Abstract
This paper investigates the influence of an explosive load, due to a terrorist action, on the behavior of a long or a suspension bridge, and studies the explosion characteristics and their effect on the bridge. The purpose of this paper is not to investigate the consequences of the loss of structural elements. The main subject is to determine the critical magnitudes of the explosions that a bridge could suffer, to indicate the possible points where the explosives can be placed, the combination of positions and also the simultaneous action or the action with time hysteresis of the explosions. The theoretical formulation is based on a continuum approach which has been used in literature to analyze such long or suspension bridges. The analysis is carried out with the modal superposition method, and the resulting differential equations are solved using the second Duhamel’s integral.
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References
USAEC. The effects of Nuclear Weapons, 1957, 1973+, 1986, Printing Office, Washington, DC.
U.S. Department of the Army Technical Manual: TM5–1300, Structures to resist the effects of accidental explosions. United States Department of the Army, Navy and Air Force, USA (1990)
U.S. Department of Defense Unified Facilities Criteria, DoD Minimum antiterrorism standards for buildings (2002)
American Society of Civil Engineers, Minimum design loads for buildings and other structures (2002)
EN 1990:2002 Eurocode—Basis of structural design (2002)
prEN 1991-1-7, Eurocode 1—Action on structures, General actions - Accidental actions European Standard
Cowper, G.R., Symonds, P.S.: Strain Hardening and Strain Rate Effect in the Impact Loading of Cantilever Beams. Brown University, Division of Applied Mathematics report, (1957)
Baker, W.E., Cox, P.A., Westine, P.S., Kulesz, J.J., Strehlow, R.A.: Explosion Hazard and Evaluation, vol. 198. Elsevier, New York (2012)
Ghali, A., Tadros, G.: Bridge progressive collapse vulnerability. J. Struct. Eng. 123(2), 227–231 (1997)
Manual of steel construction: Load & Resistance Factor Design. American Institute Steel Construction (2001)
Paik, J.K., Thayamballi, A.K.: Ultimate Limit State Design of Steel-Plated Structures. Wiley, Hoboken (2003)
Ray, J.C., Armstrong, B.J., Slawson, T.R.: Air blast environment beneath a bridge overpass, pp. 63–68. Transportation Research Record 1827, Transportation Research Board, Washington (2003)
Marchand, K., Williamson, E.B., Winget, D.G.: Analysis of blast loads on bridge substructures. In: Proceedings of the Structures and Materials, pp. 151–160. Wit Press, Southampton (2004)
Anwarul Islam, A.K.M., Yazdani, N.: Performance of AASHTO girder bridges under blast loading. Eng. Struct. 30(7), 1922–1937 (2008)
Kiger, S.A., Salim H.A., Ibrahim, A.: Bridge Vulnerability Assessment and Mitigation Against Explosions. Midwest Transportation Consortium. Iowa State University (2010)
Williamson, E.B., Oguzhan, B., Williams, G.D., Davis, C.E.: Blast-resistant highway bridges: design and detailing guidelines. TRB’s National Cooperative Highway Research Program (NCHRP) Report 645 (2010)
Bi, K., Ren, W.X., Cheng, P.F., Hao, H.: Domino-type progressive collapse analysis of a multi-span simply-supported bridge: a case study. Eng. Struct. 90, 172–182 (2015)
Baylot, J.T., Ray, J.C., Hall, R.L.: Prediction method for response of steel bridge beams and girders to blast and fragment loads, pp. 69–74. Transportation Research Record 1827, Transportation Research Board, Washington (2003)
Miyachi, K., Nakamura, S., Manda, A.: Progressive collapse analysis of steel truss bridges and evaluation of ductility. J. Constr. Steel Res. 78, 192–200 (2012)
Baker, W.E.: Explosions in Air. University of Texas Press, Austin (1973)
Scott, B.D., Park, R., Priestley, M.J.N.: Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates. ACI J. 79(1), 13–27 (1982)
