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The collapsible tubular mast (CTM) can be compactly folded for transport and deployed in orbit to serve as a key structural element. Once deployed, the CTM is vulnerable to buckling under axial load and bending moments, compromising its load-bearing capacity. The intricate relationship between the CTM's cross-section and its buckling behavior poses a significant challenge for designers. This is due to the ultra-thin nature of the CTM, which gives rise to highly localized buckling modes rather than global ones. To overcome this challenge, we developed surrogate models using a neural network (NN) trained with data from finite element analysis (FEA). These NN-based surrogate models provide high computational accuracy in predicting nonlinear buckling loads under axial force and bending moments around the two principal axes of the CTM's cross-section, achieving R 2 values of 0.9906 , 0.9987 , and 0.9628 , respectively. These models also significantly improve computational efficiency, reducing prediction time to a fraction of a second compared to several minutes with FEA. Furthermore, the NN-based surrogate models enable the usage of the non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization (MOO) of the CTMs. These models can be integrated in the NSGA-II algorithm to evaluate the objective function of existing and new individuals until a set of 1000 non-dominated solutions, i.e., cross-sectional configurations optimizing buckling performance, is identified. The proposed approach enables the design of ultra-thin CTMs with optimized stability and structural integrity by promoting design decisions based on the quantitative information provided by the NN-based surrogate models. [ABSTRACT FROM AUTHOR]

A new type of shuttle-shaped double-restrained buckling-restrained brace (SDR-BRB) is proposed, which adopts the form of a shuttle-shaped deformation section similar to its bending moment distribution as the external restraining system. The SDR-BRB has the advantages of superlong size, high load-carrying capacity, and lightweight components, and is suitable for use in large-span spatial structures and bridge structures with an exposed BRB. First, the calculation formula of the elastic buckling load of a pin-ended SDR-BRB is derived based on the equilibrium method, which is verified through the eigenvalue buckling analysis method, and the effects of the main geometric parameters on its elastic buckling behavior are evaluated. The effects of multiple key factors on the load-carrying capacity of the SDR-BRB are then studied by parametric analysis. The results show that the restraining ratio, initial imperfection, and gap have significant effects on the ultimate load-carrying capacity and overall stability of the SDR-BRB, while the effect of the diameter–thickness ratio is relatively small. On this basis, the fitting formula of the critical restraining ratio of the SDR-BRB considering the influences of initial imperfection and gap is proposed and verified by finite element analysis. The research lays a foundation for further research into the elastic–plastic hysteretic behavior and design method of an SDR-BRB. [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]

The present study assessed the Bailey Bridge's condition and investigated its adaptation as a permanent structure, targeted the Acrow Bailey Bridge in Japan. Field diagnostic loading experiments were performed under various loading conditions, such as dynamic and static loading tests. The onsite data were obtained using a transducer, friction strain gauge, target measurements for the image processing approach, and accelerometer. From the field measurements, the deflection and stresses of the bridge were found to operate within the linear elastic region. The bridge was then accurately modeled based on the in situ geometric configuration of the bridge, and Finite Element Analysis was performed. The model's accuracy was validated with the onsite data under the linear elastic domain. The model was deployed to check for resistance of critical members. A nonlinear analysis based on the linear and nonlinear buckling method was performed to determine the subject bridge's Serviceability Limit State and Ultimate Limit State. The results showed that the first out-of-plane eigenvalue buckling analysis could monolithically assess bridge members. Further, the study established digital twin models resolve for historical data through in situ modeling measurements. Therefore, the findings obtained in this study highlight the bridge's Structural Health Condition, bearing capacity, and propose a framework for adaptation as a permanent structure. [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]

In practice, the elastic lateral‐torsional buckling of doubly symmetric I‐section steel members is analyzed assuming free warping at supports. However, welded stiffeners, bolted end‐plate connections or column base plates maintain elastically the opposite flange out‐of‐plane rotations and thus induce substantial warping restraints. This paper proposes analytical formulations for the evaluation of the elastic critical bending moment for lateral‐torsional buckling of beams taking into account warping restraints at supports. Assuming series of displacement and rotation fields containing one or two terms, the energy method permits to derive expressions of the critical bending moment under constant and linear distribution of the bending moment. A single expression of the warping coefficient kw is proposed whatever the shape of the bending moment diagram. The factor C1 can be conveniently calculated by multiplying two coefficients that depend on the shape of the bending moment diagram and on the warping restraint stiffness, respectively. Finite Elements analyses of beams with warping restraints at supports have been performed considering a beam element model developed with LTBeamN and a shell element model created in ANSYS. The analytical model is in good agreement with the numerical results obtained by the two finite element models. [ABSTRACT FROM AUTHOR]

