Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

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

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1985_A7 M58.pdf [ 11.26MB ]
Metadata
JSON: 831-1.0062485.json
JSON-LD: 831-1.0062485-ld.json
RDF/XML (Pretty): 831-1.0062485-rdf.xml
RDF/JSON: 831-1.0062485-rdf.json
Turtle: 831-1.0062485-turtle.txt
N-Triples: 831-1.0062485-rdf-ntriples.txt
Original Record: 831-1.0062485-source.json
Full Text
831-1.0062485-fulltext.txt
Citation
831-1.0062485.ris

Full Text

PSEUDO NON-LINEAR SEISMIC ANALYSIS FOR DAMAGE EVALUATION OF CONCRETE STRUCTURES by SUBODH KUMAR MITAL B. Tech., Indian I n s t i t u t e of Technology Kanpur, INDIA 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE • i n FACULTY OF GRADUATE STUDIES Department of C i v i l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF May, © Subodh Kumar BRITISH COLUMBIA 1985 M i t a l , May,1985 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the THE UNIVERSITY OF BRITISH COLUMBIA, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r re f e r e n c e and study. I f u r t h e r agree that permission f o r ex t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of C i v i l E n g i n e e r i n g THE UNIVERSITY OF BRITISH COLUMBIA 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: May,1985 ABSTRACT I n e l a s t i c behavior i s i n e v i t a b l e i n most s t r u c t u r e s s u b j e c t e d to strong earthquake f o r c e s . Any r a t i o n a l design procedure, t h e r e f o r e , should attempt to estimate the amount of i n e l a s t i c behavior to be expected i n each member of the s t r u c t u r e . Methods of dynamic response a n a l y s i s based on l i n e a r e l a s t i c assumptions can be c a r r i e d out c o n v e n i e n t l y and e c o n o m i c a l l y . Such methods, however, can not provide any d i r e c t i n f o r m a t i o n on the i n e l a s t i c behavior of the s t r u c t u r e . On the other hand, time-step a n a l y s i s programs can ' t r u l y ' simulate the n o n - l i n e a r behavior of the s t r u c t u r e but are seldom used because of t h e i r c ost and complexity. There i s , t h e r e f o r e , a need f o r p r a c t i c a l and e f f i c i e n t methods which can account f o r the i n e l a s t i c b e h avior. Some methods f o r e s t i m a t i n g the i n e l a s t i c response and damage p a t t e r n s of s t r u c t u r e s under ground motions are presented. One i s the M o d i f i e d S u b s t i t u t e S t r u c t u r e Method which i s now r e v i s e d so that the s t r u c t u r e can be analysed f o r g r a v i t y loads p r i o r to the seismic a n a l y s i s . The other method which i s proposed here uses a s t a t i c a n a l y s i s . The s t r u c t u r e i s f i r s t a nalysed f o r g r a v i t y loads and then l a t e r a l seismic f o r c e s (as given by the a p p r o p r i a t e codes) are a p p l i e d . The amplitude of the l a t e r a l f o r c e s i s g r a d u a l l y i n c r e a s e d , m a i n t a i n i n g the s p e c i f i e d p a t t e r n ; a p l a s t i c hinge i s pl a c e d where a member has y i e l d e d and the s t r u c t u r e s t i f f n e s s matrix r e v i s e d each time. T h i s process i i i s c o n tinued u n t i l the s t r u c t u r e has reached a predetermined displacement. At t h i s p o i n t , the r o t a t i o n of the p l a s t i c hinges i s known and then the member c u r v a t u r e d u c t i l i t i e s can be c a l c u l a t e d . T h u s , an idea i s obtained, of the damage p a t t e r n i n the s t r u c t u r e . A computer program has a l s o been w r i t t e n f o r a n a l y s i n g the s t r u c t u r e s by 'Freeman's Method' to p r e d i c t the i n e l a s t i c response of s t r u c t u r e s under severe ground motion. The method giv e s the o v e r a l l i n e l a s t i c response without p r e d i c t i n g the p a t t e r n of l o c a l damage. These v a r i o u s methods are then compared by a n a l y z i n g two i d e a l i z e d s t r u c t u r e s . A t h i r d , r e a l s t r u c t u r e , an o f f i c e / r e s i d e n t i a l b u i l d i n g in downtown Vancouver i s a l s o a nalysed by these methods and the r e s u l t s compared with those obtained by a time-step a n a l y s i s program DRAIN-2D. These methods appear to give good r e s u l t s and i t i s hoped that they w i l l be found u s e f u l by p r a c t i s i n g e n g i n e e r s . A user's guide and the l i s t i n g of these programs are i n c l u d e d i n the appendices. Table of Contents ABSTRACT i i LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i i 1 . INTRODUCTION 1 1 . 1 BACKGROUND 1 1.2 PURPOSE OF THIS STUDY 7 1 . 3 SCOPE 9 2. MODIFIED SUBSTITUTE STRUCTURE METHOD AND FREEMAN'S METHOD 11 2.1 MODIFIED SUBSTITUTE STRUCTURE METHOD 11 2 . 2 FREEMAN ' S METHOD ..18 2.2.1 DETERMINATION OF THE CAPACITY CURVE 19 2.2.2 DETERMINATION OF THE DEMAND CURVE 21 3. STATIC DAMAGE EVALUATION METHOD 2 7 3.1 METHOD 27 3.2 COMPUTER PROGRAM CONCEPT 3 5 4. MATHEMATICAL MODELLING: ASSUMPTIONS AND COMMENTS 39 4.1 NECESSARY ASSUMPTIONS 39 4.2 ASSUMPTIONS MADE IN PRESENT ANALYSES 42 5. EXAMPLES 45 5.1 TEST STRUCTURE 1 48 5.2 TEST STRUCTURE 2 54 5.3 TEST STRUCTURE 3 61 6. CONCLUSIONS 7 3 REFRENCES 75 APPENDIX A 77 APPENDIX B 1 08 i v APPENDIX APPENDIX LIST OF FIGURES F i g . Page 2.1 DUCTILITY AND DAMAGE RATIO 12 2.2 CAPACITY : SPECTRAL ACCELERATION VS. EFFECTIVE PERIOD 22 2.3 DEMAND : SPECTRAL ACCELERATION VS. EFFECTIVE PERIOD 23 2.4 RECONCILIATION OF CAPACITY AND DEMAND 24 3.1 FORCE DISPLACEMENT CURVE 31 3.2 MOMENT CURVATURE DIAGRAM 33 5.1 TEST STRUCTURE 1 50 5.2 TIME-STEP ANALYSIS RESULTS (cur v a t u r e d u c t i l i t i e s ) 51 5.3(a) AVERAGE OF TIME-STEP ANALYSES (cu r v a t u r e d u c t i l i t i e s ) . . . . 52 5.3(b) EDAM : CURVATURE DUCTILITIES 52 5.3(c) STATIC DAMAGE METHOD : CURV. DUCT. () SENSITIVITY INDEX 53 5.3(d) RESULTS FROM FREEMAN'S METHOD 53 5.4 TEST STRUCTURE 2 56 5.5 TIME-STEP ANALYSIS RESULTS (cur v a t u r e d u c t i l i t i e s ) 57 v i 5.6(a) AVERAGE OF TIME-STEP ANALYSES (cu r v a t u r e d u c t i l i t i e s ) 58 5.6(b) EDAM : CURVATURE DUCTILITIES 58 5.6(c) STATIC DAMAGE EVALUATION : CURV. DUCT. () SENSITIVITY INDEX 59 5.6(d) RESULTS FROM FREEMAN'S METHOD 59 5.7(a) EDAM : CURV. DUCT.(REVERSE SEISMIC FORCES).. 60 5.7(b) STATIC METHOD : CURV. DUCT. FOR REVERSE SEISMIC FORCES; () SENSITIVITY INDEX 60 5.8 TEST STRUCTURE 3 64 5.9(a) TIME-STEP ANALYSIS : EL-CENTRO N-S COMP. (curv a t u r e d u c t i l i t i e s ) . . 65 5.9(b) TIME-STEP ANALYSIS : EL-CENTRO E-W COMP. (cu r v a t u r e d u c t i l i t i e s ) 66 5.9(c) TIME-STEP ANALYSIS : TAFT N21E COMP. (curv a t u r e d u c t i l i t i e s ) 67 5.9(d) TIME-STEP ANALYSIS : TAFT S69W COMP. (cu r v a t u r e d u c t i l i t i e s ) 68 5.10 AVERAGE OF TIME-STEP ANALYSES 69 5.11 EDAM : CURVATURE DUCTILITIES 7 0 5.12 STATIC DAMAGE METHOD : CURVATURE DUCTILITIES () SENSITIVITY INDEX 71 5.13 RESULTS FROM FREEMAN'S METHOD 7 2 ACKNOWLEDGEMENTS The author expresses h i s s i n c e r e g r a t i t u d e to h i s a d v i s o r s Dr. N.D. Nathan, Dr. D.L. Anderson and Dr. S. Cherry. S p e c i a l thanks are due to Dr. Nathan f o r h i s va l u a b l e guidance and constant encouragement d u r i n g the course of t h i s work. The author a l s o wishes to thank h i s f e l l o w graduate student Conroy Lum f o r h i s advice during t h i s work. Thanks are a l s o due to Mr. N i g e l Brown of Read Jones and C h r i s t o f f e r s o n who prov i d e d us with b u i l d i n g drawings and necessary inf o r m a t i o n to c a r r y out a part of t h i s work. The f i n a n c i a l support i n the form of a Reasearch A s s i s t a n t s h i p from N a t u r a l Sciences and En g i n e e r i n g Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. v i i i 1. INTRODUCTION 1 . 1 BACKGROUND As per the c u r r e n t design codes philosophy, when a s t r u c t u r e i s subjected to severe ground motion, many of i t s members are expected to go we l l past t h e i r e l a s t i c range and in many cases, the s t r u c t u r e w i l l form a mechanism. Even i f a mechanism should form, the s t r u c t u r e should not c o l l a p s e because the loads are dynamic and a l s o because of d u c t i l i t y . I f i t has been p r o p e r l y designed and d e t a i l e d , i t w i l l d i s s i p a t e energy, input to i t . I t has long been the o b j e c t i v e of re s e a r c h e r s to f i n d out how much damage each member s u f f e r s f o r a given type of earthquake motion, so that i t can be designed to e x h i b i t that much d u c t i l i t y without undue damage or f a i l u r e . In the average design o f f i c e and f o r an average s t r u c t u r e a q u a s i - s t a t i c a n a l y s i s f o r e q u i v a l e n t seismic f o r c e s i s done. These l a t e r a l f o r c e s depend upon the expected peak ground a c c e l e r a t i o n d u r i n g the l i f e of the s t r u c t u r e , the fundamental p e r i o d of v i b r a t i o n of the s t r u c t u r e , the inherent d u c t i l i t y a v a i l a b l e i n that s t r u c t u r a l form, the p r o p e r t i e s of the s o i l l y i n g underneath the s t r u c t u r e , and of course, the mass d i s t r i b u t i o n . Knowing these f o r c e s an o r d i n a r y s t a t i c a n a l y s i s i s done to f i n d the necessary y i e l d f o r c e s i n v a r i o u s members, and the s t r u c t u r e i s then designed f o r that s t r e n g t h and d e t a i l e d to ensure that the members have the d u c t i l i t y assumed to be inherent 1 2 i n t h a t s t r u c t u r a l form. The b a s i c assumption i n these c u r r e n t code procedures i s t h a t under a severe ground motion the s t r u c t u r e w i l l y i e l d but i t s u l t i m a t e displacement w i l l be equal to the displacement had i t remained completely e l a s t i c d u r i n g that p a r t i c u l a r ground motion. T h i s means that i f . a p a r t i c u l a r s t r u c t u r a l form i s capable of more d u c t i l i t y i t can be designed f o r a lower s e i s m i c f o r c e l e v e l as compared to a s t r u c t u r a l form with l i t t l e or no d u c t i l i t y . In e f f e c t i t i s a q u e s t i o n of choosing a proper combination of s t r e n g t h and d u c t i l i t y so that the s t r u c t u r e under severe ground motion responds with an a c c e p t a b l e l e v e l of damage. I t i s then the r e s p o n s i b i l i t y of the designer to ensure by proper design and d e t a i l i n g that the s t r u c t u r e f a i l s i n the f l e x u r e mode and that the f a i l u r e modes a s s o c i a t e d with a x i a l l o ad, shear and bond do not occur before the f l e x u r a l f a i l u r e of the member. T h i s approach r a i s e s s e v e r a l q u e s t i o n s . The way n o n - l i n e a r behavior i s accounted f o r i s as f o l l o w s : the i n e l a s t i c response spectrum i s determined by d i v i d i n g the e l a s t i c response spectrum by the a p p r o p r i a t e d u c t i l i t y and then using t h i s to estimate the l a t e r a l f o r c e s . T h i s assumes that the d u c t i l i t y demand i s un i f o r m l y d i s t r i b u t e d over the s t r u c t u r e ; but t h i s i s not the case i n r e a l s t r u c t u r e s , where there are i n v a r i a b l y areas of high demand and other areas which absorb l i t t l e or no energy. Thus the assumption of a smeared value of d u c t i l i t y , as i t were, does not t e l l 3 us anything about the 'bad' or 'weak' spots i n the s t r u c t u r e . I t a l s o assumes that the s t r u c t u r e v i b r a t e s e s s e n t i a l l y i n i t s f i r s t mode, and that the base shear i s d i s t r i b u t e d a c c o r d i n g l y ; although i f the height to width r a t i o exceeds some value, some account i s taken of the higher modes, when part of the base shear i s pl a c e d at the top of the s t r u c t u r e . T h i s method i s simple to apply and works reasonably w e l l f o r a 'uniform' or ' r e g u l a r ' s t r u c t u r e i . e . i f the mass i s d i s t r i b u t e d uniformly over the s t r u c t u r e and s t i f f n e s s of the s t r u c t u r e i s a l s o uniform. But with ' i r r e g u l a r ' s t r u c t u r e s such as those having setbacks or sudden changes i n s t i f f n e s s or i f the mass i s not un i f o r m l y d i s t r i b u t e d i . e . where the c o n t r i b u t i o n s of higher modes may be s i g n i f i c a n t , t h i s method does not give reasonable r e s u l t s and c e r t a i n l y does not give any idea of the damage p a t t e r n i n the s t r u c t u r e . On the other hand, a complex time h i s t o r y a n a l y s i s computer program can ' t r u l y ' simulate the n o n - l i n e a r behavior of s t r u c t u r a l elements, but these programs are expensive t o use and time consuming with regard to the p r e p a r a t i o n of input data and computer time r e q u i r e d . A l s o they depend upon assumptions of n o n - l i n e a r behavior of the s t r u c t u r e that cannot always be w e l l d e f i n e d . In these programs the ground motion i s entered i n the form of a d i g i t i z e d r e c o r d of a p a r t i c u l a r earthquake r a t h e r than as a response spectrum. U n f o r t u n a t e l y , d e s p i t e the recent 4 a d v a n c e s i n s e i s m o l o g i c a l s t u d i e s and t h e i n c r e a s e d number of a v a i l a b l e s e i s m i c r e c o r d s , a l o t o f u n c e r t a i n t y r e m a i n s w i t h r e s p e c t t o t h e n a t u r e o f t h e e a r t h q u a k e t o w h i c h a s t r u c t u r e may be s u b j e c t e d d u r i n g i t s l i f e t i m e . At b e s t we can o n l y e s t i m a t e a r a n g e o f g r o u n d a c c e l e r a t i o n i n a p a r t i c u l a r s e i s m i c zone where t h e s t r u c t u r e i s l o c a t e d . So t o g e t a r e a s o n a b l e p r e d i c t i o n o f s t r u c t u r a l b e h a v i o r i n f u t u r e g r o u n d e x c i t a t i o n s s e v e r a l a n a l y s e s a r e r e q u i r e d w i t h d i f f e r e n t s t r u c t u r a l p r o p e r t i e s and d i f f r e n t e a r t h q u a k e r e c o r d s . T h i s w i l l mean a d d i t i o n a l r u n s o f t h e program, and t h u s a d d i t i o n a l c o s t t o t h e d e s i g n e r , w h i c h makes s u c h programs e v e n more u n p o p u l a r w i t h t h e d e s i g n e r s w o r k i n g i n t h e a v e r a g e d e s i g n o f f i c e d e s i g n i n g t h e a v e r a g e c i v i l e n g i n e e r i n g s t r u c t u r e . Thus t h e use o f t h e s e methods i s " l i m i t e d t o : 1 . L a r g e a n d e x p e n s i v e p r o j e c t s where enough f u n d s and t e c h n i c a l r e s o u r c e s c a n be j u s t i f i e d i n t h e d e s i g n p r o c e s s due t o t h e enormous c o s t o f t h e p r o j e c t s t h e m s e l v e s . 2. R e s e a r c h o r i n t h e a c a d e m i c e n v i r o n m e n t , where t h e y f i n d t h e i r maximum u s a g e . S i n c e t h e s e t i m e - s t e p a n a l y s i s p rograms g i v e t h e b e s t r e p r e s e n t a t i o n of t h e ' t r u e ' n o n - l i n e a r b e h a v i o r o f t h e s t r u c t u r e , any method w h i c h i s i n t e n d e d t o a p p r o x i m a t e t h e n o n - l i n e a r b e h a v i o r i s u s u a l l y compared w i t h them t o see how c l o s e l y t h e t r u e b e h a v i o r o f t h e s t r u c t u r e i s a p p r o a c h e d . 5 Thus we attempt here t o achieve a method which i s somewhere i n between, which i s e a s i e r to use and l e s s expensive than a time-step a n a l y s i s method, but which n e v e r t h e l e s s approximates the n o n - l i n e a r behavior and give s reasonably good r e s u l t s . Two t h i n g s are important to make i t popular i n a design o f f i c e : The form of the input data should be s i m i l a r to what would be used i n an o r d i n a r y s t a t i c a n a l y s i s ; It should be based on some s o r t of envelope of the past earthquake records that are a v a i l a b l e i n s t e a d of on a s i n g l e event. A method which s a t i s f i e s these c r i t e r i a and i s based on a dynamic modal a n a l y s i s was introduced by Shibat a and Sozen 1. T h i s method i s c a l l e d the ' S u b s t i t u t e S t r u c t u r e Method' and takes i n t o account the y i e l d i n g of a member by reducing i t s s t i f f n e s s by the s o - c a l l e d 'damage r a t i o ' , and r e p l a c i n g the r e a l s t r u c t u r e by a f i c t i t i o u s s t r u c t u r e with reduced s t i f f n e s s ; hence the name ' S u b s t i t u t e S t r u c t u r e Method'. T h i s was intended to be a design method wherein the designer chooses a c c e p t a b l e v a l u e s of 'damage r a t i o s ' f o r d i f f r e n t members; r e p l a c e s the r e a l s t r u c t u r e with a f i c t i t i o u s one; and then performs an o r d i n a r y modal a n a l y s i s of the s u b s t i t u t e s t r u c t u r e t o get the l e v e l of y i e l d f o r c e s f o r which the v a r i o u s members should be designed. I t should be noted t h a t t h i s procedure i s not an i t e r a t i v e procedure. Y o s h i d a 2 extended the same idea and i n t r o d u c e d the 'Modified S u b s t i t u t e S t r u c t u r e Method'. The procedure has 6 been d e s c r i b e d i n more d e t a i l i n chapter 2 . T h i s method i s meant to be a r e t r o f i t or a design check procedure, that i s the p r o p e r t i e s and s t r e n g t h of the s t r u c t u r e being known, t h i s method computes the damage r a t i o s f o r v a r i o u s members by e l a s t i c modal a n a l y s i s i n which the reduced f l e x u r e s t i f f n e s s and e q u i v a l e n t v i s c o u s damping f a c t o r s are used i t e r a t i v e l y u n t i l convergence i s achieved: i . e . u n t i l the s t i f f n e s s reduced by the c u r r e n t damage r a t i o s l e a d to the c o r r e c t y i e l d moments, or the o r i g i n a l s t i f f n e s s leads to f o r c e s below y i e l d . As a r e s u l t of t h i s a n a l y s i s , we get a damage p a t t e r n i n the s t r u c t u r e which i s expected to occur i f i t i s subjected to the type and i n t e n s i t y of ground motion which was represented by the l i n e a r response spectrum which we used i n the a n a l y s i s . Metten 3 r e v i s e d the method so that i t c o u l d a l s o analyze coupled s t r u c t u r a l w a l l s along with framed s t r u c t u r e s . Then H u i u s t u d i e d and r e s o l v e d some problems which had hindered proper convergence in c e r t a i n cases. I t has been r e p o r t e d that t h i s method appears to work we l l f o r d i f f e r e n t kinds of s t r u c t u r e s . Freeman 5 a l s o i n t r o d u c e d a method which estimates the i n e l a s t i c response of R/C s t r u c t u r e s . T h i s method uses a simple idea to take i n t o account the n o n - l i n e a r behavior of s t r u c t u r e s under severe ground motion. I t i s a l s o meant to be a r e t r o f i t procedure. T h i s method i s e x p l a i n e d i n a l i t t l e more d e t a i l i n the f o l l o w i n g chapter. Once the s t r u c t u r a l p r o p e r t i e s and s t r e n g t h of the members are known, the c a p a c i t y of the s t r u c t u r e i s determined by combining an 7 e l a s t i c a n a l y s i s with some gen e r a l b i l i n e a r approximations. The demand of a p a r t i c u l a r earthquake i s represented by a l i n e a r response spectrum i n which the damping in c r e a s e s as the p e r i o d i n c r e a s e s from the value at f i r s t y i e l d to the maximum value at the maximum response. The. c a p a c i t y of the s t r u c t u r e and the demand of the ground motion are r e c o n c i l e d to get the e f f e c t i v e response p e r i o d of v i b r a t i o n and the percentage of c r i t i c a l damping at peak response of s t r u c t u r e . T h i s a n a l y s i s then r e s u l t s i n the estimated value of peak s t r u c t u r a l response, s y s t e m / t i p d u c t i l i t y demand, e f f e c t i v e response p e r i o d of v i b r a t i o n , i n e l a s t i c c a p a c i t y used and the remaining reserve c a p a c i t y of the s t r u c t u r e under that p a r t i c u l a r type of ground motion. Freeman used h i s method to f i n d the peak responses of two i d e n t i c a l 7-story frame s t r u c t u r e s under' the San Fernando 1971 earthquake. He r e p o r t e d 5 that the method seemed to work w e l l and the r e s u l t s obtained were q u i t e good as compared to the data obtained from the recorded motion of the a c t u a l s t r u c t u r e s . However, t h i s procedure only leads to an estimate of system d u c t i l i t y demand, but g i v e s no estimate of the l o c a l damage p a t t e r n . 1.2 PURPOSE OF THIS STUDY Var i o u s methods that c o u l d be used i n the approximate i n e l a s t i c s e i s m i c a n a l y s i s were d i s c u s s e d i n the p r e v i o u s s e c t i o n . The si m p l e s t and most widely used method i n common engin e e r i n g p r a c t i c e i s the e q u i v a l e n t l a t e r a l f o r c e 8 procedure with a q u a s i - s t a t i c a n a l y s i s ; but, as was d i s c u s s e d above, the estimate of i n e l a s t i c behavior i s q u e s t i o n a b l e , e s p e c i a l l y i f the s t r u c t u r e i s not ' r e g u l a r ' . On the other extreme there are time-step a n a l y s i s programs which, because of t h e i r complexity and c o s t , are r a r e l y used in common e n g i n e e r i n g p r a c t i c e . I t was intended to study those methods which t r y to f i l l t h i s gap and a l s o to come up with a q u a s i - s t a t i c method f o r the same purpose with the f o l l o w i n g p o i n t s : 1. The n o n - l i n e a r behavior i s represented by a l i n e a r approximat ion; 2. The method i s able to r e f l e c t the damage p a t t e r n i n the s t r u c t u r e with reasonable accuracy as compared to a time - s t e p method; 3 . The input i s s i m i l a r to what i s g e n e r a l l y used f o r an o r d i n a r y s t a t i c a n a l y s i s so as to enhance a c c e p t a b i l i t y i n an average design o f f i c e ; The main purpose of t h i s study was to apply a l l these methods to a r e a l s t r u c t u r e and to compare the r e s u l t s with those of time-step a n a l y s i s program DRAIN-2D. I t i s a n t i c i p a t e d that these programs should be used i n the f o l l o w i n g way:- once the engineer has designed a s t r u c t u r e a c c o r d i n g to the e x i s t i n g design codes, and f i x e d the s i z e s and strengths of v a r i o u s members, he may check by these methods whether the s t r u c t u r e w i l l behave i n the way he a n t i c i p a t e d or whether the design needs a r e v i s i o n i n the 'weak' or 'bad' spots. 9 From v a r i o u s methods, we get c u r v a t u r e d u c t i l i t y demand as a measure of damage. We must then ensure that a p a r t i c u l a r d e sign can be and i s d e t a i l e d so that i t i s ab l e to undergo t h a t amount of damage. 1.3 SCOPE We f i r s t d e s c r i b e the M o d i f i e d S u b s t i t u t e S t r u c t u r e method and Freeman's method f o r earthquake response p r e d i c t i o n of s t r u c t u r e s . Only a b r i e f summary w i l l be presented here as they are w e l l documented i n r e f s . ( 2 , 3 , 4 , 5 ) . Then the ' S t a t i c Damage E v a l u a t i o n Method' i s presented in a subsequent chapter. The theory behind t h i s method i s d i s c u s s e d . Mathematical modelling i s a very important part of a n a l y s i s , e s p e c i a l l y i n se i s m i c a n a l y s i s . V a r i o u s assumptions i n making a mathematical model that can g r e a t l y a f f e c t the outcome of the a n a l y s i s are d i s c u s s e d . An attempt has been made to d i s t i n g u i s h between the necessary assumptions that are u s u a l l y made i n a se i s m i c a n a l y s i s , and assumptions that are made du r i n g the course of the present study, mainly to s i m p l i f y the work. T e s t i n g of the method and comparison with other procedures, a g a i n , i s a very important p a r t of the work. F i r s t a 2-bay, 4-story r e g u l a r framed s t r u c t u r e i s analyzed by v a r i o u s a v a i l a b l e methods and the r e s u l t s compared with those of the time-step a n a l y s i s program DRAIN-2D. A 3-bay, 10 3 - s t o r y ' i r r e g u l a r ' framed s t r u c t u r e has a l s o been analyzed by v a r i o u s procedures and the r e s u l t s compared with those of the time-step a n a l y s i s program. Then a r e a l s t r u c t u r e which i s an o f f i c e / r e s i d e n t i a l b u i l d i n g i n downtown Vancouver i s modelled and analyzed and the r e s u l t s compared with the same time-step a n a l y s i s program r e s u l t s t o see how these methods work on a r e a l b u i l d i n g which was designed by the present c o n v e n t i o n a l methods. In the f i n a l chapter the c o n c l u s i o n s of t h i s t h e s i s are presented . Areas where f u r t h e r work i s needed are a l s o mentioned. I t i s hoped that by reading t h i s work de s i g n e r s w i l l be a b l e to convince themselves of the value of these methods which are easy to use and which take i n t o account the i n e l a s t i c behavior of the s t r u c t u r e in a r a t i o n a l way. 2 . MODIFIED SUBSTITUTE STRUCTURE METHOD AND FREEMAN'S METHOD 2 . 1 MODIFIED SUBSTITUTE STRUCTURE METHOD Th i s method was developed from the ' S u b s t i t u t e S t r u c t u r e Method' which was proposed by Shibata and Sozen 1. The ' S u b s t i t u t e S t r u c t u r e Method' was intended to be a design method wherein the designer would choose an acce p t a b l e l e v e l of damage i n each member and then analyse a s u b s t i t u t e s t r u c t u r e with reduced s t i f f n e s s and a f i c t i t i o u s value of v i s c o u s damping to account f o r the h y s t e r e t i c energy l o s t i n a r e a l i n e l a s t i c member. The r e s u l t of t h i s a n a l y s i s leads to the y i e l d f o r c e s f o r which v a r i o u s members should be designed. The same idea i s extended i n the 'Modified S u b s t i t u t e S t r u c t u r e Method', which i s intended to be used f o r r e t r o f i t purposes i . e . to analyse an e x i s t i n g r e i n f o r c e d concrete s t r u c t u r e f o r p r e d i c t i o n of the damage caused by severe ground motion. I t i s suggested here that i t a l s o has an important a p p l i c a t i o n as a f i n a l check i n a s s e s s i n g the probable behavior and damage p a t t e r n of a s t r u c t u r e designed by the code procedures. Obviously, f o r such a s t r u c t u r e , member s i z e s and y i e l d moments f o r the members are known and the a n a l y s i s leads to p r e d i c t e d damage r a t i o s corresponding to that ground motion. 'Damage r a t i o ' i s d e f i n e d as the r a t i o of the i n i t i a l s t i f f n e s s to the reduced s t i f f n e s s . (Refer to f i g u r e 2 . 1 , which shows a moment-rotation curve f o r a member subjected to a n t i - s y m m e t r i c a l end moments) 1 1 1 2 D u c t i l i t y , on the other hand, i s d e f i n e d as the r a t i o of the f i n a l end r o t a t i o n to the y i e l d r o t a t i o n i . e . In the f i g u r e 2 . 1 : 6. D u c t i l i t y u n_ e where 0 = End r o t a t i o n of the member at moment M n n and 0^ = End r o t a t i o n of the member at y i e l d On the other hand, damage r a t i o TJ i s d e f i n e d as: slope OA _ K_ n slope OB ~ K I f the s t r a i n hardening r a t i o 's' i s known, then damage r a t i o and d u c t i l i t y are r e l a t e d by the simple e x p r e s s i o n : 1 + U - 1 ).s ! "^-K.s n ROTATION, 6 F i g . 2 . 1 . DUCTILITY AND DAMAGE RATIO 1 3 We can see that the damage r a t i o i s always l e s s than the d u c t i l i t y , unless the s t r a i n hardening r a t i o i s zero i . e . except f o r the p e r f e c t l y e l a s t o - p l a s t i c case, when they are i d e n t i c a l l y e q u a l . Since t h i s procedure makes use of the mo d i f i e d s t i f f n e s s and damping p r o p e r t i e s which were d e r i v e d from dynamic t e s t s on co n c r e t e s t r u c t u r e s 7 , i t s use i s p r e s e n t l y r e s t r i c t e d to r e i n f o r c e d concrete s t r u c t u r e s . With some m o d i f i c a t i o n s i n the damping valu e s t h i s method can p o s s i b l y be extended to s t e e l s t r u c t u r e s . The suggested damping r a t i o f o r each of the s u b s t i t u t e members i s given by: where 17 i s the damage r a t i o I t i s assumed that each of the members c o n t r i b u t e s to the s t r u c t u r a l modal damping i n p r o p o r t i o n to i t s f l e x u r a l energy, which i n turn depends upon the member end moments. To o b t a i n a damping f a c t o r f o r e n t i r e s t r u c t u r e , a weighted average of member damping values i s taken, the weight f a c t o r being the s t r a i n energy of each element. The procedure used i n the M o d i f i e d S u b s t i t u t e S t r u c t u r e Method i s as f o l l o w s : 1. Read the s t r u c t u r e data, form the e l a s t i c s t i f f n e s s matrix ( i . e . with a l l damage r a t i o s set equal to one), and s o l v e the s t r u c t u r e f o r any g r a v i t y loads to f i n d the member f o r c e s . 0 s = 0.02 + 0.2 ( 1 - -) 1 4 Form the mass matrix and perform a modal a n a l y s i s , assuming e l a s t i c behavior, using a s p e c i f i e d l i n e a r response spectrum with s p e c i f i e d peak ground a c c e l e r a t i o n . In the f i r s t i t e r a t i o n a s p e c i f i e d smeared damping f a c t o r f o r each mode i s used. F i n d the RSS f o r c e s due to seismic loads and add them to the f o r c e s due to g r a v i t y l o a d s . Then r e f i n e the valu e s of the damping f a c t o r f o r each mode based on the member end moments as suggested e a r l i e r . Compare the end moments with the y i e l d moment of each member and l o c a t e the members where the end moments exceed the y i e l d moment. In such members the damage r a t i o i s m o d i f i e d at both ends of the member t o : M 1 17 = M - (1-S) + s.M, y 1 where:-17 = damage r a t i o f o r the next i t e r a t i o n s = s t r a i n hardening r a t i o as d e f i n e d p r e v i o u s l y M1 = moment at the corresponding end of the member Mv = y i e l d moment of the member Thus we can have two d i f f e r e n t damage r a t i o s f o r each member. They are combined to get a 6x6 s t i f f n e s s matrix f o r the s u b s t i t u t e member, and combining those we get the o v e r a l l s t i f f n e s s matrix. We then recompute s u b s t i t u t e s t r u c t u r e damping r a t i o s , p e r i o d s , mode shapes and member f o r c e s (member f o r c e s due to g r a v i t y 15 loads added to the RSS f o r c e s due to seismic loads) 6. Repeat steps 4 and 5, modifying the damage r a t i o s as f o l l o w s : ^n+1 = ^n M n M . (1-s) + S-Mn where:-r j n + 1 = damage r a t i o i n (n+1)1"*1 i t e r a t i o n M n = member end moment i n n i t e r a t i o n T h i s process i s continued u n t i l convergence i s achieved. To a c c e l e r a t e the convergence process and to reduce the number of i t e r a t i o n s two c r i t e r i a are used: If the damage r a t i o i s high ( > 5) then convergence i s made to depend on the change i n the damage r a t i o s between s u c c e s i v e c y c l e s ; i f the damage r a t i o i s low, i . e . ( l < Damage R a t i o < 5) then the convergence i s made to depend upon the change i n the end moments between s u c c e s i v e i t e r a t i o n c y c l e s . Thus the r e s u l t s of the a n a l y s i s are the f i n a l damage r a t i o s f o r a l l the members. I f the damage r a t i o f o r a member i s l e s s than one then that member has remained e l a s t i c d u r i n g that ground motion. F i n a l l y , i n a r e t r o f i t procedure, i t remains to be determined whether a member i s capable of going through the degree of deformation i n d i c a t e d by the c a l c u l a t e d damage r a t i o . The f o l l o w i n g changes have been made i n the l a s t , v e r s i o n of t h i s method, which was c a l l e d Edam2: I t i s now p o s s i b l e to analyze the s t r u c t u r e f o r g r a v i t y l o a d s, p r i o r to the seismic a n a l y s i s . At the time of 1 6 w r i t i n g t h i s t h e s i s the s t a t i c loads can only be input i n two ways: e i t h e r they can be s t a t i c nodal loads i . e . s t a t i c loads a p p l i e d d i r e c t l y at the nodes, or they can be u n i f o r m l y d i s t r i b u t e d loads on the members. Thus i f there are other types of s t a t i c l o a d i n g on the member such as p o i n t loads or t r i a n g u l a r loads e t c . , then the f i r s t o p t i o n can be used and f i x e d end nodal f o r c e s corresponding to these loads should be found and input as s t a t i c nodal l o a d s . The Young's modulus of e l a s t i c i t y need not be same f o r the whole s t r u c t u r e . I t i s read as a p a r t of the member data, so that d i f f e r e n t members can have d i f f e r e n t values of Young's modulus. This a l l o w s f o r the f a c t that in a h i g h - r i s e s t r u c t u r e d i f f e r e n t grades of concrete are used over the height of the s t r u c t u r e . When there are g r a v i t y loads to be compared with the modal f o r c e s , the d i r e c t i o n of the l a t t e r becomes important; thus i t i s necessary to c o n s i d e r two cases. The g r a v i t y f o r c e s are combined f i r s t with f i r s t mode fo r c e s i n the p o s i t i v e x - d i r e c t i o n , and second with the f i r s t mode f o r c e s i n the other d i r e c t i o n . P r o v i s i o n i s made f o r the program to be run a second time with the f o r c e s combined i n the second way. The program has been changed so that we get both the damage r a t i o s and c u r v a t u r e d u c t i l i t i e s f o r the members. Thus, i t i s p o s s i b l e now to compare the r e s u l t s from a l l the methods, by the same measure of damage i . e . the 17 cu r v a t u r e d u c t i l i t y demand. From the r e s u l t s of EDAM, we get RSS displacements, r o t a t i o n s and the damage r a t i o s at both ends of the members. For a member, once we have the f i n a l end r o t a t i o n 8 , we n can get the r o t a t i o n at y i e l d as: (See F i g . 2.1) ( 1 - T J . S ) e = 0_ y d - S ) . T ? then, the r o t a t i o n of the p l a s t i c hinge 6^ i s , 6 = 0 - 0 p n y which i s converted to the p l a s t i c c u r v a t u r e $ , based on P some assumed p l a s t i c hinge l e n g t h . In t h i s method, the p l a s t i c hinge length has been assumed to be one-twentieth of the member len g t h ( i . e . about one beam depth). Thus, $ = P_ = P  P Lp 0.05(member length) then, the c u r v a t u r e d u c t i l i t y i s given by $ C D . = 1 + -P— y M v where $ i s the y i e l d c u r v a t u r e = - y — y E l where M^ = y i e l d moment of the member EI = f l e x u r a l s t i f f n e s s of the member For member ends, which are r e s t r a i n e d a g a i n s t r o t a t i o n , the f i n a l end r o t a t i o n w i l l be zero, even though the member might have s u f f e r e d some damage at t h i s end. In t h i s 18 s i t u a t i o n , the r o t a t i o n at the other end of the member and the moment (and thus the curvature) diagram are known. From these v a l u e s , we can compute the r o t a t i o n at the end of the p l a s t i c hinge r e g i o n , while the other end, being f i x e d , has zero r o t a t i o n . Thus, knowing the f i n a l r o t a t i o n at the hinge l o c a t i o n , we c a l c u l a t e the c u r v a t u r e d u c t i l i t y i n e x a c t l y the same manner as we d i d p r e v i o u s l y . Since i n most s t r u c t u r e s , most of the response i s i n the f i r s t mode, the r o t a t i o n s and the bending moments for the c a l c u l a t i o n of c u r v a t u r e d u c t i l i t y , have been taken from the f i r s t mode and the values due to s t a t i c loads have been added. Thus, these bending moments and shears are i n e q u i l i b r i u m u n l i k e the RSS v a l u e s . The r e v i s e d program along with the user's manual i s l i s t e d i n appendix A. 2.2 FREEMAN'S METHOD Freeman proposed t h i s method 5 as an approximate procedure which takes i n t o account e x p l i c i t l y the i n e l a s t i c behavior of the s t r u c t u r e . He used i t to determine the response of two almost i d e n t i c a l b u i l d i n g s - 7-story framed r e i n f o r c e d concrete Holiday Inn Motor Ho t e l s i n C a l i f o r n i a -to the Feb 9, 1971 San Fernando earthquake. In t h i s method an e l a s t i c mathematical model of the s t r u c t u r e i s f i r s t formed, i . e . s t i f f n e s s and mass matrices are assembled in the usual way; knowing the s t r u c t u r a l p r o p e r t i e s , the e l a s t i c time p e r i o d and other dynamic 19 response p r o p e r t i e s are c a l c u l a t e d . An a p p r o p r i a t e l i n e a r response spectrum i s a l s o s e l e c t e d with a chosen peak ground a c c e l e r a t i o n . To c a l c u l a t e the i n e l a s t i c response of the s t r u c t u r e two curves are r e q u i r e d : a) the ' c a p a c i t y curve' r e p r e s e n t i n g the c a p a c i t y of the s t r u c t u r e , and b) the 'demand curve', which r e p r e s e n t s the demand put on the s t r u c t u r e by a p a r t i c u l a r ground motion. 