Buildings with high seismic risk. Unsafe Buildings

Transcription

1 Buildings with high seismic risk Unsafe Buildings

2 AN EQUIVALENT LINEARIZATION PROCEDURE FOR DISPLACEMENT-BASED SEISMIC ASSESSMENT M. Selim GÜNAY and Haluk SUCUOĞLU Middle East Technical University Ankara, Turkey

3 A displacement-based equivalent linearization procedure combining the advantages of Linear elastic analysis: 3D, multi-modal, conventional Capacity analysis: reliable estimation of maximum forces received by members and components

4 EQUIVALENT LINEARIZATION PROCEDURE Linear Elastic Demand Analysis Capacity Analysis Equivalent Linear System with Reduced Stiffness Linear Elastic Analysis of the Equivalent Linear System Decision on the Seismic Performance Based on Member Chord Rotations

5 A) DEMAND ANALYSIS 3D modal spectrum analysis Cracked section stiffnesses Internal forces and chord rotations at member ends Directions of the first mode along seismic excitation prevail

6 B) CAPACITY ANALYSIS STEP 1 : Moment Capacities of Beams STEP 2 : Axial Forces in Columns STEP 3 : Moment Capacities of Columns STEP 4 : BCCR values at the Joints Correction of Beam End Moments STEP 5 : Prediction of Potential Yielding Member Ends Determination of Base Shear Capacity

7 CAPACITY ANALYSIS Step 2 : Calculation of the Axial Forces in Columns Linear Elastic Analysis N G Limit Analysis N EQ N G N EQ Linear Elastic Analysis N G + N EQ M GI q M GJ Limit Analysis M CI + M GI M CJ - M GJ M CI q M CJ + = N G N G N EQ N EQ N EQ - N G N EQ + N G M CJ - M GJ M CI + M GI M CJ - M GJ V J V I V J N EQ

8 CAPACITY ANALYSIS Step 2 : Calculation of the Axial Forces in Columns Vertical components of the strut forces should be considered in the calculation of axial forces Ny F Step 3 : Calculation of the Moment Capacities of Columns N N G + N EQ M C M

9 CAPACITY ANALYSIS Step 4 : Calculation of BCCR Values at the Joints M CU F M CL M CR BCCR = M M CL CU + M + M CR CB M CB BCCR < 1 BCCR > 1 No modification for beam-end moments Beam end moment capacities are divided by BCCR Step 2 : Recalculation of the Axial Forces of Columns Step 3 : Recalculation of the Moment Capacities of Columns Step 4 : Recalculation of BCCR Values at the Joints

10 CAPACITY ANALYSIS Step 5 : Prediction of the Potential Yielding Member Ends BCCR > 1.10 Column ends BCCR < 0.90 Beam ends 0.90 BCCR 1.10 Column & Beam Ends Determination of the Base Shear Capacity V y h M cap V y N EQ

11 EQUIVALENT LINEAR SYSTEM Determination of the Final Distribution of Yielding Member Ends DCR=Force demand to capacity ratio at the member end DCR > 1 DCR < 1 Member end yields Member end does not yield Reduction of Moment of Inertia of a Member M M e M M e M y2 M eff M y k k M y1 k θ y θ e = θ in CR k θ y1 θ e = θ in θ y2 CR Relation between moment and chord rotation when both ends yield Relation between moment and chord rotation at the non-yielding end when only one end yields

12 EQUIVALENT LINEAR SYSTEM Reduction of Moment of Inertia of a Member Case No yielding Reduced Moment of Inertia I cr Yielding at one end Icr DCR Y Yielding at both ends Icr MAX (DCRI,DCR J)

13 δ LINEAR ELASTIC ANALYSIS OF THE EQUIVALENT SYSTEM Modal spectrum analysis of the equivalent linear system V V e V eq k o k 1 δ e δ in? Chord rotations < Chord rotation limits Damage states of members? Maximum shear force < Shear capacity of the member

