Simultaneous analytical design of ductility and shear capacity in reinforced concrete columns

The seismic design of transverse reinforcement in reinforced concrete columns requires the simultaneous satisfaction of ductility and shear requirements, which are commonly treated through separate procedures. This study develops an analytical framework for the direct design of transverse reinforcement in rectangular RC columns subjected to axial force, uniaxial bending, and shear demands. Closed-form strain relationships are derived for the Damage Limitation and Near Collapse conditions, which are used to evaluate sectional curvature ductility capacity. These relationships are subsequently inverted to obtain the transverse reinforcement required by a prescribed curvature-ductility demand. The resulting ductility-controlled reinforcement requirement is combined with a mechanically based shear-capacity model through a piecewise closed-form inversion, allowing the governing design condition and the transition between shear-controlled and ductility-controlled responses to be identified analytically. The explicit ductility inversion is derived for symmetric longitudinal reinforcement and is applicable within the formal domain of the compact formulation, while the shear design remains subject to the calibration limits of the adopted capacity model. The proposed formulation is expressed in nondimensional form and can incorporate different code-specific confinement relationships. The accuracy of the analytical developments is assessed through independent fiber-section analyses, which confirm the validity of both the sectional equilibrium formulation and the curvature-based design procedure over a broad range of RC column sections. The results show that the proposed approach provides a direct and transparent procedure for the simultaneous design of transverse reinforcement while preserving the mechanical interpretation.