Buckling Of Arches Research Articles

Rigid body qualified curved beam approach for lateral torsional buckling of arches

The curved beam finite element approach based on the potential energy formulation is widely recognized as a versatile tool for lateral torsional buckling analysis of arches. However, there exist a variety of potentials, which were developed with distinct assumptions. The diversity of energy-based curved beam theories introduces confusions in practical applications. This paper aims to examine various potential energy formulations as to whether or not they obey the rigid body rule which is a prerequisite for valid second-order analysis. The induced moments at the ends of curved beam element that have been neglected from and/or the distributed moments that should be removed from available potentials are identified to help them become rigid body qualified. Based on the revised potential functional, a curved beam finite element formulation has been developed to effectively predict yet with less effort the out-of-plane critical load for circular and parabolic arches subject to various loading and constraint conditions. The results of numerical examples demonstrate that a potential energy formulation eligible for describing the out-of-plane behavior of curved beam is required to be rigid body qualified by fulfilling two aspects: (i) the neglected end moments that are imperative for satisfying the rigid body rule must be considered unless the virtual work done by them vanishes, and (ii) undesirable distributed moments that may be induced when undergoing the rigid body motion should be removed by considering all essential potential components.

Out-Plane Buckling of Arches with Variable Cross-Section

The variable cross-section arch is widely used in practical engineering because of its beautiful arc and excellent mechanical properties. However, there is still no systematic and comprehensive study on the out-plane buckling of variable cross-section arches. In view of this, this paper is focused on the elastic analytical research of out-plane buckling of arches with variable cross-sections under a uniformly distributed radial local load. The pre-buckling and out-plane buckling behavior of a variable cross-sectional arch under an external load is quite different from that of an arch with a uniform cross-section. Castigliano’s second theorem is used to establish pre-buckling force method equilibrium equations for variable cross-sectional arches under a uniformly distributed radial local load, and corresponding analytical solutions of normal stress, axial compression, and the bending moments are obtained. Based on the energy method and the Ritz method, analytical solutions of the critical load for the elastic out-plane buckling of arches with variable cross-sections are derived. Comparisons with ANSYS results indicated that the analytical solutions are able to accurately predict the pre-buckling internal forces and critical out-plane buckling load of variable cross-section arches subjected to a uniformly distributed radial local load. It is found that the internal forces and the out-plane buckling load of an arch are significantly affected by the variation of cross-sectional height. As the ratio of the arch’s cross-sectional height increases, the bending moment decreases, and the axial force and critical out-plane buckling load increase. Analytical solutions of pre-buckling internal force and critical out-plane buckling load problems for arches with variable cross-sections have a wider significance since they can provide an effective explicit analytic method for the optimal design of arch structures.

Nonlinear forced vibration and dynamic buckling of FG graphene-reinforced porous arches under impulsive loading

Nonlinear forced vibration and dynamic buckling of fixed functionally graded graphene platelet-reinforced (FG-GPLRC) porous arches under impulsive loading are investigated. The porosity coefficient varies along the thickness of arch based on a power law distribution with uniform dispersion of graphene platelets (GPLs) in the whole arch. The FG-GPLRC porous arch is made of closed-cell metal foams whose effective materials properties are determined by the volume fraction distribution of materials together with Halpin–Tsai model. The nonlinear motion equations of the FG-GPLRC porous under impulsive loading are derived by employed Hamilton’s principle, and numerically solved by Runge–Kutta (RK) method combined with the differential quadrature method (DQM). Based on the Budiansky–Roth (B-R) criterion of dynamic buckling, the critical dynamic buckling load of the arch is also determined. Two case studies are conducted to show the determination of the dynamic buckling load of the arch, and good accuracy of the developed method in predicting the critical dynamic buckling load of both shallow and deep arches is also verified. Numerical results show that the nonlinear forced vibration and dynamic buckling of arches are quite sensitive to impulsive load duration. In addition, FG-GPLRC porous arches have significantly higher critical dynamic buckling load when undergoing instantaneous impact loading.

