Method to Solve Bond Differential‐Equation System in Prestressed Concrete

Abstract

Considering the difference in the bond behavior between the ordinary reinforcement and the tendons, which are placed in grouted ducts, first a differential equation is formulated to describe the relationship between slip and strains of steels and concrete in prestressed concrete members. In the second step a numerical method is developed to solve the differential‐equation system for single cracks and stabilized crack patterns. The method is based on the application of Runge‐Kutta method for the numerical integration and on the Newton method for the optimization of the vector function. The method presented here allows the calculation of crack width, the stiffness, and the redistribution of stresses between ordinary reinforcement and tendon in prestressed concrete members. An example is provided demonstrating the practical applicability of the method. The presented method is also suitable for reinforced concrete.