2 2 2

The critical load for the symmetric buckling mode is Pcr = 4p2EI/L2 by letting sin(kL/2) = 0. The buckling load for the antisymmetric buckling mode is Pcr = 80.8EI/L2 by letting the bracket term in Equation 2.268 equal zero.

2.12.2.4 Column with One End Fixed and One End Free

The boundary conditions for a fixed-free column are (Figure 2.114c): at the fixed end y (x = 0)=y'(x = 0)= 0 (2 .269)

and at the free end the moment M = Ely'' is equal to zero y "(x = L)= 0 (2 .270)

and the shear force V = —dM/dx = —Ely'" is equal to Py', which is the transverse component of P acting at the free end of the column.

V = —Ely''' = Py' (2 . 271) It follows that the shear force condition at the free end has the form y''' + k2y' = 0 (2 .272) Using the boundary conditions at the fixed end, we have

B + D = 0 and Ak + C = 0 (2 .273) The boundary conditions at the free end give

A sin kL + B cos kL = 0 and C = 0 (2 .274) In matrix form, Equations 2.273 and 2.274 can be written as

0 0

Post a comment