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Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939

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BuyFindarrow_forward

Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

Repeat Problem 10.1 for the element shown in Figure 10.35.

10.1 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).

images

Figure 10.35

(a)

To determine

Calculate the maximum and minimum principal stresses.

Explanation

Given information:

The normal stress along x axis (σx) is 2,193lb/ft2.

The normal stress along y axis (σy) is 3,906lb/ft2.

The shear stress along xy axis (τxy) is 919lb/ft2.

The angle (θ) is 168°.

Calculation:

Calculate the maximum principal stress (σ1) using the relation.

σ1=σy+σx2+[σy+σx2]2+τxy2

Substitute 2,193lb/ft2 for σx, 3,906lb/ft2 for σy, and 919lb/ft2 for τxy.

σ1=3,906+2,1932+[3,9062,1932]2+9192=3,049.5+1,578,153.25=3,049.5+1,256.25=4,305

(b)

To determine

Calculate the normal and shear stresses on plane AB.

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