Effects of approximations in analyses of beams of open thin-walled cross-section - part II: 3-D non-linear behaviour

In a companion paper, the effects of approximations in the flexural-torsion al stability analysis of beams was studied, and it was shown that a second- order rotation matrix was sufficiently accurate for a flexural-torsional st ability analysis. However, the second-order rotation matrix is not necessar ily accurate in formulating finite element model for a 3-D non-linear analy sis of thin-walled beams of open cross-section. The approximations in the s econd-order rotation matrix may introduce 'self-straining' due to superimpo sed rigid-body motions, which may lead to physically incorrect predictions of the 3-D non-linear behaviour of beams. In a 3-D non-linear elastic-plast ic analysis, numerical integration over the cross-section is usually used t o check the yield criterion and to calculate the stress increments, the str ess resultants, the elastic-plastic stress-strain matrix and the tangent mo dulus matrix. A scheme of the arrangement of sampling points over the cross -section that is not consistent with the strain distributions may lead to i ncorrect predictions of the 3-D non-linear elastic-plastic behaviour of bea ms. This paper investigates the effects of approximations on the 3-D non-linear analysis of beams. It is found that a finite element model for 3-D non-lin ear analysis based on the second-order rotation matrix leads to over-stiff predictions of the flexural-torsional buckling and postbuckling response an d to an overestimate of the maximum load-carrying capacities of beams in so me cases. To perform a correct 3-D non-linear analysis of beams, an accurat e model of the rotations must be used. A scheme of the arrangement of sampl ing points over the cross-section that is consistent with both the longitud inal normal and shear strain distributions is needed to predict the correct 3-D non-linear elastic-plastic behaviour of beams. Copyright (C) 2001 John Wiley & Sons, Ltd.