26.3 : 다른 끝 조건이 있는 기둥에 대한 오일러의 공식

Euler's formula for a pin-ended column expresses critical loading using the modulus of elasticity, moment of inertia of the cross-section, and length of the column.

The corresponding critical stress is expressed by dividing Euler's formula by the cross-sectional area. Here, the length of the column over the radius of gyration of the cross-section is defined as the slenderness ratio of the column. 

Euler's formula can be extended to columns having different end connections by calculating the effective buckling length that measures the load-bearing capacity of the column.

The effective length of the column is expressed as the product of the length of the column to the empirical constant k.

For columns with one end fixed and the other end free, the value of k is 2. On the other hand, for the columns with both ends fixed, k is 0.5.

For the columns with one end fixed and the other end pinned, k is 0.7.

Utilizing these values of k, Euler's formula can be extended to columns with different end connections.