  We analyze spherical dust collapse with non-vanishing radial pressure, $\Pi$,
and vanishing tangential stresses. Considering a barotropic equation of state,
$\Pi=\gamma\rho$, we obtain an analytical solution in closed form---which is
exact for $\gamma=-1,0$, and approximate otherwise---near the center of
symmetry (where the curvature singularity forms). We study the formation,
visibility, and curvature strength of singularities in the resulting spacetime.
We find that visible, Tipler strong singularities can develop from generic
initial data. Radial pressure alters the spectrum of possible endstates for
collapse, increasing the parameter space region that contains no visible
singularities, but cannot by itself prevent the formation of visible
singularities for sufficiently low values of the energy density. Known results
from pressureless dust are recovered in the $\gamma=0$ limit.
