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Cold-formed steel haunched portal frames are popular structures in industrial and housing applications. They are mostly used as sheds, garages, and shelters, and are common in rural areas. Cold-formed steel portal frames with spans of up to 30 m (100 ft) are now being constructed in Australia. As these large structures are fairly new to the market, there is limited data on their behavior and design recommendations. An experimental program was carried out on a series of portal frame systems composed of back-to-back lipped channels for the columns, rafters, and knee braces. The system consisted of three frames connected in parallel with purlins to simulate a free standing structure, with a span of 14 m (46 ft), column height of 5.3 m (17 ft), and apex height of 7 m (23 ft). Several configurations were tested including variations in the knee connection, sleeve stiffeners in the columns and rafters, and loading of either gravity only or combined horizontal and gravity loads. Deflections were recorded at various locations to measure global and local movements of the structural members. A total of eight frames with unbraced columns were tested and one frame with braced columns. Experimental results are presented herein including frame strengths and failure modes for the various frame configurations and loading conditions, as well as quantified moment-rotation relations for the column base connection. The contributions and effects of the different knee connections and sleeve stiffeners are presented. The overall frame behavior of these structures and suggested design considerations are discussed.

Cold-formed steel haunched portal frames are popular structures in industrial and residential sectors. They are commonly used in rural areas for sheds, garages, and shelters, and are now being constructed with spans of up to 30 m in Australia. As these large structures are relatively new to the market, there is limited data on their behavior and design recommendations, including connection stiffness and design. Numerical and experimental parametric studies were conducted on a haunched portal frame composed of back-to-back lipped channel sections bolted through the webs for the main frame members, and back-to-back L-brackets bolted though the webs at the connections. An advanced shell finite element model was created and validated with experimental results to confirm the suitability of the modeling technique. The validated finite element model was then used for parametric studies to determine the effects of various components of the frame, including column base connection stiffness and modifications to the knee brace-to-column connection design, on the frame capacity and behavior. An experimental program was conducted to quantify column base connection stiffness where the connection was comprised of L-brackets bolted through the column flanges at the base. Stiffness was quantified for bending about the column major and minor axes for various thickness L-brackets and for a U-bracket. Apex in-plane connection stiffness was quantified experimentally for several rafter channel thicknesses and depths. Discussions of the results of the parametric studies are presented in addition to the resulting design recommendations for constructing effective long-span cold-formed steel portal frames.

This paper presents quantitative investigations on the collapse behavior of steel portal frames exposed to standard fires. The complete collapse process is divided into safe, alert, dangerous and collapse stages. These four stages are to warn firefighters to make timely reactions to stay, ready to evacuate, and must evacuate, respectively. Numerical models are established and validated against fire tests on a full-scale steel portal frame. Based on the key displacements of the heated columns and rafters, the four stages are quantitatively determined in terms of visible phenomena and warning times. It is found that one should be ready to evacuate when the heated rafter shows large deflections, and must evacuate when the heated column moves back to its initial position. The 1 h, 2 h, 3 h fire rating of protected steel portal frames can be used to estimate the ready-evacuate, must-evacuate and collapse warning time, respectively. The findings from this preliminary study aim to provide references for firefighters to make wise decisions to evacuate timely and safety from the fire scene.

This paper presents experimental investigations on the collapse behavior of a full-scale 36 m × 12 m steel portal frame exposed to natural fires. Extensive thermal and structural responses of the frame are measured and presented. The frame collapses after 15-min fire exposure with a critical temperature of about 1100 °C in the heated column. The measured gas temperature history has a short growth period of 3 min, and reaches its peak temperature of 1100 °C within 8 min (400 °C higher than standard fire). It is found that a two-zone model can be assumed with uniform temperature distribution in the lower and upper half region, respectively. The temperature gap of these two zones reaches 200 °C. The gas temperature at top region decreases due to the deformation-induced opening of roof and fire walls. The surface facing the environment has higher gas temperatures than that inside the fire compartment (more than 200 °C). The temperature of rafters beyond the fire compartment reaches 700 °C due to the spread hot smoke. Outward bending of the external unexposed column and pulling out of corner column base are observed, which should be prevented in practical design to mitigate fire spread to adjacent buildings and ensure life safety of fire fighters. Numerical simulation is conducted and compared to experimental results which can be used for calibrating numerical models.

