• Structural Engineering and Mechanics
• /
• v.45 no.4
• /
• pp.569-594
• /
• 2013

The free vibration of axially functionally graded tapered arches including shear deformation and rotatory inertia are studied through solving the governing differential equation of motion. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches with hinged-hinged, hinged-clamped and clamped-clamped end restraints. In this study Differential Quadrature element of lowest order (DQEL) or Lagrangian Interpolation technique is applied to solve the problems. Three general taper types for rectangular section are considered. The lowest four natural frequencies are calculated and compared with the published results.

• Journal of KSNVE
• /
• v.10 no.2
• /
• pp.353-360
• /
• 2000

Numerical methods are developed for calculating the natural frequencies and mode shapes of the tapered cantilever arches with variable curvature. The differential equations governing the free vibrations of such arches are derived and solved numerically, in which the effect of rotatory inertia is included. The parabolic shape is chosen as the arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch with variable curvature while both the prime and quadratic arched members are considered as the tapered arch. Comparisons the natural jfrequencies between this study and finite element method SAP 90 seve to validate the numerical method developed herein. The lowest four natural frequencies are reported as a function of four non-dimensional system parameters. The effects of both the rotatory inertia and cross-sectional shape are reported. Also, the typical mode shapes of stress resultants as well as the displacements are reported.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.4 no.1
• /
• pp.69-77
• /
• 1984

In this paper, the governing differential equations for the free vibration of uniform parabolic arches are derived on the basis of equilibrium equations of a small element of arch rib and the D'Alembert principle. A trial eigen value method is used for determining the natural frequencies and mode shapes. And the Runge-Kutta fourth order integration technique is also used in this method to perform the integration of the differential equations. A detailed study is made of the first mode for the symmetrical and anti-symmetrical vibrations of hinged arches with the Span length equal to 10 m. The effects of the rise of arch, the radius of gyration and the rotary inertia on free vibrations are presented in detail in curves and table.

• Journal of Korean Society of Steel Construction
• /
• v.17 no.2 s.75
• /
• pp.161-171
• /
• 2005

When the in-plane flexural rigidity is small in relation to the applied load, the arch ribs may buckle to the in-plane direction. Designers should therefore determine the in-plane buckling strength. To determine the buckling strength of arch ribs, designers have to consider the material nonlinear response. But in the case of arch ribs having large slenderness ratio, arch ribs may buckle in the elastic range, and when the arch ribs have low slenderness ratio, elastic buckling strength is useful in the preliminary design. In this paper, elastic buckling strength of arch ribs, which are frequently used in practical design, is studied using nonlinear finite element method. In general, the relation between flexural rigidity and elastic buckling strength is linear. As seen from the results, however, when the arch ribs have low slenderness ratio, the relation between flexural rigidity and elastic buckling strength is nonlinear.

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

• 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.

• 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.