Closed Cross Section Research Articles

Limit states of thin-walled composite structures with closed sections under axial compression

The subjects of the study were thin-walled composite columns with closed cross sections manufactured using the autoclave technique. The composite profiles were characterized by the fact that they had a constant height and arrangement of laminate layers, however, varied cross-sectional shapes. The study was conducted using several interdisciplinary experimental research methods and advanced numerical simulations. In the course of the research, both forms of structural stability loss were registered, and damage to composite structures was assessed. In the course of the research, the influence of the shape of the cross-section on the stability and load-carrying capacity of the structure was evaluated. A measurable effect of the conducted research was the determination of the structure's post-buckling equilibrium paths, which made it possible to determine the structure's behavior in the full range of loading. In addition, the author's numerical models developed enabled validation of parallel experimental studies. The developed numerical models were based on a failure criterion known as progressive failure analysis - which allowed a thorough assessment of the failure mechanism of the composite material.

Pure distortion of symmetric box beams with hinged walls

This paper is concerned with the analysis of the pure torsion and distortion of straight box beams with trapezial cross-sections and hinged walls. A one-dimensional mechanical model for this kind of system subjected to anti-symmetric loads on the end cross-sections and no warping constraints is developed. The distortional stiffness of the system is provided by the torsional rigidity of the wall panels. The cross-sectional kinematic condition for which torsion and distortion are uncoupled has been determined. Novel explicit expressions of the internal and external distortional moments, the distortion constant, and the distortional warping pattern have been deduced; they can be directly translated to the classical distortion theory. Results of representative test cases with different section shapes and loads show excellent agreement with finite element models using shell elements. The model is a first step to analyse bridge decks with a distortionable central cell for wind engineering applications. Finally, an extension of the model, including the distortional stiffness provided by the frame bending stiffness of the cross-section walls, is presented. The extended model is applicable to assess the large-scale torsional–distortional effects in long beams with closed cross sections.

Experimental and numerical study on mechanical performance of single shear bolted connections with novel elliptical one-sided bolts

One-sided bolts, which typically employed for connecting components with closed cross section, often present complexities in both construction and installation. Addressing the limitations of conventional one-sided bolts, this study introduces a novel variant distinguished by its elliptical head, offering ease of installation without the need for specialized tools. Due to the special shape of the bolt head, the mechanical properties of the bolt need to be studied in depth. To investigate the shear properties of the novel elliptical one-sided bolts, three sets of single lap shear experiments were conducted. Subsequently, finite element numerical analyses were employed to simulate these experiments, facilitating the development of a reliable finite element model. Furthermore, parametric analyses were undertaken to examine the influence of various parameters on the ultimate shearing capacity and displacement of joints. The findings indicate that the shear capacity of the single lap joint employing novel elliptical one-sided bolts closely rivals that of ordinary hexagonal bolts with equivalent diameters. However, an enhancement in slip resistance capacity is observed in the novel elliptical one-sided bolt joints compared to hexagonal bolts. Notably, the parameters of the bolt exert a more pronounced impact on the ultimate shearing capacity and displacement of joints when contrasted with parameters associated with the plates. The recommended torque coefficient for the novel elliptical one-sided bolt is established as 0.2, and it is recommended to use appropriate torque to ensure the slip performance of the joint during practical application.

A new theoretical method for torsional-flexural vibrations response of thin-walled beams with closed cross-sections under uniform distributed moving load

This article presents a new theoretical method for the torsional-flexural vibration response of a thin-walled beam with closed cross sections under a uniformly distributed moving load. Based on Vlasov’s theory and restrained torsion theory, a comprehensive equation of motion for torsional flexural vibration is established by considering the effects of additional torque caused by the change of the shear center and the center of mass and the warpage coefficient. Using the Fourier transform, Laplace transform, and their inverse transformations, the torsional-flexural vibration response expression of thin-walled beams with closed cross-sections under a uniformly distributed moving load was derived. The results calculated by the analytical solutions in this study were compared with those from finite element method, demonstrating the reliability and superiority of the analytical solutions. Compared with the method that ignores the warpage coefficient, the lateral displacement and torsion angle of the beam calculated by the proposed theoretical method decreased by more than 12.00%. The effect of the cross-sectional properties on the natural frequency of the torsional-flexural vibration of thin-walled beams is analyzed, and the results show that the moment of inertia and mass per unit length have a considerable influence on the torsional-flexural frequency, which increases with the moment of inertia and decreases with an increase in the mass per unit length. The influences of the load magnitude, load velocity, and load eccentricity on the dynamic response were further investigated. According to the results, the lateral displacement of the beam increased significantly with increases in the load eccentricity and load magnitude. In practical engineering, the conclusions of this study can be used to limit the torsional-flexural vibration response of simple maglev support bridges to ensure the safety of vehicles and passengers.

