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In a steel supporting scaffold system, timber bearers impose a restraint on the rotation of scaffold U-head. This rotational restraint can be modelled by a rotational spring in structural analysis. To quantify the moment-rotation response of the U-head-timber bearer interface, a series of U-head sub-assembly tests were conducted, with a wide variation of parameters including applied load level, U-head configurations, and moisture content ratios of the timber bearers and joists. The relationship between the rotational stiffness and applied load is determined. A simplified procedure is proposed to implement this rotational restraint in nonlinear finite element analysis.

This paper describes a study that led to the development of an FE model for the advanced analysis of storage rack frames. The FE model is shell element-based and incorporates geometric imperfections and the semi-rigid behaviour of the pallet beam-to-upright connections. The procedure to model geometric imperfections shifts the nodes of the model according to the superimposed shapes of pure buckling modes and covers frame, member and sectional type of imperfections. The semi-rigid behaviour of connections is implemented in the model by a point-based moment-rotation relation at the intersections between members. Furthermore, the study discusses the appropriate moment-rotation curve from the available component tests to add to the model. The strength and deflection results of failure analysis are then validated against the results of four full-scale tests and the statistics of model uncertainty are obtained. Finally, strength predictions are obtained for two illustrative storage rack frames.

The load-carrying capacity of shell structures and shell-like space frames can be sensitive to initial geometric imperfections. Conventional methods of modeling geometric imperfections have focused on estimating the lower bound of the load-carrying capacity of reticulated shells. This paper proposes a random field model for the initial geometric imperfection of reticulated shell structures. The model accounts for the spatial distribution of the initial geometric imperfections, in which the correlation between imperfections at two different nodes depends on the length and number of the connecting members between the two nodes. The paper also presents the findings of the measurements of the initial geometric imperfections of a real reticulated shell structure. Based on the measurement data, the statistical characteristics of the random field model are determined. The role of initial geometric imperfections on structural ultimate strength is examined using numerical examples.

The system-based design of steel structures using advanced analysis leads to a more efficient structural design process and achieves a more uniform level of structural system reliability. The main impediment to adopting this method in practical applications is the apparent difficulty in assigning an appropriate resistance factor to structural systems. In this paper, the reliability assessment and derivation of system resistance factors for a series of 3D low-to-mid-rise steel frames are presented, taking into account the inherent uncertainties in material and geometric properties, and the model uncertainty of advanced analysis. Braced and unbraced (sway) frames with regular and irregular configurations are analysed under gravity loads and the system resistance factors are derived for different target reliability levels. The frames are selected to provide different system failure modes such as sway instability and/or member failure. Recommendations are made for the appropriate target reliabilities and associated system resistance factors for use in designing 3D steel frames at system level by advanced analysis.

Local and distortional buckling reduces the flexural and warping rigidities of steel frames. As a result, the sway buckling load of locally unstable unbraced frames is reduced and sway deflections increase at a faster rate than corresponding locally stable unbraced frames. This leads to greater second order moments and potentially premature collapse, since commonly, unbraced steel frames are designed using elastic analyses (2nd order or 1st order with moment amplification) which assume unreduced values of the flexural and warping rigidities. This paper investigates the effects of second order moments induced by local and/or distortional buckling of the uprights of steel storage rack frames. Using results from the accompanying experimental investigation, calibrated FE models are used to predict the strength of steel storage rack frames with increasingly slender cross-sections. The FE strengths are compared to design strength predictions and conclusions are drawn about the extent to which current specifications are able to accommodate second order moments generated by local and/or distortional buckling.

This paper presents an experimental investigation into locally unstable ultra-light-gauge steel storage rack frames that are prone to flexural-torsional buckling. The aim of the research was to understand how local instabilities and interactive buckling affect the strength of ultra-light gauge frames and to create reliable data through a controlled experimental investigation. A total of twelve full scale tests were conducted in the Civil Engineering Structures Laboratory at the University of Sydney. Prior to testing, the geometric imperfections of each member were measured, as were the material properties of the cold-rolled sections and the virgin steel from which the sections were formed. The cross-sectional deformations, ultimate loads and observations regarding failure modes were accurately captured and documented. The tests were also successful in capturing the post-ultimate response of the frames as well as the rotational stiffness of the beam-to-upright connections. Results from nominally identical tests were in good agreement. The tests provide comprehensive data for assessing the effects of interactive buckling and the extent to which cross-sectional deformations amplify the second-order deformations in locally unstable storage rack frames.

