• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.665-677
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• 2023

In the present study, the limit point buckling and postbuckling behaviors of sinusoidal, shallow arches with pinned supports subjected to localized sinusoidal loading, based on the Euler-Bernoulli beam theory, are numerically analyzed. There are some studies on the buckling of sinusoidal shallow arches under the effect of sinusoidal loading. However, in these studies, the sinusoidal loading acts along the horizontal projection of the entire shallow arch. No study has been found in the relevant literature pertaining to the stability of the shallow arches subjected to various lengths of sinusoidal loading. Therefore, the purpose of this paper is to contribute to the literature by examining the effect of the length of the localized sinusoidal loading and the initial rise of the shallow arch on the limit point buckling and postbuckling behaviors. Equilibrium paths corresponding to certain values of the length of the localized sinusoidal loading and various values of the initial rise parameter are presented. It has been observed that the length of the sinusoidal loading and the initial rise parameter affects the transition from no buckling to limit point instability remarkably. The deformed configurations of the sinusoidal shallow arch under localized loading regarding buckling and postbuckling states are illustrated, as well. The effects of the length of the localized sinusoidal loading on the internal forces of the shallow arch are investigated during various stages of the loading.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.1A
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• pp.79-87
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• 2008

This paper investigates the in-plane stability of fixed shallow arches. The shape of the arches is parabolic and the uniformly distributed load is used in the study. The nonlinear governing equilibrium equation of the general arch is adopted to derive the incremental form of the load-displacement relationship and the buckling load of the fixed shallow arches. From the results, it is found that buckling modes (symmetric or asymmetric) of the arches are closely related to the dimensionless rise H, which is the function of slenderness ratio and the rise to span ratio of such arches. Moreover, the threshold of different buckling modes and buckling load for fixed shallow arches are proposed. A series of finite element analysis are conducted and then compared with proposed ones. From the comparative study, the proposed formula provides the good prediction of the buckling load of fixed shallow arches.

• Journal of Korean Society of Steel Construction
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• v.18 no.4
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• pp.427-436
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• 2006

The classical buckling theory assumes that prebuckling behavior is linear and that the effect of prebuckling deformations on buckling can be ignored. However, when the rise to span ratio decreases, prebuckling deformation cannot be ignored and the symetrical buckling strength can be smaler than the asymetrical buckling strength. Finally, arches can fail due to snap-through buckling. This paper investigates the non-linear behavior and strength of pin-ended parabolic shallow arches using the non-linear governing differential equation of shallow arches. These results were compared with the solution for the symmetrical buckling load of pin-ended parabolic shallow arches was suggested.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.2
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• pp.43-54
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• 1992

For shallow arches with large dynamic loading, linear analysis is no longer considered as practical and accurate. In this study, a method is presented for the dynamic analysis of shallow arches in which geometric nonlinearity must be considered. A program is developed for the analysis of the nonlinear dynamic behavior and for evaluation of critical buckling loads of shallow arches. Geometric nonlinearity is modeled using Lagrangian description of the motion. The finite element analysis procedure is used to solve the dynamic equation of motion and Newmark method is adopted in the approximation of time integration. A shallow arch subject to radial step loads is analyzed. The results are compared with those from other researches to verify the developed program. The behavior of arches is analyzed using the non-dimensional time, load, and shape parameters. It is shown that geometric nonlinearity should be considered in the analysis of shallow arches and probability of buckling failure is getting higher as arches are getting shallower. It is confirmed that arches with the same shape parameter have the same deflection ratio at the same time parameter when arches are loaded with the same parametric load. In addition, it is proved that buckling of arches with the same shape parameter occurs at the same load parameter. Circular arches, which are under a single or uniform normal load, are analyzed for comparison. A parabolic arch with radial step load is also analyzed. It is verified that the developed program is applicable for those problems.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.3
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• pp.1-9
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• 1986

