Deflection of a perforated Beam

[Leo Baldwin]

Trying to find moment of inertia in^4) for a steel beam that looks like the attached (22 gauge steel).
Finding MOI for any beam is easy if it has no side holes.
Not sure if it helps, but I can actually have SolidoWorks FEA analysis done to get the total deflection.
I need to find the MOI (in^4) to be able to quickly get deflection calc with varying loads/spans.

 

[phamENG]

For quick checks? look at the MOI for the section ignoring the area of the web that's removed. In other words, find the MOI for the flanges and the little bit of the web between the flanges and the smaller holes - ignore the rest. Use the neutral axis through the middle of the web, of course. It's the flanges that are doing the heavy lifting anyway - the web is just there to transfer shear.

 

[WARose]

I've typically used a conjugate beam/moment area method to get the deflection on something like that. (Unless I used FEA.) Don't know if you can back out of that with a equivalent MOI.

 

[KootK]

Like phamENG suggested, I'd normally just model the member as two solid angles separated in space and representing the portions of the cross section always beyond the extremes of the penetrations. For something like this, shear deformation might be of some significance (as might shear buckling). A poor man's way to capture that might be to take the effective [Ix] just discussed and reduce that by 15% or so as we sometimes do with trusses.

 

[Leo Baldwin]

Phew - glad my top/bottom flanges are continuous
Thank you guys! I think I will do just that and ignore the about 4" of the web..

I am guessing the same 'ignorance' would apply to section modulus?

 

[KootK]

I would say so, yes.

 

[dik]

If you have lots of them, I'd suggest a load test to determine ratio of Ieff/Ic. I'd suspect the real I value would be better than 80% of the solid section.

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

-Dik

 

[rb1957]

do you think shear deflection could be an issue ?

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

 

[dhengr]

Leo Baldwin:
I would think that the manufacturer might have some literature, a tabulation, method for calculating, the effective section properties for the structural use of their products. They must know they will be needed, from time to time. I’d ask them for this info. If we don’t know how to calc. these basic props., and how to treat that web geometry, how do we know that we are modeling the section properly for a FEA program? Thus, do we (can we) trust the FEA results?

 

[Leo Baldwin]

Good points guys!
here's what I come up with:

 

[Aesur]

I agree with using the last one, especially if this is just a quick check.

 

[Leo Baldwin]

Thank you!

 

[dold]

Out of curiosity, what is the member going to be used for? 22ga seems awfully thin for a purlin, or any sort of load bearing member for that matter. Knocking on the door of web slenderness limits also. I wonder if a reduced effective thickness of the web would be a consideration? Similar to how one would calc properties of a perforated light gauge panel.

 

[Leo Baldwin]

Dold;
a series of these at 12" o/c get fused inside EPS formwork panels for concrete floors. So plenty of lateral support - they only span about 6ft between aluma shoring beams and support up to a max of about 120psf... Or plf. They are non-structural - after concrete cures they turn from shoring into finishing furring.

 

[dold]

Gotcha. Interesting.

 

[dhengr]

Leo Baldwin:
In truth, I suspect that section acts kinda like a small stl. truss, with the horiz. (top & bot.) chords as you show in your last section view (the red view), to the right, and diag. chord members making up the solid diag. stl. web material btwn. the punched holes, and connecting the top & bot. chord members. The diags. are crossing diags. centered around each large hole.

 

[dik]

I'm pretty sure it will be greater than the 3rd one = 0.797493... My WAG was 0.8 x 0.987943 = 0.790354, but we're splittin' hairs.

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

-Dik

 

[rb1957]

you could consider the web as a truss ... straight elements diagonally between the holes

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

 

[MIStructE_IRE]

Kloeckner metals have some very sophisticated free software to cover cellular beams - however even they’re not brave enough to introduce the additional smaller holes you have there!

Vierendeel bending/buckling will be difficult to justify with those smaller holes in place. A very interesting make and break thesis for someone!

 

[rb1957]

yeah, those little holes are pretty much cosmetic, in that they won't save much weight but they look "sexier" ?

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