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44 for spacing of A1035 spirals were also examined and revisions (1999) model that has been calibrated for concrete strengths have been recommended. up to 15 ksi. 2.7.1 Column Capacity Results Parametric studies were conducted to determine whether Representative moment-curvature relationships and axial columns reinforced with A1035 longitudinal and transverse load-moment (P-M) interaction diagrams are shown in Fig- reinforcement will reveal any unexpected results compared to ures 28a and 28b, respectively, for a 24-inch diameter non- columns reinforced with commonly used A615 steel. Other seismic, spirally reinforced column using #3, #4, and #5 steel types (A706, A496, A82, and A955) were not initially spirals and 10-ksi concrete. The moment-curvature responses included in the parametric studies in order to first evaluate were generated for an axial load corresponding to 0.1f c Ag the results for A1035 reinforcement. where Ag is the column gross section area. The complete set of results is provided in Ward (2009). The variation in the moment-curvature diagrams is due to the differences in Details reinforcement ratios. The columns reinforced with A615 The parametric studies were performed by analyzing have more longitudinal bars and hence a greater stiffness. 270 cases with the variables shown in Table 22. For all cases, The reduced stiffness of columns with A1035 bars needs to the amount of longitudinal steel for columns reinforced with be taken into account for design of bridges subjected to seis- ASTM A615 and ASTM A1035 bars was determined by using mic loads. The different sizes of transverse steel do not sig- a target reinforcement ratio of 4% and 2%, respectively. Spac- nificantly influence the moment-curvature relationships. ing for the transverse reinforcement was determined using This trend should be expected because the properties of AASHTO 5.10.6 and The column overall concrete (confined and unconfined cores) do not apprecia- dimensions were arbitrarily selected to cover a wide range bly influence the response of members with small axial of practical column dimensions. The complete details of all loads. Moreover, as discussed previously, the confined con- 270 cases are provided in Appendix G. crete properties are not affected by the size of transverse bars. The axial load-moment interaction diagrams (see Fig- ure 28b) for columns with A615 and A1035 reinforcement Modeling vary primarily because of the larger amount of A615 longi- A fiber analysis program called XTRACT (Imbsen 2007) tudinal reinforcement. For a given type of steel (A615 or was used to perform detailed cross-sectional fiber analyses. A1035), the size of transverse reinforcement does not affect The stress-strain relationship for ASTM A615 reinforcement the interaction diagrams. was based on an available model that replicates typical behav- The aforementioned results and discussions do not suggest ior of such bars. A user-defined material model, in which dis- any unexpected responses when A1035 steel is used. In com- crete strain and stress data points were input, was used to parison to A1035, the strengths and properties of other steel represent the stress-strain relationship of ASTM A1035. The types (A706, A496, A82, and A955) are closer to the charac- strain and stress values for each data point were established teristics of A615. Since the responses of columns with A1035 from an appropriate Ramberg-Osgood function (Appendix A). steel do not suggest any unusual or unexpected trends, it was The material behaviors of the unconfined concrete shell and deemed unnecessary to perform similar parametric studies confined concrete core were based on the Razvi and Saatcioglu for A706, A496, A82, and A955. Table 22. Variables for column parametric studies. Variable Value/Description Square tied columns designed and detailed for seismic loads; Column Type Circular spirally reinforced columns used in non-seismic regions; and Circular spirally reinforced columns for bridges subjected to seismic loads. Type of ASTM A615 with fy = 60 ksi and ASTM A1035 with fy = 120 ksi (for Reinforcement longitudinal and transverse bars) Column Size Square column dimension or diameter = 18, 24, 36, 48, 60 in. Transverse #3, #4, and #5 Reinforcement Concrete f'c = 5, 10, 15 ksi Strength