Dynamic stability of parabolic shallow arches, which are supported by hinges at both ends, is investigated. The Runge-Kutta method is used to perform time integrations of the differential equations of motion with proper boundary conditions. Based on Budiansky-Roth criterion, dynamic critical load combinations are evaluated numerically for cases of step loads of infinite duration and impulse loads, individually. The results are plotted to get interaction curves. The loci of the dynamic critical loads, which are obtained in this study, are proposed as boundaries between the dynamic stability and instability regions for the parabolic shallow arches. The results for the parabolic shallow arches are also compared with those for sinusoidal arches of the same arch rises. According to the investigation, the dynamic stability regions for the parabolic arches are larger than those for the sinusoidal arches. However, it is shown that the arch rise is the more governing factor than the shape.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.2
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• pp.39-48
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• 1990

For shallow circular arches with large dynamic loading, use of linear analysis is no longer considered as practical and accurate. In this study, a method is presented for the dynamic analysis of the shallow circular arches in which geometric nonlinearity is dominant. A program is developed for analysis of the nonlinear dynamic behavior and for evaluation of the critical buckling loads of the shallow circular arches. Geometric nonlinearity is modeled using Lagrangian description of the motion and finite element analysis procedure is used to solve the dynamic equations of motion in which Newmark method is adopted as a time marching scheme. A shallow circular arch subject to radial step load is analyzed and the results are compared with those from other researches to verify the developed program. The critical buckling loads of shallow arches are evaluated using the non-dimensional parameter. Also, the results are compared with those from linear analysis.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.2
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• pp.87-94
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• 1998

Behavioral characteristics of shallow circular arches with dynamic loading and different end conditions are analysed. Geometric nonlinearity is modelled using Lagrangian description of the motion. The finite element analysis procedure is used to solve the dynamic equation of motion, and the Newmark method is adopted in the approximation of time integration. The behavior of arches is analysed using the buckling criterion and non-dimensional time, load and shape parameters which Humphreys suggested. But a new deflection-ratio formula including the effect of horizontal displacement plus vertical displacement is presented to apply for the non-symmetric buckling problems. Through the model analysis, it's confirmed that fix-ended arches have higher buckling stability than hinge-ended arches, and arches with the same shape parameter have the same deflection ratio at the same time parameter when loaded with the same parametric load.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.869-890
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• 2022

We develop a rigorous mathematical framework for studying dynamic behavior of cracked beams and shallow arches. The governing equations are derived from the first principles, and stated in terms of the subdifferentials of the bending and the axial potential energies. The existence and the uniqueness of the solutions is established under various conditions. The corresponding mathematical tools dealing with vector-valued functions are comprehensively developed. The motion of beams and arches is studied under the assumptions of the weak and strong damping. The presence of cracks forces weaker regularity results for the arch motion, as compared to the beam case.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2000.10a
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• pp.213-218
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• 2000

This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations are assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Sinusoidal arches with hinged-hinged and clamped-clamped end constraints are considered in analysis. The frequency equations (lowest symmetical and antisymmetrical natural frequency equations) are obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated.

• Computational Structural Engineering
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• v.7 no.1
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• pp.69-81
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• 1994

This paper summarizes a dynamic analysis of the shallow circular arches under dynamic loading, considering the geometric nonlinearity. The major emphasis is placed on the development of computer program, which is utilized for the analysis of the nonlinear dynamic behavior and for the evaluation of the critical buckling loads of the shallow circular arches. Geometric nonlinearity is modeled using Lagrangian description of the motion and a finite element analysis procedure is used to solve the dynamic equation of motion. A circular arch subject to normal step load is analyzed and the results are compared with those from other researches to verify the developed program. The critical buckling loads of arches are estimated using the non-dimensional time, load and shape parameters and the results are also compared with those from the linear analysis. It is found that geometric nonlinearity plays and important role in the analysis of shallow arches and the probability of buckling failure is getting higher as arches become shallower.