Numerical investigation of channel columns with complex stiffeners—part I: test verification

A numerical investigation on fixed-ended cold-formed steel channel columns with complex stiffeners subjected to axial load is described in this paper. The complex stiffeners of the channel sections consist of simple lips with return lips. The specimens were brake-pressed from high strength zinc-coated structural steel sheets having a nominal yield stress of 450 MPa. A non-linear finite element model is developed and verified against experimental results of fixed-ended channel columns with complex stiffeners. Initial geometric imperfections and material non-linearity are included in the model. The calibrated model is shown to provide accurate predictions of the experimental ultimate loads and failure modes of the tested columns.     

Behavior of channel shear connectors, Part II: Analytical study

In this second part of the two companion papers an effective numerical model is proposed using finite element method to simulate the push-out test of channel shear connectors. The focus is on the shear capacity of channel shear connectors embedded in a solid reinforced concrete slab under monotonic loading. The model has been validated against test results presented in Part (I) and compared with data given in North American design codes. Parametric studies using this nonlinear model are performed to investigate the variations in concrete strength, channel dimensions and the orientation of the channel. The results show that the concrete strength, web and flange thicknesses of the channel and the length of the channel are significant parameters in determining the ultimate strength of channel shear connectors, whereas the height of the channel section is not a significant parameter. Also, changing the orientation of the channel causes a change in the stiffness and the ultimate strength of the shear connector.     

Aluminum alloy tubular columns—Part II: Parametric study and design using direct strength method

A parametric study of aluminum alloy columns of square and rectangular hollow sections was performed using finite element analysis (FEA). The columns were compressed between fixed ends. The parametric study included 120 columns with and without transverse welds at the ends of the columns. An accurate and reliable finite element model was used for the parametric study. Design approaches for aluminum alloy tubular columns with and without transverse welds were proposed. Column strengths predicted by the FEA were compared with the design strengths calculated using the current American, Australian/New Zealand and European specifications for aluminum structures. In addition, the direct strength method (DSM), which was developed for cold-formed carbon steel members, was used in this study for aluminum alloy columns. The design strengths calculated using the DSM were compared with the numerical results. Furthermore, design rules modified from the DSM were proposed. It is shown that the proposed design rules accurately predicted the ultimate strengths of aluminum welded and non-welded columns. The reliability of the current and proposed design rules was evaluated using reliability analysis.     

Design for openings in cold-formed steel channel stub columns

This paper is concerned with the ultimate load capacity of perforated cold-formed steel channel stub columns. A design equation has been developed to determine the ultimate load capacity of perforated channel short columns containing either single or multiple openings of square, circular and manufacturer's opening shape. The equation is based on extensive parametric studies carried out using finite element modelling on plain and lipped channel sections containing openings. A wide range of parameters such as plate slenderness, opening shapes and sizes have been considered in the study. Web plate slenderness and opening area ratio are the two main variables used to derive the design equations. The accuracy of the proposed design equation is established by comparison with a number of experimental and finite element results reported by other researchers.     

Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners

This paper presents an experimental investigation and a finite element analysis on cold-formed channels with inclined simple edge stiffeners compressed between pinned ends. Compression tests of pin-ended channel columns with inclined simple edge stiffeners have not been performed till now. A total of 36 channel specimens including three different cross sections with different edge stiffener inclined angles and column lengths were tested. Detailed measurements of initial geometric imperfections and material properties of the specimens were also conducted before the above tests. Failure modes include local buckling, distortional buckling, flexural buckling and interaction among these buckling modes were observed in tests. The results indicate that inclined angle and loading position significantly affect the ultimate load-carrying capacity and failure mode of specimens. Moreover, a non-linear finite element model was developed and verified against tests. Geometric and material non-linearities were included in the model. Results from the finite element analysis agree well with experimentally ultimate loads and failure modes. However, it should be improved on prediction for certain displacement.     

Experimental investigation of thin-walled complex section concrete-filled steel stub columns

An innovative X section with intermediate stiffeners of thin-walled concrete-filled steel stub was proposed in this study. The X section was firstly brake-pressed from structural steel sheets to form three edges open section with intermediate stiffener in each edge, then a plate with intermediate stiffener was welded to the open section to form the closed section. The intermediate stiffener was designed to enhance the local buckling stress of the thin-walled specimens. Stub column tests of both hollow steel tubes and concrete-filled steel tubes were performed. Material properties of the self-compacting concrete and steel used in the test specimens were also measured. Design methods specified in current design standard and proposed by other researchers are used to predict the design strengths of test specimens. It is shown that the predicted design strengths are conservative.     

