Equal-leg Angle Research Articles

Experiment and design of cold-formed steel equal-leg lipped angle under axial compression

To study the buckling behavior and the design method of the load-carrying capacity of cold-formed thin-walled lipped angle, axial compression tests were carried out on 32 lipped angle columns with different sections and slenderness ratios which were manufactured with high strength zinc-coated grades G450 structural steel sheets. The experimental results showed that the long column with a small width-to-thickness ratio displayed global flexural-torsional buckling, local buckling was found for the short column with a large width-to-thickness ratio. Other specimens demonstrated interactive buckling with local buckling and flexural-torsional buckling. The specimens with torsional buckling all showed post-torsional buckling strength. Then ABAQUS finite element software was used to simulate the lipped angle specimens. The simulation results were in good agreement with the test results about buckling modes and ultimate strength which indicated that the established finite element analysis model was reasonable and feasible. Therefore, the influences of the slenderness ratio, width-thickness ratio, and width ratio of the leg to lip on the ultimate strength of cold-formed thin-walled lipped angle were analyzed using finite element software. The analysis showed that the ultimate capacity of the angle decreased greatly with the increase of the slenderness ratio. The ultimate capacity increased in the range of width-to-thickness ratios of 15–30 when the angles had the same lengths. The increasing of the width of the lips increased the ultimate capacity, but the increase of the ultimate capacity of the angles would lower when local buckling occurred at the lips. Finally, based on the test results, the modified effective width method and direct strength method were proposed to calculate the capacity of the cold-formed thin-walled lipped angle under axial compression. The comparison between the predicted results with the test and finite element analysis showed that the proposed methods were accurate and feasible.

Pin-ended stainless steel equal-leg angle section members under compression and major-axis bending: Experimentation, FE modelling and design

The behaviour and design of cylindrically-pinned stainless steel equal-leg angle section members under compression and compression combined with strong-axis bending are investigated herein. 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 by means of shell finite element modelling formulated within ABAQUS and validated against experimental data. A numerical parametric study is then presented considering both hot-rolled and cold-formed stainless steel equal-leg angle section columns alongside beam–columns with a wide range of cross-section and member geometries. Finally, new design proposals for cylindrically-pinned stainless steel equal-leg angle section members under compression and compression plus major-axis bending are developed and verified against the results of physical experiments and numerical simulations. 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.

Tests, simulations and design of aluminium alloy equal-leg angle section stub columns after exposure to fire

This paper reports experimental and numerical studies on the compression resistances of aluminium alloy equal-leg angle section stub columns after exposure to fire. An experimental programme was first conducted, including heating tests, eight post-fire material coupon tests and sixteen post-fire stub column tests. Following the experimental programme, a numerical modelling programme was conducted, where finite-element models were developed and validated. The validated models were then used to perform parametric studies to derive additional numerical data. Based on the obtained test and numerical data, the relevant design rules used in Europe, China, America, Australia and New Zealand as well as the continuous strength method were assessed. The assessment results generally show that the current international standards lead to significant conservative and scattered design resistances when used for the post-fire design of aluminium alloy equal-leg angle sections under compression, particularly for those after exposure to elevated temperatures of 300 °C to 550 °C, due to the neglect of significant post-fire material strain hardening. The continuous strength method is found to provide greatly improved design accuracy and consistency over the European, Chinese, American and Australian/New Zealand standards for the post-fire design of aluminium alloy equal-leg angle sections, since it accounts for the post-fire material hardening.

Stability bearing capacity of equal-leg angle steel columns with end connection joints

This study investigated the stability bearing capacity of Q355 equal-leg angle steel columns with end connection joints for transmission towers and proposed a new design method for stable bearing capacity. A total of 39 structural tests were conducted considering the connection joints. The test results, including the failure modes and load-response histories, were reported. The numerical simulations were conducted and validated using multiple comparisons. An extensive parametric study based on a calibrated finite-element model was conducted to investigate several influential parameters. The critical elastic buckling load of a three-span continuous beam with rigid or elastic supports was derived, and the relationship between the effective length coefficients and the support stiffness was obtained. Based on the experimental and numerical simulation results, a stable bearing capacity design method applicable to equal-leg angle steel columns with end connection joints was proposed. It is shown that the proposed design method improves the consistency and reliability of the prediction of the ultimate strength.

