Curved Beam in Plan 4

[dik]

Does anyone have formulae to calculate shear, flexure and bending moment for a circular beam in plan supported on the four sides? The issue is as shown below. I know it's 'plenty strong' (the material is BAR 3/8x1-1/2 and it's part of a railing system), but I would like to be able to put some numbers on it... Thanks

I seem to recall a design book by Reynolds from decades back (from a project in the late 60s) that had curved beams with shears, moments and torsion based on the angle and fixed ends...

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

-Dik

 

[canwesteng]

What kind of support is at the ends of the round beams, and they are just rectangular bar? If you know they are plenty strong, pretend they are simply supported at the ends, and torsionally pinned, and just use statics to compute flexure and torsion.

The screen shot looks like an elevation not a plan to fwiw.

 

[dik]

Thanks canwest... I was hoping that there was a simple formula to calculate the shear, torsion and flexure that I could plug into an SMath program. I can simplify it as you noted... using a simple span for moment due to point load, ignoring any fixity, treating it as a fixed end condition and using the distance from the chord to the circumference for torsion... but, was hoping for something a little more elegant that I might be able to used for an large radius HSS section, someday.

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

-Dik

 

[XR250]

What are doing with your life, Dik?
Where is the demand coming from? Looks like a decorative portion of a guardrail (in elevation)

 

[dik]

XR... not sure... I just like interesting problems. I'm bored, so in my spare time, I like to write SMath programs for solutions. I have no concerns about sealing the design as it stands... I know it's 'good for strong' and I can connect everything with 1/2" of 3/16 fillet weld on each side. One of my many 'personal quirks', I just like numbers.

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

-Dik

 

[WARose]

I'd check Roark's....but just about everytime I've done a horizontally curved beam, it's been with a FEA program.

 

[dik]

Thanks WARose, they have one with fixed ends that I found and could use... I was thinking it was a common enough problem that there would be a solution for a single point load at mid span of one of the quadrants...

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

-Dik

 

[SandwichEngine]

There's always AISC design guide 33 for curved member design.

 

[dik]

Thanks SWE... I didn't think about that one...

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

-Dik

 

[OldDawgNewTricks]

I was thinking it was a common enough problem that there would be a solution for a single point load at mid span of one of the quadrants...

As others mentioned, Roark's and AISC DG 33 are good references. Another good reference is Structural Concrete Theory and Design by Hassoun and Al-Manaseer. Although it's a concrete textbook, the analysis part should still apply. Here's what they have to say about a similar case to the one you mentioned:

[Edit: blurry images deleted]

 

[Toby43]

SCI publication P281 deals with curved members on plan aswell.

 

[JStephen]

With an even number of support points and symmetrical loading and supports, simplest approach is to take half of the circle as a free body, sum moments about the diameter, and find the bending moment at any point. Then knowing that, take 1/4 of the circle as a free body and sum moments to find torsion.

 

[dik]

OldDawg... can you make a picture of what you posted that is more clear? It looks like it's what I'm looking for. I can't distinguish between the thetas, and betas. Thanks

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

-Dik

 

[dik]

I think I've got them figured out...

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

-Dik

 

[robyengIT]

Dik, what about these tables (free download)?

https://mega.nz/file/Ud0WlRoI#uaIxDlqZ7AX6kbUAb8CKtKByepEU0xXtp5X6YXn5ixg

 

[OldDawgNewTricks]

dik, attempting to attach a pdf excerpt...

 

[dik]

Thanks OldDawg... that's great. It will give me something to ponder this weekend.

roby... I'll take a look.

This is a bit of work just to be able to confirm a little BAR structure in a guard works. It's obvious visually that it's way 'over built'. It's just the way I approach things... most people wouldn't bother.

Thanks for your help gentlemen...

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

-Dik

 

[canwesteng]

Hey old dawg, what text did that come from?

 

[Celt83]

I believe it is from the Hassoun conrete text book, I grabbed a copy of the 6th edition recently which has some good chapters on creep/shrinkage and stairs as well.
ABE Books Link

I'm making a thing:

http://www.thestructuraltoolbox.com

(It's no Kootware and it will probably break but it's alive!)

 

[KootK]

1) I doubt that there's a canned formula in existence anywhere that would do a decent job of this particular situation given the boundary conditions.

2) The perfect moment and torsion restraint at each end of each quadrant segment will tend to lock things up pretty good.

3) Torsional effects should be pretty much irrelevant for a bar section this stocky and this short.

4) To the extent that the bar warps at all, that will likely devolve into a torsion couple formed by two opposing arches.

5) LTB is a non-issue at the proportions being considered.

5) I'd just take the plate segment shown below, straighten it out, and run a normal beam Von Mises check on flexural stress + shear stress. Maybe deflection if you care. For anything fancier than this to be of any legitimate worth sounds like FEM to me.