Analysis Results

The Sherman Oaks building was analyzed in OpenSees (McKenna, 1997), incorporating foundation springs and dashpots described above. Details for the development and calibration of the Baseline Model (MB) are described in Appendix A. Adjustments to the shear modulus for cracked concrete, Rayleigh damping, and structural mass and stiffness were used to produce a reasonably close match to recordings from the 1994 Northridge earthquake. Based on calibration studies, Model MB was considered a reasonable engineering approximation for the Sherman Oaks building. Using this model as a basis, alternative modeling

configurations for the Sherman Oaks building were developed and studied, and the resulting response quantities were compared for the following variants:

 Model MB.1, which examined the importance of flexibility in subterranean structural elements (walls and slabs);

 Model MB.2, which examined the importance of nonlinearity in foundation springs by not allowing tension (allowing gap formation);

 Model 4, which removed the effects of depth-variable ground motions and considered the use of free-field motions (versus foundation input motions);

 Model 3, which fixed the far ends of foundation springs against displacement and applied input motions at the base slab level;

 Model 2, which ignored the effects of embedment by omitting the surrounding soil and assumed a fixed base at the foundation level; and

 Model 1, which ignored the response of the subterranean levels by assuming a rigid base at the ground level.

Fundamental periods of vibration for each of the model variants are shown in Table 7-6. The resulting modeled periods were only modestly affected by different idealizations of the soil-foundation interface.

Table 7-6 Comparison of Fundamental Periods for Alternative Foundation Modeling Configurations for the Sherman Oaks Building

Model

Fundamental Period (sec)

Longitudinal Transverse

MB (Baseline Model) 2.67 2.72

MB.1 (rigid subterranean structure) 2.35 2.68

MB.2 (no tension in foundation springs) 2.65 2.73

Model 4 (bathtub) 2.67 2.72

Model 3 (fixed horizontal springs) 2.34 2.65

Model 2 (fixed at foundation) 2.67 2.71

Model 1 (fixed at grade) 2.34 2.67

Comparisons of computed displacement histories, maximum displacement, drift ratios, story shear coefficients, and peak floor accelerations between Model MB and the other models are shown in Figures 7-11 through 7-15. A summary of peak response quantities from all foundation modeling configurations is shown in Figure 7-16.

Model MB.1 and Model MB.2. Results for Model MB.1 in Figure 7-11 showed that rigid subterranean structural elements caused an increase structural response,

particularly in the NS direction, likely due to the change in period. In the case of Model MB.2, results in Figure 7-11 showed that allowing geometric nonlinearities (i.e., gap formation) had no discernible impact on response. This suggests that gaps would not be expected to form in the foundation springs between the soil and the basement walls, and supports the equivalent-linear soil-foundation modeling assumptions suggested in Section 7.1.3.

Model 4. Results for Model 4 in Figure 7-12 showed that the bathtub model introduces negligible changes in displacement response over the height of the structure (i.e., less than 3.6% different at the roof level). Changes in story drift and story shear force profiles were also negligible. Peak floor accelerations were most sensitive to the change in modeling configuration. Values above the ground level were relatively unaffected, but values in the subterranean levels were sensitive to the

use of free field motions (results marked ‘4b’) versus foundation input motions (results marked ‘4a’).

Model 3. Results for Model 3 in Figure 7-13 showed the least agreement with Model MB. Fixing the upper-level foundation springs against displacement, and applying input motions to the base slab, caused large differences in all response quantities including building vibration periods, displacement histories, drift ratios, and story shears. Given the significant discrepancies observed, use of this modeling configuration is not recommended.

Model 2. Results for Model 2 in Figure 7-14 showed that modeling the subterranean levels, even while ignoring the effects of the surrounding soil, can provide good results for some response quantities. Model 2 exhibited good agreement for building vibration periods and displacement histories. Reasonable agreement was observed for maximum displacement and drift ratios, but story shears and peak floor

accelerations differed more significantly, particularly in the subterranean levels.

Model 1. Results for Model 1 indicated that ignoring the subterranean levels significantly alters the period of vibration. As a result, displacement histories were more out-of-phase than most other modeling configurations, as shown in Figure 7-15.

Differences in story drifts, story shears, and peak floor accelerations were relatively large (up to 50% different) in some cases.

In Figure 7-16, peak displacement, drift, and story shear response quantities from all modeling configurations were synthesized and plotted in a single figure. Results for Model 3 are clear outliers for each of the parameters considered. Results for Model 4 are closest to Model MB, followed by Model 2, and then Model 1. Differences in response quantities, when they occurred, were generally greater in the subterranean levels than in the levels above grade.

Figure 7-11 Comparison of displacements, drifts, story shears, and accelerations between Model MB, MB.1 and MB.2 for the Sherman Oaks building.

Figure 7-12 Comparison of displacements, drifts, story shears, and accelerations between Model MB and Model 4 for the Sherman Oaks building.

Figure 7-13 Comparison of displacements, drifts, story shears, and accelerations between Model MB and Model 3 for the Sherman Oaks building.

Figure 7-14 Comparison of displacements, drifts, story shears, and accelerations between Model MB and Model 2 for the Sherman Oaks building.

Figure 7-15 Comparison of displacements, drifts, story shears, and accelerations between Model MB and Model 1 for the Sherman Oaks building.

Figure 7-16 Comparison of peak displacements, drift ratios, and story shears from all model configurations, in the transverse direction.