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UBC Theses and Dissertations

Longitudinal nonlinear seismic response of long bridges Hsi, Yung 1998

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LONGITUDINAL NONLINEAR SEISMIC RESPONSE OF LONG BRIDGES b y  YUNG HSI  B . A . S c ,  A  T  H  E  S  T  I  H  S  E  S  R  T h e  U  B  M  U n i v e r s i t y  I  E  Q  U  I  M  A  S  T  T  R  E  T  E  E  M  R  D  I  E  N  O  F  o  N  T  P  f B r i t i s h  A  R  F  O  S  A  P  P  L  T  I  I  R  E  A  L  T  H  D  C o l u m b i a ,  F  E  S  C  U  L  F  I  D  E  G  R  E  N  I  L  L  E  C  1 9 8 6  M  E  E  N  O  F  E  i n  T  H  E  F  A  C  U  L  T  Y  O  D e p a r t m e n t  W e  a c c e p t t o  T  H  E  U  N  I  V  E  R  F  o  t h i s  G  R  A  D  f C i v i l  t h e s i s  I  T  Y  O  F  A p r i l  ©  B  A  T  E  S  T  U  D  I  E  S  E n g i n e e r i n g  a s  t h e r e q u i r e d  S  U  c o n f o r m i n g  s t a n d a r d  R  I  T  I  S  H  1 9 9 8  Y u n g H s i ,  1 9 9 8  C  O  L  U  M  B  I  T  A  O  F  In  presenting  degree  this  at the  thesis  in  University of  partial  fulfilment  British Columbia,  freely available for reference and study. copying  of  department  this or  thesis by  for scholarly  his  publication of this thesis  or  her  the  I agree  requirements  may  representatives.  It  be is  an  Department of The University of British Columbia Vancouver, Canada  advanced  that the Library shall make it  I further agree that  purposes  for  permission  granted  for extensive  by the head  understood  that  for financial gain shall not be allowed without  permission.  DE-6 (2/88)  of  of  my  copying  or  my written  ABSTRACT  W h i l e  a s  s e i s m i c  c o l u m n  D e c k  f a i l u r e s ,  u n s e a t i n g  g e n e r a t e d  T h i s  s t u d y  b e n t s .  T  u s e d  e  p l a y e d  a n  s t r e n g t h  t h e  o  o  r e s u l t i n g  a s  i  n t h e  m o d e l l i n g  t h a n  i  a n d  i  i  n r e d u c i n g  n o t a  n t h i s  n l i m i t i n g  i m p o r t a n t  w a s  i  n  t h e  i s n o t a s  d a m a g e  1 9 9 4  m o t i o n s  friction  t h e r e s t r a i n e r  s i g n i f i c a n t l y  f t h e b e n t  e x t e n s i v e  g r o u n d  s t r e n g t h ,  f t h e r e s t r a i n e r  p a r t  u n s e a t i n g  i  c  o  m  n t h e  N o r t h r i d g e  m  o  n  a n  b r i d g e s  o c c u r r e n c e  t h e y  e a r t h q u a k e ,  a f f e c t .  a n d  h a s  s u b j e c t .  p e r f o r m e d  o t h e r s  a s  g e n e r a t e d  o p e n i n g  d e c k  c a u s e  r e c e n t l y  t h e r e s t r a i n e r  g a p  from  n e v e r t h e l e s s  a r t i f i c i a l l y  i n i t i a l  i m p o r t a n t  s t r e n g t h  t h e y  i n t e r e s t  i n c l u d e  c o m p u t e r  m o r e  i n  h  f a i l u r e s  h a p p e n e d  r e n e w e d  p a r a m e t e r s  T h e  b r i d g e  s t u d y  t h e r a n g e  a f f e c t e d  i  f a c t o r  j o i n t .  ii  s i m u l a t e  n t h e j o i n t  s l a c k  w a s  o  a n d  n o t  d i s c o v e r e d  i  n t h e  i  s t r e n g t h  p a r a m e t e r s  n t h e e x p a n s i o n  o  f t h e j o i n t .  e x p a n s i o n  n d e t e r m i n i n g  e a r t h q u a k e .  t h e y i e l d  s o m e  t h e p e r f o r m a n c e  i  t h e  T h e  o  f t h e  e x a m i n e d .  t h a t  f m o v e m e n t  t h e m o v e m e n t  s i g n i f i c a n t  t o  h o w  j o i n t .  m u c h  m a y  j o i n t .  b e  T h e  F r i c t i o n  a l s o  H o w e v e r ,  t h e  t r a v e l  w o u l d  o c c u r  TABLE OF CONTENTS  A  B  S  T  R  T  A  B  L  E  A  C  O  T  F  C  L I S T  O  F  T  A  B  L I S T  O  F  F  I  G  O  N  T  L  E  S  U  R  E  E  N  T  S  O v e r v i e w  1.2  F a c t o r s  1.2.2  S o i l  1.2.3  E x p a n s i o n J o i n t s  1.2.4  S k e w e d  1.2.5  F r i c t i o n  1.2.6  I n i t i a l  1.2.7  D a m p i n g  1.2.8  C o l u m n  T h e s i s  i  v  i  i  1  L o n g i t u d i n a l  N o n - U n i f o r m  1.4  i  1  1.2.1  O b j e c t i v e  i  iix  I n f l u e n c i n g  1.3  i  S  C H A P T E R 1 INTRODUCTION 1.1  i  G r o u n d  B r i d g e s  C u r v e d  6  7  H i n g e s )  B r i d g e s  8  9  1 0  1 1  G a p  a n d  L o n g  S o i l - S t r u c t u r e I n t e r a c t i o n  ( E x p a n s i o n  a n d  o f  M o t i o n  A m p l i f i c a t i o n a n d  J o i n t s  R e s p o n s e  O p e n i n g  a n d  R e s t r a i n e r  S l a c k  1 1  1 2  S t i f f n e s s ,  S c o p e  o f  S t r e n g t h  a n d  D u c t i l i t y  S t u d y  1 2  1 3  O r g a n i s a t i o n  1 3  i i i  CHAPTER 2 EXPANSION JOINTS  15  2.1 Introduction  15  2.2 The Typical Bridge Bent  15  2.3 Expansion Joint Locations, Geometry and Makeup  17  2.4 Elastomeric Bearing Pads  18  2.5 Deck Movements  21  2.6 Seat Widths  22  2.7 Restrainers  23  CHAPTER 3 ANALYSIS SOFTWARE  24  3.1 Introduction  24  3.2 The DRAIN-2DX Computer Program  25  3.3 General Features of DRATN-2DX  26  3.4 Element Type One  28  3.5 Element Type Two  29  3.6 Element Type Nine  31  3.7 Modifications to the DRAIN-2DX Source Code  32  3.8 Solution Techniques  32  3.9 Numerical Integration  33  3.10 Differential Support Excitation  38  3.11 The EXTR-D Data Extraction Program  38  CHAPTER 4 ANALYTICAL MODELLING  41  4.1 Introduction  41  4.2 Choice of Earthquake Records  41  4.3 Target Spectrum  42  4.4 Generation of Displacement Records  43  4.5 Bridge Frames  47  iv  4 . 6  4 . 5 . 1  B a s i c  4 . 5 . 2  B e a m - C o l u m n  4 . 5 . 3  E x p a n s i o n  4 . 5 . 4  D a m p i n g  D  R  A  I  N  -  2  B e n t  D  X  M o d e l  4 8  E l e m e n t s  4 9  S t r u t s  5 1  5 2  I n t e g r a t i o n  P a r a m e t e r s  5 3  CHAPTER 5 TWO-BENT FRAMES  54  5 . 1  I n t r o d u c t i o n  ,  5 4  5 . 2  A n a l y s i s  P a r a m e t e r s  5 . 3  A n a l y s i s  a n d  5 . 4  A n a l y s i s  S e t Y  0  F  0  R  0  5 7  5 . 5  A n a l y s i s  S e t Y  0  F  0  R  1  8 0  5 . 6  A n a l y s i s  S e t Y  0  F  0  R  2  8 5  5 . 7  A n a l y s i s  S e t Y  0  F  1  R  0  8 7  5 . 8  A n a l y s i s  S e t Y  0  F  2  R  0  8 9  5 . 9  A n a l y s i s  S e t Y  1  F  0  R  0  9 1  5 5  M o d e l  I d e n t i f i c a t i o n  5 6  5 . 1 0  A n a l y s i s  S e t Y  2  F  0  R  0  9 2  5 . 1 1  A n a l y s i s  S e t Y  2  F  0  R  2  9 5  CHAPTER 6 FIVE-BENT FRAMES  96  6.1  I n t r o d u c t i o n  9 6  6 . 2  A n a l y s i s  P a r a m e t e r s  9 7  6 . 3  A n a l y s i s  S e t Y  0  F  3  R  0  9 9  6 . 4  A n a l y s i s  S e t Y  0  F  0  R  1  1 0 1  6 . 5  A n a l y s i s  S e t Y  0  F  1  R  0  1 0 1  6 . 6  A n a l y s i s  S e t Y  0  F  1  R  1  1 0 4  6 . 7  A n a l y s i s  S e t Y  0  F  2  R  1  1 0 4  6 . 8  D o u b l e  M a g n i t u d e  E a r t h q u a k e s  1 0 7  v  6.8.1 Analysis Set 2Y0F0R1  107  6.8.2 Analysis Set 2Y0F1R0  109  6.8.3 Analysis Sets 2Y0F1R1 and 2Y0F2R1  110  6.9 Analysis Set Y1F0R0  Ill  6.10 Analysis Set Y2F0R0  Ill  6.11 Analysis Sets Y1F0R1 and Y2F0R1  113  C H A P T E R 7 S U M M A R Y AND CONCLUSIONS  115  7.1 Introduction  115  7.2 Summary  116  7.2.1 Effect of Delay  116  7.2.2 Effect of Bent Yield Strength  117  7.2.3 Effect of Friction  117  7.2.4 Effect of Restrainer Strength  117  7.3 Conclusions  118  7.4 Recommendations for Further Research  119  REFERENCES  120  APPENDIX A SOURCE CODE FOR T H E EXTR-D EXTRACTION PROGRAM  vi  122  LIST OF TABLES  T a b l e  4 . 5 . 1  D e t a i l s  T a b l e  5 . 3 . 1  S y m b o l s  T a b l e  5 . 4 . 1  T a b l e  5 . 4 . 2  T a b l e  5 . 5 . 1  5 . 5 . 2  T a b l e  5 . 6 . 1  5 . 6 . 2  a n d  M  u  a  x  T a b l e  5 . 7 . 1  5 . 7 . 2  T a b l e  5 . 8 . 1  5 . 8 . 2  5 . 9 . 1  m  M  u  a  x  j o i n t  i  m  m  a n d  M  u  x  i  m  m  a n d  M  u  x  i  m  m  a n d  M  u  a  f m  j o i n t  H e i g h t  f o r  o  i  m  m  o  f m  j o i n t  o  f m  j o i n t  i  m  u  m  j o i n t  t h e A n a l y s i s  m  u  a n a l y s i s  m  p e a k  F r a m e s ,  r e s p o n s e s S e t Y  a  x  i  0  m  F  u  0  m  i R  S e t Y  a  x  i  m  F  u  0  m  S e t Y  a  x  i  m  F  u  m  i  S e t Y  a  x  i  0  m  F  u  m  S e t Y  F  2  r e s p o n s e s S e t Y  i  1  F  0  a n d  f r a m e s  5 6  b e t w e e n  S e t Y  0  F  0  R  A d j a c e n t  s h e a r s  a n d  R  n o r m a l i z e d  E q u a l -  0  7 2  F r a m e s ,  b e t w e e n  S e t Y  0  F  0  R  A d j a c e n t  s h e a r s  f o r t h e A n a l y s i s  n E q u a l - H e i g h t  E q u a l -  1  8 3  F r a m e s ,  a n d  b e t w e e n  S e t Y  0  F  0  R  A d j a c e n t  E q u a l -  2  8 5  F r a m e s ,  2  8 6  i R  n E q u a l - H e i g h t  i R  s h e a r s  a n d  b e t w e e n  S e t Y  0  F  1  R  A d j a c e n t  E q u a l -  0  8 7  F r a m e s , 8 8  n o r m a l i z e d  s h e a r s  f o r t h e A n a l y s i s  n E q u a l - H e i g h t  a n d  b e t w e e n  S e t Y  A  d  0  F  2  j a c e n t  R  E q u a l -  0  8 9  F r a m e s ,  0  i R  n o r m a l i z e d  f o r t h e A n a l y s i s  0  F r a m e s ,  0  s h e a r s  4 9  8 4  p e a k  r e s p o n s e s  n o r m a l i z e d  n E q u a l - H e i g h t  p e a k  1  n o r m a l i z e d  s t u d y  1  F r a m e s ,  r e s p o n s e s  s e t f o rt h e t w o - b e n t  f o r t h e A n a l y s i s  p e a k  0  n t h i s  7 3  F r a m e s ,  0  i  0  R  r e s p o n s e s  a s b e n t s  n E q u a l - H e i g h t  F r a m e s ,  0  u s e d  f o r t h e A n a l y s i s  p e a k  r e s p o n s e s  A d j a c e n t  t h e A n a l y s i s x  i  A d j a c e n t  t h e A n a l y s i s  x  x  A d j a c e n t  C o m p a r i s o n  M  f m  j o i n t  C o m p a r i s o n  a  o  t h e A n a l y s i s  H e i g h t  a  A d j a c e n t  C o m p a r i s o n  a  f m  t h e A n a l y s i s  H e i g h t  a  t o i d e n t i f y  t h e A n a l y s i s  a n d  f o r T a b l e  m  H e i g h t  f o r  T a b l e  i  o  b e a m - c o l u m n s  A d j a c e n t  C o m p a r i s o n  f o r  T a b l e  u s e d  C o m p a r i s o n  f o r  T a b l e  f t h e f i v e  H e i g h t  f o r  T a b l e  o  9 0 n E q u a l - H e i g h t  0  a n d  A  d  j a c e n t  F r a m e s , 9 1  vil  T a b l e  5 . 1 0 . 1  M  T a b l e  5 . 1 1 . 1  M  a  x  f o r a  i  m  u  m  j o i n t  r e s p o n s e s  t h e A n a l y s i s x  f o r  i  m  u  m  S e t Y  j o i n t  F  0  R  r e s p o n s e s  t h e A n a l y s i s  S e t Y  2  F  0  T a b l e  6 . 2 . 2  S y m b o l s  T a b l e  6 . 8 . 1 . 1  M  a  x  i  m  u  m  p e a k  frame  T a b l e  6 . 8 . 1 . 2  M  a  x  i  m  u  m  p e a k  j o i n t  r e s p o n s e  T a b l e  6 . 8 . 2 . 1  M  a  x  i  m  u  m  p e a k  j o i n t  T a b l e  6 . 8 . 3 . 1  M  a  x  i  m  u  m  p e a k  j o i n t  a  n  d  T a b l e  6 . 9 . 1  T a b l e  6 . 1 0 . 1  S h e a r  6 . 1 0 . 2  6 . 1 1 . 1  6 . 1 1 . 2  2  R  1  F  0  0  1  F  0  R  0  1  F  0  R  1  o  a n d  1  F  0  R  1  o  n  o  a F  2  Y  2  a  F  2  x  m o d a l  a n a l y s i s  a n a l y s i s  s e t f o r t h e  f o r A n a l y s i s  9 7  f i v e - b e n t  frames  9 8  S e t 2  Y  0  F  0  R  f o r A n a l y s i s  S e t 2 Y  0  F  0  R  1  1 0 8  r e s p o n s e  f o r A n a l y s i s  S e t 2  0  F  1  R  0  1 0 9  r e s p o n s e  f o r A n a l y s i s  S e t s  Y  2  Y  0  F  1  1  R  1 0 8  1  0  i  R  m  m o d a l  p e a k  frame  a n a l y s i s  r e s p o n s e s  I  f o r A n a l y s i s  l  l  S e t s 1 1 2  m  u  m  p e a k  j o i n t  r e s p o n s e s  f o r A n a l y s i s  S e t s 1 1 2  m  u  m  p e a k  frame  r e s p o n s e s  f o r A n a l y s i s  S e t s  1  i R  u  a  0  i  x 0  m  w i t h  0  R  x  a F  i R  0  a  f m Y  x 0  F  f m  o d  2  f m Y  a n d  a  a  r e s p o n s e  d e s i g n e d  f m Y  a n d  C o m p a r i s o n Y  F r a m e s ,  1 1 0  c a p a c i t y  R  A d j a c e n t  l  C o m p a r i s o n Y  T a b l e  F  C o m p a r i s o n Y  T a b l e  0  C o m p a r i s o n Y  T a b l e  Y  a n d  9 5  w i t h  i d e n t i f y  F r a m e s ,  2  S h e a r  t o  A d j a c e n t  9 2 n E q u a l - H e i g h t  6 . 2 . 1  u s e d  d e s i g n e d  R  a n d  0 i  T a b l e  2  c a p a c i t y  2  i n E q u a l - H e i g h t  1 1 3  m  u  m  p e a k  j o i n t  l  r e s p o n s e s  f o r A n a l y s i s  S e t s 1 1 3  v i i i  LIST OF FIGURES  F i g .  1.1.1  A e r i a l  v i e w ,  l o o k i n g  I n t e r c h a n g e f o r e g r o u n d  F i g .  1.1.2  1.1.3  5 / S t a t e  c r u s h e d h a s  b e n t  j o i n t  R o u t e s e a t  1 4  a n d  C o l l a p s e d N o r t h r i d g e  F i g .  2 . 2 . 1  T y p i c a l ( b )  F i g .  2 . 3 . 1  2  o n  n e a r  s o u t h , 1 4  t h e  b e n t  v e r t i c a l  o f  s p a n s  t h e  o f  N o r t h  t h e  l e f t  4  a n d  t o  i n t h e t h i s  3  l e f t  N o r t h  1 4 i n  t h e 2  C o n n e c t o r  T h e  s p a n  ( s t i l l  t h e  R o u t e L o c a t e d  C o n n e c t o r  N o r t h  b e n t  s p a n  5 / S t a t e  e a r t h q u a k e .  I n t e r c h a n g e .  a t  s t a n d i n g )  o f  b e n t  C o n n e c t o r  n o r t h - l o o k i n g  t h e  l o c a t e d  b e t w e e n  h a s  c o l l a p s e d ,  2  2  o f  v i e w  t h e  I n t e r s t a t e  s h o w i n g  a r m  s p a n  o f  t h e  n e a r  N o r t h r i d g e  G a v i n  b e n t  I n t e r s t a t e  C a n y o n  4  i n  t h e  5 / S t a t e  S o u t h b o u n d R o u t e  1 4  e a r t h q u a k e  3  U n d e r c r o s s i n g  a f t e r  t h e  1 9 9 4  e a r t h q u a k e  b r i d g e  b e n t  j o i n t s  4  c o n f i g u r a t i o n s :  b r i d g e ,  o n  ( c )  c a p b e a m :  ( a )  b r i d g e  ( a )  s i n g l e - d e c k e r  s e c t i o n  b r i d g e ,  A - A  l o c a t i o n s ,  ( b )  1 6  c l o s e - u p , ( c )  w i t h  r e s t r a i n e r  F i g .  2 . 3 . 2  E x p a n s i o n  1 7  j o i n t s  a t  q u a r t e r - s p a n : ( a )  l o c a t i o n s ,  ( b ) c l o s e - u p ,  ( c )  w i t h  r e s t r a i n e r  F i g .  2 . 3 . 3  C o n t i n u i t y  1 8  a t  r o a d  l e v e l :  ( a )  g r o u t - e n c a s e d  f i n g e r s  F i g .  2 . 4 . 1  D e t a i l s  5 /  c r u s h e d 3  u n s e a t e d  1 9 9 4  i n t h e  I n t e r s t a t e  o f f s e t  O v e r h e a d  a f t e r  t h e  c o l l a p s e d  s u p p o r t e d  d o u b l e - d e c k e r  E x p a n s i o n  o f  N o r t h r i d g e  I n t e r c h a n g e ,  a n d  I n t e r c h a n g e  1.1.5  R o u t e  N o r t h - l o o k i n g v i e w S e p a r a t i o n  F i g .  l o o k i n g  s i m p l y  E x p a n s i o n  h i n g e  1.1.4  t h e  1 9 9 4  p a r t i a l l y  v i e w ,  S t a t e  F i g .  i s t h e  I n t e r s t a t e  a s  s o u t h ,  t h e  E l e v a t i o n  t h e  F i g .  a f t e r  m e t a l  p l a t e ,  ( b )  m e t a l 1 9  o f  a n  e l a s t o m e r i c  b e a r i n g  p a d  ix  2 0  F i g .  3.4.1  T h e  i n e l a s t i c  t r u s s  c o m p o n e n t s  t o  c o m p r e s s i o n ,  F i g .  3.5.1  T h e ( b )  p a r a l l e l  a n d  F i g .  3.9.1  N u m e r i c a l  F i g .  3 . 1 1 . 1  F i g .  4.3.1  T h e  F i g .  4.4.1  A c c e l e r a t i o n ,  B a s i c  S a n  4 . 5 . 1 :  ( a )  F i g .  4 . 5 . 2  B a s i c  F i g .  4 . 5 . 3  T h e  o  m  a  w i t h  s t r a i n  f l e x u r a l  r i g i d  t e n s i o n  e n d  h a r d e n i n g ,  s t i f f n e s s  v e l o c i t y  a n d  f o r a  u s i n g  l o g i c  a n d 2 8  z o n e s ,  ( c )  e l e m e n t  r e l a t i o n s h i p  f o r  T o t a l  P e a k t h e  a  o f  t y p e  n i n e  c o n s t a n t  t h e  E  X  T  e l e m e n t  a v e r a g e  R  -  D  3 1  a c c e l e r a t i o n  e x t r a c t i o n  p r o g r a m  S p e c t r u m  a n d  d i s p l a c e m e n t  e a r t h q u a k e ,  C i t y  a n d  b u t  t i m e  a l t e r e d  d i s p l a c e m e n t  e a r t h q u a k e ,  n o d a l  v e l o c i t y  a n d  b u t  h i s t o r i e s ,  t o  t i m e  a l t e r e d  d i s p l a c e m e n t  e a r t h q u a k e ,  f i t  t h e  b a s e d  H y b r i d  o n  t h e  R o c k  t o  h i s t o r i e s , f i tt h e  b a s e d  H y b r i d  o n  t h e  R o c k  b u t  t i m e  a l t e r e d  t o  h i s t o r i e s , f i t  t h e  b a s e d  H y b r i d  o n  u s e d  n o d a l L  frame t h r e e  b a s i c  H  M  C  ( b )  i n  f i v e - b e n t  t h e  R o c k  f r a m e  t w o - b e n t  c o m p o n e n t  0  1  ,  a n d  M  C  a n d  0  1  ,  j o i n t  a n d  u s e d  f o r t h e ( b )  h i s t o r i e s  f o r  t i m e  t i m e  i n  t h e  h i s t o r i e s  L L L P 0 1 ,  i n  f i v e - b e n t  e l e m e n t s ,  r e s p o n s e s  e a r t h q u a k e s  4 7  a n d  H H L P 0 1 ,  d i s p l a c e m e n t L  t h e  4 4  d i s p l a c e m e n t  H  3 9  4 4  f r a m e ,  t h r e e  . .  3 5  4 4  v e l o c i t y  e l e m e n t  . . . .  4 3  f o r c e - d e f o r m a t i o n r e l a t i o n s h i p t h e  T o t a l  i n  d e s i g n  T a r g e t  P r i e t a  t w o - b e n t  L L S F 0 1 ,  5 . 4 . 3  ( a )  i n  c o m p r e s s i o n  S p e c t r u m  H H S F 0 1 ,  F i g .  y i e l d i n  p a r a l l e l  S p e c t r u m  L  F i g .  5 . 4 . 2  a c h i e v e  a n d  i n t e g r a t i o n  F e r n a n d o  A c c e l e r a t i o n , 1 9 8 9  F i g .  R o c k  M e x i c o  T a r g e t  s t e p  a l g o r i t h m  A c c e l e r a t i o n , 1 9 8 5  5.4.1  e l e m e n t :  ( b )  S p e c t r u m  T a r g e t  F i g .  t i m e  H y b r i d  T a r g e t  ( a )  t o  ( c )  b u c k l i n g  f o r c e - d e f o r m a t i o n r e l a t i o n s h i p  1 9 7 1  4.4.1  h a r d e n i n g ,  t e n s i o n ,  f o r c e s ,  o r i e n t a t i o n ,  3 0  T h e  F i g .  ( a )  e l e m e n t  3.6.1  4 . 4 . 2  i n  c o m p o n e n t s  F i g .  F i g .  s t r a i n  y i e l d  b e a m - c o l u m n  d e f o r m a t i o n s t h e  e l e m e n t :  a c h i e v e  ( d )  i n e l a s t i c  b a r  i n  f o r  A n a l y s i s  -»  x  t h e  e x p a n s i o n  H H ,  A n a l y s i s  frame  H  H  0  F  a t 0  R  S e t  S e t  Y  v a r i o u s 0  0  5 1  m o d e l s 0  i n Y  s t r u t : m o d e l  i n  L L ,  A n a l y s i s  Y  4 8  c o m b i n e d  frame  f o r  frame S e t  t h e  f r a m e s  F  0  R  0  5 8  m o d e l s F  0  R  0  5 9  d e l a y s 6 0  F i g .  5 . 4 . 4  C o m p a r i s o n H  F i g .  5 . 4 . 5  H  M  C  0  1  5 . 4 . 6  C o m p a r i s o n  F i g .  5 . 4 . 7  H  S  F  0  1  5 . 4 . 8  i n  F i g .  5 . 4 . 9  i n  F i g .  5 . 4 . 1 0  f r a m e  5 . 4 . 1 1  f r a m e  P e a k  F i g .  5 . 4 . 1 2  F i g .  5 . 4 . 1 3  o  o  F  0  5 . 4 . 1 4  a n d j o i n t  1  i n  F i g .  5 . 4 . 1 5  P e a k i n  F i g .  5 . 4 . 1 6  P e a k i n  F i g .  5 . 4 . 1 7  F i g .  5 . 5 . 1  frame  C o m p a r i s o n A n a l y s i s  o  S e t s  n o d a l R  0  0  i  i  6 2  H  H  M  C  h i s t o r i e s  0  R  0  1  a n d  b e t w e e n  0  6 4  b e t w e e n  H  H  S  F  I I a t v a r i o u s 0  F  0  0  1  a n d  J a t v a r i o u s F  f r a m e  R  0  frame  L  S e t Y  0  6 9  K  a t v a r i o u s  F  0  L  h i s t o r i e s  F  F  0  R  0  R  7 0  d e l a y s  0  7 1  h i s t o r i e s  R  d e l a y s  0  a t v a r i o u s  t i m e 0  d e l a y s  0  K  S e t Y  S e t Y  b e t w e e n  0  7 4  b e t w e e n  L  L  S  F  0  1  a n d  0  7 5  f o r  f o r  f o r  n A n a l y s i s  f o r  n A n a l y s i s  d i s p l a c e m e n t  a n d Y 0 F 0 R 1 ,  frame  H  I  S e t Y  0  F  f r a m e  n A n a l y s i s  xi  6 8  J  0  d e l a y s  0  0  f o r  R  R  frame  n A n a l y s i s  r e s p o n s e s  e a r t h q u a k e s  0  F  0  S e t Y  f o r  t i m e 0  r e s p o n s e s  e a r t h q u a k e s  F  i  F  d i s p l a c e m e n t  r e s p o n s e s  e a r t h q u a k e s  0  frame  n A n a l y s i s  i  t i m e  S e t Y  f o r  r e s p o n s e s  e a r t h q u a k e s  0  f o r  n A n a l y s i s  S e t Y  f t o t a l Y  i  R  6 5  r e s p o n s e s i  0  0  n A n a l y s i s  f o r c e  a n d j o i n t  t h e t h r e e  i  f s h e a r  a n d j o i n t  frame  R  F  b e t w e e n  S e t Y  r e s p o n s e s  n A n a l y s i s  a n d j o i n t  t h e t h r e e  P e a k i n  frame  t h e t h r e e  0  n o d a l  a n d j o i n t  t h e t h r e e  F  0  b e t w e e n  6 3  n A n a l y s i s  a n d L L S F 0 9 ,  frame  0  h i s t o r i e s  0  h i s t o r i e s  r e s p o n s e s  f t o t a l  R  t i m e  e a r t h q u a k e s  o  0  n A n a l y s i s  i  S e t Y  h i s t o r i e s  F  r e s p o n s e s i  t i m e  d i s p l a c e m e n t  e a r t h q u a k e s  o  0  n A n a l y s i s  S e t Y  a n d j o i n t  i  n A n a l y s i s  t i m e  f o r c e  a n d j o i n t  C o m p a r i s o n  P e a k  i  e a r t h q u a k e s  frame  i  S e t Y  e a r t h q u a k e s  C o m p a r i s o n S  ,  n o d a l  f s h e a r  t h e t h r e e  L  6  d i s p l a c e m e n t  f o r c e  n A n a l y s i s  L L S F 0 9 ,  F i g .  f t o t a l  f r a m e  P e a k  L  0  f s h e a r  t h e t h r e e  i n  C  a n d j o i n t  t h e t h r e e  i n  F i g .  i  t h e t h r e e  P e a k  M  n A n a l y s i s  C o m p a r i s o n  P e a k  H  n o d a l  a n d H H S F 1 1 ,  H H S F 1 1 ,  F i g .  o i  C o m p a r i s o n H  f t o t a l  a n d H  F J H M C 0 6 ,  F i g .  o  0  R  0  F  frame  J  K  S e t Y  0  F  frame  K  S e t Y  0  0  7 6  0  R  7 7  7 8  a t v a r i o u s 0  R  d e l a y s  0  d e l a y s  0  h i s t o r i e s  f o r m o d e l  d e l a y s  0  a t v a r i o u s  L F  R  d e l a y s  0  I J a t v a r i o u s  S e t Y  t i m e  a t v a r i o u s  I T M C 0 6  7 9  b e t w e e n 8 1  F i g .  5 . 5 . 2  C o m p a r i s o n Y  F i g .  0  F  5 . 1 0 . 1  0  R  0  o  a n d  s h e a r  C o m p a r i s o n A n a l y s i s  F i g .  f  5 . 1 0 . 2  0  F  0  R  o  S e t s  C o m p a r i s o n  Y  f o r c e  Y 0 F 0 R 1 ,  0  a n d  f i v e - b e n t  o  f t o t a l F  0  n o d a l  Y  0  f  s h e a r  R  0  w i t h  a n d  f o r c e  Y 2 F 0 R 0 ,  f r a m e  t i m e  h i s t o r i e s  f o r m o d e l  b e t w e e n  A n a l y s i s  S e t s  I I M C 0 6  8 2  d i s p l a c e m e n t Y 2 F 0 R 0 ,  t i m e  H  H  h i s t o r i e s  f o r m o d e l  h i s t o r i e s  f o r m o d e l  e x p a n s i o n  t i m e  S  1  b e t w e e n  1  H  S  F  1  1  A n a l y s i s  9 3  S e t s  9 4  F i g .  6 . 1 . 1  T h e  F i g .  6 . 3 . 1  P e a k  v a l u e s  f o r t h e  A n a l y s i s  S e t  Y  0  F  3  R  0  1 0 0  F i g .  6 . 4 . 1  P e a k  v a l u e s  f o r t h e  A n a l y s i s  S e t  Y  0  F  0  R  1  1 0 2  F i g .  6 . 5 . 1  P e a k  v a l u e s  f o r t h e  A n a l y s i s  S e t  Y  0  F  1  R  0  1 0 3  F i g .  6 . 6 . 1  P e a k  v a l u e s  f o r t h e  A n a l y s i s  S e t  Y  0  F  1  R  1  1 0 5  F i g .  6 . 7 . 1  P e a k  v a l u e s  f o r t h e  A n a l y s i s  S e t  Y  0  F  2  R  1  1 0 6  xii  j o i n t s  F  H  b e t w e e n  9 7  CHAPTER INTRODUCTION  1.1  A  O V E R V I E W  b r i d g e  i s  r a i l r o a d ,  a n o t h e r  o r  b u i l d i n g  t h e  d i s a s t e r ,  a n d  o t h e r  a r e a s  f o r  o  f  w o u l d  from  i  n w h i c h  a  b r i d g e  a i d s  ( W e r n e r ,  t h e b r i d g e  s t r u c t u r e  o n e  f  ( H o u g h t o n  r o a d s  t o  a n d  o n l y  f a c i l i t a t e  i  w h i c h  t o a n o t h e r .  s e r v e s  t o t h e a f f e c t e d  t o r e m a i n  a s  a s  a r e a s ,  a  I t c a n  f t h e h i g h w a y  s h o u l d  w e l l  I n t h i s  r o u t e  a s  s e n s e ,  a f t e r  a n d  h e l p  r e s c u e  i t s o r i g i n a l  1  b e  o n e  I n  e a r t h q u a k e  i t a s  p u r p o s e  a s  t o  o r  h e l p  b e  a n  a  o r  m o v e  a n o t h e r .  a  U n l i k e  f t h e  a  b e y o n d  s c a l e  s u p p l i e s  from  c o m p e l l i n g  e x p r e s s w a y .  f  h i g h w a y  l a r g e  m e d i c a l  o  t o u c h e s  w e l l  o t h e r  i t i s  a r e t h e  b r i d g e  o  o v e r  p a r t s  t h e y  t h e i n j u r e d  m o r e  w h e n  n m a n y  s u c h ,  p a r t  s o m e  w a t e r w a y ,  t o p a s s  c a n e x t e n d  s e r v i c e s r e m o v e  c o u l d  a s  i  f u n c t i o n ,  u s e  c a n  f a c t ,  a n d  i t s i m p o r t a n c e  a n  a  d e s i g n e d  p l a c e  t o  w h o  o v e r  m o v e m e n t ,  s y s t e m ,  i tc e a s e  p o s t - d i s a s t e r a c c e s s  t h a n  a l s o  m e e t .  f r o m  t h o s e  p a s s a g e  t r a f f i c  t r a n s p o r t a t i o n l i f e l i n e  t h i s  f u n c t i o n a l  p r o v i d e s  t h e r o a d w a y s  t h e o n l y ,  I m m e d i a t e l y  I r o n i c a l l y ,  1 9 8 0 ) .  i t s o c c u p a n t s  n i t s c o m m u n i t y  p l a c e  o  a n d  c o n t i n u o u s  t o h a v e  s o m e t i m e s  a f f e c t  s p a n s  M i f f l i n ,  a r e f r e q u e n t l y p a r t  i ti s l o c a t e d .  1 9 8 7 ) .  w h i c h  o r u n d e s i r a b l e  d i r e c t ,  a l l t h o s e  t o g o  a r e a  o  b r i d g e s  m o s t  w h i c h  l i v e s  s y s t e m  s e r i e s  i n c o n v e n i e n t  a n d  a  o b s t a c l e s  o r  A m e r i c a ,  f a s t e s t  t h e  o t h e r  r o a d  o t h e r w i s e  N o r t h  e s s e n t i a l l y  t h o s e  r e a s o n  CHAPTER 1: INTRODUCTION  §1.1 OVERVIEW 2  1.1.1: Aerial view, looking south, of the Interstate 5/State Route 14 Interchange after the 1994 Northridge earthquake. Located in the foreground is the partially collapsed North Connector (Courtesy Dr. C . E . Ventura, Dept. O f C i v i l Engineering, U B C ) . F i g u r e  Figure 1.1.2: Elevation view, looking south,  of the North Connector at the Interstate 5/State Route 14 Interchange. The span located between the crushed bent 2 on the left and bent 3 (still standing) has collapsed, as has the simply supported span to the left of bent 2 (Courtesy Dr. C . E . Ventura, Dept. O f C i v i l Engineering, U B C ) .  CHAPTER 1: INTRODUCTION  §1.1 OVERVIEW 3  Figure 1.1.3: Expansion joint near bent 4 in the North Connector of the Interstate 5/State Route 14 Interchange, this north-looking view showing crushed hinge seat and vertical offset (Courtesy Dr. C.E. Ventura, Dept. Of Civil Engineering, UBC).  Figure 1.1.4: North-looking view of unseated span near bent 4 in the Southbound Separation and Overhead arm of the Interstate 5/State Route 14 Interchange after the 1994 Northridge earthquake (Courtesy Dr. C.E. Ventura, Dept. Of Civil Engineering, UBC).  CHAPTER 1: INTRODUCTION  §1.1 OVERVIEW 4  Figure 1.1.5: Collapsed spans in the Gavin Canyon Undercrossing after the 1994 Northridge earthquake (Courtesy Dr. C.E. Ventura, Dept. Of Civil Engineering, UBC). For these reasons, and because bridges are typically fairly large and expensive structures, their failures in earthquakes have attracted much attention in the engineering community as well as in the media, especially given the number of large magnitude earthquakes in recent memory. Though many bridge failures resulted from the failure of columns supporting the superstructure, some of the more spectacular failures in concrete bridges came about as a result of bridge decks becoming unseated and falling off their supports.  Deck unseating was considered to have been a possible cause for some of the bridge failures in the 1994 Northridge earthquake. Displayed in Figs. 1.1.1 to 1.1.3 is the partial collapse of the North Connector of the highway interchange at Interstate 5 (15) and State Route 14 (SRI4), and in Fig. 1.1.4, the unseated span in the Southbound Separation and Overhead arm. Fig. 1.1.5 shows the collapsed spans in the Gavin Canyon Undercrossing.  CHAPTER 1 : INTRODUCTION B y  t h e i r  v e r y  s u s c e p t i b l e  t o  t h e  e x p a n s i o n  t h e  c o l l a p s e  a n d  n a t u r e ,  d e c k  S k e w e d  i n  ( N a t i o n a l  t h e  a t  b y  t h e  t o  t h e  f o r  1 9 7 1  i n  w a s  p u t  t o  e x p a n s i o n  i n  f o r  a r e  p a r t ,  a l s o  f o r  t h e  p l a c e  t h e  b r i d g e  t o  j o i n t  s e a t s  t h e  o f  a s  1 4  t o  s p a n s  i n  o f  s o m e  h i n g e  w e l l  l e a d  a s  i n  t h e  t h e y  l a r g e r  c a n  t h e  w h i c h  S o u t h b o u n d  i n  t h e  b e  m o r e  m o v e m e n t s  m e c h a n i s m  1 9 9 4  l e d  i n  t o  S e p a r a t i o n  N o r t h r i d g e  1 9 9 5 ) .  u n s e a t i n g  S k e w e d  t h a n  j o i n t s  G a v i n  t h o s e  w e r e  w h i c h  t h o u g h t  C a n y o n  t o  l i e  b e  U n d e r c r o s s i n g  1 9 9 5 ) .  w h i c h  a  n u m b e r  T r a n s p o r t a t i o n  A  B r i d g e  T h e  b r i d g e s  r e s t r a i n e r s  t o  R e s e a r c h ,  d e c k  b r i d g e s .  1 2 6 0  c a n  s u c h ,  I n t e r c h a n g e  s p e c i f i c a t i o n s .  e x i s t i n g  A s  p o s s i b l e  R e s e a r c h ,  D e p a r t m e n t  w i t h  o n e  b r i d g e .  e a r t h q u a k e ,  o f  b e  E n g i n e e r i n g  E n g i n e e r i n g  s u p e r s t r u c t u r e s  t o  R o u t e  c o l l a p s e  u p g r a d e  c u r v e d .  c u r v a t u r e  v u l n e r a b l e  o f  d e s i g n  b e  C o n n e c t o r  5 / S t a t e  m o r e  F e r n a n d o  t h e  N o r t h  E a r t h q u a k e  E a r t h q u a k e  S a n  t h e  t o  t h e i r  c o n s i d e r e d  d i r e c t i o n  u n s e a t i n g ,  i n  w a s  t e n d  s i n c e  I n t e r s t a t e  C e n t e r  m o d i f i e d  r e i n f o r c e m e n t  n a r r o w  t h e  j o i n t s  l e a s t  d e c k  i m m e d i a t e l y  s e c t i o n s  i n  c o n n e c t o r s  f a i l u r e s  l o s s  t r a n s v e r s e  C e n t e r  F o l l o w i n g  S e a t  ( N a t i o n a l  r e s p o n s i b l e ,  ( B S R P )  a r m  e x p a n s i o n  s q u a r e l y  c a u s e d  u n s e a t i n g  s e v e r a l  O v e r h e a d  e a r t h q u a k e  h i g h w a y  j o i n t s .  o f  § 1 . 1 OVERVIEW 5  i n  b r i d g e  i n i t i a l  b y  w a s  w e r e  ( C a l T r a n s )  R e t r o f i t  p h a s e  1 9 9 1 )  a n c h o r i n g  f a i l u r e s  C a l i f o r n i a  S e i s m i c  ( R o b e r t s ,  a n d  o f  P r o g r a m  t o  p r o v i d e  c o n n e c t i n g  s u p e r s t r u c t u r e  a l l  e l e m e n t s  s u b s t r u c t u r e .  R e c e n t  d e c k  u n s e a t i n g  c l o s e l y  e x a m i n e  U n l i k e  t h o s e  t h e  f a i l u r e s ,  l o n g i t u d i n a l  i n i t i a t e d  i n  t h e  h o w e v e r ,  s e i s m i c  b r i d g e  h a v e  u r g e d  r e s p o n s e  b e n t s ,  t h e s e  o f  d e s i g n e r s  b r i d g e s  f a i l u r e  a n d  r e s e a r c h e r s  c o n t a i n i n g  m o d e s  c a n  t o  e x p a n s i o n  o c c u r  e v e n  m o r e  j o i n t s .  w h e n  t h e  CHAPTER 1: INTRODUCTION i n t e g r i t y  i s  o n l y  o  f t h e b e n t  a s  s h a k e s  g o o d  t h e b r i d g e ,  p a r t i c u l a r l y  1.2  c o l u m n s  i t s w e a k e s t  c a u s i n g  a d e p t  i s n o t i n q u e s t i o n .  l i n k .  i t t o  a t e x p o s i n g  T h i s  I t i s n o w  b e n d  a n d  w i d e l y  t w i s t  i n a d e q u a c i e s  r e a f f i r m s t h e o l d a x i o m  a n d  r e c o g n i z e d  t h e  i n t h e s e  l o a d  t h a t  p a t h s  t o  a n  t h a t  a  s t r u c t u r e  e a r t h q u a k e ,  c o n s t a n t l y  a s i t  c h a n g e ,  i s  j o i n t s  FACTORS INFLUENCING LONGITUDINAL RESPONSE OF L O N G BRIDGES  W h i l e  e x p a n s i o n  c o m p l i c a t e d  A  l o n g  b y  b r i d g e  s e v e r a l  o f  a s  §1.2 FACTORS INFLUENCING RESPONSE ... 6  b e n t s  g a p s  n t h e  b e t w e e n  o v e r  w h i c h  T h o u g h  t h e s e  e x p a n s i o n  l o n g  c a n  b e  e a c h  T h e  e i t h e r  a r e a s  o t h e r  m a y  s i d e  t h e b e n t s  o  f s o m e  f a  f t h e s e  from  w i t h  b r i d g e .  f a c t o r s  e x p e r i e n c e  e a c h  o t h e r ,  p h a s e  w h i c h  s o  a n d  F u r t h e r m o r e ,  c a n  o r  b e  a n d  h o w  f t h e  m o r e  w i t h  from  t h a t  o  f t h i s  b e n t s  m o t i o n s  s e v e r e  m a y  s o  s i m p l e  t h a t  w h i c h  T h e  c a u s e  t e r r a i n  t h e y  e f f e c t s  t h e  b i g g e r  e f f e c t s  p r o f i l e  c a n  h a v e  m o d e l s ,  u n c e r t a i n  w i l l  a r e  l e n g t h  r e a c h i n g  a n a l y t i c a l  i tr e m a i n s  m o r e  r e s e a r c h .  p o u n d i n g  t h e v a r y i n g  c o m b i n e d  i s m a d e  m o t i o n s .  b e n t  h e i g h t s  e a r t h q u a k e s ,  t h e i r  s o  g r o u n d  o  v a r y i n g  d e d u c e d  p a s t  i s t h e f o c u s  g r o u n d  t h a t  m o t i o n s  c a n h a v e  t h e p r o b l e m  c o n d i t i o n s ,  d i f f e r e n t  a n t i c i p a t e d  f t h e j o i n t .  o  s o i l  e x c i t a t i o n ,  o u t - o f  f r e q u e n c i e s .  d e s i g n e r s ,  b r i d g e s ,  e x p e r i e n c e  o r i g i n a l l y  o  b r i d g e  d i f f e r e n t  s u p p o r t  r e s u l t i n g  t h a n  t o  i n l o n g  w i t h  n a t u r a l  i n t e r a c t  o  f a c t o r s  c a n e x t e n d ,  o b s e r v e d  m a y  r e s p o n s e  o v e r  j o i n t s  b r i d g e s  d i f f e r e n t  f a c t o r s  o v e r a l l  o n  c h a l l e n g e  t o d i f f e r e n t i a l  d e l a y e d .  t h e e f f e c t s  s o m e  f r o m  l e a d  t h e d e c k s  d i s t i n c t l y  a n d  m a y  a  a d d i t i o n a l  e x t e n d  a w a y  a r e t i m e  i  p r e s e n t  s e v e r a l  m a y  s p a n s  t h e b r i d g e  j o i n t s  a l t e r  h o w  t h e  CHAPTER 1: INTRODUCTION O t h e r  f a c t o r s  a c c o u n t  i  n a  i n t e r a c t i o n ,  T h e  y i e l d  S o m e  o  t h e i n i t i a l  s t r e n g t h s ,  o  a l t e r e d  i n f l u e n c e ,  i  o n e  o  i  f a  f a c t o r s  d u c t i l i t i e s  n m o r e  t o  o  d e t a i l  i  i n v o l v e d ,  a n o t h e r  t o i n c l u d e  i  a n d  a r e d i s c u s s e d  i  o  b r i d g e  i n c l u d e  a n d r e s t r a i n e r  a n d  f f a c t o r s  a n a l y s i s  r e s e a r c h  S u c h  o p e n i n g  s t i f f n e s s e s  i ti s d i f f i c u l t  c o n s i d e r i n g  t o  t o  i  a s s e s s  d e t e r m i n e  t h e u n i f o r m i t y  r e c o r d e d  R e s e a r c h  f  t h e  a b o u t  W a v e  a t t h e  ( B o l t ,  f r e q u e n c y  o  f r e q u e n c y ,  b u t s p a t i a l l y  t h e r e  s e i s m i c  s l a c k  i  i  n g e n e r a l m u s t  a l s o  s o i l  a m p l i f i c a t i o n  a n d  n t h e e x p a n s i o n  f t h e b e n t s  w i l l  a l s o  n o r d e r  m o d e l  t o  a l l o  n C h a p t e r  t h e b r i d g e  c a p t u r e  t h e  f t h e m  n a  i  f u l l  j o i n t  b e  t a k e n  i n t o  s o i l - s t r u c t u r e  a n d  i n f l u e n c e  n t h e s u b s e c t i o n s w h i c h  a n d b e c a u s e  c o u l d  b e  f i v e  l a r g e  b e h a v i o u r  s o u r c e  n t h e a n a l y s i s .  c o h e r e n c e .  a n o t h e r  c o n t e n t .  t h e  d e t e r m i n e  i m p l e m e n t e d  t h a t  s t u d y .  a r e d i s c u s s e d  n t h i s  e s s e n t i a l  o n  g a p  t h e r e s p o n s e  d a m p i n g .  t h e  r e s p o n s e .  f o l l o w .  m o d e l s  e f f e c t s  r e s e a r c h  m a y  o  f  n e e d  e a c h  p r o j e c t .  T  t o  b e  f a c t o r ' s  h  e  f a c t o r s  4 .  NON-UNIFORM GROUND MOTION  B e f o r e  w a y  i n f l u e n c e  f t h e n u m b e r  f r o m  c h o s e n  m a y  c o m p r e h e n s i v e  f t h e s e  B e c a u s e  1.2.1  w h i c h  §1.2 FACTORS INFLUENCING RESPONSE ... 7  a n d  S e i s m i c  o  t h e  c o h e r e n c e ,  H e r t z ,  b  t i m e ,  A b r a h a m s o n  t h e r e  y  i  n a t u r e  o  f  m o t i o n s  w a v e s  v a r y  d e f i n i t i o n ,  Y e h ,  1985)  t w o  e x p r e s s e d  d o m i n a t e  e v e n  o v e r  f t h e b r i d g e ,  a n d  h o w  a n d  n e a r b y  i  n t e r m s  f  w a v e  a b o v e  t h i s  r e l a t i v e l y  i t w i l l  o  f o n e  o  f  i s  b e  O n e  l o c a t i o n s  f o r e x a m p l e ,  o  i t  s p a t i a l l y .  d e p e n d e n c e  d e p e n d e n c e  a c c e l e r a t i o n s  m o t i o n s  o n  s h o w s ,  s i g n i f i c a n t  o  t e m p o r a l l y  i s t h e l i n e a r  a n d  n g r o u n d  e x c i t a t i o n  i m p i n g i n g  i t i s u s u a l l y  i s a  c o m p o n e n t s  t h e  a n d  i n c o h e r e n t g r o u n d  v a r i a t i o n s  f t h e v a r i o u s  g r o u n d  f t h e g r o u n d  s a m e  o  i s t o  s i g n a l  f r e q u e n c y  t h a t  u p  t o  a  c o h e r e n c e  o  f r e q u e n c y ,  s o  s h o r t  n  d i s t a n c e s .  CHAPTER 1 : INTRODUCTION A  n  e a r t h q u a k e  s u r f a c e  a n d  d i f f e r e n t  t r a v e l  b o d y  a s s u m e d  a f f e c t  t o  r e f l e c t i o n  a n d  t o  1.2.2 T h e  o n  e a c h  o  f a u l t  f w h i c h  f r o m  a  t h e r e s p e c t i v e  a n d  p o i n t  s o u r c e  t h a t  t h e s o i l s  a n d  b e n t s  i  n a  p h e n o m e n o n  w i t h  m a y  F u r t h e r m o r e ,  a m p l i t u d e  T h i s  l i n e  a n  e x t e n d e d  r e a c h  t h e  a n d  I n  t h e e n t i r e  a s  w i l l  t h e  g e n e r a t e  t h r o u g h  s i t u a t i o n  s i t e  l e n g t h  s t i l l  c a n  a t d i f f e r e n t  m e d i a  t h e b r i d g e  b r i d g e  i s k n o w n  s i t e  t h e i d e a l i z e d  r e a c h  u n d e r  l a r g e  t h e b r i d g e  n o n - u n i f o r m  p h a s e .  l e n g t h  t i m e s  w h i c h  t h a t  r e l a t i v e l y  o  a n d  t h e  w i t h  w a v e s  t h e w a v e s  a r e  u n d i s t u r b e d  f t h e b r i d g e  e x p e r i e n c e  n u m e r o u s  h a v e  i d e n t i c a l  travelling wave effect,  t h e  b u t  a n d  b y  s a m e  p h a s e -  t h e  b r i d g e  differential support excitation.  SOIL AMPLIFICATION AND SOIL-STRUCTURE INTERACTION  w h i c h  w a v e s  r e s p o n s e  o  i ti s e r e c t e d  t r a v e l  e f f e c t  w i l l  u p  f a  a n d  t h r o u g h  D u r i n g  M e x i c o  C i t y  a s  w i t h  I t i s b e l i e v e d  w h i c h  e n e r g y  soil amplification,  t h e m o r e  t h a n  a m p l i t u d e s  o v e r  1 0 , 0 0 0  t h a t  r e m a i n  o  t h e  p r e d o m i n a n t l y  w a s  b e l i e v e d  f a t a l i t i e s  c e r t a i n  f  o  t o  i  t o  s u f f e r e d  a m p l i t u d e s  f  0 . 2 5 g -  l a y e r  h i g h  p a r t l y  n t h a t  b o t h  t h e p r o p e r t i e s  ( R o e s s e t ,  c a n  b e  r a n g e s ,  c o m p a r e d  o  f s o f t  t o  ( M  t o  l a k e  R  a n d  )  t h e  b e d  s t r a i n s ,  t h r e e  1 9 9 3 ) .  m o d i f i e d .  m a g n i t u d e  s h e a r i n g  n t h e t w o  b e  i  b y  f r e q u e n c y  R i c h t e r  l a r g e  e l a s t i c  a f f e c t e d  f i t s f o u n d a t i o n  t h e w a v e  a c c e l e r a t i o n s  o n  m o t i o n s  l a y e r s ,  o  p e a k  s i t e s  a n d  c h a r a c t e r i s t i c s  e a r t h q u a k e  a d j a c e n t  s i t s  s e v e r e l y  1 9 8 5  e x p e r i e n c e d  r o c k .  c a n b e  t h e  C i t y  k n o w n  t h e  i n c r e a s e t h e w a v e  o t h e r s .  g r o u n d  s t r u c t u r e  t h e s o i l  M e x i c o  a n d  a  t h e i r  r e f r a c t i o n ,  e x p e r i e n c e  s e i s m i c  o v e r  b o t h  e x c i t a t i o n .  s a i d  o n  a n g l e s .  o r i g i n a t e  c o m p o s i t i o n ,  i s  w a v e s ,  i n c i d e n t  c a n  s h i f t e d  o c c u r r i n g  § 1 . 2 FACTORS INFLUENCING RESPONSE... 8  s e c o n d  A  o  s  T h i s  8 . 1 ,  0 . 0 5 g -  f o r  f i l t e r i n g  e x a m p l e ,  d e p o s i t s , o n  p e r i o d .  t h e m  r e c o r d e d  g e n e r a t e d  s o i l  s e i s m i c  d e c r e a s e  o n  w h i c h  m o d i f i e d  T h i s  r e s p o n s i b l e f o r t h e m a s s i v e  e a r t h q u a k e .  f t h e  e f f e c t ,  d a m a g e  CHAPTER 1 : INTRODUCTION T h e  s t r u c t u r e  r e s p o n s e  a t  e m b e d d e d  t h e  t h e  g i v e  r i s e  t o  t r a n s m i t t e d  i n t o  d e f o r m a t i o n  i n  o f  t h e  a s  w e l l  1.2.3 T h e s e  i n  t h e  e r e c t e d  t o  o n  s h e a r s  a n d  o n e  o f  a n y  s o i l ,  c a n  t h e  s t r u c t u r e  o r  a t  m o t i o n s  l e s s  i n t e r a c t  d i f f e r e n c e  s p e a k i n g ,  b e  a l s o  i s  i n  t h e i r  b u i l t  o n  t h e  s a m e  t h e  f o u n d a t i o n  o f  t h e  l e v e l  s o i l  s i g n i f i c a n t  w i t h  i t , w i l l  i n  t h e  w i l l  t h e  o t h e r ,  p r o p e r t i e s , t h e  b e  f r e e  t e n d  p a r t i c l e s .  t h a n  e a c h  T h i s  o f  f r o m  a  t h a t  t h e  r e d u c e  t h e  a m p l i t u d e  c a l l e d  kinematic  t y p e  o f  c a s e  i n  i n  e f f e c t ,  f o l l o w i n g  m o t i o n s  d i f f e r e n t  f i e l d  t o  r e s u l t i n g  o f  a n  s o i l - s t r u c t u r e  a n d  r e s i s t e d  s o i l  w i l l  t h u s  t h a t  t h e  m o m e n t s  b y  t h e  a g a i n  b e  f o u n d a t i o n ,  d i f f e r e n t  w o u l d  b e  a c t i n g  s o i l .  a l t e r  t h e  t h e  i n e r t i a  o n  U n l e s s  m o t i o n s  f r o m  r e c o r d e d  t h e  i n  t h e  o f  o n e  t h e  t h e  t h e  g e n e r a t e d  f o u n d a t i o n ,  s o i l  t h e  s o i l  f o r c e s  i s  f o u n d a t i o n  w i t h o u t  w h i c h  e x t r e m e l y  f o u n d a t i o n .  t h e  b y  i n  s t i f f ,  T h e  w i l l  i t s v i b r a t i o n s  t u r n  t h e  m o t i o n  b e  r e s u l t i n g  a t  e x p e r i e n c e  f o u n d a t i o n ' s  m u s t  t h e  b y  b a s e  i t s e l f ,  p r e s e n c e .  EXPANSION JOINTS (EXPANSION HINGES) j o i n t s  a r e  u s e d  t e m p e r a t u r e .  b r i d g e  f o r  a s  i t s i t s  inertial interaction.  b a s e  s t r u c t u r e w i l l  t h e  t h o u g h t  a s  t h e  o f  r o t a t i o n a l  i s u s u a l l y  s t r u c t u r e i s  b e f o r e  G e n e r a l l y  a n d  k n o w n  w h i c h  B e c a u s e  e v e n  s u r f a c e  t r a n s l a t i o n a l  i n t e r a c t i o n  w i l l  f r e e  o n  b o t h .  