Lateral–torsional buckling of cold-formed zed-purlins partial-laterally restrained by metal sheeting

This paper presents an analytical model for predicting the lateral–torsional buckling of cold-formed zed-purlins partial-laterally restrained by metal sheeting for both down and uplift loadings. The critical load is determined by using energy methods. The focus of the study is to investigate the individual influences of restraints provided by the sheeting and by interval anti-sag bars, the variation of moment distribution along the longitudinal axis, and boundary conditions on the lateral–torsional buckling behaviour of the purlin.     

Stress and Buckling Analysis of Cold-formed Zed-purlins Partially Restrained by Steel Sheeting

This paper presents an analysis model for cold-formed purlin-sheeting systems subjected to wind uplitt loading in which the restraint of the sheeting to the purlin is taken into account by using two springs representing the translational and rotational restraints provided by the sheeting.The set of equations is solved by means of trigonometric series and finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the "pure bending" stress. The influence of spring stiffness and fixing position of the purlin and sheeting on the stresses resulted in the cross-section of the purlin is discussed in details.     

Column tests of cold-formed steel non-symmetric lipped angle sections

The geometry of angle sections is simple, but the behaviour and design calculations of angle sections can be quite complicated. Furthermore, lipped angle sections with unequal flange widths form a non-symmetric section and the behaviour of the section is even more complicated than a singly-symmetric angle section with equal flange widths. A test program on cold-formed steel non-symmetric lipped angle columns is presented. The non-symmetric angle sections were brake-pressed from high strength structural steel sheets having nominal yield stresses of 450 and 550 MPa with plate thicknesses of 1.0, 1.5 and 1.9 mm. The material properties of the column specimens were obtained by tensile coupon tests. The behaviour and strengths of cold-formed steel non-symmetric lipped angle columns were investigated. The test strengths are compared with the design strengths calculated using the North American Specification for the design of cold-formed steel structural members. In addition, the current design rules in the North American Specification for cold-formed steel non-symmetric lipped angle columns are assessed using reliability analysis. It is shown that the design strengths are generally quite conservative.     

Structural behavior of lapped cold-formed steel Z sections with generic bolted configurations

In order to improve the buildability of cold-formed steel structures, a series of research and development projects have been undertaken by the authors to study the structural behavior of bolted moment connections between cold-formed steel sections. As one of the major applications of cold-formed steel sections in building construction is modern roof structures with multi-span purlin systems, an extensive experimental and theoretical investigation on the structural behavior of lapped moment connections between cold-formed steel Z sections was carried out. Both generic configurations with high structural efficiency were adopted, namely, Config. W4 and W6, in which only the webs of the sections were bolted together for easy installation. Moreover, an analysis and design method was proposed to assess both the moment resistance and the effective flexural rigidity of the generic lapped connections. The research work aims to provide understanding on the structural behavior of cold-formed steel Z sections with lapped connections, and hence, to develop a set of rational design rules for multi-span purlin systems with overlaps.In order to verify the applicability of the proposed analysis and design method for other commonly adopted connection configurations, namely, Config. W2F2 and W4F2 where bolts were installed to both section webs and flanges within the lapped connections, an experimental and theoretical investigation on a total of 12 one point load tests on lapped cold-formed steel Z sections were carried out. Among all tests, section failure under combined bending and shear at the ends of lap was found to be critical while twisting of the lapped Z sections was apparent throughout the entire deformation ranges. In general, the structural behavior of lapped connections with Config. W2F2 and W4F2 was found to be similar to those with Config. W4 and W6.Moreover, the formulation of the proposed analysis and design method was modified to accommodate the presence of the flange bolts, and back analysis of the lapped Z sections against combined bending and shear using the proposed method was performed. After careful calibration against test data, the method was shown to be structurally adequate and efficient for lapped connections with Config. W2F2 and W4F2. Moreover, simple design expressions were also proposed for the evaluation of effective flexural rigidities of the lapped connections. Comparison on the structural behavior between the two sets of connection configurations was also presented.     

