Circular Arches Research Articles

In-Plane Stability Analysis of Circular Box Arches with Sinusoidal Corrugated Webs

In-Plane Stability Analysis of Circular Box Arches with Sinusoidal Corrugated Webs

Об устойчивости круговых подкрепленных арок в случае пространственной деформации

The work considers a circular arch loaded with uniformly distributed normal pressure directed towards the centre. The ends of the arch are attached with cables, one end of which is attached to the arc of the arch at an appropriate angle, and the distance between the points of attachment of the cables cannot be increased. We estimated pressure values, at which curved equilibrium forms of the arch are possible, and the smallest of these values is found, which is the critical force.

Nonlinear static analysis of masonry structures with mortar joints and cracking units by optimization‐based rigid block models

AbstractA rigid block model with elasto‐plastic softening interfaces is developed for nonlinear static analysis of masonry structures subject to monotonic loading. Cracking, crushing, and shear failures are taken into account at interfaces, following a simple micro‐modeling approach. An optimization‐based formulation is used for the solution of the equation systems governing the behavior of the rigid block assemblage. A simple incremental solution procedure is implemented to take into account the material softening behavior and the effects of large displacements on equilibrium conditions. The interface models are validated against tension and shear tests on bi‐block prisms from the literature. Applications to numerical and experimental out‐of‐plane loaded masonry walls as well as to circular arches with mortar joints are presented to evaluate the effects of tensile strength and the accuracy of the developed model against responses involving P‐Δ effects. Comparisons with experimental tests on shear walls also involving cracking of the units in the failure mechanisms are finally reported to discuss the potentialities and limitations of the proposed modeling approach.

Free Vibration of Ogival Circular Arch

This study aims to analyze the free vibration of an ogival arch in which two symmetrical arched shapes are discontinuously met at the mid-arc. Differential equations governing the free vibration of an ogival circular arch were derived, where the rotatory inertia and shear deformation effects are included. The governing equations were numerically solved to calculate natural frequencies and mode shapes. In numerical solution methods, the symmetric and anti-symmetric boundary conditions at the mid-arc were focused rather than the boundary conditions of supported end due to the discontinuity of the mid-arc. For the first time, the free vibration problem for discontinuous arches, such as ogival arches, is solved in this study. Calculation results of this study for natural frequencies are compared well with those of the finite element method. The effects of various arch parameters on natural frequencies were highlighted and discussed in detail.

Convergence-Related Serviceability Limit States of Segmental Tunnel Rings: Lessons Learned from Structural Analysis of Real-Scale Tests

An extended hybrid method for the analysis of the symmetric structural behavior of segmental tunnel linings is proposed. Their deformations cannot be determined by the traditional hybrid methods when the convergences are close to the serviceability limit states (SLSs). Two real-scale tests are employed for the validation of the proposed method. It involves structural analysis that is based on transfer relations. They represent analytical solutions of the linear theory of thin circular arches, and they contain the symmetric mode of rigid-body displacements. The method is termed hybrid because it is based on two types of input, namely the external loading and experimental data of displacements monitored during the test. It is termed extended because, additionally, the vertical and horizontal convergences are employed to produce more accurate structural deformations than obtained by the traditional hybrid method. The latter is found to be unsuitable for structural analysis after sudden failure has occurred in the vicinity of segmental interfaces. At the respective load steps, the structures were in convergence-related serviceability class C, referring to endangered serviceability. The local failures occurring at these load steps resulted in a rapid increase in the structural deformations and fast attainment of the SLS. If, in convergence-related serviceability class C, local failures at segmental interfaces are detected, the strengthening of the structure is necessary. This cannot be delayed to the attainment of serviceability class D, i.e., to reaching the SLS.

A finite strain theory for incompressible rubber-like circular arches with an application

A theory for incompressible rubber-like circular arches, undergoing finite strains and rotations, with an application to the stability of Mooney-Rivlin, doubly fixed, thin beams having initially small circular imperfections under uniformly distributed radial loads, is presented. The essence of considering transverse normal strain is emphasized for an incompressible rubber-like material. The effects of the thickness, initial curvature, and perturbation terms of the pseudo strain components on the buckling loads and central deflections are investigated. The thresholds of buckling are observed to depend on the values of the curvature of the initially imperfect beam for the chosen nonlinear material.

