Slender Members Research Articles

Experimental study of cold-drawn duplex stainless steel circular tubes under axial compression

Cold-drawing is one of the typical cold-forming techniques in producing stainless steel circular hollow sections (CHS). Compared with cold-rolling, cold-drawing can produce large scale stainless steel tubes which have wide applications in highly corrosive environment. Nevertheless, few researches have been carried out on the duplex stainless steel CHS columns. In this paper, cold-drawn duplex S22053 stainless steel CHS of three types of cross-sections were tested, including 8 material tensile coupon tests, 6 axially compressed stub column tests and 7 axially compressed long column tests. The material stress-strain curves of the cold-drawn CHS tubes, ultimate loads and failure modes of the stub and long columns were obtained. It has been revealed that material properties of cold-drawn stainless steel CHS tubes are close to those of the virgin plate in the annealed state. Moreover, all the stub columns show local buckling in “elephant foot” mode, while all the long columns undergo overall flexural buckling, among which a long column specimen with the nominal length of 700 mm（CHS-700） shows local buckling after the peak load due to the interaction of axial compression and second-order bending moment. Furthermore, comparing the test values with the predicted values based on the European, American, Australian/New Zealand and Chinese design codes, and the calculation methods available in literatures, it is concluded that the predicted values of the stub columns and the long columns with relatively large member slenderness are all lower than the test values, while the predicted values using the design methods except that in the Chinese design code are higher than the test values for the long columns with relatively small member slenderness. Chinese design code could provide safety predictions for cold-drawn duplex stainless steel CHS columns.

Numerical investigation on behaviour and design of cold-formed steel built-up column composed of lipped sigma channels

This article aims at investigating the structural response and predicting the ultimate resistance of cold-formed steel built-up columns composed of lipped sigma sections with pinned ends. For this purpose, a numerical model is established by using the finite element code ABAQUS. The finite element models include geometric, material nonlinearity. The effects of initial local and overall geometric imperfections have been taken into consideration in the finite element modelling. The results of the nonlinear finite element analysis were validated with the available experimental results present in the literature. A parametric study was carried out using the developed finite element model to study the effect of member slenderness, height-to-width ratio and depth of trapezoidal stiffener on the ultimate resistance of cold-formed steel closed built-up columns. On the basis of the parametric results, presented herein, appropriateness of the current direct strength method in the North American Specification for cold-formed steel columns is assessed. Based on such comparison, design expression is proposed to provide reliable design strength prediction of cold-formed steel built-up column composed of lipped sigma sections and verified through reliability analysis.

Load-carrying capacity of semi-rigid double-layer grid structures with initial crookedness of member

The main aim of the present study is to investigate the effect of joint bending stiffness and initial crookedness of member on load-carrying capacity of double-layer grid with different member slenderness ratios. Firstly, a mechanical model of semi-rigidly jointed double-layer grid with initial crookedness of member is developed, followed by verification of two simple grid structures. Then, the influence of joint bending stiffness and random initial crookedness of member on load-carrying capacity of double-layer grid is systematically investigated. Finally, failure mechanism and destructive process of the double-layer grid are discussed. The results indicate that the load-carrying capacity of double-layer grid with initial crookedness of member is remarkably affected by joint bending stiffness, especially for double-layer grid with slender member. The limit load of double-layer grid markedly decreases when κ less than 1.5–2. The effect of initial crookedness of member on load-carrying capacity of double-layer grid has a close relationship with member slenderness ratio. With the increase of member slenderness ratio, the limit load reduction gradually increases. The distribution of random initial crookedness of member distinctly affects the limit load of double-layer grid, and some of them can observably reduce the limit load, especially for double-layer grid with large member slenderness ratio. The failure mode of imperfect double-layer grid is affected by distribution of initial crookedness of member and joint bending stiffness. The existence of random initial crookedness of member can aggravate P-Δ effect, and some compression members of double-layer grid lose their stability prematurely, which further leads to the instability of whole double-layer grid.

