Circular slab under uniformly distributed load: If a simply supported circular slab of radius R carries a total uniformly distributed load W (i.e., load intensity w = W / (π R^2)), what is the maximum radial bending moment at the centre of the slab (per unit width)?

Introduction / Context:For circular slabs supported along the circumference and subjected to a uniformly distributed load, classic plate theory gives closed-form coefficients for bending moments. The peak radial moment occurs at the centre; knowing this coefficient is essential for reinforcement design in the radial direction.

Given Data / Assumptions:

• Circular slab of radius R.
• Simply supported at the edge.
• Total uniformly distributed load W over the area (so w = W / (π R^2)).

Concept / Approach:For a simply supported circular slab under UDL w (force per unit area), the maximum radial moment at the centre is given by M_r,max = (3 w R^2) / 16 per unit width. Substituting w = W / (π R^2) simplifies the expression in terms of total load W.

Step-by-Step Solution:Start with M_r,max = (3 w R^2) / 16.Use w = W / (π R^2).Then M_r,max = (3 / 16) * (W / (π R^2)) * R^2 = 3 W / (16 π).

Verification / Alternative check:Dimensional consistency: W has dimensions of force; dividing by π gives force; the coefficient 3/16 is dimensionless; the result is bending moment per unit width, which is in force–length units once the per-unit-width interpretation is acknowledged from plate theory conventions.

Why Other Options Are Wrong:W/π and W/(2π): Miss the correct coefficient; overestimate moment.W/(8π): Undercounts by a factor of 3/2.W/(4π): Also incorrect coefficient.

Common Pitfalls:

• Confusing simply supported with clamped edges (different coefficients).
• Mixing up total load W and intensity w.

Final Answer:3 W / (16 π)