Hi, new to the forum, I have a couple questions about stress in a beam that I am currently working with.
The beam is a length of 2"X2"X3/16" square tubing. I have an equation for normal stress being equal to moment divided by section modulus.
The tubing is welded in several place leading up to the applied force point, I have calculated the moment around the last welded location closest to the applied load. That point is also the last supported location. Also, the A500 B material has a yield strength of 46ksi
I look up the section modulus to be 0.64 and the moment is 19,500 lbs. So, normal stress = 19500 / 0.64 = 30,500psi. Since that result is well below 46,000psi, I am good, yes? Or have I even used that equation correctly?
Secondly, I know section modulus(S) = moment of inertia(I) / distance the farthest stressed point is away from the neutral axis (c). I look up (S) to be 0.64, but (I) is also 0.64, so that (S) figure must have the neutral axis in the center of the beam. If the neutral axis is in the center, then (S) = 0.64 / 1 because (c) has to be 1". However, in my moderate statics education, I would have thought that (c) would have to be 2". Because the tube is supported at the bottom, I initially thought it would be bending around that bottom point making the neutral axis right there at the bottom and that would make (c) equal to 2"
So my second question: Should I calculate with (c) being 2", doubling the calculated stress in the tube and just wait for it to fail? Or is the initial calculation with (c) being 1" correct?
Thanks in advance and any help at all is greatly appreciated. Also, this is not a homework problem or something I am considering building out in the garage to hang heavy objects over head. It's something (long story short) my crazy, entitled, impulsive, demanding boss threw me into.
Well, a sketch of the situation would go a long way towards helping us understand what is going on. Your verbal description of the first problem may be clear to you, but It does not make a lot of sens to me. I have not even looked at the second problem for the same reason.
stiched-weld.gif
Thank you again. You can see in the sketch, it is a tube welded to a base structure at two points. The moment about point A is 19,500 lbXin. I just wanted to make sure I used the equation (stress = moment / section modulus) correctly.
My second question was really just if I should consider the bending point to be at point A or if it should be considered to be the section at point A, as in the entire tube cross section there.
Last edited by Kelly_Bramble; 12-21-2012 at 02:29 PM. Reason: Attached picture in forum
Hi Wayne, hate to be difficult, but where is the load? Is it evenly distributed over the free length, or a point load at the end of the tube like a crane-jib?
If I think I understand the second part, the entire cross-section is involved in the calculated strength of the beam. If considering just the absolute point "A", that would be like using a 3/16" x 2" flat bar??? No?? I may not be grasping what you are trying to get at here though.
Step 1 is a free body diagram, and that is impossible without dimensions of supports and loads.
Also, "moment is 19,500 lbs" is wrong. It is either in-lbs or ft-lbs. Which?
And, just because the moment about A as created by the load is 19,500 __-lbs doesn't mean that is the maximum moment the beam sees. That question can only be answered with a complete free body diagram (see above).
Pinkerton, there are several point loads that I used to get a sumation of moments. I believe you have helped me with my main question. If it were not the entire cross section that counts, but just point A, I would have calculated a much smaller section modulus and it would double the stress calculation. From what I have read up on in the last few days, I beleive I am good there.
jboggs, Sorry, 19,500 lbs is a typo, it is supposed to be in in-lbs as in my second post. Originaly, I had just grabbed my easy stress equation and went to town. Since it only required a moment to be known, I didn't set up a free-body diagram. Now that you mention that though, I will dust off my strengths book and try to set it up properly. I have never laid out a free-body diagram without simple hinge or roller supports, but with the welded supports I suspect it should be treated as a cantilevered beam, in which case I should get the same results. If I don't get my head fully wrapped around that, I may link a more detailed sketch with dimensions later.
Whoa back Wayne. I do not believe I "answered" anything. As JB points out, lengths and load points are all critical to the correct calculations. We cannot confirm anything without the actual details to calculate. I was merely guessing at what you were asking.
We cannot use that 19,500 as a guide to what might be correct. Be careful as it looks like you are assuming a lot of stuff slightly outside your domain of Engineering knowledge. Given that almost 20,000 in-lbs is a serious load, you would be well advised to get some paid for Engineering assistance with that. Or at least present the entire problem here for some brave soul to jump in and give you some figures.
This could be especially important if humans have access to anywhere closely related with the finished system when under load.
beam-deflection.jpg dimensioned sketch
Here is everything I have, basically. I attempted to set up a free-body diagram and if there were all hinged supports I would be able to, but the welded supports are more than I know how to do. I know I should use the moment to get a reactive force (would be upwards) on support 1 and therefore its supportive force (would be downwards). Then add that to all other downward forces to get the upwards supportive force at support 2, but the welds got me hung up.
I thought about just setting a free-body diagram up as if the supports were hinged supports, but that wouldn't be accurate and I don't know how askew that would be from the actual.
Last edited by Kelly_Bramble; 12-21-2012 at 08:57 AM. Reason: Attach image directly
The classical solution , M/z doesn't work IMO, since the support at the A is not truly clamped, so the upper fibre stress would be much less.
If you could better clamp the section at A, your solution would be OK.
If that is not possible, then you would probably need a stress program to get a reliable result.
See attachment - close - just make assumptions about weld...Originally Posted by sickwayne77
Beam-Deflection-cantilever.jpg
Better yet....
Welding engineering and design
I made the case some time back to have the setup analyzed for a handful specific stress points, I'll make that case again. I had a statics course quite a while back and taught myself strengths shortly afterwards. I feel ok about how I used the math, but less so about how I applied it.
Thank you everyone.
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