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Pseudo non-linear seismic analysis for damage evaluation of concrete structures Mital, Subodh Kumar 1985

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PSEUDO NON-LINEAR SEISMIC ANALYSIS FOR DAMAGE EVALUATION OF CONCRETE STRUCTURES  by SUBODH KUMAR MITAL B.  Tech.,  Indian  Institute  of Technology  K a n p u r , INDIA 1981  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  •in FACULTY OF GRADUATE STUDIES Department  We a c c e p t to  THE  of C i v i l  this  thesis  the required  Engineering  as  conforming  standard  UNIVERSITY OF BRITISH  COLUMBIA  May, 1985 ©  Subodh Kumar M i t a l ,  May,1985  In  presenting  requirements  this  thesis  in  that  available  permission  scholarly  for  purposes or  understood  that gain  the  reference  by  may his  be or  copying  shall  not  her  of  the  of C i v i l  Engineering  THE UNIVERSITY OF BRITISH COLUMBIA 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  D a t e : May,1985  this  by  the  Head  i t  agree  thesis  representatives.  allowed  make  I further  of  or p u b l i c a t i o n be  shall  and s t u d y .  granted  permission.  Department  Library  for extensive copying  Department  financial  fulfilment  f o r an a d v a n c e d d e g r e e a t t h e THE UNIVERSITY OF  BRITISH COLUMBIA, I a g r e e t h a t freely  partial  of It  for my is  of t h i s t h e s i s f o r  without  my  written  ABSTRACT Inelastic  behavior  is  inevitable  subjected  to  procedure,  t h e r e f o r e , should attempt  of  strong earthquake  inelastic  behavior  linear and  elastic  most  structures  f o r c e s . Any r a t i o n a l to estimate  t o be e x p e c t e d  s t r u c t u r e . Methods o f dynamic  in  the  design amount  i n e a c h member o f t h e  response  analysis  a s s u m p t i o n s c a n be c a r r i e d  based  on  out c o n v e n i e n t l y  e c o n o m i c a l l y . Such methods, however, c a n n o t p r o v i d e any  direct  information  on  the  inelastic  s t r u c t u r e . On t h e o t h e r hand,  time-step  can  non-linear  'truly'  structure  simulate  the  b u t a r e s e l d o m used  complexity. efficient  There  because  behavior analysis  which  can  of  account  programs  behavior  i s , t h e r e f o r e , a need  methods  of the  their  of  the  cost  and  f o r p r a c t i c a l and  f o r the  inelastic  behavior. Some methods f o r e s t i m a t i n g t h e i n e l a s t i c damage  patterns  of  structures  under  ground  presented.  One i s t h e M o d i f i e d S u b s t i t u t e  which  now r e v i s e d  for  is  gravity The  analysis. and  then  t o the seismic  method w h i c h  seismic  analysed  f o r c e s (as given  c o d e s ) a r e a p p l i e d . The a m p l i t u d e gradually plastic  increased,  hinge  structure  motions a r e  Structure  here  uses a  for gravity  of the l a t e r a l  maintaining  matrix  revised  i i  static loads  by t h e a p p r o p r i a t e forces  the s p e c i f i e d  each time.  is  pattern; a  i s p l a c e d where a member h a s y i e l d e d  stiffness  Method  analysis.  i s proposed  The s t r u c t u r e i s f i r s t lateral  and  so t h a t t h e s t r u c t u r e c a n be a n a l y s e d  loads p r i o r  other  response  This  and the process  is continued u n t i l  the s t r u c t u r e  d i s p l a c e m e n t . At t h i s hinges can  is  known  and then  the  by  response  method  predicting These two  gives  analysed  various  the  methods  structures.  by  the  plastic  ductilities the  damage  T h e s e methods a p p e a r will  inelastic  A  and  predict  response  i n the appendices.  motion. without  third, in  real  by a n a l y z i n g  structure,  downtown V a n c o u v e r  the  results  and  by p r a c t i s i n g of  these  it  an  i s also  compared  t i m e - s t e p a n a l y s i s program  useful  the  damage.  A u s e r ' s guide and the l i s t i n g included  to  severe ground  t o g i v e good r e s u l t s  be f o u n d  for analysing  a r e t h e n compared  building  a  Method' under  overall  by t h e s e methods  obtained  they  'Freeman's  the p a t t e r n of l o c a l  idealized  been w r i t t e n  of s t r u c t u r e s  office/residential  those  of  i s o b t a i n e d , of  p r o g r a m has a l s o  structures  inelastic The  predetermined  i n the s t r u c t u r e .  A computer the  rotation  a  t h e member c u r v a t u r e  be c a l c u l a t e d . T h u s , an i d e a  pattern  that  point,  has reached  with  DRAIN-2D. is  hoped  engineers. programs  are  T a b l e of C o n t e n t s ABSTRACT  i i  L I S T OF FIGURES  vi  ACKNOWLEDGEMENTS 1.  viii  INTRODUCTION  1  1 . 1 BACKGROUND  1  1.2 PURPOSE OF THIS STUDY  7  1 . 3 SCOPE 2.  MODIFIED METHOD  9 SUBSTITUTE STRUCTURE METHOD AND  FREEMAN'S 11  2.1 MODIFIED SUBSTITUTE STRUCTURE METHOD 2 . 2 FREEMAN ' S METHOD 2.2.1  ..18  DETERMINATION OF THE CAPACITY CURVE  2.2.2 DETERMINATION OF THE DEMAND CURVE 3.  4.  5.  6.  11  19 21  STATIC DAMAGE EVALUATION METHOD  27  3.1 METHOD  27  3.2 COMPUTER PROGRAM CONCEPT  35  MATHEMATICAL MODELLING: ASSUMPTIONS AND COMMENTS  39  4.1 NECESSARY ASSUMPTIONS  39  4.2 ASSUMPTIONS MADE IN PRESENT ANALYSES  42  EXAMPLES  45  5.1 TEST STRUCTURE 1  48  5.2 TEST STRUCTURE 2  54  5.3 TEST STRUCTURE 3  61  CONCLUSIONS  73  REFRENCES  75  APPENDIX A  77  APPENDIX B  1 08 iv  APPENDIX APPENDIX  L I S T OF  FIGURES  Fig.  Page  2.1  DUCTILITY AND  2.2  CAPACITY  DAMAGE RATIO  12  : SPECTRAL ACCELERATION  VS.  E F F E C T I V E PERIOD 2.3  DEMAND  22  : SPECTRAL ACCELERATION  VS.  E F F E C T I V E PERIOD  23  2.4  RECONCILIATION OF CAPACITY AND  DEMAND  3.1  FORCE DISPLACEMENT  CURVE  31  3.2  MOMENT CURVATURE DIAGRAM  33  5.1  TEST STRUCTURE  50  5.2  TIME-STEP ANALYSIS  5.3(a)  (curvature d u c t i l i t i e s ) AVERAGE OF TIME-STEP ANALYSES  1  24  RESULTS  (curvature d u c t i l i t i e s ) . . . . 5.3(b)  EDAM  : CURVATURE D U C T I L I T I E S  5.3(c)  STATIC DAMAGE METHOD : CURV. DUCT. () S E N S I T I V I T Y INDEX  51  52 52  53  5.3(d)  RESULTS FROM FREEMAN'S METHOD  53  5.4  TEST STRUCTURE 2  56  5.5  TIME-STEP ANALYSIS (curvature  RESULTS  ductilities) vi  57  5.6(a)  AVERAGE OF TIME-STEP  ANALYSES  (curvature d u c t i l i t i e s ) 5.6(b)  EDAM  5.6(c)  STATIC DAMAGE EVALUATION  58  : CURVATURE D U C T I L I T I E S  58  : CURV. DUCT.  () S E N S I T I V I T Y INDEX 5.6(d)  RESULTS FROM FREEMAN'S METHOD  5.7(a)  EDAM  5.7(b)  STATIC METHOD : CURV. DUCT. FOR  TEST STRUCTURE 3  5.9(a)  TIME-STEP  5.9(d)  FORCES)..  REVERSE  ANALYSIS  60  SEISMIC  () SENSITIVITY INDEX  5.8  5.9(c)  59  : CURV. DUCT.(REVERSE SEISMIC  FORCES;  5.9(b)  59  60 64  : EL-CENTRO N-S  COMP.  (curvature d u c t i l i t i e s ) . . TIME-STEP ANALYSIS : EL-CENTRO E-W COMP. (curvature d u c t i l i t i e s ) TIME-STEP ANALYSIS : TAFT N21E COMP. (curvature d u c t i l i t i e s ) TIME-STEP ANALYSIS : TAFT S69W COMP. (curvature d u c t i l i t i e s )  5.10  AVERAGE OF TIME-STEP  ANALYSES  5.11  EDAM  5.12  STATIC DAMAGE METHOD : CURVATURE D U C T I L I T I E S  5.13  () S E N S I T I V I T Y INDEX RESULTS FROM FREEMAN'S METHOD  : CURVATURE D U C T I L I T I E S  65 66 67  68 69 70  71 72  ACKNOWLEDGEMENTS The  author  advisors  Dr.  Cherry.  Special  valuable  student  N.D.  thanks and  Dr.  D.L.  due  to  constant  are  Christofferson  and  necessary  also  wishes  also  to h i s  A n d e r s o n a n d D r . S.  Dr.  Nathan  for his during the  t o thank h i s f e l l o w  who p r o v i d e d  us  to carry  support  from N a t u r a l  o f Canada  during  due t o Mr. N i g e l  information  financial  Assistantship  gratitude  encouragement  C o n r o y Lum f o r h i s a d v i c e  and  Council  are  sincere  work.  author  Thanks  The  his  Nathan,  guidance  course of t h i s The  expresses  in  this  work.  Brown o f Read  with  building  out a p a r t  the  form  of  a  viii  acknowledged.  Jones  drawings  of t h i s  S c i e n c e s and E n g i n e e r i n g  i s gratefully  graduate  work.  Reasearch Research  1.  INTRODUCTION  1 . 1 BACKGROUND As  per the current  structure  i s subjected  members a r e e x p e c t e d in  many c a s e s ,  If  the loads  i t h a s been  dissipate  member that  the  structure forces  is  expected  structural  forces  the  to  its  r a n g e and  form a mechanism. Even i f should  not  collapse  because of d u c t i l i t y .  and  detailed, has  o u t how  exhibit  design  These  long  much  that  office  it  will  been  the  damage  much  lateral  each  ductility  period  average  for equivalent  seismic  for  depend  during of  ductility  upon  the l i f e  vibration available  of the s o i l  the  of the of  in  the that  l y i n g underneath  t h e mass d i s t r i b u t i o n . Knowing  static  analysis  in various  f o r that  an  forces  acceleration  an o r d i n a r y  and  analysis  inherent  forces  a  failure.  and o f c o u r s e ,  yield  when  t y p e o f e a r t h q u a k e m o t i o n , so  form, t h e p r o p e r t i e s  then d e s i g n e d  that  given  fundamental  the  structure,  necessary is  a  ground  the  their elastic  i t . It  to find  quasi-static  peak  structure,  these  to  designed  done.  structure,  the  for  average  a  will  designed  input  undue damage o r  In  past  form, t h e s t r u c t u r e  of r e s e a r c h e r s  i t c a n be  without  t o go w e l l  properly  suffers  philosophy,  a r e dynamic and a l s o  energy,  objective  codes  t o s e v e r e g r o u n d m o t i o n , many o f  the s t r u c t u r e  a mechanism s h o u l d because  design  strength  members, and t h e s t r u c t u r e and  members have t h e d u c t i l i t y  1  i s done t o f i n d t h e  detailed  to  assumed t o be  ensure inherent  2  in  that  structural  The is  that  yield  basic  assumption  under a s e v e r e but  particular structural designed  ground  ground form  form  lower with  more  seismic force  so t h a t  responds  w i t h an a c c e p t a b l e l e v e l  and and  that  and  the s t r u c t u r e  of the d e s i g n e r  detailing  that  bond  do  not  under  be e q u a l  elastic  level  to the that  i f . a particular it  can  be  a s compared t o a  severe  In e f f e c t  it  is  o f s t r e n g t h and ground  motion  of damage. I t i s t h e n t h e  fails  by  proper  design  i n t h e f l e x u r e mode  modes a s s o c i a t e d w i t h a x i a l occur  will  during  ductility  t o ensure  the s t r u c t u r e  the f a i l u r e  will  combination  ductility  responsibility  structure  o r no d u c t i l i t y .  a proper  procedures  the  T h i s means t h a t of  little  q u e s t i o n of choosing  motion  completely  motion.  i s capable a  c u r r e n t code  displacement  had i t r e m a i n e d  for  structural  i n these  i t s ultimate  displacement  a  form.  before the f l e x u r a l  load,  failure  shear of the  member. This  approach  non-linear  behavior  inelastic  response  elastic  response  using this  that  the d u c t i l i t y but  several  i s accounted spectrum  spectrum  then  structure;  raises  this  is  is  i s determined  the l a t e r a l  not  follows:  the  by d i v i d i n g t h e ductility  forces.  in real  of high  demand  areas  o r no e n e r g y .  of  way  the case  areas  little  The  a smeared v a l u e o f d u c t i l i t y ,  and  T h i s assumes  i s uniformly distributed  where t h e r e a r e i n v a r i a b l y which absorb  as  by t h e a p p r o p r i a t e  to estimate demand  for  questions.  Thus t h e  a s i t were, d o e s  over  the  structures, and  other  assumption not  tell  3 us  anything  about  the  structure.  It  essentially  in its first  distributed ratio  top  method  some  the  spots  in  structure  the  if  base  is  o f t h e base s h e a r  the  vibrates shear  the height  account  is  simple  to apply  f o r a 'uniform' or ' r e g u l a r '  structure  structures  is  such  stiffness  i.e.  over  also  is  t o width  taken  of  i s placed  where  the  a t the  But  i . e . i f t h e mass  is  not  contributions  of  does not g i v e  with  'irregular'  s e t b a c k s o r sudden  t h i s method does n o t  certainly  reasonably  t h e s t r u c t u r e and s t i f f n e s s o f  as those having  the  and works  structure  uniform.  o r i f t h e mass  significant,  in  that  although  when p a r t  d i s t r i b u t e d uniformly  the  and  'weak'  of the s t r u c t u r e .  well  in  or  mode, and t h a t  some v a l u e ,  modes,  This  is  assumes  accordingly;  exceeds  higher  also  'bad'  uniformly higher  give  any i d e a  changes  distributed  modes  may  be  reasonable  results  o f t h e damage  pattern  the s t r u c t u r e . On  the  other  computer  program  behavior  of  hand, can  preparation t h e y depend structure  of  that  cannot  programs the ground motion digitized  record  response  spectrum.  with  is  be  well  entered  in  of a p a r t i c u l a r earthquake Unfortunately,  regard  time  of non-linear  always  non-linear  t h e s e programs a r e  and computer  upon a s s u m p t i o n s  the  but  consuming  data  time h i s t o r y a n a l y s i s  simulate  elements,  time  input  complex  'truly'  structural  e x p e n s i v e t o u s e and  a  to  required.  behavior  the  despite  the  In t h e s e  form  rather  Also  of  defined.  the  of  a  than as a  the  recent  4  advances of  in  seismological  available  with  respect  structure can  only  get  future  a  the  zone  prediction  will  even  average  more  the  of  structural analyses  design  and  office  structure.  with  the  the  a  best  we  in  a  is located.  So  behavior  in  are  of  required  the  program, makes  designers  use  the of  with  earthquake  which  designing  Thus  which At  diffrent  designer,  unpopular  to  acceleration  a d d i t i o n a l runs  to  remains  structure  properties  mean  uncertainty  the  excitations several  This  number  its lifetime.  ground  where  increased  earthquake  of  range  the  l o t of  a  a d d i t i o n a l cost  limited  a  during  structural  engineering  of  and  subjected  seismic  ground  programs  1.  be  records,  nature  reasonable  records.  the  the  estimate  different  thus  to  may  particular to  seismic  studies  and such  working  average these  in  civil  methods i s "  to:  Large  and  expensive  technical process  projects  resources due  to  can  the  where  be  enough  justified  enormous  cost  of  funds  in  the  the  and  design  projects  themselves. 2.  Research their  or  the  maximum  programs  behavior  the  behavior  intended  usually  to  compared of  academic  usage.  give  non-linear is  in  the  environment,  Since best  of  the  them  structure  time-step  they  find  analysis  representation  of  the  'true'  s t r u c t u r e , any  method  which  approximate with  these  where  to is  the  non-linear  see  how  closely  approached.  behavior the  is true  5 Thus  we  attempt  somewhere i n between, expensive  than  nevertheless reasonably popular The  a  to  achieve  which  is  easier  time-step  good r e s u l t s .  i n a design  should  earthquake  data  be b a s e d records  modal  that  is  Method'  and  reducing  i t s stiffness  takes  and  gives  the real  stiffness;  be  similar  hence  was  of  on  a  introduced  by S h i b a t a and  'Substitute  the y i e l d i n g  name  t o be a d e s i g n values  replaces  Yoshida  2  this  o f a member by  of  the  procedure  extended the  Substitute  should  structure  'damage  real  structure  Structure  and  for  with  a  modal a n a l y s i s of y i e l d  be d e s i g n e d .  idea  with  Structure  ratios'  i s n o t an i t e r a t i v e same  and  method w h e r e i n t h e  p e r f o r m s an o r d i n a r y  t h e v a r i o u s members that  Structure  'Substitute  the s u b s t i t u t e s t r u c t u r e t o get the l e v e l  'Modified  what  and i s b a s e d on  the  the  chooses acceptable  one; and t h e n  noted  to  criteria  s t r u c t u r e by a f i c t i t i o u s  fictitious  which  t o make i t  by t h e s o - c a l l e d 'damage r a t i o ' ,  members;  be  behavior  static analysis;  these  into account  diffrent  for  which  are available instead  called  Method'. T h i s was i n t e n d e d  of  but  on some s o r t of e n v e l o p e o f t h e p a s t  analysis  1  designer  less  method,  are important  should  i n an o r d i n a r y  S o z e n . T h i s method  reduced  and  event.  dynamic  replacing  use  office:  A method w h i c h s a t i s f i e s a  to  analysis  Two t h i n g s  form of t h e i n p u t  single  a method w h i c h i s  approximates the non-linear  would be u s e d It  here  It  forces should  procedure.  introduced  the  Method'. The p r o c e d u r e has  6  been  described  meant t o be the  i n more d e t a i l  a retrofit  properties  and  elastic  stiffness  modal  and  iteratively stiffness correct  f o r c e s below y i e l d .  if  m o t i o n w h i c h was  that with  used  it  problems cases. well  I t has  type by  and the  coupled  hindered  proper  structures.  Freeman  introduced  response  idea  to take  structures  under  a retrofit  little  more  structural  of  get  a  to  occur ground  spectrum method  This  detail  the  in  the  some  in c e r t a i n  t h i s method a p p e a r s t o work  estimates  structures. This the  non-linear  method  is  following  strength  structure  so  along  the  method u s e s a behavior  s e v e r e g r o u n d m o t i o n . I t i s a l s o meant  procedure.  of  to  resolved  a method w h i c h  i n t o account  p r o p e r t i e s and  capacity  R/C  the  leads  of  response  the  to  i s expected  convergence  kinds  also  used  s t r u c t u r a l walls  for different 5  lead  r e v i s e d the  that  of  are  stiffness  s t u d i e d and  u  flexure  i.e. until  intensity  3  is  known,  a n a l y s i s , we  linear  analysis. Metten  a l s o analyze  been  this  reported  simple  the  of  is  members  reduced  factors  original  s t r u c t u r e which  represented  had  the  damage r a t i o s  the  result  the  various  i s achieved:  s t r u c t u r e s . Then H u i  which  inelastic  be  or  for  damping  current  a  to  i n the  could  framed  As  i n the  i t i s subjected  w h i c h we  the  that  s t r u c t u r e being  which  convergence by  the  in  viscous  moments,  pattern  of  2 . T h i s method  check p r o c e d u r e ,  damage r a t i o s  analysis  until  yield  damage  the  equivalent  reduced  a design  strength  t h i s method computes by  or  in chapter  of  the  explained chapter.  Once  members a r e  i s determined  by  in  of to a the  known,  combining  an  7 elastic The  a n a l y s i s with  demand  linear the  period  to  get  the  effective  i n w h i c h t h e damping i n c r e a s e s  as  damping  a n a l y s i s then  his  response  period  frame  e a r t h q u a k e . He and  the  obtained  structures. estimate  from  damage  peak  response  of value  of v i b r a t i o n , i n e l a s t i c  capacity  capacity  of  that  5  responses under'  the  the  structure  recorded  this  of  two  San  used  identical  Fernando  1971  t h e method seemed t o work  were q u i t e  of s y s t e m d u c t i l i t y  the l o c a l  at  demand,  peak  the  However,  of the  ductility  structures reported  the  t y p e o f g r o u n d m o t i o n . Freeman  the r e s u l t s o b t a i n e d  data  to  of v i b r a t i o n and t h e  system/tip  reserve  particular  method t o f i n d  7-story  yield  r e s u l t s i n the estimated  peak s t r u c t u r a l r e s p o n s e ,  that  at f i r s t  response p e r i o d  u s e d and t h e r e m a i n i n g  of  a  of t h e g r o u n d m o t i o n a r e r e c o n c i l e d  critical  structure. This  under  represented  a t t h e maximum r e s p o n s e . The. c a p a c i t y  of  effective  is  approximations. by  from t h e v a l u e  and t h e demand  percentage  of  spectrum  increases  value  structure  bilinear  of a p a r t i c u l a r earthquake  response  maximum  some g e n e r a l  well  good a s compared t o t h e motion  procedure  of  only  the leads  demand, b u t g i v e s  no  actual to  an  estimate  pattern.  1.2 PURPOSE OF THIS STUDY Various  methods  that  inelastic  seismic  section.  The s i m p l e s t  engineering  could  be  used  in  a n a l y s i s were d i s c u s s e d  practice  and most w i d e l y is  the  the approximate the  previous  u s e d method  i n common  equivalent  in  lateral  force  8 procedure  with  discussed  above,  questionable, On  a  quasi-static the  estimate  especially  the  other  used  to study to with 1.  inelastic  extreme  there  are  as  was  behavior i s  time-step  complexity  and  i n common e n g i n e e r i n g p r a c t i c e .  those  come  of  but,  i f the s t r u c t u r e i s not ' r e g u l a r ' .  programs w h i c h , b e c a u s e o f t h e i r rarely  analysis;  methods w h i c h t r y t o f i l l  up w i t h a q u a s i - s t a t i c  analysis  cost,  I t was  this  gap  are  intended and  also  method f o r t h e same p u r p o s e  the f o l l o w i n g p o i n t s : The n o n - l i n e a r  behavior  is  represented  by  a  linear  approximat ion; 2.  3.  The  method  i s able to r e f l e c t  structure  with  time-step  method;  The  input  ordinary  is  static  reasonable  similar  The  main p u r p o s e o f  methods those  structure the  i s g e n e r a l l y used  to  acceptability  study  was  to  apply  a l l these  s t r u c t u r e and t o compare t h e r e s u l t s  way:-  programs s h o u l d  once  engineer  the  anticipated  design  whether t h e s t r u c t u r e w i l l o r whether  'weak' o r 'bad' s p o t s .  the design  with  DRAIN-2D.  that these  according to the e x i s t i n g  methods  a  f o r an  has  be used i n designed  codes,  behave  a  and f i x e d  s i z e s a n d s t r e n g t h s o f v a r i o u s members, he may c h e c k  these he  compared  office;  this  i s anticipated  following  as  so a s t o enhance  of t i m e - s t e p a n a l y s i s program It  the  to a real  accuracy  t o what  analysis  i n an a v e r a g e d e s i g n  t h e damage p a t t e r n i n t h e  by  i n t h e way  needs a r e v i s i o n  i n the  9  From v a r i o u s methods, we g e t c u r v a t u r e d u c t i l i t y as  a  measure  particular to  1.3  of  damage.  design  We  must  then  can be and i s d e t a i l e d  u n d e r g o t h a t amount  ensure  demand that  a  so t h a t  i t i s able  Substitute  Structure  earthquake  response  o f damage.  SCOPE We  first  method  describe  and  prediction  the  Freeman's  method  of s t r u c t u r e s .  presented  here  as  Modified  Only  for a  they  brief  are  summary  well  will  documented  be in  refs.(2,3,4,5). Then t h e ' S t a t i c in  Damage E v a l u a t i o n Method'  a s u b s e q u e n t c h a p t e r . The t h e o r y  behind  i s presented  this  method  is  part  of  discussed. Mathematical analysis,  especially  assumptions affect has  modelling  is  in  a  seismic  i n making a m a t h e m a t i c a l  t h e outcome of t h e a n a l y s i s  been  made  to  distinguish  assumptions  that are usually  assumptions  t h a t a r e made d u r i n g  study, mainly Testing procedures, First by  to simplify of  the  again,  is  important analysis.  Various  model t h a t c a n  greatly  a r e d i s c u s s e d . An between  the  attempt  necessary  made i n a s e i s m i c a n a l y s i s , the course  of  the  and  present  t h e work.  method  a 2-bay, 4 - s t o r y  various  those  very  a  and  very  comparison  important  r e g u l a r framed  other  p a r t of t h e work.  structure i s  a v a i l a b l e methods and t h e r e s u l t s  of t h e t i m e - s t e p a n a l y s i s  with  analyzed  compared  p r o g r a m DRAIN-2D.  A  with  3-bay,  10  3-story by  'irregular'  framed  various procedures  the  time-step  is  an  and  analysis  s t r u c t u r e has the  and  time-step work on  analyzed  analysis  a real  conventional In  the  and  building the  program  building  w h i c h was  final  chapter  mentioned.  I t i s hoped t h a t by able  Areas  the  .  be  those  structure  compared w i t h  t o see  how  designed  by  of  which  the  is  same  these  methods  the  present  methods.  presented  will  analyzed  i n downtown V a n c o u v e r  results  results  been  compared w i t h  p r o g r a m . Then a r e a l  office/residential  modelled  results  also  where  c o n c l u s i o n s of  further  to c o n v i n c e  work  reading  themselves  work  the  value  take  into  of  t o use  and  the  of  s t r u c t u r e in a r a t i o n a l  behavior  the  are also  designers  methods w h i c h a r e e a s y inelastic  which  thesis  i s needed a r e  this of  this  these  account way.  2.  2.1  MODIFIED SUBSTITUTE STRUCTURE METHOD AND FREEMAN'S  MODIFIED SUBSTITUTE STRUCTURE METHOD This  method  Structure The  was  developed  method level  substitute  s t r u c t u r e with  lost  analysis should  the  was  damping  in a real  to  stiffness  account  inelastic  and S o z e n . 1  would  to  be  choose  a an  analyse a  and a  fictitious  f o r the  hysteretic  member. The r e s u l t  of t h i s  f o r c e s f o r which v a r i o u s  members  be d e s i g n e d . same i d e a  i s extended  S t r u c t u r e Method', w h i c h purposes  i n the  i s intended  i . e . to analyse  structure  an  for prediction  of  the here  important  final  application  probable  behavior  by  code  the  member s i z e s  as  and y i e l d  a n a l y s i s leads  the  (Refer  to figure member  for retrofit  reinforced  concrete  damage c a u s e d that check  by s e v e r e  i t also  Obviously,  has an  i n assessing the  f o r such  designed  a structure,  moments f o r t h e members a r e known a n d  t o p r e d i c t e d damage r a t i o s  to t h a t ground motion. of  Substitute  and damage p a t t e r n o f a s t r u c t u r e  procedures.  ratio  a  'Modified  t o be u s e d  existing  ground motion. I t i s suggested  a  'Substitute  intended  designer  reduced  leads t o the y i e l d  The  the  the  o f damage i n e a c h member a n d then  of v i s c o u s  energy  Method'  wherein  acceptable  value  from  Method' w h i c h was p r o p o s e d by S h i b a t a  'Substitute Structure  design  for  METHOD  'Damage  initial  stiffness  2 . 1 , which subjected  ratio'  shows to  11  corresponding  i s defined  t o the reduced a  stiffness.  moment-rotation  anti-symmetrical  as t h e  curve  end moments)  1 2  Ductility, final In  on t h e o t h e r  end r o t a t i o n  hand,  i s defined  t o the y i e l d  as the r a t i o  of the  rotation i . e .  the figure 2 . 1 : 6.  Ductility  where and  0 = End r o t a t i o n n  0^ = End r o t a t i o n  On t h e o t h e r  the s t r a i n  ratio  e  o f t h e member a t moment  M  n  o f t h e member a t y i e l d  h a n d , damage r a t i o  n  If  n_  u  TJ i s d e f i n e d a s :  s l o p e OA _ K_ s l o p e OB ~ K  hardening  ratio  's'  and d u c t i l i t y a r e r e l a t e d  1  + U  -  1  is  known,  by t h e s i m p l e  then  expression:  ).s  ! "^-K.s  n  Fig.  2.1.  DUCTILITY AND  damage  ROTATION, 6 DAMAGE RATIO  1 3 We  can  see  ductility, except  that  unless  t h e damage r a t i o the s t r a i n  stiffness dynamic  this  t e s t s on c o n c r e t e to  be e x t e n d e d The  i s given  is  concrete  is  ratio  = 0.02 + 0.2  s  assumed  which  that  i n turn  a damping  a v e r a g e o f member the s t r a i n  were  modified  derived  from  i t s use i s p r e s e n t l y  structures. t h i s method  With  some  can p o s s i b l y  f o r each of the s u b s t i t u t e  e a c h o f t h e members c o n t r i b u t e s in proportion  energy used  to  for entire  of each  end moments.  structure,  i s taken,  to  i t s flexural  depends upon t h e member  factor  a  weighted  the weight  factor  element.  i n the M o d i f i e d  Substitute  Structure  follows:  Read t h e s t r u c t u r e matrix  the  ( 1 - -)  damping v a l u e s  The p r o c e d u r e i s as  of  ratio  s t r u c t u r a l modal damping  Method  when t h e y a r e  structures.  where 17 i s t h e damage  To o b t a i n  zero i . e .  by:  0  energy,  which  i n t h e damping v a l u e s  to s t e e l  use  7  s u g g e s t e d damping  It  makes  structures ,  reinforced  modifications  members  procedure  and damping p r o p e r t i e s  restricted  being  ratio  equal.  Since  1.  hardening  l e s s than the  f o r the p e r f e c t l y e l a s t o - p l a s t i c case,  identically  the  i s always  data,  form  the  elastic  ( i . e . w i t h a l l damage r a t i o s s e t e q u a l  and  solve  the  member  the s t r u c t u r e forces.  f o r any g r a v i t y  loads  stiffness to one), to  find  1 4  Form t h e mass assuming  matrix  elastic  response  a  modal  using  a  specified  with  In the f i r s t  factor  perform  behavior,  spectrum  acceleration. damping  and  specified iteration  analysis, linear  peak  ground  a specified  smeared  f o r e a c h mode i s u s e d .  Find  t h e RSS f o r c e s due t o s e i s m i c l o a d s and a d d them t o  the  f o r c e s due t o g r a v i t y  of  t h e damping  factor  the  end  ratio  the  the  yield  the values  on t h e  member  earlier.  moments w i t h t h e y i e l d  member and l o c a t e exceed  refine  f o r e a c h mode b a s e d  end moments a s s u g g e s t e d Compare  l o a d s . Then  members  moment.  where  In  moment o f e a c h  the  end  moments  s u c h members t h e damage  i s m o d i f i e d a t b o t h ends o f t h e member t o :  M  1  17 = - ( 1 - S ) + s.M,  M y  1  where:17 = damage r a t i o s = strain M  hardening  ratio  iteration  as d e f i n e d  previously  = moment a t t h e c o r r e s p o n d i n g end o f t h e member  1  M  f o r the next  = v  yield  moment o f t h e member  Thus we c a n have two d i f f e r e n t member. for  They a r e c o m b i n e d  damage  ratios  to get a 6x6 s t i f f n e s s  t h e s u b s t i t u t e member, and c o m b i n i n g  the  overall  substitute shapes  and  stiffness  structure member  matrix.  damping  forces  for  We  ratios,  those then  each  matrix we  get  recompute  periods,  mode  (member f o r c e s due t o g r a v i t y  15 l o a d s added 6.  Repeat  t o t h e RSS f o r c e s due t o s e i s m i c  steps  4  and  loads)  5, m o d i f y i n g t h e damage r a t i o s a s  follows: M ^n+1  ^n  =  M  n . (1-s) +  S-M  n  where:rj M  = member  n  This  = damage r a t i o  n + 1  end moment  is  low,  convergence  is  moments between Thus ratios  less  than  that  remains  going  made  <  results  one  succesive cycles;  i f t h e damage  Ratio  <  5)  iteration  calculated The version  member  damage  a r e the f i n a l  deformation  changes  have  been  o f t h i s method, w h i c h was c a l l e d i s now p o s s i b l e prior  f o r a member  has remained  a member  damage  elastic  procedure,  i s c a p a b l e of  indicated  by  the  ratio.  following  loads,  i n t h e end  in a retrofit  t o be d e t e r m i n e d whether of  the  cycles.  of the a n a l y s i s  that  then  upon t h e change  ground motion. F i n a l l y ,  through the degree  It  I f t h e damage r a t i o i s on t h e change  depend  then  number  i s made t o depend  Damage  to  succesive  i s a c h i e v e d . To  f o r a l l t h e members. I f t h e damage r a t i o  during it  the  between  i.e.(l  convergence  are used:  ( > 5) t h e n c o n v e r g e n c e  ratio  is  iteration  p r o c e s s and t o r e d u c e t h e  two c r i t e r i a  t h e damage r a t i o s  iteration  1  in n  the convergence  iterations  high in  1  process i s continued u n t i l  accelerate of  i n (n+1) "*  made  in  analysis.  last,  Edam2:  to analyze the s t r u c t u r e  to the seismic  the  At  for gravity  the  time  of  16  writing in  this  thesis  the s t a t i c  two ways: e i t h e r  static be  loads  they  c a n be s t a t i c  applied directly  uniformly  loads can only  distributed  such  as  loads or t r i a n g u l a r  first  o p t i o n c a n be u s e d  as  static  The  nodal  of s t a t i c  and  these  loads  so  values  When modal  different  the height are  forces,  end  should  be f o u n d  nodal  can  gravity  the  loads  direction  f o r c e s a r e combined  mode f o r c e s i n t h e o t h e r  made  for  f o r c e s combined  Thus,  i n the second  and c u r v a t u r e  by  the  of  that  concrete  latter  to consider  first  with  same  becomes  two c a s e s . first  mode  and second w i t h the  direction.  Provision time  is  with the  way. so t h a t  we  ductilities  i t i s p o s s i b l e now t o compare methods,  different  f o r the fact  t o be r u n a s e c o n d  p r o g r a m h a s been c h a n g e d  damage r a t i o s  have  the  x-direction,  first  program  of t h e member  grades  of  The  the  for  t o be compared w i t h t h e  i t i s necessary  i n the p o s i t i v e  same  of the s t r u c t u r e .  thus  forces  forces  and i n p u t  need n o t be  members  important; gravity  member  l o a d s e t c . , then the  o f Young's m o d u l u s . T h i s a l l o w s  there  can  loads.  that  used over  the  fixed  a high-rise structure different  are  the  on  whole s t r u c t u r e . I t i s r e a d a s a p a r t  data,  The  loading  Young's m o d u l u s o f e l a s t i c i t y  the  in  to  loads i . e .  l o a d s on t h e members. Thus i f  types  corresponding  nodal  input  a t the nodes, or they  there are other point  be  get  both  the  f o r t h e members.  the r e s u l t s  from a l l  measure o f damage  i . e . the  17 curvature  d u c t i l i t y demand.  From t h e r e s u l t s  o f EDAM,  we  r o t a t i o n s a n d t h e damage r a t i o s F o r a member,  get  at both  once we have t h e f i n a l  RSS  displacements,  ends o f t h e members.  end r o t a t i o n  8  ,  we  , based  on  n can  get the r o t a t i o n  -  ( 1  e  0_ d  - S).T?  the r o t a t i o n 6 p  which  a s : (See F i g . 2.1)  TJ.S)  =  y  then,  at y i e l d  =  of t h e p l a s t i c  hinge  6^ i s ,  0 - 0 n y  is  converted  t o the p l a s t i c  curvature $ P  some assumed plastic of  plastic  hinge  t h e member  $  =  =  P_  P  Lp  then,  hinge  length  length.  In  this  h a s been assumed t o be  l e n g t h ( i . e . about P 0.05(member  method,  the  one-twentieth  one beam d e p t h ) .  Thus,  length)  the c u r v a t u r e d u c t i l i t y  i s g i v e n by  $  CD.  = 1 + -P— y  v where $ i s the y i e l d curvature = - — El where M^ = y i e l d moment o f t h e member M  y  y  EI  = flexural  stiffness  o f t h e member  F o r member ends, w h i c h a r e r e s t r a i n e d the  final  might  end r o t a t i o n  have  suffered  w i l l be z e r o , even some  damage  at  against  rotation,  though the this  end.  member In t h i s  18 situation,  the  t h e moment  (and  these  hinge  the  we  at the  can  compute t h e  region, while  Since  i n most  first  mode,  we  first  added.  mode and  Thus,  final  equilibrium The listed  2.2  unlike  revised  rotations  and  bending  t h e RSS  From of  fixed, at  ductility  the  in  the has  hinge  exactly  response  the bending  moments  is  moments f o r  have been t a k e n  and  in  from  l o a d s have been shears  are  in  manual  is  values. the  user's  A.  proposed  procedure  which t a k e s  behavior  of  response  of  reinforced  structure  the two  this  9,  structure.  almost  1971  this  assembled  properties,  San  method  is first  the  in  method  i n t o account He  5  as  explicitly used  the elastic  7-story  time  the  framed  in C a l i f o r n i a -  mathematical  i . e . s t i f f n e s s and  usual  inelastic  earthquake.  elastic  formed,  approximate  the  Inn M o t o r H o t e l s  Fernando an  an  i t to determine  identical buildings-  concrete Holiday  the Feb In  are  and  FREEMAN'S METHOD Freeman  to  t h e end  rotation  to s t a t i c  program a l o n g w i t h  i n appendix  known.  being  most of the  t h e v a l u e s due  these  at  end,  t h e c a l c u l a t i o n of c u r v a t u r e d u c t i l i t y , the  t h e member  previously.  structures, the  of  rotation  the c u r v a t u r e did  end  diagram are  the o t h e r  knowing t h e  calculate  same manner as  other  the c u r v a t u r e )  r o t a t i o n . Thus,  location, the  thus  v a l u e s , we  plastic zero  rotation  way;  model of  mass  knowing t h e  period  and  the  matrices structural  other  dynamic  19 response p r o p e r t i e s response  spectrum  are calculated.  i s also  An  appropriate  linear  s e l e c t e d w i t h a c h o s e n peak  ground  accelerat ion. To two  calculate  curves  are  representing  the  required:  the  capacity  'demand c u r v e ' , w h i c h structure  inelastic  response of the s t r u c t u r e  a) of  the the  represents  by a p a r t i c u l a r g r o u n d  'capacity  structure,  the  demand  the  determining  put  the  of the s t r u c t u r e  only  motion.  