[en] A one-dimensional Vlasov-Poisson model for sheet beams is reviewed and extended to provide a simple framework for analysis of space-charge effects. Centroid and rms envelope equations including image charge effects are derived and reasonable parameter equivalences with commonly employed 2D transverse models of unbunched beams are established. This sheet beam model is then applied to analyze several problems of fundamental interest. A sheet beam thermal equilibrium distribution in a continuous focusing channel is constructed and shown to have analogous properties to two- d three-dimensional thermal equilibrium models in terms of the equilibrium structure and Deybe screening properties. The simpler formulation for sheet beams is exploited to explicitly calculate the distribution of particle oscillation frequencies within a thermal equilibrium beam. It is shown that as space-charge intensity increases, the frequency distribution becomes broad, suggesting that beams with strong space-charge can have improved stability.