Beam Of Rectangular Section Research Articles

Instability of FGM rectangular hollow section (RHS) beam element under combined bending and compressive loads

Instability of FGM rectangular hollow section (RHS) beam element under combined bending and compressive loads

Cold-formed stainless steel beams with single web hole at elevated temperatures

Steel structures are often used in buildings due to their advantage in weight-to-strength ratio. However, their structural capacity deteriorates in fire as the temperature of the structures rises. Investigation of cold-formed stainless steel (CFSS) structures at elevated temperatures is still limited, especially for rectangular hollow section (RHS) beams having a single web hole in the mid-span (perforated web). Therefore, a numerical investigation was conducted to evaluate the current design provisions to calculate the strength of such beams at elevated temperatures ranging from 22 - 900 °C. A total of 400 specimens of stainless steel grades austenitic (EN 1.4301) and lean duplex (EN 1.4162) were considered. The investigation used finite element analysis (FEA) to simulate the behaviour of RHS beams with perforated web under pure bending. The finite element (FE) model was validated against a series of experimental results available in literature. The comparison between flexural strengths obtained from FEA with design values calculated from the current design rules showed that the design rules are conservative. However, they are not always reliable and safe for RHS beams without and with a perforated web for the two material grades at elevated temperatures. In this study, only the design rules specified by Eurocode 3 are shown to be reliable and safe.

Optimisation and testing of simply‐supported WAAM beams

AbstractThe design and performance of optimised wire and arc additively manufactured (WAAM) rectangular hollow section (RHS) beams, with varying material strengths and thicknesses along their lengths, are investigated in this study. Simply‐supported beams under three‐point bending were considered. Size optimisation of the RHS beams was carried out by fixing the nominal outer profile and varying the local thicknesses and steel grades in discrete steps to accommodate the variation of the bending moment along the member length. Two optimised beam specimens were manufactured via WAAM and tested, and were shown to have excellent load‐carrying capacities at greatly reduced self‐weights compared with the conventionally manufactured beams, indicating a considerable increase in their structural efficiency. This study confirms the feasibility of combining materials with different thicknesses and steel grades using WAAM, which provides structural engineers with further design freedom and opportunities to minimise material use.

Multiple-input multiple-output active vibration control of a composite sandwich beam by fractional order positive position feedback

Positive Position Feedback (PPF) is an active vibration control algorithm widely employed for the vibration mitigation of thin-walled structures equipped with active flexural patches. Fractional order PPF (FOPPF) is a recent development of PPF that has been shown to achieve substantially better spillover characteristics, thanks to the inclusion of fractional calculus. However, so far, FOPPF literature has focused almost exclusively on single-input–single-output (SISO) applications, with little consideration of multiple-input-multiple-output (MIMO) capabilities and no experimental work on the subject. To fill this gap, a MIMO FOPPF control architecture was tested numerically and experimentally on a cantilever composite sandwich beam of rectangular section. The feedback algorithm involved two piezoelectric actuators and two piezoelectric sensors in a collocated configuration for the control of the lowest four resonances of the beam, excited by a random external excitation. The participation matrices, necessary for the simulation of the response of the electromechanical system, were obtained with a recently developed experimental method. The fractional orders of derivation, together with other controller parameters such as gain, resonant frequency and damping ratio, were chosen according to an optimization algorithm aimed at the vibration amplitude reduction of the first four resonances of the controlled system. As a result, the performance of the vibration control resulted superior to the equivalent PPF with integer exponents, both in simulations and experiments.

Fire resistance of austenitic stainless steel beams with rectangular hollow sections

AbstractThis paper presents a study on the structural behaviour of stainless steel profiles under fire conditions. An experimental campaign of three‐point bending tests on rectangular hollow section beams of the grade 1.4301 (also known as 304) were conducted, considering both steady‐state and transient state conditions. Prior to those tests, the mechanical characterization of the stainless steel was investigated. The constitutive laws obtained by tensile tests at high temperatures are compared with those recommended in Eurocode 3, whose respective material models were recently proposed for modifications, still requiring complete validation. In addition, numerical modelling of the bending tests has been performed afterwards achieving close approximation to the observed experimental results. Finally, analytical methods to predict the load‐deflection behaviour are also presented. Good agreement between the considered methodologies was attained validating their application on the prediction of the fire behaviour of stainless steel beams.