the c a p a c i t y  CURVE  f u n d a m e n t a l mode o f v i b r a t i o n i s c o n s i d e r e d ,  for  simplicity;  response, of  and b) t h e on  2.2.1 DETERMINATION OF THE CAPACITY In  curve'  regular  i n any c a s e ,  vibration.  same  in  way  as  The  capacity  structure  depends  strength  or  to  upon  redundancy  of ' r e s e r v e  first  i s found  the which  the  s t r u c t u r e s the  due t o t h e  curve  in  according  6  availability  i s mainly  suggested  Technique' ,  and u n i f o r m  the  energy'  'Reserve the  Energy  damage of  structure,  or  mode  i n much t h e  availability  in  mainly  ductility  to  a  reserve and  the  in  the  structure. From  the  mathematical  structure  and  the  structural  members, t h e e l a s t i c  terms  of  spectral  fundamental p e r i o d since  known  the s t r u c t u r e  elastic elastic  capacities  capacity  acceleration  of v i b r a t i o n  model  is  as  a  found  of of  the the  threshold  in  function  of  as  follows:  i s assumed t o v i b r a t e e s s e n t i a l l y i n  20  the  first  mode, a l a t e r a l  mode c o r r e s p o n d i n g major  members  to yield  i s  elastic  spectral  acceleration  displacement To  the  developed reduced  spectral  i n which  strong  form  i n the girders  range,  elastic  simple  bi-linear  values  of  response  ( i t should  so p l a s t i c  while  model,  be  hinges  t h e columns  t h e moment  for  level  this  that  the  cracked  model  concrete  new an  section,  displacement  capacity. This displacement  ) a s we know t h e t i m e  five  and  to  expected  to  To d e v e l o p of  a  the  value and then factors  A  lateral  acceptable  peak  I t i s suggested  then  capacity  that  girders  inertia  of the structure  (AS^)  noted  model.  displacement  displacement  greatly  participation  i s determined.  equals  model i s  are expected  are  of  represents  of the structure  i fthe elastic  (AS  roof  structure  f o r weak  t o 5% o f t h e e l a s t i c  reduced  that,  spectral  this  the  d u r i n g t h e ground motion).  calculated  displacement  of  displacement and  are assigned  p e r i o d s , mode s h a p e s a n d m o d a l  are  period,  a new m a t h e m a t i c a l  a l l the girders  columns;  remain  i s  of  factor  values associated with  elastic  and  the  the  code d e s i g n p h i l o s o p h y c a l l s  girders  the time  participation  the characteristics  stiffness  current  Knowing  number  a r e computed.  estimate  beyond  mode  structure,  i n the first  in a substantial  determined.  mode s h a p e a n d t h e f i r s t the  roof displacement  i s based  the  times  on  inelastic  the  elastic  i s converted to  spectral  acceleration  p e r i o d o f t h e new m o d e l  of the  21  structure  (beyond  cumulative  values  the of  elastic  spectral  spectral  displacement  effective  period  range)  and  acceleration  can  be  o f v i b r a t i o n (T  f  f  used  then S  to  the  ,  a  find  and the  ):  1 )  Once  we  get  these  acceleration limit  and t h e  bi-linear noting  time  peak  that  same i d e a  accuracy  period  on  curve, limit  curve  nothing  is  a  t o do w i t h  required,  one  better  the  motion.  upon  the  can get a m u l t i l i n e a r c a p a c i t y  by an a p p r o p r i a t e r e s u l t s these  to the s i t e ,  motions a t the s i t e . required in  representing  linear  spectra  spectra  or the spectra  damping  of  demand c h a r a c t e r i s t i c s o f t h e g r o u n d m o t i o n a r e  represented  are  simple  ). I t i s worth  c a n be e x t e n d e d , a n d , d e p e n d i n g  DETERMINATION OF THE DEMAND CURVE  site,  a  t h e ground  2.2.2  scaled  get  property  (see F i g 2.2(b) ).  For  spectral  i . e . the e l a s t i c  we  curve  The  the  (see F i g 2 . 2 ( a )  curve  the capacity having  points  response  capacity  structure, The  vs.  two  obtained  the  equivalent  recorded  two v a l u e s  the  shapes  e s p e c i a l l y f o r the  from t h e  Then a t l e a s t  elastic  spectrum.  c a n be s t a n d a r d  developed  - one r e p r e s e n t i n g the  response  ground  o f damping  equivalent  structure, viscous  and  viscous  the  damping  in  other the  22  e l a s t i c EFF.  e l a s t i c  PERIOD,  T  e  f  E F F . PERIOD,  f  (a) Fig.  2.2. CAPACITY  T  g  f  f  (b)  : SPECTRAL ACCELERATION VS. E F F E C T I V E PERIOD  structure  at the  assumed  that  between  these  from  the  excursion. response spectrum shown  the  effective  two v a l u e s , elastic  Knowing spectra  fora  inelastic damping  with  limit  to  these  particular  varies  the  roof  the  maximum  values  f o r various  excursion.  and  values  structure  response  we  have  is  at  reconciliation  linearly  displacement inelastic  having  linear  o f damping  a demand  is  developed  these the  two  curves,  the  intersection,  or  o f t h e demand a n d t h e c a p a c i t y  intersection  is  below  the  elastic  as  intersect  predicted at curve.  capacity,  s t r u c t u r a l , damage i s a n t i c i p a t e d . I f t h e two not  It is  i n F i g 2.3. Once  this  maximum  curves  the If. no do  a t a l l , b e c a u s e t h e demand a t a l l p o i n t s  e x c e e d s t h e maximum c a p a c i t y  of the s t r u c t u r e ,  t h e n 100%  23  damping d.  PERIOD,  elastic Fig.  T  2.3. DEMAND : SPECTRAL ACCELERATION VS. E F F E C T I V E PERIOD damage o r c o l l a p s e  of the s t r u c t u r e  the  is  intersection  capacity  curve,  evaluated. effective from  between spectral the  peak  time p e r i o d curves,  t h e two  acceleration a r e read  response  spectra  used  to  obtain  the  the  peak r o o f  displacement. This  is  then  demand  compared  that  and  of the  and  be the  directly  to  p a r t i c u l a r ground  the  capacities motion.  peak  The  spectral  be r e l a t e d t o  spectral  the e l a s t i c  estimate  reserve  curves.  and t h e e f f e c t i v e t i m e p e r i o d o f  from e q . ( 1 ) , w h i c h c a n a l s o  to  If  ( s e e F i g 2.4) Damping i s i n t e r p o l a t e d  displacement  displacements  region  response parameters can  of the s t r u c t u r e  damped  are  anticipated.  inelastic  spectral  acceleration  structure  the  then v a r i o u s  The  the  in  is  displacement  and maximum  system/tip  spectral ductility  of the s t r u c t u r e  under  24  This response  method  only  parameters,  ductility,  but  and  a d e s i g n e r , who  design the  situation,  members  earthquake  of  i s assesing o r who an  this  Freeman's method. The structure, The  a  structural  of  anything  The  latter  individual  system/tip about  is  structure  program:  1.  elastic  has  been  which  to  written  analyzes  p r o b l e m may  model  in  response a  concern  noted  i s based  on  with  a  shear  regard  of  both.  to  the  concrete  Spectrum  < o w cu to  Capacity  PERIOD,  RECONCILIATION OF  CAPACITY AND  by  wall  o  2.4.  of  the  structures  the c r a c k e d  Transition  Fig.  a  future  during  frame s t r u c t u r e or a c o m b i n a t i o n  computer  important  members the  the  situation.  f o l l o w i n g p o i n t s must be  The  estimate  us  existing  work  overall  i s determining  in a r e t r o f i t  of  tell  structure.  A computer p r o g r a m course  the  g i v e s an  i t d o e s not  damage p a t t e r n i n t h e to  gives  DEMAND  T  25 section,  so t h e maximum i n e l a s t i c  structure elastic 2.  Since  has  been  threshold  assumed  before  to  be f i v e  the  the  beams  columns,  will  of  that  this  was  adopted  other 3.  It  the  beams  at  have y i e l d e d .  assumption  i s somewhat  i n order  plastic  point  a  point  when  I t c a n be a r g u e d  arbitrary  t o make t h i s  of the  but i t  method a g r e e  with  methods.  is  possible  applicable  to  gravity  analyze loads  the  structure  for  p r i o r t o the a n a l y s i s f o r  seismic  loads.  At the time of  writing  static  loads  can  i n two ways: t h e y c a n  either or  as  If  one  the  a uniformly has  twice fact  in that  deflect results This  other  types  they  should  that  this in  both  an  forces  of  on t h e members.  be c o n v e r t e d  t o one o f  putting  each  structure This  that  a t t h e nodes  loading  i n the data. should  method  does  not  the  may  tell  i n the s t r u c t u r e  effective  time  be  i s t o account  earthquake,  ways;  thesis  static  before  method.  this  lead  to  us a n y t h i n g  but  period,  i t  run  f o r the  structure  and t h e maximum o f t h e two s h o u l d  damage p a t t e r n the  input  d i s t r i b u t e d load  types mentioned  I t i s suggested  about  be  be a p p l i e d a s g e n e r a l i z e d  distributions,  4.  the  times the  form  the y i e l d  s t r u c t u r e h a s been assumed t o be half  of  displacement.  in a structure  hinges  capacity  will  different be t a k e n . about the  does  effective  tell  us  viscous  26 damping, response  spectral of  acceleration  the s t r u c t u r e ,  inelastic  capacity  It  t o use and  i s easy  used  same a s would be u s e d T h i s method it used  should  be  noted  i t to predict  structures  to thus  recorded  motion  investigation non-structural these elements structural The  of the  ordinary  static  agreed  earthquake well  considered  elements  the  i n the a n a l y s i s  he  frame and  with  the the  detailed  participation  of  indicated  that  in affecting  the  play  a significant  role  response  t o the ground  motion.  B.  but  that  5  identical  quite  the  stage  o f t h e s t r u c t u r e s . A l s o a more  which  is  analysis.  p r o g r a m a l o n g w i t h t h e u s e r ' s manual  in appendix  remaining.  reported  of two  Fernando  demand,  data  at t h i s  Freeman has  197 1 San  obtained  input  approximate  the response  the  responses  that  reserve capacity  form  i n an  i s quite  d i s p l a c e m e n t a t peak  system/tip d u c t i l i t y  and  the  and  is  listed  3.  3.1  METHOD The  sense  p r o p o s e d method that  properties  it  are  performance  of  Many b u i l d i n g s seismic  quite  code  areas  any  It  existing that  the  the  fact,  they  the  more o r  less  Before following  structures  for a  existed,  in  the  might  need  of  the that  20  to  t o be  the  the  the  for  the  changed  i t becomes more  reanalyzed or  to  locate  stiffening.  i s expected  modification.  that  checked  code-designed  to evaluate  earthquake.  c o d e s have  and  the  following  strengthening method  the  evaluate  future  years,  'reasonably'  procedure,  to  arise  structures  also  are,  to  identify  actual  ductility  assumption  implicit  The  d u c t i l i t y demand w i l l  be  uniform. this  method  restrictions  The  s y s t e m can  2.  The  structure  3.  Reinforcement their  inelastic  past  whose  ago,  seismic  structures  require  1.  that  used  need t o be  estimated  code  member  then  t o behave  members w h i c h  structures  long  main v a l u e  going  in  be  need t o c o n f i r m  be  can  ' r e t r o f i t ' method,  were d e s i g n e d  for c r i t i c a l  demand may in  known.  to  requirements. Since  where  However, from  applied  drastically  important  is also a  is  codes that  present  in  STATIC DAMAGE EVALUATION METHOD  be  are  is  not  i n one  yield  detail,  vertical  joints  to withstand  deformation without  27  plane  under s t a t i c  of a l l members and ability  in  the  noted:  analyzed  should  described  are  repeated  significant  only.  loads known  alone. such  reversals  strength  of  dacay  28 can  be e s t i m a t e d .  These a r e t h e b a s i c other  common  analysis  in  structural  knowing data  the  method. any  components  Some  seismic  do  not  etc., are discussed  The method works  lateral  loads;  static  i n the  properties, matrix  member  analyzed  forces  and Then  f o r c e s , a s c a l c u l a t e d by t h e  and a q u a s i - s t a t i c  t h e same e l a s t i c  is  of t h e  forces are calculated.  seismic  code, a r e a p p l i e d ,  with  member  i n and t h e s t i f f n e s s  gravity  due t o t h e s e  equivalent  elastic  i s f o r m e d . Then t h e s t r u c t u r e  applicable  deflections  done  chapter.  the  i s read  structure  building  the  way:  First,  the  non-structural  i n the following  following  for  that  with the s t r u c t u r a l response,  detail  elastic  in  a s s u m p t i o n s w h i c h a r e made d u r i n g  e.g.  interfere  assumptions  stiffness  analysis  is  m a t r i x . The r e s u l t i n g  member end moments, due t o l a t e r a l  seismic  scanned  o f moment t o t h e ' l a t e r a l  to find  the highest  moment' c a p a c i t y moments  which  of t h i s the  member  additional freedom)  then  plastic  by t h i s  the  the  resulting  the s t a t i c At  from  ratio  first  forces  multiplied from  ( i . e . the actual  resulting  inverse  load  moment c a p a c i t y  static  gives  the l a t e r a l  hinge w i l l from  gravity  the  minus t h e  loads  load  then  ) . The  factor  at  form. D e f l e c t i o n s and lateral  loads  are  f a c t o r , a n d added t o t h o s e r e s u l t i n g  loads.  location  node  ratio  forces, are  (or  of f i r s t an  i s introduced  plastic  additional  h i n g e o r h i n g e s , an  rotational  on t o p o f t h e p r e v i o u s  degree  of  node w i t h t h e  29 same  x  a n d y c o - o r d i n a t e s , a n d t h e same x a n d y d e g r e e s o f  freedom, to  but with a d i f f e r e n t  account  permits  rotation  structure a  f o r the fact  stiffness  different of  lateral  loads  the The  matrix  this  quasi-static  that a plastic  respect  structure,  response  scanned  with  the load  form.  Member  forces  and  and  added  to the previous  is  added.  the  s t r u c t u r e i s approximated  structure and  a  until  new  To  which  estimate  displacement static  loads  found,  and  i s called  resulting plus i s  linear  in  end  moments  capacity.  load  plastic  resulting  i s  factor,  hinge  will  from  this  of the load  factor  plastic  hinge  reassembled  process  and t h e  the u l t i m a t e roof  lateral  A. F o r t h e d e s i g n  of  roof  displacement.  displacement  elastic  loads  i s continued  a p r e - c a l c u l a t e d value  roof  of  linear.  applied lateral  added. T h i s  the  to  the non-linear behavior  matrix  ultimate  applied ordinary  moment  as piece-wise  the unfactored called  The  end moments a r e  and a second  analysis,  hinge  this  have  previous  the second  values,  the s t r u c t u r e reaches  displacement  the  f o r the o r i g i n a l l y  plastic  s i n c e we now  same  o f member  by t h e i n c r e m e n t  stiffness  analyzed  The  the  deflections  are multiplied  the  node.  the resulting  plus  analysis  Again  by  ratio  a t which  in this  freedom  definition,  hinge.  p o r t i o n of bending  ratio,  factor  by  adjoining  plastic  Again  unused  Thus  the  calculated  inverse of t h i s  gives  a  the largest  previously  hinge,  of  structure to the o r i g i n a l l y  analysis.  to find  to  degree  i s reassembled,  with  new  i s  rotational  ,  the  s t r u c t u r e from the seismic  loads  i s  of the s t r u c t u r e ,  30  these  unfactored  factors. above but  It  are  they  not  the  acting  Now,  when by  on  the  K  material damping  and  of  structural be in  the  the  It  fact,  The structure  of  shear  formula  mentioned the  NBCC , 8  factor a  number  is calculated  as  i s used:  2.8  K  of  factor  to  3.0  the  a  a  ultimate  of Canada  that  structure  the  depends upon  the  the  structure various  supplement gives  9  the  designer  the  to  an  the  allowable might  K . M i s always  s t r u c t u r a l forms. been t a k e n a  to K  s t r u c t u r a l f o r m , he for  types  structure  product  chooses  by  implied  be  In 2.9,  factor i s , in  system/tip  2.9/K.  displacement by,  of  M , f o r w h i c h the  particular  i s then g i v e n  the  f a c t o r has  approximately  and  represents  a c t i o n . For  for various  this  when  formula  capacity  i s observed  to  designing  ductility  base  inelastic  Code  method  corresponding  load  simultaneously.  above  Commentary  that,  by  combination  construction,  and  ductility  present  implying  the  of  Building  r a n g e of  suggested  load  following  in  damping  designed.  factors  r e d u c e d p r o b a b i l i t y of  seismic  type  structures,  National  the  energy a b s o r p t i o n  both v i s c o u s  load  appropriate  = A.S.K.I.F.W  factor and  the  structure  NBCC, t h e V  The  the  the  f a c t o r s a as  load  i n t o account  loads  m u l t i p l i e d by  that  a m u l t i p l i e d by  are  suggested  are  i s worth n o t i n g  which t a k e s of  loads  that  is  allowed  in  a  31 where:A  =  lateral  loads LF  plus  = load  roof  the unfactored  by  we  factor  know t h a t  the performance  hence  the  load  displacement. Now ultimate motion designed allowed whatever  the  factor  (See F i g .  to y i e l d force  i s divided  produced the  and respond  Fig.  i n the design  i t  are divided moments,  by <f> t o g e t t h e u l t i m a t e  3.1)  to that  level  used  <j> t o g e t t h e member y i e l d  assumption  essentially  t o respond  loads  f o r t h e member  factor  basic  the s t a t i c  loads  t h e r e s u l t i n g member f o r c e s  displacement is  r e s u l t i n g from  seismic  f a c t o r on l a t e r a l  4> = p e r f o r m a n c e Since  displacement  i n the a n a l y s i s  in a structure same  whether  earthquake  the  by t h e  ground  the s t r u c t u r e i s  elastically  i n an i n e l a s t i c  yields,  i s that the  or  is  manner. Thus a t  maximum  displacement  3.1. FORCE DISPLACEMENT CURVE  32 attained  will  be A^ .  Thus t h e l a t e r a l plastic  hinges  reaches  a  placed  roof  displacement  A  u  loads  a r e i n c r e a s e d g r a d u a l l y , and t h e  successively,  displacement  A^  until  .  In  if  ductilities  member  with  a  the  small  of the l a s t  structure  computational structure account  stiffness  hinge  the  structure  attains  calculate the  formation,  matrix  is  member.  are  a total  in  to  order  to so  Then  up  this  of A  of  plastic  some  length  for  Studies a t the U n i v e r s i t y of Canterbury,  suggest  that the p l a s t i c  0.65 t i m e s  the o v e r a l l  members. A  recommended  value  length  member d e p t h of  a s a good o v e r a l l  =  taking  into is  loads;  the  until  the  .  u  we  have  to curvature,  hinge.  hinge  the  ductilities hinges  the  Then  lateral  roof displacement  rotation  prevent  structure  down  t h e member c u r v a t u r e  member  that  apply.  or  w h i c h r e q u i r e s us t o assume  concrete  to a roof  placed at the  reassembled,  applied  scaled  is  unstable,  continues  originally  deflections  to  member  calculate  corresponding  stiffness  becoming  fictitious  for  convert  flexural  from  resulting  To  the  as d e s c r i b e d l a t e r ; but  ductilities  algorithm  this  solved  this  i n t h e f o l l o w i n g manner: a f i c t i t i o u s  very  location  then  form a c o l l a p s e mechanism we  curvature  displacement  to  are calculated  t h e s t r u c t u r e does  the  reaching  t h e s t r u c t u r e may o r may n o t form a c o l l a p s e  mechanism. I f i t does n o t form a mechanism curvature  the s t r u c t u r e  the  plastic  New  Zealand  may v a r y  from  0.35  for solid reinforced 0.5(depth)  has  been  average v a l u e . These f i n d i n g s  have been w e l l summarized We  by M a n d e r  1 0  .  know: $  p  = $ - $ u y  See F i g . 3.2 The p l a s t i c  curvature  $  we know t h a t t h e y i e l d  9 E—  =  curvature  =  6 E_ 0.5 d e p t h o f a member  i s g i v e n by  M  $  = y y  where: My = y i e l d EI then  EI  moment o f t h e member  = Flexural  stiffness  t h e member c u r v a t u r e  o f t h e member  d u c t i l i t y (CD.)  '  Fig.  i s g i v e n by:  CURVATURE, 4>  3.2. MOMENT CURVATURE DIAGRAM  34  CD. y or  CD.  1 +  =  <i>  y  Thus  the  curvature  structure  ductilities  for  each  a r e c a l c u l a t e d and the expected  member damage  in  the  pattern  is  i s increased  by  known. Then, 10%  the ultimate  and c u r v a t u r e  recalculated, ultimate  ductility  displacement demands  corresponding  roof  'Sensitivity  roof  to  Index'  Sensitivity  Index  =  increased  Then,  i s defined  u  f o r a l l t h e members  this  displacement.  A  an  value  index  are of  called  as:  A(CURV.  DUCT.)  0.1  where: A(CURV. at  a  DUCT.) member  =  increase  end  due  i n the curvature to  10%  ductility  increase  demand  in ultimate  roof  di splacement Thus,  for  index,  i t means  ground  motion,  demand  could  particularly  during  member  that  be  a  high  slight  increase  careful  results demands  ground  judgment  of  sensitivity  in  curvature  designer  such  that  motion.  to  the  The  of  value  increase  in  in detailing  the  ductility  his  with  significant.  a particular  exercise  for  the  Essentially, curvature  a  peak  ductility  should  be  members.  this  analysis  are Then,  determine  the  are  p u t on e a c h the  designer  whether  a  the  member must  particular  35 member  has  detailed  sufficient  available  i n t h e manner s u g g e s t e d  revision  of  the  analysis  also  design  gives  the  corresponding  to  plastic  . The code  that  hinges  the  load and  over  factors  it  will  behave  according  structure possible of  vary  yield  a t the l a s t that  widely to  the  t o ensure uniform K factor  ductility,  representing  This  hinge  these  formation is  very  which w i l l  should  not  F o r an i d e a l  be a s narrow  and t o j u s t i f y  the d u c t i l i t y  and  as  t h e use damping  PROGRAM CONCEPT  p r o g r a m u s e s t h e same c o n c e p t s a s a r e u s e d  static  plane  structural analysis.  which  does  an e l a s t i c  minor m o d i f i c a t i o n s  plane  I f a program  i n any  is  available  structural analysis,  w i t h some  i t c a n be c h a n g e d  into  t h e form u s e d  in  program. The  structure  elements. A n a l y s i s find  of  i n t h e system.  3.2 COMPUTER  this  idea  are uniformly  assumptions.  factors  loads  demand and t h e y i e l d  the s t r u c t u r e ,  code  this  the  formation)  the d u c t i l i t y over  on  range  at f i r s t  a  of the v a r i o u s  pattern  hinge  whether  lateral  based  But i f t h e  factor  t h i s range of l o a d  a single  inherent  the  on  formation  is implicitly  when  In a d d i t i o n ,  factors  sequential  and  indicates  pattern  necessary.  the s t r u c t u r e .  factor  by t h e c o d e , o r  load  ( i . e . the load  the load  wide,  the  ductility  distributed  is  curvature d u c t i l i t y  the nodal  i s i d e a l i z e d as a  planar  i s done by t h e D i r e c t  global  displacements  assemblage  of  S t i f f n e s s Method t o  and  thus  the  member  36  forces. any  E a c h node c a n h a v e  typical  degrees zero  plane  of freedom  in  the  to  the  structure,  substantially  the f i r s t  for  the e l a s t i c  can  the  A  load of  converted  applied  directly  stiffness  from  node  of  freedom  i s  of  t o be  unknowns  static  solved  member loads i s  for  member  earlier,  nodal  applied  directly  to  l o a d o n t h e member.  on t h e n o d e s , a r e r e a d main  forces  the static  f o r c e s , as c a l c u l a t e d  and  read  matrix  individual  the  distributed  matrix  of  i n t h e r o u t i n e SDFBAN.  as loads  i n the  i s  provides  locations i s  for  mentioned  seismic  to a load vector  elastic  lateral  lateral  a s some o t h e r  the stiffness  displacements,  be i n p u t e i t h e r  same  of the problem  Then  method  as  the  t h e numbers of nodes.  equations  However,  has  numbers  vector  Cholesky's  has  i n the idealization  the size  in  no d e g r e e o f  provision s t i l l  the total  nodes or as a u n i f o r m l y  and  node  degree  freedom  of the program.  the global nodal  equivalent  same  times  as  i s a provisionfor  ground,  i fa  structure i s built  by  found.  the  p r o p e r t i e s and j o i n t  matrices.  should  code,  same  thus three  and the system  be  loads  than  part  displacements  the  freedom  o r d e l e t e d . I f a node  displacement  permits  reduced;  in  The  but  of  There  t h e nodes. T h i s  f o r member  stiffness  node;  substantial  be much l e s s Data  then  both  analyst with  Knowing  to that  to  or r o t a t i o n a l  the  formed,  relative  structure,  assigned  may  t o be c o m b i n e d  i s assigned  translational  degrees  frame a n a l y s i s .  displacement  freedom  three  routine. this  forces, the structure i s solved again  by  the  i n and  With  the  load  vector of  by  Cholesky's  37  method is  ( u s e o f t h e same e l a s t i c  justified  static  loads  seismic  to  no  member  are  i s allowed  forces  found  the  highest  in  ratio  o f moment c a p a c i t y , be  increased,  plastic  due  the  to  same  to yield the  a plastic  equivalent  manner. Then t h e each  member  i f the l a t e r a l end  would  additional assigned  node  is  restrained against  placed  a t t h e member  t h e same x a n d y c o - o r d i n a t e s ,  degrees  different  loads  of  freedom  as  the  rotation,  with  adjoining  node,but  and  with a  r o t a t i o n a l d e g r e e o f f r e e d o m . I f a member end  d e g r e e o f freedom;  unknowns NU i s i n c r e a s e d  i n e i t h e r case  stiffness  matrix  is  structure  stiffness  matrix  i s reassembled.  lateral i n t h e main  a mechanism calculated  is  again  loads.  routine:  i n the routine roof  analyzed  Then  ( i . e . whethter  the  rechecked,  whether  number  SBFBAN  for  the  the  program  has  reaching  of the overall  f o r two  has formed  of the v a r i a b l e  is  A  close  to  'ratio'  zero),  reached , then  of  originally  checks  the s t r u c t u r e  the value  displacement  mechanism h a s formed b e f o r e  the  and  was  t o have a  by one . Then t h e h a l f - w i d t h  structure  structure  the  an  node i s  t h e same x  rotational  The  so  end. T h i s  f i x e d , t h e e x i s t i n g node i s now a l l o w e d  whether  were  l o c a t i o n , the  initially  things  member  form the f i r s t  h i n g e h a s formed a t t h a t  member end i s no l o n g e r  applied  under  o f t h e end moment t o t h e u n u s e d  because,  that  matrix  hinge.  Since  y  member  stiffness  RATIO s c a n s t h e moment a t b o t h ends o f  find  part  alone);  forces  routine to  because  structure  . the  If  or a  analysis  38 is  continued  is  reached.  as p r e v i o u s l y d i s c u s s e d u n t i l In e i t h e r  corresponding the  manner  displacement  the  members a s d e f i n e d The  in  and  program a l o n g  a p p e n d i x C. S i n c e  check  a  structure setup  again  feature,  attractive  it  is  t o use even  are calculated in  increased  i s computed  roof  for a l l  i n s e c t i o n 3.1 . with  t h e u s e r ' s manual u s e d  program  design,  Data  supposedly or  to  hoped,  will  check  an  is listed be u s e d t o existing  t h e e a s e of t h e  is essentially  have been u s e d by t h e d e s i g n e r this  ductilities  . Then, t h e c u r v a t u r e  index  f o r a future seismic hazard,  is significant.  u  for slightly  senstivity  this  preliminary  of A  i n s e c t i o n 3.1  are calculated  displacement  t h e member c u r v a t u r e  to a roof displacement described  ductilities  the  case,  this  data  t h e same a s would  i n h i s p r e l i m i n a r y d e s i g n and will  make t h i s  i n ordinary design  p r o g r a m more  situations.  4. MATHEMATICAL MODELLING: ASSUMPTIONS AND Mathematical modelling i s process  for  analyzing  the  an  important  structures  earthquake  like  ground  routinely  made  i n the mathematical  affect  m o t i o n s . Many  and a s s u m p t i o n s  made  for  of  the  response  assumptions  that  to are  can g r e a t l y  are discussed  h a s been made t o d i f f r e n t i a t e  assumptions  part  model, which  t h e outcome o f t h e a n a l y s i s ,  attempt  COMMENTS  here.  An  between t h e n e c e s s a r y  i n the present analyses.  4.1 NECESSARY ASSUMPTIONS The whether  first to  decision use  i n the c o n s t r u c t i o n  the  cracked,  concrete  s e c t i o n . That depends,  on  magnitude  the  small  motions,  concrete  will  section the  participation partitions, at  floor of  such  exterior about  the  members, t h e m a t h e m a t i c a l concrete  sections;  non-structural concrete  situation,  sections  thus reducing  the  of  model  include  should  elastic  of major  should include neglect  capacity  small  elements include  as  interior  For  large  structural  fully  cracked  the p a r t i c i p a t i o n of  the s t i f f n e s s  39  for  also  cases.  limit  or  transformed  elements  I t c a n be a r g u e d  increases  structural  Therefore,  and t h e s t a i r  elastic  f o r very  a l l structural  It  i t might  elements.  Initially,  elements,  non-structural  walls  is  for a particular motion.  slabs.  model  transformed  participate.  properties  a  or  t h e m a t h e m a t i c a l model s h o u l d  including  motions  lateral  a l l resisting  non-structural, motions,  of  uncracked  of  that  use of  gross  of the s t r u c t u r e ,  displacements  ,  and  40 shortening  the period  b a s e d on c r a c k e d period  of v i b r a t i o n  concrete  sections,  of v i b r a t i o n i s higher.  periods  of  real  . ' I f the e l a s t i c  buildings  the  initial  I t i s found  increase  that  as  model i s  . predicted the natural  an  earthquake  progresses. It the  h a s been r e p o r t e d  gross  measured  section  initial  concrete  that  cracked  frame-wall  cracking  to  structure,  better  the  the  i n the  better  with the cracked measured  same  study  estimates  of t h e  s e c t i o n model, which  redistribution  in a  although  the  with  reported  structure.  of In  t h e m a t h e m a t i c a l model  frame  Thus t h e a x i a l wall-frame together.  construction, deformation  construction, I t i s only  able  to  loads  transferring  internal the  is  f o r c e s as  course  of  the  i s b a s e d on t h e c r a c k e d  level.  floor  from  the  such  loads,  slabs  slabs  i.e. floor  exterior floor  load.  slabs  that  they  t r a n s f e r the  walls  to  slabs  are  stressed  as a  arising  from  these  deformations  small,  also  axial  t i e t h e frame and c o r e  the  core.  In  i t i s commonly assumed t h a t a l l  d e f l e c t i o n s o f frame and c o r e This  little  of t h e beams i s i n s i g n i f i c a n t . I n  a c t a s one u n i t  are usually  horizontal  beams c a r r y  because of t h e f l o o r  i n shear. Since  stresses  one  been  that  1 1  section.  In  membrane  the  correlates  I t has a l s o  develops  concrete  of  study  compare b e t t e r  s e c t i o n models p r o d u c e d  present'study  lateral  periods  i n t e r a c t i o n than a g r o s s  attributed  are  vibration periods  section  displacements.  i n a recent  helps  to  are  reduce  equal  the  at  any  s i z e of t h e  41 problem. The  core  integrated generally the since  at  and  the  frame of  the  base w i t h v e r y  assumed t h a t  rotation the  of  core  the  and  to  they  restrained  are  buildings  stiff  these provide foundation  the  connected  tall  massive  frame  a rigid  the  from  i s ignored.  by  in  and  Further,  region  rigid  displacement  It i s  connection  basement  retaining walls  usually  basement w a l l s .  system  in  are  floor the  are  slabs, lateral  di rect ion. As any floor  mentioned e a r l i e r ,  one  level  level  becomes  the  horizontal  i s assumed t o be  i s lumped a t  diagonal  one  and  equal,  point.  this  results  in  the c a l c u l a t i o n s .  Selection  of  damping v a l u e s  material,  type  non-structural viscous  included  with  the  following  which  experimental  i n the  uncracked  earthquake  i s present  require  which  that tested  mass  a  s t a t e and  rather  upon  the of  equivalent  recent  f o u n d by  viscous was  is a  of  frame-wall  damping  each  matrix  distribution  value  at  considerable  depends  and  t e s t s on  viscous  concluded  assumption  structure  mathematical model. A  structures  the  a  mass a t  for a structure  construction  f o r the  has  frame-wall critical  of  equivalent  decrement,  in  e l e m e n t s . We  damping  which  One  Damping  the the  of  task.  so  Thus  simplification  difficult  displacement  study  1 1  structures, logarithmic  damping  for  approximately  the  2%  of  r a n g e d between 4 and  8%  simulations. i s a l s o worth m e n t i o n i n g h e r e ,  in a l l seismic  a n a l y s i s except  in  and  time-step  42 procedures, vibrates the  is  this:  i n both  static  during  directions.  equilibrium a  a  ground motion a s t r u c t u r e  I t v i b r a t e s to e i t h e r  position;  analysis  or  psuedo  structure  i s pushed o n l y t o one  y e t whenever we  non-linear  seismic  side.  i n t h e members w h i c h c o u l d have  (due  static  to the  being  symmetric),  gravity had  the  earthquake,  i t i s assumed t h a t t h e h i n g e not  structure  affect  vibrates  the hinge  a  been  a modal the  sequence different  s t r u c t u r e not  s t r u c t u r e been p u s h e d  Since  does  get  to the  direction.  sequence  the  l o a d s o r due  do  of  analysis,  Thus we  of y i e l d i n g  side  i n the  both  ways i n an  formation  formation  other  in  i n the  one other  sequence. The  soil-structure  Such e f f e c t s thus  be  will  likely  interaction  undoubtedly to  reduce  is  normally  complicate their  the  v a l u e as  ignored.  methods,  simple  and  tools  for  design.  4.2  ASSUMPTIONS MADE IN PRESENT ANALYSES Some  present  assumptions  to s i m p l i f y  usable  absolutely First, plane  have  work a r e d i s c u s s e d h e r e .  made m a i n l y more  which  only.  significant inelastic  in  an  the I t has  during  the  T h e s e a s s u m p t i o n s have  been  t h e work and  average  necessary  been  design  t o make office,  f o r the a n a l y s i s  structure also  stiffness  can  been  d e c a y due  deformations  in  the  be  made  per  these but  t o the  are  not  se.  analyzed  assumed  they  methods  i n one  that repeated  members,  vertical  there  is  reversals  though  in  no of the  43  time-step analysis  program  c h o o s e a beam e l e m e n t At into  this  account  significant are  stage, P-A  with degrading  not c a p a b l e of t a k i n g f o r t h e columns  assumed  to  to input  point  t h e s e methods, 'Static one  moment the  To Method'  worth  and n e g a t i v e  Building  the  Method', for  K,  of  forces  I  structure, should  are  f o r e a c h member, t h e u s e r moment  only.  here,  i s that  Method'  ina l l  and  the  the user can s p e c i f y  only  each  the  to  be  results  obtained  member.  the  Thus,  same  levels.  from o t h e r  seismic  A study  for  Canada  1977,  and F e t c . ,  the  both  1 2  Evaluation methods, we  forces  of the N a t i o n a l  suggests that  fora  to  given  T,  the  we c a n c a l c u l a t e t h e i m p l i e d  earthquake  be s c a l e d  to the  which c o r r e l a t e d t h e  earthquake analyses  peak g r o u n d a c c e l e r a t i o n . In m a k i n g a  spectra  programs  o n c e we know t h e f u n d a m e n t a l t i m e p e r i o d n,  be  b e n d i n g moments.  and dynamic  Code  structure,  that  axial  compare t h e r e s u l t s o f t h e ' S t a t i c Damage  quasi-static  taking  i s assumed t o be t h e same f o r b o t h ends o f  accelerations  factors  no  'Freeman's  i t i s a l s o assumed  with  to  the y i e l d - i n t e r a c t ion  mentioning  need t o c o r r e l a t e t h e q u a s i - s t a t i c ground  of  t h e computer  that  of the y i e l d  o f moment c a p a c i t y  member;  positive  (note  i . e . 'Edam',  capacity  possible  t h e columns, which c o u l d  into account  Damage E v a l u a t i o n  value  in  i n beams). T h u s ,  one v a l u e  Another  is  stiffness.  structures. Also,  surfaces  has  it  t h e programs a r e not c a p a b l e effects  in t a l l  act  DRAIN-2D,  that  dynamic  records value  or of  analysis  of  the response implied  peak  44  ground would  acceleration,  so t h e  seismic  c o r r e s p o n d to those used  forces  on  the  i n the q u a s i - s t a t i c  structure analysis.  