Response of a slender cylindrical member under Breaking wave impact

A slender cylindrical member is the fundamental component of many coastal and offshore structures. It is essential to understand the action of breaking waves on structural members since, when these members are subjected to wave impact load, the structural damages and failures may be catastrophic. In the present study, an experimental investigation has been carried out to measure the response of the slender vertical cylinder subjected to breaking wave impact. Pressure measurements were made in order to estimate the total force acting on the structure. An empirical relation is established between total impact force and the wave steepness parameter which dictates the intensity of the breaking. Pressure rise time is an important parameter dictating the impact event. Simultaneous acceleration and strain measurements were made to evaluate the response of the cylinder. Deflection has been derived from structure acceleration. The deflection due to the moderate plunging differs by two order more than severe plunging events. Strain rate is another important consideration for the impact loading. The higher strain rate increases the resistance of the material. Under the breaking wave impact on the cylinder, the strain rate varies from2 to 10−4.

Non-constant biaxial bending capacity assessment of CFST columns through interaction diagrams

The mechanical response of concrete-filled steel tubular (CFST) columns subjected to pure compression or uniaxial bending was studied in depth over the last decades. However, the available research results on CFST columns under biaxial bending are still scarce and the lack of experimental tests for this loading situation is evident. At the same time, the design provisions in Eurocode 4 Part 1.1 for verifying the stability of CFST columns under biaxial bending make use of a simplistic interaction curve, which needs to be revised. This paper presents the outcome of a numerical investigation on slender CFST columns subjected to biaxial bending. Eccentricities differing in minor and major axis, as well as varying end moment ratios are considered in the numerical model. A parametric study is conducted for assessing the current design guidelines of EN1994-1-1. Different aspect ratios, member slenderness, reinforcement ratios and load eccentricities are studied, covering both constant and variable bending moment distribution. The numerical results are subsequently compared to the design provisions of EN1994-1-1, showing that the current interaction equation results overly conservative. An alternative interaction equation is developed by the authors, leading to a more accurate yet conservative proposal.

Instability analysis of a filament-wound composite tube subjected to compression/bending

The aim of this study is to investigate the global buckling of a relatively long composite cord–rubber tube subjected to axial compression and its cross-sectional instability due to bending by a macromechanical nonlinear finite element (FE) model (nonlinear buckling analysis). Composite reinforcement layers are modelled as transversely isotropic ones, while elastomer liners are described by a hyperelastic material model that assumes incompressibility. Force–displacement, equivalent strain, equivalent stress results along with oblateness and curvature results for the complete process have been presented. It is justified that bending leads to ovalization of the cross section and results in a loss of the load-carrying capacity of the tube. Strain states in reinforcement layers have been presented, which imply that the probable failure modes of the reinforcement layers are both delamination and yarn-matrix debonding. There is a significant increase in strains due to cross-sectional instability, which proves that the effect of cross-sectional instability on material behaviour of the tube is crucial. A parametric analysis has been performed to investigate the effect of the member slenderness ratio on cross-sectional instability of the composite tube. It shows that Brazier force is inversely proportional to the slenderness ratio. It further shows that higher oblateness parameters occur in case of a lower slenderness ratio and that cross-sectional instability takes place at a lower dimensionless displacement in case of a lower slenderness ratio. FE results have been validated by a compression/bending test experiment conducted on a tensile test machine.

Concurrent structural optimization of buckling-resistant trusses and their initial imperfections

This paper presents a new approach for truss optimization against buckling that incorporates both the structural design and the imposed initial imperfections. Euler buckling of slender members, global buckling and stability of sequences of bars are all considered by optimizing the geometric nonlinear response, instead of by imposing a large number of constraints. The proposed optimization problem formulation consists of two alternating steps: (1) Shape optimization that aims to find the worst-case imperfection shape of the joints’ positions; (2) Sizing-topology optimization that aims to find the minimum volume of a buckling-resistant structure with the given optimized imperfection. Sensitivity analysis for the two optimization phases follows the adjoint method and solutions are obtained using first-order sequential approximate methods. It is shown that optimizing the imperfection shape stabilizes the convergence as acute instantaneous buckling is avoided. Several numerical examples demonstrate the capability of the proposed formulation to generate buckling-resistant designs with robustness against imperfections.

