Question

In the design of beams for the limit state of collapse in flexure as per IS: 456-2000, let the maximum strain in concrete be limited to 0.0025, (in place of 0.0035). For this situation, consider a rectangular beam section with breadth as 250 mm, effective depth as 350 mm, area of tensioned steel as 1500 mm${}^2$ and characteristic strengths of concrete and steel as 30 MPa and 250 MPa respectively. The depth of neutral axis for the balanced failure is

• A. 140 mm
• B. 156 mm
• C. 168 mm
• D. 185 mm

Answer 1

The correct option is B 156 mm

(i) Maximum strain in concrete = 0.0025
(ii) As per the assumption of limit state design, maximum strain in tension reinforcement at the time of collapse should not be less than
$\frac{0.87f_y}{E_s}+0.002$
Above two condition will result into maximum depth of N.A. or depth of N.A. for balanced failure.

$DepthofN.A.=x_u$

$\frac{x_u}{0.0025}=\frac{(d-x_u)}{\frac{0.87f_y}{E_s}+0.002}$



$\frac{0.87f_y}{E_s}+0.002$



$\Rightarrow x_u(\frac{0.87f_y}{E_s}+0.002+0.0025)=0.0025d$

$x_u=\frac{0.0025\times 350}{\frac{0.87\times 250}{2\times {10}^5}+0.0045}$

= 156.6 mm