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Application of Pushover Analysis to the Design of Structures Containing Dissipative Elements Martin S. Williams 1 and Denis E. Clément 2 1 University of.

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Presentation on theme: "Application of Pushover Analysis to the Design of Structures Containing Dissipative Elements Martin S. Williams 1 and Denis E. Clément 2 1 University of."— Presentation transcript:

1 Application of Pushover Analysis to the Design of Structures Containing Dissipative Elements Martin S. Williams 1 and Denis E. Clément 2 1 University of Oxford, UK 2 Thomas Jundt Civil Engineers, Geneva, Switzerland 13 th 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) 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 Seismic energy dissipated through hysteresis of short, replaceable knee elements:

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

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.


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