5. As  mentioned  methods given  earlier,  i s to predict earthquake  actual  As  the  testing a  structure  essential pseudo of  t o check  For structure Static the  that  i t  is difficult  these  prediction to  the  methods  t o do an is  dynamic  a  ground  done  analysis  o f t h e damage  results  pattern  motion,  obtained  it  from  methods, a r e c o m p a r a b l e  is  other  t o those  analysis.  t h i s purpose,  two i d e a l i z e d  were a n a l y z e d  by  test  a l l these  same s t r u c t u r e s were a n a l y z e d DRAIN-2D  t h e damage  location  represented  f r a m e s and a r e a l  methods  were  to  sized  medium  test  chosen  i . e . . Edam,  the  model  the cracked  c o l u m n s was t a k e n while  so t h a t t h e y  is  transformed  as o n e - h a l f  the c r a c k e d  t h e beams a n d t h e s h e a r  based  demands  member  s i z e s and  represent  in  moment  the small  structures.  The  cracked  of the gross  section  moment  of t h e  concrete  of i n e r t i a  f o r the  moment o f  of i n e r t i a f o r  w a l l s e c t i o n s was t a k e n  45  the  actual  the modelling  on  transformed  and  to a designer.  concrete made  analysis  were compared. The e x t e n t  structures,  were  time-step  ductility  reinforced  assumptions  structures:sections,  by  a  o f t h e damage a r e o f i n t e r e s t  dimensions  following  by  and t h e r e s u l t s  In t h e i d e a l i z e d  inertia,  o f t h e s t r u c t u r e s under a  non-linear  subjected  approximate  Damage E v a l u a t i o n Method and Freeman's M e t h o d . Then,  program of  of  'true'  non-linear analysis  the time-step  g o a l of these  Since  p r o d u c e s t h e most a c c u r a t e in  the  the behavior  motion.  experiment,  analytically.  EXAMPLES  as o n e - t h i r d  46 of  the gross section As  per  the  CAN3-A23.3-M77, taken  moment o f i n e r t i a . current  the  load  a s 1.8 i n t h e S t a t i c  capacity  reduction  0.9,  the y i e l d  thus  seismic  forces.  which  member d e p t h . Evaluation plastic  for  in  method,  0 for flexure  hinge  h a s been t a k e n a s twice the  l e n g t h o f 0.05 t i m e s  most c a s e s other  i s approximately hand,  i f the user  l e n g t h i s taken  in  as one-half  t o 0.05 t i m e s  the S t a t i c  Damage E v a l u a t i o n method, t h e that  the r e s u l t s  the  Static  the  code  a r e based  the  member  equal  to the  Static  Damage  i n p u t s t h e member d e p t h , t h e  i t defaults  so  is  Damage E v a l u a t i o n method, a n d t h e  forces are approximately  the  design  seismic loads, a  on  otherwise  chosen  concrete  In Edam, t h e c u r v a t u r e d u c t i l i t i e s  On  hinge  factor  factor  on an assumed p l a s t i c length,  code  t h e member  t h e member latter  depth,  l e n g t h . In option  c a n be compared w i t h t h o s e  is from  Edam. Since code  Damage E v a l u a t i o n method a p p l i e s t h e  s e i s m i c f o r c e s on t h e s t r u c t u r e ,  chosen  for  analysis Centro  four NS,  discussed scaled  to  Freeman's  earthquake El  r e c o r d s were c h o s e n ;  Centro  peak  EW,  Taft  N21E  c h a p t e r , ground  implied  ground  motion  of  period  of each  0.21g was t a k e n of  the  earthquake  spectrum  is  method. F o r t h e t i m e - s t e p  and  motions  motion  t o t h e code s e i s m i c f o r c e s .  fundamental duration  and  i n the l a s t  correspond ground  Edam  t h e NBCC  they Taft  being  r e c o r d was t a k e n  to  be  the forces  peak  which c o r r e s p o n d s  structures  El  S69W. A s  have  so t h a t  Thus a  were  implied to the  tested.  The  i n a manner s o  47  that  t h e maximum damage i n t h e  structure  occured during  d u r a t i o n . U n l e s s otherwise mentioned, the of  the  size  earthquake  of  the  time-step  one-tenth  of  structure  e.g.  response  is  size  of t h e  period below,  of  in  a n a l y s e s was methods.  a  mainly time the  noted  was  the time p e r i o d  the s i z e  unless  r e c o r d s were t a k e n  of  due  to the  structure  be  of t h e t i m e  first  we  t o compare  that  of t h e  mode. In t h e  the average with  mode of  assume  the  as of  The  approximately  results  the time  examples  0.02 four  the the  t h r e e modes, t h e n  s t e p i s taken  o t h e r w i s e . Then,  be  as o n e - t e n t h  third  seconds  f o r the a n a l y s i s . to  if  taken  i n the  10  the s i g n i f i c a n t  structure,  step w i l l  taken  taken  first  that  seconds time-step of  other  48  5.1  T E S T STRUCTURE  1  The  two-bay,.four-story  frame  o f F i g . 5.1  structure.  Both  bays  a r e 30  feet  are  high.  Floor  weight  f o r each  12  feet  taken  as  bigger  than  the  100  the  i s t h e same  fundamental  seconds.  Response  earthquake computer  analyses demands  records,  have  been  plastic  hinge  The  maximum  mean  curvature larger  5.3(a)  obtained  in  this  11  iterations  the  from  case  was  seconds.  shows  as  the  shows  Edam. 5.4  The  sum  Fig.  shows  given  by S t a t i c  index  structure  period the  Damage  f o r t h e member, has  been  1.32  to  the  ductility of  the  history.  inches.  The  to the  member. non-linear  ductility roof  was  demands  displacement  achieved  after  of the s t r u c t u r e  Evaluation shown  by  non-linear  curvature  pushed  i s 1.1  was  four  square  of  load.  correspond  of  Convergence time  5.3(c)  4.37  the curvature  inches.  load  values  f o r each  average  root  size  i n the response  demands  the  beams a r e  The  the  max.  was  is  were computed  of  i n f i g . 5.2,  and the f i n a l  sensitivity  Here,  recorded  demands  story  . The c u r v a t u r e the  stories  structure  earlier,  test  stories  structure  test  displacement  F i g . 5.3(b)  as  demands  roof  as a  distributed  Results  c a l c u l a t e d from  o f t h e two d u c t i l i t y  analyses.  1.81  of the  F i g . 5.2  rotation,  the  The g r a v i t y  the  mentioned  in  ductility  Fig.  of  DRAIN-2D.  of  beams.  as a u n i f o r m l y period  shown  story  used  and a l l the  and second  throughout.  histories  program  are  first  and f o u r t h  on a l l t h e beams  The  four  The  the t h i r d  columns  kip/ft  kips.  wide  was  t o an  ductility  method,  i n the  was  with  brackets.  ultimate  roof  4 9  displacement  of  results  by Freeman's  period  given  inches.  Finally,  method.  a t t h e maximum r e s p o n s e was  If  we  compare  non-linear compared columns the  5 . 5 7  on  beams  curvature computed  the the would  5.3(d)  methods  non-linear first  1.86  ductility  from the n o n - l i n e a r  the  pseudo  have c o r r e c t l y p r e d i c t e d , analysis  damage.  demands  time  seconds.  s t o r y would y i e l d  suffer  shows t h e  Here, the e f f e c t i v e  t h e r e s u l t s , i t i s seen t h a t  analysis to  Fig.  is  The within  results, and a l s o , variation 20%  analysis results.  that  when the  that a l l in  of t h e  the values  50  My  "  115 k - f t  n  135  (N  1 35 11 5 135 1 25  CM  135 11 5  135  CM  5  135 125 135  135  135  125  125 165  165  165  W W  W W  TO 30'  30'  E = 3760 k s i Floor  weight  Gravity  load  i s 100 k i p s  at a l l l e v e l s  on a l l beams i s 1.1 k / f t Size  Beams First  and s e c o n d  story  Third  and f o u r t h  story  18" X 18" 15" X 18" 20"  Columns  Fig.  5.1. TEST STRUCTURE 1  X 20"  51  3.0  2.55  4.8  4.9  3.9  3.92  6.67  6.62  4.14  4. 1  6.7  6.63  3.4  3.28  2.24  3.1  El  3. 1  Centro  3.87  1 .05 5.43  1 .7 5.43  8.96  9.1  NS  El  3.2  4.22  5.46  5.48  1 .06  4.5  4.6  Taft  4. 1 :  4.85 1.15 4.3 3.15  3.2  N21E  Fig.  4.8  4.84  1 .8 4.7 9  4.79  Taft  5.2. TIME-STEP ANALYSIS (curvature  EW  3.5  4.81  .6. 1  6.15  Centro  RESULTS  ductilities)  S69W  5.2  5.2  5.4  5.4 1.55  4.4  4.4  5.0  4.7  Fig.  5 . 3 ( a ) . AVERAGE OF TIME-STEP ANALYSES (curvature d u c t i l i t i e s )  2.8  2.5  3.6  3.5  4.1  4.0  3.8  3.7  6.6  Fig.  6.0  5.3(b).  EDAM  : CURVATURE  7  DUCTILITIES  3.8(3.6)  3.4(3.8)  5.0(4.4)  5.0(4.4)  5.8(5.5)  5.8(5.7)  5.1(6.5)  5.0(6.7)  3.5(9.0)  Fig.  3.8(8.7)  5.3(c).  3.8(9.0)  STATIC DAMAGE METHOD : CURV. DUCT. ()Sensitivity  P  R  E  D  I  C  T  E  P E R I O O ( S E C ) S P E C .  A C C L ( G )  DAMPING(%) S P E C .  D  R  E  S  Index  P  O  N  S  E  1 . 8 S 0 . 1 7 2 3 . 0  D I S P ( F T )  0 . 4 8 2  D U C T I L I T Y  DEMAND  4 .1  I N E L A S T I C  CAPACITY  64  USED RESERVE  Fig.  CAPACITY  3 6  5 . 3 ( d ) . RESULTS FROM FREEMAN'S METHOD  54 5.2 TEST STRUCTURE The  three-bay,  the  second  feet.  kips  t e s t s t r u c t u r e . The w i d t h o f a l l t h e b a y s story  f o r the f i r s t  5.4  Member  and s e c o n d  The  fundamental Response  same  earthquake  four  Results  of  ductility  period  t h e two d u c t i l i t y Fig.  5.6(a)  analyses.  Fig.  shows  the  sensitivity curvature  were  analyses  5.6(b)  index  ductilty  2.8  for  100  f o r the top so  are  the  on a l l  the  beams  structure test  was  structure  0.89 to the  by  a r e shown  i n F i g . 5.5 .  rotations been  inches.  DRAIN-2D.  during  converted roof  Again,  the  to  the  displacement the  curvature  to the larger  f o r e a c h member.  the  average  shows  the  of  four  results  after 5 iterations  the s t r u c t u r e from  are  computed  hinge have  demands  shows  results  and  i n F i g . 5.5 c o r r e s p o n d  C o n v e r g e n c e was a c h i e v e d of  t h e s e c o n d and  weights  demands. The mean max. was  20  moments a r e shown i n  the  of t h i s  records,  demands shown  period  of  history,  structure  is  load.  of the p l a s t i c  ductility  this  and y i e l d  histories  response  curvature  time  The f l o o r  i s 1.0 k i p / f t  the non-linear  Maximum v a l u e s entire  load  distributed  seconds.  of  while  f l o o r s and 85 k i p s  properties  . The g r a v i t y  a uniformly  for  i s 17 f e e t h i g h ,  A l l t h e beams a r e o f t h e same s i z e  columns.  as  frame o f F i g . 5.4 was t a k e n as  s t o r i e s a r e 12 f e e t h i g h .  floor.  Fig.  three-story  The f i r s t  third  2  the each  demand shown  was  1.1  Static  from  Edam.  the  final  seconds. F i g .  5.6(c)  method,  member shown in  and  non-linear  the  with  i n brackets.  figures  the The  mentioned  55 above, a r e member. 3.5  the  The  inches,  Static  l a r g e r of  two  root-mean-square while  the  method was  obtained  the  ductility  roof  ultimate  2.7  inches.  displacement  roof  Fig.  at  the  max.  5.7(a) and  displacement  this  method,  1.3  seconds.  r e s p o n s e was  5.7(b) show t h e  each  i n Edam in  F i g . 5.6(b) shows t h e  from Freeman's method. In  time p e r i o d  demands f o r  ductility  was the  results  effective  demands  in  the  s t r u c t u r e , i f i t i s pushed  i n the  (-)ve  x-direction i.e.  the  seismic  i n the  (-)ve  x-direction.  If from  we  Edam  time-step static  compare  the  in  method, t h e top  results,  very  well  analysis results.  methods. The increase  applied the  compare  method a r e  because  the  f o r c e s are  generally  maximum r o o f sensitivity the first  story  The  the  with  than  displacement  ultimate  shows,  roof  curvature  ductility  sensitive  t o the  have  the  demands, as  increase  i n the  the  ductilities  computed  ductilities in  other  is less that  right  maximum  in  in a  increase  they  are  level  of g r o u n d  the  other slight  i n the hand  from  methods,  than for  displacement  s t o r y columns and will  those  curvature  less  index  curvature  static  beam  in  in  the  relatively motion.  more  56  M  y  = 85 k - f t  Weight  85  85 110  CN  110  100  100  04  11 0  125  125  100  160  160  20'  100  h  ^—  kips  100  kips  1 60  160  20'  100  125  125 100  100  kips  20'  ^  >f  E = 3600 k s i Gravity  load  on a l l beams  i s 1.0 k / f t  Beams  17.7" X 19.7"(450 X 500)  Columns  19.7" X 19.7"(500 X 500)  Fig.  5.4. TEST STRUCTURE 2  57  1 .86  1.7  2.2  2.9  3.23  2.2  2.42  5.04  4.42  5.4  5.83  4.56  3.58  4.0  1 .33  4.1  4.72  4.0  4.02  3.24  2.83  _ El  Centro  El  NS  2.4  3.2  C e n t r o EW  2.36  2. 1  1.9 3.83  4 .26  4.95  2.9  3.33  4.0  5.43  4.66  5.6  5.9  4.77  5.7  3.23  4.0  Taft  Fig.  4.0  3.33  3.83  N21E  4.4  Taft  5.5. TIME-STEP ANALYSIS (curvature  4.4  S69W  RESULTS  ductilities)  2.78  5.55  3.47  2.0  1.75  3.23  3.75  4.6  4.1  Fig.  5.36  3.5  4.05  5 . 6 ( a ) . AVERAGE OF TIME-STEP ANALYSES (curvature 1.5  ductilities)  1.3  1 .3 2.3  2.4  2.8  1 .72 4.3  3.2  Fig.  4.1  3.82  5 . 6 ( b ) . EDAM  4.9  3.85  : CURVATURE  DUCTILITIES  0.0(12.1)  2.1(3.8)  2.0(3.8)  2.4(4.0)  4.1(5.8)  3.7(5.8)  4.3(6.3)  2.1 (7.6)  1.6(7.7)  Fig.  5.6(c).  2.1(7.7)  1.8(7.3)  STATIC DAMAGE EVALUATION : CURV. DUCT. ( ) S e n s i t i v i t y Index P  R  E  D  I  C  T  E  P E R I O D ( S E C ) S P E C .  A C C L ( G )  DAMPING(%) S P E C .  D  R  E  S  P  O  N  S  E  1 . 3 0 0 . 2 3 1 4 . 0  D I S P ( F T )  0 . 3 1 6  D U C T I L I T Y  DEMAND  4 . 3  I N E L A S T I C  CAPACITY  7 0  USED RESERVE  Fig.  CAPACITY  3 0  5 . 6 ( d ) . RESULTS FROM FREEMAN'S METHOD  60  1.9  2.4  2.6  2.7  1 .3 4.1  5.1  3.4  . 5 . 7 ( a ) . EDAM  3.9  4.5(6.4)  11 .9(7.4)  3.9  : CURV. DUCT. (REVERSE 0.0(11.5)  1.9(4.5)  4.2  FORCES)  1.01(2.7)  2.2(4.0)  2.4(4.0)  3.8(5.9)  4.1(5.9)  2.3(7.7)  SEISMIC  2.4(7.7)  1.9(7.7)  5 . 7 ( b ) . STATIC METHOD : CURV. DUCT. FOR REVERSE FORCES; ( ) S e n s i t i v i t y Index  SEISMIC  61 5.3  TEST STRUCTURE 3  The  third  test  structure  office-cum-residential V a n c o u v e r . The  typical  building, floor  plan  floor  exterior  columns, a t the p e r i m e t e r  in  20  t o 30  feet  the middle.  reinforced three  approximately  floor  concrete  (mezzanine  through  residential  floors  and  previous  calculating assuming  higher lb./ft was  taken  The 10  was  items;  w e i g h t was  assumed on t o be  200  floor,  30 MPa  spaced  shear  walls  post-tensioned  flat  h i g h and  the  floors.  9'2"  It  office the  floor  upper  from  the  three  as  data  on  discussed  in  was  made  i s l o c a t e d on  taken.  A  a l l floors  materials  for partitions  allowance  the  uniform except  has  high.  stuctural  weight  and  and other  for  heavy  r o o f , where a  weight  at  by  the  of  150  r o o f , where  lb./ft . 2  g r a d e of c o n c r e t e  t h  of  s t o r y masses were e s t i m a t e d  of  an  It consists  building,  d r a w i n g s and  The  A  typical  modelled  uniform  X 90'.  at t y p i c a l  are  downtown .  of c o u p l e d  A  18)  in  an  i n F i g . 5.8  the  a  11'4"  (16 t h r o u g h  equipment, which  was  2  thick  is  weight  average  uniform  of  is  levels.  structural  the  mechanical  the  8"  15)  chapter.  miscellaneous  it  slab,  structure  architectural the  system  underground p a r k i n g  The  120'  centers with a core  The  is  situated i s shown  typical  at  is  analyzed  used  from  10  i s 35 MPa  t h  floor  to  from  foundation  to  15  floor  25  t h  and  V Vi  MPa  from  15  from  8"  14"  X  36".  to At  floor and  the  upwards. S h e a r w a l l t h i c k n e s s  column time  size  building  varies was  from  20"  designed,  X  30"  i t was  varies to  30"  assumed  62 that  the  forces  ductile  central  on t h e s t r u c t u r e ;  modelled  here,  c o r e would r e s i s t  b u t t h e way t h e s t r u c t u r e  some l a t e r a l  forces  columns. To e s t i m a t e the y i e l d and  reinforcement,  gravity  the  l o a d h a s been  coefficient seismic  K  of  a l l the l a t e r a l  the  moment  axial  taken  be r e s i s t e d  for  a  f o r c e which  into  NBCC  will  has  been  by t h e  given  section  i s caused  by t h e  account.  The  numerical  to estimate the q u a s i - s t a t i c  8  f o r c e s h a s been t a k e n a s  1.0  .  Ground  motion  is  assumed t o be i n t h e N-S d i r e c t i o n .  In t h e a n a l y s i s  the  have been c o n s i d e r e d .  first  10 modes o f t h e s t r u c t u r e  The 1.11  fundamental  seconds.  structure the  Again,  time-step  analysis  calculated  of  the e l a s t i c  response ground  histories  motions,  program  from  structure of  analyses.  damage;  a l l the  remained  elastic  n o t shown  deflection  DRAIN-2D.  x-direction, Fig.  a r e shown  the  figures.  wall  motion, The  suffered  sections  have  hence the columns  maximum  average  tip  was 8.7", and i n t h e -ve  shows t h e c u r v a t u r e d u c t i l i t i e s  time p e r i o d  ductilities  shear  beams have  of the  3.2".  5.11  displacement  and  t h e +ve x - d i r e c t i o n  EDAM. C o n v e r g e n c e final  columns  the coupling  this  Curvature  the response h i s t o r i e s  d u r i n g t h e ground  in  in  Only  was  were computed by  F i g . 5.9(a) t o 5 . 9 ( d ) . F i g . 5.10 shows t h e a v e r a g e  time-step  are  the  t o t h e same f o u r  ductilities in  period  by Edam,  was with  was a c h i e v e d  in  was 2.33 s e c o n d s . 7.4".  F i g . 5.12  sensitivity  15  a s g i v e n by  iterations  and  the  The r o o t - s u m - s q u a r e t i p shows  indices  the  curvature  g i v e n by t h e S t a t i c  63 Damage this  Evaluation  method. The U l t i m a t e  c a s e was 5.7". F i n a l l y ,  Fig.  t i p displacement  5.13  shows  the  in  results  from Freeman's method. In  e a c h o f t h e methods a b o v e , none o f  shear-wall all  sections  t h e methods a r e  demand g i v e n upper other roof  from  we  same  method,  see  the  do t h o s e  from  method, the  above  Static  Evaluation  value  methods  o f 0.05 for  writing  has  typical  of  assumption, the  accurately  the  comparison  with  other  coupling  option. beams,  and p r o b a b l y  damage  ratios,  reflected.  given  analysis, However,  coupling  gives  span  the r e s u l t s the  Edam, In this  pattern the  a s s u g g e s t e d by extremely  hinge  retained  length, for  a l l  which, a t the time of short is  stubby  probably  members, n o t a good  erroneous q u a n t i t a t i v e  although  Static  although  beams a r e  was  by  the ultimate  i . e . Edam and  i n p u t . As f o r p l a s t i c  times  no  beams o f  i n d i c a t e t h e same g e n e r a l  results,  t o earthquake  method,  comparisons,  different.  or  ductility  f o r the c o u p l i n g  non-linear  are considerably  The  compared t o t h o s e  f r o m a p p r o x i m a t e methods Evaluation  columns  ductilities in  pattern.  i n the s t a t i c  As  sensitive  for  because i s less.  values  the  the  displacement  Damage  the  in  are generally less  methods,  obtained  as  have y i e l d e d . C u r v a t u r e  by t h e s t a t i c  floors,  the  the  pattern  values  should  be  exterior  columns  Typical Floor  Fig.  Plan  5.8. TEST STRUCTURE 3  0.0 ,0.0 ,  6.6  t ,  6.6  .  —I  i  iq.q  56.2  21.0  ^2.4  (  19.6  ,32.3!  ,  11.1  ,27.6, • (  .-,  9.4  ?2.0,  I  18-7  ,  6  ,  9  , I  1.? - 3  17.6 ,17.8,  ]  6.5  0.0 87.9  i-  1 1 .9 ,  j  12.0 , 12.0  17.8  11.5 ,  ,16.9,  10.2 10.5  i  8  <  1  i  ,4.6 ,  FIG.  5 . 9 ( a ) . TIME-STEP ANALYSIS : EL-CENTRO N~S COMP. (curvature d u c t i l i t i e s )  .5.1  9.5  , 5.2  ,  -.  ,5.2  ,9.4,. 9.1  [  116.2  25.8  77.4  28.3  ,76.8  27.5  52.0  17.7  49.3  i  1  ,  R  14.6  43.0  25.4  ^8.6  22.7  ,32. 5,  19.7  ,?9-R  18.5  ? 6 , 9  I  22.7  .8.9  -*—  i 1  16.9  ,  14.6 11.5  l  <  i "•' i  i  ,  ,16.8,  FIG.  6  45.1  !  -  7  *  2  i  =  5 . 9 ( b ) . TIME-STEP ANALYSIS : EL-CENTRO E-W COMP. (curvature d u c t i l i t i e s )  0.0  6 . 1 , 6-0  , 0.0 • i n.o  5.8  80.0  17.5  ,48.6  18.0 i  I  15.8  42.6 .  ,, 7 3 . 6 ,  7.9 5.9  18.4 ,13.3,  I  '  3  '  7  I 10-5  7.7  ,8.3  ,  7.0  ! 10-0,  8.0  10.3,  8  ,  1  7.5  ,9.3 ,7.2  ,  1  i 3.1  6  *  4  i I  —' i  1  1 FIG.  r —  4.2 I  I—  -  8.2  1  i  i  I  l  .1 , 10.5  ,  J  i  i  5 . 9 ( c ) . TIME-STEP ANALYSIS : TAFT N21E COMP. (curvature d u c t i l i t i e s )  , 2.2 , 1  2.1 ,  ,  -  |  7  8  7.6  ,1.9, —  1  7.8  i  l  21 -fi  , 96.0 ,  61.9  23. 1 21.3 12.2  , 35.4, 1  I  ,30.3,  I  1  1  9  '  7  12.8  I  10.4  , 15.6  11.0  15.9  !  11.2  15.0,  10.6  r  1 1  ,12.6,  9.3  ! R.5 ,  7.1 4.0  2.R 1  FIG.  I  I  1  r  3  14.4  1  1  '  I  i  V  0  7.6  ,23.9, 1  1  t  t" i  —i  i  4  5 . 9 ( d ) . TIME-STEP ANALYSIS : TAFT S69W COMP. (curvature d u c t i l i t i e s )  3.7*  7.5  *  ,  i  ... 3.7 i  i  7.5,  *  7.3,  , 3.7  21.3  95.0 61 .0  22.6 1  i  21.1  57.2  12.2  . 35.8, i  i  ,  31 . 4 , 26. 1  8.2  23.0  14.6  19.7, I  13.0  19.0  12.7  18.5  12.5  17.3  11.8  14.7  10.4  10.8  8.3  ,4.9 ,  8.1  I  r  Fig.  •  10.6  —i  i •  i  ! ,  (  i  i _.  _i  5.10. AVERAGE OF TIME-STEP ANALYSES * average  of o n l y  two  e/q  records  70  , 6 . 6  i  6  ,  , i  ,  i  8  ... i  , 7.0, ,  1  , 45.8,  4.4  , i  4.5  4  '  i 1  7  i  t34,2I  u.  ,  l  12.0  l  12.4 , 9.1  27.2 ..  g  27.5, i  2  7  i  7  , 28.6, , 28.3, »  , 21 .7  1  L  ,  ,  1  -  5  ,  14.2 ...  i  13.6 ,. i  i  12.6 , l  I  11.1, 9.3 7.0  ,  •  i  4.5  r  , 2.3 , i i 'i1  14.7 . i  ,  13.9  —  !  i  ... ,  , 18.2  ,9.1  14.9 ,«  , 26.2,-. -  :  1  9. 3 fi  i  —1  ,27.5,-  , 24.3, i i  t  1  -I  (  !I ....  F I G . 5.11. EDAM  ,  1.1  , i | ;  0.0  ,  i  , r  : CURVATURE D U C T I L I T I E S  71  0 . 0 ( 0 . 0 )  .0.0(11.2)  ,,1.4(11.9)  j _  7 . 8 ( 2 2 . 4 )  j —  ,7.4(19.7)  r-  ,9.6(23.  4 . 3 ( 7 . 2 )  —  i  4 . 8 ( 1 2 . 7 ) _ l  ,  5 . 3 ( 5 . 0 )  1  r— I  9 . 7 (1 3 . 5 )  l  J  1 1 . 9 ( 1 7 . 0 } —  1 3 . 3 ( 1 9 . 1 V —  1  \  ,  —  ]  —  1  1) j —  8 . 9 ( 1 9 . 7 )  i  1 0 . 4 ( 1 5 . 3 )  I  ,10.6(21.3)  1  , 1 2 . 4 ( 2 2 . 4 )  L  _  1  ,  , 1 4 . 5 ( 2 3 . 8 Jj—_  1  , 1 7 . 0 ( 2 2 . 0 )|—- — , '  ,1 6 . 6 ( 2 0 . 2 ) ^  )j_  1  1 3 . 3 ( 1 8 . 0 ) —  1——  21  .0(27.0)1  2 2 . 3 ( 2 4 . 4 )  21  J  i  ,13.2(14.5)^-  ,  ,1.8(1.3)  i —  ,  j — i c  _  ,  I  3 . 4 ( 0 . 8 )  ! _  ,1.3(0.1)  £_ — j  ,  1—-  . 3 ( 2 2 . 3 ) _ i i  1 9 . 5 ( 1 9 . 5 ) — l ... 1 6 . 6 ( 1 6 . 1 )  I—i  i  ,6.3(6.6)  1  2 2 . 5 ( 2 5 . 9 )  ,16.7(23.2),—  ,10. 1 ( 1 0 . 7 )  1  2 1 . 0 ( 2 6 . 7 )  ,15.9(23.8)r— —1  ,15.4(17.7  1 1 . 4 ( 1 6 . 2 )  1  1 2 . 7 ( 1 1 . 9 )' 8 . 2 ( 7 . 6 )  0 . 0 ( 1 3 . 5 )  —  r —  i L  0 . 0 ( 0 . 0 )  , —  0 . 0 ( 0 . 0 )  .j—  F I G . 5.12. STATIC DAMAGE METHOD :CURVATURE D U C T I L I T I E S ( ) S e n s i t i v i t y Index  72  P R E D I C T E D  * * * * * * * * * * * * * * * * * * *  R E S P O N S E  a * * * * * * * * * * * * * - * * * * * * * * * * * ' * *  PERIOD(SEC)  1.38  SPEC. ACCL(G)  0.23G •  DAMPING(%)  3.0  SPEC. DISP(FT)  0.365  DUCTILITY DEMAND  3.8  INELASTIC CAPACITY USED  54  RESERVE CAPACITY  46  F I G . 5.13. RESULTS FROM FREEMAN'S METHOD  6. CONCLUSIONS Two methods f o r a n a l y s i n g t h e structures is  t o severe  response  of  g r o u n d m o t i o n , have been p r e s e n t e d .  One  b a s e d on t h e e l a s t i c  the  structure  yielding  in  pattern,  which  ductility  into  is  These  account  and  the  excitation.  t o be e i t h e r  linear.  represented  demand, t h a t  earthquake intended  modal a n a l y s i s and t h e o t h e r  piece-wise  members  have  shown  results all  good  The  main  as a check  cases,  on t h e  predict  a  by  curvature  the  of  of high  ductility  demand.  has  see  during  the  methods i s  procedure.  by  these  methods a r e c o r r e c t l y  energy a b s o r p t i o n  difficult  or  to  M e t h o d . The r e s u l t s  seems  to  underestimate  able  the  methods, to the  value  revised  CAN3-A23.3-M84, the  displacement  Code  gives yield  of the  high  ultimate  be p u s h e d used  i n the often  when compared w i t h t h e  methods. T h i s needs f u r t h e r i n v e s t i g a t i o n , the  of  the  show t h a t t h e method the  to p r e d i c t  areas  determine  t o which the s t r u c t u r e should  Static  between  an  design  agreement o f r e s u l t s when compared  proved  displacement  since  damage  preliminary  retrofit  structures analyzed  these  the areas  other  methods t a k e t h e  would use  assumes  o f a ' t r u e ' n o n - l i n e a r a n a l y s i s p r o g r a m DRAIN-2D. I n  the  It  here  members  or a s a u s e f u l p a r t o f a r a t i o n a l Three d i f f e r e n t  non-linear  f o r Design  of C o n c r e t e  especially Structures  slightly  different  relationships  moments,  ductility  and  structure  in  view  f a c t o r s and c a p a c i t y r e d u c t i o n f a c t o r s  73  of  the  ultimate new  on t h e m a t e r i a l s .  load  74 The the  member  writing span.  of the p l a s t i c  Edam, t h a t  error,  actual  hinge  i s evidently  d e p t h . F o r ease of m o d e l l i n g ,  However,  serious the  length  i t would be  in  short  s o an o p t i o n  equal  stubby  to  member d e p t h t o o v e r r i d e  quasi-static  analysis. seismic  They p r o v i d e  a n a l y s i s , give  to a true  non-linear  minor  changes  static  analyses.  popular  analysis  are  a very  this  and  way  required  the data  i n the average design  gap  between  non-linear  of  performing  good r e s u l t s i n c o m p a r i s o n are  in  features,  entering  value.  'true'  a n a l y s i s and  These  for  a wide  of  can lead t o  default  the  efficient  reasonably  one-twentieth  be p r o v i d e d  However, t h e p r o p o s e d methods f i l l the  i t was assumed i n  members t h i s  should  related to  easy  to file  use. used  i t i s hoped, w i l l  office.  Only  i n the  make them  REFRENCES 1.  Shibata,  A.  and  'Substitute Journal Jan. 2.  Structure  1976,  pp  Substitute R/C  Metten,  Andrew  Resistant  thesis,  Vancouver  'Psuedo  No.  ST1,  October  of  Analysis  of  t h e s i s , U n i v e r s i t y of  Canada, March  1979  Structure Coupled  Method As A D e s i g n Structural  of  British  Walls', Columbia,  1981  Seismic A n a l y s i s ' , Master's  British  Columbia,  Vancouver  thesis, Canada,  1984  Freeman, Sigmund 'Prediction  Motion',  Blume, John 'Design  A.  o f R e s p o n s e of C o n c r e t e B u i l d i n g s  SP-55 A m e r i c a n  The  Douglas  A, Newmark N.M.  of  McHenry  Concrete I n s t i t u t e , and  Motions',  Illinois,  1961  P. and  Sozen  Portland  M.A.  75  pp  to  Severe  Symposium  1978,  589-605  Corning  Multistory Reinforced  Earthquake  Gulkan,  For  H.Y.  Non-Linear  University  Method  University  Canada, M a r c h  H u i , Lawrence  Ground  Vancouver  Substitute  Seismic  Master's  7.  R/C,  W.F.  Modified For  Structure  Structures', Master's  Columbia,  Aid  6.  In  1 - 18  British  'The  5.  Method F o r S e i s m i c D e s i g n  Y o s h i d a , Sumio  Existing  4.  M.A.,  o f S t r u c t u r a l D i v i s i o n , ASCE, V o l . 102,  'Modified  3.  Sozen,  L.H.,  Conrete B u i l d i n g s  Cement A s s o c i a t i o n ,  For  Skokie  76 'Inelastic  Response o f R e i n f o r c e d  Earthquake Dec. 8.  Journal  Structures  of A C I , V o l . 71, No.  To 12,  1974, pp 604-610  National  Building  National 9.  Motions',  Concrete  Code  of  Research C o u n c i l  by N a t i o n a l  1980,  issued  o f Canada, O t t a w a ,  Supplement t o the N a t i o n a l issued  Canada  B u i l d i n g Code  Research Council  of  by  Canada  o f Canada  1980,  Canada,  Ottawa,  Ph.D.  thesis  New  Zealand,  Canada 10. Mander,  J.B.  'Seismic  Design  University Feb. 11.  of  '.Seismic  Canterbury,  Piers', Christchurch,  P.  Analysis  of R/C  Frame-wall  Structural Engineering,  1984, pp.  Structures' , Journal  ASCE, V o l . 110 No.  11,  Nov.  2619-2634  12. A n d e r s o n D.L., 'Correlation of  Bridge  1984  Moehle, Jack  of  of  The  N a t h a n N.D.  of S t a t i c  National  and C h e r r y  And Dynamic Building  Code  S.  Earthquake of  P r o c e e d i n g s of T h i r d C a n a d i a n C o n f e r e n c e Engineering  Montreal,  Canada  Analysis  Canada on  1977',  Earthquake  1979, V o l 1, pp. 653-662  APPENDIX A EDAM PROGRAM INPUT  1.  PROBLEM  INITIATION  :  INELAS, NMODES, NPRINT, ISPEC,  AMAX, DAMPIN,  (415,2F10.2,15) INELAS  :  one  Maximum  number  analysis; NMODES  :  Number  of  of  modes  card  iterations  0 for elastic  KOU  modal  for inelastic analysis  (^10) t o be i n c l u d e d  i n the  analysis NPRINT  :  Number  of  forces ISPEC  modes f o r w h i c h d i s p l a c e m e n t s a n d  will  : I n p u t spectum  be  printed  t y p e :-  1 = Spectrum  'A' f r o m S h i b a t a  2 = Spectrum  'B' from Y o s h i d a  3 = Spectrum  'C  4 = National  Building  and Sozen  from Y o s h i d a Code  Spectrum  5 = San F e r n a n d o E a r t h q u a k e S90W S p e c t r u m 6  =  C.I.T.  Simulated  Earthquake  type  C-2  Spectrum AMAX  : Maximum  DAMPIN  : Elastic  ground a c c e l e r a t i o n or  fraction KOU  :  initial  of c r i t i c a l  (g)  damping  expressed  as  damping  1 = First  mode f o r c e s  i n +ve  2 = First  mode f o r c e s  i n t h e -ve x - d i r e c t i o n  (See  Note  1) 77  x-direction  a  78 2.  TITLE TITLE  (20A4)  Problem t i t l e 3.  one o f maximum 80 c h a r a c t e r  card  length  STRUCTURAL INFORMATION : NRJ, NRM, HARD, NCONJT, NCDJT, NCDOD, NCDIDS, NCDMS one  (2I5,F10.2,5I5)  NRJ  : Number o f j o i n t s  NRM  : Number o f members i n t h e s t r u c t u r e  HARD  :  Strain  NCONJT  :  i n the s t r u c t u r e  hardening  initial  stiffness  Number  of  ratio,  'control  as  :  Number  of  generation NCDOD  :  Number  commands  :  for  ( S e e N o t e 2) joints  co-ordinate  (See Note 4 )  ( S e e N o t e 5) :  I J T , X, Y (I5,2F10.1)  one c a r d / c o n t r o l  joint  : J o i n t number, i n any s e q u e n c e  X : x c o - o r d i n a t e of the j o i n t ( f t . ) Y : y co-ordinate of the j o i n t ( f t . ) 5.  with  : Number o f commands f o r s p e c i f y i n g lumped m a s s e s  CONTROL JOINTS CO-ORDINATES  IJT  with  ( S e e N o t e 3)  Number o f commands f o r s p e c i f y i n g j o i n t s  at j o i n t s 4.  f o r which the  o f commands f o r s p e c i f y i n g j o i n t s  i d e n t i c a l displacements NCDMS  p r o p o r t i o n of  (See N o t e 2)  zero displacements NCDIDS  a  joints'  co-ordinates are specified NCDJT  card  COMMANDS FOR GENERATION OF JOINT CO-ORDINATES  :  79 Omit  i f t h e r e a r e no g e n e r a t i o n  IJT,  L J T , NJT, KDIF  commands  (415)  one card/command  IJT  : Joint  number  at the beginning  LJT  : Joint  number  a t the end of g e n e r a t i o n  NJT  : Number o f j o i n t s t o be g e n e r a t e d  KDIF  :  Joint  number  difference  nodes on t h e l i n e  of g e n e r a t i o n  to  line  along  the l i n e  between two s u c c e s s i v e  (constant).  assumed t o be e q u a l  line  I f blank  or  zero  1  COMMANDS FOR JOINTS WITH ZERO DISPLACEMENTS : Omit  i f no j o i n t s  restrained  t o have z e r o  IJT,  KDOF(1), K D 0 F ( 2 ) , KDOF(3 ) , L J T , KDIF  (13,518) IJT  displacements  one card/command :  Joint  covered KD0F(1)  : Code  number, by t h i s  or  first  i n the s e r i e s  command  f o r X displacement,  displacements  joint  0 i frestrained  in x direction,  1  from  i f free  to  displace KDOF(2)  : Code  f o r Y displacement  KDOF(3)  : Code  for rotation  LJT leave KDIF  : Last blank  in this  for a single  : Joint in  joint  number  this  assumed  series,  joint  difference  series  punch 0 o r  between s u c c e s i v e  (constant),  t o be e q u a l  i f blank  joints or zero  to1  COMMANDS FOR JOINTS WITH IDENTICAL DISPLACEMENTS : Omit  i f  no  joints  restrained  to  have  identical  80  d i splacements MDOF, NJT, I J O I N T ( N J T ) (215,1415) MDOF  one  : Displacement  NJT  :  IJOINT  code  for  x displacement  2  for  y displacement  3  for  rotation  Number  of  (max.  14)  : List  of  joints  nodes  increasing 8.  card/command  covered  covered  by  by  this  this  command  command,  order  MEMBER INFORMATION : MN,JNL,JNG,KL,KG,E,G,AREA,CRMOM,BMCAP,EXTL,EXTG,AV (515,2F10. 1,F8.1,2F10.1,3F6.2) MN  : Member  number  JNL  : Lesser joint  JNG  : Greater  KL  : Fixity  one card/member  joint  number number  code a t l e s s e r  joint  0 : Pinned 1 : Fixed KG  : Fixity  code a t g r e a t e r  E  : Young's Modulus ( k s i )  G  : S h e a r Modulus ( k s i )  joint  (0 i f s h e a r d e f l e c t i o n s a r e t o be n e g l e c t e d ) AREA CRMOM  : Cross-sectional  a r e a o f t h e member ( i n )  : Moment o f i n e r t i a  BMCAP : Y i e l d  2  o f t h e member ( i n " )  moment o f t h e member  (k-ft)  in  81  EXTL  : Rigid  extension  on t h e l e s s e r  end  joint  of t h e  on t h e g r e a t e r e n d j o i n t  of t h e  member ( f t . ) EXTG  : Rigid  extension  member ( f t . ) AV  : Shear area (0 i f s h e a r  Note  o f t h e member ( i n ) 2  deflections  a r e t o be n e g l e c t e d )  : If E, G, AREA, CRMOM, BMCAP, EXTL, EXTG,  left  blank  AV  are  or g i v e n zero f o r a member, same v a l u e s as  f o r the previous member w i l l be assumed. 9.  COMMANDS FOR LUMPED MASSES AT THE JOINTS : I J T , WTX, WTY, WTR, J J T , KDIF (15,3F10.2,215) IJT  : Joint this  one card/command  number o r f i r s t  joint  i n a s e r i e s c o v e r e d by  command  WTX : Weight a s s o c i a t e d w i t h  x-displacement (kip)  WTY : Weight a s s o c i a t e d w i t h y - d i s p l a c e m e n t ( k i p ) WTR : R o t a t i o n a l w e i g h t JJT  : Number o f l a s t l e a v e blank  KDIF  : Joint in  joint  i n the  for a single  number d i f f e r e n c e  this  assumed  series  series,  to  0 or  successive  joints  joint between  (constant),  t o be e q u a l  punch  i f blank  or zero  1  10. STATIC LOAD INFORMATION : NJLS, NLGCJ,  NML, NLGCM  (415) NJLS NLGCJ  one c a r d : Number o f j o i n t s  l o a d e d by s t a t i c  loads  : Number o f g e n e r a t i o n commands f o r  static  loads  82  applied NML  : Number o f members l o a d e d static  NLGCM  :  Cards A.  by u n i f o r m l y  distributed  load  Number o f g e n e r a t i o n on  11.  d i r e c t l y a t t h e nodes (See Note 6)  t h e members  FOR  STATIC  for static  loads  (See N o t e 6)  11A and 11B a r e o m i t t e d  COMMANDS  commands  i f NJLS i s z e r o .  LOADS APPLIED DIRECTLY ON THE  JOINTS : Omit  i f NLGCJ  i s zero  FX, FY, FM, NNOD, NODN(NNOD) (3F10.1,1015)  one card/command  FX  : Load  in x-direction (kip)  FY  : Load  in Y-direction (kip)  FM : Moment  (k-ft)  NNOD : Number o f j o i n t s t o be c o v e r e d NODN :  List  of  increasing  joints  covered  by  by t h i s command this  command  in  order OR  B. STATIC LOADS APPLIED DIRECTLY AT JOINTS : input  this  i f NLGCJ = 0  N, FX, FY, FM (15,3F10.1) N  : Node  one c a r d / l o a d e d  number  FX  : Load  i n the x - d i r e c t i o n ( k i p )  FY  : Load  i n the y - d i r e c t i o n ( k i p )  FM : Moment NOTE  :  joint  (k-ft)  ONLY  CARDS  11A  OR  11B ARE TO BE INPUT  IN THE  83 DATA, NOT BOTH. Cards  12A and 12B t o be o m i t t e d  i f NML e q u a l s  zero.  A. COMMANDS FOR STATIC MEMBER LOADS : Omit  i f NLGCM  i s zero.  W, NMEM, MR (NMEM) (F6.1,1415)  one card/command  W : Uniformly  distributed  downward l o a d  load  :  List  of  increasing  member  (k/ft),  by t h i s  command  positive  NMEM : Number o f members c o v e r e d MR  on t h e  members  covered  by  this  command i n  order OR  B. STATIC MEMBER LOADS : Omit  i f NLGCM  MMR,  W  i s not z e r o .  (I5,F10.4) MMR  : Member  one c a r d / l o a d e d number  W : Uniformly NOTE  distributed  : ONLY CARDS  WHEN NML  member  12A OR  s t a t i c load  12B TO BE  IS NOT ZERO, NOT BOTH.  (kip/ft)  INPUT  IN  THE  DATA  1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  c C C C C C C C C C  c  C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C  •••••* MODAL ANALYSIS PROGRAM ORIGINAL PROGRAM TITLED MSSM.S FIRST EDITION TITLED EDAM SECONO EDITION TITLED EDAM2 THIRD- EDITION TITLED E0AM3 *  * EDAM3  •••••+  BY" SUMIO YOSHIDA BY ANDREW W.F. METTEN BY LAWRENCE H.Y. HUI BY SUBODH KUMAR MITAL ' *  1979 1981 1984 1985  PROGRAM DIMENSIONED FOR A MAXIMUM OF :2S0 MEMBERS 200 JOINTS 100 ASSIGNED MASSES 10 EIGENVALUES 300 UNKNOWNS (NUMBER OF UNKNOWNS)*(HALF  BANDWIDTH) IS LESS THAN 8000  • NOTE - PRITZ IS A UBC:MATRIX LIBRARY SUBROUTINE FOR SOLVING EIGENVALUES VARIABLE DEFINITIONS:KL,KG  - JOINT TYPE : FIXED JOINT • 1 PINNED JOINT » O CROSS-SECTIONAL AREA MOMENT OF INERTIA OF CRACKED SECTION BENDING MOMENT CAPACITY OF SECTION DAMAGE RATIO OF MEMBER D.O.F. NO. IDENTIFIED BY JOINT NO. NO(K.I) - K - 1 (X-DOF). 2 (Y-OOF). 3 (R-DOF) I • JOINT NO. NP D.O.F. NO. IDENTIFIED BY MEMBER NO. NP(K.I) - K • DOF 1 TO 6 FOR STANDARD MEMBER I - MEMBER NO. XM LENGTH OF FLEXIBLE PORTION OF BEAM IN X-OIRECTION YM LENGTH OF FLEXIBLE PORTION OF BEAM IN Y-DIRECTION DM • TRUE LENGTH OF FLEXIBLE PORTION OF BEAM F - LOAD VECTOR EXTL, EXTG - LENGTH OF.