Thin-walled Open Profiles Research Articles

Numerical Analyses of Deformation Mechanisms in a Novel Dimensional Calibration Technique for Thin-Walled, Open Extrusions

High dimensional accuracy is of crucial importance in digital manufacturing to guarantee production capability and product performance. For manufacturing of thin-walled complex extrusions, it is often challenging to meet the tight dimensional tolerance requirements for automated mass production, due to dimensional imperfections and variations accumulated from the thermo-mechanical processing history. Recently, a new calibration technique, called Transverse Stretch and Local Bending, was developed, enabling significant improvement of the dimensional accuracy of thin-walled open profiles at a low cost. However, the deformation mechanisms have not been well understood, which in turn affect the process design for achieving high-precision products. In this study, a through-process finite element model was established and experimentally verified, which is used as a tool to investigate the mechanisms in the calibration process. It is found that the gap opening is mainly reduced in the inserting stage, but the calibration stage plays a key role in achieving high-precision products after unloading. The critical factor to achieve high dimensional accuracy is reducing the through-thickness gradients on both the profile bottom and sidewall. By controlling the total vertical displacement in the transverse stretch and local bending, the stress gradients can be effectively reduced, and the dimensional deviation caused by springback after unloading can be well mitigated. This fundamental study will benefit the industry to obtain high-precision extrusions.

Lateral-torsional buckling of partially protected steel I-beams exposed to fire

This paper proposes a new model for thin-walled open profiles able to predict bending-torsion buckling of thermally restrained steel I beams with bi- and mono-symmetric cross-sections. Refined nonlinear kinematics accounts for the shifts of the centroid and shear centre generated by the thermal gradient. The eigenvalue problem derived from geometrically nonlinear balance equations is solved via power series and Newton-Raphson technique. Several examples are presented; the results are compared with those provided by Abaqus simulation and the literature.

Investigation of a Method for Strengthening Perforated Cold-Formed Steel Profiles under Compression Loads

Cold-formed steel (CFS) storage rack structures are extensively used in various industries to store products in safe and secure warehouses before distribution to the market. Thin-walled open profiles that are typically used in storage rack structures are prone to loss of stability due to different buckling modes such as local, distortional, torsional and flexural, or any interaction between these modes. In this paper, an efficient way of increasing ultimate capacity of upright frames under compression load is proposed using bolts and spacers which are added externally to the section with certain pitches along the height. Hereinto, experimental tests on 81 upright frames with different thicknesses and different heights were conducted, and the effect of employing reinforcement strategies was examined through the failure mode and ultimate load results. Non-linear finite element analyses were also performed to investigate the effect of different reinforcement spacing on the upright performance. The results showed that the reinforcement method could restrain upright flange and consequently increase the distortional strength of the upright profiles. This method can also be effective for any other light gauged steel open section with perforation. It was also observed that the reinforcement approach is much more useful for short length upright frames compared to the taller frames.

Compressive buckling for symmetric TWB with non-zero warping stiffness

Torsion and bending/torsion buckling may occur for compressed thin-walled open profiles used in engineering and architecture applications. We report experimental results provided by PZT pickups stuck on thin-walled aluminium beams with open modified cruciform cross-section, exhibiting non-zero warping stiffness. The buckling loads and the natural frequencies corresponding to various compressive forces were detected for free and (at least partially) restrained warping of the ends of the specimens. The results are compared with those of a FEM (commercial) and an in-house numerical code that examines the stability of non-trivial equilibrium paths in a dynamic setting. The results seem new and confirm that: (a) PZT pickups can be efficient in extracting modal parameters of thin-walled beams; (b) the numerical simulations are robust and accurate in finding the buckling loads in all analyzed configurations.

Modeling distortional shear in thin-walled elastic beams

In this paper, the theoretical background and the numerical analyses of an advanced beam finite element that relaxes the hypothesis of the cross-section non-deformability are presented. The corresponding new modes, called distortional modes, are added to the modes describing the behavior of a classical thin-walled beam: tension/compression, bending and torsion. For instance, a load acting in a cross-sectional plane of a beam is considered to induce not only bending and torsion but also distortion. The distortion produces non-uniform shear and axial stresses together with a non-uniform warping of the cross-section. These resulting effects, significant for very thin-walled open profiles (and thin-walled closed profiles with high distortional loadings), are shown in this paper to be important when compared to bending and torsion stresses even in simple loading cases.

Closed-form analysis of thin-walled composite I-beams considering non-classical effects

In this work, a closed-form analysis of thin-walled open profile composite beams such as I-beam has been performed. The analysis includes the effects of elastic couplings, shell wall thickness, transverse shear deformation, torsion warping, and constrained warping. A mixed beam approach based on Reissner’s semi-complementary energy functional is used to derive the beam force–displacement relations. A closed-form solution for the static response of both symmetric and anti-symmetric layup beams with transverse shear couplings is derived. The beams considered have the boundary condition of one end fixed and the other end warping restrained and are subjected to unit bending or torque load at the beam tip. The shear flow distribution related with the applied forces and moments along the contour of the beam is also identified. The static results of composite I-beams have been validated against those of detailed two-dimensional finite element analysis. The effects of warping restraint and transverse shear deformation on the static behavior of open-section composite beams are investigated in the analysis.

Influence of warping-pretwist coupling on the torsional vibration of centrifugally-stressed cantilevers with thin-walled open-profiles

A nonlinear torsional vibration theory for multifilament models of centrifugally-stressed and pretwisted cantilevers with thin-walled open-profiles is developed from D'Alembert's principle. Warp deformation and a moderately large twist about the elastic axis are assumed in describing the dynamical torsional motion. The extensional strain is eliminated by invoking equilibrium of extensional stresses along the elastic axis. The refined derivation here reveals significant warping-pretwist coupling terms resulting from the Wagner effect and warping shear stresses, which have been ignored in thin-walled bar vibration theories hitherto. Approximate torsional frequencies are drawn from the linear terms of the resulting nonlinear boundary-value equations using a finite difference procedure with first- and second-order central differences. As the length-to-leg ratio (L/b) and leg-to-thickness ratio (b/t of typical open-profile cantilevers are varied, the individual and collective effects of warping and pretwist on the torsional frequencies are compared to exact solutions. Finally, the relative importance of centrifugal stiffening and/or softening terms, warping-pretwist coupling terms, and inertial warping-tension coupling terms is pointed out.

Closed-form effects of warping and pretwist on the torsional vibration of thin-walled open-profile cantilevers

Theoretical natural frequencies are determined for the first three modes of torsional vibration of pretwisted cantilevers with thin-walled open profiles. The equation of motion and boundary conditions are derived from a multifilament model of a pretwisted thin-walled bar undergoing warp deformation and a moderately large twist about the elastic axis. Closed-form torsional frequencies and mode shapes are derived from the linear terms of the resulting nonlinear equations. As the length-to-leg ratio ( L/b) and leg-to-thickness ratio ( b/t) of typical open-profile cantilevers are varied, the individual and collective effects of warping and pretwist on the torsional frequencies are qualitatively defined. The refined derivation and closed-form solutions presented here reveal significant destiffening of the torsional frequencies due to warping-pretwist coupling in cantilevers having pretwisted unsymmetrical open-profiles. These coupling effects, which have been ignored in thin-walled bar vibration theories heretofore, are brought out by the Wagner effect and warping shear stresses acting on the profile.