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This article addresses the problem of determining the solicitation and deformation of beams with geometric imperfection, also called real beams under a compression action. This calculation is performed by applying the Finite Transfer Method numerical procedure under first-order effects with the entire compression action applied instantaneously and applying the action gradually under second-order effects. The results obtained by this procedure for real sinusoidal or parabolic beams are presented and compared. To verify the potential of the numerical procedure, the first and second-order effects of a beam with variable section are presented. New analytical formulations of the bending moment and the transverse deformation in the beam with sinusoidal imperfection subjected to compression are also obtained, under first and second-order analysis. The maximum failure load of the beams is determined based on their initial deformation. The results of solicitation and deformation of the real beam under compression are compared, applying the analytical expressions obtained and the numerical procedure cited. The beams under study are profiles with different geometric characteristics, which shows that it is possible to obtain maximum failure load results by varying the relationships between lengths, areas and slenderness. The increase in second-order bending moments causes the failure that originates in the beam, making it clear that this approach reproduces the buckling phenomenon. The article demonstrates that through the Finite Transfer Method the calculation of first and second-order effects can be addressed in beams of any type of directrix and of constant or variable section. [ABSTRACT FROM AUTHOR]

The direct strength method (DSM) has become an alternative to the effective width method (EWM) to compute the bending moment capacity of cold-formed channel sections. The traditional EWM examines the nominal moment capacity by the PURLIN program. DSM uses a signature curve from tests on many Australian channel sections to obtain design moment capacity for local and distortional buckling modes. Moreover, the non-linear analysis performed by Strand7 will be compared with the current DSM curve. In general, these comparisons of results are in good agreement: the THIN-WALL program results and the linear static analysis results in Strand7; the moment capacity calculated by the PURLIN program (EWM) and the DSM curve in the local buckling mode; the non-linear analysis results in Strand7 and the DSM curve for each buckling mode. The outcome of this study will benefit structural engineers by providing them with design methods analysis. [ABSTRACT FROM AUTHOR]

This paper studies the stability of space structures consisting of longitudinal, open-section thin-shells transversely connected by thin rods subjected to a pure bending moment. Localization of deformation, which plays a paramount role in the nonlinear post-buckling regime of these structures and is extremely sensitive to imperfections, is investigated through probing experiments. As the structures are bent, a probe locally displaces the edge of the thin shells, creating local dimple imperfections. The range of moments for which the early buckling of the structures can be triggered by this perturbation is determined, as well as the energy barrier separating the pre-buckling and post-buckling states. The stability of the local buckling mode is then illustrated by a stability landscape, and probing is extended to the entire structure to reveal alternate buckling modes disconnected from the structure's fundamental path. These results can be used to formulate efficient buckling criteria and pave the way to operating these structures close to their buckling limits, and even in their post-buckling regime, therefore significantly reducing their mass. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'. [ABSTRACT FROM AUTHOR]

The main aim of the study is an assessment of models suitability for steel beams made of thin-walled cold-formed sigma profiles with respect to different numerical descriptions used in buckling analysis. The analyses are carried out for the sigma profile beam with the height of 140 mm and the span of 2.20 m. The Finite Element (FE) numerical models are developed in the Abaqus program. The boundary conditions are introduced in the formof the so-called fork support with the use of displacement limitations. The beams are discretized using S4R shell finite elements with S4R linear and S8R quadratic shape functions. Local and global instability behaviour is investigated using linear buckling analysis and the models are verified by the comparison with theoretical critical bending moment obtained from the analytical formulae based on the Vlasow beam theory of the thin-walled elements. In addition, the engineering analysis of buckling is carried out for a simple shell (plate) model of the separated cross-section flange wall using the Boundary Element Method (BEM). Special attention was paid to critical bending moment calculated on the basis of the Vlasov beam theory, which does not take into account the loss of local stability or contour deformation. Numerical shell FE models are investigated, which enable a multimodal buckling analysis taking into account interactive buckling. The eigenvalues and shape of first three buckling modes for selected numerical models are calculated but the values of critical bending moments are identified basing on the eigenvalue obtained for the first buckling mode. [ABSTRACT FROM AUTHOR]

Based on the negative Poisson ’s ratio effect of the re-entrant honeycomb, the finite element simulation of its buckling mechanical properties was carried out, and 2 buckling modes other than those of the traditional hexagonal honeycomb structures were obtained. The beam-column theory was applied to analyze the buckling strength and mechanism of the 2 buckling modes, where the equilibrium equations including the beam end bending moments and rotation angles were established. The stability equation was built through application of the buckling critical condition, and then the analytical expression of the buckling strength was obtained. The re-entrant honeycomb specimen was printed with the additive manufacturing technology, and its buckling performance was verified by experiments. The results show that, the buckling modes vary significantly under different biaxial loading conditions; the re-entrant honeycomb would buckle under biaxial tension due to the auxetic effect, being quite different from the traditional honeycomb structure; the typical buckling bifurcation phenomenon emerges in the analysis of the buckling failure surfaces under biaxial stress states. This research provides a significant guide for the study on the failure of re-entrant honeycomb structures due to instability, and the active application of this instability to achieve special mechanical properties. [ABSTRACT FROM AUTHOR]

Built-up radially battened columns (RBCs), comprising several identical circular steel tubes interconnected by multiple radial-shaped battens, represent an innovative column design that combines aesthetic appeal with exceptional load-bearing capacity. This makes them well-suited for architectural applications in large public buildings such as stations and airports. The axial compressive strength design methods for the built-up RBC have been extensively explored in the authors' prior studies. However, in real-world engineering applications, built-up RBCs may experience simultaneous axial compression and varying directional bending moments, particularly when considering potential eccentric compression or wind and earthquake loads in public buildings. Currently, strength design methods for this loading condition are still lacking. To address this deficiency, this paper primarily delves into the failure mechanism and strength design methods for built-up RBCs experiencing combined axial compression and arbitrary directional bending moments. Initially, the sectional strength of the built-up RBC is investigated by using a shell finite element model (FEM) for the built-up RBC. It is revealed that the compression-bending sectional strength of the built-up RBC exhibits significant differences with varying bending directions and tube numbers. Moreover, in some bending directions, the M - N sectional strength curve of the built-up RBC exhibits convexity. By integrating theoretically derived equations grounded in the principles of materials mechanics with FEM numerical calculations, concise and practical design equations are proposed for accurately predicting the sectional strength of the built-up RBC under combined axial compression and arbitrary directional bending moments. Subsequently, The buckling strength of the built-up RBC is studied using the FEM, considering initial geometrical imperfections consistent with first-order flexural buckling and accounting for geometric nonlinearity. It is noted that the bending direction of the built-up RBC may deviate during loading. Besides, the M - N buckling strength curve of the built-up RBC is not as convex as its M - N sectional strength curve. Based on calculations from numerous examples, practical design equations for predicting the buckling strength for the built-up RBC under axial compression and any directional bending moments are introduced. The key findings of this paper contribute to the compression-bending strength design of RBCs, enriching RBC design theory and promoting the widespread application of built-up RBCs in actual engineering projects. [Display omitted] • The M - N strength of RBCs varies with different bending directions and tube numbers. • The M - N sectional strength curve of the built-up RBC is convex. • The built-up RBC's bending direction may deviate during loading. • The M - N buckling strength curve of RBCs is less convex compared to its M - N sectional strength. • The M - N strength of RBCs can be predicted by a quadratic function. [ABSTRACT FROM AUTHOR]