The design of steel frames by advanced analysis (second-order inelastic analysis with imperfections) of overall system behaviour is permitted in the American steel specification AISC360-10 and the Australian Standard AS4100. In both specifications, the strength of a structural frame can be determined by a rigorous system nonlinear analysis in lieu of checking member resistances to the specific provisions of the Specification, provided that the limit states covered by the Specification equations are detected by the inelastic analysis, and a comparable or higher level of structural reliability is achieved by the inelastic analysis than by member-based design. This system-based, design-by-advanced analysis approach is termed “Direct Design Method” (DDM). In DDM, a system resistance factor is applied to the frame strength. The system factor in AISC360-10 was adopted without considering its impact on frame reliability. This paper describes the framework for developing reliability-based system resistance factors suitable for use with DDM. A simple frame is used to demonstrate the procedures. Appropriate system resistance factors for various load cases and design recommendations are presented in a companion paper [1] based on the system reliability analyses of a series of steel frames.

The paper presents an experimental investigation into the structural performance of cold-formed steel pitched portal frames subject to local and distortional buckling prior to global sway failure. The columns and rafters were constructed from back-to-back lipped channel sections, and the apex and eave joints comprised brackets bolted to both the webs and flanges of the channel sections. Three frames were tested, subjected to different combinations of horizontal and vertical loads. In all tests, lateral and torsional restraints effectively constrained the frames to deform in their own plane. Local buckling developed at a relatively early stage of loading while distortional buckling occurred when the loads were near ultimate. The occurrence of local and distortional buckling reduced the horizontal stiffness and ultimate load significantly. Failure occurred when a spatial plastic hinge formed at the top of the columns in the vicinity of the eave joints. Component tests, including tests on tension coupons and apex and eave joints, were also conducted to obtain the material and connection properties of the frames. A critical appraisal is made of the accuracy of existing design guidelines to predict the ultimate strength of the frames tested experimentally, including the interactive effect of local, distortional and overall sway buckling.

In the design of steel portal frames, second order effects are usually accounted for by using a second order elastic analysis to calculate the deformations and internal actions of the frame. In this analysis, one-dimensional beam elements are employed irrespective of whether the cross-sections of members are slender or non-slender. However, frames composed of members with slender cross-sections may buckle in local and/or distortional modes before reaching the ultimate limit state. In this case, the flexural rigidity of the frame is reduced when local/distortional buckling occurs, and as a result it undergoes larger sway deflections than had local/distortional buckling not occurred. The additional second order moments thus caused by local/distortional bucking are not accounted for in current design provisions. In this paper, the additional second-order effects caused by the development of local/distortional buckling are studied by comparing numerically determined ultimate capacities with design capacities. The numerical ultimate strengths are based on previously calibrated geometric and material nonlinear shell finite element models, and the design capacities are determined using the Australian Standard for Cold-formed Steel Structures AS/NZS 4600. A simplified approach to account for local/distortional buckling in beam-element-based design is also proposed. The focus is on portal frames subject to in-plane sway failure.

The paper describes the modeling of pitched roof cold-formed steel portal frames with slender cross-sections. Two types of finite element models are introduced: a shell finite element model and a modified beam finite element model. The shell element model involves explicit modeling of each structural member and accounts for the semi-rigid behavior of apex and eave joints by incorporating spring-like elements. The beam element model utilizes a reduced tangent rigidity method to account for cross-sectional instability. Both models are compared with results of experimentally tested portal frames, and good agreement is demonstrated.

This paper presents a rational procedure for implementing geometric imperfections into inelastic large displacement (“advanced”) analysis. The procedure uses a statistical approach that considers the reliability of the structural strength of a selection of well-documented tests of thin-walled members and frames. The aim of the study is to derive a statistical procedure for implementing imperfections in shell-element based advanced analyses and to determine an appropriate interval of half-wavelengths and number of eigenmodes to incorporate when modelling geometric imperfections. To achieve this, a analysis of strength as a function of imperfection spectra for 20 storage rack uprights and 56 frame members was conducted using finite element analysis (FEA). All FEA models were calibrated against completed experimental results. Based on the results, practical recommendations for modelling cross-sectional and member imperfections in advanced analysis for individual uprights and storage rack frames are provided.

The companion paper [1] presents a theory to account for the effects of local and/or distortional buckling in a seven degrees of freedom beam finite element analysis. The theory considers the effect of local and/or distortional buckling as a reduction in tangent rigidities, and determines the reduced tangent rigidities by an a priori post-local or post-distortional buckling analysis of a short length of section. In this paper, the presented method is incorporated into the open source software package OpenSees which was previously modified to account for warping effects [2] . The accuracy of the method is validated by comparison with shell element results for beams, columns and frames.