Direct analysis method for noncompact and slender concrete-filled steel tube members

The concrete-filled steel tube (CFT) members made of noncompact/slender sections, experiencing complex behaviors such as local buckling, concrete confinement and slippage between the components, have been increasingly used in the practical engineering structures. However, few reliable design methods were available until the latest AISC 360-16, in which two types of methods are firstly provided. The first one uses P-M interaction curves with reduced or effective stiffness method while the second adopts effective stress-strain relationships based on the fiber section approach. The beneficial effects due to the restraint of steel tube have been implicitly considered in both of them. The first method approximately accounts for the member stiffness and employs the effective length method for stability design while the second method does not fully fulfill the requirements of direct analysis specified in AISC 360-16 as lack of consideration of slenderness effects and initial geometrical imperfections. This paper proposes a flexibility-based beam-column with member imperfections and incorporates the effective stress-strain models into the fiber section for direct analysis of noncompact/slender CFT members. The gradual change of member stiffness and the actual section capacity can be accurately reflected in the analysis process and as a result, the traditional effective length method is no longer required in the proposed direct analysis. It is also found that the initial imperfection of L/1000 is insufficient for CFT members. Some useful recommendations in line with AISC 360-16 are provided for practical design. Several experimental tests demonstrate the accuracy and robustness of the proposed method.

Influence of infill properties on flexural rigidity of 3D-printed structural members

ABSTRACTThis paper characterises the flexural properties of relatively slender structural members (beams) manufactured using a FDM-based 3D printer. The primary goal is to assess the influence of infill properties on flexural rigidity through a parametric investigation. Infill percentage, infill orientation, and member thickness provided the parametric variation. The beams were tested by three-point bending, free vibration, and buckling. The tests showed that flexural rigidity varied linearly with infill percentage over most of the range considered, but fell off quickly below 10% infill. The optimal infill percentage that maximised specific flexural rigidity (flexural rigidity to length density) of the beams was determined to be between 10% and 20%.

A new species of Plaumanniola Costa Lima in French Guiana (Coleoptera: Staphylinidae).

The genus Plaumanniola Costa Lima, 1962 was a subject of several taxonomical and morphological studies. It is one of very few scydmaenines originally placed not only in a different beetle family, but even a superfamily. The first species of Plaumanniola, P. sanctaecatharinae Costa Lima, 1962 was confused with myrmecophilous spider beetles and placed in a new subfamily Plaumanniolinae of Ptinidae. Transferred to Scydmaenidae by Lawrence Reichardt (1966), it remained placed as a separate subfamily, and after merging the ant-like stone beetles with Staphylinidae, as a tribe Plaumanniolini of Scydmaenitae (Newton Franz 1998; Grebennikov Newton 2009). Franz (1990) redescribed P. sanctaecatharinae, but Jałoszyński (2013) found his redescription to have been based on a misidentified new species, which he described as P. regina Jałoszyński, 2013. The latter author illustrated previously unknown morphological structures, redefined Plaumanniola and discussed its possible close affinities with Glandulariini (Jałoszyński 2013). The unusually stout and flattened body, with especially flat and broad head (interpreted as possible adaptations towards myrmecophily, e.g., Lenko (1972)), differentiated Plaumanniolini from all other Scydmaeninae, but no other characters were found to support a separate position of this monogeneric tribe. Shortly later, a relatively slender P. simplicissima Jałoszyński, 2014 was described on the basis of material collected in Bolivia. Finally, a discovery made by Jałoszyński (2016) that Euconnus octosetosus Franz, 1994, was in fact a strikingly slender member of Plaumanniola, and that the aedeagus of Plaumanniola highly resembles that of Euconnus (Rhomboconnus Franz, 1986), lead to placing Plaumanniolini as a junior synonym of Glandulariini. It is possible that in future Plaumanniola will be reduced to a subgenus of Euconnus.

