Thin-walled Box Sections Research Articles

A novel approach for the optimum cross-section design of thin-walled box section beams subject to oblique bending based on both adequate-strength and local stability conditions

This study presents a new analytical procedure developed for the optimum cross-section design of the thin-walled box sections subject to oblique bending. The box sections designed in this study have been assumed to be achieved by hollowing out the rectangular solid sections at different subtraction ratios including arbitrary, optimum, and maximum. The optimum subtraction ratio has been determined based on the adequate-strength condition while the maximum subtraction ratio has been determined taking into account both adequate-strength and local buckling conditions. The optimal design of the box sections for the arbitrary subtraction ratio has been attained by minimizing the maximum normal stress, taking into account the adequate-strength condition. Conversely, the cross-sections of the box profiles for the optimum and maximum subtraction ratios have been optimized by minimizing their cross-section area, accounting for the defined combined strength condition involving adequate- strength and local stability requirements. An equivalent box section design model that allows checking the local stability of the box sections possessing dissimilar wall segment thicknesses has been developed to perform the local buckling control on the designed optimum box sections with unequal wall thicknesses. The new local stability conditions have been defined relying on this developed equivalent box section design model. The analytical results, validated through numerical predictions obtained from linear elastic local buckling and post-buckling analyses performed using Abaqus software, have shown that the optimally designed box section achieves substantial material savings per unit length compared to its corresponding equivalent box section.

Interactive buckling behaviour of Q420–Q960 steel welded thin-walled H-section long column

Considering the broad application prospect of high-strength steel (HSS) in engineering structure, and the limitations present in existing studies on interactive buckling of HSS welded thin-walled box-section long column, both test and finite element analysis were employed to investigate the interactive buckling behavior exhibited by 12 specimens fabricated from Q420–Q960 steels. The detailed analysis considered various aspects, including the failure mode, axial deformation, interaction of local and overall buckling deformation, and the ultimate bearing capacity. Observations revealed that the utilization rate of steel strength diminished with an escalation in both the plate width–thickness ratio and steel strength. An increase in the plate width–thickness ratio correlated with an earlier onset of local buckling, and the influence of steel strength was found to be negligible. More importantly, the limit of the plate width–thickness ratio for columns undergoing interactive buckling increased with a rise in column slenderness and decreased with an increase in steel strength. Taking into account the influence of column slenderness and steel strength, a novel calculation formula for determining the limit of the plate width–thickness ratio was derived. It is noteworthy that Eurocode 3 and JGJ/T 483–2020 were found too conservative for calculating the ultimate bearing capacity, while ANSI/AISC 360–22 was found suitable. Additionally, a calculation method for the ultimate bearing capacity of Q420–Q960 steel welded thin-walled H-section long column was proposed based on the direct strength method.

Stability design of cold-formed high and ultra-high strength steel thin-walled box sections using effective stress-strain model

This paper proposes an effective stress-strain model for integrated analysis and design of cold-formed steel structures with thin-walled sections. The study focuses on square and rectangular hollow sections made from high and ultra-high strength steel. Initially, a shell-finite element model (SFEM) was developed and validated using experimental data, specifically for cold-formed members subjected to axial compression. Subsequently, a comprehensive parametric study is conducted to establish the stress-strain relationship model through nonlinear finite element analysis. The proposed model incorporates material nonlinearity, cold-forming effect, local plate imperfection, and residual stresses into a unified stress-strain curve, leading to advanced structural analysis and design of cold-formed structures using simple one-dimensional beam-column element. Subsequently, the proposed method is then implemented in the conventional finite beam-column element analysis, demonstrating consistent agreement with both experimental tests and sophisticated finite shell element results. Finally, the robustness and validation of the proposed method are established, and its application is exemplified through the design of a modular integrated construction (MiC) structure. This study highlights the versatility and reliability of the proposed approach for the analysis and design of cold-formed steel structures.

