Question

A simply supported rectangular concrete beam of span 8 m has to be prestressed with a force of 1600 kN. The tendon is of parabolic profile having zero eccentricity at the supports. The beam has to carry an external uniformly distributed load of intensity 30 kN/m. Neglecting the self-weight of the beam, the maximum dip (in meters upto two decimal place) of the tendon at the mid-span to balance the external load should be ______.

• A. 0.15

Answer 1

The correct option is A 0.15

Prestressing force = 1600 kN



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

$=\frac{30\times 8^2}{8}=240kNm$

Shape of tendon profile will follow the shape of bending moment diagram and for equilibrium of the section having maximum Bending Moment,

$M_{max}=Pe$

$\Rightarrow 240kNm=1600kN\times e$

$\Rightarrow \frac{240kN\times {10}^{3}mm}{1600kN}=e$

e = 150 mm

= 0.15 m