Question

The singly reinforced concrete beam section shown in the figure (not drawn to the scale) is made of M25 grade concrete and Fe 500 grade reinforcing steel. The total cross- sectional area of the tension steel is 942 mm${}^2.$




As per limit state design of IS 456:2000, the design moment capacity (in kN.m round off to two decimal places) of the beam section is _____________.

• A. 158.27

Answer 1

The correct option is A 158.27
M25 ; Fe500

$A_{st}=942m{m}^2$

$x_{ulimit}=0.46d=0.46\times 450=207mm$

For calculation of depth of NA

$0.36f_{ck}b{x}_u=0.87f_y{A}_{st}$

$\Rightarrow 0.36\times 25\times 300\times x_u=0.87\times 500\times 942$

$\Rightarrow x_u=151.76mm<x_{ulimit}$

So, under reinforcement section.
Moment of resisting for under reinforced section.

$MR=0.36f_{ck}b{x}_u(d-0.42x_u)$

$=0.36\times 25\times 300\times 151.76(450-0.42\times 151.76)$

$=158271135.3Nmm$

$=158.27kNm$