Out-of-Plane Instability and Vibrations of a Flexible Circular Arch Under a Moving Load

Flexible lightweight arched structures are finding increasing use as components in smart engineering applications. Such structures are prone to various types of instability under moving transverse loads. Here, we study deformation and vibration of a hinged circular arch under a uniformly moving point load using geometrically-exact rod theory to allow for large pre- and post-buckling deformations. We first consider the quasi-statics problem, without inertia. We find that for arches with relatively large opening angle ([Formula: see text]160[Formula: see text]) a sufficiently large traversing load will induce an out-of-plane flopping instability, instead of the in-plane collapse (snap-through) that dominates failure of arches with smaller opening angle. In a subsequent dynamics study, with full account of inertia, we then explore the effect of the speed of the load on this lateral buckling. We find speed to have a delaying (or even suppressing) effect on the onset of three-dimensional bending–torsional vibrations and instability. Based on numerical computations we propose a power law describing this effect. Our results highlight the role of inertia in the onset of elastic instability.

Approximate closed-form solutions for free vibration of circular arches with discrete lateral braces

Discrete lateral braces are commonly employed to enhance the out-of-plane stability of arches. However, these braces generate coupling effects among vibration modes, which significantly impact the vibration characteristics of the arches. This paper presents an analytical solution for the free vibration analysis of two-hinged arches with equally-spaced lateral translational and/or rotational braces. A simplified method of evaluating the fundamental frequency for the out-of-plane vibration of arches with equally-spaced lateral braces is introduced. The method relies on the conventional approach of representing arch braces through elastic springs, but here the out-of-plane deflection of the braced arch is constructed by adding related coupled sinusoidal functions to that of the unbraced arch, satisfying both the boundary and kinematic conditions. Subsequently, the fundamental frequency and threshold bracing stiffness or stiffness requirement are derived using the Rayleigh–Ritz method. Finite element analysis (FEA) is applied to investigate the flexural-torsional vibration mode and fundamental frequency of arches with discrete braces, and the results from FEA closely match the theoretical predictions. The effects of number of lateral translational and/or rotational brace, out-of-plane slenderness, included angle, bracing stiffness and bracing position on the fundamental frequency are comprehensively analyzed. It is found that when the fundamental frequency of the braced arch increases due to changes in bracing stiffness, the mode shape displays more intricate behavior, rather than following a straightforward low-to-high mode growth pattern. Furthermore, it is observed that in some cases, the addition of rotational bracing stiffness can markedly enhance the maximum fundamental frequency of the arch with both translational and rotational braces.

In-Plane Vibrations of Deep Sandwich Arches with Different End Conditions Based on a Logarithmic Shear Deformation Theory

This paper deals with the vibrational frequencies of deep sandwich arches to enhance their application domain and possibly use them for energy harvesting. The circular arch with porous nanocomposite core and titanium alloy face sheets having different end conditions is numerically analyzed. The middle core of the sandwich arch is made of a six-layered porous aluminum reinforced with graphene nanoplatelets. The kinematic equations are formulated in this study based on the higher-order shear deformation theory using a logarithmic function of radius. The effective properties of the nanocomposite media are modeled by employing the Halpin–Tsai modified rule. The equations of motion are determined by applying the principle of virtual displacement. The partial differential equations are reduced using the generalized differential quadrature technique to solving an algebraic eigenvalue problem. Novel numerical results are given to show the effects of geometrical parameters, material properties, and boundary conditions on the vibrations of deep sandwich arch.

Experimental and theoretical investigations on out-of-plane buckling of circular aluminum arches with web openings under a central concentrated load

Perforated arches with cellular openings are widely used as roof beams in various buildings due to the functional and appearance requirements of architecture. Perforated arches under a central concentrated load may suffer from out-of-plane buckling when the load reaches to a critical value. This paper presents the analytical solution based on the energy method to predict the critical load of perforated arches under a central concentrated load. Experimental tests and finite element analyses are also carried out for perforated circular aluminum arch specimens to validate the present analytical solution. Good agreement between the analytical, experimental, and numerical results is demonstrated. The present results show that the size of web openings and the slenderness of the arch could affect the out-of-plane buckling behavior of perforated arches significantly. The arch with larger web perforations or larger slenderness ratio has the lower critical load of out-of-plane buckling.

