Question

For a prestressed cantilever beam of size $200mm\times 400mm$ with prestressing force of $500kN$. The beam is subjected to uniformly distributed load (inclusive of self weight) of $4kN/m$. The span of beam is $6m$. The distance (in mm, rounded off to two decimal places) of the cable from the soffit of the beam at the fixed end for no tensile stress in during service conditions is _______.

• A. 277

Answer 1

The correct option is A 277
Let the eccentricity of cable from centre line be e.Tensile stress at top fibre $=0$
$\therefore$ In cantilever beam, tensile stress may be generated at top fibre side.
$\frac{P}{A}+\frac{Pe}{Z}-\frac{M}{Z}=0$
$M=\frac{w{l}^2}{2}=\frac{4\times 6^2}{2}=72kN-m$
$Z=\frac{b{d}^2}{6}=\frac{200\times (400{)}^2}{6}=5333333.33m{m}^2$
$P=500kN$
$\therefore \frac{500\times {10}^3}{200\times 400}+\frac{500\times {10}^3\times e}{5333333.33}-\frac{72\times {10}^6}{5333333.33}=0$
$e=77.33mm$
Distance of cable from soffit $=200+77.33=277.33mm$