Question 2.15: A prismatic column of square cross section (dimensions b × b......

The column is sketched in Figure 2.26. The weight of the column and the applied load P are axial forces. First we write down an expression for axial stress and later we obtain permissible height of the column.

Weight of the column = Volume × Unit Weight

= b²h . w

Total load on the column = (P + b²h . w)

Stress in the column = \sigma_c

\sigma_{ c }=\frac{\left(P+b^2 h w\right)}{b^2}=\frac{P}{b^2}+h w

∴        h=\frac{1}{w}\left\lgroup\sigma_{ c }-\frac{P}{b^2} \right\rgroup=\frac{b^2 \sigma_{ c }-P}{w b^2}