{"@context":{"@language":"en","Affiliation":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","AggregatedSourceRepository":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","Campus":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","Creator":"http:\/\/purl.org\/dc\/terms\/creator","DateAvailable":"http:\/\/purl.org\/dc\/terms\/issued","DateIssued":"http:\/\/purl.org\/dc\/terms\/issued","Degree":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","DegreeGrantor":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","Description":"http:\/\/purl.org\/dc\/terms\/description","DigitalResourceOriginalRecord":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","Extent":"http:\/\/purl.org\/dc\/terms\/extent","FileFormat":"http:\/\/purl.org\/dc\/elements\/1.1\/format","FullText":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","Genre":"http:\/\/www.europeana.eu\/schemas\/edm\/hasType","GraduationDate":"http:\/\/vivoweb.org\/ontology\/core#dateIssued","IsShownAt":"http:\/\/www.europeana.eu\/schemas\/edm\/isShownAt","Language":"http:\/\/purl.org\/dc\/terms\/language","Program":"https:\/\/open.library.ubc.ca\/terms#degreeDiscipline","Provider":"http:\/\/www.europeana.eu\/schemas\/edm\/provider","Publisher":"http:\/\/purl.org\/dc\/terms\/publisher","Rights":"http:\/\/purl.org\/dc\/terms\/rights","ScholarlyLevel":"https:\/\/open.library.ubc.ca\/terms#scholarLevel","Title":"http:\/\/purl.org\/dc\/terms\/title","Type":"http:\/\/purl.org\/dc\/terms\/type","URI":"https:\/\/open.library.ubc.ca\/terms#identifierURI","SortDate":"http:\/\/purl.org\/dc\/terms\/date"},"Affiliation":[{"@value":"Applied Science, Faculty of","@language":"en"},{"@value":"Civil Engineering, Department of","@language":"en"}],"AggregatedSourceRepository":[{"@value":"DSpace","@language":"en"}],"Campus":[{"@value":"UBCV","@language":"en"}],"Creator":[{"@value":"English, Daryl S.","@language":"en"}],"DateAvailable":[{"@value":"2009-02-06T22:43:20Z","@language":"en"}],"DateIssued":[{"@value":"1996","@language":"en"}],"Degree":[{"@value":"Master of Applied Science - MASc","@language":"en"}],"DegreeGrantor":[{"@value":"University of British Columbia","@language":"en"}],"Description":[{"@value":"The Ministry of Transportation and Highways of British Columbia has conducted a\r\nseismic assessment and upgrade initiative for many of its major bridges. Many deficiencies\r\nhad been noted in the reinforced concrete approach bents of these bridges and the\r\nconsequences of recent failures caused by earthquake loading have emphasized the need for\r\nretrofitting to be carried out on bridges with deficiencies.\r\nSince the costs of rehabilitating the bridge bents are significant, a scale model testing\r\nprogram was devised. Models of bents comprising the details of the approach spans of the\r\nOak Street Bridge were cast and then subjected to slow cyclic lateral load testing. The\r\nspecimens were instrumented externally with linear potentiometers, and internally using strain\r\ngauges bonded to the reinforcement.\r\nThe objectives of the test program were primarily to confirm the seismic deficiencies in\r\nthe as-built bents and to prove the adequacy of proposed economical retrofit schemes for twocolumn\r\nbridge bents. Particular to this thesis, the test program was also intended to produce\r\ndata for further research that would contribute to the art of retrofit design. The strain gauge\r\ndata obtained from the test program presented the opportunity to derive section curvatures at\r\ndiscrete locations wifJiin the specimens for various stages of loading.\r\nThe data obtained from the strain gauges of the models were analyzed. Curvature\r\ndistributions for two of the retrofit schemes that performed particularly well were derived.\r\nThe distributions were integrated to give deflections which were then compared with the\r\nmeasured displacements. The errors in the calculated displacements ranged from -3% to\r\n+21%.Using the theoretical member properties, combined with the known material\r\nproperties, analytical curvature distributions were derived using the non-linear analysis\r\nprogram DRAIN-2DX. The shapes of the distributions and the peak curvature values were\r\nthe focus of interest and using moment-curvature relationships, estimates of peak concrete\r\nstrains were predicted and compared with peak strain capacities. The strain capacities were\r\nderived from theory that accounts for the level of confinement provided by transverse\r\nreinforcement in a section. It was estimated that the architectural fillet region of the beamcolumn\r\njoint region, when in compression, was able to provide confinement enough to sustain\r\nconcrete strains of the order of 0.013. The same fillet region retrofitted with high strength\r\nfiberglass wraps was estimated to be capable of ultimate concrete strains of approximately\r\n0.027.\r\nThe experimentally derived curvatures were then compared with those obtained\r\nanalytically. It was found that the curvature distributions and the peak values compared\r\nreasonably well, which increased the confidence in the ability of the analysis to predict the\r\nflexural behaviour of retrofitted two-column bridge bents. The inclusion of joint shear\r\ndeformations reduced the curvature demand in the plastic hinge regions and improved the\r\nagreement between the experimental and analytical curvatures.\r\nIt is felt that the deterioration of the bond between the concrete and the reinforcement,\r\ncaused by the cyclic nature of the tests, facilitated the derivation of reasonable approximations\r\nto the curvature distributions by reducing the tension stiffening effect on the reinforcement.\r\nThis deterioration of the bond, particularly in the plastic hinge regions, decreased the\r\nvariations of experimental curvatures occurring between cracks.","@language":"en"}],"DigitalResourceOriginalRecord":[{"@value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/4261?expand=metadata","@language":"en"}],"Extent":[{"@value":"13371111 bytes","@language":"en"}],"FileFormat":[{"@value":"application\/pdf","@language":"en"}],"FullText":[{"@value":"COMPARISON OF NON-LINEAR A N A L Y T I C A L A N D E X P E R I M E N T A L C U R V A T U R E DISTRIBUTIONS IN T W O - C O L U M N BRIDGE BENTS by DARYL S. ENGLISH B.A.Sc, The University of British Columbia, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1996 \u00a9 Daryl S. English, 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of &v\u00a3>\/\/^&<\u00a3 a <\/> (0 -20 OQ -40 -60 -80 -100 -120 -140 -5 -4 -2 - 1 0 1 2 Joint Displacement (in) Figure 5.2 Latera l L o a d Displacement Response for O S B 2 In 0 S B 2 , diagonal cracks formed in the beam in nearly the same location as in 0 S B 1 . Photos 5.3 and 5.4 can be compared with Photos 5.1 and 5.2. These cracks however, did not open as wide, even at large displacement levels, as shown in Photo 5.5. A lso, the cap beam did not fail in shear. Photos 5.2., 5.3 and 5.4 o f the two tests are taken at approximately the same displacement and show the much improved crack control in 0 S B 2 as compared to 0 S B 1 . Flexural shear cracks formed in the columns and in the region of the fillet, shown in Photo 5.6, gradually getting wider and longer as the ductility level increased. Photo 5.6 shows the south column after the first push cycle of ductility level 6. U p until the last displacement sequence, when a sudden column shear failure occurred, there was very little strength degradation, with the three hysteresis curves at each sequence nearly falling on top of each other. See Fig. 5.2. On the last loading cycle, which was initially a push, the tension column (North Column) failed suddenly in shear on the subsequent pull portion o f the cycle. Here, tension column refers to the column with reduced axial load caused by the overturning moment from the lateral loading. This sudden shear failure at a ductility o f 6 produced the wide diagonal crack in the column as shown in Photo 5.7. Photos 5.5 and 5.6 were taken at the same displacement as Photo 5.7 and shows the shear crack in the cap beam had grown to be quite wide at this displacement. The retrofit scheme used for specimen OSB2 was successful in forcing flexural hinging into the tops of the columns, producing modest ductility, and increasing the lateral load capacity o f the bent. Unfortunately the ultimate strength of the cap beam retrofit was not determined because of the column shear failure. However, the size o f the shear crack in the cap beam was of concern and indicated the possibility of a brittle shear failure in the cap beam had the columns been strengthened which would have increased the demand on the cap beam. Therefore, retrofit measures that further increased the shear capacity o f the cap beam and columns were considered. 