The vertical and horizontal stresses at a certain point in soil are as follows: σx = 50 kPa σx = 100 kPa τzx = - 20 kPa a) Determine magnitudes and directions of the major and minor principal stresses. b) Determine magnitude and direction of maximum shear stress. c) Determine the normal and shear stresses acting on a soil element inclined at 60 clockwise from the horizontal plane.

The vertical and horizontal stresses at a certain point in soil are as follows: σx = 50 kPa σx = 100 kPa τzx = - 20 kPa a) Determine magnitudes and directions of the major and minor principal stresses. b) Determine magnitude and direction of maximum shear stress. c) Determine the normal and shear stresses acting on a soil element inclined at 60 clockwise from the horizontal plane.

Principles of Geotechnical Engineering (MindTap Course List)

9th Edition

ISBN:9781305970939

Author:Braja M. Das, Khaled Sobhan

Publisher:Braja M. Das, Khaled Sobhan

Chapter10: Stresses In A Soil Mass

Section: Chapter Questions

Problem 10.2P

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The normal stresses acting on two orthogonal planes of a soil sample are 250 kN/m2 and 110 kN/m2 a. Major principal stress b. Minor principal stress c. Normal stress on a plane inclined 60° to the direction of the major principal stress d. Shear stress on a plane inclined 60° to the direction of the major principal stress
kN The magnitude of stresses of the soil element represented by the figure below are o, = 250; m Oy = 180 , and t= 80, m2 kN kN ,and 0 = 25°, determine the following: a. Magnitudes of the principal stresses. b. Normal stress on plane AB. c. Shear stress on plane AB. B
PROBLEM 2 (15 points): The magnitude of stresses of the soil element represented by the figure below are oz = 250 kN and t= 80 kN m² Oy = 180- , and 0 = 25°, determine the following: m2 a. Magnitudes of the principal stresses. b. Normal stress on plane AB. c. Shear stress on plane AB. B A
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Subject: Soil Mechanics
3 1. (a) An element of soil is subjected to the two-dimensional stresses shown in Figure Q1. 0, = 150 =-30 = 30 60° o, = 75 (All in kPa) Figure Q1 (1) Determine the normal and shear stresses on the P and Q planes which are orthogonal (ii) Determine the magnitudes and directions of the major and minor principal stresse (b) An undrained direct shear test with a hanger mass of 32 kg was performed on a sample of saturated clay. The plan dimensions of the shear box were 60 x 60 mm. The undrained shear strength of the clay is known to be Cu = 60 kPa. The critical state friction angle of the clay is known to be d'ern = 22°. What pore water pressure (u) in kPa, would the sample experience at the ultimate state? (c) Given that the pore pressure calculated from part (b) was negative, explain what this implies about the volume change that would have occurred to the sample (dilative or contractive) if the test was done under drained conditions.
a.What is the value of the maximum stress in kPa? b.What is the value of the normal stress acting at the plane AB in kPa? c.What is the value of the shear stress acting at the plane AB in kPa?
A soil specimen (100 mm × 100 mm × 100 mm) is subjected to the forces shown in Figure below. Determine (a) the magnitude of the principal stresses, (b) the orientation of the principal stress plane to the horizontal, (c) the maximum shear stress, and (d) the normal and shear stresses on a plane inclined at 208 clockwise to the horizontal. 8 kN 2 kN 12 kN 4 kN
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Soil sample size is (21cm×21cm)
2. The state plane stress in a mass of dense cohesionless sand (c=0) is described by the following stresses: Normal stress on horizontal plane = 100 kPa Normal stress on vertical plane = 50 kPa Shear stress on horizontal and vertical planes = ± 30 kPa Determine by means of the Mohr circle the magnitude and direction of the principal stresses. Is this state of stress safe against failure assuming φ= 30o?