Several steel design specifications worldwide have incorporated provisions for designing through inelastic analysis of overall system behavior. However, requirements for minimum system reliability have been implemented in such design-by-inelastic analysis methods through a simple adaptation of resistance factors originally developed from member reliability considerations. This paper examines system resistance factors through a system reliability analysis of two steel moment frames subjected to combined gravity and wind loads. The frames are designed using second-order inelastic analysis and their strength and serviceability reliabilities are evaluated. The effects on the system reliabilities of system resistance factor and wind-to-gravity load ratio are examined. The paper also identifies some research issues that should be addressed prior to implementing a system reliability-based design methodology.

The paper describes finite element analyses using the program ABAQUS 6.14 of cold-rolled alluminium alloy 5052 channel sections in stub column tests. Aluminium structural members have been used considerably in not only roof systems but also primary load-bearing components due to such advantages as superior corrosion resistance, light weight, ease of maintenance, constructability and recyclability. While the majority of aluminum structural applications are formed by extrusion, recently, aluminum Z- and C- sections have been successfully cold-formed from aluminium coil using existing rollers for cold-formed steel sections. The results of nonlinear analysis by the finite element method (FEM) depend on the measured input parameters such as the material properties, actual initial geometric imperfections and forming-induced residual stresses. The paper summaries the results of the finite element nonlinear simulations of the stub column tests on channel sections performed at the University of Sydney. The FEM results are compared and calibrated against the tests. The effect of the measured input parameters is also discussed thoroughly.

This paper presents a comprehensive parametric study on the ultimate strength of perforated cold-formed steel columns using the finite element (FE) package ABAQUS. FE models were developed ...

The parametric study of the ultimate strength of perforated cold-formed steel columns is presented in a companion paper. The parameters include five cross-section types (i.e., C, stiffened ...

Concrete-filled stainless steel tubular (CFSST) columns have attracted increasing research interests in recent years; however, It seems that the behavior of this type of innovative column u...

Cold-formed steel sections are widely used in many applications such as structural frames, scaffolding systems, purlins and storage racks. In particular, cold-formed steel portal frames can be an alternative to conventional hot-rolled steel portal frames for industrial, rural and residential low rise buildings. The advantages of using cold-formed steels include a higher strength-to-weight ratio and reduced material, erection and transportation costs. Over the past two decades a number of researchers [1] to [3] have undertaken tests on cold-formed steel portal frames. The tests mainly focused on the behaviour of joints, and employed relatively stocky sections. Hence, they provided little insight into the effects of cross-sectional instability on the overall stability of the frame. In this paper, three portal frame tests are described, the main purpose of which was to study the effect of cross-sectional instability on the two-dimensional sway failure of cold-formed steel. The tests demonstrated significant local and distortional buckling before reaching the ultimate load. Finite element models were calibrated against the tests. The calibrated models therefore can be used for a parametric study to investigate the significance of the additional second-order effects caused by local/distortional bucking. The paper details the tests and the numerical simulations.

A simple approach is developed in this paper which considers the effect of partial warping continuity through the joints of thin-walled steel frames when using beam finite element analysis. Using a condensed stiffness matrix for the joint generated by the substructuring technique, warping springs are introduced to represent the condition of partial warping restraint at intersections between members. The performance of the proposed model is demonstrated through a number of numerical examples. Excellent agreement is achieved between the results of beam finite element analysis using the suggested joint model and accurate shell finite element analysis.

Stowell's solution [1] for the buckling behaviour of flange elements in compression was premised on the assumption that the element was fixed against flexural rotations at the ends, a condition representing relatively thick elements for which the thickness dimension is adequate to prevent rotations. This paper presents a solution similar to Stowell's which is applicable to pin-ended flange elements. Aspects not considered in Stowell's work, such as the use of elliptic functions to describe the gradual change of mode shape from sinusoidal to essentially linear, and the gradual and asymptotic changes in axial rigidity in the post-buckling range are described in the paper. The paper also presents comparisons between the behaviour of pin-ended and fixed-ended flange elements. Finally, simple strength equations for flange elements in uniform compression based on the first yield criterion are derived.

This paper presents an experimental investigation into the behaviour of ultra light-gauge steel storage rack uprights subjected to compression. Two different types of members with varying lengths are tested and while the combined effects of local and distortional buckling are investigated, special attention is given to longer specimens that fail by flexural–torsional buckling in combination with local and distortional buckling. Deformations experienced during testing by all of the specimens were measured and observations regarding failure modes have been documented. In addition, the geometric imperfections of each member were measured before testing, as were the material properties of the cold-rolled sections and the virgin steel from which the sections were formed. This paper details the observed failure modes, the recorded ultimate strengths and the load-deflection responses. Design capacities calculated from AS/NZS 4084 (2012) [1] , RMI (2012) [2] and EN 15512 (2009) [3] specifications are then evaluated and compared to the experimental results obtained.The evaluation of international specificationsdetermined that EN 15512 (2009) [3] is more accurate in predicting ultimate loads of sections undergoing interactive buckling than both AS/NZS 4804 (2012) [1] and RMI (2012) [2] .

