Holooly Plus Logo
Holooly Plus Logo

Question 6.12: A single concentrated load of 1000 kN acts at the ground sur...

A single concentrated load of 1000 kN acts at the ground surface. Construct an isobar for \sigma_{z}=40 kN / m ^{2} by making use of the Boussinesq equation.

The Blue Check Mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

From Eq. (6.la) we have

 

I_{B}=\text { Boussinesq stress coefficient }=\frac{3}{2 \pi} \frac{1}{\left[1+(r / z)^{2}\right]^{5 / 2}} (6.1a)

 

\sigma_{z}=\frac{3 Q}{2 \pi z^{2}}\left[\frac{1}{1+(r / z)^{2}}\right]^{5 / 2}

 

We may now write by rearranging an equation for the radial distance r as

 

r=\sqrt{z} \sqrt{\frac{3 Q}{2 \pi z^{2} \sigma_{z}}^{2 / 5}-1}

 

Now for Q=1000 kN , \sigma_{z}=40 kN / m ^{2}, \text { we obtain the values of } r_{1}, r_{2}, r_{3}, etc. for different depths z_{1}, z_{2}, z_{3}, etc. The values so obtained are

 

z(m) r(m)
0.25 1.34
0.5 1.36
1.0 1.30
2.0 1.04
3.0 0.60
3.455 0.00

 

The isobar for \sigma_{z}=40 kN / m ^{2} may be obtained by plotting z against r as shown in Fig. Ex. 6.12.

6.12

Related Answered Questions

A raft foundation of the size given in Fig. Ex. 6.10 carries a uniformly distributed load of 300 kN/m^2. Estimate the vertical pressure at a depth 9 m below the point O marked in the figure.

Verified Answer:
The depth at which \sigma_{z} requi...

A 3 m high embankment is to be constructed as shown in Fig. Ex. 6. 11. If the unit weight of soil used in the embankment is 19.0 kN/m^3, calculate the vertical stress due to the embankment loading at points P1, P2, and P3.

Verified Answer:
q=\gamma H=19 \times 3=57 kN / m ^{2}, z=3 ...

A concentrated load of 1000 kN is applied at the ground surface. Compute the vertical pressure (i) at a depth of 4 m below the load, (ii) at a distance of 3 m at the same depth. Use Boussinesq’s equation.

Verified Answer:
The equation is   \sigma_{z}=\frac{Q}{...

A concentrated load of 45000 Ib acts at foundation level at a depth of 6.56 ft below ground surface. Find the vertical stress along the axis of the load at a depth of 32.8 ft and at a radial distance of 16.4 ft at the same depth by (a) Boussinesq, and (b) Westergaard formulae for μ = 0. Neglect the

Verified Answer:
(a) Boussinesq Eq. (6.la)   I_{B}=\tex...

A rectangular raft of size 30 x 12 m founded at a depth of 2.5 m below the ground surface is subjected to a uniform pressure of 150 kPa. Assume the center of the area is the origin of coordinates (0, 0). and the corners have coordinates (6, 15). Calculate stresses at a depth of 20 m below the

Verified Answer:
Equations (a) Boussinesq: \sigma_{z}=\frac{...

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

Verified Answer:
From Eq. (6.4), we have   \sigma_{z}=\...

ABCD is a raft foundation of a multi-story building [Fig. 6. 9(b)] wherein AB = 65.6 ft, and BC = 39.6 ft. The uniformly distributed load q over the raft is 73 10 lb/ft^2. Determine σz at a depth of 19.7 ft below point O [Fig. 6.9(b)] wherein AA1 = 13.12 ft and A1O = 19.68 ft. Use Fig. 6.8.

Verified Answer:
Rectangles are constructed as shown in [Fig. 6.9(b...

A rectangular raft of size 30 x 12 m founded on the ground surface is subjected to a uniform pressure of 150 kN/m^2. Assume the center of the area as the origin of coordinates (0,0), and corners with coordinates (6, 15). Calculate the induced stress at a depth of 20 m by the exact method at

Verified Answer:
Divide the rectangle 12 x 30 m into four equal par...

A water tank is required to be constructed with a circular foundation having a diameter of 16 m founded at a depth of 2 m below the ground surface. The estimated distributed load on the foundation is 325 kN/m^2. Assuming that the subsoil extends to a great depth and is isotropic and homogeneous,

Verified Answer:
q=325 kN / m ^{2}, R_{0}=8 m. The r...

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.

Verified Answer:
The radius of a fictitious circular footing of are...