Inelastic lateral stability of wide flange beams under biaxial end moments | |
| Author | Chesada Kasemset |
| Call Number | AIT Diss. no.D8 |
| Subject(s) | Elasticity Elastic plates and shells |
| Note | A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Engineering of the Asian Institute of Technology, Bangkok, Thailand. |
| Publisher | Asian Institute of Technology |
| Abstract | A consistent one dimensional theory of thin-walled members of open section subjected to the action of axial force, biaxial bending and torsional moments is derived based on a set of simple assumptions and the virtual work principle. The strain-displacement relations are obtained by reducing the three dimensional finite strain-displacement relations in view of the assumptions and subsequently used in the virtual work equation to yield the equilibrium equations and the associated boundary conditions. In view of the strain-displacement relations, the force-displace¬ment relations are obtained by the definition of stress resultants. The latter are linearized and substituted in the equilibrium equations which lead to the governing differential equations in terms of displacements. These nonhomogeneous governing equations are derived in terms of general loading functions and reduce, for the homogeneous case when linearized, to those obtained by Timoshenko and, with slight difference, to those derived by Vlasov. The solutions to the nonlinear equations for simple loading conditions are obtained and compared with those obtained from the linearized equations. In the second phase of the study, a numerical integration scheme is proposed to investigate the inelastic behavior of simply supported beams subjected to symmetrical biaxial end moments. Taking advantage of symmetry, the problem is treated as cantilever beams subjected to biaxial end moments at the free end. Instead of dealing with the equilibrium equations derived at the load level which contain the derivatives of the products of stress resultants and displacements, the second order moment equilibrium equations used in the proposed numerical integration scheme involve the products of the stress resultants and the derivatives of the displacements. The latter allow the numerical integration to be carried out without iteration between consecutive stations. The ultimate load carrying capacity of the member is obtained with the aid of an extension of Harness criterion for in-plane problems. The latter is formulated as a nonlinear programing problem which is transformed by the penalty function method presented by Fiacco and McCormick to an unconstrained maximization problem. The optimizing scheme suggested by Fletcher and Powell is used to obtain the numerical solutions. The solutions for several wide flange sections are obtained and the ultimate moments and corresponding displacements are plotted against an argument, λ, which is a function of length, sectional dimensions and yield stress. The eigenvalue solutions obtained for beams subjected to in-plane symmetrical end moments are also presented for comparison. |
| Year | 1973 |
| Type | Dissertation |
| School | AIT Publication (Year <=1978) |
| Department | Other Field of Studies (No Department) |
| Academic Program/FoS | Dissertation (D) (Year <=1978) |
| Chairperson(s) | Lee, S. L.;Nishino, F.; |
| Degree | Thesis (Ph.D.) - Asian Institute of Technology, 1973 |