Steel tubing strength

I'm trying to determine the best square tube steel to get for my theatrical flats project.  Price is a big concern.

I can get (these are rough estimate numbers)
- 1" 16ga for $1.15/ft
- 1" 14ga for $1.24/ft
- 1.25" 16ga for $2/ft

The weight per foot of the 1" 14ga is almost identical to the 1.25" 16ga, which means the 1.25" would be stronger, but how much stronger?  Worth 60% more cost?

All of them are overkill for the sake of constructing scenery and rigging to fly, but I'm thinking more about transporting, storing, volunteers dropping them, etc.  I'm thinking resistance to bending.

Is there an ASTM resource that shows modulus, deflection, etc that I can compare?

1.25" seems like overkill. No science. Just my gut. 

I'm assuming for simplicity that your Strength of all the materials will be sufficient.  What it sounds like you are more concerned about its Stiffness.

Stiffness of a member is a lot of math based on length of span, loading applied, material properties and geometry of cross section.  Since all of these are the same type of metal and the only thing that varies is the tube geometry we can greatly simplify the beam deflection equation to what we care about.   GROSSLY oversimplified the beam equation becomes

Deflection = X / I

where I is the moment of inertia of the cross section and X is an arbitrary number that is the simplification of all the rest of that stuff we talked about.  

Moment of inertia of a square is

(WxH)^3/12. 

Where W is width, H is height.  Of note is that the Height dimension is CUBED so Inertia is DOMINATED by height.  This is why I beams are I-shaped.  It increased the height of the section while decreasing it's material usage.

Moment of Inertia of a Hollow Tube is

(Wo x Ho^3)/12 - (Wi x Hi^3)/12

Wo / Ho is Width/Height outer dimension, Wi / Hi is Width/Height inner dimension, so Wi=Wo-2*Wall, Hi=Hi-2*Wall.

So since Stiffness puts the Inertia on the bottom an INCREASE in inertia results in a DECREASE in deflection.  For things like buckling formulas or peak bending stress the relationship is the same, increased inertia always reduces the stress in the beam making it more resistant to bending/buckling.

So to your question.

The difference between 14 ga and 16 ga will be a very minor increase in stiffness for the weight cost.   The 1.25 tube will be MUCH stiffer if that's important to you.  basically 2x as stiff.

Notice I'm not bothering with raw numbers here.  The other factors all are the same so I can easily give a relative deflection between the tubes but if you wanted empirical numbers I would need much more information.

I would probably just use the 1x1 16ga to save money and keep spans down, but I have no idea what you are building.

How is this stuff built? Since the larger tube is double the bending strength, can you use half as much? That would be a net cost savings. But there's a lot of reasons why that might not be possible to do so.

Also..  of note.   The LMP360 contains 116' of 1×1-16ga.  When I bought it it was only $0.68/ft.

I just got a quote at $1.04/ft.  

Tube dents could be an issue with the thinner gauge, especially if you are concerned about drops.

I dont think there is enough here to make the call.  a lot determines on how you will be building.  As previously said, if you go with bigger tubing will it cut down on total length of tubing?  are we talking about 10' of tubing overall or talking 10,000 feet of tubing.  are you concerned about structural damage to the tubing or cosmetic damage to the tubing.  Just as the LM360, most Locosts are built with 1x1 16ga sq tubing including mine and it si not easy to dent.    You have to smack it rather hard with a hammer to dent it  or drop it off the roof.    The original Lotus 7s were 3/4" 18ga.   The other thing to consider is if you make it out of the heavier tubing, are your crews more likely to drop or damage it moving it around due to the extra weight?   Lighter tubes are easier to move around without damage.  

I would start with the 16ga 1"x1" and build the first one to get a feel for it then determine path forward for the rest.

For more detail on what is being built,  head over to my other thread.

1x1x14ga and 1.25x1.25x16ga are 18% and 27% heavier than 1x1x16ga respectively. It's not much on short tubes, but if somebody wants to carry multiple full sticks it can make a difference in the ease of doing so.

In my experience, 1x1x16ga is reasonably handling damage resistant.

FieroReinke said:

I dont think there is enough here to make the call.  a lot determines on how you will be building.  As previously said, if you go with bigger tubing will it cut down on total length of tubing? 

