Stiffness factor for member in beam

[fonseh]

Homework Statement

In this question , I don't understand why the KBC is 4EI / L ...

Homework Equations

The Attempt at a Solution

I was told that for the far end pinned or roller supported , the K = 3EI / L , so shouldn't the KBC = 3EI / L.. Is the author wrong ?

In the 3rd photo , we can see that for far end pinned supported , k = 3EI / L , not 4EI / L

 

[haruspex]

for the far end pinned or roller supported , the K = 3EI / L , so shouldn't the KBC = 3EI / L.. Is the author wrong ?

BC is only a segment of the beam ABCD. The "far end" of BC from B is D.
Think about it: if D were just a pin then the beam could rotate a bit about D, allowing it equally to rotate a little about C. But with D fixed, it is much harder for there to be any rotation about C.

 

[fonseh]

BC is only a segment of the beam ABCD. The "far end" of BC from B is D.
Think about it: if D were just a pin then the beam could rotate a bit about D, allowing it equally to rotate a little about C. But with D fixed, it is much harder for there to be any rotation about C.

So , in this problem , the far end of AB is D , as D s pinned , so the KAB is 3EI / L ? If D is fixed , then KAB would be 4EI / L ?

 

[haruspex]

So , in this problem , the far end of AB is D , as D s pinned , so the KAB is 3EI / L ? If D is fixed , then KAB would be 4EI / L ?

That's my understanding. But please bear in mind that my entire knowledge of the subject comes from the textbook extracts you have posted.

 

[fonseh]

That's my understanding. But please bear in mind that my entire knowledge of the subject comes from the textbook extracts you have posted.

May I know which part ? Can you highlighted it ?

 

[haruspex]

May I know which part ? Can you highlighted it ?

I have not noticed an actual definition of "far end" but just thinking about how I would expect a beam to behave it is clear that if any part of a beam is unable to rotate at all it will make the beam stiffer at all joints. Hence that is how I interpret the term.