Research On Human-Induced Vibration Analysis And Comfort Assessment Method Of Stadium Stand Structures

Stadiums are a necessary component of urban construction.As a construction designed to accommodate large crowds for leisure and sports activities,the comfort of stadiums has an important impact on their use and function.With the continuous expansion of the stadium,the stadium stand structure is developing towards low frequency and large span.However,the lower natural frequency is closer to the humaninduced load frequency,which makes the stand structure more likely to produce a large vibration response under the action of human-induced loads,which may cause discomfort to users at least,and cause crowd panic at worst,causing security incidents.Among them,structural vibration accidents caused by jumping loads account for a large proportion.Therefore,the human-induced vibration response and comfort assessment of the stand structures in stadiums have received more and more attention.In addition,human comfort is a complex issue influenced by psychological and physical factors,and the comfort assessment based on single factors can often lead to deviations.Therefore,it is necessary to establish a systematic multi-factor comfort assessment method for the stand structure of large stadiums including the vibration responses.This paper conducts a systematic study on the vibration comfort and comprehensive assessment method of the stand structure of large-scale stadiums under jumping loads.Firstly,a fine jumping load model is established.Secondly,the crowd jumping load model was established considering four random variables,and the random vibration response analysis method of structures was optimized based on the crowd jumping reduction factor,which can be used to calculate the vibration response of stand structures under the action of jumping load.Then,a vibration comfort assessment method for the stand structure based on the root mean square acceleration and predicted discomfort percentage model is presented.Finally,a multi-factor comfort assessment method for the stand structure based on the fuzzy analytic hierarchy process and entropy weight method is proposed.The main work of this paper includes the following aspects:(1)Establishing a single-person jumping load modelBased on the jumping experiment database,a practical single-person random jumping load model considering different pulse forms was established.Firstly,a comprehensive database of single-person jumping loads was established based on experiments of 11 jumping frequencies and 108 subjects.Furthermore,refined singleperson jumping load models incorporating "single peak","mixed" and "double peak"pulse shapes were developed based on the database,which accurately describes the jumping load characteristics and randomness.In addition,based on the jumping load database,the variation law of the characteristic parameters of the single jumping loads with frequency is analyzed.(2)Random vibration analysis model of stand structures under the crowd jumping load.Considering the inconsistency of the crowd jumping load,the calculation formula of the crowd reduction factor is given by using the multivariate stochastic simulation method.Based on the single-person jumping load model and considering the crowd reduction factor for multiple-person jumping,a crowd jumping load model was established.The model can reflect both intra-individual and inter-individual differences in jumping.The crowd reduction factor is introduced into the random vibration analysis method of the stand structures,which improves the calculation accuracy of the analysis method.Additionally,the random vibration analysis method is simplified by using the fast calculation formula of the jumping load power spectrum.The accuracy of the model was validated by measured results of vibration responses.Besides,the calculation results of the random vibration responses model and the fine time domain model are compared to verify the efficiency of the random vibration responses model.(3)Assessment method of vibration comfort for stand structuresTo optimize the existing quantitative assessment method of vibration perception,this paper uses fuzzy statistical experiments to improve the membership function in the predicted uncomfortable rate(PUR)model based on fuzzy reliability theory.An assessment model(arms-PUR model)for the vibration comfort of the stand structures considering the vibration response and the predicted uncomfortable rate is proposed,which can be used for structural reliability and optimal design.The rationality and effectiveness of the model were confirmed by comparing measured stand vibration responses with audience comfort surveys conducted during sporting events.(4)Comprehensive assessment method for multi-factor comfort for stand structuresOn the basis of considering vibration,a comprehensive assessment method for the comfort of the stand structure is established.In this paper,empirical measurements and survey investigations were conducted to explore the relationship between various environmental parameters and comfort assessment indicators.Also,the formulas for calculating each comfort index were established.Moreover,considering the combined influence of subjective and objective factors,a comprehensive assessment method for the multi-factor comfort of stand structures,which is the FAHP-EM method,was proposed.The effectiveness of the proposed method was confirmed through measured test results and survey investigations.If the values for the physical parameters are given,the comprehensive comfort assessment index could be calculated by this formula.The designers and users of the large-scale stands can use the comprehensive comfort assessment index to better balance the relationship between energy use and human comfort.This paper solves a series of problems in the human-induced vibration analysis and comfort assessment in the stadium stand,and provides a basis for the revision of the relevant regulations on the comfort of the stand structure in the code.