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Anonymous Poster

Beam deflection

12/14/2010 12:32 AM

Here is a question for the gear heads out there from a gEEk:

I recently had a brainstorm for a great new consumer product. One of the components is a round tube roughly 24" long x 1" dia made of steel. As an engineer I dutifully sought out and applied the beam bending equation. I was able to find online calculators that gave me quick answers. Then I dutifully did a test. The calculators were wrong. Way wrong!!! I did them manually. The calculations were wrong, but matched the online calculators. I consulted a gear head. He said I'm using the equations correctly.

SOOO, here's the question. Why are the equations wrong? Test it yourself. Not even close.

"Work the problem from the beginning until you get stuck. Then work backwards from the answer. In the middle, lick and rub."

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#1

Re: Beam deflection

12/14/2010 12:43 AM

This description is inadequate. Please try again, explaining all loads and end connections on this pipe cum beam. In particular uniform vs concentrated load.

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#2

Re: Beam deflection

12/14/2010 12:45 AM

I worked it three different ways and it came out right every time. I don't know why you can't see it.

Oh, now I get it. Easy mistake to make, I've done it before myself.

You forgot to put the hole in the tube.

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#3
In reply to #2

Re: Beam deflection

12/14/2010 12:50 AM

Yeah, but be careful--if I.D. > O.D., then the hole is on the outside, which throws the calculations off.

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#4
In reply to #3

Re: Beam deflection

12/14/2010 12:58 AM

I've made that mistake before, too. But, the dumbest thing I ever did was to make the hole longer than the tube. It's impossible to get rid of the excess hole. There's nothing to cut.

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#5
In reply to #4

Re: Beam deflection

12/14/2010 1:11 AM

Make both mistakes, you get a Klein bottle, and no end of problems...for one, it doesn't hold water.

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#6
In reply to #5

Re: Beam deflection

12/14/2010 1:30 AM

That's cause there's no place for the cork.

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#9
In reply to #4

Re: Beam deflection

12/14/2010 7:35 AM

Fer Gawd's sakes, just take the extra length, color it with a black Sharpie and sell it to the Large Hadron Collider people. They've been looking for one of those.

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#10
In reply to #9

Re: Beam deflection

12/14/2010 7:37 AM
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#42
In reply to #4

Re: Beam deflection

03/26/2012 9:08 AM

You are right but you can cut if first you fill it with the material you took off.

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#7

Re: Beam deflection

12/14/2010 2:15 AM

"What wretched scoundrel stole the cork from my lunch?"

--W.C. Fields

[Thread deflection = k√(number of posts). It's a random walk.]

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#8

Re: Beam deflection

12/14/2010 4:21 AM

Gotta remember most of these calc's are only valid for 'small deflections'.
Lets hope one of the mech eng guys wanders past.
In the mean time you need to post your actual results and calculations to get a meaningful answer.

Oh and if you think the deflection on a bar is tricky, he should try making a longbow from a Yew log.
The bottom line is, it's the reality that matters rather than the calculation, no amount of equations will change the actual deflection of the beam.
Del

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#11
In reply to #8

Re: Beam deflection

12/14/2010 9:46 AM

Del,

I read last night a post about how the responses to questions were harsh and discouraged real questions. So I posted a real question. Apart from you and maybe one other person, clearly the people on this blog are self involved morons. The moderator should start removing them from the system.

Round tube beam, steel, 24" length x .625" OD x .065" wall. 25 lbs force at the midpoint, both ends supported but not fixed.

Calculated results are .85" of deflection. Real results deflection not even measurable w/o serious equipment.

I understand that reality is what matter, which is why I did the test. It amazes me that the calculations are so far off, which leads me to think I am applying them wrong or that there is some correction that brings me from theory to reality. Here is the real problem: if you can't trust the calculations, you can't perform optimization. To buy the correct size tubing to support the load, you have to buy the tubes and do trial and error.

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#12
In reply to #11

Re: Beam deflection

12/14/2010 9:56 AM

Guest,

Before you run off at the mouth about how you were dissed, please reread your pitifully inadequate first post.