* RIGID END TITLE • TITLE (80 CHARACTERS) SDAMP > STRUCTURAL DAMPING AV SHEAR AREA DAMB - DAMAGE RAIO IN THE (I-1)TH ITERATION MDOF - D.O.F. NO. FOR MASSES IDENTIFIED BY MASS NO. AMASS - LUMPED MASS ( I N UNITS OF WEIGHT) INDENTIFY BY D.O.F. NO. EVAL • EIGENVALUE FOR EACH.MODE EVEC • MODE SHAPE EVEC(K.I) - K - MASS NO. I " MODE NO. BETAM • SMEARED SUBSTITUTE DAMPING FOR EACH MODE LOCK - CONTROL DIFFERENT STAGE OF ITERATION. CORRESPOND TO SUBROUTINE STACHK WHICH IS USED TO STABILIZE CONVERGENCE LOCK - O • USUAL CONVERGENCE PROCEDURE 1 • BINARY SEARCH ROUTINE IN EFFECT  AREA CRMOM BMCAP DAMRAT ND  • '  59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 1 10 111 112 1 13 114 115 116  C C C C C C C  OLDTN OLOSA  2 - PROGRAM CONVERGED - STORE THE PERIOD OF THE LAST ITERATION • STORE UPPER AND LOWER BOUND SA VALUES  DOUBLE PRECISION STIFFNESS MATRIX REAL*8 S(30000). DSOOOOO). DET. DRATIO, DBLE. DVL(500)  C DIMENSION K L ( 2 5 0 ) , KG(250). AREA(250). CRM0M(250). BMCAP(2S0). 1 ND(3.2O0). NP(6.250). XM(250). YM(250), DM(250). F(50O). 2 EXTL(250). EXTG(250). T I T L E ( 2 0 ) . SDAMP(250). AV(250) DIMENSION DAMB(2.250), MDOFOOO). 0LDTN(2), 0LDSA(3). 1 DAMRAT(2.250) DIMENSION AMASS(50O). E V A L O O ) . EVEC( SCO. 10). BETAM(10). 1 DEFL(500), SAXIAL(250). SHEAR1(2S0). S8ML(250). 2 SBMG(250). VL(50O). E ( 2 5 0 ) . N0ON(2O), MR(15). MML(IOO). 3 FEMOOO.4). G(250). SHEAR2(2SO) CALL FTNCMO('EQUATE 99-SPRINT;') C C C C C C C C C C C C  IUNIT DEFINES THE INPUT AND OUTPUT FILES :IUNIT-5 IUNIT-6 IUNIT»7 IUNIT-8  IS DATA SOURCE FILE IS TEMPORARY STORAGE FOR INTERMEDIATE DATA IS FINAL OUTPUT FILE IS DAMAGE RATIO FILE ( SEPARATE FROM OTHER FINAL OUTPUT FILE TO MAKE PLOTTING OF RESULTS EASIER ) IUNIT • 7  CALL CONTRL TO READ IN DATA OF STURCTURE. TITLE AND PROGRAM OPTIONS. CALL CONTRL(TITLE. NRJ. NRM. 7, AMAX. ISPEC. OAMPIN. INELAS. 1 NMODES. NPRINT. HARO. KOU. NCONJT, NCDJT, NCDOD. NCDIDS. 2 NCDMS)  C C C  IDIM DIMENSIONS THE STIFFNESS MATRIX FOR SUBROUTINES IDIM - 30000  C C C C  CALL SETUP TO READ AND TO ECHO PRINT MEMBER AND JOINT OATA -HALF BANDWIDTH AND NUMBER OF UNKNOWNS ARE CALCULATED CALL SETUP(NRM. E. G, XM, YM, DM, NO, NP, AREA, CRMOM, DAMRAT, 1 NRJ. AV, KL. KG, NU. NB. SDAMP. BMCAP, IUNIT, EXTL. EXTG. 2 NCONJT, NCDJT, NCDOD. NCDIDS)  C C C C  SET IFLAG EQUAL TO 1 IF ONLY ONE ITERATION IS REOUIREO HERE IFLAG IS SET EQUAL TO O  C C C C  CHECK IF IDIM HAS BEEN ASSIGNED LARGE ENOUGH LSTM - LENGTH OF ONE-DIMENSIONAL STIFFNESS MATRIX  IFLAG • 0  LSTM - NU • NB IF (LSTM .GT. IDIM) WRITE (7.10) LSTM. IDIM 10 FORMAT (///'PROGRAM STOPPED'. //'LENGTH OF STIFFNESS MATRIX-', 16,  CO  1 (7 1 18 119 120 121 122 123 124 12S 126 127 128 129 130 131 132 133 134 135 135 137 138 139 140 14 1 142 143 144 145 146 147 .148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174  1 /'PROVIDED STORAGE (IDIM)-'. 16) IF (LSTM .GT. IDIM) STOP  C C C c  ICOUNT IS THE NUMBER OF TIMES MAIN MSSM SUBROUTINE IS CALI ICOUNT IS INITIALIZED TO ZERO HERE. ICOUNT " 0  c c c c  CALL MASS TO READ AND ASSIGN MASSES TO NODES -ASSEMBLE THE MASS MATRIX : AMASS  c c c c  REASSIGN OUTPUT TO* TEMPORARY FILE 6  c c c c c  CALL MASS(NU. ND. AMASS, IUNIT. NRO. MDOF. NCDMS)  IUNIT « 6 IF ONLY ELASTIC ANALYSIS IS REQUIRED: RESET CONTROL FLAGS SET I FLAG"1 TO INDICATE ONLY ONE ITERATION IS REOUIRED IF (INELAS .NE. 0) GO TO 20 WRITE (7.50) IUNIT - 7 I FLAG - 1 WRITE (7,50) 20 CONTINUE  c c c c C36 C C c c C37 C C44 C C C38 C C C C c c c c c c  DO 35 KOU"1,2 IF(K0U.E0.2)G0 TO 36 GO TO 38 CONTINUE 00 37 MBR"1,NRM DAMRAT(1,MBR)°1.0 DAMRAT(2.MBR)•1.0 S0AMP(MSR)»0.02 CONTINUE WRITE(7,44) FORMAT(///,'FIRST MODE FORCES IN THE REVERSE DIRECTION') IUNIT-6 IFLAG-0 CONTINUE SET THE MAXIMUM NUMBER OF ITERATIONS. IMAX - 1 IF (INELAS .NE. 0) IMAX - INELAS IM - IMAX - 1 I • THE NUMBER OF ITERATIONS PERFORMED I -0 SET LOCK TO 0 FOR NORMAL CONVERGENCE PROCEDURE LOCK • 0  175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201* 202 2C3 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232  C C C  BETA IS A FACTOR USED IN SPEEDING CONVERGENCE (0 <BETA < 1). BETA - O. EFFECTIVELY SHUTS OFF CONVERGENCE SPEEDING ROUTINE  C C C C C  SET ERROR RATIO OF MOMENTS OF YIELDED MEMBERS (BMERR). A VALUE OF 0.05 HERE ENSURES YIELDED MEMBERS ARE WITHIN 5 PERCENT OF THEIR CAPACITY.  C C C C C C C C C C  C C C C C C C C C  C C C C C C  BETA • O.  BMERR . O.OS - SET CONVERGENCE LIMIT FOR CHANGE IN DAMAGE RATIO DAMERR - 0.01 ENSURES THAT THE MAXIMUM DAMAGE RATIO CHANGE • IN THE FINAL ITERATION IS ONE PERCENT - FOR DAMAGE RATIOS ABOVE 5.0 - THOSE DAMAGE RATIOS BELOW 5.0 WILL CONVERGE TO THEIR ABSOLUTE VALUE DIFFERENCE BEING TEN TIMES THE RATIO DAMERR - 0.01 INITIALIZE ARRAY USED IN SPEEDING OF CONVERGENCE. 00 30 MEM - 1. NRM OAMB(1,MEM) - OAMRAT(1.MEM) DAMB(2,MEM) > DAMRAT(2.MEM) 30 CONTINUE FINISHED INPUT OF DATA AND INITIAL ACTIVITIES. BEGIN LOOP FOR MSS METHOD. INCREMENT ITERATION COUNTER :40 I - I • 1 WRITE (IUNIT.50) 50 FORMAT (• '. 110('-')) WRITE (IUNIT,60) I 60 FORMAT ('-'. 'ITERATION NUMBER', 14) CALL BUILD TO COMPUTE THE MEMBER AND GLOBAL STIFFNESS MATRIX CALL BUILD(NU. NB. XM, YM. DM, NP, AREA. CRMOM, AV. E. G. DAMRAT. 1 KL, KG. NRM. S. IDIM, EXTL, EXTG) CALL SCHECK TO CHECK THE CONDITION OF THE STIFFNESS MATRIX  CALL SCHECK(S. NU, NB, IDIM, IUNIT. SRATIO) IF(K0U.E0.2)G0 TO 51 IF (I .GT. 1) GO TO 410 DO 70 IM • t, NU 70 VL(IM) - O. C ANALYZE FOR STATIC LOADS READ (5,80) NJLS. NLGCJ, NML. NLGCM 80 FORMAT (415) WRITE (7,90) NJLS. NML 90 FORMAT (//. 'HO. OF JOINTS LOADED •'. 14, 5X, 1 'NO. OF MEMBERS LOAOEO •', 14. /) C  CO  233 234 235 236 237 238 239 240 24 1 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290  I F ( N J L S .EO. O .AND. NML .EO. O ) CO TO 4 0 0 I F ( N J L S .EO. O ) GO TO 2 3 0 WRITE (6.)00) 1 0 0 FORMAT (///. ' G E N E R A T I O N COMMANOS FOR S T A T I C L O A D S A P P L I E D TO THE 1N00ES'. //) I F ( N L G C J .NE. O ) GO TO 120 WRITE ( 7 . 1 1 0 ) . 1 1 0 FORMAT ('NONE'.. / ) GO TO 1 8 0 120 CONTINUE WRITE (7.130) 1 3 0 FORMAT (//. 5 X . ' F X ( K I P S ) ' . 6X. ' F Y ( K I P S ) ' . 6 X . ' F M ( K - F T ) ' , 5 X . 1 'NO. OF NODES'. 8 X . ' L I S T OF NODES'. / ) DO 1 7 0 I - 1. N L G C J READ ( 5 . 1 4 0 ) F X , F Y . FM, NNOD. ( N O D N ( J ) . J - 1 , N N O D ) 140 FORMAT ( 3 F 8 . 1 . 1 1 1 5 ) WRITE ( 7 . 1 5 0 ) F X . F Y , FM. NNOD. ( N D D N ( J ) . J - 1 , N N O D ) 150 FORMAT (/. F 8 . 1 . 6X, F 8 . 1 . 6 X . F 8 . 1 , I S . 5 X . 1 0 1 5 ) DO 1 6 0 J • 1. NNOD NN - N O D N ( J ) N1 • N D ( 1 . N N ) N2 " ND ( 2 , NN ) N3 - N 0 ( 3 . N N ) V L ( N 1 ) » V L ( N 1 ) * FX V L ( N 2 ) - V L ( N 2 ) + FY V L ( N 3 ) • V L ( N 3 ) + FM 160 CONTINUE 170 CONTINUE GO TO 2 3 0 180 CONTINUE WRITE (7.190) 1 9 0 FORMAT ( 8 X . ' J N ' . 8X, ' F X ( K I P S ) ' . 8X. ' F Y ( K I P S ) ' , 8 X . ' F M ( K - F T ) ' , 1 /) DO 2 2 0 1 - 1 . N J L S R E A D ( 5 . 2 0 0 ) N. F X . F Y . FM 200 FORMAT ( 1 5 . 3 F 1 0 . 2 ) WRITE ( 7 . 2 1 0 ) N. F X . F Y . FM 210 FORMAT ( 1 1 0 . 3 ( 8 X . F 1 0 . 2 ) ) M1 • N D ( I . N ) M2' - N D ( 2 . N ) M3 - N D O . N ) VL(M1) - VL(M1) FX V L ( M 2 ) - V L ( M 2 ) • FY V L ( M 3 ) • V L ( M 3 ) + FM 2 2 0 CONTINUE 2 3 0 CONTINUE I F (NML .EO. O ) GO TO 3 6 0 WRITE (7.240) 2 4 0 FORMAT (///. ' G E N E R A T I O N COMMANDS FOR MEMBER L O A D S ' . / / ) I F ( N L G C M . N E . O ) GO TO 2 5 0 WRITE (7.110) GO TO 3 1 0 250 CONTINUE WRITE (7,260) 2 6 0 FORMAT (//, 'U.D.L. ( K / F T ) ' , S X . 'NO. OF MEMBERS'. 8 X . 1 ' L I S T OF MEMBERS', / ) JM • 1 DO 3 0 0 I - 1, N L G C M  291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 3 10 311 312 313 314 315 316. 317 318 319 . 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348  READ ( 5 . 2 7 0 ) W, NMEM, ( M R ( J ) , J - 1 , N M E M ) FORMAT ( F 8 . 1 . 1 4 1 5 ) WRITE ( 7 , 2 8 0 ) W. NMEM. ( M R ( J ) , J - 1 , N M E M ) FORMAT ( F 8 . 1 . 5 X . 1 5 . 8 X . 1 3 1 5 ) 280 0 0 2 9 0 J - 1. NMEM MMR > MR(J) M M L ( J M ) - MMR C A L L GEN2(MMR, W, XM. K L . K G . N P . V L , J M . F E M ) JM - JM * 1 CONTINUE 290 3 0 0 CONTINUE GO TO 3 6 0 3 1 0 CONTINUE WRITE (7.320) 3 2 0 FORMAT (/. 'MEMBER NO.', IOX. ' U . D . L . ( K / F T ) ' . /) DO 3 5 0 MEM - 1. NML READ ( 5 , 3 3 0 ) MMR. W WRITE ( 7 . 3 4 0 ) MMR. W FORMAT ( 1 5 . F 1 0 . 2 ) 330 FORMAT ( 1 6 . 15X. F 1 2 . 2 ) 340 MML(MEM) - MMR C A L L G E N 2 ( MMR. W. XM, K L , K G . NP, V L , MEM. FEM) 3 5 0 CONTINUE 3 6 0 CONTINUE C O N V E R T LOAD V E C T O R TO O O U B L E P R E C I S I O N DO 3 7 0 I N • 1, NU D VL(IN) - DBLE(VL(IN)) 370 C A L L S D F B A N TO S O L V E AX-B DRAT 10 • 1 . 0 - 1 6 SAVE S T I F F N E S S MATRIX INK - NU * NB DO 3 8 0 J - 1. INK 380 D S ( J ) « S ( J ) C A L L S D F B A N ( D S . D V L . NU, NB. 1. D R A T I O , D E T . J E X P . 1) C O N V E R T S O L N . V E C T O R D V L TO S I N G L E P R E C I S I O N DO 3 9 0 J - 1. NU 390 D E F L ( J ) - SNGL(DVL(J)) F I N D MEMBER F O R C E S DUE TO G R A V I T Y L O A D S C A L L MEMFO(NRM. XM. YM. DM. A V . N P , O E F L . E X T L , E X T G . A R E A . E . G. 1I CRMOM, K L . K G . S A X I A L . S H E A R 1, S H E A R 2 , S B M L . SBMG. NML, MML, 2 FEM) 40O CONTINUE 4 10 C O N T I N U E C A L L E I G E N TO C O M P U T E T H E F R E Q U E N C I E S AND MODE S H A P E S FOR THE S U B S T I T U T E STRUCTURE 270  C  C C  C  C  C C C  CALL  c c c c  11  E I G E N ( N U . NB, S, I D I M , AMASS, E V A L . I S P E C , AMAX, I C O U N T , MOOF. I N E L A S )  INSERT HEADINGS ANALYSIS ONLY)  FOR  ITERATION  PROGRESS  EVEC.  (FOR  I F ( I N E L A S .EO. 0 .OR. I C O U N T .NE. 0 ) GO TO WRITE (7.50) WRITE (7,420) 4 2 0 FORMAT (' '. / / 2 5 X . ' I N E L A S T I C R E S U L T S ' / / ) WRITE (7.50) W R I T E ( 7 . 4 3 0 ) DAMERR  NMOOES.  IUNIT,  INELASTIC  450  CO  349 3S0 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 37S 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406  C C C C C C C C C C C C  C C C C C c c c c c c c c c c c c  c  WRITE (7.440) WRITE (99.440) 430 FORMAT (/. ' OAMERR • '. F5.2. /) 440 FORMAT ('-'. 'ITERATION ', IX, 'NO. ABOVE OAMOIF' , 3X. 1 'S MATRIX '. 2X. 'SMEAREO'/' NO.'. 5X. 'CAPACITY'. 14X, 2 'RATIO '. 2X. 'DAMPING') 450 CONTINUE AFTER 9 ITERATIONS BETA IS REASSIGNED FROM 0.0 TO 0.8 IF NO. ABOVE CAPACITY • 0. SET BETA-0.0 IF (I .GE. 9) BETA • 0.80 IF(ISIGN.EO.O) BETA-0.0 DVARY - THE LARGEST DAMAGE RATIO DIFFERENCE BETWEEN THIS AND THE LAST ITERATION DVARY • 0.0 CALL MODS - THE MAIN SUBROUTINE FOR THE MSSM -  CALL M003(IC0UNT. ISPEC, NRJ. NRM. NU, NB. NMOOES. S. IDIM. NO, 1 NP, XM, YM. DM, AREA. AV. CRMOM, OAMRAT. KL. KG. SDAMP, 2 BMCAP, E. G. AMASS. EVEC. EVAL. AMAX. ISIGN. IUNIT. BETA. 3 BMERR. IFLAG. EXTL. EXTG. BETAM. DAMB, DVARY. INELAS. DAMPIN. 4 NPRINT. HARD. OLOTN, OLDSA, LOCK. SAXIAL. SHEAR 1. SHEAR2. 5 SBML. SBMG. OEFL. KOU) IF (LOCK .EO. 1) PAMERR - 0.005 IF ONLY DOING ELASTIC ANALYSIS THEN STOP PROGRAM IF (INELAS .EO. 0) GO TO 580 - OUTPUT DAMAGE RATIOS ON UNIT 8 - OUTPUT NUMBER OF MEMBER IN EXCESS OF CAPACITY AND LARGEST DIFFERENCE FROM PREVIOUS ITERATION DAMAGE RATIOS - OUTPUT RATIO OF LARGEST TO SMALLEST NUMBER IN DIAGONAL OF STIFFNESS MATRIX (SRATIO) WRITE (7.460) I. I SIGN, DVARY. SRATIO. BETAM(1) WRITE (99.460) I. ISIGN. DVARY. SRATIO. BETAM(1) 460 FORMAT (• '. 14. 7X, 14, SX. F7.3. 2X, E10.3. 3X, F7.S) - IFLAG IS MODIFIED FROM 0 TO 1 WHEN NO MEMBER IS ABOVE CAPACITY ONE FINAL ITERATION IS PERFORMED - THE FOLLOWING LINES CHECK FOR YIELDING OF ALL MEMBERS AND THE MAXIMUM NUMBER OF ITERATIONS IF (IFLAG .EO. 1 .AND. I .GE. IMAX) GO TO 500 IF (IFLAG .EO. 1) GO TO 480 IF (I .EO. 1 .AND. ISIGN .EO. 0) GO TO 520 IF (I .GE. IM) GO TO 470 ADERR • ABS(DVARY) IF (ISIGN .EO. 0 .AND. ADERR .LT. DAMERR) GO TO 470 GO TO 40 470 CONTINUE  407 408 409 410 41 1 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 4 30 431 432 433* 434 435 436 437 438 439 440 44 1 442 443 444 445 446 447 448 449 450 451 452 453 454 4S5 456 457 458 459 460 461 462 463 464  C  C  C  C  C C C C C C  I FLAG • 1 IF (I .GE. IM .AND. LOCK .EO. 1) LOCK • 2 IF (LOCK .NE. 1) IUNIT - 7 GO TO 40 480 CONTINUE WRITE (IUNIT.490) I 490 FORMAT ('-', SX. 'NO. OF ITERATIONS •'. 15///) GO TO 540 500 CONTINUE WRITE (IUNIT.510) I 510 FORMAT ('-', 5X. 'DOES NOT CONVERGE AFTER', 15. ' 1 ) GO TO 540  ITERATIONS'///  520 CONTINUE ICOUNT - 0 IFLAG « 1 IUNIT - 7 WRITE (IUNIT.530) 530 FORMAT ('-'. 5X, 'MEMBERS DO NOT YIELD '///) GO TO 40 540 CONTINUE WHITE (IUNIT.550) BETA. BMERR 550 FORMAT ('-'. 5X. 'BETA-'. F5.3, ///5X, 'BENDING MOMENT ERROR-', 1 FB.6///) WRITE (IUNIT.560) DAMERR 560 FORMAT (' ', 'DAMAGE RATIO ERROR", F6.3) 570 CONTINUE 580 STOP END SUBROUTINE CONTRLt TITLE, NRJ, NRM. IUNIT. AMAX. ISPEC. DAMPIN, 1 INELAS. NMODES. NPRINT. HARD. KOU. NCONJT. NCDJT. 2 NCDOD. NCDIDS. NCDMS)  DIMENSION TITLE(20) C C READ IN PROGRAM OPTIONS c READ (5.10) INELAS, NMOOES. NPRINT. ISPEC. AMAX. DAMPIN. KOU 10 FORMAT (415, 2F10.2. 15) C DAMPIN IS THE PROPORTION OF CRITICAL OAMPING USED IN ELASTIC C ANALYSIS OR THE FIRST ITERATION OF THE MSSM. c c NPRINT IS A FLAG SET IF MODAL FORCES AND DISPLACEMENTS ARE REQUIRED c IF NPRINT-0 ONLY RMS FORCES ANO DISPLACEMENTS WILL BE PRINTED. c IF NPRINT IS GREATER THAN ZERO THAT NUMBER OF MODES (UP TO NMODES) c WILL HAVE THEIR FORCES ANO DISPLACEMENTS PRINTED. c c INELAS IS A FLAG INDICATING IF ONLY AN ELASTIC ANALYSIS IS REOUIRED c IF 1NELAS-0 THEN ELASTIC ANALYSIS ONLY WILL BE PERFORMED. CD  465 466 467 468 469 470 47 1 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522  C C C C  IF INELAS IS GREATER THAN ZERO THEN THIS IS THE MAXIMUM NUMBER OF ITERATIONS THAT WILL BE PERFORMED OURING INELASTIC ANALYSIS. ECHO PRINT PROGRAM OPTIONS WRITE (IUNIT.20) 20 WRITE (IUNIT,30) NMODES 30 FORMAT (' ', 'MAXIMUM NUMBER OF MODES IN ANALYSIS'. 14) IF (INELAS .EO. 0) WRITE (IUNIT.40) 40 FORMAT (• ', 'ELASTIC ANALYSIS REQUESTED') IF (INELAS .NE. 0) WRITE (IUNIT.50) INELAS SO FORMAT (' '. 'INELASTIC ANALYSIS MAXIMUM ITERATIONS'', 14) IF (INELAS .EO. 0) WRITE (IUNIT.60) DAMPIN 60 FORMAT (' '. 'FRACTION OF CRITICAL DAMPING"'. F6.4) IF (INELAS .GT. 0) WRITE (IUNIT,70) DAMPIN 70 FORMAT (' ', 'INITIAL DAMPING RATIO" '. F6.3) WRITE (IUNIT.80) NPRINT 80 FORMAT (' ', 'NUMBER OF MOOES TO HAVE OUTPUT PRINTED"', 13)  C WRITE (IUNIT.90) WRITE (IUNIT.100) AMAX 90 FORMAT ('-'. 'SEISMIC INPUT') 100 FORMAT ('-', 'MAXIMUM ACCELERATION"', F5.3. ' TIMES GRAVITY') IF (KOU .EO. 2) WRITE (IUNIT.110) 1 10 FORMAT ('- IN THE REVERSE DIRECTION') 120 FORMAT (///I10('-')) IF (ISPEC .EO. 1) WRITE (IUNIT.130) IF (ISPEC .EO. 2) WRITE (IUNIT.140) IF (ISPEC .EO. 3) WRITE (IUNIT,150) IF (ISPEC .EO. 4) WRITE (IUNIT.160) IF (ISPEC .EO. 5) WRITE (IUNIT.170) IF (I SPEC .EQ. 6) WRITE (IUNIT,180) IF (ISPEC .GE. 7) WRITE (IUNIT,190) ISPEC WRITE (IUNIT,120) 130 FORMAT (' ', 'SPECTRUM A USED') 140 FORMAT (' '. 'SPECTRUM B USED') 150 FORMAT C '. 'SPECTRUM C USED') 160 FORMAT (' '. 'NATIONAL BUILOING CODE SPECTRUM USEO') 170 FORMAT (' '. 'SAN FERNANDO E/O. HOLIDAY INN. LONGITUDINAL DIRN 180 FORMAT (' '. 'CIT/SIMULATED EARTHOUAKE TYPE C-2 SPECTRUM') 190 FORMAT (' '. 'ERROR-SPECTRUM TYPE*. 13. ' IS NOT VALID') IF (ISPEC .NE. 4) GO TO 230 DPCNT • 100.0 •• DAMPIN C CALL SPECTR(ISPEC. DAMPIN, 1 SDBND)  1.0. AMAX. SA, 6.283. SABND. SVBND.  C WRITE 200 FORMAT 1 WRITE 210 FORMAT 1 WRITE 220 FORMAT 1 C C  (IUNIT.200) DPCNT, SABND (' ', F5.2. '% DAMPING SPECTRAL ACCEL. BOUND-', F6.3. "' -G') (IUNIT.210) SD8N0 (' ', ' DISPLACEMENT BOUNO-'. F6.3, ' IN') (IUNIT.220) SVBND (' '. ' VELOCITY BOUNO-'. F6.3. ' IN/SEC)  READ IN TITLE  523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542' 543 544 545 546 547 548 549' 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580  C 230 READ (5.240) ( T I T L E ( I ) . I " 1 . 2 0 ) C C C  READ IN NRJ.NRM READ (5.250) NRd. WRITE (IUNIT.260) WRITE (IUNIT,270) WRITE (IUNIT.280) WRITE (IUNIT,290) WRITE (IUNIT.120)  NRM, HARD, NCONJT. NCDJT, NCDOD. NCDIDS, NCDMS ( T I T L E ( I ) . I - 1.20) HARD NRJ, NRM  C C 240 250 260 270 280 290  RETURN FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT 1 END  (20A4) (215. F10.2. 515) ('1', 20A4) (/5X. 'STRAIN HARDENING RATIO - '. F8.3) (///HOC*')) ('-'. 'NO. OF JOINTS', ' -'. 15. 10X, 'NO. OF MEMBERS -'. 15)  C C C SUBROUTINE SETUP(NRM. E, G. XM. YM. DM. ND. NP. AREA. CRMOM. 1 DAMRAT, NRJ, AV. KL, KG. NU, NB. SDAMP, 8MCAP, IUNIT. 2 EXTL, EXTG. NCONJT, NCDJT. NCDOD. NCDIDS) C C C C C C  •  • SET UP THE FRAME DATA  DIMENSION 1 2 3 DIMENSION C C C C C C C  C  KL(NRM). KG(NRM). AREA(NRM). CRMOM(NRM). SDAMP(NRM), DAMRAT(2,NRM). AV(NRM), N0(3.NRJ). NP(6.NRM), XM(NRM), YM(NRM). EXTL(NRM), EXTG(NRM). DM(NRM). KDDF(3), IJ0INT(4O). G(NRM) X(20O). Y(200). J N L ( 2 5 0 ) . JNG(250). BMCAP(NRM). E(NRM)  X ( I ) AND Y ( I ) IN FEET MEMBER EXTENSIONS EXTG AND EXTL ARE IN FEET. AREA(I) IN SQ. INCHES: CRMOM(I) IN INCHES**4 CONVERTED TO FOOT UNITS IN ROUTINE INITIALIZE COORDINATES DO 10 I • I, NRJ X ( I ) - 999000. 10 Y ( I ) • 999000. READ CONTROL NODE CORDINATES WRITE (7.20) 20 FORMAT (//, 'CONTROL NODE COORDINATES'. ///. 'NOOE'. 6X. 1 'X-COORD', 6X, 'Y-COORO', /) DO 50 I • 1 , NCONJT READ (5.30) I J T , X ( I J T ) , Y ( I J T ) 30 FORMAT (15. 2F10.1) WRITE (7.40) I J T , X ( I J T ) . Y ( I J T ) 40 FORMAT (15. 2F13.3) CO CO  561 5S2 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638  50 CONTINUE NODE GENERATION COMMANDS WRITE (7.60) 60 FORMAT (///' NODE GENERATION COMMANDS'/) IF (NCDJT .NE. O) GO TO 80 WRITE (7.70) 70 FORMAT (//, 'NONE') GO TO 130 80 WRITE (7.90) 90 FORMAT (/2X, 'FIRST'. 4X. 'LAST', 4X. 'NO. OF'. 4X. 'NODE'. /. 2X 1 'NODE*. 5X. 'NODE'. 4X. 'NODES', 5X. 'DIFF'. /) DO 120 I • 1. NCOJT READ (5.100) IJT. LJT. NJT. KDIF 1O0 FORMAT (415) IF (KDIF .EO. O) KDIF - 1 WRITE (7.110) IJT, LJT. NJT. KOIF 110 FORMAT (16. 318) CALL GEN1(X, Y, IJT, LJT, NJT, KDIF) 120 CONTINUE C GENERATE UNSPECIFIED JOINT COORDINATES 130 I « 1 140 I - I + 1 IF (I .GT. NRJ) GO TO 160 IF (X(I) .NE. 999000.) GO TO 140 IJT • I - 1 LJT - IJT 150 LJT • LJT + 1 IF (LJT .GT. NRJ) GO TO 160 IF (X(LJT) .EO. 999000.) GO TO 150 NJT • LJT - IJT - 1 CALL GENKX, Y. IJT. LJT. NJT. 1) I • LJT GO TO 140 160 CONTINUE C ASSIGNING 0.0.F. TO THE NODES 00 170 1 - 1 . NRJ DO 170 J • 1, 3 170 ND(J.I) • 1 C ZERO DISPLACEMENTS WRITE (7.180) 180 FORMAT (/, 'ZERO DISPLACEMENT COMMANDS'. //) IF (NCDOD .NE. O) GO TO 190 WRITE (7.70) GO TO 270 190 WRITE (7.200) 200 FORMAT (/. 'FIRST', 6X. 'X'. 6X, 'Y'. 4X. 'ROTN', 4X, 'LAST'. 4X. 1 'NODE', /. 'NODE', 7X, 'DDF', 4X. 'DOF'. 3X. 'DOF', 4X. 2 'NODE', 4X, 'DIFF'. /) DO 260 I - 1. NCOOO READ (5.210) IJT. (KDOF(J),J"1.3), LJT. KDIF 210 FORMAT (615) WRITE (7.220) IJT. (KOOF(J).J*1.3). LJT. KDIF 220 FORMAT (13. 518) DO 230 J • 1. 3 230 NO(J.IJT) - KDOF(J) IF (LJT .EO. O) GO TO 260 IF (KDIF .EO. O) KDIF • 1 NJT - (LJT - IJT) / KOIF C  639 640 64 1 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696  00 250 II • 1. NJT IJT - IJT • KOIF 00 240 J • 1. 3 240 ND(J.IJT) - KDOF(J) 250 CONTINUE 260 CONTINUE C IDENTICAL DISPLACEMENT 270 CONTINUE WRITE (7.280) 280 FORMAT (///, 'EOUAL DISPLACEMENT COMMANDS '. /) IF (NCDIDS .NE. 0) GO TO 290 WRITE (7.70) GO TO 350 290 WRITE (7.300) 300'FORMAT (//, 'DISP'. 4X. 'NO. OF'. /, 'CODE ' . 4X.'NODES'. 6X. 1 'LIST OF NODES'. /) 00 340 1 - 1 . NCDIDS READ (5.310) MKDOF, NJT, (IJOINT(IU).IU- 1.NJT) 310 FORMAT (215, 1415) .... WRITE (7,320) MKDOF, NJT. (IJOINT(IU).IU -1 .NJT) 320 FORMAT (14. 18. 6X. 1415) II - IJOINTO) DO 330 IM - 2, NJT IK - IJOINT(IM) 330 ND(MKDOF.IK) - - I I 340 CONTINUE C - TO SET UP ND ARRAY 350 NU » 0 WRITE (7.400) 00 390 I " 1. NRJ DO 380 J - 1. 3 IF (ND(J.I) .NE. 1) GO TO 360 NU - NU • 1 ND(J.I) - NU GO TO 380 360 IF (ND(J.I) .NE. 0) GO TO 370 ND ( J,I ) - 0 GO TO 380 370 II • -ND(J.I) ND(J.I) « N0(J.II ) 380 CONTINUE WRITE (7,410) I. X(I). Y(I). (ND(J.I).J- 1.3) 390 CONTINUE 400 FORMAT (/. 3X. 'JN'. 5X. 'X-COORD'. 5X. 'Y -COORD'. 5X, 'NDX'. 1 'NDY', 5X, 'NDR', /) 410 FORMAT (14. 2F13.2. 16. 5X. 14. 5X. 14) C C WRITE (IUNIT.580) WRITE (IUNIT.590) WRITE (IUNIT.60O) c c READ IN MEMBER DATA AND COMPUTE THE HALF BANDWIDTH (NB) c HALF BANDWIDTH"MAX DEGREE OF FREEDOM-MIN DEGREE OF FREEDOM +1 c c NB - 0 c 09 (0  697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754  00 560 MBR • 1. NRM READ (5.610) MN. JNL(MBR). JNG(MBR). KL(MBR), KG(MBR), E(MBR), G(MBR). AREA(MBR). CRMOM(MBR). BMCAP(MBR), EXTL(MBR). EXTG(MBR). AV(MBR) IF (£(MBR) .EO. 0.0) E(MBR) - E(MBR - 1) IF (AREA(MBR) .EO. 0.) AREA(MBR) • AREA(MBR - 1) IF (CRMOM(MBR)•.EO. 0.) CRMOM(MBR) * CRMOM(MBR - 1) IF (BMCAP(MBR)..EO. 0.) BMCAP(MBR) > BMCAP(MBR - 1) IF (MBR .EO. 1) GO TO 420 IF (G(MBR) .EO. 0.) G(MBR) • G(MBR - 1) IF (AV(MBR) .EO. 0.) AV(MBR) • AV(MBR - 1) 420 CONTINUE IF DAMAGE RATIOS ARE LESS THAN ONE SET EQUAL TO ONE C 1 2  C  C  C  c c c c  DAMRAT(1.MBR) - 1.0 DAMRAT(2,MBR) - 1.0 COMPUTE MEMBER LENGTH (OM)-LENGTH BETWEEN JOINTS-RIGID EXTENSIONS JL " JNL(MBR) JG - JNG(MBR) XM(MBR) - X ( J G ) - X ( J L ) VM(MBR) - Y ( J G ) - Y ( J L ) DM(MBR) - SORT ( ( XM(MBR ) ) • • 2 • (YM( MBR ) ) " 2 ) EXTSUM - EXTL(MBR) * EXTG(MBR) XM(MBR) « XM(MBR) • (1.0 - EXTSUM/OM(MBR)) YM(MBR) " YM(MBR) • (1.0 - EXTSUM/OM(MBR)) RESET NEGATIVE VALUES OF ZERO TO ZERO IF (YM(MBR) .GT. - 0.01 .AND. YM(MBR) .LT. 0.01) YM(MBR) • 0. 0 IF (XM(MBR) .GT. - 0.01 .AND. XM(MBR) .LT. 0.01) XM(MBR) • 0.0 DM(MBR) - DM(MBR) - EXTSUM CHECK FOR NEGATIVE LENGTHS OF MEMBER (PROBABLY CAUSED BY INCORRECT USE OF MEMBER EXTENSIONS)  430 1  IF (OM(MBR) .GT. 0.0) GO TO 440 WRITE (7.430) MBR FORMAT (' '. ///'PROGRAM HALTED:ZERO OR -VE LENGTH FOR MEMBER'. 16) STOP  c  440  CONTINUE  c  YLEN - YM(M3R) c c c  PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON VERTICAL MEMBERS. IF (EXTSUM .NE. 0.0 .AND. YLEN .GT. 0.2) WRITE (7,450) I 450 FORMAT (' '. -ERROR-HAVE END EXTENSIONS ON NON-HORIZONTAL 1 MEMBER NO.'. 13) PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON c A NON FIX-FIX TYPE MEMBER c KLSUM > KL(MBR) * KG(MBR) IF (EXTSUM .NE. 0.0 .AND. KLSUM .NE. 2) WRITE (7.460) MBR 460 FORMAT (' '. 'ERROR-HAVE RIGID EXTENSIONS ON HINGEO MEMBER". 14) c c c c  GIVE MEMBERS INITIAL ELASTIC OAMPING SDAMP(MBR) - 0.02 ASSIGN MEMBER DEGREES OF FREEDOM  755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812  NP(1.MBR) - N 0 ( 1 . J L ) NP(2.MBR) • ND(2.JL) NP(3.MBR) • N D O . J L ) NP(4.MBR) > ND(1.JG) NP(S.MBR) - ND(2.JG) NP(6.MBR) - ND(3.JG) 1 DETERMINE THE HIGHEST DEGREE OF FREEDOM FOR EACH MEMBER STORING THE RESULT IN 'MAX' MAX - 0  C C c  470 480 490 c c c c c  DO 490 K • 1, 6 IF (NP(K.MBR) - MAX) 480, 480. 470 MAX • NP(K.MBR) CONTINUE CONTINUE  DETERMINE THE MINIMUM DEGREE OF FREEDOM FOR EACH MEMBER,NOTE THAT 1 FOR STRUCTURES WITH GREATER THAN 330 JOINTS INITIAL VALUE OF MIN 1 WILL HAVE TO BE INCREASED FROM ITS PRESTENT POINT OF 1000. 1 MIN • 1000  c  500 510 520 530  DO 530 K - 1, 6 IF (NP(K.MBR)) 520. 520. 500 IF (NP(K.MBR) - MIN) 510. 520. 520 MIN « NP(K.MBR) CONTINUE CONTINUE  540 550  NBB » MAX - MIN + 1 IF (NBB - NB) 550. 550, 540 NB > NBB CONTINUE  c  c c c  PRINT MEMBER DATA AND CONVERT TO FOOT UNITS. WRITE (IUNIT,620) MBR. JNL(MBR), JNG(MBR), EXTL(MBR), DM(MBR), 1 EXTG(MBR). XM(MBR). YM(MBR). AREA(MBR), CRMOM(MBR). AV(MBR), 2 BMCAP(MBR), KL(MBR), KG(MBR). E(MBR) 560 CONTINUE DO 570 MBR - 1. NRM E(MBR) - E(MBR) • 144. G(MBR) • G(MBR) • 144. AREA(MBR) • AREA(MBR) / 144.0 AV(MBR) - AV(MBR) / 144.0 CRMOM(MBR) « CRMOM(MBR) / 20736.0  c  570 CONTINUE c c c  PRINT THE NO. OF DEGREES' OF FREEDOM AND THE HALF BANDWIDTH WRITE WRITE  c c c c  (IUNIT.630) NU (IUNIT.640) NB  01 OUTPUT THE ASSIGNED DEGREES OF RETURN  FREEDOM.  <0  O  813 814 815 816 817 818 819 820 821 822 823 824 825 826 B27 828 829 830 831 832 833 834 835 836 837 838 839 840 84 1 842 843 844 845 846 847 848 849 850 851 852 653 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870  C C C c c c c c c c c c c c c c c c c  c c c c c c c c c c  580 FORMAT (•-', 'MEMBER DATA') 590 FORMAT (/' MN JNL JNG EXTL LENGTH EXTG XM(FT) YM(FT) 1 3X. ' AREA I (CRACKED) AV. 7X. 'MOMENT' , 2X. 'KL' , IX 2 'KG'. 5X. ' E') 600 FORMAT C '. 19X. '(FEET)'. 29X. '(SO.IN)', 3X. '(IN"4)', 2X. 1 '(SO.IN)'. 3X. 'CAPACITY'. 13X. 'KSI') 610 FORMAT (515. 2F10.1. F8.1. 2F12.1. 3F6.2) 620 FORMAT (' '. 13.- 214, F7.3. F9.4. F7.3, 2F9.4. F8.1, F15.1, F8.: 1 F10.2. 213, F10.1) 630 FORMAT (//. 'NO.OF DEGREES OF FREEDOM OF STRUCTURE -'. 15) 640 FORMAT (//' HALF BANDWIDTH OF STIFFNESS MATRIX -'. 15, /) ENO SUBROUTINE BUILD(NU, NB. XM, YM. OM. NP. AREA, CRMOM, AV, E. G. 1 DAMRAT. KL, KG, NRM. S. IDIM, EXTL. EXTG)  - THIS SUBROUTINE WORKS IN DOUBLE PRECISION - THIS SUBROUTINE CALCULATES THE STIFFNESS MATRIX OF EACH MEMBER AND ADDS IT INTO THE STRUCTURE STIFFNESS MATRIX. - THE FINAL STIFFNESS MATRIX S IS RETURNED. - THIS SUBROUTINE IS SIMILAR TO ONE THAT WOULD BE USED IN NORMAL FRAME ANALYSIS. - DIFFERENCES INCLUDE USING CRACKED MOMENT OF INERTIA INSTEAD OF THE GROSS SECTION. DAMAGE RATIOS ARE USED AND FLEXURAL STIFFNESSES MODIFIED ACCORDING TO THESE RATIOS. IDIM IS THE DIMENSIONING SIZE OF THE STRUCTURE STIFFNESS MATRIX INTERNAL FOOT UNITS FOR STIFFNESS MATRIX REAL'S SM(21). S(IOIM) DIMENSION XM(NRM), YM(NRM), DM(NRM), NP(6.NRM). AREA(NRM). 1 CRMOM(NRM), AV(NRM), DAMRAT(2,NRM), KL(NRM), KG(NRM) DIMENSION EXTL(NRM), EXTG(NRM), E(NRM), G(NRM) REAL'S RF. GMOD. CMOMI. 0RATI(6), F, H REAL'8 LONE, LONEX. LONEY, LTWO, LTWOX, LTWOY. AVI REAL'8 YMI, DMI. DM2, XM2. YM2. XMI, AREAI , EMOD. XM2F. YM2F, 1 XMYMF REAL'S DBLE ZERO STRUCTURE STIFFNESS MATRIX DO 10 I - 1, IDIM S(I) - 0.0000 10 CONTINUE BEGIN MEMBER LOOP DO 200 I • 1. NRM ZERD MEMBER STIFFNESS NATRIX DO 20 J • 1. 21 SM(O) - 0.0000  871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 '910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928  C C C  20  C C c c  c  c c c  c c c c  CONTINUE ASSIGN MEMBER PROPERTIES TO DOUBLE PRECESION VARIABLES CONVERT EftG TO DOUBLE PRECISION EMOD - DBLE(E(I)) GMOO - DBLE(G(I)) LONE • DBLE(EXTL(I)) LTWO - OBLE(EXTG(I)) YMI - DBLE(YM(I)) DMI - OBLE(DM(I)) XMI - D8LE(XM(I)) AREAI • DBLE(AREA(I ) ) CMOMI - OBLE(CRMOM(I)) AVI - DBLE(AV(I)) OBTAIN EFFECTIVE DAMAGE RATIO FROM 'DAMCAL' CALL DAMCAL(DAMRAT, DRATI, I)  DM2 » DMI • DMI XM2 - XMI • XMI YM2 - YMI • YMI XMYM • XMI • YMI F • AREAI • EMOD / (DMI*DM2) H " 0.0000 SHEAR DEFLECTIONS ARE IGNORED WHENEVER G OH AV IS ZERD. IF (AV(I) .EO. 0.0 .OR. G(I) .EO. 0.) GO TO 30 H - 12.0D00 * EMOD * CMOMI / (AVI'GMOD*DM2) 30 XM2F • XM2 • F YM2F • YM2 * F XMYMF » XMYM » F FILL IN PIN-PIN SECTION OF MEMBER STIFFNESS MATRIX SM( 1 ) • XM2F SM(2) - XMYMF SM(4) - -XM2F SM(5) " -XMYMF SM(7) • YM2F SM(9) « -XMYMF SM(10) • -YM2F SM(16) • XM2F SM(17) • XMYMF SM(19) « YM2F IF (KL(I) + KG(I) - 1) 100. 40. 50 VALUES OF F CALCULATED HERE DIFFER FROM STANDARD BUILD SUBROUTINE BY DIVIDING BY THE DAMAGE RATIOS. 40  F - 3.0000 * EMOD • CMOMI / (DM2*DM2*DMI•(1.ODOO+H/4.ODOO)) GO TO 60 50 F - 12.0000 * EMOD • CMOMI / (0M2'DM2*DMI•(1 O00O*H)) c RF IS A FACTOR COMMON TO THE ENTIRE MATRIX FOR ADDITION OF c STIFFNESS DUE TO RIGID BEAM END EXTENSIONS. RF - 12.ODOO • EMOD • CMOMI / (DM2-DM2) / (1.D0*H) c c FILL IN TERMS WHICH ARE COMMON TO PIN-FIX,FIX-PIN,AND c FIX-FIX MEMBERS  (0  929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 94 7 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986  C  60 C  C c c  c c c  c  LONEY • LONE * LONEX " LONE • LTWOY • LTWO • LTWOX • LTWO • XM2F • XM2 • F YM2F • YM2 • F XMYMF • XMYM • 0M2F - DM2 • F  YMI • RF • 0RATI(4) XMI • RF • DRATI(4) YMI • RF • 0RATI(5) XMI • RF • DRATI(5) • DRATI(6) • 0RATI(6) F • DRAT 1(6)  SM(1) • SM(1) + YM2F SM(2) - SM(2) - XMYMF SM(4) - SM(4) - YM2F SM(S) - SM(5) • XMYMF SM(7) • SM(7) + XM2F SM(9) • SM(9) • XMYMF SM( 10) - SM(10) - XM2F SM(16) • SM(16) * YM2F SM(17) « SM(17) - XMYMF SM(19) • SM(19) • XM2F IF (KL(I) - KG(I)) 70, 80. 90 FILL IN REMAINING PIN-FIX TERMS 70  SM(6) • -YMI • DM2F • DRATI(5) SM(11) • XMI • DM2F • DRATI(5) SM(18) - -SM(6) SM(20) - -SM(11) SM(21) - DM2 • DM2F • DRAT 1(2) GO TO 100 FILL IN REMAINING FIX-FIX TERMS  80  SM(3) • -YMI • DM2F « 0.5D00 * DRATI(4) SM(6) - SM(3) / DRATI(4) • DRATI(5) SM(8) « XMI • DM2F • 0.5D0O " DRATI(4) SM(11) • SM(B) / DRATI(4) » DRAT 1(5) SM(12) • DM2 * DM2F • (4.0DOO+H) / 12.0000 • DRATI(1) SM(13) - -SM(3) SM(14) • -SM(8) SM(15) - DM2 • DM2F * (2.0D00-H) / 12.0000 • DRATI(3) SM(18) * -SM(6) SM(20) - -SM(11) SM(21) - SM(12) / DRATI(1) • DRATI(2) ADD IN TERMS FDR RIGID END EXTENSIONS. SM(3) • SM(3) - (LONEY) SM(6) « SM(6) - (LTWOY) SM(8) • SM(8) • LONEX SM(I1) - SM(11) + LTWOX SM(12) - SM(12) • (L0NE*DMI*(DMI + LONE) *RF ) • DRATI(1) SM(13) - SM(13) + LONEY SMI 14) ' SM(14) - LONEX SM(15) • SM(15) + ((LONE*LTWO*DMI) • (DM2*(LONE * LTW0)/2.ODOO)) I • RF • DRATI(3) SM(18) * SM(18) • LTWOY SM(20) • SM(20) - LTWOX SM(21) - SM(21) • (DM2«LTW0 + (DMI*(LTWO*LTWO))) • RF • DRATI(2) GO TO 100  987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1O02 1003 1004 1005 1006 1007 1008 1009 1010 101 1 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044  C C  c  c c c c  FILL IN REMAINING FIX-PIN TERMS 90  100  ADD THE MEMBER STIFFNESS MATRIX SM INTO THE STRUCTURE STIFFNESS MATRIX S. NB1 • NB - 1  c c  110 120 130 140 150 160 170  c c c c c c c c c c c c  SM(3) » -YMI • DM2F « DRATI(4) SM(8) • XMI • DM2F • DRATI(4) SM(12) - DM2 • DM2F • DRATI(1) SM(13) - -SM(3) SM(14) - -SM(8) CONTINUE  180 190  DO 190 J - 1. 6 IF (NP(d.D) 190, 190. 110 di » ( J - 1) • (12 - J) / 2 DO 180 L - d. 6 IF (NP(L.I)) 180. 180. 120 IF (NP(d.I) - NP(L.D) 150. 130. 160 IF (L - <J) 140, 150. 140 K - (NP(L.I) - 1) • NB1 • NP(J.I) N - U1 + L S(K) - S(K) • 2.0000 • SM(N) GO TO 180 K • (NP(J.I) - 1) • NB1 + NP(L.I) GO TO 170 K - (NP(L.I) - 1) * NB1 • NP(J.I) N • U1 + L S(K) - S(K) + SM(N) CONTINUE CONTINUE  200 CONTINUE RETURN END SUBROUTINE DAMCAL(DAMRAT, DRATI, NOM) EFFECTIVE DAMAGE RATIO CALCULATION DIMENSION DAMRAT(2.VJ0M) REAL'S DRATI(6), DBLE DRAT 1(1) • DBLE(DAMRAT(1.NOM)) DRAT I(2) • DBLE(DAMRAT(2.NOM)) DRATIO) • 1.D0 / ( .09SD0+.2D0*(DRATI( 1) • DRATI (2)) • .50500 1DRATI(1)*DRATI(2)) DRATI(1) » 1.DO / DRATI(1) DRATK2) • 1.D0 / DRATI ( 2 ) (0  1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1 100 1 101 1 102  C c c c c c c c c c c c c c c c c c c c  c  c c  DRATK4) • (2.00«DRATI(1) • DRATIO)) / 3.00 DRATI(S) • (2.DO*0RATI(2) + DRATIO)) / 3.00 0RATK6) '- (DRATI(I) • DRAT1 (2) + 0RATI(3)) / 3.DO RETURN END  SUBROUTINE MASS(NU. ND. AMASS. IUNIT. NRJ. MDOF. NCDMS)  THIS SUBROUTINE SETS UP THE MASS MATRIX ND(J.I)-DEGREES OF FREEDOM OF I TH JOINT WTX . WTY .WTR "X-MASS , Y-MASS. ROT .MASS IN FORCE UNITStKIPS OR IN-KIPS) AMASSOI-MASS MATRIX, I IS THE DEGREE OF FREEDOM OF APPLIED MASS MASSES ARE LUMPED AT NODES. THE MASS MATRIX IS DIAGONAL1 ZED. DIMENSION ND(3,NRJ). MDOF(100). AMASS(NU) ZERO MASS MATRIX DO 10 I • 1, NU AMASStI) - 0. 10 CONTINUE WRITE (7.20) 20 FORMAT (///. 'MASS GENERATION COMMANDS*. //. 'FIRST NODE'. 4X. 1 'X-MASS'. 4X. 'Y-MASS', 4X. 'ROTN MASS', 3X, 'LAST NODE' 2 3X. 'NODE OIFF.'. /) DO 80 I • 1. NCDMS READ (5.30) IJT. WTX. WTY, WTR. JJT. KDIF 30 FORMAT (15. 3F10.2. 215) WRITE (7.40) IJT, WTX, WTY. WTR. JJT. KDIF 40 FORMAT (15. 3X. 3F10.2. 4X. 15. 8X. IS) IF (KDIF .EO. 0) KDIF - 1 IF (JJT .EO. 0) GO TO 50 NJT • (JJT - IJT) / KDIF + 1 GO TO 60 50 NJT » 1 60 CONTINUE DO 70 J • 1 . NJT N1 • ND(1.IJT) N2 - ND(2.IJT) N3 - NDO.IJT) AMASS(NI) - AMASS(NI) * WTX / 32.2 AMASS(N2) • AMASS(N2) + WTY / 32.2 AMASS(N3) - AMASS(NS) + WTR / 32.2 IJT • IJT • KDIF 70 CONTINUE 80 CONTINUE OUTPUT THE DEGREES OF FREEDOM WITH MASS ANO ASSIGNED MASS .  103 C 104 105 106 C 107 108 109 110 111 112 113 1 14 C 115 116 117 118 119 120 121 122 123 124 125 126 C 127 C 128 C 129 130 131 C 132 C 133 C 134 C 135 C 136 C 137 C 138 C 139 C 140 C 141 C 142 C 143 C 144 C 145 C 146 C 147 C 148 C 149 150 151 152 153 ' C 154 C 155 156 157 C 158 C 159 C 160  JCNT • 1 WRITE (IUNIT.100) DO 90 IDOF - 1. NU RMASS • AMASS(IDOF) IF (RMASS .EO. 0.0) GO TO 90 MDOF(JCNT) - IDOF WRITE (IUNIT.110) JCNT. MDOF(JCNT). RMASS JCNT • JCNT + 1 90 CONTINUE 100 FORMAT ('-'. 'MASS NO. DOF'. 2X. 'ASSIGNED MASS (KIP"SEC"'2/FT)') 110 FORMAT (' '. 2X. 13. 3X. 13, 9X. F10.5) RETURN 120 FORMAT (15) 130 FORMAT (///110(""1) 140 FORMAT ('-', 'NO. OF NODES WITH MASS'. ' -'. 15) 150 FORMAT (/7X. 'JN'. 3X, 'X-MASS*. 4X. 'Y-MASS'. 2X, 'ROT.MASS') 160 FORMAT (' '. 12X. '(KIPS)'. 4X. '(KIPS)'. 2X. '(IN-KIPS)') 170 FORMAT (15, 3F10.0) 180 FORMAT (' '. 5X. 14. 3F10.3) END SUBROUTINE EIGEN(NU, NB. S. IDIM. AMASS. EVAL. EVEC. NMODES, 1 IUNIT. I SPEC, AMAX, ICOUNT, MDOF, INELAS) »  «•»  •  *  •  THIS SUBROUTINE COMPUTES A SPECIFIED NO. OF NATURAL FREQUENCIES AND ASSOCIATED MODE SHAPES NU»NO. OF DEGREES OF FREEDOM NB-HALF BANDWIDTH NMODES"*NO. OF MODE SHAPES TO BE COMPUTED IF NMODES IS ZERO OR IS GREATER THAN THE NUMBER OF STRUCTURE MASSES THEN NMODES WILL BE ASSIGNED THE NUMBER OF STRUCTURE MASSES. AMASS(I)-MASS MATRIX MCOUNT"NUMBER OF NONZERO MASSES S(I('STIFFNESS MATRIX STORED BY COLUMNS EVAL(I)*NATURAL FREQUENCIES EVEC( I . J)"=MODE SHAPES REAL'S OVEC(500.10). DVAL(10). CMASS(SOO), SDI30000) REAL*8 S(IDIM) DIMENSION AMASS(NU). EVAL(NMODES). EVEC(500,NMODES). MOOF(IOO) REAL'S DBLE ZERO DUMMY MASS MATRIX CMASS DO 10 ITRY - 1. 500 10 CMASS(ITRY) • O.ODO COMPUTE THE NUMBER OF NONZERO MASS MATRIX ENTRIES MCOUNT - O (0 u  1161 1162 1 163 1 164 1165 1166 1167 1168 116S 1 170 1171 1172 1 173 1 174 1175 1 176 1 177 1 178 1 179 1 180 1 181 1 182 1183 1184 1 185 1 186 1187 1188 1189 1190 1191 1192 1193 1194 1 195 1 196 1197 1198 1199 1200 1201 1202 1203 1204 120S 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218  C  C C C C C  c c c c c c c c c c c c c c c c c c c c c c c  c  DO 20 I • 1, NU CMASSU) • DBLE(AMASS(I)) IF (AMASS(I) .EO. 0.) GO TO 20 MCDUNT - MCOUNT + 1 20 CONTINUE IF (NMODES .GT. MCOUNT) NMODES • MCOUNT IF (NMODES .EO. 0) NMODES - MCOUNT IF (IUNIT .EO. 6 .AND. ICOUNT .GT. 25) GO TO 30 WRITE (IUNIT.160) NMODES CONTINUE 30 CALL PRITZ TO COMPUTE EIGENVALUES AND EIGENVECTORS CREATE A OUPLICATE STRUCTURE MATRIX (SD) (DESTROYED IN PRITZ) CALCULATE USEFUL LENGTH OF STIFFNESS MATRIX (LSTM) LSTM - (NU) • NB DO 40 I - 1. LSTM SOU) - S(I) 40 CONTINUE SET CONVERGENCE CRITERIA FOR PRITZ. MAKE NEGATIVE IF RESIDUALS .NOT DESIRED. DEPS • 1.00-10 IF (IUNIT .NE. 7) DEPS « (-1.000) * OEPS CALL EIGENVALUE FINOING ROUTINE CALL PRITZ(SO. CMASS. NU. N8. 1. OVAL. DVEC. 500. NMODES. DEPS. 1 &140) CONVERT MATRICES TO SINGLE PRECESION PRINT EIGENVALUES AND EIGENVECTORS(MODE SHAPES) EIGENVALUES (EVAL) ARE THE VALUES OF OMEGA SOUARED. SKIP PRINTING INTERMEDIATE DATA AFTER SEVERAL CYCLES. IF (ICOUNT .GT. 3 .AND. IUNIT .EO. 6) GO TO 70 WRITE (IUNIT.17C) WRITE (IUNIT.210) NMODES WRITE (IUNIT. 2 3 0 H I . I - 1 . NMODES) DO 60 ID-1.NU WRITE(IUNIT.SO) ID.(DVEC(IO.J), J*1.NMODES) 50 FORMAT (• ', 13, 10F11.6) 60 CONTINUE 70 CONTINUE CONVERT MEM8ERS OF EVAL FROM OMEGA SOUARED TO OMEGA CONVERT EIGENVECTORS TO ONLY INCLUDE DEGREES OF FREEDOM WITH MASS ASSIGNED TO THEM DO 80 MAS • 1. MCOUNT IVAR • MDOF(MAS) 00 80 MOD • 1, NMODES EVEC(MAS.MOO) • SNGL(OVEC(IVAR.MOD)) 80 CONTINUE  1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 •1273 1274 1275 1276  IF (ICOUNT .EO. 0 ) WRITE (7.90) 90 FORMAT (• ', //' INITIAL ELASTIC PERIOD IF (ICOUNT .EO. O) IUNIT • 7 WRITE (IUNIT.180) WRITE (IUNIT,190) C C  ')  COMPUTE FREQUENCIES AND PERIODS DO 100 JUICE • 1, NMODES 100 EVAL(JUICE) - SNGL(DVAL(JUICE))  C DO  110 I " 1. NMODES EVAL1 " E V A L ( I ) E V A L ( I ) • SORT(EVALI) WN • E V A L ( I ) PERIOD ' 6.283153 / WN FREQ » 1 / PERIOD IF (ICOUNT .GT. 25 .AND. IUNIT .EO. 6) GO TO 110 CALL SPECTR(ISPEC. 0.02. PERIOD. AMAX. SA. WN. SABND. SVBND. 1 SDBNO) WRITE (IUNIT.200) I . EVAL1, E V A L ( I ) . FREO. PERIOD, SA 110 CONTINUE IF (ICOUNT .EQ. O .AND. INELAS .NE. 0) IUNIT « 6 C C C C C  IF (ICOUNT .GT. 5 .AND. IUNIT .EO. 6) GO TO 130 WRITE (IUNIT.220) NMODES WRITE (IUNIT.240)(I,1-1.NMODES) DO 120 1-1.MCOUNT WRITE (IUNIT.50) I,(EVEC(I.J).J-1.NMODES) 120 CONTINUE  C 130 CONTINUE C RETURN WRITE (IUNIT.150) FORMAT (' ', 'CRAPOUT IN PRITZ') FORMAT ('-'. 'NO. OF MODES TO BE ANALI ZED -'. IS///1 I O C * ' ) / / / ) FORMAT ( / / / H O C * ' ) ) FORMAT (/5X. 'MODES'. 4X. 'EIGENVALUES'. 6X. 'NATURAL FREQUENCIES' 1 , 13X. 'PERIODS'. IOX. 'SA') 190 FORMAT (' '. SOX. '(RAD/SEC)'. 5X. ' (CYCS/SEC)'. 8X. '(SECS)'. 4X. 1 '(2 PERCENT DAMPING)') 200 FORMAT (' '. 5X, 15. 5F15.4) 210 FORMAT (/'TOTAL MODE SHAPES CORRESPONDING TO FIRST'. IS, IX. 1 'FREQUENCIES') 220 FORMAT (/'MASS MODE SHAPES CORRESPONDING TO FIRST'. 15. 1X, 1 'FREQUENCIES') 230 FORMAT (/' DOF'. 18. 9111) 240 FORMAT (/'MASS', 10111) 250 FORMAT (' '. 10F12.6) RETURN END 140 150 160 170 180  C C C  *  *  SUBROUTINE M0D3( ICOUNT. ISPEC, 1 ND. NP. XM, YM, DM. 2 SDAMP, BMCAP, E. G, 3 IUNIT, BETA. BMERR.  NRJ. NRM. NU. NB. NMODES. S. IDIM. AREA. AV. CRMOM. DAMRAT. KL. KG. AMASS. EVEC. EVAL, AMAX, IS1GN. 1F LAG. EXTL. EXTG, BETAM, OAMB,  CO  1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334  C C C C C C C C C  C C C C  C C  C C C  C C  C C  4 S  OVARY. INELAS. DAMPIN, NPRINT, HARD,* OLDTN, OLDSA. LOCK, SAXIAL, SHEAR 1, SHEAR2, SBML, SBMG, DEFL, KOU)  ............................................... SUBSTITUTE STRUCTURE METHOD FOR RETROFIT THIS SUBROUTINE COMPUTES JOINT DISPLACEMENTS AND MEMBER FORCES NEW DAMAGE RATIOS' WILL BE CALCULATED AND RETURNED. REAL*8 S(IDIM), DF(500), ORATIO; DET DIMENSION 1 2 3 DIMENSION 1 2 DIMENSION 1 2 CALCULATE  NOO.NRJ) . NP(6,NRM), XM(NRM), YM(NRM), DM(NRM). AREA(NRM), CRMOM(NRM), DAMRAT(2,NRM), KL(NRM). KG(NRM), EVEC(500,NMODES), EVAL(NMODES), SDAMP(NRM), AV(NRM), AMASS(NU) BMASS(500), IDOF(SOO). ALPHA(20). RMS(8.250). F(500), EXTL(NRM). EXTG(NRM). BMCAP(NRM). DAMB(2,NRM), BETAM(NMODES). 0LDTN(1). 