#14640 - 12/04/07 02:04 PM
Elbow center of gravity
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Registered: 09/30/02
Posts: 24
Loc: Mexico
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Can somebody give me the formula how to obtain the elbow center of gravity.
Thanks, Sergio Antonio Rivera
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Seranto
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#14641 - 12/04/07 03:11 PM
Re: Elbow center of gravity
[Re: Sergio Antonio Rivera]
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Member
Registered: 10/18/01
Posts: 285
Loc: Houston, TX
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Unless it is a reducing elbow, it will be at the midpoint along the centerline.
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Loren Brown Director of Technical Support CADWorx & Analysis Solutions Intergraph Process, Power, & Marine 12777 Jones Road, Ste. 480, Houston, TX 77070 USA
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#14646 - 12/05/07 01:33 AM
Re: Elbow center of gravity
[Re: Sergio Antonio Rivera]
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Member
Registered: 06/23/07
Posts: 285
Loc: Manila, Philippines
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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!
Edited by bom (12/05/07 01:42 AM)
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BOM
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#14649 - 12/05/07 08:28 AM
Re: Elbow center of gravity
[Re: Sergio Antonio Rivera]
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Member
Registered: 01/11/04
Posts: 383
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Roark's Formulas for Stress and Strain, Warren C. Young and Richard G. Budynas, McGraw-Hill, Seventh Edition
Attachments
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Regards,
Jouko jouko@jat.co.za
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#14654 - 12/05/07 09:22 AM
Re: Elbow center of gravity
[Re: Jouko]
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Member
Registered: 09/30/02
Posts: 24
Loc: Mexico
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I appreciate a lot all the atention that you gave.
Thanks and regards, Sergio Antonio Rivera
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Seranto
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#14655 - 12/05/07 09:24 AM
Re: Elbow center of gravity
[Re: Jouko]
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Member
Registered: 10/18/01
Posts: 285
Loc: Houston, TX
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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.
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Loren Brown Director of Technical Support CADWorx & Analysis Solutions Intergraph Process, Power, & Marine 12777 Jones Road, Ste. 480, Houston, TX 77070 USA
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#14669 - 12/05/07 11:23 PM
Re: Elbow center of gravity
[Re: Loren Brown]
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Member
Registered: 06/23/07
Posts: 285
Loc: Manila, Philippines
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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!
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BOM
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#14699 - 12/06/07 08:40 AM
Re: Elbow center of gravity
[Re: bom]
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Member
Registered: 09/29/07
Posts: 798
Loc: Romania
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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,
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#14711 - 12/06/07 01:36 PM
Re: Elbow center of gravity
[Re: mariog]
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Member
Registered: 01/11/04
Posts: 383
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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....
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Jouko jouko@jat.co.za
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#14731 - 12/07/07 02:40 AM
Re: Elbow center of gravity
[Re: Sergio Antonio Rivera]
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Member
Registered: 09/29/07
Posts: 798
Loc: Romania
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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
Attachments
199-Elbowcenterofgravity.pdf (1049 downloads)
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#14738 - 12/07/07 05:55 AM
Re: Elbow center of gravity
[Re: mariog]
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Member
Registered: 11/11/05
Posts: 24
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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
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#14739 - 12/07/07 06:05 AM
Re: Elbow center of gravity
[Re: OG]
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Member
Registered: 09/29/07
Posts: 798
Loc: Romania
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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
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#14759 - 12/08/07 09:37 PM
Re: Elbow center of gravity
[Re: Jouko]
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Member
Registered: 12/15/99
Posts: 40
Loc: Houston, TX, USA
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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.
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#14760 - 12/08/07 10:05 PM
Re: Elbow center of gravity
[Re: Darren_Yin]
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Member
Registered: 01/11/04
Posts: 383
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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.
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Regards,
Jouko jouko@jat.co.za
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#14761 - 12/09/07 08:11 AM
Re: Elbow center of gravity
[Re: Jouko]
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Member
Registered: 03/25/02
Posts: 1110
Loc: U.S.A.
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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.....
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John C. Luf
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