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• A response spectrum to predict structural responses under crowd jumping loads is derived by stochastic vibration theory. • The closed-form expression of the response spectrum is established. • The response spectrum is verified by measurements of a real floor. A major challenge in the vibration performance assessment of structures under crowd jumping loads is the lack of efficient prediction models. With the challenge in mind, this study develops a multi-mode response spectrum for multi-harmonic crowd jumping loads to predict the root mean square value of structural accelerations according to the stochastic vibration theory. The response spectrum is applicable to structures with arbitrary vibration modes, because crowd jumping loads are regarded as multi-point excitations. A random field model proposed by the author is used to derive the closed-form expression of the single-mode response induced by individual jumping loads of a single-harmonic. Furthermore, the closed-form expressions of the correlation coefficients for different load harmonics, different vibration modes, and different jumping persons are established based on the random field model. The performance of the response spectrum is evaluated for two floors, and the results indicate the feasibility of the proposed approach to predicting structural accelerations subjected to crowd jumping loads. [ABSTRACT FROM AUTHOR]

Existing dynamic load factors (DLF) for crowd jumping loads are modeled by identifying the peaks and energies from the corresponding Fourier amplitude spectrum, which may underestimate and overestimate structural responses, respectively. Based on the principle of equal structural responses, this study herein develops an equivalent DLF, using the frequency response function to weight and integrate the power spectral density (PSD) matrix of crowd jumping loads. Firstly, massive PSD matrices of different crowd sizes and different metronome frequencies are simulated using a random field model of crowd jumping loads. Thereafter, the equivalent DLF of different structural damping ratios, crowd sizes, metronome frequencies, and non-exceedance probabilities are investigated, and a model of the equivalent DLF is established accordingly. It is believed that this model could provide an efficient and accurate way to conduct reliability design for structures subjected to crowd jumping loads. [ABSTRACT FROM AUTHOR]

• The equation of motion of a crowd-structure coupled system is established. • Structural acceleration responses are derived by stochastic vibration theory. • Two tests on a bridge model and a real floor are conducted to verify the methods. Modern slender structures such as cantilever stands and long-span floors are quite sensitive to vibrations induced by crowd jumping. Existing human-structure interaction models cannot consider human body parameter variabilities and apply to jumping-induced vibration analysis of structures with closely-spaced and complex vibration modes and passive crowd. This paper herein aims to derive the equation of motion and its spectral analysis solution of an advanced model for the crowd-structure coupled system. Each person on a structure is treated as a separate spring-mass-damper, and the structure is treated as a multi-degree-of-freedom system. Each person is classified as active crowd or passive crowd according to whether he/she exerts dynamic forces on the structure. Then, the equation of motion of the crowd-structure coupled system is derived, and its spectral analysis solution is established by the stochastic vibration theory and the state space method. The frequency response function is adopted to analyze dynamic properties of the coupled system. With a previously-proposed random field model for crowd jumping loads, vibration responses of the coupled system are analyzed. Comparisons between the simulations and the results from two experiments demonstrate the feasibility of the proposed spectral analysis method. [ABSTRACT FROM AUTHOR]

Highlights • A random field model for crowd jumping load is proposed. • Experiments are conducted on a jumping group of 48 persons using 3D MCT. • Structural responses are predicted by the stochastic vibration theory. Abstract A reliable model for crowd jumping loads is a prerequisite to an accurate prediction of a long-span structure's response when subjected to crowd motion triggered by music and other mass appeal events. Because of the lack of crowd jumping experimental data, crowd jumping load models are scarce with few data available on this type of synchronisation among people. Inspired by the random field model of earthquake excitations, this study attempts to develop a random field model for crowd jumping loads based on extensive records from unique crowd jumping load experiments. A framework for the random field model of crowd jumping is first proposed, in which auto-power spectral density (PSD) and cross-PSD functions of individual and group jumping loads are defined. The auto-PSD was obtained by updating a model in a previous study. Experiments were conducted on a jumping group of 48 persons using a 3D motion capture technology. A cross-PSD model for any two persons in a jumping group was then developed based on the experimental data. Having obtained a PSD matrix for crowd jumping, the structural response could then be predicted by the stochastic vibration theory. Finally, the feasibility of the model was verified by comparing the measured responses of an existing floor with the prediction responses using the proposed model. [ABSTRACT FROM AUTHOR]