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Thin-walled shell structures are characterised by a lightweight structural form with high strength. The importance of using cylinders and cones has long been known to engineers and designers in various engineering disciplines and they are widely used in shell form. In this work, the buckling and post-buckling behaviour of thin-walled cylindrical shells with geometric imperfections was investigated under vacuum-type pressure loads. Ten shell models with dents of two depths and lengths were designed for experimental tests: the dents were the thickness or twice the thickness of the shell, while their lengths were half or one-third of the height of the model. Carbon-fibre-reinforced polymer (CFRP) was used to retrofit some of the dented models. Test results from the CFRP specimens and the non-CFRP specimens were then compared with each other and with theoretical calculations.

Cold-formed steel members are usually used as purlins in buildings to support roof cladding and thus they can be treated as beams restrained fully or partially in the lateral and torsional directions. However, when these beams are subjected to wind suction loading, their free flange is in compression, which may cause web–flange distortional buckling (WFDB). This paper presents an analytical study on the WFDB of zed-section purlins when subjected to uplift bending. A simplified model is proposed to describe the WFDB of partially restrained purlins, from which the formula for calculating the critical stress of the WFDB is derived. The present model is validated by the results obtained from the finite strip analysis.

Purpose To present a surgical technique and case presentation of internal chandelier-assisted macular buckling for myopic foveoschisis. Methods Review of patient clinical features, visual-acuity and optical coherence tomography (OCT) results following internal chandelier-assisted macular buckling for myopic foveoschisis. Results A 48-year-old highly myopic female (axial length 29.85mm) underwent internal chandelier-assisted macular buckling for myopic foveoschisis with macular detachment. The best-corrected visual acuity improved from 20/150 to 20/40. Post-operative OCT confirmed central buckle positioning and demonstrated resolved foveoschisis and macular detachment. There were no complications. Conclusions Internal chandelier-assisted macular buckling is a valuable tool to optimize buckle position and patient outcomes.

Buckling-restrained steel plate shear walls have been developed that can markedly alleviate the shortcomings of ordinary steel plate shear wall systems. A parametric study was carried out on finite-element models of buckling-restrained steel plate shear walls, to which cyclic and non-linear static analyses in accordance with the ATC-24 loading protocol were applied. Based on the results acquired from the hysteretic curves, an increase in concrete compressive strength does not markedly affect the ductility and energy dissipation capacity. Moreover, it was observed that as the width of the gap between the concrete panel and steel plate grew, energy dissipation and the response modification factor were reduced. In addition, the results indicated that an increase in the concrete compressive strength improved both shear capacity and initial stiffness. Accordingly, based on a comparison between the rate of improvement in shear capacity arising from an increase in strength of the concrete panels, frame and steel plate, it is concluded that it would be much more rational to increase the concrete strength so that greater shear capacity could be achieved.

Purpose To evaluate the outcomes and complications of scleral buckle surgery alone or combined with pneumatic retinopexy (pneumatic buckle) for the treatment of primary rhegmatogenous retinal detachment. Design Retrospective chart review. Participants Two hundred thirteen patients with rhegmatogenous retinal detachment of whom 101 underwent primary scleral buckle surgery at Rabin Medical Center in 2005–2015 (SB group) and 112 underwent pneumatic buckle surgery at Royal Alexandra Hospital in 2013–2015 (PB group). Methods All patients were followed for ≥12 months. Data on clinical and surgical parameters, outcome, and complications were collected from the medical files. Main Outcome Measures Best corrected visual acuity and anatomical outcomes. Results At 12 months, average best corrected visual acuity was 0.3 logMar in the SB group and 0.42 logMar in the PB group ( P Conclusion Scleral buckle surgery alone is efficient for the treatment of rhegmatogenous retinal detachment. Its combination with pneumatic retinopexy usually has no significant added value in terms of anatomical reattachment rate. Outcomes of Pneumatic buckling vs Scleral Buckling for RRD

Investigation of different potential instability phenomena is an essential part of a study of the structural behaviour of double-layer braced barrel vaults. In this context, the effects of the use of a reinforced concrete (RC) topping in composite action with double-layer grid-works on the instability behaviour of such structures were studied. Two types of double-layer flat grids and barrel vaults were considered: without any integral RC topping (non-composite grid-works) and with a RC topping in composite action with the spatial grid (composite grid-works). The primary models were selected and designed adopting a consistent procedure utilising the weight–density method. Initially, elastic buckling analyses were performed. Complementary studies included a series of non-linear finite-element analyses accounting for geometric and material non-linearities emphasising structural stability and the post-buckling behaviour. It was found that the presence of a rather thin layer of RC covering, in composite action with double-layer grids, increased both the initial buckling and the ultimate strengths of such structures substantially, and also significantly improved their post-buckling behaviour, resulting in much improved reliability against progressive failure and sudden loss of strength.

An interaction function was constructed based on the axial compression/tension and shear loads of orthotropic plates. The coefficients of the polynomial function were determined by uniaxial test results. Buckling interaction and failure interaction formulae under combined axial tension/compression and shear loads were established. Based on the uniaxial load test results of orthotropic plates, the buckling load and bearing capacity under any proportion of the combined loads could be predicted by using the proposed interaction formulae. The buckling interaction curves and failure envelopes predicted by the proposed interaction formulae were in excellent agreement with the test results.

