PE-09c-Boussinesq

PE-09c-Boussinesq - 220 *Stress01: Stress increase at a...

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Unformatted text preview: 220 *Stress01: Stress increase at a point from several surface point loads. (Revision: Aug-08) Point loads of 2000, 4000, and 6000 lbs act at points A, B and C respectively, as shown below. Determine the increase in vertical stress at a depth of 10 feet below point D. Solution. Using the Boussinesq (1883) table on page 202 for vertical point loads, the vertical increase in stress contributed by each at a depth z =10 feet is found by, ( ) 1 5/2 2 2 2 3 1 2 / 1 z P P p I z z r z & = = + Increase in the load at: P (lbs) r (ft) z (ft) r/z I 1 p (psf) & p from A 2,000 (10 2 +5 2 ) 1/2 = 11.18 10 1.12 0.0626 1.25 & p from B 4,000 (10 2 +5 2 ) 1/2 = 11.18 10 1.12 0.0626 2.50 & p from C 6,000 5 10 0.50 0.2733 16.40 Total = 20.2 psf Therefore, the vertical stress increase at D from the three loads A, B and C is 20.2 psf . A 10 feet B 10 feet C 5 feet D 221 *Stress-02: Find the stress under a rectangular footing. (Revision: Aug-08) Determine the vertical stress increase in a point at a depth of 6 m below the center of the invert of a newly built spread footing, 3 m by 4 m in area, placed on the ground surface carrying a columnar axial load of N = 2,000 kN . Solution: The Boussinesq solution for a rectangular loaded area only admits finding stresses below a corner of the loaded area. Therefore, the footing must be cut so that the load is at a corner (shown as the quarter of the area), where the reduced footing dimensions for the shaded area are B 1 = 1.5 m and L 1 = 2.0 m....
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PE-09c-Boussinesq - 220 *Stress01: Stress increase at a...

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