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Hinge zone tie spacing in reinforced concrete tilt-up frame panels Dew, Michael 2000

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HINGE ZONE TIE SPACING IN REINFORCED CONCRETE TILT-UP FRAME PANELS by MICHAEL DEW B.Sc. (ENG) (CIVIL) University of Cape Town, 1997 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 2000 ©Michael-John Dew, 2000 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, 1 agree that the Library shall make it freely available for reference and study. 1 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 Cl|/|i 6/1/ QH/Vef gt/VCr The University of British Columbia Vancouver, Canada Date ie AU\L DE-6 (2/88) ABSTRACT Tilt-up concrete buildings have concrete walls, supported on a concrete floor slab, and a light weight roof system. The exterior concrete walls, which are typically 190 mm thick with two layers of reinforcement, are cast on the floor slab and then lifted into position. Recently two storey panels with large window openings at both ground and first floor levels have become popular. The result is that the wall panels, n which form lateral load" resisting system, have become more like frames than walls. Given that the panels are typically only 190 mm thick, the members have very high depth to width ratios. The performance under cyclic earthquake loading of reinforced concrete frame members with these depth to width ratios is not well understood. Furthermore, since the code was written with more traditional cross sections in mind, the tie spacing rules it provides are not necessarily applicable to tilt-up frame panels. The frame panels are designed so that all inelastic deformations during an earthquake will result from flexural hinging in the frame members. The research reported in this thesis investigated the effect of hinge zone tie spacing on the displacement ductility of reinforced concrete tilt-up frame panels. The results of tests done on six full scale quarter frame panels with three different tie spacings are presented. The test specimens contained typical longitudinal reinforcement and were dimensionally representative of typical tilt-up frame panels. It was found that hinge zone tie spacing can determine the mode of failure and have a significant effect on panel ductility. The hinge zone tie spacings tested were 100 mm, 200 mm and 300 mm. The mode of failure for the 200 mm and 300 mm specimens was buckling of the longitudinal steel reinforcement in compression after the cover concrete had spalled. The 100 mm tie spacing was sufficiently close to prevent buckling of the longitudinal reinforcement after loss of the cover concrete. The 100 mm specimens failed via either local out of plane buckling of the entire hinge zone reinforcement cage, or by pullout of the longitudinal beam steel resulting from loss of bond within the hinge zone. It was found that the ultimate load attained and maintained during the ductile range was influenced by the tie spacing. The 100 mm and 200 mm tie spacing specimens attained and maintained a maximum bending moment similar to the ultimate flexural strength calculated assuming a maximum compressive strain in the concrete of 0.0035. The 300 mm tie spacing specimens only attained and maintained a bending moment approximately equal to that at first yielding of the longitudinal steel. Since the ductilities for the different tie spacings were calculated using different strength assumptions they are not directly comparable, nevertheless the full frame displacement ductilities achieved for the 100 mm, 200 mm and 300 mm tie spacings were 5.7, 3.9 and 4.7 respectively. n TABLE OF CONTENTS: Abstract List of tables List of figures Acknowledgments 1 Introduction 1.1 Origin of interest 1.2 Procedure of investigation 1.3 Scope and limitations 1.4 Plan of development 2 Problem definition 2.1 Description of type of Panel being researched 2.2 Expected mode of failure 2.3 Design procedure currently being applied 2.4 Applicability of code rules currently being applied 3 Literature review 3.1 Aim of review 3.2 Summaries of relevant articles 3.3 Conclusions of literature review 4 Mode of failure, test specimen, setup and procedure and material properties 4.1 Determination of mode of failure 4.2 Test specimen details 4.2.1 Classification of transverse reinforcement 4.2.2 Test panel configuration 4.2.3 Cross sectional dimensions and details of the test specimens 4.3 Test setup 4.3.1 Positions of supports for the test specimens 4.3.2 Hardware required for the test 4.4 Testing procedure 4.4.1 Loading procedure 4.4.2 Data recording 4.5 Material properties 4.5.1 Concrete properties 4.5.2 Reinforcing steel properties 5 Observed behavior during testing 5.1 Behavior common to all specimens 5.2 Behavior of 100 mm tie spacing specimens 5.2.1 1st Specimen 5.2.2 2nd Specimen 5.3 Behavior of 200 mm tie spacing specimens 5.3.1 1st Specimen 5.3.2 2nd Specimen 5.4 Behavior of 300 mm (and 2nd 200 mm) tie spacing specimens 5.4.1 Overall behavior of specimens 5.4.2 Specific behavior of 200 mm tie spacing specimen 5.4.3 Specific behavior of first 300 mm tie spacing specimen 5.4.4 Specific behavior of second 300 mm tie spacing specimen 6 Test results - Generation of leg load deflection plots 6.1 Assumptions used and plan of presentation of test results 6.2 Computation of top of leg deflections 6.2.1 Methods of computation of top of leg deflection 6.2.2 Top of leg deflection calculations for test # 1, first 200 mm specimen 41 6.2.3 Top of leg deflection calculations for test # 2, first 100 mm specimen 42 6.2.4 Top of leg deflection calculations for tests #'s 3-6 and evaluation of 42 methods used 6.3 Plotting of load vs. leg deflection graphs 43 6.3.1 Method of plotting of load vs. leg deflection graphs 43 6.3.2 Load deflection graph for test #1, first 200 mm specimen 44 6.3.3 Load deflection graphs for test #'s 2-6 44 6.4 Interpretation of strain readings taken during testing 44 6.4.1 Effectiveness of strain measuring method 44 6.4.2 Hinge zone strain readings 45 6.4.3 Beam strain readings 45 7 Interpretation and analysis of test results 56 7.1 Plan of presentation for result analysis 56 7.2 Comments on observed test behavior 56 7.3 Determination of yield point of leg 56 7.4 Development of bi-linear plots and method of determination of plastic 57 displacement of legs 7.5 Calculation of displacement ductility and corresponding force reduction factors 61 7.5.1 Displacement ductility defined 61 7.5.2 Determination of yield displacement of frame 62 7.5.3 Determination of ultimate displacement of frame 62 7.5.4 Calculation of ud and corresponding force reduction factors, R 63 8 Conclusions and recommendations 64 8.1 Mode of failure 64 8.2 Effect of tie spacing on ultimate load attained 64 8.3 Effect of tie spacing on ductility and buckling of longitudinal reinforcement 64 8.4 Effectiveness of test setup and testing procedure 66 8.5 Recommendations 66 Bibliography 67 Appendix I - Figures frequently referenced 68 Appendix II - Frame analysis at yield 74 Appendix III - Test Hardware 87 Appendix IV - Photographs 93 Appendix V - Test data 102 Appendix VI - Frame analysis for displacement at ultimate strength 116 iv LIST OF TABLES page 1. Yield moment for leg 18 2. Yield moment for beam 19 3. Yield moment for modified beam 20 4. Results of concrete testing done at UBC 29 5. Reinforcing steel test results 30 6. Test specimen behavior 32 7. Summary of behavior of 200 mm and 300 mm tie spacing specimens 37 8. Estimation of yield displacement 57 9. Ultimate flexural capacity of leg 60 10. Calculation of displacement ductilities and force reduction factors 63 LIST OF FIGURES 1. Test panel dimensions 22 2. Leg reinforcement 24 3. Test set-up forces 26 4. Load vs. Top of leg deflection - Test 1, 200 mm ties 43 5. Load vs. Top of leg deflection - Test 2, 100 mm ties 44 6. Load vs. Top of leg deflection - Test 3, 300 mm ties 45 7. Load vs. Top of leg deflection - Test 4, 300 mm ties 46 8. Load vs. Top of leg deflection - Test 5, 100 mm ties 47 9. Load vs. Top of leg deflection - Test 6, 200 mm ties 48 10. Leg displacement diagram 50 11. Load vs. leg deflection - Test 1, 200 mm ties 51 12. Load vs. leg deflection - Tests 2 - 6 52 13. Beam moment curvature - Test 6, 200 mm ties 54 14. 100 mm peaks and curve fit 59 15. 200 mm peaks and curve fit 59 16. 300 mm peaks and curve fit 59 1-1 Frame dimensions and bending moment diagram 69 1-2 Test setup 70 1-3 Reinforcement details 71 1-4 Load pattern 72 1-5 Load vs. leg deflection - Tests 2-6 73 v ACKNOWLEDGMENTS Research assistantship was provided by the Natural Sciences and Engineering Research Council through a research grant to Dr. R.G. Sexsmith. Further funding was provided in the form of the St. John's College Charles C C Wong Memorial Fellowship. Generous donations were made by local contractors and suppliers in terms of materials and time for the construction of the panels. Special thanks are extended to the following companies for their contributions: • Beedie Construction Co Ltd. for the construction of the panels. • Cut Rite Steel for the donation of and fixing of the panel reinforcement. • LaFarge Canada Inc. for the donation of the concrete. • Phoenix Trucking for the donation of shipping services. • Richform Construction Supply Co. Ltd. for the supply of the coil rods cast into the Specimen. • Steels Industrial Products Ltd. for donating the lifting inserts. • Sterling Crane for the lifting of the panels. A committee consisting of representatives from Structural Engineering Consultants of British Colombia (SECBC) consulting firms was formed to guide the testing program. The task of the committee was to identify the issues of concern to designers involved with tilt-up buildings, and to ensure the testing program was designed such that these issues were addressed. The committee was chaired by Gerry Weiler of Weiler Smith Bowers (WSB) Consulting Structural Engineers, and the following people attended the meetings in which the testing program was planned and/or reviewed. Dr. Robert Sexsmith UBC Dr. Perry Adebar UBC Michael Dew UBC James Lam Bianco Lam Patrick Lam CWMM Kevin Lemieux Weiler Smith Bowers Tim Loo Omnicron Jim Mutrie JKK Ron Thompson Read Jones Christofferson Gerry Weiler Weiler Smith Bowers Thanks are extended to the members of the SECBC committee for their involvement in this research and I would personally like to thank Dr. Sexsmith for his help as my thesis supervisor and Gerry Weiler for the guidance and support he provided over the course of this research project. vi 1 INTRODUCTION 1.1 Origin of interest In the past tilt-up concrete construction has been popular for warehouses and other buildings in which rectangular panels with few or no openings were appropriate. Tilt-up construction is however being increasingly used for two storey office buildings. For these buildings architects prefer panels with large window openings at both ground and first floor levels. The result is that many modern tilt-up panels are more like frames than walls. Since the panels are typically only 190 mm thick and the depths of the frame members can range between 800 mm and 1500 mm, the resulting frame members have depth to width ratios of between 4:1 and 8:1. In contrast, traditional concrete frame members have depth to width ratios of between 1:1 and 2:1. The code was written with traditional concrete cross sections in mind and some of the rules for tie spacings in the expected hinge regions are given in terms of member dimensions. When the code rules are applied to the members of tilt-up frame panels, the rules which are given in terms of least member dimensions almost always control. Thus the applicability of the code rules to the members of tilt-up frame panels is questioned. The relationship between hinge zone tie spacing and the displacement ductility of frames with members having depth to width ratios in excess of 2:1 has not been extensively tested. It was therefore decided to test a set of frame panel specimens under cyclic loads to evaluate what amount of transverse reinforcement is necessary in order to provide acceptable seismic resistance. The same size of reinforcing bars were used in all of the tests, but the spacing of the ties within the expected hinge region was varied. 1.2 Procedure of investigation A literature review was done and revealed that little testing has been done to investigate the relationship between tie spacing and ductility of frame members with large depth to width ratios. A key issue was to decide what hinge zone tie spacings should be tested. In order to detennine what tie spacings have been previously tested a literature review was done and the results of the review have been outlined in chapter 3. Six full scale test specimens which represented one quarter of a full frame panel were tested. All of the specimens were subjected to the same pattern of cyclic loading, applied at the bottom of the leg. Measurements which enabled the plotting of load vs. leg displacement graphs were recorded. Since it is reasonable to assume that all of the plastic deformation of the frame occurs in hinges which form in the leg members, the plastic displacement of the frame was estimated from the load vs. leg displacement plots. 1 Measurements which enabled the estimation of the elastic stiffness's of the frame members were also taken. Given the elastic stiffness's of the frame members, the frame yield displacement was obtained. Using the frame yield displacement, and the plastic displacements from the load vs. leg deflection plots, the displacement ductility of a full frame panel with the respective hinge zone tie spacing was estimated. Thus it was possible to observe the effect of hinge zone tie spacing on the ductility of tilt-up frame panels. 1.3 Scope and limitations Since the test specimens were expensive to construct and transport, it was considered reasonable to expect six specimens to be produced. It was decided to test three different hinge zone tie spacings, testing two specimens for each tie spacing. Thus the results of the testing done in this thesis cannot be considered to statistically significant, but do provide an indication of how the ductility of the frame members of tilt-up frame panels is related to hinge zone tie spacing. The following variables were kept constant in all of the test specimens; concrete strength, reinforcement grade, longitudinal reinforcement configuration, non hinge zone tie spacing, load sequence characteristics. A limitation of the test setup adopted was that the axial load present in actual tilt-up frame panels was not modeled. The results of this thesis are therefore only applicable to tilt-up frame panels in which the axial forces are sufficiently low such that they do not significantly effect ductility. Tilt up panels with typical dimensions and large window openings may be vulnerable to possible out of plane or lateral torsional buckling. This might be especially true for tall panels which are not laterally supported at mid-height by an intermediate floor. This is not a common design condition, but buckling should be considered when this situation does occur. It was decided that the lateral buckling of the panels is a separate issue which is too large to be incorporated into the current study. Lateral buckling of the frames is considered to be an unacceptable mode of failure since it would result in the collapse of the wall with little warning. If lateral stability is considered to be a problem, it would be necessary to ensure that all panels are provided with adequate lateral support. In laterally supported panels, the development of plastic hinges would be the critical failure mode and hence the results of the tests proposed for this research will be useful. 1.4 Plan of development The thesis report begins with an outline of the problem in chapter 2. A literature review which researched previous work on this topic is contained in chapter 3. The details of the tests are described in chapter 4 and 2 the observations, results and interpretation of results are covered in chapters 5, 6 and 7 respectively. The conclusions drawn from the test series are listed in chapter 8. There are five figures which are referenced many times throughout the thesis. For convenience these figures have been placed together in Appendix I and have been numbered 1-1 to 1-5. 3 2 PROBLEM DEFINITION 2.1 Description of type of panel being researched Tilt-up concrete buildings have concrete walls, supported on a concrete floor slab, and a light weight roof system. Roof systems typically consist of structural steel beams, open web steel joists and steel decking. The exterior concrete walls, which are typically 190 mm thick with two layers of reinforcement, are cast on the floor slab and then lifted into position. The walls, which also serve as the exterior face of the building, are temporarily braced until the roof is constructed. In the completed building, the concrete walls resist vertical loads as well as lateral loads from wind and/or earthquakes. The roof acts as a flexible diaphragm, transferring the lateral loads to the perimeter concrete shear walls. The vertical and lateral loads are transferred from the walls to the concrete floor slab via steel connections which are formed by welding together steel plates which are embedded into each of the walls and the floor slab. The connection between the panel and the floor slab prevents translation, but offers very little rotational restraint. This connection between the wall and the floor slab is therefore considered a pin connection for analysis purposes. Tilt up wall panels with large openings at the first and ground floor levels are becoming increasingly popular. The two large openings result in a panel which is more like a frame than a wall, see Figure I-la in Appendix I. Given that the panels are typically only 190 mm thick, the shear resisting system consists of reinforced concrete frames which have members with very high depth to width ratios. The legs typically have depth to width ratios between 4:1 and 5:1, and the beams can have depth to width ratios as high as 8:1. The performance under cyclic earthquake loading of reinforced concrete frame members with these depth to width ratios is not well understood. 2.2 Expected mode of failure To investigate the mode of failure of frame panels, typical loads were applied to a panel of typical dimensions, (Figure 1-1 of Appendix I), with typical reinforcement (Figure 1-3 of Appendix I). Given the connections have sufficient strength and that lateral torsional buckling of the whole frame panel is prevented, failure of the tilt-up wall system will occur via shear, or preferably via flexural hinging in the frame members. For the preferred mode of flexural hinging, in order to determine in which members hinging will occur, it is necessary to compare the bending moments in the frame members as the loads are increased to the flexural capacities of the frame members. 4 In typical tilt-up frame panels the beam members have significantly deeper cross sections than the leg members and the flexural capacities of the beam members are correspondingly higher. As increasingly large lateral loads, and corresponding vertical loads, are applied to the tilt-up frame panels, the bending moments in the legs of the panel reach their flexural capacity before the bending moments in the beam reach the beam flexural capacity. Therefore failure of the panel will occur via hinging of the leg members. A full quantitative description of the development of the hinges is given in section 4.2. 2.3 Design procedure currently being applied Assuming the roof to panel and panel to floor connections have sufficient strength, failure of the tilt-up system will occur via flexural hinging in the frame members of the panels. Design forces for tilt-up buildings are generally calculated using a force reduction factor, R, of approximately 2. CSA A23.3-941 specifies that a force reduction factor of exactly 2 be used. Therefore, according to CSA A23.3-941 the frame panels should be designed and detailed such that they provide sufficient ductility to justify the use of a force reduction factor of 2. Since the panels with large openings described above are, according to clause 23.5.3 of CSA A23.31, effectively frames, designers in the Vancouver, Canada, region are currently applying the plastic hinge detailing rules applicable to frame members requiring nominal ductility (Clause 21.9 of CSA A23.31). 2.4 Applicability of code rules currently being applied The design and detailing guidelines given in the code provisions of the American Concrete institute, and the Canadian Standards Association, were derived with traditional concrete cross sections in mind i.e. members with depth to width ratios of 1:1 or 2:1. Therefore the applicability of the rules provided by these codes for the design and detailing of tilt-up frame members which have depth to width ratios of 4:1 to 8:1 is questioned. In particular the rules for the spacing of ties in the expected hinge regions are of concern. Cross sections of typical tilt-up frame members are shown in Figure 1-3 of Appendix I. It is clear that these cross sections are very different from the square cross sections of traditional concrete frame members. The research for this thesis began with a careful study of CSA A23.3' and of the Concrete Design Handbook of the Canadian Portland Cement Association20. The study included an evaluation of how the code was interpreted in the design of an actual tilt-up frame building constructed on Vancouver Island. The main findings of this study are stated below. All references to the "code" refer to CSA A23.3'. When the current code hinge zone tie spacing rules are applied to tilt-up frame members (code1 clauses 21.9.2.1 and 21.9.2.2), the spacing rules given as a fraction of the least member dimension often control. 5 Since the tilt up frame members have cross sections very different to the cross sections the code was written for, the applicability of these rules is questioned. The rules for how far the hinge zone ties should be extended down the member (code' clauses 21.9.2.1 and 21.9.2.2) are also given in terms of member dimensions. The hinge zone distance for typical tilt-up frame panels is twice the member depth from the joint in the case of beams. These rules may be overly conservative for the members of tilt-up frame panels which have very deep sections. The d/2 rule for tie spacing in the non hinge zones of beams (code1 clause 21.9.2.1.3) often results in a very large spacing, 700 mm for the frame being considered in this study, for example. This spacing is larger than the maximum spacing for distributed reinforcement in walls, so again the applicability of the code rules is questioned. The joint detailing rule which limits the maximum bar size passing through joint regions (code1 clause 21.9.2.4.4) is very easily satisfied. This is a result of the large joint sizes. However, the ease with which this requirement is satisfied is an indication that the code was not intended for the section dimensions typically found in tilt-up frame panels. The conclusion of the study done on CSA A23.31 and the Concrete Design Handbook of the Canadian Portland Cement Association20 was that the code rules are not necessarily applicable to tilt-up frame panels. In particular it was concluded that experimental research into what tie spacings should be used in the hinge zones of tit-up frame members would be useful. 