Monosymmetric Beams Research Articles

Behaviour, design, and reliability of monosymmetric I-beams at elevated temperature

Steel is the preferred choice among structural designers because of its exceptional properties compared to other available materials. However, steel is vulnerable to fire risk, as its material characteristics deteriorate rapidly at high temperatures. It results in the instability and failure of unsupported flexural components. In the present study, a numerical analysis is conducted to explore how load patterns and temperatures impact the failure characteristics of monosymmetric I-section beams. The numerical model is validated using existing experimental tests conducted at elevated temperatures. Subsequently, the validated model is employed for the numerical study. The analysis uses the ABAQUS software. The study is conducted for beam lengths ranging from 2.5 to 20 m, incorporating different degrees of monosymmetry. The behaviour of the beams is evaluated under steady and transient-state thermal conditions, using ISO 834 fire, considering uniform/non-uniform loading patterns on the beam. The results highlighted the shortcomings in Eurocode 3 provisions related to the failure patterns of monosymmetric I-beams, particularly for cases involving point loads and uniform moments. Subsequently, a proposed new methodology for calculating design capacity for monosymmetric beams is adopted from past literature and evaluated to ensure its reliability and accuracy in predicting monosymmetric beam capacities at elevated temperatures.

A spatial stability theory of thin-walled steel beams pre-stressed by spatially inclined un-bonded cables and its FE formulation

A spatial stability theory of mono-symmetric thin-walled steel beams pre-stressed (PS) by spatially inclined cables is firstly derived using an energy method where it is assumed that deviators are rigid. Its FE formulation is then presented under bonded/un-bonded multi-deviator conditions. After that, validity and accuracy of the present formulation is demonstrated through numerical examples. Finally, effects of initial tension, deviator numbers, inclined cable profiles, and un-bonded/bonded conditions on lateral-torsional buckling (LTB) of the PS bi-/mono-symmetric beams are investigated under external loadings. Particularly, new findings on LTB characteristics of the PS beams are presented with a specific emphasis on the effects of increasing initial tension.

Bending–torsion coupled wave in thin-walled mono-symmetric metabeam: A non-dimensional analysis

The influence of the periodic resonators on wave dispersion of a thin-walled mono-symmetric beam is studied in this paper. The primary focus is to develop a non-dimensional framework to investigate the coupled bending–torsion wave propagation analytically. The resonators are placed eccentrically and are capable to form a subwavelength attenuation band in the beam due to its periodicity. The governing equations corresponding to the bending and torsional motion of a metabeam are presented in a dimensionless form, including the warping effect. The transfer matrix approach is adopted to obtain the dispersive phenomena using the Bloch–Floquet principle. The modal characteristics of a mono-symmetric beam without a resonator are computed from the frequency response function and are validated with finite element results. Subsequently, the impact of various non-dimensional parameters on the attenuation band and band merging, conversion, and bifurcation phenomena are investigated through a comprehensive parametric study. It is observed that the occurrence of the band gap primarily depends on the resonator properties and its location. A substantial band gap is achieved in the low-frequency range, which will be useful for the application in the field of vibration control and acoustics.

Separating and detecting the vertical and torsional mode shapes of thin-walled girders from vehicle’s contact responses by wavelet transform

The contribution of this paper is to separate and detect the vertical and torsional-flexural mode shapes of thin-walled girders from the traced contact responses of the two wheels of a single-axle test vehicle. To start, closed-form solutions are derived for the vertical, lateral, and torsional vibrations of a mono-symmetric beam. Next, the two wheels’ contact responses back-calculated from the vehicle’s responses are manipulated to yield separately the vertical and torsional responses of the bridge, which are free of vehicle’s frequencies. Then, the wavelet transform is employed to recover the respective vertical and torsional mode shapes. The present treatment on mode shape recovery of thin-walled girders is an extension of the previous work on frequency identification. This study indicates that: (1) the vertical and torsional mode can be separated and detected from the respective responses by the wavelet transform with no knowledge of relative shape amplitudes; (2) more modal properties of the bridge can be detected from the contact than vehicle response; (3) the proposed method for mode shape recovery is robust with regard to various factors; and (4) ongoing traffic facilitates the recovery of bridge mode shapes, including the torsional ones, even under pavement roughness.

