Question

A singly reinforced rectangular concrete beam has a width of 200 mm and an effective depth of 300 mm. If the critical neutral axis depth coefficient is 0.48, then the limiting value of the moment of resistance of the beam will be close to: (Use M-20 grade of concrete and Fe-415 steel)

• A. 30 kNm
• B. 40 kNm
• C. 50 kNm
• D. 60 kNm

Hint:

For limit state design of singly reinforced beams, use \(M_{lim} = 0.36 f_{ck} b x_{u,max}(d - 0.42 x_{u,max})\).

Answer 1

The Correct Option is C

Step 1: Formula for limiting moment of resistance.
The limiting moment of resistance for a singly reinforced beam is given by: \[ M_{lim} = 0.36 \, f_{ck} \, b \, x_{u,max} \left(d - 0.42x_{u,max}\right) \] where: - \( f_{ck} = 20 \, \text{N/mm}^2 \) (M-20 concrete), - \( b = 200 \, \text{mm} \), - \( d = 300 \, \text{mm} \), - \( x_{u,max} = 0.48d = 0.48 \times 300 = 144 \, \text{mm}. \)

Step 2: Substitution.
\[ M_{lim} = 0.36 \times 20 \times 200 \times 144 \times (300 - 0.42 \times 144) \] First compute: \[ 300 - 0.42 \times 144 = 300 - 60.48 = 239.52 \, \text{mm}. \] Now: \[ M_{lim} = 0.36 \times 20 \times 200 \times 144 \times 239.52 \] \[ M_{lim} = 498,99000 \, \text{Nmm} \approx 5.0 \times 10^7 \, \text{Nmm} \] Convert to kNm: \[ M_{lim} = \frac{5.0 \times 10^7}{10^6} = 50 \, \text{kNm}. \]

Step 3: Conclusion.
The limiting moment of resistance is approximately \(\, 50 \, \text{kNm}.\)