A reliability assessment formulation for stiffened panels using the Model Correction Factor Method (MCFM) is derived from semi-empirical design equations of the IACS Common Structural Rules (CSR) for double-hull oil tankers. The approach consists of using the IACS-CSR buckling strength requirements of stiffened panels as a simplified response model that is calibrated iteratively at the design points calculated by the first-order reliability method using the results of non-linear finite element analysis of the stiffened panel. The approach is applied to a deck stiffened panel of a Suezmax oil tanker, designed according to the CSR for Double Hull Oil Tankers that has been used in the development of codes for the structural design of ships. The stiffened panels are subjected to uniaxial compressive loads induced by the hull girder vertical bending moment in a typical seagoing operational condition of the oil tanker in full load. It is shown that the application of the MCFM leads to a fast convergence towards the design point since the IACS-CSR formulation can capture the correct failure mode of the stiffened panels and the important mechanical features related to the prediction of their ultimate strength providing a convenient response surface model for reliability assessment. • This paper presents a reliability assessment for stiffened panels using the Model Correction Factor Method. • The IACS-CSR buckling strength requirements of stiffened panels as a simplified response model that is calibrated. • The approach is applied to a deck stiffened panel of a Suezmax tanker, designed according to the Common Structural Rules. • The stiffened panels are subjected to uniaxial compressive loads induced by the hull girder vertical bending moment. • The application of MCFM leads to a fast convergence since the IACS-CSR formulation can capture the correct failure mode. [ABSTRACT FROM AUTHOR]

• The results of more than 4 000 non-linear shell F.E. computations are presented, detailed and analysed. • Prior to the numerical parametric studies, the numerical models were validated against test data on full-scale specimens, as detailed in the companion paper. • Various parameters such as the base cross-section profile, the bending moment distribution, the size and position of the openings, the steel grade and member slenderness have been studied. • Besides, a dedicated design model is presented. Systematic comparisons with the results of software ACB+, which is by far the most highly used tool in design practice, are described. • A significantly improved performance of the proposed design approach in terms of accuracy, consistency and reliability is demonstrated. The present paper investigates the lateral torsional buckling resistance of cellular steel beams numerically. Such beams are quite sensitive to lateral instability owing to a substantial increase in depth of the cross-section with respect to the base profile. While a companion paper was dedicated to (i) characterising experimentally the behaviour of cellular and Angelina beams and to (ii) validating dedicated non-linear shell F.E. models, this paper details the results of extensive numerical studies. Several key parameters in the structural response are investigated, such as the base cross-section profile, bending moment distribution, size and position of the openings, steel grade and member slenderness. The results have further been used to assess an original design proposal for the lateral torsional buckling resistance of such girders. The improved design rules are shown to provide accurate yet safe ultimate load predictions. Also, in comparison with existing and available design rules, the proposal is seen to allow for substantially higher design loads – still safe-sided –, potentially leading to significant material savings. [ABSTRACT FROM AUTHOR]

The current Eurocode 3 rules for buckling of welded I-section members are based on the assumption of hot-rolled flanges. However, flame-cut flanges are widely used in practice and induce significantly different residual stress distributions, affecting the lateral-torsional buckling resistance. Experimental tests and finite element analyses considering residual stress distributions clearly highlighted the beneficial effect of flame-cut flanges compared with hot-rolled flanges on the lateral-torsional buckling resistance of welded I-beams. To complete these preliminary results, a large number of non-linear finite element analyses are performed considering welded beams made of hot-rolled or flame-cut flanges. The beams are composed of steel grades S275 and S355. Numerical results confirm the influence of the flange fabrication process on the buckling behaviour. Eurocode 3 rules are found to be overly conservative for welded beams made of flame-cut flanges. Consequently, proposals are made that are more suitable for estimates of the lateral-torsional buckling resistance of welded beams made of flame-cut flanges. The code rules are also very conservative for welded beams made of hot-rolled flanges with a medium-to-high slenderness. A design method is thus proposed to improve the prediction accuracy of the lateral-torsional buckling resistance of slender welded beams made of hot-rolled flanges. The novel design method from prEurocode 3 provides acceptable values of the buckling resistance for welded beams made of flame-cut flanges but is restricted to uniform doubly symmetric beams. An extension of its scope to mono-symmetric uniform beams as well as tapered beams is thus suggested. An enhanced imperfection factor is proposed, adapted to welded beams made of flame-cut flanges. • Design method to compute the LTB resistance of welded beams with flame-cut flanges using the Eurocode 3 buckling curves. • Design method to compute the LTB resistance of welded beams depending on their geometry, flange fabrication process and bending moment distribution. • Adaptation of the new verification format of prEN 1993–1-1 for lateral-torsional buckling to tapered and/or mono-symmetric beams. [ABSTRACT FROM AUTHOR]

In practical applications, asymmetric sandwich panels with tapered and junction regions are frequently used. Under uniaxial compressions, asymmetric sandwich panels are collapsed with complex failure mechanism, and its mechanical behaviour is affected by tapered regions. For structure safety consideration, it is necessary to systematically investigate the stability and damage behavior of full-scaled asymmetric sandwich panels under uniaxial compression experimentally and numerically. For comparison, symmetric sandwich panels were also studied. Quasi-static compression tests and numerical modeling were conducted. Experimental data were sufficiently recorded and carefully analyzed. Meanwhile a nonlinear finite element model was advanced for evaluating stability and predicting failure behaviours and load-bearing capacity of test specimen. Comparisons between numerical predictions and experimental measurements showed that a good agreement was achieved. The tapered region had significant influence on stability behavior and load-bearing capacity. It intensified the asymmetry and introduced additional bending moments into asymmetric sandwich panels and thus caused early local buckling. Thicker core thickness enhanced the structural stiffness and load-bearing capacity. Large amounts of matrix cracking, fibre push-out and core-skin delamination were captured in asymmetric sandwich panels. Overall, buckling occurred in symmetric sandwich panels instead of local buckling in asymmetric sandwich panels, and brittle fibre breakage dominated the failure. [ABSTRACT FROM AUTHOR]

The buckling behavior of latticed columns had been widely investigated based on the theory of Euler, Engesser and Timoshenko shear beam. Although these methods had been formulated and proved to be accurate in case of special assumptions, the influences of lacing bars on the buckling behavior of latticed columns were unclear. This paper modeled a general four-legged latticed column to study the influence of the cross-section characteristics of lacing bars along with their imperfections on the buckling capacity of latticed columns. Three loading conditions and four geometric imperfect models were built to testify the performance of lacing bars. To calculate the buckling load of latticed columns with imperfections accurately, advanced nonlinear analytical procedures using Newton-Raphson incremental-iterative method (ANAP-NR) and Risk arc-length incremental-iterative method (ANAP-Risk) were developed, and then validated by FE software ABAQUS. The current data in the paper show the maximum variation on the critical buckling load of latticed columns, caused by the cross-section area, the bending moment of inertia outer lacing plane, and the imperfections of lacing bars, could reach 68%, 30%, and 25%. The analytical results indicate the great importance of lacing bars on the buckling capacity of latticed columns. [ABSTRACT FROM AUTHOR]

