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 be determined by treating each column as a beam supported at one end, with the load applied at the unsupported end?   Modified by dalecyr at Tue, Jan 25, 2011, 15:18:21

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: Is this Beam Bending Equation correctly applied?
: Is this Beam Bending Equation correctly applied? -- dalecyr	Post Reply	Top of thread	Engineering Forum

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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: Is this Beam Bending Equation correctly applied?
: Is this Beam Bending Equation correctly applied? -- dalecyr	Post Reply	Top of thread	Engineering Forum

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. Hint: It is a STRUCTURE! 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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: : Is this Beam Bending Equation correctly applied?
: : Is this Beam Bending Equation correctly applied? -- Pinkerton	Post Reply	Top of thread	Engineering Forum

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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: : : Is this Beam Bending Equation correctly applied?
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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, can those 4 columns be treated as one column of 2x2x.125? or 2x2x.250?

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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. I do not know the right question to ask. I do not know how to figure out the right question to ask. Maybe I do not belong on this forum. I apologize. dale

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: : : : : : Is this Beam Bending Equation correctly applied? -- dalecyr	Post Reply	Top of thread	Engineering Forum

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. All I was suggesting is that you seem to stop thinking at the first option that looks good and thus go with that as the method for that problem. You need to consider all options. Often you may find two or more ways to achieve the same end result. In fact that is always a good cross-check if you have that luxury. 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. ****************************************** For example: if each column is 1x1x.125 inches, can those 4 columns be treated as one column of 2x2x.125? or 2x2x.250? ****************************************** 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, <<>> so hang around for a while longer. 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 to calculate column buckling, to no avail. (I can not believe that I missed the page that Kelly pointed out) This is a pretty thourough site; so I thought maybe buckling is like a sheer load; technically, there's no such thing as sheer load; it's just a very complex interaction of compression and tension loads confined to a very small space. I had to give up on that one. Dave hinted that I should consider the whole, ie: as a structure. There are, of course, no methods on this site to calculate ratings for 'structures'. My post about "...can those 4 columns be treated as one..." was an attempt to discern whether or not those columns being connected into a structure made the math differant than simply calculating them as single components. You confirmed that is not the case. In other words, the formulas obviously show that 4 little ones do not equal one big one. (yes, I *did* do those calculations) And you confirmed that even tho they are connected as a structure, 4 little ones *still* do not equal one big one. Not knowing how to proceed with the drawing as a structure, I had to give up on that. Even tho the drawing shows a 'structure', a structure is made up of components. Not wanting to waste everyone's time by detailing my thought process, (er.. at least not lately anyway (and *this* post aside)), I was hoping that calculating the bending force would result in a more conservative number than the buckling force. I have confirmed this by running through the formula that Kelly pointed out. I have to confess that I did not understand your comment "But remember that **the supports on each end** of the beam resist rotation, like a cantilever support." I must have an incorrect understanding of a cantilevered beam; I thought, by definition, a cantilevered beam was supported, and therefore resisted rotation, on only one end. That is why I did not respond to that post. It is pretty obvious that I do not know enough to know how to figure this out, and I am at a complete loss to come up with the correct question. (Theorems required axioms; if you have no (or no appropriate) axioms, no amount of logical thinking will produce a viable theorem.) In one of my part time jobs, as a rigger, I regularly suspend (literally) tens of thousands of pounds over people's heads. These are static loads, dynamic loads, and sometimes unexpected shock loads. Point loads, uniformly distributed loads, combinations thereof, cantilever loads, ***negative loads***!!! (a truss that was resisting a 4000 pound downward load at each end, suddenly gets a 2000 pound *upward* force at 34 degrees from vertical at one end) I can not afford for my calulations to be wrong, ever. I know that designing a rack for my pickup, so that I can transport my extension ladder does not carry the same liability, but my rigger mentality forces me to run the numbers. So, this is what I have decide to do: I have figuratively turned the above drawing on it's side. Assuming (actually, hoping) that a beam can not support a greater load than the same size column, and using the results from the formula on this site titled: "Calculation Cantilevered Beam with One Load Applied at End", and knowing that I do not know if a structure increases or decreases the load handling ability over just individual components, (especially in this widely spaced configuration, rigidly attached at only one 'end') I was just going to increase the safety factor of the individual column components from 2:1 to something more like 10:1, and hope for the best. Oh yea. I doubt that Dave has read this far, but in case he has: thanks for the pep talk. ;) Comments? Modified by dalecyr at Sun, Jan 30, 2011, 00:03:44

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