Keywords: capacity spectrum method, unreinforced masonry, multi-surface failure criterion, numerical simulation, seismic design.

Although masonry is one of the oldest building materials, the design of masonry buildings is typically based on simple linear elastic material laws and empirical rules, which normally leads to uneconomic structural designs. Especially, because the demands of today's architectural trends of transparent buildings with openings and a minimal number of shear walls, can not be achieved by the use of linear models in the case of high lateral loads caused by earthquakes. Hence there is a need for nonlinear models to take all pertinent failure modes into account, in order to mirror the nonlinear anisotropic behaviour and the post-peak load-carrying capacity, which might be the reason why masonry buildings are able to withstand seismic loading. It is evident that the use of such sophisticated models is not a realistic alternative for the engineering practice. Infact, the procedure of capacity assessment should be simple enough to make it comprehensible for structural engineers, yet precise enough to satisfy the demands of the current standards.

In the present paper a new approach for the seismic design of masonry buildings based on the capacity spectrum method [1], generalised to three dimensional masonry buildings, is presented. The use of the capacity spectrum method, which calculates the maximum displacement by the intersection of the capacity curve and a reduced response spectrum, is simple enough for the engineering practice, yet its application so far has been rather limited. The design procedure developed can be applied to buildings which are regular in elevation and regular or irregular in ground plan. In the case of irregular ground plans, the mass and stiffness centre differ and the equivalent mechanical system is a three dimensional cantilever system with eccentricity and two degrees of freedoms, considering the torsional effects.

A central issue is the data acquisition of the capacity characteristics for masonry shear walls. In order to facilitate the design process for the practising engineer, a database of capacity curves is built up depending on the material, the geometry and the vertical loading. Its entries are provided by the experimental data as well as from nonlinear FEM calculations using an elasto-plastic material model. It is based on a multi-surface plasticity theory including the Return Mapping Procedure for local iteration at the integration point level. The anisotropic elastic and inelastic behaviour depends on the orientation of the masonry joints. On this basis, it is possible to simulate masonry-specific failure. Moreover, the damage mechanisms and progressions can be followed because of its failure mode dependent hardening and softening laws.

The capacity curve for the whole building is determined using the assumptions that the ultimate state is characterised by a highly nonlinear brittle behaviour of the ground floor, while the upper floors remains linear elastic, i.e. the shear walls carry only horizontal forces about their strong axes, and that the floor slabs are totally rigid in plane. For practical application the capacity curve is approximated by a defined number of calculation points to reduce the computation time. For each point the resulting base shear corresponding to the horizontal displacement is calculated by considering the capacity curves of the single walls and torsional effects. Afterwards the capacity curve obtained is converted to the capacity spectrum taking into account the stiffness reduction of the building and its modified shape of vibration.

The seismic safety of the building is verified on the basis of the Performance Point, i.e. the intersection point of the demand spectrum and the capacity spectrum. Within the seismic safety check, all requirements of the standards, e.g. simultaneously acting components of the seismic input or accidental torsional effects, are considered.

Finally, a comparison of the simplified response spectrum method with the capacity spectrum method presented is given. The differences and application limits of each method are discussed. By means of the proposed procedure the behaviour factor can be evaluated depending on the building geometry, wall configuration and materials. The results show that the capacity spectrum procedure is suited much more specifically to the seismic behaviour of masonry than the forced-based design procedures.

1

ATC-40: "Seismic Evaluation and Retrofit of Concrete Buildings", Applied Technology Council, Vol. 1, 1996.

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