The vertical stress z under the corner of a rectangular area subjected to a uniform load

Chapter 17, Problem 17.16

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The vertical stress z under the corner of a rectangular area subjected to a uniform load of intensity q is given by the solution of Boussinesqs equation: = q 4 2mn m2 + n2 + 1 m2 + n2 + 1 + m2n2 m2 + n2 + 2 m2 + n2 + 1 + sin1 2mn m2 + n2 + 1 m2 + n2 + 1 + m2n2 Because this equation is inconvenient to solve manually, it has been reformulated as z = q fz(m, n) where fz(m, n) is called the influence value, and m and n are dimensionless ratios, with m = a/z and n = b/z and a and b are defined in Fig. P17.16. The influence value is then tabulated, a portion of which is given in Table P17.16. If a = 4.6 and b = 14, use a third-order interpolating polynomial to compute z at a depth 10 m below the corner of a rectangular footing that is subject to a total load of 100 t (metric tons). Express your answer in tonnes per square meter. Note that q is equal to the load per area.

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