A comparative study on the initial in-plane stiffness of masonry walls with openings

Masonry buildings have been used for centuries in various locations around the world, including areas with high seismicity. Studies about the behavior of masonry structural components subjected to lateral loadings and retrofitting techniques for improving their performance have gained much attraction lately. Various simplified methods have been presented in the literature for the seismic vulnerability assessment of masonry buildings. The initial in-plane stiffness of masonry walls is a key parameter which significantly affects the nonlinear backbone curve of the masonry walls as well as their ultimate in-plane strength.
Different simplified analytical methods have been proposed for deriving the initial in-plane stiffness of masonry buildings with regular or irregular openings by considering the flexible spandrels that can translate and rotate under lateral load and flexible piers’ endings. In the analytical methods, the initial in-plane stiffness of each pier will be computed from the equations by considering the geometry of each component as input. Each structural component is considered as a spring and the stiffness of the whole system is computed based on equations of springs in series or in parallel.
The finite element method is considered as a reliable tool for verifying the analytical methods. For this purpose, a homogenization method has been employed for modeling the masonry walls and lateral loads have been applied on the walls with the assumption of linear material to derive the initial in-plane stiffness of the walls. For this purpose, three categories of masonry walls have been considered with one, two, and three openings where the openings’ geometries also vary to investigate the effect of opening placements and irregularities on the initial in-plane stiffness of the walls. Afterwards, the stiffnesses computed from the analytical methods are compared with the stiffnesses that have been derived from the finite element analysis to investigate the accuracy of the analytical methods. It is shown that the analytical methods can be utilized for deriving the initial in-plane stiffness of masonry walls with openings, providing fast and accurate solutions in comparison to more detailed and time-consuming finite element implementations.