Experiments on sheathed cold-formed steel studs in compression

The stability and strength of cold-formed steel lipped C-section columns (studs) with sheathing attached to the flanges is the subject of this paper. Stud configurations both with and without sheathing, either oriented strand board or gypsum board, are tested for failure in compression. A total of twenty-six tests covering short, intermediate and long specimens, varied sheathing configurations, and varied end boundary conditions are completed. Dimensions and geometric imperfections of the specimens are measured in detail. The measured geometric imperfections are reduced to scalar magnitudes consistent with local, distortional, and global buckling modes. During the testing, mid-height cross-section deformations are recorded using five position transducers. The deformations indicate the impact of the different combinations of sheathing, and of the end boundary conditions, on the strength and stability of the studs. Composite action between the stud and sheathing, and isolating direct loading of the sheathing, are shown to be significant in determining the strength and controlling limit state of the stud. Tested strengths are compared with existing North American (American Iron and Steel Institute) specification methods and potential improvements are explored.     

Design of steel sheathed cold-formed steel framed shear walls

A method for the design of steel sheathed cold-formed steel framed shear walls has been developed for inclusion in the American Iron and Steel Institute's North American standards for lateral design using a comprehensive database of single-storey shear wall tests carried out in Canada and in the United States. The wall configurations differed in terms of wall aspect ratio, framing and sheathing thickness, screw fastener schedule and framing reinforcement. The Equivalent Energy Elastic–Plastic (EEEP) analysis approach was used to derive key design information from the test data, including: nominal shear resistance, a resistance factor, an over-strength factor for capacity based seismic design and ‘test-based’ seismic force modification factors for ductility and over-strength.     

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.     

Steel sheathed cold-formed steel framed shear walls subjected to lateral and gravity loading

The design of steel sheathed cold-formed steel (CFS) framed shear walls is not addressed in Canadian design standards. A program of displacement based loading tests was carried out on single-storey shear walls of various configurations to investigate their performance and to establish a comprehensive database of information. The walls, which were subjected to lateral loading and combined lateral plus gravity loading, differed in sheathing thickness, screw fastener detailing, framing thickness, aspect ratio and framing reinforcement. The performance under loading was directly related to the sheathing connection pattern; however, when the framing elements were not blocked tension field forces resulted in significant damage to the chord studs. Details of the test program and general results are presented in this paper.     

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.     

Efficiency reduction due to shear lag on bolted cold-formed steel angles

This work presents 66 new experimental tests carried out on cold-formed steel angles fastened with bolts and under tension. In order to calculate tension-members’ ultimate capacity, net-section failure is considered. The shear-lag phenomenon reduces net-section capacity. This reduction is computed through the reduction coefficient which is a function of two parameters: length of the connection and distance of the shear plane to the centroid of the cross-section. This article examines the reduction coefficient performance based upon the new tests and data available in the literature, comprising a total of 108 lab tests. A new expression for the net-section reduction coefficient is suggested.     

Knowledge-based global optimization of cold-formed steel columns

Cold-formed steel member cross-section shapes are difficult to optimize because of the nonlinear behavior of such members under buckling loads. Traditional gradient-based optimization schemes, employing deterministic design specifications for the objective function, are inefficient and severely limited in their ability to search the full solution space of member cross-sections. Herein, a new global optimization approach that is well suited for optimization of such cross-sections is introduced. There are two distinguishing characteristics of this approach: (1) it operates within a low-dimensional expert-based feature space rather than the high-dimensional design space of cross-section parameters; and (2) it uses a numerical implementation of the direct strength method (DSM) for the objective function. Through the use of Bayesian classification trees, the most significant coordinates of the expert-based feature space are defined; these coordinates are of low dimension and are in terms of features which provide insight into structural behavior. The classification trees are then used to efficiently generate candidate member cross-section prototypes for subsequent refined local optimization.Optimization results are presented for three structurally distinguishable length regimes to provide proof-of-concept of the proposed scheme. It is demonstrated that an expert-based feature space and its associated classification tree can effectively encapsulate the knowledge gained in the design optimization process and can be subsequently used as a starting framework for related design optimization problems. This is, in essence, a highly efficient knowledge transfer mechanism that is absent in most optimization schemes. Optimization of thin-walled members stands to benefit greatly from the combination of more flexible and general design methodologies (e.g., the DSM) and novel, emerging, optimization schemes such as the one presented herein.     

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.     

