channel strength shelf reinforcement

[BFBOB]

Here's a question for you structural engineers: How does the strength of a beam made of channel vary with orientation? Let's make it simple. The channel is symmetrical, and of uniform thickness. Think of it as three sides of a square tube. Consider it a classical beam, supported at each end and uniformly loaded. Is it stronger with the open side up, down, sideways, or does it matter?

My application: reinforcement under some flimsy plastic shelves. they're almost strong enough, and I have a few pieces of aluminum channel about 1/2" on a side and 1/16" thick.

Sure, I could try it and see, but where's the sport in that?? I'd really like to see some sort of analysis just for the intellectual exercise. My initial thought experiment tells me that open side up is the worst because the open edges will buckle under compression pretty easily. Open side down is next because the open edges are relatively thin and will stretch under tension. Best is open side sideways. Then it acts more like an H beam. But, its strength is then asymmetrical and it may twist.

Any thoughts?

 

[er3456df]

I'm going to say "empty side up", but I'm not positive. Just what I've heard.

 

[Strouty]

I would like to hear qualified answers, good question.

 

[readhead]

Need more info. Span? Weight to support, now and possible? Alloy? Seems like a pretty small section that could be bent by hand. The simple answer is web verticle.

 

[CJKaz]

With the engineering term in parenthesis:

Your thinking is correct. You want to maximize the amount of material at a distance from the center of your channel (neutral axis). The "I" beam is the most common use of these properties. With the open end up you have little material at the top, it will "buckle" Open end down, the channel will bend more. Open to the side, you have equal material at the top & bottom (flanges). Think of your section is like an "I" beam with the center (web) offset to the side. It will twist, but you'll likely never notice it (shear center).

Many of the calculations boil down to a factor called section modulus which is published for a variety of shapes. A search for terms such as beam bending, moment of inertia will give all of the exhausting calculations.

 

[Modern Jess]

The Unistrut General Engineering Catalog has this cryptic bit of information:

The stiffness of the beam’s cross-sectional shape is measured by its “Moment Of Inertia” or "I". The larger a beam’s "I", the stiffer it is and the less it will deflect. A beam’s "I" can change for each major axis. The "I" of both major axes (I 1-1 and I 2-2) are provided.

Digging deeper, we find this chart associated with each type of unistrut they sell. This one is for the basic P1000:

So with a better value for I, Axis 2-2 seems to be the preferred one. But which axis is which? Well, they don't exactly go out of their way to make it clear. There are a couple of numbers buried in the dimensional diagram:

But even with that, it's tough (at least for a layman such as myself) to figure out which axis is which.

 

[Modern Jess]

Here's some more data that either makes it clearer or muddier, depending on the day of the week.

Looking at the Unistrut P5000 series, we see that has a rectangular section, rather than a square one. The axis numbers are labeled in the same fashion as the P1000 series:

This is what Unistrut has to say about the moment of inertia of the P5000 series:

Here, Axis 1-1 is clearly favored with a better I value.

What conclusions can we draw from this? Well, I can infer what this means for myself, but since I'm not actually a qualified professional, I'm somewhat hesitant to state it out loud.

EDIT: And I note with some amusement that while Unistrut does indicate which axis is stiffer, it says nothing about the two directions of that axis. In other words, whether the open side is up or down does not seem to matter.

 

[bczygan]

Here's a question for you structural engineers: How does the strength of a beam made of channel vary with orientation? Let's make it simple. The channel is symmetrical, and of uniform thickness. Think of it as three sides of a square tube. Consider it a classical beam, supported at each end and uniformly loaded. Is it stronger with the open side up, down, sideways, or does it matter?

My application: reinforcement under some flimsy plastic shelves. they're almost strong enough, and I have a few pieces of aluminum channel about 1/2" on a side and 1/16" thick.

Sure, I could try it and see, but where's the sport in that?? I'd really like to see some sort of analysis just for the intellectual exercise. My initial thought experiment tells me that open side up is the worst because the open edges will buckle under compression pretty easily. Open side down is next because the open edges are relatively thin and will stretch under tension. Best is open side sideways. Then it acts more like an H beam. But, its strength is then asymmetrical and it may twist.

Any thoughts?

Sideways is the answer based on your example as well as the typical channel section.
As you surmised, you need a top web to resist compression and a bottom web to resist tension and a vertical web to do both and connect the top and bottom webs. Exact proportions of the parts of the section are more ideal in a typical channel than in what you are using.

 

[bczygan]

Note that they show the axis closer to the closed end, giving the open end more meat to match it.

 

[Rickenbackerman]

I'm an engineer, maybe I can offer some insight.