Design of cold-formed steel unequal angle compression members

Cold-formed steel unequal angles are non-symmetric sections. The design procedure of non-symmetric sections subjected to axial compression load could be quite difficult. The unequal angle columns may fail by different buckling modes, such as local, flexural and flexural–torsional buckling as well as interaction of these buckling modes. The purpose of this study is to investigate the behaviour and design of cold-formed steel unequal angle columns. A nonlinear finite element analysis was conducted to investigate the strength and behaviour of unequal angle columns. The measured initial local and overall geometric imperfections as well as the material properties of the angle specimens were included in the finite element model. The finite element analysis was performed on fixed-ended columns for different lengths ranged from stub to long columns. It is demonstrated that the finite element model closely predicted the experimental ultimate loads and the behaviour of cold-formed steel unequal angle columns. Hence, the model was used for an extensive parametric study of cross-section geometries. The column strengths obtained from the parametric study were compared with the design strengths calculated using the North American Specification for cold-formed steel structural members. It is shown that the current design rules are generally unconservative for short and intermediate column lengths for the unequal angles. Therefore, design rules of cold-formed steel unequal angle columns are proposed.     

Influence of lateral restraint on lateral-torsional buckling of cold-formed steel purlins

In this paper, the influence of the lateral restraint provided by cladding on the lateral-torsional buckling of zed-purlin beams is investigated in detail. The analysis is performed using the energy method. The influence of the lateral restraint on the critical load is discussed for beams with various different boundary conditions, loading positions, with and without interval anti-sag bars.     

Experimental analysis on cold-formed steel beams subjected to fire

The great majority of the studies in this area emphasise further the structural behaviour of cold-formed steel members by means of analytical approximation and purely numerical methods. In addition, they generally only take into account the structural behaviour of members with just one profile. On the contrary, this paper reports a series of flexural tests under fire conditions focused on cold-formed galvanised steel beams consisting on compound cold-formed steel profiles which are often used in floors and roofs of warehouses and industrial buildings. The main objective of this research was to assess the failure modes, the critical temperature and the critical time of the studied beams. Other important goals of this research work were also to investigate the influence of the cross-sections, the axial restraint to the thermal elongation of the beam and the rotational stiffness of the beam supports. Finally, the results showed above all that the critical temperature of a cold-formed steel beam might be strongly affected by the axial restraint to the thermal elongation of the beam.     

Experimental and numerical analysis on the structural behaviour of cold-formed steel beams

A research study on the structural behaviour of cold formed steel beams with C-, I-, R- and 2R-shaped cross-sections at ambient temperature is presented, based on the results of a large programme of experimental tests and numerical simulations. Firstly, several four-point bending tests were carried out in order to assess mainly the failure loads and failure modes of the beams. Secondly, a suitable finite element model was developed to compare with the experimental results, and finally, a parametric study was undertaken in order to investigate the influence of the thickness, height and length of the beams on its structural behaviour.     

Buckling strength of steel plating with elastically restrained edges

The twin aims of the present study are to investigate the buckling strength characteristics of steel plating elastically restrained at their edges and also to develop simple design formulations for buckling strength as a function of the torsional rigidity of support members that provide the rotational restraints along either one set of edges or all (four) edges. The characteristic equation for the buckling strength of steel plating that is elastically restrained along either long or short edges while the other edges are simply supported was derived by an analytical method. Using the computed results obtained by directly solving the buckling characteristic equation, closed-form expressions of the buckling strength of the plating with one set of edges elastically restrained while the other set of edges is simply supported are derived empirically by curve fitting. Based on the insights developed in the present study, approximate equations for the buckling strength for plating with all edges elastically restrained are proposed as a function of a relevant combination of the three simpler edge condition cases (i.e., long edges elastically restrained/short edges simply supported, long edges simply supported/short edges elastically restrained, and all edges simply supported). The effect of distortion of support members before the plating buckles is also approximately accounted for. The validity of the proposed closed-form buckling strength design formulations is studied by a comparison with theoretical and numerical solutions.     

