This paper presents a generic modelling of composite steel-concrete beams with elastic shear connection. It builds on the well-known seminal technique of Newmark, Siess and Viest, in order to formulate the partial interaction formulation for solution under a variety of end conditions, and lends itself well for modification to enable direct quantification of effects such as shrinkage, creep, and limited shear connection slip capacity. This application is possible because the governing differential equations are set up and solved in a fashion whereby inclusion of the kinematic and static end conditions merely requires a statement of the appropriate constants of integration that are generated in the solution of the linear differential equations. The method is applied in the paper for the solution of the well-studied behaviour of simply supported beams with partial interaction, as well as to provide solutions for a beam encastr$acute{e}$ at its ends, and for a propped cantilever.