From what I have read. The reason this theory is necesary, is because in thick and short beams the shear strain energy is greater than normal strain energy caused by bending moments. So deformation caused by shear forces will be more significant than deformations caused by bending moments. This makes sense because thick and short beams have a great flexural rigidity and the bending moments are small compared with shear forces.
at 1:00 (Since there is no transverse loading): by that you mean there is no force parallel to axis? because if you would say otherwise, we have a load which is perpendicular to axis. (Which in my understanding, should be called as transverse loading). Am I missing something?
Additionally, maybe i don't understand, but is the last picture correct? How can the end be a straight line if you have to account for compression on top and tension at the bottom?
Maybe I got something wrong, but as far as i know the neutral axis is defined as the axis which retain perpendicularity AFTER the beam has been deformed, that's why for this particular shape is in the middle, because after the cubes are deformed, only the middle of the cube remains perpendicular. I don't understand why would you define the neutral axis before bending. And shear in a beam under deflection is always present, why would you neglect it?
If I recall correctly, it can be defined before or after any elastic deformation, as the neutral axis should remain at the same place before and after deflection. And I believe the effects of shear on deflection are neglected because they are usually much smaller than the effects of normal stresses, and for most situations they aren't crucial to the integrity of a given part.
Excellent. best video on difference between Euler and Timoshenko theory on youtube. plz make more videos, u can charge some fees to make it public , but, please make more videos. Good teachers are very very rare. God bless you.
This comments really old, but this is a good explanation of something you would learn in a strengths of materials class which is normally a second year engineering course.