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10.1 A soil element is subjected to the boundary stresses shown in the figure below. Determine...
10.2 A soil element is subjected to the boundary stresses shown in the following figure. Determine...
10.2 A soil element is subjected to the boundary stresses shown in the following figure. Determine analytically (not graphically) the normal stress Og and the shear stress τθ on the θ plane as identified. Note that only the magnitudes of the shear stress are shown in the figure. Their correct signs will be determined according to the sign convention of Figure 10.2 for the analytical equations.
Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below...
Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude 0,1 = 35 MPa, oyl = 57 MPa, and Tryl = 41 MPa Oy Txy Determine the principal normal stresses 01 and 02, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle...
5, A soil element inside a 20° natural soil slope carries total vertical stress (%) of...
5, A soil element inside a 20° natural soil slope carries total vertical stress (%) of 140 kPa, total horizontal stress (on) of 80 kPa and shear stress (Tvh) of 15 kPa Canticlockwise shear stress on vertical plane). The pore-water pressure (u) inside the element is 30 kPa. The critical state angle of friction of the soil is 30o and its undrained shear strength is 40 kPa. (a) Draw the Mohr's stress circles for this element in terms of total...
(a) If the wide-flange beam shown in Figure Q4a is subjected to a shear of V = 23 kN
(a) If the wide-flange beam shown in Figure Q4a is subjected to a shear of V = 23 kN i. Calculate the moment of inertia of the cross section about the neutral axis.ii. Determine the shear stress on the web at A.(b) The state of stress at a point is shown on the element in Figure Q4b. Determine graphically using Mohr's circle i. The principal stresses. ii. The orientation of the principal planes.iii. The maximum in-plane shear stress and average normal stress at...
Horizontal The stresses shown in the figure are applied at a point in a dry clayey...
Horizontal The stresses shown in the figure are applied at a point in a dry clayey sand soil mass. A- 50 kPa and B-120 kPa The shear strength parameters of the clayey sand are: 8kPa and ф-28° 0-25 a) The value of the shear stress, т, is slowly increased. What value would cause shear failure at the point in kPa? b) At failure what angle in degrees would the failure plane make with the horizontal at the point?
(10 points) The major and minor principal stresses measured in a soil element are equal to 200 and 100 kPa, respectively. The soil is a dry sand with an internal friction angle of 32 degrees and a co...
(10 points) The major and minor principal stresses measured in a soil element are equal to 200 and 100 kPa, respectively. The soil is a dry sand with an internal friction angle of 32 degrees and a cohesion intercept of zero, when the soil will be loaded, additional compressive stress increments of ơs and ơs/4 will be superimposed on σι and σ, respectively. Determine the maximum possible value of ơs such that the shear strength will not be exceeded in...
EXERCISE 7 (10 PTS) (A) Determine the normal and shear stresses acting on the plane for...
EXERCISE 7 (10 PTS) (A) Determine the normal and shear stresses acting on the plane for a - 30°. You are required to use the Pole Method by plotting all your graphical constructions to exact scale Given the stresses acting on an infinitesimal element of soil in the field, as shown below (B) Using the same construction from part (A), determine the major and minor principal stresses, illustrating the orientation of the corresponding planes on which the act (C) Using...
The figure shows an element of soil at the interface between two dry sand layers on a a-32° slope...
The figure shows an element of soil at the interface between two dry sand layers on a a-32° slope The interface is d=7 m below the ground surface and ror both sand layers the friction angle is φ=30, and Ko= 0.41 Assume that the shear stress is zero on both the vertical and horizontal planes. Va1 (dry unit weight of sand layer 1) - 19 kN/m3 Ys2 (dry unit weight of sand layer 2) 20 kN/m Dry Sand (Yai Dry...
4. Shear Strength A sample of cohesive soil with undrained shear strength of 30 Kpa is beng tested in a triaxial est with a confining pressure of 15 Kpa (see the figure below). Sketch the failure...
4. Shear Strength A sample of cohesive soil with undrained shear strength of 30 Kpa is beng tested in a triaxial est with a confining pressure of 15 Kpa (see the figure below). Sketch the failure envelope and Mohr's circle representing the state of stress at failure. Evaluate the following: (i) The vertical axial stress at failure. (ii) The major and minor principal stresses at failure (ii) The orientation of failure plane with respect to horizontal plane. (iv) The normal...
