An Iterative Difference Method for Calculating the Force Acting on Prestressed Members

When a force is applied to a prestressed component, the tension T in the prestressed tendons varies due to their curved arrangement and the friction between them and the corrugated ducts. Additionally, the curvature of the prestressed tendons generates normal force P in the curve's normal direction, which in turn creates friction F. The tension T, normal force P, and friction F all induce internal stress within the concrete. For certain specialized structures, the internal stress is directly linked to the normal force P; thus, accurately calculating the structural stress requires first determining the normal force. Accurate algorithms for the tension T are available. The normal pressure P and friction F can be approximated through differential methods, though they are not feasible for practical engineering applications. To address the need for tension force calculations in prestress design, based on Newton's law of force balance, a rapid and precise method for calculating tension forces has been proposed by using a differential approach and iterative methods. A set of general differential equations for simultaneously calculating the tension force T, friction force F, and normal force P have been derived. The equations enable the computation of forces in various complex prestressed components, offering a robust computational tool for prestressed component design.