We investigate the formation of beta-sheet structures in proteins without sequence-dependent side-chain interactions. To accomplish this, we introduce a model which explicitly incorporates both solvation effects and the angular dependence (on the protein backbone) of hydrogen bond formation. The thermodynamics of this model is studied by exploring the density of states for the entire system and the local couplings in a partially folded structure. Our results suggest that solvation dynamics together with the H-bond angular dependence gives rise to a generic cooperativity in this class of systems; this result explains why pathological aggregates involving beta-sheet cores can form from many different proteins. Our work provides the foundation for the construction of phenomenological models to investigate topology effects in beta-sheet folding and the competition between native folding and nonspecific aggregation.