Nonlinear force-based 3D beam model with bond-slip and time-staged prestressing for RC and PC structures

This contribution presents a three-dimensional force-based Timoshenko beam formulation for the nonlinear analysis of prestressed concrete members with evolving bond-slip interaction. A set of slip degrees of freedom is introduced at the element level to represent the relative displacement between tendons and concrete, governed by a nonlinear bond law and compatible with arbitrary tendon layouts. Prestressing can be applied through initial strains, imposed slip, or force-controlled loading, and the element naturally accommodates staged activation, grouting, and time-dependent losses due to shrinkage, creep, and relaxation. Tendon strains are obtained by projecting the beam deformation field onto the tendon axis through an isoparametric mapping, enabling the simulation of curved bonded or unbonded tendons. Concrete behavior is modeled through a three-dimensional damage-plasticity law, while tendons and reinforcing steel follow uniaxial nonlinear constitutive models. The resulting element combines force interpolation, explicit slip kinematics, and consistent sectional integration within a computationally efficient force-based framework. A validation study on prestressed CFRP-strengthened beams demonstrates the ability of the model to capture bond degradation, anchorage softening, prestress losses, and rupture-induced force redistribution. The formulation provides an efficient and general tool for simulating prestressed concrete structures with complex tendon configurations, partial bonding, and staged construction effects.