Structural Behaviour of Cold-Formed Steel Built-Up Closed Cross-section Columns - Assessing the Influence of Parameters and Design Methods

Structural behaviour of cold-formed steel (CFS) built-up closed cross-section columns subjected to local, global, and local–global interactive failure is investigated. The objective is to assess the appropriateness of six different Direct Strength Method (DSM) based designs proposed by various researchers including the current AISI codification. A total of 595 built-up column test results from the existing literature were used for assessment. The comparison of test results and design predictions indicated that the primary influential parameters that inhibit or induce the local–global interaction failure in closed cross-section built-up columns were not well incorporated into the designs. Owing to that, the DSM design predictions are largely scattered; conservative by a maximum of 258% and unconservative by 60%. The reliability analysis was carried out to statistically assess the design methods. It is found that five out of six designs are reliable but do not represent the actual structural behavioral trend. Following this, representative sample results and failure modes were analyzed for identifying the influential parameter that causes design methods to result in inaccurate failure load. The analysis shows that the strength of the column increases with a decrease in intermediate fastener spacing (less than the local buckling halfwave length) due to the flange overlapping effect while the column strength decreases due to local–global interactive buckling caused by a larger intermediate fastener spacing (higher than the local buckling halfwave length). Finally, the paper presents future directions on how the DSM should evolve for the accurate design of built-up closed cross–section columns.

Numerical study of the thermo-mechanical behavior of steel–timber structures exposed to fire

The latest trends in the construction industry related to sustainable buildings, has driven the use of timber as a construction material. One example is the continuous increase of timber structural elements made of Cross-Laminated Timber (CLT) walls and floors. In this context, Steel–Timber Composite (STC) floors, composed of CLT slabs and steel beams, represent a new alternative to traditional floor systems. Some advantages of STC structures are a reduction of the building mass and better thermal insulation, among others. Despite these benefits, the response of timber structures under a fire scenario remains a consistent concern. To address this issue, in this paper the thermo-mechanical response of STC structures exposed to fire is investigated. To this end, a one way coupled Computational Fluid Dynamics (CFD) and Finite Element Method (FEM) approach was employed. The software Fire Dynamics Simulator (FDS) was used for the CFD fire analyses and ANSYS for the FEM transient heat transfer and thermo-mechanical analyses. Three different STC floor structural configurations, having similar pre-fire performance, were proposed to assess their response when subjected to a given fire scenario. A representative room of a residential building was defined to simulate an accidental fire scenario to which the STC floor structures were exposed. The material properties and fire features were adopted in accordance with the Eurocode Standard and recent investigations found in the literature. The results indicated that after a 30 min fire exposure the CLT slabs showed a 25 mm thick charred layer on their exposed surface. Furthermore, compression failure was identified in the CLT slab upper fibres. Regarding to the steel beams, local buckling, and fracture in the area next to the end supports was observed. Overall, STC structures with closed cross sections steel beams showed a better fire performance than those that included open cross sections such as I-shaped ones.

Processing Q&P steels by hot-metal gas forming: Influence of local cooling rates on the properties and microstructure of a 3rd generation AHSS

Tube hydroforming is a well-established process in industry for producing complex shaped parts with closed cross section geometry and high geometrical accuracy. Hot-metal gas forming (HMGF) extends the conventional tube hydroforming process by a complex thermo-mechanical approach and thus potentially enables the complex processing of tubes from the relatively new class of quenching & partitioning-steels (Q&P steels). To prove the feasibility of an integrated Q&P treatment in the HMGF process, a simple demonstrator geometry is considered in the present study. The applied forming pressure is limited to 70 MPa, resulting in incomplete forming of the parts in the corner areas. The resulting, locally varying contact situation between workpiece and die allows the investigation of different cooling rates and their influence on local microstructural changes and on the corresponding mechanical properties. A numerical finite element simulation is used to estimate local cooling rates in three different areas of the tube (maximum cooling rates between 60 and 280 K/s), which are then correlated with hardness measurements and typical microstructural features. The hardness distribution is inhomogeneous over the cross section of the part (varies about 150 HV), with a minimum in the areas without die contact during quenching. Ferritic areas are observed in these regions due to the significantly lower cooling rates. Tensile tests show that the stress-strain behavior after the shortest partitioning time of 10 min is not only better from an energy efficiency point of view, but also provides both high strength (Rm =2050 MPa) and high ultimate strain (19.7 %), while longer partitioning times result in inferior properties. Thus, the present study shows that the Q&P treatment can be integrated into the HMGF process, but the local cooling rates must be taken into account as they strongly influence the final mechanical properties of the workpiece.

