Angle Section Beams Research Articles

Testing, FE modelling and design of pin-ended stainless steel equal-leg angle section columns and beam–columns

The behaviour and design of pin-ended stainless steel equal-leg angle section members under compression and compression plus minor-axis bending are investigated herein. The studied members are cylindrically pinned about the minor axis. An experimental investigation, including material testing, initial geometric imperfection measurements and physical tests on hot-rolled stainless steel equal-leg angle section members is first presented. Numerical models are developed and validated against the new experimental data. A numerical parametric study is then presented considering both hot-rolled and cold-formed stainless steel angle section columns alongside beam–columns with a wide range of slenderness values. Finally, new design proposals for pin-ended stainless steel equal-leg angle section members under compression and combined compression and minor-axis bending are developed and verified against the results of existing physical experiments, as well as the newly-generated test and numerical results. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the EN 1990 procedure.

Testing, numerical analysis and design of stainless steel equal-leg angle section beams

The stability and design of stainless steel equal-leg angle section members subjected to uniaxial bending are studied herein. An experimental investigation, comprising material testing, initial geometric imperfection measurements and physical tests on hot-rolled austenitic stainless steel equal-leg angle section beams is first presented. The test results are then used to validate shell finite element models developed within ABAQUS, which are in turn used to undertake numerical parametric studies that consider both hot-rolled and cold-formed equal-leg angle section beams in austenitic, duplex and ferritic stainless steel with a wide range of slenderness values. Recent studies have shown that for angles under major-axis bending, both lateral-torsional and local buckling can arise, while under minor-axis bending, lateral-torsional buckling and Brazier-type flattening can occur. When designing for major-axis bending according to Eurocode 3, both local and lateral-torsional buckling are considered; it is shown herein that equal-leg angle sections under major-axis bending can be designed using a normalised slenderness based on the minimum of the local and lateral-torsional elastic buckling moments, while also considering their ratio. Under minor-axis bending, however, in comparison with the current provisions in Eurocode 3 that only require cross-section checks, it is shown that both safer and more accurate resistance predictions can be achieved when account is taken for lateral-torsional buckling and Brazier-type flattening. New design proposals for stainless steel equal-leg angle section beams, covering both major- and minor-axis bending, are therefore developed. The proposed design rules offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the procedure provided in EN 1990.

Testing, simulation and design of steel equal-leg angle section beams

The stability and design of steel equal-leg angle section members subjected to uniaxial bending are studied herein. An experimental investigation, comprising material testing, initial geometric imperfection measurements and physical tests on hot-rolled steel equal-leg angle section beams is first presented. The test results, in combination with existing experimental data on steel equal-leg angle section beams collected from the literature, are then used for the validation of numerical (shell finite element) models, developed within the commercial package ABAQUS. Next, a numerical parametric study is presented considering both hot-rolled and cold-formed steel angle section beams with a wide range of slenderness values. In major-axis bending, both lateral-torsional and local buckling were observed, with the former characterised by lateral deflection and twist of the cross-section along the member length but no cross-section deformation and the latter by relative twist and transverse bending of the outstands. In minor-axis bending, lateral-torsional buckling and Brazier flattening were observed, with the latter characterised by splaying of the outstands. Note that, for equal-leg angles under minor-axis bending, lateral-torsional buckling is dominant when the cross-section tips are in compression, while Brazier flattening is more influential when the cross-section tips are in tension. When designing for major-axis bending according to Eurocode 3, both local and lateral-torsional buckling are considered; it is shown herein that equal-leg angle section beams under major-axis bending can be designed using a normalised slenderness based on the minimum of the local and lateral-torsional elastic buckling moments, while also considering the ratio of the local to the lateral-torsional elastic buckling moments. For minor-axis bending, Eurocode 3 only requires cross-section checks; this is found to result in unsafe predictions in some cases. It is shown that both safer and more accurate resistance predictions can be achieved when lateral-torsional buckling and Brazier flattening are accounted for in the design of equal-leg angle section beams under minor-axis bending, using a normalised slenderness, based on the minimum of the lateral-torsional and Brazier flattening critical buckling moments. Finally, new design proposals for steel equal-leg angle section beams, covering both major- and minor-axis bending, are developed and verified against the experimental and numerical results. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.0, is verified following the EN 1990 procedure.

