Strength of Shapes

1
Strength of Shapes!

• The shape of a structure affects how strong it
  is. Rectangles, arches, and triangles are the
  most common shapes used to build big structures.
• To understand which shapes should be used it is
  important to know what forces act on them.

2
Forces in Tension and Compression
How do we define a force?
A force is a push or pull exerted by one object
on another.
A tensile force expands or lengthens the object
it is acting on.
A compressive force compresses or shortens the
object it is acting on.
Try it out here!
3
Forces in Tension and Compression
The rope is in tension
The stand is in compression.
4
Forces on Shapes
Engineers consider shapes under heavy loads when
building large structures.
Triangles are the only shapes that cannot be
deformed without changing the length of one of
its sides Arches are strong because the force
resulting from a heavy load placed at the top
spreads down the sides to the foundation. A group
of arches placed around a central point creates a
dome, which distributes loads down through
curving sides to the foundation.
Shapes Lab (click here)
Use the slider to apply weight to each shape and
see how they react
5
Triangles
Bank of China Tower
Eiffel Tower
Stansted Airport
Centre Pompidou
6
Arches
Musee d'Orsay
San Lorenzo, Florence
Roman Colosseum
Iron Bridge at Coalbrookdale
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Domes
Florence Cathedral
Suleyman Mosque
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Applications
Psyclone Rollercoaster- triangles in structure
US Pavilion at Expo '67 - spherical structure
made of triangles
Dome tent -poles bent into arches with nylon
fabric in tension.
Campo Volantin Footbridge - arch with cables in
tension
9
Newton's Laws
When an object is at rest or moving with a
constant velocity, it will stay at rest or moving
with a constant velocity until is is subjected to
an unbalanced force.
To understand these forces we must first define
force.
How do we define force?
10
Newton's Laws

• If an unbalanced force, F, is applied to a mass,
  m, then the mass will experience an acceleration,
  a.
• F ma

11
Newton's Laws

• Every force of action between objects has an
  equal, opposite, and collinear reaction.
• Basically, what is pushing down must be pushing
  up if the object is not accelerating!
• If the object is not accelerating the sum of all
  the forces must equal zero.

12
Static Equilibrium
Static Equilibrium is the state of an object when
it is at rest or moving with a constant velocity.
There may be several forces acting on the object.
If they are canceling each other out the object
is not accelerating, then it is in a state of
static equilibrium.