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This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the ‘pure bending’ stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress.

Open cross-section, thin-walled, cold-formed steel columns have at least three competing buckling modes: local, distortional, and Euler ~i.e., flexural or flexural-torsional ! buckling. Closed-form prediction of the buckling stress in the local mode, including interaction of the connected elements, and the distortional mode, including consideration of the elastic and geometric stiffness at the web/flange juncture, are provided and shown to agree well with numerical methods. Numerical analyses and experiments indicate postbuckling capacity in the distortional mode is lower than in the local mode. Current North American design specifications for cold-formed steel columns ignore local buckling interaction and do not provide an explicit check for distortional buckling. Existing experiments on cold-formed channel, zed, and rack columns indicate inconsistency and systematic error in current design methods and provide validation for alternative methods. A new method is proposed for design that explicitly incorporates local, distortional and Euler buckling, does not require calculations of effective width and/or effective properties, gives reliable predictions devoid of systematic error, and provides a means to introduce rational analysis for elastic buckling prediction into the design of thin-walled columns.

This research aims to identify and characterize the behavior of dissimilarly sheathed, load bearing, cold-formed steel studs under axial and lateral load. A series of tests on single studs, set in track, and sheathed with either oriented strand board, gypsum board, or combinations thereof are completed. The tests approximate the behavior of a sheathed stud within a larger wall. In each test, a predetermined level of axial load (or displacement) is introduced into the stud and lateral displacement (load) is then applied and increased until failure. This configuration results in axial load, bending, and (potentially) torsion on the stud. Observed failure modes for studs sheathed on only one face include torsion and/or fastener pull-through. For studs sheathed on both faces, failure modes include torsion, local buckling, fastener pull-through, and bearing (particularly for gypsum-sheathed studs). Analysis of the torsional response indicates the important role of the sheathing in limiting torsion and ...

The primary objective of this paper is to evaluate and compare design methods for locally slender steel columns. Three design methods utilized for such columns in the United States are explored: (1) the Q-factor method; (2) the unified effective width method; and (3) the direct strength method. The design strength formulas for locally slender W-section columns for all methods are provided in a common notation. The expressions highlight the prominent role of elastic local (cross-section) slenderness. A nonlinear shell finite-element analysis parametric study on short, intermediate, and long columns is conducted to explore the divergence in the design methods as a function of local slenderness. Recommendations for advancing the design methods are offered. In particular, based on the parametric study, an effective width method alternative is provided.

This paper characterizes mechanical properties of hollow sphere (HS) steel foam, and applies calibrated Deshpande–Fleck plasticity to mechanical simulations of steel foam components. Foamed steel, steel with internal voids, provides enhanced bending rigidity, exceptional energy dissipation, and the potential to mitigate local instability. The experimental characterization of the hollow sphere foam encompasses compressive yield stress and densification strain, compressive plastic Poisson’s ratio, compressive unloading modulus, as well as tensile elastic modulus, tensile unloading modulus, tensile yield stress, tensile fracture strain, and shear yield stress and fracture strain. Since HS steel foam is compressible under triaxial pressure, Deshpande–Fleck plasticity of compressible metals was calibrated and employed in simulations. Plastic Poisson’s ratio, measured in a uniaxial test, is an important metric of foam compressibility, and it affects the response of the foam to multi-axial loadings significantly. This work is part of a larger effort to help develop steel foam as a material with relevance to civil engineering applications.

The connections of welded steel moment frames undergo a complex multiaxial state of stress that leads to high levels of stress triaxiality. As triaxiality increases, the propensity for fracture increases. Classic engineering models of fracture and modern microscale models of fracture mechanisms explicitly consider the role of triaxiality. Nonetheless, triaxiality is generally not directly considered by structural engineers. In this paper, triaxiality is defined as the ratio of the maximum principal stress to the von Mises stress. Triaxiality and maximum principal stress demands are investigated for tests on fractured notched round bars, small-scale tension specimens, and a full-scale moment connection. Based on analysis of the tests, it is proposed that, for fractures driven by triaxiality demands, the maximum principal stress at fracture is a function of the level of triaxiality. Calculation of the triaxiality demands requires 3D nonlinear analysis and depends on the loading, connection geometry, and pos...

