The tangents at A and B are perpendicular to the radii at A and B, and also we know that the angle between two non-parallel lines is equal to the angle between their normals.
@@erikoui Thank you. If proof is that easy, why waste time at 3:55 - 4:02 saying: "You can prove that the angle at O is d.theta for yourself if you'd like" , when in the same amount of time you could have said: "The tangents at A and B are perpendicular to the radii at A and B, and also we know that the angle between two non-parallel lines is equal to the angle between their normals." ?
Hi erikoui, I, too, am fascinated with the mathematics describing how a beam deflects. So much in fact I developed an explanation for the 3b1b SoME (linked below). Basically cutting the beam into many many segments seeing how they interact and then resolving the total result. Check it out. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4B2OVDku75c.html
So it means that if the applied force is not a point force at the free end, but is a function of location x, then we cannot use the simplified version of the Bernoulli beam, right? I mean then we need to integrate the equation four times in order to figure out the displacements of beam, am I correct?
That is an excellent question. Bernoulli beam theory still applies and d_theta/d_x is just a function (the derivative of theta, or the second derivative of the bending moment function M(x)). In the case of several loads (e.g. two point loads or a udl with a point load at an arbitrary point) you would calculate the deflection as if each load was applied on its own, and then add up the results (assuming the beam acts linearly elastic). Hope this helps!
Correct, the top floor had more degradation than below, due to being exposed the most. Also, only a few column caps failed, and the rest of the slab probably slowed down the falling pieces.
I have a bit of a hard time understanding your accent, so I'd appreciate it if you could add closed captions and make sure they don't cover up visuals in the video since the automatic CC _does_ cover some visuals
Hi Brenda, it's just stock footage, no symbolisms were intended. The smoke comes from an incense stick close to the camera. Hope that clears up your questions :)
Thanks for a great explanation. Posted 12 days before Champlain Towers, the timing is uncanny. I have included an end screen link in my video for viewers to understand punch "thru" better.
Hey thanks for the help! One question....what is the constant 'Q' representing at the end of the formulation? It's referring to a value of heat transfer....but where? Cheers.
@@erikoui One more question! Do you have any resources on spatial AND time-dependent FEA? Preferably from you as I enjoy your teaching style. I have found other resources online, so no worries if you have nothing on the topic!
@@BurningRoman Unfortunately I do not have anything on the topic. With time-dependent differential equations, while you could technically aporoximate a solution by treating time as a dimension, it is the norm to use a time-stepping method in conjunction with FEA. I may make a video on this at a later stage.