Thermally induced instability on asymmetric buckling analysis of pinned-fixed FG-GPLRC arches

In the present work, an analytical study on the asymmetric static and dynamic buckling of a pinned-fixed functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) arch under thermal conditions is presented. The reinforcement of graphene nanoplatelets (GPLs) is dispersed along arch thickness by following a power law distribution. Making use of the modified Halpin–Tsai micromechanical model and energy method, the static buckling load of the arch under an arbitrary radial point load and the dynamic buckling load of the arch under an arbitrary radial step point load can be derived, which could be applied to determine the existence of dynamic buckling and the phenomenon of multiple limit points under a static state. A numerical analysis is conducted to verify the accuracy of the analytical method, a good prediction on the static and dynamic buckling of the pinned-fixed FG-GPLRC arch is demonstrated. In this study, the influence of GPLs weight fraction, concentration and geometry on the static and dynamic buckling of the arch is comprehensively discussed. The dynamic and static buckling loads of the arch are found to be sensitive to applied load position under various elevated temperatures. Arch buckling load decreases as the power law index increases, but it increases as temperature rises. It is also found that the present approach is able to trace the postbuckling paths of the arch for stability analysis. Besides, accurate first-known thermal buckling solutions are also presented.

Out-of-plane buckling strength of free standing singly symmetric hollow pinned circular arches

This study deals with the out-of-plane flexural torsional buckling strength of singly symmetric free-standing circular arches with a hollow cross-section. The behavior of such arches is investigated numerically in terms of the out of plane critical elastic buckling load and ultimate load carrying capacity when such arches are subject to a radial pressure that creates uniform axial compression. Prediction methodologies proposed by other researchers for flexural torsional buckling of arches with an I-shaped cross-section, as well as American, European, and Australian code provisions for flexural buckling of compression members are slightly modified and compared with numerically obtained critical elastic buckling loads and ultimate load carrying capacities. All investigations are conducted using validated shell finite element simulations. A parametric study is conducted to evaluate the influence of arch depth, wall thickness, subtended angle, arch radius, yield strength, initial imperfections, and residual stresses on the 3D elastic-plastic behavior of such arches. It is concluded that it is not necessary to use eigenvalue buckling analysis to obtain critical elastic buckling loads for improving capacity predictions and that such loads may be obtained using existing formulations with slight modifications. Additionally, existing code provisions for flexural buckling of compression members may be used with minor modifications to predict the out-of-plane flexural torsional buckling capacity of such arches. Also, prediction methodologies proposed by other researchers for flexural torsional buckling of I-shaped arches may also be used with slight modifications and resulted in the most accurate, consistent, and design appropriate capacity predictions.

Stability of steel arches strengthened by textile membranes

The stabilization effect of textile membranes on in-plane and out-of-plane stability of a steel arch supporting the membranes is investigated. Model of a large membrane structure using Ferrari ® Précontraint 702S fabric was tested in laboratory under various loadings and the resulting deflection/stress values are presented. The numerical model employed SOFiSTiK software and 3D geometrically nonlinear analysis with imperfections (3D GNIA). The model was validated comparing the results with the arch and membranes behavior at tests. The prime goal of the article is an extensive stability study of the large barrel-type textile roofs supported by a row of steel arches. The behavior of the both arches alone and those stabilized by the membranes is studied using geometrically nonlinear analysis (3D GNA) to design properly the supporting arches followed by linear buckling analysis (3D LBA) to find critical in-plane and out-of-plane loads in the form of buckling length factors. The study covers a variety of arch geometries, boundary conditions, membrane prestressings and loadings. The detailed analysis of buckling of arches alone resulted into refining of the buckling length factors currently used in standards. The summarized results of a wide spectrum of arches stabilized by membranes declare the decisive role of membranes for both in-plane and out-of-plane loss of the arch stability and may simply be used for a preliminary design of the supporting arches.

