008 Minimum Stiffness Of Translational Spring To Change The Buckling Mode

In practical engineering, there are debates in several cases where the buckling shape and mode would not be clear. In such a case, the minimum stiffness of one element can be determined, and the buckling mode can be understood based on that. In the figure, a cantilever beam with the bending rigidity of EI is subjected to a compressive load, p. The beam’s free end is supported by a translational spring with the constant of c.

Determine the critical value of spring coefficient c so that the buckling shape of the compressive element would change from the free end to a supported one.

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