Frames with inclined legs using slope-deflection method

[Ashu2912]

Homework Statement

This is a diagram from "Structural Analysis" by Aslam Kassimalli while solving frames using slope-deflection method. In the figure, the tangent to the deflected shape at C^` is parallel to the original member AC implying that the slope at C is zero. However, later they have considered θ_C (the slope at C) as an unknown while writing the slope deflection equations. Why so?

Homework Equations

The Attempt at a Solution

 

[pongo38]

I don't think you can assume that the tangent at C' (the prime symbol ' is not clear enough in the figure) is parallel to AC. The tangent at D' is not visibly parallel to BD, and shouldn't be. In general, I would expect both C and D to rotate somewhat, because the rotation is only partially restrained by the stiffness of the attached members.