Limit State Method MCQ with answer and solution

Concept

Perfect bond means no slip, so strain in steel equals strain in the surrounding concrete at the same level.

Formula

ε_s = ε_c (at the level of steel)

Step-by-step solution

1. Bond is the grip between steel bar and concrete. 2. With proper bond, the bar does not slip inside concrete. 3. So steel and the concrete around it deform together. 4. Equal deformation means equal strain: ε_s = ε_c. 5. This is called strain compatibility. Answer is (D).

Explanation

Proper bond stops slip between the bar and concrete. So both materials have the same strain at the same point. This strain compatibility is a basic assumption in RC design.

Why the other options are wrong

A: Forces in steel and concrete are not equal; they depend on area and stiffness. B: Stresses differ because E of steel and E of concrete are different (σ = E × ε). C: 'Bending compatibility' is not a standard term in RC design.

Shortcut

Bond = no slip = same strain.

Common mistake

Choosing stress compatibility. Strain is the same, but stress is different because modulus is different (modular ratio m).