Help Understanding Transposing Formula in Roarks Formulas for Stress and Strain

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SUMMARY

The discussion centers on solving the equation presented in Roark's Formulas for Stress and Strain: 4.4661/n - 2(2.331)1/n + 1 = 0. The approximate solution provided in the text is n = 2.86, which is incorrect. Using Maple 14, the accurate solution is found to be n ≈ 2.82. An alternative interpretation of the equation yields n ≈ 2.80. The conversation highlights the limitations of algebraic methods for such equations and suggests numerical methods as a viable solution approach.

PREREQUISITES
  • Understanding of numerical methods, specifically Newton's method.
  • Familiarity with Maple 14 software for mathematical computations.
  • Basic algebra and equation manipulation skills.
  • Knowledge of Roark's Formulas for Stress and Strain as a reference text.
NEXT STEPS
  • Explore the capabilities of Maple 14 for solving nonlinear equations.
  • Learn about Newton's method and its application in numerical analysis.
  • Investigate alternative numerical methods for solving equations, such as the bisection method.
  • Review the various editions of Roark's Formulas for Stress and Strain for updated methodologies.
USEFUL FOR

Students and professionals in engineering, particularly those studying mechanics of materials, as well as anyone seeking to improve their skills in numerical methods and mathematical software applications.

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Homework Statement



Hi, I'm looking through Roarks Formulas for Stress and Strain and I am having difficulty following one of the examples. Unfortunately my maths isn't as good as I would like. Hopefully someone can explain to me the steps taken to find the solution.

Homework Equations



The book states the following expression:

4.4661/n - 2(2.331)1/n + 1 = 0

From this it finds n = 2.86, unfortunately only the answer is given an no explanation. Can someone help?

Thanks
 
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There is no simple "algebraic" method to combine 4.4661/n and 2.3311/n so no simple "algebraic" method to solve that equation. You could do it graphically or using some numerical method such as Newton's method. And "2.86" is only an approximate solution, not exact.
 
Colnago said:

Homework Statement



Hi, I'm looking through Roarks Formulas for Stress and Strain and I am having difficulty following one of the examples. Unfortunately my maths isn't as good as I would like. Hopefully someone can explain to me the steps taken to find the solution.

Homework Equations



The book states the following expression:

4.4661/n - 2(2.331)1/n + 1 = 0

From this it finds n = 2.86, unfortunately only the answer is given an no explanation. Can someone help?

Thanks

For the solution of the problem *exactly as it is written*, Maple 14 gets n = 2.822595780, which rounds off to n ≈ 2.82 (NOT 2.86). If we assume, instead, that the equation should really by
(67/15)^{1/n} - 2(7/3)^{1/n} + 1=0
the solution becomes n = 2.795724837, which rounds off to n ≈ 2.80 (again, NOT 2.86).

Note: Maple uses numerical methods to solve such equations.
 
Roark is an old, old text which has several editions. When the equation in the OP was originally solved, the author (or one of his students) might have been using a slide rule or a set of log tables and counting on his fingers and toes.
 
Hey, don't knock counting on your fingers and toes! I do it all the time.
 
HallsofIvy said:
Hey, don't knock counting on your fingers and toes! I do it all the time.
In binary, I trust?
 

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