Lecture 3 - S 13 Rectangular Surface Loads: (Boussinesq...

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13 S Rectangular Surface Loads: (Boussinesq solution - the "mn" method)) o This method determines the vertical stress Δσ v at a point P under the corner of a rectangular loaded area using footing dimensions normalized to the depth z: m = B/z n = L/z (note that m and n are interchangeable in the formula) + + + + + + + + + + + π × = × = σ Δ - 1 n m n m mn sin 1 n m 2 n m 1 n m n m mn 2 1 q I q 2 2 2 2 1 2 2 2 2 2 2 2 2 v The sin -1 quantity is calculated in radians (not degrees) . o Fortunately the above formula is also presented in both charts (handout) and tables (Das). o Example 1: Find the stress increase beneath the footing corner (P) at a depth of 6 ft. m = B/z = 3/6 = 0.5 n = L/z = 6/6 = 1.0 Go to chart, find I 0.122 Δσ v = 0.122 (1000 psf) = 122 psf o The integration of the Boussinesq point formula over various loaded areas implies that the influence of a one given load does not affect another. This works because the soil is assumed to be linear elastic, and therefore the effects may be “ superposed”. Superposition may be carried further and used to superpose entire loaded areas – say two
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This note was uploaded on 09/12/2011 for the course CEG 4012 taught by Professor Staff during the Fall '08 term at University of Florida.

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Lecture 3 - S 13 Rectangular Surface Loads: (Boussinesq...

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