Solid Mechanics: Strain Energy

When an elastic body is deformed, work is done. The energy used up is stored in the body as
strain energy and it may be regained by allowing the body to relax. The best example of this
is a clockwork device which stores strain energy and then gives it up.

We will examine strain energy associated with the most common forms of stress encountered
in structures and use it to calculate the deflection of structures. Strain energy is usually given
the symbol U.
Consider a bar of length L and cross sectional area A. If a tensile force is applied it stretches
and the graph of force v extension is usually a straight line as shown. When the force reaches
a value of F and corresponding extension x, the work done (W) is the area under the graph.
Hence W = Fx/2. (The same as the average force x extension).
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On completion of this tutorial you should be able to do the following.

Define strain energy due to a direct stress.

Define strain energy due to pure shear stress.

Define strain energy due to pure torsion.

Define strain energy due to pure bending.

Use strain energy to determine the deflection of simple
rectangular and circular structures.

Explain the affect of impact loading on the deflection of
structures.

Explain the affect of a suddenly applied load.

Explain the theorem of Castigliano.

Calculate the deflection of simple structures by applying
Castigliano’s theorem.