Comparisons were made between the magnitude and distribution of total floor forces that were obtained from the analytical models with rigid, simple and complex foundations for the 9 storey stiff buildings. The results for the flexible 9 storey buildings are presented in Section 3.1.3. The results represent the average maximum total force envelope for all of the time history records.
0 1000 2000 3000 1 2 3 4 5 6 7 8 9 L e v e l Force (kN)
Comparison of maximum average envelope forces between a structure with foundation compliance and a structure with rigid foundation
assumption SR 1:0.85 No FC FC 0 1000 2000 3000 1 2 3 4 5 6 7 8 9 L e v e l Force (kN)
Comparison of maximum average envelope forces between a structure with foundation compliance and a structure with rigid foundation
assumption SR 1:1.69
No FC FC
Figure 3%6 Comparison between maximum average total force envelopes
for complex foundation and rigid foundation models for the stiff structure
with SR 1:0.85
Figure 3%7 Comparison between maximum average total force envelopes
for complex foundation and rigid foundation models for the stiff structure
with SR 1:1.69 0 1000 2000 3000 1 2 3 4 5 6 7 8 9 L e v e l Force (kN)
Comparison of maximum average envelope forces between a structure with foundation compliance and a structure with rigid foundation
assumption SR 1:0.85 SF FC 0 1000 2000 3000 1 2 3 4 5 6 7 8 9 L e v e l Force (kN)
Comparison of maximum average envelope forces between a structure with foundation compliance and a structure with rigid foundation
assumption SR 1:1.69
SF
FC
Figure 3%8 Comparison between maximum average total force envelopes
for complex foundation and simple foundation model for the stiff structure
with SR 1:0.85
Figure 3%9 Comparison between maximum average total force envelopes
for complex foundation and simple foundation model for the stiff structure
with SR 1:1.69
Figure 3 6 to Figure 3 9 showed some interesting comparisons of the total average floor force results for the rigid (No FC) and simple foundation (SF) to the complex foundation (FC) results. It can be seen that the simple foundation does not provide any benefits in estimating the magnitude of floor forces compared to the results, of the much simpler, rigid foundation
assumption. The comparison of the average maximum total floor forces for the rigid and complex foundation indicated that for all levels, except level 1, the rigid foundation results were found to overestimate the complex foundation results. This was particularly so at level 9 of the structure.
The reason the rigid foundation structure underestimates the forces at level 1 of the structure is because this part of the structure inherently incurs smaller relative displacements of the lateral force resisting elements when the foundation is rigid compared to the structure with a flexible foundation. This is shown in Figure 3 10. The differences in the displacements, indicated by the figure, also explain why the total forces at level 9 of the structure are larger for the rigid foundation structure compared to the foundation compliant structure (shown by Figure 3 6 and Figure 3 7). The increase of displacements, due to including the flexibility of the foundation, would result in larger relative differences of the frame and the wall deformation patterns (differences could vary for different frame to wall stiffness ratios). This subsequently induces greater transfer forces leading to smaller total forces (as the magnitude of transfer forces in the link elements are opposite magnitude to inertial forces) as shown in the total forces at level 9 in Figure 3 6 and Figure 3 7.
(a) Rigid Foundation assumption (b) Foundation compliant Figure 3%10 Affects of the increase in overall flexibility of the structure
These results indicted that the rigid foundation provided conservative results for all levels except level 1; this is possibly due to the smaller displacements that were estimated by this model. The prediction of displacements directly influence the magnitudes of transfer forces, therefore the simplification of using a rigid foundation model for analysing these types of structures could lead to incorrect predictions of transfer forces.
0 1000 2000 1 2 3 4 5 6 7 8 9 L e v e l Force (kN)
Comparison of maximum average envelope of transfer forces between a structure with foundation compliance and a structure with rigid
foundation assumption SR 1:0.85 No FC FC 0 500 1000 1500 1 2 3 4 5 6 7 8 9 L e v e l Force (kN)
Comparison of maximum average envelope of inertial forces between a structure with foundation
compliance and a structure with rigid foundation assumption SR 1:0.85
No FC FC
Figure 3%11 Comparison of maximum average envelope of transfer forces between a structure with foundation compliance and a structure with rigid
foundation assumption SR 1:0.85
Figure 3%12 Comparison of maximum average envelope of inertial forces between a structure with foundation compliance and a structure with rigid
foundation assumption SR 1:0.85
Figure 3 11 and Figure 3 12 provide comparisons between the magnitude of transfer and inertial forces for the rigid and complex foundations. The transfer and inertial floor force results shown here, for the stiffness ratio of SR 1:0.85 were similar for the structures with stiffness ratios of SR 1:1.69. These figures indicate that the underestimation of total floor forces for the rigid foundation assumption at level 1 is due to the poor estimation of transfer forces at level 1. Transfer forces are poorly estimated due to the increase in displacements which occur for the complex foundation structure, as described above and shown in Figure 3 10.
These figures also indicate that the inertial forces are overestimated by the structure with the rigid foundation assumption. The inertial forces are overestimated by the structure with the rigid foundation assumption due to the shorter fundamental period of the structure, compared to the structure which includes the foundation flexibility. The shorter period, stiffer structure, induces larger acceleration or inertial forces in accordance with the acceleration response spectra.