Talk:Euler-Bernoulli beam equation
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I forgot to login before creating this article. --Yannick 23:42, 17 Jun 2005 (UTC)
Contents |
[edit] Suggestions for Further Work
[edit] History
- I'm curious as to when the theory was proven by laboratory experiment.
- The nature of Bernoulli's and Euler's collaboration could be expanded.
- Stephen Timoshenko's History of Strength of Materials (Dover Publications, Inc., New York, 1983) would probably provide more information. Anybody got a copy?
--Yannick 23:42, 17 Jun 2005 (UTC)
For number 1, I was led to believe that it was derived using laboratory experiment. I was told by a prof that this was found by measuring displacements of actual beams using a grid. - EndingPop 22 Dec 2005
- In my classes, the prof told us that Euler and Bernoulli derived the equations from the full theory of elasticity matrices, which were already known, and empirical proof came later. I still have extensive notes on the derivation.--Yannick 18:34, 3 July 2006 (UTC)
[edit] Addendum
Two more assumptions are:
Material should be homogeneous.
Material should have continuity.
- I believe those are assumptions of the theory of elasticity, not of beam theory.--Yannick 04:23, 18 September 2006 (UTC)
Maximum deflection for the four elementary loading cases must be added.
1) Cantilever (one end fixed, other free)
2) Cantilever prop (one end fixed, other pinned)
3) Simply-supported (both ends pinned)
4) Fixed-Fixed (both ends fixed)
I would also like to add few diagrams. I am busy with exams these days. I would like to expand this article once I am finished with exams.
Note: We referred R. C. Hibbeler for our "Engineering Mechanics", "Strength of Materials" and "Structural Analysis" couse. Hibbeler have'nt properly credited Euler-Bernoulli for this equation. We just call it classical equation.
Stress / Deflection = Moment / Inertia = Elasticity / Curvature
Yannick: I believe our library has the book u mentioned. I will confirm it though. Thanks for increasing my knowledge regarding this equation.
H.A., third year Civil Engineering Student.
Just found this page. I'm a (semi) retired CE who is reviewing material learned and forgotten thirty years ago.
I am thinking of adding a section on simplified beam theory which uses these assumptions:
1) Linearly elastic, isotropic 2) Small deflections 3) Shear negligible.
It's not as complete as Timoshenko beam theory, but 99.9% of structures are designed this way.
-James0011
- That would be more useful than the current page. Having both would make it much more complete. - EndingPop 00:55, 13 June 2006 (UTC)
[edit] Please don't edit equations recklessly
I basically reverted the main equations in the "practical simplification" section. My main reason is that a major error was introduced on December 22, 2005, by 131.151.65.70 simply by changing '=' signs to '+' signs. However, I also reverted other ongoing degradation of the equations. I changed the load variable back to 'P' from 'F' for consistency, because F was defined earlier in the article as internal axial force. I'm guessing it was originally changed to match the diagram, but changes like that should try to make the ENTIRE article consistent, not just one section. In this case, I would prefer changing the diagram to show a tip load of 'P', but if we go with 'F', then the variable for internal axial force should change to something else for the whole article. I also reverted 69.241.225.246's recent change at the same time because although concise equations may be pleasing to mathematicians, they make it harder for the intended audience (engineers) to read, and key information was lost in the edit: that these equations give the MAXIMUM deflection and stress for any point in the beam. Also, if we are going to express these equations as proper functions of '(x)', then 'My' should also be expressed as 'My(x)'. I didn't want to do that because this is a basic example section which should minimize the potential to confuse newbies.
No doubt there is a way to formulate these equations that will satisfy everyone's concerns, and I'll try to work on it if I get a chance. But if you want to take a try at it, please look at the entire equation, and see how it fits in with the rest of the article. A small change can really mess things up.--Yannick 04:14, 18 September 2006 (UTC)
I think there is an Error in the deflection ODE solution: it should be diveded by 3 instead of multiplied by 2. Pleae check me out!
[edit] Cantilever Image
That image of the cantilevered beam in the Boundary Considerations section seems wrong to me. In the image, the free end remains horizontal. This seems to imply that there is zero rotation, but non-zero deflection at the end of the beam. Somehow we've fixed rotations and not displacements, which isn't a possible BC presented in the section. If I'm wrong on this, could someone please explain why? - EndingPop 22:16, 3 March 2007 (UTC)
Good point. Fixed.
Ben pcc 03:36, 6 March 2007 (UTC)
