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 10.4P
(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.
Subject: Soil Mechanics
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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- 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 08arrow_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_forwardDetermine the average normal stress developed on the cross section as shown inFigure 1.arrow_forward
- 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 ABarrow_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_forwardLimiting states 1. The MC describes the state of stress of our point in the field. That is, the MC shows us the values of the two principal stresses and the value of the maximum shear stress that the point is sustaining in the field. Consider a point in a geostatic soil mass. For our point, o'vo = 100 kPa and o'ho = 40 kPa. Take a sheet of paper and draw the Mohr Circle for this point carefully. 2. Now, we know that o'ho is a principal stress because t = 0 on the vertical plane (in the field). Similarly, o'vo is a principal stress because t = 0 on the horizontal plane (in the field). What is the value of t on the plane inclined 45 degrees clockwise from the horizontal? Go ahead and use your drawn MC to find this value. The value should be t = 30 kPa. 3. Note that the value found (t = 30 kPa) is the maximum shear stress that the point is supporting in the field, as it is under o'v = 100 kPa and o'h = 40 kPa. Consider now a situation in which o'h remains at 40 kPa, but o'y grows to 120…arrow_forward
- Q2 Shown in Figure 1 is the two-dimensional state of stresses at a certain point within a soil mass. Determir the stresses acting on the horizontal and vertical planes passing through that point and show them in a skete 65 kNImarrow_forwardHelp pleasearrow_forwardI want Normal stress developed in segment AB. A homogeneous bar with a cross-sectional area of 400 mm2 is attached to fixed supports as shown inthe figure. It is subjected to lateral forces P1 = 20 kN and P2 = 50 kN. Determine the normal stressdeveloped in segments AB and BC. Answer: σAB = 80.55 MPaarrow_forward
- Question (1) A steel rod of diameter D = 50 mm has a tensile yield strength of 345 MPa supports an axial load P = 50 kN and a vertical load R = 2 kN acting at the end of an 0.8 m long arm. Calculate the strength factor of safety using (a) the maximum normal stress theory, (b) the maximum shear stress theory and (c) the distortion energy theory. y 0.8 m Question (2)arrow_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
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