Finding the elastic limit in a cantilever beam 1

[weatherbird]

I have a problem where I have a structural member modeled as a cantilever beam. I have all the material specs for the material being used. I can calculate the deflection and reactions, but what I am looking for is the force required to reach the elastic limit of the material. In other words I am trying to calculate the deflection at which this structural member will actually bend, and not return to it's normal state. I have searched the internet and text books, and even my steel construction manual but cannot find a formula or set of formulas to do this. Does anyone know where I can find this information?

Thanks,

Michael Weathers
Mechanical Engineer
General Shale Brick

 

[SWComposites]

Roark, Formulas for Stress and Strain

 

[Twoballcane]

Ummmm...hmmmm...I hope this is not a homework problem because it sure sounds like one because this is such a basic question. The ductile material will reach elastic limit when the Von Mises stress reaches the material's yield strength. Did you take Failure Theory in college?

Tobalcane
"If you avoid failure, you also avoid success."

 

[GregTirevold]

Well one thing about material specifications is that they typically are stated in an "at least X" type format. For example A36 steel has a yield point of "at least 36,000psi" but improved mill practices mean that particular piece of A36 may actually have a yield point of 44ksi or maybe even 50ksi.

So when you calculate the Von-Mises stress you need to compare it to the yield point stress. The question then becomes are you trying to find the force you can be SURE it will hold without reaching the elastic limit or are you trying to predict how much force it will REALLY take to reach the limit. These are two different things, with the second much harder to accomplish without significant testing of material from the specific supplier's process.

http://www.linkedin.com/in/gregtirevold

 

[ione]

Weathebird,

Is your cantilever made of a ductile material? If not (i.e. concrete) the Von Mises criterion does not apply.

I was wondering this as I noted your Company is involved concrete/masonry business.

 

[drawoh]

weatherbird,

If you are analyzing your cantilever beam using double integration, you are calculating bending moments. This all should be explained in your mechanics of materials textbook.

JHG

 

[weatherbird]

This is not a homework assignment, but rather a task given to me with very little time to complete it due to other irons in the fire.

The material is SAE 4150 the is hardened to 58 Rockwell. Although I do work for a brick manufacturer, I am actually part of a division that designs and builds the process equipment for the various plants.

This most likely is a simple problem, but the problem is that I am several years removed from my education, with the majority of the years spent doing things that did not require analysis, such as drawing. This is most likely the reason that I have struggled with this problem.

This is a design for a tool, in which we need to prove that the material with work in extreme instances. The people involved will recognize the amount of force needed to achieve permanent deformation easier than they can see other information that I can put in front of them.

Thanks for the feedback, I will shuffle back through my textbooks to see what I can find. If you have any other information, please share.

Thanks
Michael Weathers
Mechanical Engineer
General Shale Brick

 

[Twoballcane]

If you can get your hands on a Mehcanical Engineering Desing by Shigley,would be a good start.

Tobalcane
"If you avoid failure, you also avoid success."

 

[rb1957]

the OP sounds like a working engineer, and i'd bet that if he had a copy of Roark (et al) he'd used it.

so, you have a cantilever, with a constant I (yes?) and a length L ... what's the loading point load or distributed ?

if you can do the math, develop the equation for M(x), with x=0 at the fixed end (this way to constants of integration are zero).

oh, i remembered, you want the maximum stress in the beam (at the cantilevered end, x=0) to be = yield. bending stress = My/I (for an I-beam y = 1/2 the depth of the beam) ... so now you can determine the load applied to the beam to create plastic deformation ... continue ...

integrate twice for EI*d(x). and the deflection at the tip, x=L, d(L) is simple to determine.

that said there are plenty of on-line calculators that'll solve cantilever beams for you.

 

[Bobber1]

Calculate the section modulus of the beam.

Using the yield stress of the beam material, calculate the equivalent moment = yield stress x section modulus.

Determine the force that causes this moment by the cantilever bending equation,
force = moment found above / beam span

 

[GregLocock]

The equation of direct interest is M/I=sigma/y, where y is the distance of the outermost fibre from the neutral axis.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[israelkk]

At 58RC hardness the elastic limit is very close to the ultimate tensile strength with very little elongation and reduction of area. Therefore, the beam will probably will not have a permanent bend but more likely to have a brittle break if loaded to the ultimate tensile strength.

 

[zekeman]

"I can calculate the deflection and reactions, but what I am looking for is the force required to reach the elastic limit of the material"

Well, if you can do this, then tell us where the forces are located and give one set of forces that will put the beam in equilibrium.

From that and the stress formulae that have been suggested, you can then find the set of forces that will cause failure, since the failure forces and corresponding deflections and stresses are linearly related.

I.e., if you double the force(s), you double the stresses everywhere up until the elestic limit at which point , as IsaelK, suggests it will be near failure.

 

[desertfox]

Hi weatherbird

Here are two links giving bending formula for beams going completely plastic.
I don't know what section of beam your using so I can't comment further, however if your only interested in the extremities of the beam going into yield, then the standard beam formula given in earlier an post can be transposed to give the maximum bending moment to achieve yield, from which you can work back and get the maximum force

http://web.mit.edu/2.31/

http://www/fall01/beam.pdf

http://books.google.co.uk/books?id=P0yyTfWJIEgC&pg=PA350&lpg=PA350&dq=plastic+bending

+beams&source=bl&ots=hNp6niy_E0&sig=b7x3hbAPPCauUDqNEPQsCxc
aqto&hl=en&ei=d4CTTNq2Msb84AaV543YAw&sa=X&oi=book_result&ct
=result&resnum=4&ved=0CDAQ6AEwAzgK#v=onepage&q=plastic%20bending%20beams&f=false


desertfox