Experimental and numerical investigations of hot-rolled austenitic stainless steel equal-leg angle sections

The present paper reports a thorough experimental and numerical study on the cross-section behaviour and resistances of hot-rolled austenitic stainless steel equal-leg angle section structural members. The experimental programme was performed on a total of five different angle sections, and involved ten stub column tests and ten laterally restrained 4-point bending tests about the cross-section geometric axes (parallel to the angle legs), together with measurements on material properties and initial local geometric imperfections. The testing programme was followed by a systematic finite element simulation programme, where the developed numerical models were firstly validated against the experimentally derived results and then employed to carry out parametric studies for the purpose of generating further structural performance data over a broader range of cross-section dimensions. The numerically derived results were then employed together with the test data to assess the accuracy of the established design rules for hot-rolled austenitic stainless steel equal-leg angle section stub columns and beams given in the European code. The results of the assessment revealed an overly high level of conservatism and scatter of the European code in predicting cross-section capacities of hot-rolled austenitic stainless steel equal-leg angle section stub columns and beams, which can be mainly attributed to the neglect of the beneficial material strain hardening. The continuous strength method (CSM) is a well-established design approach, taking due account of material strain hardening in the determination of cross-section resistances, and has been recently extended to cover the design of mono-symmetric and asymmetric stainless steel open sections in compression and bending about an axis that is not one of symmetry. The CSM was assessed against the experimental and numerical results on hot-rolled austenitic stainless steel equal-leg angle section stub columns and laterally restrained beams, and shown to result in substantially more precise and consistent cross-section capacity predictions than the European code.

Brazier Effect of Thin Angle-Section Beams under Bending

Thin-walled section beams have Brazier effect to exhibit a nonlinear response to bending moments, which is a geometric nonlinearity problem and different from eigenvalue problem. This paper is aimed at investigating the Brazier effect in thin-walled angle-section beams subjected to pure bending about its weak axis. The derivation using energy method is presented to predict the maximum bending moment and section deformation. Both numerical analyses and experimental results were used to show the validity of the proposed formula. Numerical results show that the boundary condition can influence the results due to the end effect, and that the influence tends to be negligible when the length of angle beam goes up to 30 times as the length of beam side. When the collapse in experiments is governed by Brazier flattening, the moment vs. curvature curve deviates significantly from the linear beam theory, but coincides well with the proposed formula in consideration of the restraint due to limited span of experimental setup. It can be concluded that the proposed formula shows good agreement with numerical results and experimental results.

Modal characteristics of cracked thin walled unsymmetrical cross-sectional steel beams curved in plan

The paper aims to develop a generalized Finite Element (FE) model for multiple cracked thin-walled curved beams by taking account of the warping effects in the cracked section. Modal features such as natural frequencies and mode shapes for cracked and uncracked curved beam have been presented for sections having one axis of symmetry and with no axis of symmetry for various crack parameters. Theoretical results have been validated by laboratory vibration test on steel channel and angle section beams. The study reveals that cracked curved thin-walled beams behave differently under vibratory load compared to that with straight beams.

Nonlinear instability of angle section beams under uniformly distributed loads

This paper presents a study on the flattening behavior of angle-section beams of finite length subjected to uniformly distributed transverse loads. Analytical solutions for static instabilities of angle-section beams when they are bent about their weak axis are derived using energy methods. The basic assumptions used in the present study are that the total strain energy of an angle-section beam subjected to a uniformly distributed load can be simplified into a two-stage process. One is the bending response of the two legs behaving as the plate; the other is the bending response as a beam with flattened section. The nonlinear instability is derived by applying the minimum potential energy principle and the corresponding static critical moments associated with the section flattening-induced buckling are determined. To validate the analytical solution developed, nonlinear finite element analyses are also conducted. Good agreement between the present solution and the FEA results is demonstrated.

A hybrid approach to detect crack parameters using measured natural frequencies in thin walled angle section steel beams

Present study outlines a hybrid approach using Finite Element Method (FEM)–Response Surface Method (RSM)–Genetic Algorithm (GA) to predict the crack parameters, namely crack position and crack depth ratio with the help of only the measured natural frequencies of cracked thin walled beams. Numerical experimental trials of cracked beams have been conducted based on design of experiment (DOE) approach using an improved Finite element model. The improvement has been achieved by consideration of warping stiffness in cracked angle section beam. Thereafter, regression analysis has been conducted to construct Response Surface Function (RSF). Optimum crack parameters were then calculated using GA by minimizing an objective function which has been formed as the root mean square (RMS) of the residuals between RSFs and measured frequencies. Results of the study indicate that, the proposed approach performs with excellent accuracy and it does not require the response of an uncracked beam as benchmark information.

