Weakening a Cantilever Beam in One Direction (but not the other)

[Haf]

I have a unique application that essentially boils down to a cantilevered beam with a load acting perpendicular to the end of the beam. The unique part of the problem is this: we want the beam to be stout with the load acting in one direction (let’s say downward), and we want it to fail with the load acting in the other direction (let’s say upward). The cantilever is made of steel and is rectangular in cross section.

Our concept is this. We’re thinking of making a thin cut (using a 0.001” thick EDM wire) near the base of the cantilever. The cut would be perpendicular to the beam and would start at the bottom and move towards the center of the beam. At the end of the cut we would make a circle with the wire to reduce stress concentrations. So, looking from the side, the cut would look kind of like a lollipop. If necessary (and feasible), the thin cut would be filled with shimstock.

With the load acting downward, the part of the beam that is cut will be in compression, so our hope is that the effects of the cut being there will be minimal. This, of course, implies that the cut must be well on the compression side of the neutral axis. With the load acting upward, the part of the beam with the cut is in tension, and we essentially have a thinner beam. Also, we have a nice stress concentration at the end of the cut that will help with failure when the load is acting upward.

One complication is that the load is acting dynamically (think of hitting the end of the cantilever with a sledgehammer). That means there will be shock waves and rarefaction waves running around.

What are your thoughts on this concept? Its simplicity is driving me nuts. I can’t help but think there’s a “gotcha” somewhere!

Thanks,

Haf

Note: this question was also posted in the "Stuctural Engineering other topics" forum.

 

[hacksaw]

you succeeded in creating a tremendous stress concentration that weakens the overall structure. there is no mystery.

suggest that examine the localized stresses and how materials fail.

 

[henerythe8th]

Of course there are other things to consider; for instance, reducing the area that resists the shear force...
No matter what scheme you use, plan on doing a fair amount of testing. The testing should be performed for a couple of reasons: the published values for yield and ultimate strength of the material that you are using are less than they actually are in the piece that you are using, and in fact will vary from piece to piece (you may want to consider purchasing sufficient material for your test and actual installation from the same "heat&quot.
I previously did a bit of work for a farmer that wanted an implement to "fail" at a certain force and sized a "shear bolt" accordingly. After doing some testing, it took a considerable amount of "extra" force to make the "bolt" fail (due to the published minimum strength-my calcs were incorrect) and we ended up reducing the diameter of the bolt by cutting a "break" groove in the "bolt" to reduce the diameter and therefore strength to achieve "failure" at the appropriate force.

 

[sancat]

Two things come up to my mind:

What about flexo-torsional buckling? If the load will be applied on one extreme of the beam, you could have failure due to this kind of buckling. An H shape has a not so high torsional stiffness, a T shape has even less.

An I have experienced the same that Henery states: there is a minimum yield guarantee for some material, but the maximum yield value is not easy to know. Thus a material is guaranteed to not yield below certain value, but there is not stated that you will not receive for "free" a "better" material

sancat

 

[GregLocock]

I don't think there's anything wrong in principle with your design, but man is it ugly.

A more elegant approach would be to use a stick and a rope, in a triangle.





Cheers

Greg Locock

 

[ivymike]

Shucks, Greg, I was going to suggest a "living-hinged" attachment with a reinforcement on one side, but yours is even better.

 

[Haf]

Thanks for the comments.

Unfortunately, hinges, rope supports, support brackets, etc. are not possible with our design constraints.

Likewise, relatively complicated cross sections (T-shape, H-shape) are not an option.

I agree the design is relatively ugly, but will it work? As has been pointed out, a stress concentration is introduced at the end of the EDM cut. Our attempt is to mitigate this problem by putting in a stress relieving hole and locating the end of the cut relatively close to the neutral axis (but on the compression side) where stresses are relatively low.

Let me be more specific with my question. Let's say we have a 6 inch thick cantilever beam. We make the EDM cut 2.75" long, so that a 3.25" thickness is left. Will that beam be stronger than say a 5" thick beam with no cut?