Shape optimization of reticulated shells with constraints on member instabilities

ABSTRACTReticulated shell structures are commonly adopted because of their large spanning capacity and novel appearance. These structures generally comprise slender beam members, which may cause the buckling of entire structures. A shape-finding method is proposed in this study to eliminate the bending moment while optimizing the member buckling capacity of reticulated shell structures. The bending stiffness of connections can be accurately considered in the topology optimization analysis. This study can systematically be adopted for designing, analysing and optimizing such structures. All of the work presented was conducted using a general finite element analysis program and can be easily mastered by engineering designers while avoiding tedious programming work.

Structural performance of cold-formed high strength steel tubular columns

This paper presents a numerical investigation into the structural performance of cold-formed high strength steel tubular columns with square, rectangular and circular cross-sections. A finite element model was developed and validated against experimental results on the cold-formed high strength steel tubular columns. Parametric studies using the validated finite element model were carried out to determine the strengths of cold-formed tubular columns with various cross-sectional dimensions, member slenderness values, geometric imperfections and steel grades of S700, S900 and S1100. It was found that increasing the steel grade of the columns led to higher normalised column strengths which were less severely affected by geometric imperfections. The effect of material tensile strength to yield strength ratio on the column strengths was found to be insignificant. Based on the experimental results in literature and the results obtained from parametric studies, the applicability of the design rules in European, Australian and American Standards to cold-formed high strength steel tubular columns was evaluated. The reliability of the design rules was also assessed by performing reliability analysis. The design rules in these standards provide conservative predictions for the strengths of cold-formed high strength steel tubular columns. Recommendations on the column buckling curve selection are discussed. An improved column buckling curve expression considering the increment in normalised column strength with increasing steel grade is also proposed.

Design for lateral stability of slender timber beams considering slip in the lateral bracing system

The present study investigates the significance of potential slip in the bracings of simply supported slender timber members. Three bracing configurations are considered. The first case is that of a timber beam braced at one point at mid-span, the second one braced at two points and the third one braced at three points. Possible slip in the bracing members can for example be due to joint deformation, initial crookedness of purlins and slack (or relaxation) of cables in the stabilizing bay (catenary action). In this study, it is shown that slip in the bracing system can result in a reduced load-bearing capacity (due to larger beam stresses) of the beams. Also, the greater the slip, the greater lateral deflections and consequent bracing forces of the braced member. A simplified approach, using a larger initial geometrical imperfection, to account for potential slip in bracings is also evaluated. This approach is found to work reasonably well in terms of stresses and bracing forces, but underestimates the lateral displacements.

Prediction of dynamic response of semi-submersible floating offshore wind turbine using augmented Morison's equation with frequency dependent hydrodynamic coefficients

Abstract A fully coupled nonlinear simulation tool using Morison's equation is developed to predict the dynamic response of floating offshore wind turbine (FOWT) system. Water tank tests are conducted to investigate hydrodynamic coefficients and the performance of the simulation tool under different sea states. Three issues are discussed in this paper. First, correction factors for the added mass and drag coefficients are proposed to account for the effects of frequency dependent hydrodynamic coefficients, and the effects of these correction factors on the global matrices are validated by the forced oscillation tests. Then, the effects of the frequency dependent hydrodynamic coefficients and the axial Froude-Krylov force on slender members are clarified by the free decay tests and water tank tests with regular and irregular waves. Finally, the dynamic behavior of mooring system on the fairlead tension is investigated by using quasi-static and dynamic models, respectively. The dynamic responses of FOWT with improved hydrodynamic models agree well with those measured in the water tank tests.

