The subject matter of this paper is the interaction of flexure and compression in steel beam-columns with fixed-roller boundary conditions. It is shown that, for those end restraints, the effective length factor approach is inaccurate to account for geometric non-linearity.The paper then presents a formula to predict the strength of steel members subjected to simultaneous axial compression and transverse load, allowing for the formation of plastic hinges one following the other with a considerable gap. The formula is devoted to quantitative safety assessment, as it is more accurate than conventional formulas, and also to the design phase, as it is simple to use.The paper gives a detailed account of the formulation and provides some examples that show differences from the results obtained from conventional and code formulas.