P

Vext P dX

FIGURE 2.114 Column with (a) pinned ends, (b) fixed ends, and (c) fixed-free ends.

If A = C = 0, the solution is trivial. Therefore, to obtain a nontrivial solution, the determinant of the coefficient matrix of Equation 2.255 must be zero, that is,

-AK2 sin

kL =

0 0

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