Correct Answer - Option 1 : Cantilever
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.
