Fig. 8.39. Concentrated load on a semi-infinite plate.

Consider a force P per unit width of the plate applied as a line load normal to the surface - see Fig. 8.39. The plate will be considered as equivalent to a semi-infinite solid, that is, one that extends to infinity in the x and y directions below the horizon, 9 = ±f. The plate is assumed to be of unit width. It is convenient to use cylindrical polars again for this problem.

Using Boussinesq's solutions^ for a semi-infinite body, Alfred-Aimé Flamant obtained (in 1892)^the stress distribution for the present case. He showed that on any semi-circumference round the load point the stress is entirely radial, that is: age = x^ = 0 and arr will be a principal stress. He used a stress function of the type given in eqn. (8.110), namely: (p = Cr6smd which predicts stresses:

0 0

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