Angle Members Research Articles

Local buckling of steel equal angle members with normal and high strengths

Steel angle sections have been widely accepted with the development of steel structures, and such members made by high strength steel (HSS) sections are also increasingly used in buildings and bridges, and especially in transmission towers and long span trusses. Compared to normal strength steels, HSS exhibits different mechanical properties, which can cause different local buckling behavior. A finite element analysis (FEA) was performed in this paper to investigate the local buckling of steel equal angle members with different strengths under axial compression, where the residual stresses and the initial geometric imperfections of specimens were accurately described. Through this work, the relationship of the ultimate local buckling stress of steel equal angle members under axial compression as a function of steel strength and width-to-thickness ratio was established. By comparing the FEA results with the international design specifications (ANSI/AISC 360-10 and Eurocode 3), a modified design formula was developed and corresponding design suggestions were proposed, to take into account the effects of steel strength.

The structural effect of bolted splices on retrofitted transmission tower angle members

This paper examines the structural behavior of compound members used for transmission tower legs, constructed from steel angles that have been retrofitted by attaching additional parallel angle members. To study the load transfer mechanism between the original member and the reinforcing component as well as the influence of splice joints in the original tower structures, a group of static experimental tests have been conducted. A 3D nonlinear finite element model was developed in ABAQUS after considering the clearance between bolts and holes and the contact interaction between bolts and member surfaces in all of the connections. The detailed 3D model was then simplified to a one dimensional model through the use of spring elements to simulate connectors and splices, and beam elements to represent original and reinforcing members. Numerical results based on the simplified model agreed well with those from the 3D model and experimental tests. A parametric study showed that the stiffness change and bolt-slip phenomenon in the splicing joint and the connectors play an important role in the structural behavior of the retrofitted system. Enhancement of the load-carrying capability and load-sharing rate for reinforcing members can be achieved by optimizing the connector joint parameters.

Fuse performance on bracing of concentrically steel braced frames under cyclic loading

This paper describes the development of ductile fuse system for steel angle bracings to reduce the seismic demand to the connections of concentrically braced frames. In such type of structure, the connections often need reinforcement to resist the tensile capacity of the bracing to comply with the capacity design procedure recommended by most design codes. In this research, various models of ductile fuses consisting of smoothly reduced angle section are placed on the X-bracing of a braced frame. The fuses are designed to reduce the tensile capacity of braced members to the capacity of the bolted connections. To evaluate the performance of the fuse system, two different thicknesses of single angle members with leg width of 64mm part of an X-bracing are tested cyclically in a 1.75-m high frame representing a building story. It was observed that the braced frame with fuse could be used to reduce seismic load demand to the connections sufficiently to avoid connection strengthening that would result from the application of the capacity design principles. It was observed that properly designed fuse system in braced frame showed stable hysteretic response under cyclic loading and maintained adequate ductility with a reasonable compromise on the compressive strength of braced members. Finally, based on the study results, most efficient fuse patterns are identified for practical design applications.

Wind forces on single and shielded angle members in lattice structures

In this paper, the aerodynamic loads on simplified lattice structures are evaluated taking into account the force on each individual member rather than the conventional methods accounting for the overall truss through solidity ratio and global shielding coefficients. Wind tunnel tests were conducted on single angle members to determine the aerodynamic force coefficients corrected for a blockage effect. Aerodynamic force coefficients were also determined for angle members in the wake of an upstream one to assess the shielding effects. The results show that blockage plays a critical role in the determination of aerodynamic force on angle members with wind tunnel measurements. The experimental results also show three phases for the effect of shielding. The proposed approach based on the contributions of each member of lattice structures allows for the determination of the side force in addition to the drag force. The wind force on typical trusses calculated by this method is compared to the results of methods proposed in different codes.