Sediment transport and riverbed evolution of sinking streams in a dammed karst river

Little knowledge has been gained about the mechanics of the sediment transport and riverbed evolution of sinking streams in a karst river, because of inadequate data of field investigation and laboratory experiments. Numerical simulation of mixed flow and sediment transport on moveable riverbed in sinking streams is seldom reported, due to difficulties in modeling irregular closed cross-sections (CS). In this study, a unified hydrodynamic and sediment transport model is developed for the free-surface and the pressurized mixed reaches of a karst river with sinking streams, where a technique of symmetric shadow subgrid is proposed to describe and account for an irregular closed CS and its riverbed evolution. Mechanics of riverbed evolution of sinking streams in a dammed karst river are studied using a real karst-river reservoir (Jiayan reservoir), which is still conducted in a data-scarce environment. Under damming effects, a delta deposition of sediment develops at the end of reservoir backwater and steps forward. It is found that the deposition delta is able to go through the sinking streams while a narrow passage is finally reserved in sinking streams and keeps conveying flow. The riverbed elevation of a closed CS, mainly determined by the lower one of CS ceiling and reservoir water level, is dynamically stable. In a dammed karst river, a fully developed (shrunk) sinking stream has periodic morphological dynamics, one cycle of which can be described as a successive process of “siltation → reduction of conveyance area → flow lag upstream of sinking streams → large hydraulic gradient → increase of velocity → large sediment transport capacity → erosion of closed CS → increase of conveyance area”. Sensitivity studies of the parameters of the hydrodynamic and the sediment transport models are performed, whose results indicate that the periodic morphological dynamics of a fully developed sinking stream in a dammed karst river is not changed. The sinking stream in a dammed karst river will not be silted completely, when the condition for forming a large gradient of piezometric head along a sinking stream is not broken by special geomorphologies or anthropogenic influences. This fact is supported by both the numerical simulations and our field investigation of sinking streams in an existing karst-river reservoir.

Experimental Characterization of Static Behavior of a New GFRP–Metal Space Truss Deployable Bridge: Comparative Case Study

A new glass fiber-reinforced-polymer (GFRP)–metal box-truss composite girder was developed for use in lightweight deployable vehicular bridges with favorable torsional resistance for large spans. This paper describes the experimental characterization of the static behavior of the latest structure characterized by a closed cross section, with a comparative study on an early version having an open cross section. The structural form of the new structure differed considerably from that of the early version. Nondestructive tests with symmetrical and unsymmetrical static loadings were conducted on a newly fabricated prototype to identify the characteristic flexural and torsional performances of the new structure. Additionally, a comparative evaluation of the experimental behavior in terms of load–displacement and load–strain responses was conducted between the new structure and the early version. Favorable results demonstrated that the new structure enabled satisfactory static performances in terms of deployable bridge applications. The resulting comparisons indicated that the new structure featured a flexural resistance identical to that of the early version. However, the addition of lower plane-truss transverse braces in the new design significantly increased the torsional resistance of the space truss system. The overall torsional rigidity of the new structure approximately corresponded to 2.36 times that of the early version. Moreover, the stress state in the extrusion-type GFRP tubular elements of the space truss system was significantly improved. Compared to the early version, the latest structure is more appropriate for use in the primary load-carrying superstructures of large-span deployable bridges under critical unsymmetrical service loading conditions.

Optimization of steel frames with the choice of materials’ grades with restrictions on general and local stability, strength and stiffness

A computational scheme for the optimal design of steel flat frames made of thin-walled rods with closed cross sections has been developed. The structural elements’ total cost is minimized by searching for the materials’ grades and the rods’ cross sections sizes on the variable parameters’ discrete sets. The rods are separately grouped according to the condition of using one steel grade and the criterion for the cross sections’ identity. Active restrictions on the overall structural system’s stability, local stability of the rods’ walls, strength and stiffness are taken into account. The optimization process using a genetic algorithm using a mixed approach to the mutation procedure, a selection option that provides the inoperative design options, and a single-point crossing-over procedure for the simple exclusions from consideration is implemented. The deformable object stress-strain state analysis is carried out on the rod finite element model’s basis. The assessment of ensuring overall stability is carried out by checking the positive definiteness of the tangent stiffness matrix of a finite element system. Local stability using an analytical relationship for rectangular plates, generally subjected to compression-tension and bending in their plane is confirmed. The results of optimization of a three-span frame made of square pipes are presented. Steel grades and profiles were selected for the groups of the structural system’s rods.