This study aims to investigate the seismic performance of an innovative cold-formed steel (CFS) moment-resisting frame experimentally and analytically. A half-scale CFS moment-resisting portal frame was tested under static monotonic loading until failure. The frame consisted of two box-shaped columns (face-to-face channels connected with inside plates), a back-to-back lipped channel beam section and fully moment-resisting CFS bolted connections. During experimental tests, damage mostly concentrated at the top and bottom of the CFS columns due to the web crippling of the channels close to the connections, while no fracture or obvious slippage was observed at the connection zones. A detailed Finite Element (FE) model was developed using ABAQUS by taking into account the material non-linearity and geometrical imperfections. The lateral load-displacement behaviour, ultimate strength and failure modes predicted by the model were in very good agreement with the experimental results. The validated FE model was then used to assess the effects of key design parameters on the lateral load capacity, ultimate displacement, energy dissipation, ductility, and ductility reduction factor of the frame. It is shown that the proposed system can provide good seismic performance subjected to the appropriate design of the main structural elements. Increasing the axial load ratio of the columns by 50% resulted in 26%, 62%, and 50% decrease in the ultimate lateral load, energy dissipation capacity, and ductility ratio of the CFS frame, respectively. However, the energy dissipation capacity and the ductility ratio of the proposed system increased significantly by decreasing the width-to-thickness ratio of the columns.

The work presented in this paper investigates the strength of moment-resisiting apex brackets of cold-formed steel portal frames. The results of two previously reported full-scale portal frame tests, where the frames failed through buckling of the apex bracket, were used to validate a finite element model that included material nonlinearity, geometric imperfections, and bolt bearing behaviour. From portal frame test results as well as the finite element results, the importance of appropriate detailing for the apex brackets for strength is demonstrated. A simplified finite element model of the apex bracket is then presented, again validated against previously reported experimental tests. The effects of geometrical parameters of the brackets, bolt-group configuration, and yield stress of brackets were investigated through a parametric study comprising 648 models. From the results of this parametric study, design equations are proposed that can be used by practicing engineers to predict the strength of apex brackets used for cold-formed steel portal frames.

This study employs a detailed 3-D numerical modeling to investigate the fire-resistance behavior of the damaged steel portal frame with reduced beam section (RBS) connections. Ignoring the material damage parameters, and the detrimental influence of residual stresses and geometrical imperfections in the previous numerical researches has given an unrealistic response in the subsequent fire analyses. Damages were induced by the cyclic loading protocol and considering damage parameters. Then, mechanical-thermal analysis was carried out by adopting a standard fire scenario, as per ISO-834. The analysis results indicate the necessity of considering damage parameters to improve the reliability of the approach. It is revealed that fire develops thermal stresses in the bottom flange of the RBS beam. These stresses lead to severe deformation in the RBS zone, thus influencing its vital performance. Damages induced by cyclic loading drastically reduce the fire-resistance period of the frame. Once the maximum drift exceeds three times the yield limit, the steel frame is practically not capable of resisting fire. Applying extra fire load to the frame with residual lateral displacement, when the maximum lateral displacement is greater than the yield limit, the frame can only sustain the stability for less than 2 min, which will also diminish by increasing the axial column load. Through conducting a subsequent case study, it was found that the fire-resistance time of the frame is increased by decreasing the DoI of the structure at equal cyclic loadings.

