Open Section Beams Research Articles

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.

Dynamic Response Analysis of Open Section Structures with Warping Restraint Conditions and Impact Load Durations

The response analysis of frame structure with open section beams considering warping conditions and short duration load have been performed. When a beam of frame structure is subjected under torsional moment, the cross section will deform a warping as well as twist. For some thin-walled sections warping will be large, and accompanying warping restraint will induce axial and shear stresses and reduce the twist of beam which stiffens the beam in torsion. Because of impact or blast loads, the wave propagation effects become increasingly important as load duration decreases. This paper presents that a warping restraint in finite element model effects the behavior of beam deformation, dynamic mode shape and response analysis. The computer modelling of frame is discussed in linear beam element model and linear thin shell element model, also presents a correlation between computer predicted and actual experimental results for static deflection, natural frequencies and mode shapes of frame. A method to estimate the number of normal modes that are important is discussed.

The Influence of the Layer Arrangement on the Distortional Post-Buckling Behavior of Open Section Beams.

The paper deals with the design of the stacking sequence of layers in the laminate beams with open-cross sections in order to create the desired behavior in the post-buckling range. Laminate beams with channel and lipped channel cross-sections made of glass fiber reinforced polymer (GFRP) laminate with different layer arrangements (symmetrical and nonsymmetrical) have been considered. In case of the nonsymmetrical stacking sequences, hygro-thermally curvature stable (HTCS) laminates have been taken into account. Pure bending was assumed as the type of load. In the case of beams with open cross-sections, this load type can cause the lateral-distortional buckling mode. A parametric study was performed to analyze the influence of layer arrangement on post-buckling behavior. The finite element method was used to developed numerical models and conduct simulations. Additionally, the experimental tests of the channel section beams were performed in order to validate the developed numerical models.

Modification of the deflection formula for prestressed concrete hollow slab based on Timoshenko theory

PurposeTimoshenko deformation calculation theory is suited to open section beam, which is not suited to closed section beam due to the difference stress distribution between the open and the closed section beam. This study aims to modify the deflection formula for prestressed concrete hollow slab (closed section beam) based on the Timoshenko theory.Design/methodology/approach(1) The deflection curves of the prestressed concrete hollow slab beam were obtained under a single point force; (2) linear phases of the deflection values, which were calculated by Timoshenko theory and ABAQUS, were compared with the measured values; (3) a modified coefficient related to the loading location was obtained to modify the Timoshenko theoretical formula in calculating the deflection of the prestressed concrete hollow slab.Findings(1) There is a large difference between the calculated values and the measured values at 4.3 < a/H < 7.7, and the differences are between 24 and 33 percent; (2) the Timoshenko deflection formula has been modified to fit for the calculation of the prestressed concrete hollow slab. The mean of f/ft is 1.01, and the variation coefficient is 0.09 after modification. Therefore, the modified formula can be better applied in the deflection calculation of the prestressed concrete hollow slab.Originality/valueThe Timoshenko theory is the most classical theory, which is often used to calculate the deformation of beams. The modified deflection formula for prestressed concrete hollow slab based on the Timoshenko theory is reliable and convenient, which can help engineers to calculate the deflection for closed section beam quickly.

Seismic Behavior of a Novel Blind Bolted Flush End-Plate Connection to Strengthened Concrete-Filled Steel Tube Columns

Modified blind bolts (Hollo-Bolt) and a locally strengthened steel tube column in the panel zone were created to overcome the moment-resisting problem for the bolted connections between concrete-filled hollow section columns and open section beams and to enhance the performance of connections. The cyclic loading was conducted on a total of six modified anchored blind bolted flush end-plate connections to concrete-filled steel tube (CFST) columns. The key parameters investigated were the tube wall thickness, end-plate thickness, blind bolt anchorage method, and beam section. The failure mode, hysteretic behavior, strength, stiffness, ductility, and energy dissipation capacity of the connections were analyzed and evaluated with all details. The results indicated that connections with modified anchored blind bolts and locally strengthened steel tubes could avoid the premature failure of CFST column and exhibit an improved behavior with a favorable strength, stiffness, and stiffness degradation. The test observations reveal two representative failure modes, and the tube wall thickness and blind bolt anchorage method have a significant effect on the resultant failure mode. Moreover, the use of thin endplate and weak beam can effectively enhance the hysteretic behavior of joints, ductility, and energy dissipation capacity; and the change in anchoring method has little effect on the stiffness. Finite element (FE) analysis models were established for the aforementioned connections. The numerical models were validated against the experimental results and exhibited good agreement. Finally, based on the component method, an initial stiffness calculation method was established for the connections.

