Lateral Torsional Buckling Strength Research Articles

Effects of un-bonded deviators on the out-of-plane buckling of steel H-beams pre-stressed by a straight tendon cable

The out-of-plane buckling characteristics of a pre-stressed (PS) system that consists of a steel H-beam, rectilinear tendon cable, anchorages and deviators is newly reported, in which the girder is subjected to combined compressive force and bending moment introduced by the tendon. For this, new lateral-torsional buckling theories were analytically formulated and solved for the PS system having no deviator, one intermediate deviator, two deviators at regular intervals and multiple deviators. In order to verify the validity of the proposed theories, numerical examples for the PS system are given and compared with the analysis results by ABAQUS models, which are composed of thin-walled beam, rigid beam and truss cable elements. The results showed that un-bonded deviators installed externally restrain lateral and torsional deformations of the steel beam sufficiently strongly to greatly improve its lateral-torsional buckling strength.

Experimental and numerical evaluation of inelastic lateral-torsional buckling of I-section cantilevers

A primary failure mode for thin-walled steel members is lateral-torsional buckling (LTB), in which steel cantilever beams experience nonuniform twisting and buckling about their weak axes. Analytical and numerical studies related to the elastic LTB of cantilevers abound. However, comprehensive analytical and experimental studies focusing on the inelastic LTB behaviour of cantilevers are rare. Therefore, this study intends to establish a numerical procedure verified with experimental results to evaluate the inelastic LTB strength of steel cantilevers with an I-section. First, an experimental study was performed, in which nine steel cantilever beams with different slenderness and load-height levels were tested. Load–displacement behaviours of steel cantilevers were investigated by measuring lateral and vertical displacements and rotations under the effect of a monotonic end-point load. Subsequently, a two-step numerical procedure is introduced. The elastic LTB loads and the related mode-shapes were determined in the first step, and the nonlinear load-deflection behaviours were evaluated in the second step based on the Riks method. Finally, numerical and experimental results were compared, thereby demonstrating that the presented numerical analysis can be used for predicting the buckling loads, vertical displacements, and torsional rotations at an acceptable level in the design stage.

Effect of beam-deck connection flexibility on lateral torsional buckling strength of wooden twin-beams

Abstract Two finite element solutions are developed for the lateral torsional buckling analysis of timber beam-deck assemblies consisting of two beams braced by decking through fasteners. In contrast to past solutions, both solutions capture the rotational flexibility provided by the connections between the deck boards and the beams. The first solution is intended for systems with partial lateral restraint provided by the deck boards allowing lateral sway while the second solution is intended for systems that are restrained from lateral movement at the deck level. An experimental program is conducted to quantify the rotational stiffness of beam-deck connections for different types of fasteners and the results are input into the finite element formulations to evaluate the corresponding buckling capacities for beam-deck systems. The results indicate that the buckling capacity of beam-deck systems can be significantly increased with commonly used fasteners while high-capacity fasteners can achieve buckling capacities nearly identical to those where rigid rotational connections are assumed.

Neural networks for lateral torsional buckling strength assessment of cellular steel I-beams

An artificial neural network model was developed as a reliable modeling method for simulating and predicting the ultimate force capacities of cellular steel beams. The required data in training, va...

Lateral-Torsional Buckling Behaviour of Triangularly Corrugated Web Beam

Lateral torsional buckling (LTB) is a common failure mode of large span beams. In this phenomenon, the beam becomes unstable along the unbraced length. This instability of beams can be identified by out-of-plane deflection and twisting. In this paper LTB strength of triangularly corrugated web beams under bending condition is investigated. Examined steel beams consist of two flanges and a thin triangularly corrugated web, connected by automatic welding. In the literature, the LTB strength problem of steel beams was dealt with mostly for steel beams with plate, sinusoidal and trapezoidal corrugated webs. Researches of the LTB behaviour of beams with triangularly corrugated webs were found out to be very limited. A parametric study is carried out for various beam spans and corrugation densities. A general-purpose finite element program (ABAQUS) was used. The corrugation densities adopted in this study represent practical geometries, which are common used for such structures in building practice. Plot showing the influence of compressed flange slenderness on value of reduction factor for LTB is presented. It is determined that existing buckling curves poorly describe the change of reduction factor depending on slenderness of compressed flange for triangularly corrugated web beams. Finally, recommendations were proposed for the design of simple supported steel beams with corrugated webs against lateral torsional buckling in accordance with numerical results.

