Kirişlerdeki büyük yer değiştirmeler üzerine bazı yeni çözümler

Abstract

Large deflections which become under various loading on bearer systems are well knownand there are many researches on this subject. Since this subject is very important, relatedstudies are going on currently. The obtained results by linearization can be sufficient in manycases of the engineering fields. However, the well known curvature relation of elastic curve isnot linear and as that of real material?s stress-strain relation. Taking this fact intoconsideration, large deflections cannot be analyzed by analytic methods all the times. Whenthis is the case, approximate and numerical methods should be used. In this thesis, weightedresidual and Runge-Kutta methods are mostly used. Both material and geometrical nonlinearityare investigated jointly in most of the sections of the thesis.The introduction part of the thesis includes the state of the art, the aim of this research and thecontribution to literature.In section 2, Firstly, the relation of stress-strain of beam material is assumed as Ludwick typeand then large deflections of cantilever beam which is subjected to moment at the free end arecalculated. Then the same process is applied to the type of cubical and logarithmic stressstrainrelations.In section 3, the large deflections of the cantilever beam which is subjected to concentratedload at the free end are calculated using different methods and finally, the compared resultsare presented.In sections 4 and 5, the large deflections of the uniform distributed loaded simple beams andcombined loaded cantilever beams are calculated by numerical methods using curvaturemomentequations which are obtained by assuming different arc lengths.In sections 6 and 7, composite beams are investigated. In section 6, composite cantileverbeams which is subjected to concentrated load for only geometrical non-linearity isconsidered. In section 7, for both non-linearity, the large deflections of the compositecantilever beams which is subjected to moment at the free end are calculated for Ludwick,cubical, and logarithmic types of stress-strain relations.In section 8, the large deflections of the non-linear bimodulus cantilever beam which issubjected to moment at the free end are investigated for cubical and logarithmic materials.Afterward, the large deflections of the linear bimodulus cantilever beam which is subjected toconcentrated load at the free end or subjected to combined load are calculated by assumingdifferent arc length. The same process is applied to uniform distributed loaded linearbimodulus simple beams and obtained results for each cases are presented in the tables.In this thesis, simple and understandable solutions have been proposed instead of knowncomplex solutions from the previous studies in this area. Also, some new solutions have beenpresented for less encountered composite and bimodulus beams.