Is Nonlinear Dynamic Analysis Ever Useful? -- The Case of A Partially Constructed 54 Story Building That Did Not Satisfy Seismic Code Requirements --

Farzad Naeim, Ph.D., S.E., Esq. John A. Martin & Associates, Inc.

Los Angeles, California

Mohsen Rahnama, Ph.D. RMS, Inc.

Newark, California

Abstract This paper presents the application of linear and nonlinear performance based seismic design methodologies for solving a complex mixture of engineering and economical issues. A 54 story residential building was constructed to the 38th floor when it was discovered by a technical review panel that it does not meet the letter of the governing building code requirements. More specifically, the structural system of the building consisted of shear walls and slabs only. The local code, similar to IBC and UBC provisions, did not permit such a system for buildings taller than 160 feet (about 10 to 12 stories tall). This building, however, was significantly taller. The question therefore was, whether code noncompliance meant that the building was not safe for occupancy. A series of linear and nonlinear investigations were performed based on the FEMA-356 methodologies. Application of linear dynamic procedure (LDP) and nonlinear dynamic procedure (NDP) appeared to suggest markedly different performance issues with the structure. A closer scrutiny, however, showed that the results obtained from the procedures, were not that different, if they were evaluated with the limitations of LDP in mind. Schemes were devised to modify the construction of the upper floors, not yet built, in order to produce a building that would meet the desired seismic performance objectives. The construction of upper floors of the building is now underway.

Introduction A 54 story residential building in a zone of high seismicity was constructed to the 38th floor when construction stopped because of a dispute over the building’s safety during the anticipated major earthquakes. The details of why the building construction permit was issued and the construction were allowed to such a substantial level, are complex issues which are beyond the scope of this paper. Briefly stated, the structural system of the building consisted of shear walls and slabs only. The local code, similar to IBC and UBC provisions, did not permit such a system for buildings taller than 160 feet. This building, however, is about 500 ft (160 m) tall. In addition, ductile detailing procedures usually followed in zones of high seismicity were not followed to the extent normally desired. A panel of experts was established to decide whether the code noncompliance meant that the building was not safe for occupancy. A series of linear and nonlinear investigations were performed based on the FEMA-356 performance based design methodologies (FEMA, 2000). Strategies were worked out to positively improve the seismic performance of this building by primarily modifying the design of the upper floors, not yet built. The improved design substantially satisfies the FEMA-356 life safety objective in accordance with the nonlinear dynamic procedure (NDP). The construction of the upper floors of the building is now underway.

Description of the Building This building is a 54 story reinforced concrete structure consisting of three wings with identical plan dimensions each approximately 48 meters by 22 meters. The three wings referred to as wing A, B and C are at 120 degree from each other and have no expansions/seismic joints. Figure 1 shows a typical floor plan for the building. The wall layouts for wings A and B are exactly identical. Due to different apartment layout at wing C, however, the layout of walls in this wing is different in a minor way from those on wings A and B.

Wing A

Wing C Wing B

Spine Wall

Cross Wall

Figure 1. A typical floor plan of the building

The structural system consists of solid floor and roof slabs spanning to transverse and longitudinal walls. These walls provide gravity as well as wind and seismic resistance for the building. Due to the unique geometry and design of the building, lateral translational resistance is provided by the longitudinal walls (spines) and torsion is resisted solely by the transverse walls (cross walls). The walls have no seismic boundary elements along either exterior edges or interior openings. Reinforcement detailing is typically non-ductile except possibly for coupling beams of the transverse walls. It was assumed that this additional reinforcement was indeed included in the construction of the building at all floors. Foundation consists of a reinforced concrete mat with variable and substantial thickness. To our knowledge, this is the only building of this height in a zone of high seismicity which relies solely on shear walls as its lateral load resisting system. Most, if not all, building codes developed with seismic regions in mind prohibit use of shear wall systems as the only lateral force resisting system for buildings taller than 160 feet (approximately 50 meters). In United States for example, various editions of the Uniform Building Code starting with the 1976 edition (ICBO, 1976) as well as the 2000

International Building Code (ICC, 2000) would not permit such a design. The same was true in the locality this building was built where the governing code did not allow such a design for a building of this height. Several pictures of the partially constructed building which illustrate the various components of the building are presented in Figures 2 to 5.

Figure 2. A view of the building under construction

Figure 3. A typical cross wall coupling beam or lintel.

Figure 4. A view of a typical floor slab and cross walls

Figure 5. Typical slab reinforcement

The expert panel was told that the design engineers relied solely on the longitudinal walls (spines) for lateral load resistance and did not count on transverse walls to participate in resisting lateral forces. Because the three spine walls concur at the center of the building, they cannot provide the building with any torsional resistance. The torsional resistance must come from the transverse walls. Because of the large height-to-width ratio of the transverse walls and their relative flexibility, the first dynamic mode of this building is a torsional one with a fundamental period in excess of 3.3 seconds. Although this building is basically a symmetric building in plan and elevation, the rotational components of earthquake ground motions and accidental as well as actual plan eccentricities can subject the building to a significant amount of torsion during its response to major earthquakes.

