David A. Roke

Design Concepts for Damage-Free Seismic-Resistant Self-Centering Steel Concentrically Braced Frames

Conventional concentrically-braced frame (CBF) systems have limited drift capacity before brace buckling and related damage leads to deterioration in strength and stiffness. Under the NSF funded NEESR-SG research program, a new type of CBF is being developed with increased drift capacity before damage and decreased permanent drift under seismic loading. These self-centering CBF (SC-CBF) systems are intended to provide significant non-linear drift capacity while limiting damage and residual drift, and are motivated by the goal of minimizing structural damage under seismic loading. At low levels of lateral load, the response of an SC-CBF is similar to that of a conventional CBF. At higher levels of lateral load, the fundamental lateral load behavior of the SC-CBF system is rocking about the base of the compression column, which occurs when the column under tension from overturning moment decompresses and uplifts at the foundation. To control the uplift, high strength post-tensioning (PT) bars, oriented vertically over the height of the SC-CBF, prestress the frame to the foundation. The SC-CBF is designed to decompress at the base at a selected level of lateral loading, initiating a rigid-body rotation (rocking) of the frame. The PT bars provide a restoring force to return the CBF to the foundation (to self-center the CBF). The rocking response substantially influences the member forces that develop in the frame members (beams, columns, and braces) and induces deformation and eventually yielding of the PT bars. To minimize structural damage before PT bar yield, the frame members are designed to resist the internal forces that develop at PT yield. The paper presents the results of an analytical study of SC-CBFs. Dynamic analysis results demonstrate the expected drift capacity and self-centering behavior of the system. Modal decomposition of these analysis results shows that the first mode response is effectively limited by the rocking behavior; however, the higher modes are also excited by the rocking response. Based on these analysis results an improved design method is presented that accounts for the higher mode contributions to the member forces of the SC-CBF.

Assessment of artificial neural network and genetic programming as predictive tools

Two major soft computing techniques, ANN and GP, are evaluated in detail.A case study in punching shear modeling of RC slabs is modeled.The models are compared based on model complexity, statistical validation and parametric study.Overfitting potential of the models is evaluated and suggestions are provided.The results indicate model acceptance criteria should include engineering analysis. Soft computing techniques have been widely used during the last two decades for nonlinear system modeling, specifically as predictive tools. In this study, the performances of two well-known soft computing predictive techniques, artificial neural network (ANN) and genetic programming (GP), are evaluated based on several criteria, including over-fitting potential. A case study in punching shear prediction of RC slabs is modeled here using a hybrid ANN (which includes simulated annealing and multi-layer perception) and an established GP variant called gene expression programming. The ANN and GP results are compared to values determined from several design codes. For more verification, external validation and parametric studies were also conducted. The results of this study indicate that model acceptance criteria should include engineering analysis from parametric studies.

Decision Tree Approach for Soil Liquefaction Assessment

In the current study, the performances of some decision tree (DT) techniques are evaluated for postearthquake soil liquefaction assessment. A database containing 620 records of seismic parameters and soil properties is used in this study. Three decision tree techniques are used here in two different ways, considering statistical and engineering points of view, to develop decision rules. The DT results are compared to the logistic regression (LR) model. The results of this study indicate that the DTs not only successfully predict liquefaction but they can also outperform the LR model. The best DT models are interpreted and evaluated based on an engineering point of view.

Large-Scale Experimental Studies of Damage-Free Self-Centering Concentrically-Braced Frame under Seismic Loading

Conventional concentrically-braced frame (CBF) systems have limited drift capacity before brace buckling and related damage leads to deterioration in strength and stiffness. A new type of CBF is being developed which has greater drift capacity before damage and which develops less permanent (residual) drift under seismic loading. This self-centering CBF (SC-CBF) system is motivated by the goal of minimizing structural damage under seismic loading and is intended to provide significant non-linear drift capacity while limiting damage and residual drift. The fundamental lateral load behavior of the SC-CBF system is rocking on its base, which occurs when the column under tension from overturning moment decompresses and uplifts from its support. The SC-CBF is designed to decompress at the base at a selected level of lateral loading, initiating a rigid-body rotation (rocking) of the frame. Vertically-aligned post-tensioning (PT) steel resists this uplift and provides a restoring force to return the SC-CBF to its support (to re-center the system). Experimental results show that SC-CBFs can be designed to sustain no significant structural damage under the design basis earthquake and only minor structural damage under the maximum considered earthquake.

