13th World Conference on Earthquake Engineering Vancouver, August 2004 Application of Pushover Analysis to the Design of Structures Containing Dissipative Elements Martin S. Williams1 and Denis E. Clément2 1 University of Oxford, UK 2 Thomas Jundt Civil Engineers, Geneva, Switzerland 13th World Conference on Earthquake Engineering Vancouver, August 2004

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

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

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:

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

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:

Pushover analysis EC 8: FEMA 356: ATC 40: capacity spectrum method 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

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)

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

Estimated roof displacements

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:

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

Inter-storey drifts under design earthquake 5-storey KBF

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

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

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.