How to Solve Lame's Equation for A and B

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Discussion Overview

The discussion revolves around solving Lame's equation for the constants A and B in the context of a homework problem involving a steel pipe's internal pressure and allowable stress. Participants are attempting to derive these constants using simultaneous equations derived from the given stress equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the equations σr = A - B/r² and σtheta = A + B/r², and attempts to solve for A and B given specific values.
  • Another participant suggests using one equation to express A in terms of B, or vice versa, and substituting back into the other equation to solve.
  • Multiple participants express confusion about the algebraic manipulations required to isolate A or B, with requests for clarification and elaboration on the steps involved.
  • There are repeated assertions that the algebra involved is straightforward, yet some participants struggle with the basic algebraic concepts and manipulations.
  • One participant attempts to clarify the relationship between A and B but is met with further confusion regarding the signs and expressions used.
  • Another participant emphasizes the importance of careful algebraic manipulation and suggests that a lack of understanding in basic algebra may hinder solving more complex problems.

Areas of Agreement / Disagreement

There is no consensus on the correct approach to isolate A and B, as participants express varying levels of understanding and confusion about the algebra involved. Some participants provide hints while others struggle to follow the suggested steps.

Contextual Notes

Participants have not reached a resolution on the correct method to solve for A and B, and there are indications of misunderstandings regarding algebraic principles that may affect the problem-solving process.

Jud
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Homework Statement


A steel pipe is 200mm internal diameter and 20mm thick. Calculate the safe internal pressure if the allowable stress is not to exceed 140Mpa.

Homework Equations


σr = A-B/r^2[/B]
and
σtheta = A+B/r^2

The Attempt at a Solution



Right so, I've got two equations...

(eq1)140MPa =A+B/0.1^2
and
(eq2)0 = A-B/0.12^2


I need help getting A and B. Answers (A=57.38)and (B=0.826)

I know I need to use simultaneous equations. Could someone please give me a step by step solution as I'm stuck.

I have so far done -(eq2)+(eq1) to cancel out A.
and got
...140MPa = B/0.1^2 + B/0.12^2

I'm not sure what to do next to get B.
 
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Hint: use eq. 2 to get A in terms of B (or vice versa). Substitute back into eq. 1 and solve.
 
SteamKing said:
Hint: use eq. 2 to get A in terms of B (or vice versa). Substitute back into eq. 1 and solve.
I don't understand, sorry. Could you elaborate with the values please.
 
Jud said:
I don't understand, sorry. Could you elaborate with the values please.

It's very simple. You've got A - B/0.12^2 = 0. Find A in terms of B, or B in terms of A.

Once you have found an expression for A or B, substitute that expression back into eq. 1, which will then be one equation in one unknown.

You're in algebra 101 here.
 
SteamKing said:
It's very simple. You've got A - B/0.12^2 = 0. Find A in terms of B, or B in terms of A.

Once you have found an expression for A or B, substitute that expression back into eq. 1, which will then be one equation in one unknown.

You're in algebra 101 here.

I.e. B = A/0.12^2

So,
140MPa = A + (A/0.12^2)/0.1^2?
 
Jud said:
I.e. B = A/0.12^2

Uh, not quite. Remember, you've got

A - B/0.12^2 = 0

How did you come up with

B = A/0.12^2 ?
 
Jud, starting with A - B/0.12^2 = 0, solve for B, without skipping steps.
 
Mark44 said:
Jud, starting with A - B/0.12^2 = 0, solve for B, without skipping steps.

A = -B/0.12^2

A(0.12^2) = -B
 
Jud said:
A = -B/0.12^2

A(0.12^2) = -B

So you're saying if A - 5 = 0, then A = -5. Check your work again.
 
  • #10
SteamKing said:
So you're saying if A - 5 = 0, then A = -5. Check your work again.

-A(0.12^2) = -B

So, 140MPa = A + - A(0.12^2)/0.1^2
 
  • #11
Jud said:
-A(0.12^2) = -B

You can multiply both sides of the equation by -1 to obtain

A(0.12^2) = B

So, 140MPa = A + - A(0.12^2)/0.1^2

And how would you solve for A?

Friendly advice: I don't know anything about your academic background, but your apparent lack of understanding of algebra is going to prevent you from solving more complex problems than this. Try to take time and remedy this gap in your mathematical knowledge. ;)
 

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