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The focus of the present study is to rigidize the toroidal member of an inflatable space antenna using a novel rigidization technique. This technique involves embedding heat-actuated Shape Memory Alloy (SMA) wires between laminated Kapton layers to provide structural strength. Finite Element Analysis (FEA) is performed to assess the strength of the torus under a heating environment. The analysis considers the approach of constraining torus deployment in all directions, simulating the conditions it would experience during deployment and operation. By subjecting the torus to a heating environment, the behavior of the SMA wires can be observed, which in turn affects the rigidity and strength of the structure. In addition to the numerical analysis, experiments are conducted to verify the feasibility of the design and strategy. The material properties of the involved materials, such as Kapton and SMA wires, have been determined through separate experimental investigations and incorporated into the FEA tool as input parameters. Furthermore, a parametric study is conducted to examine the impact of design and material parameters on the strength of the toroidal structure. The study demonstrates that a 1-meter diameter toroidal structure based on SMA wires can offer structural strength during partial or complete venting scenarios. [ABSTRACT FROM AUTHOR]