Enhancing flange local buckling strength of pultruded GFRP open-section beams

In this work, the use of pultruded GFRP web stiffeners to enhance the flange local buckling behavior of pultruded GFRP open-section beams was proposed and demonstrated through a numerical study. The buckling strength of the GFRP I-beam was successfully increased by up to 207% via this approach. The influences of the stiffener geometry and spacing were investigated. The buckling strength of the GFRP I-beam increased as the stiffener width increased and the stiffener spacing decreased. Epoxy adhesive was found to provide a sufficient bonding effect between the web stiffeners and the beams. In addition, a design approach was proposed to predict the increased buckling strength of GFRP I-beams strengthened with web stiffeners. A comparison with finite element analysis and experimental results showed that the design equation was able to provide uniformly conservative predictions. Additionally, practical design suggestions were provided to ensure the best performance of the web stiffeners. The strengthening approach addressed in this work could potentially permit a longer span of GFRP profiles and a wider application of GFRP structures.

A theory of torsion of thin-walled beams of arbitrary open sections with influence of shear

A novel theory of torsion of thin walled beams (“shear deformable beams”) of arbitrary open cross-sections with influence of shear (TTTS) is presented. The theory is based on the classical Vlasov’s theory of thin-walled beams of open cross-section, as well on the Timoshenko’s beam bending theory. The theory is valid for general thin-walled open cross-section shapes, for distributed and concentrated transverse torsion loads and for isotropic materials. Four parameters due to shear warping are introduced. Closed-form analytical solutions for three-dimensional expressions of the normal and shear stresses are obtained. Under general transverse loads, reduced to moments of torsion with respect to the cross-section principal pole (by Vlasov’s theory), for arbitrary cross-sections, the beam will be subjected to torsion with influence of shear and in addition to bending due to shear in the beam principal planes and to tension/compression due to shear. The theory is tested by comparing it to the classical Vlasov’s thin-walled beam theory and to the finite element method using shell elements, as well as to some results in literatures.

Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

The paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

Rationalization of cross-sections of the composite reinforced concrete span structure of bridges with a monolithic reinforced concrete roadway slab

The article presents the developed rationalization technique of composite steel reinforced concrete sections with steel open section beams based on the criterion of equal strength of the section elements that are extremely distant from the neutral line. Algorithms for search for geometric parameters of a composite section limited to a certain range of values are implemented to achieve the equal strength condition. The dimensions of the individual elements which are parts of the cross-section are obtained from the condition of the constant ratio of the distances from the neutral axis to the extreme concrete and steel fibers. The numerical methods were used for calculation of continuous three-span composite reinforce concrete bridge. The technique implements the steps of bridge construction, taking into account the contact yield of the composite section, the redistribution of forces between the elements, and the effect of elastic-plastic and rheological properties of materials. The generalized kinetic curve was utilized for evaluation of concrete creep together with the phenomenological equations for the development of deformations based on a colloid-chemical representation of the mechanism for long-term concrete deformation. The proposed methodology is implemented in the LIRA-SAPR software package based on the Building Information Model Technology (BIM) and the Finite Element Method (FEM).

Non-linear torsional vibration of lengthy thin-walled simply supported beam of open section resting on Winkler foundation

The aim of this paper is to study the non-linear torsional vibrations of lengthy thin-walled simply supported beam of open section resting on Winkler foundation. The governing differential equation of motion is derived. An effort has been made to obtain and solve the governing differential equation of large amplitude torsional vibrations of doubly symmetric thin-walled beams of open section with simply supported boundary. Approximate solutions are obtained for simply supported beams using the well-known Galerkin’s method. Plots specifying the effect of large amplitudes on nonlinear frequency of torsional vibrations for various non-dimensional beam constants are furnished. From the present study, we observe, that for lower values of Winkler stiffness parameter λ≤0.1, the non-linear frequency increases drastically as β increases. Also, it is noticed that as the value of Winkler stiffness parameter λ increases, the influence of β decreases. For higher values of λ≥30, the effect of β in the present range 0–0.1 on non-linear frequency seems to be negligible.

