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 ?
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Aw1/w2 = l2^4 / l1^4
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Bw1/w2 = l1^2 / l2^2
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Cw1/w2 = l1^4 / l2^4
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Dw1/w2 = l2 / l1
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Ew1/w2 = l1 / l2
Answer
Correct Answer: w1/w2 = l2^4 / l1^4
Explanation
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:
Use standard result: w1 : w2 = l2^4 : l1^4.Therefore, w1/w2 = l2^4 / l1^4.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