Nonlinear finite element simulation of unbonded prestressed concrete beams

Prestressed concrete with internal unbonded tendons has been recognized as an excellent structural option for beams and slabs and is employed worlwide. Numerical solutions for the analysis of such structures are still an active field of research. This work presents a finite element model for the physical and geometrical nonlinear analysis of prestressed concrete beams with unbonded internal tendons, under short-term loading. The reinforced concrete beam is modeled by Euler-Bernoulli nonlinear plane frame elements and a total Lagrangian approach. The prestressing tendon is modeled by a single polygonal element embedded in a specified subset of the frame elements. Due to lack of strain compatibility between the concrete and the tendon at a given cross-section, the cable strain is computed from the displacements of all associated frame elements. Geometric and material nonlinearities are considered for both the reinforced concrete beam and the prestressing tendons. The internal force vector and corresponding tangent stiffness matrix of each element under large displacements are derived consistently, and novel expressions for the tangent stiffness operator which ensure the convergence rates of the Newton-Raphson scheme are developed. The accuracy of the formulation is assessed by comparison with experimental tests, with very good results.