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Improved Continuum Model for Free Vibration Analysis of Suspension Bridges
Gwon, Sun-Gil,Choi, Dong-Ho American Society of Civil Engineers,Engineering Me 2017 Journal of engineering mechanics Vol.143 No.7
<P>An improved continuum model of three-span suspension bridges has been developed to study the effects of hanger extensibility on free vertical vibrations. This model can be applied to both hinged and continuous girders. To obtain the equations of motion, coupled differential equations describing the vertical deflections of the main cable and the girder are derived with dimensionless parameters. Following the Galerkin method, with shape functions for the main cable and for hinged and continuous girders, equations of motion are obtained in matrix form. A compatibility equation is used to eliminate the additional horizontal force of the main cable in the equations. Natural frequencies of hinged and continuous suspension bridges are evaluated as a function of six dimensionless parameters: the relative elastic bending stiffness of the girder, the relative elastic axial stiffness of the main cable, the relative elastic axial stiffness of the hangers, the relative mass of the girder, the relative length of the side span, and the ratio of the main span sag to the maximum hanger length. Parametric studies are conducted in which each of these parameters is varied individually to observe its effect on the natural frequencies and to identify differences between a conventional model with inextensible hangers and the improved model with extensible hangers. It is found that hanger extensibility affects the natural frequencies and mode shapes of higher modes for suspension bridges with a large relative girder stiffness. This effect is slightly more pronounced for antisymmetric modes and continuous bridges. In addition, even for a bridge with a large relative girder stiffness, the hanger extensibility rarely affects the natural frequencies of higher modes if the bridge either has a large relative mass of the girder or a large relative length of the side span. (C) 2017 American Society of Civil Engineers.</P>
Gwon, Sun-Gil,Choi, Dong-Ho Elsevier 2018 ENGINEERING STRUCTURES Vol.161 No.-
<P><B>Abstract</B></P> <P>In this paper, a continuum model is proposed for static and dynamic analyses of a three-span suspension bridge with three-dimensionally curved main cables. To obtain equations of motion for this model, coupled differential equations are derived for vertical displacements of a main cable and a girder as well as lateral displacements of a main cable subjected to external loads. A compatibility equation of a three-dimensionally curved cable is also derived. Utilizing the Galerkin method, the equations of motion are obtained in matrix form. A case study bridge is used to verify the continuum model against a finite element model. Verification results show that, for distributed static loads on the girder and temperature changes in the main cable and the hangers and for dynamic moving loads on the girder, the continuum model can accurately determine static and dynamic responses, namely displacements, velocities, accelerations, bending moments, and shear forces of the girder and additional horizontal forces in the main cable.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A continuum model for a suspension bridge with three-dimensionally curved main cables is newly proposed. </LI> <LI> This model considers extensible hangers and a continuous girder as well as 3D cables. </LI> <LI> A case study bridge is used to verify this model against a finite element model. </LI> <LI> This model can accurately determine the static and dynamic responses of the bridge. </LI> </UL> </P>
권순길 ( Gwon Sun Gil ),김상현 ( Kim Sang Hyeon ),이정익 ( Lee Jeong Ig ),서장원 ( Seo Jang Won ),장재원 ( Jang Jae Won ),김순배 ( Kim Sun Bae ),박정식 ( Park Jeong Sig ) 대한신장학회 2003 Kidney Research and Clinical Practice Vol.22 No.3
배 경 : 만성신부전에서 관상동맥 질환의 유병률은 정상인에 비해 증가되어 있으며 죽상경화증이 신기능을 저하시킬 수도 있다고 생각되나 아직까지 이에 대한 정확한 보고는 되어있지 않다. 맥압은 죽상경화의 정도를 반영하며 신부전 환자에서 증가되어 있어, 이에 저자들은 죽상동맥경화에 따른 관상동맥 질환과 맥압의 변화가 신부전을 진행시키는지에 대한 관련성을 비교 검토하고자한다. 방 법 : 서울아산병원에서 3년 이상 추적 관찰이 가능하였던 경증의 만성신부전 환자들을 대상으로 심혈관조영술로 관상동맥질환 여부를 검사하였고 혈청 크레아티닌 농도 및 여러 변수들을 추적 관찰하여 관상동맥질환의 유무에 따른 신부전의 진행 여부를 비교하였으며, 다변량회귀분석을 통해 신부전을 진행시킬 수 있는 여러 변수들의 관련성 여부를 검토하였다. 또한 맥압의 증가가 신부전에 주는 영향 및 이와 관련된 여러 변수들을 비교 분석하였다. 결 과 : 전체 87명 (남자 54 여자 33명)의 환자들 중 45명이 관상동맥질환이 있었으며 42명은 없었다. 관상동맥질환이 있던 45명 중 34명 (76%)에서 신부전이 진행되었으며, 관상동맥질환이 없는 42명 가운데는 22명 (52%)이 신부전의 진행을 보였다. 여러 요인들 중 신부전의 진행과 유의하게 관련된 요인으로는 평균 동맥압, 맥압, 당뇨병성 신증, 24시간 요단백, 혈청 총 콜레스테롤 농도가 있었으며 들 중 특히 맥압이 관상동맥질환과 관련이 있었다. 결 론 : 죽상경화에 의한 관상동맥질환 및 맥압의 증가는 경도의 만성신부전 환자에서 신부전의 진행과 유의한 관련이 있는 것으로 사료된다. Background : Patients with end-stage renal disease have farther excess rate of coronary artery disease (CAD) than nonuremic population. There is a possibility that artherocslerosis may aggravate renal insufficiency, but it is not certain. Pulse pressure was also significantly increased in patients with chronic renal disese (CRD), and had been implicated in the development of atherocclerosis. The purpose fo this study is to identify the association of atherosclerotic CAD and pulse pressure with renal disease progression in patients with mild CRD Method : The patients with mild CRD who had been followed up more than 3 years in Asan medical center, Seoul, Korea, were included. We evaluated their CAD via coronary angiography, and followed up their serum creatinine levels and other parameters assumed to be associated with progression of CRD. All clinical and laboratory parameters were analyzed by multivariate logictic method. And we examined the association between pulse pressure and progression of CRD with related factors via multivariate logistic analysis. Results: Total 87 patients (54 were men and 33 were women) were included in this study. 45 patients had coronary heart disease and 42 had not. Comparison of CRD progression between the patients who had CAD (n=45) and those who not (n=42) showed a significant difference (76% vs 52%, p<0.05). Mean arterial pressure, pulse pressure, presence of diabetic nephrophthy, 24hour urine protein, total cholesterol were the parameters associated with the progression of CRD. Among of them, proteinuria and mean arterial pressure were independent risk factors for renal disease progression. Therer was a significant association between CAD and pulse pressure. Conclusion: Atherosclerotic CAD and increased pulse pressure were associated with renal disease progression in the patients with mild renal insufficiency. (Korean J Nephrol 2003;22(3):313-320)