Experimental tests have previously shown that the strength of bolted moment-connections between cold-formed steel channel members, where the connections are formed through an array of bolts in the web, is dependent on the length of the bolt-group. This reduced strength has been observed in tests on portal frame joints as well as overlapped purlin joints. For a long bolt-group length, an upper bound would be the full in-plane major axis moment-capacity of the section, which can be predicted using the conventional Direct Strength Method (DSM). For a short bolt-group length, in the order of the depth of the section, a reasonable lower bound to the reduced strength can be predicted by using the DSM, modified to include the effect of the bimoment at the connection. In this paper, a parametric study is performed covering sections of different values of slenderness.

Cold-formed steel trusses are a popular form of construction for light-weight buildings, particularly portal frame structures for which spans up to 25 m are increasingly common. A novel pin-jointed truss connector named the Howick Rivet Connector (HRC) has been tested, firstly in a T-joint arrangement, then in a truss assemblage to determine its reliable strength and stiffness. Results show that the HRC performs similarly to a bolted connection in heavy steel in terms of failure modes observed, loads reached and proportionality limit. Finite element models of both T-joints and trusses tested show good agreement with experimental results, particularly in the transition from elastic to inelastic behaviour.

An innovative type of replaceable moment-resisting viscoelastic damper (RMVD) was developed to increase the level of inherent damping of steel moment frame buildings to control wind-induced and/or earthquake-induced dynamic vibrations. The RMVDs are installed in lieu of existing steel moment connections, which occupies no additional architectural space. The system level damping of the steel moment frames could be increased from the viscoelastic segment of the RMVDs. Besides, the proposed damper exhibits passively adaptive performance. The energy dissipation mechanism of the RMVD could be easily shifted between the viscoelastic segment and fuse segment under different levels of inter-story drifts. The sacrificial fuse segment of the damper, which could be easily replaced after an earthquake event, provides ductile and stable performance when the inter-story drifts exceed a predefined threshold. The paper first presents a systemic investigation of the performance of viscoelastic material. Then, a series of dynamic experimental studies were carried out on the viscoelastic segment when subjected to input motions that feature different frequencies and magnitudes, providing a comprehensive overview of the damper performance. Furthermore, the numerical simulation of the damper is provided at the component level. Finally, a steel portal frame is simulated as a case study to present the structural performance with the dampers under static pushover loads. The result of the study shows that the energy dissipation capacity of steel moment frames could be improved throughout the implementation of such devices.

The paper presents a study on the seismic cross-aisle behaviour of drive-in steel storage racks obtained from full-scale shake table tests. The objectives of the study are to determine the natural frequency and damping from full-scale tests as well as the inelastic response of drive-in rack frames when subjected to seismic excitation including modes of vibration, 3D behaviour, base shear and damage propagation. Two different framing systems are considered in this study. One frame is fully braced in the cross-aisle direction with the diagonal braces extending from top to bottom, whereas the second frame is more flexible relying mainly on a portal frame type of stiffness and bending capacity of uprights in resisting the earthquake-induced actions. Different waveforms are used in the tests, obtained from actual ground motion records at various locations around the world. The paper also presents a comparison between the behavior of the two systems highlighting the key characteristics, advantages and disadvantages of each.

Inelastic design methods allow for larger application of loads on sections than elastic design methods, due to the redistribution of yield stress through the depth of the section. Sections that can reach the full plastic capacity and maintain it for sufficient rotation are considered applicable for plastic mechanism design, resulting in more economical structural solutions. Cold-formed steel channel sections are used extensively in portal frame structures in agricultural and light industrial/commercial applications, structures well suited to plastic design, however may currently only be designed elastically. To address this limitation in design standards, experimental and numerical analyses on the inelastic bending capacity of cold-formed channel sections are performed, and design rules to account for such behaviour are developed. Design rules are prepared using the hot-rolled steel specification methodology of classifying a section as compact, non-compact or slender (according to the Australian Standards) and Classes 1, 2, 3 and 4 (according to the European Standards). Proposals for the Australian standard are shown to provide accurate and reliable capacity predictions for cold-formed steel channel sections whose bending capacity exceeds the elastic limit.

