Simplified Model for Analyzing Soft Impacts on Structures: Validation on Steel Beams
Publication: Journal of Structural Engineering
Volume 150, Issue 12
Abstract
Traditionally, simplified methods have been used to try to solve and understand impacts. These simplified methods sometimes assume hypotheses that excessively limit their applicability or are not sufficiently simplified and require numerical solutions. To analyze the influence of projectile flexibility in the structural response to impacts, finite element (FE) models are commonly used due to the limitations of simplified methods. This article proposes a new simplified model that enables the calculation of both structural displacement and contact force during an impact on simple structures, which can be represented as a spring-mass system, such as beams. The model takes into account projectile deformation and the effect of gravitational force on the structural response, providing an analytical solution. The proposed formulation has been validated by means of experimental impact tests and with finite-element models of impacts on beams. The effect of gravity, multiple impacts, and the influence of projectile flexibility when defining soft or hard impact are discussed in depth in this article. This research enables the calculation of complex impacts in an easy way while also facilitating the understanding of the phenomenon and the key parameters for managing it.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
We would like to thank Simulsoft Ingenieros España for lending the Midas NFX software for use in this research, which has been of great help.
References
AASHTO. 2020. LRFD bridge design specifications. Washington, DC: AASHTO.
Abrate, S. 2001. “Modeling of impacts on composite structures.” Compos. Struct. 51 (2): 129–138. https://doi.org/10.1016/S0263-8223(00)00138-0.
Alonso, J., J. A. Parra, A. Pacios, and M. C. Huerta. 2019. “Similarity index: A procedure for comparing impact time histories validated with soft impact test.” Eng. Struct. 198 (Nov): 109513. https://doi.org/10.1016/j.engstruct.2019.109513.
Al-Thairy, H., and Y. C. Wang. 2013. “A simplified analytical method for predicting the critical velocity of transverse rigid body impact on steel columns.” Int. J. Impact Eng. 58 (Aug): 39–54. https://doi.org/10.1016/j.ijimpeng.2013.02.004.
Al-Thairy, H., and Y. C. Wang. 2014. “Simplified FE vehicle model for assessing the vulnerability of axially compressed steel columns against vehicle frontal impact.” J. Construct. Steel Res. 102 (Nov): 190–203. https://doi.org/10.1016/j.jcsr.2014.07.005.
CEN (European Committee for Standardization). 1991. Accidental actions. Eurocode 1-BS EN 1991-1-7. Brussels, Belgium: CEN.
Chen, L., H. Wu, and T. Liu. 2021. “Vehicle collision with bridge piers: A state-of-the-art review.” Adv. Struct. Eng. 24 (2): 385–400. https://doi.org/10.1177/1369433220953510.
Chopra, A. K. 1995. Dynamics of structures. Part 1. Hoboken, NJ: Prentice-Hall.
Dally, J. W., and W. F. Riley. 1978. Experimental stress analysis. New York: McGraw Hill.
Goldsmith, W. 2001. Impact. North Chelmsford, MA: Courier Corporation.
Gridnev, S., and I. Ravodin. 2018. “Finite element modeling of a moving load using contact conditions.” Theor. Found. Civ. Eng. 196 (Sep): 01044. https://doi.org/10.1051/matecconf/201819601044.
Gurbuz, T., A. Ilki, D. P. Thambiratnam, and N. Perera. 2019. “Low-elevation impact tests of axially loaded reinforced concrete columns.” ACI Struct. J. 116 (1): 117–128. https://doi.org/10.14359/51710862.
Hao, H. 2015. “Predictions of structural response to dynamic loads of different loading rates.” Int. J. Prot. Struct. 6 (4): 585–605. https://doi.org/10.1260/2041-4196.6.4.585.
Hoffmann, K. 2012. An introduction to stress analysis and transducer design using strain gauges. Darmstadt, Germany: HBM Test and Measurement.
Iriarte, X., J. Aginaga, G. Gainza, J. Ros, and J. Bacaicoa. 2021. “Optimal strain-gauge placement for mechanical load estimation in circular cross-section shafts.” Measurement 174 (Apr): 108938. https://doi.org/10.1016/j.measurement.2020.108938.
Jin, L., Y. Lan, R. Zhang, and X. Du. 2020. “Impact resistance of RC beams under different combinations of mass and velocity: Mesoscale numerical analysis.” Arch. Civ. Mech. Eng. 20 (4): 1–21. https://doi.org/10.1007/s43452-020-00129-8.
Lam, N. T. K., H. H. Tsang, and E. F. Gad. 2010. “Simulations of response to low velocity impact by spreadsheet.” Int. J. Struct. Stab. Dyn. 10 (3): 483–499. https://doi.org/10.1142/S0219455410003580.
