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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 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 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 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]

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]

Hull girder ultimate strength is an essential parameter for the ship's structural design. Numerous research studies have been done about hull girder bending. However, few experimental tests have been carried out due to the fabrication cost, the difficulty of monitoring loads, and mapping surfaces of models on large- and medium-scale. This paper conducted a four-point bending test of a small-scale hull box girder. The dimensions of the box girder model are defined from geometric slenderness ratios representing a double bottom panel at the midship of a typical Suezmax tanker. Numerical finite element models are developed, where the friction coefficient between the model and its supports is determined based on experimental correlation. The numerical models with different initial imperfection distributions are considered to perform ultimate strength analyses. Initial imperfections implemented in the models are based on least-squares regression of the geometric imperfections measured from the experimental models. Strain gauges were installed at the upper panel and obtained measurements compared with local numerical strains. Both experimental and numerical models showed that the upper panel of the box girder presented initial structural failure in the plating between stiffeners, which evolved to the stiffeners, following the expected buckling sequence of a reinforced panel. IACS formulation and direct methods have been employed to evaluate the ultimate bending moment. A correlation between the theoretical and experimental results indicates that the IACS formulation better predicts the ultimate bending moment, with the additional advantage of estimating the curvature. This paper also provides methodology and parameters for future studies of the ultimate strength of ship panels with different slenderness ratios. • Ship ultimate longitudinal strength based on box girder modeling. • Laboratory test of small-scale box girder using four-point bending. • Numerical and experimental correlation for different initial imperfection distributions. • Box girder bending strength, including IACS formulation. [ABSTRACT FROM AUTHOR]

This paper presents an exact solution for the boundary-value problem which describes the linear buckling of axially compressed circular cylindrical panels with stringers attached to the straight edges. The boundary conditions differ from the classical simply supported ones, often assumed for design purposes, in the sense that the torsion resisted by the stringers are also taken into account. The presence of the stringers makes the results reported herein of practical interest and valuable as benchmark data. [ABSTRACT FROM AUTHOR]

A computationally efficient framework is presented to design fibre steered laminates in cylindrical shells, stiffened with longitudinal stiffeners, optimally. The framework is comprised of a semi-analytical analysis approach and a multi-step optimisation framework, and is applied for maximum buckling capacity design of fibre steered laminates of two stiffened cylinders, with different thickness to radius ratios, under bending moment. If the maximum buckling capacity designs are material failure critical, strength is imposed as a constraint in the optimisation problem. Comparisons of buckling capacity of steered fibre laminates with those of straight fibre laminates are shown and validated. Finally, to gain in-depth understanding of the way buckling capacity is improved by fibre steering, the axial section load and the critical buckling modes of straight and steered fibre laminates are compared. [ABSTRACT FROM AUTHOR]

The paper studies the influence of internal pressure on circular thin-walled pipes ( D / t > 150 ) subjected to pure bending. Both straight pipes and curved pipes are analysed. Both yield and buckling failures are considered. It is shown that internal pressure decreases the limiting load for yield but increases the limiting load for buckling. The study is mainly FEA-based. A formula to predict critical moment given by linear buckling analysis is proposed. Comments on difference between linear and non-linear analysis results are given. It is shown that a pipe curvature opposite to the bending moment can increase the critical load. It is shown that cylindrical thin-walled shells have an optimal value of internal pressure to which limiting load for yield and critical buckling moment are equal, corresponding to an optimal use of material. [ABSTRACT FROM AUTHOR]

The lateral buckling analysis of cold-formed thin walled beams subjected to pure bending moments has been performed. The critical buckling loads are estimated based an optimization criteria. The estimated critical buckling stresses are compared with the published results, they show excellent agreement. The effect of the beam length, radius and thickness of the flanges and the length of the extended open flanges, on the critical buckling stresses have been studied for several combinations of the geometric parameters of the beam. Among the three beams, the critical buckling moments for the beam with the extended open flanges are found to be the maximum. However, considering the material and manufacturing costs, beams with rounded cross section are efficient in resisting the buckling loads. [ABSTRACT FROM AUTHOR]