Site-Specific Ground Motions Site-specific design spectra corresponding to exceedance probabilities of 10% in 50 years and 2% in 50 years were developed. Ensembles of seven pairs of recorded time histories were selected so that on average they represented the level of hazard depicted by the corresponding design spectrum. Figure 6 shows the 10% in 50 years design spectrum and the response spectra of the selected seven ground motions. The selected ground motion time histories were then scaled according to the FEMA-356 scaling procedure is to match or exceed the design spectrum in the range of 20% to 150% of the first translational period of the building. Since the best estimate of the initial first translational period of the building calculated per FEMA-356 requirements was 1.1 seconds, therefore the matching was performed for the period range of 0.22 to 1.65 seconds. The scaling factors utilized to produce a FEMA-356 compliant suite of seven time history pairs for the 10% in 50 year event varied from 1.00 to 1.39. The resulting scaled average spectrum of the selected ground motions is compared to the design spectrum in Figure 7. Please note that the average of SRSS of the seven pairs is above the 1.4 times design spectrum at the period range of interest and the fact that none of the scale factors are either unreasonably small or unreasonably large. The same scale factor is applied to both component of each time history as required by FEMA-356 provisions.

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Figure 6. 10% in 50 years design spectrum and response spectra of selected ground motions

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Figure 7. Average responses spectrum of FEMA –356 scaled time histories Evaluations Based on Linear Dynamic Procedure (LDP) LDP evaluations were performed by a local committee of engineers where initially the accidental eccentricity was not modeled and the first mode (purely torsional) was dismissed as a numerical anomaly and not a physical characteristic of the building. Response spectrum analysis was used. The FEMA-356 provisions for accidental eccentricity associated with the LDP procedure, however, significantly penalize a building with such a configuration. As a matter of fact, calculations show that the building should have been subjected to 15% rather than the usual 5% eccentricity commonly used. This would have substantially worsened the already dire prediction obtained by LDP for this building summarized as: • The demand on the lintels of the transverse walls was

significantly larger than their capacities. • The axial stress on the lower levels of the transverse

walls significantly exceeded their capacities • The main central walls would satisfy the capacity

requirements and would not need modification. The situation with transverse walls based on LDP was so out of control that a practical solution based on LDP seemed unattainable to the local committee of engineers. As a result, assistance of an expert group was sought to evaluate the building using the nonlinear dynamic procedure (NDP).

Evaluations Based on Linear Dynamic Procedure (LDP) Two fully three dimensional nonlinear computer models of the building were constructed. The first model utilized the PERFORM-3D computer program (Primary Model) and the second was constructed using the ADINA computer program (Verification Model). Here the results of the Primary Model are presented only. The PERFORM-3D computer model was composed of nonlinear walls and nonlinear beams. Flexural nonlinearity of walls was captured via the use of nonlinear fiber elements, modeling fibers of vertical concrete and steel layers. Flexural nonlinearity of the lintels was found to be non-controlling as all these beams invariably failed in shear. Shear behavior of walls and beams was modeled as elastic-plastic shear hinges. The effect of stiffness degradation in reducing the energy dissipation capacity of members was also included in this model. The total number of degrees of freedom contained in this model was approximately 48,000. This program uses a trilinear backbone with an optional strength drop as the basic nonlinear material model for steel reinforcement in tension and for concrete in compression (see Figure 8). The control points are identified by Y, U, L, and R. This is fully consistent with the nonlinear material models of FEMA-356.

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Figure 8. Primary nonlinear material behavior model (from Powel 2002). As required by FEMA 356 the expected material strengths rather than specified values were used. The tensile capacity of concrete was ignored. Although a value of approximately 10% of compressive strength may be used as tensile strength for concrete, inclusion of tensile strength is known to create significant additional nonlinear events and corresponding inter-step corrections which were not worthwhile for the nominal advantages that one could obtain by inclusion of tensile strength of concrete. Hysteretic stiffness degradation and pinching

effects were considered. A view of the 3-D nonlinear model is shown in Figure 9.

Figure 9. A view of the Perform-3D computer model

The NDP evaluation revealed that due to limited capacity of the lintels of transverse walls no excessive axial stress is produced on the lower levels of transverse walls. Contrary to LDP evaluation, however, NDP results indicated significant demand and not enough capacity on the wall segments in between successive door openings

on alternative floors on the main walls. As a matter of fact, more than 40% of entire hysteretic energy was consumed by the main (spine) walls. The overall energy balance picture for the nonlinear time history analyses and the concentration of hysteretic energy at the mail walls are shown in Figures 10 and 11, respectively. The results also indicated that on average, the demand on lintels were within the acceptable range. Further retrofit studies indicated that if the spine walls of the 16 unconstructed upper floors are thickened and cross-bar detailing as shown in Figure 12 is utilized, the demand on the lower floor coupling panels of main walls are reduced and the building can be brought to substantial compliance with FEMA-356 life safety objectives. Conclusion The construction of the building resumed shortly after the above findings reflecting the suggested modification of design and detailing on the yet unconstructed upper floors. Application of advanced analysis techniques and use of the newly developed performance based design methodologies saved a significant investment and preserved what will be the tallest residential building in a zone of high seismicity.

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Figure 10. Energy balance and energy consumed by elastic and inelastic actions at the end of each analysis

Figure 11. Energy versus time (top) and percent of hysteretic energy consumed by spine of Wing C (bottom) for a typical nonlinear time history analysis.

Figure 12. Cross-bar details as shown here combined with thickening of the main walls on the upper floors would bring the building in substantial compliance with the FEMA 356 life safety objective

References Federal Emergency Management Agency (FEMA), 2000, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, FEMA-356, Washington, D.C., US.A.

International Conference of Building Officials (ICBO), 1976, Uniform Building Code – 1976 Edition, Whittier, California, USA. International Code Council (ICC), 2002, International Building Code, Falls Church, Virginia, USA.