The buckling behaviour of cold-formed steel (CFS) Sigma sections in purlin-sheeting systems is investigated by Finite Element Analysis (FEA) in this paper. A total of 434 specimens with different web heights, thicknesses and lengths are simulated. The comparison of the longitudinal stress distributions obtained from the EN1993-1–3 and FEA is presented. The moment capacities and load–displacement curves of Sigma sections are predicted by FEA. The significant influence of the distortional-lateral torsional buckling interaction on the performance of Sigma purlins is illustrated. The modified Direct Strength Method (DSM) formulae are proposed to predict the flexural capacities of partially restrained Sigma sections under uniformly distributed uplift loading (UDUL).

The present paper treats the lateral torsional buckling (LTB) of castellated rectangular hollow section (CRHS) beams. For the purpose, an analytical model was proposed to provide critical buckling loads in (LTB) resistance. In the present model two types of web openings are considered, referring to rectangular and hexagonal shape perforating. The sectional geometrical properties attributed to each type of opening are controlled by selecting the appropriate value of the reduction parameter. Ritz method is applied in order to found the governing equilibrium equations, following the critical buckling loads are determined from the eigenvalue problem imposed to the tangential stiffness matrix. The validity of the elastic lateral buckling resistances evaluated by the proposed method is checked with the finite element simulation using ABAQUS software. The numerical results for cantilevers and simply supported CRHS beams, with hexagonal and rectangular web openings, are presented for both short and long-span beams.

This paper presents an experimental and numerical investigation into the stability of normal and high strength steel circular hollow section (CHS) columns. Two cold-formed S700 CHS profiles – 139.7×4 and 139.7×5 (in mm), were studied in the experimental programme, and twelve column tests (six on each profile), together with accompanying material tests, were performed. The load-deformation histories and key results from the tests are reported. Following the physical testing, a numerical simulation campaign was conducted. The developed finite element (FE) models for CHS columns were initially validated against the test results. Parametric studies were then carried out, where 2000 additional buckling resistance data were numerically generated for hot-finished and cold-formed CHS columns, covering steel grades from S355 to S900. The obtained test and FE results, together with existing experimental data from the literature, were used to assess the current Eurocode 3 stability design rules. It was shown that the normalised performance of CHS columns is influenced by the yield strength, which is not fully captured by the EC3 design approach. The somewhat conservative Class 3 slenderness limit for compression further worsen the accuracy for those with slender cross-sections. Improvements to the EC3 design rules were proposed to address these shortcomings, including (a) modified Ayrton-Perry formulae enabling a continuous transition of buckling curves across the yield strength spectrum and (b) a new Class 3 limit for CHS in compression. The modified EC3 approach was assessed and shown to improve the accuracy and consistency of resistance predictions over the current EC3 approach, while meeting the Eurocode structural reliability requirements.

This study presents the results of a refined numerical investigation meant at understanding the time-dependent cyclic behavior of reinforced concrete (RC) bridge columns under chlorides-induced corrosion. The chloride ingress in the cross-section of the bridge column is simulated, taking into account the effects of temperature, humidity, aging, and corrosion-induced cover cracking. Once the partial differential equations governing such multiphysics problem are solved through the finite-element method, the loss of reinforcement steel bars cross-section is calculated based on the estimated corrosion current density. The nonlinear cyclic response of the RC bridge column under corrosion is, thus, determined by discretizing its cross-sections into several unidirectional fibers. In particular, the nonlinear modeling of the corroded longitudinal rebars exploits a novel proposal for the estimation of the ultimate strain in tension and also accounts for buckling under compression. A parametric numerical study is finally conducted for a real case study to unfold the role of corrosion pattern and buckling mode of the longitudinal rebars on the time variation of capacity and ductility of RC bridge columns.

In the present paper the variant of computational methods of stability and initial post-buckling behavior of isotropic shells was generalized with respect to laminated composite shells. Using methods of the asymptotic analysis of the Timoshenko–Mindlin theory, the relationships for calculation of shells with the small geometrical imperfections of the different shapes have been produced. On the basis of obtained equations, the technique of calculation of a non-linear pre-buckling state, limiting loads and bifurcation, and also initial post-buckling behavior of laminated cylindrical shells at an axial compression and external pressure have been worked out. The results of calculation for the shells made of glass fiber-reinforced plastic and carbon fiber-reinforced plastic with multimodal imperfections and dimple imperfections have been presented. The features of transformation of the interacting modes of imperfections have been researched.

The yielding segment of the core plate is surrounded by the restraining member, making it difficult to directly inspect the buckling-restrained brace (BRB) after earthquakes. A new BRB, of which the core plate can be directly inspected without disassembling the BRB, is proposed. Only the edge of the core plate is restrained. The simulation models are verified based on previous tests, and the influence of the key parameters on the performance of the partially restrained buckling-restrained brace (PBRB) is compared based on 22 models. The design recommendation for PBRB is summarized. The main conclusions are as follows: The increase of the weak-axis gap d between the core plate and the restraining member can decrease the hysteretic energy-dissipation capacity and increase the weak-axis deformation of the core plate. The weak-axis deformation f of the core plate is selected as the performance evaluation criteria of PBRB, and it is recommended to be controlled within the core plate thickness t. When the unrestrained width-to-thickness ratio bu/t is constant, the change of the maximum weak-axis bulging deformation fmax with the core plate thickness t is not obvious. To ensure that the new PBRB shows satisfied ductility after one strong earthquake and no damage after three strong earthquakes, the two performance levels and corresponding evaluation criteria are proposed, and the design recommendation for key parameters unrestrained width-to-thickness ratio (bu/t) and restrained width-to-thickness (b-bu)/t are given.

