How to Solve Lame's Equation for A and B

[Jud]

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.

 

[SteamKing]

Hint: use eq. 2 to get A in terms of B (or vice versa). Substitute back into eq. 1 and solve.

 

[Jud]

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.

 

[SteamKing]

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.

 

[Jud]

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?

 

[SteamKing]

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 ?

 

[Mark44]

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

 

[Jud]

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

 

[SteamKing]

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.

 

[Jud]

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

 

[SteamKing]

-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. ;)