Comparative behaviour of ‘I beam- RHS column’ joints with and without web weld

This paper presents the results of an experimental and numerical comparative study for beam-column joints constructed of welding open section beams to rectangular hollow section columns between welding the entire beam profile and welding only the beam flanges. Since flanges of open section beams contribute most to the joint stiffness and moment resistance, welding the flanges only has the potential of achieving nearly the same joint stiffness and moment resistance as welding the entire beam profile while reducing the cost of welding considerably. However, it is necessary to quantify the effects. Furthermore, since the beam web is conventionally considered to resist the beam shear force, it is also necessary to investigate whether premature shear failure will occur in the case of welding the flanges only.This paper presents the results of 27 tests and accompanying detailed numerical modelling to provide further insight. The tests considered the effects of different welding arrangements, different dimensions and different beam to RHS width ratios.The experimental observations suggest that due to flexibility of the RHS face, the contributions of the beam web weld to the total joint stiffness and moment resistance are much lower than those of the beam web to the beam section. Furthermore, if only the beam flanges are welded, the flange welds have much higher shear resistances than would be applied in realistic applications.Based on these findings, the characteristics of welded open section beam to RHS column joints can be quantified by using the contributions of the beam flanges only.

Open-section origami beams for energy absorption

A series of novel open-section beams employing origami geometries were developed. These beams overcame the Brazier's effect, and they can provide more constant bending resistance and overall higher energy absorption than conventional open-section beams. Numerical simulations and experiments were used to validate these designs and showed that properly designed origami beams can achieve 23.0–40.0% higher energy absorption and 12.7–20.7% lower load uniformity than conventional beams under quasi-static loading.

Spectral Dynamic Analysis of Torsional Vibrations of Thin-Walled Open Section Beams Restrained Against Warping at One End and Transversely Restrained at the Other End

The present paper deals with spectral dynamic analysis of free torsional vibration of doubly symmetric thin-walled beams of open section. Spectral frequency equation is derived in this paper for the case of rotationally restrained doubly-symmetric thin-walled beam with one end rotationally restrained and transversely restrained at the other end. The resulting transcendental frequency equation with appropriate boundary conditions is derived and is solved for varying values of warping parameter and the rotational and transverse restraint parameter. The influence of rotational restraint parameter, transverse restraint parameter and warping parameter on the free torsional vibration frequencies is investigated in detail. A MATLAB computer program is developed to solve the spectral frequency equation derived in this paper. Numerical results for natural frequencies for various values of rotational and transverse restraint parameters for various values of warping parameter are obtained and presented in both tabular as well as graphical form showing the influence of these parameters on the first fundamental torsional frequency parameter.

Behaviour and design of cold-formed steel built-up section beams with different screw arrangements

An experimental and numerical investigation of cold-formed steel built-up beams with different screw arrangements is presented in this paper. A total of 35 beams were tested under four-point bending with different screw arrangements in the moment span. The built-up sections were assembled using self-tapping screws from either two lipped channels connected back-to-back at the web to form an open section or two plain channels connected face-to-face at the flanges to form a closed section. Finite element (FE) models have been developed and validated against the test results for the built-up open section beams and built-up closed section beams, respectively. It is shown that the FE models can accurately predict the behaviour of cold-formed steel built-up beams with different screw arrangements. A parametric study on built-up beams with larger span and various screw spacing was further carried out using the verified FE models. The test and numerical results were compared with the design strengths predicted by the direct strength method (DSM) for cold-formed steel structures, with contingent considerations of the screws when determining the elastic buckling moments in the finite strip analysis. A reliability analysis was performed to evaluate the reliability of the current DSM equations. It is shown that the current DSM equations can predict the design strengths of built-up open section beams well in this study, with the assumption that the strength of the built-up section is the sum of two component profiles. However, the design equations for local buckling strength are generally conservative for the built-up closed section beams failed by local buckling. Meanwhile, the design equations for lateral-torsional buckling (LTB) strength cannot be directly used for the built-up closed section beams with relatively large screw spacing that failed by LTB with cross section distortion or separation of two component channels. It should be noted that LTB mode with cross section distortion was found in built-up closed section beams with large screw spacing. A modified design rule based on DSM is then proposed, which is shown to improve the accuracy of the predicted strengths. Moreover, the maximum longitudinal screw spacing for built-up closed section beams was also recommended for design practice.

