@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix dc: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Civil Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Seethaler, Markus"@en ; dcterms:issued "2009-01-17T20:22:39Z"@en, "1995"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """The Ministry of Transportation and Highways (MOTH) of British Columbia has initiated an upgrade program for its bridges. Among them is Oak Street Bridge, which spans the Fraser River between Vancouver and Richmond. The Ministry of Transportation and Highways of British Columbia decided to supplement the seismic assessment of the Oak Street Bridge by large scale tests of the bridge bents at the structures laboratories of the University of British Columbia. The proposed tests consists of slow cyclic loading through increasing displacements. The test series consists of five specimens of the Oak Street Bridge, with various retrofits and an as built version, and one as built specimen representing the Queensborough Bridge. A test setup to conduct the tests was designed and installed in the UBC structures laboratory. Predictions of the response of the prototype and the test specimen were conducted to establish a testing regime and loading sequence for the slow cyclic testing program. Various analysis methods were used to assess the seismic performance of the as built bridge bent. The first test, an as built model of the Oak Street Bridge bent, supplied the data of the experimental response to compare to the analytical predictions, and gave some further insight into the failure modes, and established the ultimate strengths. The severe deficiencies in shear reinforcement in the cap beam of the bents made an accurate prediction of the response of the bridge bent very difficult. The experimental investigation resulted in much improved understanding of the seismic performance of this very typical structural component of many bridge approaches in the Lower Mainland of British Columbia."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/3745?expand=metadata"@en ; dcterms:extent "6726006 bytes"@en ; dc:format "application/pdf"@en ; skos:note "C Y C L I C R E S P O N S E O F O A K S T R E E T B R I D G E B E N T S by MARKUS SEETHALER B.A.Sc, The University of Toronto, 1989 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 APRIL, 1995 ©MarkusF. Seethaler, 1995 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 £-j>t\\U €N£t i ' /vJ€g£4 The University of British Columbia Vancouver, Canada Date ^ • ATm): R = juA for short period structures (T sz CO $ m 5 0 0 4 5 0 4 0 0 3 5 0 3 0 0 2 5 0 2 0 0 150 100 50 0 i i F lexu r e | ' jf > \\ \\ A_| Sec t iona l Yie Iding I ^ h p o r l | O H CCU | r r I n 0 1 2 3 4 5 D i sp lacemen t at the Left Jo int (in) Fig. 3.16 Flexure and shear response of the bent. 3.8 Conclusions The desired response for this structure is a ductile flexural mechanism that ensures sufficient ductility to withstand the anticipated seismic loadings in a favourable way. The analysis of the various elements of the bent showed that the beam column joint, as well as the columns themselves, are not the critical elements. The cap beam however is suspected to fail in shear in a possible brittle manner at a lower base shear than flexural hinging will occur in the cap beam, which is definitely an undesired response. Nonetheless entirely different failure mechanisms are conceivable, for example a stagewise flexural degradation of the moment capacity due to debonding of the reinforcement or an nominal ductile shear failure. The experimental test series sheds some light onto these matters. C H A P T E R 4 D Y N A M I C A N A L Y S I S O F T H E P R O T O T Y P E 4.1 Introduction One of the more complex problems in reinforced concrete behaviour is the analysis of plastic nonlinear response to random excitations such as earthquakes. Plastic behavior of reinforced concrete by itself is difficult to deal with; dynamic effects only add to the complexity. To make an analysis at all manageable many simplifications have to be made. The difficulty arises as to what assumptions can be made and still capture the main features of the response. Two types of analysis were performed: a linear spectral analysis and a time step analysis. The non linear time step analysis lends itself to a comparison with the pushover analysis of the previous chapter. Such an analysis is performed on the prototype using three earthquake records which were modified to fit the surface spectral accelerations of the Oak Street Bridge. 4.2. DRAIN-2DX Commercially there are several general purpose finite element programs available such as ADINA, ABACUS, ANSYS, etc. They allow the user to define their own constitutive relationships and develop new element types. Most of these software programs however have evolved from a mechanical engineering perspective and support aspects such as heat transfer, stress concentration, etc. The program used in this project was DRATN-2DX which is geared towards structural engineering and can perform a nonlinear time step analysis as well as a spectral response analysis. It is available through the National Information Service for Earthquake Engineering (NISEE) at the Earthquake Research Center at University of California at Berkeley. 45 46 DRATN-2DX is one of the first programs to handle nonlinear time step analysis of two dimensional frames and was first developed in 1973 by Dr. Powell at UC Berkeley. In its newest release it now incorporates modules to calculate mode shapes and spectral responses. It features a very limited number of different elements i.e. truss element, beam-column elements, a simple connection element, a structural panel element, and a link element. There are no provisions to calculate hysteretic strength or stiffness degradation. 4.3 Spectral Analysis of the Prototype The Ministry of Transportation and Highways retained consultants to develop design spectra for the Oak Street Bridge. The surface spectrum applicable for bent S28 is the one for S31 depicted in Fig 4.1. 5% damping is assumed for this spectrum. Q I 1 I I I I I I I 0 0.5 1 1.5 2 2 .5 3 3.5 4 P e r i o d (sec) Fig. 4.1 Spectrum for Oak Street Bridge bent S31. The spectral analysis was performed with DRATN-2DX. The model uses a simplified system of masses (see Fig 4.2). 47 Model MS-V2 of the previous chapter is used here. The first five natural periods are listed in Table 4.1: Table 4.1 Natural periods for bent S28. Mode Period 1 0.69 sec 2 0.17 sec 3 0.12 sec 4 0.07 sec 5 0.04 sec The combined spectral response of five modes is superimposed with the dead load forces in Fig. 4.3 The maximum bending moments in the cap beam at the face of the columns are 6550 kip-ft and 5040 kip-ft for the negative moment and positive moment respectively. The axial load from the spectral analysis is 637 kips, which when 48 superimposed with the axial load of the dead load of 554 kips, yields 1190 kips in compression and 83 kips in tension for uplift. The bending moment for the column in compression at the top of the column just below the joint is 5500 kip-ft and at the bottom of the column is 6730 kip-ft. in the uplift case the bending moment at the top of the column is 5960 kip-ft, and at the bottom of the column it is 6990 kip-ft. The maximum horizontal spectral displacement at the beam/column joints is 3.5\". Fig. 4.3 Spectral analysis results including the dead load and the flexural capacities (bending moments in kip-ft). In Fig. 4.3 the demand from the spectral analysis is compared with the flexural capacities calculated in the previous chapter. The shaded areas indicate where the demand exceeds the capacity. In the left joint region the demand exceeds the capacity by the largest margin, which coincides with the location of the first hinge of the pushover 49 analysis. The second hinge at the right joint in the cap beam also shows a large demand/capacity ratio. The approximate yield displacement from the pushover analysis in the previous chapter is about 2\". The displacement ductility demand is therefore 1.75. This is a fairly low value but not uncommon in older concrete bridge bents. 4.4 Nonlinear Time Step Analysis of the Prototype The earthquake records supplied by the soil consultants have been modified to reflect site specific soil amplifications. An attempt is made to keep the computer models for both programs as similar as possible to the models used previously. The cross sectional properties including the parameters for the yield surfaces have been adopted from the sectional analyses in chapter 3. 4.4.1 Earthquake Records The soil consultants retained by the MOTH, Dames and Moore (1991), supplied a series of earthquake records for the Oak Street Bridge listed in Table 4.2. Table 4.2 Earthquake records for the Oak Street Bridge. Place Date Site PGA PGV San Fernando 9-Feb-1971 Griffith Park Observatory 0.180 0.205 San Fernando 9-Feb-1971 3838 Lankershim Blvd. 0.150 0.150 San Fernando 9-Feb-1971 231 Figueroa Street 0.200 0.167 These acceleration records are rock or firm soil records. Since the foundation of the bridge is on very soft soil, significant soil amplification is to be expected. When comparing the spectra of the records with the design spectrum of Figure 4.1 it is apparent that the design spectrum has incorporated some soft soil amplification. The acceleration 50 as well as the time base of these firm soil earthquake records are therefore scaled to obtain a spectral response closer to the design spectrum. The scaling factors for each record are listed in Table 4.3. In Fig 4.4 the spectra for the modified earthquake records are shown in comparison with the design spectrum. Table 4.3 Scaling factors. Record Acceleration Scale Time Scale Griffith Park Observatory 1.38 1.5 3838 Lankershim Blvd. 1.07 2.5 234 Figueroa Street 1.06 2.0 Period (sec) Fig. 4.4 Modified spectra. 4.4.2 DRATN-2DX Results The geometry and stiffness of the computer model are the same as the ones used for the spectral analysis. Minimal strain hardening is used. Also P-A effects were ignored in the following analyses. The time history analyses show yielding in the beams and eventually in the columns similar to the pushover analysis. The relative displacements between the top and bottom of the bent for all three earthquake records are plotted in Fi: 4.5 to Fig. 4.7. 