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5. Static response of MEMS 321
critical buckling load can be calculated for each case following the procedure
used in determining the critical load for a pinned-pined column, as detailed in
Chen and Lui [6] or Chajes [7]. The critical load can be expressed in the
generic manner:
where is called the effective length and is calculated by means of the
effective-length factor K as:
Figure 5.56 Combinations of ideal boundary conditions for beam-columns in buckling: (a)
guided-fixed (K = 0.5), (b) pinned-fixed (K = 0.7), (c) pinned-pinned (K = 1), (d) fixed-fixed
(K = 1), (e) free-fixed (K = 2), (f) fixed-pinned (K = 2)
Figure 5.56, which shows other combinations of boundary conditions for
beam-columns subjected to buckling, also gives the corresponding values of
K – after Chen and Lui [6].
Another measure of the elastic buckling is the critical stress, which is
produced by the compression load, and which can be calculated as:
By using the radius of gyration, which is defined as:
