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In the presence of softening section constitutive relations, classical beam theories predict erroneous strain singularities, and the corresponding force/flexibility-based (FB) beam-column element formulations result in strain localization and loss of response objectivity, i.e., divergence, rather than convergence, with progressive mesh refinements. To address this challenge, various FB element formulations have been proposed in the literature. One of these formulations is the so-called "gradient inelastic" (GI) FB formulation, which is a two-node element formulation that eliminates the strain localization and achieves response objectivity through strain gradient nonlocality relations. Although a single two-node GI element can effectively simulate an entire beam or column, simulating such a member via multiple two-node GI elements in series (e.g., to apply intermediate point loads, to more accurately capture geometric nonlinearities, or to represent cross-section variation) would not lead to accurate response predictions. This is because, in a model with multiple two-node GI elements in series, the nonlocality relations are not enforced at the intermediate/connection nodes between adjacent elements. Instead, end member boundary conditions (BCs) are enforced at those connection nodes because the two-node GI formulation has been designed to simulate an entire member. To tackle this shortcoming, this paper proposes an innovative multinode GI FB element formulation. To enforce the nonlocality relations at the connection nodes, two different sets of mathematically admissible section strain compatibility conditions (CCs) are adopted. The multinode formulations using both sets of CCs are evaluated through several simulation examples, including beams and columns subjected to various loads. The evaluations demonstrate the ability of both element formulations to produce objective softening responses, while one set of CCs is found to more closely predict the responses of previously tested RC beams under midspan loading. [ABSTRACT FROM AUTHOR]

The present paper deals with the optimal design of nonprismatic beams, i.e., beams with variable cross section. To set the optimization problem, Euler-Bernoulli unshearable beam theory is considered and the elastica equation expressing the transverse displacement as a function of the applied loads is reformulated into a system of four differential equations involving kinematic components and internal forces. The optimal solution (in terms of volume) must satisfy two constraints: the maximum Von Mises equivalent stress must not exceed an (ideal) strength, and the maximum vertical displacement is limited to a fraction of beam length. To evaluate the maximum equivalent stress in the beam, normal and shear stresses have been considered. The former was evaluated through the Navier formula, and the latter through a formula derived from Jourawsky and holding for straight and untwisted beams with bisymmetric variable cross sections. The optimal solutions as function of material unit weight, maximum strength, and applied load are presented and discussed. It is shown that the binding constraint is usually represented by the maximum stress in the beam, and that applied load and strength affect the solution more than material unit weight. To maintain the generality of the solution, the nondimensionalization according to Buckingham Π -theorem is implemented and a design abacus is proposed. [ABSTRACT FROM AUTHOR]

Due to the strength reduction at the bent corners of fiber-reinforced polymer (FRP) stirrups, the high tensile strength of FRP reinforcement cannot be fully utilized in concrete structures. Although numerous experimental investigations have been conducted to study the reduced bent-corner strength, the mechanism of the strength reduction at bent corners has not been fully understood. This paper presents numerical research into the bent-corner strength of FRP stirrups with rectangular cross sections. Refined finite-element models are established based on Hashin's failure criterion and their validities are verified against six groups of 18 FRP stirrup specimens. Analyses of stress concentration in the elastic range and damage accumulation afterward are conducted to explain the mechanism of strength reduction at the bent corners of FRP stirrups. Further parametric analyses are conducted to quantitatively evaluate the contributing factors to the bent-corner strength and an empirical prediction equation is proposed. This research shows that the bond, compressive stress from concrete, and FRP material anisotropy are the critical contributors to the tensile stress concentration in the elastic range at the bent corners, which accounts for 7%, 48%, and 45% of the tensile stress concentration, respectively. The parametric analyses show that better bonding at the bent corners could potentially result in lower strength; the concrete properties and FRP width have limited influence on the bent-corner strength; and the bent-corner strength has logarithmic relation with the bent radius and thickness ratio of (R/t). This work reveals the critical mechanism of strength reduction of FRP stirrups at bent corners in concrete structures and potentially provides the opportunity for more efficient material use of FRP reinforcement. [ABSTRACT FROM AUTHOR]

Rebar buckling and fracture have been experimentally observed to cause significant degradation of the mechanical properties of reinforced concrete (RC) elements and should be accounted for in the analysis of RC structures. While data on the material properties of steel rebar are widely available, test data on rebar buckling remain scarce. This paper proposes a macromechanical model capable of predicting rebar buckling responses solely on the basis of steel material properties and the rebar geometry, even when rebar buckling experimental data are not available. This is achieved by computationally building the uniaxial stress-strain constitutive response at each analysis step through the equilibrium in the deformed configuration of the buckled rebar and through the cross-sectional constitutive response. The equilibrium in the deformed configuration is treated in a manner consistent with the corotational formulation, while the cross-sectional constitutive response is built through integration of a uniaxial damage plasticity model over the cross-section area. Rebar buckling is triggered by an initial imperfection, while low-cycle fatigue effects are reproduced through the uniaxial damage plasticity steel material model, without the need for cycle-counting algorithms. The proposed model is translated to a computer code, calibrated to a set of experimental data, validated to separate test data, and subsequently used in the analysis of an experimentally studied RC column that experienced rebar buckling under cyclic loading. Using the proposed model, the analysis captured the response of the RC column and the experimentally observed strength deterioration due to rebar buckling. [ABSTRACT FROM AUTHOR]

With the increasing demand for vertical isolation in the engineering field, the compressive behavior of low–shape factor (LSF) lead-rubber bearings (LRBs) needs to be further explored. However, the conventional simulation method of lead boundary conditions cannot accurately capture the actual compressive behavior of LSF bearings. Some scientific literature has reported this, but there is a lack of detailed studies to explain it. By comparing the experimental data and numerical simulation results of LSF bearings, the problem of this research is put forward. Thus, a refined numerical simulation method of lead boundary conditions is proposed in this paper based on the manufacturing process of LRBs. Assumed contact types, friction coefficients, and filling ratios of the lead plug are considered as variables of lead boundary conditions. The first shape factor and lead plug diameter are considered bearings variables. The compressive behavior of LRBs, including stiffness, deformation, and stress–strain distribution, are discussed through detailed analysis. The main study results indicate that contact types and filling ratios of lead plugs have a significant influence on the compressive behavior of LSF bearings, and the friction coefficient is negligible. The proposed refined simulation method is capable of capturing LRBs' mechanical behavior with better accuracy than the conventional model under different stresses, especially LSF bearings. However, the conventional numerical modeling method is recommended for LRBs with high shape factors (e.g., 30–50). Finally, an empirical formula is established based on refined simulation results. [ABSTRACT FROM AUTHOR]

Application of fiber-reinforced polymer (FRP) composites in the strengthening of reinforced concrete (RC) structures has become an increasingly accepted engineering practice. In particular, the use of externally bonded FRP wraps as a confining material for concrete can enhance both the compressive strength and the ultimate strain of concrete, making it suitable for strengthening and/or seismic retrofit of existing RC columns. This paper focuses on a recently developed analysis-oriented iterative FRP-and-steel confinement model for concrete and proposes a new optimization procedure to obtain an analytical expression for the corresponding monotonic envelope, reduce the associated computational cost, and increase the corresponding numerical robustness. Several analytical functions were evaluated in terms of their capability to fit the iteratively-generated stress-strain monotonic envelope for confined concrete. The newly proposed analytical formulation of the confined concrete stress-strain model was compared with the original iterative formulation in terms of computational cost for two examples of nonlinear seismic response analyses for: (1) an experimentally-tested concrete-filled FRP tube bridge column of a two-column bridge pier; and (2) a five-span bridge structure with FRP-retrofitted RC piers. It is found that the use of the newly proposed optimization-based analytical monotonic envelope can reduce by more than 30% the computational time associated with the original iteration-based monotonic envelope with negligible changes in the structural response prediction at both global and local levels. [ABSTRACT FROM AUTHOR]

Stiffness modifiers are used in linear structural analysis programs to recognize the low-strain amplitude nonlinear material stress–strain response and support the design of reinforced concrete structures. For example, stiffness modifiers are used to account for the reduction in stiffness that results mainly from crack development and propagation, bar bond slip between cracks, and bar bond slip of the longitudinal reinforcement developed beyond the column ends. This paper presents a primarily mechanistic model to compute the stiffness modifiers for reinforced concrete rectangular columns to support the seismic design of reinforced concrete structures. The model accounts for five modes of deformation found in columns and is calibrated against a database of test results reported in the literature on 38 large-section columns that exhibited ductile response. The paper also describes a simplified equation for use in seismic design. The simplified equation was calibrated through an extensive parametric analysis of the model. The mean, median and coefficient of variation of the ratios of the stiffness modifiers computed from the recorded response of test columns and the model output were 1.02, 1.00, and 0.18, respectively, and those calculated by the simplified equation for the same ratios were 0.95, 0.98, and 0.18, respectively. [ABSTRACT FROM AUTHOR]

As inelastic design for wind is embraced by the engineering community, there is an increasing demand for computational tools that enable the investigation of the nonlinear behavior of wind-excited structures and subsequent development of performance criteria. To address this need, a probabilistic collapse assessment framework for steel structures is proposed in this paper. The framework is based on the integration of a high-fidelity fiber-based nonlinear structural modeling environment with a wind-tunnel-informed stochastic wind load model to perform nonlinear time history analysis. General uncertainty is propagated using a stratified sampling scheme enabling the efficient estimation of reliabilities associated with rare events. The adopted models for simulating high-fidelity nonlinear structural behavior were found, in general, to be adequate for capturing phenomena, including progressive yielding, buckling, and low-cycle fatigue, that are essential for wind induced collapse analysis. In particular, the adopted fatigue model was found to be capable of predicting damage and potential fiber/section fracture associated with non–fully reversing stress-strain cycles that are characteristic of wind loading. Through illustration on a 45-story archetype steel building, critical discussions on the types of observed collapse mechanisms, the difference between along-wind and across-wind nonlinear behavior, reliabilities associated with first yield, and collapse are presented. A probabilistic description of the residual and peak story drifts is also provided through development of fragility functions. [ABSTRACT FROM AUTHOR]

There is no doubt that the strength and ductility of concrete structures can be enhanced significantly by lateral confining with steel or fiber reinforced polymer (FRP). Nevertheless, studying the mechanical response of eccentrically loaded confined concrete has received little attention compared to the study of a concentrically loaded concrete structure. To achieve a better fundamental understanding of the mechanical behavior of eccentrically loaded concrete under nonuniform confinement, an experimental study with analytical modeling was conducted in this work. A total of 100 concrete cubic specimens were tested with eccentric loadings and various lateral confinements from a fabricated apparatus that can simulate and generate passive confining pressure. Furthermore, this study successfully extended a well-established stress-strain model, originally proposed for eccentrically loaded FRP-confined circular concrete columns, to nonuniformly confined concrete cubes. The applicability and modification of this eccentricity-based model are verified and developed with the test results in this work. This paper concluded that there is good accuracy and agreement between the theoretical predictions and test results. [ABSTRACT FROM AUTHOR]

Reinforced concrete (RC) structures are subjected to combinations of axial, shear, flexure, and torsional loading during an earthquake event. Comprehensive understanding of the behavior of shear panels is essential to predict the response of members under combined loading. This work focuses on the analytical modeling of RC shear panel elements. A baseline fixed strut-angle model (FSAM) was initially proposed for the shear behavior of RC panel elements, satisfying the three basic principles of mechanics: stress equilibrium, strain compatibility, and material constitutive behavior. The FSAM was later modified to consider the effect of dowel action and aggregate interlock through empirical relationships. Use of modified FSAM formulations for the estimation of the monotonic response of shear panels with different reinforcement ratios in longitudinal and transverse directions leads to loss of convergence after yielding of the transverse reinforcement. Thus, an accurate estimation of postyield response is not possible using the existing FSAM, which is critical for seismic design. This paper presents an improved algorithm for FSAM by employing experimentally validated constitutive relationships for the aggregate interlock mechanism. Comprehensive correlation studies considering parameters including the amount of reinforcement and concrete strength are reported to understand the improved FSAM. Predictions of the improved FSAM for shear panels with unequal reinforcement are better than those derived using the existing FSAM approach. [ABSTRACT FROM AUTHOR]