Effect of Bolt Slippage and Joint Eccentricity on the Response of Lattice Structure with Non-Uniform Settlement

Lattice transimission towers are commonly made of angles bolted together directly or through gussets. And angle members are usually subjected to high axial force with eccentricity. Conventional structural analysis softwares solve such problems with the assumption of regarding the bolted connection as a rigid joint connection and ignored the effect of joint eccentricity. Thus the calculated internal forces of the structure members are bigger than those of real measurements, and the calculated structure deformation are smaller than the experimental ones under the same load. The main reasons for the discrepancy between the experimental results and the analytical solutions are bolt slippage and joint eccentricity. In this paper, the displacement-load curves of the bolted connections are introduced into the finite element simulation, revealing the effect of bolt slippage on the static response of lattice structure. The simulation results show that the bolt slippage causes the redistribution of the member internal forces of the lattice structure and increases the displacement of the lattice structure. The proposed algorithm and simulation results would provide good reference for further engineering applications.

Elastic Flexural-Torsional Buckling of Beam-Column with Equal-Leg Angle Cross-Section

The flexural-torsional buckling of equal-leg angle member under compression is analyzed and calculated. Based on General bending theory and the section properties of angle, the governing equations of the spatial buckling are presented and the formula of Wagner effect coefficient is deduced. The method can also be used for beam-columns with any type section, and the computational efficiency is much higher than numerical methods. The critical buckling loads of equal-leg angle members with different sizes are calculated and the column curves of critical load and slenderness ratio are plotted which will guide efficiently the actual engineering design.

Buckling resistance of perforated steel angle members

The detrimental effect due to perforations on the buckling resistance of perforated hot-rolled steel L-shaped members in compression is evaluated in the current paper.FEM numerical models are used in order to carry out buckling and non linear analyses with the aim of detecting both the critical and the collapse load of the studied elements in case of one or more holes.The obtained results show that, although the critical load is not strongly influenced by the presence of holes, the load bearing capacity, when members are characterized by middle–low slenderness, could be significantly diminished when drillings of common sizes are applied on one of the two section legs, meaning that current methods given by the codes are not fully conservative. As a consequence, specific stability curves are determined and proposed as useful alternative design procedure.

Recommendations for Shear Lag Factors for Longitudinally Welded Tension Members

Section J2.2b of the 2010 AISC Specification for Structural Steel Buildings requires the length of longitudinal welds, used to connect flat plate tension members, to be greater in length than the distance between the longitudinal welds. Currently, weld lengths less than the distance between the welds are not permitted for connections of flat plate members.The procedure for the calculation of the shear lag factor, U, for this type of connection is given by Case 4 in Table D3.1 of the AISC Specification, where U is a function of the length of the longitudinal weld and the width of the plate. Although Case 4 is explicitly defined for plates only, the generally accepted practice in the design of similar welded connections of angles, channels, tees and wide flange members is to apply the same limitation on weld length, and calculate the effect of shear lag as given by Case 2 in Table D3.1 of the AISC Specification, while ignoring shear lag effects with weld lengths between one and two times the distance between the welds. Furthermore, for connection geometries meeting those for Case 2 or Case 4, there is no guideline for considering connection strengths where the longitudinal welds on each side of the member have unequal lengths (e.g., skewed web members or braces), or weld lengths less than the distance between the welds.This paper presents recommendations for a generalized design procedure for welded connections of plate, angle, channel, and tee tension members regardless of the length of the weld or if the length of the longitudinal welds are unequal. A summary of the treatment of various current building codes/specifications (AISC and CSA) on this topic is presented along with the results of several published experimental research projects that evaluated the behavior of these types of connections. Two analytical models are presented, and recommendations for changes to the current AISC Specification are made, followed by an example problem illustrating the practical application of the recommendations.