0LDSA(1) OEFL(NU). SAXIAL(NRM). SHEAR 1(NRM) , SBML(NRM), SBMG(NRM). MSIGN(250.2), E(NRM). G(NRM), SHEAR2(NRM), FC0(5OO). BMLCD(250), 8MGCD(250) THE MODAL PARTICIPATION FACTOR :-  J J • TEMPORARY VARIABLE USED IN THE FOLLOEWING LOOP ONLY JJ • 1 00 10 JDOF • 1 , NU IF (AMASS(JDOF) .EO. O.) GO TO 10 BMASS(JJ) • AMASS(JDOF) IDOF(JJ) • JDOF JJ - JJ+ 1 10 CONTINUE MCOUNT • J J - 1 DO 30 MODE - 1. NMODES AMT - O. AMB • O. EIGEN VALUES ARE STORED AS FOLLOWS EVEC(MASS NO.,MODE NO.) DO 20 J - 1, MCOUNT AMT • AMT + BMASS(J) « EVEC(J.MODE) AMB - AMB • BMASS(J) • ( ( EVEC( J . MODE ) ) " 2 ) 20 CONTINUE ALPHA(MODE) • AMT / AMB 30 CONTINUE IF ( I COUNT . GT. 25 .ANO. IUNIT .EO. 6) GO TO 50 WRITE (IUNIT.420) DO 40 MODE ' 1. NMODES WRITE (IUNIT,430) MODE, ALPHA(MODE) 40 CONTINUE 50 CONTINUE WHEN KK"1. MODAL FORCES FOR UNDAMPED SUBSTITUTE STRUCTURE ARE  1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392  COMPUTED. THEY ARE USED TO COMPUTE 'SMEARED' DAMPING VALUES, WHICH ARE USED TO CALCULATE THE ACTUAL RESPONSE DF THE SUBSTITUTE STRUCTURE  C C C C  INDEX - 1  C  DO 410 KK " 1, 2  C C  SET PRINT FLAG FOR MODAL OUTPUT (0-OFF) INTPR - 1 IF (KK .EO. 1) INTPR • 0 IF (IFLAG .EO. 0 .OR. NPRINT .EO. 0) INTPR • 0 IF (ICOUNT .NE. 0) GO TO 70  c c c  c c c  c c  60  SET DAMPING RATIOS TO 'APPROPIATE* VALUES FOR INITIAL TRIAL. DO 60 MODEA • 1 . NMODES BETAM(MODEA) - DAMPIN CONTINUE  70  ICOUNT « ICOUNT + 1 WRITE (IUNIT.450) GO TO 4 10 SHRMS - 0. ZERO  DO 80 I • 1. 250 DO 80 J " 1. 8 RMS(J.I) • 0. CONTINUE  80  OUTPUT THE SMEARED DAMPING RATIOS (FOR DAMPED CASES) IF (IUNIT .EO. 6 .AND. ICOUNT .GT. 25) GO TO 120 IF (KK . EO. 1) GO TO 120  c  WRITE (IUNIT.100)  c c c c c c c c c  RMS(J.I)  DO 90 MODE - 1. NMODES WRITE (IUNIT.110) MODE, BETAM(MODE) CONTINUE  90 100 1 10  FORMAT ('-', 'MODE'. 2X. 'SMEARED DAMPING RATIO') FORMAT (' '. 1X. 13, 7X. F10.5) CALCULATE THE MODAL DISPLACEMENT VECTOR DO 320 MODEN • 1, NMODES  120  CALCULATE NATURAL PERIOD ANO CALL SPECTA  1 1  TN - 6.28318531 / (EVAL(MODEN)) WN • EVAL(MODEN) DAMP - BETAM(MODEN) IF (MODEN .NE. 1 .OR. LOCK .EO. 0) CALL SPECTRfI SPEC. DAMP, TN. AMAX, SA. WN, SABND. SVBNO. SDBND) IF (MODEN .EO. 1) CALL STACHKtOLDSA, SA, OLDTN. TN. ISPEC. LOCK, ICOUNT, IFLAG. IUNIT. AMAX, DAMP, KK)  1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 14 13 1414 1415 1416 1417 1418 14 19 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 144 1 1442 1443 1444 1445 1446 1447 1448 1449 1450  1 C C  130  LIST MEMBER FORCES IF DOING ELASTIC ANLYSIS ONLY  c  140  c c c c  c c c  CHECK IF MODAL PARTICIPATION FACTOR IS ZERO IF ALPHA IS ZERO MODAL FORCES AND DISPLACEMENTS WILL BE ZERO  170  c c c  IF (ALPHA(MOOEN) .NE. 0.0) GO TO 170 WRITE (IUNIT.160) FORMAT (/' MODAL PARTICIPATION .FORCES AND DISPL.-ZERO') GO TO 320 CONTINUE ZERO LOAD VECTOR  180  DO 180 J • 1. NU F(J> - 0. COMPUTE LOAD VECTOR FAC • SA • ALPHA(MODEN) • 32.2  c c c c c c  c c c  IF (INTPR .EO.] 0 ) GO TO 150 IF (NPRINT .LT. MODEN) GO TO 150 WRITE (IUNIT.450) WRITE (IUNIT,140) MODEN FORMAT (' '. 'MODE NUMBER'. 13, ' MODAL FORCES AND OISPLACEMEN  ITS') WRITE (IUNIT.440) CONTINUE 150  160  c c c  IF (HODEN .EO. 1 .ANO. KK .EO. 2) WRITE (99.130) TN, SA IF (MODEN .EO. 1 .ANO. KK .EO. 2 .ANO. 1 FLAG .NE. 1) WRITE (7.130) TN. SA FORMAT (50X. •< PERIOD •', F6.3. 2X. 'SA -', F6.3. ' >')  NOTE THAT AS THESE FORCES ARE BEING GENERATED FROM A LATERAL EXCITATION SPECTRUM THAT ONLY 'X MASSES' SHOULD BE USEO. IN OTHER WORDS LATERAL ACCELERATION SHOULD NOT CAUSE NON HORIZONTAL INERTIA FORCES DIRECTLY.  190  FF - 0. DO 190 J • 1, MCOUNT 11 « IDOF(O) F ( I 1 ) - EVEC(J.MODEN) • FAC • FF • FF * F ( I 1 ) CONTINUE  AMASSU1)  CALCULATE THE BASE SHEAR  200 210  IF (KK .EO. 1) GO TO 200 SHRMS • SHRMS + FF •* 2 IF (MODEN .LT. NMODES) GO TO 200 SHRMS • SORT(SHRMS) CONTINUE CONVERT SINGLE PRECISION FORCE MATRIX TO DOUBLE PRECISION DO 210 IFREE • 1. NU DF(I FREE) • D8LE(F(IFREE ) ) COMPUTE DEFLECTIONS BY CALLING SUBROUTINE SDFBAN  1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 150O 1501 1502 1503 1504 1505 1506 1507 1508  C C C  • 1 MOTE THAT NO SOLUTION IMPROVING ITERATIONS WILL BE PERFORMED. SCALING WILL BE PERFORMED TO IMPROVE THE SOLUTION WHEN NSCALE.NE.O  NSCALE • 1  C  DRATIO - 1.00-16 CALL SOFBAN(S. DF. NU. NB. INDEX. DRATIO. DET. JEXP. NSCALE) C C C C  C  SDFBAN EXITS WITH DF BEING THE. DISPLACEMENT MATRIX  220  CONVERT DOUBLE PRECISION DISPLACEMENTS TO SINGLE PRECISION 00 220 JFREE > 1. NU F ( J F R E E ) - SNGL(DF(JFREE)) CONTINUE INDEX - INDEX + 1  C C C  CALCULATE RMS DISPLACEMENTS.  230  240  250 C C C  260  270  C C C C  280 290  DO 260 JNT - 1, NRJ DX • 0. DY - 0. OR - 0. N1 - ND(1.JNT) N2 - ND(2,JNT) N3 - NDO.JNT) IF (N1 .EO. 0 ) GO TO 230 DX - F(N1) RMS(I.JNT) • RMS(I.JNT) + DX 2 CONTINUE IF (N2 .EO. 0 ) GO TO 240 DY - F(N2) RMS(2,JNT) » RMS(2,JNT) + DY 2 CONTINUE IF (N3 .EO. 0 ) GO TO 250 DR • F(N3) RMSO.JNT) » RMSO.JNT) • DR •• 2 CONTINUE IF (INTPR .EO. 0) GO TO 260 IF (NPRINT .LT. MOOEN) GO TO 260 OUTPUT MOOAL DEFLECTIONS FOR REQUIRED MODES WRITE (IUNIT.470) JNT, DX, DY. DR CONTINUE STORE FINAL FIRST MODE DEFLECTIONS FOR CURVATURE DUCTILITY CALCULATIONS IF (IFLAG .EQ. 1 .ANO. IUNIT .EQ. 7) GO TO 270 GO TO 290 CONTINUE IF (MODEN .NE. 1) GO TO 290 DO 280 JF - 1, NU FCD(JF) - F ( J F ) • DEFL(JF) CONTINUE CONTINUE CALL FORCE TO CALCULATE MEMBER FORCES AND SMEARED DAMPING RATIOS.FORCES DUE TO E/O LOADS ONLY CALL FORCE(NRM, XM, YM, DM, AV. NP. F. EXTL. EXTG. AREA. E. G, ID 05  1509 1510 151 1 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 154 1 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566  1 2 3 C C  COMPUTE ANO WRITE MODAL CONTRIBUTION FACTOR CONMOD • SA • ALPHA(MODEN) WRITEtIUNIT.550) MODEN. CONMOD FORMAT (' '. "MODE '. 13. 3X, 'CONTRIBUTION FACTOR-', F8.5) OUTPUT SPECTRAL- ACCELERATION.  C c c c c  300  310 320  c c  NPRINT. CRMOM, DAMRAT,. INTPR, KL, KG, KK, SDAMP. NMODES, IUNIT. IFLAG, MODEN, ICOUNT, RMS. BETAM, MSIGN, SHEAR 1, SHEAR2. BMLCD, BMGCO)  1  IF(INTPR.EO.O.OR.MODEN.GT.NPRINT) GO TO 570 WRITE(IUNIT,560) DAMP. TN,SA FORMAT (' ', 'DAMPING-'. F6.4. ' PERIOO-', F6.4. ' SEC. SA-'. F5.3) CONTINUE IF (KK .EO. 1) GO TO 410  c c c  PRINT RMS DISPLACEMENTS ANO FORCES  c  330 340 c c c  IF (IUNIT .EO. 6 .AND. ICOUNT .GT. 25) GO TO 340 WRITE (IUNIT,450) OUTPUT THE COUNT OF ENTRANCES INTO M0D3 WRITE (6.330) ICOUNT FORMAT (' ', 'ICOUNT-'. 13) WRITE (IUNIT,460) WRITE (IUNIT.440) CONTINUE CONVERT SOUARE OF RMS DISPLACEMENTS TO RMS DISPLACEMENTS.  350 c  360 370 380  390  400  00 350 1 - 1 . NRJ DO 350 J « 1. 3 RMS(J.I) • SORT(RMS(J,I)) CONTINUE ADD TO THESE RMS DISP.DISP DUE TO GRAVITY LOADS DO 380 1 - 1 . NRJ J1 • ND(1,I) J2 • ND(2.1) J3 - NOO.I) IF (J1 .EO. 0) GO TO 360 RMS(I.I) • RMSO.I) • O E F L ( J I ) IF (J2 .EO. 0) GO TO 370 RMS(2,I) • RMS(2.I) + 0 E F L ( J 2 ) IF (J3 .EO. 0) GO TO 380 RMSO.I) - RMSO.I) + DEFL(J3) CONTINUE IF (ICOUNT .GT. 25 .AND. IUNIT .EO. 6) GO TO 390 DO 390 I - 1, NRJ WRITE (IUNIT.470) I . (RMS(J,I),J-1,3) CONTINUE IF (ICOUNT .GT. 25 .AND. IUNIT .EO. 6) GO TO 400 WRITE (IUNIT,480) WRITE (IUNIT.490) SHRMS IF (ICOUNT .GT. 35 .ANO. IUNIT .EO. 6) GO TO 400 WRITE (IUNIT,500) CONTINUE  1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624  C C C  CALL DAMOD TO MODIFY DAMAGE RATIOS  CALL DAMOD(RMS. NRM, DAMB. BMCAP, DVARY, IFLAG, BETA, HARD, 1 ICOUNT. IUNIT. BMERR. OAMRAT. ISIGN. SDAMP. SAXIAL. SHEAR 1, 2 SHEAR2, SBML, SBMG,' MSIGN. KOU. FCD. BMLCO. BMGCD. NP, OM, 3 E. CRMOM, NU) 410 CONTINUE C -C ICOUNT - ICOUNT • 1 RETURN 420 FORMAT ('-', 'MODAL PARTICIPATION FACTOR', /) 430 FORMAT (' '. 5X. 'MODE', 15. 5X. F10.5. 5X. F10.5) 440 FORMAT ('-'. 7X. 'JOINT NO.'. 10X. 'X-DISP(FT)'. 10X. 1 'Y-OISP(FT) '. 7X. 'ROTAT10N(RAD)') 450 FORMAT ('-'. 110('•*)) 460 FORMAT ('-'. 'ROOT MEAN SOUARE DISPLACEMENTS') 470 FORMAT (' '. 6X, 110, 3F20.4) 480 FORMAT ('-'. 'ROOT MEAN SOUARE FORCES') 490 FORMAT CO*. 7X, 'RSS BASE SHEAR -'. F10.3, ' KIPS') 500 FORMAT ('-'. 8X. 'MN', 10X, 'AXIAL*. 10X, 'SHEARL*. 9X. 'SHEARG', 1 10X, 'BML', 12X. 'BMG', 9X. 'MOMENT', 10X, 'DAMAGE'/21X, 2 'KIPS'. 12X. 'KIPS', 12X. 'KIPS'. 2 ( 9 X . ' ( K - F T ) ' ) . 8X. 3 'CAPACITY', 9X, 'RATIO') END C C • • •••• C SUBROUTINE FORCEfNRM. XM, YM. DM. AV, NP. F, EXTL, EXTG. AREA. E, 1 G. NPRINT. CRMOM, DAMRAT. INTPR. KL, KG. KK. SDAMP. 2 NMODES. IUNIT, IFLAG, MODEN. ICOUNT. RMS. BETAM. MSIGN. 3 SHEAR 1, SHEAR2, BMLCD, BMGCD) C C C C THIS SUBROUTINE CALCULATES AXIAL,SHEAR FORCES C BENDING MOMENT (RETURN AS RMS(4-8.JOINT NO.)). C AND SMEARED DAMPING FACTOR (BETAM) C RMS(5.MEM) - SHEAR AT LESSER END C RMS(S.MEM) » SHEAR AT GREATER END C •*• NOTE •*• C AT THIS STAGE RMS(1,JNT)-(RMS DISPLACEMENT)SOUARED OF X DISPLACEMENT. C COMPUTE MEMBER FORCES USING DISPLACEMENTS FROM INDIVIDUAL MODES C NOTE THAT ' ENGINEERING' SIGN CONVENTION IS USED HERE. C DIMENSION XM(NRM), YM(NRM), DM(NRM), AV(NRM). NP(6.NRM), 1 MSIGN(250.2). 0 ( 6 ) . F(50O). EXTL(NRM), EXTG(NRM). 2 KL(NRM). KG(NRM), P I ( 2 5 0 ) . RMS(8.250). SDAMP(NRM), 3 BETAM(NMODES), E(NRM), G(NRM), SUMDAM(250), ZETA(10). 4 AREA(NRM), CRMOM(NRM), DAMRAT(2,NRM), SHEAR1(NRM), 5 SHEAR2(NRM), BMLCO(NRM), BMGCD(NRM) REAL'S ORATI(6) C SIGPI - O. C C INSERT MODAL MEMBER FORCE HEADINGS C  CO ~1  162S 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682  C C  IF (INTPR .NE. 0 .ANO. NPRINT .GE. MODEN) WRITE (IUNIT.10) 10 FORMAT (' '. /8X. 'MN'. 10X. 'AXIAL'. IOX. 'SHEARL'. 9X. 'SHEARG'. 1 12X. 'BML', 12X. 'BMG', /21X. 'KIPS'. 12X. 'KIPS', 12X. 2 'KIPS'. 2 ( 9 X . ' ( K - F T ) ' ) )  c  00 190 I • 1. NRM.'  c c c c c c c c  XL.YL OL BMG BML  20  c c c  c c c c  c c  X,Y COMPONENTS TRUE LENGTH OF BENDING MOMENT BENDING MOMENT  OF MEMBER LENGTH RESPECTIVELY MEMBER AT GREATER JOINT NO. END OF MEMBER. AT THE LESSER JOINT NO. END.  XL - XM(I) YL " YM(I) DL - DM(I) AVI - A V ( I )  c  c c c  • • •  30 40  DO 40 MEMDOF * 1 . 6 NI • NP(MEMDOF,I) IF (N1) 30. 30. 20 D(MEMDOF) • F(N1) GO TO 40 D(MEMDOF) • 0. CONTINUE  MOOIFY END DISPLACEMENTS FOR HORIZONTAL MEMBERS WITH END EXTENSIONS FORMULA ONLY WORKS FOR HORIZONTAL MEMBERS N3 • NP(3,I) IF (N3 .EO. 0) GO TO 50 D(2) - 0 ( 2 ) + ( F ( N 3 ) ) • E X T L ( I ) CONTINUE 50 N6 • NP(6.I) IF (N6 .EO. 0) GO TO 60 D(5) - D(5) - ( F ( N 6 ) ) • EXTG(I) CONTINUE 60 PRINT OUT MEMBER END DISPLACEMENTS FOR DEBUG 1F(I COUNT.GT.1) GO TO 80 WRITE(6.70) I.(D(M).M'1,6) 70 FORMAT (' '. 'MEMB NO.-'. 13. 'DISPL-'. 6F10.5) CONTINUE 80 AXIAL • (AREA(1)*E(I )/DL* *2) • (D(4)'XL • D(5)'YL - D(1)»XL - D( 1 2)*YL) GET EFFECTIVE DAMAGE RATIO CALL DAMCALtDAMRAT, DRATI, I ) EISI • CRMOM(I) • E ( I ) GFACT-FACTOR TO COMPUTE EFFECT OF SHEAR DEFL. ON MEMBER FORCES GFACT-0.0 IMPLIES THAT NO SHEAR DEFLECTION INCLUDED. GFACT - 0.0 IF (AVI .EO. 0.0 .OR. G ( I ) .EO. 0.0) GO TO 90 GFACT - 12.0 • EISI / (AVI*G(I)*DL*DL) * DRATI(6) CONTINUE 90 ASSIGN DISPLACEMENTS TO THEIR RESPECTIVE MEMBER DEGREES OF  1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740  FREEDOM CHECK FOR PIN-PIN MEMBERS IF ( K L ( I ) .EO. 0 .AND. KG(I) .EO. 0 ) GO TO 120 DELT • ( ( 0 ( 5 ) - 0(2>)*XL • ( D O ) - D(4))«YL) / DL BML - ( 2 . 0 * E I S I / ( D L * ( 1 . 0 + GFACT))) * ((3.O'DELT'DRATI(4)/DL) 1 ( D ( 6 ) * ( 1 . 0 - GFACT/2.0)*DRATI<3)) - (2,0'D(3)•(1.0 • GFACT/4.0)* 2 ORATI(I))) BMG • - ( 2 . 0 * E I S I / ( D L * ( 1 . 0 + GFACT))) • ((3.O'DELT'DRATI(5)/DL) 1 ( D ( 3 ) ' ( 1 . 0 - GFACT/2.0)*DRATI(3)) - (2.0*D(6)•(1.0 • GFACT/4.O) 2 'DRATI(2))) SHEAR • ( 6 . 0 ' E I S I / ( D L - D L ) ) • ( ( 0 ( 3 ) ' D R A T I ( 4 ) • D(6)'DRATI(5) - ( 1 2.0*DELT»DRAT1(6)/DL))/(1.0 * GFACT)) C BMG-BML+SHEAR'DL IF ( K L ( I ) - K G ( I ) ) 100. 130. 110 C ADJUST PIN-FIX MEMBER FORCES. 100 BMG » BMG + BML • (1.0 - GFACT/2.0) / (2.0*(1.0 • GFACT/4.0)) SHEAR - SHEAR + 1.5 • BML / (DL) BML - 0. GO TO 130 C AOJUST FIX-PIN MEMBER FORCES. 110 BML - BML * BMG • (1.0 - GFACT/2.0) / (2.0*(1.0 • GFACT/4.0)) SHEAR - SHEAR - 1.5 • BMG / (DL) BMG - O. GO TO 130 F I L L IN MEMBER FORCES FOR PIN-PIN MEMBERS. c 120 BMG • 0. BML - 0. SHEAR - 0. 130 CONTINUE C  c c c  COMPUTE THE RELATIVE FLEXURAL STRAIN ENERGY  1 140  c c  c  c c  IF (KK .EO. 2) GO TO 140 P I ( I ) - (BML*BML*DRATI(2) + BMG*BMG*DRATI(1) + BML*BMG*DRATI(3)) • 2. • DL / EISI / (16.*DRAT1(1)*DRATI(2) - 4*(DRATI(3)**2.)) SIGPI « SIGPI + P I ( I ) CONTINUE  PRINT OUT FORCES FOR EACH MEMBER IF ELASTIC CASE DESIRED. IF (INTPR .EO. 0) GO TO 160 ASHEAR - SHEAR 1(1) + SHEAR BSHEAR - S H E A R 2 0 ) • SHEAR IF (NPRINT .GE. MODEN) WRITE (IUNIT,150) I . AXIAL. ASHEAR, 1 BSHEAR, BML, BMG 150 FORMAT (6X. 15. 7F15.3) 160 CONTINUE IF (MODEN .GT. 1) GO TO 170 IF (BML .LE. 0.) MSIGN(I,1) • IF (BML .GT. 0.) MSIGN(I.I) • IF (BMG .LE. 0.) MSIGN(I.2) IF (BMG .GT. 0.) MSIGN(I,2) • 170 CONTINUE ACCUMULATE ABSOLUTE SUM AND RMS RMS(4,I) RMS(5.I) RMS(6,I) RMS(7,1)  • -  RMS(4,I) RMS(5.1) RMS(6.I) RMS(7.I)  + + + •  -1 1 -1 1 SUM  AXIAL " 2 SHEAR •• 2 BML •• 2 BMG •• 2  (0 CO  1741 1742 1743 1744 1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 1793 1794 1795 1796 1797 1798  C  C C C C C C  C C C C C  STORE FIRST MODE B.M. IN FINAL ITERATIONS FOR CURV. DUCT. IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 180 IF (MODEN .NE. 1) GO TO 180 BMLCO(I) - BML BMGCD(I) - BMG 180 CONTINUE 190 CONTINUE COMPUTE THE SMEARED DAMPING FOR EACH MODE  ,  IF (KK .EO. 2) GO TO 260 ' SUMDAM- THE PRODUCT OF MEMBER STRAIN ENERGY*MEMBER DAMPING. ZETA(MODEN) • O. 00 200 1 - 1 . NRM SUMOAM(I) - P I ( I ) • SDAMP(I) ZETA(MOOEN) « ZETA(MODEN) + SUMOAM(I) 200 CONTINUE IF (SIGPI . EO. 0.0) WRITE (IUNIT.210) 210 FORMAT (' '. "ERROR-DIVIDED BY ZERO WHILE CALCULATING SMEARED 1 DAMPING") BETAM-SMEAREO SUBSTITUTE DAMPING FOR THE M TH MODE. BETAM(MOOEN) - ZETA(MOOEN) / SIGPI PRINT DAMPING  INFORMATION FROM FINAL ITERATION.  IF (IFLAG .EO. O) GO TO 260 WRITE (6.220) SIGPI. MODEN. BETAM(MODEN) 220 FORMAT (' '. 'TOTAL FLEX. STR. ENERGY-', F10.3. 3X. 'MODE NUMBER', 1 12. 3X. 'SMEARED DAMPING FACTOR-'. F7.S) WRITE (6.230) C DO 250 MEMB - 1. NRM 230 FORMAT (' '. 'MEMBER NO.', 3X. 'STRAIN ENERGY' , 3X. 1 "MEMBER DAMPING', 3X, 'MEMBER DAMPING*STRAIN ENERGY') WRITE (6.240) MEMB. PI(MEMB), SDAMP(MEMB), SUMDAM(MEMB) 240 FORMAT (' '. 3X, 13, 10X. E10.3, BX. E10.3. I3X, F11.7) 250 CONTINUE 260 CONTINUE RETURN END C C C  *• SUBROUTINE 1 2 3  C C C  * DIMENSION 1 2 3 4  **  DAMOD(RMS. NRM, DAMB, BMCAP, OVARY. IFLAG. BETA, HARD, ICOUNT, IUNIT, BMERR, DAMRAT, ISIGN, SDAMP. SAX1AL, SHEAR 1, SHEAR2, SBML. SBMG. MSIGN, KOU. FCD. BMLCD, BMGCD. NP. DM, E, CRMOM, NU) *  "  *  *  **•  RMS(8,250). DAMB(2.NRM). BMCAP(NRM), DAMRAT(2.NRM), SOAMP(NRM), DAMDL0(2). SAXIAL(NRM). SHEAR 1(NRM), SBML(NRM), SBMG(NRM). MSIGN(250.2). SHEAR2(NRM), FCD(NU), eMLCO(NRM), BMGCD(NRM), NP(6.NRM). OM(NRM), E(NRM), CRMOM(NRM), C0(2,250)  1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 1825 1826 1827 1828 1829 1830 1B31 1832 1833 1834 1835 1836 1837 1838 1839 1840 1841 1842 .343 1144 1145 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856  C C C C  MODIFY DAMAGE RATIOS ISIGN IS A COUNT OF THE NUMBER OF MEMBERS WITH WHICH THE RATIO OF THE ABSOLUTE VALUE OF THE DIFFERENCE BETWEEN THE LARGEST RMS BENDING MOMENT ANO ULTIMATE MOMENT TO ULTIMATE MOMENT IS IN EXCESS OF 'BMERR'. ISIGN IS INITIALIZED TO ZERO HERE.  c C  c c  ISIGN - 0  c  DO  c c 10 20  c  c  30 40  50 60  70  10 MEM • 1. NRM  CONVERT SOUARE OF RMS AXIAL. SHEAR ANO MOMENT TO RMS VALUE. DO 10 J • 4. 7 RMS(J.MEM) - SORT(RMS(J.MEM)) CONTINUE IF (KOU .EO. 2) GO TO 20 GO TO 40 CONTINUE DO 30 I - 1. NRM MSIGN(I.I) - -MSIGN(I.I) MS1GN(I,2) - -MSIGNU.2) CONTINUE ADD STATIC FORCES TO FIRST MODE FORCES FOR CURV DUCT. CALCUL. IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 60 DO 50 I - 1. NRM KSIGN • 1 IF (KOU .EO. 2) KSIGN - -1 BMLCO(I) • KSIGN • BMLCO(I) + SBML(I) BMGCD(I) - KSIGN • BMGCD(I) + SBMG(I) CONTINUE CONTINUE ADD MEMBER FORCES DUE TO GRAVITY LOADS & E/O LOADS DO 70 1 • 1. NRM RMS(4.I) - RMS(4.I) • SAXIAL(I) RMS(8.I) - RMS(5.I) • SHEAR2(I) RMS(5.I) • RMS(S.I) • SHEAR 1 ( I ) RMS(G.I) - MSIGN(I.I) * RMS(6,I) • SBML(I) RMSO.I) • MSIGN(I,2) * RMSO.I) + SBMG(I) RMS(G.I) - ABS(RMS(6.I)) RMSO.I) - ABS(RMS(7,I)) CONTINUE 00 310 MEM • 1. NRM DO 90 L - 1. 2  c c c c  SET DAMOLD AS THE DAMAGE RATIO IN THE (I-2)TH ITERATION OAMB AS THE DAMAGE RATIO IN THE ( I - I ) T H ITERATION.  c c c  CALCULATE NEW DAMAGE RATIO  DAMOLD(L) • DAMB(L.MEM) DAMB(L.MEM) - DAMRAT(L.MEM)  80  IF (DAMRAT(L.MEM) .GT. 1.0) GO TO 80 DAMRAT(L.MEM) - RMS(5 • L.MEM) / BMCAP(MEM) • DAMRAT(L.MEM) GO TO 90 TEMP - RMS(5 • L.MEM) * DAMRAT(L.MEM) DAMRAT(L.MEM) - TEMP / (BMCAP(MEM)*(1 - HARD) * HARD-TEMP) to (0  1857 1858 1859 1860 1861 1862 1863 .1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 19O0 1901 1902 1903 1904 190S 1906 1907 1908 1909 1910 1911 1912 1913 1914  C  c c  •c  c c c c c c c  90  CONTINUE OUTPUT THE RMS AXIAL SHEARS ANO MOMENT.  IF (ICOUNT .CT. 35 .AND. IUNIT .EO. 6) GO TO 160 DAMAX • OAMRAT(1.MEM) IF (DAMRAT(2.MEM) .GT. DAMRAT(1.MEM)) OAMAX » DAMRAT(2,MEM) WRITE (IUNIT.100) MEM, RMS(4.MEM), RMS(5,MEM), RMS(B.MEM). 1 RMSI6.MEM), RMS(7,MEM), BMCAP(MEM), DAMAX FORMAT (6X. I S . 7F15.3) 100 IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 150 CALCULATE MEMBER CURVATURE DUCTILITIES AT BOTH ENDS OF MEM8ER CD(1.MEM) - 0. C0(2.MEM) • 0. IF (OAMRAT(1.MEM) .LE. 1.) GO TO 120 IF (NP(S.MEM) .EO. 0) GO TO 110 N1 > NPO.MEM) THETAY - ( 1 . - DAMRAT(I.MEM)'HARD) • FCD(N1) / (DAMRAT(1.MEM)'( 1. - HARD)) 1 THETAP - ABS(FCD(N1)) - ABS(THETAY) CD(t.MEM) - 1. + THETAP • E(MEM) • CRMOM(MEM) / (0.05'DM(MEM)* 1 BMCAP(MEM)) GO TO 120 CONTINUE 110 BM1 • BMLCD(MEM) BM2 • BMGCD(MEM) DAMAGE - OAMRAT(1.MEM) CALL CDUCT(C01, BM1. BM2. NP. NRM. MEM. DM, FCO. NU, DAMAGE, E. CRMOM. BMCAP, HARD) 1 CD(1.MEM) - CD 1 CONTINUE 120 IF (DAMRAT(2,MEM) .LE. 1.) GO TO 140 IF (NP(6.M£M) .EO. 0) GO TO 130 N1 - NP(6.MEM) THETAY • ( 1 . - DAMRAT(2.MEM)'HARD) • FCD(NI) / (DAMRAT(2,MEM)•( 1 1. - HARD)) THETAP - ABS(FC0(N1)) - ABS(THETAY) CD(2.MEM) • 1. + THETAP • E(MEM) • CRMOM(MEM) / (0.05'DM(MEM)• 1 BMCAP(MEM)) GO TO 140 CONTINUE 130 BM1 * BMLCD(MEM) BM2 • BMGCD(MEM) DAMAGE • DAMRAT(2,MEM) CALL CDUCT(CD2, BM1. BM2, NP, NRM, MEM. DM, FCO, NU. DAMAGE. E, CRMOM, BMCAP, HARD) 1 CD(2.MEM) • CD2 CONTINUE 140 CONTINUE ISO 160  00 240 L • 1. 2 DO NOT ALTER DAMAGE RATIOS OF LESS THAN UNITY IF (DAMRAT(L,MEM) .LT. 1.0) GO TO 230 CONVERGENCE SPEEDING ROUTINE FOLLOWS.  1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 194 1 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972  1 1 C  DAMDIF  C 170 180 190 200 210 220 230 240  1  C C C C C  C C C  IF (DAMRAT(L.MEM) .LT. 5.0) DERROR • (DAMRAT(L.MEM) - DAMB(L, MEM)) / 10.0 IF (DAMRAT(L,MEM) .GE. 5.0) DERROR • (DAMRAT(L.MEM) - DAMB(L, MEM)) / DAMRAT(L,MEM) IF (ABS(DERROR) .GT. ABS(DVARY)) OVARY - DERROR > OAMRAT(L.MEM)  - DAMB(L.MEM)  IF (DAMOLD(L) - DAMB(L.MEM)) 170. 230. CONTINUE IF (DAMDIF) 190. 230. 180 DAMRAT(L.MEM) • DAMRAT(L.MEM) + BETA • GO TO 230 OAMRAT(L.MEM) • DAMRAT(L,MEM) - BETA • GO TO 230 CONTINUE IF (DAMDIF) 220, 230. 210 CONTINUE 0AMRAT(L.MEM) • DAMRAT(L.MEM) - BETA • GO TO 230 CONTINUE DAMRAT(L.MEM) - DAMRAT(L.MEM) * BETA • CONTINUE IF (DAMRAT(L,MEM) .LT. 1.0 .AND. IFLAG 1 .0 CONTINUE  200 (DAMDIF) (DAMDIF)  (DAMDIF) (DAMDIF) .NE. 1) DAMRAT(L.MEM)  DAMAGE RATIOS CANNOT BE LESS THAN 1.0 IN LAST ITERATION SKIP RESETTING DAMAGE RATIOS LESS THAN UNITY IF (OAMRATfI.MEM) .LE. 1.0 .AND. DAMRAT(2,MEM) .LE. 1.0) GO TO 290 FIND THE BIGGEST OF THE SOUARE OF THE RMS BENDING MOMENT('BIG) IF (RMS(6,MEM) - RMS(7,MEM)) 250. 250. 260 250 BMBIG - RMS(7,MEM) DAM * DAMRAT(2.MEM) GO TO 270 260 BMBIG • RMS(6,MEM) DAM • DAMRAT(1.MEM) 270 CONTINUE 11  BMSH • INCREASED MOMENT CAPACITY DUE TO STRAIN HARDENING  BMSH - BMCAP(MEM) * (1 - HARD) / (1 - HARD'DAM) CHECK • (BMBIG - 8MSH) / BMSH IF (CHECK .GT. BMERR) ISIGN • I SIGN + 1 C COMPUTE DAMPING VALUE FOR THE MEMBER SDAMP(MEM) • 0.0 DO 280 L - 1, 2 DAM • OAMRAT(L.MEM) - 1 280 SDAMP(MEM) - SOAMP(MEM) + ((HARD'DAM + 1)'DAM) / (1 - DAMRAT(L. 11 MEM)"HARD ) SDAMP(MEM) • 0.15915494 • SOAMP(MEM) / (DAMRAT(1,MEM) • DAMRAT( 1 2.MEM)) + .02 GO TO 300 290 SDAMP(MEM) - 0 . 0 2 300 CONTINUE 310 CONTINUE  1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 19B3 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2 COO 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 201 1 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030  IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 350 WRITE (IUNIT.320) 320 FORMAT (//. 25X. 'CURVATURE DUCTILITIES'. /. 20X. 33('-*). /. IOX, 1 'MN'. 14X. 'LESSER END'. 13X, 'GREATER ENO', /) 00 340 MEM • 1, NRM WRITE (IUNIT.330) MEM, CD(1,MEM). C0(2.MEM) 330 FORMAT (7X, IS .• 2( 17X, F9 . 3) ) 340 CONTINUE 350 CONTINUE RETURN END  C C C •••••• C SUBROUTINE STACHK(OLDSA. SA, OLOTN, TN, ISPEC. LOCK, ICOUNT. 1 IFLAG. IUNIT. AMAX. DAMP. KK) C C C C C THE INTENTION OF THIS SUBROUTINE IS TO DEAL WITH CONVERGENCE C INSTABILITY CAUSED BY STEEP SPECTRUM CONTOUR C• DIMENSION 0LDTN(1), OLDSA(I) C IF (LOCK .GT. O) GO TO 90 C IF (ICOUNT .LT. 4) RETURN IF (ICOUNT .EO. 4 .AND. KK .EO. 1) GO TO 20 IF (ICOUNT .EO. 5 .AND. KK .EO. 1) GO TO 10 IF (KK .EO. 2) GO TO 30 01F1 • OLDTN( 2) - OLOTN( 1 ) 0IF2 " OLDTN(I) - TN IF (DIF1 .LT. - 0.005 .AND. DIF2 .GT. 0.005) GO TO 40 IF (DIF1 .GT. 0.005 .AND. DIF2 .LT. - 0.005) GO TO 40 10 OLDTNt2) • OLDTN(1) 20 OLDTN(1) - TN RETURN C 30 0LDSA(2) • SA • (6. + 100.'DAMP) / 8. RETURN C C INSTABILITY DETECTED : START BINARY SEARCH ROUTINE C 40 WRITE (99.150) WRITE (7.150) WRITE (99,50) ICOUNT WRITE (7,50) ICOUNT 50 FORMAT (/3X. 'CONVERGENCE PROBLEM OCCURRED AT ITERATION NO. ', 12, 1 ' :'/3X. 'SPECIAL CONVERGENCE ROUTINE IS NOW IN EFFECT'/3X, 2 'START BINARY SEARCH PROCEDURE -') KCOUNT • O LOCK - 1 OLOSA(I) • SA • (6. • 100.'DAMP) / 8. C C FIND UPPER BOUNO ANO LOWER BOUND SA(» 2% OAMPING) C - SET OLOSA(1)>UPPER BOUND. OLDSA(2)-LOWER BOUND  2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088  C C  c C c c c c  c c c c  c  c  c  0LDSA(3).TRIAL SA(0 2X DAMPING) IF (0LDSA(2) .LT. OLDSA(I)) GO TO 60 TEMP - OL0SA(1) OLDSA(1) - 0LDSA(2) 0LDSA(2) « TEMP 60 WRITE (99,70) OLDSA(I). 0LDSA(2) WRITE (7.70) OLDSA(I). 0LDSA(2) WRITE (99.140) WRITE (7.140) 70 FORMAT (/3X, 'UPPER BOUND SA • ', F7.5. 4X, 'LOWER BOUND SA - '. 1 F7.5/) 80 OLDSAO) • (OLDSA(I) • 0LDSA(2)) / 2. CALCULATE SA AND CHECK FOR CONVERGENCE (IFLAG'1) 90 SA • OLDSA(3) • 8. / (6. + 100.*DAMP) IF (IFLAG .EO. 1 .AND. KK .EO. 2) GO TO 100 RETURN CHECK FOR REAL CONVERGENCE 100 CALL SPECTROSPEC, DAMP. TN, AMAX, SAA. 0.. 0., 0.. 0.) SADIF - ABS(SA - SAA) / SAA IF (LOCK .EO. 2) GO TO 170 KCOUNT • KCOUNT • 1 WRITE (99.110) KCOUNT. SADIF WRITE (7.110) KCOUNT. SADIF 110 FORMAT (/. ' , 12. 55('-'), 'SADIF . '. F6.4) CONVERGENCE LIMIT FOR SA IS 0.015 IF (SADIF .LE. 0.015) GO TO 120 GO TO 160 120 WRITE (99,130) WRITE (7.130) 130 FORMAT (/50X. 'PROGRAM CONVERGED (SAERR-0.015)') 140 FORMAT ('-', 'ITERATION '. IX, 'NO. ABOVE DAMOIF', 3X. 1 'S MATRIX '. 2X. 'SMEARED'/' NO.'. 5X, 'CAPACITY', 14X, 2 'RATIO ', 2X, 'DAMPING') 150 FORMAT (/80('-')) IFLAG • 0 LOCK • 2 RETURN 160 IF (SA .GT. SAA) OLDSA(I) - OLDSAO) IF (SA .LT. SAA) 0LDSA(2) • 0LDSA(3) IFLAG " 0 GO TO 80 170 WRITE (99.180) SA. SAA. SADIF WRITE (7.180) SA, SAA. SADIF 180 FORMAT (/' *. 'SA • '. F7.S, 3X. 'SA(ACTUAL) • '. F7.5. 3X. 1 'SADIF - '. F7.5/) RETURN END  2089 2090 2091 2092 2093 2094 2095 2096 2097 2098 2099 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 21 lO 2111 2112 2113 2114 2115 2116 2117 21 18 2119 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 2131 2132 2133 2134 2135 2136 2137 2138 2139 2140 2141 2142 2143 2144 2145 2146  C c c c c c c c c c c c c c c c c c c c c  c c c  c c c  SUBROUTINE SPECTR(ISPEC. DAMP. TN. AMAX, SA, WN. SABND, SVBND, 1 SDBNO)  ISPEC-1 IF SPECTRUM A IS USED «2 IF SPECTRUM B IS USED •3 IF SPECTRUM C IS USED •4 IF NBC SPECTRUM IS USED •5 IF SAN FERNANDO E/O RECORD 143 IS USED •6 IF SIMULATED E/O C-2 IS USED OAMP-OAMPING FACTOR (FRACTION OF CRITICAL DAMPING) TN -NATURAL PERIOD IN SECONDS AMAX"MAXIMUM GROUND ACCELERATION (FRACTION OF G) SA -RESPONSE ACCELERATION (FRACTION OF G) WN -NATURAL FREQUENCY IN RADIANS PER SECOND. CALL FTNCMD('EQUATE 99-SPRINT;') GO TO (10. 20. 70. 110. 140. 150). ISPEC SPECTRUM A 10 IF IF IF GO  (TN .LT. 0.15) SA - 25. * AMAX • TN (TN .GE . 0.15 .ANO. TN .LT. 0.4) SA - 3.75 • AMAX (TN .GT . 0.4) SA • 1.5 • AMAX / TN TO 100  SPECTRUM B 20 CONTINUE IF (TN .LT. 0.1875) GO TO 30 IF (TN .LT. 0.53333333) GO TO 40 IF (TN .LT. 1.6666667) GO TO 50 IF (TN .LT. 1.81666667) GO TO 60 SA - 2. • AMAX , / (TN - 0.75) GO TO 100 30 SA • 20. * AMAX • TN GO TO 100 40 SA - 3.75 • AMAX GO TO 100 50 SA - 2. • AMAX , / TN GO TO 100 60 SA • 1.875 ' AMAX GO TO 100 SPECTRUM C 70 CONTINUE IF (TN .LT. 0.15) GO TO 80 IF (TN .LT. 0.38333333) GO TO 90 SA • 0.5 • AMAX / (TN - 0.25) GO TO 100 80 SA - 25. • AMAX • TN GO TO 100 90 SA • 3.75 • AMAX  2147 2148 2149 2150 2151 2152 2153 2154 2155 2156 2157 2158 2159 2160 2161 2162 2163 2 164 2165 2166 2167 2168 2169 2170 2171 2172 2173 2174 2175 2176 2177 2178 2179 2180 2181 2182 2183 2184 2185 2186 2187 2188 2189 2190 2191 2192 2193 2194 2195 2196 2197 2198 2199 2200 2201 2202 2203 2204  100 CONTINUE SA - SA • 8. / (6. • 100.-OAMP) RETURN  C c NBC SPECTRUM c 110 CONTINUE SV • 40.0 • AMAX SD - 32.0 • AMAX SACC - 1 . 0 * AMAX c PRINT OUT A CAUTION NOTE SHOULD DAMPING BE LESS THAN 0.5% IF (DAMP .LT. 0.005) WRITE (7.120) 120 FORMAT (' ', 'CAUTION-DAMPING LESS THAN 0.5%') c c COMPUTE MULTIPLICATION FACTOR FOR ACCELERATION AT DESIREO DAMPING IF (DAMP .LE. 0.02) AML - 4.2 • ((0.02 - DAMP)/0.015) • 1.6 IF (DAMP .GT. .02 .AND. DAMP .LE. .05) AML - 3.0 • ((.05 - DAMP)/. 103) * 1.2 IF (DAMP .GT. 0.05 .AND. DAMP .LE. 0.1) AML - 2.2 + ((0.1 - DAMP)/ 10.05) * 0.8 IF (DAMP .GT. 0.10) AML - 1.0 + (O.OO - DAMP)/0.90) * 1.2 c c COMPUTE MULTIPLICATION FACTOR FOR VELOCITY AT DESIRED DAMPING. IF (DAMP .LE. 0.02) VML - 2.5 • ((0.02 - DAMPJ/0.015) • 0.8 IF (DAMP .GT. .02 .AND. DAMP .LE. .05) VML * 2.0 + ((.05 - DAMP)/. 103) « 0.5 IF (DAMP .GT. .05 .AND. DAMP .LE. 0.1) VML - 1.7 + ((0.1 - DAMP)/ 10.05) • 0.3 IF (DAMP .GT. 0.10) VML • 1.0 • ((1.00 - DAMP)/0.90) * 0.7 c c COMPUTE MULTIPLICATION FACTOR FOR DISPLACEMENT AT DESIRED DAMPING. IF (DAMP .LE. 0.02) DML - 2.5 * ((0.02 - DAMP)/O.OI5) • 0.5 IF (DAMP .GT. 0.02) DML - VML c c COMPUTE BOUNDS USING DAMPING FACTORS COMPUTED ALREADY SDBNO - SD * DML SABND * SACC • AML SVBND - SV * VML c COMPUTE WHICH IS THE APPROPIATE BOUND. c CONVERT FROM IN/SEC**2 TO FRACTION OF G BY DEVIDING BY 386.4 c SAATAP • SVBND * WN / 386.4 IF (SAATAP .GT. SABND) SA - SABND IF (SAATAP .GT. SABND) GO TO 130 SDATCP - SVBND / WN IF (SDATCP .GT. SDBND) SA • SDBNO • WN • WN / 386.4 IF (SOATCP .GT. SDBND) GO TO 130 c c IF HAVE NOT YET GONE TO STEP 180 THEN NATURAL FREOUENCY LIES ON c VELOCITY BOUND. c SA - SVBND • WN / 386.4 c SA IS RETURNED AS A FRACTION OF GRAVITY. G c 130 RETURN c c SAN FERNANDO E/O, HOLIDAY INN. LONGITUDINAL DIRECTION c  o fO  2205 2206 2207 2208 2209 2210 2211 2212 2213 2214 2215 2216 2217 2218 2219 2220 2221 2222 2223 2224 2225 2226 2227 2228 2229 2230 2231 2232 2233 2234 2235 2236 2237 2238 2239 2240 2241 2242 2243 2244 2245 2246 2247 2248 2249 2250 2251 2252 2253 2254 2255 2256 2257 2258 2259 2260 2261 2262  140 IF (TN .LE. IF (TN .GT. IF (TN .GT. 1AMAX IF (TN .GT. IF (TN .GT. IF (TN .GT. GO TO 100 C C C  CIT/SIMULATED  0.2) SA > (1.013 • 11.605»TN) • AMAX 0.2 .AND. TN .LE. 0.62) SA • 3.334 • AMAX 0.62 .AND. TN .LE. 0.82) SA • (5.750 - 3.896'TN) • 0.82 .AND. TN .LE. 1.7) SA « (2.772 - 0.265'TN) • AMAX 1.7 .AND. TN . LE. 2.4) SA • (3.263 - 0.554'TN) • AMAX 2.4) GO TO 160  EARTHQUAKE C-2  150 IF (TN .LT. 0.17) SA • (0.6216 • 22.432'TN) • AMAX IF (TN .GE. 0.17 .AND. TN . LT. 0.51) SA » 4.435 • AMAX IF (TN .GE. 0.51 .AND. TN .LT. 0.58) SA • (21.831 - 34.11'TN) • 1AMAX IF (TN .GE. 0.58 .AND. TN . LT. 1.8) SA - (2.723 - 1.164'TN) • AMAX IF (TN .GE. 1.8 .AND. TN .LE. 2.4) SA • (1.457 - 0.461'TN) • AMAX IF (TN .GT. 2.4) GO TO 160 GO TO 100 160 WRITE (99.170) TN 170 FORMAT (/. 5X. 'PERIOD - '. F10.3. ' IS OUT OF THE SPECTRUM') RETURN END C C C C C C C C C C C C C  **• SUBROUTINE SCHECMS. NU, NB. IOIM, IUNIT. SRATIO)  THIS SUBROUTINE CHECKS THAT ALL DIAGONAL STIFFNESS MATRIX ELEMENTS ARE POSITIVE NUMBERS GREATER THAN ZERO. IT ALSO DETERMINES THE RATIO BETWEEN THE LARGEST AND SMALLEST MEMBERS ON THE DIAGONAL THIS WILL GIVE SOME INDICATION AS TO THE CONDITIONING OF THE STIFFNESS MATRIX MATRIX REAL'S S(IDIM) REAL'S SMIN. SMAX, OIAG. RATIO  C C C C C C C C C  THE STIFFNESS MATRIX IS STORED AS A COLUMN VECTOR. ONLY THE THE LOWER TRIANGLE ELEMENTS BEING STORED (BY COLUMNS) S ( 1 ) IS ON THE DIAGONAL AS IS S(1*NB).S(1*2'NB).ETC. NB IS THE HALF BANDWIDTH OF THE STIFFNESS MATRIX INITIALIZE THE LARGEST  ANO  SMALLEST VALUES OF DIAGONAL (SMAX.SMIN)  SMIN • 1.0045 SMAX • -1.0000 C  C  DO 50 IDOF • 1, NU IELEM - ((IDOF - 1)'NB) • 1 DIAG * S(IELEM) COMPUTE IF DIAGONAL ELEMENT IS ZERO OR NEGATIVE IF (DIAG .NE. O.ODOO) GO TO 20 WRITE (7.10) IDOF 10 FORMAT (///' PROGRAM HALTED-A ZERO IS ON THE DIAGONAL OF STIFFNE  2263 2264 2265 2266 2267 2268 2269 2270 2271 2272 2273 2274 2275 2276 2277 2278 2279 2280 2281 2282 2283 2284 2285 2286 2287 2288 2289 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 2307 2308 2309 2310 231 1 2312 2313 2314 2315 2316 2317 2318 2319 2320  1 SSMATRIX'. //'EXAMINE DEGREE OF FREEDOM '. 14) STOP  C 20 30  1 C C C  40  CONTINUE IF (DIAG .GT. 0.0) GO TO 40 WRITE (7.30) IDOF FORMAT (///' PROGRAM HALTED-NEGATIVE ELEMENT ON DIAGONAL OF ', 'STIFFNESS MATRIX', //' EXAMINE DEGREE OF FREEDOM'. 14) STOP CONTINUE  DETERMINE IF THE DIAGONAL ELEMENT UNDER EXAMINATION IS THE LARGEST SMALLEST OF THE DIAGONAL ELEMENTS. IF (DIAG .GT. SMAX) SMAX • DIAG IF (OIAG .LT. SMIN) SMIN • DIAG  OR  C 50 CONTINUE C WRITE (IUNIT.60) 60 FORMAT (/' ALL ELEMENTS OF MAIN DIAGONAL OF STIFFNESS MATRIX'. 1 ' ARE POSITIVE DEFINITE') C C C  COMPUTE AND  PRINT  RATIO OF LARGEST  TO SMALLEST  RATIO - SMAX / SMIN SRATIO - SNGL(RATIO) WRITE (IUNIT.70) SRATIO 70 FORMAT (' *. 'RATIO OF LARGEST TO SMALLEST 1 'MATRIX ELEMENT I S ' . E10.3) RETURN END  DIAGONAL ELEMENTS  DIAGONAL STIFFNESS',  C C SUBROUTINE SDFBAN(A, C C C C C C  c c c c c c c c c c c c  B. N. M, LT. RATIO. DET, NCN,  NSCALE)  THIS ROUTINE SOLVES SYSTEM OF EONS. AX'B WHERE A IS *TVE DEFINITE SYMMETRIC BAND MATRIX. BY CHOLESKY'S METHOD. LOWER HALF BAND ONLY (INCLUDING THE DIAGONAL) OF A IS STORED COLUMN BY COLUMN IN A 1 DIMENSIONAL ARRAY. SOLUTIONS X ARE RETURNEO IN ARRAY B. OPTIONAL SCALING OF MATRIX A IS AVAILABLE N - ORDER OF MATRIX A. M - LENGTH OF LOWER HALF BAND. DETERMINANT OF A - DET'( 10"NCN) . 1 . E-15< | DET | < 1 . E 15 LT-1 IF ONLY 1 8 VECTOR OR IF FIRST OF SEVERAL. LT NOT - 1 FOR SUBSEQUENT B VECTORS. RATIO • SMALLEST RATIO OF 2 ELEMENTS ON MAIN DIAGONAL OF TRANSFORMED A >1.E-7. NSCALE'O IF SCALING NOT REQUIRED. IMPLICIT REAL'8(A - H.O DIMENSION A ( 1 ) . B ( 1 ) REAL'S MULT(6000) IF (M .EO. 1) GO TO 80 MM » M - 1 NM - N • M  - Z)  o u  3321 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 2360 2361 2362 2363 2364 2365 2366 2367 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378  cC C C  NM1  • NM - MM  DUMMY STATEMENT INSERTED FOR COMPATIBILITY WITHI ASSEMBLER l F ( L T . L E . O ) RETURN  VERSION.  IF (LT .NE. 1) GO TO 340 IF (NSCALE .EO. 0) GO TO 60 00 10 I * 1, N C C C C  MATRIX SCALED BY DIVIDING ROW I AND COLUMN I BY S O R T ( A ( I . I ) ) . SUCH THAT DIAGONAL ELEMENTS A ( I . I ) ARE 1.  10  20 30  40 50 60 C C C C C C  II • (I - 1) • M • 1 IF ( A ( I I ) .LE. 0.0) GO TO 120 MULT(I) . 1.0 / DSORT(A(II)) KK - 1 00 50 I • 1. N II • (I - 1) • M • 1 JEND • II • MM IMN » (I - 1) * M - N IF (IMN .GT. 0) JEND • JEND - IMN DO 20 J • 11. JEND A ( J ) • A ( J ) • MULT(I) CONTINUE DO 30 J - KK. I I . MM A ( J ) • A ( J ) • MULT(I) IF (KK .GE. M) GO TO 40 KK • KK * 1 GO TO 50 KK • KK • M CONTINUE MP • M * 1  TRANSFORMATION OF A. A IS TRANSFORMED INTO A LOWER TRIANGULAR MATRIX L SUCH THAT A •L.LT (LT'TRANSPOSE OF L . ) . IF Y'LT.X THEN L.Y -B. ERROR RETURN TAKEN IF RATIO*1.E-7 KK - 2 NCN - 0 DET - 0. FAC - RATIO IF (A( 1 ) GT. 0. ) GO TO 70 NROW • 1 RATIO • A(1) GO TO 310 70 DET • A ( 1 ) A(1) • 1. / DS0RT(A(1)) BIGL - A O ) SML • A(1 ) A(2) • A(2) • A(1) TEMP • A(MP) - A(2) * A(2) IF (TEMP .LT. 0.0) RATIO - TEMP IF (TEMP .EO. 0.0) RATIO • 0.0 IF (TEMP .GT. 0.0) GO TO 140 NROW • 2 GO TO 310 80 DET • 1.00  2379 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 2390 2391 2392 2393 2394 2395 2396 2397 2398 2399 2400 2401 2402 2403 2404 2405 2406 2407 2408 2409 24 10 241 1 2412 2413 2414 2415 2416 2417 2418 .'419 2120 2 121 2-22 2<23 2424 2425 2426 2427 2428 2429 2430 2431 2432 2433 2434 2435 2436  90 100 110 120 130 140  150 160 170 180 190  200 210 220  NCN • O DO 110 I • 1. N DET - DET • A ( I ) IF ( A ( I ) .EO. 0.0) GO TO 120 IF (DET .GT. 1.E-15) GO TO 90 DET • DET • 1.E*15 NCN • NCN - 15 GO TO 100 IF (OET .LT. 1.E+15) GO TO 100 DET • DET • 1.E- 15 NCN - NCN • 15 CONTINUE B(I) - B(I) / A(I) RETURN RATIO > A ( I ) NROW • I GO TO 310 A(MP) • 1.0 / DSORT(TEMP) DET - DET • TEMP IF (A(MP) .GT. BIGL) BIGL - A(MP) IF (A(MP) .LT. SML) SML • A(MP) IF (N .EO. 2) GO TO 290 MP • MP + M DO 280 J - MP. NM 1 , M JP - J - MM MZC - O IF (KK .GE. M) GO TO 150 KK • KK • 1 II • 1 JC » 1 GO TO 160 KK • KK • M II « KK - MM JC - KK - MM DO 180 I - KK, J P . MM IF ( A ( I ) .EO. 0.) GO TO 170 GO TO 190 JC « JC + M MZC - MZC • 1 ASUM1 • O.DO GO TO 240 MMZC » MM • MZC II - I I • M2C KM * KK + MMZC A(KM) • A(KM) • A ( J C ) IF (KM .GE. J P ) GO TO 220 K J • KM • MM DO 210 I • K J , J P . MM ASUM2 - O.DO IM • I - MM II » I I + 1 KI « II.+ MMZC DO 200 K - KM, IM, MM ASUM2 • ASUM2 + A ( K I ) • A(K) KI » K l * MM A ( I ) • ( A ( I ) - ASUM2) • A ( K I ) CONTINUE ASUM1 'O.DO  2437 2438 2439 2440 2441 2442 2443 2444 244S 2446 2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494  00 230 K • KM, UP. MM ASUM1 • ASUM1 * A(K) • A ( K ) S • A ( J ) - ASUM1 IF (S .LT. 0.) RATIO • S IF (S .EO. 0.) RATIO • 0. IF (S .GT. 0.) GO TO 250 NROW - ( J • MM)' / M GO TO 310 250 A ( J ) • 1. / OSQRT(S) OET - DET • S IF (DET .GT. 1.E-15) GO TO 260 DET • OET • 1.E+15 NCN • NCN - 15 GO TO 270 260 IF (DET .LT. 1.E*15) GO TO 270 DET - DET • 1.E-15 NCN • NCN • 15 270 CONTINUE IF ( A ( J ) .GT. BIGL) BIGL • A ( d ) IF ( A ( J ) .LT. SML) SML - A ( J ) 280 CONTINUE 290 IF (SML .LE. FAC'BIGL) GO TO 300. GO TO 330 300 RATIO • 0. RETURN 310 WRITE (6.320) NROW 320 FORMAT ( ' 0 " « S Y S T E M IS NOT POSITIVE DEFINITE', 1 ' ERROR CONDITION OCCURREDl IN ROW'. 14) RETURN 330 RATIO - SML / BIGL 340 CALL DSBANO(A. MULT. B. N, M. NSCALE) RETURN END SUBROUTINE DSBAND(A. MULT. B. N, M. NSCALE) IMPLICIT REAL*B(A - H.O - Z) DIMENSION A ( 1 ) , 8 ( 1 ) REAL'S MULT(1) MM « M - 1 NM » N • M NM1 • NM - MM 230 240  C C C C C C  THE FOLLOWING STATEMENTS SOLVE FOR L.YB BY A FORWARDS HENCE FOR X FROM LT.X-Y BY A BACKWARDS SUBSTITUTION. IF SCALING OPTION USED. B IS SCALEO AND NORMALISED BEFORE SUBSTITUTION BEGINS. 10 SUM • O.DO IF (NSCALE .EQ. 0 ) GO TO 40 DO 20 I ' 1. N B ( I ) • B ( I ) • MULT(I) SUM - SUM « B ( l ) • B ( I ) 20 CONTINUE ELENB - DSORT(SUM) DO 30 I • 1. N 30 B ( I ) - B ( I ) / ELENB 40 B ( 1 ) • B(1) • A ( 1 ) KK • 1 Kl • 1  2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 251 1 2512 2513 2514 2515 ' 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552  1  d • 1 1 80 L • 2. N DO BSUM1 - O.DO LM > L - 1 J - J + M IF (KK .GE. M) GO TO 50 KK ' KK + 1 GO TO 60 50 KK • KK + M Kl • K l * 1 OK • KK 60 DO 70 K - K l . LM BSUM1 • BSUM1 + A ( J K ) • B ( K ) UK > JK CONTINUE 70 A(J) 80 1B ( L ) - ( B ( L ) - BSUM1) 90 1B(N) • B(N) « A(NM1) 1 NMM ' NM1 1 NN • N -1 1 ND • N 1 DO 110 L " 1, NN BSUM2 - O.DO NL • N - L 1 NL1 - N - L NMM - NMM - M NJ1 - NMM IF (L .GE. M) ND • ND - 1 DO 100 K - NL1. ND NJ1 » NJ1 + 1 BSUM2 « BSUM2 + A(NJ1) B(K) CONTINUE ioo B(NL) • (B(NL) - BSUM2) • A(NMM) IF (NSCALE .EO. O) GO TO 130 1 10 DO 120 I " 1, N MULT(I) 120 1  4  130 C C  C C  I i1  END 1  SUBROUTINE MEMFO(NRM, XM. YM, DM, AV. NP. F, EXTL. EXTG. AREA. E. 1 G. CRMOM. KL. KG.AXIAL. SHEAR 1. SHEAR2. BML. BMG. NML. MML. FEM) 2 DIMENSION 1 2 DIMENSION 1 1  I  XM(NRM), YM(NRM), DM(NRM), AV(NRM), NP(6.NRM) F ( 5 0 0 ) . D ( 6 ) . EXTL(NRM). EXTG(NRM). KL(NRM), KG(NRM). AREA(NRM). CRMOM(NRM). E(NRM). MML(IOO). FEM(100.4) AXIAL(NRM). SHEAR 1(NRM) . BML(NRM), BMG(NRM), G(NRM). SHEAR2 (NRM ) , SHEAR(250)  C 1 DO  110 1 • 1. NRM XL • XM(I) YL • YM(I) OL • DM(I) AV1 - A V ( I ) DO 30 MEMDOF • 1. 6 N1 > NP(MEMDOF.I) IF ( N I ) 20. 20. 10 O  Ul  2553 2554 2555 2556 2S57 2558 2559 2560 2561 2S62 2563 2564 2565 2S66 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2S92 2593 2594 2595 2S96 2597 2598 2599 2600 2601 2602 2603 . 2604 2605 2606 2607 2608 2609 2610  10  C C  C  C C  c  c  c  D(MEMOOF) • F(N1) GO TO 30 O(HEMOOF) • 0. CONTINUE HOOIFY END DISP FOR HORZ MEMBERSWITH ENO EXT.(VALIO FOR HORZ. MEMBERS ONLY) N3 • NP(3.I) IF (N3 .EO. 0) 00 TO 40 D(2) - 0(2) • (F(N3)) • EXTL(I) 40 CONTINUE N6 • NP ( 6, I ) IF (N6 .EO. 0) GO TO 50 0(5) - D(S) - (F(N6)) • EXTG(I) 50 CONTINUE AXIAL(I) • (AREA(I)"E(I)/DL«-2) * (D(4)*XL • D(5)*YL - D(1)«XL 1 D(2)*YL) EI5I > CRMOM(I) • E(I) INCLUOE SHEAR OEFL. GFACT'O MEANS NO SHEAR OEFL. GFACT • 0. IF (AVI .EO. 0.0 .OR. G(I) .EO. 0.0) GO TO 60 GFACT » 12.0 * EISI / (AV1*G(I)*DL*0L) 60 CONTINUE ASSIGN DISP TO RESPECTIVE D.O.F. CHECK FOR PIN-PIN MEMBERS IF (KL(I) .EO. 0 .AND. KG(I) .EO. 0) GO TO 90 DELT • ((0(5) - D(2))*XL + (DO) - 0(4))*YL) / DL BML(I) • (2.0*EISI/(DL*(1.0 + GFACT))) • ((3.O-DELT/DL) - (D(6)* (1.0 - GFACT/2.0)) - (2.0*D(3)*(1.0 + GFACT/4.0))) BMG(I) • -(2.0'EISI/(DL"O .0 + GFACT))) • ((3.0'DELT/DL) - (D(3) •O.O - GFACT/2.0)) - (2.0*D(6)»(1.0 + GFACT/4.0))) SHEAR(I) - (6.0*EISI/(DL*0L)) • ((D(3) • D(6) - (2.O'OELT/OL))/( 1 1.0+ GFACT ) ) IF (KL(I) - KG(I)) 70. 