6 3 LITERATURE REVIEW 3.1 Aim of review The objective of this research project was to determine the relationship between hinge zone tie spacing and the displacement ductility of tilt-up frame panels. Tie spacing effects the ductility of the frame members because it will determine when, if at all, the longitudinal steel will buckle in compression. Since the load carrying capacity of a member is likely to drop when the longitudinal reinforcement buckles, buckling often marks the end of the ductile range. Although a large amount of testing involving buckling of compression reinforcement has been done on members with low depth to width ratios, there is not a satisfactory amount of information on members with depth to width ratios commonly used in tilt-up panels. The main aim of the literature review was to look at previous research for guidelines as to what tie spacings should be tested. Twenty four articles directly related to the testing being done for this research were found. A brief overview of each of the 24 relevant articles is provided below in date sequence. The relevance to the tests being done for this research is commented on. The contents of the article are given in regular font and the additional comments relevant to this research are shown in italics. The ratio of tie spacing to longitudinal bar diameter, called the S/D ratio, is commonly used to describe tie spacing. In some of the cases in which the authors did not mention S/D ratios in their articles, these ratios have been calculated and included in the comments in italics. 3.2 Summaries of relevant articles G. Agrawal, L Tulin, K. Gerstle (1965)4 "Response of doubly reinforced concrete beams to cyclic loading" Journal of American Concrete Institute, 62-51, P823-834 Three beams with a 3" wide 4" deep cross section were tested under cyclic loading. The beams were longitudinally reinforced with #4 bars. Each beam had two longitudinal bars, one at the top and one at the bottom. Transverse reinforcement consisted of 1/4" rectangular ties at 2.6" spacing. No buckling failures occurred. These tests suggest that S/D ratios of 2.6/0.5 = 5.2 are adequate to prevent buckling of the longitudinal reinforcement. However only three beams were tested and the scaling may influence the results. Furthermore since there was relatively little tensile reinforcement, the compressive stresses in the concrete would have been small and therefore the outward pressure on the longitudinal steel from the bulging of the concrete in compression would have been low. 1 N. Bums, C. Seiss(1966)5 "Plastic hinging in reinforced concrete" Journal of Structural Engineering, ASCE, vol. 92 # ST5, Oct. P45-64 Cyclic (not reverse) testing was done on 39 under-reinforced beams (no axial load) which had aspect ratios of 2:1. The beams were simply supported and the load was applied at midspan. In 18 of the beams the load was applied through a column stub which was cast integrally on the top of the beam at midspan. The column stub was intended to model the beam/column joint. In the other 21 specimens the load was applied through a column stub which was cast integrally on the top and the bottom of the beam. Again the intent of the column stub was to model the beam/column joint. The 6" x 12" cross sections were longitudinally reinforced with #6 and/or #8 bars. The transverse reinforcement consisted of #3 rectangular ties at 6" spacing. Buckling of longitudinal bars preceded failure, but this only occurred once the cover had spalled. Once the cover had been lost, "bulging" of the core contributed to the buckling of the longitudinal steel. It was found that #6 and #8 bars buckled within a 6" spacing. #6 (19 mm) at 6" (152 mm) and #8 (25 mm) bars at 6" (152 mm) spacings give S/D ratios of 8 and 6 respectively. N. Burns, C. Seiss(1966)s "Repeated and reverse loading in reinforced concrete" Journal of Structural Engineering, ASCE vol. 92 #ST5, Oct. P65-78 Three beams with 2:1 aspect ratios were tested under reverse cyclic loading. The beams had the same properties as the set of 21 specimens described in the previous reference i.e. this is a second paper from the same set of experimental tests. This second paper was written to describe the effect of reverse cyclic loading as opposed to cyclic loading applied in one direction only which was covered in the first paper. Buckling failures did occur and again buckling took place over one 6" tie spacing. #6 (19 mm) bars at 6" (152 mm) centers gives an S/D ratio of 152/19=8 W.Ruiz, G. Winter (1969)16 "Reinforced concrete beams under repeated loads" Journal of Structural Engineering, ASCE vol. 95 #ST6, June, PI 189 8 18 simply supported beams with a 8" wide and 11" deep cross section were tested under cyclic loading. The reinforcing properties as well as the loading patterns were varied. Six of the 18 specimens had compression steel and ties at the critical section, while the other 12 had only tension steel. The tensile steel consisted of either 2 or 3 bars which were either #6 or #7 bars. Where compression steel was used, it consisted of a single bar placed at the midpoint of the top side of the rectangular stirrups. Buckling of the single compression bars was observed. Since stirrups are not very effective in restraining bars at a mid point of one of their sides, it is not surprising that these bars buckled. Given the very different reinforcement configurations in this test, compared to those of the tilt-up panel frame legs, the findings of this paper are not particularly useful for the tilt-up frame panel research. R. Brown, J Jirsa (1971)7 "Reinforced concrete beams under load reversals" Journal of American Concrete Institute, 68-39, P380-390 Twelve beams with a 6" x 12" cross section were tested under cyclic loading. The beams were longitudinally reinforced with four #6 or #8 bars, one in each comer. Transverse reinforcement consisted of #3 closed stirrups at 2" spacing. No buckling failures occurred. It was found that increasing the number of stirrups to improve confinement increased the number of cycles to failure. These tests indicate that S/D ratios of 2/0.75 =2.7 are adequate to prevent buckling of the longitudinal reinforcement. Since no buckling failures were observed an indication of how close this S/D ratio is to the limit was not obtained, but it is likely that an S/D ratio of 2.7 is substantially lower than would be required to prevent buckling of the longitudinal reinforcement. Ties spaced with an S/D ratio of 2.7 would however offer a large amount of confinement. J. Wight, M. Sozen(1975)'7 "Strength decay of reinforced concrete columns under shear reversals" Journal of Structural Engineering, ASCE, vol. 101 #ST5, May, P1053 The 12 specimens tested had aspect ratios of 2:1. Reinforcement consisted of four #6 longitudinal bars, one in each corner of the #2 or #3 rectangular stirrups. The main focus of this research was to investigate the shear behavior under cyclic loading and not much emphasis was placed on the buckling of the longitudinal steel. The authors recommended that the tie spacing should be less than 1/4 of the depth of the beam, but it seems that this is recommended as a shear consideration as opposed to a reinforcement stability consideration. 9 N. Gosain, R. Brown, J. Jirsa (1977)8 "Shear requirements for load reversal in reinforced concrete members" Journal of Structural Engineering, ASCE, vol. 103 #ST4, July, PI461 This paper summarizes and comments on experimental tests done by other researchers. The paper suggests that a S/D ratio of 6 should be used where buckling of longitudinal reinforcement over a single tie spacing needs to be prevented. The paper mentions other studies (Berto and Popov EERC Report 75-15) which suggested that s/d ratios of between 6 and 8 would be acceptable. The paper also describes the mechanics of buckling of longitudinal reinforcement bars in compression. C. Scribner, J. Wight (1980)' "Strength decay of reinforced concrete beams under load reversal" Journal of Structural Engineering, ASCE, vol. 106 #ST4, April, P861 14 T-shaped specimens were tested under cyclic loading. The T-shaped specimens represented the beam and columns of a concrete frame. Eight of the specimens were at 1/2 scale and the other six were full scale. A reverse cyclic load was applied to the beam of the specimen and the effect of tie spacing on the behavior of the hinge which formed in the beam was observed. A number of buckling failures of the #6 and #8 longitudinal bars were observed. These tests indicated that large ties are needed to prevent the buckling of longitudinal reinforcement. It is mentioned that ties as large as the longitudinal reinforcement would be adequate. Buckling often occurred over 3 or 4 tie spacings which suggested that the ties act as elastic supports rather than rigid supports between which buckling takes place. Tie stiffness is therefore very important. The authors drew the following conclusions from the tests: • The longitudinal steel only buckled once the cover reinforcement had been spalled. • Larger ties are more effective than smaller ties in delaying the buckling of longitudinal reinforcement. • Beam twist or shear deformations, which result in relative displacement of the compression bar over the spalled region, lead to buckling at reduced loads. The comment that ties as large as the longitudinal reinforcement should be used is probably conservative since the code says that ties need be only half as large as the longitudinal bars. The test set-up used by Scribner and Wight was similar to the test setup used for the testing reported in this thesis. 10 B. Scott, R. Park, M. Priestley (1982)18 "Stress strain behavior of concrete confined by overlapping hoops at low and high strain rates" Journal of American Concrete Institute, 79-2, P13-27 Twenty five 450 mm square, 1200 mm high, columns were tested. The specimens had between 8 and 12 longitudinal bars and the transverse reinforcement consisted of a varied arrangement of square and/or octagonal steel hoops. The loading applied was monotonic compression and it was either concentrically or eccentrically applied. The loading rate was varied to investigate the effect of strain rate on strength. The tests performed indicated that a S/D ratio of 2.7 to 4.9 was adequate to delay buckling until another mode of failure took place. The loading used in the above tests was pure axial compression and therefore the S/D ratios derived would not be applicable to the tilt-up frame members in which flexure dominates. C. Scribner(1986)10 "Reinforcement buckling in reinforced concrete flexural members" Journal of American Concrete Institute, 83-85, P966-973 This paper contained details on buckling mechanics of compression reinforcement. Tests were done and it was found that even large closely spaced ties did not always prevent buckling of the longitudinal bars at large flexural displacements. Buckling over one and more tie spacings was observed. It was found that if buckling over more than one tie spacing is to be prevented, the tie diameter should be at least half of the longitudinal bar diameter. It was queried whether the large flexural displacements at which longitudinal bar buckling takes place are realistic. This query is valid because the drift requirements required for serviceability are 1.5% of interstorey height. The author felt that since other parts of the code are based on large displacement tests the tie spacing requirements for longitudinal bar buckling should also be based on large displacement tests. The author felt that for the purposes of an analytical model for buckling over multiple tie spacings, it would be good to assume that buckling takes place over 3 tie spacings. The plastic hinge region is generally d/2 long, where d is the depth of the hinging member. Ties are likely to be spaced at approximately d/4. The first tie is typically a half tie spacing from the support i.e. d/8. The fourth tie will 11 therefore typically be at 678 + (3 x 6/4) = 7/8d i.e. near the end of the hinge region. The first and fourth ties are likely to be well held, the first one is near the support and the fourth one is in or near an area where the concrete has not spalled. Buckling is therefore likely to take place between the first and the fourth ties, over a distance of 3/4d i.e. 3 times the tie spacing of d/4. M. Papia, G. Russo, G. Zingone (1988)" "Instability of longitudinal bars in RC columns" Journal of Structural Engineering, ASCE, vol. 112 #2, P445 A mathematical model was developed to predict the behavior of reinforcing bars in compression. Uniaxial compression tests on reinforced concrete specimens were done to check the accuracy of the model. The model represented the ties as elastic springs such that buckling over more than one tie spacing could be evaluated. In the tests it was found that when buckling occurs over many tie spacings, the ties are damaged and this results in a loss of confinement which leads to a premature failure of the concrete. Tie stiffness is therefore important. Failure under uniaxial compression will always involve the buckling of the longitudinal steel, no matter what the tie spacing, and no recommendations for tie spacings were given. M. Saatcioglu, G Ozcebe (1989)12 "Response of RC columns to simulated seismic loading" Structural Journal of American Concrete Institute, 86-sl, P3-12 Fourteen full scale columns were tested under slowly applied lateral load reversals. The columns were tested under a range of axial loads. One of the main aims of the tests was to investigate the effect of axial load on the seismic behavior of RC columns. It was found that as the axial load was increased the yield load of the column increased but the ductility decreased. The opposite was found to be true for axial tension i.e. the yield was reached sooner but the columns were more ductile. It was found that an axial load equal to 20% of the design axial load capacity had a significant effect on the behavior and ductility of the column. The longitudinal steel consisted of 25 mm bars and the ties were at 150 mm c/c. No buckling of longitudinal reinforcement was observed. Further tests were done with ties at 75 mm and 50 mm c/c. The closer spacings were used to improve confinement. The 75 mm spacing gave similar results to the 150 mm spacing, but the 50 mm spacing gave significantly more ductility. 12 The axial loads in the legs of tilt-up frame panels will typically be less than 10% of the nominal axial compressive capacity, (see section 4.1.4). This is less than the 20% value which was found to have a significant effect on ductility. These tests indicate that an S/D ratio of 150/25 = 6 is adequate to prevent buckling of the longitudinal reinforcement. S. Mau, (1990)13 "Effect of tie spacing on inelastic buckling of reinforcing bars" Structural Journal of American Concrete Institute, 87-S69, P671-677 A finite element study to predict the buckling behavior of reinforcing bars was done. The study used the stress strain behavior for typical high yield steel. The critical S/D ratio was found to be in the range of 5-7 depending on the stain hardening behavior of the steel. If the S/D ratio is less than the critical value, and the ties have adequate stiffness to prevent buckling over many tie spacings, then the longitudinal bars will not buckle but will follow the stress strain curve for the steel. If the S/D ratio is greater than the critical S/D ratio, then as the longitudinal bars reach yield they will become unstable and buckle. It was found that strain hardening may delay buckling of the longitudinal steel if the S/D ratio is close to the critical S/D ratio. The tilt-up panel tests will have a minimum S/D ratio of 5. This paper indicates that this spacing should be adequate to prevent buckling. G. Monti, C Nuti (1992)14 "Non-linear cyclic behavior of reinforcement bars including buckling" Journal of Structural Engineering, ASCE, vol. 112 #12, P3268 Tests were done on steel reinforcing bars i.e. not on reinforced concrete members. These test results were used to check a mathematical model which was developed to predict the behavior, including buckling, of longitudinal reinforcing bars in compression in reinforced concrete members. The bars were tested by loading lengths of reinforcing bar in compression. The tests done indicated that a S/D ratio less than 5 is required to avoid buckling problems. Since the test specimens were clamped at their ends, the test would only represent buckling over a single tie spacing. Furthermore these bar test results can only be used to predict the behavior of reinforcing bars restrained by ties, if it is assumed that the fixity applied to the longitudinal bars by the ties is the same as the fixity applied to the test specimen bars by the testing machine. The tilt-up panel tests will have a 13 minimum S/D ratio of 5. Therefore the tests reported in the above mentioned paper suggest that this ratio should be adequate to prevent buckling. A. Azizmamini, S. Baum Kuska, P. Brungardt, E. Hatfield (1994)15 "Seismic behavior of square high strength concrete columns" Structural Journal of American Concrete Institute, 91-S33, P336-345 Nine 2/3 scale columns were tested. The test columns had #6 bars running longitudinally. The maximum spacing of the #3 transverse reinforcement bars was 2 5/8". Buckling of the longitudinal reinforcement preceded failure. When the spacing was decreased from 2 5/8" to 1 5/8" the maximum deflection increased by 40%. It was found that so long as the axial load is less than 20% of the axial load capacity reasonable ductilities are achieved. It was found that the hinge region extended to a distance equal to the depth of the beam from the support. The 2 5/8 " spacing gives a S/D ratio of 66/19 = 3.5 and the 1 5/8 " spacing gives a S/D ratio of 41/19 = 2.2. The S/D ratios required to prevent buckling in these tests are lower than those found in the other literature. This is as a result of the high axial loads used in the tests. It is likely that S/D ratios as low as 3.5 would not be required in tilt-up frame panels where axial loads are less than 10% of their nominal axial load capacity. S. Pantazopoula (1998)19 "Detailing for reinforcement stability in RC members" Journal of Structural Engineering, ASCE, vol. 124 #6, P623-P641 The author analyzed a database of over 300 columns tested under cyclic, axial and/or flexural, loading. Based on the tests a mathematical model to predict critical tie spacing was formulated. This paper also contains a description of compression reinforcement buckling mechanics. It was reported that buckling may only take place at strains 5 times the yield strain, but this depends on the tie arrangement effectiveness and on the composite action of the rebar and the concrete. The author found that experimental reports for axial strain at buckling vary widely and this, according to the author, is as a result of different test set-ups as well as the subjective judgment of when buckling takes place i.e. usually done by eye. Involved mathematical equations which use concrete strains to predict critical tie spacing are provided. 14 3.3 Conclusions of literature review All of the testing reported in the literature was performed on members with depth to width ratios of less than 2:1. A number of different load configurations were used in the tests reported in the literature. Members were subjected to monotonic, cyclic or reverse cyclic loading and the loads were axial and/or flexural. Although the load configurations and test specimens were widely varied it is felt that they will give some indication of what type of behavior can be expected in the testing of this research. The following conclusions were drawn from the literature review: • Buckling of the longitudinal reinforcement only occurs once the cover concrete has spalled. In some cases the buckling and spalling occur simultaneously. • The longitudinal bars will only buckle once they have yielded in compression. • Strain hardening of the longitudinal steel may delay buckling. • Bulging of the core concrete in compression results in an outward force being exerted on the longitudinal steel. This contributes to buckling. • Buckling can take place over one or more than one tie spacing. • It was found that buckling over a single tie spacing began to occur when the ratio of tie spacing to longitudinal bar diameter (S/D ratio) reaches 6 to 8. • S/D ratios of 4 to 5 were found to be adequate to prevent buckling of the longitudinal reinforcement even at high flexural displacements. • Buckling failures occur over more than one tie spacing when the ties are not large enough to restrain the longitudinal steel. In order to prevent this it was found that the tie thickness should not be less than half of the longitudinal bar thickness. • Axial load does have an effect on ductility and axial loads equal to 20% of the axial compressive capacity of the member were found to have a significant effect on ductility. A discussion on the effect of axial load on the ductility of tilt-up frame panel members is contained in section 4.2.2. 15 4 MODE OF FAILURE, TEST SPECIMEN, SET-UP AND PROCEDURE, AND MATERIAL PROPERTIES An investigation into the mode of failure of tilt-up frame panels is outlined in section 4.1. The selection of the test specimen properties, the test set-up and the testing procedure are explained in sections 4.2, 4.3 and 4.4 respectively. The properties of the test specimen materials are provided in section 4.5. 4.1 Deterrnination of mode of failure Failure of the tilt-up wall system will often occur via flexural hinging in the frame members. In order to study the exact mode of failure, a typical frame panel was considered. The dimensions of the frame panel studied are shown in Figure I-la in Appendix I and the reinforcement considered for the test specimen is shown in Figure 1-3 of Appendix I. It was expected that failure of the tilt-up frame panels would occur via the formation of flexural hinges in the legs below the lower beam. In order to confirm this, the following was done: flexural capacities of the leg and beam members were calculated by doing layer analyses using the typical frame section properties shown in Figures 1-1 and 1-3 of Appendix I. The flexural capacities from the layer analyses were then compared to the frame bending moments obtained from a linear elastic analysis using loads large enough to cause yielding of the frame members. In order to calculate the flexural capacities of the frame members the yield strength of the reinforcing steel used to construct the specimens was required. Since no tests were done on the reinforcing steel until after the testing of the panels, the yield strength was estimated to be 450 MPa for the purposes of these calculations. (The tests done later on the reinforcement indicated it to have a yield strength of 453 MPa.) Layer analyses were done to determine the yield moments of the frame members assuming the strain in the bottom reinforcement to be 450/200 000 = 0.00225. The top strain was then varied until an axial load equal to zero was obtained and the corresponding moment was assumed to be the yield moment. A spreadsheet was developed to perform these yield moment calculations. The spreadsheet assumed the steel to have bi-linear stress strain behavior and used the tension stiffening model proposed by Collins and Mitchell21 using the tensile cracking stress of the concrete. The concrete compression force model proposed by Collins and Mitchell21 was used to calculate the compressive force in the concrete. All of the material performance factors were assumed to be equal to 1. 