Stability criteria for roller-bent circular-hollow-section steel arches

The structural stability of steel arches comprising Circular-Hollow-Sections (CHS) is examined in the present study. Appropriate finite element models are developed, accounting for geometry and material nonlinearities, as well as, incorporating residual stresses and geometric imperfections of roller-bent arches. A verification study is first performed to evaluate the accuracy of the proposed finite element modeling, followed by sensitivity analyses aiming at estimating the effects of residual stresses and geometric imperfections on the structural response. Findings reveal that the magnitude of geometric imperfections and the distribution of residual stresses significantly affect the arch's buckling resistance. An extensive parametric study is carried out to assess the spatial stability of arches comprising a wide range of non-dimensional slenderness, commonly encountered in the civil engineering practice. Based on the results of parametric analyses, suitable parameters are determined for the in-plane and out-of-plane buckling. Finally, stability criteria are proposed via regression analyses, which are used to define relevant buckling curves according to structural steel design standards.

Nonlinear dynamic buckling of fixed shallow arches under impact loading: An analytical and experimental study

This paper presents analytical and experimental investigations on the in-plane nonlinear dynamic buckling of an elastic fixed shallow arch subjected to a central impact load generated by a free-falling object. The analytical method for determining the critical weight and impact velocity of the falling object for dynamic buckling is developed based on the principle of conservation of energy in association with the nonlinear equilibrium path of the arch. The experimental investigation is carried out using a test frame designed by authors and the finite element analysis is also conducted. Comparisons with the experimental and finite element results show that the analytical method can accurately detect dynamic buckling of arches under impact action. It is found that the required weight of the falling object for dynamic buckling is much related to the velocity impacting on the crown of the arch, and decreases with an increase of the impact velocity. It is also found that the weight of the falling object for dynamic buckling is always smaller than the corresponding static buckling load of the arch, indicating that the dynamic buckling of an arch under an impact load is more critical than its static counterpart.

TORSIONAL STIFFNESS AS AN INFLUENCE PARAMETER ON ARCH STABILITY

Arch bridge springs can be connected to concrete abutments either by prestressing bars or by connectors. In both options, the torsional stiffness is substantially reduced, compared to the full arch cross sectional area. The influence of this lack of torsional stiffness on arch buckling is being researched, both numerically and experimentally. To reduce any residual stress during tests, wooden rods that simulate the arch were submerged in water and subsequently bent to the desired shape. Imperfections of the arch samples are measured. Two unequal concentrated loads are applied to the samples, thus simulating the effect of movable loads across half of the arch span. During loading, lateral deflections were measured until elastic buckling occurred. The simulation of more flexible rotation of the springs required replacing the cross section by thin equivalent side plates. Since all parameters have not been isolated, the results are limited yet. However, comparing the failure load of similar conditions, the reduction of torsion stiffness by 81.48% reduces the failure load by 26.3%. This indicates that total prevention of axial rotation may not be imperative for arch bridges.

In-plane non-linear elastic stability of arches subjected to multi-pattern distributed load

Abstract This paper proposes a numerical and an approximate analytical method for the in-plane non-linear elastic stability of arches under the multi-pattern distributed load. There are six key parts in this paper. Firstly, the approximate analytical solution for funicular axis of arches subjected to the multi-pattern distributed load is derived from the approximations of linear elastic bending moment and horizontal reaction force in the arch end. Secondly, the numerical solution of the in-plane non-linear elastic equilibrium equation is solved by using the shooting method and the bisection method simultaneously. Thirdly, the approximate analytical solutions for the in-plane non-linear elastic equilibrium are derived according to the approximate analytical solution for funicular arch axis obtained from the first part, the simplified strain-displacement expression in Cartesian coordinate system and the virtual work principle. Fourthly, a key parameter is proposed to transform the approximate analytical solutions into the corresponding equations of catenary and parabolic arches. Fifthly, the in-plane non-linear elastic symmetric and asymmetric buckling of arches under the multi-pattern distributed load is derived analytically. Lastly, the in-plane non-linear elastic buckling behaviors of arches subjected to multi-pattern distributed load are deduced based on the obtained analytical solutions. The multi-pattern distributed load with the uniformly distributed load along the span and the uniformly distributed load along the arch is selected as example to verify the proposed method. Comparisons with numerical solutions demonstrate that the proposed approximate analytical solutions for the funicular arch axis and linear elastic horizontal reaction force agree well with the results of Runge-Kutta method and the proposed approximate buckling predictions have sufficient accuracy compared with the results of finite element method in different rise-to-span ratios, relative slenderness and arch axis parameters.

