Column Buckling (Continuous System)

[@aminamiripour6583]

Awesome! Just one question In Equation 4, Shouldn't it be +r1(square)c1 - r2(square)c2?? Because the second derivative of Cosh(r1x) is positive r1(square)cosh(r1x) not negative.

[@Freeball99]

Yes, you're correct. It appears that I made a "typo" miscopying from my notes. However, the rest of it is correct - i.e that C1 = C3 =0. It turns out in this particular case that the sign error made no difference to the result. Thanks for catching that.

[@Tomwit]

I think that was the best and most insightful explanation of buckling I've heard so far. Great video!

[@Omar-sj7wl]

Great work! You are one of my favorite engineering education video makers. Although the production value isn't that high, the videos are clear and concise.

[@moaqirahmad5948]

FANTASTIC ...... I was requesting this topic for so long and finally you have made it. I didn't know that one get to buckling through vibration equation... thank you sooo... much.

[@terokemp4810]

I can remember from FEM classes that if the stiffness matrix goes to zero under compressive loads that equals to buckling. This solution deriving from beam theory, and harmonic modes is really beautiful. This raises the thought that this is probably what they tried to teach me many times but I was just way too slow to connect the dots.

[@xiaoliyuan3172]

For n=2, 3, 4…., is that what we usually call 2nd, 3rd , 4th buckling mode. This video is helpful to understand buckle

[@Freeball99]

Correct. n refers to the mode number.

[@AlirezaRezaee]

Can you do one video on plate buckling ? The 2D nature of the problem makes it more fun.

[@Freeball99]

I will get there eventually, but for now I still have some more beam videos to make before moving on to plates.

[@augustowanderlind7963]

Hello Andy, I hope you are healthfull! First of all, your videos are pure gold. They are helping me a lot in study and research. I'm a professor of civil engineering in Brazil and work with lattice structures for towers. I would like know what software/hardware you use for make yours videos. Because of the pandemic situation, I am teatching, at the most of time, from home. Sorry for my bad english. Best Regards.

[@Freeball99]

I’m using an app called “Paper” by WeTransfer. Running on a 13 inch iPad Pro and using an Apple Pencil. Movies are captured on my Mac using QuickTime. The mic is a Blue Yeti. The voice is mine.

[@augustowanderlind7963]

@@Freeball99 thanks!

[@xiaoliyuan3172]

Hi Andy, your video is so great. I had a question, why we define the natural frequency being zero as the point of buckling?

[@Freeball99]

We are trying to get a static result out of a dynamic model. By setting the frequency to zero, we are finding the point when the effective stiffness of the column goes to 0. At this point, it cannot support a load.

[@xiaoliyuan3172]

Also, is there anyway we can explain why steel is much easier to buckle than concrete?

[@Freeball99]

Steel is way stronger and stiffer than concrete, however, it is also much more expensive to produce. Steel column tend to buckle because they are very slender in order to keep the cost down. If steel columns were made as thick as concrete columns, then they would surely be much harder to buckle than the equivalent concrete structure. From an engineering point-of-view, we would like the tensile strength properties of the steel AND the cheap and compressive properties of the concrete. On the other hand, steel is susceptible to fire damage and concrete is brittle and cracks easily (which severely reduces its tensile strength). This is why a combination of the two is used to make reinforced concrete in practice.

[@xiaoliyuan3172]

Hi Andy, you video is so great! I had a question, is there any reason we define the natural frequency being zero as the buckling? How does each buckling mode shape contributes to the column deformation if the column is under real excitations rather than free vibration? Is there any rule for buckling mode superimposition?