Local and Global Interactive Buckling Capacity of Thin-Walled Box-Section Members of BS700 High-Strength Steel under Axial Compression

The local and global buckling capacity of the thin-walled box-section members formed by cold bending of ten BS700 high-strength steel (HSS) specimens are experimentally determined through an axial compression test. The mechanical properties of the materials are evaluated through material performance test, and a material model suitable for finite element analysis is proposed. The initial geometric imperfection of the members is measured, and it is found that the maximum initial deflection can be 1/1000 of the length of the members, as specified in the Chinese code. Based on the test, the ultimate bearing capacity and failure modes of the component with local and global interactive buckling are obtained. Further, a finite element model is established, and the corresponding results are compared with the test results. Furthermore, the test results are compared with those obtained using the existing specifications. The results show that the failure modes of the specimens are primarily local and global buckling failure. The influence of residual stress and initial geometric imperfection is considered in the proposed finite element model. Comparing the ultimate bearing capacity and load-displacement curves with the corresponding test results, it is found that the finite element model can effectively reproduce the test results. By comparing the test results with those obtained based on the steel structure design codes of China, the United States, and Europe, it is found that the test results are all higher than the existing code results, and the Chinese and European codes are relatively conservative with a difference of more than 20%, while the difference between the test results and the American code results is nearly 10%. Therefore, it is necessary to further improve the calculation methods of local and global buckling capacity of thin-walled box-section members of BS700 HSS under axial compression.

Shear Lag Effects on Pedestrian-Induced Vibration and TMD-Based Vibration Control of Footbridges

The shear lag effect (SLE) is one of the vital mechanical characteristics of structures with thin-walled box sections. While most existing studies of the SLE focus on the static response of footbridges, pedestrian-induced vibration deserves more attention since it represents the actual response of footbridges during their practical service process. A theoretical framework is proposed to consider the corresponding SLE. Firstly, the SLE on the natural frequencies of the structure can be considered with a reduction ratio to the corresponding case without considering the SLE. Results show it is more necessary to consider the SLE for footbridges with smaller span-width ratios, smaller section thickness-width ratios and lower height-width ratios. The SLE may result in significant reductions in the natural frequencies of the structures. These reductions in the predicted natural frequencies due to the SLE may further result in inaccuracy in the prediction of pedestrian-induced vibrations of footbridges. Furthermore, the most often applied mitigation measures may not be reliably designed. This may result in very significant reduction in the effectiveness of vibration mitigation measures. To consider the SLE on pedestrian-induced vibration and tuned-mass-damper-based vibration control of typical footbridges with thin-walled box sections, a simplified strategy is proposed.

Experimental research on local buckling of BS700 high-strength steel thin-walled box-section members under axial compression

Experimental research on local buckling of BS700 high-strength steel thin-walled box-section members under axial compression

Symplectic analysis of thin-walled curved box girders with torsion, distortion and shear lag warping effects

Shear lag effect and torsional and distortional warping can significantly affect the performance of thin-walled curved box girders used in modern bridge engineering. The structural behaviour of these bridges exhibits complexity due to coupled bending and torsion together with warping effects of non-uniform torsion, distortion and shear lag. A practical method of analysis, based on the symplectic approach, with the same perspective as the Higher Order Beam Theories, is presented for overcoming the difficulties of numerical approaches via the Finite Element Method. In this paper, the Hamiltonian Structural Analysis method implements the analysis of the shear lag effect together with non-uniform torsion and distortion, for curved box girder bridges. The examples given can allow engineers to evaluate the effects of the negative shear lag phenomenon and the distribution of axial stresses in box slabs and webs, due to different warping effects, which strongly influence thin-walled box sections subjected to point loads and restrained areas.

Research on overall stability of BS700 high-strength steel columns with box section

To study the overall stability of BS700 high-strength steel axially compressed columns with box section, the axial compression tests of 10 thin-walled box section columns were conducted in this paper, and the numerical calculation was completed using the finite element method. Moreover, the factor of initial geometric imperfections was considered during the processes of testing and analysis. The test results showed that the failure mode of BS700 high-strength steel columns with box sections was bending buckling. 1/1000 of the member length mentioned in the Code for Design of Steel structures (GB50017–2017) could be used as the maximum initial imperfection. Compared with the curves of the 3c type in the GB50017–2017 and Eurocode specifications, the long-column test results and finite element analysis results were evidently larger and close to those of 3b types in GB50017–2017 and Eurocode 3b (8% larger on average). Moreover, although the ANSI/AISC 360–10 specifications coincided well, this standard tended to be dangerous because it prescribed a relatively low slenderness ratio. Therefore, the curves of the 3b type stipulated in GB50017–2017 and Eurocode were recommended.

