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A contribution to the study of the performance of steel pipe piles welded to concrete pier cap beams… Steunenberg, Mark 1996

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A CONTRIBUTION TO THE STUDY OF THE PERFORMANCE OF STEEL PIPE PILES WELDED TO CONCRETE PIER CAP BEAMS UNDER SEISMIC LOADS by MARK STEUNENBERG B.A.Sc, The University of British Columbia, 1994 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1996 © Mark Steunenberg 1996 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT ii ABSTRACT The Ministry of Transportation and Highways of B.C. implemented a modular bridge program in the Province. In the case of a seismic event, ductility is intended to be achieved through yielding of the steel pipe piles. Each pile has a full strength, overhead weld connecting it to an embedded plate which is cast into the precast concrete abutments and pile caps. The steel piles are intended to undergo plastic hinging; however, a high quality overhead weld is not easy to achieve under adverse site conditions. The performance of the weld under seismic loads is not the only concern. There is limited information on the design of large embedded plates using deformed bar concrete anchors made from deformed wire. This investigation focused on the connection between the steel pile and the concrete cap beam. Two full scale pile segments underwent reversed cyclic loading in order to determine the strength and ductility of the connection. Non-linear, two dimensional modelling and linear, three dimensional finite element modelling was performed. The first specimen failed by the desired plastic hinging. The flail strength weld between the pipe and embedded plate did not fail. The strength and ductility of the connection was as predicted. However, there were initial signs that the deformed anchor bars welded to the embedded plate were debonding. The second specimen was a slightly larger pipe welded to the same concrete beam. The second specimen experienced an embedded plate anchorage failure. The strength and ductility were both well below the desired levels. Although the anchors were longer than the recommended development length, the majority of bars slipped rather than fractured. This slippage led to the low strength and poor ductility. The higher than specified anchor strengths combined with the effects of cyclic loading have been identified as the primary reasons for the disturbing debonding which was observed. { TABLE OF CONTENTS iii T A B L E O F C O N T E N T S ABSTRACT ii TABLE OF CONTENTS iii LIST OF TABLES vi LIST OF FIGURES vii ACKNOWLEDGEMENT ix 1.0 INTRODUCTION 1 1.1 BACKGROUND 1 1.2 OBJECTIVES 4 1.3 SCOPE 4 2.0 THEORETICAL BACKGROUND 5 2.1 DESIGN PHILOSOPHY 5 2.1.1 Ductility 5 2.1.2 Capacity Design 6 2.1.3 Overstrength Factor 7 2.2 FAILURE MODES 8 2.2.1 Elastic Buckling of the Pipe Wall 8 2.2.2 Plastic Hinge Formation in Pipe Pile 8 2.2.3 Lamellar Tearing of Embedded Plate 10 2.2.4 Embedded Plate Anchorage Failure 11 2.2.5 Yielding of the Embedded Plate 13 2.2.6 Pile Cap Beam Failure in Shear or Flexure 14 2.2.7 Weld Failure Between Pipe and Embedded Plate 14 3.0 EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 16 3.1 GENERAL 16 3.2 TEST SPECIMENS #1 AND #2 16 3.2.1 Reinforced Concrete Beam .«• 17 3.2.2 Steel Pipe Pile 21 3.2.3 Overhead Welding 23 3.3 TEST SETUP 26 3.4 LOADING SEQUENCE 28 3.5 INSTRUMENTATION 30 3.5.1 Test Specimen #1 30 3.5.2 Test Specimen #2 32 TABLE OF CONTENTS TABLE OF CONTENTS (continued) 4.0 T E S T R E S U L T S 3-4.1 G E N E R A L 3-4.2 T E S T S P E C I M E N #1 3: 4.2.1 Hysteresis Curves 3: 4.2.2 Deformed Bar Strains 3' 4.2.3 Qualitative Observations 3! 4.2.4 Additional Observations Following Test #1 4' 4.3 T E S T S P E C I M E N #2 4 4.3.1 Hysteresis Curves 4' 4.3.2 Deformed Bar Strains 4: 4.3.3 Qualitative Observations 4' 4.3.4 Additional Observations Following Test #2 5: 5.0 A N A L Y T I C A L M O D E L L I N G 61 5.1 S I M P L E M O D E L 6< 5.1.1 Pipe Bending 61 5.1.2 Embedded Plate Rotation 6-5.2 F IN ITE E L E M E N T M O D E L 6' 5.2.1 Model Description 6' 6.0 C O M P A R I S O N B E T W E E N A N A L Y T I C A L & E X P E R I M E N T A L W O R K 7 6.1 S P E C I M E N #1 7! 6.1.1 Strains Below Yield In Anchorage Bars For Specimen #1 7. 6.1.2 Tensile Strains In Deformed Bar Anchors 7. 6.1.3 Compressive Strains In Deformed Bar Anchors 7< 6.1.4 Comparison at Yield and Maximum Moments 7: 6.1.5 Three Dimensional Distribution to Anchors 7" 6.1.6 Finite Element Model Stress Contours 8< 6.2 S P E C I M E N #2 8: 6.2.1 Slippage O f Deformed Bar Anchors In Specimen #2 8i 6.2.2 Comparison at Yield and Maximum Moments 81 6.2.3 Three Dimensional Distribution to Anchors 8' 6.2.4 Finite Element Model Stress Contours 8 ( 7.0 D I S C U S S I O N OF D E F O R M E D B A R S L I P P A G E 9: 7.1 P A R A M E T E R S I N F L U E N C I N G B O N D S T R E N G T H 9: 7.1.1 Concrete Strength 9: 7.1.2 Monotonic versus Reversed Cyclic Loading 9. 7.1.3 Steel Bar Deformations 9 7.2 E X P L A N A T I O N F O R B A R S L I P P A G E 9-7.2.1 Actual Stress Strain Relationship 9: 7.2.2 Reversed Cyclic Loading 9i TABLE OF CONTENTS v TABLE OF CONTENTS (continued) 7.3 P R O G R E S S I O N O F D E S I G N A P P R O A C H E S F O R D 2 L A N C H O R S 97 7.3.1 Present Approach Based on Specified Yield Stress With Large Ductility 97 7.3.2 Anchorage Strength Based on Actual Steel Properties 98 7.3.3 Anchorage Strength Considering Bond Failure 99 7.3.4 Anchorage Strength Considering Effects of Cyclic Loading 100 7.4 C H A N G E S T O T H E A N C H O R A G E S Y S T E M 100 7.4.1 Continue to use Nelson D 2 L Anchors 101 7.4.2 Use Conventional Reinforcing Steel 102 8.0 C O M P U T E R I Z E D D E S I G N A I D 104 8.1 P R O G R A M B A S I C S 104 8.1.1 Worksheets 105 8.1.2 Input and Output 106 8.1.3 Checks 107 8.1.4 Interactive Buttons 107 8.1.5 Quick Reference Tables 108 8.2 P R O G R A M C O M P O N E N T S 109 8.2.1 Steel Pipe, M p [ P l P E ] 109 8.2.2 Concrete Beam, V r [ B E A M ] , M r f B E A M ] 110 8.2.3 Embedded Plate Anchorage, M r [ A N C H ] 110 8.2.4 Plate Yielding At Pipe Edge, M y f P L A T E ] I l l 8.2.5 Summary Sheet, S U M M A R Y I l l 9.0 A L T E R N A T I V E C O N N E C T I O N S 112 9.1 C H A N G E S T O T H E S T E E L PIPE A N D O V E R H E A D W E L D 112 9.1.1 Steel Pipe Collar 113 9.1.2 Stiffeners Added to Connection 114 9.1.3 Holes Put into Pipe 115 9.2 C H A N G E S T O T H E A N C H O R A G E 116 9.2.1 Longer Nelson D 2 L Deformed Bars 116 9.2.2 End Plates 116 9.2.3 Hooked Ends 116 9.2.3 Conventional Rebar 117 10.0 S U M M A R Y 118 10.1 C O N C L U S I O N S 118 10.2 R E C O M M E N D A T I O N S 120 R E F E R E N C E S 121 A P P E N D I X A M A T E R I A L P R O P E R T I E S 123 A P P E N D I X B . . . W E L D E R S T I C K E T A N D P R O C E D U R E S H E E T 127 A P P E N D I X C N E L S O N S Y S T E M P R O D U C T A N D E M B E D M E N T C A T A L O G U E 129 A P P E N D I X D C A L C U L A T I O N S F O R S P E C I M E N #1 131 A P P E N D I X E C A L C U L A T I O N S F O R S P E C I M E N #2.. 140 A P P E N D I X I S O U R C E C O D E F O R P R O G R A M ' B E N D ' 143 LIST OF T A B L E S LIST OF TABLES Table 3.1- Pile size and grade used in tests Table 3.2 - Loading Regime for Specimen #1 Table 3.3 - Loading Regime for Specimen #2 Table 4 .1- Moment capacities for specimen #1 Table 4.2 - Observed strains and catalogue specified yield strains Table 4.3 - Moment Capacities Table 4.4 - Classification of failures of anchorage bars Table 6.1 - Bond Stresses at Various Load Sequences Table 6.2 - Comparison for specimen #1 Table 6.3 - Variation of plate deflection across plate width for specimen #1 Table 6.4 - Average strain in extreme row for specimen #1 Table 6.5 - Comparison for specimen #2 Table 7.1 - Data obtained from literature on bond strength Table 7.2 - Development length comparison for D2L bars and conventional rebar LIST OF FIGURES vii L I S T O F F I G U R E S Figure 1.1- Typical modular bridge section 1 Figure 1.2 - Overhead welding in progress 2 Figure 2.1- Typical force versus displacement curve for a ductile element 6 Figure 2.2 - Axial Stress Distribution at Plastic Moment 9 Figure 2.3 - Laminations potentially trap flaws during plate rolling 10 Figure 2.4 - Linear strain assumption and resulting typical stress distribution 12 Figure 2.5 - Potential Plate Yielding At Pipe Edge 13 Figure 2.6 - Pipe collar concept 15 Figure 2.7 - Site installation of pipe collar 15 Figure 3.1- Reinforced concrete beam 18 Figure 3.2 - Embedded plate layout 18 Figure 3.3 - Stud welding procedure 19 Figure 3.4 - Formwork and reinforcing steel ready for pouring 20 Figure 3.5 - General layout of test specimens 22 Figure 3.6 - Overhead weld detail for specimen #1 24 Figure 3.7 - Overhead weld detail for specimen #2 24 Figure 3.8 - Overhead welding replicates field conditions (specimen #1) 25 Figure 3.9 - Overhead weld replicates site conditions (specimen #2) 25 Figure 3.10- Test specimen in loading frame 26 Figure 3.11- Possible Uplift Forces in Piles 27 Figure 3.12 - Two loading sequences 28 Figure 3.13 - Strain gauges on embedded plate for test 1 30 Figure 3.14 - LVDT locations on test specimen #1 31 Figure 3.15- Operational strain gauges on embedded plate for test 2 32 Figure 3.16- LVDT locations on test specimen #2 33 Figure 4.1 - Specimen in loading frame 34 Figure 4.2 - Load-deformation characteristics of Test Specimen 1 36 Figure 4.3 - Strain history in bar R1C3 37 Figure 4.4 - Strain history in bar R6C3 38 Figure 4.5 - Slight bulge on left side of pipe (sequence I, cycle 1) 40 Figure 4.6 - Increasing bulge on right side of pipe (sequence I, cycle 3) 40 Figure 4.7 - Specimen at maximum deflection (Sequence J, cycle 1) 41 Figure 4.8 - Plastic hinging in pile (sequence J, cycle 1) 42 Figure 4.9 - Initial crack forming on left side of pipe (sequence J, cycle 2) 42 Figure 4.10 - Failure in the plastic hinge region 43 Figure 4.11- Minor uplift of the embedded plate 43 Figure 4.12- Location of tiny cracks due to arc strikes 44 Figure 4.13 - Cracks due to arc strikes 45 Figure 4.14 - Cracks due to arc strikes 45 Figure 5.1 - Assumed stress versus strain relationship for steel pipes 61 Figure 5.2 - Typical strain and stress profile for a given curvature 62 Figure 5.3 - Curvature prior to any pipe yielding 63 Figure 5.4 - Curvature distribution once the yield force is exceeded 63 Figure 5.5 - Typical stress-strain curve for concrete 65 LIST OF FIGURES viii L I S T O F F I G U R E S (continued) Figure 5.6 - Code simplified versus discretized layer stress distribution 65 Figure 5.7 - Displacement at jack due to plate rotation 66 Figure 5.8 - Finite element model of specimen #1 69 Figure 5.9 - Finite element model of specimen #2 70 Figure 6.1- Predicted and Observed Load-Displacement Response of Specimen #1 72 Figure 6.2 - Maximum tensile strains during last two sequences for Bar R1C3 74 Figure 6.3 - Maximum tensile strains during last two sequences for Bar R6C3 74 Figure 6.4 - Bond stress calculated from strain gauge readings 76 Figure 6.5 - Maximum compressive strains during last two sequences for Bar R1C3 77 Figure 6.6 - Maximum compressive strains during last two sequences for Bar R6C3 77 Figure 6.7 - Stress contour Sx (front view) 81 Figure 6.8 - Stress contour Sx (top view) 81 Figure 6.9 - Stress contour Sy (back view) 82 Figure 6.10 - Stress contour Sz 84 Figure 6.11- Stress contour Sz (back view) 84 Figure 6.12 - Predicted and Observed Load-Displacement Response of Specimen #2 85 Figure 6.13 - Plate uplift measured on the right side of the connection (@ LVDT 1) 87 Figure 6.14 - Plate uplift measured on the left side of the connection (@ LVDT 4) 87 Figure 6.15 - Stress contour Sx (back view) 90 Figure 6.16 - Stress contour Sy (back view) 90 Figure 6.17 - Stress contour Sz 91 Figure 6.18 - Stress contour Sz (back view) 91 Figure 7.1 - Deformed bars (Nelson bar on top, conventional bar on bottom) 94 Figure 7.2 - Idealized and actual stress-strain curves for 15M - D2L Anchors 95 Figure 7.3 - Stress distribution based on specified yield stress and large ductility 97 Figure 7.4 - Stress distribution based on actual steel strength and low ductility 98 Figure 7.5 - Stress distribution based on actual steel strength and bond failure 99 Figure 7.6 - Actual failure based on actual steel strength, bond failure and cyclic loading 100 Figure 7.7 - Stress distribution using conventional reinforcing steel 102 Figure 8.1- MAIN directory in ANCHOR spreadsheet 105 Figure 8.2 - Calculation sheet