Le = KL
L = Actual length of the column between its supports
K = Constant value dependent on the end fixity of the column as following.
- A pinned-end column is guided so that the end of the column cannot sway from side to side, but it can rotate with no resistance at the end.
- A fixed-end column is held against rotation at the support.
The higher constant value of K as shown as the "practical values" in the above table is recommended because in reality it is particularly difficult to achieve a true fixed-end column because of lacking of rigidity of the support.
The slenderness ratio is the ratio of the effective length of the column to the least radius of gyration.
Slenderness ratio = Le/r_min = KL/r_min
The slenderness ratio will be used to select the method of performing the analysis of straight, centrally loaded columns. Two methods will be presented in the next post.
- The Euler formula for long, slender columns
- The J. B. Johnson formula for short columns