Surface Rust Detection Using Ultrasonic Waves in a Cylindrical Geometry by Finite Element Simulation

Detection of early-stage corrosion on slender steel members is crucial for preventing buckling failures of steel structures. An active photoacoustic fiber optic sensor (FOS) system is reported herein for the early-stage steel corrosion detection of steel plates and rebars using surface ultrasonic waves. The objective of this study is to investigate a potential method for detecting surface corrosion/rust of steel rods using numerically simulated surface ultrasonic waves. The finite element method (FEM) was applied in the simulation of propagating ultrasonic waves on steel rod models. The pitch-catch mode of damage detection was adopted, in which one source (transmitter) and one sensor (receiver) were considered. In this research, radial displacements at the receiver were simulated and analyzed by short-time Fourier transform (STFT) for detecting, locating, and quantifying surface rust located between the transmitter and the receiver. From our time domain and frequency domain analyses, it was found that the presence, location, and dimensions (length, width, and depth) of surface rust can be estimated by ultrasonic wave propagation.

Experimental and numerical study on lateral stability of temporary structures

This paper investigates the lateral performance of temporary structures, which consist of slender members and corresponding joints, under both vertical and horizontal loads. The ultimate bearing capacity, failure modes and the strain distribution of members are illustrated. Experimental results indicate that the lateral stability of the temporary structures is weaker than the vertical stability. Diagonal bracings are the main load-bearing members which resist horizontal loads while the horizontal bars are used to keep stress low. Based on the joint mechanical parameters and the probabilistic models of initial geometric imperfection, the stochastic finite element models (SFEMs) using the Monte Carlo method have been established. The models can consider the semi-rigid performances of joints and initial geometric imperfection. The numerical results demonstrate consistency with structural tests data. Moreover, the influences of structural layers and spans are analysed based on the SFEM. Multiple factors, including spans, layers and upper vertical loads, should be considered when the lateral capacity of temporary structures is calculated. A rapid prediction formula of the lateral stability of temporary structure has been obtained.

Revolving entrance doors: Machines or structural elements?

Revolving entrance doors—usually built as some kind of all glass structure—are part of many publicly accessible buildings. As the architectural demands rise regarding transparency and slenderness of facade members, the entrance doors have to and do go along with these demands. But even if the facade is designed carefully and verified according all relevant standards, the revolving doors are usually considered as a machine, coming with some certificate. This point of view is mostly shared by the manufacturer and the basis for the call for proposals. The certificates provided by the door manufacturer considers the electrical safety, the safety aspects for people handling and using the doors regarding the risk of persons being jammed or hit by the turning door leaves, but not the structural safety of the door system in means of resistance to live, dead, wind or earthquake loads. If we look at the design and verification effort made for standard facade elements, even windows on the one hand, and the different failure consequences for windows and revolving doors on the other hand, it becomes obvious that especially to non-standard and large-scale doors should be paid some attention regarding its structural safety. Below the legal situation of revolving doors is considered in the European context and two quite different examples of revolving doors are discussed regarding their structural assessment.

Wind resistant size optimization of geometrically nonlinear lattice structures using a modified optimality criterion method