2.2.1 DETERMINATION OF THE CAPACITY CURVE In determining the c a p a c i t y of the s t r u c t u r e only the fundamental mode of v i b r a t i o n i s c o n s i d e r e d , mainly f o r s i m p l i c i t y ; i n r e g u l a r and uniform s t r u c t u r e s the response, in any case, i s mainly due to the f i r s t mode of v i b r a t i o n . The c a p a c i t y curve i s found i n much the same way as suggested i n the 'Reserve Energy Technique' 6, a c c o r d i n g to which the damage to a s t r u c t u r e depends upon the a v a i l a b i l i t y of reserve s t r e n g t h or redundancy i n the s t r u c t u r e , and the a v a i l a b i l i t y of 'reserve energy' or d u c t i l i t y i n the s t r u c t u r e . From the mathematical e l a s t i c model of the s t r u c t u r e and the known e l a s t i c c a p a c i t i e s of the s t r u c t u r a l members, the e l a s t i c c a p a c i t y t h r e s h o l d i n terms of s p e c t r a l a c c e l e r a t i o n as a f u n c t i o n of fundamental p e r i o d of v i b r a t i o n i s found as f o l l o w s : s i n c e the s t r u c t u r e i s assumed to v i b r a t e e s s e n t i a l l y i n 20 t h e f i r s t mode, a l a t e r a l r o o f d i s p l a c e m e n t i n t h e f i r s t mode c o r r e s p o n d i n g t o y i e l d i n a s u b s t a n t i a l number o f m a j o r members i s d e t e r m i n e d . K n o w i n g t h e t i m e p e r i o d , mode s h a p e a n d t h e f i r s t mode p a r t i c i p a t i o n f a c t o r o f t h e e l a s t i c s t r u c t u r e , t h e s p e c t r a l d i s p l a c e m e n t a n d s p e c t r a l a c c e l e r a t i o n v a l u e s a s s o c i a t e d w i t h t h i s r o o f d i s p l a c e m e n t a r e c o m p u t e d . To e s t i m a t e t h e c h a r a c t e r i s t i c s o f t h e s t r u c t u r e b e y o n d t h e e l a s t i c r a n g e , a new m a t h e m a t i c a l m o d e l i s d e v e l o p e d i n w h i c h a l l t h e g i r d e r s a r e a s s i g n e d g r e a t l y r e d u c e d s t i f f n e s s v a l u e s ( i t s h o u l d be n o t e d t h a t c u r r e n t c o d e d e s i g n p h i l o s o p h y c a l l s f o r weak g i r d e r s a nd s t r o n g c o l u m n s ; so p l a s t i c h i n g e s a r e e x p e c t e d t o f o r m i n t h e g i r d e r s w h i l e t h e c o l u m n s a r e e x p e c t e d t o r e m a i n e l a s t i c d u r i n g t h e g r o u n d m o t i o n ) . To d e v e l o p a s i m p l e b i - l i n e a r m o d e l , t h e moment o f i n e r t i a o f t h e g i r d e r s i s r e d u c e d t o 5% o f t h e e l a s t i c v a l u e a n d t h e n t h e p e r i o d s , mode s h a p e s a n d modal p a r t i c i p a t i o n f a c t o r s a r e c a l c u l a t e d f o r t h i s new m o d e l . A l a t e r a l d i s p l a c e m e n t l e v e l t h a t r e p r e s e n t s an a c c e p t a b l e peak r e s p o n s e o f t h e s t r u c t u r e i s d e t e r m i n e d . I t i s s u g g e s t e d t h a t , i f t h e e l a s t i c m o d e l o f t h e s t r u c t u r e i s b a s e d on t h e c r a c k e d c o n c r e t e s e c t i o n , t h e n t h e i n e l a s t i c d i s p l a c e m e n t c a p a c i t y e q u a l s f i v e t i m e s t h e e l a s t i c d i s p l a c e m e n t c a p a c i t y . T h i s d i s p l a c e m e n t i s c o n v e r t e d t o s p e c t r a l d i s p l a c e m e n t ( A S ^ ) and s p e c t r a l a c c e l e r a t i o n ( A S ) a s we know t h e t i m e p e r i o d o f t h e new m o d e l o f t h e 21 s t r u c t u r e (beyond the e l a s t i c range) and then the cumulative values of s p e c t r a l a c c e l e r a t i o n S a , and s p e c t r a l displacement can be used to f i n d the e f f e c t i v e p e r i o d of v i b r a t i o n (T f f ): 1 ) Once we get these two p o i n t s on the s p e c t r a l a c c e l e r a t i o n vs. time p e r i o d curve, i . e . the e l a s t i c l i m i t and the peak response l i m i t we get a simple b i - l i n e a r c a p a c i t y curve (see F i g 2 . 2 ( a ) ). I t i s worth noting that the c a p a c i t y curve i s a prop e r t y of the s t r u c t u r e , having nothing to do with the ground motion. The same idea can be extended, and, depending upon the accuracy r e q u i r e d , one can get a m u l t i l i n e a r c a p a c i t y curve (see F i g 2 . 2(b) ). 2 . 2 . 2 DETERMINATION OF THE DEMAND CURVE The demand c h a r a c t e r i s t i c s of the ground motion are represented by an a p p r o p r i a t e l i n e a r response spectrum. For b e t t e r r e s u l t s these s p e c t r a can be standard shapes s c a l e d to the s i t e , s p e c t r a developed e s p e c i a l l y f o r the s i t e , or the s p e c t r a o b t a i n e d from the recorded ground motions at the s i t e . Then at l e a s t two values of damping are r e q u i r e d - one r e p r e s e n t i n g the e q u i v a l e n t v i s c o u s damping i n the e l a s t i c s t r u c t u r e , and the other r e p r e s e n t i n g the e q u i v a l e n t v i s c o u s damping i n the 22 e l a s t i c e l a s t i c E F F . P E R I O D , T e f f E F F . P E R I O D , T g f f (a) (b) F i g . 2.2. CAPACITY : SPECTRAL ACCELERATION VS. EFFECTIVE PERIOD s t r u c t u r e at the maximum i n e l a s t i c e x c u r s i o n . I t i s assumed that the e f f e c t i v e damping v a r i e s l i n e a r l y between these two v a l u e s , with the roof displacement from the e l a s t i c l i m i t to the maximum i n e l a s t i c e x c u r s i o n . Knowing these val u e s and having l i n e a r response s p e c t r a f o r v a r i o u s v a l u e s of damping a demand spectrum f o r a p a r t i c u l a r s t r u c t u r e i s developed as shown i n F i g 2.3. Once we have these two cu r v e s , the p r e d i c t e d response i s at the i n t e r s e c t i o n , or at the r e c o n c i l i a t i o n of the demand and the c a p a c i t y c urve. I f . t h i s i n t e r s e c t i o n i s below the e l a s t i c c a p a c i t y , no s t r u c t u r a l , damage i s a n t i c i p a t e d . I f the two curves do not i n t e r s e c t at a l l , because the demand at a l l p o i n t s exceeds the maximum c a p a c i t y of the s t r u c t u r e , then 100% 23 damping d. e l a s t i c PERIOD, T F i g . 2.3. DEMAND : SPECTRAL ACCELERATION VS. EFFECTIVE PERIOD damage or c o l l a p s e of the s t r u c t u r e i s a n t i c i p a t e d . I f the i n t e r s e c t i o n i s i n the i n e l a s t i c r e g i o n of the c a p a c i t y curve, then v a r i o u s response parameters can be ev a l u a t e d . The peak s p e c t r a l a c c e l e r a t i o n and the e f f e c t i v e time p e r i o d of the s t r u c t u r e are read d i r e c t l y from the c u r v e s , (see F i g 2.4) Damping i s i n t e r p o l a t e d between the two damped response s p e c t r a c u r v e s . The s p e c t r a l a c c e l e r a t i o n and the e f f e c t i v e time p e r i o d of the s t r u c t u r e are used to o b t a i n the peak s p e c t r a l displacement from eq. (1), which can a l s o be r e l a t e d to the peak roof displacement. T h i s s p e c t r a l displacement i s then compared to the e l a s t i c and maximum s p e c t r a l displacements to estimate the sy s t e m / t i p d u c t i l i t y demand and re s e r v e c a p a c i t i e s of the s t r u c t u r e under that p a r t i c u l a r ground motion. 24 T h i s method on l y g i v e s the o v e r a l l s t r u c t u r a l response parameters, and g i v e s an estimate of s y s t e m / t i p d u c t i l i t y , but i t does not t e l l us anything about the damage p a t t e r n i n the s t r u c t u r e . The l a t t e r i s important to a d e s i g n e r , who i s a s s e s i n g i n d i v i d u a l members i n a design s i t u a t i o n , or who i s determining the response of the members of an e x i s t i n g s t r u c t u r e to a f u t u r e earthquake i n a r e t r o f i t s i t u a t i o n . A computer program has been w r i t t e n d u r i n g the course of t h i s work which analyzes s t r u c t u r e s by Freeman's method. The problem may concern a shear w a l l s t r u c t u r e , a frame s t r u c t u r e or a combination of both. The f o l l o w i n g p o i n t s must be noted with regard to the computer program: 1. The e l a s t i c model i s based on the cracked c o n c r e t e T r a n s i t i o n S p e c t r u m o w cu to o < C a p a c i t y PERIOD, T F i g . 2.4. RECONCILIATION OF CAPACITY AND DEMAND 25 s e c t i o n , so the maximum i n e l a s t i c c a p a c i t y of the s t r u c t u r e has been assumed to be f i v e times the e l a s t i c t h r e s h o l d displacement. 2. Since i n a s t r u c t u r e the beams w i l l form p l a s t i c hinges before the columns, the y i e l d p o i n t of the s t r u c t u r e has been assumed to be at a point when h a l f of the beams have y i e l d e d . I t can be argued t h a t t h i s assumption i s somewhat a r b i t r a r y but i t was adopted i n order to make t h i s method agree with other methods. 3. I t i s p o s s i b l e to analyze the s t r u c t u r e f o r a p p l i c a b l e g r a v i t y loads p r i o r to the a n a l y s i s f o r seismic l o a d s . At the time of w r i t i n g t h i s t h e s i s s t a t i c loads can be input i n two ways: they can e i t h e r be a p p l i e d as g e n e r a l i z e d f o r c e s at the nodes or as a unif o r m l y d i s t r i b u t e d l o a d on the members. If one has other types of s t a t i c l o a d i n g d i s t r i b u t i o n s , they should be converted to one of the types mentioned before p u t t i n g i n the data. 4. I t i s suggested that each s t r u c t u r e should be run twice i n t h i s method. T h i s i s to account f o r the f a c t that in an earthquake, the s t r u c t u r e w i l l d e f l e c t both ways; that may l e a d to d i f f e r e n t r e s u l t s and the maximum of the two should be taken. T h i s method does not t e l l us anything about the damage p a t t e r n i n the s t r u c t u r e but i t does t e l l us about the e f f e c t i v e time p e r i o d , e f f e c t i v e v i s c o u s 26 damping, s p e c t r a l a c c e l e r a t i o n and displacement at peak response of the s t r u c t u r e , system/tip d u c t i l i t y demand, i n e l a s t i c c a p a c i t y used and reserve c a p a c i t y remaining. It i s easy to use and the form of the input data i s the same as would be used i n an o r d i n a r y s t a t i c a n a l y s i s . T h i s method i s q u i t e approximate at t h i s stage but i t should be noted that Freeman has r e p o r t e d 5 that he used i t to p r e d i c t the response of two i d e n t i c a l frame s t r u c t u r e s to the 197 1 San Fernando earthquake and the responses thus obtained agreed q u i t e w e l l with the recorded motion of the s t r u c t u r e s . A l s o a more d e t a i l e d i n v e s t i g a t i o n which c o n s i d e r e d the p a r t i c i p a t i o n of n o n - s t r u c t u r a l elements i n the a n a l y s i s i n d i c a t e d that these elements play a s i g n i f i c a n t r o l e i n a f f e c t i n g the s t r u c t u r a l response to the ground motion. The program along with the user's manual i s l i s t e d i n appendix B. 3. STATIC DAMAGE EVALUATION METHOD 3.1 METHOD The proposed method i s a l s o a ' r e t r o f i t ' method, in the sense t h a t i t i s a p p l i e d to s t r u c t u r e s whose member p r o p e r t i e s are known. I t can be used to evaluate the performance of e x i s t i n g s t r u c t u r e s f o r a f u t u r e earthquake. Many b u i l d i n g s that were designed long ago, f o l l o w i n g the s e i s m i c codes that then e x i s t e d , need to be checked f o r the present code requirements. Since seismic codes have changed q u i t e d r a s t i c a l l y i n the past 20 years, i t becomes more important f o r c r i t i c a l s t r u c t u r e s to be r e a n a l y z e d to l o c a t e areas where they might need s t r e n g t h e n i n g or s t i f f e n i n g . However, the main value of the method i s expected to a r i s e from the need to confirm that code-designed s t r u c t u r e s are, i n f a c t , going to behave 'reasonably' and a l s o to i d e n t i f y any members which r e q u i r e m o d i f i c a t i o n . The a c t u a l d u c t i l i t y demand may be estimated to e v a l u a t e the assumption i m p l i c i t i n the code procedure, that the d u c t i l i t y demand w i l l be more or l e s s uniform. Before t h i s method i s d e s c r i b e d i n d e t a i l , the f o l l o w i n g r e s t r i c t i o n s are noted: 1. The system can be analyzed i n one v e r t i c a l plane o n l y . 2. The s t r u c t u r e should not y i e l d under s t a t i c loads alone. 3. Reinforcement of a l l members and j o i n t s are known such that t h e i r a b i l i t y to withstand repeated r e v e r s a l s of i n e l a s t i c deformation without s i g n i f i c a n t s t r e n g t h dacay 27 28 can be estimated. These are the basic assumptions i n the method. Some other common assumptions which are made d u r i n g any seismic a n a l y s i s e.g. that n o n - s t r u c t u r a l components do not i n t e r f e r e with the s t r u c t u r a l response, e t c . , are d i s c u s s e d i n d e t a i l i n the f o l l o w i n g chapter. The method works i n the f o l l o w i n g way: F i r s t , knowing the e l a s t i c member p r o p e r t i e s , s t r u c t u r a l data i s read i n and the s t i f f n e s s matrix of the e l a s t i c s t r u c t u r e i s formed. Then the s t r u c t u r e i s analyzed f o r the a p p l i c a b l e g r a v i t y loads; member f o r c e s and d e f l e c t i o n s due to these s t a t i c f o r c e s are c a l c u l a t e d . Then the e q u i v a l e n t l a t e r a l s eismic f o r c e s , as c a l c u l a t e d by the b u i l d i n g code, are a p p l i e d , and a q u a s i - s t a t i c a n a l y s i s i s done with the same e l a s t i c s t i f f n e s s m atrix. The r e s u l t i n g member end moments, due to l a t e r a l seismic f o r c e s , are then scanned to f i n d the highest r a t i o of moment to the ' l a t e r a l moment' c a p a c i t y ( i . e . the a c t u a l moment c a p a c i t y minus the moments r e s u l t i n g from the s t a t i c g r a v i t y loads ). The i n v e r s e of t h i s r a t i o then g i v e s the l a t e r a l load f a c t o r at which the f i r s t p l a s t i c hinge w i l l form. D e f l e c t i o n s and member f o r c e s r e s u l t i n g from the l a t e r a l loads are m u l t i p l i e d by t h i s load f a c t o r , and added to those r e s u l t i n g from the s t a t i c l o a d s . At the l o c a t i o n of f i r s t p l a s t i c hinge or hinges, an a d d i t i o n a l node (or an a d d i t i o n a l r o t a t i o n a l degree of freedom) i s int r o d u c e d on top of the pr e v i o u s node with the 29 same x a n d y c o - o r d i n a t e s , a n d t h e same x and y d e g r e e s o f f r e e d o m , b u t w i t h a d i f f e r e n t r o t a t i o n a l d e g r e e o f f r e e d o m t o a c c o u n t f o r t h e f a c t t h a t a p l a s t i c h i n g e , by d e f i n i t i o n , p e r m i t s r o t a t i o n w i t h r e s p e c t t o t h e a d j o i n i n g node. The s t r u c t u r e s t i f f n e s s m a t r i x i s r e a s s e m b l e d , s i n c e we now h a v e a d i f f e r e n t s t r u c t u r e , w i t h a p l a s t i c h i n g e . The l i n e a r r e s p o n s e o f t h i s new s t r u c t u r e t o t h e o r i g i n a l l y a p p l i e d l a t e r a l l o a d s i s c a l c u l a t e d by t h e same o r d i n a r y q u a s i - s t a t i c a n a l y s i s . A g a i n t h e r e s u l t i n g end moments a r e s c a n n e d t o f i n d t h e l a r g e s t r a t i o o f member end moments t o t h e p r e v i o u s l y u n u s e d p o r t i o n o f b e n d i n g moment c a p a c i t y . The i n v e r s e o f t h i s r a t i o , p l u s t h e p r e v i o u s l o a d f a c t o r , g i v e s t h e l o a d f a c t o r a t w h i c h t h e s e c o n d p l a s t i c h i n g e w i l l f o r m . Member f o r c e s a n d d e f l e c t i o n s r e s u l t i n g f r o m t h i s a n a l y s i s a r e m u l t i p l i e d by t h e i n c r e m e n t o f t h e l o a d f a c t o r a nd a d d e d t o t h e p r e v i o u s v a l u e s , a n d a s e c o n d p l a s t i c h i n g e i s a d d e d . Thus i n t h i s a n a l y s i s , t h e n o n - l i n e a r b e h a v i o r o f t h e s t r u c t u r e i s a p p r o x i m a t e d a s p i e c e - w i s e l i n e a r . A g a i n t h e s t i f f n e s s m a t r i x i s r e a s s e m b l e d a n d t h e s t r u c t u r e a n a l y z e d f o r t h e o r i g i n a l l y a p p l i e d l a t e r a l l o a d s a n d a new p l a s t i c h i n g e a d d e d . T h i s p r o c e s s i s c o n t i n u e d u n t i l t h e s t r u c t u r e r e a c h e s a p r e - c a l c u l a t e d v a l u e o f r o o f d i s p l a c e m e n t w h i c h i s c a l l e d t h e u l t i m a t e r o o f d i s p l a c e m e n t . To e s t i m a t e t h i s u l t i m a t e r o o f d i s p l a c e m e n t , t h e d i s p l a c e m e n t r e s u l t i n g i n t h e e l a s t i c s t r u c t u r e f r o m t h e s t a t i c l o a d s p l u s t h e u n f a c t o r e d l a t e r a l s e i s m i c l o a d s i s f o u n d , a n d i s c a l l e d A. F o r t h e d e s i g n o f t h e s t r u c t u r e , 30 these u n f a c t o r e d loads are m u l t i p l i e d by a p p r o p r i a t e load f a c t o r s . I t i s worth n o t i n g that the load f a c t o r s mentioned above are not the l o a d f a c t o r s a as suggested by the NBCC 8, but they are a m u l t i p l i e d by the l o a d combination f a c t o r which takes i n t o account the reduced p r o b a b i l i t y of a number of loads a c t i n g on the s t r u c t u r e s i m u l t a n e o u s l y . Now, when the seismic base shear i s c a l c u l a t e d as suggested by NBCC, the f o l l o w i n g formula i s used: V = A.S .K.I.F.W The K f a c t o r i n the above formula r e p r e s e n t s the m a t e r i a l and type of c o n s t r u c t i o n , and depends upon the damping and energy a b s o r p t i o n c a p a c i t y of the s t r u c t u r e by both v i s c o u s damping and i n e l a s t i c a c t i o n . For v a r i o u s types of s t r u c t u r e s , Commentary K of the supplement to the N a t i o n a l B u i l d i n g Code of Canada 9 gives the a l l o w a b l e s t r u c t u r a l d u c t i l i t y f a c t o r M , for which the s t r u c t u r e might be designed. I t i s observed that the product K . M i s always in the range of 2.8 to 3.0 f o r v a r i o u s s t r u c t u r a l forms. In the present method t h i s f a c t o r has been taken to be 2.9, implying t h a t , when a designer chooses a K f a c t o r c orresponding to a p a r t i c u l a r s t r u c t u r a l form, he i s , i n f a c t , d e s i g n i n g the s t r u c t u r e f o r an i m p l i e d s y s t e m / t i p d u c t i l i t y of approximately 2 . 9 / K . The u l t i m a t e displacement that i s allowed in a s t r u c t u r e i s then given by, 31 where:-A = l a t e r a l roof displacement r e s u l t i n g from the s t a t i c loads p l u s the u n f a c t o r e d seismic l o a d s LF = l o a d f a c t o r on l a t e r a l loads used i n the design 4> = performance f a c t o r f o r the member Since we know that the r e s u l t i n g member f o r c e s are d i v i d e d by the performance f a c t o r <j> to get the member y i e l d moments, hence the load f a c t o r i s d i v i d e d by <f> to get the u l t i m a t e displacement. (See F i g . 3.1) Now the b a s i c assumption i n the a n a l y s i s i s that the u l t i m a t e displacement produced i n a s t r u c t u r e by the ground motion i s e s s e n t i a l l y the same whether the s t r u c t u r e i s designed to respond to that earthquake e l a s t i c a l l y or i s allowed to y i e l d and respond i n an i n e l a s t i c manner. Thus at whatever f o r c e l e v e l i t y i e l d s , the maximum displacement F i g . 3.1. FORCE DISPLACEMENT CURVE 32 a t t a i n e d w i l l be A^ . Thus the l a t e r a l loads are i n c r e a s e d g r a d u a l l y , and the p l a s t i c hinges p l a c e d s u c c e s s i v e l y , u n t i l the s t r u c t u r e reaches a roof displacement A^ . In reaching t h i s displacement A u the s t r u c t u r e may or may not form a c o l l a p s e mechanism. If i t does not form a mechanism then the member cu r v a t u r e d u c t i l i t i e s are c a l c u l a t e d as d e s c r i b e d l a t e r ; but i f the s t r u c t u r e does form a c o l l a p s e mechanism we c a l c u l a t e the member c u r v a t u r e d u c t i l i t i e s corresponding to a roof displacement i n the f o l l o w i n g manner: a f i c t i t i o u s member with a very s m a l l f l e x u r a l s t i f f n e s s i s pl a c e d at the l o c a t i o n of the l a s t hinge formation, i n order to prevent the s t r u c t u r e from becoming u n s t a b l e , so that the computational a l g o r i t h m c o n t i n u e s to apply. Then the s t r u c t u r e s t i f f n e s s matrix i s reassembled, t a k i n g i n t o account t h i s f i c t i t i o u s member. Then t h i s s t r u c t u r e i s sol v e d f o r the o r i g i n a l l y a p p l i e d l a t e r a l loads; the r e s u l t i n g d e f l e c t i o n s are s c a l e d up or down u n t i l the s t r u c t u r e a t t a i n s a t o t a l roof displacement of A u . To c a l c u l a t e the member c u r v a t u r e d u c t i l i t i e s we have to convert the r o t a t i o n of p l a s t i c hinges to c u r v a t u r e , which r e q u i r e s us to assume some l e n g t h f o r the p l a s t i c hinge. S t u d i e s at the U n i v e r s i t y of Canterbury, New Zealand suggest t h a t the p l a s t i c hinge l e n g t h may vary from 0.35 to 0.65 times the o v e r a l l member depth f o r s o l i d r e i n f o r c e d c o n c r e t e members. A value of = 0.5(depth) has been recommended as a good o v e r a l l average v a l u e . These f i n d i n g s have been w e l l summarized by Mander 1 0. We know: $ = $ - $ p u y See F i g . 3.2 9 6 The p l a s t i c c u r v a t u r e $ = E— = E_ 0.5 depth we know that the y i e l d c u r v a t u r e of a member i s given by M $ = y y EI where: My = y i e l d moment of the member EI = F l e x u r a l s t i f f n e s s of the member then the member curva t u r e d u c t i l i t y ( C D.) i s given by: ' CURVATURE, 4> F i g . 3.2. MOMENT CURVATURE DIAGRAM 34 C D . y o r C D . = 1 + <i> y Thus t h e c u r v a t u r e d u c t i l i t i e s f o r e a c h member i n t h e s t r u c t u r e a r e c a l c u l a t e d and t h e e x p e c t e d damage p a t t e r n i s known. Then, t h e u l t i m a t e r o o f d i s p l a c e m e n t A u i s i n c r e a s e d by 10% and c u r v a t u r e d u c t i l i t y demands f o r a l l t h e members a r e r e c a l c u l a t e d , c o r r e s p o n d i n g t o t h i s i n c r e a s e d v a l u e o f u l t i m a t e r o o f d i s p l a c e m e n t . T h e n , an i n d e x c a l l e d ' S e n s i t i v i t y Index' i s d e f i n e d a s : A(CURV. DUCT.) = i n c r e a s e i n t h e c u r v a t u r e d u c t i l i t y demand a t a member end due t o 10% i n c r e a s e i n u l t i m a t e r o o f d i s p l a c e m e n t Thus, f o r a member w i t h h i g h v a l u e o f s e n s i t i v i t y i n d e x , i t means t h a t f o r a s l i g h t i n c r e a s e i n t h e peak g r o u n d m o t i o n , t h e i n c r e a s e i n t h e c u r v a t u r e d u c t i l i t y demand c o u l d be s i g n i f i c a n t . The d e s i g n e r s h o u l d be p a r t i c u l a r l y c a r e f u l i n d e t a i l i n g s u c h members. E s s e n t i a l l y , t h e r e s u l t s o f t h i s a n a l y s i s a r e t h e c u r v a t u r e d u c t i l i t y demands t h a t a r e put on e a c h member d u r i n g a p a r t i c u l a r g r o u n d m o t i o n . Then, t h e d e s i g n e r must e x e r c i s e h i s judgment t o d e t e r m i n e whether a p a r t i c u l a r S e n s i t i v i t y Index = A(CURV. DUCT.) 0.1 where: 35 member has s u f f i c i e n t a v a i l a b l e c u r v a t u r e d u c t i l i t y when d e t a i l e d i n the manner suggested by the code, or whether a r e v i s i o n of the design i s necessary. In a d d i t i o n , t h i s a n a l y s i s a l s o g i v e s the loa d f a c t o r s on l a t e r a l loads corresponding to the s e q u e n t i a l formation of the v a r i o u s p l a s t i c hinges . The code i s i m p l i c i t l y based on the idea that the d u c t i l i t y and the y i e l d p a t t e r n are un i f o r m l y d i s t r i b u t e d over the s t r u c t u r e . But i f the range of these l o a d f a c t o r s ( i . e . the load f a c t o r at f i r s t hinge formation and the loa d f a c t o r at the l a s t hinge formation) i s very wide, i t i n d i c a t e s that the d u c t i l i t y demand and the y i e l d p a t t e r n w i l l vary widely over the s t r u c t u r e , which w i l l not behave a c c o r d i n g to the code assumptions. For an i d e a l s t r u c t u r e t h i s range of loa d f a c t o r s should be as narrow as p o s s i b l e to ensure uniform d u c t i l i t y , and to j u s t i f y the use of a s i n g l e K f a c t o r r e p r e s e n t i n g the d u c t i l i t y and damping inherent i n the system. 3.2 COMPUTER PROGRAM CONCEPT Th i s program uses the same concepts as are used i n any s t a t i c plane s t r u c t u r a l a n a l y s i s . If a program i s a v a i l a b l e which does an e l a s t i c plane s t r u c t u r a l a n a l y s i s , with some minor m o d i f i c a t i o n s i t can be changed i n t o the form used i n t h i s program. The s t r u c t u r e i s i d e a l i z e d as a plan a r assemblage of elements. A n a l y s i s i s done by the D i r e c t S t i f f n e s s Method to f i n d the nodal g l o b a l displacements and thus the member 36 f o r c e s . E a c h node c a n h a v e t h r e e d e g r e e s o f f r e e d o m a s i n any t y p i c a l p l a n e f r a m e a n a l y s i s . T h e r e i s a p r o v i s i o n f o r d e g r e e s o f f r e e d o m t o be c o m b i n e d o r d e l e t e d . I f a node h a s z e r o d i s p l a c e m e n t r e l a t i v e t o t h e g r o u n d , no d e g r e e o f f r e e d o m i s a s s i g n e d t o t h a t n ode; i f a node h a s t h e same t r a n s l a t i o n a l o r r o t a t i o n a l d i s p l a c e m e n t a s some o t h e r node i n t h e s t r u c t u r e , t h e n t h e same d e g r e e o f f r e e d o m i s a s s i g n e d t o b o t h t h e n o d e s . T h i s p r o v i s i o n s t i l l p r o v i d e s t h e a n a l y s t w i t h s u b s t a n t i a l f r e e d o m i n t h e i d e a l i z a t i o n o f t h e s t r u c t u r e , b u t p e r m i t s t h e s i z e o f t h e p r o b l e m t o be s u b s t a n t i a l l y r e d u c e d ; t h u s t h e t o t a l numbers o f unknowns may be much l e s s t h a n t h r e e t i m e s t h e numbers o f n o d e s . D a t a f o r member p r o p e r t i e s a n d j o i n t l o c a t i o n s i s r e a d i n t h e f i r s t p a r t o f t h e p r o g r a m . Then t h e s t i f f n e s s m a t r i x f o r t h e e l a s t i c s t r u c t u r e i s b u i l t f r o m i n d i v i d u a l member s t i f f n e s s m a t r i c e s . A l o a d v e c t o r f o r s t a t i c l o a d s i s f o r m e d , a n d t h e s y s t e m o f e q u a t i o n s i s s o l v e d f o r n o d a l d i s p l a c e m e n t s by C h o l e s k y ' s method i n t h e r o u t i n e SDFBAN. K n o w i n g t h e g l o b a l n o d a l d i s p l a c e m e n t s , t h e member f o r c e s c a n be f o u n d . H owever, a s m e n t i o n e d e a r l i e r , t h e s t a t i c l o a d s s h o u l d be i n p u t e i t h e r a s l o a d s a p p l i e d d i r e c t l y t o t h e n o d e s o r a s a u n i f o r m l y d i s t r i b u t e d l o a d on t h e member. The e q u i v a l e n t l a t e r a l s e i s m i c f o r c e s , a s c a l c u l a t e d by t h e c o d e , a n d a p p l i e d d i r e c t l y on t h e n o d e s , a r e r e a d i n and c o n v e r t e d t o a l o a d v e c t o r i n t h e mai n r o u t i n e . W i t h t h e same e l a s t i c s t i f f n e s s m a t r i x a n d t h i s l o a d v e c t o r o f l a t e r a l f o r c e s , t h e s t r u c t u r e i s s o l v e d a g a i n by C h o l e s k y ' s 37 method (use of the same e l a s t i c s t r u c t u r e s t i f f n e s s matrix i s j u s t i f i e d because no member i s allowed to y i e l d under s t a t i c loads a l o n e ) ; member f o r c e s due to the e q u i v a l e n t seismic f o r c e s are found i n the same manner. Then the ro u t i n e RATIO scans the moment at both ends of each member to f i n d the hig h e s t r a t i o of the end moment to the unused part of moment c a p a c i t y , because, i f the l a t e r a l loads were to be i n c r e a s e d , that member end would form the f i r s t p l a s t i c hinge. Since a p l a s t i c hinge has formed at that l o c a t i o n , the member end i s no longer r e s t r a i n e d a g a i n s t r o t a t i o n , so an a d d i t i o n a l node i s pl a c e d at the member end. T h i s node i s assigned the same x and y c o - o r d i n a t e s , with the same x and y degrees of freedom as the a d j o i n i n g node,but with a d i f f e r e n t r o t a t i o n a l degree of freedom. If a member end was i n i t i a l l y f i x e d , the e x i s t i n g node i s now allowed to have a r o t a t i o n a l degree of freedom; i n e i t h e r case the number of unknowns NU i s i n c r e a s e d by one . Then the h a l f - w i d t h of the s t r u c t u r e s t i f f n e s s matrix i s rechecked, and the o v e r a l l s t r u c t u r e s t i f f n e s s matrix i s reassembled. The s t r u c t u r e i s again analyzed f o r the o r i g i n a l l y a p p l i e d l a t e r a l l o a d s . Then the program checks f o r two th i n g s i n the main r o u t i n e : whether the s t r u c t u r e has formed a mechanism ( i . e . whethter the value of the v a r i a b l e ' r a t i o ' c a l c u l a t e d i n the r o u t i n e SBFBAN i s c l o s e to z e r o ) , or whether the roof displacement has reached . I f a mechanism has formed before r e a c h i n g A , then the a n a l y s i s 38 i s continued as p r e v i o u s l y d i s c u s s e d u n t i l t h i s displacement i s reached. In e i t h e r case, the member c u r v a t u r e d u c t i l i t i e s c o r responding to a roof displacement of A u are c a l c u l a t e d i n the manner d e s c r i b e d i n s e c t i o n 3.1 . Then, the cu r v a t u r e d u c t i l i t i e s are c a l c u l a t e d again f o r s l i g h t l y i n c r e a s e d roof displacement and the s e n s t i v i t y index i s computed f o r a l l the members as d e f i n e d i n s e c t i o n 3.1 . The program along with the user's manual used i s l i s t e d i n appendix C. Since t h i s program supposedly w i l l be used to check a p r e l i m i n a r y design, or to check an e x i s t i n g s t r u c t u r e f o r a f u t u r e seismic hazard, the ease of the data setup i s s i g n i f i c a n t . Data i s e s s e n t i a l l y the same as would have been used by the designer i n h i s p r e l i m i n a r y design and t h i s f e a t u r e , i t i s hoped, w i l l make t h i s program more a t t r a c t i v e to use even i n o r d i n a r y design s i t u a t i o n s . 4. MATHEMATICAL MODELLING: ASSUMPTIONS AND COMMENTS Mathematical m o d e l l i n g i s an important p a r t of the process f o r a n a l y z i n g the s t r u c t u r e s f o r response to earthquake l i k e ground motions. Many assumptions that are r o u t i n e l y made in the mathematical model, which can g r e a t l y a f f e c t the outcome of the a n a l y s i s , are d i s c u s s e d here. An attempt has been made to d i f f r e n t i a t e between the necessary assumptions and assumptions made i n the present a n a l y s e s . 4.1 NECESSARY ASSUMPTIONS The f i r s t d e c i s i o n i n the c o n s t r u c t i o n of a model i s whether to use the cracked, uncracked or transformed concr e t e s e c t i o n . That depends, f o r a p a r t i c u l a r s i t u a t i o n , on the magnitude of l a t e r a l motion. I n i t i a l l y , f o r very small motions, a l l r e s i s t i n g elements, s t r u c t u r a l or n o n - s t r u c t u r a l , w i l l p a r t i c i p a t e . T h e r e f o r e , f o r small motions, the mathematical model should i n c l u d e transformed concr e t e s e c t i o n p r o p e r t i e s of a l l s t r u c t u r a l elements i n c l u d i n g the f l o o r s l a b s . I t should a l s o i n c l u d e p a r t i c i p a t i o n of such n o n - s t r u c t u r a l elements as i n t e r i o r p a r t i t i o n s , e x t e r i o r w a l l s and the s t a i r c a s es. For l a r g e motions at about the e l a s t i c l i m i t of major s t r u c t u r a l members, the mathematical model should i n c l u d e f u l l y cracked concr e t e s e c t i o n s ; i t might n e g l e c t the p a r t i c i p a t i o n of n o n - s t r u c t u r a l elements. I t can be argued that use of gross c o n c r e t e s e c t i o n s i n c r e a s e s the s t i f f n e s s of the s t r u c t u r e , thus reducing the e l a s t i c c a p a c i t y displacements , and 39 40 s h o r t e n i n g the p e r i o d of v i b r a t i o n . ' I f the e l a s t i c model i s based on cracked c o n c r e t e s e c t i o n s , the i n i t i a l . p r e d i c t e d p e r i o d of v i b r a t i o n i s higher. I t i s found that the n a t u r a l p e r i o d s of r e a l b u i l d i n g s i n c r e a s e as an earthquake pr o g r e s s e s . I t has been r e p o r t e d i n a recent s t u d y 1 1 t h a t although the gross s e c t i o n v i b r a t i o n p e r i o d s compare b e t t e r with the measured i n i t i a l p e r i o d s of the s t r u c t u r e , the cracked concrete s e c t i o n c o r r e l a t e s b e t t e r with the measured displacements. I t has a l s o been repo r t e d i n the same study that cracked s e c t i o n models produced b e t t e r estimates of the frame-wall i n t e r a c t i o n than a gross s e c t i o n model, which i s a t t r i b u t e d to the r e d i s t r i b u t i o n of i n t e r n a l f o r c e s as c r a c k i n g develops in a s t r u c t u r e . In the course of the present'study the mathematical model i s based on the cracked concrete s e c t i o n . In frame c o n s t r u c t i o n , beams c a r r y l i t t l e a x i a l l o a d . Thus the a x i a l deformation of the beams i s i n s i g n i f i c a n t . In wall-frame c o n s t r u c t i o n , f l o o r s l a b s t i e the frame and core t o g e t h e r . I t i s only because of the f l o o r s l a b s that they are able to act as one u n i t i . e . f l o o r s l a b s t r a n s f e r the l a t e r a l loads from the e x t e r i o r w a l l s to the core. In t r a n s f e r r i n g such loads, f l o o r s l a b s are s t r e s s e d as a membrane i n shear. Since deformations a r i s i n g from these s t r e s s e s are u s u a l l y s m a l l , i t i s commonly assumed that a l l h o r i z o n t a l d e f l e c t i o n s of frame and core are equal at any one l e v e l . T h i s a l s o helps to reduce the s i z e of the 41 problem. The core and the frame of t a l l b u i l d i n g s are u s u a l l y i n t e g r a t e d at the base with very s t i f f basement w a l l s . I t i s g e n e r a l l y assumed that these provide a r i g i d connection and the r o t a t i o n of the foundation system i s ignored. F u r t h e r , s i n c e the core and the frame in the basement region are connected to massive r e t a i n i n g w a l l s by r i g i d f l o o r s l a b s , they are r e s t r a i n e d from displacement in the l a t e r a l d i r e c t i o n . As mentioned e a r l i e r , the h o r i z o n t a l displacement at any one l e v e l i s assumed to be equal, so the mass at each f l o o r l e v e l i s lumped at one p o i n t . Thus the mass matrix becomes d i a g o n a l and t h i s r e s u l t s in c o n s i d e r a b l e s i m p l i f i c a t i o n of the c a l c u l a t i o n s . S e l e c t i o n of damping values f o r a s t r u c t u r e i s a r a t h e r d i f f i c u l t t a s k . Damping in a s t r u c t u r e depends upon the m a t e r i a l , type of c o n s t r u c t i o n and d i s t r i b u t i o n of n o n - s t r u c t u r a l elements. We r e q u i r e a value of e q u i v a l e n t v i s c o u s damping f o r the mathematical model. A recent s t u d y 1 1 which i n c l u d e d experimental t e s t s on frame-wall s t r u c t u r e s , with the e q u i v a l e n t v i s c o u s damping found by l o g a r i t h m i c decrement, has concluded that v i s c o u s damping f o r the frame-wall s t r u c t u r e s t e s t e d was approximately 2% of c r i t i c a l i n the uncracked s t a t e and ranged between 4 and 8% f o l l o w i n g the earthquake s i m u l a t i o n s . One assumption which i s a l s o worth mentioning here, and which i s present i n a l l seismic a n a l y s i s except i n time-step 42 procedures, i s t h i s : d u r i n g a ground motion a s t r u c t u r e v i b r a t e s i n both d i r e c t i o n s . I t v i b r a t e s to e i t h e r s i d e of the s t a t i c e q u i l i b r i u m p o s i t i o n ; yet whenever we do a modal a n a l y s i s or a psuedo n o n - l i n e a r seismic a n a l y s i s , the s t r u c t u r e i s pushed only to one s i d e . Thus we get a sequence of y i e l d i n g i n the members which c o u l d have been d i f f e r e n t (due to the s t a t i c g r a v i t y loads or due to the s t r u c t u r e not being symmetric), had the s t r u c t u r e been pushed i n the other d i r e c t i o n . Since the s t r u c t u r e v i b r a t e s both ways in an earthquake, i t i s assumed that the hinge formation i n one sequence does not a f f e c t the hinge formation i n the other sequence. The s o i l - s t r u c t u r e i n t e r a c t i o n i s normally i g n o r e d . Such e f f e c t s w i l l undoubtedly complicate the methods, and thus be l i k e l y to reduce t h e i r value as simple t o o l s f o r d e s i g n . 4.2 ASSUMPTIONS MADE IN PRESENT ANALYSES Some assumptions which have been made d u r i n g the present work are d i s c u s s e d here. These assumptions have been made mainly to s i m p l i f y the work and to make these methods more usable i n an average design o f f i c e , but they are not a b s o l u t e l y necessary f o r the a n a l y s i s per se. F i r s t , the s t r u c t u r e can be analyzed i n one v e r t i c a l plane o n l y . It has a l s o been assumed that there i s no s i g n i f i c a n t s t i f f n e s s decay due to the repeated r e v e r s a l s of i n e l a s t i c deformations i n the members, though i n the 4 3 t i m e - s t e p a n a l y s i s program DRAIN-2D, i t i s p o s s i b l e to choose a beam element with degrading s t i f f n e s s . At t h i s stage, the programs are not capable of t a k i n g i n t o account P-A e f f e c t s in the columns, which co u l d be s i g n i f i c a n t in t a l l s t r u c t u r e s . A l s o , the computer programs are not capable of t a k i n g i n t o account the y i e l d - i n t e r a c t ion s u r f a c e s f o r the columns (note that no a x i a l f o r c e s are assumed to act i n beams). Thus, f o r each member, the user has to input one value of the y i e l d moment on l y . Another p o i n t worth mentioning here, i s that in a l l these methods, i . e . 