Using the T-matrix theory, we have performed an analytical study of the collective fast normal modes of an arbitrary system of loops. The obtained results allow to assess the dynamical effects of the interaction of loops and the frequency shifts with respect to the individual loops in an arcade as a function of the number of tubes. Furthermore, the frequency shifts of a multi-stranded loop formed by several tens or hundreds of strands with respect to a monolithic one, as well as the implications on the loop motion, have been also investigated.