f o u n d a t i o n .  interaction,  A f t e r  i n  s o i l  f o u n d a t i o n ,  r e c o r d e d  t h e  t h e  c h a n g e s  m a s s l e s s  o f  a n d  § 1 . 2 FACTORS INFLUENCING RESPONSE ... 9  d e c k  l a r g e  i s  a  b r i d g e  I t i s p o s s i b l e  c o n t i n u o u s .  b r i d g e s .  e x p a n s i o n  i n  j o i n t s  M  a  n  y  l o c a t e d  s u c h  i n  t o  a c c o m m o d a t e  s m a l l  b r i d g e s  H o w e v e r ,  b r i d g e s  t h r o u g h o u t  t h i s  t o  p l a c e  p r a c t i c e  c o n s t r u c t e d  t h e  i t s c h a n g e  l e n g t h  i s  i n  o f  t h e  n o t  t h e  t h e  i n  l e n g t h  j o i n t  a t  a l w a y s  l a s t  f o u r  b r i d g e ,  a t  r e s u l t i n g  o n e  e n d  s o  p r a c t i c a l  d e c a d e s  e v e r y  o r  t h i r d  from  t h a t  c h a n g e s  t h e  e n t i r e  o r  e v e n  p o s s i b l e  s o  h a v e  m u l t i p l e  o r  f o u r t h  s p a n .  CHAPTER 1 : INTRODUCTION R e c e n t  e a r t h q u a k e s  e x p a n s i o n  n u m b e r  j o i n t s .  o f  b e c o m i n g  s u b j e c t  1.2.4 I t  t o  e x p a n s i o n  t o  o p e n e d  a l s o  h a p p e n  a n  e n d  i n  s a m e  u n c o m m o n  p e r p e n d i c u l a r  b u t  j o i n t s  r e s p o n s e  t h e  t h e r e  i s  p l a c e d  n e w  a  n o w  i n  s u p p o r t .  o f  d e m o n s t r a t e d  a  a  b r i d g e s ,  b r i d g e ,  t e n d e n c y  b r i d g e ,  T h o u g h  t h e r e  a n d  t h e  a n d  t h i s  i s  t o  f o r  a  r e t r o f i t  i n a d e q u a t e l y  d e s i g n e r s  p o s s i b l e , t o  h e l p s  n e e d  o f  b r i d g e  w h e r e  p r a c t i c e  s t i l l  h o w  l i a b i l i t y  t o  r e d u c e  o l d e r  h a v e  t h e  d e t e r m i n e  s o  m i n i m i z e  t h e  r i s k  h o w  b r i d g e s  t o  d e s i g n e d  l e n g t h  t h e  c h a n g e  o f  b r i d g e  d e c k s  t h e s e  j o i n t s  a f f e c t  t h a t  t h e y  w i l l  n o t  b e  i s  n o t  r i s k .  SKEWED JOINTS AND C U R V E D BRIDGES  i s n o t  a s k e w  a t  u n s e a t e d  s e i s m i c  c l e a r l y  H e n c e ,  e x p a n s i o n  a c c o m m o d a t e d  t h e  h a v e  § 1 . 2 FACTORS INFLUENCING RESPONSE ... 1 0  j o i n t s  t h e  n o t  i n  o n l y  o f  t h e  w h e n  t h e r e  b r i d g e  s i t u a t i o n .  a l . , 1 9 9 5 ;  C u r v e d  b r i d g e s ,  s i m i l a r  p r o b l e m .  t h e r e  w h i c h  T h e  o f  a n  t h e  p a r a l l e l  T h e  o r  t o  r o t a t i o n a l  t h e i r  t h e  t h a t  u s e d  e x t r a  I n  t h e  l o n g i t u d i n a l  m a n y  s u c h  a n g l e  o f  c u m u l a t i v e  b e t w e e n  t h e  l a r g e  G a v i n  s e a t  w i d t h s  E a r t h q u a k e  E n g i n e e r i n g  i n  c o n n e c t o r s ,  I 5 / S R 1 4  h i g h w a y  i n t e r c h a n g e  a r e  g o o d  a r e  t h e  a d j a c e n t  i t t o  b e  d e c k s ,  o f t e n  a g g r a v a t i n g  b r i d g e  n e e d e d  a l s o  a n d  h e n c e  m o v e m e n t s  i n  i n  R e s e a r c h ,  a r e  a n d  a l l o w s  f u r t h e r  C a n y o n  b e n t s  j o i n t  S u c h  e f f e c t  t h e  o b s t a c l e ,  t h e  m o v e m e n t s .  a l i g n m e n t  c a s e s ,  u n d e r l y i n g  m o v e m e n t  s e c t i o n c o l l a p s e s o f  f o r  w h o s e  s k e w e d  l o n g i t u d i n a l  C e n t e r  i n  b r i d g e  w a t e r w a y .  e a r t h q u a k e ,  f r e q u e n t l y  f a i l u r e s  o r  a  b r i d g e .  e v i d e n c e  N a t i o n a l  f i n d  s e t  t r a n s v e r s e  d e c k  o f f e r e d  a r e  o f t e n  i s r e l a t i v e  d u r i n g  T h e  t o  r o a d w a y  a r e  a x i s  i s r e l a t i v e  e a r t h q u a k e  e t  A m e r i c a  u n d e r l y i n g  c o n j u n c t i o n  u n f a v o u r a b l e  N o r t h r i d g e  t h e  N o r t h  l o n g i t u d i n a l  w h e n  ( M i t c h e l l  t o  i n  t h e  s u c h  a n  1 9 9 4  c a s e s  1 9 9 5 ) .  s u s c e p t i b l e t o  e x a m p l e s .  a  CHAPTER 1 : INTRODUCTION  1.2.5  FRICTION  U n d e r  b r i d g e  i d e a l  m a y  p r e s e n c e  a b i l i t y ,  b e  c i r c u m s t a n c e s ,  f r e e l y  o f  o p e n i n g  o f  c a n  t h e  e f f e c t i v e  i n p a s t  t h e  r e s p o n s e  i n  o f  f u n c t i o n  e x t r e m e  a f f e c t  t h e  g a p  t h e  a n d  t h e  a n  b e  n o  f r i c t i o n  w i t h o u t  i n d u c i n g  j o i n t s  p u r p o s e  d e c k s ,  a t  c a n  l e a s t  t o  a n d  t h e  i n  t h e  o f  t h e  t h e i r  a  m a y  d e c k  j o i n t  d e c k  t h i s  h e l p  s o  a n d  c l o s i n g  t h e  b e i n g  t h e  T h e  h i n d r a n c e  r e d u c e  s e c t i o n  t h a t  s e c t i o n s .  o p e n i n g  H o w e v e r ,  f r i c t i o n  p o s s i b i l i t y  i n  l i m i t  d e g r e e .  T h e  e x p a n s i o n  s t r e s s e s  s e v e r e l y  a  e a r t h q u a k e .  a s  r e l a t i v e  s t i f f  g a p  t h e  b e t w e e n  a m b i e n t  m o v e m e n t  E n o u g h  t o  c a n  a r e  v a r y  t h e  b y  s l a c k  o r  a n d  T h e y  c o u l d  r e l a t i v e  u n s e a t e d .  d i s a n c h o r  c a n  5 0  m m  t h e  f r o m  o r  y i e l d  m o r e .  o f  o f  i n  s p a c e  a s  t o  u s e d  o r  b e  t o  t h e  a s  t h a t  f a i r l y  i n t e r f e r e  r e s t r a i n e r s  a r e  e a r t h q u a k e .  i m p o r t a n t  b r i d g e .  f a c t o r s  t h e  a r e  n o t  t h e  a n  t h a t  s e c t i o n s  p a r a m e t e r s  t h e  O t h e r  s t r e n g t h  s o  a n  t h e s e  l o c a t i o n  a  s h o w n  t h a t  d e c k  p l a y  H o w e v e r ,  t h e  b e e n  e n s u r e  t h e  c o n c e i v a b l y  a t  d e c k  r e s t r a i n e r  t o  i s  R e s t r a i n e r s  b r i d g e  h a v e  e a c h  I t i s i m p o r t a n t  v a r i a t i o n s  s t i f f n e s s  i n  T h i s  r i s e s .  a d j a c e n t  p i e r .  e x c i t a t i o n .  t o  d e c k s .  t e m p e r a t u r e  i s p l a c e d  c o u l d  u p  a d j a c e n t  b e t w e e n  d e c k s .  s e i s m i c  t e m p e r a t u r e  t h e y  s l a c k  r e s t r a i n e r  j o i n t s  r e s p o n s e  i n t h e  r e s t r a i n e r s  a n d  a m b i e n t  c l i m a t e s ,  t h e  w h e n  c h a n g e s  o p e n i n g  t h e  j o i n t  i n t o  o f  i t s s u p p o r t i n g c a p b e a m  l e n g t h  e x p a n s i o n  o f  w i d t h  e a r t h q u a k e s .  a n c h o r e d ,  i n i t i a l  t h e  e x p a n d  d e c k  t h e r m a l  p r o p e r l y  a  o f  d u r i n g  a d j a c e n t  t o  l i m i t i n g  b e t w e e n  T h e  t h e i r  a d v a n t a g e  r e f e r s  d e c k s  m e a n s  w i t h  c o n t r a c t  i n t e r f a c e  d e f e a t  b e t w e e n  s h o u l d  INITIAL GAP OPENING AND RESTRAINER S L A C K  b r i d g e  a  a n  t h e r e  a n d  i n t h e  w o u l d  i n t o  m o v e m e n t s  1.2.6  e x p a n d  f r i c t i o n  w h i c h  t u r n e d  G a p  § 1 . 2 FACTORS INFLUENCING RESPONSE ... 1 1  r o l e  a r e  F o r  w h i c h  r e s t r a i n e r .  i n  t h e  u s u a l l y  b r i d g e s  c a n  a l s o  CHAPTER 1 : INTRODUCTION  1.2.7  DAMPING  A l t h o u g h  a  p a r t  l e s s  i  t h e o p e n i n g  n d a m p i n g  d e s c r i b e  s t r u c t u r e .  t h e  f r o m  o  T h e  1.2.8  t y p i c a l  a  t h e  o n  o  o  f v i e w .  o  f a  b e  c a p t u r e d  c a n  b e  e v e n  b y  u s i n g  a n  r e s p o n s e  t o  o  f a  s t r u c t u r e  t h a t  t o  i d e n t i f y ,  p r e s e n t  i  m u c h  r e a l  d a m p i n g ,  a n d  e a s i l y .  u n d e r s t o o d ,  c o n c r e t e  p l a y  n a n y  r e l a t i v e l y  i s w e l l  m o s t  t o  v i s c o u s  q u a n t i f i e d  a c c e p t e d  f i v e  m e c h a n i s m s  e q u i v a l e n t  e x p e r i m e n t a l l y  t h r e e  a i r r e s i s t a n c e a r e t h o u g h t  d i s s i p a t i o n  I t i s g e n e r a l l y  f a b o u t  a n d  s t r u c t u r e , i ti s i m p o s s i b l e  f t h e e n e r g y  t h e d y n a m i c  n t h e r a n g e  a  l a r g e b r i d g e ,  n e x t ,  d u r i n g  a n  p o s t  m a k i n g  b e h a v i o u r  d e s i g n e r  T h i s  o n e  s e t o  c u r v e ,  w i l l  p l a y  a s  a n  t h a t  f c o l u m n s  o  e v e n t ,  b e h a v i o u r  u s e  d i f f i c u l t  t h e s t i f f n e s s  y i e l d  m a y  m e a n s  i tv e r y  e a r t h q u a k e  d e f o r m a t i o n  D e t a i l i n g  c o l u m n  l e n g t h s .  F u r t h e r m o r e ,  T h e  i  p o i n t  r a t i o  f m i c r o c r a c k s  r e s p o n s e  a l l o  c a n  d a m p i n g  d a m p i n g  d o u b t ,  b r i d g e ,  d i f f e r e n t  a  r a t i o  e f f e c t  o  a t  s t r u c t u r e s  T h e  l e a s t  h a v e  p e r c e n t .  C O L U M N STIFFNESS, STRENGTH AND DUCTILITY  W i t h o u t  I n  o v e r a l l  a c a d e m i c  d a m p i n g  c l o s i n g  m a t h e m a t i c a l l y ,  f v i s c o u s  a n  a n d  t h e v i b r a t i o n a l  c o r r e s p o n d i n g  e f f e c t  a  § 1 . 2 FACTORS INFLUENCING RESPONSE ... 1 2  o  p l a y s  t h e  a s  s t r e n g t h  i m p o r t a n t  f t h e s e  r o l e  a  n a  c o l u m n s  d i f f e r e n t  c r a c k s  m a y  a n d  n o t b e  f o r a  h a s  y i e l d  m a y  o  a  a s  s e i s m i c  s e t o  s t r e n g t h  i d e a l  a s  d u r i n g  t h e d e s i r e d  a s  a  s e c t i o n a l  d e p i c t e d  i  d u c t i l i t i e s .  a  s l i g h t l y  s t i f f n e s s .  d u c t i l i t y  from  s i g n i f i c a n t l y ,  a r e a  n a  c y c l i c  f  I n  w h o l e .  s o m e t i m e s  l a r g e  o  d i f f e r e n t  a n d / o r  f t h e b r i d g e  c h a n g e ,  r e s p o n s e .  f c o l u m n s  s l i g h t l y  i t s e f f e c t i v e  d e g r a d e s  n r e a c h i n g  b r i d g e ' s  s e c t i o n  c o l u m n s  t y p i c a l l y  i  i  t h e b e h a v i o u r  b r i d g e  c o l u m n s  r o l e  c r o s s  h a v e  t h e c o n c r e t e  f t h e s e  s e c t i o n  o  t o p r e d i c t  f c o n c r e t e  l a r g e  s a m e  e a c h  m a y  a  d e c r e a s e s .  b i l i n e a r  f o r c e -  d i s p l a c e m e n t s .  CHAPTER 1: INTRODUCTION  1.3  b r i d g e  w i t h o u t  p r i o r  g e n e r a t e d  m u c h  f i r s t  t o  a t t e m p t  t o  a s  t o  t h e y  T h i s  h o w  s t u d y  r e s t r a i n e r  s e t s  s e c o n d  o f  t a k e n  t h e  a n d  t h e  d i s t i n c t  w a s  t h e  d i f f e r e n t i a l  a n d  a t  c o m p a r e d  T h r e e  s u p p o r t  f r a m e s .  i n  n o  c a n  t i m e  i s o l a t e  w i t h  t o  t h e  t h o s e  b e  f r o m  o n  e f f e c t  t h e  T h e  a n d  o b j e c t  t o  s e i s m i c  j o i n t ,  a s  a  i n f l u e n c e s .  f i v e - b e n t  o f f e r  j o i n t s  t h a n  t h i s  i t  h a v e  s e e m s  r e s e a r c h  i s  r e c o m m e n d a t i o n s  r e s p o n s e  i n t o  o f  s t u d y  l o n g  c a b l e  w e r e  u s e d  b r i d g e s  p r e s e n c e ,  i n  t h e s e  a c c o u n t .  t w o - b e n t  f r a m e s ,  w a s  r u d i m e n t a r y  T h e  h a p p e n  j o i n t s .  r e c o r d s  u s i n g  p a r a m e t r i c  o f  r e s t r a i n e r  i s t a k e n  c a n  e x p a n s i o n  e x p a n s i o n  f i r s t  a n d  c o m p l i c a t e d  e a r t h q u a k e  c o n s i d e r e d  t h e  o f  e x p a n s i o n  o f f i c i a l  t h e i r  i s m o r e  t h e  a r t i f i c i a l  c o n c l u s i v e ,  c o n t a i n i n g  i n v o l v e d .  d e s i g n  j o i n t s  t h e  s o  p a r a m e t e r s ,  p e r f o r m e d ,  f r a m e s  a  b r i d g e s  e x c i t a t i o n  T h o u g h  i s  h o w e v e r ,  t h e s e  i n  f o r c e s  s i m u l a t i o n s w e r e  o n e  o f  e x p a n s i o n  s t r e n g t h s .  t w o - b e n t  v a r i e d  o f  o f  p a r a m e t e r s  a c c o u n t  f r i c t i o n  b e n t  f i v e - b e n t  o n  e f f e c t  o f  s o m e  i n t o  u n s e a t i n g  p r o b l e m ,  n u m b e r  o f  d e c k  r e s p o n s e  T h e  e f f e c t s  v a r y i n g  s t r e n g t h s  e x t r a p o l a t e d  T h e  w i t h  a n d  l a r g e  b e  f r o m  s e i s m i c  i n t e r e s t .  t h e  e x a m i n e s  s i m u l a t i o n s  1.4  t h e  m a y  u s i n g  p a r a m e t e r  o f  i s o l a t e  s i m u l a t i o n s ,  r e s u l t i n g  t h e  r e c e n t  b e c a u s e  c o n n e c t i o n  T w o  f a i l u r e  w a r n i n g ,  a t  t h e  13  OBJECTIVE AND SCOPE OF STUDY  B e c a u s e  i n  §1.3 OBJECTIVE AND SCOPE OF STUDY  r e s u l t s  a n d  t h e  p e r f o r m e d ,  t h e  s u b s t i t u t e .  from  t h i s  E a c h  s t u d y  a r e  f r a m e s .  THESIS ORGANISATION n e x t  c h a p t e r  p a r a m e t e r s  i n  e x a m i n e s  t h e i r  t h e  d e s i g n  l o c a t i o n s  a n d  a n d  p h y s i c a l  i m p l e m e n t a t i o n  m a k e u p  a r e  o f  e x p a n s i o n  e x p l a i n e d .  j o i n t s .  S o m e  o f  CHAPTER 1: INTRODUCTION C h a p t e r  3  p r e s e n t s  i n t r o d u c e s  It  a l s o  T h e  f i l e s  o f  4.  T h i s  5  b e n t  frames,  c h a p t e r  a n d  t h e r e s u l t s  C h a p t e r  u s e d  a n a l y s i s  i n s o l v i n g  w r i t t e n  g e n e r a t i o n  d e s c r i b e s  f i v e - b e n t  a n d  t h e  t o  s o f t w a r e  u s e d  f o r t h e s e  f o r t h e s t r u c t u r a l  e x t r a c t s p e c i f i c  s i m u l a t i o n s ,  r e s p o n s e s  r e s u l t s  i  f r o m  n t h e  t h e  a n d  m o d e l .  l a r g e  d a t a  s o f t w a r e .  t h e  a l s o  f  frames  6  f a r t i f i c i a l  t h e m o d e l l i n g  u s e d  f o r t h e  o  i n t h e  a n a l y s e s  p r e s e n t s  o  e a r t h q u a k e  r e c o r d s  f t h e e x p a n s i o n  a r e d e s c r i b e d  j o i n t  a n d  t h e  i n  d e t a i l s  s i m u l a t i o n s .  p e r f o r m e d  t h e r e s u l t s  o n  t h e  e q u a l - h e i g h t  f o r t h e a n a l y s e s  p e r f o r m e d  a n d  o n  a d j a c e n t  t h e  f i v e -  c h a p t e r  a l s o  frames.  s u m m a r y  d r a w s  a n d  o  p r o g r a m  t h e a n a l y s i s  p r e s e n t s  t w o - b e n t  m e t h o d  t h e c o m p u t e r  s p e c t r u m  t h e t w o - b e n t  C h a p t e r  A  from  r e s p o n s e  C h a p t e r  d e s c r i p t i o n  t h e n u m e r i c a l  d e s c r i b e s  o u t p u t  a  §1.4 THESIS ORGANISATION 14  s o m e  o  f t h e  f i n d i n g s  c o n c l u s i o n s  a n d  from  t h i s  o f f e r s  r e s e a r c h  i s p r e s e n t e d  r e c o m m e n d a t i o n s  o n  i n C h a p t e r  t h e d e s i g n  o  7 .  T h i s  f e x p a n s i o n  j o i n t s .  2  CHAPTER  EXPANSION JOINTS  2.1  INTRODUCTION  B e c a u s e  e x p a n s i o n  f o u n d a t i o n ,  d e s i g n  a n d  e x p e c t e d  t h e y  m u s t  p l a c e m e n t  t e m p e r a t u r e  e x p a n s i o n  j o i n t  e n v i r o n m e n t  o f  c a b l e  o f  s u p p o r t e d  2.2  j o i n t s  t o  a n d  t h e  d i r e c t l y  b e  o f  i n c l u d e d  e x p a n s i o n  e x t r e m e s  n e x t .  i t s b e a r i n g  r e s t r a i n e r s  a n d  s p a n s  i n  T h e  i n  s e a t  u n s e a t e d  h o w  t h e  b r i d g e  t h e  T h e  s e l e c t i o n  i n  o f  S o m e  t h e  o f  t h e  t h e  a r e  s i z e  e x p a n s i o n  e v e n t  o f  a n  a  n  t h e  a n d  p a d  b r i d g e  i n t h e  M  o f  b r i d g e ,  s l i d i n g  m o d e r n  c a r r i e d  a n a l y s i s .  n o m i n a l  l o c a t i o n  w i d t h s  l o a d s  s t r u c t u r a l  j o i n t s .  c a p a c i t y .  l o n g e r  b e i n g  a f f e c t  y  f a c t o r s  t h e  c o d e s  t o  t r a n s m i t t e d  o p e n i n g  m a y  j o i n t s  a n d  d e c k  t h e  i n f l u e n c e  t h e  d e p e n d s  l e n g t h  d e p e n d  w i l l  t o  o n  f r o m  t h e  t h e  t h e  o n e  a m b i e n t  r e c o m m e n d  m i n i m i z e  o n  t h e  u s e  p o s s i b i l i t y  e a r t h q u a k e .  T H E TYPICAL BRIDGE B E N T  E x p a n s i o n  c o n c r e t e  j o i n t s  b r i d g e ,  p e r p e n d i c u l a r  t o  a r e  a  t h e  u s e d  i n  b o t h  t r a n s v e r s e  s p a n  o f  t h e  s i n g l e -  b e a m ,  b r i d g e ,  a n d  d o u b l e - d e c k e r  c o m m o n l y  i s u s e d  1 5  t o  r e f e r r e d  c o n n e c t  t h e  t o  b r i d g e s .  a s  t h e  c o l u m n  I n  a  s i n g l e - d e c k e r  c a p b e a m  t o p s  i n a  b e n t  a n d  t o  l y i n g  e v e n l y  CHAPTER 2: EXPANSION JOINTS  §2.2 T H E TYPICAL BRIDGE BENT  Upper deck  Bridge deck  Girders -  16  • • • • • • • • • T  Capbeam  r»-A — Columns  m ' d l  •  (a)  i  (c)  t h e  l o a d  (b)  I n  t o  i n  g i r d e r s  a  a n y  b e a m .  f u l l  T h e  h e i g h t  s i t o n  e x p a n s i o n  d e c k e r  o n  t h e  a n d  w i t h  t h e  j o i n t s  b r i d g e s .  t h e  t h e  t h e  b e  c o l u m n s .  b r i d g e  b e n t .  c a p b e a m  t h e  (a)  s i n g l e - d e c k e r  b o x  c r o s s  T h e  a r e  a n d  b r i d g e  b r i d g e ,  ( b ) d o u b l e - d e c k e r  c o n s i s t  c o n n e c t e d  w h i c h  e x t e n d  b e a m  ( F i g .  2.2.1(b),  p l a c e d  a t  c o n d i t i o n s ,  e v e r y  t h e  n u m b e r  c a p b e a m ,  d e c k  g i r d e r s  i t s a m b i e n t  t h e  o n  t h e r e  i s u s u a l l y  c a s t  o f  c a n  t r a f f i c  b e  l a n e s  t w o  o r  a n d  m o r e  m o n o l i t h i c a l l y  w i t h  2.2.1(a)).  u s u a l l y  T h e s e  D e p e n d i n g  c o l u m n s  ( F i g .  b e n t s  b r i d g e .  t h e  c o n f i g u r a t i o n s :  t h e  b r i d g e  b r i d g e ,  m a y  i n t o  o f  b r i d g e ,  o f  d e c k s  m o n o l i t h i c a l l y  D e p e n d i n g  w e i g h t  p a r t i c u l a r  w h i c h  b e n t  A - A .  c a p a c i t y  d o u b l e - d e c k e r  t h e  b r i d g e  s e c t i o n  d e c k ' s  c a r r y i n g  c o l u m n s  t h e  t h e  •  • Columns -  T y p i c a l  b r i d g e  d i s t r i b u t e  •  • cross beam  (C)  Figure 2.2.1:  •  Cross beam -  section A - A  b r i d g e ,  •  Beam-column joint -  box girder  .  Lower deck  JZ  t h i r d  o r  o f  t w o  t o  e a c h  f r o m  o n e  ( c ) ) ,  a n d  e x t e r i o r  b e n t  w i t h  o t h e r  f o u r t h  o t h e r  c o l u m n s  a t  t o  m i d - h e i g h t  t h e  n e x t  e x p a n s i o n  f a c t o r s  s p a n ,  w h i c h  j o i n t s  w h i c h  f o r b o t h  a r e  a  u s u a l l y  i n  c o m e  s i n g l e -  b y  e x t e n d  c r o s s  c a s t  t h e  d e c k .  i n t o  p l a y ,  a n d  d o u b l e -  CHAPTER 2: EXPANSION JOINTS  §2.3 EXPANSION JOINT LOCATIONS ... 17  2.3 EXPANSION JOINT LOCATIONS, GEOMETRY AND MAKEUP  Bridge deck and girder  Expansion joints (see figures below for details)  ^  (a)  2 0 mm (typ.)  -Bearing pads  P«r  FS1  Restrainer (steel cable) U— Bridge capbeam  Bridge girder  (c)  (b) Figure 2.3.1:  E x p a n s i o n  t r a n s f e r  2.3.2.  j o i n t s  I n m o s t  c a p b e a m  t w o  g i r d e r s  m o v e m e n t  s u c h  w h e r e  m e e t  o  a r e a l l o w e d  o n e  o  o  n  s y s t e m s ,  t h e y  a  f s e v e r a l  t h e  t h e g i r d e r s  a r e s t r u c t u r a l l y  c a p b e a m ,  b u t t h e y  e x p a n s i o n  t o s l i d e  a  f o r m s ,  l o c a t i o n s ,  d e p e n d i n g  m e t h o d .  a r e f i x e d  T  k  e  o  o  o v e r  y i s u s u a l l y  a r e a l l o w e d  i s p l a c e d  t o e a c h  w  t o s l i d e  i  p a r t w a y  o t h e r .  (b)  o n  f t h e s e  t o t h e i r  c o n t i n u o u s  s h e a r  j o i n t  r e l a t i v e  (a)  c a p b e a m :  a n d i t s c o n s t r u c t i o n  o v e r  I f  j o i n t s  t a k e  f t h e g i r d e r s ,  t h e c a p b e a m .  d e c k s  m a y  m e c h a n i s m ,  t h e  t o  E x p a n s i o n  t h e b r i d g e ' s  a r e s h o w n  s u p p o r t s  s u c h  b  y  n p l a c e  A  t  t h e d e c k ,  r e s t r a i n e r .  d e c k  s p a n ,  l o a d  2.3.1  a n d  e m b e d d e d  i  n F i g s .  l o c a t i o n s  t o p r e v e n t  n t h e l o n g i t u d i n a l  a l o n g  i  w i t h  d o w e l s  s u p p o r t s .  p u t i  (c)  c l o s e - u p ,  a n y  d i r e c t i o n  a s i  n F i g .  n  w h e r e  l a t e r a l  r e l a t i v e  2.3.2,  t h e  CHAPTER 2: EXPANSION JOINTS  §2.4 ELASTOMERIC BEARING PADS  18  Bridge girders  (b) Figure 2.3.2:  I n  b o t h  l o a d  t o  a s  E x p a n s i o n  s y s t e m s ,  b e a r i n g  m e t a l  t h e  m e t a l  t e e t h )  ( c )  j o i n t s  a t  c o n t i n u i t y  p l a t e  t h a t  t o  s p a n  m e s h  q u a r t e r - s p a n :  a t  t h e  t h e  a c r o s s  r o a d  g a p ,  t h e  o r  g a p  (a)  l e v e l  b y  c a n  t h e  ( F i g  l o c a t i o n s ,  b e  u s e  (b)  c l o s e - u p ,  a c h i e v e d  o f  m e t a l  b y  (c)  u s i n g  f i n g e r s  a  w i t h  r e s t r a i n e r .  g r o u t - e n c a s e d  ( s o m e t i m e s  r e f e r r e d  2.3.3).  2.4 ELASTOMERIC BEARING PADS A t  t h e  p o i n t  o f  e i t h e r  ( n a t u r a l  w h e r e  s y n t h e t i c  r u b b e r ) .  d e t e r i o r a t i o n ,  s l i d i n g  i s a l l o w e d  t o  p o l y c h l o r o p r e n e  T h o u g h  n a t u r a l  N e o p r e n e  r u b b e r  i s  t a k e  p l a c e ,  ( N e o p r e n e  e x h i b i t s  p r e f e r r e d  f o r  t h e  d e c k  W R T )  g r e a t e r  s e v e r a l  o r ,  s i t s  o n  m o r e  a n  c o m m o n l y ,  r e s i s t a n c e  r e a s o n s .  e l a s t o m e r i c  t o  o z o n e  N a t u r a l  p a d  m a d e  p o l y i s o p r e n e  a n d  r u b b e r  c h e m i c a l  r e t a i n s  i t s  CHAPTER 2: EXPANSION JOINTS  §2.4 ELASTOMERIC BEARING PADS  19  Metal fingers  Road surface  Compressible grout  Metal plate'  Foam backing  ELEV VIEW  PLAN  ( b )  Figure 2.3.3:  d e s i r a b l e  6 0  ° C ) ,  C o n t i n u i t y  d e s i g n  h a s  a  c e n t u r y ,  p a d  s o  m o v e m e n t s  I t  s h o u l d  T h e r e  b e  a b l e  b e  t o  l o w  a b l e  f u r t h e r  d e s i g n e r ' s  o f  m a n u a l  r e s i s t a n c e ,  e x c e e d  7 % ,  m u s t  n o t  e x c e e d  15%.  a c c e l e r a t e  h a r d n e s s  r u b b e r  w i t h  a n d  c r i t e r i a  t h e  T h e s e  t h e  r a t e  t o t a l  o f  m  a r e  a n d  e n d  t h e  a  x  m  u  t o  p l a t e ,  ( f r o m  t e m p e r a t u r e s  o f  i n  t h e  l o a d s  h e a v y  (b)  a b o u t  a s  - 3 0  w e l l  f i n g e r s .  ° C  a s  c h o i c e  o f  m a t e r i a l ,  t o  v i b r a t i o n s  t o  a b o u t  b e t t e r  e n g i n e e r i n g  d e f l e c t i o n ,  a n d  m e t a l  f o r  t h e  a c c e p t  c r e e p  o v e r  a  b e a r i n g  h o r i z o n t a l  i n d u c e d  b y  t r a f f i c .  r o t a t i o n .  m  s t r a i n  s e t  r a n g e  u s e d  b e a r i n g  i  m e t a l  v e r t i c a l  i m p a c t  s l i g h t  v e r t i c a l  c r e e p  b e e n  m i n i m u m  t h e  f i g u r e s  c o l d  R e g a r d l e s s  w h i c h  1985),  i n  h a s  a b s o r b  a c c o m m o d a t e  a n d  t e m p e r a t u r e  q u a n t i t y .  l o a d s  ( G o o d c o ,  n o t  w i l l  k n o w n  g r o u t - e n c a s e d  l a r g e r  v a r i a b l e  c a r r y  t o  a  n a t u r a l  t e c h n i c a l  m u s t  w h i c h  a  (a)  l e v e l :  o v e r  l e s s  M o r e o v e r ,  w i t h  a l s o  a r e  a n d  i t i s m o r e  s h o u l d  r o a d  p r o p e r t i e s  l o w e r  c h a r a c t e r i s t i c s .  a t  m u s t  s a t i s f y .  c o m p r e s s i v e  f r o m  l i m i t  w e a t h e r  p a d  v e r t i c a l  t h e  s t r a i n  i n  u n d e r  d e f l e c t i o n  m a g n i t u d e  c r a c k i n g  A c c o r d i n g  t h e  o f  t h e  v e r t i c a l  a n d  e n d  i n t e r n a l  s i d e w a l l s  t o  o f  t h e  o n e  l o a d  r o t a t i o n  s t r e s s e s  b e a r i n g  CHAPTER 2 : EXPANSION JOINTS  § 2 . 4 ELASTOMERIC BEARING PADS 2 0  • Shear 6tudsStesi top p'.ate-  ^  Bearlng pad •  '-/ Keeper bars: (all around)  Figure 2.4.1:  p a d .  T h e  s h e a r  e x p r e s s e d  B e c a u s e  u n d e r  a s  s t e e l ,  p r o c e s s  u n d e r  o f  a s  m e a s u r e d  d o  o r  s h i m s  m m  i s  t h e  b a s e  n o t  a s  p l a n  a  a n d  a n y  m u c h  r e s u l t  i n  t o p  o f  s p e c i a l  t h i s  t h e  c o n c r e t e )  o f  t h e  t h e y  t o  b e  n o t  b u l g i n g  p l a t e s ,  b o n d e d  a r e  m a d e  t h e  b y  t h e  l a r g e r  m o s t  t h e  m a d e  e n c a s e d  t h e  t h a n  i t s b a s e  o f  i t s  a n d  o f  t h e  p l a c e m e n t  t h e  o n e  M  2  5  0  m o l d i n g  e l a s t o m e r ,  a t m o s p h e r e .  a b o u t  v e r t i c a l  G 4 0 . 2 1  d u r i n g  i n  d e f l e c t i o n  H e n c e ,  h o r i z o n t a l  e l a s t o m e r  f r o m  t o  5 0 % .  b e a r i n g .  t y p i c a l l y  t h e m  n o  r e l a t i v e  f l u i d ,  o f  c o m p l e t e l y  p r o t e c t  o f  t o  p a d  e x c e e d  d e f o r m a t i o n ,  b e a r i n g  b e  t h e  i n c o m p r e s s i b l e  T h e s e  a r e  o f  s h o u l d  l a t e r a l  c o e f f i c i e n t  s h o u l d  m o v e m e n t  l a t e r a l  p a d .  d i s t a n c e  d i m e n s i o n s  a n  t h e  a l l o y s  p a d .  h e i g h t ,  l i k e  B e c a u s e  i n t r a p l a t e  f o r  t h e  t h i c k n e s s ,  h e a t .  Bottom: plate  b e a r i n g  b e a r i n g ' s  b e a r i n g  c i r c u m s t a n c e s ,  ( 0 . 3 3  b y  l i m i t i n g  t h e  ( 1 / 8 " )  t h e  t h e  b y  i n  n e e d  t h a t  t w o  o f  b e h a v e s  r e d u c e d  3  Pintfll — /  e l a s t o m e r i c  o c c u r s  p r e s s u r e  n o r m a l  m o u n t i n g  a n  b e  a b o u t  r e q u i r e m e n t  U n d e r  l o a d  c a n  p l a t e s  s m a l l e r  s t r a i n ,  e l a s t o m e r  p l a t e s  a n d  o f  p r o p o r t i o n  v e r t i c a l  s t e e l  s t e e l  a  t h e  d e f l e c t i o n  o f  D e t a i l s  Polished stainle66 eteel  -PTFE  Steel shims -  t h e  T h e  q u a r t e r  o n l y  o f  t h e  p a d .  f r i c t i o n  s u f f i c i e n t  t o  b e t w e e n  k e e p  t h e  i t t h e r e .  e l a s t o m e r  a n d  H o w e v e r ,  i n  t h e  c a s e s  CHAPTER 2 : EXPANSION JOINTS w h e r e  t h e  g r o u t e d  b a r  m o u n t i n g  b a s e  c o n c r e t e o r  s u r r o u n d s  T e f l o n )  b e  s l i d i n g  b e t w e e n  t h e  i s s t e e l  ( w i t h  o t h e r r e l a t i v e l y  u s e d .  T h e r e  s u r f a c e  d e c k  § 2 . 5 DECK MOVEMENTS 2 1  a n d  i s  t h e  a r e  u s e d  e l a s t o m e r - s t e e l  s l i p p e r y  a l s o  s o  b e a r i n g  a n  c a s e s  t h a t  p a d  s u r f a c e s ,  t h e  i n  i t i s s u g g e s t e d  w h i c h  a  t h a n  o f  t h a t  f r i c t i o n  a  p i n t e l  o f  o r  p o l y t e t r a f l u o r o e t h y l e n e  m o v e m e n t s  r a t h e r  c o e f f i c i e n t  m o s t l y  w i t h i n  t h e  o c c u r  b e a r i n g  i n  p a d  t h e  0 . 2 0 )  c o m p l e t e  ( P T F E ,  c o n t a c t  ( F i g .  o r  o r  p o i n t  2 . 4 . 1 ) .  2.5 D E C K M O V E M E N T S O n c e  t h e  b r i d g e  c r e e p  a n d  s h r i n k a g e c a n  s i z e  s i x  o f  t h e  b r i d g e  m o n t h s  r e s u l t s  d e c k  a f t e r  f r o m  i s p o u r e d ,  d e c k  t h e  a n d  t h e r m a l  a n d  o f  t e m p e r a t u r e  a n d  T h e  M a y ,  m  a  x  i  8 0  m e t r e s .  3 0  m e t r e s ,  o n e  4 0  m  u  d e c k  m  a n d  e x p a n s i o n  d e g r e e s  a l . ,  o n  i n t h e  t h r o u g h  s h o r t e n i n g  t e m p e r a t u r e ,  F r o m  t h e  s l a b ,  d e c k  w e r e  a m b i e n t  w a s  a g r e e m e n t  t o  s h o w e d  t h i s  c u r i n g  o f  t h e s e  p o i n t  a  t h e  e f f e c t s  o n ,  t h e  p r o c e s s ,  d e c k .  d u r i n g  D e p e n d i n g  b e c o m e  m a j o r i t y  t h e  t h e  n e x t  s m a l l  m m  w o u l d  n o r m a l  c o m p a r e d  ( f r o m  o t h e r  p l a c e d  d e c k ' s  d u r i n g  c h a n g e d  s e r v i c e ,  w i t h  w h i c h  u p o n  n e g l i g i b l e  t h e  a b o u t  o f  d e c k  m o v e m e n t s  t h e  b e n t  m o v e m e n t s  b y  2 8  m o v e m e n t s  d e g r e e s  c o r r e s p o n d i n g t e m p e r a t u r e  3 5  w i t h  j o i n t s  t h a t  t e m p e r a t u r e  e x p e r i e n c e d a  e x p a n s i o n  i n t h e  r o l e  a m b i e n t  1 9 9 5 )  m o v e m e n t  i s i n  j o i n t  t h e  W h i l e  s l a b  d e c k  T h i s  e t  t r a f f i c  c h a n g e s .  t h e  m a j o r  g o e s  e f f e c t s .  ( P e n t a s  e f f e c t s  a  c o n c r e t e  c o n c r e t e i s p o u r e d .  M e a s u r e m e n t s  t h e  p l a y  t h e  b e  c h a n g e  a t  t o  e s t i m a t e s .  e a c h  9 0  - 2 0  t h i r d  m e t r e s .  i n l e n g t h ,  a s  I n  + 1 5  a  s p a n ,  t h e  f o r d e c k  b r i d g e  A s s u m i n g  b e t w e e n  d i f f e r e n t i a l  m m )  t h e  w i t h  o f  t e m p e r a t u r e  f o l l o w i n g  3 9  p l a c e d  d e c k  c a l c u l a t i o n  f r o m  D e c e m b e r  l e n g t h s  b e n t s  c o n t i n u o u s  a  r e s u l t i n g  d e g r e e s .  o f  u p  a t  e v e r y  l e n g t h  from  d i f f e r e n t i a l  s h o w s ,  t o  o f  w o u l d  CHAPTER 2 : EXPANSION JOINTS b e  a b o u t  4 0  m m .  m e a s u r e m e n t  T h i s  w o u l d  T  h  t o h a v e  a l l o w  e  n o m i n a l  b e e n  c o l l e c t e d  w e r e  t h e  n o t a l w a y s  o t h e r .  s o m e  t h e  d a t a  t h e o p e n i n g  T  j o i n t s  h  e  f t h e o p e n i n g  a t t h e m e d i a n  f r o m  =  ( 0 . 0 0 0 0 1  -  3 9 . 6  i n s t r u m e n t e d  t w o  s o  n t h e e x p a n s i o n  t e m p e r a t u r e ,  - 2 0  s h o u l d  t o + 2 0  b e  j o i n t ,  a  a s s u m i n g  m i n i m u m  o  t h i s  f 2 0  m m .  e x p a n s i o n  j o i n t  m m .  l / ° C ) ( 4 0 ° C ) ( 9 0  0 0 0 f f j 7 w )  mm  a n o m a l i e s .  t h a t  a l s o  w e r e  T h e  t h e o p e n i n g  b r i d g e  T h e s e  i  at\TL  =  s h o w e d  o t h e r s .  o  t o r a n g e  s y m m e t r i c a l ,  t h a n  b e a r i n g  a l s o  s i z e  t a k e n  Al  T h e  § 2 . 6 SEAT WIDTHS 2 2  b o t h  m o v e m e n t s  w a s  u n d e r w e n t  b e l i e v e d  w i d e r  a t a n y g i v e n  o  n  o n e  n o n r e v e r s i b l e  t o b e  c a u s e d  b  y  s i d e  o  f t h e b r i d g e  m o v e m e n t s ,  m o r e  t h e r e s t r a i n i n g  t h a n  s o  e f f e c t s  a t  o  f  p a d s .  2.6 SEAT WIDTHS M o s t  b r i d g e s  w o u l d  h a v e  f a i l u r e s  c o n s t r u c t e d b e f o r e  b e e n  r e s u l t e d  a d e q u a t e  f r o m  t h a t  t h e s e a t w i d t h s  m  i  i  n  m  u  m  e x a m p l e ,  s e a t  d e c k  r e c o m m e n d  t o  a b s o r b  u n s e a t i n g  n e e d e d  w i d t h s  t o  1 9 7 0  t o b e  b e  h a d  E q n . ( 2 . 6 . 1 )  i  s e a t  t h e t h e r m a l  i  n t h e 1 9 7 1  i n c r e a s e d .  u s e d  a  d e c k  S a n  S o m e  n e x p a n s i o n  w i d t h  i  l e n g t h  j o i n t s .  c o d e s  T  h  e  f 5 0  i  t o  n a  e a r t h q u a k e ,  n o w  1 9 9 0  t h e m i n i m u m  S  o  c h a n g e s  F e r n a n d o  b r i d g e  f o r c a l c u l a t i n g  n t h e o r d e r  o f f e r  m m .  T h i s  b r i d g e .  i t w a s  W  h  e  n  r e a l i z e d  s u g g e s t i o n s  C a l T r a n s  s e a t  7 5  o  n  g u i d e l i n e s ,  t h e  f o r  w i d t h ,  2  N =  ( 3 0 5  + 2.5L + 10H)  1  * 760 mm  + 8 0 0 0  w h e r e  N  i s t h e r e q u i r e d  s e a t  w i d t h  i  n m i l l i m e t r e s ,  (2.6.1)  )  L  i s t h e  l e n g t h  i  n m e t r e s  t o  t h e  n e x t  CHAPTER 2: EXPANSION JOINTS a d j a c e n t  d e c k ,  e x p a n s i o n  a n d  S  j o i n t ,  i s t h e s k e w  H  o  §2.7 RESTRAINERS 23  i s t h e a v e r a g e  f t h e a b u t m e n t  h e i g h t  i  i  n m e t r e s  n d e g r e e s  o  f c o l u m n s  ( C a l T r a n s  s u p p o r t i n g  t h e  b r i d g e  1 9 9 0 ) .  2.7 RESTRAINERS R e s t r a i n e r s  k e e p  t o  t h e s t r u c t u r e  r e t r o f i t  c a n  a l s o  b e  b e  h a v e  a  d e f e c t  t o g e t h e r  j o i n t s  d u r i n g  w h e r e  a r e c a b l e s  o  u s i n g  a  d y n a m i c  r e s t r a i n e r s  a n d  f a i l  h a v e  s o o n e r  t h e l a r g e r  T h e  w i t h  r e d u n d a n c y ,  l o n g i t u d i n a l  s h a k i n g  i  c o n v e n i e n t  s e a t  w i d t h s  s o m e  C a l T r a n s  a n a l y s i s ,  t h a n  t h e  n o t b e  i n s t a l l e d  f t h e b r i d g e .  l i m i t  t h e s e v e r e  i tm a y  n c o n j u n c t i o n w i t h  d e s i g n e d  t h a t  n e x p a n s i o n  j o i n t s  o p e r a t i o n  r e c o m m e n d s  w i l l  i  r e s t r a i n e r s  n o r m a l  t h e s e  u s e d  i  t i e d  e x p a n s i o n  T y p i c a l l y ,  t h e  i n s t a l l e d  I  t o  s l a c k  M  e  e n s u r e  a s  e x p e c t e d .  t h e r e  m  o  m o v e m e n t  n a n  t o  t o  s o  e a r t h q u a k e .  e x t e n d  a d d  t h a t  a n o t h e r  t h e y  a d e q u a t e  T h e y  d o  o  f  t h a t  a  u s e d  s a f e t y .  s u g g e s t  a b i l i t y .  a n d  T h e y  n o t i n t e r f e r e  ( 1 9 8 9 )  c h a n c e  a r e  w i d t h .  m e a s u r e  s t r e t c h i n g  a  n t h e j o i n t  t h e s e a t  t o D e s i g n e r s  i s a l w a y s  i  I t  s i n g l e  w i t h  t h a t  a l s o  u n i t  CHAPTER ANALYSIS SOFTWARE  3.1  INTRODUCTION  T h e  m o d e l l i n g  j o i n t s  a r e  b e a r i n g  a b l e  t h e  t o  i n t e r p r e t  t h a t  t h e  t h e  p o i n t s ,  t r a v e l l i n g  A n a l y s i s  o f  i n  o f  t h i s  b r i e f  w h i c h  o f  s t u d y ,  l o o k  a t  c a n  u s e d  i n  c o m p u t e r  a n d  w i t h  a t  a s  a  w e l l  w h i c h  j o i n t s ,  t h e m .  p r o g r a m  w a v e .  O n e  t h e  t e c h n i q u e s  b r i d g e  o f  d e a l s  b e t w e e n  p r o g r a m  i s  l a r g e .  t h e  p r o g r a m ,  s p e c i f i c  T h e  i n  r e s u l t s  n e x t  e x p a n s i o n  2 4  t h e  D  o r  A  T  o f  N  2  o f  D  t h e  p r o g r a m .  t h e  X  t o  a n d  T h i s  e x a m i n e s  A  t o  T  h o w  -  m u s t  c a l c u l a t e  t h e  X  t h e s e  a t  e f f e c t  p r o v i d e s  e l e m e n t s  D  a l s o  R e s p o n s e  c h a p t e r  2  b e  r e c o r d  r e f l e c t  c h a p t e r  N  l o a d  b r i d g e s , i t i s  m e m b e r  R  t h e s e  o t h e r  ( D y n a m i c  T h e  D  m o s t  t h a t  e a r t h q u a k e  p o i n t s ,  -  f a c t  r e s p o n s e  s p a n  t h e  v e r s i o n ) .  f r o m  l i k e  c l o s e d ,  l o n g  t h e s e  R  t h e  b r i d g e ' s  w i t h  s o m e  c h a p t e r  j o i n t s .  t h e  i n p u t  b y  m u c h  o p e n e d  a c c e p t  e m p l o y e d  e x t r a c t  w i t h  b e h a v e s  b e  s t u d y  t o  c o m p l i c a t e d  S t r u c t u r e s , e x t e n d e d  a s  a  i s  c a l c u l a t e  t h e y  d e l a y  s u c h  c a p a b i l i t i e s  r a t h e r  t o  t h i s  a b l e  t i m e  t h e  w r i t t e n t o  u s e d  w h e t h e r  b e  o f  j o i n t s  o t h e r w i s e  B e c a u s e  o f  b e c o m e  m o d e l l i n g  t h e s e  e x p a n s i o n  p r o g r a m  2 - D i m e n s i o n a l  p r o g r a m  t i m e s  s y s t e m  i n t e r v a l s  i n c i d e n t  s o m e  a  c o m p u t e r  s t a t e  I N e l a s t i c  d e s c r i p t i o n  a r e  T h e  c o n t a i n i n g  f o r c e s t r a n s m i t t e d a c r o s s  t h e  i n  b r i d g e  s t r u c t u r e s .  m u l t i p l e  a  a  d i s c o n t i n u i t i e s  e s s e n t i a l  o f  o f  e n d s  o u t p u t  u s e d  w i t h  a  f i l e s ,  c a p a b i l i t i e s  CHAPTER  ANALYSIS SOFTWARE  3:  THE  § 3 . 2  D  R  A  I  N  -  2  D  COMPUTER PROGRAM  X  2 5  3.2 T H E D R A I N - 2 D X COMPUTER PROGRAM T h e  D  R  A  F  e f f e c t i v e  N  t o  D  A  T  a n d  N  S i n c e  -  2  D  X  ,  t h e  t y p e s  t y p e s  t r u s s  s o  t h a t  s o  t h e  i m p r o v e d ,  b a s e  t h e  A s  a s  p r o g r a m .  e l e m e n t  w i t h  m a n y  P e r s o n a l  s y s t e m  o r  o n  t o  m i n i m i z e  n e w  2  D  2  o n e  a n d  i n  D  c o n s i s t s  s e t  o f  o f  c a n  t h e  a  c  m  D  P C  R  o  A  L  T h e  2  o f  a n d  D  X  t o  b a s e  h a s  t h e  e a c h  T h e  t h e  o f  t h e  A  N  I  b e e n  p r o g r a m  b a s e  i s t r a n s f e r r e d  t h e  D  X  m e m b e r s .  b e t w e e n  m o d u l e s .  t h e  e l e m e n t  c o n t r o l  t o  t y p e s  l i b r a r y ,  r e w r i t t e n  T y p i c a l  h a s  y e a r s ,  ( A l l a h a b a d i ,  m a n a g e s  s e v e r a l  y e t  p r o g r a m .  a n a l y s e s  w h i c h  e l e m e n t  s i m p l e  O v e r  2  m o r e  o f  a  s u b s t a n t i a l l y  p r o g r a m  e l e m e n t  a s  o r i g i n a l  -  s u b r o u t i n e s  E x i s t i n g  t o  R  i n c l u d e  f o r  1 9 7 0 s  l i m i t e d .  D  s t r u c t u r a l  e l e m e n t s .  n  L a h e y ' s  u s i n g  -  a n d  a  c l a s s e s  a d d e d  m  N  e a r l y  r a t h e r  1 9 8 2 )  I  o f  t h e  c a p a b i l i t i e s  s u b r o u t i n e s  s t r u c t u r e  l a n g u a g e .  u s i n g  A  m o d u l a r .  b e  o  s o f t w a r e ,  R  i n  w e r e  t h e  i n f o r m a t i o n  r e m a i n  a b o u t  c l a s s  e x t e n d  1 9 8 7 ,  d i f f e r e n t  t y p e s  ( P C )  t o  t i m e  m a n a g e m e n t ,  a m o u n t  c a n  p r o g r a m m i n g  t h a t  b e a m - c o l u m n  t h r o u g h  e n g i n e e r i n g  a t  r e l e a s e d  ( G o l a f s h a n i ,  m e m o r y  t h e  e l e m e n t  8 0 4 8 6  -  d e f i n e  I n f o r m a t i o n  a n  N  a n d  d e s i g n  C o m p u t e r  I  D R A L N - 2 D ,  e l e m e n t s  s u b r o u t i n e s  T R A N s l a t i o n )  c l a s s  b a r  u s e d  A  a n d  l i k e  f i r s t  d e v e l o p e d  d e v e l o p m e n t  i n p u t  p r o g r a m  a n d  R  a n a l y s i s ,  a r e  t o  D  w a s  c a p a b i l i t i e s  b e e n  a r e  m u c h  p r o g r a m  I t s  h a v e  i t s d a t a  E l e m e n t  d e t a i l s ,  t o o l .  i t so r i g i n a l  c o n t r o l s  a r e  c o m p u t e r  v e r s i o n s  i m p r o v e  R  D  v e r s i o n s  s u c h  1 9 8 7 ) .  2  a n a l y s i s  i m p r o v e d  T w o  -  c a n  b e  w i t h o u t  t h e  b a s e  O  T  t y p e s .  e l e m e n t  t h e  d e a l  d a t a  e l e m e n t  w i t h ,  a l t e r e d  a n d  o r  c h a n g i n g  t h e  p r o g r a m  a n d  i n t e r f a c e .  N  -  2  D  X  i s w r i t t e n  i n t h e  s o u r c e  c o d e  c a n  F  R  c o m p i l e r  O  R  T  M i c r o s o f t ' s  A  N  F  O  R  T  R  b e  A  F  R  R  c o m p i l e d t o  N  o n  t h e  M  S  A  N  r u n  -  D  ( F O R m u l a  o n  O  P o w e r S t a t i o n  S  a n  8 0 3 8 6  o p e r a t i n g  c o m p i l e r  o n  CHAPTER W i n d o w s .  u s i n g  S u n  c o m p i l e r .  1 . 1 0  S y s t e m  s o u r c e  c o d e  s i m u l a t i o n s  1 9 9 3 )  o n  ( S u n O S )  GENERAL FEATURES OF  § 3 . 3  a  c a n  b e  i n t h i s  S u n  c o m p i l e d  s t u d y  w e r e  S P A R C s t a t i o n  v e r s i o n  4 . 1 . 4 ,  w i t h  r u n  o n  a  a l lp e r f o r m e d  5  3 2  t o  U  N  I  X  U  D  R  A  N  I  X  I  N  -  2  D  u s i n g  o f  2 6  w o r k s t a t i o n  D  R  A  I  N  w o r k s t a t i o n r u n n i n g  m e g a b y t e s  X  -  2  o n  D  X  t h e  R A M .  GENERAL FEATURES OF D R A I N - 2 D X D  R  A  I  N  e l e m e n t s  -  2  D  X  ,  e x a m p l e ,  o f  t r u s s  t h e  d i f f e r e n t  t h e  m a t r i x  m a y  s t r u c t u r e  a n y  s a v e d  b e  d e t a i l s .  s p e c t r u m  t y p i c a l  a x i a l  y i e l d  i s  c a n  H e n c e ,  a n a l y s i s  o  d  e  c a n  T h e  a n d  b e  t y p e  t w o  s a m e  b e  s e v e r a l  c a n  i n t o  s t r u c t u r a l  g r o u p s  t w o  v a r i o u s  o f  o f  t y p e s .  t r u s s  c a n  b e  b e  n o n l i n e a r  T y p e  b e a m - c o l u m n  o f b e a m - c o l u m n  t o  o f  t r a n s l a t i o n a l  c h a r a c t e r i s t i c s  g r o u p s  i s a s s u m e d  d a m p i n g  h a v e  c o n s i s t s  s e v e r a l  m a s s  C l a s s i c a l  a t t h e  i t i s p o s s i b l e  f o r v a r i o u s  s h a p e s  c l a s s i f i e d  m a y  s t r u c t u r e  n o d e  a s s e m b l a g e  c a n  b a r  a p p l i e d ,  s o  a n a l y s i s  c a n  o n e  o n e ,  f o r  e l e m e n t s .  b e  g r o u p e d  e l e m e n t s ,  e l e m e n t s ,  l u m p e d  a n d  a t  t h e  t h a t  e a c h  e a c h  w i t h  n o d e s ,  t h e  s o  d a m p i n g  s t i f f n e s s - p r o p o r t i o n a l .  s a v e d  a n a l y z e d  M  s t r e n g t h ,  d i a g o n a l .  b e  a r e  a n d  t h e r e  t w o - d i m e n s i o n a l  E a c h  p o s s e s s i n g t h e  s t r u c t u r e ,  a  1 9 9 3 ) .  e l e m e n t s  a n d  a n d / o r  a s  E l e m e n t s  b a r  c a p a c i t y .  m a s s -  s t a t e  s t a t e .  c a n  t y p e  m a t r i x  b e  T h e  l o a d i n g  a  m o m e n t  m a s s  s t r u c t u r e  s a m e  m o d e l l e d  ( P r a k a s h ,  c o n s i s t s  W i t h i n  t h a t  n o d e s  f r e e d o m .  t o g e t h e r .  