Thin-walled cold-formed steel members have wide applications in building structures. They can be used as individual structural framing members or as panels and decks. In general, cold-formed steel beams have open sections where centroid and shear center do not coincide. When a transverse load is applied away from the shear center it causes torque. Because of the open nature of the sections, torsion induces warping in the beam. This paper summarizes the research on the behavior of cold-formed steel beams subject to torsion and bending. The attention is focused on beams subject to torque, because of the effect of transverse loads not applied at the shear center. A simple geometric nonlinear analysis method, based on satisfying equilibrium in the deformed configuration, is examined and used to predict the behavior of the beams. Simple geometric analyses, finite element analyses and finite strip analyses are performed and compared with experimental results. The influence of typical support conditions is studied and they are found to produce partial warping restraint at the ends. This effect is accounted for by introducing hypothetical springs. The magnitude of the spring stiffness is assessed for commonly used connections. Other factors that affect the behavior of cold-formed steel members, such as local buckling, are also studied.

The moment capacity of a laterally braced cold-formed steel flexural member with edge stiffened flanges (e.g., a channel or zee section) may be affected adversely by local or distortional buckling. New procedures for hand prediction of the buckling stress in the local and distortional mode are presented and verified. Numerical investigations are employed to highlight postbuckling behavior unique to the distortional mode. Compared with the local mode, the distortional mode is shown to have (1) heightened imperfection sensitivity, (2) lower postbuckling capacity, and (3) the ability to control the failure mechanism even in cases when the elastic buckling stress in the local mode is lower than in the distortional mode. Traditional design methods do not explicitly recognize distortional buckling, nor do they account for the observed phenomena in this mode. A new design method that integrates distortional buckling into the unified effective width approach, currently used in most cold-formed steel design specifications, is presented. For each element a local buckling stress and a reduced distortional buckling stress are compared to determine the effective width. Comparison with experimental tests shows that the new approach is more consistent and reliable than existing design methods.

A new procedure for calculating the effective width of stiffened elements with multiple longitudinal intermediate stiffeners is presented. The method determines the critical stress for distortional buckling of the entire stiffened element as a unit, and local buckling of the subelement plates between stiffeners. Approximate expressions for calculating distortional buckling are verified via comparison to numerical methods. The effective width of the element is determined using Winter's equation based on the governing buckling stress. Reduced postbuckling capacity in the distortional mode is considered. Comparison to experimental data and numerical analysis shows the resulting method is a reliable predictor of the flexural capacity of cold-formed steel members with multiple longitudinal intermediate stiffeners in the compression flange.

Thin-walled, cold-formed steel members exhibit a complicated post-buckling regime that is difficult to predict. Today, advanced computational modeling supplements experimental investigation. Accuracy of computational models relies significantly on the characterization of selected inputs. No consensus exists on distributions or magnitudes to be used for modeling geometric imperfections and for modeling residual stresses of cold-formed steel members. In order to provide additional information existing data is collected and analyzed and new experiments performed. Simple rules of thumb and probabilistic concepts are advanced for characterization of both quantities. The importance of the modeling assumptions are shown in the examples. The ideas are summarized in a preliminary set of guidelines for computational modeling of imperfections and residual stresses.

The statistical characteristics (mean and variance) of the ultimate strength of cold-formed steel plates in uniform compression and pure bending are calculated and compared to deterministic approximations. Three quantities: plate thickness, longitudinal flexural residual stress magnitude and first mode imperfection magnitude, are treated as random variables. Based on existing experimental data, appropriate probability distributions are determined for the three random variables. The ultimate strength calculations are performed numerically using the finite element method (FEM). The statistical characteristics are calculated using two methods: Monte Carlo simulation and Taylor series approximation. The results are compared to the deterministic design approach of the American Iron and Steel Institute (AISI) Specification for the design of cold-formed structural members.

