Open Section Beams Research Articles

A cradle-to-site life cycle analysis of laser-cut passing-through tubular joints under different seismic conditions

Steel circular hollow sections (CHS) offer a number of advantages compared to their open section counterparts such as better resistance under tension, compression, bending in all directions and an overall reduction of structural weight, required material for corrosion and fire protection. Nevertheless, the traditional methods to connect open section beams to CHS columns often demand a significant amount of fabrication work, leading to high expenditure and resource consumption – therefore limiting their use in the current industry. These issues can be solved with an automatized joint fabrication. To that purpose, this article proposes two innovative “passing-through” I-to-CHS joints, achieved via laser cutting technology (LCT). Experimental and numerical studies were conducted to assess the joint fabrication aspects as well as the structural performance of the proposed joints. The results showed that the proposed joints can offer respectively 2.5- and 10-times larger strength and stiffness properties compared to a conventional directly welded I-to-CHS joint having similar section properties for the beam and the column. However, this study focuses on the environmental sustainability and economic feasibility of the proposed joints. A cradle-to-site life cycle analysis is conducted using multi-storey frame structures. The environmental and economic impact of the proposed joints are compared with different types of existing I-to-CHS joints in order to assess their possible benefits and limitations. Thanks to the savings in the raw material, surface treatment and transportation resources, it could be stated that, the passing-through approach with LCT offers approximately 32−42% reduction in the construction and fabrication costs of the multi-storey structures while reducing the CO2 emissions by 24−28%, compared to the directly welded I-to-CHS joints.

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Generalized strain-based finite element for non-linear stability analysis of beams with thin-walled open cross-section

Based on the generalized strain theory a shear-deformable finite element is developed for nonlinear stability analysis of thin-walled open-section beams in multibody systems. In this formulation a finite number of deformations, characterized as generalized strains, is defined which are related to dual stress resultants in a co-rotational frame. The stiffness formulation is based on a second-order approximation of the local elastic displacement field. Timoshenko’s beam theory and Vlasov’s modified thin-walled beam theory are used to include the shear strain effects due to non-uniform bending and restrained warping torsion and their mutual coupling effects. Axial shortening associated with the Wagner Hypothesis is taken into account such that the nonlinear behaviour of the beam is predicted accurately, especially under large torsion. Coupling between bending and torsional deformation due to non-coincident centroid and shear centre is modelled using a second-order cross-section transformation matrix. Cubic Hermitian polynomials are used as shape functions for the lateral displacements and twist rotation to derive the elastic and geometric stiffness matrices. Geometric nonlinearities associated with axial elongation and bending curvatures are described by additional torsion, bending and warping-related quadratic deformation terms yielding a set of modified deformations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. The accuracy and the computational efficiency of the new beam element is demonstrated in several static and dynamic examples.

A comparative experimental study on blind‐bolted beam connections to square steel tubular columns filled with polyurethane foam or concrete

AbstractIn the last two decades blind‐bolted connections have been developed to allow bolting of open section beams (e.g, I‐beam) to steel hollow section (SHS) columns where access from all sides of the column is not possible. Filling the tubular column with concrete in the vicinity of the beam‐to‐column connection has been shown to improve the anchoring mechanism of the blind‐bolted connection thereby increasing the strength and stiffness of the connection and reducing the column face deformation, however it adversely affects the joint ductility. This study introduces polyurethane foam filled steel tubular columns in combination with a new anchoring arrangement employing hollo‐bolts to develop a novel connection between the SHS columns and open section beams that provides a better combination of stiffness, strength and ductility. To investigate the behaviour of the proposed arrangement, monotonic pull‐out tests of blind bolted T‐stub connections anchored to foam‐filled steel tubular (FFT) and concrete‐filled steel tubular (CFT) columns using holloBolts were conducted. Benchmark tests on unfilled SHS columns were also conducted for comparison. The FFT in conjunction with the proposed anchoring mechanism was shown to provide a good stiffness as the CFT columns, and almost similar ductility to that of the unfilled steel tube blind‐bolted connection. Hence it is concluded that employing foam instead of concrete as an infill leads to favourable combination of strength and ductility, thus rendering FFT an attractive light alternative to CFT sections when ductility of the joint is an important design consideration.

Buckling instability of Vlasov thin-walled open-section beams: The Euler–Prandtl coupled problem

In the field of structural mechanics, the study of elastic stability is a very important stage in the design of slender, thin, and/or shallow elements. The loss of stability can lead to the global collapse of the structural element. This is achieved when the load applied to the structure reaches the critical value.There are two fundamental instabilities in rectilinear beams: the axial buckling, due to the axial force, and the lateral–torsional buckling, due to the bending moment. In general, these two instabilities may interact, when both axial force and bending moments are applied at the same time.The present paper will illustrate a three-dimensional coupled formulation, including Vlasov’s Theory for thin-walled open-section beams. The compactness of the final expressions, made even more evident by the matrix formulation, allows us for a very convenient use in the case of automatic computations.

