PSI - Issue 14

Angitha Vijayan et al. / Procedia Structural Integrity 14 (2019) 696–704 Angitha Vijayan et al. / Structural Integrity Procedia 00 (2018) 000 – 000 Here, is the unity normalized mode shape ordinate of the empty structure at the location of th individual. , and are the mass, stiffness and damping coefficient respectively of the same individual. These characteristics of individuals can be obtained from appropriate experiments. Fig. 3 shows the dominant mode shape of empty structure, location of an individual on the structure and the corresponding mode shape ordinate. If all the people are located at the midspan of the structure, then the mode shape ordinate is unity and maximum interaction happens. There is no interaction when people are located at the supports. Mode shape ordinate is zero for that case. 699 4

Fig. 2. (a) Line diagram of human body; (b) Representation of human body as a SDoF system.

2.3. Development of model for CS system The SDoF systems representing the empty structure and crowd are vertically connected to form a 2DoF system that represents the CS system as shown in Fig. 4.

Fig. 3. Demonstration of determination of equivalent SDOF model for crowd.

Fig. 4. 2DoF crowd-structure system.

An assumption is made that the crowd is always in contact with the structure. Therefore, the effect of activities such as jumping cannot be studied using this model. Further, walking crowd is modelled as equivalent stationary crowd (walking without changing the location) for the ease of computation ( Racic et al., 2009, Shahabpoor et al., 2017). This is similar to walking on treadmills at several locations. The dynamic effects created by this model on the occupied structure would be the same as actual walking crowd. The effect of crowd walking along the structure is modelled by distributing the individuals uniformly along the span. Each person is modelled to be walking at that particular location. Based on the crowd activity, crowd exerts a force, ( ) on the structure and structure develops reaction to it forming an internal force pair. The coupled equations of motion for the 2DoF system is represented as ̈( ) + ̇ + = ( ) (4) The above equation is expanded as [ 0 0 ] { ̈ ̈ ( ) ( ) } + [ + − − ] { ̇ ( ) ̇ ( ) } + [ + − − ] { ( ) ( ) } = { − ( ( ) ) } (5) In the equation, ̈ , ̇ and are the acceleration, velocity and displacement of the empty structure in vertical direction. Similarly, ̈ , ̇ and are the acceleration velocity, and displacement of crowd in vertical direction.