10 20 25 30 15 Time (sec) Fig. 4.5 Relative displacement history (Griffith Park Observatory record) 52 0 5 10 15 20 25 30 35 40 Time (sec) Fig. 4.7 Relative displacement history (234 Figueroa Street record). The dynamic analysis of the prototype show that yielding occurs at various locations, but due to some strain hardening the computer model does not become unstable as soon as four hinges have developed and a mechanism has formed. The computer models survive the earthquake record to the end without collapsing. The displacements of the spectral modal analysis are some what higher than the ones from the dynamic time history analyses. The response at and beyond the first natural period is the determining factor for the dynamic performance, and the spectra of the modified acceleration records are smaller than the design spectra in that range, which explains this discrepancy. Therefore it is recommended to use the displacements obtained from the spectral analysis for determining the displacement demands even though these are elastic responses. C H A P T E R 5 P R E D I C T I O N O F T H E M O D E L S P E C I M E N B E H A V I O U R 5.1 Introduction This chapter introduces the test model and an assessment of its behaviour. The choice of suitable scale is discussed, followed by a number of analyses in order to develop a basis for understanding the performance of the test specimen. The elastic demands due to dead load and lateral load are determined in order to establish sectional forces. Flexural capacities are calculated using accepted analysis methods, with the aid of computer programs developed by CALTRANS. The effect of shear crack openings on flexural capacity is assessed, as it appears that this particular structure is rather vulnerable to this effect due to the many longitudinal bar cutoffs and low span/depth ratio. A push over analysis is performed with reduced flexural capacities induced by diagonal shear cracks. Sectional shear capacities are calculated using several design code expressions to establish the onset of shear failure. Shear combined with flexural behaviour is analyzed using the modified compression field theory. The anticipated response of the test specimen is governed by a not well understood moment shear interaction, which makes a conclusive prediction exceedingly difficult. 5.2 The Test Model It is usually not feasible to do experiments at full scale. In this particular test a scale of 0. 5 was initially selected as it results in dimensions suitable to the laboratory capabilities such as height of the available crane, and specimen weights that are manageable. Also, preliminary calculations showed that maximum loads at this scale were achievable with existing equipment. Due to height limitations of the testing facilities, the 53 54 model only represents the upper half of the columns with the cap beam. The inflection points of the prototype columns are assumed to be approximately at midheight and so the footings of the model are pinned at this location to allow rotation. The final scale factor chosen was 0.45 as this permits scaling of the prototype #11 bars to #5 bars in the model. The columns are 21.5\" square and have a height to the underside of the cap beam of 81\". The cap beam dimensions are 19\" by 27\" and the total length is 280\". A drawing of the model by Klohn-Crippen is shown in Appendix A. Loads are scaled so that stresses remain the same, thus they are scaled by the factor 0.452. The superimposed dead load from the superstructure of the prototype is 900 kips, adding the self weight of the cap beam of 133 kips the total self weight is 1033 kips at the tops of the columns. The total dead load required to achieve the same stresses in the model columns is 209 kips. The self weight of the model cap beam and the testing frame setup is 14 kips. The additional dead load that must be applied through the dead load system is 209 - 14 = 195 kips. For each of the five dead load points 39 kips are required. 5.3 Elastic Demand Calculations Figure 5.1 shows a diagram of a portion of the specimen, and identifies column regions, general beam regions, a haunch region, and a joint region. To account for cracking of the concrete the flexural stiffness were reduced to 30% of the gross moment of inertia (Ig) for the cap beam general section and 25% of Ig for the column and the haunch section. The cross sectional properties are listed in Table 5.1. 55 RIGID B E A M C O L U M N J O I N T C O L U M N C E N T R E L I N E H A U N C H R E G I O N Fig. 5.1 Cap beam sections. Table 5.1 Sectional properties. Section Area (in2) I, (in4) % ofIe Cap beam - general 513 9,350 30 Cap beam - haunch 608 12,970 25 Column 462 4,450 25 The analytical model of the nodes and the elements is a scaled down version of the MS-V2 model in Chapter 3, depicted in Figure 5.2. 56 100 38.6 Fig. 5.2 Computer model for elastic demand calculations (forces in kips). Table 5.2 Computer model node coordinates. Node X- Coord Y- Coord Node X- Coord Y- Coord 1 0.00 94.50 17 223.00 94.50 2 8.00 94.50 18 233.00 94.50 3 27.13 94.50 19 252.87 94.50 4 46.25 94.50 20 272.00 94.50 5 57.00 94.50 21 280.00 94.50 6 67.75 94.50 22 57.00 0.00 7 72.50 94.50 23 57.00 29.75 8 81.25 94.50 24 57.00 59.50 9 94.75 94.50 25 57.00 70.25 10 117.38 94.50 26 57.00 81.00 11 140.00 94.50 27 223.00 0.00 12 162.62 94.50 28 223.00 29.75 13 185.25 94.50 29 223.00 59.50 14 198.75 94.50 30 223.00 70.25 15 207.50 94.50 31 223.00 81.00 16 212.25 94.50 32 140.00 135.00 57 For purpose of elastic demand calculations, a loading consisting of the vertical dead loads and a lateral load of 100 kips was used. The results of an elastic analysis are shown in the Figures 5.3 to 5.6. The column shear forces and bending moments for the dead load are omitted since they are insignificant. 57.9 1 1 •— 1 19.3 38.6 38.6 19.3 57.9 Fig. 5.3 Shear force diagram for the dead load (forces in kips). 45 Fig. 5.4 Bending moment diagram for dead load (moments in kip-ft). 58 50 50 ' — i — 56.9 Fig. 5.5 Shear force diagram for the lateral load of 100 kips (forces in kips). Fig. 5.6 Bending moment diagram for a lateral load of 100 kips (moments in kip-ft). From the geometry the shear demand in the mid portion of the cap beam for a given base shear Veq is 569 Vb=l93 + Ve flx— (5.1) 59 and the shear in the column is (5.2) 5.4 Flexural Analysis. A sectional analysis was carried out using CALTRANS's programs BEAM303 and COL604R. a) Flexural Capacities of the Cap Beam: The longitudinal reinforcement in the cap beam curtails rapidly both at the top and bottom. The moment capacity is calculated for each section that has different reinforcement and assumed to hold up to a point where the cutoff bars are able to develop their yield strength. For #5 bars the development length is given by ACI318-89 code as A theoretical difference between top and bottom bars is neglected here for simplification and thus the development length was taken as 12\". The results of the sectional analysis of the cap beam are listed in Table 5.3 for both positive and negative moment. The material properties were adapted from in situ tests of the existing bridge bent as mentioned in Chapter 3. The ultimate concrete strain was set to 0.005 as recommended by Paulay and Priestley (1992). The position given in Table 5.3 is the distance from the face of the column to the point where the bars are fully developed. 0.042 VX7 8.40\" or/d 0.00039//, 12.2\" 60 Table 5.3. Moment capacities of cap beam. #top #bot top bot +My position -My position bars bars cover cover (+M) (-M) (in) (in) (kip-ft) (in) (kip-ft) (in) 11 4 2.08 1.0 163 1.25 391 12.25 9 6 1.90 1.0 237 31.75 344 20.25 7 7 1.63 1.0 275 42.25 279 27.25 6 9 1.63 1.28 340 46.25 237 37.25 4 11 1.63 1.43 395 60.25 160 47.25 2 13 1.63 1.92 439 66.25 88 60.25 For sections with little shear reinforcement, as soon as significant 45° shear cracks open, the negative moment capacity gets reduced to the moment capacity at a distance d (depth of the section) closer to the centre of the cap beam (see Fig 5.7). This moment capacity is shown in Fig 5.8 as the reduced moment capacity due to shear. Fig. 5.7 Bending moment reduction due to shear cracks for negative moment. Fig 5.8 also shows the moment demand for a series of values of lateral load Veq. Based on this figure, the cap beam should start to yield at a base shear a little less than 40 kips at about the quarter point of the cap beam due to the reduced moment capacity. 61 Somewhere above 40 kips of lateral load, enough shear cracks will develop to reduce the negative moment capacity. In positive bending, yielding would occur at about 70 kips lateral load. 7 2 . 2 5 \" Fig. 5.8 Flexural capacity/demand for the cap beam (push to the right). b) Flexural Capacity of the Column. The reinforcement remains the same over the height of the columns and so only one section had to be analyzed. Due to axial load effects, matching the capacity to the demand for the columns is an iterative process (see Table 5.4). 62 Table 5.4 Column capacity iterations. Veq P My-Capacity My-Demand A (kips) (kips) (kip-ft) (kip-ft) (kip-ft) 0 103.5 284 16 +268 100 184.8 338 353 -15 95 180.7 335 338 -3 96.5 182.0 336 342 -6 94.5 180.2 335 335 0 The critical base shear for the columns in flexure is 94.5 kips. By comparison, in Section 5.4 (a) it was seen that for purely flexural behavior, the critical region was the cap beam, where yielding would occur at an approximate base shear of 40 kips. 5.5. Push Over Analysis of the Test Model. DRATN-2DX was used to do a push over analysis of the model. The computer model is identical to the simple models used before. The negative moment yield values are the reduced yield moments at a distance d (depth of section) from the haunch towards the centre of the cap beam to account for a reduction in moment capacity due to shear cracking (see Table 5.5). Table 5.5 DRAJJN-2DX cross sectional parameters for the test model. Parameters Cap Beam - general Cap Beam - haunch Column E (ksi) 4650 4650 4650 A (in2) 513 608 462.5 Ie(in4) 9350 12970 4450 Pc (kips) - - 2580 Pb (kips) - - 310 Mb (kip-in) - - 5088 +M y (kip-in) 1870 1800 2665 -My (kip-in) 2750 5500 2665 Pt (kips) - - 248 63 The load deflection results of the pushover analysis are plotted in Fig. 5.9. The two hinges to form a mechanism in the bridge bent develop in close sequence of increasing base shears. The first hinge occurs at the right hand side of the cap beam in the region of the maximum negative moment, assuming the lateral load is applied from the left to the right. The second hinge presents itself at the left hand side in the region of maximum positive moment. An ultimate base shear of around 65 kips can be sustained by this model of the bridge bent in flexural manner. The push over analysis assumes that the critical section is just at the face of the column, but as can be seen in Fig 5.8 the critical section is closer to the quarter point of the cap beam, which has a lower sectional moment capacity than the one at the face of the column. This explains the higher ultimate base shear for the push over analysis. The aspect of shear is explored in the following section. 