The Flattening Behaviour of Angle Section Beams Subjected to Pure Bending

The flattening behaviour of angle section beams subjected to pure bending is studied in this paper. Analytical solutions for static instabilities of angle section beams subjected to pure bending about its weak axis are derived using energy methods. Nonlinear finite element model using the code ANSYS is developed to simulate nonlinear snap-through instability of angle section beams under pure bending. The optimization assumption about flattening shape of the leg is proposed, through comparison of between the present solutions, experimental results, and the finite element results.

Geometric nonlinear bending response and buckling of angle-section beams under pure bending

In this paper, the geometric nonlinear bending response of angle-section beams of finite length is investigated by using energy methods. The basic assumptions used in the present study are that the total strain energy of an angle-section beam subjected to pure bending can be simplified into a two-stage process. One is the bending response of the two legs behaving as the plate; the other is the overall bending response as a beam with flattened section. The nonlinear bending response is derived by applying the minimum potential energy principle and the corresponding static and dynamic critical moments associated with the section flattening-induced buckling are determined. To validate the analytical solution developed, geometric nonlinear finite element analyses are also conducted. Good agreement between the present solution and the FEA results is demonstrated.

Nonlinear instability of angle section beams subjected to static and dynamic sudden step loads

This paper presents a study on the flattening behaviour of angle section beams subjected to pure bending. Analytical solutions for both static and dynamic instabilities of angle section beams subjected to pure bending about its weak axis are derived using energy methods. The results show that the dynamic instability of angle section beams under the action of a sudden step moment occurs at a moment about 71% of the corresponding critical static moment, but the deformations of the longitudinal curvature and flattening at the critical dynamic state are almost twice of those corresponding to the static instability case.

Analysis of equal leg single-angle section beams subjected to biaxial bending and constant axial compressive force

Single-angle section beams are generally loaded parallel to their geometrical axes and their cross-sections are not symmetrical to their principal axes. Even equal leg angle beams have only one symmetrical axis. Many types of loading cause biaxial bending and axial forces in these members. Since single-angle section beams are slender members, they also need to be analyzed in terms of flexural buckling, lateral torsional buckling and local buckling effects. In this study, a calculation procedure is presented to analyze the nominal loads of equal leg angle section beams loaded vertically to the axis of the beam. It is assumed that the axial force is composed of a constant compressive force. The constant axial force is only taken into consideration for the uniform compressive stress and the second-degree effects caused in the cross-section. Thus only the biaxial bending moments remain. The first yield, full plastic and critical lateral torsional buckling moments for biaxial bending are calculated with respect to the slenderness of the beam and the axial force. The nominal design force on the cross-section is calculated according to the load and resistance factor design rules. The analysis proposed for the constant axial load can also be used for other axial forces, by using an iterative calculation procedure.

Biaxial Bending and Torsion of Steel Equal Angle Section Beams

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.

Elastic, full plastic and lateral torsional buckling analysis of steel single-angle section beams subjected to biaxial bending

Flexural strength limits of steel single-angle section beams should be calculated based on the full plastic moment capacities, local buckling resistance and lateral torsional buckling capacities of the angle sections. The angle section beams are generally under the effect of external loads applied along the direction of geometrical axes parallel to their legs, so that they cause simultaneous biaxial bending about both principal axes. The behavior of angle sections under biaxial bending is complicated. The stress distribution of the critical points of the section cannot be easily determined since all specific points need to be checked. Furthermore, the design specifications require the consideration of the full plastic moment capacities of angle sections. This brings up the question of determining the required increase in first yield moment in order to attain full plastic moment capacities. Since single-angle section beams are thin walled slender structural members, they cannot be designed only according to their elastic and plastic moment capacities. Lateral torsional buckling and local buckling cases need to be considered in determining nominal design moments. In this study, the bending moment about the minor principal axis is assumed to be less than or equal to the moment about the major principal axis. Under that condition the first yield moment capacities, the interaction diagrams between first yield and full plastic moment capacities and critical lateral torsional buckling moments are calculated. These values are obtained by means of dimensionless coefficients, and design procedures have been given for the case of biaxial bending for single-angle section beams taking LRFD [LRFD Load and resistance factor design of single-angle members. Chicago (IL): American Institute of Steel Construction; 2000] rules into account.

