Gaussian quadrature in 1D FEM

[LRJ]

Hopefully a straightforward question: do the elements in a 1D FE model need to be the same length for Gaussian quadrature to be appropriate (i.e. selection of Gauss points and Gauss weights)? I read somewhere that this was the case, though I can't see why it should be the case.

 

[LRJ]

Another question which is related to the above: why do we bother using Gaussian quadrature at all for 1D beam elements which we already know the stiffness matrix, mass matrix, etc. for? Is there actually any need for weightings and Gauss points at all for these matrices given that we're only interested in nodal displacements and reactions?