Published in Structural Engineering and Applied Mechanics, January 31, 2020, pages 1-53.
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 <1.5 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 > 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 <Tp/Tn>1.5 . 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< 0.5 or Tp/Tn>1.5 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< 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< 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.
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