From accident investigations it is found that under some unknown conditions the energy absorbing capacity and anti-overriding function of anti-climber are greatly reduced due to the serious vertical buckling. In order to analyse the vertical buckling mechanism of collided anti-climber, a simulation strategy based on the coupling finite element method and multi-body dynamics is proposed in this paper. A numerical model of anti-climber is established and validated with the quasi-static crush test. The simulation results indicate that in some train collisions the maximal overriding speed can increase as large as 1.5 m/s. Under this condition, large constraint force and bending moment are induced and applied on the collided anti-climber, resulting in a serious vertical buckling. Besides that, the initial vertical offset is identified as another important factor. Generally speaking, the buckling degree as well as the deterioration of energy absorption capacity of collided anti-climber becomes more severe with the increase of initial offset. Moreover, when the two factors (initial vertical offset and overriding speed) are coupled together, the crush behaviour of anti-climber is more complex. If the bending moments, which are induced by the initial vertical offset and overriding speed respectively, are in the same direction, the collided anti-climber is buckled seriously. On the other hand, if these bending moments are in the opposite directions, they are counteracted. As a result, the collided anti-climber is buckled less seriously and has more capacity to absorb the collision energy. [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]

Featured Application: The research results included in the paper can be widely used in designing thin-walled steel elements for use in construction. The use of the presented calculation model for the calculation of continuous beams allows for more optimal and economical design of sections of this element class under resistance conditions. In this model, the real behavior of thin-walled beams under load was taken into account much more precisely in relation to the Eurocode. This made it possible to use the resistance reserves resulting from the effect of longitudinal stress variation and the elastic restraint of the thin-walled cross-section walls. In modern steel construction, thin-walled elements with Class 4 cross-sections are commonly used. For the sake of the computation of such elements according to European Eurocode 3 (EC3), simplified computational models are applied. These models do not account for important parameters that affect the behavior of a structure susceptible to local stability loss. This study discussed the effect of local buckling on the design ultimate resistance of a continuous beam with a thin-walled Class 4 I-shaped cross-section. In the investigations, a more accurate computational model was employed. A new calculation model was proposed, based on the analysis of local buckling separately for the span segment and the support segment of the first span, which are characterized by different distributions of bending moments. Critical stress was determined using the critical plate method (CPM), taking into account the effect of the mutual elastic restraint of the cross-section walls. The stability analysis also accounted for the effect of longitudinal stress variation resulting from the varied distribution of bending moments along the continuous beam length. The results of the calculations were compared with the numerical simulations using the finite element method. The obtained results showed very good congruence. The phenomena mentioned above are not taken into consideration in the computational model provided in EC3. Based on the critical stress calculated as above, "local" critical moments were determined. These constitute a limit on the validity of the Vlasov theory of thin-walled bars. Design ultimate resistance of the I-shaped cross-section was determined from the plastic yield condition of the most compressed edge under the assumptions specified in the study. Detailed calculations were performed for I-sections welded from thin metal sheets, and for sections made from two cold-formed channels (2C). The impact of the following factors on the critical resistance and design ultimate resistance of the midspan and support cross-sections was analyzed: (1) longitudinal stress variation, (2) relative plate slenderness of the flange, and (3) span length of the continuous beam. The results were compared with the outcomes obtained for box sections with the same contour dimensions, and also with those produced acc. EC3. It was shown that compared with calculations acc. EC3, those performed in accordance with the CPM described much more accurately the behavior of the uniformly loaded continuous beam with a thin-walled section. This could lead to a more effective design of structures of this class. [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]

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]

This study proposes a novel buckling-restrained brace (BRB) using multiple round steel core bars to increase the feasible strength of BRBs utilizing steel bars with roll-threaded screw ends. The buckling restraining members of the proposed BRB consists of multiple primary tubes and a secondary tube. The primary tube directly restrains the buckling of each core bar, and the secondary tube restrains the buckling of the primary tube through spacers. This paper first describes the configuration of the proposed BRB and the design method of buckling restrainers, in which the spacer spacing is assumed to be the buckling length of the primary tube. Subsequently, cyclic loading tests of three specimens with different spacer spacing are presented to demonstrate the mechanical behavior of the proposed BRB, such as the hysteresis behavior, axial force, and bending moment of the primary tubes. The test results indicated that fulfilling the requirement of spacer spacing is essential for achieving stable behavior of the primary tubes and steel core bars. Finally, finite element analyses of buckling-restrained units of the proposed BRB with different combinations of primary tubes and spacer spacing are presented to verify the design method. The results of the parametric analyses indicated that the proposed design formula can provide a conservative evaluation of the stability of the primary tube. • A buckling-restrained brace using multiple round steel core bars was proposed. • The buckling restrainer consists of primary and secondary tubes. • Cyclic loading tests validated the performance of the proposed BRB. • FEA of buckling-restrained units verified the design of primary tubes. [ABSTRACT FROM AUTHOR]

