Design of Tubing

I am assuming that cost is a concern as well, right?

How about dimensional restrictions on the tube?

Also are there other requirements? Such as a need to run rollers through the tubing, or ................?

Cost is a concern, but solution is more important.

Largest diameter to fit current application accessories is 100mm OD

If you are limited to a maximum of 100 mm (four inches), there is no solution to the problem. If the diameter can be increased as required, the solution is very easy. Simply calculate the moment of inertia required to satisfy the deflection criteria.

Δ = 5WL³/384EI

or I = 5WL³/384EΔ.

With the values given and steel tube with E = 29,000,000 psi,

I = 5 * 250 (29*12)³/(384 * 29e6 * 1/16) = 75.7 in⁴

An 8.625" OD pipe with 0.322 wall thickness has I = 72.5 which is pretty close.

Careful ba/ael -

In this situation I think you would have to include the weight of the pipe as well - sch 40 - 8" pipe has a weight of 28.55 lbs/foot; which is three times the amount of the loading (250 lbs/29 ft = 8.62 lbs/ft).

My questions for the original poster (Paul?) -

1. I assume by span that you mean horizontal, correct?
2. Does the material have to be aluminum or can it be something else?
3. Does "tube" only mean round, or can it be any cross-sectional area to fit in 100 mm x 100 mm?
   

I don't have an answer right now, but I am thinking along the lines of a small truss - possibly aluminum.

In any case 1/16" deflection over 29' is going to be tough.

Guest continued ..............

I also wanted to confirm the end connections - are they 'pinned' (such as ba/ael assumed) or can they be considered rigid/'fixed'.

I assumed that the 1/16" deflection pertains to live load only. Dead load deflection is already in place before the live load is added, right? In any case, the entire problem seems a bit absurd because a deflection of 1/16th of an inch over a 29 foot span is virtually unachievable unless very stiff beams are used.

It is not difficult to prove that a live load deflection of 1/16" combined with a maximum depth of 4" is not possible using any materials known to man.

Good points -

I have been pondering this for awhile, and have come to the conclusion that to even come close with a 4" depth - you would need to model the ends as rigid so that the deflection equation would be:

d = Wl³/384EI

thus, from your earlier work - 'I' would only need to be 14.5 in⁴, which is a little more reasonable and could be done with 4" XXS steel pipe (I=15.3 in⁴)

You are quite right! With fixed ends, the deflection is only one fifth as much as the simple span deflection. But complete fixity is not readily available at each end of the beam. From a practical standpoint, the problem can be solved only with a deeper beam.

There are fiberglass tubes, or pipe used for petroleum tank installations. I would think that this product could be reinforced if needed to obtain the stiffness you desire. What about thick wall stainless steel?

To avoid any excessive stresses in your piping system, the deflection is calculated from the following equation:

Δ = 5 W L⁴ / (384 E I)

where, W (lb/in), L (in), E (psi) & I (in⁴)

And the recommended deflection must be within the following limits:

NPS ¾" : 3/8", NPS 1" : 1/2", NPS 1.1/2" : 3/4", NPS from 2" up to 24" : 1", and NPS 30" : 7/8"

I agree with your expression for deflection, but disagree with your comment about excessive stresses. Deflection has nothing to do with stress and visa versa.

Due to pipe sagging, there is a max. deflection in the mid-span. And this deflection means localization and intensification of higher stresses at mid-span, where Tension at bottom of pipe cross section and Compression at top of pipe cross section. And for this reason, we have to avoid severe deflections which means severe stresses at pipe mid-Span.

To reduce the deflection:

1. Minimize the span L between the pipe supports

2. Increase the pipe section modolous I (dia. & pipe wall thickness).

3. Selecting of a pipe material with higher modolous of elasticity E.

Hello Abdel Halim Galala,

Do you consider 1/16" deflection in a 29 foot span to be a severe deflection?

Hello ba/ael,

The deflection of 1/16" in a 29 foot span is very good, and practically I think is difficult to be attained.

Hello Abdel Halim Galala,

I agree.

The only material that will meet the deflection criteria mentioned is a double skinned carbon fiber tube. Space between the skins would need to be glass micro-spheres in epoxy foam, It is quite a costly solution though.

Another potential solution is a tapered tube--larger OD in the center. Then as it deflects the top surface would be perfectly horizontal.providing even take-up.