Cost-benefit evaluation of self-centring concentrically braced frames considering uncertainties

Abstract Self-centring concentrically braced frame (SC-CBF) systems have been developed to reduce post-earthquake damages in braced frames. However, due to special details required by the SC-CBF system, the construction cost of an SC-CBF is expected to be higher than that of a conventional CBF. In this study, the seismic performance and economic effectiveness of two prototype buildings utilising SC-CBFs are assessed and compared with buildings utilising conventional CBFs by evaluating the annual probabilities of exceeding various damage levels, expected annual losses, life cycle costs (under seismic hazard) and economic benefit of using SC-CBFs considering prevailing uncertainties. The results of this study show that the SC-CBF buildings have lower drift-related losses but higher acceleration-related losses. The SC-CBF is found to be beneficial for the 6-storey configuration, but not for the 10-storey configuration. For the 6-storey buildings studied here, if the construction cost of the SC-CBF is assumed to be twice that of the CBF, the pay-off time is expected to be 12 to 21 years, with a probability of 68%, considering the uncertainties in the demand, capacity, loss parameters and initial construction costs. Finally, appropriate probabilistic engineering demand parameter model formulation is critical for generating accurate loss analysis results.

Engineering optimization using interior search algorithm

A new global optimization algorithm, the interior search algorithm (ISA), is introduced for solving engineering optimization problems. The ISA has been recently proposed and has two new search operators, composition optimization and mirror search. In the current study, the optimization process starts with composition optimization and linearly switches to mirror search. For validation against engineering optimization problems, ISA is applied to several benchmark engineering problems reported in the literature. The optimal solutions obtained by ISA are better than the best solutions obtained by the other methods representative of the state-of-the-art in optimization algorithms.

Structural and Nonstructural Performance Evaluation of Self- Centering Concentrically Braced Frames Under Seismic Loading

Self-centering concentrically braced frame (SC-CBF) systems have higher drift capacity than conventional CBF systems prior to damage. To fully demonstrate the effectiveness of SC-CBF systems, a comparison study is performed considering both structural and nonstructural seismic performance. First, two prototype buildings are designed with the same configuration but different lateral load resisting systems (CBF or SC-CBF exclusively). Nonlinear dynamic analysis is conducted using finite element numerical modeling to obtain seismic responses under a suite of earthquake records with various hazard levels. The numerical results are then utilized to build probabilistic demand models of inter-story drift, floor acceleration, and roof acceleration. Finally, fragility curves for structural and nonstructural components are generated for various performance levels with demands and capacities. The comparison of the fragilities of the two structural systems reveals that the SC-CBF has better seismic performance than the conventional CBF; however, nonstructural components must be designed for higher force demands in the SC-CBF.

Life cycle cost-benefit evaluation of self-centering and conventional concentrically braced frames