5.4 Test O S B 4 - Vert ical ly and Horizontal ly Post-Tensioned C a p Beam wi th C o l u m n Jackets The hysteretic response of specimen OSB4 is shown in Fig. 5.3 and shows very good performance to a ductility level of 9. In this, and subsequent tests, the displacement controlled cycles were all measured from the zero displacement position and so the ductility levels in both the push and pull directions are essentially the same. The overall hysteretic performance proved to be very effective by forcing hinges into the tops of the columns in the region of the fillet. The specimen eventually failed in flexure in the column region above the column jackets as evidenced by spalling o f the cover concrete and buckling o f the vertical column reinforcement. The first cycle to a ductility level o f 12 showed a strength loss when compared to the previous sequence, and subsequent cycles had approximately a 15% loss in each cycle. 42 6 8 10 12 740 720 700 80 60 40 \"Or \u2022S- 20 \u00ab. (0 0) 0 \u2022c CO 0) <0 n -20 OQ-40 -60 -80 -100 -120 -140 South \u2014' -4 - 2 - 1 0 1 2 Joint Displacement On) Figure 5.3 La tera l L o a d Displacement Response for OSB4 At low ductility levels, flexure and shear cracks developed in the cap beam, as shown in Photo 5.8 taken at a ductility of 4, but these did not widen or grow as the test progressed and the beam retrofit was successful in forcing the damage into column flexure. Photos 5.9 and 5.10 show the north column and joint region at ductility levels o f 4 and 6 respectively. A t ductility 4, there is considerable cracking in the column but little cracking in the joint. A t ductility 6, the cracks are wider in the column and there are the beginnings of diagonal cracks across the joint. A t a ductility level of 9 some spalling occurred near the column corner bars, as seen in Photos 5.11 and 5.12, which allowed the corner bars to buckle. Photo 5.12 also shows the bottom end of one of the vertical Dywidag post-tensioned bars that were installed to increase the beam shear resistance and provide confinement to the top horizontal beam reinforcement. Photo 5.13 shows the damage at a ductility o f 12. At this displacement level there was much more spalling o f the cover concrete, more bars had buckled and some of the reinforcement had fractured. As the cycling progressed, more of the vertical bars fractured and this lead to the degradation and reduction in strength with each additional cycle as shown in Fig. 5.3. Photo 5.13 also shows that some of the diagonal cracks in the joint had joined up to form one diagonal crack extending the full length of the joint from lower right to upper left. However, this crack did not open to any appreciable extent. This retrofit scheme proved to increase the shear capacity o f the cap beam, increase the bond strength between the concrete and the cap beam's top reinforcement, and the column jackets provided increased confinement and capacity to the columns. Shear failures in the cap beam and columns were precluded and damage to the joint region was minimal. Although the retrofit performed extremely well, the curvature demand on the plastic hinge regions was large and subsequently, because of a lack of significant confinement in the fillet region, spalling o f concrete and buckling o f reinforcement lead to rapid degradation between cycles. Thus the confinement provided in the plastic hinge regions of the last retrofit measure, specimen O S B 5 , extended higher into the fillet region than the steel jackets used on OSB4 . This was expected to reduce the spalling of concrete that was observed in the hinge regions of specimen OSB4. 5 . 5 Test O S B 5 - Prestressed C a p Beam with Fiberglass Wraps on the C a p B e a m and Co lumns Photos 4.7 and 4.8 showed specimen O S B 5 at the beginning of the test and the extent o f the fiberglass wraps on the cap beam and columns. The hysteretic load-displacement response is shown in Fig. 5.4. The performance of this retrofit was exceptional up to a displacement ductility level o f 9 where the test had to be terminated because of limitations in the displacement capacity of the loading system. The confining effect and the flexibility of the fiberglass wraps which reduced column damage are evident by comparing the hysteretic loops of O S B 4 and O S B 5 at displacement levels slightly greater than 4 inches. Refer to Figs. 5.3 and 5.4. Note that the hysteresis loops for O S B 5 show much less degradation than the loops for O S B 4 . 45 HA= 1 2 4 6 8 1 0 - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 Joint Displacement On) Figure 5.4 La tera l L o a d Displacement Response for OSB5 This specimen was more flexible than specimen OSB4 which had full length steel column jackets, thus the yield displacement was larger, and so even though the maximum displacement was greater than in the previous tests the ductility level was not as high. Since the fiberglass wrap retrofit was designed to be similar in strength to OSB4, the decision was made to subject the specimen to the same loading regime as OSB4. For this reason the ductility values on the caption board in the OSB5 photos, for example shown as U3.0 in Photo 5.14, are in error. The actual displacement ductility is approximately 75% of the amount shown on the caption board. Photos 5.14 and 5.15 show the south cap beam and joint regions after three cycles at a displacement ductility of just over 2. The cracks that are marked were very small. The cracks occurring under the fiberglass wrap were not visible, and the lines drawn on the fiberglass wrap indicate the extent of debonding of the fiberglass from the concrete. For instance, in Photo 5.14 the area enclosing the number 3.0 indicates that this area became unbonded sometime during the sequence at U3.0, or a ductility of about 2.2. The actual debonding took place between the concrete and the white acrylic type paint that had been used to paint the specimen. If the fiberglass had been applied directly to the concrete, the bond between the wrap and the specimen would have been better, however, the debonding did not appear to adversely affect the performance of the fiberglass retrofit. A s the loading progressed more cracks developed in the joint area but not in the short central length o f the beam that was visible. Photos 5.16 and 5.17 show the cracks at ductilities of 6.5 and 9 respectively. At peak deflection all these cracks were relatively small, including those in the joint region. The dark patch seen in Photos 5.16 and 5.17 is the area where