This paper focuses on the investigation into global stability design of grid cylindrical-lattice shell (GCLS) under combined axial compression and moments. This study is an extension of previous researches carried out by the authours in the elastic buckling and axially load-bearing capacity of GCLSs (Zhu et al., 2021, 2022). Accordingly the elastic buckling load and global compression stability coefficient of GCLS loaded axially are employed. The finite element model adopted in this study has been validated by previous researches (Zhu et al., 2021, 2022; Guo et al., 2017). First the elastic buckling behaviours of GCLS under pure bending moments is explored by using eigenvalue buckling analysis. The obtained results demonstrate the effects of the bending moment direction, the beam-column stiffness ratio, the diameter-height ratio of GCLS, the number of columns, and the number of storeys of GCLS on the elastic buckling load of GCLS. Subsequently, the ultimate stability capacity of GCLS under pure bending moment are investigated numerically by using a large number of numerical examples in the common range of engineering applications. Accordingly, a design formula is established based on a relationship between the bending stability coefficient φ M and the compression normalized slenderness ratio λ N , namely the φ M - λ N curve for predicting pure bending-bearing stability capacity. Finally, the interaction design formula for predicting the stability capacity of GCLS under combined axial compression and moment is proposed conservatively by introducing axial compression stability coefficient and bending moment stability coefficient. This interaction design formula is further validated by employing a large number of the numerical examples and provides fundamentals for designing GCLSs in practice. [Display omitted] • Elastic buckling behavior of Grid Cylindrical-Lattice Shells (GCLSs) under combined axial compression and bending moment is investigated. • Stability curve φ M - λ N of GCLSs under bending moment is obtained by using numerical examples. • Stability capacity design of GCLS under combined axial compression and bending moment is proposed according to an interactive formula of N/N u ∼ M/M u. [ABSTRACT FROM AUTHOR]

Analytical formulations for the evaluation of the critical bending moment for lateral-torsional buckling of a beam taking into account warping restraints at supports are proposed in this paper. A theoretically exact solution is firstly derived from differential equilibrium equations using infinite power series for the twist rotation. Next, the deflected shape is approximated using a single or several base functions for the displacement and rotation fields. The energy method is then used to derive approximate expressions of the critical bending moment of beams subjected to various loading conditions: constant/linear bending moment distributions, mid-span pointwise transverse force or uniformly distributed load. The warping coefficient k w does not depend on the bending moment diagram. The equivalent uniform moment factor C 1 can be conveniently expressed as a product of two coefficients, one related to the bending moment distribution and the other to the warping restraints stiffness. Finite Element analyses of beams with warping restraints at supports have been performed considering a shell elements model created in ANSYS and a beam elements model developed in LTBeamN. • Theoretical exact solution for lateral-torsional buckling with warping restraints • Approximate analytical expressions of M cr in Eurocode 3 format • A single expression of the warping factor k w. • Warping stiffness limit characterizing semi-rigid joints [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical investigations of the buckling behaviour and resistance of S960 ultra-high strength steel slender welded I-section beam–columns under combined compression and minor-axis bending moment. An experimental programme, including initial geometric imperfection measurements and eight beam–column tests, was firstly conducted. The test procedures, setups and results were fully reported. Following the experimental programme, a numerical modelling programme was carried out, with finite element models initially developed and validated against the test results and then employed to conduct parametric studies to generate further numerical data. On the basis of the test and numerical data, the relevant design interaction curves, as provided in the European code, Australian standard and American specification, were evaluated for their applicability to S960 ultra-high strength steel slender welded I-section beam–columns. The evaluation results revealed that all three codified design interaction curves lead to conservative resistance predictions, mainly owing to the conservative end points (i.e. column buckling strength and cross-section minor-axis bending resistance). Finally, a revised Eurocode design interaction curve, with improved compression end point determined from more accurate column buckling curve and bending end point determined from the direct strength method, was finally proposed, and shown to result in more accurate resistance predictions for S960 ultra-high strength steel slender welded I-section beam–columns than the codified design interaction curves. • The buckling behaviour of S960 ultra-high strength steel slender welded I-section beam–columns is studied. • Eight beam–column tests on S960 ultra-high strength steel slender welded I-sections are conducted. • FE models are developed and validated against the test results and then used to perform parametric studies. • The applicability of the relevant codified design interaction curves is assessed, revealing inaccuracy. • A new design interaction curve is proposed, resulting in more accurate failure load predictions. [ABSTRACT FROM AUTHOR]

