Strain-path-dependent stress-strain model for ultrahigh-performance concrete columns constrained by stirrups

The incorporation of steel fibers improves the microscopic ductility of ultrahigh-performance concrete (UHPC) materials, and their macroscopic ductility can also be improved by the restraining effect of composite stirrups. Two defects can be found in the stress-strain model of UHPC restrained by stirrups based on the design-oriented method: the restraint coefficient of the stirrup is the effective restraint coefficient at the peak state of the specimen, while the variation in the restraint stress of the stirrup with the axial-hoop strain relationship (strain path) is ignored. In this study, a strain-path-dependent stress-strain model for UHPC constrained by stirrups and fibers is proposed through a database with 10 sets of test results on UHPC columns, which alleviates the shortcomings of the design-oriented model. (1) On the basis of the axial-hoop strain relationship curve in the test results, an axial-hoop strain model of UHPC restrained by stirrups is established. (2) The variation in the restraint stress of the stirrup with strain path is considered. (3) On the basis of the stress-strain model of actively constrained concrete, an iterative method of subsections is adopted, and a UHPC stress-strain model restrained by stirrup based on strain path is established. Results show that the established axial-hoop strain equation can better predict the hoop strain of UHPC restrained by stirrups and steel fibers, the calculated value of peak stress of UHPC constrained by stirrups based on strain path is in good agreement with the test results, and the outcomes of the path-dependent stress-strain model are in better agreement with the experimental results than those of the design-oriented stress-strain model.