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The feasible and practical stiffness combinations of the lower and upper structures shown in Figure 3.9 (b) of Example 3-1 is compared with those shown in Figure 3.10 (b) of Example 3-2. From Figure 3.9 (b), it is seen that majority of the feasible and practical stiffness combinations of the lower and upper structures of Example 3-2 will result in that the overall stiffness ratio Rk to be located in area 4

of Figure 3.6 (b) or (c). The area 4 signifies that the two-stage analysis procedure is applicable. As previously discussed in section 3.3, if the overall stiffness ratio Rk is located in area 4, the lower

structure has no effect on the upper one, and the upper structure can be considered as an independent building fixed to ground. Therefore, there is almost no interaction between the lower and upper structures in terms of mass and stiffness. The drift limit of the upper 6-storey CFS frame of Example 3-2 can be satisfied by considering the stiffness of CFS shear wall alone. However, all the feasible and practical stiffness combinations of Example 3-1 have yielded that the overall stiffness ratio between the lower and upper structures Rk to be located in area 1 of Figure 3.6 (a), as shown in Figure

3.9 (b). As previous discussed in section 3.3.1 and 3.3.3, if the overall stiffness ratio is located in the area 1 of Figure 3.6 (a), the interactions between lower and upper structure in terms of mass and stiffness should be accounted for in the design and analysis. Therefore, the feasible stiffness combinations of the lower and upper structures of Example 3-1 are greatly affected by the interactions between lower and upper structures in terms of mass and stiffness.

The difference of the stiffness combination characteristics between the two examples is primarily resulted from the difference of the mass associated with the lower structures between the two buildings. Considering the numbers of storey of the lower structure are 6 and 2 for the buildings in Examples 3-1 and 3-2, respectively, the resulted overall mass ratio between the lower and upper structures, Rm, of the building in Example 3-1 is 4.56, which is much greater than that of Example 3-2,

i.e., 0.76, as shown in Table 3.6. Recall that the effect of the overall mas ratio Rm on the shear-force-

amplification factor αU discussed in section 3.3.1. A larger value of the overall mass ratio Rm would

result in a more significant amplification of the shear force for the upper structure. Therefore, the calculated critical shear-force-amplification factors of Example 3-1 are much greater than those of Example 3-2, as shown in Table 3.4. In addition, with a larger value of the overall mass ratio, the critical storey-stiffness ratios of the upper structure of Example 3-1 are also much greater than those of Example 3-2, especially for the storey-stiffness ratio of the upper structure associated with the two-

Table 3.6: Design comparison between Examples 3-1 and 3-2

lower structure upper structure Rm

CFS shear wall length (m)

number of columns in RC moment frame

Example 3-1 6-storey RC frame 3-storey CFS frame 4.56 33.47 ~ 51.17 10.47 ~16.0

Example 3-2 2-storey RC frame 6-storey CFS frame 0.76 30.45 ~ 73.20 4.10 ~ 16.0

stage analysis procedure rkU2stg. The storey-stiffness ratio of the upper structure associated with the

two-stage analysis procedure rkU2stg for Example 3-1 is significantly greater than that of Example 3-2

with the values of rkU2stg for Example 3-1 and Example 3-2 respectively being 81.41 and 2.69, as

shown Table 3.5. With larger values of shear-force-amplification factors and critical storey-stiffness ratios, the interactions between the lower and upper structures in terms of mass and stiffness associated with Example 3-1 have a more significant effect on the stiffness combinations compared to that of Example 3-2.

Intuitively, people may think that the minimum required CFS shear wall length for the 3-storey CFS frame in Example 3-1 should be less than that for the 6-storey CFS frame in Example 3-2. However, due to the large shear-force-amplification effect associated with Example 3-1, the minimum required CFS shear wall length for the 3-storey CFS structure in Example 3-1 is greater than that for the 6-storey CFS structure in Example 3-2, with each of them respectively being 33.47 m and 30.45m, as shown in Table 3.6. Nevertheless, the maximum feasible and practical CFS shear wall length of Example 3-1, i.e., 51.71 m, is less than that of Example 3-2, i.e., 73.2 m, as shown in Table 3.6. The maximum CFS shear wall lengths for both examples are limited by the structure layout, as shown Figure 3.8. The maximum CFS shear wall length 6.1m × 3 ×4 = 73.2 m of Example 3.2 is limited by the total available wall length, while the maximum CFS shear wall length 51.71 m for Example 3-2 is limited by the total number of columns in the RC frame. To ensure that the maximum storey-drift occur at the upper structure, the storey-stiffness ratio should not be less than the calculated rkU1, as discussed in section 1.3.2. The value of rkU1 for Example 3-1, i.e., 4.41, is greater

than that of Example 3-2, i.e., 1.89, as shown in Figure 3.5. As to Example 3-1, if the CFS shear wall length is greater than 51.71 m, to ensure the storey-stiffness of the lower structure kL be not less than

rkU1kU, the required number of columns in the RC moment frame becomes greater than 16. Therefore,

the maximum CFS shear wall length for Example 3-1 is limited to 51.71 m rather than 73.2m. As to Example 3-2, since value of the minimum storey-stiffness ratio rku1 is relatively small, the required

number of column can be less than 16 even if the CFS shear wall length is 73.2m, as shown in Figure 3.9 (b).

From the previous discussion, it is seen since the number of the storey and total seismic weight of the lower structure is greater than those of the upper structure in Example 3-1, the required stiffness of the upper structure is greatly affected by the interactions between lower and upper structures in terms of mass and stiffness. However, as to Example 3-2, since the number of the storey and total seismic weight of the lower structure is less than those of the upper structure, such interactions have less effect on the required stiffness of the upper structure. The required lateral stiffness of the upper structure can be determined without considering the influence of the lower structure.