阻尼对空爆荷载等效静载动力系数的影响

耿少波; 罗干; 陈佳龙; 赵洲

doi:10.11883/bzycj-2021-0036

阻尼对空爆荷载等效静载动力系数的影响

doi: 10.11883/bzycj-2021-0036

中北大学土木工程学科部，山西太原 030051

基金项目: 国家自然科学基金（51408558）

详细信息

作者简介:
耿少波（1982－　），男，博士，副教授，gengshaobo@nuc.edu.cn

中图分类号: O383.2
计量
- 文章访问数: 450
- HTML全文浏览量: 264
- PDF下载量: 63
- 被引次数: 0
出版历程
- 收稿日期: 2021-01-23
- 录用日期: 2021-12-13
- 修回日期: 2021-06-08
- 网络出版日期: 2022-01-04
- 刊出日期: 2022-02-28

Effect of damping on equivalent static load dynamic factor of air blast load

Department of Civil Engineering, North University of China, Taiyuan 030051, Shanxi, China

摘要

摘要: 为考查阻尼参数对空爆荷载等效静载动力系数的影响，理论推导了空爆荷载下结构等效单自由体系弹塑性位移解及延性比解，设计并计算了阻尼比0.000 1～0.1、延性比1～4的20种典型工况的动力系数，并与现行抗爆设计规范动力系数公式结果进行了对比。结果表明：阻尼比小于0.000 1时可基本代表无阻尼状态，阻尼比0.01的动力系数比无阻尼的最大降低幅度为2.08%，数值差异很小，因此阻尼比为0.01以内时，可忽略阻尼对动力系数的影响；阻尼比0.05的动力系数比无阻尼的降低幅度约9.92%，数值差异较大，认为阻尼比0.05以上时将具有明显的经济效益；现行设计规范动力系数更适用于柔性结构体系，运用于刚性结构抗爆设计时，计算误差较大，对阻尼比较小的结构设计更不利。
- 空爆荷载 /
- 等效静载 /
- 等效单自由度体系 /
- 动力系数 /
- 阻尼比
Abstract: In order to examine the effect of damping on the equivalent static load dynamic factor of the air blast loading, the solutions of the elastoplastic displacement and ductility ratio were derived by the structural equivalent single degree of freedom (SDOF) method for the air blast loading. According to the relationship between the duration of the air blast loading and the duration required for the structural members to complete elastic vibration, the members are divided into two types: rigid members and flexible members. Twenty typical calculation cases, including damping ratios from 0.000 1 to 0.1 and ductility ratios from 1 to 4, were completed and compared with the dynamic factor formula results of the current blast resistant design code. The results show as follow. A ductility ratio less than 0.000 1 can be regarded as a state without damping. The relative error of the dynamic factor between the calculation results with a damping ratio of 0.01 and without damping is less than 2.08%. This relative error is so small that the damping effect with a damping ratio less than 0.01 can be ignored. The dynamic factor with a damping ratio of 0.05 is about 9.92% lower than the one without damping. This relative error is so great that considering the damping ratio will have obvious economic benefits for the blast resistant design when its value is greater than 0.05. Based on the elastic design, the calculation results from the current blast resistant code formula are in good agreement with those from the derived formula in this paper, and the value of the dynamic factor calculated from the code is between the results of damping ratios of 0.01 and 0.05. Furthermore, the current air blast resistant design code formula is more suitable for flexible structure systems. When the code formula is applied to calculate the dynamic factor of rigid members, there will be a large calculation error, which is more unfavorable for members with small damping.
- air blast loading /
- equivalent static load /
- equivalent single degree of freedom /
- dynamical factor /
- damping ratio

HTML全文

图 1 理想弹塑性的含阻尼等效单自由度体系

Figure 1. Elastic-perfectly plastic SDOF vibration system with damping

下载: 全尺寸图片幻灯片

图 2 本文工况计算结果与文献公式的比较

Figure 2. Comparison of the results from the calculation cases and from the code formula