The behavior and design of cold-formed steel sections with single and multiple intermediate stiffeners in the compression, flange is investigated. Existing experimental data are used to evaluate critically the AISI specification and Eurocode. For bending strength prediction of sections with multiple intermediate stiffeners, the AISI specification can be quite unconservative and Eurocode often Yields overly conservative results. Existing experimental data are used to calibrate a finite element model. An extensive parametric study is conducted using the finite element model. The results of the study are used to gain a better understanding of the behavior of these elements, and to help evaluate alternatives to the existing design procedures. Based on the existing data and the finite element stud two alternatives to the existing strength prediction procedures are advanced.

In eukaryotic cells the actin-cytoskeletal network provides stiffness and the driving force that contributes to changes in cell shape and cell motility, but the elastic behavior of this network is not well understood. In this paper a two dimensional form-finding model is proposed to investigate the elasticity of the actin filament network. Utilizing an initially random array of actin filaments and actin-cross-linking proteins the form-finding model iterates until the random array is brought into a stable equilibrium configuration. With some care given to actin filament density and length, distance between host sites for cross-linkers, and overall domain size the resulting configurations from the form-finding model are found to be topologically similar to cytoskeletal networks in real cells. The resulting network may then be mechanically exercised to explore how the actin filaments deform and align under load and the sensitivity of the network's stiffness to actin filament density, length, etc. Results of the model are consistent with the experimental literature, e.g. actin filaments tend to re-orient in the direction of stretching; and the filament relative density, filament length, and actin-cross-linking protein's relative density, control the actin-network stiffness. The model provides a ready means of extension to more complicated domains and a three-dimensional form-finding model is under development as well as models studying the formation of actin bundles.

The Dallas Cowboys Practice Facility (DCPF) was a large, fabric-covered, lightweight steel truss structure that collapsed in May 2009. News coverage of the event was quick to identify high winds as the cause of the failure, but in reality, there were a number of design errors which caused failure of the structure in winds far less severe than the nominal design wind speed. This paper presents the results of our failure investigation, including a comparison of the wind loads used in the original design to the provisions of ASCE 7, an analysis of the strength of the steel trusses, and the results of a 3D finite element model of the structure including the outer fabric covering. Portions of the original design that did not meet accepted codes and standards are highlighted and discussed. Based on these results and photographs of the collapsed structure, a likely initial failure mechanism and progressive collapse sequence is proposed. The results of our analysis and proposed failure sequence are compared to the investigation performed by the National Institute of Standards and Technology (NIST). Based on the design errors identified by both investigations, recommendations related to the design of lightweight fabric-covered structures are made. BACKGROUND AND HISTORY The Dallas Cowboys Practice Facility was a large, fabric-covered steel structure approximately 204 ft x 406 ft in plan. Although described by some reports as a “tent” structure, the main vertical and lateral structural system of the facility was a series of steel trusses, which were made up of several prefabricated segments that were assembled in the field. Trusses were spaced 15 ft on center along the length of the structure, and were supported on caissons connected by grade beams. Truss chord members were cold-formed, 5 in.-diameter circular HSS, and web members were hotrolled single and double 3x3 angles. In the direction perpendicular to the ridge, lateral resistance was provided by the trusses. In the direction parallel to the ridge, lateral resistance was provided by a purlin and sway cable system. A structural plan of the facility and an elevation of one of the trusses is shown in Figure 1.

The Direct Strength Method is an entirely new design procedure for cold-formed steel member design, and was formally adopted into AISI Standards (AISI-S100-07). The method integrates computational determination of cross-section stability and maps the stability to appropriate limit states for design in a highly compact and efficient format. This new design method does not rely on effective width and is able to provide a consistent design methodology for general cold-formed steel cross-sections. This workshop on the Direct Strength Method provides attendees with (a) background and examples, (b) the latest advances including members with holes, and (c) an industry perspective for a company utilizing the method in new product development.

The asymmetry of a bevel-tip needle results in the needle naturally bending when it is inserted into soft tissue. In this study we present a mechanics-based model that calculates the deflection of the needle embedded in an elastic medium. Microscopic observations for several needle- gel interactions were used to characterize the interactions at the bevel tip and along the needle shaft. The model design was guided by microscopic observations of several needle- gel interactions. The energy-based model formulation incor- porates tissue-specific parameters such as rupture toughness, nonlinear material elasticity, and interaction stiffness, and needle geometric and material properties. Simulation results follow similar trends (deflection and radius of curvature) to those observed in macroscopic experimental studies of a robot- driven needle interacting with different kinds of gels. These results contribute to a mechanics-based model of robotic needle steering, extending previous work on kinematic models.

