一种计算预应力构件作用力的迭代差分方法

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

对预应力构件施加作用力时,由于预应力筋往往是曲线布置,同时预应力筋与波纹管之间存在摩擦,使得预应力筋的拉力T会发生变化,同时预应力筋曲率的存在,会在曲线法向方向产生法向压力P,法向压力产生摩擦力F。拉力T、法向压力P、摩擦力F都会在混凝土内产生内应力。对于某些特殊形式的结构,内应力只是直接与法向压力P有关,只有得到法向力才能准确计算结构应力。拉力T目前已有准确的计算方法,法向压力P、摩擦力F可以有微分解,但工程上却无法使用。针对预应力设计中张拉力的计算需求,根据牛顿力的平衡定律,使用差分形式,借助于迭代方法,提出了一种快捷准确的张拉作用力计算方法,推导了同步计算张拉力T、摩擦力F和法向压力P的一般性的差分计算方程组,使用该方程组可计算各种复杂预应力构件的作用力,为预应力构件设计提供强大的计算工具。

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.