Intermittently stiffened cold-formed steel GFRP composite lightweight built-up beams: Experimental investigation and performance assessment

Previous attempts to develop lightweight cold-formed steel (CFS) composite sections have successfully improved their buckling strengths but have been limited to unstiffened profiles only. This paper reports the results of an experimental program on the flexural behavior of newly developed CFSGFRP (Glass Fiber Reinforced Plastic) composite built-up open-section beams. In total, six large-scale specimens were tested under four-point loading with simply supported boundary conditions. To counter the inherent limitation of premature local buckling in the thin-walled CFS sections under compressive stresses, various combinations of intermittent stiffening and GFRP plank packing were adopted to improve the performance of the CFS GFRP lightweight composite beam specimens. The intermittent stiffening and GFRP plank packing were used judiciously in the compression flange and the web region of the specimens. A conventional open-section built-up beam was fabricated using two plain channels fastened through the web as a benchmark to evaluate the flexural performance of the composite beams. Furthermore, a hot-rolled steel beam with equivalent dimensions was also tested to give a broader comparison. The flexural performance of all the beams was assessed in terms of peak strength, initial stiffness, load–deformation​ response, failure modes and strength-to-weight parameter. The results confirmed the structural feasibility of adopting GFRP to form CFS lightweight built-up beams. The incorporation of GFRP planks significantly improved the flexural capacity by about 180% compared to the conventional CFS built-up beams. They also helped in attaining about 80% of the equivalent hot-rolled steel beam’s flexural strength, resulting in highly efficient built-up beams for practical applications.

DSM Formula for Local-Global Interaction Buckling of Cold-Formed Stainless Steel I-Beams

The paper presents a set of Direct Strength Method (DSM) formulae for cold-formed stainless steel I-section beams. On basis of a carefully calibrated FE model for stainless steel open-section beams featuring local-global interaction buckling, an extensive database was first established. The existing DSM formula of the best prediction performance was commented on for its drawbacks. For improved strength prediction, a traditional-form DSM formula was proposed first, and novel two-phase DSM formulae were derived on basis of a deep insight into the varying trend of the member strengths. The two-phase DSM formulae were found to be very powerful predictors yielding more accurate strength predictions over the whole range of slenderness and avoiding undue conservatism for intermediate and short members. A considerable boost in design strength by up to 39% can be achieved with the two-phase DSM formula. The DSM curves were developed with a due reliability level to fit into the current design codes.

Analytical and Experimental Study on Cold-Formed Steel Built-Up Sections for Bending.

In the construction of steel structures, the two most common types of structural members are hot-formed and cold-formed members. This paper mainly describes the analytical and experimental research on the strength and characteristics of CFS bolted built-up sigma sections having different structural arrangements under bending. The cross-sectional dimensions for the parametric study were selected by the sizes available in the market. In this paper, ANSYS workbench software was used to perform FE modeling and observe the local, flexural, and interaction of these buckling. Then, experimental study was performed by varying the arrangement of open section beams between face-to-face and back-to-back, connected using bolts or fasteners different spacings. Further, we conducted bending tests on cold-formed steel built-up members having simple edge stiffeners in the middle. Comparing both analytical and experimental studies, the results indicate that the back-to-back connected built-up beam section provides a flexural capacity higher than the face-to-face built-up section. Moreover, increasing the bolt spacing enhanced the load-carrying capacity of back-to-back sigma section built-up beams. It has also been discovered that the flexural strength of beams is primarily determined by bolt spacing or itsposition.

Experimental and Numerical Study on the Flexural Behavior of Cold-Formed Steel Multi-Limb Built-Up Section Beams

Cold-formed steel (CFS) is a typical green building material with the merits of being low-cost, lightweight, high-strength, and recyclable. CFS built-up section beams are widely used in CFS frames owing to their outstanding mechanical properties. However, a simplified and accurate method for calculating the flexural moment capacity of multi-limb built-up beams is missing in specifications. In this study, the flexural behaviors of CFS four-limb built-up beams with closed and open sections are investigated via experiments and finite element (FE) modeling. Firstly, the flexural moment capacities and failure modes of the beams are obtained by four-point bending experiments. The ultimate load capacity of the new open section beam is found to be higher than that of the closed section beam, and the failure mode is local buckling of the web and upper flange. Then, the FE models validated by the tests are developed to conduct an extensive parametric study. Numerical results show that the flexural moment capacity increases with the thickness and web depth. Finally, a simplified calculation method for the flexural moment capacities of the closed and open section beams is proposed by considering the reduction factor of gross section modulus of the built-up section.

