1 Context and formulation of problem
By tradition, the design of masonry structures subject to seismic loads is initially linear and based on anticipated loads. The nonlinear structural safety margins are then simplified with the aid of a so-called behaviour coefficient q, which accounts for the deformability of the structure as a function of the employed material (steel, reinforced concrete, masonry, wood, etc.). Used in combination with elevated seismic loads according to the latest earthquake standard, the q value 1.5 specified for unreinforced masonry according to DIN 4149 and DIN EN 1998 can thwart the calculatory verification of provenly reliable types of construction in earthquake-prone regions of Germany, despite their having demonstrated structural stability during past seismic events.
With a view to rectifying this discrepancy, Bachmann and Lang (2002) developed a deformation-based verification concept (the capacity spectrum method). That concept, however, applied only to regular masonry structures and did not account for the effects of cyclical wall stress in the nonlinear range. With the financial assistance of the umbrella organization for masonry and residential construction in Germany (Deutsche Gesellschaft für Mauerwerks- und Wohnungsbau e.V. - DGfM), the Chair of Department for Structural Design and Building Physics at RWTH Aachen University improved the method to enable analysis of arbitrary layout configurations with allowance for the effects of torsion.
Realistic structural design according to the new, deformation-based concept is, however, only possible if the cyclic-load deformation curves of the walls are available for diverse load levels and geometries of a brick-and-mortar combination. Such a basis for application of the new deformation-based concept to brick masonry, though, did not exist. This was due both to incomplete test results and to the lack of a conceptual approach to the systematic arrangement of the curves in the analytical software.
The targeted goal was to develop a new method for the systematic analysis of shear wall curves as input values for deformation-based structural design according to the capacity spectrum method.
Experimental shear wall trials and numerical simulations were performed for the purpose of defining a load-deformation curve matrix. A special interpolation algorithm was developed to enable the requisite interpolation between the curves and subsequent prototypical application to a real semi-detached house. The application was examined by Landesstelle für Bautechnik in Tübingen and found to be correct. However, it eventually came to light that the generation of a representable matrix chart of load-deformation curves would be diseconomical due to the large number of trials required. Consequently, an entirely new concept was devised. The new concept was derived by systematically analyzing the load-deformation curves obtained in the course of both the present project and the EU project ESECMaSE (2009) with regard to maximum loads and deformability levels.
The load deformation curves are bilinearly approximable by definition of an initial stiffness, a maximum load and a maximum deformation. This bilinear approximation can then be used for the random approximation of boundary conditions for shear walls and shear wall curves. This renders interpolation unnecessary.
The concept has since been incorporated into the national application document of DIN EN 1998-1 (2010) and is now available for practical application using the special masonry structure software MINEA (2012). Hence, the concept was put into practice even before the project terminated, thus underlining the inherent usefulness of the project.
This research project was conducted by the Research Alliance of the Brick and Tile Industry Regd (FGZ). Under project number AiF 15824N, it was promoted by BMWi through the German Federation of Industrial Research Associations “Otto von Guericke“ Regd (AiF) and implemented in cooperation with the Chair of Department for Structural Design and Building Physics at RWTH Aachen University.
The purpose of this research project was achieved. The 49-page final report is available from the Research Alliance of the Brick and Tile Industry Regd (FGZ) in Berlin.