grout was applied to form a smooth radius for the application o f the fiberglass in the fillet region. The fiberglass wraps however, did not reach the full height o f the grouted region and a portion o f the grout subsequently became loose during testing and was removed. Its removal did not represent spalling of the cover concrete although spalling did occur at one corner as described below. Photos 5.18 and 5.19 show the specimen after the completion o f the test to ductility 9, after the fiberglass wrap had been removed, and the cracks under the fiberglass marked. Photo 5.18 shows cracking in the south column extending well down the length o f the column. These cracks had essentially closed under the self weight o f the specimen when the photo was taken. Photo 5.19 shows the south cap beam section which had only a few small diagonal cracks. There may have been a slight tendency for the cracks to turn in the horizontal direction at the top of the beam, which would indicate a potential for bond failure and spalling o f the top cover concrete, but there did not appear to be any spalling and the small width o f the cracks would indicate that there had not been bond failure. The north end of the beam had only one diagonal crack under the fiberglass wrap During the sequence to ductility 9 a small amount of spalling took place at one corner on the interior face of the north column just above the fiberglass wrap and allowed the corner column bar to buckle. This is shown in Photo 5.20 which also shows the extent o f the spalling that took place underneath the top of the fiberglass wrap. In this photo the top of the fiberglass wrap was at the bottom of the buckle, level with the bottom of the white patch under the letter N , thus the spalling mostly took place above the wrap. In contrast to the steel jackets used in specimen OSB4 , the fiberglass wraps did not restrict the length of plastic hinge that formed as evidenced by the well distributed cracking observed on the columns after the wraps were removed. Refer to Photo 5.18. This, combined with the fact that a larger area of the plastic hinge region was confined by the wraps than in specimen OSB4 , OSB5 was able to undergo larger displacements before concrete began to spall and the reinforcement buckled. The flexibility of the wraps permitted large displacements, with reduced ductility demand, and the confinement provided by the wraps reduced the amount of damage suffered by the bent throughout the test. It was for these reasons that the condition of specimen OSB5 at a given displacement was always better than the condition of specimen OSB4 at the same displacement. This observation became quite profound at the end of the testing sequence, near the 4 inch displacement level. 49 C H A P T E R 6 - A N A L Y T I C A L P R E D I C T I O N S 6.1 Overv iew Clearly, avoiding brittle shear failures such as shear failures is desirable in the event o f an earthquake. It is the intent of the designer to obtain a ductile, and flexurally dominated response from a structure. In doing so, members designed to undergo inelastic deformations in the form of plastic hinges require provision of sufficient transverse reinforcement in the form of spirals or rectangular tie arrangements to provide effective confinement, prevent buckling o f longitudinal reinforcement, and prevent shear failure. Currently design information is available for retrofit schemes that include steel column jackets (Chai, Priestley and Seible, 1991) and more recently, fiberglass jackets ( S E Q U A D , 1993). Although there are recommendations that aid in predicting plastic hinge lengths, there is little information available on predicting the curvature distributions that arise due to particular loadings on as-built or retrofitted structures. After observing and comparing the behaviour of specimens O S B 4 and O S B 5 , it was decided to attempt analytical predictions of their behaviour and determine i f the curvature distributions within these two specimens could be predicted, since their response was predominately flexural. From these distributions, the peak curvatures, peak curvature ductility demand, the ultimate compressive strain in the concrete and the reinforcement strains could be determined. Firstly, predictions of the overall lateral displacement response for specimens O S B 4 and O S B 5 were carried out using the analysis program D R A I N - 2 D X , which is a non-linear analysis package that can be used for static or dynamic analyses. D R A I N - 2 D X was used to perform a simple push-over analysis for the two specimens in an attempt to compare the predicted behaviour with the observed hysteretic envelope. P-A effects were included in the analyses. After the overall prediction of the force-deflection relationship was determined, curvature distributions over the length of the cap beam and the columns were derived from the DRAIN - 2 D X output. These were calculated by taking the difference in the rotations at the ends of each element and dividing by the element length. The shape of the distributions and peak curvature values were then compared to those derived experimentally from the internal instrumentation o f each specimen, as shown in Fig. 3.3. Estimates o f the peak concrete strains, 8 C , in the plastic hinge regions, were then obtained from the appropriate curvatures. 6.2 D R A I N - 2 D X Models 6.2.1 Noda l Arrangements The specimens were first discretized into stick models comprised of a series o f nodes and bending members. The nodal arrangements for both specimens O S B 4 and O S B 5 were identical. Nodes were placed at the locations of longitudinal strain gauges in the real model, at the points o f application of dead and lateral load, and at section changes in the cap beam and beam-column joint regions. Additional nodes were placed in regions expected to undergo inelastic displacements, namely, in the tops of the columns just below the beam-column joints. Figure 6.1 shows the model used, including the locations of the dead and applied lateral loads. The numbers indicate the node numbering scheme that was used. In all, there were 66 nodes and 66 elements per specimen. Table 6.1 lists the nodal coordinates o f the computer models which are consistent with the set of axes shown in Fig. 6.1. Figure 6.1 Noda l Arrangements for Specimens O S B 4 and O S B 5 52 Table 6.1 Noda l Coordinates for Specimens O S B 4 and O S B 5 Node X - C o o r d . Y - C o o r d . Node X - C o o r d . Y - C o o r d . Number (in) On) Number (in) (in) C a p Beam South Co lumn 100 0.0 97.8 200 57.0 0.0 101 8.0 97.8 201 57.0 12.5 102 43.3 97.8 202 57.0 24.0 103 50.5 97.8 203 57.0 37.5 104 57.0 97.8 204 57.0 50.0 105 63.5 97.8 205 57.0 62.5 106 71.3 97.8 206 57.0 66.0 107 72.5 97.8 207 57.0 69.7 108 78.8 97.8 208 57.0 73.3 109 84.5 97.8 209 57.0 76.3 110 86.1 97.8 210 57.0 78.9 111 94.0 97.8 211 57.0 81.6 112 99.5 97.8 212 57.0 84.3 113 105.5 97.8 213 57.0 94.8 114 109.5 97.8 115 115.6 97.8 116 119.5 97.8 Nor th Co lumn 117 129.5 97.8 300 223.0 0.0 118 140.0 97.8 301 223.0 12.5 119 150.5 97.8 302 223.0 24.0 120 160.5 97.8 303 223.0 37.5 121 164.7 97.8 304 223.0 50.0 122 170.5 97.8 305 223.0 62.5 123 174.5 97.8 306 223.0 66.0 124 180.5 97.8 307 223.0 69.7 125 186.0 97.8 308 223.0 73.3 126 193.9 97.8 309 223.0 76.3 127 195.5 97.8 310 223.0 78.9 128 201.3 97.8 311 223.0 81.6 129 207.5 97.8 312 223.0 84.3 130 208.8 97.8 313 223.0 94.8 131 216.5 97.8 132 223.0 97.8 133 229.5 97.8 A - F r a m e Peak 134 236.8 97.8 400 140.0 138.3 135 272.0 97.8 136 280.0 97.8 53 6.2.2 F lexura l Analysis Moment-curvature relationships were derived for all the structural sections within the