Presented research aims to prove the appearance of lateral-distortional buckling mode by observing the beams' deflection characteristics. Eight-layer channel and lip-channel cross-section glass fibre reinforced polymer (GFRP) beams subjected to pure bending in the web plane were discussed. The Finite Element Method and the Semi-Analytical Method were used to perform all calculations. Deflection angles at the beams' ends show that the lateral deflection sharply increases from load close to critical one and in the post-buckling range. It was observed that for simply supported beams subjected to bending, the lateral-distortional global buckling mode is accompanied by rotation at support in the flange plane. In the FEM approach, the lowest buckling mode is usually considered in beams subjected to bending, and the angle of rotation in the load plane corresponding to the critical bending moment is only analysed. However, in the interactive buckling analysis, the horizontal rotation at the supports is accompanied by the global mode, and its impact is often neglected due to its high bifurcation value compared to the lowest mode. Moreover, in the paper, the influence of this mode on the equilibrium paths, the critical buckling load, the load-carrying capacity, distributions of internal membrane forces, and vertical and horizontal angle of rotation was investigated. [ABSTRACT FROM AUTHOR]

• Buckling of elliptic cylinders with varied slenderness and eccentricity is studied. • Fast performance overviews are attained for FRP components through shell analyses. • Lamination parameters are used to express the stiffness properties in compact form. • The utilized methods provide design bases for optimizing FRP structural components. Structural members made of fiber-reinforced polymers (FRP) attract increasing attention in the development of novel architectural systems that challenge the standard design methodologies. Cylindrical surfaces constitute one of the typical geometric sets obtained with the FRP component fabrication. This paper explores the influences of two geometric parameters on the buckling performance of elliptical cylinders: inverse slenderness (ratio of minimum diameter to height) and eccentricity (ratio of radii along semi-axes). The overall stiffness properties are defined using lamination parameters. This analysis method eliminates the dependency of optimal solutions on the initial assumptions regarding the laminate configuration, which needs to be explicitly described in multi-layer modeling. Finite element analyses are utilized to compute buckling loads of the cylinders under axial compression force and bi-axial bending moments. The optimal lamination parameters and buckling stresses are determined for various parameters, and the lamination parameters corresponding to the optimal and simple [±45°] angle-ply design points are presented in the lamination parameter plane via Miki's diagram. The results reveal the level of performance that can be achieved by a specific geometry and provide guidelines for the optimal design of elliptical laminated cylinders against buckling. [ABSTRACT FROM AUTHOR]

Wrinkling behavior of buried pressure pipeline under strike-slip fault movement was investigated by finite element method. Effects of fault displacement, internal pressure, diameter-thick ratio and dip angle on the wrinkling modes and longitudinal strain of pipeline were discussed. The results show that there are two wrinkling locations of buried pipeline under fault displacement. There is only one wrinkle on A part, but more than two wrinkles on B part. Buckling mode of buried steel pipeline presents three states under different internal pressures. They are collapse state, critical state between collapse and wrinkling, and wrinkling state. The greater diameter-thick ratio can enhance the ability to resistance to bending moment. The bending curve of pipeline changes from S-shape to Z-shape with the increasing of diameter-thick ratio. Wrinkling is more serious with the increasing of fault displacement and diameter-thick ratio. There are two wrinkling modes of B part pipeline when dip angle ß = 0°~45°. [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]