Failure mechanism and retrofitting strategy of transmission tower structures under ice load

An experimental study was conducted on two pairs of subassemblages of a typical 500kV transmission tower of the same type as those suffered the most severe damage during ice disaster in South China in 2008. The objectives are to study the failure mechanism of transmission towers under extreme load of freezing rain and to investigate the pertinent retrofitting strategy for increasing the load-carrying capacity of towers so as to prevent their collapse. The difference between specimens in each pair is that one had an additional diaphragm as measures of retrofitting while the other did not. The mechanical behavior, failure mode, strain and deformation at critical points, of the specimens were studied. The test results revealed that buckling of the main leg was the predominant failure mode of structures. For the two subassemblages without diaphragm, the out-of-plane deformations in the joints of diagonal bracings were relatively large and the buckled main angle members exhibited apparent torsion, which significantly decreased the load-carrying capacity of specimens. But for the two subassemblages with diaphragms, the out-of-plane deformations of cross-bracings were markedly inhibited by the added diaphragms and the buckling mode of the main member approached flexural buckling without torsion. As a result, the ultimate strength was increased by 18.3% and 17.6% for the single-panel and double-panel tower subassemblages respectively. It shows that the addition of the diaphragm significantly improved the mechanical performance of transmission towers by reducing the torsional effect on main members and inhibiting the out-of-plane deformation of diagonal braces.

Theoretical and experimental study of cold‐formed steel double angle members under compression

Theoretical and experimental study of cold‐formed steel double angle members under compression

Effect of corrosion on the buckling of steel angle members – experimental study

The aim of this work is to study the effect of corrosion on the buckling behaviour and resistance of corroded steel angle section members. The influences of the corrosion location and the loss of cross-section are studied by experimental investigations, where the corrosion is modelled by artificial thickness reduction. Compressive buckling tests are carried out on twenty-four specimens. Different corrosion damages are modelled, like uniform, pitting and local corrosion in the specimens. The buckling behaviour and the relationship of the corrosion reduction and the resistance decrease are determined.

Study on the Local Buckling Behavior of Steel Equal Angle Members under Axial Compression with the Steel Strength Variation

High strength steel sections have been increasingly used in buildings and bridges, and steel angles have also been widely used in many steel structures, especially in transmission towers and long span trusses. However, high strength steel exhibits mechanical properties that are quite different from ordinary strength steel, and hence, the local buckling behavior of steel equal angle members under axial compression varies with the steel strength. However, there is a lack of research on the relationship of the local buckling behavior of steel equal angle members under axial compression with the steel strength. A finite element model is developed in this paper to analyze the local buckling behavior of steel equal angle members under axial compression, and study its relationship with the steel strength and the width-to-thickness ratio of the angle leg. The finite element analysis (FEA) results are compared with the corresponding design method in the American code AISC 360-05, which provides a reference for the related design.

