Estimating the Impact Force and Dissipated Energy of Adjacent Buildings during Earthquake in Terms of Hysteresis Curves

Since buildings are individually built close to each other, seismic excitation is caused the buildings experience lateral displacement and collides with each other due to different material, height and vibration modes. Structural pounding, which may occur because of earthquake between two adjacent buildings with different dynamic characteristics, has been an interesting research topic during the last few decades in field of earthquake engineering. Many researchers have intensively studied building pounding, impact and dissipated energy between adjacent buildings during earthquakes. In order to calculate the impact and energy absorption, numerical investigations need to have an unreal link element, which is involved spring and dashpot and is located at the conjunction top level of buildings. Recently, several mathematic equations have been justified to determine impact value and energy dissipation during collision. Most of researchers have used numerical methods to simulate the problem of earthquakeinduces pounding between adjacent buildings. Investigation of building pounding can be addressed in two different paths: experimental analyses and analytical analyses. To measure the impact force during collisions and lateral displacement of adjacent structures, software used need to define a specific link element at the connection level between the buildings analyzed. These link elements can be significantly different so as to insure a complete agreement between analytical and experimental results based on type of link elements. The mathematical equations correspond to the modeling by distinct link elements could be calculated by different approaches. The main different concepts used on link elements correspond to appropriate use of gap, spring and damper in the link elements. As periods of the adjacent colliding buildings are conceptually different, the link elements should be able to allow and translate the different behavior of buildings during seismic excitations. In this study, two new mathematical equations are proposed to measure the impact force and energy dissipation. The results based on the proposed equations are compared with those of the available equations. Since there is a need to have a reference curve to select impact velocity based on coefficient of restitution, several impact velocities and CRs were evaluated. By using the latter curve, results could be evaluated. Finally, based on coefficient of restitution and using a steady-state response of single degree of freedom system due to the external force, a new equation of motion is suggested to estimate the impact damping ratio.