Two-way slab simply supported on all four edges carrying uniformly distributed load w: If l1 and l2 are the longer and shorter spans respectively, the load split into w1 on strips parallel to l2 and w2 on strips parallel to l1 is in the ratio ?

Introduction / Context:
In classic plate theory for simply supported rectangular slabs under uniform load, the load distribution to orthogonal strip actions relates to the spans to the fourth power. This gives a convenient way to apportion load effects for preliminary design or educational problems.

Given Data / Assumptions:

• Two-way slab, simply supported on all sides.
• Uniformly distributed load w.
• Strips considered parallel to l2 (carrying w1) and parallel to l1 (carrying w2).

Concept / Approach:

Deflection and stiffness of plate action lead to a fourth-power span dependency. Hence the load split is proportional to the fourth power of the orthogonal spans.

Step-by-Step Solution:

Verification / Alternative check:

Many textbooks present the same fourth-power law for load apportionment in simply supported two-way plates under UDL.

Why Other Options Are Wrong:

Ratios with 2nd power, 1st power, or inverted fourth power contradict the plate-theory result used for such educational distribution.

Common Pitfalls:

Confusing which span is associated with which strip; swapping l1 and l2 leads to the reciprocal.

Final Answer:

w1/w2 = l2^4 / l1^4