Moment of inertia - curved flat bar

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Discussion Overview

The discussion revolves around calculating the moment of inertia for a formed flat bar with a uniform curve. Participants explore various methods and resources for deriving or estimating the moment of inertia, including references to specific editions of Roark's Formulas for Stress and Strain.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in calculating the moment of inertia for a curved flat bar and seeks assistance.
  • Another participant suggests that the problem may be a homework question and points to Roark's Formulas as a potential resource for the solution.
  • A participant confirms that their edition of Roark's includes the relevant information, while another mentions that their edition lacks it.
  • One participant questions whether the section is thick or thin and proposes that calculus could be used to determine the moment of inertia.
  • Another participant suggests using integration to find the moment of inertia due to the curvature, while also recommending a rough estimate using a rectangular cross-section formula.
  • A link to an external webpage is provided for further information on area moment of inertia.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best method to calculate the moment of inertia, with multiple approaches and resources being suggested. There is also uncertainty regarding the applicability of different editions of Roark's Formulas.

Contextual Notes

Some assumptions about the geometry of the bar and the nature of the section (thick vs. thin) remain unresolved. The discussion includes references to specific mathematical methods and resources without establishing a definitive approach.

Bearcat_w
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I am trying to calculate the moment of inertia of a formed (uniform curve) flat bar. I have attached a sketch . The bar is 5/8" thick x 1" wide. I'm stumped.
 

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    Curved plate.jpg
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Is this a homework problem where you need to come up with the derivation?

Roark's Formulas for Stress and Strain has the answer to that exact section, in Appendix A, Table A.1 (Properties of Sections).
 
Thanks for the fast reply. Exactly what I needed. My 5th Edition Roark lacks the appendix!
 
I have the Seventh edition and it has it, and from what I can tell the Sixth edition has it as well. Time to get a new Roark's!
 
hi there..
i think you are trying to find the stress at a section in this problem..
is this a thick or a thin section? With some calculus we can figure out what will be the moment of inertia..
 
If your looking for an exact answer you would have integrate it using:

Ixy=∫xydA since it is curved

Honestly though I would just get a rough estimate with a simple rectangular cross-section area moment of inertia equation

I=1/12bh^3

or I would use a program like Solidworks that would calculate it for me.

If you want to know more about area moment of inertia this is a good web page that gives a basic overview

http://sbainvent.com/strength_of_materials/area-moment-of-inertia.php
 

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