16 The spreadsheet calculations for the yield moments of the leg and the beam are contained in Tables 1-3. Table 1 contains the yield moment calculation for the leg of the typical frame panel considered. The leg reinforcement considered is shown in Figure 1-3 of Appendix I. Table 2 contains the yield moment calculation for the beam of the typical frame panel considered. The beam reinforcement is shown in Figure 1-3 of Appendix I. Table 3 contains the yield moment calculation for the beam of a frame panel reinforced as shown in Figure 1-3 of except using 10M bars for the distributed instead of the 15M bars shown in Figure 1-3. Knowing the yield moments of the frame members, vertical and transverse loads (with typical relative proportions) were applied to the frame and increased until yield moments were reached in either the legs or the beams. This procedure indicated that flexural hinges will form in the legs below the lower beam joint before yielding begins in the beams. The first yield bending moment diagram is shown in Figure I-lb in Appendix I. Note that the moments in the top of the legs are, on average, equal to the calculated yield moment of 271 kNm, see Table 1. The full frame analysis for first yielding, including all relevant input and output, is contained in Appendix II. In SAAP 2000, the computer program used for the frame analysis, U refers to displacement and R refers to rotation. The displacements are given in meters (m) and the rotations in radians. P is axial load, V is shear, T is torsion and M3 is the moment about the Y axis. The forces and moments have units of Newtons (N) and Newton.meters (Nm) respectively. In the joints definition section, the joint restraints are described by six numbers which are each either zero or one. A zero indicates that the restraint was not applied while a one indicates that it was applied. The first three numbers refer to translation in the X, Y and Z directions respectively, and the last three refer to rotation about the X, Y and Z axes respectively. In the material properties section, special materials called "legmat" and "beammat" were defined with moduli of elasticity's such that the stiffnesses of the legs and beams were in proportion. For the frame structure of Figure I-la, by comparing the shear forces from the frame analysis to the shear capacities of the members, it is clear that flexural hinges will form prior to shear failure of the frame members, therefore shear failure will not be critical and flexural hinging will be the controlling mechanism. The shear resistances offered by the concrete, Vc, are very close to the shear loads in the legs and beams of the panels. Therefore only a minimum amount of transverse reinforcement would be required for shear strength. However, substantially more than minimum transverse reinforcement is used since it is required to prevent the buckling of the longitudinal reinforcement. Contribution to shear strength is a secondary purpose of the transverse reinforcement. Since joint failure was not considered to be an issue, the joint regions were modeled using infinitely stiff short frame members in the computer analysis. 17 TABLE 1 - YIELD MOMENT CALCULATION FOR LEG fc' (MPa)= 30 Ect(MPa) = 30124.7 ult strain = -0.00199 fr (MPa) = 1.81 str@cracking 6.0084E-05 Depth to bot strain (mm)= 740 alphal = 0.7 Width of C flange (mm) = 190 alpha2= 1 d to bot of flange (mm) = Width of web (mm) = Depth to CA (mm) 800 190 400 Top strain -8.51780E-04 Axial force (N) Moments (Nmm) Bot.strain 2.26500E-03 cone C -422878 cone C 139323521 Betal 0.694375614 concT 89697 cone T 5.67E+6 Alphal 0.528094952 steel 331386 steel 125946115 c (mm) 202.2334589 -1.794E+3 270934962 phi 4.212E-06 CONCRETE FORCES Comp (N) -422.702E+3 (rectangular stress block) 10 LAYERS OF CONCRETE IN COMPRESSION: Moment (kNm) = Shrinkage strain: 271 0.00E+00 Layer Depth strain cf f (MPa) d to bot of layer Area •N (N) lever (mm) M (Nmm) 1 10.1 -809.19E-6 -19.4 20.2 3842 -74639 -390 29100726 2 30.3 -724.0E-6 -17.8 40.4 3842 -68574 -370 25349389 3 50.6 -638.8E-6 -16.2 60.7 3842 -62088 -349 21696005 4 70.8 -553.7E-6 -14.4 80.9 3842 -55180 -329 18166154 5 91.0 -468.5E-6 -12.5 101.1 3842 -47850 -309 14785418 6 111.2 -383.3E-6 -10.4 121.3 3842 -40099 -289 11579380 7 131.5 -298.1E-6 -8.3 141.6 3842 -31926 -269 8573621 8 151.7 -212.9E-6 -6.1 161.8 3842 -23331 -248 5793723 g 171.9 -127.8E-6 -3.7 182.0 3842 -14315 -228 3265268 10 192.1 -42.6E-6 -1.3 202.2 3842 -4877 -208 1013837 38.42E+3 -422.88E+3 139323521 TENSILE FORCES - See C&M P135 for equation &143 for area zone d to cent. strain cf f (MPa) Area N (N) lever (mm) M (Nmm) 1 740 0.002265 0.614 32300 19826 340 6740753 2 520 0.0013384 0.697 43700 30455 120 3654560 3 280 0.0003275 0.902 43700 39417 -120 -4729987 4 60 -0.0005991 0.000 32300 0 -340 0 5 -0.0008518 0.000 0 0 -400 0 6 -0.0008518 0.000 0 0 -400 0 7 -0.0008518 0.000 0 0 -400 0 89.70E+3 5.67E+6 STEEL FORCES Layer AREA fy Depth strain from phi strain sf MPa N (N) lever (mm) M (Nmm) 1 600 450 740 0.002265 0.002265 450.0 270000 340 91800000 2 400 450 520 0.001338 0.001338 267.7 107071 120 12848541.41 3 400 450 280 0.000328 0.000328 65.5 26203 -120 -3144404.76 4 600 450 60 -0.000599 -0.000599 -119.8 -71888 -340 24441978.81 -0.000852 -0.000852 0.0 0 -400 0 -0.000852 -0.000852 0.0 0 -400 0 -0.000852 -0.000852 0.0 0 -400 0 -0.000852 -0.000852 0.0 0 -400 0 -0.000852 -0.000852 0.0 0 -400 0 -0.000852 -0.000852 0.0 0 -400 0 -0.000852 -0.000852 0.0 0 -400 0 -0.000852 -0.000852 0.0 0 -400 0 3.31E+05 1.26E+08 18 TABLE 2 - YIELD MOMENT CALCULATION FOR BEAM fc' (MPa)= 30 Ect(MPa) = 30124.7 ult strain = •0.00199 fr (MPa) = 1.81 str@cracking 6.0084E-05 Depth to bot strain (mm)= 1340 alphal = 0.7 Width of C flange (mm) = 190 alpha2= 1 d to bot of flange (mm) = Width of web (mm) = Depth to CA (mm) 1400 190 700 Top strain -6.84420E-04 Axial force (N) Moments (Nmm) Bot.strain 2.26500E-03 cone C -539471 cone C 319635005 Betal 0.688226997 concT 128450 cone T 11.29E+6 Alphal 0.442109542 steel 409234 steel 251283135 c (mm) 310.9502207 -1.786E+3 582208049 phi 2.201 E-06 CONCRETE FORCES Comp (N) -539.296E+3 (rectangular stress block) 10 LAYERS OF CONCRETE IN COMPRESSION: Moments (kNm) = Shrinkage strain: 583 0.00E+00 Layer Depth strain cf f (MPa) d to bot of layer Area N (N) lever (mm) M (Nmm) 1 15.5 -650.20E-6 -16.4 31.1 5908 -96833 -684 66277445 2 46.6 -581.8E-6 -15.0 62.2 5908 -88419 -653 57769122 3 77.7 -513.3E-6 -13.5 93.3 5908 -79586 -622 49523590 4 108.8 -444.9E-6 -11.9 124.4 5908 -70335 -591 41579899 5 139.9 -376.4E-6 -10.3 155.5 5908 -60666 -560 33977095 6 171.0 -308.0E-6 -8.6 186.6 5908 -50577 -529 26754228 7 202.1 -239.5E-6 -6.8 217.7 5908 -40070 -498 19950344 8 233.2 -171.1E-6 -4.9 248.8 5908 -29145 -467 13604491 9 264.3 -102.7E-6 -3.0 279.9 5908 -17801 -436 7755718 10 295.4 -34.2E-6 -1.0 311.0 5908 -6038 -405 2443073 59.08E+3 -539.47E+3 319635005 TENSILE FORCES - See C&M P135 for equation &143 for area zone d to cent. strain cf f (MPa) Area N (N) lever (mm) M (Nmm) 1 60 -0.0005524 0.000 39900 0 -640 0 2 380 0.000152 0.993 42750 42460 -320 -13587075 3 700 0.0008563 0.766 42750 32741 0 0 4 1020 0.0015607 0.673 42750 28759 320 9202984 5 1340 0.002265 0.614 39900 24491 640 15674000 6 -0.0006844 0.000 0 0 -700 0 7 -0.0006844 0.000 0 0 -700 0 128.45E+3 11.29E+6 STEEL FORCES Layer AREA fy Depth strain from phi strain sf MPa N (N) lever (mm) M (Nmm) 1 600 450 60 -0.000552 -0.000552 -110.5 -66282.77 -640 42420972.9 2 400 450 380 0.000152 0.000152 30.4 12159 -320 -3890756.78 3 400 450 700 0.000856 0.000856 171.3 68506 0 0 4 400 450 1020 0.001561 0.001561 312.1 124853 320 39952918.93 5 600 450 1340 0.002265 0.002265 450.0 270000 640 172800000 -0.000684 -0.000684 0.0 0 -700 0 -0.000684 -0.000684 0.0 0 -700 0 -0.000684 -0.000684 0.0 0 -700 0 -0.000684 -0.000684 0.0 0 -700 0 -0.000684 -0.000684 0.0 0 -700 0 -0.000684 -0.000684 0.0 0 -700 0 -0.000684 -0.000684 0.0 0 -700 0 4.09E+05 2.51 E+08 19 TABLE 3 - YIELD MOMENT CALCULATION FOR BEAM (REINFORCED AS SHOWN IN FIGURE 1-3 OF APPENDIX I, EXCEPT ASSUMING 10M DISTRIBUTED BARS INSTEAD OF 15M) fc' (MPa)= 30 Depth to bot strain (mm)= Width of C flange (mm) = d to bot of flange (mm) = Width of web (mm) = Depth to CA (mm) Ect(MPa)= 30124.7 1340 190 1400 190 700 ult strain = -0.00199 fr (MPa) = 1.81 str@cracking 6.0084E-05 alpha1= 0.7 alpha2= 1 Axial force (N) Top strain -5.86554E-04 Bot.strain 2.26500E-03 Betal 0.684808481 Alphal 0.387826776 c(mm) 275.6329917 phi 2.128E-06 CONCRETE FORCES Comp (N) -417.266E+3 (rectangular stress block) 10 LAYERS OF CONCRETE IN COMPRESSION: Moments (Nmm) cone C -417380 cone T 92278 steel 323303 -1.799E+3 cone C 252588076 cone T 13.12E+6 steel 225474190 491183300 Moments (kNm) = 492 Shrinkage strain: 0.00E+00 Layer Depth strain cf f (MPa) d to bot of layer Area N (N) lever (mm) M (Nmm) 1 13.8 -557.23E-6 -14.4 27.6 5237 -75613 -686 51886952 2 41.3 -498.6E-6 -13.1 55.1 5237 -68812 -659 45323267 3 68.9 -439.9E-6 -11.8 82.7 5237 -61738 -631 38962517 4 96.5 -381.3E-6 -10.4 110.3 5237 -54392 -604 32827235 5 124.0 -322.6E-6 -8.9 137.8 5237 -46774 -576 26939957 6 151.6 -263.9E-6 -7.4 165.4 5237 -38882 -548 21323217 7 179.2 -205.3E-6 -5.9 192.9 5237 -30719 -521 15999549 8 206.7 -146.6E-6 -4.3 220.5 5237 -22283 -493 10991488 9 234.3 -88.0E-6 -2.6 248.1 5237 -13574 -466 6321569 10 261.9 -29.3E-6 -0.9 275.6 5237 -4593 -438 2012326 52.37E+3 -417.38E+3 252588076 TENSILE FORCES - See C&M P135 for equation &143 for area zone d to cent. strain cf f (MPa) Area N (N) lever (mm) M (Nmm) 1 60 -0.0004589 0.000 39900 0 -640 0 2 380 0.0002221 0.950 28500 27084 -320 -8666897 3 700 0.0009031 0.758 28500 21597 0 0 4 1020 0.001584 0.670 28500 19106 320 6113931 5 1340 0.002265 0.614 39900 24491 640 15674000 6 -0.0005866 0.000 0 0 -700 0 7 -0.0005866 0.000 0 0 -700 0 92.28E+3 13.12E+6 STEEL FORCES Layer AREA fy Depth strain from phi strain sf MPa N(N) lever (mm) M (Nmm) 1 600 450 60 -0.000459 -0.000459 -91.8 -55064.697 -640 35241406.28 2 200 450 380 0.000222 0.000222 44.4 8884 -320 -2842824.21 3 200 450 700 0.000903 0.000903 180.6 36123 0 0 4 200 450 1020 0.001584 0.001584 316.8 63361 320 20275608.07 5 600 450 1340 0.002265 0.002265 450.0 270000 640 172800000 -0.000587 -0.000587 0.0 0 -700 0 -0.000587 -0.000587 0.0 0 -700 0 -0.000587 -0.000587 0.0 0 -700 0 -0.000587 -0.000587 0.0 0 -700 0 -0.000587 -0.000587 0.0 0 -700 0 -0.000587 -0.000587 0.0 0 -700 0 -0.000587 -0.000587 0.0 0 -700 0 3.23E+05 2.25E+08 20 The assumption of flexural hinging taking place in the legs may not always be true. In this case the maximum beam moment of 429 kNm obtained from the linear elastic analysis is less than the yield moment for the beam which was calculated to be 583 kNm, see Table 2. However, if 10M bars were used for distributed reinforcement in the beam instead of 15M bars, the beam yield moment would reduce to 492 kNm, see Table 3. This would still result in hinges in the legs before yielding begins in the beam. However this may not always be the case and the flexural strengths of the members should always be compared to the expected moments to determine where failure will occur. All regions in which hinging is expected should be detailed accordingly. The cover concrete will spall as flexural hinging begins and a drop in flexural capacity is expected when the longitudinal steel buckles in compression. After the cover concrete has spalled, the remaining core concrete in compression will "bulge out" between the ties, pushing on the longitudinal compression reinforcing bars and inclining them to buckle. The tendency of the longitudinal reinforcing bars to buckle in compression will be affected by the spacing of the ties in the hinge region and on whether or not the bars have already been yielded in tension. Prior yielding in tension results in a decrease in stiffness, known as the Baushinger effect, and this will increase the likelihood of buckling. Further details on the mechanics of failure involving buckling of longitudinal reinforcement in compression can be found in References 8 and 10. 4.2 Test specimen details 4.2.1 Classification of transverse reinforcement There is a question as to whether it is strictly correct to describe the ties and stirrups in the frame members as confinement reinforcement. Concrete under large compressive stresses will strain significantly in the transverse direction unless it is confined. Lateral ties or "confinement reinforcement" is used to hold the concrete together to prevent expansion. This increases the effective compressive strength of the concrete. Since the ties in the legs of the panels are not resisting a compression failure of the concrete, they should not be classified primarily as "confinement" reinforcement. The primary purpose of the stirrups and ties is to prevent the buckling of the longitudinal bars under cyclic loads and it would therefore be more correct to describe the transverse reinforcement as "anti-buckling" reinforcement. The stirrups will also provide confinement to the concrete core, so the ties and stirrups are acting partially as confinement steel. A third purpose of the transverse reinforcement is to provide shear resistance. 21 4.2.2 Test panel configuration Test specimen properties were selected such that the test specimen would exhibit the same failure mechanisms that would take place in real tilt-up frame panels i.e. plastic hinging in the leg of the panel. The test panel dimensions are shown in Figure 1. 900 mm 3'0" 7 T — 7 T -2000 mm 6'3" -7T Cyclic loading 7T-750mm 2'6" 1500 mm 5' 3000 mm 10' 7T-THICKNESS = 190 mm FIGURE 1 - TEST PANEL DIMENSIONS Since the failure mode in the real frame panels would be the formation of flexural hinges in the legs of the panel, it is important that this also be the failure mechanism in the test panel. The proposed test specimen is proportioned to have a flexural hinge failure. The interaction of the column in which the hinge forms with the adjacent joint region is equally important. The proposed test specimen includes the joint region and therefore the column joint interaction will be well modeled. Although the eventual failure mechanism would involve the formation of a plastic hinge in the lower leg of the frame, it would be beneficial to observe the level of damage in the joint and adjoining column and beam when failure occurred in the leg. Therefore a test specimen which included a portion of the frame beam was used. The final test panel shape is shown in Figure 1-2 in Appendix I. In order to ensure that the shear to moment ratios in the leg and in the beam would be exactly the same as in the real panel it was necessary to apply the reactions at the inflection points of the bending moment diagram under lateral loads, see Figure I-lb of Appendix I. Trucking restrictions limited the length of the beam of the test specimen. Therefore a 22 steel extension beam was used to ensure the beam reaction was applied at the inflection point of the bending moment diagram. The stiffness of the steel extension beam is significantly less than that of the concrete beam. However, since the test setup is statically determinate the member forces are not affected. Another advantage of the statically determinate test set-up was that a single force measurement would enable the computation of shear forces and bending moments at all points in the test specimen. The axial load present in tilt-up frame panels was not modeled in the test since it would have significantly complicated the test to model the axial loads accurately. Axial compression delays yielding but decreases ductility. Conversely, axial tension results in earlier yielding but more ductility. The maximum axial compression in the frame legs at failure is of the order of 350 kN. The maximum axial tension in the frame legs at failure is of the order of 50 kN. (See frame analysis contained in Appendix II.) The nominal axial compressive capacity of a 190 mm x 800 mm concrete section with four 20M bars and four 15M bars longitudinally is 3380 kN. Therefore tension in the frame legs is likely to be less than 5% of the nominal axial compressive capacity, and the compression in the frame legs is likely to be about 10% of the nominal axial compressive capacity. Saatcioglu & Ozcebe12 found that an axial load of 20% of the member axial compressive capacity had a significant effect on the behavior and ductility of the 14 full scale columns they subjected to slowly applied lateral load reversals. However Azizinamini et al15 found that as long as the axial load is less than 20% of the axial capacity of the member, reasonable ductilities were achieved in the nine 2/3 scale columns they tested under reverse cyclic loading. The panels were tested without axial load in the legs as the axial loads were sufficiently low so as not to significantly effect the ductility results. The model was not scaled. Scaling problems include a lack of reinforcing steel in smaller sizes and the difficulties involved in scaling of concrete (the coarse aggregate can be scaled down but then the size ratio of the large to small aggregate is changed.) Furthermore given that the size of defects in concrete is generally independent of the size of the coarse aggregate, in the scaled down specimen a given defect would have a larger effect than it would have had in a full size test specimen. The reasons for testing a full size test were, therefore: • good representation of behavior and failure of real structure. • opportunity to observe behavior of "non-failure regions" as failure is approached. Six test specimens, with the same concrete outline, but different reinforcement configurations were tested. 4.2.3 Cross sectional dimensions and details of the test specimens The longitudinal steel in the legs of frame panels is proportioned to resist bending moments caused by eccentrically applied gravity loads, and in plane bending moments caused by lateral loads from wind or 23 seismic loads. Longitudinal reinforcement details which are typical for tilt-up frame panel legs were used for the test panels (see Figure 1-3 in Appendix I). A specimen with a 190 mm wide and 800 mm deep leg, longitudinally reinforced as shown in Figure 2, was tested. 190(7.5") H H 800 (2'7") FIGURE 2 - LEG REINFORCEMENT The reinforcement configuration for the whole test specimen is shown in Figure 1-3 in Appendix I. The strictest code rules (Clause 21.9.2.2.1 of reference 1 and clause 21.10.5.1 of reference 2) result in a tie spacing of half the least member dimension. In a typical panel, 190 mm thick, the resulting spacing is 95 mm. Previous research5,6'7'8,1213'14 has found that tie spacing to longitudinal bar diameter ratios (S/D ratios) of between 5 and 8 are adequate to prevent buckling of longitudinal steel. Given that 20M bars are the largest bars commonly used in the legs of tilt-up frame panels, a tie spacing of 100 mm would be adequate, according to the most conservative previous research, to prevent premature buckling of the longitudinal reinforcement. Designers have used hinge region tie spacings of between 95 mm and 300 mm. Since six test specimens were available it was decided to test three different tie spacings, with two specimens per spacing. The tie spacings tested were 100 mm (S/D = 5), 200 mm (S/D = 10) and 300 mm (S/D = 15). In the test specimens these tie spacings started lm below the beam joint and were extended up through the joint and into the leg above the beam. Below the hinge region, and in the beam, a tie spacing of 400 mm was used. All transverse reinforcement consisted of closed leg ties or stirrups. Shear stresses in the frame members are generally low and minimum shear reinforcement is sufficient as far as shear strength is concerned. A 1 x 20M Each face 2 x 15M Each face NOTE: The transverse reinforcement consisted of closed leg ties and stirrups < 1 x 20M Each face 24 / 4.3 Test setup 4.3.1 Positions of supports for the test specimens In order for the tests to be representative of the behavior of real portal frame panels it was necessary to choose a support configuration which would give similar member forces to those found in a full panel loaded until failure. The test specimen setup is shown in Figure 1-2 of Appendix I. A frame analysis was done to determine the bending moments and shear and axial forces at first yielding of the prototype frame members. Since the longitudinal reinforcement of the members was pre-defined, the yield bending moments could be calculated. The method by which this was done is explained in section 4.1. The loads on the frame were increased until moments large enough to cause yielding were reached. Yielding occurred first in the legs, just below the lower header beam. The loads which were large enough to cause yielding and the resulting bending moment diagram are shown in Figure I-lb in Appendix I. The self weight of the frame members was also considered in the analysis. The full yield analysis input and results are contained in Appendix II. The position and type of supports applied to the test panel were chosen such that the member forces in the test panel were as close to those determined for the full panel as possible. It was found that this could best be achieved by placing a hinge support at the inflection point in the upper column, point A in Figure 3, and a roller support near the inflection point in the lower header beam, point B in Figure 3. I V a Summing moments about A: load x da c = V b x db d Therefore V b = load x d a c / d M M d b = V b x dd b = load x d a c Therefore the moment in the beam does not depend on dad, dd c or d M FIGURE 3 - TEST SETUP FORCES Member BD has been referred to as the "beam" of the test specimen in the discussion below i.e. it represents the lower beam in the real panel. Since leg DC will be made the same length as in the leg in the real panel, the moment and shear forces in it will be the same as in the real structure. As shown in Figure 3, the moment in the beam at point D does not H, V B V zr OOP -X-D 25 depend on the length of the beam i.e. it only depends on length d^. Therefore, given that the hinge at A is at the inflection point of the bending moment diagram and that the length of the leg is the same as in the real structure, the bending moment in the beam will be exactly the same as in the real structure. Since M d b and M d c are the same as in the real structure, moment equilibrium of the joint implies that the M d a , the moment in the upper column, will be exactly the same as in the real structure. As length db d is increased the reaction V b , and therefore the shear force in the beam, will decrease. Since, as shown in Figure 3, the moment in the beam does not depend on length dM, it is possible to vary length d M until the reaction V b is such that the shear force in the beam is the same as in the real panel. Therefore the following can be said about the test panel: 1. The distribution of moments in the test panel will be the same as in the actual structure (This is very important since the mode of failure is flexural hinging). 