The Edward H. Angle Research Prize

Twenty years ago at a lodge in Sun Valley, Idaho, Dr Ram Nanda was awarded the first Edward H. Angle Research Prize. What is this award? What does it mean and what has happened to it since then? The award was originally established by the Board of Directors of the Angle Foundation in 1987. The motion establishing the award read in part, ‘‘... Edward H. Angle Research Prize to be presented at each Biennial Meeting of The E. H. Angle Education and Research Foundation to the member publishing the outstanding article in The Angle Orthodontist during the preceding biennium.’’ Thereafter, the award was presented at every biennial meeting since 1981. Most recently, at the 2009 Angle Biennial Meeting the award went to James A McNamara, Jr and co-author Yan Gu. A list of all awardees can be found by going to http://www.angle.org and, in the lower right hand corner of the page, click on ‘‘To view the names of all prize recipients in previous years click here’’. The list is also printed in the The Angle Orthodontist in the March issue of even numbered years. The Angle Orthodontist was established in 1931 by a small group of Angle’s students shortly after Dr Angle’s death. The newly widowed Mother Angle was the first editor. However, The Edward H. Angle Research Prize was not adopted by the Board of the Angle Foundation until 1987 and the first award was in 1991. Since the original motion called for the prize to be awarded to, ‘‘... member publishing the outstanding article in The Angle Orthodontist during the preceding biennium’’ it is not surprising that the motion was a relatively internal matter. Some believed that this limitation applied to the The Angle Orthodontist as well, but the electronic age has accelerated the development of a substantial international following for the journal. This is clearly exemplified by the obvious fact that most of the articles in the journal are now authored by non-Angle Society members. The apparent incongruity between the journal’s international character and the relatively internal Edward H. Angle Research prize was recognized long ago. The issue has never been about whether or not nonSociety members should be recognized. The answer to this question was never in dispute. Rather the question has been much more about how to preserve the honor and prestige earned by the work of former winners while also recognizing the role of all contemporary contributors. Like all changes that impact on many people, any change in the award would have numerous difficult practical questions. What if a winning paper has a nonAngle member as author and an Angle member as a coauthor? Or vice versa? All such imaginable combinations do occur. Should there one award or are their multiple awards? Historically the Edward H. Angle Research Prize also has had a small cash award. How would a new system handle this? Some believe that a prize should be awarded in both clinical research and basic research categories. Apart from the difficulties in sorting manuscripts into these discrete categories, others support the role of the journal in bringing clinical and basic work together in support of evidence based clinical procedures. In its broadest sense, basic research means research undertaken without an application in mind; applied research means research undertaken with an application in mind and clinical research simply means there are patients involved. Many think we would have great difficulty sorting the published articles into such discrete categories upon which all could agree. There is no doubt that this award has grown in prestige and the original fundamental purpose of the award must be remembered. Some believe the award can serve a very useful purpose as an incentive for high quality research. With Edward H. Angle as the putative founding father of modern orthodontics in mind, one highly regarded orthodontist suggested to me that this prize could thus serve a function analogous to an orthodontic Nobel Prize. The Nobel Prize is an interdisciplinary award with several categories and worldwide competition. Is this a model to emulate? The prize(s?) could conceivably bring a win-win situation to all involved. Any review and possible changes in the award could, at the very least, only be constructive and bring greater kudos and peer recognition for all our authors.

Prediction of the tensile capacity of cold formed angles experiencing shear lag

The present study deals with the shear lag phenomenon in cold formed angles under tension, which are connected on one leg. A new expression for shear lag factor which represents the net section reduction coefficient has been suggested in the present paper. The proposed expression based on the regression analysis of 108 experimental results reported in the literature is validated by experiments involving net section failure in angles under tension. Totally 18 experiments were carried out on single angles fastened with bolts to the gusset plates under tension loaded upto net section rupture mode of failure. The experimental test parameters considered are number of bolts, pitch and shear lag distances and ratio of connected leg length to unconnected leg length. The tensile capacities are evaluated by various specifications such as AS/NZS:4600:2005, NAS:2001, AISC:2005, BS:5950-Part5:1998, IS:800-2007 and the proposed equation. A comparative study of tensile capacities predicted based on various codes and the experiment results is presented in this paper. For the tested range of specimens, both NAS:2001 and AISC:2005 standards over-predicted the capacities for all the specimens. The IS:800-2007 and AS/NZS 4600:2005 predictions are good for the specimens with three bolted connections and unconservative in the case of specimen with two bolts. Both BS:5950-Part-5:1998 and the proposed equation for IS:801 predict good estimate of the tensile capacity of cold formed angle members. The proposed equation for cold formed steel tension members, which is in the same format of IS:800 (2007) (Indian code for Hot rolled steel design), has been demonstrated to be good.

Full plastic capacity of equal angle sections under biaxial bending and normal force

Steel angle members are usually designed by elastic methods, which may lead to uneconomical design. In order to make use of the plastic reserves of the section, the knowledge of its exact failure surface is important. In this study, it is shown that idealizing the section with lines of no thickness, which is common in the literature, entails a significant error when the neutral axis intersects a leg at a small angle. A simple interaction formula is proposed, which is shown to be very accurate based on an exhaustive analysis of all common angle sections listed in the tables. Further increase in accuracy is achieved through analytical relations for the cross-sectional properties, both elastic and plastic, that are derived. The proposed analysis forms the base of inelastic design and does not address stability issues.