'Edam', 'Freeman's Method' and the ' S t a t i c Damage E v a l u a t i o n Method', the user can s p e c i f y only one value of moment c a p a c i t y f o r each member. Thus, the moment c a p a c i t y i s assumed to be the same f o r both ends of the member; i t i s a l s o assumed to be the same f o r both p o s i t i v e and negative bending moments. To compare the r e s u l t s of the ' S t a t i c Damage E v a l u a t i o n Method' with the r e s u l t s o b t a i n e d from other methods, we need t o c o r r e l a t e the q u a s i - s t a t i c seismic f o r c e s to the ground a c c e l e r a t i o n s l e v e l s . A s t u d y 1 2 which c o r r e l a t e d the q u a s i - s t a t i c and dynamic earthquake analyses of the N a t i o n a l B u i l d i n g Code of Canada 1977, suggests that f o r a given s t r u c t u r e , once we know the fundamental time p e r i o d T, the f a c t o r s K, n, I and F e t c . , we can c a l c u l a t e the im p l i e d peak ground a c c e l e r a t i o n . In making a dynamic a n a l y s i s of tha t s t r u c t u r e , the earthquake records or the response s p e c t r a should be s c a l e d to that value of i m p l i e d peak 44 g r o u n d a c c e l e r a t i o n , s o t h e s e i s m i c f o r c e s on t h e s t r u c t u r e w o u l d c o r r e s p o n d t o t h o s e u s e d i n t h e q u a s i - s t a t i c a n a l y s i s . 5. EXAMPLES As mentioned e a r l i e r , the goal of these approximate methods i s to p r e d i c t the behavior of the s t r u c t u r e s under a given earthquake motion. Since i t i s d i f f i c u l t to do an a c t u a l experiment, t e s t i n g of these methods i s done a n a l y t i c a l l y . As a ' t r u e ' n o n - l i n e a r dynamic a n a l y s i s produces the most a c c u r a t e p r e d i c t i o n of the damage p a t t e r n in the s t r u c t u r e s u b j e c t e d to a ground motion, i t i s e s s e n t i a l to check that the r e s u l t s obtained from other pseudo n o n - l i n e a r a n a l y s i s methods, are comparable to those of the time-step a n a l y s i s . For t h i s purpose, two i d e a l i z e d t e s t frames and a r e a l s t r u c t u r e were analyzed by a l l these methods i.e.. Edam, S t a t i c Damage E v a l u a t i o n Method and Freeman's Method. Then, the same s t r u c t u r e s were an a l y z e d by a time-step a n a l y s i s program DRAIN-2D and the r e s u l t s were compared. The extent of the damage rep r e s e n t e d by d u c t i l i t y demands and the l o c a t i o n of the damage a r e of i n t e r e s t to a d e s i g n e r . In the i d e a l i z e d t e s t s t r u c t u r e s , member s i z e s and the dimensions were chosen so that they represent a c t u a l small to medium s i z e d r e i n f o r c e d concrete s t r u c t u r e s . The f o l l o w i n g assumptions were made in the m o d e l l i n g of the s t r u c t u r e s : - the model i s based on cr a c k e d concrete s e c t i o n s , the cracked transformed moment of i n e r t i a f o r the columns was taken as one-half of the gross s e c t i o n moment of i n e r t i a , while the c r a c k e d transformed moment of i n e r t i a f o r the beams and the shear w a l l s e c t i o n s was taken as o n e - t h i r d 45 46 of the gross s e c t i o n moment of i n e r t i a . As per the c u r r e n t code f o r concre t e design CAN3-A23.3-M77, the load f a c t o r on seismic loads, a i s taken as 1.8 in the S t a t i c Damage E v a l u a t i o n method, and the c a p a c i t y r e d u c t i o n f a c t o r 0 f o r f l e x u r e has been taken as 0.9, thus the y i e l d f o r c e s are approximately twice the code seismic f o r c e s . In Edam, the cu r v a t u r e d u c t i l i t i e s are based on an assumed p l a s t i c hinge l e n g t h of 0.05 times the member le n g t h , which in most cases i s approximately equal to the member depth. On the other hand, i n the S t a t i c Damage E v a l u a t i o n method, i f the user inputs the member depth, the p l a s t i c hinge l e n g t h i s taken as one-half the member depth, otherwise i t d e f a u l t s to 0.05 times the member l e n g t h . In the S t a t i c Damage E v a l u a t i o n method, the l a t t e r o p t i o n i s chosen so that the r e s u l t s can be compared with those from Edam. Since the S t a t i c Damage E v a l u a t i o n method a p p l i e s the code seismic f o r c e s on the s t r u c t u r e , the NBCC spectrum i s chosen f o r Edam and Freeman's method. For the time-step a n a l y s i s four earthquake records were chosen; they were E l Centro NS, E l Centro EW, T a f t N21E and T a f t S69W. As d i s c u s s e d i n the l a s t chapter, ground motions have to be s c a l e d to peak i m p l i e d ground motion so that the f o r c e s correspond to the code seismic f o r c e s . Thus a peak i m p l i e d ground motion of 0.21g was taken which corresponds to the fundamental p e r i o d of the s t r u c t u r e s being t e s t e d . The d u r a t i o n of each earthquake r e c o r d was taken i n a manner so 47 that the maximum damage i n the s t r u c t u r e occured d u r i n g that d u r a t i o n . Unless otherwise mentioned, the f i r s t 10 seconds of the earthquake records were taken f o r the a n a l y s i s . The s i z e of the time-step was taken to be approximately one-tenth of the time p e r i o d of the s i g n i f i c a n t mode of the s t r u c t u r e e.g. i n a s t r u c t u r e , i f we assume that the response i s mainly due to the f i r s t three modes, then the s i z e of the time step w i l l be taken as one-tenth of the time p e r i o d of the s t r u c t u r e i n the t h i r d mode. In the examples below, the s i z e of the time step i s taken as 0.02 seconds unless noted otherwise. Then, the average of four time-step analyses was taken to compare with the r e s u l t s of other methods. 4 8 5.1 TEST STRUCTURE 1 The t w o - b a y , . f o u r - s t o r y frame o f F i g . 5.1 was u s e d as a t e s t s t r u c t u r e . B o t h bays a r e 30 f e e t wide and a l l t h e s t o r i e s a r e 12 f e e t h i g h . F l o o r w e i g h t f o r e a c h o f t h e s t o r i e s i s t a k e n a s 100 k i p s . The f i r s t and s e c o n d s t o r y beams a r e b i g g e r t h a n t h e t h i r d and f o u r t h s t o r y beams. The s i z e of t h e c o l u m n s i s t h e same t h r o u g h o u t . The g r a v i t y l o a d i s 1.1 k i p / f t on a l l t h e beams as a u n i f o r m l y d i s t r i b u t e d l o a d . The f u n d a m e n t a l p e r i o d o f t h e s t r u c t u r e was 1.32 s e c o n d s . Response h i s t o r i e s o f t h e t e s t s t r u c t u r e t o t h e f o u r e a r t h q u a k e r e c o r d s , m e n t i o n e d e a r l i e r , were computed by t h e computer program DRAIN-2D. R e s u l t s of t h e n o n - l i n e a r a n a l y s e s a r e shown i n F i g . 5.2 . The c u r v a t u r e d u c t i l i t y demands have been c a l c u l a t e d f r o m t h e max. v a l u e s o f t h e p l a s t i c h i n g e r o t a t i o n , r e c o r d e d i n t h e r e s p o n s e h i s t o r y . The mean maximum r o o f d i s p l a c e m e n t was 4.37 i n c h e s . The c u r v a t u r e d u c t i l i t y demands i n f i g . 5.2, c o r r e s p o n d t o t h e l a r g e r of t h e two d u c t i l i t y demands f o r e a c h member. F i g . 5.3(a) shows t h e a v e r a g e o f f o u r n o n - l i n e a r a n a l y s e s . F i g . 5.3(b) shows t h e c u r v a t u r e d u c t i l i t y demands as o b t a i n e d from Edam. The r o o t sum s q u a r e r o o f d i s p l a c e m e n t i n t h i s c a s e was 5.4 i n c h e s . C o n v e r g e n c e was a c h i e v e d a f t e r 11 i t e r a t i o n s and t h e f i n a l t i m e p e r i o d of t h e s t r u c t u r e was 1.81 s e c o n d s . F i g . 5 . 3 ( c ) shows t h e c u r v a t u r e d u c t i l i t y demands as g i v e n by S t a t i c Damage E v a l u a t i o n method, w i t h t h e s e n s i t i v i t y i n d e x f o r t h e member, shown i n t h e b r a c k e t s . H e r e , t h e s t r u c t u r e has been p u s h e d t o an u l t i m a t e r o o f 4 9 displacement of 5 . 5 7 inches. F i n a l l y , F i g . 5 . 3 ( d ) shows the r e s u l t s given by Freeman's method. Here, the e f f e c t i v e time p e r i o d at the maximum response was 1 . 8 6 seconds. If we compare the r e s u l t s , i t i s seen that the pseudo n o n - l i n e a r a n a l y s i s methods have c o r r e c t l y p r e d i c t e d , when compared to the n o n - l i n e a r a n a l y s i s r e s u l t s , that the columns on the f i r s t s t o r y would y i e l d and a l s o , that a l l the beams would s u f f e r damage. The v a r i a t i o n i n the cu r v a t u r e d u c t i l i t y demands i s w i t h i n 2 0 % of the valu e s computed from the n o n - l i n e a r a n a l y s i s r e s u l t s . 5 0 My " 115 k - f t n 5 (N CM 135 1 1 5 CM 135 1 25 135 125 165 W W 30' 1 35 1 1 5 135 125 135 125 165 TO 30' 135 135 135 165 W W E = 3760 k s i F l o o r weight i s 100 kips at a l l l e v e l s G r a v i t y l o a d on a l l beams i s 1.1 k / f t Beams F i r s t and second s t o r y T h i r d and f o u r t h s t o r y Columns S i z e 18" X 18" 15" X 18" 20" X 20" F i g . 5.1. TEST STRUCTURE 1 51 3.0 2.55 3.9 3.92 4.14 4. 1 3.4 3.28 2.24 3.1 E l Centro NS 3.87 4.22 5.48 5.46 6.15 .6. 1 1 .06 4.79 1 .8 4.7 9 4.5 4.6 : 3. 1 T a f t N21E 4.8 4.9 6.67 6.62 6.7 6.63 1 .05 1 .7 5.43 5.43 8.96 9.1 E l Centro EW 3.2 3.5 4.81 4.8 4.84 4.85 4. 1 1.15 4.3 3.2 3.15 T a f t S69W F i g . 5.2. TIME-STEP ANALYSIS RESULTS ( c u r v a t u r e d u c t i l i t i e s ) 5.2 5.2 5.4 5.4 4.4 1.55 4.4 4.7 5.0 F i g . 5.3(a). AVERAGE OF TIME-STEP ANALYSES (cu r v a t u r e d u c t i l i t i e s ) 2.8 2.5 3.6 3.5 4.1 4.0 3.8 3.7 6.6 6.0 7 F i g . 5.3(b). EDAM : CURVATURE DUCTILITIES 3.8(3.6) 3.4(3.8) 5.0(4.4) 5.0(4.4) 5.8(5.5) 5.8(5.7) 5.1(6.5) 5.0(6.7) 3.5(9.0) 3.8(8.7) 3.8(9.0) F i g . 5.3(c). STATIC DAMAGE METHOD : CURV. DUCT. ( ) S e n s i t i v i t y Index P R E D I C T E D R E S P O N S E P E R I O O ( S E C ) 1 . 8 S S P E C . A C C L ( G ) 0 . 1 7 2 D A M P I N G ( % ) 3 . 0 S P E C . D I S P ( F T ) 0 . 4 8 2 D U C T I L I T Y D E M A N D 4 . 1 I N E L A S T I C C A P A C I T Y 6 4 U S E D R E S E R V E C A P A C I T Y 3 6 F i g . 5.3(d). RESULTS FROM FREEMAN'S METHOD 54 5.2 TEST STRUCTURE 2 The three-bay, t h r e e - s t o r y frame of F i g . 5.4 was taken as the second t e s t s t r u c t u r e . The width of a l l the bays i s 20 f e e t . The f i r s t s t o r y i s 17 f e e t high, while the second and t h i r d s t o r i e s are 12 f e e t h i g h . The f l o o r weights are 100 kips for the f i r s t and second f l o o r s and 85 kips f o r the top f l o o r . A l l the beams are of the same s i z e and so are the columns. Member p r o p e r t i e s and y i e l d moments are shown i n F i g . 5.4 . The g r a v i t y l o a d i s 1.0 k i p / f t on a l l the beams as a un i f o r m l y d i s t r i b u t e d l o a d . The fundamental p e r i o d of the s t r u c t u r e was 0.89 seconds. Response h i s t o r i e s of t h i s t e s t s t r u c t u r e to the same four earthquake r e c o r d s , were computed by DRAIN-2D. R e s u l t s of the n o n - l i n e a r analyses are shown i n F i g . 5.5 . Maximum value s of the p l a s t i c hinge r o t a t i o n s d u r i n g the e n t i r e response h i s t o r y , have been converted to the cur v a t u r e d u c t i l i t y demands. The mean max. roof displacement fo r t h i s s t r u c t u r e was 2.8 inches. Again, the cu r v a t u r e d u c t i l i t y demands shown i n F i g . 5.5 correspond to the l a r g e r of the two d u c t i l i t y demands f o r each member. F i g . 5.6(a) shows the average of four n o n - l i n e a r a n a l y s e s . F i g . 5.6(b) shows the r e s u l t s from Edam. Convergence was achieved a f t e r 5 i t e r a t i o n s and the f i n a l time p e r i o d of the s t r u c t u r e was 1.1 seconds. F i g . 5.6(c) shows the r e s u l t s from the S t a t i c method, with the s e n s i t i v i t y index f o r each member shown i n b r a c k e t s . The cu r v a t u r e d u c t i l t y demand shown i n the f i g u r e s mentioned 55 above, are the l a r g e r of the two d u c t i l i t y demands f o r each member. The root-mean-square roof displacement i n Edam was 3.5 inches, while the u l t i m a t e roof displacement i n the S t a t i c method was 2.7 inches. F i g . 5.6(b) shows the r e s u l t s obtained from Freeman's method. In t h i s method, e f f e c t i v e time p e r i o d at the max. response was 1.3 seconds. F i g . 5.7(a) and 5.7(b) show the d u c t i l i t y demands in the s t r u c t u r e , i f i t i s pushed in the (-)ve x - d i r e c t i o n i . e . the seismic f o r c e s are a p p l i e d i n the (-)ve x - d i r e c t i o n . If we compare the r e s u l t s , the curvature d u c t i l i t i e s from Edam compare very well with those computed from time-step a n a l y s i s r e s u l t s . The c u r v a t u r e d u c t i l i t i e s in the s t a t i c method are g e n e r a l l y l e s s than in other methods, because the maximum roof displacement i s l e s s than i n other methods. The s e n s i t i v i t y index shows, that f o r a s l i g h t i n c r e a s e i n the u l t i m a t e roof displacement i n the s t a t i c method, the f i r s t s t o r y columns and the r i g h t hand beam in the top s t o r y w i l l have the maximum in c r e a s e i n the c u r v a t u r e d u c t i l i t y demands, as they are r e l a t i v e l y more s e n s i t i v e to the i n c r e a s e i n the l e v e l of ground motion. 5 6 CN 04 M y = 85 k - f t 85 100 110 100 1 1 0 100 125 100 125 100 125 100 160 160 160 Weight 85 kips 110 100 kips 125 100 kips 1 60 20' 20' 20' h ^— ^ >f E = 3600 k s i G r a v i t y l o a d on a l l beams i s 1.0 k / f t Beams 17.7" X 19.7"(450 X 500) Columns 19.7" X 19.7"(500 X 500) F i g . 5.4. TEST STRUCTURE 2 1 .86 1.7 2.2 2.9 3.23 5.04 4.42 5.4 3.58 4.0 4.1 E l Centro NS 2.4 3.2 1.9 3.83 4 .26 4.95 5.43 4.66 5.6 3.23 4.0 4.0 T a f t N21E 3.33 5 7 1 .33 2.2 2.42 2.83 5.83 4.56 4.72 3.24 4.02 _ 4.0 E l Centro EW 2.36 2. 1 2.9 3.33 4.0 5.9 4.77 5.7 3.83 4.4 4.4 T a f t S69W F i g . 5.5. TIME-STEP ANALYSIS RESULTS ( c u r v a t u r e d u c t i l i t i e s ) 2.0 1.75 2.78 3.23 3.75 5.55 4.6 5.36 3.47 4.1 4.05 3.5 F i g . 5.6(a). AVERAGE OF TIME-STEP ANALYSES ( c u r v a t u r e d u c t i l i t i e s ) 1.5 1.3 1 .3 2.3 2.4 2.8 1 .72 4.3 4.1 4.9 3.2 3.82 3.85 F i g . 5.6(b). EDAM : CURVATURE DUCTILITIES 0.0(12.1) 2.1(3.8) 2.0(3.8) 2.4(4.0) 4.1(5.8) 3.7(5.8) 4.3(6.3) 1.6(7.7) 2.1 (7.6) 2.1(7.7) 1.8(7.3) F i g . 5.6(c). STATIC DAMAGE EVALUATION : CURV. DUCT. ( ) S e n s i t i v i t y Index P R E D I C T E D R E S P O N S E P E R I O D ( S E C ) 1 . 3 0 S P E C . A C C L ( G ) 0 . 2 3 1 D A M P I N G ( % ) 4 . 0 S P E C . D I S P ( F T ) 0 . 3 1 6 D U C T I L I T Y D E M A N D 4 . 3 I N E L A S T I C C A P A C I T Y 7 0 U S E D R E S E R V E C A P A C I T Y 3 0 F i g . 5.6(d). RESULTS FROM FREEMAN'S METHOD 1.9 60 2.6 2.4 2.7 5.1 1 .3 4.1 4.2 3.4 3.9 3.9 . 5.7(a). EDAM : CURV. DUCT. (REVERSE SEISMIC FORCES) 0.0(11.5) 1.01(2.7) 1.9(4.5) 2.2(4.0) 2.4(4.0) 4.5(6.4) 3.8(5.9) 4.1(5.9) 11 .9(7.4) 2.3(7.7) 2.4(7.7) 1.9(7.7) 5.7(b). STATIC METHOD : CURV. DUCT. FOR REVERSE SEISMIC FORCES; ( ) S e n s i t i v i t y Index 61 5.3 TEST STRUCTURE 3 The t h i r d t e s t s t r u c t u r e analyzed i s an o f f i c e - c u m - r e s i d e n t i a l b u i l d i n g , s i t u a t e d i n downtown Vancouver. The t y p i c a l f l o o r plan i s shown i n F i g . 5.8 . A t y p i c a l f l o o r i s approximately 120' X 90'. I t c o n s i s t s of e x t e r i o r columns, at the perimeter of the b u i l d i n g , spaced at 20 to 30 feet c e n t e r s with a core of coupled shear w a l l s in the middle. The f l o o r system i s a p o s t - t e n s i o n e d f l a t r e i n f o r c e d concrete s l a b , 8" t h i c k at t y p i c a l f l o o r s . I t has three underground parking l e v e l s . A t y p i c a l o f f i c e f l o o r (mezzanine through 15) i s 11'4" high and the upper three r e s i d e n t i a l f l o o r s (16 through 18) are 9'2" h i g h . The s t r u c t u r e was modelled from the data on a r c h i t e c t u r a l and s t r u c t u r a l drawings and as d i s c u s s e d i n the p r e v i o u s chapter. The s t o r y masses were estimated by c a l c u l a t i n g the weight of the s t u c t u r a l m a t e r i a l s and assuming average uniform weight f o r p a r t i t i o n s and other m i s c e l l a n e o u s items; an allowance was made f o r heavy mechanical equipment, which i s l o c a t e d on the r o o f , where a higher uniform weight was taken. A uniform weight of 150 l b . / f t 2 was assumed on a l l f l o o r s except at the r o o f , where i t was taken to be 200 l b . / f t 2 . The grade of concrete used i s 35 MPa from f o u n d a t i o n to the 1 0 t h f l o o r , 30 MPa from 1 0 t h f l o o r to 1 5 t h f l o o r and 25 V Vi MPa from 15 f l o o r upwards. Shear w a l l t h i c k n e s s v a r i e s from 8" to 14" and column s i z e v a r i e s from 20" X 30" to 30" X 36". At the time b u i l d i n g was designed, i t was assumed 62 that the d u c t i l e c e n t r a l core would r e s i s t a l l the l a t e r a l f o r c e s on the s t r u c t u r e ; but the way the s t r u c t u r e has been modelled here, some l a t e r a l f o r c e s w i l l be r e s i s t e d by the columns. To estimate the y i e l d moment f o r a given s e c t i o n and reinforcement, the a x i a l f o r c e which i s caused by the g r a v i t y l o a d has been taken i n t o account. The numerical c o e f f i c i e n t K of the NBCC 8 to estimate the q u a s i - s t a t i c s e i s m i c f o r c e s has been taken as 1.0 . Ground motion i s assumed to be i n the N-S d i r e c t i o n . In the a n a l y s i s by Edam, the f i r s t 10 modes of the s t r u c t u r e have been c o n s i d e r e d . The fundamental p e r i o d of the e l a s t i c s t r u c t u r e was 1.11 seconds. Again, the response h i s t o r i e s of t h i s s t r u c t u r e to the same four ground motions, were computed by the time-step a n a l y s i s program DRAIN-2D. Curvature d u c t i l i t i e s c a l c u l a t e d from the response h i s t o r i e s are shown in F i g . 5.9(a) to 5.9(d). F i g . 5.10 shows the average of the time-step a n a l y s e s . Only the c o u p l i n g beams have s u f f e r e d damage; a l l the columns and shear w a l l s e c t i o n s have remained e l a s t i c d u r i n g the ground motion, hence the columns are not shown i n the f i g u r e s . The maximum average t i p d e f l e c t i o n i n the +ve x - d i r e c t i o n was 8.7", and in the -ve x - d i r e c t i o n , 3.2". F i g . 5.11 shows the cu r v a t u r e d u c t i l i t i e s as given by EDAM. Convergence was achieved i n 15 i t e r a t i o n s and the f i n a l time p e r i o d was 2.33 seconds. The root-sum-square t i p displacement was 7.4". F i g . 5.12 shows the cu r v a t u r e d u c t i l i t i e s with s e n s i t i v i t y i n d i c e s g i v e n by the S t a t i c 63 Damage E v a l u a t i o n method. The Ul t i m a t e t i p displacement i n t h i s case was 5.7". F i n a l l y , F i g . 5.13 shows the r e s u l t s from Freeman's method. In each of the methods above, none of the columns or she a r - w a l l s e c t i o n s have y i e l d e d . Curvature d u c t i l i t i e s i n a l l the methods are i n the same p a t t e r n . The d u c t i l i t y demand given by the s t a t i c method, f o r the c o u p l i n g beams of upper f l o o r s , are g e n e r a l l y l e s s compared to those given by other methods, because i n the s t a t i c method, the u l t i m a t e roof displacement i s l e s s . As we see from the above comparisons, the r e s u l t s o b t ained from approximate methods i . e . Edam and the S t a t i c Damage E v a l u a t i o n method, i n d i c a t e the same general p a t t e r n as do those from the n o n - l i n e a r a n a l y s i s , although the values are c o n s i d e r a b l y d i f f e r e n t . However, as suggested by the S t a t i c E v a l u a t i o n r e s u l t s , c o u p l i n g beams are extremely s e n s i t i v e to earthquake input. As f o r p l a s t i c hinge l e n g t h , the value of 0.05 times the span was r e t a i n e d f o r a l l methods f o r comparison with Edam, which, at the time of w r i t i n g has no other o p t i o n . In short stubby members, t y p i c a l of c o u p l i n g beams, t h i s i s probably not a good assumption, and probably g i v e s erroneous q u a n t i t a t i v e values f o r the damage r a t i o s , although the p a t t e r n should be a c c u r a t e l y r e f l e c t e d . e x t e r i o r columns T y p i c a l F l o o r P l a n F i g . 5.8. TEST STRUCTURE 3 0.0 6.6 ,0.0 , t i - ] , 6.6 . 0.0 6.5 87.9 i —I iq .q 56.2 21.0 ^2.4 ( 19.6 ,32.3! , 11.1 ,27.6, • .-, 9.4 , ( ?2.0, I 6 , 9 I 18-7 , 1.? - 3 17.6 1 1 .9 j ,17.8, , 12.0 , 1 7 . 8 12.0 ,16.9, 11.5 , 10.2 10.5 i 8 < 1 i ,4.6 , FIG. 5 . 9 ( a ) . TIME-STEP ANALYSIS : EL-CENTRO N~S COMP. (curvature d u c t i l i t i e s ) .5.1 9.5 , 5.2 , - . , 9 . 4 , . -,5.2 [ 9.1 116.2 25.8 77.4 28.3 ,76.8 27.5 52.0 17.7 49.3 i 1 6 , R i 45.1 14.6 43.0 25.4 ^8.6 22.7 ,32. 5, 19.7 ,?9-R 18.5 ! ? 6 , 9 I , 16.9 22.7 , 14.6 ,16.8, 11.5 .8.9 l 7 * 2 i -*— < i i 1 "•' i = FIG. 5.9(b). TIME-STEP ANALYSIS : EL-CENTRO E-W COMP. ( c u r v a t u r e d u c t i l i t i e s ) 0 . 0 6 . 1 , , 0 . 0 6-0 • i n . o 5 .8 8 0 . 0 1 7 . 5 , 4 8 . 6 1 8 . 0 I i 4 2 . 6 1 5 . 8 ,, 7 3 . 6 , . 7 . 9 18.4 5 . 9 , , 1 3 . 3 , I 3 ' 7 ' I I 10 -5 7 . 7 , 8 . 3 , 7 . 0 ! 10-0, 8 . 0 , 1 0 . 5 .1 l -8 . 2 10.3, 1 8 , 1 i i , 9 . 3 7 . 5 , 7 . 2 , 1 6 * 4 r — 3.1 i i 4 . 2 I I I— —' i J 1 i 1 i FIG. 5.9(c). TIME-STEP ANALYSIS : TAFT N21E COMP. (curv a t u r e d u c t i l i t i e s ) , 2.2 , 7.8 , 1 2.1 , 1 7 - 8 | ,1.9, 7.6 — l i , 96.0 21 -fi 61.9 , 23. 1 21.3 , 35.4, 12.2 1 I ,30.3, I 1 0 ' 3 I ,23.9, 7.6 ! 1 I 1 1 9 ' 7 I 12.8 r 14.4 10.4 , 15.6 11.0 i I 15.9 1 1 11.2 1 15.0, 10.6 ,12.6, 9.3 ! R.5 , 7.1 2.R 4.0 1 t" V 1 t i —i i 4 r FIG. 5.9(d). TIME-STEP ANALYSIS : TAFT S69W COMP. (curvature d u c t i l i t i e s ) 3.7* 7.5 * ... 3.7 i , 7.5, i i * , 3.7 7.3, 95.0 21.3 61 .0 22.6 i 1 57.2 21.1 . 35.8, 12.2 i i 31 .4 , , 10.6 ! 26. 1 8.2 , 23.0 14.6 19.7, 13.0 I I 19.0 12.7 18.5 12.5 17.3 11.8 14.7 10.4 10.8 8.3 ,4.9 , 8.1 ( • — i i • i i r _i i _. F i g . 5.10. AVERAGE OF TIME-STEP ANALYSES * average of o n l y two e/q r e c o r d s 70 , 6 . 6 , , 4.4 , i 6 , 8 i i i 4.5 , 7.0, , .. i i 1 4 ' 7 1 , 45.8, t 3 4 , 2 I i u. , 12.0 l l 12.4 , 27.2 9.1 ( .. 27.5, g t i 2 7 - 7I 1 1 i 9. 3 f-, 28.6, i i 14.9 ,-, 28.3, , —1 ! « 14.7 . » ,27.5,-i i , 14.2 ... , 26.2,-. - 13.6 ,. , 24.3, , i i 12.6 , i i : , 21 .7 i l ... , 11.1, 1 L , 18.2 , 9.3 , • 13.9 7.0 ,9.1 r I i 4.5 , 2.3 , , 1.1 i i 1 1 - 5 I , 0.0 , — 'i ! i i ; r .... | , FIG. 5.11. EDAM : CURVATURE DUCTILITIES 7 1 0 . 0 ( 0 . 0 ) 4 . 3 ( 7 . 2 ) . 0 . 0 ( 1 1 . 2 ) — i i — 4 . 8 ( 1 2 . 7 ) _ , , 1 . 4 ( 1 1 . 9 ) j _ 1 l , 5 . 3 ( 5 . 0 ) r— 7 . 8 ( 2 2 . 4 ) j — 1 I 9 . 7 (1 3 . 5 ) , 7 . 4 ( 1 9 . 7 ) r-l J 1 1 . 9 ( 1 7 . 0 } — , 9 . 6 ( 2 3 . 1 ) j — 1 3 . 3 ( 1 9 . 1 V — 8 . 9 ( 1 9 . 7 ) ] — 1 \ , 1 0 . 4 ( 1 5 . 3 ) , 1 0 . 6 ( 2 1 . 3 ) I 1 1 1 1 . 4 ( 1 6 . 2 ) , 1 2 . 4 ( 2 2 . 4 ) L _ 1 1 1 3 . 3 ( 1 8 . 0 ) — , 1 4 . 5 ( 2 3 . 8 Jj—_ 1 1—— , 21 . 0 ( 2 7 . 0 ) -, 1 5 . 9 ( 2 3 . 8 ) r — 1 1 — 1 2 1 . 0 ( 2 6 . 7 ) , 1 6 . 7 ( 2 3 . 2 ) , — 2 2 . 5 ( 2 5 . 9 ) , 1 7 . 0 ( 2 2 . 0 )|—-— , 2 2 . 3 ( 2 4 . 4 ) ,1 6 . 6 ( 2 0 . 2 ) ^ ' 1 1—-21 . 3 ( 2 2 . 3 ) _ , 1 5 . 4 ( 1 7 . 7 ) j _ J i i 1 9 . 5 ( 1 9 . 5 ) — , 1 3 . 2 ( 1 4 . 5 ) ^ -i l ... , 1 6 . 6 ( 1 6 . 1 ) , 1 0 . 1 ( 1 0 . 7 ) i I — i , 1 2 . 7 ( 1 1 . 9 ) , 6 . 3 ( 6 . 6 ) j — i — ' — 8 . 2 ( 7 . 6 ) r — , 1 . 8 ( 1 . 3 ) c _ i i , 0 . 0 ( 1 3 . 5 ) 3 . 4 ( 0 . 8 ) ! _ I L , 0 . 0 ( 0 . 0 ) , — , 1 . 3 ( 0 . 1 ) £ _ — j 0 . 0 ( 0 . 0 ) . j — FIG. 5.12. STATIC DAMAGE METHOD :CURVATURE DUCTILITIES ( ) S e n s i t i v i t y Index 7 2 P R E D I C T E D R E S P O N S E * * * * * * * * * * * * * * * * * * * a * * * * * * * * * * * * * - * * * * * * * * * * * ' * * PERIOD(SEC) 1.38 SPEC. ACCL(G) 0.23G • DAMPING(%) 3.0 SPEC. DISP(FT) 0.365 DUCTILITY DEMAND 3.8 INELASTIC CAPACITY 54 USED RESERVE CAPACITY 46 FIG. 5.13. RESULTS FROM FREEMAN'S METHOD 6. CONCLUSIONS Two methods f o r a n a l y s i n g the n o n - l i n e a r response of s t r u c t u r e s to severe ground motion, have been presented. One i s based on the e l a s t i c modal a n a l y s i s and the other assumes the s t r u c t u r e piece-wise l i n e a r . These methods take the y i e l d i n g i n members i n t o account and p r e d i c t a damage p a t t e r n , which i s represented here by the cu r v a t u r e d u c t i l i t y demand, that the members would see during an earthquake e x c i t a t i o n . The main use of the methods i s intended to be e i t h e r as a check on the p r e l i m i n a r y design or as a u s e f u l part of a r a t i o n a l r e t r o f i t procedure. Three d i f f e r e n t s t r u c t u r e s analyzed by these methods, have shown good agreement of r e s u l t s when compared to the r e s u l t s of a 'true' n o n - l i n e a r a n a l y s i s program DRAIN-2D. In a l l the cases, these methods are c o r r e c t l y a b l e to p r e d i c t the areas of high energy a b s o r p t i o n or the areas of high d u c t i l i t y demand. I t has proved d i f f i c u l t to determine the u l t i m a t e displacement to which the s t r u c t u r e should be pushed i n the S t a t i c Method. The r e s u l t s show t h a t the method used o f t e n seems to underestimate the value when compared with the other methods. T h i s needs f u r t h e r i n v e s t i g a t i o n , e s p e c i a l l y s i n c e the r e v i s e d Code f o r Design of Concrete S t r u c t u r e s CAN3-A23.3-M84, g i v e s s l i g h t l y d i f f e r e n t r e l a t i o n s h i p s between the y i e l d moments, d u c t i l i t y and u l t i m a t e displacement of the s t r u c t u r e i n view of the new l o a d f a c t o r s and c a p a c i t y r e d u c t i o n f a c t o r s on the m a t e r i a l s . 73 74 The l e n g t h of the p l a s t i c hinge i s e v i d e n t l y r e l a t e d to the member depth. For ease of m o d e l l i n g , i t was assumed i n w r i t i n g Edam, th a t i t would be equal to one-twentieth of span. However, i n short stubby members t h i s can le a d t o s e r i o u s e r r o r , so an o p t i o n should be pro v i d e d f o r e n t e r i n g the a c t u a l member depth to o v e r r i d e t h i s d e f a u l t v a l u e . However, the proposed methods f i l l a wide gap between the q u a s i - s t a t i c a n a l y s i s and the 'true' n o n - l i n e a r a n a l y s i s . They pr o v i d e a very e f f i c i e n t way of performing seismic a n a l y s i s , give reasonably good r e s u l t s i n comparison to a true n o n - l i n e a r a n a l y s i s and are easy to use. Only minor changes are r e q u i r e d i n the data f i l e used in the s t a t i c a n a l y s e s . These f e a t u r e s , i t i s hoped, w i l l make them popular i n the average design o f f i c e . REFRENCES 1. S h i b a t a , A. and Sozen, M.A., ' S u b s t i t u t e S t r u c t u r e Method For Seismic Design In R/C, J o u r n a l of S t r u c t u r a l D i v i s i o n , ASCE, V o l . 102, No. ST1, Jan. 1976, pp 1 - 18 2. Yoshida, Sumio 'Modified S u b s t i t u t e S t r u c t u r e Method For A n a l y s i s of E x i s t i n g R/C S t r u c t u r e s ' , Master's t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver Canada, March 1979 3. Metten, Andrew W.F. 'The M o d i f i e d S u b s t i t u t e S t r u c t u r e Method As A Design A i d For Seismic R e s i s t a n t Coupled S t r u c t u r a l W a l l s ' , Master's t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver Canada, March 1981 4. Hui, Lawrence H.Y. 'Psuedo Non-Linear Seismic A n a l y s i s ' , Master's t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver Canada, October 1984 5. Freeman, Sigmund A. ' P r e d i c t i o n of Response of Concrete B u i l d i n g s to Severe Ground Motion', The Douglas McHenry Symposium 1978, SP-55 American Concrete I n s t i t u t e , pp 589-605 6. Blume, John A, Newmark N.M. and Corning L.H., 'Design of M u l t i s t o r y R e i n f o r c e d Conrete B u i l d i n g s For Earthquake Motions', P o r t l a n d Cement A s s o c i a t i o n , Skokie I l l i n o i s , 1961 7. Gulkan, P. and Sozen M.A. 75 76 ' I n e l a s t i c Response of R e i n f o r c e d Concrete S t r u c t u r e s To Earthquake Motions', J o u r n a l of ACI, V o l . 71, No. 12, Dec. 1974, pp 604-610 8. N a t i o n a l B u i l d i n g Code of Canada 1980, issued by N a t i o n a l Research C o u n c i l of Canada, Ottawa, Canada 9. Supplement to the N a t i o n a l B u i l d i n g Code of Canada 1980, iss u e d by N a t i o n a l Research C o u n c i l of Canada, Ottawa, Canada 10. Mander, J.B. 'Seismic Design of Bridge P i e r s ' , Ph.D. t h e s i s U n i v e r s i t y of Canterbury, C h r i s t c h u r c h , New Zealand, Feb. 1984 11. Moehle, Jack P. '.Seismic A n a l y s i s of R/C Frame-wall S t r u c t u r e s ' , J o u r n a l of S t r u c t u r a l E n g i n e e r i n g , ASCE, V o l . 110 No. 11, Nov. 1984, pp. 2619-2634 12. Anderson D.L., Nathan N.D. and Cherry S. ' C o r r e l a t i o n of S t a t i c And Dynamic Earthquake A n a l y s i s of The N a t i o n a l B u i l d i n g Code of Canada 1977', Proceedings of T h i r d Canadian Conference on Earthquake E n g i n e e r i n g Montreal, Canada 1979, Vol 1, pp. 653-662 APPENDIX A EDAM  PROGRAM INPUT 1. PROBLEM INITIATION : INELAS, NMODES, NPRINT, ISPEC, AMAX, DAMPIN, KOU (415,2F10.2,15) one c a r d INELAS : Maximum number of i t e r a t i o n s f o r i n e l a s t i c a n a l y s i s ; 0 f o r e l a s t i c modal a n a l y s i s NMODES : Number of modes (^10) to be inc l u d e d i n the a n a l y s i s NPRINT : Number of modes f o r which displacements and f o r c e s w i l l be p r i n t e d ISPEC : Input spectum type :-1 = Spectrum 'A' from Shibata and Sozen 2 = Spectrum 'B' from Yoshida 3 = Spectrum 'C from Yoshida 4 = N a t i o n a l B u i l d i n g Code Spectrum 5 = San Fernando Earthquake S90W Spectrum 6 = C.I.T. Simulated Earthquake type C-2 Spectrum AMAX : Maximum ground a c c e l e r a t i o n (g) DAMPIN : E l a s t i c or i n i t i a l damping expressed as a f r a c t i o n of c r i t i c a l damping KOU : 1 = F i r s t mode f o r c e s i n +ve x - d i r e c t i o n 2 = F i r s t mode f o r c e s i n the -ve x - d i r e c t i o n (See Note 1) 77 78 2. TITLE TITLE (20A4) one c a r d Problem t i t l e of maximum 80 c h a r a c t e r l e n g t h 3. STRUCTURAL INFORMATION : NRJ, NRM, HARD, NCONJT, NCDJT, NCDOD, NCDIDS, NCDMS NRJ : Number of j o i n t s i n the s t r u c t u r e NRM : Number of members i n the s t r u c t u r e HARD : S t r a i n h a r d e n i n g r a t i o , as a p r o p o r t i o n of i n i t i a l s t i f f n e s s NCONJT : Number of ' c o n t r o l j o i n t s ' f o r which the c o - o r d i n a t e s a re s p e c i f i e d (See Note 2) NCDJT : Number of commands f o r j o i n t s c o - o r d i n a t e g e n e r a t i o n (See Note 2) NCDOD : Number of commands f o r s p e c i f y i n g j o i n t s w i t h z e r o d i s p l a c e m e n t s (See Note 3) NCDIDS : Number of commands f o r s p e c i f y i n g j o i n t s w i t h i d e n t i c a l d i s p l a c e m e n t s (See Note 4 ) NCDMS : Number of commands f o r s p e c i f y i n g lumped masses at j o i n t s (See Note 5) 4 . CONTROL JOINTS CO-ORDINATES : I J T , X, Y (I5,2F10.1) one c a r d / c o n t r o l j o i n t IJT : J o i n t number, i n any sequence X : x c o - o r d i n a t e of the j o i n t ( f t . ) Y : y c o - o r d i n a t e of the j o i n t ( f t . ) 5. COMMANDS FOR GENERATION OF JOINT CO-ORDINATES : (2I5,F10.2,5I5) one c a r d 79 Omit i f there are no generation commands IJT, LJT, NJT, KDIF (415) one card/command IJT : J o i n t number at the beginning of gen e r a t i o n l i n e LJT : J o i n t number at the end of gen e r a t i o n l i n e NJT : Number of j o i n t s to be generated along the l i n e KDIF : J o i n t number d i f f e r e n c e between two s u c c e s s i v e nodes on the l i n e ( c o n s t a n t ) . I f blank or zero assumed t o be equal to 1 COMMANDS FOR JOINTS WITH ZERO DISPLACEMENTS : Omit i f no j o i n t s r e s t r a i n e d to have zero displacements IJT, KDOF(1), KD0F(2), KDOF(3 ) , LJT , KDIF (13,518) one card/command IJT : J o i n t number, or f i r s t j o i n t i n the s e r i e s covered by t h i s command KD0F(1) : Code f o r X displacement, 0 i f r e s t r a i n e d from displacements i n x d i r e c t i o n , 1 i f free to d i s p l a c e KDOF(2) : Code f o r Y displacement KDOF(3) : Code f o r r o t a t i o n LJT : Last j o i n t i n t h i s s e r i e s , punch 0 or leave blank f o r a s i n g l e j o i n t KDIF : J o i n t number d i f f e r e n c e between s u c c e s i v e j o i n t s i n t h i s s e r i e s ( c o n s t a n t ) , i f blank or zero assumed to be equal to 1 COMMANDS FOR JOINTS WITH IDENTICAL DISPLACEMENTS : Omit i f no j o i n t s r e s t r a i n e d to have i d e n t i c a l 80 d i splacements MDOF, NJT, IJOINT(NJT) (215,1415) one card/command MDOF : Displacement code for x displacement 2 for y displacement 3 for r o t a t i o n NJT : Number of j o i n t s covered by t h i s command (max. 14) IJOINT : L i s t of nodes covered by t h i s command, i n i n c r e a s i n g order 8. MEMBER INFORMATION : MN,JNL,JNG,KL,KG,E,G,AREA,CRMOM,BMCAP,EXTL,EXTG,AV (515,2F10. 1,F8.1,2F10.1,3F6.2) one card/member MN : Member number JNL : Lesser j o i n t number JNG : Greater j o i n t number KL : F i x i t y code at l e s s e r j o i n t 0 : Pinned 1 : F i x e d KG : F i x i t y code at g r e a t e r j o i n t E : Young's Modulus ( k s i ) G : Shear Modulus ( k s i ) (0 i f shear d e f l e c t i o n s are to be neglected) AREA : C r o s s - s e c t i o n a l area of the member ( i n 2 ) CRMOM : Moment of i n e r t i a of the member ( i n " ) BMCAP : Y i e l d moment of the member ( k - f t ) 81 EXTL : R i g i d extension on the l e s s e r end j o i n t of the member ( f t . ) EXTG : R i g i d extension on the g r e a t e r end j o i n t of the member ( f t . ) AV : Shear area of the member ( i n 2 ) (0 i f shear d e f l e c t i o n s are to be neglected) Note : If E, G, AREA, CRMOM, BMCAP, EXTL, EXTG, AV are l e f t blank or given zero for a member, same values as for the previous member w i l l be assumed. 9. COMMANDS FOR LUMPED MASSES AT THE JOINTS : IJT, WTX, WTY, WTR, JJT, KDIF (15,3F10.2,215) one card/command IJT : J o i n t number or f i r s t j o i n t i n a s e r i e s covered by t h i s command WTX : Weight a s s o c i a t e d with x-displacement (kip) WTY : Weight a s s o c i a t e d with y-displacement (kip) WTR : R o t a t i o n a l weight JJT : Number of l a s t j o i n t i n the s e r i e s , punch 0 or leave blank f o r a s i n g l e j o i n t KDIF : J o i n t number d i f f e r e n c e between s u c c e s s i v e j o i n t s i n t h i s s e r i e s ( c o n s t a n t ) , i f blank or zero assumed to be equal to 1 10. STATIC LOAD INFORMATION : NJLS, NLGCJ, NML, NLGCM (415) one c a r d NJLS : Number of j o i n t s loaded by s t a t i c loads NLGCJ : Number of generat i o n commands f o r s t a t i c loads 82 a p p l i e d d i r e c t l y at the nodes (See Note 6) NML : Number of members loaded by un i f o r m l y d i s t r i b u t e d s t a t i c load NLGCM : Number of gen e r a t i o n commands f o r s t a t i c loads on the members (See Note 6) 11. Cards 11A and 11B are omitted i f NJLS i s zero. A. COMMANDS FOR STATIC LOADS APPLIED DIRECTLY ON THE  JOINTS : Omit i f NLGCJ i s zero FX, FY, FM, NNOD, NODN(NNOD) (3F10.1,1015) one card/command FX : Load i n x - d i r e c t i o n (kip) FY : Load i n Y - d i r e c t i o n (kip) FM : Moment ( k - f t ) NNOD : Number of j o i n t s to be covered by t h i s command NODN : L i s t of j o i n t s covered by t h i s command i n i n c r e a s i n g order O R B. STATIC LOADS APPLIED DIRECTLY AT JOINTS : input t h i s i f NLGCJ = 0 N, FX, FY, FM (15,3F10.1) one card/loaded j o i n t N : Node number FX : Load i n the x - d i r e c t i o n ( k i p) FY : Load i n the y - d i r e c t i o n ( k i p ) FM : Moment ( k - f t ) NOTE : ONLY CARDS 11A OR 11B ARE TO BE INPUT IN THE 83 DATA, NOT BOTH. Cards 12A and 12B to be omitted i f NML equals z e r o . A. COMMANDS FOR STATIC MEMBER LOADS : Omit i f NLGCM i s zero. W, NMEM, MR (NMEM) (F6.1,1415) one card/command W : Uniformly d i s t r i b u t e d l o a d on the member ( k / f t ) , downward load p o s i t i v e NMEM : Number of members covered by t h i s command MR : L i s t of members covered by t h i s command i n i n c r e a s i n g order OR B. STATIC MEMBER LOADS : Omit i f NLGCM i s not zero. MMR, W (I5,F10.4) one card/loaded member MMR : Member number W : Uniformly d i s t r i b u t e d s t a t i c l o a d ( k i p / f t ) NOTE : ONLY CARDS 12A OR 12B TO BE INPUT IN THE DATA WHEN NML IS NOT ZERO, NOT BOTH. 1 c 2 C 3 C 4 C •••••* MODAL ANALYSIS PROGRAM * EDAM3 •••••+ 5 C 6 C ORIGINAL PROGRAM TITLED MSSM.S BY" SUMIO YOSHIDA 1979 7 C FIRST EDITION TITLED EDAM BY ANDREW W.F. METTEN 1981 8 C SECONO EDITION TITLED EDAM2 BY LAWRENCE H.Y. HUI 1984 9 C THIRD- EDITION TITLED E0AM3 BY SUBODH KUMAR MITAL 1985 10 C * ' * 1 1 c 12 C PROGRAM DIMENSIONED FOR A MAXIMUM OF :-13 C 14 C 2S0 MEMBERS 15 C 200 JOINTS 16 C 100 ASSIGNED MASSES 17 C 10 EIGENVALUES 18 C 300 UNKNOWNS 19 C (NUMBER OF UNKNOWNS)*(HALF BANDWIDTH) IS LESS THAN 8000 20 C 21 C • NOTE - PRITZ IS A UBC:MATRIX LIBRARY SUBROUTINE 22 C FOR SOLVING EIGENVALUES 23 C 24 C VARIABLE DEFINITIONS:-25 C 26 C KL,KG - JOINT TYPE : FIXED JOINT • 1 27 C PINNED JOINT » O 28 C AREA - CROSS-SECTIONAL AREA 29 C CRMOM - MOMENT OF INERTIA OF CRACKED SECTION 30 C BMCAP • BENDING MOMENT CAPACITY OF SECTION 31 C DAMRAT ' DAMAGE RATIO OF MEMBER 32 C ND D.O.F. NO. IDENTIFIED BY JOINT NO. 33 C NO(K.I) - K - 1 (X-DOF). 2 (Y-OOF). 3 (R-DOF) 34 C I • JOINT NO. 35 C NP D.O.F. NO. IDENTIFIED BY MEMBER NO. 36 C NP(K.I) - K • DOF 1 TO 6 FOR STANDARD MEMBER 37 C I - MEMBER NO. 38 C XM LENGTH OF FLEXIBLE PORTION OF BEAM IN X-OIRECTION 39 C YM LENGTH OF FLEXIBLE PORTION OF BEAM IN Y-DIRECTION 40 C DM • TRUE LENGTH OF FLEXIBLE PORTION OF BEAM 4 1 C F - LOAD VECTOR 42 C EXTL, EXTG - LENGTH OF.