Correct Answer - Option 2 : 13 kNm/m
Concept:
Moment of resistance for under reinforced beam is given by:
MOR = 0.87× fy × Ast(d - 0.42Xu)
Where, Xu = Depth of neutral axis, Ast = Area of reinforcement
Depth of neutral axis is calculated as:
Compression force = Tension force
0.36 fck b Xu = 0.87 fy Ast
Calculation:
Given,
d = 100 mm, c/c spacing between bar = 200 mm
M20 and Fe415
Taking b = 1000 mm for slab ,Calculating Ast,
Ast = \(\left ( \dfrac{1000.A_{\phi }}{\rm Spacing} \right )\)
\(A_{st}= \dfrac{1000× \frac{\pi }{4}× 10^{2}}{200}\) = 393 mm2
We know that,
Depth of Neutral Axis (xu):
\(X_{u}= \left ( \dfrac{0.87f_{y}.A_{st}}{0.36f_{ck}.b} \right )\)
\(X_{u}= \left ( \dfrac{0.87× 415× 393}{0.36× 20 × 1000} \right )\)= 19.6 mm
MOR is given as:
Mu = 0.87 fy.Ast.(d - 0.42Xu)
Mu = 0.87×415× 393 (100- 0.42 × 19.6)
Mu = 141892.65 × 91.768 = 13021204.7 N-mm
Mu = 13.0 kN-m