for plastic moment of pipe 106 Figure 8.3 - Print and iterate simplified by interactive buttons 108 Figure 8.4 - Various worksheets available in ANCHOR 109 Figure 8.5 - Embedded plate layout generated by computer I l l Figure 9.1 - Pipe collar concept 113 Figure 9.2 - Stiffener plate concept 114 Figure 9.3 - Holes in pipe concept 115 Figure 9.4 - Decision tree for possible changes to the connection 117 A C K N O W L E D G E M E N T ix ACKNOWLEDGEMENT Funding for this research was provided in part by the Ministry of Transportation and Highways of British Columbia. The Ministry's financial contribution is greatly appreciated. In addition, the Bridge Engineering Branch in Victoria supplied much needed information throughout the course of the research. Additional funding was given by the Canadian Institute of Steel Construction. Thanks in particular to Rob Third, B.C. Regional director for the CISC. Other funding was through operating and personal grants from NSERC. All financial support from the above parties is greatly valued. Advisors at the University of British Columbia were Dr. S.F. Stiemer and Dr. R.G. Sexsmith from the Department of Civil Engineering. Their constant encouragement and availability is appreciated. Mr. Paul Symons, laboratory technician in Department of Civil Engineering, was always helpful in the structures laboratory. This project could not have been performed without his expertise and support. Solid Rock Steel Fabricating Co. provided ample space and equipment when constructing the test specimens. This free service made the project run more smoothly. Special thanks to the company pesident, Benny Steunenberg, for his cooperation. CHAPTER 1 - INTRODUCTION 1.0 INTRODUCTION 1.1 BACKGROUND The Ministry of Transportation and Highways of the Province of British Columbia has developed a Modular Bridge Program that aims at optimizing cost by reducing designing, detailing and construction time. The Modular Bridge Program is comprised of a system of bridges where major components are all pre-designed and pre-fabricated. The components are fabricated in a plant and shipped to the construction site where they are bolted, welded or grouted together. This results in a considerable reduction in site construction time and cost. The superstructure consists of precast concrete twin box cell box girders laid side by side to form the bridge deck. Typical spans range from 8 to 20 metres. The substructure is made up of a precast concrete cap beam welded to steel pipe or H piles. Figure 1.1 shows the conceptual layout of a typical modular bridge section. Figure 1.2 shows the actual construction practice of field welding the piles to embedded plates. CONCRETE HOLLOW BDX GIRDERS EMBEDDED PLATE / WELDED CONNECTION PRECAST PIER/ABUTMENT PILE CAP STEEL PIPE Y PILES / — r K t U H o I r l L K / f t D U I n t N I r J.L GRDUND LEVEL EMBEDDED PLATE AND ANCHDR BARS Figure 1.1 - Typical modular bridge section CHAPTER 1 - INTRODUCTION 2 Figure 1.2 - Overhead welding in progress Use of the modular bridge system is most applicable in remote locations where ready-mix concrete is not available or very costly. It is also an effective system when project schedules require the bridge construction time to be as short as possible. A typical single span bridge can be erected in a few days. These modular bridges can also be erected in colder months, thus providing more flexibility for project schedules. Better quality control of structural members can also be achieved since fabrication takes place in a controlled plant environment. C H A P T E R 1 - I N T R O D U C T I O N 3 Prior to 1994, the modular system was used on ten bridges in British Columbia; however, in each case seismic loads did not govern the design. These locations include Dawson Creek, Quesnel, Vernon and 100 Mile House. Due to the initial success of the modular bridge program, the planning and construction of numerous other modular bridges has proceeded. Some of these new bridges are located in areas where seismic activity is anticipated. Placing these bridges in potentially seismically active zones introduces the possibility for significantly higher lateral loads within the structure. These loads on the connection between the steel pile and the concrete pier pose design issues which did not govern in the non-seismic design of modular bridges. Seismic design introduces many new considerations as failure modes previously insignificant become more relevant. In addition, the need for ductile behaviour influences the design and details of the bridge. The structural efficiency and monetary savings linked to the modular bridge program relies heavily on the simplicity of the members and the method of connecting members in the field. Connections in bridges often dictate whether the structure possesses adequate ductility, or exhibits brittle failure. Depending on the quality of the overhead weld between the pile and pile cap, the bridge may or may not behave in a ductile manner. An additional concern is that detailed design guidelines for the steel anchors welded to the embedded plate are scarce. Typically research information focuses on one specific connection or anchor type that was tested. This in turn does not allow for application of the design equations to other areas of research and design. For these reasons, it was deemed necessary to perform tests to better understand the behaviour of the connection. The research was performed in coordination with the Ministry of Transportation and Highways and the University of British Columbia. CHAPTER 1 - INTRODUCTION 4 1.2 OBJECTIVES The purpose of this research was to investigate the seismic behaviour of the connection between the steel pile and concrete beam. The primary objective was to determine whether plastic hinging the pile could be achieved prior to a weld failure between the pipe and embedded plate. While investigating plastic hinging, it was also important to obtain the strength and ductility of the connection. It was also necessary to study the behaviour of the embedded plate anchorage since little was known about the strength of the anchorage system. Forcing an anchorage failure would produce valuable information regarding the strength, ductility and failure mode of the anchorage. In addition, the effect of the embedded plate flexibility on the distribution of strains to the numerous anchors was of interest. In light of the above objectives, changes to the present design assumptions could be recommended. Furthermore, alternative connections between the steel pile and concrete beam could be explored. 1.3 SCOPE The research was performed at the Department of Civil Engineering, University of British Columbia. The testing program consisted of reversed cyclic loading of two specimens. Each specimen was designed with different failure modes in mind, such that the pipe and anchorage failures could be observed. These tests also satisfied the goal of observing the weld between the pipe and plate through numerous cycles at a large stress range. A simple two dimensional, non-linear model was compared to the experimental results. Finite element modelling proved to be an effective means of examining the influence of plate flexibility. Finally, a computer based design tool was developed. CHAPTER 2 - THEORETICAL BACKGROUND 5 2.0 THEORETICAL BACKGROUND 2.1 DESIGN PHILOSOPHY The present seismic design of the connection recognizes the need for a ductile structure, and adopts the capacity design philosophy. Ductility and capacity design are explained later in this section. It is reasonable to expect bridges to remain elastic and undamaged for small to moderate earthquakes; however, it is widely accepted that it is too costly to design a structure to remain undamaged in a severe earthquake. Therefore, under a severe earthquake, the seismic design philosophy accepts the possibility of structural damage and plastic deformations. However, the structure in question should not collapse. Ductility and capacity design both aid in achieving this philosophy. 2.1.1 Ductility Ductility is a measure of a structure's ability to undergo inelastic deformations prior to failure. In the majority of bridges, the most desirable ductile behaviour is achieved by flexural yielding in the columns.1 In the case of this research, if ductility is to be achieved in the piles, it is essential that the pile be a compact section. Compact sections ensure that plastic deformations through yielding can be achieved, rather than premature buckling of the member. Figure 2.1 presents a typical force versus displacement curve for ductile members subjected to loading above their yield level. The yield displacement, Ay, is defined as the displacement at the yield force level, Fy. A given displacement ductility is defined as the multiple "Seismic Design and Retrofit Manual for Highway Bridges", U.S. Department of Transportation, 1987 CHAPTER 2 - THEORETICAL BACKGROUND 6 of the yield displacement. For instance, a displacement ductility of 3 would be achieved by displacing the member a total of 3\x, without decrease of the force level. (J. = Ay 3[i ^ Figure 2.1 - Typica l force versus displacement curve for ductile elements 2.1.2 Capacity Design Capacity design essentially states that all components of a structure be designed such that the predicted failure mode is one that is desired and exhibits adequate ductility. For example, brittle shear failure within the concrete cap beam should be avoided by ensuring that plastic hinging in the pile occurs first. Undesirable failure modes could also be ductile modes. For example, excessive yielding of the anchorage bars welded to the embedded plate may be considered a ductile failure mode. However, the damage would be difficult to inspect and repair. In the case of the modular bridge, the plastic moment capacity of the pipe pile should be less than the moment resistance of the embedded plate anchorage. This should ensure that the failure mode would not only be ductile, but also accessible for visual inspection and potential repair. CHAPTER 2 - THEORETICAL BACKGROUND 7 2.1.3 Overstrength Factor One additional concept in the capacity design approach is the overstrength factor. The overstrength factor is a means of accounting for material strengths which are possibly higher than anticipated. In order to ensure that plastic hinging occurs in the pile, an overstrength factor is added to the yield strength of the pile. This in turn forces the designer to make the embedded plate anchorage stronger. Presently, the Ministry of Transportation and Highways (MoTH) of B.C. performs design calculations based on a minimum overstrength factor of (J)Q = 1.25. The overstrength factor, (J>0, is defined as follows: <t>o = Md(anchorage/Mi(pipe) M i(pipe) is the ideal, unfactored moment resistance of the pipe. The yield strength of the pipe is the specified design yield strength. M<i(anchorage) is the dependable, factored moment resistance of the embedded plate anchorage, and is given by: anchorage) i(anchorage) Mi(anchorage) is the ideal, unfactored moment resistance of the anchorage based on the specified yield strengths. Abridge is the bridge performance factor and is usually assigned a value of 0.85. Capacity design combined with the overstrength factor is meant to provide a high probability that plastic hinge formation within the piles occurs before other failure modes. Moreover, when combined with the concept of ductility, a solid basis for an effective seismic design is formed. CHAPTER 2 - THEORETICAL BACKGROUND 8 2.2 F A I L U R E M O D E S Identification of all failure modes within the entire connection is critical to the proper application of the capacity design approach. These include possible failures within the steel pipe, concrete beam, anchorage bars, embedded plate, and the relevant welds in the connection. 2.2.1 Elast ic Buck l ing of the Pipe W a l l Large axial compressive stresses induced by pipe bending can cause the pipe wall to buckle in the elastic range. Guidelines have been set in place to ensure that compact sections are always used when ductility is desired. Compact sections are sections which can undergo extensive deformations beyond their yield strain, thus providing adequate ductility. Elastic buckling of the pipe should not occur provided the following diameter to thickness ratio is satisfied. D/t < 18000/Fy(pipe) [CAN/CSA-S6-88, Table 15] Even if the effects of reverse cyclic loading could affect this limit on the the D/t ratio, the pipes used in both specimens were well below this limit. Also, a reasonable material overstrength is presumably taken into consideration by the code formula. 