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The characteristic equation becomes k cos kL = 0

Since k cannot be zero, we must have cos kL = 0 or np kL = —, n = 1,3,5,... 2

The smallest root (n = 1) gives the lowest critical load of the column p2 EI

The boundary conditions for columns with various end conditions are summarized in Table 2.2. 2.12.2.5 Column Effective Length Factor

The effective length factor, K, of columns with different end boundary conditions can be obtained by equating the Pcr load obtained from the buckling analysis with the Euler load of a pinned-end column of effective length KL

p2 EI

The effective length factor can be obtained as

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