Bauhaus Summer School

Simplified non-linear analysis of unreinforced masonry walls with irregular opening layouts

Masonry is a heterogeneous, discontinuous, and anisotropic material with distinct rupture or stress surfaces. The mechanical properties of such a system are largely influenced by the constitutive materials and construction methods. Thus, the type of masonry units, construction method, and material properties have a significant influence on the performance of unreinforced masonry (URM) against lateral loads. Masonry failure due to lateral loads is characterized by its heavy weight, high stiffness, and low tensile strength. The global stability of URM depends on the behavior of individual elements of the structure. 

In recent years, the adoption of performance-based earthquake engineering concepts has led to the application of many non-linear static procedures in the seismic assessment of buildings such as the capacity spectrum and the N2 methods. This kind of approach generally requires the comparison of seismic demand with the building capacity, expressed in terms of displacements. This comparison can be obtained by idealizing the actual building response with an equivalent single-degree-of-freedom (SDOF) oscillator. Within this framework, the assessment of structures can be achieved by means of a non-linear static analysis (pushover), in which the structure undergoes a pattern of increasing lateral loads describing the seismic forces and the displacement of a control node is monitored during the loading process. 

The choice of a structural model able to perform the pushover analysis of masonry structures is of prime importance. The choice between accurate (FEM) and simplified models (EFM) is governed by a balanced compromise between the desired accuracy and complexity of a structural model. For instance, in the vulnerability assessment of a large stock of existing buildings, the adoption of finite element models (FEM) becomes unsustainable from a practical point of view and so the equivalent frame model (EFM) can be an effective alternative, provided that the main hypothesis is carefully investigated. The equivalent frame approach idealizes masonry as an assemblage of vertical (pier) and horizontal (spandrel) elements. Piers are the primary load-resistant elements in both gravity and lateral direction. Spandrels are secondary elements that couple the piers in the case of lateral loads. The pier and spandrel elements are interconnected by rigid offsets. Each element of the equivalent frame is modeled by a well-defined constitutive law. This approach introduces strong simplifications and thus its accuracy depends on the consistency of adopted assumptions for the actual structural problem. 

This project aims to introduce the participants to advanced modeling techniques for the nonlinear analysis of URM walls with irregular opening layouts. The project begins with the elaboration of existing ground plans by transformation into digital drawings. In the next step, available façade information and dimensions will be elaborated and correlated with the ground plan information. The elaborated ground plans will be transformed into an equivalent frame to perform numerical studies. The building capacity and corresponding performance objectives for different seismic acceleration levels will be determined. Finally, the results will be summarized and presented by considering building type-specific fragility functions.