Table 3 <strong>The</strong> results of limit load multiplier for irregular nodal layout Nodes 83 293 446 631 λ 3.108 2.203 2.215 1.575 Q γ 12.432 8.813 8.500 6.287 errors 97% 40% 35% 0.04% Runtime (s) 0.1 35 194 1169 By comparing the results of limit load parameter listed in Tables1, 2 and 3 (see Figure 5), it is very apparent that the accuracy of limit load parameter for regular nodal layout is higher than that of irregular layout. However, the reason of difference between two nodal layouts is not analysed here, and it will be further studied in the following research works. CONCLUSIONS AND DISCUSSIONS In this paper, a new formulation of upper bound approach based on RPIM and nonlinear programming is proposed. In the present method, the CTM integration method is used to calculate the internal dissipation, and the direct iterative algorithm is used to solve nonlinear programming for finding the optimal value of limit loading parameter of vertical slope. By the classical vertical slope stability problem, the validity of the present method is verified in this paper. <strong>The</strong> accuracy of limit loading parameter mainly depends on the number of field nodes and integral points. On the other hand, the accuracy of limit loading parameter for regular nodal layout is higher than that of irregular layout. <strong>The</strong> reasons of different accuracy need to be further studied. It may be carried out from the following two aspects, i.e., the CTM integration method and interpolation of RPIM shape function. ACKNOWLEDGMENTS <strong>The</strong> first author appreciates the useful comments from Prof H.S. Yu of <strong>University</strong> of Nottingham. <strong>The</strong> work was partly supported by Research Grants Council of <strong>Hong</strong> <strong>Kong</strong> (under grant No. 623609). REFERENCES Anderheggen, E., Knöpfel, H. (1972). “Finite element limit analysis using linear programming”, International Journal of Solids and Structures, 8, 1413-1431. Beissel, S., Belytschko T. (1996). “Nodal integration of the element-free Galerkin method”, Computer Methods in Applied Mechanics and Engineering, 139, 49-74. Belytschko, T., Lu, Y.Y., Gu, L. (1994). “Element-free Galerkin methods”, International Journal for Numerical Methods in Engineering, 37, 229-256. Bottero, A., Negre, R., Pastor, J., Turgeman, S. (1980). “Finite Element Method and Limit Analysis <strong>The</strong>ory for Soil Mechanics Problems”, Computer Methods in Applied Mechanics and Engineering, 22, 131-149. Capsoni, A., Corradi, L. (1997). “ A finite element formulation of the rigid plastic limit analysis problem”, International Journal for Numerical Methods in Engineering, 40, 2063-2086. Chen, J.S., Wu, C.T., Yoon, S., You, Y. (2001). “A stabilized conforming nodal integration for Galerkin mesh-free methods”, International Journal for Numerical Methods in Engineering, 50, 435-466. Chen, J.S, Yoon, S., Wu, C.T. (2002). “Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods”, International Journal for Numerical Methods in Engineering, 53, 2587-2615. Chen, W.F. (1975). “Limit Analysis and Soil Plasticity”, New York: Elsevier Scientific Publishing Co. Chen, S., Liu, Y., Cen, Z. (2008). “Lower-bound limit analysis by using the EFG method and non-linear programming”, International Journal for Numerical Methods in Engineering, 74, 391-415. Chen, Z. (2002). “Limit analysis of the classic problems of soil mechanics”, Chinese Journal of Geotechnical Engineering, 24(1), 1-11. (in Chinese) Ciria, H., Peraire, J., Bonet, J. (2008). “Mesh adaptive computation of upper and lower bounds in limit analysis”, International Journal for Numerical Methods in Engineering, 75, 899-944. Drucker, D.C., Prager, W. (1952). “Soil mechanics and plastic analysis or limit design”, Quarterly of Applied Mathematics, 10(2), 157-165 Kim, J., Salgado, R., Yu, H.S. (1999). “Limit analysis of soil slopes subjected to pore-water pressures”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125(1), 49-58. Kim, J., Salgado, R., Lee, J. (2002). “Stability analysis of complex soil slopes using limit analysis”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 128(7), 546-557. -345-
Khosravifard, A., Hematiyan, M.R. (2010). “A new method for meshless integration in 2D and 3D Galerkin meshfree methods”, Engineering Analysis with Boundary Elements, 34, 30-40. Krabbenhøft, K., Lyamin, A.V., Sloan, S.W. (2007). “Formulation and solution of some plasticity problems as conic programs”, International Journal of Solids and Structures, 44, 1533-1549. Krabbenhøft, K., Lyamin, A.V., Sloan, S.W. (2008). “Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming”, Communications in Numerical Methods in Engineering, 24, 1107-1119. Le, C.V., Gilbert, M., Askes, H. (2009). “Limit analysis of plates using the EFG method and second-order cone programming”, International Journal for Numerical Methods in Engineering, 78, 1532-1552. Le, C.V., Nguye-Xuan, H., Nguyen-Dang, H. (2010a). “Upper and lower bound limit analysis of plates using FEM and second-order cone programming”, Computer and Structures, 88, 65-73. Le, C.V., Nguye-Xuan, H., Askes, H., Bordas, S. P. A., Rabczuk, T., Nguyen-Vinh, H. (2010b). “A