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Seismic vulnerability assessment

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Seismic vulnerability assessment Powered By Docstoc
					              ARISTOTLE UNIVERSITY OF THESSALONIKI
              CIVIL      ENGINEERING       DEPARTMENT
              LABORATORY   OF   REINFORCED   CONCRETE




     3D
 PUSHOVER
 ANALYSIS:                                           COMPILED
THE ISSUE OF
                                              GREGORY G. PENELIS
  TORSION
                                               ANDREAS J. KAPPOS


12th European Conference on Earthquake Engineering
           LONDON – SEPTEMBER 2002
INTRODUCTION
 Torsional strain is often observed on damaged
  buildings after earthquakes
 This effect is more transparent in the nonlinear

  response of stuctures (I.e. severe damage)
 The nonlinear analysis of buildings is gradually
  being introduced in codes and guidelines (ATC-
  40, FEMA 273 & 356, HAZUS, RISK-UE etc)-
  mainly by utilising the more perceptible by the
  practicing engineer PUSHOVER ANALYSIS.
INELASTIC TORSION TO DATE:
     STATE OF THE ART
   Two “categories” of reports:
    (Α) The theoretical study of inelastic torsion
    (Β) The design of torsionally restrained new buildings
    From these:
    The static eccentricity is modified as the elastic center CR
    shifts towards the center of shear CS. (PAULAY).
    The limit surface BST (BASE SHEAR TORSION) defined
    by triads of points corresponding to different failure
    mechanisms (Chopra).
From the state of the art the issue of
nonconvergence between static nonlinear analysis
and dynamic nonlinear analysis is obvious.
- All approaches seem to be case sensitive to the
excitation
- The modal loads (elastic) seem to be the load
vector approximating the dynamic nonlinear
analysis better
           SCOPE OF WORK
 The primary results of a 3D static nonlinear
 analysis methodology for the assessment of the
 vulnerability of structures which converges with
 the results of 3D dynamic nonlinear analysis.
Α) Definition of an appropriate load vector for the
 static nonlinear analysis
Β) Definition of the equivalent single dof oscillator
 for the spectral assessment of the vulnerability
 under a specific excitation.
C) The introduction of the excitation.
          PRINCIPLES OF THE
           METHODOLOGY
Α) LOAD      VECTOR: One that causes the same
  displacement and torque on a structure using static
  linear analysis as the ones calculated by elastic spectral
  dynamic analysis (icluding all important modes). A
  kind of modal loads…
Β) EQUIVALEN SDOF OSCILATOR: (For translation &
  torque) The methodology of Saidi& Sozen (1981)
  which defined the sdof oscillator for translation was
  modified to take into account the torsional effect.
C) SPECTRA: Mean normalised inelastic acceleration-
  displacement spectra (ADRS)
        ONE STOREY BUILDING (1)
1)   Selection of accelerograms (3-5) which are normalised
     (acc. Pga or Ι)
2)   Calculation of the mean elastic spectra of the selected
     accelerograms and execution of spectral dynamic
     analysis in order to define the elastic translation and
     rotation of the center of mass.
3)   The displacement vector of step 2 is used as a constraint
     in order to calculate the corresponding load vector.
4)   Calculation of the modification factors for the sdof
     oscillator..
      ONE STOREY BUILDING (2)
ψδ = P1/M1                                   (1)
ψΜ = -1                                      (2)
c1 = (m  uy22 + Jm  θz22) / m uy2         (3)
c2 = (uy2  ψδ + ψM  θz2 )/ ψδ              (4)
m* = muy2                                   (5)
Where
ψδ, ψΜ: parameters related to the modal loads,
P1, M1 : the load vector defined by step 3
c1, c2: parameters for the tranformation of a mdof to a
    sdof system,
In general parameter c1 corresponds to displacements and
parameter c2 to loading.
υy1       static   elastic        P1   normalization                              uy2 = 1

  }                              }                                   }                         }
θz1   Analysis with constraint    M1   of displacement vector                     θz2 =θz1/uy1

