Hollow Section Beams Research Articles

Experimental and numerical investigation on the multi-optimization of reinforcing the side members of the vehicle structure

The aim of this study is to investigate the improvement in the strength of a top-hat profile hollow-section beam used in a vehicle structure by attaching different shapes of internal reinforcements. The base structure of the beam was first considered as a hat-shape structure which was jointed to a flat plate using spot-welds. Three types of sheet metal reinforcements were formed and attached inside the beam’s structure. Then, they were tested experimentally under low-velocity lateral impact. Also, a numerical simulation is being developed using LS-DYNA explicit code and validated using experimental data. Valid numerical configuration is used to conduct an optimization study on cross-sectional shape of the internal reinforcing component. Optimizations are carried out using single- and multi-objective methods based on Genetic Algorithm approach and the suggested optimum solutions are compared with experimental results. Moreover, to discuss the feasibility of applied reinforcements on side section of a vehicle’s body-in-white, a realistic side-pole crash test is simulated using a validated vehicle model and performance of improved chassis is compared with basic model and results are presented, discussed and commented upon.

Design of cold-formed steel SHS and RHS beam–columns considering the influence of steel grade

The structural behaviour and design of cold-formed steel square and rectangular hollow section (SHS and RHS) beam–columns, made of both normal and high strength steels, are investigated in the present study through a comprehensive numerical modelling programme. Refined finite element (FE) models were first established and calibrated against a collection of existing cold-formed steel member test results from the literature. Following this, an extensive parametric study was undertaken to expand the cold-formed steel beam–column data pool, covering a wider range of steel grades, cross-section geometries, member slendernesses and loading combinations. Results from the parametric study were then used to examine the accuracy of the current codified beam–column design methods, provided in the European Standards EN 1993-1-1 (2005) and EN 1993-1-12 (2007) as well as the American Specification AISC 360-16 (2016). The comparisons revealed that the codified design rules provide varying levels of accuracy in predicting the ultimate resistances of cold-formed steel beam–columns depending on the steel grade. An improved design approach, compatible with current codified design rules in EN 1993-1-1 (2005), is proposed that features (1) recently developed column buckling curves that reflect the increasing normalised column buckling resistance with increasing steel yield strength; (2) bending moment resistances calculated using the Continuous Strength Method (CSM) and (3) new interaction curves for cold-formed steel beam–columns, which are anchored to these more accurate end points. The newly proposed design approach is shown to yield more accurate and consistent resistance predictions over current design provisions for cold-formed steel SHS and RHS beam–columns made of different steel grades, and its reliability has also been statistically verified in accordance with EN 1990.

Performance and design of RAC-filled steel RHS beams

Research on steel hollow sections filled with recycled aggregate concrete (RAC) has been recently gained attention across the world. This is because the RAC-filled steel hollow section reuse the waste concrete, while, still achieving good structural performance. This paper studies the static performance of RAC-filled steel rectangular hollow section (RHS) beams. Ten beams with various recycled coarse aggregate (RCA) replacement ratio (r), depth-to-width ratio (β) and width-to-thickness ratio (B/t) were tested. The results show that, after the mid-span deflection exceeds 6% of effective span, the top flange of the tube and part of the adjacent side walls of the tube buckled in the pure bending zone for all tests, whilst cracking was observed at the bottom flange of the tube within pure bending zone of some beams. Accordingly, for the concrete core, both crushing at the tube buckling position and cracks extended towards the compression zone are observed. The moment-deflection (strain) relationship of the specimens can be divided into three key stages, namely, elastic, elastic-plastic and hardening. In general, moment capacity and flexural stiffness of the specimens reduce with the augment of B/t and the decrease of β under the same width. A finite element (FE) model that can efficiently reproduce the failure process and moment-deformation curves of RAC-filled steel RHS beams is also developed, and the FE is further used to discover the influence of r and β on working mechanism of such composite beams. Finally, based on the parametric analysis, the design equations for moment capacity of RAC-filled steel RHS beams are developed, and the accuracy of the simplified equations is verified by the experimental results. Meanwhile, the test results also proved that the approach in ACI 318 code is the more suitable method for the flexural stiffness prediction of RAC-filled steel RHS beams.

