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Nowadays, buildings are built without 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 earthquake occurrence, and severe damages 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 office, 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 centers have to be protected against the damages due to the significance of such structures prior and after earthquake. Many researchers have studied building pounding to calculate the dissipated energy and the impact force between two buildings during earthquake. For this challenge, they need to have a link element, which describes impact by using spring and dashpot. Several mathematical equations were suggested to calculate two mentioned parameters. In this paper, based on mathematic relation, a new relation of damping term of impact formula is simulated to measure impact force and energy dissipation. The results of this formula are compared with another suggested formula. As it was mentioned, different materials used in building constructions cause various dynamic behaviors during earthquake. Concrete structures are typically more rigid than steel structures in similar conditions. Consequently, lateral displacements of concrete buildings may also be less than lateral displacements of similar steel structures as stiffness of concrete buildings causes decrease in natural periods during earthquake. Naturally, large lateral nonlinear displacements under time history lateral loading in concrete structures may not be observed. Buildings can collide with adjacent buildings in left and right directions. For concrete buildings, however, the impact of pounding may be more significant than those on steel structures in most situations Many researchers have suggested new relations in terms of impact to increase the dissipated energy. Based on mathematic relation, they showed that energy dissipation depends significantly on stiffness, impact velocity and coefficient of restitution. 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 dissipated energy, a new relation between CR and impact velocity is suggested. As it seems that it is a need to have a reference curve to select impact velocity based on coefficient of restitution, several impact velocity and CR were evaluated. Using this curve, all of results can be optimized. Finally, a new equation of motion is assumed to select the best impact velocity and coefficient of restitution.

Keywords: Impact, Impact Velocity, Dissipated Energy, Damping

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