Question

A prestressed concrete rectangular beam has area of cross-seciton equal to $36000m{m}^2$ and moment of inertia of $2.7\times {10}^{8}m{m}^4$. A prestressing force of 195 kN is applied by tendons at an eccentricity of 55 mm from neutral axis.
The loss of stress in steel due to creep of concrete is ____ $N/m{m}^2$.
[Take $E_s=2\times {10}^{5}N/m{m}^2,E_C=3\times {10}^{5}N/m{m}^2$ and creep coefficient = 1.50]

• A. 76

Answer 1

The correct option is A 76
Modular ratio, $m=\frac{E_s}{E_c}=\frac{2\times {10}^5}{3\times {10}^4}=\frac{20}{3}$

Stress in concrete at the level of steel is,

$f_c=\frac{P}{A}+\frac{P{e}^2}{I}$

$=\frac{195\times {10}^3}{36000}+\frac{195\times {10}^3\times {55}^2}{2.7\times {10}^8}$

$\simeq 7.6N/m{m}^2$

Loss of stress in steel due to creep of concrete is given by

$=\varphi m{f}_c$

$=1.5\times \frac{20}{3}\times 7.6=76N/m{m}^2$