* RIGID END 43 C TITLE • TITLE (80 CHARACTERS) 44 C SDAMP > STRUCTURAL DAMPING 45 C AV SHEAR AREA 46 C DAMB - DAMAGE RAIO IN THE (I-1)TH ITERATION 47 C MDOF - D.O.F. NO. FOR MASSES IDENTIFIED BY MASS NO. 48 C AMASS - LUMPED MASS (IN UNITS OF WEIGHT) INDENTIFY BY 49 C D.O.F. NO. 50 C EVAL • EIGENVALUE FOR EACH.MODE 51 C EVEC • MODE SHAPE 52 C EVEC(K.I) - K - MASS NO. 53 C I " MODE NO. 54 C BETAM • SMEARED SUBSTITUTE DAMPING FOR EACH MODE 55 C LOCK - CONTROL DIFFERENT STAGE OF ITERATION. CORRESPOND TO 56 C SUBROUTINE STACHK WHICH IS USED TO STABILIZE CONVERGENCE 57 C LOCK - O • USUAL CONVERGENCE PROCEDURE 58 C 1 • BINARY SEARCH ROUTINE IN EFFECT 59 C 2 - PROGRAM CONVERGED 60 C OLDTN - STORE THE PERIOD OF THE LAST ITERATION 61 C OLOSA • STORE UPPER AND LOWER BOUND SA VALUES 62 C 63 C 64 C DOUBLE PRECISION STIFFNESS MATRIX 65 C 66 REAL*8 S(30000). DSOOOOO). DET. DRATIO, DBLE. DVL(500) 67 C 68 DIMENSION KL(250), KG(250). AREA(250). CRM0M(250). BMCAP(2S0). 69 1 ND(3.2O0). NP(6.250). XM(250). YM(250), DM(250). F(50O). 70 2 EXTL(250). EXTG(250). TITLE(20). SDAMP(250). AV(250) 71 DIMENSION DAMB(2.250), MDOFOOO). 0LDTN(2), 0LDSA(3). 72 1 DAMRAT(2.250) 73 DIMENSION AMASS(50O). EVALOO). EVEC( SCO. 10). BETAM(10). 74 1 DEFL(500), SAXIAL(250). SHEAR1(2S0). S8ML(250). 75 2 SBMG(250). VL(50O). E(250). N0ON(2O), MR(15). MML(IOO). 76 3 FEMOOO.4). G(250). SHEAR2(2SO) 77 CALL FTNCMO('EQUATE 99-SPRINT;') 78 C 79 C IUNIT DEFINES THE INPUT AND OUTPUT FILES :-80 C 81 C IUNIT-5 IS DATA SOURCE FILE 82 C IUNIT-6 IS TEMPORARY STORAGE FOR INTERMEDIATE DATA 83 C IUNIT»7 IS FINAL OUTPUT FILE 84 C IUNIT-8 IS DAMAGE RATIO FILE ( SEPARATE FROM OTHER FINAL 85 C OUTPUT FILE TO MAKE PLOTTING OF RESULTS EASIER ) 86 IUNIT • 7 87 C 88 C CALL CONTRL TO READ IN DATA OF STURCTURE. TITLE AND PROGRAM 89 C OPTIONS. 90 C 91 CALL CONTRL(TITLE. NRJ. NRM. 7, AMAX. ISPEC. OAMPIN. INELAS. 92 1 NMODES. NPRINT. HARO. KOU. NCONJT, NCDJT, NCDOD. NCDIDS. 93 2 NCDMS) 94 C 95 C IDIM DIMENSIONS THE STIFFNESS MATRIX FOR SUBROUTINES 96 C 97 IDIM - 30000 98 C 99 C CALL SETUP TO READ AND TO ECHO PRINT MEMBER AND JOINT OATA 100 C -HALF BANDWIDTH AND NUMBER OF UNKNOWNS ARE CALCULATED 101 C 102 CALL SETUP(NRM. E. G, XM, YM, DM, NO, NP, AREA, CRMOM, DAMRAT, 103 1 NRJ. AV, KL. KG, NU. NB. SDAMP. BMCAP, IUNIT, EXTL. EXTG. 104 2 NCONJT, NCDJT, NCDOD. NCDIDS) 105 C 106 C SET IFLAG EQUAL TO 1 IF ONLY ONE ITERATION IS REOUIREO 107 C HERE IFLAG IS SET EQUAL TO O 108 C 109 IFLAG • 0 1 10 C 111 C CHECK IF IDIM HAS BEEN ASSIGNED LARGE ENOUGH 112 C LSTM - LENGTH OF ONE-DIMENSIONAL STIFFNESS MATRIX 1 13 C 114 LSTM - NU • NB 115 IF (LSTM .GT. IDIM) WRITE (7.10) LSTM. IDIM 116 10 FORMAT (///'PROGRAM STOPPED'. //'LENGTH OF STIFFNESS MATRIX-', 16, CO 1 (7 1 /'PROVIDED STORAGE (IDIM)-'. 16) 1 18 IF (LSTM .GT. IDIM) STOP 119 C 120 C ICOUNT IS THE NUMBER OF TIMES MAIN MSSM SUBROUTINE IS CALI 121 C ICOUNT IS INITIALIZED TO ZERO HERE. 122 c 123 ICOUNT " 0 124 c 12S c CALL MASS TO READ AND ASSIGN MASSES TO NODES 126 c -ASSEMBLE THE MASS MATRIX : AMASS 127 c 128 CALL MASS(NU. ND. AMASS, IUNIT. NRO. MDOF. NCDMS) 129 c 130 c 131 c REASSIGN OUTPUT TO* TEMPORARY FILE 6 132 c 133 IUNIT « 6 134 135 c c 135 c IF ONLY ELASTIC ANALYSIS IS REQUIRED: RESET CONTROL FLAGS 137 c SET I FLAG"1 TO INDICATE ONLY ONE ITERATION IS REOUIRED 138 c 139 IF (INELAS .NE. 0) GO TO 20 140 WRITE (7.50) 14 1 IUNIT - 7 142 I FLAG - 1 143 WRITE (7,50) 144 145 20 CONTINUE c 146 c DO 35 KOU"1,2 147 c IF(K0U.E0.2)G0 TO 36 .148 c GO TO 38 149 C36 CONTINUE 150 C 00 37 MBR"1,NRM 151 C DAMRAT(1,MBR)°1.0 152 c DAMRAT(2.MBR)•1.0 153 c S0AMP(MSR)»0.02 154 C37 CONTINUE 155 C WRITE(7,44) 156 C44 FORMAT(///,'FIRST MODE FORCES IN THE REVERSE DIRECTION') 157 C IUNIT-6 158 C IFLAG-0 159 C38 CONTINUE 160 C 161 C SET THE MAXIMUM NUMBER OF ITERATIONS. 162 C 163 IMAX - 1 164 IF (INELAS .NE. 0) IMAX - INELAS 165 IM - IMAX - 1 166 C 167 c I • THE NUMBER OF ITERATIONS PERFORMED 168 c 169 I - 0 170 c 171 c SET LOCK TO 0 FOR NORMAL CONVERGENCE PROCEDURE 172 c 173 LOCK • 0 174 c 175 C BETA IS A FACTOR USED IN SPEEDING CONVERGENCE (0 <BETA < 1). 176 C BETA - O. EFFECTIVELY SHUTS OFF CONVERGENCE SPEEDING ROUTINE 177 C 178 BETA • O. 179 C 180 C SET ERROR RATIO OF MOMENTS OF YIELDED MEMBERS (BMERR). 181 C A VALUE OF 0.05 HERE ENSURES YIELDED MEMBERS ARE WITHIN 182 C 5 PERCENT OF THEIR CAPACITY. 183 C 184 BMERR . O.OS 185 C 186 C - SET CONVERGENCE LIMIT FOR CHANGE IN DAMAGE RATIO 187 C 188 C DAMERR - 0.01 ENSURES THAT THE MAXIMUM DAMAGE RATIO CHANGE 189 C • IN THE FINAL ITERATION IS ONE PERCENT - FOR DAMAGE RATIOS 190 C ABOVE 5.0 191 C - THOSE DAMAGE RATIOS BELOW 5.0 WILL CONVERGE TO THEIR 192 C ABSOLUTE VALUE DIFFERENCE BEING TEN TIMES THE RATIO 193 C 194 DAMERR - 0.01 195 C INITIALIZE ARRAY USED IN SPEEDING OF CONVERGENCE. 196 00 30 MEM - 1. NRM 197 OAMB(1,MEM) - OAMRAT(1.MEM) 198 DAMB(2,MEM) > DAMRAT(2.MEM) 199 30 CONTINUE 200 C 201* C 202 C FINISHED INPUT OF DATA AND INITIAL ACTIVITIES. 2C3 C BEGIN LOOP FOR MSS METHOD. 204 C 205 C 206 C 207 C INCREMENT ITERATION COUNTER :-208 C 209 40 I - I • 1 210 WRITE (IUNIT.50) 211 50 FORMAT (• '. 110('-')) 212 WRITE (IUNIT,60) I 213 60 FORMAT ('-'. 'ITERATION NUMBER', 14) 214 C 215 C CALL BUILD TO COMPUTE THE MEMBER AND GLOBAL STIFFNESS MATRIX 216 C 217 CALL BUILD(NU. NB. XM, YM. DM, NP, AREA. CRMOM, AV. E. G. DAMRAT. 218 1 KL, KG. NRM. S. IDIM, EXTL, EXTG) 219 C 220 C CALL SCHECK TO CHECK THE CONDITION OF THE STIFFNESS MATRIX 221 C 222 CALL SCHECK(S. NU, NB, IDIM, IUNIT. SRATIO) 223 C IF(K0U.E0.2)G0 TO 51 224 IF (I .GT. 1) GO TO 410 225 DO 70 IM • t, NU 226 70 VL(IM) - O. 227 C ANALYZE FOR STATIC LOADS 228 READ (5,80) NJLS. NLGCJ, NML. NLGCM 229 80 FORMAT (415) 230 WRITE (7,90) NJLS. NML 231 90 FORMAT (//. 'HO. OF JOINTS LOADED •'. 14, 5X, 232 1 'NO. OF MEMBERS LOAOEO •', 14. /) CO 233 IF ( N J L S .EO. O .AND. NML .EO. O) CO TO 400 234 IF ( N J L S .EO. O) GO TO 230 235 WRITE ( 6 . ) 0 0 ) 236 100 FORMAT (///. 'GENERATION COMMANOS FOR STATIC LOADS APPLIED TO THE 237 1N00ES'. //) 238 IF ( N L G C J .NE. O) GO TO 120 239 WRITE ( 7 . 1 1 0 ) . 240 110 FORMAT ('NONE'.. /) 24 1 GO TO 180 242 120 CONTINUE 243 WRITE ( 7 . 1 3 0 ) 244 130 FORMAT (//. 5X. ' F X ( K I P S ) ' . 6X. ' F Y ( K I P S ) ' . 6X. ' F M ( K - F T ) ' , 5X. 245 1 'NO. OF NODES'. 8X. 'LIST OF NODES'. /) 246 DO 170 I - 1. NLGCJ 247 READ ( 5 . 1 4 0 ) FX, FY. FM, NNOD. (NODN(J).J-1,NNOD) 248 140 FORMAT ( 3 F 8 . 1 . 1115) 249 WRITE ( 7 . 1 5 0 ) FX. FY, FM. NNOD. (NDDN(J).J-1,NNOD) 250 150 FORMAT (/. F 8 . 1 . 6X, F 8 . 1 . 6X. F8.1, I S . 5X. 1015) 251 DO 160 J • 1. NNOD 252 NN - NODN(J) 253 N1 • ND(1.NN) 254 N2 " ND ( 2 , NN ) 255 N3 - N0(3.NN) 256 V L ( N 1 ) » V L ( N 1 ) * FX 257 V L ( N 2 ) - V L ( N 2 ) + FY 258 V L ( N 3 ) • V L ( N 3 ) + FM 259 160 CONTINUE 260 170 CONTINUE 261 GO TO 230 262 180 CONTINUE 263 WRITE ( 7 . 1 9 0 ) 264 190 FORMAT ( 8 X . 'JN'. 8X, ' F X ( K I P S ) ' . 8X. ' F Y ( K I P S ) ' , 8X. 'FM ( K - F T ) ' , 265 1 /) 266 DO 220 1 - 1 . NJL S 267 READ ( 5 . 2 0 0 ) N. FX. FY. FM 268 200 FORMAT ( 1 5 . 3F10.2) 269 WRITE ( 7 . 2 1 0 ) N. FX. FY. FM 270 210 FORMAT ( 1 1 0 . 3 ( 8 X . F 1 0 . 2 ) ) 271 M1 • ND(I.N) 272 M2' - ND(2.N) 273 M3 - NDO.N) 274 VL(M1) - VL(M1) FX 275 VL(M2) - VL(M2) • FY 276 VL(M3) • VL(M3) + FM 277 220 CONTINUE 278 230 CONTINUE 279 IF (NML .EO. O) GO TO 360 280 WRITE ( 7 . 2 4 0 ) 281 240 FORMAT (///. 'GENERATION COMMANDS FOR MEMBER LOADS'. //) 282 IF (NLGCM . NE. O) GO TO 250 283 WRITE ( 7 . 1 1 0 ) 284 GO TO 310 285 250 CONTINUE 286 WRITE ( 7 , 2 6 0 ) 287 260 FORMAT (//, 'U.D.L. ( K / F T ) ' , SX. 'NO. OF MEMBERS'. 8X. 288 1 ' L I S T OF MEMBERS', /) 289 JM • 1 290 DO 300 I - 1, NLGCM 291 READ ( 5 . 2 7 0 ) W, NMEM, (MR(J),J-1,NMEM) 292 270 FORMAT ( F 8 . 1 . 1415) 293 WRITE ( 7 , 2 8 0 ) W. NMEM. (MR(J),J-1,NMEM) 294 280 FORMAT ( F 8 . 1 . 5X. 15. 8X. 1315) 295 00 290 J - 1. NMEM 296 MMR > MR(J) 297 MML(JM) - MMR 298 CALL GEN2(MMR, W, XM. KL. KG. NP. VL, JM. FEM) 299 JM - JM * 1 300 290 CONTINUE 301 300 CONTINUE 302 GO TO 360 303 310 CONTINUE 304 WRITE ( 7 . 3 2 0 ) 305 320 FORMAT (/. 'MEMBER NO.', IOX. ' U . D . L . ( K / F T ) ' . /) 306 DO 350 MEM - 1. NML 307 READ ( 5 , 3 3 0 ) MMR. W 308 WRITE ( 7 . 3 4 0 ) MMR. W 309 330 FORMAT ( 1 5 . F 1 0 . 2 ) 3 10 340 FORMAT ( 1 6 . 15X. F12.2) 311 MML(MEM) - MMR 312 CALL GEN2( MMR. W. XM, KL, KG. NP, VL, MEM. FEM) 313 350 CONTINUE 314 360 CONTINUE 315 C CONVERT LOAD VECTOR TO OOUBLE PRECISION 316. DO 370 IN • 1, NU 317 370 D V L ( I N ) - D B L E ( V L ( I N ) ) 318 C CALL SDFBAN TO SOLVE AX-B 319 . DRAT 10 • 1.0-16 320 C SAVE S T I F F N E S S MATRIX 321 INK - NU * NB 322 DO 380 J - 1. INK 323 380 D S ( J ) « S ( J ) 324 CALL SDFBAN(DS. DVL. NU, NB. 1. DRATIO, DET. J E X P . 1) 325 C CONVERT SOLN. VECTOR DVL TO SINGLE PRECISION 326 DO 390 J - 1. NU 327 390 D E F L ( J ) - S N G L ( D V L ( J ) ) 328 C FIND MEMBER FORCES DUE TO GRAVITY LOADS 329 CALL MEMFO(NRM. XM. YM. DM. AV. NP, OEFL. EXTL, EXTG. AREA. E. G. 330 1 I CRMOM, KL. KG. SAXIAL. SHEAR 1, SHEAR2, SBML. SBMG. NML, MML, 331 2 FEM) 332 40O CONTINUE 333 4 10 CONTINUE 334 C CALL EIGEN TO COMPUTE THE FREQUENCIES AND MODE SHAPES FOR 335 C THE SUBSTITUTE STRUCTURE 336 C 337 CALL EIGEN(NU. NB, S, IDIM, AMASS, EVAL. EVEC. NMOOES. IUNIT, 338 1 1 I SPEC, AMAX, ICOUNT, MOOF. INELAS) 339 c 340 c INSERT HEADINGS FOR ITERATION PROGRESS (FOR INE L A S T I C 341 c ANALYSIS ONLY) 342 c 343 IF ( I N E L A S .EO. 0 .OR. ICOUNT .NE. 0 ) GO TO 450 344 WRITE ( 7 . 5 0 ) 345 WRITE ( 7 , 4 2 0 ) 346 420 FORMAT (' '. //25X. ' I N E L A S T I C RESULTS'//) 347 WRITE ( 7 . 5 0 ) 348 WRITE ( 7 . 4 3 0 ) DAMERR CO 349 WRITE (7.440) 407 I FLAG • 1 3S0 WRITE (99.440) 408 IF (I .GE. IM .AND. LOCK .EO. 1) LOCK • 2 351 430 FORMAT (/. ' OAMERR • '. F5.2. /) 409 IF (LOCK .NE. 1) IUNIT - 7 352 440 FORMAT ('-'. 'ITERATION ', IX, 'NO. ABOVE OAMOIF' , 3X. 410 GO TO 40 353 1 'S MATRIX '. 2X. 'SMEAREO'/' NO.'. 5X. 'CAPACITY'. 14X, 41 1 C 354 2 'RATIO '. 2X. 'DAMPING') 412 480 CONTINUE 355 450 CONTINUE 413 WRITE (IUNIT.490) I 356 C 414 490 FORMAT ('-', SX. 'NO. OF ITERATIONS •'. 15///) 357 C AFTER 9 ITERATIONS BETA IS REASSIGNED FROM 0.0 TO 0.8 415 GO TO 540 358 C IF NO. ABOVE CAPACITY • 0. SET BETA-0.0 416 C 359 C 417 500 CONTINUE 360 IF (I .GE. 9) BETA • 0.80 418 WRITE (IUNIT.510) I 361 C IF(ISIGN.EO.O) BETA-0.0 419 510 FORMAT ('-', 5X. 'DOES NOT CONVERGE AFTER', 15. ' ITERATIONS'/// 362 C 420 1 ) 363 C DVARY - THE LARGEST DAMAGE RATIO DIFFERENCE BETWEEN THIS AND 421 GO TO 540 364 C THE LAST ITERATION 422 C 365 C 423 520 CONTINUE 366 DVARY • 0.0 424 ICOUNT - 0 367 C 425 IFLAG « 1 368 C CALL MODS - THE MAIN SUBROUTINE FOR THE MSSM 426 IUNIT - 7 369 C - 427 WRITE (IUNIT.530) 370 CALL M003(IC0UNT. ISPEC, NRJ. NRM. NU, NB. NMOOES. S. IDIM. NO, 428 530 FORMAT ('-'. 5X, 'MEMBERS DO NOT YIELD '///) 371 1 NP, XM, YM. DM, AREA. AV. CRMOM, OAMRAT. KL. KG. SDAMP, 429 GO TO 40 372 2 BMCAP, E. G. AMASS. EVEC. EVAL. AMAX. ISIGN. IUNIT. BETA. 4 30 C 373 3 BMERR. IFLAG. EXTL. EXTG. BETAM. DAMB, DVARY. INELAS. DAMPIN. 431 540 CONTINUE 374 4 NPRINT. HARD. OLOTN, OLDSA, LOCK. SAXIAL. SHEAR 1. SHEAR2. 432 WHITE (IUNIT.550) BETA. BMERR 37S 5 SBML. SBMG. OEFL. KOU) 433* 550 FORMAT ('-'. 5X. 'BETA-'. F5.3, ///5X, 'BENDING MOMENT ERROR-', 376 IF (LOCK .EO. 1) PAMERR - 0.005 434 1 FB.6///) 377 C 435 WRITE (IUNIT.560) DAMERR 378 C IF ONLY DOING ELASTIC ANALYSIS THEN STOP PROGRAM 436 560 FORMAT (' ', 'DAMAGE RATIO ERROR", F6.3) 379 IF (INELAS .EO. 0) GO TO 580 437 570 CONTINUE 380 C 438 580 STOP 381 C - OUTPUT DAMAGE RATIOS ON UNIT 8 439 END 382 C - OUTPUT NUMBER OF MEMBER IN EXCESS OF CAPACITY AND LARGEST 440 C 383 c DIFFERENCE FROM PREVIOUS ITERATION DAMAGE RATIOS 44 1 C 384 c - OUTPUT RATIO OF LARGEST TO SMALLEST NUMBER IN DIAGONAL 442 C 385 c OF STIFFNESS MATRIX (SRATIO) 443 SUBROUTINE CONTRLt TITLE, NRJ, NRM. IUNIT. AMAX. ISPEC. DAMPIN, 386 c 444 1 INELAS. NMODES. NPRINT. HARD. KOU. NCONJT. NCDJT. 387 WRITE (7.460) I. I SIGN, DVARY. SRATIO. BETAM(1) 445 2 NCDOD. NCDIDS. NCDMS) 388 WRITE (99.460) I. ISIGN. DVARY. SRATIO. BETAM(1) 446 C 389 460 FORMAT (• '. 14. 7X, 14, SX. F7.3. 2X, E10.3. 3X, F7.S) 447 C 390 c 448 C 391 c 449 DIMENSION TITLE(20) 392 c 450 C 393 c - IFLAG IS MODIFIED FROM 0 TO 1 WHEN NO MEMBER IS ABOVE CAPACITY 451 C READ IN PROGRAM OPTIONS 394 c ONE FINAL ITERATION IS PERFORMED 452 c 395 c - THE FOLLOWING LINES CHECK FOR YIELDING OF ALL MEMBERS AND THE 453 READ (5.10) INELAS, NMOOES. NPRINT. ISPEC. AMAX. DAMPIN. KOU 396 c MAXIMUM NUMBER OF ITERATIONS 454 10 FORMAT (415, 2F10.2. 15) 397 c 4S5 C DAMPIN IS THE PROPORTION OF CRITICAL OAMPING USED IN ELASTIC 398 IF (IFLAG .EO. 1 .AND. I .GE. IMAX) GO TO 500 456 C ANALYSIS OR THE FIRST ITERATION OF THE MSSM. 399 IF (IFLAG .EO. 1) GO TO 480 457 c 400 IF (I .EO. 1 .AND. ISIGN .EO. 0) GO TO 520 458 c NPRINT IS A FLAG SET IF MODAL FORCES AND DISPLACEMENTS ARE REQUIRED 401 IF (I .GE. IM) GO TO 470 459 c IF NPRINT-0 ONLY RMS FORCES ANO DISPLACEMENTS WILL BE PRINTED. 402 ADERR • ABS(DVARY) 460 c IF NPRINT IS GREATER THAN ZERO THAT NUMBER OF MODES (UP TO NMODES) 403 IF (ISIGN .EO. 0 .AND. ADERR .LT. DAMERR) GO TO 470 461 c WILL HAVE THEIR FORCES ANO DISPLACEMENTS PRINTED. 404 GO TO 40 462 c 405 c 463 c INELAS IS A FLAG INDICATING IF ONLY AN ELASTIC ANALYSIS IS REOUIRED 406 470 CONTINUE 464 c IF 1NELAS-0 THEN ELASTIC ANALYSIS ONLY WILL BE PERFORMED. CD 465 C IF INELAS IS GREATER THAN ZERO THEN THIS IS THE MAXIMUM NUMBER OF 466 C ITERATIONS THAT WILL BE PERFORMED OURING INELASTIC ANALYSIS. 467 C 468 C ECHO PRINT PROGRAM OPTIONS 469 WRITE (IUNIT.20) 470 20 47 1 WRITE (IUNIT,30) NMODES 472 30 FORMAT (' ', 'MAXIMUM NUMBER OF MODES IN ANALYSIS'. 14) 473 IF (INELAS .EO. 0) WRITE (IUNIT.40) 474 40 FORMAT (• ', 'ELASTIC ANALYSIS REQUESTED') 475 IF (INELAS .NE. 0) WRITE (IUNIT.50) INELAS 476 SO FORMAT (' '. 'INELASTIC ANALYSIS MAXIMUM ITERATIONS'', 14) 477 IF (INELAS .EO. 0) WRITE (IUNIT.60) DAMPIN 478 60 FORMAT (' '. 'FRACTION OF CRITICAL DAMPING"'. F6.4) 479 IF (INELAS .GT. 0) WRITE (IUNIT,70) DAMPIN 480 70 FORMAT (' ', 'INITIAL DAMPING RATIO" '. F6.3) 481 WRITE (IUNIT.80) NPRINT 482 80 FORMAT (' ', 'NUMBER OF MOOES TO HAVE OUTPUT PRINTED"', 13) 483 C 484 WRITE (IUNIT.90) 485 WRITE (IUNIT.100) AMAX 486 90 FORMAT ('-'. 'SEISMIC INPUT') 487 100 FORMAT ('-', 'MAXIMUM ACCELERATION"', F5.3. ' TIMES GRAVITY') 488 IF (KOU .EO. 2) WRITE (IUNIT.110) 489 1 10 FORMAT ('- IN THE REVERSE DIRECTION') 490 120 FORMAT (///I10('-')) 491 IF (ISPEC .EO. 1) WRITE (IUNIT.130) 492 IF (ISPEC .EO. 2) WRITE (IUNIT.140) 493 IF (ISPEC .EO. 3) WRITE (IUNIT,150) 494 IF (ISPEC .EO. 4) WRITE (IUNIT.160) 495 IF (ISPEC .EO. 5) WRITE (IUNIT.170) 496 IF (I SPEC .EQ. 6) WRITE (IUNIT,180) 497 IF (ISPEC .GE. 7) WRITE (IUNIT,190) ISPEC 498 WRITE (IUNIT,120) 499 130 FORMAT (' ', 'SPECTRUM A USED') 500 140 FORMAT (' '. 'SPECTRUM B USED') 501 150 FORMAT C '. 'SPECTRUM C USED') 502 160 FORMAT (' '. 'NATIONAL BUILOING CODE SPECTRUM USEO') 503 170 FORMAT (' '. 'SAN FERNANDO E/O. HOLIDAY INN. LONGITUDINAL DIRN 504 180 FORMAT (' '. 'CIT/SIMULATED EARTHOUAKE TYPE C-2 SPECTRUM') 505 190 FORMAT (' '. 'ERROR-SPECTRUM TYPE*. 13. ' IS NOT VALID') 506 IF (ISPEC .NE. 4) GO TO 230 507 DPCNT • 100.0 •• DAMPIN 508 C 509 CALL SPECTR(ISPEC. DAMPIN, 1.0. AMAX. SA, 6.283. SABND. SVBND. 510 1 SDBND) 511 C 512 WRITE (IUNIT.200) DPCNT, SABND 513 200 FORMAT (' ', F5.2. '% DAMPING SPECTRAL ACCEL. BOUND-', F6.3. 514 1 "' -G') 515 WRITE (IUNIT.210) SD8N0 516 210 FORMAT (' ', ' DISPLACEMENT BOUNO-'. F6.3, 517 1 ' IN') 518 WRITE (IUNIT.220) SVBND 519 220 FORMAT (' '. ' VELOCITY BOUNO-'. F6.3. 520 1 ' IN/SEC) 521 C 522 C READ IN TITLE 523 C 524 230 READ (5.240) (TITLE(I).I"1.20) 525 C 526 C READ IN NRJ.NRM 527 C 528 READ (5.250) NRd. NRM, HARD, NCONJT. NCDJT, NCDOD. NCDIDS, NCDMS 529 WRITE (IUNIT.260) (TITLE(I).I - 1.20) 530 WRITE (IUNIT,270) HARD 531 WRITE (IUNIT.280) 532 WRITE (IUNIT,290) NRJ, NRM 533 WRITE (IUNIT.120) 534 C 535 C 536 RETURN 537 240 FORMAT (20A4) 538 250 FORMAT (215. F10.2. 515) 539 260 FORMAT ('1', 20A4) 540 270 FORMAT (/5X. 'STRAIN HARDENING RATIO - '. F8.3) 541 280 FORMAT (///HOC*')) 542' 290 FORMAT ('-'. 'NO. OF JOINTS', ' -'. 15. 10X, 'NO. OF MEMBERS -'. 543 1 15) 544 END 545 C 546 C 547 C 548 SUBROUTINE SETUP(NRM. E, G. XM. YM. DM. ND. NP. AREA. CRMOM. 549' 1 DAMRAT, NRJ, AV. KL, KG. NU, NB. SDAMP, 8MCAP, IUNIT. 550 2 EXTL, EXTG. NCONJT, NCDJT. NCDOD. NCDIDS) 551 C 552 C • • 553 C 554 C 555 C SET UP THE FRAME DATA 556 C 557 DIMENSION KL(NRM). KG(NRM). AREA(NRM). CRMOM(NRM). SDAMP(NRM), 558 1 DAMRAT(2,NRM). AV(NRM), N0(3.NRJ). NP(6.NRM), XM(NRM), 559 2 YM(NRM). EXTL(NRM), EXTG(NRM). DM(NRM). KDDF(3), 560 3 IJ0INT(4O). G(NRM) 561 DIMENSION X(20O). Y(200). JNL(250). JNG(250). BMCAP(NRM). E(NRM) 562 C 563 C 564 C X(I) AND Y(I) IN FEET 565 C MEMBER EXTENSIONS EXTG AND EXTL ARE IN FEET. 566 C AREA(I) IN SQ. INCHES: CRMOM(I) IN INCHES**4 567 C CONVERTED TO FOOT UNITS IN ROUTINE 568 C INITIALIZE COORDINATES 569 DO 10 I • I, NRJ 570 X(I) - 999000. 571 10 Y(I) • 999000. 572 C READ CONTROL NODE CORDINATES 573 WRITE (7.20) 574 20 FORMAT (//, 'CONTROL NODE COORDINATES'. ///. 'NOOE'. 6X. 575 1 'X-COORD', 6X, 'Y-COORO', /) 576 DO 50 I • 1 , NCONJT 577 READ (5.30) IJT, X(IJT), Y(IJT) 578 30 FORMAT (15. 2F10.1) 579 WRITE (7.40) IJT, X(IJT). Y(IJT) 580 40 FORMAT (15. 2F13.3) CO CO 561 50 CONTINUE 5S2 C NODE GENERATION COMMANDS 583 WRITE (7.60) 584 60 FORMAT (///' NODE GENERATION COMMANDS'/) 585 IF (NCDJT .NE. O) GO TO 80 586 WRITE (7.70) 587 70 FORMAT (//, 'NONE') 588 GO TO 130 589 80 WRITE (7.90) 590 90 FORMAT (/2X, 'FIRST'. 4X. 'LAST', 4X. 'NO. OF'. 4X. 'NODE'. /. 2X 591 1 'NODE*. 5X. 'NODE'. 4X. 'NODES', 5X. 'DIFF'. /) 592 DO 120 I • 1. NCOJT 593 READ (5.100) IJT. LJT. NJT. KDIF 594 1O0 FORMAT (415) 595 IF (KDIF .EO. O) KDIF - 1 596 WRITE (7.110) IJT, LJT. NJT. KOIF 597 110 FORMAT (16. 318) 598 CALL GEN1(X, Y, IJT, LJT, NJT, KDIF) 599 120 CONTINUE 600 C GENERATE UNSPECIFIED JOINT COORDINATES 601 130 I « 1 602 140 I - I + 1 603 IF (I .GT. NRJ) GO TO 160 604 IF (X(I) .NE. 999000.) GO TO 140 605 IJT • I - 1 606 LJT - IJT 607 150 LJT • LJT + 1 608 IF (LJT .GT. NRJ) GO TO 160 609 IF (X(LJT) .EO. 999000.) GO TO 150 610 NJT • LJT - IJT - 1 611 CALL GENKX, Y. IJT. LJT. NJT. 1) 612 I • LJT 613 GO TO 140 614 160 CONTINUE 615 C ASSIGNING 0.0.F. TO THE NODES 616 00 170 1 - 1 . NRJ 617 DO 170 J • 1, 3 618 170 ND(J.I) • 1 619 C ZERO DISPLACEMENTS 620 WRITE (7.180) 621 180 FORMAT (/, 'ZERO DISPLACEMENT COMMANDS'. //) 622 IF (NCDOD .NE. O) GO TO 190 623 WRITE (7.70) 624 GO TO 270 625 190 WRITE (7.200) 626 200 FORMAT (/. 'FIRST', 6X. 'X'. 6X, 'Y'. 4X. 'ROTN', 4X, 'LAST'. 4X. 627 1 'NODE', /. 'NODE', 7X, 'DDF', 4X. 'DOF'. 3X. 'DOF', 4X. 628 2 'NODE', 4X, 'DIFF'. /) 629 DO 260 I - 1. NCOOO 630 READ (5.210) IJT. (KDOF(J),J"1.3), LJT. KDIF 631 210 FORMAT (615) 632 WRITE (7.220) IJT. (KOOF(J).J*1.3). LJT. KDIF 633 220 FORMAT (13. 518) 634 DO 230 J • 1. 3 635 230 NO(J.IJT) - KDOF(J) 636 IF (LJT .EO. O) GO TO 260 637 IF (KDIF .EO. O) KDIF • 1 638 NJT - (LJT - IJT) / KOIF 639 00 250 II • 1. NJT 640 IJT - IJT • KOIF 64 1 00 240 J • 1. 3 642 240 ND(J.IJT) - KDOF(J) 643 250 CONTINUE 644 260 CONTINUE 645 C IDENTICAL DISPLACEMENT 646 270 CONTINUE 647 WRITE (7.280) 648 280 FORMAT (///, 'EOUAL DISPLACEMENT COMMANDS '. /) 649 IF (NCDIDS .NE. 0) GO TO 290 650 WRITE (7.70) 651 GO TO 350 652 290 WRITE (7.300) 653 300'FORMAT (//, 'DISP'. 4X. 'NO. OF'. /, 'CODE ' . 4X. 'NODES'. 6X. 654 1 'LIST OF NODES'. /) 655 00 340 1 - 1 . NCDIDS 656 READ (5.310) MKDOF, NJT, (IJOINT(IU).IU- 1.NJT) 657 310 FORMAT (215, 1415) 658 WRITE (7,320) MKDOF, NJT. (IJOINT(IU).IU -1 .NJT) .... 659 320 FORMAT (14. 18. 6X. 1415) 660 II - IJOINTO) 661 DO 330 IM - 2, NJT 662 IK - IJOINT(IM) 663 330 ND(MKDOF.IK) - -II 664 340 CONTINUE 665 C - TO SET UP ND ARRAY 666 350 NU » 0 667 WRITE (7.400) 668 00 390 I " 1. NRJ 669 DO 380 J - 1. 3 670 IF (ND(J.I) .NE. 1) GO TO 360 671 NU - NU • 1 672 ND(J.I) - NU 673 GO TO 380 674 360 IF (ND(J.I) .NE. 0) GO TO 370 675 ND ( J,I ) - 0 676 GO TO 380 677 370 II • -ND(J.I) 678 ND(J.I) « N0(J.II ) 679 380 CONTINUE 680 WRITE (7,410) I. X(I). Y(I). (ND(J.I).J- 1.3) 681 390 CONTINUE 682 400 FORMAT (/. 3X. 'JN'. 5X. 'X-COORD'. 5X. 'Y -COORD' . 5X, 'NDX'. 683 1 'NDY', 5X, 'NDR', /) 684 410 FORMAT (14. 2F13.2. 16. 5X. 14. 5X. 14) 685 C 686 C 687 WRITE (IUNIT.580) 688 WRITE (IUNIT.590) 689 WRITE (IUNIT.60O) 690 c 691 c READ IN MEMBER DATA AND COMPUTE THE HALF BANDWIDTH (NB) 692 c HALF BANDWIDTH"MAX DEGREE OF FREEDOM-MIN DEGREE OF FREEDOM +1 693 c 694 c 695 NB - 0 696 c 09 (0 697 00 560 MBR • 1. NRM 698 READ (5.610) MN. JNL(MBR). JNG(MBR). KL(MBR), KG(MBR), E(MBR), 699 1 G(MBR). AREA(MBR). CRMOM(MBR). BMCAP(MBR), EXTL(MBR). EXTG(MBR). 700 2 AV(MBR) 701 IF (£(MBR) .EO. 0.0) E(MBR) - E(MBR - 1) 702 IF (AREA(MBR) .EO. 0.) AREA(MBR) • AREA(MBR - 1) 703 IF (CRMOM(MBR)•.EO. 0.) CRMOM(MBR) * CRMOM(MBR - 1) 704 IF (BMCAP(MBR)..EO. 0.) BMCAP(MBR) > BMCAP(MBR - 1) 705 IF (MBR .EO. 1) GO TO 420 706 IF (G(MBR) .EO. 0.) G(MBR) • G(MBR - 1) 707 IF (AV(MBR) .EO. 0.) AV(MBR) • AV(MBR - 1) 708 420 CONTINUE 709 C IF DAMAGE RATIOS ARE LESS THAN ONE SET EQUAL TO ONE 710 C 711 DAMRAT(1.MBR) - 1.0 712 DAMRAT(2,MBR) - 1.0 713 C COMPUTE MEMBER LENGTH (OM)-LENGTH BETWEEN JOINTS-RIGID EXTENSIONS 714 JL " JNL(MBR) 715 JG - JNG(MBR) 716 XM(MBR) - X(JG) - X(JL) 717 VM(MBR) - Y(JG) - Y(JL) 718 DM(MBR) - SORT ( ( XM(MBR ) ) • • 2 • (YM( MBR ) ) " 2 ) 719 EXTSUM - EXTL(MBR) * EXTG(MBR) 720 XM(MBR) « XM(MBR) • (1.0 - EXTSUM/OM(MBR)) 721 YM(MBR) " YM(MBR) • (1.0 - EXTSUM/OM(MBR)) 722 C RESET NEGATIVE VALUES OF ZERO TO ZERO 723 IF (YM(MBR) .GT. - 0.01 .AND. YM(MBR) .LT. 0.01) YM(MBR) • 0. 0 724 IF (XM(MBR) .GT. - 0.01 .AND. XM(MBR) .LT. 0.01) XM(MBR) • 0. 0 725 DM(MBR) - DM(MBR) - EXTSUM 726 c 727 c CHECK FOR NEGATIVE LENGTHS OF MEMBER 728 c (PROBABLY CAUSED BY INCORRECT USE OF MEMBER EXTENSIONS) 729 c 730 IF (OM(MBR) .GT. 0.0) GO TO 440 731 WRITE (7.430) MBR 732 430 FORMAT (' '. ///'PROGRAM HALTED:ZERO OR -VE LENGTH FOR MEMBER'. 733 1 16) 734 STOP 735 c 736 440 CONTINUE 737 c 738 YLEN - YM(M3R) 739 c 740 c PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS 741 c ON VERTICAL MEMBERS. 742 IF (EXTSUM .NE. 0.0 .AND. YLEN .GT. 0.2) WRITE (7,450) I 743 450 FORMAT (' '. -ERROR-HAVE END EXTENSIONS ON NON-HORIZONTAL 744 1 MEMBER NO.'. 13) 745 c PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON 746 c A NON FIX-FIX TYPE MEMBER 747 KLSUM > KL(MBR) * KG(MBR) 748 IF (EXTSUM .NE. 0.0 .AND. KLSUM .NE. 2) WRITE (7.460) MBR 749 460 FORMAT (' '. 'ERROR-HAVE RIGID EXTENSIONS ON HINGEO MEMBER". 14) 750 c 751 c GIVE MEMBERS INITIAL ELASTIC OAMPING 752 SDAMP(MBR) - 0.02 753 c 754 c ASSIGN MEMBER DEGREES OF FREEDOM 755 756 757 758 759 760 761 C 1 762 C 763 764 c 765 766 767 470 768 480 769 490 770 c 771 c 1 772 c 1 773 c 1 774 c 775 776 c 777 778 779 500 780 510 781 520 782 530 783 c 784 785 786 540 787 550 788 c 789 c 790 c 791 792 793 794 560 795 796 797 798 799 800 801 c 802 570 803 c 804 c 805 c 806 807 808 c 809 c 01 810 c 811 c 812 NP(1.MBR) - N0(1.JL) NP(2.MBR) • ND(2.JL) NP(3.MBR) • NDO.JL) NP(4.MBR) > ND(1.JG) NP(S.MBR) - ND(2.JG) NP(6.MBR) - ND(3.JG) DETERMINE THE HIGHEST DEGREE OF FREEDOM FOR EACH MEMBER STORING THE RESULT IN 'MAX' MAX - 0 DO 490 K • 1, 6 IF (NP(K.MBR) - MAX) 480, 480. 470 MAX • NP(K.MBR) CONTINUE CONTINUE DETERMINE THE MINIMUM DEGREE OF FREEDOM FOR EACH MEMBER,NOTE THAT FOR STRUCTURES WITH GREATER THAN 330 JOINTS INITIAL VALUE OF MIN WILL HAVE TO BE INCREASED FROM ITS PRESTENT POINT OF 1000. MIN • 1000 DO 530 K - 1, 6 IF (NP(K.MBR)) 520. 520. 500 IF (NP(K.MBR) - MIN) 510. 520. 520 MIN « NP(K.MBR) CONTINUE CONTINUE NBB » MAX - MIN + 1 IF (NBB - NB) 550. 550, 540 NB > NBB CONTINUE PRINT MEMBER DATA AND CONVERT TO FOOT UNITS. WRITE (IUNIT,620) MBR. JNL(MBR), JNG(MBR), EXTL(MBR), DM(MBR), 1 EXTG(MBR). XM(MBR). YM(MBR). AREA(MBR), CRMOM(MBR). AV(MBR), 2 BMCAP(MBR), KL(MBR), KG(MBR). E(MBR) CONTINUE DO 570 MBR - 1. NRM E(MBR) - E(MBR) • 144. G(MBR) • G(MBR) • 144. AREA(MBR) • AREA(MBR) / 144.0 AV(MBR) - AV(MBR) / 144.0 CRMOM(MBR) « CRMOM(MBR) / 20736.0 CONTINUE PRINT THE NO. OF DEGREES' OF FREEDOM AND THE HALF BANDWIDTH WRITE (IUNIT.630) NU WRITE (IUNIT.640) NB OUTPUT THE ASSIGNED DEGREES OF FREEDOM. RETURN <0 O 813 580 FORMAT (•-', 'MEMBER DATA') 814 590 FORMAT (/' MN JNL JNG EXTL LENGTH EXTG XM(FT) YM(FT) 815 1 3X. ' AREA I (CRACKED) AV. 7X. 'MOMENT' , 2X. 'KL' , IX 816 2 'KG'. 5X. ' E') 817 600 FORMAT C '. 19X. '(FEET)'. 29X. '(SO.IN)', 3X. '(IN"4)', 2X. 818 1 '(SO.IN)'. 3X. 'CAPACITY'. 13X. 'KSI') 819 610 FORMAT (515. 2F10.1. F8.1. 2F12.1. 3F6.2) 820 620 FORMAT (' '. 13.- 214, F7.3. F9.4. F7.3, 2F9.4. F8.1, F15.1, F8.: 821 1 F10.2. 213, F10.1) 822 630 FORMAT (//. 'NO.OF DEGREES OF FREEDOM OF STRUCTURE -'. 15) 823 640 FORMAT (//' HALF BANDWIDTH OF STIFFNESS MATRIX -'. 15, /) 824 ENO 825 C 826 C B27 C 828 SUBROUTINE BUILD(NU, NB. XM, YM. OM. NP. AREA, CRMOM, AV, E. G. 829 1 DAMRAT. KL, KG, NRM. S. IDIM, EXTL. EXTG) 830 831 c c 832 c 833 c 834 c - THIS SUBROUTINE WORKS IN DOUBLE PRECISION 835 c - THIS SUBROUTINE CALCULATES THE STIFFNESS MATRIX OF EACH 836 c MEMBER AND ADDS IT INTO THE STRUCTURE STIFFNESS MATRIX. 837 c - THE FINAL STIFFNESS MATRIX S IS RETURNED. 838 c - THIS SUBROUTINE IS SIMILAR TO ONE THAT WOULD BE USED IN 839 c NORMAL FRAME ANALYSIS. 840 c - DIFFERENCES INCLUDE USING CRACKED MOMENT OF INERTIA INSTEAD 84 1 c OF THE GROSS SECTION. DAMAGE RATIOS ARE USED AND FLEXURAL 842 c STIFFNESSES MODIFIED ACCORDING TO THESE RATIOS. 843 c IDIM IS THE DIMENSIONING SIZE OF THE STRUCTURE STIFFNESS MATRIX 844 c INTERNAL FOOT UNITS FOR STIFFNESS MATRIX 845 c 846 REAL'S SM(21). S(IOIM) 847 DIMENSION XM(NRM), YM(NRM), DM(NRM), NP(6.NRM). AREA(NRM). 848 1 CRMOM(NRM), AV(NRM), DAMRAT(2,NRM), KL(NRM), KG(NRM) 849 DIMENSION EXTL(NRM), EXTG(NRM), E(NRM), G(NRM) 850 REAL'S RF. GMOD. CMOMI. 0RATI(6), F, H 851 REAL'8 LONE, LONEX. LONEY, LTWO, LTWOX, LTWOY. AVI 852 REAL'8 YMI, DMI. DM2, XM2. YM2. XMI, AREAI , EMOD. XM2F. YM2F, 653 1 XMYMF 854 REAL'S DBLE 855 c 856 c ZERO STRUCTURE STIFFNESS MATRIX 857 c 858 DO 10 I - 1, IDIM 859 S(I) - 0.0000 860 10 CONTINUE 861 c 862 c 863 c BEGIN MEMBER LOOP 864 c 865 DO 200 I • 1. NRM 866 c 867 c ZERD MEMBER STIFFNESS NATRIX 868 c 869 DO 20 J • 1. 21 870 SM(O) - 0.0000 871 20 CONTINUE 872 C 873 C ASSIGN MEMBER PROPERTIES TO DOUBLE PRECESION VARIABLES 874 C CONVERT E ft G TO DOUBLE PRECISION 875 EMOD - DBLE(E(I)) 876 GMOO - DBLE(G(I)) 877 LONE • DBLE(EXTL(I)) 878 LTWO - OBLE(EXTG(I)) 879 YMI - DBLE(YM(I)) 880 DMI - OBLE(DM(I)) 881 XMI - D8LE(XM(I)) 882 AREAI • DBLE(AREA(I ) ) 883 CMOMI - OBLE(CRMOM(I)) 884 AVI - DBLE(AV(I)) 885 C 886 C OBTAIN EFFECTIVE DAMAGE RATIO FROM 'DAMCAL' 887 c 888 CALL DAMCAL(DAMRAT, DRATI, I) 889 c 890 DM2 » DMI • DMI 891 XM2 - XMI • XMI 892 YM2 - YMI • YMI 893 XMYM • XMI • YMI 894 F • AREAI • EMOD / (DMI*DM2) 895 H " 0.0000 896 c SHEAR DEFLECTIONS ARE IGNORED WHENEVER G OH AV IS ZERD. 897 IF (AV(I) .EO. 0.0 .OR. G(I) .EO. 0.) GO TO 30 898 H - 12.0D00 * EMOD * CMOMI / (AVI'GMOD*DM2) 899 30 XM2F • XM2 • F 900 YM2F • YM2 * F 901 XMYMF » XMYM » F 902 c 903 c FILL IN PIN-PIN SECTION OF MEMBER STIFFNESS MATRIX 904 c 905 SM( 1 ) • XM2F 906 SM(2) - XMYMF 907 SM(4) - -XM2F 908 SM(5) " -XMYMF 909 SM(7) • YM2F '910 SM(9) « -XMYMF 911 SM(10) • -YM2F 912 SM(16) • XM2F 913 SM(17) • XMYMF 914 SM(19) « YM2F 915 IF (KL(I) + KG(I) - 1) 100. 40. 50 916 c 917 c VALUES OF F CALCULATED HERE DIFFER FROM STANDARD BUILD 918 c SUBROUTINE BY DIVIDING BY THE DAMAGE RATIOS. 919 c 920 40 F - 3.0000 * EMOD • CMOMI / (DM2*DM2*DMI•(1.ODOO+H/4.ODOO)) 921 GO TO 60 922 50 F - 12.0000 * EMOD • CMOMI / (0M2'DM2*DMI•(1 O00O*H)) 923 c RF IS A FACTOR COMMON TO THE ENTIRE MATRIX FOR ADDITION OF 924 c STIFFNESS DUE TO RIGID BEAM END EXTENSIONS. 925 RF - 12.ODOO • EMOD • CMOMI / (DM2-DM2) / (1.D0*H) 926 c 927 c FILL IN TERMS WHICH ARE COMMON TO PIN-FIX,FIX-PIN,AND 928 c FIX-FIX MEMBERS (0 929 C 930 LONEY • LONE * YMI • RF • 0RATI(4) 931 LONEX " LONE • XMI • RF • DRATI(4) 932 LTWOY • LTWO • YMI • RF • 0RATI(5) 933 LTWOX • LTWO • XMI • RF • DRATI(5) 934 60 XM2F • XM2 • F • DRATI(6) 935 YM2F • YM2 • F • 0RATI(6) 936 XMYMF • XMYM • F • DRAT 1(6) 937 0M2F - DM2 • F 938 C 939 SM(1) • SM(1) + YM2F 940 SM(2) - SM(2) - XMYMF 941 SM(4) - SM(4) - YM2F 942 SM(S) - SM(5) • XMYMF 943 SM(7) • SM(7) + XM2F 944 SM(9) • SM(9) • XMYMF 945 SM( 10) - SM(10) - XM2F 946 SM(16) • SM(16) * YM2F 94 7 SM(17) « SM(17) - XMYMF 948 SM(19) • SM(19) • XM2F 949 IF (KL(I) - KG(I)) 70, 80. 90 950 C 951 c FILL IN REMAINING PIN-FIX TERMS 952 c 953 70 SM(6) • -YMI • DM2F • DRATI(5) 954 SM(11) • XMI • DM2F • DRATI(5) 955 SM(18) - -SM(6) 956 SM(20) - -SM(11) 957 SM(21) - DM2 • DM2F • DRAT 1(2) 958 GO TO 100 959 c 960 c FILL IN REMAINING FIX-FIX TERMS 961 c 962 80 SM(3) • -YMI • DM2F « 0.5D00 * DRATI(4) 963 SM(6) - SM(3) / DRATI(4) • DRATI(5) 964 SM(8) « XMI • DM2F • 0.5D0O " DRATI(4) 965 SM(11) • SM(B) / DRATI(4) » DRAT 1(5) 966 SM(12) • DM2 * DM2F • (4.0DOO+H) / 12.0000 • DRATI(1) 967 SM(13) - -SM(3) 968 SM(14) • -SM(8) 969 SM(15) - DM2 • DM2F * (2.0D00-H) / 12.0000 • DRATI(3) 970 SM(18) * -SM(6) 971 SM(20) - -SM(11) 972 SM(21) - SM(12) / DRATI(1) • DRATI(2) 973 c ADD IN TERMS FDR RIGID END EXTENSIONS. 974 SM(3) • SM(3) - (LONEY) 975 SM(6) « SM(6) - (LTWOY) 976 SM(8) • SM(8) • LONEX 977 SM(I1) - SM(11) + LTWOX 978 SM(12) - SM(12) • (L0NE*DMI*(DMI + LONE) *RF ) • DRATI(1) 979 SM(13) - SM(13) + LONEY 980 SMI 14) ' SM(14) - LONEX 981 SM(15) • SM(15) + ((LONE*LTWO*DMI) • (DM2*(LONE * LTW0)/2.ODOO)) 982 I • RF • DRATI(3) 983 SM(18) * SM(18) • LTWOY 984 SM(20) • SM(20) - LTWOX 985 SM(21) - SM(21) • (DM2«LTW0 + (DMI*(LTWO*LTWO))) • RF • DRATI(2) 986 GO TO 100 987 C 988 C FILL IN REMAINING FIX-PIN TERMS 989 c 990 90 SM(3) » -YMI • DM2F « DRATI(4) 991 SM(8) • XMI • DM2F • DRATI(4) 992 SM(12) - DM2 • DM2F • DRATI(1) 993 SM(13) - -SM(3) 994 SM(14) - -SM(8) 995 100 CONTINUE 996 c 997 c ADD THE MEMBER STIFFNESS MATRIX SM INTO THE STRUCTURE 998 c STIFFNESS MATRIX S. 999 c 1000 NB1 • NB - 1 1001 c 1O02 DO 190 J - 1. 6 1003 IF (NP(d.D) 190, 190. 110 1004 110 di » (J - 1) • (12 - J) / 2 1005 c 1006 DO 180 L - d. 6 1007 IF (NP(L.I)) 180. 180. 120 1008 120 IF (NP(d.I) - NP(L.D) 150. 130. 160 1009 130 IF (L - <J) 140, 150. 140 1010 140 K - (NP(L.I) - 1) • NB1 • NP(J.I) 101 1 N - U1 + L 1012 S(K) - S(K) • 2.0000 • SM(N) 1013 GO TO 180 1014 150 K • (NP(J.I) - 1) • NB1 + NP(L.I) 1015 GO TO 170 1016 160 K - (NP(L.I) - 1) * NB1 • NP(J.I) 1017 170 N • U1 + L 1018 S(K) - S(K) + SM(N) 1019 180 CONTINUE 1020 c 1021 190 CONTINUE 1022 c 1023 200 CONTINUE 1024 c 1025 RETURN 1026 END 1027 1028 c c 1029 c 1030 SUBROUTINE DAMCAL(DAMRAT, DRATI, NOM) 1031 1032 c c 1033 c 1034 c EFFECTIVE DAMAGE RATIO CALCULATION 1035 c 1036 DIMENSION DAMRAT(2.VJ0M) 1037 REAL'S DRATI(6), DBLE 1038 c 1039 DRAT 1(1) • DBLE(DAMRAT(1.NOM)) 1040 DRAT I(2) • DBLE(DAMRAT(2.NOM)) 1041 DRATIO) • 1.D0 / ( .09SD0+.2D0*(DRATI( 1) • DRATI (2)) • .50500 1042 1DRATI(1)*DRATI(2)) 1043 DRATI(1) » 1.DO / DRATI(1) 1044 DRATK2) • 1.D0 / DRATI ( 2 ) (0 1045 DRATK4) • (2.00«DRATI(1) • DRATIO)) / 3.00 1046 DRATI(S) • (2.DO*0RATI(2) + DRATIO)) / 3.00 1047 0RATK6) '- (DRATI(I) • DRAT1 (2) + 0RATI(3)) / 3.DO 1048 RETURN 1049 END 1050 1051 C c 1052 c 1053 SUBROUTINE MASS(NU. ND. AMASS. IUNIT. NRJ. MDOF. NCDMS) 1054 1055 c c 1056 c 1057 c 1058 c THIS SUBROUTINE SETS UP THE MASS MATRIX 1059 c 1060 c ND(J.I)-DEGREES OF FREEDOM OF I TH JOINT 1061 c WTX . WTY .WTR "X-MASS , Y-MASS. ROT .MASS IN FORCE UNITStKIPS OR IN-KIPS) 1062 c AMASSOI-MASS MATRIX, I IS THE DEGREE OF FREEDOM OF APPLIED MASS 1063 c 1064 c MASSES ARE LUMPED AT NODES. THE MASS MATRIX IS DIAGONAL1 ZED. 1065 c 1066 DIMENSION ND(3,NRJ). MDOF(100). AMASS(NU) 1067 c 1068 c 1069 c 1070 c ZERO MASS MATRIX 1071 c 1072 DO 10 I • 1, NU 1073 AMASStI) - 0. 1074 10 CONTINUE 1075 c 1076 WRITE (7.20) 1077 20 FORMAT (///. 'MASS GENERATION COMMANDS*. //. 'FIRST NODE'. 4X. 1078 1 'X-MASS'. 4X. 'Y-MASS', 4X. 'ROTN MASS', 3X, 'LAST NODE' 1079 2 3X. 'NODE OIFF.'. /) 1080 DO 80 I • 1. NCDMS 1081 READ (5.30) IJT. WTX. WTY, WTR. JJT. KDIF 1082 30 FORMAT (15. 3F10.2. 215) 1083 WRITE (7.40) IJT, WTX, WTY. WTR. JJT. KDIF 1084 40 FORMAT (15. 3X. 3F10.2. 4X. 15. 8X. IS) 1085 IF (KDIF .EO. 0) KDIF - 1 1086 IF (JJT .EO. 0) GO TO 50 1087 NJT • (JJT - IJT) / KDIF + 1 1088 GO TO 60 1089 50 NJT » 1 1090 60 CONTINUE 1091 DO 70 J • 1 . NJT 1092 N1 • ND(1.IJT) 1093 N2 - ND(2.IJT) 1094 N3 - NDO.IJT) 1095 AMASS(NI) - AMASS(NI) * WTX / 32.2 1096 AMASS(N2) • AMASS(N2) + WTY / 32.2 1097 AMASS(N3) - AMASS(NS) + WTR / 32.2 1098 IJT • IJT • KDIF 1099 70 CONTINUE 1 100 80 CONTINUE 1 101 c 1 102 c OUTPUT THE DEGREES OF FREEDOM WITH MASS ANO ASSIGNED MASS . 103 C 104 JCNT • 1 105 WRITE (IUNIT.100) 106 C 107 DO 90 IDOF - 1. NU 108 RMASS • AMASS(IDOF) 109 IF (RMASS .EO. 0.0) GO TO 90 110 MDOF(JCNT) - IDOF 111 WRITE (IUNIT.110) JCNT. MDOF(JCNT). RMASS 112 JCNT • JCNT + 1 113 90 CONTINUE 1 14 C 115 100 FORMAT ('-'. 'MASS NO. DOF'. 2X. 'ASSIGNED MASS (KIP"SEC"'2/FT)') 116 110 FORMAT (' '. 2X. 13. 3X. 13, 9X. F10.5) 117 RETURN 118 120 FORMAT (15) 119 130 FORMAT (///110(""1) 120 140 FORMAT ('-', 'NO. OF NODES WITH MASS'. ' -'. 15) 121 150 FORMAT (/7X. 'JN'. 3X, 'X-MASS*. 4X. 'Y-MASS'. 2X, 'ROT.MASS') 122 160 FORMAT (' '. 12X. '(KIPS)'. 4X. '(KIPS)'. 2X. '(IN-KIPS)') 123 170 FORMAT (15, 3F10.0) 124 180 FORMAT (' '. 5X. 14. 3F10.3) 125 END 126 C 127 C 128 C 129 SUBROUTINE EIGEN(NU, NB. S. IDIM. AMASS. EVAL. EVEC. NMODES, 130 1 IUNIT. I SPEC, AMAX, ICOUNT, MDOF, INELAS) 131 C 132 C » «•» • * • 133 C 134 C 135 C THIS SUBROUTINE COMPUTES A SPECIFIED NO. OF NATURAL FREQUENCIES 136 C AND ASSOCIATED MODE SHAPES 137 C 138 C NU»NO. OF DEGREES OF FREEDOM 139 C NB-HALF BANDWIDTH 140 C NMODES"*NO. OF MODE SHAPES TO BE COMPUTED 141 C IF NMODES IS ZERO OR IS GREATER THAN THE NUMBER OF STRUCTURE 142 C MASSES THEN NMODES WILL BE ASSIGNED THE NUMBER OF STRUCTURE 143 C MASSES. 144 C AMASS(I)-MASS MATRIX MCOUNT"NUMBER OF NONZERO MASSES 145 C S(I('STIFFNESS MATRIX STORED BY COLUMNS 146 C EVAL(I)*NATURAL FREQUENCIES 147 C EVEC( I . J)"=MODE SHAPES 148 C 149 REAL'S OVEC(500.10). DVAL(10). CMASS(SOO), SDI30000) 150 REAL*8 S(IDIM) 151 DIMENSION AMASS(NU). EVAL(NMODES). EVEC(500,NMODES). MOOF(IOO) 152 REAL'S DBLE 153 ' C 154 C ZERO DUMMY MASS MATRIX CMASS 155 DO 10 ITRY - 1. 500 156 10 CMASS(ITRY) • O.ODO 157 C 158 C COMPUTE THE NUMBER OF NONZERO MASS MATRIX ENTRIES 159 C 160 MCOUNT - O (0 u 1161 C 1162 DO 20 I • 1, NU 1 163 CMASSU) • DBLE(AMASS(I)) 1 164 IF (AMASS(I) .EO. 0.) GO TO 20 1165 MCDUNT - MCOUNT + 1 1166 20 CONTINUE 1167 IF (NMODES .GT. MCOUNT) NMODES • MCOUNT 1168 IF (NMODES .EO. 0) NMODES - MCOUNT 116S IF (IUNIT .EO. 6 .AND. ICOUNT .GT. 25) GO TO 30 1 170 WRITE (IUNIT.160) NMODES 1171 30 CONTINUE 1172 C 1 173 C CALL PRITZ TO COMPUTE EIGENVALUES AND EIGENVECTORS 1 174 C CREATE A OUPLICATE STRUCTURE MATRIX (SD) (DESTROYED IN PRITZ) 1175 C 1 176 C CALCULATE USEFUL LENGTH OF STIFFNESS MATRIX (LSTM) 1 177 LSTM - (NU) • NB 1 178 c 1 179 DO 40 I - 1. LSTM 1 180 SOU) - S(I) 1 181 40 CONTINUE 1 182 c 1183 c SET CONVERGENCE CRITERIA FOR PRITZ. MAKE NEGATIVE IF 1184 c RESIDUALS .NOT DESIRED. 1 185 c 1 186 DEPS • 1.00-10 1187 IF (IUNIT .NE. 7) DEPS « (-1.000) * OEPS 1188 c 1189 c CALL EIGENVALUE FINOING ROUTINE 1190 CALL PRITZ(SO. CMASS. NU. N8. 1. OVAL. DVEC. 500. NMODES. DEPS. 1191 1 &140) 1192 c 1193 c CONVERT MATRICES TO SINGLE PRECESION 1194 c 1 195 c PRINT EIGENVALUES AND EIGENVECTORS(MODE SHAPES) 1 196 c EIGENVALUES (EVAL) ARE THE VALUES OF OMEGA SOUARED. 1197 c 1198 c SKIP PRINTING INTERMEDIATE DATA AFTER SEVERAL CYCLES. 1199 IF (ICOUNT .GT. 3 .AND. IUNIT .EO. 6) GO TO 70 1200 WRITE (IUNIT.17C) 1201 c WRITE (IUNIT.210) NMODES 1202 c WRITE (IUNIT. 230HI.I-1. NMODES) 1203 c DO 60 ID-1.NU 1204 c WRITE(IUNIT.SO) ID.(DVEC(IO.J), J*1.NMODES) 120S 50 FORMAT (• ', 13, 10F11.6) 1206 60 CONTINUE 1207 c 1208 70 CONTINUE 1209 c CONVERT MEM8ERS OF EVAL FROM OMEGA SOUARED TO OMEGA 1210 c 1211 c CONVERT EIGENVECTORS TO ONLY INCLUDE DEGREES OF FREEDOM 1212 c WITH MASS ASSIGNED TO THEM 1213 DO 80 MAS • 1. MCOUNT 1214 IVAR • MDOF(MAS) 1215 00 80 MOD • 1, NMODES 1216 EVEC(MAS.MOO) • SNGL(OVEC(IVAR.MOD)) 1217 80 CONTINUE 1218 c 1219 IF (ICOUNT .EO. 0) WRITE (7.90) 1220 90 FORMAT (• ', //' INITIAL ELASTIC PERIOD ') 1221 IF (ICOUNT .EO. O) IUNIT • 7 1222 WRITE (IUNIT.180) 1223 WRITE (IUNIT,190) 1224 C 1225 C COMPUTE FREQUENCIES AND PERIODS 1226 DO 100 JUICE • 1, NMODES 1227 100 EVAL(JUICE) - SNGL(DVAL(JUICE)) 1228 C 1229 DO 110 I " 1. NMODES 1230 EVAL1 " EVAL(I) 1231 EVAL(I) • SORT(EVALI) 1232 WN • EVAL(I) 1233 PERIOD ' 6.283153 / WN 1234 FREQ » 1 / PERIOD 1235 IF (ICOUNT .GT. 25 .AND. IUNIT .EO. 6) GO TO 110 1236 CALL SPECTR(ISPEC. 0.02. PERIOD. AMAX. SA. WN. SABND. SVBND. 1237 1 SDBNO) 1238 WRITE (IUNIT.200) I. EVAL1, EVAL(I). FREO. PERIOD, SA 1239 110 CONTINUE 1240 IF (ICOUNT .EQ. O .AND. INELAS .NE. 0) IUNIT « 6 1241 C 1242 IF (ICOUNT .GT. 5 .AND. IUNIT .EO. 6) GO TO 130 1243 C WRITE (IUNIT.220) NMODES 1244 C WRITE (IUNIT.240)(I,1-1.NMODES) 1245 C DO 120 1-1.MCOUNT 1246 C WRITE (IUNIT.50) I,(EVEC(I.J).J-1.NMODES) 1247 120 CONTINUE 1248 C 1249 130 CONTINUE 1250 C 1251 RETURN 1252 140 WRITE (IUNIT.150) 1253 150 FORMAT (' ', 'CRAPOUT IN PRITZ') 1254 160 FORMAT ('-'. 'NO. OF MODES TO BE ANALI ZED -'. IS///1 IOC *')///) 1255 170 FORMAT (///HOC*')) 1256 180 FORMAT (/5X. 'MODES'. 4X. 'EIGENVALUES'. 6X. 'NATURAL FREQUENCIES' 1257 1 , 13X. 'PERIODS'. IOX. 'SA') 1258 190 FORMAT (' '. SOX. '(RAD/SEC)'. 5X. ' (CYCS/SEC)'. 8X. '(SECS)'. 4X. 1259 1 '(2 PERCENT DAMPING)') 1260 200 FORMAT (' '. 5X, 15. 5F15.4) 1261 210 FORMAT (/'TOTAL MODE SHAPES CORRESPONDING TO FIRST'. IS, IX. 1262 1 'FREQUENCIES') 1263 220 FORMAT (/'MASS MODE SHAPES CORRESPONDING TO FIRST'. 15. 1X, 1264 1 'FREQUENCIES') 1265 230 FORMAT (/' DOF'. 18. 9111) 1266 240 FORMAT (/'MASS', 10111) 1267 250 FORMAT (' '. 10F12.6) 1268 RETURN 1269 END 1270 C 1271 C * * 1272 C •1273 SUBROUTINE M0D3( ICOUNT. ISPEC, NRJ. NRM. NU. NB. NMODES. S. IDIM. 1274 1 ND. NP. XM, YM, DM. AREA. AV. CRMOM. DAMRAT. KL. KG. 1275 2 SDAMP, BMCAP, E. G, AMASS. EVEC. EVAL, AMAX, IS1GN. 1276 3 IUNIT, BETA. BMERR. 1F LAG. EXTL. EXTG, BETAM, OAMB, CO 1277 4 OVARY. INELAS. DAMPIN, NPRINT, HARD,* OLDTN, OLDSA. 1278 S LOCK, SAXIAL, SHEAR 1, SHEAR2, SBML, SBMG, DEFL, KOU) 1279 C 1280 C ............................................... 1281 C 1282 C SUBSTITUTE STRUCTURE METHOD FOR RETROFIT 1283 C 1284 C THIS SUBROUTINE COMPUTES JOINT DISPLACEMENTS AND MEMBER FORCES 1285 C NEW DAMAGE RATIOS' WILL BE CALCULATED AND RETURNED. 1286 C 1287 REAL*8 S(IDIM), DF(500), ORATIO; DET 1288 C 1289 DIMENSION NOO.NRJ) . NP(6,NRM), XM(NRM), YM(NRM), DM(NRM). 1290 1 AREA(NRM), CRMOM(NRM), DAMRAT(2,NRM), KL(NRM). KG(NRM), 1291 2 EVEC(500,NMODES), EVAL(NMODES), SDAMP(NRM), AV(NRM), 1292 3 AMASS(NU) 1293 DIMENSION BMASS(500), IDOF(SOO). ALPHA(20). RMS(8.250). F(500), 1294 1 EXTL(NRM). EXTG(NRM). BMCAP(NRM). DAMB(2,NRM), 1295 2 BETAM(NMODES). 0LDTN(1). 