At the end of the 19th century, H. A. Janssen discovered that the bottom floor pressure in a cylindrical container of granular material asymptotes exponentially to a value less than the weight of the material i.e., the pressure becomes independent of the fill height of the column. This phenomenon is investigated using discrete element simulations of inelastic, frictional spheres in a cylindrical vessel having a particle-to-cylinder diameter ratio at approximately 13.3 or 26.6, with varying bed heights in both cases. The axial pressure profile and the load experienced by a piston that is supporting the granular column are computed. In order to activate frictional forces at the wall contacts either the piston (or equivalently the cylinder wall), is slowly displaced at a rate so as to maintain quasi-static conditions. Various combinations of wall and inter-particle friction coefficients are examined. The simulated behavior of the load vs. fill level was found to fit well to the functional form of Janssen's theory. Moreover, quantitative comparisons are in agreement with experimental measurements from the literature. Results are critically discussed in the framework of the assumptions implicit in Janssen's theory.