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Is this Beam Bending Equation correctly applied? | |||
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Posted by: dalecyr ® 01/25/2011, 15:03:00 Author Profile eMail author Edit |
Referencing the attached picture;
assuming a rectangular box constructed of tubing as shown; assuming a load adequately supported, sitting on top of the box; assuming the bottom of the box is securely attached; assuming an additional lateral force applied to the load; assuming each column bears exactly 1/4 the vertical and lateral loads; Using a specific load, can the lateral deflection of each column
Modified by dalecyr at Tue, Jan 25, 2011, 15:18:21 |
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: Is this Beam Bending Equation correctly applied? | |||
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Posted by: Kelly Bramble ® 01/29/2011, 07:41:55 Author Profile eMail author Edit |
Well, to calculate the column loading there are cook-book solutions that represent this loading situation. A statics free-body diagram is needed to define and then calculate the specific applied loading. Though, as all of you know the results are only an estimate as actual resultant loading and applied stresses and strains is given by the combination of assembly imperfections of the materials and welded connections. So, for a quick estimate of a similar column loading configuration and the potential buckling of the column see: Eulers Equation Colmun Bucking I want to repeat that this is an estimate and not a perfect case for the Eulers equations, however if your design is 1.5X to 3X stronger under loading then the minimum calculated then the design should be adequate. It is early, and I have been running hard all week, however I would use the "Pinned-Pinned" Effective Length Constant. I think EE needs to create calculators for these equations... soon. Modified by Kelly Bramble at Sat, Jan 29, 2011, 07:45:43 |
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Posted by: Pinkerton ® 01/25/2011, 15:17:54 Author Profile eMail author Edit |
Nope. You're not thinking this through. I'll give an answer when you ask the right question.
The lateral load needs defining in direction and force. Uniform or sudden? Any possibility to twist the "box" or lozenge in any or several planes? Offset lateral load? So many answers so little time. ;) Dave |
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Posted by: jboggs ® 01/25/2011, 18:33:04 Author Profile eMail author Edit |
"Using a specific load, can the lateral deflection of each column be determined by treating each column as a beam supported at one end, with the load applied at the unsupported end?" Basically, yes. But remember that the supports on each end of the beam resist rotation, like a cantilever support. |
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Posted by: dalecyr ® 01/26/2011, 20:49:44 Author Profile eMail author Edit |
For the purposes of calculating deflection,
since each column is connected to its neighboring column, can the four columns shown above be treated as one larger column? For example: if each column is 1x1x.125 inches,
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Posted by: jboggs ® 01/27/2011, 12:11:36 Author Profile eMail author Edit |
Bending strength isn't necessarily linearly proportional to external dimensions. I would recommend applying 1/4th of the load to a single leg. |
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Posted by: dalecyr ® 01/28/2011, 20:36:33 Author Profile eMail author Edit |
Dave: I have thought about this for a few days.
Maybe I do not belong on this forum.
dale |
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Posted by: Pinkerton ® 01/29/2011, 10:12:36 Author Profile eMail author Edit |
Dale, JB was guiding you so I left it to him to follow through with it. Now, get someone to toss your pacifier back into the baby carriage and you get back into the fold here.
Many years back I bought a very high-end programmable Casio calculator (back in the TI-59 days) that had inbuilt routines for all manner of Engineering stuff. I used one such routine to calculate the size pipe needed for a 25' wide x 10' tall gate. Had I not cross-checked I would never have known that the calculator had a flawed algorithm and had provided an incorrect size. The questions you asked about up-sizing suggested stabbing in the dark. If you assumed that premise to be correct, then you should have dragged out the formulas and done some alternative calcs for deflection. You would have quickly seen that the following made no sense. ******************************************
If you look back over my posts to anyone you will see I usually answer with more of a suggestion or question than a direct answer. You are wanting to learn this stuff, I will not give the direct answers. I don't care if others do provide direct information, but it is not how I work. Not meaning to sound pompous or superior, but it takes years of study to understand all this stuff and if you want to get good at this, even as a hobby, then you have to follow that path to learn. Well, learn from me anyway. We -- and I think I can speak generally for the group, still love ya, ya big lug, << All I am saying is think things through and don't grab at the first solution that sounds plausible. I have said it before, "everything in Engineering is logical," and that means it can be figured out by the thought process. Dave Modified by Pinkerton at Sat, Jan 29, 2011, 10:15:07 |
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Posted by: jboggs ® 01/29/2011, 11:28:55 Author Profile eMail author Edit |
Dale,
I didn't see a response to my suggestion. It is possible to calculate the deflection of your structure with the lateral load. Think about it this way: "beams" are resisting the sideward load. All things being equal they are all probably carrying an equal share of the load. That means each one is deflecting as it would under 1/4 of the total load. For your beam diagram, just turn it sideways so that the load is vertical and the beam horizontal, and pick out the appropriate formulas from Roark's, Mark's, Machinery's Handbook, or this website. |
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Posted by: jboggs ® 01/29/2011, 11:33:24 Author Profile eMail author Edit |
Dale,
After reading Kelly's post above I realized that you might be talking about column buckling. I thought you were just talking about sideward deflection under lateral load. Are you talking about column buckling? If so, that's a whole different thing, and follow Kelly's advice. |
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Posted by: dalecyr ® 01/29/2011, 18:25:58 Author Profile eMail author Edit |
jb: I have spent hours on this site searching for a method
I had to give up on that one. Dave hinted that I should consider the whole,
There are, of course, no methods on this site
My post about "...can those 4 columns be treated as one..."
You confirmed that is not the case.
Not knowing how to proceed with the drawing as a structure,
Even tho the drawing shows a 'structure',
Not wanting to waste everyone's time by detailing my thought process,
I have confirmed this by running through
I have to confess that I did not understand your comment
I must have an incorrect understanding of a cantilevered beam;
It is pretty obvious that I do not know enough
(Theorems required axioms; if you have no (or no appropriate) axioms,
In one of my part time jobs, as a rigger,
I can not afford for my calulations to be wrong, ever. I know that designing a rack for my pickup,
I have figuratively turned the above drawing on it's side. Assuming (actually, hoping) that a beam can not support
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