Cyclic axial response and energy dissipation of cold-formed steel framing members

This paper summarizes results from an experimental program that investigated the cyclic axial behavior and energy dissipation of cold-formed steel C—sections structural framing members. Fully characterized cyclic axial load–deformation response of individual members is necessary to facilitate performance-based design of cold-formed steel building systems. Specimen cross-section dimensions and lengths were selected to isolate specific buckling modes (i.e., local, distortional or global buckling). The cyclic loading protocol was adapted from FEMA 461 with target displacements based on elastic buckling properties. Cyclic response showed large post-buckling deformations, pinching, strength and stiffness degradation. Damage accumulated within one half-wave after buckling. The total hysteretic energy dissipated within the damaged half-wave decreased with increasing cross-section slenderness. More energy dissipation comes at the cost of less cumulative axial deformation before tensile rupture.     

Analysis of the post-buckling behavior of a purlin built from thin-walled cold-formed C profile

The paper presents an example of the design of a simply supported C purlin according to the European and Polish standards that create possibility of acquirement material savings by taking into consideration the post-buckling state of the section. The results obtained according to the standard way are compared with the numerical results by means of program [MARC MSC.MARC vK7.3 User Manual. Theory, MARC Analysis Reasearch Corp., 1998, USA].     

Fuzzy optimization of cold-formed steel sheeting using genetic algorithms

In this paper, genetic algorithms are applied for optimization of dimensions of cold-formed steel trapezoidal sheeting. The objective of the optimization is to obtain the minimum weight subjected to the given constraints in accordance with Eurocode 3, Part 1.3. In traditional optimization, these constraints are defined with crisp number. However, in practical engineering, constraints with a small certain percentage of violation can be acceptable. Thus, in this research, sheeting is optimized to satisfy the constraints considering the fuzziness so that the optimization is more practical from the engineering point of view. The better performance of introducing the fuzziness into a constraints-handling technique has been demonstrated with a design example.     

An experimental investigation on the seismic behavior of cold-formed steel walls sheathed by thin steel plates

The use of cold-formed steel (CFS) frames has grown extensively in recent years, particularly in the earthquake-prone regions. However, the behavior of lateral resisting systems in CFS structures under seismic loads has not been scrutinized in detail. Towards this, an experimental investigation has been conducted on cold formed steel frames sheathed by thin galvanized steel plates, the results of which are presented here. The experiments involve 24 full-scale steel plated walls tested under cyclic loading with different configurations of studs and screws. Of particular interest were the specimens׳ maximum lateral load capacity and the load-deformation behavior as well as a rational estimation of the seismic response modification factor, R. The study also evaluates the failure modes of the systems. The main factors contributing to the ductile response of these shear walls are also discussed in order to suggest improvements so that the walls respond plastically with a significant drift and without any risk of brittle failure.     

Buckling restrained braces as structural fuses for the seismic retrofit of reinforced concrete bridge bents

A structural fuse concept is proposed in which easily replaceable ductile structural steel elements are added to an RC bridge bent to increase its strength and stiffness, and also designed to sustain the seismic demand and dissipate all the seismic energy through hysteretic behavior of the fuses, while keeping the RC bridge piers elastic. While this concept could be implemented in both new and existing bridges, the focus here is on the retrofit of non-ductile reinforced concrete bridge bents. Several types of structural fuses can be used and implemented in bridges; the focus in this paper is on using Buckling Restrained Braces (BRB) for the retrofit of RC bridge bents. The results of a parametric formulation conducted introducing key parameters for the design procedure of the fuse system, validated by nonlinear time history analyses are presented. A proposed design procedure, using BRBs as metallic structural fuses, is found to be sufficiently reliable to design structural fuse systems with satisfactory seismic performance. A graphical representation to help find admissible solutions is used, and shows that the region of admissible solution decreases when the frame strength ratio increases as a larger fuse element is required to achieve an effective structural fuse concept.     

Global optimization of cold-formed steel channel sections

Cold-formed steel sections have an important advantage which is the great flexibility of cross-sectional profiles and sizes available to structural steel designers. However, this flexibility makes the selection of the most economical section difficult for a particular situation. This paper presents a global optimization method for designing the cross-section of channel beams subjected to uniformly distributed transverse loading. The optimization of the cross-section is performed using the trust-region method (TRM) based on the failure modes of yielding strength, deflection limitation, local buckling, distortional buckling and lateral–torsional buckling. Numerical examples include the comparisons of the optimized sections obtained based on the applications of BS 5950-5 standard and the recently developed ENV-1993-1-3.     