The objective of this paper is to provide analytical expressions for the elastic cross-section local buckling stress, including element interaction, of hot-rolled steel structural shapes. The cross-section local buckling stress is determined by finite strip analysis. Local stability of each cross-section is considered in axial compression, as well as positive and negative bending about the major and minor axis. All sections in the AISC shapes database are considered, with the exception of pipe sections. The local buckling stresses are converted into plate buckling coefficients ( k 's) and simplified expressions provided for all observed k 's. The plate buckling coefficients ( k 's) from the finite strip analysis are also compared to the values inherently assumed in the AISC Specification. Significant differences between assumed (AISC) and calculated k values are observed.

This paper demonstrates how to decompose general stability solutions into useful subclasses of buckling modes through formal definition of the mechanical assumptions that underlie a class of buckling modes. For example, a thin-walled lipped channel column as typically used in cold-formed steel can have its buckling mode response decomposed into local, distortional, global, and other (transverse shear and extension) modes. The solution is performed by writing a series of constraint equations that are consistent with the mechanical assumptions of a given buckling class. The mechanical assumptions that defined the buckling classes were determined so as to be consistent with those used in Generalized Beam Theory (see e.g., Silvestre and Camotim 2002a,b) The resulting constraint equations may be used to constrain the solution before analysis, and thereby provide the opportunity to perform significant model reduction, or may be employed after the analysis to identify the buckling classes that participate in a given buckling mode. This paper shows the framework for this process in the context of the finite strip method (building off of Adany and Schafer 2004, 2005a,b) and discusses some of the interesting outcomes that result from the application of this approach. Of particular interest, and discussed here, is the definition of global buckling modes, and the treatment of members with rounded corners — each of which provide certain challenges with respect to traditional definitions of the buckling classes. Examples are provided to illustrate the technique and challenges. The long-term goal of the work is to implement the procedures in general purpose finite element codes and thus enable modal decomposition to become a widely available tool for analyzing thin-walled member cross-section stability.

Actin-crosslinking proteins organize actin filaments into dynamic and complex subcellular scaffolds that orchestrate important mechanical functions, including cell motility and adhesion. Recent mutation studies have shown that individual crosslinking proteins often play seemingly non-essential roles, leading to the hypothesis that they have considerable redundancy in function. We report live-cell, in vitro, and theoretical studies testing the mechanical role of the two ubiquitous actin-crosslinking proteins, alpha-actinin and fascin, which co-localize to stress fibers and the basis of filopodia. Using live-cell particle tracking microrheology, we show that the addition of alpha-actinin and fascin elicits a cell mechanical response that is significantly greater than that originated by alpha-actinin or fascin alone. These live-cell measurements are supported by quantitative rheological measurements with reconstituted actin filament networks containing pure proteins that show that alpha-actinin and fascin can work in concert to generate enhanced cell stiffness. Computational simulations using finite element modeling qualitatively reproduce and explain the functional synergy of alpha-actinin and fascin. These findings highlight the cooperative activity of fascin and alpha-actinin and provide a strong rationale that an evolutionary advantage might be conferred by the cooperative action of multiple actin-crosslinking proteins with overlapping but non-identical biochemical properties. Thus the combination of structural proteins with similar function can provide the cell with unique properties that are required for biologically optimal responses.

The organization of filamentous actin (F-actin) in resilient networks is coordinated by various F-actin cross-linking proteins. The relative tolerance of cells to null mutations of genes that code for a single actin cross-linking protein suggests that the functions of those proteins are highly redundant. This apparent functional redundancy may, however, reflect the limited resolution of available assays in assessing the mechanical role of F-actin cross-linking/bundling proteins. Using reconstituted F-actin networks and rheological methods, we demonstrate how alpha-actinin and fascin, two F-actin cross-linking/bundling proteins that co-localize along stress fibers and in lamellipodia, could synergistically enhance the resilience of F-actin networks in vitro. These two proteins can generate microfilament arrays that "yield" at a strain amplitude that is much larger than each one of the proteins separately. F-actin/alpha-actinin/fascin networks display strain-induced hardening, whereby the network "stiffens" under shear deformations, a phenomenon that is non-existent in F-actin/fascin networks and much weaker in F-actin/alpha-actinin networks. Strain-hardening is further enhanced at high rates of deformation and high concentrations of actin cross-linking proteins. A simplified model suggests that the optimum results of the competition between the increased stiffness of bundles and their decreased density of cross-links. Our studies support a re-evaluation of the notion of functional redundancy among cytoskeletal regulatory proteins.

