Variability and Accuracy of Target Displacement from Nonlinear Static Procedures

This paper compares the target displacement estimate from four current nonlinear static procedures—FEMA-356 CM, ASCE41 CM, ATC-40 CSM, and FEMA-440 CSM—with the value derived from recorded motions of five strongly shaken reinforced concrete buildings.This comparison provides useful insight into two important questions: (1) how much does the target displacement vary among the four nonlinear static procedures? and (2) can the engineering profession “accurately” predict the response of a real building during an earthquake event using currently available modeling techniques and pushover analysis procedures? It is shown that these procedures may lead to significantly different estimates of the target displacement, particularly for short-period buildings responding in the nonlinear range. Furthermore, various nonlinear static procedures applied to nonlinear models developed using generally accepted engineering practice provide either significant over estimation or under estimation of the target roof displacement when compared to the value derived from recorded motions

Evaluation of a Substitute Structure Method to Estimate Seismic Displacement Demand in Piers and Wharves

This paper compares seismic displacement from the MOTEMS and the ASCE/COPRI 61-14 substitute structure method (SSM) with results from the nonlinear response history analysis (NLRHA). It is found that the SSM is biased toward overpredicting displacement demand for short-period systems and under-predicting displacement demand for long-period systems. The overprediction was found to be excessive for very-short period systems (i.e., systems with periods shorter than the period at which the design spectrum transitions from linearly increasing spectral acceleration to constant spectral acceleration). It is recommended that the SSM not be used for such systems. It is also recommended that the SSM not be used for long-period systems (i.e., systems with periods longer than the period at which the design spectrum transitions from constant spectral acceleration to constant spectral velocity), where it underpredicts displacement demand and may lead to unconservative design. The SSM provides reasonable results (within 20% of results from NLRHA) for systems with periods in the constant spectral acceleration region of the design spectrum

Seismic Response of Linear and Non-Linear Asymmetric Systems With Non-Linear Fluid Viscous Dampers

This investigation is concerned with the seismic response of one‐story, one‐way asymmetric linear and non‐linear systems with non‐linear fluid viscous dampers. The seismic responses are computed for a suite of 20 ground motions developed for the SAC studies and the median values examined. Reviewed first is the behaviour of single‐degree‐of‐freedom systems to harmonic and earthquake loading. The presented results for harmonic loading are used to explain a few peculiar trends—such as reduction in deformation and increase in damper force of short‐period systems with increasing damper non‐linearity—for earthquake loading. Subsequently, the seismic responses of linear and non‐linear asymmetric‐plan systems with non‐linear dampers are compared with those having equivalent linear dampers. The presented results are used to investigate the effects of damper non‐linearity and its influence on the effects of plan asymmetry. Finally, the design implications of the presented results are discussed

Seismic Behaviour of Asymmetric Buildings With Supplemental Damping

This paper investigates the response of asymmetric‐plan buildings with supplemental viscous damping to harmonic ground motion using modal analysis techniques. It is shown that most modal parameters, except dynamic amplification factors (DAFs), are affected very little by the plan‐wise distribution of supplemental damping in the practical range of system parameters. Plan‐wise distribution of supplemental damping significantly influences the DAFs, which, in turn, influence the modal deformations. These trends are directly related to the apparent modal damping ratios; the first modal damping ratio increases while the second decreases as CSD moves from right to left of the system plan, and their values increase with larger plan‐wise spread of the supplemental damping. The largest reduction in the flexible edge deformation occurs when damping in the first mode is maximized by distributing the supplemental damping such that the damping eccentricity takes on the largest value with algebraic sign opposite to the structural eccentricity

Effects of Supplemental Viscous Damping on Seismic Response of Asymmetric-Plan Systems

Coupling between lateral and torsional motions may lead to much larger edge deformations in asymmetric‐plan systems compared to systems with a symmetric plan. Supplemental viscous damping has been found to be effective in reducing deformations in the symmetric‐plan system. This investigation examined how supplemental damping affects the edge deformations in asymmetric‐plan systems. First, the parameters that characterize supplemental viscous damping and its plan‐wise distribution were identified, and then the effects of these parameters on edge deformations were investigated. It was found that supplemental damping reduces edge deformations and that reductions by a factor of up three are feasible with proper selection of system parameters. Furthermore, viscous damping may be used to reduce edge deformations in asymmetric‐plan systems to levels equal to or smaller than those in the corresponding symmetric‐plan system

Evaluation of In-Ground Plastic-Hinge Length and Depth for Piles in Marine Oil Terminals

This investigation evaluated the current recommendations for plastic-hinge length and depth for piles in marine oil terminals considering nonlinear pile and soil behavior, as well as two seismic design levels: Level 1 and Level 2. It was found that the plastic-hinge length depends on seismic design level, whereas depth is independent of seismic design level. For pre-stressed concrete piles, the current plastic-hinge length recommendations were generally found to be adequate for seismic design Level 2, but provided much smaller plastic-hinge length for Level 1. For hollow-steel piles, the current plastic-hinge length recommendation was generally found to be adequate for sands, but provided much smaller plastic-hinge length for clays for both seismic design levels. Furthermore, the current recommendations lead to much shallower plastic-hinge depth than that found in this investigation

