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3.2.2 Perform3D  Model  Description  

The  Perform3D  model  was  constructed  to  replicate  STEEL  models  as  closely  as  possible.  

All   elements   were   given   a   fiber   cross   section   with   fiber   areas   matching   those   in   STEEL   as   discussed   in   Section   1.5.5.   Each   fiber   was   designated   with   the   same   material   model   and   the   appropriate   fiber   area   reductions   were   applied   for   fixed   end   connections   and   pinned   connections.  For  brace  elements  an  actual  moment  release  element  was  applied  to  either  end   of   the   compound   element   to   simulate   the   manner   with   which   STEEL   treats   braces.   For   each   Perform  compound  element  a  rigid  end  offset  was  applied  to  either  end  with  the  appropriate   length   matching   that   of   STEEL.   Furthermore,   shear   deformation   in   beams   and   columns   was   enabled  using  shear  areas  defined  by,  

𝐴!"= 𝑑𝑡!  

𝐴!"= 2𝑏𝑡!  

Where  𝐴!"   is   the   shear   area   along   the   web   and  𝐴!"is   the   shear   area   along   the   flanges.   The   shear  modulus  was  found  using,  

𝐺 = 𝐸 2 1+𝑣  

Where  E  is  the  Young’s  Modulus  and  𝑣  is  the  Poisson’s  ratio  taken  to  be  0.3.  

  As   STEEL   is   a   2D   analysis   software,   special   restraints   needed   to   be   placed   on   the   Perform3D  model  to  ensure  that  out-­‐of-­‐plane  behavior  was  eliminated.  Therefore,  all  non-­‐base   nodes  were  given  fixed  conditions  for  the  H2,  RH1,  RZ  directions.  All  base  nodes  were  given  full   fixed  conditions.  

   

3.2.3 Material  Model  Description  

Due  to  limitations  in  both  STEEL  and  Perform3D,  it  is  not  possible  to  get  an  exact  match   in   the   material   model.   As   discussed   previously,   the   STEEL   material   model   is   symmetric   and   consists   of   a   linear   elastic   region,   followed   by   a   region   of   constant   stress,   which   is   then   preceded  by  a  strain  hardening  region  represented  by  a  cubic  ellipse.  Following  this  the  curve   will  then  drop  to  a  defined  residual  value.  In  Perform3D,  the  nonlinear,  non-­‐buckling  material   model   consists   of   a   linear   elastic   region,   followed   by   a   secondary   linear   region,   leading   to   a   region  of  constant  stress  before  reaching  a  region  of  negative  slope  before  ultimately  dropping   to  a  residual  value.  

In  an  attempt  to  match  these  material  models  as  closely  as  possible,  the  material  used   for  the  ETABS  to  STEEL  comparison  described  in  Section  3.1.3  was  modified.  The  steel  material   model  begins  with  a  linear  slope  of    199.95  GPa  (29000  ksi),  yielding  at  344.737  MPa  (50  ksi).  

The   region   of   constant   stress   continues   until   a   strain   of   0.004   where   a   cubic   ellipse   with   an   intersection  slope  of  3467257  MPa  (502883  ksi)  and  ultimate  stress  of  448.1  MPa  (65  ksi)  at  a   strain  of  0.11.  At  a  strain  of  0.205  the  STEEL  material  model  drops  to  a  residual  stress  of  0  MPa   (0  ksi).  

The   Perform3D   model   also   has   a   linear   slope   of   199.95   GPa   (29000   ksi)   with   a   yield   stress  of  344.747  MPa  (50  ksi).  The  secondary  linear  region  ends  at  a  stress  of  441.26  (64  ksi)   and  a  strain  of  0.05.  The  region  of  constant  stress  ends  at  a  strain  of  0.16  and  then  decreases  to   a   stress   of   344.747   MPa   (50   ksi)   at   a   strain   of   0.207272.   The   Perform3D   material   will   then   remain  at  this  stress  until  a  strain  of  0.218181  after  which  it  drops  to  0  stress.  An  image  of  this   can  be  seen  in  Figure  3-­‐28.  

Figure  3-­‐28  -­‐  Material  Model  Description  -­‐    Perform3D  vs.  STEEL    

   

