Nonlinear Drift Demands on Moment-Resisting Stiff Frames
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1 NATO SfP977 Seismic Assessment and Rehabilitation of Existing Buildings CLOSING WORKSHOP ĐSTANBUL MAY JUNE 5 Nonlinear Drift Demands on Moment-Resisting Stiff Frames Aslı Metin and Department of Civil Engineering Middle East Technical University
2 Introductory remarks A realistic seismic performance evaluation requires the estimation of deformation demands associated with the lateral strength capacity of the system for a given seismic hazard. Choice of deformation demand measure depends on the selected performance level at a given seismic hazard.
3 Drift related demand measures Maximum roof and interstory drift, variation of maximum story drift along the building height are useful if the performance targets of interest are related to downtime and monetary losses. Estimation of these parameters are still challenged by many factors; record to record variability, complex nonlinear structural behavior, intricate relation between the structure and ground-motion.
4 Present state of practice Reduce MDOF into an equivalent SDOF system using NSPs (pushover) Determine the equivalent SDOF maximum response from an approximate procedure (DCM, CSM, MADRS etc) or directly from nonlinear response history analysis. From this information extrapolate the MDOF deformation demands using empirical MDOF SDOF relationships
5 Objective Using a total of ground motions and 8 moment-resisting frames (MRFs) of different story levels Variation of maximum roof and maximum interstory drift; height-wise variation of story drift for MRFs Adequacy of first mode approach in describing the expected drift demands on stiff MRFs. Verification of a new procedure to estimate the maximum interstory drift ratio (MIDR) for MRFs.
6 Ground-motions soil site (NEHRP C and D) records 5.7 < M < km < d <.5 km Records without pulse signals Ground-motions are divided into two equal bins to represent different seismic hazard
7 Median spectra 5 GROUP I Group I 5 GROUP II Group II PSA (cm/s ) 5 PSA (cm/s ) Period (s) Period (s) On average, Group I ground motions represent a higher hazard level el
8 Frame models Smoothed spectra for the ground-motion bins are used to design MRFs of -, 5-, 7- and 9-story levels that comply the recent codes Model frames are special MRFs No lateral stiffness reduction along the height for Group I frames Uniform lateral stiffness reduction along the height for Group II frames
9 Global capacity envelopes.6 GROUP I Pushover Curves - Group I.6 GROUP II Pushover Curves - Group II Base Shear Coefficient.5.. story 5 story 7 story 9 story Base Shear Coefficient.5.. story 5 story 7 story 9 story Roof Displacement (cm) Roof Displacement (cm) Pushover analysis using height invariant inverse triangular loading Fundamental period range is approximately n SPECIAL STIFF MOMENT- RESISTING FRAME
10 Nonlinear RHA vs. Capacity envelopes Group I story - Group I 5 story - Group I. 7 story - Group I 9 story - Group I.5 Base Shear Coefficient.. Base Shear Coefficient. Base Shear Coefficient Base Shear Coefficient 6 8 Roof Displacement (cm) Roof Displacement (cm) Roof Displacement (cm) Roof Displacement (cm) story - Group II 5 story - Group II Group II 7 story - Group II 9 story - Group II Base Shear Coefficient.. Base Shear Coefficient. Base Shear Coefficient Base Shear Coefficient Roof Displacement (cm) Roof Displacement (cm) Roof Displacement (cm) Roof Displacement (cm)
11 Nonlinear RHA: Maximum roof versus maximum interstory drift MIDR (%).6. GROUP I MRDR vs. MIDR - Inelastic - MIDR (%).6. GROUP II MRDR vs. MIDR - Inelastic story 5 story 7 story 9 story Series MRDR (%).8.6. story 5 story 7 story 9 story Series MRDR (%) MIDR =.6( e.5mrdr ) (Stiff MRFs conforming the codes with T <. s and R < 7)
12 Definition of R.6 Elastic force level, F e Lateral Force R = F e /F y Yield force level, Capacity curve from pushover and its bilinear idealization Design force level Elastic displacement Yield 5 displacement Lateral Displacement
13 Nonlinear RHA: Maximum roof & interstory drifts as a function of R R GROUP I story 5 story 7 story 9 story R GROUP I story 5 story 7 story 9 story Inelastic to elastic maximum roof drift ratio as a function of R R MRDR ie /MRDR e GROUP II story 5 story 7 story 9 story R MIDR ie /MIDR e GROUP II story 5 story 7 story 9 story Inelastic to elastic maximum interstory drift ratio as a function of R MRDR ie /MRDR e MIDR ie /MIDR e
14 Nonlinear RHA: Typical variation of maximum story drifts Group I: 7 story GROUP I Maximum Story Drift Ratio (%) Group I: 9 story GROUP I Maximum Story Drift Ratio (%) Group II: 7 story GROUP II Maximum Story Drift Ratio (%) Group II: 9 story GROUP II Maximum Story Drift Ratio (%). The overall behavior resembles first mode dominant behavior. The maximum interstory drift variation shows more scatter particularly for Group II frames
15 Dispersion (COV) COV.6.5 story 5 story Group I Group II story COV.6.5 Group I Group II 5 story.... Story Level 5 Story Level COV.6 Group I Group II 7 story COV.6 Group I Group II 9 story Story Level Story Level 7 story 9 story
16 Φ Γ Φ Γ Statistics to relate SDOF to MDOF deformations using first mode Relates elastic MDOF - SDOF Group I Group II Fractiles,e x,e top,e /S d,e top,i /S d,i,e x,e top,e /S d,e top,i /S d,i -story 5% 8% story 5% 8% story 5% 8% story 5% 8% good agreement agreement is not as for median inelastic median good as in Group I ratios are smaller
17 Lateral deformation profiles 9 9 Story - Elastic story - Inelastic Story Displacement (cm) Story Displacement (cm) Concentration of plastic hinging at lower levels results lesser roof drifts in nonlinear behavior
18 Statistical evaluation First mode approach: MIDR = h [ Γ φ S ( T, 5%, )] MRDR =,, e d, i, ideal ξ H e = R [ ] n n Γ φ φ S ( T, ξ 5%, ), e, e, e d, i, ideal = R max RHA using idealized bilinear curves from PO particular for each model New procedure: MIDR( T, ξ, ρ) = γ ( T, ρ) γ ( T, ρ) GSDRsh ; γ = c + ; γ GSDR sh πh =.7 sin H S d, i ( T, ideal, ξ = H c T 5%, R) = e Regression expressions using first mode behavior ( c + c / T )
19 Error statistics (Error = Approximate/Exact) st mode approach MRDR st mode approach MIDR New method MIDR Group I Error Group II Group I Error Group II Group I Error Group II 5% 5% 5% 5% 5% 5% -story.. -story story..7 5-story.9. 5-story.9. 5-story..7 7-story.. 7-story story..5 9-story.9. 9-story story..
20 Conclusions Variation of story drifts are sensitive to the structural configuration. First mode approach, on average, tends to overestimate the roof drift for stiff MRFs. Maximum interstory drift cannot be estimated successfully by this approach. A new procedure that has been tested on elastic frames seems to be promising for nonlinear behavior.
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