A uniform symmetric cross-section cantilever beam of length L is subjected to a
transverse force P at the free end, as shown in the figure. The Young's modulus of
the material is E and the moment of inertia is I. Ignoring the contributions due to
transverse shear, the strain energy stored in the beam is _____.
Options:
(A) P2L3
6EI
(B) PL3
3EI
(C) PL3
6EI
(D) P2L3
3EI
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.29)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Structural Mechanics** under *Aerospace Structures* (1 Mark, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Structural Mechanics.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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