What I understood is : - We use Euler formula when the Buckling stress is less than or equal to the Yielding stress and this case applies for long columns only [ high slenderness ratio ( Kl/r ) ]. In reality we might use intermediate or short columns so for the intermediate and short columns we use Tables based on empirical equations to find the Allowable Buckling Load by comparing it with the value of ( Kl/r ) of the column under study. - The moment of Inertia with respect to x-x was (Ix) less than (Iy) , the x-x axis is called the weak axis and the y-y axis is called the strong axis so logically the buckling failure starts from the weak axis , in practice the use Bracing in the side of the weak axis to strengthen it and minimize Buckling effect.
hi first of I gotta say I'm loving the video. I just wanted to ask a weird question... how can the beam be pinned in both the x-x plane and the y-y plane lol nothing major, it made for an easier example. for that to be true it would have to be on a ball joint or something right?
I am working on a project where I have to design a wheel using spokes. I am cross referencing a previous design and for some odd reason the spokes are curved toward the bottom. How would I calculate the Pcr of a curved spoke? Thanks!
Hi Structurefree, Thank you for your videos, they are awesome. Keep it up! But i have one question about this video. I know that the yield stress is given, but is there anyway to calculate it? or it is so a material property which is found out empirically? Cheers Sam
Dear structure free Very interesting talk. Can you use this mathematics to determine the buckle point in any given stock or the s&p 500 or the DJIA? If you look at the 2008 GFC, 1987 selloff or the 1929 crash would this buckle point appear in the mathematics do you think? Any kind thoughts appreciated.
That's an interesting question. I know that people use differential equations to try and model the market and there is the discipline of mathematical finance. I'm more of a buy and hold investor. If I could predict the future.....hmmmmmm....ballin.
Do you have any videos on web shear and flexural buckling for box girders? Also, I'm not sure if you are Canadian or not but I am from the University of Toronto and our civ102 professor (Michael Collins) derived equations for shear cracking in reinforced concrete which are used by our provincial and federal code for concrete structures (and I think he recently managed to get it adopted by the Americans due to its improved accuracy over the ones currently used) and I was wondering if you could do a few videos on those ones.
Here I am again watching you vids for the PE four years after. I was asking myself the same question: why not use P= pi^2 EA/ (Kl/r)^2 . Scroll down the comment section only to find out I asked the same questions four years ago. LOL.
If you calculate that a column will both yield and buckle at the same applied load, does it have the ultimate capacity to carry that load? And if not, how do you calculate the ultimate capacity of an intermediate column? A column which has a yield strength and an ultimate strength in the same vicinity. Are buckling and yielding both independent failure modes for a column? Or in the event of an intermediate column, does a combined failure mode occur?
+carultch the euler buckling equation has a lot of assumptions built into it (linear elastic material, no crookedness, etc.) unless the column is more like a pedestal (really really small slenderness ratio), it will buckle first. There is also inelastic buckling behavior which typically occurs as you decrease slenderness ratio and that topic is typically covered in a second course in mechanics or an introductory design course.
I don't understand why you would have to use the variation of the Euler's equation to solve this problem. Demonstration purposes? The P = pi^2EI/(KL)^2 is much easier and quicker to use.
WHY70122 It really doesn't matter either way. I personally like to use the slenderness ratio (KL/r) since it is a dimensionless measure of slenderness for a given member. It makes it convenient to compare column members, also the AISC manual uses the slenderness ratio in its tables and in the specifications and provides values for the radius of gyration in the cross-section properties table.
I have been studying an effect that I observed many years ago in my teens. In the last few year I have learn about Euler’s column and contain column studies. I think my observation is a variation of his contained column theory. Is my variation well known and studied? As of late, it’s starting to look like a good model of the particle in a box problem. Maybe I am just trying to read too much into it but it has some interesting proprieties that I think people in the know should look at.
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-wrBsqiE0vG4.html the engineer test video is not as exciting as yours but I hope you find in interesting. Hope you will try the effect and or comment on it. I think it rate as a variation of Euler’s contain column work. Yes-no maybe?