I-beam to square hollow column blind bolted moment connection: Experimental and numerical study

This paper presents the results of experimental investigations and numerical analyses carried out to investigate the performance of new blind bolted moment-resisting connections between square hollow section columns and open section beams, referred to herein as the extended and flush end plate. Eight full-scale specimens comprising four extended end plate and four flush end plate exterior connections were tested under monotonic loading. The moment-rotation curves, failure mode, initial stiffness and connection classification of the joints were obtained and discussed. The results showed that the end plate type has a significant influence on the flexural capacity as well as the rotational stiffness of the proposed blind bolted connection. Furthermore, the test also showed that for specific column sizes, an increase in the beam size and end plate thickness could reduce the connection strength. The experimental specimens were also simulated using finite element models and compared with the experimental results. Comparison amongst the experimental and three-dimensional finite element (FE) models shows that the modeling of finite element analyses for the prediction of the connection behavior is sufficiently accurate.

A buckling and postbuckling analysis of axially loaded thin-walled beams with point-symmetric open section using corotational finite element formulation

The axially loaded thin-walled beams with point symmetric open section are studied using a corotational finite element formulation. The kinematics of the beam element is described in the current element coordinate system. The element nodal forces are derived using the virtual work principle, and consistent second order linearization of the fully geometrically non-linear beam theory. Different axial load systems with the same centric resultant axial force but different resultant bimoments are considered. Numerical examples studied show that the effects of bimoments on the buckling and postbuckling behavior of point symmetric open section beams are remarked.

Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation

The problem of the post-buckling response of a simply supported thin-walled beam subjected to an axial compressive load and supported by the Winkler–Pasternak foundation is studied in this paper. The strains are assumed to be small and elastic. The shear deformations and the in-plane cross-sectional deformations are assumed to be negligible. The post-buckling paths of the simply supported beam are determined for different values of the Winkler and Pasternak stiffness parameters. Bifurcation points are found.

Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation

Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation

Design of cold-formed steel built-up sections with web perforations subjected to bending

The flexural behaviour including the moment capacities and failure modes of cold-formed steel built-up sections with circular web holes was investigated. Finite element analysis was performed on a wide range of cold-formed steel built-up section beams with different sizes of perforations under four-point bending. The built-up sections included both I-shaped open sections assembled from two lipped channels back-to-back and box-shaped closed sections assembled from two plain channels face-to-face. Finite element (FE) models have been developed to simulate the simply-supported cold-formed steel built-up section beams. The FE models for the built-up open sections and built-up closed sections were verified against the test results that have been conducted by the authors. The validated models were employed to carry out extensive parametric studies on cold-formed steel built-up section beams with various section slenderness and hole sizes. The beam strengths obtained from the numerical analysis together with the available test data were compared with the design strengths calculated from the current direct strength method (DSM). The critical elastic local and distortional buckling moments including the influence of holes that are required in DSM calculation were determined by rational finite strip analysis. It is shown that the DSM formulae in the North American Specification AISI S100-16 are capable for predicting the design strengths of the built-up open section beams with holes, while are quite conservative for the closed section beams with holes. Modifications are proposed for the DSM formulae for built-up closed section beams with holes. In this study, the current DSM was extended to cover the cold-formed steel built-up open and closed section beams with holes.

01.04: Joints between open section beams and tubular columns: New configuration for semi‐rigid and moment resistant bolted joints

ABSTRACTThe appealing shape and the mechanical properties of the tubular members are the main responsible for their growing popularity amongst architects and engineers. However, their potential hasn't been properly explored due difficulties encountered in the joints conception and design, with special emphasis on the bolted joints if rigid and/or full strength behaviour is required for the joint.Currently, in the European regulation scenario, the guidance for the joints design is given in the EN 1993‐1‐8. The recommendations for joints with tubular members are given in its seventh chapter, where only welded solutions are considered. Bolted solutions aren't referred, and no guidance is given to predict the joints rotational stiffness and rotation capacity. However, a window is left open in the standard sixth chapter with the given method to predict the joints structural properties (component method). The method is applicable to joints in frames of any type, independently of its configuration and of the joined members’ sections. Once known the nonlinear response of each joint basic component, commonly represented by force‐displacement curves, the component method can be used to predict the joint structural properties.Regarding the current lack of information in this subject, the authors propose a new configuration for joints connecting open section beams to rectangular or square hollow section columns. The configuration was conceived with the double purpose of getting a joint with bending moment resistance capacity and with high initial rotational stiffness. Furthermore, looking on the current regulation scenario, it would be desirable that joints with the proposed configuration could be designed by the component method. Thus, the authors identified the joint active basic components, and are developing experimental work in the sense of establish the force‐displacement curves which represent the nonlinear response of the new basic components. The experimental work, already developed, on the basic components structural response is here summarily presented.