Flexure Torsion Research Articles

Experimental and numerical investigations into torsional-flexural behaviours of railway composite sleepers and bearers

Abstract Fibre-reinforced foamed urethane (FFU) composite sleepers and bearers are safety-critical components installed in complex railway switches and crossings. Not only does they need to provide vertical track support, the composite sleepers and bearers must also endure longitudinal and lateral actions stemming from complex wheel and rail interactions. In reality, the railway bearers at crossing noses are susceptible to coupling torsional-flexural loading. The complex non-linear behaviours have never been investigated numerically nor experimentally. It is thus necessary to comprehend torsional-flexural behaviours of FFU composite sleepers and bearers through finite element and experimental approaches. 3D finite element modelling of FFU composite beams have been established to predict the non-linear coupling behaviours. Three specimens of FFU beams have been prepared for robust experiments under each load case. Our studies exhibit excellent agreement between numerical and experimental results. The ductile failure behaviours (post yield point) have been observed from the experiments. Considerable effects of load eccentricity on the flexure–torsion behaviours of the composite members can also be noted. In addition, the load-eccentricity curves have been identified to portray the non-linear behaviour of the railway components under coupling flexural and torsional loadings. The new insights considering their load–displacement relationships, modes of failure and damage, flexural and torsional interactions are the precursors for railway engineers to design and adopt FFU composite sleepers and bearers in practice where complex wheel/rail interface generally causes coupling torsional and vertical loading conditions.

Combined bending-torsion and compression-bending-torsion behaviours of reinforced concrete-filled thin-walled corrugated steel tubes

Reinforced concrete-filled thin-walled galvanized corrugated steel tube (RCFCST) is a novel composite member that has application potential in extremely corrosive environments and seismic activity regions. A series of preliminary works have been conducted on its compressive, flexural, shear, and torsional behaviour. However, the combined loading condition is almost inevitable in practice. The correlations between the flexural and torsional behaviour of RCFCSTs are unique due to the special spiral corrugated profile, which is unclear and needs to be addressed. This paper, therefore, presents an experimental investigation of the RCFCST under combined bending-torsion and compression-bending-torsion loads, encompassing the main test variables of torsion-to-bending ratios, torsional directions, and axial compression ratios. The loading set-up and instruments have been introduced in detail. The failure modes, lateral load versus lateral displacement curves, bending moment versus flexural lateral displacement curves, torsion moment versus torsional angle curves, and strain distributions are carefully addressed. The working mechanisms of the RCFCST under monotonic combined loads are discussed, with a particular explanation of the dependent behaviour on the torsion-to-bending ratios and torsional directions. The applicability of the existing design methods for the bearing capacity of RCFCST specimens under combined loads is examined carefully, with specific design suggestions proposed.

Flexure–Torsion Response of Compressed Open Reinforced-Concrete Cores: Experimental Strain Gradients, Numerical Methods, and Interaction Diagrams

Flexure–Torsion Response of Compressed Open Reinforced-Concrete Cores: Experimental Strain Gradients, Numerical Methods, and Interaction Diagrams

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

Flexural Torsional Buckling of a Beam from the Dee Bridge of 1846 - Analytical and Finite Element Analyses

The Industrial Revolution in Victorian England was a period marked by rapid development of the machine industry, accompanied by new technologies in metallurgy and a need for transport between economic areas that was fast, cheap and convenient. This is a period when the railway transport arose and in a short time acquired an image familiar to us to this day. Passage of train sets across rivers and hard-to-reach areas requires transport facilities. In this period, an extremely large number of bridges and aqueducts were built, which have different constructive solutions, different technologies are applied and they are made of different materials, depending on the preference of their creator. This paper examines the collapse of one of the beams of the Dee Bridge on 24 May 1847. The analysis carried out shows the irrationality of the cross-sectional dimensions and types of girder supports witch generate large compressive forces in the beam, leading to flexural torsional buckling.

