Question

A concrete beam of rectangular cross-section of 200 mm x 400 mm is pre-stressed with a force 400 kN at eccentricity 100 mm. The maximum compressive stress in the concrete is

• A. 12.5 N/mm${}^2$
• B. 7.5 N/mm${}^2$
• C. 5.0 N/mm${}^2$
• D. 2.5 N/mm${}^2$

Answer 1

The correct option is A 12.5 N/mm${}^2$

Cross sectional area,
$A=200\times 400=8\times {10}^{4}m{m}^2$
Moment of inertia,
$I=\frac{200\times {400}^3}{12}$
Prestressing force

$P=400kN=4\times {10}^5$ N
Eccentricity,
e = 100 mm
Maximum compressive stress
$=\frac{P}{A}+\frac{My}{I}$
$=\frac{P}{A}+\frac{\left(Pe\right).D/2}{I}$
$=\frac{4\times {10}^5}{8\times {10}^4}+\frac{4\times {10}^5\times 100\left(400/2\right)}{\frac{200\times {400}^3}{12}}$
$=12.5N/m{m}^2$