0LDSA(1) 1296 DIMENSION OEFL(NU). SAXIAL(NRM). SHEAR 1(NRM) , SBML(NRM), 1297 1 SBMG(NRM). MSIGN(250.2), E(NRM). G(NRM), SHEAR2(NRM), 1298 2 FC0(5OO). BMLCD(250), 8MGCD(250) 1299 C CALCULATE THE MODAL PARTICIPATION FACTOR :-1300 C 1301 C J J • TEMPORARY VARIABLE USED IN THE FOLLOEWING LOOP ONLY 1302 J J • 1 1303 C 1304 00 10 JDOF • 1 , NU 1305 IF (AMASS(JDOF) .EO. O.) GO TO 10 1306 BMASS(JJ) • AMASS(JDOF) 1307 IDOF(JJ) • JDOF 1308 J J - J J + 1 1309 10 CONTINUE 1310 C 1311 MCOUNT • J J - 1 1312 C 1313 DO 30 MODE - 1. NMODES 1314 AMT - O. 1315 AMB • O. 1316 C 1317 C EIGEN VALUES ARE STORED AS FOLLOWS EVEC(MASS NO.,MODE NO.) 1318 C 1319 DO 20 J - 1, MCOUNT 1320 AMT • AMT + BMASS(J) « EVEC(J.MODE) 1321 AMB - AMB • BMASS(J) • ( ( EVEC( J. MODE ) ) "2 ) 1322 20 CONTINUE 1323 ALPHA(MODE) • AMT / AMB 1324 30 CONTINUE 1325 C 1326 IF (I COUNT . GT. 25 .ANO. IUNIT .EO. 6) GO TO 50 1327 WRITE (IUNIT.420) 1328 C 1329 DO 40 MODE ' 1. NMODES 1330 WRITE (IUNIT,430) MODE, ALPHA(MODE) 1331 40 CONTINUE 1332 50 CONTINUE 1333 C 1334 C WHEN KK"1. MODAL FORCES FOR UNDAMPED SUBSTITUTE STRUCTURE ARE 1335 C COMPUTED. THEY ARE USED TO COMPUTE 'SMEARED' DAMPING VALUES, 1336 C WHICH ARE USED TO CALCULATE THE ACTUAL RESPONSE DF THE 1337 C SUBSTITUTE STRUCTURE 1338 C 1339 1340 INDEX - 1 C 1341 DO 410 KK " 1, 2 1342 C 1343 C SET PRINT FLAG FOR MODAL OUTPUT (0-OFF) 1344 INTPR - 1 1345 IF (KK .EO. 1) INTPR • 0 1346 IF (IFLAG .EO. 0 .OR. NPRINT .EO. 0) INTPR • 0 1347 IF (ICOUNT .NE. 0) GO TO 70 1348 c 1349 c SET DAMPING RATIOS TO 'APPROPIATE* VALUES FOR INITIAL TRIAL. 1350 DO 60 MODEA • 1 . NMODES 1351 BETAM(MODEA) - DAMPIN 1352 60 CONTINUE 1353 c 1354 ICOUNT « ICOUNT + 1 1355 WRITE (IUNIT.450) 1356 GO TO 4 10 1357 70 SHRMS - 0. 1358 c 1359 c ZERO RMS(J.I) 1360 c 1361 DO 80 I • 1. 250 1362 DO 80 J " 1. 8 1363 RMS(J.I) • 0. 1364 80 CONTINUE 1365 c 1366 c OUTPUT THE SMEARED DAMPING RATIOS (FOR DAMPED CASES) 1367 IF (IUNIT .EO. 6 .AND. ICOUNT .GT. 25) GO TO 120 1368 IF (KK . EO. 1) GO TO 120 1369 c 1370 WRITE (IUNIT.100) 1371 c 1372 DO 90 MODE - 1. NMODES 1373 WRITE (IUNIT.110) MODE, BETAM(MODE) 1374 90 CONTINUE 1375 c 1376 100 FORMAT ('-', 'MODE'. 2X. 'SMEARED DAMPING RATIO') 1377 1378 1 10 FORMAT (' '. 1X. 13, 7X. F10.5) c 1379 c 1380 c CALCULATE THE MODAL DISPLACEMENT VECTOR 1381 c 1382 120 DO 320 MODEN • 1, NMODES 1383 c 1384 c CALCULATE NATURAL PERIOD ANO CALL SPECTA 1385 c 1386 TN - 6.28318531 / (EVAL(MODEN)) 1387 WN • EVAL(MODEN) 1388 DAMP - BETAM(MODEN) 1389 IF (MODEN .NE. 1 .OR. LOCK .EO. 0) CALL SPECTRfI SPEC. DAMP, 1390 1 TN. AMAX, SA. WN, SABND. SVBNO. SDBND) 1391 IF (MODEN .EO. 1) CALL STACHKtOLDSA, SA, OLDTN. TN. ISPEC. 1392 1 LOCK, ICOUNT, IFLAG. IUNIT. AMAX, DAMP, KK) 1393 IF (HODEN .EO. 1 .ANO. KK .EO. 2) WRITE (99.130) TN, SA 1394 IF (MODEN .EO. 1 .ANO. KK .EO. 2 .ANO. 1 FLAG .NE. 1) 1395 1 WRITE (7.130) TN. SA 1396 130 FORMAT (50X. •< PERIOD •', F6.3. 2X. 'SA -', F6.3. ' >') 1397 C 1398 C LIST MEMBER FORCES IF DOING ELASTIC ANLYSIS ONLY 1399 c 1400 IF (INTPR .EO.] 0) GO TO 150 1401 IF (NPRINT .LT. MODEN) GO TO 150 1402 WRITE (IUNIT.450) 1403 WRITE (IUNIT,140) MODEN 1404 140 FORMAT (' '. 'MODE NUMBER'. 13, ' MODAL FORCES AND OISPLACEMEN 1405 ITS') 1406 WRITE (IUNIT.440) 1407 150 CONTINUE 1408 c 1409 c CHECK IF MODAL PARTICIPATION FACTOR IS ZERO 1410 c IF ALPHA IS ZERO MODAL FORCES AND DISPLACEMENTS WILL BE ZERO 1411 c 1412 IF (ALPHA(MOOEN) .NE. 0.0) GO TO 170 14 13 WRITE (IUNIT.160) 1414 160 FORMAT (/' MODAL PARTICIPATION .FORCES AND DISPL.-ZERO') 1415 GO TO 320 1416 170 CONTINUE 1417 c 1418 c ZERO LOAD VECTOR 14 19 c 1420 DO 180 J • 1. NU 1421 180 F(J> - 0. 1422 c 1423 c COMPUTE LOAD VECTOR 1424 c 1425 FAC • SA • ALPHA(MODEN) • 32.2 1426 c 1427 c NOTE THAT AS THESE FORCES ARE BEING GENERATED FROM A 1428 c LATERAL EXCITATION SPECTRUM THAT ONLY 'X MASSES' SHOULD 1429 c BE USEO. IN OTHER WORDS LATERAL ACCELERATION SHOULD NOT 1430 c CAUSE NON HORIZONTAL INERTIA FORCES DIRECTLY. 1431 c 1432 FF - 0. 1433 DO 190 J • 1, MCOUNT 1434 11 « IDOF(O) 1435 F(I1) - EVEC(J.MODEN) • FAC • AMASSU1) 1436 FF • FF * F(I 1 ) 1437 190 CONTINUE 1438 c 1439 c CALCULATE THE BASE SHEAR 1440 c 144 1 IF (KK .EO. 1) GO TO 200 1442 SHRMS • SHRMS + FF •* 2 1443 IF (MODEN .LT. NMODES) GO TO 200 1444 SHRMS • SORT(SHRMS) 1445 200 CONTINUE 1446 c CONVERT SINGLE PRECISION FORCE MATRIX TO DOUBLE PRECISION 1447 DO 210 IFREE • 1. NU 1448 210 DF(I FREE) • D8LE(F(IFREE ) ) 1449 c 1450 c COMPUTE DEFLECTIONS BY CALLING SUBROUTINE SDFBAN 1451 C • 1 MOTE THAT NO SOLUTION IMPROVING ITERATIONS WILL BE PERFORMED. 1452 C SCALING WILL BE PERFORMED TO IMPROVE THE SOLUTION WHEN NSCALE.NE.O 1453 C 1454 NSCALE • 1 1455 C 1456 DRATIO - 1.00-16 1457 CALL SOFBAN(S. DF. NU. NB. INDEX. DRATIO. DET. JEXP. NSCALE) 1458 C 1459 C SDFBAN EXITS WITH DF BEING THE. DISPLACEMENT MATRIX 1460 C 1461 C CONVERT DOUBLE PRECISION DISPLACEMENTS TO SINGLE PRECISION 1462 00 220 JFREE > 1. NU 1463 F(JFREE) - SNGL(DF(JFREE)) 1464 220 CONTINUE 1465 C 1466 INDEX - INDEX + 1 1467 C 1468 C CALCULATE RMS DISPLACEMENTS. 1469 C 1470 DO 260 JNT - 1, NRJ 1471 DX • 0. 1472 DY - 0. 1473 OR - 0. 1474 N1 - ND(1.JNT) 1475 N2 - ND(2,JNT) 1476 N3 - NDO.JNT) 1477 IF (N1 .EO. 0) GO TO 230 1478 DX - F(N1) 1479 RMS(I.JNT) • RMS(I.JNT) + DX 2 1480 230 CONTINUE 1481 IF (N2 .EO. 0) GO TO 240 1482 DY - F(N2) 1483 RMS(2,JNT) » RMS(2,JNT) + DY 2 1484 240 CONTINUE 1485 IF (N3 .EO. 0) GO TO 250 1486 DR • F(N3) 1487 RMSO.JNT) » RMSO.JNT) • DR •• 2 1488 250 CONTINUE 1489 IF (INTPR .EO. 0) GO TO 260 1490 IF (NPRINT .LT. MOOEN) GO TO 260 1491 C OUTPUT MOOAL DEFLECTIONS FOR REQUIRED MODES 1492 WRITE (IUNIT.470) JNT, DX, DY. DR 1493 260 CONTINUE 1494 C STORE FINAL FIRST MODE DEFLECTIONS FOR CURVATURE DUCTILITY 1495 C CALCULATIONS 1496 IF (IFLAG .EQ. 1 .ANO. IUNIT .EQ. 7) GO TO 270 1497 GO TO 290 1498 270 CONTINUE 1499 IF (MODEN .NE. 1) GO TO 290 150O DO 280 JF - 1, NU 1501 FCD(JF) - F(JF) • DEFL(JF) 1502 280 CONTINUE 1503 290 CONTINUE 1504 C 1505 C CALL FORCE TO CALCULATE MEMBER FORCES AND SMEARED 1506 C DAMPING RATIOS.FORCES DUE TO E/O LOADS ONLY 1507 C 1508 CALL FORCE(NRM, XM, YM, DM, AV. NP. F. EXTL. EXTG. AREA. E. G, ID 05 1509 1 NPRINT. CRMOM, DAMRAT,. INTPR, KL, KG, KK, SDAMP. NMODES, 1510 2 IUNIT. IFLAG, MODEN, ICOUNT, RMS. BETAM, MSIGN, SHEAR 1, 151 1 3 SHEAR2. BMLCD, BMGCO) 1512 C 1513 C COMPUTE ANO WRITE MODAL CONTRIBUTION FACTOR 1514 CONMOD • SA • ALPHA(MODEN) 1515 C WRITEtIUNIT.550) MODEN. CONMOD 1516 300 FORMAT (' '. "MODE '. 13. 3X, 'CONTRIBUTION FACTOR-', F8.5) 1517 c OUTPUT SPECTRAL- ACCELERATION. 1518 c 1519 c IF(INTPR.EO.O.OR.MODEN.GT.NPRINT) GO TO 570 1520 c WRITE(IUNIT,560) DAMP. TN,SA 1521 310 FORMAT (' ', 'DAMPING-'. F6.4. ' PERIOO-', F6.4. ' SEC. SA-'. 1522 1 F5.3) 1523 320 CONTINUE 1524 c 1525 c 1526 IF (KK .EO. 1) GO TO 410 1527 c 1528 c PRINT RMS DISPLACEMENTS ANO FORCES 1529 c 1530 IF (IUNIT .EO. 6 .AND. ICOUNT .GT. 25) GO TO 340 1531 WRITE (IUNIT,450) 1532 c OUTPUT THE COUNT OF ENTRANCES INTO M0D3 1533 WRITE (6.330) ICOUNT 1534 330 FORMAT (' ', 'ICOUNT-'. 13) 1535 WRITE (IUNIT,460) 1536 WRITE (IUNIT.440) 1537 340 CONTINUE 1538 c 1539 c CONVERT SOUARE OF RMS DISPLACEMENTS TO RMS DISPLACEMENTS. 1540 c 154 1 00 350 1 - 1 . NRJ 1542 DO 350 J « 1. 3 1543 RMS(J.I) • SORT(RMS(J,I)) 1544 350 CONTINUE 1545 c ADD TO THESE RMS DISP.DISP DUE TO GRAVITY LOADS 1546 DO 380 1 - 1 . NRJ 1547 J1 • ND(1,I) 1548 J2 • ND(2.1) 1549 J3 - NOO.I) 1550 IF (J1 .EO. 0) GO TO 360 1551 RMS(I.I) • RMSO.I) • OEFL(JI) 1552 360 IF (J2 .EO. 0) GO TO 370 1553 RMS(2,I) • RMS(2.I) + 0EFL(J2) 1554 370 IF (J3 .EO. 0) GO TO 380 1555 RMSO.I) - RMSO.I) + DEFL(J3) 1556 380 CONTINUE 1557 IF (ICOUNT .GT. 25 .AND. IUNIT .EO. 6) GO TO 390 1558 DO 390 I - 1, NRJ 1559 WRITE (IUNIT.470) I. (RMS(J,I),J-1,3) 1560 390 CONTINUE 1561 IF (ICOUNT .GT. 25 .AND. IUNIT .EO. 6) GO TO 400 1562 WRITE (IUNIT,480) 1563 WRITE (IUNIT.490) SHRMS 1564 IF (ICOUNT .GT. 35 .ANO. IUNIT .EO. 6) GO TO 400 1565 WRITE (IUNIT,500) 1566 400 CONTINUE 1567 C 1568 C CALL DAMOD TO MODIFY DAMAGE RATIOS 1569 C 1570 CALL DAMOD(RMS. NRM, DAMB. BMCAP, DVARY, IFLAG, BETA, HARD, 1571 1 ICOUNT. IUNIT. BMERR. OAMRAT. ISIGN. SDAMP. SAXIAL. SHEAR 1, 1572 2 SHEAR2, SBML, SBMG,' MSIGN. KOU. FCD. BMLCO. BMGCD. NP, OM, 1573 3 E. CRMOM, NU) 1574 410 CONTINUE 1575 C --1576 C 1577 ICOUNT - ICOUNT • 1 1578 RETURN 1579 420 FORMAT ('-', 'MODAL PARTICIPATION FACTOR', /) 1580 430 FORMAT (' '. 5X. 'MODE', 15. 5X. F10.5. 5X. F10.5) 1581 440 FORMAT ('-'. 7X. 'JOINT NO.'. 10X. 'X-DISP(FT)'. 10X. 1582 1 'Y-OISP(FT) '. 7X. 'ROTAT10N(RAD)') 1583 450 FORMAT ('-'. 110('•*)) 1584 460 FORMAT ('-'. 'ROOT MEAN SOUARE DISPLACEMENTS') 1585 470 FORMAT (' '. 6X, 110, 3F20.4) 1586 480 FORMAT ('-'. 'ROOT MEAN SOUARE FORCES') 1587 490 FORMAT CO*. 7X, 'RSS BASE SHEAR -'. F10.3, ' KIPS') 1588 500 FORMAT ('-'. 8X. 'MN', 10X, 'AXIAL*. 10X, 'SHEARL*. 9X. 'SHEARG', 1589 1 10X, 'BML', 12X. 'BMG', 9X. 'MOMENT', 10X, 'DAMAGE'/21X, 1590 2 'KIPS'. 12X. 'KIPS', 12X. 'KIPS'. 2(9X.'(K-FT)'). 8X. 1591 3 'CAPACITY', 9X, 'RATIO') 1592 END 1593 C 1594 C • • •••• 1595 C 1596 SUBROUTINE FORCEfNRM. XM, YM. DM. AV, NP. F, EXTL, EXTG. AREA. E, 1597 1 G. NPRINT. CRMOM, DAMRAT. INTPR. KL, KG. KK. SDAMP. 1598 2 NMODES. IUNIT, IFLAG, MODEN. ICOUNT. RMS. BETAM. MSIGN. 1599 3 SHEAR 1, SHEAR2, BMLCD, BMGCD) 1600 C 1601 C 1602 C 1603 C THIS SUBROUTINE CALCULATES AXIAL,SHEAR FORCES 1604 C BENDING MOMENT (RETURN AS RMS(4-8.JOINT NO.)). 1605 C AND SMEARED DAMPING FACTOR (BETAM) 1606 C RMS(5.MEM) - SHEAR AT LESSER END 1607 C RMS(S.MEM) » SHEAR AT GREATER END 1608 C •*• NOTE •*• 1609 C AT THIS STAGE RMS(1,JNT)-(RMS DISPLACEMENT)SOUARED OF X DISPLACEMENT. 1610 C COMPUTE MEMBER FORCES USING DISPLACEMENTS FROM INDIVIDUAL MODES 1611 C NOTE THAT ' ENGINEERING' SIGN CONVENTION IS USED HERE. 1612 C 1613 DIMENSION XM(NRM), YM(NRM), DM(NRM), AV(NRM). NP(6.NRM), 1614 1 MSIGN(250.2). 0(6). F(50O). EXTL(NRM), EXTG(NRM). 1615 2 KL(NRM). KG(NRM), PI(250). RMS(8.250). SDAMP(NRM), 1616 3 BETAM(NMODES), E(NRM), G(NRM), SUMDAM(250), ZETA(10). 1617 4 AREA(NRM), CRMOM(NRM), DAMRAT(2,NRM), SHEAR1(NRM), 1618 5 SHEAR2(NRM), BMLCO(NRM), BMGCD(NRM) 1619 REAL'S ORATI(6) 1620 C 1621 SIGPI - O. 1622 C 1623 C INSERT MODAL MEMBER FORCE HEADINGS 1624 C CO ~1 162S IF (INTPR .NE. 0 .ANO. NPRINT .GE. MODEN) WRITE (IUNIT.10) 1683 C FREEDOM CHECK FOR PIN-PIN MEMBERS 1626 10 FORMAT (' '. /8X. 'MN'. 10X. 'AXIAL'. IOX. 'SHEARL'. 9X. 'SHEARG'. 1684 IF (KL(I) .EO. 0 .AND. KG(I) .EO. 0) GO TO 120 1627 1 12X. 'BML', 12X. 'BMG', /21X. 'KIPS'. 12X. 'KIPS', 12X. 1685 DELT • ((0(5) - 0(2>)*XL • (DO) - D(4))«YL) / DL 1628 2 'KIPS'. 2(9X.'(K-FT)')) 1686 BML - (2.0*EISI/(DL*(1.0 + GFACT))) * ((3.O'DELT'DRATI(4)/DL) -1629 C 1687 1 (D(6)*(1.0 - GFACT/2.0)*DRATI<3)) - (2,0'D(3)•(1.0 • GFACT/4.0)* 1630 C 1688 2 ORATI(I))) 1631 c 1689 BMG • -(2.0*EISI/(DL*(1.0 + GFACT))) • ((3.O'DELT'DRATI(5)/DL) -1632 00 190 I • 1. NRM.' 1690 1 (D(3)'(1.0 - GFACT/2.0)*DRATI(3)) - (2.0*D(6)•(1.0 • GFACT/4.O) 1633 c 1691 2 'DRATI(2))) 1634 c 1692 SHEAR • (6.0'EISI/(DL-DL)) • ((0(3)'DRATI(4) • D(6)'DRATI(5) - ( 1635 c 1693 1 2.0*DELT»DRAT1(6)/DL))/(1.0 * GFACT)) 1636 c XL.YL - X,Y COMPONENTS OF MEMBER LENGTH RESPECTIVELY 1694 C BMG-BML+SHEAR'DL 1637 c OL • TRUE LENGTH OF MEMBER 1695 IF (KL(I) - KG(I)) 100. 130. 110 1638 c BMG • BENDING MOMENT AT GREATER JOINT NO. END OF MEMBER. 1696 C ADJUST PIN-FIX MEMBER FORCES. 1639 c BML • BENDING MOMENT AT THE LESSER JOINT NO. END. 1697 100 BMG » BMG + BML • (1.0 - GFACT/2.0) / (2.0*(1.0 • GFACT/4.0)) 1640 c 1698 SHEAR - SHEAR + 1.5 • BML / (DL) 1641 XL - XM(I) 1699 BML - 0. 1642 YL " YM(I) 1700 GO TO 130 1643 DL - DM(I) 1701 C AOJUST FIX-PIN MEMBER FORCES. 1644 AVI - AV(I) 1702 110 BML - BML * BMG • (1.0 - GFACT/2.0) / (2.0*(1.0 • GFACT/4.0)) 1645 c 1703 SHEAR - SHEAR - 1.5 • BMG / (DL) 1646 DO 40 MEMDOF * 1 . 6 1704 BMG - O. 1647 NI • NP(MEMDOF,I) 1705 GO TO 130 1648 IF (N1) 30. 30. 20 1706 c FILL IN MEMBER FORCES FOR PIN-PIN MEMBERS. 1649 20 D(MEMDOF) • F(N1) 1707 120 BMG • 0. 1650 GO TO 40 1708 BML - 0. 1651 30 D(MEMDOF) • 0. 1709 SHEAR - 0. 1652 40 CONTINUE 1710 130 CONTINUE 1653 c 1711 c 1654 c MOOIFY END DISPLACEMENTS FOR HORIZONTAL MEMBERS WITH END 1712 c COMPUTE THE RELATIVE FLEXURAL STRAIN ENERGY 1655 c EXTENSIONS FORMULA ONLY WORKS FOR HORIZONTAL MEMBERS 1713 c 1656 N3 • NP(3,I) 1714 IF (KK .EO. 2) GO TO 140 1657 IF (N3 .EO. 0) GO TO 50 1715 PI ( I ) - (BML*BML*DRATI(2) + BMG*BMG*DRATI(1) + BML*BMG*DRATI(3)) 1658 D(2) - 0(2) + (F(N3)) • EXTL(I) 1716 1 • 2. • DL / EISI / (16.*DRAT1(1)*DRATI(2) - 4*(DRATI(3)**2.)) 1659 50 CONTINUE 1717 SIGPI « SIGPI + PI(I) 1660 N6 • NP(6.I) 1718 140 CONTINUE 1661 IF (N6 .EO. 0) GO TO 60 1719 c 1662 D(5) - D(5) - (F(N6)) • EXTG(I) 1720 c PRINT OUT FORCES FOR EACH MEMBER IF ELASTIC CASE DESIRED. 1663 60 CONTINUE 1721 IF (INTPR .EO. 0) GO TO 160 1664 c PRINT OUT MEMBER END DISPLACEMENTS FOR DEBUG 1722 ASHEAR - SHEAR 1(1) + SHEAR 1665 c 1F(I COUNT.GT.1) GO TO 80 1723 BSHEAR - SHEAR20) • SHEAR 1666 c WRITE(6.70) I.(D(M).M'1,6) 1724 IF (NPRINT .GE. MODEN) WRITE (IUNIT,150) I. AXIAL. ASHEAR, 1667 70 FORMAT (' '. 'MEMB NO.-'. 13. 'DISPL-'. 6F10.5) 1725 1 BSHEAR, BML, BMG 1668 80 CONTINUE 1726 150 FORMAT (6X. 15. 7F15.3) 1669 AXIAL • (AREA(1)*E(I )/DL* *2) • (D(4)'XL • D(5)'YL - D(1)»XL - D( 1727 160 CONTINUE 1670 1 2)*YL) 1728 c IF (MODEN .GT. 1) GO TO 170 1671 c GET EFFECTIVE DAMAGE RATIO 1729 1672 CALL DAMCALtDAMRAT, DRATI, I) 1730 IF (BML .LE. 0.) MSIGN(I,1) • -1 1673 EISI • CRMOM(I) • E(I) 1731 IF (BML .GT. 0.) MSIGN(I.I) • 1 1674 c 1732 IF (BMG .LE. 0.) MSIGN(I.2) - -1 1675 c GFACT-FACTOR TO COMPUTE EFFECT OF SHEAR DEFL. ON MEMBER FORCES 1733 IF (BMG .GT. 0.) MSIGN(I,2) • 1 1676 c GFACT-0.0 IMPLIES THAT NO SHEAR DEFLECTION INCLUDED. 1734 170 CONTINUE 1677 GFACT - 0.0 1735 c ACCUMULATE ABSOLUTE SUM AND RMS SUM 1678 IF (AVI .EO. 0.0 .OR. G(I) .EO. 0.0) GO TO 90 1736 c 1679 GFACT - 12.0 • EISI / (AVI*G(I)*DL*DL) * DRATI(6) 1737 RMS(4,I) - RMS(4,I) + AXIAL " 2 1680 90 CONTINUE 1738 RMS(5.I) • RMS(5.1) + SHEAR •• 2 1681 c 1739 RMS(6,I) - RMS(6.I) + BML •• 2 1682 c ASSIGN DISPLACEMENTS TO THEIR RESPECTIVE MEMBER DEGREES OF 1740 RMS(7,1) - RMS(7.I) • BMG •• 2 (0 CO 1741 C STORE FIRST MODE B.M. IN FINAL ITERATIONS FOR CURV. DUCT. 1742 IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 180 1743 IF (MODEN .NE. 1) GO TO 180 1744 BMLCO(I) - BML 1745 BMGCD(I) - BMG 1746 180 CONTINUE 1747 190 CONTINUE 1748 C 1749 C 1750 C COMPUTE THE SMEARED DAMPING FOR EACH MODE , 1751 C 1752 IF (KK .EO. 2) GO TO 260 1753 C ' 1754 C SUMDAM- THE PRODUCT OF MEMBER STRAIN ENERGY*MEMBER DAMPING. 1755 ZETA(MODEN) • O. 1756 00 200 1 - 1 . NRM 1757 SUMOAM(I) - P I ( I ) • SDAMP(I) 1758 ZETA(MOOEN) « ZETA(MODEN) + SUMOAM(I) 1759 200 CONTINUE 1760 IF (SIGPI . EO. 0.0) WRITE (IUNIT.210) 1761 210 FORMAT (' '. "ERROR-DIVIDED BY ZERO WHILE CALCULATING SMEARED 1762 1 DAMPING") 1763 C 1764 C BETAM-SMEAREO SUBSTITUTE DAMPING FOR THE M TH MODE. 1765 BETAM(MOOEN) - ZETA(MOOEN) / SIGPI 1766 C 1767 C PRINT DAMPING INFORMATION FROM FINAL ITERATION. 1768 C 1769 IF (IFLAG .EO. O) GO TO 260 1770 WRITE (6.220) SIGPI. MODEN. BETAM(MODEN) 1771 220 FORMAT (' '. 'TOTAL FLEX. STR. ENERGY-', F10.3. 3X. 'MODE NUMBER', 1772 1 12. 3X. 'SMEARED DAMPING FACTOR-'. F7.S) 1773 WRITE (6.230) 1774 C 1775 DO 250 MEMB - 1. NRM 1776 230 FORMAT (' '. 'MEMBER NO.', 3X. 'STRAIN ENERGY' , 3X. 1777 1 "MEMBER DAMPING', 3X, 'MEMBER DAMPING*STRAIN ENERGY') 1778 WRITE (6.240) MEMB. PI(MEMB), SDAMP(MEMB), SUMDAM(MEMB) 1779 240 FORMAT (' '. 3X, 13, 10X. E10.3, BX. E10.3. I3X, F11.7) 1780 250 CONTINUE 1781 260 CONTINUE 1782 RETURN 1783 END 1784 C 1785 C *• ** 1786 C 1787 SUBROUTINE DAMOD(RMS. NRM, DAMB, BMCAP, OVARY. IFLAG. BETA, HARD, 1788 1 ICOUNT, IUNIT, BMERR, DAMRAT, ISIGN, SDAMP. SAX1AL, 1789 2 SHEAR 1, SHEAR2, SBML. SBMG. MSIGN, KOU. FCD. BMLCD, 1790 3 BMGCD. NP. DM, E, CRMOM, NU) 1791 C 1792 C * * " * * **• 1793 C 1794 DIMENSION RMS(8,250). DAMB(2.NRM). BMCAP(NRM), DAMRAT(2.NRM), 1795 1 SOAMP(NRM), DAMDL0(2). SAXIAL(NRM). SHEAR 1(NRM), 1796 2 SBML(NRM), SBMG(NRM). MSIGN(250.2). SHEAR2(NRM), 1797 3 FCD(NU), eMLCO(NRM), BMGCD(NRM), NP(6.NRM). OM(NRM), 1798 4 E(NRM), CRMOM(NRM), C0(2,250) 1799 C MODIFY DAMAGE RATIOS 1800 C 1801 C ISIGN IS A COUNT OF THE NUMBER OF MEMBERS WITH WHICH THE RATIO 1802 C OF THE ABSOLUTE VALUE OF THE DIFFERENCE BETWEEN THE LARGEST RMS 1803 c BENDING MOMENT ANO ULTIMATE MOMENT TO ULTIMATE MOMENT IS IN 1804 C EXCESS OF 'BMERR'. 1805 c ISIGN IS INITIALIZED TO ZERO HERE. 1806 c 1807 ISIGN - 0 1808 c 1809 DO 10 MEM • 1. NRM 1810 c 1811 c CONVERT SOUARE OF RMS AXIAL. SHEAR ANO MOMENT TO RMS VALUE. 1812 DO 10 J • 4. 7 1813 RMS(J.MEM) - SORT(RMS(J.MEM)) 1814 10 CONTINUE 1815 IF (KOU .EO. 2) GO TO 20 1816 GO TO 40 1817 20 CONTINUE 1818 DO 30 I - 1. NRM 1819 MSIGN(I.I) - -MSIGN(I.I) 1820 30 MS1GN(I,2) - -MSIGNU.2) 1821 40 CONTINUE 1822 c ADD STATIC FORCES TO FIRST MODE FORCES FOR CURV DUCT. CALCUL. 1823 IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 60 1824 DO 50 I - 1. NRM 1825 KSIGN • 1 1826 IF (KOU .EO. 2) KSIGN - -1 1827 BMLCO(I) • KSIGN • BMLCO(I) + SBML(I) 1828 BMGCD(I) - KSIGN • BMGCD(I) + SBMG(I) 1829 50 CONTINUE 1830 60 CONTINUE 1B31 c ADD MEMBER FORCES DUE TO GRAVITY LOADS & E/O LOADS 1832 DO 70 1 • 1. NRM 1833 RMS(4.I) - RMS(4.I) • SAXIAL(I) 1834 RMS(8.I) - RMS(5.I) • SHEAR2(I) 1835 RMS(5.I) • RMS(S.I) • SHEAR 1(I) 1836 RMS(G.I) - MSIGN(I.I) * RMS(6,I) • SBML(I) 1837 RMSO.I) • MSIGN(I,2) * RMSO.I) + SBMG(I) 1838 RMS(G.I) - ABS(RMS(6.I)) 1839 RMSO.I) - ABS(RMS(7,I)) 1840 70 CONTINUE 1841 00 310 MEM • 1. NRM 1842 DO 90 L - 1. 2 .343 c 1144 c SET DAMOLD AS THE DAMAGE RATIO IN THE (I-2)TH ITERATION 1145 c OAMB AS THE DAMAGE RATIO IN THE (I-I)TH ITERATION. 1846 c 1847 DAMOLD(L) • DAMB(L.MEM) 1848 DAMB(L.MEM) - DAMRAT(L.MEM) 1849 c 1850 c CALCULATE NEW DAMAGE RATIO 1851 c 1852 IF (DAMRAT(L.MEM) .GT. 1.0) GO TO 80 1853 DAMRAT(L.MEM) - RMS(5 • L.MEM) / BMCAP(MEM) • DAMRAT(L.MEM) 1854 GO TO 90 1855 80 TEMP - RMS(5 • L.MEM) * DAMRAT(L.MEM) 1856 DAMRAT(L.MEM) - TEMP / (BMCAP(MEM)*(1 - HARD) * HARD-TEMP) to (0 1857 90 CONTINUE 1858 C 1859 c OUTPUT THE RMS AXIAL SHEARS ANO MOMENT. 1860 c 1861 IF (ICOUNT .CT. 35 .AND. IUNIT .EO. 6) GO TO 160 1862 DAMAX • OAMRAT(1.MEM) 1863 IF (DAMRAT(2.MEM) .GT. DAMRAT(1.MEM)) OAMAX » DAMRAT(2,MEM) .1864 WRITE (IUNIT.100) MEM, RMS(4.MEM), RMS(5,MEM), RMS(B.MEM). 1865 1 RMSI6.MEM), RMS(7,MEM), BMCAP(MEM), DAMAX 1866 100 FORMAT (6X. IS. 7F15.3) 1867 IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 150 1868 •c CALCULATE MEMBER CURVATURE DUCTILITIES AT BOTH ENDS OF MEM8ER 1869 CD(1.MEM) - 0. 1870 C0(2.MEM) • 0. 1871 IF (OAMRAT(1.MEM) .LE. 1.) GO TO 120 1872 IF (NP(S.MEM) .EO. 0) GO TO 110 1873 N1 > NPO.MEM) 1874 THETAY - (1. - DAMRAT(I.MEM)'HARD) • FCD(N1) / (DAMRAT(1.MEM) '( 1875 1 1. - HARD)) 1876 THETAP - ABS(FCD(N1)) - ABS(THETAY) 1877 CD(t.MEM) - 1. + THETAP • E(MEM) • CRMOM(MEM) / (0.05'DM(MEM) * 1878 1 BMCAP(MEM)) 1879 GO TO 120 1880 110 CONTINUE 1881 BM1 • BMLCD(MEM) 1882 BM2 • BMGCD(MEM) 1883 DAMAGE - OAMRAT(1.MEM) 1884 CALL CDUCT(C01, BM1. BM2. NP. NRM. MEM. DM, FCO. NU, DAMAGE, E. 1885 1 CRMOM. BMCAP, HARD) 1886 CD(1.MEM) - CD 1 1887 120 CONTINUE 1888 IF (DAMRAT(2,MEM) .LE. 1.) GO TO 140 1889 IF (NP(6.M£M) .EO. 0) GO TO 130 1890 N1 - NP(6.MEM) 1891 THETAY • (1. - DAMRAT(2.MEM)'HARD) • FCD(NI) / (DAMRAT(2,MEM) •( 1892 1 1. - HARD)) 1893 THETAP - ABS(FC0(N1)) - ABS(THETAY) 1894 CD(2.MEM) • 1. + THETAP • E(MEM) • CRMOM(MEM) / (0.05'DM(MEM) • 1895 1 BMCAP(MEM)) 1896 GO TO 140 1897 130 CONTINUE 1898 BM1 * BMLCD(MEM) 1899 BM2 • BMGCD(MEM) 19O0 DAMAGE • DAMRAT(2,MEM) 1901 CALL CDUCT(CD2, BM1. BM2, NP, NRM, MEM. DM, FCO, NU. DAMAGE. E, 1902 1 CRMOM, BMCAP, HARD) 1903 CD(2.MEM) • CD2 1904 140 CONTINUE 190S ISO CONTINUE 1906 c 1907 160 00 240 L • 1. 2 1908 c 1909 c DO NOT ALTER DAMAGE RATIOS OF LESS THAN UNITY 1910 c 1911 IF (DAMRAT(L,MEM) .LT. 1.0) GO TO 230 1912 c 1913 c CONVERGENCE SPEEDING ROUTINE FOLLOWS. 1914 c 1915 IF (DAMRAT(L.MEM) .LT. 5.0) DERROR • (DAMRAT(L.MEM) - DAMB(L, 1916 1 MEM)) / 10.0 1917 IF (DAMRAT(L,MEM) .GE. 5.0) DERROR • (DAMRAT(L.MEM) - DAMB(L, 1918 1 MEM)) / DAMRAT(L,MEM) 1919 IF (ABS(DERROR) .GT. ABS(DVARY)) OVARY - DERROR 1920 C 1921 DAMDIF > OAMRAT(L.MEM) - DAMB(L.MEM) 1922 C 1923 IF (DAMOLD(L) - DAMB(L.MEM)) 170. 230. 200 1924 170 CONTINUE 1925 IF (DAMDIF) 190. 230. 180 1926 180 DAMRAT(L.MEM) • DAMRAT(L.MEM) + BETA • (DAMDIF) 1927 GO TO 230 1928 190 OAMRAT(L.MEM) • DAMRAT(L,MEM) - BETA • (DAMDIF) 1929 GO TO 230 1930 200 CONTINUE 1931 IF (DAMDIF) 220, 230. 210 1932 210 CONTINUE 1933 0AMRAT(L.MEM) • DAMRAT(L.MEM) - BETA • (DAMDIF) 1934 GO TO 230 1935 220 CONTINUE 1936 DAMRAT(L.MEM) - DAMRAT(L.MEM) * BETA • (DAMDIF) 1937 230 CONTINUE 1938 IF (DAMRAT(L,MEM) .LT. 1.0 .AND. IFLAG .NE. 1) DAMRAT(L.MEM) 1939 1 1 .0 1940 240 CONTINUE 194 1 C 1942 C DAMAGE RATIOS CANNOT BE LESS THAN 1.0 1943 C IN LAST ITERATION SKIP RESETTING DAMAGE RATIOS LESS THAN UNITY 1944 C 1945 IF (OAMRATfI.MEM) .LE. 1.0 .AND. DAMRAT(2,MEM) .LE. 1.0) 1946 1 1 GO TO 290 1947 C FIND THE BIGGEST OF THE SOUARE OF THE RMS BENDING MOMENT('BIG) 1948 IF (RMS(6,MEM) - RMS(7,MEM)) 250. 250. 260 1949 250 BMBIG - RMS(7,MEM) 1950 DAM * DAMRAT(2.MEM) 1951 GO TO 270 1952 260 BMBIG • RMS(6,MEM) 1953 DAM • DAMRAT(1.MEM) 1954 270 CONTINUE 1955 C 1956 C BMSH • INCREASED MOMENT CAPACITY DUE TO STRAIN HARDENING 1957 C 1958 BMSH - BMCAP(MEM) * (1 - HARD) / (1 - HARD'DAM) 1959 CHECK • (BMBIG - 8MSH) / BMSH 1960 IF (CHECK .GT. BMERR) ISIGN • I SIGN + 1 1961 C COMPUTE DAMPING VALUE FOR THE MEMBER 1962 SDAMP(MEM) • 0.0 1963 DO 280 L - 1, 2 1964 DAM • OAMRAT(L.MEM) - 1 1965 280 SDAMP(MEM) - SOAMP(MEM) + ((HARD'DAM + 1)'DAM) / (1 - DAMRAT(L. 1966 1 1 MEM)"HARD ) 1967 SDAMP(MEM) • 0.15915494 • SOAMP(MEM) / (DAMRAT(1,MEM) • DAMRAT( 1968 1 2.MEM)) + .02 1969 GO TO 300 1970 290 SDAMP(MEM) -0.02 1971 300 CONTINUE 1972 310 CONTINUE 1973 IF (IFLAG .NE. 1 .OR. IUNIT .NE. 7) GO TO 350 1974 WRITE (IUNIT.320) 1975 320 FORMAT (//. 25X. 'CURVATURE DUCTILITIES'. /. 20X. 33('-*). /. IOX, 1976 1 'MN'. 14X. 'LESSER END'. 13X, 'GREATER ENO', /) 1977 00 340 MEM • 1, NRM 1978 WRITE (IUNIT.330) MEM, CD(1,MEM). C0(2.MEM) 1979 330 FORMAT (7X, IS .• 2( 17X, F9 . 3) ) 1980 340 CONTINUE 1981 350 CONTINUE 1982 RETURN 19B3 END 1984 C 1985 C 1986 C •••••• 1987 C 1988 SUBROUTINE STACHK(OLDSA. SA, OLOTN, TN, ISPEC. LOCK, ICOUNT. 1989 1 IFLAG. IUNIT. AMAX. DAMP. KK) 1990 C 1991 C 1992 C 1993 C 1994 C THE INTENTION OF THIS SUBROUTINE IS TO DEAL WITH CONVERGENCE 1995 C INSTABILITY CAUSED BY STEEP SPECTRUM CONTOUR 1996 C • 1997 DIMENSION 0LDTN(1), OLDSA(I) 1998 C 1999 IF (LOCK .GT. O) GO TO 90 2 COO C 2001 IF (ICOUNT .LT. 4) RETURN 2002 IF (ICOUNT .EO. 4 .AND. KK .EO. 1) GO TO 20 2003 IF (ICOUNT .EO. 5 .AND. KK .EO. 1) GO TO 10 2004 IF (KK .EO. 2) GO TO 30 2005 01F1 • OLDTN( 2) - OLOTN( 1 ) 2006 0IF2 " OLDTN(I) - TN 2007 IF (DIF1 .LT. - 0.005 .AND. DIF2 .GT. 0.005) GO TO 40 2008 IF (DIF1 .GT. 0.005 .AND. DIF2 .LT. - 0.005) GO TO 40 2009 10 OLDTNt2) • OLDTN(1) 2010 20 OLDTN(1) - TN 201 1 RETURN 2012 C 2013 30 0LDSA(2) • SA • (6. + 100.'DAMP) / 8. 2014 RETURN 2015 C 2016 C INSTABILITY DETECTED : START BINARY SEARCH ROUTINE 2017 C 2018 40 WRITE (99.150) 2019 WRITE (7.150) 2020 WRITE (99,50) ICOUNT 2021 WRITE (7,50) ICOUNT 2022 50 FORMAT (/3X. 'CONVERGENCE PROBLEM OCCURRED AT ITERATION NO. ', 12, 2023 1 ' :'/3X. 'SPECIAL CONVERGENCE ROUTINE IS NOW IN EFFECT'/3X, 2024 2 'START BINARY SEARCH PROCEDURE -') 2025 KCOUNT • O 2026 LOCK - 1 2027 OLOSA(I) • SA • (6. • 100.'DAMP) / 8. 2028 C 2029 C FIND UPPER BOUNO ANO LOWER BOUND SA(» 2% OAMPING) 2030 C - SET OLOSA(1)>UPPER BOUND. OLDSA(2)-LOWER BOUND 2031 C 0LDSA(3).TRIAL SA(0 2X DAMPING) 2032 C 2033 IF (0LDSA(2) .LT. OLDSA(I)) GO TO 60 2034 TEMP - OL0SA(1) 2035 OLDSA(1) - 0LDSA(2) 2036 0LDSA(2) « TEMP 2037 60 WRITE (99,70) OLDSA(I). 0LDSA(2) 2038 WRITE (7.70) OLDSA(I). 0LDSA(2) 2039 WRITE (99.140) 2040 WRITE (7.140) 2041 70 FORMAT (/3X, 'UPPER BOUND SA • ', F7.5. 4X, 'LOWER BOUND SA - '. 2042 1 F7.5/) 2043 80 OLDSAO) • (OLDSA(I) • 0LDSA(2)) / 2. 2044 c 2045 C CALCULATE SA AND CHECK FOR CONVERGENCE (IFLAG'1) 2046 c 2047 90 SA • OLDSA(3) • 8. / (6. + 100.*DAMP) 2048 IF (IFLAG .EO. 1 .AND. KK .EO. 2) GO TO 100 2049 RETURN 2050 c 2051 c CHECK FOR REAL CONVERGENCE 2052 c 2053 100 CALL SPECTROSPEC, DAMP. TN, AMAX, SAA. 0.. 0., 0.. 0.) 2054 SADIF - ABS(SA - SAA) / SAA 2055 IF (LOCK .EO. 2) GO TO 170 2056 KCOUNT • KCOUNT • 1 2057 WRITE (99.110) KCOUNT. SADIF 2058 WRITE (7.110) KCOUNT. SADIF 2059 110 FORMAT (/. ' , 12. 55('-'), 'SADIF . '. F6.4) 2060 c 2061 c CONVERGENCE LIMIT FOR SA IS 0.015 2062 c 2063 IF (SADIF .LE. 0.015) GO TO 120 2064 GO TO 160 2065 c 2066 120 WRITE (99,130) 2067 WRITE (7.130) 2068 130 FORMAT (/50X. 'PROGRAM CONVERGED (SAERR-0.015)') 2069 140 FORMAT ('-', 'ITERATION '. IX, 'NO. ABOVE DAMOIF', 3X. 2070 1 'S MATRIX '. 2X. 'SMEARED'/' NO.'. 5X, 'CAPACITY', 14X, 2071 2 'RATIO ', 2X, 'DAMPING') 2072 150 FORMAT (/80('-')) 2073 IFLAG • 0 2074 LOCK • 2 2075 RETURN 2076 c 2077 160 IF (SA .GT. SAA) OLDSA(I) - OLDSAO) 2078 IF (SA .LT. SAA) 0LDSA(2) • 0LDSA(3) 2079 IFLAG " 0 2080 GO TO 80 2081 c 2082 170 WRITE (99.180) SA. SAA. SADIF 2083 WRITE (7.180) SA, SAA. SADIF 2084 180 FORMAT (/' *. 'SA • '. F7.S, 3X. 'SA(ACTUAL) • '. F7.5. 3X. 2085 1 'SADIF - '. F7.5/) 2086 RETURN 2087 END 2088 c 2089 C 2090 c 2091 SUBROUTINE SPECTR(ISPEC. DAMP. TN. AMAX, SA, WN. SABND, SVBND, 2092 1 SDBNO) 2093 c 2094 c 2095 c 2096 c 2097 c ISPEC-1 IF SPECTRUM A IS USED 2098 c «2 IF SPECTRUM B IS USED 2099 c •3 IF SPECTRUM C IS USED 2100 c •4 IF NBC SPECTRUM IS USED 2101 c •5 IF SAN FERNANDO E/O RECORD 143 IS USED 2102 c •6 IF SIMULATED E/O C-2 IS USED 2103 c OAMP-OAMPING FACTOR (FRACTION OF CRITICAL DAMPING) 2104 c TN -NATURAL PERIOD IN SECONDS 2105 c AMAX"MAXIMUM GROUND ACCELERATION (FRACTION OF G) 2106 c SA -RESPONSE ACCELERATION (FRACTION OF G) 2107 c WN -NATURAL FREQUENCY IN RADIANS PER SECOND. 2108 c 2109 CALL FTNCMD('EQUATE 99-SPRINT;') 21 lO GO TO (10. 20. 70. 110. 140. 150). ISPEC 2111 c 2112 c SPECTRUM A 2113 c 2114 10 IF (TN .LT . 0.15) SA - 25. * AMAX • TN 2115 IF (TN .GE . 0.15 .ANO. TN .LT. 0.4) SA - 3.75 • AMAX 2116 IF (TN .GT . 0.4) SA • 1.5 • AMAX / TN 2117 GO TO 100 21 18 c 2119 c SPECTRUM B 2120 c 2121 20 CONTINUE 2122 IF (TN .LT . 0.1875) GO TO 30 2123 IF (TN .LT . 0.53333333) GO TO 40 2124 IF (TN .LT . 1.6666667) GO TO 50 2125 IF (TN .LT . 1.81666667) GO TO 60 2126 SA - 2. • , AMAX / (TN - 0.75) 2127 GO TO 100 2128 30 SA • 20. * AMAX • TN 2129 GO TO 100 2130 40 SA - 3.75 • AMAX 2131 GO TO 100 2132 50 SA - 2. • , AMAX / TN 2133 GO TO 100 2134 60 SA • 1.875 ' AMAX 2135 GO TO 100 2136 c 2137 c SPECTRUM C 2138 c 2139 70 CONTINUE 2140 IF (TN .LT . 0.15) GO TO 80 2141 IF (TN .LT . 0.38333333) GO TO 90 2142 SA • 0.5 • AMAX / (TN - 0.25) 2143 GO TO 100 2144 80 SA - 25. • AMAX • TN 2145 GO TO 100 2146 90 SA • 3.75 • AMAX 2147 100 CONTINUE 2148 SA - SA • 8. / (6. • 100.-OAMP) 2149 RETURN 2150 C 2151 c NBC SPECTRUM 2152 c 2153 110 CONTINUE 2154 SV • 40.0 • AMAX 2155 SD - 32.0 • AMAX 2156 SACC - 1 . 0 * AMAX 2157 c PRINT OUT A CAUTION NOTE SHOULD DAMPING BE LESS THAN 0.5% 2158 IF (DAMP .LT. 0.005) WRITE (7.120) 2159 120 FORMAT (' ', 'CAUTION-DAMPING LESS THAN 0.5%') 2160 c 2161 c COMPUTE MULTIPLICATION FACTOR FOR ACCELERATION AT DESIREO DAMPING 2162 IF (DAMP .LE. 0.02) AML - 4.2 • ((0.02 - DAMP)/0.015) • 1.6 2163 IF (DAMP .GT. .02 .AND. DAMP .LE. .05) AML - 3.0 • ((.05 - DAMP)/. 2 164 103) * 1.2 2165 IF (DAMP .GT. 0.05 .AND. DAMP .LE. 0.1) AML - 2.2 + ((0.1 - DAMP)/ 2166 10.05) * 0.8 2167 IF (DAMP .GT. 0.10) AML - 1.0 + (O.OO - DAMP)/0.90) * 1.2 2168 c 2169 c COMPUTE MULTIPLICATION FACTOR FOR VELOCITY AT DESIRED DAMPING. 2170 IF (DAMP .LE. 0.02) VML - 2.5 • ((0.02 - DAMPJ/0.015) • 0.8 2171 IF (DAMP .GT. .02 .AND. DAMP .LE. .05) VML * 2.0 + ((.05 - DAMP)/. 2172 103) « 0.5 2173 IF (DAMP .GT. .05 .AND. DAMP .LE. 0.1) VML - 1.7 + ((0.1 - DAMP)/ 2174 10.05) • 0.3 2175 IF (DAMP .GT. 0.10) VML • 1.0 • ((1.00 - DAMP)/0.90) * 0.7 2176 c 2177 c COMPUTE MULTIPLICATION FACTOR FOR DISPLACEMENT AT DESIRED DAMPING. 2178 IF (DAMP .LE. 0.02) DML - 2.5 * ((0.02 - DAMP)/O.OI5) • 0.5 2179 IF (DAMP .GT. 0.02) DML - VML 2180 c 2181 c COMPUTE BOUNDS USING DAMPING FACTORS COMPUTED ALREADY 2182 SDBNO - SD * DML 2183 SABND * SACC • AML 2184 SVBND - SV * VML 2185 c COMPUTE WHICH IS THE APPROPIATE BOUND. 2186 c CONVERT FROM IN/SEC**2 TO FRACTION OF G BY DEVIDING BY 386.4 2187 c 2188 SAATAP • SVBND * WN / 386.4 2189 IF (SAATAP .GT. SABND) SA - SABND 2190 IF (SAATAP .GT. SABND) GO TO 130 2191 SDATCP - SVBND / WN 2192 IF (SDATCP .GT. SDBND) SA • SDBNO • WN • WN / 386.4 2193 IF (SOATCP .GT. SDBND) GO TO 130 2194 c 2195 c IF HAVE NOT YET GONE TO STEP 180 THEN NATURAL FREOUENCY LIES ON 2196 c VELOCITY BOUND. 2197 c 2198 SA - SVBND • WN / 386.4 2199 c SA IS RETURNED AS A FRACTION OF GRAVITY. G 2200 c 2201 130 RETURN 2202 c 2203 c SAN FERNANDO E/O, HOLIDAY INN. LONGITUDINAL DIRECTION 2204 c o fO 2205 140 IF (TN .LE. 0.2) SA > (1.013 • 11.605»TN) • AMAX 2206 IF (TN .GT. 0.2 .AND. TN .LE. 0.62) SA • 3.334 • AMAX 2207 IF (TN .GT. 0.62 .AND. TN .LE. 0.82) SA • (5.750 - 3.896'TN) • 2208 1AMAX 2209 IF (TN .GT. 0.82 .AND. TN .LE. 1.7) SA « (2.772 - 0.265'TN) • AMAX 2210 IF (TN .GT. 1.7 .AND. TN . LE. 2.4) SA • (3.263 - 0.554'TN) • AMAX 2211 IF (TN .GT. 2.4) GO TO 160 2212 GO TO 100 2213 C 2214 C CIT/SIMULATED EARTHQUAKE C-2 2215 C 2216 150 IF (TN .LT. 0.17) SA • (0.6216 • 22.432'TN) • AMAX 2217 IF (TN .GE. 0.17 .AND. TN . LT. 0.51) SA » 4.435 • AMAX 2218 IF (TN .GE. 0.51 .AND. TN .LT. 0.58) SA • (21.831 - 34.11'TN) • 2219 1AMAX 2220 IF (TN .GE. 0.58 .AND. TN . LT. 1.8) SA - (2.723 - 1.164'TN) • AMAX 2221 IF (TN .GE. 1.8 .AND. TN .LE. 2.4) SA • (1.457 - 0.461'TN) • AMAX 2222 IF (TN .GT. 2.4) GO TO 160 2223 GO TO 100 2224 160 WRITE (99.170) TN 2225 170 FORMAT (/. 5X. 'PERIOD - '. F10.3. ' IS OUT OF THE SPECTRUM') 2226 RETURN 2227 END 2228 C 2229 C **• 2230 C 2231 SUBROUTINE SCHECMS. NU, NB. IOIM, IUNIT. SRATIO) 2232 C 2233 C 2234 C 2235 C THIS SUBROUTINE CHECKS THAT ALL DIAGONAL STIFFNESS MATRIX 2236 C ELEMENTS ARE POSITIVE NUMBERS GREATER THAN ZERO. IT ALSO DETERMINES 2237 C THE RATIO BETWEEN THE LARGEST AND SMALLEST MEMBERS ON THE DIAGONAL 2238 C THIS WILL GIVE SOME INDICATION AS TO THE CONDITIONING OF THE 2239 C STIFFNESS MATRIX 2240 C MATRIX 2241 C 2242 REAL'S S(IDIM) 2243 REAL'S SMIN. SMAX, OIAG. RATIO 2244 C 2245 C 2246 C THE STIFFNESS MATRIX IS STORED AS A COLUMN VECTOR. ONLY THE 2247 C THE LOWER TRIANGLE ELEMENTS BEING STORED (BY COLUMNS) 2248 C S(1) IS ON THE DIAGONAL AS IS S(1*NB).S(1*2'NB).ETC. 2249 C NB IS THE HALF BANDWIDTH OF THE STIFFNESS MATRIX 2250 C 2251 C INITIALIZE THE LARGEST ANO SMALLEST VALUES OF DIAGONAL (SMAX.SMIN) 2252 C 2253 SMIN • 1.0045 2254 SMAX • -1.0000 2255 C 2256 DO 50 IDOF • 1, NU 2257 IELEM - ((IDOF - 1)'NB) • 1 2258 DIAG * S(IELEM) 2259 C COMPUTE IF DIAGONAL ELEMENT IS ZERO OR NEGATIVE 2260 IF (DIAG .NE. O.ODOO) GO TO 20 2261 WRITE (7.10) IDOF 2262 10 FORMAT (///' PROGRAM HALTED-A ZERO IS ON THE DIAGONAL OF STIFFNE 2263 1 SSMATRIX'. //'EXAMINE DEGREE OF FREEDOM '. 14) 2264 STOP 2265 C 2266 20 CONTINUE 2267 IF (DIAG .GT. 0.0) GO TO 40 2268 WRITE (7.30) IDOF 2269 30 FORMAT (///' PROGRAM HALTED-NEGATIVE ELEMENT ON DIAGONAL OF ', 2270 1 'STIFFNESS MATRIX', //' EXAMINE DEGREE OF FREEDOM'. 14) 2271 STOP 2272 40 CONTINUE 2273 C 2274 C DETERMINE IF THE DIAGONAL ELEMENT UNDER EXAMINATION IS THE LARGEST OR 2275 C SMALLEST OF THE DIAGONAL ELEMENTS. 2276 IF (DIAG .GT. SMAX) SMAX • DIAG 2277 IF (OIAG .LT. SMIN) SMIN • DIAG 2278 C 2279 50 CONTINUE 2280 C 2281 WRITE (IUNIT.60) 2282 60 FORMAT (/' ALL ELEMENTS OF MAIN DIAGONAL OF STIFFNESS MATRIX'. 2283 1 ' ARE POSITIVE DEFINITE') 2284 C 2285 C COMPUTE AND PRINT RATIO OF LARGEST TO SMALLEST DIAGONAL ELEMENTS 2286 C 2287 RATIO - SMAX / SMIN 2288 SRATIO - SNGL(RATIO) 2289 WRITE (IUNIT.70) SRATIO 2290 70 FORMAT (' *. 'RATIO OF LARGEST TO SMALLEST DIAGONAL STIFFNESS', 2291 1 'MATRIX ELEMENT IS'. E10.3) 2292 RETURN 2293 END 2294 C 2295 C 2296 SUBROUTINE SDFBAN(A, B. N. M, LT. RATIO. DET, NCN, NSCALE) 2297 C 2298 C 2299 C THIS ROUTINE SOLVES SYSTEM OF EONS. AX'B WHERE A IS *TVE DEFINITE 2300 C SYMMETRIC BAND MATRIX. BY CHOLESKY'S METHOD. 2301 C LOWER HALF BAND ONLY (INCLUDING THE DIAGONAL) OF A IS STORED 2302 C COLUMN BY COLUMN IN A 1 DIMENSIONAL ARRAY. 2303 c SOLUTIONS X ARE RETURNEO IN ARRAY B. 2304 c OPTIONAL SCALING OF MATRIX A IS AVAILABLE 2305 c N - ORDER OF MATRIX A. 2306 c M - LENGTH OF LOWER HALF BAND. 2307 c DETERMINANT OF A - DET'( 10"NCN) . 1 . E-15< | DET | < 1 . E 15 2308 c LT-1 IF ONLY 1 8 VECTOR OR IF FIRST OF SEVERAL. LT NOT - 1 FOR 2309 c SUBSEQUENT B VECTORS. 2310 c RATIO • SMALLEST RATIO OF 2 ELEMENTS ON MAIN DIAGONAL OF 231 1 c TRANSFORMED A >1.E-7. 2312 c NSCALE'O IF SCALING NOT REQUIRED. 2313 c 2314 c 2315 IMPLICIT REAL'8(A - H.O - Z) 2316 DIMENSION A(1). B(1) 2317 REAL'S MULT(6000) 2318 IF (M .EO. 1) GO TO 80 2319 MM » M - 1 2320 NM - N • M o u 3321 NM1 • NM - MM 2379 2322 c 2380 2323 C DUMMY STATEMENT INSERTED FOR COMPATIBILITY WITH I ASSEMBLER VERSION. 2381 2324 C lF(LT.LE.O) RETURN 2382 2325 C 2383 2326 IF (LT .NE. 1) GO TO 340 2384 2327 IF (NSCALE .EO. 0) GO TO 60 2385 2328 00 10 I * 1, N 2386 2329 C 2387 2330 C MATRIX SCALED BY DIVIDING ROW I AND COLUMN I BY SORT(A(I.I)). SUCH 2388 2331 C THAT DIAGONAL ELEMENTS A(I.I) ARE 1. 2389 2332 C 2390 2333 II • (I - 1) • M • 1 2391 2334 IF (A(II) .LE. 0.0) GO TO 120 2392 2335 10 MULT(I) . 1.0 / DSORT(A(II)) 2393 2336 KK - 1 2394 2337 00 50 I • 1. N 2395 2338 II • (I - 1) • M • 1 2396 2339 JEND • II • MM 2397 2340 IMN » (I - 1) * M - N 2398 2341 IF (IMN .GT. 0) JEND • JEND - IMN 2399 2342 DO 20 J • 11. JEND 2400 2343 A(J) • A(J) • MULT(I) 2401 2344 20 CONTINUE 2402 2345 DO 30 J - KK. I I . MM 2403 2346 30 A(J) • A(J) • MULT(I) 2404 2347 IF (KK .GE. M) GO TO 40 2405 2348 KK • KK * 1 2406 2349 GO TO 50 2407 2350 40 KK • KK • M 2408 2351 50 CONTINUE 2409 2352 60 MP • M * 1 24 10 2353 C 241 1 2354 C TRANSFORMATION OF A. 2412 2355 C A IS TRANSFORMED INTO A LOWER TRIANGULAR MATRIX L SUCH THAT A •L.LT 2413 2356 C (LT'TRANSPOSE OF L.). IF Y'LT.X THEN L.Y -B. 2414 2357 C ERROR RETURN TAKEN IF RATIO*1.E-7 2415 2358 C 2416 2359 KK - 2 2417 2360 NCN - 0 2418 2361 DET - 0. .'419 2362 FAC - RATIO 2120 2363 IF (A( 1 ) GT. 0. ) GO TO 70 2 121 2364 NROW • 1 2-22 2365 RATIO • A(1) 2<23 2366 GO TO 310 2424 2367 70 DET • A(1) 2425 2368 A(1) • 1. / DS0RT(A(1)) 2426 2369 BIGL - A O ) 2427 2370 SML • A(1 ) 2428 2371 A(2) • A(2) • A(1) 2429 2372 TEMP • A(MP) - A(2) * A(2) 2430 2373 IF (TEMP .LT. 0.0) RATIO - TEMP 2431 2374 IF (TEMP .EO. 0.0) RATIO • 0.0 2432 2375 IF (TEMP .GT. 0.0) GO TO 140 2433 2376 NROW • 2 2434 2377 GO TO 310 2435 2378 80 DET • 1.00 2436 NCN • O DO 110 I • 1. N DET - DET • A(I) IF (A(I) .EO. 0.0) GO TO 120 IF (DET .GT. 1.E-15) GO TO 90 DET • DET • 1.E*15 NCN • NCN - 15 GO TO 100 90 IF (OET .LT. 1.E+15) GO TO 100 DET • DET • 1.E- 15 NCN - NCN • 15 100 CONTINUE 110 B(I) - B(I) / A(I) RETURN 120 RATIO > A(I) 130 NROW • I GO TO 310 140 A(MP) • 1.0 / DSORT(TEMP) DET - DET • TEMP IF (A(MP) .GT. BIGL) BIGL - A(MP) IF (A(MP) .LT. SML) SML • A(MP) IF (N .EO. 2) GO TO 290 MP • MP + M DO 280 J - MP. NM 1 , M JP - J - MM MZC - O IF (KK .GE. M) GO TO 150 KK • KK • 1 II • 1 JC » 1 GO TO 160 150 KK • KK • M II « KK - MM JC - KK - MM 160 DO 180 I - KK, JP. MM IF (A(I) .EO. 0.) GO TO 170 GO TO 190 170 JC « JC + M 180 MZC - MZC • 1 ASUM1 • O.DO GO TO 240 190 MMZC » MM • MZC II - II • M2C KM * KK + MMZC A(KM) • A(KM) • A(JC) IF (KM .GE. JP) GO TO 220 KJ • KM • MM DO 210 I • KJ, JP. MM ASUM2 - O.DO IM • I - MM II » II + 1 KI « II.+ MMZC DO 200 K - KM, IM, MM ASUM2 • ASUM2 + A(KI) • A(K) 200 KI » Kl * MM 210 A(I) • (A(I) - ASUM2) • A(KI) 220 CONTINUE ASUM1 'O.DO 2437 00 230 K • KM, UP. MM 2495 1 2438 230 ASUM1 • ASUM1 * A(K) • A(K) 2496 1 2439 240 S • A(J) - ASUM1 2497 2440 IF (S .LT. 0.) RATIO • S 2498 2441 IF (S .EO. 0.) RATIO • 0. 2499 2442 IF (S .GT. 0.) GO TO 250 2500 2443 NROW - ( J • MM)' / M 2501 2444 GO TO 310 2502 244S 250 A(J) • 1. / OSQRT(S) 2503 50 2446 OET - DET • S 2504 2447 IF (DET .GT. 1.E-15) GO TO 260 2505 60 2448 DET • OET • 1.E+15 2506 2449 NCN • NCN - 15 2507 2450 GO TO 270 2508 2451 260 IF (DET .LT. 1.E*15) GO TO 270 2509 70 2452 DET - DET • 1.E-15 2510 80 1 2453 NCN • NCN • 15 251 1 90 1 2454 270 CONTINUE 2512 1 2455 IF (A(J) .GT. BIGL) BIGL • A(d) 2513 1 2456 IF (A(J) .LT. SML) SML - A(J) 2514 1 2457 280 CONTINUE 2515 1 2458 290 IF (SML .LE. FAC'BIGL) GO TO 300. ' 2516 2459 GO TO 330 2517 2460 300 RATIO • 0. 2518 2461 RETURN 2519 2462 310 WRITE (6.320) NROW 2520 2463 320 FORMAT ('0"«SYSTEM IS NOT POSITIVE DEFINITE', 2521 2464 1 ' ERROR CONDITION OCCURRED l IN ROW'. 14) 2522 2465 RETURN 2523 2466 330 RATIO - SML / BIGL 2524 2467 340 CALL DSBANO(A. MULT. B. N, M. NSCALE) 2525 ioo 2468 RETURN 2526 1 10 I 2469 END 2527 2470 SUBROUTINE DSBAND(A. MULT. B. N, M. NSCALE) 2528 i 2471 IMPLICIT REAL*B(A - H.O - Z) 2529 120 1 2472 DIMENSION A(1), 8(1) 2530 130 1 2473 REAL'S MULT(1) 2531 1 2474 MM « M - 1 2532 C 2475 NM » N • M 2533 C 2476 NM1 • NM - MM 2534 2477 C 2535 1 2478 C THE FOLLOWING STATEMENTS SOLVE FOR L.Y-B BY A FORWARDS 2536 2 2479 C HENCE FOR X FROM LT.X-Y BY A BACKWARDS SUBSTITUTION. 2537 C 2480 C IF SCALING OPTION USED. B IS SCALEO AND NORMALISED BEFORE 2538 C 2481 C SUBSTITUTION BEGINS. 2539 I 2482 C 2540 1 2483 10 SUM • O.DO 2541 2 2484 IF (NSCALE .EQ. 0) GO TO 40 2542 1 2485 DO 20 I ' 1. N 2543 1 2486 B(I) • B(I) • MULT(I) 2544 C 2487 SUM - SUM « B ( l ) • B(I) 2545 1 2488 20 CONTINUE 2546 2489 ELENB - DSORT(SUM) 2547 2490 DO 30 I • 1. N 2548 2491 30 B(I) - B(I) / ELENB 2549 2492 40 B(1) • B(1) • A(1) 2550 2493 KK • 1 2551 2494 Kl • 1 2552 2. N O.DO - 1 M .GE. M) GO TO 50 + 1 M 1 K l . LM BSUM1 + A(JK) • B(K) A(J) d • 1 DO 80 L • BSUM1 -LM > L J - J + IF (KK KK ' KK GO TO 60 KK • KK + Kl • K l * OK • KK DO 70 K -BSUM1 • UK > JK 4 CONTINUE B(L) - (B(L) B(N) • B(N) « NMM ' NM1 NN • N - 1 ND • N DO 110 L " 1, NN BSUM2 - O.DO NL • N - L NL1 - N - L NMM - NMM - M NJ1 - NMM IF (L .GE. M) ND • ND - 1 DO 100 K - NL1. ND NJ1 » NJ1 + 1 BSUM2 « BSUM2 + A(NJ1) CONTINUE B(NL) • (B(NL) - BSUM2) • A(NMM) IF (NSCALE .EO. O) GO TO 130 DO 120 I " 1, N - BSUM1) A(NM1) 1 B(K) MULT(I) END SUBROUTINE MEMFO(NRM, XM. YM, G. CRMOM. KL. KG. MML. FEM) DM, AV. NP. F, EXTL. EXTG. AREA. E. AXIAL. SHEAR 1. SHEAR2. BML. BMG. NML. DIMENSION XM(NRM), YM(NRM), DM(NRM), AV(NRM), NP(6.NRM) D(6). EXTL(NRM). EXTG(NRM). KL(NRM), KG(NRM). F(500). AREA(NRM). CRMOM(NRM). DIMENSION AXIAL(NRM). SHEAR2 (NRM ) DO 110 1 • 1. NRM XL • XM(I) YL • YM(I) OL • DM(I) AV1 - AV(I) DO 30 MEMDOF • 1. 6 N1 > NP(MEMDOF.I) IF (NI) 20. 20. 10 E(NRM). MML(IOO). FEM(100.4) SHEAR 1(NRM) . BML(NRM), BMG(NRM), G(NRM). , SHEAR(250) O Ul 2553 10 D(MEMOOF) • F(N1) 2554 GO TO 30 2555 20 O(HEMOOF) • 0. 2556 30 CONTINUE 2S57 C HOOIFY END DISP FOR HORZ MEMBERSWITH ENO EXT.(VALIO FOR 2558 C HORZ. MEMBERS ONLY) 2559 N3 • NP(3.I) 2560 IF (N3 .EO. 0) 00 TO 40 2561 D(2) - 0(2) • (F(N3)) • EXTL(I) 2S62 40 CONTINUE 2563 N6 • NP ( 6, I ) 2564 IF (N6 .EO. 0) GO TO 50 2565 0(5) - D(S) - (F(N6)) • EXTG(I) 2S66 50 CONTINUE 2567 AXIAL(I) • (AREA(I)"E(I)/DL«-2) * (D(4)*XL • D(5)*YL - D(1)«XL -2568 1 D(2)*YL) 2569 EI5I > CRMOM(I) • E(I) 2570 C INCLUOE SHEAR OEFL. GFACT'O MEANS NO SHEAR OEFL. 2571 GFACT • 0. 2572 IF (AVI .EO. 0.0 .OR. G(I) .EO. 0.0) GO TO 60 2573 GFACT » 12.0 * EISI / (AV1*G(I)*DL*0L) 2574 60 CONTINUE 2575 C ASSIGN DISP TO RESPECTIVE D.O.F. 2576 C CHECK FOR PIN-PIN MEMBERS 2577 IF (KL(I) .EO. 0 .AND. KG(I) .EO. 0) GO TO 90 2578 DELT • ((0(5) - D(2))*XL + (DO) - 0(4))*YL) / DL 2579 BML(I) • (2.0*EISI/(DL*(1.0 + GFACT))) • ((3.O-DELT/DL) - (D(6)* 2580 (1.0 - GFACT/2.0)) - (2.0*D(3)*(1.0 + GFACT/4.0))) 2581 BMG(I) • -(2.0'EISI/(DL"O .0 + GFACT))) • ((3.0'DELT/DL) - (D(3) 2582 •O.O - GFACT/2.0)) - (2.0*D(6)»(1.0 + GFACT/4.0))) 2583 SHEAR(I) - (6.0*EISI/(DL*0L)) • ((D(3) • D(6) - (2.O'OELT/OL))/( 2584 1 1.0+ GFACT ) ) 2585 IF (KL(I) - KG(I)) 70. 