Method of superposition example #1: simply supported beam
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- เผยแพร่เมื่อ 14 ต.ค. 2024
- Check out www.engineer4f... for more free structural analysis tutorials. The course covers shear force and bending moment diagram review, method of superposition, moment area method, force method, displacement method, slope deflection method, and 3 moment equation.
This tutorial goes through a statically determinate slope & deflection example problem using the method of superposition. The simply supported beam has a point load and a distributed load, and we use a table of slopes/deflections for common beam loading to speed up the calculation.
Here is the table from the video: www.engineer4f... you will also find similar tables in any mechanics of materials or structural analysis textbook.
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Thanks for watching, The Struggle Is REAL!
Thanks man, some douchbag professor put a problem just like this in a review video but decided he was gonna do a "separate video" to solve it which I couldn't find. Thanks again. Big Stress Reliever!
Simply explained. Please keep it up, Thank you ❤
What happens if the point of deflection you want to find is not at the point load? Like if they say find the deflection 1m from a but point load is 2m away? I hope you respond
Moment area method is a good way, especially when seeking the max deflection. Check out videos 19 - 28 here: engineer4free.com/structural-analysis I recommend watching them all to learn the method, but the last one in particular (video 28) might be similar to what you're looking for
How to know if I have to use the curve ekvation? Why arent we using that for the single load?
I know this is an old video but is there anyway to use this method to find where the slope is 0 on the beam/the exact location of maximum deflection?
You're probably best off using the moment area method to find the locations of zero slope for a non-symmetrical structure. Check out videos 19-28 here: engineer4free.com/structural-analysis Video 28 specificaly goes over an example on that, but I'd recommend watching the other videos in the section as they build up knowledge and context on how to use the method.
Thank you very much. Took a look and it was a great help.
Awesome, glad to hear it!! =)
thanks sir it was helpful.
i appreciate it
What is the definition of X. I don’t get how you get X.
x is the horizontal distance from point A. If L = 8, then x at midspan is 4. Check out videos 15 - 18 here: engineer4free.com/structural-analaysis for more in depth explanation of this method.
Thank you for saving me 30 min of hair pulling 🙌
Does this method work for finding moments across the beam as well?
Superposition applies to internal bending moments too. If you had two loads on a structure, you could draw that structure twice, with only one of the loads present in each diagram. If you solve the internal bending moment at some point in both diagrams, then you can take the sum of them as the actual internal bending moment at that point in the actual structure with both loads. Same goes for internal shear, and reaction forces.
Engineer4Free Thanks for the quick reply. Allright, that sounds awesome. But what if i want to draw a moment/shear diagram for the entire beam, i.e I have the lenght set to x. Could I still use superposition?
You could, but I wouldn't normally recommend it. If you are drawing the SFD & BMD for a statically determinate beam, I would first solve for what the reactions are for the whole beam with all loads acting on it, and then draw the SFD in one go, and then draw the BMD based off the info in the SFD. If you split the loads into separate diagrams your pretty much going to double or triple the work (like if there are two or three loads in total). I made a bunch of videos on SFD & BMD, they are videos 1-9 here: engineer4free.com/structural-analysis That is the method I usually use, it's "the fast way" where you don't really find the moment function in terms of x. It pretty much works flawlessly with combinations of point loads and uniformly distributed loads. If you're asked to find moment in terms of x before plotting the BMD on a statically determinate problem, you have to do it the "longer way," which you can get the hang of in videos 66-72 here: engineer4free.com/statics. Even though most often it's easier and quicker to do it the fast way, it's still a good idea to understand why it works via the longer way. If you are doing problems that are statically indeterminate, then there are several methods at your disposal, which I cover many in detail at engineer4free.com/structural-analysis. One last mention, is that video 39 in the structural analysis course goes over adding two BMDs using the principle of superposition, and ultimately I mention in that video that it's almost never worth it to solve problems that way. I encourage watching the tutorials that I linked above, if you do you'll have a pretty good understanding of drawing SFDs & BMDs. I'd recommend watching the statics ones first, then the structural analysis ones should be a breeze after. Hope that helps!
Thank you very much. Engineering is a hard program to study, but thankfully there are kind and informational guys like you. I'll most definetly check your videos out.
You're welcome! Engineering is a really tough program and I'm glad I can help :)
thanks
you're welcome homie
Was EI given? or do we have to find it ourselves? I have no information on it.
EI in this video is given, it's 100x10^6Nm^2 written at the very top middle of the screen at the beginning of the video in black. EI is often just given in these types of problems. Otherwise you need to be given the cross section and material so you can calculate it or look it up in a table.