New buckling optimal solutions for curved composite panels are presented in terms of principle of virtual work and sequential permutation search (SPS) algorithm. By utilizing the principle of virtual displacements, the buckling load is calculated and the accuracy of the derived buckling solutions is verified by comparison with experimental data and numerical results. SPS utilizes the inherent mechanical properties of composite laminates in which the bending stiffness of the outer layers is more sensitive than those close to the mid-surface. Curved composite panels exhibit a variety of length-to-arc ratios and radius-to-length ratios, under axial compression, pure shear, and combined loadings, are optimized. Some of the results are compared with the global optima obtained by enumeration method, and SPS shows good robustness in locating the global optima. In addition, the buckling load carrying capacity of optimized curved composite panels can be improved by as much as twice over cross-ply laminates. Low computational costs of SPS algorithm imply its potential for solving high-dimensional discrete variable optimization problems of composite structures.

In this article, we studied the instability phenomenon of plate buckling made of steel (E36-S355), and magnetorheological elastomer subject to compression loading. The study of the magnetic field intensity influence on the buckling instability of compressed hybrid plates is done by a mathematical development using the Ritz approach and by a numerical simulation under the Abaqus software. The obtained results show clearly that we can control the instabilities of the adaptive smart plate’s behavior by the magnetic field, and the orientation angle of pseudo-fibers formed by the iron particles; depending on the variation of the angle direction of the magnetic field.

Recently, the collapse of space truss structures has been a public concern, often triggered by local damages of key components. The enhancement effects of buckling-controlled methods on the damaged members of space truss structures are systematically investigated by the detailed numerical analysis. Different local damages are introduced to the members to discuss the influence of damage positions and levels on the bearing capacity and displacement ductility. The sensitivity analysis is also performed to select representative damage modes. Compressive sleeve columns are designed and simulated for the damaged tubes, and the simulation method is verified by the reference tests. Moreover, parametric analysis is carried out to analyze the influence of the protrusion length, stiffness ratio and gap on the post-buckling behavior of members, including the failure mode, bearing capacity, enhancement effect and displacement ductility. Different designs of the outer tubes are proposed for the inner tubes with various damages. The principle in this work can effectively guide the reinforcement of the damaged members.

The present study is aimed to estimate the influence of the web distortion on the elastic (Lr) and plastic (Lp) limiting lengths given in the American Institute of Steel Construction (AISC code) for the lateral torsional buckling behavior of steel beams. For this aim, the W44x335 beam is adopted in the buckling analyses carried out by the ABAQUS finite element (FE) program. The strain results at mid-height of the web at mid-span of the beam are taken into account as monitoring parameters. The web strain results are found highly greater than the yield strain value when L/Lr is equal to 1.0. Hence, the elastic limiting length (Lr) is required to be considered greater than the calculated length as per the code formulation. The section is obtained to reach the maximum strain value at the web before the unbraced length (L) is equal to the plastic limiting length (Lp). Therefore, the calculated Lp is estimated with the given analytical formulation to be highly shorter than the length through the FE analysis. These outcomes prove that the formulations of the limiting lengths proposed in the AISC code don’t consider the influence of the web distortion that is predicted to lead to reducing the torsional and warping rigidity of the section. With the study, it is proposed to determine a reduction coefficient by performing more numerical analyzes for different cross sections and free openings in the regulation.

The finite element model-based design of steel structures is getting increasing attention by designers, especially in the case of buckling problems of welded plated structures and by the static check of the interacting stability behaviour. The FEM-based design approach is introduced and standardised in the EN 1993–1-5 Annex C providing the ability to calculate the buckling resistance based on direct resistance check by geometrical and material non-linear analysis using imperfections (GMNIA). By this design process, the application of imperfections (shape and magnitude) has a large impact on the computed buckling resistance. It is especially true if the interacting stability phenomenon (interaction of plate and column-like behaviour) is to be analysed. The general way to consider imperfections in FE models is the application of equivalent geometric imperfections covering the effect of residual stresses and geometric imperfections. Several previous investigations prove the application of equivalent geometric imperfections can lead to conservative resistance, especially in the case of the interacting stability problem because the application of two different equivalent geometric imperfections leads to duplication of the residual stresses. Therefore, it is highly important to determine the appropriate imperfection shape and size for buckling problems. The current paper deals with the determination of local plate buckling-type imperfection, which can be further applied in numerical models used for interacting stability problems, which is the next step of the planned research program. Within the current paper, the necessary imperfection magnitudes are determined for welded square box-section columns for various steel grades (S235 – S960) to perfectly match the local buckling resistance proved by test results and gives design proposals for FEM-based design approaches.

The outstand flanges of aluminium alloy angles are sensitive to local buckling due to the low elastic modulus of material. To improve the sectional buckling stress, lips could be introduced to improve the stability behaviour of the outstand flanges. This paper presents an equilibrium approach and a simplified energy method for the local and distortional buckling of extruded aluminium alloy lipped angle columns. Closed form solutions for local buckling and distortional buckling are proposed. The equivalent flexural rigidity and torsional rigidity of the lip are two main factors affecting the sectional buckling behaviour. As distinct from double-sided symmetrical edge stiffeners, the bending of a single-sided edge stiffener can lead to in-plane compressive deformation of the adjacent flange. Based on the edge-stiffened flange model, the equivalent flexural rigidity of the lip is obtained from finite element (FE) analysis. To validate the proposed analytical methods, the elastic buckling coefficients of lipped angles with varying dimensions are obtained from eigenvalue buckling analysis. Lips of different thicknesses are considered to study the effect of torsional rigidity. Comparing with FE results, the proposed equilibrium approach shows excellent accuracy for both local and distortional buckling stresses. The closed form solution given by energy method can also well predict the sectional buckling stress. Finally, parametric studies are carried out to further investigate the effects of flexural and torsional rigidities of lips and the slenderness ratios of flanges on the elastic buckling behaviour. Some design remarks are concluded to provide valuable reference for the application of extruded aluminium alloy lipped angles in practice.

