Elastic Stability of Flexible Columns

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Mechanics of solids

Text of Elastic Stability of Flexible Columns

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Elastic stability of Flexible columnsChapter 9IntroductionA system is said to be in a state of stable equilibrium if, for all possible geometrically admissible small displacements from the equilibrium conditions, restoring forces arise which tend to accelerate the system back toward the equilibrium position.

Elastic stability

The borderline between stability and instability occurs when P=2kL. This value is designated as the critical load or the buckling load.

The equilibrium requirement results from balancing torques in the deformed configuration of Fig. (b).

Examples of Instability

Elastic stability of flexible columns

A truss ABC supports a load W at joint B, as shown in the figure. The length L1 of member AB is fixed, but the length of strut BC varies as the angle is changed. Strut BC has a solid circular cross section. Joint B restrained against displacement perpendicular to the plane of the truss. Assuming the collapse occurs by buckling of the strut, determine the angle for minimum weight of the strut.