LTB analysis of pre-stressed mono-symmetric thin-walled beams with deviators under non-uniform bending moments using a simplified FEM

A FE formulation has been newly presented for the lateral-torsional buckling (LTB) analysis of an externally pre-stressed (PS) steel beam, possessing deviators under non-uniform bending moments. Firstly, the total potential energies of the PS mono-symmetric thin-walled beams in possession of un-bonded/bonded deviators are derived depending on the number of deviators. Afterwards, the in-plane solutions of the PS mono-symmetric simple/cantilever beams under the lateral load can be analytically derived through the use of discontinuous functions. A simplified FE procedure is then developed based on the total potential energy, taking into consideration the effects of double tendons. Finally, the critical buckling loads of simple and cantilever PS mono-symmetric beams which were subjected to the non-uniform moments with the increasing of deviators are evaluated using the FEM and Rayleigh-Ritz method. As a result, the FE solutions were found to be very well matched to solutions by Ritz method and Abaqus. Additionally, the effects of double tendons, eccentricity, and the initial tension on LTB of the PS beam system were investigated with the increase of un-bonded/bonded deviators.

Scanning and separating vertical and torsional–flexural frequencies of thin-walled girder bridges by a single-axle test vehicle

An effective procedure is proposed for scanning and separating the vertical (flexural) and torsional–flexural frequencies of thin-walled girder bridges by a moving single-axle test vehicle, modeled as a two degree-of-freedom (DOF) system to account for the vertical and rocking motions. The response of the vehicle is not directly used, since it may mask the bridge frequencies by self frequencies. Instead, the wheel-bridge contact responses are used for being free of vehicle’s frequencies. To start, closed-form solutions are derived for the vertical, lateral, and torsional vibrations of the mono-symmetric beam. Then, the contact responses are calculated from the vehicle responses, considering the discrete nature of field data. The vertical and torsional–flexural frequencies of the bridge are separated by using the vertical and rocking motions derived from the contact responses without prior knowledge of the mode shapes. The proposed technique is numerically validated with the following conclusions: (1) the wheels’ contact responses outperform the vehicle response in that more high frequencies of the bridge can be detected; (2) the torsional–flexural​ frequencies can better be detected from the wheel closer to the bridge edge; and (3) the vertical and torsional–flexural frequencies of bridges can be successfully separated by the proposed procedure even in the presence of pavement roughness, which is helpful for field applications.

Internal instability of thin-walled beams under harmonic moving loads

Frequent resonance may result in excessive vibrations and endanger the safety of bridges. Firstly, the governing equations of motion are derived for the vertical, lateral and torsional vibrations of a mono-symmetric thin-walled box beam under a harmonic moving load. Then the resonance conditions are derived by letting the denominator of the response of concern equal to zero. For the mono-symmetric beam, the vertical resonance is uncoupled, but the torsional and lateral resonances are coupled. When in vertical resonance, the vertical motion of the beam will diverge by growing to a maximum during the acting period of the moving load. Similar phenomenon exists for the torsional–flexural resonance. A specific case occurs when the above two resonance frequencies coincide, for which the critical length of the beam can be determined. The phenomenon of simultaneous resonance is a kind of internal instability featured by the fact that the beam can transform repetitively from the vertical mode to the torsional–flexural mode, and vice versa, with no additional energy input. To avoid the inherent internal instability, a beam should be designed with a length not equal or close to the critical length presented in this paper. All the aforementioned resonances have been extensively studied for cases involving both harmonic and random moving loads and validated by the finite element analysis.

