(2) A double clamped beam is shown in Figure 1. The distance between the clamps is...

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(2) A double clamped beam is shown in Figure 1. The distance between the clamps is L. The beam has cross-sectional area moment of inertia, I, cross-sectional area, A, and Young's modulus, E. Take the x-coordinate coincident with the neutral axis of the beam in its undeformed configuration, and the origin at the axial center of the undeformed beam. The vertical displacement is denoted as, w = w(x) and the clamped ends require that w(+L/2) = 0 and w'(L/2) = 0. The beam is placed in a uniaxial compression such that there is an initial compressive force of Po carried along the neutral axis of the beam. Use von Krmn beam theory to show that the buckling force is |Pc| = 4(/L)EI. Since both Po and P are compressive and assuming that [Po| > |Pc|, show that the amplitude, 8= w(x = 0), of the post-buckling behavior can be approximated as d = 4 [R-1]/. y L FIGURE 1. Schematic diagram of buckled double clamped beam. (2) A double clamped beam is shown in Figure 1. The distance between the clamps is L. The beam has cross-sectional area moment of inertia, I, cross-sectional area, A, and Young's modulus, E. Take the x-coordinate coincident with the neutral axis of the beam in its undeformed configuration, and the origin at the axial center of the undeformed beam. The vertical displacement is denoted as, w = w(x) and the clamped ends require that w(+L/2) = 0 and w'(L/2) = 0. The beam is placed in a uniaxial compression such that there is an initial compressive force of Po carried along the neutral axis of the beam. Use von Krmn beam theory to show that the buckling force is |Pc| = 4(/L)EI. Since both Po and P are compressive and assuming that [Po| > |Pc|, show that the amplitude, 8= w(x = 0), of the post-buckling behavior can be approximated as d = 4 [R-1]/. y L FIGURE 1. Schematic diagram of buckled double clamped beam.