Question

Assume straight line instead of parabola for stress strain curve of concrete as follows and partial factor of safety as 1.0

A rectangular under-reinforced concrete section of 300 mm width and 500 mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16 mm diameter.
Concrete mix is M-20

The depth of the neutral axis from the compressive fibre is

• A. 76 mm
• B. 81 mm
• C. 87 mm
• D. 100 mm

Answer 1

The correct option is A 76 mm



For depth of Neutral Axis $x_u$
C= T
Area of stress diagram $\times$ width = T
$\frac{1}{2}[\frac{3}{7}{x}_u+x_u]\times 0.67f_{ck}\times 300=0.87f_y.A_{st}$
$\frac{1}{2}\times \frac{10}{7}{x}_u\times 0.67\times 20\times 300$
$=0.87\times 415\times 3\times \frac{\pi \times {16}^2}{4}$
$x_u=75.844$ mm
$\underset{–}{\sim }$76 mm