Question

A prestressed concrete beam 300 mm wide and 600 mm deep is prestressed using 5 high tension bars of 12 mm $\varphi$ provided at 220 mm from the soffit of the beam. The effective stress in steel is $800N/m{m}^2$. The bending moment that must be applied to the section to just avoid tension at the soffit of the beam is ______ kNm.

• A. 81.36

Answer 1

The correct option is A 81.36
$P=800\times 5\times \frac{\pi }{4}\times {12}^2$
$=452389N$
$e=300-220=80mm$

The bending moment required so that the tension at the soffit is just avoided will be given by

$\frac{P}{A}+\frac{Pe}{Z}-\frac{M}{Z}=0$

$\Rightarrow \frac{452389}{300\times 600}+\frac{452389\times 80}{\left(\frac{300\times {600}^2}{6}\right)}-\frac{M}{\left(\frac{300\times {600}^2}{6}\right)}=0$

$\Rightarrow 2.51+2.01-\frac{M}{18\times {10}^6}=0$

$\Rightarrow M=81.36\times {10}^{6}Nmm$

$=81.36kNm$