Design of direct-formed square and rectangular hollow section beams

A complementary experimental study showed that the flexural member design rules in the North American steel design standards (AISC 360–16 and CSA S16-19) can be excessively conservative for direct-formed regular- and high-strength steel square and rectangular hollow sections (hereinafter collectively referred to as RHS). It was also found that post-production hot-dip galvanizing can further improve member flexural behaviours through effective reduction of cold-forming-induced residual stresses. In this study, the experimental results of 22 full-scale beam tests from the complementary experimental study are used to validate non-linear finite element (FE) models. The FE models are developed using previously measured stress-strain relationships, residual stresses, and geometric imperfections. A subsequent parametric study including 788 beam models is performed to cover extended ranges of cross-sectional dimensions. The applicability of the existing slenderness limits and flexural design formulae are examined using the experimental and numerical data. The results justify the use of less stringent slenderness limits and higher design curves for direct-formed regular- and high-strength RHS beams (untreated and galvanized). Modifications to the existing design rules are proposed. Based on reliability analyses, the modified approaches are proven accurate and provide adequate safety margins.

Simplified analytical method for lateral torsional buckling assessment of RHS beams with web openings

The present paper treats the lateral torsional buckling (LTB) of castellated rectangular hollow section (CRHS) beams. For the purpose, an analytical model was proposed to provide critical buckling loads in (LTB) resistance. In the present model two types of web openings are considered, referring to rectangular and hexagonal shape perforating. The sectional geometrical properties attributed to each type of opening are controlled by selecting the appropriate value of the reduction parameter. Ritz method is applied in order to found the governing equilibrium equations, following the critical buckling loads are determined from the eigenvalue problem imposed to the tangential stiffness matrix. The validity of the elastic lateral buckling resistances evaluated by the proposed method is checked with the finite element simulation using ABAQUS software. The numerical results for cantilevers and simply supported CRHS beams, with hexagonal and rectangular web openings, are presented for both short and long-span beams.

Torsional behavior of reinforced recycled aggregate flowing concrete hollow section beams

Fifteen reinforced concrete beams made with recycled aggregates and flowing concrete, which were tested under pure torsion to study the torsional behavior. The major parameters in this study were the percent of the recycled aggregates and the number of transverse reinforcements. The torsional response and crack behavior were investigated in this study. From the results, it can be noted that the increase of the recycled aggregate led to a decrease in the critical and ultimate torque of the beam, also, the increasing the number of transverse reinforcements led to the enhancement of the critical and ultimate torque. Numerical analysis by finite element method was conducted and gave a good indicator for agreement in the results of critical and ultimate load between the numerical and experimental study, as well as the angle of twisting of the beam. The second approach was Hsu᾽s softened truss model, the model proves it can predict the critical and ultimate torque for the beam and showed its ability to describe the behavior of the beams before and after cracks.

Experimental investigation of direct-formed square and rectangular hollow section beams

This paper presents an experimental study on the flexural behaviours of new-generation direct-formed square and rectangular hollow sections (collectively referred to as RHS herein). A total of 22 beam specimens covering wide ranges of cross-sectional dimensions and nominal yield stresses (350 and 690 MPa) are tested. The results are compared to those from previously tested indirect-formed and hot-finished RHS to study the effect of different production processes. The effects of post-production hot-dip galvanizing on residual stresses and flexural behaviours are also studied. The applicability of slenderness limits and flexural design formulae in the current North American steel design standards are examined using the experimental data. The experimental results demonstrate that the existing flexural design rules are generally conservative for direct-formed RHS (ungalvanized and galvanized).

