8-5.  Rectangular columns are used to support a roof. The ends of a column are pin connected. The dimension of the column is shown in the figure. If the modulus of elasticity follows a normal distribution , determined the distribution of the critical load of the column. Assume that Euler’s formula is valid.

Solution:

According to the cross section of the column, we can get

,   (Controls!)

Since the ends of the column are pin connected, . Thus the critical buckling load of this column can be calculated by

Thus

The critical load of the column follows a normal distribution of .   Ans.