Reinforced concrete beam safety check: A beam of width 25 cm with an effective lever arm (jd) of 40 cm resists a shear force of 6 t; the permissible (safe) shear stress is 5 kg/cm² and the applied bending moment is 24 t·m. Assess the beam's adequacy in shear under these conditions.

Introduction / Context:

This problem tests the fundamental shear capacity check for a reinforced concrete (R.C.C.) beam using working-stress style calculations. Even if a beam satisfies bending, it must also be verified that the nominal shear stress does not exceed the permissible (safe) shear stress for the concrete section.

Given Data / Assumptions:

• Beam breadth (b) = 25 cm.
• Effective lever arm (jd) ≈ 40 cm (used as the effective depth for shear check in this classic formulation).
• Shear force V = 6 t = 6000 kg.
• Permissible shear stress τ_perm = 5 kg/cm².
• Applied bending moment M = 24 t·m (given for completeness, but the governing check here is shear).

Concept / Approach:

For preliminary shear safety under working stress methods, the nominal shear stress is estimated as τ_v = V / (b * jd). If τ_v > τ_perm, the section is unsafe in shear, regardless of its adequacy in bending. Appropriate remedies include providing shear reinforcement (stirrups), increasing section size, or reducing shear by layout changes.

Step-by-Step Solution:

Verification / Alternative check:

Even if bending is satisfactory (M given as 24 t·m), shear governs because τ_v surpasses τ_perm. Introducing adequate shear reinforcement might help, but as stated, the current check indicates a shear shortfall.

Why Other Options Are Wrong:

• is safe / is over safe: Contradicted by τ_v > τ_perm.
• needs redesigning: Vague; the precise verdict is that it is unsafe in shear (redesign or extra shear steel is needed).
• safe in bending but unsafe in shear: Although true descriptively, the asked judgment focuses on shear adequacy; standard answer is ‘‘is unsafe in shear’’.

Common Pitfalls:

• Mixing units (tonne vs kg) or using total depth instead of effective lever arm for shear check in this classic exam style.
• Assuming bending adequacy implies shear adequacy; both checks are independent.

Final Answer:

is unsafe in shear