H.1 Structure B
Wall on BL1
In this section, the evaluation of the wall on BL1 of structure A and B is presented, according to the Tier 3c method. The depicted analysis corresponds to the first ground motion record, GM1, and a PGA value of 0.15 g.
As can be seen in Figure H.1, the deformation of the spring that represents BL1 is significantly higher for structure B, compared to structure A. This is a result of the substantial reduction in capacity of the BBC that corresponds to BL1 of structure B, as depicted in Figure G.3. Due to the increased deformation of BL1, the wall on the specific building layer shows nonlinear behavior, yielding higher wall deformations, as shown in respectively Figure H.2 and H.3. Hence, the UC values for the wall on BL1 of structure B are higher than the UC values for the wall on BL1 of structure A.
a) structure A b) structure B
Figure H.1: Deformation BL1 (Tier 3c, GM1, PGA = 0.15 g).
a) structure A b) structure B
Figure H.2: Hysteresis wall springs of wall on BL1 (Tier 3c, GM1, PGA = 0.15 g).
Results sensitivity study page 128
a) structure A b) structure B Figure H.3: Relative deformation wall on BL1 (Tier 3c, GM1, PGA = 0.15 g).
Wall on BL2
In this section, the evaluation of the wall on BL2 of structure A and B is presented, according to the Tier 3c method. The depicted analysis corresponds to the tenth ground motion record, GM10, and a PGA value of 0.15 g.
As can be seen in Figure H.4, the deformation of the spring that represents BL2 is significantly reduced for structure B, compared to structure A. This is expected to be the result of the soft-story mechanism that applies for BL1. Due to the reduced displacement time history that is subjected to the analyzed wall, the wall shows only linear behavior, resulting in relatively low wall deformations, as shown in respectively Figure H.5 and H.6. Hence, the UC values for the wall on BL2 of structure B are lower than the UC values for the wall on BL2 of structure A.
a) structure A b) structure B
Figure H.4: Deformation BL2 (Tier 3c, GM10, PGA = 0.15 g).
H.1 Structure B page 129
a) structure A b) structure B
Figure H.5: Hysteresis wall springs of wall on BL2 (Tier 3c, GM10, PGA = 0.15 g).
a) structure A b) structure B
Figure H.6: Relative deformation wall on BL2 (Tier 3c, GM10, PGA = 0.15 g).
H.2 Structure C
Wall on BL1
In this section, the evaluation of the wall on BL1 of structure A and C is presented, according to the Tier 3c method. The depicted analysis corresponds to the first ground motion record, GM1, and a PGA value of 0.15 g.
In Figure H.7, it can be seen that the deformation of the spring that represents the lateral behavior of BL1 of structure C shows a minor reduction compared to the same spring in structure A. Although the wall on BL1 of structure C therefore gets subjected to a reduced displacement time history, the resulting relative wall deformation is higher, as shown in Figure H.9. This can be explained by the fact that BC1 applies for the analyzed wall in structure C, while the wall in structure A corresponds to BC3. Hence, the wall in structure C corresponds to a reduced capacity curve, as shown in Figure G.4.
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a) structure A b) structure C Figure H.7: Deformation BL1 (Tier 3c, GM1, PGA = 0.15 g).
a) structure A b) structure C
Figure H.8: Hysteresis wall springs of wall on BL1 (Tier 3c, GM1, PGA = 0.15 g).
a) structure A b) structure C
Figure H.9: Relative deformation wall on BL1 (Tier 3c, GM1, PGA = 0.15 g).
Wall on BL2
In this section, the evaluation of the wall on BL2 of structure A and C is presented, according to the Tier 3c method. The depicted analysis corresponds to the first ground motion record, GM1, and a PGA value of 0.15 g.
For the wall on BL2 of structure C, similar observations apply as for the wall on BL1 of the same structure. As shown in Figure H.10, the deformation of the spring that represents the lateral behavior of BL2 of structure C shows a minor reduction compared to the same spring in structure A. Although the analyzed wall thus gets subjected to a reduced displacement time history, the resulting relative wall deformation is higher for the wall in structure C, compared to the wall in structure A. Again,
H.2 Structure C page 131
this can be explained by the difference in the capacity curves of the analyzed walls, as is the result of the different boundary conditions. For the wall on BL2 of structure A, BC3 applies, whereas for the wall on BL2 of structure C, BC0 applies. In Figure G.4, the capacity curves are depicted.
a) structure A b) structure C
Figure H.10: Deformation BL2 (Tier 3c, GM1, PGA = 0.15 g).
a) structure A b) structure C
Figure H.11: Hysteresis wall springs of wall on BL2 (Tier 3c, GM1, PGA = 0.15 g).
a) structure A b) structure C
Figure H.12: Relative deformation wall on BL2 (Tier 3c, GM1, PGA = 0.15 g).
