In this paper, a 1D discrete element is formulated for analysis of reinforced concrete frames with catenary action. A force-based formulation is developed based on the total secant stiffness approach and an associated direct iterative solution scheme is derived. The effect of material nonlinearity as well as softening of concrete under compression is taken into account and a nonlocal averaging technique is employed to maintain the objectivity of displacement and force responses. Concerning geometrical nonlinearities, the fibre strains are assumed to be small; however, the effect of transverse displacement on the axial strain is large and it is taken into account as well as the effect of shear on the axial force. Using a Simpson integration scheme, together with a piecewise interpolation of curvature, the deformed shape of the element is consistently updated. The formulation is verified with numerical examples.