2. All the shear forces, apart from the shear forces in member DA, will be the same as in the real structure. The error in the shear force in member DA is not considered to be critical. 3. The axial forces in the test panel are not the same as in the real structure, but since only column DA, which is not expected to fail, has any axial force at all, this is considered to be acceptable because the axial forces in the real structure are low. As can be seen from the shear force diagrams contained in Appendix II, the shear forces vary along the length of the beam. Since it would not be practical to change the length dbd in the test every time the load direction changes, d M has been chosen to be representative of the shear forces in the beam throughout the loading sequence. It was found that the length d M required to give a representative shear force in member bd was in excess of 4m. Since it would not be practical or economical to have a test specimens with beams 4m long, an attachable steel extension beam was used to increase the length of the beam. The stiffness differences between the concrete and steel members will be of no consequence because the test set-up is statically determinate. 4.3.2 Hardware required for the test In some cases the hardware required for the tests was available, and in other cases it had to be manufactured. The hardware, as positioned in the final test setup, is shown in Figure 1-2 in Appendix I. The Drawings from which the hardware was constructed are shown irrAppendix III. 26 The panel was tested on the strongfloor in the structures lab at UBC. The panel was tested in a "lying down" position and was supported 300 mm above the strong floor. The test panel rested on low friction teflon pads to ensure that minimal jacking force was used to resist friction during testing. A jack with a 100 kip (445 kN) load capacity and a 24" (620 mm) stroke was used to load the test specimen at the bottom of the leg, 2900 mm below the bottom of the beam. A horizontal thrust support was required for the jack. Since the jacking force was reasonably low, up to 140 kN, and was applied quite close to the floor, about 300 mm, the strength requirements for the jack support were not very large. A column stub was modified and bolted to the floor to serve as a thrust support for the jack. A steel extension beam was attached to the end of the beam of the test specimen. The roller support at the end of the steel extension beam, point B in Figure 3, was provided by placing rollers, which were found in the structures lab, between the steel beam and horizontal thrust supports. Thrust supports were placed on either side of the steel extension beam. A hinge connection was required at the top of the column such that free rotation, but no translational movement, was permitted. The part of the hinge attached to the top of the column was connected to threaded bars which were cast into the test specimen. 4.4 Testing procedure 4.4.1 Loading procedure Using the leg reinforcement shown in Figure 1-3 of Appendix I, the yield force was calculated to be approximately 93 kN (fy = 450 MPa, fc' = 30 MPa). The specimens were loaded using sequences consisting of three cycles. A cycle, which would begin at zero displacement, consisted of a push in one direction followed by a pull in the opposite direction, and then a return to zero displacement. The reverse cyclic loading sequence shown in Figure 1-4 of Appendix I was followed. The displacement at 75 kN was multiplied by 4/3 to predict the yield displacement, d, which was used as the basis for the rest of the loading which was done under displacement control. It is important to note that the 75 kN displacement used to calculate the yield displacement, was the 75 kN displacement for the test panel in the test set-up. This would be different to the 75 kN displacement for the leg alone and different to the 75 kN displacement of the full frame panel. Similarly the predicted yield displacement i.e. 4/3 times the 75 kN displacement, is the test panel yield displacement. 27 4.4.2 Data recording Load and displacement readings from the jack were electronically captured. A LVDT was placed at the top of the leg to measure the movement of the top of the leg. The only information it was essential to measure was the load and deflection readings from the jack and the deflection readings at the top of the leg. With this information it was possible to plot the load deflection diagrams for the leg and hence determine the panel ductilities corresponding to the respective tie spacings. However other readings were also taken during the test. At each load increment concrete strains on opposite sides of the beam were electronically recorded using LVDT's. This enables the plotting of the moment curvature diagram for the beam which allows the elastic stiffness of the beam to be estimated. The deflections recorded by the jack included deflections resulting from deformations occurring in the beam of the test specimen. The rotation of the joint was required to calculate the deflection of the LEG of the test specimen. This rotation was calculated using the deflection measured at the top of the leg and assuming rigid body motion of the joint region about the hinge connection shown in Figure 1-2 in Appendix I. As a check on the rotations a laser pointer was glued to the center of the joint and the movement of the laser dot on a piece of paper 8m away from the pointer was measured. Using the movement of the laser dot it was possible to calculate the rotation of the joint at each load stage. A comparison of the joint rotations obtained from each of the methods is made in chapter 6. At each load increment concrete strains on opposite sides of the leg in the hinge zone were electronically recorded using LVDT's, and mechanically recorded using dial gauges. From the strain measurements it is possible to obtain curvatures and hence plot moment curvature diagrams for the hinge regions of the specimens. The strains were typically measured over 400 mm of the hinge zone. In some cases the 400 mm measuring length extended into the joint region and in other cases it started and finished within the leg. In order to attach the strain measuring apparatus to the test specimen the following method was used: 100 mm long steel studs were cut from 10 mm diameter round bar. The studs were hammered into holes which had been drilled into the top face of the test specimens. Horizontal bars which spanned the 400 mm gauge length were attached to the top of the studs using 90° clamps. Where dial gauges were used, the gauges were attached to steel studs which were inserted into the top of the test specimen as described above. Where LVDT's were used, the LVDT's were held in plastic clamps which were epoxy glued to the specimen. A number of the photographs contained in Appendix IV show the placement of the strain measuring apparatus on the test specimens. The effectiveness of these methods of measuring strain is described in chapter 6. 28 4.5 Material properties 4.5.1 Concrete properties The specified 28 day strength of the concrete was 30 MPa. The test panels were cast from the same batch of concrete that was used to cast the panels being used for the actual building on site. Deltiac Testing and Engineering LTD did the quality control testing for the concrete used in the panels. The average 28 day strength reported by Deltiac was 33.0 MPa. Six cylinders were cast and tested in the materials laboratory at the University of British Columbia (UBC). These six cylinders were cured under exactly the same conditions as the panels. One of the six cylinders was tested on the same day as each of the six test specimens were tested. The results from these tests are contained in Table 4 below. Casting took place on Wednesday the 14th of July 1999 and the test panels and the cylinders were moved to the structures laboratory at UBC on the 21st of July 1999. Table 4 - RESULTS OF CONCRETE TESTING DONE AT UBC Cylinder # Date Age (days) Strength (MPa) 1 7 September 55 21.3 2 21 September 69 25.3 3 29 September 77 21.9 4 5 October 83 21.6 5 20 October 98 23.8 6 4 November 113 23.9 It is clear from Table 4 that the 28 day strength of the cylinders tested at UBC would have been significantly less than 30 MPa. However the curing of the cylinders tested at UBC was the same as the curing of the test panels and these particularly dry curing conditions may have contributed to the low strengths shown in Table 4. The cylinders were removed from their plastic molds when the formwork was stripped from the test panels i.e. three days after casting. The cylinders then spent four days outdoors before being moved into the structures lab at UBC, where they were placed alongside the test panels. These dry and exposed curing conditions would partly account for the low strengths of the cylinders tested at UBC. An additional reason for low strength could be that the cylinders cast on site may not have been adequately compacted. A concrete strength of 30 MPa was assumed in the yield load calculations. However, it was found that the yield load calculation was not very sensitive to the concrete strength assumed for the calculation. 29 4.5.2 Reinforcing steel properties A number of pieces of the 20M bar used in the legs were cut from the test panels for testing. The yield strain of the 20M bars was required in order to calculate the yield moment of the leg, see section 4.1. Since the first four pieces tested behaved similarly, no additional tests were done. Table 5 below summarizes the results of the tests. Table 5 - REINFORCING STEEL TEST RESULTS TEST PANEL # Yield Strength (MPa) Ultimate Strength (MPa) Elongation (%) 2 449.5 726 15.5 2 453.7 732 14.0 3 451.6 727 13.5 3 455.7 743 15.5 The yield strength was determined by 0.5% extension under load. 30 5 OBSERVED BEHAVIOR DURING TESTING Unless otherwise indicated, all the figures referenced in this chapter can be found in Appendix IV. Load sequences names like "3d" are often used. This means that the maximum displacements of that load sequence were equal to 3 times the yield displacement. In order to understand the explanations given in this chapter it is important to have a full understanding of the load cycles and load sequences described in section 4.4.1. Again it is noted that the yield displacement is the yield displacement for the system, and therefore includes the elastic displacement of the steel extension beam. Table 6 indicates at which load stages the spalling of cover and buckling of reinforcement took place for each of the test specimens. A full description of the behavior of the individual test specimens follows. 5.1 Behavior common to all specimens The behavior of all the specimens was similar prior to yielding of the longitudinal steel. This is not surprising given that the longitudinal reinforcement was the same in each of them. Assuming a modulus of rupture stress of 3.29 MPa (Equation 8-8 of Reference 1) the cracking load was estimated, using the transformed section, to be 26 kN. The first flexural cracks appeared during the 25 kN load sequence and by the end of the 25 kN load sequence typically only one or two small flexural cracks had formed. In order to ensure that the positions of the cracks were visible in the photographs, lines were drawn with a marker pen over the cracks on the specimens. Therefore what might appear to be large cracks are actually the marker pen lines. The crack thicknesses are indicated by the numbers alongside the cracks. By the end of the 50 kN load sequence cracks as large as 0.35 mm had formed and the spacing of cracks in the future hinge zone was typically 150 mm to 200 mm. The 50 kN load sequence ended with the 12th load cycle. The cracking in the first 100 mm specimen at the end of the 12th cycle is shown in Figure IV-1 of Appendix IV. The extent of cracking shown in Figure IV-1 is typical of the cracking in all of the specimens at the end of the 50 kN load stage. 31 T A B L E 6 - T E S T S P E C I M E N B E H A V I O R Load Jack 100 mm ties 200 mm ties 300 mm ties Stage Load first second first second (kN) specimen specimen specimen specimen 0 0 1 25 2 -25 3 25 4 -25 5 25 6 -25 7 50 8 -50 9 50 10 -50 11 50 12 -50 13 75 14 -75 15 - 75 16 -75 17 75 18 -75 19 d 20 -d 21 d 22 -d 23 d 24 -d 25 1.5d 26 -1.5d 27 1.5d 28 -1.5d 29 1.5d 30 -1.5d 31 2d 32 -2d 33 2d 34 -2d 35 2d Spalling Spalling & Buckling (outside) 36 -2d Spalling Spalling & Buckling (inside) 37 3d Spalling Buckling (outside) 38 -3d Spalling Buckling (inside) 39 3d Buckling (outside) 40 -3d Buckling (inside) 41 3d Spalling Spalling 42 -3d Spalling Spalling 43 4d 44 -4d 45 4d Beam steel bond failure 46 -4d 47 4d Vert, crack into beam 48 -4d 49 300 mm Buckling of entire 50 -300 mm I reinforcement cage 32 At the end of the yield displacement load sequence cracks as large as 2.0 mm had formed and the spacing of cracks in the future hinge zone was typically 100 mm to 150 mm. The yield displacement load sequence ended with the 24th load cycle. The cracking in the first 100 mm specimen at the end of the 24th load cycle is shown in Figure IV-2 of Appendix IV. The extent of cracking shown in Figure IV-2 is typical of the cracking in all of the specimens at the end of the yield displacement load cycle. The largest crack shown in Figure IV-2 is 1.8 mm wide and runs from the beam leg intersection diagonally into the joint. In all of the specimens the largest flexural crack at any given load stage would start at the leg beam intersection and run diagonally into the joint region. It is of interest to note that this large crack would be partially controlled by the diagonal 15M bars which are placed at the leg beam intersection, see Figure 1-3 of Appendix I. The code intention for these diagonal bars was to control shrinkage cracks, but clearly they will also have an effect on the location of the flexural hinge. After yielding of the longitudinal steel the specimens with different tie spacings behaved differently but there was still some common behavior. Even though the longitudinal steel started yielding during the Id load sequence, the earliest the cover ever spalled was at the end of the 2d load sequence, this occurred in both of the 300 mm specimens. The cover of the 200 mm tie spacing specimens spalled in the 3d load sequence. The extent of cracking in the 200 mm tie spacing specimen at the end of the 2d load sequence is shown in Figure IV-3 of Appendix IV. It can be seen from Figure IV-3 that the cracking on the outside of the leg extended up into the joint region. Figure IV-3 also shows the extent of cracking in the joint region and in the part of the beam adjacent to the joint. As would be expected, there was more diagonal cracking in the specimens with larger tie spacings. As shown in Figure IV-3 of Appendix IV, at the end of the 2d load sequence there was a 1.25 mm diagonal crack in the 200 mm tie spacing specimen. Since the shear is constant along the length of the leg and the tie spacing was increased to 400 mm in the part of the leg more than lm from the joint, there was more shear cracking in the region of the leg below the area detailed for ductility. The hinge regions (regions of yielding) appeared to extend approximately 800 mm below the joint, and up into the joint. The large 4.5 mm crack visible in Figure IV-3 of Appendix IV formed approximately 250 mm into the joint region. It is therefore clear that the zone of yielding of the longitudinal reinforcement extended well into the joint region. 33 5.2 Behavior of 100 mm tie spacing specimens 5.2.1 1st Specimen The cover first spalled during the third cycle of the 3d loading sequence. Severe cracks, many in excess of 3 mm, were present in the joint region during hinging and the crushing and tensile straining of concrete associated with the hinging extended into the joint region. By the end of the 4d load sequence the cover had extensively spalled, especially on the outside face leg. It can be seen from Figure IV-4 in Appendix IV that by the end of the 4d load sequence, which ended with load cycle 48, the cover had spalled over 7 tie spacings (700 mm), and had extended 2.5 tie spacings (250 mm) into the joint region. During the third cycle of the 4d load sequence the bottom longitudinal beam reinforcement, which is anchored in the part of the joint just above the top of the leg, underwent a bond failure and pulled out of the joint. This bond failure occurred as a consequence of the repeated cyclic loading causing excessive tensile straining in the lower region of the joint. The large crack associated with this bond failure can be seen in Figure IV-5 of Appendix IV. The pullout of the longitudinal beam bar led to a failure, with corresponding drop in capacity, in the "pushing" direction. However there was no failure in the pulling direction. When the leg was pulled the large crack closed and the hinge continued to develop for the pulling direction. However, even though no failure was observed, the load reached with each successive load cycle at the same displacement was reduced. This is largely as a result of the Baushinger effect i.e. as the steel was yielded again and again, the stiffness decreased more and more. The result being that with each successive straining of the steel to give the same displacement, the load would be successively lower. Since the jack had only a 600 mm stroke the specimen could only be deflected 300 mm either way. It was therefore not possible to see if the specimen would maintain its "pulling" capacity at higher displacements. Since failure had already taken place in one direction it was decided that it would not be worthwhile to move the jack such that the specimen could be "pulled" further. By the end of the test, the region in which cover had spalled on the outside face had grown considerably compared to when the pullout of the longitudinal beam bars occurred. The spalling just prior to the beam steel pullout is shown in Figure IV-4 of Appendix IV and the spalling at the end of the test is shown in Figure IV-6. (It can also be seen in Figure IV-6 how the large crack visible in Figure IV-5 closed when the specimen was pulled.) Figure IV-6 shows that the region of spalling at the end of the test extended over 10 tie spacings (1000 mm), extending 400 mm into the joint and 600 mm down the leg. It is clear from this 34 photograph that 100 m ties are very effective for preventing buckling of the longitudinal steel even at very high strains. 5.2.2 2nd Specimen The cover spalled during the third cycle of the 3d loading sequence. Bond failure of the bottom longitudinal beam steel was not the primary cause of failure in the second 100 mm tie spacing specimen. A large crack did form, running from the leg beam intersection, extending vertically up the beam joint interface. Figure IV-7, which was taken at the end of the first push of the 4.3 d load sequence, shows the spalling of the concrete and the crack extending vertically up into the beam. There was not a significant decrease in load carrying capacity in the pushing direction with the formation of this vertical crack. Before full bond failure occurred, the face concrete spalled off the leg and all eight of the longitudinal bars in the leg (four on each face) buckled out of plane. All the longitudinal bars in the hinge zone buckled in the same mode and in the same direction. The out of plane buckling of the whole hinge zone reinforcement cage is clearly shown in Figure IV-8. The first bars to buckle were the top face distribution reinforcement bars. These bars are not restrained from buckling by the ties since they are in the center of the long side of the ties, see Figure 1-3 of Appendix I. Since the leg buckled up it is likely that the top face distribution bars buckled before the bottom face distribution bars. It is likely that the top face distribution bars buckled first because the quality of the top face concrete would be lower than the quality of the bottom face concrete i.e. as a result of bleeding and more exposed early curing conditions. Once the top distribution bars had buckled out of plane there was a tendency for the whole hinge zone reinforcement cage to undergo local out of plane buckling. The ties prevent in plane buckling of the outside longitudinal bars but are ineffective if all the longitudinal bars buckle in the same direction. 5.3 Behavior of 200 mm tie spacing specimens 5.3.1 1st Specimen The first 200 mm tie spacing specimen was the first of the six specimens tested. A number of problems occurred during the first test. The first major problem was with the load calibration in the computer. The load scale was set incorrectly and the maximum load the computer could read was 96.8 kN. Unfortunately this load was very close to the expected yield load and by the time the problem was detected the specimen had yielded and the yielding portion of load deflection plot had not been recorded. 35 A second problem occurred when the pushing direction roller supports (see Figure 1-2 of Appendix I) moved 20 mm during the first load cycle of the 1.5d load sequence. The moving of the support was a result of the bolts connecting the support to the strong floor not being sufficiently tensioned. Since the roller supports were only pushed in one direction, it was possible to fill in the 20 mm gap and continue. However during the first cycle of the 2d load sequence the hinge support (see Figure 1-2 of Appendix I) moved. Since the hinge support was required to carry loads in two directions it would slide forward and back as the loading continued. Therefore the specimen was loaded to failure by pushing it in one direction. The resulting test was therefore one in which a specimen with a 200 mm tie spacing was subjected to a degree of cyclic loading and then pushed monotonically until failure. This test gave an indication of how cyclic loading reduced the ability of the specimen to achieve the maximum displacement. By comparing the maximum displacement of this 200 mm tie spacing specimen, which had a relatively small amount of cyclic loading, to the maximum displacement of the 200 mm tie spacing specimen which was subjected to increasing cyclic loads to failure, the effect of cyclic loading on maximum displacement achieved could be observed. Failure in the 200 mm tie spacing specimen loaded monotonically to failure occurred via buckling of the longitudinal steel which occurred after the concrete had spalled. After failure had occurred the loads which the specimen could resist were significantly less and it was therefore possible to apply cyclic loads once again i.e. the loads were too low to cause sliding of the supports. After a few cycles the longitudinal steel ruptured in tension. The steel on both sides of the specimen leg ruptured. For subsequent tests, bigger, stronger bolts were used and the jacking force was significantly increased to ensure there were no further sliding problems. 