Simplified Analysis of Asymmetric Structures With Supplemental Damping

This study investigated the effects of neglecting off‐diagonal terms of the transformed damping matrix on the seismic response of non‐proportionally damped asymmetric‐plan systems with the specific aim of identifying the range of system parameters for which this simplification can be used without introducing significant errors in the response. For this purpose, a procedure is presented in which modal damping ratios computed by neglecting off‐diagonal terms of the transformed damping matrix are used in the traditional modal analysis. The effects of the simplification are evaluated first by comparing the aforementioned modal damping ratios with the apparent damping ratios obtained from the complex‐valued eigenanalysis. The variation of a parameter that was defined by Warburton and Soni as an indicator of the errors introduced by the simplification is examined next. Finally, edge deformations obtained from the simplified procedure are compared with those obtained from the direct integration of the equations of motion. It is found that the simplified procedure may be used without introducing significant errors in response for most practical values of the system parameters. Furthermore, estimates of the edge deformations, in general, tend to be on the conservative side

Evaluation of Seismic Force Provisions for Ancillary Systems in Piers and Wharves Considering Effects of Nonlinearity

Much of the prior research on understanding seismic response of secondary systems and development of code provisions was conducted either for nuclear power plant facilities or buildings. Most marine structures differ from nuclear power plant facilities or buildings in that the marine structures can be idealized as one-story building type systems. Furthermore, most previous studies have been limited to linear elastic behavior of both primary and secondary systems. The objectives of this study are to (1) understand effects of nonlinearity, both in primary and secondary systems, on seismic forces in secondary systems, and (2) evaluate seismic force provisions proposed in MOTEMS that were based on linear elastic studies for secondary system considering effects nonlinearity. Since primary systems of concern in this investigation are marine structures such as piers, wharves, and marine oil terminals, which can be idealized as single-degree-of-freedom (SDOF) systems, this study utilized a simple model with two degrees of freedom, one representing the marine structure and the other representing the ancillary component. This investigation used the SAC ground motion set consisting of 20 ground motions from 10 sites for 10% probability of exceedance in 50 years for a site in Los Angeles, California. This investigation first studies the effects of damping in the secondary system on forces in the secondary systems. This investigation led to the conclusion that the damping has negligible effects on force in the secondary system for low values of the ratio of the secondary and primary system periods (say less than 0.5) regardless of the primary system period or ratio of the mass of the secondary and primary systems. For larger values of the period ratio, however, force may be 10% to 35% higher in secondary systems with 2% damping compared to systems with 5% damping. Based on this analysis, 2% damping in the secondary system was used in this investigation. Most previous investigation on nonlinear SDF systems have been focused on seismic displacement demands. It has been found that displacement of systems with non-zero post-yield stiffness is lower than the corresponding elastic-perfectly-plastic SDF systems. However, the effects of non-zero post-yield stiffness is not clear. Therefore, this investigation next examined the effects of post-yield stiffness on system forces. It was found that very-short period system with strength lower than the strength required for it to remain elastic may experience force which may even be higher than force in the corresponding linear-elastic system. Therefore, it recommended that very-short period (or stiff) systems not be designed for strengths much lower than the elastic-level strength. While post-yield stiffness of primary system is often better known, e.g., nonlinear pushover analysis, such may not always be the case for secondary systems. Therefore, careful consideration must be given to force-based design of stiff (or short-period) secondary systems when post-yield stiffness is not known. The investigation next focused on the effects of nonlinearity in primary and secondary systems on seismic forces in secondary systems. This investigation led to the following conclusions: Nonlinearity in the primary system alone leads to: (1) significant reduction of forces in the secondary systems with Tp/Tn \u3c1.5 because nonlinearity in the primary system results in lower acceleration transmitted to the base of the secondary system, which in turn leads to lower force in the secondary system, (2) minimal reduction of forces for systems with Tp/Tn \u3e 1.5 indicating that force in very flexible secondary system is insensitive to nonlinearity in the primary system, and (3) largest reduction for systems for which Tp/Tn is close to one. These trends are essentially independent of period of the primary system. Nonlinearity in the secondary system alone leads to: (1) excessive deformation and force, which may be higher than those in corresponding linear elastic systems, for very-short period secondary system with strength lower than the strength required for it to remain elastic, i.e., Rp higher than 1.0, and (2) these trends are most prominent for lower values of u and reduce as u increases but are essentially independent of period of the primary system. It is recommended that very-short period (or stiff) secondary systems not be designed for Rp higher than 1.0. Nonlinearity in both primary and secondary systems generally reduces forces in the secondary system. The exception occurs for very stiff secondary systems, i.e., very low Tp/Tn values, where force in nonlinear secondary system exceeds that in its linear-elastic counterpart. The other trends are similar to those noted for systems with nonlinearity in the secondary systems only. Finally, this investigation evaluated the MOTEMS seismic force provisions for secondary system considering effects nonlinearity. This work led to the following conclusions and recommendations: When both primary and secondary systems are expected to remain within the linear elastic range, the MOTEMS simplified and alternate formula may significantly underestimate the force in the secondary system for the period ratios 0.5 \u3cTp/Tn\u3e1.5 . Therefore, it is recommended that engineers avoid systems within this period range. When both primary and secondary systems are expected to remain within the linear elastic range, the MOTEMS simplified formula leads to significant overestimation which can exceed 100% for period ratios Tp/Tn\u3c 0.5 or Tp/Tn\u3e1.5 but the alternate formula reduces this overestimation and generally provides forces that are very close to those from response history analysis. When the secondary systems are expected to responds beyond the linear elastic range, both the simplified and alternate MOTEMS formulas may lead to significant underestimation of forces in the secondary system even for period ratios Tp/Tn\u3c 0.5 . Therefore, it is recommended that either engineers are cautioned against designing secondary systems in this period range for forces much lower than those required to remain linear elastic. The higher forces in nonlinear secondary system with period ratio Tp/Tn\u3c 0.5 may occur in secondary systems with non-zero post-yield stiffness. Therefore, engineers are also cautioned to design secondary systems with post-yield stiffness to be as close to zero as possible. The MOTEMS alternate formula reduces overestimation or provides very good estimates of forces in the secondary systems compared to the simplified formula. The MOTEMS alternate formula is preferable when information on period ratio, Tp/Tn is available