100. 80 PIN-FIX MEMBER FORCES 70 BMG(I) • BMG(I) • 8MLU) • O.O - GFACT/2.0) / (2.0*0.0 • GFACT/4.0)) SHEAR(I) • SHEAR(I) • 1.5 * BML(I) / DL BML(I) - 0. GO TO 100 FIX-PIN MEMBERS 80 BML(I) * BML(I) + BMG(I) * (1 .0 - GFACT/2.0) / (2.0*0.0 + GFACT/4.0)) " SHEAR(I) - SHEAR(I) - 1.5 * BMG(I) / DL BMG(I) • 0. GO TO 100 PIN-PIN MEMBERS 90 BML(I) • 0. BMG(I) • 0. SHEAR(I) - 0. 100 CONTINUE SHE ARK I) • SHEAR(I) SHEAR2(I) • SHEAR(I) 110 CONTINUE IF (NML .EO. 0) GO TO 150 DO 140 1 * 1 . NRM DO 120 J " 1. NML IF (I .EO. MML(J)) GO TO 130 120 CONTINUE 20 30  2611 2612 2613 2614 261S 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668  GO TO 140 CONTINUE BML(I) - BML(I) * FEM(J,2) BMG(I) • BMG(I) + FEM(J.4) SHEAR 1(1) - SHEAR(I) • FEM(J.I) SHEAR2U) • SHEAR(I) - FEM(J.3) 140 CONTINUE 150 CONTINUE RETURN END  130  SUBROUTINE GEN1(X. Y, IdT. LJT. NJT. KDIF) GENERATES NODES ALONG STRAIGHT LINE DIMENSION X(32S). Y(32S) XI « X(IJT) YI • Y(IJT) DX - X(LJT) - XI DY - Y(LJT) - YI OX - OX / FLOAT(NJT D DY • DY / FLOAT(NJT 1) DO 10 I - 1 . NJT IJT - IJT • KDIF XI - XI • DX YI - YI + DY X(IJT) • XI Y(IJT) - YI 10 RETURN END SUBROUTINE GEN2(MMR, W, XM. KL. KG. NP. F, JL. FEM) DIMENSION XM(200). KL(200). KG(20O). NP{6.200). F(500). FEMO00.4) IF R3 R6 R2 RS GO IF R3 R6 R2 R5 GO R3 R6 R2 R5 GO R2 R3  (KL(MMR) + KG(MMR) - 1) 50. 20. 10 -W • XM(MMR) • XM(MMR) / 12. -R3 -0.5 • W « XM(MMR) R2 TO 60 KL(MMR) - KG(MMR)) 30, 70. 40 O. W « XM(MMR) • XM(MMR) / 8. -0.5 • V • XM(MMR) - R6 / XM(MMR) -0.5 • V • XM(MMR) + R6 / XM(MMR) TO 60 W * XM(MMR) " XM(MMR) / 8. O. -0.5 • W • XM(MMR) - R3 / XM(MMR) -0.5 * W • XM(MMR) + R3 / XM(MMR) TO 60 -0.5 • W • XM(MMR) 0. O  at  2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725 2726  C C  R5 • R2 R6 - 0. 60 CONTINUE d i • NPO.MMR) d2 • NPO.MMR) d3 • NP(2.MMR) d4 • NP(5,MMR) F ( d 3 ) - F(d3) • R2 F ( d 4 ) • F ( d 4 ) • R5 F ( d l ) • F ( d l ) • US F ( J 2 ) • F ( d 2 ) * R6 FEM(dL.I) • -R2 FEM(dL.2) - R3 FEM(dL.3) » -RS FEM(dL.4) > -R6 70 CONTINUE RETURN ENO ••••  „  SUBROUTINE CDUCT'CD, BM1. BM2, NP, NRM. 1 E. CRMOM, BMCAP, HARO) C C C C  C  C  2727 2728 2729 2730 2731 2732 2733 2734  MEM.  DM,  FCD. NU. DAMAGE,  ....................... CONVERTS DAMAGE RATIOS TO CURVATURE DUCTILITIES DIMENSION NP(6.NRM), DM(NRM), FCD(NU). BMCAP(NRM), E(NRM), 1 CRMOM(NRM) CHECK WHETHER MEMBER IS IN DOUBLE OR SINGLE CURVATURE IF (BM1 .LT. 0.) GO TO 10 IF (BM2 .LT. O.) GO TO 50 GO TO 20 10 IF (BM2 .LT. O.) GO TO 20 GO TO 50 20 CONTINUE MEMBER IS IN SINGLE CURVATURE B l - BMt - 8M2 BM • ABS(B1) • 0.95 IF (NPO.MEM) . EO. 0) GO TO 30 THETA - (ABS(BMI) • BM) • 0.95 • OM(MEM) / (2.*E(MEM)*CRMOM(MEM)) N1 - NPO.MEM) GO TO 40 30 THETA - (ABS(BM2) • BM) • 0.95 • DM(MEM) / (2. *E(MEM)*CRMOM(MEM) ) NI • NPO.MEM) 40 CONTINUE ROTN • ABS(FCD(N1)) - THETA THETAP • ROTN - ROTN * ( 1 . - DAMAGE'HARD) / (OAMAGE*(1. - HARD)) CD • 1. • THETAP • E(MEM) • CRMOM(MEM) / (0.05*DM(MEM)*BMCAP(MEM)) GO TO 60 50 CONTINUE MEMBER IS IN DOUBLE CURVATURE IF (NPO.MEM) . EO. 0) BMX • BM2 IF (NPO.MEM) . EO. O) BMX • BM1 XI • ABS(BMX) / (ABS(BMI) * ABS(BM2)) X2 • 0.95 - XI BM - ABS(BMX) • X2 / XI THETA1 » A8SI8MX) • XI • DM(MEM) / (2.*E(MEM)•CRMOM(MEM)) THETA2 • BM • X2 • DM(MEM) / (2.*E(MEM)*CRMOM(MEM)) IF (NPO.MEM) . EO. O) N1 • NPO.MEM)  IF (NPO.MEM) .EO. O) NI - NPO.MEM) ROTN . FCO(NI) ROTN • ABS(ROTN) • THETA1 - THETA2 THETAP - ROTN - ROTN • ( 1 . - DAMAGE*HARD) / (DAMAGE'd - HARD)) CONTINUE* ™ ' ' ' I <005*DM(MEM)*BMCAP(MEM)) RETURN END E  T  A  P  E  <  M  E  M  >  C  R  M  0  M  <  M  E  M  APPENDIX B FREEMAN'S  METHOD  PROGRAM INPUT  Use  any  consistent  conversion 1.  of u n i t s  of  units,  there  internal  i n t h e program.  (20A4)  Problem t i t l e  one c a r d o f maximum  80 c h a r a c t e r  length  SEISMIC LOAD INFORMATION : ISPEC,  AMAX, KOU, GG  (I5,F10.5,I5,F8.2) ISPEC  KOU  'A' from S h i b a t a  2 = National  Building  : Maximum :  t y p e :-  1 = Spectrum  Code  and Sozen  Spectrum  g r o u n d a c c e l e r a t i o n (g)  1 = First  mode  forces  i n +ve x - d i r e c t i o n  2 = First  mode  forces  i n t h e -ve x - d i r e c t i o n  (See GG  one c a r d  : I n p u t spectum  AMAX  3.  i s no  TITLE : TITLE  2.  set  Note  : Acceleration  1)  due t o g r a v i t y (g)  STRUCTURAL INFORMATION : NRM,  NMB,  NRJ, NCONJT, NCDJT, NCDOD, NCDIDS, NCDMS  (215,F10.2,515)  one c a r d  NRM  : Number o f members  NMB  : Number o f beams i n t h e s t r u c t u r e  NRJ  : Number o f j o i n t s  NCONJT  :  Number  of  i n the s t r u c t u r e  i n the s t r u c t u r e 'control  108  joints'  for  which  the  109 co-ordinates are specified NCDJT  :  Number  of  generation  commands  for  zero displacements  NCDMS  joints  specifying  for specifying  displacements  : Number o f commands at  co-ordinate  joints  with  joints  with  (See Note 3)  : Number o f commands identical  for joints  (See Note 2)  NCDOD : Number o f commands  NCDIDS  (See Note 2)  (See Note 4)  for specifying  lumped  masses  (See Note 5)  CONTROL JOINTS CO-ORDINATES : IJT,  X, Y  (15,2F10.1) IJT X  : Joint  one c a r d / c o n t r o l  joint  number, i n any s e q u e n c e  : x co-ordinate  of the j o i n t  Y : y co-ordinate  of the j o i n t  COMMANDS FOR GENERATION OF JOINT CO-ORDINATES : Omit  i f t h e r e a r e no g e n e r a t i o n  IJT,  L J T , NJT, KDIF  (415)  commands  one card/command  IJT  : Joint  number a t t h e b e g i n n i n g  LJT  : Joint  number a t t h e e n d o f g e n e r a t i o n  NJT  : Number o f j o i n t s  KDIF  :  Joint  t o be g e n e r a t e d  the line  two s u c c e s s i v e  ( c o n s t a n t ) . I f blank  t o be e q u a l  line  line  along  number d i f f e r e n c e between  nodes on t h e l i n e assumed  of generation  or  zero  to1  COMMANDS FOR JOINTS WITH ZERO DISPLACEMENTS : Omit  i f no j o i n t s  r e s t r a i n e d t o have z e r o  displacements  1 10 IJT,  KDOF(1),  KDOF(2), KDOF(3), L J T , KDIF  (13,518) IJT  one card/command  : Joint  number, o r  covered KDOF(1)  : Code  by t h i s  first  joint  in  the  series  command  for X displacement,  displacements  in  x  0 i f restrained  direction,  from  1 i f free to  displace KDOF(2)  : Code  f o r Y displacement  KDOF(3)  : Code  for rotation  LJT  : Last  joint  blank KDIF  : Joint in  for a single  this  series  i f no  0 or leave  joint between  succesive  i f blank  joints  or  zero  to1  WITH IDENTICAL  joints  punch  (constant),  t o be e q u a l  COMMANDS FOR JOINTS Omit  series,  number d i f f e r e n c e  assumed 7.  in this  restrained  DISPLACEMENTS : to  have  identical  displacements MDOF, NJT, I J O I N T ( N J T ) (215,1415) MDOF  one card/command  : Displacement  code :  1 : for x displacement  NJT  :  2  : for y displacement  3  : for rotation  Number  of  joints  covered  by  this  command  (max. 14) IJOINT  : List  of  increasing  nodes order  covered  by  this  command,  in  111 8.  MEMBER INFORMATION : MN,JNL,JNG,KL,KG,E,G,AREA,CRMOM,BMCAP,EXTL,EXTG,AV (515,2F10.1 ,F8.2,F15.3,F15.3,3F8.2) one card/member MN  : Member number  JNL  : Lesser  JNG  : Greater  KL  : Fixity 0  joint  number  joint  number  code a t l e s s e r  joint  : Pinned  1 : Fixed KG : F i x i t y  code a t g r e a t e r  E  : Young's Modulus  G  : Shear (0  AREA CRMOM  joint  Modulus  i f shear  deflections  : Cross-sectional  area  : Moment o f i n e r t i a  a r e t o be  neglected)  o f t h e member  o f t h e member  BMCAP : Y i e l d moment o f t h e member EXTL  : Rigid  extension  on t h e l e s s e r  end ' j o i n t  of  the  on t h e g r e a t e r end j o i n t  of  the  AV  are  member EXTG  : Rigid  extension  member AV  : Shear area (0  Note  left for 9.  i f shear  o f t h e member deflections  a r e t o be  neglected)  : I f E , G, AREA, CRMOM, BMCAP, EXTL, EXTG,  blank  or  g i v e n z e r o f o r a member, same v a l u e s a s  t h e p r e v i o u s member w i l l  DAMPING VALUES : DAMP1, DAMP2  be assumed.  1 12 (2F5.3) DAMP1  one c a r d  : Damping  i n the e l a s t i c  s t r u c t u r e (% o f  value  maximum  critical  damping) DAMP2 : Damping critical 10.  at  the  (%  of  damping)  COMMANDS FOR LUMPED MASSES AT THE JOINTS : I J T , WTX,  WTY,  WTR,  J J T , KDIF  (I 5,3F10.2,215) IJT  : Joint this  one card/command  number o r f i r s t  joint  in a series  : Weight a s s o c i a t e d w i t h  x-displacement  WTY  : Weight a s s o c i a t e d w i t h  y-displacement  WTR  : Rotational :  Number  leave KDIF  by  weight of  blank  : Joint in  covered  command  WTX  JJT  last  joint  for a single  i n the s e r i e s ,  punch 0 o r  joint  number d i f f e r e n c e between s u c c e s s i v e  this  series  assumed 11.  response  (constant),  t o be e q u a l  if  blank  or  joints zero  to 1  STATIC LOAD INFORMATION : NJLS, NLGCJ, NML,  NLGCM  (415) NJLS NLGCJ  one c a r d : Number o f j o i n t s :  Number o f g e n e r a t i o n  applied NML  directly  :  by s t a t i c commands  loads for static  loads  a t t h e nodes (See Note 6)  : Number o f members l o a d e d static  NLGCM  loaded  by u n i f o r m l y  distributed  load  Number o f g e n e r a t i o n  commands  for static  loads  11 3  on Cards  t h e members  (See Note 6)  12A a n d 12B a r e o m i t t e d  A. COMMANDS FOR STATIC LOADS  i f NJLS APPLIED  i s zero. DIRECTLY  ON  THE  JOINTS : Omit  i f NLGCJ  i s zero  FX, FY, FM, NNOD, NODN(NNOD) (3F10.1,1015)  one card/command  FX  : Load  in x-direction  FY  : Load  i n Y-direction  FM  : Moment  NNOD : Number o f j o i n t s t o be c o v e r e d NODN  :  List  of  increasing  joints  covered  by t h i s  by  this  command command i n  order OR  B. STATIC LOADS APPLIED DIRECTLY AT JOINTS : input  this  i f NLGCJ = 0  N, FX, FY, FM (15,3F10.1) N  : Node  one c a r d / l o a d e d  joint  number  FX  : Load  i n the x - d i r e c t i o n  FY  : Load  i n the y - d i r e c t i o n  FM  : Moment  NOTE : ONLY CARDS  12A OR  12B ARE  TO  BE  INPUT  IN  DATA, NOT BOTH. Cards  13A a n d 13B t o be o m i t t e d  i f NML e q u a l s  A. COMMANDS FOR STATIC MEMBER LOADS : Omit  i f NLGCM  i s zero.  zero.  THE  11 4 W, NMEM, MR(NMEM) (F6.1,1415)  one card/command  W : Uniformly  distributed  downward l o a d NMEM  load  positive  : Number o f members c o v e r e d  MR :  List  of  increasing  on t h e member,  members  by t h i s  covered  by  command  this  command  in  order  OR B. STATIC MEMBER LOADS : Omit  i f NLGCM  i s not zero.  MMR, W (I5,F10.4) MMR  : Member  one c a r d / l o a d e d number  W : Uniformly NOTE  :  ONLY  member  distributed CARDS  static  load  13A OR 13B TO BE INPUT IN THE DATA  WHEN NML IS NOT ZERO, NOT BOTH.  1 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  REAL-B C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C  SOOOOO)  FREEMAN'S METHOD FOR EARTHQUAKE RESPONSE PREDICTION • • THIS METHOD CONSIDERS ONLY FUNDAMENTAL MODE OF VIBRATION PROGRAM DIMENSIONED FOR A MAXIMUM OF :250 MEM8ERS 200 JOINTS 100 ASSIGNED  MASSES  VARIABLE DEFINITIONS:KL.KG  '  - JOINT TYPE  : FIXED JOINT • 1 PINNED JOINT » 0 AREA - CROSS-SECTIONAL AREA CRMOM - MOMENT OF INERTIA OF GROSS SECTION BMCAP - BENDING MOMENT CAPACITY OF SECTION ND D.O.F. NO. IDENTIFIED BY JOINT NO. ND(K.I) - K • 1 (X-DOF). 2 (Y-DOF). 3 (R-OOF) I - JOINT NO. NP 0.0.F. NO. IDENTIFIED BY MEMBER NO. NP(K.I) - K • OOF 1 TO 6 FOR STANDARD MEMBER I « MEMBER NO. XM • LENGTH OF FLEXIBLE PORTION OF BEAM IN X-DIRECTION YM LENGTH OF FLEXIBLE PORTION OF BEAM IN Y-DIRECTION DM . TRUE LENGTH OF FLEXIBLE PORTION OF BEAM F • LOAD VECTOR EXTL,EXTG - LENGTH OF RIGID END TITLE - TITLE (80 CHARACTERS) AV • SHEAR AREA MDOF - 0.0.F. NO. FOR MASSES IDENTIFIED BY MASS NO. AMASS • LUMPED MASS ( I N UNITS OF WEIGHT) IN0ENT1FY BY D.O.F. NO. EVAL • EIGENVALUE EVEC • MODE SHAPE EVEC(K.I) - K - MASS NO. I • MODE NO. SOEL • ELASTIC MODEL SPECTRAL DISPLACEMENT SAEL - ELASTIC MODEL SPECTRAL ACCELERATION RMAX • ROOF DISPLACEMENT AT YEILDING OF STRUCTURE DAMP 1 • EFFECTIVE DAMPING FOR ELASTIC MOOEL OF STR. DAMP2 » EFF. DAMPING FOR MAX. INELASTIC EXCURSION  DIMENSION KL(250). KG(250). AREA(2S0). CRM0M(2S0). BMCAP(250). 1 NDO.200). NP(6.250). XM(2S0). YM(250). DM(250). F(SOO). 2 EXTL(250), EXTG(2S0). T I T L E ( 2 0 ) . AV(2S0). MDOF(IOO). 3 AMASS(500). EVAL(IO). EVECI500,10). ALPHA(IO). DAMP(20), 4 T ( 4 0 ) , E ( 2 5 0 ) . G(250) CALL FTNCMO('EQUATE 99-SPRINT:') CALL CONTRL(NRJ, NRM, NMB. ISPEC. AMAX. KOU. NCONJT. NCDJT, NCDOD,  59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 1 14 115 116  1  C C  C  C  C  NCOIDS. NCDMS. GG) IDIM • 30000 CALL SETUP(NRM. E. G. XM. YM, DM. NO. NP, AREA. CRMOM. NRJ. AV. 1 KL, KG. NU. NB. BMCAP, EXTL. EXTG, DAMP 1. DAMP2, NCONJT. 2 NCDJT. NCDOD, NCDIDS) CALL MASS(NU. ND. AMASS. NRJ. MDOF. NCDMS, GG) CALL BUILD(NU, NB, XM, YM, OM, NP. AREA. CRMOM, AV. E. G, KL, KG, 1 NRM. S, IOIM. EXTL, EXTG) CALL SCHECK(S, NU. NB, IDIM. SRATIO) CALL EIGEN(NU. NB, S. IDIM. AMASS. EVAL. EVEC, 1. MDOF. PERIOD. 1 WN) CALL M0D3(NRJ. NRM. NU. NB. S. IDIM. NO. NP. XM. YM. OM. AREA. AV, 1 CRMOM, KL. KG. BMCAP, E. G, AMASS, EVEC, EVAL. EXTL. EXTG. 2 NMB. ALPHA, RMAX. KOU. GG) WRITE (6.10) 10 FORMAT (//. 'RESULTS FOR INELASTIC MODEL OF STRUCTURE') WHEN HALF OF THE BEAMS YIELDEO STR. ASSUMED YIELDED ASSIGN SX S T I F F . VALUE TO BEAMS;BEAMS NUMBERED FIRST DO 20 I > 1, NMB CRMOM(I) " 0.05 • CRMOM(I) 20 CONTINUE MODE SHAPES NORMALIZED S . T . A ( I . J ) AT ROOF IS UNITY SO » RMAX 7 ALPHA(1) SDEL - SD SAEL • WN • WN * SD SAEL - SAEL / GG TP - PERIOD CALL BUILD(NU. NB, XM, YM, DM, NP, AREA. CRMOM. AV. E. G, KL. KG. 1 NRM. S. IOIM. EXTL. EXTG) CALL SCHECK(S. NU. NB. IDIM. SRATIO) CALL EIGEN(NU, NB. S. IDIM. AMASS. EVAL. EVEC. 1. MDOF, PERIOD. 1 WN) CALCULATE MODAL PARTICAPATION FACTOR MCOUNT • 0 00 30 I • 1 , NU IF (AMASS(I) .EO. 0.) GO TO 30 MCOUNT - MCOUNT + 1 30 CONTINUE AMT - 0. AMB • 0. 00 40 J • I. NU AMT • AMT + AMASS(J) * E V E C ( J . I ) AMB « AMB • AMASS(J) • ( ( E V E C ( J , 1 ) ) * * 2 ) 40 CONTINUE ALPHA(1) • AMT / AMB WRITE (6.50) ALPHA(1) 50 FORMAT (//. 'FIRST MOOE PARTICIPATION FACTOR-'. F5.2) SOI - 5.0 • RMAX / ALPHA(I) SA 1 - WN * WN * SD 1 SA1 • SA1 / GG NOW MAKE COMBINEO MODEL S02 - SD * S01 SACOMB - SAEL + SA1 OMSQ • GG * SACOMB / S02 OMEGA • SORT(OMSO) TPR » 6.283153 / OMEGA WRITE (6.60)  117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 14 1 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174  WRITE (6.70) TP. SAEL 70 FORMAT (/. ' ELASTIC MODEL'. //. 'TIME PERIOD-', F6.3. ' S E C . IOX. 1 'SPEC ACCL(G)-', F7.3) WRITE (6.80) TPR. SAC0M8 80 FORMAT (/, 'COMBINED MODEL'. //, 'TIME PERIOD''. F6.3. ' S E C . IOX. 1 'SPEC ACCL(G)"'. F7.3) WRITE (6.90) 90 FORMAT (//, 'DEMAND SPECTRUM', /, ' ') C DEMAND TRANSITION CURVE WRITE (6,100) WRITE (6,110) TP, DAMP 1 T(1) • TP DAMP(1) • DAMP 1 100 FORMAT (/. SX. 'TIME PD.', 10X, 'DAMPINGU OF CRIT.)') 110 FORMAT (7X, FS.3. 15X, F5.1) 0 • 5.0 • RMAX / (DAMP2 - DAMP 1) ROOFOI • RMAX DI - 1.0 DO 120 I • 2, 15 DAMP(l) » DAMP 1 + 01 ROOFDI • ROOFDI * 0 SPDISP » ROOFDI / ALPHA(1) COMBSD - SD + SPDISP SPACL - WN • WN • SPDISP SPACL - SPACL / GG COMBSA - SAEL + SPACL OMSO - GG • COMBSA / COMBSD OMEGA - SORT(OMSO) T ( I ) - 6.283153 / OMEGA WRITE (6,110) T ( I ) . DAMP(I) IF (DAMP(I) .EO. DAMP2) GO TO 130 DI - D1 • 1.0 120 CONTINUE 130 CONTINUE NM - DAMP2 - DAMP 1 + 1. C HAVE NM VALUES OF T & DAMP; DAMP NOW CONVERTED TO FRACTIONS DO 140 IU • 1. NM 140 OAMP(IU) - DAMP(IU) / 100. TN • TP DO 180 I • 1. 40 CALL SPECTR(OAMP, T. SA, ISPEC, AMAX, NM, TN) IF (TN .EO. TP) GO TO 160 150 CONTINUE SACAP • (SACOMB - SAEL) • (TN - TP) / (TPR - TP) + SAEL SACH - SA - SACAP IF (SACH .LE. 0.05 .AND. SACH .GE. - 0.05) GO TO 200 CELT - (SA - SACAP) / 4. TN • TN • OELT GO TO 180 160 CONTINUE IF (SA .GE. SAEL) GO TO 150 WRITE (6.170) 170 FORMAT (/. 5X. 'IN THIS PARTICULAR EO. STRUCTURE REMAINS ELASTIC I, THUS NO OAMAGE') STOP 180 CONTINUE WRITE (6.190) 190 FORMAT ( 'CAPACITY & DEMAND CANNOT BE RECONCILED')  175 176 177 178 179 1B0 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 20O 201 202 203 204 205 206 207 208 209 210 21 1 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232  STOP 200 CONTINUE WRITE (6,210) • 210 FORMAT (///. 8X. ' P R E D I C T E D  220 230 240  250 260 270 280 290 300 310 C C C C C C  R E S P O N S E ' . / .  5X,  SD • GG * SA * TN • TN / ( 4 . • 3 . 14593*3. 141593) DUCTIL - SO / SOEL ICU - (SO - SDEL) • 100. / SD1 1RCAP - 100 - ICU DO 230 I - 2, NM IF (TN .GT. T ( 1 ) ) GO TO 230 TX - ( T ( I - 1) • T ( I ) ) / 2. IF (TN .GT. TX) GO TO 220 DPG • DAMP(I - 1) GO TO 240 DPG » DAMP(I) GO TO 240 CONTINUE CONTINUE DPG - 100. • DPG WRITE (6.250) TN WRITE (6.260) SA WRITE (6.270) DPG WRITE (6.280) SD WRITE (6.290) DUCTIL WRITE (6.30O) ICU WRITE (6.310) 1RCAP FORMAT (/, SX. 'PERIOD(SEC)'. 10X. F5.2) FORMAT (/. SX. 'SPEC. ACCL(G)'. 9X, FS.3) FORMAT (/. 5X. 'DAMPING(X)'. IOX, FS.1) FORMAT (/. 5X. 'SPEC. O I S P ( F T ) ' , 8X. F5.3) FORMAT (/, 5X. 'DUCTILITY DEMAND'. 4X. F5.1) FORMAT (/. 5X. 'INELASTIC CAPACITY'. 2X. 14. /. 5X. 'USEO') FORMAT (/. 5X. 'RESERVE CAPACITY', 4X. 14) STOP END  • **•«•*••***••*•«*««•••«•*•••*"""«*••"•"•*** SUBROUTINE CONTRL(NRJ, NRM. NMB. ISPEC. AMAX. KOU. NCONJT, NCDJT. 1 NCDOD, NCDIDS. NCDMS. GG) DIMENSION T I T L E ( 2 0 ) READ (5.60) ( T I T L E ( I ) , I - 1 , 2 0 ) READ (5.70) ISPEC. AMAX. KOU. GG READ (5.80) NRM, NMB. NRJ, NCONJT, NCDJT. NCDOO, NCDIDS. NCDMS WRITE (6.60) ( T I T L E d ),I«1 .20) WRITE (6.90) NRJ, NRM, NMB IF (ISPEC .EO. 1) WRITE (6.30) IF (ISPEC .EO. 2) WRITE (6.40) IF (KOU .EO. 2) WRITE (6,10) 10 FORMAT ('IN THE REVERSE DIRECTION') WRITE (6.50) AMAX WRITE (6.20) GG 20 FORMAT (/. 'ACCL. DUE TO GRAVITY " '. F8.2. /) 30 FORMAT (/, '-SPECTRUM A USED') 01  233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 2B3 284 285 286 287 288 289 290  40 50 60 70 80 90  C C C c c c 'c c c c  c c c  FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT 1 RETURN END  (/. '-NBC SPECTRUM USED') (/. '-MAX ACCL.-'. F5.3. 'TIMES GRAVITY') (20A4) (15, F10.S, 15. F8.2) (815) (/. 'NO.OF JOINTS •', 14, (OX. 'NO.OF MEMBERS •'. 14. IOX, 'NO OF BEAMS •'. 14)  SUBROUTINE SETUP(NRM, E. G, XM. YM. DM. ND. NP, AREA. CRMOM. NRJ. 1 AV, KL, KG, NU, NB, BMCAP, EXTL. EXTG. DAMP 1, DAMP2, 2 NCONJT. NCDJT. NCDOD. NCDIDS)  SET UP THE FRAME DATA DIMENSION 1 2 DIMENSION  KL(NRM). KG(NRM), AREA(NRM), CRMOM(NRM), BMCAP(NRM), AV(NRM), NDO.NRJ), NP(6.NRM). XM(NRM). YM(NRM). EXTL(NRM). EXTG(NRM), OM(NRM), E(NRM). G(NRM) X(200). Y(200), JNL(250), JNG(250). KD0F(3). IJ0INT(40)  INITIALIZE COORDINATES DO 10 I • 1. NRJ X(I) • 999000. 10 Y(I) - 999000. c REAO CONTROL NODE CORDINATES WRITE (6.20) 20 FORMAT (//. 'CONTROL NODE COORDINATES'. ///. 'NODE', 6X. 1 'X-COORO'. 6X. 'Y-COORD'. /) DO 50 I - 1 , NCONJT READ (5.30) IJT." X(IJT). Y(IJT) 30 FORMAT (IS. 2F10.1) WRITE (6.40) IJT. X(IJT), Y(IJT) 40 FORMAT (IS. 2F13.3) SO CONTINUE c NODE GENERATION COMMANDS WRITE (6.60) 60 FORMAT (///' NODE GENERATION COMMANDS'/) IF (NCDJT .NE. 0) GO TO 80 WRITE (6.70) 70 FORMAT (//, 'NONE') GO TO 130 80 WRITE (6.90) 90 FORMAT (/2X. 'FIRST', 4X. 'LAST', 4X. 'NO. OF'. 4X. 'NODE'. /. 2X 1 'NOOE'. 5X. 'NODE*. 4X. 'NODES', SX, 'OIFF'. /) DO 120 I - 1. NCDJT READ (5,100) IJT. LJT. NJT. KDIF 100 FORMAT (415) IF (KDIF .EO. 0) KDIF • 1 WRITE (6.110) IJT. LJT. NJT. KOIF  291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 34 1 34 2 343 344 345 346 347 348  110  C  C C  C  FORMAT (16, 318) CALL GENKX. Y. IJT, LJT, NJT, KDIF) 120 CONTINUE GENERATE UNSPECIFIED JOINT COORDINATES 130 I - 1 140 1 * 1 + 1 IF (I .GT. NRJ) GO TO 160 IF (X(I) .NE. 999000.) GO TO 140 IJT • I - 1 LJT • IJT 150 LJT - LJT • 1 IF (LJT .GT. NRJ) GO TO 160 IF (X(LJT) .EO. 999O00.) GO TO 150 NJT » LJT - IJT - 1 CALL GENKX. Y. IJT. LJT, NJT, 1) I - LJT GO TO 140 160 CONTINUE ASSIGNING 0.0.F. TO THE NODES DO 170 I » 1. NRJ DO 170 J » 1. 3 170 ND(J.I) « 1 ZERO DISPLACEMENTS WRITE (6.180) 180 FORMAT (/. 'ZERO DISPLACEMENT COMMANDS'. //) IF (NCDOD .NE. 0) GO TO 190 WRITE (6.70) GO TO 270 190 WRITE (6,200) 200 FORMAT (/. 'FIRST', 6X, 'X'. 6X. 'Y', 4X, 'ROTN'. 4X, 'LAST'. 4X, 11 'NODE'. /. 'NODE', 7X, 'OOF'. 4X. 'OOF'. 3X. 'DOF', 4X. 2 'NODE'. 4X. 'OIFF'. /) DO 260 I - 1. NCDOD READ (5.210) IJT, (KDOF(J).J»1.3). LJT. KDIF 210 FORMAT (615) WRITE (6.220) IJT. (KDOF(J).J-1.3). LJT. KDIF 220 FORMAT (13. 518) DO 230 J - 1. 3 230 ND(J.IJT) - KDOF(J) IF (LJT .EO. 0) GO TO 260 IF (KOIF .EO. 0) KDIF • 1 NJT « (LJT - IJT) / KOIF 00 250 II • 1. NJT IJT - IJT + KDIF DO 240 J • 1. 3 240 NO(J.IJT) - KDOF(J) 250 CONTINUE 260 CONTINUE IOENTICAL DISPLACEMENT 270 CONTINUE WRITE (6,280) 280 FORMAT (///. 'EOUAL DISPLACEMENT COMMANOS '. /) IF (NCDIDS .NE. 0) GO TO 290 WRITE (6.70) GO TO 350 290 WRITE (6.30O) 300 FORMAT (//. 'DISP'. 4X. 'NO. OF', /, 'CODE'. 4X. 'NODES'. 6X, 1 'LIST OF NOOES'. /)  349 350 351 352 353 354 355 35S ' 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 3SO 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406  DO 340 1 - 1 . NCDIDS READ (5.310) MKDOF, NJT. (IJOINT(IU).IU-1.NJT) FORMAT (215. 1415) WRITE (6.320) MKDOF. NJT, (IJOINT(IU).IU-1.NJT) 320 FORMAT (13. 18. 6X. 1415) II • IJOINT(I) 00 330 IM '- 2. NJT IK - IJOINT(IM) 330 NO(MKDOF.IK) • -II 340 CONTINUE C TO SET UP NO ARRAY 350 NU • 0 WRITE (6,400) DO 390 1 - 1 . NRJ DO 380 J - 1, 3 IF (ND(J.I) .NE. 1) GO TO 360 NU - NU + 1 ND( J. I ) - NU GO TO 380 360 IF (NO(J.I) .NE. 0) GO TO 370 ND(J.I) • 0 GO TO 380 370 II - -ND(J.I) NO(J.I) • ND(J.II) 380 CONTINUE WRITE (6.410) I. X(I). Y(I). (ND(J,I).J-1.3) 390 CONTINUE 400 FORMAT (/. 3X. 'JN'. 5X, 'X-COORD*. 5X. 'Y-COORO'. 5X. 'NDX', 5X, 1 'NOY', 5X, 'NOR'. /) 410 FORMAT (14. 2F13.2. 16. 5X. 14, 5X. 14) C WRITE (6.580) WRITE (6.590) WRITE (6.600) C C READ IN MEMBER DATA ANO COMPUTE THE HALF BANDWIOTH (NB) C HALF BANDWIDTH-MAX DEGREE OF FREEDOM-MIN DEGREE OF FREEDOM +1 C C NB • 0 310  DO 560 MBR - 1. NRM READ (5.610) MN. JNL(MBR), JNG(M8R), KL(MBR). KG(MBR), E(MBR), 1 G(MBR), AREA(MBR). CRMOM(MBR), BMCAP(MBR), EXTL(MBR), EXTG(MBR) 2 AV(MBR) C C COMPUTE MEMBER LENGTH (DM)-LENGTH BETWEEN JOINTS-RIGID EXTENSIONS JL • JNL(MBR) JG - JNG(MBR) XM(MBR) • X(JG) - X(JL) YM(MBR) • Y(JG) - Y(JL) DM(MBR) - S0RT((XM(MBR))* 2 • (YM(MBR))**2) EXTSUM • EXTL(MBR) + EXTG(MBR) XM(MBR) - XM(MBR) - (1.0 - EXTSUM/DM(MBR)) YM(MBR) - YM(MBR) • (1.0 - EXTSUM/DM(MBR)) C RESET NEGATIVE VALUES OF ZERO TO ZERO IF (YM(MBR) .GT. - O.01 .ANO. YM(MBR) .LT. 0.01) YM(MBR) - 0.0 ,  407 40B 409 410 411 412 413 4 14 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 44 1 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464  IF (XM(MBR) .GT. - 0.01 .AND. XM(MBR) .LT. 0.01) XM(MBR) - 0.0 DM(MBR) • OM(MBR) - EXTSUM  C C CHECK FOR NEGATIVE LENGTHS OF MEMBER c (PROBABLY CAUSED BY INCORRECT USE OF MEMBER EXTENSIONS) c IF (DM(MBR) .GT. 0.0) GO TO 430 WRITE (6.420) MBR 420 FORMAT (' '. ///'PROGRAM HALTED:ZERO OR -VE LENGTH FOR MEMBER', 1 16) STOP c 430 CONTINUE c YLEN - YM(MBR) c c PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS c ON VERTICAL MEMBERS. IF (EXTSUM .NE. 0.0 .AND. YLEN .GT. 0.2) WRITE (6.440) I 440 FORMAT (' ', 'ERROR-HAVE END EXTENSIONS ON NON-HORIZONTAL 1 MEMBER NO.', 13) c PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON c A NON FIX-FIX TYPE MEMBER KLSUM - KL(MBR) • KG(MBR) IF (EXTSUM .NE . 0.0 .AND. KLSUM .NE. 2) WRITE (6,450) MBR 450 FORMAT (' '. 'ERROR-HAVE RIGID EXTENSIONS ON HINGED MEMBER'. I< c c c ASSIGN MEMBER DEGREES OF FREEDOM NP(1.MBR) - ND(1.JL) NP(2..MBR) - N0(2.JL) NP(3.MBR) - ND(3.JL) NP(4.MBR) - ND(1.JG) NP(5.M8R) » ND(2.JG) NP(6,MBR) - ND(3.JG) c DETERMINE THE HIGHEST DEGREE OF FREEDOM FOR EACH MEMBER STORING c THE RESULT IN 'MAX' MAX - 0 c DO 480 K • 1, 6 IF (NP(K.MBR) - MAX) 470. 470, 460 460 MAX - NP(K.MBR) 470 CONTINUE 480 CONTINUE c c DETERMINE THE MINIMUM DEGREE OF FREEDOM FOR EACH MEMBER.NOTE THAT c FOR STRUCTURES WITH GREATER THAN 330 JOINTS INITIAL VALUE OF MIN c WILL HAVE TO BE INCREASED FROM ITS PRESTENT POINT OF 1000. c c WILL HAVE TO BE INCREASEO FROM ITS PRESTENT POINT OF 1000. c MIN • 1000 c 00 520 K • 1 . 6 IF (NP(K.MBR)) 510. 510. 490 490 IF (NP(K.MBR) - MIN) 500. 510. 510 500 MIN - NP(K.MBR) 510 CONTINUE 09  465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522  C  520  CONTINUE  NBB • MAX - MIN • 1 IF (NBB - NB) 540. 540. 530 530 NB • NBB 540 CONTINUE IF (E(MBR) .EO. 0.) E(MBR) - E(MBR - 1) IF (MBR .EO. 1) GO TO 550 IF (G(MBR) .EO. 0.) G(MBR) • G(MBR - 1) IF (AV(MBR) .EO. 0.) AV(MBR) - AV(MBR - 1) 550 CONTINUE IF (AREA(MBR) .EO. 0.) AREA(MBR) • AREA(MBR - 1) IF (CRMOM(MBR) .EO. O.) CRMOM(MBR) • CRMOM(MBR - 1) IF (BMCAP(MBR) .EO. O.) BMCAP(MBR) » BMCAP(MBR - 1) C PRINT MEMBER OATA C WRITE (6,620) MBR. JNL(MBR). JNG(MBR), EXTL(MBR). OM(MBR). 1 EXTG(MBR). XM(MBR), YM(MBR), AREA(MBR), CRMOM(MBR). AV(MBR), 2 BMCAP(MBR), KL(MBR). KG(MBR), E(MBR) 560 CONTINUE C PRINT THE NO. OF DEGREES OF FREEDOM AND THE HALF BANDWIDTH C WRITE (6.630) NU WRITE (6.640) NB C READ DAMPING VALUES READ (5.570) DAMP 1, DAMP2 570 FORMAT (2F5.3) RETURN 580 FORMAT ('-'. 'MEMBER DATA') S90 FORMAT (/• MN JNL JNG EXTL LENGTH EXTG XM YM 1 2X. 'AREA MOM OF I AV, 7X. 'MOMENT', 3X. 'KL'. 2 IX. 'KG'. 5X. ' E ') 600 FORMAT (85X. 'CAPACITY') 610 FORMAT (515. 2F10.1. F8.2, F15.3. F10.1. 3F8.2) 620 FORMAT (• '. 13. 214, F7.1, F9.2, F7.1, 2F9.2, F8.2. F15.3. F8.2. 1 F10.1. 213. F10.1) 630 FORMAT (//. 'NO.OF DEGREES OF FREEDOM OF STRUCTURE «'. 15) 640 FORMAT (/' HALF BANDWIDTH OF STIFFNESS MATRIX »'. 15) END C C C C SUBROUTINE BUILD(NU, NB, XM, YM. DM, NP, AREA, CRMOM. AV, E, G, 1 KL. KG. NRM, S. IDIM. EXTL. EXTG) C C • »••• »••» • C C C THIS SUBROUTINE WORKS IN DOUBLE PRECISION C THIS SUBROUTINE CALCULATES THE STIFFNESS MATRIX OF EACH C MEMBER AND ADDS IT INTO THE STRUCTURE STIFFNESS MATRIX. C THE FINAL STIFFNESS MATRIX S IS RETURNED. C THIS SUBROUTINE IS SIMILAR TO ONE THAT WOULD BE USED IN NORMAL C FRAME ANALYSIS. C IOIM IS THE DIMENSIONING SIZE OF THE STRUCTURE STIFFNESS MATRIX. C REAL'S SM(21), S(IDIM)  523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 5B0  DIMENSION XM(NRM) , YM(NRM) , DM(NRM), " 1 CRMOM(NRM). AV(NRM). KL(NRM). KG(NRM), EXTL(NRM). 2 EXTG(NRM), E(NRM) REAL*8 RF. GMOD, CMOMI, F, H REAL'S LONE. LONEX. LONEY. LTWO. LTWOX. LTWOY. AVI REAL'S YMI. OMI. DM2. XM2. YM2. XMI. AREAI. EMOD. XM2F. YM2F. 1 XMYMF REAL'S DBLE ZERO STRUCTURE STIFFNESS MATRIX G ( N  C C C C c c c  DO 10 I • 1. IDIM S(I) • 0.0000 10 CONTINUE BEGIN MEMBER LOOP DO 200 I • 1, NRM  c c c  ZERO MEMBER STIFFNESS NATRIX 20  c c  c  c  c c c  DO 20 J • t. 21 SM(J) - 0.0000 CONTINUE  ASSIGN MEMBER PROPERTIES TO DOUBLE PRECESION VARIABLES EMOD - DBLE(EU)) GMOD - DBLE(G(I)) LONE - OBLE(EXTL(I)) LTWO - DBLE(EXTG(I)) YMI » DBLE(YM(I)) OMI • DBLE(DM(I)) XMI - DBLE(XM(I)) AREAI • OBLE(AREA(I)) CMOMI • DBLE(CRMOM(I)) AVI - D8LE(AV(I>) 0M2 - OMI • DMI XM2 • XMI • XMI YM2 " YMI • YMI XMYM - XMI • YMI F • AREAI * EMOD / (DMI*DM2) H ' 0.0000 SHEAR DEFLECTIONS ARE IGNORED WHENEVER G OR AV IS ZERO. IF (AV(I) .EO. 0.0 .OR. G(l) .EO. 0.) GO TO 30 H « 12.0000 • EMOO ' CMOMI / (AVI'GM0D*0M2) 30 XM2F • XM2 • F YM2F - YM2 • F XMYMF ' XMYM • F FILL IN PIN-PIN SECTION OF MEMBER STIFFNESS MATRIX ' SM( 1 ) • XM2F SM(2) « XMYMF SM(4) • -XM2F SM(S) • -XMYMF SM(7) - YM2F  M )  581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638  C C  SM(9) • -XMYMF SM(10) - -YM2F SM(16) • XM2F SM(17) • XMYMF SM(19) • YM2F IF (KL(I) • KG(I) - 1) 100. 40. 50 40  F • 3.0000 • EMOO * CMOMI / (DM2*DM2*DMI*(1.0000+H/4.1 GO TO 60 50 F - 12.0000 * EMOD • CMOMI / (DM2*DM2 *DMI *(1.ODOO+H)) C RF IS A FACTOR COMMON TO THE ENTIRE MATRIX FOR ADDITION OF C DUE! TO RIGID BEAM END EXTENSIONS. RF » 12.ODOO • EMOO * CMOMI / (DM2*DM2) / (1.D0+H) C c FILL IN TERMS WHICH ARE COMMON TO PIN-FIX,FIX-PIN.ANO c FIX-FIX MEMBERS c LONEY - LONE * YMI • RF LONEX - LONE • XMI * RF LTWOY - LTWO • YMI • RF LTWOX - LTWO * XMI • RF 60 XM2F - XM2 * F YM2F - YM2 • F XMYMF • XMYM • F 0M2F • 0M2 • F c SM( 1 ) - SM( 1 ) + YM2F SM(2) • SM(2) - XMYMF SM(4) • SM(4) - YM2F SM(5) • SM(5) + XMYMF SM(7) • SM(7) • XM2F SM(9) - SM(9) + XMYMF SM(10) - SM(10) - XM2F SM(16) - SM(16) + YM2F SM(17) • SM(17) - XMYMF SM(19) - SM(19) • XM2F IF <KL(I) - KG(I)) 70. 80. 90 c c FILL IN REMAINING PIN-FIX TERMS c 70 SM(6) • -YMI • DM2F SM( 11) • XMI * DM2F SM(18) • -SM(6) SM(20) - -SM(11) SM(21) - DM2 * DM2F GO TO 100 c c FILL IN REMAINING FIX-FIX TERMS c 80 SM(3) • -YMI • DM2F • 0.5000 SM(6) - SM(3) SM(8) • XMI • DM2F • 0.5000 SM(11) - SM(8) SM(12) - 0M2 * DM2F • (4.ODOO+H) / 12.ODOO SM(13) • -SM(3) SM(14) - -SM(8) SM(15) - DM2 • DM2F • (2.0D00-H) / 12.0000  639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696  SM(18) • -SM(6) SM(20) • -SM(11) SM(21) • SM(12) ADD IN TERMS FOR RIGID END EXTENSIONS. SM(3) • SM(3) - (LONEY) SM(6) • SM(6) - (LTWOY) SM(8) - SM(8) LONEX SM(11) SM(11) • LTWOX SM(12) SM(12) • (LONE"OMI«(DMI + LONE)*RF) SM(13) SM(13) • LONEY SM(14) SM(14) - LONEX SM(15) SM(IS) • ((LONE*LTWO*DMI) + (DM2*(LONE + LTW0)/2.0000)) • RF SM(18) SM(18) LTWOY SM(20) LTWOX SM(20) (DM2"LTWO + (DMI*(LTWO*LTWO))) * RF SM(21) SM(21) GO TO 100 FILL IN REMAINING FIX-PIN TERMS SM(3) • -YMI • DM2F 90 SM(8) - XMI • DM2F SM(12) • DM2 • DM2F SM(13) - -SM(3) SM(14) • -SM(8) CONTINUE ADD THE MEMBER STIFFNESS MATRIX SM INTO THE STRUCTURE STIFFNESS MATRIX S. NB 1 NB 1 DO 190 d « 1. 6 IF (NP(d.I)) 190. 190, 110 Jl • (d - 1) • (12 - d) / 2 120 130 140  150 160 170 1B0 190  DO 180 L • d. 6 IF (NP(L.D) 180. 180, 120 IF (NP(d.I) - NP(L.I)) ISO. 130, 160 IF (L - d) 140. 150. 140 K - (NP(L.I) - 1) • NB1 • NP(d.I) N - di • L S(K) • S(K) + 2.0000 • SM(N) GO TO'180 K - (NP(d.I) - 1) • NB1 + NP(L.I) GO TO 170 K - (NP(L.I) - 1) * NB1 • NP(d.I) N • di + L S(K) • S(K) • SM(N) CONTINUE CONTINUE  200 CONTINUE RETURN END O  697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748. 749 750 751 752 753 754  C C C C C C C c c c c c c c c c c c c c  SUBROUTINE SDFBAN(A. B. N. M. LT, RATIO. DET, NCN. NSCALE)  THIS ROUTINE SOLVES SYSTEM OF EONS. AX'B WHERE A IS +TVE DEFINITE SYMMETRIC BAND MATRIX. BY CHOLESKY'S METHOD. LOWER HALF BAND. ONLY (INCLUDING THE DIAGONAL) OF A IS STORED COLUMN BY COLUMN IN A 1 DIMENSIONAL ARRAY. SOLUTIONS X ARE RETURNED IN ARRAY B. OPTIONAL SCALING OF MATRIX A IS AVAILABLE N - ORDER OF MATRIX A. M - LENGTH OF LOWER HALF BAND. DETERMINANT OF A - OET'(10"NCN). 1.E-15<|DET|<1.E15 LT»1 IF ONLY 1 B VECTOR OR IF FIRST OF SEVERAL. LT NOT « 1 FOR SUBSEQUENT B VECTORS. RATIO • SMALLEST RATIO OF 2 ELEMENTS ON MAIN DIAGONAL OF TRANSFORMED A >1.E-7. NSCALE-0 IF SCALING NOT REQUIRED. IMPLICIT REAL'8(A - H.O - Z) DIMENSION A ( 1 ) , 8 ( 1 ) REAL'S MULT(4000) IF (M .EQ. 1) GO TO 80 MM - M - 1 NM - N • M NM1 - NM - MM  c c c c  DUMMY STATEMENT INSERTED FOR COMPATIBILITY WITH ASSEMBLER VERSION IF(LT.LE.O) RETURN  c c c c  MATRIX SCALED BY DIVIDING ROW I ANO COLUMN I BY SORT(A(I.I)), SUCH THAT DIAGONAL ELEMENTS A ( I , I ) ARE 1.  IF (LT .NE. 1) GO TO 340 IF (NSCALE .EO. 0) GO TO 60 DO 10 I • 1, N  10  20 30  40 50  II • ( I - 1) » M + 1 IF ( A ( I I ) .LE. 0.0) GO TO 120 MULT(I) - 1.0 / DSQRT(AUI)) KK • 1 DO 50 I • 1 , N II • ( I - 1) • M • 1 JENO - I I 'MM IMN - ( I - 1) + M - N IF (IMN .GT. 0) JEND • JEND - IMN DO 20 J • I I , JEND A ( J ) - A ( J ) • MULT(I) CONTINUE DO 30 J • KK, I I , MM A(d) • A ( J ) • MULT(I) IF (KK .GE. M) GO TO 40 KK • KK + 1 GO TO 50 KK - KK * M CONTINUE  755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812  C C C C C C  60 MP - M + 1 TRANSFORMATION OF A. A IS TRANSFORMED INTO A LOWER TRIANGULAR MATRIX L SUCH THAT A'L.LT (LT-TRANSPOSE OF L . ) . IF Y-LT.X THEN L.Y'B. ERROR RETURN TAKEN IF RATI0<1.E-7 KK - 2 NCN - 0 DET - 0. FAC • RATIO IF (A(1) .GT. O.) GO TO 70 NROW - 1 RATIO • A ( 1 ) GO TO 310 70 DET - A(1) A(1) « 1. / OSQRT(A(1)) BIGL • A(1) SML - A(1) A(2) - A(2) • A{1) TEMP - A(MP) - A ( 2 ) • A(2) IF (TEMP .LT. 0.0) RATIO • TEMP IF (TEMP .EO. 0.0) RATIO • 0.0 IF (TEMP .GT. 0.0) GO TO 140 NROW • 2 GO TO 310 80 DET • 1.DO NCN • O DO 1 10 I - 1 . N OET • DET * A ( I ) IF ( A ( I ) .EQ. 0.0) GO TO 120 IF (DET .GT. 1.E-15) GO TO 90 DET - DET • 1.E+15 NCN - NCN - 15 GO TO 100 .90 IF (DET .LT. 1.E-M5) GO TO 100 DET • DET • 1.E-15 NCN « NCN + 15 lOO CONTINUE 110 B ( I ) - 8 ( 1 ) / A O ) RETURN 120 RATIO - A ( I ) 130 NROW ' I GO TO 310 140 A(MP) - 1.0 / DSQRT(TEMP) DET - DET * TEMP IF (A(MP) .GT. BIGL) BIGL • A(MP) IF (A(MP) .LT. SML) SML • A(MP) IF (N .EO. 2) GO TO 290 MP " MP + M DO 280 J * MP. NM1, M JP - J - MM MZC " O IF (KK .GE. M) GO TO 150 KK - KK + 1 II • 1 JC • 1 GO TO 160 (O  813 814 813 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870  • KK • M • KK - MM - KK - MM 180 I • KK, OP. MM' 160 IF ( A ( I ) .EO. 0.) GO TO 170 GO TO 190 OC • OC • M 170 MZC • MZC + 1 180 ASUM1 - O.DO GO TO 240 MMZC • MM • MZC 190 II « I I + MZC KM - KK + MMZC A(KM) • A(KM) • A(OC) IF (KM .GE. OP) GO TO 220 KO * KM + MM DO 210 I • KO, OP, MM ASUM2 - O.DO IM • I - MM II - II + 1 K l • II «• MMZC DO 200 K • KM, IM. MM ASUM2 - ASUM2 + A ( K I ) « A(K) K l • K l + MM 200 A ( I ) - ( A ( I ) - ASUM2) • A(KI) 210 CONTINUE 220 ASUM1 • O.DO DO 230 K • KM, OP, MM ASUM1 - ASUM1 + A(K) « A(K) 230 S • A ( d ) - ASUMI 240 IF (S .LT. 0.) RATIO - S IF (S .EO. 0.) RATIO - 0. IF (S .GT. 0.) GO TO 250 NROW - (0 + MM) / M GO TO 310 A ( J ) - 1. / DSORT(S) 250 DET " DET • S IF (DET .GT. 1.E-15) GO TO 260 DET - OET • I.E+15 NCN • NCN - 15 GO TO 270 IF (OET .LT. I.E+15) GO TO 270 260 DET • DET • 1.E-15 NCN • NCN • 15 CONTINUE 270 IF ( A ( 0 ) .GT. BIGL) BIGL • A(0) IF ( A ( 0 ) .LT. SML) SML - A(0) 280 CONTINUE 290 IF (SML .LE. F A C B I G L ) GO TO 300 GO TO 330 300 RATIO - 0. RETURN 310 WRITE (6.320) NROW 320 FORMAT ('0** SYSTEM IS NOT POSITIVE DEFINITE', 1 ' ERROR CONDITION OCCURRED IN ROW', 14) RETURN 330 RATIO - SML / BIGL 340 CALL DSBANO(A, MULT. B, N, M, NSCALE) 150  KK II OC 00  ,  871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 9O0 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 92 1 922 923 924 925 926 927 928  RETURN END SUBROUTINE OSBANO(A, MULT, 8. N. M. NSCALE) IMPLICIT REAL*B(A - H.O - Z ) DIMENSION A( 1), B ( 1 ) REAL'8 MULT(1) MM • M - 1 NM • N • M NM1 • NM - MM C C C C C C  THE FOLLOWING STATEMENTS SOLVE FOR L.Y'B BY A FORWARDS HENCE FOR X FROM LT.X-Y BY A BACKWARDS SUBSTITUTION. IF SCALING OPTION USED. B IS SCALED AND NORMALISED BEFORE SUBSTITUTION BEGINS. 10 SUM - O.DO IF (NSCALE .EO. 0) GO TO 40 DO 20 I - 1, N B ( I ) - B ( I ) » MULT(I) SUM - SUM • B ( I ) • B ( I ) 20 CONTINUE ELENB • OSORT(SUM) DO 30 I - 1. N 30 B ( I ) - B ( I ) / ELENB 40 B(1) - B ( 1 ) • A(1) KK " 1 K1 • 1 0 • 1 DO 80 L - 2. N BSUM1 • O.DO LM - L - 1 0 • 0 • M IF (KK .GE. M) GO TO 50 KK • KK + 1 GO TO 60 KK - KK + M 50 Kl • K l • 1 OK • KK 60 DO 70 K - K l . LM BSUM1 • BSUM1 * A(OK) • B ( K ) OK • OK + MM CONTINUE 70 80 B ( L ) - ( B ( L ) - 8SUM1) • A ( 0 ) 90 B(N) • B(N) ' A(NM1) NMM • NM1 NN • N - 1 ND • N DO 110 L * 1, NN BSUM2 • O.DO NL - N - L NL1 • N - L + 1 NMM • NMM - M NJ1 • NMM IF ( L .GE. M) NO " NO - 1 DO 100 K • NL1 . ND Ndl • N01 • 1 BSUM2 • BSUM2 + A(NJ1) • B ( K ) 100 CONTINUE  929 930 931 932 933 934 935 936 937 938 939 940 94 1 94 2 943 944 945 946 947 948 949 950 951 9S2 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986  110 B(NL) • (B(NL) - BSUM2) • A(NMM) IF (NSCALE .EO. 0) GO TO 130 00 120 I - 1. N 120 B(I) - B(I) • ELENB • MULT(I) 130 RETURN END C c  SUBROUTINE EIGEN(NU. NB, S. IDIM. AMASS. EVAL. EVEC. NMODES. MDOF. 1 PERIOD. WN)  c c THIS SUBROUTINE COMPUTES A SPECIFIED NO. OF NATURAL FREQUENCIES c AND ASSOCIATED MODE SHAPES c c NU-NO. OF DEGREES OF FREEDOM c NB'HALF BANDWIDTH c NMODES'NO. OF MODE SHAPES TO BE COMPUTED c IF NMOOES IS ZERO OR IS GREATER THAN THE NUMBER OF STRUCTURE c MASSES THEN NMODES WILL BE ASSIGNED THE NUMBER OF STRUCTURE c MASSES. c AMASS(II'MASS MATRIX MCOUNT * NUMB E R OF NONZERO MASSES c S(I)»STIFFNESS MATRIX STORED BY COLUMNS c EVAL(I)"NATURAL FREQUENCIES c EVEC(I,J)-MODE SHAPES c REAL'S OVEC(500. 10). OVALOO), CMASS(SOO). SDOOOOO) REAL'S S(IDIM) DIMENSION AMASS(NU). EVAL(NMODES) , EVEC(500,NMODES). MDOF(1O0) REAL'8 DBLE c c ZERO DUMMY MASS MATRIX CMASS DO 10 I TRY - 1, 500 10 CMASS(ITRY) - O.ODO c c COMPUTE THE NUMBER OF NONZERO MASS MATRIX ENTRIES c MCOUNT - 0 c DO 20 I • 1, NU CMASS(I) » DBLE(AMASS(I)) IF (AMASS(I) .EQ. 0.) GO TO 20 MCOUNT • MCOUNT • 1 20 CONTINUE 30 CONTINUE c c CALL SPRIT TO COMPUTE EIGENVALUES AND EIGENVECTORS c CREATE A DUPLICATE STRUCTURE MATRIX (SD) (OESTROYEO IN SPRIT) c c CALCULATE USEFUL LENGTH OF STIFFNESS MATRIX (LSTM) LSTM • (NU) • NB c 00 40 I • 1. LSTM SD(1) - S(I) 40 CONTINUE c SET CONVERGENCE CRITERIA FOR SPRIT. MAKE NEGATIVE IF RESIDUALS NOT c DESIRED. c  987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044  DEPS - 1.00-10 DEPS • (-1.000) * DEPS  C C CALL EIGENVALUE FINDING ROUTINE CALL PRITZISD. CMASS, NU. N8. 1. DVAL. DVEC. 500. NMODES, DEPS, 1 &60) C CONVERT EI GEN VECTORS TO SINGLE PRECISION 00 50 MAS • 1. NU 50 EVEC(MAS.I) • SNGL(DVEC(MAS.1)) EVAL(1) - SNGL(DVAL(1)) EVAL1 - EVAL(1) EVAL(1) - SORT(EVALI) WN * EVAL(1) PERIOD - 6.283153 / WN FREO • 1 / PERIOD WRITE (6,70) WN. PERIOO RETURN 60 WRITE (6.80) 70 FORMAT (//. 'NAT. FREO."'. F5.2. 5X, 'TIME PERIOO-'. F5.2. ' S E C . 