Inelastic Lateral Buckling Resistance of Stepped I-beam with Compact Section and Continuous Bracing

Continuous multispan beams in bridges experiences high negative moment at interior supports and the top flanges of these beams are laterally braced due to the concrete slab or steel deck above it. The negative moment can be resisted by increasing the cross sections of the beams at the supports. An earlier study on the elastic lateral torsional buckling of stepped beam with continuous lateral bracing was conducted to propose new design equations. The main focus of this study is to continue the previous research considering the inelastic buckling of stepped beams. ABAQUS, a finite element method program was used to conduct the buckling analysis of the beams. A total of five different load cases were used in the analysis. The effects of the residual stress and geometric imperfection were also considered for the inelastic buckling strength. Results showed that the inelastic buckling strength exceeds the plastic moment of the section and it is not needed to focus on the inelastic range when computing the lateral torsional buckling strength.

Distortional Lateral Torsional Buckling Analysis of Beams with Overhangs

AbstractThe present study investigated the effect of web distortion on the lateral torsional buckling strength of Gerber systems. Toward this goal, a number of modifications were introduced into tw...

Yielding and lateral torsional buckling limit states for butterfly-shaped shear links

A promising type of hysteretic damper used for seismic energy dissipation consists of a steel plate with cutouts leaving butterfly-shaped links that undergo flexural yielding when the plate is subjected to shear deformations. Butterfly-shaped links, which have linearly varying width between larger ends and a smaller middle section, have been shown in previous research to possess substantial ductility and stable energy dissipation capability, but can be prone to other limit states such as lateral torsional buckling (LTB) or shear yielding.The current work examines the three potential limit states of LTB, flexural yielding and shear yielding, and develops methods to predict which limit state will control along with the associated strength. First, the governing differential equation for elastic LTB of a butterfly-shaped link is formulated and a relatively simple equation is developed to predict the critical shear force associated with elastic LTB. The shear yielding and flexural yielding limit states are then described and equations are presented to predict the associated shear strength of the butterfly-shaped links. The accuracy of the equations is then evaluated against a series of finite element (FE) models that are validated against previous experiments.It was found that butterfly-shaped links that are thick enough to prevent lateral torsional buckling, experience a progression of limit states including: (1) yielding in one mode (flexural or shear), (2) geometric hardening associated with increasing tension forces in the links, and (3) further yielding associated with biaxial stresses. The equation developed for lateral torsional buckling produced an average LTB strength that was within 4% of the FE model results and the equations for flexural yielding and shear yielding predicted the strength of the FE models within 3% on average.

Cross-Section Properties and Elastic Lateral-Torsional Buckling Capacity of Steel Delta Girders

In this paper, the behavior of slender steel delta girders (SDG) is investigated both analytically and numerically. In the analytical analysis, closed-form equations for cross-section properties of SDG are derived. They are then compared with solutions obtained numerically. Using these cross-section properties, the theoretical elastic lateral-torsional buckling (LTB) strength of these girders are determined and compared with results obtained from a finite element analysis. The results show that the theoretical LTB equation derived for general open monosymmetric I-sections can be applied to these delta girders. Additionally, it is shown that a simplified expression for the coefficient of monosymmetry $$\beta_{x}$$ derived for I-sections can be used in the computation of LTB strength for SDG. A parametric study is then performed to demonstrate the effectiveness of SDG in achieving a favorable strength-to-weight ratio when compared to standard I-section members. Based on the results of this parametric study, it is recommended that the height and width of the delta region of the cross-section be equal to two-fifth the height of the web and three-quarter the width of the compression flange, respectively.

Lateral torsional buckling of welded wide flange beams under constant moment

The structural steel design specification in Canada, CSA S16-14, uses the same equations for the design of rolled and welded shape beams for lateral torsional buckling (LTB). A recent study has shown that the current design equations might overestimate the capacity of welded wide flange (WWF) beams. This paper evaluates the performance of the current design equations in providing LTB capacities of welded I-shape beams (WWF beams). An extensive finite element (FE) analysis is performed for simply supported WWF beams subjected to constant moment. In total, 256 FE models are analyzed and it is observed that both CSA and AISC overestimate the LTB capacity of welded I-shape beams by as much as 37%, particularly when residual stress measured at Lehigh University is used in the analysis. Also, the Eurocode is found to be conservative and the proposed equation by MacPhedran and Grondin in 2011 provides better predictions of LTB strengths of WWF shapes than the current CSA approach.