Design procedures for cold-formed stainless steel built-up columns assembled from equal-leg angles

In this paper, the structural behaviour of cold-formed stainless steel (CFSS) built-up T- and cruciform-section columns is studied experimentally and numerically, and the effect of discrete fasteners on their flexural and torsional rigidity is considered. To build the singly symmetrical built-up T-section columns, two equal-leg angle sections made of lean-duplex grade EN 1.4162 were assembled back-to-back. The doubly symmetrical built-up cruciform-section columns were composed of four star-oriented equal-leg angle sections made of austenitic grade EN 1.4301. They were connected using M8 bolts of class 8.8. Two pin-ended built-up T-section columns with length of 1000 mm, and four built-up cruciform-section columns with lengths of 600 mm and 2400 mm with semi-rigid support conditions, were tested under pure axial compression. As observed in the tests, built-up T-section columns experienced flexural-torsional buckling failure, whereas built-up cruciform-section columns failed in torsional buckling mode. Finite element models were validated against the conducted experiments and used to perform a parametric study of the structural behaviour of CFSS built-up T- and cruciform-section columns. The study included the column length, cross-sectional dimensions and bolt spacing as variables. The experimental and numerical data, i.e., the column strengths and failure modes, were compared against the results obtained based on the European and North American Specifications alongside a recent method established for cold-formed carbon steel equivalents and based on the Direct Strength Method (DSM). It is shown that the DSM-based approach predicts the ultimate buckling resistances of the considered built-up columns more accurately than the available codified design methods.

Assessment of design procedures for the buckling resistance of hot-rolled steel equal leg angles under concentric and eccentric compression

This work presents an extensive advanced numerical study calibrated with recent experimental results available in the literature on the buckling behavior of hot-rolled steel angles under concentric and eccentric compression to support the ongoing revision in Europe of the design rules for angles concentrically and eccentrically loaded in compression. The numerical results were used for the assessment of existing design procedures commonly applied in practice (Eurocodes and AISC), as well as new recently proposed recommendations. In general, the current analytical rules do not present good agreement with the experimental and calibrated numerical results, even showing unsafe results for some slenderness ranges. In case of fixed members in eccentric compression, these design rules are extremely conservative, reaching ratios rN (numerical versus analytical resistances) in excess of 2. The new proposals resulting from the project ANGELHY present an improved agreement with the numerical results, showing that they may efficiently replace the current design rules in the Eurocodes. However, for concentric compression, a reliability assessment shows that the required partial factor is γM1* = 1.1.

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.

Analysis of the stability behavior of cross bracings in transmission towers based on experiments and numerical simulations

Angle steel towers are widely used in various transmission lines owing to their convenient connections, easy availability, simple production processes, and high efficiencies. Cross bracings play an important role in resisting wire tension, wind, and snow loads as the main support components ensuring the stability of an angled steel tower. Thus, an analysis of the buckling resistance of cross bracings is significant in improving the bearing capacity of transmission towers. In this study, full-scale tests of equal-leg and unequal-leg angles in planar tower sections were conducted. The influence of the axial force ratio on the stability of a cross bracing was studied based on numerical simulations and compared with the current codes. The results revealed that the failure mode of an equal-leg angle cross bracing was always out-of-plane buckling, whereas the final failure mode of an unequal-leg angle steel cross bracing could be out-of-plane buckling or both out-of-plane and in-plane co-buckling. With an increase in the axial force ratio, the buckling resistance of the cross bracing decreased rapidly, with over 40% decline in the amplitude. The buckling resistance of the unequal-leg angle was approximately 20% higher than that of the equal-leg angle at all axial force ratios. Compared with the current codes for tower structures, we discovered that the code values and finite-element results were considerably different. Notably, the calculation methods of ASCE 10-15 and EN1993-3-1 neglect the variation in the effective length with the axial force ratio. Although DL/T 5154-2012 considers the effect of the axial force ratio, the values are all greater than the finite-element results. The findings of this study can help elucidate the cross bracing stability in angle steel lattice towers.