Lets look at the tube cross section in pure bending... Sigma (stress) = M*c/I. M = applied moment (torque). c = distance from the neutral axis of the cross section to the outer fiber. I = moment of inertia for the cross section.

Since you said the tubing is square, everything in the equation stays the same except for I. I drew it up real quick in some software I have - 1/2" by 1/2" tubing with a 1/16" wall.

Iyy= 0.0032857 Izz= 0.0021254
Iyy is with the open end to the left or right (same result)
Izz is with the open end at the top or bottom (again, same result)

So, Iyy is stronger - open end left or right. Problem is, you have to consider the whole scenario - the shelf itself is part of the cross section, too! I'd reckon that open side up would be the strongest since in that case you're closing out the open side of the U with the shelf, giving you a boxed-in cross section.

 

[bczygan]

I'm an engineer, maybe I can offer some insight.

Lets look at the tube cross section in pure bending... Sigma (stress) = M*c/I. M = applied moment (torque). c = distance from the neutral axis of the cross section to the outer fiber. I = moment of inertia for the cross section.

Since you said the tubing is square, everything in the equation stays the same except for I. I drew it up real quick in some software I have - 1/2" by 1/2" tubing with a 1/16" wall.

Iyy= 0.0032857 Izz= 0.0021254
Iyy is with the open end to the left or right (same result)
Izz is with the open end at the top or bottom (again, same result)

So, Iyy is stronger - open end left or right. Problem is, you have to consider the whole scenario - the shelf itself is part of the cross section, too! I'd reckon that open side up would be the strongest since in that case you're closing out the open side of the U with the shelf, giving you a boxed-in cross section.

That would be true, but only if you could make the shelf truly part of the cross section by a continuous connection the length of both open legs of the channel. If both the shelf and channel were of the same material, plastic or metal, they could be glued or welded continuously. But they are not. So the strongest is with the open part facing outward, giving the least span of the shelf from channel to channel, all the way around. But the neatest is with the open to the inside.

 

[Rickenbackerman]

That would be true, but only if you could make the shelf truly part of the cross section by a continuous connection the length of both open legs of the channel.

In theory, yes. But in reality I believe a bolted (or screwed) connection every four-six inches or so would approximate a continuous connection. Besides, I could make the same argument: C-shaped cross sections are absolutely terrible in torsion, and with the open end facing left or right, you've got an offset cross section (inducing torsion under bending) and would also need a continuous connection in that case to resist torsion, no?

BTW, OP - you said "open side up is the worst because the open edges will buckle under compression pretty easily". That would be true, if the open edges were in compression - they're not! With the open face up and the tubing under the shelf, the edges of the legs of the U will be in pure tension. Tension = no buckling.

 

[bczygan]

In theory, yes. But in reality I believe a bolted (or screwed) connection every four-six inches or so would approximate a continuous connection. Besides, I could make the same argument: C-shaped cross sections are absolutely terrible in torsion, and with the open end facing left or right, you've got an offset cross section (inducing torsion under bending) and would also need a continuous connection in that case to resist torsion, no?

BTW, OP - you said "open side up is the worst because the open edges will buckle under compression pretty easily". That would be true, if the open edges were in compression - they're not! With the open face up and the tubing under the shelf, the edges of the legs of the U will be in pure tension. Tension = no buckling.

Isn't it true that the entire channel would only be solely in tension if the continuous connection to the shelf was true, AND the shelf section was substantial enough that the neutral axis was between it and the channel and the shelf took all the compression? How substantial is the plastic shelf? What are the expected loads?

 

[Rickenbackerman]

I didn't say anything about the "entire channel". The bottom of the channel will obviously be in compression. The top of the channel would be in tension as long as the neutral axis is somewhere below the top of the tubing, and since the OP said the shelf material was pretty wimpy, I assumed it would be. And I'm still not really buying your "continuous connection" argument - if that were the case bridges wouldn't be held together with bolts! I realize that is a pretty generalized statement, but I think you get my point.

Good discussion! But I gotta roll for the night. I'll check in on this thread tomorrow...

 

[bczygan]

I didn't say anything about the "entire channel". The bottom of the channel will obviously be in compression. The top of the channel would be in tension as long as the neutral axis is somewhere below the top of the tubing, and since the OP said the shelf material was pretty wimpy, I assumed it would be. And I'm still not really buying your "continuous connection" argument - if that were the case bridges wouldn't be held together with bolts! I realize that is a pretty generalized statement, but I think you get my point.

Good discussion! But I gotta roll for the night. I'll check in on this thread tomorrow...

It is getting late, and we're getting tired(You mixed up tension and compression). And you are right, it should be continuous enough of a connection. Bolts are a good example.

