Development of a Real-Time Test Method for Structures

Application of Pushover Analysis to the Design of Structures Containing Dissipative Elements Martin S. Williams1 and Denis E. Clment2 University of Oxford, UK 2 Thomas Jundt Civil Engineers, Geneva, Switzerland 1 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: Cross brace Knee element 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:

Short cantilever shear stiffness Brace Brace Connecting bracket Knee element Connection stiffness Rigid offset Truss element axial stiffness Beam element flexural stiffness Hysteresis response of model Element properties chosen semi-empirically Comparison with full-scale cyclic test data: 600 Force (kN) 300 0 -300 Physical test Drain-2DX -600 -20 -10 0 Deflection (mm) 10

20 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: Knee braced bay 5.2m ELEVATION: 5.2m ELEVATION: 5.2m 6m 6m 6m Pushover analysis EC 8: F modal and uniform load patterns simplify pushover curve to elastic-perfectly plastic d 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 F d 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) Comparison with EC8 spectrum, TH1-5 Typical EC8 spectrum-compatible time history 3 0.5 0 -0.5 -1 0 5 10 15 20 Acceleration (g)

Accn (g) 1 EC8 TH1 TH2 2 TH3 TH4 TH5 1 Time (s) 0 0 1 2 Period (s) 3 Pushover curves Results shown for 5-storey frame Post-yield stiffness ~16% of elastic stiffness As a result, EC8 under-estimates initial stiffness Modal load pattern 1500 Uniform load pattern 1500 1000 1000

Pushover 500 Pushover 500 EC8 EC8 FEMA356 FEMA356 0 0 0 50 100 Displacement [mm] 150 0 50 100 Displacement [mm] 150 Estimated roof displacements 10-storey KBF EC8 Modal EC8 Uniform FEMA Modal

10-storey MRF FEMA Uniform ATC Modal ATC Uniform Multi-modal 5-storey KBF 0.8 1 1.2 1.4 1.6 Roof disp from pushover Mean roof disp from TH analyses 1.8 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: 0.15g 0.35g Yielded knee element 0.5g Plastic hinge Element yielding 5-storey frame EC8 pushover analysis under uniform loading: 0.15g

0.35g Yielded knee element 0.5g Plastic hinge 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 EC 8 FEMA 356 ATC 40 5 5 5 4 4 4 3 3 3 2 2 2

1 1 1 0 0 0 0.5 1 Storey drift (%) 0 0 0.5 Storey drift (%) 1 0 0.5 Storey drift (%) Time history analysis: Mean Mean +/- st. dev. Pushover analysis: Uniform Modal

1 Inter-storey drifts under design earthquake 10-storey MRF (i.e. before retrofit): EC8 FEMA 356 ATC 40 Modal Pushover 10 10 10 10 9 9 9 9 8 8 8 8 7 7 7

7 6 6 6 6 5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 1

1 1 1 0 0 0 1 2 0 0 Drift (%) 1 2 0 0 Drift (%) 1 2 0 Drift (%) 1 Drift (%) Time history analysis: Mean

Mean +/- st. dev. Pushover analysis: Uniform Modal 2 Inter-storey drifts under design earthquake 10-storey KBF (i.e. after retrofit with knee elements): EC8 FEMA 356 ATC 40 Modal Pushover 10 10 10 10 9 9 9 9 8 8 8 8

7 7 7 7 6 6 6 6 5 5 5 5 4 4 4 4 3 3 3 3 2 2

2 2 1 1 1 1 0 0 0 1 2 0 0 Drift (%) 1 2 0 0 Drift (%) 1 2 0 Drift (%)

1 Drift (%) Time history analysis: Mean Mean +/- st. dev. Pushover analysis: Uniform Modal 2 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.