  We propose a model that explains the reduction of $T_c$ due to the pinning of
stripes by planar impurity co-doping in cuprates. A geometrical argument about
the planar fraction of carriers affected by stripe pinning leads to a a linear
$T_c$ suppression as a function of impurity concentration $z$. The critical
value $z_c$ for the vanishing of superconductivity is shown to scale like
$T_c^2$ in the under-doped regime and becomes universal in the optimally- and
over-doped regimes. Our theory agrees very well with the experimental data in
single- and bi-layer cuprates co-doped with Zn, Li, Co, etc...
