In a singly reinforced rectangular section, the limiting moment of resistance is reached when
- AThe neutral axis lies in the tension zone
- BThe tensile reinforcement yields and concrete crushes simultaneouslyCorrect
- CThe compressive stress in concrete reaches 0.446 fck
- DThe strain in concrete reaches 0.002
Solution
Concept
Limiting state of resistance in balanced sections
Formula
εcu = 0.0035, εst ≥ 0.87·fy/Es + 0.002
Step-by-step solution
1. As per IS 456:2000, a balanced (limiting) section design corresponds to balanced failure criteria. 2. In a balanced section, the maximum compressive strain in concrete reaches 0.0035 simultaneously with the steel reaching its yield strain. 3. At this balanced condition, the section develops its maximum permissible limiting moment of resistance Mu,lim. 4. Hence, the limiting moment is reached when tensile steel yields and concrete crushes simultaneously. Answer: B
Explanation
In limit state design of reinforced concrete beams, the limiting (balanced) moment of resistance is defined by the simultaneous arrival of extreme concrete compressive strain at 0.0035 and tensile steel tensile strain at its yield strain (0.87 fy/Es + 0.002).
Why the other options are wrong
A) In a beam section, the neutral axis separates compressive and tensile zones, not lying solely in tension. C) 0.446 fck is design compressive strength of concrete, not the failure condition. D) 0.002 is the strain at which concrete reaches maximum stress in the parabolic region, not ultimate strain.
Shortcut
Limiting section = Balanced section = Simultaneous steel yield and concrete crushing.
Common mistake
Thinking concrete crushing alone without steel yield represents the balanced limiting state.
Correct answer: B) The tensile reinforcement yields and concrete crushes simultaneously