A dent is a typical defect found in oil and gas pipelines and poses a significant threat to their safety and integrity. In this study, the buckling behavior and limit strain capacity of pipelines with kinked dents under bending moment loads were investigated. First, four-point bending tests of full-scale pipelines with kinked dents were conducted in a laboratory, and the critical buckling load and strain response of the pipelines during buckling failure were tested. The test results revealed that the existence of kinked dents, specifically those with large depths, could weaken the bending resistance of the pipelines. During the buckling process of the pipeline, a considerable compressive strain was generated at the bottom center of the dent, which was considerably higher than the strain value at the corresponding position of the intact pipeline. However, the strain at both axial sides of the dent gradually changed from compressive strain at the initial bending stage to tensile strain after buckling failure. Then, nonlinear finite element (FE) models of buckling failure for pipelines with kinked dents under bending moment loads were developed, and the reliability of the FE models was verified through comparison with the test results. In addition, a parametric sensitivity study was conducted to determine the effect of parameters, such as dent depth, dent angle, diameter-to-thickness ratio of the pipe, and yield ratio of the pipe steel, on the compressive strain capacity of the pipeline. Finally, based on a large number of FE simulation results, a model for predicting the buckling compressive strain capacity of pipelines with kinked dents was developed, which can be used for evaluating buckling instability failure of pipelines with kinked dents subjected to bending moment loads. • A strain-based assessment method for dented pipelines under bending loads. • A finite element model for buckling analysis on dented pipeline. • A bending test of buckling failure of pipelines with kinked dents. • Dependence of the compressive strain capacity on pipe geometry and steel material. • The critical compressive strain of buckling as a function of dent depth, angle. [ABSTRACT FROM AUTHOR]

This work presents an investigation on the compressive strain capacity of resisting buckling on an X80 steel corroded pipeline subjected to a bending moment using nonlinear finite element analysis (FEA) validated by full-scale tests. The modelling results indicate that the existing strain-based assessment method is not suitable for pipelines with deep corrosion and has certain application limitations. Consequently, a new evaluation method based on far-field strain was developed to predict the buckling failure of corroded pipelines subjected to bending loads. The influence of the corrosion shape type, corrosion size (i.e., depth d , length L , and width w), pipe geometry, and internal pressure on the critical buckling strain capacity and critical buckling moment of the pipeline were studied using parameter sensitivity analysis to verify the proposed strain criteria. The results illustrate that the variation trends between the critical buckling strain and the critical buckling moment with each factor were consistent, indicating that the proposed novel strain-based evaluation method is effective and applicable. In addition, the buckling resistance of a pipeline with rectangular corrosion is relatively weaker than that with a semi-spherical corrosion pit or cylindrical grooved corrosion under the same defect size. Further, the critical compressive strain capacity of a corroded pipeline is primarily affected by the depth and width of the corrosion, whereas the effect of the corrosion length is relatively insignificant. Moreover, the critical length and width of the corrosion defect affecting the bending capacity of resisting buckling were determined as L / D t = 20 and w / π D = 0. 5 , respectively. • A novel strain-based assessment method of local buckling of corroded pipelines. • Determined the effect of defect geometry on critical compressive strain capacity. • Determined the critical defect size that affect the pipe buckling strain capacity. [ABSTRACT FROM AUTHOR]

A new model depicting the buckling configuration of a tubular string in a three-dimensional curved wellbore is proposed. During modeling, the toolface angle is considered, and the sinusoidal buckling and helical buckling of the tubular string are considered on the basis of alignment with either the lower curved side or the outer curved side of the wellbore. After modeling, the energy method is used to solve the model, and the critical buckling load, which is related to the relationship between the buckling configuration and the axial load, can be obtained. The critical buckling loads calculated using the model presented in this paper are consistent with the measured data from published experiments and the trends of the He and Kyllingstad model. The results of the new model also show that with an increasing wellbore curvature, the influence of the toolface angle on the critical buckling load and the characteristic parameters of the buckling configuration (wavelength, amplitude, and pitch) decreases. Based on the expressions for the quantitative relationships between these characteristic parameters and the axial load, procedures for calculating the contact force and the bending moment are given. The results for the contact force show that the calculated values from the Johancsik et al. model and the Mitchell model are the average values calculated using the procedures presented in this paper for tubular strings under sinusoidal buckling and helical buckling, respectively. The calculation results show that the influence of the toolface angle on the bending moment of a tubular string under helical buckling is less than that under sinusoidal buckling. By using this model, not only can the critical buckling loads, contact forces and bending moments of tubular strings in three-dimensional curved wellbores be calculated, but the trends of these calculated values with the buckling configuration can also be identified to guide the selection of the control parameters for tubular strings in the field. • A buckling model for a tubular string in a three-dimensional curved wellbore is established. • The critical buckling loads and the parameters (wavelength, amplitude, and helix pitch) can be obtained by the model. • The critical buckling loads calculated by the model are consistent with the values measured in published experiments. • Based on the buckling model, the contact force and bending moment of the tubular string can be determined. [ABSTRACT FROM AUTHOR]

