The Effect of a Top Flexible Restraint on a Two-Bodies Vertical Spanning Wall

In unreinforced masonry structures, one of the most dangerous events that can occur during earthquakes is an out-of-plane mechanism. This type of response significantly changes if the wall is restrained by a horizontal element, like a floor, a roof or tie rods. The collapse, in this case, could take place for slipping/failure of the connection to the diaphragm or for overturning of the wall, following the formation of a crack at an intermediate height between the base and the top. Further, to evaluate the response of these kind of mechanisms, the assumption of a rigid top support can be too crude especially in case of a timber diaphragm or small diameter and large length tie rods. In this context, in order to capture the complex dynamic behavior of the wall, formed by two stacked rigid bodies (free to rock) connected to a spring, a specific analytical model (updated to account for additional masses active on the wall only during the earthquake) is used. For slender walls connected to a flexible restraint, the flexural out-of-plane mechanism is recurrent. These walls are common in the Emilia-Romagna region of Italy. For this reason, a building portfolio in Emilia is analyzed to derive mean and standard deviation of a log-normal distribution of the main parameters of the system. The variation of relevant parameters is investigated, in order to evaluate the effect of the elastic restraint at the top. The results of the analysis highlighted that stiff diaphragm can significantly reduce the rotations. Additionally, the study on the effect of the wall size pointed out how the top spring causes a reverse scale effect.