For flexural thin-walled section beams, the ultimate strength is significantly affected by the interaction of different local buckling modes associated with combined bending and shear stresses. This paper provides a comprehensive analytical and numerical study of elastic buckling of thin-walled channels subjected to different combinations of bending and shear stresses. The commercial ABAQUS software package using Finite Element Method (FEM) has been used to perform the elastic buckling analyses of the channel sections. The results are benchmarked against those from the Semi-Analytical Finite Strip Method (SAFSM) for the cases of pure bending and shear only. Two typical types of channels with and without lips are selected for investigation. To study the effect of different combinations of bending and shear on the buckling stresses, different normal stress distributions and equilibrating shear stresses are applied at two end cross-sections of the channels to maintain static equilibrium. Different types of interactions which occur during the buckling analyses are studied by varying the ratios of bending moments resulting from the modelled longitudinal stresses. A new concept for the elastic local buckling interaction based on the Average Bending Moment (ABM) at buckling is provided. In addition, an explicit approach for local buckling loads of channels under different combinations of bending and shear is also introduced for the practical design use. The results from this explicit solution for elastic buckling can be used as direct inputs for an explicit Direct Strength Method (DSM) design of members under combined bending and shear. • A comprehensive study of elastic buckling of thin-walled channels under combined bending and shear stresses is performed • ABAQUS software package using FEM is used to conduct elastic buckling analyses of thin-walled channel sections • Results are benchmarked against those from the Semi-Analytical Finite Strip Method for the cases of pure bending and shear only cases • A new concept for elastic local buckling interaction based on the Average Bending Moment (ABM) at buckling is provided • Results from the explicit solution for elastic buckling analyses can be used in the Direct Strength Method (DSM) of design [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper (Gonçalves and Camotim, 2013 [1]), the authors presented an investigation concerning the buckling (bifurcation) behaviour of uniformly compressed thin-walled tubes with regular polygonal cross-sections (RCPS). The present paper complements the previous work by addressing the local and distortional buckling behaviour of RCPS members subjected to bending or torsion and aims at providing a novel insight into these phenomena. In particular, the specialization of Generalized Beam Theory (GBT) for RCPS, as recently proposed in Gonçalves and Camotim (2013) [2], is employed to obtain closed-form analytical solutions and also to carry out parametric studies by means of numerical analyses which are both computationally efficient (due to the small number of d.o.f. involved) and clarifying (due to the modal decomposition features of GBT). For validation purposes, solutions taken from the literature and also standard shell finite element model results are employed. [Copyright &y& Elsevier]

Abstract: Trapezoidal sheeting of thin-walled steel is applied frequently for roofing and cladding. As such, it is loaded by a concentrated load (at the support) and a bending moment. A recently developed model to predict the sheeting's failure behaviour leaves the question open whether mode jumping (the phenomenon where a plate dynamically changes its buckling mode during an increasing load) should be taken into account in the model. This article presents the analytical and finite element modelling of square and long plates, which, depending on the boundary conditions, may represent the compressed flange of trapezoidal sheeting. The analytical modelling is based on the combination of several displacement functions and using the principle of minimal potential energy. Hereafter the stability of each part of the resulting equilibrium curves is determined. A spin-off of the analytical model is an analytical expression for a current curve-fitted based prediction formula for the post/pre-buckling stiffness ratio by Rhodes. Furthermore, the accuracy range of a solution by Williams and Walker for the far-post buckling behaviour can be confirmed. The finite element modelling has been carried out by implicit dynamic, and explicit (dynamic) simulations. Both for the load levels and the buckling mode sequences, the analytical and finite element models give equivalent results. It is concluded that for the specific boundary conditions that represent the situation of a compressed flange for trapezoidal sheeting, it is very likely that mode jumping will not occur. [Copyright &y& Elsevier]

• Tests and numerical analysis of specimens with large width-thickness ratios. • Elastic-plastic local buckling and its effects on hysteretic behaviour of beam-columns. • Design formula for bearing capacity of Q690 high strength beam-columns. To evaluate local buckling and its effect on the hysteretic performance of high-strength Q690 thin-walled H-section beam-columns, cyclic testing was carried out on four H-section columns composed of plates with a nominal yield strength of 690 MPa. Based on China's standard for the design of steel structures (GB 50010-2017), the four H-section columns are categorized as S4 and S5 sections, and the axial load ratio of the columns is 0.2 and 0.35. After the test, the failure mode, second-order effect of bending moment, hysteresis curve, bearing capacity, backbone curve, energy dissipation, ductility and stiffness degradation of the specimens were investigated. The failure mode of the specimens is elastic–plastic local buckling of the column bottom flange and web. The ductility coefficient of the specimens is 2.08–3.04, and they have certain specific deformation and energy dissipation capacities. Following this, a finite element model was established to simulate the hysteretic performance of the Q690 thin-walled H-section beam-columns. The failure mode and hysteresis curve obtained by the finite element simulation corresponded well with the tests. Based on this agreement, a parametric study was carried out to investigate the influence of the flange width-thickness ratio, web width-thickness ratio, and axial load ratio on the local buckling and hysteretic performance of H-section beam-columns. The variation trend of the backbone curve and the bearing capacity were further investigated by the finite element parametric analysis. Finally, a prediction formula for the beam-column bearing capacity was proposed based on the finite element results. The comparison with the test results shows that the proposed formula has sufficient accuracy and can be used in engineering design. [ABSTRACT FROM AUTHOR]