Beam & Shell Models for Composite Straight or Curved Bridge Decks with Intermediate Diaphragms & Assessment of Design Specifications

In this research effort, the generalized warping and distortional problem of straight or horizontally curved composite beams of arbitrary cross section, loading and boundary conditions is presented. An inclined plane of curvature is considered. Additionally, the stiffness of diaphragmatic plates has been introduced in the formulation in order to compare with the case where rigid diaphragms are assumed. Isogeometric tools (NURBS) are employed in order to obtain the results for the 1D formulation and 3D shell models are developed in FEM commercial software for composite cross sections with diaphragms. The number of intermediate diaphragms according to bridges design specifications is compared to the analyzed diaphragmatic arrangements in order to assess the overall structural behavior of bridges decks. For this purpose, examples of curved beam models with open or closed cross sections and various arrangements of diaphragms have been studied.

Displacement modes of a thin-walled beam model with deformable cross sections

A novel one dimensional beam model for analysis of prismatic thin-walled beams with deformable cross sections is introduced and a novel cross section mode determination procedure, which leads to the three dimensional beam displacement modes, is derived. The first order beam model for linear analysis includes: shear deformations related to both Timoshenko and Mindlin-Reissner type shear deformations, the warping effects of torsion, cross section distortion with related warping effects, as well as the Poisson effect with transverse displacements due to normal stress. The generality of the model allows it to handle open, closed and multi-cell cross sections with branched walls. The cross section analysis procedure leads to two types of beam displacement modes referred to as distortional beam modes and fundamental beam modes, with exponential and polynomial variations along the beam axis, respectively. It turns out that each of the beam deformation modes consists of a sum of one to four cross section displacement fields each with an individual axial variation. The displacement modes can facilitate the formulation of an advanced thin-walled beam element. The beam displacement modes will be illustrated for an open and a closed cross section.

Validation of Bredt\u2019s formulas for beams with hollow cross sections by the method of asymptotic splitting for pure torsion and their extension to shear force bending

The equations governing pure torsion of prismatic beams with thin-walled closed cross sections, known as Bredt’s formulas, are verified using the method of asymptotic splitting. In particular, the strong formulation of the Saint-Venant problem of a straight beam is expanded asymptotically. We begin by validating well-known technical assumptions for the shear stress distribution. Furthermore, the influence of a transverse force acting on the beam is considered. This shear force causes a deformation of the cross section, and therefore an adaption of Bredt’s formulas is needed. Two distinct formulations of the shear center, called the kinematic and the energetic shear center, are obtained. The latter is verified in numerical experiments.

Validation of Bredt's formulas by the method of asymptotic splitting

AbstractThe equations describing torsion of prismatic bars with thin‐walled closed cross sections, known as Bredt's formulas, are verified using the method of asymptotic splitting. In particular, the strong formulation of the Saint Venant problem of a straight beam is expanded asymptotically. At first, well‐known technical assumptions of the shear stress distribution are validated. Further, the influence of a transverse force acting on the beam is considered. This shear force causes a deformation of the cross section and therefore an adaption of Bredt's formulas. Two distinct formulations of the shear center, called the kinematic and the energetic shear center, are obtained. The latter are verified in numerical experiments.

A Finite Strip for the Vibration Analysis of Rotating Toroidal Shell Under Internal Pressure

In this paper, a finite strip for vibration analysis of rotating toroidal shells subjected to internal pressure is developed. The expressions for strain and kinetic energies are formulated in a previous paper in which vibrations of a toroidal shell with a closed cross section are analyzed using the Rayleigh–Ritz method (RRM) and Fourier series. In this paper, however, the variation of displacements u, v, and w with the meridional coordinate is modeled through a discretization with a number of finite strips. The variation of the displacements with the circumferential coordinate is taken into account exactly by using simple sine and cosine functions of the circumferential coordinate. A unique argument nφ+ω t is used in order to be able to capture traveling modes due to the shell rotation. The finite strip properties, i.e., the stiffness matrix, the geometric stiffness matrix, and the mass matrices, are defined by employing bar and beam shape functions, and by minimizing the strain and kinetic energies. In order to improve the convergence of the results, also a strip of a higher-order is developed. The application of the finite strip method is illustrated in cases of toroidal shells with closed and open cross sections. The obtained results are compared with those determined by the RRM and the finite element method (FEM).

