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This and the next image are from:
Yukio Ueda, “Elastic, elastic-plastic and plastic buckling of plates with residual stresses”, Ph.D. Dissertation, Department of Civil Engineering, Lehigh University, 1962
ABSTRACT: Welded built-up members are being used more frequently in steel construction due to economy, convenience and aesthetics. The residual stresses produced in the members as a result of the welding play an important role in the buckling strength of the members. This dissertation presents the results of an investigation into the elastic, elastic-plastic and plastic buckling of steel plates containing residual stresses. Particular attention is given to the local buckling of built-up columns of box-shaped cross section. The material of the members is steel with a stress-strain relationship assumed to be elastic perfectly plastic, and with a Poisson's ratio of 0.3 in the elastic range and 0.5 in the plastic range. The analysis of the behavior of the plate material in the plastic range was based on both the secant modulus deformation theory and the flow theory. The theorem of minimum potential energy was applied to solve the buckling problem. A simplified residual stress distribution was used in the analysis. Analytical solutions were obtained for the elastic, elastic-plastic and plastic buckling of a plate simply supported at the loading edges with the other edges elastically restrained or simply supported or fixed. Numerical examples of the analytical solution were presented for the study on the strength of local buckling of square built-up columns, that is, case (a) above. This study showed that the first term of the series of the assumed deflection function was sufficient to investigate the elastic, elastic-plastic and plastic buckling of the plate with residual stresses. An experimental study was performed on two short columns to check the theory for the square built-up column of the numerical examples. Good agreement was obtained with the results of the numerical calculation for elastic buckling and for elastic-plastic buckling, based on the secant modulus deformation theory. The experiments also showed that the ultimate load was very close to the critical buckling load for the elastic-plastic buckling, but that the post buckling strength was large for the elastic buckling.
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