## 1 Introduction  
The wide application of frame-supported structures serves the increasing demand for modern buildings that are designed and constructed with multiple functions for various purposes. However, the uneven distribution of stiffness and mass in the vertical direction may induce a sudden change in structural stiffness under seismic influence, which undermines the overall structure [1; 2; 3]. Framework-masonry structures (FM structures), with a design scheme where the upper part is relatively stronger than the lower part, have poor seismic resistance based on their behavior in previous earthquakes [4]. The Olive View Medical Center in San Fernando, for instance, suffered from crashed ground columns and buckled reinforced steel in the main building [5; 6]. Another example occurred in Skopje, Yugoslavia. A five-storey building on October Street (literally translated) was heavily damaged at the ground floor which consisted of stores with no partition wall, while the upper floors--primarily partitioned residences--were only slightly damaged. [7]. These findings were confirmed in China, where FM structure stands were some of the most extensively damaged structures in both Wenchuan and Yushu earthquakes (in Sichuan and Qinghai Province, respectively) [8]. Comparatively, the masonry structure of framework seismic walls presents a good choice in terms of city reconstruction and business decentralization. The China Academy of Building Research conducted an experimental study on the seismic performance of a 1/2-scale-seven-floor brick house with a seismic wall framework. The conclusions indicate that, as the weak layer emerges, elastic-plastic deformation takes place in a collective manner, which means that severe damage is likely to occur. Therefore, the study suggests that the stiffness ratio at the interim layer falls somewhere between 1.2 and 2.0 [9]. Xi'an University of Architecture and Technology conducted quasi-dynamic response tests to using 1/2-scale models, where a two-layer framework seismic wall supports a four-layer brick house. The results show the peak values for the seismic shear force and for the moment occur at the interim layer, which remains vulnerable to external force. Therefore, to enhance the lateral stiffness and load-bearing performance in the horizontal direction, structural columns are added to the middle of the interim layer for further support. In the meantime, the stiffness ratio between the third layer and the second layer is between 1.2 and 1.4, whereas that between the second and the first should not exceed 1.4 [4]. The frame-work shear wall structure delivers strong performance in seismic resistance. Although a ground shear wall with increased wall thickness can cope with any sudden change in stiffness at the interim layer, its overuse undermines the layout design and the daily function of the building. At the same time, frame-supported columns tend to be underused as they bear only limited shear force during earthquakes [10]. Both Japan and South Korea have placed frame-supported shear wall structures under quasi-dynamic and vibration tests. The majority of the structural damage is noticed in the frame, whereas the upper structure remains in the elastic stage. In other words, the overall specimen is unevenly damaged [11; 12]. The Southeast University of China (Jiangsu Province) scaled a reinforced framework structure with the bottom layer of a large bay supported by specially shaped columns to 1/6 of the prototype and performed seismic simulations on a vibration test rig. The damage could be categorized as structural damage of the beam hinge. As the plastic hinge at the beam end develops, the wall corners crack; therefore, stronger corner design is highly recommended [13]. Several researchers and scholars have studied the seismic design of frame-supported structures, which tend to display an uneven distribution of stiffness and mass. The results show that the inter-layer displacement and ductility increase with decreasing stiffness and strength of the first layer.