FIGURE 2.125 Buckling stress coefficients for uniaxially compressed plate.

Values of k for plates with several different boundary and loading conditions are given in Figure 2.126. Circular Plates

The critical value of the compressive forces Nr uniformly distributed around the edge of a circular plate of radius r0 clamped along the edge (Figure 2.127) can be determined by r2 d2f + ^ df f _ Qr2 dr2 dr D

where f is the angle between the axis of revolution of the plate surface and any normal to the plate, r is the distance of any point from the center of the plate, and Q is the shearing force per unit of length. When there are no lateral forces acting on the plate, the solution of Equation 2.356 involves Bessel function of the first order of the first and second kinds and the resulting critical value of Nr is obtained as

The critical value of Nr for the plate when the edge is simply supported can be obtained in the same way as

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