Four identical hollow cylindrical cloumns of steel support a big structure of mass 50.000 kg. the inner and outer radii of each column are 30 cm and 60 cm respectively. Assume the load distribution to be uniform , calculate the compressional strain of each column. the Young's modulus of steel is `2.0 xx 10^(11) Pa`.

Explanation

Load on each column, `F = (50,000)/(4) kg wt = (50000 xx 9.8)/(4) N`
`A = pi (r_(2)^(2)-r_(1)^(2)) = 22/7 [(0.60)^(2)-(0.30)^(2)] = 22/7 xx 0.27 m^(2)` ltbr. Compression strain `=(F//A)/(Y) = (F)/(AY) = (50,000 xx 9.8)/(4 xx (22/7 xx 0.27) xx 2.0 xx 10^(11)) = 7.21 xx 10^(-7)`.