Dynamic impact factors for simply supported bridges with different cross-section types DENG Lu HE Wei WANG Fang

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1 34 14 JOURNAL OF VIBRATION AND SHOCK Vol. 34 No JTJ JTG D IM 5 IM IM IM IM IM U44 A DOI /j. cnki. js Dynamic impact factors for simply supported bridges with different cross-section types DENG LuHE WeiWANG Fang College of Ciil EngineeringHunan UniersityChangsha China Abstract In the General Code for Design of Highway Bridges and CulertsnamelyJTJ and JTG D the impact factor IM is specified as the function of the length of bridge span and the fundamental frequency of bridgerespectiely. These codes proisions consider only one parameter that has influence on ehicle-bridge interaction system. Howeersome studies hae suggested that the use of single parameter may be insufficient to account for dynamic impact of moing ehicles. In this study the finite-element models of fie bridges based on standard drawings were built. The IMs of these bridges were calculated using numerical methods suitable for different cases. The rationality of code proisions was examined. The IMs for bridges of three different cross sections with the same span length and fundamental frequency were then compared. The results show that under aerage road surface condition the IMs calculated are lower than those specified in JTG D but are relatiely consistent with these specified in JTJ neerthelessunder poor road surface conditionboth design codes significantly underestimate the IM there exists significant ariation of IM for bridges with the same span length and fundamental frequency but different cross sections indicating that ealuating IM using either span length or fundamental frequency alone is not accurate generally and engineers should also pay attention to the difference in IM due to cross-section types. Key words ehicle-bridge interaction dynamic impact factor code proisions numerical simulation finiteelement analysis IM JJ denglu@ hnu. edu. cn IM = δ d δ s δ d δ s

2 ~ 3 3 ~ d b + { C b C b db [ d C b C ] + { d Kb K b d [ K ] { b d = F br + F { g F M [ b M ] K b r 2 MCK d b F g F b r F r 1 HSB r g 2 T - 1 T Box HSB Ansys 3D 2. 2 Ansys 14-2% T m T /2 mm Fig. 1 1 /2 Cross section of the bridges unit mm 1 Tab. 1 Detailed properties of the fie bridges /m /Hz IM T - 2 T Fig Axle ehicle model

3 Fig Axle ehicle model 3 Tab. 2 Major parameters of 3 ehicles under study 1# 2# 3# GVW /t M 1 /t I 1 zx / kg m I 1 zy / kg m M 2 /t I 2 zx / kg m I 2 zy / kg m m 1 /t K 1 u / kn m C 1 u / kn s m K 1 l / kn m C 1 l / kn s m m 2 /t K 2 u / kn m C 2 u / kn s m K 2 l / kn m C 2 l / kn s m m 3 /t K 3 u / kn m C 3 u / kn s m K 3 l / kn m C 3 l / kn s m L 1 /m L 2 /m L 3 /m L 4 /m L 5 /m L 6 /m b /m mm Fig. 4 Vehicle loading position unit mm Fig. 5 Road roughness IM Tab. 3 Calculation cases for IM 3 3 1# 2# 3# 5 10 m /s 15 m /s 20 m /s 25 m /s 30 m /s 6 δ d δ s HSB - 1 3# 17 Fig. 6 Typical dynamic and static response ISO

4 t 3# t 2#IM IM IM ~ Hz IM IM - 20 IM IM 89 T % 04 IM 89 /Hz IM Fig. 7 Variation of mean IMs against roughness IM HSB IM IM 8 8 IM 89 2 IM IM 165% ~ 208% 8 IM Fig. 8 Variation of mean IMs against ehicle t 1# IM HSB - 1 HSB - 2 2# IM Tab. 4 Fundamental frequencies of the three ehicles 1# 2# 3# 4. 2 IM IM IM 5 IM T - 2 IM % ~ 22% 2 69% ~ 140% % ~ 58. 2% Tab. 5 Statistic result of numbers of oer-code-specified-alue eents and maximum relatie ariation between simulated alue and code-specified alue 1. HSB T Box T HSB /% /% IM 9 9 3

5 # 3# AASHTO m /s # 20 m /s Fig. 9 Variation of IM with change in roughness leel and ehicle type 9 IM IM Φ IM max IM min ξ L /% Φ ξ IM ξ f /% ξ = IM max - IM min 5 100% 4 IM min 5 ξ ξ L 3 IM ξ f 3 IM 45 ξ L ξ f 6 ξ f ξ L 1 04 IM 89 ξ L 31% % ξ f ξ L ξ f 25% 25% IM 153% IM 102% 4 IM ξ L ξ f 31% L f 30% 6 IM ξ Tab. 6 Statistics results of ξ

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