This paper examines the quasi-static cyclic behavior,lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy(SMA) link-bars.Moment-curvature constitutive relationships are formulated and analysis tools are developed for the PT column,including a modified four-spring model prepared for the SMA bars.The suggested system is exemplified using a column with an aspect ratio of 7.5 and twelve 36.5 mm diameter NiTi martensitic SMA bars.A post-tensioning force of 40% to 60% of the tendon yield strength is applied in order to obtain a self re-centering system,considering the residual stress of the martensitic SMA bars.The cyclic response results show that the lateral strength remains consistently around 10% of the total vertical load and the equivalent viscous damping ratios reach 10%-12% of critical.When large diameter NiTi superelastic SMA bars are incorporated into the column system,the cyclic response varies substantially.The creep behavior of the superelastic SMA bar is accounted for since it affects the re-centering capability of the column.Two examples are presented to emphasize the modeling sensitivities for these special bars and quantify their cyclic behavior effects within the column assembly. This paper examines the quasi-static cyclic behavior, lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy (SMA) link-bars. Moment-curvature constitutive relationships are formulated and analysis tools are developed for the PT column, including a modified four-spring model for the SMA bars. suggested system is using using a column with an aspect ratio of 7.5 and twelve 36.5 mm diameter NiTi martensitic SMA bars. A post-tensioning force of 40% to 60% of the tendon yield strength is applied in order to obtain a self re-centering system, considering the residual stress of the martensitic SMA bars. cyclic response results show that the lateral strength remains consistently around 10% of the total vertical load and the equivalent visitive damping ratios reach 10% -12% of critical .When large diameter NiTi superelastic SMA bars are incorporated into the column system, the c yclic response variations of the creep behavior of the superelastic SMA bar is accounted for for it affects the re-centering capability of the column. Two examples are presented to emphasize the modeling sensitivities for these special bars and quantify their cyclic behavior effects within the column assembly.