Q.44 In the design of T beam, If Mu > Mu,lim then the section is designed as a _______ Where Mu = Ultimate flexural strength of beam, Mu,lim = limiting moment of resistance of a beam
- AOver reinforced section
- BDoubly reinforced sectionCorrect
- Cunder reinforced section
- DSingly reinforced section
Solution
Concept
When the factored moment is more than the limiting moment of resistance, a singly reinforced section is not enough, so compression steel is added (doubly reinforced section).
Formula
Mu - Mu,lim = fsc × Asc × (d - d')
Step-by-step solution
1. Find Mu,lim of the T-beam section with xu = xu,max. 2. Compare Mu with Mu,lim. 3. If Mu ≤ Mu,lim, design as singly reinforced (under-reinforced) section. 4. If Mu > Mu,lim, the extra moment (Mu - Mu,lim) is resisted by compression steel plus extra tension steel. 5. So the section is designed as a doubly reinforced section. Answer is (B).
Explanation
IS 456 limits the neutral axis depth to xu,max to make the failure ductile. If the moment is more than Mu,lim, we cannot simply add more tension steel. Instead we add compression steel and matching tension steel, so the section becomes doubly reinforced.
Why the other options are wrong
A: Over-reinforced sections give brittle failure and are not allowed in limit state design. C: An under-reinforced section can carry only up to Mu,lim. D: A singly reinforced section is used only when Mu ≤ Mu,lim.
Shortcut
Mu > Mu,lim means doubly reinforced. Mu ≤ Mu,lim means singly reinforced.
Common mistake
Adding only more tension steel. This pushes xu above xu,max and makes the section over-reinforced.
Correct answer: B) Doubly reinforced section