Variational modelling of local–global mode interaction in long rectangular hollow section struts with Ramberg–Osgood type material nonlinearity

A variational model describing the nonlinear mode interaction in thin-walled box-section struts under pure axial compression made from a nonlinear material obeying the Ramberg–Osgood law is presented. The formulation combines continuous displacement functions and generalized coordinates, leading to the derivation of a system of differential and integral equations that describe the static equilibrium response of the strut. Solving the system of equations using numerical continuation techniques reveals the strongly unstable post-buckling response arising from combined geometrical and material nonlinearities during the interactive buckling of the global and local buckling modes—the resulting behaviour being more unstable with decreasing material hardening. A finite element (FE) model is also devised and reveals very similar post-buckling behaviour as highlighted in the variational model. The results compare very well in terms of the mechanical destabilization and the post-buckling deformation, which verifies the analytical model.

Buckling-resistant topological design using sensitivities to variations in localised nominal stiffness

Thin-walled structures are extensively used in aerospace, automotive and mechanical engineering applications due to their high strength- and stiffness-to-weight ratios. However, the performance of these structures tends to be heavily influenced by localised features such as manufacturing defects or design details included for non-structural reasons, e.g. inspection cut-outs. Understanding the sensitivity of structural performance to these nominal stiffness variations, and especially their spatial distribution through the volume of the structure, is important to the designer. We propose a new methodology, the Localised Nominal Stiffness method, to quantify the sensitivity of buckling performance to the distribution of nominal stiffness variations across the structure. The underpinning idea involves reducing the stiffness in small localised regions of the structure and quantifying the ensuing variation in linear buckling capacity before returning the stiffness to its original value. The process is repeated for all locations ensuring coverage of the entire structural domain, which leads to a sensitivity map. In practice, each location corresponds to an element in a finite element mesh. Focusing on structures subject to buckling constraints, and with the aim of using highly efficient structural analysis, we identify sensitivities using the hierarchical Unified Formulation. The resulting sensitivity contour maps can be used to identify regions of the structure where defects or removal of material (for lightweighting) would not significantly affect buckling and post-buckling performance. The effectiveness of the method is tested through three examples: a simply-supported plate; a simply-supported, thin-walled box-section column; and a thin shell with simply-supported and clamped boundary conditions. In all cases, the buckling performance of structures can be maintained with reduced structural weight.

An improved method for analyzing shear lag in thin-walled box-section beam with arbitrary width of cantilever flange

The shear lag effect can significantly affect the performance of wide-box structures, and even becomes one of the most important influencing factors endangering structural safety. This paper develops a theoretical analysis method, which is designated as PM analysis for analyzing shear lag phenomenon in thin-walled box-section beam with arbitrary width of cantilever flange. In this method, the introduction of initial shear rotation (or initial shear strain) γ0i, due to the effect of web restraint on flanges, is innovatively proposed and further employed in describing the additional warping displacement in top lateral cantilever flanges, and a practical and straightforward procedure of coefficient α3 is designed (DP) based on the proposed assumptions. In addition, a modified method to PM-DP analysis is developed for improving the defects of the hypothesis of shear-lag warping displacements in top lateral cantilever flanges, that is, PM-DP(M) analysis. The differential equations for generalized displacement w(x) and the standard magnitude of shear-lag warping displacement U(x) of the beam are deduced by means of the principle of minimum potential energy (MPE) and solved with the given boundary conditions. Numerous models of thin-walled box-section with arbitrary width of top lateral cantilever flanges under distributed load are chosen and built through a software program (ABAQUS). The results obtained from PM analysis (PM-LB, PM-DP and PM-DP(M)) are summarized into a series of curves indicating the distribution of normal stress and the displacements for various examples, and compared to those obtained from the finite element method (FEM). The study widely demonstrates the strong applicability and high precision of PM-DP(M) analysis, which can be considered as an ideal solution in predicting shear lag effect for thin-walled box-section beam with arbitrary width of cantilever flange and, possibly, be adopted as valuable reference for the design of related thin-walled structures.