                                                       Μέσο υάσμα επιταχύνσεων


                                             12
                                              10
                                           )
                                           2
                                           Ac 8
                                           c
                                               6                                 Elastic
                                           (m/
                                           se 4
                   CM                      c 2
                                              0
                                                   0    1         2        3
                                                              Τ(sec)




                                         Translation – Rotation:υy1, θz1

                     Excitation
             ONE STOREY BUILDING (3)
5)   Pushover analysis with the load vector at Center of Mass (P1,
     M1). The P-δ curve of the multi dof -> single dof using c1, c2
     Ρ* = c2 p/m*         δ* = c1 uy      (6)
6)   For the selected accelerograms the mean inelastic normalised
     spectra (A-D) are calculated. The demand is defined for several
     ductilities (I.e. Fajfar-Dolsek, 2000)
7)   The P-δ curve of the sdof is plotted on the demand spectraand the
     performace point is defined. This is the target displacement of
     the sdof -> u*targ.
8)   The target displacement of the mdof is calculated
       utarg = u*targ / c1                  (7)
     and the target rotation (Rtarg) as it is defined by the pushover
     analysis (P-θ curve) of the mdof for the target dispacement utarg
                    RESULTS - COMPARISON
     Σηρεπηικά μη δεζμευμένο κηίριο                        Σηρεπηικά δεζμευμένο κηίριο
                                                         Torsionally Restrained
     Torsionally Unrestrained
                                                                             Τ3


                                      Τ2                                                 Τ2
Τ1                                                  Τ1




                                                                             Τ3




                                           Στ.4: Μονώροθο κηίριο
Α) Comparison of the P-δ and Ρ-θ curves of the pushover analysis
   (steps 1-3 &5) with the corresponding dynamic envelope
Β) Calculation of the target displacement and rotation using pushover
   analysis with inelastic spectra and comparison with the results of
   nonlinear time history analysis.
                                  Α) P-δ and Ρ-θ curves
          The dynamic envelope is calculated for the 1st set
           of 4 accellerograms using:
           T.UR :40 time history nonlinear analysis
           T.R. : 80 time history nonlinear analysis
       1)Lp-Tr e s ur e Is l-Tr . -κανονικοποιημένο                 4)Kobe -HYOGO KEN - l-κανονικοποιημένο


4                                                            4
2                                                            2
0                                                            0
-2 0            5               10              15      20   -2 0     5        10         15        20        25   30

-4                                                           -4
-6                                                           -6


           2)L P-L ick -lab -tr -κανο νικο πο ιη μένο                3)Nor thr idge -Ne w hall Fir e Station-L-
                                                                                κανονικοποιημένο
6
4                                                            6
                                                             4
2
                                                              2
0
                                                              0
-2 0            5               10              15      20
                                                             -2 0          5              10             15        20
-4                                                           -4
-6                                                           -6
                                                                        TORSIONALLY UNRESTRAINED
                                                                P o ly n o m ia l f it t o 4 0 in e la s t ic t im e h is t o r y d y n a m ic a n a ly s e s a n d
                                                                                       c o m p a r is o n w it h t h e p u s h o v e r c u r v e   Torsionally Unrestrained Building (T.U)                                                                                                                                 Torsionally Restraine
                                                                                                                                                                                                                                            P o ly n o m ia l f it t o 4 0 in e la s t ic t im e h is t o r y d y n a m ic a n a ly s e s a n d
                                                                                                                                                                                                                                                                  c o m p a r is o n w it h t h e p u s h o v e r c u r v e
                                                                                                                     P -δ c ur ve
                                                                                                                                                                                                                                                                                         P -θ c ur ve

                           2500
                                                                                                                                                                                                                          2500


                           2000
                                                                                                                                                                                                                          2000
                                                                                                                                                                                                                                                                  W2
             P ( Um a x ) ( k N)




                                                                                                                                       W1                                                                                                                                                                                  W1