The global buckling behaviour of hot-rolled stainless steel channel section beam–columns under combined compression and minor-axis bending moment has been studied based on testing and numerical modelling and reported in this paper. A testing programme was conducted on ten hot-rolled austenitic stainless steel channel section beam–columns, with five buckling towards webs and the other five buckling towards flange tips. This was followed by a numerical modelling programme, in which finite element models were firstly developed and validated against the test results and then used to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions, member effective lengths and loading combinations. The test and numerical results were adopted to assess the current design interaction curves given in the European code and American guide, both of which were found to result in inaccurate and scattered failure load predictions. The inaccuracy of the codified design interaction curves stems from the inaccurate end points (i.e. the member resistances under pure compression and pure bending) and the inappropriate shape. To address these shortcomings, a new design interaction curve was developed firstly through the adoption of more accurate end points and secondly through the derivation of a more proper shape. The proposed design interaction curve was shown to yield accurate and consistent failure load predictions for hot-rolled stainless steel channel section beam–columns. The reliability of the new proposal was also confirmed by means of statistical analyses. • The buckling behaviour of hot-rolled stainless steel channel section beam–columns is studied. • Ten beam–column tests were conducted. • FE models were firstly developed and validated against the test results and then adopted to perform parametric studies. • The codified design interaction curves were assessed, indicating inaccuracy. • A new design interaction curves was proposed, with the accuracy and reliability demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a theoretical analysis of the linear and nonlinear elastic in-plane behaviour and buckling of pinned–fixed circular arches that are subjected to a radial load distributed uniformly around the arch axis. In contrast to most previously reported studies, the pinned support and fixed support of a pinned–fixed arch provide different boundary conditions at each of its ends. Because of this, the structural behaviour of a pinned–fixed arch is quite different from that of a pinned–pinned or a fixed–fixed arch. The linear and nonlinear analyses show that the uniform radial load produces both an unsymmetrical bending moment and an axial compressive force in pinned–fixed arches; particularly in shallow pinned–fixed arches, the unsymmetrical bending moments are significant prior to in-plane buckling. It is found that a pinned–fixed arch under a uniform radial load can buckle in a limit point mode, but cannot buckle in a bifurcation mode. This is quite different from pinned–pinned or fixed–fixed arches under a uniform radial load that may buckle in a bifurcation mode and in a limit point mode. Analytical solutions for the nonlinear equilibrium path and limit point buckling load of shallow pinned–fixed circular arches are derived. Comparisons with finite element results show that the analytical solutions can predict the nonlinear equilibrium path and the nonlinear buckling and postbuckling behaviour of shallow pinned–fixed arches accurately. Although these solutions are derived for shallow pinned–fixed arches, comparisons with finite element results have demonstrated that they can also provide reasonably good predictions for the nonlinear buckling load of deep pinned–fixed arches under a uniform radial load. [Copyright &y& Elsevier]

Abstract: For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames. [Copyright &y& Elsevier]

The assessment of the design buckling resistance of single members is usually based either directly on the elastic buckling resistance of the member or indirectly on its non-dimensional slenderness computed from the elastic buckling resistance. Specifically, Eurocode 3 buckling curves define the buckling reduction factors as a function of non-dimensional slenderness and, according to EC3 "General Method", these curves may also be used for non-uniform members. In this context, a new procedure will be presented for the computation of the elastic critical moment of tapered members. As is well known, the elastic critical moment strongly depends on both the bending moment diagram and end support restrictions. For uniform members, elastic critical moments may be computed using a relatively simple formula in which the bending moment distribution is taken into account by an equivalent uniform moment factor, and the end support restrictions are introduced through the buckling length. Unfortunately, this formula has not been extended to tapered members and, as a consequence, the elastic critical moment for tapered beams must be obtained using numerical methods such as the finite element methods. Based on a comprehensive parametric study for the elastic critical moment of tapered beams with different moment diagrams, this paper offers a new procedure, called the Equivalent Moment Approach, for the substitution of a tapered beam with any moment diagram by an equivalent uniform beam. One advantage of the present procedure is that closed form expressions valid for uniform beam can be generalized and used for tapered beams. [ABSTRACT FROM AUTHOR]

Abstract: The newly developed p-M diagram provides a means for readily evaluating the collapse and/or buckling load of pressure equipment with external flaws simultaneously subjected to internal pressure, p and external bending moment, M due to earthquake, etc. In this paper, some FEAs for large diameter vessels with an external flaw were conducted under (1) pure external bending moment, and (2) subjected simultaneously to both internal pressure and external bending moment, in order to determine the plastic collapse load by applying the twice-elastic slope (TES) as recommended by the ASME and to determine the buckling load. The p-M line adopted in the Ibaraki FFS rule based on the measured yield stress indicates that the safety margin for the TES loads at the LTA is about 1.2–1.8, and 1.5–2.0 for the buckling loads. The Ibaraki FFS rule that prevents buckling by applying Donnell''s equation of FS=2 can assure adequate levels of integrity and safety. [Copyright &y& Elsevier]

