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UBC Theses and Dissertations

The lateral-torsional buckling of doubly symmetric wide flange sections De Vall, Ronald H.

Abstract

In this thesis, a stiffness matrix which includes the non-linear effects of principal plane shears, moments and axial loads on lateral and torsional deflections is developed for a doubly symmetric wide flange section. Initially, an exact eight by eight linear matrix is developed for an element of constant section properties. The eight allowable deflections allows the independent representation of the deflections of either flange at either end. The non-linear effects are included in the differential equations by considering the effect of the primary stresses on the equilibrium of a dis-placed element. Two approximations are then introduced. The first consists of a numerical technique for solving the differential equations. The second consists of a simplification of the boundary conditions in solving the differential equations. Using these two approximations, the non-linear portion of the matrix is then built. Several structures are then analyzed. Each structure is divided into several elements. This allows beams of non-constant section properties to be analyzed, and increases the accuracy of the results of the approximate matrices. The results of these analyses are then compared to theoretical results and tabulated. It is seen that the matrix gives good agreement for all cases tested.

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