approximation by the ideal gas law

Gas Constant = Rg = Cp – Cv

Energy Balance of Unit Mass of Air

dq = Energy increment input Cv = Specific Heat Constant Volume dT = Increase in Internal Energy pdv = Work Done by Volume Expansion

Energy Balance with Ideal Gas Substitution Specific Volume = v = 1/ρ 1/ρ

Ideal Gas

Adiabatic Relationships If there is no input or output of heat then dq = 0 and:

Therefore:

Since Rg = Cp – Cv and γ = Cp / Cv

Adiabatic Relationships Taking the ln of both sides & where C = constant

Therefore:

& Using the Perfect Gas Law implies also that

&

Adiabatic Lapse Rate If we consider the static condition of air, then focus on a horizontal slice of that air (δ (δz). The pressure at the bottom of the slice will be greater than at the top by and amount (δ (δp) equal to weight per unit area of the air slice. The height is measured as positive direction up.

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

Adiabatic Lapse Rate Substituting equations in for p and ρ.

It follows that

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

Which translates into about 10 ˚C per 1000 meters in height (5.5˚F per 1000 Ft). The air density ratio to that at see level is given by.

Adiabatic Lapse Rate Take the example of Denver Colorado altitude of 1637 M.

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

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

Coriolis Effect The coriolis effect is the deflection of an object that is affected by a rotating frame of reference

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

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

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

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


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


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

Hurricanes are example of extreme low pressure systems. This explains why a hurricane flow is counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. Images: www.newmediastudio.org/.../Spiral_Winds.html

Cyclones & Anticyclones •Cyclones, rotating winds around low pressures, can generate very high winds. In the northern hemisphere the rotation is counterclockwise. •Anticyclones, rotating winds around high pressure, are associated with generally lighter winds and the rotation is clockwise in the northern hemisphere. •Rotation directions are switched in the southern hemisphere

Hurricane - Scale

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

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

•Winds speeds can vary from 72mph to 300mph •Only the most critical structures are designed to resist these forces •Only 2 percent of tornados produce wind speeds over 200mph •Conditions are most favorable over flat plains during the summer months

Tornado Winds – Fujita Scale F-# F0

Intensity Phrase Wind Speed Gale tornado

40-72 mph

Type of Damage Done Some damage to chimneys; breaks branches off trees; pushes over shallow-rooted trees; damages sign boards.

Moderate tornado 73-112 mph

The 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 mph

Considerable 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 mph

F1

F4 F5

F6

Devastating tornado

207-260 mph

Incredible tornado 261-318 mph

Inconceivable tornado

319-379 mph

Roof and some walls torn off well constructed houses; trains overturned; most trees in forces uprooted

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

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

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

Wind Effects on Buildings Lecture 2

Turbulence •Wind is rarely free of turbulence •Caused by friction with earths surface as well as thermal effects •At very high speeds the friction effect dominates •Need to examine how the presence of turbulence enters into the equations of motion

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

Equations for the Motion of Air •Conservation of Mass •Momentum Equations •Coriolis Terms •Shear Stress Terms •Viscosity

Based on lecture by Peter Erwin, 2008

Conservation of Mass Mass 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 Mass Mass 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 Mass Continuity 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 Balance X-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=


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

From the continuity equation:

Hence x-momentum =

Momentum Balance Y & Z-Directions Similar equations follow for the momentum in the other 2 directions:

Y-direction =

Z-direction =

Inclusion of Coriolis Terms X-direction =

Y-direction =

Z-direction =

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

Shear force due to shear stresses

Viscosity and kinematic viscosity

Where µ = viscosity

Where V = kinematic viscosity

Navier Stokes Equations General equations for the motion of air X-momentum equation:

Y-momentum equation:

Z-momentum equation:

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

Computational Fluid Dynamics

Lecture 1 - BTES

Recommend Documents