Flexural behaviour and strength of cold-formed steel L-headers

Cold-formed steel headers are structural components used over wall openings in cold-formed steel residential and light commercial construction. Recently, there has been an increased interest in cold-formed L-headers among homebuilders primarily due to their ease of installation and low material cost. The findings from an extensive laboratory testing program, of full-scale single and double cold-formed steel L-headers are presented in this paper. The objective of the research was to investigate the flexural behaviour and strength of L-headers under both gravity and uplift loads. Based on the results improved ultimate strength design expressions and new deflection expressions for a wide range of L-header assemblies have been proposed.     

Experiments on cold-formed steel columns with holes

The objective of this paper is to observe and quantify the relationship between elastic buckling and the tested response of cold-formed steel columns with holes. Compression tests were conducted on 24 short and intermediate length cold-formed steel columns with and without slotted web holes. For each specimen, a shell finite element eigenbuckling analysis was also conducted such that the influence of the boundary conditions and the hole on local, distortional, and global elastic buckling response could also be captured. Slotted web holes may modify the local and distortional elastic buckling half-wavelengths, and may also change the critical elastic buckling loads. Experimentally, slotted web holes are shown to have a minimal influence on the tested ultimate strength in the specimens considered, although post-peak ductility is decreased in some cases. Tangible connections are observed between elastic buckling and load–displacement response during the tests, including mode switching between local and distortional buckling. The columns are tested with friction-bearing boundary conditions where the columns ends are milled flat and parallel, and bear directly on steel platens. These boundary conditions, which greatly speed specimen preparation, are determined to be viable for evaluating the tested response of short and intermediate length columns, although the post-peak response of intermediate length specimens must be considered with care.     

Modal analysis of cold-formed pallet rack structures with semi-rigid connections

The three dimensional (3D) model of conventional pallet racking systems were prepared using the finite element program ANSYS and free vibration modal analysis carried out on conventional pallet racks with the 18 types of column sections developed along with semi-rigid connection. The stiffness of the connector was tested using the conventional cantilever method and also using a double cantilever method. Non-linear finite element analysis of both the tests was carried out. From the experimental study on connection and finite element modal analysis, a simple analytical model that captures the seismic behavior of storage racks in their down aisle direction is proposed. The model is aimed at developing simplified equation for the fundamental period of storage racks in their down aisle direction. A parametric study was carried out to find out fundamental mode shape and time period. Finite element method is used for the accuracy and appropriateness of cold-formed steel frame.     

Inelastic performance of cold-formed steel strap braced walls

The inelastic performance of sixteen 2.44 m×2.44 m cold-formed steel strap braced walls was evaluated experimentally. The performance was affected by the holddown detail, which in many cases did not allow the test specimens to reach or maintain a yield capacity and severely diminished the overall system ductility. “Test-based” R_d×R_o values of 3.65, 2.11 and 1.72 indicate the low ductility levels, which were not adequate to warrant the use of a seismic response modification coefficient of R=4.0 in design. Capacity design of the SFRS elements must account for the overstrength of the strap material.     

Detailing recommendations for 1.83 m wide cold-formed steel shear walls with steel sheathing

The paper presents an experimental investigation on 1.83 m wide, 2.44 m high cold-formed steel (CFS) stud framed shear walls using steel sheet sheathing. Four wall configurations were studied through monotonic and cyclic tests. The test results indicated that besides the sheet buckling and screw pull out, the buckling of interior studs might occur for the 1.83 m CFS walls. To prevent the failure in the studs, special detailing was developed in this research. It was discovered that the special detailing could increase both the shear strength and the ductility of the shear walls. The research also found that the codified nominal shear strengths can be conservatively used for walls with an aspect ratio of 3:2. Based on the test results, the nominal seismic shear strength for 1.83 m wide CFS shear walls was established for design purposes.     

Monotonic shear tests of cold-formed steel wall frames with sheathing

This research is focused on the experimental study of the structural strength of cold-formed steel wall frames with sheathing under monotonic shear loading. Two aspect ratios, 1.0 and 2.0 were utilized in the design of wall specimens. Three different kinds of sheathing material, gypsum board, calcium silicate board, and oriented-strand board, with two different thicknesses (9 and 12 mm) were adopted in the test specimens. The ultimate strength, stiffness, energy absorption, and ductility ratio were studied for each test specimen. In final, the ductility ratios of the cold-formed steel wall frames similar to the wall configuration conducted in this study are proposed.     

