An analytical study on SMA beam-column actuators for anti-buckling phenomenon.

• Comprehensive examination of prismatic shape memory alloy (SMA) beam-columns and their resistance against buckling. • Integration of analytical and semi-analytical methods to understand the process of straightening the column and prevent buckling. • Development of a mathematical model that provides a step-by-step explanation of the anti-buckling phenomenon. • Identification of nine different stages of stress-height diagrams resulting from the complex stress–strain behavior of SMA materials. • Derivation of corresponding forces and moments for each stage using analytical methods, facilitating the design of SMA structures. • Highlighting that achieving a uniform strain distribution across all sections of the column is the primary reason for beam-column straightening, rather than relying on an even distribution of stress. • Demonstrating that the process of achieving a uniform strain distribution led to a gradual decrease in the curvature of the beam-column, ultimately reaching zero curvature. The present paper focuses on studying the anti-buckling behavior of prismatic martensitic shape memory alloy (SMA) beam-columns. It combines analytical and semi-analytical approaches to investigate the process of column straightening for anti-buckling. We try to comprehensively describe this phenomenon and develop a mathematical model to formulate each step of the anti-buckling problem. Due to the complex stress–strain behavior of SMA material, nine different stages of stress-height diagrams may potentially occur during this effect; thus, for facilitating the design process of SMA structures, corresponding forces and moments to each stage, are analytically derived. Our demonstration establishes that the primary cause of beam-column straightening is not the uniformity of stress, but rather the achievement of uniform strain across all fibers of the cross-section. This uniform strain distribution implies that the curvature of the beam-column diminishes to zero. [ABSTRACT FROM AUTHOR]