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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 ?

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 roller22

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  • $\begingroup$ I've just posted an answer to your other recent question. This question looks to be along similar lines; the answer to the other question may also apply here. $\endgroup$ – AndyT Jan 23 '17 at 10:45
  • $\begingroup$ Ok, @AndyT , i understand that the statement In order to draw the deflected shape properly, the capacity of the beam to resist the applied function must be removed so the beam can deflect when the function is applied. For the cantilever , why we cant replace it with roller instead of double roller ? What 's the difference between double and single roller ? $\endgroup$ – kelvinmacks Jan 23 '17 at 11:41
  • $\begingroup$ continuous from previous comment , 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 $\endgroup$ – kelvinmacks Jan 23 '17 at 11:42
  • $\begingroup$ Why we need to use double roller for case iv ? $\endgroup$ – kelvinmacks Jan 23 '17 at 11:42
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The answer is in your quote/picture:

If the support A is cantilever type, a double roller guide must be used at A since this type of support will then transmit both a moment MA at the fixed support and axial load, RAx but will not transmit RAy.

In other words, we want the influence for the vertical reaction, so we release the vertical support degree of freedom only, and leave the other supported degrees of freedom alone.

As far as iv) goes, I can see three rollers in the picture. This is analogous to a "double roller": it will transmit axial load and moment but not shear load.

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    $\begingroup$ @kelvinmacks - Yes, the double roller enables the beam to move upwards and downwards. How could vertical shear be transmitted across that interface? Shear is a force resisting two adjacent "faces" moving relative to one another. $\endgroup$ – AndyT Jan 23 '17 at 12:42
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    $\begingroup$ RAy is the Reaction at A in the y direction. With a beam on only one side, the reaction would be equal to the shear. "Transmit vertical shear" means that... vertical shear will be transmitted (passed/carried) from one side to the other (or in this case, from the beam into the support). If you still don't understand what "transmit vertical shear" means then you really need to go back to the beginning of your engineering course and stop trying to understand more advanced topics like influence lines. $\endgroup$ – AndyT Jan 23 '17 at 15:49
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    $\begingroup$ Every time I am talking about whether or not vertical shear is transmitted, I'm talking about at the place under consideration. For the reaction at the cantilever support (ii), it is about whether shear can be transmitted from the beam to the support: when you introduce the roller no shear can be transmitted across that joint. For part way along the beam (iv) it is about whether shear can be transmitted from the right of point B to the left of point B: when you introduce the roller no shear can be transmitted across that joint. $\endgroup$ – AndyT Jan 23 '17 at 16:22
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    $\begingroup$ Anywhere that we haven't introduced a roller/joint the shear can be transmitted as it is in a normal beam. $\endgroup$ – AndyT Jan 23 '17 at 16:22
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    $\begingroup$ 1. The influence line is the deflected shape, not the shear force diagram. 2. For case (ii) vertical shear can be transmitted throughout the beam except it can't be transmitted from the beam to the support. For case (iv) shear can be transmitted from the end of the beam, as far as B, but it can't be transmitted over the roller at B. It can then be transmitted anywhere from the left of B through the beam to the support at A. Would you like me to point out where I've already explained this point no2, or are you now able to read my previous comments and understand? $\endgroup$ – AndyT Jan 23 '17 at 17:23

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