Question

An reinforced beam of effective size $250mm\times 400mm$ is reinforced by $3$ nos. $16\varphi$ bars of grade $Fe415$. If the reinforcement is changed by $6$ nos. of mild steel bars of diameter $16mm$, the shift (in mm) of neutral axis as per IS $456:2000$ is _______.(The grade of concrete used is $M25$).

• A. 19

Answer 1

The correct option is A 19
Given, $b=250mm,d=400mm$
Case-1: $A_{st}=3nos.$ of $16\varphi =603.2m{m}^2$
$C=T$
$0.362f_{ck}b{x}_u=0.87f_y{A}_{st}$
$0.362\times 25\times 250x_u=0.87\times 415\times 603.12$
$x_u=96.3mm$
$x_{u,lim}=0.48d=192mm>x_u,$ under reinforced section.
Case-2: $A_{st}=6nos.$ of $16\varphi =1206.4m{m}^2$
$C=T$
$0.362f_{ck}b{x}_u=0.87f_y{A}_{st}$
$x_u=\frac{0.87\times 250\times 1206.4}{0.362\times 25\times 250}=115.97mm$
$x_{u,lim}=0.53d=212mm>x_u,$ under reinforced section.
Shift in neutral axis $=x_u^{\prime }-x_u$
$=19.67mm$