Structural behaviour of cold-formed steel built-up closed section beam–columns

In order to examine the beam–column behaviour of cold-formed steel (CFS) built-up closed sections, a numerical study was performed and is presented in this paper. The finite element model with careful considerations of material nonlinearity and initial geometric imperfections was established for the thin-walled section components under eccentric compression and verified against the existing experimental results. Then, the calibrated finite element model was adopted to obtain the numerical predictions of additional 280 beam–columns over an extensive scope of sectional geometries and initial loading eccentricities. Underpinned by the newly generated numerical predictions of 280 members and the existing test results of 30 specimens, the design approaches using codified interaction formulae and a bi-linear interaction expression proposed in the recent research for CFS built-up open section beam–columns together with the nominal compressive and flexural resistances determined by direct strength method (DSM) were assessed for thin-walled built-up closed section members under combined loading. Based on the nominal resistances determined by DSM, the interaction formulae in the ANSI/AISC 360 and EN 1993-1-3 as well as the available bi-linear interaction expression were overall unconservative for the design of built-up closed section beam–columns, while the interaction curve specified in the AISI S100 generally offered slightly conservative strength predictions. Furthermore, it was revealed that the interaction relationship in the AS/NZS 4600 and the bi-linear interaction expression modified in this study could provide accurate predictions for the CFS built-up closed section beam–columns, whereas the predictions obtained by the modified bi-linear interaction expression were overall less scattered.

Experimental investigation of four-point bending of thin walled open section steel beam loaded and set in the shear center

Thin walled cold formed structures were, and still are, very popular structural elements used in mechanical engineering. Modern technology and the progress in materials engineering allow to fabricate various shapes of thin walled cold formed components. Therefore, combinations between technology possibilities, material properties, loads and engineering requirements are wide and unlimited for thin walled components. The aim of this paper is to perform an experimental study of cold formed C-channel steel beams under four-points bending loads based on the global and the local buckling phenomena. A test rig was developed with a specially designed support system to subject thin-walled steel beams to a four-point bending load, where the support and loads were applied to the shear center of the open section steel beam. It is shown that it is not possible to completely eliminate the torque load on a thin-walled beam with an open section where load and support are applied in the shear center because investigated beams weren’t ideal made. Thin walled open section beams are very sensitive for boundary conditions and geometrical accuracy. The force of gravity is also working. The presented research methodology can be improved and do test with other open section thin walled beams.

Exact solutions for thin-walled composite open section beams using a unified state space coupled field formulation

Thin-walled open section composite beams (TWOSCB) used extensively in aerospace structures exhibit several non-classical effects such as torsional warping, warping shear, material coupling, and shear deformation. Arbitrary cross-section and material coupling make the governing equations highly coupled and difficult to solve analytically. In this paper, a unified coupled-field formulation is developed to analyze TWOSCB accommodating all non-classical effects. Using the state-space method to derive analytical expressions for displacements and forces, Vlasov solutions of isotropic beams are recovered. Results obtained for arbitrarily laminated mono-symmetric composite channel and I-section beams subjected to bending and torsion loads show excellent agreement with available results in the literature.

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors’ earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section’s area properties that are necessary to axial and shear stress calculations within the structure’s thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.

Vibration and buckling optimization of thin-walled functionally graded open-section beams

This study presents vibration and buckling optimization of thin-walled functionally graded (FG) beams with bi-symmetric I-shape and channel-section. Material properties are assumed to vary through-the-contour direction by a non-monotonic function. A piece-wise cubic Hermite interpolation is used to estimate the volume fractions of the constituent phases. Based on Vlasov’s thin-walled theory, the beam element with two-node fourteen degrees of freedom is developed. Differential evolution (DE) is employed as an optimizer to solve the optimization problems. N-point volume fraction through-the-contour direction is considered as the design variables. A dimensionless objective function is formulated on the grounds of the optimization of frequency criterion and buckling load. Results of the study are presented graphically. Optimal results are obtained to be significant for several specific design of thin-walled beams.

Flexural analysis of thin-walled laminated composite beams with arbitrary open sections and shear influence

Analytic model for the flexural analysis of thin-walled laminated composite beams with arbitrary open sections and shear influence is presented. Model is based on general Vlasov’s theory of thin-walled beams of open sections, as well as on Timoshenko’s beam bending theory. The shear strain in the beam middle surface is taken into analysis, i.e. the out-of-plane warping of the cross-section due to shear. Analytic expressions for the stresses and displacements with the shear influence are derived in closed analytic form. Beams subjected to general transverse load reduced to principal pole are considered. The influence of shear deformations and fiber angle on stress and displacement distributions is investigated. Beams with different height-to-span ratios and different boundary conditions are analyzed. The accuracy of the presented model is verified by comparing the results with the finite element solutions utilizing shell elements, as well as with the results from the available literature. Very good agreement between analytical and numerical results is obtained.

