A consistent force-based prestressed beam model with curvilinear tendons and bond–slip

This study proposes a unified force-based formulation for three-dimensional Timoshenko beam elements that includes the classical fiber-section approach, the bond–slip effects in arbitrarily curved or draped prestressing tendons, the multiple construction stages and the time dependent losses such as concrete creep, shrinkage, and steel relaxation. The concrete fibers follow a three-dimensional damage-plasticity law, and the tendon-concrete interaction evolves through internal variables that reflect the grouting sequence. Even though different mixed formulations can be used, this paper presents the force-based formulation, that provides the best approximation of the bond behavior. All the mentioned aspects are coupled in a framework within the same element state determination problem. Validation against representative experimental tests shows that the proposed formulation reproduces full nonlinear load–displacement curves, tendon bond–slip profiles, and failure modes that conventional flexure-only, perfectly bonded models cannot capture. Both in the bonded and unbonded tests, the response is reproduced with only three beam elements, while in the CFRP-strengthened beam tests, peak load and initial stiffness are predicted within 10% of the experiments’ results. The proposed element can simulate the nonlinear response of prestressed concrete beams, incorporating time-dependent losses, arbitrary tendon geometries, segmental construction, staged prestressing, and bond conditions ranging from fully bonded to fully unbonded.