64 5.6 Shear Capacity. The sectional shear capacity was computed using the ACI318 and the ACI/ASCE shear formulae. Since the axial load of the column depends on the lateral load, which in turn determines the shear in the column, some iterations are required to find the shear capacity and the corresponding axial load; assuming the load is governed by shear. a) ACI 318-89 : (imperial units). V. = Kfyd V=2 2000,4 b) ACI/ASCE: (imperial units) (5.3) (5.4) (5.5) v = v + v +v Kfyd Vc=(0*$ + 12Qpw)f£bwd Vp = 0.2P (5.6) (5.7) (5.8) (5.9) The shear calculations were done for a typical cap beam and a column section. The parameters are listed in Table 5.6. 65 Table 5.6 Cross sectional parameters. Parameter Cap Beam Column Gross areaAg(in) 513 462.25 Effective height d (in) 23 17.2 Width bw (in) 19 21.5 Concrete strength f'c (psi) 6000 6000 Reinforcement yield strength fy (psi) 50,000 50,000 Shear reinforcement Av (in) 0.08 0.051 Tie spacing s (in) 16 5.375 Reinforcement ratio pw 0.00363 0.0537 Axial load P,NU (lb.) 0 varies The two codes yielded quite different results. The ACI/ASCE approach results in a lower base shear failure load as indicated in Table 5.7. V„ is the sectional shear capacity of various sections. To normalize the results the corresponding base shears Veq were calculated. Table 5.7 Shear capacities. Section Code Vn VeQ Cap Beam ACI 318 73.5 95.3 ACI/ASCE 49.3 52.7 Column ACI 318 65.3 130.6 ACI/ASCE 54.1 108.2 It should be noted that all code shear formulae assume a minimum amount of shear reinforcement at a minimum stirrup spacing of d/2, in this case 13.5 in. The provided stirrup spacing in the middle of the cap beam is 16 in. The minimum shear reinforcement for the cap beam section at that spacing should be 0.31 in . The transverse reinforcement 2 provided is 0.08 in . Very little research has been conducted with lightly reinforced concrete members subjected to large shears (see Pessiki et al. (1990)). 66 To find some bounds on the capacity of the bent the ACI/ASCE approach was chosen. In this approach the shear capacity is dependent on the amount of tension steel in the section, which accounts for the contribution of the longitudinal steel towards the shear capacity of the section. The shear capacity is then dependent on how much of the tension steel has been mobilized to withstand the negative bending of the cap beam. An increase in lateral load increases the negative moment near the centre of the beam. At exact centre, M„eg is zero due to lateral load. Since the negative steel curtails towards the centre of the beam, fewer and fewer bars are available to resist the longitudinal demand from the shear. Therefore the shear capacity diminishes towards the middle of the cap beam. The code formula (e.g. 5.5) is conservative in this region due to low bending moments. At a fairly low base shear of 35 kips the shear capacity exceeds the demand close to the centre of the cap beam as shown in Fig 5.10. Since Table 5.7 and Fig. 5.10 are based on the ACI/ASCE code approach the significance of the longitudinal reinforcement on the shear capacity becomes apparent. For the columns there is no cutoff of the reinforcement. The shear capacity is to some extent dependent on the axial load, which in the ACI/ASCE formula is accounted for in the Vp term of equation (5.9). Some iterations are required to obtain the critical base shear corresponding to the minimum shear capacity. For any of the code approaches, shear in the columns is not predicted to be the critical failure mode. 67 80 60 a. x co 20 CENTRE OF CAP BEAM ^ 1 SHEAR CAPACITY GOVERNED BY TOP STEEL SHEAR CAPACITY GOVERNED BY BOTTOM STEEL - i I— o 0 z SHEAR DEMAND FOR gj LATERAL LOAD OF j 50 m 35 kips 200 -150 -100 — z U J -50 7% 100 BENDING MOMENT DEMAND FOR A LATERAL LOAD OF 35 kips Fig. 5.10 Shear analysis for the cap beam at a lateral load of 35 kips. The shear formulae used by these codes are conservative in their estimation of the shear capacities. Usually the highest shear occurs near supports. For simple supported beams there is virtually no bending moment at the supports, whereas for continuous beams the highest moments occur near the supports. The ACI/ASCE code formula takes this into account to make the shear capacity dependent on the amount of longitudinal steel, which usually corresponds to the bending moment demand in the region. 5.7 Modified Compression Field Theory. Here the capacities of the cap beam are analyzed based on the modified compression field theory similar to Chapter 3 using the program RESPONSE. Three sections with different steel areas were chosen for the sectional analysis. The locations of these sections are at the points of the full development of the top reinforcement and are shown in Fig. 5.11. 68 © 0 © Fig. 5.11 Sections for the RESPONSE analysis. The reinforcement of the individual sections is listed in Table 5.8. Table 5.8 Reinforcement in the analysis sections. Section No. of Top Bars No. of Bottom Bars Av fin*) On) 1 9 4 0.19 7.4 2 6 4 0.13 13.5 3 4 7 0.08 16 From the elastic force demand calculation earlier in the chapter the moment/shear ratios were determined and are used here to analyze the interaction between shear and flexure (see Table 5.9), similar to Chapter 3. 69 Table 5.9 Elastic demand constants and ratios. Cap Beam Section No dN/dV Mo dM/dV Vo dVo/dV LEFT 1 2.4 0.0 44.6 +4.69 33.9 1.76 LEFT 2 2.4 0.0 44.5 +3.56 33.9 1.76 LEFT 3 2.4 0.0 44.5 +2.44 33.9 1.76 RIGHT 1 2.4 0.0 44.6 -4.69 -33.9 1.76 RIGHT 2 2.4 0.0 44.5 -3.56 -33.9 1.76 RIGHT 3 2.4 0.0 44.5 -2.44 -33.9 1.76 The RESPONSE results are listed in Table 5.10. Table 5.10 RESPONSE results. Cap Beam Section Veq M V N kips kip-ft kips kips LEFT 1 81.1 170.2 26.8 2.2 LEFT 2 91.8 161.8 32.9 2.4 LEFT 3 141.6 193.7 61.2 2.4 RIGHT 1 80.3 -259.8 64.9 2.3 RIGHT 2 71.9 -169.4 60.1 2.4 RIGHT 3 69.2 -98.4 58.6 2.9 The critical base shear of 69.2 kips is governed by the RIGHT 3 section and is significantly higher than the 35 kips obtained from the ACI/ASCE approach and the 40 kips obtained by the modified sectional capacity analysis also at the quarter point of the cap beam. The negative flexural capacity of 98 kip-ft for the RESPONSE analysis is only slightly higher than the critical moment capacity of 88 kip-ft from the CALTRANS's program BEAM303. RESPONSE however gives an ultimate force state at which the section fails, whereas BEANO 03 provides an idealized yielding response. 70 It is difficult to estimate to what degree the bending moment capacity is reduced due to shear. Some of the shear is resisted by the longitudinal steel, partly as a tension tie in the traditional shear truss model, and partly as a simple dowel action. A rather crude estimate of the onset of nonlinear behavior is 40 Kips of base shear and the maximum expected base shear is about 70 kips. Nevertheless considering all the uncertainties the testing program is very much justified. C H A P T E R 6 T E S T S E T U P 6.1 Introduction The test set up was specifically designed to carry out the experiment on the Oak Street Bridge Bent Test at the UBC Structures Laboratories. The scale of 45% and the outside expected performance envelopes were established by Klohn-Cripppen. The fabrication of the specimens was tendered out to a local contractor and was done off-site. The contractor had to meet some stringent material specifications to ensure reasonable representation of the existing structure. The test frame was designed as part of this thesis and was contracted out to a local steel fabricator. The data acquisition system relies upon the available system in the structures labs at UBC. 6.2 Material Properties of the Test Specimen The contractor was given a window for the concrete strengths of 4.8 to 5.5 ksi. Obtaining reinforcement steel at a yield strength of 50 ksi was more difficult. The contractor had to get the main reinforcing steel in the United States. The ties and stirrups are standard wire sizes and could be procured in Canada. The wires had to be annealed to reach the required yield strengths. This proved to be more complicated than anticipated, since the original yield strengths of the material and the consequent cold working was not exactly known. Some experimenting was required. However in one of the batches the yield strength was very close to the desired values. 71 72 6.3 The Loading Frame The test setup, shown in Fig 6.1, was designed specifically to test the specimens representing a typical two column bent of the Oak Street Bridge at a scale of 0.45. Klohn-Crippen set the maximum lateral design load to 150 kips and the maximum displacement to ± 3\" for all the specimens, including the retrofitted ones. A hydraulic jack with a stroke of 12\" and a capacity of 225 kips was available. The reaction frame was designed for the full jack capacity; the remainder of the test setup was designed for the 150 kips. Since the test program is particularly interested in the cap beam and the beam column joint response, an important concern was the lateral load application into the cap beam. A triangular load truss was devised to introduce the lateral loads. The vertical dead loads were introduced at five bearing points. Since the bearings at the footings simulated the inflection points of the columns, they had to provide freedom of rotation, but withstand uplift. 6.3.1 Reaction Frame. The reaction frame system consists of two A-frames connected at the top by a spreader beam onto which the actuator is attached. Some lateral bracing perpendicular to the main axis of the test setup provides lateral stability and enough strength to temporarily brace the specimen for erection. Both supports and the reaction frame are tied together at the floor level; the A frames are therefore self equilibrating for the lateral loads, but rely on the strong floor for vertical reactions to resist overturning. 