1. 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

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: 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

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.