Multiple equilibria of pinned FGP-GPLRC circular arches under a half-span distributed radial load

This article presents a theoretical analysis on the multiple equilibria of pinned functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) circular arches subjected to a half-span distributed radial load. The effective material properties of the arch with different porosity distribution modes are approximated via a modified Halpin–Tsai micromechanical model. The decoupled neutral-plane-based governing equations are then built in the framework of the principle of minimum potential energy, from which analytical solutions for the radial displacement at an arbitrary point on the arch axis are derived. Utilizing a perturbation method, the possible buckling modes are discussed. The complete buckling evolution process of bending moment and vertical displacement are followed, meanwhile the critical geometrical parameters that control buckling behaviors switching are identified. To validate the presented analytical solutions, Finite element (FE) analysis is carried out. An in-depth parameter analysis is performed subsequently to evaluate the fluences of porosity distributions, GPL weight fraction, and porosity coefficient on the multiple equilibria path of arches. It was found that the pinned FGP-GPLRC arches could buckle only in a limit point mode under a half-span distributed radial load. When λ ≥ 8.36 , the multiple equilibria phenomenon occurs and the external force corresponding to inflexion point vanishes.

In-plane nonlinear buckling analysis and design method of concrete-filled steel tubular catenary arches

The prevalence of concrete-filled steel tubular (CFST) catenary arches, renowned for the optimal load-bearing efficiency, has shown a marked increase over the past decades. To date, extensive research has been conducted into the nonlinear buckling behaviors and elastic-plastic strength of circular and parabolic CFST arches, grounded on the assumption that the curvature of the arch axis remains a specific constant. However, for CFST catenary arches, this assumption is not appropriate, given the substantial variation in curvature along the arch rib, and the influence of the arch axis is not adequately addressed in the existing design codes. Therefore, in this paper, a more precise strain expression is employed to conduct the nonlinear buckling analysis on CFST catenary arches. The analytic solutions for both symmetric snap-through buckling and anti-symmetric bifurcation buckling loads are obtained. In addition, a validated finite element (FE) model is adopted to investigate the influence of key parameters, including the slenderness ratio, the arch-axis coefficient, the rise-to-span ratio, and the steel ratio, on the in-plane stability bearing capacity of CFST catenary arches subjected to axial compression. Moreover, the obtained numerical results are utilized for comparison with the prediction results calculated by the existing design codes for CFST or steel arches. The comparison results indicate that the existing design codes have tended to overestimate the in-plane strength of CFST catenary arches, mainly due to the ignorance of the influence of pre-buckling deformation. Thus, based on the nonlinear buckling analysis results, a revised lower-bound design formula for predicting the in-plane stability bearing capacity of CFST catenary arches under axial compression is proposed, considering the influence of the rise-to-span ratio and the steel ratio.

Reliability assessment of circular steel arches with elastic restraints using hybrid ANN-MCS technique

Reliability assessment of circular steel arches with elastic restraints using hybrid ANN-MCS technique

Archicarbons: New Carbon Allotropes Build from Circular Arches of Carbon Atoms as Building Blocks

Molecular and periodic allotropes based on cyclo[18]carbon, known as archicarbons, were investigated using density functional theory (DFT) in both molecular and periodic models. This study explores the physicochemical characteristics of these exquisite carbon allotropes, including various molecular archicarbons (spiro[18]carbon, bicyclo[8]carbon, 0-tricyclo[8] carbon, 0-bi(cyclo[19]carbon), 1-bi(cyclo[19]carbon), and 0-fused[18]carbon) and periodic archicarbons (poly-spiro[8]carbon, poly-0-bi(cyclo[8]carbon), poly-1-bi(cyclo[8]carbon)). Most proposed molecular archicarbons showed higher cohesive energy than cyclo[18]carbon, except for bicyclo[8]carbon, which suggests that those may be experimentally observable. Proposed synthetic routes for both molecular and periodic archicarbons are suggested, highlighting their potential, particularly in semiconductor applications, and paving the way for further exploration of their distinct electronic properties.

Nonlinear buckling and post-buckling analyses of functionally graded circular shallow arches

Snap-through analysis of thin, functionally graded (FG), fixed, circular shallow arches subjected to uniformly distributed vertical load is examined in this paper. The modulus of elasticity varies gradually along with the normal to the axis of the arch in alliance with the power law form. The solution of the geometrically nonlinear problem is carried out by using a numerical scheme accounting for the moderately large deflections theory based on small strain and moderate rotation in the von Kármán sense. The combined effect of the parameters that is, the power law index, the ratio of the modulus of elasticity and the modified slenderness ratio on the support reactions, the snap-buckling and post-buckling behaviors of the fixed circular shallow arches are examined. It is found that the lowest buckling load is considerably affected by the variation of these parameters. In addition, the effects of the material distribution on internal forces, deformed configurations and rotation angle are presented at various stages of the deformation.

