Lipped Channel Beams Research Articles

GBT-based buckling analysis of thin-walled members with non-standard support conditions

This paper reports on the use of a recently developed Generalised Beam Theory (GBT) formulation, and corresponding finite element implementation, to analyse the local and global buckling behaviour of thin-walled members with arbitrary loading and support conditions — this formulation takes into account longitudinal normal stress gradients and the ensuing pre-buckling shear stresses. After presenting an overview of the main concepts and procedures involved in the performance of a GBT-based (beam finite element) member buckling analysis, one addresses in detail the incorporation of non-standard support conditions, such as (i) full or partial localised displacement or rotation restraints, (ii) rigid or elastic intermediate supports or (iii) end supports corresponding to angle connections. In order to illustrate the application and capabilities of the proposed GBT-based approach, one presents and discusses numerical results concerning cold-formed steel (i) lipped channel beams and (ii) lipped I-section beams and columns with various “non-standard” support conditions — while the beams are acted by uniformly distributed or mid-span point loads, applied at the shear centre axis, the columns are subjected to uniform compression. In particular, it is possible to assess the influence of the different support conditions on the beam and column buckling behaviour (critical buckling loads and mode shapes). For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code A nsys.

GBT FORMULATION TO ANALYZE THE BUCKLING BEHAVIOR OF THIN-WALLED MEMBERS SUBJECTED TO NON-UNIFORM BENDING

In this paper, one investigates the local-plate, distortional and global buckling behavior of thin-walled steel beams subjected to non-uniform bending moment diagrams, i.e. under the presence of longitudinal stress gradients. One begins by deriving a novel formulation based on Generalized Beam Theory (GBT), which (i) can handle beams with arbitrary open cross-sections and (ii) incorporates all the effects stemming from the presence of longitudinally varying stress distributions. This formulation is numerically implemented by means of the finite element method: one (i) develops a GBT-based beam finite element, which accounts for the stiffness reduction associated to applied longitudinal stresses with linear, quadratic and cubic variation, as well as to the ensuing shear stresses, and (ii) addresses the derivation of the equilibrium equation system that needs to be solved in the context of a GBT buckling analysis. Then, in order to illustrate the application and capabilities of the proposed GBT-based formulation and finite element implementation, one presents and discusses numerical results concerning (i) rectangular plates under longitudinally varying stresses and pure shear, (ii) I-section cantilevers subjected to uniform major axis bending, tip point loads and uniformly distributed loads, and (iii) simply supported lipped channel beams subjected to uniform major axis bending, mid-span point loads and uniformly distributed loads — by taking full advantage of the GBT modal nature, one is able to acquire an in-depth understanding on the influence of the longitudinal stress gradients and shear stresses on the beam local and global buckling behavior. For validation purposes, the GBT results are compared with values either (i) yielded by shell finite element analyses, performed in the code ANSYS, or (ii) reported in the literature. Finally, the computational efficiency of the proposed GBT-based beam finite element is briefly assessed.

Fatigue behaviour of welded steel tubular structures: Gowda, S.S. and Hakola, I. Conf. Fatigue and Fracture in Steel and Concrete Structures, ISFF '91, Madras, India, Dec 1991 Vol 2 (Oxford & IBH Publishing Co. Pvt. Ltd, New Delhi, India, 1991) 697–713

Present paper investigates an efficiency of application of vertical stiffeners in the web of cold-formed C-section beams under local concentrated loading. The stiffeners would be cold-formed – an I-section cut is made on the web and the cut edges are folded into the inner side of the profile. A lipped channel beam with a length of 1 m was selected to investigate the efficiency of vertical web stiffeners. As a validation of rational stiffener parameters requires an extensive experimental program that is time-consuming and prohibitively expensive, thus, the numerical modelling using finite element method (FEM) was adopted. The numerical modelling was performed according to the standardized methodology of American Iron and Steel Institute (AISI) covering four loading and boundary conditions: 1) interior-one-flange (IOF); 2) interior-two-flange (ITF); 3) end-one-flange (EOF); and 4) end-two-flange (ETF). The influence of stiffeners geometry on the ultimate stiffened web crippling strength was assessed using the data from the numerical modelling of one hundred specimens. The obtained results were compared to the ultimate web crippling capacity of unstiffened beams. The relationships of load-vertical web displacement and load-horizontal web displacement were derived. The analysis of the obtained results formulated the directions for a further research.

