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 obtained as per IS: 456-2000 differs from the depth of neutral axis obtained in case of from compression fibre is

• A. 15 mm
• B. 20 mm
• C. 25 mm
• D. 32 mm

Answer 1

The correct option is C 25 mm




For depth of Neutral Axis $x_u$
C= T

Area of stress diagram $\times$ width = T

$\frac{1}{2}[\frac{3}{7}{x}_u+x_u]\times 0.67f_{ck}\times 300=0.87f_y.A_{st}$

$\frac{1}{2}\times \frac{10}{7}{x}_u\times 0.67\times 20\times 300=0.87\times 415\times 3\times \frac{\pi \times {16}^2}{4}$

$x_u=75.844mm$
$x_u\simeq 76mm$
Depth of NA as per IS : 456
C = T
$0.36f_{ck}b.x_u=0.87f_y{A}_{st}$
$0.36\times 20\times 300x_u=0.87\times 415\times 3\times \frac{\pi \times {16}^2}{4}$
$x_u=100.824$ mm
Neutral axis differs by (100.824-75.84)
= 24.98
= 25 mm