3.2.4 Perform3D  Analysis  Limitations  

While  conducting  several  of  the  linear  elastic  time  history  analyses  in  Perform3D  it  was   noticed   that   for   the   specific   models,   namely   the   two   brace   frame   and   twenty   story   moment   frame,  while  STEEL  and  Perform3D  yielded  similar  results  for  both  the  elastic  stiffness,  initial   release   point,   mass,   and   period;   following   the   removal   of   the   horizontal   acceleration   the   Perform3D   model   exhibited   practically   no   damping.   While   the   exact   method   is   not   perfectly   clear   it   was   revealed   by   CSI   customer   support   that   for   steel   fiber   elements   0%   of   the   axial   stiffness  for  Rayleigh  damping  is  used  [20].  This  was  done  by  the  Perform3D  programmers  to   combat   excessive   energy   dissipation   found   in   their   analyses   when   these   axial   fibers   yield,   resulting  in  an  axial  expansion.  The  issue  is  said  to  be  caused  by  coupling  between  the  bending   and   axial   affects   that   is   generally   not   present   before   yielding   or   cracking.   Through   their   own   analyses   it   was   found   that   this   affect   resulted   in   excessive   energy   dissipation   when   using     stiffness  proportional  Rayleigh  damping  [20].  The  decision  to  remove  axial  stiffness  from  steel   fiber  elements  was  done  to  yield  a  more  conservative  answer  in  users’  analyses.    

For   most   users   this   affect   will   not   cause   a   large   error   in   their   simulation   because,   in   general,  fiber  elements  are  only  used  in  small,  localized  regions.  However,  in  order  to  achieve  a   valid   comparison   between   these   two   softwares   the   usage   of   fiber   elements   throughout   the   Perform3D   model   results   in   a   practically   no   damping   being   applied   in   specific   models.   As   a   result,  the  free  vibration  analysis  for  both  chevron  brace  frame  models  as  well  as  the  twenty   story   model   resulted   in   a   solution   which   could   not   be   properly   compared   to   the   results   of   STEEL.   However,   for   each   of   these   models   the   static   stiffness,   initial   release   point   from   the   analysis   can   still   be   compared   as   well   as   the   results   from   the   pushover   analysis.   For   the  

cantilever  column,  three  story  moment  frame,  and  two  bay  three  story  moment  frame  models   this   approximation   of   no   axial   damping   done   by   Perform3D   is   small   enough   that   a   relatively   accurate   comparison   can   still   be   made   from   the   free   vibration   analysis   as   these   models   act   primarily  in  bending.  

Additionally,   Perform3D   does   not   include   geometric   updating.   While   for   most   typical   analyses  this  will  not  result  in  a  considerable  difference,  when  calculating  the  ultimate  capacity   of  the  building  as  well  as  determine  at  what  drift  the  structure  experiences  geometric  instability   the  lack  of  geometric  updating  can  begin  to  play  a  large  difference.  It  is  therefore  expected  that   at  very  large  strains  the  results  of  the  STEEL  and  Perform  analyses  will  diverge  and  it  is  expected   for   some   of   the   more   realistically   weighted   buildings   that   the   STEEL   analyses   will   become   unstable   at   a   lower   drift.   Furthermore,   for   extremely   high   drifts   it   was   seen   that   the   results   from  the  STEEL  pushover  analysis  can  show  a  rapid  increase  in  base  shear  following  the  collapse   of  the  structure.  It  is  believed  this  is  caused  by  the  manner  in  which  STEEL  conducts  pushover   analyses.  Due  to  the  monotonically  increasing  applied  accelerations  the  amount  of  force  being   applied  to  the  structure  increases  regardless  of  whether  the  structure  is  capable  of  resisting  this   force.  However,  since  this  force  must  be  resolved  in  the  system  the  base  shear  of  the  structure   will   continue   to   increase.   Through   examining   the   deformed   shape   of   the   structure   it   is   clear   that   this   increase   in   base   shear   is   not   indicative   of   an   increase   in   structural   capacity   post-­‐

collapse  but  rather  an  artifact  of  conducting  a  force  controlled  analysis.  

   

3.2.5 Analysis  Discussion  

A   total   of   six   models   were   analyzed   in   both   STEEL   and   Perform   and   their   results   compared.   Each   model   was   chosen   to   test   a   specific   feature   of   STEEL   to   determine   how   the   assumptions   compare   to   those   of   Perform.   The   models   begin   with   a   simple   three   element   cantilever  column  followed  by  a  three  story  single  bay  moment  frame  and  a  three  story  single   bay   chevron   brace   frame.   From   here,   the   models   increase   in   complexity   to   a   two   bay   three   story  moment  frame  and  then  a  two  bay  three  story  chevron  brace  frame.  Lastly,  a  twenty  story   moment  frame  based  on  Hall’s  U20  building  [1]  was  analyzed.  

For   some   of   these   models,   properties   such   as   the   section   sizes   and   masses   may   be   considered   nonrealistic,   however,   as   the   goal   of   this   study   was   to   compare   the   results   of   Perform  and  STEEL  the  actual  specifics  of  the  models  are  not  as  important  as  the  comparative   results  from  the  two  software  systems.  Often,  particular  masses  or  section  sizes  were  chosen  to   encourage  a  specific  type  of  nonlinear  behavior  or  to  simplify  the  model  so  as  to  reduce  the   number  of  variables  for  comparison.  

 

   

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