Large roofs and sports stadiums

Wind loading and structural response

Lecture 20 Dr. J.D. Holmes

Large roofs and sports stadiums

• Entertainment centres, exhibition centres, sports arenas etc

• Quasi-steady approach is not applicable

• Resonant effects can be significant

• Bending moments in arches and domes are sensitive to distribution of wind load

Large roofs and sports stadiums

• General flow characteristics :

• Mainly attached flow on large roofs

Separation “bubble”

Stagnation Point

Fluctuating re-attachment point

Shear layer positions:High turbulenceLow turbulence

Large roofs and sports stadiums

• General flow characteristics :

• On arched roof, separation occurs downstream of apex

Separation point

Large roofs and sports stadiums

• Mean pressure distributions :

• Fluctuations in pressure will generate downwards pressures for short times

U.W.O. Wind-tunnel tests

1.0Cp

Large roofs and sports stadiums

• Mean net pressure distributions (cantilevered stadium roof):

gap at rear reduces net pressures

-1.3-1.2

-1.1-1.0

-0.7-0.6

-0.4-0.2

-0.1

-0.8

0.00.20.1

0.1

0.0

-1.4

C/L

blocked at rear

Large roofs and sports stadiums

• Arched roof :

wind loads depend strongly on R/S (rise/span)

less strongly on L/S and he/S

L

S

R

he

Large roofs and sports stadiums

• Arched roof (Cp) :

R/S = 0.2 he/R = 0.45 L/S = 1.0 = 0o

+0.4

-0.4-0.8

+0.3

0

+0.2

-0.3

-0.6-0.3 +0.5-0.5

-0.4-0.5

-0.25

increasing L/S pressures on roof become more negative

Large roofs and sports stadiums

• Arched roof (Cp) :-0.3

0

-0.7

+0.2

-1.0

-0.4-0.5

-0.7

+0.4

+0.3

0

+0.2+0.3

+0.2

-0.4

0

-0.2-0.7

-0.6

-0.6-0.5

-0.5

-0.4+0.1

-0.45

-0.5-0.6

-0.7

-0.9 higher negative values

Large roofs and sports stadiums

• Arched roof (Cp) :

-0.2

-0.25-0.3 -0.4

-0.5

-0.7

-0.9

+0.4

+0.2

+0.5

0-0.7

-0.5-0.3

-0.2-0.15 -0.5

-0.15

R/S = 0.5 he/R = 0.45 L/S = 1.0 = 0o

lower negative values

positive

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Instantaneous pressure distributions vary greatly from time to time due to turbulence, vortex generation etc. Shapes may vary greatly from the mean pressure distribution

Need to identify those distributions which produce maximum load effects

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Wind-tunnel methods for design wind loads :

1) Direct approach : simultaneous time histories from the whole roof are recorded and stored. Later weighted with structural influence coefficients to obtain time histories of load effects. Instantaneous pressure distributions are identified and averaged.

2) Correlations between pressure fluctuations at different parts of the roof are measured and used to determine effective static load distributions (Lecture 13, Chapter 5)

Correlations for separated parts of a large roof are low: hence potential for significant reduction in peak effective loads and peak load effects (b.m.’s, axial forces etc.)

Arch roof (Kasperski,1992) :

Extrem e load d istribution for the support reaction, R

Extrem e load d istribution for the bending m om ent at C

G ust pressure envelope

C =0.5pCR

45

+

-

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Sydney Olympics, 2000

Superdome Stadium Australia

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Sydney Olympics, 2000 - 1/500 wind-tunnel model

Stadium AustraliaSuperdome

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Stadium Australia (Sydney Olympics, 2000)

2 2

2 3

2 4

1 9

2 0

2 1

1 8

1 7

1 61 41 3

1 5

1 21 0741

2 5

6

118

93

N

Panel layout for wind-tunnel testing

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Stadium Australia (Sydney Olympics, 2000)

20

40

60

80

100

120

140

160

180

20

40

-0.4

-0.8

-1.2

WSW wind pressure coefficient for minimum load in Member 23 Area 8

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Stadium Australia (Sydney Olympics, 2000)

20406080100120140160

180

20

40

0.40.2

0

ESE wind pressure coefficient for max load in Member 1454 Main arch

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Superdome (Sydney Olympics, 2000)

12

3

4

5

6

7 8 9

10

11

12

13

14

1516

17

18

19 20 21

22

23

24

25

26

27

28

Large roofs and sports stadiums

• Structural loads - effective static load distributions

Superdome (Sydney Olympics, 2000)

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28Panel Number

Pre

ssu

re /k

Pa

Extreme pressure limits Correlation approach Direct approach

WSW

SSE

Effective static load distributions for axial loads in a particular roof member

Large roofs and sports stadiums

• Structural loads - contribution from resonant modes

Usually not significant for roofs supported all round or on two sides

Very large roofs may have several modes below 1 Hertz

- contributions to load effects depend on similarity of mode shapes with influence lines

May be significant for cantilevered roofs :

0Time

Vertical upwards

End of Lecture 20

John Holmes225-405-3789 JHolmes@lsu.edu