**Objective -** There is a need for more complete understanding of the collapse likelihood of current code-compliant (ASCE/SEI 7) buildings in "design level" earthquakes. The objective of this project is to evaluate by analysis the collapse probabilities of a suite of steel buildings for a series of increasingly severe earthquake ground motions for a suite of code-compliant (ASCE/SEI 7) steel buildings that were designed for the ASCE/SEI 7 - ASCE/SEI 41. The probabilities of collapse will be determined using the methodology outlined in FEMA P695 (FEMA 2009). The work will assess how these probabilities compare with the collapse objective presumed in ASCE/SEI 7. This assess will either validate the basis of current code (ASCE/SEI 7) provisions or provide the technical basis for targeted changes to those provisions.

**Background -** The proposed project evolved from work that was initiated in FY 2014 to perform two specific tasks concerning seismic design of buildings using ASCE/SEI 7 (ASCE 2010):

- Approximate structural period relationship: In linear analysis methods that are prescribed by ASCE/SEI 7, earthquake-induced lateral loads are approximated using a linear response spectrum of a single degree of freedom oscillator; a building structure's fundamental period of vibration is related via the spectrum to the acceleration that excites the mass of the structure and thus creates earthquake-induced forces. ASCE/SEI 7 provides methods to approximate the fundamental vibration period. Disparities between a building's actual fundamental period and the approximate building period used in ASCE/SEI 7 design calculations impact resulting building performance. In research completed to date, impacts of ASCE/SEI 7 fundamental period approximations have been assessed in over 50 special moment frames that have been designed and evaluated. A preliminary improved structural period relationship has been proposed this formulation requires final development and testing.
- Vertical distribution of design lateral earthquake forces: The prescriptive lateral force distribution procedures in ASCE/SEI 7 approximate the demands induced in over the height of a building by ground motion shaking using a simplified approach. The true distribution of demands depends on a variety of variables, including how uniformly stiffness, strength, and mass are distributed along the height of a building, and how much higher frequency modes contribute to the response. ASCE/SEI 7 provides additional approximations of the impacts of these variables on the actual distribution of demands. However, work by others has shown large uncertainties in the ASCE/SEI 7 approximations. The impacts of these uncertainties on design need to be assessed. This work has not been started.

The findings of the ASCE/SEI 41 (ASCE 2013) project on steel special moment frames, special concentrically and eccentrically braced frames were recently published in three reports (Harris and Speicher 2015a, 2015b and 2015c). These reports identified the need of quantifying the collapse probability of the archetype buildings studied, to develop meaningful quantitative links between ASCE/SEI 41 and ASCE/SEI 7, and to investigate whether ASCE/SEI 7 meets its own performance objective. NIST researchers do not believe that this work has not been performed comprehensively before now. In peer reviews of the project that has been completed and published, this work has been identified as being more urgent than the original two tasks discussed above. In addition, other external input received from the structural engineering community and members of the NEHRP Advisory Committee on Earthquake Hazards Reduction (ACEHR) also confirm the need for such a study. Accordingly the modified research approach proposed here has been developed to quantify the collapse probability of ASCE/SEI 7 code-compliant buildings, followed later by completing he original two tasks. Performing the collapse assessment study will benefit the two original tasks, by (1) developing a framework to test the findings of the approximate period task, and (2) providing a significant amount of data to investigate the lateral force distribution along the height of a building. This will result in a superior research product that will not only complete what was originally proposed but also will more rigorously identify the performance impacts.

**What is the new technical idea?** Among other features, performance-based seismic engineering (PBSE) is intended to let the structural engineer develop earthquake-resistant building design solutions that are more efficient and cost effective than those obtained using the prescriptive building code requirements found in ASCE/SEI 7, which is intended for general use. NIST GCR 09-917-2 (NIST 2009) identified the need for further research and refinement of the PBSE methodologies in U.S. model building codes. NIST GCR 12-917-20 (NIST 2012) then identified the need for advanced seismic design criteria so that a structural system designed using ASCE/SEI 7 would more accurately meet the intended collapse objective in the design basis earthquake. In attempt to address these needs, a multi-year project was undertaken to assess the correlation between ASCE/SEI 7 and its PBSE counterpart, ASCE/SEI 41, which was initially created for existing building assessment (Harris and Speicher 2015a, 2015b, and 2015c). One key recommendation from this research, NIST (2012), was the need to conduct collapse assessments of a suite of buildings to determine whether these buildings were meeting the intended performance objectives of ASCE/SEI 7; this recommendation was also made by the peer review team that oversaw this research and others from the community.