Lateral-torsional buckling of channel beams

A theoretical and experimental study of the buckling behaviour of channel beams with unbraced longitudinal edge stiffeners, bent in such a way that the stiffeners are in compression, is presented. For a relatively short length of beam loaded in such a manner, the beam will buckle symmetrically. However, for a relatively long beam the lateral-torsional buckling may well be the governing mode of failure. The investigations presented here are confined to the latter case of lipped channel beam sections subjected to pure bending. A semi-analytical, semi-numerical approach is used in the theoretical analysis to predict the critical lateral-torsional buckling moments of such beams. Comparison between the theoretical and experimental results is presented and the agreements obtained are reasonably good.

Distortional buckling of thin-web beam-columns

An approximate finite element method of analysis is developed for the distortional buckling of beam-columns. The member consists of a flexible web, to which is connected two rigid flange assemblies of arbitrary shape which remain undistorted during buckling. The method permits an economic computer analysis to be made of elastic distortional buckling of members under various conditions of loading, end support and restraint. Following studies of the convergence and accuracy of the buckling solutions, the method is used to demonstrate the effects of web distortion on the elastic buckling of lipped channel beams under moment gradient.

The Local Buckling and Post Local Buckling Behaviour of Thin-Walled Beams

SummaryThis paper presents a theoretical analysis of the behaviour of thin-walled lipped channel beams subjected to end moments. In the analysis the beam section is assumed to be composed of a number of flat plates, joined at the edges. The mechanics of local instability of the walls of the beam are examined from a consideration of the strain energy stored in the component plates, and critical moments to cause local buckling are evaluated. The behaviour of the beam after local buckling is studied using a semi-energy method, whereby the stress and deflection systems throughout the section are linked by solving von Kármán’s compatibility equation for the component plates and the stress and deflection magnitudes are found from energy considerations. As collapse of the beam is approached, a simple plasticity analysis is incorporated in the theory in order to evaluate the collapse moment for the beam.The results of the analysis are compared with the findings of an extensive experimental investigation and it is shown that the theory is very accurate in its prescription of the experimental stresses and deflections. Comparison of the theoretical and experimental collapse moments also verifies the validity of the theoretical analysis.

Tank built with horizontal staves : ( Engineering News-Record, Vol. 129, No. 19.)

Present paper investigates an efficiency of application of vertical stiffeners in the web of cold-formed C-section beams under local concentrated loading. The stiffeners would be cold-formed – an I-section cut is made on the web and the cut edges are folded into the inner side of the profile. A lipped channel beam with a length of 1 m was selected to investigate the efficiency of vertical web stiffeners. As a validation of rational stiffener parameters requires an extensive experimental program that is time-consuming and prohibitively expensive, thus, the numerical modelling using finite element method (FEM) was adopted. The numerical modelling was performed according to the standardized methodology of American Iron and Steel Institute (AISI) covering four loading and boundary conditions: 1) interior-one-flange (IOF); 2) interior-two-flange (ITF); 3) end-one-flange (EOF); and 4) end-two-flange (ETF). The influence of stiffeners geometry on the ultimate stiffened web crippling strength was assessed using the data from the numerical modelling of one hundred specimens. The obtained results were compared to the ultimate web crippling capacity of unstiffened beams. The relationships of load-vertical web displacement and load-horizontal web displacement were derived. The analysis of the obtained results formulated the directions for a further research.