2.2.2 Plast ic H inge Format ion in Pipe Pi le For compact sections, the pipe undergoes yielding across the entire cross section due to bending (tension on one side, compression on the other). Figure 2.2 shows the corresponding state of stress for the plastic hinging case. This is the most desirable failure mode because it is ductile and should produce good energy dissipation characteristics. Also, steel tends to be reliable CHAPTER 2 - THEORETICAL BACKGROUND 9 serving as a ductile material. In the current test, the shear2 and axial3 forces were too small to significantly alter the plastic moment capacity of the pipe. The plastic moment in the pipe occurs at the value Mp(Pipe) given by the following equation: Mp(pjpe) — Fy(pipe)*Z Z is the plastic modulus of the pipe section, and can be expressed as follows: Z = D3*[l-(l-2*t/D)3]/6 Applied Moment / =Mp(pipe) ( Pipe Diameter \ = P i r T S ens tres ile ises Compressive Stresses Figure 2.2 - Axial Stress Distribution at Plastic Moment Sherman, "Tests of Circular Steel Tubes in Bending", ASCE Structural Journal, November 1976 Johnston, "Guide to Stability Design Criteria for Metal Structures", 1976 CHAPTER 2 - THEORETICAL BACKGROUND 10 2.2.3 Lamellar Tearing of Embedded Plate Lamellar tearing results from high tensile stresses acting perpendicular to the rolling direction of the plate. As illustrated by Figure 2.3, small flaws trapped during the rolling process may lead to an unanticipated sudden failure.4 In critical applications, testing of the plate is performed to detect potential flaws. For example, testing was used on portions of the Alex Fraser bridge where numerous vital connections possessed the potential for catastrophic lamellar tearing. Rolling Direction Thickness of Plate Trapped Imperfection ^ ^ ^ " " A V ^ from Rolling Plate Laminations Embedded Plate t t t Large Tensile Stresses Figure 2.3 - Laminations potentially trap flaws during plate rolling 4 Boyd (ed), "Brittle Fracture in Steel Structures", 1970 CHAPTER 2 - THEORETICAL BACKGROUND 11 2.2.4 Embedded Plate Anchorage Failure The anchorage design currently performed by the MoTH relies on steel bar information provided in the Nelson Stud Welding Applications - Concrete Connections catalogue (Hereafter referred to as the Nelson catalogue). The relevant excerpts of this catalogue are presented in Appendix C: the information relates to the steel anchorage bars and their necessary embedment length, as well as the specified yield stress of the bars. It should be noted that previous research has shown that bond deterioration of conventional reinforcing steel under cyclic loading could occur when bond stresses reach 80% of the monotonic bond strength.5 ' 6 An adequate bar spacing must be maintained, otherwise a group effect failure could occur. Failure of the bar in the heat affected zone of the weld to the plate is also a possible failure mode. Attempting to account for these characteristics within the anchorage system should lead us to a ductile design. Figure 2.4 shows how the St. Venant's assumption of is utilized (plane sections remaining plane). This is essentially the concept of a linear strain distribution to the deformed bar anchors. Also, all of the bars across the width of the plate are assumed to receive equal strains. In other words, three dimensional effects in distributions of strains are neglected. Finally, the "rectangular stress block"7 is used to simulate the compressive force due to the concrete. Hawkins & Mitchell, "Seismic Response of Composite Shear Connectors", ASCE Structural Journal, September 1984 Eligehausen & Popov, "Behavior of Deformed Bars Anchored at Interior Joints Under Seismic Excitations", 4th Canadian Conference on Earthquake Engineering CAN/CSA-S6-88, "Design of Highway Bridges", 1990 CHAPTER 2 - THEORETICAL BACKGROUND 12 The moment resistance resulting from these assumptions is as follows: Mr(anchorage) = ^ bridge * {Z [Td(i)*def(i)] - C(plate)*rB*Cem/2} The tensile force in each row of bars and the compressive concrete force are as follows: Td(i) = ar0Vv(i) * A r o w ( i) and C^ute) = af c * p\c The term def(i) is the distance from the plate edge to the row "i", and cem is the depth to the neutral axis. o"roW(i) is the stress in the bars of row "i", and A,0W(i) is the total area of bars in row "i". P and a are empirical terms defining the dimensions of the rectangular compression block, and f c is the compressive strength of the concrete. ~ 7 Tension / I / I / Embedded Plate ^ Deformed bars anchored in concrete Strain Distribution Compression Iy(bar) Stress Distribution Figure 2.4 - Linear strain assumption and resulting typical stress distribution CHAPTER 2 - THEORETICAL BACKGROUND 13 2.2.5 Y ie ld ing of the Embedded Plate The design of the anchorage system assumes that strains are distributed linearly along the length of the plate. Therefore, the plate must have sufficient strength such that it does not yield in bending. If the plate were to yield, assumptions regarding the distribution of forces to the anchors would be violated.8 The figure below shows how yielding at the edge of the pipe could occur due to the compressive reaction in the concrete. The compressive reaction has been shown as rectangular because the plate yielding is checked at the anchorage ultimate moment resistance. The yield moment of the plate is calculated assuming that the entire width of the plate contributes to the bending resistance: My(piate) = <j>bridge * Fy(Piate) * S/6 S is the section modulus of the pipe, and could be expressed as: S = l/6*width*(thickness)2 z Steel Pipe 'Potential Plate Yielding Steel Plate / / / / t t t t t Compressive Reaction Due To Concrete Concrete Beam Figure 2.5 - Potential Plate Y ie ld ing A t Pipe Edge Cannon,, "Flexible Baseplates: Effect of Plate Flexibility and Preload on Anchor Loading and Capacity", ACI Structural Journal, May-June 1992 CHAPTER 2 - THEORETICAL BACKGROUND 14 2.2.6 Pile Cap Beam Failure in Shear or Flexure The concrete beam must also be designed for adequate shear and moment resistance. The strength of the beam becomes more of a concern when larger pile sizes are used. This is because the beam must be capable of resisting the pipe's plastic moment capacity in order to ensure plastic hinging in the pile. The factored strengths for bending and shear are as follows: M^bean,) = Abridge * { Z [F(i)*St(i)] - C(COnc)*P*c/2} V^beam) = Abridge * (V. + Vc) [CAN/CSA S6-88, 8.6.6.1.1] F(i) is the force in the bars of row "i" and st(i> is the distance from the top of the beam to row "i". 2.2.7 Weld Failure Between Pipe and Embedded Plate Performing an overhead complete penetration weld is challenging. Consistent weld quality is often difficult to achieve. Even though the theoretical strength of the weld is significantly higher than that of the pipe, possible fatigue cracking of the weld is of great concern when cyclic loading produces a large range of stresses.9 This fracture could occur in the weld material, or in the heat affected zone of the weld. Insisting on qualified welders and appropriate welding procedures is intended to reduce the likelihood of weld failures. Having inspectors present during the welding process is an additional measure taken by MoTH to minimize poor welds. Due to concerns regarding potential weld failure, the Ministry's seismic design currently includes a pipe collar (Figure 2.6). The collar increases the cross sectional area of the weld, thus reducing the stresses in the weld and likelihood of weld failure. The tests were performed without the collar, because the weld was theoretically strong enough without it. Figure 2.7 shows how the collar is installed at the site with the aid of a bolt to make the collar fit closely around the pile. 9 Masubuchi, "Analysis of Welded Structures", 1980 CHAPTER 2 - THEORETICAL BACKGROUND 15 EMBEDDED P L A T E AND C O N C R E T E BEAM A B D V E 3 0 0 < CP PER P I L E AND C D L L A R P I L E H A L P S E C T I D N TD PIT P I L E PRCIPILE P I P E P I L E E L E V A T I O N Figure 2.6 - Pipe collar concept Figure 2.7 - Site installation of pipe collar CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 16 3.0 EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 3.1 G E N E R A L The most general and essential data required from the testing are the load-deformation characteristics (hysteresis curves). The curves can be obtained from the reversed cyclic loading of the specimens. Other important data includes the rotation of the embedded plate relative to the concrete beam, and strains in the deformed bar anchors. This will provide much needed information on the behaviour of the embedded plate. Potential fatigue and failure of the complete penetration overhead weld is also an area of significant interest. Understanding the importance of these parameters allows for the implementation of an effective test plan which will address these issues. 3.2 T E S T S P E C I M E N S #1 A N D #2 Both test specimens consisted of the same short, reinforced concrete beam. An embedded plate was cast into the concrete beam. Once the beam had cured, a steel pipe pile was welded in the overhead position to the embedded plate. The materials and constructions methods laid out in the Ministry of Transportation and Highways standard specifications were followed as closely as conditions allowed. The first test was performed with a smaller pile size which did not exceed the predicted resistance of the anchorage. That is, the plastic moment of the pipe was expected to be approximately equal to the yield moment of the anchorage. This ensured that this first test focused on the plastic hinge formation or possible weld failure. CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 17 Following the first test, the steel pipe was removed from the embedded plate. A larger pipe was then welded to the same reinforced concrete beam that was used for the first test. The second test was a simulation of what could occur in the real construction situation. That is, the plastic moment capacity of the pile based on an overstrength factor of § = 1.25 was intended to match the theoretical factored moment resistance of the anchorage. 3.2.1 Reinforced Concrete Beam The reinforcing steel consisted of 30M and 15M longitudinal reinforcement, and 15M stirrups (400 MPa). High strength concrete typically produces a higher bond strength with steel anchors. This in turn reduces the necessary development length of the steel anchorage bars. For this reason, the MoTH design incorporates a concrete strength of 45 MPa. The concrete pouring data and subsequent compressive strengths are contained in Appendix A. The embedded steel plate was a 600 x 650 x 50 mm (350 MPa) complete with thirty (30) Nelson deformed bar anchors. The anchors were product type D2L and were 15M x 600 mm long (483 MPa). Figure 3.1 presents the concrete beam, complete with reinforcing details. Figure 3.2 shows the details of the embedded plate, along with the bar reference numbers of R1C1 through R6C5. CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 18 6 - 30M BARS TCP 8< BOTTOM 15M STIRRUPS 12 200 4 - 15M BARS EMBEDDED PLATE CENTERED IN BEAM 1700 750 J 1 1 800 650 BEAM ELEVATION Figure 3.1 - Reinforced concrete beam NOTES 1- CONCRETE TO BE 45 MPa 2 - MAINTAIN 50mn CDVER 3 - TIE WIRE A L L INTERSECTIONS 8 5 120 120 120 120 8 5 37 105 105 105 105 105 38 * ^ -Q O O O o -o o o o o o o o O o o o o o o o o R1C1 R2C1 R3C1 R4C1 R5C1 R6C1 o R1C2 R 2 C 2 R3C2 R4C2 R5C2 R 6 C 2 R1C3 R 2 C 3 R3C3 R 4 C 3 R5C3 R 6 C 3 o R1C4 R2C4 R3C4 R4C4 R5C4 R6C4 o R1C5 R 2 C 5 R3C5 R4C5 R5C5 R 6 C 5 PL 6 5 0 x 6 0 0 x 5 0 ( 3 5 0 V ) 15Mx600 LDNG D2L N E L S D N DEFEiRMED BAR TO BE WELDED IN ACCORDANCE WITH MANUFACTURER 'S RECOMMENDATIONS (30 IN TOTAL) Figure 3.2 - Embedded plate layout C H A P T E R 3 - E X P E R I M E N T A L APPROACH FOR T E S T SPECIMENS #1 & #2 19 The welding of the deformed bar anchors to the embedded plate was performed by a Division 1 shop employee using a special stud gun. The stud gun machine has prescribed temperature settings and arc times for various bar diameters. The bars are placed in the shaft of the gun along with a porcelain mold just prior to welding. The mold confines the weld material to the area surrounding the bar. Following the weld, the mold can be broken to allow for visual inspection of the weld quality. The weld is performed in about one second. Figure 3.3 is a photograph which was taken while the weld