  We establish the existence of a scaling limit $\mathcal{E}_p$ of discrete
$p$-energies on the graphs approximating generalized Sierpi\'{n}ski carpets for
$p > \dim_{\text{ARC}}(\textsf{SC})$, where $\dim_{\text{ARC}}(\textsf{SC})$ is
the Ahlfors regular conformal dimension of the underlying generalized
Sierpi\'{n}ski carpet. Furthermore, the function space $\mathcal{F}_{p}$
defined as the collection of functions with finite $p$-energies is shown to be
a reflexive and separable Banach space that is dense in the set of continuous
functions with respect to the supremum norm. In particular, $(\mathcal{E}_2,
\mathcal{F}_2)$ recovers the canonical regular Dirichlet form constructed by
Barlow and Bass or Kusuoka and Zhou. We also provide $\mathcal{E}_{p}$-energy
measures associated with the constructed $p$-energy and investigate its basic
properties like self-similarity and chain rule.
