Topic: Mechanics of Materials
A rigid horizontal bar AB is supported by two wires CE & DF of lengths L and 2L. If each wire has cross-sectional area A, the tensile stresses σ₁ (in CE) and σ₂ (in DF) are respectively.
- A. 3P/5A and 6P/5A
- B. 2P/5A and 4P/5A
- C. 3P/A and 6P/A
- D. P/A each
Answer: D. P/A each
Explanation: From the geometry of similar triangles formed by deflection, Δ₂ = 2Δ₁. Since Δ = PL/AE, we get (P₂*2L)/AE = 2 * (P₁*L)/AE, which simplifies to P₂ = P₁. From moment equilibrium about A, 3P = P₁ + 2P₂. Substituting P₁=P₂ gives 3P = 3P₁, so P₁=P₂=P. Stress = P/A for both.