Haf

 

[trainguy]

Here's what's wrong with it :

1) - what about shear stresses? Are they within allowable values at your reduced section? A cut is a cut, and even though you believe you've restored what you need for bending, shear will have to be checked at the narrow (top) section, and this stress will have to be combined with your normal stresses. I don't know why, but my spider sense is whispering "shear failure ...shear failure..."

2) Sancat is right on re: flexural / torsional buckling. Imagine the stability of your section outboard of the cut assuming ONLY the top part of the rectangle over the whole length past the cut. Doesn't look as rosy, does it... Or maybe it does if you've checked it... There are few things in the beam world less stable than a cantilever.

That's my 2 cents.

 

[strokersix]

Haf,

Do you have room for a bolted flange welded to the fixed end of the beam? If so, then you can arrange the bolt pattern such that a fastener failure will limit the structure strength in the upward direction and the beam itself will limit the strength in the downward direction.

Mike

 

[chicopee]

Where you have the proposed cut, the position of the N.A. has move upward in the remaining solid portion of the bar. Instead of making that proposed cut at the base of the beam, about using an irregular cross section whereby the N.A. is closer to the bottom of the beam therefore failure would occur on the upward stroke of the force and you would not have to worry about the rarefraction of the shock wave. Realize that failure of the suggested bar may not come as a clean break but instead as a bend.

 

[diamondjim]

Hal,
Do you have room to put in 2 welded triangles
towards the compressive side of the upward
beam and not weld them to the horizontal beam.
It would serve to resist the downward force but
do nothing when the upward force was applied.
It seems like this might be a practical solution.
The triangles would serve as shear bosses.

Another thought would be to have a c shape type
plate on the far side which would act as a shear
plate when a downward load was applied, and as a
free hinge when an upward force was applied.

Another thought would be to create two horizontal
beams with an overhanging portion to take the
downward force. The upper beam could be bolted
near the far side of the beams. There would be
very little load in the downward side acting on
the bolt, but would be tremendous on the upward
side due to the moment arm.

 

[BATman2]

Haf,

You mentioned dynamic loading. If the tension is high enough to initiate yielding, and it occurs frequently, fatique needs to be considered as well. If the tension load is frequent, I would abandon the notch concept all together. I would work with a buckle trigger of some type, a "plastic" hinge design using the flanges, or the fastener concept Strokersix noted.

When you say "fail" I assume you mean substantial yielding or buckling. Or do you need this thing to break away completely?

Boozer




Regarding actual material strength values, I'd have a sample tested to be sure.

 

[Haf]

Boozer,

The loading is dynamic but it is a one time event, so fatigue is not an issue.

While I appreciate input on alternate designs, as I mentioned before, our design constraints are such that fasteners, hinges, non-rectangular cross sections, etc. are not an option.

To make things easier, forget I said anything about beam failure. I haven't been entirely honest about the specifics anyway. Suffice it to say that we have a specific reason for making the EDM cut that I'd rather not get into.

Haf

 

[BATman2]

Haf,

Understood, you've got totally fixed "constraints", I've been there too. In that case, I would do the math to check the stresses; FEA if you got a package available. (non-linear ideally) then test it, maybe more than once depending on the criticality of the application!!!

Good luck,
Boozer

 

[sancat]

Haf,
I understand you have a plate, with some thickness, say 1 inch, and 6 inches deep. If you do cut it with EDM, and finish it with a loop, I think you will have your intended effect, it will have a higher load capacity downwards that upwards but if you only think about 1st order stability.
If you add buckling load to your analysis, I think that the 5 inches beam will have a higher resistance.
Ipolar for 6x1 inch is 18.5 inch4
Ipolar for 5x1 inch is 10.8 inch4
Ipolar for 3.25x1 inch is 3.13 inch4
I dont have the exact geometry for your configuration, but as you see, there are different torsional resistances for different beam depths, and therefore, different resistance to buckling due to torso-flexural failure
sancat

 

[borjame]

Not knowing how the load is applied i.e. is it an impact from another object or is there a piece attached to the beam that push/pulls, here is my two cents.

Use two beams, one on top of the other with top beam smaller than the bottom. When you push down both beams work together but when you pull up only the top beam would be affected. Waala.