5.3.2 2nd Specimen The failure of the specimens with hinge zone ties spaced at 200 mm was similar in nature to the failure of the specimens with ties spaced at 300 mm. Therefore the failure observations for the second 200 mm specimen have been considered in section 5.4 alongside the observations of the 300 mm specimens. 36 5.4 Behavior of 300 mm (and 2nd 200 mm) tie spacing specimens 5.4.1 Overall behavior of specimens The failure of the second 200 mm tie spacing specimen and both of the 300 mm tie spacing specimens were all controlled by in plane buckling of the outside longitudinal bars. Buckling always occurred over one tie spacing. The behavior of the 300 mm and the 2nd 200 mm tie spacing specimens is summarized in Table 7. Table 7 - Summary of behavior of 200 mm and 300 mm tie spacing specimens 200 mm specimen 1st 300 mm specimen 2nd 300 mm specimen Start of spalling. 1st cycle of 3d sequence 3rd cycle of 2d sequence 3rd cycle of 2d sequence Buckling of steel on outside face. 2nd cycle of 3d sequence 1st cycle of 3d sequence 3rd cycle of 2d sequence Buckling of steel on inside face. 2nd cycle of 3d sequence 1st cycle of 3d sequence 3rd cycle of 2d sequence 5.4.2 Specific behavior of 200 mm tie spacing specimen Although the first buckling of the longitudinal steel in the 200 mm tie spacing specimen occurred during the 2nd cycle of the 3d load sequence, this initial buckling was not very severe. See Figure IV-9 of Appendix IV. It can be seen from Figure IV-9 that the buckling took place in a plane at 45° to the face of the leg. Although in Figure IV-9 it appears that only the bottom bar has buckled, the top bar has also buckled, but since it has buckled towards the camera, this buckling is not clear. Although there was a decrease in load carrying capacity associated with this initial buckling, the decrease was not very large. Figure IV-10 of Appendix IV shows the extent of buckling on the outside face of the member after the pushing portion of the first cycle of the 4d load sequence. By this stage the buckling was severe with a correspondingly large decrease in load carrying capacity. Again it is noted that buckling always occurred over one tie spacing. Although it happened once the load carrying capacity had dropped significantly, it is interesting to note that the longitudinal steel ruptured in tension. Shortly after the rupturing of the longitudinal steel the cover on the face of the leg spalled and the face reinforcing bars on the top face of the specimen buckled up. This buckling was similar to that observed in the second 100 mm tie spacing specimen although in this case out of plane buckling of the whole reinforcement cage did not take place. 37 5.4.3 Specific behavior of first 300 mm tie spacing specimen As can be seen from the times of spalling and buckling in Table 7, the buckling of the longitudinal steel in the 300 mm tie spacing specimens occurred in the same cycle, or one cycle after, the cover spalled. The rapid succession of spalling and buckling can be seen by referring to Figures IV-11, IV-12 and IV-13 in Appendix IV. Figure IV-11 shows the first 300 mm tie spacing specimen at the end of the 2d load sequence. At this stage the cracking was quite severe and a small amount of surface cover had spalled on the inside face of the leg. Figure IV-12 shows the spalled cover and buckled reinforcement on the outside face of the leg at the end of the pushing half of the first cycle of the 4d load sequence i.e. just half a load cycle after the picture in Figure IV-11 was taken. As in the 200 mm tie spacing specimen, the buckling took place in a plane at 45° to the face of the leg. Again it appears that only the bottom bar has buckled, but actually the top bar has also buckled. The spalling of cover and buckling of longitudinal reinforcement on the inside face of the leg took place during load stage 38 i.e. the second half of the first cycle of the 4d load sequence. The damage at load stage 38 is shown in Figure IV-13 of Appendix IV. The rapid succession of spalling and buckling is clear when it is considered that the pictures in Figures IV-11 and IV-13 were taken only one load cycle apart. 5.4.4 Specific behavior of second 300 mm tie spacing specimen In the second 300 mm tie spacing specimen the succession of spalling and buckling was even more rapid, with both occurring in the same half load cycle i.e. the third cycle of the 2d load sequence. The damage in the specimen at the end of the 1.5d load sequence can be seen in Figure IV-14 of Appendix IV. It is interesting to note the relatively large shear cracks (1.0 mm) in the hinge region. Shear cracks did not form to this extent in the specimens with closer hinge zone tie spacings. Since the buckling took place immediately after / as spalling occurred, no pictures of the specimen in the spalled but not buckled condition were taken. Figure IV-15 of Appendix IV shows the buckled bars on the outside face of the specimen. Spalling and buckling of the bars on the outside face took place during the first half of the third cycle of the 2d load sequence i.e. load stage 35. Note how by this stage the diagonal shear cracks had increased in width to be 1.8 mm. The longitudinal steel on the inside of the leg buckled during the second half of the third cycle of the 2d load sequence i.e. load stage 36. During the first half of the first cycle of the 3d load sequence a significant amount of damage occurred. Firstly further spalling and buckling took place on the outside of the leg. Secondly, the face cover of the leg spalled and the 38 longitudinal bars on the face of the leg buckled up. This is clearly shown in Figure IV-16 which was taken at the end of the first cycle of the 3d load sequence i.e. load stage 37. 39 6. TEST RESULTS - GENERATION OF LEG LOAD DEFLECTION PLOTS 6.1 Assumptions used and plan of presentation of test results The primary objective of this thesis was to determine the relationship between hinge zone tie spacing and the ductility of full size tilt-up frame panels. It is assumed that the plastic displacement of the full panel results entirely from the plastic rotation of the hinges which form in the top of the legs. Thus the main objective of the tests was to obtain leg load displacement plots for the respective tie spacings. This would provide the plastic displacement capacity of the legs, and therefore the plastic displacement capacity of the entire frame. The raw load displacement readings from the jack require interpretation and modification since they include deflections resulting from deformation of the steel extension beam. In order to obtain the leg deflection values corresponding to the recorded loads it was necessary to subtract deflections resulting from deformation of the parts of the test specimen other than the leg from the jack deflection readings. Referring to Figure 1-2 of Appendix I, the joint would move laterally when load was applied to the bottom of the leg because the support at the end of the beam was a roller support. This lateral movement would be included in the deflections recorded by the jack. Furthermore, the deformation of the test specimen beam as well as the steel extension beam would also contribute to rotation of the joint. This joint rotation would result in deflections at the bottom of the leg which would also be included in the deflections measured by the jack. Since it was necessary to obtain LEG load deflection plots, these deflections which originated from outside of the leg would have to be subtracted from the deflections measured by the jack. In order to calculate the magnitude of the bottom of leg deflections resulting from firstly lateral movement of the joint and secondly from joint rotations, it was necessary to calculate top of leg deflections. The computation of top of leg deflections is explained in section 6.2. The plotting of leg load vs. deflection graphs is explained in section 6.3. Strain measurements were recorded during the tests so that moment curvature plots could be generated. The success of the strain recording methods and the interpretation of the results is explained in section 6.4. Since the computer recorded load and deflection values at either 2 or 5 second intervals, each test had up to 2000 data points. All manipulation of data and calculations were done using Microsoft Excel. Extracts of the recorded test data are contained in Appendix V. The complete set of test data is available from the author at michaeljohndew@hotmail.com. 40 6.2 Computation of top of leg deflections 6.2.1 Methods of computation of top of leg deflection Three different methods were used to determine the top of leg deflections. In each of the methods it was assumed that there was rigid body motion of the joint and upper leg of the test specimen (see Figure 1-2 of Appendix I). Using this rigid body motion assumption, each of the methods calculated the rotation of the joint and then used the joint rotation to calculate the movement of the top of the leg. Given that there was relatively little cracking in the upper region of the joint and in the leg above the joint, the rigid body motion assumption seems reasonable. The three methods used to calculate top of leg deflections were as follows: 1. The most basic method involved direct measurement of the movement of the joint region using a regular 300 mm ruler. The ruler was suspended above the specimen and the movement of a line which was drawn on the specimen was recorded. The distance of the measuring point from the hinge of the test setup was recorded and it was used to calculate joint rotation. The joint rotation was then used to calculate the movement of the top of the leg using simple trigonometry. 2. For the second method, a laser pointer was glued to the top of the specimens in the middle of the joint region. The movement of the laser dot was monitored on a piece of paper positioned 8 m away. Using simple trigonometry it was possible to find the of rotation of the joint. The joint rotation was then used to calculate the movement of the top of the leg using the assumption of rigid body motion of the joint and upper leg. 3. Before the third test an extra LVDT became available and for the third to sixth tests, the top of leg deflections were measured using the LVDT. The LVDT recorded the top of leg deflections at 2 second intervals and matched them to corresponding load readings recorded by the jack. The distance of the LVDT from the hinge of the test setup was measured and used to calculate joint rotation. The joint rotation was then used to calculate the top of leg deflection using the assumption of rigid body motion for the joint and top leg. 6.2.2 Top of leg deflection calculations for test # 1, first 200 mm specimen For test one only method 1 described in section 6.2.1 above was used. However this method was used twice. Firstly the lateral movement of the joint was measured as described above. Secondly, the lateral movement of the connection between the concrete beam of the test specimen and the steel extension beam was measured. Assuming axial rigidity of concrete beam of the test specimen, and using the measured "vertical" (as viewed in Figure 1-2 of Appendix I) distance from the hinge of the test setup to the point of measurement, the rotation of the joint was calculated. The joint rotation was then used to calculate top of leg deflection. 41 The results of the two calculations are shown in Figure 4. The average of the two best fit lines was used to obtain top of leg deflections from the load values recorded by the jack i.e. this equation was programmed into the spreadsheet such that the top of leg deflections for each recorded load could be calculated. This was done in the Excel spreadsheet containing the recorded test data. 6.2.3 Top of leg deflection calculations for test # 2, first 100 mm specimen Methods one and two described in section 6.2.1 above were used to calculate the top of leg deflections for test 2. The results of the two methods are shown in Figure 5. The average of the best fit lines was used to obtain top of leg deflections from the load values recorded by the jack i.e. this equation was programmed into the spreadsheet such that the top of leg deflections for each recorded load could be calculated. This was done in the Excel spreadsheet containing the recorded test data. 6.2.4 Top of leg deflection calculations for tests #'s 3-6 and evaluation of methods used All three methods described in section 6.2.1 above were used to calculate the top of leg deflections for tests 3 to 6. The results of the three methods for specimens 3 to 6 are shown in Figures 6 to 9. Comparing the top of leg deflection results from the three methods revealed the following: The ruler method was reasonably accurate. However an assumption of the ruler method was that the load deflection movement of the top of the leg was the same as the unload deflection movement of the top of the leg. The LVDT load vs. top of leg deflection results indicate that this assumption is not true, see Figures 6 to 9. The LVDT results suggest that as the load was reduced, the beam and joint parts of the test set-up recovered first and the deflections in the leg recovered more slowly. This could be explained by the greater degree of cracking in the leg compared to the beam. Since the beam had relatively little cracking, once the load was reduced the beam was easily able to return to its original shape. In the leg where the cracking was more severe, as the load was reduced the cracks would not close completely. Only once the load direction had been reversed would the cracks be forced closed. This type of pinched hysteresis loop is typically observed in members with high shear. Although the leg failure was flexurally dominated, there was a degree of shear cracking, particularly below the hinge zone where the tie spacing was 400 mm. For specimens one and two, the use of the fitted line to calculate the load vs. top of leg deflection involved assuming that the load deflection movement of the top of the leg was the same as the unload deflection movement of the top of the leg. As explained above, this is not a true assumption and as a result the load 42 CO CD "h E E o o CM CO CD C O "-4—' o M — CD Q CD CD O CL o (fl E E o o CN <fl 0) c o u a> o= V O O) o —I o Q. o > T3 (0 O - 8 -E c co 'o a> —3 m © ® i _a> a) ZJ £. i i ro ro a) CD c c Lj _ i o o o in C D CD •—-~ T— co CO 00 co ST • 6 _oa + X ULE — T— i i C D CD m " O in L U i i C O >» I D •4> E E, c o O a **-0) Q -csr (N^ t) Peon CO > "O 03 O CD < Q - o) E "O ro ro £ ~ ® E ro £ E • b 2 E o CN co co co CM co co CM co co co CD LO CD CD CO CD CD oo oo co oo CD oo CM CD CM in CD 00 1 CD I CO CO oq CD I cq CD CD in Ti-en 43 (nm) pecn o o cn E «> E I CD ~— 44 (A Q) i— E E o o ro c o o CO Q * $ »•-o a o I-V) > •a ro O s Tf co ca co ro o co — a> '-' c? •£ Al •4 -4 ( N i ) P E O T O ro E" f i CD £ E o o CO 00 CD c o o CD Q cn CD CL o r-w > " O CO o in 0) E E o o CO in r-0) a cn o Q. o I— in > •a ro o (Nt) Peon h-CD i_ ZJ Lu 2 * O (D E i t -_j ro 12 o ra a: ~ 0 „ f N I N S 46 o o o T f CD E E o o in to h-c o o Q) »+— CD Q CD CD CL O H CO > XJ CD O in o E E o o (A 4> C g o a; Q O) 0) Q. (A > ra o (NM) PEOT 00 0 LL T3 0) o — 2 o O- • 2 £ ^ E •R «> ro o £5, 1 £ o lo P T f T f 47 CO CD E E o o CN co" to CD I— CD Q D) CD CL O 1-> TD CD O _J O CO -3 i a> CD i— Cf) Ll co o. w ^ o ra E o ^ 2 S3 5 i — CO i cv =5 i 0L_ ra o ;* 3 |o|S 48 deflection shape of the leg will not be correct. Since the ruler measurements were taken during the loading stage, the line fitted to the ruler measurements will be accurate for loading, but inaccurate for unloading. Therefore the loading part of the leg load deflection diagram will be accurate but the unloading part will not. The result of the error is that the unloading part of the leg load deflection plots for tests one and two are steeper than they should be. This effect can be observed by comparing the load deflection plots of the first and second tests to the load deflection plots of the third to sixth tests, see Figure 1-5 of Appendix I to compare test 2 to tests 3 to 6. Since it was clear that the top of leg deflection results obtained from the LVDT at the top of the leg were the most accurate, they were used to calculate the bottom of leg deflections for specimens 3 to 6. The top of leg deflection equations obtained from the ruler and laser data points were not used for specimens 3 to 6 but are shown in Figures 6 to 9 for comparison purposes. 6.3 Plotting of load vs. leg deflection graphs 6.3.1 Method of plotting of load vs. leg deflection graphs As explained above, in order to obtain the leg deflection it was necessary to subtract the following quantities from the deflection value recorded by the jack: 1. Deflection resulting from lateral movement of the joint. 2. Deflection resulting from rotation of the joint. The magnitude of the sum of the above quantities was calculated as follows: • The distance from the center of the hinge to the top of the leg, Ljoint, was constant for all of the tests (2225 mm). • The distance from the center of the hinge to the point of force application at the bottom of the leg, L j a c k , was constant for all of the tests (5125 mm). • The top of leg deflection calculated as described in section 6.2 above was multiplied by the ratio Ljac l t/L j I ) inI to obtain dsys, the "system" displacement at the bottom of the leg i.e. displacement resulting from lateral movement of the joint, d j o i m, as well as from rotation of the joint, d^. The quantities used in this calculation are illustrated in Figure 10. 49 Ljoint FIGURE 10 - LEG DISPLACEMENT DIAGRAM. It is clear from Figure 10 that the total displacement at the bottom of the joint, dsys, resulting from non leg deformations, is equal to djoint plus <!„,,. The calculation of dsys was done in excel and subtracted from the deflection recorded by the jack to obtain the leg deflection. Thus it was possible to plot load vs. leg deflection graphs. 6.3.2 Load deflection graph for test #1, first 200 mm specimen As explained in chapter 5, a number of problems were experienced during test # 1, the first 200 mm specimen. The results of test #1 are not considered in the analyses done in chapter 7. The load vs. LEG deflection plot for test #1 is shown in Figure 11. 6.3.3 Load deflection graphs for test #'s 2-6 The load vs. LEG deflection plots for test #'s 2-6 are shown in Figure 12 as well as in Figure 1-5 of Appendix I. These plots are analyzed and interpreted in chapter 7. 6.4 Interpretation of stain readings taken during testing 6.4.1 Effectiveness of strain measuring method Concrete strains were measured in the hinge region of the legs and in the beams of the specimens. The method by which the LVDT's and dial gauges were attached to the specimens was explained in section 4.4.2. The strain readings obtained at low loads, before significant cracking had occurred, appeared to be reasonably good. However once severe flexural cracks had developed this method of recording strains proved to be ineffective. The flexural cracks had a tendency to pass through the holes into which the inserts had been placed. It is possible that the drilling which was done to create the insert holes caused microcracking of the concrete around the holes resulting in an area of damaged concrete which "attracted" 50 o (m) peon 51 Figure 12 - Load vs. Leg Def lecJ ionOeste^e Figure 12a Jack Load vs LEG Deflection • Test 2,100mm Ties Figure 12b Jack Load vs LEG Deflection - Test 5.100mm Ties Figure 12e Jack Load vs LEG Deflection - Test 3, 300mm Ties Figure 12f Jack Load vs LEG Defection-Test 4, 300mm Ties flexural cracks. The result of the cracks passing through the holes was that the inserts became loose. Since the gauge length for the strain readings was typically only 400 mm, even a small amount of movement would ruin the results. 6.4.2 Hinge zone strain readings Since there was severe cracking in the hinge zone, the problems with the strain measuring system described in section 6.4.1 above were particularly severe. The results were in fact so erratic that they have not been presented. 6.4.3 Beam strain readings Since there was a lesser degree of flexural cracking in the beam, the results of the beam strain measurements were reasonably good. The strains measured on the top and bottom of the beam were used to obtain curvature values which were used to plot a moment curvature plot for the beam. The process by which the readings from the LVDT's at the top and bottom of the beam were translated into a moment curvature plot was as follows: 1. Displacement values were recorded by the LVDT's at either 2 or 5 second intervals. 2. The zero load displacements measured by the LVDT's at the beginning of the test were subtracted from the LVDT displacements at each recorded load to give displacements relative to zero load. 3. The displacements were divided by the gauge length, typically 400 mm, to give strain values. 4. The differences between the strains at the top and bottom of the beam were divided by the distance between the LVDT's at the top and bottom of the beam. The resulting value was the curvature of the beam at the given load. 5. Using the corresponding load recorded by the jack, the roller reaction was found by surnming moments about the hinge of the test set-up, see Figure 1-2 of Appendix I. This was possible since the test setup was statically determinate. The moment associated with the curvature calculated in step 4 above, was assumed to be equal to the roller reaction multiplied by the distance from the roller to the center of the gauge length of the LVDT's at the top and bottom of the beam. 6. The moment curvature graph was plotted using the curvature values from step 4 and moment values from step 5. Beam strains were recorded using LVDT's in tests one and six. However, it seems that one of the LVDT's recording the beam strain readings in test number one was faulty and therefore the results were discarded. The beam strain readings from test number six were well recorded and the resulting moment curvature plot is shown in Figure 13. 53 (uifW) luaiuow The plot in Figure 13 also contains the response of the beam section predicted using Response 200022. The gradient of the post cracking prediction of Response 200022 agrees well with the line fitted through the moment curvature values recorded from the beam during test 6. From the gradient of the beam moment curvature plot the beam stiffness could be estimated. It was fortunate that the beam moment curvature plot could be generated because the elastic stiffness obtained from this plot was used in the elastic analysis to determine the yield displacement of the frame. This is explained further in chapter 7. 