On the saturated impulse for a circular hollow beam under pressure pulse loading

The saturated impulse phenomenon, which may occur in a hollow beam with a circular cross-section, is examined when a rectangular pressure pulse loading is applied uniformly on the upper surface of the beam. A simplified 2DoF model of the dynamic response of a relatively long circular hollow section beam is developed to explore the role of the local and global deformations build up simultaneously during the beam response. In order to simplify the analytical formulation, the elastic deformations of the hollow beam are neglected, and a rigid-plastic method of analysis is applied. Finite element simulations using an elastic, perfectly plastic material model are carried out to verify the proposed analytical model and to reveal the influence of the elasticity on the beam response. The limit of the pressure pulse loading, beyond which saturated impulse is not defined for a hollow beam, is obtained numerically. The responses of hollow beams with lengths between 800 and 1200 mm, radius of 40 mm and several wall thicknesses are analysed. It is observed that the proposed 2DoF model can predict satisfactory the local and global saturated deflections while the saturated pressure pulse duration is underestimated due to the disregard of the stored elastic energy in the beam. It is suggested that the analytically predicted saturated impulse can be used as a lower bound estimate for the saturated impulse for a given beam geometry.

A unified approach for austenitic and ferritic stainless steel CHS beam–columns subjected to eccentric loading

This paper develops a unified approach for assessing structural behaviour of austenitic and ferritic stainless steel circular hollow section (CHS) beam–columns​ under eccentric loading. This approach is based on combining a deformation-based method and collapse theory for stainless steel CHS beam–columns.A normalised M–N–Φ relationship of stainless steel CHS was derived based on a fibre model; the approach incorporated deformation capacity and strain hardening based on continuous strength method (CSM). The novelty of this paper is to present a closed-form solution for generating axial-load–end-moment interaction curves of the stainless steel CHS beam–column by combining the normalised M–N–Φ equation with a general beam–column equation. Besides, a critical normalised mid-height curvature was determined, which could be used to differentiate cross-section local buckling failure from global stability failure of stainless steel CHS beam–columns under combined loading. The proposed approach related the strengths of beam–columns to the effective column lengths by introducing a new non-dimensional slenderness ratio for stainless steel CHS beam–columns. It also provided an explicit way to consider the effect of column imperfections on the strengths of stainless steel CHS beam–columns. Accuracy of the derived normalised interaction curves was assessed by comparing the predictions against the test and numerical results for a wide range of non-dimensional slenderness ratios and different classes of CHS cross-sections for both stainless steel grades. A high level of accuracy and consistency was achieved in predicting the strengths of both short and long stainless steel CHS beam–columns for both types of steel grade.

Higher-order beam bending theory for static, free vibration, and buckling analysis of thin-walled rectangular hollow section beams

In higher-order beam theories, cross-sectional deformations causing complex responses of thin-walled beams are considered as additional degrees of freedom. To fully capture their bending responses, enriched sectional modes departing from Vlasov’s assumptions have been utilized in recent studies. However, due to these bending-related modes, no available higher-order beam bending theory has established explicit stress-generalized force relations that are fully consistent with those by the classical beam theories and earlier studies based on Vlasov’s assumptions. If they are available, physical significance of the bending-related generalized forces can be readily understood. In addition, equilibrium conditions at a joint of multiple thin-walled beams can be explicitly derived. Here, we newly propose a higher-order beam bending theory that not only includes as many bending-related sectional modes as desired, but also provides the desired explicit stress-generalized force relations. To this end, we establish a recursive analysis method that derives hierarchical bending-related sectional modes. We show that this method can yield certain relations among the sectional mode shapes, which are critical in establishing the desired explicit relations. The validity of the present theory is confirmed by calculating the static, free vibration, and buckling responses of several thin-walled rectangular hollow section beams.

