“Computational Civil Engineering - "Intersections" International Journal

“Computational Civil Engineering 2005”, International Symposium 19The displacements obtained with the incompatible element PLAN-12 are close tothose obtained in the bar theory, in the case of bending, or in the thin-walled barstheory, for the complex action of restrained torsion and bending. The differencesbetween the results are less then 2%, the finite element approach generallyoverestimating the displacements.It can be noticed (Figure 4) that the Bernoulli’s hypothesis of plane sections isrespected for bending. For the restrained torsion (Figure 5), the warping of thecross section is obvious. A comparative study of the vertical displacements at thetop of the structure (the warping effect) is given in Figure 6 and Table 1.Table 1. Vertical displacements at the top level of the structureHYFEMNASTRANNode Displacement [mm] Node Displacement [mm]Deviation%34322930313335– 3.61.78.3– 0.6– 7.3– 1.7+ 3.429303132333435– 3.52231.65678.0186– 0.48– 7.0585– 1.646+ 3.32252.202.613.51253.423.282.33Mean deviation 6.05%Figure 6. Vertical displacements at the top level of the structure, meshwork U 2 , loadingcase (c)The results suggest a good concordance of the two programs, the average gap beingaround 6.05%.