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!
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." ?
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
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bro this was the best video about this topic so far, please keep making videos like this man! congrats absolutely awesome
Excellent presentation, gave me great light into the theory of beams. pls upload more sir
Loved the history behind the assumptions and derivations, excellent video!
French audience here. Not bad on your pronunciation of "Antoine Parent" ;-). Interesting topic, not very often encountered online.
Good video burst 4:23, should be
1/rho = dtheta/ds
yes !
Look at this video, it is great. This guy was great.
Me salvaste la vida amigo
Thanks for the amazing video!
Excelente la explicación
Me when I find a channel with a fascinating video style, content that I'd enjoy, and an upload date not more recent than a year: ☹️
It’s crazy that they figured this out two centuries ago
4:13 Shouldn't the curvature 1 over ro be equal to inverse of ds over d theta?
yes seems like a mistake
Video about M= EI/ ρ ??
Legend
How accurate would you bet that Euler's equation is for real scenarios with slender columns?
I wonder how the model of a rod which can’t describe a torsion is still very popular
4:11 actually, rho = ds/dtheta
no
oh sorry didnt read wvery well
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!
@@erikoui what if the force itself is a function of location, like a distributed load, so we should integrate it four times, right?
@@Arsenic_99 That is correct.
"From Structural, to Aerospace..."
Me in Aerospace Structures class: 😢
4:00 how would you prove this ?
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." ?
There is literature that mention the equation with a negative sign. Why is that?
Probably just depends on what sign convention is used. (If you define z as up or down)
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
What do you mean, I’m learning English and I understand
What a crazy thing to ask.
This equation has been proven to be inaccurate
It is inaccurate when the assumptions used to derive the ecuation are not satisfied. Othewise it gives nice results.