Research on cold-formed steel columns

The paper summarises research on cold-formed steel columns performed by the author. Cold-formed steel members are either cold-rolled or brake-pressed into structural shapes. As a result, cold-formed steel open sections are usually singly-point- or non-symmetric. The most common types of singly-symmetric sections are channel and angle. The research focused on cold-formed steel open sections, such as plain and lipped channels, channels with simple and complex edge stiffeners as well as plain and lipped angles, and unequal angles. In addition, cold-formed steel built-up closed sections with intermediate stiffeners were investigated. Both experimental and numerical investigations into the strength and behaviour of cold-formed steel columns were conducted. The column strengths obtained from these investigations were compared with the design strengths obtained using various international standards for cold-formed steel structures. Furthermore, the behaviour and design of cold-formed steel lipped channel columns at elevated temperatures were also investigated. The paper also summarises the design recommendations for cold-formed steel columns.     

Recent developments in the design of cold-formed steel members and structures

Cold-formed steel members and structures are extremely widespread in use at the present time. The design analysis of such structures is often complex, as their behaviour can be influenced by effects, which arise due to the slenderness of members, walls and cross-sections. Prime among these effects are the various types of buckling which can occur, and which may interact with each other to promote failure at loads substantially less than those, which would be obtained in the absence of these effects. The complications induced by such effects must be taken into account in design, if the potential benefits offered by the use of such members are to be realised, and in recent design specifications this has been realised. In this paper the main types of cold-formed steel members are described, the particular characteristics affecting their design are discussed, as are the ways in which design specifications deal with these characteristics.     

Structural analysis and design assisted by testing of cold-formed steel structures

The technical and economical efficiency of cold-formed steel structures, which usually are of thin-walled sections, is strongly dependent on the ability of the designer to manage the instability problems and optimize the connection detailing associated with proper calculation models. Sometimes it is really difficult to control such types of problems by analytical calculation procedures. On this purpose, modern design codes give the possibility to apply design methodologies assisted by testing. This is, for instance, the case of EN1990 (Section 5 and Annex D) and EN1993-1-3 (testing procedures). The present paper, based on results obtained by the author and his research team, shows how test results can be used to solve and validate some complex problems of analysis and design of cold-formed steel structures, all of them being experienced by the author.     

Unified formulation for web crippling strength of cold-formed steel sheeting using stepwise regression

This study presents the availability of a stepwise regression (SR) method for the unified formulation of web crippling strength of cold-formed steel decks for various loading cases. Existing design codes offer different formulations for each loading case. However, the objective of this study is to provide an alternative unified (single) formulation to related design codes which can be used for all loading cases at the same time and should be more accurate than the separate formulations of existing design codes. The unified stepwise regression formulation is based on well established experimental results from the literature. The proposed unified SR formulation results are compared with experimental results and current design codes and found to be more accurate.     

Web crippling of cold-formed unlipped channels with flanges restrained

The paper describes a series of web crippling tests on cold-formed unlipped channels with flanges restrained (fastened) as well as channels with flanges unrestrained (unfastened). The tests were performed under end and interior two-flange loading conditions specified in the North American Specification and Australian/New Zealand Standard for cold-formed steel structures, namely end-two-flange and interior-two-flange loading conditions. The concentrated load was applied by a bearing plate at the top flange of the channels, and the reaction force applied by an identical bearing plate at the bottom flange of the channels. The bearing plates acted across the full flange widths of the channels. The flanges of the channels were either bolted to one or two bearing plates for the specimens with flanges restrained. The web crippling test strengths are compared with the design strengths obtained using the North American Specification, Australian/New Zealand Standard and American Iron and Steel Institute Specification for cold-formed steel structures. It is shown that the design strengths predicted by the North American Specification using the unfastened design rules are generally conservative, but unconservatively predicted using the fastened design rules, even when the flanges of the specimens were restrained. The design strengths predicted by the Australian/New Zealand Standard and American Iron and Steel Institute Specification are unconservative.