Flexural behaviour of cold-formed steel oval hollow section beams

This paper presents a detailed investigation into the flexural strength and behaviour of cold-formed steel oval hollow section beams. A series of four-point bending tests were conducted as part of the experimental programme. Following this, a total of 12 tested beams were simulated by a non-linear finite element analysis. Upon validation of the newly developed numerical model, a total of 36 numerical results were generated through a parametric study to assess the structural response of the oval hollow section beams over a wider range of cross-section dimensions. The experimental and numerical data were used to evaluate the applicability of five existing design methods for cold formed steel structural members, including Eurocode 3, the North American Specification, the Australian/New Zealand Standards, the direct strength method and the continuous strength method. In general, the results indicate that all the three design standards produce unconservative predictions, while the direct strength method and the continuous strength method yield relatively accurate and consistent predictions.

Potential Application of Green Composites for Cross Arm Component in Transmission Tower: A Brief Review

Recently, advanced technologies exploit materials from nonrenewable resources such as petroleum, natural gas, metal ores, and minerals. Since the depletion of these resources and environmental issues, it has brought attention to researchers to progress in the development of biodegradable materials from green composites. Most biofibres and biopolymers are obtained from agricultural waste products either from stem, leaf, stalk, or fruit. Nowadays, green composites with well-regulated life span have been widely discussed in numerous fields and applications. Some studies have shown that biofibres and biopolymers have comparable mechanical, thermal, and physical properties with glass fibre and other synthetic polymers. Thus, researchers are progressively narrowing down the development of green composite materials in many high strength applications, such as house deck and automotive components. This review focuses on the background of green composites (natural fibres and biopolymers), the manufacturing processes, potential applications in cross arm structures, and testing evaluations. This article also focuses on the specific current cross arm configurations and the pultrusion process to form squared hollow section beams. Many open issues and ideas for potential applications of green composites are analysed, and further emphases are given on the development of environmentally friendly material structures. Hence, the article is expected to deliver a state-of-art review on manufacturability and perspectives of natural fibre reinforced biopolymer composite cross arms for transmission towers.

Cyclic Behavior of Hollow Section Beam–Column Moment Connection: Experimental and Numerical Study

Steel buildings with tubular columns showed a satisfactory performance during the Honshu (2011) earthquake, unlike steel buildings in the 1994 Northridge and 1995 Kobe earthquakes, where welded moment connections showed damage in their joints. In this research, a lateral joint using a hollow structural section (HSS)-beam and HSS-column subjected to cyclic displacement was performed. Three large-scale specimens were tested and a numerical model was calibrated, reaching a good adjustment. Later, several configurations of beams and columns were evaluated using finite element (FE) models from the numerical model previously calibrated. A flexural resistance higher 0.80 Mp at 0.04 [rad] was obtained for all cases studied. The ductility factor in the 3 specimens was lower than 2.5, therefore a non-ductile behavior was controlled in the connection. This aspect is very important although a 0.8 Mp at 0.04 [rad] was achieved. Finally, the typical welded moment connection can be improved using the bolted moment connection, which allows the concentration of inelastic incursion in the beam compared with the welded solution. However, a non-ductile behavior derived from local buckling in flanges of a tubular beam can affect the seismic performance.

Energy absorption study of a new reinforced top-hat section beam under flexural loading

The aim of this study is to investigate the improvement in energy absorption of a top-hat profile hollow-section beam by attaching different shapes of internal reinforcements. The base structure of the beam was first considered as a hat shape structure which was jointed to a flat plate using spot-welds. Three types of sheet metal reinforcements were formed and attached inside the beam’s structure. Then, they were tested experimentally under quasi-static three-point bending loading condition. Also, these reinforced structures were numerically simulated using LS-DYNA explicit code. After the numerical simulation is validated using experimental data, some new cross-sections were proposed for reinforcing component, and the specimens’ performance were studied based on the total energy absorption and the specific energy absorption (SEA) parameters. Furthermore, the effects of different assembly methods, such as joint areas and arrangement of spot-welds, were numerically investigated in order to obtain the best configuration to manufacture the reinforced top-hat profile beam. The results for the best crashworthiness characteristics are presented, discussed, and commented upon.

