• Title/Summary/Keyword: Lateral deflection

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Effects of load height application and pre-buckling deflections on lateral buckling of thin-walled beams

  • Mohri, F.;Potier-Ferry, M.
    • Steel and Composite Structures
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    • v.6 no.5
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    • pp.401-415
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    • 2006
  • Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

An Analysis of the Reinforced Concrete Circular Ring Sector Plates with Arbitrary Boundary Conditions (任意의 境界條件을 갖는 鐵筋콘크리트 扇形板의 解析(II) - 第 2報 鐵筋比 및 邊長比의 影響 -)

  • Jo, Jin-Gu
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.34 no.1
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    • pp.78-86
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    • 1992
  • This paper aims at investigating the effect of steel ratio and the magnitude of edge-ratio on the mechanical characteristics of reinforced concrete ring sector plate. The influence of steel bars was taken into account by coupling stiffness matrix of the steel bar element with that of the concrete plate element without dealing with separate element of steel bar and by establishing the composite stiffness matrix, which leads to the desirable result which does not increase th number of element could be obtained. Through case studies with 6 cases various steel ratios in ring sector plate supported at four edges and 4 cases with different open angles, the influence of the steel ratio was examined. A numerical analysis to find out the effect of the steel ratio d ue to above mentioned cases was carried out by 4 boundary conditions ; all edges clamped (B.C-1), all edges simply supported (B.C-2), curvilinear two edges clamped and other edges free (B.C-3) and curvilinear two edges simply supported and other edges free(B.C-4). The main results obtained are summarized as follows : 1. The effect of steel ratio on the magnitude of lateral deflection and x-directional bending moment at the center of sector plate and the midpoint of outer and inner curvilinear edges is almost the same up to $30^{\circ}$ of open angle. Beyond $30^{\circ}$ of the angle, the larger the angle, the greater the effect of ratio. 2. In design works using balanced steel ratio, the effect of steel bar can be ignored. But for larger open angles, especially greater than $90^{\circ}$, it proves desirable to consider the effect of steel bar. 3. The effect of the arc length of center circle/straight edge on lateral deflection and bending moment is remarkable in B.C-2. For larger open angle, the effect is also noted except for B.C-3 which turn out hardly affected. 4. The effect of the radius of curvature/straight side length on lateral deflection and x-directional bending moment is noted in B.C-2. As open angle increases, B.C-1 and B.C-3 almost agree and B.C-2 approaches B.C-4.

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Effect of Pile Construction on Lateral Behavior of Single Rigid Pile in Sand (사질토 지반에서 단일 강성말뚝의 수평거동에 대한 시공방법의 영향)

  • 김병탁;김영수;서인식
    • Journal of the Korean Geotechnical Society
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    • v.15 no.6
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    • pp.29-44
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    • 1999
  • This paper shows the results of model tests on the lateral behavior of single rigid pile, which was constructed by driving, in homogeneous and non-homogeneous (two layered) NakDong River sands. The purpose of the present paper is to investigate the effect of ratio of lower layer thickness to embedded pile length, relative density of sand and pile construction conditions (Driven & Embedded piles) on the characteristics of lateral behavior of single pile. These effects can be quantified only by the results of model tests. As a model result, the lateral behavior depends upon the pile construction condition in loose-density soil more than in high-density soil. If the pile construction depends upon driving construction, the decrease of deflection remarkably increases for both loose homogeneous sand and non-homogeneous soil$(E_{h1}/E_{h2}/=0.18)$ with high thickness of upper layer but the decrease of maximum bending moment shows the opposite result to the decrease of deflection. And, with respect to deflection, it was found that the deflection ratio $(y_{Driven}y_{Embedded})$ of embedded to driven piles has the ranges of 0.65 - 0.88 $(D_r=90%)$0.38 - 0.65 $(D_r=61.8%)$ for each relative density of homogeneous soil and the range of 0.6 - 0.88 for non-homogeneous soil. Also, in this study, the experimental equation for the effects of drop height (DH) and H/L on the ratios of $y_D/y_E\; and MBM_D/MBM_ E$ is suggested from model tests.

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A Comparison between predicted and measured values for lateral bearing capacity of PHC pile in weathered Granite soil (화강풍화토 지반에 타입된 PHC 말뚝의 수평지지력에 대한 추정치와 실측치의 비교)

  • 오재화
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.42 no.5
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    • pp.144-150
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    • 2000
  • This study dealt with the comparison of lateral baring capacity for vertical PHC pile between predicted and measured values driven in weathered granite soils to build world cup gymnasium in Kwangju area. Recently, the calculation of horizontal bearing capacity of piles foundation has been considered very important for earthquake or wind resistant design in Korea. During this study , Matlock & Reese, Broms and Chang's methods were selected in prediction of lateral resistant of PHC piles. As for case study, the prediction values were compared with 5 measured ones based on ASTM. The result showed that prediction values proposed by Matlock & Reese , Chang and Broms were smaller that real values. Three proposed methods by Matlock & Reese and Chang based on lateral deflection and Broms by ultimated lateral resistance turned out valid in view of engineering practice.

