Question

A simply supported post-tensioned prestressed concrete beam of span $L$ is prestressed by a straight tendon at a uniform eccentricity 'e' below the centroidal axis. If the magnitude of prestressing force is $P$ and flexural rigidity of beam is $EI$, the maximum central deflection of the beam is

• A. $\frac{Pe{L}^2}{8EI}$ (downwards)
• B. $\frac{Pe{L}^2}{48EI}$ (upwards)
• C. $\frac{Pe{L}^3}{8EI}$ (upwards)
• D. $\frac{Pe{L}^2}{8EI}$ (upwards)

Answer 1

The correct option is D $\frac{Pe{L}^2}{8EI}$ (upwards)

Maximum central deflection,
$\delta =\frac{L^1}{8R}\frac{1}{R}=\frac{Pe}{EI}\therefore \delta =\frac{Pe{L}^2}{8EI}\left(upwards\right)$