Yığma yapılarda doğrusal olmayan artımsal analiz için bir yöntem önerisi

Masonry structures, due to their material properties especially, exceed the elastic limits and start responding in the inelastic range even after small amplitudes of load, much earlier than attaining the “point of yield”. Both in historical and modern civil masonry construction, most of the masonry structures are of unreinforced type, where the tensile strength of mortar is negligible. As a result, nonlinear behaviour in the unreinforced masonry structures is quite easy to be attained. Capturing the nonlinear response, on the other hand, especially under earthquake-like lateral loads, is quite difficult with the existing analytical tools. Available analytical approaches, material constitutive models and the existing software are not able to provide help in capturing, even for a simple 2-storey masonry, the nonlinear cyclic response. In the homogenized finite element models, the accuracy of the model largely relies on how the modelling approach handles the cracks and the crack development. The available models cause serious problems in convergence when the large level of nonlinearity is present and because cracks are difficult to follow numerically. The problem becomes even more pronounced when the type of loading dictates not only crack opening but also crack closing. Apart from the very high level of non-lineariy, masonry materials are also highly anisotropic or orthotropic. It is known that most of the construction materials exhibit certain degree of anisotropy. In cases where the anisotropy is negligible, formulation of the behaviour in section and member levels becomes significantly easier. When the behaviour of materials assumed as isotropic, such as in the case of concrete and steel, the load response can be easily demonstrated by employing well known yield or failure criteria such as Coulomb or von Mises. On the other hand, for clay bricks for example, despite the fact that the clay itself is a homogenous and isotropic material, the structure of the brick with its cores introduces certain anisotropy. Furthermore, mortar joints and the type of the bond add to the anisotropic behaviour. There are quite many difficulties in accurately modelling the behaviour of anisotropic materials. Additionally to the intrinsic difficulties in the mechanical formulation of anisotropic materials, there is also a lack of comprehensive experimental results both for pre- and post-peak behaviours. Several anisotropic plasticity models have been proposed along the last decades, both from purely theoretical and experimental standpoints as failure criteria. The difficulties in capturing the anisotropic response accurately stem from the material-dependent difficulties as well as physical problems such as the element dimensions. An entire reinforced concrete beam or column can be modelled by using two nodes at minimum, and 12 DOFs. Masonry, however, needs to be modelled with finite elements, leading thus to higher number of DOFs to be solved even for the same size of element with reinforced concrete. The inherent modelling difficulties for unreinforced masonry lead to often problematic convergence issues. In practice, nonlinear analysis of unreinforced masonry in large nonlinearity is not a feasible endeavour in most of the cases. This paper proposes a simplified step-wise method where every analysis step is linear elastic. The approach introduces displacement steps to the structure where the element stresses are cumulatively collected in a separate software where the decisions on the failure type and damage level of each element are also made. This approach cancels out the problems of non-convergence completely, leading to a more realistic analysis time ranges. The proposed approach takes into account the material inelasticity as well as the anisotropy. One of the strong points of the proposed approach is that it can easily capture the negative post-peak slope, which is characteristic of unreinforced masonry. The proposed method is applied to a load bearing piece of a historical construction just to check the consistency of the approach. The proposed method, as its current form, is applicable for monotonic loading only, whilst the adaptation of the method to cyclic loading as well as proof analyses with experiments are among future developments.