Question

A rectangular simply supported prestressed concrete beam of span L is subjected to a prestressing force of P acting centrally at and sections and the prestress tendons are parabolically draped with maximum eccentricity of $e_{max}$ at the mid span section. The uniformly distributed upward load(w) on the beam due to prestressing will be:

• A. $16P{e}_{max}/L^2$
• B. $4P{e}_{max}/L^2$
• C. $12P{e}_{max}/L^2$
• D. $8P{e}_{max}/L^2$

Answer 1

The correct option is D $8P{e}_{max}/L^2$


The parabolic cable profile actually acts like a cable in the suspension bridge. The cable has the property that at every point of it the BM is zero.



$R_v=\frac{wl}{2}$

BM at C = 0
$R_v\times \frac{l}{2}=R_H\times e_{max}+w\frac{{\left(\frac{l}{2}\right)}^2}{2}$

$\frac{wl}{2}\times \frac{l}{2}=R_H\times e_{max}+\frac{w{l}^2}{8}$

$R_H=\frac{w{l}^2}{8e_{max}}$

$Pcos\theta =\frac{w{l}^2}{8e_{max}}$

$w=\frac{8P{e}_{max}cos\theta }{l^2}$

For small value of $\theta$
$cos\theta \underset{–}{\sim }1$

$Hence,w=\frac{8P{e}_{max}}{L^2}$