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Maximum shear stress in a Mohr's circle
- a)is equal to radius of Mohr's circle
- b)is greater than radius of Mohr's circle
- c)is less than radius of Mohr's circle
- d)Could be any of the above
Correct answer is option 'A'. Can you explain this answer?
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Maximum shear stress in a Mohrs circlea)is equal to radius of Mohrs ci...
Introduction:
The Mohr's circle is a graphical representation used to determine the maximum shear stress and principal stresses in a material under combined loading. It is a useful tool in analyzing the stress state of a material and predicting its failure.
Mohr's Circle:
Mohr's circle is a graphical representation of stress transformation in materials. It is constructed by plotting the normal and shear stresses on the x and y axes of a graph. The center of the circle represents the average stress, while the radius of the circle represents the maximum shear stress.
Maximum Shear Stress:
The maximum shear stress occurs at a 45-degree angle to the normal stress axis on the Mohr's circle. It is located at the furthest point from the center of the circle. The maximum shear stress is given by the equation:
τ_max = (σ_max - σ_min) / 2
where τ_max is the maximum shear stress, σ_max is the maximum normal stress, and σ_min is the minimum normal stress.
Relation to Mohr's Circle:
The maximum shear stress on a Mohr's circle is equal to the radius of the circle. This can be proven mathematically by substituting the values of σ_max and σ_min into the equation for maximum shear stress.
τ_max = (σ_max - σ_min) / 2
= (σ_max - (σ_max + σ_min) / 2) / 2
= (σ_max - σ_max/2 - σ_min/2) / 2
= (σ_max/2 - σ_min/2) / 2
= (σ_max - σ_min) / 2
Thus, it can be observed that the maximum shear stress is equal to the radius of the Mohr's circle.
Conclusion:
In conclusion, the maximum shear stress in a Mohr's circle is equal to the radius of the circle. This relationship holds true for any stress state and is a fundamental property of Mohr's circle.
The Mohr's circle is a graphical representation used to determine the maximum shear stress and principal stresses in a material under combined loading. It is a useful tool in analyzing the stress state of a material and predicting its failure.
Mohr's Circle:
Mohr's circle is a graphical representation of stress transformation in materials. It is constructed by plotting the normal and shear stresses on the x and y axes of a graph. The center of the circle represents the average stress, while the radius of the circle represents the maximum shear stress.
Maximum Shear Stress:
The maximum shear stress occurs at a 45-degree angle to the normal stress axis on the Mohr's circle. It is located at the furthest point from the center of the circle. The maximum shear stress is given by the equation:
τ_max = (σ_max - σ_min) / 2
where τ_max is the maximum shear stress, σ_max is the maximum normal stress, and σ_min is the minimum normal stress.
Relation to Mohr's Circle:
The maximum shear stress on a Mohr's circle is equal to the radius of the circle. This can be proven mathematically by substituting the values of σ_max and σ_min into the equation for maximum shear stress.
τ_max = (σ_max - σ_min) / 2
= (σ_max - (σ_max + σ_min) / 2) / 2
= (σ_max - σ_max/2 - σ_min/2) / 2
= (σ_max/2 - σ_min/2) / 2
= (σ_max - σ_min) / 2
Thus, it can be observed that the maximum shear stress is equal to the radius of the Mohr's circle.
Conclusion:
In conclusion, the maximum shear stress in a Mohr's circle is equal to the radius of the circle. This relationship holds true for any stress state and is a fundamental property of Mohr's circle.
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Maximum shear stress in a Mohrs circlea)is equal to radius of Mohrs circleb)is greater than radius of Mohrs circlec)is less than radius of Mohrs circled)Could be any of the aboveCorrect answer is option 'A'. Can you explain this answer?
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