Study of Practical Analysis Method for Shear Warping Deformationof Composite Box Girder with Corrugated Steel Webs

Shear warping deformation is an important part of the flexural and constrained torsion analysis of composite box girder with corrugated steel webs (CBG-CSWs), which is also the main reason for the complex force analysis of box girders. A new practical theory for analyzing shear warping deformations of CBG-CSWs is presented. By introducing shear warping deflection and corresponding internal forces, the flexural deformation of CBG-CSWs is decoupled to the Euler-Bernoulli beam (EBB) flexural deformation and the shear warping deflection. On this basis, a simplified method for solving shear warping deformation using the EBB theory is proposed. According to the similarity of the governing differential equations of constrained torsion and shear warping deflection, a convenient analysis method for the constrained torsion of CBG-CSWs is derived. Based on the decoupled deformation states, a beam segment element analytical model applicable to EBB flexural deformation, shear warping deflection, and constrained torsion deformation is proposed. A variable section beam segment analysis program considering the variation of section parameters is developed for CBG-CSWs. Numerical examples of constant and variable section continuous CBG-CSWs show that the stress and deformation results obtained by the proposed method are in good agreement with the 3D finite element results, verifying the effectiveness by the proposed method. Additionally, the shear warping deformation has a great influence on the cross-sections near the concentrated load and middle supports. This impact along the beam axis decays exponentially, and the decay rate is related to the shear warping coefficient of the cross-section.

Multiagent Control of Airplane Wing Stability with “Feathers” under the Flexural Torsional Flutter

This paper proposes a novel method for the unbounded oscillation prevention of an aircraft wing under the flexural torsional flutter, an innovative multiagent attitude to control an aircraft wing with a surface consisting of managed rotating “feathers” (agents). Theoretical evaluation of the method demonstrates its high aptitude to avoid an aircraft wing’s flexural-torsional vibrations via expansion of the model’s ability to dampen the wing oscillations. It potentially allows increasing an aircraft’s speed without misgiving of the flutter. A new way to control an aircraft wing based on the Speed-Gradient methodology is suggested to increase the maximal possible flight speed without a flutter occurrence. Provided experiments demonstrate the theoretical advantage of the multiagent approach to the “feathers” rotation control.

Formulation Of The Total Potential Energy Functional Relevant To The Stability Analysis Of A Doubly Symmetric Single (DSS) Cell Thin- Walled Box Column In Line With Raleigh- Ritz Method

Purpose: This work is concerned with the formulation of peculiar Total Potential Energy Functional (TPEF) for a Doubly Symmetric Single (DSS) cell Thin -walled Box Column (TWBC). The formulated Energy Functional Equations support the stability analysis of a DSS cell thin-walled box (closed) column cross-section using Raleigh - Ritz Method (RRM) with polynomial shape functions.
 Methodology: This present formulation is based on the governing TPEF developed by Nwachukwu and others (2017). The polynomial shape functions (only the first two coordinate polynomial shape functions) for different boundary conditions were generated first, and then followed by the formulation of TPEF for different boundary conditions of the DSS cell TWBC.
 Findings: The Raleigh- Ritz based formulated TPEF equations are found suitable, handy and simple to be used in the Flexural(F) , Flexural- Torsional(FT) and Flexural- Torsional- Distortional(FTD) buckling/stability analysis of DSS cell TWBC cross-section where data obtained (critical bulking loads) will be compared with the works of other authors in subsequent papers.
 Conclusion: Henceforth it is recommended that additional work should be done using more than first two coordinate polynomial shape functions in order to increase the accuracy of RRM.

Flexural–torsional failure and DSM design of fixed-ended cold-formed steel columns at elevated temperatures

Recently, Dinis et al. (2019,2020) reported in-depth numerical investigations showing that the current Direct Strength Method (DSM) global design curve may severely underestimate the flexural–torsional (FT) failure loads of fixed-ended cold-formed steel (CFS) columns with slenderness above 1.5. This finding was based on the analysis of columns exhibiting various cross-section shapes and geometries, and covering wide slenderness ranges. Moreover, these authors used the failure load data gathered to develop, and propose a novel DSM column strength curve set that was shown to improve considerably the FT failure load prediction for those columns. The purpose of this work is to extend the scope of the previous investigations to fixed-ended CFS cold-formed columns failing in FT modes under elevated temperatures (up to 800 °C). The results presented and discussed consist of column FT post-buckling equilibrium paths and failure loads, obtained through geometrically and materially non-linear Ansys shell finite element analyses — to ensure covering wide FT slenderness ranges, several room-temperature yield stresses are considered. The model prescribed in Part 1–2 of Eurocode 3, for cold-formed steel, is adopted to describe the temperature-dependence of the steel material properties. Lastly, the numerical failure loads assembled in this work, together with numerical and experimental ones collected from the literature, are used to propose a modification of the DSM-based FT strength curve set developed by Dinis et al. (2020), making it capable of handling FT failures under elevated temperatures. Since the merit assessment of the modified strength curve set shows a visible improvement in FT failure load prediction quality, it is fair to argue that it constitutes a good starting point to search for an efficient general DSM-based design approach for CFS columns failing in FT modes at elevated temperatures.

