Based on the double member model of wall-frame structure and the corresponding transfer matrix method, the concept of frequent impedance of rigid foundation is introduced so that SSI can be taken into account. This method is more convenient and efficient compared to finite element method because of fewer structural parameters and faster calculation speed. Necessary structure parameters include 7 parameters of each storey, geometry size and total mass of foundation and elastic parameters of site soil. Totally 39 examples were calculated for 13 values of foundation mass and 3 kinds of soil, which are compared to the result of fix bottom model of upper structure. Results show that SSI does not always deduce a decrease of seismic response. Sometimes SSI may increases structural displacement evidently. The simplified method would provide structure designers an efficient tool to understand seismic behavior of wall-frame structures with various foundation and site soil.

Transfer Matrix Method was used to calculate the frequent earthquake responses of high-rise building with different facade shapes. At the premise of constant lateral rigid and same bottom storey mass and supposing that the facade shape variability is simulated by the change of storey mass, the relationship between the maximum value of seismic response and the structure total mass were obtained. Results show that up concave shapes are more optimal than down concaves, pyramid and homogeneous shape as long as the structure deformation being within a reasonable range. If the building height is the most seeking aspect of the design, an up concave shape should be adopted and the building bottom size can be amplified according to the required architecture scale. On the other hand, up concave shapes can’t adapt to a rather wide range of total mass. If the construction field is limited and the architecture scale must meet the requirement, the homogeneous shape should be adopted.

This paper established the theoretical equations of transfer matrix method for shear wall structures with large space at lower part to calculate natural vibration periods. The bottom structure is simplified as a hinged plane system with a complex frame and a complex shear wall, and the upper structure is simplified as a complex shear wall. Transfer matrixes between adjacent stories were established according to the fluctuated equations of complex members and equilibrium and displacement compatibility conditions. After multiplying the transfer matrix of every story, transfer matrix of the whole structure was established. Finally, the solving equation for the natural period was deduced by the boundary conditions. An example showed the feasibility and reliability of the method. In comparison with FEM, it is a convenient and universal method and is recommended for preliminary design of shear wall structures with large space at lower part.

This paper established the theoretical equations of transfer matrix method for frame shear wall structures to solve natural vibration and elastic response under earthquakes. Columns at each storey are combined into an equivalent shear member and shear walls are combined into an equivalent bending member. The structure is simplified as a double member system with the two members being coordinated by the in-plane infinite rigid floors. Transfer matrix of the structure was derived according to the fluctuated equations of equivalent members and the equilibrium and displacement compatibility conditions. After considering the boundary conditions at the bottom and top of structure, it presented the equations and method to solve seismic response, natural frequencies and modes of vibration of the structure. In comparison with FEM, it is a more convenient and universal method and is recommended for preliminary design of frame shear wall structures.

Using three slab models (elastic plate, elastic membrane and rigid plate), the column displacement of one storey frames with different slab-hole ratio, column size and slab thickness under horizontal earthquake were calculated to investigate the driving and limiting factor on the in-plane deformation of floor slab. An influence factor concerning structure stiffness, floor slab stiffness and representative value of gravity load was proposed on the concept of fixed zone and deformed zone. A linear relationship between in-plane deformation and the influence factor was obtained based on the statistic data of 18 examples. Results show that the effect of out-of-plane stiffness of floor slab is very small and negligible and the in-plane deformation of floor slab can be kept within a reasonable range by balancing the structure stiffness of slab strips around the hole and deducing the length-width ratio of floor slab located at deformed zone.