Veneer-based timber circular hollow section beams: Behaviour, modelling and design

Various forms of timber hollow structural profiles have either been proposed in the literature or are already commercially available. Tests performed on Circular Hollow Section (CHS) beams showed failure modes not usually encountered in timber structures. For relatively thin-walled profiles, a sudden failure in the compression zone, with the opening of the cross-section, was observed. To confidently use and market CHS timber products, design rules considering all possible failure modes must be developed. This paper presents a Finite Element (FE) model of CHS timber beams which captures all experimentally observed failure modes. Cohesive zone elements were used to model the quasi-brittle failure modes of the timber material. The model was validated against ten experimental tests performed on CHS of three different cross-sectional slenderness and manufactured from juvenile hardwood Gympie messmate (Eucalyptus cloeziana) rotary peeled veneers. The model was found to accurately capture the measured structural behaviour and resulted in an average experimental-to-predicted bending capacity ratio of 1.02. The model was also used to explain the mechanisms leading to the sudden compressive failure mode. A parametric study was finally performed on 72 CHS beams of different cross-sectional slenderness. Results showed a strong correlation between the cross-sectional slenderness ratio and section capacity. Design rules are proposed and discussed.

Experimental and numerical analysis of impactor geometric shape effects on steel beams under impact loading

This paper presents experimental and numerical studies about the effect of geometric shape of impactors (drop weight) at damage status on weak axis of rectangular hollow section (RHS) steel beams under impact loadings. To do so, six simply supported steel beam specimen with 2000 mm length have been tested on their weak axis from two different height of the drop weight as 1400 mm and 2000 mm respectively. The head geometry of the drop weight consisted of three different types namely rectangular (SPC#R), circular (SPC#C) and triangular (SPC#T), while the weight of the impactors was kept constant in all conditions. For numerical simulation of impact loading on steel beams, initially, three dimensional finite element models of the samples under impact loading were analyzed using Abaqus Explicit package program. To determine the effect of geometric shape of drop weight, five parameters namely displacement, acceleration, reaction forces, stress distribution and plastic strain have been considered comparatively. Displacement, acceleration and reaction forces were compared experimentally and numerically while, stress distribution and plastic strains were only compared numerically on verified finite element models. In the second part of the numerical study, the effect of geometric shape of impactors on square hollow section (SHS) beam was investigated. For this purpose, six simply supported steel beams’ FE models with 2000 mm length have been analyzed from two different height of the drop weight as 1400 mm and 2000 mm respectively. Obtained results show that the maximum deflections and acceleration have been occurred in the beams that were hit by the triangular headed impactor in both types of the section. In addition, the biggest plastic deformation and stress distribution have been observed in the tests where triangular headed impactors were used. The minimum damage and displacement have been occurred in the tests where rectangular shaped impactor have been used. To sum up, for a constant impact load, triangular head of impactor inflicts a bigger damage and plastic deformation on steel beam in comparison to circular and rectangular heads of impactors.

Behaviour of seawater and sea sand concrete filled FRP square hollow sections

Abstract FRP tube could serve as formwork in new constructions and the square cross-section is convenient for connections. This paper presents an experimental and theoretical study on seawater sea sand concrete (SWSSC)-filled glass/carbon/basalt FRP square hollow section (SHS) stub columns and beams. FRP SHS includes fibres oriented in ±15°, ±40° and ±75° with respect to the longitudinal axis so that the hoop and axial strengths are comparable. Both unfilled FRP SHS and SWSSC-filled FRP SHS were tested under axial compressive, three-point or four-point bending loads. SWSSC-filled FRP columns failed by FRP rupture, whereas the failure mode for beams was the crushing of compressive flanges. In this paper, the stress-strain behaviour of columns and moment-strain curves of beams were discussed and compared to the corresponding SWSSC-filled stainless steel (SS) SHS specimens. It was found that existing stress-strain models, which were originally derived for rectangular concrete confined by FRP wrap, cannot precisely capture the stress-strain response of SWSSC-filled FRP columns. Existing models are improved to more accurately predict the ultimate axial strains and stress-strain relationship. A theoretical model is proposed to estimate the moment capacity of SWSSC-filled FRP beams with reasonable accuracy.