下载: 全尺寸图片幻灯片

图 3 本文工况计算结果的相对误差

Figure 3. Relative errors of the calculation cases

下载: 全尺寸图片幻灯片

表 1 典型工况

Table 1. Typical calculation cases

工况	阻尼比 ξ	延性比 β	工况	阻尼比 ξ	延性比 β	工况	阻尼比 ξ	延性比 β	工况	阻尼比 ξ	延性比 β
C1	0.0001	1	C6	0.0001	2	C11	0.0001	3	C16	0.0001	4
C2	0.001	1	C7	0.001	2	C12	0.001	3	C17	0.001	4
C3	0.01	1	C8	0.01	2	C13	0.01	3	C18	0.01	4
C4	0.05	1	C9	0.05	2	C14	0.05	3	C19	0.05	4
C5	0.1	1	C10	0.1	2	C15	0.1	3	C20	0.1	4

下载: 导出CSV

参考文献(23)

[1]	中华人民共和国建设部, 中华人民共和国国家质量监督检验检疫总局. 人民防空地下室设计规范: GB 50038–2005 [S]. 北京: 中国标准出版社, 2006.
[2]	US Army Corps of Engineers. Structures to resist the effects of accidental explosions: TM5–1300 [S]. Washington: Department of the Army, 1990.
[3]	Canadian Standards Association. Design and assessment of buildings subjects to blast loads: CSA/S 850–12 [S]. Ontario: CSA, 2012.
[4]	中华人民共和国住房和城乡建设部. 建筑结构荷载规范: GB 50009–2012 [S]. 北京: 中国建筑工业出版社, 2012.
[5]	BIGGS J M. Introduction to structural dynamics [M]. New York: McGraw-Hill Book Company, 1964: 315−327.
[6]	GANTES C J, PNEVMATIKOS N G. Elastic-plastic response spectra for exponential blast loading [J]. International Journal of Impact Engineering, 2004, 30(3): 323–343. DOI: 10.1016/S0734-743X(03)00077-0.
[7]	RIEDEL W, FISCHER K, KRANZER C, et al. Modeling and validation of a wall-window retrofit system under blast loading [J]. Engineering Structures, 2012, 37: 235–245. DOI: 10.1016/j.engstruct.2011.12.015.
[8]	方秦, 杜茂林. 爆炸荷载作用下弹性与阻尼支承梁的动力响应 [J]. 力学与实践, 2006, 28(2): 53–56. DOI: 10.3969/j.issn.1000-0879.2006.02.012. FANG Q, DU M L. Dynamic responses of an elastically supported beams with damping subjected to blast loads [J]. Mechanics in Engineering, 2006, 28(2): 53–56. DOI: 10.3969/j.issn.1000-0879.2006.02.012.
[9]	方秦, 陈力, 杜茂林. 端部设置弹簧和阻尼器提高防护门抗力的理论与数值分析 [J]. 工程力学, 2008, 25(3): 194–199,221. FANG Q, CHEN L, DU M L. Theoretical and numerical investigations in effects of end-supported springs and dampers on increasing resistance of blast doors [J]. Engineering Mechanics, 2008, 25(3): 194–199,221.
[10]	郭东, 刘晶波, 闫秋实. 爆炸荷载作用下梁板结构反弹机理分析 [J]. 建筑结构学报, 2012, 33(2): 64–71. DOI: 10.14006/j.jzjgxb.2012.02.009. GUO D, LIU J B, YAN Q S. Rebound mechanism analysis in beams and slabs subjected to blast loading [J]. Journal of Building Structures, 2012, 33(2): 64–71. DOI: 10.14006/j.jzjgxb.2012.02.009.
[11]	陈万祥, 郭志昆, 叶均华. 爆炸荷载作用下柔性边界钢筋混凝土梁的动力响应与破坏模式分析 [J]. 兵工学报, 2011, 32(10): 1271–1277. CHEN W X, GUO Z K, YE J H. Dynamic responses and failure modes of reinforced concrete beams with flexible supports under blast loading [J]. Acta Armamentarii, 2011, 32(10): 1271–1277.
[12]	董彬, 李志军, 魏同. 爆炸荷载下建筑结构的振动控制及分析 [J]. 西安工业大学学报, 2020, 40(4): 404–409. DOI: 10.16185/j.jxatu.edu.cn.2020.04.006. DONG B, LI Z J, WEI T. Vibration control and analysis of structure under explosion load [J]. Journal of Xi’an Technological University, 2020, 40(4): 404–409. DOI: 10.16185/j.jxatu.edu.cn.2020.04.006.