73 1V-10 3/4\" Fig. 6.1 Test setup. 74 6.3.2 Dead Load System. The vertical dead load was applied at all five superstructure bearing points. The outer two loads on both ends of the specimen were applied using a spreader beam system on each side of the specimen and the center load was applied by a single actuator. All jacks were fed in series through one hydraulic loop and the pressure was controlled with one manual hydraulic reducing valve. To attain the required load of 39 kips, the hydraulic pressure in the jacks was set at 2412 psi. 6.3.3 Load Distribution System The consultants on the project assumed that only the two first interior supports of the bridge bent closest to the columns will transfer the lateral load of the bridge deck into the bent. For this reason, a triangular truss was chosen to carry actuator lateral load to the test specimen. Since some concrete dilation was expected, the load application system was designed as a determinate triangular truss. The connections of the truss elements were not pinned, but the flexibility of the members was assumed sufficient to allow for expansion of the cap beam. Oversized holes in the gusset plates make it possible to readjust the position of the truss after several load cycles. The truss was designed to withstand the maximum expected lateral load of 150 kips. 6.3.4 Bearing Assembly. The supports of columns were to simulate inflection points and therefore allow for rotational freedom, but restrain vertical and horizontal movement. Since the system is statically determinate vertically, only the horizontal reactions had to be measured. Refer to Figure 6.2 for the details of the bearing assembly. The whole bearing assembly rested on a lubricated Teflon pad, which allowed for horizontal movement, but the assembly was held in place by a thick reaction plate, which was strain gauged. It was essentially a load cell. The friction load on the Teflon pads increases with an increase of vertical load. 75 Before the first test, some calibration runs were conducted to find the correlation. The friction on the Teflon pads was very sensitive to the vertical load and it was unfortunately not very linear. At the time of the calibration, only the dead load was available to impose some vertical load; therefore the bearings could be calibrated for only a small range of vertical loads. THREADED STUDS GROOVED SOLE PLATE GROOVED ROCKER PLATE REACTION PLATE 3/8\"x101/2\"x101/2\" TEFLON PAD ELEVATION CONCRETE SPECIMEN 7/8\" THREADED STUD NOT SHOWN ABOVE FOR CLARITY LUBRICATED TEFLON PAD 1 1/2\" ATLAS SUPERIOR SHAFTING PIN x 6\" LONG SECTION A-A Fig. 6.2 Bearing assembly. 76 6.4 Data Acquisition The data acquisition system collects and measures the signals from physical sensors mounted on the specimen. The signals are conditioned, converted from analog to digital, and then stored. 6.4.1 Data Acquisition System Components Physically the system consists of five main components, a personal computer with a large hard drive, software, a signal conditioning unit including an analog to digital converter, a data acquisition board, and a large number of transducers and strain gauges, which are the actual sensors. The personal computer controls the data acquisition board driven by the software and stores the data as a ASCII file on the hard drive. In this experimental setup the computer has a 486DX 66 MHz CPU and local buses with a 210 MB hard disk. The software is a commercial data acquisition software, Lab VIEW (Laboratory Virtual Instrumentation Workbench). This program allows the user to customize his/her requirements by using virtual instruments. Instead of a written program code the program is discretized in fundamental tasks and put together with icons symbolizing the virtual instruments to one data acquisition program. The data acquisition board is mounted in the personal computer and is a multifunctional I/O board (AT-M10-16X) with an analog to digital converter and timing I/O functions. The signal conditioning unit converts and feeds the collected signals from the various data acquisition devices as an analog signal to the data acquisition board. The basic conversion in signal conditioning is amplification and filtering of the signal. The 77 system used here is called SCXI (Signal Conditioning extensions for Instrumentation) and is a high performance, multi channel system for the PC-based data acquisition board. The transducers of the physical data acquisition devices sense any applicable physical stimulus. In this particular case there were about seventy strain gauges which were mounted to the reinforcing steel, about ten displacement transducers, and three load cells. 6.4.2 External Instrumentation Six LVDT's (Linear Variable Differential Transducers) and four LMP's (Linear Motion Potentiometers) were used to measure external displacements of the specimen during the test. • LOADGELL • LVDTorLMP Fig. 6.3 External instrumentation locations. 78 The location of the LVDT's and LMP's is depicted in Fig 6.3. Four LMP's are located at the center of the joints to measure the vertical and horizontal displacement of the two joints. An LVDT was mounted to the jack and used in the loading system to control the jack movements during displacement control. Five LVDT's were placed at the north joint to read joint distortions. A load cell was placed between the jack and the loading truss to measure the load applied by the horizontal jack and was used for the actuator control under load control. For the first test this load cell did not function. Two pressure transducers were placed into the hydraulic system of the loading jack. Unfortunately this system did not compensate for the friction in the jack, which had to be removed at a later stage from the recorded data. Since the system was statically determinate vertically but indeterminate horizontally it was desirable to measure the shear in the columns by measuring the horizontal reactions through the instrumented bearings. Unfortunately the signals from these strain gauges turned out to be very noisy. 6.4.3 Internal Instrumentation About seventy strain gauges were mounted on reinforcing steel throughout the specimen as depicted on Klohn-Crippen drawing Q117-SK2 (see Appendix A). In addition, six strain gauges were placed on two aluminum strips as shown on Fig. 6.4. These aluminum strips measure internal deformations in the joint and provided a correlation with the measured external joint distortions, and were installed as shown in Fig. 6.5 in an attempt to determine joint cracking stresses, and draw conclusions on external crack patterns. ALUMINUM PLATE 3\"x1\"x1/8\" ALUMINUM SHEET 1/8\"x3/8\" STRAIN GAUGE JVWW. \"WWW WWV\\T 6\" * *• 2\" 6\" -X-Fig. 6.4 Internal deformation measurement. INTERNAL LVDT's Fig. 6.5 Arrangement of internal gauges. 80 6.5 Data Processing The data acquisition program was recently purchased by the Department of Civil Engineering at the University of British Columbia. At this time the collection of about 90 data channels is possible. The output is a simple ASCII file with all the channels readings in separate columns. The readings are all voltages between -10 Volts and +10 Volts. The standard 60 Hz analog filter, which filters the noise from the power supplies, caused a tracking problem; i.e. certain channels would overshadow adjacent channels, and therefore the filter could not be used. This resulted in considerable noise in the records. Because of the large amount of data a FORTRAN program called DP (Data Processing) was written by the author to filter the original data and to reduce the amount of data by eliminating close data points (see Appendix C). The filtering routines were adapted from Press et al. (1989). The program first reads the raw data into a large array, each channel in a separate column, which is then run through a smoothing subroutine channel by channel. The subroutine initially removes any linear trend in the data. Then it uses a Fast Fourier Transform to low-pass filter the data, and the linear trend is reinserted at the end. The user specifies a smoothing constant, which specifies the number of points over which the data is smoothed. After some experimenting, the smoothing constant was set to 15, which gives, in the opinion of the author, a reasonable fit. After the data is smoothed the voltage readings are converted to physical units, i.e. strains, displacements, and forces. Finally the data is reduced by deleting data points that lie close together. For this routine up to 20 control channels with associated different limits for the tolerance can be chosen. The result is then stored as an ASCII file. Fig. 6.6 demonstrates the effects of the filtering processes; the noisy raw data is converted to smooth filtered data. 81 -0.15 -0.17+ -0.27 TIME Fig. 6.6 Filtering on a sample of data. 6.6 Load Application (Load History) The testing procedure was in essence to load the test specimen to sequences of three cycles of lateral load or displacement at increasing predetermined levels until the specimen failed. The separate steps of the conduct of the test are discussed in more detail in Chapter 7. For this first test the load cell, which was used to control the actuator under load control, was not functional and the entire test had to be done under displacement control. The LVDT used for displacement control was on the loading jack and so the elastic deflection of the frame had to be taken into consideration in calculating the specimen displacement required for the various loading stages. The general philosophy was to have a few load sequences in the elastic range in order to calibrate the system and establish the reliability of the data acquisition system, before proceeding to the first yield level. Usually one can estimate the yield forces quite easily, but yield displacements are more difficult to predict, due to the uncertainties of the 82 actual stiffness degradation caused by the cracking of the concrete. A common approach is to load to 75% of the estimated yield load under load control, measure the displacement, and extrapolate this to the yield displacement (see Fig. 6.7). The remainder of the testing is conducted under displacement control with sequences at multiples of the yield displacement leading to a history of displacement ductility levels. W 0.75 vy ^ Actual Response ^ Idealized Response 0.75 Ay Ay Joint Displacement (in) Fig. 6.7 General