For a balanced beam section, the limit state is reached when:
- Athere is the simultaneous crushing of concrete and breaking of steel
- Bthere is the simultaneous yielding of both concrete and steel
- Cthere is the simultaneous crushing of concrete and yielding of steelCorrect
- Dthere is the simultaneous yielding of concrete and breaking of steel
Solution
Concept
In a balanced section, concrete reaches its ultimate (crushing) strain and steel reaches its yield strain at the same time.
Formula
xu,max/d = 0.0035/(0.0055 + 0.87 fy/Es)
Step-by-step solution
1. Limit state of collapse in flexure: concrete fails when strain at top fibre = 0.0035 (crushing). 2. Steel fails by yielding when its strain reaches 0.87 fy/Es + 0.002. 3. In a balanced section, both these happen at the same time. 4. So the limit state is simultaneous crushing of concrete and yielding of steel. Answer (C).
Explanation
Concrete does not yield; it fails by crushing. Steel does not break at the limit state; it yields first. In a balanced section, concrete crushing and steel yielding happen together.
Why the other options are wrong
A: Steel yields at the limit state; it does not break. B: Concrete does not yield; it crushes. D: Concrete crushes (it does not yield), and steel yields (it does not break).
Shortcut
Remember: concrete crushes, steel yields. Pick the option that says both.
Common mistake
Thinking steel breaks or concrete yields at the limit state.
Correct answer: C) there is the simultaneous crushing of concrete and yielding of steel