Understanding Support Types: Single vs Double Roller for Cantilever Structures

[fonseh]

Homework Statement

In i ) I was told that for the pinned support , we can assume to replace it with a roller , while for the cantilever , we can assume it to be supported by double roller .

For the cantilever , why we can't replace it with roller instead of double roller ? What 's the difference between double and single roller ?

Homework Equations

The Attempt at a Solution

In iv ) I was told that we can use roller guide , so from the figure , it's single roller , right ? So , IMO , the ii) was wrong , for the cantilever , we should always use [/B]single roller

 

[haruspex]

Homework Statement

In i ) I was told that for the pinned support , we can assume to replace it with a roller , while for the cantilever , we can assume it to be supported by double roller .

For the cantilever , why we can't replace it with roller instead of double roller ? What 's the difference between double and single roller ?

Homework Equations

The Attempt at a Solution

In iv ) I was told that we can use roller guide , so from the figure , it's single roller , right ? So , IMO , the ii) was wrong , for the cantilever , we should always use [/B]single roller

Took me a while, but I think I get it.
The question posed is what happens to the rest of the system if the point A is somehow displaced "vertically".
If A is only a pin, the beam can accommodate the displacement by rotating about A. So the effect is the same as if A were just a roller in the first place.
If the joint at A is a cantilever then the beam cannot rotate about it. So displacing A vertically is like the support at A being a double roller.

 

[fonseh]

Took me a while, but I think I get it.
The question posed is what happens to the rest of the system if the point A is somehow displaced "vertically".
If A is only a pin, the beam can accommodate the displacement by rotating about A. So the effect is the same as if A were just a roller in the first place.
If the joint at A is a cantilever then the beam cannot rotate about it. So displacing A vertically is like the support at A being a double roller.

Well , thanks for your explanation .But ,If A is only a pin, rotating about Av has the same effect as if A were just a roller in the first place?

Secondly , why placing a double roller at A will not allow rotation ?

 

[haruspex]

,If A is only a pin, rotating about Av has the same effect as if A were just a roller in the first place?

No. A roller is like a pin that can also slide in one direction.
The actual support at A is a pin. We are looking at the consequences of movement of that support in the vertical direction.
Pin + 1 dimensional movement = roller.
Similarly,
Fixed (cantilever) + 1 dimensional movement = double roller.

why placing a double roller at A will not allow rotation ?

That's what a double roller does. Each roller is constrained to slide in a track. Rotation would tug one of them out of the track.

See if http://www.engr.uky.edu/~gebland/CE 382/CE 382 Four Slides per Page/L4 - Support Reactions.pdf helps.