Two-way slab bending: If a slab is simply supported on all four edges and spans in two directions with equal side lengths (a square slab), by what factor is the maximum bending moment in a one-way slab reduced due to two-way action? Select the standard multiplying factor applied to w * l^2 / 8 for design in each direction.

Introduction / Context:
When a reinforced concrete slab is supported on all four sides and the side lengths are equal (a square panel), the load is carried in two directions. This two-way action reduces the bending moment in each direction compared to a one-way slab spanning in a single direction only.

Given Data / Assumptions:

• Simply supported slab on all four edges.
• Equal sides, so span along x equals span along y (square slab).
• Uniformly distributed load is considered for basic design comparison.

Concept / Approach:
In a one-way simply supported slab, the maximum midspan moment is M = w * l^2 / 8. For a square, simply supported two-way slab under uniform load, classical plate theory and standard design tables indicate that the load is shared by orthogonal strips. Each direction carries approximately half the one-way moment, giving a multiplying factor of 0.5 for design moments in each direction.

Step-by-Step Solution:
Identify base moment (one-way): M1 = w * l^2 / 8.Recognize two-way sharing for a square slab: moments distribute equally in both directions.Adopt the standard factor: Mx = My = 0.5 * (w * l^2 / 8).Hence the multiplying factor is 0.5.

Verification / Alternative check:
Design handbooks and code commentaries present coefficient tables for two-way slabs; for a square, simply supported slab, the coefficients in both directions are equal and sum to the one-way value, validating the 0.5 factor per direction.

Why Other Options Are Wrong:

• 0.2, 0.3, 0.4: Underestimate moments and would be unsafe.
• 0.7: Overestimates per-direction moment for a square panel; not economical.

Common Pitfalls:
Confusing total plate moment distribution with per-direction design moments; using one-way moments for a square two-way panel leads to overdesign.

Final Answer:
0.5