This paper provides a simplified design approach for estimating the lateral–torsional buckling (LTB) strength of the pultruded glass fiber-reinforced polymer (GFRP) composite I-beams. A detailed finite element (FE) model based on ABAQUS incorporating more realistic parameters for pultruded GFRP I-beam is developed and verified against the test results available in the relevant literature. After achieving a reliable FE model (through high degree of accuracy in the numerical validation), detailed parametric studies were undertaken by varying the section geometries as well as the span of pultruded I-beams. The selection of the sectional dimensions was based on the composite manuals available in the market, to ensure ease in the practical application of the outcomes of this study. In this analysis, simply supported beam with a uniform bending moment is considered. In accordance with the results of the FE parametric analysis, the accuracy of the theoretical LTB strengths predicted by the equations proposed for pultruded GFRP beams available in the literature is assessed. This comparison indicates that the existing method results in an over-conservative LTB strength estimates for pultruded GFRP I-beams, especially in the low and medium slenderness range. This is primarily due to a comparatively lesser impact of section imperfections on LTB resistance than high slenderness range. Therefore, to address this shortcoming, new simplified design formulations were proposed to have high accuracy of the LTB strength predictions for pultruded GFRP I-beams especially in the low and medium slenderness range. The proposed equations have been provided that might aid the structural engineers in economically designing the pultruded GFRP I-beams in the future. [ABSTRACT FROM AUTHOR]

In this paper, an experimental program is presented consisting of 13 experiments on welded stainless steel I-profile beams subjected to lateral torsional buckling, in which 11 specimens are made of the lean duplex stainless grades EN 1.4062 and EN 1.4162, while the last two specimens are made of the austenitic grade EN 1.4404. The beam heights are 160, 210, and 260 mm, and the beams have a constant flange width of 160 mm. This results in three different strong axis elastic section moduli but similar weak axis bending resistances. The range of beam buckling length covers slenderness values from 0.30 to 0.76. The geometrical imperfections of the specimens were measured using digital image correlation (DIC). The web was first measured along its whole length. Then, the beam was placed on its fork supports, and the imperfection was then remeasured once more to check the influence of both gravity and test setup. Traditional four-point bending tests were carried out, and during which, the displacements were measured using linear variable differential transformer (LVDTs), inclinometers, and DIC. In this paper, the measured ultimate moments, together with results of experiments collected in the literature, are compared to the design rules provided in EN 1993-1-4, for which a safe but rather conservative design is obtained, and to the recent proposal of Taras and Greiner dedicated to carbon steel beams. The latter provides better results for high slenderness values but can be further improved. [ABSTRACT FROM AUTHOR]

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force F , bending moment M and distributed load q (or concentrated load P) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads. [ABSTRACT FROM AUTHOR]

This paper investigates the elastic lateral-torsional buckling of shear deformable circular arches of monosymmetric steel I-section with in-plane elastic rotational end constraints under a central concentrated radial load. In previous studies of monosymmetric arches reported in the literature, their ends were considered to be fix-ended or pin-ended in the plane of their curvature. In practice, the ends of an arch are not always fix-ended or pin-ended. The ends of an arch may have elastic restraints provided by elastic foundations or other adjacent structural elements. In addition, Timoshenko shear deformations, which are inevitable for arches with small and moderate slenderness ratios, are not considered in previous studies of the topic. The major contributions of this article are the following: (1) accurate strains and deformed curvatures for monosymmetric arches, including shear deformations, are derived using position vector analysis; and (2) in-plane analyses, including the influences of the elastic rotational end restraints, are successfully carried out in two steps to obtain the accurate axial compressive force, bending moment, and shear force distributions for lateral-torsional buckling analysis. The theoretical solutions for the lateral-torsional buckling load are obtained by applying the principle of stationary potential energy together with a Rayleigh-Ritz formulation and validated by ANSYS version 15.0 modeling of the problem. [ABSTRACT FROM AUTHOR]

Structure-function-material integration design based on the buckling instability of flexible cellular structures has attracted much attention. According to the reversible and repeatable characteristics of buckling deformation, phonon bandgap switches, the autonomous drive of soft robots, programmable logic controllers, and reusable spacecraft landing buffer devices can be designed. Based on the Hamiltonian variational principle and symplectic eigen expansion, a theoretical analysis model of the symplectic stiffness method is established, and analytical expressions for the stiffness of several typical buckling modes of elastically supported beams are obtained. The analytical closed-form expressions for the macroscopic buckling strength of honeycombs are obtained according to the bending moment equilibrium equation. The buckling modes of regular hexagonal, hierarchical hexagonal, and tri-chiral honeycombs are obtained by numerical simulation and experimental verification, and some novel higher-order modes are observed. Uniaxial compression experiments reveal that these higher-order buckling modes can be triggered by adjusting the geometric parameters of the unit cells. The high agreement between experimental, numerical, and existing literature results for the failure surfaces of cellular structures verifies the effectiveness of the proposed symplectic stiffness method. In a word, the buckling modes can be designed to meet different functional requirements by changing the initial configuration of flexible cellular structures. This provides a new idea and theoretical guidance for the development of metamaterials and structures with tailored properties. • The symplectic eigen-solutions interpret the physical mechanism for all kinds of deformation patterns. • Analytical closed-form expressions for the buckling strength of cellular honeycomb structures are obtained. • Higher-order buckling modes can be triggered by adjusting the geometric parameters of the unit cell. [ABSTRACT FROM AUTHOR]

• A mathematical model for buckling and post-buckling under different torsion-bending ratios were established. • The buckling stability and load carrying capacity of the wing box were analyzed by the experiments. • By establishing a refined simulation model, the impact of different torsion-bending ratio on failure mode of the wing box. In this paper, a mathematical model for the effect of different torsion-bending ratios on buckling and failure loads under complex operating conditions was proposed, and the buckling, post-buckling and failure behavior and mechanism of carbon fiber composite wing box were studied by combining experiments and simulations. A high-precision computational simulation model was established by considering detailed bolt arrangement information, as well as damage and failure of composite materials. The predicted buckling loads, failure loads, and damage modes are in good agreement with the experimental results. The results show that, under the condition of constant bending moment, as the torque increases, the linear strain of the box section remains consistent, while the shear strain increases significantly, leading to a change in the buckling mode and failure distribution. When the torsion-bending ratio is less than 2.0, the loading form of the structure is greatly affected by the torque. On the contrary, the buckling and failure loads are exponentially close to the pure torsional state. The mathematical model and simulation model in this study can provide an important reference for the structural design and failure mechanism analysis of large composite wing boxes. [ABSTRACT FROM AUTHOR]

This article focuses on the lateral-torsional buckling resistance of girders with slender, class 4 cross-sections with a research aim to check the accuracy of the design resistance model of EN1993-1-1 and EN1993-1-5 on the coupled instability of lateral-torsional buckling and local plate buckling resistances. The current Eurocode-based design method considers in the effective cross-sectional resistance calculation that yield strength is reached in the extreme fibre of the cross-section, and the reduction factor (ρ p) related to local plate buckling is calculated based on this assumption. However, if lateral-torsional buckling occurs, maximum stress in the web can be significantly smaller at the ultimate limit state which is not considered in the effective cross-sectional resistance calculation. On the other side, EN1993-1-1 proposes to consider the effective bending moment resistance in the relative slenderness calculation of lateral-torsional buckling, which is in contradiction with the general definition of the relative slenderness ratio ( λ ¯ LT) , which should refer to the plastic resistance divided by the critical load of the structure. This article aims to check if the current Eurocode-based design rules need improvement and to check the effect of the above-mentioned specific issues on the calculated lateral-torsional buckling resistance. An extensive numerical research programme is executed to check and compare the lateral-torsional buckling resistance of class 3 (as reference) and class 4 cross-sections, and results are compared to Eurocode-based design models. [ABSTRACT FROM AUTHOR]

