A soil element is shown in Figure 10.30. Determine the following:
a) Maximum and minimum principal stresses
b) Normal and shear stresses on the plane AB
Use Equations (10.3), (10.4), (10.6), and (10.7)
Homework Answers
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.
2) The plane state of stresses at a point is as shown in the figure. Using...
2) The plane state of stresses at a point is as shown in the figure. Using the methods of your preference determine 1 ksi a) Principal stresses and maximum in-plane shear and represent them on a triangular element indicating angles and directions. 3 ksi 60° b) The normal and shear stress along plane ab
The state of stress at a point is shown on the element. Determine (a) the stress components acting on the inclined plan...
The state of stress at a point is shown on the element. Determine (a) the stress components acting on the inclined plane AB, (b) the principal stresses, and (c) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case. Sketch the results on each element. 2 ksi 3 ksi 30° 4 ksi
The state of stress at a point is shown on the element. Determine (a) the stress components acting on the inclined plan...
The state of stress at a point is shown on the element. Determine (a) the stress components acting on the inclined plane AB, (b) the principal stresses, and (c) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case. Sketch the results on each element. 2 ksi 3 ksi 30° 4 ksi
3. Figure shows a state of plane stress consists of normal stresses 60 MPa and Ly-40MPa;...
3. Figure shows a state of plane stress consists of normal stresses 60 MPa and Ly-40MPa; and unknown shear stress, The maximum principal stress was determined to be 104.34 MPa. Using Mohr's cirdle, determine a. the magnitude of the shear stress, b. the principal plane and the minimum principal stress. Then, sketch the element showing all stresses in its proper orientation, c. the maximum shear stress, associated normal stress and the orientation of the element. Then, sketch the element showing...
10.1 A soil element is subjected to the boundary stresses shown in the figure below. Determine...
10.1 A soil element is subjected to the boundary stresses shown in the figure below. Determine analytically (not graphically) the normal stress σ, and the shear stress Tg on the θ-plane as identified. Note that only the magni- tudes of the shear stress are shown in the figure. Their correct signs shall be determined according to the sign convention of Figure 10.2 for the analytical equations 40 kPa 20 kPa 20 kPa θ-plane 100 kPa 100 kPa 20 20 kPa...
The stresses on element A are as shown. Using Mohrs circle: a) Determine the stresses on...
The stresses on element A are as shown. Using Mohrs circle: a) Determine the stresses on element B and show these on a sketch of a properly oriented element. b) Determine the principal stresses and show these on a sketch of a properly oriented element. c) Determine the maximum and minimum shear stresses and associated normal stresses and show these on a sketch of a properly oriented element. у Y1 4.0 MPa 2.0 MPa A B 35° 1 1.0 MPa...
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...
a) The state of stress at a point is shown on the element in Figure Q4(a)...
a) The state of stress at a point is shown on the element in Figure Q4(a) Deternine i) The principal stresses (in-plane) and the corresponding principal planes; 1) The maximum in-plane shear stress and the orientation of the corresponding plane as well as the normal stress on that plane. 60 MPa 30 MPa 45 MPa Figure Q4(a)
When an element is oriented such that it is subjected to maximum in-plane shear stress, the...
When an element is oriented such that it is subjected to maximum in-plane shear stress, the element is also subject to: Average normal stress Undefined normal stress O Maximum normal stress O Zero normal stress Question 43 On Mohr's Circle, the sign convention is: O Positive normal stress to the right, positive shear stress down Positive normal stress to the left, positive shear stress up o Positive normal stress to the left, positive shear stress down o Positive normal stress...
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.
2) The plane state of stresses at a point is as shown in the figure. Using the methods of your preference determine 1 ksi a) Principal stresses and maximum in-plane shear and represent them on a triangular element indicating angles and directions. 3 ksi 60° b) The normal and shear stress along plane ab
The state of stress at a point is shown on the element. Determine (a) the stress components acting on the inclined plane AB, (b) the principal stresses, and (c) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case. Sketch the results on each element. 2 ksi 3 ksi 30° 4 ksi
The state of stress at a point is shown on the element. Determine (a) the stress components acting on the inclined plane AB, (b) the principal stresses, and (c) the maximum in-plane shear stress and average normal stress at the point. Specify the orientation of the element in each case. Sketch the results on each element. 2 ksi 3 ksi 30° 4 ksi
3. Figure shows a state of plane stress consists of normal stresses 60 MPa and Ly-40MPa; and unknown shear stress, The maximum principal stress was determined to be 104.34 MPa. Using Mohr's cirdle, determine a. the magnitude of the shear stress, b. the principal plane and the minimum principal stress. Then, sketch the element showing all stresses in its proper orientation, c. the maximum shear stress, associated normal stress and the orientation of the element. Then, sketch the element showing...
10.1 A soil element is subjected to the boundary stresses shown in the figure below. Determine analytically (not graphically) the normal stress σ, and the shear stress Tg on the θ-plane as identified. Note that only the magni- tudes of the shear stress are shown in the figure. Their correct signs shall be determined according to the sign convention of Figure 10.2 for the analytical equations 40 kPa 20 kPa 20 kPa θ-plane 100 kPa 100 kPa 20 20 kPa...
The stresses on element A are as shown. Using Mohrs circle: a) Determine the stresses on element B and show these on a sketch of a properly oriented element. b) Determine the principal stresses and show these on a sketch of a properly oriented element. c) Determine the maximum and minimum shear stresses and associated normal stresses and show these on a sketch of a properly oriented element. у Y1 4.0 MPa 2.0 MPa A B 35° 1 1.0 MPa...
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...
a) The state of stress at a point is shown on the element in Figure Q4(a) Deternine i) The principal stresses (in-plane) and the corresponding principal planes; 1) The maximum in-plane shear stress and the orientation of the corresponding plane as well as the normal stress on that plane. 60 MPa 30 MPa 45 MPa Figure Q4(a)
When an element is oriented such that it is subjected to maximum in-plane shear stress, the element is also subject to: Average normal stress Undefined normal stress O Maximum normal stress O Zero normal stress Question 43 On Mohr's Circle, the sign convention is: O Positive normal stress to the right, positive shear stress down Positive normal stress to the left, positive shear stress up o Positive normal stress to the left, positive shear stress down o Positive normal stress...
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