Question

In the prestressed concrete beam section shown in the given figure (all dimensions in mm in the figure), if the net losses are 15% and final prestressing force applied at 'A' is 500 kN, the initial extreme fibre stresses at tip and bottom will be respectively

• A. $-3.40N/m{m}^{2}and16.70N/m{m}^2$
• B. $-3.40N/m{m}^{2}and19.60N/m{m}^2$
• C. $-4.0N/m{m}^{2}and16.70N/m{m}^2$
• D. $-4.0N/m{m}^{2}and19.60N/m{m}^2$

Answer 1

The correct option is D $-4.0N/m{m}^{2}and19.60N/m{m}^2$

$\begin{array}{cc}& \text{Initial prestressing force,}\\ P& =\frac{500}{0.85}=588.2kN\\ e& =75mm\\ & \text{Area of beam,}\\ A& =250\times 300=75000m{m}^2\\ & \text{Top fibre stress}\\ & =\frac{P}{A}(1-\frac{6e}{d})=-3.92N/m{m}^2\\ & \text{Bottom fibre stress}\\ & =\frac{P}{A}(1+\frac{6e}{d})=19.6N/m{m}^2\end{array}$