• Magazine of the Korean Society of Agricultural Engineers
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• v.44 no.3
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• pp.92-100
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• 2002

The advent or high-strength steel has enabled the arch structures to be relatively light, durable and long-spanned by reducing the cross sectional area. On the other hand, the possibility of collapse may be increased due to the slender members which may cause the stability problems. The limit analysis to estimate the ultimate load is based on the concept of collapse mechanism that forms the plastic zone through the full transverse sections. So, it is not appropriate to apply it directly to the instability analysis of arch structures that are composed with compressive members. The objective of this study is to evaluate the ultimate load carrying capacity of the parabolic arch by using the elasto-plastic finite element model. As the rise to span ratio (h/L) varies from 0.0 to 0.5 with the increment of 0.05, the ultimate load has been calculated fur arch structures subjected to uniformly distributed vertical loads. Also, the disco-elasto-plastic analysis has been carried out to find the duration time until the behavior of arch begins to show the stable state when the estimated ultimate load is applied. It may be noted that the maximum ultimate lead of the parabolic arch occurs at h/L=0.2, and the appropriate ratio can be recommended between 0.2 and 0.3. Moreover, it is shown that the circular arch may be more suitable when the h/L ratio is less than 0.2, however, the parabolic arch can be suggested when the h/L ratio is greater than 0.3. The ultimate load carrying capacity of parabolic arch can be estimated by the well-known formula of kEI/L$^3$where the values of k have been reported in this study. In addition, there is no general tendency to obtain the duration time of arch structures subjected to the ultimate load in order to reach the steady state. Merely, it is observed that the duration time is the shortest when the h/L ratio is 0.1, and the longest when the h/L ratio is 0.2.

• Journal of the Korean Society of Hazard Mitigation
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• v.5 no.1 s.16
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• pp.55-62
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• 2005

Parabolic arch ribs are widely used in practical. In case of circular arch ribs. Inelastic in-plane buckling behaviors were investigated by Trahair(1996). Recently Yong-lin Pi & Bradford(2004) investigated about in-plane design equation for circular arch ribs. In $1970{\sim}1980$. In-plane buckling strength about parabolic arch ribs were studied by some japan researchers (Sinke, Kuranishi). Study results of Sinke & kuranishi are only valid for rise-span ratio $0.1{\sim}0.2$. In this paper. The researchers investigated about in-plane inelastic buckling behaviors of parabolic arch ribs having rise-span ratio from 0.1 to 0.4. From the results. When the rise-span ratio increase, flexural moments increase and influence of axial force to in-plane buckling strength decrease. Finally, buckling curves for parabolic arch ribs subjected distributed loading along the axis were suggested.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.6
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• pp.21-28
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• 2004

This study aims to investigate the effects of partially distributed loads on the dynamic behaviour of steel parabolic arches by using the elasto-plastic finite element model based on the Von Mises yield criteria and the Prandtl-Reuss How rule. For this purpose, the vertical and the radial load conditions were considered as a distributed loading and the loading range is varied from 40% to 100% of arch span. Normal arch and arch with initial deflection were studied. The initial deflection of arch was assumed by the sinusoidal motile of ${\omega}_i\;=\;{\\omega}_O$ sin ($n{\pi}x/L$). Several numerical examples were tested considering symmetric initial deflection when the maximum initial deflection at the apex is fixed as L/1000. The analysis resluts showed that the maximum deflection at the apex of arch was occurred when 70% of arch span was loaded. The maximum deflection at the quarter point of arch span was occurred when 50% of arch span was loaded. It is known that the optimal rise to span ratio between 0.2 and 0.3 when the vertical or radial distributed load is applied. It is verified that the influence of initial deflection of radial load case is more serious than that of vertical load case.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.2
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• pp.67-75
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• 2004

This study aims to investigate the dynamic behaviour of a parabolic arch with initial deflection by using the elasto-plastic finite element model where the von-Mises yield criteria have been adopted. The initial deflection of arch was assumed by the high order polynomial of ${\omega}_i$ = ${\omega}_o$${(1-{(2x/L)}^m)}^n$) and the sinusoidal profile of ${\omega}_i$ = ${\omega}_o$$\sin$(n$\pi$x/L). Several numerical examples were tested considering symmetric initial deflection modes when the maximum initial deflection of an arch is fixed as L/500, L/1000, L/2000 or L/5000. The effects of polynomials order on the dynamic behavior of arch were not conspicuous. The most unfavorite dynamic response occurs when the maximum initial deflection varies from L/1000 to L/4000 if the initial deflection mode is represented by high order polynomials.

