Internal Pressures: Analysis of Wind-Induced Pressure Changes in Buildings, Slides of Environmental Law and Policy

Download Internal Pressures: Analysis of Wind-Induced Pressure Changes in Buildings and more Slides Environmental Law and Policy in PDF only on Docsity!

• Wind pressure on a wall cladding or roof is always :

external wind pressure - internal pressure

• wind will affect internal pressure magnitude, except for fully sealed buildings
• Fully-sealed buildings : assume internal pressure is atmospheric pressure

(po)

• Wind-induced internal pressures significant for dominant openings - e.g. produced by flying debris

• Single opening on windward wall
• Dimensional analysis :

 1 = A3/2/Vo - where A is the area of the opening, and Vo is the internal volume

F(π,π ,π ,π ,π ) ρ U 2

1

p p C (t) 1 2 3 4 5 2 a

0 pi 

  i

2 a

0 2 ρ U 2

1

p π  - where p o is atmospheric (static) pressure

(related to Mach Number)

 3 = aUA1/2/ - where  is the dynamic viscosity of air (Reynolds Number)

U

π 4 u

  (turbulence intensity)

 5 = lu/A - where lu is the length scale of turbulence

• Single opening on windward wall
  • Helmholtz resonator model :

Air ‘slug’ moves in and out of building in response to external pressures

Air ‘slug’

Mixing of moving air is ignored

le

• Single opening on windward wall
  • ‘Stiffness’ term :

Assume adiabatic law for internal pressure and density

Since i  a , pi  po

γ pi aconstant.ρ i

i i

i i

γ- 1 γ^ i i

i i Δρ ρ

γp γρ ρ ρ

p p   

γ- 1 i i

i (^) aconstant.γρ dρ

dp 

o

a

i

i V

ρ Ax

ρ

γp  o

o V

γp Ax 

Resisting force = pi.A o

2 o

V

γp A x

 = ratio of specific heats(1.4 for air)

• Single opening on windward wall
  • ‘Damping’ term :

From steady flow through a sharp-edged orifice :

k = discharge coefficient

xx 2k

ρ ρ U U 2

k

p (^2) a  i  2 a o o   

Theoretically k =

π



• Inertial term : Δp(t). Aρa Alex

Theoretically le = πA/4 (circular opening)

• Single opening on windward wall
  • Helmholtz resonant frequency :

Effect of building flexibility :

KA = bulk modulus of air = pressure change for unit change in volume

= (a p)/, equal to  po

KB = bulk modulus for the building

ρ V [1 (K /K )]

γAp

2 π

n a e o A B

o H 

l

For low-rise buildings, KA/ KB = 0.2 to 5

(for Texas Tech field building, KA/ KB= 1.5)

• Single opening on windward wall
  • Helmholtz resonant frequency :

Type Internal Volume (m 3 )

Opening Area (m 2 )

Stiffness ratio KA/KB

Helmholtz Frequency (Hertz) Texas Tech field building

470 0.73 1.5 1.

House 600 4 0.2 2. Warehouse 5000 10 0.2 1. concert hall 15000 15 0.2 0. arena (flexible roof) 50000 20 4 0.

(measured values for Texas Tech building)

Resonant response is not high because of high damping

• Multiple openings on windward and leeward walls :

Neglecting compressibility in this case (a = 0) :

Can be used for mean internal pressures or peak pressures using quasi-steady

assumption. Need iterative solution when N is large.

ρ Qj 0 a

N 1  

where

a

e i ρ

2 p p Q kA

  (^) (modulus allows for flow from interior to exterior)

,^0 1  e j  i  j

N A p p

N is number of openings

• Multiple openings on windward and leeward walls :

Consider building with 5 openings :

Q 1 Q 2

Q 3

Q 4

Q 5

pe,1 pe,

pe,

pe, pe,

pi

inflows

outflows

A 1 pe , 1  pi  A 2 pe , 2  pi  A 3 pe , 3  pi  A 4 pe , 4  pi  A 5 pe , 5  pi

• Single windward opening and single leeward opening :

i.e. comparison with experimental data :

Used in codes and standards to predict peak pressures (quasi-steady principle)

-0.

0

0 2 4 AW^ /AL 6 8 10

C

pi

Measurements Equation (6.16)

• Multiple windward and leeward openings :

Neglect inertial terms, characteristic response time :

Characteristic frequency, nc = 1/(2c)

(^2) 3/2 pW pL L

2 o W

a o W L A B

c C C

γkp (A A )

ρ V UA A [1 (K /K )]

Aw = combined opening area on windward wall

AL = combined opening area on leeward wall

fluctuating internal pressures :

numerical solutions required if inertial terms are included

• Porous buildings :

Treated in same way as multiple windward and leeward openings :

AL = average wall porosity  total areas of leeward and side walls

Aw = average wall porosity  total windward wall area