                                                                                                                                                                                                            P ( Um a x ) ( k N)
                           1500
                                                                                                                                                                                                                          1500



                           1000                                                                                                                                                                                           1000



                                          500                                                                                                                                                                                     500



                                                     0                                                                                                                                                                              0

                                                     0 .0 0 0          0 .0 0 2           0 .0 0 4              0 .0 0 6              0 .0 0 8         0 .0 1 0             0 .0 1 2        0 .0 1 4                               0 .0 E+ 0 0      2 .0 E- 0 4         4 .0 E- 0 4      6 .0 E- 0 4         8 .0 E- 0 4        1 .0 E- 0 3         1 .2 E- 0 3

                                                                                                                            δ (m m )                                                                                                                                                         θ (r ad )

                                                                                  L P- T r e s .Is l.                          L P- L ic k L a b                         No-New h                                                                           L P- T r e s .Is l.                 L P- L ic k L a b                   No-New h

                                                                                  K o b - H y o g .K e n                       Pu s h o v e r                            Po ly n o m ia l 3 r d                                                             K o b - H y o g .K e n              Pu s h o v e r                      Po ly n o m ia l 3 r d


                                                                                                                                                                                                                                                           Figure 4: Single storey building
                                                             TORSIONALLY RESTRAINED
                                                                         Torsionally
estrained Building o(T.U) 8 0 in e la s t ic t im e h is t o r y d y n a m ic a n a ly s e s a n d Restrained Building (T.R) to 80 inelastic tim e history dynam ic analyses and
               P o ly n m ia l f it t o
                                                                                                                     Polynom ial fit
                                                                                                                                                                                                                                                              com parison w ith the pushover curve
                                                                                     c o m p a r is o n w it h t h e p u s h o v e r c u r v e
                                                                                                           P -δ c ur ve (T.R.)
                                                                                                                                                                                                                                                                                     P-θ curve (T.R.)

                                             6000
                                                                                                                                                                                                       Τ3
                                                                                                                                                                                                                                  6000
                                             5000
                                                                                    W2                                                                                                                                            5000                                 W2
                                                                                                                                                   W1
                                                                                                                                                                                                               P (Umax)(kN)
                               P ( Um a x ) ( k N)




                                             4000                                                                                                                                                                                 4000

                                             3000                                                                                                                                                                                 3000

                                             2000                                                                                                                                                                                 2000

                                                                                                                                                                                                                                  1000
                                             1000

                                                                                                                                                                                                                                         0
                                                         0
                                                                                                                                                                                                       Τ3                               0.0E+00             2.0E-03                   4.0E-03               6.0E-03                8.0E-03                   1.0E-02
                                                         0 .0 0 0     0 .0 0 5        0 .0 1 0            0 .0 1 5         0 .0 2 0         0 .0 2 5      0 .0 3 0           0 .0 3 5      0 .0 4 0
                                                                                                                                                                                                                                                                                                θ (rad)
                                                                                                                       δ (m m )

                                                                                  L P- T r e a s .Is l.                    L P- L ic k L a b                      No-New h                                                                                         LP-Treas.Isl.                       LP-LickLab                             No-New h
                                                                                  K o b - H y o g .K e n                   Pu s h o v e r                         p o ly n o m ia l 6 th                                                                           Kob-Hyog.Ken                        Pushover                               log fit
                                                                                 Figure 4: Single storey building
    Β) TARGET DISPLACEMENT &
            ROTATION
The 4 selected accelerograms scaled to pga = 0.4g
 6% deviation in displacement and 2% in rotation for
  the torsionally unrestrained building.
 W1
                                        W2


 3.7% deviation in displacement and 6.8% in

  rotation for the torsionally restrained building.




