Limiting states1. The MC describes the state of stress of our point in the field. That is, the MC shows us thevalues of the two principal stresses and the value of the maximum shear stress that thepoint 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 pointcarefully.2. Now, we know that o'ho is a principal stress because t = 0 on the vertical plane (in thefield). 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? Goahead 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 issupporting in the field, as it is under o'v = 100 kPa and o'h = 40 kPa. Consider now asituation in which o'h remains at 40 kPa, but o'y grows to 120 kPa. Draw this new MC onthe same graph you used to draw the MC for item #1 above. If you draw the second MCcorrectly, you will find that the maximum shear stress that the point is supporting is now40 kPa.4. You can now confirm that the maximum shear stress that a point in a geostatic mass feelsis equal to the radius of its MC, which is (o'v-o'h)/2. And so, the maximum shear stressdepends on how different o'v and o'h are. If o'v = o'h, then there is no shear stress felt bythe point (the MC is a point on the MC graph; on the x-axis).5. Neatly redraw the MC you drew earlier for a point with o'y = 100 kPa and o'h = 40 kPa.This time draw the MC in the space below.113

"Since you have posted a question with multiples parts, I will solve first 3 for you as per guideline"ThereforeMohr's circles are drawn in step 3 .And

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Civil Engineering

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.

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.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Solid Mechanics

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

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 kPa. Draw this new MC on
the same graph you used to draw the MC for item #1 above. If you draw the second MC
correctly, you will find that the maximum shear stress that the point is supporting is now
40 kPa.
4. You can now confirm that the maximum shear stress that a point in a geostatic mass feels
is equal to the radius of its MC, which is (o'v-o'h)/2. And so, the maximum shear stress
depends on how different o'v and o'h are. If o'v = o'h, then there is no shear stress felt by
the point (the MC is a point on the MC graph; on the x-axis).
5. Neatly redraw the MC you drew earlier for a point with o'y = 100 kPa and o'h = 40 kPa.
This time draw the MC in the space below.
113

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Step 2: Calculate the centre and radius of Mohr's circle

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Step 3: Draw Mohr's circle diagram

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Step 4: Calculate stresses at 45 degree with horizontal

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