Owing to the increase in the applications of the built-up Cold-Formed Steel (CFS) sections in the construction industry, there exists an immediate demand in standardisation of the design rules to use built-up sections as structural members. This paper presents a numerical approach to estimate the capacities and structural buckling behaviour of mono-symmetric stiffened built-up CFS homogeneous and Hybrid Double-T-Box Girders (DTBGs and HDTBGs) subjected to uniform static flexure. The geometry of these built-up sections is unique and has the combined advantages of an open 'T' section girder that offers greater resistance against flexural buckling moment and a closed box region, which resist against lateral-torsional bucking. A verified and validated Finite Element Analysis (FEA) parametric study on 120 ideal FE models of I-DTBGs and I-HDTBGs are performed using ABAQUS software. The overall non-dimensional member slenderness (λLT) considered in this study is ranging up to 1.80. This study captured the three primary modes of failures: local, distortional and lateral-torsional buckling and two interaction modes of failures viz, local plus distortional and distortional plus lateral buckling and their sub kinds. For, the DTBGs and HDTBGs with λLT 0.4 exhibits lateral buckling failure. The bending capacities of the girders and their varying buckling modes are dependent upon the increase of member slenderness and plate element stiffness. The obtained flexural capacities of these girders from FEA have been compared against the Effective Width Method (EWM) design equations as suggested in Eurocode standards. This research study identifies that there exist notable differences while assessing the buckling capacities of these DTBGs and HDTBGs using the existing design rules and their relationships. Henceforward, a new simplified and appropriate design equation is formulated, and its corresponding buckling curve is illustrated in this study. The arrived equation is, χLT = 0.13 λ 2LT − 0.65 λLT + 1.11 that is also found to be satisfactory as per reliability analysis.

The average shear-bearing ratio (β) of buckling restrained brace (BRB) is a key parameter, affecting the seismic performance of buckling restrained braced steel frames (BRBF). In order to determine the dynamic response of multi-story BRBF with different β values, two kinds of structural models are established, one is with the rigid connection of beam-column joints, and the other model has both hinged and rigid joints. The nonlinear time-history analysis of multi-story BRBF structures are carried out by selecting the seismic waves with predominant period close to the first mode period of each research model, and the seismic waves that are significantly different from it. The influence of β on the shear displacement, bending displacement and vibration mode of the structure are revealed: when β ≤ 30%, the story drift of multi-story BRBF structure is mainly shear deformation and the first vibration mode is predominant. When β increases, the bending deformation of the story drift increases. The second vibration mode of the structure is predominant when β ≈ 90%. It is suggested that the equivalent seismic force of multi-story BRBF structure with β > 30% should not be calculated by the base shear force method.

This paper presents an experimental and numerical investigation on the local buckling behaviour of a new built-up Cold-Formed Steel (CFS) homogeneous and hybrid Double-I-Box Column sections (DIBCs and HDIBCs) under axial compression. In total, 24 experimental tests are conducted, out of those 12 tests are on stub columns and the remaining 12 are on short columns. The parameters considered are hybrid ratio (Φh), section’s breadth to depth ratio (B/D) and column height (H). The columns considered in this study are having an overall slenderness (λ) less than 0.20, and the flange plate slenderness (λpf) less than 1.85. Test specimens failed in either of the following three failure modes: local buckling, yielding or by the interaction of both. In all the tested specimens, typical Bottom Zone Local Buckling (BZLB) similar to the shape of Elephant’s Foot is identified. The deformation shape is recognized by expansion (outward buckling) along the major axis and contraction (inward buckling) along the minor axis at the bottom 1/4th height of the columns in opposite faces, followed by the collapse. This kind of failure mode is a clear representation of Poisson’s ratio effect at the ends causing a restraint which then creates a local imperfection under load which leads to a localized failure at bottom zones in the stub and short columns of DIBCs and HDIBCs. BZLB phenomenon is enhanced because of the tubular cross-section geometry, boundary conditions plate element slenderness, overall slenderness of these built-up sections. The ultimate capacities of both the stub and short columns are governed by their strength limits and slenderness. Nonlinear Finite Element Analysis (FEA) is performed on experimental FE models using ABAQUS software and verified against the test results and validated with the actual structural behaviour. Further FEA is performed on 96 ideal parametric FE models considering different material properties and slenderness values. Effect of the intermediate longitudinal stiffener and the influence of edge constraints on axial strengths are also reported. The axial strengths obtained from the experimental tests and FE parametric studies are compared with the predicted results using the Effective Width Method (EWM) as suggested in the Eurocode specifications to access the feasibility of the current design rules, which is found to produce reasonable predictions albeit slightly conservative. It is found that for stub columns with λ 0.1, the experimental values are found to be 1.25 times higher than the predicted values. It is also observed that for columns having λ ≥ 0.1 0.2 with λpf > 1.2 there is a reduction in local buckling resistance of around 2.5% for each increase of λpf by 10%. Hence, it is concluded that the concentric axial compression capacities of DIBCs and HDIBCs subjected to local buckling can be computed as the arithmetic summation of effective strengths of individual channel sections calculated by using the EWM design equations, as recommended in this study. The attained results prove that these sections have a considerable local inelastic reserve strength as specified in North American standards.