cell-based smoothed finite element method for kinematic limit analysis”, International Journal for Numerical Methods in Engineering, 83, 1651-1674. Li, H.X., Yu, H.S. (2006). “Limit analysis of 2-D and 3-D structures based on an ellipsoid yield criterion”, Acta Geotechnica, 1, 179-193. Liu, G.R. (2010). “Meshfree method: moving beyond the finite element method, 2 nd ed.”, CRC press: Boca Raton, USA. Liu, G.R., Gu, Y.T. (2005). “An introduction to meshfree methods and their programming”, Spring. Liu, Y.H., Cen, Z.Z., Xu, B.Y. (1995). “A numerical method for plastic limit analysis of 3-D structures”, International Journal of Solids and Structures, 32(12), 1645-1658. Lyamin, A.V., Sloan, S.W. (2002). “Upper bound limit analysis using linear finite elements and non-linear programming”, International Journal for Numerical and Analytical Methods in Geomechanics, 26, 181-216. Lysmer, J. (1970). “Limit analysis of plane problems in soil mechanics”, Journal of the Soil Mechanics and Foundations Division, ASCE, 96(4), 1311-1334. Makrodimopoulos A., Martin, C.M. (2006). “Lower bound limit analysis of cohesive-frictional materials using second-order cone programming”, International Journal for Numerical Methods in Engineering, 66, 604-634. Makrodimopoulos A., Martin, C.M. (2007). “Upper bound limit analysis using simplex strain elements and second-order cone programming”, International Journal for Numerical and Analytical Methods in Geomechanics, 31, 835-865. Makrodimopoulos A., Martin, C.M. (2008a). “Upper bound limit analysis using discontinuous quadratic displacement fields”, Communications in Numerical Methods in Engineering, 24, 911-927. Martin, C.M., Makrodimopoulos A. (2008b). “Finite-Element Limit Analysis of Mohr-Coulomb Materials in 3D Using Semidefinite Programming”, Journal of Engineering Mechanics, ASCE, 134(4), 339-347. Makrodimopoulos A. (2010). “Remarks on some properties of conic yield restrictions in limit analysis”, International Journal for Numerical Methods in Biomedical Engineering, 2010, 26, 1449-1461. Pastor, J., Thai, T.H., Francescato, P. (2000). “New bounds for the height limit of a vertical slope”, International Journal for Numerical and Analytical Methods in Geomechanics, 24, 165-182. Sloan, S.W. (1988). “Lower bound limit analysis using finite elements and linear programming”, International Journal for Numerical and Analytical Methods in Geomechanics, 12, 61-77. Sloan, S.W. (1989). “Upper bound limit analysis using finite elements and linear programming”, International Journal for Numerical and Analytical Methods in Geomechanics, 13, 263-282. Sloan, S.W., Kleeman, P.W. (1995). “Upper bound limit analysis using discontinuous velocity fields”, Computer Methods in Applied Mechanics and Engineering, 127, 293-314. Wang, J.G., Liu, G.R. (2002). “A point interpolation meshless method based on radial basis functions”, International Journal for Numerical Methods in Engineering, 54 (11), 1623-1648. Yu, H.S., Salgado, R., Sloan, S.W., Kim, J.M. (1998). “Limit analysis versus limit equilibrium for slope stability”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124(1), 1-11. Zhang, P., Lu, M., Hwang, K. (1991). “A mathematical programming algorithm for limit analysis”, ACTA MECHANICA SINICA, 23(4), 433-442. (in Chinese) Zouain, N., Herskovits, J., Borges, L.A., Feijóo, R.A. (1993). “An iterative algorithm for limit analysis with nonlinear yield functions”, International Journal of Solids and Structures, 30, 1397-1417. -346-
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Proceedings of the 5th Cross-strait
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SCIENTIFIC COMMITTEE Chairman Jan-M
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ORGANIZING COMMITTEE Co-chairmen Yi
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设 计 大 师 金 问 鲁 教 授
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TABLE OF CONTENTS Scientific Commit
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J.T. Shi & L. Su Impact of Spatial
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Temperature Effect on Variation of
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Trace Analysis of Mechanical Respon
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Keynote Lectures
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图 1 海 峡 大 桥 三 个 路
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非 主 通 航 孔 的 跨 径 应
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图 3 空 间 结 构 按 单 元
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图 7 多 面 体 空 间 框 架
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图 14 内 蒙 古 响 沙 湾 沙
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5.3. MRF3 索 穹 顶 — 网 壳
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图 29 杭 州 黄 龙 体 育 中
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(a) 鸟 瞰 图 (b) 计 算 模 型
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As it is conventional, the displace
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⎡ n n ⎤ ⎢q 1 0( z− Li) q0(
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frequencies of interest and the tra
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Another phenomenon observed from Fi