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H.2.1 Aborted NLTH analysis
The aborted NLTH analysis that is evaluated in this section concerns the analysis of the wall on BL2 of structure C according to the Tier 3c method, as a result of the application of the tenth ground motion record, GM10, with a PGA value of 0.15 g.
Figure H.13 shows the relative deformation of the wall for a PGA value of 0.15 g. Although the NLTH analysis only gets aborted after circa 10 seconds, only the first part of the deformation time history is depicted, so that the vibration of the wall over time can still be clearly seen. It can be observed that the wall does not return to its equilibrium position after the last shown peak displacement that is obtained around 4.75 seconds.
Figure H.13: Relative deformation wall on BL2 (Tier 3c, GM10, PGA = 0.15 g).
Figures H.14a-d show the relative deformation of the wall for four lower PGA values that ascend to the PGA value of 0.15 g for which the NLTH analysis gets aborted. For these four PGA values, convergence errors do not occur. The application of ascending PGA values yields significant differ-ences in the recorded relative deformation of the analyzed wall. It can be noted that the positive peak displacement that is obtained around 4.75 seconds increases for increasing PGA values. The subsequent negative peak displacement that occurs around 5.25 seconds for a PGA value of 0.149 g seems to eventually result in OOP failure of the wall for the PGA value of 0.15 g. It is thus expected that the aborted NLTH analysis can be explained by the presence of an actual OOP failure of the analyzed URM wall, rather than by the presence of an error in the model.
H.2 Structure C page 133
a) PGA = 0.14 g b) PGA = 0.145 g
c) PGA = 0.148 g d) PGA = 0.149 g
Figure H.14: Relative deformation wall on BL2 (Tier 3c, GM10, ascending PGA values).
H.3 BC0
In this section, the evaluation of the wall on BL1 for both the original BC3 and the adapted BC0 is presented, according to the Tier 3c method. The depicted analysis corresponds to the first ground motion record, GM1, and a PGA value of 0.15 g.
In Figure H.15, it can be seen that the deformation of the spring that represents the lateral behavior of BL1 does only show minor differences due to the adapted boundary condition of the analyzed URM wall. Only in Figure H.16, the impact of the application of BC0 becomes clear. In this figure, the significant reduction of the capacity curve for the wall springs can be seen. Due to the reduced capacity curve, higher wall deformations are obtained, as shown in Figure H.17, yielding a higher UC value.
H.3 BC0 page 134
a) BC3 b) BC0 Figure H.15: Deformation BL1 (Tier 3c, GM1, PGA = 0.15 g).
a) BC3 b) BC0
Note: plotting order of curves changed for clarity
Figure H.16: Hysteresis wall springs (Tier 3c, GM1, PGA = 0.15 g).
a) BC3 b) BC0
Figure H.17: Relative deformation wall (Tier 3c, GM1, PGA = 0.15 g).
H.4 Linear behavior of BL1 and BL2
In this section, the evaluation of the wall on BL1 for both nonlinear and linear BL behavior is presented, according to the Tier 3c method. The depicted analysis corresponds to the first ground motion record, GM1, and a PGA value of 0.25 g.
From Figure H.20, it can be noted that the absence of yielding of BL1 results in smaller deformations of the spring that represents the lateral behavior of BL1. This causes a reduced displacement time history that is subjected to the analyzed wall, preventing the occurrence of nonlinear wall
H.4 Linear behavior of BL1 and BL2 page 135
behavior, as shown in Figures H.21 and H.22. Eventually, lower wall deformations are obtained, which corresponds to a lower UC value.
The moment in time that corresponds to the onset of the high differences between the relative deformations of the wall for the two analyzed structures, as shown in Figure H.23, indeed corresponds to the onset of nonlinear behavior of the wall springs in the structure that incorporates nonlinear BL behavior, as shown in Figure H.21.
a) nonlinear behavior BLs b) linear behavior BLs Figure H.18: Force BL1 (Tier 3c, GM1, PGA = 0.25 g).
a) nonlinear behavior BLs b) linear behavior BLs Figure H.19: Yielding BL1 (Tier 3c, GM1, PGA = 0.25 g).
a) nonlinear behavior BLs b) linear behavior BLs Figure H.20: Deformation BL1 (Tier 3c, GM1, PGA = 0.25 g).
H.4 Linear behavior of BL1 and BL2 page 136
a) nonlinear behavior BLs b) linear behavior BLs Figure H.21: Deformation wall springs (Tier 3c, GM1, PGA = 0.25 g).
a) nonlinear behavior BLs b) linear behavior BLs Figure H.22: Hysteresis wall springs (Tier 3c, GM1, PGA = 0.25 g).
a) nonlinear behavior BLs b) linear behavior BLs Figure H.23: Relative deformation wall (Tier 3c, GM1, PGA = 0.25 g).
H.4 Linear behavior of BL1 and BL2 page 137
Appendix