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Replace a support

  1. Jan 22, 2017 #1
    1. The problem statement, all variables and given/known data
    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 cant replace it with roller instead of double roller ? What 's the difference between double and single roller ?

    2. Relevant equations


    3. 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
    single roller
     

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  3. Jan 25, 2017 #2

    haruspex

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    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.
     
  4. Jan 25, 2017 #3
    Well , thanks for your explaination .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 ?
     
  5. Jan 25, 2017 #4

    haruspex

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    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.
    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.
     
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