Self-centering concentrically braced frame (SC-CBF) systems have been developed to increase the drift capacity of braced frames prior to structural damage. To achieve the improved seismic performance of SC-CBF system, the construction cost of an SC-CBF is expected to be higher than that of a conventional CBF. In this study, economic effectiveness of using an SC-CBF instead of a CBF in one prototype building is calculated to indicate the time that initial SC-CBF construction costs are compensated by lower earthquake-induced losses in the lifetime of the building (pay-off time). The results of this study show lower business interruption is the most significant component of the economic benefit of the SC-CBF compared to the CBF. Moreover, the pay-off time increases dramatically if the initial construction cost of the SC-CBF is more than 4% higher than the CBF. Earthquake-induced damages of buildings can cause social and economic disturbances. Selfcentering concentrically braced frame (SC-CBF) systems (Roke et al. 2009) have been developed to address the limitations of conventional CBFs by increasing drift capacity of the structure prior to damage and decreasing residual drift; thus SCCBF can mitigate losses due to earthquakes. This improved seismic performance of the SC-CBF system has been found experimentally and numerically (e.g., Roke et al. 2009; Dyanati et al. 2014, 2015). However, the construction cost of an SC-CBF is expected to be higher than that of a conventional CBF due to the special details and elements required by the SC-CBF. Therefore, it is necessary to investigate if the higher construction cost of SC-CBF system would be offset by lower earthquake-induced losses (due to better seismic performance of SC-CBF) during the life time of the building, which would demonstrate the economic effectiveness of SC-CBF systems compared with conventional CBF systems. Life cycle cost assessment has been used as a measure of the economic effectiveness of a structure. Wen & Ang (1991) and Wen & Shinozuka (1998) developed a life cycle cost formulation to investigate the cost effectiveness of an active control system in structures during earthquakes. Goda et al. (2010) used life cycle cost assessment to investigate the cost effectiveness of a seismic isolation technology. Kang & Wen (2000) used the minimum life cycle cost concept to develop an optimal design for structures under single and multiple hazards. Padgett et al. (2009) developed a retrofit strategy for bridges based on cost-benefit analysis using life-cycle cost to determine the most costeffective retrofit method that differs based on the seismic hazard characteristics of the location. Available software such as HAZUS (FEMA 2014) and PACT (FEMA 2012) have been used in the seismic performance and loss evaluation of buildings (Erberik & Elnashai 2006, Parvini sani & Banazadeh 2012) and can also be used for life 12 International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 2 cycle cost estimation. However, there is a major drawback in both software packages: they both define engineering demand parameter (EDP) models as a function of only one seismic intensity measure (IM), pseudo spectral acceleration (PSA), which may not be accurate for CBF and SC-CBF structures (as studied by Dyanati et al. 2015), eventually leading to inaccuracy in the loss estimation. In this study, the economic benefit of the SC-CBF will be studied using life cycle cost formulation. The economic benefit of the SCCBF, which is the difference between life cycle cost of SC-CBF and CBF structures, will clarify if the higher construction cost of SC-CBF will be compensated by better performance of SC-CBF. 1. SC-CBF SYSTEM The general configuration of an SC-CBF is shown in Figure 1(a). There are two sets of columns in the SC-CBF: SC-CBF columns and adjacent gravity columns. As shown in Figure 1(b), the SC-CBF columns are allowed to uplift at the base, causing a rocking response under higher levels of lateral force. Vertically oriented post-tensioning (PT) bars and gravity loads are used to resist column uplift and provide selfcentering (i.e., reducing residual drift). The rocking behavior softens the lateral force-lateral drift response of the system, thereby permitting larger lateral displacements while limiting the member force demands, avoiding yielding or buckling in the braces. 2. SEISMIC LIFE-CYCLE COST-BENEFIT MODEL Life cycle cost of a building system subjected to seismic hazard includes three components (Kang & Wen 2000): initial construction cost, including structural and non-structural component costs (C0); earthquake-induced losses or life cycle loss of the building (e.g., repair cost, business interruption, injuries) (LCL); and operation/maintenance costs during the life cycle of the building (Cm), as shown in Equation (1).         x x x x m C t LCL C t LCC    , , 0 (1) where LCC = life cycle cost of the structure; t = life time of the structure; and x = vector of design variables for the structure. Figure 1: (a) Configuration of SC-CBF; (b) Rocking behavior of SC-CBF; (c) configuration of CBF. Construction cost estimation is straightforward and can be generally estimated using expert opinions or tools such as R.S. Square Foot Costs (RS Means 2013). Maintenance and operation costs are highly related to the occupancy of the building, rather than the structural system, and can be estimated using handbooks and standards such as Facilities Maintenance & Repair Cost Data Online (RS Means 2013). The life cycle loss (LCL) estimation, on the other hand, involves more complex procedures including hazard, response, damage, and loss analysis for calculating the losses from earthquakes. If the expected annual loss (EAL) from earthquakes is known, the expected value for life cycle loss (E[LCL]) can be evaluated as follows (Porter et al. 2004):     EAL e t LCL E t      1 ] , [ x (2) where e -γt = discounted factor over time t and γ = constant discount rate per year, which is used to calculate the present value of the future losses. Assuming C0,SC-CBF = a C0,CBF (a = relative cost coefficient and a > 1) and equal maintenance/operation costs for CBF and SCCBF systems, the expected economic benefit of using an SC-CBF instead of a CBF in a building, E[BSC-CBF], can then be calculated as follows: 12 International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015 3         CBF SC CBF t CBF CBF SC

Sensitivity analysis of seismic performance assessment and consequent impacts on loss analysis

The probabilistic framework for seismic performance evaluation developed by PEER has been widely used in the literature. This framework consists of four steps: hazard analysis, response analysis, damage analysis, and loss analysis. Typically the process involves ground motion selection for numerical analysis, probabilistic model development for engineering demand parameters (EDP), and an EDP hazard calculation approach. This study investigates the impact of three aspects (i.e., the ground motion suite selected, the EDP formulation chosen, and the hazard calculation formulation adopted) on the seismic performance of an office building located in downtown Los Angeles. The result of this study shows that these three aspects have significant impacts on the seismic performance in terms of dynamic responses, demand hazard, and expected annual loss. This study also suggests that more accurate and robust performance evaluation is obtained when: (1) using a ground motion suite that contains a rich intensity measure content, (2) using vector-valued demand models that provides more accurate predictions rather than scalar-valued demand models, and (3) using joint hazard formulations when two seismic intensity measures are involved.

Seismic-Resistant Friction-Damped Braced Frame System with Buckling Restrained Columns

Conventional braced frame systems have limited drift capacity prior to brace buckling and related damage leads to deterioration in strength and stiffness. Rocking braced frame systems increase the drift capacity; however, significant higher mode effects and local yielding may result from column uplift. A friction-damped braced frame (FDBF) system with buckling-restrained columns (FDBF-BRC) is being developed to provide significant drift capacity while limiting damage and residual drift without column uplift. The FDBF-BRC system consists of beams, columns, and braces branching off a central column, and buckling restrained columns (BRCs) are incorporated into the system in the first story. The BRCs and friction generated at lateral-load bearings are used to dissipate energy to minimize the overall seismic response of the FDBF-BRC system. Vertically aligned post-tensioning bars provide additional overturning moment resistance and aid in self-centering the system to eliminate residual drift. In this study, a suite of 44 DBE-level ground motions used in FEMA P695 is numerically applied to several FDBF-BRCs to demonstrate the seismic performance of the system. The results show that the FDBF-BRC system has high ductility and energy dissipation capacity, and is an effective seismic resistant system.