Natural Period Measurement and Analysis of School Buildings with External Corridor
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摘要: 根据现有的抗震设计方法，结构基本周期是确定设计地震力大小的关键因素。中小学外廊式教学楼在历次地震中均表现出较严重的震害。为研究教学楼实际自振周期与结构设计模型的差异，本文选取4栋典型的外廊式教学楼，采用脉动法测试结构一阶平动和扭转的固有周期，并根据原设计图纸复现了结构计算模型。测试和分析结果表明：实测纵横向自振周期较经验公式估算的周期小，相差范围在8.9%～28.0%，且经验公式估算的周期介于实测值与结构分析软件计算值之间。填充墙的数量和布置形式会对结构3个方向的自振周期产生不同程度的影响，填充墙对横向的刚度作用远大于纵向，同时横墙也使结构抗扭刚度得到极大的提高。不考虑填充墙的计算模型和经验公式均无法同时准确评估3个方向的自振周期。结构整体的抗震性能与填充墙的分布形式和连接方式都有重要的联系，设计中应充分考虑填充墙的布置及参与工作状态，才能准确评估结构抗震设计及结构承载力。Abstract: According to current seismic design methods, the fundamental period of a structure is a critical parameter in determining seismic forces. School corridor buildings in primary and secondary schools have experienced varying degrees of earthquake damage in past seismic events. To investigate discrepancies between the actual natural periods and the design model assumptions for these buildings, four representative corridor school buildings were selected for study. The first-order translational and torsional frequencies were measured using the ambient vibration method. Structural calculation models were then reconstructed based on the original design drawings. The results indicate that the measured natural periods in both longitudinal and transverse directions are consistently shorter than those estimated by empirical formulas, with discrepancies ranging from 8.9% to 28.0%. The empirical formula estimates fall between the measured values and those derived from structural analysis software. Furthermore, the quantity and configuration of infilled walls significantly affect the natural periods in all three directions. Specifically, infilled walls contribute substantially more to lateral stiffness than to longitudinal stiffness, and they markedly enhance the torsional stiffness of the structures. Notably, calculation models and empirical formulas that neglect the presence of infilled walls fail to accurately predict the natural periods simultaneously in all directions. These findings underscore that the seismic response of such structures is strongly influenced by the arrangement and connection details of infilled walls. Therefore, to achieve accurate seismic force estimations and structural capacity evaluations, the configuration and mechanical behavior of infilled walls must be thoroughly incorporated into seismic design considerations.
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图 9 实测和计算周期的反应谱值
Figure 9. Response spectrum values to measured and calculated periods
表 1 测试仪器技术指标
Table 1. Technical specification of the test instruments
传感器 放大器 数据采集仪 型号 941B 型号 941型 型号 INV3062-C1（L） 量程 0.125 m/s 积分参数 直通 采样方式 分块平均 灵敏度 23 V·m/s 放大倍数 10 通道数 8 通频带 1～100 Hz 通频带 0.25～25 Hz 采样频率 100 Hz 
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表 2 结构信息和测试结果
Table 2. Structure information and test results
建筑名称 结构形式 形状 层数 长/m 宽/m 高/m 一阶周期/s 纵向 横向 扭转 妥甸小学四层教学楼 框架 矩形 4 40.2 8.7 16.2 0.249 0.266 0.225 法脿小学四层教学楼 框架 矩形 4 26.1 8.1 15.3 0.266 0.240 0.198 程江小学四层教学楼 框架 矩形 4 45.6 9 18.65 0.244 0.244 0.192 程江小学五层教学楼 框架 矩形 5 45.6 9 22.25 0.279 0.279 0.226
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表 3 结构自振周期及折减系数
Table 3. Natural periods and reduction factors
建筑名称 实测一阶周期 软件计算模型一阶周期 折减系数 纵向/s 横向/s 扭转/s 纵向/s 横向/s 扭转/s 纵向 横向 扭转 妥甸小学四层教学楼 0.249 0.266 0.225 0.560 0.592 0.586 0.45 0.45 0.38 法脿小学四层教学楼 0.266 0.240 0.198 0.546 0.572 0.490 0.49 0.42 0.40 程江小学四层楼 0.244 0.244 0.192 0.546 0.705 0.672 0.45 0.35 0.29 程江小学五层楼 0.279 0.279 0.226 0.635 0.784 0.740 0.44 0.36 0.31
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表 4 实测与经验公式对比
Table 4. Comparison between measurement and calculation with empirical formula
建筑名称 纵向 横向 实测/s 计算/s 公式/s 误差t/% 误差c/% 实测/s 计算/s 公式/s 误差t/% 误差c/% 妥甸小学 0.249 0.336 0.291 14.4 −15.5 0.266 0.355 0.319 16.6 −11.3 法脿小学 0.266 0.328 0.292 8.9 −12.3 0.240 0.343 0.312 23.1 −9.9 程江小学四层 0.244 0.328 0.302 19.2 −8.6 0.244 0.423 0.339 28.0 −24.8 程江小学五层 0.279 0.382 0.323 13.6 −18.3 0.279 0.470 0.376 25.7 −25.0 注：t为实测周期与经验公式周期的误差，c为计算模型周期与经验公式周期的误差。
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