Moment of inertia question for two plates welded together

[Jackolantern]

TL;DR Summary

two plates welded together, will the moment of inertia be as though it were one plate?

If two plates of Aluminum (both are 2" tall, and 1/2" thick) were placed over each other (see photo 1) and then welded together all around the perimeter of the second plate (the blue one) as indicated by the yellow lines in photo 2, then would the moment of inertia be calculated as if the local section (only where they are connected) was 2" by 1"? And would the same apply if the second plate was bolted to the first plate using many bolts?
second moment of area/moment of inertia = "I" in the bending stress formula sigma = My/I

 

[Lnewqban]

What other way could it be?

Please, see:
https://mathalino.com/reviewer/mechanics-and-strength-of-materials/superimposed-or-built-up-beams

https://mathalino.com/reviewer/mech.../spacing-of-rivets-or-bolts-in-built-up-beams

 

[Jackolantern]

What other way could it be?

Please, see:
https://mathalino.com/reviewer/mechanics-and-strength-of-materials/superimposed-or-built-up-beams

https://mathalino.com/reviewer/mech.../spacing-of-rivets-or-bolts-in-built-up-beams

Thank you for the links L, I really appreciate them. In the first link however it doesn't say anything about welded plates equating to one solid piece. I want to understand why it is that this first and second plate in my example can become as load bearing as a genuine fused and homogenous 2" x 1" bar when it only has two continuous weld beads connecting it. I want to know the "how" of it.

 

[Lnewqban]

Thank you for the links L, I really appreciate them. In the first link however it doesn't say anything about welded plates equating to one solid piece.

By clicking on the link located at the bottom right corner of each page of that first link, you will be taken to the next page, which has some explanation and comparison of resistance to bending between beams formed by attached and detached layers of material.

I want to understand why it is that this first and second plate in my example can become as load bearing as a genuine fused and homogenous 2" x 1" bar when it only has two continuous weld beads connecting it. I want to know the "how" of it.

The welding creates a path for the shear flow, preventing sliding of the plate respect to the square.
The additional plates locate more cross-section material away from the neutral axis (where is more helpful), increasing the moment of inertia.

Please, read from page 109 on at this link:
https://docs.google.com/file/d/0Bw8...Zjg/edit?resourcekey=0-GEkdRBIXq66OFnCBnteVSw

That is a copy of the excellent textbook (parts 1 and 2) that we used in the 80's.

 

[Jackolantern]

Thank you for the links L, I really appreciate them. In the first link however it doesn't say anything about welded plates equating to one solid piece. I want to understand why it is that this first and second plate in my example can become as load bearing as a genuine fused and homogenous 2" x 1" bar when it only has two continuous weld beads connecting it. I want to know the "how" of it.

L, one more question for you, what if you didn't weld directly around the perimeter, but instead welded a perimeter smaller than the total height and width of the second plate like in this photo? You wouldn't be able to then consider it as one piece then right?

 

[Lnewqban]

L, one more question for you, what if you didn't weld directly around the perimeter, but instead welded a perimeter smaller than the total height and width of the second plate like in this photo? You wouldn't be able to then consider it as one piece then right?

No, I wouldn't consider it as one bending-resistant effective piece.
You would be increasing the cross-section, but stress on the welding would be too big.

 

[Jackolantern]

No, I wouldn't consider it as one bending-resistant effective piece.
You would be increasing the cross-section, but stress on the welding would be too big.

Hm, I thought so too. I read through your 80's book until page 112, it did help me to better conceptualize this concept. I like what you said, "the welding creates a path to for the shear flow..", this makes me think that it is the weld being placed all the way at the bottom and top of the plate that allows it to transmit its shear flow to the the entire height of the 2nd plate, rather than just a portion of the plate if it were welded with that smaller perimeter.

If you were to only weld that small perimeter, I suppose the new cross section would look something like this?

 

[Lnewqban]

If you were to only weld that small perimeter, I suppose the new cross section would look something like this?

No, more like this:

 

[Jackolantern]

No, more like this:

View attachment 323202

No, more like this:

View attachment 323202

I see...the strength of the weld has to matter here, back to the example of the full perimeter weld as in the photo. We can only assume this as one homogenous section so long as each seam can resist the shear stress, I'm reading my own mechanics of materials book on it right now but I suppose we wouldn't be able to just say if the weld yield stress is greater than the base material then we have nothing to worry about?

 

[Lnewqban]

We can only assume this as one homogenous section so long as each seam can resist the shear stress, I'm reading my own mechanics of materials book on it right now but I suppose we wouldn't be able to just say if the weld yield stress is greater than the base material then we have nothing to worry about?

The weld is calculated based on its cross-area times length besides yield stress.

If we are still discussing two plates of Aluminum, both being 2" tall, and 1/2" thick, please consider how small this cross-section, which resists bending is.
Any welding or drilling will weaken the main 2" tall and 1/2" thick aluminum plate to some degree.

Unless the side plate is running most of the span, the single plate cross-sections located immediately next to the second plate will be exposed to more or less the same bending moment and lateral buckling.

Please, research wing aluminum spar for examples of efficient small beams in restricted spaces.

Example:
https://www.google.com/search?q=alu...g&ei=75MDZOGoJa6dp84P8-e1yAs&bih=684&biw=1007

Please, see also:
https://en.wikipedia.org/wiki/Spar_(aeronautics)

 

[Jackolantern]

The weld is calculated based on its cross-area times length besides yield stress.

If we are still discussing two plates of Aluminum, both being 2" tall, and 1/2" thick, please consider how small this cross-section, which resists bending is.
Any welding or drilling will weaken the main 2" tall and 1/2" thick aluminum plate to some degree.

Unless the side plate is running most of the span, the single plate cross-sections located immediately next to the second plate will be exposed to more or less the same bending moment and lateral buckling.

Please, research wing aluminum spar for examples of efficient small beams in restricted spaces.

Example:
https://www.google.com/search?q=alu...g&ei=75MDZOGoJa6dp84P8-e1yAs&bih=684&biw=1007

Please, see also:
https://en.wikipedia.org/wiki/Spar_(aeronautics)

You're right, but this is similar stuff we talked about in the other thread though, we need to keep on a different subject otherwise the mods will take it down.

Regarding welding, I've rechecked my analysis of my little project and the force that's caused bending will actually be smaller than anticipated, so small that I'm certain a riveted plate on each side of the HAZ will work. But there's something else I don't think I did correctly, could you check out this other thread I started?

https://www.physicsforums.com/threads/free-beam-moment-problem.1050496/#post-6861756

 

[IdBdan]

How do you bond faying surfaces for added strength? Methyl Methacrylate Adhesives

Many of the new adhesives for aluminum & steel have a strength of 30 MPa. In a test I did with Loctite HHD8000, the adhesive out performed just bolted by 12%. Also did the same test addding a 3" staggered edge weld. Not much help but a little better.

HHD800 has a shear strength of 2650psi with aluminum. I've found that a drilled and torque bolted connection after a firmly clamped adhesive cure time is best. These adhesives have spacer beads in them to allow a predetermined thickness of bond material. Over tightening with bolts during the cure can defeat that objective. And, as I found out .... it glues the bolt in the hole. A glued joint you're never removing the bolts anyway and it may be an advantage?

I look at "glue & metals?" in a whole new light now. It may not be a design you can put 100% assurance in but it's a great CYA factor.