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刚 塑 性 平 面 应 变 极 限
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采 用 数 值 极 限 分 析 法
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为 了 推 测 浅 埋 隧 洞 破
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鹤 梁 岩 壁 面 上 至 今 已
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图 6 黄 庭 坚 题 铭 “ 元
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图 16 巫 山 神 女 图 17 长
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五 、 历 年 来 研 究 过 的
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在 会 议 结 束 前 给 我 半
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图 31 院 士 建 议 文 件 的
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科 所 、 重 庆 交 通 学 院
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图 37 白 鹤 梁 题 刻 中 段
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图 46 上 下 游 水 平 交 通
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图 59 参 观 廊 道 安 装 在
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9.6. 白 鹤 梁 水 下 博 物
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(5) “ 无 压 容 器 ” 水 下
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(a) 模 型 I (b) 模 型 II (c)
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(a) 水 平 接 缝 处 螺 钉 松
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表 5 模 型 I 在 9 度 罕 遇
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1.2. 大 型 钢 结 构 设 计
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5250 5000 i= 0.07 1 i= 0.07 5000 16
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A Pb Pa Pb A Pb Pa Pb Pa Pa ax Pb P
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(a) 预 应 力 索 布 置 (b) 1/6
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图 23 150m×150m 周 边 简 支
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图 27(a) 自 重 作 用 下 结
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四 、 结 语 150m×150m 空 间
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通 过 上 述 技 术 创 新 平
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* θt r1cosθ r2cosθ2 = = (9) * 1
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圖 10 水 平 軌 枕 方 向 之
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圖 19 水 平 軌 枕 方 向 之
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向 量 r r &r r 的 變 化 率
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Experimental Program More than 60 l
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failure mode specimens, applying CF
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columns were reinforced with three
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e formed at the column base and the
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Acceleration (g) 1 0.5 0 -0.5 Simul
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Table 2 Mix Proportion of the PDCC
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observed between the formwork and c
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In the above example, the GFRP with
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构 的 加 固 修 复 , 二 是
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FRP 网 格 FRP 筋 和 索 FRP 布
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(2) 钢 筋 - 连 续 纤 维 复
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生 退 化 。 拉 伸 强 度 相
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σ tf 混 凝 土 构 件 粘 结
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新 型 抗 震 结 构 的 荷 载
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的 破 坏 过 程 也 与 柱 C-S
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拉 索 频 率 阶 数 也 低 于
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A m plitude (m m ) 6000 5000 4000 3
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产 工 艺 进 行 探 索 性 研
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Girders with Externally Prestressed
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concrete columns were documented by
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fatigue life of steel columns. Xiao
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Figure 11 Relationships between res
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20. Xiao, Y. and Wu, H. (2000). “
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phenomenon, however, cannot be cons
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ase rock; H j ( iω) , H k ( iω) a
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Numerical Results The earthquake-in
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REFERENCES Bi, K., Hao, H. and Ren,
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Figure 3 Idealised bonded joint mod
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A = 0 1 (6a) B1 = −δ f (6b) f si
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Table 1 Test and predicted flexural
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COMPARISON OF FLEXURAL DEBONDING MO
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Figure 2 Location of smart aggregat
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Figure 5 Experimental setup Figure
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Figure 15 Impact location on FRP wr
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REFERENCES Bhalla, S. and Soh, C.K.