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

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

Effect of surface loading pattern on the monosymmetric beams at elevated temperature

Nowadays constructional steel has become the desired choice of structural designers because of its structural properties over other materials. However, structural steel susceptible to fire hazard as material properties of steel decreases rapidly at high temperatures that led to the instability failure of the unrestrained flexural members. In this study, numerical analysis is carried out to investigate the effect of surface loading patterns and temperatures on the buckling behavior of monosymmetric I-section beams. The ISMB600 monosymmetric beam of lengths varying from 2.5 m to 20 m simulated and analyzed using FEM based software ABAQUS. The response of beams is studied under uniform thermal conditions as well as transient thermal condition with 50% load ratio. Considerable variation in buckling capacity is noticed at elevated temperature. Based on the present results, the loading pattern is found to exhibit a significant influence on the moment capacities. The comparison between the numerical results and codal provisions of Eurocode 3 revealed that the codal provisions of Eurocode 3 pertaining to the buckling behavior of monosymmetric I-beams lead to the over-conservative prediction for medium to high slender beams and unsafe for beams having low slenderness ratio.

Elastic critical moment for monosymmetric beams under linear moment gradients

The present study documents some inconsistencies observed when applying the lateral torsional buckling provisions of the Canadian standards of steel structures to characterize the elastic critical moments for monosymmetric beams subjected to linear moment gradients. An overview of the underlying theoretical background is presented and the reasons behind the discrepancies observed between standard-recommended solutions on one hand, and theoretical and finite element solutions on the other hand are discussed. An improved solution is then developed by generating a parametric study based on finite element analyses and developing regression equations to estimate the critical moments for monosymmetric beams under linear moments inducing double curvature. The expressions are cast in a dimensionless form as a function of four parameters. The potential use of the proposed solution is subsequently illustrated through a design example.

Inelastic lateral buckling of continuous steel beams

The inelastic behaviour of a steel beam is complicated by reductions in the section rigidities which depend on the moment distribution and residual stress pattern. The inelastic beam is effectively tapered and mono-symmetric, and iterative numerical methods need generally to be used for the analysis.The in-plane moment distribution in an inelastic continuous beam lies between the commonly assumed rigid-plastic “plastic” path and a “yield” moment path. The yield path is the more critical for lateral buckling of the continuous beams considered in this paper.Approximations of the inelastic out-of-plane moduli of continuous beams developed from closed form lateral buckling solutions for simply supported beams in uniform bending can be used in a computer program for the buckling analysis of tapered mono-symmetric beams. Residual stresses cause significant reductions in the inelastic buckling resistance.The AISC design code predicts strengths which are similar in shape but significantly higher in magnitude than the inelastic buckling resistances of simply supported beams in uniform bending. The predictions for beams with central concentrated loads are much higher than the corresponding inelastic buckling resistances. Closer but still conservative approximations are obtained by using the method of design by inelastic buckling, which can also be used for continuous beams. This method is much simpler than those used to obtain accurate predictions.

Lateral-torsional Buckling Moment of Simply Supported Unrestrained Monosymmetric Beams

The stability equations for simply supported beams were solved approximately using the Bubnov-Galerkin method. We omit the influence of displacements in the plane of bending. The analytical solutions were used for checking the stability of laterally unrestrained mono-symmetric beams. The lateral-torsional buckling (LTB) moment depends on bending distribution and on the load height effect. Each of applied concentrated and distributed loads, may have arbitrary direction and optional coordinate for the applied force along the cross section’s height. Derived equations allow for simple, yet fast control of lateral buckling moment. Numerical examples show good consistency of analytic results with those obtained from Finite Element Method (FEM) software.

Structural behavior of non-prismatic mono-symmetric beam

This paper attempts to understand the structural behavior of non prismatic channel beams subjected to bending through finite element(FE) analysis. The present study aims at shedding some light on how tapered channel beams behave by studying the effect of taper ratio on structural behavior. As a weight reduction is always desired in aerospace structures beams are tapered in order to obtain highest structural efficiency. FE analysis has been performed to study the effect of taper ratio on linear deflection, lateral torsional buckling, non-linear parameters and dynamic parameters. Taper ratio tends to affect the mechanics of tapered beams innocuously and adversely. Consequently it becomes important to understand and document the mechanics of channel tapered beams. Channel beams generally have low torsional rigidity due to the off-shear loading. The effect of loading type and location of applied load have been studied for flange taper, web taper and symmetric taper for different conditions. Among these, as the taper ratio is increased, the torsional angular deflection increases but begins to decrease when the beam is web tapered and symmetrically tapered for a mid web loaded beam. But when loaded through the shear center, an increase in the torsional angular deflection can be observed with increase in taper ratio. This indicates that a flange taper could cause an increase in torsional angular deflection with an increase in taper ratio.