100. 80 2586 c PIN-FIX MEMBER FORCES 2587 70 BMG(I) • BMG(I) • 8MLU) • O.O - GFACT/2.0) / (2.0*0.0 • 2588 GFACT/4.0)) 2589 SHEAR(I) • SHEAR(I) • 1.5 * BML(I) / DL 2590 BML(I) - 0. 2591 GO TO 100 2S92 c FIX-PIN MEMBERS 2593 80 BML(I) * BML(I) + BMG(I) * (1 .0 - GFACT/2.0) / (2.0*0.0 + 2594 GFACT/4.0)) 2595 " SHEAR(I) - SHEAR(I) - 1.5 * BMG(I) / DL 2S96 BMG(I) • 0. 2597 GO TO 100 2598 c PIN-PIN MEMBERS 2599 90 BML(I) • 0. 2600 BMG(I) • 0. 2601 SHEAR(I) - 0. 2602 100 CONTINUE 2603 . SHE ARK I) • SHEAR(I) 2604 SHEAR2(I) • SHEAR(I) 2605 110 CONTINUE 2606 IF (NML .EO. 0) GO TO 150 2607 DO 140 1 * 1 . NRM 2608 DO 120 J " 1. NML 2609 IF (I .EO. MML(J)) GO TO 130 2610 120 CONTINUE 2611 2612 2613 2614 261S 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 GO TO 140 130 CONTINUE BML(I) - BML(I) * FEM(J,2) BMG(I) • BMG(I) + FEM(J.4) SHEAR 1(1) - SHEAR(I) • FEM(J.I) SHEAR2U) • SHEAR(I) - FEM(J.3) 140 CONTINUE 150 CONTINUE RETURN END 10 SUBROUTINE GEN1(X. Y, IdT. LJT. NJT. KDIF) GENERATES NODES ALONG STRAIGHT LINE DIMENSION X(32S). Y(32S) XI « X(IJT) YI • Y(IJT) DX - X(LJT) - XI DY - Y(LJT) - YI OX - OX / FLOAT(NJT DY • DY / FLOAT(NJT DO 10 I - 1 . NJT IJT - IJT • KDIF XI - XI • DX YI - YI + DY X(IJT) • XI Y(IJT) - YI RETURN END D 1) SUBROUTINE GEN2(MMR, W, XM. KL. KG. NP. F, JL. FEM) DIMENSION XM(200). KL(200). KG(20O). NP{6.200). F(500). FEMO00.4) IF (KL(MMR) + KG(MMR) - 1) 50. 20. 10 R3 R6 R2 RS GO TO 60 R2 R3 -W • XM(MMR) • XM(MMR) / 12. -R3 -0.5 • W « XM(MMR) R2 KL(MMR) - KG(MMR)) 30, 70. 40 O. W « XM(MMR) • XM(MMR) / 8. -0.5 • V • XM(MMR) - R6 / XM(MMR) -0.5 • V • XM(MMR) + R6 / XM(MMR) IF R3 R6 R2 R5 GO TO 60 R3 R6 R2 R5 GO TO 60 W * XM(MMR) " XM(MMR) / 8. O. -0.5 • W • XM(MMR) - R3 / XM(MMR) -0.5 * W • XM(MMR) + R3 / XM(MMR) -0.5 • W • XM(MMR) 0. O at 2669 R5 • R2 2727 2670 R6 - 0. 2728 2671 60 CONTINUE 2729 2672 d i • NPO.MMR) 2730 2673 d2 • NPO.MMR) 2731 2674 d3 • NP(2.MMR) 2732 2675 d4 • NP(5,MMR) 2733 2676 F(d3) - F(d3) • R2 „ 2734 2677 F(d4) • F(d4) • R5 2678 F ( d l ) • F( d l ) • US 2679 F(J2) • F(d2) * R6 2680 FEM(dL.I) • -R2 2681 FEM(dL.2) - R3 2682 FEM(dL.3) » -RS 2683 FEM(dL.4) > -R6 2684 70 CONTINUE 2685 RETURN 2686 ENO 2687 C •••• 2688 C 2689 SUBROUTINE CDUCT'CD, BM1. BM2, NP, NRM. MEM. DM, FCD. NU. DAMAGE, 2690 1 E. CRMOM, BMCAP, HARO) 2691 C 2692 C ....................... 2693 C CONVERTS DAMAGE RATIOS TO CURVATURE DUCTILITIES 2694 DIMENSION NP(6.NRM), DM(NRM), FCD(NU). BMCAP(NRM), E(NRM), 2695 1 CRMOM(NRM) 2696 C CHECK WHETHER MEMBER IS IN DOUBLE OR SINGLE CURVATURE 2697 IF (BM1 .LT. 0.) GO TO 10 2698 IF (BM2 .LT. O.) GO TO 50 2699 GO TO 20 2700 10 IF (BM2 .LT. O.) GO TO 20 2701 GO TO 50 2702 20 CONTINUE 2703 C MEMBER IS IN SINGLE CURVATURE 2704 B l - BMt - 8M2 2705 BM • ABS(B1) • 0.95 2706 IF (NPO.MEM) . EO. 0) GO TO 30 2707 THETA - (ABS(BMI) • BM) • 0.95 • OM(MEM) / (2.*E(MEM)*CRMOM(MEM)) 2708 N1 - NPO.MEM) 2709 GO TO 40 2710 30 THETA - (ABS(BM2) • BM) • 0.95 • DM(MEM) / (2. *E(MEM)*CRMOM(MEM) ) 2711 NI • NPO.MEM) 2712 40 CONTINUE 2713 ROTN • ABS(FCD(N1)) - THETA 2714 THETAP • ROTN - ROTN * (1. - DAMAGE'HARD) / (OAMAGE*(1. - HARD)) 2715 CD • 1. • THETAP • E(MEM) • CRMOM(MEM) / (0.05*DM(MEM)*BMCAP(MEM)) 2716 GO TO 60 2717 50 CONTINUE 2718 C MEMBER IS IN DOUBLE CURVATURE 2719 IF (NPO.MEM) . EO. 0) BMX • BM2 2720 IF (NPO.MEM) . EO. O) BMX • BM1 2721 XI • ABS(BMX) / (ABS(BMI) * ABS(BM2)) 2722 X2 • 0.95 - XI 2723 BM - ABS(BMX) • X2 / XI 2724 THETA1 » A8SI8MX) • XI • DM(MEM) / (2.*E(MEM)•CRMOM(MEM)) 2725 THETA2 • BM • X2 • DM(MEM) / (2.*E(MEM)*CRMOM(MEM)) 2726 IF (NPO.MEM) . EO. O) N1 • NPO.MEM) IF (NPO.MEM) .EO. O) NI - NPO.MEM) ROTN . FCO(NI) ROTN • ABS(ROTN) • THETA1 - THETA2 THETAP - ROTN - ROTN • (1. - DAMAGE*HARD) / (DAMAGE'd - HARD)) CONTINUE* ™ E T A P ' E < M E M > ' C R M 0 M < M E M ' I <005*DM(MEM)*BMCAP(MEM)) RETURN END APPENDIX B FREEMAN'S METHOD  PROGRAM INPUT Use any c o n s i s t e n t set of u n i t s , there i s no i n t e r n a l c o n v e r s i o n of u n i t s i n the program. 1. TITLE : TITLE (20A4) one c a r d Problem t i t l e of maximum 80 c h a r a c t e r l e n g t h 2. SEISMIC LOAD INFORMATION : ISPEC, AMAX, KOU, GG (I5,F10.5,I5,F8.2) one c a r d ISPEC : Input spectum type :-1 = Spectrum 'A' from Shibata and Sozen 2 = N a t i o n a l B u i l d i n g Code Spectrum AMAX : Maximum ground a c c e l e r a t i o n (g) KOU : 1 = F i r s t mode f o r c e s i n +ve x - d i r e c t i o n 2 = F i r s t mode f o r c e s i n the -ve x - d i r e c t i o n (See Note 1) GG : A c c e l e r a t i o n due to g r a v i t y (g) 3. STRUCTURAL INFORMATION : NRM, NMB, NRJ, NCONJT, NCDJT, NCDOD, NCDIDS, NCDMS (215,F10.2,515) one c a r d NRM : Number of members i n the s t r u c t u r e NMB : Number of beams i n the s t r u c t u r e NRJ : Number of j o i n t s i n the s t r u c t u r e NCONJT : Number of ' c o n t r o l j o i n t s ' f o r which the 108 109 c o - o r d i n a t e s are s p e c i f i e d (See Note 2) NCDJT : Number of commands f o r j o i n t s c o - o r d i n a t e g e n e r a t i o n (See Note 2) NCDOD : Number of commands f o r s p e c i f y i n g j o i n t s with zero displacements (See Note 3) NCDIDS : Number of commands f o r s p e c i f y i n g j o i n t s with i d e n t i c a l displacements (See Note 4) NCDMS : Number of commands f o r s p e c i f y i n g lumped masses at j o i n t s (See Note 5) CONTROL JOINTS CO-ORDINATES : IJT, X, Y (15,2F10.1) one c a r d / c o n t r o l j o i n t IJT : J o i n t number, i n any sequence X : x co - o r d i n a t e of the j o i n t Y : y co - o r d i n a t e of the j o i n t COMMANDS FOR GENERATION OF JOINT CO-ORDINATES : Omit i f there are no generat i o n commands IJT, LJT, NJT, KDIF (415) one card/command IJT : J o i n t number at the beginning of gen e r a t i o n l i n e LJT : J o i n t number at the end of generation l i n e NJT : Number of j o i n t s to be generated along the l i n e KDIF : J o i n t number d i f f e r e n c e between two s u c c e s s i v e nodes on the l i n e ( c o n s t a n t ) . I f blank or zero assumed to be equal to 1 COMMANDS FOR JOINTS WITH ZERO DISPLACEMENTS : Omit i f no j o i n t s r e s t r a i n e d to have zero displacements 1 10 IJT, KDOF(1), KDOF(2), KDOF(3), LJT, KDIF (13,518) one card/command IJT : J o i n t number, or f i r s t j o i n t i n the s e r i e s covered by t h i s command KDOF(1) : Code f o r X displacement, 0 i f r e s t r a i n e d from displacements i n x d i r e c t i o n , 1 i f f r e e to d i s p l a c e KDOF(2) : Code f o r Y displacement KDOF(3) : Code f o r r o t a t i o n LJT : Last j o i n t i n t h i s s e r i e s , punch 0 or leave blank f o r a s i n g l e j o i n t KDIF : J o i n t number d i f f e r e n c e between s u c c e s i v e j o i n t s i n t h i s s e r i e s ( c o n s t a n t ) , i f blank or zero assumed to be equal to 1 7. COMMANDS FOR JOINTS WITH IDENTICAL DISPLACEMENTS : Omit i f no j o i n t s r e s t r a i n e d to have i d e n t i c a l displacements MDOF, NJT, IJOINT(NJT) (215,1415) one card/command MDOF : Displacement code : 1 : for x displacement 2 : for y displacement 3 : f o r r o t a t i o n NJT : Number of j o i n t s covered by t h i s command (max. 14) IJOINT : L i s t of nodes covered by t h i s command, i n i n c r e a s i n g order 111 8. MEMBER INFORMATION : MN,JNL,JNG,KL,KG,E,G,AREA,CRMOM,BMCAP,EXTL,EXTG,AV (515,2F10.1 ,F8.2,F15.3,F15.3,3F8.2) one card/member MN : Member number JNL : Lesser j o i n t number JNG : Greater j o i n t number KL : F i x i t y code at l e s s e r j o i n t 0 : Pinned 1 : F i x e d KG : F i x i t y code at gr e a t e r j o i n t E : Young's Modulus G : Shear Modulus (0 i f shear d e f l e c t i o n s are to be neglected) AREA : C r o s s - s e c t i o n a l area of the member CRMOM : Moment of i n e r t i a of the member BMCAP : Y i e l d moment of the member EXTL : R i g i d e xtension on the l e s s e r end ' j o i n t of the member EXTG : R i g i d e xtension on the gr e a t e r end j o i n t of the member AV : Shear area of the member (0 i f shear d e f l e c t i o n s are to be neglected) Note : I f E, G, AREA, CRMOM, BMCAP, EXTL, EXTG, AV are l e f t b l a n k or g i v e n z e r o f o r a member, same v a l u e s as f o r the p r e v i o u s member w i l l be assumed. 9. DAMPING VALUES : DAMP1, DAMP2 1 12 (2F5.3) one card DAMP1 : Damping i n the e l a s t i c s t r u c t u r e (% of c r i t i c a l damping) DAMP2 : Damping value at the maximum response (% of c r i t i c a l damping) 10. COMMANDS FOR LUMPED MASSES AT THE JOINTS : IJT, WTX, WTY, WTR, JJT, KDIF (I 5,3F10.2,215) one card/command IJT : J o i n t number or f i r s t j o i n t in a s e r i e s covered by t h i s command WTX : Weight a s s o c i a t e d with x-displacement WTY : Weight a s s o c i a t e d with y-displacement WTR : R o t a t i o n a l weight JJT : Number of l a s t j o i n t in the s e r i e s , punch 0 or leave blank f o r a s i n g l e j o i n t KDIF : J o i n t number d i f f e r e n c e between s u c c e s s i v e j o i n t s i n t h i s s e r i e s ( c o n s t a n t ) , i f blank or zero assumed to be equal to 1 11. STATIC LOAD INFORMATION : NJLS, NLGCJ, NML, NLGCM (415) one card NJLS : Number of j o i n t s loaded by s t a t i c loads NLGCJ : Number of generation commands f o r s t a t i c loads a p p l i e d d i r e c t l y at the nodes (See Note 6) NML : Number of members loaded by unif o r m l y d i s t r i b u t e d s t a t i c l o a d NLGCM : Number of genera t i o n commands f o r s t a t i c loads 1 1 3 on the members (See Note 6) Cards 12A and 12B are omitted i f NJLS i s zero. A. COMMANDS FOR STATIC LOADS APPLIED DIRECTLY ON THE  JOINTS : Omit i f NLGCJ i s zero FX, FY, FM, NNOD, NODN(NNOD) (3F10.1,1015) one card/command FX : Load i n x - d i r e c t i o n FY : Load i n Y - d i r e c t i o n FM : Moment NNOD : Number of j o i n t s t o be covered by t h i s command NODN : L i s t of j o i n t s covered by t h i s command i n i n c r e a s i n g order OR B. STATIC LOADS APPLIED DIRECTLY AT JOINTS : input t h i s i f NLGCJ = 0 N, FX, FY, FM (15,3F10.1) one card/loaded j o i n t N : Node number FX : Load i n the x - d i r e c t i o n FY : Load i n the y - d i r e c t i o n FM : Moment NOTE : ONLY CARDS 12A OR 12B ARE TO BE INPUT IN THE DATA, NOT BOTH. Cards 13A and 13B to be omitted i f NML equals zero. A. COMMANDS FOR STATIC MEMBER LOADS : Omit i f NLGCM i s zero. 1 1 4 W, NMEM, MR(NMEM) (F6.1,1415) one card/command W : Uniformly d i s t r i b u t e d load on the member, downward loa d p o s i t i v e NMEM : Number of members covered by t h i s command MR : L i s t of members covered by t h i s command i n i n c r e a s i n g order OR B. STATIC MEMBER LOADS : Omit i f NLGCM i s not zero. MMR, W (I5,F10.4) one card/loaded member MMR : Member number W : Uniformly d i s t r i b u t e d s t a t i c load NOTE : ONLY CARDS 13A OR 13B TO BE INPUT IN THE DATA WHEN NML IS NOT ZERO, NOT BOTH. 1 REAL-B SOOOOO) 2 C 3 C 4 C 5 C FREEMAN'S METHOD FOR EARTHQUAKE RESPONSE PREDICTION 6 C 7 C • • 8 C THIS METHOD CONSIDERS ONLY FUNDAMENTAL MODE OF VIBRATION 9 C 10 C PROGRAM DIMENSIONED FOR A MAXIMUM OF :-I I C 12 C 250 MEM8ERS 13 C 200 JOINTS 14 C 100 ASSIGNED MASSES 15 C 16 C VARIABLE DEFINITIONS:-17 C 18 C KL.KG - JOINT TYPE : FIXED JOINT • 1 19 C PINNED JOINT » 0 20 C AREA - CROSS-SECTIONAL AREA 21 C CRMOM - MOMENT OF INERTIA OF GROSS SECTION 22 C BMCAP - BENDING MOMENT CAPACITY OF SECTION 23 C ND D.O.F. NO. IDENTIFIED BY JOINT NO. 24 C ND(K.I) - K • 1 (X-DOF). 2 (Y-DOF). 3 (R-OOF) 25 C I - JOINT NO. 26 C NP 0.0.F. NO. IDENTIFIED BY MEMBER NO. 27 C NP(K.I) - K • OOF 1 TO 6 FOR STANDARD MEMBER 28 C I « MEMBER NO. 29 C ' XM • LENGTH OF FLEXIBLE PORTION OF BEAM IN X-DIRECTION 30 C YM LENGTH OF FLEXIBLE PORTION OF BEAM IN Y-DIRECTION 31 C DM . TRUE LENGTH OF FLEXIBLE PORTION OF BEAM 32 C F • LOAD VECTOR 33 C EXTL,EXTG - LENGTH OF RIGID END 34 C TITLE - TITLE (80 CHARACTERS) 35 C AV • SHEAR AREA 36 C MDOF - 0.0.F. NO. FOR MASSES IDENTIFIED BY MASS NO. 37 C AMASS • LUMPED MASS (IN UNITS OF WEIGHT) IN0ENT1FY BY 38 C D.O.F. NO. 39 C EVAL • EIGENVALUE 40 C EVEC • MODE SHAPE 41 C EVEC(K.I) - K - MASS NO. 42 C I • MODE NO. 43 C SOEL • ELASTIC MODEL SPECTRAL DISPLACEMENT 44 C SAEL - ELASTIC MODEL SPECTRAL ACCELERATION 45 C RMAX • ROOF DISPLACEMENT AT YEILDING OF STRUCTURE 46 C DAMP 1 • EFFECTIVE DAMPING FOR ELASTIC MOOEL OF STR. 47 C DAMP2 » EFF. DAMPING FOR MAX. INELASTIC EXCURSION 48 C 49 C 50 C 51 C 52 DIMENSION KL(250). KG(250). AREA(2S0). CRM0M(2S0). BMCAP(250). 53 1 NDO.200). NP(6.250). XM(2S0). YM(250). DM(250). F(SOO). 54 2 EXTL(250), EXTG(2S0). TITLE(20). AV(2S0). MDOF(IOO). 55 3 AMASS(500). EVAL(IO). EVECI500,10). ALPHA(IO). DAMP(20), 56 4 T(40), E(250). G(250) 57 CALL FTNCMO('EQUATE 99-SPRINT:') 58 CALL CONTRL(NRJ, NRM, NMB. ISPEC. AMAX. KOU. NCONJT. NCDJT, NCDOD, 59 1 NCOIDS. NCDMS. GG) 60 IDIM • 30000 61 CALL SETUP(NRM. E. G. XM. YM, DM. NO. NP, AREA. CRMOM. NRJ. AV. 62 1 KL, KG. NU. NB. BMCAP, EXTL. EXTG, DAMP 1. DAMP2, NCONJT. 63 2 NCDJT. NCDOD, NCDIDS) 64 CALL MASS(NU. ND. AMASS. NRJ. MDOF. NCDMS, GG) 65 CALL BUILD(NU, NB, XM, YM, OM, NP. AREA. CRMOM, AV. E. G, KL, KG, 66 1 NRM. S, IOIM. EXTL, EXTG) 67 CALL SCHECK(S, NU. NB, IDIM. SRATIO) 68 CALL EIGEN(NU. NB, S. IDIM. AMASS. EVAL. EVEC, 1. MDOF. PERIOD. 69 1 WN) 70 CALL M0D3(NRJ. NRM. NU. NB. S. IDIM. NO. NP. XM. YM. OM. AREA. AV, 71 1 CRMOM, KL. KG. BMCAP, E. G, AMASS, EVEC, EVAL. EXTL. EXTG. 72 2 NMB. ALPHA, RMAX. KOU. GG) 73 WRITE (6.10) 74 10 FORMAT (//. 'RESULTS FOR INELASTIC MODEL OF STRUCTURE') 75 C WHEN HALF OF THE BEAMS YIELDEO STR. ASSUMED YIELDED ASSIGN SX 76 C STIFF. VALUE TO BEAMS;BEAMS NUMBERED FIRST 77 DO 20 I > 1, NMB 78 CRMOM(I) " 0.05 • CRMOM(I) 79 20 CONTINUE 80 C MODE SHAPES NORMALIZED S.T.A(I.J) AT ROOF IS UNITY 81 SO » RMAX 7 ALPHA(1) 82 SDEL - SD 83 SAEL • WN • WN * SD 84 SAEL - SAEL / GG 85 TP - PERIOD 86 CALL BUILD(NU. NB, XM, YM, DM, NP, AREA. CRMOM. AV. E. G, KL. KG. 87 1 NRM. S. IOIM. EXTL. EXTG) 88 CALL SCHECK(S. NU. NB. IDIM. SRATIO) 89 CALL EIGEN(NU, NB. S. IDIM. AMASS. EVAL. EVEC. 1. MDOF, PERIOD. 90 1 WN) 91 C CALCULATE MODAL PARTICAPATION FACTOR 92 MCOUNT • 0 93 00 30 I • 1 , NU 94 IF (AMASS(I) .EO. 0.) GO TO 30 95 MCOUNT - MCOUNT + 1 96 30 CONTINUE 97 AMT - 0. 98 AMB • 0. 99 00 40 J • I. NU 100 AMT • AMT + AMASS(J) * EVEC(J.I) 101 AMB « AMB • AMASS(J) • ((EVEC(J,1))**2) 102 40 CONTINUE 103 ALPHA(1) • AMT / AMB 104 WRITE (6.50) ALPHA(1) 105 50 FORMAT (//. 'FIRST MOOE PARTICIPATION FACTOR-'. F5.2) 106 SOI - 5.0 • RMAX / ALPHA(I) 107 SA 1 - WN * WN * SD 1 108 SA1 • SA1 / GG 109 C NOW MAKE COMBINEO MODEL 110 S02 - SD * S01 111 SACOMB - SAEL + SA1 112 OMSQ • GG * SACOMB / S02 113 OMEGA • SORT(OMSO) 1 14 TPR » 6.283153 / OMEGA 115 WRITE (6.60) 116 117 WRITE (6.70) TP. SAEL 118 70 FORMAT (/. ' ELASTIC MODEL'. //. 'TIME PERIOD-', F6.3. 'SEC. IOX. 119 1 'SPEC ACCL(G)-', F7.3) 120 WRITE (6.80) TPR. SAC0M8 121 80 FORMAT (/, 'COMBINED MODEL'. //, 'TIME PERIOD''. F6.3. 'SEC. IOX. 122 1 'SPEC ACCL(G)"'. F7.3) 123 WRITE (6.90) 124 90 FORMAT (//, 'DEMAND SPECTRUM', /, ' ') 125 C DEMAND TRANSITION CURVE 126 WRITE (6,100) 127 WRITE (6,110) TP, DAMP 1 128 T(1) • TP 129 DAMP(1) • DAMP 1 130 100 FORMAT (/. SX. 'TIME PD.', 10X, 'DAMPINGU OF CRIT.)') 131 110 FORMAT (7X, FS.3. 15X, F5.1) 132 0 • 5.0 • RMAX / (DAMP2 - DAMP 1) 133 ROOFOI • RMAX 134 DI - 1.0 135 DO 120 I • 2, 15 136 DAMP(l) » DAMP 1 + 01 137 ROOFDI • ROOFDI * 0 138 SPDISP » ROOFDI / ALPHA(1) 139 COMBSD - SD + SPDISP 140 SPACL - WN • WN • SPDISP 14 1 SPACL - SPACL / GG 142 COMBSA - SAEL + SPACL 143 OMSO - GG • COMBSA / COMBSD 144 OMEGA - SORT(OMSO) 145 T(I) - 6.283153 / OMEGA 146 WRITE (6,110) T ( I ) . DAMP(I) 147 IF (DAMP(I) .EO. DAMP2) GO TO 130 148 DI - D1 • 1.0 149 120 CONTINUE 150 130 CONTINUE 151 NM - DAMP2 - DAMP 1 + 1. 152 C HAVE NM VALUES OF T & DAMP; DAMP NOW CONVERTED TO FRACTIONS 153 DO 140 IU • 1. NM 154 140 OAMP(IU) - DAMP(IU) / 100. 155 TN • TP 156 DO 180 I • 1. 40 157 CALL SPECTR(OAMP, T. SA, ISPEC, AMAX, NM, TN) 158 IF (TN .EO. TP) GO TO 160 159 150 CONTINUE 160 SACAP • (SACOMB - SAEL) • (TN - TP) / (TPR - TP) + SAEL 161 SACH - SA - SACAP 162 IF (SACH .LE. 0.05 .AND. SACH .GE. - 0.05) GO TO 200 163 CELT - (SA - SACAP) / 4. 164 TN • TN • OELT 165 GO TO 180 166 160 CONTINUE 167 IF (SA .GE. SAEL) GO TO 150 168 WRITE (6.170) 169 170 FORMAT (/. 5X. 'IN THIS PARTICULAR EO. STRUCTURE REMAINS ELASTIC 170 I, THUS NO OAMAGE') 171 STOP 172 180 CONTINUE 173 WRITE (6.190) 174 190 FORMAT ( 'CAPACITY & DEMAND CANNOT BE RECONCILED') 175 STOP 176 200 CONTINUE 177 WRITE (6,210) • 178 179 210 FORMAT (///. 8X. ' P R E D I C T E D R E S P O N S E ' . / . 5X, 1B0 SD • GG * SA * TN • TN / (4.•3. 14593*3. 141593) 181 DUCTIL - SO / SOEL 182 ICU - (SO - SDEL) • 100. / SD1 183 1RCAP - 100 - ICU 184 DO 230 I - 2, NM 185 IF (TN .GT. T(1) ) GO TO 230 186 TX - (T(I - 1) • T(I)) / 2. 187 IF (TN .GT. TX) GO TO 220 188 DPG • DAMP(I - 1) 189 GO TO 240 190 220 DPG » DAMP(I) 191 GO TO 240 192 230 CONTINUE 193 240 CONTINUE 194 DPG - 100. • DPG 195 WRITE (6.250) TN 196 WRITE (6.260) SA 197 WRITE (6.270) DPG 198 WRITE (6.280) SD 199 WRITE (6.290) DUCTIL 20O WRITE (6.30O) ICU 201 WRITE (6.310) 1RCAP 202 250 FORMAT (/, SX. 'PERIOD(SEC)'. 10X. F5.2) 203 260 FORMAT (/. SX. 'SPEC. ACCL(G)'. 9X, FS.3) 204 270 FORMAT (/. 5X. 'DAMPING(X)'. IOX, FS.1) 205 280 FORMAT (/. 5X. 'SPEC. OISP(FT)', 8X. F5.3) 206 290 FORMAT (/, 5X. 'DUCTILITY DEMAND'. 4X. F5.1) 207 300 FORMAT (/. 5X. 'INELASTIC CAPACITY'. 2X. 14. /. 5X. 'USEO') 208 310 FORMAT (/. 5X. 'RESERVE CAPACITY', 4X. 14) 209 STOP 210 END 21 1 C 212 C 213 C • **•«•*••***••*•«*««•••«•*•••*"""«*••"•"•*** 214 C 215 SUBROUTINE CONTRL(NRJ, NRM. NMB. ISPEC. AMAX. KOU. NCONJT, NCDJT. 216 1 NCDOD, NCDIDS. NCDMS. GG) 217 C 218 C 219 DIMENSION TITLE(20) 220 READ (5.60) (TITLE(I),I-1,20) 221 READ (5.70) ISPEC. AMAX. KOU. GG 222 READ (5.80) NRM, NMB. NRJ, NCONJT, NCDJT. NCDOO, NCDIDS. NCDMS 223 WRITE (6.60) ( T I T L E d ),I«1 .20) 224 WRITE (6.90) NRJ, NRM, NMB 225 IF (ISPEC .EO. 1) WRITE (6.30) 226 IF (ISPEC .EO. 2) WRITE (6.40) 227 IF (KOU .EO. 2) WRITE (6,10) 228 10 FORMAT ('IN THE REVERSE DIRECTION') 229 WRITE (6.50) AMAX 230 WRITE (6.20) GG 231 20 FORMAT (/. 'ACCL. DUE TO GRAVITY " '. F8.2. /) 232 30 FORMAT (/, '-SPECTRUM A USED') 01 233 40 FORMAT (/. '-NBC SPECTRUM USED') 234 50 FORMAT (/. '-MAX ACCL.-'. F5.3. 'TIMES GRAVITY') 235 60 FORMAT (20A4) 236 70 FORMAT (15, F10.S, 15. F8.2) 237 80 FORMAT (815) 238 90 FORMAT (/. 'NO.OF JOINTS •', 14, (OX. 'NO.OF MEMBERS •'. 14. IOX, 239 1 'NO OF BEAMS •'. 14) 240 RETURN 241 END 242 243 C 244 C 245 C 246 c 247 SUBROUTINE SETUP(NRM, E. G, XM. YM. DM. ND. NP, AREA. CRMOM. NRJ. 248 1 AV, KL, KG, NU, NB, BMCAP, EXTL. EXTG. DAMP 1, DAMP2, 249 2 NCONJT. NCDJT. NCDOD. NCDIDS) 250 c 251 c 252 ' c 253 c 254 c SET UP THE FRAME DATA 255 c 256 DIMENSION KL(NRM). KG(NRM), AREA(NRM), CRMOM(NRM), BMCAP(NRM), 257 1 AV(NRM), NDO.NRJ), NP(6.NRM). XM(NRM). YM(NRM). 258 2 EXTL(NRM). EXTG(NRM), OM(NRM), E(NRM). G(NRM) 259 DIMENSION X(200). Y(200), JNL(250), JNG(250). KD0F(3). IJ0INT(40) 260 c 261 c 262 c INITIALIZE COORDINATES 263 DO 10 I • 1. NRJ 264 X(I) • 999000. 265 10 Y(I) - 999000. 266 c REAO CONTROL NODE CORDINATES 267 WRITE (6.20) 268 20 FORMAT (//. 'CONTROL NODE COORDINATES'. ///. 'NODE', 6X. 269 1 'X-COORO'. 6X. 'Y-COORD'. /) 270 DO 50 I - 1 , NCONJT 271 READ (5.30) IJT." X(IJT). Y(IJT) 272 30 FORMAT (IS. 2F10.1) 273 WRITE (6.40) IJT. X(IJT), Y(IJT) 274 40 FORMAT (IS. 2F13.3) 275 SO CONTINUE 276 c NODE GENERATION COMMANDS 277 WRITE (6.60) 278 60 FORMAT (///' NODE GENERATION COMMANDS'/) 279 IF (NCDJT .NE. 0) GO TO 80 280 WRITE (6.70) 281 70 FORMAT (//, 'NONE') 282 GO TO 130 2B3 80 WRITE (6.90) 284 90 FORMAT (/2X. 'FIRST', 4X. 'LAST', 4X. 'NO. OF'. 4X. 'NODE'. /. 2X 285 1 'NOOE'. 5X. 'NODE*. 4X. 'NODES', SX, 'OIFF'. /) 286 DO 120 I - 1. NCDJT 287 READ (5,100) IJT. LJT. NJT. KDIF 288 100 FORMAT (415) 289 IF (KDIF .EO. 0) KDIF • 1 290 WRITE (6.110) IJT. LJT. NJT. KOIF 291 110 FORMAT (16, 318) 292 CALL GENKX. Y. IJT, LJT, NJT, KDIF) 293 120 CONTINUE 294 C GENERATE UNSPECIFIED JOINT COORDINATES 295 130 I - 1 296 140 1 * 1 + 1 297 IF (I .GT. NRJ) GO TO 160 298 IF (X(I) .NE. 999000.) GO TO 140 299 IJT • I - 1 300 LJT • IJT 301 150 LJT - LJT • 1 302 IF (LJT .GT. NRJ) GO TO 160 303 IF (X(LJT) .EO. 999O00.) GO TO 150 304 NJT » LJT - IJT - 1 305 CALL GENKX. Y. IJT. LJT, NJT, 1) 306 I - LJT 307 GO TO 140 308 160 CONTINUE 309 C ASSIGNING 0.0.F. TO THE NODES 310 DO 170 I » 1. NRJ 311 DO 170 J » 1. 3 312 170 ND(J.I) « 1 313 C ZERO DISPLACEMENTS 314 WRITE (6.180) 315 180 FORMAT (/. 'ZERO DISPLACEMENT COMMANDS'. //) 316 IF (NCDOD .NE. 0) GO TO 190 317 WRITE (6.70) 318 GO TO 270 319 190 WRITE (6,200) 320 200 FORMAT (/. 'FIRST', 6X, 'X'. 6X. 'Y', 4X, 'ROTN'. 4X, 'LAST'. 4X, 321 1 1 'NODE'. /. 'NODE', 7X, 'OOF'. 4X. 'OOF'. 3X. 'DOF', 4X. 322 2 'NODE'. 4X. 'OIFF'. /) 323 DO 260 I - 1. NCDOD 324 READ (5.210) IJT, (KDOF(J).J»1.3). LJT. KDIF 325 210 FORMAT (615) 326 WRITE (6.220) IJT. (KDOF(J).J-1.3). LJT. KDIF 327 220 FORMAT (13. 518) 328 DO 230 J - 1. 3 329 230 ND(J.IJT) - KDOF(J) 330 IF (LJT .EO. 0) GO TO 260 331 IF (KOIF .EO. 0) KDIF • 1 332 NJT « (LJT - IJT) / KOIF 333 00 250 II • 1. NJT 334 IJT - IJT + KDIF 335 DO 240 J • 1. 3 336 240 NO(J.IJT) - KDOF(J) 337 250 CONTINUE 338 260 CONTINUE 339 C IOENTICAL DISPLACEMENT 340 270 CONTINUE 34 1 WRITE (6,280) 34 2 280 FORMAT (///. 'EOUAL DISPLACEMENT COMMANOS '. /) 343 IF (NCDIDS .NE. 0) GO TO 290 344 WRITE (6.70) 345 GO TO 350 346 290 WRITE (6.30O) 347 300 FORMAT (//. 'DISP'. 4X. 'NO. OF', /, 'CODE'. 4X. 'NODES'. 6X, 348 1 'LIST OF NOOES'. /) 349 DO 340 1 - 1 . NCDIDS 350 READ (5.310) MKDOF, NJT. (IJOINT(IU).IU-1.NJT) 351 310 FORMAT (215. 1415) 352 WRITE (6.320) MKDOF. NJT, (IJOINT(IU).IU-1.NJT) 353 320 FORMAT (13. 18. 6X. 1415) 354 II • IJOINT(I) 355 00 330 IM '- 2. NJT 35S ' IK - IJOINT(IM) 357 330 NO(MKDOF.IK) • -II 358 340 CONTINUE 359 C TO SET UP NO ARRAY 360 350 NU • 0 361 WRITE (6,400) 362 DO 390 1 - 1 . NRJ 363 DO 380 J - 1, 3 364 IF (ND(J.I) .NE. 1) GO TO 360 365 NU - NU + 1 366 ND( J. I ) - NU 367 GO TO 380 368 360 IF (NO(J.I) .NE. 0) GO TO 370 369 ND(J.I) • 0 370 GO TO 380 371 370 II - -ND(J.I) 372 NO(J.I) • ND(J.II) 373 380 CONTINUE 374 WRITE (6.410) I. X(I). Y(I). (ND(J,I).J-1.3) 375 390 CONTINUE 376 400 FORMAT (/. 3X. 'JN'. 5X, 'X-COORD*. 5X. 'Y-COORO'. 5X. 'NDX', 5X, 377 1 'NOY', 5X, 'NOR'. /) 378 410 FORMAT (14. 2F13.2. 16. 5X. 14, 5X. 14) 379 C 3SO WRITE (6.580) 381 WRITE (6.590) 382 WRITE (6.600) 383 C 384 C READ IN MEMBER DATA ANO COMPUTE THE HALF BANDWIOTH (NB) 385 C HALF BANDWIDTH-MAX DEGREE OF FREEDOM-MIN DEGREE OF FREEDOM +1 386 C 387 C 388 NB • 0 389 390 DO 560 MBR - 1. NRM 391 READ (5.610) MN. JNL(MBR), JNG(M8R), KL(MBR). KG(MBR), E(MBR), 392 1 G(MBR), AREA(MBR). CRMOM(MBR), BMCAP(MBR), EXTL(MBR), EXTG(MBR) 393 2 AV(MBR) 394 395 C 396 C COMPUTE MEMBER LENGTH (DM)-LENGTH BETWEEN JOINTS-RIGID EXTENSIONS 397 JL • JNL(MBR) 398 JG - JNG(MBR) 399 XM(MBR) • X(JG) - X(JL) 400 YM(MBR) • Y(JG) - Y(JL) 401 DM(MBR) - S0RT((XM(MBR))*,2 • (YM(MBR))**2) 402 EXTSUM • EXTL(MBR) + EXTG(MBR) 403 XM(MBR) - XM(MBR) - (1.0 - EXTSUM/DM(MBR)) 404 YM(MBR) - YM(MBR) • (1.0 - EXTSUM/DM(MBR)) 405 C RESET NEGATIVE VALUES OF ZERO TO ZERO 406 IF (YM(MBR) .GT. - O.01 .ANO. YM(MBR) .LT. 0.01) YM(MBR) - 0.0 407 IF (XM(MBR) .GT. - 0.01 .AND. XM(MBR) .LT. 0.01) XM(MBR) - 0.0 40B DM(MBR) • OM(MBR) - EXTSUM 409 C 410 C CHECK FOR NEGATIVE LENGTHS OF MEMBER 411 c (PROBABLY CAUSED BY INCORRECT USE OF MEMBER EXTENSIONS) 412 c 413 IF (DM(MBR) .GT. 0.0) GO TO 430 4 14 WRITE (6.420) MBR 415 420 FORMAT (' '. ///'PROGRAM HALTED:ZERO OR -VE LENGTH FOR MEMBER', 416 1 16) 417 STOP 418 c 419 430 CONTINUE 420 c 421 YLEN - YM(MBR) 422 c 423 c PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS 424 c ON VERTICAL MEMBERS. 425 IF (EXTSUM .NE. 0.0 .AND. YLEN .GT. 0.2) WRITE (6.440) I 426 440 FORMAT (' ', 'ERROR-HAVE END EXTENSIONS ON NON-HORIZONTAL 427 1 MEMBER NO.', 13) 428 c PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON 429 c A NON FIX-FIX TYPE MEMBER 430 KLSUM - KL(MBR) • KG(MBR) 431 IF (EXTSUM .NE . 0.0 .AND. KLSUM .NE. 2) WRITE (6,450) MBR 432 450 FORMAT (' '. 'ERROR-HAVE RIGID EXTENSIONS ON HINGED MEMBER'. I< 433 c 434 c 435 c ASSIGN MEMBER DEGREES OF FREEDOM 436 NP(1.MBR) - ND(1.JL) 437 NP(2..MBR) - N0(2.JL) 438 NP(3.MBR) - ND(3.JL) 439 NP(4.MBR) - ND(1.JG) 440 NP(5.M8R) » ND(2.JG) 44 1 NP(6,MBR) - ND(3.JG) 442 c DETERMINE THE HIGHEST DEGREE OF FREEDOM FOR EACH MEMBER STORING 443 c THE RESULT IN 'MAX' 444 MAX - 0 445 c 446 DO 480 K • 1, 6 447 IF (NP(K.MBR) - MAX) 470. 470, 460 448 460 MAX - NP(K.MBR) 449 470 CONTINUE 450 480 CONTINUE 451 c 452 c DETERMINE THE MINIMUM DEGREE OF FREEDOM FOR EACH MEMBER.NOTE THAT 453 c FOR STRUCTURES WITH GREATER THAN 330 JOINTS INITIAL VALUE OF MIN 454 c WILL HAVE TO BE INCREASED FROM ITS PRESTENT POINT OF 1000. 455 c 456 c WILL HAVE TO BE INCREASEO FROM ITS PRESTENT POINT OF 1000. 457 c 458 MIN • 1000 459 c 460 00 520 K • 1 . 6 461 IF (NP(K.MBR)) 510. 510. 490 462 490 IF (NP(K.MBR) - MIN) 500. 510. 510 463 500 MIN - NP(K.MBR) 464 510 CONTINUE 09 465 520 CONTINUE 466 C 467 NBB • MAX - MIN • 1 468 IF (NBB - NB) 540. 540. 530 469 530 NB • NBB 470 540 CONTINUE 471 IF (E(MBR) .EO. 0.) E(MBR) - E(MBR - 1) 472 IF (MBR .EO. 1) GO TO 550 473 IF (G(MBR) .EO. 0.) G(MBR) • G(MBR - 1) 474 IF (AV(MBR) .EO. 0.) AV(MBR) - AV(MBR - 1) 475 550 CONTINUE 476 IF (AREA(MBR) .EO. 0.) AREA(MBR) • AREA(MBR - 1) 477 IF (CRMOM(MBR) .EO. O.) CRMOM(MBR) • CRMOM(MBR - 1) 478 IF (BMCAP(MBR) .EO. O.) BMCAP(MBR) » BMCAP(MBR - 1) 479 C PRINT MEMBER OATA 480 C 481 WRITE (6,620) MBR. JNL(MBR). JNG(MBR), EXTL(MBR). OM(MBR). 482 1 EXTG(MBR). XM(MBR), YM(MBR), AREA(MBR), CRMOM(MBR). AV(MBR), 483 2 BMCAP(MBR), KL(MBR). KG(MBR), E(MBR) 484 560 CONTINUE 485 C PRINT THE NO. OF DEGREES OF FREEDOM AND THE HALF BANDWIDTH 486 C 487 WRITE (6.630) NU 488 WRITE (6.640) NB 489 C READ DAMPING VALUES 490 READ (5.570) DAMP 1, DAMP2 491 570 FORMAT (2F5.3) 492 RETURN 493 580 FORMAT ('-'. 'MEMBER DATA') 494 S90 FORMAT (/• MN JNL JNG EXTL LENGTH EXTG XM YM 495 1 2X. 'AREA MOM OF I AV, 7X. 'MOMENT', 3X. 'KL'. 496 2 IX. 'KG'. 5X. ' E ') 497 600 FORMAT (85X. 'CAPACITY') 498 610 FORMAT (515. 2F10.1. F8.2, F15.3. F10.1. 3F8.2) 499 620 FORMAT (• '. 13. 214, F7.1, F9.2, F7.1, 2F9.2, F8.2. F15.3. F8.2. 500 1 F10.1. 213. F10.1) 501 630 FORMAT (//. 'NO.OF DEGREES OF FREEDOM OF STRUCTURE «'. 15) 502 640 FORMAT (/' HALF BANDWIDTH OF STIFFNESS MATRIX »'. 15) 503 END 504 C 505 C 506 C 507 C 508 SUBROUTINE BUILD(NU, NB, XM, YM. DM, NP, AREA, CRMOM. AV, E, G, 509 1 KL. KG. NRM, S. IDIM. EXTL. EXTG) 510 C 511 C • »••• »••» • 512 C 513 C 514 C THIS SUBROUTINE WORKS IN DOUBLE PRECISION 515 C THIS SUBROUTINE CALCULATES THE STIFFNESS MATRIX OF EACH 516 C MEMBER AND ADDS IT INTO THE STRUCTURE STIFFNESS MATRIX. 517 C THE FINAL STIFFNESS MATRIX S IS RETURNED. 518 C THIS SUBROUTINE IS SIMILAR TO ONE THAT WOULD BE USED IN NORMAL 519 C FRAME ANALYSIS. 520 C IOIM IS THE DIMENSIONING SIZE OF THE STRUCTURE STIFFNESS MATRIX. 521 C 522 REAL'S SM(21), S(IDIM) 523 524 525 526 527 528 529 530 531 C 532 C 533 C 534 535 536 537 C 538 c 539 c 540 c 541 542 c 543 c 544 c 545 546 547 548 c 549 c 550 551 552 553 554 555 556 557 558 559 560 c 561 562 563 564 565 566 567 c 568 569 570 571 572 573 c 574 c 575 c 576 577 578 579 5B0 DIMENSION XM(NRM) , YM(NRM) , DM(NRM), G ( N" M )-1 CRMOM(NRM). AV(NRM). KL(NRM). KG(NRM), EXTL(NRM). 2 EXTG(NRM), E(NRM) REAL*8 RF. GMOD, CMOMI, F, H REAL'S LONE. LONEX. LONEY. LTWO. LTWOX. LTWOY. AVI REAL'S YMI. OMI. DM2. XM2. YM2. XMI. AREAI. EMOD. XM2F. YM2F. 1 XMYMF REAL'S DBLE ZERO STRUCTURE STIFFNESS MATRIX DO 10 I • 1. IDIM S(I) • 0.0000 10 CONTINUE BEGIN MEMBER LOOP DO 200 I • 1, NRM ZERO MEMBER STIFFNESS NATRIX DO 20 J • t. 21 SM(J) - 0.0000 20 CONTINUE ASSIGN MEMBER PROPERTIES TO DOUBLE PRECESION VARIABLES EMOD - DBLE(EU)) GMOD - DBLE(G(I)) LONE - OBLE(EXTL(I)) LTWO - DBLE(EXTG(I)) YMI » DBLE(YM(I)) OMI • DBLE(DM(I)) XMI - DBLE(XM(I)) AREAI • OBLE(AREA(I)) CMOMI • DBLE(CRMOM(I)) AVI - D8LE(AV(I>) 0M2 - OMI • DMI XM2 • XMI • XMI YM2 " YMI • YMI XMYM - XMI • YMI F • AREAI * EMOD / (DMI*DM2) H ' 0.0000 SHEAR DEFLECTIONS ARE IGNORED WHENEVER G OR AV IS ZERO. IF (AV(I) .EO. 0.0 .OR. G(l) .EO. 0.) GO TO 30 H « 12.0000 • EMOO ' CMOMI / (AVI'GM0D*0M2) 30 XM2F • XM2 • F YM2F - YM2 • F XMYMF ' XMYM • F FILL IN PIN-PIN SECTION OF MEMBER STIFFNESS MATRIX ' SM( 1 ) • XM2F SM(2) « XMYMF SM(4) • -XM2F SM(S) • -XMYMF SM(7) - YM2F 581 SM(9) • -XMYMF 582 SM(10) - -YM2F 583 SM(16) • XM2F 584 SM(17) • XMYMF 585 SM(19) • YM2F 586 IF (KL(I) • KG(I) - 1) 100. 40. 50 587 C 588 C 589 40 F • 3.0000 • EMOO * CMOMI / (DM2*DM2*DMI*(1.0000+H/4.1 590 GO TO 60 591 50 F - 12.0000 * EMOD • CMOMI / (DM2*DM2 *DMI *(1.ODOO+H)) 592 C RF IS A FACTOR COMMON TO THE ENTIRE MATRIX FOR ADDITION OF 593 C DUE ! TO RIGID BEAM END EXTENSIONS. 594 RF » 12.ODOO • EMOO * CMOMI / (DM2*DM2) / (1.D0+H) 595 C 596 c FILL IN TERMS WHICH ARE COMMON TO PIN-FIX,FIX-PIN.ANO 597 c FIX-FIX MEMBERS 598 c 599 LONEY - LONE * YMI • RF 600 LONEX - LONE • XMI * RF 601 LTWOY - LTWO • YMI • RF 602 LTWOX - LTWO * XMI • RF 603 60 XM2F - XM2 * F 604 YM2F - YM2 • F 605 XMYMF • XMYM • F 606 0M2F • 0M2 • F 607 c 608 SM( 1 ) - SM( 1 ) + YM2F 609 SM(2) • SM(2) - XMYMF 610 SM(4) • SM(4) - YM2F 611 SM(5) • SM(5) + XMYMF 612 SM(7) • SM(7) • XM2F 613 SM(9) - SM(9) + XMYMF 614 SM(10) - SM(10) - XM2F 615 SM(16) - SM(16) + YM2F 616 SM(17) • SM(17) - XMYMF 617 SM(19) - SM(19) • XM2F 618 IF <KL(I) - KG(I)) 70. 80. 90 619 c 620 c FILL IN REMAINING PIN-FIX TERMS 621 c 622 70 SM(6) • -YMI • DM2F 623 SM( 11) • XMI * DM2F 624 SM(18) • -SM(6) 625 SM(20) - -SM(11) 626 SM(21) - DM2 * DM2F 627 GO TO 100 628 c 629 c FILL IN REMAINING FIX-FIX TERMS 630 c 631 80 SM(3) • -YMI • DM2F • 0.5000 632 SM(6) - SM(3) 633 SM(8) • XMI • DM2F • 0.5000 634 SM(11) - SM(8) 635 SM(12) - 0M2 * DM2F • (4.ODOO+H) / 12.ODOO 636 SM(13) • -SM(3) 637 SM(14) - -SM(8) 638 SM(15) - DM2 • DM2F • (2.0D00-H) / 12.0000 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 SM(18) • -SM(6) SM(20) • -SM(11) SM(21) • SM(12) ADD IN TERMS FOR RIGID END EXTENSIONS. SM(3) • SM(3) - (LONEY) SM(6) • SM(6) -SM(8) - SM(8) SM(11) SM(12) SM(13) SM(14) SM(15) • RF SM(18) SM(20) SM(21) GO TO 100 SM(11) SM(12) SM(13) SM(14) SM(IS) SM(18) SM(20) SM(21) (LTWOY) LONEX • LTWOX • (LONE"OMI«(DMI + LONE)*RF) • LONEY - LONEX • ((LONE*LTWO*DMI) + (DM2*(LONE + LTW0)/2.0000)) LTWOY LTWOX (DM2"LTWO + (DMI*(LTWO*LTWO))) * RF 90 FILL IN REMAINING FIX-PIN TERMS SM(3) • -YMI • DM2F SM(8) - XMI • DM2F SM(12) • DM2 • DM2F SM(13) - -SM(3) SM(14) • -SM(8) CONTINUE ADD THE MEMBER STIFFNESS MATRIX SM INTO THE STRUCTURE STIFFNESS MATRIX S. NB 1 NB 1 120 130 140 150 160 170 DO 190 d « 1. 6 IF (NP(d.I)) 190. 190, 110 Jl • (d - 1) • (12 - d) / 2 DO 180 L • d. 6 IF (NP(L.D) 180. 180, 120 IF (NP(d.I) - NP(L.I)) ISO. 130, 160 IF (L - d) 140. 150. 140 K - (NP(L.I) - 1) • NB1 • NP(d.I) N - di • L S(K) • S(K) + 2.0000 • SM(N) GO TO'180 K - (NP(d.I) - 1) • NB1 + NP(L.I) GO TO 170 K - (NP(L.I) - 1) * NB1 • NP(d.I) N • di + L S(K) • S(K) • SM(N) CONTINUE 1B0 190 CONTINUE 200 CONTINUE RETURN END O 697 C 698 SUBROUTINE SDFBAN(A. B. N. M. LT, RATIO. DET, NCN. NSCALE) 699 C 700 C 701 C 702 C THIS ROUTINE SOLVES SYSTEM OF EONS. AX'B WHERE A IS +TVE DEFINITE 703 C SYMMETRIC BAND MATRIX. BY CHOLESKY'S METHOD. 704 C LOWER HALF BAND. ONLY (INCLUDING THE DIAGONAL) OF A IS STORED 705 c COLUMN BY COLUMN IN A 1 DIMENSIONAL ARRAY. 706 c SOLUTIONS X ARE RETURNED IN ARRAY B. 707 c OPTIONAL SCALING OF MATRIX A IS AVAILABLE 708 c N - ORDER OF MATRIX A. 709 c M - LENGTH OF LOWER HALF BAND. 710 c DETERMINANT OF A - OET'(10"NCN). 1.E-15<|DET|<1.E15 711 c LT»1 IF ONLY 1 B VECTOR OR IF FIRST OF SEVERAL. LT NOT « 1 FOR 712 c SUBSEQUENT B VECTORS. 713 c RATIO • SMALLEST RATIO OF 2 ELEMENTS ON MAIN DIAGONAL OF 714 c TRANSFORMED A >1.E-7. 715 c NSCALE-0 IF SCALING NOT REQUIRED. 716 c 717 c 718 IMPLICIT REAL'8(A - H.O - Z) 719 DIMENSION A(1), 8(1) 720 REAL'S MULT(4000) 721 IF (M .EQ. 1) GO TO 80 722 MM - M - 1 723 NM - N • M 724 NM1 - NM - MM 725 c 726 c DUMMY STATEMENT INSERTED FOR COMPATIBILITY WITH ASSEMBLER VERSION 727 c IF(LT.LE.O) RETURN 728 c 729 IF (LT .NE. 1) GO TO 340 730 IF (NSCALE .EO. 0) GO TO 60 731 DO 10 I • 1, N 732 c 733 c MATRIX SCALED BY DIVIDING ROW I ANO COLUMN I BY SORT(A(I.I)), SUCH 734 c THAT DIAGONAL ELEMENTS A(I,I) ARE 1. 735 c 736 II • (I - 1) » M + 1 737 IF ( A ( I I ) .LE. 0.0) GO TO 120 738 10 MULT(I) - 1.0 / DSQRT(AUI)) 739 KK • 1 740 DO 50 I • 1 , N 741 II • (I - 1) • M • 1 742 JENO - II 'MM 743 IMN - (I - 1) + M - N 744 IF (IMN .GT. 0) JEND • JEND - IMN 745 DO 20 J • I I , JEND 746 A(J) - A(J) • MULT(I) 747 20 CONTINUE 748. DO 30 J • KK, I I , MM 749 30 A(d) • A(J) • MULT(I) 750 IF (KK .GE. M) GO TO 40 751 KK • KK + 1 752 GO TO 50 753 40 KK - KK * M 754 50 CONTINUE 755 60 MP - M + 1 756 C 757 C TRANSFORMATION OF A. 758 C A IS TRANSFORMED INTO A LOWER TRIANGULAR MATRIX L SUCH THAT A'L.LT 759 C (LT-TRANSPOSE OF L . ) . IF Y-LT.X THEN L.Y'B. 760 C ERROR RETURN TAKEN IF RATI0<1.E-7 761 C 762 KK - 2 763 NCN - 0 764 DET - 0. 765 FAC • RATIO 766 IF (A(1) .GT. O.) GO TO 70 767 NROW - 1 768 RATIO • A(1) 769 GO TO 310 770 70 DET - A(1) 771 A(1) « 1. / OSQRT(A(1)) 772 BIGL • A(1) 773 SML - A(1) 774 A(2) - A(2) • A{1) 775 TEMP - A(MP) - A(2) • A(2) 776 IF (TEMP .LT. 0.0) RATIO • TEMP 777 IF (TEMP .EO. 0.0) RATIO • 0.0 778 IF (TEMP .GT. 0.0) GO TO 140 779 NROW • 2 780 GO TO 310 781 80 DET • 1.DO 782 NCN • O 783 DO 1 10 I - 1 . N 784 OET • DET * A(I) 785 IF (A(I) .EQ. 0.0) GO TO 120 786 IF (DET .GT. 1.E-15) GO TO 90 787 DET - DET • 1.E+15 788 NCN - NCN - 15 789 GO TO 100 790 .90 IF (DET .LT. 1.E-M5) GO TO 100 791 DET • DET • 1.E-15 792 NCN « NCN + 15 793 lOO CONTINUE 794 110 B(I) - 8(1) / AO) 795 RETURN 796 120 RATIO - A(I) 797 130 NROW ' I 798 GO TO 310 799 140 A(MP) - 1.0 / DSQRT(TEMP) 800 DET - DET * TEMP 801 IF (A(MP) .GT. BIGL) BIGL • A(MP) 802 IF (A(MP) .LT. SML) SML • A(MP) 803 IF (N .EO. 2) GO TO 290 804 MP " MP + M 805 DO 280 J * MP. NM1, M 806 JP - J - MM 807 MZC " O 808 IF (KK .GE. M) GO TO 150 809 KK - KK + 1 810 II • 1 811 JC • 1 812 GO TO 160 (O 813 150 KK • KK • M 871 RETURN 814 II • KK - MM 872 END 813 OC - KK - MM 873 SUBROUTINE OSBANO(A, MULT, 8. N. M. NSCALE) 816 160 00 180 I • KK, OP. MM' 874 IMPLICIT REAL*B(A - H.O - Z) 817 IF (A(I) .EO. 0.) GO TO 170 875 DIMENSION A( 1), B(1) 818 GO TO 190 876 REAL'8 MULT(1) 819 170 OC • OC • M 877 MM • M - 1 820 180 MZC • MZC + 1 878 NM • N • M 821 ASUM1 - O.DO 879 NM1 • NM - MM 822 GO TO 240 880 C 823 190 MMZC • MM • MZC 881 C THE FOLLOWING STATEMENTS SOLVE FOR L.Y'B BY A FORWARDS 824 II « II + MZC 882 C HENCE FOR X FROM LT.X-Y BY A BACKWARDS SUBSTITUTION. 825 KM - KK + MMZC 883 C IF SCALING OPTION USED. B IS SCALED AND NORMALISED BEFORE 826 A(KM) • A(KM) • A(OC) 884 C SUBSTITUTION BEGINS. 827 IF (KM .GE. OP) GO TO 220 885 C 828 KO * KM + MM 886 10 SUM - O.DO 829 DO 210 I • KO, OP, MM 887 IF (NSCALE .EO. 0) GO TO 40 830 ASUM2 - O.DO 888 DO 20 I - 1, N 831 IM • I - MM 889 B(I) - B(I) » MULT(I) 832 II - II + 1 890 SUM - SUM • B(I) • B(I) 833 Kl • II «• MMZC 891 20 CONTINUE 834 DO 200 K • KM, IM. MM 892 ELENB • OSORT(SUM) 835 ASUM2 - ASUM2 + A(KI) « A(K) 893 DO 30 I - 1. N 836 200 Kl • Kl + MM 894 30 B(I) - B(I) / ELENB 837 210 A(I) - (A(I) - ASUM2) • A(KI) 895 40 B(1) - B(1) • A(1) 838 220 CONTINUE 896 KK " 1 839 ASUM1 • O.DO 897 K1 • 1 840 DO 230 K • KM, OP, MM 898 0 • 1 841 230 ASUM1 - ASUM1 + A(K) « A(K) 899 DO 80 L - 2. N 842 240 S • A(d) - ASUMI 9O0 BSUM1 • O.DO 843 IF (S .LT. 0.) RATIO - S 901 LM - L - 1 844 IF (S .EO. 0.) RATIO - 0. 902 0 • 0 • M 845 IF (S .GT. 0.) GO TO 250 903 IF (KK .GE. M) GO TO 50 846 NROW - (0 + MM) / M 904 KK • KK + 1 847 GO TO 310 905 GO TO 60 848 250 A(J) - 1. / DSORT(S) 906 50 KK - KK + M 849 DET " DET • S 907 Kl • Kl • 1 850 IF (DET .GT. 1.E-15) GO TO 260 908 60 OK • KK 851 DET - OET • I.E+15 909 DO 70 K - K l . LM 852 NCN • NCN - 15 910 BSUM1 • BSUM1 * A(OK) • B(K) 853 GO TO 270 911 OK • OK + MM 854 260 IF (OET .LT. I.E+15) GO TO 270 912 70 CONTINUE 855 DET • DET • 1.E-15 913 80 B(L) - (B(L) - 8SUM1) • A(0) 856 NCN • NCN • 15 914 90 B(N) • B(N) ' A(NM1) 857 270 CONTINUE 915 NMM • NM1 858 IF (A(0) .GT. BIGL) BIGL • A(0) 916 NN • N - 1 859 IF (A(0) .LT. SML) SML - A(0) 917 ND • N 860 280 CONTINUE 918 DO 110 L * 1, NN 861 290 IF (SML .LE. FACBIGL) GO TO 300 919 BSUM2 • O.DO 862 GO TO 330 920 NL - N - L 863 300 RATIO - 0. 92 1 NL1 • N - L + 1 864 RETURN 922 NMM • NMM - M 865 310 WRITE (6.320) NROW 923 NJ1 • NMM 866 320 FORMAT ('0**,SYSTEM IS NOT POSITIVE DEFINITE', 924 IF (L .GE. M) NO " NO - 1 867 1 ' ERROR CONDITION OCCURRED IN ROW', 14) 925 DO 100 K • NL1 . ND 868 RETURN 926 Ndl • N01 • 1 869 330 RATIO - SML / BIGL 927 BSUM2 • BSUM2 + A(NJ1) • B(K) 870 340 CALL DSBANO(A, MULT. B, N, M, NSCALE) 928 100 CONTINUE 929 110 B(NL) • (B(NL) - BSUM2) • A(NMM) 930 IF (NSCALE .EO. 0) GO TO 130 931 00 120 I - 1. N 932 120 B(I) - B(I) • ELENB • MULT(I) 933 130 RETURN 934 935 END C 936 c 937 SUBROUTINE EIGEN(NU. NB, S. IDIM. AMASS. EVAL. EVEC. NMODES. MDOF. 938 1 PERIOD. WN) 939 940 c 94 1 c THIS SUBROUTINE COMPUTES A SPECIFIED NO. OF NATURAL FREQUENCIES 94 2 c AND ASSOCIATED MODE SHAPES 943 c 944 c NU-NO. OF DEGREES OF FREEDOM 945 c NB'HALF BANDWIDTH 946 c NMODES'NO. OF MODE SHAPES TO BE COMPUTED 947 c IF NMOOES IS ZERO OR IS GREATER THAN THE NUMBER OF STRUCTURE 948 c MASSES THEN NMODES WILL BE ASSIGNED THE NUMBER OF STRUCTURE 949 c MASSES. 950 c AMASS(II'MASS MATRIX MCOUNT * NUMB E R OF NONZERO MASSES 951 c S(I)»STIFFNESS MATRIX STORED BY COLUMNS 9S2 c EVAL(I)"NATURAL FREQUENCIES 953 c EVEC(I,J)-MODE SHAPES 954 c 955 REAL'S OVEC(500. 10). OVALOO), CMASS(SOO). SDOOOOO) 956 REAL'S S(IDIM) 957 DIMENSION AMASS(NU). EVAL(NMODES) , EVEC(500,NMODES). MDOF(1O0) 958 REAL'8 DBLE 959 c 960 c ZERO DUMMY MASS MATRIX CMASS 961 DO 10 I TRY - 1, 500 962 10 CMASS(ITRY) - O.ODO 963 c 964 c COMPUTE THE NUMBER OF NONZERO MASS MATRIX ENTRIES 965 c 966 MCOUNT - 0 967 c 968 DO 20 I • 1, NU 969 CMASS(I) » DBLE(AMASS(I)) 970 IF (AMASS(I) .EQ. 0.) GO TO 20 971 MCOUNT • MCOUNT • 1 972 20 CONTINUE 973 30 CONTINUE 974 c 975 c CALL SPRIT TO COMPUTE EIGENVALUES AND EIGENVECTORS 976 c CREATE A DUPLICATE STRUCTURE MATRIX (SD) (OESTROYEO IN SPRIT) 977 c 978 c CALCULATE USEFUL LENGTH OF STIFFNESS MATRIX (LSTM) 979 LSTM • (NU) • NB 980 c 981 00 40 I • 1. LSTM 982 SD(1) - S(I) 983 40 CONTINUE 984 c SET CONVERGENCE CRITERIA FOR SPRIT. MAKE NEGATIVE IF RESIDUALS NOT 985 c DESIRED. 986 c 987 DEPS - 1.00-10 988 DEPS • (-1.000) * DEPS 989 C 990 C CALL EIGENVALUE FINDING ROUTINE 991 CALL PRITZISD. CMASS, NU. N8. 