Concept explainers
(a)
Calculate the maximum and minimum principal stresses.
(a)
Answer to Problem 10.1P
The maximum principal stress
The minimum principal stress
Explanation of Solution
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)
Calculate the normal and shear stresses on plane AB.
(b)
Answer to Problem 10.1P
The normal stress on plane AB
The shear stress on plane AB
Explanation of Solution
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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Chapter 10 Solutions
MindTap Engineering for Das/Sobhan's Principles of Geotechnical Engineering, 9th Edition, [Instant Access], 2 terms (12 months)
- A soil element is shown in the figure below. Determine the following: (in kPa) a. Maximum Principal Stress b. Minimum Principal Stress c. Normal Stress on plane AB d. Shear Stress on plane ABarrow_forwardA soil element is shown in the figure below.  Determine the following: (in kPa) a. Maximum and Minimum Principal Stress c. Normal Stress and Shear Stress on plane ABarrow_forwardRefer to Figure 10.46. A flexible circular area of radius 6 m is uniformly loaded. Given: q = 565 kN/m2. Using Newmarks chart, determine the increase in vertical stress, z, at point A. Figure 10.46arrow_forward
- Use Eq. (6.14) to determine the stress increase () at z = 10 ft below the center of the area described in Problem 6.5. 6.5 Refer to Figure 6.6, which shows a flexible rectangular area. Given: B1 = 4 ft, B2 = 6 ft, L1, = 8 ft, and L2 = 10 ft. If the area is subjected to a uniform load of 3000 lb/ft2, determine the stress increase at a depth of 10 ft located immediately below point O. Figure 6.6 Stress below any point of a loaded flexible rectangular areaarrow_forwardFor the stress soil element shown, determine the following using the Pole Method. A. The major principal stress B.The minor principal stress C. Normal stress on plane AE D. Shear stress on plane AEarrow_forwardA soil element is shown in the figure. Determine the following: 300 psf 1. a. Maximum and minimum principal stresses b. Normal and shear stresses on plane AB 250 psf 80 psf A + 35⁰ + B 80 psfarrow_forward
- 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 Aarrow_forwardUse Eq. (6.14) to determine the stress increase Δσ at z = 10 ft below the center of the area described in Problem 6.5.arrow_forwardStresses acting on an infinitesimal soil element are shown in the figure (with o₂ > 0). The major and minor principal stresses are o, and o3, respectively. Considering the compressive stresses as positive, which one of the following expressions correctly represents the angle between the major principal stress plane and the horizontal plane? ox Tzx ·0xarrow_forward
- 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. Barrow_forward8. The following figure consists of a line load and point load acting on the surface of a soil mass X1=4.5 m X2=3.5 m r2 Y2=2.5 m Line load 50 kN/m Z= 6m Point load 100 kN A Calculate the increase in the vertical stress at the soil element A.arrow_forward6. A cylindrical sample of soil is iso-tropically compressed at 150 KPa under drained condition. Subsequently, the axial stress was held constant and the radial stress was increased to 300 kPa under an undrained condition. (a) Calculate the initial mean effective stress and deviatoric stress. Create a graph with the x-axis as p, p' and the y-axis as q (p, q space). Plot these values in (p, ) space. (b) Calculate the increase in mean total stress and deviatoric stress. (c) Plot the total and effective stress paths (assume the soil is a linear, isotropic, elastic material). (d) Determine the slopes of the total and effective stress paths and the maximum excess porewater pressure for each space.arrow_forward
- Principles of Geotechnical Engineering (MindTap C...Civil EngineeringISBN:9781305970939Author:Braja M. Das, Khaled SobhanPublisher:Cengage LearningPrinciples of Foundation Engineering (MindTap Cou...Civil EngineeringISBN:9781305081550Author:Braja M. DasPublisher:Cengage Learning