d i f f e r e n t  a t  i s  o f  o f  a  s t r u c t u r e  d e g r e e s  E l e m e n t s  w i t h  a  c o n n e c t e d  r o t a t i o n a l  a  t h e  T h e  ( N o v e m b e r ,  O p e r a t i n g  3.3 I n  A l t e r n a t i v e l y ,  Til  t h e  v e r s i o n  ANALYSIS SOFTWARE  3:  a n d  e n d  t o  o f  a n y  i n p u t  l o a d i n g  p e r i o d s c a n  p e r f o r m e d  f o r  a n  t h e  a n a l y s i s ,  s t r u c t u r e  p a t t e r n s  b e  a n d  i n  o n e  s u b s e q u e n t l y  c a l c u l a t e d  u n s t r e s s e d  d a t a  f o r a n y  s t a t e .  b e  r e s t a r t e d  c o m p u t e r  b y  s t a t e ,  s i m p l y  a n d  r u n ,  f r o m  a n d  t h e  d e f i n i n g  t h e  l i n e a r  r e s p o n s e  CHAPTER  3 :  W h e r e a s  s t a t i c  i  n o w  U  p  o  I  N  -  2  c a n t h e n  file.  D  b e  R  A  t h e i r  a n a l y s i s  p e r f o r m e d .  t o  o b t a i n  w i t h o u t  a n d  T h e  h i g h  a n d  d a t a  t h e n o d e s  i n  t h i s  R  A  r e s e a r c h .  I  h  e  a n d  s m a l l  -  2  D  T h e i r  a n d o u t p u t  d e s c r i p t i o n s  b e  a n d / o r  w i t h  l a r g e  file  T  h  e  files  h a s  o  o  f  .ECH  file  e n e r g y  i  i  files,  a n d  b  e c h o  A .  f o l l o w e d  t y p e s ,  y  b  y  o  D  X  a  d y n a m i c  t h e  p r o g r a m  a n d  i m p o s e d  s t r u c t u r e ,  a n d  s t a t e .  i  n t h e  e x t e n s i o n s  d e p e n d  A  n  o n  t i m e  i t  m  u  a  x  i  m  c a n  s t e p  m  v a l u e s  d a t a ,  i n f o r m a t i o n .  o  s t r u c t u r e  f t h e  d e s i r e d  d e s c r i p t i o n  t h e d e s c r i p t i o n  f w h i c h  t h e  p o s s i b l e  f t h e i n p u t  l o a d  t o  n o d a l  a n a l y s i s  m a k e s  o  2 7  l i n e a r  s p e c i f i e d  t h e i n p u t  T h e  2  a n d  s p e c i f i e d  u n b a l a n c e d  f o l l o w e d  e l e m e n t  file.  T h i s  a n  -  f o r s e l e c t e d  a n d t o o b t a i n  c o n t a i n s  a  w o u l d  a t  N  n t h e d a m a g e d  r e s u l t s  o u t  L  t h a t  filename  o u t p u t  p r i n t e d  s o  n a m e  g e n e r a t e d  n A p p e n d i x  p r o p e r t i e s ,  s i xd i f f e r e n t  f o l l o w .  u n i q u e  h i s t o r y  A  s t a t i c  d a m a g e  f t h e a n a l y s i s .  o u t p u t  a r e s h o w n  a  t o t h e . O U T  f t h e s t r u c t u r e  a n d  files  t i m e  o  t o  R  v e l o c i t i e s  b u t d i f f e r e n t  r e s u l t s  c o n t a i n i n g  i n i t i a l  b e h a v i o u r  u s i n g  f i l e n a m e ,  a d d e d ,  D  f o l l o w i n g  n o n l i n e a r  p e r f o r m e d  f f i l e s  t y p e  a n a l y s i s  b e e n  s p e c i f i e d  o u t a t t h e e n d  s t e p .  h a v e  t h e s t r u c t u r e ' s  s e t o  s t e p s ,  c o o r d i n a t e s  c u r r e n t l y  c a n p e r f o r m  c a n  a n d  e x t r e m e l y  g  X  a r e w r i t t e n  p r i n t e d  o  D  d y n a m i c  m o d u l e s  e n v e l o p e  f t h e d e s c r i p t i o n  X  2  t h e s a m e  t i m e  l  a  n u m b e r  a t e a c h  t h e i r  -  a n a l y s i s  r e s p o n s e s  w i t h o u t  o  N  e x c i t a t i o n ,  g e n e r a t e s  e x a c t  r e s u l t s  i n p u t  N  X  s o l u t i o n  c o n s i s t s  i n c l u d e s  D  v e r y  i s a  S a m p l e  D  I  n o n l i n e a r  t o i n v e s t i g a t e  a l l h a v e  o u t r e s u l t s  a n a l y s e s .  e l e m e n t s .  2  A  a  a n a l y s i s  d y n a m i c  I f r e q u e s t e d ,  a c c u r a c y  i n p u t  -  R  s u p p o r t  a p p l i e d  T  e n v e l o p e  file  a  N  f D  d y n a m i c  e l e m e n t  w i t h  p r i n t i n g  t h e . S L O  w  files  c o n t e n t .  d i s p l a c e m e n t s  a n d  I  T h e s e  p e r f o r m e d  e  o  GENERAL FEATURES OF  § 3 . 3  p e r f o r m  v e r s i o n  H e n c e ,  e x e c u t i o n ,  i n t e r v a l s ,  N  o n l y  d i f f e r e n t i a l  i n d i c a t e  b e  c o u l d  o r d e r .  l o a d s .  d a t a  D  t h e c u r r e n t  n a n y  l o a d s  n  i n p u t  A  c o n s i d e r  d y n a m i c  s t a t i c  R  a n a l y s i s ,  a n a l y s e s  c a n  D  ANALYSIS SOFTWARE  t h r e e  o  f t h e  a r e  u s e d  CHAPTER 3 : ANALYSIS SOFTWARE  § 3 . 4 ELEMENT TYPE O N E 28  3.4 E L E M E N T T Y P E O N E  NodeJ  Figure 3.4.1: a c h i e v e i n  s t r a i n  i n e l a s t i c  h a r d e n i n g ,  ©  t r u s s y i e l d  b a r i  (a)  e l e m e n t :  n t e n s i o n  a n d  o r i e n t a t i o n ,  c o m p r e s s i o n ,  (b)  p a r a l l e l  ( d ) y i e l d  i  c o m p o n e n t s  n t e n s i o n ,  t o  b u c k l i n g  c o m p r e s s i o n .  DRAIN-2DX  a x i a l  m a y  T h e  Axial Force  f o r c e s  b e  d e f i n e s  ( P o w e l l ,  o r i e n t e d  S t r a i n  h a r d e n i n g  e l a s t i c  a n d  i  c o r r e s p o n d i n g  1 9 9 3 ) .  n a n y  d i r e c t i o n  w h i c h  S t a t i c  f i x e d  t y p e  l o a d s  e n d  o n e  I t c a n b e  i s m o d e l l e d  a n o t h e r  c o n s i d e r e d .  e l e m e n t  i  a s  u s e d  a n  t o m o d e l  i s e l a s t i c  f o r c e s .  t r u s s  t r u s s  b a r c a p a b l e  m e m b e r s  a n d  o f  t r a n s m i t t i n g  s i m p l e  o n l y  c o l u m n s ,  a n d  c o m p o n e n t s ,  o n e  ( F i g . 3 . 4 . 1 ( a ) ) .  n t h e p r o g r a m  a l o n g  i n e l a s t i c  a n d  t h e  b y  p e r f e c t l y  e l e m e n t  c o m b i n i n g  p l a s t i c  l e n g t h  t w o  p a r a l l e l  ( F i g . 3 . 4 . 1 ( b ) ) .  c a n  b e  c o n s i d e r e d  P - A  b y  e f f e c t s  c a n  s p e c i f y i n g  b e  t h e  CHAPTER 3: ANALYSIS SOFTWARE T w o  b e  i n  I f  a l t e r n a t i v e  s p e c i f i e d  t e n s i o n ,  t o  m o d e s  y i e l d  b u t  t o  o f  s t i f f n e s s - p r o p o r t i o n a l  p a r a l l e l  w i t h  b a r  e l e m e n t .  b a r  e l e m e n t  e a c h  t h a t  t h e  a r e  g r o u p  e l a s t i c a l l y  d a m p i n g  e l e m e n t .  T h e  a r e  t y p e  b e a m s  f l a n k e d  i s  t y p e  o n  h i n g e s  t h e  T h e  a t  c a n  y i e l d  b e  i s a  e n d s  b y  a  e n e r g y  a s  l i n e a r  i s P  i n  d y n a m i c  l o g  f i l e s ,  s o  t h a t  e l a s t i c  a n a l y s i s ,  t h e  t y p e .  3.4.1(c),  F i g .  d a m p i n g  i n i t i a l  b y  i n  e l e m e n t  o r  I t  t o  m a y  y i e l d  3.4.1(d).  F i g .  t h e  a b s o r b e d  s o l u t i o n  s h o w n  v i s c o u s  t i m e s  f o r a n y  a s  f o r t h i s  v i s c o u s  t h e y  e l e m e n t  i s a d d e d  s t i f f n e s s  o f  e v e n  i  ft h e  d a m p i n g  m a y  b e  i n  t h e  t r u s s  b a s e  t r u s s  e l e m e n t s  c h e c k e d  t o  i n  e n s u r e  s i m p l e  b y  i n p a r a l l e l  i n  Two  m o m e n t  t h e  t h r o u g h  t h e  a n d  h i n g e s  c a n  W  t o  h  e  n  t a k e  ( F i g .  y i e l d i n g  p l a c e  b e  i n t e r a c t i o n  t o  s p e c i f i e d  T h e  y i e l d  s t e e l  o f  i s r e a c h e d ,  i n  t h e  i n c r e a s e ,  b e  e f f e c t  s u r f a c e .  a n  e l a s t i c  t h e  a x i a l  f o r c e  e l e m e n t  i n  a n d  b e n d i n g  i n e l a s t i c  f o r m a t i o n  o f  p l a s t i c  c o m p o n e n t ,  s i m u l a t i n g  a t  c o n c r e t e  i n e l a s t i c  h a r d e n i n g  i n e l a s t i c  d i f f e r e n t  o f  r e i n f o r c e d  o f  S t r a i n  c o n s i s t s  o n l y  t o  a n d  e s s e n t i a l l y  3.5.1(a)).  e l e m e n t  c o n t i n u e s  n e g a t i v e b e n d i n g .  P - M  I t c o n s i s t s  z o n e s  i n e l a s t i c  3.5.1(b)).  f o r m o d e l l i n g  1993).  e n d  c o m p o n e n t  t h e  a  r i g i d  i s a s s u m e d  e l a s t i c  f o r  e l e m e n t  ( P o w e l l ,  t h a t  ( F i g .  f o r p o s i t i v e  s p e c i f i e d  i n e l a s t i c  o p t i o n a l  a s s u m i n g  m o m e n t s  a n d  i n t h e  b e a m - c o l u m n s  c o n s t a n t  m o m e n t s  e l e m e n t ,  t w o  b o t h  c o m p o n e n t s  c o m p r e s s i o n ,  c o n s t a n t  o f  s p e c i f i e d  r e a s o n a b l e .  a n d  m o d e l l e d  i n  b e  c o m p r e s s i o n ,  I t s v i s c o s i t y  r e m a i n s  s h o w n  a n d  m a y  i s s p e c i f i e d ,  a m o u n t s  3.5 E L E M E N T T Y P E E l e m e n t  b e h a v i o u r  t e n s i o n  v i s c o s i t y  y i e l d s .  e l e m e n t  t h e y  b a s i c  T h i s  i n e l a s t i c  i n b o t h  b u c k l e  §3.5 ELEMENT TYPE T w o 29  t h e  o n  s t r a i n  t w o  w h i l e  h a r d e n i n g .  e n d s  b e n d i n g  o f  t h e  s t r e n g t h  § 3 . 5 ELEMENT TYPE T w o 3 0  CHAPTER 3 : ANALYSIS SOFTWARE  Elastic-plastic component with ideal (non-hardening) plastic hinges  Combine^ .  Moment  NodeJ Elastic-plastic component \Rigid none Node I cotnp°J*?L.  Elastic Strain hardening component is a simple elastic element  Curvature  (a)  (b)  EndJ  M. M.  1  *«  0  EI L  k..  0  j.  I  End I  Figure 3.5.1: c o m p o n e n t s s t i f f n e s s  E l e m e n t s  s t i f f n e s s  w i t h  S t a t i c  b e  t a k e n  A s  i n  t h e  i n t r o d u c i n g  i n t o  t r u s s  a  o f  k,  k  u  o f  e n e r g y  b y  s e c t i o n s  a b s o r b e d  ky  t h e  c a n  e l e m e n t  l e n g t h  (a)  w i t h  rigid  e n d  d e f o r m a t i o n s  c o n s i d e r e d  e l a s t i c  o f  t h e  t h e  b e a m  e l e m e n t ,  z o n e s ,  a n d  f o r c e s ,  t h e  (b) a n d  o r  i n i t i a l  d a m p i n g  a r e  P - A  f o r c e s  e n d  p a r a l l e l f l e x u r a l  i s  f o r a n y  d i s p l a y e d  f l e x u r a l  e f f e c t s  f r o m  c a n  o t h e r  b e  c a u s e s ,  f o r c e s .  t a k e n  I t s v i s c o s i t y  c o n s t a n t  e l e m e n t s  a p p r o p r i a t e  ( F i g . 3 . 5 . 1 ( c ) ) .  i n p a r a l l e l .  r e m a i n s  d a m p i n g  s p e c i f y i n g  c o r r e s p o n d i n g f i x e d  e l e m e n t  a n d  b y  e l e m e n t ,  s t i f f n e s s - p r o p o r t i o n a l  d a m p i n g  b y  b e  f o r t h e  s p e c i f y i n g  e l e m e n t s ,  b a s i c  e l e m e n t :  ©  e l e m e n t .  a l o n g  v i s c o u s  t h e  h a r d e n i n g ,  a n d  u  a c c o u n t  l i n e a r  s t i f f n e s s  c r o s s  l o a d s  b a r  b e a m - c o l u m n  s t r a i n  f o r t h e  v a r i a b l e  c o e f f i c i e n t s  c a n  a m o u n t s  i n e l a s t i c  a c h i e v e  r e l a t i o n s h i p  c o n s i d e r e d .  e l a s t i c  T h e  t o  i s  i n t o  P  t i m e s  d y n a m i c  i n  t h e  a c c o u n t  t h e  i n i t i a l  a n a l y s i s .  s o l u t i o n  b y  l o g  T h e  f i l e .  CHAPTER 3: ANALYSIS SOFTWARE  §3.6 ELEMENT TYPE NINE  31  3.6 E L E M E N T T Y P E NINE  Force (tension or compression) Elastic f  An initial state can be a prestress force or initial gap/slack. —  Deformation (extension or shortening)  Gap opening or slack in cable  Figure 3.6.1:  A  r e l a t i v e l y  i s  e s s e n t i a l l y  w i t h  a n  T h e  n e w  a  a d d i t i o n , t h e  s i m p l e  i n i t i a l  a r b i t r a r y  f o r c e - d e f o r m a t i o n  g a p  i n e l a s t i c  o r  o r i e n t a t i o n ,  a  b u t  d e f o r m a t i o n  r e l a t i o n s h i p  i t  i n  a c t s  o n l y  t e n s i o n .  p o s i t i v e  I n  a  o r  W  o r  h  I n  o r  m o r e  e  n  t h i s  s e n s e .  p r e s t r a i n e d t o  e l a s t i c a l l y  t w o  m o d e ,  s e n s e .  p o s i t i v e  i t h a s  I n  a  m o d e ,  s p e c i f i e d  a n  f i n i t e  i t i s u s e d  i n F i g .  a  g a p  t o  s t a t e ,  f o r c e s  t h i s  n e g a t i v e  I n d e e d ,  e l e m e n t s  i n  a  a n d  W  a n d  h  u p  n  b e  I t  o f  t o  e l e m e n t .  t h e  m o d e l  1993).  b e  m a d e  i t i s u s e d  e l e m e n t  m o d e s  u s e d  c a n  i t a c t s  c a n  n i n e  ( P o w e l l ,  w h e n  d e f o r m a t i o n .  p a r a l l e l .  b e  t h i s  e  t y p e  c o m p r e s s i o n / t e n s i o n  e l e m e n t  c a b l e ,  e l e m e n t  c o m p l e x  a  a  c a n  t h o u g h  o p e n s  m o d e l  i s  s l a c k  3.6.1.  f o r c e s  f o r  w h i c h  i n i t i a l  l e n g t h ,  t e n s i l e  i t s i n i t i a l  t h e s e  w i t h  a n d  e l e m e n t  e l e m e n t ,  c o m p r e s s i v e  i n e l a s t i c a l l y .  o f  n i n e  b a r  i s s h o w n  c o m p r e s s i o n ,  t h i s  c o m p r e s s i o n .  c a b l e  t y p e  r e l a t i o n s h i p  t o  n e t  o n l y  i n  a r e  a l s o  b e h a v i o u r  b e  t o  a r e  a  m a y  b e  t o  c o n s i d e r e d  s p e c i f i e d  t o  f o r c e -  b e c o m e s  i t g o e s  s p e c i f i e d  h a v e  s l a c k  t o  f o r c e  u n l o a d  o b t a i n e d  a n  e l e m e n t ,  i t  c o n s i d e r e d  a n d  h a s  T h e  b e a r i n g  o n  I t  e l e m e n t  e l e m e n t  s m a l l .  a  e l e m e n t .  b e a r i n g  a c t i n g  t e n s i o n ,  p r e l o a d e d  c a n  v e r y  f o r c e  l e n g t h e n i n g  a  T h i s  m o d e l  s h o r t e n i n g  l i n k  b y  a  i n  h a v e  l e v e l ,  e i t h e r  p l a c i n g  CHAPTER 3 : ANALYSIS SOFTWARE P - A  e f f e c t s  d a m p i n g  o r  i s  e l e m e n t ' s  v i s c o u s  3.7  f o r  s p e c i f i e d ,  i n i t i a l  d a m p i n g  a  c a n n o t  l i n e a r  s t i f f n e s s ,  i s  e l e m e n t s  a r e  m o d i f i c a t i o n s w e r e  e l e m e n t  s h e a r  U  l o a d s  c u r r e n t l y  v i s c o u s  a d d e d  i n  s h o w n  b e  t a k e n  i n t o  d a m p i n g  e l e m e n t ,  p a r a l l e l .  T h e  i n  t h e  s o l u t i o n  a c c o u n t .  w i t h  a m o u n t s  l o g  I f  s t i f f n e s s - p r o p o r t i o n a l  s t i f f n e s s  o f  p  e n e r g y  t i m e s  t h e  a b s o r b e d  b a s i c  b y  t h e  f i l e .  MODIFICATIONS TO THE D R A I N - 2 D X SOURCE C O D E  M i n o r  a  e l e m e n t  § 3 . 7 MODIFICATIONS TO THE SOURCE CODE 3 2  N  t y p e  f o r c e s  I  X  w e r e  M o s t  r e a d a b i l i t y  a r e  o f  t w o .  m o r e  w a s  m o r e  p l a t f o r m , t h e  l e t t e r s .  t y p e  t w o  o f  T h e  t h e  s h o w n  i n  c r i t i c a l  c h a n g e s  c o l u m n  t o  i n t h e  i n  b e  SOLUTION TECHNIQUES  T h e  s t a t i c  a s  s c h e m e  t h a n  a l s o  a l l o w s  n o d e s ,  a  a r e  s i g n i f i c a n t  a  t h e  e l a s t i c - p l a s t i c  p e r f o r m e d  c h a n g e  i t e r a t i o n  d e t a i l e d  A  I  N  -  2  X  s h e a r  r e s e a r c h .  s o u r c e  B e c a u s e  w e r e  f o r m a t  o u t p u t  a n d  f i l e  o n  s o u r c e  f o r c e s  c o d e  h e a d i n g s  v i s i b l e  D  c o d e .  T h e  i n s t e a d  t h e  o f  a l l c o n v e r t e d  c o l u m n s  s c r e e n  a x i a l  m o d e l l i n g  m o d i f i c a t i o n s  w e r e  t i m e  m a d e  w e r e  w a s  from  p e r f o r m e d  c a p i t a l  t o  m a t c h e d  i n  A  u p  l  t o  f o r  a s  o n  s m a l l  e n h a n c e  s o m e  s c r o l l i n g .  r e s u l t s  d e f o r m a t i o n s ,  m a d e  s m a l l e r  w i t h o u t  h i s t o r y  t h e  e l e m e n t  c a s e s  s o  l s u c h  t h a t  c h a n g e s  A .  3.8  d e f i n e d  R  o u t p u t  t h e  w o u l d  D  i n c l u d e  t h i s  o u t p u t  w i d t h s  A p p e n d i x  t o  w e r e  T h e  d e t a i l s  a n a l y s e s  t h e  m o d i f i e d  o u t p u t .  e l e m e n t  t o  f i l e n a m e s  o t h e r  t h e  m a d e  i n  m e t h o d ,  c a l c u l a t i o n  w o r k  o n  t h e  u s i n g  a n  s t i f f n e s s .  t h o u g h  o f  I n  e v e n t - t o - e v e n t  s o m e  i t m a y  e n e r g y  e l e m e n t s ,  w a y s ,  r e q u i r e  b a l a n c e ,  k i n e t i c  t h i s  m o r e  w h i c h  e n e r g y  s c h e m e ,  i s a  s i m p l e r  c o m p u t e r  a c c o u n t s  a n d  w h e r e  e a c h  i s  a n d  m o r e  r e l i a b l e  t i m e .  T h i s  s c h e m e  f o r e x t e r n a l  d a m p i n g  e v e n t  w o r k .  w o r k  T h e s e  o n  t h e  e n e r g y  CHAPTER 3 : ANALYSIS SOFTWARE v a l u e s  a n  s h o u l d  i n d i c a t i o n  T h e  s o ,  t h e  t h i s  o f  t h e  p r o g r a m  s t e p  l o a d  t a k e  e v e n t  t h e  b e  t h e  s i z e  o f  i t s  c o n t r o l  t h e  o n  e x a c t  h o w  v e l o c i t y  a t  a  s t e p  t h e  e i t h e r  w i t h i n  n o t  t i m e  t h e  b r i n g  T h i s  f o r t h e  o f  t h e  t o  c a n  a t  i m b a l a n c e  s t e p s .  o f  b e  t h e  c a n  e f f e c t i v e  s t e p  a r e  s p e c i f i e d .  b e  t o l e r a n c e s  s p e c i f i e d  a t  f o r  t h i s  u n t i l  s t e p s  a n o t h e r  i s  u s i n g  e l e m e n t  c a n  c h o s e n ,  p r o g r a m  t o  t h e  p o i n t  i n t e g r a t i o n  p e r f o r m e d  I f  p r o p o r t i o n  c h a n g e s  i s e x c e e d e d .  f o r e a c h  e a c h  e v e n t .  c a l c u l a t e d  t i m e  T h e  o f  s o l v e s  i s a d j u s t e d  b e  b e  a n  t h e  a n d  s t e p - b y - s t e p  m a y  e n d  r e a c h e d  e v e n t  I f v a r i a b l e  t h e s e  b e  t i m e  T h e  s t e p - e n d s  a l s o  t h e  w i l l  A t  c a l c u l a t e s  m a t r i x  t h e  v e c t o r .  e i t h e r  c o r r e c t i o n s  o f  m u s t  h a s  p r o g r a m  s t i f f n e s s  t i m e  f o r c e s  w h e n  t o l e r a n c e s  s t r u c t u r e  a d j u s t e d m a t r i x  l o a d  e n e r g y  i n t e g r a t i o n .  e l e m e n t  r e m a i n d e r  f o r i m p u l s e  o v e r s h o o t  t h e  T h e  t h e  v a r i a b l e  a c c o r d i n g l y  i n  s t r u c t u r e  e l e m e n t .  a n d  s t e p - b y - s t e p  a p p r o a c h .  t o  r e m a i n d e r  a  s u b s t a n t i a l  c o r r e c t l y .  e l e m e n t s  T h e  o r  A  p e r f o r m e d  r e q u i r e d  s t e p s  a n a l y s i s .  u s i n g  o f  c o n s t a n t  s t e p  t h e  f r a c t i o n a l  t o l e r a n c e s  E v e n t  E v e n t  i m p r o v e  t o  b e t t e r  a n a l y s i s .  p r o c e d u r e  t h e  f a n y  a f f e c t e d  a n d  t i m e  3.9 NUMERICAL T h e  w a s  d i s p l a c e m e n t s  e r r o r  n e x t  o f  p e r f o r m e d  u s i n g  t h a t  t h e  u s i n g  b a l a n c e .  a r e  e n d  d i s p l a c e m e n t s .  N o d a l  l o w e r  c o m p u t a t i o n s  e n e r g y  n o d a l  m a t r i x  p e r f o r m e d  a n d  i n  a c c o u n t  o c c u r s .  t h e  e v a l u a t e s i  v e c t o r  i n t o  a t  a n a l y s i s  i s r e p e a t e d  a d j u s t e d  u p p e r  t h e  a n a l y s e s  c o r r e s p o n d i n g  t o  c h e c k e d  t h a t  d y n a m i c  s t e p ,  b e  § 3 . 9 NUMERICAL INTEGRATION 3 3  INTEGRATION a n d  a c c e l e r a t i o n  t h e  b e g i n n i n g  p a r a m e t e r s  i s  o f  a s s u m e d  t h e  s t e p  u s e d  t o  a r e  i n  v a r y  u s e d  t h e  i n  a s  n u m e r i c a l  t h e  t i m e  i n i t i a l  s t e p - b y - s t e p  i n c r e m e n t s .  c o n d i t i o n s  t o  i n t e g r a t i o n  T h e  s o l v e  d e p e n d  d i s p l a c e m e n t  f o r t h e  m o t i o n  a n d  o f  CHAPTER 3 : ANALYSIS SOFTWARE t h e  m a s s  W i t h  a t t h e e n d  t h e u s e  r e s u l t s  w i t h  P e n z i e n ,  t h e  o  f t h e s t e p ,  f s u i t a b l y  r e l a t i v e l y  1 9 7 5 ) .  I f  d i s p l a c e m e n t  m a s s  o  c a n b e  i n  o f  a  b  y  f/t)  = =  f/t)  =f (u,u)  T h e  cu  p(t)  d y n a m i c  e q u a t i o n  y  t h e  t a k i n g  o f  t i m e  t h e d i f f e r e n c e  r e p r e s e n t i n g  m o t i o n ,  I f  t h e  t h e m a s s ,  s m a l l  i m p o r t a n t  d a m p i n g  t i m e  o  " / / ' , ) ]  At,  c o n s i d e r a t i o n ,  r e c a l c u l a t e d  u s i n g  a n  + /  D  f (t)  f  s y s t e m ,  y i e l d  c o n c e p t  u=d u/dt ,  e x c e l l e n t  ( C l o u g h  u=u(t)  t h e v a r i a b l e  2  a n d  t o  s t e p .  a n d  d e n o t e s  2  t h e m o t i o n  o f  t h e  m o t i o n  =  s  f o r  a n  p(t)  ( 3 . 9 . 1 )  i n e l a s t i c  E q n s .  WT>  t h e n  + /  i  n t h a t  -/ (',)]  +  D  o  i n  A a ,  s y s t e m ,  c A w ,  t i m e  ( 3 . 9 . 2 ) ,  kku^  At,  - / s C ' , ) ]  i  =  b e c o m e s  ( 3 . 9 . 2 )  t h a t  c a n b e  =  e l e m e n t  t,  =  2  a n d  t,  +  t  2  At,  t o  a n  r e p r e s e n t  e q u a t i o n  o b t a i n e d .  C i )  t o r e m a i n  r e w r i t t e n  A p ( r , )  t  P ( ' 2 ) ~P  i n t e g r a t i o n  f a n  t+At,  a t  a n d u s i n g  s u c h  i s a s s u m e d  a n  l a t e r  P  c a n b e  t h a t  t i m e  = (t+Af)  i n t e r v a l  [/"A)  m a t r i x  +  s h o r t  i n t e r v a l  t h e e q u a t i o n  +  a n d  f t h e s y s t e m  s t i f f n e s s  a  ( r + A r )  ( 3 . 9 . 1 )  a n d i s t h e r e a s o n  a d j u s t e d  S  f t h e t i m e  f t h e m a s s  +  e v a l u a t e d  ( f + A f )  a n d s t i f f n e s s  i n t e r v a l  o  f o u n d  i t s s i m p l e  u-du/dt  t h a t  b e e n  f o rt h e n e x t  f o r c e ,  f o r c e  w h e n  a n d e n d o  t h e m o t i o n  Wi)  d a m p i n g  b e t w e e n  a t t h e b e g i n n i n g  +  d e s p i t e  (SDOF)  e q u a t i o n  h a s  c o n d i t i o n s  l o a d .  / / f + A r )  B  m e t h o d  e f f o r t ,  s u c h  D  i s t h e r e s i s t i n g  i s t h e e x t e r n a l  t h i s  i n i t i a l  f o r c e ,  i s t h e v i s c o u s  s  t,  f (t)  +  b e c o m e  f r e e d o m  t h e d y n a m i c  i s t h e i n e r t i a  f (t) D  a n d  mil  o f  a t t i m e  fff)  w h e r e  n t u r n  s t e p s ,  d e g r e e  m  m a s s  d e s c r i b e d  t i m e  i  c o m p u t a t i o n a l  s i n g l e  t h e  w h i c h  s m a l l  l i t t l e  § 3 . 9 NUMERICAL INTEGRATION 3 4  a s  s t e p  e v e n t  ( 3 . 9 . 3 )  t h e s a m e  E q n . ( 3 . 9 . 4 ) .  m u s t  b e  t h r o u g h o u t  T h i s  i s  s u b d i v i d e d  a n  a n d  h a p p e n s .  ( 3 . 9 . 4 )  CHAPTER 3 : ANALYSIS SOFTWARE  § 3 . 9 Nu M ERIC AL INTEGRATION 3 5  If in a SDOF system, the variable u = u(t) is  Acceleration (constant)  used to denote the position of a mass m at  "2  time t, such thatu=du and u=du. , and that dt dt  Au,  2  u, is its position at t and u at t , and At the n  2  2  time increment during this interval, then the Velocity (linear)  motion of the mass at the end of this time increment, assuming a constant average  Au,  acceleration, so that the velocity increases linearly and the displacement quadratically in this time interval, shall be given as Ail,  =  Aiij  _2  2it,  -  time  -Af-  Displacement\ (quadratic)  At  and  Au,  Aii, = _4_Au, - Ait, - 2u. (At) At 2  Figure 3.9.1: S i n c e  D  c h a n g e  R  A  T  N  w o u l d  q u a d r a t i c  -  N u m e r i c a l  2  D  X  b  e  t i m e  a s s u m e s  l i n e a r  ( F i g . 3 . 9 . 1 ) .  w i t h  s t e p  a  i n t e g r a t i o n  c o n s t a n t  t i m e ,  a  M a t h e m a t i c a l l y ,  1  "l  +  { a n d  t h e  (  • U  An, {  « 2  2  d i s p l a c e m e n t  l  n  J  c h a n g e  J. + U  2  «jAr +  •  2  At =  a tt i m e  \  J  At =  u\  t,  (( ii,  a v e r a g e  dt h e  t h e  u s i n g  a  c o n s t a n t  a c c e l e r a t i o n  c o r r e s p o n d i n g  v e l o c i t y  +(ii +Au ) 1  1  i n  a v e r a g e  e a c h  zi'j Ar + Aii  l  t i m e  s t e p ,  d i s p l a c e m e n t  c h a n g e  t,  a tt i m e  m  At = w'jAr + A w ' j  t h e  c h a n g e  a  y b  At  v e l o c i t y  w o u l d  e e x p r e s s e d  b  e  a s  (3.9.5)  a s  +(ii +Au )\ x  l  At = ii.At + Au,— 1  \  a c c e l e r a t i o n .  At] At — 2  . .  = u.At 1  .. (Ar)  + a,-—— 1  2  1  2  A  2  .. (Ar)  (3.9.6) 2  + Aw.-i—'— 1  4  C H A P T E R 3: A N A L Y S I S SOFTWARE  E q n s .  Au,  (3.9.5)  a n d  a r e e x p r e s s e d  (3.9.6)  i  m  a  n t e r m s  y  o  b  § 3 . 9 N U M E R I C A L INTEGRATION 3 6  e r e a r r a n g e d  i n t o  E q n s .  (3.9.7)  a  n  d  (3.9.8),  s o t h a t  Au,  a  n  d  Au  f  r  AM, = (AM, - w'jAf)  (3.9.7)  Ar  M,Ar - zi', (Ar)  2  AM,  AM, -  (3.9.8)  (AO  2  C o m b i n i n g  (3.9.7)  E q n s .  a n d  (3.9.8),  • 2  „..  A M , —  - 2M.  A  'At  e q u a t i o n  c a n b  . 4  „ .. (3.9.9)  - M . — - 2M.  ' Ao At 2 l  1  (  1  l a s t  4  1  AM.  T h i s  .  = Au,  e s u b s t i t u t e d  = A M . — - 2M.  'At  f o r  Au,  i  (3.9.10)  1  n E q n .  (3.9.5)  t o o b t a i n  a  n e x p r e s s i o n  2 AM, — - 2M, = M,Ar + A « , y  4  S u b s t i t u t i n g  f o r  E q n s .  t h e i n t e r v a l  m  4  I  At  (3.9.10)  n  o  w  = AM,  a n d  4  (AO  2  1  i n t o  (3.9.12)  At  E q n .  (3.9.4),  t h e d y n a m i c  e q u a t i o n  o f  m o t i o n  b e c o m e s  AM , - — M• , - 0 " -A 2M, 2  . 4 M , — - 2M.  (AO  (3.9.12)  Au,  (3.9.11)  ''At  AM.  f o r  At  1  +C  —AM, -2M,  ^ Ar  1  1  + kAu = Ap(fj) x  (3.9.13)  CHAPTER 3 : ANALYSIS SOFTWARE T h i s  e q u a t i o n  m o v e d  a r e  t o t h e  m o v e d  m  a  l e f t  y  a  t o t h e  b e  n  r e a r r a n g e d  dr e p r e s e n t e d  r i g h t  § 3 . 9 NUMERICAL INTEGRATION 3 7  a  n  i n t o  y k\  b  t h e  a  d r e p r e s e n t e d  n  d a l lt e r m s  b  y  Ap(t),  4  k =  RAu, = Ap(tj),  f o r m  a  a s s o c i a t e d  n  d t h e n  i n  w i t h  s o l v e d  w h i c h  a l l c o n s t a n t s a r e  k n o w n  f o r  i n i t i a l  c o n d i t i o n s  Au  r  7  2  (3.9.14)  m + —c + k (At) Ar 2  4P(',) = 4P(',)  Au,  O n c e  i sk n o w n ,  v e l o c i t y  m a s s  n  a t t h e  s y s t e m ,  T h e  a  e  n  t h e y  d o  a r e  i s  t o l i m i t  e r r o r s  e a c h  b e  t h e  f r o m  t i m e  j u s t  a  t i m e  i  b  y  u s e d  d u r i n g  w i t h  s t e p s  i  f o r  a  o  a  t o t a l  e x p r e s s i n g  «','  a r e  k e p t  p e r i o d  o  m  L P d )  a  n  At,  ( 2 w  O  F  i  a  n  d h e n c e  w e r e  s y s t e m  nD  R  A  T  N  -  a c c e l e r a t i o n  m  c o i n c i d e s  s m a l l .  a  i  a  s i n g l e  nm a t r i x  w i t h  T  h  c o r r e c t .  e g e n e r a l  b e i m p o s e d  D  t h e  O  F  f o r m .  m e t h o d s  H o w e v e r , t h e  r u l e  t o a v o i d  a t t h e  f  n  N e w m a r k ' s  T i m e - s t e p p i n g  F u r t h e r m o r e ,  y  f o r  o  i  o  f  t h u m b  t h e s m a l l  b e g i n n i n g  o  f  a s  -/ (',)] s  X  t h ec h a n g e  t h em o t i o n  e x p r e s s e d  i s n o ts t r i c t l y  s t r u c t u r e .  c o n d i t i o n  D  t o f i n d  1 9 9 5 ) .  s u f f i c i e n t l y  ft h e  2  t o e v a l u a t e  d e v e l o p e d  w h e n  ( C h o p r a ,  w h i c h  (3.9.15)  . ) c  d ( 3 . 9 . 1 2 )  e q u a t i o n s  y=\ll  e q u i l i b r i u m  —  D  u s e d  d  t h ei n i t i a l  =  ( 3 . 9 . 1 0 )  fa c c e l e r a t i o n ,  s t e p s  t o 1 / 1 0 t h e  n  1  t h e s e  m e t h o d  a  1  i n t e r v a l  m u l t i p l e  p = l / 4  t i m e  nE q n s .  A l t h o u g h  v a r i a t i o n  f t h e  Ar  t h et i m e  a c c e l e r a t i o n  a c c u m u l a t i n g ,  s t e p ,  e  a s v a l i d  l i n e a r  s m a l l  nb  i n t e r v a l .  m e t h o d  a s s u m e  w i l l  ft h e  c o n s t a n t  t i m e - s t e p p i n g  e r r o r s  a  d a c c e l e r a t i o n  a v e r a g e  u s u a l l y  i t c  m +  +  (3.9.16)  CHAPTER 3: ANALYSIS SOFTWARE  3.10  g r o u n d  b e  d e l a y s  m a y  a t  s u p p o r t  m o t i o n s  a t  a c h i e v e d  b y  a t  e a c h  e a c h  T h e  m o t i o n s  o f  t h e  t o  t h e  i s  a d j u s t e d  t h e  F o r  d i f f e r e n t  a r e  b e  m o d e l l e d  F o r  s a m e  f i l t e r i n g  i n  f o u n d a t i o n s  g r o u n d  f o u n d a t i o n s  a r e  e l e m e n t s  t a n g e n t  b y  a n  t h e  a d d i t i o n a l  i n t r o d u c e d  d y n a m i c  i n i t i a l  e n s u r e  3.11  s u p p o r t .  u s i n g  s u p p o r t s  a d d i t i o n a l  T o  e a c h  c a n  o n  p r o g r a m  s i m i l a r  d i s p l a c e m e n t  o n  e f f e c t s ,  t h e  d i s s i m i l a r  a n d  b y  s o i l s ,  r e c o r d  s o i l s ,  c o m p l e t e l y  s p e c i f y i n g  t h e  t h e  w i t h  e a r t h q u a k e  t r a v e l l i n g  w a v e  s u c c e s s i v e l y  b o d y  d i f f e r e n t  t h e  w a v e s  o f  r e c o r d s  l o n g e r  t h e  m a y  e f f e c t  t i m e  e a r t h q u a k e  b e  s p e c i f i e d  s u p p o r t .  s p r i n g  s i d e s  e x c i t a t i o n  s u p p o r t .  e x p e r i e n c e  T h e s e  n o  38  DIFFERENTIAL SUPPORT EXCITATION  D i f f e r e n t i a l  c a n  §3.10 DIFFERENTIAL SUPPORT EXCITATION  s p r i n g  s p e c i f i e d  n e e d  t o  e q u a t i o n  s t i f f n e s s  e q u i v a l e n t  p r o p e r  i n t o  t h e  t h r o u g h  b e  o f  m o t i o n .  a t  o f  e a c h  T h e  t i m e  s p r i n g  c o d e s  e f f e c t  s t i f f n e s s  o f  f o r c e  a t  e a c h  t h e s e  t h e  t i m e  o f  a t  i t s  a f f e c t e d  s p r i n g s  c o n t r i b u t i o n  e a c h  b a l a n c e s ,  s u p p o r t s  f o r  a s s o c i a t e d d e g r e e s  s p r i n g  e n e r g y  t h r o u g h  r e s t r a i n t  T h e  f o r t h e  a d d i t i o n a l  c a l c u l a t i o n  t h e  d e f i n e d .  m a t r i x  d e f o r m a t i o n  s t r u c t u r e  o f  p r o g r a m  i n  n o d e ,  i s r e f l e c t e d  t h e  t h e  a l s o  T h e  s o  i s  s o l u t i o n  b o t h  a d d e d  l o a d  k e e p s  t h a t  o n  s p r i n g s  f r e e d o m .  s t e p  f o u n d a t i o n s .  v e c t o r  p r o c e s s .  t r a c k  o f  t h e  N  X  c a n  s t e p .  T H E E X T R - D D A T A EXTRACTION PROGRAM  D e p e n d i n g  p r o d u c e  r e s u l t s  l i m i t e d  o n  o u t p u t  t o  t o  b e  a  t h e  s i z e  f i l e s  i n  s p e c i f i e d  p a r t i c u l a r  o f  t h e  e x c e s s  t i m e  o f  6 5  s t e p s  u s e d  a n d  m e g a b y t e s .  f o r p a r t i c u l a r  n o d e s  d i s p l a c e m e n t  o r  a n d  f o r c e .  t h e  o u t p u t  A l t h o u g h  e l e m e n t s ,  I f n o d a l  t h e  s p e c i f i e d ,  p r o g r a m  i t d o e s  r e s u l t s  a r e  n o t  D  R  A  T  a l l o w s  a l l o w  s p e c i f i e d ,  t h e  -  2  t i m e  D  h i s t o r y  r e s u l t s  f o r  t o  e x a m p l e ,  b e  i t  CHAPTER 3 : ANALYSIS SOFTWARE  § 3 . 1 1 T H E E X T R - D EXTRACTION PROGRAM 3 9  Determine name of DRAIN-2DXoutput file  Determine extraction parameters, and write to the input parameter file.  Determine name of input parameterfile,and open it.  Interactive input Batch input  Determine node details (displacement type, total number of nodes, node number and direction.  Read appropriate data from the DRAJN-2DX outputfileand write to the results file.  Determine element details (total number of elements, element type, group, number, end andforce). (  End^\  Figure 3.11.1:  o u t p u t s  i n  t h ex -  t h et i m e  c o d e ,  a t  c o d e  i n  d e s i g n  a  a n d y - t r a n s l a t i o n s  a s w e l l  a s t h er o t a t i o n s .  t i m e  h i n g e  o u t p u t ,  s t e p .  T h i s  a  nb e  A p p e n d i x  d a t a  k n o w n  d e s i g n  f o u n d  B .  i  s t e p  a  n  d s h e a r  t h ef i l e s  m a d e  f r o m  a s E  X  T  -  D  f o r c e s ,  c a n s t i l l  ,  o u t p u t  E  X  F  T  o  R  -  D  rt y p e  a n d f o r e a c h  o u t p u t  t w o  e  r o t a t i o n ,  f i l e  s i z e s  l a r g e  t o w r i t e  e x t r a c t i o n  a  F  i  O  c  ft i m e  R  T  R  n  a  a  e l e m e n t s ,  d o  n  ft h e  r e c o r d  a  y i e l d  n e g a t i v e  s i g n i f i c a n t l y  r e d u c e d  r e s u l t s  c o m p u t e r  n  a  d  h i s t o r y  N  e a c h  e l e m e n t ,  d p o s i t i v e  nb e  A  p r o g r a m .  a r e  n e e d e d  p r o g r a m  t o  f i l e s .  a c c e p t s  S a m p l e  t h e  t h eh i n g e  g e tq u i t e  i n t e r a c t i v e  i sd i s p l a y e d  C.  o f  a n d t i m e ,  i ti m p e r a t i v e  a n d l o g i c  nA p p e n d i x  d l o g i c  A l t h o u g h  t h e s e  R  n  n u m b e r  r o t a t i o n s .  d a t a  a l g o r i t h m  a  m o m e n t s  t h er e q u i r e d  p r o g r a m ,  c  i n c l u d e s  p l a s t i c  s e l e c t i v e  e x t r a c t  b a s i c  a l g o r i t h r n  t h eb e n d i n g  e a c h  T h i s  B a s i c  h i s t o r y  a c c u m u l a t e d  w i t h  Check all parameters, and write to input parameter file.  i  nt h ef l o w  i n p u t  a  n  a s w e l l  c h a r t  d o u t p u t  a s b a t c h  i  i n p u t  nF i g . 3 . 1 1 . 1 ,  f i l e s  f o r  E  X  T  R  -  f o r m a t s .  a  D  n  d t h e  a r e  T  h  e  s o u r c e  i n c l u d e d  CHAPTER  3 :  I f  g r o u p  a  l a r g e  r e q u i r e d  It  t h e n  u s i n g  f r o m  s t o r e s  i n p u t  u n d e r g o n e .  t a k e  m a i n t a i n ,  b e e n  t h e  T h e  t h o u g h  a n  u s e r  t o  e r r o r  -  D  a l l o w s  i  n a  f i l e  a c t i v e l y  l i n e s  b e e n  X  t h e s a m e  t h e f i r s t  f i l e  s o  m a y  b e  c o n t r o l  h a s b e e n  f t o p d o w n  p o s s i b l e ,  r e c o v e r y  s t e a d i l y  a r e f o u n d  s o  i  n e a c h  t h a t  R  -  D  EXTRACTION PROGRAM 40  s t r u c t u r e ,  e x t r a c t i o n  s u b s e q u e n t  e d i t e d  t h e  T  p r o v i d e d  e x t r a c t i o n  o  o p t i o n  s e c t i o n ,  d e s i g n .  f e x e c u t i o n  t h a t  i m p r o v e d  t h r o u g h  a n d  a n d  t o  t h e s a m e  b e  d o n e  e x t r a c t i o n s  t h a t  r e s u l t s  a r e  i n t e r a c t i v e l y .  m a y  b e  i t s f o r m a t t i n g  p r o c e s s  w i t h o u t  i n c o r r e c t  r a t h e r  t h a n  T h i s  p a r a m e t e r s  s t a r t i n g  u s i n g  m a k e s  e f f i c i e n c y .  t h e v a r i o u s  t h e p r o g r a m  s u b s t a n t i a l l y r e w r i t t e n  m o d u l a r  a t t h e e x p e n s e  w h e r e  R  o n  E  d o n e  i s n o t  u s i n g  t h e  t i m e .  p r o g r a m  o  T  p a r a m e t e r  c a p a b i l i t y h a s  a d v a n t a g e  a d d e d  u s e r  e a c h  X  p a r a m e t e r s  T h e  t h e  C o m m e n t  p o i n t .  f u l l  f o r m a t .  E  THE  § 3 . 1 1  a r e p e r f o r m e d  a n a l y s i s ,  t h e e x t r a c t i o n  p r o g r a m ' s  t h i s  f a n a l y s e s  a l l o w i n g  i n t e r a c t i v e  at  o  e a c h  t h e b a t c h  c h a n g e d ,  T h e  ANALYSIS SOFTWARE  a  s t r u c t u r e d  c h e c k i n g  a r e d e t e c t e d  f r o m  i sr e l a t i v e l y  t h e p r o g r a m  E r r o r  t h e  r e v i s i o n s  e r r o r  r o u t i n e s  b e g i n n i n g .  f r e e  a p p r o a c h ,  r e l a t i v e l y  a t d a t a  i t h a s  e n t r y ,  e a s y  h a v e  t o  t o  a l s o  a l l o w i n g  CHAPTER T  1  ANALYTICAL MODELLING  4.1  INTRODUCTION  T h e  r e s u l t s  a n d  m o d e l l i n g  e f f e c t i v e l y  r e m a i n s  o  a  c h a p t e r  u s e d  i  s i m u l a t i o n  p a r a m e t e r s  z e r o  t h e b e s t  T h i s  a n d  f c o m p u t e r  c h a n c e  a n  d o  m e a n s  I t a l s o  s e l e c t e d  i  o n  a s  m u c h  t h e  o  e x a c t  f g e n e r a t i n g  n t h e D  R  a n  e m p l o y e d  d e s c r i b e s  A  s o m e  L  N  -  2  o n  t h e s e l e c t i o n  e a r t h q u a k e  e a r t h q u a k e ' s  t h e p r o c e d u r e s  n t h e s i m u l a t i o n s .  t h e p a r a m e t e r s  t h e y  t h a t  p o s s i b l e  d e s c r i b e s  a s  d e p e n d  D  r e c o r d s  o  t o  t h e s e  f t h e p a r a m e t e r s  X  A l t h o u g h  r e c o r d  r e c o r d  f o r g e n e r a t i n g  f a p p r o p r i a t e  u s e d .  a c c e l e r a t i o n  a r t i f i c i a l  o  w i l l  f i ta  b e  u s e d  i  t h e r e  i s  r e p e a t e d , i t  g i v e n  a r t i f i c i a l  m o d e l s  s p e c t r u m .  r e c o r d s  n t h e b r i d g e  t o  b e  m o d e l s  s i m u l a t i o n s .  4.2 CHOICE OF EARTHQUAKE RECORDS T h r e e  S a n  F e r n a n d o ,  r e c o r d  t h e  a r t i f i c i a l  w a s  i n h e r e n t  e a r t h q u a k e  1 9 8 5  c h o s e n  r e c o r d s  M e x i c o  b e c a u s e ,  d e f i c i e n c y  i  C i t y  w e r e  a n d  a m o n g  u s e d  t h e  o t h e r  n t h e b r i d g e  i  1 9 8 9  n t h e a n a l y s e s .  L  o  r e a s o n s ,  d e s i g n  m  a  P r i e t a  i tw a s  w e r e  e a r t h q u a k e s .  t h e f i r s t  s p e c i f i c a t i o n s  4 1  T h e s e  o  b a s e d  T h e  t o r e v e a l ,  f t h a t  t i m e ,  o n  o n  S a n  a  t h e  F e r n a n d o  l a r g e  i n c l u d i n g  1 9 7 1  s c a l e ,  t h o s e  f o r  CHAPTER 4 : ANALYTICAL MODELLING e x p a n s i o n  H u g h e s .  o f  j o i n t s .  T h e  M e x i c o .  T h e  L  o  t h r e e  m  M e x i c o  T h i s  a c c e l e r a t i o n  a  T h i s  r e c o r d  C i t y  r e c o r d  o n e , u n l i k e  w a s  P r i e t a  w a s  a  § 4 . 3 TARGET SPECTRUM 4 2  t a k e n  c a m e  t y p i c a l  f r o m  f r o m  u n t i l  a b o u t  r e c o r d  f r o m  D i a m o n d  a c c e l e r a t i o n  r e c o r d s  w e r e  1 5  d i g i t i z e d  S t a t i o n  A e r o p u e r t o  e a r t h q u a k e  n o t r e a c h e d  c a m e  A r r a y  r e c o r d ,  s e c o n d s  a t 0 . 0 2  ( S i t e  ( S t a t i o n  I D  A  d i s p l a y s  a f t e r  H e i g h t s  4  a  Z  I  H  N o .  )  s l o w  1 2 6 )  o n  E D  5 8 1 3 0 )  i  L a k e  t h e w e s t  b u i l d u p ,  n S a n  c o a s t  a n d  t h e a c c e l e r o m e t e r w a s  ( S i t e  a t  p e a k  t r i g g e r e d .  F r a n c i s c o .  A  l  l  s e c o n d s .  4.3 T A R G E T SPECTRUM A c c o r d i n g  C a n a d a  t h e  h a p p e n e d  h e l p  d i r e c t i o n  p l a t e s  i n  o  f 6 0 °  a n d  o  s i n g l e  D r .  t h e  t h a t  a t  o  i  r e c o r d s  s h o u l d  a n d  E n v i r o n m e n t a l S u r v e y  1 8 0 0  f  o  m  R o c k  w i l l  a t  J a p a n .  r e s u l t  m  ( C a n a d i a n  t h a t  6  i  n a  i  t h e s a m e  B o b r o w s k y  o  o  f  e  n  t h e l o c k  s a m e  a  c o n t e n t ,  o  m  m  D r .  D a v i d  W a s h i n g t o n ,  o  T h i s  n  t h e  a n d  S u r v e y  a n d  D r .  t h e  o  t w o  i  n  E q u a l  s p e c t r u m  n a n y  i  n  g i v e n  c o m p a r i s o n .  f t h e  K e n j i  a  s t r a i n  f t h e  f C a n a d a ,  Y a m a g u c h i  t h e  t h e e a r t h q u a k e s ,  f o r  o  o  i  f  D i s p l a y e d  s a m e  r e s p o n s e  b a s i s  ( i n  i s r e f l e c t e d  m a t c h e d .  t o  m a x i m u m  c  b e t w e e n  o  W i t h  e a s t w a r d  t h e e n v e l o p e  m a t c h e d  c o a s t  1 9 9 8 ) .  r e l e a s i n g  c r u s t .  w e r e  f r o m  f t h e G e o l o g i c a l  S u r v e y ,  U n i v e r s i t y  h  r e c o r d s  f r e q u e n c y  p r o v i d e  t h e w e s t  d i s p l a c e d  n t h e e a r t h ' s  B e i n g  t h e  o n  e a r t h q u a k e ,  i s d e r i v e d  f o r V a n c o u v e r .  G e o l o g i c a l  W  m e g a t h r u s t  S p e c t r u m  h e n c e  i s b e i n g  p e r y e a r .  a l lt h e e a r t h q u a k e  a n d  e a r t h q u a k e  B r o a d c a s t i n g C o r p . ,  V i c t o r i a  m m  a p p r o x i m a t e l y  t h e  s u b d u c t i o n  d e f o r m a t i o n  a l lh a v e  s t r u c t u r e ,  S t a t e s  1 7 0 0  f a b o u t  T a r g e t  S p e c t r a  m a j o r  s h o w  t o w h i c h  D r . P e t e r  H e a l t h o  r a t e  p r o d u c e  f f r e e d o m  C l a g u e  f J a n 2 6 ,  i tw o u l d  n t h i s  S u b d u c t i o n  f t h e U n i t e d  G e o l o g i c a l  a t a  o v e r c o m e ,  t h e H y b r i d  o  o  t h e l a s t  m e a s u r e m e n t s  f t h e s p e c t r u m  l e a s t ,  J o h n  t h e n i g h t  a z i m u t h )  t h e s e  d e g r e e  A t w a t e r  g e o l o g i s t s ' ,  s a t e l l i t e s ,  F i g . 4 . 3 . 1 ,  t h e o r y  o n  a c c u m u l a t e d  e n s u r e s  o f  f  s e l e c t i o n  R i s k  1  o  i s f i n a l l y  e n e r g y  t h e  t o r e s e a r c h  D r .  B r i a n  D e p a r t m e n t  S a t a k e  o  f  t h e  CHAPTER 4 : ANALYTICAL MODELLING  § 4 . 4 GENERATION OF DISPL. RECORDS 4 3  600  0.01  0.10  1.00 P e r i o d  F i g u r e  4.4  4.3.1  : T h e  g e n e r a t i o n  T h e  t a r g e t  s p e c t r u m .  p r o g r a m  S y n t h  S  P  f i r s t  o f  s t e p s .  E  E  C  t o  T a r g e t  i s t o  t h e  b e  S p e c t r u m .  t i m e  s t e p  i s  h i s t o r y .  b a s e l i n e  d r i f t s  s t e p  u s i n g  T h i s  t h e  t i m e s  1 9 8 9 )  i s  i s  t o  a  o n  a  a c c e l e r a t i o n  s e v e r a l  i n  b a s e d  a c c e l e r a t i o n  ( F i l i a t r a u l t ,  n e x t  a n  a c h i e v e d  a r t i f i c i a l  T h e  r e c o r d  g e n e r a t e  e x e c u t e d  p r o g r a m  d i s p l a c e m e n t  d i s p l a c e m e n t  T h i s  s p e c t r u m .  p r o d u c e  a  s t e p  o u t p u t s  n e e d s  d e s i r e d  t o  R o c k  ( s e e s )  GENERATION OF DISPLACEMENT RECORDS  T h e  R  H y b r i d  10.00  t o  f o r  s o m e w h a t  final  a  a c c e l e r a t i o n  h i s t o r y  S y n t h  t h a t  a s  p r o d u c t .  T h i s  w e l l  t h e  t h e  n u m e r i c a l  t r i c k y  w h i c h  p r o g r a m  h i s t o r y  a c c u r a c y ,  v e r i f y  p e r f o r m  t i m e  t h e  t i m e  r e a l  d o u b l e  p r o c e s s ,  e r r o r  a s  c a n  i n v o l v e s  c o n f o r m s  t o  ( N a u m o s k i ,  a s  final  o u t p u t  r e c o r d  i t s  i s  i s  r u n  s u f f i c i e n t l y  i n t e g r a t i o n  n u m e r i c a l  b e  t h e  t o  d e s i r e d  1 9 8 5 ) .  s p e c t r u m .  r e c o r d  s e v e r a l  T h i s  B e c a u s e  t h r o u g h  t h e  c l o s e  t o  t h e  p r o d u c e  t h e  i n t e g r a t i o n s  r e m o v e d  b y  a  t e n d  s e r i e s  o f  CHAPTER 4 : ANALYTICAL MODELLING  § 4 . 4 GENERATION OF DISPL. RECORDS 4 4  - 2 0 0  o <D  o >  4  1 2  c  0  /V A  / \  v  s ID O  -2  5  -4  A  V  iS on  -6  1 0  2 0  T i m e  F i g u r e  4 . 4 . 