Numerical Investigation of Flexural Behavior of Reinforced Concrete (RC) T-Beams Strengthened with Pre-Stressed Iron-Based (FeMnSiCrNi) Shape Memory Alloy Bars

Shape memory alloy (SMA) is a material that can change shape in response to external stimuli such as temperature, stress, or magnetic fields. SMA types include nitinol (nickel-titanium), copper-aluminum-nickel, copper-zinc-aluminum, iron-manganese-silicon, and various nickel-titanium-X alloys, each exhibiting unique shape memory properties for different applications. Reinforced concrete (RC) T-beams strengthened and pre-stressed with Fe-SMA bars are numerically investigated for their flexural response under the influence of various parameters. The bars are embedded in a concrete layer attached to the beam’s soffit. Based on the numerical results, it was found that increasing the compression strength from 30 to 60 MPa slightly improves the beam’s strength (by 2%), but it significantly increases its ductility by approximately 45%. As opposed to this, the strength and ductility of the pre-stressed T-beam are considerably improved by using a larger diameter of Fe-SMA bars. Specifically, using 12 mm Fe-SMA bar over 6 mm resulted in 65% and 47% greater strength and ductility, respectively. Furthermore, this study examines the importance of considering the flange in the flexural design of pre-stressed beams. It is seen that considering a 500 mm flange width enhanced the ductility by 25% compared to the rectangular-section beam. The authors recommend further experimental work to validate and supplement the calculations and methodology used in the current numerical analysis.

Semi-empirical synergetic analysis of the shear capacity of steel fibre reinforced concrete slender beams of rectangular-sections without stirrups

Although steel fibre reinforced concrete (SFRC) has been widely used in various engineering structures, there is a lack of a reliable and unified method for predicting the shear capacity of reinforced SFRC slender beams. After conducting an extensive review of previous studies on the slender beams of rectangular-section without stirrups and the SFRC with the cold-drawn hook-end steel fibre, a database was developed based on 280 reinforced SFRC slender beams that failed in shear accompanied by 37 reinforced SFRC slender beams failed in flexure and 71 reinforced conventional concrete beams failed in shear. The comparison between the experimental results and the results predicted using existing formulae revealed that a more accurate empirical model is required to evaluate the effects of multi-factors on the shear strength of the reinforced SFRC slender beams without stirrups. Based on the model of the critical shear crack, a semi-empirical synergetic equation is developed to predict the shear capacity of reinforced SFRC slender beams without stirrups. The enhanced shear resistance of SFRC in the shear-compression zone, the dowel action of longitudinal tensile steel bars, the aggregate interlock between sides of critical shear crack, and the shear resistance of steel fibres across the shear cracks as well as the size effect of sectional depth are considered. Good prediction results with small dispersion can be obtained using the proposed semi-empirical model. Conservative and simplified equations are also provided as the lower bound of the experimental shear strength of the reinforced SFRC slender beams without stirrups for easier implementation of the proposed model in real engineering design practice.

Analysis, Comparison and Optimization of T-type Section Beam and Rectangular Section Beam based on Engineering Training

The research on the optimization of T-beam under the condition that both T-beam and rectangular section beam meet the section bearing capacity. Through theoretical calculation, component fabrication, experiment, and data collection and analysis, fully explore the advantages of a T-beam, optimize the experimental beam transport process, and apply it to practical teaching to improve the safety and convenience of the experimental process.

Design of cold-formed high strength steel square and rectangular hollow section beam–columns

Cold-formed high strength steel (CFHSS) square and rectangular hollow section (SHS and RHS) beam–columns were investigated in this study with an objective to evaluate the applicability of existing design rules given in American, Australian and European codes for SHS and RHS beam–columns of S700, S900 and S1100 steel grades, and subsequently, provide economical and reliable design rule for CFHSS SHS and RHS beam–columns. A comprehensive numerical investigation was performed in this study, where the values of flat width-to-thickness ratio of the tubular sections ranged from 7.5 to 96. The constitutive model developed for CFHSS tubular members was used in the numerical investigation. Global and local geometric imperfections were also included in the numerical models. In total, 465 data were compared with the nominal capacities predicted from American, Australian and European codes, including 390 numerical data obtained in this investigation. The safety levels of design rules given in these standards were examined by performing a reliability analysis. It has been demonstrated that the current design rules given in the American, Australian and European codes provide conservative predictions. A modified design method based on the recommendations given in European code was proposed in this study. Overall, it has been proved that the proposed design rule provides accurate and reliable predictions for the design of cold-formed S700, S900 and S1100 steel grades SHS and RHS beam–columns.

