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Unformatted text preview: iew of Pertinent Engineering Principles Euler Buckling load for Linear Elastic Bars Consider an ideal straight, prismatic bar composed of a linearly elastic material and subjected to an axial compressive load as shown in Figure 4. Figure 4. Pinned Bar under Compressive Load If the bar is ideal, then it will remain straight under all levels of load P . Suppose that the bar is subjected to a slight lateral disturbance as the load is increased from zero. For low levels of axial load, when the disturbance is removed, the bar will return to the straight condition. However, at a certain critical value of the axial load, a slight disturbance will result in very large lateral deflection of the bar and the bar will remain in the deflected condition even though the disturbance is removed. This critical load, called the Euler buckling load, is given by: PCR 2EI L2 (1) where PCR is the maximum load that the bar can sustain without buckling, E is the modulus of Elasticity (Young’s modulus), I is the moment of inertia of the cross section, and L is the length of the bar. For a bar with circular cross section, Equation (1) reduces to PCR EA2 4L2 (2)...
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