Floor Systems – Filler joists supporting slabs: When may their spans be treated as approximately equal for analysis and detailing?
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AIf longest span is within 5% of the shortest
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BIf longest span is within 10% of the shortest
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CIf longest span is within 15% of the shortest
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DIf longest span is within 20% of the shortest
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EOnly when spans are exactly equal
Answer
Correct Answer: If longest span is within 10% of the shortest
Explanation
Introduction:In joisted slabs, small variations in joist span may be ignored to simplify analysis. Recognizing an acceptable tolerance avoids unnecessary differentiation in design loads and reinforcement.
Given Data / Assumptions:
- Parallel filler joists supporting a slab.
- Uniform loading and similar boundary conditions.
- Interest: how close spans must be to assume equality.
Concept / Approach:
When the longest span does not exceed the shortest span by more than about 10%, stiffness and deflection differences are modest. Treating spans as equal is typically acceptable for pragmatic design and layout.
Step-by-Step Solution:
1) Measure shortest and longest spans.2) Compute percentage difference = (longest − shortest) / shortest * 100.3) If ≤ 10%, proceed with equal-span assumptions for design tables and detailing.Verification / Alternative check:
Elastic deflection and moment comparisons show small deviations within ±10% length variation under uniform loading.
Why Other Options Are Wrong:
5% is overly restrictive; 15% and 20% may lead to noticeable redistribution; exact equality is unnecessary in practice.
Common Pitfalls:
Ignoring differences in support conditions or load patterns; using equal span assumption when one bay is much longer.
Final Answer:
If longest span is within 10% of the shortest