Formula - Strain energy - simply supported beam due to bending moment

Q.  What is the strain energy stored in a simply supported beam due to bending moment?
- Published on 21 Sep 15

a. ∫ (M2/EI)
b. ∫ (M2/2EI)
c. ∫ (M/2EI)
d. ∫ (2M/EI)

ANSWER: ∫ (M2/2EI)

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    Discussion

  • Sravanthi   -Posted on 24 Nov 15


    - When a beam is subjected to bending moment, it deflects by an angle θ as shown above.

    - Therefore, workdone = (1 / 2) M dθ

    But strain energy = workdone

    Since, d2y / dx2 = M / EI = dθ / dx

    dθ = (M / EI) dx ---------- (2)

    Substituting the value of dθ in eq (1),

    strain energy = (1 / 2) M dθ

    = (1 / 2) M x (M / EI) dx

    Strain energy = ∫ [M2 / 2EI] dx

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