Calculation of the ultimate stress of unbonded tendons in prestressed concrete members considering the rotation capacity

Experimental observations have shown that the stress in unbounded tendons may increase significantly at failure in partially prestressed and prestressed concrete beams and slabs. Many experimental and analytical studies have been carried out over the past four decades to predict ultimate tendon stress at flexural failure, and formulae with different degrees of sophistication, based on different approaches, physical models and experimental tests, have been suggested. According to several models in the literature, including the strain compatibility approach, the total elongation of unbonded prestressing steel between the end anchorages (and the consequent stress increment) is mainly caused by the plastic deformation that occurs in the plastic region of the critical sections of the members. For this reason, the stress increment in unbounded tendons at the ultimate conditions should be evaluated taking into account the wide scattering observed in the plastic rotation capacity, and adopting an appropriate safety level. This paper critically reviews the design formulae that can be found in the literature and proposes a new approach that is able to improve some critical aspects of the existing formulations, in particular concerning the rotation capacity of the members.