Chapter 10, Problem 10.1P

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9th Edition

Braja M. Das + 1 other

ISBN: 9781305970939

Textbook Problem

A soil element is shown in Figure 10.34. Determine the following:

**a.**Maximum and minimum principal stresses**b.**Normal and shear stresses on plane*AB*

Use Eqs. (10.3), (10.4), (10.6), and (10.7).

(a)

To determine

Calculate the maximum and minimum principal stresses.

Answer

The maximum principal stress

The minimum principal stress

Explanation

**Given information:**

The normal stress along *x* axis

The normal stress along *y* axis

The shear stress along *xy* axis

**Calculation:**

Find the horizontal angle as follows:

Calculate the maximum principal stress

Substitute

Hence, the maximum principal stress

Calculate the minimum principal stress

Substitute

Hence, the minimum principal stress

(b)

To determine

Calculate the normal and shear stresses on plane *AB*.

Answer

The normal stress on plane *AB*

The shear stress on plane *AB*

Explanation

**Given information:**

The normal stress along *x* axis

The normal stress along *y* axis

The shear stress along *xy* axis

The angle

**Calculation:**

Calculate the normal stress

Substitute

Hence, the normal stress on plane *AB*

Calculate the shear stress

Substitute

Therefore, the shear stress on plane *AB*

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