• KSCE Journal of Civil and Environmental Engineering Research
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• v.41 no.3
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• pp.191-200
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• 2021

This paper deals with the boundary conditions of the stress resultants at the mid-arc for free vibration analyses of the arch. The considered arch is a horseshoe symmetric elliptic arch. The work dealing with the boundary conditions of the deflection at both ends of the arch has already been reported in the open literature. This revisited paper aims to study the suitability of the boundary conditions of the stress resultants at the mid-arc to be replaced by the boundary condition at both ends. In this study, the boundary conditions of the stress resultants at the mid-arc are newly derived based on the theory of the previous work, and natural frequencies and mode shapes are obtained using the new boundary conditions of the stress resultants. The numerical results of this paper confirm that the new boundary conditions have been validated according to previous studies and results of finite element ADINA.

• Computational Structural Engineering : An International Journal
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• v.1 no.1
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• pp.49-57
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• 2001

This paper presents exact solutions for the modal stress-resultant distributions for vibrating rectangular Mindlin plates involving two opposite sides simply supported while the other two sides free. These exact stress-resultants of vibrating plates with free edges, hitherto unavailable, are very important because they serve as benchmark solutions for checking numerical solutions and methods. Using the exact solutions of a square plate, this paper highlights the problem of determining accurate stress-resultants, especially the transverse shear forces and twisting moments in thin plates, when employing the widely used numerical methods such as the Ritz method and the finite element method. Thus, this study shows that there is a need for researchers to develop refinements to the Ritz method and the finite element method for determining very accurate stress-resultants in vibrating plates with free edges.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2001.10a
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• pp.198-201
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• 2001

This paper deals with the Automatic Analysis of Continuous Beams with Variable Cross-Section. Based on the principle of superpositon and the method of consistent deformations, the governing differential equation is derived for the deflection and stress resultants of such continuous beam. The effects of variable load conditions, the end constraints on the deflection and the stress resultants are analyzed. It is expected that the results obtained herein can be used practically in the structural engineering.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.41-49
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• 2002

An efficient algorithm automatically determining cross sectional properties of thin-walled beams is developed using the minimum information about geometry of the cross section. This scheme is applied to automatic calculation of normal and shear stress distribution corresponding to stress resultants as well as sectional constants for complex open and closed thin-walled sections. Numerical examples evaluating section constants and stress distributions is presented and compared with the available reference's results.

• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.707-720
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• 2005

The bending stress formula that taking into account the transverse deformation is developed for plane-curved, untwisted isotropic beams subjected to loadings that result in deformations in the plane of curvature. In order to account the transverse Poisson contraction effect, a new constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures for a curved plate is derived in a $6{\times}6$ matrix form. This constitutive relation will provide the fundamental basis to the analyses of curved structures composing of isotropic or anisotropic materials. Then, the bending stress formula of a curved isotropic beam can be deduced from this newly developed curved plate theory. The stress predictions by the present analysis are compared to those by the analysis that neglected the Poisson contraction effect. The results show that the Poisson effect becomes more significant as the Poisson ratio and the curvature are getting larger.

• Steel and Composite Structures
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• v.19 no.2
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• pp.327-348
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• 2015

A numerical procedure is presented that provides ultimate curvature and moment domains for composite rectangular and circular cross-sections of reinforced concrete columns with or without an embedded steel section subjected to combined axial loading and biaxial bending. The stress resultants for the concrete and reinforcement bars are calculated using fiber analysis and the stress resultants for the encased structural steel are evaluated using an exact integration of the stress-strain curve over the area of the steel section. A dimensionless formula is proposed that can be used for any section with similar normalized geometric and mechanical parameters. The contribution of each material to the bearing capacity of a section (resistance load and moments) is calculated separately so that the influence of each geometric or mechanical parameter on the bearing capacity can be investigated separately.

• Structural Monitoring and Maintenance
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• v.4 no.3
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• pp.269-299
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• 2017

This paper presents a Level III damage evaluation methodology, which simultaneously, identifies the location, the extent, and the severity of stiffness damage in deep beams. Deep beams are structural elements with relatively high aspect (depth-to-length) ratios whose response are no longer based on the simplified Euler-Bernoulli theory. The proposed methodology is developed on the bases of the force-displacement relations of the Timoshenko beam theory and the concept of invariant stress resultants, which states that the net internal force existing at any cross-section of the beam is not affected by the inflicted damage, provided that the external loadings in the undamaged and damaged beams are identical. Irrespective of the aspect ratios, local changes in both the flexural and the shear stiffnesses of beam-type structures may be detected using the approach presented in this paper.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.131-150
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• 2006

Exact analytical solutions for in-plane static problems of planar curved beams with variable curvatures and variable cross-sections are derived by using the initial value method. The governing equations include the axial extension and shear deformation effects. The fundamental matrix required by the initial value method is obtained analytically. Then, the displacements, slopes and stress resultants are found analytically along the beam axis by using the fundamental matrix. The results are given in analytical forms. In order to show the advantages of the method, some examples are solved and the results are compared with the existing results in the literature. One of the advantages of the proposed method is that the high degree of statically indeterminacy adds no extra difficulty to the solution. For some examples, the deformed shape along the beam axis is determined and plotted and also the slope and stress resultants are given in tables.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.11a
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• pp.105-108
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• 2004

In general, the nonlinear behavior of composite structures composing of steel and concrete is analyzed on the basis of the assumption of the perfect bond actions in steel-concrete interface in which the interface slip or separation is not allowed. The assumption is based on the fact that the full interface bond behavior is provided with the mechanical connectors of studs. However, since the number and spacing of the studs are determined by the stress resultants calculated in the interface area, the interface analysis is required to evaluate the stress resultants. This paper describes the nonlinear steel-concrete interface behavior considering the two interface failure mechanisms of slip and separation. Elastoplastic constitutive relation is developed. thru the formulation framework using the two energy dissipation mechanisms. As the result, the steel plate push-out tests sandwitched between concrete blocks are analyzed and compared with the test results with which the good agreements are observed.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.459-475
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• 2005

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.