Buckling problem of composite plates is of importance since it is commonly encountered in thin-walled structural components in engineering. Buckling resistance design of composite plates involves the design of laminate stacking sequence exhibiting high dimensional discrete variables owing to the combination and permutation of ply orientations of layers. In this work, a sequential permutation search (SPS) optimization algorithm is presented for the stacking sequence design of composite rectangular plates accounting for the inherent physical-mechanical behavior of composite laminates. Owing to that the governing equation for buckling of composite rectangular plates is a linear homogeneous equation on bending stiffness parameters, the convexity of flexural lamination parameters and sensitivity of bending stiffness are utilized to construct sensitive detection techniques and linear search procedures. Moreover, to increase the robustness of SPS, a sign optimization algorithm (SOA) is coupled in SPS to regulate bending-twisting coupling effects. The SPS algorithm is applied to the buckling resistance design of composite rectangular plates exhibiting various boundaries under axial compression, where the Rayleigh-Ritz method is developed to perform the buckling analysis. Optimal results of SPS are compared against layerwise optimization approach (LOA) and genetic algorithm (GA), illustrating its reliability and efficiency.

Stability checking is an essential element of the dimensioning of steel frame structures. One of the stability checking methods allowed by EN 1993-1-1 is the so-called general method of assessing structural stability, based on buckling curves and relative structure slenderness λ ¯ op {\bar \lambda _{op}} usually determined through numerical analyses. But this method is not widely used because of the limited computing capabilities of the engineering programs dedicated to static load analyses and difficulties in interpreting the results of the computations. The commonly used computer programs enable one to determine the shape of buckling and critical load amplifier αcr , from which one cannot directly determine the risk of buckling of a real structure. This paper presents a modified and innovative approach to the general method of assessing structural stability, which uses only three parameters, that is, the type of cross section, cross-section strength utilisation and αcr , to determine a member’s/structure’s bearing capacity mobilisation from the stability condition. The problem solution is presented in the form of simple formulas and legible diagrams. Finally, synthetic conclusions are formulated.

Even though high-strength steel has been widely used across the world, the global buckling behaviour of high-strength steel beams has yet to be systematically investigated through experimental tests and numerical simulations. This paper describes an experimental and numerical study of the lateral-torsional buckling resistance of welded Q690 steel beams. Eight beams with doubly-symmetric cross-sections and different height-to-width ratios were tested under a concentrated point load. To allow free lateral deflections, a special loading system was designed and erected at the mid-span of steel beams. The applied load remained in the vertical direction during the whole loading process, despite significant rotations and lateral deflections of the beam. The critical bending moment of steel beams was quantified in the experimental tests. Besides, numerical models were established by using ABAQUS and initial imperfections were properly defined in the model. Direct comparisons were made among numerical results of steel beams of different steel grades and design curves in different standards. Based on experimental and numerical results, recommendations were provided for the lateral-torsional buckling design of Q690 steel beams. It was suggested that GB50017-2003 and GB50017-201X can predict the buckling resistance of Q690 steel beams with slightly conservative results, Eurocode 3 yields rather conservative estimations, but ANSI/AISC360-10 significantly overestimates the buckling resistance.

I-shaped hoisting spreader beams are widely used in practice when lifting heavy objects by crane. In general, I-shaped beams that are subjected to a bending moment may be sensitive to lateral torsional buckling. Eurocode 3 (1993-1-1 [1]) provides a calculation method to determine the lateral torsional buckling resistance using buckling curves. The method requires the elastic critical moment to calculate the relative slenderness. Different solutions for elastic critical mo-ments are available which usually require fork end conditions. However, hoisting spreader beams do not have fork end conditions nor do they have lateral supports. Thus, the available calculation methods cannot be used and a new method is developed. A numerical model is vali-dated against an experiment and subsequently used to investigate different types of spreader beam configurations. First a method to determine the elastic critical moment of a hoisting spreader beam is developed. Then the lateral torsional buckling resistance is evaluated using the buckling curves. The applicable buckling curve is determined by choosing the least conservative curve that can be used with a partial factor of 1.0. This results in buckling curve d to evaluate the lateral torsional buckling resistance of hoisting spreader beams.

In this paper, a high order finite element model for buckling and post-buckling analysis of a functionally graded material (FGM) plate is proposed. The study is performed considering a functionally graded material plate under different loadings and solicitations. The analysis is based on the classical thin-plate kinematics of von Karman by considering a quadrilateral finite element with four nodes and five degrees of freedom per node. Static equilibrium equations are obtained using the principle of potential energy. The resolution of the stability nonlinear equations is done using a high order algorithm so-called Asymptotic Numerical Method (ANM). This method is based on the Taylor series expansion and continuation techniques. The validity and accuracy of the proposed model is then tested by numerical comparisons of rectangular and perforated plates with the results obtained by the Abaqus industrial software and with those given in the literature

This paper presents the use of Fredholm–Volterra integro-differential equation approach for determining the critical buckling load and natural frequencies of periodically supported nonprismatic Eul...

A numerical study has been carried out to know the lateral torsional buckling of hot rolled steel I beam strengthened using steel plate at the bottom flange. A linear and non-linear analytical study has been carried out using Abaqus software to know the behaviour of beams. For this analysis, ISMB500 is strengthened using a steel plate by varying the thickness of the steel plate. Welded connection is used for connecting the steel plate and bottom flange of a steel beam. The research work aims to determine the ultimate bending strength of the unstrengthened and strengthened I beam. The load deflection behaviour of strengthened and unstrengthned beams was also studied in this research work. Strengthening of steel beam using a steel plate significantly increases the load carrying capacity of steel I beam between 6% and 22%. The percentage of increasing load carrying capacity is depend upon the thickness of plate.

