Concept explainers
Repeat Prob. 3–15 for:
(a) σx = 28 MPa, σy = 7 MPa, τxy = 6 MPa cw
(b) σx = 9 MPa, σy = –6 MPa, τxy = 3 MPa cw
(c) σx = –4 MPa, σy = 12 MPa, τxy = 7 MPa ccw
(d) σx = 6 MPa, σy = –5 MPa, τxy = 8 MPa ccw
(a)
The principle normal stress.
The shear stress.
The angle from
Answer to Problem 16P
The principle normal stress
The shear stress is
The angle from
Explanation of Solution
Write the coordinates of the points through which the Mohr’s circle pass.
Here, the stress along x face is
Draw the
Write the formula for the center point.
Here, the center point is
Write the expression for the angle between the line joining points A and B with
Here, the angle made by the diameter with positive x-axis in the counterclockwise direction is
Write the expression of the radius of circle.
Write the expression maximum in plane normal stress.
Here, the maximum in plane normal stress are
Write the expression of maximum in plane shear stress.
Here, the maximum shear stress is
Write the expression for the angle of maximum shear plane.
Here, the angle is
Conclusion:
Substitute the value
Draw the Mohr’s circle diagram.
The Figure (1) shows the Mohr’s circle diagram.
Figure (1)
Substitute the value
Substitute the value
Thus, the angle from
Substitute the value
Substitute the value
Thus, the principle normal stress
Substitute the value
Thus, the principle normal stress
Substitute the value
Thus, the shear stress is
Substitute the value
The Figure (2) shows the maximum in plane normal stress distribution about the plane.
Figure (2)
The Figure (3) shows stress distribution at maximum shear stress plane.
Figure (3)
(b)
The principle normal stress.
The shear stress.
The angle from
Answer to Problem 16P
The principle normal stress
The shear stress is
The angle from
Explanation of Solution
Write the coordinates of the points through which the Mohr’s circle pass.
Draw the
Write the formula for the center point.
Write the expression for the angle between the line joining points A and B with
Write the expression of the radius of circle.
Write the expression maximum in plane normal stress.
Write the expression of maximum in plane shear stress.
Write the expression for the angle of maximum shear plane.
Write the expression for the angle between the line joining points A and B with
Conclusion:
Substitute
Substitute
Draw the Mohr’s circle diagram.
The Figure (4) shows the Mohr’s circle diagram.
Figure (4)
Substitute the value
Substitute the value
Thus, the angle from
Substitute the value
Substitute
Thus, the principle normal stress
Substitute
Thus, the principle normal stress
Substitute the value
Thus, the shear stress is
Substitute the value
The Figure (5) shows the maximum in plane normal stress distribution about the plane.
Figure (5)
The Figure (6) shows stress distribution at maximum shear stress plane.
Figure (6)
Thus, the principle normal stress
(c)
The principle normal stress.
The shear stress.
The angle from
Answer to Problem 16P
The principle normal stress
The shear stress is
The angle from
Explanation of Solution
Write the coordinates of the points through which the Mohr’s circle pass.
Draw the
Write the formula for the center point.
Write the expression for the angle between the line joining points A and B with
Write the expression of the radius of circle.
Write the expression maximum in plane normal stress.
Write the expression of maximum in plane shear stress.
Write the expression for the angle of maximum shear plane.
Conclusion:
Substitute the value
Substitute
Draw the Mohr’s circle diagram.
Figure (7) shows the Mohr’s circle diagram.
Figure (7)
Substitute the value
Substitute the value
Substitute the value
Substitute the value
Substitute the value
Substitute the value
Substitute the value
The Figure (8) shows the maximum in plane normal stress distribution about the plane.
Figure (8)
The Figure (9) shows stress distribution at maximum shear stress plane.
Figure (9)
Thus, the he principle normal stress
(d)
The principle normal stress.
The shear stress.
The angle from
Answer to Problem 16P
The principle normal stress
The shear stress is
The angle from
Explanation of Solution
Write the coordinates of the points through which the Mohr’s circle pass.
Draw the
Write the formula for the center point.
Write the expression for the angle between the line joining points A and B with
Write the expression of the radius of circle.
Write the expression maximum in plane normal stress.
Write the expression of maximum in plane shear stress.
Write the expression for the angle of maximum shear plane.
Write the expression for the angle between the line joining points A and B with
Conclusion:
Substitute
Substitute
Draw the Mohr’s circle diagram.
The Figure (10) shows the Mohr’s circle diagram.
Figure (10)
Substitute the value
Substitute the value
Substitute the value
Substitute the value
Substitute the value
Substitute the value
Substitute the value
The Figure (11) shows the maximum in plane normal stress distribution about the plane.
Figure (11)
The Figure (12) shows stress distribution at maximum shear stress plane.
Figure (12)
Thus, the principle normal stress
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Chapter 3 Solutions
Loose Leaf for Shigley's Mechanical Engineering Design Format: LooseLeaf
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