specimens to determine the various yield surfaces, including column axial load-moment interaction diagrams, and the post-elastic behaviour. A s indicated in Drawing Q117-11, Appendix B , the longitudinal reinforcement in the cap beam has many cut-off locations. The moment capacity was calculated for each section created by the cut-off locations and the sections were determined by assuming a particular development length for the main #5 bars. The basic development length given by the C A N -A23.3-M84 code for #5 bars in tension and compression is ld = 0.042 \u00b1j== (Imperial Units, psi) = 7.68 in. where the steel yield strength w a s , \/ , = 49500 psi, the area of each bar Ab = 0.307 in 2 , and the average compressive strength o f the concrete for both specimens was fc \u00ab 6900 psi. Fo r analysis purposes, the development length for the #5 reinforcement was set to 7.5 in. This value was considered to be conservative because of the conservatism inherent in the concrete design code and due to the levels of post-tensioning and increased transverse reinforcement present in both specimens OSB4 and OSB5 that increased the level o f confinement for the main reinforcement. Shown in Table 6.2 are the flexural capacities and the effective concrete moments o f inertia used for the cap beams of both specimens OSB4 and OSB5 . The capacities were determined considering the post-tensioning force in the cap beam of 342 psi for both specimens. The internally bonded tendon of OSB4 was not considered in the flexural analysis and thus its stiffening and post yield strengthening effects were ignored. This omission did not greatly affect the results of the D R A I N - 2 D X analysis since the cap beams in both tests did not reach flexural capacity. The X coordinates indicated in Table 6.2 correspond with those listed in Table 6.1 and the sections listed are symmetric about the cap beam centerline which has an X coordinate o f 140 in. Table 6.2 C a p Beam Section Capacit ies and Inertias X-Coord ina te (inches) Section Number Positive Capaci ty (Mv +) (kip. in) Negative Capac i ty (My -) (kip. in) Inert ia Ie ( in 4) 0.0 1 3300 6570 17500 43.3 2 3600 8800 21500 63.5 3 3600 6800 21500 71.3 3 3600 6800 17500 84.5 4 3640 5290 17500 94.0 5 4320 4290 17500 99.5 6 4320 4290 17500 105.5 7 4680 4210 17500 109.5 8 5360 3570 17500 119.5 9 6000 2890 17500 129.5 10 6650 2880 17500 140.0 Since flexural stiffness is influenced greatly by the extent of cracking in the section, and the degree of cracking over the length of members changes significantly, effective section inertias were calculated using 0.6.1^088 for the columns and O.SSJgross for the cap beam, as recommended in Paulay and Priestley (1992). Ideally, the section inertias could have been varied along the lengths of the cap beam and columns to reflect the degree of cracking at different locations throughout the bent and perhaps better partially account for the true non-linear flexural response of the members. Since the variation o f the section inertias mainly affects the response of the structure in the linear range, and the primary concern o f this thesis was to examine the structure response in the post-elastic range, this was not done. A simple expression relating the modulus of elasticity of the concrete to the square root o f the compressive strength was used from CAN-A23 .3 -M84 and is given as Ec = 57000 \/^7*7 (Imperial Units, psi) = 4735000 psi = 4735 ksi where the concrete compressive strength\/ ' c , was taken as 6900 psi. The computer program used to derive moment-curvature relationships for each section was one that used theory proposed by Mander, Priestley and Park (1988). The theory attempts to account for the effects of confinement provided by transverse reinforcement. A n energy balance approach is used to predict the ultimate longitudinal compressive strain capacity o f the concrete based upon the fracture of the transverse reinforcement. The strain energy capacity of the transverse reinforcement is equated with the strain energy stored in the concrete as a result of the confinement provided. The constitutive relationship for the concrete is predicted by calculating a maximum compressive concrete strain and an increased compressive strength based upon the reinforcing details of the section. Strain hardening of the reinforcing steel is accounted for in the program. The program output includes both the 56 concrete and steel strains for given curvatures. Shown in F ig. 6.2 below is the typical column section interaction diagram derived from the program. The moment values shown are the yield moments for the range of axial loads i f a the moment-curvature response is approximated by a bilinear relationship. This approximation is shown in F ig . 6.5. A similar interaction diagram was derived for the column fillet regions. 500 .3500 I 1 1 J 1 1 1 1 1 -10000 -7500 -5000 -2500 0 2500 5000 7500 10000 Moment (kip*in) Figure 6.2 Column Section Interaction Diagram 6.2.3 Accounting for Joint Shear Deformations The version of D R A I N - 2 D X used for the analysis cannot directly model joint shear deformations that result from the joint forces. That is, the program did not allow for a rotation in the joint region due to the joint shear stresses arising during the test. Only beam shear deformations transverse to the members' axes are permitted by the program. In order to account for the true joint shear deformations measured by the L V D T setup at the north joint, the shear area over the length of the column sections was reduced. The calculated shear distortion over the length of the column was forced to equal the measured joint shear strain multiplied by the column length. Shown in Table 7.1 of Chapter 7 are the joint shear strains for specimens O S B 4 and O S B 5 when the bents were displaced to the north. The shear stress giving rise to the calculated shear deformation was thus from the column shear force, not the joint shear stress. This method of accounting for shear deformations occurring in the joints predicts the same deflected shape of the columns as observed during testing and thus does not affect the prediction o f flexural deformations in the cap beam and columns. Joint shear deformations, member flexural deformations and member shear deformations constitute the contributions to the overall bent deflection. For a given displacement, accounting for the shear deformation in the joints reduces the flexural demand in the other regions of the bent. Thus with large joint shear deformations, there is less demand on the plastic hinge regions throughout the structure. 6.2.4 Post Processing of D R A I N - 2 D X Results After the overall model response was generated, the nodal rotations were analyzed and reduced to average curvatures over the length of the cap beam and columns. The nodal rotations from the D R A I N - 2 D X output files were extracted with the program E X developed by the author. The source code, including a brief explanation of the program, is provided in Appendix D. The E X program reads the output file for a particular analysis segment and extracts the rotational histories for each node and stores them in arrays. The program then reads in the locations of the nodal coordinates from an input file called ex.nod and calculates the distance between nodes. The rotations for each end o f each element are summed and divided by the element length to obtain the average curvature for that particular element. The average curvature is then assigned to the element midpoint. These curvatures and midpoint locations are then written to an output file called ex.out where they can be further manipulated or plotted. 