Simulation Of Stochastic Crowd Load And Analysis Of Vibration Response For Large-span Floor

The serviceability of human-induced vibrations is an increasingly important and noticeable issue in modern structural design,such as large-span floors,footbridges,elevated pedestrian corridors,sports grandstands,long-cantilever structures and flexible stairs.The primary research of human-induced vibrations is the dynamic force model induced by human walking.Walking loads generated by individuals are the basic research of crowd loads and to generate crowd loads,thus it is critical to understand the characteristics of individual continuous walking forces.There are two main experimental approaches to collect measured human walking forces: direct measurements and indirect measurements.However a few domestic researches compare the walking forces from the two measurements.Most domestic and foreign scholars believe that the walking force parameters follow normal distributions,such as walking frequency,walking length,dynamic load factors,phases and so on,but the detailed analysis of these parameters is lack.Two methods of traditional direct force measurements utilizing force plates and indirect tests based on accelerometers are applied to carry out walking loading experiments simultaneously in the present study.A single footfall force model and continuous walking force models are established using experimental data.The differences of walking loads obtained by the two methods are compared and analyzed.Then the vertical vibration responses of a long-span steel-concrete composite floor and a footbridge under human walking forces are analyzed.The main research work and conclusions in this paper are as follows:1.Individual walking forces are collected simultaneously by a combination of direct force measurements using three force plates and indirect tests using novel MEMS AH100 B accelerometers.A total of 66 healthy adults are tested under free-walking conditions and four fixed-frequency walking conditions(i.e.,1.5Hz,1.8Hz,2.0Hz and 2.3Hz),and 2444 groups of effective acceleration curves and 7332 effective single footfall load curves are obtained.2.Based on the measured single footfall load curves,the statistical characteristics of temporal and spatial parameters of gait(i.e.,walking frequency,the duration of single footfall load,double support time,the proportion of double support time to single step time,step length,single footfall characteristic forces,characteristic time,impulse and equivalent force)and the relationship between each other are analyzed.A Fourier series model of the single footfall force including the first five harmonics is constructed,and the statistical characteristics and distributions of each dynamic load factors and phase angles are analyzed in detail.The first and second-order dynamic load factors can be represented as linear functions of walking frequency,and the remaining dynamic load factors can be represented as constants.The distribution of each parameter is carefully analyzed by six commonly used distribution types.Comparisons with the existing single footfall force models in the literature show that different single footfall force models vary by different test objects and sample data,and the model proposed in this study can reflect reasonably the basic properties of the single footfall when individuals walking,which can be utilized to analyze the structure vibration under human walking force.3.Using the experimental records collected directly by the force plates,continuous walking force curves are obtained using two extension methods based on single steps and two subsequent steps,respectively,and a single-step extended continuous walking force model(i.e.,Model I)and a double-steps extended continuous walking force model(i.e.,Model II)are established.Meanwhile,a continuous walking force model based on accelerations of the body center of mass from indirect inertial measurements is proposed(i.e.,Model III).The parameters characteristics and distributing disciplinarian of the three force models are analyzed.By comparing the differences among the above three walking force models,we conclude that: since Model I takes into account the characteristics of each single steps,the calculated walking frequency range is larger;Model III investigates a real continuous walking period,which can reflect the variability between each step in an individual's true continuous walking load;Model II is similar to Model III.Thus Model III is more reasonable and reliable to represent human continuous walking force.The phase angles have highly discreteness so that it is very difficult to make effective comparative analysis.Different load models with different values of phase angles will certainly cause different vibration responses for actual structures with complex modes.4.Taking a typical large-span steel-concrete composite experimental floor as an example,the acceleration responses under free-walking crowd loads are analyzed.Considering the randomness of the walking frequency,phase angles,and dynamic load factors under free-walking condition,stochastic crowd walking loads are applied to the structure simulated by ANSYS software,using Monte Carlo method.The results show that,when single walking loads are used to create stochastic crowd walking loads,the greater the randomness of gait parameters,the greater the randomness of the calculated structural response;the maximum calculated acceleration basically follows normal distribution under free-walking case.5.Human-induced vibration serviceability problems of the first mast cable-stayed footbridge in Nanjing are studied using a combination of finite-element simulations and field experiments.A finite element model of full bridge is established by ANSYS software for modal analysis,while ambient vibration tests are conducted to validate the modal properties.The first vertical frequency of the footbridge is less than 3Hz within the sensitive frequency range of human activities.Thus the vibration responses need to be calculated while the tuned mass dampers(TMD)are installed to control the vertical vibration.Then the dynamic responses of the bridge before and after the installation of TMD are determined experimentally under various moving crowd excitations,and the actual damping effect is evaluated.Meanwhile,three continuous walking load models obtained by three different methods in this paper are applied to the finite element model of the bridge.By comparing the calculated results with the measured results,it is found that the acceleration-based walking load model(i.e.,Model ?)is more reasonable for calculating the structural response.