Help Understanding Transposing Formula in Roarks Formulas for Stress and Strain

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Homework Help Overview

The discussion revolves around understanding a specific equation from Roark's Formulas for Stress and Strain, particularly the expression involving the variable n: 4.4661/n - 2(2.331)1/n + 1 = 0. Participants express difficulty in following the steps to arrive at the solution, which is stated to be n = 2.86.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants note the lack of a straightforward algebraic method to solve the equation and suggest alternative approaches such as graphical or numerical methods. Others question the accuracy of the provided solution and propose different interpretations of the equation that yield varying results for n.

Discussion Status

The discussion is ongoing, with participants exploring different methods and interpretations of the equation. Some guidance has been offered regarding numerical methods, but there is no explicit consensus on the correct approach or solution.

Contextual Notes

Participants mention that the equation may have been derived using older methods, and there is a suggestion that the original text may have discrepancies across different editions. The discussion highlights the potential for varying interpretations of the equation.

Colnago
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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
[tex](67/15)^{1/n} - 2(7/3)^{1/n} + 1=0[/tex]
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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