Question

A single reinforced rectangular concrete beam has a width of 150 mm and an effective depth of 330 mm. The characteristic compressive strength of concrete is 20 MPa and the characteristic tensile strength of steel is 415 MPa. Adopt the stress block for concrete as given in IS : 456-2000 and take limiting value of depth of neutral axis as 0.48 times the effective depth of the beam.The limiting area of tension steel in mm${}^2$ is

• A. 473.9
• B. 412.3
• C. 373.9
• D. 312.3

Answer 1

The correct option is A 473.9

Limiting value of depth of neutral axis
= 0.48d
= 0.48 $\times$ 330
$x_{umax}=158.4$ mm

Moment of resistance,
$M=0.36f_{ck}b{x}_u(d-0.42x_u)$
Limiting value of moment of resistance when
$x_u=x_{umax}$
$M_{ulim}=0.36f_{ck}.b{x}_{umax}(d-0.42x_{umax})$
$=0.36\times 20\times 150\times 158.4(330-0.42\times 158.4)$
$=45.07\times {10}^6$ N-mm
= 45.07 kN-m
$M_{ulim}=45.07\times {10}^6$
=$0.87\times 415A_{st}(330-0.42\times 158.4)$
$\Rightarrow A_{st}=473.79m{m}^2$