The block diagrams below show states of stress on soil elements. For each state of stress,...
The block diagrams below show states of stress on soil elements.
For each state of stress, perform the following tasks:
1. Sketch a Mohr circle of stress
2. Identify the major and minor principal stresses, σ1 and σ3,
and the maximum shear stress, τmax
3. Compute the mean stress and shear stress invariants, p and q.
Note that p = 1⁄2(σ1+ σ3) and q = σ1-σ3 for two-dimensional stress
conditions where we ignore the intermediate principal stress,
σ2.
4. Identify...
10.2 A soil element is subjected to the boundary stresses shown in the following figure. Determine analytically (not graphically) the normal stress Og and the shear stress τθ on the θ plane as identified. Note that only the magnitudes of the shear stress are shown in the figure. Their correct signs will be determined according to the sign convention of Figure 10.2 for the analytical equations.
Part A - Normal Stresses, Shear, and Angles The stress element shown in the figure below is subjected to the indicated stresses of magnitude 0,1 = 35 MPa, oyl = 57 MPa, and Tryl = 41 MPa Oy Txy Determine the principal normal stresses 01 and 02, the maximum in-plane shear stress Tmax,in-plane, and the angles at which they occur relative to the given stress element. Follow the sign convention. Suppose that when the element is oriented at an angle...
5, A soil element inside a 20° natural soil slope carries total vertical stress (%) of 140 kPa, total horizontal stress (on) of 80 kPa and shear stress (Tvh) of 15 kPa Canticlockwise shear stress on vertical plane). The pore-water pressure (u) inside the element is 30 kPa. The critical state angle of friction of the soil is 30o and its undrained shear strength is 40 kPa. (a) Draw the Mohr's stress circles for this element in terms of total...
Horizontal The stresses shown in the figure are applied at a point in a dry clayey sand soil mass. A- 50 kPa and B-120 kPa The shear strength parameters of the clayey sand are: 8kPa and ф-28° 0-25 a) The value of the shear stress, т, is slowly increased. What value would cause shear failure at the point in kPa? b) At failure what angle in degrees would the failure plane make with the horizontal at the point?
(10 points) The major and minor principal stresses measured in a soil element are equal to 200 and 100 kPa, respectively. The soil is a dry sand with an internal friction angle of 32 degrees and a cohesion intercept of zero, when the soil will be loaded, additional compressive stress increments of ơs and ơs/4 will be superimposed on σι and σ, respectively. Determine the maximum possible value of ơs such that the shear strength will not be exceeded in...
EXERCISE 7 (10 PTS) (A) Determine the normal and shear stresses acting on the plane for a - 30°. You are required to use the Pole Method by plotting all your graphical constructions to exact scale Given the stresses acting on an infinitesimal element of soil in the field, as shown below (B) Using the same construction from part (A), determine the major and minor principal stresses, illustrating the orientation of the corresponding planes on which the act (C) Using...
The figure shows an element of soil at the interface between two dry sand layers on a a-32° slope The interface is d=7 m below the ground surface and ror both sand layers the friction angle is φ=30, and Ko= 0.41 Assume that the shear stress is zero on both the vertical and horizontal planes. Va1 (dry unit weight of sand layer 1) - 19 kN/m3 Ys2 (dry unit weight of sand layer 2) 20 kN/m Dry Sand (Yai Dry...
4. Shear Strength A sample of cohesive soil with undrained shear strength of 30 Kpa is beng tested in a triaxial est with a confining pressure of 15 Kpa (see the figure below). Sketch the failure envelope and Mohr's circle representing the state of stress at failure. Evaluate the following: (i) The vertical axial stress at failure. (ii) The major and minor principal stresses at failure (ii) The orientation of failure plane with respect to horizontal plane. (iv) The normal...
The block diagrams below show states of stress on soil elements.
For each state of stress, perform the following tasks:
1. Sketch a Mohr circle of stress
2. Identify the major and minor principal stresses, σ1 and σ3,
and the maximum shear stress, τmax
3. Compute the mean stress and shear stress invariants, p and q.
Note that p = 1⁄2(σ1+ σ3) and q = σ1-σ3 for two-dimensional stress
conditions where we ignore the intermediate principal stress,
σ2.
4. Identify...
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