Mathematical formulation of the space curvature of the tendon in the PC structures

This paper presents the mathematical formulation of the space curvature of the prestressing tendon in the nonlinear analysis of prestressed concrete (PC) structures. The nonlinear behaviour of prestressed tendons is described by the one dimensional elasto-viscoplastic model. The tendon element geometry is described by the second order space function which is determined by its projections. These elements make it possible to model arbitrarily curved prestressing tendons in space, thus they can be determined independently of the three-dimensional (3D) finite element mesh. This is very important in the case when the prestressing tendon can not be located in a plane. The transfer of prestressing force on the concrete was modelled numerically. The developed model makes it possible to compute prestressing structures in phases: before prestressing, during prestressing and after prestressing. The described models are implemented in the computer programme for a 3D analysis of the prestressed concrete structures where the structures are discretized by three-dimensional finite elements with an embedded one-dimensional element of prestressed tendons