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Physics notes -
Materials and their use in structures
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Compression and tension
A structure is in compression (tension) when it is pushed (pulled) at the two ends.
According to Newton's Third Law, the structure exerts a reaction force on the objects pushing or pulling it.
Compression and tension can co-exist within a structure:
Example 1 A cantilevered beam bends under its own weight.
Example 2 A beam supported at its two ends, i.e. a simply supported beam, bends under its own weight.
Example 3 A truss, a network of beams joined together in rigid triangles, supports a load.
Shear
Shear refers to the sliding of a layer over another layer in a structure. It may occur when a structure experiences a sideways or twisting force.
Example 1 Cantilevered beam under its own weight.
Example 2 Flag pole in the wind.
Example 3 A rotating propeller.
Stress
Consider a beam of non-uniform cross-section in tension (or compression).
Tension in the beam is the same along the entire length, which is equal to $F$, but the stress $\sigma$ which is defined as $\sigma=\frac{F}{A}$, where $A$ is the cross-sectional area, is different at different positions.
Since $\sigma \propto \frac{1}{A}$, therefore stress is highest at the narrowest section where fracture is most likely to occur.
The unit for stress $\sigma$ is $\mathrm{Nm}^{-2}$, or Pa (pascals).
Larger units are $\mathrm{MPa}\left(10^{6} \mathrm{~Pa}\right), \mathrm{GPa}\left(10^{9} \mathrm{~Pa}\right)$.
Physics notes - Materials and their use in structures
©Copyright 2009 itute.com
Free download and print from www.itute.com
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