Inclined composite guardrails/safety barriers – Numerical and experimental evaluation of their transverse stiffnesses and compliance with standards

Three-point flexure and axial torsion tests were undertaken to establish the longitudinal elastic flexural and in-plane shear moduli of pultruded GFRP tubes. They were used to define one-dimensional two-node beam elements for modelling single- and two-bay inclined guardrails with inclinations up to 60°. Subsequently, three-dimensional FE models were developed to analyse more accurately single- and two-bay 30° inclined guardrails. The results from these analyses were compared with those of full-scale load tests on 30° inclined guardrails subjected to transverse normal preload, usability, and ultimate loads applied to the handrails. It is shown that the analysis results based one-dimensional elements significantly underestimate the mean handrail deflections and over-estimate the guardrails’ transverse stiffness. By contrast, using three-dimensional elements in the FE models give more accurate predictions, with mean handrail deflections 9% and 14–16% lower than single- and two-bay test values respectively. The corresponding percentages for mean transverse stiffnesses are 10% and 12.5 – 14.3% higher respectively. It was also observed that the responses of the guardrails were linear, the residual deflections on unloading were less than permitted for the preload, usability and ultimate loads. Furthermore, neither the single- nor the two-bay 30° inclined guardrails sustained any damage.

Nonlocal Analysis of the Flexural-Torsional Stability for FG Tapered Thin-Walled Beam-Columns.

This paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according to the Eringen nonlocal elasticity assumptions. The stability equations of the problem and the associated boundary conditions are derived based on the Vlasov thin-walled beam theory and energy method, accounting for the coupled interaction between axial and bending forces. The coupled equilibrium equations are solved numerically by means of the differential quadrature method (DQM) to determine the flexural–torsional buckling loads associated to the selected structural system. A parametric study is performed to check for the influence of some meaningful input parameters, such as the power-law index, the nonlocal parameter, the axial load eccentricity, the mode number and the tapering ratio, on the flexural–torsional buckling load of tapered thin-walled FG nanobeam-columns, whose results could be used as valid benchmarks for further computational validations of similar nanosystems.

Analysis of Structural Vibrations of Vertical Axis Wind Turbine Blades via Hamilton’s Principle — Part 3: Pitch Angle and Equilibrium State

Pitch angle is one of the most important parameters of wind turbine blade. This study is aimed to investigate the effect of the pitch angle on the deformation of a VAWT. Lagrangian mechanics and Euler’s beam theory are used to derive the motion equations of linear structural vibration for straight blade vertical axis wind turbine blade with the pitch angle [Formula: see text]. The complete equations of motion take account of the 4-DOF deformation of flexural–flexural–torsion–extension as well as the material damping. Vibration analysis of generalized displacement about the equilibrium state (GDAES) is carried out with respect to the displacement of the equilibrium state (DOES), which is separated from the motion of vibration. After simplifying the equilibrium equation of 4-DOF into 1-DOF system, the exact solution of displacement [Formula: see text] of the equilibrium state is derived. The correction [Formula: see text] of [Formula: see text] due to the pitch angle and the characteristics of [Formula: see text] with constant linear speed are analyzed. Furthermore, we investigate the coupling effect of lateral bending and axial extension of the blade on [Formula: see text] is analyzed. Finally, the exact solution of [Formula: see text] is verified by the central difference method.

Effect of fiber content and their hybridization on bending and torsional strength of hybrid epoxy composites reinforced with carbon and sugar palm fibers

This study aims to investigate the effect of fiber hybridization of sugar palm yarn fiber with carbon fiber reinforced epoxy composites. In this work, sugar palm yarn composites were reinforced with epoxy at varying fiber loads of 5, 10, 15, and 20 wt % using the hand lay-up process. The hybrid composites were fabricated from two types of fabric: sugar palm yarn of 250 tex and carbon fiber as the reinforcements, and epoxy resin as the matrix. The ratios of 85 : 15 and 80 : 20 were selected for the ratio between the matrix and reinforcement in the hybrid composite. The ratios of 50 : 50 and 60 : 40 were selected for the ratio between sugar palm yarn and carbon fiber. The mechanical properties of the composites were characterized according to the flexural test (ASTM D790) and torsion test (ASTM D5279). It was found that the increasing flexural and torsion properties of the non-hybrid composite at fiber loading of 15 wt % were 7.40% and 75.61%, respectively, compared to other fiber loading composites. For hybrid composites, the experimental results reveal that the highest flexural and torsion properties were achieved at the ratio of 85/15 reinforcement and 60/40 for the fiber ratio of hybrid sugar palm yarn/carbon fiber-reinforced composites. The results from this study suggest that the hybrid composite has a better performance regarding both flexural and torsion properties. The different ratio between matrix and reinforcement has a significant effect on the performance of sugar palm composites. It can be concluded that this type of composite can be utilized for beam, construction applications, and automotive components that demand high flexural strength and high torsional forces.

