Chapter 10, Problem 10.7P

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9th Edition

Braja M. Das + 1 other

ISBN: 9781305970939

Textbook Problem

Point loads of magnitude 125, 250, and 500 kN act at *B*, *C*, and *D*, respectively (Figure 10.40). Determine the increase in vertical stress at a depth of 10 m below the point *A*. Use Boussinesq’s equation.

**Figure 10.40**

To determine

Calculate the increase in vertical stress at a depth of *A* by using Boussinesq’s equation.

Explanation

**Given information:**

The magnitude of load at *B*

The magnitude of load at *C*

The magnitude of load at *D*

The depth below point *A*

**Calculation:**

Calculate the distance *A* using the relation.

Here, *x* is the distance of a point from *A* along *x* axis and *y* is the distance of a point from *A* along *y* axis.

Show the location of points *A*, *B*, *C*, and *D* as in Figure 1.

Refer to Figure 1.

Calculate the distance *B* from *A* as shown below.

Substitute *x* and *y* in Equation (1).

Similarly, calculate the distance

Calculate the ratio

For point *B*,

Substitute *r* and *z*.

Similarly, calculate the ratio

Calculate the value of influence factor

Refer Table 10.1 “Variation of

Take the value of

Similarly, take the value of

Calculate the increase in vertical stress

Calculate the increase in vertical stress *B* as shown below.

Substitute *P*, *z*, and

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