Behaviour and design of cold-formed steel built-up section beams with different screw arrangements

An experimental and numerical investigation of cold-formed steel built-up beams with different screw arrangements is presented in this paper. A total of 35 beams were tested under four-point bending with different screw arrangements in the moment span. The built-up sections were assembled using self-tapping screws from either two lipped channels connected back-to-back at the web to form an open section or two plain channels connected face-to-face at the flanges to form a closed section. Finite element (FE) models have been developed and validated against the test results for the built-up open section beams and built-up closed section beams, respectively. It is shown that the FE models can accurately predict the behaviour of cold-formed steel built-up beams with different screw arrangements. A parametric study on built-up beams with larger span and various screw spacing was further carried out using the verified FE models. The test and numerical results were compared with the design strengths predicted by the direct strength method (DSM) for cold-formed steel structures, with contingent considerations of the screws when determining the elastic buckling moments in the finite strip analysis. A reliability analysis was performed to evaluate the reliability of the current DSM equations. It is shown that the current DSM equations can predict the design strengths of built-up open section beams well in this study, with the assumption that the strength of the built-up section is the sum of two component profiles. However, the design equations for local buckling strength are generally conservative for the built-up closed section beams failed by local buckling. Meanwhile, the design equations for lateral-torsional buckling (LTB) strength cannot be directly used for the built-up closed section beams with relatively large screw spacing that failed by LTB with cross section distortion or separation of two component channels. It should be noted that LTB mode with cross section distortion was found in built-up closed section beams with large screw spacing. A modified design rule based on DSM is then proposed, which is shown to improve the accuracy of the predicted strengths. Moreover, the maximum longitudinal screw spacing for built-up closed section beams was also recommended for design practice.

Applicability of North American standards for lateral torsional buckling of welded I-beams

Design specifications in North America, unlike their European counterpart, use same equations for design of rolled and welded shape beams for lateral torsional buckling (LTB). A recent study by MacPhedran and Grondin (2011) has shown that the current Canadian design equations might overestimate the capacity of welded wide flange (WWF) beams, which are welded I-shapes, requiring further investigation. This paper evaluates the performance of the current design equations for LTB capacities of welded I-shape beams. Nonlinear Finite Element (FE) analysis is performed for simply supported WWF beams subjected to constant moment, linear and nonlinear moment gradient. Three types of linear moment gradients are investigated: end moment ratios of 0.5, 0.0, and − 1.0. Also, two types of transverse loadings are considered: a concentrated load at mid-span and uniformly distributed load along the length, and applied at the top flange, shear center, and at the bottom flange. In total, 416 FE models are analyzed and it is observed that for constant moment loading both CSA and AISC overestimate the LTB capacity of welded I-shape beams by as much as 37%. FE analysis also shows that current CSA strength curve overestimates significantly the strength of WWF beams by as much as 40% for end moment ratio of 0.5. For transverse loading, current CSA strength curve overestimates the capacity significantly for top flange loading and underestimates for bottom flange loading. Also, Eurocode is found to be conservative for all cases and the proposed equation by MacPhedran and Grondin (2011) provides better predictions of LTB strengths of WWF shapes than the current CSA approach.

Assessment of I-Section Member LTB Resistances Considering Experimental Test Data and Practical Inelastic Buckling Design Calculations

The current AASHTO and AISC Specification equations characterizing the lateral-torsional buckling (LTB) resistance of steel I-section members are the same, with minor exceptions, and are based in large part on unified provisions calibrated to experimental data. This paper takes a fresh look at the correlation of the flexural strength predictions from these equations with a large experimental data set compiled from research worldwide. To account fully for the moment gradient and end restraint effects present in the physical tests, the study employs practical buckling calculations using inelastic stiffness reduction factors (SRFs) based on the design resistance equations. The study focuses on uniform bending tests as well as moment gradient tests in which the transverse loads are applied at braced locations. Reliability indices are estimated in the context of building design. It is shown that a proposed modified form of the current resistance equations provides a more uniform level of reliability, as a function of the LTB slenderness, consistent with the target intended in the AISC Specification. The paper also calls attention to the limited experimental data pertaining to the inelastic LTB resistances in certain cases. The paper concludes by providing additional recommendations for LTB strength calculations in routine design, including illustrative plots conveying the impact of the proposed changes.