• Structural Engineering and Mechanics
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• v.8 no.5
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• pp.465-476
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• 1999

A structural optimization process is presented for arches with varying cross-section. The optimality criteria method is used to develop a recursive relationship for the design variables considering displacement, stresses and minimum depth constraints. The depth at the crown and at the support are taken as design variables first. Then the approach is extended by taking the depth values of each joint as design variable. The curved beam element of constant cross section is used to model the parabolic and circular arches with varying cross section. A number of design examples are presented to demonstrate the application of the method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.942-947
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• 2004

The differential equations governing free, in-plane vibrations of stepped non-circuiar arches are derived as nondimensional forms including the effects of rotatory inertia, shear deformation and axial deformation. The governing equations are solved numerically to obtain frequencies and mode shapes. The lowest four natural frequencies and mode shapes are calculated for the stepped parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of arch rise to span length ratios, slenderness ratios, section ratios, and discontinuous sector ratios are considered. The effect of rotatory inertia and shear deformation on natural frequencies is reported. Typical mode shapes of vibrating arches are also presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.846-851
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• 2003

The differential equations governing free, in-plane vibrations of non-circular arches with non-uniform cross-section, including the effects of rotatory inertia, shear deformation and axial deformation, are derived and solved numerically to obtain frequencies. The lowest four natural frequencies are calculated for the prime parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. Three general taper types for rectangular section are considered. A wide range of arch rise to span length ratios, slenderness ratios, and section ratios are considered. The agreement with results determined by means of a finite element method is good from an engineering viewpoint.

• Magazine of the Korean Society of Agricultural Engineers
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• v.45 no.2
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• pp.78-85
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• 2003

This study aims to investigate the effect of partially distributed loads on the static behavior of parabolic arches by using the elastic-plastic finite element model. For this purpose, the vertical, the radial, and the anti-symmetric load cases are considered, and the ratio of loading range and arch span is increased from 20% to 100%. Also, the elastic-visco-plastic analysis has been carried out to estimate the elapse time to reach the stable state of arches when the ultimate load obtained by the finite element analysis is applied. It is noted that the ultimate load carrying capacities of parabolic arches are 6.929 tf/$m^2$ for the radial load case, and 8.057 tf/$m^2$ for the vertical load case. On the other hand, the ultimate load is drastically reduced as 2.659 tf/$m^2$ for the anti-symmetric load case. It is also shown that the maximum ultimate load occurs at the full ranging distributed load, however, the minimum ultimate loads of the radial and vortical load cases are obtained by 2.336 tf/$m^2$, 2.256 tf/$m^2$, respectively, when the partially distributed load is applied at the 40% range of full arch span.

• 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.

• Structural Engineering and Mechanics
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• v.39 no.6
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• pp.751-765
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• 2011

The present paper deals with the identification of a concentrated damage in an elastic parabolic arch through the minimization of an objective function which measures the differences between numerical and experimental values of static displacements. The damage consists in a notch that reduces the height of the cross section at a given abscissa and therefore causes a variation in the flexural stiffness of the structure. The analytical values of static displacements due to applied loads are calculated by means of the principle of virtual work for both the undamaged and damaged arch. First, pseudo-experimental data are used to study the inverse problem and investigate whether a unique solution can occur or not. Various damage intensities are considered to assess the reliability of the identification procedure. Then, the identification procedure is applied to an experimental case, where displacements are measured on a prototype arch. The identified values of damage parameters, i.e., location and intensity, are compared to those obtained by means of a dynamic identification technique performed on the same structure.