1 :  F e r n a n d o  A c c e l e r a t i o n ,  e a r t h q u a k e ,  b u t  v e l o c i t y  a l t e r e d  t o  a n d  3 0  ( s e e s )  d i s p l a c e m e n t  f i tt h e  H y b r i d  4 0  t i m e  R o c k  h i s t o r i e s ,  T a r g e t  b a s e d  S p e c t r u m .  o n  t h e  1 9 7 1  S a n  CHAPTER 4 : ANALYTICAL MODELLING  § 4 . 4 GENERATION OF DISPL. RECORDS 4 5  2 0 0  •2  >  -io - 1 5  - 2 0  0  1 0  2 0  T i m e  F i g u r e M e x i c o  4 . 4 . 2 : C i t y  A c c e l e r a t i o n ,  e a r t h q u a k e ,  b u t  v e l o c i t y a l t e r e d  a n d t o  3 0  ( s e e s )  d i s p l a c e m e n t  f i tt h e  4 0  H y b r i d  t i m e  R o c k  h i s t o r i e s ,  T a r g e t  b a s e d  S p e c t r u m .  o n  t h e  1 9 8 5  CHAPTER 4: ANALYTICAL MODELLING  F i g u r e L  o  m  a  4 . 4 . 3 : P r i e t a  A c c e l e r a t i o n ,  e a r t h q u a k e ,  b u t  v e l o c i t y a l t e r e d  §4.4 GENERATION OF DISPL. RECORDS 46  a n d t o  d i s p l a c e m e n t  f i t t h e  H y b r i d  t i m e  R o c k  h i s t o r i e s ,  T a r g e t  b a s e d  S p e c t r u m .  o n  t h e  1 9 8 9  CHAPTER 4 : ANALYTICAL MODELLING c o r r e c t i o n  p r o c e d u r e s ,  n u m e r i c a l l y  v e l o c i t y  4 . 4 . 2  b y  a n d  a n d  u s i n g  a s  p r o p o s e d  t h e  d i s p l a c e m e n t  V  U  -  t i m e  P  O  § 4 . 5 BRIDGE FRAMES 4 7  b y  I  N  T  H u d s o n  I I  h i s t o r i e s  ( 1 9 7 9 ) .  p r o g r a m  from  T h e  p r o c e d u r e s  ( M a x w e l l ,  t h e t h r e e  1 9 9 1 ) .  e a r t h q u a k e s  a r e  w e r e  T h e  s h o w n  p e r f o r m e d  a c c e l e r a t i o n ,  i n F i g s  4 . 4 . 1 ,  4 . 4 . 3 .  4.5 BRIDGE FRAMES  F i g u r e  T w o  d i s t i n c t  c o l u m n  a  4 . 5 . 1 :  B r i d g e  s e t s  o  e l e m e n t s  l e n g t h  o  f d e c k  c o n n e c t e d  f  c o n t a i n i n g  t h r o u g h  f o u r  i n t h e  t h e  r e s p o n s e .  t w o - b e n t  frames  frames  i n b o t h  p a r a m e t e r s  o v e r a l l  frames:  T h e  b e  w e r e  u s e d  T h e  a n  e x p a n s i o n  e a c h  frames  o  f i r s t  e x t r a p o l a t e d  s e t o  s t r u t ,  t o  f  B r i d g e  frames  c o n t a i n s  o n e  w e r e  a p p l y  f i v e - b e n t  w h e r e a s  a l t e r e d  frames  ( b )  s t u d y .  f w h i c h  w e r e  f i v e - b e n t  frame,  i n t h i s  frames.  d e c k s ,  t w o - b e n t  c a n  ( a ) t w o - b e n t  t o  a t  t h e n  a  frame.  b e n t s  c o n s i s t s  t h e  a n  a  o  s e c o n d  f t w o  t i m e  t o  t o  m o d e l .  b e n t s  s e t c o n s i s t s  e x p a n s i o n  s t u d i e d  l a r g e r  a r e r e p r e s e n t e d  s e e  s t r u t  h o w  s e e  i  b y  b e a m -  c o n n e c t e d  o  f f i v e  ( F i g . 4 . 5 . 1 ) .  e a c h  ft h e  w o u l d  r e s u l t s  from  b y  b e n t s  T h e  a f f e c t  t h e  CHAPTER 4 : ANALYTICAL MODELLING  4.5.1  § 4 . 5 BRIDGE FRAMES 4 8  BASIC B E N T M O D E L  equivalent  • This node has only horizontal translational DOF  -±  Truss bar element - This strut is made up of three elements placed in parallel: 1. compression link element, representing bulkheads, 2. tension link element, representing restrainer, and 3. truss bar element, representing joint friction. Beam-column element •  F i g u r e  4 . 5 . 2 :  I n  b o t h  t h e t w o -  i s  r e p r e s e n t e d b y  t h e  i n  t o p  h a l f  s e r i e s .  o t h e r  O n e  i s t h e  4 . 5 . 2 ) .  o  T h e  D O F .  T h e  e l a s t i c  a n d  B a s i c  a n d  a  e l e m e n t s  u s e d  f i v e - b e n t  f r a m e s  b e a m - c o l u m n  f t h e c o l u m n s .  s t r u t  s h o r t  t w o  d e c k  p l a c e d  d i s c u s s e d  i  t r u s s  s t r u t s  s t r u t s  n m o r e  b a r  s t r u t  c o n s i d e r e d  i  n  h i g h  e l e m e n t  u s e d  d e t a i l  i  n t h e  i  T h e  n t h i s  w i t h  s t u d y ,  a  a  n o d e  a n d  i n t h i s  m a s s  e a c h  a t t h e t o p  t h e  i s o n l y  y i e l d  v a l u e s  s e c t i o n s .  T h e  t o  d e c k  o  g i v e n  a s  e l e m e n t s  a n d  b y  a n d  t w o  t h e  o  a  s t r u t  t h e  d e c k  d e c k  s t r u t s  g i r d e r s ,  h o r i z o n t a l  a r e  f t h e  t h e  f t h e e x p a n s i o n  t h e y  e x p a n s i o n  s e c t i o n  r e p r e s e n t  a t t h e m a s s  w h i c h  s t u d y .  f r a m e s .  t h r e e - s p a n  t h e b e h a v i o u r  b e a m - c o l u m n  f o l l o w i n g  f i v e - b e n t  r e p r e s e n t s  t o r e p r e s e n t  b y  a n d  a r e c o n n e c t e d  w h i c h  s t i f f n e s s  c r i t i c a l  p a r a l l e l .  u s e d  e l e m e n t s  a r e c o n n e c t e d  h a v e  t w o - b e n t  e l e m e n t  T h e s e  e x p a n s i o n  a r e n o t  e l e m e n t s  i s a  i n t h e  a n d  p l a c e d  a n d  j o i n t  t h e  ( F i g .  t r a n s l a t i o n a l  e x p e c t e d  i s m a d e  e x p a n s i o n  t o  u p  r e m a i n  o  f  s t r u t s  t h r e e  a r e  CHAPTER 4 : ANALYTICAL MODELLING  § 4 . 5 BRIDGE FRAMES 4 9  4.5.2 B E A M - C O L U M N ELEMENTS T a b l e  4 . 5 . 1 :  D e t a i l s  o  f t h e  five  b e a m - c o l u m n s  T B  M a s s ,  m  ( k i l o g r a m s )  H e i g h t ,  3 E I  L  ( m )  ( k N . m  2  )  S t i f f n e s s ,  k  P e r i o d ,  ( s e e s )  T  S p e c t r a l  S p e c t r a l  S h e a r  M  o  m  D  R  A  ( k N / m )  n  I  t  N  -  A  c  e  ,  S  ( k N . m )  2  D  X  S h e a r  S F  M  a  x  M o m e n t  C  M  a  x  S h e a r  M  C  M  a  x  M  o  [ m . S  . L ]  m  e  ( k N )  n  t  P  M  a  x  S h e a r  L  P  M  a  x  M o m e n t  H  B e n t  I  i  n t h i s  s t u d y .  T B e n t  1  T J  B  e  n  t  K  B  e  n  t  L  9 5 0 2 4 5 .  9 5 0 2 4 5 .  9 5 0 2 4 5 .  9 5 0 2 4 5 .  9 5 0 2 4 5 .  1 5 . 8 9 4  1 3 . 6 9 7  1 1 . 3 0 7  8 . 6 2 9  5 . 4 3 6  3 . 7 6 5 5 E 7 -  3 . 7 6 5 5 E 7  3 . 7 6 5 5 E 7  3 . 7 6 5 5 E 7  3 . 7 6 5 5 E 7  9 3 7 8 . 5 4  1 4 6 5 4 . 0  2 6 0 5 1 . 5  5 8 6 1 5 . 9  2 3 4 4 6 3 .  2 . 0  1 . 6  1.2  0 . 8  0 . 4  0 . 9 5 0 0 0  1 . 1 9 0 4 6  1 . 6 4 5 2 4  2 . 4 8 0 0 0  4 . 2 0 0 0 0  9 0 2 . 7 3 2  1 1 3 1 . 2 2  1 5 6 3 . 3 8  2 3 5 6 . 6 1  3 9 9 1 . 0 3  1 4 3 4 8 .  1 5 4 9 4 .  1 7 6 7 6 .  2 0 3 3 4 .  2 1 6 9 4 .  8 6 6 . 9 5  1 1 5 9 . 8  1 6 2 2 . 7  2 4 1 8 . 1  4 2 6 1 . 5  0 . 9 6 0 4  1 . 0 2 5 3  1 . 0 3 7 9  1 . 0 2 6 1  1 . 0 6 7 8  8 8 0 . 8 1  1 1 7 3 . 1  1 5 5 9 . 6  2 3 5 6 . 2  3 8 8 4 . 9  ( n o r m ' d )  0 . 9 7 5 7  1 . 0 3 7 0  0 . 9 9 7 6  0 . 9 9 9 9  0 . 9 7 3 4  ( k N )  8 9 9 . 0 0  1 1 3 0 . 8  1 5 8 4 . 6  2 3 5 3 . 9  3 9 8 1 . 7  ( n o r m ' d )  0 . 9 9 5 9  0 . 9 9 9 6  1 . 0 1 3 6  0 . 9 9 8 9  0 . 9 9 7 7  8 8 0 . 8 4  1 1 6 8 . 1  1 5 9 1 . 9  2 4 3 3 . 7  4 2 3 1 . 1  1 4 0 0 0  1 6 0 0 0  1 8 0 0 0  2 1 0 0 0  2 3 0 0 0  C a p a c i t y :  C a p a c i t y  n  A  ( n o r m ' d )  L  e  )  ( k N )  M  m  t  T  b e n t s  R e s p o n s e :  x  o  2  [ m . S J  a  M  ( m / s e c  A  M  S h e a r  ]  [2%-/m/k]  S F  D e s i g n  3  n  a s  R e s p o n s e :  ( k N )  e  [ 3 E I / L  e  u s e d  t  ( k N )  C a p a c i t y  ( k N . m )  CHAPTER 4: ANALYTICAL MODELLING I n  a  t y p i c a l  d e p e n d s  m o r e  b r i d g e ,  i n  p a r t  f l e x i b l e  o n  a n d  B e a m - c o l u m n s  u s e d  i n  i n  t h e  T h e  d i f f e r e n t  s p e c t r a l  a n d  t h e y  a s  D  S  O  i n  t h i s  t h e  w i t h i n  t a b l e  f i v e  b e e n  A l l  a r e  t o  t h e  a n  t h e  e l a s t i c  r o u n d e d  A  I  m o d e l s  w e r e  s p e c t r a l  d e m a n d s  o f f , a n d  -  2  i n  t u r n  a  a r e  u s e d  t h a n  i n t h i s  f r a m e s ,  o f  t h e s e  d i r e c t l y  r e s p o n s e  s h o w s  t o  s p e c t r a l  n o r m a l  v a l u e s  t h e  t o  m e t r i c  t h e  v a l u e s .  t h e  r e f l e c t  a r e  H y b r i d  o f  R o c k  t h e  t a r g e t  s p e c t r u m .  w h e r e a s  c o m p a r i s o n .  t i m e  T h e  s y n t h e s i z e d  t h e  h i s t o r y ,  v a r i a t i o n  r e c o r d s  T h e s e  h e i g h t  4.5.1.  a c t  b e n t s  a r e  t h e  t o  v a l u e s  v a l u e s  a r e  e x c e p t i o n  v a l u e s  v a l u e s  c l o s e  t h e y  s h e a r  t h e s e  t h e s e  c o m e  t h e  m o m e n t  W i t h  a r e  S p e c t r u m ,  w h e n  T h e  a r e  s e c t i o n .  i n T a b l e  w h e n  50 b e n t  b e n t s  T a r g e t  a l l o f  o f  s a m e  b e n t s  d e m a n d s  a  b e n t s  a c c o r d i n g t o  e l a s t i c  u n i t s ,  t h e  s h o w n  t h e s e  o f  T a l l e r  t h i s .  a r r a n g e d  d e m a n d  p e r i o d  w i t h  t h e  F e r n a n d o  r e s p o n s e  T h e  i t s h e i g h t .  o n e s  t o  a r e  f o r c o n v e n i e n t  S a n  a l t h o u g h  s t u d y  f r o m  D  f i t t e d  o f  b e a m - c o l u m n s  s t r e n g t h  h i s t o r i e s  m i d s p a n .  s h o r t e r  a n d  p r o b a b l e  X  t h e  f u n c t i o n  v i b r a t i o n  t w o - b e n t  t h e i r  t h a t  t o w a r d s  t h e  t i m e  r e s p o n s e  t h e  o f  i n  d e r i v e d  r e s p o n s e  i s p r o o f  s e l e c t e d  o f  N  t o  e x p r e s s e d  f i ti s n o t  n o t e d .  R  i s  h e i g h t s  i n t h e  i n d i c a t i o n  o f  w h i c h  h e i g h t  c h a r a c t e r i s t i c s  v a l u e s  b e n t ' s  p e r f o r m a n c e  o t h e r w i s e  F  T h e  D  i n  l o n g e r p e r i o d  d i f f e r e n t  T h e  p e r c e n t  a r b i t r a r i l y  t h e  O  r e s p o n s e  s p e c t r u m ,  o n  D  s h o r t e s t  s p e c t r a l  T h e  S  a  f r a m e s .  r e s p o n s e  a s  n o r m a l i z e d  o f  f i v e  m o d e l s .  s u b j e c t e d  i n c r e a s e  p e r m u t a t i o n s  p r o v i d e  F  b e n t s  i t s s t i f f n e s s ,  h a v e  o f  f i v e - b e n t  t h e  §4.5 BRIDGE FRAMES  f r o m  t h e  f a l l  t h e  d e s i r e d  p r e c i s e .  d e s i g n  o f  t h e  c a p a c i t i e s  t h e s e  b e n t s  i n t h e  i n t h e  c o r r e s p o n d i n g  c o m p a r i s o n s  o f  b e n t s  t h r e e  s h e a r  i n  l a s t  t h i s  t w o  r o w s  o f  e a r t h q u a k e s .  c a p a c i t i e s  s t u d y  w i l l  a r e  b e  T a b l e  T h e  a r e  m o m e n t  s h o w n  b a s e d  4.5.1  o n  i n  t h e  t h e s e  l o o s e l y  b a s e d  c a p a c i t i e s  l a s t  h a v e  s e c o n d  n u m b e r s  r o w .  u n l e s s  CHAPTER 4 : ANALYTICAL MODELLING  4.5.3  § 4 . 5 BRIDGE FRAMES 5 1  EXPANSION STRUTS  tension force  tension force  truss bar to model friction —7  • link element to model restrainer  gap closing gap closing  gap opening  gap opening  • link element to model bulkheads compression force  compression force  (a) F i g u r e b a s i c  T h e  4 . 5 . 3 :  T h e  c o m p o n e n t  e x p a n s i o n  p l a c e d  c o m p r e s s i o n  t e n s i o n  t r u s s  h a s  b a r  b e e n  T h e  t h e  o n l y ,  e l e m e n t s ,  b e t w e e n  o n l y ,  t o  w i t h  a  f o u n d  u s e d  t o  t o  i n  t h e  t h e  t h e  b u t  i n  j o i n t  t h e  o p e n i n g  i s  i n i t i a l l y  i n i t i a l  b e g i n s  c o m p l e t e l y  c o n c r e t e  i n  t h e  s u b j e c t e d  f r i c t i o n  t o  i n  c l o s e  c l o s e d  a t  a n d  b u l k h e a d s  t h e  t h e  l o w  t o  a l m o s t  f u r t h e r  t h e  f o r t h e  a t  t h e  n e w  c o m b i n a t i o n  T h e r e  c a b l e .  t o  f o r c e  t h e  a t  a r e  T h e  m o d e l  b r i d g e s  c o m b i n e d  c o m p r e s s i o n  t o  e x p a n s i o n  e x p a n s i o n  v a l u e ,  i s o v e r c o m e ,  b e g i n  a  s t r u t .  c o m p r e s s i o n ,  c o n s t a n t  i s  r e s t r a i n e r  y i e l d  r e l a t i v e l y  j o i n t  w i l l  o f  f o r t h e  s t r u t :  ( a )  t h e  t h r e e  m o d e l .  b u l k h e a d s  o f  u s e d  m o d e l s  p o i n t s  r e s p o n s e  e v e n  c o m b i n e d  b r i d g e  e n d  s t i f f n e s s  e x i s t  t h e  t h e  m o d e l  m o d e l  h i g h  ( b )  f o r c e - d e f o r m a t i o n r e l a t i o n s h i p  u n t i l  i s  f o r c e - d e f o r m a t i o n r e l a t i o n s h i p  s t r u t  i n p a r a l l e l  ( b )  m o d e l  A s  ( f r o m  w i l l  e x p e r i e n c e  A '  t o  c a u s e  t h i r d  e t  g a p  B').  t h e  o n e  f o r  a n d  t h e  o n e  f o r  e l e m e n t  i n  C  i s a n  t h e  i n e l a s t i c  j o i n t ,  i n F i g . 4 . 5 . 3 ( b ) .  d e c r e a s e  B',  t h e  b u l k h e a d s  c r u s h i n g w h e n  o t h e r  w h i c h  1 9 9 5 ) .  c o n t i n u e s  A t  e l e m e n t s  e l e m e n t s ,  a l . ,  n o t  b a s i c  l i n k  f r i c t i o n  d o e s  t h e  t h r e e  j o i n t ,  i s s h o w n  o p e n i n g  A'.  t w o  t h e  ( P e n t a s  o f  i s  t o  h  e  n  s i g n i f i c a n t l y  d e c r e a s e ,  e x p a n s i o n  t o  W  d e f o r m .  r e a c h e d .  t h e  j o i n t  T h e  CHAPTER 4 : ANALYTICAL MODELLING I n  t e n s i o n ,  u p  a t p o i n t  r e s t r a i n e r  b o t h  t h e j o i n t  B.  I ft e n s i o n  r e a c h e s  l i n k  i n i t i a l  5 0 6 3 1  i s  u p  o p e n i n g  M N / m .  T h e  s e t a t 5 1 7 8 8 3  u p .  T h e  s l a c k  c o n t i n u e s , t h e r e s t r a i n e r  e l a s t i c  a r e s p e c i f i e d  t o b u i l d  g a p  t o o p e n  i t s m a x i m u m  e l e m e n t s  d e f o r m a t i o n s  T h e  b e g i n s  § 4 . 5 BRIDGE FRAMES 5 2  i  n  w a s  i n i t i a l  k N / m .  i n t h e r e s t r a i n e r  b e g i n s  d e f o r m a t i o n  t o u n l o a d  t o s t r a i n  l i m i t ,  a n d  c a b l e  i  i s c o m p l e t e l y  n t e n s i o n .  y i e l d i n g  i n e l a s t i c a l l y , i ti s p o s s i b l e  A  t  b e g i n s  p o i n t  t o  t a k e n  C,  o c c u r .  f o rp e r m a n e n t  t h e  A  s  i n e l a s t i c  e a c h .  s e t a t 2 0  s l a c k  T h e s e  i  m m ,  a n d  t h e b u l k h e a d  n t h e r e s t r a i n e r  p a r a m e t e r s  i s s e t a t 4 0  a r e l e f t  c o m p r e s s i o n  m m ,  u n c h a n g e d  i  a n d  s t i f f n e s s  t h e r e s t r a i n e r  n t h i s  i s s e t a t  s t i f f n e s s  s t u d y .  4.5.4 DAMPING T h e  g e n e r a t i o n o  w h i c h  h a s  i s a  a n  t y p i c a l  f t h e a r t i f i c i a l  v a l u e  e q u i v a l e n t  p r o d u c e  a  m  a  x  i  m  o  u  m  D a m p i n g  i s s e tt o 5  w i l l  d i f f e r i n g  h a v e  f a c t o r  i  e l e m e n t  p l a c e d  n o r d e r  g r o u p  i  n a  t o  f 5  %  u s e d  %  o  f c r i t i c a l  s t i f f n e s s e s .  t o c o n t a i n  s e p a r a t e  w h i c h  n t h e b e n t s .  a c h i e v e  t h e  5  %  m a t c h e s  a  l i n k  w i t h  m e a n s  s u b j e c t e d  b e n t s  r a t i o .  d i f f e r e n t  T h e  T h i s  t h e t a r g e t  r e q u i r e  d a m p i n g  g r o u p .  p e r f o r m e d  w h e n  t h e f i v e  w i l l  w i t h  w a s  s t r u c t u r e s .  d a m p i n g ,  S i n c e  E a c h  e l e m e n t s  e l e m e n t  h i s t o r i e s  f o rc o n c r e t e  r e s p o n s e  i  t i m e  %  t h a t  t o  o  a  t h e s e  S  f c r i t i c a l  D  O  F  t i m e  d a m p i n g ,  m o d e l  w h i c h  h i s t o r i e s ,  w i l l  s p e c t r u m .  H  t o L  d i f f e r e n t  S i n c e  D  R  m e c h a n i c a l  e l e m e n t s  5  a l lh a v e  s t i f f n e s s  A  I  N  -  2  D  d i f f e r e n t  p r o p o r t i o n a l  X  d o e s  c h a r a c t e r i s t i c s ,  a r e n o t g i v e n  l e n g t h s ,  a n y  n o t  e a c h  t h e y  d a m p i n g  a l l o w  b e n t  d a m p i n g .  a n y  w a s  CHAPTER  4 :  ANALYTICAL MODELLING  § 4 . 6 D  4.6 D R A I N - 2 D X INTEGRATION T h e  m o s t  w e r e  p a r a m e t e r s  i m p o r t a n t  n e e d e d  A n o t h e r  t o  o  b  y  e s p e c i a l l y  t o o b t a i n  i m p o r t a n t  u s e v e r y  s m a l l  i  n D  f t h e s e  a s c e r t a i n e d  d i s c o v e r e d ,  w a s  u s e d  R  A  I  N  -  2  i s t h e s i z e  p e r f o r m i n g  f o r m o d e l s  r e l i a b l e  p a r a m e t e r  n u m b e r s  a  R  A  J  N  -  2  D  INTEGRATION PARAMETERS  X  5 3  PARAMETERS  D  X  s i m u l a t i o n s  o  f t h e i n t e g r a t i o n  s e c o n d  c o n t a i n i n g  c a n  a n a l y s i s  l i n k  s i g n i f i c a n t l y  t i m e  s t e p .  u s i n g  e l e m e n t s ,  T  t i m e  t h a t  a  h  e  a f f e c t  t h e r e s u l t s .  a c c u r a c y  s t e p s  t i m e  h a l f  s t e p  a s  o  o  f t h e  b i g .  f 0 . 0 0 5  T  h  e  r e s u l t s  I t  w a s  s e c o n d s  r e s u l t s .  i s t h e f o r c e  t o m i n i m i z e  a n d m o m e n t  e r r o r s  i  o v e r s h o o t  n t h e e n e r g y  t o l e r a n c e .  b a l a n c e .  I t w a s  n e c e s s a r y  CHAPTER TWO-BENT FRAMES  5.1 A  INTRODUCTION  p r e l i m i n a r y  a n d  w i t h  a n  a  e x p a n s i o n  l e t t e r  p e r m u t a t i o n s  a t  a  T h e  t i m e  b e n t  i n  b e n t s  t h e  t o  w h i c h  w h i c h  t h r e e  i n c l u d e  o f  a r e  t h e  n a m e d  frames  c o n s i s t  o f  t a l l e s t  n i n e  i s o l a t e  T h e  g e n e r a t e d  c o l u m n  f o r t h e  f o u r  p e r f o r m a n c e  p e r f o r m e d  F i v e  t o  L  e f f e c t  a f t e r  o f  t h e i r  o f  t w o  frame  b e n t s  w a s  d i s p l a c e m e n t  s t r e n g t h ,  o f  friction  b e n t s  s h o r t e s t  p a r a m e t e r s  w o u l d  h a v e  c o n s t i t u e n t  w h i c h  w o u l d  F r a m e s  a r e  d i f f e r e n t  e x a m i n e d  t i m e  c o n s i s t i n g  d i f f e r e n t  T h e  e a c h  b e n t s  f r a m e s  f o r t h e  frames.  E q u a l - H e i g h t  e a c h  y i e l d  u s i n g  ( F i g .4 . 5 . 1 ( a ) ) .  t o t a l  a r r a n g e m e n t .  F r a m e s ,  T h e  H  f o r a  a n d  w a s  s t r u t  from  o r d e r  f r a m e s ,  h e i g h t  s t u d y  u n d e r  j o i n t ,  5 4  ( T a b l e  u s e d  t h e  a p p e a r  H H ,  T h e  t w o  b e n t s  o f v a r y i n g  b e n t s ,  i n  t h i s  a r e  H I ,  d i f f e r e n t  K  a n d  K  o t h e r  i n  T h e  s t r e n g t h  o n e  m o d e l s .  o f  e q u a l -  a  f i v e -  A d j a c e n t  K L .  a n d  s t u d i e d  v a r i e d  frames  a n d  d e c k  d i f f e r e n t  b r i d g e  L L .  a  i d e n t i f i e d  i n  w e r e  e a c h  s i t u a t i o n s ,  y i e l d  u s e d  t h e  b y  e a c h  f i v e  t o  I J , J  p a r a m e t e r s  r e s t r a i n e r  o f  o f  a d j a c e n t  a r e  s t u d y  r e s p o n s e  c o n s i s t  j o i n e d  h e i g h t s ,  4 . 5 . 1 ) ,  I I , J J , K  h e i g h t s ,  h i s t o r i e s .  i n t h e  o n  o f  i n  u s i n g  t h e  a n d  e a c h  o f  m o d e l l i n g  t i m e  d e l a y .  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 2 ANALYSIS PARAMETERS 5 5  5.2 ANALYSIS PARAMETERS T h r e e  b y  d i f f e r e n t  Y O ,  Y  l  a n d  t h e  s t r e n g t h  t h e  c a s e  t h e  s p e c t r a l  a  o f  F l  a n d  w o u l d  t h e  a  F o r c e  s h e a r  F 2 .  b e  c a s e  s l i d i n g  t h e  T h r e e  a n d  v a l u e s  o n  r e s t r a i n e r  d e t e r m i n e  r e s t r a i n e r  w e r e  s l a c k  t o  a n d  t o  a  x  i  u  4 0  t o  m  m m .  5  t h e  a r e  n o  o f  c a s e  t o  r e a c h  a n  t h e  o f  t h e  t h i s  ( 2 3 3 0  s t u d y .  d e m a n d  p e r f o r m e d  n o  w i t h  f r i c t i o n .  l o c k e d  T h e s e  a r e  i n i t i a l  i n  t o  f o r c e  g a p  t o  c o r r e s p o n d s  F  i s s e t  R  F  s h o r t  k N )  o f  t o  e q u a l  4.  t o  S u c h  d u c t i l i t y .  f o r m  i  f  b y  F O ,  f r i c t i o n  c o r r e s p o n d s  t h e  j o i n t s  c a s e  f o r m  d e t e r m i n e  d e t e r m i n e  a t  j o i n t  i n t e r f a c e  w i t h o u t  w a s  t o  T e f l o n  s t u d i e d  t o  s e e  t o g e t h e r .  d e n o t e d  i s p r e s e n t .  i s  a n  ( 7 8 4 . 8  T h i s  c o r r e s p o n d s  r e s t r a i n e r  a n  l  l  s h o r t  d i s p l a c e m e n t  e x p a n s i o n  r e s t r a i n e r  R 2  a  a r e  F  r e a c t i o n  o f  o f  d e n o t e d  u s e d  Y  s t r e n g t h  c a s e  i n  u s e d  b e n t s .  r e q u i r e d  w a s  d e n o t e d  w a s  y i e l d  t h e  T h i s  i n f i n i t e  k N ) -  t o  e a r t h q u a k e .  b e n t s  w h e n  t h e  a r e  v e r t i c a l  a n d  t h e  T h e s e  friction.  c a s e  from  t h e  r e p r e s e n t a t i v e  w h e n  i n  y i e l d i n g ,  c o r r e s p o n d s  d u r i n g  %  n o  m e a n i n g  a n a l y s e s .  o f  t h e  s t r e n g t h  1,  d e t a i l e d  m o s t  u s e d  0.25mg  l a n a l y s e s  o f  t o  r e s p o n s e  o f  m  2  c a s e  s t r e n g t h s w e r e  m  c a s e  o f  s t r e n g t h s a r e  r e s p o n s e  o f  Y 2  t h e s e  j o i n t s  c o r r e s p o n d s  s t r e n g t h  l  t h e  i s t h e  a n d  T h e s e  c a s e  e l a s t i c  4 . 5 . 1 ) .  i n  e x p a n s i o n  b r i d g e ' s  t h e  A  ( F R F )  u s e d  c o r r e s p o n d s  y i e l d  F a c t o r  d e s i g n e d  u s e d .  t h e  a n  e q u i v a l e n t  F 2  t h e  R O  e a r t h q u a k e .  i n  d e c k s ,  r e s t r a i n e r  R 2 .  b e  t o  o b t a i n  ( T a b l e  c o r r e s p o n d s  s u r f a c e s .  e f f e c t  d e m a n d  f r i c t i o n  t h e  t o  R e d u c t i o n  d e s i r a b l e  o f  s t r e n g t h s w e r e  c o r r e s p o n d s  n e e d e d  s h o u l d  F O  y i e l d  Y O  d e m a n d  f r i c t i o n  b e t w e e n  t o  Y 2 .  b e a m - c o l u m n  T h r e e  R l  c o l u m n  t o  l i k e l y  a  i n  R  s h o r t  l  f o r m  c o r r e s p o n d s  n o n - y i e l d i n g  t o  o p e n i n g  e x p e r i e n c e  o f  2 0  b y  m m  R O ,  t o  a  r e s t r a i n e r ,  i n  a n d  a  l a r g e  i n i t i a l  CHAPTER 5: TWO-BENT FRAMES  §5.3 ANALYSIS & MODEL IDENTIFICATION  56  5.3 ANALYSIS AND M O D E L IDENTIFICATION T a b l e  5 . 3 . 1 :  S y m b o l s  u s e d  P a r a m e t e r  Y i e l d  s t r e n g t h  F r i c t i o n  i n  o  f  b e n t  j o i n t  R e s t r a i n e r  s t r e n g t h  t o i d e n t i f y  a n a l y s i s  n  a n a l y s i s  c o n s i s t  ( F O )  a  o  n  a n a l y s e s  d e l a y s  f a n a l y s e s  d n o  P a r a m e t e r  Y O  E l a s t i c  Y  S p e c t r a l  l  F O  N o  F I  F r i c t i o n  F 2  I n f i n i t e  R O  N o  R  R e s t r a i n e r  p e r f o r m e d  h i s t o r y  s y m b o l ,  w i t h i n  u s e d  w i t h  d i f f e r e n c e  1  o  n  e a c h  F  a n a l y s i s  f o r S  b e t w e e n  a  w i t h  o  b e n t s  ft h e  n i n e  f r o m  b  y  o  0 . 0  =  7 8 4 . 8  f r i c t i o n  o  ft i m e  ft h e  E q n .  d e l a y  M  C  y  f  4  N  ( l o c k e d  j o i n t s )  A  a t 0 . 2 5 m g  t h ea n a l y s i s  ( Y O ) ,  t y p i c a l  o  ft h e  s e c o n d s  i  n0 . 0 5  t h e i r  f o r M e x i c o  T  h  a t t h es u p p o r t s  P  Y  k  N  )  0  R  0  w o u l d  i  nt h e  j o i n t s  i n c l u d e  e a r t h q u a k e s ,  o  b  a  n  d  t h ee a r t h q u a k e  m  a  y  w i t h  i n c r e m e n t s .  i s d e n o t e d  i sd e n o t e d  F  s e tw o u l d  s e c o n d  f o r L  0  f r i c t i o n  b e n t s ,  e e a r t h q u a k e  a n d L  n o  t h r e e  c o n s t i t u e n t  C i t y ,  ( 2 3 3 0  s e t  a n a l y s i s  e a c h  a p p l i e d .  e a r t h q u a k e  o  r e s t r a i n e r  e l a s t i c a l l y  u s i n g  t o 0 . 5  b  k  y i e l d s  H e n c e ,  5 . 3 . 1 ) .  s e t a r ei d e n t i f i e d  ( F R F )  r e s t r a i n e r  u s e d .  f r a m e s ,  F a c t o r  f r i c t i o n  r e s p o n d i n g  ( R O ) ( T a b l e  n F e r n a n d o ,  a r r i v a l  t o 1 1 , a s g i v e n  t h ep a r a m e t e r s  v a r y i n g  a n d t h ea m o u n t  S  y  c a p a c i t y  R e d u c t i o n  N o n - y i e l d i n g  p r e s e n t  s u p p o r t s  e a c h  b  V a r i a t i o n  s h e a r  F o r c e  l  f r a m e s .  r e s p o n s e  Y 2  p e r f o r m e d  r e s t r a i n e r  b e t w e e n  M o d e l s  f r o m  s e t i s i d e n t i f i e d  f o r t h et w o - b e n t  I d e n t i f i c a t i o n  R 2  A  s e t  b  y  a  t w o  P r i e t a .  a  n u m b e r  T  h  e  t i m e  l e t t e r  t i m e  r a n g i n g  ( 5 . 3 . 1 ) .  Time Delay (seconds) - (number-I)  *  0 . 0 5  seconds  ( 5 . 3 . 1 )  CHAPTER A c c o r d i n g  b e n t  o f  I  o n  0 . 2 5  T h e  i n  t h e  5.4  a n d  H  a  a n d  r i g h t .  f i r s t  frame,  L L S F 0 1 ,  t h e  L  m a s s e s  t h e  w i t h  a  i s  v a l u e s  S  D  O  F  v e r y  p o s i t i o n s  o f  d e l a y  t h e  b e  b e n t  k N  a  f r a m e  e a r t h q u a k e  t o  4 . 5 . 1 )  o f  w i t h  t i m e  a  f o r e a c h  b e n t  n u m b e r  a n d  d e n o t e d  i n  1  a  o n  b e n t  H  h i s t o r y ,  b y  V  I  o n  w i t h  F  0  t h e  a  a n a l y s i s  R  0  5 7  l e f t  t i m e  o n  s h e a r  t h e  b e  a n d  d e l a y  t h e  t h e  a n d  M  l  b e n t  b y  d e s i g n  r e s p o n s e s  l e f t  n a m e d  w i t h  i s d e n o t e d  H e n c e ,  T h e  H  w o u l d  i s d e n o t e d  l e f t .  k N .  f o r b e n t  b e n t s  b e n t  g i v e n  t h e  V I = 1 1 6 8 . 1  t h e s e  t h e  m a s s e s  5 . 4 . 1 ,  e i t h e r  b e  s h e a r  b o t h  V 2  t h e  s h e a r  o f  t h e s e  f o r b e n t  a n d  I  M 2 .  m o m e n t  l a r g e r  b e n t  ( m o d e l s  r e s p o n s e s ,  H H S F 0 1 ,  r e s p o n s e s  i n  b e n t s  a r e  b e n t s  b e g i n s  H  H  M  a l l t h r e e  m o v i n g  i n  n o  C  f r i c t i o n  0  1  ,  H  H  L  a n d  P  e a r t h q u a k e s  p h a s e ,  e a c h  0  1  n o  t o  m a t c h  a c t s  a s  a n  5 . 4 . 2 ) .  t h e  i n t e r a c t i o n  t h e  e l a s t i c  d e l a y  b e t w e e n  o n l y  a t  n o  B e c a u s e  ( F i g s .  s e t , t h e  w i t h  w i t h  m a x i m u m  i n t e r a c t i o n  c o u l d  frames  F r a m e s  c l o s e l y .  m o d e l  a n a l y s i s  r e s p o n s e  w i t h  c o m p a r e s  L L L P 0 1 ) ,  i n c r e a s e d ,  i n t h i s  g i v e n  ,  o f  0  Y0F0R0  a n a l y s e s  1  m o m e n t  ( T a b l e  c o r r e s p o n d i n g  C  0  c a p a c i t i e s  w o u l d  L  M  c o n s i s t s  F e r n a n d o  V H = 8 8 0 . 8 4  E q u a l - H e i g h t  i n d e p e n d e n t  a p p l i e d  b e  I n  s p e c t r a l  d e l a y  o f  S a n  s t a r t i n g  a n a l y s i s  T h e  s e t  a n d  I w o u l d  t h e  H I S F 0 6  Y  s u p p o r t s .  d e s i g n  s h e a r  i n t h e  2 - b e n t  r e s t r a i n e r .  o n  t h e  ANALYSIS SET  T h i s  A s  m o m e n t  ANALYSIS SET  § 5 . 4  m o d e l  s u b j e c t e d t o  b e t w e e n  p o s i t i o n  b e n t s  c o n v e n t i o n ,  r i g h t ,  w h e r e a s  b e n t s  o n  t h i s  s e c o n d s  b e n t ' s  f o r  t o  t h e  s h e a r  l e t t e r ,  TWO-BENT FRAMES .  5:  o r  o f  i s t h e  i m p a c t  i m p a c t ,  t h e  s m a l l e r t h a n  t o  o c c u r .  b e t w e e n  p e a k  t h e  t h e  s h e a r  s p e c t r a l  A s  n o  r e s t r a i n e r  d e c k s .  f o r c e s  s h e a r  i n  i s  D e p e n d i n g  a n  a n a l y s i s  r e s p o n s e .  CHAPTER 5: TWO-BENT FRAMES  H  §5.4 ANALYSIS SET Y 0 F 0 R 0  58  YdFORO-HHEQOl  0.10  c  s  CD  o 0.05 <D  0.00 o  X  -  •0.05  Displ. of ground — Displ. of mass 1 — Displ. of mass 2  i  O o  y  -0.10  o  0.10 Hi  0.05  O  0.00  -  u X •  -0.05  Displ. of ground Displ. of mass 1 Displ. of mass 2 J  o  ai -0.10  o o  0.10 c  o E 0.05 o u C3  z o  PH J X X I  o.oo -0.05  Displ. of ground^ — Displ. of mass 1 ^— Displ. of mass 2J  o  Pi o [i, o  >  -0.10 20  10  30  40  Time (sees)  F i g u r e  5 . 4 . 1 :  HHMC01  a n d  T o t a l  n o d a l  HHLP01,  d i s p l a c e m e n t i n t h e  A n a l y s i s  t i m e  h i s t o r i e s  S e t  Y0F0R0.  f o r F r a m e  HH,  i n m o d e l s  HHSF01,  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 4  ANALYSIS SET Y  0  F  0  R  0  5 9  Y0F0R0-LLEQ01  0.10 c  cu  0.05  £ u  _s 3. 0.00 o IX,  in -J •  o Pi o u~ o  •0.05  Displ. of ground — Displ. of mass 1 — Displ. of mass 2 J  -0.10  0.10 c  u £ u u  0.05  Z o  0.00  CJ  2 -0.05  - J  Displ. of ground^ — Displ. of mass 1 — Displ. of mass 2 J  •  o  pi  o -0.10 HH o >&  0.10  a CD  0.05  E  CL)  O  0.00 o  P—i  -0.05  Displ. of ground ^ Displ. of mass 1 — Displ. of mass 2 J  o  Pi o O  >  -0.10 10  20 T i m e  F i g u r e L  L  M  C  0  5 . 4 . 2 : 1  a n d  T o t a l  n o d a l  L L L P 0 1 ,  d i s p l a c e m e n t  i n t h e A n a l y s i s  t i m e S e t  40  ( s e e s )  h i s t o r i e s  Y 0 F 0 R 0 .  f o r f r a m e  L  L  ,  i n m o d e l s  L L S F 0 1 ,  CHAPTER 5: TWO-BENT FRAMES  §5.4 ANALYSIS SETYOFORO 60  0.15  C  c  v  CJ  o  0.10  a  0.05  o  S  U eg  u San Fernando^ — Mexico City \^— Loma Prieta J  r  San Fernando"' — Mexico City .— Loma Prieta  I  0.00  T3 CJ N  O  1.4 0J  N  1.2 1.0  o c  C  0.8 u  C3  JS  0.6  OJ  0.4  CL.  C  cu  CJ  San Fernando"' — Mexico City — Loma Prieta J  0.2  OJ  CQ  0.0  O.  ^ — San Fernando^ — Mexico City — Loma Prieta J  c OJ  CC  Peak gap opening (mm)  Peak contact forces (kN) 10000  120  7500  90  5000  60  2500  San Fernando — Mexico City <— Loma Prieta . 0.0  0.1  0.2  0.3  0.4  0.5  30  San Fernando — Mexico City — Loma Prieta , 0.0  0.1  Time delay (sees)  F i g u r e  5 . 4 . 3 :  e a r t h q u a k e s  P e a k  f r a m e  i n A n a l y s i s  a  S e t  n  d j o i n t  r e s p o n s e s  Y0F0R0.  0.2  0.3  0.4  0.5  Time delay (sees)  f o r f r a m e  H  H  a tv a r i o u s  d e l a y s  i  nt h e  t h r e e  CHAPTER 5: TWO-BENT FRAMES S h o w n  p e a k  i n  i  n F i g . 5.4.3  n o r m a l i z e d  t h em o d e l s  p r o d u c e s  a g a i n s t  a  i  t i m e  f o r c e s ,  p e a k  F f F D V I C  d i f f e r e n t  d e l a y  st h e v a r i a t i o n  s h e a r  H H S F ,  §5.4 ANALYSIS SET Y 0 F 0 R 0 61  p e a k  a  n  w i t h  c o n t a c t  d F i H L P .  r e s p o n s e  t o p r o d u c e  a  t i m e  i  p l o t  d e l a y  f o r c e s  E a c h  o  a  n  nt h ep e a k  d p e a k  a  s i n g l e  n  t o t a l  n o d a l  g a p o p e n i n g s  ft h e e l e v e n  nt h e f r a m e  w i t h  a  i  d e l a y  d t h e j o i n t .  m a x i m u m  c a s e s  T h e s e  v a l u e  d i s p l a c e m e n t s ,  1  f o rb e n t s  i  ne a c h  p e a k s  k n o w n  c  a  n  2  d  e a r t h q u a k e  a  n b e  a s t h e  p l o t t e d  maximum  peak response.  I t  i s h e l p f u l  t h e  t o d e f i n e  p u r p o s e s  r e s p o n s e  i  o  ft h i s  normalized response  a  f o r q u a n t i t i e s  r e s e a r c h , t h en o r m a l i z e d  na n a n a l y s i s  e x p r e s s e d  a s a  s h e a r  m u l t i p l e  o  f o r a  s u c h  b e n t  ft h e b e n t ' s  a s s h e a r  i sd e f i n e d  s p e c t r a l  a  n  d m o m e n t .  a s t h eb e n t ' s  s h e a r  r e s p o n s e ,  F  o  r  s h e a r  a s  g i v e n  b y E q n . (5.4.1). , . Normalized shear response -  shear response  (5.4.1) spectral response  I f  a  i t s  b e n t ' s  c a n b e  a s a  s e e n  m a x i m u m  nm o d e l  w o u l d  T  H  b e  r e p o n s e .  n F i g .  (122.3% o  e a r t h q u a k e .  r e s p o n s e  T  m u l t i p l e ' o f  i  e a r t h q u a k e .  i  s h e a r  i t s s p e c t r a l  e x p r e s s e d  2  s h e a r  n o r m a l i z e d  t h a n  I t  p e a k  h  g i v e n  A  u n i t y .  e  b e n t ' s  f o r e x a m p l e ,  f  o  V H ,  h  e p e a k  H  S  F  s h e a r  T  h  r  i  1.223  n b e n t  f o r c e  e p e a k  a n a l y s i s  n u m b e r  p e a k  V  H  2  t h a t  )  l a r g e r  t h e p e a k  o c c u r s  b  g a p o p e n i n g s  a s i t s s p e c t r a l  1.0  t h a n  i n d i c a t e s  s h e a r  a  s h e a r  r e s p o n s e ,  r e s p o n s e  i s t h e p e a k  s h e a r  b i g g e r  r e s p o n s e  r e s p o n s e .  w h e n  i s r e d u c e d  i st h e s a m e  n o r m a l i z e d  s p e c t r a l  5.4.3,  T  1.  na  t h e b e n t ' s  e m a x i m u m  l  h  i  n o r m a l i z e d  t h e d e l a y  w h e n  y  a b o u t  i s  0.20  t h e d e l a y  15%  g e n e r a l l y  i  s h e a r  i  s e c o n d s  i s 0.25  nb e n t  i n c r e a s e  1  n b e n t  i  n  d a b o u t  a s d e l a y  r e a c h e s  n t h e M e x i c o  s e c o n d s  a  1  i  C i t y  n t h e  35%  i  t h e  s a m e  n  i s i n c r e a s e d .  b e n t  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 4 ANALYSIS SETYOFORO 6 2  Y0F0R0-HHMC06DP  0.10 c CD  s  0.05  CD CD  a ~ o  0.00  u  s  -0.05  o ci o o  -0.10  Displ. o f ground ^ D i s p l . o f mass 1 — D i s p l . o f mass 2 J  I  0.10 c CD  s  0.05  -o  0.00  CD CD C"5  o U  -0.05  X I o ci o  -0.10  tin  o  10000 CD CD  ZCD  7500  c O CD  5000  ©  U  2500 o O UH O  10  20  30  40  Time (sees)  F i g u r e  5 . 4 . 4 :  H  6  H  M  C  0  ,  i  C o m p a r i s o n nA n a l y s i s  o  S e t  ft o t a l  n o d a l  Y 0 F 0 R 0 .  d i s p l a c e m e n t  t i m e  h i s t o r i e s  b e t w e e n  H  H  M  C  0  1  a n d  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 4  ANALYSIS SET Y  0  F  0  R  0  6 3  Y0F0R0-HHMC06SH  1000 OJ  500 3 o J3 O U  % I  -500  o  — Shear in bent 1 — Shear in bent 1  & o o  1000  5  1000  o  500 u VO  o U  i  -500  o o  Shear in bent 1 , — Shear in bent 2 J  P  -1000  S  10000  u o  C O o VO  o  X  7500  5000  2 5 0 0  •  o ci o o  0 10  20  30  40  Time (sees)  F i g u r e i n  5 . 4 . 5 :  A n a l y s i s  C o m p a r i s o n  S e t  Y 0 F 0 R 0 .  o  f s h e a r  f o r c e  t i m e  h i s t o r i e s  b e t w e e n  H  H  M  C  0  1  a n d  H  H  M  C  0  6  ,  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 4  ANALYSIS SET  Y  0  F  0  R  H  S  F  0  1  0  6 4  Time (sees)  F i g u r e  5 . 4 . 6 :  H H S F 1 1 ,  i  C o m p a r i s o n  n A n a l y s i s  S e t  o  f t o t a l  n o d a l  Y 0 F 0 R 0 .  d i s p l a c e m e n t  t i m e  h i s t o r i e s  b e t w e e n  H  a n d  CHAPTER 5: TWO-BENT FRAMES  2  §5.4 ANALYSIS SETYOFORO 65  YOFORO-HHSF11SH  1000  CJ  500  ,o CU  -  0  o '—  C/j  X  K &  o  -500 — Shear in bent 1 — Shear in bent 2  o  >- •1000  1000  — Shear in bent 1 , — Shear in bent 2 .  10000  cu  7500  s  e o  X  i  5000 2500  o o UL.  o  >  10 T i m e  F i g u r e  5 . 4 . 7 :  A n a l y s i s  S e t  C o m p a r i s o n  Y0F0R0.  o  f s h e a r  30  20  f o r c e  t i m e  40  ( s e e s )  h i s t o r i e s  b e t w e e n  HHSF01  a  n  d  HHSF11,  i  n  CHAPTER I n  5 :  m o d e l  H  i m p a c t s ,  a n d  M  C  f o r c e  a n d  h a v i n g  H  t o w a r d s  5 . 4 . 5 .  e n e r g y  M  l  t o M  l  m a k e s  a  d i r e c t i o n .  a c c e l e r a t i o n  p e a k  o n e  f  t h e  r e d u c e s  T h e  t o  m o d e l  at  a b o u t  b y  t h e  a  c a u s e s  b e n t s ,  m a y  l a r g e  s e c o n d s  g r o u n d  g r o u n d  i s  c o r r e s p o n d i n g  M  2  t y p e  i n F i g s .  o  o f  p e a k  t o  b o t h  a n d  w i t h  s h e a r  s h e a r  f o r c e .  l e f t ,  m a s s  M 2  M 2  l  t o  s n a p  T h e  w h e n  A  s  O  n a  H  M  n  l  t h e  A  1  h a s  M  C  M  l  0  ,  a  F  1  b e g u n  i  0  6 6  t h e l e f t  a f t e r  a l s o  m o v i n g  s o m e  o  e x c u r s i o n  i n a  T h e  f  d i s p l a c e m e n t ,  M  a n  f i r s t  l a r g e r  i n t h e  k i n e t i c  l  ,  a n d  r e s p o n s e  f i t s  i n c r e a s e  t i m e ,  o  o  f t h i s  m o v i n g  T h i s  h a n d ,  R  F i g s .  r e s u l t i n g  i m p a c t .  0  n  r e s u l t  t h e r i g h t .  o  w h i l e  a  l a r g e r  f a t  i m p a c t  l e a s t  w h i c h  parasympathetic.  f o rm o d e l  f o r c e  r e a c h  H  t r a n s f e r  s  ,  0  d i s p l a c e m e n t  t o w a r d s  t o  0  o t h e r  M  H  Y  c l o s e l y - s p a c e d  n o d a l  t h e p e a k  c a l l e d  a n d  l a r g e  2  C  l a r g e  r e l a t i v e  s h e a r  t h e m a s s e s  a  M  p o s i t i v e  b e  M  t w o  m a s s  t o w a r d s  h i s t o r i e s  i n  H  i n c r e a s e  m a y  m a s s e s  r e s u l t i n g  i  t h e  p e a k  w i t h  t h e l e f t .  b a c k  t o  f  m o d e l  t h e g r o u n d  p o s i t i v e  t e n d s  o  t o t a l  t o  u p  i n m o d e l  r e s u l t i n g  t i m e  T h e  c a u s e s  t o w a r d s  t h a n  i n v o l v e d  5 . 4 . 7 .  r e s u l t  i s a c c e l e r a t i n g  m o d e r a t e ,  l a r g e r  f o r c e  a  c a t c h e s  c u r t a i l i n g  a  a s  i s c o m p a r e d  sympathetic.  t o t h e r i g h t .  t h e  M  w h i c h  a s  t h e e a r t h q u a k e ,  t o  6  t h e l e f t ,  M 2 ,  M 2 ,  b e n t s  a n d  0  m o t i o n s  t o w a r d s  f i m p a c t ,  5 . 4 . 6  m o v e m e n t  m o v i n g  l  d e s c r i b e d  r e s p o n s e  i n t o  t h e i r  e x p e r i e n c e s  d i s p l a c e m e n t  F T H S F O l  C  w h e n  c a u s e s  t o c a t c h u p  b e  M  r e l a t i v e l y  i s m o v i n g  B e n t  T h i s  t h o u g h  e v e n t u a l l y  l  H  e x c u r s i o n .  c o n t i n u e  from  f o r c e .  n o d a l  5  M  H  o c c u r s  t h e e a r t h q u a k e .  e x c u r s i o n t o t h e l e f t  l  T h i s  s h e a r  i n t o  h a p p e n s  p o s i t i v e  b o t h  M  n p e a k  s e c o n d s  i m p a c t  l a r g e r  W h i l e  t h e p e a k  t o t a l  a s  i  f o rm o d e l  i m p a c t ,  i tf o rM 2 .  s h e a r  o  f i r s t  t r a n s f e r r e d  i n c r e a s i n g  1 6 . 3  h i s t o r i e s  T h i s  o p p o s i t e  i s  a n d  ANALYSIS SET  § 5 . 4  i n c r e a s e  t h e m a x i m u m  s h e a r .  e n e r g y  t h e  T h e  n e g a t i v e  i n  ,  1 4 . 8  t h e l e f t .  i m p a c t ,  6  t i m e  r e a c h e d  k i n e t i c  0  a t a b o u t  s h e a r  5 . 4 . 4  TWO-BENT FRAMES  2  t h e i r  H  H  S  F  i n m o d e l  1  1  H  H  i s  S  a r e c a t a p u l t e d  p e a k  r e l a t i v e  p o s i t i v e  F  0  t o  c o m p a r e d  1  o c c u r s  t h e  r i g h t  e x c u r s i o n s ,  d i s p l a c e m e n t  a n d  t h e  CHAPTER I n  TWO-BENT FRAMES  5 :  m o d e l  H H S F 1 1 ,  e q u a l l y  l a r g e  c a t a p u l t  e f f e c t ,  r e s u l t  i  i n s t a n t  M  l  n a  d e l a y  t o w a r d s  e x c u r s i o n  f o rM  t h e i m p a c t  e f f e c t ) ,  l  f r o m  .  M  2  s i g n i f i c a n t l y  s c e n a r i o s a b o v e  t h e  p e a k  c o n t a c t  S h o w n  i  n  d e c k s  o n  E q u a l - H e i g h t  B o t h  f o r c e  F i g s .  t h e f r a m e s  w h e n  t h e  m i n i m u m .  T h e  f t h e  K  a p p e a r s  g a p  5 . 4 . 1 1  a n d  i s a b o u t  p e a k  g a p  L  h a l f  w h e n  L  Y  a t t h e  r e s u l t s  o p e n i n g  a r e  t h e  s h e a r  .  t h e  n a t u r a l  o p e n i n g s  i m p a c t  o c c u r s ,  s h o w  d e l a y  t h a t  t i m e  w i t h  p e a k  p e r i o d  a  p e a k  t h e  o  g e n e r a l  n  s h e a r  o  i  f t h e  d e l a y  f o r c e s  c o n t a c t  b e n t ,  i n c r e a s e  i  n  t h e d e l a y  i s  s t o r e d  H  S  F  I n  1  ,  t h e  t r a n s f e r  b e n t ,  f a c t ,  f o r  f o r c e ,  t h e  s u p p o r t s .  t o t a l  g a p  a  0  d e l a y .  e i t h e r  t h e  r e a c h  n  p o s i t i v e  n o  s h e a r  s h e a r  n  e  n o w  a c h i e v e  p e a k  a n  t h e  h  i s  e n e r g y  t h e p e a k  t h e p e a k  a s  t h e  f o r c e s  i  H  w i t h  b e t w e e n  i n  a n d  t o  i m p a c t .  n t h e p e a k  n  s p l i t  W  a n d  n m o d e l  f o r c e s  67  0  i  f t r a v e l .  r e d u c e d  t h e r e s u l t i n g  t i m e  t i m e  a  R  f o r a  r e d u c t i o n  t h e c a s e  i s i n c r e a s e d  p e a k  f t h e  i  o  f m o t i o n ,  a  0  d i r e c t i o n s  s t o p  i tr e q u i r e s  t o  t r e n d  c o n t a c t  w h i l e  o  i td i d i  w h i c h  F  e x p e r i e n c e  v i r t u a l  r e s u l t s  c o m p a r e d  a r o u n d  t o  0  i n o p p o s i t e  w i t h  e x c u r s i o n  t h e  a  p h a s e  s h e a r  v a r i a t i o n  I t a p p e a r s  t o  c o u p l e d  a p p r o x i m a t e  a s  f o r c e s ,  ,  b e g i n s  i t s d i r e c t i o n  i t s n e x t  l  l  s u p p o r t s  h e a d i n g  r e v e r s e  n M  d e c r e a s e  a n  M  c o m e  d i s p l a c e m e n t  m o t i o n  t o b e  t o  p o s i t i v e  a n  o r  s  d i s p l a c e m e n t ,  r e d u c e d  g r o u n d  n o r m a l i z e d  I I , J J , K  d e l a y  t o  t h a t  l  e n t e r e d  t h e p e a k  i n c r e a s e  t h e p e a k  5 . 4 . 8  p e a k  o  r e l a t i v e  i t s r e l a t i v e  M  i  A  m a s s e s  i n s t a n t l y  f m o m e n t u m  r e a c h e s  e i t h e r  T h e s e  a l r e a d y  e x p e r i e n c e  t h e r e  a n d  o  t o  m o t i o n s  m a s s e s .  c a u s i n g  M 2  h a s  l o s s  i l l u s t r a t e  t h e n a t u r e  d i s p l a c e m e n t s ,  f o r  c a n  F r a m e s ,  c a u s i n g  r e d u c e s  b e n t s  t h e t w o  i m p a c t ,  r e d u c e d  n e v e r  T h e  d e p e n d i n g  T h e  t h e  e f f e c t .  b e t w e e n  a n d  t h e g r o u n d  t o t h e l e f t .  t h e g r o u n d  c a t a p u l t  t w o  t r a v e l l i n g  t h e l e f t .  e n e r g y  b e t w e e n  b e t w e e n  p a r a s y m p a t h e t i c  i t s m o t i o n ,  p o t e n t i a l  a s  i s s t i l l  ( t h eh i c c u p  m o v i n g  d e l a y  i n r e s p o n s e  M 2  l a r g e  r e s u m e s  t h e l a r g e  ANALYSIS SET  § 5 . 4  n o d a l  o p e n i n g s  m  f o r c e s  a  x  i  m  r e a c h  i n c r e a s e d .  u  m  a  CHAPTER 5: TWO-BENT FRAMES  § 5 . 4 ANALYSIS S E T Y O F O R O 68  0.15  c -D  a  u £ CD CD  s  0.10  - J  CD  a  ca  CL)  -A cci  0.05  CD  Q-  San Fernando' - Mexico City V;— Loma Prieta J  San Fernando' — Mexico City — Loma Prieta J 0.00  T3 N  o e  1.4 T3 CD N  1.2 1.0  O  C  0.8 C9  ed CD -£= CO  M a  o  a. c CD  CQ  "J  J=  0.6  CO  0.4  San Fernando" — Mexico City .