  The Bresse system is a valid model for arched beams which reduces to the
classical Timoshenko system when the arch curvature $\ell=0$. Our first result
shows the Timoshenko system as a singular limit of the Bresse system as $\ell
\to 0$. The remaining results are concerned with the long-time dynamics of
Bresse systems. In a general framework, allowing nonlinear damping and forcing
terms, we prove the existence of a smooth global attractor with finite fractal
dimension and exponential attractors as well. We also compare the Bresse system
with the Timoshenko system, in the sense of upper semicontinuity of their
attractors as $\ell \to 0$.
