Design of Beams MCQ with answer and solution

Concept

When the nominal shear stress τ_v is more than the shear strength of concrete τ_c, shear reinforcement (stirrups or bent-up bars) is provided.

Formula

τ_v = V_u / (b × d); V_us = V_u − τ_c × b × d; S_v = 0.87 × f_y × A_sv × d / V_us

Step-by-step solution

1. Find the nominal shear stress: τ_v = V_u / (b × d). 2. Compare τ_v with the design shear strength of concrete, τ_c. 3. If τ_v > τ_c, concrete alone cannot resist the shear. 4. Provide shear reinforcement (vertical stirrups, bent-up bars or inclined stirrups) for the extra shear V_us. 5. Check that τ_v ≤ τ_c,max. If not, increase the section size. 6. So the answer is shear reinforcement, (A).

Explanation

Shear in a beam causes diagonal tension cracks near the supports. Stirrups and bent-up bars cross these cracks and resist the shear that the concrete cannot carry. So shear reinforcement strengthens the beam against shear stress.

Why the other options are wrong

(B) Tension reinforcement resists the bending moment, not shear. (C) Side face reinforcement controls cracks on the sides of deep beams (depth > 750 mm). (D) Compression reinforcement adds bending capacity in doubly reinforced beams.

Shortcut

Shear stress means shear reinforcement (stirrups).

Common mistake

Thinking more tension steel alone handles shear. It only slightly increases τ_c, it does not replace stirrups.