On the unloading action of torques in beams reinforced concrete coffered floors

The purpose of this work is the qualitative and quantitative identification of the unloading effect in the beams of direct coffered floors from the action of torques. To solve the problem in the computer complex SCAD, the bending and torsional moments in the beams of a direct coffered floor hinged along the contour with a plan size of 8.0 8.0 m with different widths of the beams installed with a step of 1.0 m were determined. As a computer model, a rod finite element model of beams of rectangular section with a direct application of a linear load to them according to the law of a triangle was used, as the most accurate finite element method. Analytical calculation of the structure is carried out. The calculation data of computer models showed that as the width of the beams increases, the torques in them increase, while the span bending moments decrease. The width of the support contour beam affects the support bending moment of the span beams, which occurs at the point of their joining. The paper presents graphs of the dependence of the values of the span bending moment, the support moment and the torque on the width of the caisson beams. The analytical method for calculating coffered floors does not take into account the rigidity of the support contour, the presence of torques in the beams, their effect on bending span moments and deflections of the structure. This is one of the reasons for the discrepancy between the data compared by the researchers.

Characterization of strength, modulus, and fatigue damage properties of cement stabilized macadam based on the double modulus theory

• Flexural tensile strengths calculated with tensile and compressive differences are reduced by nearly 20 % when compared to those calculated without tensile and compressive differences. • A power function decay model of the tension–compression moduli of cement stabilized macadam was established in the four-point bending fatigue test. • The fatigue damage model of cement stabilized macadam was established and its accuracy was verified. Cement stabilized macadam (CSM) is a mixture created by combining cement as a binding material, water, and various particle sizes of minerals. The cement stabilized macadam material exhibits different moduli in tension and compression due to both its mechanical properties and the mechanical response in the asphalt pavement structure. To explore the strength, modulus and fatigue damage characteristics of CSM under different tensile and compressive modulus, this paper carried out the research. The calculation formulas for flexural tensile strength and tension–compression modulus were derived based on the difference in tension–compression modulus. A four-point bending strength test of CSM was carried out. Four-point bending fatigue tests with varying stress ratios were performed. It reveals deterioration laws of tension–compression modulus during fatigue process. The double logarithmic fatigue equation of CSM, as well as its nonlinear fatigue damage evolution equation, are established based on fatigue life results. The results of an analytical solution for fatigue life of rectangular section beams based on damage mechanics were obtained and compared to the results of four-point bending fatigue tests. The results reveal that the modulus of CSM differs in tension and compression. The calculated flexural tensile strength with the tension and compression difference is nearly 20 % lower than without the difference. The calculation approach that does not account for the difference in tension and compression overestimates the flexural tensile strength of CSM. The tension–compression moduli of CSM exhibit a power function decay law in the four-point bending fatigue processes. In the first stage, the dynamic modulus decays at a steady rate, accounting for 90 % of total fatigue life. The second stage in the life ratio of 0.9 occurs when the decay rate of the modulus rapidly increases and enters the stage of sharp decay. Based on the results of the four-point bending test, the modulus decay model was created. The decay parameter m has an exponential relationship with the stress ratio. The relative errors between the mean values of fatigue life tests and the predicted values of the analytical solutions range from 10.8 to 30.6 percent. The established fatigue damage equation for CSM can better reflect its fatigue damage evolution law. The research findings have great significance to solve the determination of pavement materials parameters based on the difference in tension and compression modulus. It also has a specific reference value for asphalt pavement design theory and calculation method when the varied modulus of tension and compression are considered.

Analysis of springback for multiple bending considering nonlinear unloading-reloading behavior, stress inheritance and Bauschinger effect

Multiple bending faces more challenges in accurate springback prediction for difficult-to-form metals such as aluminum alloys and high-strength steels. This is attributed to stress inheritance (the effect of residual stress on subsequent bending), the Bauschinger effect and nonlinear unloading-reloading behavior, which have a more significant effect on the springback of difficult-to-form metals. A new analytical model considering these key factors was established, and the solution method of a series of key equations were given. The Chaboche hardening model and two elastic models (chord modulus and nonlinear elastic model) were used to characterize the constitutive properties. Experiments were performed to verify the analytical model, and the effects of the above three factors on springback were investigated. The results show that the analytical results are in good agreement with the experimental results, and the average relative error of the 6061 aluminum alloy rectangular section beam under two cycles of positive and reverse pure bending is within 3 %. Compared with the existing models, the analytical model established in this study has higher prediction accuracy and faster solution speed. • A new analytical model of springback for multiple bending was established. • Yoshida and Amaishi nonlinear elastic model was introduced in the analytical model. • Nonlinear unloading-reloading behavior, stress inheritance and the Bauschinger effect are comprehensively considered. • Accurate prediction of springback for multiple bending was achieved, and the effect of the three factors on springback was investigated.

