  In this paper we show that bending a finite volume hyperbolic $d$-manifold
$M$ along a totally geodesic hypersurface $\Sigma$ results in a properly convex
projective structure on $M$ with finite volume. We also discuss various
geometric properties of bent manifolds and algebraic properties of their
fundamental groups. We then use this result to show in each dimension $d\geq 3$
there are examples finite volume, but non-compact, properly convex
$d$-manifolds. Furthermore, we show that the examples can be chosen to be
either strictly convex or non-strictly convex.
