PSI - Issue 14

Angitha Vijayan et al. / Procedia Structural Integrity 14 (2019) 696–704

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Angitha Vijayan et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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1. Introduction

Several newly built structures have shown baffling resonance when subjected to dynamic crowd loads. The London Millennium Bridge had exhibited severe lateral sway on the day of its inauguration and had to be close down for renovation. Similar incident was reported for Pont-de-Solférino in Paris. Complaints of excessive structural vibrations were reported from the crowds of Mancheste r United’s Old Trafford Stadium and Morumbi Stadium in Brazil. In both the cases, tuned mass dampers were fitted to the stadiums inorder to reduce the vibration levels. Due to such occurrences, there has been growing interest in this subject. Structures such as footbridges, grandstands or floors subjected to rhythmic crowd activities have had trouble in satisfying the serviceability criteria for vibrations when subjected to dynamic crowd loads. The modern trend in architecture utilizes more slender structures resulting in lower natural frequencies. This when coupled with dynamic crowd loads makes the structure susceptible to excessive vibrations and dangerously affects the safety and comfort of the occupants. A mass-spring-damper interaction system was suggested by Sachse et al. (2003) to model occupied structure. Two degrees of freedom (2DoF) human structure dynamic interaction models were successfully adopted by various authors viz. Dougill et al. (2006) and Vasilatou (2017). Jones et al. (2011) have conducted studies on existing structures to verify the reliability of equivalent mass-spring damper models for predicting the response of structures subjected to crowd loads. Current available guidelines such as Canadian, ISO and UK were considered and it was found that UK recommendations were able to replicate the responses of crowd structure interaction at certain points of the structure. According to them, Canadian guidance lacks reliable precision whereas ISO 10137 is highly conservative and overestimates the responses of the crowd-structure interaction system. Racic et al. (2009) were the first to adequately conduct a research on the aspects of human walking forces. A very comprehensive review dealing with different experimental and analytical characterizations of pedestrian loading was done. They have introduced methods for the indirect measurement of several walking forces varying with time. Experimental observations of walking forces using a treadmill and a force plate were also included. This paper was able to bridge the gap between human gait biomechanics and civil engineering dynamics. Shahabpoor et al. (2017) have performed extensive experimental studies on crowd structure interaction. They have compared the modal properties of empty structure with that of occupied structure for walking and standing crowd. They have inferred from their studies that an appropriately modelled 2DoF system could represent the actual crowd-structure (CS) interaction successfully. The study is limited to the analysis of a single structure with fixed geometry and material properties. It is observed from the existing literature that the studies on crowd structure interaction gained attention only three decades back. Hence, the same demands further investigations. No work has been reported in Indian scenario to the best of a uthors’ knowledge . Furthermore, Indian codes consider the presence of crowd on structures as live loads, which is inadequate for capturing the interaction of crowd with the structure. In the present work, crowd occupied structure is modeled as a 2DoF system and the significance of crowd load on structures is demonstrated. The present work is limited to only vertical vibrations. The factors such as crowd size, crowd location and crowd activity are considered for the analysis. The comfort level of people standing on the structure is also estimated for the cases analyzed. The trend of variation of natural frequency of the occupied structure with variation in crowd properties obtained is compared with the trend reported in literature. 2. Methodology The main aspect of the present work is to determine the properties and response of the CS system where the structure and crowd interact with each other. In order to obtain these, a 2DoF system is developed. The first degree of the 2DoF system represents the vertical motion of the structure and the second degree represents the vertical motion of crowd. Modal properties are obtained for this interacting system. The force exerted by the crowd on the structure depends on the crowd activity and the structure develops reaction to it. These two forces constitute an internal force pair (Jones, 2011). The response of the system is affected by this force. The outputs from the analysis are the modal properties and the response of the CS system whereas the inputs for the analysis are the properties of the empty structure and crowd characteristics. A simple structure which represents both footbridge and long-span slender floor is adopted for the analysis. The crowd structure model is validated with experimental results reported in literature. The steps followed in this work to analyze the crowd structure system are determination of modal