7A04-T6 high-strength aluminium alloy SHS and RHS beams under pure bending—Testing, modelling and design recommendations

This paper presents both experimental and numerical investigations into the flexural behaviour of 7A04-T6 high-strength aluminium alloy rectangular and square hollow section (RHS/SHS) beams subjected to four-point bending. A total of 15 bending tests were conducted on RHS and SHS beams with non-slender and slender cross-sections. The test set-up, instrumentation, experimental procedure and results, including measured material properties, failure modes, moment capacities of specimens, were fully reported. Based on the developed and validated finite element (FE) models, an extensive parametric study over a wide range of cross-section slenderness and width-to-height ratios was carried out. Following this, moment capacities obtained from the tests and FE analyses were used to assess the accuracy of current codified design methods provided by the European code (EN 1999-1-1:2007), Chinese standard (GB 50429-2007) and American Aluminium Design Manual (ADM 2015). It is shown that the predicted design resistances were generally conservative up to 37%. Towards meeting the need of a more comprehensive design method, the continuous strength method (CSM) was extended to the 7A04-T6 high-strength aluminium alloy SHS and RHS beams under pure bending and proved to be more accurate for predicting the moment capacity. Finally, the reliability of these four design methods were calculated and confirmed to satisfy the corresponding target reliability indices.

Design Aids for Beams of Rectangular Cross Section with Parabolic Haunches: Part 2

In this paper, the most used design aids for beams of rectangular section with parabolic haunches are presented. The beam is found subjected to concentrated load localized anywhere on the beam, and takes into account the bending and shear deformations to obtain the fixed-end moments factors, which is the main contribution of this research work. The first part of this work presents the design aids for the same type of beams to obtain the carry-over factors, the stiffness factors, and the fixed-end moments factors are obtained for a uniformly distributed load. The variables and the simplifications are the same as in the part 1. Also, a numerical example is shown using the design aids, and it is compared with the equations previously presented by the authors in a paper prior to this document, and the results are equal to a three-digit approximation. Therefore, design aids provide a great tool of help for structural engineers by the greatly time-savings.

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.

Study on different moduli T-section beams: Pure bending elastic solution and PMMA experiment

In order to accurately analyze the bending problem of T-section beams, a novel analytical method is proposed based on the simplified mechanical model of T-section beams with different tension and compression moduli. Firstly, the expressions of the neutral layer position, normal stress, bending stiffness and displacement of the four-point bending test beam of two types of T-section beams are derived based on the classical beam theory. Then, the expressions of the rectangular section beam are obtained by degenerating the expressions of T-section. Finally, the proposed method is verified via the finite element simulation and the four-point bending test beam of two types of T-section beams with Polymethyl methacrylate (PMMA). From the comparative analysis, the theoretical solutions of the proposed analytical method agree well with the results of the experimental data and the finite element. The flexural modulus can be obtained accurately by the proposed method with the compression and tensile moduli of the beam, which can be used as an efficient and theoretical approach to determine the flexural modulus of the T beam instead of conducting bending experiments.

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.

Design Aids for Beams of Rectangular Cross Section with Parabolic Haunches: Part 1

In this paper, the most used design aids for beams of rectangular section with parabolic haunches are presented. The variables considered are: the heights at its two ends vary parabolically, the width of the beam is constant, and the height in the central part is constant. The beam is found subjected to a uniformly distributed load, which takes into account the bending and shear deformations to obtain the fixed-end moments factors, the carry-over factors and the stiffness factors, which is the main contribution of this research work. The simplifications are: the heights at its two ends are equal, as these are the most used by aesthetics in architectural constructions, and the total height of the beam in the central part is considered of 0.10 of the length of the beam according to the ACI (American Concrete Institute) code for deflection control. Also, a numerical example is shown using the design aids, and it is compared with the equations previously described by the authors in an article prior to this document, and the results are equal to a three-digit approximation. Therefore, design aids provide a great tool of help for structural engineers by the greatly time-savings.