This article presents a study on the impact of the screw location and the diaphragm effects on the buckling behavior of the simply supported C/Z-section purlins under wind uplift loadings. The diaphragm effects provided by the sheeting and the warping-torsional effect induced by load eccentricity are taken into account in the differential equations of the nonlinear twisting flexural-torsional model. The biaxial bending moments, bi-moments, as well as the flexural-torsional buckling load of the purlin can be numerically obtained with the proposed model. The global, local, and distortional buckling interaction behavior and the limit states capacities are formulated based on the modified Direct Strength Method. The effects of both the restraints provided by the sheeting and impact of the screw location on the mechanical performance of the purlins are evaluated with the proposed method. The relationship between the buckling load and rotational restraint stiffness is also provided. The proposed methodology will contribute to the assessment of buckling capacity of purlin-sheeting systems. [ABSTRACT FROM AUTHOR]

The non-linear in-plane stability of pin-ended circular shallow arches is analytically investigated. The arches are made of functionally graded material with the material properties varying along the thickness. The external load is a radial concentrated force in the direct vicinity of the crown. The effect of the bending moment on the membrane strain is included in the one-dimensional model. The equations of the pre-buckling and buckled equilibrium are derived using the principle of minimum potential energy. Analytical solutions are found for both bifurcation and limit point buckling. Extensive parametric studies are performed to find and demonstrate the effect of various parameters on the buckling load and in-plane behaviour. It is found that most arches have multiple stable and unstable equilibria and the number of equilibria increases with the modified slenderness. When the load is applied exactly at the crown, the lowest buckling load is related to bifurcation buckling for most geometries and material compositions but when there is a small imperfection in the load position, only limit point buckling is possible. The position of the load can have quite a huge influence on the buckling load, therefore pin-ended functionally graded shallow arches are sensitive to small imperfections in the load position. • The sensitivity of shallow arches to small loading imperfections is studied. • The arches are made of transversely FGM. • The effect of various geometrical-material parameters is investigated analytically. • Results show that the load position has huge influence on the buckling behaviour. [ABSTRACT FROM AUTHOR]

Continuous composite beams can present a global instability known as lateral distortional buckling (LDB). The design code EN 1994-1-1:2004 provides a procedure for the verification of this ultimate limit state, in which the resistant bending moment is calculated considering the behavior of the inverted “U-frame” mechanism. An essential parameter for the determination of this moment is the rotational stiffness of the composite beam, which depends on the web stiffness. The EN 1994-1-1:2004 procedure is restricted to composite beams with solid-web steel sections without openings. This paper presents several numerical analyses of the web rotational stiffness of castellated sections such as Anglo-saxon, Litzka and Peiner typologies. Finally, based on numerical results obtained, three different adjustment coefficients were proposed for the Anglo-Saxon, Litzka and Peiner typologies for the calculation of the web rotational stiffness of the castellated profile. The proposed coefficients provided an excellent adjustment between the results obtained numerically and those obtained from the classical formulation of the plate theory, with an average deviation of 2%, indicating low dispersion and homogeneous results. [ABSTRACT FROM AUTHOR]

• BB-BC algorithm is used to obtain optimum CFS beam sections at ULS and SLS based on EC3. • Twelve prototypes are optimised by considering manufacturing and design constraints. • Flexural capacity and stiffness of optimum CFS beams increased by up to 58% and 44%. • Detailed FE models with geometric imperfections confirm the adequacy of the results. • Folded flange channels generally provide the best design solutions at SLS and ULS. Cold-formed steel (CFS) elements are increasingly used as main structural members in modern construction practice. While flexibility of CFS cross-sectional shape allows achieving higher load carrying capacities by using more efficient shapes, obtaining optimum design solutions can be a challenging task due to end-use constraints and complex behaviour of CFS elements controlled by local, global and distortional buckling modes. This study aims to develop a practical methodology for optimum design of CFS beam sections with maximum flexural strength and minimum deflection under ultimate and serviceability load conditions, respectively, in accordance with Eurocode 3 by taking into account manufacturing and end-use design constrains. Population-based Big Bang–Big Crunch Optimisation method is employed to obtain optimum design solutions for twelve different CFS cross-sectional prototypes. To verify the flexural strength and stiffness of the optimum beam sections, detailed nonlinear finite element (FE) models are developed using ABAQUS by considering both material nonlinearity and initial geometrical imperfections. It is shown that the optimised sections based on serviceability limit state (SLS) and ultimate limit state (ULS) can provide, respectively, up to 44% higher effective stiffness and 58% higher bending moment capacity compared to a standard lipped channel beam section with the same plate width and thickness. Using plain channel and folded-flange sections generally leads to the best design solutions for SLS and ULS conditions, respectively. Finally, the results of detailed FE models are used to evaluate the adequacy of EC3 proposed procedures to estimate CFS beam capacity and deflection at ULS and SLS, respectively. [ABSTRACT FROM AUTHOR]

This study investigates the load-bearing behavior of timber members subjected to combined compression and bending based on the guidelines of the standard Eurocode 5. In this context, two design approaches are stated to account for flexural buckling: the effective length method and the second-order analysis. Although Eurocode 5 states that second-order analysis can be carried out to check the stability of beam-columns, it does not mention how to formulate this analysis. This study investigates this case in order to develop alternative interaction formulae to check the stability of timber members subjected to simultaneously acting axial compression and bending moments with risk of buckling failure. The second-order analysis advanced in this article can be an alternative tool to be used by the structural engineer to assess the stability of axially loaded members subjected to the risk of flexural buckling failure. [ABSTRACT FROM AUTHOR]

Microtubules (MTs) in living cells are frequently bend, e.g., with a mean curvature of about 0.4 rad/μm in fibroblast cells [Odde et al., J. Cell Sci. 112, 3283 (1999)]. This raises a natural question whether bending buckling can occur in a MT. In this paper, an orthotropic model is developed to investigate buckling of MTs upon bending and torsion. A critical buckling curvature for a bent MT is predicted to be about 0.03 rad/μm (to which the corresponding bending moment is 0.85 nN nm), indicating that MTs in living cells are likely buckled. Buckling behavior of torsional MTs is also studied, and a critical buckling torque of 0.077 nN nm is obtained. Comparison to the results from an isotropic model shows that anisotropic properties of the MT wall have severe effect on the mechanical behavior of MTs. [ABSTRACT FROM AUTHOR]

This paper presents an in-depth numerical investigation into the local buckling behaviour and develops advanced machine learning (ML) -based design methods for high strength steel (HSS) welded I-section beams for predicting the ultimate bending moment resistance under bending. Though HSS welded I-sections are commonly used in construction industry, the interaction effect between the flange and web plates as well as the relatively simplified design formulae result in limited accuracy of ultimate bending moment prediction and complex endeavour is involved for sections subject to local buckling. Finite element models are firstly developed and validated against the collected experimental test data, after which an extensive parametric study is carried out covering a larger range of cross-section slenderness and steel grades. Five ML models including Linear regressor (LR), Support vector regressor (SVR), Artificial neural network (ANN), Random forest regressor (RFR) and Boosting algorithm (XGBoost) were subsequently developed based on the test dataset (experimental and numerical data) to train and test the ML models. Though the current design codes of EN 1993-1-12 and AISC 360-16 can generally provide accurate cross-section classifications with appropriate slenderness limits, the ultimate bending moment resistance predictions are overconservative, particularly for slender sections. The developed ML models outperformed the codified design methods with notable improvements and can be employed in predicting the ultimate bending moment resistance of HSS welded I-section beams under bending. • Finite element modelling of high strength steel I-section is presented. • An extensive parametric study comprising 548 numerical models is carried out. • Slenderness limits specified in existing design codes are assessed. • Five machine learning models for predicting ultimate bending moment resistance is developed. • The performance of the developed machine learning models is evaluated. [ABSTRACT FROM AUTHOR]