05.25: Lateral torsional buckling investigation on welded Q460GJ structural steel unrestrained singly‐symmetric beams under a point load

ABSTRACTThis paper reports the results of experimental tests and parametric analyses for the lateral torsional buckling (LTB) strengths of welded singly‐symmetric I‐shaped cross‐section beams fabricated from Q460GJ structural steel plates. Simply supported beams with varying lengths and sectional dimensions were tested by using a special testing system. In order to achieve the ideal loading condition and the simply supported boundary condition, a special testing system including the and the loading system and supporting system was invented and used in the experimental tests, and the testing system was verified. Meanwhile, a finite element model established by a finite element program ABAQUS, correlated well with the experimental result, was used to conduct the parametric studies. The result showed that the finite element model can be useful in simulation. Thus, the parametric studies were conducted, using the verified finite element model, to investigate the effect of member slenderness and height‐to‐width ratio. It is well known that each design specification has its own background and compiling principles, and the formula of each design code is very difficult. Q460GJ structural steel is a new material, thus, it is very hard to say which design code is more suitable to predict the lateral torsional buckling strengths of welded H‐shaped sectional beams fabricated from Q460GJ structural steel plates. While comparing the test results and the parametric studies results with the prediction of some design code including Chinese design code GB50017‐201X (2012) and GB50017‐2003 (2003), American code (ANSI/AISC360‐10, 2010) and EC3 (2005), some important conclusions can be found. The results demonstrate that the global stability design methods in GB50017‐201X (2012) and EC3 (2005) for rolled sections or equivalent welded sections may be more appropriate for Q460GJ structural steel beams. In addition, the design methods in GB50017‐2003 (2003) and the American code (ANSI/AISC360‐10, 2010) may not be conservative for Q460GJ structural steel beams.

繰返し曲げせん断力を受けるH形断面テーパー梁の座屈形式と塑性変形性能

Web-tapered tapered H-shaped beams, which have a continuous reduction in section, have been utilized in steel-frame structures for more efficient utilization of structural materials. On the other hand, section stiffness decreases along a beam's axis, and the member stress increases. For this reason, it is more important to investigate the buckling behavior and the progress of the plasticity of a tapered H-shaped beam than that of a uniform H-shaped beam. In the past, the authors investigated elastic plate buckling strength and lateral torsional buckling strength using an energy method and numerical analysis. An estimation method and formula were proposed in those research studies. This study examines the inelastic buckling strength and plastic deformation capacity of Web-tapered H-shaped beams with depth tapered through by a cyclic loading test and numerical analysis. Twelve tapered beams and five normal straight beams were tested. The cyclic behavior and collapse mode of these specimens were investigated. In addition, multiple simulations using numerical analyses were carried out. Then, the collapse mode and plastic deformation capacity of the tapered beam were evaluated by using indexes that were determined on the basis of the elastic buckling strength. First, it is clear that the behavior and collapse mode of tapered beams are changed by the following characteristics: taper gradient, flange plate slenderness, web plate slenderness, and lateral bracing length. The skeleton curves of each specimen are taken from the load-displacement relationships obtained by a cyclic loading test. Using these skeleton curves, the effects of a tapered gradient on the performance of an H-section beam are examined. The value of the plastic deformation capacities of beams collapsed by web plate buckling or lateral torsional buckling are estimated from the eigenvalue of each tapered beam. This means that the plastic deformation capacity increases when the eigenvalue is higher. On the other hand, the values of the plastic deformation capacity of a beam collapsed by flange plate buckling are almost the same without regard to its own eigenvalue. Because the flange plate buckling strength decreases when the tapered gradient is steep, and plastic reason in flange is longer. Second, the effect of a cyclic load on tapered beams is considered. It is evident that beams with low plate slenderness and large plastic deformation capacity are affected by cyclic loads. That value The plastic deformation capacity of these beams decreases by cyclic loading. Third, the authors propose a new plate buckling slenderness index (WFγ) and lateral buckling slenderness index (γb). These slenderness indexes are obtained from the elastic buckling strength. It is clear that the collapse mode of a tapered beam can be classified using these indexes. In the range of WFγ / γb > 2.4, the collapse mode is plate local buckling, and in the range of WFγ / γb < 2.4, the collapse mode is lateral torsional buckling. Finally, the maximum strengths and plastic deformation capacities of tapered beams are estimated by using the plate buckling slenderness index and lateral buckling slenderness index when the collapse mode of tapered beams is classified by these indexes. The elastic buckling strength of the tapered beams do not decrease as a result of the coupled instability effect between the plate local buckling and lateral torsional buckling. However, the maximum strength and the plastic deformation capacity decrease as a result of these effects.

Analysis and Design of Stabilizer Plates in Single-Plate Shear Connections

Single-plate shear connections experience some magnitude of torsional moment, either due to the lateral torsional buckling phenomena or due to the effects of lap eccentricity. When the required torsional strength of the connection exceeds the available torsional strength of the connection, the designer has two options: alter the geometry of the connection to increase the torsional resistance of the connecting plate or provide stabilizer plates. Thornton and Fortney (2011) provide analysis techniques for accounting for the effects of lap eccentricity and lateral torsional buckling strength. Part 10 of the Manual (Steel Construction Manual, 14th ed., 2011) presents a summary of the equations used for such an evaluation. However, no discussion was provided by Thornton and Fortney with regard to the size and detailing of a stabilizer plate when such a plate is required. This paper presents recommendations for the analysis with regard to appropriate stabilizer plate cross-sectional dimensions and the attachment of the stabilizer plate to the connecting material and support. Three different types of stabilizer plates are presented along with recommendations for the design and detailing of the stabilizer plates; the impact that each type has on the design of the single-plate shear connection and the supporting column is presented as well.

