Moment of Inertia of Circular Tube Cross Section at an Angle 13

[dik]

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.

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

-Dik

 

[azcats]

Does that get weird because the apparent wall thickness will be different across the cut?

 

[desertfox]

Hi dik

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-moments-of-inertia

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

 

[JStephen]

If you tilt a tube or rod so you have an elliptical area in a cross section, the moment of inertia in one direction increases by 1/cos(theta) and in the other direction increases by (1/cos(theta))^3.
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.

 

[KootK]

Is this for a weld or the member itself? I'm not sure that elliptical treatment would even be valid for the member.

 

[dik]

Thanks... I knew it wasn't easy... else I'd have posted the question on facebook or something of that ilk... I'll take a gander at the fox's post... it looks promising. If I have a solid elipse? and take away the equivalent inner ellipse, it should accommodate the difference in wall thickness due to the cut...

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

-Dik

 

[dik]

Koot... It's for a weld... and the difference between a tube with no angle and a circle is wildly different... it's to accommodate guardrails welded on a slope.

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

-Dik

 

[Agent666]

If you find a formula for solid ellipse then outside minus inside with different minor/major axis dimensions.

https://engineervsheep.com

 

[rb1957]

my I for a solid ellipse is pi*a^3*b/4 (like pi*r^4/4 for a circle), a is major semi-axis, b is minor semi axis, I about minor axis
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 ?

 

[dik]

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

 

[rb1957]

from Bruhn ...

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

 

[dik]

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.

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

-Dik

 

[dik]

Does Bruhn have a formula about the weak axis?

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

-Dik

 

[271828]

The properties for a half ellipse are in Part 17 of the AISC Manual. Seems like one could use those to derive the properties for an entire ellipse.

 

[Agent666]

Does Bruhn have a formula about the weak axis?

Swap a and b...

https://engineervsheep.com

 

[PEinc]

Can you draw the ellipse in AutoCAD and then use MassProp command to calculate the moment of inertia.

http://www.PeirceEngineering.com

 

[rb1957]

"Does Bruhn have a formula about the weak axis?"

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

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

 

[KootK]

Actually, I don't think this is valid even for the welds. Using the ellipse shape implicitly assumes that you're delivering load perpendicular to your tube walls which is surely inconsistent with your tube design. You could do the ellipse thing but, then, you'd just have to turn around and take the parallel to tube component of that anyhow. And that would just get you back to the circle.

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

 

[dik]

koot... it's not exact and I'm happy with it for welds... it's close enough... pi*a*b^3/4 works... thanks, gentlemen... problem solved...


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

 

[KootK]

In my opinion it's not just inexact dik. Rather, it's wholly incorrect to use the ellipse without adjusting for the component of weld resistance that would be parallel to the tube walls.