Stability and Resistance of Steel Continuous Beams with Thin-Walled Box Sections

AbstractThe issues of local stability and ultimate resistance of a continuous beam with thin-walled box section (Class 4) were reduced to the analysis of the local buckling of bilaterally elastically restrained internal plate of the compression flange at longitudinal stress variation. Critical stress of the local buckling was determined using the so-called Critical Plate Method (CPM). In the method, the effect of the elastic restraint of the component walls of the bar section and the effect of longitudinal stress variation that results from varying distribution of bending moments were taken into account. On that basis, appropriate effective characteristics of reliable sections were determined. Additionally, ultimate resistances of those sections were estimated. The impact of longitudinal stress variation and of the degree of elastic restraint of longitudinal edges on, respectively, the local buckling of compression flanges in the span section (p) and support section (s) was analysed. The influence of the span length of the continuous beam and of the relative plate slenderness of the compression flange on the critical ultimate resistance of box sections was examined.

Free Vibrations of Thin-Walled Box-Section Bars Allowing for Shear Strains

Purpose. The purpose is to study free vibrations of thin-walled bar with combined bisymmetrical section allowing for the effects of shear strains.Methods. We used the main hypothesis of V.Z. Vlasov concerning thin-walled bars. Solving motion equations analytically, we used the method of initial parameters and the known methods for differential equations solution. In the natural experiment we applied Autodesk Inventor system. In the course of the natural experiment on shaker, we used the method of smooth change in the frequency of sinusoidal vibrations.Results. We provide the analytical solutions of the shapes and the natural frequencies of thin-walled bar with combined bisymmetrical section allowing for shears caused by bends and constrained torsion. We compared the results of the calculations conducted in CAE system and the results of the full-scale experiment to determine the frequencies of vibrations of box beam.Conclusions. The results showed that the analytical calculations are in good compliance with the results of numerical and physical experiments and can be used for dynamic calculations of thin-walled structural elements, in particular, for the prevention of the destruction of structures in the event of resonance phenomena.

Load capacity probabilistic sensitivity analysis of thin-walled beams

The paper deals with the load carrying capacity probabilistic variance-based sensitivity analysis of thin-walled box-section girders subjected to pure bending. The lower- and upper-bound load capacity estimation is performed using two different analytical methods. The sensitivity analysis performed is based on the methodology of the Monte-Carlo method. The analysis is carried out using the polynomial decomposition and multi-dimensional linear regression. The sample results obtained are presented in diagrams and pie charts showing the sensitivity of load capacity to different random input variables (material properties and geometrical parameters). The variance-based analysis (Anova) of lower-bound and upper-bound load capacity estimation is carried out, from which some conclusions are derived, if (and how) assumed changes in standard deviations of input variables influence the magnitude of the load capacity and differences in upper-bound and lower-bound load capacity estimations. The results of Anova tests are shown in sample histograms. Some final conclusions concerning the efficiency of the applied models and the statistically significant influence of input random variables (yield stress, wall thickness, height and length of the beam) upon the upper-bound and lower bound estimation of the load capacity as well as the difference of these two estimations, are presented.

High-speed deformation of a high-strength coated thin plate

The punch with cone-shaped working part impact into aluminum alloy thin-walled structures is mathematical modelled applying thermo-mechanical coupling of the physical processes during their deformation. The nonlinear physical properties contain a nonlinear stress-strain rate dependence of temperature. To solve the contact problem the sliding boundary conditions (friction) on moving bodies introduced. Numerical simulation of impact process performed using the finite element method and the independent Lagrange-Euler approach for two variants of the thin-walled box structure. The solution of the dynamic viscous plastic contact problem allowed to determine and to design the stress-strain fields in the thin-walled box section. For comparison, the deformation process of the similar aluminum construction with an additional rib considered when the punch with the conical working part impact. Analysis of stress-strain state for two various types of structural geometries demonstrated that mounting the additional medial rib into its design let redistribute the stress fields and significantly reduce the plastic deformation area during the impact because of four fold increasing in its contact stiffness. Such modification of the structure rigidity may improve the strength properties of the entire composite security device applying changes only to its part.

