A rectangular beam 20 cm wide carries a maximum shear force of 10,000 kg. If the corresponding maximum shear stress is 30 kg/cm², what is the depth of the beam?

Introduction / Context:
Shear stress distribution in beams is non-uniform. For rectangular sections, the maximum shear stress is related to the average shear stress by a factor of 1.5. This principle is used to calculate the unknown dimension of a beam under load.

Given Data / Assumptions:

• Width (b) = 20 cm.
• Shear force (V) = 10,000 kg.
• Maximum shear stress (τmax) = 30 kg/cm².
• Material assumed homogeneous and elastic.

Concept / Approach:
Formula for maximum shear stress in a rectangle: τmax = 1.5 * V / (b * d) Rearranging: d = 1.5 * V / (b * τmax)

Step-by-Step Solution:
τmax = 30 kg/cm².V = 10,000 kg.b = 20 cm.d = (1.5 * 10,000) / (20 * 30) = 15,000 / 600 = 25 cm.

Verification / Alternative check:
Check average shear stress = V / (b * d) = 10,000 / (20 * 25) = 20 kg/cm². Maximum shear stress = 1.5 × 20 = 30 kg/cm², which matches given data.

Why Other Options Are Wrong:

• 15 cm, 20 cm, 30 cm: do not satisfy the shear stress relation.

Common Pitfalls:

• Using average shear stress formula instead of maximum shear stress for rectangular sections.

Final Answer:
25 cm