1 //) 80 FORMAT ('CRAPOUT IN SPRIT') END C c • • *•• SUBROUTINE M0D3(NRd, NRM. NU. NB, S. IDIM, ND. NP. XM. YM, DM, 1 AREA, AV, CRMOM, KL. KG. BMCAP. E. G. AMASS. EVEC. 2 EVAL, EXTL. EXTG, NMB. ALPHA. RMAX. KOU, GG) C " " " REAL'8 SOOOOO). OF(SOO). DRATIO. DET DIMENSION ND(3.NRJ), NP(6,NRM), XM(NRM). YM(NRM), DM(NRM). 1 AREA(NRM), CRMOM(NRM). KL(NRM). KG(NRM), EVEC(50O,1), 2 E(NRM), G(NRM), EVAL(1), AV(NRM). AMASS(NU), BMASS(500). 3 IDOF(500). ALPHA(10), F(500). BMCAP(NRM), EXTL(NRM). 4 EXTG(NRM), 0EFL(5O0). SAXIAL(250). SHEARL(250). 5 SHEARG(250). SBML(250). SBMG(250). N0DN(20). MR(15). 6 MML(tOO). FEM(100.4) C CALCULATE MODAL PARTICIPATION FACTOR MCOUNT • O DO 10 1 • 1. NU IF (AMASS(I) .EO. O.O) GO TO 10 MCOUNT - MCOUNT + 1 10 CONTINUE AMT • O. AMB « 0. DO 20 J - 1, NU AMT • AMT + AMASS(J) • EVEC(J,1) AMB - AMB + AMASS! J) * ( ( EVEC( J. 1 ) ) "2 ) 20 CONTINUE ALPHA(1) - AMT / AMB WRITE (6,30) ALPHA(1) 30 FORMAT ('FIRST MODE PARTICIPATION FACTOR-'. F5.2) C ANALYZE FOR STATIC LOADS READ (5.40) NJLS, NLGCJ, NML. NLGCM 40 FORMAT (415) WRITE (6.50) NJLS. NML 50 FORMAT (//. 'NO. OF JOINTS LOADED-'. 14. 5X. 'NO. OF MEMBERS LOADE 10-'. 14) DO 60 I • 1. NU  1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1 100 1101 1102  60 F ( I ) - 0. IF (NLJS .£0. 0 .ANO. NML . CO. O) GO TO 350 IF (NJLS .EO. O) GO TO 200 WRITE (6.70) 70 FORMAT (///. 'GENERATION COMMANDS FOR STATIC LOADS APPLIED TO THE 1N0DES'. //) IF (NLGCJ .NE'. O) GO TO 90 WRITE (6.80) 80 FORMAT ('NONE'. /) GO TO 150 90 CONTINUE 00 140 1 - 1 . NLGCJ WRITE (6.100) 1O0 FORMAT (//. SX. 'FX'. 10X. 'FY'. 10X. 'FM'. 5X. 'NO. OF NODES'. 1 7X. 'LIST OF NODES'. /) READ (S.110) FX. FY. FM, NNOD, (NODN(N),N"1.NNOD) 110 FORMAT (3F8.1. 1115) WRITE (6.120) FX, FY, FM, NNOD, (NODN(N),N-1.NNOD) 120 FORMAT (/. F8.1. 6X. FB.1. 6X, F8.1, 15, SX. 1015) DO 130 J • 1. NNOD NN » NODN(J) N1 - N0(1.NN) N2 - ND(2,NN) N3 - ND ( 3 . NN) F(N1) - F ( N I ) • FX F(N2) - F(N2) • FY F(N3) - F(N3) * FM 130 CONTINUE 140 CONTINUE GO TO 210 150 CONTINUE WRITE (6.170) DO 190 I • I. NJLS READ (5.160) N, FX, FY. FM 160 FORMAT (15, 3F10.S) 170 FORMAT (8X, 'JN.'. 10X, ' FX '. 10X. ' F Y ', 10X, ' FM' WRITE (6.180) N. FX, FY, FM 180 FORMAT (110. 3(8X.F10.5)) Ml - ND(1.N) M2 - ND(2.N) H3 - N0(3,N) F(M1) - F(M1) • FX F(M2) • F(M2) • FY F(M3) - F(M3) + FM 190 CONTINUE 20O CONTINUE 210 CONTINUE IF (NML .EO. O) GO TO 350 WRITE (6.220) 220 FORMAT (///. 'GENERATION COMMANDS FOR MEMBER LOADS'. //) IF (NLGCM .NE. 0) GO TO 230 WRITE (6,80) GO TO 290 230 CONTINUE WRITE (6.240) 240 FORMAT (//. 'U.O.L.'. 5X, 'NO. OF MEMBERS'. 8X. 'LIST OF MEMBERS' 1 /) JM - 1 "  1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1 114 1115 1 116 1117. 1118 1119 1120 1121 1122 1123 1124 1125 1 126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1 136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1 160  C C C C  C C  C  DO 280 I - 1. NLGCM READ (5.250) W. NMEM, (MR(J).J-1.NMEM) 250 FORMAT (F8.1. 1415) WRITE (6.260) W. NMEM. (MR(J).J-1.NMEM) 260 FORMAT ( F 6 . 1 . 4X. IS. BX. 1315) DO 270 J • 1. NMEM MMR • MR(J) MML(JM) - MMR CALL GEN2(MMR, W. XM. KL. KG, NP, F. JM. FEM) JM • JM + 1 270 CONTINUE 280 CONTINUE GO TO 340 290 CONTINUE WRITE (6.300) 300 FORMAT ('MEMBER NO.', 10X. 'UNIF. DIST. LOAD') DO 330 MEM • 1. NML READ (5,310) MMR, W WRITE (6.320) MMR, W 310 FORMAT (15. F10.4) 320 FORMAT (16. 15X. F10.2) MML(MEM) • MMR CALL GEN2(MMR, W, XM. KL, KG. NP, F, MEM. FEM) 330 CONTINUE 340 CONTINUE 350 CONTINUE CONVERT LOAD VECTOR TO DOUBLE PRECISION DO 360 J • 1, NU 360 D F ( J ) - D B L E ( F ( J ) ) CALL SDFBAN TO SOLVE AX-B DRATIO » 1.0-16 CALL SDFBAN(S, DF, NU, NB, 1. DRATIO. DET. JEXP. 1) CONVERT SOLN. VECTOR DF TO SINGLE PRECISION DO 370 J - 1 . NU 370 D E F L ( J ) - S N G L ( D F ( J ) ) CALCULATE MEMBER FORCES DUE TO STATIC LOADS CALL MEMFOtNHM. XM, YM, DM. AV. NP. DEFL. EXTL, EXTG. AREA. E. G, 1 CRMOM. KL. KG, SAXIAL. SHEARL, SHEARG. SBML. SBMG, NML. MML. 2 FEM) ZERO LOAD VECTOR DO 380 J - 1, NU 380 F ( J ) - O. COMPUTE LOAD VECTOR SA - 0.41 FAC • SA • ALPHA(1) • GG DO 390 J - 1, NU F ( J ) • E V E C ( J . I ) • FAC * AMASS(J) / 5. OF(J) " DBLE(F(J)) 390 CONTINUE IF (KOU .EO. 2) GO TO 400 " GO TO 410 400 DO 4 10 J - 1. NU DF(J) - -OF(J) 410 CONTINUE CALL SDFBAN NSCALE • 1 DRATIO - 1.00-16 INDEX - 2  ro  1161 1162 1163 1164 1165 M66 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 •1209 1210 1211 1212 1213 1214 1215 1216 1217 1218  CALL SOFBAN(S, DF, NU. NB. INDEX, DRATIO. DET, JEXP. NSCALE) OO 420 dF - 1, NU F(dF) - SNGL(DF(dF)) 420 CONTINUE WRITE (6,430) 430 FORMAT (//. .'dT. DISP. AND MEMBER FORCES AT THE YIELD OF STRUCTURE I S ' . /) WRITE (6.440) 440 FORMAT (/13X, ' J N ' . 13X, 'X-OISP.', 13X. 'Y-DISP.'. 10X. 1 'ROTATION'. /) C CALCULATE MEMBER FORCES OUE TO E/O FORCES CALL FORCE(NRM, XM. YM. DM. AV, NP. F, EXTL, EXTG, AREA, E. G. 1 CRMOM. KL. KG. NO, NMB. NRJ. BMCAP. RMAX. SAXIAL. SHEARL. 2 SHEARG, SBML, SBMG, OEFL. NU) RETURN END C •••• • SUBROUTINE FORCE(NRM. XM, YM, DM, AV. NP, F, EXTL, EXTG. AREA. E, 1 . G, CRMOM. KL, KG, NO, NMB, NRd. BMCAP, RMAX, SAXIAL, 2 SHEARL, SHEARG, S8ML, SBMG. DEFL. NU) C DIMENSION XM(NRM). YM(NRM), DM(NRM), AV(NRM), NP(S.NRM). F(NU). 1 D(6). EXTL(NRM), EXTG(NRM), KL(NRM). KG(NRM), G(NRM), 2 AREA(NRM). CRMDM(NRM). ND(3.NRJ). BMCAP(NRM), E(NRM) DIMENSION AXIAL(2S0), SHEAR(250). BML(250). BMG(250) DIMENSION SAXIAL(NRM), SHEARL(NRM), SBML(NRM), SBMG(NRM), 1 DEFL(NU), SHEARG(NRM) 10 FORMAT (/12X. 'MN'. 10X. 'AXIAL', IOX, 'SHEARL', 12X. 'SHEARG', 1 12X, 'BML'. 12X, 'BMG', /) DD 120 1 * 1 , NRM XL - XM(I) YL - YM(I) DL • DM(I) AV1 - AV(I) DO 40 MEMDOF - 1 , 6 N1 • NP(MEMDOF.I) IF (NI) 30. 30. 20 20 D(MEMDOF) • F(N1) GO TO 40 30 D(MEMDOF) • 0. 40 CONTINUE C MODIFY END DISP FOR HORZ MEMBERSWITH END EXT.(VALID FOR C HORZ. MEMBERS ONLY) N3 - NP(3,I) IF (N3 .EO. 0) GO TO 50 0(2) - D(2) • (F(N3)) • EXTL(I) 50 CONTINUE N6 • NP(6.I) IF (N6 .EO. O) GO TO 60 0(5) > 0(5) - (F(N6)) • EXTG(I) 60 CONTINUE AXIAL(I) • (AREA(I)«E(I)/DL**2) • (D(4)«XL • D(5)'YL - D(1)*XL 1 D(2)*YL) EISI • CRMOM(I) • E(I) C INCLUDE SHEAR DEFL. GFACT-0 MEANS NO SHEAR OEFL. GFACT - 0. IF (AVI .EO. 0.0 .OR. GO) .EO. 0.0) GO TO 70 GFACT • 12.0 • EISI / (AV1*G(I)*DL*OL)  1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276  C C  C  C  C  C  70  CONTINUE ASSIGN DISP TO RESPECTIVE D.O.F. CHECK FOR PIN-PIN MEMBERS IF (KL(I) .EO. O .AND. KG(I) .EO. 0) GO TO 100 DELT • ((D(5) - D(2))«XL • (0(1) - D(4))«YL) / DL BML(I) • (2.0*EISI/(DL*(1.0 • GFACT))) • ((3 O'DELT/OL) - (D(6)« 1 (1.0 - GFACT/2.0)) - (2.0*D(3)•(I.O • GFACT/4.O))) BMG(I) - -(2.0'EI SI/(OL*(1.0 • GFACT))) • ((3.0'OELT/DL) - (0(3) 1 «(1.0 - GFACT/2.0)) - (2.0'D(6)•(1.0 • GFACT/4.O))) SHEAR(I) • (6.0»E1SI/(0L"0L)) • ((0(3) • D(4) - (2.O'DELT/OL))/( 1 1.0+ GFACT)) IF (KL(I) - KG(I)) 80. 110. 90 PIN-FIX MEMBER FORCES 80 BMG(I) • BMG(I) * BML(I) • (1.0 - GFACT/2.0) / (2.0*(1.0 • 1 GFACT/4.O)) SHEAR(I) - SHEAR(I) • 1.5 • BML(I) / DL BML(I) - O. GO TO 1 10 FIX-PIN MEMBERS 90 BML(I) • BML(I) • BMG(I) • (1.0 - GFACT/2.0) / (2.0*(1.0 + 1 GFACT/4.0)) SHEAR(I) . SHEAR(I) - 1.5 • BMG(I) / DL BMG(I) - 0. GO TO 110 PIN-PIN MEMBERS 100 BML(I) • 0. BMG(I) • O. SHEAR(I) • 0. 110 CONTINUE 120 CONTINUE FAC • 1.0 130 KOUNT - O DO 150 M - 1. NRM AMOM • SBML(M) • BML(M) AMOG • SBMG(M) • BMG(M) AMOM ' ABS(AMOM) AMOG > ABS(AMOG) IF (AMOM .LT. AMOG) AMOM - AMOG AMU ' AMOM / BMCAP(M) IF (AMU .GE. 0.95) GO TO 140 GO TO 150 140 KOUNT - KOUNT + 1 150 CONTINUE NM - 1 • NMB / 2 IF (KOUNT .GE. NM) GO TO 170 FAC • 1.02 • FAC DO 160 J • 1. NRM AXIAL(J) • 1.05 • AXIAL(J) SHEAR(J) • 1.05 • SHEAR(J) BML(J) ' 1.05 • BML(J) 160 BMG(J) - 1.05 • BMG(J) GO TO 130 170 CONTINUE WRITE DISP. & MEM FORCES NOW DO 180 JF - 1. NU 180 F(JF) - FAC • F(JF) • DEFL(JF) RMAX • -10.0 DO 230 JNT - 1. NRJ Ul  1277 1278 1279 1280 1281 1282 1283 1284 128S 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 •1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334  OX • 0. or • o. OR - 0. N1 • NOI1.JNT) N2 • N0(2.dNT) N3 - N0(3.JNT) IF (N1 .EO. 0) GO TO 190 OX • F(N1) 190 CONTINUE IF (N2 .EQ. 0) GO TO 200 DY • FCN2) 200 CONTINUE IF (N3 .EO. 0) GO TO 210 DR - F(N3) 210 CONTINUE WRITE (6.220) JNT. OX, OY. DR DX • ABS(DX) IF (DX .GT. RMAX) RMAX • DX 220 FORMAT (6X. 110. 3F20.4) 230 CONTINUE WRITE (6.10) DO 240 IM • 1, NRM AXIAL(IM) - AXIAL(IM) + SAXIAL(IM) SHEARL(IM) - SHEAR(IM) » SHEARL(IM) SHEARG(IM) » SHEAR(IM) + SHEARG(IM) BML(IM) « BML(IM) + SBML(IM) BMG(IM) • BMG(IM) + SBMG(IM) WRITE (6.250) IM, AXIAL(IM), SHEARL(IM). SHEARG(IM). BML(IM). 1 BMG(IM) 240 CONTINUE 250 FORMAT (10X, 15, 5F15.3) WRITE (6.260) RMAX 260 FORMAT (//, 'AT ROOF DISP OF', F6.3, ' STRUCTURE YIELOED') RETURN END C C C C C C C c c c c c c c c C c c c  SUBROUTINE MASS(NU, ND, AMASS. NRJ. MDOF. NCDMS. GG)  THIS SUBROUTINE SETS UP THE MASS MATRIX N0(J.I)-DEGREES OF FREEDOM OF I TH JOINT WTX,WTY.WTR-X-MASS.Y-MASS.ROT.MASS AMASS(I)-MASS MATRIX.I IS THE DEGREE OF FREEDOM OF APPLIEO MASS MASSES ARE LUMPEO AT NOOES. THE MASS MATRIX IS DIAGONAL I ZED. DIMENSION NOO.NRJ), MOOF(IOO). AMASS(NU) ZERO MASS MATRIX DO 10 I • 1, NU AMASS(I) • 0.  1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1386 1387 1388 1389 1390 1391 1392  C  C C C  C C  C C C c c c c c c c c  10 CONTINUE WRITE (6.20) 20 FORMAT (///. 'MASS GENERATION COMMANDS'. //, 'FIRST NODE', 4X. 1 'X-MASS'. 4X. 'Y-MASS'. 3X. 'ROTN MASS'. 3X. 'LAST NODE'. 2 3X. 'NODE DIFF'. /) DO 80 I - 1. NCOMS READ (5.30) IJT, WTX, WTY, WTR. JJT. KDIF 30 FORMAT (15, 3F10.1. 215) WRITE (6.40) IJT. WTX. WTY, WTR. JJT, KDIF 40 FORMAT (15. 3X, 3F10.1. 4X, 15. 4X. 15) IF (KDIF .EQ. 0) KDIF - 1 IF (JJT .EO. 0) GO TO 50 NJT - (JJT - IJT) / KDIF • 1 GO TO 60 50 CONTINUE NJT • 1 60 CONTINUE DO 70 J • 1 . NJT N1 - ND(1,IJT) N2 • N0(2.IJT) N3 - NOO.IJT) AMASS(NI) - AMASS(Nt) + WTX / GG AMASS(N2) - AMASS(N2) • WTY / GG AMASS(N3) • AMASS(N3) + WTR / GG IJT - IJT » KOIF 70 CONTINUE 80 CONTINUE OUTPUT THE DEGREES OF FREEDOM WITH MASS AND ASSIGNED MASS. JCNT - 1 WRITE (6.100) DO 90 IDOF • 1. NU RMASS - AMASS(IDOF) IF (RMASS .EO. 0.0) GO TO 90 MDOF(JCNT) - IOOF WRITE (6.110) JCNT, MOOF(JCNT). RMASS JCNT - JCNT • 1 90 CONTINUE 100 FORMAT (*-'. 'MASS NO. OOF'. 6X. 'ASSIGNED MASS *) 110 FORMAT (' '. 2X. 13. 3X. 13. 9X. F10.5) RETURN END SUBROUTINE SCHECK(S, NU. NB, IDIM, SRATIO) THIS SUBROUTINE CHECKS THAT ALL DIAGONAL STIFFNESS MATRIX ELEMENTS ARE POSITIVE NUMBERS GREATER THAN ZERO. IT ALSO DETERMINES THE RATIO BETWEEN THE LARGEST ANO SMALLEST MEMBERS ON THE DIAGONAL THIS WILL GIVE SOME INDICATION AS TO THE CONDITIONING OF THE STIFFNESS MATRIX MATRIX ro  •  1393 1394 1393 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450  C REAL'S S ( I O I M ) R E A L ' S S M I N . SMAX. D I A G . RATIO C C C C C C C C C  THE S T I F F N E S S MATRIX I S STORED AS A COLUMN VECTOR. ONLY THE THE LOWER TRIANGLE ELEMENTS BEING STORED (BY COLUMNS) S ( 1 ) I S ON THE DIAGONAL AS I S S ( 1 ' N B ) . S ( 1 + 2 ' N B ) , E T C . NB I S THE H A L F BANDWIDTH OF THE S T I F F N E S S MATRIX I N I T I A L I Z E THE LARGEST ANO  SMALLEST VALUES OF DIAGONAL  (SMAX.SMIN)  SMIN - 1.0045 SMAX • - 1 . 0 0 0 0 C  C  DO 5 0 IDOF - 1. NU IELEM • ((IDOF - 1)*NB) • 1 DIAG • S ( I E L E M ) COMPUTE I F DIAGONAL ELEMENT I S ZERO OR NEGATIVE I F ( D I A G .NE. 0 . 0 0 0 0 ) GO TO 20 WRITE ( 6 . 1 0 ) IOOF 10 FORMAT (///' PROGRAM HALTED-A ZERO I S ON THE DIAGONAL OF i S T I F F N E 1SSMATRIX', //'EXAMINE DEGREE OF FREEDOM '. 1 4 ) STOP  C 20 30 1 40 C C C  CONTINUE I F ( D I A G .GT. 0 . 0 ) GO TO 40 WRITE ( 6 . 3 0 ) IDOF FORMAT (///' PROGRAM HALTED-NEGATIVE ELEMENT ON DIAGONAL OF '. 'STIFFNESS MATRIX'. //' EXAMINE DEGREE OF FREEDOM'. 1 4 ) STOP CONTINUE  DETERMINE I F THE DIAGONAL ELEMENT UNDER EXAMINATION I S THE LARGEST OR SMALLEST OF THE DIAGONAL ELEMENTS. I F ( D I A G .GT. SMAX) SMAX - DIAG I F ( D I A G .LT. SMIN) SMIN - DIAG  C 5 0 CONTINUE C WRITE ( 6 , 6 0 ) 6 0 FORMAT (/' A L L ELEMENTS OF MAIN DIAGONAL OF S T I F F N E S S MATRIX', 1 ' ARE P O S I T I V E D E F I N I T E ' ) C C C  COMPUTE ANO  PRINT RATIO OF LARGEST TO SMALLEST DIAGONAL  RATIO • SMAX / SMIN SRATIO - S N G L ( R A T I O ) WRITE ( 6 . 7 0 ) SRATIO 7 0 FORMAT (/. 'RATIO OF LARGEST TO SMALLEST DIAGONAL 1 'MATRIX ELEMENT I S ' . E 1 0 . 3 )  ELEMENTS  STIFFNESS'.  C RETURN END C C  •  •  '  SUBROUTINE SPECTR(DAMP. T. SA. I S P E C . AMAX. NM. C  ' TN)  '  1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508  C C C C C C C C  C C C  DIMENSION D A M P ( 2 0 ) . T ( 4 0 ) . S A C ( 2 ) I S P E C - 1 I F SPECTRUM A ( S H I B A T A & - 2 I F NBC SPECTRUM I S USED - 3  SOZEN) I S  USED  C A L L FTNCMD('EQUATE 9 9 - S P R I N T ; ' ) GO TO ( 1 0 . 8 0 ) . I S P E C SPECTRUM A 10 I F ( T N .GT. T ( 1 ) ) GO TO 3 0 DAMPIN • O A M P ( 1 ) 2 0 I F ( T N .LT. 0 . 1 5 ) SA • 2 5 . • AMAX • TN I F ( T N .GE. 0.15 .ANO. TN .LT. 0 . 4 ) SA • 3 .75 * AMAX I F ( T N .GE. 0 . 4 ) SA • 1.5 • AMAX / TN SA - SA • 8. / ( 6 . + 100.'DAMPIN) RETURN 3 0 CONTINUE I F ( T N .LT. T ( N M ) ) GO TO 4 0 DAMP IN - OAMP(NM) GO TO 2 0 4 0 CONTINUE DO 6 0 I • 2. NM I F ( T N .GT. T ( I ) ) GO TO 6 0 DO 5 0 J - 1. 2 K • I - 2 + J IF ( T ( K ) .LT. O . I S ) SA - 2 5 . • AMAX • T O O I F ( T ( K ) .GE. .15 .AND. T ( K ) .LT. 0.4) SA - 3 . 7 5 I F ( T ( K ) .GE.- 0 . 4 ) SA • 1.5 • AMAX / T( K ) S A C ( v l ) - SA • 8. / ( 6 . + 100. ' D A M P ( K ) ) 50 SA - ( S A C ( 2 ) - S A C ( D ) • ( T N - T ( I - 1 ) ) / ( T ( I ) 1 SAC(1) GO TO 7 0 CONTINUE 60 7 0 CONTINUE RETURN NBC  SPECTRUM  8 0 CONTINUE SV • 4 0 . • AMAX SD • 3 2 . • AMAX SACC - 1. • AMAX I F ( T N .GT. T ( 1 ) ) GO TO 100 DAMPIN - O A M P ( 1 ) 9 0 CONTINUE C A L L M U L T ( T N , DAMPIN. SV. SD, SACC. S A C L ) SA - SACL RETURN 1 0 0 I F ( T N .LT. T ( N M ) ) GO TO 110 DAMPIN - DAMP(NM) GO TO 9 0 110 CONTINUE 0 0 130 I • 2, NM I F ( T N .GT. T ( I ) ) GO TO 130 0 0 120 J - 1, 2 K • I - 2 • d  to •~1  (509 1310 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 '536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566  TP • T(K) OAMPIN • OAMP(K) CALL MULT(TP, DAMPIN. SV, SD. SACC. SACL) 120 SAC(d) • SACL SA - (SAC(2) - SAC(1)) • (TN - T ( I - 1)) / ( T ( I ) - T ( I - 1)) • 1 SAC(1) GO TO 140 • 130 CONTINUE 140 CONTINUE RETURN END C SUBROUTINE MULT(TPR, DAMP. SV. SD, SACC, SACL) C • . • C PRINT OUT A CAUTION NOTE SHOULO DAMPING BE LESS THAN 0.5% IF (DAMP .LT. 0.005) WRITE (7.10) 10 FORMAT (" '. 'CAUTION-DAMPING LESS THAN 0.5%') WN - 6.283153 / TPR C COMPUTE MULTIPLICATION FACTOR FOR ACCELERATION AT DESIREO DAMPING IF (DAMP .LE. 0.02) AML • 4.2 + ((0.02 - DAMPJ/0.015) • 1.6 IF (DAMP .GT. .02 .AND. OAMP .LE. .05) AML • 3.0 • ((.OS - DAMP)/ 103) • 1.2 IF (DAMP .GT. 0.05 .AND. DAMP .LE. 0.1) AML - 2.2 + ((0.1 - DAMP)/ 10.05) • 0.8 IF (DAMP .GT. 0.10) AML » 1.0 + ((1.00 - DAMPj/0.90) • 1.2 C C COMPUTE MULTIPLICATION FACTOR FOR VELOCITY AT DESIRED DAMPING. IF (DAMP .LE. 0.02) VML • 2.5 + ((0.02 - DAMP)/0.015) • 0.8 IF (DAMP .GT. .02 .AND. DAMP .LE. .05) VML • 2.0 • ((.OS - DAMP)/. 103) • 0.5 IF (DAMP .GT. .OS .AND. DAMP .LE. 0.1) VML « 1.7 + ((0.1 - DAMP)/ 10.05) • 0.3 IF (DAMP .GT. 0.10) VML • 1.0 + ((1.00 - DAMP)/0.90) • 0.7 C C COMPUTE MULTIPLICATION FACTOR FOR DISPLACEMENT AT OESIRED OAMPING. IF (DAMP .LE. 0.02) DML • 2.5 + ((0.02 - DAMP)/0.015) * 0.5 IF (DAMP .GT. 0.02) DML • VML C C COMPUTE BOUNDS USING OAMPING FACTORS COMPUTED ALREADY SDBND - SD * DML SABND - SACC • AML SV8ND • SV • VML . C COMPUTE WHICH IS THE APPROPIATE BOUND. C CONVERT FROM I N / S E C ' 2 TO FRACTION OF G BY DEVIDING BY 386.4 C SAATAP • SVBND • WN / 386.4 IF (SAATAP .GT. SABND) SACL • SABND IF (SAATAP .GT. SABND) GO TO 20 SDATCP - SVBND / WN IF (SDATCP .GT. SDBND) SACL - SDBNO • WN • WN / 386.4 IF (SDATCP .GT. SDBND) GO TO 20 C C IF HAVE NOT YET GONE TO STEP 180 THEN NATURAL FREOUENCY LIES ON C VELOCITY BOUND. C SACL • SVBND • WN / 386.4 C SA IS RETURNED AS A FRACTION OF GRAVITY. G 20 RETURN  1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1S86 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 161 1 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624  END I C  C  C  c c  c  c c  c  SUBROUTINE MEMFOfNRM. XM. YM. DM. AV. NP. F. EXTL. EXTG. AREA. E. 1 G. CRMOM, KL. KG. AXIAL. SHEARL, SHEARG. BML. BMG. NML. 2 MML, FEM) DIMENSION 1 1 2 DIMENSION 1 1  XM(NRM). YM(NRM), DM(NRM). AV(NRM). NP(6.NRM). F ( 5 0 0 ) . D(6) EXTL(NRM), EXTG(NRM). KL(NRM), KG(NRM). AREA(NRM). CRMOM(NRM). E(NRM). G(NRM). MML(IOO). FEM(100.4) AXIAL(NRM). SHEAR(250). BML(NRM), BMG(NRM), SHEARL(NRM). SHEARG(NRM)  DO 1  110 I - 1. NRM XL • XM(I) YL - YM(I) DL » DM(I) AV1 - A V ( I ) 00 30 MEMDOF - 1 . 6 NI • NP(MEMDOF.I) IF (NI) 20. 20. 10 D(MEMDOF) - F(N1) 10 GO TO 30 D(MEMDOF) - O. 20 CONTINUE 30 MODIFY END DISP FOR HORZ MEMBERSWITH END EXT.(VALID FDR HORZ. MEMBERS ONLY) N3 - NP(3.I) IF (N3 .EO. O) GO TO 40 D(2) - 0 ( 2 ) + ( F ( N 3 ) ) • E X T L ( I ) CONTINUE 40 N6 - NP(6.I) IF (N6 .EO. 0) GO TO 50 0 ( 5 ) - 0 ( 5 ) - ( F ( N 6 ) ) • EXTG(I) CONTINUE , . SO A X I A L ( I ) - ( A R E A ( I ) « E ( I ) / 0 L " 2 ) • (D(4)«XL + 0<5)'YL - O O J ' X L 1I 0(2)*YL) EISI " CRMOM(I) • E ( I ) INCLUOE SHEAR DEFL. GFACT'O MEANS NO SHEAR DEFL. GFACT » O. IF (AV1 .EO. 0.0 .OR. G ( I ) .EO. 0.0) GO TO 60 GFACT - 12.0 • EISI / (AV1*G(I)*DL*DL) CONTINUE 60 ASSIGN DISP TO RESPECTIVE 0.0.F. CHECK FOR PIN-PIN MEMBERS IF ( K L ( I ) .EO. O .ANO. K G ( I ) .EO. O) GO TO 90 DELT • ( ( D ( 5 ) - 0(2))<XL + ( D O ) - D ( 4 ) ) - Y L ) / DL BML(I) - ( 2 . 0 ' E I S I / ( D L ' ( 1 . 0 • GFACT))) • ((3.0*DELT/DL) - (D(6)« 1 ( 1 . 0 - GFACT/2.0)) - ( 2 . 0 * D ( 3 ) ' ( 1 . 0 • GFACT/4.0))) BMG(I) • -(2.0*EISI/(DL«(1.0 • GFACT))) • ((3.O'DELT/DL) - (D(3) 1 1 »(1.0 - GFACT/2.0)) - ( 2 . 0 ' 0 ( 6 ) « ( t . O • GFACT/4.0))) SHEAR(l) - <6.0'EISI/(DL«DL)) • ( ( 0 ( 3 ) + D(6) - (2.O'DELT/DL))/( 1 1.0 + GFACT)) IF ( K L ( I ) - K G ( I ) ) 70. 100. 80 PIN-FIX MEMBER FORCES 70 BMG(I) - BMG(I) • BML(I) * O.O - GFACT/2.0) / ( 2 . 0 ' d . O * 1 1 GFACT/4.O)) SHEAR(I) - SHEAR(I) • 1.5 • BML(I) / OL B M L ( l ) - O.  09  1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682  GO TO 100 FIX-PIN MEMBERS 80 BML(I) - BML(I) + BMG(I) * (1.0 - GFACT/2.0) / <2.0«(1 .0 + 1 1 GFACT/4.0)) SHEARfI) « SHEAR(I) - 1.5 • BMG(I) / DL BMG(I) - 0. GO TO 100 C PIN-PIN MEMBERS 90 BML(I) • 0. BMG(I) • 0. SHEAR ( I ) . 0. CONTINUE too SHEARL(I) - SHEAR(I) SHEARG(I) - SHEAR(I) 110 CONTINUE IF (NML .EO. 0) GO TO 150 DO 140 I • 1. NRM 00 120 J • 1 . NML IF ( I .EO. MML(J)) GO TO 130 120 CONTINUE GO TO 140 130 CONTINUE BML(I) • BML(I) + FEM(J.2) BMG(I) - BMG(I) + FEM(J.4) SHEARL(I) - SHEAR(I) • FEM(J.I) SHEARG(I) - SHEAR(I) - FEM(J,3) 140 CONTINUE 150 CONTINUE RETURN END C C SUBROUTINE GENKX. Y, I J T . LJT, NJT.KDIF) C C C GENERATES NODES ALONG STRAIGHT LINE c DIMENSION X(325), Y(325) XI - X ( I J T ) YI • Y ( I J T ) DX • X ( L J T ) - XI DY • Y ( L J T ) - YI DX • DX / FLOAT(NJT + 1) DY . DY / FLOAT(NJT • 1) 00 10 I • 1. NJT IJT « IJT + KDIF XI - XI + DX YI • YI • DY X ( I J T ) - XI 10 Y ( I J T ) - YI RETURN END C  c c c c  -  1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 1713 1714 1715 1716 1717 1718 1719 1720  C  IF (KL(MMR) + KG(MMR) - 1) 50. 20. 10 10 R3 • -W * XM(MMR) • XM(MMR) / 12. R6 - -R3 R2 - -0.5 • W • XM(MMR) R5 - R2 GO TO 60 20 IF (KL(MMR) - KG(MMR)) 30. 70. 40 30 R3 • 0. R6 - W • XM(MMR) • XM(MMR) / 8. R2 - -0.5 • W * XM(MMR) - R6 / XM(MMR) R5 • -0.5 • W • XM(MMR) • R6 / XM(MMR) GO TO 60 40 R3 • -V • XM(MMR) • XM(MMR) / 8. R6 • 0. R2 - -0.5 • W • XM(MMR) - R3 / XM(MMR) R5 • -0.5 • W • XM(MMR) + R3 / XM(MMR) GO TO 60 50 R2 • -O.S • V • XM(MMR) R3 - O. R5 » R2 R6 • 0. 60 CONTINUE J1 • NPO.MMR) J2 « NPO.MMR) J 3 » NPO.MMR) J4 - NPO.MMR) F ( J 3 ) ' F ( J 3 ) + R2 F ( J 4 ) • F ( J 4 ) + RS F ( J 1 ) • F ( J 1 ) * R3 F ( J 2 ) - F ( J 2 ) • R6 FEM(JL.1) » -R2 FEM(JL,2) " R3 FEM(JL.S) - -R5 FEM(JL,4) - -R6 70 CONTINUE RETURN END  SUBROUTINE GEN2(MMR. W. XM. KL. KG. NP, F, J L .FEM) DIMENSION XM(200). K L ( 2 0 0 ) . KG(200). NP(6.2O0) , F ( 5 0 0 ) . FEM(100.4)  to to  APPENDIX C  STATIC DAMAGE EVALUATION METHOD PROGRAM INPUT  Use any c o n s i s t e n t conversion 1.  of  units,  there  no  internal  of u n i t s i n the program.  (20A4)  one c a r d  Problem t i t l e  o f maximum 80 c h a r a c t e r  length  STRUCTURAL INFORMATION : NRM,  NRJ, NCONJT, NCDJT, NCDOD, NCDIDS  (615)  one c a r d  NRM  : Number o f members i n t h e s t r u c t u r e  NRJ  : Number of j o i n t s  NCONJT  :  Number  of  i n the s t r u c t u r e 'control  co-ordinates NCDJT  :  Number  of  generation  zero NCDIDS  commands  for  (See N o t e  : Number o f commands  for  which  (See N o t e 2) joints  specifying  co-ordinate  joints  with  joints  with  ( S e e Note 3) for specifying  displacements  (See N o t e  4)  CONTROL JOINTS CO-ORDINATES : I J T , X, Y (15,2F10.1) IJT  : Joint  one c a r d / c o n t r o l number,  X : x co-ordinate  i n any s e q u e n c e of the j o i n t  130  the  2)  for  displacements  identical  joints'  are specified  NCDOD : Number o f commands  3.  is  TITLE : TITLE  2.  set  joint  131 Y : y co-ordinate of the j o i n t COMMANDS FOR GENERATION OF JOINT CQ-QRDINATES : Omit  i f t h e r e a r e no g e n e r a t i o n commands  I J T , L J T , NJT, KDIF (415)  one card/command  IJT  : Joint  number  at the beginning of generation  LJT  : Joint  number  a t t h e end of g e n e r a t i o n  NJT  : Number o f j o i n t s  KDIF  :  Joint  number  t o be g e n e r a t e d difference  nodes on t h e l i n e  line  along  the l i n e  between two s u c c e s s i v e  (constant). If  assumed t o be e q u a l  line  blank  or  zero  to1  COMMANDS FOR JOINTS WITH ZERO DISPLACEMENTS : Omit  i f no j o i n t s  restrained  t o have z e r o  IJT,  KDOF(1), K D 0 F ( 2 ) , K D O F ( 3 ) , L J T , KDIF  (13,518) . IJT  displacements  one card/command :  Joint  covered KD0F(1)  number, by t h i s  or  first  i n the series  command  : Code f o r X d i s p l a c e m e n t , displacements  joint  0 i frestrained  in x direction,  1  i f free  from to  displace KDOF(2)  : Code  for Y displacement  KD0F(3)  : Code  for rotation  LJT  : Last  joint  blank KDIF  : Joint in  for a single  number  this  in this  series, joint  difference  series  punch 0 o r l e a v e  between s u c c e s i v e  (constant),  assumed t o be e q u a l  to1  i f blank  joints or zero  1 32 COMMANDS FOR JOINTS WITH IDENTICAL DISPLACEMENTS : Omit  if  no  joints  restrained  to  have  identical  displacements MDOF, NJT, I J O I N T ( N J T ) (215,1415) MDOF  one card/command  : Displacement  code :  1 : f o r x displacement 2 : f o r y displacement 3 : for rotation NJT  :  IJOINT  Number  of  (max.  14)  : List  of  joints  nodes  increasing  covered  covered  by  by  this  this  command  command,  in  order  MEMBER INFORMATION : MN,JNL,JNG,KL,KG,E,G,AREA,CRMOM,DEPTH,BMCAP,EXTL,EXTG,AV (515,2F10.1,F8.2,F15.1,F6.1,F10.1,3F8.2) MN  : Member number  JNL  : Lesser  JNG  : Greater  KL  one card/member  : Fixity  joint  number  joint  number  code a t l e s s e r  joint  0 : Pinned 1 : Fixed KG  : Fixity  code a t g r e a t e r  E  : Young's M o d u l u s  G  : Shear  Modulus  (0 i f s h e a r AREA  joint  deflections  : Cross-sectional  a r e t o be n e g l e c t e d )  a r e a o f t h e member  133 CRMOM  : Moment o f i n e r t i a  DEPTH  : D e p t h o f t h e member; hinge  BMCAP : Y i e l d EXTL  : Rigid  o f t h e member i f given  l e n g t h assumed  zero,  plastic  0.05(Member L e n g t h )  moment o f t h e member extension  on t h e l e s s e r  end  joint  of the  on t h e g r e a t e r e n d j o i n t  of the  member EXTG  : Rigid  extension  member AV  : Shear area (0  Note AV  i f shear d e f l e c t i o n s  a r e t o be n e g l e c t e d )  : I f E , G, AREA, CRMOM, DEPTH, BMCAP, are  values 8.  o f t h e member  left  blank  or  given  zero  a s f o r t h e p r e v i o u s member w i l l  EXTL,  EXTG,  f o r a member, same be assumed.  STATIC LOAD INFORMATION :. NJLS, NLGCJ, NML, NLGCM, NJL (515) NJLS  one c a r d : Number o f j o i n t s  NLGCJ  : Number o f g e n e r a t i o n applied  NML  NLGCM  a t t h e nodes  : Number o f j o i n t s  COMMANDS  JOINTS :  static  loads  (See Note 6)  by u n i f o r m l y  distributed  commands f o r  static  loads  t h e members (See N o t e 6) loaded  C a r d s 9A a n d 9B a r e o m i t t e d A.  loads  load  : Number o f g e n e r a t i o n on  9.  directly  by s t a t i c  commands f o r  : Number o f members l o a d e d static  NJL  loaded  FOR  STATIC  by s e i s m i c  i f NJLS  load  i s zero.  LOADS APPLIED DIRECTLY  ON THE  1 34  Omit  i f NLGCJ  i s zero  FX, FY, FM, NNOD, NODN(NNOD) (3F10.1,1015)  one card/command  FX  : Load i n x - d i r e c t i o n  FY  : Load i n Y - d i r e c t i o n  FM  : Moment  NNOD NODN  : Number o f j o i n t s t o be c o v e r e d :  List  of  increasing  joints  covered  by t h i s command  by  this  command i n  order  OR B. STATIC LOADS APPLIED DIRECTLY AT JOINTS : input  this  i f NLGCJ = 0  N, FX, FY, FM (I5,3F10.1) N  : Node  one c a r d / l o a d e d  joint  number  FX  : Load i n the x - d i r e c t i o n  FY  : Load  FM  : Moment  i n the y - d i r e c t i o n  NOTE : ONLY CARDS 9A OR 9B ARE TO BE INPUT  IN THE  NOT BOTH. Cards  10A a n d 10B t o be o m i t t e d  A. COMMANDS Omit  i f NML e q u a l s  zero.  FOR STATIC MEMBER LOADS :  i f NLGCM  i s zero.  W, NMEM, MR(NMEM) (F6.1,1415) W : Uniformly downward  one card/command d i s t r i b u t e d load load  positive  on t h e member,  DATA,  135 NMEM : Number o f members c o v e r e d MR  :  List  of  members  increasing  by t h i s  covered  by  command  this  command  in  order OR  B.  STATIC MEMBER LOADS :  Omit  i f NLGCM  i s not zero.  MMR, W (I5,F10.4) MMR  one c a r d / l o a d e d  : Member  number  W : Uniformly NOTE  :  member  ONLY  distributed CARDS  static  load  1 OA OR 1 OB TO BE INPUT IN THE DATA  WHEN NML IS NOT ZERO, NOT BOTH. 11. LOAD FACTOR AND K FACTOR FLOAD, DUCTK (2F10.2)  one c a r d  FLOAD  : Load  factor  DUCTK  : K factor  u s e d on t h e s e i s m i c  used  loads  i n A.S.K.I.F.W f o r m u l a e  12. SEISMIC LOADS N, FX, FY, FM (I5,3F10.5) N  : Node number  FX  : Load  i n the x - d i r e c t i o n  FY  : Load  i n the y - d i r e c t i o n  FM  : Moment  one c a r d / l o a d e d  joint  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 SO 51 52 S3 54 55 56 57 58  C c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c  c  STATIC DAMAGE EVALUATION METHOD METHOD TO CHECK DESIGN OONE BY CODE FORCEStOUASI STATIC ANALYST REAL'S S(190000). OBLE. DVL(500). SMS(200.21) PROGRAM DIMENSIONED FOR A MAXIMUM OF :200 MEMBERS 200 JOINTS VARIABLE DEFINITIONS:Kl.. KG  - JOINT TYPE : FIXED JOINT • 1 PINNED JOINT • 0 CROSS-SECTIONAL AREA MOMENT OF INERTIA OF GROSS SECTION BENOING MOMENT CAPACITY OF SECTION 0.0.F. NO. IOENTIFI ED BY JOINT NO. NO(K.I) - K • 1 (X-DOF), 2 (Y-DOF), 3 (R-OOF) I » JOINT NO. NP " D.O.F. NO. IDENTIFIED BY MEMBER NO. NP(K.I) - K - OOF 1 TO 6 FOR STANOARO MEMBER I - MEMBER NO. XM - LENGTH OF FLEXI8LE PORTION OF BEAM IN X-DIRECTION YM » LENGTH OF FLEXIBLE PORTION OF BEAM IN Y-DIRECTION DM • TRUE LENGTH OF FLEXIBLE PORTION OF BEAM EXTL.EXTG - LENGTH OF RIGID END TITLE - TITLE (80 CHARACTERS) AV • SHEAR AREA FL(I) • LOAD FACTOR AT WHICH I TH HINGE FORMS YCR - YIELD CURVATURE PCR • PLASTIC CURVATURE AREA CRMOM BMCAP NO  « • -  REAL'S OET. ORATIO DIMENSION KL(20O). KGC200), AREAC200). CRM0M(2OO), BMCAP(200.3), 1 ND(3,32S), NP(6.200). XM(200). YM(200). OM(200). 2 EXTL(20O). EXTGC200), AV(200). TITLE(20). VLC5O0). 3 AXIAL(200). SHEARL(ZOO), SHEARG(200). BML(200). 4 • BMG(200). DEFLC500). F(500). RAXIAL(200), SHEAR 1(200), 5 SHEAR2(200). RBML(200). RBMG(20O). FL(200), JNL(200). 6 JNG(200). X(325). Y(325), R0TN(2.325). NDEF(2.325). 7 CD(200.2). SI(2). HL(200), YCR(200). PL(500). E(200). 8 G(200). N00NI20), MR(1S), MML(IOO), FEM(100.4) CALL FTNCMOt'EQUATE 99'SPRINT;') CALL CONTRL(NRJ. NCONJT. NCDJT. NCDOD. NCDIDS, NRM). CALL SETUPCNRM, E, G. XM. YM, DM. NO. NP, AREA, CRMOM. NRJ. AV. 1 KL, KG. NU, NB. BMCAP. EXTL. EXTG, JNL. JNG. X. Y, YCR. HL, 2 NCONJT. NCDJT, NCDOD, NCDIDS) IDIM • 190000 ASSEMBLE STIFFNESS MATRIX  39 60 61 62 63 64 65 66 67 68 69 70 71 .72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116  MMAX • O CALL BUILD(NU. NB. XM. YM. DM. NP. AREA. CRMOM. AV. E. G. KL. KG. 1 NRM, S, IDIM. EXTL. EXTG. SMS. MMAX) CALL SCHECK(S. NU. NB. IDIM, SRATIO) C FORM LOAD VECTOR.GRAVITY LOADS & E/O FORCES AS GIVEN BY NBCC 00 10 I - 1, 500 PL(I) - 0. 10 VL(I) » 0. READ (5.380) NJLS. NLGCJ. NML. NLGCM. NJL WRITE (6.20) 20 FORMAT (//. ' -JOINT AND MEMBER LOADS') C READ STATIC LOADS;MEMBER LOADS ONLY UDL DO 30 J • 1. NRM RAXIAL(J) - 0. SHEAR 1 ( J) - O. SHEAR2(J) - O. RBML(J) » 0. 30 R8MG(J) • 0. DO 40 J - 1, 500 40 OEFL(J) - 0. IF (NJLS .EO. 0 .ANO. NML .EQ. 0) GO TO 320 IF (NJLS .EQ. 0) GO TO 190 WRITE (6,50) 50 FORMAT (///, 'GENERATION COMMANDS FOR STATIC LOADS APPLIED DIRECTL 1Y TO THE NODES', /) IF (NLGCJ .NE. 0) GO TO 70 WRITE (6,60) 60 FORMAT (//, 'NONE'. /) GO TO 140 70 CONTINUE DO 130 I - 1. NLGCJ WRITE (6.80) 80 FORMAT (//, SX. 'FX'.. IOX. 'FY'. 13X. 'FM'. 10X. 'NO. OF NODES'. 1 /) READ (S.90) FX. FY. FM. NNOD, (NOON(N),N-1.NNOD) 90 FORMAT (3F10.1. 1015) WRITE (6.100) FX. FY, FM. NNOD 100 FORMAT (/, F6.1. 6X, F10.1. 6X, F10.1. IOX. IS) C C WRITE (6.110) (NODN(N).N'1.NNOD) 110 FORMAT (/, 'LIST OF NODES', //. 16IS) 00 120 J • 1, NNOD NN ' NODN(J) NI • N0(1.NN) N2 • ND ( 2 , NN ) N3 - ND ( 3 , NN) PL(N1) - PL(N1) + FX PL(N2) • PL(N2) + FY PL(N3) • PL(N3) • FM 120 CONTINUE 130 CONTINUE GO TO 190 140 CONTINUE WRITE (6.150) 150 FORMAT (' -JN'. 13X, 'FX '. IOX, 'FY ', IOX, ' FM', /) 00 180 NJ • 1, NJLS READ (S.160) N. FX, FY. FM  U  cn  117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174  WRITE (6.170) N, FX. FY. FM FORMAT (15. 3F10.5) FORMAT (14. 3(10X.F10.2)) N1 ' ND(I.N) N2 " N0(2.N) N3 • N0(3.N) PL(N1) - PL(N1) + FX PL(N2) - PL(N2) • FY P U N S ) - PL(N3) + FM 180 CONTINUE 190 CONTINUE IF (NML .EO. 0) GO TO 320 WRITE (6.200) 200 FORMAT (///. "GENERATION COMMANDS FOR MEMBER LOADS'. /) IF (NLGCM .NE. O) GO TO 210 WRITE (6.60) GO TO 270 210 CONTINUE WRITE (6.220) 220 FORMAT (//. 3X, 'U.D.L.'. 3X. 'NO. OF MEMBERS'. 13X. 1 'LIST OF MEMBERS', /) JM * 1 DO 260 I • 1. NLGCM REAO (5.230) W. NMEM, (MR(J).J>1.NMEM) 230 FORMAT (F6.1. 1415) WRITE (6.240) W. NMEM, (MR(J),J-1,NMEM) 240 FORMAT (F6.1. 5X. 15. 11X. 1315) 00 250 J - 1 . NMEM MMR • MR(J) MML(JM) - MMR CALL GEN2(MMR. W, XM, KL. KG. NP. PL. JM, FEM) JM • JM + 1 250 CONTINUE 260 CONTINUE GO TO 320 270 CONTINUE WRITE (6.280) 280 FORMAT (5X. 'MEMBER NO.'. 10X. 'UNIF. DIST. LOAD') 00 310 J • 1. NML READ (5.290) MMR. W WRITE (6.300) MMR, W 290 FORMAT (15. F10.4) 300 FORMAT (5X. 16. 15X. F10.2) MML(J) - MMR CALL GEN2(MMR. W. XM. KL. KG. NP, PL. J . FEM) 310 CONTINUE 320 CONTINUE C READ SEISMIC FORCE LOAD FACTOR FLOAO ANO VALUE OF K USED C IN ASKIFW FORMULAE REAO (5.330) FLOAO. OUCTK 330 FORMAT (2F10.2) WRITE (6.340) FLOAO. DUCTK 340 FORMAT (/. 'SEISMIC FORCE LOAO FACTOR •', F5.2. //. 1 • 'VALUE OF K FOR THIS STRUCTURE -'. FS.2) C READ E/O LOADS (AS PER NBCC) WRITE (6.350) 350 FORMAT (/. 5X. 'EARTHQUAKE LOADS') WRITE (6.400) 160 170  '  175 176 177 178 179 180 181 182 183 184 185 186 187 -188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232  C C  C  C C  C C C C  00 360 J - 1. NJL READ (5.390) N. FX. FY, FM WRITE (6.410) N. FX, FY, FM M1 - ND(1,N) M2 - ND(2.N) M3 - ND(3.N) VL(M1) - VL(M1) • FX VL(M2) • VL(M2) + FY VL(M3) - VL(M3) + FM 360 CONTINUE IF (NJLS .EQ. 0 .AND. NML .EO. O) GO TO 450 SOLVE THE STRUCTURE FOR GRAVITY LOADS CONVERT LOADS TO DOUBLE PRECISION DO 370 I • 1 . NU 370 0 V L ( I ) - O S L E ( P L ( I ) ) 380 FORMAT (515) 390 FORMAT (15. 3F10.5) 400 FORMAT (5X, ' J N ' . 9X. ' F X '. 9X, ' FY '. 9X, ' FM'. /) 410 FORMAT (/. 17. 3 ( 8 X . F 1 0 . 2 ) ) CALL SDFBAN TO SOLVE AX»B(GRAVITY LOADS) DRATIO • 1.D-16 INK - NU • NB CALL SDFBAN(S, DVL, NU. NB. 1. DRATIO. DET. JEXP. 1. KTR) DVL NOW IS SOLN. VECTOR.CONVERT IT TO SINGLE PRECISION 00 420 J - 1. NU 420 F ( J ) - S N G U D V L ( J ) ) FINO OUT MEMBER FORCES DUE TO STATIC LOADS ML I - NML CALL FORCEtNRM, XM. YM, DM. AV, NP, F. EXTL. EXTG. AREA. E. G. 1 CRMOM. KL. KG. AXIAL. SHEARL. SHEARG. BML. BMG. ML I . MML, 2 FEM) 00 430 I • 1, NRM RAXIAL(I) • A X I A L ( I ) SHEAR 1(1) • SHEARL(I) SHEAR2U) - SHEARG(I) RBML(I) > BML(I) 430 RBMG(I) • BMG(I) DO 440 I " 1, 500 440 D E F L ( I ) - F ( I ) 450 CONTINUE DO 460 1 - 1 . 2 DO 460 J - 1 . NRM NDEF(I.J) - -9 460 ROTN(I.J) - O. DO 470 J - 1. NU 470 OVL(J) • D B L E ( V L ( J ) ) CALL SDFBAN TO SOLVE AX-B(FOR E/O LOADS) DRATIO • 1.D-16 CALL SDFBAN(S. DVL. NU. NB. 2. DRATIO, DET. JEXP, 1. KTR) CONVERT SOLN. VECTOR OVL TO SINGLE PRECISION 00 480 J • 1. NU 480 F ( J ) • SNGL(DVL(J)) FINDING A NOOE AT THE TOP OF THE STRUCTURE TO FINO SYSTEM DUCTILITY XD1 - 0. 00 500 1 - 1 , NRJ I I - NO(I.I) IF ( I t .EQ. O) GO TO 500  233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290  XD2 • A B S ( F ( I 1 ) ) IF (XD2 .GT. X01) GO TO 490 GO TO 500 490 CONTINUE X01 • X02 NTOP • I 500 CONTINUE K • ND(1.NTOP) YDEFL - DEFL(K) + F ( K ) UOEFL - FLOAO • 2.9 • YDEFL / DUCTK WRITE (6.510) YOEFL. UOEFL 510 FORMAT (/, 'YIELD TIP DISP. F10.3. 5X. 'ULTIMATE TIP OISP. 1 F10.3. /) FINO MEMBER FORCES DUE TO E/O LOADS ML I • 0 CALL FORCE(NRM, XM. YM, OM, AV. NP F. EXTL. EXTG. AREA, E. G, 1 CRMOM, KL, KG. AXIAL. SHEARL. SHEARG. BML, BMG, MLI, MML, 2 FEM) LSENS • 1 IKOUNT - 0 DO 1060 IOV • 1. 200 HAVE MEMBER FORCES,FIND LOAD FACTOR AT WHICH PLASTIC HINGE FORMS 00 580 1 * 1. NRM RBL ABS(RBML(I)) RBG ABS(RBMG(I)) IF (RBML(I) .LE. 0.0 .AND.. BML(I) .LT. 0.0) GO TO 520 IF (RBML(I) .GT. 0.0 .AND.. BML(I) .GT. 0.0) GO TO 520 IF (R8ML(I) .LE. 0.0 .AND.. BML(I) .GT. 0.0) GO TO 530 IF (RBML(I) .GT. 0.0 .AND.. BML(I) .LT. 0.0) GO TO 530 520 8MCAP(I,2) • BMCAP(I, D - RBL GO TO 540 BMCAP(I,2) « BMCAP(I, 1) • RBL 530 CONTINUE 540 IF (RBMG(I) .LE. 0.0 .AND. BMG(I) .LT. 0.0) GO TO 550 IF (RBMG(I) .GT. 0.0 .AND., BMG(I) .GT. 0.0) GO TO 550 IF (RBMG(I) .LE. 0.0 .AND. BMG(I) .GT. 0.0) GO TO 560 IF (RBMG(I) .GT. 0.0 .AND.. 8MG(I) .LT. 0.0) GO TO 560 550 BMCAP(I.3) - BMCAP(I, 1) " RBG GO TO 570 BMCAP(I,3) • BMCAP(I, 1) • RBG 560 CONTINUE 570 CONTINUE 580 CALL RATIO(BML, BMG, BMCAP. NRM, FACT. KL. KG. MMAX. ICT. LSENS) IF (IOV .EO. 1) GO TO 590 FL(IOV) • FL(IOV - 1) • FACT GO TO 600 FL(IOV) . FACT 590 CONTINUE 600 WRITE (99.610) FL(IOV) L(IOV) IF (LSENS .EO. 1) WRITE (6.610) FL FORMAT ('AT A LOAO FACTOR OF F6 3) 00 620 I • 1. NRM FACT • AXIAL(I) RAXIAL(I) • RAXIAL(I) FACT • SHEARL(I) SHEAR1(I) - SHEARI(I) FACT * SHEARG(I) SHEAR2(I ) • SHEAR2II) BML( I) RBML(I) • RBML(I) • FACT RBMG(I) • RBMG(I) » FACT • BMG( I) 620 CONTINUE  291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348  C C  C  C  C  C C  K » ND(1.NTOP) UOEFL • ABS(UDEFL) TIPD - OEFL(K) • FACT • F ( K ) TIPD " ABS(TIPD) IF (TIPD .LT. UDEFL .AND. IKOUNT .EO. 1) GO TO 680 IF (TIPO .LT. UDEFL) GO TO 660 FACT 1 • (UDEFL - ABS(OEFL(K)) ) / A B S ( F ( K ) ) • ADD UP THE DEFLECTIONS CORRESPONDING TO TIP DEFLECTION OF CALCULATED VALUE 00 630 I - 1. NU D E F L ( I ) • D E F L ( I ) + FACT 1 • F ( I ) 630 CONTINUE IF (LSENS .EO. 1) WRITE (6.640) 640 FORMAT ('THIS PLASTIC HINGE NOT CONSIDERED AS TIP DISP. IS'. / 1 'MORE THAN CALCULATED ULT. TIP DISP'. //) IF (IKOUNT .EO. 1) GO TO 1250 IF (LSENS .EO. 1) CALL CURVO(NRM. CD, NOEF, NP, DEFL. ROTN. HL, 1 YCR, LSENS. IKOUNT) 00 650 I • 1. NU D E F L ( I ) • D E F L ( I ) - FACT 1 • F ( I ) 650 CONTINUE 660 CONTINUE IF (LSENS .EO. 2) UOEFL - 1.1 • UOEFL UDEFL « ABS(UDEFL) K - ND(1.NTOP) TIPD ' DEFL(K) + FACT • F ( K ) TIPD " ABS(TIPD) IF (TIPD .LT. UDEFL) GO TO 680 FACT 1 • (UDEFL - ABS(OEFL(K) ) ) / ABS(F(K) ) NOW AOD UP THE DEFL UP TO INCREASED TIP DEFL. DO 670 I - 1. NU D E F L ( I ) - D E F L ( I ) + FACT 1 • F ( I ) 670 CONTINUE GO TO 1250 680 CONTINUE AOD UP THE DEFLECTIONS 00 690 I - 1. NU D E F L ( I ) • D E F L ( I ) • FACT » F ( I ) 690 CONTINUE IF (ICT .EO. 1) N1 - NP(3,MMAX) IF (ICT .EO. 2) N1 - NP(G.MMAX) NOEF(ICT,MMAX) • N1 IF (N1 .EO. 0) GO TO 700 ROTN(ICT.MMAX) - DEFL(N1) 700 CONTINUE IF (LSENS .EO. 1) WRITE (6,710) TIPD 710 FORMAT (' TIP DISP • '. F10.3) IF (ICT .EO. 2) GO TO 740 ICT'1 -PLASTIC HINGE FORMED AT LESSER END OF MEMBER MMAX IF (NP(3,MMAX)) 720, 720. 730 720 J L - JNL(MMAX) N0(3,JL) - NU + 1 NU • NU • 1 NP(3.MMAX) - N O O . J L ) GO TO 770 730 CONTINUE ADO A NEW NODE-.NODE ON TOP OF ONE ANOTHER CAPABLE OF HAVING DIFFRENT ROTATIONS  01  349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406  C 740 750  760  770 C  780 790 800  810 820 830 840 C C 850 860 870 880  NRJ - NRJ + 1 NU • NU + 1 JL - JNL(MMAX) N0(1,NRJ) " ND(1 ,0L) ND(2.NRJ) • ND(2.JL) X(NRJ) - X ( J L ) Y(NRJ) • Y ( J L ) N0(3.NRJ) - NU JNL(MMAX) • NRJ NPO.MMAX) • NU GO TO 770 DO SAME THING;HINGE FORMED AT GREATER END OF MEM8ER MMAX CONTINUE IF (NPO.MMAX)) 750. 750. 760 JG - JNG(MMAX) NOO.JG) • NU • 1 NU - NU + 1 NP(6.MMAX) - NOO.JG) GO TO 770 CONTINUE NRJ " NRJ + 1 NU - NU + 1 JG • JNG(MMAX) ND(1.NRJ) - ND(1.JG) NDO.NRJ) • ND(2.JG) X(NRJ) - X(JG) Y(NRJ) • Y(JG) NDO.NRJ) - NU JNG(MMAX) • NRJ NPO.MMAX) - NU CONTINUE SEE WHETHER HALF WIDTH OF STIFFNESS MATRIX CHANGED MAX • 0 DO 800 K • 1. 6 IF (NP(K.MMAX) - MAX) 790, 790. 780 MAX - NP(K.MMAX) CONTINUE CONTINUE MIN - 1000 00 840 K - 1. 6 IF (NP(K.MMAX)) 830, 830. 810 IF (NP(K.MMAX) - MIN) 820. 820. 