Tubular steel towers are the most common design solution for supporting medium-to-high-rise wind turbines. Notwithstanding, historical failure incidence records reveal buckling modes as a common type of failure of shell structures. It is thus necessary to revisit the towers' performance against bending-compression interactions that could unchain buckling modes. The present investigation scrutinises buckling performances of a cylindrical steel shell under combined load, by means of the energy method. Within the proposed framework, the differential equations to obtain dimensionless expressions showed the energy-displacement relations taking place along the shell surface. Furthermore, shell models integrated with initial imperfection have been embedded into finite element algorithms based on the Riks method. The results show buckling evolution paths largely affected by bending moments lead to section distortions (oval-shaped) that in turn change the strain energy dissipation routine and section curvature. The shell geometrical parameters also show a strong influence on buckling effects seemingly linked to a noticeable reduction of the shell bearing capacity during the combined loading scenarios. [ABSTRACT FROM AUTHOR]

• Cantilevers are very different from simply supported beams. • Cantilevers have different restraints and moment and yielding patterns. • Yielding in steel cantilevers varies with moment distribution and residual stresses. • Yielding reduces out-of-plane section rigidities. • Lateral buckling resistance is affected by moment distribution and reduced rigidities. • Beam buckling design rules are inappropriate for cantilevers. Steel cantilevers are very different from the simply supported beams under uniform bending which provide the basis for designing steel members against lateral buckling. Cantilevers have different end restraint conditions, while the most critical loading condition for cantilevers is one of concentrated end load leading to a linear moment distribution. Thus the elastic lateral buckling formulations for uniform bending of simply supported beams used more generally for design are inappropriate for cantilevers. The mono-symmetric yield patterns in simply supported beams with residual stresses in uniform bending are of opposite sense to those of cantilevers because of the opposite sense of the bending moments. Thus formulations which take account of the effect of mono-symmetry on the inelastic lateral buckling of simply supported beams are inappropriate for cantilevers. Further, the linear cantilever moment distribution leads to very localised yielding instead of the uniform yielding of beams under uniform bending. This paper studies the inelastic lateral buckling of cantilevers in order to produce better design guidance than that currently based on the inelastic buckling of simply supported beams in uniform bending. The effects of mono-symmetry on the elastic buckling of beams and cantilevers are first investigated, and then the effects of the mono-symmetric non-uniform yielding patterns which complicate the prediction of the inelastic buckling resistances of cantilevers are studied. Cantilevers with reduced (instead of rigid) end warping restraints occur in overhanging beams, and so the effects of yielding on overhanging segments are also studied. These studies are used to develop simple approximate methods for designing cantilevers and overhanging segments against inelastic lateral buckling. [ABSTRACT FROM AUTHOR]

The current slenderness limits are significantly different in international design codes for cold-formed Circular Hollow Sections (CHS) under pure bending. This paper aims to use the Finite Element (FE) method to understand the behaviour of cold-formed CHS under pure bending and to propose new design rules. The model is calibrated by comparing its predicted load-deflection curves with previously published experimental data. In total, 21 specimens were modelled with diameter-to-thickness ratios ranging from 13 to 122. The current slenderness limits in the present international steel specifications were examined using the FE model and their suitability for cold-formed CHS is discussed. The effect of section slenderness on rotation capacity has been examined where the predicted variation of rotation capacity against section slenderness has been compared to the experimental results. A new equation for the amount of initial geometrical imperfection as a function of section slenderness has been developed and proposed for design purposes. The ovalisation deformation ratio and the critical strain at local buckling were determined and compared for compact, non-compact and slender sections. The progressive bending deformations of CHS at 10 critical steps have been presented and compared for the three cross sectional types, in particular at the maximum moment and bending rotation. In general, a good agreement has been obtained between the predicted strengths and ductilities using the current FE models and those of the experimental data of cold-formed CHS. • Using finite element method to determine the slenderness limit of cold-formed steel tubes and compared to the previous experimental results. • The effect of geometrical imperfections on the deformation cold-formed CHS has been examined. • The rotation capacity has been presented for CHS. • The ovalisation of compact, non-compact and slender section has been analysed. • The buckling mechanism has been analysed by using strain analysis, the critical strain at maximum moment has been determined and compared to the theoretical results. [ABSTRACT FROM AUTHOR]