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Seismic  Performance  of  Shear  Wall  Buildings  with  Gravity-­‐Induced  

Lateral  Demands  

Michael  Dupuis  Tyler  Best  Ken  Elwood  

Don  Anderson    

Dept.  of  Civil  Engineering    University  of  BriCsh  Columbia  

 LATBSDC  Annual  MeeAng  –  3  May  2013  

Gravity-­‐Induced  Lateral  Demand  (GILD)    on  SFRS  

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Gravity  systems  resulAng  in  GILD  

BMD  

BIG.dk  

In  design:    Vancouver,  Canada     Grand  Chancellor,  Christchurch,  New  Zealand    

Real  buildings…  

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What  FDL /Fy  will  cause  the  structure  to  experience    “much  larger”  driXs  than  predicted  by  elasAc  analysis?    

MGILD

VGILD

SDOF  Study  

Fyt

Clough  Fyc

k

a = FGILD /Fy    

FGILD  

SDOF  Study  

•  The  yield  strengths  of  the  model  were  adjusted  to  suit  the  applied  load,  FDL =  aFy  :  

Fyt =  Fy+FDL =  Fy(1+a)    

Fyc =  -­‐Fy+FDL =  -­‐Fy(1-­‐a)    

Fyt =Fy+FDL

Fyc=-Fy+FDL

F

D

Fy

-Fy

•  Applied  load  amplificaAon  factor,  b:            RaAo  of  peak  displacement  from  system  with  applied  load  to    peak  displacement  from  system  without  applied  load.  

)0()0(

max

max

=Δ≠Δ=

ααβ

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Varia>on  of  Mean b with  α  

Influence  of  reducing  nega>ve  yield  strength  

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MDOF  Study  

•  Concrete  core  walls  •  N  =  5,  10,  20,  30,  40,  50  storeys  •  Yielding  was  assumed  to  occur  within  a  plasAc  hinge  length  of  0.5lw

•  The  hinge  zone  was  assumed  to  not  exceed  the  height  of  the  first  storey  

•  Fibre  model  used  for  hinge  region  to  get  realisAc  hystereAc  response  

•  Limited  degradaAon  in  model    (except  P-­‐d)    •  Non-­‐conservaAve  assessment  of  collapse.  

•  Assumed  building  was  constructed  straight.  

MDOF  Study  

PlasAc  hinge  

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Core  Wall  Fibre  Model  

No.  Storeys  

tweb  (mm)  

tflange  (mm)  

bw  (mm)  

lw  (mm)  

f’c  (MPa)  

5   300   300   4600   4600   25  

10   300   450   6000   5500   30  

20   450   550   8000   7500   35  

30   600   700   9000   9000   40  

40   700   800   11500   10750   45  

50   800   850   13500   13750   50  

Fibre  secAon  hysteresis  examples  

-­‐150,000  

-­‐100,000  

-­‐50,000  

0  

50,000  

100,000  

150,000  

200,000  

-­‐1.0   -­‐0.5   0.0   0.5   1.0   1.5  

Moment  (kNm)  

Curvature  (rad/km)  -­‐150,000  

-­‐100,000  

-­‐50,000  

0  

50,000  

100,000  

150,000  

200,000  

-­‐1.0   -­‐0.5   0.0   0.5   1.0   1.5  

Mom

ent  (kN

m)  

Curvature  (rad/km)  

High  axial  load  on  wall  

R  =  2.0,  α  =  0.1  

Low  axial  load  on  wall  

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Models  and  MoAons  

DefiniAons  𝛼= 𝑀↓𝐺𝐼𝐿𝐷 /𝑀↓𝑦    

𝑅↓𝛼=0 = 𝑀↓𝐸  𝑚𝑎𝑥 /𝑀↓𝑦    

My  =  MEmax/R  

MGILD    

My  =  MEmax/R  

My  =  MEmax/Ra=0  MGILD    

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•  Example  –  Vancouver:  •  Ra=0  =  4.0  •  a =  0.4  

•  Higher  a =  More  slope  required  •  Taller  Structure  =  Less  slope  •  Higher  Ra=0  =  Less  slope  

Inclined  Columns  

N  =  5  

Slope  =  5.7ᵒ  

N  =  50  

Slope  =  1.7ᵒ  

CanAlevered  shear  wall    varying  axial  loads  

  𝑅↓𝛼=0 =4.0  and  𝛼=0.4  

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CanAlever  Wall  

20  storey,   𝑅↓𝛼=0 =2.0  

Coupled  Wall  

20  storey,   𝑅↓𝛼=0 =2.0  

𝛼=0.4  𝛼=0.0   𝛼=0.2  

𝛼=0.4  𝛼=0.0   𝛼=0.2  

Coupling  beam     𝑅↓𝛼=0 =4.0  

𝛼=0.4  𝛼=0.0  

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Braced  Frames  •  8  storey,  Ra=0  =  4    

𝛼=0.2  𝛼=0.0  

Applied  Load  AmplificaAon  Factor  

)0()0(

)0()0(

max

max

max

max

=≠≈

=Δ≠Δ=

αθαθ

ααβ

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DeformaAon  Demand  AmplificaAon  𝛽= ∆(𝑅↓𝛼=0 ,𝛼)/∆( 𝑅↓𝛼=0 ,𝛼=0)   

𝑅↓𝛼=0 =2.0  

Can>levered   Coupled  

DeformaAon  Demand  AmplificaAon  

𝑅↓𝛼=0 =2.0  

Coupled  Walls  

𝑅↓𝛼=0 =6.0  

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Variability  

𝐶𝑜𝑢𝑝𝑙𝑒𝑑,   𝛼=0.2,  𝑅↓𝛼=0 =2.0  

RecommendaAon  Need  limit  on  a  above  which  linear  analysis  cannot    provide  a  reliable  esAmate  of  deformaAon  demands.  