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-of-Plane Stability Analysis of the Circular Box Arch with Sinusoidal Corrugated Webs

This paper presents an arch structure called the circular box arch with sinusoidal corrugated webs (CBASCW). This study investigates the out-of-plane elastic buckling behavior and elastoplastic stability capacity of the arch through a combined approach of theoretical derivation and finite element simulation. The section stiffness of the arch, including flexural stiffness, shear stiffness, and torsional stiffness, is achieved through theoretical derivation. Additionally, the elastic buckling load in both pure compression and pure bending states is derived. A simplified model is also introduced, which can conveniently simulate the internal force and deformation of the arch. The elastoplastic instability mechanism and failure mode are studied under various loading conditions, including uniform radial load, end bending moment, vertical load uniformly distributed in full-span, and vertical load uniformly distributed in half-span. Furthermore, the stability curves of the arch under conditions of pure compression and pure bending are graphed by incorporating stability coefficient and regularized slenderness ratio. According to the simulation results obtained from the simplified model and the analysis of stability curves, a design formula for stability capacity is proposed.

Flexural–torsional buckling of steel circular arches with I-section under central concentrated load in elevated-temperature environment

This article reports the fire resistance experiments conducted on I-section circular steel arches, as well as the observed out-of-plane flexural–torsional buckling (FTB) behavior and in-depth finite element numerical simulation results. The test was carried out using a large fire test furnace to provide a real fire environment with a nonuniform temperature field. A specially designed loading device allowed for unconstrained out-of-plane deformation of the specimens inside the furnace, thereby achieving effective load conditions and noncoupled response of the components. Numerical analyses were performed using a combination of the general codes Fluent and Abaqus, with the former used for heat transfer analyses, and a structural FE model including the loading device and complex geometric imperfections was established based on the measured data. Thus, accurate simulation of the out-of-plane behavior of the steel arches at elevated temperature was achieved. On this basis, an in-depth parametric study was carried out to investigate the effects of temperature field variations, load ratio (LR), and geometric imperfection. The analysis results show that FTB occurs at nonuniform temperatures for the arches under concentrated load, and the difference in temperature distribution in fire has a minimal effect on the FTB behavior. LR is negatively correlated with critical temperature; the smaller the LR, the more significant the weakening of critical loads by fire. The effect of initial geometrical imperfections on FTB at elevated temperatures is similar to that at ambient temperatures, and the effect on the critical temperature of FTB can almost be ignored when the imperfection amplitude is less than S/400.

Experimental research and engineering application on bearing capacity of concrete-filled steel tube circular arch

The bearing property and deformation failure law of the CFST circular arch were investigated in order to provide direction for the optimization of the concrete-filled steel tube (CFST) support. The flexural bearing capacity test of the 194 mm × 10 mm CFST was performed initially in this study. It was primarily explored how bearing capacity and deformation of circular arches were affected by the slip of the arch foot and anti-bending strengthening, and the neutral layer migration rule and anti-bending strengthening mechanism of circular arches were examined. The bearing performance of the circular arch under the condition of the concentrated load of the vault and the usual uniform load of the entire span is then simulated in an orthogonal test by numerical simulation in order to extend the experimental investigation. The effect of variables including the steel tube’s outer diameter, thickness, slip of the arch foot, and the ratio of the arch rise to span on the bearing capacity of the circular arch is examined. The study demonstrates that under focused stress on the arch top or full-span normal uniform loading, the arch foot slip is the most important element impacting the CFST support’s bearing capacity. In steel tubes with the same outer diameter and wall thickness, the vector span ratio has a bigger influence than anti-bending strengthening. When the span ratio is the same, the influence of the outer diameter and wall thickness are equal and outweigh the influence of bending strengthening. The circular arch with an outside diameter of 168 mm, a wall thickness of 10 mm, and a rise-span ratio of 0.207 has the best performance characteristics under the influence of concentrated load, and the ultimate failure mechanism is local waist drum deformation failure. Based on the aforementioned study findings, the circular CFST support’s buckling deformation and drum deformation are examined, and a composite support consisting of “anchor net spray + CFST support” is directed for the north three deep track downhill of Yangcheng Coal Mine. Two failure types expose the failure mechanism and provide a technique for optimization. The support had contributed to the circular CFST arc arch’s best bearing performance in the event of waist drum deformation and failure.

Natural vibrations of circular nanoarches of piecewise constant thickness

The free vibrations of elastic circular arches made of a nano-material are considered. A method of determination of eigenfrequencies of nanoarches weakened with stable cracks is developed making use of the concept of the massless spring and Eringen's nonlocal theory of elasticity. The aim of the paper is to evaluate the sensitivity of eigenfrequencies on the geometrical and physical parameters of the nanoarch.