Analytical investigation of the behavior of concrete beams reinforced with multiple circular superelastic shape memory alloy bars

A new analytical model is developed for concrete composite beams reinforced with multiple superelastic shape memory alloy (SMA) circular bars and subjected to bending. The model is derived based on the three-dimensional (3D) ZM model for SMAs combined with Timoshenko beam theory. Mathematic formulas are first developed to predict and describe the internal material structure of the composite taking into account solid phase transformation in the SMA bars. Analytical expressions are then obtained for the moment-curvature and shear force-shear strain relations. The present work is the first to derive nonlinear expressions for the axial stress and elastic moduli of regions experiencing phase transformation within SMA in the vertical y–coordinate and the evolution of phase transformation along the axial and transverse directions in the SMA bars during unloading. The proposed model is validated against 3D finite element analysis (FEA) results for the same beam. It is found that the superelasticity of the beam is further enhanced with temperature closer to austenitic finish temperature, higher SMA volume percentage, higher number of SMA bars, and location of SMA bars further away from the neutral plane. In contrast, the magnitude of the austenitic and martensitic moduli were found to have negligible influence on superelasticity.