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 at a depth of 2 m below the ground surface. Use Boussinesq’s method for line loads.
Question 6.4: Three parallel strip footings 3 m wide each and 5 m apart ce...
From Eq. (6.4), we have
\sigma_{z}=\frac{q}{z} \frac{2 / \pi}{\left[1+(x / z)^{2}\right]^{2}}=\frac{q}{z} I_{z} (6.4)
\sigma_{z}=\frac{q}{z} \frac{2 / \pi}{\left[1+(x / z)^{2}\right]^{2}}=\frac{q}{z} I_{z}
The stress at A (Fig. Ex. 6.4) is
\left(\sigma_{z}\right)_{A}=\frac{2 \times 200}{3.14 \times 3}\left[\frac{1}{1+(0 / 3)^{2}}\right]^{2}+\frac{2 \times 150}{3.14 \times 3}\left[\frac{1}{1+(5 / 3)^{2}}\right]^{2}
+\frac{2 \times 100}{3.14 \times 3}\left[\frac{1}{1+(10 / 3)^{2}}\right]^{2}=45 kN / m ^{2}
The stress at B
\left(\sigma_{z}\right)_{B}=\frac{2 \times 200}{3 \pi}\left[\frac{1}{1+(5 / 3)^{2}}\right]^{2}+\frac{2 \times 150}{3 \pi}\left[\frac{1}{1+(0 / 3)^{2}}\right]^{2}
+\frac{2 \times 100}{3 \pi}\left[\frac{1}{1+(5 / 3)^{2}}\right]^{2}=36.3 kN / m ^{2}
The stress at C
\left(\sigma_{z}\right)_{C}=\frac{2 \times 200}{3 \pi} \frac{1}{1+(10 / 3)^{2}}^{2}+\frac{2 \times 150}{3 \pi} \frac{1}{1+(5 / 3)^{2}}^{2}+\frac{2 \times 100}{3 \pi}=23.74 kN / m ^{2}
Related Answered Questions
From Eq. (6.la) we have
I_{B}=\text ...
(a) Boussinesq Eq. (6.la)
I_{B}=\tex...
Equations (a) Boussinesq: \sigma_{z}=\frac{...
Rectangles are constructed as shown in [Fig. 6.9(b...
Divide the rectangle 12 x 30 m into four equal par...
q=325 kN / m ^{2}, R_{0}=8 m. The r...