13 th World Conference on Earthquake Engineering Vancouver, August 2004

1. Application of Pushover Analysis to the Design of Structures Containing Dissipative ElementsMartin S. Williams1 and Denis E. Clément21 University of Oxford, UK2 Thomas Jundt Civil Engineers, Geneva, Switzerland 13th World Conference on Earthquake Engineering Vancouver, August 2004

2. Outline • Introduction to knee braced frames • Modelling using Drain-2DX • Five and ten-storey frame designs • Pushover and time-history analyses • Results • Conclusions and future work

3. Introduction to knee braced frames (KBFs) Seismic energy dissipated through hysteresis of short, replaceable knee elements: Knee elements can be designed to: • Yield early, maximizing protection to main frame • Yield in web shear rather than flexure • Remain stable under large non-linear excursions

4. Modelling a knee element using Drain-2DX An assemblage of standard truss and beam elements was used to represent observed shear, flexural and axial behaviour:

5. Hysteresis response of model • Element properties chosen semi-empirically • Comparison with full-scale cyclic test data:

6. Frame designs Designed to EC8, PGA = 0.35g Five-storey frame – designed as KBF: Ten-storey frame – designed as ductile MRF, then retrofitted: PLAN: PLAN: ELEVATION: ELEVATION:

7. Pushover analysis • EC 8: • modal and uniform load patterns • simplify pushover curve to elastic-perfectly plastic • FEMA 356: • other load patterns (e.g. adaptive) permitted, but not used here • simplify to bi-linear with post-yield stiffness equal to   initial stiffness • ATC 40: capacity spectrum method • Modal pushover (Chopra and Goel, 2002): combine results of pushovers using first few modal load patterns

8. Time history analyses • 30 time-histories generated using SIMQKE • Compatible with EC8 Type 1 spectrum, soil type C • Analysed using DRAIN-2DX (Newmark implicit integration scheme)

9. Pushover curves • Results shown for 5-storey frame • Post-yield stiffness ~16% of elastic stiffness • As a result, EC8 under-estimates initial stiffness

10. Estimated roof displacements

11. Element yielding • In 5-storey frame, all knee elements yielded and all main elements remained elastic under design earthquake • In 10-storey retrofitted frame, limited plasticity occurred in main frame under design earthquake • e.g. 5-storey frame - EC8 pushover analysis under modal loading:

12. Element yielding • 5-storey frame – EC8 pushover analysis under uniform loading: • Time history analyses: • first knee element yield at around 0.08g • no hinges in main frame elements below 0.56g

13. Inter-storey drifts under design earthquake • 5-storey KBF

14. Inter-storey drifts under design earthquake • 10-storey MRF (i.e. before retrofit):

15. Inter-storey drifts under design earthquake • 10-storey KBF (i.e. after retrofit with knee elements):

16. Conclusions • A Drain-2DX knee element model capable of representing shear, flexural and axial behaviour has been developed and validated. • Pushover analyses of 5 and10-storey knee braced frames showed that they possess high ductility (~6) and post-yield stiffness (~16%). • In time-history analyses, knee elements began to yield at just 0.08g but remained stable up to 0.56g. • Use of pushover analysis does not necessarily lead to optimal design. Multi-modal pushover offers some advantages in this respect. • In comparison with time-history analyses, FEMA 356 pushover approach gave most consistent results, EC8 approach appears highly conservative for this type of structure.