Composite pipe was commonly used in many chemical processes in the petrochemical and pulp and paper industries to convey corrosive fluid suction. Many composite pipe designers currently use conventional metallic pipe standards which do not take the anisotropic nature of composite materials into account. Generally composite pipes replace copper, steel, pvc pipe for hot and cold water piping. In this study an analytical model was developed for buckling of orthotropic composite pipe under external pressure. This pipeline is subjected to two equal and opposite axial pushes then the stress induced at different sections of the body is plotted. It is observed that because of the compressive load the length of the body will decrease and the cross-sectional area of the material will increase as the lateral dimensions change.

This paper investigates the structural performance of concrete-filled stainless steel tubular (CFSST) columns composed of rectangular and square sections. A fiber-based mathematical model is developed to simulate the nonlinear performance of such columns loaded concentrically accounting for the local buckling of steel tube. An accurate lateral pressure model, as well as a strength degradation parameter are proposed based on the existing test results and incorporated in the mathematical modeling developed. A large test dataset is used to validate the accuracy of the numerical prediction. The mathematical model is employed to study the sensitivities of important column parameters on their axial behavior. The accuracy of the existing confinement model of rectangular CFST columns is evaluated in predicting the performance of CFSST short columns. Furthermore, the accuracy of the existing codified design models as well as and the simplified design model proposed in this study to quantify the ultimate compressive strength of such columns is investigated. An accurate artificial neural network (ANN) model along with the GUI feature is developed for the design engineers as a tool to predict their ultimate axial strengths.

Introduction and Importance Neurological deterioration due to buckling of the ligamentum flavum (LF) is an uncommon complication after anterior cervical corpectomy or discectomy with fusion. Case Presentation In this report, we present the case of a 66-year-old male who underwent anterior cervical partial corpectomy of C5 and discectomy of prolapsed C5-C6 with fusion. Postsurgery, the patient displayed signs of neurological deterioration. Upon immediate cervical magnetic resonance imaging (MRI), posterior canal stenosis and severe compression with cord signal due to LF buckling were detected. A posterior laminectomy procedure and canal decompression at the C5-C6 level with bone fusion were performed. Clinical Discussion Patient presented with walking difficulty, then walking disability, followed by bilateral upper and lower limb paresthesia with burning sensation. Examination showed ⅘ muscle strength in both handgrips. Further investigation showed brisk deep tendon reflexes, positive Hoffman sign unilaterally, equivocal Babinski sign, and progressive quadriparesis. Magnetic resonance imaging showed mild and diffuse building of some cervical discs, with spinal cord progression. We performed an anterior cervical corpectomy and fusion (ACCF) and anterior cervical discectomy and fusion (ACDF); a titanium mesh with plates and screws was used for fusion, with removal of a calcified and herniated subligamentous disc. Postoperatively, upper and lower limb strength deteriorated; immediate cervical and thoracic MRI showed LF buckling, which caused canal stenosis and severe compression. Urgent posterior laminectomy and canal decompression with bone fusion was scheduled on the same day. The patient underwent physiotherapy and regained upper and lower limb strength and his ability to walk. Conclusion This indicates the possibility of neurological deterioration as a result of LF buckling, which may be a result of LF thickening accompanied by hyperextension in the cervical region. In this regard, immediate imaging following signs of neurological complications after anterior cervical corpectomy or discectomy warrants early detection, which results in a better prognosis.

PURPOSE To investigate the long-term effect of scleral buckling on corneal biomechanics and the effect of change of scleral properties on intraocular pressure (IOP) measurements. METHODS This is a prospective case series, patients with rhegmatogenous retinal detachment prepared for scleral buckling were included. Goldmann applanation tonometry was used to measure IOP (GAT IOP). Ocular Response Analyzer (ORA) was used to measure corneal hysteresis (CH), corneal resistance factor (CRF), goldmann-corrected IOP (IOPg), and corneal-compensated IOP (IOPcc) preoperatively, and 1, 3, and 6 months postoperatively. RESULTS Thirty-three eyes included in the final analysis, with an average age 38.4 ± 16.2 years. CH and CRF decreased significantly at first, third, sixth months post-scleral buckling; however, this effect decreased with time as follows; preoperative: 8.9 ± 1.5 and 8.5 ± 2.1, first month: 6.8 ± 1.6 and 7.1 ± 1.8 (P value = 0.00, 0.002), third month: 7.8 ± 1.5 and 7.6 ± 1.6 (P value = 0.001, 0.008), and sixth month: 7.7 ± 1.3 and 7.6 ± 1.7 (P value = 0.002, 0.055). IOP cc was 19.3 ± 3.6, 17.1 ± 4, and 17.6 ± 2.9 at 1, 3, and 6 months, and these readings were significantly higher than GAT (13.6 ± 7.6, 12.4 ± 5.1, and 12.1 ± 2.9, P values = 0.00) and IOPg (14.9 ± 3.6, 13.5 ± 4.1, and 13.9 ± 3.5, P values = 0.00). The change in CH at each visit is correlated with the difference between the IOPcc and GAT measurements. CONCLUSION The conventional Goldmann applanation tonometry underestimates post buckle IOP measurements due corneal biomechanics changes. ORA might be an alternative and accurate method of measurement; however, further investigation is warranted.