Lee, Y., J. F. Hamilton, and J. W. Sullivan. 1983. “The lumped parameter method for elastic impact problems.” J. Appl. Mech. 50 (4a): 823–827. https://doi.org/10.1115/1.3167152.
Louw, J. M., G. Maritz, and M. J. Loedolff. 1992. “The behaviour of RC columns under impact loading.” J. Civ. Eng. 34 (11): 371–378. https://doi.org/10.10520/AJA10212019_18182.
Sánchez-Haro, J. 2017. “Development of theory on impacts: Simplified method of calculation of impacts in structures.” Ph.D. thesis, Structural Dept., Univ. of Cantabria.
Sánchez-Haro, J., I. Lombillo, and G. Capellán. 2022. “Equivalent static force in heavy mass impacts on structures.” Int. J. Struct. Stab. Dyn. 22 (2): 2250025. https://doi.org/10.1142/S0219455422500250.
Sánchez-Haro, J., I. Lombillo, and G. Capellán. 2023. “Simplified model to consider influence of gravity on impacts on structures: Experimental and numerical validation.” Int. J. Impact Eng. 173 (Mar): 104474. https://doi.org/10.1016/j.ijimpeng.2022.104474.
Sharma, H., S. Hurlebaus, and P. Gardoni. 2012. “Performance-based response evaluation of reinforced concrete columns subject to vehicle impact.” Int. J. Impact Eng. 43 (May): 52–62. https://doi.org/10.1016/j.ijimpeng.2011.11.007.
Stronge, W. J. 2004. Impact mechanics. Cambridge, UK: Cambridge Univ.
Suthan, R., V. Jayakumar, and S. Madhu. 2018. “Evaluation of mechanical properties of Kevlar fibre epoxy composites: An experimental study.” Int. J. Veh. Struct. Syst. 10 (6): 389–394. https://doi.org/10.4273/ijvss.10.6.02.
Utzeri, M., M. Sasso, G. Chiappini, and S. Lenci. 2021. “Modelling of low-velocity impacts on composite beams in large displacement.” Fract. Struct. Integr. 15 (58): 254–271. https://doi.org/10.3221/IGF-ESIS.58.19.
Viviani, L., A. Consolaro, M. Maffeis, and G. Royer-Carfagni. 2021. “Engineered modelling of the soft-body impact test on glazed surfaces.” Eng. Struct. 226 (Jan): 111315. https://doi.org/10.1016/j.engstruct.2020.111315.
Yang, Y., N. T. K. Lam, and L. Zhang. 2012a. “Estimation of response of plate structure subject to low veloctiy impact by a solid object.” Int. J. Struct. Stab. Dyn. 12 (6): 1250053. https://doi.org/10.1142/S0219455412500538.
Yang, Y., N. T. K. Lam, and L. Zhang. 2012b. “Evaluation of simplified methods of estimating beam responses to impact.” Int. J. Struct. Stab. Dyn. 12 (3): 1250016. https://doi.org/10.1142/S0219455412500162.
Zhang, C., G. Gholipour, and A. A. Mousavi. 2021. “State-of-the-art review on responses of RC structures subjected to lateral impact loads.” Arch. Comput. Methods Eng. 28 (4): 2477–2507. https://doi.org/10.1007/s11831-020-09467-5.
Zhao, D., W. Yi, and S. K. Kunnath. 2017. “Shear mechanisms in reinforced concrete beams under impact loading.” J. Struct. Eng. 143 (9): 04017089. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001818.
Zhao, W., and J. Qian. 2019. “Dynamic response and shear demand of reinforced concrete beams subjected to impact loading.” Int. J. Struct. Stab. Dyn. 19 (8): 1950091. https://doi.org/10.1142/S0219455419500913.
Zhao, W., and J. Ye. 2022. “Dynamic behavior and damage assessment of RC columns subjected to lateral soft impact.” Eng. Struct. 251 (Jan): 113476. https://doi.org/10.1016/j.engstruct.2021.113476.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 150 • Issue 12 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jan 18, 2024
Accepted: Jun 20, 2024
Published online: Sep 24, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 24, 2025
ASCE Technical Topics:
- Analysis (by type)
- Beams
- Continuum mechanics
- Dynamic loads
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Finite element method
- Methodology (by type)
- Models (by type)
- Numerical analysis
- Numerical methods
- Projectile penetration
- Research methods (by type)
- Solid mechanics
- Steel beams
- Steel structures
- Structural analysis
- Structural dynamics
- Structural engineering
- Structural members
- Structural models
- Structural systems
- Structures (by type)
- Validation
Authors
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