For a rectangular beam of size b × d, with yield stress of steel f y, area of steel A st, concrete with characteristic strength f ck, for under-reinforced section, neutral axis to depth ratio is given by
- Axu/d = 0.87 fy Ast / (0.36 fck b d)Correct
- Bxu/d = 0.87 fy b d / (0.36 fck Ast)
- Cxu/d = fy Ast / (fck b d)
- DNone of the above
Solution
Concept
Depth of neutral axis from equilibrium
Formula
0.36 fck b xu = 0.87 fy Ast
Step-by-step solution
1. Compression C = 0.36 fck b xu; tension T = 0.87 fy Ast. 2. C = T ⇒ xu/d = 0.87 fy Ast / (0.36 fck b d).
Explanation
In an under-reinforced section steel yields; equating the forces gives the neutral axis depth.
Why the other options are wrong
B has Ast and bd interchanged; C uses neither factor.
Shortcut
xu/d = 2.42 (fy/fck)(Ast/bd).
Common mistake
Interchanging Ast and bd.
Correct answer: A) xu/d = 0.87 fy Ast / (0.36 fck b d)