Behaviour of anchorage zones for prestressed concrete

by T.J.Ibell

Research on the analysis of anchorage zones for prestressed concrete continues due to inconsistencies and contradictions encountered both in existing theories and experimental findings. Present design methods generally assume elastic behaviour of the anchorage zone. The amount of steel reinforcement required is determined according to the magnitude of the calculated elastic tensile force. For the steel reinforcement to contribute significantly to the behaviour of the anchorage zone, however, cracking of the concrete must occur, which violates the initial assumptions. It was therefore decided to formulate upper- and lower-bound plasticity solutions to the problem, which would model the problem more rationally.

To provide a basis against which such theoretical models could be validated, a series of tests on concrete prisms, with and without steel reinforcement, and strip-loaded through rigid plates, was carried out. It was found that, in general, initial cracking occurred along the central axis of the specimens, followed at a higher load by wedging failure beneath the loading plate. However, as the steel reinforcement percentage was increased, lateral out-of-plane wedging occurred. This behaviour was partially prevented by the presence of cross-links in the stirrups, positioned to `tie' the legs together and maintain plane strain conditions.

Upper-bound plasticity solutions to the problem, under assumed plane strain conditions, showed promising correlation with the experimental results. Predictions from a simple lower-bound model, based on equilibrium of the prism at ultimate failure, also approximated the experimental results reasonably well. However, both models assumed only planar behaviour of the prisms. In addition, the presence of ducts could not be modelled by these methods and the load capacities to first cracking of the prisms could not be predicted.

Therefore, a generalised lower-bound method was developed to overcome these limitations. It was decided to divide the problem into two stages. The first stage involved the determination of the resistance to cracking of the prism, under suitable assumptions of steel stresses, by carrying out a linear elastic finite element analysis of the prism. The maximum tensile principal stress was found, compared with a simple tension cut-off criterion and the cracking load capacity of the prism predicted. Thereafter, a central bursting crack was assumed to have occurred along the length of the prism. The steel reinforcement was assumed to have yielded and a second linear elastic finite element analysis was performed. Stresses along potential wedging planes were determined and averaged, under the assumption that such redistribution could occur in a ductile manner at failure. This stress state was applied to the Modified Coulomb failure criterion and the predicted failure capacity determined in this way.

This method was applied to both strip- and patch-loaded specimens, under many varying parameters. The method was shown to be capable of predicting both the failure loads and behaviours of such test specimens.

It is concluded that this generalised plasticity method of analysis has much potential for use in anchorage zone design.

Keywords:- Prestressed concrete, anchorage zones, plasticity, Modified Coulomb failure criterion, finite elements.