Soroushian, P., Choi, K., Alhamad, A.: Dynamic constitutive behavior of concrete. ACI J. 83(2), 251–258 (1987)
CEB-FIP model code: Comite´ Euro-international du Be´ton Trow-bridge, p. 1993. Redwood books, Wiltshire (1990)
Malvar, L.J., Crawford, J.E.: Dynamic Increase Factors for Concrete. Twenty-Eighth DDESB Seminar, Orlando (1998)
Xu, Z., Lu, X., Guan, H., Lu, X., Ren, A.: Progressive-collapse simulation and critical region identification of a stone arch bridge. J. Perform. Constr. Facil. 27, 43–52 (2013)
Son, J., Astaneh-Asl, A.: Blast protection of cable-stayed and suspension bridges. In: Proceedings of the TCLEE Conference on Lifeline Earthquake Engineering in a Multihazard Environment, pp. 1–12. ASCE, Reston (2009)
Hao, H., Tang, E.K.C.: Numerical simulation of a cable-stayed bridge response to blast loads, Part II: damage prediction and FRP strengthening. Eng. Struct. 32(10), 3193–3205 (2010)
Cai, J., Xu, Y., Zhuang, L., Feng, J., Zhang, J.: Comparison of various procedures for progressive collapse analysis of cable-stayed bridges. J. Zhejiang Univ. Sci. A 13(5), 323–334 (2012)
Hashemi, S.K., Bradford, M.A., Valipour, H.R.: Dynamic response of cable-stayed bridge under blast load. Eng. Struct. 127, 719–736 (2016)
Sherbaph, M.: Study and Investigation of the Effects of the Explosion on Suspension Bridges. MSc dissertation, University of Tabriz, Department of Civil Engineering (2013) (In Persian)
Ray, J.C.: Validation of numerical modeling and analysis of steel bridge towers subjected to blast loadings. In: Proceedings of the Structures Congress and Expositions, pp. 1–10. ASCE, Reston (2006)
Tang, E.K.C., Hao, H.: Numerical simulation of a cable-stayed bridge response to blast loads, Part I: model development and response calculations. Eng. Struct. 32(10), 3180–3192 (2010)
Ibarhim, A., Salim, H., Rahman, N.A.: Progressive collapse of post-tensioned box girder bridges under blast loads using applied element method. In: Structures Congress, pp. 2291–2300. ASCE, Reston (2012)
Tian, L., Huang, F.: Numerical simulation for progressive collapse of continuous girder bridge subjected to ship collision based on three-stage simulation method. Adv. Mater. Res. 790, 362–366 (2013). https://doi.org/10.4028/www.scientific.net/AMR.790.36
Tian, L., Huang, F.: Numerical simulation for progressive collapse of continuous girder bridge subjected to ship impact. Trans. Tianjin Univ. 20, 250–256 (2014). https://doi.org/10.1007/s12209-014-2216-8
Farahmand-Tabar, S., Barghian, M., Vahabzadeh, M.: Investigation of the progressive collapse in a suspension bridge under the explosive load. Int. J. Steel Struct. 19(6), 2039–2050 (2019)
Fujikura, S., Bruneau, M.: Experimental investigation of seismically resistant bridge piers under blast loading. J. Bridg. Eng. 10(1061), 63–71 (2011)
Pan, Y., Ventura C.E., Cheung M.M.S.: Performance of highway bridges subjected to blast loads. https://doi.org/10.1016/j.engstruct.2017.08.028 (2017)
Michaltsos, G.T., Sophianopoulos, D.S.: Suspension bridges under blast loads: a preliminary linearized approach. Arch. Appl. Mech. (2021). https://doi.org/10.1007/s00419-021-01991-5
Qi, X.J., Liu, Q., Shang, F.J.: Dynamic response of concrete arch bridge under blast loading. J. Appl. Mech. Mater. 501–504, 1283–1286 (2014)
Ma, L.L., Wu, H., Fang, Q.: Damage mode and dynamic response of RC girder bridge under explosions. Eng. Struct. (2021). https://doi.org/10.1016/j.engstruct.2021.112676Get
Wawranek, A., Steinhard, O.: Theory und berechnung der Stahlbrücken. Springer, Berlin (1958)
Michaltsos, G.T., Raftoyiannis, I.G.: Bridges’ Dynamics. Bentham Sciences Publ, UAE (2012)
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Michaltsos, G.T., Avraam, T. Bridges under explosive loads a preliminary linearized approach. Arch Appl Mech 92, 2041–2059 (2022). https://doi.org/10.1007/s00419-022-02148-8
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DOI: https://doi.org/10.1007/s00419-022-02148-8