was in progress. Figure 3.3 - Stud welding procedure CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 20 The reinforcing steel cage and formwork were built at the same time as the embedded plate. After these components were fabricated, pouring of the concrete commenced. Pouring the concrete included the tasks of vibrating, determining air content, and the pouring of test cylinders Figure 3.4 shows the reinforcing and embedded plate in the formwork prior to pouring of the concrete. Figure 3.4 - Formwork and reinforcing steel ready for pouring CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 21 3.2.2 Steel Pipe Pi le For reasons previously discussed, the pipe size was increased for the second specimen. Table 3.1 summarizes the grade and size for each test. The actual yield stress was obtained from the mill testing certificates provided by the pipe manufacturer (Appendix A). The general layout and dimensions of the test specimens are shown on Figure 3.5. Specimen #1 Specimen #2 Pile Size 324<j> x 12.7 mm 406(b x 12.7 mm Grade A252 Grade 3 A53 Grade B Minimum Specified Yield Stress [MPa] 310 241 Actual Yield Stress [MPa] 410 338 Overstrength = Actual/Specified 1.32 1.40 Table 3.1 - Pi le sizes and grades used in tests It should be noted that the grade used in the second test was A53 Grade B. This grade is the same as A252 Grade 2. The Ministry typically specifies a pipe which is A252 Grade 2, with a minimum yield stress of 241 MPa. The only difference is that the A53 Grade B steel goes through more stringent mill tests with respect to performance checks. When selling A252 Grade 2 pipe (ay = 241 MPa), most pipe suppliers simply supply A252 Grade 3 (rjy = 310 MPa). In fact, it was rather difficult to locate steel piles with a yield stress near 241 MPa. Note that for both specimens, the overstrength factor shown in Table 3.1 is in excess of the assumed design overstrength factor of § 0 = 1.25. The pipe supplier's philosophy is, "stronger is better". However, in the case of seismic design, this is not always the case. The modular bridge exemplifies this, where the stronger pipe may force failure into another region of the connection. CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 EMBEDDED P L A T E PL 6 5 0 x 6 0 0 x 5 0 (GRADE 3 5 0 V ) 850 1700 SPECIMEN 1 3 2 4 DIA x 12,7 P IPE P I LE ( A 2 5 2 GRADE 3)| SPECIMEN 2 406 DIA x 12,7 P IPE P I LE (A53 GRADEB) ' T COMPLETE I p—<PENETRATION I / TO BE DDNE | / IN THE |/ OVERHEAD 1 POSITION yrm 850 2 2 3 5 800 750x800 DP CONCRETE BEAM 3 7 5 3 7 5 750 ELEVATION SIDE VIEW Figure 3.5 - General layout of test specimens CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 23 3.2.3 Overhead Welding The bridge inspector of the MoTH Bridge Inspection Branch stated two conditions that typically provide a rationale to avoid the need for extensive testing of the overhead weld1. Firstly, a MoTH bridge inspector must be present during the performance of the weld. Secondly, the bridge inspector's familiarity with the welder's workmanship on past projects is beneficial. These two conditions were satisfied in the case of the overhead welds. Also, ultrasonic or x-ray inspection of a weld are non-conclusive when only one side of the weld is accessible. Therefore, it was decided to proceed with the project without having testing of the weld. For both specimens, the weld between the pile and embedded plate was performed in the overhead position. This complete penetration weld was performed by CWB (Canadian Welding Bureau) certified welders from a Division 1 shop. The welders have done extensive work for the Ministry in the past. The weld was also performed under the supervision of MoTH bridge inspectors in order to replicate field conditions. The tickets for the two welders and the welding procedure sheet are contained in Appendix B. The first pipe was purchased with a bevel already on the pipe end. Although the angle of the bevel was not very large, it was not altered. This would save some money, as the bevel was within the minimal requirements for a bevel angle. The second pipe was purchased with no bevel, and thus needed to have the bevel made with a torch. At this time, the welder advised that in his experiences, a greater angle for the bevel would be more representative of the real construction situation. Figures 3.6 and 3.7 present the typical welding details for specimens #1 and #2, respectively. i As per discussions with Bob Matthews, MoTH Bridge Inspector, July 1994. CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 24 C O N C R E T E B E A M A B O V E 50nn THICK EMBEDDED PLATE 50 BACKUP BAR F B 5 0 x 5 ( R O L L E D ) -WELD DDNE IN 5 P A S S E S 30 ' PIPE BEVEL -12.7mm PIPE WALL -12.7 Figure 3.6 - Overhead weld detail for specimen #1 C O N C R E T E B E A M A B D V E 4 50nn THICK EMBEDDED PLATE 4 50 i >\~ WELD DDNE IN 5 P A S S E S / / * \ 40 ' PIPE BEVEL BACKUP BAR E B 5 0 x 5 ( R O L L E D ) V V ^ - 1 2 . 7 m m PIPE WALL h—12.7 Figure 3.7 - Overhead weld detail for specimen #2 CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 25 CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 26 3.3 TEST SETUP In order to simulate seismic loads on the connection, a test frame was used which was large and strong enough to accommodate the test specimen. The cyclic horizontal load was applied by means of a 445 kN (50 ton) hydraulic jack which had a maximum stroke of ± 300 mm. The jack was mounted on one of the test frame columns. Both test specimens were secured to the test frame by means of prestressed Dywidag bars and spreader beams as shown in Figure 3.10. The dywidag bars extended to the underside of the 600 mm thick concrete laboratory floor. 350 WIDE TEST FRAME 1220 c CONCRETE /~BEAM o A - A 1 1220 PIPE COLLAR, 890 445 kN CAPACITY 600nn TOTAL STROKE ±300 STROKE £252 JACK LENGTH SPREADER BEAMS 8. DYVIDAG BARS 1950 aoo Z Z Z Z ^ Z ] / / / / I / / / / / . / / / / / / / / / / / / 40- 1220 CONCRETE SLAB FLDDR 1700 Figure 3.10- Test specimen in loading frame CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 27 The usual vertical load, possibly simulating dead load, was not applied to the specimens. A set of piles in a bridge application would experience uplift as well as downward forces depending on the position of the pile in the set. This scenario is demonstrated in Figure 3.11. Therefore, it was deemed to be realistic enough to set the average vertical force to zero. H r— 1 H 1 1 \ 1 \ Rl R ^ / 1 R3 / R 4 2 / R 5 R 6 R7 POTENTIAL POR PILE UPLIPT PORCES Figure 3.11- Possible Uplift Forces in Piles CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 28 3.4 LOADING SEQUENCE The loading regime for the tests was not meant to simulate any particular earthquake, but rather subject the specimens to a series of increasing cyclic loads. The low frequency testing of the connections allowed for a more controlled monitoring of the specimen. Each test specimen underwent reversed cyclic loading of increasing amplitudes. At each amplitude, the specimen was cycled a specified number of times, thus completing one sequence. DISPLACEMENT ' AMPLITUDE 0+1) . . . DISPLACEMENT \ \ \ AMPLITUDE f O - f - A A A / \ / \ / \ J1YCLE 7 CYCLE 2_ JCYCLE J_ | \ / \ / PERIOD T I J I \J Y ^ SEQUENCE (i) SEQUENCE Figure 3.12 - Two loading sequences Initially, the specimens were loaded by a load controlled hydraulic cylinder. This means that the specimens were loaded to a specified force, and the corresponding displacement was measured. Prior to testing, the yield loads of the specimens had been calculated. The specimens were loaded up to 75% of their respective yield force, at which point the displacement was measured. The yield displacement of the specimen was calculated as being 4/3 (1/75%) times this measured displacement. The jack was then changed from "load control" to "displacement control", which means that the specimen is loaded up to a specified deflection and the corresponding load is measured. Detailed loading sequences are given in Tables 3.2 and 3.3. TIME CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 29 LOAD SEQUENCE PERIOD CYCLES MAXIMUM AMPLITUDE MEASURED DEFLECTION A 3 minutes 2 10 kN 1.5 mm B 3 2 40 6.0 C 3 2 80 12 D 3 2 115 14 E 3 2 153 18 F 3 3 l.lu. 33 G 3 3 1.7u 50 H 3 3 2.4^ 71 I 4 6 3.9u 117 J 4 3 8.3(j. 250 mm Table 3.2 - Loading Regime for Specimen #1 LOAD SEQUENCE PERIOD CYCLES MAXIMUM AMPLITUDE MEASURED DEFLECTION A 3 minutes 2 10 kN 0.6 mm B 3 2 34 2.1 C 3 2 68 4.2 D 3 2 115 8.5 E 3 2 203 13 F 3 3 1.2u 40 G 3 3 1.3u 45 H 3 3 1.8u 62 I 3 3 2.2^ 75 Table 3.3 - Loading Regime for Specimen #2 CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 30 3.5 I N S T R U M E N T A T I O N Linearly Varying Displacement Transducers (LVDT's) were used extensively to monitor the movements of both test specimens. To aid in checking for potential yielding of the bars, strain gauges were mounted on two of the bars welded to the steel plate 3.5.1 Test Specimen #1 Strain gauges monitored the behaviour of the bar anchors on the embedded plate. Three strain gauges were mounted on each of the two outermost bars to monitor the strain. The strain gauge data could lead to numerous conclusions including: a) Excessive yielding in the bars, indicated by bar strains exceeding the yield strain. b) Failure of the weld between the bar and plate, or fracture of the bar. No strain in the bar could indicate no force in the bar, and thus a failure has possibly occurred. c) Different strains at the increasing depths of the bar could lead to an understanding of the required development length for the bars. BAR R1C3 BAR R6C3 -600-A o o o o o o o o o o o A 650 A - A STRAIN GAUGES ON THESE TWO BARS DNLY Figure 3.13 - Strain gauges on embedded plate for test 1 CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 31 Figure 3.14 presents the location of the various LVDT's on specimen 1. LVDT's 3 & 11 measured the vertical displacements of the concrete beam, and LVDT 5 measured the horizontal displacement of the block. These measurements determine how much of the displacement measured at the jack is due to beam rotation and translation. These effects of beam rotation and translation are then subtracted from the jack displacement record to determine the "true deflection" due to embedded plate rotation and cantilever pipe deflection. LVDT 1 was installed near the edge of the embedded plate and could be compared to LVDT 6 in order to investigate the variation of embedded plate deflection across the plate. 1700 943 23 22 —JACK LDAD 18B0 I 4*1 240 I—— 6 I • MEASURES HORIZONTAL DISPLACEMENTS | MEASURES V E R T I C A L DISPLACEMENTS Figure 3.14 - LVDT locations on test specimen #1 CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 32 3.5.2 Test Specimen #2 Following the test on specimen 1, it was realized that one of the strain gauges was no longer functioning correctly. Then prior to testing the second specimen, it was discovered that three more strain gauges had been damaged. This was possibly due to two reasons. Firstly, handling of the specimen with chains and straps could have led to excessive pulling on the wires leading to damage. Secondly, preheating of the second specimen prior to performing the overhead weld could have led to melting of wires or other heat related damage. Unfortunately this led to only two strain gauges being available for data acquisition during testing of the second specimen. The loss of the strain gauges was unfortunate, but it did not spoil the second test. It will be shown later that the maximum strains in the bars were reached during the first test. This means that the main purpose of the strain gauges was served in the first test. That is, obtaining the maximum strain in the bars. BAR R1C3 A - A TWO GAUGES OPERATIONAL ON THIS BAR D.NLY Figure 3.15 - Operational strain gauges on embedded plate for test 2 CHAPTER 3 - EXPERIMENTAL APPROACH FOR TEST SPECIMENS #1 & #2 33 Figure 3.16 presents the location of the numerous LVDT's on specimen 2. LVDT's 2 & 5 measured the vertical displacements of the concrete beam. Therefore, the effect of beam rotation can then be subtracted from the jack displacement record to show the "true deflection" due to embedded plate rotation and cantilever pipe deflection. LVDT 3 was installed near the edge of the embedded plate and could be compared to LVDT 4 in order to investigate the variation of embedded plate deflection across the plate. 