Calculate the maximum and minimum principal stresses using the principles of Mohr’s circles.

Question

Limiting 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…

Answer 1

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Chapter 10, Problem 10.3P

(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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Limiting 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…

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.

I 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 MPa