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Pressure-impulse diagrams using coupled single degree of freedom systems subjected to blast load

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Abstract

Pressure-Impulse (P-I) diagrams, a widely popularized approach, relate different damage levels and are utilized in the preliminary design of structural elements subjected to blast loading. In the presented paper, P-I diagrams generated using coupled Single Degree of Freedom (SDOF) model subjected to blast loading are studied. It may be noted that these P-I diagrams for the blast in the dynamic and impulsive regime are very different from those derived by applying the uncoupled SDOF approach. The resultant P-I diagrams are further compared with those based on Timoshenko beam theory, including the higher modes effect. The findings are intended to shed light on how to develop simpler, more accurate methods for calculating the combined reaction of structural parts exposed to various blast loading ranges. The effect of shear and flexure resistance ratio on P-I diagrams has been studied parametrically. P-I diagrams show only small fluctuations as they approach quasi-static regimes, indicating that they are not sensitive to the shear and flexure resistance ratio for a distant range of blast loadings.

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References

  • Abedini, M., Mutalib, A. A., Baharom, S., & Hao, H. (2013). Reliability analysis of P-I diagram formula for RC column subjected to blast load. In Proceedings of World Academy of Science, Engineering and Technology (vol. 7 no. 8, pp. 253–257)

  • Abedini, M., Mutalib, A. A., Raman, S. N., Alipour, R., & Akhlaghi, E. (2019). Pressure-impulse (P–I) diagrams for reinforced concrete (RC) structures. Archives Computational Methods Engineering., 26, 733.

    Article  Google Scholar 

  • Bhatt, A., Bhargava, P., & Maheshwari, P. (2021). Contribution of higher modes in the dynamic response of reinforced concrete member subjected to blast IOP Conference Series. Earth and Environment Sciences, 871, 012003. https://doi.org/10.1088/1755-1315/871/1/012003

    Article  Google Scholar 

  • Bhatt, A., Bhargava, P., & Maheshwari, P. (2023). Coupled SDOF system approach for reinforced concrete beams subjected to blast loading. Engineering Structures, 22, 4435 (under communication)

    Google Scholar 

  • Biggs, J. M. (1964). Introduction to Structural Dynamics. Mc Graw Hill Book Company. https://doi.org/10.1007/978-3-7091-2656-1_2

    Article  Google Scholar 

  • Campidelli, M., & Viola, E. (2007). An analytical-numerical method to analyze the single degree of freedom models under air blast loading. Journal of Sound and Vibration, 302(1–2), 260–286. https://doi.org/10.1016/j.jsv.2006.11.024

    Article  Google Scholar 

  • Chopra, A. K. (2012). Dynamics of structures. Prentice Hall 4th edition

  • Cormie, D., Mays, C., & Smith, P. (2009). Blast effects on buildings (2nd ed.). Thomas Telford Ltd.

    Book  Google Scholar 

  • Department of Defense, UFC 3–340–02. (2008). Structures to resist the effects of the accidental explosions. Technical Report, Unified Facilities Criteria

  • Dragos, J., & Wu, C. (2014). Interaction between direct shear and flexural responses for blast loaded one-way reinforced concrete slabs using a finite element model. Engineering Structures, 72, 193–202. https://doi.org/10.1016/j.engstruct.2014.04.043

    Article  Google Scholar 

  • Fallah, A. S., & Louca, L. A. (2007). Pressure-impulse diagrams for elastic-plastic-hardening and softening single-degree-of-freedom models subjected to blast loading. International Journal of Impact Engineering, 34(4), 823–842. https://doi.org/10.1016/j.ijimpeng.2006.01.007

    Article  Google Scholar 

  • Gantes, C. J., & Pnevmatikos, N. G. (2004). Elastic-plastic response spectra for exponential blast loading. International Journal of Impact Engineering, 30(3), 323–343. https://doi.org/10.1016/S0734-743X(03)00077-0

    Article  Google Scholar 

  • Han, S. M., Benaroya, H., & Wei, T. (1999). Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and Vibrations, 225(5), 935–988. https://doi.org/10.1006/jsvi.1999.2257

    Article  MATH  Google Scholar 

  • Ibrahim, Y. E., Ismail, M. A., & Nabil, M. (2017). Response of Reinforced Concrete Frame Structures under Blast Loading. Procedia Engineering, 171, 890–898. https://doi.org/10.1016/j.proeng.2017.01.384

    Article  Google Scholar 

  • Jayasooriya, R. (2010). Vulnerability and damage analysis of reinforced concrete framed buildings, PhD thesis

  • Jones, N., & Alves, M. (2004). Post-failure motion of beams under blast loads. Structural Materials, 15, 3–12.

