This report presents the results of the Phase 2 of a study dealing with the effect of diaphragm flexibility on the seismic response of single-story buildings. While Phase 1 of the study considered the elastic response of the buildings, the present phase focuses on the nonlinear response of the building. It is assumed that the nonlinearity is confined to the lateral load resisting system that supports the diaphragm, while the diaphragm itself remains elastic. The building is modeled by a simple beam supported on springs. The latter represent the supporting lateral load resisting systems. Both flexural and shear deformations in the beam (diaphragm) are accounted for.
Shear deformation plays an important role in determining the stiffness of the diaphragm and in certain types of diaphragms such deformation may be significantly larger than the flexural deformation. Shear deformation must therefore be taken into account in an analysis of the diaphragm. The flexibility of the diaphragm also causes substantial lengthening of the building period, which would lead to a reduction in the base shear. Because of nonlinearity in the Seismic Force Resisting System (SFRS) and the presence of many eras in the time history of response when the diaphragm is vibrating as a free system, the higher elastic modes of the building become major contributors to the response. This increases the displacement of the SFRS and hence the ductility demand placed on it, and changes the pattern of the distribution of inertia forces across the length of the diaphragm.
The maximum nonlinear displacement of the SFRS and hence the ductility demand on it increases with the flexibility of the diaphragm as measured by the ratio of the maximum static elastic displacement of the diaphragm and that of the top of SFRS under a uniformly distributed lateral load on the diaphragm. The changed distribution of the inertia forces implies that the maximum moment in the diaphragm is not much different from that obtained by assuming that the inertia forces are uniformly distributed.
A simplified procedure for design of single storey structures with flexible diaphragms under seismic loads was proposed. The procedure accounts for the influence of the flexibility of the diaphragm on the seismic performance of the vertical SFRS, either through increase in the seismic ductility demand, or through reduction of the Rd factor for the SFRS. The developed procedure and modified Rd factors to account for the increased seismic demand on the vertical SFRS presented in this report formed the basis for the code change proposal that was presented to the NBCC Standing Committee on Earthquake Design (SCED) and considered for inclusion in the 2015 edition of NBCC.
