GATE CE 2022 Set 2 — Question 32
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Geotechnical Engineering → Stress Distribution in Soils → Boussinesq's Theory
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Question
A concentrically loaded isolated square footing of size carries a concentrated vertical load of . Considering Boussinesq’s theory of stress distribution, the maximum depth (in m) of the pressure bulb corresponding to of the vertical load intensity will be ___________. (round off to two decimal places)
Correct answer
4.35 to 4.39
Solution
1.Calculate the vertical load intensity ():
The load intensity is the total load divided by the area of the footing.2.Determine the stress value for the pressure bulb ():
The pressure bulb corresponds to an isobar where the vertical stress is of the applied load intensity.3.Apply Boussinesq's equation for vertical stress:
For a point load , the vertical stress at depth directly below the load () is given by:Substituting the known values:4.Solve for the maximum depth ():
Rounding to two decimal places, the maximum depth is .Continue learning with Success Tracker
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