Residual stress and compression buckling of large welded equal-leg steel angles

In recent years, the use of large angle columns increased in response to the booming constructions of ultra-high-voltage (UHV) transmission towers. Although steel column stability had been studied extensively, fundamental researches on large welded angles were insufficient; the compression buckling strengths of such angles before and after galvanization were unclear. Therefore, this paper measured the residual stresses of welded L300 × 30 and L300 × 20 sections with the sectioning method. There were six non-galvanized and six galvanized specimens. It was found that hot-dip galvanization followed by immediate water cooling altered the residual stresses greatly. Based on the test data, two types of residual stress distribution models were proposed: one was for the non-galvanized welded angles and the other was for the galvanized ones. Next, finite element analyses using ABAQUS were conducted to study the influences of geometric imperfections, galvanization and through-thickness stress variations on the buckling strengths of welded angle columns. Finally, buckling strengths covering a wide range of slenderness ratios were calculated, forming the buckling curves of the large welded equal-leg angles. These curves were then compared with the existing Chinese, European and American design codes. The column design recommendations for the large welded equal-leg angles were given: it was suggested to use GB 50017 curve a, EC3 curve a0, or ASCE 10 curve with λx,n ≤ 1 to design such angle columns.

Stability of equal-leg angle section braces with torsional restraints

Cross bracing using the single leg angle sections are connected on both sides at the joints, affecting the stability capacity of the cross bracing because of the torque. The study on the stability capacity of equal-leg angle sections with the effects of torsional restraints at joints was insufficient. Additionally, there is no clear guidance from relevant design codes. In this study, an end constraint was designed to simulate the effect of torsional restraints for the angle sections. A total of 105 specimens of angle sections, divided into three kinds of pieces (A, B, C), were tested under three boundary conditions. Additionally, Finite Element Method modeling to study the effects of end constraint was parallelly conducted. Class B specimens had the worst stability. When the slenderness ratio is <120, the stability capacity of Class C specimens is larger. When the slenderness ratio is larger than 120, Class A specimens have better stability. The stability capacity of the equal-leg angle sections is positively related to the stiffness of the end constraint, when the stiffness is less than or equal to 200 kN•m/θ, the change of the stability capacity appears more dramatic, when the stiffness exceeds 200 kN•m/θ, the increase becomes slower. The effect of the slenderness ratio and the ratio of the torsional stiffness at nodes to the bending stiffness of columns were quantified through the stability capacities obtained from the experiment and FEMs to propose a modified method for effective length coefficients, which could optimize transmission tower design.

Phenomenological hysteretic model for fixed-end steel equal-leg angle: Development and application

Hysteretic behaviors of steel members are of great significance in the assessment of the realistic ultimate capacity of steel structures subjected to dynamic overloads (e.g. strong earthquakes). To this end, this paper intends to develop a new phenomenological hysteretic model for capturing the inelastic behaviors of steel equal-leg angles, which is extensively used in a latticed steel tower. Specifically, cyclic tests of steel angles were performed, and a 3D finite element (FE) model is developed and validated based on the experimental results. Numerical parametric analyses are then performed to investigate the influences of slenderness ratios, width-to-thickness ratios, and initial imperfections on the hysteretic behaviors of steel equal-leg angles. Based on the parametric results, a phenomenological hysteretic model is proposed to replicate the hysteretic behaviors of steel angles, and its accuracy is demonstrated by further comparing against the experimental results. Finally, the proposed phenomenological hysteretic model is coded into the commercial package ABAQUS and used to simulate the dynamic responses and collapse of a latticed tower under severe earthquakes. The results show that the proposed phenomenological hysteretic model shows high fidelity in reproducing the nonlinear hysteretic behaviors of steel equal-leg angles subjected to cyclic loads. This research can enrich the existing hysteretic models of steel members and provide an accurate method for estimating the realistic responses of steel structures subjected to strong dynamic overloads.

