001 Buckling Loads and Shape Modes of Rigid Element, Translational 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 transitional 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. If the undrained shear strength of soil is 10𝑘𝑃𝑎, determine the buckling load numerically.
5. For three Circular Hollow Sections (CHS), determine the Euler buckling load and check which buckling mode would occur first.
6. Model the system in FEM software and compare your results.

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