The vertical stress z under the corner of a rectangular area subjected to a uniform load of intensity q is given by the solution

The vertical stress σ_z under the corner of a rectangular area subjected to a uniform load of intensity q is given by the solution of Boussinesq’s equation:

Because this equation is inconvenient to solve manually, it has been reformulated as

Σz = qfz (m, n)

Where ƒ_z(m, n) is called the influence value and m and n are dimensionless ratios, with m = α/z and n = b/z and α and b as defined in Figure. The influence value is then tabulated, a portion of

which is given in Table P20.26. If α = 4.6 and b = 14, use a third-order interpolating polynomial to compute σ 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.

2nn /m? +n? +1 m +n? + 2 m2 +n2 +1+ m2n? m2 +n? +1 4T 2mn /m? +n2 +1 m2 + n2 + 1+m2n? + sin-