The Bravern is a massive, 3 million-square-foot, mixed-use development that covers a 4.5-acre site. Located in Bellevue, Wash., a thriving Seattle suburb, The Bravern includes two class-A office towers and two exclusive condominium towers. These four high-rise buildings are situated over a three-story podium showcasing over 300,000 square feet of high-end retail space and 3,100 parking stalls located on seven levels of below-grade parking. DCI Engineers applied a performance-based design philosophy to analyze the seismic force resisting systems for this project in order to control the cost of the structure, while still ensuring a safe and practical design.

Performance-based design
In order to minimize costs and maximize leasable floor space, special reinforced concrete shear cores were used as the lateral force resisting system for each of the four towers of The Bravern. This project was designed based on the 2003 International Building Code and ASCE 7-02. Based on these codes, The Bravern falls within seismic design category D. The code limits the building height to 160 feet for this design category and lateral system. An exception in the code allows the height to be increased to 240 feet in buildings that satisfy special redundancy and torsional requirements. The Bravern’s two office towers are 160 feet and 276 feet tall, and the two residential towers are each 365 feet tall. Therefore, three of the four towers exceeded the 240 foot height limit of the code and an alternative design procedure was required.

The building codes use a prescriptive design procedure. The prescriptive approach is intended to prevent significant damage during a moderate seismic event and ensure for the life and safety of a building’s occupants during a Maximum Considered Earthquake (MCE). However, this method does not provide the designer any means to assess what level of damage could actually occur in a structure. Alternatively, performance-based design is intended to allow designers to quantify the performance of a structure based upon a specified loading condition and a desired level of operation. Hence, a performance-based assessment was chosen as the alternative design procedure to demonstrate that the behavior of the buildings at The Bravern would surpass the intended life safety requirements of the code during a seismic event.

Peer review
A performance-based assessment and non-linear analysis require a seismic review by an independent, registered design professional. The third party reviewer, or peer reviewer, is selected by the building department to evaluate the entire seismic system and all supporting calculations.

Unlike a typical code level design, a performance-based design does not have standard criteria that must be met. As a result, the peer reviewer has a great deal of latitude in terms of what parameters may be required for the analysis. Hence, the process creates a level of uncertainty in terms of the amount of time and level of commitment a performance-based design will require to be reviewed.

Throughout the peer review process, the structural drawings—along with supporting calculations and the computer models—were submitted for review, verification, and comments. In order to facilitate the process, DCI submitted seismic design criteria to the peer reviewer prior to the start of the analysis. This ensured that both the design and review teams had consensus on the criterion that was to be used during the design of the lateral system. Throughout the extensive review process, comments addressing proposed modifications and questions concerning the lateral system were addressed by the design team. Once the peer reviewer approved all comments and responses—and was confident that the design was complete—the building department then issued a structural permit for the project.

To avoid the potentially long peer review process, project teams that have tight time constraints will often look for alternatives to the performance-based design approach. One such alternative is the use of a codified dual system which incorporates a central core in conjunction with a steel or concrete moment frame. Since the building code recognizes the inherent redundancy provided by two lateral systems, there is no code prescribed height limit as may be required for other lateral framing options. However, the dual system creates added cost and architectural restrictions for the structure, which the project owner must be willing to accept.

Performance levels
DCI Engineers evaluated the buildings at both elastic (linear) and plastic (non-linear) performance levels. A non-linear model is able to account for the yielding behavior of the structural elements by including the plastic range strength and stiffness of the materials. As a result, the non-linear model can identify those areas of the structure that yield during a given loading condition. This type of modeling more accurately replicates how and where the seismic energy will be dissipated by the yielding of the elements, and what the realistic deformations of the structure will be during a seismic event. This allows the engineer to limit the yielding locations of the building lateral system to specific, more desirable areas.

Elastic (linear) analysis
Two linear analyses were used for the initial design of all the building’s lateral elements. These consisted of a response spectrum analysis and linear time history analysis. Both were performed with the code prescribed forces using the three dimensional analysis program ETABS from Computers & Structures.

Response spectrum analysis is a dynamic analysis that uses the actual mass distribution within the structure to calculate the building period and resulting base shear. Separate models were created for each of the towers during the linear response spectrum analysis. The results were normalized to the code level forces and used for the initial strength design of the coupling beams and the shear cores.

The linear time history analysis uses seven pairs of site specific, MCE level ground motions provided by a geotechnical engineer. These earthquake ground motions have a 2 percent probability of exceedance within a 50 year period. An elaborate model, which included all four towers, the retail podium, and seven levels of below-grade parking, was created to run this analysis. The earthquake time histories were applied in two orthogonal directions creating 14 earthquake conditions. Mean plus sigma of the results from these 14 earthquake runs was used for the design forces. The data from this analysis was primarily used for the design of floor diaphragms, connections below the podium level, and basement walls. This resulted in a design that allowed the diaphragms and the basement walls to behave in an elastic manner under MCE level forces.

