Limit State Method MCQ with answer and solution

Concept

IS 456-2000 limits the nominal shear stress τ_v in a beam to τ_c,max, which depends on concrete grade.

Formula

τ_v = V_u / (b × d) ≤ τ_c,max

Step-by-step solution

1. Open IS 456-2000, Table 20: maximum shear stress τ_c,max for limit state design. 2. Values are M20 = 2.8, M25 = 3.1, M30 = 3.5, M35 = 3.7, M40 and above = 4.0 N/mm². 3. For M25, τ_c,max = 3.1 N/mm². 4. So the answer is (B).

Explanation

IS 456 gives an upper limit on shear stress in beams for each concrete grade. For M25 this limit is 3.1 N/mm². If τ_v is more than this value, the section must be redesigned, because stirrups alone cannot help.

Why the other options are wrong

A (3.4): not a value in the table. C (3.5): this is for M30. D (2.8): this is for M20.

Shortcut

Remember the series 2.8, 3.1, 3.5, 3.7, 4.0 for M20 to M40.

Common mistake

Mixing up grades (2.8 is for M20, 3.5 is for M30), or using the working stress table values instead of the limit state values.