Although multiple-model structural identification (MM ST-ID) approaches appear to offer clear, conceptual benefits over singlemodel approaches, they have not yet been employed within a transparent scenario that will allow quantitative comparison, critique, and refinement. To fill this gap, the research reported in this paper aimed to (1) implement and compare current MM ST-ID approaches on a physical laboratory model to establish their accuracy and identify their merits and shortcomings, and (2) identify the ability to refine MM ST-ID methods by weighing observations based on their correlation with the desired predictions. The scenario implemented used modal parameters as the observations, and static displacements and strains as the desired predictions. The various MM ST-ID methods were evaluated based on how their prediction distributions agreed with the actual responses of the physical model. The results indicated that while all methods were successful in bounding the actual responses, the Bayesian updating approach proved to be the most efficient in terms of required number of simulations, and was able to produce prediction distributions with the smallest bounds (while still incorporating all measured responses). In addition, the mean of the MM ST-ID prediction distributions did not coincide with the model that had the largest weight (i.e., the highest likelihood), which indicates that single model approaches not only are unable to provide estimates of variability, but may produce biased predictions. Finally, through a second set of scenarios, the research reported in this paper showed how prediction distributions may be improved by weighing observations based on their correlation with the desired predictions. [ABSTRACT FROM AUTHOR]

Ultrahigh toughness cementitious composite is a cementitious material that exhibits the characteristic of pseudo strain hardening under uniaxial tension, and has potential use in structures that experience repeated or fatigue loads. A series of quasi-static, dynamic, and fatigue tests were performed to evaluate the frequency effect on the compressive fatigue behavior of this material; in this paper the results are reported. It is found that the fatigue life and deformation pattern are influenced by loading frequency. The relationship between the secondary strain rate, the secondary strain rate per cycle, and the fatigue life is illustrated and equations applied to predict the fatigue life of specimen are developed. The failure strain of each loading frequency is found to follow the Weibull distribution. Based on the distribution of the static failure strain at the same stress level, a probabilistic model of the fatigue failure strain is proposed to describe the frequency effect, which gets a considerable agreement with the experimental results. [ABSTRACT FROM AUTHOR]

Available capacity models for the assessment of seismic capacity of RC columns are mainly based on experimental tests under axial load and uniaxial bending. Furthermore, experimental tests have been mainly performed on columns representative of new constructions. To analyze the effects of biaxial bending on the seismic performances of existing RC columns with design characteristics nonconforming to present day seismic codes and practices, this paper presents the results of a first stage of tests on RC columns under both axial load and biaxial bending, which effectively simulate the seismic actions. In particular, this paper presents results of four tests on full-scale square columns reinforced with plain bars subjected to constant axial load and biaxial cyclic actions. Two different cyclic displacement paths were investigated: horizontal displacements with an inclination angle of 45 or 30°, with respect to the cross-section principal axes. The influence of biaxial bending actions on the global behavior of existing RC columns in terms of stiffness, strength, deformation capacity, and the effects of different horizontal displacements orientation on their performances are herein investigated and discussed; the comparison with experimental outcomes provided by uniaxial bending tests on companion specimens are also presented. Experimental findings showed that biaxial bending actions affect columns rotational capacity more than strength. The rotational capacity reduction because of biaxial bending actions, even if more significant than the flexural capacity reduction, is not currently taken into account in the available seismic guidelines related to existing RC buildings. [ABSTRACT FROM AUTHOR]

This paper deals with the ultimate strength and design of fixed-ended lipped channel columns experiencing local-distortional buckling mode interaction. First, the paper reports the results of an experimental investigation involving a set of 26 columns with several cross-section dimensions and yield stresses that were tested to determine their failure loads and also to provide experimental evidence of the occurrence of local-distortional mode interaction. These results consist of the column geometries, material properties, initial geometric imperfections, nonlinear equilibrium paths, and ultimate strength values. Then, after comparing the experimental column ultimate loads with the estimates provided by the current direct strength method (DSM) design curves against local and distortional failures, which clearly show that they lead to inaccurate and often very unsafe ultimate strength estimates, the paper presents and assesses the quality of DSM-based design procedures based on approaches providing nominal strengths against local-distortional and distortional-local interactive failures. Next, an in-depth comparison is made between all the experimental ultimate strength results available in the literature and their estimates provided by the preceding DSM design procedures. Finally, the paper closes with design considerations and recommendations, motivated by the conclusions drawn from this investigation. [ABSTRACT FROM AUTHOR]

The strength of thin-walled stainless steel columns has been investigated extensively over the last few years. In European standards, the concept of section classification for determining the cross section capacity is used. In this system, for Class 4 cross sections, the effective width method (EWM) must be used to account for the effect of local buckling. Because of the complexity and limitations of this method, other methods have been developed, such as the direct strength method (DSM) for cold-formed thin-walled profiles and the continuous strength method (CSM), initially established for members made of nonlinear metallic materials. In the CSM, to take advantage of strain hardening, a deformation-based design approach using a continuous relationship between the cross-sectional slenderness and the cross-sectional deformation capacity is used. To a large extent, the CSM yields accurate predictions, especially in the low slenderness range where the current DSM design procedures for members submitted to pure compression tend to produce conservative predictions for materials with pronounced strain hardening such as stainless steel alloys. The present paper presents an extension of the traditional DSM, which provides accurate design strength predictions in the low slenderness range for stainless steel thin-walled section columns failing by distortional, local, and overall buckling. It contains practical information concerning the reference experimental data and draws conclusions about the justification of the proposed analytical formula. The paper is divided into three main parts: the description of the database, the establishment of the design model, and a reliability analysis of the method. [ABSTRACT FROM AUTHOR]

This paper investigates the fatigue behavior of reinforced concrete beams at low temperatures compared to similar beams tested in fatigue at room temperature. Four large-scale steel-reinforced beams (200 × 400 × 4,200 mm) were fabricated and tested. All of the beams had temperature differentials over their depth to simulate solar radiation and in-service temperature of the bridges. Two beams had stirrups while the other two had no shear reinforcement. One beam of each type was tested at room temperature and the other at low temperature. The beams were cyclically loaded to failure with a stress range representative of the ratio of live to dead loads found in most bridges. This study showed that the fatigue life of the reinforced concrete improved at low temperature and this improvement was much more pronounced when shear reinforcement was not present. In fact, low temperature changed the mode of failure of the reinforced concrete beams without stirrups from shear to flexural fatigue failure as a result of the higher shear strength and stiffness of the reinforced concrete, the lower number of cracks with smaller widths, and improved fatigue properties of steel at low temperature. The results showed that the fatigue life of the reinforced concrete beam without shear reinforcement at room temperature primarily depended on the concrete and concrete-to-steel bond while fatigue lives of the other beams depended on the stresses in the tensile reinforcement. The strains and stiffness degradation were much lower in the low-temperature beams compared to their room-temperature counterparts. The findings of this study showed that the contribution of concrete to the performance of the beam under either static or cyclic load becomes more pronounced at low temperatures. [ABSTRACT FROM AUTHOR]