This paper presents some closed form solutions for the buckling problem of periodic Vierendeel girders subjected to compressive axial loads. These are obtained by studying a geometrically non-linear ideal discrete beam, composed of cells or panels that deform only according to the inner forces transferring modes of the girder unit cell. In particular, the recursive equations governing the equilibrium of this discrete system are derived by the virtual works principle. Then, they are exactly solved and formulae for the critical loads are achieved. Although the ideal girder deforms with geometrically not compatible longitudinal shear strains, it gives very accurate predictions in a wide range of conditions of technical interest. These theoretical results are used as starting point for the analysis of the stiffening effect yielding a Euler critical load significantly higher than the buckling load evaluated on the basis of the classical Engesser's assumptions. Specifically, by an ideal girder auxiliary solution, the discrete systems of self-equilibrated inner bending moments (self-moments) restoring the longitudinal shear strains compatibility are studied and it is shown that the axial loads under which these moments exist are accurate critical loads estimates of the real girder. Closed form solutions are obtained also for this problem and a simplified formula is derived for evaluating real girders buckling loads. The applicability of the reported solutions is verified by a validation study based on a series of finite element girder models. • Closed form solutions for the axial load critical responses of a periodic Vierendeel girder. • A discrete girder model by the unit cell inner forces transferring modes. • Analysis and solution of girder recursive equilibrium equations. • Stiffening 'discrete effect' of web rods and joints explained in terms of self-moments. • Improved solutions for critical axial loads response by cells shear strains compatibility. [ABSTRACT FROM AUTHOR]

Along with the promotion of green construction, prefabricated single-layer reticulated shells (PSLRS) with assembled joints have been increasingly applied in large-span buildings. However, the frequent joint assembly errors during the manual installation will not only weaken the mechanical properties of the joints, but also affect the overall stability of PSLRS. Therefore, the adverse effects of joint assembly errors on both aspects were studied in this paper. Firstly, the flexural performance of a modified bolted splice joint was numerically simulated, and its performance degradation under different joint assembly errors was investigated. Then on this basis, the PSLRS computational model with the joint performance imperfections was established, and three imperfection analysis methods, J-SIMM, J-CIMM, and J-EIM, were proposed to estimate the reliable bearing capacity. Based on these methods, the most unfavorable imperfection distribution modes of cylindrical PSLRS were obtained, and the imperfection sensitivity under different boundary conditions was analyzed. The results showed that the initial joint assembly errors significantly reduced the joint's flexural stiffness and ultimate bending moment, thereby changing the buckling mode of PSLRS and leading to premature structural failure. Especially for the cylindrical PSLRS supported at the two longitudinal edges, its stability bearing capacity was significantly reduced under the influence of initial joint performance imperfections. Nevertheless, the proposed method J-EIM still obtained the lower limit of the bearing capacity with fewer calculations compared to the stochastic method, which provides practical guidance for the structural design of PSLRS. [Display omitted] • A modified bolted splice joint that can connect large-section latticed shell members was proposed. • The flexural performance of assembled joints was investigated with the initial assembly errors considered. • The sensitivity of prefabricated single-layer reticulated shells to the joint performance imperfections was analyzed. • Two deterministic imperfection mode methods of the joint performance were proposed for the reliable bearing capacity. • The coupling effects between the joint performance imperfections and geometric imperfections were studied. [ABSTRACT FROM AUTHOR]

In this paper we have discussed the frictional buckling behavior of a slender rod constrained in a horizontal cylinder. Buckling and post-buckling behaviors including the onset of helical buckling and subsequent axial force transfer are interpreted in a new way. Helical buckling and concomitant low force transfer efficiency which would prevent further axial extended reach is important to engineering structures, such as coiled tubing operations in petroleum industry. By means of the beam-column method, new governing differential equation of frictional buckling are derived to predict critical buckling force. We also investigate the transfer efficiency of axial force quantifying the effect of axial friction on rod lockup phenomenon in post-buckling analyses by perturbation solution. The coupling effect between axial force and friction is solved for the first time in this paper. The bending moment at the lock-up limit which would cause the rod to rupture is also analyzed. Finally, we have compared the proposed model with experimental results to verify its validity. Through these analyses, we have provided another interpretation to the existing experiment and numerical simulation results of frictional buckling. The derived results are simple and convenient for a problem in industrial practice. • New buckling differential equations of frictionally, cylindrically restrained rod are derived. • Critical buckling loads of frictional buckling are solved from the new buckling equations. • Analytical solutions about axial force transfer efficiency are derived by perturbation solution. • Good agreement is found between the theory and experimental results. [ABSTRACT FROM AUTHOR]

• Stiffness reduction method developed for LTB assessment of tapered beams. • Proposed method eliminates the need to use member design equations. • Comprehensive verification of the stiffness reduction method against shell FE results. • The proposed approach compared against Eurocode 3. • Illustration of the accuracy of proposed method for laterally braced tapered beams. A stiffness reduction method for the lateral-torsional buckling (LTB) assessment of welded web-tapered steel beams is presented in this study. The method is implemented by (i) modelling a tapered steel beam using elastic beam finite elements specifically developed to represent the elastic instability response of tapered steel members, (ii) reducing the Young's modulus E and shear modulus G of each element through a stiffness reduction function considering the bending moments and cross-section properties at the middle of each element and (iii) performing an elastic Linear Buckling Analysis of the beam with reduced stiffness, referred to as LBA-SR herein. Since the adverse influence of the development of plasticity and imperfections on the ultimate member strengths are fully accounted for through stiffness reduction, the presented method does not require any further global instability assessment using member design equations; thus, the proposed method is both direct and practical. Verification of the method is shown for a wide range of web-tapered steel beams using results from nonlinear shell finite element modelling. [ABSTRACT FROM AUTHOR]

Great attention has been given in the last few years to steel–concrete composite beams due to the gains in strength that can be obtained with the small cost of installing a shear connection between the steel profile and the concrete slab. In continuous and semicontinuous composite beams close to the internal supports, hogging bending moments are developed and the compressed bottom flange may buckle laterally in an unstable way known as the lateral-distortional buckling, characterized by a horizontal displacement and twist of the bottom flange with an out-of-plane distortion of the web. In the literature, several formulations were proposed to determine the critical moment for this type of buckling. Among them, some of the most relevant are presented by [K. Roik, G. Hanswille and J. Kina, Solution for the lateral torsional buckling problem of composite beams (in German), Stahlbau59 (1990)] and [G. Hanswille, J. Lindner and D. Munich, Lateral torsional buckling of composite beams (in German), Stahlbau67 (1998)]. In the present work, a new procedure is developed to determine the elastic critical moment of lateral–distortional buckling of composite beams under uniform hogging moment. To assess and calibrate this procedure, 7 772 numerical models were analyzed by the finite element code ANSYS and the results were compared with the ones obtained from the new proposed formulas. The procedure presented excellent agreement with the numerical results, with an average deviation of 2.33% from the computational simulations. The formulations of [K. Roik, G. Hanswille and J. Kina, Solution for the lateral torsional buckling problem of composite beams (in German), Stahlbau59 (1990)] and [G. Hanswille, J. Lindner and D. Munich, Lateral torsional buckling of composite beams (in German), Stahlbau67 (1998)] did not lead to such satisfactory results, presenting an average deviation of 12.41% and 16.51%, respectively. [ABSTRACT FROM AUTHOR]

