Influence of actual imperfection on strength, buckling and limit load of thinwalled beams and columns with nonstandard C-sections

Cold-formed, thin-walled beams and columns are popular structural members. They are made of thin, cold-rolled steel sheets by using cold-rolling or edge bending machines. The dimensional accuracy of those beams and columns is dependent on manufacturing machines, which can be manually or numerically controlled, and the operators’ experience. If the cross-sections of beams and columns are complicated, the actual members may differ from their counterparts. This project extends the range of methods used for experimental investigations of thin-walled coldformed beams and columns to optical measuring techniques (optical deformation analysis). This is a continuation of earlier researches conducted in the Division of Strength of Materials and Structures at Poznan University of Technology. The aim of the project is a global look at the mechanics of thin-walled cold-formed beams using experimental methods taking into account geometric imperfections. Measurements do not restrict to some points where strain gauges are glued or recording single parameters, e.g. load. The deformation and strains of the entire external surface of a beam are recorded like in FEA. In this way geometrical imperfections, local and distortional buckling that are typical of open, thinwalled beams can be exactly monitored and analysed. New channel beams and columns with non-standard crosssection are considered in this project. Obtained experimental results will be compared with the results of finite element analyses, constrained and unconstrained Finite Strip Method (FSM, CuFEM) and some new analytical formulas. Optical deformation analysis allows to make not only a quantitative comparison, i.e. comparing parameters (stresses or strains) in some points, but also qualitative one, i.e. the deformation and buckling mode of entire beams can be compared. According to the authors’ knowledge, the influence of actual geometrical imperfection on the strength and stability of thin-walled cold-formed beams was not evaluated by optical measuring techniques. Therefore this project popularise these techniques, validating and checking their usefulness to such structural members. Preliminary researches refer to sigma channels with corrugated flanges. Their imperfections reduce the geometrical properties of cross-section even by 4.2% (the 1st principle moment of inertia) and rotate the principle axes by 0.98° in relation to the global coordinate system, i.e. actual profiles are not fully symmetrical. The beams were scanned using a high resolution camera and then the generated cloud of 3d points was converted into a surface model using OPTOCAD software. The strength and stability of actual and ideal beams subjected to pure bending were analysed using Finite Element Method and SolidWorks Simulation. The numerical model included material and geometrical non-linearities. The obtained results, i.e. critical moment, stresses and deflections, were compared with each other. The influence of the beam length on the results was also evaluated. Simply supported beams subjected to pure bending were considered, because channels usually carry transverse loads. Preliminary investigations confirm a well-known fact that such thin-walled, cold-formed channel beams cannot be analysed using static linear analysis based on classical beam theory. The stress distribution in the plane parallel to the neutral axis, e.g. in the flange, is not uniform and the shape of cross-section changes as load (bending moment) increases. In order to accurately simulate the behaviour of beams geometrical and material nonlinearities need to be included in numerical models. The used true stress-strain curve was based on the actual tensile tests of specimens cut from the beams. The strength and stability of actual, scanned beams were compared with the strength and stability of their idealized counterparts that did not included edge radiuses. Imperfections reduce the maximum bending moment (limit load) by 3.0-5.4% so a little bit more than the geometrical properties of cross-sections. The difference between stresses of scanned and theoretical beams may be even 8.3-13.8%. This is three times bigger than the reduction of geometrical properties of cross-section.