14 DECISION on SEISMIC PERFORMANCE Base shear capacity Distribution of yielding member ends Damage states of members

15 CASE STUDY BUILDINGS The equivalent linearization procedure was implemented on three buildings CASE STUDY I : EIGHT STORY BUILDING AT CEYHAN CASE STUDY II : FOUR STORY BUILDING AT DINAR CASE STUDY III : FIVE STORY BUILDING AT DUZCE

16 CASE STUDY BUILDINGS A Four Five Eight Story Building B C D E y x F

17 RESULTS For comparison with pushover analysis, only the first mode is taken into account Axial Forces in Columns Label AF Pushover (KN) (1) AF Estimated (KN) (2) Ratio (2/1) MC Pushover (KNm) (1) MC Estimated (KNm) (2) Ratio (2/1) C C C C C C C D D D D Five Story Building at Düzce

18 RESULTS Axial Forces in Columns Label AF Pushover (KN) (1) AF Estimated (KN) (2) Ratio (2/1) MC Pushover (KNm) (1) MC Estimated (KNm) (2) Ratio (2/1) B B B B B B A A A A A A Four Story Building at Dinar

19 RESULTS Base Shear Capacities CASE Pushover (KN) Estimated (KN) Estimated / Pushover Eight Story Building Four Story Building Five Story Building Y Five Story Building X

20 RESULTS Distributions of Yielding Member Ends Pushover Equivalent Linearization Procedure Frame A Frame C Frame D Frame B Frame A Frame C Frame D Frame B Eight Story Building at Ceyhan

21 RESULTS Distributions of Yielding Member Ends Pushover Equivalent Linearization Procedure FRAME B FRAME A Four Story Building at Dinar

22 RESULTS Distributions of Yielding Member Ends Pushover Equivalent Linearization Procedure Frame C Five Story Building at Düzce Frame D

23 RESULTS Chord Rotations Five Story Building at Düzce: X Direction Model (Beams) CR (Elastic Analysis w/o Stiffness Reduction) CC = beams adjacent to columns beams adjacent to shearwalls CR (Equivalent Linear Procedure) CC = beams adjacent to columns beams adjacent to shearwalls CR (Pushover) CR (Pushover) No reduction in stiffness Reduction in stiffness

24 RESULTS Chord Rotations Five Story Building at Düzce: X Direction Model (Columns) CR (Elastic Analysis w/o Stiffness Reduction) CC = columns shearwalls CR (Equivalent Linear Procedure) CC = columns shearwalls CR (Pushover) CR (Pushover) No reduction in stiffness Reduction in stiffness

25 RESULTS Chord Rotations Eight Story Building at Ceyhan CR (Equivalent Linear Procedure) beams adjacent to columns beams adjacent to shearwalls CC= CR (Equivalent Linear Procedure) columns shearwalls CC= CR (Pushover) CR (Pushover) Beams Columns

26 RESULTS Chord Rotations Four Story Building at Dinar CR (Equivalent Linear Procedure) CC= CR (Equivalent Linear Procedure) CC= CR (Pushover) CR (Pushover) Beams Columns

27 RESULTS Chord Rotations Five Story Building at Düzce (Y Direction Model) CR (Equivalent Linear Procedure) beams adjacent to columns beams adjacent to shearwalls CR (Pushover) CC = CR (Equivalent Linear Procedure) columns shearwalls CC = CR (Pushover) Beams Columns

28 CONCLUSIONS Predictions of base shear capacity, axial forces and moment capacities of columns, distributions of yielding member ends and chord rotations obtained with the equivalent linearization procedure are sufficiently accurate. Conventional linear elastic analysis (simple, standard and familiar) Errors are small compared to true nonlinear (pushover) analysis Equivalent linearization procedure may serve as a simple seismic assessment tool as an alternative to nonlinear analysis.

29 THANK YOU