A truss member of length $L$, cross-sectional area $A$, and Young's modulus $E$ carries an axial force $F$ due to external flight loads. To determine the deflection at a joint along a specified direction, a virtual dummy unit load is applied at that joint, inducing an internal virtual force $f$ in the member. By the unit load method, the deflection contribution of this single member is:

(A) $\Delta = \frac{F f L}{A E}$

(B) $\Delta = \frac{F^2 L}{2 A E}$

(C) $\Delta = \frac{f^2 L}{2 A E}$

(D) $\Delta = \frac{F L}{A E}$

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles By the Principle of Virtual Work (Unit Load Method for trusses): $$1 \cdot \Delta = \sum_{i=1}^N \frac{F_i f_i L_i}{A_i E_i}$$ where: - $F_i$ is the actual axial force in member $i$ caused by real applied loads - $f_i$ is the virtual axial force in member $i$ caused by a fictitious unit load ($1\text{ N}$) applied at the target degree of freedom - $\frac{F_i L_i}{A_i E_i} = \Delta L_i$ is the real axial elongation/contraction of the member. ### 2. Analytical Verification For a single member, the virtual work done is: $$\Delta = f \cdot \Delta L = \frac{F f L}{A E}$$ ### 3. Distractor Forensics - **Option B:** Strain energy stored in the member $U = \frac{F^2 L}{2 A E}$. - **Option D:** Real elongation $\Delta L = \frac{F L}{A E}$ of the member itself, not projected onto the degree of freedom. ### 4. Exam Trap & Standard Reference - **Trap Alert:** Always remember that internal virtual work is linear in the product $F f L / (AE)$. - **Standard Reference:** Megson, T.H.G., *Aircraft Structures for Engineering Students*, Chapter 5.

← Prev Question Next Question →