— Loma Prieta  0.2  U D.  San l'ernando — Mexico City .— Loma Prieta  •i—'  c CD  0.0  CQ  Peak gap opening (mm)  Peak contact forces (kN) 12000  120  9000  90  6000  60  3000  «-» San Fernando — Mexico City — Loma Prieta , 0.0  0.1  0.2  0.3  0.4  0.5  30  San Fernando - Mexico City V;— Loma Prieta y  0.0  Time delay (sees)  F i g u r e  5 . 4 . 8 :  e a r t h q u a k e s  x  i  P e a k  f r a m e  nA n a l y s i s  a  S e t  n  dj o i n t  r e s p o n s e s  Y 0 F 0 R 0 .  0.1  0.2  0.3  0.4  0.5  Time delay (sees)  f o rf r a m e  I I a t v a r i o u s  d e l a y s  i  nt h e t h r e e  CHAPTER 5: TWO-BENT FRAMES  §5.4 ANALYSIS S E T Y O F O R O 69  0.15  a  G CJ  U  £ u JS  0.10  CJ  CL  o  0.05  CJ  «»•» San Fernando^ — Mexico City ;— Loma Prieta J  D.  San Fernando — Mexico City — Loma Prieta  04  0.00  1.4 TJ CJ N  CJ  N  O  1.2 1.0  o c  0.8 ed OJ  C3 CJ  0.6  J =  ir,  CO  CJ  c  c  M a  0.4  San Fernando^ — Mexico City — Loma Prieta J  0.2  CJ  0.0  cj  • San Fernando — Mexico City -— Loma Prieta J  a  cj  CC  Peak gap opening (mm)  Peak contact forces (kN) 16000  120  12000  90  8000  60  4000  San Fernando Mexico City Loma Prieta ,  30  San Fernando\ — Mexico City — Loma Prieta  0 0.0  0.1  0.2  0.3  0.4  0.5  0.0  Time delay (sees)  F i g u r e  5 . 4 . 9 :  e a r t h q u a k e s  i  P e a k  frame  n A n a l y s i s  a S e t  n  dj o i n t  r e s p o n s e s  Y0F0R0.  0.1  0.2  0.3  0.4  0.5  Time delay (sees)  f o rf r a m e  J  Ja t v a r i o u s  d e l a y s  i  nt  h  e t h r e e  CHAPTER 5: TWO-BENT FRAMES  §5.4 ANALYSIS SET Y 0 F 0 R 0 70  0.15 CO  •*—>  a CJ  E  OJ  c  u  £  0.10  u o cd  O  J2  D_ cd «  0.05 — San Fernando — Mexico City — Loma Prieta J  San Fernando" — Mexico City \;— Loma Prieta J  tN  0.00  1.4  Time delay (sees)  F i g u r e  5 . 4 . 1 0 :  e a r t h q u a k e s  i  P e a k  f r a m e  n A n a l y s i s  a  S e t  n  d j o i n t  r e s p o n s e s  Y0F0R0.  Time delay (sees)  f o rf r a m e  K  K  a tv a r i o u s  d e l a y s  i  n t h e t h r e e  CHAPTER 5: TWO-BENT FRAMES  §5.4 ANALYSIS SET Y 0 F 0 R 0  71  0.15  C  c CJ  w o  0.10  n. in  a  a.  D  Kmzwm  3  0.05  co  ™ San Fernando — Mexico City — Loma Prieta .  CL CN  — San Fernando^ — Mexico City — Loma Prieta J  0.00  F i g u r e  5 . 4 . 1 1 :  e a r t h q u a k e s  i  P e a k  f r a m e  n A n a l y s i s  S e t  a n d j o i n t  r e s p o n s e s  Y0F0R0.  f o rf r a m e  L  L  a t v a r i o u s  d e l a y s  i  n t h e  t h r e e  CHAPTER 5 : TWO-BENT FRAMES T a b l e  5 . 4 . 1 :  A d j a c e n t  C o m p a r i s o n  F r a m e s ,  o f  f o r t h e  m  a  x  i  m  A n a y s i s  u  m  S e t  p e a k  n o r m a l i z e d  ( f o r  s h e a r s  b e t w e e n  E q u a l - H t .  S h e a r  N o r m a l i z e d  F r a m e s )  E a r t h q u a k e  H  S F  1 . 0 8 2  1 . 0 6 4  M  C  1 . 2 2 3  1 . 1 5 1  L P  1 . 0 9 4  1 . 0 5 7  S F  1 . 0 3 8  1 . 0 2 7  M  C  1 . 0 1 5  1 . 1 2 8  L P  1 . 0 0 5  0 . 9 8 6  S F  1 . 1 3 0  1 . 0 4 5  M  C  1 . 1 1 0  1 . 0 8 2  L P  1 . 1 6 2  0 . 9 9 1  S F  1 . 0 9 3  1 . 5 0 9  M  1 . 1 0 9  1 . 0 5 8  L P  0 . 9 6 7  1 . 1 4 8  S F  1 . 6 5 9  1 . 4 4 7  M  0 . 9 4 8  0 . 9 6 8  1 . 4 7 4  1 . 2 2 2  J  K  L  C  C  L P  G e n e r a l l y  i n  t h e  s p e a k i n g ,  f r a m e  w h e n  t h e i r  s h e a r  f o r c e s  a l s o  b e n t ' s  h a v e  t h e  r e s p o n s e s  i n  f o l l o w s  b o t h  t h a t  m o v e m e n t  t h i s  a g r e e s  s a m e  a r e  w i t h  n a t u r a l  1 8 0  t h e o r e t i c a l  p e r i o d ,  d e g r e e s  0  F  0  R  0  7 2  E q u a l - H e i g h t  B e n t  I  Y  a n d  Y 0 F 0 R 0 .  N o r m a l i z e d  I t  ANALYSIS SET  § 5 . 4  o u t  ( f o r  i n t e r p r e t a t i o n s  i t f o l l o w s  t h a t  o f  r e s u l t i n g  p h a s e ,  t h e  o f  m o s t  i n  t h e  r e s p o n s e .  s e v e r e  t h e  S h e a r  A d j a c e n t  i m p a c t  l a r g e s t  F r a m e s )  I f b o t h  b e n t s  w o u l d  o c c u r  d e c r e a s e  i n  p e a k  b e n t s .  t h e  g a p  o p e n i n g  i s p h a s e - s h i f t e d .  I n  w i l l  t h e  b e  i n c r e a s e d w i t h  t a l l e r  a n d  m o r e  i n c r e a s i n g  f l e x i b l e  b e n t s ,  d e l a y ,  t h e  a s  p h a s e  t h e  s e c o n d  c h a n g e  i n  CHAPTER T a b l e  TWO-BENT FRAMES  5:  5 . 4 . 2 :  A n a l y s i s  M  S e t  a  x  i  m  m  j o i n t  r e s p o n s e s  i n  E q u a l - H e i g h t  a n d  ANALYSIS SET A d j a c e n t  Y  0  F  0  a  x  i  m  u  F r i c t i o n  F r a m e  H  F r a m e s ,  m  M  ( k N )  a  x  i  m  u  I m p a c t  m  M a x .  ( k N )  R e s t r a i n e r  F o r c e  M  ( k N )  a  x  i  m  u  9 4 . 7  I I  0.0  1 0 9 4 5 . 0  0.0  1 1 2 . 0  J J  0.0  1 4 6 1 0 . 0  0 . 0  1 1 0 . 9  K  K  0 . 0  1 6 4 5 1 . 0  0.0  1 1 9 . 9  L  L  0 . 0  1 7 3 8 7 . 0  0.0  9 1 . 4  H I  0 . 0  9 5 8 2 . 7  0.0  1 1 7 . 6  I J  0 . 0  1 1 1 5 6 . 0  0.0  1 0 9 . 5  J K  0 . 0  1 3 8 6 5 . 0  0.0  1 1 4 . 5  K  0.0  2 0 3 4 3 . 0  0.0  1 2 2 . 8  L  t h e  o f  I n  t o t a l  t h e  r e s p o n s e  t h e  g r o u n d  e x t e n t  c a n  t h i s  t h e  s h e a r  a l m o s t  s l i g h t  b e n t  0  b e n t s ,  o f  t h e  a  b e  p e r f e c t ,  o f  t h e  r a n d o m  n o t  n a t u r e  i n c r e a s e  i n c r e a s e d  %  o v e r  i n  i n  a  V  L  t h e  l a r g e  t h e  b y  6  5  %  s h e a r  o v e r  2  a  t h e  g r o u n d  p e a k  i n b e n t  r e l a t i v e  t h r o u g h  a s  o f  V  t h e  p h a s e  t h e  L  o f  i n  1  t h e  b a s e  o f  I n  o f  L L L P 1 1 .  b e n t ' s  p h a s e  m o t i o n  i n b e n t  t h e  r e l a t i v e  m a k e  c h a n g e  G a p  d i s p l a c e m e n t s  u p  a  i s m o r e  l a r g e  o f  t h e  p o r t i o n  d i r e c t l y  a  o f  r e s u l t  c h a n g e .  r e s p o n s e  m o d e l  i n t h e  a n d  i n  d i s p l a c e m e n t s  m o t i o n s .  d i s p l a c e m e n t  i n c r e a s e  c h a n g e  g r o u n d  m a s s e s ,  t r e n d  w i l l  p h a s e  t h e  g o i n g  i n c r e a s e s  r e s u l t e d  s t i f f e r  f r o m  d i s p l a c e m e n t  w a s  5  a n d  m o r e  d i s p l a c e m e n t s  s i g n i f i c a n t l y  p e a k  b y  b y  c o m e s  s h o r t e r  n o d a l  H o w e v e r ,  f o r  ( m m )  0.0  b e n t .  7 3  O p e n i n g  8 8 5 7 . 2  b e n t ' s  0  m  0.0  t h e  R  Y 0 F 0 R 0 .  M  H  u  § 5 . 4  t h e  m a s s e s  s o m e  a  b e n t  m o d e l  T h e s e  b e n t ,  s h e a r .  b u t  i s i n f l u e n c e d  c a s e s ,  t h e  ( F i g s .  5 . 4 . 1 2  L L S F 0 9 ,  i n c r e a s e s  t h e  h i g h  t o  a  s y m p a t h e t i c  a n d  a n d  w e r e  i m p a c t s  5 . 4 . 1 3 ) .  i t w a s  o f  T h e  i n c r e a s e d  c a u s e d  s t i f f n e s s  c e r t a i n  b y  t h i s  o n l y  s h o r t  CHAPTER 5 : TWO-BENT FRAMES  B  § 5 . 4 ANALYSIS SETYOFORO 7 4  Y0F0RO-LLSF09DP  0.08  C CD  E  CD CD  0.04  P.  0.00 o  U00  J  —1 -0.04  *=* Displ. of ground — Displ. of mass 1 . — Displ. of mass 2  I  o O u. o -0.08  g  0.08  o E  0.04  CJ  od  0.00 o  —1 I  -0.04  Displ. of ground — Displ. of mass 1 — Displ. of mass 2  O O  to -0.08 o >§  16000  CD CJ  CJ  ed C o  CD  8000  O Lu CO  -J —1 I  o ai o u, o  4000  >-  10 Time (sees)  F i g u r e  5 . 4 . 1 2 :  L L S F 0 9 ,  C o m p a r i s o n  i n A n a l y s i s  S e t  o  f t o t a l  Y 0 F 0 R 0 .  n o d a l  d i s p l a c e m e n t  t i m e  h i s t o r i e s  b e t w e e n  L  L  S  F  0  1  a  n  d  CHAPTER 5 : TWO-BENT FRAMES  |  § 5 . 4  ANALYSIS SET  Y  0  F  0  R  0  7 5  YOF0R0-LLSFO9SH  4000  CU CJ  c3  O  to 2 -4000 to  o ai o to p  — —  Shear in bent 1 Shear in bent 2  -8000  4000 cu CJ  cu  -C  CO ON  o to CO  -4000  -J  —1  o  o to ° -8000  §  16000  cu  o £ 12000 4-1  CU  s  o cu  O o to  8000  CO  —I  —1  4000  o o o 4 T i m e  F i g u r e  5 . 4 . 1 3 :  A n a l y s i s  S e t  C o m p a r i s o n  Y 0 F 0 R 0 .  o  f s h e a r  f o r c e  10  6  t i m e  ( s e e s )  h i s t o r i e s  b e t w e e n  L  L  S  F  0  1  a n d  L L S F 0 9 ,  i  n  CHAPTER 5: TWO-BENT FRAMES  §5.4 ANALYSIS SET Y 0 F 0 R 0 76  0.15  c  cu cu u ed  M  a <u  E  0.10  CD  CJ CCJ  cd  0.05  CJ  CL  CL  San Fernando^ Mexico City Loma Prieta  ed  0.00  San Fernando^ — Mexico City ,— Loma Prieta  tN  2  1.4 cu N  O  e cd tu  cd  u a. c u CQ  T3 CJ  N  1.2 1.0  O  C  0.8 Cd CU  J3  0.6  co  _^  0.4  cu  San Fernando^ — Mexico City V;— Loma Prieta  0.2 0.0  c_  San Fernando"'! — Mexico City — Loma Prieta J  CN  c cj CQ  Peak contact forces (kN)  Peak gap opening (mm)  10000  120  7500  90  5000  60  2500  — San Fernando — Mexico City -— Loma Prieta , 0.0  0.1  0.2  0.3  0.4  0.5  30  • San Fernando — Mexico City -— Loma Prieta y 0.0  0.1  Time delay (sees)  F i g u r e  5 . 4 . 1 4 :  e a r t h q u a k e s  P e a k  f r a m e  i n A n a l y s i s  S e t  a  n  d j o i n t  r e s p o n s e s  Y0F0R0.  0.2  0.3  0.4  0.5  Time delay (sees)  f o r f r a m e  H  I  a tv a r i o u s  d e l a y s  i  nt h e t h r e e  c  CD  s  0.10  u  o cd  CL) CL  0.05 ^ S a n Fernando^ — Mexico City \^— Loma Prieta  cd  0.00  i  0.15  77  1  §5.4 ANALYSIS SET Y 0 F 0 R 0  Mass 2 pe ak displace merits (m)  CHAPTER 5: TWO-BENT FRAMES  ^ San Fernando"; — Mexico City \;— Loma Prieta J  1.4  Peak contact forces (kN)  0.0  0.1  0.2  0.3  0.4  Peak gap opening (mm)  0.5  0.0  0.1  Time delay (sees)  F i g u r e  5 . 4 . 1 5 :  e a r t h q u a k e s  i  P e a k  f r a m e  n A n a l y s i s  S e t  a n d  j o i n t  Y0F0R0.  r e s p o n s e s  0.2  0.3  0.4  0.5  Time delay (sees)  f o r f r a m e  I J a t  v a r i o u s  d e l a y s  i n t h e  t h r e e  CHAPTER 5: TWO-BENT FRAMES  §5.4 ANALYSIS SET Y 0 F 0 R 0 78  0.15  a  a CO CO  o  0.10  CO 6 CO  0.05  -Li 1)  o ca  C3  cz CO CL  CL  San Fernando^ - Mexico City — Loma Prieta  rl  0.00  -o  -a CO  CO  O  O  a  c  N  cz CO  .C  Xi  CO  s  cd oj  CL  '  C CQ  c_  San Fernando Mexico City — Loma Prieta  San Fernando^ — Mexico City — Loma Prieta  rl  13 0J  CQ  Peak gap opening ( m m )  Peak contact forces (kN) 120  16000  12000  8000  4000  San Fernando —— Mexico City — Loma Prieta 0.0  0.1  0.2  0.3  0.4  — Mexico City •— Loma Prieta 0.5  0.0  0.1  Time delay (sees)  F i g u r e  5 . 4 . 1 6 :  e a r t h q u a k e s  P e a k  f r a m e  i n A n a l y s i s  a  S e t  n  d j o i n t  r e s p o n s e s  Y0F0R0.  0.2  0.3  0.4  0.5  Time delay (sees)  f o r f r a m e  J  K a tv a r i o u s  d e l a y s  i  nt h e t h r e e  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 4  ANALYSIS SET  Y  0  F  0  R  0  7 9  0.15  C u  c  4)  0.10  o o  CO CO BJ  CL  ci co  L^  0.05  CO  a.  San Fernando^ — Mexico City -— Loma Prieta J  cn  a 0.00  ft  San Fernando'— Mexico City — Loma Prieta  C3  2  Peak gap opening (mm)  Peak contact forces (kN) 20000 San Fernando^ Mexico City Loma Prieta J  15000  10000  5000  San Fernando Mexico City Loma Prieta J  0.0  0.1  0.2  0.3  0.4  0.5  0.0  0.1  Time delay (sees)  F i g u r e  5 . 4 . 1 7 :  e a r t h q u a k e s  i  P e a k  f r a m e  nA n a l y s i s  a  S e t  n  dj o i n t  r e s p o n s e s  Y 0 F 0 R 0 .  0.2  0.3  0.4  0.5  Time delay (sees)  f o rf r a m e  K  L  a tv a r i o u s  d e l a y s  i  nt h e t h r e e  CHAPTER W  h  e  n  m  a  x  i  TWO-BENT FRAMES  5:  A d j a c e n t  m  u  m  F r a m e s  p e a k  s h e a r s  c o r r e s p o n d i n g  b e n t s  T h e  i m p a c t s  m  a n d  a  x  t h e  i  m  a  m  u  x  i  m  m  a r e  u  m  s u b j e c t e d  w e r e  i n  t h e  t o  r e d u c e d  t h e  i n  E q u a l - H e i g h t  f o r t h e s e  p e a k  § 5 . 5  g a p  f r a m e s  o p e n i n g s  s a m e  m o s t  t i m e  c a s e s ,  F r a m e s  w h e n  ( T a b l e  g e n e r a l l y  f o r t h e s e  h i s t o r i e s  ( F i g s .  S e t  5 . 4 . 1 4  c o m p a r e d  t o  Y  t o  t h e  0  F  0  R  1  8 0  5 . 4 . 1 7 ) ,  r e s p o n s e s  t h e  o f  5 . 4 . 1 ) .  i n c r e a s e a s  f r a m e s  A n a l y s i s  v a r i e d  t h e  b e n t s  b e t w e e n  g e t  9 1  s h o r t e r  a n d  a n d  1 2 3  s u f f e r ,  m m  ( T a b l e  5 . 4 . 2 ) .  5.5  ANALYSIS SET Y 0 F 0 R 1  T h i s  s e t  b u t  w i t h  n o t  a  a n a l y s i s  a  r e s t r a i n e r  a c t i v a t e d  n e e d e d  m  o f  x  i  from  m  t o  u  m o d e l s  T h e r e  t h e  p e a k  t h e  s h e a r  b e f o r e  i n c r e a s e d  t h e  s i n g l e  w i t h  d i s p l a y  i n  t h e  t a l l e r  o f  t h e  r e s t r a i n e r  g a p  a  ( H  i n  c a s e  L ,  a d d i t i o n  r e a c h e d  i n t h e  o f  t h e  I ) .  a  S F  a t  w i t h  s e t Y  6 0  m m  F  0  t h e r e  s e c o n d s .  f r a m e  w i t h  R  0  T h e  t h e  t h e  m  a  x  i  T h e  t a l l e r  u  e x a c t  e a r t h q u a k e  f r a m e s ,  t h e y  t h e  m  t h e  r e s p o n s e ,  F r a m e s ,  w e r e  m  m  a  x  5.5.1  frames.  f r i c t i o n ,  r e s t r a i n e r  a m o u n t  t i m e  o f  r e m a i n  e s t a b l i s h e d  i n  s h e a r  u  m  s h e a r s  m  5 . 5 . 2 )  T h e  p e a k  a  x  i  i n  m  s h o w  i m p a c t s  u  t h e  m  t h e s e  5 . 5 . 1 ) .  a c t u a l l y  A d j a c e n t  p e a k  t h a t  n o w  T h e  u n c h a n g e d  i  m  w a s  d e l a y  h i s t o r y .  ( T a b l e  p e a k  a n d  t h e  n o  i s a c t i v a t e d  r e d u c t i o n i n t h e  ( F i g s .  o f  b e n t  r e s t r a i n e r  w h e r e  i s s o m e  b e h a v i o u r  a n d  b e c a u s e  w h e n  r e s u l t s  e l a s t i c  E q u a l - H e i g h t  0 . 1 0  e a c h  0  w i t h  t h e  e a r t h q u a k e )  h i s t o r y  s u b s e q u e n t  I n  l e a s t  r e s t r a i n e r .  t h o u g h  T i m e  f r a m e s  e s p e c i a l l y  a n a l y s i s  p a t t e r n ,  a n d  v a r i e s  c a s e s ,  i n  o f  0.25mg.  e x c e e d e d  m a n y  ( b e n t  a l t e r s  a t  r e s t r a i n e r  s i m i l a r  b e n t s  r e s p o n s e  y i e l d s  o p e n i n g  c a s e  t h e  t h e  d e l a y  c o r r e s p o n d i n g  i s a  F r a m e s  w h i c h  u n t i l  a c t i v a t e  m  t h e  c o m p a r e s  s h e a r s  a c t i v a t i o n  h a p p e n  a t  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 5  A n a l y s i s  S e tY  0  F  0  R  1  8 1  Y0F0RI-IIMC06DP  0.10 c  CD  0.05  CD  u C3  0.00  •tl  •o o  u  IB  -0.05  o ci o u, o >  1  -0.10  Displ. of ground^ Displ. of mass 1 Displ. of mass 2  0.10  a CD  0.05  E CJ  o ca  0.00  VO  o U  -0.05 o o  Displ. of ground Displ. of mass 1 Displ. of mass 2  -0.10  >-  10000  i  Contact force Restrainer force  5  7500  VD  5000  a  o u  + of o o  2500  0  >H  20  10 T i m e  F i g u r e Y  0  F  0  R  5 . 5 . 1 : 0  a  n  C o m p a r i s o n  d Y 0 F 0 R 1 ,  o  ft o t a l  f o r m o d e l  n o d a l  40  ( s e e s )  d i s p l a c e m e n t  I I M C 0 6 .  30  t i m e  h i s t o r i e s  b e t w e e n  A n a l y s i s  S e t s  CHAPTER 5: TWO-BENT FRAMES  §5.5  A n a l y s i s  S e tY  F  0  R  82  1  Y0F0R1-I1MC06SH  1000 CD CJ  0  500  u*  a  03  CD  JS  co  VO O  U  T o ci o  -500  °  -1000  |  1000  F  LL.  CO  CD CJ  500  LH  eg  u. re  CD  J3  CO  VO  o U  2  -500  5  o fa £ -1000 0  g  10000 Contact force ] Restrainer force I  CO  1  7500  vo  5000  o U  2  4,  2500  o LL. O  llll 10  20 T i m e  F i g u r e  5 . 5 . 2 :  Y 0 F 0 R 1 ,  C o m p a r i s o n  f o r m o d e l  o  f s h e a r  I I M C 0 6 .  f o r c e  t i m e  30  40  ( s e e s )  h i s t o r i e s  b e t w e e n  A n a l y s i s  S e t s  Y  0  F  0  R  0  a  n  d  CHAPTER T a b l e  5 :  TWO-BENT FRAMES  5 . 5 . 1 :  A d j a c e n t  C o m p a r i s o n  F r a m e s ,  f o rt h e  o  f m  A  n  a  x  § 5 . 6 A n a l y s i s  i  a y s i s  m  u  m  p e a k  S e t  n o r m a l i z e d  b e t w e e n  2  8 3  E q u a l - H e i g h t  a n d  s h e a r  E a r t h q u a k e  H  S F  1 . 0 8 2  1 . 0 2 4  M  C  1 . 2 0 5  1 . 1 0 2  L  P  1 . 0 9 4  1 . 0 1 7  S F  1 . 0 3 8  1 . 0 2 7  M  C  1 . 0 1 5  1 . 0 8 4  L  P  1 . 0 0 5  0 . 9 1 7  S F  1 . 1 3 0  1 . 0 1 8  M  C  1 . 1 1 0  1 . 1 4 7  L  P  1 . 1 6 2  0 . 9 9 1  S F  1 . 0 2 3  1 . 5 1 2  M  1 . 0 6 2  1 . 0 5 3  0 . 9 6 7  1 . 1 4 8  S F  1 . 8 9 4  1 . 4 3 3  M  1 . 0 9 4  1 . 0 2 2  1 . 4 5 0  1 . 1 2 3  J  K  C  L  L  P  C  L  d i f f e r e n t  p o i n t s  c o r r e s p o n d i n g  T h e  a d d i t i o n  o p e n i n g .  S e t  g a p  P  n t i m e ,  c a s e s  o  f a  W h e r e a s  Y 0 F 0 R 0 ,  p e a k  i  E q u a l - H t .  N o r m a l i z e d  B e n t  I  w i t h o u t  r e s t r a i n e r  t h e m  t h o s e  o p e n i n g s  l e a d i n g  a  x  i  t o n e w  0  F  0  R  Y 0 F 0 R 1 .  N o r m a l i z e d ( f o r  s h e a r s  S e t Y  p e a k  F r a m e s )  s h e a r s  w h i c h  ( f o r  m a y  b e  s h e a r  A d j a c e n t  F r a m e s )  l a r g e r  o r s m a l l e r  n t h e m  a  t h a n  t h e  r e s t r a i n e r s .  r e s u l t e d  m  u  n u m b e r s  a r e u s u a l l y  m  n o w  i  p e a k  n a  t o  o p e n i n g s  r a n g e  l a r g e r  3 0  i  f r o m  n c a s e s  4  0  %  r e d u c t i o n  v a r i e d  6 3  t o  w h e r e  8 8  f r o m  m m .  i  9 1  T  t o  h  e  t h e r e s t r a i n e r  1 2 3  m  m  x  i  m  i  u  m  p e a k  n t h e  r e d u c t i o n s  h a s r e a c h e d  i  n  g a p  A n a l y s i s  m  a  x  y i e l d .  i  m  u  m  CHAPTER 5: TWO-BENT FRAMES T a b l e  5 . 5 . 2 :  A n a l y s i s  M  a  x  i  m  u  m  j o i n t  §5.6 A  r e s p o n s e  i  n E q u a l - H e i g h t  a  n  d  n a l y s i s  Y 0 F 0 R 2 84  S e t  A d j a c e n t  F r a m e s ,  f  M  a  x  i  m  F r i c t i o n  u  m  M  ( k N )  a  x  i  m  I m p a c t  u  m  M a x .  R e s t r a i n e r  F o r c e  ( k N )  M  ( k N )  a  x  i  m  u  m  O p e n i n g  6435.5  1749.1  63.4  I I  0.0  8750.1  2348.8  68.0  J J  0.0  11651.0  2356.6  69.5  KK  0.0  13226.0  2422.1  82.2  L  0.0  18452.0  2396.1  77.2  H I  0.0  7473.6  2348.6  68.0  I J  0.0  9277.5  2349.1  68.1  L  J  K  0.0  12047.0  2380.8  74.2  K  L  0.0  14904.0  2452.1  88.0  r e s t r a i n e r  i n v a r i a b l y  F r a m e s  u p o n  T h e  b e n t s  t o l i m i t  i  nt u r n  d o  w a s  e v e n  a r em u c h  w i t h  f r a m e s ,  s u f f e r ,  t o r e d u c e  c o n t r i b u t e d  s o  o  2330  T  h a s  n o  h  T h e r e  y i e l d e d .  F r a m e s ,  d o  i n  f r a m e  y i e l d  w i t h  a s t h em o t i o n  a t t h e s u p p o r t s .  o  f w h e t h e r  n o t b e n d  m a s s ,  a s  r e s u l t i n g  fp h a s e  i m p a c t  E x c e p t  e r e s t r a i n e r s  d e l a y  t h e y  t h eo u to  L L ) .  k N .  i r r e s p e c t i v e  f t h e  t o r e d u c e d  ( f r a m e  t h er e s t r a i n e r  a t  y i e l d i n g .  t h ed i s p l a c e m e n t  h e l p  s e t  nt h eE q u a l - H e i g h t  f p h a s e ,  a l lb u t o n e c a s e  w h e r e  i  n t h e s h o r t e r  r e s t r a i n e r s  T h i s  f o r  i  s t r e n g t h  t o r e s t r a i n e r  t h e y  o u t o  f r e q u e n t l y  S h o r t e r  y i e l d  l e a d s  t h a n  g e n e r a l l y  t h e  G  a  p  ( m m )  0.0  H  T h e  r  Y0F0R1.  S e t  F r a m e  H  o  m o t i o n  f o r c e s .  i su s u a l l y  T  a  h  i  H  ,  l e s s  t h e  i n c r e a s e  d e l a y  b e t w e e n  w h e n  l a r g e r  s t r a i n  i  i  l a r g e r  u  m  r e d u c t i o n  p e a k  i  b e n t s  y i e l d  f e q u a l  a r e  m o r e  h e i g h t .  i s  c a l l e d  nt h e r e s t r a i n e r .  e m  m  d e l a y  A d j a c e n t  t h e r e s t r a i n e r  t h eg a p o p e n i n g  x  i n  n t h e  a l s o  a r e o  w h e n  a  i  u n e q u a l  R e s t r a i n e r s  t h e b e n t s  e a s i l y  na  H  e x c e e d s  i m p a c t s  np e a k  a r e  i m p a c t s  60  m m .  r e d u c e d  i  n  c a s e s  CHAPTER  5.6  TWO-BENT FRAMES  5:  § 5 . 6  A n a l y s i s  S e t  Y  5 . 6 . 1 :  A d j a c e n t  2  8 5  C o m p a r i s o n  F r a m e s ,  o f  f o r t h e  m  a  x  i  m  A n a y s i s  u  m  p e a k  S e t  n o r m a l i z e d  0  R  b e t w e e n  E q u a l - H e i g h t  a n d  Y 0 F 0 R 2 .  N o r m a l i z e d  s h e a r  H  S F  1 . 0 8 2  1 . 0 2 4  M  C  1 . 2 0 5  1 . 1 0 2  L P  1 . 0 9 4  1 . 0 1 7  S F  1 . 0 3 8  • 1 . 0 2 7  M  C  1 . 0 1 5  1 . 0 8 4  L P  1 . 0 0 5  0 . 9 1 7  S F  1 . 1 3 0  1 . 0 1 8  M  C  1 . 1 1 0  1 . 1 4 7  L P  1 . 1 6 2  0 . 9 9 1  S F  1 . 0 2 3  1 . 5 6 1  M  1 . 0 6 2  1 . 0 5 3  L P  0 . 9 6 7  1 . 1 4 8  S F  1 . 7 7 5  1 . 5 0 3  M  C  1 . 0 0 0  1 . 4 4 4  L  P  1 . 4 5 0  1 . 1 2 3  J  K  L  T h i s  s e t  o f  u n c h a n g e d  m a y  b e  e x a m i n e s  r e s t r a i n e r .  c o m p a r e d  t h e  r e s t r a i n e r  F e r n a n d o  C  a n a l y s i s  n o n - y i e l d i n g  t o  c a s e .  h a s  r e c o r d ,  E q u a l - H t .  N o r m a l i z e d  E a r t h q u a k e  I  ( f o r  s h e a r s  B e n t  t h e  F  ANALYSIS SET Y 0 F 0 R 2  T a b l e  t h i s  0  i n  M o s t  t h e  T h e  c o m e  t h e  i n t o  w h i c h  m  r e s p o n s e  o f  t h e  p r e v i o u s  a  x  i  p l a y ,  t h e  m  u  a s  m  m  a  x  o f  i  a n a l y s i s  p e a k  m  f r a m e s  u  m  s e t  s h e a r  i s f r e q u e n t l y  d i s p l a c e m e n t s  F r a m e s )  w i t h  p e a k  t h e  p e a k  e l a s t i c  s h e a r  ( T a b l e  c o u l d  ( f o r  5 . 5 . 1 ) .  h a v e  c a s e  v e r y  A d j a c e n t  b e n t s ,  v a l u e s  T h e r e  h a p p e n e d  w i t h  e a r l y .  m o d e l s  n o  ( T a b l e  a r e  t w o  b e f o r e  s h e a r F r a m e s )  f r i c t i o n ,  5 . 6 . 1 )  a n d  r e m a i n  r e a s o n s  t h e  s u b j e c t e d  e f f e c t s  t o  a  t h e  w h y  o f  S a n  CHAPTER T a b l e  TWO-BENT FRAMES  5 :  5 . 6 . 2 :  A n a l y s i s  M  a  x  i  m  M  r e s p o n s e  i  n  E q u a l - H e i g h t  a n d  A d j a c e n t  0  F  0  F r a m e s ,  a  x  H  i  m  u  m  M  ( k N )  a  x  i  m  u  I m p a c t  m  M a x .  ( k N )  R e s t r a i n e r  F o r c e  M  ( k N )  a  x  i  m  u  m  ( m m )  6 3 . 4  I I  0 . 0  8 7 5 0 . 1  3 3 0 2 . 4  6 6 . 4  J J  0 . 0  1 1 6 5 1 . 0  3 4 4 6 . 6  6 6 . 7  0 . 0  1 3 2 2 6 . 0  5 2 0 3 . 2  7 0 . 0  L  0 . 0  1 7 7 7 1 . 0  5 7 7 4 . 5  7 1 . 1  H I  0 . 0  7 4 7 3 . 6  3 4 6 1 . 2  6 6 . 7  I J  0 . 0  9 2 7 7 . 5  3 4 8 9 . 3  6 6 . 7  J K  0 . 0  1 2 0 4 7 . 0  3 9 4 5 . 3  6 7 . 6  K  0 . 0  1 5 3 3 2 . 0  6 1 0 6 . 8  7 1 . 8  K  L  r e a c h  y i e l d .  r e a c h e d  S h o w n  i  r e s t r a i n e r  r e a s o n  T h i s  1 . 0 8 4  w a s  V  I  n T a b l e  t o  l e a d  p u l l i n g  o n  o n e  e x t r e m e  h a l f  b e n t s ,  t i m e s  a s  t h e p e a k  b e n t  t h e m a x i m u m  t o  S e t  h i g h e r  ( f r a m e  l a r g e r  b e n t  t h a n  K  K  H  s h e a r s  r e a c h e d  1 . 0 2 4  r e s p o n s e  g a p  o p e n i n g  Y 0 F 0 R 1 .  p e a k  f o rt h i s  O  s h e a r s ,  n  i  t h e  a s  t h e r e l a t i v e  L  C  i  n t h e M  t h e y i e l d  p u l l e d  i  V  H  n c a s e s  i  w h e r e  n m o d e l  o n  ( 2 3 3 0  b e n t  L ,  n e a c h  a n d  i  c a s e ,  o t h e r  t h e r e s t r a i n e r  H I S F 0 4  a n d  h a n d ,  o n e  b e n t  L  a n d  A l t h o u g h  t h e r e d u c t i o n  u s i n g  b e n t  t o  o n  t h e r e s t r a i n e r  n Y 0 F 0 R 1 ,  t h e n  s e t .  d i s p l a c e m e n t  e a r t h q u a k e ) ,  k N )  a n a l y s i s  i t a l l o w s  i n c r e a s i n g  ,  o c c u r  d  i  d n o t  t h e w a y  b e n t  I J M C 0 5 .  i s t h e j o i n t  a n o t h e r ,  c a s e  f i r s t  n m o d e l  A n a l y s i s  o c c a s i o n a l l y  f o r c e  i s t h a t  t h e w a y  5 . 6 . 2  r e d u c e s  c o m p a r e d  i  8 6  G a p  O p e n i n g  1 7 4 9 . 1  p o s s i b l e  2  •  F r i c t i o n  A n o t h e r  R  f o r t h e  6 4 3 5 . 5  L  a  j o i n t  S e t Y  0 . 0  K  I  m  S e t Y 0 F 0 R 2 .  F r a m e  H  u  § 5 . 6 A n a l y s i s  s u c h  t h e b e n t  o n  a  a  a  t h e p e a k  K .  s i g n i f i c a n t  r e s t r a i n e r  m  b e i n g  d e v e l o p e d  b e n t  n o n - y i e l d i n g  i s n o t  e x e r c i s e  i n c r e a s e d  p u l l e d  a  u  c  h  l a r g e r  p u l l e d .  f o r c e  s h e a r  c a n  t w o  i  n  I n  a n d  b o t h  CHAPTER  5.7  5 :  TWO-BENT FRAMES  5 . 7 . 1 :  A d j a c e n t  C o m p a r i s o n  F r a m e s ,  S e t Y  f o rt h e  o  f m  A  n  a  x  i  m  a y s i s  u  m  p e a k  S e t  n o r m a l i z e d  b e t w e e n  s h e a r  S F  1 . 0 0 8  0 . 9 3 2  M  1 . 0 2 4  0 . 9 1 7  L P  1 . 0 3 0  0 . 9 3 3  S F  0 . 9 9 6  1 . 0 9 5  M  1 . 0 2 4  1 . 0 6 4  L P  0 . 9 8 1  1 . 0 9 1  S F  1 . 0 1 9  1 . 0 7 5  M  0 . 9 8 1  1 . 0 9 3  L P  1 . 0 4 8  1 . 1 1 5  S F  0 . 9 9 4  1 . 1 0 0  M  0 . 9 6 8  1 . 1 5 3  L P  0 . 9 6 7  1 . 1 3 7  S F  1 . 6 4 3  0 . 9 5 9  M  1 . 0 0 9  1 . 0 7 4  1 . 4 4 6  1 . 4 7 3  L  E q u a l - H t .  N o r m a l i z e d  H  K  C  C  C  C  C  L P  T h i s  b u t  i st h e a n a l y s i s  w i t h  n o  r e s p o n s e .  i n  t h e j o i n t  I n  t h ej o i n t s  d e c k s  s e tp e r f o r m e d  r e s t r a i n e r .  I n a  f a i r l y  w a s  t o m a k e  T h e  l a r g e  w e r e  o n  p o r t i o n  o  o  w i t h  F r a m e s )  e l a s t i c  f f r i c t i o n  f t h e a n a l y s e s  l a r g e  m o b i l i z e d , a  c o n t a c t .  f r a m e s  p r e s e n c e  n o t s u f f i c i e n t l y  t h a t  1  R  0  E q u a l - H e i g h t  E a r t h q u a k e  J  F  8 7  a n d  Y 0 F 1 R 0 .  N o r m a l i z e d ( f o r  s h e a r s  B e n t  I  0  Y0F1R0  ANALYSIS S E T  T a b l e  § 5 . 7 A n a l y s i s  i  s u b s t a n t i a l  b e n t s ,  n t h e j o i n t  p e r f o r m e d ,  t o o v e r c o m e  ( f o r  a n d j o i n t  h a s  d  i  a  a n d  dn o t m o v e  f r i c t i o n  s i g n i f i c a n t  t h e f o r c e  t h e f r i c t i o n ,  n u m b e r  A d j a c e n t  w h i c h  t h e j o i n t  s h e a r F r a m e s )  a t 7 8 4 . 8  e f f e c t  w a s  i t s  d e v e l o p e d  s t a y e d  s u f f i c i e n t l y  o n  k N ,  l o c k e d .  f o r t h e  t w o  CHAPTER T a b l e  TWO-BENT FRAMES  5 :  5 . 7 . 2 :  A n a l y s i s  M  a  x  i  m  m  j o i n t  r e s p o n s e  i n  E q u a l - H e i g h t  a n d  A n a l y s i s  S e t Y  A d j a c e n t  0  F  1  F r a m e s ,  M  a  x  i  m  u  F r i c t i o n  H  m  M  ( k N )  a  x  i  m  I m p a c t  u  m  M a x .  ( k N )  R e s t r a i n e r  F o r c e  M  ( k N )  a  x  i  m  u  m  O p e n i n g  0 . 0  0 . 0  2 0 . 0  I I  5 5 1 . 6  0 . 0  0 . 0  2 0 . 0  J J  7 8 4 . 8  0 . 0  0 . 0  2 0 . 4  K  7 8 4 . 8  1 0 9 5 8 . 0  0 . 0  8 0 . 1  L  L  7 8 4 . 8  1 1 3 8 9 . 0  0 . 0  8 5 . 1  H I  4 1 4 . 2  0 . 0  0 . 0  2 0 . 0  I J  5 9 8 . 1  0 . 0  0 . 0  2 0 . 0  J K  7 8 4 . 8  2 8 7 0 . 0  0 . 0  4 4 . 9  K  7 8 4 . 8  1 1 7 3 6 . 0  0 . 0  1 0 3 . 0  t h e  L  j o i n t  t r u e  m a d e  b e t w e e n  t h e  T a b l e  n o  d e c k s  5 . 7 . 1  f r i c t i o n  j o i n t  E v e n  a s  m e c h a n i s m ,  t h r o u g h o u t  I n  t h e  frame  i m p a c t e d ,  s h o w s  I n  ( Y 0 F 0 R 0 ) ,  t h e  t h e r e  o  a r e  h e l p i n g  t o  i  t h e  f o u r  s h e a r  i  m  frames,  u  t h e E q u a l - H e i g h t  H H ,  n o t  t h e  I I ,H I  a n d  I J ,i  s u f f i c i e n t l y  t h e  j o i n t  friction  i n t h e b e n t s .  i n c r e a s e s , b u t  x  b u t  I n  F r a m e s ,  n a l l t h r e e  f o r c o n t a c t  s h o w e d  w a s  G a p  t o  i n c r e a s i n g  f i n a l l y  o v e r c o m e  5 . 7 . 2 .  f r i c t i o n  a  i n f r a m e s  m o b i l i z e d ,  r e d i s t r i b u t i n g  t h e m  F r a m e s .  i n c r e a s e d , u n t i l  n T a b l e  s o m e  o v e r c o m e ,  r e d u c e  d e l a y s  r e m a i n i n g  f n o r m a l i z e d  i t i s i n e s s e n c e  i t i s f i n a l l y  w a s  s u p p o r t s  s h o w n  t h e v a r i a t i o n  A d j a c e n t  t h e v a r i o u s  b e t w e e n  a s  a n d  J J ,t h e j o i n t  d e c k s .  t h e d e l a y  i m m o b i l i z e d ,  w h e n  t h e E q u a l - H e i g h t  l o c k e d  r e c o r d s .  m o b i l i z a t i o n  a n d  f o rb o t h  s t a y e d  e a r t h q u a k e  b e  8 8  ( m m )  K  w a s  0  f o r  3 5 5 . 8  T h i s  R  S e t Y 0 F 1 R 0 .  F r a m e  H  u  § 5 . 7  c a n  m  t h e  s t i l l  d e c k  a l s o  s o m e  s h e a r  a c t  a s  i m p a c t .  C o m p a r e d  d e c r e a s e s .  d e m a n d  a n  t o  B  b e t w e e n  e f f e c t i v e  t h e c a s e  y  k e e p i n g  t h e  e n e r g y  w i t h  t w o  t h e  b e n t s .  d i s s i p a t i o n  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 8  A n a l y s i s  S e t Y  0  F  2  R  0  8 9  5.8 ANALYSIS SET Y 0 F 2 R 0 T a b l e  5 . 8 . 1 :  A d j a c e n t  C o m p a r i s o n  F r a m e s ,  f o rt h e  o  f m  A  n  a  x  i  m  a y s i s  u  m  p e a k  S e t  n o r m a l i z e d  s h e a r s  b e t w e e n  E q u a l - H e i g h t  Y 0 F 2 R 0 .  N o r m a l i z e d  s h e a r  N o r m a l i z e d  B e n t  E a r t h q u a k e  H  S F  1 . 0 0 8  0 . 9 3 2  M  1 . 0 2 4  0 . 9 1 7  L P  1 . 0 3 0  0 . 9 3 3  S F  0 . 9 9 6  1 . 0 9 5  M  1 . 0 2 4  1 . 0 6 4  L P  0 . 9 8 1  1 . 0 9 1  S F  1 . 0 1 9  1 . 0 7 5  M  0 . 9 8 1  1 . 0 9 3  L P  1 . 0 4 8  1 . 1 1 5  S F  1 . 0 5 8  1 . 3 8 7  M  1 . 0 8 9  1 . 3 4 0  L P  1 . 0 5 7  1 . 4 8 6  S F  2 . 1 0 1  1 . 2 1 3  M  1 . 9 3 0  1 . 4 6 9  1 . 9 4 3  1 . 2 8 7  I  J  K  L  ( f o r  E q u a l - H t .  C  C  C  C  C  L P  T h i s  i st h e a n a l y s i s  r e s t r a i n e r .  G e n e r a l l y  t o g e t h e r  i n c r e a s e d  m  m  a  i n  x  i  m  u  T a b l e  s e tp e r f o r m e d  s p e a k i n g ,  w i t h  d e l a y  p e a k  n o r m a l i z e d  5 . 8 . 2 .  C o m p a r e d  e x p e r i e n c e  a  l a r g e r  m  a  x  i  m  t i m e ,  t o  m  f r a m e s  t h e f o r c e  s h e a r s  u  o n  w i t h  r e q u i r e d  f o r b o t h  t h e p r e v i o u s  s h e a r .  F r a m e s )  e l a s t i c  t o k e e p  i  n T a b l e  a n a l y s i s  ( f o r  b e n t s  a n d  t h e t w o  t h e E q u a l - H e i g h t  a r e s h o w n  p e a k  a n d  5 . 8 . 1 ,  i n f i n i t e  b e n t s  i  n e a c h  t h e j o i n t  s e t ( Y 0 F 1 R 0 ) ,  t h e  F r a m e s )  f r i c t i o n ,  a n d t h e A d j a c e n t  a n d  s h e a r  A d j a c e n t  w i t h  f r a m e  a c t i n g  F r a m e s .  f o r c e s  s h o r t e r  a r e  b e n t s  n o  T h e  s h o w n  h e r e  CHAPTER T a b l e  5 :  TWO-BENT FRAMES  5 . 8 . 2 :  A n a l y s i s  M  a  x  i  m  M  j o i n t  a  x  i  m  u  F r i c t i o n  H  r e s p o n s e  i  n  E q u a l - H e i g h t  a n d  A d j a c e n t  0  F  m  M  ( k N )  a  x  i  m  I m p a c t  u  m  M a x .  ( k N )  R e s t r a i n e r  F o r c e  M  ( k N )  a  x  i  m  u  0 . 0  2 0 . 0  I I  5 5 1 . 6  0 . 0  0 . 0  2 0 . 0  J J  9 7 0 . 7  0 . 0  0 . 0  2 0 . 0  2 1 5 2 . 5  0 . 0  0 . 0  2 0 . 0  8 1 6 0 . 7  0 . 0  0 . 0  2 0 . 0  K  L  H I  4 1 4 . 2  0 . 0  0 . 0  2 0 . 0  I J  5 9 8 . 1  0 . 0  0 . 0  2 0 . 0  J K  1 2 8 1 . 3  0 . 0  0 . 0  2 0 . 0  K  3 6 0 9 . 2  0 . 0  0 . 0  2 0 . 0  I n  L  t h e p r e v i o u s  j o i n t  I n  b e n t s .  T h i s  x  i n s t a n c e ,  S i n c e  g r o u n d  a  t h e l o c k e d  h i g h e r  i s e s p e c i a l l y  i  m  u  m  p e a k  t o  a  t h e d e c k s  d i s p l a c e m e n t  b e n t .  w h e n  t h e b e n t s  m o t i o n ,  t r a n s l a t e s  h o l d  c a s e ,  i s m o b i l i z e d , r e l e a s i n g  t h i s  R  0  9 0  f o r t h e  j o i n t  s h e a r  L  o  f  2 . 0 0  a b o u t  ,  i  V  8 1 6 1  w h e n  a n d  l o w e r i n g  L  k N ,  a s  a t t h e d e c k  n w h i c h  d i s p l a c e m e n t  r e a c h e s  b e n t  L  n t h e d e f o r m e d  c o n s i d e r e d  d i s p l a c e m e n t s  f f r a m e  n t h e s h o r t  i  e n e r g y ,  a p a r t  o  g r o u n d  f o r c e  c a n b e  s p r e a d  r e l a t i v e  t o g e t h e r  i  t h e s p r i n g  c a n n o t  t r u e  l a r g e  t h e i n e r t i a  o c c u r  a  w h e n  t h e  d i f f e r e n t i a l .  w h i c h  i ti s a p p l i e d  i s l a r g e  a s  a  d e l a y  T h e  m  a  x  e n o u g h  h o r i z o n t a l  r e s u l t i n g  o  f b e n t  f o r c e  i  L  s u p p o r t  i  m  u  t h e  t h e  b e n t .  t w o  d i f f e r e n t i a l  n h i g h e r  s h e a r s .  e x c i t a t i o n  f r i c t i o n  t o c a u s e  n t h e  t h e  c o n t r i b u t e s t o  n  m  i  b e t w e e n  i  f o r c e  G a p ( m m )  t h e f r i c t i o n ,  t o a c c o m m o d a t e  s t i f f n e s s  l a r g e  s h e a r  c o n n e c t i o n  n t h e b e n t s ,  t h e h i g h  e x c e e d s  t h e p e a k  r i g i d  l e v e l  i  b e n t  m  O p e n i n g  0 . 0  L  2  F r a m e s ,  3 5 5 . 8  K  m  m  S e t Y  S e t Y 0 F 2 R 0 .  F r a m e  H  u  § 5 . 8 A n a l y s i s  a  3 5  a t t h e d e c k  m  a l s o  r e q u i r e d  m  n o d e  a  t o  r e l a t i v e  o  f t h e  CHAPTER 5: TWO-BENT FRAMES  §5.9  5.9  ANALYSIS SET Y 1 F 0 R 0  T h i s  a n a l y s i s  d e m a n d ,  l i s t e d  v a l u e s  t h e s e  w i t h  f o r  r e a c h e d  m  a  n o  x  y i e l d  i  m  u  m  h e r e .  S e t  M  a  f o r  x  a n d  p e a k  T h e  r e a c h e d  5 . 9 . 1 :  A n a l y s i s  t h e  f r i c t i o n  e s t a b l i s h e d  w e r e  T a b l e  s e t c o m p a r e s  i  m  n o  a  n o r m a l i z e d  x  i  c a s e s  u  o f  m  m  u  m  I n  s h e a r  o f  j o i n t  w h e r e  j o i n t  f r a m e s  r e s t r a i n e r s .  p e r f o r m a n c e  m  i n  r e s p o n s e  t h e  r e s p o n s e  f i v e  a n d  i n  S e t  T h e s e  c a s e s  r e m a i n  o p e n i n g s  r e m a i n e d  a n d  s p e c t r a l  o f  s a m e  c a s e s  r e m a i n  30  t h e  u n c h a n g e d .  a l s o  e l a s t i c  E q u a l - H e i g h t  t h e  Y 0 F 0 R 0 , 25  1.00.  g a p  h a v e  s t r e n g t h s e t t o  Y1F0R0  S e t  M  a  x  i  m  F r i c t i o n  u  m  M  ( k N )  a  x  i  m  I m p a c t  u  M a x .  m  ( k N )  0.0  8 8 5 7 . 2  I I  0.0  J J  H  A d j a c e n t  F r a m e s ,  f o r  R e s t r a i n e r  F o r c e  M  a  x  i  m  u  m  O p e n i n g  ( k N )  0.0  1 2 1 . 0  1 0 9 4 5 . 0  0 . 0 .  1 1 2 . 0  0.0  1 4 6 1 0 . 0  0 . 0  1 1 0 . 9  1 2 6 . 9  L  L  0 . 0  1 4 2 4 3 . 0  0.0  9 1 . 4  H I  0.0  9 5 8 2 . 7  0.0  1 1 7 . 6  I J  0.0  1 1 1 5 6 . 0  0.0  1 0 9 . 5  J K  0.0  1 3 8 6 5 . 0  0.0  1 1 4 . 5  K  0.0  2 0 3 4 3 . 0  0.0  1 2 2 . 8  L  t h e  0  g a p  F  0  R  s p e c t r a l  H o w e v e r ,  d e c r e a s e d ,  t h e  a s  t h e  o p e n i n g s  0  u s u a l l y  m a x i m u m  s h e a r  t h e r e  v a l u e s  d e m a n d .  a r e  t h o u g h  c a s e s ,  t h i s  i n c r e a s e ,  T h i s  s u c h  d e c r e a s e  w e r e  i n  i s n o t  c o m p a r e d  e s t a b l i s h e d  i s t r u e  a s  w h e n  f o r t h e  I I M C 0 4  w h e n  m a j o r i t y  a n d  s i g n i f i c a n t ,  t o  c o r r e s p o n d i n g  t h e  o f  s h e a r  c a s e s  L L S F 0 5 ,  a n d  t h e s e  r e s p o n s e  w h e n  w h e r e  c a s e s  t h e  a r e  a  c a s e s  w a s  b e n t  p e a k  n o t  i n  G a p ( m m )  0 . 0  Y  o f  5.9.1).  ( T a b l e  1 6 4 5 1 . 0  t h e  n o w  u n c h a n g e d ,  0 . 0  i f  v a l u e s  M o s t  K  p e a k  s h e a r  h a v e  K  T h e  91  Y 1 F 0 R 0 .  F r a m e  H  A n a l y s i s  o t h e r  b e n t s  s h e a r  e x c e e d e d  f o r c e s  t h e  w i t h  A n a l y s i s  Y 0 F 0 R 0 ,  g r e a t e r  r e a c h e s  o p e n i n g s  c o m m o n .  t h a n  y i e l d .  h a v e  CHAPTER 5: TWO-BENT FRAMES  5.10  A n a l y s i s  S e t  Y2F0R0  5 . 1 0 . 1 :  M  a  x  i  M  m  a  u  x  m  i  j o i n t  m  F r i c t i o n  F r a m e  H  u  r e s p o n s e  m  M  ( k N )  a  i n  x  i  E q u a l - H e i g h t  m  u  I m p a c t  m  a n d  M a x .  ( k N )  A d j a c e n t  R e s t r a i n e r  F o r c e  F r a m e s ,  M  ( k N )  a  x  i  m  u  f o r  m  ( m m )  3 8 7 4 . 4  0 . 0  1 7 5 . 1  I I  0 . 0  5 6 7 1 . 3  0 . 0  1 6 9 . 0  J J  0.0  6 4 1 2 . 8  0 . 0  1 5 4 . 6  K  K  0 . 0  8 9 9 9 . 4  0 . 0  1 4 6 . 0  L  L  0.0  8 7 7 1 . 9  0 . 0  1 1 3 . 1  H I  0 . 0  4 3 2 6 . 0  0 . 0  1 4 8 . 2  I J  0 . 0  5 7 3 5 . 1  0.0  1 4 8 . 8  J K  0 . 0  6 8 9 1 . 7  0.0  1 4 4 . 1  K  0 . 0  7 6 4 2 . 9  0.0  1 1 3 . 8  L  T h i s  s e t  o f  n o  f i r s t  t w o  o f  a n a l y s i s  f r i c t i o n  s u b s t a n t i a l  d e c k s  n e v e r  a r r i v e s  l a t e r  c a u s e s  a n o t h e r  e x p l a i n s  f r o m  t h e  e a c h  i n  a n d  n o  i m p a c t  c o m e  t h e  c a u s e s  i n t o  a  a n d  r e s u l t i n g  i n c r e a s e  t h a t  i n t h e  f i r s t  r e s p o n s e  A  l  l b e n t s  s u f f i c i e n t  c o n t a c t  e a r t h q u a k e  a f t e r  t h e  r e s t r a i n e r .  i m p a c t ,  l a r g e  o t h e r  c o m p a r e s  a g a i n  o f  b e n t s  i n  p e a k  ( F i g . 5 . 1 0 . 1  l o w e r  t h e  p e a k  o p e n i n g s .  i m p a c t .  a l lf r a m e s  p e r m a n e n t  e s t a b l i s h e s  i n  d e s i g n e d  h a v e  a n d  i m p a c t  i n  5 . 1 0 . 2 ) .  i n  t h e  Y  f o r c e s  b e n t s  a r e  a  f o r c e  y i e l d e d .  d e f o r m a t i o n  p e a k  T h e  w i t h  t h e  T h e  0  F  0  I n  r e d u c t i o n  m o s t  b e n t s ,  l a r g e r  R  ( T a b l e  0  p e r m a n e n t l y  t h a t  m o t i o n  5 . 1 0 . 1 ) .  f a c t o r  c a s e s ,  s u c h  a n a l y s i s  t h e  G a p  O p e n i n g  0.0  4,  92  ANALYSIS SET Y 2 F 0 R 0  T a b l e  H  §5.10  s e t  T h i s  d i s p l a c e d  t h e  t h e  w h i c h  n e v e r  a l s o  a w a y  CHAPTER 5: TWO-BENT FRAMES  §5.10  A n a l y s i s  S e t  Y2F0R0-HHSF11DP  0.10 a E CO  o cd  Y 2 F 0 R 0 93  0.05  D-  Z, o.oo CO  X X•  -0.05  f • Displ. of ground Displ. of mass 1 — Displ. of mass 2  o  ci  o  HH o  -0.10  0.10  Displ. of ground • Displ. of mass 1 Displ. plf mass 2  c CJ  E  CO  0.05  CJ  cd  5. CO  0.00  CO  X•  -0.05  o  ci o  -0.10  £  10000  fD O  o cd  7500  4—*  c  o  "  5000  CL. CO  X X o  i  2500  ci o u.  10  20 T i m e  F i g u r e  5 . 1 0 . 1 :  Y0F0R0  a n d  C o m p a r i s o n  Y2F0R0,  i  o  f t o t a l  n m o d e l  n o d a l  40  ( s e e s )  d i s p l a c e m e n t  HHSF11.  30  t i m e  h i s t o r i e s  b e t w e e n  A n a l y s i s  S e t s  CHAPTER 5 : TWO-BENT FRAMES  § 5 . 1 0  A n a l y s i s  S e tY  2  F  0  R  0  9 4  1000 CD  O  3—i  500  a  H cd cu  LL.  m X Xi  -500  o  oi  Shear in bent 1 — Shear in bent 2  o  UH  CN  •1000  10000 cu o •~ o  7500  cd  *  5000  UL-  m X X  2500  I  o  cC o  tN  20  10 T i m e  F i g u r e  5 . 1 0 . 2 :  Y 2 F 0 R 0 ,  i  C o m p a r i s o n  nm o d e l  o  H H S F 1 1 .  fs h e a r  f o r c e  t i m e  40  30  ( s e e s )  h i s t o r i e s  b e t w e e n  A n a l y s i s  S e t s  Y  0  F  0  R  0  a n d  CHAPTER  5 :  TWO-BENT FRAMES  § 5 . 1 1 A n a l y s i s  S e t Y  2  F  0  R  2  9 5  5.11 ANALYSIS SET Y 2 F 0 R 2 T a b l e  5 . 1 1 . 1 :  A n a l y s i s  M  a  x  i  m  u  m  j o i n t  r e s p o n s e  i  n  i  m  E q u a l - H e i g h t  a n d  A d j a c e n t  F r a m e s ,  f o r t h e  S e t Y 2 F 0 R 2 .  M  a  x  i  m  u  F r i c t i o n  F r a m e  m  M  ( k N )  a  x  I m p a c t  u  m  M a x .  ( k N )  R e s t r a i n e r  F o r c e  M  ( k N )  a  x  i  m  u  m  0 . 0  4 2 3 4 . 4  2 3 3 5 . 1  6 4 . 5  I I  0 . 0  5 0 6 9 . 8  2 2 9 7 . 4  6 4 . 4  J J  0 . 0  7 8 6 1 . 3  2 3 3 2 . 4  6 4 . 5  0 . 0  9 7 6 2 . 9  3 2 6 9 . 3  6 6 . 3  L  0 . 0  1 0 2 2 8 . 0  4 0 5 1 . 5  6 7 . 8  H I  0 . 0  4 2 7 9 . 4  2 4 9 2 . 7  6 4 . 8  0 . 0  7 3 8 7 . 5  2 7 3 4 . 8  6 5 . 3  0 . 0  7 2 0 9 . 0  3 0 0 1 . 5  6 5 . 8  0 . 0  9 2 7 8 . 7  3 7 7 8 . 4  6 7 . 3  H  K  L  H  K  U  J  K  K  L  T h i s  s e to  o f  a n d  4 ,  Y i e l d i n g  a r e  f a n a l y s i s  c o m p a r e s  i s d i f f e r e n t  o  f r o m  f t h e b e n t s ,  s l i g h t l y  s u b s t a n t i a l l y  d i f f e r e n t  r e d u c e d .  l i k e  t h e p e r f o r m a n c e  t h e p r e v i o u s  i  f r o m  s e t i  n t h e p r e v i o u s  A n a l y s i s  o  f b e n t s  n t h a t  a n a l y s i s  S e t  a  d e s i g n e d  w i t h  n o n - y i e l d i n g  Y 2 F 0 R 0 ,  b u t  t h e  m  a  a  f o r c e  x  i  T h e  m  u  m  m  a  ( m m )  r e d u c t i o n  r e s t r a i n e r h a s  s e t , i s u n i v e r s a l .  G a p  O p e n i n g  x  g a p  i  m  b e e n  u  m  f a c t o r  a d d e d .  i m p a c t s  o p e n i n g s  a r e  CHAPTER V FIVE-BENT FRAMES  6.1 INTRODUCTION T h e  f i v e - b e n t  f r a m e  c a p t u r e s  t h e e f f e c t  c o n s i s t s  o  w i t h  T h e  b e n t  f b e n t s  L  j o i n t  p a r a m e t e r s  h  e  b e n t  n  1  e v e n l y  t h a t  a r r a n g e d  o  s t u d i e d  friction,  i  r e m a i n  i  r e a l i s t i c  b e t w e e n  b e n t  frames  s t r e n g t h  u n c h a n g e d  w a s  a n d  a t 2 0  t h e f i r s t ,  a n d b e n t  b e t w e e n  a d j a c e n t  b e n t s .  b e t w e e n  b e n t s  1  a n d  m u l t i p l e  h e i g h t ,  a n a l y s i s .  t i m e  m  m  5  i  s t a r t i n g  u n d e r  T h e s e  T h e  a n d  m m ,  t h e l a s t ,  H e n c e ,  b e n t s  d e l a y .  w a v e  t h a n  4 0  w i t h  t h e d e l a y  2 .  9 6  b y  b e n t  a  v a r i o u s  i n i t i a l  H  f r a m e ,  a n d  a n  u s i n g  a n d  frame  a n d  e n d i n g  e x p a n s i o n  a r e t h e b e n t  o p e n i n g  i t b e t t e r  T h e  t h e l e f t  s i t u a t i o n s ,  g a p  a s  e x c i t a t i o n .  o n  d e c k  p a r a m e t e r s  s o m e  y i e l d  s t r u t .  o  f t h e  s t r e n g t h ,  r e s t r a i n e r  s l a c k  r e s p e c t i v e l y .  