The cognition of the effect of cutout on the capacity of loading bearing and the buckling behavior of the cylindrical shells is crucial in designing of structures of automobiles, airplanes and marine structures. In this article, the simulation and analyzing of steel cylindrical shells with different lengths and diameters, including elliptical cutout, under bending moment with using of the numerical finite elements method was done. Furthermore, the effect of changing of cutout dimensions and the ratio of the length to diameter on buckling behavior and post buckling of cylindrical shells are studied. Finally, the relations for finding of buckling moment of these structures were presented. [ABSTRACT FROM AUTHOR]

Buckling of concentric tubular strings in pipe is an essential problem in the fields of medical, biological, and nanomaterials, especially in petroleum engineering. Completely different from the buckling of the classic Euler compression columns, the buckling of concentric tubular strings involves geometric nonlinearity and contact nonlinearity, and has more complicated geometric deformations and buckling configurations. In this paper, a finite element method combining the spatial beam element and the two-layer contact gap element is proposed, and a virtual transient dynamic method is introduced to solve the static buckling of concentric tubular strings. The internal concentric tubular strings are discretized into spatial beam elements, and the contact relationships between tubular strings are described by two-layer contact gap element. Meanwhile, the larger damping is used to attenuate the dynamic response of the system, so as to find the static part of the transient dynamic solution. Appropriate damping and element length are determined by numerical simulation. The structural characteristics and contact states of eight post-buckling configurations are studied. The helix pitch values of specific configurations are in good agreement with the theoretical solutions. In addition, the distribution of bending moment, shear force and contact force in various post-buckling configurations is studied. For the full helical buckling, it is found that there is only one non-contact section in the transition section of inner tube and two non-contact sections in the transition section of middle tube. The research results of this paper provide a theoretical basis and reference for further study on the buckling of multi-layer concentric tubular strings. • Finite element method and transient dynamics method are used to solve the static buckling of concentric tubular strings in pipe. • Eight post-buckling configurations as axial compression force increases for concentric tubular strings in pipe. • Transition section includes only one non-contact section for inner tube while includes two non-contact section for middle tube. [ABSTRACT FROM AUTHOR]

Abstract: In finite element methods that are based on position and slope coordinates, a representation of axial and bending deformation by means of an elastic line approach has become popular. Such beam and plate formulations based on the so-called absolute nodal coordinate formulation have not yet been verified sufficiently enough with respect to analytical results or classical nonlinear rod theories. Examining the existing planar absolute nodal coordinate element, which uses a curvature proportional bending strain expression, it turns out that the deformation does not fully agree with the solution of the geometrically exact theory and, even more serious, the normal force is incorrect. A correction based on the classical ideas of the extensible elastica and geometrically exact theories is applied and a consistent strain energy and bending moment relations are derived. The strain energy of the solid finite element formulation of the absolute nodal coordinate beam is based on the St. Venant–Kirchhoff material: therefore, the strain energy is derived for the latter case and compared to classical nonlinear rod theories. The error in the original absolute nodal coordinate formulation is documented by numerical examples. The numerical example of a large deformation cantilever beam shows that the normal force is incorrect when using the previous approach, while a perfect agreement between the absolute nodal coordinate formulation and the extensible elastica can be gained when applying the proposed modifications. The numerical examples show a very good agreement of reference analytical and numerical solutions with the solutions of the proposed beam formulation for the case of large deformation pre-curved static and dynamic problems, including buckling and eigenvalue analysis. The resulting beam formulation does not employ rotational degrees of freedom and therefore has advantages compared to classical beam elements regarding energy-momentum conservation. [Copyright &y& Elsevier]

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]

Abstract: The durability of thermal barrier coatings (TBCs) employed in most turbine engines is limited by delamination, both within the coating and at the coating–substrate interface. A test used for evaluating the mixed-mode toughness pertinent to such delaminations has been fully-analyzed by determining the steady-state energy release rate, the mode mixity and the critical length for buckling. An analytic solution based on beam theory establishes basic estimates and scaling relationships. Selected finite-element calculations have been used to affirm the fidelity of the results. The energy release rate attains steady-state, but the phase angle changes throughout because of a small (but significant) bending moment induced at the supports. The coating buckles at a critical delamination length, whereupon the energy release rate increases rapidly and violates steady state. The solutions are used to re-interpret measurements reported in the literature for an electron beam physically deposited TBC. [Copyright &y& Elsevier]