    Google Scholar 

  • Kadid, A. (2008). Stiffened plates subjected to uniform blast loading. Journal of Civil Engineering and Management, 14(3), 155–161. https://doi.org/10.3846/1392-3730.2008.14.11

    Article  Google Scholar 

  • Krauthammer, T. (2008). Pressure-impulse diagrams and their applications. In Modern Protective Structures, Civil and Environmental Engineering. https://doi.org/10.1201/9781420015423.ch8

    Article  Google Scholar 

  • Krauthammer, T., Astarlioglu, S., Blasko, J., Soh, T. B., & Ng, P. H. (2008). Pressure-impulse diagrams for the behavior assessment of structural components. International Journal of Impact Engineering, 35(8), 771–783. https://doi.org/10.1016/j.ijimpeng.2007.12.004

    Article  Google Scholar 

  • Li, Q. M., & Meng, H. (2002). Pulse loading shape effects on pressure–impulse diagram of an elastic-plastic, single-degree-of-freedom structural model. Journal of Engineering Mechanics ASCE, 44, 1985–1998.

    MATH  Google Scholar 

  • Liu, L., Zong, Z., Tang, B., & Li, M. (2018). Damage Assessment of an RC Pier under Noncontact Blast Loading Based on P - I Curves. Shock and Vibration. https://doi.org/10.1155/2018/9204036

    Article  Google Scholar 

  • Ngo, T., Mendis, P., Gupta, A., & Ramsay, J. (2007). Blast loading and blast effects on structures - An overview. Electronic Journal of Structural Engineering, 7, 76–91.

    Article  Google Scholar 

  • Ross, T. J. (1986). Impulsive direct shear failure in RC slab. Journal of Structural Engineering ASCE, 1, 1661–1677.

    Google Scholar 

  • Shi, H., Salim, H., & Ma, G. (2012). Using P-I diagram method to assess the failure modes of rigid-plastic beams subjected to triangular impulsive loads. International Journal of Protective Structures, 3(3), 333–353. https://doi.org/10.1260/2041-4196.3.3.333

    Article  Google Scholar 

  • Slawson, B. T. R. (1984). Dynamic shear failure of shallow-buried flat-roofed reinforced concrete structures subjected to blast loading. Technical Report SL-84–7 Structures Laboratory US Army Waterways Experiment Station, Vicksburg, MS.

  • Smith, P. D., & Hetherington J. G. (1994). Blast and ballistic loading of structures. CRC Press

  • Syed, Z. I., Liew, M. S., Hasan, M. H., & Venkatesan, S. (2014). Single-degree-of-freedom based pressure-impulse diagrams for blast damage assessment. Applied Mechanics and Materials, 567, 499–504. https://doi.org/10.4028/www.scientific.net/AMM.567.499

    Article  Google Scholar 

  • Van Der Meer, L. J., Kerstens, J. G. M., & Bakker, M. C. M. (2010). P-I diagrams for linear-elastic cantilevered Timoshenko beams including higher modes of vibration. Heron, 55(1), 51–83.

    Google Scholar 

  • Wu, C. (2012). Research Development on Protection of Structures against Blast Loading at the University Of Adelaide. Australian Journal of Structural Engineering, 13(1), 97–109. https://doi.org/10.7158/13287982.2012.11465102

    Article  Google Scholar 

  • Xu, J., Wu, C., & Li, Z. X. (2014). Analysis of direct shear failure mode for RC slabs under external explosive loading. International Journal of Impact Engineering, 69, 136–148. https://doi.org/10.1016/j.ijimpeng.2014.02.018

    Article  Google Scholar 

  • Youngdahl, C. K. (1970). Correlation parameters for eliminating the effect of pulse shape on dynamic plastic deformation. Journal of Applied Mechanics Transactions ASME, 37(3), 744–752. https://doi.org/10.1115/1.3408605

    Article  MATH  Google Scholar 

  • Yu, R., Zhang, D., Chen, L., & Yan, H. (2018). Non-dimensional pressure–impulse diagrams for blast-loaded reinforced concrete beam-columns referred to different failure modes. Advances of Structural Engineering, 21(14), 2114–2129. https://doi.org/10.1177/1369433218768085

    Article  Google Scholar 

  • Zhang, C., Gholipour, G., & Mousavi, A. A. (2019). Nonlinear dynamic behavior of simply-supported RC beams subjected to combined impact-blast loading. Engineering Structures, 181, 124–142. https://doi.org/10.1016/j.engstruct.2018.12.014

    Article  Google Scholar 

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  1. Department of Civil Engineering, IIT Roorkee, Roorkee, 247667, India

    Anita Bhatt & Pradeep Bhargava

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  1. Anita Bhatt
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Anita Bhatt wrote the main manuscript text and prepared all figures reported in manuscript. Pradeep Bhargava provided valuable guidance. All authors reviewed the manuscript.

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Correspondence to Anita Bhatt.

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Bhatt, A., Bhargava, P. Pressure-impulse diagrams using coupled single degree of freedom systems subjected to blast load. Asian J Civ Eng 24, 3893–3905 (2023). https://doi.org/10.1007/s42107-023-00705-2

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