6.3 OSB4 Response The push over analysis was done by imposing a deflection at the top of the A-frame as was shown in F ig. 3.1 and modeled in Fig. 6.1. The predicted push-over response of O S B 4 is compared to the observed hysteresis curves in Fig. 6.3 and is labeled 'Dra in-2DX prediction1. It can be seen from this figure that the model behaviour envelopes the southbound (positive joint displacement) hysteresis curves reasonably well except perhaps in the one to two inch displacement range where the D R A I N - 2 D X prediction matches the second and third cycles of each sequence as opposed to the first. The D R A I N - 2 D X prediction is symmetric, unlike the observed hysteresis curves for specimen OSB4. There appears to be no justification for this unsymmetrical response since the specifications for the specimens were symmetric. It is coincidence that the analytical prediction which was derived from the details indicated on the structural drawings in Appendix B coincides with the southbound deflection curves which always followed the northbound curves in the loading sequence. 59 -120 -140 I 1 -J 1 1 1 1 1 1 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 Joint Displacement (in) Figure 6.3 Analy t ica l Latera l L o a d Displacement Response for O S B 4 It can be seen that the load for the model continues to increase beyond the 4 inch displacement when the real structure begins to degrade rapidly. This is a result o f the bilinear moment-curvature relationship used by DRAIN -2DX for each member. It should be noted that DRAIN -2DX, at present, does not have a hysteretic model that allows for cyclic degradation. This limitation did not however, affect the results o f the simple push-over analysis that was performed. The curvature distributions obtained at different ductility levels from the post processing of the DRAIN -2DX analysis were then plotted for the cap beam and columns. Figure 6.4 shows the curvatures obtained for the cap beam. The figure shows the increasing progression of curvatures as the displacement level increases but that they increase more rapidly in the linear range than in the post-elastic range. This was expected since the D R A I N -2DX prediction indicated that there was no flexural yielding of any of the beam elements and the force levels remained relatively constant at the higher displacements. The curvatures towards the north end of the beam are higher because of larger moments due to dead load effects at low ductility levels, and higher column moment capacity due to the increased axial load in the leading 'compression column' at the higher ductility levels. 61 A,P \u2022 0.00008 T Figure 6.4 Analy t ica l C a p Beam Curvatures for O S B 4 The columns were the only elements to undergo inelastic deformations and the capacity of the elements increase due to the strain hardening effect. As a result, the elastic portions o f the bent, particularly the cap beam, undergo slightly greater deformations as the flexural demand increases. This trend is evident in Fig. 6.4. Figure 6.5 shows the bilinear approximation to the real moment-curvature response of a section and the post-elastic slope used by D R A I N - 2 D X . This slope can vary depending on what is chosen as M y and which part o f the real response curve one is trying to model. In the work presented here the strain hardening slope, denoted by a , varied from 0.005 to 0.02. 62 F igure 6.5 Idealized Member Flexural Response Used by D R A I N - 2 D X Shown in F ig. 6.6 is the progression of curvatures in the columns for the same ductility levels presented for the cap beam. Recall that the south (left column in the figure) column would be subjected to a tensile reaction at the base due to the northbound lateral displacement. It is evident from the figure that the steel jackets were extremely stiff and forced deformations into localized regions above the tops of the jackets. The abrupt decrease in curvature that occurs about half way up the architectural fillet, or 78 inches from the column base, is due to a discrete section change that occurs at nodes #209 and #309 in the D R A I N - 2 D X model. Refer to Fig. 6.1 and Table 6.1 for the nodal locations. The second distinct drop that occurs in the beam column joint region at 89 inches from the column bases is also due to a section capacity change located at nodes #212 and #312. 63 * MA =6.0 \u2022 MA =4-0 -MA =3.0 * MA =2.0 A MA =1-2 \u2022 MA =0.9 \u2022 MA = 0.65 Hi y IO CM IO O O O \u00a9 \u00abM O O O O O O O \u00b0 . \u00a9' \u00b0 . O* \u00b0 . C> Curvature (1\/in) Curvature (1\/in) Figure 6.6 Analy t ica l Co lumn Curvatures for O S B 4 It can be seen that for each displacement level, the south column curvatures are greater than the curvatures in the north column. Keeping in mind that the response of specimen 0 S B 4 was primarily flexural in nature, this behaviour would be expected since the curvatures in the cap beam are less at the south end. This means that the cap beam rotation at the south end is less than at the north end, and thus in order to maintain compatibility o f the members, the curvatures and deflection of the south column must be greater than that o f the north column. Refer to Figs. 6.4 and 6.6 for clarification. Shown in Table 6.3 are the predicted peak curvatures and the corresponding estimated concrete strains for ductility levels ranging from 2.0 to 12.0. The displacement indicated is the average horizontal displacement of the north and south joints. The peak concrete compressive strains s c were calculated using the 'Mander' program which calculates strains for 64 specified axial loads and curvatures. The respective compressive loads in the south and north columns in the inelastic range of the response are approximately 10 and 180 kips. Table 6.3 Peak Analytical Curvatures for the Plastic Hinge Regions of O S B 4 Ductility Displ. South Column North Column A (in) Curvature Ductility Strain Curvature Ductility Strain , in the plastic hinge region did not allow for input of such particular geometry constraints. Thus in order to predict the flexural response of the fillet region, the confinement parameters for the section in the program were modified so that the predicted response of the section could reach curvatures of the order of 0.0055 rad\/in., which was approximately the maximum curvature predicted in the D R A I N - 2 D X analyses. The confinement is primarily dependent on the tie arrangement and so, the area, the axial stiffness and the strength o f the ties were kept the same, and the spacing of the ties was varied until the column section could attain peak curvatures of about 0.0055 1\/in. The equivalent spacing of the 9 Ga. (0.15 in. diameter) ties, predicted by the program, to attain the peak curvatures, was 0.5 in. The predicted maximum concrete strain capacity, e c u , for this level of confinement was 0.017. Between ductility levels 9 and 12 in the real test of OSB4 is when significant degradation of the specimen occurred. See Photos 5.12 and 5.13. The analysis would predict that the architectural fillet regions and steel jackets appeared to provide confinement enough to attain a maximum concrete strain slightly less than 0.017. The Mander' program predicted and ultimate strain capacity o f the steel, e s u , of approximately 0.16. From tensile tests performed on the #5 reinforcement, the ultimate strain capacity was observed to be about 0.158. For the peak curvature value of 0.00538, the corresponding steel strain is approximately 0.098 which is well below the capacity o f the steel. Spalling o f concrete above the steel jackets was first observed to occur at ductility level 6 during