Principles of Geotechnical Engineering (MindTap Course List)
9th Edition
ISBN: 9781305970939
Author: Braja M. Das, Khaled Sobhan
Publisher: Cengage Learning
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Chapter 10, Problem 10.5P
(a)
To determine
Calculate the maximum and minimum principal stresses using the pole method.
(b)
To determine
Calculate the normal and shear stresses on plane AB using the pole method.
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A soil element is shown in the figure. Determine the following
Major principal stress
Minor principal stress
Normal stress on plane AB
Shear stress on plane AB
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
A soil element is shown in Figure 10.38. Using the pole meathod, determine:
a. Maximum and minimum principle stresses.
b. Normal and shear stresses on plane AB
Solve this problem three ways: first via equations, second via Mohr’s circle and the two-theta method, and third via Mohr’s circle and the origin of planes. All methods should give the same answer.
Chapter 10 Solutions
Principles of Geotechnical Engineering (MindTap Course List)
Ch. 10 - Prob. 10.1PCh. 10 - Prob. 10.2PCh. 10 - Prob. 10.3PCh. 10 - Prob. 10.4PCh. 10 - Prob. 10.5PCh. 10 - Prob. 10.6PCh. 10 - Point loads of magnitude 125, 250, and 500 kN act...Ch. 10 - Refer to Figure 10.41. Determine the vertical...Ch. 10 - For the same line loads given in Problem 10.8,...Ch. 10 - Refer to Figure 10.41. Given: q2 = 3800 lb/ft, x1...
Ch. 10 - Refer to Figure 10.42. Due to application of line...Ch. 10 - Refer to Figure 10.43. A strip load of q = 1450...Ch. 10 - Repeat Problem 10.12 for q = 700 kN/m2, B = 8 m,...Ch. 10 - Prob. 10.14PCh. 10 - For the embankment shown in Figure 10.45,...Ch. 10 - Refer to Figure 10.46. A flexible circular area of...Ch. 10 - Refer to Figure 10.47. A flexible rectangular area...Ch. 10 - Refer to the flexible loaded rectangular area...Ch. 10 - Prob. 10.19PCh. 10 - Prob. 10.20PCh. 10 - Refer to Figure 10.48. If R = 4 m and hw = height...Ch. 10 - Refer to Figure 10.49. For the linearly increasing...Ch. 10 - EB and FG are two planes inside a soil element...Ch. 10 - A soil element beneath a pave ment experiences...
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- Refer 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_forwardRefer to Figure 10.43. A strip load of q = 1450 lb/ft2 is applied over a width with B = 48 ft. Determine the increase in vertical stress at point A located z = 21 ft below the surface. Given x = 28.8 ft. Figure 10.43arrow_forwardRead the question carefully and give me right solution according to the question. Please don't miss anything. Thank youarrow_forward
- A 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_forwardSoil sample size is (21cm×21cm)arrow_forward7. A soil element is subjected to a combination of normal and shear stresses, as shown in the following figure. The corresponding Mohr's circle of stress is provided, and some points (with Coordinates) and lines are added to assist you. Complete the following 1) Which point represents the normal and shear stresses on the horizontal plane PQ? 2) Which point represents the normal and shear stresses on the vertical plane QN? 3) Which point represents the pole of this Mohr circle? 4) Which point represents the normal and shear stresses on plane MN? 5) Which point represents the major principal stress? 6) Which point represents the minor principal stress? Note: all dashed lines are parallel to each other with the inclination angle given. b(72, 40) 40 a(112, 40) 457 30 112 kPa c(52,20) j(132,20) 20 40 kPa - P. 10 M 七 d(47,0) i(137,0) to 72 kPa -10 40 kPa e(52,-20) h(132,-20) 45 -20 -30 -40 g(112,-40) A72,-40) 90 100 110 120 130 140 150 30 40 50 60 70 80 Normal Stress, kPa Shear Stress, kPaarrow_forward
- ELABORATE Try solving the following problem: Practice Problem: Refer to Figure 3.12. Determine the vertical stress increase Aoz, at point A with the following values: q = 75 lb/ft; x = 6 ft; z = 5 ft. STAR Line load = q Figure 3.12 Aσ₂arrow_forwardkN 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_forwardQ.1 The state of stress at a point in a soil mass is eiven below, Determine the principal stresses and also the octahedral normal and shear stresses. 50 30 25 Stress state (soil) 30 40 25 kPa 25 25 08arrow_forward
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