It won't cut down on overall length needed for the project.  It's more of a "what's my minimum strength needed"

The answer is nebulous because in actual use, any of them are overkill.  It's the durability of storage, transport, etc.

Would angle be sufficient instead of square tube?

nocones said:

I'm assuming for simplicity that your Strength of all the materials will be sufficient.  What it sounds like you are more concerned about its Stiffness.

Stiffness of a member is a lot of math based on length of span, loading applied, material properties and geometry of cross section.  Since all of these are the same type of metal and the only thing that varies is the tube geometry we can greatly simplify the beam deflection equation to what we care about.   GROSSLY oversimplified the beam equation becomes

Deflection = X / I

where I is the moment of inertia of the cross section and X is an arbitrary number that is the simplification of all the rest of that stuff we talked about.  

Moment of inertia of a square is

(WxH)^3/12. 

Where W is width, H is height.  Of note is that the Height dimension is CUBED so Inertia is DOMINATED by height.  This is why I beams are I-shaped.  It increased the height of the section while decreasing it's material usage.

Moment of Inertia of a Hollow Tube is

(Wo x Ho^3)/12 - (Wi x Hi^3)/12

Wo / Ho is Width/Height outer dimension, Wi / Hi is Width/Height inner dimension, so Wi=Wo-2*Wall, Hi=Hi-2*Wall.

So since Stiffness puts the Inertia on the bottom an INCREASE in inertia results in a DECREASE in deflection.  For things like buckling formulas or peak bending stress the relationship is the same, increased inertia always reduces the stress in the beam making it more resistant to bending/buckling.

So to your question.

The difference between 14 ga and 16 ga will be a very minor increase in stiffness for the weight cost.   The 1.25 tube will be MUCH stiffer if that's important to you.  basically 2x as stiff.

Notice I'm not bothering with raw numbers here.  The other factors all are the same so I can easily give a relative deflection between the tubes but if you wanted empirical numbers I would need much more information.

I would probably just use the 1x1 16ga to save money and keep spans down, but I have no idea what you are building.

This is excellent.  Just for clarity, the percentages at the right side of that chart are relative numbers based on an unknown force?  So like if I had equal spans of each tube and hung a weight in the middle, in theory, the deflection might hypothetically look like:

1" 16 ga might deflect 10mm
1" 14 ga might deflect 8.7mm
1.25" 16 ga might deflect 4.9mm

Am I extrapolating correctly?  I know it's totally not scientific and all relative, I just know there are times when volunteers step where they shouldn't, or assume something is beefier than it actually is.  Having the extra rigidity before yield might mean that an accidental step or drop might save it.  I guess I'm thinking that if it cuts my accidental bends in half, it might be worth it.

All three formats are dancing around 1 lb/ft.  The smallest is .83 lbs and the heaviest is 1.03 per foot, so it's not like a massive weight difference.

wae said:

Would angle be sufficient instead of square tube?

Likely, yes, but the added rigidity of tube means I can get by with less weight.  Tube also offers other benefits when hanging/rigging.

In reply to Curtis73 (Forum Supporter) :

Yes it's relative deflection with the classic 1*1-16ga being "100%".  Load does not apply through a squared term so it should just be linear.  I can take a stab at figuring up the load required to actually bend a tube but from personal experience at 6' spans 1" is beyond a 240lb person as I tested it when I used it for the spar on the LMP360 wing.

Also.. as an additional option.  I noticed 1-5/8 steel studs are ~$6.50/10'..  so $.65/ft.  Which..  is pretty cheap.    They are listed at 2.4lbs/10' so .25lbs/ft so they would make some light panels.  

In reply to nocones :

I think your description and math are a great thing.  I'm not sure that additional mathing will add anymore clarity.

I actually have enough 3/4" 16 ga to built a test piece.  If it holds up, then I'm sure 1" 16ga will.  My longest span is 8'.  It's a 4x8 theatrical wall unit that looks like this and gets skinned with 5mm lauan.

nocones said:

Also.. as an additional option.  I noticed 1-5/8 steel studs are ~$6.50/10'..  so $.65/ft.  Which..  is pretty cheap.    They are listed at 2.4lbs/10' so .25lbs/ft so they would make some light panels.  

