Deflection Analysis of Beams from Vehicle Velocity

Keywords: Vehicle-bridge interaction (VBI), Bridge dynamics,, Bridge deflection.


In this work, the modeling and calculations referring to the deflection of special artworks are presented. The type train is modeled as two degrees of freedom and mobile base, with the bridge deck being considered the mobile base. The base is treated as an elastic beam, according to the Euler-Bernoulli theory. The fundamental assumption made is that the relative displacements between the vehicle and the bridges are synchronous. This allows the calculation of natural frequencies, eigenvalues and normal modes of vibration of the beam. The temporal response of the beam deflection is obtained, assuming that the vehicle employs, at each instant of time, an impulse load on the beam. Numerical simulations are performed to improve the understanding of the dynamic behavior of the structure.



Download data is not yet available.


Q. Zou, L. Deng, T. Guo, and X. Yin, “Comparative Study of Different Numerical Models for Vehicle–Bridge Interaction Analysis”. World Scientific Publishing Company, vol. 16, no. 28, 2016.

Y. B. Yang, B. H. Lin, “Vehicle–bridge interaction analysis by dynamic condensation method”. Journal Struct. Eng., ASCE, vol.121, pp. 1636-1643, 1995.

X. Q. Zhu, S. S. Law, “Structural Health Monitoring Based on Vehicle-Bridge Interaction: Accomplishments and Challenges”. Advances in Structural Engineering, vol. 18, pp.1999-2015, 2015.

T. Hayashikawa, N. Watanabe, “Dynamic behavior of continuous beams with moving loads”.Journal of Engineering Mechanics Division, ASCE, vol. 107, pp. 229-246, 1981.

K. Matsuoka, H. Tanaka, “Drive-by deflection estimation method for simple support bridgesbased on track irregularities measured on a traveling train”. Mechanical Systems and Signal Processing, vol. 182, pp. 109-149, 2023.

R. Corbally, A. Malekjafarian, “Bridge damage detection using operating deflection shape ratiosobtained from a passing vehicle”. Journal of Sound and Vibration, vol. 27, pp.117-125, 2022.

H. C. Kwon, M. C. Kim, I. W. Lee, “Vibration Control of Bridges Under Moving Loads”. Computer e Structures, vol. 66, pp. 473-480, 1998.

Y. B. Yang, C. W. Lin, J. D. Yau, “Extracting bridge frequencies from the dynamic response of a passing vehicle”. Journal of Sound and Vibration, vol. 272, pp. 471-493, 2004.

M. V. Meyer, D. Cantero, R. Lenner, “Dynamics of long multi-trailer heavy vehicles crossingshort to medium span length bridges”. Engineering Structures, vol. 247, pp. 113-149, 2021.

S. S. Rao, Mechanical vibrations”, 5º ed., Pearson, Miami. 2010.

L. Meirovitch, Computational methods in structural dynamics, Springer Science & BusinessMedia 1980.

How to Cite
W. da Silva, V. Rocha, R. Tintaya Mollo, and M. Rabelo, “Deflection Analysis of Beams from Vehicle Velocity”, LAJC, vol. 10, no. 2, pp. 74-83, Jul. 2023.
Research Articles for the Regular Issue