A beam carries a uniform distributed load through its length. In which of the following configurations will the strain energy be maximum?

Concept:

Strain energy:

It is defined as the energy adsorption of material due to strain under an applied load. It is also equal to the work done on a specimen by an external force. It can be denoted by U.

\({\bf{U}} = \mathop \smallint \limits_0^{\bf{L}} \frac{{{{\bf{M}}^2}{\bf{dx}}}}{{2{\bf{EI}}}}\)

Where,

M = Maximum moment, E = Elastic modulus, I = Moment of inertia.

Explanation:

Strain energy will be maximum when the maximum moment will be high.

Maximum moment for different types of beam:

For the cantilever beam, \({\bf{M}} = \frac{{{\bf{W}}{{\bf{L}}^2}}}{2}\)

For Fixed-beam, \({\bf{M}} = \frac{{{\bf{W}}{{\bf{L}}^2}}}{{12}}\)

For simply supported beam, \({\bf{M}} = \frac{{{\bf{W}}{{\bf{L}}^2}}}{8}\)

For propped cantilever beam, \({\bf{M}} = \frac{{{\bf{W}}{{\bf{L}}^2}}}{8}\)

Hence, Strain energy for the uniformly distributed load will be maximum in the cantilever beam.