Loading on an elastic half space:

Line loading

Here we will discuss the stresses and deformations on an elastic half space loaded one dimensionally over a strip.

Consider normal and shear loading of the elastic half space under plane strain conditions. Stress equilibrium relation under plane strain approximation:

(4.1)

where the normal and shear stress components are related to the shear stresses as:

(4.2)

Conversely, the strain components in terms of stresses are written as:

(4.3)