-­‐  Weak  correlaCon  with  T  and  R    ignore  

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Probability  of  Collapse    

0.0    

0.2    

0.4    

0.6    

0.8    

1.0    

0   1   2   3   4   5  

Prob

ability  of  C

ollapse  

Sa  (T1  =  3.0  s)  [g]  

alpha=0.0  

alpha=0.4  

𝐶𝑜𝑢𝑝𝑙𝑒𝑑,  𝑁=30,  𝑅↓𝛼=0 =2.0  

Proposed  Structural  Irregularity  2015  NaConal  Building  Code  of  Canada  

Type   Irregularity Type and Definition   Notes  

1  Vertical Stiffness Irregularity  Vertical stiffness irregularity shall be considered to exist when the lateral stiffness of the SFRS in a storey is less than 70% of the stiffness of any adjacent storey, or less than 80% of the average stiffness of the three storeys above or below.  

(1) (3) (7)  

…   …  

7  Torsional Sensitivity- to be considered when diaphragms are not flexible.  Torsional sensitivity shall be considered to exist when the ratio B calculated according to Sentence 4.1.8.11(9) exceeds 1.7.  

(1) (3) (4) (7)  

8  Non-orthogonal Systems  A “Non-orthogonal System” irregularity shall be considered to exist when the SFRS is not oriented along a set of orthogonal axes.  

(5) (7)  

9 Gravity-Induced Lateral Demand Irregularity A gravity-induced lateral demand irregularity on the SFRS shall be considered to exist where the ratio α calculated according to Sentence 4.1.8.10.(4) exceeds 0.1 for SFRS with self-centering characteristics and 0.03 for other systems.

(3) (7) (4)

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Proposed  Structural  Irregularity  2015  NaConal  Building  Code  of  Canada  

       where:  a  =  QG  /  Qy  

–  QG  =  gravity-­‐induced  lateral  demand  on  the  SFRS  at  the  base  of  the  yielding  system    

–  Qy  =  the  resistance  of  the  yielding  mechanism  required  to  resists  the  minimum  earthquake  loads        ≥  overstrength  x  reduced  design  earthquake  force    

Systems  with  self-­‐centering  characteris>cs  

Other  systems   Code  Requirement  

0.0 ≤ a  <  0.1   0.0  ≤ a  <  0.03   No  requirements  

0.1  ≤ a  <  0.2   0.03 ≤ a  <  0.05   MulAply  displacements  by  1.2  

0.2  ≤ a   0.05 ≤ a   Nonlinear  response  history  analysis  

where  IEFaSa(0.2)  ≥  0.5g  

What  acAon  should  be  used  for  QG?  

QG

QG

QG

QG

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Conclusions  

•  Gravity-­‐induced  lateral  demands  can  result  in  amplified  displacement  demands  and  increased  collapse  potenAal.  –  Large  hysteresis  à  more  suscepAble  to  ratcheAng  

•  Need  NL  analysis  for  QGILD  >  0.05Qy  

–  Self-­‐centering  à  less  suscepAble  to  ratcheAng    •  Need  NL  analysis  for  QGILD  >  0.1Qy  

•  Weakening  system  in  opposite  direcAon  from  GILD  can  improve  performance.  

•  Further  studies  required…  

THANK  YOU!  QuesAons?  

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Case  Studies  

Case  Study Descrip>on

𝛽↓𝑚𝑎𝑥  𝛽

𝛽↓𝐶𝑎𝑠𝑒  𝑆𝑡𝑢𝑑𝑦 /𝛽↓𝐴𝑟𝑐ℎ𝑒𝑡𝑦

𝑝𝑒  

Archetype  (30  storey  coupled  shear  wall  building,  α=0.2,   R↓α=0 =4.0,  Coupling  RaAo  =  0.70) 1.98 1.54a 1

Gravity  System  Irregularity

Inclined  Columns  over  Lobby 1.21 1.09a 0.71

Eccentric  Floor  Spans 2.27 1.77a 1.15

Strengthened  Coupling  Beams

Coupling  RaAo  =  0.77 1.92   1.43  a 0.93

Coupling  RaAo  =  0.84 1.83 1.39a 0.90

Subduc>on  Ground  Mo>ons

2010  Chile  Earthquake -­‐ 2.03b 1.32

2011  Tohoku  Earthquake -­‐ 1.62b 1.05

ConsideraAon  of  verAcal  ground  moAon  à  no  difference  

aMedian  from  the  ten  crustal  ground  moAons  used  in  the  study;  bValue  from  a  single  ground  moAon.  

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Adebar  et  al  2007  

CanAlevered  Walls  N  =  30  stories  R  =  4    

Alpha    =  0.4  

0 2 4 6 8 100

0.5

1

1.5

2

Maximum Interstory Drift [%]

Sa(T

1) [g]

0 2 4 6 8 100

0.5

1

1.5

2

Maximum Interstory Drift [%]

Sa(T

1) [g]

LA  Vancouver  

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Varia>on  of  Mean γ with  α  

Varia>on  of  Mean b with  α  

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VariaAon  of  b  with  R