The strain energy U due to bending is (where M is bending moment, EI is flexural rigidity and dx is short length of beam.)
- A∫ (M² dx / 2EI)Correct
- B∫ (M dx / 3EI)²
- C∫ (M² dx / 3EI)
- D∫ (M dx / 2EI)²
Solution
Concept
Bending strain energy
Formula
U = ∫ M² dx / 2EI
Step-by-step solution
1. Work done on an element = ½ M dθ with dθ = M dx / EI. 2. dU = M² dx / 2EI, so U = ∫ M² dx / 2EI.
Explanation
The strain energy stored in bending is half the product of moment and rotation, integrated along the length.
Why the other options are wrong
The other forms have the factor 3 or square the integral, which is not the energy expression.
Shortcut
U = ∫M²dx/2EI.
Common mistake
Squaring the whole integral.
Correct answer: A) ∫ (M² dx / 2EI)