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-torsional stability analysis of beams was studied, and it was shown that a second-order rotation matrix was sufficiently accurate for a flexural-torsional stability analysis. However, the second-order rotation matrix is not necessarily accurate in formulating finite element model for a 3-D non-linear analysis of thin-walled beams of open cross-section. The approximations in the second-order rotation matrix may introduce ‘self-straining’ due to superimposed 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–plastic analysis, numerical integration over the cross-section is usually used to check the yield criterion and to calculate the stress increments, the stress resultants, the elastic–plastic stress–strain matrix and the tangent modulus matrix. A scheme of the arrangement of sampling points over the cross-section that is not consistent with the strain distributions may lead to incorrect predictions of the 3-D non-linear elastic–plastic behaviour of beams. 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-linear analysis based on the second-order rotation matrix leads to over-stiff predictions of the flexural-torsional buckling and postbuckling response and to an overestimate of the maximum load-carrying capacities of beams in some cases. To perform a correct 3-D non-linear analysis of beams, an accurate model of the rotations must be used. A scheme of the arrangement of sampling points over the cross-section that is consistent with both the longitudinal normal and shear strain distributions is needed to predict the correct 3-D non-linear elastic–plastic behaviour of beams. Copyright © 2001 John Wiley & Sons, Ltd.