1. DVAL. DVEC. 500. NMODES, DEPS, 992 1 &60) 993 C CONVERT EI GEN VECTORS TO SINGLE PRECISION 994 00 50 MAS • 1. NU 995 50 EVEC(MAS.I) • SNGL(DVEC(MAS.1)) 996 EVAL(1) - SNGL(DVAL(1)) 997 EVAL1 - EVAL(1) 998 EVAL(1) - SORT(EVALI) 999 WN * EVAL(1) 1000 PERIOD - 6.283153 / WN 1001 FREO • 1 / PERIOD 1002 WRITE (6,70) WN. PERIOO 1003 RETURN 1004 60 WRITE (6.80) 1005 70 FORMAT (//. 'NAT. FREO."'. F5.2. 5X, 'TIME PERIOO-'. F5.2. 'SEC. 1006 1 //) 1007 80 FORMAT ('CRAPOUT IN SPRIT') 1008 END 1009 C 1010 c • • *•• 1011 SUBROUTINE M0D3(NRd, NRM. NU. NB, S. IDIM, ND. NP. XM. YM, DM, 1012 1 AREA, AV, CRMOM, KL. KG. BMCAP. E. G. AMASS. EVEC. 1013 2 EVAL, EXTL. EXTG, NMB. ALPHA. RMAX. KOU, GG) 1014 C " " " 1015 REAL'8 SOOOOO). OF(SOO). DRATIO. DET 1016 DIMENSION ND(3.NRJ), NP(6,NRM), XM(NRM). YM(NRM), DM(NRM). 1017 1 AREA(NRM), CRMOM(NRM). KL(NRM). KG(NRM), EVEC(50O,1), 1018 2 E(NRM), G(NRM), EVAL(1), AV(NRM). AMASS(NU), BMASS(500). 1019 3 IDOF(500). ALPHA(10), F(500). BMCAP(NRM), EXTL(NRM). 1020 4 EXTG(NRM), 0EFL(5O0). SAXIAL(250). SHEARL(250). 1021 5 SHEARG(250). SBML(250). SBMG(250). N0DN(20). MR(15). 1022 6 MML(tOO). FEM(100.4) 1023 C CALCULATE MODAL PARTICIPATION FACTOR 1024 MCOUNT • O 1025 DO 10 1 • 1. NU 1026 IF (AMASS(I) .EO. O.O) GO TO 10 1027 MCOUNT - MCOUNT + 1 1028 10 CONTINUE 1029 AMT • O. 1030 AMB « 0. 1031 DO 20 J - 1, NU 1032 AMT • AMT + AMASS(J) • EVEC(J,1) 1033 AMB - AMB + AMASS! J) * ( ( EVEC( J. 1 ) ) "2 ) 1034 20 CONTINUE 1035 ALPHA(1) - AMT / AMB 1036 WRITE (6,30) ALPHA(1) 1037 30 FORMAT ('FIRST MODE PARTICIPATION FACTOR-'. F5.2) 1038 C ANALYZE FOR STATIC LOADS 1039 READ (5.40) NJLS, NLGCJ, NML. NLGCM 1040 40 FORMAT (415) 1041 WRITE (6.50) NJLS. NML 1042 50 FORMAT (//. 'NO. OF JOINTS LOADED-'. 14. 5X. 'NO. OF MEMBERS LOADE 1043 10-'. 14) 1044 DO 60 I • 1. NU 1045 60 F(I) - 0. 1046 IF (NLJS .£0. 0 .ANO. NML . CO. O) GO TO 350 1047 IF (NJLS .EO. O) GO TO 200 1048 WRITE (6.70) 1049 70 FORMAT (///. 'GENERATION COMMANDS FOR STATIC LOADS APPLIED TO THE 1050 1N0DES'. //) 1051 IF (NLGCJ .NE'. O) GO TO 90 1052 WRITE (6.80) 1053 80 FORMAT ('NONE'. /) 1054 GO TO 150 1055 90 CONTINUE 1056 00 140 1 - 1 . NLGCJ 1057 WRITE (6.100) 1058 1O0 FORMAT (//. SX. 'FX'. 10X. 'FY'. 10X. 'FM'. 5X. 'NO. OF NODES'. 1059 1 7X. 'LIST OF NODES'. /) 1060 READ (S.110) FX. FY. FM, NNOD, (NODN(N),N"1.NNOD) 1061 110 FORMAT (3F8.1. 1115) 1062 WRITE (6.120) FX, FY, FM, NNOD, (NODN(N),N-1.NNOD) 1063 120 FORMAT (/. F8.1. 6X. FB.1. 6X, F8.1, 15, SX. 1015) 1064 DO 130 J • 1. NNOD 1065 NN » NODN(J) 1066 N1 - N0(1.NN) 1067 N2 - ND(2,NN) 1068 N3 - ND ( 3 . NN) 1069 F(N1) - F(NI) • FX 1070 F(N2) - F(N2) • FY 1071 F(N3) - F(N3) * FM 1072 130 CONTINUE 1073 140 CONTINUE 1074 GO TO 210 1075 150 CONTINUE 1076 WRITE (6.170) 1077 DO 190 I • I. NJLS 1078 READ (5.160) N, FX, FY. FM 1079 160 FORMAT (15, 3F10.S) 1080 170 FORMAT (8X, 'JN.'. 10X, ' FX '. 10X. 'FY ', 10X, ' FM' 1081 WRITE (6.180) N. FX, FY, FM 1082 180 FORMAT (110. 3(8X.F10.5)) 1083 Ml - ND(1.N) 1084 M2 - ND(2.N) 1085 H3 - N0(3,N) 1086 F(M1) - F(M1) • FX 1087 F(M2) • F(M2) • FY 1088 F(M3) - F(M3) + FM 1089 190 CONTINUE 1090 20O CONTINUE 1091 210 CONTINUE 1092 IF (NML .EO. O) GO TO 350 1093 WRITE (6.220) 1094 220 FORMAT (///. 'GENERATION COMMANDS FOR MEMBER LOADS'. //) 1095 IF (NLGCM .NE. 0) GO TO 230 1096 WRITE (6,80) 1097 GO TO 290 1098 230 CONTINUE 1099 WRITE (6.240) 1 100 240 FORMAT (//. 'U.O.L.'. 5X, 'NO. OF MEMBERS'. 8X. 'LIST OF MEMBERS' 1101 1 /) 1102 JM - 1 " 1103 DO 280 I - 1. NLGCM 1104 READ (5.250) W. NMEM, (MR(J).J-1.NMEM) 1105 250 FORMAT (F8.1. 1415) 1106 WRITE (6.260) W. NMEM. (MR(J).J-1.NMEM) 1107 260 FORMAT (F6.1. 4X. IS. BX. 1315) 1108 DO 270 J • 1. NMEM 1109 MMR • MR(J) 1110 MML(JM) - MMR 1111 CALL GEN2(MMR, W. XM. KL. KG, NP, F. JM. FEM) 1112 JM • JM + 1 1113 270 CONTINUE 1 114 280 CONTINUE 1115 GO TO 340 1 116 290 CONTINUE 1117. WRITE (6.300) 1118 300 FORMAT ('MEMBER NO.', 10X. 'UNIF. DIST. LOAD') 1119 DO 330 MEM • 1. NML 1120 READ (5,310) MMR, W 1121 WRITE (6.320) MMR, W 1122 310 FORMAT (15. F10.4) 1123 320 FORMAT (16. 15X. F10.2) 1124 MML(MEM) • MMR 1125 CALL GEN2(MMR, W, XM. KL, KG. NP, F, MEM. FEM) 1 126 330 CONTINUE 1127 340 CONTINUE 1128 350 CONTINUE 1129 C CONVERT LOAD VECTOR TO DOUBLE PRECISION 1130 DO 360 J • 1, NU 1131 360 DF(J) - D B L E ( F ( J ) ) 1132 C CALL SDFBAN TO SOLVE AX-B 1133 DRATIO » 1.0-16 1134 CALL SDFBAN(S, DF, NU, NB, 1. DRATIO. DET. JEXP. 1) 1135 C CONVERT SOLN. VECTOR DF TO SINGLE PRECISION 1 136 DO 370 J - 1 . NU 1137 370 DEFL(J) - SNGL(DF(J)) 1138 C CALCULATE MEMBER FORCES DUE TO STATIC LOADS 1139 CALL MEMFOtNHM. XM, YM, DM. AV. NP. DEFL. EXTL, EXTG. AREA. E. G, 1140 1 CRMOM. KL. KG, SAXIAL. SHEARL, SHEARG. SBML. SBMG, NML. MML. 1141 2 FEM) 1142 C ZERO LOAD VECTOR 1143 DO 380 J - 1, NU 1144 380 F(J) - O. 1145 C COMPUTE LOAD VECTOR 1146 SA - 0.41 1147 FAC • SA • ALPHA(1) • GG 1148 DO 390 J - 1, NU 1149 F(J) • EVEC(J.I) • FAC * AMASS(J) / 5. 1150 OF(J) " DBLE(F(J)) 1151 390 CONTINUE 1152 IF (KOU .EO. 2) GO TO 400 1153 " GO TO 410 1154 400 DO 4 10 J - 1. NU 1155 DF(J) - -OF(J) 1156 410 CONTINUE 1157 C CALL SDFBAN 1158 NSCALE • 1 1159 DRATIO - 1.00-16 1 160 INDEX - 2 ro 1161 CALL SOFBAN(S, DF, NU. NB. INDEX, DRATIO. DET, JEXP. NSCALE) 1162 OO 420 dF - 1, NU 1163 F(dF) - SNGL(DF(dF)) 1164 420 CONTINUE 1165 WRITE (6,430) M66 430 FORMAT (//. .'dT. DISP. AND MEMBER FORCES AT THE YIELD OF STRUCTURE 1167 IS'. /) 1168 WRITE (6.440) 1169 440 FORMAT (/13X, ' JN ' . 13X, 'X-OISP.', 13X. 'Y-DISP.'. 10X. 1170 1 'ROTATION'. /) 1171 C CALCULATE MEMBER FORCES OUE TO E/O FORCES 1172 CALL FORCE(NRM, XM. YM. DM. AV, NP. F, EXTL, EXTG, AREA, E. G. 1173 1 CRMOM. KL. KG. NO, NMB. NRJ. BMCAP. RMAX. SAXIAL. SHEARL. 1174 2 SHEARG, SBML, SBMG, OEFL. NU) 1175 RETURN 1176 END 1177 C •••• • 1178 SUBROUTINE FORCE(NRM. XM, YM, DM, AV. NP, F, EXTL, EXTG. AREA. E, 1179 1 . G, CRMOM. KL, KG, NO, NMB, NRd. BMCAP, RMAX, SAXIAL, 1180 2 SHEARL, SHEARG, S8ML, SBMG. DEFL. NU) 1181 C 1182 DIMENSION XM(NRM). YM(NRM), DM(NRM), AV(NRM), NP(S.NRM). F(NU). 1183 1 D(6). EXTL(NRM), EXTG(NRM), KL(NRM). KG(NRM), G(NRM), 1184 2 AREA(NRM). CRMDM(NRM). ND(3.NRJ). BMCAP(NRM), E(NRM) 1185 DIMENSION AXIAL(2S0), SHEAR(250). BML(250). BMG(250) 1186 DIMENSION SAXIAL(NRM), SHEARL(NRM), SBML(NRM), SBMG(NRM), 1187 1 DEFL(NU), SHEARG(NRM) 1188 10 FORMAT (/12X. 'MN'. 10X. 'AXIAL', IOX, 'SHEARL', 12X. 'SHEARG', 1189 1 12X, 'BML'. 12X, 'BMG', /) 1190 DD 120 1 * 1 , NRM 1191 XL - XM(I) 1192 YL - YM(I) 1193 DL • DM(I) 1194 AV1 - AV(I) 1195 DO 40 MEMDOF - 1 , 6 1196 N1 • NP(MEMDOF.I) 1197 IF (NI) 30. 30. 20 1198 20 D(MEMDOF) • F(N1) 1199 GO TO 40 1200 30 D(MEMDOF) • 0. 1201 40 CONTINUE 1202 C MODIFY END DISP FOR HORZ MEMBERSWITH END EXT.(VALID FOR 1203 C HORZ. MEMBERS ONLY) 1204 N3 - NP(3,I) 1205 IF (N3 .EO. 0) GO TO 50 1206 0(2) - D(2) • (F(N3)) • EXTL(I) 1207 50 CONTINUE 1208 N6 • NP(6.I) •1209 IF (N6 .EO. O) GO TO 60 1210 0(5) > 0(5) - (F(N6)) • EXTG(I) 1211 60 CONTINUE 1212 AXIAL(I) • (AREA(I)«E(I)/DL**2) • (D(4)«XL • D(5)'YL - D(1)*XL -1213 1 D(2)*YL) 1214 EISI • CRMOM(I) • E(I) 1215 C INCLUDE SHEAR DEFL. GFACT-0 MEANS NO SHEAR OEFL. 1216 GFACT - 0. 1217 IF (AVI .EO. 0.0 .OR. GO) .EO. 0.0) GO TO 70 1218 GFACT • 12.0 • EISI / (AV1*G(I)*DL*OL) 1219 70 CONTINUE 1220 C ASSIGN DISP TO RESPECTIVE D.O.F. 1221 C CHECK FOR PIN-PIN MEMBERS 1222 IF (KL(I) .EO. O .AND. KG(I) .EO. 0) GO TO 100 1223 DELT • ((D(5) - D(2))«XL • (0(1) - D(4))«YL) / DL 1224 BML(I) • (2.0*EISI/(DL*(1.0 • GFACT))) • ((3 O'DELT/OL) - (D(6)« 1225 1 (1.0 - GFACT/2.0)) - (2.0*D(3)•(I.O • GFACT/4.O))) 1226 BMG(I) - -(2.0'EI SI/(OL*(1.0 • GFACT))) • ((3.0'OELT/DL) - (0(3) 1227 1 «(1.0 - GFACT/2.0)) - (2.0'D(6)•(1.0 • GFACT/4.O))) 1228 SHEAR(I) • (6.0»E1SI/(0L"0L)) • ((0(3) • D(4) - (2.O'DELT/OL))/( 1229 1 1.0+ GFACT)) 1230 IF (KL(I) - KG(I)) 80. 110. 90 1231 C PIN-FIX MEMBER FORCES 1232 80 BMG(I) • BMG(I) * BML(I) • (1.0 - GFACT/2.0) / (2.0*(1.0 • 1233 1 GFACT/4.O)) 1234 SHEAR(I) - SHEAR(I) • 1.5 • BML(I) / DL 1235 BML(I) - O. 1236 GO TO 1 10 1237 C FIX-PIN MEMBERS 1238 90 BML(I) • BML(I) • BMG(I) • (1.0 - GFACT/2.0) / (2.0*(1.0 + 1239 1 GFACT/4.0)) 1240 SHEAR(I) . SHEAR(I) - 1.5 • BMG(I) / DL 1241 BMG(I) - 0. 1242 GO TO 110 1243 C PIN-PIN MEMBERS 1244 100 BML(I) • 0. 1245 BMG(I) • O. 1246 SHEAR(I) • 0. 1247 110 CONTINUE 1248 120 CONTINUE 1249 FAC • 1.0 1250 130 KOUNT - O 1251 DO 150 M - 1. NRM 1252 AMOM • SBML(M) • BML(M) 1253 AMOG • SBMG(M) • BMG(M) 1254 AMOM ' ABS(AMOM) 1255 AMOG > ABS(AMOG) 1256 IF (AMOM .LT. AMOG) AMOM - AMOG 1257 AMU ' AMOM / BMCAP(M) 1258 IF (AMU .GE. 0.95) GO TO 140 1259 GO TO 150 1260 140 KOUNT - KOUNT + 1 1261 150 CONTINUE 1262 NM - 1 • NMB / 2 1263 IF (KOUNT .GE. NM) GO TO 170 1264 FAC • 1.02 • FAC 1265 DO 160 J • 1. NRM 1266 AXIAL(J) • 1.05 • AXIAL(J) 1267 SHEAR(J) • 1.05 • SHEAR(J) 1268 BML(J) ' 1.05 • BML(J) 1269 160 BMG(J) - 1.05 • BMG(J) 1270 GO TO 130 1271 170 CONTINUE 1272 C WRITE DISP. & MEM FORCES NOW 1273 DO 180 JF - 1. NU 1274 180 F(JF) - FAC • F(JF) • DEFL(JF) 1275 RMAX • -10.0 1276 DO 230 JNT - 1. NRJ Ul 1277 OX • 0. 1278 or • o. 1279 OR - 0. 1280 N1 • NOI1.JNT) 1281 N2 • N0(2.dNT) 1282 N3 - N0(3.JNT) 1283 IF (N1 .EO. 0) GO TO 190 1284 OX • F(N1) 128S 190 CONTINUE 1286 IF (N2 .EQ. 0) GO TO 200 1287 DY • FCN2) 1288 200 CONTINUE 1289 IF (N3 .EO. 0) GO TO 210 1290 DR - F(N3) 1291 210 CONTINUE 1292 WRITE (6.220) JNT. OX, OY. DR 1293 DX • ABS(DX) 1294 IF (DX .GT. RMAX) RMAX • DX 1295 220 FORMAT (6X. 110. 3F20.4) 1296 230 CONTINUE 1297 WRITE (6.10) 1298 DO 240 IM • 1, NRM 1299 AXIAL(IM) - AXIAL(IM) + SAXIAL(IM) 1300 SHEARL(IM) - SHEAR(IM) » SHEARL(IM) 1301 SHEARG(IM) » SHEAR(IM) + SHEARG(IM) 1302 BML(IM) « BML(IM) + SBML(IM) 1303 BMG(IM) • BMG(IM) + SBMG(IM) 1304 WRITE (6.250) IM, AXIAL(IM), SHEARL(IM). SHEARG(IM). BML(IM). 1305 1 BMG(IM) 1306 240 CONTINUE 1307 250 FORMAT (10X, 15, 5F15.3) 1308 WRITE (6.260) RMAX 1309 260 FORMAT (//, 'AT ROOF DISP OF', F6.3, ' STRUCTURE YIELOED') 1310 RETURN 1311 END 1312 C 1313 C SUBROUTINE MASS(NU, ND, AMASS. NRJ. MDOF. NCDMS. GG) 1314 1315 C 1316 C 1317 C 1318 C •1319 C THIS SUBROUTINE SETS UP THE MASS MATRIX 1320 c 1321 c N0(J.I)-DEGREES OF FREEDOM OF I TH JOINT 1322 c WTX,WTY.WTR-X-MASS.Y-MASS.ROT.MASS 1323 c AMASS(I)-MASS MATRIX.I IS THE DEGREE OF FREEDOM OF APPLIEO MASS 1324 c 1325 c 1326 c MASSES ARE LUMPEO AT NOOES. THE MASS MATRIX IS DIAGONAL I ZED. 1327 c 1328 DIMENSION NOO.NRJ), MOOF(IOO). AMASS(NU) 1329 C 1330 c 1331 c ZERO MASS MATRIX 1332 c 1333 DO 10 I • 1, NU 1334 AMASS(I) • 0. 1335 10 CONTINUE 1336 C 1337 WRITE (6.20) 1338 20 FORMAT (///. 'MASS GENERATION COMMANDS'. //, 'FIRST NODE', 4X. 1339 1 'X-MASS'. 4X. 'Y-MASS'. 3X. 'ROTN MASS'. 3X. 'LAST NODE'. 1340 2 3X. 'NODE DIFF'. /) 1341 DO 80 I - 1. NCOMS 1342 READ (5.30) IJT, WTX, WTY, WTR. JJT. KDIF 1343 30 FORMAT (15, 3F10.1. 215) 1344 WRITE (6.40) IJT. WTX. WTY, WTR. JJT, KDIF 1345 40 FORMAT (15. 3X, 3F10.1. 4X, 15. 4X. 15) 1346 IF (KDIF .EQ. 0) KDIF - 1 1347 IF (JJT .EO. 0) GO TO 50 1348 NJT - (JJT - IJT) / KDIF • 1 1349 GO TO 60 1350 50 CONTINUE 1351 NJT • 1 1352 60 CONTINUE 1353 DO 70 J • 1 . NJT 1354 N1 - ND(1,IJT) 1355 N2 • N0(2.IJT) 1356 N3 - NOO.IJT) 1357 AMASS(NI) - AMASS(Nt) + WTX / GG 1358 AMASS(N2) - AMASS(N2) • WTY / GG 1359 AMASS(N3) • AMASS(N3) + WTR / GG 1360 IJT - IJT » KOIF 1361 70 CONTINUE 1362 80 CONTINUE 1363 C OUTPUT THE DEGREES OF FREEDOM WITH MASS AND ASSIGNED MASS. 1364 C 1365 JCNT - 1 1366 WRITE (6.100) 1367 C 1368 DO 90 IDOF • 1. NU 1369 RMASS - AMASS(IDOF) 1370 IF (RMASS .EO. 0.0) GO TO 90 1371 MDOF(JCNT) - IOOF 1372 WRITE (6.110) JCNT, MOOF(JCNT). RMASS 1373 JCNT - JCNT • 1 1374 90 CONTINUE 1375 C 1376 C 1377 100 FORMAT (*-'. 'MASS NO. OOF'. 6X. 'ASSIGNED MASS *) 1378 110 FORMAT (' '. 2X. 13. 3X. 13. 9X. F10.5) 1379 RETURN 1380 END 1381 C 1382 C 1383 SUBROUTINE SCHECK(S, NU. NB, IDIM, SRATIO) 1384 C 1386 c c 1387 c THIS SUBROUTINE CHECKS THAT ALL DIAGONAL STIFFNESS MATRIX 1388 c ELEMENTS ARE POSITIVE NUMBERS GREATER THAN ZERO. IT ALSO DETERMINES 1389 c THE RATIO BETWEEN THE LARGEST ANO SMALLEST MEMBERS ON THE DIAGONAL 1390 c THIS WILL GIVE SOME INDICATION AS TO THE CONDITIONING OF THE 1391 c STIFFNESS MATRIX 1392 c MATRIX ro 1393 C 1394 REAL'S S ( I O I M ) 1393 REAL'S SMIN. SMAX. DIAG. RATIO 1396 C 1397 C • 1398 C THE STIFFNESS MATRIX IS STORED AS A COLUMN VECTOR. ONLY THE 1399 C THE LOWER TRIANGLE ELEMENTS BEING STORED (BY COLUMNS) 1400 C S ( 1 ) IS ON THE DIAGONAL AS IS S(1'NB).S(1+2'NB),ETC. 1401 C NB IS THE HALF BANDWIDTH OF THE STIFFNESS MATRIX 1402 C 1403 C I N I T I A L I Z E THE LARGEST ANO SMALLEST VALUES OF DIAGONAL (SMAX.SMIN) 1404 C 1405 SMIN - 1.0045 1406 SMAX • -1.0000 1407 C 1408 DO 50 IDOF - 1. NU 1409 IELEM • ((IDOF - 1)*NB) • 1 1410 DIAG • S(IELEM) 1411 C COMPUTE IF DIAGONAL ELEMENT IS ZERO OR NEGATIVE 1412 IF (DIAG .NE. 0.0000) GO TO 20 1413 WRITE ( 6 . 1 0 ) IOOF 1414 10 FORMAT (///' PROGRAM HALTED-A ZERO IS ON THE DIAGONAL OF iSTIFFNE 1415 1SSMATRIX', //'EXAMINE DEGREE OF FREEDOM '. 14) 1416 STOP 1417 C 1418 20 CONTINUE 1419 IF (DIAG .GT. 0.0) GO TO 40 1420 WRITE (6.30) IDOF 1421 30 FORMAT (///' PROGRAM HALTED-NEGATIVE ELEMENT ON DIAGONAL OF '. 1422 1 'STIFFNESS MATRIX'. //' EXAMINE DEGREE OF FREEDOM'. 14) 1423 STOP 1424 40 CONTINUE 1425 C 1426 C DETERMINE IF THE DIAGONAL ELEMENT UNDER EXAMINATION IS THE LARGEST OR 1427 C SMALLEST OF THE DIAGONAL ELEMENTS. 1428 IF (DIAG .GT. SMAX) SMAX - DIAG 1429 IF (DIAG .LT. SMIN) SMIN - DIAG 1430 C 1431 50 CONTINUE 1432 C 1433 WRITE ( 6 , 6 0 ) 1434 60 FORMAT (/' ALL ELEMENTS OF MAIN DIAGONAL OF STIFFNESS MATRIX', 1435 1 ' ARE POSITIVE DEFINITE') 1436 C 1437 C COMPUTE ANO PRINT RATIO OF LARGEST TO SMALLEST DIAGONAL ELEMENTS 1438 C 1439 RATIO • SMAX / SMIN 1440 SRATIO - SNGL(RATIO) 1441 WRITE ( 6 . 7 0 ) SRATIO 1442 70 FORMAT (/. 'RATIO OF LARGEST TO SMALLEST DIAGONAL STIFFNESS'. 1443 1 'MATRIX ELEMENT I S ' . E10.3) 1444 C 1445 RETURN 1446 END 1447 C • • ' ' ' 1448 C 1449 SUBROUTINE SPECTR(DAMP. T. SA. ISPEC. AMAX. NM. TN) 1450 C 1451 C DIMENSION DAMP(20). T ( 4 0 ) . SAC(2) 1452 1453 C ISPEC- 1 IF SPECTRUM A (SHIBATA & SOZEN) IS USED 1454 C - 2 IF NBC SPECTRUM IS USED 1455 C - 3 1456 C 1457 CALL FTNCMD('EQUATE 99-SPRINT;') 1458 GO TO ( 1 0 . 8 0 ) . ISPEC 1459 C 1460 C SPECTRUM A 1461 C 1462 10 IF (TN .GT. T ( 1 ) ) GO TO 30 1463 DAMPIN • OAMP(1) 1464 20 IF (TN .LT. 0.15) SA • 25. • AMAX • TN 1465 IF (TN .GE. 0.15 .ANO. TN .LT. 0.4) SA • 3 .75 * AMAX 1466 IF (TN .GE. 0.4) SA • 1.5 • AMAX / TN 1467 SA - SA • 8. / ( 6 . + 100.'DAMPIN) 1468 RETURN 1469 30 CONTINUE 1470 IF (TN .LT. T(NM)) GO TO 40 1471 DAMP IN - OAMP(NM) 1472 GO TO 20 1473 40 CONTINUE 1474 DO 60 I • 2. NM 1475 IF (TN .GT. T ( I ) ) GO TO 60 1476 DO 50 J - 1. 2 1477 K • I - 2 + J 1478 IF ( T ( K ) .LT. O.IS) SA - 25. • AMAX • TOO 1479 IF ( T ( K ) .GE. .15 .AND. T(K) .LT. 0.4) SA - 3.75 1480 IF ( T ( K ) .GE.- 0.4) SA • 1.5 • AMAX / T( K) 1481 50 SAC(vl) - SA • 8. / ( 6 . + 100. 'DAMP(K)) 1482 SA - ( S A C ( 2 ) - S A C ( D ) • (TN - T ( I - 1 )) / ( T ( I ) -1483 1 SAC(1) 1484 GO TO 70 1485 60 CONTINUE 1486 70 CONTINUE 1487 RETURN 1488 C 1489 C NBC SPECTRUM 1490 C 1491 80 CONTINUE 1492 SV • 40. • AMAX 1493 SD • 32. • AMAX 1494 SACC - 1. • AMAX 1495 IF (TN .GT. T ( 1 ) ) GO TO 100 1496 DAMPIN - OAMP(1) 1497 90 CONTINUE 1498 CALL MULT(TN, DAMPIN. SV. SD, SACC. SACL) 1499 SA - SACL 1500 RETURN 1501 100 IF (TN .LT. T(NM)) GO TO 110 1502 DAMPIN - DAMP(NM) 1503 GO TO 90 1504 110 CONTINUE 1505 00 130 I • 2, NM 1506 IF (TN .GT. T ( I ) ) GO TO 130 1507 00 120 J - 1, 2 1508 K • I - 2 • d to •~1 (509 TP • T(K) 1310 OAMPIN • OAMP(K) 1511 CALL MULT(TP, DAMPIN. SV, SD. SACC. SACL) 1512 120 SAC(d) • SACL 1513 SA - (SAC(2) - SAC(1)) • (TN - T(I - 1)) / (T(I) - T(I - 1)) • 1514 1 SAC(1) 1515 GO TO 140 • 1516 130 CONTINUE 1517 140 CONTINUE 1518 RETURN 1519 END 1520 C 1521 SUBROUTINE MULT(TPR, DAMP. SV. SD, SACC, SACL) 1522 C • . • 1523 C PRINT OUT A CAUTION NOTE SHOULO DAMPING BE LESS THAN 0.5% 1524 IF (DAMP .LT. 0.005) WRITE (7.10) 1525 10 FORMAT (" '. 'CAUTION-DAMPING LESS THAN 0.5%') 1526 WN - 6.283153 / TPR 1527 C COMPUTE MULTIPLICATION FACTOR FOR ACCELERATION AT DESIREO DAMPING 1528 IF (DAMP .LE. 0.02) AML • 4.2 + ((0.02 - DAMPJ/0.015) • 1.6 1529 IF (DAMP .GT. .02 .AND. OAMP .LE. .05) AML • 3.0 • ((.OS - DAMP)/ 1530 103) • 1.2 1531 IF (DAMP .GT. 0.05 .AND. DAMP .LE. 0.1) AML - 2.2 + ((0.1 - DAMP)/ 1532 10.05) • 0.8 1533 IF (DAMP .GT. 0.10) AML » 1.0 + ((1.00 - DAMPj/0.90) • 1.2 1534 C 1535 C COMPUTE MULTIPLICATION FACTOR FOR VELOCITY AT DESIRED DAMPING. '536 IF (DAMP .LE. 0.02) VML • 2.5 + ((0.02 - DAMP)/0.015) • 0.8 1537 IF (DAMP .GT. .02 .AND. DAMP .LE. .05) VML • 2.0 • ((.OS - DAMP)/. 1538 103) • 0.5 1539 IF (DAMP .GT. .OS .AND. DAMP .LE. 0.1) VML « 1.7 + ((0.1 - DAMP)/ 1540 10.05) • 0.3 1541 IF (DAMP .GT. 0.10) VML • 1.0 + ((1.00 - DAMP)/0.90) • 0.7 1542 C 1543 C COMPUTE MULTIPLICATION FACTOR FOR DISPLACEMENT AT OESIRED OAMPING. 1544 IF (DAMP .LE. 0.02) DML • 2.5 + ((0.02 - DAMP)/0.015) * 0.5 1545 IF (DAMP .GT. 0.02) DML • VML 1546 C 1547 C COMPUTE BOUNDS USING OAMPING FACTORS COMPUTED ALREADY 1548 SDBND - SD * DML 1549 SABND - SACC • AML 1550 SV8ND • SV • VML 1551 . C COMPUTE WHICH IS THE APPROPIATE BOUND. 1552 C CONVERT FROM IN/SEC'2 TO FRACTION OF G BY DEVIDING BY 386.4 1553 C 1554 SAATAP • SVBND • WN / 386.4 1555 IF (SAATAP .GT. SABND) SACL • SABND 1556 IF (SAATAP .GT. SABND) GO TO 20 1557 SDATCP - SVBND / WN 1558 IF (SDATCP .GT. SDBND) SACL - SDBNO • WN • WN / 386.4 1559 IF (SDATCP .GT. SDBND) GO TO 20 1560 C 1561 C IF HAVE NOT YET GONE TO STEP 180 THEN NATURAL FREOUENCY LIES ON 1562 C VELOCITY BOUND. 1563 C 1564 SACL • SVBND • WN / 386.4 1565 C SA IS RETURNED AS A FRACTION OF GRAVITY. G 1566 20 RETURN 1567 I 1568 C 1569 1570 1 1571 2 1572 C 1573 1 1574 1 1575 2 1576 1 1577 1 1578 C 1579 1 1580 1581 1582 1583 1584 1585 1S86 1587 10 1588 1589 20 1590 30 1591 c 1592 c 1593 1594 1595 1596 40 1597 1598 1599 1600 SO 1601 1602 1 1603 1604 c 1605 1606 1607 1608 60 1609 c 1610 c 161 1 1612 1613 1614 1 1615 1616 1 1617 1618 1 1619 1620 c 1621 70 1622 1 1623 1624 END SUBROUTINE MEMFOfNRM. XM. YM. DM. AV. NP. F. EXTL. EXTG. AREA. E. G. CRMOM, KL. KG. AXIAL. SHEARL, SHEARG. BML. BMG. NML. MML, FEM) DIMENSION XM(NRM). YM(NRM), DM(NRM). AV(NRM). NP(6.NRM). F(500). D(6) EXTL(NRM), EXTG(NRM). KL(NRM), KG(NRM). AREA(NRM). CRMOM(NRM). E(NRM). G(NRM). MML(IOO). FEM(100.4) DIMENSION AXIAL(NRM). SHEAR(250). BML(NRM), BMG(NRM), SHEARL(NRM). SHEARG(NRM) DO 110 I - 1. NRM XL • XM(I) YL - YM(I) DL » DM(I) AV1 - AV(I) 00 30 MEMDOF - 1 . 6 NI • NP(MEMDOF.I) IF (NI) 20. 20. 10 D(MEMDOF) - F(N1) GO TO 30 D(MEMDOF) - O. CONTINUE MODIFY END DISP FOR HORZ MEMBERSWITH END EXT.(VALID FDR HORZ. MEMBERS ONLY) N3 - NP(3.I) IF (N3 .EO. O) GO TO 40 D(2) - 0(2) + (F(N3)) • EXTL(I) CONTINUE N6 - NP(6.I) IF (N6 .EO. 0) GO TO 50 0(5) - 0(5) - (F(N6)) • EXTG(I) CONTINUE , . AXIAL(I) - (AREA(I)«E(I)/0L"2) • (D(4)«XL + 0<5)'YL - OOJ'XL -I 0(2)*YL) EISI " CRMOM(I) • E(I) INCLUOE SHEAR DEFL. GFACT'O MEANS NO SHEAR DEFL. GFACT » O. IF (AV1 .EO. 0.0 .OR. G(I) .EO. 0.0) GO TO 60 GFACT - 12.0 • EISI / (AV1*G(I)*DL*DL) CONTINUE ASSIGN DISP TO RESPECTIVE 0.0.F. CHECK FOR PIN-PIN MEMBERS IF (KL(I) .EO. O .ANO. KG(I) .EO. O) GO TO 90 DELT • ((D(5) - 0(2))<XL + (DO) - D(4))-YL) / DL BML(I) - (2.0'EISI/(DL'(1.0 • GFACT))) • ((3.0*DELT/DL) - (D(6)« (1.0 - GFACT/2.0)) - (2.0*D(3)'(1.0 • GFACT/4.0))) BMG(I) • -(2.0*EISI/(DL«(1.0 • GFACT))) • ((3.O'DELT/DL) - (D(3) 1 »(1.0 - GFACT/2.0)) - (2.0'0(6 )« ( t.O • GFACT/4.0))) SHEAR(l) - <6.0'EISI/(DL«DL)) • ((0(3) + D(6) - (2.O'DELT/DL))/( 1.0 + GFACT)) IF (KL(I) - KG(I)) 70. 100. 80 PIN-FIX MEMBER FORCES BMG(I) - BMG(I) • BML(I) * O.O - GFACT/2.0) / (2.0'd.O * 1 GFACT/4.O)) SHEAR(I) - SHEAR(I) • 1.5 • BML(I) / OL BML(l) - O. 09 1625 GO TO 100 1683 C 1626 C FIX-PIN MEMBERS 1684 IF (KL(MMR) + KG(MMR) - 1) 50. 20. 10 1627 80 BML(I) - BML(I) + BMG(I) * (1.0 - GFACT/2.0) / <2.0«(1 .0 + 1685 10 R3 • -W * XM(MMR) • XM(MMR) / 12. 1628 1  GFACT/4.0)) 1686 R6 - -R3 1629 SHEARfI) « SHEAR(I) - 1.5 • BMG(I) / DL 1687 R2 - -0.5 • W • XM(MMR) 1630 BMG(I) - 0. 1688 R5 - R2 1631 GO TO 100 1689 GO TO 60 1632 C PIN-PIN MEMBERS 1690 20 IF (KL(MMR) - KG(MMR)) 30. 70. 40 1633 90 BML(I) • 0. 1691 30 R3 • 0. 1634 BMG(I) • 0. 1692 R6 - W • XM(MMR) • XM(MMR) / 8. 1635 SHEAR ( I ) . 0. 1693 R2 - -0.5 • W * XM(MMR) - R6 / XM(MMR) 1636 too CONTINUE 1694 R5 • -0.5 • W • XM(MMR) • R6 / XM(MMR) 1637 SHEARL(I) - SHEAR(I) 1695 GO TO 60 1638 SHEARG(I) - SHEAR(I) 1696 40 R3 • -V • XM(MMR) • XM(MMR) / 8. 1639 110 CONTINUE 1697 R6 • 0. 1640 IF (NML .EO. 0) GO TO 150 - 1698 R2 - -0.5 • W • XM(MMR) - R3 / XM(MMR) 1641 DO 140 I • 1. NRM 1699 R5 • -0.5 • W • XM(MMR) + R3 / XM(MMR) 1642 00 120 J • 1 . NML 1700 GO TO 60 1643 IF (I .EO. MML(J)) GO TO 130 1701 50 R2 • -O.S • V • XM(MMR) 1644 120 CONTINUE 1702 R3 - O. 1645 GO TO 140 1703 R5 » R2 1646 130 CONTINUE 1704 R6 • 0. 1647 BML(I) • BML(I) + FEM(J.2) 1705 60 CONTINUE 1648 BMG(I) - BMG(I) + FEM(J.4) 1706 J1 • NPO.MMR) 1649 SHEARL(I) - SHEAR(I) • FEM(J.I) 1707 J2 « NPO.MMR) 1650 SHEARG(I) - SHEAR(I) - FEM(J,3) 1708 J3 » NPO.MMR) 1651 140 CONTINUE 1709 J4 - NPO.MMR) 1652 150 CONTINUE 1710 F(J3) ' F(J3) + R2 1653 RETURN 1711 F(J4) • F(J4) + RS 1654 END 1712 F(J1) • F(J1) * R3 1655 C 1713 F(J2) - F(J2) • R6 1656 C 1714 FEM(JL.1) » -R2 1657 SUBROUTINE GENKX. Y, IJT. LJT, NJT. KDIF) 1715 FEM(JL,2) " R3 1658 C 1716 FEM(JL.S) - -R5 1659 C 1717 FEM(JL,4) - -R6 1660 C 1718 70 CONTINUE 1661 c GENERATES NODES ALONG STRAIGHT LINE 1719 RETURN 1662 DIMENSION X(325), Y(325) 1720 END 1663 XI - X(IJT) 1664 YI • Y(IJT) 1665 DX • X(LJT) - XI 1666 DY • Y(LJT) - YI 1667 DX • DX / FLOAT(NJT + 1) 1668 DY . DY / FLOAT(NJT • 1) 1669 00 10 I • 1. NJT 1670 IJT « IJT + KDIF 1671 XI - XI + DX 1672 YI • YI • DY 1673 X(IJT) - XI 1674 10 Y(IJT) - YI 1675 RETURN 1676 END 1677 c 1678 c 1679 SUBROUTINE GEN2(MMR. W. XM. KL. KG. NP, F, JL. FEM) 1680 c 1681 c 1682 DIMENSION XM(200). KL(200). KG(200). NP(6.2O0) , F(500). FEM(100.4) to to APPENDIX C STATIC DAMAGE EVALUATION METHOD  PROGRAM INPUT Use any c o n s i s t e n t set of u n i t s , there i s no i n t e r n a l c o n v e r s i o n of u n i t s i n the program. 1. TITLE : TITLE (20A4) one c a r d Problem t i t l e of maximum 80 c h a r a c t e r l e n g t h 2. STRUCTURAL INFORMATION : NRM, NRJ, NCONJT, NCDJT, NCDOD, NCDIDS (615) one c a r d NRM : Number of members i n the s t r u c t u r e NRJ : Number of j o i n t s i n the s t r u c t u r e NCONJT : Number of ' c o n t r o l j o i n t s ' f o r which the co - o r d i n a t e s are s p e c i f i e d (See Note 2) NCDJT : Number of commands f o r j o i n t s c o - o r d i n a t e generation (See Note 2) NCDOD : Number of commands f o r s p e c i f y i n g j o i n t s with zero displacements (See Note 3) NCDIDS : Number of commands f o r s p e c i f y i n g j o i n t s with i d e n t i c a l displacements (See Note 4) 3. CONTROL JOINTS CO-ORDINATES : IJT, X, Y (15,2F10.1) one c a r d / c o n t r o l j o i n t IJT : J o i n t number, i n any sequence X : x c o - o r d i n a t e of the j o i n t 130 131 Y : y co - o r d i n a t e of the j o i n t COMMANDS FOR GENERATION OF JOINT CQ-QRDINATES : Omit i f there are no ge n e r a t i o n commands IJT, LJT, NJT, KDIF (415) one card/command IJT : J o i n t number at the beginning of generat i o n l i n e LJT : J o i n t number at the end of generation l i n e NJT : Number of j o i n t s to be generated along the l i n e KDIF : J o i n t number d i f f e r e n c e between two s u c c e s s i v e nodes on the l i n e ( c o n s t a n t ) . If blank or zero assumed to be equal to 1 COMMANDS FOR JOINTS WITH ZERO DISPLACEMENTS : Omit i f no j o i n t s r e s t r a i n e d to have zero displacements IJT, KDOF(1), KD0F(2), KDOF(3), LJT, KDIF (13,518) one card/command . IJT : J o i n t number, or f i r s t j o i n t i n the s e r i e s covered by t h i s command KD0F(1) : Code f o r X displacement, 0 i f r e s t r a i n e d from displacements i n x d i r e c t i o n , 1 i f f r e e to d i s p l a c e KDOF(2) : Code for Y displacement KD0F(3) : Code for r o t a t i o n LJT : Last j o i n t i n t h i s s e r i e s , punch 0 or leave blank f o r a s i n g l e j o i n t KDIF : J o i n t number d i f f e r e n c e between s u c c e s i v e j o i n t s i n t h i s s e r i e s ( c o n s t a n t ) , i f blank or zero assumed to be equal to 1 1 32 COMMANDS FOR JOINTS WITH IDENTICAL DISPLACEMENTS : Omit i f no j o i n t s r e s t r a i n e d to have i d e n t i c a l displacements MDOF, NJT, I JOINT(NJT) (215,1415) one card/command MDOF : Displacement code : 1 : f o r x displacement 2 : f o r y displacement 3 : f o r r o t a t i o n NJT : Number of j o i n t s covered by t h i s command (max. 14) IJOINT : L i s t of nodes covered by t h i s command, i n i n c r e a s i n g order MEMBER INFORMATION : MN,JNL,JNG,KL,KG,E,G,AREA,CRMOM,DEPTH,BMCAP,EXTL,EXTG,AV (515,2F10.1,F8.2,F15.1,F6.1,F10.1,3F8.2) one card/member MN : Member number JNL : Lesser j o i n t number JNG : Greater j o i n t number KL : F i x i t y code at l e s s e r j o i n t 0 : Pinned 1 : F i x e d KG : F i x i t y code at g r e a t e r j o i n t E : Young's Modulus G : Shear Modulus (0 i f shear d e f l e c t i o n s are to be neglected) AREA : C r o s s - s e c t i o n a l area of the member 133 CRMOM : Moment of i n e r t i a of the member DEPTH : Depth of the member; i f given zero, p l a s t i c hinge length assumed 0.05(Member Length) BMCAP : Y i e l d moment of the member EXTL : R i g i d extension on the l e s s e r end j o i n t of the member EXTG : R i g i d extension on the g r e a t e r end j o i n t of the member AV : Shear area of the member (0 i f shear d e f l e c t i o n s are to be neglected) Note : If E, G, AREA, CRMOM, DEPTH, BMCAP, EXTL, EXTG, AV are l e f t blank or given zero f o r a member, same values as f o r the prev i o u s member w i l l be assumed. 8. STATIC LOAD INFORMATION :. NJLS, NLGCJ, NML, NLGCM, NJL (515) one card NJLS : Number of j o i n t s loaded by s t a t i c loads NLGCJ : Number of generat i o n commands f o r s t a t i c loads a p p l i e d d i r e c t l y at the nodes (See Note 6) NML : Number of members loaded by un i f o r m l y d i s t r i b u t e d s t a t i c load NLGCM : Number of generation commands f o r s t a t i c loads on the members (See Note 6) NJL : Number of j o i n t s loaded by se i s m i c l o a d 9. Cards 9A and 9B are omitted i f NJLS i s zero. A. COMMANDS FOR STATIC LOADS APPLIED DIRECTLY ON THE JOINTS : 1 34 Omit i f NLGCJ i s zero FX, FY, FM, NNOD, NODN(NNOD) (3F10.1,1015) one card/command FX : Load i n x - d i r e c t i o n FY : Load i n Y - d i r e c t i o n FM : Moment NNOD : Number of j o i n t s to be covered by t h i s command NODN : L i s t of j o i n t s covered by t h i s command i n i n c r e a s i n g order OR B. STATIC LOADS APPLIED DIRECTLY AT JOINTS : input t h i s i f NLGCJ = 0 N, FX, FY, FM (I5,3F10.1) one card/loaded j o i n t N : Node number FX : Load i n the x - d i r e c t i o n FY : Load i n the y - d i r e c t i o n FM : Moment NOTE : ONLY CARDS 9A OR 9B ARE TO BE INPUT IN THE DATA, NOT BOTH. Cards 10A and 10B to be omitted i f NML equals z e r o . A. COMMANDS FOR STATIC MEMBER LOADS : Omit i f NLGCM i s zero. W, NMEM, MR(NMEM) (F6.1,1415) one card/command W : Uniformly d i s t r i b u t e d load on the member, downward load p o s i t i v e 135 NMEM : Number of members covered by t h i s command MR : L i s t of members covered by t h i s command i n i n c r e a s i n g order OR B. STATIC MEMBER LOADS : Omit i f NLGCM i s not zero. MMR, W (I5,F10.4) one card/loaded member MMR : Member number W : Uniformly d i s t r i b u t e d s t a t i c load NOTE : ONLY CARDS 1 OA OR 1 OB TO BE INPUT IN THE DATA WHEN NML IS NOT ZERO, NOT BOTH. 11. LOAD FACTOR AND K FACTOR FLOAD, DUCTK (2F10.2) one card FLOAD : Load f a c t o r used on the seismic loads DUCTK : K f a c t o r used i n A.S.K.I.F.W formulae 12. SEISMIC LOADS N, FX, FY, FM (I5,3F10.5) one card/loaded j o i n t N : Node number FX : Load i n the x - d i r e c t i o n FY : Load i n the y - d i r e c t i o n FM : Moment 1 C 2 c 3 c STATIC DAMAGE EVALUATION METHOD 4 5 6 c c c METHOD TO CHECK DESIGN OONE BY CODE FORCEStOUASI STATIC ANALYST 7 8 c REAL'S S(190000). OBLE. DVL(500). SMS(200.21) 9 c PROGRAM DIMENSIONED FOR A MAXIMUM OF :-10 c 200 MEMBERS 1 1 c 200 JOINTS 12 c 13 c VARIABLE DEFINITIONS:-14 c 15 c Kl.. KG - JOINT TYPE : FIXED JOINT • 1 16 c PINNED JOINT • 0 17 c AREA - CROSS-SECTIONAL AREA 18 c CRMOM « MOMENT OF INERTIA OF GROSS SECTION 19 c BMCAP • BENOING MOMENT CAPACITY OF SECTION 20 c NO - 0.0.F. NO. IOENTIFI ED BY JOINT NO. 21 c NO(K.I) - K • 1 (X-DOF), 2 (Y-DOF), 3 (R-OOF) 22 c I » JOINT NO. 23 c NP " D.O.F. NO. IDENTIFIED BY MEMBER NO. 24 c NP(K.I) - K - OOF 1 TO 6 FOR STANOARO MEMBER 25 c I - MEMBER NO. 26 c XM - LENGTH OF FLEXI8LE PORTION OF BEAM IN X-DIRECTION 27 c YM » LENGTH OF FLEXIBLE PORTION OF BEAM IN Y-DIRECTION 28 c DM • TRUE LENGTH OF FLEXIBLE PORTION OF BEAM 29 c EXTL.EXTG - LENGTH OF RIGID END 30 c TITLE - TITLE (80 CHARACTERS) 31 c AV • SHEAR AREA 32 c FL(I) • LOAD FACTOR AT WHICH I TH HINGE FORMS 33 c YCR - YIELD CURVATURE 34 c PCR • PLASTIC CURVATURE 35 c 36 c 37 c 38 c 39 c 40 c 41 c 42 REAL'S OET. ORATIO 43 DIMENSION KL(20O). KGC200), AREAC200). CRM0M(2OO), BMCAP(200.3), 44 1 ND(3,32S), NP(6.200). XM(200). YM(200). OM(200). 45 2 EXTL(20O). EXTGC200), AV(200). TITLE(20). VLC5O0). 46 3 AXIAL(200). SHEARL(ZOO), SHEARG(200). BML(200). 47 4 • BMG(200). DEFLC500). F(500). RAXIAL(200), SHEAR 1(200), 48 5 SHEAR2(200). RBML(200). RBMG(20O). FL(200), JNL(200). 49 6 JNG(200). X(325). Y(325), R0TN(2.325). NDEF(2.325). SO 7 CD(200.2). SI(2). HL(200), YCR(200). PL(500). E(200). 51 8 G(200). N00NI20), MR(1S), MML(IOO), FEM(100.4) 52 CALL FTNCMOt'EQUATE 99'SPRINT;') S3 CALL CONTRL(NRJ. NCONJT. NCDJT. NCDOD. NCDIDS, NRM). 54 CALL SETUPCNRM, E, G. XM. YM, DM. NO. NP, AREA, CRMOM. NRJ. AV. 55 1 KL, KG. NU, NB. BMCAP. EXTL. EXTG, JNL. JNG. X. Y, YCR. HL, 56 2 NCONJT. NCDJT, NCDOD, NCDIDS) 57 IDIM • 190000 58 c ASSEMBLE STIFFNESS MATRIX 39 MMAX • O 60 CALL BUILD(NU. NB. XM. YM. DM. NP. AREA. CRMOM. AV. E. G. KL. KG. 61 1 NRM, S, IDIM. EXTL. EXTG. SMS. MMAX) 62 CALL SCHECK(S. NU. NB. IDIM, SRATIO) 63 C FORM LOAD VECTOR.GRAVITY LOADS & E/O FORCES AS GIVEN BY NBCC 64 00 10 I - 1, 500 65 PL(I) - 0. 66 10 VL(I) » 0. 67 READ (5.380) NJLS. NLGCJ. NML. NLGCM. NJL 68 WRITE (6.20) 69 20 FORMAT (//. ' -JOINT AND MEMBER LOADS') 70 C READ STATIC LOADS;MEMBER LOADS ONLY UDL 71 DO 30 J • 1. NRM .72 RAXIAL(J) - 0. 73 SHEAR 1 ( J) - O. 74 SHEAR2(J) - O. 75 RBML(J) » 0. 76 30 R8MG(J) • 0. 77 DO 40 J - 1, 500 78 40 OEFL(J) - 0. 79 IF (NJLS .EO. 0 .ANO. NML .EQ. 0) GO TO 320 80 IF (NJLS .EQ. 0) GO TO 190 81 WRITE (6,50) 82 50 FORMAT (///, 'GENERATION COMMANDS FOR STATIC LOADS APPLIED DIRECTL 83 1Y TO THE NODES', /) 84 IF (NLGCJ .NE. 0) GO TO 70 85 WRITE (6,60) 86 60 FORMAT (//, 'NONE'. /) 87 GO TO 140 88 70 CONTINUE 89 DO 130 I - 1. NLGCJ 90 WRITE (6.80) 91 80 FORMAT (//, SX. 'FX'.. IOX. 'FY'. 13X. 'FM'. 10X. 'NO. OF NODES'. 92 1 /) 93 READ (S.90) FX. FY. FM. NNOD, (NOON(N),N-1.NNOD) 94 90 FORMAT (3F10.1. 1015) 95 WRITE (6.100) FX. FY, FM. NNOD 96 100 FORMAT (/, F6.1. 6X, F10.1. 6X, F10.1. IOX. IS) 97 C 98 C 99 WRITE (6.110) (NODN(N).N'1.NNOD) 100 110 FORMAT (/, 'LIST OF NODES', //. 16IS) 101 00 120 J • 1, NNOD 102 NN ' NODN(J) 103 NI • N0(1.NN) 104 N2 • ND ( 2 , NN ) 105 N3 - ND ( 3 , NN) 106 PL(N1) - PL(N1) + FX 107 PL(N2) • PL(N2) + FY 108 PL(N3) • PL(N3) • FM 109 120 CONTINUE 110 130 CONTINUE 111 GO TO 190 112 140 CONTINUE 113 WRITE (6.150) 114 150 FORMAT (' -JN'. 13X, 'FX '. IOX, 'FY ', IOX, ' FM', /) 115 00 180 NJ • 1, NJLS 116 READ (S.160) N. FX, FY. FM U cn 117 WRITE (6.170) N, FX. FY. FM 118 160 FORMAT (15. 3F10.5) 119 170 FORMAT (14. 3(10X.F10.2)) 120 N1 ' ND(I.N) 121 N2 " N0(2.N) 122 N3 • N0(3.N) 123 PL(N1) - PL(N1) + FX 124 PL(N2) - PL(N2) • FY 125 PUNS) - PL(N3) + FM 126 180 CONTINUE 127 190 CONTINUE 128 IF (NML .EO. 0) GO TO 320 129 WRITE (6.200) 130 200 FORMAT (///. "GENERATION COMMANDS FOR MEMBER LOADS'. /) 131 IF (NLGCM .NE. O) GO TO 210 132 WRITE (6.60) 133 GO TO 270 134 210 CONTINUE 135 WRITE (6.220) 136 220 FORMAT (//. 3X, 'U.D.L.'. 3X. 'NO. OF MEMBERS'. 13X. 137 1 'LIST OF MEMBERS', /) 138 JM * 1 139 DO 260 I • 1. NLGCM 140 REAO (5.230) W. NMEM, (MR(J).J>1.NMEM) 141 230 FORMAT (F6.1. 1415) 142 WRITE (6.240) W. NMEM, (MR(J),J-1,NMEM) 143 240 FORMAT (F6.1. 5X. 15. 11X. 1315) 144 00 250 J - 1 . NMEM 145 MMR • MR(J) 146 MML(JM) - MMR 147 CALL GEN2(MMR. W, XM, KL. KG. NP. PL. JM, FEM) 148 JM • JM + 1 149 250 CONTINUE 150 260 CONTINUE 151 GO TO 320 152 270 CONTINUE 153 WRITE (6.280) 154 280 FORMAT (5X. 'MEMBER NO.'. 10X. 'UNIF. DIST. LOAD') 155 00 310 J • 1. NML 156 READ (5.290) MMR. W 157 WRITE (6.300) MMR, W 158 290 FORMAT (15. F10.4) 159 300 FORMAT (5X. 16. 15X. F10.2) 160 MML(J) - MMR 161 CALL GEN2(MMR. W. XM. KL. KG. NP, PL. J . FEM) 162 310 CONTINUE 163 320 CONTINUE 164 C READ SEISMIC FORCE LOAD FACTOR FLOAO ANO VALUE OF K USED 165 ' C IN ASKIFW FORMULAE 166 REAO (5.330) FLOAO. OUCTK 167 330 FORMAT (2F10.2) 168 WRITE (6.340) FLOAO. DUCTK 169 340 FORMAT (/. 'SEISMIC FORCE LOAO FACTOR •', F5.2. //. 170 1 • 'VALUE OF K FOR THIS STRUCTURE -'. FS.2) 171 C READ E/O LOADS (AS PER NBCC) 172 WRITE (6.350) 173 350 FORMAT (/. 5X. 'EARTHQUAKE LOADS') 174 WRITE (6.400) 175 00 360 J - 1. NJL 176 READ (5.390) N. FX. FY, FM 177 WRITE (6.410) N. FX, FY, FM 178 M1 - ND(1,N) 179 M2 - ND(2.N) 180 M3 - ND(3.N) 181 VL(M1) - VL(M1) • FX 182 VL(M2) • VL(M2) + FY 183 VL(M3) - VL(M3) + FM 184 360 CONTINUE 185 IF (NJLS .EQ. 0 .AND. NML .EO. O) GO TO 450 186 C SOLVE THE STRUCTURE FOR GRAVITY LOADS 187 C CONVERT LOADS TO DOUBLE PRECISION -188 DO 370 I • 1 . NU 189 370 0VL(I) - OSLE(PL(I)) 190 380 FORMAT (515) 191 390 FORMAT (15. 3F10.5) 192 400 FORMAT (5X, ' JN'. 9X. ' F X '. 9X, ' FY '. 9X, ' FM'. /) 193 410 FORMAT (/. 17. 3(8X.F10.2)) 194 C CALL SDFBAN TO SOLVE AX»B(GRAVITY LOADS) 195 DRATIO • 1.D-16 196 INK - NU • NB 197 CALL SDFBAN(S, DVL, NU. NB. 1. DRATIO. DET. JEXP. 1. KTR) 198 C DVL NOW IS SOLN. VECTOR.CONVERT IT TO SINGLE PRECISION 199 00 420 J - 1. NU 200 420 F(J) - SNGUDVL(J)) 201 C FINO OUT MEMBER FORCES DUE TO STATIC LOADS 202 ML I - NML 203 CALL FORCEtNRM, XM. YM, DM. AV, NP, F. EXTL. EXTG. AREA. E. G. 204 1 CRMOM. KL. KG. AXIAL. SHEARL. SHEARG. BML. BMG. ML I . MML, 205 2 FEM) 206 00 430 I • 1, NRM 207 RAXIAL(I) • AXIAL(I) 208 SHEAR 1(1) • SHEARL(I) 209 SHEAR2U) - SHEARG(I) 210 RBML(I) > BML(I) 211 430 RBMG(I) • BMG(I) 212 DO 440 I " 1, 500 213 440 DEFL(I) - F(I) 214 450 CONTINUE 215 DO 460 1 - 1 . 2 216 DO 460 J - 1 . NRM 217 NDEF(I.J) - -9 218 460 ROTN(I.J) - O. 219 DO 470 J - 1. NU 220 470 OVL(J) • DBLE(VL(J)) 221 C CALL SDFBAN TO SOLVE AX-B(FOR E/O LOADS) 222 DRATIO • 1.D-16 223 CALL SDFBAN(S. DVL. NU. NB. 2. DRATIO, DET. JEXP, 1. KTR) 224 C CONVERT SOLN. VECTOR OVL TO SINGLE PRECISION 225 00 480 J • 1. NU 226 480 F(J) • SNGL(DVL(J)) 227 C FINDING A NOOE AT THE TOP OF THE STRUCTURE TO FINO 228 C SYSTEM DUCTILITY 229 XD1 - 0. 230 00 500 1 - 1 , NRJ 231 II - NO(I.I) 232 IF (It .EQ. O) GO TO 500 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 XD2 • ABS(F(I1)) IF (XD2 .GT. X01) GO TO 490 GO TO 500 490 CONTINUE X01 • X02 NTOP • I 500 CONTINUE K • ND(1.NTOP) YDEFL - DEFL(K) + F(K) UOEFL - FLOAO • 2.9 • YDEFL / DUCTK WRITE (6.510) YOEFL. UOEFL 510 FORMAT (/, 'YIELD TIP DISP. 1 F10.3. /) FINO MEMBER FORCES DUE TO E/O LOADS ML I • 0 F10.3. 5X. 'ULTIMATE TIP OISP. XM. YM, OM, AV. NP KG. AXIAL. SHEARL. F. EXTL. EXTG. AREA, E. G, SHEARG. BML, BMG, MLI, MML, CALL FORCE(NRM, 1 CRMOM, KL, 2 FEM) LSENS • 1 IKOUNT - 0 DO 1060 IOV • 1. 200 HAVE MEMBER FORCES,FIND LOAD FACTOR AT WHICH PLASTIC HINGE FORMS 00 580 1 * 1. NRM RBL RBG ABS(RBML(I)) ABS(RBMG(I)) 258 IF (RBML(I) .LE. 0.0 .AND. . BML(I) .LT. 0.0) GO TO 520 259 IF (RBML(I) .GT. 0.0 .AND. . BML(I) .GT. 0.0) GO TO 520 260 IF (R8ML(I) .LE. 0.0 .AND. . BML(I) .GT. 0.0) GO TO 530 261 IF (RBML(I) .GT. 0.0 .AND. . BML(I) .LT. 0.0) GO TO 530 262 520 8MCAP(I,2) • BMCAP(I, D - RBL 263 GO TO 540 264 530 BMCAP(I,2) « BMCAP(I, 1) • RBL 265 540 CONTINUE 266 IF (RBMG(I) .LE. 0.0 .AND. BMG(I) .LT. 0.0) GO TO 550 267 IF (RBMG(I) .GT. 0.0 .AND. , BMG(I) .GT. 0.0) GO TO 550 268 IF (RBMG(I) .LE. 0.0 .AND. BMG(I) .GT. 0.0) GO TO 560 269 IF (RBMG(I) .GT. 0.0 .AND. . 8MG(I) .LT. 0.0) GO TO 560 270 550 BMCAP(I.3) - BMCAP(I, 1) " RBG 271 GO TO 570 272 560 BMCAP(I,3) • BMCAP(I, 1) • RBG 273 570 CONTINUE 274 580 CONTINUE 590 600 CALL RATIO(BML, BMG, BMCAP. NRM, FACT. KL. KG. MMAX. ICT. LSENS) IF (IOV .EO. 1) GO TO 590 FL(IOV) • FL(IOV - 1) • FACT GO TO 600 FL(IOV) . FACT CONTINUE WRITE (99.610) FL(IOV) IF (LSENS .EO. 1) WRITE (6.610) FL 620 FORMAT ('AT A 00 620 I • 1. RAXIAL(I) SHEAR1(I) SHEAR2(I ) RBML(I) • RBMG(I) • RBMG(I) » FACT • BMG( CONTINUE LOAO FACTOR OF NRM • RAXIAL(I) - SHEARI(I) • SHEAR2II) RBML(I) • FACT F6 FACT • FACT • FACT * BML( L(IOV) 3) AXIAL(I) SHEARL(I) SHEARG(I) I) I) 291 K » ND(1.NTOP) 292 UOEFL • ABS(UDEFL) 293 TIPD - OEFL(K) • FACT • F(K) 294 TIPD " ABS(TIPD) 295 IF (TIPD .LT. UDEFL .AND. IKOUNT .EO. 1) GO TO 680 296 IF (TIPO .LT. UDEFL) GO TO 660 297 FACT 1 • (UDEFL - ABS(OEFL(K)) ) / ABS(F(K)) • 298 C ADD UP THE DEFLECTIONS CORRESPONDING TO TIP DEFLECTION 299 C OF CALCULATED VALUE 300 00 630 I - 1. NU 301 DEFL(I) • DEFL(I) + FACT 1 • F(I) 302 630 CONTINUE 303 IF (LSENS .EO. 1) WRITE (6.640) 304 640 FORMAT ('THIS PLASTIC HINGE NOT CONSIDERED AS TIP DISP. IS'. / 305 1 'MORE THAN CALCULATED ULT. TIP DISP'. //) 306 IF (IKOUNT .EO. 1) GO TO 1250 307 IF (LSENS .EO. 1) CALL CURVO(NRM. CD, NOEF, NP, DEFL. ROTN. HL, 308 1 YCR, LSENS. IKOUNT) 309 00 650 I • 1. NU 310 DEFL(I) • DEFL(I) - FACT 1 • F(I) 311 650 CONTINUE 312 660 CONTINUE 313 IF (LSENS .EO. 2) UOEFL - 1.1 • UOEFL 314 UDEFL « ABS(UDEFL) 315 K - ND(1.NTOP) 316 TIPD ' DEFL(K) + FACT • F(K) 317 TIPD " ABS(TIPD) 318 IF (TIPD .LT. UDEFL) GO TO 680 319 FACT 1 • (UDEFL - ABS(OEFL(K) ) ) / ABS(F(K) ) 320 C NOW AOD UP THE DEFL UP TO INCREASED TIP DEFL. 321 DO 670 I - 1. NU 322 DEFL(I) - DEFL(I) + FACT 1 • F(I) 323 670 CONTINUE 324 GO TO 1250 325 680 CONTINUE 326 C AOD UP THE DEFLECTIONS 327 00 690 I - 1. NU 328 DEFL(I) • DEFL(I) • FACT » F(I) 329 690 CONTINUE 330 IF (ICT .EO. 1) N1 - NP(3,MMAX) 331 IF (ICT .EO. 2) N1 - NP(G.MMAX) 332 NOEF(ICT,MMAX) • N1 333 IF (N1 .EO. 0) GO TO 700 334 ROTN(ICT.MMAX) - DEFL(N1) 335 700 CONTINUE 336 IF (LSENS .EO. 1) WRITE (6,710) TIPD 337 710 FORMAT (' TIP DISP • '. F10.3) 338 IF (ICT .EO. 2) GO TO 740 339 C ICT'1 -PLASTIC HINGE FORMED AT LESSER END OF MEMBER MMAX 340 IF (NP(3,MMAX)) 720, 720. 730 341 720 JL - JNL(MMAX) 342 N0(3,JL) - NU + 1 343 NU • NU • 1 344 NP(3.MMAX) - NOO.JL) 345 GO TO 770 346 730 CONTINUE 347 C ADO A NEW NODE-.NODE ON TOP OF ONE ANOTHER CAPABLE OF HAVING 348 C DIFFRENT ROTATIONS 01 349 NRJ - NRJ + 1 407 C STRUCTURE IS LINEAR FOR THE UNUSED PART OF THE BENDING MOMENT 350 NU • NU + 1 408 C EQUIVALENT TO REDUCING THE BENDING MOMENT CAPACITY 351 JL - JNL(MMAX) 409 C CHECK FOR A POSSIBLE JT.ROTATION MECHANISM 352 N0(1,NRJ) " ND(1 ,0L) 410 00 910 I • 1. NRJ 353 ND(2.NRJ) • ND(2.JL) 411 00 890 J - 1. NRM 354 X(NRJ) - X(JL) 412 IF (I .EQ. JNL(J)) GO TO 910 355 Y(NRJ) • Y(JL) 413 IF (I .EO. JNG(J)) GO TO 910 356 N0(3.NRJ) - NU 414 890 CONTINUE 357 JNL(MMAX) • NRJ 415 WRITE (6.900) I 358 NPO.MMAX) • NU 416 900 FORMAT ('JOINT ROTATION MECHANISM FORMED AT JT NO.'