Buckling and Torsion of Steel Unequal Angle Beams

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 any 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 behavior of restrained beams, a third has studied the lateral buckling of unrestrained beams, and a fourth the biaxial bending of unrestrained beams. In each paper, simple design methods have been developed. In a companion paper an approximate method of predicting the second-order deflections and twist rotations of steel angle section beams under major axis bending and torsion is developed. The 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 of the series and the lateral buckling proposals of the third paper to approximate the member capacities. This method is extended to steel unequal angle beams in the present paper.

Biaxial Bending of Steel Angle Section Beams

The loads applied to angle beams usually act out of the principal planes so that they cause simultaneous biaxial bending about both principal axes. The general practice for designing unbraced beams...

Lateral Buckling Strengths of Steel Angle Section Beams

The design of unbraced steel angle section beams against biaxial bending and torsion requires the ability to predict their lateral buckling strengths when bent about the major principal axis. Present design code formulations of lateral buckling strength are based on research on doubly symmetric I-section beams, and may be inappropriate for monosymmetric and asymmetric angle section beams. This paper presents close approximations for the elastic lateral buckling moments of equal and unequal angle section beams loaded by uniformly distributed loads which act at or away from the shear center. Small and large twist rotation elastic analyses of angle section beams with initial twist rotations are used with interaction equations for the biaxial bending section moment capacities to investigate present design code formulations for lateral buckling strength. It is found that these code formulations are unnecessarily conservative, especially at high slendernesses, where the moment capacities predicted by them may be less than the minor axis section capacity instead of greater. An improved formulation is proposed which is simpler and more economic than the present formulations. The use of the elastic lateral buckling approximations in the improved design moment capacity formulation is demonstrated in a worked example.

Moment Capacities of Steel Angle Sections

Steel angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion. However, the recommendations of many design codes are unnecessarily conservative when applied to the bending of angle section beams, or are of limited application, or fail to consider some effects which are thought to be important. In this paper, consideration is given to the first-order elastic analysis of the biaxial bending of angle section beams including the effects of elastic restraints, and proposals are developed for the section moment capacities of angle sections under biaxial bending which approximate the effects of full plasticity in compact sections, first yield in semicompact sections, and local buckling in slender sections. Proposals are developed for the bearing, shear, and uniform torsion capacities of angle section beams in a companion paper. The proposals in this and the companion paper can be used to design steel angle section beams which are laterally restrained so that...

Bearing, Shear, and Torsion Capacities of Steel Angle Sections

Steel angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion. However, many design codes do not have any 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. In this paper, proposals are developed for the section capacities of angle sections under bearing, shear, and uniform torsion. In a companion paper, consideration is given to the first-order elastic analysis of the biaxial bending of angle section beams, including the effects of restraints, and proposals are developed for the section moment capacities of angle sections under biaxial bending. The proposals in this and the companion paper can be used to design steel angle section beams which are laterally restrained so that lateral buckling and second-order effects are unimportant.

Variable twist torsion tests on carbon fibre composite beams

A detailed experimental programme of work is presented which examines the constrained torsional response of carbon fibre composite beams for the cantilevered configuration with torque applied at the free end. The behaviour of open-section beams and that of single-cell closed-section box beams is reported and discussed and the experimental findings are shown to corroborate simple engineering theoretical approaches. Tests have been carried out on zed and angle-section beams and thus the effects of primary and secondary warping restraint respectively on the torsional response of open-section beams are examined. The behaviour of zed-section beams is governed, in the main, by primary effects and that of angle-section beams is associated solely with secondary effects. The stress distributions along the beams and around the cross-sections are determined from the measured strains during test obtained from surface bonded strain gauges and comparison of these with theory is shown to be in good agreement. The essential differences in response to constrained torsion between open and closed-section beams are detailed in the paper and the importance of experimental tests in the analysis of composite structures is highlighted.