Hybrid frames composed of steel, concrete and composite members are widely used to-date due to their structural efficiency and economy as alternatives to traditional bare steel system, especially in high-rise buildings. However, the present design of this structural form is both inconvenient and inconsistent as it needs several separated design codes for bare steel (BS), reinforced concrete (RC) and steel-concrete composite (SCC) elements. This paper proposes a second-order design method which requires only section capacity check without the need of using prescriptive formulae in different codes for various structural forms. The member-based design using linear analysis and the effective length assumption is replaced by the iterative second-order analysis. Using the Pointwise-Equilibrium-Polynomial (PEP) element, which allows for member P-δ effects and initial imperfections in conjunction with a robust nonlinear incremental-iterative procedure, the nonlinear response of individual members and the structural system is captured directly and used for structure resistance checks. The sectional failure surface method is introduced for member strength checking. In the generation of failure surfaces of the arbitrarily shaped cross sections, the stress distribution along the concrete component is considered by an equivalent stress block or a number of segments and the entire structural steel section will be meshed into fibres for determination of section capacity. Verifications of the proposed integrated analysis and design method based on section capacity check are conducted using several examples with accuracy of the method demonstrated.

This paper describes a study into the fire behaviour of steel portal frame buildings at elevated temperatures using the finite element programme SAFIR. The finite element analysis carried out in this report is three dimensional and covers different support conditions at the column bases, the presence of axial restraints provided by the end walls, different fire severities within the building, different levels of out-of-plane restraint to the columns and the effect of concrete encasement to the columns. From a large number of analyses, it is shown that the bases of the steel portal frames at the foundations must be designed and constructed with some level of fixity to ensure that the structure will deform in an acceptable way during fire, with no outwards collapse of the walls. The analyses also show that to avoid sidesway (i.e. collapse outwards) it is not necessary for steel portal frame columns to be fire-protected unless the designer wishes to ensure that the columns and the wall panels remain standing, during and after the fire.

Traditionally, the steel portal frame design assumes that beam-to-column joints are rigid or pinned. However, it is largely recognized that the great majority of joints do not exhibit such idealized behaviour transmitting bending moments with non-negligible rotations. These joints are called semi-rigid and their design should be performed according to their actual structural behaviour. When minor axis beam-to-column joints are considered, the adopted design process generally assumes a flexible response although this is not true for the great majority of structural joints. Minor axis joints present a distinct behaviour that differentiates them from major axis joints. In fact, the absence of transverse stiffeners implies that the column web must resist all the tensile and compressive forces arising from the beam flanges in bending, akin to a plate supported on its vertical sides. In order to evaluate this component’s behaviour, this paper presents a comparison between results obtained from a finite element model analysis and experiments. The experimental programme was based on the use of reflection photoelasticity techniques to determine the column web stress and strain distribution present in minor axis semi-rigid joints. This technique, although widely used for determining stress and strain distributions in other applications, was first used in this investigation to determine the semi-rigid joints structural response.

A series of tests were executed for H-shaped beams whose flanges were connected to end-plate by non-completely penetrated welds. The welds were designed by equal capacity rule and the beams were mainly composed of non-compact or slender elements. The parameters introduced are width–thickness ratios of beam flange and web, end-plate thickness, angle between flange plane and end-plate plane and so on. 24 pieces of specimens were tested to failure under monotonic loading and 6 under cyclic loading. For comparison, a few of the specimens are those with completely penetrated groove welds. Finite element (FE) analysis was also carried out to study the effect of parameter change on the resistance of the welds. The parameters involved end-plate thickness, weld size, column flange thickness and bolt gauge. The results show that thinner end-plate and greater bolt gauge will deteriorate the resistance of weld. As long as the components are properly designed, as done in tests, the connections will not fail at the welds no matter what kind of weld form is adopted. In addition, weld form has no obvious effect on the ultimate loads and cyclic behavior of specimens. It is confirmed that the non-completely penetrated welds connecting flanges of H-shaped beams and end-plates can be used both under static loading and seismic loading in low-rise building structure where local buckling of the member is the predominant factor.