Lateral-torsional buckling behavior of hot-rolled steel beams with flange upstands

The lateral-torsional buckling behavior of hot-rolled steel beams has been studied extensively. Much of the research carried out has been limited to doubly symmetric beams and a few other common geometries. The study of monosymmetric and non-symmetric geometries has not been as extensive. This paper presents a study of the lateral-torsional buckling behavior of monosymmetric beams having the monosymmetry introduced by flange end upstands. The study is carried out using finite element modelling. The behavior is investigated for various spans and with various heights of upstands. It is observed that the upstands increase the critical buckling moment of the section but that this increase diminishes with increase in upstand height. It is further observed that this unique behavior could be influenced by a movement in the relative position of the shear center to the geometric centroid as the flange upstands are adjusted. In addition there exists for these geometries unique points where the monosymmetric sections have properties typically associated with doubly symmetric sections. It is shown that the relative position of the shear center and centroid have some influence on the strength gain pattern observed.

Torsional flexural steady state response of monosymmetric thin-walled beams under harmonic loads

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.

Bending and buckling of tapered steel beam structures

This paper describes an efficient finite element method of analysing the elastic in-plane bending and out-of-plane buckling of indeterminate beam structures whose members may be tapered and of mono-symmetric I cross-section. The structure’s loading includes concentrated moments and concentrated or uniformly distributed off-axis transverse and longitudinal forces, and its deformations may be prevented or resisted by concentrated or continuous rigid or elastic off-axis restraints.Tapered finite element formulations are developed by numerical integration instead of the closed forms often used for uniform elements. Difficulties in specifying the load positions for tapered mono-symmetric members caused by the variations of the centroidal and shear centre axes are avoided by using an arbitrary axis system based on the web mid-line. Account is taken of additional Wagner torque terms arising from the inclination of the shear centre axis.A computer program based on this method is used to analyse a number of examples of the elastic in-plane bending of tapered cantilevers and built-in beams, and very close agreement is found between its predictions and closed form solutions.The program’s predictions of the elastic out-of-plane flexural–torsional buckling of a large number of uniform and tapered doubly and mono-symmetric beams and cantilevers under various loading and restraint conditions are generally in close agreement with existing predictions and test results. The common approximation in which tapered elements are replaced by uniform elements is shown to converge slowly, and to lead to incorrect predictions for tapered mono-symmetric beams.

균일모멘트가 작용하는 일축대칭 I형 양단 스텝보의 비탄성 횡-비틀림 좌굴에 관한 해석적 연구

연속경간을 가지는 I형강 교량은 내부 지점 부근에 상대적으로 큰 부모멘트가 발생하게 된다. 따라서 경제적인 단면 활용을 위하여 내부지점부위의 상부 및 하부 플랜지에 플레이트를 보강한 변단면을 사용하고 있다. 본 논문에서는 기존 탄성 횡-비틀림 좌굴식에 관한 연구를 토대로 하여 비탄성 구간에 있는 일축대칭 I형 양단 스텝보의 횡-비틀림 좌굴강도 해석을 실시하였다. 유한요소해석 프로그램인 ABAQUS가 사용되었으며, 회귀분석프로그램을 활용하여 간편 설계식을 제안하였다. 양단 스텝보에 순수휨이 작용할 때를 고려하였으며, 비선형 해석을 위해 잔류응력 및 초기변형을 고려하였다. 본 연구를 통하여 개발 제안된 식은 일축대칭 스텝보의 비탄성 횡-비틀림 좌굴 강도에 널리 사용될 수 있으며 유사연구에 크게 기여할 것이다. The cross-sections of continuous multi-span beams are sometimes suddenly increased or stepped at the interior supports of continuous beams to resist high negative moments. This paper investigates inelastic lateral-torsional buckling of monosymmetric stepped I-beams subjected to pure bending. A three-dimensional finite-element program ABAQUS and a regression program were used to analytically develop new design equation. The flange thickness ratio, flange width ratio and stepped length ratio were considered as parameters of this study. The combined effects of residual stresses and geometric imperfection on inelastic lateral-torsional buckling of beams are considered. The proposed solution can be easily used to calculation for inelastic lateral torsional buckling strengths of monosymmetric beams with doubly stepped cross sections and to develop new design equations for inelastic lateral-torsional buckling resistances of stepped beams.

