Internal Forces Calculations - Steel Bundles

[dmaier]

Hello,

I am having a difficult time to try and figure out this problem for work.

I have steel piping bundled together in a hexagonal pattern that is strapped together [band-it strapping]. There have been instances of excess amounts of weight when these bundles are being stacked upon one another sometimes causing the bottom bundle's strapping to break and then stacks falling [and making a mess].

I am looking for some help as to try and figure out the forces acting inside the bundle to get a representation to see where the most outward force is located [and value/direction] to note where the bands are breaking and at what force the bands can withstand.

I welcome all help. I have attached a file to give a illustration.

Thanks,

D

 

[dmaier]

Thank you for you help!!

I did it in a different way individualizing pipes, I will upload my calcs next week. My output was the same as BAretired's 1.155F.

 

[dmaier]

Here is the way I came up with the values.

 

[Brad805]

I was annoyed by my silly comments and was pondering a simple analysis method for this in SAP. I came up with the attached tension/compression only members to idealize the structure. I assumed a 2.82" diameter (2" X and 2" Y). I thought I would post it.

 

[BAretired]

dmaier: Using your numbering system, Pipes 13 and 16 cannot be in equilibrium without an additional force normal to the strap. The strap is incapable of delivering such a force unless it deflects. If it deflects, Pipe 13 and 16 move outward and downward, normal to the strap. When that happens, Pipes 8 and 12 move downard and inward as they rely on pipes 13 and 16 for support. Precisely how this affects the overall statics is not clear without examining the new position of each pipe.

When additional load is placed above by placing more bundles on top of the first one, the eccentricity of balls 13 and 16 increases due to increased compression between Pipes 8-13-17.

The simplest remedy is to put a shim between the strap and Pipe 13 and also between the strap and Pipe 16 such that the harp in the strap is sufficient to hold Pipe #13 and #16 in position for all loading conditions.

Brad805: Your analysis requires tension where no tension is available and cannot be correct (see above).


BA

 

[Brad805]

BA, yes I see there is a 3lb tensile force where it should not exist. Oh well, it was only 20min. I like the block idea, but I wonder how well that will work if they are using an automated system like you posted earlier.

 

[BAretired]

Shims or blocks likely would not work well with an automated system similar to the one in the earlier video. But it is not clear how high those bundles are intended to be stacked. There must be a limit and the supplier should stipulate what that limit is.

BA

 

[dmaier]

So to sum up, what method is correct? There has been a lot of input, and I thank you all for that!, but with what method would provide the accurate value?

From this:
-----
So, for a stack of four bundles we have:

P = 19*4W = 76W
where W = unit weight of one pipe times the strap spacing

T = 0.5P = 38W (KootK)

T = (3*19W + 18W)cos 30 = 64.95W (Robbiee)

T = 0.385P = 29.26W (BAretired)

Interesting!
----

All are different values through different methods! KootK if your method is correct can you please be more detailed? Your drawing is confusing me, sorry.

This is a, in a sense, simplified value as there are other factors being neglected, as BAretired has pointed out [ie. pipe deflection internally, stretching of the strap itself, crimping of the strap, etc.]. Though even this will give a rule of thumb that a factor of safety can be applied to for strapping and stacking purposes.

 

[BAretired]

Consider the equilibrium of Pipe #13 (and #16). See attached link. Pipe #13 has a gravity load W which must be resisted by components as shown. To hold the pipe in position, a force of W/2 is required acting normal to the strap.

The strap spans from the tangent point of Pipe #8 to the tangent point of Pipe #17, a span of 2D where D is the diameter of the pipe. The moment of a simple beam of span L and concentrated load P at midpoint is M = PL/4 or in this case, M = (W/2)2D/4 = WD/4.

The tension T in the strap required to provide a reaction of W/2 at midspan is T = M/t = WD/4t where t is the offset from a straight line or, in this case the thickness of the required shim. If t = 0, the strap tension is infinite but after the strap begins to strain, t increases above 0.

If we know the initial strap tension, we can calculate offset t required to hold Pipe #13 in position. If T[sub]init[/sub] = 30W then t = WD/(4*30W) = D/120. For D = 12", t = 0.10", say a 1/8" shim.

If the initial prestress is only 10W, then t[sub]req'd[/sub] = D/40 = 0.30".

BA

 

[KootK]

KootK if your method is correct can you please be more detailed?

I no longer have faith in my solution dmaier. Moreover, I'm driving myself quite mad trying to sort it out. I've been checking our various solutions for equilibrium at the top and bottom joints. Nothing checks out.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Ussuri]

How much preload/pretension to you apply when strapping these together? The differing tools will apply a different preload, so even in the absence of gravity loading the load in the strap is in equilibrium with the pipes.