This collapse assessment will be performed following the methodology developed in FEMA P695 (FEMA 2009) to systematically quantify and assess the nonlinear performance of a building, and to determine the probability of collapse in a "standardized" manner. NIST GCR 10-917-8 (2010) studied the FEMA P695 methodology and concluded that is a valuable tool for analyzing a structural system to support its properties' inclusion in model buildings codes. As a consequence, FEMA P695 has been accepted as the best currently available methodology to establish the collapse probability of a seismic force-resisting system and the methodology will be referenced in the upcoming ASCE/SEI 7-16 standard.

In this research, the previously mentioned suite of archetype buildings will be evaluated, with the probability of collapse established for each building and compared with the intended design performance objective. This is accomplished by running nonlinear dynamic analyses using a suite of ground motions scaled at various intensity levels to predict the responses of the buildings from elastic into the nonlinear range of response and finally to collapse. Final results will be presented in terms of a probability of collapse at different ground motion intensities. The probability of collapse at a maximum intensity level (the maximum considered earthquake event) will be quantified in this study for each building, and then compared with the intended target collapse probability prescribed in ASCE/SEI 7. This comparison will provide unique information that examines the intended probability of collapse in ASCE/SEI 7, and also complete the next step toward investigating the consistency between ASCE/SEI 7 and ASCE/SEI 41. Using these results, the Harris and Speicher recommendations will be calibrated and extended to further improve current PBSE provisions in ASCE/SEI 41 that target equivalent performance to that of a new building.

A complementary task will be performed to investigate the effects of the already-proposed NIST approximate period formulation on the probability of collapse. For example, if the collapse probability of the archetype buildings is known, how does the collapse probability change if the proposed NIST procedure is used for approximate period determination during design? If the performance is improved, then that confirms the efficacy of the proposal and will aid in the implementation process with ASCE/SEI 7. A secondary complementary task will be conducted to investigate the vertical force distribution induced in the building at various intensities of the imposed ground motions.

**What is the research plan? **The FEMA P695 methodology will be exercised to measure the collapse probabilities of the suite of steel archetype buildings designed for the Harris and Speicher study. The heart of the P695 process is incremental dynamic analysis (IDA) (Vamvatsikos and Cornell 2002). In IDA, the nonlinear building model is first developed and dynamically analyzed for a scaled selected ground motion. The response of the building (usually in terms of the roof drift ratio) is recorded. The nonlinear dynamic analysis is repeated by incrementally increasing the scale factor of the input ground motion, until the building collapses in the analysis. The same analysis is then repeated for a suite of 44 ground motions. The result of analyses is presented in the form of a cumulative distribution function, known as a "fragility curve," that present probability of exceeding a specific damage state (such as collapse) at a given intensity measure.

An initial investigation will center on whether two-dimensional (2-D) or three-dimensional (3-D) models are required for this work. Many researchers investigating the probability of collapse via IDA use 2-D models to avoid the complexity of analyzing 3-D models. This issue will be investigated in relation to the building suite to determine whether 2-D or 3-D modeling should more appropriately be used.

Next, the 4-story steel special moment frame (SMF) model will be developed and calibrated in OpenSEES (McKenna 2000). This process will then be repeated for the 8- and 16-story SMFs. The effects of the various design and analysis assumptions will also be investigated in relation to the seismic performance and associated collapse probabilities to complement the IDA results. These items will include investigating the effects of linear static and dynamic design approaches, the sensitivity to the modeling and solutions algorithm assumptions, and the effects of the manner in which IDA is performed. The systematic collapse investigation will be conducted using the FEMA P-695 Toolkit developed as part of NIST GCR 12-917-20.

As a complementary task, the recent research conducted at NIST covering the effects of seismic risk category on the approximate fundamental period of a building will be completed and documented in a journal paper submitted to WERB. Using this new approximation, a redesigned 4-story SMF will be evaluated using FEMA P695 to determine whether the collapse probability is improved. Depending on the results, this may be repeated for all three building heights.

Another complementary task will be completed is that of using the results of the FEMA P695 analysis to characterize the lateral force distribution along the height of the building. Performing FEMA P695 analyses will provide a large data set on the shape and variability of the force distribution at various intensity levels ranges from the elastic response up to the collapse. Compiling this data improves the understanding from the lateral demand distribution, and provides insights on the potential improvements for the lateral force distribution method prescribed in ASCE/SEI 7.

Contingent of the findings of the above-mentioned tasks, other lateral load-resisting systems, such as buckling-restrained brace frames and special concentrically braced frames may be investigated in a similar manner. Those systems have been studied by Harris and Speicher using the same approach as that for SMF buildings.

Given that data from this research can be used to develop improved fragility functions, NEHRP researchers will follow closely the ongoing research at the Community Resilience Center of Excellence to assess possible areas of future collaboration.