Keywords: bridges, dynamics, modal analysis, harmonic, vibrations, traffic loads.

Harmonic moving loads comprise a sizeable part of the traffic loads that bridges suffer over their lifetime. Pavement roughness, vehicle suspension, and bridge- vehicle interaction induce harmonic excitations on roadway bridges. Also, the unbalanced weight on the driving wheels of steam locomotives introduces load fluctuation on the railway bridges. Ignoring these cyclic effects of traffic loads has been the source of significant error that many researchers have asserted through their investigations. In this paper, the dynamic responses of single span girder bridges are investigated under the influence of moving sinusoidal loads. The parameters of the sinusoidal moving loads that affect the response are defined and their significance on the response parameters is quantified. A computer program based on the modal analysis technique is developed to calculate the bridge vertical displacement and bending moment responses. The numerical output is validated versus the existing numerical examples and found to be in a complete agreement. The vehicular frequency, speed, and the amplitude of the harmonic load fluctuation are found to have significant influence on the bridge behaviour. Also, the response at resonance is found to be abnormally amplified. The results indicate that satisfactory prediction of the bridge dynamic response requires accurate information about the frequency and the amplitude of the harmonic portion of the vehicular load.

Summary and Conclusions

The bridge response under harmonic moving force as a portion of the vehicular load is investigated. Road surface roughness, vehicle suspension, bridge-vehicle interaction, as well as the unbalanced weight on the driving wheels of steam locomotives induces traffic load fluctuation. The impact criteria in most bridge codes ignore these cyclic effects of traffic. The current study has been devoted to investigate the significance of including these effects on the bridge dynamic response. After formulating the problem, the response calculations have been carried out using a computer program developed to fulfill this task, the significance of the harmonic load portion and its parameters on the bridge response are presented and discussed. The following conclusions can be drawn:

1. A reliable bridge design procedure necessitates a satisfactory accurate prediction of the bridge dynamic response, which in turn requires accurate information of the frequencies and amplitudes of any oscillatory moving forces the bridge may encounter.
2. The bridge dynamic response under the influence of harmonic moving force is oscillatory in nature, which intensifies the risk of fatigue failure. The magnitude of this risk depends on the amplitude and frequency of the harmonic excitation.
3. Besides, an amplification of the bridge dynamic response may occur when the harmonic load frequency is in the neighborhood of any of the bridge natural frequencies, even for small harmonic load amplitudes. A response amplification as high as 16 times the static response is found for harmonic load amplitude of 70% of the total vehicle weight, with frequency matches the bridge fundamental frequency.
4. The effect of the vehicular speed on the bridge dynamic response is also frequency dependent. On one hand, for force frequencies in the vicinity of the bridge natural frequencies, increasing the speed acts like vibration damper, where it decreases the maximum response. While, on the other hand, increasing the vehicle speed, increases the dynamic response for the rest of the force frequency range.

1

Ishac, I.I., and Swailem, M.K., (2000), "Dynamic Behaviour of Steel Simple Span Railway Bridges Traveled by Trains.", Mansoura Engineering Journal, (MEJ), Faculty of Engineering, Mansoura Univ., Egypt, Vol. 25, No. 1.

2

Kou, J.W., and DeWolf, J.T., (1997), "Vibrational Behaviour of Continuous Span Highway Bridge Influencing Variables.", J. Structural Engineering., ASCE, Vol. 123, No. 3. doi:10.1061/(ASCE)0733-9445(1997)123:3(333)

3

Kwon, H.C., Kim, M.C., and Lee, I.W., (1998), "Vibration Control of Bridges under Moving Loads.", J. Computers & Structures, Vol. 66, No. 4. doi:10.1016/S0045-7949(97)00087-4

4

Martin, T.M., (2000), "Effect of Design Parameters on the Dynamic Response of Bridge", VTRC Report No. 00-R23, Virginia Transportation Research Council, Charlottesville.

5

Warburton, G.B., (1976), "The Dynamical Behaviour of Structures", 2nd Ed., Pergamon Press Oxford, England.

6

Yang, Y.B., and Yau, J.D., (1997), "Vehicle-Bridge Interaction Element for Dynamic Analysis.", J. Structural Engineering., ASCE, Vol. 123, No. 11. 1997. doi:10.1061/(ASCE)0733-9445(1997)123:11(1512)

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £123 +P&P)