The direct strength method (DSM) design rules for cold-formed steel members in shear have been incorporated recently into the North American specification for the design of cold-formed steel structural members and are being implemented in the Australian cold-formed steel structures standard. The method, which was calibrated for unperforated members only, requires two inputs including the buckling load Vcr and the shear yielding load Vy. For members with square web cutouts, Vcr can be computed by either the spline finite strip method or the tabulated values based on the shear buckling coefficients kv as in previous studies or the finite element method. However, Vy has not been accurately formulated including holes. This paper represents a practical model to obtain Vy for members with central openings subjected predominantly to shear. The model ranges from very small holes where traditional shear yielding predominates to large holes where Vierendeel action dominates. The model is verified with the DSM design formulas using the predominantly shear tests recently conducted at the University of Sydney and Queensland University of Technology with both square and circular web openings and for shear spans with aspect ratio of 1.0. [ABSTRACT FROM AUTHOR]

In moderate seismic regions, engineers are permitted to use a response modification coefficient, R, of 3 in the design of steel systems without any specific seismic detailing or proportioning requirements. Recent research, however, has raised questions regarding the reliability of concentrically braced frame (CBF) systems designed using the R ¼ 3 provision because their performance under the maximum considered earthquake seismic hazard is inherently dependent on reserve capacity--lateral force-resisting capacity outside the primary seismic force-resisting system (SFRS). In a previous study by the authors, two full-scale two-story CBF tests were conducted to better understand seismic behavior and associated reserve capacity after significant damage in the primary SFRS. These tests were (1) an R ¼ 3 chevron; and (2) an R ¼ 3.25 split-x ordinary concentrically braced frame (OCBF). To complement the experimental program, a numerical parametric study was conducted to further distinguish the influence that two design parameters--system type and system configuration--have on overall system behavior including non-ductile limit states and reserve capacity. Although the prototype frames studied were designed for the same building and location, they exhibited a wide variety of limit states. The occurrence of particular classes of mechanisms and their associated reserve capacities was influenced by the system type and system configuration. Specific reserve capacity mechanisms depended on the location of damage within the primary SFRS. Predicting these damage locations is difficult because they depend on as-built weld overstrength. This paper explores the classes of reserve capacity mechanisms that were observed both experimentally and in the companion numerical simulations. [ABSTRACT FROM AUTHOR]

A new type of lightweight shear walls made with a laminated bamboo (glubam) stud frame and ply-bamboo sheathing panels is introduced in this paper. The lateral loading experiments of such shear walls and corresponding similar lightweight wood shear walls with three different panel-frame nailing connections and two thicknesses of sheathing panels were performed, in accordance with international standards. Test results demonstrate that the lightweight glubam shear walls have similar performance as conventional lightweight wood-frame shear walls, with higher initial stiffness and peak load, but less ductility. An increase in nail diameter can improve the load-bearing capacity of the shear walls until the failure mode of panel-frame connection changes from yielding of the nails to pull-through of nails from the ply-bamboo panels. Increased panel thickness can increase the bearing capacity and deformability of the shear walls when the failure pattern of panel-frame connection changes from panel failure to nail yielding. A new uplift hold-down device and improved design of edge studs were used to increase the ductile performance of glubam shear walls. [ABSTRACT FROM AUTHOR]

Longitudinal cracks in wood beams of heavy timber structures are commonly seen and can impair the load-carrying capacity of such beams. This paper presents the experimental and numerical modeling results on 35 pieces of full-scale wood beams with saw kerfs that simulate lengthwise checks. The influences of the checks and self-tapping screws used for retrofitting purposes were identified based on the normalized load-carrying capacity of the tested beams. It was found that a longitudinal check (up to 2/3 of the beam span) may cause a resistance loss up to 46.2% compared to an unchecked beam, and the use of self-tapping screws may increase the resistance to no less than 86% of that of an unchecked beam. A three-dimensional (3D) finite-element method based model was developed and verified to further quantify the stress intensity factor at the check tip. Based on the modeling and test results, a simple formula was established for prediction of the stress intensity factor, considering the geometry of the checks and the contribution of the self-tapping screws. The generated formula was verified with good agreement and therefore can be used for determination of the shear resistance of checked wood beams and the required screw spacing for retrofitting purposes. [ABSTRACT FROM AUTHOR]

Tension field theory assumes that after elastic shear buckling has occurred, compressive stresses in the web plate do not increase; therefore, postbuckling shear strength solely results from the development of tensile stresses within a defined diagonal tension field. Finite-element analyses have found this fundamental assumption to be invalid and a new theory (compression theory) was proposed that bases the development of postbuckling shear strength mostly on the compressive response of the plate (tension plays a secondary role). Previous work has validated compression theory against a wide variety of published experimental data at ambient temperature. This paper shows that compression theory can predict the ultimate postbuckling shear strength of steel web plates up to temperatures of 1,100°C. This finding is significant because steel plate girders subjected to fire loading are highly susceptible to web shear buckling. Experimentally validated finite-element models are used to develop temperature-dependent multiplicative parameters to permit the use of compression theory to calculate ultimate postbuckling shear strength at elevated temperatures. Comparisons with published experimental data show that predictions of ultimate postbuckling shear strength from compression theory closely agree with the literature. [ABSTRACT FROM AUTHOR]

The mechanism method, based on the particularization of limit design to masonry structures proposed by Heyman, is certainly a very suitable procedure for the analysis of no-tension material arches, especially because of its simplicity. The literature largely treats the method under the hypothesis of infinite compressive strength of the material, whereas fewer studies are devoted to finite compression strength. In this paper the latter case is revisited with reference to masonry arch bridges, assuming a rigid-perfect plastic model for the material and using a nondimensional formulation. In this way, results are derived and discussed for a wide range of parameters. The results are compared with those obtained using Heyman's hypotheses. [ABSTRACT FROM AUTHOR]