Probabilistic bearing capacity assessment for unequal-leg angle cross-bracings in transmission towers

Unequal-leg angle (ULA) cross-bracings in transmission towers could be adopted to provide more efficient engineering design and save material in some cases, but the buckling behavior of them receives quite less attention than that of equal-leg angle (ELA) cross-bracings. This paper studies the stability bearing capacity and reliability of ULA cross-bracings in transmission towers. Firstly, the experimental study on a full-scale ULA cross-bracing is investigated, and the establishment and validation of its finite element model are also carried out. Then, the bearing capacity prediction for ULA cross-bracings based on the Kriging metamodel is conducted on the basis of experimental and numerical investigations, and the accuracy assessment and comparison with design codes are also proceeded. Finally, based on the Kriging metamodel and Monte Carlo simulation, the reliability of ULA cross-bracings is assessed under the probabilistic framework. The results show that the Kriging metamodel performs the satisfactory accuracy to predict the stability bearing capacity of ULA cross-bracings, while predicted results of design codes are relatively conservative. Furthermore, the reliability of ULA cross-bracings is affected by their thickness, steel grade and tension-compression ratio, where the increase of thickness may be a quite efficient way to increase their reliability.

Structural behaviour and design of press-braked S690 high strength steel angle section long columns

A testing and numerical modelling programme has been conducted to investigate the flexural buckling behaviour and resistance of press-braked S690 high strength steel angle section long columns. The testing programme adopted two press-braked S690 high strength steel equal-leg angle sections and included initial geometric imperfection measurements as well as twelve pin-ended column tests. The testing programme was accompanied by a numerical modelling programme, including a validation study, where finite element models were developed and validated against the test results, and a parametric study, where the validated finite element models were used to generate further numerical data over a wide range of cross-section dimensions and member effective lengths. The obtained test and numerical data were used to evaluate the existing design rules for press-braked S690 high strength steel angle section long columns, as specified in the North American specification, Australian/New Zealand standard and European code. The evaluation results revealed that the North American specification and Australian/New Zealand standard result in a high level of design accuracy and consistency, while the Eurocode leads to excessively conservative and scattered failure load predictions. Finally, a new design approach was proposed and shown to offer more accurate and consistent failure load predictions, with less calculation works, than the design codes.

Experiment and Design Method of Cold-Formed Thin-Walled Steel Double-Lipped Equal-Leg Angle under Axial Compression

The cold-formed steel (CFS) double-lipped equal-leg angle is widely used in modular container houses and cold-formed steel buildings. To study the buckling behavior and bearing capacity design method of the cold-formed steel (CFS) double-lipped equal-leg angle under axial compression, 24 CFS double-lipped equal-leg angles with different sections and slenderness ratios the axial compression were conducted. The test results showed that the distortional buckling occurs for specimens with a small width-to-thickness ratio and small slenderness ratio. The buckling interactive with distortional and global flexural buckling was observed for the specimens with small width-to-thickness ratios and large slenderness ratios. The specimens with large width-to-thickness ratios and small slenderness ratios showed interactive buckling with local and distortion buckling. The specimens with large width-to-thickness ratios and large slenderness ratio developed interactive buckling with local, distortional, and global flexural buckling. The finite element model established by ABAQUS software was used to simulate and analyze the test. The buckling modes and the load-carrying capacities analyzed by the finite element model agreed with the test results, which showed that the developed finite element model was feasible to analyze the buckling and bearing capacity of the CFS double-lipped equal-leg angles. The experimental results were compared with those calculated by the direct strength method in the North American standard and the effective width method in the Chinese standard. The comparisons indicated that the calculated results are very conservative with maximum value 36% and 51% for direct strength method and effective width method, respectively. The coefficient of variation was 0.276 and 0.397, respectively. Finally, the modified direct strength method and the modified effective width method were proposed based on the experimental results. The comparison on the ultimate strength between test results and calculated results by using the modified method showed a good agreement. The modified method can be as a proposed desigh method for the ultimate strength of the CFS double-lipped equal-leg angles under axial compression.