[13]	杜志鹏, 汪玉, 杜俭业, 等. 舰船水下爆炸鞭状运动中的阻尼效应 [J]. 船海工程, 2008, 37(5): 95–98. DOI: 10.3963/j.issn.1671-7953.2008.05.027. DU Z P, WANG Y, DU J Y, et al. Damping effects on the whipping response of warship subjected to an underwater explosion [J]. Ship and Ocean Engineering, 2008, 37(5): 95–98. DOI: 10.3963/j.issn.1671-7953.2008.05.027.
[14]	LIU Y, YAN J B, HUANG F L. Behavior of reinforced concrete beams and columns subjected to blast loading [J]. Defence Technology, 2018, 14(5): 550–559. DOI: 10.1016/j.dt.2018.07.026.
[15]	NASSR A A, YAGI T, MARUYAMA T, et al. Damage and wave propagation characteristics in thin GFRP panels subjected to impact by steel balls at relatively low-velocities [J]. International Journal of Impact Engineering, 2018, 111: 21–33. DOI: 10.1016/j.ijimpeng.2017.08.007.
[16]	ZHANG F R, WU C Q, ZHAO X L, et al. Experimental study of CFDST columns infilled with UHPC under close-range blast loading [J]. International Journal of Impact Engineering, 2016, 93: 184–195. DOI: 10.1016/j.ijimpeng.2016.01.011.
[17]	LIU S F, ZHOU Y Z, ZHOU J N, et al. Blast responses of concrete beams reinforced with GFRP bars: Experimental research and equivalent static analysis [J]. Composite Structures, 2019, 226(10): 111271. DOI: 10.1016/j.compstruct.2019.111271.
[18]	NAGATA M, BEPPU M, ICHINO H, et al. Method for evaluating the displacement response of RC beams subjected to close-in explosion using modified SDOF model [J]. Engineering Structures, 2018, 157: 105–118. DOI: 10.1016/j.engstruct.2017.11.067.
[19]	SYED Z I, RAMAN S N, NGO T, et al. The failure behavior of reinforced concrete panels under far-field and near-field blast effects [J]. Structures, 2018, 14: 220–229. DOI: 10.1016/j.istruc.2018.03.009.
[20]	RITCHIE C B, PACKER J A, SEICA M V, et al. Behaviour and analysis of concrete-filled rectangular hollow sections subject to blast loading [J]. Journal of Constructional Steel Research, 2018, 147: 340–359. DOI: 10.1016/j.jcsr.2018.04.027.
[21]	SHI Y C, XIONG W, LI Z X, et al. Experimental studies on the local damage and fragments of unreinforced masonry walls under close-in explosions [J]. International Journal of Impact Engineering, 2016, 90: 122–131. DOI: 10.1016/j.ijimpeng.2015.12.002.
[22]	FOGLAR M, HAJEK R, KOVAR M, et al. Blast performance of RC panels with waste steel fibers [J]. Construction and Building Materials, 2015, 94: 536–546. DOI: 10.1016/j.conbuildmat.2015.07.082.
[23]	耿少波, 李洪, 葛培杰. 考虑跃迁的指数型炸药空爆荷载等效静载动力系数 [J]. 爆炸与冲击, 2019, 39(3): 032201. DOI: 10.11883/bzycj-2018-0048. GENG S B, LI H, GE P J. Equivalent static load dynamical coefficient for exponential air blast loading with transition [J]. Explosion and Shock Waves, 2019, 39(3): 032201. DOI: 10.11883/bzycj-2018-0048.