Floor Systems – Filler joists supporting slabs: When may their spans be treated as approximately equal for analysis and detailing?

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:

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