the real test. See Photo 6.1. From the predicted behaviour, this would indicate a spalling strain, s s p , of about 0.0075. This strain is somewhat greater than what is normally considered the spalling strain of concrete. This higher strain most likely is due to the confining effect of the fillet region and the steel jacket. Joint shear deformations for OSB4 were not detected by the external L V D T system until the later stages of the test when the joint region showed diagonal cracking. Consequently, in the range up to and including ductility level 4.0, the joint shear deformations in the D R A I N - 2 D X model were was assumed to remain linear in behaviour. This assumption is consistent with the observed behaviour of the beam column joint by comparing Photos 5.9 and 5.10. A t ductility level 4, as shown in Photo 5.9, there are no visible cracks extending across the joint and at ductility level 6, as in Photo 5.10, there are two cracks running from the upper left towards the lower right. The external L V D T system indicated shear deformations at ductility levels 6, 9 and 12. Recall Photo 5.13 which shows the north joint at a ductility o f 12 where there are two narrow cracks running from bottom right to top left on the north joint, and none running from the lower left to the top right. Presumably the difference in damage observed between the north and south directions was a result o f the different moments and joint shears arising in the joints due to the change in section capacity caused by the difference in axial load between the two columns. Recall that the pushover analysis was performed by imposing a northbound deflection to the bent. 6.4 O S B S Response Nearly the identical procedure to that used for analysis of O S B 4 was carried out to predict the overall response of specimen OSB5. Shown in Fig. 6.7 is the predicted analytical response of specimen OSB5 compared to the observed hysteresis curves. Again, the D R A I N -2 D X response envelopes the hysteresis curves reasonably well for the southbound portion o f the curves and under-predicts the load in the north direction. The D R A I N - 2 D X response matches well with the first cycle in each sequence which may be expected because as stated before, only a static push over analysis was performed and D R A I N - 2 D X does not account for degradation between cycles. 67 10 -140 - 5 - 4 - 3 -2 -1 0 1 2 3 4 5 Joint Displacement On) Figure 6.7 Analy t ica l Latera l L o a d Displacement Response for O S B 5 Shown in Fig. 6.8 are the predicted cap beam curvatures for ductility levels 0.6 to 6.0. A s was the case in OSB4 , cap beam curvatures in specimen OSB5 increase with increasing displacement until flexural yielding of the bent occurs, beyond which the curvatures increase only slightly. Since the peak loads reached by the specimens were approximately the same, 68 and yielding occurred primarily in the columns, the magnitudes of cap beam curvatures for specimens O S B 4 and OSB5 are nearly identical in the non-linear displacement range. The slight difference arises in the linear range where the magnitudes are slightly less in O SB 5 than O S B 4 because OSB5 had more flexible columns. The yield displacement for OSB5 was approximately 0.5 inch. A,P \u2022 0.00008 T Figure 6.8 Analy t ica l C a p Beam Curvatures for O S B 5 Shown in Fig. 6.9 are the predicted column curvatures for specimen O S B 5 . The curvatures were, as expected, more distributed than those predicted for OSB4 . The peak column curvatures occur in approximately the same locations as specimen O S B 4 , but because 69 the fiberglass wraps provided an insignificant contribution to the flexural stiffness of the columns, longer plastic hinges developed for the columns in specimen O S B 5 . The peak curvatures were consequently greater in OSB4 than in OSB5 for a given displacement. Photos 5.13 and 5.18 show the plastic hinge regions of specimens O S B 4 and OSB5 respectively at a displacement o f 4.3 inches. It can easily be seen from these photographs that there was much more localized flexural demand and damage in specimen O S B 4 than OSB5 . A,P 10 \u00a9 \u00a7 \u00a9' 3 \u00a9a io f 1 all 1 Eg i ...1:1-. - -\u2022 \/ \u2022 ' i' \u2022\"' \u2022 . i '\"]\u2022 i i i i i CM \u00a9 o' I O CM \u00a7 o' + MA=60 \u2022MA =4.0 -MA =3.0 * MA =2-0 \u00b1MA = 10 \u2022 MA = 0-8 + MA = 06 Curvature (1\/in) Curvature (1\/in) Figure 6.9 Analy t ica l Co lumn Curvatures for O S B 5 The curvatures in the south column are uniformly greater than those in the north column for ductilities up to 3.0, as was observed in the analysis o f OSB4 . The peak curvatures for the north and south columns of OSB5 however, are nearly identical for displacement ductilities 4.0 and 6.0. The curvatures in the south column, particularly for these ductility levels, are more distributed than those in the north column resulting in a larger south column deflection that is required to maintain displacement compatibility o f the cap beam and 70 columns. Also the south joint region experienced some significant diagonal cracking at these displacement levels which contributed to the overall deflection of the bent and reduced the flexural demand on the hinge region. See Photo 5.18. The diagonal cracking in the south joint region shown in the photo runs primarily from the bottom left to top right which coincides with joint forces induced by a northbound deflection. Note that there are no cracks seen running from bottom right to the top left of the joint region. Consequently, for the analysis, the shear deformations of the north joint were assumed to remain linear and the shear area in the north column was not reduced since larger shear strains were not detected there during testing. The 'Mander' program used to predict the flexural capacities o f the sections assumes only steel to be used as transverse reinforcement and prescribes the elastic modulus of transverse reinforcement to be that of steel. The modulus o f steel is approximately 9 times that measured for the fiberglass wraps. In order to model the confinement effect o f the fiberglass wrap accurately, the details of the transverse reinforcement were modified in the program. The wrap was first assumed to consist of discrete ties spaced at 0.5 in. The area of the 'wrap ties' was then reduced to get the correct axial stiffness per 0.5 in. o f wrap. Because the area o f the ties had been reduced, the ultimate stress o f the 'wrap ties' was increased so that the ultimate strength was correct. The predicted ultimate strain capacity o f the concrete s c u , for the columns wrapped in fiberglass was 0.027. A t the peak curvature o f 0.0033, the predicted steel strain, e s , is approximately 0.061 which is below the peak strain capacity o f the steel, s s u , o f about 0.16. Shown below in Table 6.4 are the peak curvatures calculated for the plastic hinge regions for specimen OSB5. Concrete strains corresponding to these curvatures were 71 calculated using the 'Mander' program. The bent displacement indicated in Table 6.4 is the average horizontal displacement of the joints. 