Reconstruction of 3d Model Based on CT Scan Image Information of Human Ridge Cone Bone

Aiming at the manufacturing process of individualized human body skeleton model in medical rehabilitation engineering, the three dimensional geometry model of human body skeleton model has been reconstructed for based on the image of the bone obtained from the computed tomography (ct) scan using the CAD software. In the Modeling process, the CT scan of the two-dimensional CT images of bone cross section in the online data extract, after interpolation and fitting method to generate a set of closed cross section lines, such as recycled curve skin generate ideal bone surface, and eventually generate human bones of three-dimensional entity model.

Experimental and numerical investigation on dynamic properties of thin-walled GFRP buckled columns

this paper analyses the numerical and experimental results to evaluate the dynamic properties of pultruded GFRP (Glass-Fiber Reinforced Polymers) buckled columns. The profiles are made of glass fiber reinforcement and thermosetting vinylester matrix with thin-walled open or closed cross section. The buckling phenomena of the column with fixed ends were evaluated with a non-destructive method based on experimental modal data through dynamic identification procedure.Numerical analysis has been carried out through Finite Element models calibrated considering two consecutive stages that involve the local and global scale: i) parametric natural frequencies analysis to model the different cross sections taking into account the stiffness of the rotational constraint between the wall segments of the thin walled pultruded profiles; ii) buckling analysis to identify the inaccuracies in the specimen or in the experimental apparatus through global flexural displacements which increase continuously with the axial load.Experimental, theoretical and numerical results were compared in order to know the wall segment effects of GFRP columns in free vibration field when affected by buckling phenomena.The results allow to investigate the significant role that the manufacturing imperfections of pultruded material play in the structural performance of GFRP buckled columns.

Enhancing the structural performance of steel channel sections by CFRP strengthening

The aim of this test study was to achieve an in-situ strengthening technique to retrofit the deteriorated tall steel structures using carbon fiber-reinforced polymer (CFRP). A total of 20 structural steel channel sections with various retrofitting configurations were tested to arrive at an optimal strengthening technique to improve the buckling mode of failure of structural steel channel section under flexural loading. An approach of transforming the open cross section to closed cross section was used to increase the torsional resistance of channel sections. The various parameters such as type of CFRP fabric, wrapping configuration (skin and closed wrap) and number of CFRP layers were also included in this study. The results indicate that the closed wrapped configuration with an additional (final) layer of bi-directional CFRP fabric provides the higher strength and stiffness compared to control and skin wrapped specimen due to the confinement of hoop directional fibers. This study also proves that the lateral torsional buckling (LTB) mode of failure of open cross section specimens can be improved by appropriate CFRP strengthening techniques.

Unified theory for analysis of curved thin-walled girders with open and closed cross section through HSA method

The behaviour of thin-walled structures is deeply influenced by non-uniform torsion and cross section distortion. In this paper the extension of the Hamiltonian Structural Analysis (HSA) Method to thin-walled straight and curved beams is presented. The proposed method solves the structural elastic problem of thin-walled beams through the definition of a Hamiltonian system composed of 1st order differential equations. The method allows engineers to solve the elastic problem by introducing the degrees of freedom and the corresponding compatibility equations, founding equilibrium equations in the variational form. The methodology is explained in the framework of the so-called Generalized Beam Theory, considering beams on elastic foundation and thin-walled structures with non-uniform torsion and distortion in a unified theory for open and closed cross section considering the shear deformability of the wall midline. The exact solution is found for straight and horizontally curved beams and distortion of box section is directly solved avoiding the analysis through the Beam on Elastic Foundation (BEF) analogy. Numerical applications are given in order to show the wide range of applicability of the proposed method and to validate it through comparisons with literature data.

An experiment and FE simulation for the development of a SPFC1180 AHSS one-body door impact beam about a car side collision

This paper presents a new one-body door impact beam that was developed to protect an occupant when a car is involved in a side collision. SPFC1180 Advanced High Strength Steel (AHSS) was used to improve the impact energy absorbability and the small door dent to ensure safety inside of the car. To obtain the proper closed cross section shape of the door impact beam, several designs with the same inside area were considered by conducting a finite element (FE) bending analysis using the ANSYS Mechanical software. FE door modeling was validated with the impact simulation package of the LS-DYNA software, and the results were compared to those from the door module test. The validated door beam model was also subjected to a side collision test of a complete vehicle following the FMVSS 214 regulation using a parallel computing simulation, and a comparison was carried out for the pipe-typed door beam using a virtual structural test applicability. The results indicate that the SPFC1180 one-body door impact beam can exhibit an equivalent reaction force and can decrease manufacturing costs and weight when compared to a pipe typed door beam as a result of the AHSS material, simple manufacturing process, and one-body closed-section shape design.