S3 : Stadium Roof Design

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S3 Stadium Roof Design Cantilever Roof Design
Experiment
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Cantilever Roof Design
Liberty Stadium Location Swansea Home to
Swansea City football and Ospreys Rugby
Team Capacity 20,000 Built in 2005
Twickenham during the construction of the South
Stand.
forum.skyscraperpage.com
P29
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Cantilever Roof Design
Shanghai Sports Centre Stadium Location
China Home to All sports, but football
mainly Capacity 80,000 Built in 1997
Its unique curving roof is the worlds longest
cantilevered roof truss structure with fabric
canopy, spanning 300metres.
eap.ucop.edu
P30
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Cut out and calculate y
Roof
Depth of Counter Weight, y
Counter Weight
Mast
Cut Away
Fold to make a stand
Cut
Cut Away
Clockwise Roof Moment Area x mass per cm² x
gravity x lever arm Anticlockwise Counter Weight
Moment Width x y x mass per cm² x gravity x
lever arm Equating the two expressions finds a
value for y for the roof to balance
P31
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Design roof and balance
The roof balances when the counter weight is
reduced to depth y as the moments about the mast
(the pivot) are equal.
Cut out a design for the cantilever roof which
will hang above spectators.
The clockwise roof moment will be reduced, the
anticlockwise counter weight moment also needs to
be reduced. Progressively reduce its depth,
checking regularly if it balances.
P32
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Centre of gravity of roof
Trace the shape onto the piece of card that was
removed earlier. How can you find its centre of
gravity?
Punch a hole and hang the roof off a drawing pin.
Ensuring that the roof can swing freely, allow it
to settle and draw a vertical line from the pin
downwards.
This line will go through the centre of
gravity. If repeated the point where the lines
cross will be the centre of gravity.
P33
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Calculate area of new roof
Again in order to balance the clockwise and
anticlockwise moments about the mast must equal.
So we can calculate a value for the area of the
roof, A.
b
From measuring, D 4.1cm b 5.7 cm Clockwise
roof moment 0.08 x 9.81 x A x (5.7 1)
5.26A Ncm Anticlockwise moment 0.08 x 9.81 x
4.1 x 7 x 4.5 101 Ncm Equating the two gives A
101/5.26 19.3cm²
D
P34
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Check area
Another way to calculate area is to trace the
shape onto square paper and count the
squares. This methods gives A 20cm² What is the
percentage difference? Difference (20 19.3) /
19.3 3.6 Does this confirm the earlier
calculation?
P35
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More concentrated counter-weight
The area of the counter weight can be reduced if
a more concentrated mass is used, such as coins.
This will improve the appearance of the roof
structure.
The clockwise moment from the roof 5.26 x A
5.26 x 19.3 101.5 Ncm Anti-clockwise moment
from card counter weight 0.08 x 9.8 x 3 x 3 x
(1.5 1) 17.6 Ncm The centre of gravity of
any coin will be in the middle. If the coins,
with mass M, are placed in the middle of a 3cm x
3cm then Anti-clockwise moment from coins M
x 9.8 x (1.5 1) 24.5M Equating the clockwise
and anticlockwise moments gives M (101.5
17.6) / 24.5 3.42 grams
P36
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Achieving balance
A 1 pence piece weighs 3.56 grams so is the
closest to the required weight of
3.42grams. Initially when it is selotaped in
placed the structure does not balance as the
weight is too big How can this be rectified?
The anticlockwise moment is too big so needs to
be decreased. Moving the penny closer to the mast
will decreased its lever arm and its moment,
allowing it to balance.
P37
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Like a Tower crane
The system of a overhanging cantilever with a
counter balancing weight is exactly the same as
how a crane works. The long arm carries the
lifting gear whilst the short arm carries the
counterweight. How will the mass of the counter
weight be decided?
The maximum load on the crane will come when the
lifting gear is at the very end of the arm. The
lever arm for the moment is the greatest
here. This counterweight is often made up of very
heavy concrete blocks as it must be able to
balance this maximum moment.
P38
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Tying the roof down
A stadium roof very rarely looks like a crane, so
where does the counter weight go? By altering the
vertical height of the weight, the balancing
effect is not compromised, so we can lower the
weight until it is out of sight, underground.

1. Punch a hole through the middle of where the coin
   was located to get the structure to balance.
2. Stick the coins to a piece of string and tie
   down the roof by tying the string through the
   hole.

The cantilever roof now hangs as if unsupported
creating a dramatic looking stadium roof.
P39