Steel structural members and frames always indicate imperfections to various degrees. These include initial out-of-straightness and initial out-of-plumb due to manufacturing and erection tolerances. In general, the shape and magnitude of geometric imperfections may have a significant influence on the response of a structure, and hence need to be modelled accurately when determining the load carrying capacity of a steel frame by advanced structural analysis. Most conveniently, geometric imperfections can be introduced in structural models as scaled eigenmodes obtained a priori from an elastic buckling analysis. However, it remains unanswered how many eigenmodes need to be incorporated and how to choose the scaling factors of each mode. This paper presents a study of how the strength of steel frames varies with the number and magnitudes of eigenmodes. Frames with random geometric imperfections are produced using the statistics of measurements of out-of-plumb and member imperfections, and analysed using advanced geometric and material nonlinear analysis. The imperfections are then resolved into eigenmodes and a second set of advanced analysis is carried out using a finite number of modes to represent the imperfections. Conclusions are drawn about the appropriate number and magnitudes of eigenmodes to use in advanced structural analyses of steel frames.

This paper analyses the influence of horizontal bracing restraints provided by the friction between pallet bases and rail beams on the static behaviour and design of steel drive-in storage racks. The pallet bracing restraints are shown to significantly influence the structural behaviour of the rack, and their effect on the bending moment distribution of the uprights is studied in the paper. The 2D single upright model proposed by Godley is improved in this study by including the restraints provided by the plan flexural stiffness of the rail beams and the friction between the pallets and rail beams. The improved 2D model was found to accurately reproduce the bending moment distributions obtained using 3D advanced finite element analysis. The 2D single upright model is used to analyse 36 drive-in racks under various load case combinations. The paper evaluates the influence of the pallet bracing restraints on the ultimate capacity of drive-in racks, clarifies the loading pattern(s) governing the structural design and determines the friction coefficient, or strength of a restraining device, required to prevent the pallets from sliding. It is shown that while restraints from pallets could potentially be considered in design, they would not lead to more economic structural solutions.

Structural systems made of high-strength and/or high-ductility metals are usually also rather slender, which means that their structural behaviour and ultimate strength are often governed by a combination of plasticity and instability effects. Currently, the rigorous numerical analysis of such systems can only be achieved by resorting to complex and computationally costly shell finite element simulations. This work aims at supplying to designers/researchers with an efficient and structurally clarifying alternative to assess the geometrically and/or materially non-linear behaviour (up to and beyond the ultimate load) of prismatic thin-walled members, such as those built from cold-formed steel. The proposed approach is based on Generalised Beam Theory (GBT) and is suitable for members exhibiting arbitrary deformation patterns (e.g., global, local, distortional, shear) and made of non-linear isotropic materials (e.g., carbon/stainless steel grades or aluminum alloys). The paper begins by providing an overview of the physically and geometrically non-linear GBT formulation recently developed and validated by the authors, which is followed by the presentation and thorough discussion of several illustrative numerical results concerning the structural responses of 5 members (beams and columns) made of distinct (linear, bi-linear or highly non-linear) materials. The GBT results consist of equilibrium paths, modal participation diagrams and amplitude functions, stress contours, displacement profiles and collapse mechanisms – some of which are compared with Abaqus shell finite element analysis (SFEA) values. An excellent correlation is found in all cases and, moreover, it is shown that GBT analyses including judiciously selected deformation mode sets involve only 25% (on average) of the number of d.o.f. required by similarly accurate SFEA. Moreover, it is clearly evidenced that the GBT modal nature makes it possible to acquire in-depth knowledge on the member behavioural mechanics in the elastic and elastic–plastic regimes.

This paper concerns storage rack frames and describes a study that led to the development of an FE model sufficiently accurate and simultaneously simple to be adopted by professional engineers. The presented FE model pays particular attention to storage rack frames susceptible to local/distortional buckling and down-aisle sway buckling. The influence of several strength parameters is also assessed with a special focus on the moment-rotation curve of the semi-rigid joints, including the detailed connection between members discretised into shell elements, and the modelling of perforations.