Analysis of aluminum front bumper beam for heavy quadricycles under impact loading

A heavy quadricycle is a small four-wheeled vehicle suitable for urban mobility owing to its compact, lightweight and energy-efficient advantages. However, such small vehicles have a comparatively short crumple zone leading to a higher risk of occupant injury in case of frontal collision. In this paper, the structural performance and energy absorption of aluminum alloy AA6063-T6 thin-walled front bumper beams for heavy quadricycles are studied. Mechanical characteristics of the beams with simple cross-sectional profiles, i.e., square, rectangle and double-cell rectangle as well as a commercially available bumper beam of a heavy quadricycle under cylindrical-rod impact loading are investigated through finite element analysis using LS-DYNA. A parametric study is also performed to examine the effects of open and closed sections, different cross-sectional shapes and various fillet radii on impact responses of the bumper beam including energy absorption, specific energy absorption, peak force, and crush force efficiency. The results show that although section profiles with sharp corners possess higher energy absorption, a larger fillet radius could mitigate the unfavourable peak force from impact up to 40%. The partition plate of the double-cell rectangle section induces a much higher peak force compared to others. In addition, when comparing an open-section beam with closed-section beams, it is found that an open-cell hat-shape model with fillet radius of 8 mm is the most efficient design. The crush force efficiency and peak force of the section are 32% higher and 17% lower, respectively, when compared to the closed-cell section with fillet radius of 8 mm.

Buckling analysis of open-section beams with thin-walled functionally graded materials along the contour direction

The buckling and lateral buckling of thin-walled functionally graded (FG) open-section beams with various types of material distributions are studied. The approach is based on assumption that the volume fraction of particles varies through the contour direction according to a power law. The governing buckling equation and a finite element method have been developed to formulate the problem. Warping of cross-section and all the structural coupling coming from anisotropy of material are taken into account in this study. The critical load is obtained for thin-walled FG channel-section with arbitrary distributions of material. The lateral buckling parameter and mechanism are expressed for thin-walled FG mono-symmetric I-section beam under uniformly distributed load and pure bending with several types of material distributions. For the validity of the proposed theory, the number comparisons are compared with those of formerly published work. The effects of the material distribution, load height and span-to-height on the buckling characteristics are examined in detail and highlighted.

Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems

This paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.

General Stiffness Matrix for a Thin-Walled, Open-Section Beam Structure

This paper is to review the theory of thin-walled beam structures of the open cross-section. There is scant information on the performance of structures made from thin-walled beam elements, particularly those of open sections, where the behavior is considerably complicated by the coupling of tensile, bending and torsional loading modes. In the combined loading theory of thin-walled structures, it is useful to mention that for a thin-walled beam, the value of direct stress at a point on the cross-section depends on its position, the geometrical properties of the cross-section and the applied loading. This applies whether the thin-walled section is closed or open but this study will be directed primarily at the latter. Theoretical analyses of structures are fairly well established, considered in multi-various applications by many scientists. However, due to the present interest in lightweight structures, it is necessary to specify where the present theory lies. It does not, for example, deal with compression and the consequent failure modes under global and local buckling. Indeed, with the inclusion of strut buckling failure and any other unforeseen collapse modes, the need was perceived for further research into the subject. Presently, a survey of the published works has shown in the following: 1) The assumptions used in deriving the underlying theory of thin-walled beams are not clearly stated or easily understood; 2) The transformations of a load system from arbitrary axis to those at the relevant centre of rotation are incomplete. Thus, an incorrect stress distribution may result in; 3) Several methods are found in the recent literature for analyzing the behaviour of thin-walled open section beams under combined loading. These reveal the need appears for further study upon their torsion/flexural behaviour when referred to any arbitrary axis, a common case found in practice. This review covers the following areas: 1) Refinement to existing theory to clarify those observations made in 1 - 3 above; 2) Derivation of a general elastic stiffness matrix for combined loading; 3) Calculation of the stress distribution on the cross-section of a thin-walled beam. A general transformation matrix that accounts for a load system applied at an arbitrary point on the cross-section will be published in a future paper.

Free vibration of thin-walled open-section beams with functionally graded materials along the contour direction

An investigation of free vibration of a thin-walled beams with functionally graded materials (FGMs) is presented. The mechanical properties of thin-walled beam are assumed to vary along the contour direction of the thin-walled cross section. Governing differential equations are derived by means of Hamilton's principle. A finite element model is developed to formulate the problem. The natural frequencies and corresponding vibrational modes are obtained for thin-walled FG mono-symmetric I- and channel-sections beams with several different types of material distributions. A numerical comparison is carried out to show the validity of the proposed theory with available results in the literature. Furthermore, effects of gradual law and volume fraction of ceramic on the natural frequencies of beams are also studied.