• Proceedings of the Korea Concrete Institute Conference
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• 2000.10a
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• pp.211-216
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• 2000

Numerical studies were carried out to develop the moment magnifier method for long-term behavior of flat plates, subjected to combined in-plane compressive and transverse loads. Nonlinear finite element analyses were performed for the numerical studies. Through the numerical studies, the long term behavior of the flat plate subjected to uniform or nonuniform floor load was investigated, and creep effects on the degradation of strength and stiffness of the slabs were examined. As the result, the creep factor was developed to epitomizes with creep effect on the flat plate. The moment magnifier method using the creep factor was developed for long-term behavior of flat plates. Also, the design examples are shown for verification of proposed design method.

• Magazine of the Korea Concrete Institute
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• v.11 no.1
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• pp.243-254
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• 1999

This paper presents a numerical study for developing the moment magnifier method that is applicable to RC flat plates subject to combined axial compressive and floor load. For the nonlinear finite element analysis, a computer program addressing material and geometric nonlinearities was developed. The flat plates to be studied are designed in accordance with the Direct Design Method in Korean Building Code for Structural Concrete. This paper proposes the buckling force and the moment magnification factor for the flat plate under the governing load condition that is the combined vertical and subsequently applied uniaxial compressive load. The buckling force is defined with two ingredients: the buckling coefficient and the effective flexural rigidity. Parametric studies are performed to investigate variations of the buckling coefficient and the effective flexural rigidity. Based on the numerical results, this paper provides the design values of the buckling coefficient and the effective flexural rigidity, and the design procedure for the moment magnifier method.

• International Journal of Concrete Structures and Materials
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• v.8 no.2
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• pp.99-116
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• 2014

The American Concrete Institute (ACI) 318-11 permits the use of the moment magnifier method for computing the design ultimate strength of slender reinforced concrete columns that are part of braced frames. This computed strength is influenced by the column effective length factor K, the equivalent uniform bending moment diagram factor $C_m$ and the effective flexural stiffness EI among other factors. For this study, 2,960 simple braced frames subjected to short-term loads were simulated to investigate the effect of using different methods of calculating the effective length factor K when computing the strength of columns in these frames. The theoretically computed column ultimate strengths were compared to the ultimate strengths of the same columns computed from the ACI moment magnifier method using different combinations of equations for K and EI. This study shows that for computing the column ultimate strength, the current practice of using the Jackson-Moreland Alignment Chart is the most accurate method for determining the effective length factor. The study also shows that for computing the column ultimate strength, the accuracy of the moment magnifier method can be further improved by replacing the current ACI equation for EI with a nonlinear equation for EI that includes variables affecting the column stiffness and proposed in an earlier investigation.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.04a
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• pp.507-512
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• 2000

This paper presents a design procedure using the moment magnifier method that is applicable to RC flat plates subjected to combined axial compressive and uniform or non-uniform floor load. Based on the numerical results, the design values of the buckling coefficient and the effective flexural rigidity, that define the buckling force, have been proposed. Using these design values, this paper provides the design procedure for the moment magnifier method.

• Magazine of the Korea Concrete Institute
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• v.7 no.1
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• pp.156-164
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• 1995

P-${\Delta}$ analysis by use of the equivalent colurnn stiffness determined by Momcnt curvature-Thrust curves provides relatively precise analytical results for unbraced reinforced concrete columns, however it needs a complicated arialytical procedure. Equ~valent col~rnn stiffness equations are proposed for a simple analytical procedure which are ckterrnined by the Moment-Curvature Thrust curves of the practically useable sections. Thc proposed stiffness equations are appiled to P-${\Delta}$ analysis and rnornent magnifier method to compare with the selected test result. Use of the proposed stiffness equations may slrnplify the P-${\Delta}$ i.rialvtica1 procedure and improve the accuracy of moment magnifier niethod.

• Journal of the Korea Concrete Institute
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• v.13 no.1
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• pp.38-45
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• 2001

Numerical studies were carried out to develop the moment magnifier method for long-term behavior of flat plates, subjected to combined in-plane compressive and transverse loads. Nonlinear finite element analyses were performed for the numerical studies. Through the numerical studies, the long term behavior of the flat plate subjected to uniform or nonuniform floor load was investigated, and creep effects on the degradation of strength and stiffness of the slabs were examined. As a result, the creep factor was implemented to describe the creep effect on the flat plate. The moment magnifier method using the creep factor was developed for long-term behavior of flat plates. Also, the design examples were shown for the verification of the proposed design method.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.87-96
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• 1992

Moment Magnifier Method has been generally used in estimation of total column moment induced by geometric nonlinearity for reinforced concrete slender column design, however second order analysis such as P-${\Delta}$ method has been recommended by Code for better result. Member stiffness estimation is the most significant factor for accuracy of second order analysis. Equivalent Column stiffness based on theoretically obtained moment-curvature-thrust relationship has been proposed and the analytical results of the proposed method, MacGregor-Hage Method, Furlong's Method, and Moment Magnifier Method are compared with experimentally obtained data.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.67-79
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• 1991

Geomrtric nonlinearity of axially and laterally loaded reinforced concrete slender columns has been generally considered by use of second order analysis such as $P-{\Delta}$ method. Complex procedure in second order analysis may not be a difficult problem with computer aid, however it has been seldom used in design offices because of the need of carefully decided input data. In lieu of second order analyses, the Korean and the American concrete codes have adopted the moment magnifier method. It is known, however, that this method results in too conservative design in some cases. Accuracy of the moment magnifier method to the experimentally obtained data has been reviewed and an improved method has been proposed for better result.

• 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.

• 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.