Keywords: impact, impact velocity, dissipated energy, damping.

Nowadays, buildings are built without the required separation distance as many engineers do not consider building pounding effects. If adjacent buildings are not separated properly from each other, pounding can occur upon the occurrence of an earthquake, and severe damage to the buildings can be observed even if they are well designed and constructed. Engineers should realize that building pounding is a serious hazard and it has to be considered during design and construction of buildings. There are many residential building complexes, service offices, agencies, schools and hospital in cities around the world which are located next to each other as the cost of land is high. In this term, hospitals with emergency facilities and emergency centres have to be protected against the damage of such structures prior and after an earthquake.

Many researchers have studied building pounding to calculate the dissipated energy and the impact force between two buildings during an earthquake. For this challenge, they need to have a link element, which describes the impact by using a spring and a dashpot. Several mathematical equations were suggested to calculate the two parameters, dissipated energy and impact force.

Energy absorption is calculated using the stiffness of the spring, the impact velocity and the coefficient of restitution (CR). As researchers can select different coefficients of restitution, various results are calculated in each analysis. In order to integrate the results of the analyses and evaluate pounding, the dissipated energy having different coefficient of restitutions and based on mathematical relations, a new equation of the damping term of the impact formula is simulated to measure the impact force and energy dissipation. Using the equation presented and selecting different coefficients of restitution, dissipated energies can be calculated co-ordinately. The equation provides a damping equation of motion based on the stiffness, impact velocity, masses and four unknown parameters, which are called 'n-o-r-a'. Considering the suggested equation for all parameters, integrated results using different coefficient of restitutions are provided.

Researchers have suggested new relations in terms of impact to increase the dissipated energy. Based on a mathematical relation, they showed that energy dissipation depends significantly on the stiffness, impact velocity and coefficient of restitution (CR). For this challenge, by using a suggested link element, a new formula is presented to calculate the impact force and energy dissipation. To optimize the results of the dissipated energy, a new relation between CR and the impact velocity is suggested. It is shown that a reference curve is used to select the impact velocity based on coefficient of restitution, several impact velocities and CR were evaluated. By using this curve, all of the results can be optimized. Finally, a new equation of motion is assumed to select the best impact velocity and coefficient of restitution.

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