Dynamic one-sided out-of-plane behavior of unreinforced-masonry wall restrained by elasto-plastic tie-rods

Past earthquakes have shown the high vulnerability of existing masonry buildings, particularly to out-of-plane local collapse mechanisms. Such mechanisms can be prevented if façades are restrained by tie rods improving the connections to perpendiculars walls. Whereas in the past only static models have been proposed, herein the nonlinear equation of motion of a monolithic wall restrained by a tie rod is presented. The façade, resting on a foundation and adjacent to transverse walls, rotates only around one base pivot and has one degree of freedom. Its thickness is explicitly accounted for and the tie rod is modeled as a linear elastic—perfectly plastic spring, with limited displacement capacity. The model is used to investigate the response to variations of wall geometry (height/thickness ratio, thickness), tie rod features (vertical position, length, prestress level), and material characteristics (elastic modulus, ultimate elongation, yield strength) typical of historical iron. The most relevant parameter is the steel strength, whereas other characteristics play minor roles allowing to recommend reduced values for pre-tensioning forces. The force-based procedure customary in Italy for tie design is reasonably safe and involves protection also against collapse, although probably not enough as desirable.