test responses. Table 6.1 shows the target loading history of the first test. A more detailed account of the actual test loads and displacements are given in Chapter 7. One should note that since the first test was conducted entirely under displacement control, only a very crude estimate of the 75% of yield could be made and consequently an exact yield point was not clearly established. Table 6.1 Target loading sequence for the first test. SEQ A (in) Comments C 0.04 D 0.08 E 0.12 40 kips F 0.20 50 kips G 0.25 65 kips 1.0 Ay H 0.45 1.5 Ay I 0.65 2.0 Ay J 0.90 3.0 Ay K 1.25 4.0 Ay C H A P T E R 7 I N T E R P R E T A T I O N O F T E S T R E S U L T S 7.1 Introduction The discussion is restricted to the first test of the series, the as-built model of Oak Street Bridge Bent S28. Some of the data acquisition devices responded quite well, notably the LVDTs (Linear Variable Displacement Transducer) and the LMPs (Linear Motion Potentiometer) on the joints and the actuator, as well as the pressure transducers in the hydraulic system of the lateral load actuator. Most of the other devices however gave fairly noisy responses. The LVDTs arranged at the joint at the North end registered very little joint distortions. The two internal LVDTs placed in the same joint also showed very small signatures. Also, no visual cracks were observed at the joints, which indicates that the beam/column joints did not undergo any significant deformations. The column shear load cell readings were noisy but a trend could be detected. Most of the strain gauges mounted on the reinforcement gave recordings throughout the test; only a very few did not function from the start. The detailed observations of the test are listed in Table 7.1, which references a few photographs taken during the test. The load deflection curves were developed as a primary record of the response of the test specimen. To ascertain the working condition of the strain gauges a closer examination was made of the strain gauges on the top of the cap beam. The measured maximum strains for a particular sequence in the elastic range at various locations along the cap beam were compared to the analytical values at the same base shear. Finally an explanation of the failure of the specimen is attempted. 84 85 7.2 Event Table The test was broken up into sequences denoted by ascending letters as described in Table 7.1. Each sequence represents two to three cycles at one load level. Cycle A pushes to the North (right) and cycle B pulls to the South (left). At the beginning of all the sequences, all the load control devices were balanced and zeroed, i.e. the load cell, the pressure transducers and the LVDT on the lateral jack. The scan rate for the data acquisition system was set to 2 scans per second. When first switched on, about 50 scans of the whole system were recorded and the dead load was slowly applied. Another 50 scans are taken with only the dead load in place before the lateral load is applied. The load was manipulated by a load controller which in turn controls a servo valve in the hydraulic loop of the lateral load actuator. The load application follows a preset loading function generated by a separate unit. Usually a sinusoidal wave form is used so that the load application slows down at its peaks allowing observation of the specimen at the critical instances. The load was held at the peak of each cycle to mark the cracks on the specimen with felt pens and to take pictures. The data acquisition system was turned off at the end of each sequence and a preliminary data analysis was done to ensure that the data had been properly recorded. This process was repeated for each sequence. A detailed account of all the observations during the test is given in Table 7.1. A series of photographs were taken throughout the test. A few of them are compiled in Appendix B. 86 Table 7.1 The Event Table. SEQ C Y C A (in) LD (kips) H Comments Photo A low level loading sequence B low level loading sequence C 0.04 20 low level loading sequence D 0.08 30 few flexural cracks developed on the top of the cap beam E 1A 0.12 40 development of 45deg shear cracks at the top of the north end of the cap beam and flexural cracks on the bottom of the south end of the cap beam IB more cracks developing opposite and symmetrical to cycle 1A 3A no more additional cracks 3B no more additional cracks B. l F 1A 0.20 50 few more shear cracks IB only a few more cracks G 1A 0.25 65 1.0 more cracks, the load seemed to be dropping off when holding at the max IB same as above 3B the shear cracks in the cap beam were widening to 0.9 mm (one major crack on the north end of the beam); some of the shear cracks were now horizontal at the top of the cap beam and indicating debonding of the top reinforcement close to the centre of the beam B.2 H 1A 0.45 1.5 major shear crack at the back of the specimen IB major shear crack opening on the top and the side, crack widths 4.0 mm 3A shear cracks at the north end 2.0 mm 3B shear crack width 4.0 mm I 1A IB 0.65 2.0 shear crack widths 7.0 mm shear crack widths 7.0 mm B.3 B.4 SEQ : Sequence CYC: Cycle A : Joint Displacement in inches. LD : Target Load in kips ju : Ductility Level 87 Table 7.1 The Event Table (continued). SEQ C Y C A (in) L D (kips) Comments Photo J 0.90 3.0 before starting the loading the top A-frame was readjusted by undoing the 12 bolts on the north side; some release was observed; the concrete dilated a little and the frame put some constraint onto the beam 1A shear crack width 12.0 mm; some of the wiring on the reinforcing became visible in the cracks; the load was slowly decreasing while holding at the max. displacement; spalling on the back side IB the load was still decreasing while the displacement is on hold; severe bulging and debonding on the top of the beam at the south end. the shear cracks reach 13.0 mm; after removal of lose concrete, rebar became exposed 2A more spalling 2B a large piece of concrete fell off at the middle of the cap beam and exposed reinforcing steel 3A more spalling B.5 3B more spalling, rubble was falling into the cracks B.6 K 1A 1.25 4.0 severe cracking, the specimen started to fall apart; debonding at the top of the beam, shear failure occurred and the load dropped to zero B.7 IB dramatic damage, but the load could still be held in this direction B.8/B.9 SEQ : Sequence CYC: Cycle A : Joint Displacement in inches. LD : Target Load in kips //: Ductility Level 88 7.3 Load - Deflection Curves The overall response of the bent is best represented by load deflection curves, which plot the total lateral loads against the average horizontal joint displacements. Since the lateral load was measured by the pressure transducers in the hydraulic loop of the loading jack, the load readings include the friction in the hydraulic system. The friction acts against the direction of the jack movement and therefore leads to higher load readings than actually applied onto the specimen. Comparing loading and unloading sequences in the purely elastic range an average friction component of 5 kips was detected, which was manually removed from the jack load readings. The base shears given in the following discussions are corrected for the friction. Table 7. 2 Loading history. SEQ Base Shear expected (kips) Base Shear measured (kips) jack disp. (LVDT) expected (in) jack disp. (LVDT) measured (in) expected joint disp. (in) measured joint disp. (in) C 20 0.14 0.10 D 30 29 0.21 0.18 0.15 0.08 E 40 33 0.28 0.22 0.20 0.12 F 50 43 0.35 0.34 0.25 0.19 G 65 48 0.46 0.43 0.33 0.25 1 H 57 0.63 0.67 0.50 0.46 1.5 I 55 0.80 0.85 0.67 0.63 2 J 45 1.06 1.16 0.93 0.90 3 K 14 1.36 1.24 1.25 4 Since the load cell on the main actuator was not functional, the entire test had to be performed under displacement control. The displacement is controlled by the feed back from the LVDT mounted on the lateral load actuator. These jack displacements also 89 include a component from the elastic deflection of the reaction frame which was analytically determined to be 0.02\" per 10 kips. Later on it was discovered however that the elastic deformation of the frame is closer to 0.03\" per 10 kips. A first yield was anticipated at 65 kips at a joint displacement of 0.33\". The expected and the actual load history is listed in Table. 7.2. Several shear cracks in the cap beam started to form at a relatively low level, sequence E, at a base shear of 33 kips (see photo B. 1 and Fig. 7.1). This coincides with an anticipated shear failure from the analysis. From that point on there is a slight stiffness degradation up to sequence G, the estimated yield displacement based on flexural yielding. Large cracks started to form on the top of the specimen indicating debonding of the top reinforcement (see photo B.2). The little vertical reinforcement provided was not sufficient to confine the longitudinal steel. At ductility level 1.5, sequence H, the hysteresis loops start to open up showing plastic deformation. Strength was still increasing and the maximum base shear of about 60 kips was reached at that point. The first cycle of sequence I (u=2.0), see Fig. 7.2, shows little strength degradation, however the following cycles show severe strength degradation. The debonding of the top reinforcement progressed with each load cycle. Degradation continued with each cycle of sequence J and then on the first cycle of sequence K the beam failed completely at the negative moment (south) end. At this stage the bent continued to carry the dead load and could still resist a small amount of lateral load as the north end of the beam had not yet failed. At the failed south end the shear was being carried by tension in the bottom bars, see Photo B.8 and B.9. At the ultimate load stage virtually complete strength loss was observed in a brittle shear failure of the cap beam. BASE SHEAR (Kips) Fig. 7.1 Load deflection curve up to sequence H. O O O O o O O 00 CO ^* CM cjl ^ Cp BASE SHEAR (kips) Fig. 7.2 Load deflection for 0SB1. 