Three parallel strip footings 3 m wide each and 5 m apart center to center transmit contact pressures of 200, 150 and 100 kN/m^2 respectively. Calculate the vertical stress due to the combined loads beneath the centers of each footing at a depth of 3 m below the base. Assume the footings are placed at a depth of 2 m

Question

Three parallel strip footings 3 m wide each and 5 m apart center to center transmit contact pressures of 200, 150 and 100 [latex]kN / m ^{2}[/latex] respectively. Calculate the vertical stress due to the combined loads beneath the centers of each footing at a depth of 3 m below the base. Assume the footings are placed at a depth of 2 m at a depth of 2 m below the ground surface. Use Boussinesq's method for line loads.

Accepted Answer

From Eq. (6.4), we have

[latex]\sigma_{z}=\frac{q}{z} \frac{2 / \pi}{\left[1+(x / z)^{2} ight]^{2}}=\frac{q}{z} I_{z}[/latex] (6.4)

[latex]\sigma_{z}=\frac{q}{z} \frac{2 / \pi}{\left[1+(x / z)^{2} ight]^{2}}=\frac{q}{z} I_{z}[/latex]

The stress at A (Fig. Ex. 6.4) is

[latex]\left(\sigma_{z} ight)_{A}=\frac{2 imes 200}{3.14 imes 3}\left[\frac{1}{1+(0 / 3)^{2}} ight]^{2}+\frac{2 imes 150}{3.14 imes 3}\left[\frac{1}{1+(5 / 3)^{2}} ight]^{2}[/latex]

[latex]+\frac{2 imes 100}{3.14 imes 3}\left[\frac{1}{1+(10 / 3)^{2}} ight]^{2}=45 kN / m ^{2}[/latex]

The stress at B

[latex]\left(\sigma_{z} ight)_{B}=\frac{2 imes 200}{3 \pi}\left[\frac{1}{1+(5 / 3)^{2}} ight]^{2}+\frac{2 imes 150}{3 \pi}\left[\frac{1}{1+(0 / 3)^{2}} ight]^{2}[/latex]

[latex]+\frac{2 imes 100}{3 \pi}\left[\frac{1}{1+(5 / 3)^{2}} ight]^{2}=36.3 kN / m ^{2}[/latex]

The stress at C

[latex]\left(\sigma_{z} ight)_{C}=\frac{2 imes 200}{3 \pi} \frac{1}{1+(10 / 3)^{2}}^{2}+\frac{2 imes 150}{3 \pi} \frac{1}{1+(5 / 3)^{2}}^{2}+\frac{2 imes 100}{3 \pi}=23.74 kN / m ^{2}[/latex]

Question 6.4: Three parallel strip footings 3 m wide each and 5 m apart ce...

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