Cantilevered beam question - real life scenerio

[dalecyr]

Cantilevered load forces:


Referring to the attached diagram;
Assuming a pipe, forming a cantilevered beam;
assuming the pipe is restricted from moving upward on the left end;
assuming the pipe is restricted from moving downward by resting on a concrete shelf, as shown;
assuming a load placed at any point along the cantilevered portion of the beam;

In perusing the available formulas,
it seems this is the correct one to use
to determine the suitability of this arrangement to carry the load.

http://www.engineersedge.com/beam_bending/beam_bending9.htm



But, intuitively, it seems to me that there is a more critical point,
namely, the point at the edge of the concrete shelf supporting the pipe.



I'm not sure why, but it seems to me that the pipe would fail at this point,
by "kinking", before it would fail by bending over-all.



If this is correct, which formula do I use to determine the weight at which the pipe would "kink"?
Thoughts?

[Cake of Doom]

Sorry for the late reply.

You'll need to keep an eye on the stress and strain along the bend radius as it deflects, increasing the weight until it reaches failure or exceeds it's permissible limits. This is how kinks and wrinkles form.

Wall thickness and material strength will be the big players in this game. If you really want to slug it out, you can use work/energy methods but as you'll want to change factors as you go, I'd recommend using a good FEA package.

[dalecyr]

Thanks for your reply.


Cake: you seem to concur that kinking at the support boundary is the first failure mode.


Although I understand the principals used in FEA,
I don't have access to a Finite Element Analysis package,
and my calculus hasn't been dusted off for over 30 years.


I suppose I could setup a 'test to destruction'...
but I'd much rather do it mathematically.


I'm pretty sure we are well under a desired safety factor of 5:1.
(I'm thinking we are more like 10:1 or 12:1)


But "pretty sure" is not where I like to operate.


So, going against all of Dave's admonitions,
I'm going to ask for help from "some anonymous forum participate on the internet".


The pipe is Schedule 80, 1.5", steel;
wall thickness is .020";
pipe length is 60";
unsupported length is 40";
load is centered at 50" from the left end, 10" from the free, unsupported end;
the load is 75 lbs.


Thoughts, comments, smart remarks?

[Cake of Doom]

A good "quick check" is Mapp / MoR = < 1.0

For a small section like this I'd ideally like to see that come out around 0.050 mark, to indicate low bending.

I'd be happy that the section wouldn't kink or buckle with that figure.

[dalecyr]

Um... ya got me on those variable names.

Happily, I'm about to learn something.
Mapp?
MoR?

[Cake of Doom]

Sorry; I don't know how to do subtext on here so everything looks odd.

Mapp = Maximum applied moment.

MoR = The sections Moment of Resistance.

Have you worked out the reaction (including section self weight) at the shelf edge? You could always use that value for a local buckling check.

Whilst these "checks" aren't as thorough as the stress/strain formulae, they are still pretty handy for most situations

[dalecyr]

Thanks.
This will get me close enough to tell if further investigation is required.

[Kelly_Bramble]

But, intuitively, it seems to me that there is a more critical point, namely, the point at the edge of the concrete shelf supporting the pipe.

I'm not sure why, but it seems to me that the pipe would fail at this point, by "kinking", before it would fail by bending over-all.

I'm quite sure that the equations assume distributed loading or contact at the interaction point. Moreover, I agree that a pipe is going to fail or "kink" faster with point loading as opposed to distributed loading.

If this is a serious in service design, I would FOS it at least x 6 or more without a proper analysis or change the loading at that edge to full distributed.

[dalecyr]

According to this website:
https://answers.**********/question/i...3001827AAqN27Z
What is the formula for maximum moment?

I assume you mean bending moment in Structural Engineering.
If so, it depends what structure you are applying the load to, what load type you are applying, and where you are applying it on the structure.
For a simply-supported beam of length L and a point load W applied at its midpoint: WL/4 (max moment at the midpoint)
If the total load is the same (W), but applied uniformly along the structure: WL/8 (max moment at the midpoint)
For a cantilever beam length L with point load W applied at its end: WL (max moment at the support)
If the total load is the same (W), but applied uniformly along the structure: WL/2 (max moment at the support)

So, I use M=WL.

If I remember correctly:
Moment of Resistance = Moment of Inertia / Distance to neutral axis

Right?

[Cake of Doom]

With one little correction. For a UDL it should be WL^2/8. That's not important right now but I couldn't let it go.

Depending on your material grade, you should be getting ~1.2 kNm bending resistance from your tube.

So, providing my memory is still good for feet, inches, barleycorns and hogsheads, I make the moment from the load (no self weight included)
0.41 kNm.

0.41/1.2 = 0.34 < 1 .'. ok

Not as low as I'd like and not including any additional factors but it works on paper.

If this is a serious in service design, I would FOS it at least x 6 or more without a proper analysis or change the loading at that edge to full distributed.

This is good advice too. Distributing the load at the fulcrum point will help out, and be more friendly to the concrete beneath it. The higher FoS is good move too as any "bounce" will magnify the force at the fulcrum.

[dalecyr]

Thanks for your reply.


If I understand everything correctly, the Factor of Safety is only about 3:1.
Below the accepted industry standard (5:1) for this application.


Although the configuration of the load makes it difficult to distribute along the pipe,
I can easily distribute the load across two of these contraptions,
giving an acceptable FOS.


Thanks Cake and Kelly, for your input.

[Kelly_Bramble]

If I understand everything correctly, the Factor of Safety is only about 3:1.
Below the accepted industry standard (5:1) for this application.

Yes, 3:1 not cool in this application. You may in fact need way more than 5:1..

See this document:

Factor of Safety

[dalecyr]

Thanks for citing that document.
I have not run across it before.



According to that document, item 1 applies.
The component, and its load, are static, once installed.
There are no dynamic forces.
There is no shock load.
There are no wear points due to movement.


However, the load, a theatrical lighting instrument, is suspended over people.


In our industry, theatrical and arena rigging,
this increases item 1 from a FOS of 3
to a FOS of 5 for this type of component.