DESIGN FORMULA FOR REHABILITATED ANGLE STEEL MEMBER USING CARBON FIBER REINFORCED PLASTIC PLATES

The authors have developed a tensile force strengthening method using bonded carbon fiber reinforced plastic (CFRP) plate to enhance the life of existing buildings.A rehabilitation technique for compressive force strengthening as well as tensile force strengthening is required to enhance the strength and deformation of steel structure members. This paper reports the results of compressive loading tests on an angle steel brace before and after rehabilitation using bonded CFRP plates. These results show enhanced compressive force carrying capacity and deformation capacity as follows. 1) Although buckling tests showed enhanced flexural rigidity, there was no increment of axial stiffness. 2) An elastic buckling formula using the experimental flexural rigidity from a three-point bending test, gave a conservative evaluation of load carrying capacity. 3) Taking into count the contribution of CFRP up to the elastic limit strain of the steel member, its load carrying capacity could be evaluated from the formula of Design Standard for Steel Structures of AIJ. 4) The CFRP must be bonded over the full length of the angle member.

On the local and global buckling behaviour of angle, T-section and cruciform thin-walled members

This paper reports the results of an investigation aimed at providing fresh insight on the mechanics underlying the local and global buckling behaviour of angle, T-section and cruciform thin-walled steel members (columns, beams and beam-columns). Due to the lack of primary warping resistance, members displaying these cross-section shapes possess a minute torsional stiffness and, therefore, are highly susceptible to buckling phenomena involving torsion – moreover, it is often hard to distinguish between torsion and local deformations. Almost all the numerical results presented are obtained by means of Generalised Beam Theory (GBT) analyses and, taking advantage of its unique modal features, it is possible to shed some new light on how to characterise and/or distinguish the local and global buckling modes of the above thin-walled members. Finally, some comments are made concerning the development of a rational and efficient (safe and economic) approach for their design.

Compression strength of corroded steel angle members

Steel structures corrode when exposed to the environment, and their capacity is reduced accordingly. In practice, when a member is found corroded during inspection, it is necessary to estimate the residual capacity of corroded members in order to decide whether to change the member, repair it or just remove corrosion and re-protect the member. The objective of this article is to provide data to engineers on the structural behavior of corroded steel angle members under compressive load. Sixteen angle members were corroded with an accelerated procedure and then tested in compression. Eight uncorroded members were also tested in compression. The influence of corrosion on compressive capacity was measured and compared to analytical methods accounting for weight loss. Recommendations are drawn from this research to provide guidance to engineers on how to evaluate compressive capacity of corroded members. Needs for future work are also highlighted.

Design Aspects of Single-Angle Members

Used since the very beginning of steel construction, single angle members are found in many different kinds of structures. Nearly all single-angle members are eccentrically loaded in some fashion, yet truss chords, tower legs and similar members not carrying transverse loads are usually designed as centrally loaded members. The ANSI/AISC 360-05 Specification for Structural Steel Buildings prescribes complex design calculations for eccentrically loaded single angles, but also provides simplified equations that adjust the KL/r ratio to account for eccentricities and end restraints. The purpose of this paper is to examine the possibility of simpler calculations and to explore the behavior of single-angle members.

Design of angle trusses by codes and second-order analysis with experimental verification

Popular national design codes provide varied buckling formulae for design of trusses composed of angle members under different end conditions. The reliability of these design methods highly depends on the accuracy in estimating the effective length, slenderness modification equations and the interaction equations. To date, design method using the second-order analysis has become popular because it captures directly the behavior in analysis and eliminates the error in a linear analysis and design such as assumption of the effective length factor. In this paper, the predicted failure loads of the angle trusses by different codified method would be compared with test results. Further, a refined second-order analysis method is proposed here to the design of angle trusses composed of single angle members with accuracy verified by comparing the predicted and the test results.