Investigation on Buckling Behaviour of GFRP Angle Sections with Bolted Connections in Lattice Towers

Glass fibre-reinforced polymer (GFRP) angle is an emerging alternative material to conventional steel angle sections in transmission line (TL)/communication towers, because of their superior characteristics such as high strength to weight ratio, high tensile strength, better corrosion resistance, light in weight for handling and transportation, etc. The GFRP angle sections are used as leg, bracing, tie and redundant members in towers, in which these members are subjected to reversal of tensile and compressive forces due to wind. The compression strength is mainly governed by the buckling characteristics of angle sections. There is lack of design criteria concerning the use of GFRP angle sections with bolted connections in lattice towers. In the present study, experimental investigation is conducted on concentrically loaded GFRP angle sections with bolted connections in TL/communication towers. The material properties were determined based on compression and in-plane shear coupon test. The existing mathematical model to determine the buckling characteristics such as torsional–flexural, flexure and pure torsion is considered. The theoretical approach to determine its limiting effective length governing the transition from torsional–flexural to flexural buckling mode for GFRP angle sections with bolted connections is proposed in this paper. The proposed formulation is validated with experimental investigation conducted at component level on GFRP angle sections with bolted connections at both ends for different slenderness ratios ranging from 40 to 100 along with numerical investigation using FEA software, ANSYS. Experimental investigation was also carried out for validation at sub-structural level on ‘X’-braced panel made entirely of GFRP angle sections. The panel failed prematurely during testing, and the reason for this failure was observed due to excessive bending stress exerted on the free length of stub member. Based on the results of the investigations, suitable recommendations for use of GFRP angle sections in lattice tower are proposed.

Evaluating the performance of a configurable finite element model as a tool in composite catheter design

Currently there are limited predictive modeling tools available for composite interventional catheter design. Most interventional catheter development involves iteration based design. Composite interventional catheters typically consist of a PTFE inner layer wrapped with a fine strand, metal reinforcement layer covered with a TPE (thermoplastic elastomer) outer layer. Fast reliable computational based techniques for early stage catheter design would limit the number of prototypes required to get to concept or design freeze stage therefore reducing development time. This paper’s goal is to examine how effective FEA is as a technique for predicting the performance of a composite catheter shaft. The steps taken and challenges overcome in creating a configurable FE model for a spirally reinforced composite catheter are outlined. The paper presents Finite Element (FE) generated data for tensile yield. This is a fundamental performance parameter in interventional catheter design. Catheters are designed to operate below their yield point. Models developed for simulating tensile yield can likely be adapted to simulate other performance characteristics such as flexural properties and torsion characteristics as part of future work. Data from FEA analysis is compared with data from physically testing catheters built to the same specification as that used in the FE model configuration.

Elastoplastic Flexure of Round Steel Beams. 1. Springback Coefficient

Round steel beams are widely used in metallurgy, manufacturing, and construction. It is often irreplaceable in the production of machines and mechanical equipment on account of its excellent corrosion resistance and remarkable strength. Cylindrical springs for road and railroad vehicles are manufactured from round beams by means of special bending machines. Round beams also serve as blanks in the production of seamless pipe for the oil and gas industry. Stepped round beams are used as rollers in rolling and straightening mills. Steel rebar is manufactured from round beams of similar size. Outside Russia, the main producers of continuous-casting machines for the production of round billet are SMS Demag (Germany), Danieli (Italy), SMS Concast (Switzerland), and Siemens VAI (Austria). Russian producers include AO Chusovskii Metallurgicheskii Zavod, PAO Chelyabinskii Metallurgicheskii Kombinat, AO Volzhskii Trunbnyi Zavod, OAO Nizhneserginskii Metizno-Metallurgicheskii Zavod, AO Chepetskii Mekhanicheskii Zavod, PAO Severskii Trubnyi Zavod, and PAO Taganrogskii Metallurgicheskii Zavod. In the manufacture of parts from round beams and their use, they often experience elastic or elastoplastic flexure or complex torsion and flexure. In the present work, we propose an analytical method of calculating the residual curvature of round steel beams in elastoplastic flexure. In the calculations, the residual curvature of the round beam after flexure and the bending moments of the beam cross section in flexure are determined as a function of the beam radius, the Young’s modulus, the yield point, and the hardening modulus of the steel. The results may be widely used at manufacturing and metallurgical plants.

