Question

An reinforced beam of size $250mm\times 500mm$ (overall) is reinforced with $2$ nos. of $16mm$ dia bars in compression side and $4$ nos. of $20mm$ dia bars in tension side. The effective cover to both reinforcement is $40mm$. The grade of materials used are $M20$ and $Fe415$ respectively. The stress in steel (on compression side) may be taken from table below:For balanced failure, the moment of resistance (in kNm, round off to two decimals) is _______kN-m.

• A. 203

Answer 1

The correct option is A 203
$A_{st}=4\times \frac{\pi }{4}\times {20}^2=1256.6m{m}^2$
$A_{sc}=2\times \frac{\pi }{4}\times {16}^2=402m{m}^2$
$\frac{d^{\prime }}{d}=\frac{40}{460}=0.0869$
$\therefore f_{sc}=358-\frac{(358-352)}{(0.10-0.05)}(0.0869-0.05)$
$=353.57MPa$
For balanced failure, $x_u=x_{u,lim}=0.48d=0.48\times 460=220.8mm$
For $Fe415,x_{u,lim}=0.48d$

$M_{u,lim}=0.362f_{ck}b{x}_u(d-0.416x_u)+(f_{sc}-0.447f_{ck})A_{sc}(d-d^{\prime })$
$=0.362\times 20\times 250\times 220.8(460-0.416\times 220.8)$
$+(353.57-0.447\times 20)\times 402(460-40)$
$=(147.13+58.19)kNm$
$=205.32kN-m$