Finding Centroids

[DanMarotta]

Using Mathcad to find the centroid location of general shapes.

How'd he do? Would you take a different approach in finding centroids?

[f.kohlhepp]

BostonDan wrote:

Using Mathcad to find the centroid location of general shapes.

How'd he do? Would you take a different approach in finding centroids?

Tough to say.

Video??

[MikeArmstrong]

Do you want a worksheet as an example?

Mike

BTW - will the example worksheet be available to download?

[DanMarotta]

Up to you Mike on whether you want to post a worksheet example. I haven't seen anything on the forums about centroids

You'll have to ask the author. This video I pulled from YouTube.

[MikeArmstrong]

A slightly different approach as the attached sheet calculates a composite centroid in order to calculate the bending stress generated in the jack, might be worth a glance though.

Mike

[MikeArmstrong]

Improved example added.

Mike

[f.kohlhepp]

Dan;

I'm sorry, please help an old man out. I have searched this site high and low for this video, even searching the videos tab, to no avail. Where in h*ll is the video you're talking about? Or is my (work) computer stripping a link?

[RichardJ]

Where in h*ll is the video you're talking about? Or is my (work) computer stripping a link?

It's right there, embedded in Dan's post. It's a YouTube video, so maybe your IT dept has stripped the link? Here's the URL for the video:

http://www.youtube.com/watch?v=SqhqwBMAbRs

[DanMarotta]

Sorry Fred, Richard may be right. Your IT dept may have blocked you from accessing the YouTube site.

That doesn't mean you're left out. How do you find centroids using Mathcad?

[f.kohlhepp · Accepted solution]

Your IT dept may have blocked you from accessing the YouTube site.

They have.

But centroids 'R Us:

[MikeArmstrong]

Fred,

That is a fantastic worksheet, excellent piece of work

Dan - give thread the correct answer star, I would consider this worksheet more valuable than the video.

Mike

[MikeArmstrong]

Fred,

If you have the time would you try to use your sheet for the shapes in my, worksheet "Example2". I have tried numerous times and failed to get it to work.

Cheers in advance

Mike

[f.kohlhepp]

Mike Armstrong wrote:

Fred,

If you have the time would you try to use your sheet for the shapes in my, worksheet "Example2". I have tried numerous times and failed to get it to work.

Cheers in advance

Mike

If you put Example2 into version 11, I'll be happy to try.

[MikeArmstrong]

Attached is my example saved in M11 format.

Mike

[f.kohlhepp]

Attached.

For a very nasty surprise, disable the declaration on TOL.

[wayne]

f.Kohlhepp,

Interesting. Numerical methods can be tricky. In your example, the linterp functions works, in mine, which had two vertical
elements it did not work.

Numerical integration with functions with large steps can have problems, though Mathcad is pretty good at integrating acorss
steps, just takes a little longer. In the double integral method, it takes even longer, so I try to avoid double integration, numerically.

I attached the revisions that I made, in 11; If epsilon is set to 1, it will not work. Seting epsilon very close to 1 works,
and the cacluation time is not noticeable. I am guessing that is the case becasue the numerical integation is not across a
substantial vertical step.

Any comments on this?

Thanks

Wayne

[f.kohlhepp]

Interesting way to reduce the number of integrations.

I have expanded the original sheet to compute the second moments as well, but I can see that your single integration scheme has definite value.

[MikeArmstrong]

Cheers wayne for your help.

Would you be able to add a few notes to your worksheet, maybe where you have worked out the Iyy and Ixx. I haven't done this for a long time and its really bugging me.

Mike

[wayne]

Mike,

Hope this helps,

Wayne

[MikeArmstrong]

Cheers for the explanation Wayne, much appreciated.

Mike

[MikeArmstrong]

Cheers Fred.

I'm not sure if its worth while using Integrals for such a problem. My example seems simple. Simple = good for me.

Mike

[f.kohlhepp]

I'm not sure if its worth while using Integrals for such a problem. My example seems simple. Simple = good for me.

Mike;

I agree that for your example integration is an unnecessary and potentially error-ridden path. Simple is usually much better. The integration method derives from "first principles," though, so it has the advantage of being rigorously correct (once you get rid of numerical integration errors.) Since I'm usually trying to sort out odd-shaped structures, this method has advantages for me.

Fred

[MikeArmstrong]

Fred,

I am very grateful for the time you have spent. This is a learning curve for me using integrals. I have only ever used them for very simple problems.

I still don't fully understand how your area function works!!!!

Mike

[BillWadsworth]

Mike, have a look at this, it is a sheet I posted back in 06/07/06 which does the same job but slightly differently. I did the intergrations by hand to get expressions for the area, 1st mom. of area, etc., under each line segment; the sheet then just evaluates the expressions. (It is a re-hashed BASIC program). It is something I first saw done on a HP 9800 programmable calculator at a meeting at the Institution of Civil Engineers in London in about 1965. I went back and struggled until I got it working on my machine (the office machine actually, they cost £2500 at that time). So, I have implemented it on every computer I have had since then and use it quite frequently. Just remember to traverse the area clockwise, holes can be accommodated by going round them anti-clockwise).

Bill Wadsworth.

[MikeArmstrong]

Cheers for the example Bill, much appreciated.

Mike

[f.kohlhepp]

I still don't fully understand how your area function works!!!!

Maybe this will help.

[MikeArmstrong]

Fred,

That is a superb worksheet. You should create a document with Integrals as the title. This could be of great benefit for members, like me trying to understand the use of integrals.

Mike

[MJG]

The approach looks good to me. I am a little disappointed, however, that units were not used in the example. It's good that he's solving by integration rather than just teaching to look up equations from a book, but the numbers have no meaning without units.

[MikeArmstrong]

Dan,

Its a good example but not very practical. He doesn't explain how he gets the curve function f(x) and for the second example he just makes a curve up. Unless I'm wrong this method can only be used if the curve function is given.

Mike

[RichardJ]

Its a good example but not very practical. He doesn't explain how he gets the curve function f(x) and for the second example he just makes a curve up. Unless I'm wrong this method can only be used if the curve function is given.

Follow Fred's example, and use interpolation to generate the function. Using the closed spline from Tom's spline routines may be a better choice than linterp in some cases though.