Lattice structures normally have slender members and light weight, high flexibility and small damping ratios. Hence, their structural behavior may be affected by the geometric nonlinearity and they are prone to large displacements and safety issues due to wind loads. Optimal design of such nonlinear and flexible structures is difficult and complicated. This paper presents an automatic optimizing flow for the integrated wind-induced response analysis and wind-resistant optimal design of linear and non-linear lattice structures based on the modified Optimality Criterion (OC) algorithm. The method for structural dynamic analysis and wind-induced response of lattice structure is developed by combining Proper Orthogonal Decomposition (POD) with Load Dependent Ritz (LDR) vector method, together with the Harmonic Excitation Method (HEM) and Load Response Correlation (LRC) method. Meanwhile the quadratic programming method is used to evaluate the Lagrange multipliers in the modified optimality criterion method. Based on the derived design sensitivity analysis results for the nodal displacements, element stresses and nonlinear critical load factor of linear and nonlinear space frame structures in a companion paper, an automatic optimizing flow is then established by adopting the Application Programming Interface (API) of SAP2000 to integrate the wind-induced response, design sensitivity analysis and wind-resistant optimal design of space frame structural system. The proposed automatic optimizing flow is then applied to the optimized process of a lattice structure under dynamic wind loading. It is found that for the lattice structure, the geometric non-linear analysis and the constraint of nonlinear critical load factor need to be considered in their optimization, meanwhile updating on the time-history of wind loads and Equivalent Static Wind Loads (ESWL) is necessary as result of the variations in the design member size during the optimization process. It is also found that the maximum displacement constraint is the most important factor in the optimization of the lattice structure and maximum stress of structural elements are normally found to be inactive constraints during the optimization procedure. In the case that a low limit for the maximum displacement is pre-set, the nonlinear critical load factor becomes the important constraint. Optimized results from this study would be helpful to those involved in wind resistant analysis and optimization design research for such lattice structures.

Compressive behaviour of eccentrically loaded slender masonry columns confined by FRP

Fibre Reinforced Polymer (FRP) confinement represents an effective tool for retrofitting masonry piers or columns enhancing their structural performance. This technique has been widely studied in the literature mainly with reference to short columns, while no extensive information is available on the influence of second order effects on its efficacy in case of slender members. Within this framework, the presented study concerns a simplified method able to assess the effects of FRP confinement on the compressive behaviour of slender masonry columns. A proper constitutive law of FRP confined masonry in compression is adopted for performing a sectional analysis, in which also considerations are made on the increase of ultimate moment and curvature depending on the role of some key parameters. The effect of column slenderness is evaluated using a simple analytical iterative procedure, making it possible to calculate the allowable slenderness ratios as function of the maximum drift, taking into account both strength and stability. The effect of slenderness on eccentrically loaded columns is finally examined through a finite element model used for validating the results of the proposed analytical procedure, allowing also to draw safety domains useful for design/verification purposes. It is shown as the column’s slenderness affects the efficiency of confinement, being the latter negligible for values of normalized length greater than 20.

Numerical Investigation on the Buckling Failure of Slender Tubular Member with Cutout Presence

Pitting corrosion often leads to the creation of small holes in steel tubular member of platform structures when a protective coating is damaged. A single pit on slender compression element can cause a significant reduction in the buckling capacity of the member. Euler formula is no longer applicable for determining the critical buckling load when cutout presence on the member. This research was conducted to numerically study the effect of a circular hole on the buckling capacity of slender steel tubular member. A variation on hole positions was at 0.125 L, 0.25 L, 0.375 L, and 0.5 L, where L is the length of the member. The hole was taken to be 0.5 pipe diameter. Two nonlinear geometric 3D Finite Element models were developed to analyzed the member critical buckling load: (a) buckling analysis, where the problem was formulated as eigenvalue problem based on the nonlinear incremental equilibrium equations, and (b) nonlinear analysis, where the nonlinear equilibrium equations were developed and solved by several schemes to get the load – deflection curve. For the both models, the tubular member was discretized into: (a) shell elements, and (b) solid elements. The numerical results were verified by experimental investigation. The results showed that: (a) the presence of cutout reduced the buckling load significantly, (b) the reduction ranging from 3% to 10% depending on the hole positions, (c) the maximum reduction occurs when the hole position was in the middle of the member length, (d) compared to experimental results, the critical buckling load obtained from buckling analysis deviated 1~4% while those of nonlinear analysis deviated 1~5%, (e) the buckling mode corresponded with member bent away to opposite side of the cutout position.