This paper presents some new and valuable numerical results for the thermo-mechanical buckling analysis of bidirectional porous functionally graded plates with uniform and non-uniform temperature rise. The strong form formulation is implemented for thermo-mechanical buckling in the framework of higher-order shear deformation theory. The material property with four schemes of porosity distribution of bidirectional porous functionally graded plate is taken by a modified power law. The governing differential equations are accomplished utilizing the principle of virtual works. The multi-quadric radial basis function is implemented for discretizing the governing differential equations. The multi-quadric radial basis function Euclidean norm is modified to analyze the square as well as rectangular plates without changing the shape parameters. Convergence and validation studies are performed to show the accuracy, effectiveness, and consistency of the present meshfree collocation method. The influence of different porosity distributions, span to thickness ratios, aspect ratios, grading index, temperature raise, boundary conditions, and porosity index on thermomechanical buckling load is evaluated. Some novel results for the bidirectional porous functionally graded plate are also enumerated that can be utilized as benchmark results for future reference.

Deterministic and stochastic bending and buckling characteristics of antisymmetric cross-ply and angle-ply laminated composite plates are thoroughly examined. Partial differential equations for cross-ply and angle-ply laminates are derived using the three variable refined shear deformation theory based on the Hamilton principle. Deterministic Navier’s solutions are obtained for specific boundary conditions and numerical results are validated with the first-order and third-order shear deformation theories. Two stochastic sampling methods, namely Monte Carlo simulation and Latin hypercube sampling, are presented and analyzed to determine the optimal one based on convergence studies and criteria of sampling errors. Comprehensive probability characteristics of stochastic bending deflections and stochastic critical buckling loads of antisymmetric cross-ply and angle-ply laminated composite plates are investigated using the optimal sampling technique. Probability distribution functions of various stochastic cases provide good assessments for the effects of each inevitable source uncertainty on the bending and buckling behaviors of the laminated composites. This study presents a good alternative for the classical and expensive Monte Carlo simulations and provides a fundamental understanding of bending and buckling statistics of laminated composites.

Analytical solution to the buckling problems of stiffened panels subjected to in-plane compressive loads is presented. The total potential energy functional of stiffened panel is obtained by the summation of that of a line continuum and stiffened panel derived from elastic principles of mechanics. Minimizing the resulting equation with respect to deflection coefficient and rearranging gives the expression for obtaining the buckling load of stiffened panel. Exact deflection functions were substituted directly in the new solution and various edge conditions were considered in this analysis. Obtained results were compared with analytical results of previous works. The method is computationally efficient for complex edge conditions and gives high numerical accuracy.

This study aims to introduce a novel optimal structural design framework for buckling-restrained braces (BRBs) in multi-story buildings. Five artificial intelligence (AI) algorithms, including particle swarm optimization (PSO), shuffled frog-leaping algorithm (SFLA), interior search algorithm (ISA), hybrid of bat and particle swarm optimization (BAT-PSO), and political optimizer, which is recently proposed, are adopted for the optimum design of BRB systems. In the proposed optimization process, the BRB cross-sectional area is taken as the objective function considering the stiffness-strength criteria. As a result, by optimizing the BRB cross-sectional area, the weight of BRBs will reduce. Two mostly-used cross-sectional profiles for all-steel BRBs (circular and rectangular) are considered. In general, the optimized solutions using AI algorithms were more cost effective and exhibited considerably better structural performance in terms of global buckling requirements in comparison to other conventional BRB designs. The results showed that BAT-PSO worked the best in terms of objective function value and computational time. The design solutions obtained using BAT-PSO were lighter (35% for circular profiles and 20% for rectangular profiles), and had superior performance in terms of both stiffness and strength in comparison with the conventional BRB designs. It was also shown that using circular profile can reduce the weight of BRB elements by around 15% compared to rectangular profile. The results of this study should prove useful in more efficient design of BRB systems in common practice.

A method is presented for evaluating the axial critical loads and deformed shapes of a Vierendeel periodic girder. They are obtained by solving the large-deflections equilibrium problem of a micro-polar equivalent model. The elastic properties of this model have been derived from those of an ideal girder whose cells may deform only according to the inner forces transferring modes of the unit cell. In particular, the strain energy density of the equivalent medium is obtained by evaluating the limit of the girder elastic energy for the cell to girder size ratio tending to zero. To solve Engesser/Haringx discord, the large deflections equilibrium equations are deduced by the virtual work principle, without any a priori assumption on the shear force. For this aim, also the external work of the substitute medium is evaluated by the same procedure as the strain energy density. Actually, it is first written for the ideal girder under the assumption of negligibility of the axial effects at the cell-scale, then specialized for the continuous medium by examining the limit value for cell to girder size ratio going to zero. Closed form solutions for the critical deformed shapes are given, together with an accurate formula for the girder buckling load

With the tremendous development of additive manufacturing technology in recent years, porous infill structures with well-designed topology configurations have been widely used in various physical fields. The porous infill structure may be prone to thermo-mechanical buckling failure under certain extreme thermal conditions due to temperature gradient effects and delicate local details of the porous infill structure.Therefore, a topological optimization design method, which considers the influence of the thermo-solid coupling field on the buckling performance of the porous infill structure, is proposed by using the projection approach merged with the Solid Isotropic Material with Penalization (SIMP) method. Critical buckling load factors obtained with thermal-elastic equilibrium and linear buckling analysis are employed to measure the buckling performance of the structure. Numerical examples show that the proposed method can effectively improve the buckling performance of the porous infill structure under the thermo-mechanical environment.

