Baseline Model Development

Response history analysis of a three-dimensional model of the soil-foundation-structure system of the Sherman Oaks building was performed using OpenSees, Open System for Earthquake Engineering Simulation (McKenna, 1997; OpenSees, 2011).

This model was based on a previous OpenSees structural model of the building provided by the California Strong Motion Instrumentation Program (CSMIP), and United States Geological Survey (USGS). Construction drawings of the Sherman Oaks building were made available for inspection through the auspices of CSMIP.

The structural system and foundation configuration of the Sherman Oaks building are described in Chapter 7.

Renderings of the Sherman Oaks building configuration are provided in Figure A-1.

The renderings include cut-away views showing details in the first story, basement, and foundation regions. The structural configuration in the first story and basement levels were modeled in a simplified manner to keep the structural modeling aspects tractable, and to focus on comparisons between variations in the idealization of the soil-foundation interface.

In the first story of the building, the one-story extension of the structure along the south longitudinal face of the building (shown in Figure A-1) was not included in the structural model (i.e., both the mass and the stiffness of the one-story extension were excluded). In the basement region, the geometry was simplified such that the shear walls were placed in-line with the perimeter frames of the superstructure. This kept the footprint of the model at 21.9 m wide by 57.6 m long (72 ft by 189 ft) from foundation to roof. Although this geometric simplification was made, the flexibility inherent in the real configuration was captured through elastic connecting springs modeled with the stiffness properties of the horizontal slab components that

interconnect the frame lines of the superstructure with the basement wall lines. This is shown schematically in Figure A-2.

Figure A-1 Renderings of the Sherman Oaks building, including cut-away views showing structural details in the first story, basement, and foundation regions.

Figure A-2 Schematic illustration of elastic springs connecting the framing lines of the superstructure with the wall lines in the basement levels.

The superstructure of the Sherman Oaks building model is a three-dimensional frame of fiber elements (nonlinearBeamColumn in OpenSees). The model is a centerline model that does not include finite joint elements. The two basement levels include fiber element beams and columns, basement slabs, shear walls, and basement grade beams. A rigid diaphragm constraint is used at each floor level.

Fiber elements are composed of both core and cover concrete materials (Concrete04 in OpenSees) and reinforcing steel materials (Steel02 in OpenSees). Fiber elements model flexural behavior using nonlinear concrete and steel material models. Shear and torsional flexibilities are modeled to be linear-elastic, and are combined together into a single component model using the SectionAggregator approach in OpenSees.

An expected yield strength of 462 MPa (67 ksi) was used for the grade 60 steel (Melchers, 1999). This value is slightly lower than, but still comparable to, an expected yield strength of 517 MPa (75 ksi), which is suggested in ASCE/SEI 41-06 (ASCE, 2007). An expected initial stiffness of 20,000 GPa (29,000 ksi) was used, along with a post-yield hardening stiffness of 2% of the initial stiffness. A nominal concrete strength of 35 MPa (5.0 ksi) was included in the model, without provision for expected strength. Use of nominal concrete strength in lieu of expected strength was judged to have minimal impact on the structural response predictions because of the mild nonlinearity experienced in the Northridge earthquake.

The calculated building mass included the mass of all structural elements (beams, columns, and slabs); 0.5 kPa (10 psf) for partitions; 0.6 kPa (12 psf) for mechanical, electrical, and plumbing components; and 25% of the design live load taken as 0.6 kPa (12 psf) for a design live load of 2.5 kPa (50 psf). These masses are accounted for both above and below grade.

Damping was modeled as 4.5% Rayleigh damping, anchored to the first and second mode periods of the building (2.9 sec and 1.0 sec, respectively). This level of damping is a calibrated value, which is discussed below. In developing the Rayleigh damping matrix, degrees-of-freedom associated with foundation springs were excluded. This was necessary to avoid double counting of foundation damping because the soil-foundation model included dashpots at these degrees-of-freedom.

Basement shear walls are 30 cm (1 ft) thick, modeled in the simplified manner described above (and shown in Figure A-2). Figure A-2 shows how the moment resisting frame, simplified shear wall, and slab elements connect to the framing nodes in the two basement levels of the building. At each connection location, the nodes are placed at the same coordinates in the model (but are shown offset in Figure A-2 to illustrate the connectivity). Vertical and rotational degrees of freedom are constrained together for all nodes at each connection location. Figure A-2 also depicts the rigid beams needed to support the simplified shear wall models and the soil springs at the base of the building (soil dashpots are not shown). Stiffness in the

plane of the shear walls was computed based on shear behavior using G=0.4Ec, as recommended in PEER/ATC-72-1, Modeling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings (ATC, 2010), E_c=23,200 MPa (3,370 ksi), and a factor to account for the cracked properties of the wall (another calibrated value discussed below). The out-of-plane stiffness of the walls was not included in the model.

The stiffness and damping properties of the soil are modeled using vertical and horizontal springs and dashpots, as described in Chapter 7. Soil springs are linear-elastic (with model variant MB.2 considering the no-tension gap springs). Dashpots are linear in all model variations.

The depth-variable nature of input ground motions over the height of the basement walls were specified using the MultipleSupportExcitation approach in OpenSees. In this approach, the acceleration, velocity, and displacement acceleration-histories are all specified at each subterranean level. Specifying each ground motion history removes the need to integrate motions within OpenSees.