002 Buckling Loads and Shape Modes of Rigid Element, Rotational Spring

Four rigid bars form a compressive element under applied compressive load at point B. It is assumed that the bars are hinged and connected at their intersection. At one end, the element is supported by a hinge, and at the other end, point B, the element is supported by a roller. The system is assumed to be a 2D structure. At the intersections, there are three rotational springs with a spring coefficient of k. Each rigid bar is the length of l.

1. Determine the total potential energy of the system.
2. Determine the buckling loads.
3. Determine the buckling shape modes.
4. Assume the rotational spring coefficient is 2000 kN.m/rad and determine the buckling loads numerically.
5. Model the system in FEM software and compare your results.

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