qualitative influence line of pinned support

For the highlighted part , why we need to replace the support at A with a roller guide ? We could see at A , it's a pinned support , right ?

Pinned support will resist horizontal and vertical reaction , why the author said it will not resist vertical force ? Is the author wrong ?

1 Answer

The answer is in your quote/picture:

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.

The Muller-Breslau principle is that the influence line is equal to: the deflected shape of the relevant force/moment at the relevant location if the resistance to the effect at the location of interest is removed.

In order to find the influence line for a vertical reaction at A, we therefore want to find the deflected shape for a vertical force at A, when there is no vertical support at A.

If we had left the vertical support in at A, then a vertical force applied at A would give us no deflection, and hence the influence line would be zero everywhere. Clearly that's wrong, as we know a force applied just next to A would give us a reaction at A!