55 7 INTERPRETATION AND ANALYSIS OF TEST RESULTS 7.1 Plan of presentation for result analysis As explained in chapter 5 a number of problems were experienced during test #1, the first 200 mm specimen. Therefore the results of that specimen have not been considered in the interpretation and analysis of test results done in this chapter. In chapter 6 the load vs. leg displacement plots for each of the tests were developed and these plots are shown in chapter 6 and in Figure 1-5 of Appendix I. There is information shown on the force displacement plots of Figure 1-5 of Appendix I which was not mentioned in chapter 6: the bi-linear plots and the yield points. The calculation of the yield points is explained in section 7.3. and the generation of the bi-linear plots is explained in section 7.4. The calculation of displacement ductility and the corresponding force reduction factors is done in section 7.5. 7.2 Comments on observed test behavior The load displacement plots from each of the two 100 mm specimens, fig I-5a and I-5b in Appendix I, are similar. Even though the modes of failure were different, failure occurred at similar loads and displacements and this accounts for the similarity of the load displacement hysteresis plots. The load displacement plots from each of the two 300 mm specimens, fig I-5e and I-5f, also appear similar. This is not surprising given that the modes of failure were the same. Although buckling occurred during different load sequences for each of the two 300 mm tie spacing specimens, it occurred only one load cycle apart and therefore the behavior can be assumed to be consistent. Given the consistency of performance of the 300 mm specimens, it is assumed that the 200 mm spacing load deflection plot, Figure I-5c of Appendix I, is representative of 200 mm spacing performance even though only one test result is available. 7.3 Determination of yield point of leg The load vs. leg deflection plots in Figure 1-5 of Appendix I contain small triangular markers which indicate the yield point of the legs. Since the legs have a significant quantity of distributed reinforcement, see Figure 1-3 of Appendix I, the force displacement curve is rounded in the yielding region and does not have a well defined yield point. Therefore, in order to estimate the yield load, the following method which involved the use of a layered analysis to determine the yield moment, was used: 56 • Tests indicated the steel to have a yield strength of 453 MPa, see chapter 4. • It was assumed that the strain at a depth of 740 mm was 453/200 000 = 0.002265. • The top strain was varied until an axial load equal to zero was obtained. • The corresponding moment (271 kNm) was assumed to be the yield moment. • Assuming a lever arm of 2.9 m, see Figure 1-2 of Appendix I, a yield force of 93 kN was calculated. Thus the yield load was found via a theoretical calculation, but using the yield strength obtained from tests done on reinforcement taken from the test specimens. The following method was used to obtain the yield displacement: The average displacement at approximately 75% of the yield load (70 kN) was found considering the loads and displacements for both directions from all of the tests. In other words, the absolute values of the displacements at 70 kN and at -70 kN for each test specimen were obtained from the test data. The yield displacement was assumed to be equal to 93/70 times the average displacement at 70 kN. As shown in Table 8, the average displacement at 70 kN was found to be 13.8 mm which resulted in a predicted yield displacement of 18.3 mm. TABLE 8 - ESTIMATION OF YIELD DISPLACEMENT TEST # d @ 70 kN (mm) d @ - 70 kN (mm) Average (mm) 1 14 -14.3 14.2 2 10.4 -14.7 12.6 3 17.5 -8.1 12.8 4 16.1 -15 15.6 5 17 -8.3 12.7 6 15.1 -14.3 14.7 Ave. from all tests 13.8 Predicted yield disp. 18.3 The yield point was assumed to be at a load of 93 kN and a displacement of 18.3 mm. The yield points were assumed to be the same for each of the test specimens and are shown as triangular markers on the load vs. leg deflection plots of Figure 1-5 of Appendix I. 7.4 Development of bi-linear plots and method of determination of plastic displacement of legs The bi -linear plots were constructed to provide a simple representation of the specimen behavior as well as to allow the determination of the plastic displacement of the legs of the test specimens. Plastic 57 displacement is calculated by subtracting the yield displacement from the ultimate displacement. The determination of the yield displacement (18.3 mm at 93 kN) was explained in section 7.3. The ultimate displacement is defined as the displacement to which a specimen can be deformed while retaining its load carrying capacity. However, it is noticed from the hysteresis loops, Figure 1-5 of Appendix I, that with each successive cycle to the same displacement, the load reached is reduced. This is partly a result of the Baushinger effect and partly a result of the decrease in stiffness of the test specimen as cracking increases. There is typically a large decrease in the load attained between the first and second cycles, while the loads obtained in the second and third cycles are fairly similar. In other words, by the third cycle the decrease has somewhat stabilized. Load and deflection readings at the peak of each post yielding load cycle in each load sequence were extracted from the test data and are listed in Appendix V. Also contained in Appendix V are plots which show the post yielding cycle peaks. The decrease in load attained with each successive cycle at the same displacement can clearly be seen. It is also clear from the plots that the decrease in load attained stabilizes by the third cycle. Figures 14, 15 and 16 show the absolute values of the load and deflection values for the first, second and third post yielding cycle peaks for the 100 mm, 200 mm and 300 mm test specimens respectively. For the 100 mm and 300 mm specimens, the results for both specimens with the respective tie spacings are plotted. The ductile range is considered to end when the specimen can no longer maintain a prescribed strength. For a specimen to be considered to be maintaining it's load carrying capacity, it was considered necessary for it to reach the prescribed load capacity on the third cycle of each load sequence. A question arises as to what the prescribed load capacity should be. Referring to Figure 14 for the 100 mm tie spacing specimen, and Figure 15 for the 200 mm tie spacing specimen, it is observed that the third cycle peaks are significantly above the yield load of 93 kN. Furthermore it is likely that in design, the capacity of the leg would be assumed to be larger than the strength corresponding to first yield. Once the lateral forces have been reduced by the appropriate force reduction factor, the longitudinal reinforcement would be designed assuming a maximum compressive strain in the concrete of 0.0035, with a layer analysis. The result would be that the distributed bars, most of which would be yielding, would contribute to the strength and therefore the ultimate moment assumed would be greater than the first yield moment. The calculation of the ultimate strength of the leg of the test specimen is shown in Table 9. It was assumed that there was no tension stiffening as it is unlikely that tension stiffening would be used by a typical engineer when designing the leg of a tilt-up frame panel. 58 160 140 120 100 FIGURE 14 -100 mm peaks and curve fit 50 o 1st cycle x 2nd cycle A 3rd cycle —A— fit 100 150 Leg deflection (mm) X x X X 200 250 140 120 80 60 40 20 FIGURE 15 - 200 mm peaks and curve fit 50 o 1st cycle x 2nd Cycle A 3rd cycle -*-fit 100 150 Leg deflection (mm) 200 250 140 120 100 =r 80 j 60 FIGURE 16 - 300mm peaks and curve fit o ° o , x ° * A» X A o 1 st cycle x 2nd cycle A 3rd cycle -*-m 100 150 Leg Deflection (mm) 200 250 59 TABLE 9 - ULTIMATE FLEXURAL CAPACITY OF I FO ASSUMING BOTTOM 3 LAYERS OF STEEL YIELD: fc' (MPa)= 30 Depth to bot strain (mm)= Width of C flange (mm) = d to bot of flange (mm) = Width of web (mm) Depth to CA (mm) = Ect(MPa) = 30124.7 740 190 800 190 400 ult strain = -0.00199 fr (MPa) = 0.00 str@cracking 0 alpha1= 0.7 alpha2= 1 Top strain -3.50000E-03 Bot.strain 2.06427E-02 Betal 0.902342126 Alphal 0.806718693 c(mm) 107.2788048 Axial force (N) Moments (Nmrrrt cone C -446699 cone C 157027225 concT 0 cone T OOO.OOE+O steel 446702 steel 155345338 3.217E+0 nents (kNm) = ge strain: 312372563 pni CONCRE1 Comp (N) 10 LAYER 3.263E-05 rE FORCES -445.125E+3 S OF CONCRE (rectangular TE IN COMP stress block RESSION: Mon Shrinkc 312.37 0.00E+00 Layer Depth strain cf f (MPa) d to bot of layer Area N(N) lever (mm) M (Nmm) 1 5.4 -3.33E-3 -16.6 10.7 2038 -33747 -395 13317890 2 16.1 -3.0E-3 -22.7 21.5 2038 -46245 -384 17753988 3 26.8 -2.6E-3 -27.0 32.2 2038 -54967 -373 20512584 4 37.5 -2.3E-3 -29.4 42.9 2038 -59912 -362 21715220 5 48.3 -1.9E-3 -30.0 53.6 2038 -61080 -352 21483441 6 59.0 -1.6E-3 -28.7 64.4 2038 -58472 -341 19938792 7 69.7 -1.2E-3 -25.6 75.1 2038 -52087 -330 17202817 8 80.5 -875.0E-6 -20.6 85.8 2038 -41926 -320 13397059 9 91.2 -525.0E-6 -13.7 96.6 2038 -27988 -309 8643063 10 101.9 -175.0E-6 -5.0 107.3 2038 -10273 -298 3062373 20.38E+3 -446.70E+3 157027225 1 CIN&ILt r -UKUbij - bee u&M H135 for equation &143 for area zone d to cent. strain cf f (MPa) Area N (N) lever (mm) M (Nmm) 1 740 0.0206427 0.000 32300 0 340 0 2 520 0.0134651 0.000 43700 0 120 0 3 280 0.0056351 0.000 43700 0 -120 0 4 60 -0.0015425 0.000 32300 0 -340 0 5 -0.0035 0.000 0 0 -400 0 6 -0.0035 0.000 0 0 -400 0 7 -0.0035 0.000 0 0 -400 0 000.00E+0 000.00E+0 SIEtL r-u Layer AREA fy Depth strain from phi strain sf MPa N (N) lever (mm) M (Nmm) 1 600 453 740 0.020643 0.020643 453.0 271800 340 92412000 2 400 450 520 0.013465 0.013465 450.0 180000 120 21600000 3 400 450 280 0.005635 0.005635 450.0 180000 -120 -21600000 4 600 453 60 -0.001542 -0.001542 -308.5 -185098 -340 62933338 -0.003500 -0.003500 0.0 0 -400 0 -0.003500 -0.003500 0.0 0 -400 0 -0.003500 -0.003500 0.0 0 -400 0 -0.003500 -0.003500 0.0 0 -400 0 -0.003500 -0.003500 0.0 0 -400 0 -0.003500 -0.003500 0.0 0 -400 0 -0.003500 -0.003500 0.0 0 -400 0 -0.003500 -0.003500 0.0 0 -400 0 4.47E+05 1.55E+08 60 The ultimate moment was found to be 312 kNm. Using a lever arm of 2.9m the ultimate load is found to be 107 kN. Since this is the strength which would likely be used in the design, it is the strength which the leg would have to maintain while in the ductile range. Furthermore the displacement which corresponds to this load should be used as the "yield displacement" in the displacement ductility calculation. Assuming a linear range with an elastic stiffness based on the calculations of section 7.3, the displacement corresponding to a load of 107 kN was found to be 21.1 mm. Since the 100 mm and 200 mm tie spacing specimens maintain strengths substantially larger than the first yield strength, it is appropriate to utilize this strength in design and to also use it as the threshold strength which the third cycle peaks must exceed while in the ductile range. Thus for the 100 mm and 200 mm tie spacing specimens the bi-linear curve consisted firstly of a line from the origin to the point defined by a load of 107 kN and displacement of 21.1 mm and secondly of a horizontal line starting from this point and extending in the direction of increasing displacements. The ultimate displacement will be assumed to be where a line connecting the third cycle peaks crosses the horizontal portion of the bi-linear plot. Thus the ultimate displacements for the 100 mm (see Figure 14) and 200 mm (see Figure 15) tie spacings were taken as 200 mm and 130 mm respectively. Referring to Figure 16 it is observed that the third cycle peaks for the 300 mm specimens generally do not reach the ultimate strength of 107 kN. If 107 kN was taken to be the threshold strength, the 300 mm specimens would have no ductility at all. Thus it seems that the full ultimate strength cannot be attained with a tie spacing of 300 mm. Therefore the design strength should be assumed to be the first yield strength for sections with ties at 300 mm while an ultimate strength based on a compressive concrete strain of 0.0035 can be used when ties are spaced at 100 mm or 200 mm. This idea of having different design strengths is similar to the method used in a number of steel design codes in which, depending on the class of section, different design assumptions are used. For the 300 mm tie spacings the bi-linear curve consisted firstly of a line from the origin to the point defined by a load of 93 kN and displacement of 18.3 mm and secondly of a horizontal line starting from this point and extending in the direction of increasing displacement. An ultimate displacement of 140 mm was obtained from Figure 16. To obtain the plastic displacement of the legs, the yield displacement was subtracted from the ultimate displacement. 7.5 Calculation of displacement ductility and corresponding force reduction factors 7.5.1 Displacement ductility defined Displacement ductility, ud, is defined as follows: 61 d max M dispi, lacement d (Equation 7.5.1.1 ) yield Therefore to calculate displacement ductility, the yield displacement of the frame and the ultimate displacement of the frame are required: 7.5.2 Determination of yield displacement of frame A linear elastic analysis of the frame shown in Figure I-la of Appendix I was done using a basic structural analysis computer program. In order to run the program stiffness' for the frame members were required. Using the leg yield displacement and corresponding yield load found in section 7.3, the elastic stiffness of the leg of the frame was estimated, using equation 7.5.2.1, to be 41.3 x 106 N.m 2 . The elastic stiffness of the beam was obtained from the moment curvature plot generated from the beam strain readings electronically recorded during the testing, and was calculated to be 237.7 x 106 N.m2 (see Figure 13). Using the above mentioned stiffness' for the leg and the beam in the computer analysis, the frame yield displacement was calculated to be 33 mm. The full frame analysis at first yield is contained in Appendix II. The loads used and the corresponding bending moment diagram are also shown on Figure I-lb of Appendix I. Note that the moments in the top of the legs are, on average, approximately equal to the leg first yield moment of 271 kNm. Thus the frame displacement obtained from this analysis was the frame first yield displacement and was used as the yield displacement in the displacement ductility calculation for the 300 mm tie spacing calculation. A second analysis, contained in Appendix VII was done in which the loads were increased until the moments in the tops of the legs were equal to the ultimate moment of 312 kNm, see Table 9. The frame displacement obtained from this analysis was the ultimate moment displacement and was used in the displacement ductility calculation for the 100 mm and 200 mm tie spacings. Apart from the hinge action which spread into the joint regions, there was relatively little cracking and therefore relatively little joint deformation in the tests. Therefore the joints were modeled using infinitely rigid short frame members for the computer analyses. 7.5.3 Determination of ultimate displacement of frame It is assumed that after yielding begins in the leg, all subsequent displacement is a result of plastic rotation of the hinge i.e. assume the plastic displacement of the frame equals the plastic displacement of leg. d = PL3 (Equation 7.5.1.1 ) 3EI 62 Therefore the ultimate displacement of the frame is assumed to equal the yield displacement of the frame (from the computer analysis) plus the plastic displacement of the leg. Since the plastic displacement of the leg can be obtained from the leg load deflection plots, the ultimate displacement of the frame, and therefore the displacement ductility, can now be calculated. 7.5.4 Calculation of u.d and corresponding force reduction factors, R The natural period of vibration of buildings using tilt-up wall panels as the lateral load resistance system would be in the order of 0.2 seconds i.e. typically two storey buildings. Therefore the natural period of vibration would be less than the peak spectral period which is approximately 0.5 seconds. Therefore the equal displacement principle is not applicable and the equal energy rule should be applied. The following relationship between displacement ductility, ud, and the force reduction factor, R, is obtained when the equal energy rule is applied: R = V 2 P displacement ~ 1 (Equation 7.5.4.1 ) The calculation of the displacement ductilites and corresponding force reduction factors is shown below in Table 10. Table 10 - Calculation of ductilities and force reduction factors Hinge zone tie spacing: 100 mm 200 mm 300 mm Leg ultimate displacement (mm). 200 130 140 Plastic displacement (mm)<a) 179 109 122 Frame yield displacement (mm) 38 38 33 Frame ultimate displacement (mm)(b> 217 147 155 u d ( c ) 5.7 3.9 4.7 R(d> 3.3 2.6 2.9 (a) Subtract leg yield displacement (18 mm for 300 mm spacing and 21 mm for 100 mm and 200 mm spacings) from maximum leg displacement. (b) Frame yield displacement plus plastic displacement. (c) Displacement ductility, calculated using equation 7.5.1.1. (d) Force reduction factor, calculated using equation 7.5.4.1. The relative magnitudes of the displacement ductilities and the force reduction factors are discussed in chapter 8. 63 8 CONCLUSIONS AND RECOMMENDATIONS 8.1 Mode of failure The results of the tests done on the six tilt-up frame panels tested indicated that flexural hinges will form in the top of the first storey legs before failure of the panel takes place. The hinge region was found to be approximately equal to the depth of the leg. It was further found that hinging extends up into the joint region. Although there was significant cracking in the joint region and in the ends of the beams at failure, yielding of the beam steel did not appear to have occurred when failure of the leg took place. Diagonal shear cracks did form in both the legs and beams of the test specimens, but in no case did shear failure occur. Shear cracking was more severe in the specimens with larger tie spacings. The 100 mm specimens indicated that tie spacing can effect the mode of ultimate failure. In each of the 100 mm specimens the ties held the core together very effectively, the result being that failure occurred via either longitudinal beam steel pullout or local buckling of the entire reinforcement cage. 8.2 Effect of tie spacing on ultimate strength attained As explained in section 7.4, in order for a specimen to be considered to have attained a particular strength, it is necessary for it to obtain that strength even on the third cycle of a given load sequence. Two maximum strengths were considered; ultimate strength of 312 kNm (force of 107 kN) and first yielding strength of 271 kNm (force of 93 kN). It is evident from figures 14 and 15 that the 100 mm and 200 mm tie spacing specimens both attained and maintained the ultimate load of 107 kN. The 300 mm specimen however did not attain the ultimate strength of 107 kN. It is therefore concluded that in design, if the tie spacing is small, less than 200 mm, then it is appropriate to calculate the leg flexural strength assuming a maximum compressive concrete strain of 0.0035 and account for the resistance offered by the distributed bars which are likely also yielding. However if the tie spacing is large, greater than 200 mm, then the ultimate strength should be considered to be equal to the strength at first yielding of the bottom reinforcement. This type of approach is commonly used in steel design i.e. the design assumptions are dependent on the class of section. 8.3 Effect of tie spacing on ductility and buckling of longitudinal reinforcement Hinge zone tie spacing determines the mode of failure and has a significant effect on panel ductility. Table 10 indicates that larger ductilities can be expected from a 300 mm tie spacing than from a 200 mm spacing. This does not mean that the performance of the 300 mm spacing specimens was better than that of the 200 mm spacing specimens, in fact the opposite is true. A higher threshold load was used to calculate the ductility for the 200 mm specimens i.e. the end of the ductile range for the 200 mm specimens was assumed to occur when the load dropped below 107 kN, while the end of the ductile range for the 300 mm specimens was assumed to occur when the load dropped below 93 kN. 64 The ductilities calculated in table 10 for the 100 mm (5.7) and 200 mm (3.9) tie spacings can be directly compared because they were calculated using the same assumptions. From this comparison it is clear that decreasing the tie spacing from 200 mm to 100 mm had a significant positive effect on ductility. A force reduction factor of 2 is currently prescribed in CSA A23.31 for the design of tilt-up panels. The testing done in this research indicates that this force reduction factor is appropriate for tie spacings up to 200 mm even if the full ultimate strength is assumed to be the strength retained during the ductile range. However, if the tie spacing is greater than 200 mm, a force reduction factor of 2 would be unconservative unless the maximum strength is assumed to be equal to the strength at first yielding of the longitudinal steel. Previous research910" has found that, depending on the tie stiffness, buckling can occur over multiple tie spacings. Scribner and Wight9 suggested that ties as large as the longitudinal steel may be required to prevent buckling over multiple tie spacings. All buckling observed in these tests occurred over single tie spacings. Therefore these tests indicate that ties which are half of the size of the longitudinal bars are adequately stiff to prevent buckling over multiple tie spacings. Previous researchers5'6'7'8'2'314 have observed buckling of flexural reinforcement in a number of different test setups. The S/D ratios recommended where buckling of longitudinal reinforcement is required, range between 5 and 8. The 100 mm tie spacing was sufficiently close to prevent buckling of the longitudinal bars after loss of the cover concrete. For the 100 mm tie spacing specimen which failed via local buckling of the whole hinge zone reinforcement cage, failure was initiated by out of plane buckling of the distribution reinforcement bars and not by buckling of the edge face bars which the rectangular ties were restraining. Therefore these tests indicate that a S/D ratio of 5 is adequate to prevent buckling of the longitudinal bars in compression. The out of plane buckling failure of the 100 mm tie spacing specimen could be delayed by using cross ties to restrain the distributed reinforcement bars in the hinge region. For the 100 mm tie spacing specimen in which failure resulted from pullout of the bottom longitudinal beam bar, the failure could be delayed by hooking the ends of the bars which pulled out. However, since in the two specimens tested each failure was observed once, it is concluded that if either one of the failure modes is prevented, then failure would simply occur via the other mode at approximately the same time. Therefore if failure is to be significantly delayed, cross ties should be added and the bottom longitudinal beam bars should be hooked. 