Mechanical Engineering Exam > Mechanical Engineering Questions > Which one of following is NOT correct?a)Inter...
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Which one of following is NOT correct?
- a)Intermediate principal stress is ignored when applying the maximum principal stress
theory - b)The maximum shear stress theory gives the most accurate results amongst all the failure
theories - c)As per the maximum strain energy theory, failure occurs when the strain energy per unit
volume exceeds a critical value - d)As per the maximum distortion energy theory, failure occurs when the distortion energy
per unit volume exceeds a critical value
Correct answer is option 'B'. Can you explain this answer?
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Which one of following is NOT correct?a)Intermediate principal stress ...
Introduction:
In the field of mechanical engineering, various failure theories are used to predict the failure of materials and structures under different loading conditions. These theories help in determining the critical values of stress, strain, or energy at which failure occurs. Among these failure theories, one of the options provided is incorrect. Let's analyze each option to identify the correct answer.
Analysis of each option:
a) Intermediate principal stress is ignored when applying the maximum principal stress theory:
The maximum principal stress theory, also known as the Rankine theory, assumes that failure occurs when the maximum principal stress exceeds the material's ultimate strength. In this theory, the intermediate principal stress is not considered, and only the maximum principal stress is taken into account. Therefore, option 'a' is correct.
b) The maximum shear stress theory gives the most accurate results amongst all the failure theories:
This statement is incorrect. The maximum shear stress theory, also known as the Tresca theory, assumes that failure occurs when the maximum shear stress exceeds the material's yield strength. However, this theory is not always the most accurate because it neglects the effects of normal stresses. Therefore, option 'b' is incorrect.
c) As per the maximum strain energy theory, failure occurs when the strain energy per unit volume exceeds a critical value:
The maximum strain energy theory, also known as the Saint-Venant theory, assumes that failure occurs when the strain energy per unit volume exceeds a critical value. This theory considers both shear and normal strains, making it applicable for ductile materials. Therefore, option 'c' is correct.
d) As per the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value:
The maximum distortion energy theory, also known as the von Mises theory or the octahedral shear stress theory, assumes that failure occurs when the distortion energy per unit volume exceeds a critical value. This theory is widely used for predicting failure in ductile materials under complex loading conditions. Therefore, option 'd' is correct.
Conclusion:
After analyzing each option, we can conclude that option 'b' is not correct. The maximum shear stress theory does not always give the most accurate results among all the failure theories.
In the field of mechanical engineering, various failure theories are used to predict the failure of materials and structures under different loading conditions. These theories help in determining the critical values of stress, strain, or energy at which failure occurs. Among these failure theories, one of the options provided is incorrect. Let's analyze each option to identify the correct answer.
Analysis of each option:
a) Intermediate principal stress is ignored when applying the maximum principal stress theory:
The maximum principal stress theory, also known as the Rankine theory, assumes that failure occurs when the maximum principal stress exceeds the material's ultimate strength. In this theory, the intermediate principal stress is not considered, and only the maximum principal stress is taken into account. Therefore, option 'a' is correct.
b) The maximum shear stress theory gives the most accurate results amongst all the failure theories:
This statement is incorrect. The maximum shear stress theory, also known as the Tresca theory, assumes that failure occurs when the maximum shear stress exceeds the material's yield strength. However, this theory is not always the most accurate because it neglects the effects of normal stresses. Therefore, option 'b' is incorrect.
c) As per the maximum strain energy theory, failure occurs when the strain energy per unit volume exceeds a critical value:
The maximum strain energy theory, also known as the Saint-Venant theory, assumes that failure occurs when the strain energy per unit volume exceeds a critical value. This theory considers both shear and normal strains, making it applicable for ductile materials. Therefore, option 'c' is correct.
d) As per the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value:
The maximum distortion energy theory, also known as the von Mises theory or the octahedral shear stress theory, assumes that failure occurs when the distortion energy per unit volume exceeds a critical value. This theory is widely used for predicting failure in ductile materials under complex loading conditions. Therefore, option 'd' is correct.
Conclusion:
After analyzing each option, we can conclude that option 'b' is not correct. The maximum shear stress theory does not always give the most accurate results among all the failure theories.
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Which one of following is NOT correct?a)Intermediate principal stress is ignored when applying the maximum principal stresstheoryb)The maximum shear stress theory gives the most accurate results amongst all the failuretheoriesc)As per the maximum strain energy theory, failure occurs when the strain energy per unitvolume exceeds a critical valued)As per the maximum distortion energy theory, failure occurs when the distortion energyper unit volume exceeds a critical valueCorrect answer is option 'B'. Can you explain this answer?
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