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A Study on Lateral Bearing Capacity of PHC Piles Driven Vertically in Decomposed Granite and Clayey Soil (화강토와 점토지반에 연직으로 타입된 PHC말뚝의 수평지지력에 관한 연구(지반공학))

  • 문영민;이문수;이대재
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • 2000.10a
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    • pp.466-470
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    • 2000
  • Recently, the calculation of horizontal bearing capacity of piles foundation has been considered very important for earthquake or wind resistant design in Korea. This study deals with the lateral resistance of PHC pile instead of vertical capacity for earthquake resistant design as well as wind. As case study, the prediction values were compared with measured ones based on ASTM. During this research, Matlock & Reese, Davisson & Gill, Broms and Chang's methods were selected in calculating prediction of lateral resistance of PHC piles. In decomposed granite and clayey soils, The result showed that prediction values proposed by Matlock & Reese(Davisson & Gill), Chang and Broms were smaller values than real values. four proposed methods by Matlock & Reese(Davisson & Gill) and Chang based on lateral deflection and Broms by ultimate lateral resistance turned out valid in view of engineering practice.

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Deformation Behavior and Slope Stability Effect of Anchored Retention Walls Installed in Cut Slope (절개사면에 설치된 앵커지지 합벽의 변형거동 및 사면안정효과)

  • Hong Won-Pyo;Han Jung-Geun
    • Journal of the Korean Geotechnical Society
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    • v.20 no.9
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    • pp.57-64
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    • 2004
  • In order to establish the design method of anchored retention walls in cut slope, the behavior of anchored retention walls and backside ground needs to be investigated and checked in detail. In this study, the behavior of anchored retention walls was investigated by instrumentation installed in cut slope for an apartment construction site stabilized by a row of piles and anchored retention walls. When the anchor was installed at each excavating stages, the horizontal deflection of retention wall decreased, while the horizontal deformation of backside ground increased. The deflection of anchored retention wall decreased as the anchor was prestressed. The prestressed anchor farce has a great effect on the deflection of retention walls, while it has little effect on the deformation of its backside ground. The maximum horizontal deflection of anchored retention walls was developed between $1\%\;and\;4\%$ of excavation depth, which are $2\~8$ times larger than max. horizontal deflection of anchored retention walls including rock layers with backside horizontal ground. Meanwhile, SLOPILE (ver. 3.0) program analyzes the slope stability effects for anchored retention walls. As a result of analysis on slope stability analysis, the lateral earth pressure applied at anchored retention piles could be used as the mean values of empirical lateral pressures using anchored retention wall with horizontal ground at its backside.

Vibration Analysis of Wedge Type Bar by Ritz Method (Ritz법을 이용한 쐐기형 봉의 진동 해석)

  • Park Sok-Chu
    • Journal of Advanced Marine Engineering and Technology
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    • v.29 no.8
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    • pp.877-882
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    • 2005
  • This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Enen if the solution of Bessel's function exists. as Bessel function is a series function. we must got the solution by numerical method Hereby the author Proposes the ununiform beam solution of the matrix method by Ritz's method. and Proposes a new deflection shape function.

Vibration Analysis of Tapered Bar (경사진 봉의 진동 해석)

  • 박석주
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.984-987
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    • 2003
  • This paper discusses the lateral vibration of a bar which has its tip free. The uniform bar has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function, or mathematical solution could not be existed. Even if the solution of Bessel's function exists. as Bessel function is a series function, we must get the solution by numerical method, Hereof the author proposes the solution of the matrix method by Ritz's method, and proposes a new deflection shape

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Case Analysis of Abutment Displacement and Pavement settlement (교대변위 및 도로침하에 대한 사례분석)

  • 박찬호;김수일
    • Proceedings of the Korean Geotechical Society Conference
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    • 1994.03a
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    • pp.19-30
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    • 1994
  • This paper reports a case study of aboutment displacement and pavement settlement observed at the construction site for highway bridges. The emphasis was on quantifying the horizontal deflections of about and pavement settlement on the backfill surface. It is shown that in soft clay, bridge aboutments on pile foundations are subjected to lateral earth pressures due to lateral soil movement. Based on the results analyzed, the earth pressure was predicted by deflection shape of piles based on the results of a numerical analysis and an analytical study. Also, the long term settlement of soil below pavement was estimated.

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Experimental Investigation on the Creep Behavior of Pultruded FRP Composite Columns (인발성형 FRP 복합소재 기둥부재의 크리프거동에 대한 실험적 분석)

  • Kang, Jin Ook;Abdul Hamid Zureick
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2003.10a
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    • pp.299-306
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    • 2003
  • This paper presents the results of an experimental investigation pertaining to the creep behavior of fiber-reinforced polymeric (FRP) pultruded components subjected to sustained eccentric axial loading. Six different axial load/eccentricity combinations were investigated through the experiments. The test duration of these experiments was 2,000 hours (90 days), during which the mid-height lateral deflections of the components were recorded continually. Analytical formulations based on the Schapery's quasielastic method and a power law model were used for the prediction of the creep lateral deflection.

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