Cold-formed steel structures are the theme of this month’s special issue of the Journal. The majority of the papers appearing are from the Seventeenth International Specialty Conference on ColdFormed Steel Structures, which was held in Orlando, Florida in October of 2004. This biannual conference, which is an important forum for research and practice exchange in the field, is ably organized by Professor Roger LaBoube of the Center for ColdFormed Steel Structures at the University of Missouri-Rolla. This issue provides expanded versions of the most highly regarded papers from this conference as selected by the members of the ASCE-SEI Committee on Cold-Formed Steel of the TAC on Metals. The Committee on Cold-Formed Steel also performed nearly all of the paper reviews. Committee members include R. LaBoube, J. Fisher, W. Kile, J. Larson, G. Polard, T. Sputo, W. Easterling, H. Salim, R. Serrette, W. Allen, B. Schafer, R. Lindenberg, T. Roecker, L. Xu, N. Rahman, E. Di Girolamo, and C. Rogers.

Corrigendum to “Steel foam for structures: A review of applications, manufacturing and material properties” [Journal of Constructional Steel Research 71 (2012) 1–10] B.H. Smith , S. Szyniszewski , J.F. Hajjar , B.W. Schafer ⁎, S.R. Arwade a a Dept. of Civil & Env. Engg. University of Massachusetts, Amherst, MA 01003, USA b Dept. of Civil Engg., Johns Hopkins University, Baltimore, MD 21218, USA c Dept. of Civil & Env. Engg., Northeastern University, Boston, MA 02115, USA

This paper discusses the various design methods for sheathed walls framed from cold‐formed steel studs proposed by the American Iron and Steel Institute (AISI) since 1962. The discussion focuses on the development the equations used in the design methods, and aims to establish an understanding of the assumptions and simplifications employed. Special attention is given to the “2a” rule used since AISI (1962). The 2a rule prescribes that the buckling length of a sheathed stud shall be equal to twice the distance between fasteners (2a), in order to consider a missing fastener. A reliability study is used herein to evaluate the 2a rule, which is shown to lead to conservative strength predictions. Resistance factors are proposed as a more rational choice to take account of ineffective fasteners or construction flaws.

Cold-formed steel design can be a complicated and tedious process. Extensive use of unsymmetric sections, local buckling considerations that require iterative methods even for determining simple section properties such as moment of inertia, and numerous other complications tends to thin the ranks of those willing to design in cold-formed steel. Three recently published books on cold-formed steel design aim to explain the underlying behavior of these unique members and provide insight on the methods used in their design. With the recent publication of three up-to-date textbooks, now is a unique time to compare and contrast the available resources for engineers and educators interested in coldformed steel design. The standard-bearer is, and continues to be, W. W. Yu’s ColdFormed Steel Design ~2000, Wiley, New York!. Now in its 3rd edition with over 750 pages of text and 1,3001 referenced works, this is the definitive source. G. J. Hancock, T. M. Murray, and D. S. Ellifritt’s contribution to the field is Cold-Formed Steel Structures to the AISI Specification ~2001, Marcel Dekker, New York!. This book includes additional insight on elastic buckling behavior using numerical methods ~not in Yu’s text! and provides a compact, yet still complete, presentation of the key issues relevant to modern cold-formed steel design. The most recent addition is A. Ghersi, R. Landolfo, and F. M. Mazzolani’s Design of Metallic Cold-Formed Thin-Walled Members ~2002, Spon, London!. This book is unique from the other two in that it covers European and American design codes for cold-formed steel, and in part, for aluminum. However, the presentation is terse, with only 150 pages of text. Yu’s Cold-Formed Steel Design is presented in 14 chapters, the first 7 of which cover basic member design: compression members, flexural members, beam-columns, and material behavior. Local buckling, effective width, and other issues pertinent to cold-formed steel design are fully discussed and presented. Use of the AISI Specification, both ASD and LRFD, are fully integrated into the text with appropriate design examples. Connections are covered in Chapter 8 and specific details necessary for successfully bolting, screwing, or welding thin-walled steel components together are discussed and design examples given. The first 8 chapters summarize the theory and design methodology for conventional cold-formed steel member design and connection. The remaining 5 chapters of Yu’s text moves into application specific areas and miscellaneous topics. The application areas covered include composite-reinforced concrete-steel decking, and residential construction. These chapters are short, but have excellent reference lists. A chapter on metal buildings is surprisingly absent. However, most aspects of cold-formed steel design, as it