Shear lag effect in thin-walled box girders has been studied over several decades. However, the methods adopted in many papers have some deficiencies. In the present work, an improved displacement function for shear lag warping in a box girder with cantilever slabs is established. Based on the concept of generalized force corresponding to the generalized displacement for shear lag and the relevant geometrical properties, an improved finite-segment method is proposed to simplify the shear lag analysis of complex box girders. The homogeneous solution of the governing differential equation for shear lag is adopted as the element displacement function. The formulas of the element stiffness matrix and the equivalent nodal force vector are derived. A general formula expressed in terms of the generalized moment is presented to calculate the stress. A finite-element computer program is developed by using FORTRAN language and is used to analyze a cantilever box girder model and a continuous prestressed concrete box girder. The theoretical results are in good agreement with the test results, validating the proposed method and formulas. This paper also reveals for the first time the characteristics of the generalized moment for shear lag. [ABSTRACT FROM AUTHOR]

Forum papers are thought-provoking opinion pieces or essays founded in fact, sometimes containing speculation, on a civil engineering topic of general interest and relevance to the readership of the journal. The views expressed in this Forum article do not necessarily reflect the views of ASCE or the Editorial Board of the journal. [ABSTRACT FROM AUTHOR]

To support the repair and maintenance of steel eyebars in bridges, tension stresses are sometimes estimated from the observed member natural frequencies. Although the ends of such eyebars are often essentially fixed, a pin-ended model has typically been used to predict tensions because closed-form solutions do not exist for any other end conditions. An approximation that reflects vibrating stretched wires with fixed ends has also been used, but this still incurs considerable error at lower member slenderness and stress levels. To provide for better estimates of eyebar tensions from observed vibrations, this paper presents exact tabular solutions for determining the direct tension stress in undamped steel bars, generalized for any length or thickness, where both ends of the member are fixed or where one end is fixed and the other pinned. Approximation equations derived from these exact solutions are also developed. Examples demonstrate the application of these new tools and the potential increase in accuracy over the former methods. [ABSTRACT FROM AUTHOR]

In recent years, significant advances have been accomplished in the fields of modeling, analysis, and design of deteriorating civil engineering systems, and novel approaches to life-cycle assessment, maintenance planning, and optimal design of structural systems have been proposed. Despite these advances, life-cycle concepts are far from being explicitly addressed in design and assessment codes and effectively implemented into practice. There is, therefore, a need to promote further research in the field of life-cycle performance of structural systems under uncertainty and to fill the gap between theory and practice by incorporating life-cycle concepts in structural design and assessment codes. An effort is currently ongoing within the Structural Engineering Institute (SEI)/ASCE to meet this need. This paper is part of this effort and is aimed at presenting a review of the main principles, concepts, methods, and strategies for life-cycle assessment and design of deteriorating structural systems under uncertainty. General criteria for deterioration modeling are first presented, with emphasis on the effects of corrosion and fatigue in steel structures and chloride-induced corrosion in concrete structures. The time-variant structural performance is then investigated with reference to a set of probabilistic performance indicators, and the structural lifetime associated with a reliability target is formulated. The role of inspection and monitoring, the effects of maintenance and repair interventions, and the definition of cost-effective maintenance strategies are discussed. The concepts of life-cycle performance assessment and maintenance planning are used to formulate the life-cycle reliability-based design problem in an optimization context. [ABSTRACT FROM AUTHOR]

This paper attempts to enhance (1) the flexibility-corotational beam formulation for simulating highly geometrically nonlinear problems, and (2) the arc length method of integration to develop a robust and economical solution scheme for random quasi-static loading input. The existing flexibility-corotational formulation of a three dimensional beam is improved by (1) updating the rotation matrices by using the quaternions, and (2) proposing novel methods for tracking the displacement compatibility. Further, the cylindrical arc length method is modified by (1) introducing capabilities for handling random quasi-static loading, and (2) proposing automatic adjustment of the arc length. By using these developments several classical geometric nonlinearity problems are solved and path independency for buckling and post-buckling path with the random quasi-static loading is verified. The proposed variation in the arc length solution scheme is also shown to be better than the implementation of the arc length method in the state of the art commercial software. [ABSTRACT FROM AUTHOR]

The pull-out performance of steel rods glued into timber is well-documented, and short-term tests by many researchers have demonstrated reliable strength. The behavior of glued-in steel rods in moment-resisting beam-column joints is much more complex because of anisotropy of wood in the connection region, discontinuity of material at the interface, and the possible effects of creep of timber and stress concentrations on the joint performance. This paper describes the results of a series of long-term load tests on moment-resisting joints between glulam members and separate load tests on the various joint components, including the epoxy itself and the timber stressed perpendicular to the grain. Different types of knee joints, with rods fully epoxied along their length or epoxied only in one member and tensioned in the other, and with different geometries (with the beam extended over the column or with the column extended past the beam) were tested. Measurements were recorded to identify time-dependent stress redistribution within the test joints, creep of the joint as a whole, and possible crushing of the timber-to-timber bearing surfaces. Local deformation of timber loaded in compression perpendicular to the grain was found to contribute to excessive joint deformations in tests in which the steel rods were not glued over their full length. The test results confirm the possibility to use the transformed section method in design as presented in the first companion paper, and address a number of issues pointed out in the same paper. [ABSTRACT FROM AUTHOR]

This paper examines the assumption implicit in Cochrane's formula that stresses are uniformly distributed across the net section of a staggered bolted connection. The assumption was found to be overoptimistic for connections in steel having low ductility, leading to unconservative estimates for the tension capacity if the in-plane shear lag is not accounted for. The reduction factor of 0.9 specified in the North American specification for cold-formed steel structures partially, but not wholly, addresses the problems inherent in the code equations. This paper points out that the simplification of Cochrane's original formula into the standard formula used in steel design codes worldwide can lead to additional design capacity that may not be justified. It proposes an equation that accounts for the in-plane shear lag and incorporates Cochrane's original formula for determining the net section area. The proposed equation is demonstrated through laboratory tests on 74 staggered bolted connection specimens in 1.5 mm and 3.0 mm G450 sheet steel to be more accurate and consistent than the code equations in predicting the net section tension capacity. [ABSTRACT FROM AUTHOR]

