# Experimental Evaluation of Rigidity Center
## 1 Introduction  
Loss of life and property was experienced in the recent earthquakes in Turkey due to buildings that were not designed and constructed in accordance with the rules specified in the seismic regulations [1; 2; 3]. Although the damage was mostly caused by the material quality and design deficiencies, it has been determined that the incorrect placement of the vertical structural system elements is also a factor that increased the damage [4]. As the direction of an earthquake and the angle of the impact on buildings are uncertain, it is desirable for buildings to have sufficient earthquake performance in both the main axes. For this purpose, vertical structural system elements are placed in buildings in a way that adds strength, rigidity and ductility on both the main axes [5]. However, sometimes vertical load-carrying members can be placed asymmetrically due to architectural and economic reasons. If the layout is not well adjusted, then the rigidity center of the building moves away from the mass center. Thus, seismic force acting on the center of mass tries to rotate the building around the center of rigidity; therefore, torsion occurs in the floor [6; 7; 8]. This torsion is transferred to the vertical load-carrying members as an additional shear force. In order to determine the torsional effect realistically, the positions of the mass and rigidity center must be determined accurately [9]. When designing a building, the positions and dimensions of the columns and shear walls are decided during the architectural design, while the final dimensions of the vertical load-carrying elements are determined during the static design. The column and shear wall positions are generally not changed during the static design as it may affect the architectural plan [10; 11; 12]. While the rigidity center of reinforced concrete buildings can be determined separately for each floor, a single rigidity center can also be calculated for the building [6; 13; 14; 15; 16; 17; 18]. The following methods are generally recommended to calculate the rigidity center location:  
* Buildings are handled independently in x and y directions, and the size and location of the vertical structural elements are taken into account [5; 15; 19];
* Dependent and independent analyses in x and y directions are made by creating story stiffness matrices, and the distribution of the shear forces acting on the structural system elements is taken into account [20; 21; 22];
* The distribution of rotations under unit loading is taken into account by forming a global stiffness matrix for the building [23]. In the methods where the rigidity center is calculated by establishing stiffness matrices, the floors are generally considered rigid diaphragms [24]. It has been determined by various studies that shear walls are important in influencing the position of the rigidity center due to their large moments of inertia in the in-plane direction. For this reason, the effect of the shear wall placement on the system behavior was also investigated [25; 26]. It has been observed that drifts increase in the structures where the rigidity center and mass center move away from each other. The symmetrical placement of the shear walls on the outer axes increased the torsional rigidity and reduced the shear forces. It is recommended that the shear walls be placed symmetrically so that they do not create torsion [25; 26]. Although several analytical studies related to rigidity center locations and their effects on buildings are available, there are a limited number of experimental studies dealing with rigidity center calculations [27; 28; 29; 30; 31; 32; 33]. Half-scale single-story buildings with two spans in both directions were experimentally tested considering the torsional irregularities created by slab openings. From the test results, it was stated that the diaphragm rotation calculated from the rigidity center was found to be more reliable compared to the Turkish Building Code (TBC2018).