I need clarification Please: I keep seeing that the critical buckling formula does not include a radius of gyration only the critical stress formula. Why is the radius of gyration used here in the critical buckling formula?
Haha, It doesn't bother me if it doesn't bother you :) As for a microphone I'm not sure, just one that doesn't pick up on so much of the "p-uh" and breath-y sounds. Again, thanks for the helpful video!
Thanks for this example it was great but how come when I use the formula in regards to Length Pcr= [(pi)^2.E.I]/(KL)^2 I get a completely different answer, and in which case should I use which formula ? I'm mainly confused because the two formulas are so similar and I'm not sure when I'd need the other one
If you substitute r for sqrt(I/A) in the second formula and solve, you end up exactly with the first formula. The reason you use r is to determine which plane of axis the buckling is going to occur in, if your cross section is something simpler (like a circle) then you can just use the first one. (I know you've probably long passed this course, but hopefully someone else finds this helpful).
hello... i have been waiting for your new video!!! I have a request if you may allow me ,pleas do some videos in R C designing .. i mean take a small project like two story building and show us how to design the members all together ...i woul appreciat that ... thank you so much...
Hi! Thanks for this clear explanation. Just a question: for an arbitrary shape of the cross section, how should I compute the radius of gyration? with respect to centroidal axes only (and then find the maximum of KL/r? Is mohr's circle necessary here to find the minimum moment of inertia (but that would mean that K would change... I'm confused).
hey dude, ive been looking through your impressive vids for some way of calculating the dispersion of a force through a shaped wheel. if you have a moment look through ://scratch.mit.edu/projects/10186511/ inside the script, costume 2 of the core structure sprite or just play and click on the core to see the math in the background and click on that math to see the picture. any help is appreciated :D
TheHeartsDuff 0.7 is approximately equal to half of the square root of two. In fact, the k-factor for this condition is supposed to be sqrt(2)/2. In the condition of fixed-pinned, draw the shape that the buckling takes, and construct the sine wave shape that can meet the fixed bottom and pinned top. You will see that in order to get a vertical tangent at the bottom, while the top is free to be oriented in any direction, the way to do this is to reduce the "wavelength" of the sine curve by a factor of sqrt(2)/2 from a pinned-pinned buckling shape.
I have a quick question on the moment of inertia. Where does the (1/12) come into play and do you have any videos explaining the moment of inertia? I've watched some but don't really understand how to calculate it
probably too late to help you but for other people, moment of inertia is a geometric property meaning it is only related to the dimensions of the object. you can obtain it by integrating the (distance squared from the neutral axis) of every point on the plane. Think of it like finding the area under a graph, we know that we have to integrate the function within a certain range (definite integration). That is wat is happening under the hood. But if you have a graph of a very simple equation, say y = 1 , you would simply have a straight line and the area under it would just be a rectangle whose area you can determine by just (base, which is any range of x values) x (height, in this case 1) . Likewise, for area moment of inertia you have formulae for a lot of simple shapes , for a rectangular cross section it would be (base x height)/12 .The 1/12 came from when we performed the definite integration of the (distance squared from the neutral axis) of every point on the plane.
length of the bow-curved deflection of the column (under load) depending on the end conditions..i.e. pinned-pinned k= 1,fixed-fixed k=.5, fixed-free k=2, fixed-pinned k = .7 (depending what book u read). kL is termed the equivalent length....
Its a little complicated to explain with out a diagram but its the deflected shape that particular support configuration forms when load is applies compared with the standard configuration the Pinned-pinned support or k=1.0. The k=0.7 basically means that that proportion of L acts like the standard Pinned-Pinned support. This is known as its effective length factor. Since the formula used is derived from the pinned-pinned support the beam has to act the same way. here's a list of common k values: Pinned-Pinned = 1.0 Fixed-Pinned = 0.7 Fixed-Fixed = 0.5 Fix-Free = 2.0
