1. Off-Diagonal 2-4 Damping Technology using Semi-Active Resetable Devices Geoffrey W Rodgers, Kerry J Mulligan, J Geoffrey Chase, John B Mander, Bruce L Deam, and Athol J Carr End Cap Cylinder Piston Seal

2. Device Design Valve a) Valves CylinderPiston b) CylinderPiston Independent two chamber design allows broader range of control laws

3. Overall Customised Hysteresis Only the 2 - 4 control law does not increase base-shear Viscous Damper 1-4 Resetable 1-3 Resetable 2-4 Resetable Resist all motion Resist motion away from 0 Resist motion toward 0 Resist all velocity

4. Semi-Active Resetable Device Model Experimental Test Results Simulink Models

5. Simplified Linear Model Less computationally expensive, with no anticipated loss of accuracy or generality 1-3 control2-4 control 1-4 control

6. Response Spectra Average response spectra for different control laws How do the different control laws perform relative to one another?

7. Reduction Factors More clearly represent reductions achieved with each control law Note the apparent invariance to the type of ground motion encountered Divide results with additional stiffness by the uncontrolled case Largest reductions seen for the 1-4 device – This device acts over a larger percentage of each cycle and will consequently have longer active strokes

8. Suite Dependence Normalise the average reduction factor from each suite to the reduction factors for all ground motions to investigate suite dependence Values close to unity across the spectrum indicates an invariance to the type of ground motion (near field vs. far field) encountered – indicating a robustness of this form of control

9. Spread of Results Log-normal co-efficient of variation or dispersion factor - Indicates the spread of the results within a ground motion suite - Largest spread is seen for the 1-4 device indicating more variability - Both the 1-3 and 2-4 device show a tighter spread

10. Structural Force The base-shear force for a linear, un-damped structure - Gives an indication of the required column strength Largest reductions for the 1-4 device – consistent with other metric Similar performance for the 1-3 and 2-4 devices

11. Base-Shear The sum of the structural force and the resetable device force - Gives an indication of the required foundation strength Only the 2-4 device reduces base shear across the entire spectrum The 1-3 and 1-4 devices increase base-shear by as much as 60% The 2-4 device provides similar reductions in displacement and structural force as the 1-3 device, and also reduces base-shear

12. Control laws compared Averaging across suites more clearly indicates the relative advantage of the control laws Structural Force Base-Shear Force 1-3 and 2-4 show similar reductions in structural force, but are outperformed by the 1-4 device Only the 2-4 device reduces base-shear, whereas both the 1-3 and 1-4 increase base-shear by as much as 60%

13. Displacement Spectral Area Numerically integrate the area under the response spectra in the seismically important T = 0.5 to 2.5 second range. An indication of the average displacement reduction factor in the constant velocity region of the spectra Fit empirical equations to estimate damping reduction factors where where C = 1.43, 1.59, and 5.75 for the 1-3, 2-4 and 1-4 devices

14. How accurate are these equations? Re-plot the displacement reduction factors, with the reduction factors from the empirical equations Although variations can be seen above T = 3.0seconds, equations are appropriate over the constant velocity region from T = 0.5 – 3.0 secs Black Line is Empirical Equation

15. ADRS Acceleration-Displacement Response Spectra Relate additional resetable stiffness to design guidelines Empirical reduction factor equations create a “standard design platform” for a structural engineer to safely and effectively add resetable devices to their design.

16. Summary The 1-4 device outperforms both the 1-3 and 2-4 device for displacement response and structural force as it acts over the full response cycle, has longer active strokes, and consequently higher energy dissipation Both the 1-3 and 1-4 devices provide a reduction in structural force and displacement response, but increase base-shear up to 60% The 2-4 device reduces both structural force and base-shear All three control laws are suite invariant indicating a robustness to the type of ground motion encountered Empirical equations to approximate reduction factors allow incorporation into accepted performance based design metrics

17. Conclusions Semi-active control enables customisation of overall structural hysteresis in novel ways not available with passive systems The most applicable control law (of the selected few presented) depends on the application New purpose designed structure Retrofit application with limited foundation strength Thus, device selection and implementation is a structural design problem rather than a control systems problem The overall approach presented can be used to develop standard design metrics for any similar novel semi-active or passive systems/devices, thus creating a bridge to the design profession and a greater likelihood of uptake.

18. Experimental Work One fifth scale building fitted with pneumatic semi-active resetable devices

19. Experimental and Analytical Comparison Reductions seen in shake table tests are close to those predicted by the analytical study

20. Acknowledgements Special thanks to Ms Kerry Mulligan and Professors Chase and Mander for their assistance with this research, as well as to our co-authors This research was funded by the NZ Earthquake Commission (EQC) Research Foundation and the New Zealand Tertiary Education Commission (TEC) Bright Futures Top Achievers Doctoral Scholarship Scheme