Task 3—Development and verification of simplified design tools Juan Vargas – Junior in Civil Engineering – Vice President SCU SHPE Mark Aschheim – Professor, Structural/Earthquake Engineering

Effect of Hysteresis Type on SDOF Response Rocking Sliding  MM  V u FS V = 2 FS V = 5 SDOF simulations to evaluate effect of “element” hysteresis type on peak displacement response. For different ground motions and select short, medium, and long periods: Given Sa (or R), what ductility (displacement) demands result? Alternatively, what Sa (or R) to get ductility demands of 2 and 6? Evaluate vulnerability to overturning (tipping over) relative to conventional oscillators with P-Delta (use FEMA 440 R max equation).  Peak displacement response ratios at select periods (e.g. C x )  To what extent do initial stiffness and hysteretic type matter?  Strategies to select elements/behavior to reduce response amplitudes  May suggest scaling ground motions to match peak displacement of appropriate inelastic oscillator PmPm PmPm PmPm u

Combinations of Elements Elements… Combinations…. Are there simple methods to estimate peak displacement response for parallel combinations of elements (hysteretic types) Repeat for series combinations. Can response with series combinations be chaotic? If so, under what conditions? Validate use of “equivalent SDOF” oscillators for estimating displacement response of MDOF systems composed of mixed hysteretic types. Is it necessary to adjust first mode parameters (  1 and  1 ) for change in displaced shape due to rocking/sliding? PmPm

Development of Design Approach Can we apply Yield Point Spectra with plastic mechanism approach to design structure and foundation system? Or to structure given a foundation? Perhaps define yield point parametrically for curvilinear hysteretic behavior? Perhaps retain conventional elastic spectra and apply new C x coefficients to derive inelastic spectra? What performance limits to design for, particularly for foundations? Admissible Yield Points Inadmissible Drift Limit Ductility Limit Inelastic Spectra (Yield Point Spectra) for conventional (bilinear) hysteresis  M M   M Composite Hysteretic Behavior