Question

In an under-reinforced one-way slab with an effective depth of 100 mm, the main steel is provided as 10 mm bars at 200 mm center to center. The moment of resistance of the slab for M-20 grade concrete and Fe-415 steel will be
1. 10 kNm/m
2. 13 kNm/m
3. 27.6 kNm/m
4. 29.8 kNm/m
5.

Answer 1

Correct Answer - Option 2 : 13 kNm/m

Concept:

Moment of resistance for under reinforced beam is given by:

MOR = 0.87× f_y × Ast(d - 0.42Xu)

Where, X_u = Depth of neutral axis, A_st = Area of reinforcement

Depth of neutral axis is calculated as:

Compression force = Tension force

0.36 f_ck b X_u = 0.87 f_y A_st

Calculation:

Given,

d = 100 mm,  c/c spacing between bar = 200 mm

M20 and Fe415

Taking b = 1000 mm for slab ,Calculating A_st,

A_st = \(\left ( \dfrac{1000.A_{\phi }}{\rm Spacing} \right )\)

\(A_{st}= \dfrac{1000× \frac{\pi }{4}× 10^{2}}{200}\) = 393 mm²

We know that,

Depth of Neutral Axis (x_u):

\(X_{u}= \left ( \dfrac{0.87f_{y}.A_{st}}{0.36f_{ck}.b} \right )\)

\(X_{u}= \left ( \dfrac{0.87× 415× 393}{0.36× 20 × 1000} \right )\)= 19.6 mm 

MOR is given as:

M_u = 0.87 f_y.A_st.(d - 0.42X_u)

M_u = 0.87×415× 393 (100- 0.42 × 19.6)

M_u = 141892.65 × 91.768  = 13021204.7 N-mm

M_{u =} 13.0 kN-m