Dynamic impact of heavy long vehicles with equally spaced axles on short-span highway bridges

    Omar MOHAMMED Affiliation
    ; Arturo GONZÁLEZ Affiliation
    ; Daniel CANTERO Affiliation


Extremely large trucks with a weight exceeding the standard require a permit before they are allowed to cross the bridges of a specific route. For the purpose of safety, an escort is often employed to maintain a distance between vehicles and to ensure that the bridge load remain below the allowed maximum. Given that the speed of these large vehicles is quite slow and that the amplitude of vibrations normally declines when the vehicle mass is large, a minor dynamic amplification of the bridge response is expected. However, some of these large trucks have a unique feature characterized by “multiple equally-spaced axles”, something that is uncommon in normal vehicle. The application of axle forces at equal intervals can dynamically excite bridges to a considerable extent, even at low speeds. These “critical” low speeds are estimated a priori from the axle spacing of the truck and the main frequency of vibration of the bridge. This paper demonstrates that when the “critical” speed is unavoidable, a relatively high dynamic allowance must be added to static calculations before granting a permit to a long heavy vehicle.

Keyword : bridge dynamics, critical velocity, dynamic amplification factor (DAF), expansion joint, large trucks, permit vehicles, vehicle bridge interaction (VBI)

Mar 27, 2018
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


AASHTO. (2012). LRFD bridge design specifications, Washington, DC. American Association of State Highway Officials

(AASHO). (1962). “The AASHO road test.” Rep. 4, Special Rep. 61D, Highway Research Board, Washington, DC.

Brady, S. P., & O’Brien, E. J. (2006). Effect of vehicle velocity on the dynamic amplification of two vehicles crossing a simply supported bridge. Journal of Bridge Engineering, 11(2), 250-256.

Brady, S. P., O’Brien, E. J., & Žnidarič, A. (2006). Effect of vehicle velocity on the dynamic amplification of a vehicle crossing a simply supported bridge. Journal of Bridge Engineering, 11(2), 241-249.

Cantero, D., O’Brien, E. J., & González, A. (2010). Modelling the vehicle in vehicle–infrastructure dynamic interaction studies. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 224(2), 243-248.

Cantero, D., González, A., & O’Brien, E. J. (2011). Comparison of bridge dynamic amplification due to articulated 5-Axle trucks and large cranes. Baltic Journal of Road and Bridge Engineering, 6(1), 39-47.

Cantero, D., Arvidsson, T., O’Brien, E. J., & Karoumi, R. (2015). Train–track–bridge modelling and review of parameters. Structure and Infrastructure Engineering, 12(9), 1051-1064.

Cantero, D., & Karoumi, R. (2016). Numerical evaluation of the mid-span assumption in the calculation of total load effects in railway bridges. Engineering Structures, 107, 1-8.

Casas, J. R., & Aparicio, A. C. (2001). Computer-based bridge management system for permit vehicle routing. Computer-Aided Civil and Infrastrcuture Engineering, 16(6), 444-454.

Correia, J. P. R. R., & Branco, F. A. B. B. (2006). New methodology: permit checking of vehicular overloads. Journal of Bridge Engineering, 11(3), 274-281.

Cebon, D. (1999). Handbook of vehicle-road interaction (600 p.). Swets & Zeitlinger Lisse, The Netherlands.

Cebon, D., & Newland, D. E. (1983). Artificial generation of road surface topography by the inverse FFT method. Vehicle System Dynamics, 12(1-3), 160-165.

Deng, L., Yu, Y., Zou, Q., & Cai, C. S. (2014). State-of-the-Art review of dynamic impact factors of highway bridges. Journal of Bridge Engineering, 20(5), 1-14.

Ding, L., Hao, H., & Zhu, X. (2009). Evaluation of dynamic vehicle axle loads on bridges with different surface conditions. Journal of Sound and Vibration, 323(3-5), 826-848.

Enright, B., & O’Brien, E. J. (2013). Monte Carlo simulation of extreme traffic loading on short and medium span bridges. Structure and Infrastructure Engineering, 9(12), 1267-1282.

Fafard, M., Bennur, M., & Savard, M. (1997). A general multi-axle vehicle model to study the bridge-vehicle interaction. Engineering Computations, 14(5), 491-508.

Fu, T. T., & Cebon, D. (2002). Analysis of a truck suspension database. International Journal of Heavy Vehicle Systems, 9(4), 281-297.

González, A. (2010). Vehicle-bridge dynamic interaction using finite element modelling. In D. Moratal (Ed.), Finite Element Analysis, Sciyo, Croatia (pp. 637-662).