Resistance of Closely Spaced Back‐to‐back Connected Equal Leg Angle Sections

AbstractIn the framework of the European RFCS project ANGELHY, the resistance of built‐up members fabricated from angle sections is studied, amongst others. This paper focusses on the resistance of back‐to‐back connected angle sections. The studied built‐up members are connected through bolted packing plates. Due to the flexibility of this connection, the back‐to‐back connected members do not fully act as a single homogeneous member but the connection stiffness has to be accounted for. However, Eurocode 3 does not provide a clear and generally accepted method for the determination of the buckling resistance of back‐to‐back connected members that do not respect a limit distance of 15imin between the packing plates. This limit is very low and therefore there exists a need of a design method overcoming the limitations. Throughout this paper, a design method will be derived based on a comprehensive numerical study. The numerical model is based on solid finite elements and has been validated with physical tests. Owing to the use of solid elements, it is possible to model explicitly the bolts, the packing plates and all contact regions.

Experimental and numerical studies of stainless steel angle-to-plate connections

This paper presents experimental and numerical studies of stainless steel angle-to-plate connections failing by net section fracture. Tension tests were conducted on 16 austenitic stainless steel angle-to-plate connections, with each consisting of an equal-leg or unequal-leg angle section member bolted to gusset plates by one leg. The specimens were designed with different angle section sizes, number of bolt holes and connection lengths. The key test observed results, including the load–elongation curves as well as the failure loads and modes, were fully reported. The strain distribution at critical cross-sections and the effects of connection length, out-of-plane eccentricity and in-plane eccentricity on net section efficiency were discussed. The experimental programme was supplemented by a numerical modelling programme, where finite element models were firstly developed and validated against the test results and afterwards adopted to perform parametric studies to generate further numerical data. On the basis of the test and numerical data, the accuracy of the design rules for stainless steel angle-to-plate connections failing by net section fracture, as set out in the European code and American specification, was assessed. The assessment results revealed that the European code leads to excessively conservative and scattered failure load predictions, while the American specification yields unsafe failure load predictions. Therefore, an improved design approach was proposed and shown to provide substantially improved predictions of failure load over the design codes; the reliability of the proposed design approach was also demonstrated by statistical analyses. Besides, the existing codified and proposed design methods for carbon steel angle-to-plate connections were also assessed for their applicability to stainless steel angle-to-plate connections. It was found that the method specified in the American specification for carbon steel angle-to-plate​ connections can be safely extended to cover the design of their stainless steel counterparts.

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.

Stability of Equal-leg Angle Steel Columns with Single-clad End Connection Joints

Stability of Equal-leg Angle Steel Columns with Single-clad End Connection Joints

Compressive performance of steel-timber composite L-shaped columns under concentric loading

Steel-timber composites (STCs) have emerged in the construction of large-span structures and multistory buildings. In this paper, a novel L-shaped column fabricated using STC (L-STC) was proposed. The L-STC column consisted of equal-leg angle steel and glulam. The angle steel was bonded inside the glulam. Twenty-two L-STC columns were tested under axial compression and compared with four L-shaped glulam columns as control groups. Parameters including wood species, steel ratios and column lengths were considered. The failure modes, stiffness, load-carrying capacity and ductility of the L-STC columns were analyzed. The test results demonstrated that L-STC columns displayed a (near) full composite action. The short L-STC columns failed due to crushing failure while the long L-STC columns failed due to global buckling. The stiffness and load-carrying capacity of the L-STC columns were enhanced by more than 56% and 33%, respectively. Increasing the width of the angle legs was recommended to achieve a higher load-carrying capacity. Furthermore, a finite element analysis was developed and validated. The load distribution on components of the L-STC columns was presented, and restraining effects of the timber on steel were analyzed and discussed. It was found that enhancing the timber grades, column lengths or reducing the steel ratios offered preferable lateral restraint of timber on steel.

Design rules for equal-leg angle members subjected to compression and bending

Angle profiles are amongst the most common structural steel shapes for construction purposes. However, their specific features clearly discern them from other types of common sections, what inevitably leads to the need for the development of specific design provisions. In this paper, extensive numerical and experimental studies have been conducted to propose a complete and duly validated set of design rules for resistance and stability of angle members subjected to individual and combined internal normal forces and moments. The proposed rules are written in the format of Eurocode 3 to allow a direct inclusion in forthcoming drafts.