Two-way slab design — a slab simply supported on all edges with corners free to lift should be designed using which classical method?

Introduction / Context:
Two-way slabs distribute loads in both orthogonal directions. For slabs simply supported on all edges without corner hold-down (corners free to lift), classical elastic solutions provide moment coefficients used for preliminary and exam problems. Knowing which named formulation applies is a frequent test of fundamentals.

Given Data / Assumptions:

• Slab: simply supported on all four sides.
• No torsional steel or corner hold-down; corners may lift.
• Uniformly distributed loading considered for coefficient selection.

Concept / Approach:

The Grashoff–Rankine (also called Rankine–Grashoff) method provides moment coefficients for two-way slabs with corners free to lift. Marcus coefficients apply where torsional restraint exists at corners (or partial fixity). Rankine alone or “Rankine–Marcus” are not the standard references for this boundary case.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Compare with Marcus coefficients (for restrained corners) to see the reduction/increase in moments due to torsional fixity assumptions; values differ, confirming boundary condition sensitivity.

Why Other Options Are Wrong:

Marcus formula is for restrained corners; “Rankine” or “Grashoff” alone are incomplete references for this specific case; “Rankine–Marcus” is not the standard pairing.

Common Pitfalls (misconceptions, mistakes):

Using corner-restrained coefficients while detailing no torsional steel; ignoring aspect ratio effects.

Final Answer:

Rankine Grashoff formula