Elastic lateral-torsional buckling strength and torsional bracing stiffness requirement for monosymmetric I-beams

Elastic lateral-torsional buckling (LTB) is a common failure mode of large span beams. In this phenomenon the beam becomes unstable along the unbraced length. This instability of beams can be identified by out-of-plane deflection and twisting. Using discrete torsional braces is one of the ways to prevent LTB. In this paper the LTB strength and bracing stiffness requirements of monosymmetric I-beams with discrete torsional braces, under pure bending condition is investigated. First, an analytical solution for an unlimited number of braces is presented by using an energy approach. Then the results of the proposed equations are compared with the results of a 1-D finite element analysis and the equivalent continuous brace stiffness concept. The comparison shows that the proposed equations are in good agreement with the finite element analysis. A parametric study is carried out for various dimensions and geometrical properties of cross sections. The results show that using the monosymmetric I-sections with larger compression flange is the more economical solution. Finally, the effects of linear moment gradient conditions and the cross sectional distortion on the LTB strength and bracing stiffness requirement are investigated.

Lateral torsional buckling of steel twin plate girder systems with torsional braces only

This paper presents results of both an experimental and a finite element study on the lateral torsional buckling behaviour and strength of twin plate girder systems with only discrete torsional braces. Two scaled twin-beam specimens with different arrangements of lateral and torsional braces were tested and results were used to validate the finite element model. The finite element study considered the effect of individual brace member stiffness and the number of braces. Results showed that for twin plate girders braced with only torsional braces, the critical buckling moment has the most significant increase when the number of interior braces increases from two to three. For a given girder section, the increase in the critical moment capacity by increasing the cross-frame member size is minimal. The lateral torsional buckling moment equation as well as the brace force design procedure contained in the Canadian Highway Bridge Design Code were examined. A relationship between the ratio of provided-to-required torsional stiffness and the effective length factor was discussed.

An Evaluation on the Effect of Cross-Frame Spacing Limit on Buckling Strength of Horizontally Curved Multi-Girder Systems under Uniform Bending

This study provides an evaluation on the effect of existing cross-frame spacing limit on buckling strength of horizontally curved girder systems. Since current design specifications only consider individual buckling between cross-frames for multi-girder systems, this study utilizes global lateral torsional vertical buckling strength of such girder systems. Elastic eigen value analysis was conducted using the finite element program, ABAQUS. Models with varying degrees of curvature, flange width-to-thickness ratio of 12, 10 and 8 and span length-to-depth ratio of 16, 20 and 24 were generated and their respective maximum cross-frame spacing was computed. These models were then subjected to uniform bending in order to obtain the buckling strength and different buckling modes from the analysis. Finally, critical buckling capacity ratio (Mcurved/Mstraight) was used to establish the effect of the existing cross-frame spacing limit on the buckling strength of horizontally curved multi-girder systems. Using comparative analysis, the results showed that the existing cross-frame spacing limit gave conservative critical buckling capacity ratio for models with high degree of curvature. However, for models that yielded the maximum cross-frame spacing equal to 0.25L and low degree of curvature, the critical capacity ratio decreased significantly. A suggestion was developed based on the results of the finite element analysis to provide a better guide on the design of cross-frame spacing limit.

Lateral torsional buckling strength of unsymmetrical plate girders with corrugated webs

This paper deals with lateral torsional buckling of plate girders with corrugated webs (CWG). The research includes both theoretical and finite element analyses for un-symmetrical plate girders with corrugated webs subjected to uniform moment. A new warping constant for this un-symmetrical cross-section is derived taking into consideration the cross-sectional variation along the girder length. Trapezoidal corrugated web profile is taken into consideration in the derivation. The location of the shear center is determined and a closed form of the warping constant is derived. The un-symmetry of the web-less beam, which agrees with the case of CWG, is considered in the calculation of the lateral torsional buckling strength. The results are verified with those obtained using the finite element technique and gave good agreement. A comparison with different specifications and codes is conducted to investigate the effect of un-symmetry on the plate girder strength. The effect of cross-section geometrical configurations on the lateral torsional buckling strength under uniform moment is investigated and discussed.