18B0 1000 - J A C K LOAD 18B0 3 | -U-l 240 U— 4 I • MEASURES HORIZONTAL DISPLACEMENTS | MEASURES V E R T I C A L DISPLACEMENTS Figure 3.16 - LVDT locations on test specimen #2 CHAPTER 4 - TEST RESULTS 3 4 4.0 TEST RESULTS 4.1 G E N E R A L This chapter presents the results as observed during testing, and gives a global impression of the outcome. A more detailed comparison to analytical models is presented later in the report Both test specimens were designed according to a philosophy emphasizing ductile behavior under seismic excitations. This ductile behavior was meant to be achieved through yielding of the pipe piles. The tests were designed to investigate whether the pipes could achieve a plastic hinging failure. Undesirable failure modes of potential concern have been indicated early in this paper. Of these failure modes, failure of the weld between the pipe and the plate was of primary concern. In addition, behaviour of the embedded plate anchorage system was of interest. Figure 4.1 - Specimen in loading frame CHAPTER 4 - TEST RESULTS 35 4.2 TEST SPECIMEN #1 The pipe used in the first test had a plastic moment capacity significantly lower than the theoretical moment resistance of the embedded plate anchorage. This was meant to ensure that the plastic hinge in the pipe could be observed. It would also allow for verification that the overhead complete penetration weld between the pipe and the plate was indeed strong enough. Table 4.1 presents moment resistances based on the present design assumptions used by MoTH. The calculations are contained in Appendix D. Plastic moment capacity of pipe based on mill test certificates 505 kN*m Factored Resistance of Anchorage = 0.85) 592 kN*m Unfactored Resistance of Anchorage (<|> = 1.0) 696 kN*m Table 4.1 - Moment capacities for specimen #1 4.2.1 Hysteresis Curves The hysteresis curves obtained from this test are the most essential piece of data. From these load versus deflection plots, one can determine if the specimen possesses adequate strength and ductility. Figure 4.2 presents the force measured in the hydraulic jack's load cell and the displacement of the jack. The displacement of the jack has been corrected to eliminate the effects of beam rocking and sliding in the test frame. Complete yielding of the pipe cross section is predicted, with no loss of strength. Recall that the sequences and their corresponding force or displacement level were defined in Table 3.2. CHAPTER 4 - TEST RESULTS 36 300 300 Displacement at jack [mm] Figure 4.2 - Load-deformation characteristics of Test Specimen 1 Sequences A to F in Figure 4.2 represent the elastic response of the specimen. After sequence F, the stiffness is reduced, and yielding of the specimen begins to take place. The hysteresis curves for sequences G, H, and I indicate that a plastic load has been achieved. This is verified by the constant load exerted on the specimen at reasonably large ductility levels (uA reached 8.3). Note that for load sequence J, the load carrying capacity is quite high for the first cycle. However, the final two cycles show a drop in load resistance. This is the most definitive drop in capacity during one sequence, and is due to degradation under cyclic loading. In fact, the qualitative observations will point out the propagation of the failure crack during this final load sequence. The hysteresis curves at sequences I and J continue to be "full". This leads to the conclusion that the energy dissipation characteristics of this connection are impressive. CHAPTER 4 - TEST RESULTS 37 4.2.2 Deformed Bar Strains The capacity design philosophy encourages ductility and damage in areas which can be easily inspected and repaired. For this reason, failure of the embedded plate anchorage system was not considered desirable. Strain gauges were mounted on two of the outermost bars to check on potential yielding and bar fracture. The hysteresis curves for the two bars are presented in Figures 4.3 and 4.4. These two curves are for the gauges located 100 mm from the plate, and have been referred to previously as location A on bars R1C3 and R6C3. 300 -1500 -1000 -500 0 500 1000 1500 2000 2500 Strain Gauge Reading [microstrain] Figure 4.3 - Strain history in bar R1C3 CHAPTER 4 - TEST RESULTS 38 100 K u o u & M o -100 -300 -1500 -1000 -500 0 500 1000 1500 2000 2500 Strain Gauge Reading [microstrain] Figure 4.4 - Strain history in bar r6c3 The maximum bar strains observed in the two outermost bars indicate that the steel strains are below yield. Table 4.2 presents the observed maximum bar strains during testing on the two bars, and the yield strain based on the Nelson Catalogue guaranteed minimum yield stress of 483 MPa. BarRlC3 Bar R6C3 Observed Maximum Strains 1550x1 (T6 2200X10"6 Catalogue Yield Strain 2400X10-6 2400xl0"6 Table 4.2 - Observed strains and catalogue specified yield strains CHAPTER 4 - TEST RESULTS 39 4.2.3 Qualitative Observations Visual inspection of the test specimen can often lead to further information regarding it's behaviour. In the case of the first test specimen, the observation of plastic hinging and examination of the full strength weld for cracking were of primary interest. Observation of embedded plate uplift would further aid in characterizing the behaviour of the anchorage system. The specimen was painted with a coat of thinned white latex. Flaking of the latex would indicate highly strained regions of the pipe, and it would also allow for easy identification of cracks on the concrete beam. Apparently the coat of latex was too thick and did not flake as anticipated. Before proceeding with the test at load sequence I, the white latex was removed from the pipe and the plate. The plate and the bottom 300 mm of the pipe were then coated with a water and lime mixture. Subsequent loading produced extensive flaking of this new lime coating. The first sign of observable straining within the connection occurred during sequence G. At this stage, the edge of the embedded plate and the concrete beam began to show some movement relative to each other. Although this movement was barely visible, it continued to increase as the test progressed. Figure 4.5 shows the pipe pile beginning to bulge during sequence I. This was accompanied by flaking of the white lime mixture on the pipe. This flaking occurred on the compressive face of the pipe, but no noticeable flaking occurred on the tension face. A slight crack down the middle of the beam was also noticed. This crack began at the top of the beam, at the center of the embedded plate, and proceeded about halfway down the beam. As cycling continued at sequence I, the pipe began to bulge extensively approximately 100 mm above the welded connection. Also note in Figure 4.6 the hinging indicated by flaking of the white lime. Figure 4.6 - Increasing bulge on right side of pipe (sequence I, cycle 3) CHAPTER 4 - TEST RESULTS 4 1 During the first cycle at sequence J, increased symptoms of sequence I were noticed (Figure 4.8). During the second cycle, a small crack on the tension face of the pipe was observed (Figure 4.9). The crack was located in a region of high curvature, approximately 125 mm from the welded connection. The high curvature was a result of the extensive bulging in the pipe. Once the load was reversed, a virtually identical tension crack appeared on the other side of the pipe. The third cycle of sequence J caused the first crack which formed to propagate until complete failure occurred. Figures 4.10 and 4.11 show the failure of the pipe, as well as the minor uplift of the embedded plate. Figure 4.7 - Specimen at maximum deflection (Sequence J, cycle 1) CHAPTER 4 - TEST RESULTS 4 2 Figure 4.9 - Initial crack forming on left side of pipe (sequence J, cycle 2) Figure 4.11 - Minor uplift of the embedded plate C H A P T E R 4 - TEST RESULTS 44 4.2.4 Additional Observations Following Test #1 The cracks in the pipe which led to failure were not located in the heat affected zone of the complete penetration weld. However, after looking closer at the region near the weld, several tiny cracks were identified (Figure 4.12). These cracks are shown on Figures 4.13 and 4.14. After examining the cracks much more closely, it was discovered that the cracks were due to weld arcing on the pipe. After discussing the matter with the welder, he insisted that they were not accidental strikes, but rather purposefully located outside the weld region. This was done so that when the welding rod was brought into the welding zone, it would not start off cold. A welding rod that starts off cold could can promote microcracks in the weld. After seeing these cracks, the inspector from the bridge inspection branch of the M o T H requested that the second specimen have all of the arc strikes removed by grinding. Figure 4.12 - Location of tiny cracks due to arc strikes CHAPTER 4 - TEST RESULTS 4 5 Figure 4.14 - Cracks due to arc strikes CHAPTER 4 - TEST RESULTS 46 Both the load versus deflection characteristics and the observed actions are consistent with the anticipated plastic hinge formation in the pipe. The load-deformation hysteresis plots indicate excellent energy dissipation characteristics. Although the strain gauges indicate that yielding of the embedded bars did not occur, there is reason to believe that the deformed bars might have slipped in the concrete. The uplift of the plate supports the notion that the deformed bars might be debonding. The possibility of bar slippage is discussed in greater detail later in the report. The failure of this connection could be classified as a ductile low cycle fatigue failure within the plastic hinge region. CHAPTER 4 - TEST RESULTS 47 4.3 T E S T S P E C I M E N #2 The pipe used in the second test had a plastic moment capacity between the factored and unfactored moment resistance of the embedded plate anchorage. The predicted moment capacities based on the M o T H current design assumptions are presented in Table 4.3 (see Appendix E). Plastic moment capacity of pipe based on mill test certificates 665 kN*m Factored Resistance of Anchorage = 0.85) 592 kN*m Unfactored Resistance of Anchorage ((() = 1.0) 696 kN*m Table 4.3 - Moment Capacities 4.3.1 Hysteresis Curves Figure 4.15 presents the overall load versus displacement record for specimen 2. The displacement has been corrected to eliminate the effect of concrete beam rotation. Recall that the sequences and their corresponding force or displacement was shown in Table 3.3. 4 0 0 200 -200 -400 -30 0 30 Displacement at jack [mm] 60 90 Figure 4.15 - Load-Displacement curves for specimen #2 CHAPTER 4 - TEST RESULTS 48 Sequences A to G, although not linear, do represent the portion of the response which is relatively stable. Sequence H shows that the specimen has yielded in some manner. This indicated by the deviation from the stable curves established in sequences A to G. Sequence H also is when the specimen underwent maximum loading. The response during sequence I shows a sudden and dramatic degradation in strength. In fact, the displacement ductility achieved by specimen #2 has been estimated to be only 2.2u.. This value is approximate because the specimen was not perfectly symmetric in its response. This ductility is rather low considering that a force reduction factor of 4 would typically be assumed for connections where steel is the ductile failure mode. Energy dissipation is directly related to the concept of ductility. The energy dissipation characteristics of test specimen #2 are not as impressive as that of specimen #1. The curves tend to be slightly pinched at the larger deflections. Thus, the connection is apparently getting "sloppy" with increasing load cycles: This overall connection behavior leads to the understanding that the failure mode within the connection was not plastic hinging within the steel pipe. Insufficient load capacity and poor energy dissipation are characteristics consistent with the actual failure mode, which is discussed in detail later in this chapter. 