92 An envelope of the load deflection plots is shown in Fig 7.3 and compared to the results of the monotonic push over analysis of the model. It is seen that the actual maximum lateral load is somewhat lower than the calculated one. IB CL DC S5 CO LU CO < m 80 60 40 20 0 -20 -40 -60 -80 -1.5 / . LOAD DEFLECTION ENVELOPE \\ s \\ A \\ IPI ISH OX/PR AM Al Y S I S 1 . // -0.5 0 0.5 JOINT DISPLACEMENT (in) 1.5 Fig. 7.3 Load deflection envelope for OSB1. From the above Fig. 7.3 it can be seen that the initial stiffness of test specimen was somewhat higher than the assumed cracked one of the computer models. This is due to the effects of crack development and the associated stiffness degradation. On average however the predicted stiffness of the model is a fair representation up to the yield level. Realistically the structure failed as soon as the strength started to degrade in sequence H. The test specimen hence reached a displacement ductility of about 1.5, which is comparable to analytical displacement ductility of 1.75. At ductilities over 2 serious strength degradation was observed. This indicates adverse hysteretic behaviour, which the computer programs used herein are not able to model. Others have made attempts to capture this response pattern with some success (Kunnath et al. (1992), and Stone and 93 Taylor(1993)). The hysteresis loops indicate that the as-built bridge bent shows little energy absorption and very poor ductile behaviour. 7.4 Strain gauge results Most of the strain gauges were functional throughout the test and only a few saturated when their capacity was exceeded. From the visual observations during the test, two regions of the cap beam experienced serious damage. One is the region of shear failure just outside the haunches and the other is at the top of the cap beam, where the top reinforcement debonded at the final stages of the test. The shear failure region has very little shear reinforcement and the data from the few strain gauges is inconclusive. The strains along the top show consistent readings through most of the test until the final stages when the gauges saturated. The maximum tension strain readings are depicted in Fig. 7.4 and Fig. 7.5 up to the sequence when one of the strain gauges reached saturation. For the exact strain gauge location refer to Klohn-Crippen's Drwg Q l 17-SK2 in Appendix A. io u io w io u n co co » - CM co io to r- co cn I— I— I— I— I— I— I— h- l— CO CO CO GO CO CO CD GQ CD DISTANCE FROM CENTRELINE OF COLUMN Fig. 7.4 Strain gauge reading, top reinforcement at south end, negative moment. 94 SEQC SEQ D SEQ E -•-SEQ F - • SEQ G -o-SEQ H -o-40 20 0 DISTANCE FROM CENTRELINE OF COLUMN (in) Fig. 7.5 Strain gauge reading, top reinforcement at north end, negative moment. The maximum strains nearly reached the yield strain 0.0017. From these strains the actual forces in the reinforcing bars can be calculated. Assuming an effective sectional depth of 0.8/i, the bending moments in the section can be estimated as shown in Fig. 7.6 and Fig. 7.7. Fig 7.6 Bending moments in the cap beam at the south end of specimen. 95 Fig. 7.7 Bending moments in the cap beam at the north end of specimen. One would expect the largest moments to be at the face of the column, but the measured bending moments seem to dip in haunch region, even though the larger effective depth in this region has been taken into account. In Fig 7.8 the measured bending moments in the cap beam at a base shear of 33 kips (sequence E) are compared against the bending moments obtained from a elastic push over analysis at the same base shear. This low ductility level was chosen to demonstrate the working conditions of the strain gauges in the mostly elastic range of the test, since the analytical responses are more accurately defined. As can be seen there is reasonable agreement between the experimentally determined moments and the calculated moments, although at one point there is up to a 100% difference between the north end and the south end. Since during the entire test the 60 Hz analog filters were turned off and the sampling rate was only 2 Hz, the small signatures of the strain gauges were severely corrupted. Therefore the strain gauges for 96 this test are not a very reliable data acquisition device and at best can only indicate a trend, but by no means give an exact account of the strains they measure. Notable is the slight reduction in the measured bending moments just at the face of the column in the haunch region. 180 i Distance from Centre of Column (in) Fig 7.8 Bending moments in the cap beam at base shear 33 kips. 7.5 Comments on the Response of the Test Specimen The largest axial strains in the top rebar of the cap beam are at about the quarter point of the cap beam. This is also where most of the cracking occurred and near to a cutoff point. Initial flexural cracks developed into diagonal shear cracks in the later sequences of the test. The strain gauges attached to the stirrups in this area never seemed to register any strains vertically. The diameter of these stirrups is very small and there were no gauges right at the main diagonal crack; local yielding was the main effect on these bars. Inasmuch as neither the concrete alone provides enough capacity nor the 97 insufficient contribution of the vertical shear reinforcement, the longitudinal reinforcement added significantly to the shear capacity of the section. The failure at ultimate load was a brittle shear failure of the cap beam. The shear reinforcement at that stage was ruptured. After failure, the specimen was held together by tension in the highly deformed lower reinforcing bars. Very little cracking occurred in the beam column joints indicating that the weak element in the existing structure is definitely the cap beam. Strength retrofits of the beam and columns will put higher forces into the joints. At this stage the ductile performance of the joints is questionable due to just nominal shear reinforcement and the difficulty to strengthen the haunch region adequately. Locally the columns might still show some undesirable debonding of the main reinforcement due to the nominal confinement of the column reinforcing steel. C H A P T E R 8 C O N C L U S I O N S 8.1 Introduction This work represents the first part of a large scale testing program at UBC on the as-built and retrofitted concrete bridge bents of the Oak Street Bridge. The objective of this phase of the project was to determine the performance parameters of the intended test series, to design and implement the test setup, and to test and analyze the first test specimen, an as-built specimen. The preliminary findings indicate severe ductile deficiencies and a brittle failure mechanism at ultimate loads, which confirms initial assessments and emphasizes the need for seismic upgrading of the existing structure. When the Ministry of Transportation and Highways of British Columbia decided to pursue testing as part of the upgrading efforts of the Oak Street Bridge, the structural consultants Klohn-Crippen and representatives from UBC's structural engineering group in Civil Engineering had to decide on the scope and design parameters of the test series. Testing was deemed to be cost effective due to the large number of similar structural elements not only found in the Oak Street Bridge, but also in the Queensborough Bridge. The test specimens were to model the cap beam and parts of the columns to the first inflection point of a typical prototype bridge bent. 8.2 Analytical Predictions The analysis considered a typical prototype bent and the scaled experimental test model. Preliminary assessment and dynamic analysis was conducted on the prototype. The test model was analyzed to find the response parameters for the design of the test set up and for later comparison to the test results. 98 99 A general seismic assessment of the prototype using the 1961 AASHO design guidelines and the 1983 ATC-6 bridge design code shows a dramatic increase in seismic lateral load demand over that time period. For the original design seismic loadings were preempted by wind loadings. ATC-6 puts a lateral load demand of 470 kips on the structure, for which it was clearly not designed. Deficiencies were identified in the cap beam and the columns of the bridge bent for loads much less than the ATC-6 values. A member capacity assessment of the beam, column, and the beam/column joint indicates flexural hinging in the cap beam at a lower base shear demand than from ATC-6. The predicted hinge region in the cap beam is very poorly reinforced for shear and was suspected to have a very poor ductile response. The push over analysis using cracked sectional properties taking only flexure into account shows a first yield at 378 kips and an ultimate load of475 kips. A shear strength analysis based on the compression field theory unveiled a much lower critical base shear of 243 kips. The nonlinear dynamic analysis using three modified earthquake records gives similar ultimate loads to the push over analysis and yields a displacement ductility of 1.75, which is very low but not uncommon in older concrete structures. It was realized that this concrete structure does not meet modern minimum requirements for longitudinal and transverse reinforcement and therefore the imaginable failure mechanisms are some what dubious. In order to conduct the test yield levels and estimates of the ultimate loads and displacements had to be determined to establish a load application history. Investigating various assessment approaches a first flexural yielding the cap beam for the test model was estimated around 40 kips. The compression field theory gives an ultimate base shear of 69 kips. It is difficult to predict to what extend the longitudinal reinforcement contributes to the shear capacity and thus the interaction of flexure and shear in a poorly reinforced regions in the cap beam. The experimental tests 100 series was therefore very much justified to determine the actual response of the bridge bent. 8.3 Test Setup As part of this research various retrofit schemes were to be investigated. The maximum estimated responses were based on an assumed full retrofit using overstrength material properties. The design criteria of the test setup for strength and deflection were derived from these conservative predictions. At the time of the completion of this thesis all the test specimens have been tested and the test setup has performed to its specifications. The only defect was an eccentricity in the loading A-frame mounted to the specimen, due to inherent construction tolerances of the connection points on the test specimen itself. The loading frame started to deform laterally due to this secondary effects and had to be strengthened with a diagonal brace. In hindsight, a much greater lateral stiffness in the loading frame would have been better. A large data acquisition program was installed to record