Substructuring analysis of thin-walled box girders and nonlinear pure torsion analysis of beams

This dissertation consists of two parts. The first part presents an analysis method for thin-walled box girders which is suitable for parallel processing. The problem is formulated in such a way that the calculations of the influence coefficients and the generation and inversion of the stiffness matrix of each substructure can be carried out independently in parallel processing. Instead of solving the condensed system equilibrium equations in the traditional substructuring method, a mix of compatibility and equilibrium equations are employed. The major unknowns are the shear forces at the interfaces where the thin walls of the substructures join. The proposed substructuring method is sufficiently general to be performed on microcomputers with commercial finite-element software.;The second part presents the nonlinear finite element analysis of beams of arbitrary cross sections subjected to pure torsion. The material nonlinearity of concrete and steel, i.e., the nonlinear relationship between shear stress and shear modulus, is considered and implemented by an incremental numerical scheme. The total complementary potential energy of a twisted beam in terms of the stress function are formulated as a quadratic functional, and the minimization of the functional leads to the finite element matrix equation. The cross section of the beam is discretized into finite elements. At each increment, the shear stress of all elements of the cross section is calculated. Because of the material nonlinearity, elements at different shear stresses have different shear moduli which are continuously updated at the beginning of each increment. It is assumed that the material behaves linearly at each increment. A number of hollow circular sections and square box sections were analyzed by the proposed method and the results were compared with classic solutions and also the Bredt's formula for closed thin-walled sections. Plain concrete and reinforced concrete beams analyzed by the proposed method compare well with experimental measurements and other analytical results presented by other investigators.;Numerical examples of a cantilever thin-walled box girder and a two-span continuous thin-walled box girder and a thin-walled circular tube subject to torque are analyzed by the proposed method and the results are compared with classic solutions and other studies. The examples give satisfactory numerical solutions for stresses, displacements and shear lag effect. Estimates of reductions in computation time and computer memory for the stress matrix operation indicate that the method is numerically efficient.