Question

A reinforced concrete beam of rectangular section has a width of 300 mm and an effective depth of 500 mm. The effective cover to tension and compression steel is 40 mm each. The beam is reinforced with 4 bars of 20 mm diameter in tension and 2 bars of 16 mm diameter in compression. The grade of concrete used is M20 and steel is Fe145.
The depth of neutral axis is ____ mm.
[Assume $f_{sc}$ = 0.97 times allowable stress in tension steel]

• A. 146.53

Answer 1

The correct option is A 146.53
$A_{st}=4\times \frac{\pi }{4}\times {20}^2=1256.64m{m}^2$

$A_{sc}=2\times \frac{\pi }{4}\times {16}^2=402.12m{m}^2$

$f_{sc}=0.97(0.87\times 415)=350.22m{m}^2$

$x_{u,bal}=0.48d=0.48\times 500=240mm$

For neutral axis, C = T

$\Rightarrow 0.36f_{ck}B{x}_u+(f_{sc}-0.45f_{ck})A_{sc}=0.87\times f_y\times A_{st}$

$\Rightarrow 0.36\times 20\times 300\times x_u+(350.22-0.45\times 20)\times 402.12=0.87\times 415\times 1256.64$

$\Rightarrow x_u=146.53mm$