预应力混凝土梁弹—徐状态统一计算理论

UNIFIED CALCULATION THEORY FOR ELASTIC-CREEPING STATE OF BONDED P.C. MEMBERS

本文视有粘结的预应力混凝土梁为混凝土和预应力钢索的组合构件,推导出弹-徐状态的统一计算公式,为预应力混凝土梁的计算提出一种新的理论方法。本文讨论梁的情况,但推广到其它结构条件,原则上也无特殊困难。 全文主要内容有:1)建立预应力混凝土梁的变分原理——对弹性和徐变状态分别建立普遍化的势能原理;在建立徐变变分原理时,采用谱分解变分原理[3],并按长期形变模量的概念建立总的势能泛函,求解长期应力。2)有限元构式——按建立的变分原理,采用变形协调模型,以结点变位为未知量进行有限元构式求单元刚度矩阵。3)给出两个计算实例。 新方法计算精度高,反映出常用方法的差距,为进一步了解预应力混凝土的性态,提供了手段。

In this paper, regarding a well-bonded P.C. member as a composite element ofthe concrete and prestressing steels, a unified calculation theory for elastic-cree-ping state of the member is developed, and formulas are derived accordingly. Thenew method established here is specially for beam cases only, however, it can beextended to meet other kind of structural conditions without remarkable diffi-culty. The main contents of this paper: 1)establishing of the variational principles forelastic-creeping state of the member-the generalized potential energy principles forboth states are first established respectively, the creeping variational principle isestablished subsequently by means of the spectral resolving variational principle.Basing on the idea of long-period deformation modulus, the total potential energyfunctional expression is found for long-period stress solutions. 2) FEM formulation--according to the established variational principles, FEM formulation isworked out on compatible deformation model with the nodal displacements asunknowns, element stiffness matrices can be obtained. 3) giving two examplesdemonstrating the practical calculations. The new method yields results of high accuracy. It not only reflects thedisparity of the conventional method,but also shows us a way to the further un-derstanding of prestressed concrete behaviours.