• 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.

• Proceedings of the Korea Concrete Institute Conference
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• 1997.10a
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• pp.603-608
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• 1997

Studies on the second-order analysis of reinforced concrete columns have been chiefly dealt with symmetric section under uniaxial loading. In practical situations, however, columns are subjected to biaxial loadings. Therefore, for more accurate prediction of the behavior of concrete columns under biaxial loading, the interaction between bending moments of major and minor axes should be considered. Recently Kim & Lee proposed a numerical method of predicting the behavior of concrete columns under biaxial loading. In this paper, to investigate the behavior of concrete columns under biaxial loading and verify the validity of proposed method, a series of test were carried out for sixteen tied reinforced columns with 100${\times}$100mm square and 200${\times}$100mm rectangular sections under various loading conditions. The length of columns was 1,300mm and the concrete strength was 28MPa. The boundary conditions at the both ends were hinged and end eccentricities were equal(400mm). Proposed numerical analyses applied to the test piece were performed to predict behavior of concrete columns with square and rectangular sections under various loading conditions. Test results were also compared with those using the moment magnifier method in ACI code. The test results showed that the moment magnifier method is conservative.

• Structural Engineering and Mechanics
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• v.84 no.4
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• pp.561-573
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• 2022

This paper presents a new model to obtain the minimum area of the contact surface for rectangular isolated footings, considering that the contact surface works partially to compression (a part of the contact surface of the footing is subjected to compression and the other is not in compression or tension). The methodology is developed by integration to obtain the axial load "P", moment around the X axis "M_x" and moment around the Y axis "M_y". This document presents the simplified and precise equations of the four possible cases of footing subjected to uniaxial bending and five possible cases of footing subjected to biaxial bending. The current model considers the contact area of the footing that works totally in compression, and other models consider the contact area that works partially under compression and these are developed by very complex iterative processes. Numerical examples are presented to obtain the minimum area of rectangular footings under an axial load and moments in two directions, and the results are compared with those of other authors. The results show that the new model presents smaller areas than the other authors presented.

• Structural Engineering and Mechanics
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• v.43 no.2
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• pp.147-161
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• 2012

This paper presents a curvature method for analysis of beam-columns with different materials and arbitrary cross-section shapes and subjected to combined biaxial moments and axial load. Both material and geometric nonlinearities (the p-delta effect in this case) were incorporated. The proposed method considers biaxial curvatures and uniform normal strains of discrete cross-sections of beam-columns as basic unknowns, and seeks for a solution of the column deflection curve that satisfies force equilibrium conditions. A piecewise representation of the beam-column deflection curve is constructed based on the curvatures and angles of rotation of the segmented cross-sections. The resulting bending moments were evaluated based on the deformed column shape and the axial load. The moment curvature relationship and the beam-column deflection calculation are presented in matrix form and the Newton-Raphson method is employed to ensure fast and stable convergence. Comparison with results of analytic solutions and eccentric compression tests of wood beam-columns implies that this method is reliable and effective for beam-columns subjected to eccentric compression load, lateral bracings and complex boundary conditions.

• Journal of Korean Society of Steel Construction
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• v.14 no.5 s.60
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• pp.567-576
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• 2002

Maximum-strength concrete-ailed steel square tubular columns were tested under concentric and biaxial eccentric load. Buckling length-section depth ratio $L_k/D$, magnitude of eccentricity e, and angle of eccentric load ${\theta}$ were selected as experimental parameters. Strength and behavior were also examined. Test results showed that the maximum strength of columns under biaxial eccentric load could be predicted using the previously proposed strength formula of columns under uniaxial eccentric load. Likewise, the behavior and maximum strength of columns could be predicted using the analysis.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.21 no.7
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• pp.669-673
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• 2008

ITO thin film was deposited on PC substrate in Facing Targets Sputtering (FTS) system with various sputtering conditions. After it is applied to external bending force, we investigated how change the surface and electrical property of as-deposited ITO thin film. As the L(face-plate distance) of substrate decreases, it found that the maximum crack density is increasing at the center position and decreasing crack density as goes to the edge. So to apply same curvature (r) and bending force to PC substrate with ITO thin film, we fixed the L that is equal to curvature radius (2r). Before bending test, ITO thin films that deposited in the input current of 0.4 A and thickness of 200 nm already had biaxial tensile failure because of each different CTE (Coefficient of Thermal Expansion) and Others had been shown no bending or crack. After bending test, all samples had been shown cracks at about 200 times and as increasing the crack density, resistivity increased.

