Why are fixed end moments at AB and BC not considered when finding moment at B?

[fonseh]

Homework Statement

In this problem , i don't understand why the fixed end moment AB and fixed end moment BC arent considered ?

Homework Equations

The Attempt at a Solution

Is it because we are asked to find the moment at B , so only fixed end moment AB and fixed end moment BC arent considered ?

 

[PhanthomJay]

the supports at A and C are given as pinned joints, not fixed joints, as noted in the problem.

 

[fonseh]

Here's a list of fixed end moment , in this example , we can see that the fixed end moment AB and BA is + / - PL / 8 , why it's not 3PL / 16 as in the example in post # 1? In both example , we could see that ( example in post1) , span BC is fixed supported and

the supports at A and C are given as pinned joints, not fixed joints, as noted in the problem.

One more problem , why (FEM)BC is 3PL / 16 ?
It's clear in the the figure 636 that when one end is fixed , while the another end is pinned , then the fixed end moment is 3PL /16 ... But for the span BC , we could see that B is the roller and C is the pinned connection , there's no fixed support in the span BC

 

[PhanthomJay]

Here's a list of fixed end moment , in this example , we can see that the fixed end moment AB and BA is + / - PL / 8 , why it's not 3PL / 16 as in the example in post # 1? In both example , we could see that ( example in post1) , span BC is fixed supported and

One more problem , why (FEM)BC is 3PL / 16 ?
It's clear in the the figure 636 that when one end is fixed , while the another end is pinned , then the fixed end moment is 3PL /16 ... But for the span BC , we could see that B is the roller and C is the pinned connection , there's no fixed support in the span BC

You are correct that there are no fixed end moments at A, B, and C. But remember, these series of problems you have been working on are for statically indeterminate beams because there are more unknown external support reaction forces and moments than the number of equilibrium equations, so you have to resort to indeterminate analysis methods such as the slope-deflection approach or moment distribution method. These methods require you to assume initially that the interior joint (B) is fixed, then you release the joint from fixity and let the assumed FEM moment distribute to the other ends based on stiffness and carry over factors. In this example, in span BC, you temporarily fix joint B, and since the beam is pinned at C, you use the table for a fixed-pinned beam to get the FEM_BC of 3PL/16. After completing the analysis, you end up with only internal moments, but no external FEM moments at the supports.