A very large floating structure (VLFS) may undergo buckling and yielding under rare and extreme waves. Then, the cross section of the VLFS collapses completely. The evaluation of the consequence of collapse is critical in view of the risk analysis. In this paper, the parametric dependencies of the collapse extent of a VLFS under extreme vertical bending moments are investigated. A mathematical equation to describe the collapse behavior of the VLFS is developed taking account of the hydroelastic deformation. The whole VLFS is modeled by a segmented beam on an elastic foundation with infinite length connected via a nonlinear rotational spring assuming that a plastic hinge is formed at the collapsing section of the VLFS under the extreme vertical bending moment. By solving the equation in an analytical manner, a simple formula to predict the extent of collapse of the VLFS is developed. The results by the formula are well correlated with those by numerical simulation that has been developed by the present authors. It is shown that the characteristic length defined for a VLFS plays a key role in the collapse behavior. [ABSTRACT FROM AUTHOR]

Buckling resistance predictions resulting from flexural and flexural–torsional buckling of double tee section members subjected to compression and bending are considered. A novel analytical model is developed for establishing design criteria based on decomposition of the member buckling behaviour into in-plane and out-of-plane resistance. The former is based on second-order bending relationships of load effects of structural members with in-plane equivalent imperfections, while the latter is based on the stability theory of thin-walled open sections. First part of this study presents an analytical formulation of the in-plane buckling resistance of beam–columns. In this regard, further decomposition is postulated for the in-plane first-order bending moment diagram that results in the loading state to be the superposition of two components. The first component is related to symmetrical loading and the second to antisymmetric loading. To consider the second-order effects, prebuckling displacements generated by the abovementioned loading components are amplified with regard to the inversion of the residuum of the buckling force utilisation ratio in order to obtain approximate values of second-order displacements and internal moments. As a result, the in-plane interaction curve, expressed in dimensionless coordinates, that describes the beam–column in-plane flexural buckling resistance without considering lateral–torsional buckling effects, is obtained. The results of nonlinear finite element simulations are used for the verification of the developed analytical formulation. It is concluded that this proposal yields less conservative predictions than those based on the interaction relationships of clause 6.3.3 of Eurocode 3, Part 1–1. • The study discusses design criteria for in-plane buckling and bending behaviour. • The proposed analytical model has only one design condition. • The model is based on a linear combination of elementary resistance utilisation ratios. • The model is verified by the results from finite element simulations. • The results are compared with those from EC3 interaction equations. [ABSTRACT FROM AUTHOR]

Abstract This study presents an experimental study on the static and fatigue behavior of steel-concrete composite beams subjected to negative bending moment. A total of 10 specimens were tested, with a special focus on the effect of corroded studs. The load-carrying capacity, beam stiffness and fatigue life of specimens having different corrosion rates were evaluated. Test results showed that the specimens subjected to monotonic loading failed by local buckling while fatigue loading led to shear fracture of the studs and crack initiation followed by propagation in the steel beam. Corrosion of shear connectors had a significantly detrimental effect on the load-carrying capacity and stiffness of the composite beams. As the corrosion rate increased, the fatigue life of the beams was dramatically declined by up to 29.69%. The residual bending stiffness and slip stiffness decreased as the fatigue cycles elapsed. Highlights • Ten steel-concrete composite beams subjected to negative bending moments were tested. • The effect of corrosion of shear studs on the beam behavior was investigated. • Specimens under static loading failed by local buckling rather than stud fracture. • Specimens under fatigue loading was observed studs failure followed by beam fracture. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for determining the critical lateral-torsional buckling loads of beams subjected to arbitrarily transverse loads. This new method is developed based on the classical energy method. However, the difference of the present method from the traditional energy methods is the formulation of potential energy of external loads, which is expressed in terms of the internal bending moment and internal shear force in the pre-buckling stage regardless of the type of loading. Compared to the traditional formulations of the potential energy of external loads, not only is the present formula simple in the form, easy and convenient in the calculation, but it also provides a unified form for calculating accurate critical load of lateral-torsional buckling of the beams. [ABSTRACT FROM AUTHOR]

Abstract When the sinusoidal buckling of suspended tubular strings is transforming to helical buckling, the deformation changes drastically, which makes the tubular strings extremely unstable. The quantitative description of this buckling configuration in previous theoretical studies is not precise enough. In our current study, dynamic relaxation method is applied to carry out numerical simulation of buckling transition of suspended tubular strings. To obtain stable buckling configurations, larger Rayleigh damping is used to attenuate the dynamic effect. With the increase of axial compression load, the lateral buckling of the suspended strings suddenly becomes spiral shape with two contact points. As the string length increases, the position of the lower contact point remains almost at the same position. While the upper contact point gradually moves upward, and the helix angle between the two points increases and gradually tends to be constant. The maximum contact force is located at the lower contact point, the maximum shear force is located at the bottom of the strings, and the dimensionless distance between the location of the maximum bending moment and the well bottom is about 1.0. These loads, including the maximum contact force, maximum shear force and maximum bending moment, gradually decrease with the increasing string length and tend to be constant. The dimensionless critical load is reduced from 4.41 to 3.81 with the effect of string length. The critical load calculated in this paper is the minimum value when helical buckling just occurs. The results obtained in the current study have wide engineering applications, particularly in failure analysis and prevention of helical buckling. Highlights • Stable buckling configuration is obtained by using dynamic relaxation method. • Quantitative description of buckling deformation, shear force, bending moment and contact force are obtained. • The critical load obtained is the minimum one when the helical buckling just happens. [ABSTRACT FROM AUTHOR]

Abstract Structural design formulae for beam-columns require accurate end points (i.e. accurate resistance predictions for pure compression and pure bending), should be of suitable form to capture the interaction between the different components of loading and should take due account of the influence of a moment gradient along the member length. However, existing design rules for stainless steel beam-columns do not fully capture the interaction responses observed in experiments and numerical simulations, and are often tied to inaccurate end points; the adopted equivalent uniform moment factors can also be unconservative in the case of high moment gradients. As a consequence, previous comparisons of stainless steel beam-column experimental and finite element results with codified strength predictions have often revealed a rather high degree of scatter. This prompted the present research, to develop improved design proposals for stainless steel square hollow section (SHS) and rectangular hollow section (RHS) beam-columns under moment gradients. To this end, revised design approaches are proposed firstly through the derivation of more accurate design interaction curves for stainless steel SHS and RHS beam-columns under uniform bending moment and then through the employment of more suitable equivalent uniform moment factors, underpinned by and validated against over 1500 test and numerical data points. The new design approaches are shown to lead to improved (safe-sided, accurate and consistent) resistance predictions for stainless steel SHS and RHS beam-columns under moment gradients over the current codified design rules. Finally, statistical analyses are performed to demonstrate the reliability of the proposed approaches, according to the requirements specified in EN 1990. Highlights • Current codified design rules for stainless steel beam-columns under moment gradients were briefly reviewed. • Shortcomings in the existing design codes were identified, and methodologies for overcoming them were described. • Improved design approach for stainless steel beam-columns under moment gradients was proposed. • Assessment of the new proposal indicates a higher level of design accuracy and consistency. • The reliability of the new proposal has been confirmed by means of statistical analyses. [ABSTRACT FROM AUTHOR]

