Slope deflections method analysis of beam

[fonseh]

Homework Statement

why we need to consider 2 conditions , the beam curve downwards ( as in 11-3) and beam curve upwards ( as in 11-4) ?
What's the difference between 2 cases ?

I notice that in both cases , the author assume clockwise as positive
here are the 3 consecutive pages of notes

Homework Equations

The Attempt at a Solution

I think the second cases where the curve curve upwards is unnecessary because we can see that the curve curve downwards (U shape) in the first photos .

 

[fonseh]

why for the relative linear dispalcement , we just have to consider one scenario only , namely consider the case where the member B is displaced relative to A ? Why we don't have to consider the case where the member A is displaced relative to B ?

 

[fonseh]

Is there anything wrong with these cases ?

 

[fonseh]

Can someone explain it ?
Or we need to consider 2 cases ( where the curve curve upwards and curve downwards) because it is a must to do so ? The beam will curve like this one if we superimpose 2 graph ? The red part represent the shape of graph , while the black line represent the beam

 

[fonseh]

bump

 

[fonseh]

Bump