Initial imperfection in bolted end-plate connections is mainly induced by residual deformation of welding. Three typical initial imperfections, namely V -shape, C -shape and W -shape are identified in terms of the geometrical imperfection shapes for extended bolted end-plate connections based on a field study. Seven specimens of extended bolted end-plate connection, among which six specimens with V -shape initial imperfection and one without imperfection in the end-plates were tested, and the influence of the initial imperfection of the end-plate on the behaviour of the connections was investigated. Test results show that initial rotation stiffness of extended bolted end-plate joints decreases with increase of initial imperfection in the end-plate, however, the strength of the end-plate joints is only affected slightly by the imperfection. Besides, the thicker the end-plate is, the more reduction in the initial rotation stiffness relatively. Further parametric study on 14 extended bolted end-plate connections with three typical shapes of imperfections were conducted based on the finite element analysis. Among the three types of initial imperfection, the V -shape has the least influence, and the C -shape has the biggest influence on the initial rotation stiffness of the extended bolted end-plate joints. For initial geometrical imperfection in a V -shape, its influence on behaviour of extended bolted end-plate connections is negligible as far as the imperfection is limited to the criterion, giving H / 300 . The influence of initial imperfection in a W -shape on rotation stiffness should be acceptable if the initial imperfection is limited to the criterion. In the case of a C -shape initial imperfection in the end-plate, its influence on the rotation stiffness would be substantial; even it satisfies the requirement of the imperfection limit. The results of the study should be applicable to the bolted end-plate connections, whether flushed or extended end-plate beam to column joints in structural frames.

This paper proposes an alternative construction system for composite portal frames. The proposed process uses a perfobond rib shear connector and a connection element, denominated “T-rib” for composite action. The “T-rib” connection element was developed with the aim of transferring the forces from the reinforcing bars, used in hogging moment regions, to edge and corner column flanges. Full-scale test results of a composite semi-rigid portal frame are presented in terms of load–deflection, load–deformation and load–rotation curves.

A theoretical and experimental investigation into the factors affecting the accuracy of beam-end connector tests showed that the flexibility of the stub beam used in the cantilever test can induce errors of up to 4% in the experimentally determined moment–rotation relationships. Appropriate correction equations are derived in this paper. The corrected moment–curvature equation was then used in an investigation into the sway behaviour of racking structures under a combination of point loads normal to the ground and with proportionally increasing side loads. The experimental tests used a mirror arrangement of two portal frames lying horizontally. During each test three cycles of loading and unloading were performed before the frame was taken to its ultimate load. Initially the bending moments on both beam-to-column joints had the same sign. The percentage of side load applied to the structure was chosen so that, due to the effect of frame geometry change, reversal of bending moments occurred in one of the joints during the test. The beam and column components of the frame were numerically modelled using stability functions. The beam–column connections were semi-rigid and the experimental moment–rotation curves were incorporated into the connection behaviour. Three different theoretical models were tested: a multi-linear model proposed by the authors and two bi-linear models produced according to the FEM and SEMA codes. The agreement between theory and experiment, for all load cases (including the unloading parts of the experimental cycles), was excellent for the multi-linear model. The FEM code model overestimated the sway deflections occurring in the rack but gave accurate predictions of joint moments and could be conservatively used in design. The SEMA code consistently underestimated the sway deflections and was unable to predict joint moment reversal. Once the theoretical model had been validated, a study was then undertaken into the behaviour of a two-bay portal frame structure.

