• Structural Engineering and Mechanics
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• v.3 no.5
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• pp.511-525
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• 1995

The differential equations governing in-plane free vibrations of the elastic, catenary arch with rotatory inertia are derived in Cartesian coordinates. Frequencies and mode shapes are computed numerically for such arches with unsymmetric axes, for both clamped-clamped and hinged-hinged end constraints. The lowest four natural frequency parameters are reported, with and without rotatory inertia, as a function of three nondimensional system parameters; the span to cord length ratio e, the slenderness ratio s, and the rise to cord length ratio f. Experimental measures of frequencies and mode shapes for several laboratory-scale catenary models serve to validate the theoretical results.

• Magazine of the Korean Society of Agricultural Engineers
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• v.43 no.3
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• pp.85-93
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• 2001

In this study, a computer program considering shape imperfections of arch under dynamic loading was developed. The shape imperfection of arch was assumed as higher degree polynomial expressed as $\omega$$_{i}$ = $\omega$$_{o}$ (1-(2$\chi$/L)$^{m}$ )$^n$and sinusoidal curve such as $\omega$$_{i}$ = $\omega$$_{o}$ sin(η$\pi$$\chi$/L). In finite element formulation, the material nonlinear behavior was assumed the elasto-viscoplastic model highly corresponding to the real behavior of the material and the geometrically nonlinear behavior was modeled using Lagrangian description of motion. Also, the behavior of steel was modeled by applying yield criteria of Von Mises. The developed program was applied to the analysis of the dynamic behavior for the clamped beam subjected to the concentrated load at midspan and the results were compared with those from other research to investigate accuracy of the presented finite element program. In numerical examples, the shape imperfections of L/500, L/1,000 and L/2,000 were considered and the modes of shape imperfections of the symmetric and antisymmetric were adopted. The effects of the shape imperfections on the dynamic behavior of arch were conspicuous and results of analysis indicate that the reasonable values of arch rise to arch span ratio ranged between 0.1 and 0.3.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.340-343
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• 2007

The differential equations governing free, in-plane vibrations of non-circular arches with the translational (radial and tangential directions) and rotational springs at the ends, including the effects of rotatory inertia, shear deformation and axial deformation, are solved numerically using the corresponding boundary conditions. The lowest four natural frequencies for the parabolic geometry are calculated over a range of non-dimensional system parameters: the arch rise to span length ratio, the slenderness ratio, and the translational and rotational spring parameters.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6A
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• pp.827-833
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• 2008

This paper deals with the free vibrations of elastica shaped arches. The elastica shaped arches are formed by the post-buckled column whose arc length is always constant. The equations governing free, planar vibration of general arch in open literature are modified for applying the free vibrations of elastica shaped arch and solved numerically to obtain frequencies and mode shapes for hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effects of rotatory inertia, rise ratio and slenderness ratio on natural frequencies are presented. The frequencies of elastica shaped arches are greater than those of parabolic shaped ones. Also, typical mode shapes are presented in figures.

• Earthquakes and Structures
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• v.15 no.5
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• pp.541-553
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• 2018

In this paper a limit analysis based procedure for the rapid evaluation of the in-plane seismic capacity of masonry arch bridges is carried out. Attention has been paid to the effect of the backfill on the collapse load. A parametric investigation has been performed by varying the rise/span ratio and the results have been compared with those obtained by finite element modelling. The comparison highlights the conservative feature of the proposed model in terms of ultimate loads and a good agreement in terms of collapse mechanisms.

