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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

Using the principles of Mohr’s circles for the soil element shown in Figure 10.36, determine the following:

a. Maximum and minimum principal stresses

b. Normal and shear stresses on plane AB

images

Figure 10.36

(a)

To determine

Calculate the maximum and minimum principal stresses using the principles of Mohr’s circles.

Explanation

Given information:

The normal stress along x axis (σx) is 36kN/m2.

The normal stress along y axis (σy) is 90kN/m2.

The shear stress along xy axis (τxy) is 21kN/m2.

The plane AB inclined at an angle of 45°.

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.
  • O1 is the point of intersection of the normal stress axis with the line CB.
  • Calculate the stress on plane, by moving an angle 2θ in a counterclockwise direction from the point M along the circumference of the Mohr’s circle to reach point D.
  • The co-ordinate of point Q give the normal stress (σn) and shear stress (τn) on the given plane.
  • The ordinate of point N is the major principal stress (σ1) and ordinate of point S is the minor principal stress (σ3).

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

OO1=σx+σy2

Substitute 36kN/m2 for σx and 90kN/m2 for σy.

OO1=36+902=1262=63kN/m2

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

R=[σyσx2]2+τxy2

Substitute 36kN/m2 for σx, 90kN/m2 for σy, and 21kN/m2 for τxy.

R=[90362]2+(21)2=1,170=34

(b)

To determine

Calculate the normal and shear stresses on plane AB using the principles of Mohr’s circles.

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