The paper presents a detailed finite element (FE) model intended for studying the distortional–global interaction buckling behaviour of thin-walled stainless steel beams. The model incorporated actual measured material properties of three stainless steel alloys (austenitic S30401, ferritic S44330 and lean duplex S32101), as well as measured initial geometric imperfections. The model was verified against the experimental data presented in the companion paper [1] . A parametric study was then carried out using the calibrated model to augment the ultimate strength database The accuracy of the Australian/New Zealand (AS/NZS 4673 [2] ), American (SEI/ASCE-8 [3] ) and European (Eurocode3, Part1-4 [4] ) standards for stainless steel structures was evaluated using the available data. It was found that the current Australian/New Zealand and American design codes do not contain rules for checking distortional buckling strength nor do they account for distortional–global interaction buckling effects. The European standard accounts for distortional buckling effects by reducing the effective area of flange stiffeners using an effective thickness method, and covers the effect of distortional–global interaction by using the effective cross-section for overall buckling strength checks. The European code was therefore more conservative than the other two standards. Following the principles of the Australian and American design codes for cold-formed steel structures, additional provisions for checking distortional buckling strength were suggested to improve the current Australian/New Zealand and American stainless steel design codes. Variants of the proposed provisions to account for distortional–global interaction were also examined which resulted in generally better predictions than those of the European code. However, the distortional–global interaction effect was found to vary with the section slenderness, and none of the design provisions performed consistently better than others.

This paper presents a set of new test data for high strength concrete filled steel tubular (CFST) members subjected to transverse impact. A total of 12 circular CFST specimens and reference hollow steel tubes were tested in a drop hammer rig. The cube strength of the concrete used for the CFST members is up to 75 MPa. A finite element analysis (FEA) model is established to predict the impact behaviour of high strength CFST members, and the accuracy of which is then verified by the presented test results. Full-range analyses of the behaviour of CFST members under impact loading are then carried out using the FEA model to produce the force state, internal force distribution, and flexural capacity. Finally, a simplified model is obtained based on a parametric analysis to calculate the flexural capacity of CFST members under impact load.

Second-order inelastic analysis (advanced analysis) is a new paradigm in structural steel design. This paper examines the provisions for design by advanced analysis in the Australian Steel Standard (AS4100), and the AISC Specification (AISC 360-10). The Australian Standard AS4100 uses a reduced section yield surface to incorporate resistance factors, while AISC 360 requires that the strength and stiffness of all members and connections are reduced by a factor of 0.9 to account for the uncertainties in member strength and stiffness. Another way to incorporate the resistance factor in advanced analysis is to use a system resistance factor for the frame strength. This paper presents a case study for the design of a typical semi-rigid steel scaffold structure using these three different design-by-advanced analysis methods. The paper also discusses the challenges and research needs for developing a system-based design methodology using advanced analysis.

The paper summarizes the main new design provisions included in the recently revised Australian standard for steel storage racks. The standard features multitiered analysis provisions ranging from basic linear-elastic analysis-based provisions to highly advanced integrated design-analysis [geometric and material nonlinear analysis with imperfections (GMNIA)] provisions that allow the analysis and design to be completed in one step. The GMNIA provisions distinguish between beam element–based and shell element–based analysis according to cross section slenderness and provide rules for the imperfections to use for the two types of analysis, including imperfections in the local and distortional buckling modes for the shell element–based analysis. The selection of the system-based reliability (resistance) factor (ϕs) is discussed. The standard is seen as the most advanced design code of its type currently available for frame-type steel structures. The paper also provides an in-depth discussion about th...

Compared with austenitic or duplex stainless steels, ferritic stainless steels have no or very low nickel content. Therefore, their cost is lower and more stable than those of austenitic and duplex stainless steels, providing a more viable alternative for structural applications. They are also less affected by gradual yielding than their austenitic and duplex counterparts and thus retain elastic stiffness at relatively high stress levels more like their ordinary carbon steel counterparts. Existing stress-strain models, however, are less accurate in predicting stress-strain curves for ferritic stainless steels than for austenitic and duplex stainless steels. The paper collects a wide range of tensile test data for ferritic stainless steel coupons cut either from steel sheets or cold-formed hollow sections. Using the three basic Ramberg–Osgood parameters, stress-strain models are developed for both flat and corner ferritic stainless steels. The accuracy of the proposed models is verified by comparin...

