Limit State Method MCQ with answer and solution

Concept

Design bond stress τ_bd depends on concrete grade and type of bar (plain or deformed).

Formula

L_d = φ σ_s / (4 τ_bd)

Step-by-step solution

1. IS 456 gives τ_bd values for plain bars in a table, one value for each concrete grade (M20, M25, ...). 2. For deformed bars (HYSD), these values are increased by 60%. 3. For bars in compression, they are increased by 25%. 4. So τ_bd depends on concrete strength and the type of bar. 5. Answer is (A).

Explanation

Bond stress is the grip between steel and concrete. A stronger concrete gives better grip, and deformed (ribbed) bars grip better than plain bars. So τ_bd depends on the concrete grade and the type of bar.

Why the other options are wrong

B: Bar area or diameter affects development length L_d, not τ_bd. C: Steel strength and bar area do not decide τ_bd. D: Steel strength (σ_s) appears in the L_d formula, but τ_bd itself does not depend on it.

Shortcut

τ_bd = f(concrete grade, bar type). Deformed bar: +60%. Compression: +25%.

Common mistake

Students confuse τ_bd with L_d. L_d depends on bar diameter and steel stress, but τ_bd does not.