A methodology is developed in this paper for the design and proportioning of interventions for seismic upgrading of substandard reinforced-concrete (RC) buildings. The retrofit approach is presented in the form of a simple design tool that aims toward both demand reduction and enhancement of force and deformation supply through controlled modification of stiffness along the height of the building. This objective is achieved by engineering the translational mode-shape of the structure, so as to optimize the distribution of interstory drift. Results from the proposed approach are summarized in a spectrum format in which demand, expressed in terms of interstory drift, is related to stiffness. Design charts, which relate the characteristics of commonly used global intervention procedures to influence drift demands, are developed to facilitate the retrofit design. The intervention procedures considered in this paper are reinforced-concrete jacketing, the addition of reinforced-concrete walls, and the addition of masonry infills. The proposed methodology is also amenable to adaptation to other strengthening methods, such as the addition of cross-bracing. [ABSTRACT FROM AUTHOR]

A LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam produced by using a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. It has the beneficial characteristics of torsionally rigid closed rectangular flanges combined with the economical fabrication processes from a single strip of high-strength steel. Although the LSB sections are commonly used as flexural members, no research has been conducted on the shear behavior of LSBs. Therefore, experimental and numerical studies were conducted to investigate the shear behavior and strength of LSBs. In this research, finite-element models of LSBs were developed to investigate their nonlinear shear behavior, including their buckling characteristics and ultimate shear strength. They were validated by comparing their results with available experimental results. The models provided full details of the shear buckling and strength characteristics of LSBs and showed the presence of considerable improvements to web shear buckling in LSBs and associated postbuckling strength. This paper presents the details of the finite-element models of LSBs and the results. Both the finite-element analysis (FEA) and experimental results showed that the current design rules in cold-formed steel codes are very conservative for the shear design of LSBs. The ultimate shear capacities from FEAs confirmed the accuracy of proposed shear strength equations for LSBs on the basis of the North American specification and direct strength method (DSM) design equations. Developed finite-element models were used to investigate the reduction to shear capacity of LSBs when full-height web side plates were not used or when only one web side plate was used, and these results are also presented in this paper. [ABSTRACT FROM AUTHOR]

This paper describes and demonstrates modifications of the harmony search method to support multimodal structural optimization. Several researchers have recognized the potential of population-based optimization methods, such as genetic algorithms and particle swarm optimization, to support multimodal optimization, that is, generating a range of good alternative solutions, rather than a single best solution. Among these population-based methods is the harmony search method, which has been demonstrated to be efficient and effective in many unimodal structural optimization problems. Toward the goal of making the harmony search method more effective in multimodal optimization, this paper describes a new strategy for generating solutions called close-harmony improvisation, and a new strategy for replacing solutions called local replacement. Examples demonstrate the effect of the two strategies used individually and in tandem. The discussion compares results with conventional harmony search and finds that close-harmony improvisation consistently improves the fitness of the search results, although the effect is sometimes mild, whereas local replacement is quite effective in increasing the diversity of the search result. [ABSTRACT FROM AUTHOR]

During a fire, columns on the perimeter of a building will be subject to moments induced by both a thermal gradient and the restraint of axial expansion by adjacent heated beams, which themselves develop axial load. These members thus act as beam-columns because they are then subject to a combination of axial load plus moment caused by a combination of gravity plus thermal loading. This paper presents a two-pronged procedure to predict the behavior of the perimeter column as a beam-column, considering both the individual member response (including thermal gradients) and the global response (including the interactions of adjacent members). All methods discussed in the paper are closed-form (i.e., they require no iteration) and can therefore be solved by using a spreadsheet or simple mathematical algorithm. The framework is sufficiently simple for use in codified structural-fire design and could be included in a reference of performance-based analysis methods for steel structures. Although this paper specifically addresses the performance of columns on the perimeter of buildings, the proposed framework can be a blueprint for the performance-based analysis of other beam-columns, such as floor beams. [ABSTRACT FROM AUTHOR]

High-strength cold-formed steel sections are commonly used in a variety of applications including residential construction. These steel sections typically have a nominal yield stress of 550 MPa and the use of such high-strength material allows for a reduction in thicknesses. With this reduction in thickness, the high-strength steel can be manufactured into complex shapes including stiffeners. Such complex shapes exhibit structural instabilities such as local, distortional, and flexural-torsional buckling modes, and in some cases, interaction of the local and distortional buckling modes may occur. This paper describes the design and testing of web-stiffened high-strength steel cold-formed lipped channel columns. In order to be able to apply the direct strength method (DSM) in Section 7 of the Australian Standard AS/NZS 4600:2005 and Appendix 1 of the North American Specification to design, the steel sections must be prequalified as a compression member. The section chosen is prequalified and has nearly coincidental local buckling and distortional buckling loads as well as a flexural-torsional mode which varies with length. A series of compression tests was carried out in a 300-kN capacity SINTEC testing machine over a range of lengths with fixed-ended conditions. The varying lengths were chosen so as to observe the buckling modes and the possibility of interaction between them. The effect of the different types of failure modes is also discussed in this paper. The experimental results are then compared with design methods in the existing design standards. The methods include the effective width method and the DSM as described in the Australian Cold-Formed Steel Structures Standard and the North American Specification. It is shown that the existing standards are unconservative and new proposals for dealing with this are made. [ABSTRACT FROM AUTHOR]

This paper presents an iterative automated method for optimizing structures with multiple deflection criteria and load cases. The method is based on the principle of virtual work. Discrete sections are selected for structures with fixed geometries. An optimal structure is one which meets all strength and deflection criteria using minimal material. Four case studies are considered in this paper. A simple portal frame is presented to show how the method works. A 60-story frame is optimized to demonstrate the effectiveness of the method for large structures. A warehouse designed by professional engineers is presented to show how the method can be used for structures subjected to complex loading conditions and deflection criteria. The automated method's solution is 4.5% lighter than the engineers'. Finally, a stepped cantilever is optimized and compared to results in literature. Material savings of up to 14.4% are realized. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Design models for local buckling of fire-exposed aluminum sections are currently lacking. Based on analyses with validated finite-element models, this paper investigates local buckling of extruded sections with stress-strain relationships representative for fire-exposed aluminum alloys. Due to the fact that these stress-strain relationships are more curved than at ambient temperature, existing design models developed for ambient temperature cannot be used for fire design. This paper presents a new design model for local buckling under fire conditions. The study concludes that the local buckling resistance decreases less fast than the plastic capacity at increasing temperature. This is mainly due to the fact that the ratio between the modulus of elasticity and the 0.2% proof stress increases with increasing temperature for structural aluminum alloys. [ABSTRACT FROM AUTHOR]

