Method for a direct calculation of stress-strain state parameters at normal right-angled sections of structural members given curvilinear stress diagrams

Abstract

The paper presents a methodology and formulaefor direct calculations (without successive approximationscycles). Curvilinear material stress diagrams are employed.The formulae have been devised for the calculation ofstress-strain state parameters at normal sections of structuralmembers. They are applicable for both crack-lessmembers (e.g. for the calculation of the cracking moment)and for the calculation of sections between cracks of themembers with cracks (for the calculation of the stressstrainparameters of reinforced members, to establish the deviation of the deformation of the reinforcement from theplane sections). It is also possible to disregard the stresses.When the stresses of the tensile zone of the members aredisregarded, the formulae may be also used for the sectionsnear the crack (for the calculation of the breaking momentor the reinforcement). The direct calculation is possiblewhen we know the strain ε ε of any of the layers. In othercases, the calculations have to be repeated.The present paper presents only a part of the workdone. A case is presented when curvilinear stress diagramsof the fifth degree are used. Further papers will present theformulae employing simpler third degree curvilinear stressdiagrams or the ones employing noncurvilinear stress diagramsor the ones devised for the calculation of parametersat the sections near the crack or when the members arewith flanges.