Global optimum design of cold-formed steel hat-shape beams

Using the computational neural network model developed recently by the authors, a comprehensive parametric study is performed for global optimization of cold-formed steel hat-shape beams based on the AISI Specifications. Design curves are presented for global optimum values of the thickness, the web-depth-to-thickness ratio, and the flange width-to-thickness ratio for unbraced beams having steel yield strengths of 250 and 345 N/mm². The computational neural network model guarantees a local optimum solution. The global optimum is found by an exhaustive search that is guided by a heuristic approach to reduce the search effort. An extensive parametric study yielded insights into the behavior of cold-formed steel beams that are then used as rules to reduce the search space and guide the exhaustive search. The procedure for finding the global optimum design of cold-formed steel beams is presented in a few recursive steps. The optimum design curves presented in this article can be of great value to structural design engineers.     

Experimental investigation of cold-formed lean duplex stainless steel beam-columns

This paper describes a test program on cold-formed lean duplex stainless steel members in combined compression and minor axis bending. The test specimens were cold-rolled from flat strips of lean duplex stainless steel grade EN 1.4162. In this study, square and rectangular hollow sections were compressed at different eccentricities, in order to obtain a beam-column interaction curve for each series of tests. Initial overall geometric imperfections of the members were measured prior to testing. The ultimate loads and the failure modes of each specimen were obtained. The observed failure modes include local buckling, flexural buckling and interaction of local and flexural buckling. The test strengths obtained from this study and other available data were compared with the design strengths predicted by the American Specification, Australian/New Zealand Standard and European Code for stainless steel structures. It should be noted that these specifications do not cover the material of lean duplex stainless steel. Therefore, the suitability of the beam-column design rules in these specifications for lean duplex stainless steel is assessed in this study. Generally, these specifications are capable of predicting the beam-column strengths of the lean duplex stainless steel test specimens, and the design rules in the specifications are considered to be reliable. It is observed that the European Code generally provides quite conservative predictions for the beam-column specimens compared to the American Specification and Australian/New Zealand Standard predictions.     

Prediction of residual stresses and strains in cold-formed steel members

The objective of this paper is to provide an unambiguous mechanics-based prediction method for determination of initial residual stresses and effective plastic strains in cold-formed steel members. The method is founded on basic physical assumptions regarding plastic deformations and common industry practice in manufacturing. Sheet steel coiling and cross-section roll-forming are the manufacturing processes considered. The structural mechanics employed in the method are defined for each manufacturing stage and the end result is a series of closed-form algebraic equations for the prediction of residual stresses and strains. Prediction validity is evaluated with measured residual strains from existing experiments, and good agreement is shown. The primary motivation for the development of this method is to define the initial state of a cold-formed steel member for use in a subsequent nonlinear finite element analysis. The work also has impact on our present understanding of cold-work of forming effects in cold-formed steel members.     

Bending strength of hybrid cold-formed steel beams

For the purpose of determining the load-carrying capacity of cold-formed steel structural members, the effective width approach has been used. Since most studies were limited only to the structural members, which were assembled from the same material in a given section, this investigation was concentrated on a study of structural strength and behavior of hybrid cold-formed steel beams subjected dynamic loads. An investigation was also conducted to study the validity of effective design width formulas for the design of these specimens. The materials used in this study were 25 AK and 50 SK sheet steels. A total of 72 spot-welded closed-hat sections were tested under different strain rates. The results showed that the structural strengths including yield moment and ultimate moment of hybrid cold-formed steel beams increase with increasing strain rates. In the determination of the strength of hybrid sections, the effective cross-sectional area calculated on the basis of the dynamic yield stresses can be employed. A design procedure was also developed to compute the member strength of hybrid beams.     

Laser welded built-up cold-formed steel beams: Experimental investigations

The results of a research project aimed at designing and development a built-up cold-formed steel beam assembled by laser welding are described in this paper. The research activity was concerned with the evaluation of the applicability of laser welded connections to cold-formed members and with the assessment of the load bearing capacity of the assembled beams. With this aim, both lap-shear and U-tension tests were carried out on laser welds in order to assess the influence on connection strength of different parameters such as the gap between the steel sheets and the zinc coating. Finally, the load bearing capacity of laser welded built-up cold-formed members was investigated by four-point bending tests. Four full-scale prototypes were manufactured with different spacings of connections along the flanges in order to evaluate the effects of weld configuration on the load bearing capacity.     

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.