Three pinned-end columns of the same material have the same length and the same cross-sectional area (see figure). The columns are free to buckle in any direction. The columns have cross sections as follows: (1) a circle, (2) a square, and (3) an equilateral triangle.
Determine the ratios P1 : P2 : P3 of the critical loads for these columns.
![1642_fc13a98d-bb4d-44ad-a33b-6864724942a4.png](https://secure.tutorsglobe.com/CMSImages/1642_fc13a98d-bb4d-44ad-a33b-6864724942a4.png)