Simple Stress and Strain MCQ with answer and solution

Concept

On the engineering stress-strain curve of steel, the ultimate stress is the highest point. The rupture (breaking) stress comes after necking and is lower.

Formula

σ_u = P_max / A₀

Step-by-step solution

1. Draw the engineering stress-strain curve for mild steel. 2. The curve rises to the maximum point. This is the ultimate stress, σ_u = P_max/A₀. 3. After this point necking starts and the load falls. 4. The bar breaks at a lower load, so the rupture stress (based on A₀) is less than σ_u. 5. So statement A (rupture strength higher than ultimate strength) is NOT correct.

Explanation

For structural steel, the ultimate strength is the maximum stress on the curve. After necking, the load drops, so the rupture strength is lower than the ultimate strength. So statement A is wrong.

Why the other options are wrong

B: Correct. At yield point, extension increases without increase in load. C: Correct. Ultimate strength is the maximum stress the material can take. D: Correct. Ultimate stress = maximum load / original area.

Shortcut

Ultimate = peak of curve. Nothing (in engineering stress) is higher than the peak, so rupture < ultimate.

Common mistake

Using true stress (load / reduced neck area). True stress at rupture is higher, but standard definitions use the original area.