2.1 A uniformly distributed load ofintensity g 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 g, 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: - 0.58 qalE, -0.221q.0 0.011q, os = 0.004q, e; = 0.214q/E, v; = -0.102q/E, es - -0.112q/E]| 2a v05 2a ww7 100, ? FIGURE P2.1

2.1 A uniformly distributed load ofintensity g 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 g, 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: - 0.58 qalE, -0.221q.0 0.011q, os = 0.004q, e; = 0.214q/E, v; = -0.102q/E, es - -0.112q/E]| 2a v05 2a ww7 100, ? FIGURE P2.1

Elements Of Electromagnetics

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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

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PROBLEMS
2.1 A uniformly distributed load of intensity a 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 g. 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 -
0.011q. os = 0.004q, e; = 0.214q/E, E; = -0.102q/E, e -0.112q/E]|
0.58 qalE, o, 0.221q, o-
2a
v05
2a
FIGURE P2.1

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