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MindTap Engineering for Das/Sobhan's Principles of Geotechnical Engineering, 9th Edition, [Instant Access], 2 terms (12 months)
9th Edition
ISBN: 9781305971257
Author: Braja M. Das; Khaled Sobhan
Publisher: Cengage Learning US
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Chapter 10, Problem 10.4P
(a)
To determine
Calculate the maximum and minimum principal stresses using the principles of Mohr’s circles.
(b)
To determine
Calculate the normal and shear stresses on plane AB using the principles of Mohr’s circles.
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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
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.
Q.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
08
Chapter 10 Solutions
MindTap Engineering for Das/Sobhan's Principles of Geotechnical Engineering, 9th Edition, [Instant Access], 2 terms (12 months)
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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- 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_forwardSoil sample size is (21cm×21cm)arrow_forwardA 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 ABarrow_forward
- Do not give answer in image and hand writingarrow_forwardA 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.arrow_forwardHelp pleasearrow_forward
- A thin layer of clay subjected to drying develops internal shrinkage stresses. The state of effective stress at a point in this layer is shown in the figure (a) below. Plane stress condition can be assumed for this problem. Elastic modulus, E of clay is 15 MPa and Poisson's ratio, v is 0.35. Hooke's law is valid during drying, meaning that (o,- vo,) *3 where s,is the strain in x direction. 12 kPa 19 kPa Tx1y1 46 kPa 15° (a) Before curling (b) After curlingarrow_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_forwardN B 0 Horizontal The stresses shown in the figure are applied at a point in a dry clayey sand soil mass. A= 50 kPa and B= 125 kPa The shear strength parameters of the clayey sand are: c'= 9kPa and p'=29° 0=30° a) The value of the shear stress, T, is slowly increased. What value would cause shear failure at this point (in kPa)? b) At failure, what angle does the failure plane make with the horizontal (in degrees)?arrow_forward
- The vertical and horizontal stresses at a certain point in soil are as follows:σx = 50 kPaσx = 100 kPaτzx = - 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.arrow_forwardi need the answer quicklyarrow_forwardShow solution. The answer must be A. 36.87 B. 14arrow_forward
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