The energy dissipated per cycle and the characteristic strength of lead-rubber bearings reduce with increasing number of cycles as a result of heating of the lead core. The reduction is substantial depending on the geometric characteristics of the bearing and the speed of motion. This paper presents a theory that is capable of predicting the dependency on time of the characteristic strength and energy dissipated of lead-rubber bearings. The theory is based on predicting the temperature of the lead core and relating the temperature to the strength. A much simpler theory is also presented based on neglect of heat conduction through the steel shim and end plates of the bearing. The theory is useful in predicting the cyclic behavior of lead-rubber bearings for simplified analysis, in extrapolating experimental data from one scale to another and in developing models for dynamic response history analysis of seismically isolated structures that account for the time-dependent mechanical properties of the bearings. A companion paper presents results of eight tests of six lead-rubber bearings that provide verification of the theoretical solution. [ABSTRACT FROM AUTHOR]

The energy dissipated per cycle and the characteristic strength of lead-rubber bearings reduce with increasing number of cycles as a result of heating of the lead core. A theory which is capable of predicting the histories of temperature rise in the core, of the energy dissipated and of the characteristic strength of lead-rubber bearings has been presented in a companion paper. This paper presents a comparison of predictions of this theory to experimental results obtained in the testing of six lead-rubber bearings. The analytical predictions are found to be sufficiently accurate. Moreover, finite-element analyses results are presented that provide insight into the distribution of temperature in the lead core and end and shim plates of the bearings. These distributions confirm the assumptions made in the development of the theoretical solution. [ABSTRACT FROM AUTHOR]

This paper presents a review of the design provisions for screw-fastened cold-formed steel connections in the United States, including criteria for testing and evaluating the strength of screw fasteners. In addition, the paper examines the relationship between the connected elements/components computed connection strength and the strength of the connector (screws). Fastener strength test data from three independent manufacturers is presented and it is shown that as the thickness or yield strength of the connected elements/components is increased, the ratio of the fastener strength to the bearing/tilting strength decreases to values less than one-half in some cases. Analysis of the test data showed that even when the 2001 North American Specification (NASPEC) for the Design of Cold-Formed Steel Structural Members statistical requirements for distribution of the test data are met, the computed safety and resistance factors can exceed the recommended limits in Section E4 of the 2001 NASPEC. On this basis, it is recommended that the current language in the 2001 NASPEC be revised to specify, if necessary, limits on manufacturer computed safety and resistance factors. Finally, it is recommended that fastener tilt during screw shear strength tests be eliminated to facilitate an accurate evaluation of the shear strength of a fastener. [ABSTRACT FROM AUTHOR]

Seismic design relies on inelastic deformations through hysteretic behavior. However, this translates into damage on structural elements, permanent system deformations following an earthquake, and possibly high cost for repairs. An alternative design approach, proposed in the past, is to concentrate damage on disposable and easy to repair structural elements (i.e., “structural fuses”), whereas the main structure is designed to remain elastic or with minor inelastic deformations. The implementation of the structural fuse concept into actual buildings would benefit from a systematic and simple design procedure. Such a general procedure is proposed here for designing new or retrofitted structures. The proposed structural fuse design procedure for multi-degree-of-freedom structures relies on results of a parametric study (presented in the paper), considering the behavior of nonlinear single degree of freedom systems subjected to synthetic ground motions. Nonlinear dynamic response is presented in dimensionless charts normalized with respect to key parameters. The proposed design procedure is illustrated as an example of application using Buckling-restrained braces as metallic structural fuses. This example is used in an experimental project (which is described in a companion paper) as a proof of concept to the developed design procedure. [ABSTRACT FROM AUTHOR]

In the paper corrosion-induced crack initiation and propagation are investigated experimentally and numerically, with particular emphasis on quantifying the proportion of corrosion products that are dissipated within the concrete pores and cracks, thus reducing the pressure exerted by corrosion products on the surrounding concrete. Initially, experimental data on crack initiation and propagation obtained from accelerated corrosion tests of reinforced concrete slabs are presented. A comparison of finite-element model results and experimental data is used to estimate the amount of corrosion products penetrating into concrete pores and cracks, which is an essential parameter for prediction of corrosion initiation and propagation. It was found that the amount of corrosion products penetrating into the concrete pores before crack initiation is larger than that obtained by other researchers. The paper also showed that corrosion products do not fully fill corrosion-induced cracks in concrete immediately after their initiation as the cracks are being filled gradually over time and the thicker the concrete cover the longer it will take to fully fill a crack. [ABSTRACT FROM AUTHOR]

This paper describes the design and experimental investigation of a series of compressive tests on a stiffened cross-shaped section fabricated from cold-formed high-strength steel of 0.42 mm thickness and nominal yield stress of 550 MPa. The complex shape has been chosen so that it has a local buckling mode, two distinct distortional buckling modes, and a flexural-torsional mode. The first distortional buckling mode has a shorter buckle half wavelength and hence is classified as a short half-wavelength distortional buckling mode, while the other distortional mode has a much longer buckle half-wavelength and is classified as a long half-wavelength distortional buckling mode. The compression tests were carried out in a 300 kN capacity SINTEC testing machine over a range of lengths with fixed-ended conditions. The varying lengths were chosen so as to observe the buckling modes and the possibility of interaction between them. The experimental results are then compared with design methods in the existing design standards. The methods include the direct strength method (DSM) recently incorporated in the North American specification and the Australian Cold-Formed Steel Structures Standard AS/NZS 4600. When compared to the existing methods, the test results indicate that at intermediate and longer specimen lengths, the interaction of local and distortional buckling modes has a significant effect on the strength of the section. This paper presents the procedures taken to design the complex shape and the experiments carried out to obtain the geometric imperfections and material properties of the specimens and the test results. New design methods are proposed for the local buckling DSM curve as well as for the distortional buckling strength curves so as to account for the effects of interaction of local and distortional buckling modes. [ABSTRACT FROM AUTHOR]