In-plane nonlinear buckling analysis of circular arches considering shear deformation

A new theory for the buckling and nonlinear analysis of circular arches with shear deformation is developed, the theory is based on the variational principle in which the nonlinear strain energy of all stress components are included. For arches subjected to a uniform constant-directed radial load, internal forces and deformations including shear deformation are determined, then the buckling of arches only considering uniform axial forces and incorporating the effect of pre-buckling deformations and all internal forces are respectively carried out, with the results of the latter are fully validated by FE predictions, thus the proposed theory is verified. The buckling of arches with shear deformation is then viewed as an interactive buckling between flexural and shear buckling, Simplified formulas for the critical loads and the critical axial forces of arches for 4 types of loads are presented, the comparison shows excellent agreement between the proposed formulas and FE analysis.

Lateral-torsional buckling of arches under an arbitrary radial point load in a thermal environment incorporating shear deformations

This paper presents an analytical investigation of the thermoelastic lateral-torsional buckling of circular arches under an arbitrary radial point load in a uniform thermal environment accounting for shear deformations, which has not been reported in the literature. The interaction of thermal environment with the arbitrary load and elastic end restraints produces complex non-uniform compressive, bending, and shearing actions in the arch. The theoretical solutions of the critical load and temperature field for the elastic lateral-torsional buckling of arches accounting for shear deformations are derived. Comparisons of theoretical solutions with finite element results show that their agreements are excellent. Effects of various factors on the lateral-torsional buckling are investigated. An increase of the temperature field reduces the buckling load, while an increase of the radial load reduced the critical temperature field for buckling. The effect of shear deformations on the lateral-torsional buckling load is also explored. It is shown that the neglect of shear deformations causes errors in the prediction of the critical buckling load. When shear deformations are considered, the buckling load for arches with a small and intermediate lateral slenderness ratio under the radial point load alone is shown to be lower than that without consideration of shear deformations. However, under the uniform temperature field alone, the critical temperature field for lateral-torsional buckling of the arches considering shear deformations is higher than that neglecting shear deformations.

Effect of Impact Load on Dynamic Buckling of Steel Lattice Arch

In this study, test results and numerical simulation data are jointly analyzed to investigate the dynamic buckling of the steel arch under impact load. A series of impact tests of the triangular lattice steel arch are conducted to study the effect of the impact velocity and rise-to-span ratio on the structure buckling. The experimental results are compared with the numerical simulation ones, including arch buckling and strain data, which show the efficiency of the numerical simulation in performing the arch dynamic response calculation. It is also revealed that the impact velocity has a drastic effect on the steel arch buckling, and the arch impact resistance can be improved by increasing the rise-to-span ratio.

Study of Concrete Filled Steel Tubular Arch Bridge: A Review

In many developed countries, concrete filled steel tubular arch bridges are being constructed for roads and railway lines. The CFST arch bridges use steel tubular arches with self consolidating concrete pumped inside and the steel tube provides confinement to the concrete infill. Also, these concrete filled steel tubes have enhanced ductility, better seismic performance, aesthetic quality, lesser consumption of materials and self weight, speedy construction and small vibrations according to studies conducted earlier. Due to the presence of steel tube, local buckling of arch is delayed and reduces the ingress of moisture when exposed to harsh environmental conditions. This paper aims to find the seismic performance of CFST arch bridges in terms of seismic output and deformation when compared to conventional bridges being currently constructed.