i s a s s u m e d  t o b e  t h e t w o - b e n t  n d i f f e r e n t i a l  t o t h e n e x t  e x a m i n e d  t h e e a r t h q u a k e  i s a l w a y s  m o d e l  i s c o n n e c t e d  n t h e p r e l i m i n a r y  i s p r e s e n t ,  b r i d g e  n d e s c e n d i n g  E a c h  f t h e s e  r e s t r a i n e r  d e l a y  m o r e  f i n t e r a c t i o n  t h e r i g h t .  p e r f o r m a n c e  p a r a m e t e r s  W  o n  o  i s a  e x c i t e d  b e t w e e n  t o t r a v e l  from  ( F i g . 6 . 1 . 1 ) .  b e n t s  1  a n d  l e f t  T i m e  3  t o  r i g h t ,  d e l a y  i s t w i c e  s o  i s  a s  t h a t  a p p l i e d  l a r g e  a s  CHAPTER 6 : FIVE-BENT FRAMES  L  L  expansion joint 1  § 6 . 2 ANALYSIS PARAMETERS 9 7  L  expansion joint 2  expansion joint 4  Bent 4 (BentK)  Bent 3 (BentJ)  Bent 2 (Bent I)  Bent I (BentH)  L  expansion joint 3  BentS (BentL)  Direction of earthquake wave propagation  Figure 6.1.1:  T  h  e f i v e - b e n t  f r a m e  w i t h  e x p a n s i o n  j o i n t s .  6.2 ANALYSIS PARAMETERS Table 6.2.1  :  S h e a r  c a p a c i t y  S p e c t r a l C a p a c i t y  B e n t  d e s i g n e d  S h e a r  w i t h  a  m o d a l  M o d a l  ( k N )  a n a l y s i s .  H e i g h t  S h e a r  C a p a c i t y  ( k N )  M  o  m  e  n  t  C a p a c i t y  ( m )  ( k N . m )  1  8 8 0 . 8 4  1 1 9 3 . 6  1 5 . 8 9 4  1 8 9 7 1 . 0  2  1 1 6 8 . 1  1 3 8 5 . 0  1 3 . 6 9 7  1 8 9 7 1 . 0  3  1 5 9 1 . 9  1 6 7 7 . 8  1 1 . 3 0 7  1 8 9 7 1 . 0  4  2 4 3 3 . 7  2 1 9 8 . 5  8 . 6 2 9  1 8 9 7 1 . 0  5  4 2 3 1 . 1  3 4 9 0 . 0  5 . 4 3 6  1 8 9 7 1 . 0  T h r e e  d i f f e r e n t  r e p r e s e n t s  m a t c h e d  t h i s  t h ec a s e  t o t h et o t a l  c a p a c i t y  r e s i s t a n c e  m o d a l  b e n t  o  s t r e n g t h s a r eu s e d .  f m o d a l  s p e c t r a l  i s d i s t r i b u t e d  ( T a b l e  s h e a r  y i e l d  6 . 2 . 1 ) .  c a p a c i t y .  Y  s h e a r  s h e a r  c a p a c i t y .  d e m a n d  b e t w e e n  2  Y  T  c o r r e s p o n d s  h  ( s h o w n  t h e b e n t s  c o r r e s p o n d s  0  e t o t a l  i  s h e a r  nT a b l e  s u c h  t o t h ec a s e  t o t h ec a s e  t h a t  c a p a c i t y  4 . 5 . 1 ,  t h e y  w h e r e  a  n  F  R  F  o  fn  o  y i e l d i n g .  f t h e f i v e  d r e p e a t e d  a l lh a v e  a n  o  o  f 4  b e n t s  a b o v e ) ,  t h e s a m e  Y  l  i s  b u t  m o m e n t  i s a p p l i e d  t ot h e  CHAPTER 6: FIVE-BENT FRAMES  Table 6.2.2:  S y m b o l s  u s e d  P a r a m e t e r  Y i e l d  s t r e n g t h  o f  b e n t  t o  §6.2 ANALYSIS PARAMETERS  i d e n t i f y  a n a l y s i s  s e t  f o r t h e  I d e n t i f i c a t i o n  P a r a m e t e r  Y O  E l a s t i c  Y  M o d a l  l  i n  j o i n t  R e s t r a i n e r  E x c e p t  i n t h e  r e s p o n s e  F o u r  t h e  c a s e s  b e n t s  f r i c t i o n  r e s t r a i n e r  t h e  c a s e  T h e s e  d o u b l e  w h e r e  r e s p o n s e  s h e a r ,  t o  M o d a l  F O  N o  F I  F r i c t i o n  =  4 6 6 . 1  k  N  F 2  F r i c t i o n  =  9 3 2 . 2  k  N  F 3  I n f i n i t e  R O  N o  R l  R e s t r a i n e r  t h e  w e r e  i s s e t t o  t h e  m o d a l  u s e d .  4 6 6 . 1  c a s e  o f  t h e  F O  F 2  t h e  r e s t r a i n e r  p a r a m e t e r s  a r e  l i s t e d  e a r t h q u a k e s .  e q u a l  s h e a r ,  w i t h  a n  F  R  F  o f  4  f r i c t i o n  ( l o c k e d  j o i n t s )  y i e l d s  i s u s e d  a t  0 . 2 5 / w g  ( A n a l y s i s  S e t s  Y  ( 2 3 3 0  l  k N )  , Y 2 ) ,  t h e  s h e a r  s h e a r .  t o  c a s e  t h e  c a s e  w h e r e  t h e  o f  n o  f r i c t i o n .  f r i c t i o n  i s s e t t o  F I  i s  9 3 2 . 2  t h e  c a s e  k N ,  a n d  j o i n t s .  R O  s t r e n g t h  T a b l e  i s t h e  o b t a i n  r e s t r a i n e r  c a p a c i t y  s p e c t r a l  t o  f r i c t i o n  c o r r e s p o n d s  k N .  u s e d .  w h e r e  i n  t o  s h e a r  l o c k e d  s t r e n g t h s w e r e  m a g n i t u d e  d i s t r i b u t e d  r e s i s t a n c e  Y 2  i s n o r m a l i z e d  v a l u e s  c o r r e s p o n d s  T w o  i s  o f  f r i c t i o n  w h e r e  F 3  s t r e n g t h  f r a m e s .  V a r i a t i o n  m o m e n t  F r i c t i o n  f i v e - b e n t  98  c o r r e s p o n d s  i s s e t  6 . 2 . 2 .  t o  t o  t h e  0.25mg  S e v e r a l  a n a l y s i s  c a s e  ( 2 3 3 0  s e t s  w i t h  n o  r e s t r a i n e r ,  a n d  R  l  k N ) .  w e r e  a l s o  p e r f o r m e d  u s i n g  CHAPTER  FIVE-BENT FRAMES  6:  ANALYSIS SET  § 6 . 3  Y  0  F  3  R  0  9 9  6.3 ANALYSIS SET Y 0 F 3 R 0 T h i s  a n a l y s i s  e l a s t i c  b e n t s ,  s t i f f n e s s  t h e  o  w i t h  o  f t h e f i v e  n o d a l  p e a k  E x c e p t  f o rb e n t  t h o s e  p e a k  1  o  i  s h e a r  n t h e  frame  H I  s h e a r  i  s h e a r  T h e  u  a  h i g h e r  a n d  A s  x  i  m  t h a n  i n e r t i a  d e l a y  n t h e  ( F i g .  f o r c e s  from  L  m o t i o n s  r e s u l t s  w e l l ,  c o m p a r e d  p e a k  f r i c t i o n  i  1  h e r e  i s a  F r a m e  n t h i s  i  s t i f f n e s s  w i t h  d e l a y .  s t i f f e s t  b e n t  frame  r e l a t i v e  ( T a b l e  5  d e c r e a s e  b e n t s  c o m e  d i s p l a c e m e n t s  c a s e  a l l i n c r e a s e d  V H ,  o  l  f  T h i s  a r e l o c k e d ,  o  A  r e c o r d .  f e v e n  t h e  a n d  frame  h a s  t h e  a x i a l  t h e s h o r t e s t  l n o d e s  h a v e  f i v e ,  x  b e n t ,  s i m i l a r  p e a k  e x p e r i e n c e s  l a r g e r  a n d  p e a k  s i g n i f i c a n t l y .  i  m  F  o  r  e x a m p l e ,  1 . 0 9 5  p e a k  t o  V  I  t h e  t h e  0 . 9 3 3  t h e  V  L  i s b e c a u s e  m  a  ,  n o d a l  T h e  u n i f o r m  w i t h  n t h e t w o - b e n t  V  x  i  m  a  m  s h e a r  x  H  i  u  w h i c h  i  m  n  i  frame.  m u c h  j o i n t s  n t h i s  b e n t .  d i s p l a c e m e n t s  i n c r e a s i n g  frames,  t h e  a s  o  f  t h e  t h e  d e l a y .  m  a  m  p e a k  i s  m o v e m e n t  u  b e n t  m  t h e l o c k e d  d i s p l a c e m e n t s  t o t a l  s h e a r s  n o r m a l i z e d  i n t h e t w o - b e n t  i s 1 . 8 8 8  r e l a t i v e  p l a y .  ( Y 0 F 2 R 0 )  u  T h i s  n t h e p e a k  i n t o  m  c o m p a r e d  frame  frame.  i  S i m i l a r l y ,  w i t h  i n t h i s  i  a  5 . 8 . 1 ) .  V I , c o m p a r e d  f o rb e n t  m  ( Y 0 F 2 R 0 ) .  i s 0 . 9 6 3  a r e c a u s i n g  g r a d u a l  t h e  s i m i l a r  n t h e t w o - b e n t  b e n t s  b e t w e e n  h a v e  t h e  m o d e l s  r e c o r d  s h e a r  t o t h e c o r r e s p o n d i n g  f o r c e s  e v e n  e x p e r i e n c e  i s 1 . 0 2 0  t h e t a l l e r  n l a r g e r  i  r e a c h e d  i s i n c r e a s e d , t h e r e  b e i n g  frame  F e r n a n d o  2  t h e j o i n t s  t h e b e n d i n g  u n i f o r m ,  5 ,  S i n c e  F e r n a n d o  6 . 3 . 1 ) .  f o rb e n t  V  t h a n  b e n t  n o r m a l i z e d  1 . 2 1 3  h i g h e r  i n t h i s  S a n  t o t h e S a n  r e s t r a i n e r .  i s f a i r l y  b u t  r e s p o n s e  b u t n o  A d j a c e n t  f o rb e n t  p e a k  t h e  o u t - o f - p h a s e  m a s s e s  m  f o r c e s  t w o - b e n t  n o r m a l i z e d  m  m a s s e s  5 , t h e b e n t s  n o r m a l i z e d  f  i s m u c h  d i s p l a c e m e n t s ,  l a r g e s t  a s  t h e f r a m e ' s  l o c k e d j o i n t s  f t h e g i r d e r s  m o t i o n  t o t a l  s e t e x a m i n e s  x  i  m  A  s  u  m  CHAPTER 6: FIVE-BENT FRAMES  §6.4 ANALYSIS SET Y 0 F 0 R 1  Peak nodal displacements (m)  0.15  — —  Bent 1 Bent 2 Bent 3 —- Bent 4 — Bent 5  0.10  100  Peak normalized shears  2.0 1.5 1.0  0.05 0.5 0.0  0.00 Peak friction forces (kN)  8000 6000  60  4000  40  2000  20  Peak contact forces (kN)  15000  Peak gap openings (mm)  80  Joint 1 — Joint 2 — Joint 3 — Joint 4  10000  Joint 1 — Joint 2 — Joint 3 — Joint 4  Peak restrainer forces (kN)  2500  — — — —  2000  Joint 1 Joint 2 Joint 3 Joint 4  1500 1000  5000  500 0 0.0  0.1  0.2  0.3  0.4  0.5  0.0  Figure 6.3.1: Peak values for the Analysis Set Y 0 F 3 R 0 .  0.1  0.2  0.3  0.4  0.5  CHAPTER  6:  FIVE-BENT FRAMES  § 6 . 4  ANALYSIS SET  Y  0  F  0  R  1  1 0 1  6.4 ANALYSIS SET Y 0 F 0 R 1 T h i s  a n a l y s i s  j o i n t  f r i c t i o n ,  a s  d e l a y  b u t  a n d  p e r f o r m e d  w i t h  r e s t r a i n e r  i s i n c r e a s e d h e l p s  t h e  p e a k s  W h e r e a s  o f  s e t w a s  i  f r i c t i o n  f o r b e n t  5  n t h e p r e v i o u s  i  n o r m a l i z e d  n t h i s  d o e s  n o t  a n a l y s i s  t h e  S a n  t h e p e a k  c h a n g e  t o t a l  F e r n a n d o  a l l o w e d  f o r b e n t  5 ,  T h e  n o d a l  s i g n i f i c a n t l y  s e t , t h e m o v e m e n t  s e t h a s  e x c e p t  o n l y  s t r e n g t h s e t t o 0 . 2 5 w g .  t o r e d u c e  a n a l y s i s  s h e a r s ,  u s i n g  b e n t  a l s o  5  o  a  w i t h  d i s p l a c e m e n t s  a s  e l a s t i c  b e n t s ,  i n c r e a s e i n o u t - o f - p h a s e  d e l a y  f r e e d o m  s i m i l a r  i  a r e t i e d  ( F i g .  t o g e t h e r ,  n i t s m o v e m e n t .  d e c r e a s i n g  b e n t s ,  6 . 4 . 1 ) .  t h e  T h e  p a t t e r n  a s  n o  m o t i o n  f o r t h e t a l l e r  i s i n c r e a s e d  f a l l t h e b e n t s  m o r e  d i s p l a y  r e c o r d  l a c k  p e a k  d e l a y  i s  i n c r e a s e d .  A l l  r e s t r a i n e r s  e f f e c t i v e  E x c e p t  d e l a y  i  a r e s t r a i n e d  n r e d u c i n g  f o r j o i n t  t i m e  4 ,  t o  t h e p e a k  t h e r e  a l s o  y i e l d  g a p  ( 2 3 3 0  k N )  o p e n i n g s ,  a p p e a r s  t o b e  a  a t c e r t a i n  w h i c h  d o  g e n e r a l  d e l a y  t i m e s ,  n o t i n c r e a s e  r e d u c t i o n  i  a n d  t h e y  a p p e a r  s i g n i f i c a n t l y  n t h e p e a k  w i t h  c o n t a c t  t o  b e  d e l a y .  f o r c e s  a s  i s i n c r e a s e d .  6.5 ANALYSIS SET Y 0 F 1 R 0 T h i s  a n a l y s i s  e l a s t i c  b e n t s ,  C o m p a r e d  r e d u c e d ,  g e n e r a l  w h e n  t o  b u t  s e t w a s  p e r f o r m e d  f r i c t i o n  t h e  m o r e  r e d u c t i o n  t h e d e l a y  ( 4 6 6 . 1  p r e v i o u s  s o  k N )  a t  a n a l y s i s  f o r t h e t a l l e r  i n t h e p e a k  i s l e s s  u s i n g  t h a n  5  t h e S a n  %  f t h e n o r m a l  s e t ( Y 0 F 0 R 1 ) ,  b e n t s  n o r m a l i z e d  0 . 2  o  F e r n a n d o  s e c o n d s .  t h a n  s h e a r  t h e  g r o u n d  f o r c e  t h e  p e a k  s h o r t e r  f o r c e s ,  a t t h e j o i n t ,  t o t a l  o n e s  e v e n  m o t i o n s  n o d a l  o n  a n d  n o  T h e r e  s h o r t e r b e n t s ,  w i t h  r e s t r a i n e r .  d i s p l a c e m e n t s  ( F i g . 6 . 5 . 1 ) .  f o r t h e  t h e f r a m e  a r e  i s a l s o  a  e s p e c i a l l y  §6.5 ANALYSIS SET Y0F1R0 102  CHAPTER 6: FIVE-BENT FRAMES  Peak normalized shears  Peak nodal displacements (m) 0.15  1.2  0.10  0.8  0.05  0.4 — — —  Bent 1 Bent 2 Bent 3 Bent 4 BentS  -A  0.0  0.00  Peak gap openings (mm)  Peak friction forces (kN)  1000  — — — —  750  Joint 1 Joint 2 Joint 3 Joint 4  500  250  Peak restrainer forces (kN)  Peak contact forces (kN) 15000  Joint 1 — Joint 2 — Joint 3 — Joint 4  10000  2500 2000 1500 1000  5000 Joint 1 — Joint 2 — Joint 3 — Joint 4  500  0.0  0.1  0.2  0.3  0.4  0.5  0.0  Figure 6.4.1: Peak values for the Analysis Set Y0F0R1.  0.1  0.2  0.3  0.4  0.5  CHAPTER 6: FIVE-BENT FRAMES  §6.6 ANALYSIS SET Y 0 F 1 R 1 103  Peak normalized shears  Peak nodal displacements (m)  0.15  0.10  0.05  0.0  0.00  Peak gap openings (mm)  Peak friction forces (kN)  1000  — Joint 1 —  Joint  2  — Joint 3 — Joint 4  750  100 80 60  500 40 250  20 0 Peak contact forces (kN)  15000  Peak restrainer forces (kN)  Joint 1 — Joint 2 — Joint 3 — Joint 4  10000  2500  — — — —  2000  Joint 1 Joint 2 Joint 3 Joint 4  1500 1000  5000  500 0 0.0  Figure 6.5.1:  P e a k  0.1  v a l u e s  0.2  0.3  0.4  f o r t h e A n a l y s i s  0.5  S e t  0.0  Y0F1R0.  0.1  0.2  0.3  0.4  0.5  CHAPTER  6:  T h e  f r i c t i o n  t h e  p e a k  c a s e  g a p  FIVE-BENT FRAMES  o f n o  f r i c t i o n  o p e n i n g s  a r e  r e s t r a i n e r  h a s  t h e  t i m e  d e l a y  6.6  y i e l d  T h e  a t  m  a  a l l .  ( F i g .  i s  x  i  I n  t h e  o p e n i n g  T h i s  i n  m  i s t h e  t h e  T h i s  f o u r  6 8  a n a l y s i s  j o i n t  a n  ( 2 3 3 0  m e a n s  a s  s e t  from  w a s  f r i c t i o n  s t r e n g t h  s e t  t o  t i m e s  0 . 3 0  a s  i n  h a v e  b e e n  m o b i l i z e d .  c o n t a c t f o r c e s  o f  t h e  l e s s  p e a k  t h a n  g a p  a r e  0 . 3 0  H o w e v e r ,  s u b s t a n t i a l l y  s e c o n d s .  o p e n i n g s  Y  0  1  1 0 4  c o m p a r e d  w i t h  2  r e d u c e d .  H o w e v e r ,  b e t w e e n  F  b e n t s  T h e  t h e  4  R  p e a k  l a c k  a n d  5  o f  a  w h e n  s e c o n d s .  t h e  k N ) .  i n j o i n t  t h a t  1  r e a c h e s  o n l y  a c t i v a t e d  i n t h e  m m  o n e ,  o f  t h e  f o r t h e  T h i s  f o r t h e  g r o u n d  2 8  u n t i l  p r e v i o u s  y i e l d .  e x c e p t  F e r n a n d o  r e s p o n s e  r e a c h e s  8 8  S a n  n o t  t h e  frame  p r e v i o u s  T h e  i t w a s  t h e  r e s t r a i n e r s  m m  p e a k  i n c r e a s e  s a m e  o p e n i n g  s a m e  t h e  f o r d e l a y  o t h e r j o i n t s ,  t h e  t o  g a p  a l l j o i n t s  ANALYSIS SET  Y0F1R1  ANALYSIS SET  b e n t s ,  w i t h  s e t  u  6 . 6 . 1 ) .  o f  6.7  m  t h a t  i s g r e a t e r t h a n  0.25mg  a t  e x a c t l y  o u t  r e d u c e d  r e s u l t e d  a n a l y s i s  s h o w  ( Y 0 F 0 R 1 ) ,  ANALYSIS SET  T h i s  t o  f o r c e s  § 6 . 7  m m ,  t h e  frame  m o t i o n s  s o  t h e  d e l a y  s e t , i n w h i c h  p r e v i o u s  s e t  w i t h o u t  a t  t i m e s  4,  t h e  l e s s  i s n o  a  r e s t r a i n e r  w a s  n o t  a c t i v a t e d  l e a s t  0 . 2 5  s e c o n d s  t h a n  0 . 2 5  r e s t r a i n e r .  r e d u c e s  s e t  u s e d .  r e s t r a i n e r  t h e r e  i n j o i n t  o f  w e r e  r e a c h e d  f o r d e l a y  r e s t r a i n e r ,  a d d i t i o n  t h e  m  a  x  s e c o n d s  O n l y  i  m  u  m  o n e  g a p  r e s t r a i n e r .  Y0F2R1 p e r f o r m e d  ( 9 3 2 . 2  k N )  0.25mg.  a t  u s i n g  1 0 %  t h e  o f  S a n  t h e  F e r n a n d o  n o r m a l  f o r c e  r e c o r d  o n  b e t w e e n  t h e  f r a m e  d e c k s ,  a n d  w i t h  a  e l a s t i c  r e s t r a i n e r  CHAPTER 6 : FIVE-BENT FRAMES  §6.7 ANALYSIS SET Y 0 F 2 R 1 105  Peak normalized shears  Peak nodal displacements (m) 0.15  Bent 1 Bent 2 Bent 3 — Bent 4 — Bent 5  —  0.10  0.4  0.05  Bent 1 Bent 2 Bent 3 — Bent 4 — Bent 5  —  0.0  0.00 Peak friction forces (kN)  Peak gap openings (mm) 80  1000  — Joint 1 Joint 2 — Joint 3 — Joint 4  750  60  500  40  250  20  -H  Peak contact forces (kN)  Peak restrainer forces (kN) 2500  15000 — — — —  Joint Joint 2 —• Joint 3 — Joint 4  Joint 1 Joint 2 Joint 3 Joint 4  — — — —  2000  Joint Joint 2 Joint 3 Joint 4  10000  5000  0  ^  0.0  Figure 6.6.1:  P e a k  0.1  v a l u e s  0.2  for  0.3  0.4  t h e A n a l y s i s  0.5  S e t  0.0  Y0F1R1.  0.1  0.2  0.3  0.4  0.5  CHAPTER 6: FIVE-BENT FRAMES  §6.8 DOUBLE MAGNITUDE EARTHQUAKES 106  Peak nodal displacements (m)  0.15  — Bent 1 — Bent 2 Bent 3 — Bent 4 — Bent 5  0.10  Peak normalized shears  1.2  0.8  0.4  0.0 Peak gap openings (mm)  80  750  60  500  40 r.  250  Joint 1 Joint 2 Joint 3 — Joint 4  Peak contact forces (kN)  15000  20  Peak restrainer forces (kN)  2500 2000 -  10000  — — — —  Joint 1 Joint 2 Joint 3 Joint 4  1500 1000  5000  500  0.0  Figure 6.7.1:  P e a k  0.1  v a l u e s  0.2  for  0.3  0.4  t h e A n a l y s i s  0.5  S e t  0.0  Y0F2R1.  0.1  0.2  0.3  0.4  0.5  CHAPTER 6 : FIVE-BENT FRAMES A l t h o u g h  t o t a l  t h e j o i n t s  n o d a l  r a n g e  a s  a  l a r g e r  b e  j o i n t s  t i m e  d e l a y  a c t i v a t e d .  p e a k  T i m e  6.8  t h e  p l a c e  frames  i  m  o f  t h e  p e a k  t h e  u  t h e  2  p e a k  t h a t  o n c e  i t h a s  s h e a r  t h o s e  i n  t h e  ( F i g . 6 . 7 . 1 )  4  h a s  b e e n  t h e  d e c k s  p e a k  p r e v i o u s  r e m a i n  t o  r e a c h e d  f r i c t i o n  b e  m a d e ,  y i e l d  e x p e r i e n c e s i n t h i s  r e d u c e d  f r i c t i o n  b y  c e r t a i n  r e s t r a i n e r  o p e n i n g s  t h e  t h a n  s h o w n  i n j o i n t  b e e n  g a p  a s  b e t w e e n  t h e  h a s  friction  i n  s e t , t h e  a b o u t  t h e  p e a k  s a m e  s e t .  m o b i l i z e d ,  f o r c e  s h o w  j o i n t  a n a l y s i s  r e s t r a i n e r  m  m o r e  n o r m a l i z e d  c o n t a c t  f o r j o i n t  i n a n a l y s i s  m a g n i t u d e  j o i n t s  s e t s  e a r t h q u a k e s ,  w i t h  s u p p o r t s .  6.8.1 T h e  x  r e s u l t s  i n  b e e n  f o r j o i n t  a  r a n g e  a n d  h a v e  107  i n  o n  a v e r a g e  t h e  b y  f o r c e s  h a v e  a  a n d  ( 2 3 3 0  d o  2 0  n o t  l i m i t i n g  t h e  k N )  a n a l y s i s  a b o u t  o t h e r j o i n t s  f o r c e s ,  i t n o w  r e s t r a i n e r s  i n  t h e  s e t i s 3 3 7  m m  e f f e c t  o n  t o  p r e v i o u s  k N .  f o r e a c h  c h a n g e  t a k e s  T h e  d e l a y ,  s i g n i f i c a n t l y .  t h e  m o v e m e n t  m o b i l i z e d .  DOUBLE MAGNITUDE EARTHQUAKES  T h e  t h e  h a v e  o p e n i n g s  h i s t o r y  t a k i n g  m  frame  p r e v i o u s  W h e r e a s  s e t , t h e  g a p  t h o u g h  f o r t h e  a l l  a n a l y s i s  o f  d i s p l a c e m e n t s  t h o s e  A l t h o u g h  i n t h i s  § 6 . 8 DOUBLE MAGNITUDE EARTHQUAKES  f r i c t i o n  T h e  t o  a n d  g r o u n d  Y 0 F 0 R 1 ,  Y 0 F 1 R 0 ,  i n v e s t i g a t e  t h e  r e s t r a i n e r s .  m o t i o n s  e f f e c t  T h i s  from  Y 0 F 1 R 1  o f l a r g e r  i s a c h i e v e d  a l lt h r e e  a n d  Y  0  F  g r o u n d  b y  2  R  1  s u b j e c t e d  m o t i o n s  d o u b l i n g  e a r t h q u a k e  a r e  o n  t h e  r e c o r d s  t h e  d o u b l e  p e r f o r m a n c e  g r o u n d  a r e  t o  m o t i o n s  a t  u s e d .  ANALYSIS SET 2 Y 0 F 0 R 1 frame  d i s p l a y e d  u s e d  i n  i n  t h i s  T a b l e s  a n a l y s i s  6 . 8 . 1 . 1  a n d  s e t  i s t h e  6 . 8 . 1 . 2 ,  s a m e  a g a i n s t  a s  t h e  o n e  v a l u e s  i n Y 0 F 0 R 1 .  from  A n a l y s i s  T h e  S e t  p e a k  v a l u e s  Y 0 F 0 R 1 .  a r e  CHAPTER 6: FIVE-BENT FRAMES T a b l e  6 . 8 . 1 . 1 :  M  a  x  i  m  u  m  §6.8 DOUBLE MAGNITUDE EARTHQUAKES  p e a k  frame  A n a l y s i s  F r a m e  T o t .  D i s p l .  r e s p o n s e  S e t  f o r A n a l y s i s  ( m )  2Y0F0R1.  S e t  Y 0 F 0 R 1  A n a l y s i s  N o r m .  S h e a r  T o t .  D i s p l .  S e t  2 Y 0 F 0 R 1  ( m )  N o r m .  S h e a r  1  0 . 1 5 5  1 . 1 8 9  0 . 2 6 4  2 . 3 6 3  2  0 . 1 1 2  0 . 8 7 6  0 . 2 1 3  1 . 9 4 6  3  0 . 1 0 5  1 . 0 0 5  0 . 1 6 3  1 . 3 4 1  4  0 . 0 8 0  0 . 9 5 2  0 . 1 3 0  1 . 2 1 4  5  0 . 0 5 3  0 . 9 6 8  0 . 0 9 5  1 . 8 5 9  T h e  a n d  l a r g e r  g r o u n d  i n t h e c a s e  T h e  i n c r e a s e  T a b l e  o  m o t i o n s  f  frames  i n p e a k  6 . 8 . 1 . 2 :  M  a  x  h a v e  1,  s h e a r  i  m  u  m  2  s i g n i f i c a n t l y  a n d  w a s  p e a k  G a p  t h e p e a k  n o t  a s  j o i n t  A n a l y s i s  J o i n t  5,  i n c r e a s e d  S e t  ( m m )  l a r g e  t h e p e a k  n o r m a l i z e d  f o r  r e s p o n s e  frames  s h e a r  3  a n d  f o r A n a l y s i s  t o t a l  h a s  4,  n o d a l  a p p r o x i m a t e l y  ( k N )  G a p  d o u b l e d .  2 Y 0 F 0 R 1 .  A n a l y s i s  R e s t r a i n e r  d i s p l a c e m e n t s ,  h o w e v e r .  S e t  Y 0 F 0 R 1  S e t  ( m m )  2 Y 0 F 0 R 1  R e s t r a i n e r  1  7 0 . 7  2 3 6 2 . 7  8 8 . 8  2 4 5 6 . 3  2  7 3 . 6  2 3 7 7 . 5  1 1 8 . 6  2 5 4 0 . 9  3  7 5 . 9  2 3 8 9 . 6  1 0 4 . 2  2 5 3 6 . 3  4  7 8 . 0  2 4 0 0 . 5  1 3 1 . 9  2 5 4 1 . 6  T h e  a m p l i f i e d  o p e n i n g  m o r e  l a c k  t h e  i  n j o i n t s  e f f e c t i v e  o  f  c a s e  m o t i o n s  friction  o f  j o i n t  2 ,  3  o  f  a n d  t h e  4 .  T h e  i n r e s t r i c t i n g  i n t h e j o i n t  2 ,  t h e m  a  t h e  h a s  x  i  m a s s  m  i n c r e a s e  m o t i o n  a l s o  u  m  r e s u l t  o  i n  a  i n j o i n t  f b e n t  s i g n i f i c a n t l y  p e a k  l a r g e  i m p a c t  1,  1  i n c r e a s e  w a s  t h e  n o t  m o s t  i n c r e a s e d  i n c r e a s e d  2  a s  i n  t h e  m  l a r g e ,  f l e x i b l e  o  a  a s  6  %  from  Y  x  0  i  t h e  f t h e  t h e p o u n d i n g  3  108  m  u  m  0  R  f i v e  1  p e a k  r e s t r a i n e r  b e n t s .  b e t w e e n  F  ( k N )  t o  d e c k s .  2 6 2 8 7  g a p  w a s  T h e  I n  k N .  CHAPTER 6: FIVE-BENT FRAMES  6.8.2 T h e  ANALYSIS SET  e f f e c t  t h a t  o  d o u b l e  e x p e r i e n c e d  n o r m a l i z e d  p e a k  b y  f a  t o t a l  91%  b  s h e a r  n o d a l  Table 6.8.2.1:  M  2Y0F1R0  m a g n i t u d e  f o r c e s  h a v e  m .  a  x  i  m o r e  T  h  e l a r g e s t  m  u  m  G a p  t h a n  o c c u r s  p e a k  T  o  h  3,  i n b e n t  r e s p o n s e  S e t  Y0F1R0 I m p a c t  t h ef r a m e  i  t o t a l  ns o m e  w h e r e  o c c u r s  j o i n t  ( m m )  n  e p e a k  d o u b l e d  i n c r e a s e  A n a l y s i s  J o i n t  e a r t h q u a k e  2Y0F0R1.  y t h e o n e i n  d i s p l a c e m e n t  0.156  t o  §6.8 DOUBLE MAGNITUDE EARTHQUAKES 109  i  i  nt h i s  n o d a l  1,  n b e n t  u  k  N  d t h e  p  f r o m  0.082  m  i  f r o m  0.091  m  t o  0.230  S e t  ( m m )  I m p a c t  (  k  N  88.1  15561.0  2  69.4  6851.2  154.9  18397.0  3  66.5  5775.5  147.7  17911.0  4  87.6  6483.3  166.8  17258.0  T h e  m  a  x  d o u b l e d  i  m  s t r a i n  o  a  4.  f a  n  h  b i g g e r  T h e s e  l a r g e  f o r c e s ,  f u r t h e r  h a v e  t h a n  a r e i  m o m e n t u m .  e f f e c t i v e  i  n t h e c a s e  o  d o u b l e d  m o r e  m o v e m e n t s  a s i  o p e n i n g  g a p o p e n i n g s  t h a n  i n c r e a s e s  t o g a t h e r  i s m o r e  p e a k  m o r e  f o r c e s  d i f f e r e n t i a l  r e s t r a i n e r  w i t h  h a v e  e i m p a c t  c o n t i n u e  d p o u n d i n g  h a r d e n  a r e t h e m a x i m u m  o p e n i n g s  T  t h e d e c k s  n e v e n  p r e s e n c e  o p e n i n g  g a p  Y0F1R0.  t o  o v e r c o m e ,  i  m  f o r j o i n t  c o m p a r e d  r e s u l t  u  6.8.2.1  h  o f  ft h e g a p .  d i m p a c t  1,  f o r j o i n t  e l a r g e  g r o u n d  f t h e  1,  b e n t s .  s i n c e  a  n  d  i n t h e  3,  a  i n c r e a s i n g  t h a t  o n c e  m o t i o n s  t h e p e r c e n t a g e  2Y0F0R1,  f o r c e s  2  d u e t o t h e f a c t  a t t h et o p o  n r e d u c i n g  n  f o r j o i n t s  t r i p l e d  n p a r t  T  a  m .  2Y0F1R0  4246.2  n T a b l e  n t h e  Y0F1R0  n  31.6  i  p e a k  e s m a l l e s t i n c r e a s e i  1  S h o w n  t o  2Y0F1R0.  S e t  G a p  )  n  h  A n a l y s i s  (  a  T  g o i n g  f o r A n a l y s i s  s e t i ss i m i l a r  d i s p l a c e m e n t s  c a s e s .  i t g o e s  a n a l y s i s  B  y  n  j o i n t s .  d  b  n e a r l y  i  i s  s u p p o r t  c o m p a r i s o n ,  t h e r e s t r a i n e r  366%  y  f r i c t i o n  a tt h e  i n c r e a s e  )  t h e  n t h e g a p  c o n t i n u e s  t o  CHAPTER 6 : FIVE-BENT FRAMES  6.8.3  § 6 . 8 DOUBLE MAGNITUDE EARTHQUAKES  ANALYSIS SETS 2 Y 0 F 1 R 1 AND 2 Y 0 F 2 R 1  Table 6.8.3.1:  M  a  x  i  m  u  m  p e a k  j o i n t  A n a l y s i s  J o i n t  G a p  r e s p o n s e  S e t  ( m m )  f o r A n a l y s i s  S e t s  2 Y 0 F 1 R 1  2  Y  0  F  1  A n a l y s i s  R e s t r a i n e r  ( k N )  G a p  R  1  S e t  ( m m )  a n d  2  Y  0  2 Y 0 F 2 R 1 .  F  2  R  1  R e s t r a i n e r  ( k N )  1  6 6 . 7  2 3 4 2 . 0  3 8 . 9  0 . 0  2  8 1 . 1  2 4 1 6 . 6  6 8 . 1  2 3 4 9 . 0  3  8 1 . 9  2 4 2 0 . 8  7 5 . 3  2 3 8 6 . 6  4  1 1 0 . 9  2 5 4 0 . 5  9 5 . 1  2 4 8 8 . 9  T a b l e  a  6 . 8 . 3 . 1  d o u b l e  t h e  s h o w s  frame  i n  f r a m e  w i t h  t h e  t o  t h a n  6 0  a p p l i e d  a r e  i n  a l s o  t u r n  T h e  o r  l e s s  l e s s  p e a k  d e c r e a s e s  frames  t h e  l e a d  m m  t h a n  t o t a l  t h o s e  t h o s e  n o d a l  b e t w e e n  e i t h e r  w a y ,  t h e  from  i n A n a l y s i s  S e t  k N ) .  t h a t  i n  T h e  2 Y 0 F 1 R 1 ,  j o i n t  s o  r e s p o n s e  r e d u c t i o n  e a r t h q u a k e  t h a n  frame  S e t  t o  l a r g e r  j o i n t  ( 4 6 6 . 1  A n a l y s i s  a n d  p e a k  T h e  2 Y 0 F 1 R 1  t o  t h e j o i n t ,  l e s s  t h e  e a r t h q u a k e .  C o m p a r e d  o f  110  friction,  t h e  t h e  u s e d .  2 Y 0 F 1 R 1 .  w h e r e  o n l y  t h e  a n a l y s i s  d e p e n d i n g  o n  g a p  x  i  m  i s n o t  a n d  p e a k  T h e  g r o u n d  t w o  t h e  u  m  friction  d e c r e a s e d  i n  s h e a r  m o b i l i t y  p e r f o r m e d  ( 9 3 2 . 2  r e s t r a i n e r  o f  i n  1  t h e  t h e  t h e s e  k N )  t h e  t h a n  m o b i l i t y  f o r c e s .  h a s  b e e n  i n  I n  t h e  r e d u c e d  a m o u n t  j o i n t s  t w o  u s i n g  d i f f e r e n c e .  d e c r e a s e s  i s p r e s e n t  n o r m a l i z e d  t h i s  a t j o i n t  f o r c e s  r e s p o n s e s  m o t i o n .  p e a k  r e g a r d l e s s  p o u n d i n g  o r  friction  2 Y 0 F 2 R 1  a n d  s e t s  r e f l e c t  o p e n i n g  a c t i v a t e d ,  j o i n t  m o r e  j o i n t s  i n  g a p  a n a l y s i s  h a s  o p e n i n g s  p e a k  p e a k  o f  friction  r e s t r a i n e r  s e t s .  t h e  a  T h e  T h e  d i s p l a c e m e n t s  t w o  m  r e s t r a i n e r  r e c o r d  l a r g e r  p e a k  l a s t  2 Y 0 F 2 R 1  r e s p o n s e  t h e  i n t h e  t h e  o f  d e l a y  2 Y 0 F 2 R 1  a n a l y s i s  s e t s  a r e  a l o n e .  s h o w  b o t h  i n c r e a s e s  a n d  i n  j o i n t  c a n  t h e  t h e  a f f e c t  CHAPTER  6.9 T h e  FIVE-BENT FRAMES  6:  ANALYSIS SET  § 6 . 9  Y  s u c h  l  i n  t h e  s y m b o l  T h e  t h a t  t h e  t o t a l  a n d  n o  T a b l e  6.9.1 :  f o r  t h i s  s p e c t r a l  b e n t s  f r i c t i o n  t h e  r e s t r a i n e r ,  S h e a r  a n a l y s i s  s h e a r  a l lh a v e  a n d  c a p a c i t y  F r a m e  s t a n d s  c a p a c i t y f o r t h i s  s a m e  w a s  m o m e n t  w i t h  f o r  s h e a r  f r a m e  s t r e n g t h  a  t o  a l l t h r e e  m o d a l  d e s i g n e d  i s d i s t r i b u t e d  c a p a c i t y ( T a b l e  s u b j e c t e d  d e s i g n e d  H e i g h t  s e t  6 . 9 . 1 ) .  T h i s  e a r t h q u a k e  R  0  1 1 1  M o d a l  ( m )  S h e a r  1 3 . 6 9 7  1 3 8 5 . 0  3  1 1 . 3 0 7  1 6 7 7 . 8  4  8 . 6 2 9  2 1 9 8 . 5  5  5 . 4 3 6  3 4 9 0 . 0  s h e a r  b e f o r e  t h e  F e r n a n d o  c a p a c i t y  t a l l e r  a n d  m a y  p e a k  6.10  g a p  o n e s ,  M e x i c o  i n s t a n c e s .  t h e y  a m o n g  T h e  e i t h e r  a n d  t o  C i t y  p e a k  t h e  b e n t s  y i e l d  i n  m o r e  i n c r e a s e  o r  n o d a l  frame  c a u s e s  frequently.  e a r t h q u a k e s ,  t o t a l  t h e  B e n t  r e g a r d l e s s  d i s p l a c e m e n t s  d e c r e a s e .  T h i s  i s  frame  m o d a l  f i v e  h a s  C a p a c i t y  2  T h e  t h e  a  b e n t s  n o  j o i n t  a n a l y s i s .  1 1 9 3 . 6  T h e  0  r e c o r d s .  1 5 . 8 9 4  a n d  F  w i t h  a m o n g  1  b u t  1  ANALYSIS SET Y1FORO  a n a l y s i s .  t w o  Y  o f  5,  w h e r e a s  p e a k  t h e  s h o r t e r  b e n t s  f o r e x a m p l e ,  d e l a y ,  a n d  a l s o  t h e  c a s e  s h e a r  w i t h  t o  y i e l d s  B e n t  f o r c e s  t h e  ( k N )  1  i n  y i e l d  a l lt h e  y i e l d s  v a r y  p e a k  r e a c h  i n  S a n  o n l y  w i t h  d e l a y ,  i m p a c t  f o r c e s  o p e n i n g s .  ANALYSIS SET Y 2 F 0 R 0 b e n t s  s h e a r  i n  t h i s  c a p a c i t y .  frame  a r e  I t i s a l s o  d e s i g n e d  s u b j e c t e d  w i t h  t o  a  f o r c e  a l l t h r e e  r e d u c t i o n  f a c t o r  e a r t h q u a k e s .  o f  4  a p p l i e d  t o  t h e  m o d a l  CHAPTER 6: FIVE-BENT FRAMES T a b l e  6 . 1 0 . 1 :  C o m p a r i s o n  o f  m  a  §6.11 ANALYSIS SETS Y 1 F 0 R 1 AND Y 2 F 0 R 1 x  i  m  u  m  p e a k  f r a m e  r e s p o n s e s  f o r A n a l y s i s  112  Y1F0R0  S e t s  a n d  Y 2 F 0 R 0 .  A n a l y s i s  F r a m e  N o d a l  D i s p l .  S e t  ( m )  Y  1  F  0  R  0  A n a l y s i s  N o r m .  S h e a r  N o d a l  D i s p l .  S e t  Y  ( m )  2  F  0  R  0  N o r m .  S h e a r  1  0 . 1 6 7  ( M C )  1 . 0 0 0  ( M C )  0 . 1 3 7  ( L P )  0 . 2 5 0  ( a l l )  2  0 . 1 1 2  ( M C )  0 . 8 3 8  ( M C )  0 . 1 2 4  ( L P )  0 . 2 5 0  ( a l l )  3  0 . 1 0 6  ( M C )  0 . 9 8 4  ( S F )  0 . 0 9 8  ( L P )  0 . 2 5 0  ( a l l )  4  0 . 0 8 2  ( M C )  1 . 0 0 0  ( a l l )  0 . 0 7 9  ( S F )  0 . 2 5 0  ( a l l )  1 . 0 0 0  ( a l l )  0 . 0 8 6  ( S F )  0 . 2 5 0  ( a l l )  f r a m e  r e s p o n s e s  0 . 0 7 3  5  T a b l e  6 . 1 0 . 1  Y 2 F 0 R 0 .  w h i c h  s h e a r  s i m i l a r  j o i n t  d e l a y  r e d u c e d  t h e m a x i m u m  r e s p o n s e  t h e m  t o t h e b e n t s ,  p e a k  T a b l e  T h e  g e n e r a t e d  a p p l i e d  T h e  s h o w s  ( S F )  a  x  i  m  i sn o r m a l i z e d  m  y i e l d i n g i  r e s p o n s e s  c a s e s  u  i  p e a k  r e s p o n s e  i s i n d i c a t e d  n t h e b e n t s  i s u n i v e r s a l  ( T a b l e  n t h e  t o t h e m o d a l  t w o  6 . 1 0 . 2 )  c a n  e i t h e r  a n a l y s i s  s e t s ,  t h o u g h  f m a x i m u m  p e a k  j o i n t  f r o m  t h e A n a l y s i s  s h e a r  c a p a c i t i e s , a n d  i n p a r e n t h e s e s .  i n a l lc a s e s  i n c r e a s e  t h e  m  a  S e t s  o r  x  i  m  o  W  h  e  f d e l a y  n  m  p e a k  1  t h e  F  0  R  0  a n d  e a r t h q u a k e  t h e F  i n a l l  d e c r e a s e  u  Y  R  F  o  f 4  i s  e a r t h q u a k e s .  w h e n  c o m p a r i n g  i m p a c t  f o r c e s  a r e  a n d  s i g n i f i c a n t l y .  6 . 1 0 . 2 :  C o m p a r i s o n  o  r e s p o n s e s  f o rA n a l y s i s  S e t s  Y  1  F  0  F  0  R  0  R  0  Y 2 F 0 R 0 .  A n a l y s i s  J o i n t  G a p  ( m m )  S e t  Y  1  F  0  R  A n a l y s i s  0  I m p a c t  ( k N )  G a p  1 0 4 . 3  1  1 2 2 . 0  ( M C )  1 4 6 5 4 .  ( M C )  2  1 1 8 . 3  ( M C )  1 7 0 6 9 .  ( M C )  3  1 1 4 . 3  ( M C )  1 6 0 0 0 .  ( M C )  4  8 7 . 9  ( M C )  1 5 5 2 2 . ( S F )  1 0 9 . 2  ( m m )  ( M C )  S e t  Y  2  I m p a c t  4 8 6 7 . 6  ( k N )  (  M  C  )  ( S F )  9 5 6 6 . 9  ( S F )  1 1 5 . 6 ( M C )  8 8 9 9 . 5  ( L P )  9 0 7 0 . 2  ( S F )  9 4 . 2  ( L P )  CHAPTER 6: FIVE-BENT FRAMES  §6.11 ANALYSIS SETS Y 1 F 0 R 1 AND Y 2 F 0 R 1  113  6.11 ANALYSIS SETS Y1FOR1 AND Y2F0R1 T a b l e  6 . 1 1 . 1 :  C o m p a r i s o n  o f  m a x i m u m  p e a k  f r a m e  r e s p o n s e s  f o r A n a l y s i s  Y1F0R1  S e t s  a n d  Y 2 F 0 R 1 .  A n a l y s i s  N o d a l  F r a m e  D i s p l .  S e t  Y  ( m )  1  F  0  R  1  A n a l y s i s  N o r m .  S h e a r  N o d a l  D i s p l .  S e t  Y  ( m )  2  F  0  R  1  N o r m .  S h e a r  1  0 . 1 5 6  ( M C )  0 . 8 7 9  ( M C )  0 . 1 0 3  ( L P )  0 . 2 5 0  ( a l l )  2  0 . 1 1 2  ( M C )  0 . 7 3 4  ( M C )  0 . 0 9 1  ( L P )  0 . 2 5 0  ( a l l )  3  0 . 1 0 5  ( M C )  0 . 0 8 9  ( L P )  0 . 2 5 0  ( a l l )  4  0 . 0 7 9  ( M C )  0 . 0 7 9  ( S F )  0 . 2 5 0  ( a l l )  0 . 0 9 0  ( S F )  0 . 2 5 0  ( a l l )  0 . 0 7 3  5  A n a l y s i s  S e t Y  r e s t r a i n e r s  t h e  b e n t s  W i t h  1  F  0  t h e r e  6 . 1 1 . 2 :  i  o  ( S F )  a t 0 . 2 5 / w g .  f a  f o rm o d a l  r e s t r a i n e r ,  n a l l b u t  i s a l s o  1 . 0 0 0  a  o n e  s l i g h t  C o m p a r i s o n  o  ( S F )  ( S ,  1 . 0 0 0  i s p e r f o r m e d  a r e d e s i g n e d  d i s p l a c e m e n t s  T a b l e  1  s e t t o y i e l d  t h e a d d i t i o n  y i e l d e d ,  R  0 . 9 7 7  o n  ( a l l )  t h e f r a m e  A n a l y s i s  s h e a r ,  t h e r e  f m a x i m u m  2  b u t w i t h  ( b e n t  r e d u c t i o n  w i t h  S e t Y  a r e s l i g h t  i n s t a n c e  M )  i  5 ,  F  a  R  1  i s p e r f o r m e d  F  R  F  o  Y 2 F 0 R 1 ) .  j o i n t  d e s i g n e d  0  f  r e d u c t i o n s  n t h e p e a k  p e a k  b e n t s  s h e a r  f o rm o d a l  o n  t h e  s h e a r ,  frame  i  w i t h  n  w h i c h  t o t a l  n o d a l  4.  i  n t h e m  I n  c a s e s  f o r c e s  r e s p o n s e s  a  x  i  m  u  m  w h e r e  ( t a b l e  p e a k  t h e  b e n t  h a s  n o t  6 . 1 1 . 1 ) .  f o rA n a l y s i s  S e t s  Y  1  F  0  F  0  R  1  R  1  a n d  Y 2 F 0 R 1 .  A n a l y s i s  J o i n t  1  G a p  7 2 . 5  ( m m )  ( L P )  S e t  Y  1  F  0  R  1  A n a l y s i s  I m p a c t  ( k N )  1 5 1 2 5 .  ( L P )  ( L P )  2  7 3 . 9  ( M C )  1 4 0 8 4 .  3  6 7 . 7  ( M C )  1 4 3 2 1 . ( S F )  4  7 9 . 1  ( M C )  1 4 5 4 2 .  ( S F )  G a p  6 3 . 6  6 7 . 4  6 6 . 9  6 8 . 5  ( m m )  ( M ,  L )  ( S F )  ( M C )  ( S F )  S e t  Y  2  I m p a c t  4 7 3 1 . 7  ( k N )  (  M  C  )  8 2 6 1 . 6  ( L P )  7 1 8 6 . 7  ( S F )  7 0 8 4 . 2  ( S F )  CHAPTER 6: FIVE-BENT FRAMES 6.11.2  T a b l e  s h o w s  t h e p e a k  r e s t r a i n e r  i s v e r y  c o m p a r e d  t o t h e t w o  T h e  b i g g e s t  m  i  a  x  m  u  m  b e n e f i t  p e a k  m o d a l  s h e a r .  o c c u r s  a t j o i n t  a l s o  b e e n  e f f e c t i v e  3,  s l i g h t l y  i  a n a l y s i s  o c c u r s  g a p  I n  j o i n t  s e t s  a t j o i n t  s e t w i t h  g o i n g  f r o m  r e d u c e d .  r e s p o n s e s  n r e d u c i n g  o p e n i n g  t h e  §6.11 ANALYSIS SETS Y 1 F 0 R 1 AND Y 2 F 0 R 1  t h e m  (Y1F0R0 1,  l o c a t e d  i s r e d u c e d  FRF  116  o  m m  f  f o r t h e t w o  a  a n d  t o  i  u  m  122  m m .  p e a k  Y2F0R0)  a p p l i e d ,  67  m  b e t w e e n  f r o m  4  x  a n a l y s i s  g a p  t h e  t o  m  T h e  m o s t  73  m  m  a  x  i  m  u  m  m  a  x  i  m  u  I t c a n b e  o p e n i n g  p e r f o r m e d  t h e t w o  m m  s e t s .  w i t h o u t  f l e x i b l e  r e d u c t i o n  p e a k  t h a t  a t t h e j o i n t ,  t h e  b e n t s ,  f o r t h e b e n t s  m  s e e n  i  n  i m p a c t  114 t h e  w h e n  r e s t r a i n e r .  w h e r e  t h e  d e s i g n e d  g a p  t o  o p e n i n g  f o r c e s  h a v e  CHAPTER SUMMARY AND CONCLUSIONS  7.1 I n  INTRODUCTION p a s t  e a r t h q u a k e s ,  e x p a n s i o n  j o i n t .  e x c i t a t i o n  o n  o f  t h i s  b r i d g e s  b r i d g e  b e n t s ,  a n d  e f f e c t s  o f  u s e d ,  u s e d  t h e  b e  t o  s u c h  s t u d y  s a m e  b e e n  t h o u g h t  j o i n t s .  t h e  T h e  w e r e  e m p l o y i n g  t o  a  b e  t w o - b e n t  b y  a  a s s e s s  l a r g e r  a l o n g  t h e s e  s t u d i e d  a n d  f r a m e  f o u r  w h e t h e r  1 1 5  a n d  p o s s i b l e  f a c t o r s  d e l a y  t i m e s ,  s t r e n g t h .  a d j a c e n t  a t  a  f r a m e s .  o b s e r v a t i o n s  T h e  from  o n  m a i n  t h e  y i e l d  w e r e  a n  t i m e .  T h e  t o t a l  p u r p o s e  r e s p o n s e  o f  o f  t h e  g a p  u s e d .  t o  o f  f i v e - b e n t  t h e  t h e  s u p p o r t  f o r i n i t i a l  a t t e m p t  A  a t  s t r e n g t h  V a l u e s  r e c o r d s  i n  u n s e a t m e n t  d i f f e r e n t i a l  p r o b l e m .  p e r f o r m e d  o n e  d e c k  o t h e r  e a r t h q u a k e  t h e m  t h e  m o d e l .  f o r t h e  i n c l u d e  w a s  f r o m  w i t h  r e s t r a i n e r  T h r e e  v a r y i n g  e q u a l - h e i g h t a n d  t o  o f  j o i n t  c h o s e n .  j o i n t ,  r e s u l t i n g  r e s p o n s i b l e  e f f e c t  f a c t o r s  p a r a m e t e r s ,  p a r a m e t e r s  e x t r a p o l a t e d  t h e  f a i l u r e s  i n t h e  t o  e x p a n s i o n  s l a c k  f i v e  b r i d g e  a c t i o n s  d e t e r m i n e  v a r i o u s  i n c l u d i n g  a r e  i n  r e s t r a i n e r  t h e s e  w e r e  c o u l d  w a s  f r i c t i o n  p r e l i m i n a r y  h a v e  n o n - l i n e a r  b r i d g e ,  c o n t a i n i n g  o p e n i n g  A  T h e  t h e  r e s e a r c h  t h e r e  i s o l a t e  n i n e  frame  p r e l i m i n a r y  t h e  f r a m e s  m o d e l  s t u d y  CHAPTER 7: SUMMARY AND CONCLUSIONS  §7.2 SUMMARY 116  7.2 SUMMARY T h e  c o n c l u s i o n s r e a c h e d  b e n t  frame.  T h e r e  i s a  i  n t h e t w o - b e n t  m u c h  frame,  e s p e c i a l l y  7.2.1  E F F E C T OF D E L A Y  W  h  e  n  t h e g r o u n d  b e t w e e n  t h e  t h e  I n  m a x i m u m  r e s t r a i n e r s  m o t i o n  d i f f e r e n t  d i s p l a c e m e n t s  i n c r e a s e d .  w h e n  h i g h e r  a n d  a p p l i e d  b e n t s .  t h e p e a k  a l lt h e o t h e r  p e a k  d e g r e e  o  I n  a r e p r e s e n t  s h e a r  u s u a l l y  t h e  w e r e  o r w h e n  b e n t s  m o d e l s  f o r c e s  w i t h  t h e d i s p l a c e m e n t s  i  n a  t h e  c a s e  a n d  w i t h  i s  s h e a r  s o m e  j o i n t s ,  d e l a y  n t h e  i n c r e a s e d  t h e  d e c r e a s e  h a v e  i  f i v e -  f i v e - b e n t  l a r g e .  i tc r e a t e s  g e n e r a l  t o t h e l a r g e r  t h e b e n t s  friction  l o c k e d  a  a p p l i c a b l e  b e t w e e n  i s d e l a y e d ,  e x p e r i e n c e  o c c u r  n o t a l w a y s  f i n t e r a c t i o n  t o a d j a c e n t  m o d e l s ,  v a l u e s  f r a m e s  p e a k  a s  b e e n  t o t a l  t h e d e l a y  f o u n d  r a t h e r  i n t e r a c t i o n  n o d a l  t i m e  t o v a r y ,  t h a n  o n e  i s  b u t  w i t h  n o  d e l a y .  O  n  t h e  w i t h  o t h e r  i n c r e a s i n g  l a r g e r  p e a k  c o n t i n u e  o p e n i n g s  u n t i l  h a n d ,  d e l a y s .  o p e n i n g s  t o c a u s e  t h e r e s t r a i n e r  i n c r e a s e d .  d e l a y .  I n  a n d  b y  r e s p o n s e s ,  w i t h o u t  i m p a c t  f o r c e s ,  i  s a m e  A  a c t i v a t e d .  e f f e c t  i s  s  t h e p e a k  r e s t r a i n e r s ,  a s  n t h e e x p a n s i o n  t h e r e s t r a i n e r s .  b e c o m e s  T h e  e s p e c i a l l y  m o d e l s  i n t e r a c t i o n  a r e l i m i t e d  i n c r e a s i n g  t h e j o i n t  t h e  A f t e r  I n m o d e l s  d e l a y s  m o t i o n s  w i t h  p o i n t ,  w i t h  t h e  i tm a y  p e a k  t e n d  b e t w e e n  g a p  i n c r e a s e  o r  t h e  a s  n  g a p  i n c r e a s e  d e c r e a s e  f o r c e s  i  b e n t s  t h e p e a k  o p e n i n g s  i n c r e a s e  i m p a c t  t o  g e n e r a l l y r e s u l t  r e s t r a i n e r s ,  i s i n c r e a s e d , t h e p e a k  t h i s  e v i d e n t  o p e n i n g s ,  i n c r e a s e d  o u t - o f - p h a s e  j o i n t .  d e l a y  g a p  w i t h  d e l a y  i s  CHAPTER 7 : SUMMARY AND CONCLUSIONS  § 7 . 2 SUMMARY 117  7.2.2 E F F E C T OF BENT YIELD STRENGTH T h e  m  t h e  a  x  i  m  b e n t s  p e a k  o n  w h e n  t h e t w o - b e n t  a n d  t h i s  t o a n  r e d u c t i o n  i  o p e n i n g s  from  R  F  o  w i t h  i  t h e b e n t s  f 4 ,  n t h e p e a k  a r e r e d u c e d  t a k e s  y i e l d i n g  t h e p e a k  F  c a n e i t h e r  t h e s p e c t r a l  y i e l d i n g  c a u s e s  frames,  d e s i g n e d  f o r c e s  g a p  frames,  i m p a c t  f i v e - b e n t  a  m  i sr e d u c e d  d e p e n d i n g  I n  u  i  n t h e b e n t s  t o m o v e  o p e n i n g  t h e Y  2  t o a  i  n Y  2  a p a r t  F  0  a n d  R  v a l u e  b e n t s ,  o f j o i n t  w h e n  a s  a  4  F  0  t h e y i e l d  c o r r e s p o n d i n g  o c c u r s  o p e n  f o r t h e e x t e r i o r  n t h e c a s e  g a p  d e m a n d  w h e n  s t r e n g t h i  t o a  F  R  F  o  f  n  4 ,  p l a c e .  o p e n i n g s  a s  s h e a r  i n c r e a s e o r d e c r e a s e  u p  frames  a  F  o  f 4  i s t h e f o r c e  l a r g e  g a p  H o w e v e r ,  i s a p p l i e d  i  t h e f i r s t  c a n g e t l a r g e r  i n Y 2 F 0 R 0 .  R  b e f o r e  i  m a j o r  n t h e j o i n t .  w h e n  t h e g e n e r a l  w h e n  I n t h e  t h e b e n t s  t o t h e b e n t s .  n t h e r e s t r a i n e r  i m p a c t ,  T  o n e  h  a r e  t r e n d i s  e  i m p a c t  i s p r e s e n t .  7.2.3 E F F E C T OF FRICTION W  h  a n d  e  n  f r i c t i o n  s h e a r  b e i n g  f o r c e s  c a n b e  r e d i s t r i b u t e d ,  r e d u c e d ,  e f f e c t  i sp r e s e n t  i  n t h e e x p a n s i o n  s l i g h t l y  e s p e c i a l l y  a s i st h e m a x i m u m  o n  t h e b e h a v i o u r  o  i  t h e m a x i m u m  i n c r e a s e d o r d e c r e a s e d ,  ft h e  p e a k  f t h e j  j o i n t ,  friction  i m p a c t  i s l a r g e .  f o r c e s .  T h e  a s  T h e  p e a k  t o t a l  t h e s h e a r  m  a  p r e s e n c e  x  u  m  n o d a l  d e m a n d  i  m  p e a k  o  f f r i c t i o n  d i s p l a c e m e n t s  o n  g a p  h a s a  t h e b e n t s  o p e n i n g s  i s  a r e  d a m p i n g - l i k e  o i n t .  7.2.4 E F F E C T OF RESTRAINER STRENGTH T h e  p r e s e n c e  e x p a n s i o n  o  f a  j o i n t .  