The stability of steel storage racks in the cross-aisle direction is typically ensured by cold-formed steel bolted upright frames. Sensitive to second-order effects, accurately determining the shear stiffness of these frames is essential for seismic design and for ensuring the stability of the rack, especially for high-bay racks and racks supporting the building enclosure, where the outer rack frames must withstand cross-aisle horizontal actions due to wind loading. The main international racking specifications adopt different approaches to determining the shear stiffness of cold-formed steel storage rack upright frames. The Rack Manufacturers Institute (RMI) specification conservatively uses Timoshenko and Gere's theory. The European Specification EN 15512 recommends testing, however it is not clear whether the shear stiffness obtained using the recommended test procedure is correct. The newly revised Australian Standard AS 4084 adopted the European approach but also introduced an alternative test method for determining the combined bending and shear stiffness of upright frames in the transverse direction. This paper reviews and analyses the factors influencing the shear deformation of cold-formed steel bolted upright frames and introduces the alternative test set-up adopted in the revised Australian Standard. 36 upright frames have been tested using the two test methods, and experimental results are presented, discussed and compared with finite element analysis results. Recommendations on how to use the test outcomes in design are also provided. Based on these recommendations, the paper shows that the two test methods are not equivalent and yield different results for the transverse shear stiffness of upright frames.

Many failures of concrete structures during construction are traceable to the collapse of formwork shoring systems. A reliability analysis for typical steel scaffold shoring structures is presented herein utilizing recent survey data on geometric and mechanical properties of steel scaffold members, and a second-order inelastic structural analysis model. Published shore load surveys were analyzed to develop the probabilistic models for loads acting on scaffolds during concrete placement. The paper investigates the mode of failure, the effects of different random variables on the variability of structural strength, and the reliability of the analyzed scaffold structures. The reliability framework can be used to improve the current working load limit basis for the design of steel scaffold structures and make scaffold design risk-consistent.

Steel drive-in racks are susceptible to structural failure from accidental impact by operating forklift trucks. Under impact, the upright bends and the supported pallets may drop through the rack to cause structural collapse if the bay opening exceeds the pallet bearing width. This drop-through limit state has not been considered in existing rack design standards. This paper proposes a simple equation to calculate the equivalent static impact force based on recent tests and nonlinear dynamic analysis of drive-in steel racks. An impact load factor is developed on the basis of a structural reliability assessment, taking into account the uncertain nature of the impact force, structural resistance, and models used in structural analysis. In design practice, the bay opening is determined from factored impact loads and is not to exceed specified limits.

Steel storage racks, made of cold-formed steel, are used extensively in industry for storing goods. Two main racking systems prevail, referred to as selective racks and drive-in racks. International racking design codes deal mainly with selective racks, but limited design guidelines are available for drive-in racks. Drive-in racks require minimum floor space by storing pallets one after the other with no space between them. The forklift truck drives into the rack to store the pallets on the first-in, last-out principle. To allow forklift passage, drive-in racks can be braced only at the back (spine bracing) and at the top (plan bracing) in the down-aisle direction, resulting in a complex slender structure with poorly understood three-dimensional (3D) behavior and increased risk of collapse. Tests on drive-in rack systems to accurately capture their 3D behavior have not previously been available in the literature. This paper presents experimental results from full-scale tests conducted on a complete drive-...

This paper summarizes a recently completed research programme carried out at the University of Sydney on drive-in steel storage racks subjected to horizontal impact loads. Impact loads develop frequently during the normal operation of drive-in racks when the forklift truck strikes an upright on entering or leaving a bay, and may lead to local or global collapse. The collapse follows the bowing of the upright which may cause a pallet to drop off the supporting beam rails and initiate progressive collapse down through the bay and possibly into adjacent bays as well. The research programme comprised full-scale tests on assemblies of a four-bay-wide racking system, tests on system components, the development of finite element models capable of predicting the behaviour of the system accurately, parametric studies of the strengths and stiffnesses of steel storage racks, the development of a simple mechanical model for understanding the dynamic behaviour of the system during impact and a reliability analysis for deriving equations for the design impact loads and associated load factors. The purpose of the paper is to give an overview of the methodology adapted for the research programme and to present the main findings and final outcome of the research.

This paper presents the analytical developments of the application of the Isoparametric Spline Finite Strip Method (ISFSM) to the material inelastic and geometric nonlinear analysis of perforated thin-walled steel structures. The general theory of the ISFSM is briefly introduced. The formulations of the kinematics, strain–displacement and constitutive assumptions are presented, and the tangential stiffness matrix is derived by applying the incremental equilibrium condition. The requirements for strip continuity and boundary conditions are also discussed. In particular, the plasticity theory and the methods to integrate the ‘rate equations’ are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are highlighted. The present isoparametric spline finite strip analysis is verified against a number of analyses of perforated and non-perforated plates and plate assemblages, as described in the companion paper (Yao and Rasmussen, submitted for publication) [1] , demonstrating its accuracy and efficiency for the predictions of the inelastic post-buckling behavior of perforated thin-walled steel structures.