This paper describes the development and results of a finite element parametric study of eccentrically braced frame links having hollow rectangular cross sections (i.e., tubular links). The parametric study involves over 200 combinations of geometries and properties and is divided into two parts. Part A considers a wide range of compactness ratios and link lengths to determine appropriate compactness ratio limits such that links with tubular cross sections can achieve desired rotation levels prior to significant strength degradation from local buckling. Part B of the study involves models developed with flange compactness ratios, web compactness ratios, and stiffener spacings near the proposed design limits from Part A, and also examines links having webs and flanges with different yield stresses (i.e., hybrid links). Results of the parametric study are also used to investigate the adequacy of a method for approximating link overstrength. A companion paper describes the experimental verification of the proposed design requirements. [ABSTRACT FROM AUTHOR]

This paper investigates the consequence of using Rayleigh proportional damping in the analysis of inelastic structural systems. The discussion is presented theoretically, as well as by example through the analysis of a simple five-story structure. It is shown that when the stiffness portion of the system damping matrix is based on the original system stiffness, artificial damping is generated when the structure yields. When the damping matrix is based on the tangent stiffness but the Rayleigh proportionality constants are based on the initial stiffness, a significant but reduced amplification of damping occurs. When the damping is based on the tangent stiffness and on updated frequencies based on this stiffness, virtually no artificial damping occurs. The paper also investigates the influence on effective damping when localized yielding occurs in areas of concentrated inelasticity. In such cases, it is possible to develop artificial viscous damping forces that are extremely high, but that are not easy to detect. Such artificial damping forces may lead to completely invalid analysis. The paper ends with recommendations for performing analysis where the artificial damping is eliminated, or at least controlled. [ABSTRACT FROM AUTHOR]

In the companion paper, the nonlinear elastic stability analysis of a shallow parabolic arch with horizontal spring supports was investigated. The solution for the in-plane antisymmetric bifurcation buckling load and an approximate solution for the symmetric snap-through buckling load for shallow arches were proposed, and the effects of the stiffness of the horizontal springs on the buckling load and buckling behavior of arches were studied. When the stiffness of each of the spring supports is the same, the structural configuration replicates that of a tied arch with roller supports. This paper reports short-term experimental studies undertaken on two shallow parabolic reinforced concrete arches. The two supports of each arch were connected by a steel tie. The arches failed in an antisymmetric bifurcation buckling mode well before the maximum stress in the concrete reached its compressive strength. Both the load–deflection response and the buckling load are compared with theoretical predictions that incorporate various degrees of nonlinearity in their formulation, including the predictions derived in the companion paper. [ABSTRACT FROM AUTHOR]

This paper investigates the in-plane elastic stability of a shallow parabolic arch with horizontal spring supports subjected to a uniformly distributed vertical load. A virtual work formulation is used to establish both the nonlinear equilibrium equations and the buckling equilibrium equation for shallow arches. Analytical solutions for the in-plane buckling loads of shallow arches subjected to this loading regime are obtained, and a closed-form solution for the in-plane antisymmetric bifurcation buckling load and an approximation to the symmetric snap-through buckling load of shallow arches are proposed. Comparisons with the finite-element predictions of these buckling loads, together with the measured buckling loads of arches tested in the laboratory and reported in the companion paper, demonstrate that the analytical solutions are accurate. It is found that the effects of the stiffness of the horizontal springs on the buckling load and buckling behavior of arches are significant, and that the buckling load of an arch increases with an increase in the flexibility of the horizontal springs at the supports. Values of the slenderness that delineate the buckling modes increase with an increase of the flexibility of the horizontal springs. Values of the slenderness that distinguish between an arch (for which buckling is possible) and a beam curved in elevation (that cannot buckle in plane) also increase with an increase of the flexibility of the horizontal springs. [ABSTRACT FROM AUTHOR]

In this paper an attempt is made to automatically calculate the bifurcation of the buckling path of shallow lattice domes. This calculation is performed in a two-stage analysis of the space structure without introducing any geometrical imperfections. The method is implemented in a combined materially and geometrically nonlinear finite element analysis computer program based on an incremental/iterative Newton-Raphson solution procedure. In the first stage analysis, the load factors at which critical points occur are determined and the primary path is obtained. In the second stage analysis the perfect structure is lead toward the lowest bifurcation path using the technique described in this paper. The resulting theoretical predictions are verified by existing experimental observations on two model domes. [ABSTRACT FROM AUTHOR]

Although steel single angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion, their behavior may be extremely complicated, and the accurate prediction of their strengths very difficult. Further, many design codes do not have design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. This paper is one of a series on the behavior and design of single angle section steel beams. Two previous papers have studied the biaxial bending and torsion of restrained beams, a third has studied the lateral buckling of unrestrained beams, a fourth the biaxial bending of unrestrained beams, and a fifth and sixth the buckling and torsion of unrestrained beams. In each paper, simple design methods have been developed. In this present paper, an approximate method of predicting the second-order deflections and twist rotations of steel equal angle section beams under biaxial bending and torsion is developed. This method is then used to determine the approximate maximum biaxial bending moments in such beams, which are then used with the section moment capacity proposals of the first paper and the lateral buckling proposals of the third paper to approximate the member capacities. [ABSTRACT FROM AUTHOR]

This paper describes the buckling behavior of cold-formed steel equally lipped angle columns. The initial local imperfections, residual stresses, and corner material properties of the cold-formed steel angles have been measured experimentally and reported in this paper. An accurate finite element model was developed to carry out the buckling analysis. Both initial local and overall geometric imperfections have been incorporated in the model. The effect of residual stresses on the buckling behavior was investigated. The material nonlinearities of flat and corner portions of the angle sections were considered in the analysis. The finite element analysis was performed on equally lipped angles compressed between fixed ends for different column lengths, and column curves were obtained. The nonlinear finite element model was verified against recent experimental results. An extensive parametric study was carried out using the finite element model to study the effects of cross section geometries on the strength and behavior of lipped angle columns. The column strengths predicted by the finite element model were compared with the design strengths calculated using the North American Specification and Australian/New Zealand Standard for cold-formed steel structures. In addition, the results obtained from the finite element model were also compared with the design strengths obtained from proposed design rules. It is shown that the proposed design rules accurately predicted the column strengths for non-slender lipped angles and were quite conservative for slender lipped angles. [ABSTRACT FROM AUTHOR]