Derivation of Slope Deflection Equations - Structural Analysis

Where do the slope deflections come from? How are they determined? This is the video for you.... If you're not curious about the detailed calculations for the derivation, just hit these three sections of the video to get the gist: Overview of Displacement Methods (0:26), Description of Displacements and Sign Convention (3:00), and the derivation summary (37:51). Here's a timeline below if you want to jump around....like House of Pain:
0:00 Introduction
0:26 Overview of Displacement Methods
2:28 Beginning of Slope-Deflection Equation Derivations
3:00 Description of displacements and positive sign convention
7:32 Deriving slope deflection equations
8:08 Slope (Rotation) theta_A, detailed calculations using the integration method
21:48 Slope (Rotation) theta_B
24:00 Chord Rotation psi = Delta/L, detailed calculations using the integration method
34:42 Fixed End Moments
37:51 Summary of derivation and getting final form of slope deflection equations

[@thefreakbt]

Really helped to understand it. Months worth of learning from textbook condensed into 1 video

[@cherrytree5026]

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thank you very much for every minute of this video.

[@structurefree]

You are too kind! 😁

[@rodrigodeleon8352]

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[@Josh-zk7pf]

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[@Josh-zk7pf]

At 34:45 you said we deserve a medal, make sure my professor knows to give me one ;) hahaha

[@kuberbhatnagar2998]

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[@twigsfloat2773]

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[@OmarPerez-ff2pk]

thank you! i was lost with the information at the books but here everything is clear!

[@doolomer8873]

Best teacher ever

[@Eagle_1174]

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[@that.unknown]

you are saving my academic life.

[@anandkumarmaurya8709]

So nicely explained. Thank you sir

[@DanielLee-wz9ft]

Great content, but I have a question. When loadings are applied to the member, the member deforms. Then, we use the deformation to back-calculate the bending moment acting on the member. However, at last, we further calculate the bending moment induced by the loadings on the member again!? Wouldn't this duplicate the value we found?

[@bigguspiggus6041]

Fantastic videos, really useful.
In what order would you suggest watching the playlists if starting from scratch?

[@AlAminHossain-lw5lj]

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[@muhammad3456d]

Good work

[@yimsopanha4102]

Would you please tell me how the shape of beam with both fixed-end deforms the way you drew?

[@noortech7602]

Amazing

[@engsayidahmedshmuqtaar3372]

Thanks alot really i got from here clear understand

[@structurefree]

👍

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[@structurefree]

🙏

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[@muhammad3456d]

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[@jilagamnagendrakumar5522]

Do a vedio on flexibility matrix methods

[@structurefree]

Here's a link to part 3 a very detailed force (aka flexbility) method problem series that has 2 dofs and provides an intro to the matrix approach.
czcams.com/video/Vt8HH_A_QgI/video.html

[@adityakandpal99]

I personally think that taking the rotation in clockwise direction to be positive every time is not correct. Because if in the first case where we are studying theta(a) if we take the bending moment from the left end than if at x=0 we keep the theta(a) to be positive than we get a negative relation between the theta and end moments which is wrong rather the sign should depend on the behavior of the bending moment if that bending moment supports the theta than the theta should be taken to be positive like the case taken in this video whereas if it is opposite than take negative.

[@structurefree]

slope deflection equations are derived using a different convention than internal loading functions.

[@yimsopanha4102]

What exactly is the difference between M(AB) and FEM(AB)?
Thanks

[@structurefree]

the letters...jk

[@structurefree]

M_AB is what you are trying to solve for. the FEMs are if the ends of the beam were fixed-fixed. the FEMs account for the influence of member loading on M_AB.

[@yimsopanha4102]

@@structurefree thanks