Free walls, roofs and billboards

Free walls, roofs and billboards

Wind loading and structural response

Lecture 22 Dr. J.D. Holmes


• free-standing walls

• elevated walls and billboards

• free roofs and canopies

2ha2

1

Lwpn

Uρ

ppC

2ha2

1

LUpn

Uρ

ppC


• attached canopies

• solar panels


free-standing walls

• wind at 90o to plane of wall (lecture 8, Chapter 4)

CD = 1.2

TWO-DIMENSIONAL WALL

Ground

SQUARE WALL

CD = 1.1

Ground

reference U taken as Uh (top of wall)


free-standing walls

• wind at 90o to plane of wall (lecture 8, Chapter 4)

reference U taken as Uh (top of wall)


free-standing walls

• wind at 90o to plane of wall

Jensen Number (h/zo) = 50 to 160

Mean

Maximum

bh

0.1 1 10 100

b/h

4

3

2

1

0

Cpn


free-standing walls


Jensen Number (h/zo) = 50 to 160

0.1 1 10 100b/h

4

3

2

1

0

Cpn

Mean

Maximum

bh


free-standing walls


Net pressure difference high for first 1-2 wall heights from windward end

mean Cpn

1.6 1.0

1.9 1.4 0.7

1.1 0.8 0.6 0.4 1.6 2.2

1.8 2.7 1.4 1.1 1.0 0.8 0.7 0.6

b/h=2

b/h=3

b/h=5

b/h=10


free-standing walls


Effect of corner is to reduce largest net pressure

mean Cpn

0.1 1 10 100

y/h

4

3

2

1

0

Cpn

no corner 45

corner 45

infinite 45corner 225

no corner 225

45

225

y


Parallel free-standing walls (noise barriers on urban freeways)

-3

-2

-1

0

1

2

3

4

5

-50 -40 -30 -20 -10 0 10 20 30 40 50

wall spacing/wall height

Ne

t p

ress

ure

co

eff

icie

nts

Mean

r.m.s.

Maximum

Minimum

Shielding

significant shielding effects up to 10 wall heights separation

sh• wind at 0o to plane of walls


Billboards

• wind at 0o to plane of board

effect of elevation : increase magnitude of mean net pressure coefficient

=

=Cpn 1.5

mean Cpn


Billboards

• wind at 45o to plane of board

45o1.5 1.1

2c

c

c

Ground

mean Cpn


s

B

h

SOLID SIGN OR FREESTANDING WALL

GROUND SURFACE

CASE AWIND NORMAL TO WALL

New table proposed for ASCE-7-05

• Solid freestanding walls and solid signs

• Force coefficients Cf given as function of clearance ratio, s/h, and aspect ratio, B/s

CASE BWIND AT 45° TO WALL


Walls on bridges


0

1

2

3

4

5

0 1 2 3 4

s/h

Cp

upwindwall

Mean

r.m.s.

Maximum s

Coefficients based onU at top of wall : little effect of s/h ratio


Free-standing roofs

Usual convention : positive net pressure is downwards

pnet flat

pnet pitched

pnet troughed


Free-standing roofs

pnet


Free-standing roofs

Effect of stored goods : flow stagnates underneath - pnet goes more negative

pnet


Free-standing roofs

upper surface pressures dominate - especially near the ridge

pitched - full scale

-1.5

-1

-0.5

0

0.5

0 4.65 9.3

Distance from leading edge (m)

Me

an p

ress

ure

co

effi

cie

nt

Upper surface

Lower surface

d=9.3 m


Free-standing roofs

Cpn averaged over half a roof

pitched - model tests

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

0 30 60 90 120 150 180

angle of attack (degrees)

Cp

(m

ea

n)

5 degrees pitch 10 degrees pitch15 degrees pitch 22.5 degrees pitch30 degrees pitch

high positive and negative values for roof pitches of 22.5o and 30o


Attached canopies (over loading bays etc.)

when mounted near the top of the wall, uplift force is high

zero pitch - model scale

hhc

wc

0.0 0.5 1.0 1.5 2.0 2.5 3.0Canopy height-to-width ratio, hc/wc

hc/h =1

hc/h=0.75

hc/h=0.5

-4.0

-3.0

-2.0

-1.0

0.0

Cpn or 4.0, whichever is the lesser

c

cpn w

h1.31.0C-

or 4.0, whichever is the lesser

c

cpn w

h0.41.0C-


Solar panels

wind loads are affected by many parameters :

on roofs of buildings

d

c e

w

h1

h2


Solar panels

• ‘stand-off’ distance reduces net load normal to roof

• higher roof pitch produces less uplift force

• panel near eaves or gable ends experience higher loads

• generally better to mount parallel to roof slope ( = 0)

End of Lecture 22

John Holmes225-405-3789 [email protected]

Free walls, roofs and billboards

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