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Question 6.8: For a raft of size 98.4 x 39.36 ft, compute the stress at 65...

For a raft of size 98.4 x 39.36 ft, compute the stress at 65.6 ft depth below the center of the raft by assuming that the rectangle can be represented by an equivalent circle. The load intensity on the raft is 3133 lb / ft ^{2}.

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The radius of a fictitious circular footing of area equal to the rectangular footing of size 98.4 x 39.36 ft is

 

\pi R_{0}^{2}=98.4 \times 39.36=3873 \text { sq. } ft \text { or } R_{0}=\sqrt{\frac{3873}{\pi}}=35.12 ft

 

Use Eq. (6.21) for computing \sigma_{z} at 35.6 ft depth

 

\sigma_{z} / q=1-\left[\frac{1}{1+\left(R_{0} / z\right)^{2}}\right]^{3 / 2}=I_{z} (6.21)

 

Now, z / R_{0}=\frac{65.6}{35.12}=1.9, \text { and } r / R_{0}=0 . \text { From Fig. } 6.11, I_{2}=0.3

 

Therefore, \sigma_{z}=0.3 q=0.3 \times 3133=940 lb / ft ^{2}.

6.7

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