Failure Mechanics of Uniformly Compressed Thin-Walled Box-Section Struts

It is well known that the structural performance of thin-walled compression members is subject to the effects of local buckling and material yielding. Due to these effects, the compressive carrying capability of short strut members can be significantly reduced. This paper employs finite element simulation to examine the post-buckled response of thin-walled box-sections that covers complete loading history of the compression struts from the onset of elastic local buckling through the nonlinear elastic and elasto-plastic post-buckling phases of behaviour up to final collapse and unloading. A detailed account of the growth and redistribution of stresses on the surfaces is given in the paper. The results from finite element simulations are shown to compare well with the analytical method of analysis.

Theory of Thin-Walled, Pretwisted Composite Beams with Elastic Couplings

In this work, the structural response of thin-walled composite beams with pretwist angle is investigated by using a mixed beam approach that combines the stiffness and flexibility methods in a unified manner. The Reissner's semi-complimentary energy functional is used to derive the stiffness matrix that approximates the beam in an Euler–Bernoulli level for extension and bending and Vlasov level for torsion. The bending and torsion-related warpings induced by the pretwist effects are derived in a closed form. The developed theory is validated with available literature and detailed finite element structural analysis results using the MSC/NASTRAN. Pretwisted composite beams with rectangular solid and thin-walled box sections are illustrated to validate the current approach. Acceptable correlation has been achieved for cases considered in this study. The effects of pretwist and fiber orientation angles on the static behavior of pretwisted composite beams are also studied.

Load-carrying capacity of high-strength steel box-sections I: Stub columns

To study the load-carrying capacity of thin-walled box-section stub columns fabricated by high strength steel 18Mn2CrMoBA, uniaxial compression experiments of specimens with different geometrical dimensions were carried out. Compared with the predicted values by the AISI Code, the tested load-carrying capacities of the stub columns are much greater, which suggests that the existing effective width method should not be applicable for high strength steel stub columns. The finite element analysis based on ANSYS code was employed to simulate the deformation curves and predict the load-carrying capacities. The numerical values were generally in good agreement with the experimental values. Parameter analysis was performed to investigate the ultimate strength of the high strength steel stub column. The values obtained indicate that the width–thickness ratio of the flange and the section side ratio should be the main factors to decide the ultimate strength of the stub column. Taking the width–thickness ratio and the section side ratio as parameters, a formula to predict the loading capacity of the high strength steel stub column was put forward and proved to be effective by the tested and numerical values.

Optimum design of straight thin-walled box section beams for crashworthiness analysis

This paper provides an optimum design for regular thin-walled box section beams on their cross-sectional profiles. The thin-walled box beams with optimized cross-sectional dimensions perform ideally during the crashworthiness analysis. In this paper, the response surface method (RSM) is utilized to formulate the complex design problem. During the optimum design, the specific energy absorption (SEA) is set as the design objective, and it is constrained by the maximum crushing force ( P m ) and the cross-sectional dimensions. Detailed finite element (FE) models are created for such thin-walled box beams which are used for the design optimization. Finally, simplified FE models for these beams are also created for the same design process. Optimal design obtained with the simplified models is compared to the design achieved from the detailed models to verify the accuracy and efficiency of the simplified models.

Flexural–torsional behavior of thin-walled closed-section composite box beams

This paper presents a flexural–torsional analysis of composite box beams. A general analytical model applicable to thin-walled box section composite beams subjected to vertical and torsional load is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional responses for arbitrary laminate stacking sequence configurations, i.e. unsymmetric as well as symmetric. Governing equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for thin-walled composites beams under vertical and torsional loading, addressing the effects of fiber angle and laminate stacking sequence.