6.4 Peak Analytical Curvatures for the Plastic Hinge Regions of O S B 5 Ductility Displ. South Column North Column \/ \/ A A (in) Curvature Ductility Strain Curvature Ductility Strain $ (Mm) tH Sc \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9\" \u00a9 \u00a9' \u00a9 o' Curvature (1\/in) Curvature (1\/in) Figure 8.1 Compar ison of Curvatures at Duct i l i ty Leve l 2.1 for O S B 4 \u2022 nA=4.0 Experimental Results \u2022 HA =4.0 Analytical Results Curvature (1\/in) Curvature (1\/in) Figure 8.2 Compar ison of Curvatures at Duct i l i ty Leve l 4.0 for O S B 4 8 8 \u00a7 S \u00a7 \u00a7 \u00a9* \u00a9 o \u00a9* \u00a9 \u00a9' _ CM CM C \u00a7 8 S \u00a7 \u00a7 c \u00a9 \u2022 \u00a9 ' \u00a9 ' \u00a9 \u2022 \u00a9 ' < Curvature (1\/in) Curvature (1\/in) Figure 8.3 Compar ison of Curvatures at Duct i l i ty Leve l 5.7 for OSB4 105 Table 8.1 Measured Displacements Versus Revised Calculated Displacements for OSB4 Measured Displacement Ductility fiA Measured Displacement (in) Revised Calculated Displacement (in) Revised Percent Error South Column Closure Error terror (in) 0.8 0.28 0.29 +2 % [+4] +0.035 1.2 0.43 0.47 +9 % [+13] -0.14 2.1 0.72 0.84 +17% [+24] +0.030 3.0 1.04 1.26 +21 % [+27] +0.22 4.0 1.41 1.52 +8 % [+14] +0.15 5.7 2.01 1.96 -2 % [+2] -0.074 A s shown in Figs. 8.1 through 8.3, the experimental peak curvatures in the plastic hinge regions o f the columns are less than those predicted by D R A I N - 2 D X and the experimental distributions are also more 'spread out' over the same region. Given that the curvature distributions predicted by D R A I N - 2 D X produce a compatible set o f displacements, the relative areas under the curvature diagrams, particularly in the plastic hinge regions, can be compared to see why the experimental data may over-predict or under-predict the measured displacement. It can be seen in Figs. 8.1 to 8.3 that areas where the experimental distributions are larger than those obtained analytically would predict larger displacements than those measured. This is particularly true for ductility levels 2.1 and 4.0 where the experimental curvatures are larger over much of the plastic hinge lengths. A s evidenced in Table 8.1, a change in the curvatures in the north column resulted in changes o f the error ranging from 2% to 7%. 8.2 Specimen OSB5 Shown in figures 8.4 to 8.6 are the curvature distributions predicted by the D R A I N -2 D X model contrasted with those obtained experimentally for ductility levels 2.2, 4.0 and 6.0 106 for specimen OSB5 . It can be seen that the predicted cap beam curvatures are relatively close to those indicated by the strain gauges, especially at the larger ductilities. Similar to O S B 4 , the experimental results were always greater than the analytical results for the north end of the cap beam. The explanation for this is also due to the reduced stiffness caused by the flexural cracking in the north end of the cap beam. Larger discrepancies between the distributions arise in the joint regions. D R A T N - 2 D X tends to predict more localized curvatures with greater peak magnitudes than what were measured. As with OSB4 , curvatures equal to the moment M , divided by the flexural stiffness of the columns (EI)C oiumn, were used from the column bases up to 55 in. from the bases. This was done to account for the uncracked linear behaviour of the lower portions o f the columns. Shown in Table 8.2 below are the comparisons of the measured bent displacements versus the revised calculated displacements. Table 8.2 shows the effect that interpolation o f linear curvature values over the lower portion of the columns had on the calculation o f the measured displacement. The change in the error of calculated displacement ranged from 0% to 6%. 107 A,P \u2022 MA =2-2 Experimental Results O HA =2-2 Analytical Results CM ^ CO 00 \u00a9 CM \u00a9 \u00a9 \u00a9 \u00a9 *- _ O \u00a9 \u00a9 \u00a9 O \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 0 0 0 0 0 CM ^ CO 00 \u00a9 CM ^ \u00a9 \u00a9 \u00a9 \u00a9 * - * - * \" \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 \u00a9 Curvature (1\/in) Curvature (1\/in) Figure 8.4 Compar ison of Curvatures at Duct i l i ty Leve l 2.2 for O S B 5 Figure 8.5 Compar ison of Curvatures at Duct i l i ty Leve l 4.0 for O S B 5 A.P a -0.00006 Experimental Results o nA = 6.0 Analytical Results U) O IO c* o o \u00a9 Y - m 00 Cl s: w O o A V |!8 !!3 i si 3 \u00b0 4 A co 1 = i ^ o 0_ z C \u00a73 3 o-I\" -TTci-11 h I i 3 J iS - g is -n-2 8 3. is M .1-4 ! E 3\" \u2022 i So. 8 S i \u00a7 \u00ab s \u00a7 11 r CL \u202211* M . V M M 7f nil -* M M M I I I I WW ?3* -1' tPIERCAP \u00bbS5 1* SHAFT r r ft \u2022 o \u2022 i \u2014 , >1 t i r\u2014 n \/ OB 1 s P 1 Tx. (TrP.) A P P E N D I X C - P H O T O G R A P H S 125 Photo 3 . 2 Typica l Strain Gauge Wrapped in Protective Put ty Photo 3.4 Diagonal System of Instrumented Bars in the Nor th Jo in t Photo 4.1 Specimen OSB1 in Part ia l Formwork at A . P . S . Photo 4.2 Specimen O S B 1 Loaded on the Modi f ied A . P . S . Tra i le r Photo 4.4 Specimen OSB4 in the Testing Frame P r i o r to Test ing Photo 4.5 Installation of Fiberglass W r a p on the South E n d of the C a p Beam Photo 4.6 Start of Fiberglass W r a p on the South C o l u m n 132 Photo 4.8 C a p Beam of O S B 5 Pr io r to Testing Photo 4.9 South Co lumn and C a p Beam of O S B 5 P r i o r to Test ing Photo 5.4 O S B 2 - Nor th E n d of C a p Beam at Duct i l i ty 1.4 OAK ST BRIOGE BENT T E S T D E C 2 1993 S P E C I M E N O S B S a RF1 S E Q U E N C E J C Y C L E IB DUCTILITY 6.0 136 Photo 5.5 O S B 2 - South E n d of C a p Beam at Duct i l i ty 6 Photo 5.6 O S B 2 - Nor th C o l u m n at Duct i l i ty 1.4 Photo 5.7 O S B 2 - Nor th Co lumn Shear Fai lure at Duct i l i ty 6 139 Photo 5.10 O S B 4 - Nor th Joint at Duct i l i ty 6 Photo 5.11 O S B 4 - North Joint at Duct i l i ty 9 141 Photo 5.12 O S B 4 - Nor th Joint and Beam Underside at Duct i l i ty 9 Photo 5.17 O S B 5 - South E n d of C a p Beam and Joint at Displacement 4.3 in . 145 Photo 5.19 O S B 5 - South E n d of C a p Beam at Displacement 4.3 in . 146 Photo 5.20 OSB5 - North Column Buckled Reinforcement Photo 6.2 O S B 4 - Overal l V iew at Duct i l i ty 12 APPENDIX D - COMPUTER PROGRAM \"EX\" SOURCE CODE $debug c****************************************************************** c* Program to extract Nodal Rotations from drain output f i l e s . * c* Nodal rotations are converted to d i s t r i b u t e d curvatures. * c* * c* Output f i l e s generated by program: ex.ech,ex.out * c* Input f i l e s required by program: ex.nod,user Input * c* * c* Written by Daryl English vl.O, July,1995. * c* * c* Nodes MUST be 104 to 313 for analysis to be succes s f u l . * c* Extracted data from DRA1N2D output f i l e s i s echoed to the * c* f i l e \"ex.ech\". The present version only reads the r o t a t i o n s * c* output by Drain and calculates the curvatures. Two * c* dimensional arrays are used. The FORTRAN v3.0 compiler * c* l i m i t s the data to about 2.5 2-D arrays each 75x75. * c* c* The program counts the number of displacement\/load steps c* i n c l u d i n g any i n t e r a t i o n steps performed. So data can be c* manipulated for d i f f e r e n t specimens and d i f f e r e n t a n a l y s i s c* lengths. Lengthy analysis segments w i l l require the arrays c* to be redimensioned. * C* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * program ex character*8 prgm character*12 input1,input2,out1,out2 character*22 analtype character*80 t i t l e integer nodnum(66),nstep(75) r e a l fact(75),rotn(66,75),statn(70),delta(70),posn(70), phi(66,75),xtran(75) c********************************* c* Program I n i t i a l i z a t i o n and Name Q* ******************************* * prgm='EXTR1' write(*,750) prgm 750 format(16x,****************************************** .\/,24x,'Program ',a5,' vl.O by Daryl English', .\/,16x,'Extraction of Drain2D Nodal Rotations f o r Processing', .