 

[dmaier]

Just to point out that no shims will be intended to be used or required. This would increase cost and askew production. The point about adding the shims is not really at all dealing with the question at hand to figure out the tension the band is facing when being stacked/maximum force. The bundle itself is only held together through the use of strapping, so the strapping handles all the tension/force to keep the bundle together [when shipping, loading, stacking etc.].

As for pretension I do not know that off hand, I do know that the company is using Samuel Strapping Systems for their banding at this time [

http://www.samuelstrapping.com/en/product/product.asp?cat=2&sub=23&pid=172

-- 1-1/4" bands, most likely the 5500lb strength]. So saying this with 5500lb strength, not taking crimping or other factors into play [and for simplicity load P = T], that a bundle that weighs 5000lbs and has say 4 straps will yield a 22,000lbs breaking strength. Which in turn would say that you could stack these 4 high [22,000/5,000 = 4.4], with the bottom bundle being included in the 4.

I do get what you are saying with the normal force from the band being applied to the pipe [13], but is this still not the area of highest force contribution which would be at pipe [8], due to symmetry? As well in your calculations would t not just be the thickness of the strap not the shim?? And the 30W [I assume that is just an arbitrary pre-stress value] would that not have to take into account all other weights of pipe above/acting on it? -- Sorry, but going through this has constantly brought up doubts and frustrations to try and solve.

Ussuri can you elaborate more on your statement? Are you saying that the pretension that the straps provide is in equilibrium with the total bundle load? Which would be to say that the bundle weight would be completely handled by the strapping, and then additional straps would provide more allowable force to be applied to the bundle to withstand [makes sense]?

 

[KootK]

At the risk of adding to your frustration Dmaier, I'd like to change my answer again (attached sketch). I'm going with a strap tension of [P x sin(30 deg)] = 0.577 P.

I tackled things a little differently this time. I considered equilibrium in the stack immediately after elongation of the straps takes place. When the stack "settles" slightly, it results in horizontal gaps between each pipe and its neighbours to the left and right.

In my opinion, those gaps preclude the use of the centre diamond load path detailed in BAretired's solution. At the end of the day, my solution is BA's minus the middle diamond. Most importantly, I've checked force equilibrium at all six corners for my double diamond solution and everything balances out.

In the absence of friction on the strap, which has been our assumption thus far, the tension in the strap will be uniform around the entire bundle. The strap tension will not be at a maximum at pipe #8/#12. As a consequence, any extra strap tension required to restrain pipes #4/#7/#13/#16 will be in addition the the strap tension values that we've been kicking around for the simplified case.

Significant pre-stress would mess with my solution if it meant that the horizontal gaps that I've described never come to pass. Even so, this seems like a reasonable upper bound on the strap tension force. I'm sure that the pre-stressing is imperfect an subject to losses over time.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Brad805]

Have you considered doing test in the field? Without an estimate of the max/min prestress force this discussion seems largely academic. Is the strapping installed manually or is this done by a machine? I know from experience (woodwork hobby) that if it the strapping is installed manually the prestress force varies quite a lot. I have had bundles of wood delivered that the edges were crushed, and others where the straps were doing nothing. Granted, wood is much more variable than pipe, but I am sure you get the point. In the study I posted earlier they found the installation of the straps had a lot to do with the failure. If the straps are installed by a machine then I see where you are coming from, but you still need to get an idea of the prestress force. Presumably your shop has been doing this for quite some time. If you come back and all of a sudden say they need to do things dramatically different people will ask questions that will lead to doubt.

 

[BAretired]

I have been wondering about a few things:

[li]If the straps are pre-stressed, is the initial stress uniform all around or is it variable due to friction at each of the six corners of the bundle?[/li]

[li]Does the pre-stress force add to the force determined from statics or is it included? For example, when a bolt is pre-stressed axially, then separately loaded in tension, the tension in the bolt remains constant until the applied load exceeds the pre-stress force.
[/li]

[li]If the bundles are stacked to a height of four or five bundles, what provisions are there to ensure all bundles are properly aligned. i.e. there is no eccentricity from bundle to bundle?[/li]

[li]What diameter of pipe are we talking about?[/li]

[li]How are the bundles handled when stacking them? Two slings per bundle?[/li]

BA

 

[dmaier]

All bundles are handled in an automated setting using magnets. The bundles are strapped manually at another mill. My company is performing the automation not the production/manufacturing of the bundles, as to why we are trying to figure out max stacking, since more stacks = more space/capacity.

