Research on Dynamic Characteristics of Boarding Bridge Under the Crowd Loads
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1 nd International Conference on Architectural Engineering and New Materials (ICAENM 2017) ISBN: Research on Dynamic Characteristics of Boarding Bridge Under the Crowd Loads Conggui Pan and Xigen Zhang ABSTRACT The 45m boarding bridge is taken as the research object in this paper. The transient vibration model is established according to the transient dynamic analysis theory. Based on the dynamic analysis results of the structure under the crowd loads, the TMB vibration reduction analysis is conducted. This method can be used as a reference for analyzing the dynamic characteristics of other boarding bridges under the crowd loads. 1 INTRODUCTION As a bridge that crosses from the plane and the terminal, the boarding bridge provides a comfortable and safe walking space for passengers. As one of the important facilities, terminal boarding bridge is the level-a equipment in airport. Meanwhile, it connects directly with the aircraft, which is significant to safety responsibility. Generally, multi-channel boarding bridge consists of the rotating platform, channels, airport platform, the lifting system and other parts. For the convenience of walking, the length of the boarding bridge is often very long. However, according to the practical experience, the natural frequency of vibration is very close to the frequency of people walking, if the length of the bridge is more than 40 m, which results the resonance phenomenon. The resonance will cause the large amplitude and long-term fatigue load, resulting in the decrease of durability. The welds of steel 1 Conggui Pan, Wuhan South Four-ring Expressway Construction Management Co. Ltd, Wuhan, , China. Xigen Zhang, China Harzone, Wuhan, , China. 425
2 structures are apt to cause damage and even fracture under such fatigue loads [1]. In addition, vibration may also reduce the comfort of passengers, which causes psychological panic. TRANSIENT DYNAMICS ANALYSIS Transient dynamics analysis (also called time-history analysis) is used to determine the dynamic responses of structures under arbitrary time-dependent load. The basic equation is based on the following constitutive relation[2]: { } M u + C u + K u = F t (1) [ ]{ } [ ]{ } [ ]{ } ( ) Where [ M ] is mass matrix, [ C] is damping matrix, [ K ] is stiffness matrix, { u} is { } { } u u the node displacement vector, is the node velocity vector, is the node acceleration vector. In full transient analysis, New mark time integration method is often used, in a time interval: { n+ 1} { n} ( 1 δ ){ n} δ { n+ 1} u = u + u + u t (2) 1 2 (3) 2 { u } = { u } + { u } t + α { u } + α { u } t n+ 1 n n n n+ 1 Where α and δ are New mark integral parameter. In time tn+1: { } [ M ]{ u } + [ C]{ u } + [ K ]{ u } = F ( t ) n+ 1 n+ 1 n+ 1 (4) Rearranging Eqs.(2) and (3): { + 1} 2 { + 1} { } 1 1 un = un un un un α t α t α (5) δ ( ) { } 1 { } 426
3 { 1} { } { } { 1} (1 ) un+ = un + t δ un + tδ un+ (6) u n + 1 can be determined by Eqs. (4), (5) and (6): 1 δ [ M ] + [ C] + [ K ]{ u } = F ( t) + M u + u + u α t α t α t α t 2α { } [ ] { } { } 1 { } 2 n+ 1 2 n n n 1 δ [ ] { } 1 { } t δ C un un 2 { un} α t α 2 α Then, the values of velocity and acceleration will be obtained by (5) and (6). (7) THE EXAMPLE ANALYSIS The boarding bridge used in this paper belongs to truss bridge of three retractable tunnels. The body of the bridge consists of three tunnels A, B and C, which are constructed of glass and truss, the metal floors and the metal roofs. The length of tunnel A is 16.4m, tunnel B is m, and C is 16.75m. As shown in Figure 1, shell63elementsare used to simulate the roof and floor plates, and beam188elements are adopted to simulate the truss parts. The mesh is refined in (and near) the corner and coarsened away from the corner. Figure 1. Finite element model. With the subspace method in ANSYS software, the natural vibration characteristic are calculated in Table I. Because the sensitive frequency of pedestrian incentive load are mainly within 5Hz, it is necessary to list the first four order modals in Table I. The corresponding vibration modes are shown in Figure2. 427
4 TABLE I. MODES AND NATURAL FREQUENCY (Hz). Modal Frequency Vibration mode The first mode Transverse vibration The second mode Vertical vibration The third mode Transverse vibration The fourth mode Transverse vibration (a) The first mode (b) The second mode (c) The third mode (d) The fourth mode Figure 2. Vibration modes. Euro code EN1990has made the detailed evaluation standard about the comfort of pedestrian bridge. It adopts peak acceleration of structure vibration response as comfort evaluation criterion for pedestrian bridge. The maximum permissible vertical vibration acceleration and lateral vibration acceleration of pedestrian bridge should be controlled within the range of value given in Table II. TABLE II. COMFORT CRITERION IN EURO CODE. Vibration mode Maximum acceleration(m/s 2 ) Vertical vibration 0.7 Transverse vibration in common cases 0.2 Transverse vibration with suffusion pedestrian
