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The state of stress at a point when completely specified enables one to determine the
1. maximum shearing stress at the point
2. Stress components on any arbitrary plane containing that point
Which of the above is/are correct?
- a)1 only
- b)2 only
- c)both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'C'. Can you explain this answer?
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The state of stress at a point when completely specified enables one to determine:
1. Maximum shearing stress at the point:
When the state of stress at a point is completely specified, it means that the magnitudes and directions of all the stress components (normal and shear stresses) acting at that point are known. In such a case, one can determine the maximum shearing stress at the point.
To determine the maximum shearing stress, we need to consider the stress components acting on planes inclined at different angles with respect to the reference plane. By analyzing the magnitudes of these stress components, we can determine the plane on which the maximum shearing stress occurs. The maximum shearing stress is given by the difference between the maximum and minimum principal stresses acting on that plane.
2. Stress components on any arbitrary plane containing that point:
When the state of stress at a point is completely specified, it also enables one to determine the stress components on any arbitrary plane containing that point.
To determine the stress components on an arbitrary plane, we need to consider the normal and shear stresses acting on that plane. The normal stress is the stress component acting perpendicular to the plane, while the shear stress is the stress component acting parallel to the plane. These stress components can be determined by analyzing the equilibrium equations and the geometry of the problem.
Conclusion:
Therefore, when the state of stress at a point is completely specified, it enables us to determine both the maximum shearing stress at the point and the stress components on any arbitrary plane containing that point. Hence, option C, "both 1 and 2," is correct.
1. Maximum shearing stress at the point:
When the state of stress at a point is completely specified, it means that the magnitudes and directions of all the stress components (normal and shear stresses) acting at that point are known. In such a case, one can determine the maximum shearing stress at the point.
To determine the maximum shearing stress, we need to consider the stress components acting on planes inclined at different angles with respect to the reference plane. By analyzing the magnitudes of these stress components, we can determine the plane on which the maximum shearing stress occurs. The maximum shearing stress is given by the difference between the maximum and minimum principal stresses acting on that plane.
2. Stress components on any arbitrary plane containing that point:
When the state of stress at a point is completely specified, it also enables one to determine the stress components on any arbitrary plane containing that point.
To determine the stress components on an arbitrary plane, we need to consider the normal and shear stresses acting on that plane. The normal stress is the stress component acting perpendicular to the plane, while the shear stress is the stress component acting parallel to the plane. These stress components can be determined by analyzing the equilibrium equations and the geometry of the problem.
Conclusion:
Therefore, when the state of stress at a point is completely specified, it enables us to determine both the maximum shearing stress at the point and the stress components on any arbitrary plane containing that point. Hence, option C, "both 1 and 2," is correct.
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The state of stress at a point when completely specified enables one to determine the1. maximum shearing stress at the point2. Stress components on any arbitrary plane containing that pointWhich of the above is/are correct?a)1 onlyb)2 onlyc)both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?
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