\/,16x,\u2022****************************************************\u2022) c******************************** c* Opening input and output f i l e s Q******************************** write(*,800) keybrd=0 read(keybrd,'(al2)') i n p u t l i n f i l e = 3 koutl=4 kout2=6 input2='ex.nod' out1=*ex.ech' out2='ex.crv' write(*,805) i n p u t l write(*,807) input2 write(*,810) o u t l write(*,810) out2 o p e n ( i n f i l e , f i l e = i n p u t l , s t a t u s = ' o l d ' ) open(kout1,file=out1,status='new') open(kout2,file=out2,status='new') 800 format(\/,lx,'Enter raw data f i l e ( i n c l . extension) => ',\\) 805 format(\/,lx,'===> Opening input f i l e : ',al2) 807 format(lx,'===> Opening input f i l e : ',al2) 810 format(lx,'===> Opening output f i l e : ',al2,) c****************************************** ******* c* Find the L a t e r a l Collapse analysis segement c* and count the number of analysis steps. c* Echo extracted data to f i l e = ex.ech for v e r i f i c a t i o n . c******************************************************** ncounter=l i = l j - l 10 read(infile,900) analtype 900 format(lx,a22) if(analtype.eq.'ANALYSIS TYPE = * STAT') then ncounter=0 read(infile,1015) nodnum(i) write(*,910) nodnum(i) read(infile,1025) n s t e p ( j ) , f a c t ( j ) , x t r a n ( j ) , r o t n ( i , j ) write(kout1,1030) i n p u t l write(koutl,1035) nodnum(i) write(koutl,1040) write(koutl,1045) n s t e p ( j ) , f a c t ( j ) , r o t n ( i , j ) 910 format(\/,lx,i5,' => F i r s t node number') 1015 format(\/\/,35x,i5,) 1025 format(\/\/\/,i5,2x,el0.4,2x,el2.5,16x,el2.5) 1030 format(lx,'Data echoed from f i l e : ',al2,\/) 1035 format(lx,'Node number =>',i5) 1040 format(lx,'Step',5x,'Load Fact',8x,'R-Rotn') 1045 format(lx,i5,',',2x,el0.4,',',2x,el2.5) j - j + l endif i f ( e o f ( i n f i l e ) ) then c l o s e ( i n f i l e ) close(koutl) close(kout2) write(*,1075) 1075 format(\/,lx,'===> S t a t i c analysis segment not found < stop endif if(ncounter.eq.1) then goto 10 endif c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* Subsequent loops for f i r s t node c********************************* 20 read(infile,1050) n s t e p ( j ) , f a c t ( j ) , x t r a n ( j ) , r o t n ( i , j ) if(fact(j).gt.0.00001) then write(koutl,1060) n s t e p ( j ) , f a c t ( j ) , r o t n ( i , j ) j=j+l jmax=j-l goto 20 endif write(*,1070) jmax 1050 format(i5,2x,el0.4,2x,el2.5,16x,el2.5) 1060 format(lx,i5,',',2x,el0.4,',',2x,el2.5) 1070 format(lx,i5,' => Number of steps i n S t a t i c Analysis') c****************************************** c* Read i n the data f or a l l remaining nodes c****************************************** keof=l i=i+l read(infile,1200) nodnum(i) 1200 format(35x,i5,\/\/\/) 150 write(koutl,1205) nodnum(i) 1205 format(\/,lx,'Node number =>',i5) 40 do 100 j=l,jmax read(infile,1210) r o t n ( i , j ) 1210 format(47x,el2.5) write(koutl,1220) n s t e p ( j ) , f a c t ( j ) , r o t n ( i , j ) 1220 format(lx,i5,',',2x,el0.4,',',2x,el2.5) 100 continue i=i+l imax=i-l i f ( e o f ( i n f i l e ) ) then c l o s e ( i n f i l e ) keof=0 write(*,1300) nodnum(imax) write(*,1305) imax write(*,1310) i n p u t l 1300 format(lx,i5,' => Last node number') 1305 format(lx,i5,' => Total number of nodes') 1310 format(\/,lx,'===> Closing input f i l e : ',al2) goto 50 endif read(infile,1230) nodnum(i) write(koutl,1235) nodnum(i) 1230 format(\/,35x,i5,\/\/\/) 1235 format(\/,lx,'Node number =>',i5) 50 if(keof.eq.1) then goto 40 endif close(koutl) c******************************************* c* Read i n nodal posi t i o n s from ex.nod f i l e , c******************************************* kin2=5 open(kin2,f ile=input2,status='old') read(kin2,4000) t i t l e do 80 n=l,imax+2 read(kin2,*) statn(n) 80 continue knorth=imax+2 close(kin2) write(*,4010) input2 write(*,4015) o u t l 4000 format(a80) 4010 format(lx,'===> Closing input f i l e : ',al2) 4015 format(lx,'===> Extracted data i s echoed i n f i l e : ',al2) c**************************************** c* Calculate nodal deltas from positions, c**************************************** k=l kbeam=29 do 90 n=2,kbeam delta(k)=statn(n)-statn(n-1) k=k+l 90 continue ksouth=44 do 95 n=31,ksouth delta(k)=statn(n)-statn(n-1) k=k+l 95 continue do 97 n=46,knorth delta(k)=statn(n)-statn(n-1) k=k+l 97 continue kmax=k-l 151 c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* Cal c u l a t e s t a t i o n mid-points f o r curvatures to be p l o t t e d c*********************************************************** 1=1 do 110 n=2,kbeam posn(l)=(statn(n)+statn(n-l))\/2 1=1+1 110 continue do 120 n=31,ksouth posn(l)=(statn(n)+statn(n-l))\/2 1=1+1 120 continue do 125 n=46,knorth posn(l)=(statn(n)+statn(n-l))\/2 1=1+1 125 continue lmax=l-l c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* Calculate cap beam curvatures from nodal rotations C* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * i = l j=l k=l 1=1 do 150 i=2,kbeam do 170 j=l,jmax p h i ( k , j ) = ( r o t n ( i , j ) - r o t n ( i - l , j ) ) \/ d e l t a ( k ) 170 continue k=k+l 150 continue c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* South column curvatures calculated c************************************ do 180 i=31,43 do 190 j=l,jmax p h i ( k , j ) = ( r o t n ( i , j ) - r o t n ( i - l , j ) ) \/ d e l t a ( k ) 190 continue k=k+l 180 continue do 200 j=l,jmax p h i ( k , j ) = ( r o t n ( l , j ) - r o t n ( i - l , j ) ) \/ d e l t a ( k ) 200 continue k=k+l c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c* North column curvatures calculated c************************************ do 210 i=45,imax do 220 j=l,jmax p h i ( k , j ) = ( r o t n ( i , j ) - r o t n ( i - l , j ) ) \/ d e l t a ( k ) 220 continue k=k+l 210 continue do 230 j=l,jmax p h i ( k , j ) = ( r o t n ( 2 9 , j ) - r o t n ( i - l , j ) ) \/ d e l t a ( k ) 230 continue Q* ************* * *************************************** c* Write curvatures to ex.out f o r p l o t t i n g and ana l y s i s c****************************************************** write(kout2,4500) i n p u t l write(kout2,4510) (fact(j),j=l,jmax) write(kout2,4512) (xtran(j),j=l,jmax) do 250 k=l,28 write(kout2,4515) posn(k),(phi(k,j),j=l,jmax) 250 continue write(kout2,4520) do 260 k=29,42 write(kout2,4515) posn(k),(phi(k,j),j=l,jmax) 260 continue write(kout2,4530) do 270 k=43,kmax write(kout2,4515) posn(k),(phi(k,j),j=l,jmax) 270 continue write(*,4550) out2 4500 format(lx,'Data extracted from f i l e : ',al2,\/, lx,'Curvatures calculated are as follows:',\/\/, lx,'===> cap Beam Curvatures (1\/in) <===\u2022) 4510 format(lx,'Station ( i n ) | Load Factor =>',75(f8.4,3x,' 4512 format(13x,'|',6x,'X-tran =>',75(2x,f8.4,lx,',')) 4515 format(3x,f8.3,2x,*,',15x,75(fll.9,',')) 4520 format(lx,'===> South Column Curvatures (1\/in) <===\u2022) 4530 format(lx,'===> North Column Curvatures (1\/in) <===*) 4550 format(lx,'===> Curvature c a l c u l a t i o n s i n f i l e : ',al2 close(kout2) end ","@language":"en"}],"Genre":[{"@value":"Thesis\/Dissertation","@language":"en"}],"GraduationDate":[{"@value":"1996-05","@language":"en"}],"IsShownAt":[{"@value":"10.14288\/1.0050352","@language":"en"}],"Language":[{"@value":"eng","@language":"en"}],"Program":[{"@value":"Civil Engineering","@language":"en"}],"Provider":[{"@value":"Vancouver : University of British Columbia Library","@language":"en"}],"Publisher":[{"@value":"University of British Columbia","@language":"en"}],"Rights":[{"@value":"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https:\/\/open.library.ubc.ca\/terms_of_use.","@language":"en"}],"ScholarlyLevel":[{"@value":"Graduate","@language":"en"}],"Title":[{"@value":"Comparison of non-linear analytical and experimental curvature distributions in two-column bridge bents","@language":"en"}],"Type":[{"@value":"Text","@language":"en"}],"URI":[{"@value":"http:\/\/hdl.handle.net\/2429\/4261","@language":"en"}],"SortDate":[{"@value":"1996-12-31 AD","@language":"en"}],"@id":"doi:10.14288\/1.0050352"}