Question

When a section is subjected to the limiting moment of resistance then the actual stress in steel of a singly reinforced concrete beam of 200 mm width and 400 mm effective depth, with 4 bars of 16 mm diameter of Fe415 steel is ________ $N/m{m}^2$ [Use M20 grade concrete]

• A. 343.77

Answer 1

The correct option is A 343.77
Given data $A_{st}=\frac{\pi }{4}\times {16}^2\times 4=804.25m{m}^2$

b = 200 mm; d = 400 mm

From equilibrium of forces

T = C
$A_{st},f_{st}=0.36\times f_{ck}b{x}_{u,lim}$

$\Rightarrow f_{st}=\frac{0.36\times f_{ck}b{x}_{u,lim}}{A_{st}}$

$=\frac{0.36\times 20\times 200\times 400\times \left(0.48\right)}{804.25}$

$\therefore f_{st}=343.77N/m{m}^2$

Alternatively,

$x_{u,lim}=0.48d=0.48\left(400\right)=192mm$

$M_u,lim=0.138f_{ck}b{d}^2=0.138\left(20\right)\left(200\right)(400{)}^{2}Nmm$

= 88.32 kNm

$M_{u,lim}=f_{st},A_{st}(d-0.42x_u)$

$\Rightarrow 88.32\times {10}^6=f_{st}\left(804.25\right)(400-0.42\times 192)$

$\Rightarrow f_{st}=343.86N/m{m}^2$