Keywords: pushover analysis, masonry, multimodal, earthquake, shear wall.

Nonlinear static procedures are a common method for the structural design for earthquake loading. Usually, only the first mode shape is taken into account when deducing the behaviour of the structure. Obviously, considering only the first mode shape is only sufficiently accurate if the first mode is dominating the structural behaviour. However, for certain ground plans or mass distributions, higher modes can significantly influence the vibration characteristics of the building.

The paper presents a multimodal pushover analysis for shear wall structures. Assuming rigid floors, the structure is idealised as a multi degree of freedom system with horizontal displacements in the main direction. The paper presents three different load distributions. The first load distribution is based on the modal pushover analysis procedure by Chopra et al. [1] and the second load distribution is based on the adaptive modal combination procedure by Kalkan et al. [2]. Both load distributions are proportional to modal shape and mass distribution. In addition to that, the third distribution also takes the earthquake excitation into account [3].

With these different load distributions, the pushover analysis for shear wall structures is carried out based on single wall capacities [4]. This inherently allows nonlinearities in the individual walls and different stiffness distributions in the different storeys to be considered. The maximum displacement under earthquake loading is calculated by determining the intersection between the modal capacity curve and the design spectrum.

The proposed method with three different load vectors is illustrated using a three storey masonry building with a soft secondary storey. A detailed description of this building and the calculation is presented. To highlight the importance of taking higher modes into account, a comparative analysis is carried out between the proposed load vectors and a load vector that is based only on the first mode.

The feasibility of multimodal pushover analyses based on single wall capacities has been shown. For all load vectors, a significant influence of higher modes on the maximum displacement and interstorey drift due to earthquake loading was demonstrated. Based on these findings, it can be concluded that multimodal pushover analysis is an important design tool even for low rise shear wall buildings, especially if a soft storey is present.

1

A.K. Chopra, R.K. Goel, "A modal pushover analysis procedure to estimate seismic demands for buildings: theory and preliminary evaluation", PEER Report, 2001.

2

E. Kalkan, S. Kunnath, "Adaptive modal combination procedure for nonlinear static analysis of buildings structures", Journal of Structural Engineering, 1721-1731, 2006. doi:10.1061/(ASCE)0733-9445(2006)132:11(1721)

3

S. Kunnath, "Identification of modal combinations for nonlinear static analysis of building structures", Computer Aided Civil and Infrastructure Engineering, 19, 246-259, 2004. doi:10.1111/j.1467-8667.2004.00352.x

4

C. Gellert, C. Butenweg, "Nichtlinearer Erdbebennachweis von Mauerwerksbauten", Tagungsband zur D-A-CH-Tagung, Zürich, Schweiz, 2009.

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