Stability of thin walled beam-columns

In this research, theoretical and experimental studies on the stability of openand closed thin-walled beam-columns under the effect of axial loads or anycombinations of axial load, biaxial bending, and bimoments are carried out. Theobjective of the research is to determine the critical loads of such members and theexpected type of buckling for any member whatever this buckling is flexural, torsionalor flexural torsional mode. The study focuses on the optimal design of such membersby a new practical technique, and on simple procedures to enable the designers toassess this behavior.The second order analysis of the principal differential equations of equilibriumfor bending and torsion are presented. Closed form solution for the differentialequation which including second order terms is carried out. The values of critical loadsof the member are obtained using eigen value analysis together with Newton-Raphsonmethod. This work is dependent upon Oberbski theory which in turn is a furtherdevelopment of the general theory derived by Vlasov. The case of externally actingbimoments is studied for members having no axis of symmetry by introducing a newsectorial parameter (fJ ).eoA computer program was developed to determine different linear and sectorialproperties of open and closed thin-walled members. The program is used to study theeffect of different parameters on the stability behavior and optimal design of suchmembers.The developed computer program can perform the following three principaltasks :-• Constructing stability curves for members subjected to axial loads or interactiondiagrams for members subjected to combined loads.Optimal analysis and design of thin- walled members under different load conditions .Checking the safety of a given member configuration and load condition.Using the developed computer program, the effect of different parameters onthe stability behavior, load-carrying capacity, and optimal design is investigated. Theseparameters are :-Type and shape of the cross section,Thickness of section walls,Degree of symmetry,Member length and boundary conditions (ul.),Kind of applied loadsCross section perimeter.The study also offers the following items:A set of dimensionless curves for the determination of sectorial properties for alltypes and shapes of thin-walled cross sections.Charts for discussing the instability phenomena for any thin-walled membersconsidering the above mentioned parameters