Bill (Not an engineer but played one in a few Arch. offices).

 

[CJKaz]

Original post stated thin plastic shelf, even if connected to tube the contribution to the resulting composite beam would be negligible (yield strength of plastic vs steel). The neutral a is would still be in the tube's cross section. Compression above the neutral axis tension below.

 

[WNYflyer]

Original post stated thin plastic shelf, even if connected to tube the contribution to the resulting composite beam would be negligible (yield strength of plastic vs steel). The neutral a is would still be in the tube's cross section. Compression above the neutral axis tension below.

Or you could calculate the transformed composite section based up the Modulas of Elasticities of the differing materials. Then you could look at real stresses versus the allowables.

 

[Rickenbackerman]

It is getting late, and we're getting tired(You mixed up tension and compression). And you are right, it should be continuous enough of a connection. Bolts are a good example.

Bill (Not an engineer but played one in a few Arch. offices).

The neutral a is would still be in the tube's cross section. Compression above the neutral axis tension below.

You guys both have it backward... it's a simple cantilever beam... I found this with google search, imagine you're looking at the shelf from the side.
<img src="http://classconnection.s3.amazonaws.com/111/flashcards/445111/jpg/cantilever_beam_moment1319407839731.jpg">

And I still say that this:

Has more inertia than this:

 

[readhead]

Buy some plywood.

 

[Amarch22]

And I still say that this:

Has more inertia than this:

Agreed, provided (again) that composite action can be developed. I don't think that's happening based on (1) OP's description and two (2) almost zero strength of the plastic in compression (i.e., "flimsy").

Also,
From the OP:

Consider it a classical beam, supported at each end and uniformly loaded.

Doesn’t jive with:

You guys both have it backward... it's a simple cantilever beam...

IMHO, there are too many generalties floating around on this thread for it to be of much use (unfortunately).

 

[readhead]

The op never came back. He probably threw everything away and set fire to the garage to get rid of the shelves.

 

[Spareparts]

Beating this up real good, just get a spring scale and 3 pieces of the channel and test it yourself. Don't sound that difficult and you learn something about engineering even if it a little country

 

[darkk]

Soooooooooooooo.......who's buying the ******* beer?

 

[readhead]

No one. It fell on the floor when the shelves broke.
Oh you mean the new beer.

 

[JimVonBaden]

Are you guys taking into account the two "J" forms of the open ends? These should, in theory, add rigidity to the open side. SO, open end up, shelf on top. Add strenth by used bolts through the shelf and the appropriate spring clips to hold the bolts in tension on the "J"s.

Those curved ends, "J"s, look significant to me.

Jim

 

[Strouty]

If you wanted it to be even stronger you could put two pieces back to back and end up with a mini Ibeam.

 

[where2]

If you wanted it to be even stronger you could put two pieces back to back and end up with a mini Ibeam.

Exactly what i was thinking, but you'll need a continuous adhesion between the two pieces, so they act as one I shaped piece as load is applied.

This reminds me of college physics class for engineers problems...

 

[BFBOB]

Wow, this is a great discussion. I gave up too soon in my internet search - had forgotten all about Unistrut. For me, the Unistrut data is conclusive. The 5000 series specs were the key. It is so much taller than wide (as shown in the drawing) it just has to be stronger with the long axis vertical- and it is, by a large factor. That tells us which is axis 1 and 2 in the drawing, which is certainly not made clear. Applying that back to the nearly-square 1000 series, the data show it is stronger oriented open-side-sideways, but not by very much. As one Journalisto pointed out, the rolled edges add quite a bit of material and strength both in compression and tension, but still the shape wins out.
Several of you made arguments for the sideways orientation, noting it's like an I beam with the web off center.
So, with all this data, I decided to do a test. I supported the ends of a 2' length of the stuff on my workbench with a steel rule standing behind. I set a 10 lb weight in the middle and measured the deflection. With the open side up or down, it deflected 6/32. With the open side sideways, it only deflected 4/32.
That makes me an expert (someone whose last guess turned out to be right).
In any case, the channel is way stronger than necessary in either orientation - the shelves in question are cheap stackable in/out trays on my desk.
Thanks for a fun thought experiment!
I've seen one commercial application where wooden shelves are reinforced by formed-steel channel, and it is oriented open side sideways. But maybe that doesn't count since the channels are wrapped around the edges, probably as much for protectingthem from abrasion as stiffening.

 

[WNYflyer]

I'm an engineer, maybe I can offer some insight.

Lets look at the tube cross section in pure bending... Sigma (stress) = M*c/I. M = applied moment (torque). c = distance from the neutral axis of the cross section to the outer fiber. I = moment of inertia for the cross section.