• Magazine of the Korea Concrete Institute
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• v.9 no.2
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• pp.99-108
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• 1997

Many studies on the second-order analysis of reinforced concrete columns have been dealt for symmetric sections under uniaxial loading. However, actual columns are practically subjected to hiaxial loading. In order to more accurately predict the behavior of concrete columns under biaxial loading. the interaction between bending moments of major and minor axes should be considered. In this paper, a stiffness matrix of columns under biaxial loadings was derived and a numerical method was proposed. Numerical analyses, based on the proposed method. were performed to predict behavior of concrete columns with square and rectangular sections under various loading conditions. The analytical results were compared to those using the moment magnifier method in ACI code. It was found that the ultimate strength of concrete rectangular columns, fhr some cases of' biaxial loading conditions. calculated by the moment magnifier method was larger than the values based on the proposed method and therefore. may be ovet.'stimated.

• Journal of Korean Society of Steel Construction
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• v.14 no.6
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• pp.823-834
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• 2002

Maximum-strength concrete-filled steel square tubular columns were tested under concentric and biaxial eccentric load. Buckling length-section depth ratio $L_k/D$, magnitude of eccentricity e, and angle of eccentric load ${\theta}$ were selected as experimental parameters. Strength and behavior were also examined. Test results showed that the maximum strength of columns under biaxial eccentric load could be predicted using the previously proposed strength formula of columns undr uniaxia eccentric load. Likewise, the behavior and maximum strength of columns could be predicted using the analysis.

• Magazine of the Korea Concrete Institute
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• v.10 no.4
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• pp.113-124
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• 1998

Numerical study using nonlinear finite element analysis is done for investigating behavior of isolated reinforced concrete walls subject to combined in-plane and out-of-plane bending moments and axial force. A method for estimating the ultimate strength of wall is developed, based on the analytical results. For the nonlinear finite element analysis, a computer program addressing material and geometric nonlinearities is developed. An existing unified method combining plasticity theory and damage model is used for material model of reinforced concrete. By numerical studies, the internal force distribution in the cross section is idealized, and a new method for estimating the ultimate strength of wall is developed. According to the proposed method, variation of the interaction curve of in-plane bending moment and axial force depends on the range of the permissible axial force per unit length that is determined by the given amount of out-of-plane bending moment. As the out-of-plane bending moment increases, the interaction curve shrinks, which indicates a decrease in the ultimate strength. The proposed method is compared with an existing method using the general assumption that strain shall be directly proportional to the distance from the neutral axis. Compared with the proposed method, the existing method overestimates the ultimate strength for walls subject to low out-of-plane bending moments, and it underestimates the ultimate strength for walls subject to high out-of-plane bending moments.

• Structural Engineering and Mechanics
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• v.78 no.3
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• pp.269-280
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• 2021

Reinforced concrete (RC) structural walls with L-shaped sections are commonly used in RC buildings. The walls are often expected to sustain biaxial load and Unsymmetrical bending in an earthquake event. However, there currently exists limited experimental evidence regarding their seismic behaviour in these lateral loading directions. This paper makes experimental and numerical investigations to these walls behaviours. Experimental evidences are presented for four L-shaped wall specimens which were tested under simulated seismic load from different lateral directions. The results highlighted some distinct behaviour of L-shaped walls sustaining Unsymmetrical bending relating to their seismic performance. First, due to the Unsymmetrical bending, out-of-plane reaction forces occur for these walls, which contribute to accumulation of the out-of-plane deformations of the wall, especially when out-of-plane stiffness of the section is reduced by horizontal cracks in the cyclic load. Secondly, cracking was found to affect shear centre of the specimens loaded in the Unsymmetrical bending direction. The shear centre of these specimens distinctly differs in the flange in the positive and negative loading direction. Cracking of the flange also causes significant warping in the bottom part of the wall, which eventually lead to out-of-plane buckling failure.