Abstract
A bidirectional B-spline QR method (BB-sQRM) for the study on the crack control of the reinforced concrete (RC) beam embedded with shape memory alloy (SMA) wires is presented. In the proposed method, the discretization is performed with a set of spline nodes in two directions of the plane model, and structural displacement fields are constructed by the linear combination of the products of cubic B-spline interpolation functions. To derive the elastoplastic stiffness equation of the RC beam, an explicit form is utilized to express the elastoplastic constitutive law of concrete materials. The proposed model is compared with the ANSYS model in several numerical examples. The results not only show that the solutions given by the BB-sQRM are very close to those given by the finite element method (FEM) but also prove the high efficiency and low computational cost of the BB-sQRM. Meanwhile, the five parameters, such as depth-span ratio, thickness of concrete cover, reinforcement ratio, prestrain, and eccentricity of SMA wires, are investigated to learn their effects on the crack control. The results show that depth-span ratio of RC beams and prestrain and eccentricity of SMA wires have a significant influence on the control performance of beam cracks.
Highlights
Cracking is one of the main nonlinear characteristics of reinforced concrete (RC) structures
In view of fact that the numerical analysis for nonlinear behaviors of shape memory alloy (SMA) smart concrete beams is less and the employment of the finite element method (FEM) in modeling and analysis is more, in order to enrich the theoretical system of SMA concrete structures and to increase the diversity of methods, the B-spline QR method (BB-sQRM) is adopted in this paper to perform a nonlinear analysis of the SMA smart concrete beam, which ensures the accuracy of the results while the computational scale is reduced and the efficiency of numerical analysis improved
Based on the BB-sQRM, a new model is presented in this paper, which is used in the nonlinear analysis for crack control capability of the SMA concrete beam
Summary
Cracking is one of the main nonlinear characteristics of reinforced concrete (RC) structures. In view of fact that the numerical analysis for nonlinear behaviors of SMA smart concrete beams is less and the employment of the FEM in modeling and analysis is more, in order to enrich the theoretical system of SMA concrete structures and to increase the diversity of methods, the BB-sQRM is adopted in this paper to perform a nonlinear analysis of the SMA smart concrete beam, which ensures the accuracy of the results while the computational scale is reduced and the efficiency of numerical analysis improved. Based on the iteration method of incremental initial stress, the calculation format for nonlinear analysis of the BBsQRM is established The nonlinear behavior such as cracking of the SMA concrete beam can be analyzed by controlling the temperature of SMA wires. Several parameters, such as depth-span ratio, thickness of concrete cover, reinforcement ratio, prestrain, and eccentricity of SMA wires, will be discussed to learn their influence on the capability of crack control, which can provide supplementary and further analytical means for test methods
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