The trend for aeroengines with increasing thrust capacities requires the development of shaft technology to deal with this greater power transmission, while still restricting their dimensions and weight. Thin-walled designs can assist in achieving this objective, but are limited by their torsional collapse behaviour. By improving the understanding of the torsional buckling behaviour of shafts, this will enable improved shaft designs able to deal with the increase load capacities required. Until recently the prediction of buckling failures of such thin-walled shafts was by empirical and theoretical equations, which are, in general, unnecessarily conservative. A previous publication described the development and validation of an accurate and versatile finite element-based analysis technique for predicting the torsional buckling behaviour of thin-walled shafts. Although for a typical aeroengine drive shaft the dominant loading mode, under normal conditions, is torsion, aeroengine drive shafts will also experience bending and axial loading. The aim of this paper is to prove that the previously developed finite element buckling methodology can be used for buckling analyses of shafts under combined load situations. This paper presents validation cases for which experimental test results are compared with the results of finite element analyses, under various loading modes; it shows that the behaviour of shafts under combined loads can be accurately predicted using the finite element method. [ABSTRACT FROM AUTHOR]

Steel stiffened panels are widely used in engineering design and construction. However, numerical modeling and analysis effort for a three-dimensional (3D) stiffened panel may be notable, especially for the ultimate limit state of ship structures. Therefore, a homogenization method is outlined that transforms 3D stiffened panel into an Equivalent Single Layer (ESL) concerning the same mechanical behavior. ESL stiffnesses are obtained with a unit cell analyses based on stiffened panel where periodicity is imposed with boundary conditions based on a first-order shear deformation theory (FSDT). Stiffnesses were determined from the first derivative of a membrane force and bending moment obtained with numerical simulations. The effect of initial imperfection shape was included in the analysis to account for local and global buckling behavior. ESL with non-linear stiffness was implemented in Abaqus UGENS subroutine, allowing incremental evaluation of stiffness. Ultimate strength prediction of a steel grillage model with ESL finite element analysis was in excellent agreement with detailed 3D FEM analysis. The key in this analysis was consideration of non-linear ESL stiffness as linear analysis was unable to detect the point where ultimate strength capacity of the grillage was reached. • Homogenization method aims to transform the detailed 3D stiffened panel into an equivalent single layer (ESL). • Geometrical and material nonlinearities were considered in the stiffness calculation of ESL. • UGENS subroutine was invoked to involve the non-nonlinear membrane force and bending moment of ESL. • Ultimate strength of stiffened panel was accurately determined with current non-linear ESL approach. [ABSTRACT FROM AUTHOR]

A general method for the investigation of buckling of reinforced concrete beams subjected to axial loads and bending moments is presented. The beams ate subdivided into finite segments or line elements. The geometrical and mechanical properties of the cross-sections are described by means of the finite element method. The constitutive relationships of the materials employed may be of any type, as well as the location of the steel reinforcements. A computer program has been written and implemented on a microcomputer for practical use. Several examples show the capability of the presented approach. [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]

A systematic finite element based approach is presented to characterize the interaction between the bending moments and axial forces coming from the connected beams in 2D welded steel joints. The modelling technique is described in the paper, as well as the description of the interaction diagrams between axial forces and bending moments for a series of commercial steel sections. An initial imperfection is included in the finite element model to capture the possible buckling failure modes in the column web and the beam flanges. The approach predicts moment capacities that are very similar to those predicted by Eurocode 3 in the absence of axial forces. Interaction diagrams and moment rotation curves are shown for different levels of axial forces, as well as axial force versus displacements for different levels of bending moments. An investigation is also carried out that shows that the approach leads to axial-bending interaction curves that are path independent. Finally, a nonlinear exponential curve fitting is proposed for the axial-moment interaction diagram. • Finite element method to accurately model the resistance of 2D welded joints with axial force and bending moment interaction • Initial imperfection to capture the possible buckling failure modes in the column web and the beam flanges • Generation of axial force versus bending moment interaction diagrams • Path independent limit surfaces [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]

• The strong coupled form-finding and optimization algorithm was proposed. • The geometrical length of component can be optimized according to its internal force. • The buckling capacity of the entire structures can be optimized during form-finding analysis. • The buckling capacity of the entire structures can be significantly improved. Reticulated shell structures are commonly adopted because of their long-span feature and novel appearance. These structures generally comprise slender beam members, which may cause the buckling of entire structures. A shape-finding method is proposed in this study to eliminate the bending moment while optimizing the member buckling capacity of reticulated shell structures. The proposed method (the strong coupling form-finding and optimization algorithm) can be utilized to optimize the geometrical length of each component. The effective length factor, sectional area, and moment of inertia can be accurately considered in the optimization analysis. Member length can be optimized according to the axial force and geometrical parameter. This study can systematically be adopted in the design, analysis, and optimization of reticulated shell structures. This work was conducted using a general finite element analysis program and can be easily mastered by engineering designers while avoiding tedious programming. [ABSTRACT FROM AUTHOR]