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Splines, which were invented by Schoenberg, constitute a smooth curve between given data points. They are widely used in computer-aided designs, geometric modeling, graphics, and aerodynamic designs. This paper gives a new technique for efficient mathematical modeling of prestressing cable using B-spline curve. In prestressed concrete structures, cable profile plays an important role in reducing tension from concrete. So far, this cable was modeled, as of parabolic shape but the actual cable profile is a smooth curve. A new approach has been used in this paper for efficient modeling of cable using B-spline. This gives various other added advantages, which is not possible by any other curve. This is implemented in finite element analysis of 9-node Lagrangian element for concrete and cable model by 3-node bar element. Based on vector calculus formulation reaction of the cable on the concrete is obtained and applied on finite element nodes. Effects of friction and cable stiffness are taken into accounts. A finite element software has been developed incorporating these features. Various prestressed concrete beams of different spans have been successfully analysed and validated. It is observed, this formulation is very powerful in accurate analysis of the prestressed concrete structures.

Efficient Mathematical Model for Prestressing Cables and Its Implementation in Computer Analysis