Shallow parabolic arches have been commonly applied in engineering structures, whereas their structural behavior has not been fully investigated due to significant geometric nonlinearity. In general, a shallow parabolic arch has a tendency to suddenly buckle when it is subjected to a step load. An analytical study and a numerical simulation on the nonlinear in-plane buckling behavior of shallow parabolic arches with tension cables and pin-joints are presented. To establish nonlinear buckling equilibrium equations for shallow parabolic arches, motion equations are evaluated using Hamilton’s principle. Then, the law of conservation of energy is adopted for unstable equilibrium paths, to establish the criteria for the nonlinear buckling of these shallow arches. Closed-form solutions for the lower and upper nonlinear buckling loads of a shallow arch under step loads are obtained. The analytical solutions show that the modified slenderness ratio is an important parameter affecting buckling. Nonlinear buckling under step loads or static snap-through buckling with symmetry is impossible when the slenderness ratio is out of the given interval. Moreover, nonlinear buckling under step loads is sensitive to the stiffness of the tension cables. In comparison with an equivalent distributed step load, a central concentrated load is much more likely to induce nonlinear buckling.

PurposeExperimental mid/large scale testing of ship-like stiffened panels in compression is a quite expensive exercise that is not standard. Numerical simulations are preferred instead. Because of being relatively inexpensive (cost and time wise), most authors perform an exhaustive design space exploration arriving at a significant number of runs. This work demonstrates that the buckling response with respect to the nondimensional slenderness ratios may well be fitted with nine runs per stiffener geometry.Design/methodology/approachEfficient derivation of buckling strength formulas for stiffened panels through the employment of design of experiments (DoE) and response surface methodology (RSM) combined with numerical nonlinear experimentation over the entire range of practical geometries.FindingsThe surrogate model developed for T-bar stiffeners predicts accurately enough the ultimate stress in the practical design area, while the surrogate models for angle bars and flat bars demonstrate difference between 10 and 30% from common structural rules (CSR).Originality/valueTo the authors' best knowledge, the statistical-based formal and rigorous approach of DoE and RSM to obtaining buckling surfaces for stiffened panels is performed for the first time. The number of required observations per stiffener type has not been addressed yet as each work selects its own sampling scheme without formal reasoning. This work comes to frame the number of observations for efficient surrogate model building.

In the present research, finite element solutions of thermal post-buckling load-bearing strength of functionally graded (FG) sandwich shell structures are reported by adopting a higher-order shear deformation type kinematics. For the numerical calculation, nine nodes are considered for each element. A specialized MATLAB code is developed incorporating the present mathematical model to evaluate the numerical buckling temperature. The Green–Lagrange nonlinear strain is adopted for the formulation of the sandwich structure. The eigenvalue equation of the FG sandwich structure is solved to predict the post-buckling temperature values of the structure. Moreover, three kinds of temperature distributions across the panel thickness are assumed, viz., uniform, linear and nonlinear. In addition, the properties are described using the power law distributions. The numerical solutions are first validated and, subsequently, the impact of alterations of structural parameters, viz., the curvature ratios, core–face thickness ratios, support conditions and power law index (nZ) including the amplitude ratio on the thermal post-buckling response of FG sandwich curved panels have been studied in details. The investigation reveals different interesting outcomes, which may help for future references for the analysis and design of the graded sandwich structure.

This paper evaluates the strength of unlipped channel columns using the Direct Strength Method (DSM), which applies to the sections with either intermediate or edge stiffeners. The local buckling behaviour of plain cold-formed steel sections (CFS) with fixed-ends is studied by investigating the results of (i) 25 experimental studies published in the literature and (ii) a numerical study of 105 CFS sections. This paper reveals that the aspect ratio (web height to flange width ratio) of the cross-section significantly affects the local buckling strength of plain unlipped channel sections. The DSM local buckling strength as specified in the codes of practice ignores the effect of this parameter, resulting in unconservative designs for such columns. The difference in strength prediction can be up to about 15% for columns with a web height to flange width ratio of 3.0. At this aspect ratio, the inter-element stiffness contribution in the post-buckling stage is the minimum, resulting in a lower strength estimation. To account for this inadequacy, this paper suggests a modified DSM design procedure that accounts for the effect of stiffness contribution from the aspect ratio of the cross-section in the post-buckling stage. The proposed modified DSM design equations agree well with the results of experimental and numerical studies and preserve the target reliability of AISI- S100 (2016) for LRFD.

Gusset rotation would cause adverse influence on the buckling-restrained brace (BRB) end zone and even lead to premature buckling of the BRB end zone. However, limited studies to date referred to the gusset rotation response. To evaluate the cyclic behavior and gusset rotation response, five 1/2-scaled buckling-restrained braced frame (BRBF) subassemblages with various gusset connections, i.e., pinned gusset connection, bolted gusset connection, welded gusset connection, pinned-welded gusset connection, and pinned-bolted gusset connection, were conducted under horizontal cyclic loading. The effects of gusset connection type on the failure modes, horizontal initial stiffness, energy dissipation and rotation response of specimens were analyzed in detail. It showed that all specimens performed plump and stable hysteresis behavior. The upper gusset rotation of the specimen with pinned gusset connection was larger than that of bolted gusset connection, followed by welded connection. Meanwhile, the finite element (FE) models were established and validated by test results. Furthermore, the standard FE model of a full-scale one-story one-bay steel moment BRBF with a single diagonal BRB was developed and then extended to a large number of models to investigate the contribution of various parameters on the upper gusset rotation. Finally, the gusset rotational formulae for predicting its response, as the steel moment BRBF reached to either 2.0% or 3.0% drift, were proposed on the basis of the results of the extensive parametric analysis. It could be used to determine the rotation of the BRB end zone, and the flexural moment acting on the BRB end zone and corresponding practical design procedure can be finally derived to avoid the potential premature failure of the BRB end zone.