830 MIN • NP(K.MMAX) CONTINUE CONTINUE NBB - MAX - MIN + 1 IF (NB8 .GT. NB) NB • NBB CHECK HERE WHETHER A COLLAPSE MECHANISM HAS FORMED. IF YES GET OUT OF THIS DO LOOP GO TO 880 CONTINUE WRITE (6.860) FL(IOV) FORMAT (/. 'APPRENT COLLAPSE AT A LOAD FACTOR OF'. F6.3) GO TO 1070 CONTINUE IF (DRATIO .GT. 5.0-3) GO TO 1040 GO TO 850 CONTINUE  407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464  STRUCTURE IS LINEAR FOR THE UNUSED PART OF THE BENDING MOMENT EQUIVALENT TO REDUCING THE BENDING MOMENT CAPACITY CHECK FOR A POSSIBLE JT.ROTATION MECHANISM 00 910 I • 1. NRJ 00 890 J - 1. NRM IF ( I .EQ. J N L ( J ) ) GO TO 910 IF ( I .EO. J N G ( J ) ) GO TO 910 CONTINUE 890 WRITE (6.900) I FORMAT ('JOINT ROTATION MECHANISM FORMED AT JT NO.'. 14) 900 GO TO 850 CONTINUE 910 MS - NU * NB DO 920 I • t. MS S ( I ) - 0.0000 920 REASSEMBLE THE OVERALL STIFFNESS MATRIX C NB1 - NB - 1 DO 1020 I - 1, NRM DO 1010 J - 1 . 6 IF ( N P ( J . D ) 1010. 1010. 930 J1 - ( J - 1) • (12 - J ) / 2 930 DO 1000 L » J . 6 IF ( N P ( L . D ) 1O00. 1000. 940 IF ( N P ( J . I ) - N P ( L . I ) ) 970. 950. 980 940 IF (L - J ) 960. 970. 960 950 K • ( N P ( L . I ) - 1) • NB1 + N P ( J . I ) 960 N - J1 • L S(K) • S ( K ) + 2.ODOO • SMS(I.N) GO TO 1000 K • ( N P ( J . I ) - 1) • NB1 + N P ( L . I ) 970 GO TO 990 K • ( N P ( L . I ) - 1) • NB1 + N P ( J . I ) 980 N • J1 + L 990 S(K) • S ( K ) + SMS(I.N) CONTINUE 1000 CONTINUE 1010 CONTINUE 1020 CALL SCHECKO. NU. NB. IOIM, SRATIO) DO 1030 I - 1. NU DVL(I) • D B L E ( V L U ) ) 1030 DRATIO - 1.0-16 CALL SOFBANO. DVL. NU. NB. 1. DRATIO. DET. JEXP. 1. KTR) IF (KTR .EQ. 2) GO TO 850 IF (DRATIO) 850. 850. 870 CONTINUE 1040 DO 1050 I • 1. NU F ( I ) » SNGL(DVL(I)) 1050 CALL FORCE(NRM. XM. YM. DM. AV. NP. F. EXTL. EXTG. AREA. E. 1 CRMOM. KL. KG. AXIAL. SHEARL. SHEARG. BML, BMG) 1060 CONTINUE 1070 CONTINUE IF ( I C T .EO. 1) N • JNL(MMAX) IF (ICT .EQ. 2) N • JNG(MMAX) 00 1090 I " 1. NRJ IF ( X ( I ) .EQ. X(N) .AND. Y ( I ) .EQ. Y ( N ) ) GO TO 1080 GO TO 1090 MEM - I 1080 GO TO 1100  C C C  CO  (0  463 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 49S 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522  1090 1100 1110  C  1120  C  C C  1130 1140 1150  1160 1170 1180 1190  1200  CONTINUE I • MEM IF (I . E O . N) GO TO GO TO 1120 NRJ - NRJ • 1 I « NRJ X ( I ) • X(N) Y ( I ) - Y(N) ND( 1.1) • N0( 1..N) N D ( 2 . I ) - ND(2.N) N 0 ( 3 , I ) • ND(3.N)  1110  X(N) - X(N) - 0 . 1 0 Y(N) - Y(N) - 0 . 1 0 AOO A" FICTITIOUS MEMBER WITH VERY SMALL MOM. OF INERTIA NRM • NRM * 1 JNL(NRM) - I JNG(NRM) • N XM(NRM) - X(N) - X ( I ) YM(NRM) - Y(N) - Y ( I ) DM(NRM) • S0RT((XM(NRM))"2 + (YM(NRM) ) **2) EXTL(NRM) - 0. EXTG(NRM) - 0. KL(NRM) • 1 KG(NRM) - 1 NP(1.NRM) > N 0 ( 1 . 1 ) NP(2.NRM) • N 0 ( 2 . I ) NP(3.NRM) - N D ( 3 . I ) NP(4.NRM) • N0(1,N) NP(S.NRM) - ND(2,N) NP(6.NRM) • N0(3.N) AREA(NRM) - AREA(NRM - 1) / 100. CRMOM(NRM) - 0.01 • CRMOM(NRM - 1) AV(NRM) * 0. E(NRM) • E(NRM - 1) MMAX - NRM AT THIS STAGE SHOULD ALSO CHECK WHETHER HALF-WIDTH OF STIFFNESS MATRIX CHANGED MAX - 0 DO 1150 K - 1 . 6 IF (NP(K.MMAX) - MAX) 1140. 1140. 1130 MAX ' NP(K.MMAX) CONTINUE CONTINUE MIN - 1000 DO 1190 K • 1. 6 IF (NP(K.MMAX)) 1180. 1180. 1160 IF (NP(K.MMAX) - MIN) 1170. 1170, 1180 MIN - NP(K.MMAX) CONTINUE CONTINUE NBB • MAX - MIN » 1 IF (NBB . G T . NB) NB • NBB CALL BUILD(NU, NB, XM. YM. OM. NP, AREA. CRMOM, AV. E . G, K L . KG. 1 NRM, S, IDIM. EXTL, EXTG, SMS, MMAX) CALL SCHECMS. NU. NB. IOIM, SRATIO) 00 1200 J • 1, NU OVL(J) • DBLE(VL(J))  523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 S47 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580  DRATIO - 1.0-16 CALL SDFBAN(S. DVL. NU. NB. 1. ORATIO. OET. JEXP. 1, KTR) IF (ORATIO . G T . 5 . D - 3 ) GO TO 1220 WRITE ( 6 . 1 2 1 0 ) FORMAT ("DID NOT WORK") STOP CONTINUE 11 • ND(1.NTOP) DO 1230 K - 1. NU F(K) • SNGL(DVL(K)) SCALE UP THIS SOLN. VECTOR S . T . THE ULTIMATE ROOF DISP. IS UDEFL DI • A B S ( D E F L ( 1 1 ) ) ADISP - UDEFL - D1 FA • AOISP / A B S ( F ( I I ) ) 00 1240 K • 1. NU DEFL(K) - DEFL(K) + FA • F(K) CONTINUE NRM « NRM - 1 CALL CURVD(NRM, CD. NDEF, NP. OEFL. ROTN. HL. YCR, LSENS) CONTINUE PRINT OUT CURV. DUCT. ANO SENSITIVITY INDEX DO 1310 J - 1. NRM DO 1280 I • 1, 2 SKI) • 0. COY • 0. IF ( N D E F ( I . J ) . L T . 0) GO TO 1270 IF (I . E O . 1 ) 0 1 - NP(3,J) IF (I . E O . 2) J1 • N P ( 6 . J ) IF ( N D E F ( I . J ) . E O . 0) GO TO 1260 J2 - N D E F ( I . J ) PCR - ( D E F L ( J I ) - ( D E F L ( J 2 ) - R O T N ( I . J ) ) ) / HL(J) PCR - ABS(PCR) COY - 1. • PCR / YCR(J) SKI) - (COY - C O ( J . I ) ) / 0.. 1 GO TO 1280 CONTINUE PCR - DEFL(J1 ) / H L ( J ) PCR « ABS(PCR) COY - 1. + PCR / YCR(J) SKI) • (CDY - C D ( J . I ) ) / 0.. 1 CONTINUE CONTINUE IF (d . E O . 1) WRITE ( 6 . 1 2 9 0 ) FORMAT (10X. ' C U R V A T U R E D U C T I L I T Y DE  1210 1220  .  C C  1230  1240  C  1250  1260  1270 1280 1290 1  2 3  1300 1310 C C  . / / , 5X. 'MEMBER N O . * ,, 14X. 'LESSER E N D ' . 13X. 'GREATER E N D ' . 13X. 'SENSITIVITY INDEX". /) SENS • SI(1) IF (SENS . L T . S K 2 ) ) SENS • SI(2) WRITE ( 6 , 1 3 0 0 ) J . C O ( J . I ) . C 0 ( J , 2 ) . SENS FORMAT (SX. 15, 17X. F 9 . 3 , 17X, F 9 . 3 , 17X. F9.1) CONTINUE STOP ENO SUBROUTINE  CONTRL(NRJ,  NCONJT,  NCOJT,  NCOOO. NCOIOS.  NRM)  o  581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 60S 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638  C C  DIMENSION TITLE(20) READ ( 5 . 1 0 ) ( T I T L E ( I ) . I - 1 . 2 0 ) READ ( 5 . 3 0 ) NRM. NRJ, NCONJT, NCOJT. NCDOD, NCDIDS WRITE ( 6 , 1 0 ) ( T I T L E ( I ) . 1 - 1 . 2 0 ) WRITE ( 6 , 2 0 ) NRJ, NRM 10 FORMAT (20A4) • 20 FORMAT (/. 'NO. OF J O I N T S - ' . IS. IOX, 'NO. OF MEMBERS-', 30 FORMAT (615) RETURN END  . IS.  /)  C C  c c c c c c c c  c c c c  c  SUBROUTINE 1 2  SETUP(NRM, E . 0. XM. YM, DM. ND. NP. AREA. CRMOM. NRJ. AV. K L . KG, NU. NB. BMCAP, EXTL. EXTG, J N L , JNG, X, Y, YCR, HL, NCONJT. NCDJT. NCDOD, NCDIDS)  SET UP THE FRAME DATA DIMENSION 1 2 DIMENSION 1  KL(NRM), KG(NRM), AREA(NRM), CRMOM(NRM), BMCAP(NRM,3), AV(NRM), N 0 ( 3 , N R J ) . NP(6,NRM), XM(NRM). YM(NRM), EXTL(NRM). EXTG(NRM). OM(NRM). E(NRM), G(NRM) X ( 3 2 S ) . Y ( 3 2 5 ) , JNL(NRM), JNG(NRM). HL(NRM). YCR(NRM), K 0 0 F ( 3 ) . IJ0INT(40)  INITIALIZE COORDINATES DO 10 I - 1. NRJ X ( I ) - 999000. 10 Y ( I ) - 999O00. READ CONTROL NOOE CORDINATES WRITE ( 6 . 2 0 ) 20 FORMAT ( / / . 'CONTROL NODE COORDINATES'. / / / . ' N O D E ' . 6X. 1 'X-COORO'. 6X, 'Y-COORD'. / ) DO 50 I • 1 . NCONJT READ ( 5 , 3 0 ) I J T . X ( I J T ) , Y ( I J T ) 30 FORMAT (15. 2 F t O . 1 ) WRITE ( 6 . 4 0 ) I J T . X ( I J T ) , Y ( I J T ) 40 FORMAT ( 1 5 . 2F13.3) SO CONTINUE NODE GENERATION COMMANOS WRITE ( 6 . 6 0 ) 60 FORMAT ( / / / ' NODE GENERATION COMMANDS'/) IF (NCOJT . N E . 0) GO TO 80 WRITE ( 6 . 7 0 ) 70 FORMAT ( / / , 'NONE') GO TO 130 80 WRITE ( 6 , 9 0 ) 90 FORMAT ( / 2 X , ' F I R S T ' . 4X. ' L A S T ' . 4X, ' N O . O F ' . 4X. ' N O D E ' . / . 2X. 1 ' N O D E ' . 4X. ' N O D E ' . 4X. 'NODES'. 5X. ' O I F F ' . / ) DO 120 1 - 1 . NCDJT  639 640 64 1 642 643 644 645 646 647 648 649 650 651 •JS2 653 654 655 656 657 658 659 660 661 662 663 664 66S 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696  READ ( S . 1 0 0 ) I J T . L J T . N J T . KOIF FORMAT (4IS) IF (KDIF . E O . 0) KOIF • 1 WRITE (6.110) I J T . L J T . N J T . KDIF 110 FORMAT (16. 318) CALL G E N K X . Y . I J T . L J T . N J T . KOIF) 120 CONTINUE GENERATE UNSPECIFIEO JOINT COORDINATES 130 I • 1 140 I • I + 1 IF (I . G T . NRJ) GO TO 160 IF ( X ( I ) . N E . 9 9 9 0 0 0 . ) GO TO 140 IJT • I - 1 LJT - IJT 150 LJT - LJT + 1 IF (LJT . G T . NRJ) GO TO 160 IF ( X ( L J T ) . E Q . 9 9 9 0 0 0 . ) GO TO 150 NJT - LJT - IJT - 1 CALL G E N K X . Y. I J T . L J T . N J T . 1) I - LJT GO TO 140 160 CONTINUE ASSIGNING D . O . F . TO THE NODES DO 170 1 - 1 . NRJ DO 170 J - 1, 3 170 N D ( J . I ) • 1 ZERO DISPLACEMENTS WRITE ( 6 , 1 8 0 ) 180 FORMAT ( / . 'ZERO DISPLACEMENT COMMANDS'. / / ) IF (NCOOD . N E . 0) GO TO 190 WRITE ( 6 . 7 0 ) GO TO 270 190 WRITE (6,200) 2O0 FORMAT ( / . ' F I R S T ' . 6X. ' X ' . 6 X . ' Y ' . 4X. ' R O T N ' . 4X. ' L A S T ' , 4X 1 ' N O O E ' , / . ' N O D E ' , 7X, ' D O F ' . 4X, ' D O F ' . 5X, ' D O F ' , 4X. 2 'NODE'. 4X. ' D I F F ' . /) 00 260 I • 1. NCDOD READ (5.210) I J T . ( K D O F ( J ) . d - 1 . 3 ) . L J T . KDIF 210 FORMAT (615) WRITE ( 6 , 2 2 0 ) I J T , ( K D O F ( J ) . J - 1 ,3 ) , L J T . KDIF 220 FORMAT (13. 518) DO 230 J • 1. 3 230 N D ( J . I J T ) - KDOF(J) IF ( L J T .EQ. 0 ) GO TO 260 IF (KDIF . E Q . 0) KOIF - 1 NJT - (LJT - I J T ) / KDIF DO 250 II - 1. NJT IJT » IJT + KDIF DO 240 J • 1. 3 240 N D ( J . I J T ) « KDOF(J) 250 CONTINUE 260 CONTINUE IDENTICAL DISPLACEMENT 270 CONTINUE WRITE ( 6 . 2 8 0 ) 280 FORMAT ( / / / . 'EQUAL DISPLACEMENT COMMANDS ' . / ) IF (NCDIOS . N E . 0 ) GO TO 290 WRITE ( 6 . 7 0 ) 100  C  C  C  C  697 698 699 700 701 702 703 704 705 706 707 708 709 710 7t 1 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754  290 300  310 320  C  330 340 350  360 370 380 390 400 C  C  c c c c  410  GO TO 350 WRITE (6.300) FORMAT (//, * O I S P ' . 4X. ' N O . O F " . / . ' C O O E ' . 4X. 'NODES'. 6X. I ' L I S T OF NODES'. / ) 00 340 1 - 1 . NCDIDS REAO ( 5 . 3 1 0 ) MKDOF. N J T . ( I J O I N T ( I U ) . I U - 1 . N J T ) FORMAT (215. 1415) WRITE (6.320.) MKOOF, N J T . (I JOINT ( I U ) . IU-1 . NJT ) FORMAT (13, 18. 6X, 1415) II - IJOINT(I) 00 330 IM - 2, NJT IK • IJOINT(IM) NO(MKDOF.IK) - - I I CONTINUE TO SET UP ND ARRAY NU - 0 WRITE ( 6 . 4 0 0 ) DO 390 I - 1. NRJ DO 380 J • 1. 3 IF ( N D ( J . I ) . N E . 1) GO TO 360 NU - NU + 1 N O ( J . I ) - NU GO TO 380 IF ( N D ( J . I ) . N E . 0) GO TO 370 NO(J.I) - 0 GO TO 380 II - - N D ( J . I ) NO(J.I) - ND(J.II) CONTINUE WRITE ( 6 . 4 1 0 ) I . X ( I ) . Y ( I ) . ( N D ( J , I ) . J - 1 , 3 ) CONTINUE FORMAT (/. 3X. ' J N ' . 5X. ' X - C O O R D ' . SX. 'Y-COORO'. 5X, ' N O X ' . 5X. 1 ' N D Y ' , 5X. ' N O R ' , / ) FORMAT (14, 2 F 1 3 . 2 , 16, 5X. 14. 5X. 14) WRITE WRITE WRITE  READ IN MEMBER DATA AND COMPUTE THE HALF BANDWIDTH (NB) HALF BANDWIDTH-MAX DEGREE OF FREEDOM-MIN DEGREE OF FREEOOM +1 NB - 0 00 1 2  c c  (6.590) (6,600) (6.610)  580 MBR - 1. NRM REAO ( 5 . 6 2 0 ) MN, JNL(MBR), JNG(MBR), KL(MBR). KG(MBR), E(MBR), G(MBR), AREA(MBR), CRMOM(MBR), DEPTH, BMCAP(MBR,1), EXTL(MBR), EXTG(MBR), AV(MBR)  COMPUTE MEMBER LENGTH (OM)-LENGTH BETWEEN JOINTS-RIGID EXTENSIONS JL - JNL(MBR) JG - JNG(MBR) XM(MBR) • X(JG) - X ( J L ) YM(MBR) - Y ( J G ) - Y ( J L ) DM(MBR) • S0RT((XM(MBR))--2 + (YM(MBR))**2) EXTSUM • EXTL(MBR) + EXTG(MBR)  755 756 757 758 759 760 761 762 763 764 765 766 767 7.68 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812  C  C C C C  XM(MBR) - XM(MBR) • ( 1 . 0 - EXTSUM/OM(MBR)) YM(MBR) • YM(MBR) • ( 1 . 0 - EXTSUM/OM(MBR)) RESET NEGATIVE VALUES OF ZERO TO ZERO IF (YM(MBR) . G T . - 0.01 .AND. YM(MBR) . L T . 0 . 0 1 ) IF (XM(M8R) . G T . - 0.01 .AND. XM(MBR) . L T . 0 . 0 1 ) DM(MBR) - DM(MBR ) - EXTSUM  C C C C  • 0.0 • 0.0  CHECK FOR NEGATIVE LENGTHS OF MEMBER (PROBABLY CAUSED BY INCORRECT USE OF MEMBER EXTENSIONS)  420 C  YM(MBR) XM(MBR)  430  1  IF (DM(MBR) . G T . 0 . 0 ) GO TO 430 WRITE ( 6 . 4 2 0 ) MBR FORMAT (' ' . / / / ' P R O G R A M HALTED:ZERO OR -VE LENGTH FOR MEMBER', 16) STOP CONTINUE YLEN •  YM(MBR)  PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON VERTICAL MEMBERS. IF (EXTSUM . N E . 0 . 0 .AND. YLEN . G T . 0 . 2 ) WRITE ( 6 . 4 4 0 ) I 440 FORMAT (' ' . 'ERROR-HAVE END EXTENSIONS ON NON-HORIZONTAL 1 MEMBER N O . ' . 13) C PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON C A NON F I X - F I X TYPE MEMBER KLSUM > KL(MBR) + KG(MBR) IF (EXTSUM . N E . 0 . 0 .AND. KLSUM . N E . 2) WRITE ( 6 . 4 5 0 ) MBR 450 FORMAT (' ' . 'ERROR-HAVE RIGID EXTENSIONS ON HINGED MEMBER'. 14) C C C ASSIGN MEMBER DEGREES OF FREEDOM NP(I.MBR) - N O O . J L ) NP(2.MBR) - N D ( 2 , J L ) NPO.MBR) - N D ( 3 . J L ) NP(4,MBR) - N D ( 1 . J G ) NP(S.MBR) - N D ( 2 , J G ) NP(6,MBR) - N D ( 3 , J G ) C DETERMINE THE HIGHEST DEGREE OF FREEDOM FOR EACH MEMBER STORING C THE RESULT IN 'MAX' MAX - O C DO 480 K • 1, 6 IF (NP(K.MBR) - MAX) 470. 4 7 0 . 460 460 MAX - NP(K.MBR) 470 CONTINUE 480 ' CONTINUE C C DETERMINE THE MINIMUM OEGREE OF FREEDOM FOR EACH MEMBER.NOTE THAT C FOR STRUCTURES WITH GREATER THAN 330 JOINTS INITIAL VALUE OF MIN C WILL HAVE TO BE INCREASEO FROM ITS PRESTENT POINT OF 1000. C C WILL HAVE TO BE INCREASED FROM ITS PRESTENT POINT OF tOOO. C MIN • 1000 C 00 520 K « 1. 6  M  813 814 B15 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870  C  490 500 510 520  530 540  550  560  C C  570  IF (NP(K.MBR)) 510. 510. 490 IF (NP(K.MBR) - MIN) 500. 510. 510 MIN • NP(K.MBR) CONTINUE CONTINUE NBB • MAX - MIN + 1 IF (NBB - NB) 540. 540. 530 NB • NBB CONTINUE HL(MBR) - 0 . IF (E(M8R) . E O . 0 . ) E(MBR) • E(MBR - 1) IF (MBR . E O . 1) GO TO 550 IF (G(MBR) . E O . O . ) G(MBR) - G(MBR - 1) IF (AV(MBR) . E O . 0 . ) AV(MBR) - AV(MBR - 1) IF (HL(MBR - 1) . E O . 0 . ) GO TO 550 HL(MBR) • HL(MBR - 1) IF (HL(MBR) . E O . 0 . ) HL(MBR) > HI(MBR - 1) CONTINUE IF (AREA(MBR) . E Q . 0 . ) AREA(MBR) - AREA(MBR - 1) IF (CRMOM(MBR) . E Q . 0 . ) CRMOM(MBR) • CRMOM(MBR - 1) IF (MBR . E Q . 1) HL(MBR) « 0 . 5 • DEPTH YCR(MBR) • BMCAP(MBR,1) / (E(MBR )*CRMOM(MBR)) IF (YCR(MBR) . N E . O . ) GO TO 560 MR • MBR - 1 BMCAP(MBR.I) • BMCAP(MR.1) YCR(MBR) - BMCAP(MBR.I) / (E(MBR)* CRMOM(MBR)) CONTINUE DO 570 1 - 1 , NRM IF ( H L ( I ) . E O . O . ) H L ( I ) • 0 . 0 5 • DM(MBR) CONTINUE PRINT MEM8ER DATA  WRITE ( 6 , 6 3 0 ) MBR, JNL(MBR), JNG(MBR), EXTL(MBR), DM(MBR), 1 EXTG(MBR), XM(MBR), YM(MBR), AREA(MBR), CRMOM(MBR). AV(MBR). 2 BMCAP(MBR,1), KL(MBR). KG(MBR). E(MBR) 580 CONTINUE C PRINT THE NO. OF DEGREES OF FREEDOM AND THE HALF BANDWIDTH C WRITE (6.640) NU WRITE (6.650) NB C RETURN 590 FORMAT (//, 'MEMBER DATA') 600 FORMAT ( / ' MN JNL JNG EXTL LENGTH EXTG XM YM 1 2X, 'AREA MOM OF I A V . 7X. 'MOMENT'. 3X, ' K L ' , 2 1X. ' K G ' . 5X. ' E ' ) 610 FORMAT (85X. 'CAPACITY') 620 FORMAT (515. 2 F 1 0 . 1 , F 8 . 2 . F 1 5 . 1 . F 6 . 1 . F 1 0 . 1 . 3FB.2) 630 FORMAT (' ' , 13. 214, F 7 . 1 . F 9 . 2 . F 7 . 1 , 2 F 9 . 2 , F 8 . 2 . F 1 5 . 3 . FB. 1 F 1 0 . 1 . 213. F10.1) 640 FORMAT ( ' - ' . 'NO.OF DEGREES OF FREEOOM OF STRUCTURE • ' , 15) 650 FORMAT ( / ' HALF BANDWIDTH OF STIFFNESS MATRIX • ' . 15) END C C C SUBROUTINE BUILOtNU, NB, XM. YM, DM, NP. AREA, CRMOM. AV, E , G,  871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928  1  C  K L . K G . NRM, S.  IDIM.  EXTL. EXTG, SMS. MMAX)  C C  c c c c c c c c c c  c c  c  THIS SUBROUTINE WORKS IN DOUBLE PRECISION THIS SUBROUTINE CALCULATES THE STIFFNESS MATRIX OF EACH MEMBER AND ADDS IT INTO THE STRUCTURE STIFFNESS MATRIX. THE FINAL STIFFNESS MATRIX S IS RETURNED. THIS SUBROUTINE IS SIMILAR TO ONE THAT WOULD 8E USED IN NORMAL FRAME ANALYSIS. IDIM IS THE DIMENSIONING SIZE OF THE STRUCTURE STIFFNESS MATRIX INTERNAL FOOT UNITS FOR STIFFNESS MATRIX REAL'8 S M ( 2 I ) . S ( I D I M ) , SMS(2O0.21) DIMENSION XM(NRM). YM(NRM). DM(NRM). NP(6,NRM). AREA(NRM). 1 CRMOM(NRM). AV(NRM). KL(NRM). KG(NRM). EXTL(NRM). 2 EXTG(NRM). E(NRM). G(NRM) REAL'S R F . GMOD. CMOMI. F . H REAL'S LONE. LONEX. LONEY. LTWO. LTWOX, LTWOY, AVI REAL'S YMI, DMI. DM2. XM2. YM2. XMI. AREAI, EMOD. XM2F, YM2F, 1 XMYMF REAL'8 D8LE ZERO STRUCTURE STIFFNESS MATRIX INK • NU • NB DO 10 I - 1, INK S ( I ) - O.ODOO 10 CONTINUE N1 N2 IF IF  c c c c  8EGIN MEMBER LOOP ENTER HERE TO REBUILD MEMBER STIFFNESS MATRIX FOR MEMBER MMAX WHICH HAS JUST YIELDED & REASSEMBLE S T R . S T I F F . MATRIX DO 120 I " N I , N2  c c c c c c  • 1 • NRM (MMAX . N E . 0) N1 » MMAX (MMAX . N E . 0) N2 * MMAX  ZERO MEMBER STIFFNESS NATRIX  20  DO 20 J • 1, 21 SM(J) » O.ODOO CONTINUE  ASSIGN MEMBER PROPERTIES TO DOUBLE PRECESION CONVERT E TO DOUBLE PRECISION EMOD - D B L E ( E ( I ) ) GMOD - D B L E ( G ( I ) ) LONE • O B L E ( E X T L ( I ) ) LTWO " D B L E ( E X T G ( I ) ) YMI • D8LE(YM(I)) DMI - DBLE(OM(I)) XMI - DBLE(XM(I)) AREAI - DBLE(AREA(I)) CMOMI • DBLE(CRMOM(I)) AVI • OBLE(AV(I ) )  VARIABLES  u  929 930 931 932 933 934 935 936 937 938 939 940 94 1 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986  C  C  C C C  C C  C C C C C C  DM2 • DMI • DMI XM2 - XMI • XMI YM2 • YMI • YMI XMYM - XMI • YMI F • AREAI • EMOD / (DMI*DM2) H - O.ODOO SHEAR DEFLECTIONS ARE IGNORED WHENEVER G OR AV IS ZERO. IF ( A V ( I ) . E O . 0 . 0 .OR. G ( I ) . E O . 0 . ) GO TO 30 H • 12.ODOO • EMOD * CMOMI / (AVI"GMOD*DM2) 30 XM2F • XM2 • F YM2F - YM2 • F XMYMF » XMYM • F FILL  SECTION OF MEMBER STIFFNESS MATRIX  SM(1) - XM2F SM(2) - XMYMF SM(4) - -XM2F SM(S) - -XMYMF SM(7) - YM2F SM(9) • -XMYMF SM(10) - -YM2F SM(16) • XM2F SM(17) • XMYMF SM(19) • YM2F IF ( K L ( I ) + KG(I) -  1)  100,  40,  50  40  F • 3.ODOO * EMOD * 'CMOMI / (0M2 *DM2 *DMI*(1.ODOO+H/4.1 GO TO 60 50 F » 12.ODOO * EMOD • CMOMI / (DM2*DM2*DMI•( 1.ODOO+H)) RF IS A FACTOR COMMON TO THE ENTIRE MATRIX FOR ADDITION OF DUE TO RIGIO BEAM END EXTENSIONS. RF - 12.ODOO • EMOD • CMOMI / (DM2-DM2) / (1.D0+H) FILL IN TERMS WHICH ARE COMMON TO PIN-FIX.FIX-PIN,ANO FIX-FIX MEMBERS  60  C  IN PIN-PIN  LONEY LONEX LTWOY LTWOX XM2F • YM2F . XMYMF DM2F •  • • "  LONE LONE LTWO LTWO XM2 * YM2 • • XMYM DM2 •  SM(1) • SM(2) > SM(4) • SM(S) > SM(7) • SM(9) • SM(10) • SM(16) • SM(17) • SM(19) •  • • • • F F • F  YMI XMI YMI XMI  • • • •  RF RF RF RF  F  SM(1) • SM(2) SM(4) SM(5) • SM(7) + SM(9) • SM(10) SM(16) SM(17) SM(19)  YM2F XMYMF YM2F XMYMF XM2F XMYMF - XM2F • YM2F - XMYMF • XM2F  987 9B8 989 990 891 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044  C C C  C C C  IF ( K L ( I ) FILL 70  C  C C C  80.  90  IN REMAINING PIN-FIX TERMS  SM(6) • -YMI • DM2F SM(11) " XMI • DM2F SM(18) - -SM(6) SM(20) - -SM(11) SM(21) • DM2 • DM2F GO TO 100 FILL  80  - K G ( I ) ) 70.  IN REMAINING F I X - F I X TERMS  SM(3) • -YMI • DM2F * 0 . 5 0 0 0 SM(6) - SM(3) SM(8) • XMI • 0M2F * 0.5D00 SM(11) - SM(8) SM(12) « DM2 * DM2F * (4.ODOO+H) / 12.ODOO SM(13) • -SM(3) SM(14) • -SM(8) SM(15) • DM2 • DM2F • (2.0D00-H) / 12.ODOO SM(1B) - -SM(6) SM(20) • -SM(11) SM(21) - SM(12) ADD IN TERMS FOR RIGID END EXTENSIONS. SM(3) - SM(3) - (LONEY) SM(6) ' S M ( 6 ) - (LTWOY) SM(8) " SM(8) + LONEX SM(11) • SM(11) + LTWOX SM(12) • SM(12) + (LONE'DMI•(DMI + LONE)*RF) SM(13) - SM(13) • LONEY SM(14) • SM(14) - LONEX SM(15) - SM(15) + ((LONE*LTWO*OMI) • (DM2*(LONE 1 • RF SM(18) SM(20) SM(21) GO TO FILL  + LJWO)/2.0000))  • SM(18) + LTWOY • SM(20) - LTWOX - SM(21) + (DM2*LTW0 + (DMI * (LTWO* LTWO) ) )• • RF 100  IN REMAINING F I X - P I N  TERMS  90  SM(3) • -YMI • 0M2F SM(8) - XMI • DM2F SM(12) - DM2 • 0M2F SM(13) • -SM(3) SM(14) • -SM(8) 100 CONTINUE DO 110 J - 1. 21 110 S M S ( I . J ) • SM(J) 120 CONTINUE C ADO THE MEMBER STIFFNESS MATRIX SMS INTO THE STRUCTURE C STIFFNESS MATRIX S. C NB1 • NB - 1 DO 220 I - 1, NRM DO 210 J • 1, 6 IF ( N P ( J . I ) ) 210. 210. 130  •t.  1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067  C  130  140 150 160  170 180 190  C C C  1068 1069  C  1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102  C C C C C C  c c c c C C  c c c c c  c c c c c  200 210 220  01  •  (d  -  1)  •  (12  - d)  /  2  DO 200 I • J . 6 IF ( N P ( L . D ) 200. 200. 140 IF ( N P ( d . I ) - N P ( L . I ) ) 170. 150. 180 IF (L - d) 160, 170. 160 K • ( N P ( L . I ) - 1) • NB1 + N P ( d . I ) N • d1 • L S(K) - S(K) + 2.0D00 * SMS(I.N) GO TO 200 K - ( N P ( d . I ) - 1) • NB1 • N P ( L . I ) GO TO 190 K - ( N P ( L . I ) - 1) • NB1 + N P ( d . I ) N • di • I S(K) • S(K) + SMS(I.N) CONTINUE CONTINUE CONTINUE RETURN END SUBROUTINE  SOFBAN(A.  B.  N, M. L T ,  RATIO. DET. NCN. NSCALE.  KTR)  THIS ROUTINE SOLVES SYSTEM OF EONS. AX-B WHERE A IS +TVE DEFINITE SYMMETRIC BAND MATRIX. BY CHOLESKY'S METHOD. LOWER HALF BAND ONLY (INCLUDING THE DIAGONAL) OF A IS STORED COLUMN BY COLUMN IN A 1 DIMENSIONAL ARRAY. SOLUTIONS X ARE RETURNED IN ARRAY B. OPTIONAL SCALING OF MATRIX A IS AVAILABLE N - ORDER OF MATRIX A . M - LENGTH OF LOWER HALF BAND. DETERMINANT OF A • D E T ' ( 1 0 " N C N ) . 1 . E - 15< |DET |< 1 .E15 LT-1 IF ONLY 1 B VECTOR OR IF FIRST OF SEVERAL. LT NOT • 1 FOR SUBSEQUENT B VECTORS. RATIO • SMALLEST RATIO OF 2 ELEMENTS ON MAIN DIAGONAL OF TRANSFORMED A > 1 . E - 7 . NSCALE-0 IF SCALING NOT REQUIRED. KTR '1 IF THE SYSTEM IS POSITIVE DEFINITE •2 IF THE SYSTEM IS NOT POSITIVE DEFINITE(MECHANISM FORMED) IMPLICIT REAL*8(A - H.O - Z) DIMENSION A ( 1 ) . B(1) REAL'S MULT(20000) IF (M . E O . 1) GO TO 80 MM • M - 1 NM • N • M NM1 • NM - MM KTR • 1 DUMMY STATEMENT INSERTED FOR COMPATIBILITY WITH ASSEMBLER VERSION I F ( L T . L E . O ) RETURN IF (LT . N E . 1) GO TO 340 IF (NSCALE' . E O . 0) GO TO 60 DO 10 I - 1. N MATRIX SCALED BY DIVIDING  ROW I ANO COLUMN I BY S O R T ( A d . I ) ) .  SUCH  1103 I 104 .1105 1106 1107 1108 1109 I I 10 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1 125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1 136 1 137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 • 1156 1157 1158 1159 1160  C  C  C C C C C C  THAT DIAGONAL ELEMENTS A ( I . I )  ARE  1.  II - (I - 1) • M • 1 IF ( A ( I I ) . L E . 0 . 0 ) GO TO 120 10 MULT(I) - 1.0 / DSQRT(A(II)) KK » 1 DO 50 I • 1. N II • ( I - 1 ) • M + 1 dEND • II * MM IMN • (I - 1) + M - N IF (IMN . G T . O) dENO - dEND - IMN DO 20 d • I I . dENO A(d) • A(d) • MULT(I) 20 CONTINUE DO 30 d - KK. 11, MM 30 A(d) - A(d) • MULT(I) IF (KK . G E . M) GO TO 40 KK * KK • 1 GO TO 50 40 KK - KK • M 50 CONTINUE 60 MP • M + 1 TRANSFORMATION OF A . A IS TRANSFORMED INTO A LOWER TRIANGULAR MATRIX L SUCH THAT A - L . L T (LT'TRANSPOSE OF L . ) . IF Y ' L T . X THEN L . Y ' B . ERROR RETURN TAKEN IF RATIO<1.E-7 KK » 2 NCN « O DET - O. FAC - RATIO IF (A(1) . G T . O . ) GO TO 70 NROW » 1 RATIO - A( 1 ) GO TO 310 70 OET - A(1) A(1) • 1. / DSORT(A(1)) BIGL • A(1) SML - A(1) A(2) - A(2) • A(1) TEMP - A(MP) - A(2) • A(2) IF (TEMP . L T . 0 . 0 ) RATIO ' TEMP IF (TEMP . E Q . 0 . 0 ) RATIO - 0 . 0 IF (TEMP . G T . 0 . 0 ) GO TO 140 NROW - 2 GO TO 310 80 OET 1.D0 NCN - O DO 110 I • 1. N DET - DET • A ( I ) IF ( A ( I ) .EQ. 0.0) GO TO 120 IF (DET . G T . 1.E-1S) GO TO 90 DET - OET • I . E ' 1 5 NCN - NCN - 15 GO TO 100 90 IF (OET . L T . 1.E-M5) GO TO 100 DET - DET • 1.E-15  Ul  1 161 1162 1 163 1164 1 165 1166 1167 1168 1169 1 170 1171 1 172 1 173 1174 1175 1176 1 177 1 178 1179 1 180 1181 1182 1183 1 184 1 185 1186 1187 1 188 1 1B9 1 190 1 191 1 192 1 193 1 194 1 195 1 196 1 197 1 198 1 199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218  NCN - NCN + 15 100 CONTINUE 110 B ( I ) - B ( I ) / A l l ) RETURN 120 RATIO • A ( I ) 130 NROW - I GO TO 310 140 A(MP) - 1.0 / OSORT(TEMP) OET • DET • TEMP IF (A(MP) . G T . BIGL) BIGL • A(MP) IF (A(MP) . L T . SML) SML • A(MP) IF (N . E O . 2) GO TO 290 MP • MP + M DO 280 J - MP. NM1. M JP • J - MM MZC - 0 IF (KK . G E . M) GO TO 150 KK • KK + 1 II - 1 dC • 1 GO TO 160 150 KK • KK + M II • KK - MM dC • KK - MM DO 180 I • KK. dP. MM 160 IF ( A ( I ) . E O . 0 . ) GO TO 170 GO TO 190 170 JC • JC + M 180 MZC • MZC + 1 ASUM1 - O.DO GO TO 240 190 MMZC • MM • MZC II • II + MZC KM • KK • MMZC A(KM) - A(KM) » A(JC) IF (KM . G E . JP) GO TO 220 KO * KM **• MM DO 210 I - K d . J P , MM ASUM2 • 0 . 0 0 IM - I - MM 1 1 - 1 1 * 1 Kl - II • MMZC DO 200 K • KM, IM. MM ASUM2 • ASUM2 + A ( K I ) • A(K) 200 Kl - K l • MM 210 A ( I ) - ( A ( I ) - ASUM2) • A ( K I ) 220 CONTINUE ASUM1 • 0 . 0 0 ' DO 230 K » KM. dP, MM 230 ASUM1 ' ASUM1 + A(K) * A(K) 240 S • A(d) - ASUM1 IF (S . L T . 0 . ) RATIO • S IF (S . E O . 0 . ) RATIO • 0 . IF (S . G T . 0 . ) GO TO 250 NROW • (d + MM) / M GO TO 310 250 A(J) - 1. / DSQRT(S) DET - DET • S  1219 1220 1221 1222 1223 1224 '•225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276  260 270 280 290 300 310 320  ^  C C C C C C  330 340  IF (OET . G T . 1.E-15) GO TO 260 DET • OET • 1 .E-MS NCN • NCN - 15 GO TO 270 IF (DET . L T . I.E+15) GO TO 270 DET • OET • I . E - 1 5 NCN - NCN + 15 CONTINUE IF ( A ( J ) . G T . BIGL) BIGL • A ( J ) IF ( A ( J ) . L T . SML) SML - A ( J ) CONTINUE IF (SML . L E . FAC-BIGL) GO TO 300 GO TO 330 RATIO - 0 . RETURN WRITE ( 6 , 3 2 0 ) NROW FORMAT ( ' 0 * * " S Y S T E M IS NOT POSITIVE D E F I N I T E ' . 1 ' ERROR CONDITION OCCURRED IN ROW'. 14) KTR • 2 RETURN RATIO - SML / BIGL CALL DSBAND(A. MULT. B. N . M. NSCALE) RETURN END SUBROUTINE DS8AND(A, MULT. B . N . M. NSCALE) IMPLICIT REAL*8(A - H.O - Z) DIMENSION A ( 1 ) . B ( 1 ) REAL'S MULT(1) MM - M - 1 NM • N • M NM1 • NM - MM  THE FOLLOWING STATEMENTS SOLVE FOR L . Y - B BY A FORWARDS HENCE FDR X FROM LT.X=Y BY A BACKWARDS SUBSTITUTION. IF SCALING OPTION USEO. B IS SCALEO AND NORMALISED BEFORE SUBSTITUTION BEGINS. 10 SUM " O . D O IF (NSCALE . E O . 0) GO TO 40 DO 20 I - 1. N B ( I ) • B ( I ) • MULT(I) SUM - SUM + B ( I ) • B ( I ) 20 CONTINUE ELENB • DSORT(SUM) DO 30 I * 1, N 30 B ( I ) - B ( I ) / ELENB 40 B ( 1 ) • B(1) * A ( 1 ) KK • 1 Kl - 1 J - 1 DO 80 L • 2. N BSUM1 - O.DO LM - L - 1 J - J +M IF (KK . G E . M) GO TO 50 KK - KK + 1 GO TO 60 50 KK • KK • M  cn  1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 130O 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 131 1 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334  60  70  KI - KI • <JK • KK DO 70 K BSUM1 • JK - JK CONTINUE  1 K I . LM BSUM1 + A(JK) • MM  •  B(K)  80 BCD • (8(1.) - BSUM 1) • A(d) 90 B(N) • B(N) «. A(NM 1 ) NMM - NM1 NN > N - 1 NO - N 00 1 10 L • 1 , NN BSUM2 • O.DO NL - N - I NL1 • N - L + 1 NMM • NMM - M NJ1 > NMM IF (L . G E . M) NO • NO - 1 DO 100 K • NL1. ND Ndl • NJ1 + 1 BSUM2 - BSUM2 + A(NJ1) * B(K) 100 CONTINUE 110 B(NL) - (B(NL) - BSUM2) • A(NMM) IF (NSCALE . E O . 0) GO TO 130 DO- 120 I • 1 . N 120 8(1) • B(I) • ELENB • MULT(I) 130 RETURN END  '  C  c  c c c c c c c c c c c c c c c c C  c c c c  SUBROUTINE  SCHECK(S.  NU. NB.  IOIM,  SRATIO)  THIS SUBROUTINE CHECKS THAT ALL DIAGONAL STIFFNESS MATRIX ELEMENTS ARE POSITIVE NUMBERS GREATER THAN ZERO. IT ALSO DETERMINE! THE RATIO BETWEEN THE LARGEST AND SMALLEST MEMBERS ON THE DIAGONAL THIS WILL GIVE SOME INDICATION AS TO THE CONDITIONING OF THE STIFFNESS MATRIX MATRIX REAL'8 S(IOIM) REAL'S SMIN. SMAX, DIAG, RATIO THE STIFFNESS MATRIX IS STORED AS A COLUMN VECTOR. ONLY THE THE LOWER TRIANGLE ELEMENTS BEING STOREO (BY COLUMNS) S O ) IS ON THE DIAGONAL AS IS S( 1+NB) . S( 1 + 2'NB ) , ETC . NB IS THE HALF BANDWIDTH OF THE STIFFNESS MATRIX INITIALIZE  THE LARGEST ANO SMALLEST VALUES OF 01AGONAL (SMAX,SMIN)  DO 50 IDOF - 1. NU IELEM • ((IOOF - 1 ) » N B ) • 1 DIAG • S(IELEM) COMPUTE IF DIAGONAL ELEMENT IS ZERO OR NEGATIVE IF (DIAG . N E . 0.0000) GO TO 20  1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392  10 C  C  20  CONTINUE IF (DIAG . G T . 0 . 0 ) GO TO 40 WRITE ( 6 . 3 0 ) IOOF 30 FORMAT (///* PROGRAM HALTED-NEGATIVE ELEMENT ON DIAGONAL OF 1 'STIFFNESS MATRIX'. / / ' EXAMINE DEGREE OF FREEDOM'. STOP 40 CONTINUE 50 CONTINUE  FORCE (NRM. XM, YM. OM. AV. NP, F . EXTL. EXTG, AREA. E . G . CRMOM. K L . KG, AXIAL. SHEARL, SHEARG. BML. BMG, NML. MML, FEM) * • * * *••• DIMENSION XM(NRM), YM(NRM), DM(NRM), AV(NRM), NP(6,NRM). F ( 5 0 O ) . 1 0(6). EXTL(NRM), EXTG(NRM). KL(NRM). KG(NRM), AREA(NRM). 2 CRMOM(NRM). E(NRM) , G(NRM). MMLOOO). FEM( 100.4) DIMENSION AXIAL(NRM), SHEAR(250). BML(NRM), BMG(NRM), SHEARL(NRM), 1 SHEARG(NRM)  1 2  C  C  10 20 30  40  50  C  C  '. 14)  RETURN END  C  C C  WRITE ( 6 , 1 0 ) IDOF FORMAT ( / / / ' PROGRAM HALTED-A ZERO IS ON THE DIAGONAL OF STIFFNE 1SSMATRIX', / / ' E X A M I N E DEGREE OF FREEDOM ' , 14) STOP  60  SUBROUTINE  DO 110 I « 1. NRM XL " XM(I) YL - YM(I) DL - OM(I) AV1 • A V ( I ) DO 30 MEMDOF - 1 . 6 . N1 • NP(MEMDOF,I) IF (N1) 20. 20. 10 O(MEMDOF) - F(N1) GO TO 30 D(MEMDOF) • O. CONTINUE MODIFY END DISP FOR HORZ MEMBERSWITH END EXT.(VALIO FOR HORZ. MEMBERS ONLY) N3 • N P ( 3 . I ) IF (N3 . E O . O) GO TO 40 D(2) • D(2) + ( F ( N 3 ) ) * E X T L ( I ) CONTINUE N6 • N P ( 6 . I ) IF (N6 . E O . 0) GO TO 50 D(5) • D(5) - ( F ( N 6 ) ) * EXTG(I) CONTINUE AXIAL(I) - ( A R E A ( I ) * E ( I ) / 0 L * * 2 ) • (D(4)'XL + 0 ( S ) « Y L - D(1)'XL 1 D(2)«YL) EISI • CRMOM(I) * E O ) INCLUDE SHEAR D E F L . GFACT-0 MEANS NO SHEAR DEFL. GFACT • 0. IF (AVI . E O . 0 . 0 .OR. GO) . EO. 0 . 0 ) GO TO 60 GFACT • 12.0 • EISI / ( A V 1 - G ( I ) - D L - D L ) CONTINUE ASSIGN OISP TO RESPECTIVE D . O . F .  -  1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 141 1 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450  CHECK FOR PIN-PIN MEM8ERS IF ( K L ( I ) . E O . 0 .AND. KG(I) . E O . 0) GO TO 90 OELT • <<D(S) - D ( 2 ) ) ' X L + (0(1) - D ( 4 ) ) « Y L ) / DL BML(I) • ( 2 . 0 ' E I S I / ( D L ' ( 1 . 0 + GFACT))) * <(3.0*DELT/DL) - ( 0 ( 6 ) ' 1 (1.0 - GFACT/2.0)) - ( 2 . 0 * D ( 3 ) ' ( 1 . 0 + GFACT/4.0))) BMG(I) - - ( 2 . 0 ' E I S I / ( D L ' ( 1 . 0 • GFACT))) • ( ( 3 . 0 * D E L T / D L ) (0(3) 1 '(1.0 - GFACT/2.0)) - ( 2 . 0 ' 0 ( 6 ) ' ( 1 . 0 • GFACT/4.0))) SHEAR(I) - ( 6 . 0 ' E I S I / ( 0 L ' D D ) • ( ( 0 ( 3 ) + 0(6) - ( 2 . O * D E L T / 0 L ) ) / ( 1 1.0 • GFACT)) IF ( K L ( I ) - K G ( I ) ) 70. 100. 80 C PIN-FIX MEMBER FORCES 70 BMG(I) - BMG(I) + BML(I) • ( 1 . 0 - GFACT/2.0) / ( 2 . 0 * ( 1 . 0 • 1 GFACT/4.0)) SHEAR(I) - SHEAR(I) + 1.5 • BML(I) / DL BML(I) • 0 . GO TO 100 FIX-PIN MEMBERS C 80 BML(I) - BML(I) • BMG(I) • ( 1 . 0 - GFACT/2.0) / ( 2 . 0 " ( 1 . 0 + 1 GFACT/4.0)) SHEAR(I) • SHEAR(I) - 1.5 • BMG(I) / DL BMG(I) - 0 . GO TO 100 C PIN-PIN MEMBERS 90 BML(I) • 0 . BMG(I) - 0 . SHEAR(I) • 0 . 100 CONTINUE SHEARL(I) • SHEAR(I) SHEARG(I) ' SHEAR(I) 110 CONTINUE IF (NML . E O . 0 ) GO TO 150 00 140 I - 1. NRM 00 120 J - 1. NML IF (I . E O . MML(d)) GO TO 130 120 CONTINUE GO TO 140 130 CONTINUE BML(I) • BML(I) + FEM(d.2) BMG(I) • BMG(I) + F £ M ( d , 4 ) SHEARL(I) « SHEAR(I) + F E M ( J . I ) SHEARG(I) - SHEAR(l) - FEM(J,3) 140 CONTINUE 150 CONTINUE RETURN END C C C SUBROUTINE RATIO(BML. BMG. BMCAP. NRM, FACT. K L . KG, MMAX. I C T . 1 LSENS) C C DIMENSION BML(NRM) , BMG(NRM), BMCAP(200.3). KL(NRM), KG(NRM) CALL FTNCMD('EQUATE 9 9 - S P R I N T ; ' ) RMAXL • - 1 . 0 RMAXG • RMAXL DO 80 I • 1, NRM IF ( K L ( I ) . E O . 0) GO TO 10 C  1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 . 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508  10 20  30 40 50 60 70 80 90  100  110  120  130 C C  RATL • BML(I) / BMCAP(I.2) RATL - ABS(RATL) GO TO 20 CONTINUE RATL • - 1 . 0 CONTINUE IF ( K G ( I ) . E Q . 0) GO TO 30 RATG - BMG(I) / B M C A P U . 3 ) RATG - ABS(RATG) GO TO 40 CONTINUE RATG - - 1 . 0 CONTINUE IF (RATL . G T . RMAXL) GO TO 50 GO TO 60 RMAXL • RATL NL - I CONTINUE IF (RATG . G T . RMAXG) GO TO 70 GO TO 80 RMAXG » RATG NG • I CONTINUE IF (RMAXL . G T . RMAXG) GO TO 90 GO TO 1 10 CONTINUE FACT - 1. / RMAXL WRITE (99.100) NL IF (LSENS . E O . 1) WRITE ( 6 . 1 O 0 ) FORMAT (/. ' - P L A S T I C FAILURE AT KL(NL) " 0 MMAX • NL ICT • 1 GO TO 130 CONTINUE FACT - 1. / RMAXG WRITE (99.120) NG IF (LSENS . E O . 1) WRITE ( 6 . 1 2 0 ) FORMAT (/. ' - P L A S T I C FAILURE AT KG(NG) » 0 MMAX - NG ICT • 2 CONTINUE RETURN END SUBROUTINE EIGEN(S,  NL LESSER END OF MEMBER N O . '  NG GREATER END OF MEMBER NO'  NU, NB)  REAL'S S ( 1 2 0 0 0 0 ) , A S ( 4 0 O . 4 O 0 ) . DO 10 I - 1. NU DO 10 J • 1, I 10 A S ( I . d ) • 0 . 0 0 DO 20 I * 1. NU d 1 - 1 * N S ' ( I - 1 ) N » NB + I - 1 DO 20 J • I. N AS(d.I) - S(dl) di • di • 1  DA(120000).  DE(400)  1509 1510 1511 1512 1513 1514 1515 1516 1517 151B 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 154 1 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566  C C C C C C  C C  20 CONTINUE 11-0 DO 30 I • 1, NU DO 30 J - 1. I 1 1 - 1 1 * 1 30 DA(I1) - A S ( I . J ) CALL DSYMALCOA, NU, DE. IER. WRITE ( 6 . 4 0 ) ( D E ( I ) . I - 1.5) 40 FORMAT ( 5 F 2 0 . 1 ) RETURN END •• •* SUBROUTINE GEN1(X,  Y,  IJT.  1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586  0)  •  LJT,  NJT.  KDIF)  • GENERATES NODES ALONG STRAIGHT LINE DIMENSION X ( 3 2 5 ) . Y(325) XI - X ( I J T ) YI - Y ( I J T ) DX • X ( L J T ) - XI DY • Y ( L J T ) - YI OX - DX / FLOAT(NJT + 1) OY - DY / FLOAT(NJT • 1) 00 10 I • 1. NJT IJT - IJT + KDIF XI - XI • DX YI - YI • DY X ( I J T ) • XI 10 Y ( I J T ) - YI RETURN END ••• SUBROUTINE GEN2(MMR, W. XM. K L . KG, NP, F,  C C  » DIMENSION XM(200), K L ( 2 0 0 ) .  C 10  20 30  40  50  IF R3 R6 R2 R5 GO IF R3 R6 R2 RS GO R3 R6 R2 R5 GO R2  JL,  FEM)  * KG(200). NP(G.20O). F ( 5 0 0 ) .  (KL(MMR) . KG(MMR) - 1) 50. 20. 10 - -W • XM(MMR) - XM(MMR) / 12. • -R3 - - 0 . 5 • W • XM(MMR) • R2 TO 60 (KL(MMR) - KG(MMR)) 30, 70. 40 - O. - W • XM(MMR) * XM(MMR) / 8. • - 0 . 5 * W • XM(MMR) - R6 / XM(MMR) • - 0 . 5 • W • XM(MMR) + R6 / XM(MMR) TO 60 - -W • XM(MMR) • XM(MMR) / 8. • O. » - 0 . 5 • W • XM(MMR) - R3 / XM(MMR) • - O . S • W • XM(MMR) • R3 / XM(MMR) TO 60 • - 0 . 5 • W • XM(MMR)  FEM(  .4)  1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622  C  R3 - 0. R5 - R2 R6 - 0. 60 CONTINUE Jt • NPO.MMR) J2 - NP(6.MMR) J3 - NPO.MMR) J4 - NPO.MMR) F(J3) - F(J3) • F(J4) - F(J4) + F(J1) • F(JI) + F(J2) - F(J2) • F £ M ( J L . 1 ) - -R2 F E M ( J L , 2 ) • R3 F E M ( J L , 3 ) - -R5 F E M ( J L , 4 ) - -R6 70 CONTINUE RETURN END  C C C C C C C C C  C  1  A  R2 R5 JJ3 R6  SUBROUTINE CURVD(NRM. CD. NDEF, NP, OEFL, ROTN, H L , YCR. IKOUNT)  LSENS,  ...a........*....*....*.............................. CALCULATES CURVATURE DUCTILITIES DIMENSION C D O O O . 2) , N D E F ( 2 . 3 2 5 ) . N P O . N R M ) , O E F L O O O ) , 1 R 0 T N ( 2 . 3 2 5 ) . HL(NRM), YCR(NRM) CALCULATE CURVATURE OUCLITY BASED ON ASSUMED HINGE LENGTH OF 0.5 TIMES THE MEMBER OEPTH OR 0.05 TIMES MEMBER LENGTH DO 30 J - 1. NRM DO 20 I - 1, 2 C D ( J . I ) - 0. IF ( N D E F ( I . J ) . L T . 0) GO TO 20 IF (I . EO. 1) J1 - N P O . J ) IF (I . E O . 2) J1 • N P O . J ) IF ( N D E F ( I . J ) . E O . 0) GO TO 10 J2 - N D E F ( I . J ) PCR - (DEFL(J1) - ( 0 E F L ( J 2 ) - R O T N ( I . J ) ) ) / HL(J) PCR - ABS(PCR) C D ( J . I ) • 1. • PCR / YCR(J) GO TO 20 10 CONTINUE PCR • D E F L ( J 1 ) / HL(J) PCR - ABS(PCR) C D ( J . I ) • 1. + PCR / YCR(J) CONTINUE 20 30 CONTINUE PUSH THE STRUCTURE MORE SUCH THAT TIP OISP. INCREASES BY 10% LSENS - 2 IKOUNT - 1 RETURN END  CO  APPENDIX D  NOTE  1: As r e p o r t e d e l s e w h e r e  gravity  loads  direction to  different  and  two  with  seismic  in  generated  line  is  for 'control for  beginning  not  neccesary result  gravity  loads  x-direction  For these  joints'  the  line.  in are  (K0U=1)  with  seismic  any  member,  two  analysis  must  remaining  be  specified.  joints  c a n be  The c o - o r d i n a t e s of t h e two  a n d a t t h e end o f t h e g e n e r a t i o n  necessary  numbered  generation  such  joints.  line.  That  is,  to give generation  joints, The any  commands f o r  which a r e e q u a l l y spaced program a u t o m a t i c a l l y  generation  command  along  generates  with  equal  a n d a node number d i f f e r e n c e o f one i s s u p e r f l u o u s .  NOTE 3; S i n c e  we a r e c o n s i d e r i n g o n l y a p l a n a r  can  x-displacement, cases,  from  is  have been d e f i n e d p r e v i o u s l y .  the  joint  when  loads, the  might  f o r c e s a r e combined  resulting  a straight  the  sequentially  spacing  they  direction(KOU=2).  co-ordinates  along  at  must It  one  It  are  be c o n s i d e r e d .  the  joints  as  when t h e r e  the seismic  forces i n positive  other  NOTE 2: C o - o r d i n a t e s Then,  cases,  when g r a v i t y  the  with  becomes i m p o r t a n t .  patterns:  maximum o f t h e damage should  combined  load  damage  the other,  forces  be  of the l a t t e r  consider  combined  to  i n the t h e s i s ,  have  three  degrees  y-displacement  some j o i n t s  may be f i x e d  150  and  of  problem,  freedom,  rotation.  In  each i.e.  certain  o r r e s t r a i n e d from moving i n  151 certain of  directions.  nodes  for  Code 0 s h o u l d be a s s i g n e d t o such  that  degree  of freedom, which  leads  to greater computational  NOTE  4:  that  As  discussed  a group of  directions. direction  joints  such  reduces  the size  computer  time.  If  there  should  NOTE  earlier,  group  14 j o i n t s  are  more  than  This  of  14  in  certain  of freedom  i n that  joints. thus  joints,  t o assume  Obviously,  this  reducing the required by a s i n g l e then  command.  another  command  be g i v e n .  5: T h i s s p e c i f i c a t i o n  permits  a r e c o n s t r a i n e d t o have  NOTE 6 : I f some nodes they  the user  to input  o n l y w i t h a few l i n e s / c a r d s .  t h e masses s p e c i f i e d  loads,  identically  c a n be c o v e r e d  t h e masses a s s o c i a t e d w i t h of  i t i s reasonable  displaces  of the problem,  masses a t t h e j o i n t s joints  a  i s fixed.  efficiency.  We c a n a s s i g n t h e same d e g r e e  for  groups  this  identical  If certain  displacement,  displacement  will  joints.  or  the  c a n be g r o u p e d  have  t o g e t h e r . On s u c h  static  l o a d s c a n be s p e c i f i e d  joints  o r 13 members c a n be c o v e r e d  same  static  nodes/members  only with a single by a s i n g l e  then  be t h e sum  f o r the i n d i v i d u a l  members  lumped  command. command.  9  

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