r e s t r a i n e r  W h i l e  a n d  i t s s t r e n g t h c a n h a v e  t h e r e s t r a i n e r  c a n i  n f a c t  a  l a r g e  e f f e c t  i n c r e a s e t h e p e a k  o n  t o t a l  t h e b e h a v i o u r  n o d a l  o  f t h e  d i s p l a c e m e n t  CHAPTER 7 : SUMMARY AND CONCLUSIONS a n d  t h e p e a k  e x p a n s i o n  b e n t  j o i n t .  f r a m e s  h a s  f o r c e s  T h i s  w h e r e  c o n t r i b u t e d  w h i c h  s h e a r  t o  a  i  n a  b e n t ,  i td o e s  i sr e g a r d l e s s o  s i g n i f i c a n t l y  f w h e t h e r  n o n - y i e l d i n g r e s t r a i n e r s  s l i g h t  y i e l d e d  f u r t h e r  § 7 . 3 CONCLUSIONS 1 1 8  r e d u c t i o n  i  r e d u c e  t h e r e s t r a i n e r  ( Y 0 F 0 R 2 )  w e r e  n t h e p e a k  g a p  t h e p e a k  i s s t r a i n e d  u s e d ,  g a p  o p e n i n g  t o y i e l d .  t h e a d d i t i o n a l  o p e n i n g  c o m p a r e d  i  n t h e  I n t h e t w o -  s t r e n g t h  t o  a  o n l y  r e s t r a i n e r  ( Y 0 F 0 R 1 ) .  7.3 CONCLUSIONS B a s e d  t h e  o n  g a p  t h e f i n d i n g s  o p e n i n g  r e l a t i v e  q u a n t i t y  d o  t h a t  r e a c h e d  p e a k  t i m e  i  b e  n a  o  w h i l e  y i e l d ,  i  h i s t o r y  i n t e r p r e t e d  o  o  f  t h e  t h e m a x i m u m  n o r m a l i z e d  s h e a r  f t h e n o d a l  c o r r e c t l y .  T h e  t h i s  m  a  j o i n t  d o  x  i t b e  t o  h a v e  y i e l d  s t u d y  t h a t  d e l a y  i  m  u  m  f o r c e s  n o t r e a c h  d i s p l a c e m e n t s  r e s t r a i n e r s  t h a t  t h e j o i n t  t i m e  t h a t  a d d i t i o n  a p p e a r s  u p o n .  s a m e  T h e  r e q u i r i n g  f f r i c t i o n  d u r i n g  i ta p p e a r s  j o i n t .  o r d e c r e a s e  n t h e  m o s t  b e n t ,  r e l i e d  d i s c o v e r e d  a l l o c c u r  Y 1 F 0 R 0 ,  t h e  c a n  s t u d y ,  e x p a n s i o n  c a n i n c r e a s e  a l s o  n o t  n t h i s  t h e p r e s e n c e  e x c i t a t i o n  w a s  n a n  d i s p l a c e m e n t  A l t h o u g h  I t  i  i  f r e s t r a i n e r s  d e s i g n e d  a  r e s p o n s e ,  t h e m  p e a k  F  x  m  u  m  o  r i n s t a n c e ,  o p e n i n g s  f o r c e s  i  a n d  o n  p e a k  e f f e c t ,  f o r a n y  n m o s t  t o e n s u r e  t h a t  d u c t i l i t y .  i ti s n o t  i  c a s e s  t o  s u p p o r t  r e s p o n s e s  a n a l y s i s  g i v e n  n d e l a y  a  m o t i o n s .  a n d j o i n t  n t h e t w o - b e n t  l i m i t i n g  i n c r e a s e t h e  t h e g r o u n d  a r e r e a c h e d  i  n  d i f f e r e n t i a l  f r a m e  s h e a r  I t i s n e c e s s a r y  a n d j o i n t  b e n e f i c i a l  d e p e n d i n g  a  i  t h e a p p r o p r i a t e  f t h e b e n t  n o r m a l i z e d  g a p  y i e l d .  i  o  e f f e c t i v e  c a n ,h o w e v e r ,  w i t h  s i m i l a r l y  s t r e n g t h  c a s e .  a n d  o  a r e v e r y  f r a m e  c a s e s  a r e  h a s  w h e r e  e x a m i n e  t h e r e s u l t s  s e t  t h e  b e i n g  CHAPTER 7: SUMMARY AND CONCLUSIONS  §7.3 CONCLUSIONS  7.4 RECOMMENDATIONS FOR FURTHER T h e  c u r r e n t  s p e c t r u m .  t h a t  T h e  s u c h  b r i d g e  s t u d y  r e s t r a i n e r  w i t h  s l a c k  o n  o  e a r t h q u a k e  o  f b r i d g e s  p r e s e n t  i t sb e n t s  d i f f e r e n t i a l  i  n a  f o c u s s e d  c o n j u n c t i o n  b e h a v i o u r  h a v e  j o i n t s  d i f f e r e n t  d e p e n d i n g  c o u l d  u n d e r  e x p a n s i o n  u s e s  r e s p o n s e  s i t e s  c o u l d  r e s p o n s e  T h i s  s t u d y  o  f 4 0  s l a c k ,  c o u l d  t h e n u m b e r  w i t h  t h e  f e x p a n s i o n  m o r e  s u p p o r t  o r  j o i n t s  s o i l  a n d  s o i l s  w i t h  v e r y  i n i t i a l  T h e  j o i n t .  t o  r e s t r a i n e r s .  n e e d s  b e  a l s o  g a p  b e  T h e s e  a  o  a  r o c k  s t u d i e d , a s  t a l l e r  t a r g e t  i ti s  b e n t s .  T h e  l i k e l y  A  c h a r a c t e r i s t i c s ,  e x a m i n e d .  l o n g  a n d  i t s  b e h a v i o u r  o  f  s t u d i e d .  a r e i n i t i a l l y  p r o d u c e  w i t h  o p e n i n g  s t i f f n e s s  u s i n g  t o b e  d i f f e r e n t  a l s o  s h o u l d  w h i c h  g i v e n  p r o f i l e s  s i t e s  g e n e r a t e d  f o r b r i d g e s  w i t h  a n  j o i n t s  i n a  s o i l  s h o u l d  d i f f e r e n t l y .  e m p l o y e d  w e r e  p r o b l e m  b r i d g e  j o i n t s  b e h a v e  s o f t  e x c i t a t i o n  E x p a n s i o n  v a r y i n g  o n  RESEARCH  w h i c h  o n  s e v e r e  c u r v e d  e x p a n s i o n  m m .  l o c a t e d  f o u n d e d  s k e w e d  o n  a  r e c o r d s  119  o  f 2 0  m m  c l o s e d , o r  a n d  h a v e  f t h e r e s t r a i n e r s  p a r a m e t e r s  m o r e  s h o u l d  c o m p l e t e  c a n  b e  a n  i n i t i a l  r e s t r a i n e r s  a l s o  v a r y  s t u d i e d  p i c t u r e  o n  i  n  t h e  REFERENCES 1.  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C l i f f s ,  _  A . ,  1 9 9 1 .  T e r e n c e  D y n a m i c s  W .  D e s i g n e r s ,  a n d  a t B e r k e l e y ,  " T h e  C a l i f ,  S p e c i f i c a t i o n s ,  E n g l e w o o d  A . ,  G o o d c o  S e i s m i c  Y . T .  C a l i f . ,  b y  G o l a f s h a n i ,  E l a s t o m e r  -  o f  a n d  [ § 3 . 9 ]  F i l i a t r a u l t ,  X  C a l i f . ,  D e s i g n  p r o d u c e d  E n g i n e e r i n g ,  9.  -  B r o a d c a s t i n g  A n i l  C l o u g h ,  N  S a c r a m e n t o ,  P r e n t i c e - H a l l ,  7.  I  B e r k e l e y ,  B r i d g e  C a n a d i a n  A  U n i v e r s i t y  S a c r a m e n t o ,  T h o m p s o n ,  6.  a t  B r i d g e  S t r u c t u r e s ,  5.  R  A b r a h a m s o n  C a l i f o r n i a  S t r u c t u r e s ,  4.  D  Report No. UCB/EERC-84/13,  D i s t a n c e s , " o f  "  d i s s e r t a t i o n ,  2 ,  i n  t h e  1 9 9 5 .  1 2 0  C a l i f ,  1 9 9 1 .  D o n a l d 1 9 9 4  [ § 4 . 4 ]  A n d e r s o n ,  N o r t h r i d g e  [ § 1 . 2 . 4 ]  M u r a t  S a a t c i o g l u  E a r t h q u a k e , "  a n d  Canadian  1 5 .  N a t i o n a l i n  t h e  [ § 1 . 1 ,  1 6 .  C e n t e r  a  N ,  P e n t a s , o f  [ § 2 . 5 ,  G .  G u i d e ,  2 0 .  P e r f o r m a n c e  o f  H i g h w a y V o l .  1 0 ,  B r i d g e s  N o .  2 ,  1 9 9 5 .  R o b e r t s ,  1 9 8 5 .  R i c h a r d  o f  A r t i f i c i a l  E a r t h q u a k e  A c c l e r a t i o n  E n g i n e e r i n g  T i m e  S o f t w a r e  H i s t o r y  C o m p a t i b l e  L i b r a r y ,  M c M a s t e r  [ § 4 . 4 ]  A v e n t ,  i n C o m p o s i t e  V i j a k a  K . A .  G o p u  a n d  K e i t h  J . R e b e l l o ,  " F i e l d  S t u d y  Transportation Research Record,  B r i d g e s , "  N o .  1 4 7 6 ,  D  R  A  I  N  -  2  D  X  T y p e 0 9 ,  C i v i l  E l e m e n t a n d  D e s c r i p t i o n  T y p e l 5 ,  a n d  U s e r  V e r s i o n  E n g i n e e r i n g , U n i v e r s i t y  o f  G u i d e  C a l i f o r n i a  f o r E l e m e n t  T y p e O l ,  T y p e 0 2 ,  Report No. UCB/SEMM-93/18,  1 . 1 0 , " a t  B e r k e l e y ,  B e r k e l e y ,  C a l i f . ,  1 9 9 3 .  § 3 . 6 ]  V . ,  G .  H .  V e r s i o n  U n i v e r s i t y  R .  f o r G e n e r a t i o n  S p e c t r u m ,  O n t . ,  M o v e m e n t s  "  o f  § 3 . 5 ,  P r a k a s h ,  A . ,  T y p e 0 6 ,  D e p a r t m e n t  1 9 .  " T h e  Civil Engineering Practice,  § 4 . 5 . 3 ]  H.,  T y p e 0 4 ,  [ § 3 . 4 ,  T a r g e t  H e r o d o t o s  P o w e l l ,  P r o g r a m  H a m i l t o n ,  L o n g i t u d i n a l  1 9 9 5 .  1 8 .  S y n t h  S p e c i f i e d  U n i v e r s i t y ,  1 7 .  E n g i n e e r i n g R e s e a r c h , E a r t h q u a k e , "  § 1 . 2 . 4 ]  N a u m o s k i , w i t h  f o r E a r t h q u a k e  N o r t h r i d g e , C a l i f o r n i a ,  o f  P o w e l l , 1 . 1 0 , "  C a l i f o r n i a  J a m e s  E . ,  a n d  S.  C a m p b e l l ,  "  D  R  A  I  N  -  2  D  X  B a s e  Report No. UCB/SEMM-93/17, a t  " R e c e n t  B e r k e l e y ,  B e r k e l e y ,  A d v a n c e s  i n  C a l i f ,  S e i s m i c  1 9 9 3 .  D e s i g n  a n d  P r o g r a m  D e p a r t m e n t  D e s c r i p t i o n o f  C i v i l  a n d  U s e r  E n g i n e e r i n g ,  [ § 3 . 3 ]  R e t r o f i t  o f  C a l i f o r n i a  B r i d g e s , "  i n  Proceedings of the 4th U.S.-Japan Workshop on Earthquake Disaster Prevention for Lifeline Systems, N a t i o n a l  2 1 .  R o e s s e t ,  J o s e  Seminar, 2 2 .  W e r n e r ,  M . ,  I n s t i t u t e  " S e i s m i c  D e p a r t m e n t  S t u a r t  D.,  o f  o f  S t a n d a r d s  a n d  S o i l - S t r u c t u r e  C i v i l  " E a r t h q u a k e  T e c h n o l o g y ,  E n g i n e e r i n g R e s e a r c h  [ § 1 . 1 ]  Seismic Soil-Structure Interaction  I n t e r a c t i o n , "  E n g i n e e r i n g , U n i v e r s i t y  1 9 9 1 .  o f  N e e d s  B r i t i s h  F o r  C o l u m b i a ,  T r a n s p o r t a t i o n  1 9 9 3 .  L i f e l i n e  [ § 1 . 2 . 2 ]  S y s t e m  Abatement of Seismic Hazards to Lifelines: Proceedings of a Workshop on Development of an Action Plan, E l e m e n t s "  i n  F e d e r a l  D . C ,  V o l .  2 ,  1 9 8 7 .  E m e r g e n c y  [ § 1 . 1 ]  1 2 1  M a n a g e m e n t  A g e n c y  ( F E M A ) ,  W a s h i n g t o n ,  APPENDIX A 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*  DYNAMIC ANALYSIS RESULTS EXTRACTION PROGRAM EXTR-D Program Concept Program Source First Modification Date o f F i r s t M o d i f i c a t i o n  : : : :  Dr. D.L. Anderson Vinod Bata Yung H s i 25th May, 1993.  Further Modification Technical Consultation  : Yung H s i : Thomas Wong  Dates o f F u r t h e r  : 1 8 t h October, 1993. 1 8 t h May, 1994. 30th August, 1994. 3 r d March, 1995.  i  Modification  Most Recent C o m p i l a t i o n C u r r e n t V e r s i o n Number  Date  : 24th J u l y , 1995. : 3.00  T h i s program i s w r i t t e n t o e x t r a c t r e s u l t s from l a r g e Drain-2DX o u t p u t f i l e s t o f a c i l i t a t e t h e p l o t t i n g p r o c e s s and t h e comparison o f r e s u l t s . The program has l a r g e l y been r e w r i t t e n , u s i n g a s t r u c t u r e d approach, t o conform t o t h e c u r r e n t programming p h i l o s o p h y o f t o p down modular design. A l t h o u g h such d e s i g n s may n o t always p r o v i d e t h e most e f f i c i e n t way t o code an a l g o r i t h m , i t i s b e l i e v e d t h a t such s h o r t c o m i n g s a r e more t h a n o f f s e t by t h e r e l a t i v e ease i n m a i n t a i n i n g and u p d a t i n g t h e s e programs, e s p e c i a l l y when t h e y become more complex by each r e v i s i o n . The f i r s t m o d i f i c a t i o n added r e s u l t s e x t r a c t i o n f o r l i n k e l e m e n t s . second r e v i s i o n made p o s s i b l e t h e e x t r a c t i o n o f d e f o r m a t i o n time h i s t o r i e s f o r a l l t h e d i f f e r e n t t y p e s o f elements. An i n t e r a c t i v e i n p u t mode was t h e n added t o improve program f l e x i b i l i t y .  A  A subsequent r e v i s i o n t h e n a l l o w e d up t o t e n n o d a l d i s p l a c e m e n t a r r a y s o r t e n member f o r c e a r r a y s t o be s t o r e d i n a s i n g l e f i l e . A side e f f e c t o f t h i s update i s t h e c o n s o l i d a t i o n o f t h e e x t r a c t i o n s u b r o u t i n e s f o r a l l the elements. T h i s f i n a l v e r s i o n enables the e x t r a c t i o n of r e l a t i v e nodal displacement as l o n g as t h e r e f e r e n c e node i s g i v e n . I n o t h e r words, t h e program c a n now c a r r y out s i m p l e a r r a y a r i t h m e t i c . This r e v i s i o n also included a major r e w r i t e t o b e t t e r t a k e advantage o f t h e v a r i o u s t y p e s o f FORTRAN f u n c t i o n and s u b r o u t i n e subprograms and produce a much t i g h t e r , and much l e s s t e d i o u s , s o u r c e code. F u t u r e r e v i s i o n s may i n c l u d e a more s o p h i s t i c a t e d f i l e n a m e f i l t e r t o a l l o w f o r more f l e x i b l e f i l e n a m e i n p u t . As i t s t a n d s now, a l l f i l e n a m e s must conform t o t h e MS-DOS 8.3 f i l e - n a m i n g c o n v e n t i o n , and t h e y must be i n p u t w i t h o u t any p r e c e d i n g b l a n k s p a c e s . As w e l l , some p a r t s o f t h e c u r r e n t v e r s i o n a r e coded u n o r t h o d o x manner. Examples i n c l u d e GOTO s t a t e m e n t s a l a b e l o u t s i d e o f an I F s t r u c t u r e o r a DO l o o p from constructs. R e c o d i n g t h e s e c o n s t r u c t s may r e q u i r e a  i n a relatively which p o i n t t o the i n s i d e of these more t h o r o u g h and  123 c* c*  * *  detailed revision.  L.  c* c*  * *  MAIN PROGRAM VARIABLES:  r°*  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*  * INTEGER VARIABLES: * ISEG the d e s i r e d a n a l y s i s SEGment * RESTYP - the TYPe o f R E S u l t s d e s i r e d , * 1 f o r n o d a l d i s p l a c e m e n t s , 2 f o r element f o r c e s . * TOTNOD - t h e TOTal number o f NODes t o be p r o c e s s e d * NODE an a r r a y f o r NODE numbers * I an a r r a y c o u n t e r * J an a r r a y c o u n t e r * NSKIP - t h e o u t p u t f i l e s t o r e s e v e r y NSKIPth d a t a p o i n t * DISPL - an a r r a y f o r DISPLacement d i r e c t i o n s * TOTELM - the TOTal number o f ELeMents t o be p r o c e s s e d * ELMGR - an a r r a y f o r ELeMent GRoups * ELMNUM - an a r r a y f o r ELeMent NUMbers * ELMTYP - an a r r a y f o r ELeMent TYPes * ELMEND - an a r r a y f o r ELeMent ENDs, 1 f o r i , and 2 f o r j . * ELMFOR - an a r r a y f o r ELeMent FORces, 1 f o r a x i a l , 2 f o r shear, 3 f o r moment, 4 f o r a x i a l d e f o r m a t i o n , * and 6 f o r h i n g e r o t a t i o n . Shear d e f o r m a t i o n i s not a v a i l a b l e . * * t h e Number o f t h e SEGment NSEG * NODNUM - t h e NUMber o f t h e NODe * ELENUM - t h e NUMber o f t h e ELEment * ELEGR - the GRoup number o f t h e ELEment * RTFLAG - a FLAG t o i n d i c a t e whether R e l a T i v e d i s p l a c e m e n t i s d e s i r e d * DPLTYP - d i s p l a c e m e n t t y p e = 1 f o r r e l a t i v e d i s p l s . * 2 f o r absolute d i s p l s . * 3 f o r both. * * REAL VARIABLES: * FACTOR - an a r r a y f o r ( m u l t i p l i e r ) s c a l e f a c t o r s * ( • " • * (_ * CHARACTER VARIABLES: c* DRNOUT - name o f DRaiN-2DX OUTput f i l e * c* * INMODE - an i n d e x t o i n d i c a t e MODE (method) o f INput c* * c* FLNAME - NAME o f t h e parameter F i L e * c* L A B E L i - a r r a y s used f o r c h a r a c t e r s t r i n g comparisons * c* DIRLBL - an a r r a y c o n t a i n i n g h e a d i n g l a b e l s f o r output f i l e * c* * c* EXTERNAL UNIT NUMBERS: * c* u n i t 1 - Drain-2DX output f i l e * c* u n i t 2 - p a r a m e t e r f i l e * c* u n i t 3 - f i l e c o n t a i n i n g e x t r a c t e d r e s u l t s * c* u n i t 4 - f i l e c o n t a i n i n g e x t r a c t e d r e s u l t s * Q*******************************************************************************  c* c*  PROGRAM EXTRD  c* c*  c* c*  INTEGER  OPENFL, INMODE, CHKNUM, ISEG, RESTYP, I, J , NSKIP, DPLTYP, TOTNOD, NODE(IO), RNODE(IO), DISPL(IO), TOTELM, ELMTYP(10), ELMGR(10), ELMNUM(10), ELMEND(10), ELMFOR(10), FLAG, TOTCNT  1 2 3  REAL 1  FACTOR(IO), TIME(40005), DRAIN1(10,40005), DRAIN2(10,40005), M I N l ( l O ) , M A X l ( l O ) , AMAXl(lO), MIN2(10), MAX2(10), AMAX2(10)  C* C* CHARACTER  FILENM*12,  PRMTFL*12,  LABELI*80, LABEL2*80  C* C*  COMMON  /NODES/  TOTNOD, NODE, RNODE, DISPL  1 2 4  COMMON COMMON COMMON COMMON C* C* C* C*  Write  /ELMTS/ /DISPS/ /FILES/ /DRAIN/  TOTELM, ELMTYP, ELMGR, ELMNUM, ELMEND, NSKIP, FACTOR FILENM TIME, DRAIN1, DRAIN2  d i s p l a y header f o r program  ELMFOR  initialization.  WRITE (*,5000) C* C* Determine t h e name o f t h e Drain-2DX f i l e , and open i t . C* 1000 GOTO (1020,9000) OPENFL(1,1,1) C* C* Determine whether i n p u t i s from s c r e e n o r i n p u t f i l e . C* 1020 WRITE (*,6000) 1040 WRITE (*,6020) READ (*,8000) INMODE GOTO (1040,9000,1060) CHKNUM(INMODE,0,0,0) C* C* I f u s e r chooses t o use s c r e e n i n p u t , determine t h e name o f t h e i n p u t C* p a r a m e t e r f i l e , and open i t . I f t h e f i l e a l r e a d y e x i s t s , check t o see C* i f t h e u s e r r e a l l y s t i l l wishes t o u s e i n t e r a c t i v e i n p u t . C* 1060 I F (INMODE .EQ. 1) THEN WRITE (*,6040) GOTO (1100,9000,1080) OPENFL(1,2,2) C* C* I f u s e r d e c i d e s t o use an a l r e a d y e x i s t i n g i n p u t parameter f i l e , r e s e t C* t h e INMODE v a r i a b l e t o 2, and p r o c e e d t o t h e b a t c h p r o c e s s i n g s e c t i o n . C* 1080 INMODE = 2 PRMTFL = FILENM GOTO 1700 1100 END I F C* C* Echo t h e i n p u t parameter f i l e n a m e t o a permanent s t o r a g e f o r i n f o r m a t i o n C* v e r i f i c a t i o n b e f o r e t h e a c t u a l e x t r a c t i o n p r o c e s s . C* PRMTFL = FILENM C* C* C* ========================== INTERACTIVE INPUT ========================== C* C* I f i n p u t from s c r e e n , l e a d u s e r w i t h p r o m p t i n g q u e s t i o n s . C* Determine t h e a n a l y s i s segment, and w r i t e t o t h e i n p u t parameter f i l e . C* IF (INMODE .EQ. 1) THEN WRITE (*,6060) READ (*,8000) ISEG CALL WRTPAR(2,ISEG) C* C* Determine t h e r e s u l t type, and w r i t e t o t h e i n p u t parameter f i l e . C* 1120 WRITE (*,6080) READ (*,8000) RESTYP GOTO (1120,9000,1140) CHKNUM(1,2,1,RESTYP) 1140 CALL WRTPAR(3,RESTYP) C* C* Read i n d a t a r e q u i r e d f o r n o d a l r e s u l t s e x t r a c t i o n . C* Read i n t h e d i s p l a c e m e n t type, and w r i t e t o t h e i n p u t parameter f i l e . C* IF (RESTYP .EQ. 1) THEN 1160 WRITE (*,6100) READ (*,8000) DPLTYP GOTO (1160,9000,1180) CHKNUM(1,3,2,DPLTYP) 1180 CALL WRTPAR(4,DPLTYP) C*  C* C* C* C* C* C*  Read i n t h e a p p r o p r i a t e f i l e n a m e s , and w r i t e t o t h e i n p u t parameter f i l e s . U n i t 3 w i l l be u s e d f o r a b s o l u t e d i s p l a c e m e n t s , and u n i t 4 f o r r e l a t i v e displacements. I f b o t h a r e r e q u i r e d , b o t h u n i t s w i l l be used. The i n t e g e r f u n c t i o n subprogram OPENFL a l s o c a l l s t h e s u b r o u t i n e subprogram WRTPAR t o w r i t e t h e f i l e n a m e s t o t h e i n p u t parameter f i l e .  IF (DPLTYP .NE. 2) GOTO (1200,9000) OPENFL(1,3,3) 1200 I F (DPLTYP .NE. 1) GOTO (1220,9000) OPENFL(1,4,4) C* C* Read i n t h e n t h v a l u e t o e x t r a c t , and w r i t e t o t h e i n p u t p a r a m e t e r f i l e . C* 1220 WRITE (*,6120) READ (*,8000) NSKIP CALL WRTPAR(7,NSKIP) C* C* Zero t h e a p p r o p r i a t e a r r a y s , and d e t e r m i n e t h e t o t a l number o f nodes. C* DO 1240, 1=1, 10, 1 NODE(I) = 0 1240 CONTINUE C* 1260 WRITE (*,6140) READ (*,8000) TOTNOD GOTO (1260,9000,1280) CHKNUM(1,10,3,TOTNOD) 1280 CALL WRTPAR (8, TOTNOD) C* C* Read i n t h e node numbers, d i s p l a c e m e n t d i r e c t i o n s and s c a l e f a c t o r s . C* Echo t h e d a t a t o t h e i n p u t parameter f i l e f o r f u t u r e u s e . C* IF (DPLTYP .EQ. 1) THEN WRITE (*,6160) DO 1340, 1=1, TOTNOD, 1 1300 READ (*,*) NODE(I), D I S P L ( I ) , FACTOR(I) GOTO (1320,9000,1340) CHKNUM(1,3,4,DISPL(I)) 1320 WRITE (*,6180) GOTO 1300 1340 CONTINUE CALL WRTPAR(9,0) C* C* Read i n t h e node numbers and t h e r e f e r e n c e node numbers, as w e l l as C* the other i n f o r m a t i o n i f r e l a t i v e nodal displacements are r e q u i r e d . C* Echo t h e d a t a t o t h e i n p u t parameter f i l e f o r f u t u r e u s e . C* ELSE WRITE (*,6200) DO 1420, 1=1, TOTNOD, 1 1380 READ (*,*) NODE(I), RNODE(I), D I S P L ( I ) , FACTOR(I) GOTO (1400,9000,1420) CHKNUM(1,3,4,DISPL(I)) 1400 WRITE (*,6180) GOTO 1380 1420 CONTINUE CALL WRTPAR(10,0) END I F C* C* I d e n t i f y t h e end o f t h e f i l e w i t h a p r o p e r s p e c i f i e r . C* CALL WRTPAR(30, 0) C* C* C l o s e t h e u n i t b e f o r e moving o n t o t h e next s t e p . C* CLOSE (UNIT=2) C* C* Read i n d a t a r e q u i r e d f o r element r e s u l t s e x t r a c t i o n . C* ELSE C* C* Read i n t h e r e s u l t s output f i l e , and w r i t e t o t h e i n p u t p a r a m e t e r f i l e . C* GOTO (1460,9000) OPENFL(1,5,3)  1 2 6  c*  C* Read i n t h e n t h v a l u e t o e x t r a c t , and w r i t e t o t h e i n p u t p a r a m e t e r f i l e . C* 1460 WRITE (*,6120) READ (*,8000) NSKIP CALL WRTPAR(7,NSKIP) C* C* Zero t h e a p p r o p r i a t e a r r a y s , and determine t h e t o t a l number o f e l e m e n t s . C* DO 1480, 1=1, 10, 1 ELMGR(I) = 0 ELMNUM(I) = 0 14 8 0 CONTINUE C* 1500 WRITE (*,6220) READ (*,8000) TOTELM GOTO (1500,9000,1520) CHKNUM(1,10,3,TOTELM) 1520 CALL WRTPAR(18,TOTELM) C* C* F o r e a c h element, r e a d i n t h e element type and t h e a p p r o p r i a t e C* a d d i t i o n a l element i n f o r m a t i o n as n e c e s s a r y . C* WRITE (*,6240) DO 1660, 1=1, TOTELM, 1 1540 WRITE (*,6250) READ (*,8000) ELMTYP(I) GOTO (1540,9000,1560) CHKNUM(1,9,5,ELMTYP(I)) C* C* Read i n a p p r o p r i a t e d a t a f o r t r u s s t y p e elements. C* 1560 I F (ELMTYP(I) .EQ. 1 .OR. ELMTYP(I) .EQ. 9) THEN ELMEND(I) = 1 1580 WRITE (*,6260) READ (*,*) ELMGR(I), ELMNUM(I), ELMFOR(I), FACTOR(I) GOTO (1580,9000,1640) CHKNUM(1,7,6,ELMFOR(I)) C* C* Read i n a p p r o p r i a t e d a t a f o r beam-column type elements. C* ELSE 1600 WRITE (*,6280) READ (*,*) ELMGR(I), ELMNUM(I), ELMEND(I), 1 ELMFOR(I), FACTOR(I) GOTO (1600,9000,1620) CHKNUM(1,2,7,ELMEND(I)) 1620 GOTO (1600,9000,1640) CHKNUM(1,6,8,ELMFOR(I)) 1640 END I F 1660 CONTINUE C* C* Echo t h e d a t a t o t h e i n p u t parameter f i l e f o r f u t u r e u s e . C* CALL WRTPAR(19, 0) C* C* I d e n t i f y t h e end o f t h e f i l e w i t h a p r o p e r s p e c i f i e r . C* CALL WRTPAR(30,0) C* C* C l o s e t h e u n i t b e f o r e moving onto t h e next s t e p . C* CLOSE (UNIT=2) C* C* End o f t h e i n t e r a c t i v e i n p u t s e c t i o n . C* END I F C* C* C* ========================== PARAMETER FILE INPUT ======================= C* C* I f i n p u t from parameter f i l e , open t h e f i l e and b e g i n r e a d i n g . C* ELSE  GOTO  **  J* :* **  type.  extraction.  I F (RESTYP .EQ. 1) THEN READ (2,8040) DPLTYP GOTO (1740,9000) CHKNUM(2,3,0,DPLTYP) I F (DPLTYP .NE. 2) GOTO (1760,9000) OPENFL(2,3,3) I F (DPLTYP .NE. 1) GOTO (1780,9000) OPENFL(2,4,4) READ (2,8040) NSKIP READ (2,8040) TOTNOD GOTO (1800,9000) CHKNUM(2,10,0,TOTNOD)  Zero the a r r a y s .  1800 1820  DO 1820, 1=1, 10, 1 NODE(I) = 0 CONTINUE  Read p a s t t h e header READ (2,8060) READ (2,8060) READ (2,8060)  **  :*  GOTO 1700  Read i n d a t a r e q u i r e d f o r n o d a l r e s u l t s  1740 1760 1780  :* ;*  READ (2,8060) LABEL1 IF (LABEL1(1:5) .NE. 'Analy') BACKSPACE (UNIT=2)  READ (2,8040) ISEG READ (2,8040) RESTYP GOTO (1720,9000) CHKNUM(2,2,0,RESTYP)  1720  :* ;*  lines.  Read i n t h e a n a l y s i s segment and t h e r e s u l t  **  :* '*  PRMTFL = FILENM  Read p a s t t h e t i t l e  1700  :*  OPENFL(2,2,2)  Echo t h e i n p u t parameter f i l e n a m e t o a permanent s t o r a g e f o r i n f o r m a t i o n v e r i f i c a t i o n before the actual e x t r a c t i o n process.  1680 ** :* **  (1680,9000)  lines. LABEL1 LABEL1 LABEL1  Read i n t h e node numbers, d i s p l a c e m e n t  d i r e c t i o n s and s c a l e  IF  1840  1860  :*  (DPLTYP .EQ. 1) THEN DO 1840, 1=1, TOTNOD, 1 READ (2,8080) NODE(I), D I S P L ( I ) , FACTOR(I) GOTO (1840,9000) CHKNUM(2,3,I,DISPL(I)) CONTINUE ELSE DO 1860, 1=1, TOTNOD, 1 READ (2,8100) NODE(I), RNODE(I), D I S P L ( I ) , FACTOR(I) GOTO (1860,9000) CHKNUM(2,3,I,DISPL(I)) CONTINUE END I F  End o f n o d a l d a t a i n p u t . CLOSE  ;*  Close the u n i t .  (UNIT=2)  Read i n d a t a r e q u i r e d f o r element r e s u l t s  extraction.  ELSE 1880 1*  l*  factors.  GOTO READ READ GOTO  (1880,9000) OPENFL(2,3,3) (2,8040) NSKIP (2,8040) TOTELM (1900,9000) CHKNUM(2,10,0,TOTELM)  Zero t h e a r r a y s .  1 2 8  c*  1 900  DO 1920, 1=1, 10, ELMGR(I) = ELMNUM(I) = CONTINUE  1 920 C* C* Read p a s t t h e header C* READ (2, 8060) READ (2, 8060) READ (2, 8060) READ (2,8060)  lines. LABEL1 LABEL1 LABEL1 LABEL1  F o r e a c h element, r e a d i n t h e element type and t h e a p p r o p r i a t e a d d i t i o n a l element i n f o r m a t i o n as n e c e s s a r y .  1 1940  1 960 1 980 2 000 C* C* End C*  DO 2000, 1=1, TOTELM, 1 READ (2,8120) ELMTYP(I), ELMGR(I), ELMNUM(I), ELMEND(I) ELMFOR(I), FACTOR(I) GOTO (1940,9000) CHKNUM(2,9,I,ELMTYP(I)) IF (ELMTYP(I) .EQ. 1 .OR. ELMTYP(I) .EQ. 9) THEN GOTO (1980,9000) CHKNUM(2,7,I,ELMFOR(I)) ELSE ELMEND(I)) GOTO (1960,9000) CHKNUM (2, CHKNUM(2, ELMFOR(I)) GOTO (1980,9000) END I F CONTINUE o f element d a t a i n p u t .  CLOSE END I F END I F C* C* C* C* C* C* C*  Close the u n i t .  (UNIT=2)  FINAL CONFIRMATION P e r f o r m f i n a l check b e f o r e p r o c e e d i n g w i t h a c t u a l r e s u l t s e x t r a c t i o n . W r i t e a l l r e l e v a n t i n f o r m a t i o n t o t h e s c r e e n and ask f o r c o n f i r m a t i o n .  OPEN (UNIT=2,FILE=PRMTFL,STATUS='OLD ) 2020 READ (2,8060) LABEL1 IF (LABEL1(1:5) .NE. 'Analy') GOTO 2020 BACKSPACE (UNIT=2) C* I n s e r t b l a n k l i n e s i n t h e d i s p l a y t o s e p a r a t e t h i s s e c t i o n from t h e C* C* p r e v i o u s s e c t i o n s o t h a t t h e s c r e e n i s l e s s c l u t t e r e d . C* WRITE (*,8060) WRITE (*,8060) WRITE (*,8060) C* C* I n i t i a l i z e the e n d - o f - f i l e f l a g . As l o n g as i t has n o t r e a c h e d t h e end o f C* t h e i n p u t parameter f i l e , keep r e a d i n g and e c h o i n g t h e i n f o r m a t i o n . C* FLAG = 1 2040 I F (FLAG .EQ. 1) THEN READ (2,8060) LABEL1 IF (LABEL1(1:5) .EQ. '<EOF> ) THEN FLAG = 2 GOTO 2040 ELSE WRITE (*,8060) LABEL1 GOTO 2040 END I F END I F C* C l o s e t h e u n i t and c o n f i r m w i t h t h e u s e r t h a t t h e i n f o r m a t i o n i s c o r r e c t . C* C* 1  1  1 2 9  CLOSE (UNIT=2) WRITE (*,8060) WRITE (*,6300) READ ( * , * ) FLAG IF (FLAG .NE. 1) THEN WRITE (*,6320) GOTO 9000 END I F C* C* C*  Inform WRITE  C* C* C* C* C* C* C*  t h e u s e r t h a t t h e program i s e x t r a c t i n g  results.  (*,6340)  ==========================  PROCESSING  ====================================  Begin p r o c e s s i n g the e x t r a c t i o n s . Rewind t h e Drain-2DX u n i t and b e g i n by r e a d i n g p a s t t h e header  lines.  REWIND (UNIT=1) READ (1,8060) LABEL1 READ (1,8060) LABEL1 READ (1,8060) LABEL1 READ (1,8060) LABEL1 READ (1,8060) LABEL2 C* C* C*  Echo t h e r e l e v a n t header l i n e s  i n t o the a p p r o p r i a t e r e s u l t s output  files.  IF  (RESTYP .EQ. 1) THEN (DPLTYP .NE. 2) THEN WRITE (3,8060) LABEL1 WRITE (3,8060) LABEL2 END I F IF (DPLTYP .NE. 1) THEN WRITE (4,8060) LABEL1 WRITE (4,8060) LABEL2 WRITE (4,8060) '' END I F ELSE WRITE (3,8060) LABEL1 WRITE (3,8060) LABEL2 END I F WRITE (3,8060) '' IF  C* C* C* C* C* C* C* C* C*  F o r e a c h r e s u l t d e s i r e d ( i = l t o 10), c a l l t h e segment s e a r c h i n g s u b r o u t i n e subprogram SEGSRC t o p l a c e t h e p o i n t e r a t t h e a p p r o p r i a t e r e c o r d i n t h e Drain-2DX f i l e . Then c a l l t h e r e a d i n g s u b r o u t i n e subprogram t o r e a d i n t h e d a t a and t h e n p r o c e s s i t a c c o r d i n g l y . Note t h a t because o f t h e s p e c i a l p r o c e d u r e s r e q u i r e d t o e x t r a c t r e l a t i v e n o d a l d i s p l a c e m e n t s , t h e method o f h a n d l i n g n o d a l e x t r a c t i o n s i s s l i g h t l y d i f f e r e n t from t h a t o f h a n d l i n g t h e element r e s u l t s e x t r a c t i o n s . IF  C* C* C* C*  (RESTYP .EQ. 1) THEN DO 3100, 1=1, TOTNOD, 1  E x t r a c t the absolute nodal displacements r e g a r d l e s s o f the type o f displacements required. CALL SEGSRC(ISEG,RESTYP,1,1,FLAG) . I F (FLAG .EQ. 2) GOTO 9000 WRITE (*,6360) I, TOTNOD CALL READND(1,1,DISPL(I),TOTCNT) DO 3020, J = l , TOTCNT, 1 CALL MINMAX(J,DRAIN1(I,J),MINI(I),MAX1(I),AMAX1(I)) CONTINUE  302 0 C* C* R e l a t i v e nodal displacements w i l l C* e i t h e r 2 o r 3. C*  a l s o be r e q u i r e d when DPLTYP i s  130 IF  3060  (DPLTYP .NE. 1) THEN CALL SEGSRC(ISEG,RESTYP,DPLTYP,I,FLAG) IF (FLAG .EQ. 2) GOTO 9000 CALL READND(DPLTYP,I,DISPL(I),TOTCNT) DO 3060, J = l , TOTCNT, 1 DRAIN2(I,J) = DRAIN1(I,J) - DRAIN2(I,J) CALL MINMAX(J,DRAIN2(I,J) MIN2(I),MAX2(I),AMAX2(I)) CONTINUE END I F WRITE (*,6380) I, TOTNOD CONTINUE  3100 C* C* A f t e r a l l t h e r e q u i r e d d a t a i s o b t a i n e d , e x t r a c t e v e r y n t h element and C* s c a l e f a c t o r t h e s e and t h e extrema v a l u e s . C* WRITE (*,6440) CALL SCALE(RESTYP,TOTNOD,DPLTYP,TOTCNT,NSKIP,FACTOR, 1 MINI, MAX1, AMAX1, MIN2 , MAX2 , AMAX2) C* C* E x t r a c t t h e element r e s u l t s . Note t h a t t h e element e x t r a c t i o n s a r e C* a c c o m p l i s h e d e n t i r e l y i n t h e s u b r o u t i n e subprogram READEL, i n c l u d i n g C* f i n d i n g t h e extrema, e x t r a c t i n g o n l y t h e n t h p o i n t s , and s c a l i n g t h e C* o u t p u t r e s u l t s . C* ELSE DO 3260, 1=1, TOTELM, 1 CALL SEGSRC(ISEG,RESTYP,DPLTYP,I,FLAG) IF (FLAG .EQ. 2) GOTO 9000 WRITE (*,6400) I, TOTELM CALL READEL(I,ELMTYP(I),ELMEND(I),ELMFOR(I),TOTCNT, 1 MINI(I),MAX1(I),AMAX1(I)) WRITE (*,6420) I, TOTELM 3260 CONTINUE WRITE (*,6440) CALL SCALE(RESTYP,TOTELM,DPLTYP,TOTCNT,NSKIP,FACTOR, 1 MINI, MAX1, AMAX1, MIN2 , MAX2 , AMAX2 ) END I F P r i n t out a l l t h e r e l e v a n t a r r a y s WRITE C* C* C*  CALL  i n t o t h e r e s u l t s output  file.  (*,6460) PRNOUT(RESTYP,DPLTYP,TOTCNT,MINI,MAX1,AMAX1,MIN2,MAX2,AMAX2)  Determine i f more e x t r a c t i o n i s d e s i r e d . WRITE (*,6480) READ (* , *) FLAG IF (FLAG .EQ. 1) GOTO 1040  C* C* S c r e e n Header D i s p l a y C* S e c t i o n 5000 C* 5000 FORMAT (llllllllll.T10, 1  Format  DYNAMIC ANALYSIS RESULTS EXTRACTION PROGRAM EXTR-D V e r s i o n 3.00 f o r MS-DOS Program Concept by Dr. D.L. Anderson O r i g i n a l Program d e v e l o p e d by V i n o d B a t a Program adapted by Yung H s i DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF BRITISH COLUMBIA VANCOUVER, BC, CANADA  ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10, ,/,T10,  ,11)  C*  c*  131 C* S e c t i o n 6 000 C* 6000 FORMAT (//, 1 2 3 4 5 6 7  (/,  602 0 FORMAT 1 604 0 FORMAT 1 2 6060 FORMAT (/, 6080 FORMAT (/, 1 2 6100 FORMAT 1 2 3 4 5 6 6120 FORMAT (/, 1 6140 FORMAT (/, 1 6160 FORMAT (// 1 2 3 4 5 6180 FORMAT (/, 1 62 00 FORMAT (// 1 2 3 4 5 6 6220 FORMAT (/, ' I 1 624 0 FORMAT ( / / , 1 2 3 4 5 6 7 8 9 A B C D E F G  I n t e r a c t i v e Input  Question  Format  You must i n f o r m t h i s program what r e s u l t s ' , t o e x t r a c t , whether t h e y b e , / , d i s p l a c e m e n t s , o r f o r c e s and moments. ', You c a n do t h i s e i t h e r by i n t e r a c t i v e , / , screen input, o r through a prepared i n p u t , parameter f i l e . I f you c h o o s e , / , i n t e r a c t i v e s c r e e n i n p u t , t h e program w i l l , prompt y o u w i t h q u e s t i o n s and s t o r e ' , / , y o u r r e s p o n s e s i n an i n p u t parameter', f i l e f o r f u t u r e use.') Enter 1 f o r i n t e r a c t i v e screen input, or',/, e n t e r 2 i f y o u have a p r e p a r e d i n p u t parameter f i l e . ' ) No p r e p a r e d i n p u t parameter f i l e . The ', program w i l l c r e a t e one f o r you',/, from t h e d a t a y o u e n t e r . ' ) E n t e r t h e d e s i r e d a n a l y s i s segment number.') Do y o u want n o d a l r e s u l t s o r element r e s u l t s ? ' , / , (Enter 1 f o r nodal displacements, or',/, e n t e r 2 f o r element f o r c e s and moments.)') What t y p e o f d i s p l a c e m e n t s do you want?' ,/, (Enter 1 f o r absolute displacements,',/, 2 f o r r e l a t i v e displacements,',/, 3 f o r b o t h types o f d i s p l a c e m e n t s . -/, (Note t h a t i f you choose 3, y o u need t o ' , supply 2 filenames,',/, one f o r each type o f d i s p l a c e m e n t . ) ' ) E n t e r t h e v a l u e n ' ' , so t h a t o n l y e v e r y n t h ' value i s extracted.') How many n o d a l r e s u l t s would y o u l i k e ? ' , / , (You c a n have up t o t e n r e s u l t s p e r f i l e ..) ') E n t e r on each o f t h e subsequent l i n e s , ' , at one l i n e p e r node,',/, a: the d e s i r e d node number,',/, b: i t s d i s p l a c e m e n t d i r e c t i o n , ' , / , and',/, (1 f o r x, 2 f o r y, and 3 f o r r o t ' ' n . ) C : the m u l t i p l y i n g s c a l e f a c t o r . ' , / ) Enter the l a s t l i n e again, but with the c o r r e c t ' i n f o r m a t i o n t h i s time.') E n t e r on each o f t h e subsequent l i n e s , ' , at one l i n e p e r node,',/, a: t h e d e s i r e d node number, ,/, b: t h e r e f e r e n c e node number, ,/, i t s displacement d i r e c t i o n , ' , / , C: (1 f o r x, 2 f o r y, and 3 f o r r o t ' ' n . ) , and' , / , d: the m u l t i p l y i n g s c a l e f a c t o r . ' , / ) How many elements r e s u l t s would you l i k e ? ' , / , (You c a n have up t o t e n r e s u l t s p e r f i l e . ) ' ) E n t e r on each p a i r o f t h e subsequent l i n e s , ' , at two l i n e s p e r element,',/, some o r a l l o f t h e f o l l o w i n g d a t a : ' , / / , E n t e r , on t h e f i r s t o f each two l i n e s , ' , / , l a : t h e element type (1, 2 o r 9 ) , ' , / / , and on t h e second o f each two l i n e s , ' , / , 2a: t h e element group, 2b: t h e element number,',/, 2c: t h e element end', ( u s i n g 1 f o r i , and 2 f o r j ) , ' ,/, 2d: t h e f o r c e component ( u s i n g 1 f o r ' , a x i a l , 2 f o r shear, and 3 f o r moment,',/, 4 f o r a x i a l deformation, , 1  1  1  1  1  1 1  1  1  1  6 f o r hinge r o t a t i o n , and ,/, 7 f o r v i s c o u s f o r c e ) , and', 2e: t h e m u l t i p l y i n g s c a l e f a c t o r . ' , / / , (You w i l l be prompted f o r t h e a p p r o p r i a t e ' , data required.)',//) 6250 FORMAT (/, E n t e r element type.') 6260 FORMAT (' E n t e r el.group, el.no., f o r c e comp., ', 1 and s c a l e f a c t o r . ' ) 1  1  1 3 2  el.group, el.no., e l . e n d , ', 628 0 FORMAT (' E n t e r 1 ' f o r c e comp., and s c a l e f a c t o r . ' ) 630 0 FORMAT (' The above i n f o r m a t i o n i s what you have e n t e r e d . ', 1 ' Proceed? [l=yes, 2=abort]',/, 2 I f t h e i n f o r m a t i o n i s i n c o r r e c t , you may a b o r t ' , 3 ' t h e program, e d i t t h i s f i l e , ' , / , 4 ' and then r e - e x e c u t e t h e program u s i n g t h e ' , 5 ' batch processing option.') You may c o r r e c t t h e d a t a and', 632 0 FORMAT (' Program a b o r t e d . 1 ' r u n t h e program l a t e r u s i n g ' , / , 2 ' batch processing.') 6340 FORMAT (//,' I n i t i a t i n g r e s u l t s e x t r a c t i o n p r o c e s s ...',//) 6360 FORMAT (/,' Reading node ',12,' o f ',12,' ...') 6380 FORMAT (' Node ',12,' o f ' ,12, ' done. ') 6400 FORMAT (/,' Reading element ',12,' o f ',12,' ...') 6420 FORMAT (' Element ',12,' o f ',12,' done.') 6440 FORMAT (//,' Now commencing r e s u l t s p r o c e s s i n g ... ') 6460 FORMAT (/,' ... and w r i t i n g r e s u l t s t o f i l e ( s ) ...') 6480 FORMAT (/,' E x t r a c t i o n p r o c e s s completed.',//, 1 ' Do you w i s h t o e x t r a c t more r e s u l t s ? ', 2 ' (l=yes, 2=no)') C* C* S e c t i o n 8000 S t a n d a r d Input/Output Data F i l e Format C* C* 800 0 FORMAT (1015) 802 0 FORMAT (A12) 804 0 FORMAT (30X,I5) 806 0 FORMAT (A80) 808 0 FORMAT (15X,I5,23X,I2,12X,E9.3) 810 0 FORMAT (15X,I5,10X,I5,8X,I2,12X,E9.3) 812 0 FORMAT (II,11X,13,5X,15,3X,12,8X,12,17X,E9.3) C C C S e c t i o n 9000 Stop, and End o f Program C 900 0 STOP END C* C* C** C* INTEGER FUNCTION SUBPROGRAM OPENFlLe C* C* T h i s i n t e g e r f u n c t i o n subprogram i s w r i t t e n t o open t h e a p p r o p r i a t e u n i t C* corresponding t o a f i l e . I t f i r s t asks t h e u s e r t o e n t e r a f i l e n a m e . C* A f t e r removing any p o s s i b l e t r a i l i n g comma, i t opens t h e f i l e . If i t C* e n c o u n t e r s an unexpected f i l e s t a t u s , i t o f f e r s e r r o r r e c o v e r y r o u t e s . C* C* C* C* SUBROUTINE SUBPROGRAM VARIABLES: C* C* C* INTEGER VARIABLES: C* OPENFL - an i n t e g e r t o i n d i c a t e whether t h e OPEN F i L e o p e r a t i o n was C* s u c c e s s f u l ( l = c o n t i n u e , 2=abort, 3=batch p r o c e s s i n g ) C* I - an a r r a y c o u n t e r used i n f i l t e r i n g out commas C* INDEX - an i n d e x t o i n d i c a t e t h e q u e s t i o n t o a s k t h e u s e r c* MODE - an i n d e x t o i n d i c a t e MODE (method) o f i n p u t c* UNTNUM - t h e UNiT NUMber o f t h e f i l e t o open 1  c* c* c* c* c* c** c* c*  CHARACTER VARIABLES: FILENM - t h e NaMe o f t h e FILE t o open NAME - a NAME v a r i a b l e u s e d f o r f i l t e r i n g  INTEGER FUNCTION OPENFL(MODE,INDEX,UNTNUM)  filenames  1 3 3  c * c *  INTEGER I, MODE, INDEX, UNTNUM, RECOVR CHARACTER FILENM* 12 ', NAME*12 C* C* COMMON C* C* C* C* C*  /FILES/  FILENM  I n i t i a l i z e t h e OPENFL v a l u e t o 2 ( f o r a b o r t program). This value s u b s e q u e n t l y be r e s e t i f t h e f i l e can be s u c c e s s f u l l y opened. OPENFL = 2  C* C* C*  Read i n t h e f i l e n a m e  from t h e a p p r o p r i a t e  (MODE .EQ 1) THEN IF (INDEX EQ. 1) WRITE IF (INDEX EQ. 2) WRITE IF (INDEX EQ. 3) WRITE IF (INDEX EQ. 4) WRITE IF (INDEX EQ. 5) WRITE READ (*,8000) NAME ELSE IF (INDEX EQ. 2) THEN WRITE (*,6100) READ (*,8000) NAME END I F END I F  input u n i t .  IF  C* C* C* C*  Initialize and f i l t e r  (*,6000) (*,6020) (*,6040) (*,6060) (*,6080)  the character array with blank characters, out t h e t r a i l i n g comma, i f any.  DO 1020, 1=1, 12, 1 FILENM(I:I) = ' ' I F (NAME(I:I) .NE. ',' .AND. NAME(I:I) .NE. ') 1 FILENM(I:I) = NAME(I:I) 1020 CONTINUE C* C* F o r i n t e r a c t i v e i n p u t , t h e p r o c e s s i n g i n c l u d e s e r r o r r e c o v e r y . C* IF (MODE .EQ. 1) THEN C* C* The u n i t number 1 i s u s e d f o r t h e Drain-2DX output f i l e . C* IF (UNTNUM .EQ. 1) THEN OPEN (UNIT=l,FILE=FILENM,STATUS='OLD',ERR=1040) OPENFL = 1 GOTO 9000 C* C* E r r o r r e c o v e r y i f t h e Drain-2DX f i l e does not e x i s t . C* 1040 GOTO (1000,9000) RECOVR(l) C* C* The u n i t number 2 i s used f o r t h e i n p u t parameter f i l e . C* ELSE I F (UNTNUM .EQ. 2) THEN OPEN (UNIT=2,FILE=FILENM,STATUS='NEW ,ERR=1060) CALL WRTPAR(1,0) OPENFL = 1 GOTO 9000 C* C* E r r o r r e c o v e r y i f t h e i n p u t parameter f i l e a l r e a d y e x i s t s . C* 1060 GOTO (1080,1000,9000,1100) RECOVR(ll) 1080 OPEN (UNIT=2,FILE=FILENM,STATUS= OLD') REWIND (UNIT=2) CALL WRTPAR(1,0) OPENFL = 1 1  I  ,  will  1 3 4  GOTO 9000 C* C* T h i s b r a n c h i s u s e d i f t h e u s e r wishes t o use t h e same i n p u t C* p a r a m e t e r f i l e and go d i r e c t l y t o b a t c h p r o c e s s i n g . C* 1100 OPEN (UNIT=2,FILE=FILENM,STATUS='OLD ) OPENFL = 3 GOTO 9000 C* C* The u n i t number 3 i s used f o r a b s o l u t e n o d a l d i s p l a c e m e n t r e s u l t s o r C* t h e element r e s u l t s output f i l e , and t h e u n i t number 4, f o r r e l a t i v e C* n o d a l d i s p l a c e m e n t r e s u l t s . C* Open t h e a p p r o p r i a t e r e s u l t s output f i l e . C* ELSE OPEN (UNIT=UNTNUM,FILE=FILENM,STATUS= NEW ,ERR=1120) IF (INDEX .EQ. 3 .OR. INDEX .EQ. 4) THEN CALL WRTPAR(INDEX+2,1) ELSE CALL WRTPAR(15,1) END I F OPENFL = 1 GOTO 9000 C* C* E r r o r r e c o v e r y i f t h e r e s u l t s output f i l e a l r e a d y e x i s t s . C* 1120 GOTO (1140,1000,9000) RECOVR(12) 1140 OPEN (UNIT=UNTNUM,FILE=FILENM,STATUS= OLD') IF (INDEX .EQ. 3 .OR. INDEX .EQ. 4) THEN CALL WRTPAR(INDEX+2,1) ELSE CALL WRTPAR(15,1) END I F REWIND (UNIT=UNTNUM) OPENFL = 1 GOTO 9000 END I F C* C* I n b a t c h p r o c e s s i n g , an e r r o r c o u l d l e a d t o t h e program a b o r t i n g . C* ELSE IF (UNTNUM .EQ. 2) THEN OPEN (UNIT=2,FILE=FILENM,STATUS='OLD',ERR=1160) REWIND (UNIT=2) OPENFL = 1 GOTO 9000 C* C* E r r o r r e c o v e r y i f t h e i n p u t p a r a m e t e r f i l e does not e x i s t . C* 1160 GOTO (1000,9000) RECOVR(2) ELSE READ (2,8020) FILENM OPEN (UNIT=UNTNUM,FILE=FILENM,STATUS= NEW ,ERR=1180) OPENFL = 1 GOTO 9000 C* C* A b o r t program i f t h e r e s u l t s output f i l e a l r e a d y e x i s t s . C* 1180 WRITE (*,6120) FILENM END I F END I F C* C* C* S e c t i o n 6000 - I n t e r a c t i v e Input Q u e s t i o n Format ======================== C* 6000 FORMAT (/,' E n t e r t h e name o f t h e Drain-2DX o u t p u t f i l e . ) 6020 FORMAT (/,' E n t e r t h e name you w i s h t o use f o r t h e , 1 i n p u t parameter f i l e . ' ) 6040 FORMAT (/, E n t e r t h e name o f t h e f i l e t o w r i t e a b s o l u t e ' , l  1  1  1  1  1  1  1  1  1  1 2  nodal displacements t o . , / , (Note t h a t t h e f i l e must not a l r e a d y e x i s t . ) ' ) E n t e r t h e name o f t h e f i l e t o w r i t e r e l a t i v e ' , nodal displacements t o . ' , / , (Note t h a t t h e f i l e must not a l r e a d y e x i s t . ) ' ) E n t e r t h e name o f t h e f i l e t o w r i t e element', results to.',/, (Note t h a t t h e f i l e must not a l r e a d y e x i s t . ) ' ) E n t e r t h e name o f t h e i n p u t parameter f i l e . ' ) The output f i l e ',A12,' you s p e c i f i e d ' , already exists.',/. These f i l e s must be new. The program has a b o r t e d . ' ) 1  6060 FORMAT (/, 1 2 6080 FORMAT (/, 1 2 6100 FORMAT (/, 6120 FORMAT (/, 1 2 C* C* S e c t i o n 8000 - S t a n d a r d Input/Output Data F i l e Format =================== C* 8000 FORMAT (A12) 8020 FORMAT (30X,A12) C* C* C* S e c t i o n 9000 - Stop, and End o f Program ================================= C* 9000 RETURN END C* C* Q * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  Q* * C* INTEGER FUNCTION SUBPROGRAM RECOVeR * C* * C* T h i s i n t e g e r f u n c t i o n subprogram i s a r e c o v e r y r o u t e f o r e r r o r s made * C* during the i n t e r a c t i v e data entry process. I t w r i t e s a message t o t h e * C* s c r e e n a s k i n g i f c o r r e c t i o n i s d e s i r e d , and t h e n p r o c e e d s a c c o r d i n g l y . * C* I f t h e u s e r w i s h e s a second attempt, t h e c o n t r o l u s u a l l y r e t u r n s t o t h e * C* c a l l i n g r o u t i n e w i t h an i n t e g e r f o r t h e GOTO statement, i n d i c a t i n g t h e * C* course o f a c t i o n t o f o l l o w . * C* * C* * C* * C* SUBROUTINE SUBPROGRAM VARIABLES: * Q* * C* INTEGER VARIABLES: * C* RECOVR - a number t o i n d i c a t e t h e c o u r s e o f a c t i o n t o t a k e * C* INDEX - an INDEX t o i n d i c a t e t h e v a r i a b l e t o be checked * C* * C******************************************************************************* C* INTEGER FUNCTION RECOVR(INDEX) C* C* INTEGER INDEX CHARACTER FILENM*12  COMMON C* C* C* C* C* C*  (INDEX .LE. 10) THEN  I f index IF  C* C*  FILENM  Determine t h e c o u r s e o f a c t i o n t o t a k e b y r e a d i n g t h e index. I f i n d e x i s l e s s t h a n 10, t h e r e w i l l o n l y be two a v a i l a b l e o p t i o n s , r e t r y and a b o r t . IF  C* C* C*  /FILES/  i s 1, Drain-2DX output  (INDEX  I f index  .EQ. 1)  WRITE  file  not found.  (*,6000)  i s 2, t h e i n p u t parameter f i l e  i s n o t found.  1 3 6  IF C* C* C*  (INDEX .EQ. 2)  (*,6020)  (*,6040)  Read t h e r e s p o n s e  and p r o c e e d  accordingly.  READ (*,8000) RECOVR IF (RECOVR .NE. 1 .AND. RECOVR WRITE (*,6060) WRITE (*,6080) RECOVR = 2 ELSE I F (RECOVR .EQ. 2) THEN WRITE (*,6080) END I F C* C* C* C*  FILENM  I f i n d e x i s l e s s t h a n 10, a s k i f t h e u s e r wants t o r e t r y . WRITE  C* C* C*  WRITE  .NE. 2) THEN  I f i n d e x numbers a r e g r e a t e r t h a n 10, i t s i g n i f i e s t h a t m u l t i p l e options are a v a i l a b l e . ELSE  C* C* C* C* C* C* C* C*  I f i n d e x i s 11, i n p u t parameter f i l e n a m e a l r e a d y e x i s t s . M u l t i p l e options are a v a i l a b l e . Choose 1 t o o v e r w r i t e e x i s t i n g f i l e , 2 t o use a d i f f e r e n t f i l e n a m e , 3 t o a b o r t and s t a r t a t a l a t e r date, and 4 t o q u i t i n t e r a c t i v e mode and use b a t c h p r o c e s s i n g . IF  1  C* C* C* C* C* C* C*  (INDEX .EQ. 11) THEN WRITE (*,6100) FILENM READ (*,8000) RECOVR IF (RECOVR .NE. 1 .AND. RECOVR .NE. 2 .AND. RECOVR .NE. 3 .AND. RECOVR .NE. 4) THEN WRITE (*,6120) WRITE (*,6080) RECOVR = 3 ELSE IF (RECOVR .EQ. 3) WRITE (*,6080) END I F END I F  I f index Multiple Choose 1 2 and 3  i s 12, a r e s u l t s output f i l e n a m e a l r e a d y options are available. t o overwrite e x i s t i n g f i l e , t o use a d i f f e r e n t filename, t o a b o r t and s t a r t a t a l a t e r d a t e .  exists.  IF  (INDEX .EQ. 12) THEN WRITE (*,6140) FILENM READ (*,8000) RECOVR IF (RECOVR .NE. 1 .AND. RECOVR .NE. 2 .AND. 1 RECOVR .NE. 3) THEN WRITE (*,6160) WRITE (*,6080) RECOVR = 3 ELSE IF (RECOVR .EQ. 3) WRITE (*,6080) END I F END I F END I F C* C* C* S e c t i o n 6000 - I n t e r a c t i v e Input Q u e s t i o n Format ======================== C* 6000 FORMAT (/,' The Drain-2DX f i l e does n o t e x i s t . ' ) 6020 FORMAT (/,' The f i l e ', A12, ' does n o t e x i s t . ' ) 6040 FORMAT (' Do you w i s h t o r e t r y ? (l=retry,2=abort)') 6060 FORMAT (/,' The response t o t h i s q u e s t i o n must be e i t h e r 1 o r 2.')  608 0 FORMAT (/, 610 0 FORMAT 1 2 3 4 5 6 612 0 FORMAT (/, 614 0 FORMAT (/. 1 2 3 4 616 0 FORMAT (/, C* C* C* S e c t i o n 8000 C* 800 0 FORMAT (II) C* C* C* S e c t i o n 9000 C* 900 0 RETURN END C* C*  The program has aborted.') Input parameter f i l e ',A12,' a l r e a d y e x i s t s . ', What do you w i s h t o do?',/, (Enter 1 t o o v e r w r i t e the e x i s t i n g f i l e , ' , / , 2 t o use a f i l e o f a d i f f e r e n t name,',/, 3 t o a b o r t and s t a r t o v e r a t a l a t e r time, or 4 t o q u i t i n t e r a c t i v e mode and use t h e ' , e x i s t i n g f i l e f o r processing.',/) The response t o t h i s q u e s t i o n must be 1, 2, 3 o r 4 . ') F i l e ',A12,' a l r e a d y e x i s t s . ', What do you wish t o d o ? , / , (Enter 1 t o overwrite the e x i s t i n g f i l e , ' , / , 2 t o use a f i l e o f a d i f f e r e n t name,',/, or 3 t o a b o r t and s t a r t o v e r a t a l a t e r time. ) ' ) The response t o t h i s q u e s t i o n must be 1, 2, o r 3. ' ) 1  -  Standard  Stop,  Input/Output  Data F i l e  Format  and End o f Program  c*** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* * c* FUNCTION SUBPROGRAM CHecKNUMber * c* * c* T h i s i n t e g e r f u n c t i o n subprogram i s w r i t t e n t o v e r i f y t h e v a l i d i t y o f c* c e r t a i n i n p u t parameters. I t r e t u r n s s p e c i f i c i n t e g e r v a l u e s t o i n d i c a t e * * c* a c o u r s e o f a c t i o n when an i n p u t d a t a v a l u e i s i n v a l i d . I t c a l l s t h e c* i n t e g e r f u n c t i o n subprogram RECOVR t o w r i t e e r r o r messages t o t h e s c r e e n * c* t o i n f o r m t h e u s e r o f an i n v a l i d i n p u t and t o r e q u e s t a c o r r e c t i o n where * c* p o s s i b l e . I f no c o r r e c t i o n i s p o s s i b l e , t h e n t h e program w r i t e s an e r r o r * * c* message b e f o r e i t a b o r t s . c* c* c* INTEGER VARIABLES: c* c* c* CHKNUM an i n d e x t o i n d i c a t e t h e c o u r s e o f a c t i o n t o t a k e ( l = r e t r y , 2=abort, 3=continue) i n i n t e r a c t i v e format c* ( l = c o n t i n u e , 2=abort) i n b a t c h p r o c e s s i n g c* the MODE (method) o f i n p u t c* MODE an INDEX t o i n d i c a t e t h e c h e c k i n g r o u t i n e t o be used c* INDEX c* MSGNUM an i n d e x t o i n d i c a t e by NUMber t h e MeSsaGe t o be p r i n t e d t h e NUMber b e i n g checked f o r i t s v a l i d i t y c* NUM c* c*** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* c* c* c*  INTEGER FUNCTION CHKNUM(MODE,INDEX,MSGNUM,NUM)  INTEGER  MODE, INDEX, MSGNUM, NUM,  RECOVR  C* C* IF C* C* C* C* C* C*  (MODE .EQ. 1) THEN  The method o f i n p u t can be checked by u s i n g a z e r o i n d e x . I f t h e i n d e x i s z e r o , t h e program c o n t i n u e s t o e x e c u t e f o r c a s e s where t h e v a r i a b l e MODE i s s e t t o e i t h e r 1 o r 2. Otherwise, i t g e n e r a t e s an e r r o r message and r e q u e s t s a d a t a c o r r e c t i o n . IF  (INDEX .EQ. 0)  CHKNUM = 3  1 3 8  c* C* C*  I f i n d e x i s 2, check f o r e n t r i e s o f 1 o r 2. IF  C* C* C*  (INDEX .EQ. 2) THEN IF (NUM .GT. 2 .OR. NUM .LE. 0) THEN IF (MSGNUM .EQ. 1) WRITE (*,6000) IF (MSGNUM .EQ. 7) WRITE (*,6020) WRITE (*,6040) CHKNUM = RECOVR(0) ELSE CHKNUM = 3 END I F  I f i n d e x i s 3, check f o r e n t r i e s o f 1, 2 o r 3. ELSE I F (INDEX .EQ. 3) THEN IF (NUM .GT. 3 .OR. NUM .LE. 0) THEN IF (MSGNUM .EQ. 2) WRITE (*,6060) IF (MSGNUM .EQ. 4) WRITE (*,6080) WRITE (*,6100) CHKNUM = RECOVR(0) ELSE CHKNUM = 3 END I F  C* C* C*  I f i n d e x i s 6, check f o r e n t r i e s o f 1, 2, 3 o r 6.  1  C* C* C*  ELSE I F (INDEX .EQ. 6) THEN IF (NUM .EQ. 4 .OR. NUM .EQ. 5 .OR. NUM .GT. 6 .OR. NUM .LE. 0) THEN IF (MSGNUM .EQ. 8) WRITE (*,6120) WRITE (*,6140) CHKNUM = RECOVR(0) ELSE CHKNUM = 3 END I F  I f i n d e x i s 7, check f o r e n t r i e s o f 1, 4 o r 7. ELSE I F (INDEX .EQ. 7) THEN IF (NUM .NE. 1 .AND. NUM .NE. 4 .AND. NUM .NE. 7) THEN IF (MSGNUM .EQ. 6) WRITE (*,6120) WRITE (*,6160) CHKNUM = RECOVR(0) ELSE CHKNUM = 3 END I F  C* C* C*  I f i n d e x i s 9, check f o r e n t r i e s o f 1,  2 o r 9.  ELSE I F (INDEX .EQ. 9) THEN I F (NUM .NE. 1 .AND. NUM .NE. 2 .AND. NUM .NE. 9) THEN IF (MSGNUM .EQ. 5) WRITE (*,6180) WRITE (*,6200) CHKNUM = RECOVR(0) ELSE CHKNUM = 3 END I F C* C* C*  I f i n d e x i s 10, check t h a t  t h e e n t r y i s 10 o r l e s s .  ELSE I F (INDEX .EQ. 10) THEN IF (NUM .GT. 10 .OR. NUM .LE. 0) THEN IF (MSGNUM .EQ. 3) WRITE (*,G220) WRITE (*,624 0) CHKNUM = RECOVR(0) ELSE CHKNUM = 3 END I F  1 3 9  END I F C* C* C* C* C* C* C* C*  In batch processing, e r r o r recovery i s not p o s s i b l e . Hence, i n s t e a d o f u s i n g t h e MSGNUM t o p r i n t out a query a s k i n g i f c o r r e c t i o n i s d e s i r e d , i t w i l l now be u s e d t o p a s s t h e v a l u e o f t h e i n d e x i n t h e node o r element a r r a y so t h a t i t c a n be u s e d t o i n f o r m t h e u s e r which node o r element e n t r y i n t h e a r r a y g e n e r a t e d t h e e r r o r . ELSE I F (MODE .EQ. 2) THEN IF (INDEX .EQ. 0) CHKNUM = 3  C* C* C*  I f i n d e x i s 2, check f o r e n t r i e s o f 1 o r 2. IF  1  C* C* C*  I f i n d e x i s 3, check f o r e n t r i e s o f 1, 2 o r 3.  1  C* C* C*  ELSE I F (INDEX .EQ. 3) THEN IF (NUM .GT. 3 .OR. NUM .LE. 0) THEN IF (MSGNUM .EQ. 0) WRITE (*,S280) IF (MSGNUM .EQ. 1) WRITE (*,S281) IF (MSGNUM .EQ. 2) WRITE (*,6282) IF (MSGNUM .EQ. 3) WRITE (*,6283) I F (MSGNUM .GE. 4 .AND. MSGNUM .LE. WRITE (*,6284) MSGNUM IF (MSGNUM .EQ. 10) WRITE (*,6285) WRITE (*,6400) CHKNUM = 2 ELSE CHKNUM = 1 END I F  9)  I f i n d e x i s 6, check f o r e n t r i e s o f 1, 2, 3 o r 6.  1  1  C* C* C*  (INDEX .EQ. 2) THEN IF (NUM .GT.. 2 .OR. NUM . LE. 0) THEN IF (MSGNUM .EQ. 0) WRITE (*,6260) IF (MSGNUM .EQ. 1) WRITE (*,S261) IF (MSGNUM .EQ. 2) WRITE (*,6262) IF (MSGNUM .EQ. 3) WRITE (*,6263)IF (MSGNUM .GE. 4 .AND. MSGNUM .LE. 9) WRITE (*,6264) MSGNUM IF (MSGNUM .EQ. 10) WRITE (*,6265) WRITE (*,6400) CHKNUM = 2 ELSE CHKNUM = 1 END I F  ELSE I F (INDEX .EQ. 6) THEN IF (NUM .EQ. 4 .OR. NUM .EQ. 5 .OR. NUM .GT. 6 .OR. NUM .LE. 0) THEN IF (MSGNUM .EQ. 1) WRITE (*,6301) IF (MSGNUM .EQ. 2) WRITE (*,G302) IF (MSGNUM .EQ. 3) WRITE (*,6303) IF (MSGNUM .GE. 4 .AND. MSGNUM .LE. WRITE (*,6304) MSGNUM IF (MSGNUM .EQ. 10) WRITE (*,6305) WRITE (*,6400) CHKNUM = 2 ELSE CHKNUM = 1 END I F  9)  I f i n d e x i s 7, check f o r e n t r i e s o f 1, 4 o r 7. ELSE I F (INDEX IF (NUM .NE. IF (MSGNUM IF (MSGNUM  .EQ. 7) 1 .AND. .EQ. 1) .EQ. 2)  THEN NUM .NE. 4 .AND. NUM .NE. 7) THEN WRITE (*,6301) WRITE (*,G302)  1 4 0  IF IF  (MSGNUM .EQ. 3) WRITE (*,6303) (MSGNUM .GE. 4 .AND. MSGNUM .LE. 9) WRITE (*,6304) MSGNUM IF (MSGNUM .EQ. 10) WRITE (*,6305) WRITE (*,6400) CHKNUM = 2 ELSE CHKNUM = 1 END I F C* C* C*  I f i n d e x i s 9, check f o r e n t r i e s o f 1, 2 o r 9. ELSE I F (INDEX .EQ. 9) THEN IF (NUM .NE. 1 .AND. NUM .NE. 2 .AND. NUM .NE. 9) THEN IF (MSGNUM .EQ. 1) WRITE (*,S321) IF (MSGNUM .EQ. 2) WRITE (*,6322) IF (MSGNUM .EQ. 3) WRITE (*,6323) IF (MSGNUM .GE. 4 .AND. MSGNUM . LE. 9) WRITE (*,6324) MSGNUM IF (MSGNUM .EQ. 10)WRITE (*,6325) WRITE (*,6400) CHKNUM = 2 ELSE CHKNUM = 1 END I F If  index  i s 10, check t h a t t h e e n t r y i s 10 o r l e s s .  ELSE I F (INDEX .EQ. 10) THEN IF (NUM .GT. 10 .OR. NUM .LE. 0) THEN WRITE (*,6340) WRITE (*,6400) CHKNUM = 2 ELSE CHKNUM = 1 END I F END I F  c* c* c*  If  i n p u t mode i s o t h e r t h a n 1 o r 2, t h e n u s e e r r o r  recovery.  ELSE WRITE (*,6360) WRITE (*,6040) WRITE (*,6380) READ (*,8000) CHKNUM IF (CHKNUM .NE. 1) WRITE (*,6400) END I F  C* C* C* S e c t i o n 6000 I n t e r a c t i v e Input Q u e s t i o n Format C* 600 0 FORMAT (/, You have e n t e r e d an i n v a l i d v a l u e f o r t h e ' , 1 r e s u l t type.') 602 0 FORMAT (/,' You have e n t e r e d an i n v a l i d v a l u e f o r t h e ' , 1 ' element end.') 604 0 FORMAT ( The response t o t h i s q u e s t i o n must be e i t h e r 1 o r 2.') 606 0 FORMAT (/, ' You have e n t e r e d an i n v a l i d v a l u e f o r the , 1 displacement type. ) 608 0 FORMAT (/, ' You have e n t e r e d an i n v a l i d v a l u e f o r the , 1 ' displacement d i r e c t i o n . ' ) 610 0 FORMAT (' The response t o t h i s q u e s t i o n must be 1, 2 o r 3.') 612 0 FORMAT (/,' You have e n t e r e d an i n v a l i d v a l u e f o r t h e ' , 1 ' element f o r c e . ' ) 614 0 FORMAT (' The response t o t h i s q u e s t i o n must be 1, 2, 3 o r 6 . ') 616 0 FORMAT (' The response t o t h i s q u e s t i o n must be 1, 4 o r 7. ) 618 0 FORMAT (/,' You have e n t e r e d an i n v a l i d v a l u e f o r t h e ' , 1 element type.') 620 0 FORMAT (' The response t o t h i s q u e s t i o n must be 1, 2 o r 9. ) 622 0 FORMAT (/, You have e n t e r e d an i n v a l i d v a l u e f o r t h e , 1  1  1  1  1  1  1  1  1  1  1  1  1 4 1  6240 FORMAT 1 2 3 6260 FORMAT 1 6261 FORMAT 1 6262 FORMAT 1 6263 FORMAT 1 6264 FORMAT 1 6265 FORMAT 1 6280 FORMAT 1 6281 FORMAT 1 6282 FORMAT 1 62 83 FORMAT 1 62 84 FORMAT 1 62 85 FORMAT 1 6301 FORMAT 1 63 02 FORMAT 1 63 03 FORMAT 1 63 04 FORMAT 1 6305 FORMAT 1 6321 FORMAT 1 6322 FORMAT 1 6323 FORMAT 1 6324 FORMAT 1 6325 FORMAT 1 6340 FORMAT 1 6360 FORMAT 1 6380 FORMAT 6400 FORMAT  ' t o t a l number o f r e s u l t s d e s i r e d . ' ) ' The number o f r e s u l t s must be t e n o r l e s s , ' ' and must be a non-zero, p o s i t i v e ' , / , integer. (You c a n have up t o t e n r e s u l t s ' , ' per f i l e . ) ' ) /,' The r e s u l t t y p e you s p e c i f i e d i n ' , ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' /, ' The element end o f t h e 1 s t element i n ' ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' /, ' The element end o f t h e 2nd element i n ' ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' /,' The element end o f t h e 3 r d element i n ' ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' /,' The element end o f t h e ',11,'th element ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' ] /,' The element end o f t h e 1 0 t h element i n ' ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' ! /,' The d i s p l a c e m e n t t y p e you s p e c i f i e d i n ' y o u r i n p u t parameter f i l e i s i n v a l i d . /, The d i s p l . d i r e c t i o n o f t h e 1 s t n o d e , i n y o u r i n p u t parameter f i l e i s i n v a l i d . ' /,' The d i s p l . d i r e c t i o n o f t h e 2nd node', ' i n y o u r i n p u t parameter f i l e i s i n v a l i d . /,' The d i s p l . d i r e c t i o n o f t h e 3 r d n o d e , ' i n y o u r i n p u t parameter f i l e i s i n v a l i d . /,' The d i s p l . d i r e c t i o n o f t h e ' , 1 1 , t h node i n y o u r i n p u t parameter f i l e i s i n v a l i d . /,' The d i s p l . d i r e c t i o n o f t h e 10th n o d e , ' i n y o u r i n p u t parameter f i l e i s i n v a l i d . /,' The element f o r c e o f t h e 1 s t element i n ' , ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' ) /,' The element f o r c e o f t h e 2nd element i n ' , y o u r i n p u t parameter f i l e i s i n v a l i d . ' ) /,' The element f o r c e o f t h e 3 r d element i n ' , y o u r i n p u t parameter f i l e i s i n v a l i d . ) /,' The element f o r c e o f t h e ' , 1 1 , t h element i n y o u r i n p u t parameter f i l e i s i n v a l i d . ) /, The element f o r c e o f t h e 1 0 t h element i n , ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' ) /, The element t y p e o f t h e 1 s t element i n , ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' ) /, The element t y p e o f t h e 2nd element i n ' , ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' ) /,' The element t y p e o f t h e 3 r d element i n , y o u r i n p u t parameter f i l e i s i n v a l i d . ' ) /,' The element t y p e o f t h e ',11,'th element i n ' , ' y o u r i n p u t parameter f i l e i s i n v a l i d . ' ) /,' The element t y p e o f t h e 1 0 t h element i n ' , y o u r i n p u t parameter f i l e i s i n v a l i d . ) /, The number o f r e s u l t s you s p e c i f i e d i n ' , y o u r i n p u t parameter f i l e i s i n v a l i d . ) /,' You have e n t e r e d an i n v a l i d v a l u e f o r t h e ' , i n p u t mode. ) Do you w i s h t o r e t r y ? (l=retry,2=abort)') /,' The program has a b o r t e d . ' ) 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  C* S e c t i o n 8C 3000 C* 8000 FORMAT ( I D C* C* C* S e c t i o n 9C 3000 C* 9000 RETURN END C* C*  -  S t a n d a r d Input/Output Data F i l e  Format  Stop, and End o f Program  Q************************************************************  *******************  142  c*  *  C* C* C* C* C* C* Q*  SUBROUTINE SUBPROGRAM WRiTePARameters  * * T h i s s u b r o u t i n e subprogram i s p a s s e d a number from t h e c a l l i n g u n i t , and * w r i t e s t o t h e i n p u t parameter f i l e t h e a p p r o p r i a t e parameter, a l o n g w i t h * a n a n o t a t i o n o f t o e x p l a i n what t h a t parameter i s . * * *  C* C* C* C* C*  INTEGER INDEX NUM FILENM  Q************************************************ C*  c*  SUBROUTINE WRTPAR(INDEX,NUM)  c* c*  INTEGER  1 2  c* c*  C* C* C* C*  INDEX, NUM, TOTNOD, NODE(IO), RNODE(IO), DISPL(IO), TOTELM, ELMTYP(10), ELMGR(10), ELMNUM(10), ELMEND(10), ELMFOR(10), NSKIP REAL FACTOR(10) CHARACTER FILENM*12, ANOT1(10)*7, ANOT2(10)*11  COMMON COMMON COMMON COMMON  (INDEX -EQ. 2)  (INDEX (NUM WRITE ELSE WRITE END I F END I F  NUM  type.  .EQ. 3) THEN .EQ. 1) THEN (2,6040) NUM (2,6060)  NUM  Write the d e s i r e d nodal displacement. IF  (INDEX (NUM WRITE ELSE I F WRITE ELSE WRITE END I F END I F IF  .EQ. 4) THEN .EQ. 1) THEN (2,6080) NUM (NUM .EQ. 2) THEN (2,6100) NUM (2,6120)  NUM  Write the filenames o f the nodal output IF IF  C* C*  WRITE (2,6020)  Write the d e s i r e d r e s u l t  IF  C* C* C*  WRITE (2,6000)  W r i t e t h e d e s i r e d a n a l y s i s segment number.  IF  C* C* C*  TOTNOD, NODE, RNODE, DISPL TOTELM, ELMTYP, ELMGR, ELMNUM, ELMEND, ELMFOR NSKIP, FACTOR FILENM  (INDEX .EQ. 1)  IF C* C* C*  /NODES/ /ELMTS/ /DISPS/ /FILES/  Write the heading o f the f i l e . IF  C* C* C*  * * * * * * *******************************  VARIABLES: - a n i n d e x t o i n d i c a t e which parameter t o w r i t e - t h e NUMber t o be w r i t t e n t o t h e i n p u t parameter f i l e - a FILENaMe t o be w r i t t e n t o t h e i n p u t parameter f i l e  (INDEX .EQ. 5) (INDEX .EQ. 6)  W r i t e t h e v a l u e 'n'.  WRITE (2,6140) WRITE (2,6160)  files.  FILENM FILENM  1 4 3  c *  IF C* C* C*  (2,6180)  NUM  W r i t e t h e t o t a l number o f nodes t o e x t r a c t . IF  C* C* C*  (INDEX .EQ. 7) WRITE  (INDEX .EQ. 8) WRITE  (2,6200)  NUM  W r i t e t h e s p e c i f i c a t i o n s o f t h e nodes t o e x t r a c t . IF  (INDEX .EQ. 9) THEN WRITE (2,6220) DO 1000, 1=1, TOTNOD, 1 IF (DISPL(I) .EQ. 1) THEN ANOT1 (I) = [ x - d i r ] ' ELSE I F (DISPL(I) .EQ. 2) THEN ANOT1(I) = ' [ y - d i r ] ELSE ANOT1 (I) = ' [ r - r o t ] END I F WRITE (2,6240) NODE(I), D I S P L ( I ) , A N O T l ( I ) , FACTOR(I) 1000 CONTINUE END I F C* C* W r i t e t h e s p e c i f i c a t i o n s o f t h e nodes t o e x t r a c t . C* IF (INDEX .EQ. 10) THEN WRITE (2,6260) DO 1020, 1=1, TOTNOD, 1 IF (DISPL(I) .EQ. 1) THEN ANOT1(I) = [ x - d i r ] ' ELSE IF (DISPL(I) .EQ. 2) THEN ANOT1(I) = [ y - d i r ] ' ELSE ANOT1(I) = [ r - r o t ] ' END IF WRITE (2,6280) NODE(I), RNODE(I), D I S P L ( I ) , A N O T l ( I ) , 1 FACTOR(I) 1020 CONTINUE END I F C* C* W r i t e t h e name o f t h e r e s u l t s output f i l e . C* I F (INDEX .EQ. 15) WRITE (2,6300) FILENM C* C* W r i t e t h e t o t a l number o f elements t o e x t r a c t . C* IF (INDEX .EQ. 18) WRITE (2,6320) NUM C* C* W r i t e t h e s p e c i f i c a t i o n s o f t h e elements t o e x t r a c t . C* IF (INDEX .EQ. 19) THEN WRITE (2,6340) DO 1040, 1=1, TOTELM, 1 C* C* L a b e l t h e element t y p e s . C* IF (ELMTYP(I) .EQ. 1) THEN ANOT1 (I) = ' [ t r u s s ] ' ELSE I F (ELMTYP(I) .EQ. 2) THEN ANOT1 (I) = [beam] ' ELSE ANOT1 (I) = [exp] ' END I F C* C* L a b e l t h e f o r c e s and moments. C* IF (ELMFOR(I) .EQ. 1) THEN ANOT2(I) = [ a x i a l ] ELSE I F (ELMFOR(I) .EQ. 2) THEN 1  1  1  1  1  1  1  1  1  1  AN0T2(I) = ' [ s h e a r ] ELSE I F (ELMFOR(I) .EQ. 3) THEN ANOT2(I) = '[moment]' ELSE I F (ELMFOR(I) .EQ. 4) THEN ANOT2(I) = ' [ a x i a l - d e f ] ELSE I F (ELMFOR(I) .EQ. 6) THEN ANOT2(I) = ' [ h i n g e - r o t ] ELSE ANOT2(I) = [ v i s c f o r c e ] END I F 1  1  1  1  :* ;*  W r i t e t h e d a t a t o t h e i n p u t parameter WRITE (2,6360) 1  1040  :* **  file.  ELMTYP(I), ANOT1(I), ELMGR(I), ELMNUM(I), ELMEND(I), ELMFOR(I), ANOT2(I), FACTOR(I)  CONTINUE END I F  W r i t e a s p e c i f i e r t o i d e n t i f y t h e end o f f i l e . IF  '* **  1  (INDEX .EQ. 30) WRITE (2,6380)  I n t e r a c t i v e Input Q u e s t i o n  S e c t i o n 6000  Format  ( I f you e d i t t h i s f i l e , p l e a s e 6000 FORMAT ( INPUT PARAMETER FILE make s u r e you keep',/, 1 ==================== the o r i g i n a l formatting, or', 2 t h e program w i l l n o t ' , / , 3 4 execute p r o p e r l y . ) ' , / ) 6020 FORMAT A n a l y s i s segment number : MS) R e s u l t type : ',15,5X, [nodal', 604 0 FORMAT displacements]') 1 6060 FORMAT Result type : ',15,5X, [element', 1 f o r c e s and moments]') ',15,5X, [ a b s o l u t e , 6080 FORMAT D i s p l a c e m e n t type : 1 displacements] ) 6100 FORMAT D i s p l a c e m e n t type : ,15,5X, [ r e l a t i v e ' , displacements]') 1 Displacement type : ',15,5X, [abs. & r e l . ' 6120 FORMAT displacements]') 1 6140 FORMAT Abs. d i s p l . f i l e n a m e : ' , A12) 6160 FORMAT Rel. d i s p l . filename : ' , A12) 6180 FORMAT ',15,5X,'(only e v e r y The v a l u e ''n'' : 1 nth value i s extracted.)') T o t a l number o f nodes : ',15) 6200 FORMAT 6220 FORMAT /,14X,'Node #',21X,'Displ. D i r e c . ' , 6 X , ' S c a l e ' , . /,14X,'======',21X,'=============',6X,'=====') 1 6240 FORMAT 15X,15,23X,12,2X,A7,3X,1PE9.3) 6260 FORMAT /,14X,'Node #',6X,'Ref. N o d e ' , 6 X , ' D i s p l . D i r e c . ' , 6 X , 'Scale', 1 /,14X,'======',6X,'=========',6X,'=============',6X, 2 3 62 80 FORMAT 15X,15,10X,15,8X,12,2X,A7,3X,1PE9.3) 'Element r e s u l t s f i l e n a m e : ,A12) 6300 FORMAT 6320 FORMAT ' T o t a l number o f elements: ',15) 6340 FORMAT /,11X,'Elm Element Elm',30X,'Scale', /,'Elm. Type Gr. number End Element F o r c e ' 1 10X,'Factor', 2 3 4 10X,'======') 6360 FORMAT (II,IX,A7,3X,13,5X,15,3X,12,8X,12,2X,A12,3X,1PE9.3) 6380 FORMAT ( <EOF>') 1  1  1  1  1  1  ^* :* S e c t i o n 9000 -* 9000 RETURN END  -  Stop,  and End o f Program  ==================  145 c * c *  Q******************************************************************************* C* C* SUBROUTINE SUBPROGRAM SEGmentSeaRCh C* C* This subroutine subprogram searches the Drain-2DX output f i l e f o r the C* appropriate segment and leaves the record pointer at that location f o r C* the subroutine subprograms READND and READEL to read and extract the C* required nodal or element data. C* C* C* C* INTEGER VARIABLES: C* ISEG - an index to indicate which" analysis segment i s desired C* RESTYP - the TYPe of RESults desired, C* 1 f o r nodal displacements, 2 f o r element forces. C* I - an array counter C* DPLTYP - displacement type = 1 f o r r e l a t i v e d i s p l s . C* 2 f o r absolute d i s p l s . C* 3 f o r both. C* NSEG - the Number of the SEGment C* NODNUM - the NUMber of the NODe C* ELENUM - the NUMber of the ELEment C* ELEGR - the GRoup number of the ELEment C* Q******************************************************************************* C* C* SUBROUTINE SEGSRC(ISEG,RESTYP,DPLTYP,I,ERROR) INTEGER ISEG, RESTYP, I, ERROR, NSEG, NODNUM, ELENUM, ELEGR, 1 TOTNOD, DPLTYP, NODE(IO), RNODE(IO), DISPL(IO), 2 TOTELM, ELMTYP(10), ELMGR(10), ELMNUM(10), 3 ELMEND(IO), ELMFOR(10) CHARACTER LABEL1*29, LABEL2*31, LABEL3*20, LABEL4*14 COMMON COMMON C* C* C* C* C*  /NODES/ /ELMTS/  TOTNOD, NODE, RNODE, DISPL TOTELM, ELMTYP, ELMGR, ELMNUM, ELMEND, ELMFOR  I n i t i a l i z e the error f l a g and rewind the unit to the beginning before searching. ERROR = 1 REWIND (UNIT=1)  C* C* Begin by l o c a t i n g the correct analysis segment. C* 1000 READ (1,8000) LABEL1 IF (LABEL1 -EQ. RESULTS FOR ANALYSIS SEGMENT') THEN BACKSPACE (UNIT=1) READ (1,8020) NSEG IF (NSEG .EQ. ISEG) THEN C* C* I f nodal results are desired, look f o r the corresponding l a b e l . C* IF (RESTYP .EQ. 1) THEN 1020 READ (1,8040) LABEL2 IF (LABEL2 .EQ. ' DISPLACEMENT HISTORY OF NODE ') THEN BACKSPACE (UNIT=1) READ (1,8060) NODNUM IF (DPLTYP .EQ. 1) THEN IF (NODNUM .NE. NODE(I)) THEN GOTO 1020 END IF ELSE 1  * * * * * * * * * * * * * * * * * * * * * * *  1 4 6  IF  (NODNUM .NE. RNODE(I)) THEN GOTO 1020 END I F END IF ELSE GOTO 1020 END I F C* C* C*  I f element r e s u l t s a r e d e s i r e d ,  1040  ELSE IF (RESTYP .EQ. 2) THEN READ (1,8080) LABEL3 IF (LABEL3 .EQ. HISTORY FOR BACKSPACE (UNIT=1) 1  C* C* C* C*  look f o r the corresponding  Continue t o look f o r the c o r r e c t element group.  label.  ELEMENT ) THEN 1  element number i n t h e c o r r e c t  READ (1,8100) ELENUM, ELEGR IF (ELENUM.EQ.ELMNUM(I) .AND. ELEGR.EQ.ELMGR(I)) THEN IF (ELMTYP(I) .EQ. 1) THEN READ (1,8120) LABEL4 READ (1,8120) LABEL4 IF (LABEL4 .NE. TRUSS ELEMENT') THEN ERROR = 2 WRITE (*,6000) END IF ELSE IF (ELMTYP(I) .EQ. 2) THEN READ (1,8080) LABEL3 READ (1,8080) LABEL3 IF (LABEL3 .NE. ' BEAM COLUMN ELEMENT') THEN ERROR = 2 WRITE (*,6000) END I F ELSE I F (ELMTYP(I) .EQ. 9) THEN READ (1,8120) LABEL4 READ (1,8120) LABEL4 IF (LABEL4 .NE. ' LINK ELEMENT ') THEN ERROR = 2 WRITE (*,6000) END I F END I F 1  C* C* C*  C o n t i n u e t o l o o k i f element number and element group do n o t match. ELSE GOTO 1040 END I F  C* C* C*  C o n t i n u e t o l o o k i f t h e l a b e l does not match. ELSE GOTO 1040 END I F END I F  C* C* C*  C o n t i n u e t o l o o k i f segment number does not match. ELSE GOTO 1000 END I F  C* C* C*  C o n t i n u e t o l o o k i f t h e l a b e l does n o t match. ELSE GOTO 1000 END I F  C* C*  :*  S e c t i o n 6000  6000 FORMAT (/, 1 2 3 4 5  -  B a t c h P r o c e s s i n g D i s p l a y Format  ============  You have e n t e r e d a v a l u e f o r t h e element t y p e , t h a t does n o t c o r r e s p o n d t o ' , / , the element group you s p e c i f i e d . ', The program has a b o r t e d . Please c o r r e c t ' , / , y o u r i n p u t parameter d a t a ( f i l e ) ' , and r e r u n t h e p r o g r a m . ) 1  1  I*  '* :*  S e c t i o n 8000  8000 8020 8040 8060 8080 8100 8120 * :* * *  FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT  -  Standard  Input/Output  Data F i l e Format  (A29) (30X, 13) (A31) (30X, 110) (A20) (21X, I3,18X,I3 (A14)  Section 9 9000 000  -  Stop,  and End o f Program  9000 RETURN END  *******************************************^ I*  *  •*  SUBROUTINE SUBPROGRAM READNoDe  :* :* :*  T h i s s u b r o u t i n e subprogram reads i n t h e d e s i r e d n o d a l d i s p l a c e m e n t v a l u e s * u s i n g t h e a p p r o p r i a t e format, and r e t u r n s t o t h e c a l l i n g r o u t i n e t h e * t o t a l number o f v a l u e s r e a d i n t o t h e a r r a y . *  '*  :*  *  *  *  I*  *  I*  *  :* :* :* :*  INTEGER VARIABLES: J - an i n d e x t o count t h e t o t a l number o f v a l u e s r e a d TOTCNT - t h e TOTal CouNT, t h e t o t a l number o f v a l u e s r e a d INDEX - a number t o i n d i c a t e which component o f t h e d i s p l a c e m e n t  :* ;* I*  REAL VARIABLES: TIME - an a r r a y t o s t o r e t h e time DRAIN - an a r r a y t o s t o r e t h e d i s p l a c e m e n t s  read  *  ;* .* READND(DPLTYP,I,DISPL,TOTCNT)  INTEGER I , J , DPLTYP, DISPL, TOTCNT REAL TIME(40005), DRAIN1(10,40005), DRAIN2(10,40005) CHARACTER LABEL1*80 I*  COMMON  :* ^*  /DRAIN/  I n i t i a l i z e t h e time  TIME, DRAIN1,  DRAIN2  f l a g and t h e J c o u n t e r .  READ (1,8000) LABEL1 READ (1,8000) LABEL1 READ (1,8000) LABEL1 TIME(0) = -0.1 J =1 Read i n t h e time and d i s p l a c e m e n t s  i n the appropriate  *  * * *  I* •••a***************************************  SUBROUTINE  * * * t o read *  format.  1 4 8  LOOO I F (DPLTYP .EQ. 1) THEN IF (DISPL .EQ. 1) THEN READ (1,8020,ERR=1020) TIME(J), DRAIN1(I,J) ELSE I F (DISPL .EQ. 2) THEN READ (1,8040,ERR=1020) TIME(J), DRAIN1(I,J) ELSE READ (1,8060,ERR=1020) TIME(J), DRAIN1(I,J) END I F ELSE IF (DISPL .EQ. 1) THEN READ (1,8020,ERR=1020) TIME(J), DRAIN2(I,J) ELSE I F (DISPL .EQ. 2) THEN READ (1,8040,ERR=1020) TIME(J), DRAIN2(I,J) ELSE READ (1,8060,ERR=1020) TIME(J), DRAIN2(I,J) END I F END I F IF (TIME(J) .LT. T I M E ( J - l ) ) GOTO 1020 J = J + 1 GOTO 1000  c* c* c*  C a l c u l a t e t h e t o t a l number o f v a l u e s r e a d .  1 02 0 TOTCNT = J - 1  c* c* c* c*  S e c t i o n 8000  S t a n d a r d Input/Output  Data F i l e Format  000 FORMAT (A80) 020 FORMAT (7X,Ell.4,2X,E12.5) (7X,Ell.4,16X,E12.5) 8040 FORMAT 8060 FORMAT (7X,Ell.4,3OX,E12.5) C* C* C* S e c t i o n 9000 Stop, and End o f Program C* 9000 RETURN END C* C* C** C* SUBROUTINE SUBPROGRAM FeTCH-ELement C* C* T h i s s u b r o u t i n e subprogram reads i n t h e d e s i r e d element r e s u l t s o u t p u t C* u s i n g t h e a p p r o p r i a t e format, and r e t u r n s t o t h e c a l l i n g r o u t i n e t h e C* t o t a l number o f v a l u e s r e a d i n t o t h e a r r a y . I t t h e n c a l l s t h e s u b r o u t i n e C* subprogram MINMAX t o c a l c u l a t e t h e extrema v a l u e s . A f t e r e s t a b l i s h i n g C* t h e s e , i t c a l l s t h e s u b r o u t i n e subprogram SCALE t o c o n c a t e n a t e i t s C* e n t r i e s and t o s c a l e f a c t o r them. C* C* C* C* INTEGER VARIABLES: C* J - an i n d e x t o count t h e t o t a l number o f v a l u e s r e a d C* TOTCNT - t h e TOTal CouNT, t h e t o t a l number o f v a l u e s r e a d c* INDEX - a number t o i n d i c a t e which component o f t h e d i s p l a c e m e n t t o r e a d c*  c* c* c* c* c* c** c* c* c* c*  REAL VARIABLES: TIME - an a r r a y t o s t o r e t h e time DRAIN1 - an a r r a y t o s t o r e t h e d i s p l a c e m e n t s r e a d  SUBROUTINE  READEL(I,ELMTYP,ELMEND,ELMFOR,TOTCNT,MIN,MAX,AMAX)  1 4 9  INTEGER I, J , ELMTYP, ELMEND, ELMFOR, TOTCNT REAL TIME(40005), DRAIN1(10,40005), DRAIN2(10,40005), 1 MIN, MAX, AMAX CHARACTER LABEL1*80 C* C* COMMON C* C* C* C*  /DRAIN/  TIME, DRAIN1, DRAIN2  Read p a s t t h e h e a d e r l i n e s READ (1,8000) READ (1,8000) READ (1,8000) READ (1,8000) TIME(0) = -0.1 J = 1  and i n i t i a t e t h e time and c o u n t e r v a r i a b l e s .  LABEL1 LABEL1 LABEL1 LABEL1  C* C* P e r f o r m t h e r e a d o p e r a t i o n u s i n g t h e a p p r o p r i a t e format. C* 1000 I F (ELMTYP .EQ. 1) THEN IF (ELMFOR .EQ. 1) THEN READ (1,8020,ERR=1020) TIME(J), DRAIN1(I,J) ELSE I F (ELMFOR .EQ. 4) THEN READ (1,8040,ERR=1020) TIME(J), DRAIN1(I,J) ELSE READ (1,8060,ERR=1020) TIME(J), DRAIN1(I,J) END I F ELSE I F (ELMTYP .EQ. 2) THEN IF (ELMEND .EQ. 1) THEN IF (ELMFOR EQ. 1) READ (1, 3080,ERR=1020) TIME(J) DRAIN1(I,J) 1 TIME(J) IF (ELMFOR EQ. 2) READ (1, 3100,ERR=1020) DRAIN1(I J) 1 TIME(J) IF (ELMFOR EQ. 3) READ (1, 3120,ERR=1020) DRAIN1(I J) 1 TIME(J) IF (ELMFOR EQ. 6) READ (1, 3140,ERR=1020) DRAIN1(I J) 1 IF (TIME(J) .LT. T I M E ( J - l ) ) GOTO 1020 READ (1,8000) LABEL1 ELSE READ (1,8160,ERR=1020) TIME(J) IF (TIME(J) .LT. T I M E ( J - l ) ) GOTO 1020 IF (ELMFOR .EQ. 1) READ (1,8180,ERR=1020) DRAIN1(I,J) IF (ELMFOR .EQ. 2) READ (1,8200,ERR=1020) DRAIN1(I,J) IF (ELMFOR .EQ. 3) READ (1,8220,ERR=1020) DRAIN1(I,J) IF (ELMFOR .EQ. 6) READ (1,8240,ERR=1020) DRAIN1(I,J) END I F ELSE IF (ELMFOR -EQ. 1) THEN READ (1,8260,ERR=1020) TIME(J), DRAIN1(I,J) ELSE I F (ELMFOR .EQ. 4) THEN READ (1,8280,ERR=1020) TIME(J), DRAIN1(I,J) ELSE READ (1,8300,ERR=1020) TIME(J), DRAINl(I.J) END I F END I F C* C* Check t o see i f t h e r e a d o p e r a t i o n has r e a c h e d t h e end o f t h e segment. C* IF (TIME(J) .LT. T I M E ( J - l ) ) GOTO 1020 C* C* C a l l t h e s u b r o u t i n e subprogram MINMAX t o compare extrema. C* CALL MINMAX(J,DRAIN1(I,J),MIN,MAX,AMAX) C* C* Increment t h e c o u n t e r and c o n t i n u e t h e r e a d i n g o p e r a t i o n . C* J = J + 1  GOTO 1000 C* C* C a l c u l a t e t h e t o t a l number o f e n t r i e s i n t h e a r r a y , and c a l l t h e s u b r o u t i n e C* subprogram SCALE t o c o n c a t e n a t e t h e a r r a y and s c a l e f a c t o r t h e e n t r i e s . C* 1020 TOTCNT = J - 1 !* '*  :* >*  S e c t i o n 61000  -  Standard  Input/Output  8000 FORMAT (A80) 8020 FORMAT ( 7 X , E l l . 3,6X,E11.3) 8040 FORMAT ( 7 X , E l l . 3,28X,E11.3) 8060 FORMAT ( 7 X , E l l . 3,17X,E11.3) 8080 FORMAT (7X,E11. 4,30X,E11.3) 8100 FORMAT ( 7 X , E l l . 4,19X,Ell.3) 8120 FORMAT ( 7 X , E l l . 4,8X,E11.3) 8140 FORMAT ( 7 X , E l l . 4,41X,E11.3) 8160 FORMAT ( 7 X , E l l . 4) 8180 FORMAT ( 4 8 X , E l l .3) 8200 FORMAT ( 3 7 X , E l l -3) 8220 FORMAT ( 2 6 X , E l l .3) 8240 FORMAT ( 5 9 X , E l l .3) 8260 FORMAT ( 7 X , E l l . 4,5X,E12.4) 8280 FORMAT (7X.E11. 4,29X,E12.4) 8300 FORMAT (7X,E11. 4,17X,E12.4) C* C* C* S e c t i o n 9000 - Stop, and End o f Program C* RETURN END C* C* Q****************************************  =================================  ***************************************  (2* C*  * SUBROUTINE  SUBPROGRAM MINimum-MAXimum  * *  Q*  C* T h i s s u b r o u t i n e subprogram i s used t o d e t e r m i n e t h e maximum and minimum C* v a l u e s o f the v a r i a b l e s that are passed t o i t by the c a l l i n g r o u t i n e . C* I t e s t a b l i s h e s t h e i n i t i a l extrema when t h e c a l l i n g r o u t i n e sends i t a n C* i n d e x v a l u e o f 1. C* C* C* C* INTEGER VARIABLES: C* INDEX - an i n d e x t o i d e n t i f y t h e i t h component C* C* REAL VARIABLES: C* VALUE - t h e VALUE p a s s e d from t h e c a l l i n g r o u t i n e f o r comparison. C* MINVAL - t h e MINimum VALue c u r r e n t l y e s t a b l i s h e d C* MAXVAL - t h e MAXimum VALue c u r r e n t l y e s t a b l i s h e d C* AMAX - t h e A b s o l u t e MAXimum v a l u e c u r r e n t l y e s t a b l i s h e d C* C******************************************************************************* C* SUBROUTINE  MINMAX(INDEX,VALUE,MINVAL,MAXVAL,  AMAX)  C* C* INTEGER INDEX REAL VALUE, MINVAL, C* C* C* C*  I f this IF  MAXVAL, AMAX  i s t h e f i r s t time through, i n i t i a l i z e  (INDEX .EQ. 1) THEN MINVAL = VALUE MAXVAL = VALUE  t h e extrema  values.  * * * * * * * * * * * * * * * *  END I F C* C* C*  Do t h e c o m p a r i s o n and r e t u r n t h e extrema. IF IF IF  (VALUE .LT. MINVAL) MINVAL = VALUE (VALUE .GT. MAXVAL) MAXVAL = VALUE (ABS(MINVAL) .LT. MAXVAL) THEN AMAX = MAXVAL ELSE AMAX = MINVAL END I F C* C* C* S e c t i o n 9000 - Stop, and End o f Program ================================= C* 9000 RETURN END C* C* C******************************************************************************* c *  *  C* SUBROUTINE SUBPROGRAM SCALE * C* * C* T h i s s u b r o u t i n e subprogram c o n c a t e n a t e s an a r r a y from i t s o r i g i n a l l e n g t h * C* t o 1/nth t h a t l e n g t h . I f t h e number o f e n t r i e s cannot be e v e n l y d i v i d e d * C* b y t h e v a l u e n, t h e n i t s i m p l y drops o f f t h e l a s t few e n t r i e s . The * C* r o u t i n e a l s o p e r f o r m s t h e s c a l e f a c t o r i n g p r o c e s s a t t h e same time, * C* i n c l u d i n g t o t h e extrema v a l u e s t h a t a r e p a s s e d t o i t . * C* * r»* * C* * C* INTEGER VARIABLES: * C* TOTCNT - t h e TOTal CouNT o f t h e number o f e n t r i e s i n t h e a r r a y * C* NSKIP - t h e Number o f t h e v a l u e t o be e x t r a c t e d * C* J - a c o u n t e r t o keep t r a c k o f t h e e n t r i e s a l r e a d y p r o c e s s e d * C* * C* REAL VARIABLES: * C* TIME - t h e time a r r a y * C* DRAIN - the output a r r a y * C* FACTOR - t h e s c a l e FACTOR * C* * C******************************************************************************* C*  1  SUBROUTINE SCALE(RESTYP,TOTNUM,DPLTYP,TOTCNT,NSKIP,FACTOR, MINI, MAX1, AMAX1, MIN2 , MAX2 , AMAX2 )  C* C* INTEGER RESTYP, TOTNUM, DPLTYP, TOTCNT, NSKIP, I, J REAL TIME(40005), DRAIN1(10,40005), DRAIN2(10,40005), 1 FACTOR(IO), MINI(10), MAX1(10), AMAXl(lO), MIN2(10), 2 MAX2 (10) , AMAX2 (10) C* C* COMMON C* C* C* C* C* C*  /DRAIN/  TIME, DRAIN1, DRAIN2  C a l c u l a t e t h e new c o n c a t e n a t e d t o t a l a r r a y l e n g t h , and e x t r a c t t h e n t h value by r e - a s s i g n i n g the a r r a y content. M u l t i p l y the array contents b y t h e s c a l e f a c t o r a t t h e same time.  1000  1020  TOTCNT = INT(REAL(TOTCNT)/REAL(NSKIP)) DO 1000, J = l , TOTCNT, 1 TIME(J) = TIME(J*NSKIP) CONTINUE DO 1040, 1=1, TOTNUM, 1 DO 1020, J = l , TOTCNT, 1 DRAIN1(I,J) = DRAIN1(I,J*NSKIP)*FACT0R(I) CONTINUE  MINI(I) = MINI(I)*FACTOR(I) MAXl(I) = MAX1(I)* FACTOR(I) AMAXl(I) = AMAX1(I)* FACTOR(I) 1040 CONTINUE C* C* I f r e l a t i v e n o d a l d i s p l a c e m e n t s a r e r e q u i r e d , t h e n p e r f o r m t h e above s e t C* o f o p e r a t i o n s one more time. C* IF (RESTYP .EQ. 1 .AND. DPLTYP .NE. 1) THEN DO 1080, 1=1, TOTNUM, 1 DO 1060, J = l , TOTCNT, 1 DRAIN2(I,J) = DRAIN2(I,J*NSKIP)* FACTOR(I) 1060 CONTINUE MIN2(I) = MIN2(I)*FACTOR(I) MAX2(I) = MAX2(I)* FACTOR(I) AMAX2(I) = AMAX2(I)* FACTOR(I) 1080 CONTINUE END I F C* C* C* S e c t i o n 9000 - Stop, and End o f Program ================================= C* 9000 RETURN END C* C* Q******************************************************************************* Q* * C* SUBROUTINE SUBPROGRAM PRiNt-OUTput * Q* * C* T h i s s u b r o u t i n e subprogram i s t h e f i n a l s t e p i n t h e e x t r a c t i o n p r o c e s s . * C* I t w r i t e s the e x t r a c t e d r e s u l t s t o the a p p r o p r i a t e u n i t i n the s p e c i f i e d * C* format, and i n c l u d e s extrema v a l u e s as w e l l as p r o p e r a n o t a t i o n f o r t h e * C* d i f f e r e n t data. * C* * Q* * C* * C* CHARACTER VARIABLES: * C* DIRLBL - D I R e c t i o n LaBeL, f o r a d d i n g t i t l e s i n output f i l e s * C* * Q******************************************************************************* C* C* SUBROUTINE 1  PRNOUT(RESTYP,DPLTYP,TOTCNT,MINI,MAX1,AMAX1, MIN2 , MAX2 , AMAX2 )  INTEGER  RESTYP, DPLTYP, TOTCNT, I , J , TOTNOD, NODE(10), RNODE(IO), DISPL(IO), TOTELM, ELMTYP(10), ELMGR(10), ELMNUM(10), ELMEND(10), ELMFOR(10) REAL TIME(40005), DRAIN1(10,40005), DRAIN2(10,40005), 1 MINI(10), MAXl(lO), AMAXl(lO), MIN2(10), MAX2(10), AMAX2(10) CHARACTER DIRLBL(10)*9 1 2  COMMON COMMON COMMON C* C* C* C*  Initialize IF  /NODES/ /ELMTS/ /DRAIN/  TOTNOD, NODE, RNODE, DISPL TOTELM, ELMTYP, ELMGR, ELMNUM, ELMEND, ELMFOR TIME, DRAIN1, DRAIN2  the headings  f o r t h e columns o f t h e o u t p u t  (RESTYP .EQ. 1) THEN DO 1000, 1=1, 10, 1 DIRLBL(I) = x-dir' CONTINUE DO 1020, 1=1, TOTNOD, 1 IF (DISPL(I) .EQ. 2) DIRLBL(I) = ' IF (DISPL(I) .EQ. 3) DIRLBL(I) = ' 1  1000  y-dir' r-rot'  files.  1 5 3  1020  CONTINUE ELSE DO 1040, 1=1, 10, 1 DIRLBL(I) = axial' CONTINUE 1040 DO 1060, 1=1, TOTELM, 1 shear I F (ELMFOR(I) .EQ. 2) DIRLBL(I) DIRLBL(I) moment I F (ELMFOR(I) .EQ. 3) DIRLBL(I) axial-def IF (ELMFOR(I) .EQ. 4) DIRLBL(I) hinge-rot' IF (ELMFOR(I) .EQ. 6) viscforce' IF (ELMFOR(I) .EQ. 7) DIRLBL(I) CONTINUE 1060 END I F C* Write absolute displacements i f they are r e q u i r e d . C* C* IF (RESTYP .EQ. 1 .AND. DPLTYP .NE. 2) THEN WRITE (3, 8000) (AMAX1 (J) , J 1,TOTNOD) WRITE (3 8020) (MINI(J) J=l,TOTNOD) WRITE (3 8040) (MAX1 (J) J=l,TOTNOD) WRITE (3 8080) WRITE (3 8080) WRITE (3 8100) NODE(1) NODE(2), NODE(3), NODE(4), NODE(5), NODE(6) NODE(7), NODE(8), NODE(9) , NODE(10) (DIRLBL(J),J=l,10) WRITE (3,8120 WRITE (3,8080) DO 1080, J = l , TOTCNT, 1 WRITE (3,8140) TIME(J) (DRAIN1(I,J),1=1,TOTNOD) CONTINUE 1080 END I F C* Write r e l a t i v e displacements i f they are r e q u i r e d . C* C* IF (RESTYP .EQ. 1 .AND. DPLTYP .NE. 1) THEN (AMAX2(J), J 1,TOTNOD) WRITE (4, 3000) (MIN2(J), J=l,TOTNOD) WRITE (4, 3020) (MAX2 (J) , J=l,TOTNOD) WRITE (4,8040) WRITE (4, 3080) WRITE (4, 3080) NODE(l), NODE(2), NODE(3) NODE(4) , NODE(5) , WRITE (4, 3110) NODE(6), NODE(7), NODE(8) NODE(9), NODE(IO) (DIRLBL(J),J=l,10) WRITE (4, 3120) WRITE (4, 3080) DO 1100, J = l , TOTCNT, 1 TIME(J) (DRAIN2(I,J),1=1,TOTNOD) WRITE (4,8140 CONTINUE 1100 END I F C* W r i t e element r e s u l t s i f t h e y a r e r e q u i r e d . C* C* IF (RESTYP .EQ. 2) THEN WRITE (3,8200) (AMAX1(J) , J=l,TOTELM) WRITE (3,8220) (MINI(J), J=l,TOTELM) WRITE (3,8240) (MAX1(J) , J=l,TOTELM) WRITE (3,8080) ' WRITE (3,8260) ELMGR(1), ELMGR(2), ELMGR(3), ELMGR(4), ELMGR(5), ELMGR(6), ELMGR(7), ELMGR(8), ELMGR(9), ELMGR(10) WRITE (3,8280) ELMNUM(1), ELMNUM(2), ELMNUM(3), ELMNUM(4), ELMNUM(5), ELMNUM(6), ELMNUM(7), ELMNUM(8), ELMNUM(9), ELMNUM(10) (DIRLBL(J) J=l,10) WRITE (3,8300) WRITE (3,8080) DO 1120, J = l , TOTCNT, 1 WRITE (3,8320 TIME(J) , (DRAIN1(I,J),1=1,TOTELM) CONTINUE 1120 END I F 1  1  1  1  1  1  1 5 4  c * c  S e c t i o n 8000  -  S t a n d a r d Input/Output Data F i l e  *  8000 FORMAT ',2X,'ABS MAX',Ipl0el3.5) 8020 FORMAT ',6X,'Min',Ipl0el3.5) ',6X,'Max',lpl0el3.5) 8040 FORMAT 8080 FORMAT A80) ,9X,10(6X, 'NODE ' ,12)) 8100 FORMAT ,9X,10(5X,'RNODE ',12)) 8110 FORMAT 8120 FORMAT ,5X,'TIME',10(4X,A9)) 8140 FORMAT ,F9.4,Ipl0el3.5) ,2X,'ABS MAX',Ipl0el2.4) 8200 FORMAT ,6X,'Min',Ipl0el2.4) 8220 FORMAT ,6X,'Max',Ipl0el2.4) 8240 FORMAT 8260 FORMAT ,9X,10(4X,'GROUP ',12)) 8280 FORMAT ,9X,10(3X,'NUMBER ',12)) 8300 FORMAT ,5X,'TIME',10(3X,A9)) 8320 FORMAT ,F9.4,lpl0el2.4) C* C* Stop, and End o f Program C* S e c t i o n 9000 C* 9000 RETURN END C* C*  Format  

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