the displacement, force, and strain gauge measurements. The analysis of all the data will take quite some time and is currently being undertaken by other graduate students at UBC. A first and brief look at the readings indicate that most of the devices were functional through out the test. Since the test setup is indeterminate in the horizontal direction, some effort was put into measuring the lateral forces at the bottom column supports and still provide a rotational degree of freedom. The device provided pinned supports, and was instrumented to establish lateral reaction at each pin. Unfortunately the calibration for lateral load was crude to be of use. 101 8.4 Test Results The definition of yielding in this test is some what ambiguous. There is no distinct hinging pattern apparent. The specimen gradually developed severe cracks in the cap beam just outside the haunches. Based on the load displacement curves, the best way to define yielding is a significant deviation from the linear response, which occurred at sequence 'G ' at a measured base shear of 48 kips and a joint displacement of 0.25 in. The ultimate load was attained at sequence 'H ' at 57 kips and a displacement of 0.47 in. The following sequences showed rapid deterioration and strength degradation until the specimen failed at a base shear of 14 kips and a displacement of 1.25 in. Assuming failure as soon as strength degradation sets in a displacement ductility of 1.88 was found, which compares well with the predicted one of 1.75. Scaling the ultimate capacity to the actual bridge bent gives a base shear capacity of 281 kips, which is very much below modern lateral load demands of 470 kips. The hysteresis loops are pinched and the severe strength degradation clearly indicates the poor ductile response and the ineffective energy absorption of the as built bridge bent. Considering this very low ductility of the structure one has to assume that the lateral load demands have to be resisted essentially in the elastic region to provide a satisfactory seismic performance, which is clearly not the case here. Seismic upgrades of some sort are therefore necessary. Preliminary investigation of all the strain gauges show that most of the gauges were functional through out the test. A closer look at the gauges at the top of the cap beam revealed quite large discrepancies of up to 100% for symmetrical placed gauges, which should read similar strains. The data obtained from these gauges are to be considered with some reservation and only a trend at best in the response can be derived from these readings. 102 8.5 Conclusions The Oak Street Bridge, built in the 1950's, was recognized by the British Columbia Ministry of Transportation and Highways as being seismically deficient by today's standards. The deficiencies are in the lateral load carrying capacity, the lack of control over failure mode, and in many of the details of the steel reinforcement. The details of the reinforcing steel and the corresponding lack of ductility make a prediction of the response very difficult. This is further complicated by the fact that there are no readily accepted standards for retrofit design of bridges for improved seismic behaviour. For these reasons, the Ministry of Transportation and Highways, upon the advice of their consultants, decided that a program of experimental testing would be an effective way to determine the actual performance of the concrete bridge bents of the approach spans. The undertaking here is twofold; first to find a reasonable approach to predict the response analytically, and secondly to carry out an experimental test program to establish the actual capacity and ductility of a scaled model of the bridge bent. Various analytical examinations of the prototype and model bridge bent uncovered serious deficiencies in the cap beam. A push over analysis based on a purely flexural response shows an ultimate base shear capacity slightly below elastic (unit force reduction factor; R = 1) demands to current standards (ATC-6). However a simple shear analysis predicts a failure at a much lower base shear level and a non ductile brittle response can therefore be expected. Since there is so little transverse shear reinforcement in the cap beam, much less than the modern design guidelines require, conventional shear analyses are not quite applicable. A more refined approach based on the compression field theory indicates an interaction between shear and flexure and hence a reduction in flexural capacity due to demands on the longitudinal reinforcing bars from the shear. Yet a concise prediction of the failure mechanism in the cap beam still remains quite difficult. A 103 dynamic analysis using various modified earthquake records reveals fairly small displacement ductilities of less than two (< 2), which is not uncommon for older concrete structures. All the above analyses point at a very poor ductile response to lateral loads. The experimental test program was initiated to determine the actual response parameters and secondly to proof test a few retrofit schemes based on findings of the as built specimen. The first test, an as built one, confirmed the predicted low ductility and also the brittle response of the cap beam with little energy absorption. Also found was a significant strength degradation due to debonding of the longitudinal, which is credited to the poor confinement of the main rebars. The uncertainties to predict a response of older structures in particular to seismic attack invariable makes experimental testing the only satisfying approach to obtain their seismic response. The aspect of retrofitting these deficient structures is an even less understood issue and inspires ongoing research all over the world. B I B L I O G R A P H Y 1. AASHO 1961, Standard Specification for Highway Bridges, Washington, DC, American Association of State Highway Officials, 1961. Ed. 8, 2. ACI/ASCE Committee 426, Suggested Revisions to Shear Provisions for Building Codes, American Concrete Institute, Detroit, 1978, pp. 88. 3. ATC-6, Applied Technology Council \"Seismic Design Guidelines for Highway Bridges,\" Report ATC-6, Washington DC, Federal Highway Administration, 1981. 4. Byrne, P.M., \"Seismic Loading, Soil Modeling and Analysis,\" Proceedings of the Seismic Soil/Structure Interaction Seminar (CSCE), Vancouver, May 29, 1993. 5. Chai, Y.H., Priestley, M.J.N, and Seible, F., \"Seismic Retrofit of Circular Bridge Columns for Enhanced Flexural Performance,\" ACI StructuralJournal, v 88 n 5, 1991, pp. 572-584. 6. Choi, C.-K. and Kwak, H.-G., \"The Effect of Finite Element Mesh Size in Nonlinear Analysis of Reinforced Concrete Structures,\" Computers and Structures, v 36 n 5, 1990, pp. 807-815. 7. Clough, R.W. and Penzien, J., Dynamics of Structures, New York, McGraw-Hill, 1975. 8. Collins, M.P. and Mitchell D., Prestressed Concrete Structures, New Jersey, Prentice Hall, 1991. 9. Collins, M.P., \"Towards a Rational Theory of RC Members in Shear,\" Journal of the Structural Division, ASCE, v 104 n ST4, 1978, pp. 649-666. 10. Commentary J : Effects of Earthquakes, Supplement to the National Building Code of Canada 1990, Ottawa, National Research Council of Canada, 1990. pp. 202-220. 104 105 11. Crippen International Ltd., \"Oak Street Bridge No. 1380 - Two-Column Bent Test Program - Comparison of Five Major Bridges,\" Report prepared for the Ministry of Transportation and Highways of British Columbia, 1993. 12. Dames and Moore, \"Geotechnical Study and Seismic Evaluation - Oak Street Bridge,\" Final Report to the Ministry of Transportation and Highways of British Columbia, 1991. 13. Filippou, F.C. and Fenves, G.L., \"Nonlinear Static and Dynamic Analysis of Reinforced Concrete Members, Subassemblages and Structures,\" Seismic Workshop in San Diego 1990, pp. 195-202. 14. Filippou, F .C , \"Models of Nonlinear Static and Dynamic Analysis of Concrete Freeway Structures,\" Seismic Design and Retrofit of Bridges, Seminar Proceedings, Berkeley, 1992. 15. Hu, H.-T. and Schnobrich, W.C., \"Nonlinear Analysis of Cracked Reinforced Concrete,\" ACI Structural Journal, v 87 n 2, 1990, pp. 199-207. 16. Kunnath, S.K.; Reinhorn, A.M. and Lobo, R.F., IDARC Version 3.0 : A Program for the Inelastic Damage Analysis of Reinforced Concrete Structures (NCEER 92-0022), Buffalo, N. Y., National Centre for Earthquake Engineering Research, 1992. 17. Mander, J.B., Priestley, M.J.N, and Park, R , \"Theoretical Stress-Strain Model for Confined Concrete,\" ASCE Journal of Structural Engineering, v 114 n 8, 1988, pp. 1804-1826. 18. Mitchell, D., Tinawi, R. and Sexsmith, R.G., \"Performance of Bridges in the 1989 Loma Prieta Earthquake. Lessons of Canadian Designers,\" Canadian Journal of Civil Engineering, v 18 n 4, 1991, pp. 711-734. 19. Paulay, T. and Priestley, M.J.N., Seismic Design of Reinforced Concrete and Masonry Buildings, New York, John Wiley & Sons, 1992. 106 20. Paulay, T., Park, R. and Priestley, M.J.N., \"Reinforced Concrete Beam-Column Joints under Seismic Actions,\" ACIJournal Proceedings, v 75 n 11, 1978, pp. 585-593. 21. Pessiki, S.P.; Conley, C.H.; Gergely, P. and White, R.N., Seismic Behavior of Lightly-Reinforced Concrete Column and Beam-Column Joint Details (NCEER 90-0014), Buffalo, N.Y., National Center for Earthquake Engineering Research, 1990. 22. Powell, G., \"Observations on the Practical Application of Nonlinear Analysis,\" Seismic Design and Retrofit of Bridges, Seminar Proceedings, Berkeley, 1992. 23. Powell, G.H., DRAIN-2D user's guide, Berkeley, CA, Earthquake Engineering Research Center, University of California, 1973. 24. Press, William H.; Teukolsky, Saul A.; Flannery, Brian P. and Vetterling, William T., Numerical Recipes, The Art of Scientific Computing (FORTRAN Version), Cambridge, Cambridge University Press, 1989. 25. Priestley, M.J.N, and Calvi, G.M., \"Towards a Capacity-Design Assessment Procedure for Reinforced Concrete Frames,\" Earthquake Spectra, v 7 n 3, 1991, pp. 413-437. 26. Priestley, M.J.N, and Seible, F., \"Design of Seismic Retrofit Measures for Concrete Bridges,\" Seminar on Seismic Assessment and Retrofit of Bridges, Report SSRP -91/03, San Diego (UCSD), 1991, pp. 197-250. 27. Priestley, M.J.N., \"Seismic Assessment of Existing Concrete Bridges,\" Seminar on Seismic Assessment and Retrofit of Bridges, Report SSRP -91/03, San Diego (UCSD), 1991, pp. 82-149. 