Effects of Nonlinearity in Primary Systems on Acceleration in Secondary Systems: Piers, Wharves, and Marine Oil Terminals

This investigation examines the effects of nonlinearity in the primary system of the coupled primary-secondary systems on accelerations in the secondary systems during seismic loading. The coupled primary-secondary systems considered in this investigation are those typically found in piers, wharves, and marine oil terminals. This investigation first examines the effects of nonlinearity in the primary system on acceleration at the point of attachment of the secondary system to the primary system and found that: The acceleration at the point of attachment of the secodnary system to the primary system decreases with increasing level of nonlinearity in the primary system. This occurs because yielding in the primary system limits accelerations that can transmit through it. The recommendation by Goel (2017a) provides very good estimate of the acceleration at the point of attachment of the secondary system to the primary system in coupled primarysecondary systems when the primary systems remains linear elastic. However, it provides increasingly conservative estimate of the acceleration with increasing nonlinearity in the primary system. The recommendations in ASCE 7-10 significantly over-predict accelerations at the point of attachment of the secondary system. The level of over-prediction increases with increasing level of nonlinearity in the primary system and period of the primary system. This investigation next examined the effects of nonlinearity in the primary system on amplification of the acceleration in the secondary system due to its flexibility and found that: The trends in amplification of acceleration in the secondary system due to its flexibility of linear-elastic system no longer apply when the primary system is deformed beyond the linear elastic range. In particular, amplification of acceleration tends to be much larger when period of the secondary system is longer than period of the primary system and this difference increases with increasing level of nonlinearity in the primary system. This occurs because the effective period of the primary system elongates due to its nonlinearity and thereby reduces the effective period ratio, which has the effect of increasing amplification of acceleration in the secondary system. The nonlinearity in the primary system has minimal effect on amplification of acceleration in the secondary system when period ratio is less than 0.6. For such systems, recommendation by Goel (2017a) may be used to accurately estimate amplification of acceleration in the secondary system when the primary system is expected to be deformed beyond the linear elastic range. Finally, this investigation studied the effects on nonlinearity in the primary system on acceleration in the secondary system and found that: The recommendation in the ASCE 7-10 document for flexible secondary system generally lead to significant over-prediction of acceleration in the secondary system. The level of over-prediction increases with increasing level of nonlinearity in the primary system and increasing period of the primary system. The recommendation in the commentary of the ASCE 7-10 document also leads to overprediction, although not as large as that from the recommendation in the main body of the ASCE 7-10 document, of acceleration in the secondary system. The level of over- ii prediction increases with increasing level of nonlinearity in the primary system and increasing period of the primary system. The recommendation by Goel (2017a) provide a reasonably good estimate of acceleration in the secondary system over the entire range of vibration period of the primary system when the primary system remains in the linear elastic. However, this recommendation provides slight over-prediction when the primary system deforms beyond the linear elastic range. The recommendation in ASCE 7-10 document and by Goel (2017a) were developed based on studies of linear-elastic systems. The current investigation, which considers nonlinearity in the primary system, indicates that recommendations based on linear-elastic systems lead to conservative estimates of accelerations in secondary system even when the primary system in the coupled primary-secondary system is deformed beyond the linear-elastic range. Based on findings in this investigation, it is recommended not to design coupled primary secondary systems with period ratio between 0.6 and 1.4 and secondary systems weighing less than 20% of the primary system. For such cases, secondary systems may experience excessive accelerations that may equal to or exceed eight times the peak ground accelerations due to strong coupling between primary and secondary systems