Analysis of steel storage rack columns

Storage rack systems are structures composed of cold-formed steel structural members that are used as columns, beams and bracing. The rack columns present peculiar features in their design because they have perforations to facilitate assemblage of the system, which makes them more difficult to analyze by cold-formed steel structures design codes. There are several design codes proposed by the manufacturers associations, as the specifications of Rack Manufacturers Institute (RMI), applied in the USA along with the specification of the American Iron and Steel Institute (AISI). These codes propose experimental stub columns tests for the determination of their resistance. In this work, the commercial software, ANSYS, is used for material and geometric non-linear analysis of these columns, and the results are compared with experimental data obtained by stub column tests, for a typical section of racks manufactured in Brazil.     

An investigation of the block shear strength of coped beams with a welded clip angle connection — Part II: Numerical study

An experimental study of the block shear capacity of ten full-scale coped beams with a welded clip angle connection was presented in Part I. The test results were compared with predictions using block shear design equations in several current design standards. In general, the results showed that the existing design standards did not provide consistent predictions of the block shear capacity of coped beams with welded clip angles. In addition, the equations provided by the standards cannot accurately reflect the failure mode of the specimens observed in the tests. In order to gain a better understanding of the connection behavior, such as the stress distribution in the web near the periphery of the clip angles and the failure mechanism of the connection, an analytical study of the block shear capacity of coped beams with welded clip angles was carried out using the finite element method. Based on the limited test data and the results of the finite element analysis (FEA), a strength model was established and a design equation was proposed to evaluate the block shear strength of coped beams with welded clip angles. It was shown that the proposed design equation gave better predictions of the block shear capacity of the specimens.     

Experimental and numerical assessment of stayed steel columns

Stayed steel columns may be used as compression-resisting members of a structure presenting high slenderness ratios and fast erection requirements. The system is able to sustain a wide range of load levels and lengths with economic and reliable structural solutions. Although this structural solution dates back from the 1960s its structural behaviour is not fully understood. This fact motivated a study of the system structural behaviour by means of an experimental program followed by finite element simulations aiming to determine the most efficient structural geometries and the corresponding steel ties pre-stress force magnitudes. A series of full-scale tests were executed in 12 m pre-stressed steel columns with a 90 mm diameter. Some of the main contributions of the current study are related to the conception, development and execution of new tri-dimensional full-scale tests and the development of a finite element model calibrated against these experiments. An extensive parametric analysis based on the calibrated finite element simulation was also performed focusing on the most significant parameters that could affect the structural response, i.e., column length and diameter, pre-stress force magnitude, among others. The test and numerical results will certainly contribute to the development of updated design procedures and formulae to be introduced in future structural design codes.     

Numerical simulation of concrete encased steel composite columns

This paper investigates the behaviour of pin-ended axially loaded concrete encased steel composite columns. A nonlinear 3-D finite element model was developed to analyse the inelastic behaviour of steel, concrete, longitudinal and transverse reinforcement bars as well as the effect of concrete confinement of the concrete encased steel composite columns. The interface between the steel section and concrete, the longitudinal and transverse reinforcement bars, and the reinforcement bars and concrete were also considered that allowed the bond behaviour to be modeled and the different components to retain their profile during the deformation of the column. Furthermore, the initial overall (out-of-straightness) geometric imperfection was carefully incorporated in the model. The finite element model has been validated against published experimental results. The main objective of the study was to understand the structural response and modes of failure of the columns and to assess the composite column strengths against current design codes. The study covered slender, non-slender, stub and long concrete encased steel composite columns. The concrete strengths varied from normal to high strength (20-110 MPa). The steel section yield stresses also varied from normal to high strength (275-690 MPa). Furthermore, the variables that influence the composite column behaviour and strength comprising different slenderness ratios, concrete strength and steel yield stress were investigated in a parametric study. It is shown that the increase in structural steel strength has a small effect on the composite column strength for the columns having higher relative slenderness ratios due to the flexural buckling failure mode. The composite column strengths obtained from the finite element analysis were compared with the design strengths calculated using the American Institute for Steel Construction AISC and Eurocode 4 for composite columns. Generally, it is shown that the EC 4 accurately predicted the design strength for the concrete encased steel composite columns having a concrete cylinder strength of 30 MPa and structural steel yield stresses of 275 and 460 MPa, which are in the limits of the code, which otherwise, was generally conservative. The AISC predictions were quite conservative for all the concrete encased steel composite columns.     