4.3.2 Deformed Bar Strains Discussion of the results for specimen #1 led to the conclusion that the bars being monitored in the first test had not yet yielded. Observing the hysteresis curves in Figure 4.16 indicates that yielding of these same bars has not occurred in test 2. This is because the strains are well below the expected yield strain of 2400 microstrains. CHAPTER 4 - TEST RESULTS 49 400 -400 I 1 i 1 1 i i i -600 -400 -200 0 200 400 600 800 1000 Strain Gauge Reading [microstrain] Figure 4.16 - Strain history in bar R1C3, location A 4.3.3 Qualitative Observations Specimen #2 did not experience plastic hinging in the pipe. In fact, the pipe did not show any signs of bulging at the yield moment. Observations made during and following the test validate the notion of deformed bar slippage. Once again, to aid in visual inspection of the connection, the specimen was painted with a water and lime mixture. Flaking of the lime would indicate regions of high strain. Black markers were used to trace cracks on the concrete beam. CHAPTER 4 - TEST RESULTS 50 Sequence F corresponds to the force necessary to reach the yield moment of the pipe. Figure 4.17 shows the status of the connection as it was observed during this sequence. Notice the uplift of the plate on the left side of the connection. Also, flaking of the lime mixture on the left side of the pipe was beginning to take place. While the vertical crack on the concrete beam remained from the first test, a horizontal crack appeared. It progressed from the left spreader beam and terminated at the vertical crack. At sequence H, increased symptoms of the previous load levels were observed. For instance, Figure 4.18 shows a more dramatic plate uplift and the flaking of the lime on the pipe continues to progress. Also observed was the spalling of concrete on the top of the concrete beam. The spalling occurred between the spreader beam and the edge of the embedded plate. All three observations of plate uplift, lime flaking on the pipe, and spalling of the concrete were also noticed on the right side of the connection. The final loading was sequence I, after which the connection was deemed to have failed. Failure was defined by the inability of the connection to sustain a reasonable amount of load compared to the previous load sequence. The uplift of the plate at the extreme jack deflection amounted to more than 25 mm. Figures 4.19 shows the status of the left side of the connection at extreme deflection. Figure 4.20 was taken after failure, when some of the concrete was chiseled away from the front of the specimen. Lime flaking from both sides of the pipe indicate that substantial axial strains due to bending occurred in the pipe. In addition, note the amount of uplift along the entire length of the embedded plate (Figure 4.20). With this amount of uplift of the entire plate, it is clear that all of the Nelson D2L bars failed in some manner. CHAPTER 4 - TEST RESULTS 51 Figure 4.17 - Plate uplift and pipe straining (sequence F) Figure 4.18 - Plate uplift, pipe straining, concrete spalling (sequence H) CHAPTER 4 - TEST RESULTS 52 Figure 4.19 - Extensive plate uplift (sequence 1) \ Figure 4.20 - Removed concrete shows uplift along entire length of plate (sequence I) CHAPTER 4 - TEST RESULTS 53 4.3.4 Additional Observations Following Test #2 Removal of all of the concrete from the specimen could lead to a better understanding of the failure mode of the embedded anchorage bars. Using a jackhammer, all of the bars were exposed, and a variety of failures were observed. The three potential failure modes are weld failure, bar fracture, and bar slippage. Slip failures were interpreted as all of the bars still remaining on the plate after testing. This is because the entire plate had lifted up enough to presume all bars failed in some manner. All of the bar fractures occurred within 20 mm of the weld to the plate. While bar fracture was the anticipated failure mode, Table 4.4 shows that bar slippage dominated the typical failure mode of the bars. Figure 4.21 shows the orientation of the bars on the plate and their corresponding failure modes. Failure Mode Number of Bars Failure of bars as a percentage of the total Bar slippage 20 20/30 = 66.7% Defective weld 1 1/30 = 3.3 % Bar fracture 9 9/30 = 30 % Table 4.4 - Classification of failures of anchorage bars CHAPTER 4 - TEST RESULTS 54 jack force pipe This is the view shown below / t t concrete Weld = defective weld Bar] = bar fracture Slip = bar slippage C l C2 C3 Slip Slip Slip C4 C5 Slip Weld ( \ Bar V / Slip Slip Slip Slip Slip / \ Bar V / (Bar] rr—N Bar / s Bar v ' Bar v / Slip Bar V I Slip Slip • • • • • Slip Slip [Bar) Slip Slip • • • • • Slip Slip [Bar] Slip Slip R2 R3 R4 R5 R6 R l Figure 4.21 - Orientation of bars and failure modes Further knowledge could be gained from interpreting the significance of the location of the fractured bars on the plate.Eigth of the nine bar fractures occured in rows R4, R5 and R6. Recall that Figures 4.3 and 4.4 show that larger bar strains were observed in R6C3 than R1C3. This implies that the bond might have been stronger on the R6 side of the connection. CHAPTER 4 - TEST RESULTS 55 Also note that eight of the nine bar fractures occurred closer to the middle of the connection (R2, R4 and R5). The first reason could be that the interior bars experienced bending stresses at failure. This is because the bar remains perpendicular to the plate, but at the same time must extend vertically into the concrete. Let us assume that a plate uplift of di corresponds to the displacement necessary to cause the bars to slip. Figure 4.22 shows that the outer row has a much lower angle of plate rotation (dashed line) necessary to reach a displacement, di. However, the interior rows undergo extensive plate rotation (solid line) to achieve the displacement, di. This would in turn lead to substantial bending stresses in the bar. Figure 4.23 shows how the flexibility of the cantilever section of the plate could lead to decreased bending stresses in the outer rows. Figure 4.22 - Possible bending stresses induced in interior rows Figure 4.23 - Outer flexible regions of plate reduce bending in outer bars CHAPTER 4 - TEST RESULTS 56 Figure 4.24 shows the one bar which failed due to a defective weld. The height and form of the weld is consistent with that of the other 29 welds which did not fail. It is often very difficult to determine the quality of the weld. Still, one out of thirty bars failing by a poor weld should lead to a reasonable degree of confidence in the welding procedure. Figure 4.25 shows a typical bar fracture, which was the anticipated failure mode for all of the bars. Slight necking of the bar indicates a moderate level of ductility achieved prior to failure. Because of the difficulty in achieving consistent weld quality, the bar needed to be removed and the plate surface ground smooth prior to welding a new bar in it's place. This is indicated by the surface of the plate which has been subjected to grinding to remove the previous weld material deposit. Figure 4.26 also shows that the plate surface needed to be ground smooth, and another weld effort was made. But after the second weld attempt, a tiny region of the weld was still not satisfactory (lower left of bar on photo). Therefore, to increase confidence in the weld strength, the weld was repaired by a hand weld in the region of concern. Only this one bar was repaired with a hand weld. Figure 4.27 shows a bar which ultimately failed by slippage. However, a closer look indicates that this bar underwent large compression forces. This is hinted by the noticeable bulge approximately 30 mm from the weld. Possibly some debris from the bar slippage was transferred beneath the bar when it was in tension. And then, when the bar went into compression, it could not be pushed down as far due to the bottom of the bar being clogged with debris. Thus, higher compression forces were induced in this bar. Visual inspection of the other bars led to the conclusion that this bulging phenomena was an isolated incident. CHAPTER 4 - TEST RESULTS 57 Figure 4.25 - Bar fracture of R4C5 CHAPTER 4 - T E S T RESULTS 58 Figure 4.27 - Large compression force indicated by bulging in bar R 6 C 2 CHAPTER 4 - TEST RESULTS 59 The load versus deflection characteristics and the observations made during and following testing are not consistent with plastic hinge formation in the pipe. The load-deformation hysteresis plots do not possess the quality of energy dissipation that is desired. Although the strain gauge reading on the outermost bar indicated no strains above yield, subsequent removal of the concrete shows that a variety of bar failures occurred. Bar slippage dominated the failure modes, which will be investigated and discussed in greater detail in the following chapters. CHAPTER 5 - ANALYTICAL MODELLING 60 5.0 ANALYTICAL MODELLING This chapter outlines the two approaches used to predict the response of the specimens. A simple model has been used to predict both the linear and non-linear portions of the load displacement response. However, this approach does not consider the effects of three dimensional distribution of strains. For this reason, three dimensional, finite element modelling has been performed. The finite element model has been applied for the linear region of the response. The predictions obtained from these models will be compared to the actual test results in Chapter 6. 5.1 SIMPLE MODEL A simple, two dimensional model used for the comparative study has been developed. The displacement of the specimen is primarily due to two factors. First, the deflection of the pipe due to cantilever loading. Second, the rotation of the embedded plate in the concrete causes additional displacement at the jack location. 5.1.1 Pipe Bending The specimens were intended to undergo plastic hinging in the pipes. Thus, the predicted behaviour of the connection must include the non-linear characteristics of the steel. For simplicity, the steel was assumed to have a Young's modulus of 200,000 MPa, up to the yield stress of the two pipes. The Young's modulus would be set to zero once the yield stress was reached. This bilinear curve is illustrated graphically in Figure 5.1. CHAPTER 5 - ANALYTICAL MODELLING 61 ° 4 oy = 410 MPa (specimen 1) a y = 338 MPa (specimen 2) E = 200,000 MPa 6 Figure 5.1 - Assumed stress versus strain relationship for steel pipes Figure 5.2 shows the sequence of events leading to the calculation of the moment in the pipe. The pipe cross section was divided into 36 slices. For a given curvature, the strain in each slice was calculated. The stress was then computed based on the constitutive relationships previously shown by Figure 5.1. The axial force in each slice was equal to the stress times the area of the slice. The moment in the pipe was then calculated by summing the axial forces times the distance of the slice to the section centroid. The derivation of the moment in the pipe can be shown symbolically as follows: ai represents the stress for the given slice "i". A is the area of slice "i". In this case, the area is equal for all 36 slices. d; is the distance of slice "i" to the centroid of the pipe (shown graphically on Figure 5.2). N; is the axial force in the slice "i": it is the product of the stress times the area. M = Z [ ( O i * A i ) * d i ] = I [Ni*di] CHAPTER 5 - ANALYTICAL MODELLING 6 2 Pipe cross section Strains, e Stresses, a Figure 5.2 - Typical strain and stress profile for a given curvature When the cantilever loads are below the yielding level, the predicted deflection of the pipes is based on elastic behaviour and is given by: A = (PL3)/(3EI) P represents the cantilever force and L is the length of the cantilever. E is the Young's modulud of steel and I is the moment of Inertia for the pipe. This corresponds to integrating the curvature of the pipe along it's entire length. The total deflection, as a function of the curvature, <j>, at the base could also be expressed as: A = <t>2(L/3) Figure 5.3 shows the distribution of curvature, which is linear prior to any yielding. CHAPTER 5 - ANALYTICAL MODELLING 63 l^pipe plate jack force T P<P y L concrete curvature, (j) Figure 5.3 - Curvature prior to any pipe yielding Once the force reaches a level which produces the yield moment in the pipe, the curvature distribution in the pipe changes. Figure 5.4 shows how a specified distance of the pipe undergoes substantial straining. This region is called the plastic hinge zone, and is denoted by L p . For steel sections, the plastic hinge length is assumed to be the depth of the member. Once the plastic moment of the pipe is reached, the pipe can no longer sustain a higher load. Thus, the displacement continues to increase with a constant plastic load, Pp. Prior to this plastic load, the integrated curvatures produce a displacement as follows : A - c))y (L/3)+((J)-<|>y)Lp(L-Lp/2), where $y is the yield curvature < -jack force P y<P ^pipe L plate L concrete • curvature, <}> Figure 5.4 - Curvature distribution once the yield force is exceeded CHAPTER 5 - ANALYTICAL MODELLING 64 5.1.2 Embedded Plate Rotation The code simplified approach makes use of an equivalent rectangular stress block. This is not the most accurate representation of the