    Pushover                       Nonlinear Dynamic
               Στ.8: Μεηαηοπίζεις και ζηροθές ηοσ κηιρίοσ
     CONCLUSIONS - COMMENTS
  The Ρ-δ and Ρ-θ curves of the pushover analysis
  approximate the dynamic envelope
 The    target displacement and rotation are
  accurately calculated for the one storey building
 The implementation for multi storey buildings is
  yet to come
Problems - Observations
Α) Adaptive pushover analysis
Change in Κ -> [Φ] -> [V, T]
                        Β) Mean inelastic normalised spectra / Highly
                        damped spectra
                                 Μ έ σ ο Ικ α ν ο τ ικ ό Φ ά σ μ α ο μ α λ ο π ο ιη μ έ ν ο
                                 Mean inelastic normalised spectra
                        12                                                                         Ela s t ic



                        10                                                                         Pu s h o v e r



                         8
Ε π ι τ . (m / se c )
2




                                                                                                   Π ο λ σ ω ν σ μ ικ ή
                                                                                                   ( d u c t.= 2 )
                         6
                                                                                Mean Ικανοτικό Φάσμαν σ μ ικ normalisation
                                                                                                   Π ο σ ω τωρίς
                                                                               Μέσο inelastic spectra λwithout ή ομαλοποίηση
                                                                                                   ( d u c t.= 1 .5 )
                         4
                                                                   12                              Π ο λ σ ω ν σ μ ικ ή
                                                                                                   ( d u c t.= 1 .7 5 )
                         2
                                                                   10
                                                                                                   Π ο λ σ ω ν σ μ ικ ή
                                                    Acc (m/sec2)




                                                                                                   ( 1 .9 )
                         0                                         8
                             0     0.01         0.02                    0.03    0.04
                                                                                                                                 Elastic
                                           Μ ε τ α τ . (m )
                                                                   6
                                                                                                                                 duct.= 1.5
                                                                   4
                                                                                                                                 duct.= 2
                        Στήμα 9: Εθαρμογή ηης μεθόδοσ ηοσ ικανοηικού θάζμαηος για ηον
                                    σπολογιζμό ηης 2
                                                   μεηαηόπιζης «ζηότο» .                                                         duct.= 4
                                                                   0
                                                                         0       0.01       0.02                0.03      0.04
                                                                                          Disp (m)
C) Inconsistency of t-h inelastic analysis?



                                                                                                                 Source
Name                              Country     Date     Depth    mb            ML          Ms       Mo            Mechanism

aftershock of Friuli earthquake   Italy         9/15/76 15 km           5.7         6.2        6.06 6.3e+017 Nm oblique
                                  Uzbekista
Gazli                             n             5/17/76 13 km           6.2         6.4        7.04 1.8e+019 Nm thrust

Tabas                             Iran          9/16/78 5 km            6.4                    7.33 1.3e+020 Nm thrust


                                                                     MEAN SMOOTHENED ADRS SPECTRA
                                                                                                                             Elastic

                                                     12
                                                                                                                             Poly. (duct.= 2)
                                                     10
                                                      8
                                                                                                                             Poly. (duct.=
                                                      6                                                                      1.5)
                                                      4
                                                                                                                             Poly.
                                                      2                                                                      (duct.=1.75)
                                                      0
                                                          0      0.05              0.1           0.15         0.2            Poly. (duct.=
                                                                                                                             1.1)
               Dynamic Envelope
                              Torsionally Unrestrained 1 storey building
                                       65 Timehistory analysis
                                              P-δ curve
    7000


    6000


    5000
                                                                                                               MaxV -> disp & rot
    4000                                                                                     maxV              Maxdisp -> V & rot
V




                                                                                             maxD
    3000


    2000


    1000


       0
           0    0.02   0.04        0.06       0.08       0.1       0.12    0.14       0.16            Torsionally Unrestrained 1 storey building
                                               Δ                                                               65 Timehistory analysis
                                                                                                                      P-θ curve
                                                                               7000


                                                                               6000


                                                                               5000


                                                                               4000
                                                                                                                                                                  maxV
                                                                           V




                                                                                                                                                                  maxd
                                                                               3000


                                                                               2000


                                                                               1000


                                                                                  0
                                                                                      0       0.002    0.004         0.006         0.008           0.01   0.012
                                                                                                                       Θ