What are the variables in Roark's formulas for stress and strain?

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Discussion Overview

The discussion revolves around understanding the variables in Roark's formulas for stress and strain, particularly in the context of mechanical engineering applications involving circular plates. Participants seek clarification on specific variables and their meanings within the formulas presented in an old book on the subject.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about the variables in Roark's formulas and lists several terms including b/a, ro/a, yb, mrb, ya, and mra.
  • Another participant points out that understanding the variables requires seeing the equations in which they are used.
  • A participant provides a formula and attempts to explain the variables, suggesting that b and a are radial dimensions and that b/a is their ratio.
  • There is mention of constants (C2, C3, C5, C6, L3, L6) that are likely defined in a table within the book, which may help clarify their roles.
  • A later reply discusses the context of the problem involving two circular plates bolted to rings and pressurized, indicating a practical application of the formulas.
  • Another participant references an online calculator for Roark's formulas and suggests verifying results with hand calculations.
  • There is a suggestion to share input and output from calculations for verification purposes, indicating a collaborative approach to resolving uncertainties.

Areas of Agreement / Disagreement

Participants generally agree that the variables require further clarification and that context is important for understanding their meanings. However, there is no consensus on the specific interpretations of the variables or the formulas themselves, and the discussion remains unresolved regarding the exact definitions and applications.

Contextual Notes

The discussion highlights limitations in the available information, such as missing assumptions about the specific equations and the need for definitions of constants. The context of the application (pressurizing a cavity between plates) adds complexity to the understanding of the variables.

Who May Find This Useful

Mechanical engineers, students studying mechanics of materials, and practitioners using Roark's formulas for stress and strain in practical applications may find this discussion relevant.

kieren12345
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I have an old book on roarks formulas for stress and strain. Which seams to have the formulas I need but it doesn't have explanation of what the variables are. I am a mechanical engineer but have not studied Roarks.

Does anyone know the following?
b/a
ro/a
yb
mrb
ya
mra


Thanks
 
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I think you mean "nomenclature."

It's impossible to tell you anything about the variables you have listed without seeing the equation in which they are presented.
 
Thank you for correcting me there.

the formula I have is
yb=0
0b=0
ya=0
0a=0

mrb=-wa(C3L6-C6L3)/(C2C6-C3C5)
Qb=w(C2L6-C5L3)/(C2C6-C3C5)
mra=MrbC8+QbaC9-waL3
Qa=Qb(b/a)-(wRo/a)

any help?
 
Please list the table or section to which you are referring.
 
kieren12345 said:
I have an old book on roarks formulas for stress and strain. Which seams to have the formulas I need but it doesn't have explanation of what the variables are. I am a mechanical engineer but have not studied Roarks.

Does anyone know the following?
b/a
ro/a
yb
mrb
ya
mra


Thanks
It would help to see what section (and edition of the book) you're referring to, but it looks like a flat, circular plate.

b is a radial dimension (see figure in book)
a is a radial dimension (see figure in book)
so b/a is a ratio of the radial dimensions.
ro is also a radial dimension (generally to a line of load)
mrb refers to a radial moment at b
mra refers to a radial moment at a

mrb=-wa(C3L6-C6L3)/(C2C6-C3C5)
w is a linear load
C2, C3, C5, C6, L3, L6 are all constants. There will be a table for these constants at the beginning of the table you're looking at for the specific geometry.
etc...

If you can be more specific (what table are you using, what edition of the book, etc) it would help.
 
Please see attached word doc.

thanks

to explain abit better. I have two circular plates that is bolted to an internal and external ring, so that there is a cavity inbetween. We are giong to pressurise this cavity to 10bar and see how an internal elastomer reacts. One of the end plates is steel and one is plexiglas.

Please see 2nd attachment for drg.
 
attached
 
Kieren12345,

Nothing is attached.

I use Roark's book about once a week. All the C's and other constants can be confusing.

At the Roark website there is an online calculator. I have never used it so make sure you run some test cases and verify with some hand calcs that the program is producing the correct results.

http://www.roarksformulas.com/

Thanks
Matt
 
CFDFEAGURU said:
... make sure you run some test cases and verify with some hand calcs that the program is producing the correct results.
This is a good point, I meant to bring it up. If you do the calc per Roark, you might consider posting your input, the case used, and the output. It's easy enough for people that use Roark to verify your calculations are correct. I have spreadsheets for many of the circular plates and also access to all the cases on Mathcad.
 

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