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Question

Consider a square-shaped area ABCD on the ground with this centre at M as shown in the figure. Four concentrated vertical loads of P = 5000 kN are applied on this area, one at each corner.


The vertical stress increment (in kPa up to one decimal place) due to these loads according to the Boussinesq's equation at a point 5m right below M is
  1. 190.84

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Solution

The correct option is A 190.84
Due to one corner load

σz=3P2πz2⎜ ⎜ ⎜11+(rz)2⎟ ⎟ ⎟5/2

r=22+22=22m

z = 5 m

P = 5000 kN

σz=3×50002π×52⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢11+(225)2⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥5/2

=47.709kN/m2

So due to four load vertical stress

=4σz

=4× 47.709

=190.84kN/m2


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