Superposition of the solution for the half-space uniformly loaded along one axis gives us the solution for a strip of finite width.

**Uniform Loading over a
Finite Width **

Superposition of the
solution for the half-space uniformly loaded along one axis gives us the
solution for a strip of finite width as shown in Figure 8.6. The same result
can also be obtained by integrating the result for a line load (Section 8.1)
over the interval -*b* =< *y *=< *b*.

There are various ways to express the
solution. In Cartesian coordinates:

If we consider principal stresses, the
stress field is particularly simple:

The stress trajectories
are confocal ellipses and hyperbolas having the end points of the strip, *F*_{1},
and *F*_{2}, as foci as shown in Figure 8.6b. Both principal
stresses have constant values along any circle passing through *F*_{1}
and *F*_{2} with its center on the *x* axis (Figure 8.6c).

Moreover, the maximum shear stress has a
maximum where

Although derived from solutions with
ambiguity in the far field, this result is well behaved since every stress
component damps out to the solution for a concentrated line load *P = *2*pb*. We will see later that these results are useful

when we consider slip-line theory to
calculate the collapse load for a uni-formly loaded strip.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

Civil : Principles of Solid Mechanics : Wedges and the Half-Space : Uniform Loading over a Finite Width |

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