FE based mode interaction analysis of thin-walled steel box columns under axial compression

This paper presents the Finite Element (FE) analysis based mode interaction analysis of thin-walled steel box columns under axial compression. Earlier theoretical results on the optimum design of axially compressed box columns were validated through FE analysis. The study was then extended to cover factors that were previously omitted. These factors included column out-of-straightness, residual stresses and plasticity. Emphasis was given on imperfection sensitivity and its effect on optimum design.     

Nonlinear behavior of concrete-filled stainless steel stiffened slender tube columns

This paper investigates the nonlinear behavior of concrete-filled high strength stainless steel stiffened slender square and rectangular hollow section columns. The stiffened slender tubes had overall depth-to-plate thickness (D/t) ratios ranging 60–160. The concrete strengths covered normal and high-strength concrete. The investigation focused on short axially loaded columns. A nonlinear finite element (FE) model has been developed to study the behavior of the concrete-filled stiffened tube columns. A parametric study was conducted to investigate the effects of cross-section geometry and concrete strength on the behavior and strength of the columns. The results of the concrete-filled stiffened tube columns were compared with the results of the companion concrete-filled unstiffened tube columns. It is shown that the concrete-filled stiffened slender tube columns offer a considerable increase in the column strength and ductility than the concrete-filled unstiffened slender tube columns. The column strengths obtained from the FE analysis were compared with the design strengths calculated using the American specifications and Australian/New Zealand standards. A design equation was proposed for concrete-filled stainless steel stiffened slender tube columns. It is shown that the proposed modified equation provides more accurate design strengths compared to the American and Australian/New Zealand predictions.     

Coupled instabilities with distortional buckling in cold-formed steel lipped channel columns

The paper addresses the elastic post-buckling behaviours of cold-formed steel lipped channel simply supported columns affected by mode interaction phenomena involving distortional buckling, namely local/distortional, distortional/global (flexural-torsional) and local/distortional/global mode interaction. The results presented were obtained by means of Abaqus shell finite element analyses adopting column discretisations into fine 4-node element meshes. In order to enable a thorough assessment of all possible mode interaction effects, the column lengths and cross-section dimensions were carefully selected to ensure similar local, distortional and/or global buckling loads. One analyses otherwise identical (elastic) columns having initial geometrical imperfections (i) with various configurations (combinations of the competing critical buckling mode shapes) and (ii) sharing the same overall amplitude.     

Structural performance of cold-formed lean duplex stainless steel columns

The structural performance of cold-formed lean duplex stainless steel columns was investigated. A wide range of finite element analysis on square and rectangular hollow sections and other available data, with a total number of 259 specimens, were considered. An accurate finite element model has been created to simulate the pin-ended cold-formed lean duplex stainless steel columns. Extensive parametric study was carried out using the validated finite element model. The column strengths predicted from the parametric study together with the available data are compared with the design strengths calculated from various existing design rules for cold-formed stainless steel structures. It is shown that the existing design rules, except for the ASCE Specification as well as the stub column and full area approach, are conservative. Modifications are proposed for the AS/NZS Standard, EC3 Code, and direct strength method. Reliability analysis was performed to assess the existing and modified design rules. It is also shown that the modified design rules are able to provide a more accurate and reliable predictions for lean duplex stainless steel columns. In this study, it is suggested that the modified design rules in the AS/NZS Standard and the modified direct strength method to be used in designing cold-formed lean duplex stainless steel columns.     

Numerical parametric study on stability and deformation of tunnel face reinforced with face bolts

Although face bolting has been used as a stabilisation technique in open-face tunnelling for decades, there is still a lack of systematic ways for determining the optimum parameters of face bolts. To optimise design for face bolting in soft ground, it is necessary to understand the influences of each parameter associated with face bolting on ground response. In this note, five series of numerical parametric studies are carried out, to investigate the effects of length, density, reinforcement area, axial rigidity of face bolts and strength of soil on tunnel face stability and deformation in soft rock. Based on the ground condition, geometries of tunnel and configurations of face bolts simulated, the optimum length, density and axial rigidity of face bolts are found to be 0.6H (H = height of tunnel), 1 bolt/m² and 195 MN, respectively. The optimum axial rigidity of face bolt appears to be independent of the bolt density. The computed results also reveal that it is more effective to reduce face deformation by installing face bolts around the tunnel periphery, than installing them near the central area of the tunnel face.     

