The third equilibrium equation for forces of flexural member cross-section

Abstract

In earlier articles of the author two equilibrium equations of fairly general ZI method for calculation of real parameter values of stress-strain states for normal to longitudinal axes sections of flexural members at any loading stage are presented. It required in advance to have or to calculate by the method of successive approximation strain value of any one layer. The third equation for force static is presented in this article. The main purpose of the equation is calculation of neutral axes location in cases when external actions are given but strain value of any layer is not given in advance. Strain is calculated from other equations and then it enables calculation of values for all other parameters. Such calculation is especially relevant for reinforced concrete members with cracks in tension zone because at present calculation of neutral axes location is carried out either by empirical formula or in very approximate way.

It can be considered that creation of ZI method is finished by the third force equilibrium equation. Applica-tion of ZI method three equation system enables solution of many theoretical and practical problems. Application for particular practical problems examples of ZI method three equations in general case are presented in this article as well.

DOI: http://dx.doi.org/10.5755/j01.mech.20.2.6942