Moment of inertia question for two plates welded together

• Jackolantern
In summary, the moment of inertia for two plates welded together can be calculated by adding the individual moments of inertia for each plate and accounting for the weld between them. This calculation is important for determining the resistance of the welded plates to rotation and bending moments. The moment of inertia can also be affected by the shape and size of the plates as well as the material properties. It is a key factor in the design and analysis of welded structures.
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

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Lnewqban said:
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
Jackolantern said:
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.

Jackolantern said:
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.

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

Jackolantern said:
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?

Jackolantern said:
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
Lnewqban said:
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?

Jackolantern said:
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
Lnewqban said:
No, more like this:

View attachment 323202
Lnewqban said:
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?

Jackolantern said:
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://en.wikipedia.org/wiki/Spar_(aeronautics)

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Lnewqban said:
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://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?

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.

Lnewqban

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is also known as rotational inertia.

2. How is moment of inertia calculated for two plates welded together?

The moment of inertia for two plates welded together can be calculated by adding the individual moments of inertia of each plate, taking into account their distance from the axis of rotation.

3. What factors affect the moment of inertia for two plates welded together?

The moment of inertia for two plates welded together is affected by the mass and distribution of the plates, as well as their distance from the axis of rotation.

4. How does moment of inertia impact the rotational motion of an object?

A higher moment of inertia means that more force is required to change the rotational motion of an object. This can result in slower rotation and more stability for the object.

5. Can moment of inertia be changed for two plates welded together?

Yes, the moment of inertia for two plates welded together can be changed by altering the mass or distribution of the plates, or by changing the distance from the axis of rotation.

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