The North American construction industry has seen substantial growth in the use of cold-formed steel (CFS) framing for midrise buildings in recent years. In seismic zones, CFS-framed buildings utilize shear walls to provide the primary lateral resistance to earthquake induced loads. Although oriented strand board (OSB) and plywood panels have been traditionally used as the sheathing material for these essential components, more recently, steel sheet sheathing has emerged as a novel strategy due to its strength, ductility, ease of installation, and use of noncombustible material, among other benefits. To address the paucity of data regarding CFS-framed shear wall response within actual wall lines of buildings, a two-phased experimental effort was conducted. Wall-line assemblies were fabricated and tested with shear walls placed in-line with gravity walls. The shear walls chord stud packs include tie-rod assemblies consistent with multi-story detailing. Specimens were either unfinished or finished, and the shear walls were laid out in a symmetrical or unsymmetrical fashion within in the wall line. In addition, both Type I and Type II shear wall and anchorage detailing were investigated. In this paper, the impact of test variables governing the structural detailing of CFS-framed walls are quantified through dynamic and quasi-static tests, and a companion paper presents findings regarding the impact of architectural variations on seismic performance., (c) 2022 American Society of Civil Engineers.

In this paper the generalization of the constrained finite strip method (cFSM) is discussed. cFSM is a special version of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanics, e.g., to allow buckling only in flexural, lateral–torsional, or a distortional mode. In the original cFSM only open cross-section members are handled, here the method is extended to cover any flat-walled member, including those with closed cross-sections or cross-sections with open and closed parts. Moreover, in the original cFSM only 4 deformation classes are defined, here the deformation field is decomposed into additional, mechanically meaningful, sub-fields. Formal mechanical criteria are given for the deformation classes, and implementation of the criteria regardless of cross-section topology is illustrated. In this paper, the primary deformation classes are presented in detail. Primary deformations are associated with minimal cross-section discretization, i.e. nodal lines located at folds and ends only. This paper is accompanied by a companion, where secondary modes and additional practical aspects in the selection of base vectors for the deformation classes are discussed. With the proposed modifications the powerful cFSM capabilities of buckling mode decomposition and identification are extended to essentially arbitrary thin-walled cross-sections.

Performance-based fire design for cold-formed steel systems is in its infancy. This paper brings together existing research on cold-formed steel materials, members, and assemblages at elevated temperatures; and complementary analysis and design methods necessary for the development of analysis-based design for cold-formed steel systems under fire. Cold-formed steel systems have become popular in building construction as both load-bearing and non-load-bearing elements, primarily due to their high strength-to-weight ratio and ease of construction. Consequently, design specifications, and structural analysis tools have rapidly evolved to facilitate engineering design of these complex thin-walled members. However, in fires the performance of cold-formed steel systems are assured by prescriptive detailing and standardized testing. Today, engineering knowledge is rapidly advancing, providing the opportunity to contemplate analysis-based design as an enabling tool for general performance-based fire engineering of cold-formed steel systems. The review provided here includes experimental results on mechanical and thermal properties of cold-formed steel and temperature dependent constitutive relations, subsystem testing and computational simulations, and analysis models and exploratory methods for fire design, i.e., the building blocks towards performance-based fire design for cold-formed steel systems.