## Moment of Inertia of Circular Tube Cross Section at an Angle

## Moment of Inertia of Circular Tube Cross Section at an Angle

(OP)

Does anyone have the formula for a circular tube cut at an angle to the axis? I have one for an ellipse, but if I make the major diameter equal to the minor diameter then I get a different number than for a straight circular cross section. They should be similar/exact.

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

I haven’t got one for an ellipse but I found this site, I am thinking you could do a graphical integration on a section if it’s drawn out.

https://studylib.net/doc/8800517/calculating-momen...

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

If you look at the integral defining I, then every Y dimension becomes Y/cos(theta), that cos(theta) is a constant that can be pulled out of the integral, so you get the integral for a circular area with one of those two factors.

If you have a composite cross section that includes a tilted tube, I think that violates the assumptions made to derive beam bending in the first place, so I don't know that numbers you get using those I's are that significant. IE, the stresses won't all be tilted normal to your plan, they'll be axial in the tube.

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

https://engineervsheep.com

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

and for a tube, subtract the hole.

you "could" derive it from the ellipse equation ... (x/a)^2 + (y/b)^2 = 1 ... but who's got time for that !

another day in paradise, or is paradise one day closer ?

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Maybe have to find a better ellipse... the formula I used initially was way out of whack... by a factor of nearly 2. I figured a weld on the perimeter would be similar to a sliced tube accommodating the weld size with different major and minor axis. Thanks...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

another day in paradise, or is paradise one day closer ?

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

thanks Agent... that formula is different than the one I used... will take a gander to see how it compares to a normal circle... I used agent's welding pattern program to do one in SMath and didn't want to use it for a mathematical ellipse... in a pinch, I would have, but didn't want to.

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Swap a and b...

https://engineervsheep.com

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

www.PeirceEngineering.com

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

no, but as agent said, as his link says, swap the "a" and "b".

another day in paradise, or is paradise one day closer ?

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

As far as the formula for an ellipse goes, I'm on board with JStephen's method. When in doubt, trust the math.

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

That's what the a b^3 part works on... again thanks so much.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

BA

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

1) there would be some "stretch" improvement on the long / web sides but;

2) no improvement on the short / flange sides because pushing on them at an angle would bow them out.

Trying to think about how that pans out for for an ellipse hurts me brain.

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Sorry for the fuzzy.

I believe it's from "Solutions to Design of Weldments"

https://www.jflf.org/ProductDetails.asp?ProductCod...

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

That's how the post is designed

(I hope no one thought I was using the elliptical perimeter for the tube design)and the weld checked based on the circular perimeter as well as the elliptical perimeter. I'm aware the elliptical perimeter is a bit off... but not likely significant... the circular perimeter greatly underestimates the weld strength~~stress~~. I just wanted a bit of a handle on where it stood.I didn't mean to imply that I was using the increased section modulus based on the sloped cut. The tube stands by itself, as if it were normal and the weld is similar to that... I just wanted to get an idea of how much greater weld capacity there was if the ellipse were considered instead of the circle.Thanks gentlemen.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Regards

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

That said, my solution for the problem is to just treat it as a circle and figure the elliptical weld is a little stronger, which is quick and easy.

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Not exact, but a good ballpark. Thanks... and for small angles, it becomes a better guess.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Here's how you could obtain the inertia of an inclined section of a circular tube:

1) Create a tubular part:

2) Cut the tube using an inclined plane:

3) Obtain the inertia using the region properties:

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

and I didn't record the source for this one, either...

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

https://newtonexcelbach.com/2020/08/06/section-pro...

The example has the long axis set to root 2 x the short axis, with the inner ellipse with a radius 2 units shorter on both axes.

The observant will note that the results suggest that Iy = Ix = Ixc, which is obviously wrong. Since the origin is at the centroid of both ellipses Ix = Ixc and Iy = Iyc. I will fix that and upload to the same address.

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

BA

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

BA

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

BAretired:That's why fillet welds are not pre-qualified with a dihedral angle less than 60 degrees. See W59 figure 4.8 for example or equivalent in AWS. Once you have less than 60 degrees (or more than 135) the weld is no longer considered a fillet and must be specified as a partial penetration groove weld or like with effective throat clearly specified.For raker design (HSS tubes connected to flat plates top and bottom on a 45 degree angle) we show a cut section on our drawings through the joint so it can be clearly seen where a fillet stops and a partial penetration weld begins. Typically we indicate the effective throat required on the small angle side, and the desired fillet weld on the larger angle side. On plan we indicate this via different line thicknesses.

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

@ dik. Please, can you tell us the tube diameter and the design loads?

Regards

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

and design loads (the data columns line up... just from different parts of the program):

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

That's good information. So in this case, the minimum angle between member axis and cut plane would be 45 degrees if a fillet weld is to be used.

BA

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

For design loads See OSHA 1926.502 “Fall protection systems criteria and practices”.

Regards

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Just to clear up a bit of confusion on my part. I don't have access to W59. Is the minimum dihedral angle, for a prequalified fillet weld, 45 degrees or 60 degrees?

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

For example lets say you need a 6mm weld at 90 degrees. The equivalent leg length on a 60 degree joint would be S = 6mm*0.71 = 4.26mm. If you put a 6mm leg length then your capacity would be 1 / 0.71 (1.41x) as much as for a 6mm weld at a 90 degree joint. For the same leg length the effective throat is greater in a joint with a smaller angle and less in a joint with a larger angle.

https://app.aws.org/mwf/attachments//73/286473/SMA...

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

thanks... I would have thought it would be reversed.

Thanks for the link

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

I believe the strength of the weld is proportional to the length of the green line shown below. Doesn't seem to be precisely equal to Enable's reference, but his is conservative.

BA

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

-Dik

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

Is this railing for a nuclear power plant?

Even in a nuclear power plant they don't make it that complicated.

Sorry

Regards

## RE: Moment of Inertia of Circular Tube Cross Section at an Angle

-Dik