Generally, the mass of the below-grade levels is ignored during a seismic analysis. However, at the request of the peer reviewer, the self weight of the concrete slabs was included in order to better understand the performance of the lower level diaphragms. Due to the large size of the below-grade parking slabs, the seismic mass and base shear increased significantly. This increase in base shear was unrealistic since the model did not take into account the effects of soil damping. To mitigate this problem and account for the lateral resistance provided by the soil, horizontal springs were inserted in the model along the height of the basement. This modeling technique provided an accurate method for calculating the transfer of seismic forces from the central building cores to exterior basement walls.

In order to envelope the potential load paths for the seismic forces, two different versions of the linear time history models were created. One model was used to obtain the maximum forces in the diaphragms and basement walls. This version softened the shear cores with higher cracking values, and modeled the basement walls and diaphragms as stiffer elements with minimal cracking. As a result, maximum seismic forces were transferred to the basement walls through the diaphragms. A second version of the model was used to obtain the maximum forces in the below-grade cores. The shear cores were modeled as stiffer elements with reduced cracking values while the diaphragms and basement walls were softened by increasing the cracking coefficients. This resulted in a higher percentage of the shear forces remaining in the cores.

Plastic (non-linear) analysis
After the completion of the linear analyses, a non-linear time history analysis was performed in order to verify the non-linear performance of the elements that were designed. We used Computers & Structures’ Perform 3D for the non-linear analysis. In order to accurately study the non-linear performance, stress-strain curves were created. These curves included the inelastic range for the various materials within the structure. Separate curves were generated for both axial and shear conditions. Additional material properties were also created for the coupling beams framing the opening in the core walls. As previously noted, the preliminary designs for the coupling beam geometry and reinforcement was completed in the linear analysis. Moment rotation curves from each of these unique coupling beams were used to generate the material properties for the performance-based design.

The non-linear time history analysis used the same seven pairs of MCE level ground motions as the linear analysis. Once again, mass was added to the below-grade levels at the request of the peer reviewer. However, Rayleigh damping was used to damp out the higher modes that resulted from the mass below the seismic base.

During the 14 rounds of the analyses, the stress and strain in the elements were tracked. The strains in the flexure elements were compared to the pre-established strain limits to determine if yielding had occurred at a given location. Using this process for multiple iterations, the length of the hinge zone at the base of the tower was ascertained. Any flexural yielding outside of this hinge zone was eliminated by increasing the flexural reinforcement in that area. The stress ratios in the shear elements were checked to confirm they were below the yield limits. This ensured the shear cores performed in a flexural ductile fashion under the MCE level forces.

The non-linear analysis was used to confirm that the drift of the buildings and the coupling beam rotations were within the prescribed limits. While verifying these serviceability restrictions the average of the 14 earthquake conditions was used. A 50 percent increase above the code prescribed drift limit was used to account for the difference between MCE and Design Basis Earthquake (DBE) force levels. Additionally, the code allows a 25 percent increase in drift for non-linear analysis.

Foundations
The foundations for the tower cores were designed by comparing the linear and non-linear models while using soft diaphragms and basement walls with stiff shear cores. As noted above, both models included the mass and stiffness of the below-grade levels, as well as the soil interaction on the basement walls. With these conservative assumptions, DCI engineers were able to demonstrate that a significant amount of shear force was transferred from the central core to the exterior basement walls. This allowed the mat foundations below the tower cores to be no more than 6 feet thick, which saved on excavation and material costs.

Moving forward
The use of performance-based design provided major benefits to the design team of The Bravern. Seismic data from past earthquakes was used to create detailed loading requirements for each of the four towers based upon building periods and mass. The non-linear analysis then facilitated a thorough study of the building behaviors during those design event loads. This allowed the team to create a unique, safe, and economical design using a method that was otherwise not prescribed by the code.

As the design community strives to achieve a better understanding of how structures will behave under significant seismic events and other catastrophic loading conditions, performance-based design will continue to gain popularity. At this stage, the design philosophy is only attractive for major structures that fall outside current building code parameters and can justify the added design time and expense. However, as more research is done and additional guidelines are created, performance-based design will allow building owners, users, and designers to better understand how buildings will behave and what level of detail is required to achieve a given level of performance. 

Jeff Brink, P.E., S.E., and Anish Talati, P.E., S.E., are associates with DCI Engineers in Bellevue, Wash., and can be reached at jbrink@dci-engineers.com and atalati@dci-engineers.com, respectively.