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The RVE, occupying a geometrical do
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[ ut ] is the tangential vector if
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extended to the resolution of the n
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469.1m,f m =55%,f I =45% -50 Σ 3 -
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頭 混 凝 土 護 蓋 敲 除 ,
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發 生 夾 片 咬 合 失 敗 ,
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會 因 設 計 長 度 不 足 ,
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面 之 反 推 分 析 可 知 ,
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因 此 連 擋 土 牆 本 身 之
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⎛τ ⎞ av ⎛amax ⎞⎛σ ⎞ v
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地 液 化 与 否 初 步 判 别
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等 (2000) [15] 在 试 验 中 都
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五 、 结 论 剪 切 波 速 法
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钢 混 凝 土 相 当 于 将 型
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A g — 混 凝 土 毛 截 面 面
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5.1. 大 连 市 体 育 馆 钢
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土 梁 中 设 立 直 线 预 应
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混 凝 土 板 外 侧 , 受 力
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试 验 采 用 跨 中 两 点 对
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为 了 深 入 了 解 槽 型 钢
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笔 者 针 对 已 有 结 合 部
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(c) 波 形 钢 腹 板 工 字 型
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manner for statistical analysis, (i
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3.3.1 Software System for Instrumen
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spectrum is obtained in an approxim
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The monitoring work is composed of
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displacement influence lines and st
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Hong Kong Institution of Engineers.
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Monitoring Category Bridge Features
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9 Combination of Above Divided Sect
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Back to Routine Monitoring Not Exce
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Tsing Yi Stonecutters Figure 5 Layo
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Continuous Data Acquisition GPS Tim
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Y(+ve) Y T Temperature Distribution
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Type of Input Data Type of Data Pro
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Type of Input Data Type of Data Pro
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Type of Input Data Type of Data Pro
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Type of Input Data Type of Data Pro
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青 衣 Tsing Yi 昂 船 洲 Stonec
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Accelerometer Fixing of Portable Ac
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Tsing Yi Stonecutters Bridge Stonec
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Structural Health Data Management S
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a mean recurrence interval with ext
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The present study is concerned with
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在 此 选 取 Kondner [10] 及 Go
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SHAKING TABLE TEST PROGRAM System i
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Force (N) 600 500 400 300 200 100 N
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Figure 9 Comparison of SAF-TMD and
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_ Cumulative Frequency of Samples (
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STADIUM ROOF BRIEF Jaber Al-Ahmad I
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a) 1st modal shape Figure.7 Modal s
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1) 所 需 的 机 具 设 备 少
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Effects of Web Slenderness (d/t w )
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REFERENCES ABAQUS/Standard User’s
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规 程 [7]。 文 献 [2]、[3]
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为 探 究 球 节 点 壁 厚 对
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[4] 王 星 , 董 石 麟 , 完 海
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一 、 前 言 鋼 纜 為 斜 張
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圖 1 愛 蘭 矮 塔 斜 張 橋
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態 頻 率 後 , 由 圖 6 可 清
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素 連 接 , 假 設 兩 構 件
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The 5th Cross-strait Conference on
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图 3 半 片 梁 的 有 限 元
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加 固 前 的 钢 筋 混 凝 土
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The 5th Cross-strait Conference on
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and a corresponding shear strain of
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The 5th Cross-strait Conference on
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对 温 度 变 化 效 应 进 行
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典 型 节 点 : 在 钢 结 构
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钢 结 构 第 一 阶 振 型 为
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(a) 上 支 座 节 点 (b) 下 支
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上 部 屋 面 钢 结 构 下 部
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验 算 4、6 号 线 重 力 荷
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采 用 SAP2000, 对 各 种 截
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The 5th Cross-strait Conference on
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高 屏 溪 引 橋 共 包 含 五
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表 3 由 高 屏 溪 斜 張 橋
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圖 7 垂 直 撓 曲 第 一 振
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表 7 在 P2 橋 墩 不 同 沖