28. Schultz, A., \"Experiments on Seismic Performance of RC Frames with Hinging Columns,\" ASCE Journal of Structural Engineering, v 116 n 1, 1990, pp. 125-145. 29. Seed, R.B. and Dickenson, S.E.,\"Site-Dependent Seismic Site Response,\" Proceedings of the SecondAnual Seismic Research Workshop (CALTRANS), Sacramento, March 16 - 18, 1993. 107 30. Seible, F. and Priestley, M.J.N., \"Damage and Performance Assessment of Existing Concrete Bridges under Seismic Loads,\" Proc. U. S.-Japan Seismic Retrofit Workshop, 1990, pp. 203-222. 31. Stevens, N. J., Uzumeri, S.M., Collins, M.P. and Will, G.T., \"Constitutive Model for Reinforced Concrete Finite Element Analysis,\" ACI Structural Journal, v 88 n 1, 1991, pp. 49-59. 32. Stone, W.C. and Taylor, A.W., Seismic Performance of Circular Bridge Columns Designed in Accordance With AASHTO/CALTRANS Standards, Gaithersburg, MD, National Institute of Standards and Technology, 1993. 33. Vecchio, F.J. and Collins M.P., \"Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear,\" ACI Journal, Proceedings, v 83 n2, 1986, p. 219-231. 34. Vecchio, F.J. and Selby, R.G., \"Toward Compression-Field Analysis of Reinforced Concrete Solids,\" ASCE Journal of Structural Engineering, v 117 n 6, 1991, pp. 1740-1758. A P P E N D I X A S T R U C T U R A L D R A W I N G S Structural drawings Q l 17-01 and Q l 17-11 from KLOHN-CRIPPEN. 108 A P P E N D I X B P H O T O G R A P H S O F T H E F I R S T T E S T 112 Photograph B.2 Sequence G - Cycle 3B Photograph B.4 Sequence I - Cycle 3B Photograph B.6 Sequence J - Cycle 3B A P P E N D I X C D P - P R O G R A M C . l The DP Program c *********************************************** C DATA PROCESSING PROGRAM C VERSION 4.1 C 27. OCTOBER 1993 C *********************************************** C This program t r i e s to smooth the data with an weighted average C and conversion to actual u n i t s . Add the data reduction routine. C Try to compile i t with the Lahey compiler PROGRAM DATAFAB C *** VARIBALE DEFINITION INTEGER NCH, NCHCH, TYPE(100), I, J, K, N, NMAX REAL F(3,100), DATA(2048,100) , DLTCH(20), TOL(20), CHCH(20,3) REAL STRG, LDCELL, LVDT, LMPS, FOOTING, LINPOT, AVG, DIFF REAL PTS, DELTA, VALUE C REAL ZERO CHARACTER TITLE*40, FCNT*12, FIN*12, FOUT*12, DATE*10 CHARACTER DES(100)*8 LOGICAL SAVE c _ C *** READ COMMAND LINES WRITE (*,*) 1 THIS IS A DATA FABRICATION PROGRAM' WRITE (*,*) ' BY MARKUS SEETHALER' WRITE (*,*) ' 1 WRITE (*,*) ' ENTER THE CONTROL DATA FILE NAME : ' READ (*,*) FCNT WRITE (*,*) ' ENTER THE INPUT FILE NAME : ' READ (*,*) FIN WRITE (*,*) ' ENTER THE OUTPUT FILE NAME : ' READ (*,*) FOUT C . C *** READ CONTROL DATA FILE OPEN(UNIT=5,FILE=FCNT,STATUS='OLD') WRITE(*,*) ' READING THE CONTROL DATA FILE' READ (5, ' (A40) ') TITLE WRITE(*,*) ' ',TITLE READ (5, ' (A10) ' ) DATE 118 119 READ(5,*) NCH READ (5,*) PTS DO 10 1=1,NCH READ(5,1000) DES(I) 1000 FORMAT (A8) 10 CONTINUE DO 20 1=1,NCH READ(5,*) TYPE(I), (F(J,I),J=l,3) 20 CONTINUE READ(5,*) NCHCH DO 25 1=1,NCHCH READ(5,1500) (CHCH(I,J),J=l,3),TOL(I) 1500 FORMAT (313,4X,F8.3) 25 CONTINUE CLOSE(UNIT=5) C *** OPEN THE DATA FILES WRITE (*,*) ' OPENING THE FILES' OPEN(UNIT=6,FILE=FIN,STATUS='OLD') OPEN(UNIT=7,FILE=FOUT,STATUS='UNKNOWN') C *** PROCESS THE DATA FILE C ** READING THE DATA IN WRITE (*,*) ' READING THE DATA' N = 1 30 CONTINUE READ(6,*,END=40) (DATA(N,J),J=1,NCH) N = N +1 GOTO 30 40 CONTINUE NMAX = N - 1 C *** RUN THE SMOOTH ROUNTINE ON ONE COLUMN WRITE (*,*) ' SMOOTHING THE DATA1 DO 50 J = 1,NCH CALL SMOOFT(DATA(1,J),NMAX,PTS) 120 50 CONTINUE c C *** DATA CONVERSION TO ACTUAL UNITS WRITE (*,*) ' CONVERSION OF THE DATA TO REAL UNITS' DO 90 J=1,NCH IF (TYPE(J) .EQ. 1) THEN DO 100 K = 1,NMAX DATA(K,J) = STRG(DATA(K,J),F(1,J)) 100 CONTINUE ELSE IF (TYPE(J) .EQ. 2) THEN DO 110 K = 1,NMAX DATA(K,J) = LDCELL(DATA(K,J),F(1,J)) 110 CONTINUE ELSE IF (TYPE(J) .EQ. 3) THEN DO 120 K = 1,NMAX DATA(K, J) = LVDT (DATA(K, J) , F (1, J) ) 120 CONTINUE ELSE IF (TYPE(J) .EQ. 4) THEN DO 130 K = 1,NMAX DATA(K,J) = LMPS(DATA(K,J),F(1,J)) 130 CONTINUE ELSE IF (TYPE(J) .EQ. 5) THEN DO 140 K = 1,NMAX DATA(K,J) = FOOTING(DATA(K,J),F(1,J)) 140 CONTINUE ELSE IF (TYPE(J) .EQ. 6) THEN DO 150 K = 1,NMAX DATA(K,J) = LINPOT(DATA(K,J),F(l,J)) 150 CONTINUE ELSE WRITE (*,*) 'WE HAVE A PROBLEM!!!' STOP END IF 90 CONTINUE c C *** DATA OUTPUT WRITE (*,*) ' DATA OUTPUT' WRITE(7,1100) TITLE 1100 FORMAT (A40) WRITE(7,1200) DATE 1200 FORMAT (A10) WRITE(7,1300) 'SCAN',(DES(J),J=1,NCH) 1300 FORMAT(A7,100(1, 1 ,A8)) SAVE = .TRUE. DO 160 K = 1, NMAX DO 170 I=1,NCHCH IF (CHCH(I,2) .EQ. 1) THEN VALUE = DATA(K,CHCH(1,1)) ELSE IF (CHCH(I,2) .EQ. 2) THEN VALUE = AVG(DATA(K,CHCH(1,1)),DATA(K,CHCH(I,3))) ELSE IF (CHCH(I,2) .EQ. 3) THEN VALUE = DlFF(DATA(K,CHCH(1,1)),DATA(K,CHCH(1,3))) END IF DELTA = ABS(VALUE - DLTCH(I)) IF (DELTA .GE. TOL(I)) THEN SAVE = .TRUE. DLTCH(I) = VALUE ENDIF 170 CONTINUE IF (SAVE) THEN WRITE (7,1400) K,(DATA(K,J),J=1,NCH) 1400 FORMAT(' ',15,100 ( ' , ' , F l l . 6 ) ) WRITE(*,*) 'SCAN : ',K SAVE = .FALSE. END IF 160 CONTINUE c C *** CLOSING UP SHOP WRITE(*,*) ' THIS IS THE END OF STORY, SO FAR' CLOSE (UNIT=6) CLOSE (UNIT=7) STOP END c SUBROUTINE SMOOFT(Y,N,PTS) C *** Smooths an array Y of length n, with a window od f u l l width order C PTS neighboring points, a user supplied value, Y i s modified PARAMETER(MMAX=2 04 8) DIMENSION Y(MMAX) 122 M=2 NMIN=N+2.*PTS I IF(M.LT.NMIN)THEN M=2*M GO TO 1 ENDIF IF(M.GT.MMAX) PAUSE 'MMAX too small' CONST=(PTS/M)**2 Y1=Y(1) YN=Y(N) RN1=1./(N-l.) DO 11 J=1,N Y(J)=Y(J)-RN1*(Y1*(N-J)+YN*(J-1) ) II CONTINUE IF(N+l.LE.M)THEN DO 12 J=N+1,M Y(J)=0. 12 CONTINUE ENDIF M02=M/2 CALL REALFT(Y,M02,1) Y(1)=Y(1)/M02 FAC=1. DO 13 J=1,M02-1 K=2*J+1 IF(FAC.NE.0.)THEN FAC=AMAX1(0.,(1.-CONST*J**2)/M02) Y(K)=FAC*Y(K) Y(K+1)=FAC*Y(K+1) ELSE Y(K)=0. Y(K+1)=0. ENDIF 13 CONTINUE FAC=AMAX1(0.,(l.-0.25*PTS**2)/M02) Y(2)=FAC*Y(2) CALL REALFT(Y,M02,-1) DO 14 J=1,N Y(J)=RN1*(Yl*(N-J)+YN*(J-l))+Y(J) 14 CONTINUE RETURN END c SUBROUTINE REALFT(DATA,N, ISIGN) C *** Fourier transform w/ r e a l numbers. REAL*8 WR,WI,WPR,WPI,WTEMP,THETA DIMENSION DATA(*) THETA=6.28318530717959D0/2.0D0/DBLE(N) 123 Cl=0.5 IF (ISIGN.EQ.1) THEN C2=-0.5 CALL F0UR1(DATA,N, +1) ELSE C2=0.5 THETA=-THETA ENDIF WPR=-2.0D0*DSIN(0.5D0*THETA) **2 WPI=DSIN(THETA) WR=1.ODO+WPR WI=WPI N2P3=2*N+3 DO 11 1=2,N/2+1 11=2*1-1 12=11+1 I3=N2P3-I2 14=13+1 WRS=SNGL(WR) WIS=SNGL(WI) H1R=C1*(DATA(II)+DATA(13)) H1I=C1*(DATA(I2)-DATA(I4)) H2R=-C2*(DATA(12)+DATA(14)) H2I=C2*(DATA(I1)-DATA(I3)) DATA(II)=H1R+WRS * H2 R-WIS * H21 DATA(I2)=H1I+WRS*H2I+WIS*H2R DATA(13)=H1R-WRS*H2R+WIS*H2I DATA(I4)=-H1I+WRS*H2I+WIS*H2R WTEMP=WR WR=WR*WPR-WI*WPI+WR WI=WI*WPR+WTEMP*WPI+WI 11 CONTINUE IF (ISIGN.EQ.1) THEN H1R=DATA(1) DATA (1) =H 1R+DATA (2 ) DATA (2 ) =H1R-DATA (2) ELSE H1R=DATA(1) DATA (1)=C1* (H1R+DATA (2) ) DATA(2)=C1* (H1R-DATA(2) ) CALL FOUR1(DATA,N,-1) ENDIF RETURN END SUBROUTINE FOUR1(DATA,NN,ISIGN) REAL*8 WR,WI,WPR,WPI,WTEMP,THETA DIMENSION DATA(*) N=2*NN 124 j=l DO 11 1=1,N,2 IF(J.GT.I)THEN TEMPR=DATA(J) TEMPI=DATA(J+l) DATA(J)=DATA(I) DATA (J+l) =DATA (1+1) DATA(I)=TEMPR DATA(I+1)=TEMPI ENDIF M=N/2 1 IF ((M.GE.2).AND.(J.GT.M)) THEN J=J-M M=M/2 GO TO 1 ENDIF J=J+M 11 CONTINUE MMAX=2 2 IF (N.GT.MMAX) THEN ISTEP=2*MMAX THETA=6.28318530717959D0/(ISIGN*MMAX) WPR=-2.D0*DSIN(0.5D0*THETA) **2 WPI=DSIN(THETA) WR=1.DO WI=0.D0 DO 13 M=1,MMAX,2 DO 12 I=M,N,ISTEP J=I+MMAX TEMPR=SNGL(WR)*DATA(J)-SNGL(WI)* DATA(J+1) TEMPI=SNGL(WR)*DATA(J+1)+SNGL(WI)*DATA(J) DATA (J) =DATA (I) -TEMPR DATA (J+l) =DATA (1+1)-TEMPI DATA (I) =DATA (I) +TEMPR DATA (1+1) =DATA (1+1) +TEMPI 12 CONTINUE WTEMP=WR WR=WR*WPR-WI*WPI+WR WI=WI*WPR+WTEMP*WPI+WI 13 CONTINUE MMAX=ISTEP GO TO 2 ENDIF RETURN END c _ . REAL FUNCTION STRG (D,F) C *** COMPUTES THE STRAIN READING FOR STRAIN GAUGES C ARGUMENT DECLARATIONS REAL D,F(5) STRG = (D-F(3))/F(2)*4/F(l) RETURN END REAL FUNCTION LDCELL (D,F) C *** COMPUTES THE LOAD CELL READING C ARGUMENT DECLARATIONS REAL D,F(5) LDCELL = (D+F(2))*F(1) RETURN END REAL FUNCTION LVDT (D,F) C *** COMPUTES THE LVDT READING C ARGUMENT DECLARATIONS REAL D,F(5) LVDT = D*F(1) RETURN END REAL FUNCTION LMPS (D,F) C *** COMPUTES THE LMPS READING C ARGUMENT DECLARATIONS REAL D,F(1) LMPS = D*F(1) RETURN END REAL FUNCTION FOOTING (D, F) C *** COMPUTES THE FOOTING READING 126 C ARGUMENT DECLARATIONS REAL D,F(5) FOOTING = D*F(1) RETURN END REAL FUNCTION LINPOT (D,F) *** COMPUTES THE STRING LINEAR POT READING C ARGUMENT DECLARATIONS REAL D,F(5) LINPOT = D*F(1) RETURN END REAL FUNCTION AVG (A,B) C *** COMPUTES THE AVERAGE BETWEEN TO CHANNELS C ARGUMENT DECLARATIONS REAL A,B AVG = (A - B)/2 RETURN END REAL FUNCTION DIFF (A,B) C *** COMPUTES THE DIFFERENCE BETWEEN TWO CHANNELS C ARGUMENT DECLARATIONS REAL A, B DIFF = A - B RETURN END 127 C.2 User Guide The programs asks interactively for the filesnames of the control data file, the data file and the output file. A free format is used to read the data files. The output file has commas as delimiters. All files are ASCII files. T H E C O N T R O L DATA FILE GENERAL INFORMATION TITLE D A T E N C H PTS Alpha-numeric upto 40 character Alpha-numeric upto 10 character No. of data channels Smoothing constant D A T A CHANNEL DESIGNATION DES(l) DES(NCH) DATA CONVERSION TYPE (1),F(1..3,1) TYPE (NCH),F(NCH..3,1) F(l,*); Gauge Factor F(2,*); Excitation Voltage F(3,*); Offset TYPE = 2 ; Load Cell F(l,*); Scale Factor F(2,*) ; Offset F(3,*); N/A TYPE = 3 ; LVDT F(l,*); Scale Factor F(2,*) ; N/A F(3,*);N/A TYPE = 4 ; L V D T F(l,*); Scale Factor F(2,*); N/A F(3,*) ; N/A TYPE = 5 ; LMPS F(l,*); Scale Factor Designation of the data channels, Alpha-numeric upto 8 character TYPE: Data Acquisition Device F: Factors TYPE = 1 ; Strain Gauge F(2,*);N/A F(3,*);N/A TYPE = 6 ; Footing F(l,*); Scale Factor F(2,*) ; N/A F(3,*) ; N/A OUTPUT CONTROL NCHCH No. of output cheching controls CHCH(l,1..3),TOL(l) CHCH(NCHCFL 1. .3),TOL(NCHCH) CHCH(*,1) : First control channel No. CHCH(*,2) : Checking type = 1; just check first control channel = 2; average between first and second control ch. = 3; difference between first and second cntrl ch. TOL(*) : Tolerance of the output control. "@en ; edm:hasType "Thesis/Dissertation"@en ; vivo:dateIssued "1995-05"@en ; edm:isShownAt "10.14288/1.0050379"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Civil Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "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."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Cyclic response of Oak Street Bridge bents"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/3745"@en .