5 THE PEDESTRIAN LOAD MODEL The normal pedestrian stride frequency is between 1.6Hz (slowly walk) and 4Hz (power walk), and the average value is about 2Hz[3, 4]. In this paper, the vertical response are mainly considered under pedestrian loads. TABLE III. THE PEDESTRIAN LOAD PARAMETERS. Type of pedestrian load Velocity Stride length Stride frequency (m/s) (m) (Hz) Slowly walk Normally walk Power walk Normally running Fast running The pedestrian incentive curve is introduced here[5], as shown in Figure 3. The horizontal ordinate of single foot curve is the contact time of single foot, vertical ordinate is the vertical force. The vertical force Fcan be expressed as: F =u F static ( 8 ) Where u is the impact factor. To simulate pedestrian loads, each step using as a dynamic load applies to the structural model. Assuming that each single foot curve is the same, the overlapping time of each foot is considered as 0.1s. The equivalent pedestrian load diagram is described in Figure4. Figure 3. Single foot curve. Figure 4. Multi-step pedestrian load diagram. 429
6 THE DYNAMIC RESPONSE UNDER PEDESTRIAN LOADS In order to simplify the calculation, the pedestrian loads are equivalent to the corresponding vertical force produced by people walking at the same time. Assuming that the pedestrian stride is 0.75m, and the effective calculated length is from the end constraint point to the lifting support point. Because the width of tunnel is between 1.5m-2m, only two people can walk side by side in width. Therefore, considering the necessary gap between people(the gap is 1m), the maximal number of people in the tunnel under the working condition is n=2 34. Based on the pedestrian load theory proposed by Japanese scholars [6], the number of people walking at the same time on the bridge is 0.2n, then, the crowd vibration force is equivalent to the vertical force produced by 13.6 people walking at same time. The velocity and acceleration response curves of midspan (NODE:40324) are drawn in Figure5. As shown in Figure 5, under the pedestrian loads, the peak value of the speed is 0.189m/s, the peak of acceleration is -3.76m/s2.The comfort evaluation standard in Euro code for the vertical vibration of pedestrian bridge is not more than 0.7 m/s2intable 2. Obviously, a series of vibration reduction treatments should be adopted to improve the comfort level of the boarding bridge. (a) The velocityresponse curve (b) The acceleration response curve Figure 5. The dynamic response under pedestrian loads. VIBRATION CONTROL AND COMFORT EVALUATION The principle of vibration reduction by Tuned Mass Damper (TMD) is to couple a single degree of freedom spring quality TMD vibration system (the additional system) in the main structure (the primary system). Then, the original single degree of freedom vibration system turns into a two degree of freedom vibration system (see Figure6). The natural frequencies of the substructure will be close to the main 430
7 structure by changing the mass or stiffness of the substructure. In that case, the substructure can produce an additional inertia force in the opposite direction of vibration, making the vibration attenuation the main structure. The original vertical frequency of this boarding bridge is 4.49 Hz, and the dynamic responses of the whole system are recalculated under the quality ratio of µ = 1%, µ =2%, µ =3%, µ =4% and µ =5%. The dynamic response values are summarized in Table IV. A comprehensive consideration according to the results in Table. 4, the vibration reduction effect is good taking the quality ratio of 2%, as shown in Figure7. The peak of acceleration of the optimized structure is -0.31m/s2. TABLE IV. THE DYNAMIC RESPONSE VALUES UNDER DIFFERENT QUALITY RATIA. The quality ratio Acceleration(m/s 2 ) Vibration reduction rate % % 2% % 3% % 4% % 5% % Figure 6. TMD mechanical model. Figure 7. The acceleration response curve. CONCLUSIONS (1) It is very necessary to analyze the dynamic characteristics of boarding bridge, especially for the long-span bridge. It is easy to produce resonance for the bridge in the range of sensitive frequency. (2) According to the simplified identify model, it is convenient to estimate the dynamic response under the crowed loads. 431
8 (3) Based on the dynamic analysis results of the structure under the crowd loads, the TMB vibration reduction analysis is conducted. This kind of vibration reduction method provides a practical base for the pedestrian bridge. REFERENCES 1. Yin, X.J., Gao, X.L., et al The vibration control of the second stage of the boarding bridge project in Shanghai pudong airport, Journal of Disaster Prevention and Mitigation Engineering, pp Sheng, T.H., Yu, H.L., et al ANSYS finite element analysis principle and engineering application examples, Tsinghua University Press, Beijing. 3. DaSilva, J.G.S, Vellasco, P.C.G, et al Vibration analysis of footbridges due to vertical human loads, Computers and Structures, 85(21-22): Obata, T. and Miyamori, Y Identification of a human walking force model based on dynamic monitoring data from pedestrian bridges, Computers and Structures, 84(1): Ellingwood, B., and Tallin, A Structural service ability: floor vibrations, Journal of Structural Engineering, 110(2): Fujino, Y., Pacheo, B.M., Nakamura, S., et al Synchronisation of human walking observed during lateral vibration of a congested pedestrian bridge, Earthquake Engineering and Structural Dynamics, 22:
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