In case you forgot, here's all the information you provided: "round tube roughly 24" long x 1" dia made of steel"

Now you tell us the OD is .625, not 1" as in your first post. No mention of wall thickness in your first post, either.

So, get over your arrogant self!

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#14
In reply to #12

Re: Beam deflection

12/14/2010 10:19 AM

C'mon, give him a chance... I'm interested and I might learn something...
The discrepancy between practical and theoretical always interests me.
Ok there's a lack of good info in the first post, but it's still an interesting Q.
We get plenty of really daft Q's without scaring off the potentially informative ones.
Del
<click.. sanctimonious cat mode off>

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#15
In reply to #14

Re: Beam deflection

12/14/2010 10:30 AM

Sorry,

I'm over it now. I don't mind being admonished if I'm guilty, but that was uncalled for.

I'll bow out now so's you serious types can move forward in the pursuit of whatever it is that is the guest's goal.

Cheers.

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#24
In reply to #12

Re: Beam deflection

12/14/2010 4:56 PM

You noticed -may be- that I several times insisted on the fact that engineering is a precise profession.

Unfortunately not every body thinks the same.

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#26
In reply to #24

Re: Beam deflection

12/15/2010 9:24 AM

I agree with both of your statements.

Thanks,

Happy Holidays.

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#37
In reply to #24

Re: Beam deflection

12/19/2010 1:38 AM

"You noticed -may be- that I several times insisted on the fact that engineering is a precise profession."

I'm glad I was a meat cutter. EVERY professional I ever dealt with, lawyers, doctors, engineers, etc... was always practicing their profession, and how exact do you have to be if you're just practicing ?!?

"Unfortunately not every body thinks the same."

Edit to the truth:

Unfortunately not every body thinks...

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#40
In reply to #37

Re: Beam deflection

12/21/2010 9:15 PM

?

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#13
In reply to #11

Re: Beam deflection

12/14/2010 10:09 AM

I'm not a mech eng, but I'd assume you'd need the Youngs' modulus for the steel. If I had to guess at the most likely error, I'd hazard that you were using the formula for a beam supported at one end?
There are some great mech eng guys* here, and the other's are just joshing around, maybe it's too near to Christmas. We're mostly harmless, so forgive the levity.
Del
* ba/ael knows his stuff, maybe drop him a private message, and say Del sent you...
Oh dunno if guests can PM...
I'll PM him and suggest he looks at this thread.

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#25
In reply to #13

Re: Beam deflection

12/15/2010 9:10 AM

I've got some bad news and some good news. The bad news is that you can not calculate the deflection of a beam without knowing the elastic modulus of the material. The good news is that all steel from the lowest grade-low carbon-coat hanger steel to the highest grade M2 high speed steel, and everything in between, has the same elastic modulus of 30,000,000 psi.

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#16
In reply to #11

Re: Beam deflection

12/14/2010 1:20 PM

Guest,

I hadn't got around to reading this thread, but Del sent me a line, so here goes. I did a quick calculation and found that you are out by a factor of 16. The deflection appears to be about 0.053" using E = 30 x 106 psi.

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#18
In reply to #16

Re: Beam deflection

12/14/2010 2:14 PM

I think I see what I did wrong. I think I used the wrong 2nd moment of area. My source has one where you plug in radius and one for diameter and I think I just switched the two.

.05 is still much larger deformation than I am seeing, but for the moment we will accept the answer "Check your experiment again." :-)

Thanks! You rock.

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#20
In reply to #18

Re: Beam deflection

12/14/2010 2:32 PM

Well, I'm certainly not surprised that you would make a mistake like that.

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#17
In reply to #11

Re: Beam deflection

12/14/2010 2:00 PM

What ba/ael wrote is correct. Deflection is only 0.0528".

You can always check a result looking at the beam geometry. For instance in your case the beam has the load in the middle and is free on supports at ends so that you can consider as 2 cantilevers. For a cantilever beam f= P*L^3/(3*E*J).

P is the reaction force on support thus 1/2 of the load in the middle.

I am sure ba/ael used the right equation which is a bit different from the way I took.

