Question

A pre-tensioned rectangular beam 150 mm wide and 300 mm depth is prestressed with three straight tendons each having a cross-sectional area of 50 mm${}^2$ to an initial stress of 1200 N/mm${}^2$. The tendons are located at 100 mm from the soffit of the beam. If the modular ratio is 6 the loss of prestressing force (in kN upto one decimal place) due to the elastic deformation of concrete is ______.

• A. 4.8

Answer 1

The correct option is A 4.8

Loss due to elastic deformation $=m{f}_c=6f_c$

$f_c=\frac{P}{A}+\frac{P{e}^2}{I}$

$P=1200\times 3\times 50N$
$A=150\times 300$
e = 50 mm

$f_c=\frac{1200\times 3\times 50}{150\times 300}+\frac{1200\times 3\times 50\times {50}^2}{\frac{150\times {300}^3}{12}}$

$=4+\frac{4}{3}=\frac{16}{3}N/m{m}^2$

$Loss=6\times \frac{16}{3}=32N/m{m}^2$

$Lossinforce=32\times 3\times 50$
= 4800 N = 4.8 kN