Question

A RCC beam ($250mm\times 500mm$ overall) is subjected to service working load of $20kN/m$. The span of beam is $6m$. The characteristic compressive strength of concrete is $20MPa$ and the characteristic strength of steel is $415MPa$. The effective cover to reinforcing bar of diameter $16mm$ is $25mm$. For balanced failure, number of bars (approximate value) required are:

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is C 5

Given, $b=250mm$, $d=500-25=475mm$

$f_{ck}=20MPa$, $f_y=415MPa$

Working load $\left(W\right)=20kN/m$

$\Rightarrow$ Factored load $\left(W_u\right)=(1.5\times 20)kN/m=30kN/m$

For $M20$ & $Fe415$ grade of materials
$M_{u,lim}=0.139f_{ck}b{d}^2$
$=(0.139\times 20\times 250\times {475}^2)\times {10}^{-6}=156.81kN-m$

$M_u=\frac{W_u.l^2}{8}=\frac{(1.5\times 20)\times 6^2}{8}=135kN-m<M_{u,lim}$
Hence the section is under reinforced.

For balanced failure
$x_u=x_{u,lim}=0.48d,$ (For Fe415)
$=0.48\times 475=228mm$

$M_u=0.87f_y{A}_{st}(d-0.416x_{u,lim})$
$135\times {10}^6=0.87\times 415A_{st}(475-0.416\times 228)$
$A_{st}=983.58m{m}^2$

No.of bars $=\frac{983.58}{\frac{\pi }{4}\times {16}^2}=4.89\approx 5$