Inelastic buckling design of monosymmetric I-beams

Methods of designing steel monosymmetric I-beams against lateral buckling are not well supported by research. For this paper, the inelastic buckling of monosymmetric steel I-beams under moment gradient is studied and compared with design recommendations. For welded beams in uniform bending, inelastic buckling is initiated at moments which are often close to those which cause first yield in the compression flange. Once initiated, the inelastic buckling resistance remains constant as the slenderness decreases until strain-hardening occurs. For hot-rolled beams in uniform bending, the inelastic buckling resistance increases almost linearly as the slenderness decreases. Three regimes are significant in the inelastic buckling resistances of hot-rolled monosymmetric beams under moment gradient, depending on which flange yields first and the end moment ratio. Simple linear approximations of good accuracy are developed for designing hot-rolled monosymmetric beams in uniform bending, while less accurate but conservative approximations are developed for moment gradient. The use of these approximations is illustrated by a worked example.

Numerical method for predicting the elastic lateral distortional buckling moment of a mono-symmetric beam with web openings

When used as floor joists, the new mono-symmetric LiteSteel beam (LSB) sections require web openings to provide access for inspections and various services. The LSBs consist of two rectangular hollow flanges connected by a slender web, and are subjected to lateral distortional buckling effects in the intermediate span range. Their member capacity design formulae developed to date are based on their elastic lateral buckling moments, and only limited research has been undertaken to predict the elastic lateral buckling moments of LSBs with web openings. This paper addresses this research gap by reporting the development of web opening modelling techniques based on an equivalent reduced web thickness concept and a numerical method for predicting the elastic buckling moments of LSBs with circular web openings. The proposed numerical method was based on a formulation of the total potential energy of LSBs with circular web openings. The accuracy of the proposed method's use with the aforementioned modelling techniques was verified through comparison of its results with those of finite strip and finite element analyses of various LSBs.

Lateral buckling of beams with shear deformations – A hyperelastic formulation

The equilibrium and buckling equations are derived for the lateral buckling of a prismatic straight beam. A consistent finite strain constitutive law is used, which is based on a hyperelastic model for an isotropic material. The kinematics of the cross-sectional deformations are based on a Timoshenko type beam displacement of the cross-sectional plane using Euler angles and two shear finite rotations coupled with warping taken normal to the displaced plane. Also derived are the second order approximations to the displacements, curvatures, twist and internal actions. The constitutive relationships for the internal actions reveal new coupling terms between the bending moments, torsion and bimoment, which are functions of the cross-sectional warping and shear deformations. New Wagner type nonlinear torsion terms are derived which are functions of the warping of the cross-sectional plane, and are coupled to the twisting and shear deformations of the cross-section. Solutions are determined for the lateral buckling of a prismatic monosymmetric beam under pure bending and the flexural–torsional buckling under axial compression. For the flexural–torsional buckling problem it is found that the Euler type column buckling formula is consistent with Haringx’s column buckling formula while the torsional buckling formula is different to conventional equations. The second variation of the total potential is also derived. The effects of shear deformations are explored by examining the non-dimensional lateral buckling equation for a simply supported beam.