65 8.4 Effectiveness of test setup and testing procedure Apart from the initial problems experienced with the sliding of the supports in test #1, the test setup performed well. Given that the area of hinging extended into the joint region, it is concluded that it was worthwhile to test the full "1/4 frame" panel because it modeled the joint region well. The ability to observe the level of damage in the beam when failure occurred in the leg, and the opportunity to record strain values from the beam also made the testing of the 1/4 frame model worthwhile. The displacement data recording system worked well, however the strain recording method only worked well while until yielding began. A better means of obtaining strains would be to attach strain gauges to the longitudinal reinforcing steel where site conditions enable this. 8.5 Recommendations The tests done clearly indicate that the maximum load attained and the ductility depend on the tie spacing. It is therefore recommended that when designing the legs of tilt-up frame panels, the method used to calculate the maximum flexural strength of the legs be dependent on the spacing of the ties in the hinge region. Further testing would be required in order to obtain accurate knowledge of what strength would be appropriate to assume for each tie spacing. Based on these tests the following recommendations are made: If the hinge zone tie spacing is less than 200 mm, the ultimate strength may be calculated assuming a maximum compressive concrete strain of 0.0035 and the resistance offered by the distributed bars, which are likely yielding, should be included. If the tie spacing is greater than 200 mm, the ultimate strength should be considered to be the strength at first yielding of the bottom steel and the resistance offered by the distributed bars, which would not have yet yielded, should be included. Thus in all cases a layer analysis should be done. If the above ultimate strengths, for members with hinge zone tie spacings greater and less than 200 mm respectively, are used as the "elastic strengths" of the tilt-up frame members, the results of this research indicate that it would then be appropriate to use a force reduction factor, R, of two in design. Since the spalling of cover extended 400 mm up into the joint region and 700 mm down the leg, these tests indicate that "hinge zone tie spacing" should be applied from a distance equal to the member depth below the joint, up to the top of the joint. 66 BIBLIOGRAPHY: 1. CSA Committee A23.3, Design of Concrete Structures, Canadian Standards Association, Rexdale, Canada, 1994 2. Concrete Design Handbook, Canadian Portland Cement Association, Ottawa, 1995 3. ACI Committee 318, Building Code Requirements for Structural Concrete, American Concrete Institute, Farmington Hills, 1999 4. Agrawal, L Tulin, K. Gerstle (1965), "Response of doubly reinforced concrete beams to cyclic loading" Journal of American Concrete Institute, 62-51, P823-834 5. Burns, C. Seiss (1966), "Plastic hinging in reinforced concrete" Journal of Structural Engineering, ASCE, vol. 92 # ST5, Oct. P45-64 6. Burns, C. Seiss (1966) "Repeated and reverse loading in reinforced concrete" Journal of Structural Engineering, ASCE vol. 92 #ST5, Oct. P65-78 7. Brown, J Jirsa (1971), "Reinforced concrete beams under load reversals" Journal of American Concrete Institute, 68-39, P380-390 8. Gosain, R. Brown, J. Jirsa (1977), "Shear requirements for load reversal in reinforced concrete members" Journal of Structural Engineering, ASCE, vol. 103 #ST4, July, PI461 9. C. Scribner, J. Wight (1980), "Strength decay of reinforced concrete beams under load reversaF Journal of Structural Engineering, ASCE, vol. 106 #ST4, April, P861 10. C. Scribner (1986), "Reinforcement buckling in reinforced concrete flexural members" Journal of American Concrete Institute, 83-85, P966-973 11. Papia, G. Russo, G. Zingone (1988), "Instability of longitudinal bars in RC columns" Journal of Structural Engineering, ASCE, vol. 112 #2, P445 12. Saatcioglu, G Ozcebe (1989), "Response of RC columns to simulated seismic loading" Structural Journal of American Concrete Institute, 86-sl, P3-12 13. Mau, (1990), "Effect of tie spacing on inelastic buckling of reinforcing bars" Structural Journal of American Concrete Institute, 87-S69, P671-677 14. Monti, C Nuti(1992), "Non-linear cyclic behavior of reinforcement bars including buckling" Journal of Structural Engineering, ASCE, vol. 112 #12, P3268 15. Azizinamini, S. Baum Kuska, P. Brungardt, E. Hatfield (1994), "Seismic behavior of square high strength concrete columns" Structural Journal of American Concrete Institute, 91-S33, P336-345 16. Ruiz, G. Winter (1969), "Reinforced concrete beams under repeated loads" Journal of Structural Engineering, ASCE vol. 95 #ST6, June, PI 189 17. Wight, M. Sozen (1975), "Strength decay of reinforced concrete columns under shear reversals" Journal of Structural Engineering, ASCE, vol. 101 #ST5, May, P1053 18. Scott, R. Park, M. Priestley (1982), "Stress strain behavior of concrete confined by overlapping hoops at low and high strain rates" Journal of American Concrete Institute, 79-2, PI 3-27 19. Pantazopoula (1998), "Detailing for reinforcement stability in RC members" Journal of Structural Engineering, ASCE, vol. 124 #6, P623-P641 20. Canadian Portland Cement Association, "Concrete Design Handbook" 1995, 116 Albert Street, Ottawa, Ontario, Canada 21. Collins and Mitchell, "Prestressed Concrete Basics." 1987, first edition, Canadian Prestressed Concrete Institute, 85 Albert Street, Ottawa, Ontario, Canada 22. Response 2000, layer analysis computer program used to predict the flexural response of reinforced concrete sections. Developed at the University of toronto under the supervision of Professor Michael Collins. A version of the program can be downloaded from www.ecf.utoronto.ca/~bentz/r2k.htm 67 APPENDIX I FIGURES FREQUENTLY REFERENCED 68 •4 800 F i gu re I-la - Frame Dimensions TDP CENTRAL MEMBER UDL down = 20 kN/n IQl UDL across = 27.8 kN/m 200 159 266 F igu re I-lb - Bending Moment Diagram FIGURE 1-1 R D L L E R S U P P O R T - 2 1 7 5 -JACK H I N G E S U P P O R T r 1 7 5 T - 2 0 0 0 , 0 -3 2 0 0 o o o o o o o n I II II n ~l H h - 8 0 0 H 6 6 0 o 1 4 0 0 2 9 0 0 Figure 1-2 - Test Setup 2 x 1200nn long 15M diagonal bars £V 8 x 10M Closed leg stirrups 8 300mn c / c 2 x 20M EF (Deflect Inside longitudinal colunn steel) 3 x 15M 8 320nn c / c EF (Deflect Inside longitudinal colunn steel) • — « 2 0 M 20M 15M 10M Ties H5M LEG SECTIDN Mi 20M 15M 10M Ties &5M 15M V 4 x 10M Closed leg stirrups e 200nn c / c HINGE ZONE TIE SPACINGS 10M e 100 nn c / c 10M e 200 nn c / c 10M 8 300 nn c / c 10M e 400 nn c /c 2 x 15M EF 2 x 20M EF 20M BEAM SECTIDN F i g u r e 1 - 3 - R e i n f o r c e m e n t D e t a i l s 71 4.0. d 72 Figure 1-5 - Load vs. Leg Deflection - Tests 2-6 Figure l-5a Jack Load vs LEG Deflection • Test 2,100mm Ties -450-. Doflection (mm) Figure l-Sb Jack Load vs LEG Deflection - Test 5,100mm Ties Deflect ion (mm) Figure l-5c Jack Load vs LEG Deflection • Test 6,200mm Ties Figure l-5d - BMinear Plots 150-, - Ultimate strength plot -Yield strength plot Deflection (mm) S -ape-Figure l-5e Jack Load vs LEG Deflection - Test 3, 300mm Ties Figure l-Sf Jack Load vs LEG Deflection - Test 4,300mm Ties Deflection (mm) APPENDIX II FRAME ANALYSIS AT YIELD SAP2000 v6.10 - File:test - Deformed Shape (LOAD1) - N-m Units 75 SAP2000 January 31,2000 9:19 .-R3Sgi. 17 30698.84 &4479.7&1-331970 14»$Q. 38 8 254174 - fcHllllf 33056S Z > X SAP2000 v6.10 - File:test - Moment 3-3 Diagram (L0AD1) - N-m units 76 SAP2000 January 31,2000 9:19 ooHi # 6 1 * ?M36 20 .O,.. .ST •Ol I! j | WU ON rrv 136873 V<>; -» -y 1823-74 Z > X SAP2000 v6.10 - File:test - Shear Force 2-2 Diagram (LOADI)-N-m Units 77 SAP2000 January 31,2000 9:17 18459.4$! i I JJ5S3I. 18 z A > X -f 385291 -292286 SAP2000 v6.10 - File:test - Axial Force Diagram (LOADI)-N-m Units 78 SAP2000 V6.10 F i l e : TEST N-ra Units PAGE 1 January 31, 2000 9:30 J O I N T D I S P L A C E M E N T S JOINT LOAD UX UY 1 LOAD1 0.0000 0.0000 2 LOAD1 0.0257 0.0000 3 LOAD1 0.0271 0.0000 4 LOAD1 0.0285 0.0000 5 LOAD1 0.0321 0.0000 6 LOAD1 0.0332 0.0000 7 LOAD1 0.0332 0.0000 8 LOAD1 0.0330 0.0000 9 LOAD1 0.0330 0.0000 10 LOAD1 0.0328 0.0000 11 LOAD1 0 . 0288 0.0000 12 LOAD1 0.0273 0.0000 13 LOAD1 0.0257 0.0000 14 LOAD1 0.0000 0.0000 15 LOAD1 0.0271 0.0000 16 LOAD1 0.0273 0.0000 uz RX RY RZ 0.0000 0 . 0000 0.0117 0 . 0000 1. 132E-04 0 . 0000 2 . 092E-03 0 . 0000 1. 140E-04 0. 0000 1. 959E-03 0 . 0000 1. 127E-04 0. 0000 1. 980E-03 0 . 0000 6 . 6S0E-06 0 0000 1. 630E-03 0. 0000 5 574E-06 0 0000 1. 601E-03 0 0000 -6 350E-04 0 0000 1 597E-03 0 0000 -1 337E-03 0 0000 2 082E-04 0 0000 -1 419E-03 0 0000 2 187E-04 0 0000 -1 416E-03 0 0000 3 078E-04 0 0000 -1 .124E-03 0 . 0000 2 217E-03 0 . 0000 -1 .120E-03 0 .0000 2 .171E-03 0 . 0000 -1 .114E-03 0 . 0000 2 .299E-03 0 . 0000 0.0000 0 . 0000 0.0116 0 . 0000 -6 .638E-04 0 .0000 1 .941E-03 0 . 0000 -2 .598E-04 0 .0000 2 .149E-03 0 .0000 79 SAP2000 V6.10 F i l e : TEST N-m Units PAGE 3 January 31, 2000 9:30 F R A M E E L E M E N T FRAME LOAD LOC 1 L0AD1 0.00 1.45 2.90 F O R C E S P 24951.98 30241.58 35531.18 V2 94436.23 94436.23 94436.23 V3 00 00 00 0.00 0.00 0.00 M2 0 . 00 0.00 0.00 0 .00 -136932.50 -27386S.00 LOAD1 0.00 3 .5E-01 7.0E-01 35531.18 36807.98 38084.78 94436.23 94436.23 94436.23 00 00 00 0.00 0.00 0.00 0.00 0.00 0.00 -273865.00 -306917.69 -339970.34 LOAD1 0.00 1. OE-01 2 . OE-01 3 .0E-01 4.0E-01 44749.23 44749.23 44749.23 44749.23 44749.23 94934.64 95573.05 96211.45 96849.84 97488.24 0.00 0 . 00 0.00 0.00 0 .00 .00 . 00 . 00 .00 .00 0.00 0 . 00 0 . 00 0.00 0.00 405450.06 395924.69 386335.44 376682.38 366965.47 LOAD1 0 . 00 1 . 67 3.35 5 .02 6 . 70 44749.23 44749.23 44749.23 44749.23 44749.23 97488.24 108181.44 118874.64 129567.84 140261.03 0 . 00 0.00 0.00 0.00 0 .00 0 . 00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0 . 00 0.00 366965.47 194717.17 4557.76 -203512.75 -429494.34 LOAD1 1 2 3 4 0.00 0E-01 OE-01 OE-01 . OE-01 44749.23 44749.23 44749.23 44749.23 44749.23 140261.03 140899.44 141537.83 142176.23 142814.63 0 . 00 0.00 0.00 0 . 00 0.00 0.00 0.00 0 . 00 0 . 00 0.00 0.00 0 . 00 0 .00 0.00 0 . 00 -429494.34 -443552.34 -457674.16 -471859.84 -486109.34 LOAD1 0 . 00 3.5E-01 7 . OE-01 -289732.69 -291009.47 -292286.28 -91823.71 -91823.71 -91823.71 0.00 0 . 00 0.00 0.00 0.00 0 . 00 0.00 0 . 00 0 . 00 -330565.25 -298426.97 -266288.66 LOAD1 0.00 1 .45 2 .90 -292286.28 -297575.88 -302865.47 -91823.71 -91823.71 -91823.71 0 . 00 0.00 0.00 0 . 00 0 . 00 0.00 0 . 00 0 .00 -266288.66 -133144.33 0.00 LOAD1 0 .00 3 . 5E-01 7.0E-01 -56849.87 -55573.07 -54296.27 49687.01 49687.01 49687.01 0.00 0.00 0.00 00 00 0 . 00 00 00 0 .00 65479.70 48089.27 30698.84 80 SAP2000 v6.10 F i l e : TEST N-m Units PAGE 4 January 31, 2000 9:30 R A M E E L E M E N T F O R C E S FRAME LOAD LOC P V2 V3 T M2 9 L0AD1 00 0.00 -54296. 27 49687. 01 0 . 00 0. 00 0 . 8 . 0E-01 -51377. 88 49687. 01 0 . 00 0 . 00 0 . 00 1.60 -48459. 48 49687. 01 0. 00 0. 00 0 . 00 10 L0AD1 0. 00 0 . 00 0.00 -48459. 48 49687. 01 0. 00 3 . 5E-01 -47182 . 68 49687. 01 0 . 00 0. 00 0 . 00 7 . OE-01 -45905. 88 49687. 01 0 . 00 0 . 00 0 . 00 11 L0AD1 00 00 0.00 49687. 01 -45905. 88 0 . 00 0 . 0 . 1 OE-01 49687. 01 -45267. 48 0 . 00 0 . 00 0 00 2 OE-01 49687 01 -44629 08 0 00 0 00 0 00 3 OE-01 49687 01 -43990 68 0 00 0 00 0 00 4 OE-01 49687 01 -43352 28 0 00 0 00 0 00 12 L0AD1 00 00 0 . 00 49687 01 -43352 28 0 00 0 0 1.67 3122 02 840 91 0 00 0 00 0 00 3 .35 -43442 96 4S034 09 0 00 0 00 0 00 5.02 -90007 95 89227 28 0 00 0 00 0 00 6 .70 -136572 94 133420 47 0 00 0 00 0 00 13 L0AD1 00 00 0 . 00 -136572 94 133420 47 0 00 0 0 1 OE-01 -136572 94 134058 86 0 00 0 00 0 00 2 0E-01 -136572 94 134697 27 0 00 0 00 0 . 00 3 .OE-01 -136572 94 135335 .66 0 00 0 00 0 . 00 4 .0E-01 -136572 .94 135974 .06 0 .00 0 . 00 0 . 00 14 LOAD1 . 00 0 . 00 -135974 .06 -136572 . 94 0 .00 0 .00 0 3 .5E-01 -137250 . 86 -136572 .94 0 .00 0 .00 0 .00 7 .OE-01 -138527 .66 -136572 . 94 0 .00 0 .00 0 . 00 15 LOAD1 .00 . 00 0 . 00 -138527 .66 -136572 . 94 0 .00 0 0 S .OE-01 -141446 .06 -136572 . 94 0 .00 0 .00 0 .00 1.60 -144364 .45 -136572 . 94 0 .00 0 .00 0 . 00 16 LOAD1 .00 0 . 00 0 . 00 -144364 .45 -136572 . 94 0 . 00 0 3 .5E-01 -145641 .25 -136572 . 94 0 .00 0 .00 0 .00 7 .OE-01 -146918 . 05 -136572 . 94 0 . 00 0 .00 0 . 00 M3 30698.84 -9050.74 -48800.32 -48800.32 -66190.74 -83581.17 83581.17 88139.84 92634.66 97065.66 101432.80 101432.80 137036.06 98615.76 -13828.11 -200295.55 -200295.55 -213669.47 -227107.25 -240608.86 -254174.31 -254174.31 -206373.86 -158573.39 -158573.39 -49315.11 59943.17 59943.17 107743.63 155544.09 81 SAP2000 V6.10 F i l e : TEST January 31, 2000 9:31 J O I N T D A T A JOINT GLOBAL-X 1 -3 75000 2 -3 75000 3 -3 75000 4 -3 75000 5 -3 75000 6 -3 75000 7 -3 35000 8 3 35000 9 3 75000 10 3 75000 11 3 75000 12 3 75000 13 3 75000 14 3 75000 15 -3 35000 16 3 .35000 N-m Units PAGE 1 GLOBAL-Y GLOBAL-2 RESTRAINTS ANGLE-A ANGLE-B ANGLE-C 3 75000 0 00000 1 1 1 0 0 0 0 000 0 000 0 000 3 75000 2 90000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 3 60000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 4 30000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 5 90000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 6 60000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 6 60000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 6 60000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 6 60000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 5 90000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 4 30000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 3 60000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 2 90000 0 0 0 0 0 0 0 000 0 000 0 000 3 75000 0 00000 1 1 1 0 0 0 0 000 0 000 0 000 3 .75000 3 60000 0 0 0 0 0 0 0 000 0 000 0 000 3 .75000 3 60000 0 0 0 0 0 0 0 000 0 000 0 000 82 SAP2000 v6.10 F i l e : TEST N-m Units January 31, 2000 9:32 PAGE 1 F R A M E E L E M E N T FRAME JNT-1 JNT-2 1 1 2 2 2 3 3 3 15 4 15 16 5 16 12 6 12 13 7 13 14 8 3 4 9 4 5 10 5 6 11 6 7 12 7 8 13 8 9 14 9 10 15 10 11 16 11 12 D A T A SECTION ANGLE LEG 0 . 000 JNTLEG 0 000 JNTBM 0 000 BEAM 0 000 JNTBM 0 000 JNTLEG 0 000 LEG 0 000 JNTLEG 0 000 LEG 0 000 JNTLEG 0 000 JNTBM 0 000 BEAM 0 000 JNTBM 0 000 JNTLEG 0 . 000 LEG 0 .000 JNTLEG 0 . 000 RELEASES SEGMENTS 000000 2 000000 2 000000 4 000000 4 000000 4 000000 2 000000 2 000000 2 000000 2 000000 2 000000 4 000000 4 000000 4 000000 2 000000 2 000000 2 Rl R2 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 000 0 .000 0 000 0 .000 0 000 0 . 000 0 . 000 0 . 000 0 .000 0 .000 0 . 000 FACTOR LENGTH 1.000 2.900 1.000 0.700 1.000 0.400 1.000 6.700 1.000 0.400 1.000 0.700 1.000 2.900 1.000 0.700 1.000 1.600 1.000 0.700 1.000 0.400 1.000 6.700 1.000 0.400 1.000 0.700 1.000 1.600 1.000 0.700 83 SAP2000 V6.10 F i l e : TEST N-m Units PAGE 1 January 31, 2000 9:32 F R A M E S P A N D I S T R I B U T E D L O A D S Load Case LOAD1 FRAME TYPE DIRECTION DISTANCE-A VALUE-A DISTANCE-B VALUE-B 12 FORCE GLOBAL-Z 0.0000 -20000.0000 1.0000 -20000.0000 12 FORCE GLOBAL-X 0.0000 27800.0000 1.0000 27800.0000 12 FORCE GLOBAL-X 0.0000 40000.0000 1.0000 40000.0000 12 FORCE GLOBAL-X 0.0000 -40000.0000 1.0000 -40000.0000 84 S T A T I C STATIC CASE L0AD1 O A D C A S E S CASE SELF WT TYPE FACTOR DEAD 1.0000 1 A T E R MAT LABEL STEEL CONC LEGMAT BEAMMAT JNTMAT I A L P R O P E R T Y MODULUS OF POISSON'S ELASTICITY RATIO D A T A THERMAL WEIGHT PER UNIT VOL COEFF 1.999E+11 2 .482E+10 5.098E+09 5.472E+09 2.000E+11 0.300 1.170E-05 0.200 9.900E-06 0.200 0.000 0.200 0.000 76819.547 23561 .609 24000 . 000 24000.000 0.300 0.000 24000.000 MASS PER UNIT VOL 7827.101 2400 .680 2400.000 2400.000 2400.000 M A T E P I A L D E S I G MAT DESIGN STEEL LABEL CODE FY LEGMAT N BEAMMAT N JNTMAT N F R A M E S E C T I O N SECTION MAT SECTION WEB FLANGE FLANGE LABEL LABEL TYPE THICK WIDTH THICK BOTTOM BOTTOM BEAM BEAMMAT 0 . 000 0 . 000 0 . 000 LEG LEGMAT 0 . 000 0 .000 0 . 000 JNTLEG JNTMAT 0 . 000 0 . 000 0 . 000 JNTBM JNTMAT 0 . 000 0 . 000 0 . 000 F R A M E S E C T I O N N D A T A CONCRETE FC REBAR FY DEPTH 1 .400 0 . 800 0 . 800 1.400 CONCRETE FCS FLANGE WIDTH TOP 0 . 190 0 . 190 0 . 190 0 . 190 SECTION AREAS LABEL BEAM LEG JNTLEG JNTBM AREA TORSIONAL INERTIA MOMENTS OF INERTIA 133 122 0.266 2.927E-03 0.152 1.555E-03 0.152 1.555E-03 0.266 2.927E-03 4.345E-02 8.107E-03 8.107E-03 4.345E-02 8.002E-04 4.573E-04 4.573E-04 8.002E-04 A2 0 .222 0 .127 0.127 0 .222 REBAR FYS FLANGE THICK TOP 0.000 0 .000 0 . 000 0 . 000 SHEAR A3 0 . 222 0 .127 0.127 0 .222 85 F R A M E SECTION GYRATION LABEL S E C T I O N P R O SECTION MODULII S33 S22 P E R T Y D A T A PLASTIC MODULII Z33 Z22 BEAM 6.207E-02 8.423E-03 9.310E-02 1.263E-02 LEG 2.027E-02 4.813E-03 3.040E-02 7.220E-03 JNTLEG 2.027E-02 4.813E-03 3.040E-02 7.220E-03 JNTBM 6.207E-02 8.423E-03 9.310E-02 1.263E-02 R A M E SECTION LABEL BEAM LEG JNTLEG JNTBM S E C T I TOTAL WEIGHT 85545 . 570 32831.984 15321.587 10214.391 O N P R O TOTAL MASS 8554.558 3283.198 1532.159 1021.439 P E R T Y RADII OF R33 R22 0.404 5.485E-02 0.231 5.485E-02 0.231 5.485E-02 0.404 5.485E-02 D A T A 86 APPENDIX III TEST HARDWARE W E B A T T A C H M E N T 21mm h o l e s f o r 3 / 4 ' b o l t s 150,0 300,0 2 8 n m h o l e s f o r 1 i n c h c o i l r o d •20.0 140,0 All p l a t e a t l e a s t g r a d e 300V, 8mm f i l l e t welds c o n t i n u o u s al l a r o u n d , Weld us ing E480XX e l e c t r o d e (metr ic ) o r E70XX e l e c t r o d e (imperial) o r equ i va l en t 89 pq i o Ul U • i—i r — CJ Ld • U u IT CL -Ld LD i — i X u Q O O C J L J • >_i • CL 91 JACK SET-UP: 3@ PLAN V I EW LOAD CELL E L E V A T I D N E= — ( r — b — — n T n i —a I LOAD CELL Co 5 5 Q Q CONNECTION TD LEG DETAIL: PLAN V IEW 31 E L E V A T I D N 92 APPENDIX IV TEST PHOTOGRAPHS UNIVERSITY OF SC Tiff UP PANEL TESTS SPECIMEN S ma MM TIE SPACING LOAD STAGE IE SEP 2 01999 FIGURE IV-1 I <M»en$m OF B TUT tif nmt SPECIMEN 8 MM WW TIE SPAC»«1 iO«> STAGE 24 » asiasaf FIGURE IV-2 95 FIGURE IV-11 FIGURE IV-12 99 FIGURE IV-13 101 APPENDIX V TEST DATA ELECTRONICALLY RECORDED TEST DATA The following measurements were electronically recorded: • Jack load (kN), all tests. • Jack Displacement (mm), all tests. • Deflection at top of leg (mm), tests 3 to 6. • Strain on top face of beam, test 6. • Strain on bottom face of beam, test 6. Since each test had up to 2000 recordings of each of the above measurements, the data has not been printed. Instead it is contained on a computer disk submitted with the thesis. The data is contained within an EXCEL spreadsheet and the columns containing the data are clearly labeled. DATA RECORDED BY HAND DURING TESTING The following data was recorded by hand during the tests: • Jack Load (kN), all tests. • Jack Displacement (mm), all tests. • LVDT displacement at top of leg (mm), tests 3-6. • Ruler measurements at joint and at the foot of the leg (mm), all tests. • Position of laser dot on paper (mm), tests 2-6. This data is contained in tables, one for each test, beginning on the following page. SELECTED DATA USED FOR ANALYSIS Load and corresponding deflection values at each of the post yielding cycle peaks for tests 2-6 were extracted from the electronically recorded data. Tables containing this data as well as plots of the data are given after the tables containing the data recorded by hand during the testing. 103 T E S T 1 - 200mm TIE S P A C I N G LOAD JACK DATA Ruler Measurements STAGE LOAD (kN DISP. Connection Hinge Top of leg Foot Push Pull (mm) Left/Right Up/Down Left/Right Up/Dow Left/Right Left/Right Up/Down 0 -2.2 150 150 150 150 150 150 150 1 25 10.9 152 148 151 150 153 490 151 2 25 -13.7 147 152 149 150 147 510 149 3 25 10.9 152 148 150 150 153 490 151 4 25 -14.7 147 152 149 150 147 512 149 5 25 10.6 152 148 151 150 153 489 150 6 25 -15.6 147 153 150 150 147 512 150 7 50 26.5 155 145 152 150 157 475 152 8 50 -31.9 144 155 149 150 143 528 149 9 50 28.6 155 144 152 150 157 473 151 10 50 -33.1 144 156 149 150 143 528 150 11 50 30.3 156 144 152 150 158 471 152 12 50 -33.5 144 156 148 150 142 529 149 13 75 43.2 158 142 153 150 161 459 153 14 75 -48.1 140 157 148 150 139 543 150 15 75 44.5 158 142 153 150 161 458 154 16 75 -50.2 140 158 147 150 139 545 149 17 75 46.8 158 142 153 150 162 455 154 18 75 -51.8 139 158 147 150 137 549 150 Pushing direction roller support moved about 20mm at this stage, reference measurements re-taken 0 14 157 142 152 150 156 484 151 19 94 79 169 132 155 151 171 423 156 20 96 -51 144 152 143 149 142 540 150 21 96.8 79 168 132 155 150 170 429 156 22 90 -51 144 153 146 150 140 545 150 23 94 79 168 132 155 150 171 422 144 Hinge Support moved significantly, by this stage plastic deformation had taken place and it was therefore not possible to "re-reference" the rulers 0 30 24 96 106 180 140 167 161 185 397 147 25 96 130 182 191 26 124 157 182 137 170 162 192 345 152 27 128 170 192 28 131 186 193 29 133 200 193 30 134 236 193 31 138 254 194 32 33 -200 83mm of plastic disp Crushing of concrete Bar rupture 104 TEST 2 - 1 0 0 m m TIE SPACING LOAD J A C K D A T A Ruler Measurements STAGE LOAD (kN) DISP. Top of Hinge Foot d of dot Push Pull (mm) Left/Right Up/Down Left/Right Up/Down (mm) 0 -2 150 150 500 150 1 25 10.3 153 150 488 150 11 2 25 -11.6 149 151 507 150 -8 3 25 8.7 153 149 489 150 11 4 25 -12.5 147 150 508 150 -9 5 25 8.8 152 150 489 150 11 6 25 -12.8 146 151 508 150 -9 7 50 24.8 157 149 475 151 27 8 50 -29.2 142 151 523 150 -22 9 50 25.5 157 149 474 149 28 10 50 -30.8 141 151 524 150 -24 11 50 26.2 158 149 473 148 29 12 50 -31.5 141 151 525 150 -24 13 75 42.6 162 148 457 154 47 14 75 -45.2 138 153 538 150 -36 15 75 43.6 162 151 456 154 47 16 75 -46.9 137 157 540 150 -36 17 75 45 162 152 455 155 49 18 75 -48.4 137 158 542 150 -38 19 97 61 166 151 439 156 69 20 97.9 -61 134 159 554 150 -44 21 93.5 61 167 150 439 156 68 22 89.9 -61 134 158 553 150 -44 23 96.2 61 166 150 438 156 68 24 89 -61 135 158 553 151 -44 25 122 92 171 149 409 160 26 108 -92 132 160 580 155 27 101 92 170 149 406 165 28 105 -92 132 160 581 155 29 106 92 170 149 405 165 30 104 -92 132 160 581 155 31 95 122 172 149 380 170 32 89 -122 132 162 609 157 33 108 122 172 149 378 171 34 106 -122 131 161 605 157 35 105 122 172 149 380 171 36 100 -122 131 162 608 157 37 130 183 38 129 -183 39 117 183 40 116 -183 41 105 183 42 119 -183 43 128 244 192 2120mm 44 -244 138 from pin 45 244 190 i.e. at Ivdt 46 -244 138 stud 47 244 200 48 -244 175 1370mm 49 245 225 from pin 50 -245 175 i.e. at insert 51 245 226 52 -245 105 TEST 3 - 300mm TIE SPACING LOAD JACK DATA LVDT Ruler Measurements d of dot on STAGE LOAD (kN) DISP. @joint Top of Hinge Foot board Push Pull (mm) (mm) Left/Right Left/Right Up/Down (mm) 0 52.9 150 500 150 1 25 20.05 49.4 153 485 151 17 2 -25 -6.04 54.6 149 509 150 -7 3 25 21.1 49 154 486 151 20 4 -25 -6.34 54.7 148 509 150 -7 5 25 21.9 48.9 154 485 151 19 6 -25 -8.9 55.2 147 511 150 -7 7 50 39.6 45 157 468 152 37 8 -50 -17.9 57.8 145 522 150 -20 9 50 40.2 45 157 467 152 36 10 -50 -25.7 59.7 144 528 150 -23 11 50 42.3 44.5 158 467 151 36 12 -50 -23.1 58.6 144 528 150 -23 13 75 57.3 41.3 161 451 154 50 14 -75 -36 61 141 542 150 -34 15 75 58 41.1 161 450 155 50 16 -75 -38.6 61.6 141 543 150 -34 17 75 59.2 41 161 450 155 50 18 -75 -38.6 61.5 141 543 150 -34 19 94 74 38.2 165 434 157 59 20 -98 -54 64.5 139 558 150 -42 21 94 74 38.5 164 435 158 59 22 -97 -54 64 138 557 150 -42 23 92 74 38 163 435 157 59 24 -91 -54 64 138 556 150 -42 25 117 106 35.6 166 405 163 71 26 -117 -86 66.4 136 591 151 -50 27 . 