Slenderness-based design criteria to allow for the plastic analysis of tubular beams

The present paper focuses on the rotational capacity of H.S.S. steel sections; in particular, the influence of local buckling is accounted for by means of a new generalized cross-sectional slenderness parameter, which is used to characterize the cross-sectional rotational capacity, and, by extension, the available deformation capacity.Careful shell modelling of hollow section beams in bending was used, the numerical models being previously carefully validated against more than 50 bending tests. Extensive F.E. studies were consecutively performed, including many parameters such as various material grades, load and support arrangements, length-to-height ratios, etc. Specific attention was paid to the introduction of initial geometrical (local) imperfections, as they were shown quite influential on the rotation capacity.The paper then analyses the numerical results and points out the various influences of height-to-width ratio, shear, moment gradient, yield stress and length-to-height ratio on the available rotational capacity. In a second step, the rotational capacity demand vs. stability criterion is detailed, and related to the proposed generalized cross-sectional slenderness, which is shown to be more appropriate than the b/t ratios usually proposed in design codes. Finally, code-ready recommendations for new ways of allowing for plastic analysis in practical design following the proposed approach are given.

Moment-rotation relationship of hollow-section beam-to-column steel joints with extended end-plates

This paper presents the flexural performance of steel beam-to-column joints composed of hollow structural section beams and columns. A finite element (FE) model was developed incorporating geometrical and material nonlinearities to evaluate the behaviour of joints subjected to bending moments. The numerical outcomes were validated with experimental results and compared with EN1993-1-8. The demountability of the structure was discussed based on the tested specimen. A parametric analysis was carried out to investigate the effects of steel yield strength, end-plate thickness, beam thickness, column wall thickness, bolt diameter, number of bolts and location. Consequently, an analytical model was derived based on the component method to predict the moment-rotation relationships for the sub-assemblies with extended end-plates. The accuracy of the proposed model was calibrated by the experimental and numerical results. It is found that the FE model is fairly reliable to predict the initial stiffness and moment capacity of the joints, while EN1993-1-8 overestimates the initial stiffness extensively. The beam-to-column joints are shown to be demountable and reusable with a moment up to 53% of the ultimate moment capacity. The end-plate thickness and column wall thickness have a significant influence on the joint behaviour, and the layout of double bolt-rows in tension is recommended for joints with extended end-plates. The derived analytical model is capable of predicting the moment-rotation relationship of the structure.

Cold-formed high strength steel SHS and RHS beams at elevated temperatures

The structural responses of cold-formed high strength steel (HSS) square and rectangular hollow section (SHS and RHS) beams at elevated temperatures were examined in this study. Stress-strain relationships of cold-formed HSS at elevated temperatures were proposed and verified against material test results. The proposed stress-strain relationships were then employed in a finite element (FE) analysis to study the behaviour of cold-formed HSS SHS/RHS beams at elevated temperatures up to 1000 °C. The developed FE model was verified with available test results of cold-formed HSS SHS/RHS beams; upon verification, a total of 252 numerical flexural capacities were gained from FE analyses. The numerical results were used to investigate the suitability of existing cross-section slenderness limits to the HSS tubular sections at elevated temperatures. The applicability of current flexural design provisions in the Eurocode 3, AISC and AISI specifications to the investigated HSS tubular beams at elevated temperatures was also examined. Overall, it is shown that the codified provisions can provide quite conservative predictions; an improved design rule is proposed by modifying the direct strength method (DSM) in the AISI specification. Furthermore, reliability analyses were carried out to assess reliability levels of codified and modified provisions. It has been demonstrated that the modified DSM can produce accurate and reliable design and therefore is recommended to be used for cold-formed HSS SHS/RHS beams at elevated temperatures.