Experimental determination of fracture toughness for adhesively bonded composite joints

The characterization of fracture toughness or critical energy release rate of adhesive joint in composite structures is a key parameter. In the present study, fracture toughness of adhesively bonded composite joints is experimentally investigated for the basic fracture modes. Experiments are conducted on the double cantilever beam, end notched flexure and edge crack torsion specimens to determine the fracture toughness of three modes, namely mode-I, mode-II and mode-III. Specimens are bonded with epoxy adherent and cured at room temperature. The fracture toughness values of mode-II and mode-III are 2.6 and 4.6 times respectively of mode-I. Acoustic emission (AE) technique is also employed to aid in determining the fracture toughness of bonded joints. The results indicate that AE signals have good correlation with load–displacement behavior to determine the fracture initiation stage especially in the mode-II loading.

Strength of multi-span composite beams subjected to combined flexure and torsion

An improved understanding of the performance of composite beams subjected to combined flexure and torsion is essential for practical design as such loading states are very common in bridges for the main girder and in buildings for edge beams. Multi-span steel–concrete composite beams consisting of two steel joists and one concrete slab are concerned herein, on which an experimental study and finite element (FE) modelling analyses are presented. Eight reduced scale beams under combined flexure and torsion to varying degrees are tested, with both full and partial shear connection being incorporated. Either flexure-dominated or torsion-dominated failure modes are observed in each test depending on the ratio between the bending and torsional moments applied externally. Load-deformation responses, ultimate strengths as well as flexure–torsion interaction of all specimens are also reported and discussed. Based on the experimental outcomes, a three-dimensional FE model is developed and further validated against the test results, and an extensive range of parametric analyses are undertaken by using the FE model. It is indicated that in addition to well-known parameters relating to the concrete slab and stirrups, the torsional strength of multi-span composite beams is also sensitive to the degree of shear connection, spacing of the joists and span-to-depth ratio. Contributions of the steel joist and its constraint on the slab towards the torsional strength are increased. With respect to their flexure–torsion interaction relation, no increase in the torsional strength is observed within the presence of combined flexure, and vice versa. The interaction is insensitive generally to various parameters considered herein and the test results exhibit consistent phenomenon. Design guidance and new equations for predicting the torsional strength and the flexure–torsion interaction relation are proposed based on the test and FE analysis results as well as a comprehensive review of existing approaches in the literature.

CVBEM solution for De Saint-Venant orthotropic beams under coupled bending and torsion

The aim of this paper is to provide a solution for the coupled flexure–torsion De Saint Venant problem for orthotropic beams taking full advantage of the complex variable boundary element method (CVBEM) properly extended using a complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. The proposed method returns the complete stress field and the unitary twist rotation of the cross section at once by performing only line integrals. Numerical applications have been reported to show the validity and the efficiency of the proposed modified CVBEM to handle shear stress problems in the presence of orthotropic materials.

Seismic performance of circular RC bridge columns with flexure–torsion interaction

Reinforced concrete (RC) bridge columns for skewed, curved bridges and other kinds of irregular bridges can be subjected to combined loadings with axial load, shear force, flexure and torsion under multi-dimensional earthquake excitations. Combined loadings including torsion probably affect the seismic performance of these bridge columns. The experimental investigation on the seismic performance of circular RC bridge columns under combined cyclic bending and torsional loading is conducted in this paper. Twelve circular RC bridge column specimens are tested under various loading conditions: cyclic bending, cyclic torsion, and combined cyclic torsion and cyclic bending. Several combinations of cyclic bending and cyclic torsion are applied to evaluate the interaction between torsion and flexural capacity of bridge columns. The experimental results showed that the flexural capacity decreases and the damage tends to occur upward outside the flexural plastic hinge region as the level of applied cyclic torsion increases, and the torsional capacity decreases as the level of applied cyclic bending increases. The failure mode and deformation characteristics of RC bridge columns will be changed due to the effect of combined flexural and torsional loadings. The locking and unlocking effect of the spiral reinforcement on torsional and flexural envelopes of columns under pure torsion and combined cyclic bending and torsion is found. The influence of aspect ratio, longitudinal reinforcement ratio and type of spiral reinforcement on the seismic performance of columns under combined action with the same rotation-drift ratio is also discussed. An empirical flexural and torsional hysteretic model for circular RC columns with single spiral stirrup under combined cyclic bending and torsion is proposed based on the experimental results.