Structural properties and out-of-plane stability of roller bent steel arches

In contemporary architecture the use of steel arches has seen a significant increase. They are applied in buildings and large span bridges, combining structural design with architectural merits. For arches lacking lateral support (or freestanding arches) the out-of-plane structural stability behavior is the decisive design criterion. However, suitable methods or design rules to assess the out-of-plane structural stability resistance of arches are lacking and the collapse behavior is often unknown. Nowadays engineers have to perform laborious calculations which can lead either to conservative or nonconservative arch designs. This Ph.D. project is aimed at studying the out-of-plane structural stability behavior of steel arches, and developing design rules for these arches. The out-of-plane structural stability behavior was studied by means of geometrical and material non-linear finite element analyses including structural imperfections with ANSYS v. 11.0. The investigation was confined to wide flange circular freestanding arches which are subjected to in-plane vertical loads and manufactured by the roller bending process. The roller bending process is a manufacturing technique by which steel members are bent at ambient temperature into circular arches. It was expected that the residual stresses and mechanical properties (e.g. yield stress, ultimate tensile stress) are altered due to roller bending. Since the alteration of residual stresses and mechanical properties (imperfections) can affect the out-of-plane structural stability of freestanding steel arches, the influence of the roller bending process was studied first. Residual stress measurements and tensile tests were conducted on both straight and roller bent members to assess the influence of roller bending. In addition to the experiments, finite element simulations of the roller bending process were performed in the ANSYS v. 11.0 environment to estimate the residual stress distribution in the arches. Good agreement between the experimentally and numerically obtained residual stresses in roller bent arches was observed. Based on the experimental and numerical studies of the imperfections in roller bent arches a residual stress model and distribution of mechanical properties across the steel bent section were proposed which serve as the initial state of a roller bent arch when assessing its structural performance by means of non-linear finite element simulations. Numerical analyses showed that the residual stresses in roller bent arches have a minor influence on the load carrying capacity. However, the alterations of the mechanical properties can result in a significant reduction of the arch strength The existing column curve formulations as given in EC3 were adapted to include out-of-plane buckling of arches by altering the form of the imperfection parameter. The column curves can give an accurate prediction of the out-of-plane buckling load provided an appropriate imperfection parameter is selected and the non-dimensional slenderness is known. Based on numerous finite element calculations an imperfection parameter curve was derived which was substituted into the column curve formulation rendering a column curve for roller bent arches failing by out-of-plane buckling. Finite element results showed that multiple column curves were necessary to capture the out-of-plane buckling response of arches for various load cases and steel grades. The column curves require the determination of the non-dimensional slenderness represented by the in-plane plastic capacity and out-of-plane elastic buckling load. Since any closed form equations are lacking to approximate these buckling parameters finite element techniques were adopted. For future research it is recommended that closed-form solutions or design graphs should be derived with mechanical models to obtain the elastic-plastic buckling load of freestanding roller bent arches without using finite element analyses.

Multiple unstable equilibrium branches and non-linear dynamic buckling of shallow arches

An arch under a suddenly-applied load will oscillate about its equilibrium position. If the suddenly-applied load is sufficiently large, the oscillation may reach a position on the unstable equilibrium branch of the arch, triggering its dynamic buckling. In many cases, arches are supported by other structural members or by elastic foundations which provide elastic types of rotational restraints to the ends of the arch. When the rotational end restraints of an arch are not equal to each other, the in-plane non-linear equilibrium path of the arch may have multiple unstable branches, which will influence the dynamic buckling of the arch significantly. This paper investigates effects of multiple unstable equilibrium branches on the non-linear in-plane dynamic buckling of a shallow circular arch under a suddenly-applied central concentrated load. Two methods based on the energy approach are used to derive the dynamic buckling loads. It is found that the number and magnitude of dynamic buckling loads are influenced significantly by the number of unstable equilibrium branches, by the stiffness of the unequal rotational end restraints, and by the included angle and slenderness ratio of the arch.

