• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.1A
• /
• pp.79-87
• /
• 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 the Computational Structural Engineering Institute of Korea
• /
• v.13 no.3
• /
• pp.321-328
• /
• 2000

An improved formulation of thin-wailed curved beams with variable curvatures based on displacement field considering the second order terms of finite semitangential rotations is presented. From linearized virtual work principle by Vlasov's assumptions, the total potential energy is derived and all displacement parameters and the warping functions are defined at cendtroid axis. In developing the thin-walled curved beam element having eight degrees of freedom per a node, the cubic Hermitian polynomials are used as shape functions. In order to verify the accuracy and practical usefulness of this study, free vibrations and buckling analyses of parabolic and elliptic arche shapes with mono-symmetric sections are carried out and compared with the results analyzed by ABAQUS' shell element.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.971-976
• /
• 2002

The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in rectangular coordinates rather than in polar coordinates, in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Rectangular coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters: the rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.

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

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.12 no.12
• /
• pp.970-978
• /
• 2002

The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates. in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters the rise to chord length ratio. the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.