Question

A simply supported pre-stressed concrete beam is 6 m long and 300 mm wide. Its gross depth is 600 mm. It is pre-stressed by horizontal cable tendons at a uniform eccentricity of 100 mm. The pre-stressing tensile force in the cable tendons is 1000 kN. Neglect the self weight of beam. The maximum normal compressive stress in the beam at transfer is

• A. zero
• B. 5.55 N/mm${}^2$
• C. 11.11 N/mm${}^2$
• D. 15.68 N/mm${}^2$

Answer 1

The correct option is C 11.11 N/mm${}^2$

Prestressing tensile force,
$P=1000kN={10}^6$ N
Eccentricity, e = 100 mm
Moment of inertia,

$I=\frac{300\times {600}^3}{12}$


Maximum normal compressive stress,

$\sigma =\frac{P}{A}+\frac{\left(Pe\right)y}{I}$

$=\frac{{10}^6}{300\times 600}+\frac{({10}^6\times 100)\times \left(600/2\right)}{\frac{300\times {600}^3}{12}}$

$=11.11N/m{m}^2\left(atbottom\right)$