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: Limiting Moment of Resistance Formula.
The formula for the limiting moment of resistance of a singly reinforced beam is: \[M_{lim} = 0.36 \, f_{ck} \, b \, x_{u,max} \left(d - 0.42x_{u,max}\right)\] Parameters: - \( f_{ck} = 20 \, \text{N/mm}^2 \) (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: Calculation.
Substitute values into the formula: \[M_{lim} = 0.36 \times 20 \times 200 \times 144 \times (300 - 0.42 \times 144)\] Calculate the term in the parenthesis: \[300 - 0.42 \times 144 = 300 - 60.48 = 239.52 \, \text{mm}.\] Perform the full calculation: \[M_{lim} = 0.36 \times 20 \times 200 \times 144 \times 239.52\] \[M_{lim} = 498,99000 \, \text{Nmm} \approx 5.0 \times 10^7 \, \text{Nmm}\] Convert to kNm: \[M_{lim} = \frac{5.0 \times 10^7}{10^6} = 50 \, \text{kNm}.\]

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