Highlights • Buckling mechanism of steel core of BRBs with fixed ends is revealed. • The design criteria as well as the buckling half wavelength were validated by the quasi-static tests of five BRBs. • Compared to existing methods, the proposed design approach can ensure a proper safety margin of the stiffening part. Abstract Based on theoretical analyses, the development of buckling mode of steel core is revealed for buckling restrained braces (BRBs) with fixed ends. The formulae are derived for the bending moments of the stiffening part of the core and restraining member of BRBs. Then a global stability design method of fixed-end BRBs is proposed. The results of the contact force, flexural response and buckling half wavelength with finite-element analysis agree with the theoretical analysis. The design criteria as well as the buckling half wavelength were validated by the quasi-static tests of five BRBs. Compared to existing methods, the proposed design approach can ensure a proper safety margin of the stiffening part. [ABSTRACT FROM AUTHOR]

Long runs of cold-formed steel Z-section purlins are often segmented due to assemblage and transportation issues. The segments are commonly connected by bolts to a short cold-formed steel member similar to the purlin; this short member is typically called a sleeve; from a structural point of view, it does not guarantee a state of full continuity to the purlin. This study reports a series of 15 experiments on cold-formed steel Z-sections purlins with sleeved bolted connections tested in bending. These experiments vary cross-section height, thickness and length of sleeve, and span. This parametric experimental study seeks to better understand the flexural-buckling strength, collapse mechanism, and moment-rotation behavior of purlin-sleeve systems. Since the design of purlins with sleeved bolted connections is often limited by the serviceability limit state, in this case excessive displacement, special attention is given to accurately determining and understanding the moment-rotation behavior of purlin-sleeve systems. Based on the experimental results, an expression is proposed to predict non-linear moment-rotation behavior; the proposed expression is compared to expressions previously proposed in the literature. The proposed moment-rotation expression, when used in a simple rotation spring-beam model, leads to accurate prediction of displacement and bending moment in the purlin-sleeve system at any load stage. [ABSTRACT FROM AUTHOR]

Cold-formed steel haunched portal frames are popular structures in industrial and housing applications. They are mostly used as sheds, garages, and shelters, and are common in rural areas. Cold-formed steel portal frames with spans of up to 30 m are now being constructed in Australia. As they are relatively new to the market, current design recommendations are fairly limited. In the specific frame system analyzed herein, the column is partially restrained against twist rotation at an intermediate point where the knee brace joining the column and rafter is connected. An experimental program was carried out on a series of portal frame systems composed of back-to-back channels for the columns and rafters. It was found that changing the knee brace and knee brace-to-column connection bracket significantly affected the buckling capacity of the column, however this was not captured in design calculations. In order to correctly predict frame behavior and ultimate loads for design purposes, the column buckling capacity must be accurately calculated. This paper presents an energy method approach to calculate the buckling load of a column with an intermediate elastic torsional restraint. Various end conditions of the column are considered including column base semi-rigidity, as well as multiple loading conditions. Displacement functions are determined based on measured experimental data. The Southwell and Meck plot methods to determine column buckling loads are discussed. The column buckling loads determined from the plot methods and calculated by the energy analysis are compared to the experimental column buckling loads. It is shown that the energy method outlined herein predicts the buckling load within 6% for columns with an intermediate elastic torsional restraint. [ABSTRACT FROM AUTHOR]

• A novel polyhedral profile is developed to rehabilitate the damaged pipeline. • The polyhedral ring is characterized by functionally graded porous. • The graphene platelets are used to reinforce the polyhedral ring. • Analytical derivations are obtained to express the buckling load. • The equilibrium paths are plotted explicitly for FGP-GPLs polyhedral ring. This paper focuses on the nonlinear buckling responses of the confined functionally graded porous (FGP) lining with polyhedral shapes reinforced by graphene platelets (GPLs). The FGP-GPLs polyhedral lining is surrounded tightly and rigidly by a medium. It is assumed that the interface is smooth between the lining and pipeline. The deformation of the lining may be represented by an admissible displacement expression when a point load is applied at the crown position. Afterward, the nonlinear governing equilibrium equations are obtained explicitly by combining the thin-walled shell theory and the principle of minimum potential energy. Solving the nonlinear governing equilibrium equations yields the critical buckling load. A comparison study is strictly completed with the other closed-form solutions when the polyhedral lining reduces to a circular one. In addition, an improvement factor is quantified to understand the effect of polyhedral shapes on the bending stiffness. Finally, the effects of polyhedral shapes, porosity coefficient, weight fraction, and geometric parameters of the GPLs are explored in terms of buckling load, hoop force, and bending moment. [ABSTRACT FROM AUTHOR]

Perhaps due to the bending moment singularity at the obtuse plate corners, the existing buckling loads vary appreciably even for simply supported rhombic plate under uniaxial loading. In this paper, the buckling analysis of skew plates under various loadings is presented using the modified differential quadrature method (DQM). A complete set of equations of equilibrium, bending and twisting moments, equivalent shear forces and corner force in oblique coordinate system is given. Eight combinations of simply supported, clamped and free boundary conditions, four skew angles, and five aspect ratios are considered. Convergence studies are made for rhombic plates with the largest skew angle subjected to uniaxial and equal biaxial compressive loads. The solution accuracy is further verified by comparing the results with data obtained by the finite element method using very fine meshes. New data are tabulated and plotted for skew plates with different edge conditions, aspect ratios and skew angles, subjected to uniaxial, biaxial, as well as combined shear with uniaxial loads. Most of the data, not available thus far, may be useful for other researches in testing the validity of their numerical techniques for thin plate analysis. [ABSTRACT FROM AUTHOR]

This paper discusses the behaviour of stainless steel rectangular and square hollow sections (RHSs and SHSs) under combined constant compression and uniaxial cyclic bending. A total of 10 specimens were tested, covering a variety of section slenderness, axial load ratio, and bending direction. These test parameters were found to have evident influences on the local buckling resistance of the specimens. It was also observed that the current codified classification limits underestimate the ability of the stainless steel sections to develop plastic stresses. Moreover, the specimens exhibited low to moderate levels of ductility and energy dissipation capacity due to a relatively early occurrence of local buckling. A numerical study was subsequently conducted, shedding further light on the strength, stress pattern, ductility, and local failure behaviour of the specimens. A more extensive parametric study was then carried out, which provides basis for the proposal of a ductility-oriented design approach that aims to offer a quick yet reliable evaluation tool for predicting the available ductility supply of stainless steel RHSs/SHSs under different loading conditions. The rationality of the current major design codes for predicting the strength of stainless steel members was also evaluated, and it was found that the design codes tend to be conservative. [ABSTRACT FROM AUTHOR]

