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## Chapter: Civil : Principles of Solid Mechanics : Wedges and the Half-Space

Superposition of the solution for the half-space uniformly loaded along one axis gives us the solution for a strip of 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 =< =< 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, F1, and F2, as foci as shown in Figure 8.6b. Both principal stresses have constant values along any circle passing through F1 and F2 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 = 2pb. 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.

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

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