Civil Engineering MCQJE Level Civil Engineering
The strain energy stored in a beam subjected to pure bending moment M over length L is:
Strength of MaterialsStrength of MaterialsMEDIUM
Choose the correct answer
A
U = ML/(EI)
B
U = M²L/(2EI)
C
U = M²/(2EIL)
D
U = 2M²L/EI
Correct Answer
B. U = M²L/(2EI)
Why is this the answer?
Strain energy U = M²L/(2EI) for constant M. For varying M(x): U = ∫M²dx/(2EI). This is the basis of Castigliano''s theorem: deflection at load point δ = dU/dP. Strain energy is always positive, a scalar. Used in virtual work and unit load method for deflection of statically indeterminate structures.
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