 

[BAretired]

You didn't answer my questions. Instead you answered a question which wasn't asked. Have you considered a career in politics?

BA

 

[dmaier]

I did answer your questions.... let me elaborate:


- If the straps are pre-stressed, is the initial stress uniform all around or is it variable due to friction at each of the six corners of the bundle?
Manually strapped, I do not know if all uniform [human error], I would like to assume that it is uniform for ease. They are strapped tightly together and the pipes are snug to one another.

- Does the pre-stress force add to the force determined from statics or is it included? For example, when a bolt is pre-stressed axially, then separately loaded in tension, the tension in the bolt remains constant until the applied load exceeds the pre-stress force.
I do not know the answer to this, the bands supply sufficient force to hold the bundle itself together and maintain its [hexagonal] orientation. I would then say yes, the tension in the strapping remains constant until there is bundles stacked on top, and then and a point when n# stacks exceeds this tension.
This is where the calculations could vary as if there is a large pre-stress then there is a larger magnitude force acting normal to the pipes keeping them snug together, which would have greater strain already in the strapping [correct?]. However I do not have what they manually strap the bands to at their mill.

- If the bundles are stacked to a height of four or five bundles, what provisions are there to ensure all bundles are properly aligned. i.e. there is no eccentricity from bundle to bundle?
Bundles are handled in an automated setting, therefore assume that bundles are aligned and forces act purely vertical -- bundles are placed directly on top of one another

- What diameter of pipe are we talking about?
in this case it is a 3.5" diameter pipe, different bundle sizes can vary from <1"-12" but have different orientations

- How are the bundles handled when stacking them? Two slings per bundle?
bundles are handled using a magnet, no slings

Does this give you more insight, and help with your questions?

 

[BAretired]

dmaier:

It helps, but I have to think about it a bit more.

BA

 

[BAretired]

As for pretension I do not know that off hand, I do know that the company is using Samuel Strapping Systems for their banding at this time [

http://www.samuelstrapping.com/en/product/product....

-- 1-1/4" bands, most likely the 5500lb strength]. So saying this with 5500lb strength, not taking crimping or other factors into play [and for simplicity load P = T], that a bundle that weighs 5000lbs and has say 4 straps will yield a 22,000lbs breaking strength. Which in turn would say that you could stack these 4 high [22,000/5,000 = 4.4], with the bottom bundle being included in the 4.

If the 5500#(average breaking strength)strap is used, it is 1.25" wide x 0.031" thick for an area of 0.03875 in[sup]2[/sup]. According to my earlier analysis, the tension for a four bundle stack should be 0.385P or about 1925#. (2890# using KootK's revised analysis).

I doubt that Samuel Strapping Systems prestresses the straps to a significant degree, but this can be confirmed with them. For the present purposes, I will assume a prestress of 0.

Tensile Stress = f[sub]t[/sub] = 1925/(4 * 0.03875) = 12,420 psi
Length of strap = 12D where D is the diameter of pipe.
Average strain = f[sub]t[/sub]/E = 12,420/29e6 = 0.000428
Total strain = 0.000428*12D = 0.018" for a bundle with 3.5" OD pipe.

The total strain is small enough to be safely ignored. (Should confirm E with the supplier).

Depending on the safety factor you want, you could probably use smaller straps. Might be a good idea to get the properties of the steel used for straps, particularly the yield point.

BA

 

[BAretired]

Oops, it's getting late. Let me correct that.

If the 5500#(average breaking strength)strap is used, it is 1.25" wide x 0.031" thick for an area of 0.03875 in2. According to my earlier analysis, the tension for a four bundle stack should be 0.385P or about 1925# 7700#. (2890# 11,550# using KootK's revised analysis).

I doubt that Samuel Strapping Systems prestresses the straps to a significant degree, but this can be confirmed with them. For the present purposes, I will assume a prestress of 0.

Tensile Stress = f[sub]t[/sub] = 7700/(4*0.03875) = 49,700 psi
Length of strap = 12D where D is the diameter of pipe.
Average strain = f[sub]t[/sub]/E = 49,700/29e6 = 0.00171
Total strain = 0.00171*12D = 0.0719" for a bundle with 3.5" OD pipe.

The total strain is small enough to be safely ignored. (Should confirm E with the supplier).

Breaking strength/T[sub]max[/sub] = 22000/7700 = 2.85 (not too bad, but only 1.90 using KootK's value).

Might be a good idea to get the properties of the steel used for straps, particularly the yield point.

BA