Also, cheaper than 2x4-10 lumber

After seeing what you're doing, would channel iron be a better choice?  Might be able to be lighter and stiffer in the directions you care about, as well as being cheaper than tubing?  I haven't looked into the price of it recently since I haven't had any projects involving it, but years ago I did a project and was able to shave about 15-20% of the weight over comparable sq. tubing.

In reply to WonkoTheSane :

I can get into it more later, but the easy button is tubing.  Going with something not-tubing gets into much greater levels of fabrication for legal rigging/flying.  Being able to pass wire rope through tubing to rig means getting around a small truckload of additional forged hardware, welding, etc.

In reply to Curtis73 (Forum Supporter) :

I wasn't picturing the tubing being left open at the top. 
 

You can have the same ability to connect and hinge without any of the stuff I previously posted. 
 

Make a few connector clips that look like this:

Use pipe or round tubing that fits snugly inside your 1" square tubing. You won't need ANY bolts or nylocks, you can have 2 sided flats that hinge, and you won't need any tools to assemble. 

I do shelving systems that hold thousands of pounds that are connected to each other only by a large hairpin that slips down into the tube. 

Considering that your wood flats are built out of 1x3s, I think that the lightest steel would be fine.

SV reX said:

In reply to Curtis73 (Forum Supporter) :

I wasn't picturing the tubing being left open at the top. 
 

You can have the same ability to connect and hinge without any of the stuff I previously posted. 
 

Make a few connector clips that look like this:

Use pipe or round tubing that fits snugly inside your 1" square tubing. You won't need ANY bolts or nylocks, you can have 2 sided flats that hinge, and you won't need any tools to assemble. 

I like that idea.  One of my first thoughts was that type of thing, but with some kind of spring or adjuster screw in the middle.  As you bend the hinge, the distance between the holes will change, so a spring or means of adjustment will keep the seams tight.

VolvoHeretic said:

Considering that your wood flats are built out of 1x3s, I think that the lightest steel would be fine.

After visiting a steel yard today and comparing all three, I agree with you.  16 ga is a lot thicker than I remember.

So, for those of you asking about channel or angle, here's the longer explanation.

When rigging to fly in theater, things are a bit different than commercial/industrial.  The rules are a little more pragmatic considering you're not hanging a permanent thing like a gantry crane that will be used 18 hours a day for 75 years.  We're talking about flying a 400-lb thing for two weeks.

So, consider the picture above of the framing construction.  Let's say I need to make a suspended/flying wall that is 24' high and 16' wide. (coincidentally, I just did this exact thing tonight at a local high school)  The layout will be 3 of these walls tall and 4 wide.  SOP requires that the entire structure be held in compression, not tension.  That means the wire rope needs to attach to the bottom of the walls instead of bolting them all together and just picking it up from the top row.

Being able to pass a wire rope down through all 24' of tubing means the entire thing is under compression at the center of their mass.  The flats on the 2nd and 3rd row up (even though they're bolted together) are just floating, and entirely suspended along the center of their mass.  Theoretically, they don't even need to be bolted together.  This does two primary things:  1) makes them hang plumb, which is important when you have 6-8" between the flying pipe and, say, the next pipe full of light fixtures, and 2) removes a moment of force.  If I hang from the back of channel or angle, there is a significant amount of weight in front of the wire rope.  If the steel were compromised, there is a moment of force that would tend to cause the center of the steel to buckle forward and collapse under its own weight.  

With tubing, not only is that moment of force (mostly) removed, if it did start to buckle, it would have to overcome the entire weight of the mass under it in order to keep buckling, as the shortened distance would have to lift the entire wall.  Since the weight of one buckling flat is less than the entire wall, it can't buckle.

With channel or angle, I would have to add a pass-through every 4', and since it is overhead lifting, that pass-through has to be forged.  So I would be adding a forged eye every 4' to the framing on each plane for the cable.  Even then, if it decides to buckle, it has 4' it can freely fall since there is 4' between each eye.

As much as it's nice to say "yeah, but when would that ever happen?"... it happens a lot.  An actor bumps a flying set piece on the way up and it swings just 1".  The person operating the rope is focused on the rope and has no idea.  You get 500 lbs of scenic beauty moving at 15 mph and it whacks another flying thing on the way out.  

Does that make any sense?