Question

A doubly reinforced rectangular concrete beam has a width of 300 mm and an effective depth of 500 mm. The beam is reinforced with 2200 mm ${}^2$ of steel in tension and 628 mm${}^2$ of steel in compression. The effective cover for compressive steel is 50 mm. Assume that both tensioned and compressive steel yield. The grades of concrete and steel used are M-20 and Fe-250 respectively. The stress block parameters (rounded off to first two decimal places) for concrete shall be as per IS : 456-2000.

The depth of neutral axis is

• A. 205.30 mm
• B. 184.56 mm
• C. 160.91 mm
• D. 145.30 mm

Answer 1

The correct option is C 160.91 mm


Grade of concrete = M20
Grade of steel = Fe-250

Effective depth, d = 500 mm
Width, b = 300 mm
Both tension and compressive steel yield .
So stress in both the bar
$=0.87f_y$
$=0.87\times 250$
Depth of Neutral Axis $\left(x_u\right)$,
C = T
$0.36f_{ck}b.x_u+A_{SC}\times (0.87f_y-0.45f_{ck})$
$=0.87f_y.A_{st}$
$0.36\times 20\times 300\times x_u+628(0.87\times 250-0.45\times 20)$
$=0.87\times 250\times 2200$
$x_u=160.908$ mm
= 160.91 mm
Maximum depth of Neutral axis
= 0.53 d
=0.53$\times$500
$x_{umax}$= 265 mm
$\Rightarrow x_u<x_{umax}$
Hence O.K.