Since you said the tubing is square, everything in the equation stays the same except for I. I drew it up real quick in some software I have - 1/2" by 1/2" tubing with a 1/16" wall.

Iyy= 0.0032857 Izz= 0.0021254
Iyy is with the open end to the left or right (same result)
Izz is with the open end at the top or bottom (again, same result)

So, Iyy is stronger - open end left or right. Problem is, you have to consider the whole scenario - the shelf itself is part of the cross section, too! I'd reckon that open side up would be the strongest since in that case you're closing out the open side of the U with the shelf, giving you a boxed-in cross section.

Wow, this is a great discussion. I gave up too soon in my internet search - had forgotten all about Unistrut. For me, the Unistrut data is conclusive. The 5000 series specs were the key. It is so much taller than wide (as shown in the drawing) it just has to be stronger with the long axis vertical- and it is, by a large factor. That tells us which is axis 1 and 2 in the drawing, which is certainly not made clear. Applying that back to the nearly-square 1000 series, the data show it is stronger oriented open-side-sideways, but not by very much. As one Journalisto pointed out, the rolled edges add quite a bit of material and strength both in compression and tension, but still the shape wins out.
Several of you made arguments for the sideways orientation, noting it's like an I beam with the web off center.
So, with all this data, I decided to do a test. I supported the ends of a 2' length of the stuff on my workbench with a steel rule standing behind. I set a 10 lb weight in the middle and measured the deflection. With the open side up or down, it deflected 6/32. With the open side sideways, it only deflected 4/32.
That makes me an expert (someone whose last guess turned out to be right).
In any case, the channel is way stronger than necessary in either orientation - the shelves in question are cheap stackable in/out trays on my desk.
Thanks for a fun thought experiment!
I've seen one commercial application where wooden shelves are reinforced by formed-steel channel, and it is oriented open side sideways. But maybe that doesn't count since the channels are wrapped around the edges, probably as much for protectingthem from abrasion as stiffening.

Deflection varies with the moment of inertia "I" (Iyy, Izz) of a section. The bigger the "I" the less deflection.

So check out the ratio of Iyy to Izz values above and the ratio of your deflections you came up with..............notice anything?

Iyy divided by Izz approx. 1.5.............. 6/32 divide by 4/32 = 1.5

So you just proved/confirmed by experimentation the ratio of the "I's" of the section.

Good job

 

[CJKaz]

Hey WNYflyer, is that Bethlehem logo from the Buffalo site? Was up there several years ago and saw what was left. Sad. Lived within smelling distance of the Bethlehem PA mill back in the '80s.

This discussion brought back some long lost mechanics of materials memories. Still in there after 30+ years

 

[srmofo]

Deflection varies with the moment of inertia "I" (Iyy, Izz) of a section. The bigger the "I" the less deflection.

So check out the ratio of Iyy to Izz values above and the ratio of your deflections you came up with..............notice anything?

Iyy divided by Izz approx. 1.5.............. 9/32 divide by 6/32 = 1.5

So you just proved/confirmed by experimentation the ratio of the "I's" of the section.

Good job

Where did the 9/32 come from? 6/32 divided by 4/32 is 1.5 though

 

[WNYflyer]

Where did the 9/32 come from? 6/32 divided by 4/32 is 1.5 though

You are correct sir ! Brain Fart !!! been a very long day

 

[srmofo]

You are correct sir ! Brain Fart !!! been a very long day

Ok just making sure I wasnt the one lost...Ive been stalking this thread since the beginning and initially thought the beam would be stronger in the up/down orientation simply because it has twice as much material that way.

I never considered that that material would be put both into compression on the top half and tension in the bottom half and the fact it would be much more susceptible for the whole rig to fold up because it has less strength in the horizontal plane to resist those forces. (Basically the beam can fold like a 'V' easier, because its easier to distort)

With the open positioned sideways, The top is completely in compression, the bottom completely in tension , and the side is going to keep those from folding into the 'V'

 

[WNYflyer]

Hey WNYflyer, is that Bethlehem logo from the Buffalo site? Was up there several years ago and saw what was left. Sad. Lived within smelling distance of the Bethlehem PA mill back in the '80s.

This discussion brought back some long lost mechanics of materials memories. Still in there after 30+ years

CJKaz

I think the Avatar is from a building in Bethlehem Pa. actually. Yup, I think there is nothing much left on the lake side in Lackawanna other than the abandoned North office building and the more modern South office .

I believe across the road some facilities are now or going to be re-used for some kind of newer pipe mill. I am sure it has to do with all the natural gas production on the NY/PA border areas and such.

Smelling distance from the mill? A steel mill smells? usually it is the Coke Ovens if they have them