Thank you so much, you made a clear video, with great background, and was entertaining. I finally understand this for my HW as it made no sense in class. Big ups!
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
