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Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice because
- a)effect of direct stress is neglected
- b)pin joints are not free from friction
- c)the assumptions made in using the formula are not met in practice
- d)the material does not behave in an ideal elastic way in tension and compression
Correct answer is option 'A'. Can you explain this answer?
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Euler’s formula gives 5 to 10% error in crippling load as compar...
Euler's formula to calculate crippling load in the column
\({P_{cr}} = \frac{{{\pi ^2}EI_{mini}}}{{L_e^2}}\)
Where P = Crippling load, E = young's modulus, Imini = Minimum area moment of inertia of column, Le = Effective length of a column
The assumption made while developing Euler Formula for the crippling load of a column does not meet in the real-life practice due to which therefore Euler's formula gives 5 to 10 % error compared to experimental results or true value.
The following assumptions are made in Euler's column theory :
- The column is initially perfectly straight and the load is applied axially.
- The cross-section Of the column is uniform throughout its length.
- The column material is perfectly elastic, homogeneous, and isotropic and obeys Hooke's law.
- The length of the column is very large as compared to its lateral dimensions.
- The direct stress is very small as compared to the bending stress.
- The self-weight of the column is negligible.
- The column will fail by buckling alone.
- Pin joints are free from friction.
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Euler’s formula gives 5 to 10% error in crippling load as compar...
Leonhard Euler (1707-1783) was a Swiss mathematician, physicist, and engineer who made significant contributions to many areas of mathematics, including calculus, number theory, graph theory, and geometry. He is considered one of the greatest mathematicians of all time and is known for his prolific output, having published over 800 papers and books during his lifetime.
Some of Euler's most famous contributions include:
- Euler's formula: e^(ix) = cos(x) + i sin(x), which relates complex numbers to trigonometric functions.
- Euler's identity: e^(iπ) + 1 = 0, which is often considered the most beautiful equation in mathematics.
- Euler's theorem: a^(φ(n)) ≡ 1 (mod n), which relates the totient function to modular arithmetic.
- Euler's method: a numerical method for approximating solutions to differential equations.
- Euler's number: e, which is a fundamental constant in calculus and analysis.
Euler also made significant contributions to physics, including the study of fluid dynamics and the theory of elasticity. He is often credited with introducing the concept of a function and laying the foundation for modern analysis.
Some of Euler's most famous contributions include:
- Euler's formula: e^(ix) = cos(x) + i sin(x), which relates complex numbers to trigonometric functions.
- Euler's identity: e^(iπ) + 1 = 0, which is often considered the most beautiful equation in mathematics.
- Euler's theorem: a^(φ(n)) ≡ 1 (mod n), which relates the totient function to modular arithmetic.
- Euler's method: a numerical method for approximating solutions to differential equations.
- Euler's number: e, which is a fundamental constant in calculus and analysis.
Euler also made significant contributions to physics, including the study of fluid dynamics and the theory of elasticity. He is often credited with introducing the concept of a function and laying the foundation for modern analysis.
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Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice becausea)effect of direct stress is neglectedb)pin joints are not free from frictionc)the assumptions made in using the formula are not met in practiced)the material does not behave in an ideal elastic way in tension and compressionCorrect answer is option 'A'. Can you explain this answer?
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Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice becausea)effect of direct stress is neglectedb)pin joints are not free from frictionc)the assumptions made in using the formula are not met in practiced)the material does not behave in an ideal elastic way in tension and compressionCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice becausea)effect of direct stress is neglectedb)pin joints are not free from frictionc)the assumptions made in using the formula are not met in practiced)the material does not behave in an ideal elastic way in tension and compressionCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice becausea)effect of direct stress is neglectedb)pin joints are not free from frictionc)the assumptions made in using the formula are not met in practiced)the material does not behave in an ideal elastic way in tension and compressionCorrect answer is option 'A'. Can you explain this answer?.
Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice becausea)effect of direct stress is neglectedb)pin joints are not free from frictionc)the assumptions made in using the formula are not met in practiced)the material does not behave in an ideal elastic way in tension and compressionCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice becausea)effect of direct stress is neglectedb)pin joints are not free from frictionc)the assumptions made in using the formula are not met in practiced)the material does not behave in an ideal elastic way in tension and compressionCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Euler’s formula gives 5 to 10% error in crippling load as compared to experimental results in practice becausea)effect of direct stress is neglectedb)pin joints are not free from frictionc)the assumptions made in using the formula are not met in practiced)the material does not behave in an ideal elastic way in tension and compressionCorrect answer is option 'A'. Can you explain this answer?.
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