Elbow center of gravity

Can somebody give me the formula how to obtain the elbow center of gravity.

Thanks,
Sergio Antonio Rivera

Unless it is a reducing elbow, it will be at the midpoint along the centerline.

Problem is more complicated. Unfortunately I cannot give the simple formula. Could give few pages of complex calcs. See attached images from 3D modeller solutions.

Hi Sir Sergio,

It is easy to locate the center of gravity using the Integral calculus..
I cannot exactly remember the process of solving it and have no time to review that Book either. You can reffer that to the OLD book of Poter and Poter in Integral Calculus and Analytic Geometry, I have 4th edition in college, maybe author change in latest edition. 10minutes of studying that part is enough to learn and apply...

Usually it is done by doulbe integration process..

Regards!

Roark's Formulas for Stress and Strain, Warren C. Young and Richard G. Budynas, McGraw-Hill, Seventh Edition

I appreciate a lot all the atention that you gave.

Thanks and regards,
Sergio Antonio Rivera

That's right. After my post yesterday I investigated this further and it turns out that the CG is not along the centerline and may not even be on the bend geometry at all.

not even elbow like reducing elbow... I believe it will make the calculation more complicated. In my mathematical point of view, 3rd degree of integration maybe a solution for this(I dont remember trying to solve this one)... sloping while rotating?.. Well thats a hardstuff...

Regards!

Roark's Formula is good...but not for a segment of torus!
It’s worth to consider also the chapter title…

You may consider the following coordinate along the bisect plan of elbow:

sin(alpha)/alpha*{c+[a**2+(a - t)**2]/(4c)}

where 2*alpha is the elbow angle (and you must keep alpha in radians!)
c is the radius of elbow
a is circle radius (half of OD pipe)
t is thickness of elbow

If you are interested, I can give you a one page proof using parametric equations of torus and some triple integrals

Regards,

Agree. I made only a quick check. For that reason I left the tittle. On 45 and 90 degr 24" formula gives 15 mm out. Not good enough.

Your formula is correct for uniform thickness elbow. I assume we will not worry about WTH differences around the elbow....

OK, you may find some details in the file attached.

For me was only to have some fun by recalling mathematics and trying to help a little.

If thickness is not uniform in section, then t=t(v) and you must consider this in integration.

If we have a reducing elbow, also a=a(u), and again this are making some extra work.

Always there is the option to use a math soft. I recommend Mathcad that is reasonable for an engineer.

Regards,
Mario

Hi,

If you draw the elbow on 3-d (must be on 3d) in AutoCAD or any dwg program, you can have all the properties. CG,Ixx,Ixy(circle) , weight,Volume...etc is very quick and simple.Then select properties.

Civil guys take these properties from these packages. Imagine doing integral calculus to very irregular shapes like dams....

OG

True.

However note that the original question was "Can somebody give me the formula how to obtain the elbow center of gravity?"
It was not more than a replay to this question.
For sure, it wasn't an investigation about the most convenient way to get the result.

regards

For unsophisticated stress analysts--like me (and perhaps Loren Brown also for the above)--the “most convenient” method to find C.G. is:

To build a 10D elbow (for example) ONLY, to error-check the input, and, lo and behold, here is the C.G. The problem is, that it gives only one significant number in (ft.). How to increase the number, that I don’t know. But Loren Brown may decide to redeem himself so to share with us this knowledge.

If nothing else change your file's units. I use metric in mm. C.G. is given with an accuracy of 0.1 mm. Should be enough.

And I agree about the MathCAD. No more spread sheet formulas, which are about impossible to get correct. Anybody doing any calculations should look into MathCAD or some other similar product. No unit changes, easy to check and easy to write.

I second Darrens Thoughts although the academia displayed has been interesting....

When I get a chance I will also look through Spielvogels' work as I recall he also discussed this topic.....