González, A., O’Brien, E. J., Cantero, D., Li, Y., Dowling, J., & Žnidarič, A. (2010). Critical speed for the dynamics of truck events on bridges with a smooth road surface. Journal of Sound and Vibration, 329(11), 2127-2146.

González, A., Rowley, C., & O’Brien, E. J. (2008ª). A general solution to the identification of moving vehicle forces on a bridge. International Journal for Numerical Methods in Engineering, 75(3), 335-354.

González, A., Rattigan, P., O’Brien, E. J., & Caprani, C. (2008b). Determination of bridge lifetime dynamic amplification factor using finite element analysis of critical loading scenarios. Engineering Structures, 30, 2330-2337.

Harris, N. K., O’Brien, E. J., & González, A. (2007). Reduction of bridge dynamic amplification through adjustment of vehicle suspension damping. Journal of Sound and Vibration, 302(3), 471-485.

Honda, H., Kajikawa, Y., & Kobori, T. (1982). Roughness characteristics at expansion joint on highway bridges. Proceedings of Japan Society of Civil Engineers, 324, 173-176.

ISO 8608:1995 Mechanical Vibration-Road Roughness Surfaces.Kim, C.-W., Kawatani, M., & Kwon, Y.-R. (2007). Impact coefficient of reinforced concrete slab on a steel girder bridge. Engineering Structures, 29(4), 576-590.

Kirkegaard, P. H., Nielsen, S. R. K., & Enevoldsen, I. (1997). Heavy vehicles on minor highway bridges – dynamic modelling of vehicles and bridges (44 p.). Aalborg University, Instituttet for Bygningsteknik.

Kwasniewski, L., Wekezer, J., Roufa, G., Li, H., Ducher, J., & Malachowski, J. (2006). Experimental evaluation of dynamic effects for a selected highway bridge. Journal of Performance of Constructed Facilities, 20(3), 253-260.

Lehtonen, T., Kaijalainen, O., Pirjola, H., & Juhala, M. (2006). Measuring stiffness and damping properties of heavy dynamics tyres. Proceedings of the FISITA World Automotive Congress, October 22-27, 2006. Yokohama, Japan.

Li, H. (2005). Dynamic response of highway bridges subjected to heavy vehicles (146 p.). PhD Dissertation, Florida state University. Retrieved from

Li, J., & Su, M. (1999). The resonant vibration for simply supported girder bridge under high-speed trains. Journal of Sound and Vibration, 224(5), 897-915.

Moghimi, H., & Ronagh, H. R. (2008). Impact factors for a composite steel bridge using non-linear dynamic simulation. International Journal of Impact Engineering, 35(11), 1228-1243.

Mohammed, O., Cantero, D., González, A., & Al-Sabah, S. (2014). Dynamic amplification factor of continuous versus simply supported bridges due to the action of a moving load. Proceedings of Civil Engineering Research in Ireland, August 28−29, 2014. Belfast, UK. Retrieved from

Mohammed, O., & González, A. (2017). Static and dynamic moments for any plane within a straight solid slab bridge caused by the crossing of a truck. Engineering Structures, 150, 465-480.

O’Brien, E. J., Keogh, D., & O’Connor, A. (2014). Bridge deck analysis (2nd ed.) CRC Press. Retrieved from

Reddy, J. N. (2002). Energy principles and variational methods in applied mechanics. John Wiley & Sons. Retrieved from

Rezaiguia, A., Ouelaa, N., Laefer, D. F., & Guenfoud, S. (2015). Dynamic amplification of a multi-span, continuous orthotropic bridge deck under vehicular movement. Engineering Structures, 100, 718-730.

Rowley, C., O’Brien, E., González, A., & Znidaric, A. (2009). Experimental testing of a moving force identification bridge weigh-in-motion algorithm. Experimental Mechanics, 49(5), 743-746.

Sayers, M. W., & Karamihas, S. M. (1996). Interpretation of Road Roughness Profile Data – Final Report. University of Michigan Transportation Research Institute (UMTRI).

Shi, X., Cai, C. S., & Chen, S. (2008). Vehicle induced dynamic behavior of short-span slab bridges considering effect of approach slab condition. Journal of Bridge Engineering, 13(1), 83-92.

Vigh, A., & Kollár, L. P. (2007). Routing and permitting techniques of overweight vehicles. Journal of Bridge Engineering, 12(6), 774-784.

Yang, Y. B., Yau, J. D., & Wu. Y. S. (2004). Vehicle Bridge Interaction Dynamics with Application to High-Speed Railways (564 p.). World Scientific Publishing Co. Pte. Ltd.

Wong, J. Y. (2008). Theory of ground vehicles (592 p.). John Wiley & Sons, New York.

Send mail to Author

Send Cancel