Why do you not give the link of the calculator you used ? It could help to find where the error was made ?

If the person you "consulted" said that you used the equations the right way then there were not the right equations since we are already 2 to come with the RIGHT equations to same result. this leads to some assumptions which I do not want to write.

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#19
In reply to #17

Re: Beam deflection

12/14/2010 2:18 PM

The calculator I found online is http://www.calculatoredge.com/civil%20engg%20calculator/beam.htm#tube which still gives bogus numbers. I have contacted them before regarding the discrepancy, but no response.

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#21
In reply to #19

Re: Beam deflection

12/14/2010 2:39 PM

Guest,

It appears the online calculator is finding the deflection of a cantilever of 24" length with a concentrated load at the free end. The deflection for that beam is 16 times the deflection of a simple beam centrally loaded. The calculator is correct for the condition it is checking, but it is not immediately clear from the display what the boundary conditions are.

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#22
In reply to #19

Re: Beam deflection

12/14/2010 4:18 PM

I went to the link you provided. I do not see on the site where one is to input the type of beam support (i.e. simply supported, cantilever, etc.) or where to input the location of the load. Sounds like you should look at a different source. Here is one for supported a beam supported at both ends and single load at the center. The equation for maximum deflection (which happens to be where the load is applied) is ym = W*L^3/(48*E*I).

For your problem I calculated I to be 0.004543 in4 and used a Young's Modulus (E) of 30*106 psi. This computes to a deflection of 0.528 inches.

If this does not match what you measured experimentally, then perhaps your beam is not simply supported at both ends, your material has a different Young's Modulus of Elasticity or you may be mixing units (inches and cm, or something of that nature).

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#23
In reply to #19

Re: Beam deflection

12/14/2010 4:54 PM

You used the wrong calculator. It is difficult to imagine the level of people who give a "calculator" without asking for the type of beam.

Now if you look at what I used as approach the length of the beam (total) will be 2x the one I introduced in the equation and the load as well so that the result will be 2^3*2 times higher = 16 exactly what you obtained. Using the radius instead of the diameter you introduced same factor since the value is ^4!

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#27
In reply to #11

Re: Beam deflection

12/15/2010 11:21 AM

Be sure the material properties are correct. Steel comes in many variations.

Stainless is different than carbon steel. But even using a different modulus my

deflections were .055 for carbon steel and .057 for stainless steel.

I used the Machinery's Handbook for starters. There must be more info or something else in the setup to give you .85". This is off by over a factor of 10 which in itself is suspicious.

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#29
In reply to #27

Re: Beam deflection

12/15/2010 11:29 AM

Just to clarify I used a .625" O.D. tube x .065" wall thickness

and I got an I of .004543 inches to the fourth. I used the same equation

as above and got .055" CS vs. .057" for SS again. Unless I am making an error...

Still off by a factor of 10.

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#30
In reply to #29

Re: Beam deflection

12/15/2010 12:00 PM

About 7 (seven) hours before you wrote your comment the explanation of the factor 16 (not 10) was given.

So that you have NOT to doubt about your computations you have to only read what was written before!

The differences between the Young moduli of carbon and stainless steels are not sufficient to justify the differences between the results obtained by guest or calculator and true value.

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#28
In reply to #11

Re: Beam deflection

12/15/2010 11:27 AM

What was the type of tube? Seamless or welded? Grade of steel? Sounds like you are testing 1/2" electrical conduit not structural steel tube? All of the before mentioned will give different test results; only the structural steel tube will satisfy the formula.

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#31

Re: Beam deflection

12/15/2010 12:33 PM

Hello All,

I think I know where the discrepancy lies, and it's the value of Young's Modulus of Elasticity of Steel (Es) that's being applied in the formulas and online calculators.

When I attended engineering school for my BS Civil/Structural in the late '70's and early 80's (and MS and PHD later on + working with the USACE & private consulting practice firms spanning over 30 years) we used Es = 29,000 Ksi or 29,000,000 psi for structural steel, not the 30,000 Ksi which I see throughout this thread. Who on the Earth changed the Es value for STRUCTURAL STEEL for these online software packages, some computer tech weenie that doesn't have the engineering education, knowledge and judgement of exactly what he's writing into the code???????????? BIG SCREW-UP if you ask me!