Two-way aluminum alloy gusset joints (AAGJs) are considered to be employed in cable-stiffened aluminum alloy single-layer reticulated shell structures meshed with quadrilateral grids. In this study, a series of experiments on six AAGJs with and without shear connectors were conducted to investigate their semi-rigid behavior. Two joints were subjected to pure bending moments and others to shear loads, then their corresponding failure modes were investigated which were mainly beam rupture, beam web buckling, and bolt failure. The moment-rotation curves, shear load-rotation curves, and strain-load curves were also obtained, indicating that AAGJs are typical semi-rigid joints. Shear connectors can optimize the load transferring path and improve ductility under bending moment while enhancing shear performance significantly. A simplified theoretical AAGJ model was also established and parameterized according to the experimental results. [ABSTRACT FROM AUTHOR]

In geohazard areas, buried pipelines are subjected to permanent ground-induced deformations, which constitute major threats for their structural safety. Geohazards include seismic fault movement, liquefaction-induced lateral spreading, slope instability or soil subsidence, and are associated with the development of severe strains in the pipeline. Calculation of these strains is necessary for assessing pipeline integrity. In the present paper, an analytical methodology is presented that allows for simple and efficient pipeline strain analysis in geohazard areas. The methodology is compared with existing more elaborate analytical methodologies and finite element predictions. The analytical formulation results in closed form expressions and the model contributes to better understanding of buried pipeline behavior subjected to permanent ground-induced deformations. The proposed methodology is directly applicable to fault actions, but it can be also applicable to a wide range of geohazards. Furthermore, using this methodology, one may predict the strains developed in the pipeline wall due to ground-induced actions in a simple and efficiently manner and is suitable for the preliminary design of pipelines. [ABSTRACT FROM AUTHOR]

Unburied subsea pipelines designed to operate under high temperature and high pressure (HT/HP) conditions tend to relieve their axial compressive force by forming lateral buckles. Uncontrolled lateral buckling can lead to pipeline failure, such as collapse. Thus, controlled lateral buckling is an effective and inexpensive method to accommodate axial thermal expansion and to control pipeline lateral buckling. In this study, analytical solutions for uncontrolled and controlled lateral buckling of unburied subsea pipelines are derived. And the interaction between two adjacent buckles for controlled lateral buckling is considered. The typical behaviors of uncontrolled and controlled lateral buckling with different lengths of feed-in zone are illustrated and analyzed. The effects of length of feed-in zone and lateral soil resistance on controlled lateral buckling are also presented. The results show that shorter length of feed-in zone and smaller lateral soil resistance will lead to smaller lateral buckling amplitude, maximum bending moment and maximum axial compressive stress. Therefore, reducing the length of feed-in zone or lateral soil resistance can be an appropriate method to be used to control lateral buckling. Finally, the analytical solutions are validated by use of the finite element modelling. The analytical results show good agreement with finite element analysis results. [ABSTRACT FROM AUTHOR]

A single wave of extreme height can damage ship structures in the ocean by generating buckling midship, thus destabilizing the ship girder and causing rupture. The probability of such an extreme wave is low in reality. On the one hand, it is very costly to recreate a real ship test for the study of extreme wave conditions. On the other hand, it is difficult to carry out tests on a scale model in tank waves, because such waves are too small to damage the ship model. In this paper, a hydroelasto-buckling experiment is performed on a ship model to study the dynamic ultimate strength of the ship and dynamic course of collapse of the structure. Thus far, no method of simulation has been proposed to study this problem because the dynamic ultimate strength of the ship involves strong coupling between the nonlinearity in the ship structure and waves. Here, a hydroelasto-buckling ship model is first designed, and a test programme is determined. A buckling hinge that can collapse under the load of the tank wave is used to connect two ship girders with a hinge joint. Then, a number of single tank waves are generated by changing their wave patterns to simulate an extreme ocean wave. The dynamic rotation angle, bottom water press and acceleration at midship are measured in the experiment. Importantly, the relationship between structural response and wave patterns is analyzed. The structural response involves encountering the VBM/rotation deformation induced by the wave load and whipping the VBM/rotation deformation induced by natural structural oscillations. It is found that the ultimate strength of the ship girder can be generated by both encountering waves and the structural flutter response caused by changing wave height. Lastly, the midship water pressure and acceleration are also analyzed to discuss the influence of a large deformation of the ship structure on the fluid load. Some conclusions are presented in the paper. [ABSTRACT FROM AUTHOR]

Girders with trapezoidally corrugated web are widely used structural elements in the civil engineering praxis due to their numerous advantages. Despite, there are a relatively small number of previous investigations focusing on the determination of the bending moment resistance and the flange buckling behavior. Previous experimental and numerical investigations confirmed that the flange buckling resistance model provided by the EN1993-1-5 predicts often unsafe resistances. The summary of the previous investigations on the flange buckling behavior is presented in the companion paper (Part I) Jáger et al. [1] coupled with the introduction of an executed experimental research program investigating the flange buckling resistance of girders with corrugated web. Based on the test results an advanced FE model is developed, validated and presented in the current paper. In the first part of the study an imperfection sensitivity analysis is performed to develop proposals for applicable equivalent geometric imperfections for FEM based design method. In the second part of this paper an intensive parametric study is performed to investigate the buckling coefficient and the relationship between the relative slenderness and the reduction factor for corrugated web girders. The current paper also focuses on a new design method development for the determination of the flange buckling resistance. [ABSTRACT FROM AUTHOR]

This paper presents the result of an experimental research about the lateral torsional buckling instability during bending tests of Partially Encased Beams (PEB) at elevated temperature. A set of twenty seven four-point bending tests, grouped in ten series, were carried out to analyse the influence of relative slenderness, beam temperature and the shear bond conditions between concrete and steel in bending. In addition, this study compares the behaviour of PEB and bare steel beam under bending at room temperature. PEB specimens are based on IPE100 steel profiles, with two different lengths 2.4 m (medium series) and 3.9 m (large series), tested in bending using simple supporting conditions and exposed to different temperatures levels of 200 °C, 400 °C, and 600 °C. Two different shear bond conditions, between steel profile and lateral concrete, were analysed at 400 °C: one series with connectors formed by welded stirrups to the web and another series with natural adherence between steel and concrete, not welded stirrups. PEB attained lateral torsional buckling as deformed failure mode at the ultimate limit state, except for the case of PEB tested at 600 °C that results in a plastic hinge failure. The bending resistance was determined for the maximum load event (F u ) and for the displacement limit corresponding to L/30 (F L/30 ) and compared with the results of the Eurocode 3 part 1–2 simple calculation method, considering an adaptation of its formulae to PEB. The expected reduction in bending resistance at elevated temperature is in good agreement with the experimental reduction factor, when the deformation criterion is used. [ABSTRACT FROM AUTHOR]

The present paper describes a theoretical study on the effect of pre-buckling displacements on the elastic instability of U-shaped members. Expressions for the elastic critical bending moments under mono-axial bending and the elastic critical load amplification factor for the case of bi-axial bending are derived and validated through elastic geometrically non-linear analysis including a geometric imperfection. It will be shown that pre-buckling displacements have a non-negligible influence on the behaviour of U-shaped members, especially when subjected to minor-axis and bi-axial bending. It will be shown that, contrariwise to the natural feeling, U-shaped members under minor-axis bending may, in some cases, be sensitive to elastic instability (lateral-torsional buckling). Moreover, the validated analytical expressions show that shorter members are more sensitive to elastic instability under minor-axis bending than their longer counterparts! [ABSTRACT FROM AUTHOR]