Dynamic Increase Factor of an Equivalent SDOF Structural System for Beams with Different Support Conditions under Conventional Blast Loading
Publication: Journal of Engineering Mechanics
Volume 147, Issue 4
Abstract
This study aims to investigate the effects of the dynamic increase factor for beam structures under conventional blast loading. Combined with differential equations of an equivalent single-degree-of-freedom (SDOF) system in elastic and plastic response stages, the dynamic increase factor expression of a beam structure under conventional blast loading was derived. Based on the degree to which the structure reached the plastic stage, the dynamic increase factors under different ratios of equivalent mass-load transformation factors in the elastic stage and elastoplastic stage were analyzed. Using simply supported beams, simply supported and fixed beams, and fixed-end beams as the types of analysis beams, nine calculation conditions of the dynamic increase factor were completed. The calculation results were compared with the formula used by the Chinese blast-resistant design code. The results showed that for a beam structure design with a large ductility ratio (), a ratio of the equivalent mass-load transformation factors in the elastic and plastic stages larger than 1 would increase engineering costs. Compared with simply supported beams and simply fixed beams, the relative error caused by the different ratios for the equivalent mass-load transformation factors is smaller for fixed-end beams. The existing research ignores the equivalent mass-load transformation factor in the plastic stage and takes the ratio of the equivalent mass-load transformation factors in the elastic and plastic stages as 1. This will have a significant impact on the dynamic increase factor of simply supported beams, and the value of maximum error is approximately 18%. If the equivalent mass-load transformation factor in the plastic stage is ignored, then the error in calculating the dynamic increase factor will be small for beam structures with lower ductility ratios (), and the value of maximum error is approximately 5%.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The authors wish to gratefully acknowledge the National Natural Science Foundation of China (No. 51408558) for their support in this study.
References
Acito, M., F. Stochino, and S. Tattoni. 2011. “Structural response and reliability analysis of RC beam subjected to explosive loading.” In Vol. 82 of Applied mechanics and materials, 434–439. Kapellweg, Switzerland, Trans Tech.
Bruhl, J. C., and A. H. Varma. 2018. “Experimental evaluation of steel-plate composite walls subject to blast loads.” J. Struct. Eng. 144 (9): 04018155. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002163.
Carta, G., and F. Stochino. 2013. “Theoretical models to predict the flexural failure of reinforced concrete beams under blast loads.” Eng. Struct. 49 (Apr): 306–315. https://doi.org/10.1016/j.engstruct.2012.11.008.
Fallah, A. S., E. Nwankwo, and L. A. Louca. 2013. “Pressure-impulse diagrams for blast loaded continuous beams based on dimensional analysis.” J. Appl. Mech. 80 (5): 051011. https://doi.org/10.1115/1.4023639.
Fan, Y., L. Chen, H. Ren, P. Feng, and Q. Fang. 2019. “Blast-resistant mechanism of RC beam with kinked rebar and calculation method of dynamic resistance coefficient.” Explos. Shock Waves 39 (3): 035102.
Fang, Q., G. Cheng, and L. Chen. 2013. “The linear dynamic responses of columns subjected to blast loads.” Eng. Mech. 30 (3): 112–119. https://doi.org/10.6052/j.issn.1000-4750.2011.08.0544.
Figuli, L., C. Bedon, Z. Zvaková, Š. Jangl, and V. Kavický. 2017. “Dynamic analysis of a blast loaded steel structure.” Procedia Eng. 199 (2017): 2463–2469. https://doi.org/10.1016/j.proeng.2017.09.388.
Fujikura, S., and M. Bruneau. 2011. “Experimental investigation of seismically resistant bridge piers under blast loading.” J. Bridge Eng. 16 (1): 63–71. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000124.
Gong, S., S. Zhu, A. Zhang, and W. Jin. 2011. “Numerical simulation of blast loads and dynamic response of reinforced concrete slab subjected to close-in explosion.” [In Chinese.] J. Beijing Univ. Technol. 37 (2): 199–205.
Jones, J., C. Wu, D. J. Oehlers, A. S. Whittaker, W. Sun, S. Marks, and R. Coppola. 2009. “Finite difference analysis of simply supported RC slabs for blast loadings.” Eng. Struct. 31 (12): 2825–2832. https://doi.org/10.1016/j.engstruct.2009.07.011.
Kermani, A., A. Ashrafi, and A. Louhghalam. 2018. “A modal approach to determine direct shear of beams subjected to impulse.” Eng. Struct. 156 (Feb): 46–52. https://doi.org/10.1016/j.engstruct.2017.10.076.
Ministry of Construction of the People’s Republic of China. 2006. Code for design of civil air defense basement. GB50038-2005. Beijing: Ministry of Construction of the People’s Republic of China.
Nassr, A. A., A. G. Razaqpur, M. J. Tait, M. Campidelli, and S. Foo. 2012. “Single and multi degree of freedom analysis of steel beams under blast loading.” Nucl. Eng. Des. 242 (Jan): 63–77. https://doi.org/10.1016/j.nucengdes.2011.10.020.
Rigby, S. E., A. Tyas, and T. Bennett. 2012. “Single-degree-of-freedom response of finite targets subjected to blast loading—The influence of clearing.” Eng. Struct. 45 (Dec): 396–404. https://doi.org/10.1016/j.engstruct.2012.06.034.
Stochino, F., and G. Carta. 2014. “SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects.” Nucl. Eng. Des. 276 (Sep): 74–86. https://doi.org/10.1016/j.nucengdes.2014.05.022.
Sun, J., G. Li, and Y. Lu. 2007. “Equivalent single degree of freedom model of SRC columns under blast loading.” J. Vib. Shock 26 (6): 82–89. https://doi.org/10.13465/j.cnki.jvs.2007.06.020.
Tang, T., F. You, T. Ge, and Y. Huang. 2007. “Effects of simplified forms of explosion load on stress field of elastic zone during explosion.” [In Chinese.] Blasting 24 (2): 7–11.
Wu, J., J. Liu, and Y. Du. 2007. “Elastic-Plastic dynamic calculation and numerical analysis of assembling blast resistant wall under effect of vehicle bombs.” J. Disaster Prev. Mitigation Eng. 27 (4): 394–400. https://doi.org/10.13409/j.cnki.jdpme.2007.04.001.
Yan, J., Y. Liu, and F. Huang. 2019. “Improved SDOF approach to incorporate the effects of axial loads on the dynamic responses of steel columns subjected to blast loads.” Adv. Civ. Eng. 2019: 1–9. https://doi.org/10.1155/2019/7810542.
Yang, K., X. Yang, and N. Wang. 2001. “Equivalent static load calculation method for ground structures under chemical explosion.” [In Chinese.] Prot. Eng. 23 (2): 1–7.
Yao, S.-J., D. Zhang, F.-Y. Lu, W. Wang, and X.-G. Chen. 2016. “Damage features and dynamic response of RC beams under blast.” Eng. Fail. Anal. 62 (Apr): 103–111. https://doi.org/10.1016/j.engfailanal.2015.12.001.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 4 • April 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: May 12, 2020
Accepted: Dec 3, 2020
Published online: Jan 25, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 25, 2021
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