The theoretical developments of a material inelastic and geometric nonlinear analysis by use of the isoparametric spline finite strip method (ISFSM) are presented in a companion paper (Yao and Rasmussen (submitted) [1] ). In the present paper, the numerical implementation of the analysis is reported, including nonlinear solution techniques, inelastic material models, selective reduced integration strategies, convergence criteria, and solution procedures. The reliability and efficiency of the method are demonstrated by a number of numerical examples, including analyses of flat plates with different material plasticity models, a classical nonlinear shell problem, perforated flat and stiffened plates, and perforated stiffened channel section storage rack uprights.

The paper presents a study of the capacities of steel rack frames based on linear analysis (LA), geometric nonlinear analysis (GNA), and geometric and material nonlinear analysis (GMNIA). In the case of linear and geometric nonlinear analyses, the design is carried out to the Australian cold-formed steel structures AS/NZS4600. The study includes braced, unbraced, and semi-braced frames, and compact and noncompact cross sections. The paper shows axial force and bending moment paths for geometric and geometric and material nonlinear analyses, and explains the differences observed in the design capacities obtained using the different types of analysis based on these paths. The paper provides evidence to support the use of advanced GMNIA for the direct design of steel rack frames without the need for checking section or member capacities to a structural design standard.

This paper addresses the problem of determining the stiffness and strength of steel storage rack base plate assemblies. Base plate assemblies are usually bolted to an upright and to a concrete floor, and they are used to provide resistance against the flexural buckling of the upright and/or the overall down-aisle buckling of the frame. The semi-rigid stiffness is usually determined by means of a test of two pre-loaded uprights connected to a concrete block in a dual-actuator set-up. Guidance for conducting the test is provided in the European Standard EN 15512. However, several aspects of the test need clarification, notably the test set-up and the transducer arrangement for measuring the rotations of the base plate. This paper provides recommendations for how best to conduct the test, and proposes an alternative test method to that given in the EN 15512 Specification. The paper also identifies the contributions to the deformations of base plate assemblies, including the deformations of the supporting floor, the base plate assembly itself and the upright, and proposes simple expressions for calculating the stiffness associated with each contributing deformation where applicable. Furthermore, the paper proposes a deformation criterion for determining the ultimate design moment for base plate tests which do not attain a peak moment.

The paper addresses the problem of determining the accidental forklift truck impact forces on steel storage racks. Based on first principles of mechanics, simple models of a loaded forklift truck and a drive-in racking structure are presented. Model masses, as well as stiffness and damping coefficients are calibrated against experimental results obtained from tests of a forklift truck and a drive-in racking structure. Comparisons between experimental results and solutions obtained from the simple mechanical models show that the simple models accurately reproduce the static and dynamic behaviours of their associated structures. Based on the drive-in rack impact test results presented in a companion paper (Gilbert and Rasmussen, submitted for publication) [1] and the simple mechanical models for drive-in racks, actual impact forces are calculated and presented. Finally, using the impact test results and the simple mechanical models, the actual motion of the forklift truck body is calculated. This motion, being a common characteristic to all drive-in racking impacts, allows impact forces to be obtained for various pallet loads, impact elevations and rack characteristics. Thus, the paper concludes with a general method for calculating forces generated under forklift truck impact.

Extensively used in the industry to store goods, steel storage racks are frequently subjected to accidental impact forces from operating forklift trucks. There is currently little understanding of the nature of these impact forces, leading to occasional catastrophic failures because of inadequate structural design. International racking design codes deal with impact but use an arbitrary value of impact force with no scientific justification. This paper focuses on an impact-sensitive type of storage rack, called “drive-in racks”. Contrary to classical “selective racks”, where pallets are stored on beams and where each single pallet is always accessible, “drive-in racks” allow the forklift truck to drive into the rack to store pallets on beam rails, one after the other, on the first-in, last-out principle. This type of design leads to slender uprights in the down-aisle direction, only restrained at the base and at the top. When subjected to an impact force, the bowing of the upright triggers progressive failure by allowing the pallets to drop through. This paper presents experimental results obtained from tests on a complete full-size drive-in rack structure subjected to the impact of a forklift truck. Parametric impact studies using finite element analysis are also presented. Factors affecting the sensitivity of drive-in racking structures to impact are investigated and conclusions are drawn about the parameters most significantly influencing the progressive collapse of this type of rack under impact.

