Beitrag zum statischen nichtlinearen Erdbebennachweis von unbewehrten Mauerwerksbauten unter Berücksichtigung einer und höherer Modalformen

摘要

Construction and verification of masonry buildings under earthquake loading is usually done by determining of all relevant maximum values of forces, displacements and deformations. There are different classes of methods for the prediction of the behaviour of the construction. The main focus of this contribution lies on nonlinear static procedures, which have the advantage that no complex time history calculation is necessary and nonlinear material properties can be inherently considered. This makes them very interesting for practical application. Additionally, they allow for an explicit consideration of nonlinear reserves. Firstly the basic principles of nonlinear static procedures are described in detail and their potentials and limitations are discussed in this contribution. In the centre of interest is the procedure of DIN EN 1998-1 which will become widely used with the introduction of this standard in Germany. The basis for all these procedures is the pushover curve, which depicts the displacement of a control node for increasing horizontal loads considering the nonlinear behaviour of the system. The verification within these procedures is then done by comparing this capacity with the seismic demand taking the energy dissipation into account. Based on a comparison of different common methods with time history calculations, recommendations for a secure application and important input parameters are derived. Irrespective of the verification method, the correct estimation of the dissipated energy always plays a key role. Therefore a suitable inelastic spectrum or damping approach is necessary. Nonlinear static procedures can be subdivided into multimodal procedures and those considering only the fundamental mode. The second class of methods is sufficiently accurate if the fundamental vibration mode is dominating the structural behaviour. However, for certain ground plans or mass distributions, higher modes can have a significant influence on the vibration characteristics of the building. If higher modes have an influence on the structural behaviour under earthquake loading, multimodal procedures lead to a better match between reality and modelling result. An overview of current state-of-the-art multimodal procedures is given and an enhanced concept is developed. This concept, the nonlinear adaptive multimodal interaction analysis (AMI), is based on multiple pushover analyses to determine the maximum inter storey drift. This parameter is especially important for masonry buildings. Within one pushover analysis changes of dynamic parameters and the load distribution are considered which occur due to local failures of the structure. The load distributions are determined from combinations of all relevant modes which ensure that the most unfavourable combination for each storey is always considered. Therefore the concept is always on the safe side. For the applicability of nonlinear static procedures to unreinforced masonry buildings, a structural building model is necessary. On the one hand, the building model must represent the failure modes of single walls (flexural failure, sliding shear failure and diagonal tension shear failure) and on the other hand the structural behaviour. This includes the interaction between walls and slabs and the redistribution of loads. In this contribution a macro element is presented which captures all of these effects. Besides the structural building model, a realistic estimation of the energy dissipation of the entire building is necessary to predict the behaviour under earthquake loading by nonlinear static procedures. Especially for masonry buildings a damping model is necessary which represents the dissipated energy as a function of the failure modes of single walls. Based on experimental results a novel damping approach is presented which is shown to be capable of predicting the hysteretic damping due to the modes of failure and ductility. The presented nonlinear concept in combination with the developed damping model allows to fully exploit the capacity of masonry as a construction material. This makes masonry a viable construction material for various construction tasks again.