100 106 36.3 166 406 166 71 28 -80 -86 63.7 139 588 153 -42 29 99 106 36.2 166 405 166 69 30 -82 -86 63.8 138 588 154 -42 31 112 138 34.7 167 373 172 76 32 -106 -118 66.3 137 620 155 -50 33 104 138 34.7 167 375 172 76 34 -68 -118 64.2 137 620 156 -46 35 106 138 34.8 167 374 172 76 36 -100 -118 66 136 618 157 -50 37 112 202 33.8 167 310 181 76 106 TEST 4 - 300mm TIE SPACING LOAD JACK DATA LVDT Ruler Measurements d of dot on STAGE LOAD (kN) DISP. ©joint Top of Hinge Foot board Push Pull (mm) (mm) Left/Right LeWRight Up/Down (mm) 0 -2 57.3 150 500 150 1 25 9.73 54.9 153 490 150 10 2 25 -12 60.2 147 511 150 -12 3 25 10.1 54.8 153 490 150 10 4 25 -13.8 60.6 147 512 150 -12 5 25 10.6 54.8 152 490 151 10 6 25 -15.3 60.9 147 513 150 -12 7 50 28.15 50.7 156 473 153 27 8 50 -31.8 64.7 143 529 150 -27 9 50 31.8 50.4 157 470 153 32 10 50 -34 65.5 142 530 150 27 11 50 31.8 50.4 158 470 153 32 12 50 -34 65.8 142 533 150 -31 13 75 48.7 46.4 161 452 155 48 14 75 -51 69.4 138 549 149 -45 15 75 50.8 46.4 161 451 155 48 16 75 -54 69.8 138 549 150 -45 17 75 52 46.2 161 450 156 48 18 75 -58 70.9 137 552 150 -51 19 100 70 42.8 165 432 157 62 20 -98 -74 73 135 566 150 -61 21 94 70 43.4 163 435 158 59 22 -98 -74 73 135 568 150 -61 23 92 70 43.5 165 435 158 59 24 -96 -74 73 135 570 150 -61 25 117 106 39.6 167 398 165 75 26 -114 -110 75 132 605 152 -70 27 104 106 40.8 167 400 166 72 28 -105 -110 74.2 134 602 152 -65 29 101 106 41.3 166 398 166 72 30 -100 -110 73.9 134 604 152 -65 31 117 142 38 168 365 173 79 32 -117 -146 75.3 132 639 155 -72 33 107 142 39.4 167 366 176 77 34 -107 -146 74.5 133 635 155 -70 35 92 142 40 166 367 175 75 36 -104 -146 74.5 133 636 157 -70 Failed on the way pushing to 214mm 107 TEST 5 - 100mm TIE SPACING LOAD JACK DATA LVDT @joint (mm) Ruler Measurements d of dot on board (mm) STAGE LOAD (kN) DISP. (mm) Top of Hinge Left/Right Foot Start @DG Left/Right Up/Down 0 0 0 0 62.9 150 500 100 1 25 25 14.6 59.4 153 486 101 16 2 25 25 -11.8 65.8 147 512 100 -12 3 25 25 17.5 58.7 154 484 101 20 4 25 25 -13 66.2 147 513 100 -14 5 25 25 17.4 58.7 154 484 101 20 6 25 25 -13 66.7 147 513 100 -14 7 50 50 37 54.6 158 164 102 39 8 50 50 -26 69.3 144 528 100 -26 9 50 50 40.7 54 159 462 105 42 10 50 50 -28.5 70.1 143 529 100 -27 11 50 50 41.7 54 159 463 104 42 12 50 50 -28.7 70.1 144 528 100 -27 13 75 75 58.4 50.8 162 445 105 57 14 75 75 -44.3 73.3 139 545 100 -40 15 75 75 59 50.5 163 444 106 58 16 75 75 -46 73.5 140 546 99 -40 17 75 75 61 50.3 162 442 107 61 18 75 75 -51 74.7 139 550 99 -42 19 87 87 69 48.7 164 436 107 65 20 -99 -99 -69 76.6 137 569 99 -53 21 83 80 69 49 164 435 108 65 22 -99 -93 -69 76 136 567 100 -53 23 83 77 69 49 164 435 108 65 24 -98 -91 -69 76 136 567 100 -49 25 111 110 104 45 166 403 114 70 26 -123 -110 -104 79 136 598 101 -61 27 98 93 104 46.7 166 402 111 77 28 -113 -113 -104 79 135 598 102 -58 29 91 82 104 47.8 165 404 116 77 30 -110 -110 -104 78 135 598 103 -58 31 118 118 138 45 167 369 122 80 32 -129 -111 -138 79 134 633 104 -63 33 109 104 138 46 167 370 125 80 34 -121 -105 -138 79 134 631 105 -63 35 106 107 138 46 166 369 125 81 36 -116 -100 -138 79 135 630 105 -62 37 207 38 -138 -207 39 207 40 -121 -207 41 112 207 42 -123 -207 43 129 276 108 TEST 6 - 200mm TIE SPACING LOAD JACK DATA LVDT Ruler Measurements Dial Gauges d of dot STAGE LOAD DISP. @joint Hinge Foot Beam Outer (kN) (mm) (mm) L/R L/R Up/Down Top Bottom (mm) 0 0.15 66.2 150 500 150 4.82 5.21 1 25 14.8 61.7 155 488 151 4.86 5.22 15 2 -25 -11.5 69.5 146 513 150 4.77 5.22 -12 3 25 15.4 61.7 155 488 151 4.87 5.22 15 4 -25 -12 69 146 513 151 4.78 5.22 -12 5 25 15.1 61.7 155 488 151 4.87 5.22 15 6 -25 -13 70 146 514 150 4.78 5.22 -14 7 50 35 56 161 469 152 4.94 5.17 34 8 -50 -30 74 141 530 150 4.7 5.25 -26 9 50 37 56 161 467 152 4.97 5.14 36 10 -50 -32 74 141 532 150 4.69 5.26 -30 11 50 36 56 161 467 152 4.98 5.13 36 12 -50 -33 75 141 533 150 4.68 5.26 -30 13 75 53 52 165 450 153 5.06 4.84 49 14 -75 -44 77 139 543 150 4.51 5.3 -37 15 75 54 52 165 450 155 5.08 4.8 49 16 -75 -47 79 138 545 150 4.48 5.31 -40 17 75 56 52 165 449 155 5.09 4.78 52 18 -75 -51 78 137 549 151 4.47 5.32 -43 19 94 68 49 168 436 155 5.16 4.64 61 20 -101 -68 81 134 565 152 4.38 5.35 -53 21 91 68 49 168 437 155 5.15 4.63 61 22 -100 -68 81 135 565 152 4.4 5.35 -53 23 74 68 49 167 437 156 5.14 4.65 59 24 -100 -68 81 135 566 152 4.41 5.35 -53 25 118 102 44 172 404 161 5.21 4.36 77 26 -117 -102 83 133 598 155 4.32 5.37 -59 27 104 102 46 171 402 162 5.2 4.42 73 28 -111 -102 83 133 599 155 4.34 5.37 -59 29 101 102 46 171 403 164 5.19 4.44 73 30 -108 -102 83 133 599 155 4.36 5.36 -59 31 107 136 45 173 370 170 5.22 4.36 80 32 -119 -136 83 132 630 160 4.3 5.38 -62 33 106 136 44 173 370 170 5.21 4.4 80 34 -114 -136 82 132 631 160 4.33 5.37 -62 35 105 136 43 173 370 170 5.21 4.42 80 36 -107 -136 81 133 632 160 4.35 5.37 -62 37 123 204 40 176 305 184 5.25 4.24 93 38 -118 -204 81 132 697 165 4.27 5.36 -66 39 109 204 37 5.24 4.31 89 109 POST YIELDING CYCLE PEAKS -100 TEST TWO mm tie spacing TEST FIVE Load Stage Jack def. Load(kN) leg deflection (mm) Load stage Jack def. Load (kN) d of leg (mm) 19 d 100.833 20.34 19 d 86.171 22.86 20 -d -97.9 -25.33 20 -d -109.819 -21.08 21 d 97.428 20.8 21 d 83.334 23.11 22 -d -97.238 -26.33 22 -d -101.306 -21.67 23 d 97.144 21.65 23 d 85.509 24.57 24 -d -97.238 -27.66 24 -d -97.806 -21.87 25 1.5d 121.643 42.82 25 1.5d 111.616 47.89 26 -1.5d -113.508 -49.41 26 -1.5d -122.967 -49.73 27 1.5d 114.832 49.92 27 1.5d 99.603 50.18 28 -1.5d -106.414 -53.09 28 -1.5d -113.319 -50.93 29 1.5d 106.319 48.26 29 1.5d 101.968 54.78 30 -1.5d -104.333 -53.31 30 -1.5d -109.44 -51.28 31 2d 126.94 69.78 31 2d 117.102 79.31 32 -2d -120.035 -81.48 32 -2d -129.021 -81.38 33 2d 110.292 76.71 33 2d 110.292 76.71 34 -2d -108.022 -81.79 34 -2d -108.022 -81.79 35 2d 105.468 77.78 35 2d 105.278 81.84 36 -2d -104.806 -82.71 36 -2d -116.251 -82.53 37 3d 131.858 129.23 37 3d 128.831 140.4 38 -3d -129.493 -133 38 -3d -138.29 -142.42 39 3d 120.318 132.81 39 3d 115.683 142.83 40 -3d -121.17 -136.31 40 -3d -124.102 -138.13 41 3d 115.305 135.08 41 3d 112.846 142.69 42 -3d -119.278 -137.94 42 -3d -124.196 -143.23 43 4d 128.831 190.49 43 4d 129.115 204.4 44 -4d -133.088 -193.09 44 -4d -141.317 -203.25 45 4d 116.156 196.65 45 4d 116.346 204.85 46 -4d -123.629 -197.7 46 -4d -122.588 -202.97 47 4d 90.333 206.37 47 4d 91.752 156.41 48 -4d -122.305 -197.92 48 -4d -110.008 -207.42 49 4d 88.063 208.29 49 4d 65.551 192.12 50 -4d -111.711 -202.09 50 -4d -51.173 -202.23 51 4d 84.847 209.7 51 4d 17.405 121.66 52 -4d -109.535 -205.45 53 4d 75.672 213.31 First cycle load peaks load (kN) Leg d (mm) Second cycle load peaks Third cycle load peaks load (kN) Leg d (mm) load (kN) Leg d (mm) 19 d 100.833 20.34 21 d 97.428 20.80 23 d 97.144 21.65 20 -d -97.9 -25.33 22 -d -97.238 -26.33 24 -d -97.238 -27.66 19 d 86.171 22.86 21 d 83.334 23.11 23 d 85.509 24.57 20 -d -109.819 -21.08 22 -d -101.306 -21.67 24 -d -97.806 -21.87 25 1.5d 121.643 42.82 27 1.5d 114.832 49.92 29 1.5d 106.319 48.26 26 -1.5d -113.508 -49.41 28 -1.5d -106.414 -53.09 30 -1.5d -104.333 -53.31 25 1.5d 111.616 47.89 27 1.5d 99.603 50.18 29 1.5d 101.968 54.78 26 -1.5d -122.967 -49.73 28 -1.5d -113.319 -50.93 30 -1.5d -109.44 -51.28 31 2d 126.94 69.78 33 2d 110.292 76.71 35 2d 105.468 77.78 32 -2d -120.035 -81.48 34 -2d -108.022 -81.79 36 -2d -104.806 -82.71 31 2d 117.102 79.31 33 2d 110.292 76.71 35 2d 105.278 81.84 32 -2d -129.021 -81.38 34 -2d -108.022 -81.79 36 -2d -116.251 -82.53 37 3d 131.858 129.23 39 3d 120.318 132.81 41 3d 115.305 135.08 38 -3d -129.493 -133 40 -3d -121.17 -136.31 42 -3d -119.278 -137.94 37 3d 128.831 140.4 39 3d 115.683 142.83 41 3d 112.846 142.69 38 -3d -138.29 -142.42 40 -3d -124.102 -138.13 42 -3d -124.196 -143.23 43 4d 128.831 190.49 45 4d 116.156 196.65 47 4d 90.333 206.37 44 -4d -133.088 -193.09 46 -4d -123.629 -197.70 48 -4d -122.305 -197.92 43 4d 129.115 204.4 45 4d 116.346 204.85 48 -4d -110.008 -207.42 44 -4d -141.317 -203.25 46 -4d -122.588 -202.97 49 4d 88.063 208.29 50 -4d -111.711 -202.09 49 4d 65.551 192.12 50 -4d -51.173 -202.23 51 4d 84.847 209.70 52 -4d -109.535 -205.45 53 4d 75.672 213.31 POST YIELDING C Y C L E P E A K S - Test 2 ,100 m m ties o -4S9-100 50 o -250 -200 -150 -100 -50 -50 o o o?oo •456-o° 8 50 100 150 200 250 Leg deflection (mm) I -2 50 -200 -150 -100 -50 " D IS O o o POST YIELDING C Y C L E P E A K S • Test 5,100 m m ties wo-oo o o o 100 50 8 o -50 $ ) 0 O -150 200-CP ° 50 o o 100 150 200 250 Leg deflection (mm) 111 POST YIELDING CYCLE PEAKS - 200mm Tie spacing specimen First cycle peaks TEST 6 Load Jack Load (kN) d of leg stage def. (mm) 19 d 96.387 24.0 20 -d -105.184 -29.7 21 d 92.603 24.2 22 -d -101.4 -29.2 23 d 82.009 23.8 24 -d -99.509 -28.5 25 1.5d 119.089 47.1 26 -1.5d -120.129 -55.0 27 1.5d 105.657 48.4 28 -1.5d -112.089 -58.7 29 1.5d 105.468 51.2 30 -1.5d -108.495 -58.6 31 2d 125.426 83.3 32 -2d -121.832 -92.5 33 2d 107.927 75.9 34 -2d -116.156 -95.0 35 2d 108.967 78.6 36 -2d -112.373 -94.8 37 3d 127.413 134.2 38 -3d -131.953 -166.4 39 3d 114.832 129.1 40 -3d -95.63 -187.1 41 3d 104.995 126.6 42 -3d -102.819 -147.5 43 4d 101.306 228.0 44 -4d -88.158 -234.0 19 d 96.387 24.0 20 -d -105.2 -29.7 25 1.5d 119.09 47.1 26 -1.5d -120.1 -55.0 31 2d 125.43 83.3 32 -2d -121.8 -92.5 37 3d 127.41 134.2 38 -3d -132 -166.4 43 4d 101.31 228.0 44 -4d -88.16 -234.0 Second cycle peaks 21 d 92.603 24.2 22 -d -101.4 -29.2 27 1.5d 105.66 48.4 28 -1.5d -112.1 -58.7 33 2d 107.93 75.9 34 -2d -116.2 -95.0 39 3d 114.83 129.1 40 -3d -95.63 -187.1 Third cycle peaks 23 d 82.009 23.8 24 -d -99.51 -28.5 29 1.5d 105.47 51.2 30 -1.5d -108.5 -58.6 35 2d 108.97 78.6 36 -2d -112.4 -94.8 41 3d 105 126.6 42 -3d -102.8 -147.5 112 POST YIELDING CYCLE PEAKS - Test 6, 200 mm ties -460-g -3D0 100 50 O CD) ® O o *8 o -200 -100 ft 8 -50 X J100 -4-60-100 200 300 Leg Deflection (mm) 113 POST YIELDING CYCLE PEAKS - 300 mm TEST THREE Load Jack Load (kN) leg def Stage def. (mm) 19 d 98.09 25.92 20 -d -102.062 -16.02 21 d 96.292 27.16 22 -d -97.049 -18.48 23 d 94.684 27.02 24 -d -91.563 -17.79 25 1.5d 117.67 47.78 26 -1.5d -116.724 -40.91 27 1.5d 99.603 49.80 28 -1.5d -79.361 -49.96 29 1.5d 99.036 49.47 30 -1.5d -82.388 -49.61 31 2d 113.697 76.67 32 -2d -106.508 -73.40 33 2d 108.305 76.59 34 -2d -101.873 -70.92 35 2d 106.792 77.33 36 -2d -101.873 -74.75 37 3d 117.197 136.29 38 -3d -110.67 -133.55 39 3d 101.589 143.11 40 -3d -98.09 -143.31 41 3d 92.131 152.06 42 -3d -85.509 -153.27 43 4d 79.077 180.53 44 -4d -47.106 -163.48 tie spacing TEST FOUR Load Jack Load (kN) d of leg Stage def. (mm) 19 d 100.076 28.01 20 -d -104.711 -28.73 21 d 95.063 30.02 22 -d -100.927 -29.12 23 d 93.549 30.31 24 -d -100.36 -30.07 25 1.5d 117.008 54.12 26 -1.5d -115.4 -59.33 27 1.5d 104.333 58.37 28 -1.5d -102.346 -62.08 29 1.5d 101.589 60.31 30 -1.5d -102.252 -62.42 31 2d 117.102 87.73 32 -2d -115.873 -94.51 33 2d 107.359 90.76 34 -2d -110.765 -96.59 35 2d 97.806 93.44 36 -2d -106.508 -95.76 37 3d 103.481 130.68 38 -3d -90.05 -147 39 3d 80.023 162 40 -3d -47.106 -166.93 First cycle peaks 19 d 98.09 25.92 20 -d -102.062 -16.02 19 d 100.076 28.01 20 -d -104.711 -28.73 25 1.5d 117.67 47.78 26 -1.5d -116.724 -40.91 25 1.5d 117.008 54.12 26 -1.5d -115.4 -59.33 31 2d 113.697 76.67 32 -2d -106.508 -73.40 31 2d 117.102 87.73 32 -2d -115.873 -94.51 37 3d 117.197 136.29 38 -3d -110.67 -133.55 37 3d 103.481 130.68 38 -3d -90.05 -147 43 4d 79.077 180.53 44 -4d -47.106 -163.48 Second cycle peaks 21 d 96.292 27.16 22 -d -97.049 -18.48 21 d 95.063 30.02 22 -d -100.927 -29.12 27 1.5d 99.603 49.80 28 -1.5d -79.361 -49.96 27 1.5d 104.333 58.37 28 -1.5d -102.346 -62.08 33 2d 108.305 76.59 34 -2d -101.873 -70.92 33 2d 107.359 90.76 34 -2d -110.765 -96.59 39 3d 101.589 143.11 40 -3d -98.09 -143.31 39 3d 80.023 162 40 -3d -47.106 -166.93 Third cycle peaks 23 d 94.684 27.02 24 -d -91.563 -17.79 23 d 93.549 30.31 24 -d -100.36 -30.07 29 1.5d 99.036 49.47 30 -1.5d -82.388 -49.61 29 1.5d 101.589 60.31 30 -1.5d -102.252 -62.42 35 2d 106.792 77.33 36 -2d -101.873 -74.75 35 2d 97.806 93.44 36 -2d -106.508 -95.76 41 3d 92.131 152.06 42 -3d -85.509 -153.27 114 POST YIELDING CYCLE PEAKS - Test 3, 300 mm ties 160-50 O o o -21 bo -150 -100 <3> Moo -460-50 100 150 Leg Deflection (mm) °, -2 POST YIELDING CYCLE PEAKS - Test 4, 300 mm ties 4 6 0 -50 00 -150 -100 -50 o o -460-O O O 50 Leg Deflection (mm) 150 200 115 APPENDIX VI FRAME ANALYSIS FOR DISPLACEMENT AT ULTIMATE STRENGTH 116 SAP2000 March 13,2000 20:49 e « SAP2000 March 13,2000 20:48 IT) in O O 58*0$. 76. -•i 5, felt} •-: •IJ708I z A ->X SAP2000 v6.10 - File:test2 - Axial Force Diagram (L0AD1) - N-m Units 118 SAP2000 March 13,2000 20:48 - --• ••- 1 3 • — • fg75?6 I 0 f 107.13 z 10120?. 31 -> X SAP2000 v6.10 - File:test2 - Shear Force 2-2 Diagram (LOAD1) - N-m Units 119 SAP2000 March 13,2000 20:48 B4686.76 ••as;-z A -> X a o — i- '846 I? 21 #70 J76673| 1 38»osa T20" SAP2000 v6.10 - File:test2 - Moment 3-3 Diagram (LOAD 1) - N-m Units SAP2000 V6.10 File: TEST2 N-m Units March 13, 2000 20:37 J O I N T D I S P L A C E M E N T S JOINT LOAD UX UY UZ RX RY RZ 1 LOAD1 0.0000 0.0000 0.0000 D.0000 D.0135 0.0000 2 LOAD1 0.0296 0.0000 1.432E-04 0.0000 2.378E-03 0.0000 3 LOAD1 0.0312 0.0000 1.442E-04 0.0000 2.225E-03 0.0000 4 LOAD1 0.0327 0.0000 1.427E-04 0.0000 2.249E-03 0.0000 5 LOAD1 0.0369 0.0000 1.607E-05 0.0000 1.912E-03 0.0000 6 LOAD1 0.0382 0.0000 1.475E-05 0.0000 1.880E-03 0.0000 7 LOAD1 0.0382 0.0000 -7.377E-04 0.0000 1.875E-03 0.0000 8 LOAD1 0.0380 0.0000 -1.545E-03 0.0000 2.022E-04 0.0000 9 LOAD1 0.0380 0.0000 -1.625E-03 0.0000 2.143E-04 0.0000 10 LOAD1 0.0378 0.0000 -1.621E-03 0.0000 3.179E-04 0.0000 11 LOAD1 0.0332 0.0000 -1.281E-03 0.0000 2.582E-03 0.0000 12 LOAD1 0.0314 0.0000 -1.277E-03 0.0000 2.529E-03 0.0000 13 LOAD1 0.0296 0.0000 -1.269E-03 0.0000 2.676E-03 0.0000 14 LOAD1 0.0000 0.0000 0.0000 0.0000 0.0134 0.0000 15 LOAD1 0.0312 0.0000 -7.389E-04 0.0000 2.204E-03 0.0000 16 LOAD1 0.0314 0.0000 -2.739E-04 0.0000 2.505E-03 0.0000 J O I N T R E A C T I O N S JOINT LOAD F1 1 LOAD1 -109207 14 LOAD1 -105193 F2 F3 M1 M2 M3 0.0000-32965.1758 0.0000 0.0000 0.0000 344378.6563 0.0000 0.0000 F R A M E E L E M E N T F O R C E S 0.0000 0.0000 FRAME LOAD LOC P V2 V3 T M2 M3 1 LOAD1 0.00 32965.18 109207.34 0.00 0.00 0.00 0.00 1.45 38254.77 109207.34 0.00 0.00 0.00 -158350.58 2.90 43544.37 109207.34 0.00 0.00 0.00 -316701.16 2 LOAD1 0.00 43544.37 109207.34 0.00 0.00 0.00 -316701.16 3.5E-01 44821.17 109207.34 0.00 0.00 0.00 -354923.75 7.0E-01 46097.97 109207.34 0.00 0.00 0.00 -393146.31 3 LOAD1 0.00 52483.29 112894.13 0.00 0.00 0.00 469524.75 1.OE-01 52483.29 113532.52 2.0E-01 52483.29 114170.92 3.0E-01 52483.29 114809.32 4.0E-01 52483.29 115447.72 4 L0AD1 0.00 52483.29 115447.72 1.67 52483.29 126140.92 3.35 52483.29 136834.11 5.02 52483.29 147527.31 6.70 52483.29 158220.52 5 LOAD1 0.00 52483.29 158220.52 1.OE-01 52483.29 158858.91 2.0E-01 52483.29 159497.31 3.0E-01 52483.29 160135.70 4.0E-01 52483.29 160774.11 6 LOAD1 0.00 -331245.88 -105192.60 3.5E-01 -332522.66 -105192.60 7.0E-01 -333799.47 -105192.60 7 LOAD1 0.00 -333799.47 -105192.60 1.45 -339089.06 -105192.60 2.90 -344378.66 -105192.60 8 LOAD1 0.00 -66796.15 56724.05 3.5E-01 -65519.35 56724.05 7.0E-01 -64242.55 56724.05 9 LOAD1 0.00 -64242.55 56724.05 8.0E-01 -61324.16 56724.05 1.60 -58405.76 56724.05 10 LOAD1 0.00 -58405.76 56724.05 3.5E-01 -57128.96 56724.05 7.0E-01 -55852.16 56724.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 458203.44 0.00 446818.25 0.00 435369.25 0.00 423856.38 0.00 423856.38 0.00 221525.97 0.00 1284.44 0.00 -236868.19 0.00 -492931.91 0.00 -492931.91 0.00 -508785.84 0.00 -524703.63 0.00 -540685.25 0.00 -556730.69 0.00 -378693.25 0.00 -341875.84 0.00 -305058.44 0.00 -305058.44 0.00 -152529.22 0.00 0.00 0.00 76378.45 0.00 56525.06 0.00 36671.67 0.00 36671.67 0.00 -8707.55 0.00 -54086.76 0.00 -54086.76 0.00 -73940.15 0.00 -93793.54 11 L0AD1 0.00 1.OE-01 2.0E-01 3.0E-01 4.0E-01 12 LOAD1 0.00 1.67 3.35 5.02 -6.70 -13 LOAD1 0.00 • 1.OE-01 2.0E-01 3.0E-01 4.0E-01 14 LOAD1 0.00 • 3.5E-01 7.0E-01 15 LOAD1 0.00 • 8.0E-01 1.60 • 16 LOAD1 0.00 • 3.5E-01 7.0E-01 56724.05 -55852.16 0.00 0.00 56724.05 -55213.76 0.00 0.00 56724.05 -54575.36 0.00 0.00 56724.05 -53936.96 0.00 0.00 56724.05 -53298.56 0.00 0.00 56724.05 -53298.56 0.00 0.00 3124.07 -730.38 0.00 0.00 -50475.91 51837.81 0.00 0.00 104075.90 104405.99 0.00 0.00 157675.88 156974.17 0.00 0.00 157675.88 156974.17 0.00 0.00 -157675.88 157612.58 0.00 0.00 -157675.88 15^*^97 0.00 0.00 -157675.88 158889.38 0.00 0.00 -157675.88 159527.77 0.00 0.00 159527.77 -157675.88 0.00 0.00 -160804.56 -157675.88 0.00 0.00 -162081.36 -157675.88 0.00 0.00 162081.36 -157675.88 0.00 0.00 -164999.77 -157675.88 0.00 0.00 167918.16 -157675.88 0.00 0.00 167918.16 -157675.88 0.00 0.00 -169194.95 -157675.88 0.00 0.00 -170471.77 -157675.88 0.00 0.00 0.00 93793.54 0.00 99346.84 0.00 104836.30 0.00 110261.91 0.00 115623.69 0.00 115623.69 0.00 160872.91 0.00 118070.45 0.00 -12783.69 0.00 -231689.52 0.00 -231689.52 0.00 -247418.81 0.00 -263211.97 0.00 -279068.94 0.00 -294989.75 0.00 -294989.75 0.00 -239803.27 0.00 -184616.80 0.00 -184616.80 0.00 -58476.16 0.00 67664.46 0.00 67664.46 0.00 122850.95 0.00 178037.42 S T A T I C L O A D C A S E S S T A T I C CASE S E L F WT CASE T Y P E FACTOR LOAD1 DEAD 1.0000 123 J O I N T D A T A J O I N T GLOBAL-X G L O B A L - Y G L O B A L - Z RESTRAINTS A N G L E - A A N G L E - B A N G L E - C 1 -3 .75000 3 75000 0 .00000 1 1 1 0 0 0 0 .000 2 0 . 000 -3 . 75000 0 . 000 3 75000 2 .90000 0 0 0 0 0 0 0 .000 3 0 . 000 -3 .75000 0 . 000 3 .75000 3 . 60000 0 0 0 0 0 0 0 .000 4 0 . 000 -3 .75000 0 . 000 3 .75000 4 .30000 0 0 0 0 0 0 0 . 000 5 0 . 000 -3 .75000 0. 000 3 .75000 5 .90000 0 0 0 0 0 0 0 . 000 6 0 .000 -3 .75000 0 . 000 3 .75000 6 .60000 0 0 0 0 0 0 0 . 000 7 0 . 000 -3 .35000 0 000 3 . 75000 6 .60000 0 0 0 0 0 0 0 . 000 8 0 .000 3 .35000 0 000 3 . 75000 6 . 60000 0 0 0 0 0 0 0 . 000 9 0 . 000 3 .75000 0 000 3 . 75000 6 . 60000 0 0 0 0 0 0 0 . 000 10 0 3 000 . 75000 0 000 3 . 75000 5.90000 0 0 0 0 0 0 0 . 000 11 0 3 . 000 . 75000 0 .000 3 . 75000 4.30000 0 0 0 0 0 0 0 . 000 12 0 3 .000 .75000 0 . 000 3 .75000 3.60000 0 0 0 0 0 0 0 . 000 13 0 3 . 000 . 75000 0 . 000 3 .75000 2.90000 0 0 0 0 0 0 0 . 000 14 0 3 . 000 . 75000 0 . 000 3 .75000 0 . 00000 1 1 1 0 0 0 0 . 000 15 0 -3 . 000 .35000 0 . 000 3 .75000 3.60000 0 0 0 0 0 0 0 . 000 16 0 3 . 000 .35000 0 .000 3 .75000 3.60000 0 0 0 0 0 0 0 . 000 0 . 000 0 .000 F R A M E E L E M E N T FRAME J N T - 1 J N T - 2 R l 1 0 .000 2 0 . 000 3 0 . 000 4 0 . 000 5 0 . 000 6 0 . 000 7 0 .000 8 0 . 000 R2 FACTOR 1 2 0 .000 2 3 0 .000 3 15 0 . 000 15 16 0 . 000 16 12 0 . 000 12 13 0 . 000 13 14 0 .000 3 4 0 . 000 LEG 1. 000 J N T L E G 1.000 JNTBM 1.000 BEAM 1.000 JNTBM 1. 000 J N T L E G 1.000 L E G 1.000 J N T L E G 1.000 D A T A SECTION LENGTH 0 . 000 2 . 900 0 . 000 0 . 700 0 . 000 0 .400 0 . 000 6 .700 0.000 0 .400 0 . 000 0 .700 0 .000 2 . 900 0.000 0 .700 ANGLE RELEASES SEGMENTS 000000 000000 000000 000000 000000 000000 000000 000000 2 2 4 4 4 2 2 2 9 0 .000 10 0 . 000 11 0 . 000 12 0 . 000 13 0 . 000 14 0 .000 15 0 .000 16 0 . 000 0.000 0 . 000 0 . 000 0.000 0 . 000 0 . 000 10 0 . 000 11 5 6 7 8 9 10 11 12 0 . 000 M A T E R I A L L E G 1 .000 J N T L E G 1. 000 JNTBM 1.000 BEAM 1.000 JNTBM 1. 000 J N T L E G 1. 000 L E G 1 .000 J N T L E G 1. 000 0 . 000 1.600 0.000 0 .700 0 . 000 0.400 0 . 000 6.700 0 . 000 0.400 0 . 000 0.700 0 . 000 1.600 0 . 000 0 . 700 000000 000000 000000 000000 000000 000000 000000 000000 P R O P E R T Y D A T A MAT MODULUS OF POISSON'S THERMAL WEIGHT PER MASS PER LABEL E L A S T I C I T Y RATIO COEFF UNIT VOL UNIT VOL STEEL' 1.999E+11 0 .300 1 170E-05 76819 547 7827 101 CONC 2.482E+10 0 .200 9 900E-06 23561 609 2400 680 LEGMAT 5.098E+09 0 .200 0 . 000 24000 000 2400 000 BEAMMAT 5.472E+09 0.200 0 . 000 24000 000 2400 000 JNTMAT 2.000E+11 0 .300 0 . 000 24000 000 2400 000 SAP2000 V6 . 1 0 F i l e : TEST2 N-m U n i t s PAGE 5 M a r c h 13, 2000 20:38 M A T E R I A L D E S I G N MAT DESIGN S T E E L REBAR LABEL CODE FY FYS D A T A CONCRETE FC REBAR FY S T E E L CONC 275790304 LEGMAT BEAMMAT JNTMAT F R A M E SECTION FLANGE LABEL THICK TOP BEAM 0 . 000 L E G 0 . 000 248211296 S C N N N S E C T I O N MAT SECTION 27579030 413685504 CONCRETE FCS 27579030 WEB FLANGE L A B E L T Y P E THICK WIDTH BEAMMAT 0 . 000 LEGMAT 0 .000 BOTTOM 0 .000 0 . 000 P R O P E R T Y FLANGE THICK BOTTOM 0 . 000 0 . 000 D A T A DEPTH 1.400 0 . 800 FLANGE WIDTH TOP 0 .190 0.190 125 J N T L E G JNTMAT 0.800 0.190 0 .000 0.000 0 .000 0.000 JNTBM JNTMAT 1.400 0.190 0 .000 0.000 0 .000 0.000 F R A M E S E C T I O N P R O P E R T Y D A T A SECTION AREA TORSIONAL MOMENTS OF INERTIA SHEAR AREAS L A B E L INERTIA 133 122 A2 A3 BEAM 0 .266 2 . 9 2 7 E - 0 3 4 . 3 4 5 E - 0 2 8 . 0 0 2 E - 0 4 0 .222 0 .222 L E G 0.152 1 . 5 5 5 E - 0 3 8 .107E-03 4 . 5 7 3 E - 0 4 0 .127 0 . 127 J N T L E G 0.152 1 .555E-03 8 .107E-03 4 . 5 7 3 E - 0 4 0 .127 0 . 127 JNTBM 0.266 2 . 9 2 7 E - 0 3 4 .345E-02 8 . 0 0 2 E - 0 4 0.222 0 . 222 SAP2000 V6 . 1 0 F i l e : TEST2 N-m U n i t s PAGE 8 M a r c h 13, 2000 20:38 F R A M E S E C T I O N P R O P E R T Y D A T A SECTION SECTION MODULII PLASTIC MODULII RADII OF GYRATION L A B E L S33 S22 Z33 Z22 R33 R22 BEAM 6 . 2 0 7 E - 0 2 8 . 4 2 3 E - 0 3 9 .310E-02 1 .263E-02 0.404 5 . 4 8 5 E - 0 2 L E G 2 . 0 2 7 E - 0 2 4 . 8 1 3 E - 0 3 3 .040E-02 7 . 2 2 0 E - 0 3 0 .231 5 . 4 8 5 E - 0 2 J N T L E G 2 . 0 2 7 E - 0 2 4 . 8 1 3 E - 0 3 3 . 0 4 0 E - 0 2 7 . 2 2 0 E - 0 3 0 .231 5 . 4 8 5 E - 0 2 JNTBM 6 . 2 0 7 E - 0 2 8 . 4 2 3 E - 0 3 9 .310E-02 1 .263E-02 0.404 5 . 4 8 5 E - 0 2 SAP2000 V6 . 1 0 F i l e : TEST2 N-m U n i t s PAGE 9 M a r c h 13, 2000 20:38 F R A M E S E C T I O N P R O P E R T Y D A T A SECTION TOTAL TOTAL L A B E L WEIGHT MASS BEAM 85545.570 8554.558 L E G 32831.984 3283 .198 J N T L E G 15321.587 1532 .159 JNTBM 10214.391 1021 .439 SAP2 000 v 6 . 1 0 F i l e : TEST2 N-m U n i t s PAGE 10 M a r c h 13, 2000 20:38 S H E L L S E C T I O N P R O P E R T Y D A T A SECTION MAT SHELL MEMBRANE BENDING MATERIAL L A B E L L A B E L TYPE THICK THICK ANGLE SSEC1 CONC 1 1.000 1.000 0 .000 SAP2000 V6 . 1 0 F i l e : TEST2 N-m U n i t s PAGE 11 M a r c h 13, 2000 20:38 S H E L L S E C T I O N P R O P E R T Y D A T A SECTION TOTAL TOTAL L A B E L WEIGHT MASS SSEC1 0 .000 0.000 SAP2000 V 6 . 1 0 F i l e : TEST2 N-m U n i t s PAGE 12 M a r c h 13, 2000 20:38 G R O U P M A S S D A T A GROUP M-X M-Y M-Z A L L 14391.352 14391.352 14391.352 SAP2000 V6 . 1 0 F i l e : TEST2 N-m U n i t s PAGE 13 M a r c h 13 , 2000 20:38 F R A M E S P A N D I S T R I B U T E D L O A D S L o a d Case LOAD1 FRAME TYPE DIRECTION D I S T A N C E - A V A L U E - A D I S T A N C E - B V A L U E - B 12 FORCE GLOBAL-X 0 .0000 32000.0000 1.0000 32000 .0000 12 FORCE G L O B A L - Z 0.0000 -25000.0000 1.0000 -25000 .0000 

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