A uniformly distributed load of intensity q is applied through a circular area of radius a...
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A uniformly distributed load of intensity q is applied through a circular area of radius a on the surface of an incompressible (v = 0.5) homogeneous half-space with an elastic modu- lus E, as shown in Figure P2.1. In terms of q, a, and E, determine the vertical displacement, three principal stresses, and three principal strains at a point 2a below the surface under the edge (r = a) of the loaded area. [Answer: w = 0.58 qal E, o1 = 0.221q, o2 = 0.011q, o3 = 0.004q, ɛ1 = 0.214q/E, E2 = -0.102q/E, ɛ3 = -0.112q/E] %3D %3D %3D %3D %3D 2a E v = 0.5 2a w = ? 01, 02, 03, = ? 81, 82, E3, = ? FIGURE P2.1 A uniformly distributed load of intensity q is applied through a circular area of radius a on the surface of an incompressible (v = 0.5) homogeneous half-space with an elastic modu- lus E, as shown in Figure P2.1. In terms of q, a, and E, determine the vertical displacement, three principal stresses, and three principal strains at a point 2a below the surface under the edge (r = a) of the loaded area. [Answer: w = 0.58 qal E, o1 = 0.221q, o2 = 0.011q, o3 = 0.004q, ɛ1 = 0.214q/E, E2 = -0.102q/E, ɛ3 = -0.112q/E] %3D %3D %3D %3D %3D 2a E v = 0.5 2a w = ? 01, 02, 03, = ? 81, 82, E3, = ? FIGURE P2.1
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