The AISC "Manual of Steel Construction" lists Es = 29,000 Ksi. It appears to me that application of the incorrect Es will result in errors.......there'ss 1,000,000 psi difference in the two values!!!! Never in my life as a Structural Engineer would I even consider using Es = 30,000 Ksi. I doubt that my contemporaries would either.

Signed,

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#32
In reply to #31

Re: Beam deflection

12/15/2010 1:15 PM

30,000,000/29,000,000 ≈ 1.034. That's only a 3.4% difference, though I too am used to 29... vs 30....

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#33
In reply to #32

Re: Beam deflection

12/15/2010 1:57 PM

I agree that 29,000,000 psi is a better value for E, but as you have noted, it does not account for the whopping difference in results.

The online calculator does not state the support conditions for the beam and I believe that is the main problem. It should have stated that the calculation is for a cantilever beam with point load at the free end.

A simple beam with a point load in the middle has a deflection of PL3/48EI. A cantilevered beam with point load at the free end has a deflection of PL3/3EI. These results differ by a factor of 16.

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#34
In reply to #31

Re: Beam deflection

12/15/2010 2:04 PM

As others have pointed out, the difference between 29 and 30 million yields a 3.5% difference in deflection. Also, 29 million is correct for structural steel, but OP hasn't specified the type of steel he is using. A curious property of steel is that all carbon steels from structural, to high speed, to air and oil hardening steels, etc., etc., have an elastic modulus value between 29 and 30 million. Therefore, all carbon steels will deflect the same amount (within 3.5%) under load until they reach their elastic limit.

Signed,

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#35
In reply to #31

Re: Beam deflection

12/15/2010 2:40 PM

I hope that it was thought as an ironic joke. If not I have to ask myself a lot about several aspects in the tuition.

What signification have the mentions at the end ?

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#36

Re: Beam deflection

12/15/2010 4:53 PM

Don't know much about your application or constraints, but the circular cross section is far from optimal for the bending load as you have described it. Circular sections are often a first choice for torsion and also axial loading.

You don't appear to have a deflection problem anyway, but other shapes (e.g. I-beam) are more efficient for this bending load case.

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#38

Re: Beam deflection

12/20/2010 9:21 AM

Structural engineering is as much an art as it is a science. We set out to make sure that a structure is not too weak and not too flexible. We do not seek to find the exact stress or deflection, only to limit them.

Manufactured items and materials are made to within prescribed tolerances, thickness, out-of-roundness, chemical composition, etc.

The dimensions you provided look to be nominal, rather than exact. you don't say if the supports and load are knife edge or not, if not, the deflection will be affected.

It is not an exact science. Do not, dear grasshopper, expect exact answers.

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#39
In reply to #38

Re: Beam deflection

12/20/2010 1:20 PM

passingtongreen,

I agree that uncertainty about the modulus of elasticity and minor differences in wall thickness, diameter or out-of-roundness can affect the precision of the calculated results.

To this end, the online calculator's output was Deflection = 0.845244" and Stress = 41,271.7 psi. These figures should have been rounded to a maximum of three significant digits (more likely two) as we do not know the diameter, thickness or Young's modulus to a precision of more than two or three sig figs.

So, deflection = 0.85" and stress = 41,200 psi would have been a more appropriate output.

Using the relationship M = f*S = 41,200*0.01454 = 600"#, confirms that the online calculator was intended for a cantilevered beam loaded at the free end (M = PL = 25*24 = 600"#). For a simple beam loaded at midspan, M = PL/4 = 150"#.

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#41

Re: Beam deflection

03/25/2012 6:06 PM

Online Beam Bending Helper for fast calculations. It is Silverlight application with rich user interface (like desktop) for helping students and engineers to solve (check) Beam Bending tasks.

About the theory...
Euler-Bernoulli-Timoshenko Beam Bending theory works well for long beams (the length of beam is much more from other sizes)

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#43
In reply to #41

Re: Beam deflection

10/15/2012 5:01 AM
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