Effect of Cross Section Geometry on the Response of an SMA Column

Abstract

This numerical study investigates the effect of cross section geometry on the bending of a beam and also buckling of a column made of shape memory alloy (SMA). It incorporates superelastic SMA's non-linear stress—strain relations, including the non-symmetric behavior in tension and compression. Primarily, an arbitrary rectangular cross section is selected for analysis of the beam and column, loaded beyond the linear stress—strain relations. Then similar analysis is carried out for two different equivalent cross sections, namely, square of same area and square of same inertia, for comparing the effect of cross section geometry on the response of the beam and column. Using the equations of static equilibrium, the variations of effective modulus and bending moment for different equivalent cross sections are presented. The critical stress of the column is calculated by assuming an appropriate deflection curve for both ends hinged condition. It is found that the effective modulus depends only on the stress—strain curve. The bending moment, on the other hand, is a function of the stress—strain curve and cross section geometry. For a given load, the square of same area develops the minimum bending stress, while the square of same inertia develops the maximum bending stresses. Because of the non-symmetric stress—strain curve, the compressive stress is found to be higher than the tensile stress. It is also found that the buckling load for a column is distinctly high if the non-symmetric stress—strain curve is used in the analysis. Moreover, for a very high critical stress, the square of same area has the highest slenderness ratio, while the rectangle has the lowest slenderness ratio.