A MODAL CONDITIONAL MEAN TARGET SPECTRUM METHOD TO CONSIDER HIGHER MODE EFFECT
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摘要: 采用传统条件均值谱作为目标谱匹配选波未能有效考虑结构的高阶振型影响，针对这一缺陷，在条件均值谱方法的理论基础上，提出了一种考虑高阶振型影响的模态条件均值谱方法。该方法以振型参与质量系数作为权重，将各振型下的条件均值谱组合起来，得到一条新的目标谱，称为模态条件均值谱。设计了一座30层的钢框架-中心支撑结构，分别生成其主周期的条件均值谱、模态条件均值谱以及一致危险谱作为目标谱，各选取11条地震动进行结构动力时程分析。结果表明，考虑了结构高阶振型影响的模态条件均值谱方法得出的结构响应，明显大于不考虑高阶振型影响的传统条件均值谱的结果。建议此方法推广用于高层工程结构作为目标谱。
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关键词:
- 条件均值谱 /
- 模态条件均值谱 /
- 动力时程分析 /
- 高阶振型 /
- 钢框架-中心支撑结构
Abstract: The traditional method uses conditional mean spectrum as the target spectrum to select ground motion, which fails to effectively take into account the influence of high mode vibration of the structure. To overcome this shortcoming, a modal conditional mean spectrum method considering the influence of higher mode effect is proposed. With the weight coefficients of mode participation mass ratios, the proposed method combines the conditional mean spectrum of each mode to obtain a new target spectrum, and is called the modal conditional mean spectrum. A 30-story steel frame-center support structure was designed, and the mean conditional spectrum of interested period, modal mean conditional spectrum and uniform hazard spectrum were generated, and then 11 ground motions were selected for structural dynamic time history analysis with the 3 target spectra respectively. The results show that the structural response obtained by the modal conditional mean spectrum method considers the influence of higher mode effect of the structure, and generates obviously greater result than the traditional conditional mean spectrum. It is suggested that the proposed method be extended to high-rise structures as target spectrum. -
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图 2 一致谱、条件谱、模态谱对比
Figure 2. Comparison of uniform hazard spectrum, conditional spectrum and modal conditional spectrum
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图 4 最大层间位移角结果及其均值
Figure 4. Results of maximum inter-story drift ratio and its mean value
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图 5 层间位移角均值对比
Figure 5. Comparison of the mean value of maximum inter-story drift ratio
表 1 模型结构截面信息
Table 1 Sectional information of model structure
构件类型 楼层 截面型号 钢材型号 梁 1~3 GB-HW-350×350×10×16 Q345 4~20 GB-HW-300×300×15×15 Q345 21~30 GB-HW-300×300×10×15 Q345 柱 1~5 GB-HW-400×400×30×50 Q345 6~10 GB-HW-400×400×20×35 Q345 11~15 GB-HW-400×400×18×28 Q345 16~20 GB-HW-400×400×13×21 Q345 21~25 GB-HW-350×350×12×19 Q345 26~30 GB-HW-300×300×10×15 Q345 支撑 1~5 GB-HW-200×200×8×12 Q345 6~10 GB-HW-175×175×7.5×11 Q345 11~30 GB-HW-150×150×7×10 Q345 
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表 2 模型结构的模态分析结果
Table 2 Modal analysis results of model structure
振型 周期/s 振型参与质量系数 累计振型参与质量系数 1 3.338 298 66.1161 66.1161 2 0.987 063 17.1815 83.2976 3 0.500 022 6.5598 89.8574 4 0.325 342 3.3756 93.2329 5 0.239 905 1.8166 95.0495 6 0.189 475 1.1605 96.2100 7 0.157 273 0.7205 96.9305 8 0.133 744 0.5179 97.4485 9 0.117 012 0.3811 97.8296 10 0.103 622 0.3019 98.1314 11 0.093 573 0.2656 98.3970 12 0.085 122 0.2006 98.5976