. 14) 359 GO TO 770 417 GO TO 850 360 C DO SAME THING;HINGE FORMED AT GREATER END OF MEM8ER MMAX 418 910 CONTINUE 361 740 CONTINUE 419 MS - NU * NB 362 IF (NPO.MMAX)) 750. 750. 760 420 DO 920 I • t. MS 363 750 JG - JNG(MMAX) 421 920 S(I) - 0.0000 364 NOO.JG) • NU • 1 422 C REASSEMBLE THE OVERALL STIFFNESS MATRIX 365 NU - NU + 1 423 NB1 - NB - 1 366 NP(6.MMAX) - NOO.JG) 424 DO 1020 I - 1, NRM 367 GO TO 770 425 DO 1010 J - 1 . 6 368 760 CONTINUE 426 IF ( N P ( J . D ) 1010. 1010. 930 369 NRJ " NRJ + 1 427 930 J1 - (J - 1) • (12 - J) / 2 370 NU - NU + 1 428 DO 1000 L » J . 6 371 JG • JNG(MMAX) 429 IF ( N P ( L . D ) 1O00. 1000. 940 372 ND(1.NRJ) - ND(1.JG) 430 940 IF (NP(J.I) - NP(L.I)) 970. 950. 980 373 NDO.NRJ) • ND(2.JG) 431 950 IF (L - J) 960. 970. 960 374 X(NRJ) - X(JG) 432 960 K • (NP(L.I) - 1) • NB1 + NP(J.I) 375 Y(NRJ) • Y(JG) 433 N - J1 • L 376 NDO.NRJ) - NU 434 S(K) • S(K) + 2.ODOO • SMS(I.N) 377 JNG(MMAX) • NRJ 435 GO TO 1000 378 NPO.MMAX) - NU 436 970 K • (NP(J.I) - 1) • NB1 + NP(L.I) 379 770 CONTINUE 437 GO TO 990 380 C SEE WHETHER HALF WIDTH OF STIFFNESS MATRIX CHANGED 438 980 K • (NP(L.I) - 1) • NB1 + NP(J.I) 381 MAX • 0 439 990 N • J1 + L 382 DO 800 K • 1. 6 440 S(K) • S(K) + SMS(I.N) 383 IF (NP(K.MMAX) - MAX) 790, 790. 780 441 1000 CONTINUE 384 780 MAX - NP(K.MMAX) 442 1010 CONTINUE 385 790 CONTINUE 443 1020 CONTINUE 386 800 CONTINUE 444 CALL SCHECKO. NU. NB. IOIM, SRATIO) 387 MIN - 1000 445 DO 1030 I - 1. NU 388 00 840 K - 1. 6 446 1030 DVL(I) • DBLE(VLU)) 389 IF (NP(K.MMAX)) 830, 830. 810 447 DRATIO - 1.0-16 390 810 IF (NP(K.MMAX) - MIN) 820. 820. 830 448 CALL SOFBANO. DVL. NU. NB. 1. DRATIO. DET. JEXP. 1. KTR) 391 820 MIN • NP(K.MMAX) 449 IF (KTR .EQ. 2) GO TO 850 392 830 CONTINUE 450 IF (DRATIO) 850. 850. 870 393 840 CONTINUE 451 1040 CONTINUE 394 NBB - MAX - MIN + 1 452 DO 1050 I • 1. NU 395 IF (NB8 .GT. NB) NB • NBB 453 1050 F(I) » SNGL(DVL(I)) 396 C CHECK HERE WHETHER A COLLAPSE MECHANISM HAS FORMED. IF YES GET 454 CALL FORCE(NRM. XM. YM. DM. AV. NP. F. EXTL. EXTG. AREA. E. 397 C OUT OF THIS DO LOOP 455 1 CRMOM. KL. KG. AXIAL. SHEARL. SHEARG. BML, BMG) 398 GO TO 880 456 1060 CONTINUE 399 850 CONTINUE 457 1070 CONTINUE 400 WRITE (6.860) FL(IOV) 458 IF (ICT .EO. 1) N • JNL(MMAX) 401 860 FORMAT (/. 'APPRENT COLLAPSE AT A LOAD FACTOR OF'. F6.3) 459 IF (ICT .EQ. 2) N • JNG(MMAX) 402 GO TO 1070 460 00 1090 I " 1. NRJ 403 870 CONTINUE 461 IF (X(I) .EQ. X(N) .AND. Y(I) .EQ. Y(N)) GO TO 1080 404 IF (DRATIO .GT. 5.0-3) GO TO 1040 462 GO TO 1090 405 GO TO 850 463 1080 MEM - I 406 880 CONTINUE 464 GO TO 1100 CO (0 463 1090 CONTINUE 466 1100 I • MEM 467 IF (I .EO. N) GO TO 1110 468 GO TO 1120 469 1110 NRJ - NRJ • 1 470 I « NRJ 471 X(I ) • X(N) 472 Y(I) - Y(N) 473 ND( 1.1) • N0( 1..N) 474 ND(2.I) - ND(2.N) 475 N0(3 , I ) • ND(3.N) 476 C 477 1120 X(N) - X(N) - 0.10 478 Y(N) - Y(N) - 0.10 479 C AOO A" FICTITIOUS MEMBER WITH VERY SMALL MOM. OF INERTIA 480 NRM • NRM * 1 481 JNL(NRM) - I 482 JNG(NRM) • N 483 XM(NRM) - X(N) - X(I) 484 YM(NRM) - Y(N) - Y(I) 485 DM(NRM) • S0RT((XM(NRM))"2 + (YM(NRM) ) **2) 486 EXTL(NRM) - 0. 487 EXTG(NRM) - 0. 488 KL(NRM) • 1 489 KG(NRM) - 1 490 NP(1.NRM) > N0(1.1) 491 NP(2.NRM) • N0(2.I ) 492 NP(3.NRM) - ND(3.I) 493 NP(4.NRM) • N0(1,N) 494 NP(S.NRM) - ND(2,N) 495 NP(6.NRM) • N0(3.N) 496 AREA(NRM) - AREA(NRM - 1) / 100. 497 CRMOM(NRM) - 0.01 • CRMOM(NRM - 1) 49S AV(NRM) * 0. 499 E(NRM) • E(NRM - 1) 500 MMAX - NRM 501 C AT THIS STAGE SHOULD ALSO CHECK WHETHER HALF-WIDTH OF STIFFNESS 502 C MATRIX CHANGED 503 MAX - 0 504 DO 1150 K - 1 . 6 505 IF (NP(K.MMAX) - MAX) 1140. 1140. 1130 506 1130 MAX ' NP(K.MMAX) 507 1140 CONTINUE 508 1150 CONTINUE 509 MIN - 1000 510 DO 1190 K • 1. 6 511 IF (NP(K.MMAX)) 1180. 1180. 1160 512 1160 IF (NP(K.MMAX) - MIN) 1170. 1170, 1180 513 1170 MIN - NP(K.MMAX) 514 1180 CONTINUE 515 1190 CONTINUE 516 NBB • MAX - MIN » 1 517 IF (NBB .GT. NB) NB • NBB 518 CALL BUILD(NU, NB, XM. YM. OM. NP, AREA. CRMOM, AV. E . G, KL. KG. 519 1 NRM, S, IDIM. EXTL, EXTG, SMS, MMAX) 520 CALL SCHECMS. NU. NB. IOIM, SRATIO) 521 00 1200 J • 1, NU 522 1200 OVL(J) • DBLE(VL(J)) 523 DRATIO - 1.0-16 524 CALL SDFBAN(S. DVL. NU. NB. 1. ORATIO. OET. JEXP. 1, KTR) 525 IF (ORATIO .GT. 5.D-3) GO TO 1220 526 WRITE (6.1210) 527 1210 FORMAT ("DID NOT WORK") 528 STOP 529 1220 CONTINUE 530 11 • ND(1.NTOP) 531 DO 1230 K - 1. NU 532 1230 F(K) • SNGL(DVL(K)) 533 C SCALE UP THIS SOLN. VECTOR S . T . THE ULTIMATE ROOF DISP. 534 . C IS UDEFL 535 DI • ABS(DEFL(11)) 536 ADISP - UDEFL - D1 537 FA • AOISP / ABS(F( I I ) ) 538 00 1240 K • 1. NU 539 DEFL(K) - DEFL(K) + FA • F(K) 540 1240 CONTINUE 541 NRM « NRM - 1 542 CALL CURVD(NRM, CD. NDEF, NP. OEFL. ROTN. HL. YCR, LSENS) 543 1250 CONTINUE 544 C PRINT OUT CURV. DUCT. ANO SENSITIVITY INDEX 545 DO 1310 J - 1. NRM 546 DO 1280 I • 1, 2 S47 S K I ) • 0 . 548 COY • 0. 549 IF (NDEF(I . J ) . L T . 0) GO TO 1270 550 IF (I .EO. 1 ) 0 1 - NP(3 , J ) 551 IF (I .EO. 2) J1 • NP(6 . J ) 552 IF (NDEF(I . J ) .EO. 0) GO TO 1260 553 J2 - NDEF(I . J ) 554 PCR - (DEFL(JI ) - (DEFL(J2) - ROTN(I . J ) ) ) / HL(J) 555 PCR - ABS(PCR) 556 COY - 1. • PCR / YCR(J) 557 S K I ) - (COY - C O ( J . I ) ) / 0. . 1 558 GO TO 1280 559 1260 CONTINUE 560 PCR - DEFL(J1 ) / HL(J) 561 PCR « ABS(PCR) 562 COY - 1. + PCR / YCR(J) 563 S K I ) • (CDY - C D ( J . I ) ) / 0. . 1 564 1270 CONTINUE 565 1280 CONTINUE 566 IF (d .EO. 1) WRITE (6.1290) 567 1290 FORMAT (10X. ' C U R V A T U R E D U C T I L I T Y D E 568 1 569 2 . / / , 5X. 'MEMBER N O . * , , 14X. 'LESSER END' . 13X. 570 3 'GREATER END' . 13X. 'SENSITIVITY INDEX". / ) 571 SENS • SI(1) 572 IF (SENS . L T . S K 2 ) ) SENS • SI(2) 573 WRITE (6,1300) J . C O ( J . I ) . C 0 ( J , 2 ) . SENS 574 1300 FORMAT (SX. 15, 17X. F 9 . 3 , 17X, F 9 . 3 , 17X. F9 .1) 575 1310 CONTINUE 576 STOP 577 ENO 578 C 579 C 580 SUBROUTINE CONTRL(NRJ, NCONJT, NCOJT, NCOOO. NCOIOS. NRM) o 581 C 639 READ (S.100) I JT . L JT . NJT. KOIF 582 C 640 100 FORMAT (4IS) 583 DIMENSION TITLE(20) 64 1 IF (KDIF .EO. 0) KOIF • 1 584 READ (5.10) ( T I T L E ( I ) . I - 1 . 2 0 ) 642 WRITE (6.110) I JT. L JT . NJT. KDIF 585 READ (5.30) NRM. NRJ, NCONJT, NCOJT. NCDOD, NCDIDS 643 110 FORMAT (16. 318) 586 WRITE (6,10) (TITLE( I ) .1 -1 .20 ) . 644 CALL GENKX. Y. I JT. L J T . NJT. KOIF) 587 WRITE (6,20) NRJ, NRM 645 120 CONTINUE 588 10 FORMAT (20A4) • 646 C GENERATE UNSPECIFIEO JOINT COORDINATES 589 20 FORMAT (/. 'NO. OF JOINTS- ' . IS. IOX, 'NO. OF MEMBERS-', IS. / ) 647 130 I • 1 590 30 FORMAT (615) 648 140 I • I + 1 591 RETURN 649 IF (I .GT. NRJ) GO TO 160 592 END 650 IF (X(I) .NE. 999000.) GO TO 140 593 651 IJT • I - 1 594 C •JS2 LJT - IJT 595 C 653 150 LJT - LJT + 1 596 c 654 IF (LJT .GT. NRJ) GO TO 160 597 c 655 IF (X(LJT) .EQ. 999000.) GO TO 150 598 SUBROUTINE SETUP(NRM, E . 0. XM. YM, DM. ND. NP. AREA. CRMOM. NRJ. 656 NJT - LJT - IJT - 1 599 1 AV. KL. KG, NU. NB. BMCAP, EXTL. EXTG, JNL, JNG, X, Y, 657 CALL GENKX. Y. I JT . L J T . NJT. 1) 600 2 YCR, HL, NCONJT. NCDJT. NCDOD, NCDIDS) 658 I - LJT 601 c 659 GO TO 140 602 c 660 160 CONTINUE 603 c 661 C ASSIGNING D . O . F . TO THE NODES 604 c 662 DO 170 1 - 1 . NRJ 60S c SET UP THE FRAME DATA 663 DO 170 J - 1, 3 606 c 664 170 ND(J . I ) • 1 607 DIMENSION KL(NRM), KG(NRM), AREA(NRM), CRMOM(NRM), BMCAP(NRM,3), 66S C ZERO DISPLACEMENTS 608 1 AV(NRM), N0(3,NRJ). NP(6,NRM), XM(NRM). YM(NRM), 666 WRITE (6,180) 609 2 EXTL(NRM). EXTG(NRM). OM(NRM). E(NRM), G(NRM) 667 180 FORMAT (/. 'ZERO DISPLACEMENT COMMANDS'. / / ) 610 DIMENSION X(32S). Y(325), JNL(NRM), JNG(NRM). HL(NRM). YCR(NRM), 668 IF (NCOOD .NE. 0) GO TO 190 611 1 K00F(3). IJ0INT(40) 669 WRITE (6.70) 612 c 670 GO TO 270 613 c 671 190 WRITE (6,200) 614 c INITIALIZE COORDINATES 672 2O0 FORMAT (/. ' F I R S T ' . 6X. ' X ' . 6X. ' Y ' . 4X. ' R O T N ' . 4X. ' L A S T ' , 4X 615 DO 10 I - 1. NRJ 673 1 'NOOE' , / . ' N O D E ' , 7X, ' D O F ' . 4X, ' D O F ' . 5X, ' D O F ' , 4X. 616 X(I) - 999000. 674 2 'NODE' . 4X. ' D I F F ' . / ) 617 10 Y(I) - 999O00. 675 00 260 I • 1. NCDOD 618 c READ CONTROL NOOE CORDINATES 676 READ (5.210) I JT . (KDOF(J ) .d-1 .3 ) . L JT . KDIF 619 WRITE (6.20) 677 210 FORMAT (615) 620 20 FORMAT (//. 'CONTROL NODE COORDINATES'. / / / . 'NODE' . 6X. 678 WRITE (6,220) I JT, (KDOF(J ) . J -1 ,3 ) , L JT . KDIF 621 1 'X-COORO'. 6X, 'Y-COORD'. / ) 679 220 FORMAT (13. 518) 622 DO 50 I • 1 . NCONJT 680 DO 230 J • 1. 3 623 READ (5,30) IJT. X ( I J T ) , Y(IJT) 681 230 ND(J . I JT) - KDOF(J) 624 30 FORMAT (15. 2FtO.1) 682 IF (LJT .EQ. 0) GO TO 260 625 WRITE (6.40) I JT. X ( I JT ) , Y(IJT) 683 IF (KDIF .EQ. 0) KOIF - 1 626 40 FORMAT (15. 2F13.3) 684 NJT - (LJT - I JT) / KDIF 627 SO CONTINUE 685 DO 250 II - 1. NJT 628 c NODE GENERATION COMMANOS 686 IJT » IJT + KDIF 629 WRITE (6.60) 687 DO 240 J • 1. 3 630 60 FORMAT (/ / / ' NODE GENERATION COMMANDS'/) 688 240 ND(J . I JT) « KDOF(J) 631 IF (NCOJT .NE. 0) GO TO 80 689 250 CONTINUE 632 WRITE (6.70) 690 260 CONTINUE 633 70 FORMAT (//, 'NONE') 691 C IDENTICAL DISPLACEMENT 634 GO TO 130 692 270 CONTINUE 635 80 WRITE (6,90) 693 WRITE (6.280) 636 90 FORMAT (/2X, ' F I R S T ' . 4X. ' L A S T ' . 4X, 'NO. O F ' . 4X. 'NODE' . / . 2X. 694 280 FORMAT (/// . 'EQUAL DISPLACEMENT COMMANDS ' . / ) 637 1 'NODE' . 4X. 'NODE' . 4X. 'NODES'. 5X. ' O I F F ' . / ) 695 IF (NCDIOS .NE. 0) GO TO 290 638 DO 120 1 - 1 . NCDJT 696 WRITE (6.70) 697 GO TO 350 698 290 WRITE (6.300) 699 300 FORMAT (//, * O I S P ' . 4X. 'NO. O F " . / . 'COOE' . 4X. 'NODES'. 6X. 700 I 'LIST OF NODES'. / ) 701 00 340 1 - 1 . NCDIDS 702 REAO (5.310) MKDOF. NJT. (IJOINT(IU).IU-1.NJT) 703 310 FORMAT (215. 1415) 704 WRITE (6.320.) MKOOF, NJT. (I JOINT (IU). IU-1 . NJT ) 705 320 FORMAT (13, 18. 6X, 1415) 706 II - IJOINT(I) 707 00 330 IM - 2, NJT 708 IK • IJOINT(IM) 709 330 NO(MKDOF.IK) - -II 710 340 CONTINUE 7t 1 C TO SET UP ND ARRAY 712 350 NU - 0 713 WRITE (6.400) 714 DO 390 I - 1. NRJ 715 DO 380 J • 1. 3 716 IF (ND(J . I ) .NE. 1) GO TO 360 717 NU - NU + 1 718 NO(J . I ) - NU 719 GO TO 380 720 360 IF (ND(J . I ) .NE. 0) GO TO 370 721 NO(J . I ) - 0 722 GO TO 380 723 370 II - -ND(J . I ) 724 NO(J . I ) - ND(J . I I ) 725 380 CONTINUE 726 WRITE (6.410) I. X ( I ) . Y ( I ) . (ND(J , I ) . J -1 ,3 ) 727 390 CONTINUE 728 400 FORMAT (/. 3X. ' J N ' . 5X. 'X-COORD'. SX. 'Y-COORO'. 5X, 'NOX' . 5X. 729 1 'NDY' , 5X. 'NOR', / ) 730 410 FORMAT (14, 2F13.2, 16, 5X. 14. 5X. 14) 731 C 732 WRITE (6.590) 733 WRITE (6,600) 734 WRITE (6.610) 735 C 736 c READ IN MEMBER DATA AND COMPUTE THE HALF BANDWIDTH (NB) 737 c HALF BANDWIDTH-MAX DEGREE OF FREEDOM-MIN DEGREE OF FREEOOM +1 738 c 739 c 740 NB - 0 741 742 00 580 MBR - 1. NRM 743 REAO (5.620) MN, JNL(MBR), JNG(MBR), KL(MBR). KG(MBR), E(MBR), 744 1 G(MBR), AREA(MBR), CRMOM(MBR), DEPTH, BMCAP(MBR,1), EXTL(MBR), 745 2 EXTG(MBR), AV(MBR) 746 747 c 748 c COMPUTE MEMBER LENGTH (OM)-LENGTH BETWEEN JOINTS-RIGID EXTENSIONS 749 JL - JNL(MBR) 750 JG - JNG(MBR) 751 XM(MBR) • X(JG) - X(JL) 752 YM(MBR) - Y(JG) - Y(JL) 753 DM(MBR) • S0RT((XM(MBR))--2 + (YM(MBR))**2) 754 EXTSUM • EXTL(MBR) + EXTG(MBR) 755 XM(MBR) - XM(MBR) • (1 .0 - EXTSUM/OM(MBR)) 756 YM(MBR) • YM(MBR) • (1 .0 - EXTSUM/OM(MBR)) 757 C RESET NEGATIVE VALUES OF ZERO TO ZERO 758 IF (YM(MBR) . G T . - 0.01 .AND. YM(MBR) . L T . 0.01) YM(MBR) • 0 .0 759 IF (XM(M8R) .GT. - 0.01 .AND. XM(MBR) . L T . 0.01) XM(MBR) • 0 .0 760 DM(MBR) - DM(MBR ) - EXTSUM 761 C 762 C CHECK FOR NEGATIVE LENGTHS OF MEMBER 763 C (PROBABLY CAUSED BY INCORRECT USE OF MEMBER EXTENSIONS) 764 C 765 IF (DM(MBR) . G T . 0 .0) GO TO 430 766 WRITE (6.420) MBR 767 420 FORMAT (' ' . / / / 'PROGRAM HALTED:ZERO OR -VE LENGTH FOR MEMBER', 7.68 1 16) 769 STOP 770 C 771 430 CONTINUE 772 C 773 YLEN • YM(MBR) 774 C 775 C PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS 776 C ON VERTICAL MEMBERS. 777 IF (EXTSUM .NE. 0 .0 .AND. YLEN .GT. 0 .2 ) WRITE (6.440) I 778 440 FORMAT (' ' . 'ERROR-HAVE END EXTENSIONS ON NON-HORIZONTAL 779 1 MEMBER N O . ' . 13) 780 C PRINT ERROR MESSAGE IF ATTEMPT TO HAVE RIGID EXTENSIONS ON 781 C A NON FIX-FIX TYPE MEMBER 782 KLSUM > KL(MBR) + KG(MBR) 783 IF (EXTSUM . N E . 0 . 0 .AND. KLSUM .NE. 2) WRITE (6.450) MBR 784 450 FORMAT (' ' . 'ERROR-HAVE RIGID EXTENSIONS ON HINGED MEMBER'. 14) 785 C 786 C 787 C ASSIGN MEMBER DEGREES OF FREEDOM 788 NP(I.MBR) - N O O . J L ) 789 NP(2.MBR) - ND(2, JL) 790 NPO.MBR) - ND(3. JL) 791 NP(4,MBR) - ND(1.JG) 792 NP(S.MBR) - ND(2,JG) 793 NP(6,MBR) - ND(3,JG) 794 C DETERMINE THE HIGHEST DEGREE OF FREEDOM FOR EACH MEMBER STORING 795 C THE RESULT IN 'MAX' 796 MAX - O 797 C 798 DO 480 K • 1, 6 799 IF (NP(K.MBR) - MAX) 470. 470. 460 800 460 MAX - NP(K.MBR) 801 470 CONTINUE 802 480 ' CONTINUE 803 C 804 C DETERMINE THE MINIMUM OEGREE OF FREEDOM FOR EACH MEMBER.NOTE THAT 805 C FOR STRUCTURES WITH GREATER THAN 330 JOINTS INITIAL VALUE OF MIN 806 C WILL HAVE TO BE INCREASEO FROM ITS PRESTENT POINT OF 1000. 807 C 808 C WILL HAVE TO BE INCREASED FROM ITS PRESTENT POINT OF tOOO. 809 C 810 MIN • 1000 811 C 812 00 520 K « 1. 6 M 813 IF (NP(K.MBR)) 510. 510. 490 814 490 IF (NP(K.MBR) - MIN) 500. 510. 510 B15 500 MIN • NP(K.MBR) 816 510 CONTINUE 817 520 CONTINUE 818 C 819 NBB • MAX - MIN + 1 820 IF (NBB - NB) 540. 540. 530 821 530 NB • NBB 822 540 CONTINUE 823 HL(MBR) - 0. 824 IF (E(M8R) .EO. 0 . ) E(MBR) • E(MBR - 1) 825 IF (MBR .EO. 1) GO TO 550 826 IF (G(MBR) .EO. O.) G(MBR) - G(MBR - 1) 827 IF (AV(MBR) . E O . 0 . ) AV(MBR) - AV(MBR - 1) 828 IF (HL(MBR - 1) .EO. 0 . ) GO TO 550 829 HL(MBR) • HL(MBR - 1) 830 IF (HL(MBR) .EO. 0.) HL(MBR) > HI(MBR - 1) 831 550 CONTINUE 832 IF (AREA(MBR) .EQ. 0.) AREA(MBR) - AREA(MBR - 1) 833 IF (CRMOM(MBR) .EQ. 0 . ) CRMOM(MBR) • CRMOM(MBR - 1) 834 IF (MBR .EQ. 1) HL(MBR) « 0.5 • DEPTH 835 YCR(MBR) • BMCAP(MBR,1) / (E(MBR )*CRMOM(MBR)) 836 IF (YCR(MBR) .NE. O.) GO TO 560 837 MR • MBR - 1 838 BMCAP(MBR.I) • BMCAP(MR.1) 839 YCR(MBR) - BMCAP(MBR.I) / (E(MBR)* CRMOM(MBR)) 840 560 CONTINUE 841 DO 570 1 - 1 , NRM 842 IF (HL(I) .EO. O.) HL(I) • 0.05 • DM(MBR) 843 570 CONTINUE 844 C PRINT MEM8ER DATA 845 C 846 WRITE (6,630) MBR, JNL(MBR), JNG(MBR), EXTL(MBR), DM(MBR), 847 1 EXTG(MBR), XM(MBR), YM(MBR), AREA(MBR), CRMOM(MBR). AV(MBR). 848 2 BMCAP(MBR,1), KL(MBR). KG(MBR). E(MBR) 849 580 CONTINUE 850 C PRINT THE NO. OF DEGREES OF FREEDOM AND THE HALF BANDWIDTH 851 C 852 WRITE (6.640) NU 853 WRITE (6.650) NB 854 C 855 RETURN 856 590 FORMAT (//, 'MEMBER DATA') 857 600 FORMAT (/ ' MN JNL JNG EXTL LENGTH EXTG XM YM 858 1 2X, 'AREA MOM OF I A V . 7X. 'MOMENT'. 3X, ' K L ' , 859 2 1X. ' K G ' . 5X. ' E ') 860 610 FORMAT (85X. 'CAPACITY') 861 620 FORMAT (515. 2F10.1, F8 .2 . F15 .1 . F 6 . 1 . F10 .1 . 3FB.2) 862 630 FORMAT (' ' , 13. 214, F 7 . 1 . F 9 . 2 . F 7 . 1 , 2F9.2, F8 .2 . F15.3. FB. 863 1 F10.1 . 213. F10.1) 864 640 FORMAT ( ' - ' . 'NO.OF DEGREES OF FREEOOM OF STRUCTURE • ' , 15) 865 650 FORMAT (/ ' HALF BANDWIDTH OF STIFFNESS MATRIX • ' . 15) 866 END 867 C 868 C 869 C 870 SUBROUTINE BUILOtNU, NB, XM. YM, DM, NP. AREA, CRMOM. AV, E, G, 871 1 KL . KG. NRM, S. IDIM. EXTL. EXTG, SMS. MMAX) 872 873 C C 874 C 875 c 876 c THIS SUBROUTINE WORKS IN DOUBLE PRECISION 877 c THIS SUBROUTINE CALCULATES THE STIFFNESS MATRIX OF EACH 878 c MEMBER AND ADDS IT INTO THE STRUCTURE STIFFNESS MATRIX. 879 c THE FINAL STIFFNESS MATRIX S IS RETURNED. 880 c THIS SUBROUTINE IS SIMILAR TO ONE THAT WOULD 8E USED IN NORMAL 881 c FRAME ANALYSIS. 882 c IDIM IS THE DIMENSIONING SIZE OF THE STRUCTURE STIFFNESS MATRIX 883 c INTERNAL FOOT UNITS FOR STIFFNESS MATRIX 884 c 885 REAL'8 SM(2I) . S(IDIM), SMS(2O0.21) 886 DIMENSION XM(NRM). YM(NRM). DM(NRM). NP(6,NRM). AREA(NRM). 887 1 CRMOM(NRM). AV(NRM). KL(NRM). KG(NRM). EXTL(NRM). 888 2 EXTG(NRM). E(NRM). G(NRM) 889 REAL'S RF. GMOD. CMOMI. F. H 890 REAL'S LONE. LONEX. LONEY. LTWO. LTWOX, LTWOY, AVI 891 REAL'S YMI, DMI. DM2. XM2. YM2. XMI. AREAI, EMOD. XM2F, YM2F, 892 1 XMYMF 893 REAL'8 D8LE 894 c 895 c ZERO STRUCTURE STIFFNESS MATRIX 896 INK • NU • NB 897 DO 10 I - 1, INK 898 S(I) - O.ODOO 899 10 CONTINUE 900 c 901 N1 • 1 902 N2 • NRM 903 IF (MMAX .NE. 0) N1 » MMAX 904 IF (MMAX .NE. 0) N2 * MMAX 905 c 906 c 8EGIN MEMBER LOOP 907 c ENTER HERE TO REBUILD MEMBER STIFFNESS MATRIX FOR MEMBER 908 c MMAX WHICH HAS JUST YIELDED & REASSEMBLE STR.STIFF. MATRIX 909 DO 120 I " NI , N2 910 c 911 c ZERO MEMBER STIFFNESS NATRIX 912 c 913 DO 20 J • 1, 21 914 SM(J) » O.ODOO 915 20 CONTINUE 916 c 917 c ASSIGN MEMBER PROPERTIES TO DOUBLE PRECESION VARIABLES 918 c CONVERT E TO DOUBLE PRECISION 919 EMOD - DBLE(E(I) ) 920 GMOD - DBLE(G(I)) 921 LONE • OBLE(EXTL(I)) 922 LTWO " DBLE(EXTG(I)) 923 YMI • D8LE(YM(I)) 924 DMI - DBLE(OM(I)) 925 XMI - DBLE(XM(I)) 926 AREAI - DBLE(AREA(I)) 927 CMOMI • DBLE(CRMOM(I)) 928 AVI • OBLE(AV(I ) ) u 929 C 930 DM2 • DMI • DMI 931 XM2 - XMI • XMI 932 YM2 • YMI • YMI 933 XMYM - XMI • YMI 934 F • AREAI • EMOD / (DMI*DM2) 935 H - O.ODOO 936 C SHEAR DEFLECTIONS ARE IGNORED WHENEVER G OR AV IS ZERO. 937 IF (AV(I) .EO. 0 .0 .OR. G(I) .EO. 0 . ) GO TO 30 938 H • 12.ODOO • EMOD * CMOMI / (AVI"GMOD*DM2) 939 30 XM2F • XM2 • F 940 YM2F - YM2 • F 94 1 XMYMF » XMYM • F 942 C 943 C FILL IN PIN-PIN SECTION OF MEMBER STIFFNESS MATRIX 944 C 945 SM(1) - XM2F 946 SM(2) - XMYMF 947 SM(4) - -XM2F 948 SM(S) - -XMYMF 949 SM(7) - YM2F 950 SM(9) • -XMYMF 951 SM(10) - -YM2F 952 SM(16) • XM2F 953 SM(17) • XMYMF 954 SM(19) • YM2F 955 IF (KL(I) + KG(I) - 1) 100, 40, 50 956 C 957 C 958 40 F • 3.ODOO * EMOD * 'CMOMI / (0M2 *DM2 *DMI*(1.ODOO+H/4.1 959 GO TO 60 960 50 F » 12.ODOO * EMOD • CMOMI / (DM2*DM2*DMI•( 1.ODOO+H)) 961 C RF IS A FACTOR COMMON TO THE ENTIRE MATRIX FOR ADDITION OF 962 C DUE TO RIGIO BEAM END EXTENSIONS. 963 RF - 12.ODOO • EMOD • CMOMI / (DM2-DM2) / (1.D0+H) 964 C 965 C FILL IN TERMS WHICH ARE COMMON TO PIN-FIX.FIX-PIN,ANO 966 C FIX-FIX MEMBERS 967 C 968 LONEY - LONE • YMI • RF 969 LONEX • LONE • XMI • RF 970 LTWOY • LTWO • YMI • RF 971 LTWOX " LTWO • XMI • RF 972 60 XM2F • XM2 * F 973 YM2F . YM2 • F 974 XMYMF • XMYM • F 975 DM2F • DM2 • F 976 C 977 SM(1) • SM(1) • YM2F 978 SM(2) > SM(2) - XMYMF 979 SM(4) • SM(4) - YM2F 980 SM(S) > SM(5) • XMYMF 981 SM(7) • SM(7) + XM2F 982 SM(9) • SM(9) • XMYMF 983 SM(10) • SM(10) - XM2F 984 SM(16) • SM(16) • YM2F 985 SM(17) • SM(17) - XMYMF 986 SM(19) • SM(19) • XM2F 987 IF (KL(I) - KG(I) ) 70. 80. 90 9B8 C 989 C FILL IN REMAINING PIN-FIX TERMS 990 C 891 70 SM(6) • -YMI • DM2F 992 SM(11) " XMI • DM2F 993 SM(18) - -SM(6) 994 SM(20) - -SM(11) 995 SM(21) • DM2 • DM2F 996 GO TO 100 997 C 998 C FILL IN REMAINING FIX-FIX TERMS 999 C 1000 80 SM(3) • -YMI • DM2F * 0.5000 1001 SM(6) - SM(3) 1002 SM(8) • XMI • 0M2F * 0.5D00 1003 SM(11) - SM(8) 1004 SM(12) « DM2 * DM2F * (4.ODOO+H) / 12.ODOO 1005 SM(13) • -SM(3) 1006 SM(14) • -SM(8) 1007 SM(15) • DM2 • DM2F • (2.0D00-H) / 12.ODOO 1008 SM(1B) - -SM(6) 1009 SM(20) • -SM(11) 1010 SM(21) - SM(12) 1011 C ADD IN TERMS FOR RIGID END EXTENSIONS. 1012 SM(3) - SM(3) - (LONEY) 1013 SM(6) ' S M ( 6 ) - (LTWOY) 1014 SM(8) " SM(8) + LONEX 1015 SM(11) • SM(11) + LTWOX 1016 SM(12) • SM(12) + (LONE'DMI•(DMI + LONE)*RF) 1017 SM(13) - SM(13) • LONEY 1018 SM(14) • SM(14) - LONEX 1019 SM(15) - SM(15) + ((LONE*LTWO*OMI) • (DM2*(LONE + LJWO)/2.0000)) 1020 1 • RF 1021 1022 SM(18) • SM(18) + LTWOY 1023 SM(20) • SM(20) - LTWOX 1024 SM(21) - SM(21) + (DM2*LTW0 + (DMI * (LTWO* LTWO) ) )• • RF 1025 GO TO 100 1026 C 1027 C FILL IN REMAINING FIX-PIN TERMS 1028 C 1029 90 SM(3) • -YMI • 0M2F 1030 SM(8) - XMI • DM2F 1031 SM(12) - DM2 • 0M2F 1032 SM(13) • -SM(3) 1033 SM(14) • -SM(8) 1034 100 CONTINUE 1035 DO 110 J - 1. 21 1036 110 SMS(I.J) • SM(J) 1037 120 CONTINUE 1038 C ADO THE MEMBER STIFFNESS MATRIX SMS INTO THE STRUCTURE 1039 C STIFFNESS MATRIX S. 1040 C 1041 NB1 • NB - 1 1042 DO 220 I - 1, NRM 1043 DO 210 J • 1, 6 1044 IF (NP( J . I ) ) 210. 210. 130 •t. 1045 130 01 • (d - 1) • (12 - d) / 2 1046 C 1047 DO 200 I • J . 6 1048 IF ( N P ( L . D ) 200. 200. 140 1049 140 IF (NP(d.I ) - NP(L . I ) ) 170. 150. 180 1050 150 IF (L - d) 160, 170. 160 1051 160 K • (NP(L . I ) - 1) • NB1 + NP(d.I) 1052 N • d1 • L 1053 S(K) - S(K) + 2.0D00 * SMS(I.N) 1054 GO TO 200 1055 170 K - (NP(d.I) - 1) • NB1 • NP(L . I ) 1056 GO TO 190 1057 180 K - (NP(L. I ) - 1) • NB1 + NP(d.I) 1058 190 N • d i • I 1059 S(K) • S(K) + SMS(I.N) 1060 200 CONTINUE 1061 C 1062 210 CONTINUE 1063 C 1064 220 CONTINUE 1065 C 1066 RETURN 1067 END 1068 C NCN. NSCALE. KTR) 1069 SUBROUTINE SOFBAN(A. B. N, M. LT, RATIO. DET. 1070 C 1071 C THIS ROUTINE SOLVES SYSTEM OF EONS. AX-B WHERE A IS +TVE DEFINITE 1072 C SYMMETRIC BAND MATRIX. BY CHOLESKY'S METHOD. 1073 C LOWER HALF BAND ONLY (INCLUDING THE DIAGONAL) OF A IS STORED 1074 C COLUMN BY COLUMN IN A 1 DIMENSIONAL ARRAY. 1075 C SOLUTIONS X ARE RETURNED IN ARRAY B. 1076 c OPTIONAL SCALING OF MATRIX A IS AVAILABLE 1077 c N - ORDER OF MATRIX A. 1078 c M - LENGTH OF LOWER HALF BAND. 1079 c DETERMINANT OF A • DET'( 10"NCN) . 1 . E- 15< |DET |< 1 .E15 1080 C LT-1 IF ONLY 1 B VECTOR OR IF FIRST OF SEVERAL. LT NOT • 1 FOR 1081 C SUBSEQUENT B VECTORS. 1082 c RATIO • SMALLEST RATIO OF 2 ELEMENTS ON MAIN DIAGONAL OF 1083 c TRANSFORMED A >1.E-7. 1084 c NSCALE-0 IF SCALING NOT REQUIRED. 1085 c KTR '1 IF THE SYSTEM IS POSITIVE DEFINITE 1086 c •2 IF THE SYSTEM IS NOT POSITIVE DEFINITE(MECHANISM FORMED) 1087 IMPLICIT REAL*8(A - H.O - Z) 1088 DIMENSION A(1 ) . B(1) 1089 REAL'S MULT(20000) 1090 IF (M .EO. 1) GO TO 80 1091 MM • M - 1 1092 NM • N • M 1093 NM1 • NM - MM 1094 KTR • 1 1095 c DUMMY STATEMENT INSERTED FOR COMPATIBILITY WITH ASSEMBLER VERSION 1096 c I F ( L T . L E . O ) RETURN 1097 c 1098 IF (LT .NE. 1) GO TO 340 1099 IF (NSCALE' .EO. 0) GO TO 60 1100 DO 10 I - 1. N 1101 c S O R T ( A d . I ) ) . SUCH 1102 c MATRIX SCALED BY DIVIDING ROW I ANO COLUMN I BY 1103 C THAT DIAGONAL ELEMENTS A ( I . I ) ARE 1. I 104 C .1105 II - (I - 1) • M • 1 1106 IF (A( I I ) . L E . 0 .0) GO TO 120 1107 10 MULT(I) - 1.0 / DSQRT(A(II)) 1108 KK » 1 1109 DO 50 I • 1. N I I 10 II • ( I - 1 ) • M + 1 1111 dEND • II * MM 1112 IMN • (I - 1) + M - N 1113 IF (IMN .GT. O) dENO - dEND - IMN 1114 DO 20 d • I I . dENO 1115 A(d) • A(d) • MULT(I) 1116 20 CONTINUE 1117 DO 30 d - KK. 11, MM 1118 30 A(d) - A(d) • MULT(I) 1119 IF (KK .GE. M) GO TO 40 1120 KK * KK • 1 1121 GO TO 50 1122 40 KK - KK • M 1123 50 CONTINUE 1124 60 MP • M + 1 1 125 C 1126 C TRANSFORMATION OF A. 1127 C A IS TRANSFORMED INTO A LOWER TRIANGULAR MATRIX L SUCH THAT A - L . L T 1128 C (LT'TRANSPOSE OF L . ) . IF Y ' L T . X THEN L . Y ' B . 1129 C ERROR RETURN TAKEN IF RATIO<1.E-7 1130 C 1131 KK » 2 1132 NCN « O 1133 DET - O. 1134 FAC - RATIO 1135 IF (A(1) .GT. O . ) GO TO 70 1 136 NROW » 1 1 137 RATIO - A( 1 ) 1138 GO TO 310 1139 70 OET - A(1) 1140 A(1) • 1. / DSORT(A(1)) 1141 BIGL • A(1) 1142 SML - A(1) 1143 A(2) - A(2) • A(1) 1144 TEMP - A(MP) - A(2) • A(2) 1145 IF (TEMP . L T . 0 .0) RATIO ' TEMP 1146 IF (TEMP .EQ. 0 .0) RATIO - 0 . 0 1147 IF (TEMP .GT. 0 .0) GO TO 140 1148 NROW - 2 1149 GO TO 310 1150 80 OET - 1.D0 1151 NCN - O 1152 DO 110 I • 1. N 1153 DET - DET • A( I ) 1154 IF (A(I ) .EQ. 0 .0) GO TO 120 1155 IF (DET .GT. 1.E-1S) GO TO 90 • 1156 DET - OET • I . E ' 1 5 1157 NCN - NCN - 15 1158 GO TO 100 1159 90 IF (OET . L T . 1.E-M5) GO TO 100 1160 DET - DET • 1.E-15 Ul 1 161 NCN - NCN + 15 1219 IF (OET .GT. 1.E-15) GO TO 260 1162 100 CONTINUE 1220 DET • OET • 1 .E-MS 1 163 110 B(I) - B(I) / A l l ) 1221 NCN • NCN - 15 1164 RETURN 1222 GO TO 270 1 165 120 RATIO • A(I) 1223 260 IF (DET . L T . I.E+15) GO TO 270 1166 130 NROW - I 1224 DET • OET • I .E-15 1167 GO TO 310 '•225 NCN - NCN + 15 1168 140 A(MP) - 1.0 / OSORT(TEMP) 1226 270 CONTINUE 1169 OET • DET • TEMP 1227 IF (A(J ) .GT. BIGL) BIGL • A(J) 1 170 IF (A(MP) .GT. BIGL) BIGL • A(MP) 1228 IF (A(J ) . L T . SML) SML - A(J) 1171 IF (A(MP) . L T . SML) SML • A(MP) 1229 280 CONTINUE 1 172 IF (N .EO. 2) GO TO 290 1230 290 IF (SML . L E . FAC-BIGL) GO TO 300 1 173 MP • MP + M 1231 GO TO 330 1174 DO 280 J - MP. NM1. M 1232 300 RATIO - 0. 1175 JP • J - MM 1233 RETURN 1176 MZC - 0 1234 310 WRITE (6,320) NROW 1 177 IF (KK .GE. M) GO TO 150 1235 320 FORMAT ( ' 0 * * "SYSTEM IS NOT POSITIVE DEFINITE' . 1 178 KK • KK + 1 1236 1 ' ERROR CONDITION OCCURRED IN ROW'. 14) 1179 II - 1 1237 KTR • 2 1 180 dC • 1 1238 RETURN 1181 GO TO 160 1239 330 RATIO - SML / BIGL 1182 150 KK • KK + M 1240 340 CALL DSBAND(A. MULT. B. N. M. NSCALE) 1183 II • KK - MM 1241 ^ RETURN 1 184 dC • KK - MM 1242 END 1 185 160 DO 180 I • KK. dP. MM 1243 SUBROUTINE DS8AND(A, MULT. B. N. M. NSCALE) 1186 IF (A(I) .EO. 0 . ) GO TO 170 1244 IMPLICIT REAL*8(A - H.O - Z) 1187 GO TO 190 1245 DIMENSION A ( 1 ) . B(1) 1 188 170 JC • JC + M 1246 REAL'S MULT(1) 1 1B9 180 MZC • MZC + 1 1247 MM - M - 1 1 190 ASUM1 - O.DO 1248 NM • N • M 1 191 GO TO 240 1249 NM1 • NM - MM 1 192 190 MMZC • MM • MZC 1250 C 1 193 II • II + MZC 1251 C THE FOLLOWING STATEMENTS SOLVE FOR L .Y-B BY A FORWARDS 1 194 KM • KK • MMZC 1252 C HENCE FDR X FROM LT.X=Y BY A BACKWARDS SUBSTITUTION. 1 195 A(KM) - A(KM) » A(JC) 1253 C IF SCALING OPTION USEO. B IS SCALEO AND NORMALISED BEFORE 1 196 IF (KM .GE. JP) GO TO 220 1254 C SUBSTITUTION BEGINS. 1 197 KO * KM **• MM 1255 C 1 198 DO 210 I - Kd. JP, MM 1256 10 SUM " O . D O 1 199 ASUM2 • 0.00 1257 IF (NSCALE .EO. 0) GO TO 40 1200 IM - I - MM 1258 DO 20 I - 1. N 1201 1 1 - 1 1 * 1 1259 B(I) • B( I ) • MULT(I) 1202 Kl - II • MMZC 1260 SUM - SUM + B(I ) • B( I ) 1203 DO 200 K • KM, IM. MM 1261 20 CONTINUE 1204 ASUM2 • ASUM2 + A(KI) • A(K) 1262 ELENB • DSORT(SUM) 1205 200 Kl - K l • MM 1263 DO 30 I * 1, N 1206 210 A(I) - (A(I) - ASUM2) • A(KI) 1264 30 B(I ) - B( I ) / ELENB 1207 220 CONTINUE 1265 40 B(1) • B(1) * A(1) 1208 ASUM1 • 0.00 ' 1266 KK • 1 1209 DO 230 K » KM. dP, MM 1267 K l - 1 1210 230 ASUM1 ' ASUM1 + A(K) * A(K) 1268 J - 1 1211 240 S • A(d) - ASUM1 1269 DO 80 L • 2. N 1212 IF (S . L T . 0 . ) RATIO • S 1270 BSUM1 - O.DO 1213 IF (S .EO. 0 . ) RATIO • 0. 1271 LM - L - 1 1214 IF (S .GT. 0 . ) GO TO 250 1272 J - J + M 1215 NROW • (d + MM) / M 1273 IF (KK . G E . M) GO TO 50 1216 GO TO 310 1274 KK - KK + 1 1217 250 A(J) - 1. / DSQRT(S) 1275 GO TO 60 1218 DET - DET • S 1276 50 KK • KK • M cn 1277 KI - KI • 1 1278 60 <JK • KK 1279 DO 70 K - K I . LM 1280 BSUM1 • BSUM1 + A(JK) • B(K) 1281 JK - JK • MM 1282 70 CONTINUE 1283 80 BCD • (8(1.) - BSUM 1) • A(d) 1284 90 B(N) • B(N) «. A(NM 1 ) 1285 NMM - NM1 1286 NN > N - 1 1287 NO - N 1288 00 1 10 L • 1 , NN 1289 BSUM2 • O.DO 1290 NL - N - I 1291 NL1 • N - L + 1 1292 NMM • NMM - M 1293 NJ1 > NMM 1294 IF (L . G E . M) NO • NO - 1 1295 DO 100 K • NL1. ND 1296 ' Ndl • NJ1 + 1 1297 BSUM2 - BSUM2 + A(NJ1) * B(K) 1298 100 CONTINUE 1299 110 B(NL) - (B(NL) - BSUM2) • A(NMM) 130O IF (NSCALE .EO. 0) GO TO 130 1301 DO- 120 I • 1 . N 1302 120 8(1) • B(I) • ELENB • MULT(I) 1303 130 RETURN 1304 1305 END C 1306 c 1307 SUBROUTINE SCHECK(S. NU. NB. IOIM, SRATIO) 1308 1309 c c 1310 c 131 1 c THIS SUBROUTINE CHECKS THAT ALL DIAGONAL STIFFNESS MATRIX 1312 c ELEMENTS ARE POSITIVE NUMBERS GREATER THAN ZERO. IT ALSO DETERMINE! 1313 c THE RATIO BETWEEN THE LARGEST AND SMALLEST MEMBERS ON THE DIAGONAL 1314 c THIS WILL GIVE SOME INDICATION AS TO THE CONDITIONING OF THE 1315 c STIFFNESS MATRIX 1316 c MATRIX 1317 c 1318 REAL'8 S(IOIM) 1319 REAL'S SMIN. SMAX, DIAG, RATIO 1320 c 1321 c 1322 c THE STIFFNESS MATRIX IS STORED AS A COLUMN VECTOR. ONLY THE 1323 c THE LOWER TRIANGLE ELEMENTS BEING STOREO (BY COLUMNS) 1324 c SO) IS ON THE DIAGONAL AS IS S( 1+NB) . S( 1 + 2'NB ) , ETC . 1325 c NB IS THE HALF BANDWIDTH OF THE STIFFNESS MATRIX 1326 C 1327 c INITIALIZE THE LARGEST ANO SMALLEST VALUES OF 01AGONAL (SMAX,SMIN) 1328 c 1329 c 1330 DO 50 IDOF - 1. NU 1331 IELEM • ((IOOF - 1 ) » N B ) • 1 1332 DIAG • S(IELEM) 1333 c COMPUTE IF DIAGONAL ELEMENT IS ZERO OR NEGATIVE 1334 IF (DIAG .NE. 0.0000) GO TO 20 1335 WRITE (6,10) IDOF 1336 10 FORMAT (/ / / ' PROGRAM HALTED-A ZERO IS ON THE DIAGONAL OF STIFFNE 1337 1SSMATRIX', / / 'EXAMINE DEGREE OF FREEDOM ' , 14) 1338 STOP 1339 C 1340 20 CONTINUE 1341 IF (DIAG .GT. 0 .0) GO TO 40 1342 WRITE (6.30) IOOF 1343 30 FORMAT (///* PROGRAM HALTED-NEGATIVE ELEMENT ON DIAGONAL OF ' . 1344 1 'STIFFNESS MATRIX'. / / ' EXAMINE DEGREE OF FREEDOM'. 14) 1345 STOP 1346 40 CONTINUE 1347 50 CONTINUE 1348 C 1349 RETURN 1350 END 1351 C 1352 SUBROUTINE FORCE (NRM. XM, YM. OM. AV. NP, F. EXTL. EXTG, AREA. E . 1353 1 G. CRMOM. KL . KG, AXIAL. SHEARL, SHEARG. BML. BMG, NML. 1354 2 MML, FEM) 1355 C * • * * * • • • 1356 DIMENSION XM(NRM), YM(NRM), DM(NRM), AV(NRM), NP(6,NRM). F(50O). 1357 1 0 ( 6 ) . EXTL(NRM), EXTG(NRM). KL(NRM). KG(NRM), AREA(NRM). 1358 2 CRMOM(NRM). E(NRM) , G(NRM). MMLOOO). FEM( 100.4) 1359 DIMENSION AXIAL(NRM), SHEAR(250). BML(NRM), BMG(NRM), SHEARL(NRM), 1360 1 SHEARG(NRM) 1361 C 1362 DO 110 I « 1. NRM 1363 XL " XM(I) 1364 YL - YM(I) 1365 DL - OM(I) 1366 AV1 • AV(I) 1367 DO 30 MEMDOF - 1 . 6 1368 . N1 • NP(MEMDOF,I) 1369 IF (N1) 20. 20. 10 1370 10 O(MEMDOF) - F(N1) 1371 GO TO 30 1372 20 D(MEMDOF) • O. 1373 30 CONTINUE 1374 C MODIFY END DISP FOR HORZ MEMBERSWITH END EXT.(VALIO FOR 1375 C HORZ. MEMBERS ONLY) 1376 N3 • NP(3 . I ) 1377 IF (N3 .EO. O) GO TO 40 1378 D(2) • D(2) + (F(N3)) * EXTL(I) 1379 40 CONTINUE 1380 N6 • NP(6 . I ) 1381 IF (N6 .EO. 0) GO TO 50 1382 D(5) • D(5) - (F(N6)) * EXTG(I) 1383 50 CONTINUE 1384 AXIAL(I) - ( A R E A ( I ) * E ( I ) / 0 L * * 2 ) • (D(4) 'XL + 0 ( S ) « Y L - D(1) 'XL -1385 1 D ( 2 ) « Y L ) 1386 EISI • CRMOM(I) * EO) 1387 C INCLUDE SHEAR DEFL. GFACT-0 MEANS NO SHEAR DEFL. 1388 GFACT • 0. 1389 IF (AVI .EO. 0 .0 .OR. GO) . EO. 0 .0) GO TO 60 1390 GFACT • 12.0 • EISI / (AV1-G(I)-DL-DL) 1391 60 CONTINUE 1392 C ASSIGN OISP TO RESPECTIVE D . O . F . 1393 C CHECK FOR PIN-PIN MEM8ERS 1451 RATL • BML(I) / BMCAP(I.2) 1394 IF (KL(I) . E O . 0 .AND. KG(I) .EO. 0) GO TO 90 1452 RATL - ABS(RATL) 1395 OELT • <<D(S) - D(2)) 'XL + (0(1) - D ( 4 ) ) « Y L ) / DL 1453 GO TO 20 1396 BML(I) • ( 2 . 0 ' E I S I / ( D L ' ( 1 . 0 + GFACT))) * <(3.0*DELT/DL) - ( 0 ( 6 ) ' 1454 10 CONTINUE 1397 1 (1 .0 - GFACT/2 .0 ) ) - ( 2 . 0 * D ( 3 ) ' ( 1 . 0 + GFACT/4 .0) ) ) 1455 RATL • -1 .0 1398 BMG(I) - - ( 2 . 0 ' E I S I / ( D L ' ( 1 . 0 • GFACT))) • ( (3 .0 *DELT/DL) - (0(3) 1456 20 CONTINUE 1399 1 ' ( 1 . 0 - GFACT/2 .0) ) - ( 2 . 0 ' 0 ( 6 ) ' ( 1 . 0 • GFACT/4 .0) ) ) 1457 IF (KG(I) .EQ. 0) GO TO 30 1400 SHEAR(I) - ( 6 . 0 ' E I S I / ( 0 L ' D D ) • ((0(3) + 0(6) - ( 2 .O*DELT/0L) ) / ( 1458 RATG - BMG(I) / BMCAPU.3 ) 1401 1 1.0 • GFACT)) 1459 RATG - ABS(RATG) 1402 IF (KL(I) - KG(I)) 70. 100. 80 1460 GO TO 40 1403 C PIN-FIX MEMBER FORCES 1461 30 CONTINUE 1404 70 BMG(I) - BMG(I) + BML(I) • (1 .0 - GFACT/2.0) / ( 2 . 0 * ( 1 . 0 • 1462 RATG - -1 .0 1405 1 GFACT/4.0)) 1463 40 CONTINUE 1406 SHEAR(I) - SHEAR(I) + 1.5 • BML(I) / DL 1464 IF (RATL .GT. RMAXL) GO TO 50 1407 BML(I) • 0 . 1465 GO TO 60 1408 GO TO 100 1466 50 RMAXL • RATL 1409 C FIX-PIN MEMBERS 1467 NL - I 1410 80 BML(I) - BML(I) • BMG(I) • (1 .0 - GFACT/2.0) / ( 2 . 0 " ( 1 . 0 + 1468 60 CONTINUE 141 1 1 GFACT/4.0)) 1469 IF (RATG .GT. RMAXG) GO TO 70 1412 SHEAR(I) • SHEAR(I) - 1.5 • BMG(I) / DL 1470 GO TO 80 1413 BMG(I) - 0 . 1471 70 RMAXG » RATG 1414 GO TO 100 1472 NG • I 1415 C PIN-PIN MEMBERS 1473 80 CONTINUE 1416 90 BML(I) • 0 . 1474 IF (RMAXL .GT. RMAXG) GO TO 90 1417 BMG(I) - 0 . 1475 GO TO 1 10 1418 SHEAR(I) • 0 . 1476 90 CONTINUE 1419 100 CONTINUE 1477 FACT - 1. / RMAXL 1420 SHEARL(I) • SHEAR(I) 1478 WRITE (99.100) NL 1421 SHEARG(I) ' SHEAR(I) 1479 IF (LSENS .EO. 1) WRITE (6.1O0) NL 1422 110 CONTINUE 1480 100 FORMAT (/. ' -PLASTIC FAILURE AT LESSER END OF MEMBER N O . ' 1423 IF (NML .EO. 0) GO TO 150 1481 KL(NL) " 0 1424 00 140 I - 1. NRM 1482 MMAX • NL 1425 00 120 J - 1. NML 1483 ICT • 1 1426 IF (I . E O . MML(d)) GO TO 130 1484 GO TO 130 1427 120 CONTINUE 1485 110 CONTINUE 1428 GO TO 140 1486 FACT - 1. / RMAXG 1429 130 CONTINUE 1487 WRITE (99.120) NG 1430 BML(I) • BML(I) + FEM(d.2) 1488 IF (LSENS .EO. 1) WRITE (6.120) NG 1431 BMG(I) • BMG(I) + F £ M ( d , 4 ) 1489 120 FORMAT (/. ' -PLASTIC FAILURE AT GREATER END OF MEMBER NO' 1432 SHEARL(I) « SHEAR(I) + FEM(J .I ) 1490 KG(NG) » 0 1433 SHEARG(I) - SHEAR(l) - FEM(J,3) 1491 MMAX - NG 1434 140 CONTINUE 1492 ICT • 2 1435 150 CONTINUE 1493 130 CONTINUE 1436 RETURN 1494 RETURN 1437 END 1495 END 1438 C 1496 C SUBROUTINE EIGEN(S, NU, NB) 1439 C . 1497 1440 C 1498 C 1441 SUBROUTINE RATIO(BML. BMG. BMCAP. NRM, FACT. KL. KG, MMAX. ICT. 1499 REAL'S S(120000), AS(40O.4O0). DA(120000). DE(400) 1442 1 LSENS) 1500 DO 10 I - 1. NU 1443 C 1501 DO 10 J • 1, I 1444 C 1502 10 AS( I .d ) • 0 .00 1445 DIMENSION BML(NRM) , BMG(NRM), BMCAP(200.3). KL(NRM), KG(NRM) 1503 DO 20 I * 1. NU 1446 CALL FTNCMD('EQUATE 99-SPRINT;') 1504 d 1 - 1 * N S ' ( I - 1 ) 1447 RMAXL • -1 .0 1505 N » NB + I - 1 1448 RMAXG • RMAXL 1506 DO 20 J • I . N 1449 DO 80 I • 1, NRM 1507 AS(d . I ) - S ( d l ) 1450 IF (KL(I) . E O . 0) GO TO 10 1508 d i • d i • 1 1509 20 CONTINUE 1510 1 1 - 0 1511 DO 30 I • 1, NU 1512 DO 30 J - 1. I 1513 1 1 - 1 1 * 1 1514 30 DA(I1) - AS( I . J ) 1515 CALL DSYMALCOA, NU, DE. IER. 0) 1516 WRITE (6.40) ( D E ( I ) . I - 1.5) 1517 40 FORMAT (5F20.1) 151B RETURN 1519 END 1520 C • • • * • 1521 C 1522 SUBROUTINE GEN1(X, Y, IJT. LJT, NJT. KDIF) 1523 C 1524 C • 1525 C 1526 C GENERATES NODES ALONG STRAIGHT LINE 1527 DIMENSION X(325). Y(325) 1528 XI - X(I JT) 1529 YI - Y( I JT) 1530 DX • X(LJT) - XI 1531 DY • Y(LJT) - YI 1532 OX - DX / FLOAT(NJT + 1) 1533 OY - DY / FLOAT(NJT • 1) 1534 00 10 I • 1. NJT 1535 IJT - IJT + KDIF 1536 XI - XI • DX 1537 YI - YI • DY 1538 X(I JT) • XI 1539 10 Y(IJT) - YI 1540 RETURN 154 1 END 1542 C • • • 1543 C 1544 SUBROUTINE GEN2(MMR, W. XM. KL. KG, NP, F, JL , FEM) 1545 C 1546 C » * 1547 DIMENSION XM(200), KL(200). KG(200). NP(G.20O). F(500). FEM( 1548 C 1549 IF (KL(MMR) . KG(MMR) - 1) 50. 20. 10 1550 10 R3 - -W • XM(MMR) - XM(MMR) / 12. 1551 R6 • -R3 1552 R2 - -0.5 • W • XM(MMR) 1553 R5 • R2 1554 GO TO 60 1555 20 IF (KL(MMR) - KG(MMR)) 30, 70. 40 1556 30 R3 - O. 1557 R6 - W • XM(MMR) * XM(MMR) / 8. 1558 R2 • -0 .5 * W • XM(MMR) - R6 / XM(MMR) 1559 RS • -0 .5 • W • XM(MMR) + R6 / XM(MMR) 1560 GO TO 60 1561 40 R3 - -W • XM(MMR) • XM(MMR) / 8. 1562 R6 • O. 1563 R2 » -0.5 • W • XM(MMR) - R3 / XM(MMR) 1564 R5 • -O.S • W • XM(MMR) • R3 / XM(MMR) 1565 GO TO 60 1566 50 R2 • -0 .5 • W • XM(MMR) .4) 1567 R3 - 0. A 1568 R5 - R2 1569 R6 - 0. 1570 60 CONTINUE 1571 Jt • NPO.MMR) 1572 J2 - NP(6.MMR) 1573 J3 - NPO.MMR) 1574 J4 - NPO.MMR) 1575 F( J3) - F(J3) • R2 1576 F(J4) - F(J4) + R5 1577 F( J1) • F( J I ) + JJ3 1578 F(J2) - F(J2) • R6 1579 F £ M ( J L . 1 ) - -R2 1580 FEM(JL,2) • R3 1581 FEM(JL,3) - -R5 1582 FEM(JL,4) - -R6 1583 70 CONTINUE 1584 RETURN 1585 END 1586 C 1587 C 1588 C 1589 SUBROUTINE CURVD(NRM. CD. NDEF, NP, OEFL, ROTN, HL, YCR. LSENS, 1590 1 IKOUNT) 1591 C 1592 C . . . a . . . . . . . . * . . . . * . . . . * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1593 C 1594 C CALCULATES CURVATURE DUCTILITIES 1595 C 1596 DIMENSION CDOOO. 2) , NDEF(2.325) . NPO.NRM) , O E F L O O O ) , 1597 1 R0TN(2.325). HL(NRM), YCR(NRM) 1598 C CALCULATE CURVATURE OUCLITY BASED ON ASSUMED HINGE LENGTH 1599 C OF 0.5 TIMES THE MEMBER OEPTH OR 0.05 TIMES MEMBER LENGTH 1600 DO 30 J - 1. NRM 1601 DO 20 I - 1, 2 1602 CD(J . I ) - 0. 1603 IF (NDEF(I.J) . L T . 0) GO TO 20 1604 IF (I . EO. 1) J1 - N P O . J ) 1605 IF (I .EO. 2) J1 • N P O . J ) 1606 IF (NDEF(I.J) .EO. 0) GO TO 10 1607 J2 - NDEF(I . J ) 1608 PCR - (DEFL(J1) - (0EFL(J2) - ROTN(I . J ) ) ) / HL(J) 1609 PCR - ABS(PCR) 1610 CD(J . I ) • 1. • PCR / YCR(J) 1611 GO TO 20 1612 10 CONTINUE 1613 PCR • DEFL(J1) / HL(J) 1614 PCR - ABS(PCR) 1615 CD(J . I ) • 1. + PCR / YCR(J) 1616 20 CONTINUE 1617 30 CONTINUE 1618 C PUSH THE STRUCTURE MORE SUCH THAT TIP OISP. INCREASES BY 10% 1619 LSENS - 2 1620 IKOUNT - 1 1621 RETURN 1622 END CO APPENDIX D NOTE 1: As r e p o r t e d elsewhere i n the t h e s i s , when there are g r a v i t y l oads to be combined with the s e i s m i c loads, the d i r e c t i o n of the l a t t e r becomes important. I t i s neccesary to c o n s i d e r two load cases, as they might r e s u l t i n d i f f e r e n t damage p a t t e r n s : one when g r a v i t y loads are combined with s e i s m i c f o r c e s i n p o s i t i v e x - d i r e c t i o n (K0U=1) and the o t h e r , when g r a v i t y f o r c e s are combined with s e i s m i c f o r c e s i n the other direction(KOU=2). For any member, maximum of the damage r e s u l t i n g from these two a n a l y s i s should be c o n s i d e r e d . NOTE 2: C o - o r d i n a t e s for ' c o n t r o l j o i n t s ' must be s p e c i f i e d . Then, the c o - o r d i n a t e s f o r the remaining j o i n t s can be generated along a s t r a i g h t l i n e . The c o - o r d i n a t e s of the two j o i n t s at the beginning and at the end of the gen e r a t i o n l i n e must have been d e f i n e d p r e v i o u s l y . I t i s not necessary t o g i v e g e n e r a t i o n commands f o r s e q u e n t i a l l y numbered j o i n t s , which are e q u a l l y spaced along the g e n e r a t i o n l i n e . The program a u t o m a t i c a l l y generates such j o i n t s . That i s , any ge n e r a t i o n command with equal spacing and a node number d i f f e r e n c e of one i s s u p e r f l u o u s . NOTE 3; Si n c e we are c o n s i d e r i n g only a p l a n a r problem, each j o i n t can have three degrees of freedom, i . e . x-displacement, y-displacement and r o t a t i o n . In c e r t a i n cases, some j o i n t s may be f i x e d or r e s t r a i n e d from moving i n 150 151 c e r t a i n d i r e c t i o n s . Code 0 should be assigned to such groups of nodes f o r that degree of freedom, which i s f i x e d . T h i s le a d s to g r e a t e r computational e f f i c i e n c y . NOTE 4: As d i s c u s s e d e a r l i e r , i t i s reasonable to assume th a t a group of j o i n t s d i s p l a c e s i d e n t i c a l l y i n c e r t a i n d i r e c t i o n s . We can a s s i g n the same degree of freedom i n that d i r e c t i o n f o r such a group of j o i n t s . O b v i o u s l y , t h i s reduces the s i z e of the problem, thus reducing the r e q u i r e d computer time. 14 j o i n t s can be covered by a s i n g l e command. If there are more than 14 j o i n t s , then another command should be gi v e n . NOTE 5: T h i s s p e c i f i c a t i o n permits the user to input lumped masses at the j o i n t s only with a few l i n e s / c a r d s . I f c e r t a i n j o i n t s are c o n s t r a i n e d to have i d e n t i c a l displacement, then the masses a s s o c i a t e d with t h i s displacement w i l l be the sum of the masses s p e c i f i e d f o r the i n d i v i d u a l j o i n t s . NOTE 6 : I f some nodes or members have the same s t a t i c l o a d s , they can be grouped t o g e t h e r . On such nodes/members s t a t i c loads can be s p e c i f i e d only with a s i n g l e command. 9 j o i n t s or 13 members can be covered by a s i n g l e command. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062485/manifest

Comment

Related Items