考虑跃迁的指数型炸药空爆荷载等效静载动力系数

耿少波; 李洪; 葛培杰

doi:10.11883/bzycj-2018-0048

考虑跃迁的指数型炸药空爆荷载等效静载动力系数

doi: 10.11883/bzycj-2018-0048

耿少波^{1, 2,},
李洪¹,
葛培杰³

1.
中北大学土木工程学科部，山西太原 030051
2.
长安大学桥梁结构安全技术国家工程实验室，陕西西安 710064
3.
大连理工大学水利工程学院，辽宁大连 116024

基金项目: 国家自然科学基金（51408558）；桥梁结构安全技术国家工程实验室开放基金（2014G1502002）

详细信息

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

中图分类号: O383
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出版历程
- 收稿日期: 2018-02-02
- 修回日期: 2018-05-12
- 网络出版日期: 2019-03-25
- 刊出日期: 2019-03-01

Equivalent static load dynamical coefficient for exponential air blast loading with transition

GENG Shaobo^{1, 2
,},
LI Hong¹,
GE Peijie³

1.
Department of Civil Engineering, North University of China, Taiyuan, 030051,Shanxi, China
2.
Bridge Structure Safety Technology National Engineering Laboratory, Chang′an University, Xi’an, 710064, Shaanxi, China
3.
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, 116024, Liaoning, China

摘要

摘要: 为对比抗爆设计规范采用的线性荷载计算模式，建立了考虑跃迁的指数型衰减荷载表达式，通过爆炸荷载等效单自由度微分方程，求解了关于跃迁时长、超压峰值、指数型形状调整参数、结构自振频率与荷载作用时长的等效静载抗力动力系数表达式。根据跃迁时长与形状调整参数，分析了四种典型计算工况，结果表明：现行结构抗爆设计规范等冲量线性衰减荷载可设计范围明显偏小，动力系数在延性比β＜3.0下偏保守，而β≥3.0，wt₊＞1.4δ时偏不安全，最大偏低17.4%；跃迁时长比值越大，动力系数越大，跃迁时长比为1%～2%时，对动力系数影响程度为0.4～0.7%，指数型荷载形状调整参数对柔度特别大的结构动力系数无影响，对其它结构动力系数增大或减少影响程度不一。
- 抗爆设计 /
- 等效荷载 /
- 动力系数 /
- 跃迁荷载 /
- 指数型荷载
Abstract: Compared to linear attenuation load calculation model, exponential attenuation load with transition expression was given to build equivalent SDOF differential equations under air blast loading. The expressions, which had relationship to transition duration, overpressure peak, exponential load adjusting parameter, natural frequency and overpressure duration, were derived to solve equivalent static load dynamical coefficients. Changed with transition duration and load adjusting parameters, four typical calculation conditions results were calculated. The results show that the linear attenuation blast load’s application range is limited. When the ductility ratio β＜3.0, the dynamical coefficients from the linear attenuation blast load behaves greater value and safer characteristic. When the ductility ratio β≥3.0 and wt₊＞1.4δ, it will be lower 17.4% than the value from exponential attenuation load with transition. For the much transition duration ratio, dynamical coefficients will be greater. In the range of 1%−2% for the transition duration ratio, the effect on dynamical coefficients is greater at 0.4−0.7% and can be ignored. Exponential load adjusting parameter has no effect on structural design with great flexibility while it would lead to increase or decrease the dynamical coefficients for the structure with the general flexibility.
- anti-blast design /
- Equivalent static load /
- dynamical coefficient /
- transition load /
- exponential loading

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图 1 荷载简化及作用时长

Figure 1. Schematic diagram of load types and load durations

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图 2 线性衰减荷载与本文荷载计算模式动力系数对比

Figure 2. Dynamical coefficients comparison between linear load and exponential loading with transition

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图 3 线性衰减荷载与典型工况结果差异性比值

Figure 3. The difference ratio between linear decay load and typical calculation conditions

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表 1 工况分组

Table 1. Calculation cases

工况	t₀/t₊	δ	a	θ_I
工况1	0.01	1.464	1.27	0.2～2.8
工况2	0.01	1.6	1.61	0.2～2.8
工况3	0.02	1.464	1.27	0.2～2.8
工况4	0.02	1.6	1.61	0.2～2.8

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表 2 工况1动力系数计算K_h

Table 2. Dynamical coefficient K_h for calculation case 1

θ₊	K_h
θ₊	β=1.0	β=1.2	β=1.6	β=2	β=3	β=5
0.292 8	0.100 (1.0%)	0.085 (1.2%)	0.067 (0.0%)	0.057 (0.0%)	0.044 (0.0%)	0.033 (0.0%)
0.585 6	0.199 (0.0%)	0.168 (0.0%)	0.134 (0.7%)	0.114 (0.0%)	0.088 (0.0%)	0.065 (0.3%)
0.878 4	0.296 (−0.3%)	0.25 (0.0%)	0.199 (0.0%)	0.17 (0.0%)	0.129 (−2.4%)	0.090 (−7.3%)
1.171 2	0.389 (−0.8%)	0.328 (−0.9%)	0.261 (−0.9%)	0.220 (−2.3%)	0.162 (−6.6%)	0.110 (−9.2%)
1.464 0	0.478 (−1.7%)	0.403 (−1.7%)	0.316 (−3.1%)	0.265 (−5.1%)	0.192 (−7.0%)	0.125 (−8.3%)
1.756 8	0.562 (−2.5%)	0.472 (−2.9%)	0.368 (−4.7%)	0.307 (−5.1%)	0.221 (−5.1%)	0.138 (−4.4%)
2.049 6	0.640 (−3.4%)	0.537 (−3.8%)	0.420 (−4.1%)	0.350 (−3.4%)	0.251 (−1.4%)	0.149 (3.2%)
2.342 4	0.711 (−4.6%)	0.599 (−4.7%)	0.474 (−2.0%)	0.397 (−0.4%)	0.283 (3.0%)	0.161
2.635 2	0.774 (−6.1%)	0.652 (−5.6%)	0.519 (−1.9%)	0.446 (2.9%)	0.319 (7.9%)	0.176
2.928 0	0.830 (−7.6%)	0.700 (−6.7%)	0.557 (−2.9%)	0.476 (1.6%)	0.359 (12.8%)	0.198
3.220 8	0.877 (−9.4%)	0.740 (−8.5%)	0.589 (−5.1%)	0.504 (−0.6%)	0.404 (17.4%)	0.229
3.513 6	0.917	0.773	0.615	0.526	0.407	0.267
3.806 4	0.948	0.799	0.636	0.544	0.421	0.308
4.099 2	0.972	0.819	0.652	0.558	0.431	0.354

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