In-plane and out-of-plane one-way vertical bending behavior interaction analysis of unreinforced masonry walls with newly developed load capacity interaction curve

The structural behavior of unreinforced masonry (URM) walls under in -plane (IP) or out -of -plane (OOP) loading in masonry buildings has been extensively investigated in the public literature. However, studies focusing on the URM walls subjected to concurrent IP and OOP loadings are limited. Neglecting IP and OOP interaction effects may lead to unsafe design practices. As such, this study conducts a comprehensive numerical investigation into the behavior of URM walls under combined IP and OOP loading, focusing on the influences of aspect ratio (i.e., height-to-length ratio), slenderness ratio (i.e., height-to-thickness ratio), and pre -compression load levels. To capture the possible failure modes of URM walls under various loading scenarios, the simplified micro modeling approach is employed. The analysis results indicate that the presence of OOP loading leads to a substantial reduction in IP capacities. Longer walls, characterized by smaller AR, exhibit more pronounced IP and OOP interaction effects. Additionally, highly slender walls show significant additional moments due to second -order effects under OOP loading, thereby negatively affecting the IP capacity. Low-level pre -compression loads are beneficial in diminishing capacity interaction effects, while high pre -compression loads exert a negative influence. To facilitate the consideration of IP and OOP capacity interaction effects in an efficient manner, a simplified analytical model is developed through curve fitting, in which the effects of aspect ratio, slenderness ratio, and pre -compression load are incorporated.