This paper describes the findings from various site measurements of geometric imperfections of support scaffold systems, also known as falsework in industry. The measurements consist of out-of-straightness of the standards (uprights), out-of-plumb of the frame and loading eccentricity between the timber bearer and the U-head screw jack. The measurements were taken from different support scaffold construction sites before the pouring of concrete, representing actual initial geometric imperfections and loading eccentricity encountered in practice. The paper also reports the results of support scaffold joint tests. The tests were performed on randomly chosen used components to investigate the joint stiffness for rotations about vertical and horizontal axes. Tests were performed for various joint configurations (two-way, three-way, and four-way connections), bending axes, and loading directions. The statistical analysis of the data is presented in the paper for practical application in modelling and probabilistic assessment of support scaffold systems.

Steel support scaffold systems are characterised by the large variations of geometric and mechanical parameters, notably joint stiffness, initial geometric imperfections, yield stress and load eccentricity. This paper investigates the effects of these uncertainties on the ultimate strength of multi-storey steel support scaffold frames through a rational statistical framework and a second-order inelastic finite element analysis (advanced analysis). A series of stick type steel scaffold systems with cuplok joints were studied. The statistical data for the basic random variables were acquired through field measurements and laboratory tests. By comparison to load tests, the bias and variability of advanced analysis were estimated. The basic random variables and the model uncertainty are propagated through Monte Carlo simulation to obtain the statistics of system strength. The first-order reliability method is then employed to estimate the reliability of steel scaffold systems designed by advanced analysis.

The stability of steel storage racks, which are often unbraced, may depend solely on the pallet beam to upright connector and on the stiffness of the base plate to floor connection. This paper presents experimental results from cyclic tests performed on portal beam to upright bolted moment connections intended for cold-formed steel drive-in and drive-through storage racks. In storage racks, portal beams are typically connected to uprights by “tab connectors”, which are costly to manufacture and experience initial looseness. By simply bolting the portal beams to the uprights, bolted moment connections may represent a cost-effective alternative to “tab connectors”. A literature review shows that bolted moment connections between cold-formed steel members are economical and feasible. However, experimental results show a significant amount of looseness in the connection after an initial high moment–rotational stiffness. Being slender structures, storage racks are sensitive to the second-order P – Δ effect, and international racking specifications require the initial looseness of the tab connectors to be considered when analysing the stability of the rack in the down-aisle direction (sway motion). The non-linear cyclic behaviour of bolted moment connections is presented and explained herein. Based on finite element results, it is shown that, for drive-in and drive-through racks, the looseness in bolted moment connections can be ignored in ultimate limit states design. Finally, the paper concludes with proposing two methods, with different degree of complexity, for the design of drive-in and drive-through racks with bolted portal beam to upright bolted moment connections.

This paper presents a series of 48 full-scale tests on press-braked stainless steel lipped channel section columns subjected to concentric compression. The tests were carried out between fixed ends in the Structures Laboratory of the University of Liege and the test specimens were designed such that distortional buckling developed in the section prior to overall flexural-torsional buckling. The stainless steel alloy was 1.4003 chromium weldable steel, popularly known as 3Cr12. Three different geometries were tested using the same experimental setup. A critical summary of the standards and methods for calculating the carrying capacity of cold-formed stainless steel compression members is presented in a companion paper by the same writers.

This paper provides a critical summary of the European standards and design methods available for calculating the strength of cold-formed stainless steel compression members. The standards considered (so far mainly applied to columns failing by flexural buckling) are applied to the case of lipped channel section columns failing by combined distortional and overall flexural-torsional buckling. As observed during the tests presented in a companion paper, distortional buckling is found to have a considerable effect on the cross section resistance and is prone to interact with the global flexural-torsional mode. It is investigated how the different formulations account for the two buckling modes and their interaction and how accurate strength predictions they provide. A new direct strength method taking into account these failure modes is then presented and compared to the test results.

A detailed finite element (FE) model is presented, which was developed with the aim of studying the interaction of local and overall buckling in stainless steel columns. The model incorporates non-linear stress–strain behaviour, anisotropy, enhanced corner properties and initial imperfections. The model was verified against a program of 29 laboratory tests on stainless steel lipped channels, described in a companion paper [Becque J, Rasmussen KJR. Experimental investigation of the interaction of local and overall buckling of stainless steel lipped channel columns. Journal of Constructional Steel Research 2009; 65(8–9): 1677–84] and yielded excellent predictions of ultimate strength and specimen behaviour. The FE model was further used in parametric studies, varying both the cross-sectional slenderness and the overall slenderness. Three stainless steel alloys were considered: AISI304, AISI430 and 3Cr12. The results are compared with the governing design rules of the Australian, North American and European standards for stainless steel structures.