Load and resistance factor design of composite columns

Test capacities of composite concrete-encased steel profile and concrete-filled tube columns and beam-columns are compared with predictions of the design model of the American Institute of Steel Construction Load and Resistance Factor Design criteria. Some 300 tests were examined. It was found that the design model is conservative, but that the scatter of the tests with respect to the AISC design model is also high. A first-order second-moment reliability study revealed that the concrete-encased members exceeded the target reliability index in the design specification, but that the concrete-filled tubes had an inadequate reliability index when compared to the target value. It is recommended that both a better design model and further tests are needed to arrive at satisfactory design criteria.     

Numerical parametric study of geosynthetic reinforced soil integrated bridge system (GRS-IBS)

A 2-D finite flement model was developed in this study to conduct a FE parametric study on the effects of some variables in the performance of geosynthetic reinforced soil integrated bridge system (GRS-IBS). The variables investigated in this study include the effect of internal friction angle of backfill material, width of reinforced soil foundation (RSF), secondary reinforcement within bearing bed, setback distance, bearing width and length of reinforcement. Other important parameters such as reinforcement stiffness and spacing were previously investgated by the authors. The performance of GRS-IBS were investgated in terms of lateral facing displacement, strain distribution along reinforcement, and location of potential failure zone. The results showed that the internal friction angle of backfill material has a significant impact on the performance of GRS-IBS. The secondary reinforcement, setback distance, and bearing width have low impact on the performance of GRS-IBS. However, it was found that the width of RSF and length of reinforcement have negligible effect on the performance of GRS-IBS. Finally, the potential failure envelope of the GRS-IBS abutment was found to be a combination of punching shear failure envelope (top) that starts under the inner edge of strip footing and extends vertically downward to intersect with Rankine active failure envelope (bottom).     

Aluminum tubular sections subjected to web crippling—Part II: Proposed design equations

The web crippling design rules in the current American Aluminum Design Manual, Australian/New Zealand Standard, and European code for aluminum structures are assessed. Test strengths of aluminum square and rectangular hollow sections under end-two-flange (ETF) and interior-two-flange (ITF) loading conditions are compared with the design strengths (capacities) obtained using the aforementioned specifications. Furthermore, the test strengths are also compared with the design strengths obtained using the unified web crippling equation as specified in the North American Specification for cold-formed steel structural members. It is shown that the design strengths predicted by the aforementioned specifications are either quite conservative or unconservative, but in general the predictions are unreliable resulting from reliability analysis. Hence, two different unified web crippling equations for aluminum square and rectangular hollow sections under ETF and ITF loading conditions are proposed. The proposed unified design equation (A) uses the same technique as the North American Specification for the unified web crippling equation with new coefficients of C, C_N and C_h determined based on the test results obtained in this study. The proposed unified design equation (B) is similar to the unified web crippling equation in the NAS Specification, and the effect of the ratio N/h is also considered, where N is bearing length and h is the depth of the flat portion of web. Generally, it is shown that the proposed unified web crippling equation (B) compares well with the test results.     

FE modelling and fire resistance design of concrete filled double skin tubular columns

Concrete filled double skin tubular columns (CFDST) have excellent structural behaviour. They have been used as transmission towers and have potential to be used as building columns and bridge piers. Performance of the CFDST columns under ambient temperature has been well studied, whereas fire resistance of such columns is still a major concern. A summary of a series of fire tests on CFDST columns conducted by the authors is briefly presented in the paper. A finite element numerical model is developed to analyse the fire behaviour of CFDST columns, namely thermal and structural responses under fire exposure. The model is verified by the test results and then used to perform parametric analyses. Parameters which have significant effect on the fire behaviour of CFDST columns are identified. Based on the parametric studies, suggestions on the fire resistance design of such columns are made. Practical design tables are derived for the fire resistance design of some typical CFDST columns.     

高强冷弯薄壁型钢卷边槽形截面轴压构件试验研究及承载力分析

对63根屈服强度550MPa高强冷弯薄壁型钢卷边槽形截面轴压构件进行试验研究,分析了构件的屈曲模式和极限承载力,并将参考AISI规范、澳洲规范和北美规范及我国现行行业标准《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）计算的构件承载力与试验结果进行分析比较。在此基础上,对高强超薄壁型钢卷边槽形截面轴压构件的承载力合理计算模式进行研究。结果表明：高强超薄壁型钢卷边槽形截面轴压构件在宽厚比较大时会出现畸变屈曲模式;采用等效板件方法计算加劲板件有效宽度后,我国《低层冷弯薄壁型钢房屋建筑技术规程》（报批稿）适用于屈曲强度550MPa、厚度小于2.00mm的冷弯薄壁型钢卷边槽形截面构件承载力计算。