• Structural Engineering and Mechanics
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• v.9 no.2
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• pp.169-180
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• 2000

An optimization procedure has been prescribed for the minimum weight design of symmetrical parabolic arches subjected to arbitrary loading. The cross section is assumed to be a symmetrical box section with variable depth and flange areas. The webs are unstiffened and have constant thickness. The proposed sequential, iterative search technique determines the optimum geometrical configuration of the parabolic arch which includes the optimum depth profile and the optimum lengths and areas of the required flange plates corresponding to the prescribed number of curtailments. The study shows that the optimum value of rise to span ratio (h/L) of a parabolic arch is maximum at 0.41 for uniformly distributed loading over the entire span. For any other loading, the optimum value of h/L is less than 0.41.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.673-682
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• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• Structural Engineering and Mechanics
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• v.13 no.6
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• pp.713-730
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• 2002

This paper presents a finite element approach for determining the natural frequencies for planar inclined arches of various shapes vibrating in three-dimensional space. The profile of inclined arches, represented by undeformed centriodal axis of cross-section, is defined by the equation of plane curves expressed in the rectangular coordinates which are : circular, parabolic, sine, elliptic, and catenary shapes. In free vibration state, the arch is slightly displaced from its undeformed position. The linear relationship between curvature-torsion and axial strain is expressed in terms of the displacements in three-dimensional space. The finite element discretization along the span length is used rather than the total are length. Numerical results for arches of various shapes are given and they are in good agreement with those reported in literature. The natural frequency parameters and mode shapes are reported as functions of two nondimensional parameters: the span to cord length ratio (e) and the rise to cord length ratio (f).

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.10
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• pp.24-30
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• 2018

As the demand for underground space increases, many researchers have been studying the load reduction method using high compressible materials to solve for the stability problem of the overhead load and for the increase of the earth pressure which decreases the function of the underground structure. This paper determines the optimum soft zone and the effect of the using EPS Geofoam as a load reduction material to arch structures. A finite element analysis program, ABAQUS, is used to analyze the soil-structure interaction and the behavior of buried arch structures considering different four EPS Geofoam forms to confirm the most conservative shape. The optimum cross-sectional shape was determined by comparing the results of earth pressure reduction rate in accordance with the change of span-rise ratio and span length of the arch structure. It was confirmed that the earth pressure generated in the arch structure using the optimal soft zone selected by the numerical analysis was reduced by an average of 78%. In this study, the effect of EPS Geofoam on soil pressure reduction and its applicability to underground arch structures will provide an economical and conservative way to design underground structures and will help to increase the usability of deep underground space.

• Steel and Composite Structures
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• v.43 no.6
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• pp.785-796
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• 2022

Concrete-encased steel (CES) beam, in which structural steel is encased in a reinforced concrete (RC) section, is widely applied in high-rise buildings as transfer beams due to its high load-carrying capacity, great stiffness, and good durability. However, these CES beams are prone to shear failure because of the low shear span-to-depth ratio and the heavy load. Due to the high load-carrying capacity and the brittle failure process of the shear failure, the accurate strength prediction of CES beams significantly influences the assessment of structural safety. In current design codes, design formulas for predicting the shear strength of CES beams are based on the so-called "superposition method". This method indicates that the shear strength of CES beams can be obtained by superposing the shear strengths of the RC part and the steel shape. Nevertheless, in some cases, this method yields errors on the unsafe side because the shear strengths of these two parts cannot be achieved simultaneously. This paper clarifies the conditions at which the superposition method does not hold true, and the shear strength of CES beams is investigated using a compatible truss-arch model. Considering the deformation compatibility between the steel shape and the RC part, the method to obtain the shear strength of CES beams is proposed. Finally, the proposed model is compared with other calculation methods from codes AISC 360 (USA, North America), Eurocode 4 (Europe), YB 9082 (China, Asia), JGJ 138 (China, Asia), and AS/NZS 2327 (Australia/New Zealand, Oceania) using the available test data consisting of 45 CES beams. The results indicate that the proposed model can predict the shear strength of CES beams with sufficient accuracy and safety. Without considering the deformation compatibility, the calculation methods from the codes AISC 360, Eurocode 4, YB 9082, JGJ 138, and AS/NZS 2327 lead to excessively conservative or unsafe predictions.