Lateral-Torsional Buckling Analysis of Arches Having In-Plane Rotational End Restraints under Uniform Radial Loading

AbstractIn many cases, an arch may have in-plane elastic end restraints provided by the connected structures or elastic foundations, which may influence the elastic lateral-torsional buckling of the arch. However, little research of the lateral-torsional buckling of arches with elastic end restraints has been reported in the open literature. This paper analytically investigates the lateral-torsional buckling of pin-ended circular arches having in-plane elastic rotational end restraints under a uniform radial load. The analytical solutions for the prebuckling behavior of such an arch show that the uniform radial load produces combined axial compressive and bending actions in the arch and that the axial compressive force produced by the uniform radial load is approximately uniform along the arch axis. It is found that the stiffness of elastic rotational end restraints has significant effects on the magnitude and distribution of the axial compressive forces and bending moments. The axial compressive force de...

Elastic Stability of Circular Arches with the Open Thin-walled Monosym-metric Section Considering the Prebuckling Deformation

The effect of prebuckling in-plane deformations on the elastic flexural-torsional buckling of arches is studied in this paper. Nonlinear strain-displacement relations considering initial curvature effects and higher order prebuckling de-formation terms with curvature in deriving process are substituted into the second variation of the total potential to obtain the buckling energy equation. The analytical solutions for the flexural-torsional buckling moment of arches in uniform bending, containing the effects of the prebuckling deformation, are proposed. Also, the influence of the higher order prebuckling deformation terms with the curvature effects is investigated according to the ratio of the minor axis flexural stiffness to the major axis flexural stiffness.

Nonlinear analysis and buckling of shallow arches with unequal rotational end restraints

Arches are often supported by other structural elements which provide elastic types of restraint at both of their ends and these elastic restraints usually have different stiffnesses. This paper presents a nonlinear elastic in-plane buckling and postbuckling analysis of pin-ended shallow circular arches having elastic rotational end restraints of unequal stiffness when subjected to a uniform radial load. An energy method is used to derive the differential equations of equilibrium, and the differential equations of buckling equilibrium. The nonlinear equilibrium equation between the external load and the axial force is also established. Analytical solutions for the nonlinear in-plane behaviour and buckling loads of the arches are derived. It is found that the effects of the unequal stiffness of the rotational end restraints on the nonlinear behaviour and buckling of the arches are significant. The nonlinear buckling loads increase with an increase of the stiffness of rotational end restraints. It is also found that the pin-ended arch with elastic rotational end restraints of unequal stiffness may buckle in a limit point instability mode, but they cannot buckle in a bifurcation mode. This is different from pin-ended arches with equal rotational end restraints, which can buckle in either a limit point instability or a bifurcation mode. It is demonstrated that there exists a specific geometric parameter (as defined in the paper) that defines a switch between arches and beams curved in elevation. Comparisons with finite element results show that the analytical solutions can accurately predict the nonlinear behaviour and buckling loads of pin-ended shallow circular arches with elastic rotational end restraints of unequal stiffness. The analytical solutions are shown to reduce to those of pin-ended arches with equal rotational end restraints or without rotational end restraints, fixed arches, and pinned-fixed arches.

Buckling of parabolic arches with hangers and tie

This paper pertains to the critical load for two-hinged parabolic arches with hangers and tie. It was proved that the existence of hangers (vertical and especially slant) can lead to a significant increase of arch critical load and consequently to increase of arch capacity. It has also been shown that the convex distribution of ties (in relation to the horizontal tie) can often be very useful. The tabulated results presented in the paper allow to determine the effective (buckling) length of the arches. Furthermore, it has been noted that the recommendations of European Standard (Eurocode 3: EN 1993-2) concerning the buckling of parabolic arches with hangers and tie may quite frequently lead to unsafe design. The issues of buckling of arches presented in this paper have a practical aspect and, in author’s opinion, can find a direct application in design practice.