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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

A soil element is shown in Figure 10.38. Using the pole method, determine:

a. Maximum and minimum principal stresses

b. Normal and shear stresses on plane AB

images

Figure 10.38

(a)

To determine

Calculate the maximum and minimum principal stresses using the pole method.

Explanation

Given information:

The normal stress along x axis (σx) is 80kN/m2.

The normal stress along y axis (σy) is 160kN/m2.

The shear stress along xy axis (τxy) is 40kN/m2.

The plane AB inclined at an angle of 27°.

Calculation:

Apply the procedure to construct the Mohr’s circle as shown below.

  • Find the centre of the circle O1 located σx+σy2 from the origin.
  • Find the radius (R) of the Mohr’s circle [σyσx2]2+τxy2.
  • Sketch the Mohr’s circle once R has been determined.
  • Draw a line CP parallel to the plane. Point P is the pole.
  • Draw a line PD parallel to the plane AB. The point of intersection with Mohr’s circle is D.
  • The coordinates of Q give the stresses on the plane AB.

Sketch the Mohr’s circle for the soil element as shown in Figure 1.

Refer to Figure 1.

Calculate the centre of the Mohr’s circle from the origin (OO1) as shown below.

OO1=σx+σy2

Substitute 80kN/m2 for σx and 160kN/m2 for σy.

OO1=80+1602=2402=120kN/m2

Calculate the radius (R) Mohr’s circle as shown below.

R=[σyσx2]2+τxy2

Substitute 80kN/m2 for σx, 160kN/m2 for σy, and 40kN/m2 for τxy

(b)

To determine

Calculate the normal and shear stresses on plane AB using the pole method.

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