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表 3 地震解耦结果
Table 3 The results of seismic de-aggregation
解耦目标 震级M 震中距R/km 贡献系数 epsilon(ε) Sa(T=3.3 s) 6.25 41 20.71620 2.261303587 Sa(T=1 s) 6.25 61 12.37719 2.447757995 Sa(T=0.5 s) 6.25 41 13.18000 1.978400000 Sa(T=0.3 s) 6.25 41 13.03700 1.861600000
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表 4 选波信息
Table 4 The information of selected record
序号 地震动记录名称 台站 时间/年 震级 均方误差 调幅系数 a) 条件谱选波结果 EQ1 RSN286_ITALY_A-BIS000.AT2 "Bisaccia" 1980 6.90 0.0862 1.0259 EQ2 RSN289_ITALY_A-CTR000.AT2 "Calitri" 1980 6.90 0.1935 0.7919 EQ3 RSN740_LOMAP_ADL250.AT2 "Anderson Dam (L Abut)" 1989 6.93 0.0840 1.4927 EQ4 RSN827_CAPEMEND_FOR000.AT2 "Fortuna - Fortuna Blvd" 1992 7.01 0.0350 0.8373 EQ5 RSN1616_DUZCE_362-N.AT2 "Lamont 362" 1999 7.14 0.1404 3.1651 EQ6 RSN3750_CAPEMEND_LFS270.AT2 "Loleta Fire Station" 1992 7.01 0.1165 0.4226 EQ7 RSN3757_LANDERS_NPF090.AT2 "North Palm Springs Fire Sta #36" 1992 7.28 0.0726 0.8421 EQ8 RSN4844_CHUETSU_65007NS.AT2 "Tokamachi Matsunoyama" 2007 6.80 0.1000 1.0231 EQ9 RSN5664_IWATE_MYG005NS.AT2 "MYG005" 2008 6.90 0.2033 0.2526 EQ10 RSN5776_IWATE_54010NS.AT2 "Kami_ Miyagi Miyazaki City" 2008 6.90 0.16100 0.8655 EQ11 RSN5806_IWATE_55461NS.AT2 "Yuzawa Town" 2008 6.90 0.1667 0.5959 b) 模态谱选波结果 序号 地震动记录名称 台站 时间/年 震级 均方误差 调幅系数 EQ1 RSN289_ITALY_A-CTR000.AT2 "Calitri" 1980 6.90 0.0787 0.8142 EQ2 RSN313_CORINTH_COR--L.AT2 "Corinth" 1981 6.60 0.1513 0.6491 EQ3 RSN740_LOMAP_ADL250.AT2 "Anderson Dam (L Abut)" 1989 6.93 0.1622 1.5347 EQ4 RSN755_LOMAP_CYC195.AT2 "Coyote Lake Dam - Southwest Abutment" 1989 6.93 0.1329 0.8439 EQ5 RSN827_CAPEMEND_FOR000.AT2 "Fortuna - Fortuna Blvd" 1992 7.01 0.0692 0.8609 EQ6 RSN1616_DUZCE_362-N.AT2 "Lamont 362" 1999 7.14 0.0800 3.2543 EQ7 RSN3757_LANDERS_NPF090.AT2 "Loleta Fire Station" 1992 7.28 0.0542 0.8659 EQ8 RSN4013_SANSIMEO_36258021.AT2 "San Antonio Dam - Toe" 2003 6.52 0.0858 1.3419 EQ9 RSN4844_CHUETSU_65007NS.AT2 "Tokamachi Matsunoyama" 2007 6.80 0.0435 1.0519 EQ10 RSN4872_CHUETSU_65053NS.AT2 "Sawa Mizuguti Tokamachi" 2007 6.80 0.0850 0.8689 EQ11 RSN5806_IWATE_55461NS.AT2 "Yuzawa Town" 2008 6.90 0.0802 0.6127 c) 一致危险谱选波结果 序号 地震动记录名称 台站 时间/年 震级 均方误差 调幅系数 EQ1 RSN164_IMPVALL.H_H-CPE147.AT2 "Cerro Prieto" 1979 6.53 0.1010 1.7230 EQ2 RSN289_ITALY_A-CTR000.AT2 "Calitri" 1980 6.90 0.1310 1.6679 EQ3 RSN1614_DUZCE_1061-N.AT2 "Lamont 1061" 1999 7.14 0.1030 2.9772 EQ4 RSN1633_MANJIL_ABBAR--L.AT2 "Abbar" 1990 7.37 0.1307 0.6577 EQ5 RSN3757_LANDERS_NPF090.AT2 "North Palm Springs Fire Sta #36" 1992 7.28 0.1268 1.7737 EQ6 RSN4843_CHUETSU_65006NS.AT2 "Matsushiro Tokamachi" 2007 6.80 0.0736 1.4716 EQ7 RSN4844_CHUETSU_65007NS.AT2 "Tokamachi Matsunoyama" 2007 6.80 0.1121 2.1549 EQ8 RSN4869_CHUETSU_65042NS.AT2 "Kawaguchi" 2007 6.80 0.1272 2.5473 EQ9 RSN4882_CHUETSU_65321NS.AT2 "Ojiya City" 2007 6.80 0.1472 1.2254 EQ10 RSN5274_CHUETSU_NIG028NS.AT2 "NIG028" 2007 6.80 0.1466 2.4569 EQ11 RSN5783_IWATE_54026NS.AT2 "Semine Kurihara City" 2008 6.90 0.0855 1.7043
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