The authors have recently described a cold-formed steel portal framing system in which simple bolted moment-connections, formed through brackets, were used for the eaves and apex joints. Such connections, however, cannot be considered as rigid because of localised in-plane elongation of the bolt-holes caused by bearing against the bolt-shanks. To therefore predict the initial stiffness of such connections, it is necessary to know the initial bolt-hole elongation stiffness kb. In this paper, a finite element solid idealisation of a bolted lap-joint in shear will be described that can be used to determine kb; the results obtained are validated against experimental data. A beam idealisation of a cold-formed steel bolted moment-connection is then described, in which spring elements are used to idealise the rotational flexibility of the bolt-groups resulting from bolt-hole elongation. Using the value of kb in the beam idealisation, the deflections predicted are shown to be similar to those measured experimentally in laboratory tests conducted on the apex joint of a cold-formed steel portal frame.

Methods for the elastic-plastic analysis of plane frames were developed in the 1960s, soon after the birth of the digital computer. Much of this early work was surprisingly sophisticated and, despite the passage of time, is still state-of-the-art and well worth re-visiting. In Europe, there is renewed interest in these methods of analysis motivated by the more stringent stability requirements of Eurocode 3 and the realisation that even the humble pitched-roof portal frame is surprisingly sensitive to second-order effects. This paper will review the current state of the art, comparing the influence coefficient and full iteration methods of elastic-plastic analysis and giving consideration to the problems of positioning plastic hinges below points of maximum bending moment in beams and the ‘false mechanism’ problem. Strain hardening in plastic hinges will also be considered together with the sensitive balance between strain hardening and second-order effects.

A simplified procedure for the analysis and optimum design of frames with rigid or flexible connections is presented. The procedure is based on the elastic analysis and the allowable stress design of AISC specifications. The analysis procedure is simplified by using the secant stiffness as the average connection stiffness to approximate the connection behaviour in the analysis. A computer program is developed to find the optimum design of flexibly-jointed frames, as well as rigidly-jointed frames. A predictor-corrector scheme is employed to arrive at the optimum design. The predicted design vector is expressed in terms of true member forces by an implicit scheme. Dynamic scaling and a unique process of step size reduction are employed on the predicted design vector to avoid bypassing an optimum during the search procedure. A portal frame numerical example is employed to compare the optimum design of a flexibly-jointed frame to that of the same frame when assumed to be rigidly-jointed. The comparison is accomplished through the graphical presentation of the constraints and the objective function contours of each case in the design space. The safety of approximating the analysis of flexible frames as rigid is discussed. The global optimum solution, which is always safe for rigid or flexible analysis, is also presented. All these points are also addressed when employing a larger frame example.

Experimental and analytical research on rafter-to-column joints of portal frames built up from cold-formed sections is presented. The haunched rafter was connected to the column by bolted end-plate connection. Two full-scale frame corners were tested, applying cantilever testing mode. Effects of different structural arrangements on the connection moment-rotation performance were investigated. The ultimate behaviour of the joints was determined. On the basis of the experimental results the connections were classified according to the international proposals. An analytical method was introduced for the prediction of the strength and stiffness of the connection. A combination of a finite element model and a mechanical model was used in two steps: the finite element model for the analysis of the T-stub element of the connection (local behaviour); and the mechanical model for the analysis of the moment-rotation relationship (global behaviour). Results of comprehensive studies are reported.

The steel construction code Eurocode-3 (EC3) presents major differences when compared to the current Spanish code EA-95. In this paper the authors try to analyze the differences and their importance on the analysis and design of planar multistory frames as well as pitched roof portal frames, commonly used for commercial and industrial buildings, respectively. A careful examination is made on the different ways that EC3 allows for the analysis of sway and non-sway frames, as well as a detailed comparison with EA-95 of the methods used for structural verification of the individual members. Finally, different design comparisons are made for standard multistory planar frames as well as a pitched roof portal frame.