state of stress in the connection. Therefore, in order to model the entire moment curvature response of the embedded plate, a computer program called BEND was developed. The source code for the program, written in Turbo Pascal 5.0, is contained in Appendix I. BEND uses a more realistic stress versus strain relationship to determine the stress in the concrete (Figure 5.5). In fact, the stress-strain curve is based on a high strength concrete curve. This is applicable because of the moderately high strength concrete used in these tests. For a given section with discretized layers of concrete and steel, the computer asks the user for a curvature. Each discretized layer has a different strain based on the assumption of linearly varying strains. As shown in Figure 5.6, this produces different stresses in each layer. The program iterates until axial equilibrium is satisfied. The corresponding moment for the given curvature is then calculated. If the user continues to input several different curvatures, the entire response of the embedded plate connection is able to be calculated using this approach. The ultimate strength obtained from the discretized layer approach was verified by comparison to the code. The ultimate strengths were within 2 % of each other. CHAPTER 5 - ANALYTICAL MODELLING Figure 5.5 - Typ ica l stress-strain curve for concrete k—*5 „ ^ c, to neutral axis ^ otfc fc Figure 5.6 - Code simplif ied versus discretized layer stress distr ibut ion Once the entire moment-curvature response has been predicted, the displacement at the jack must be computed. First, the strains in the steel were converted to displacements by multiplying the strain in the steel by the bar length. This gives an angle of rotation for the plate, which can then be transferred to a displacement at the jack (Figure 5.7). CHAPTER 5 - ANALYTICAL MODELLING 66 Urowl ar s <— • Figure 5.7 - Displacement at jack due to plate rotation The prediction of embedded plate rotation shown in the previous figure uses the entire length of the steel bar to determine the bar's change of length. This is somewhat misleading due to the fact that the strain in the bar is continually decreasing with length along the bar due to bonding to the concrete. In this regard, the model will be more flexible than would be anticipated in the actual test. However, this assumption is reasonable when one considers that the majority of the displacement is due to pipe flexibility, and not plate rotation. The simple predictive model is based on deflections due to pipe bending and embedded plate rotation. It takes into account the non-linear characteristics of the steel pipe, concrete, and steel anchorage bars. The predictions obtained from the model will be used to compare with the test results of the two specimens. CHAPTER 5 - ANALYTICAL MODELLING 67 5.2 FINITE ELEMENT MODEL Finite element models have been developed to predict the linear response of the two specimens. A commercial finite element program, ANSYS V5.0, was used exclusively for modelling of the test specimens. The models would also be useful when observing any unanticipated stress concentrations near the weld between the pipe and the plate. It proved to also be effective in studying the effects of plate flexibility. The plate flexibility can affect the distribution of strains to the concrete anchors. If the plate is too flexible, it could lead to a severe violation of the assumption of linearly varying strains: the stiffness of the plate substantially alters the load distribution to the various anchors. Due to the fact that debonding of the bars was suspected, only linear finite element modelling was employed. The characteristics of the bond-slip response of the bars proved beyond the scope of this report. Also, an accurate model for the bond-slip characteristics of these D2L anchors is not available. Therefore, any non-linear modelling could provide suspect results. 5.2.1 Model Description The model consisted of elements representing the pipe, plate, anchorage bars, and concrete regions in compression. All of the elements, with the exception of the anchorage bars, were created using eight (8) node, brick like elements. In order to reduce both model development and computational time, half of the specimen was modelled according to it's symmetry. CHAPTER 5 - ANALYTICAL MODELLING 68 The anchorage bars were modelled by two node, truss elements. That is, they were capable of carrying axial forces only. Each bar had an area equal to the nominal area of 187 mm2. However, because half of the specimen was modelled, the bars along the line of symmetry had half of the area. The steel pipe, plate and anchorage bars were assumed to have a Young's modulus of 200,000 MPa. The concrete elements were assumed to have a Young's modulus equal to the secant modulus of 5000*(f c) 0 5 (MPa). The eight node concrete elements were modelled on the compressive face of the embedded plate. The contribution of concrete where the anchorage bars were in tension was assumed to be negligible. Also, it has been assumed that the concrete elements contribute to the bending stiffness of the plate. This is because the concrete elements are in compression and there are a number of deformed bar anchors providing a shear connection. Determining the location of the neutral axis was an iterative procedure because a linear analysis was employed. It was iterative because an initial guess had to be made at the layout of the concrete compressive elements. Once the program was run, the nodes needed to be checked if they were experiencing uplift or not. If the node had an upwards displacement, this would mean that any concrete elements attached to it would be in tension. Therefore, the element would need to be removed, and the analysis re-performed. The opposite case is if a node moved downward and no concrete was attached to it. This would indicate compression, and a concrete element would need to be added to the model at this location. This iterative approach was followed until the most reasonable orientation of concrete elements was obtained. CHAPTER 5 - ANALYTICAL MODELLING 69 There are only minor differences in the two models. Obviously, the second specimen had a larger pipe diameter, and was modelled as such. Also, the concrete compressive elements were rearranged for the second specimen. This is because the yield moment for specimen #2 was larger. Therefore, the orientation of the compressive reactions under the plate would need to be altered. Figures 5.8 and 5.9 show the resulting models for specimens 1 and 2, respectively. L A T E R A L L O A D ( H A L V E D F D R S Y M M E T R Y ) ITX 1880 •600-|—324 —| i i T 325 — - C O N C R E T E E L E M E N T S • S T E E L E L E M E N T S E L E V A T I O N TOP V I E W Figure 5.8 - Fini te element model of specimen #1 CHAPTER 5 - ANALYTICAL MODELLING 70 LATERAL LDAD (HALVED FDR SYMMETRY) on 1880 -600-406 — — T 325 •CONCRETE ELEMENTS STEEL ELEMENTS E L E V A T I O N TOP V IEW Figure 5.9 - Finite element model of specimen #2 CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 71 6.0 COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK The simple model described previously has been compared to the measured results on the two specimens. The simple model was a means of establishing a theoretical load versus displacement response for each of the specimens. Furthermore, finite element modelling has been used as a means of comparison to the experimental results at the yield point of the two specimens. The finite element model will allow for analysis of plate bending stresses, which could influence the distribution of strains to the various anchors. In the case of poor agreement between the theoretical and experimental results, more detailed test data will be presented as a means of explaining the discrepancies. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 72 6.1 SPECIMEN #1 Figure 6.1 presents the load-deformation history for the response of specimen #1. The darker line superimposed on the plot represents the predicted monotonic response derived from simple two dimensional model. The model prediction is a stiffer response; however, the strength correlation is excellent. The accurate prediction of the strength indicates that the theory behind the plastic moment capacity of the pipe is verified. The rest of this section attempts to explain why the connection was more flexible than anticipated. Bar slippage is the most probable reason. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 73 6.1.1 Strains Below Y ie ld In Anchorage Bars Fo r Specimen #1 Because the observed strains in the bars during testing were below yield, the only possible location that the bars could have yielded was in the first 100 mm of the bar. This is because the first 100 mm of the bar could not be monitored by the strain gauges. Yielding in the first 100 mm is unlikely due to the fact that the uplift of the plate was significantly more than could be reasonably explained by yielding over 100 mm. The amount of yielding over 100 mm would have to reach approximately 14 times the yield strain (14sy) if it were to account for the observed plate uplift of 3 mm. This is improbable because it will be shown later that in simple tension, the bars fail at a strain of about 3.5 times the yield strain (3.5sy). Therefore, the bars are not ductile enough to reach strains 14 times the yield strain. Furthermore, bar R1C3 experienced the lesser of the steel strains, but it was on the side which experienced more uplift! A more likely explanation for the embedded plate uplift is the slippage of the anchorage bars. 6.1.2 Tensile Strains In Deformed B a r Anchors Slippage of the deformed bars might at first seem unlikely, but observing the strains in the anchorage bars could potentially tell us a great deal about possible bond deterioration. Figures 6.2 and 6.3 present the maximum steel tensile strains at the three positions on the bar at different stages of testing. Sequence I and J are the two final load sequences prior to failure. Note that for virtually constant force levels, the steel strains in both bars drop substantially over the final 8 cycles. This indicates possible bar slippage due to bond deterioration. Note the particularly severe drops in strain for bar R1C3. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 600' Figure 6.2 - Maximum tensile strains during last two sequences for Bar R1C3 100 E E ^ 200 8 o .s 03 b 300 400 500 500 T Strain Gauge Reading [microstrain] 1000 1500 2000 2500 1 1 1 1 S Seq.I.Cycle 1 •O- Seq. I, Cycle 2 A- Seq. I, Cycle 3 H Seq. I, Cycle 4 •O- Seq. I, Cycle 5 •A-Seq. I, Cycle 6 #• Seq. J, Cycle 1 it Seq. J, Cycle 2 — — 600 1 • ' '' ' ' ' 1 ' 1 Figure 6.3 - Maximum tensile strains during last two sequences for Bar R6C3 CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 75 Table 6.1 presents the average bond stress due to tension in the bars at different stages of testing. Note that while bar R6C3 has relatively stable bond stresses at high loads, bar R1C3 apparently suffers a major drop in the bond stress after the first cycle of sequence I. This suggests that the maximum bond strength for bar R1C3 has been exceeded. Load Sequence and Cycle Number Jack Force (kN) Bar R6C3: Bond stress (MPa) and Force in bar (kN) Bar R1C3: Bond stress (MPa) and Force in bar (kN) Seq D, all cycles 115 2.1 MPa,. 40 kN 1.0 MPa, 24 kN Seq H, all cycles 260 2.8 MPa, 65 kN 1.2 MPa, 52 kN Seq I, cycle 1 285 3.3 MPa, 81kN 1.7 MPa, 58 kN Seq I, cycle 6 265 2.9 MPa, 69 kN 0.85 MPa, 30 kN Table 6.1 - Bond Stresses at Various Load Sequences The tabled values for bond stress in the previous table are based on the assumption of uniform bond stress. The steel strains in the specimens were converted to forces by: F = e*Esteei*Area. The maximum average bond stress along the bar is therefore: tavg = (Force at gauge 1 - Force at gauge 3)/(7c*diameter*length), where diameter = 15mm, and length between strain gauges = 400mm. This is demonstrated graphically by Figure 6.4 CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 76 X; ~7f 400mm 100mm Figure 6.4 - Bond stress calculated from strain gauge readings 6.1.3 Compressive Strains In Deformed Bar Anchors Figures 6.5 and 6.6 present the maximum steel compressive strains at the three positions on the bar during the later stages of testing. The steel compressive strains appear more stable than the tensile strains previously discussed. The compressive strains are significantly less than the tensile strains due to the contribution of the concrete on the compressive face. Also the bearing at the bottom end of the bar resisted potential slippage when the bars were in compression. Therefore, it is reasonable to speculate that when the bars were in compression they simply returned to their original position, and did not experience any more substantial slip. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 77 E £ CQ a o c o 200 o oo 3 t o o VI 300 400 500 Strain Gauge Reading [microstrain] -500 0 500 B Seq I, Cycle 1 & Seq I, Cycle 2 A-Seq I, Cycle 3 B Seq I, Cycle 4 $-Seq 1, Cycle 5 A-Seq I, Cycle 6 - m- Seq J, Cycle 1 * S e q J, Cycle 2 600 I Figure 6.5 - Maximum compressive strains during last two sequences for Bar R1C3 10 0 200 o O .s VI 300 400 500 U 600 Strain Gauge Reading [microstrain] -400 -200 T BSeq I, Cycle 1 O - Seq I, Cycle 2 * Seq I, Cycle 3 B Seq I, Cycle 4 Seq I, Cycle 5 & Seq I, Cycle 6 %• Seq J, Cycle 1 ! *-Seq J, Cycle 2 j 200 Figure 6.6 - Maximum compressive strains during last two sequences for Bar R6C3 CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 78 6.1.4 Compar ison at Y ie ld and M a x i m u m Moments The finite element modelling results were investigated at a force level necessary to achieve the yield moment in the pipe. The simple approach is essentially the code approach, except that actual material strengths are used, and the bridge performance factor, is excluded. The force is that measured in the jack, while the deflection is measured at the jack, but has been corrected to eliminate the effects of beam rocking and sliding. The outermost bar along the centerline of the beam is R6C3, because this bar experienced the largest strains. Although some local stresses in the FEM were higher than yield, the yield force was set equal to that of the simple approach. This would allow for more convenient comparison between deflections and bar strains. At Yield Moment Experimental Simple Approach Finite Element Force, Vy [kN] 200 203 203 Deflection, Dy [mm] 30 25 26 Bar Strain [microstrain] 2010 1990 2560 At Maximum Moment Force, Vp [kN] 280 269 n/a Bar Strain [microstrain] 2200 2675 n/a Table 6.2 - Compar ison for specimen #1 At the yield moment, the simple model underestimates the experimental bar strains. The high bar strains predicted by the FE analysis is due to plate flexibility across the plate's width. At the maximum moment, the simple model bar strains are larger than the measured values. This is because the experimental bar strains peaked at 2200 microstrain, and then slippage occurred. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL-& EXPERIMENTAL WORK 79 6.1.5 Three Dimensional Distr ibut ion to Anchors The code simplified approach assumes an equal distribution of force to each embedded anchor across the width of the plate. However, a more realistic deformed shape for the plate could be obtained from the FEM. During testing, LVDT 1 was placed near the plate edge on specimen #1 (recall Figure 3.14). The plate uplift at this location could then be compared to the uplift measured by LVDT 6, along the centerline of the beam. Table 6.3 presents two values of interest. The experimental value is the ratio of LVDT 1 to LVDT 6. The FEM result is for vertical nodal displacements for nodes located where the LVDTs were on the specimen. The values presented in the Table are for the side of the specimen in tension at the yield force of the pipe. Although the values are not in good agreement, they do give a general impression as to the degree of plate bending across the width of the plate. Experimental Simple Approach FEM (Douter edge)/(Dcenterline) 7 5 % 100 % (code assumption) 4 6 % Table 6.3 - Var ia t ion of plate deflection across plate width for specimen #1 Now the high bar strains predicted by the FEM in Table 6.2 can be better understood. If the average strain for one row was considered, the agreement is more impressive. The average strain could be calculated as being: ecenteriine * [1+ (Douter edge)/(Dcenteriine)]/2. The average row strain is presented in Table 6.4. The agreement is now more impressive. Experimental Simple Approach FEM Eaverage [microstrain] 2010 * [l+.75]/2 = 1760 microstrain 100 % (code assumption) = 1990 microstrain 2560 * [1+.46J72 1870 microstrain Table 6.4 - Average strain in extreme row for specimen #1 CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 80 6.1.6 Finite Element Model Stress Contours The FEM results can also be observed in the context of stress contours. From this aspect, certain problem areas could be identified as having abnormal stress concentrations. The graphical representation of the stresses can also lead to a better appreciation and "feel" for the numerical values already presented in this chapter. It is also important to gain confidence in the FEM as an acceptable means of predicting the specimen's behaviour. This could lead to using FEM as a method of exploring other connection concepts in place of the existing details. The stresses along the length of the plate are defined as Sx. Here, the effects of plate flexibility can be visually appreciated. The most significant stresses in the x-plane are in the embedded plate. The compressive side of the connection has the most substantial bending stresses inside the edge of the pipe's edge. This is because of the modelling assumption that the concrete elements contributed to the bending stiffness of the plate. On the tension side of the connection, the maximum plate bending stress occurs at the pipe's edge. Figures 6.7 and 6.8 present these stress contours. The legend shows that the plate stresses are above the yield stress of 350 MPa. However, these high stresses are localized, and the majority of the plate's width is below the yield stress. Figure 6.8 shows how the majority of plate bending is occurring across the width of the pipe. In other words, the outer regions of the plate are not resisting much of the bending stresses. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 81 OCT 27, 1995 14 : 15 : 12 , , -373.689 }==} -286 .14 mm I if?; e| pflPj -23.491 B E S i ! S s 1 S | 239 .158 5 = 326.788 L £ £ s a J 414.258 Figure 6.7 - Stress contour Sx (front view) X S H E ' 5\ '.' w OCT 27, 1995 14:21:19 • 1 -373.689 \===i -286.14 ki l ls -198.59 l l l l l -111.04 -an . 49 1 gg|g 64 .859 gil l 151.609 ™ ill:™! L—--1 414.258 Figure 6.8 - Stress contour Sx (top view) CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 82 The stresses across the width of the plate are defined as Sy. Figure 6.9 shows the state of stress looking from the back of the connection. The simple two dimensional approach used by the code assumes that all Sy stresses are equal to zero. The stress contours refute this, indicating that substantially high stresses are induced in the third dimension. O C T 2 7 , 1 9 9 5 1 4 : 1 3 : 1 4 - 3 2 5 . 8 6 3 - 2 5 4 . 9 7 9 - 1 8 4 . 0 9 5 - 1 1 3 . 2 1 1 - 4 2 . 3 2 7 2 8 . 5 5 7 9 9 . 4 4 1 7 0 . 3 2 4 2 4 1 . 2 0 8 3 1 2 . 0 9 2 Figure 6.9 - Stress contour Sy (back view) CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 83 The most fundamental stress is the axial stress in the pipe. This vertical stress is defined as Sz. Note that in Figure 6.10 the largest stresses are at the outermost fibers of the pipe. Figure 6.11 also shows the Sz contours from the back view. The most intriguing result is shown by Figure 6.10. At location A, there is a large compressive stress in the element. However, in the elements above and below this location, the stress is lower. This is most likely due to the eccentric nature of the compressive reaction from the concrete. Thus, when the stress is transferred to the pipe, there is axial force and a moment to be carried by the pipe. The legend gives stresses that are significantly higher than the actual yield stress of the pipe (410 MPa). This was expected to local conditions producing high stresses. For example, the additional bending due to the eccentric compressive reaction would increase the axial stress in the pipe. Also, extremely high stresses can be expected at abrupt changes in geometry where the pipe meets the plate. It is interesting to note that the compressive stresses were higher than the tensile stresses in the pipe. This could be observed during the test. Recall that photographs presented earlier in this report showed that flaking of the lime from the pipe first occurred on the compressive face of the pipe. This suggested that the compressive strains were larger than the tensile strains. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 84 OCT 27, 1995 14:05:54 -614.795 -492.264 -369.733 -247.282 -124.671 -2.14 120.391 242.922 365.453 487.984 OCT 27. 1995 14:09:04 . . -614.795 Lr^J -492.264 P E s s s s s r a ~369 • 733 mmm - 5 4 7 o « ^ > ™ -Itl'.tvi 1 1 1 " 2 • 1 4 SSI 120.391 HH| 242.922 365.453 1 ^ 487.984 Figure 6.10 - Stress contour Sz Figure 6.11 - Stress contour Sz (back view ) C H A P T E R 6 - COMPARISON B E T W E E N A N A L Y T I C A L & E X P E R I M E N T A L W O R K 85 6.2 SPECIMEN #2 The numerical data obtained from test 2 combined with various observations indicate that the connection did not behave as desired. In fact, the moment capacity and failure mode of the embedded plate anchorage were both disappointing. Numerous Nelson deformed bars slipped, and a low percentage experienced the desired bar fracture. However, if one considers the conclusions derived from the first test specimen regarding potential bar slippage, the failure mode might not be such a surprise after all. Figure 6.12 presents the predicted load-displacement response superimposed on the actual hysteresis curves. 400 I : : = 1 1 [ : = : : = 1 200 -200 .400 I i i i I i I i I i I i I -90 -60 -30 0 30 60 90 Displacement at jack [mm] Figure 6.12 - Predicted and Observed Load-Displacement Response of Specimen #2 CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 86 Figure 6.12 shows that the agreement between the theoretical (thick line) and actual response is poor. This can best be explained by the proposed reasoning of bar slippage. De-bonding of the anchorage bars would effect both the stiffness and strength of the connection. The photographic evidence previously presented regarding embedded plate uplift and bar slippage is verified by the numerical results. The photographs and observations suggested that unanticipated failure modes of the anchorage bars were dominating the load carrying characteristics of the connection. 6.2.1 Slippage Of Deformed Bar Anchors In Specimen #2 Discussion of the first test has already suggested that de-bonding of the Nelson deformed bars is of possible concern. With this in mind, the uplift of the embedded plate could further reinforce the notion of bar slippage. Figures 6.13 and 6.14 present the uplift of the plate during the increasing loading sequences. The uplift was measured at locations previously described as LVDT 1 and LVDT 4. The uplift of the concrete beam due to rotation of the beam has been subtracted from the LVDT readings. Thus, the plots show plate uplift relative to the concrete. The plots show that after the maximum load of « 300 kN was reached, the uplift of the embedded plate increased dramatically. In fact, the uplift was greater in later cycles when the applied force had dropped off from the maximum. The large displacements of the plate are consistent with deformed bar slippage. Although the two plots show a maximum uplift of approximately 14 mm, the LVDTs reached their maximum stroke at this point. This maximum LVDT stroke is represented by the vertical lines at plate uplift of « 14 mm. Visual inspection of the plate suggested that the uplift of the plate was closer to 25 mm at failure. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 87 -400 4 - 4 --4 0 4 8 12 16 Plate Uplift [mm] Figure 6.14 - Plate uplift measured on the left side of the connection (@ LVDT 4) C H A P T E R 6 - C O M P A R I S O N B E T W E E N A N A L Y T I C A L & E X P E R I M E N T A L W O R K 88 6.2.2 Compar ison at Y ie ld and M a x i m u m Moments As has already been discussed, specimen #2 did not behave as expected. This would cause the comparison of values in Table 6.5 below to be poor. Because the strain gauges on bar R6C3 were not functioning for the second test, the experimental bar strains presented in the Table are for barRlC3. At Yield Moment Experimental Simple Approach Finite Element Force, Vy [ k N ] 230 270 270 Deflection, Dy [mm] 34 18 18.3 Bar Strain [microstrain] 810 2675 3350 At Maximum Moment Force, Vp [ k N ] 270 351 n/a Bar Strain [microstrain] 860 3480 n/a Table 6.5 - Compar ison for specimen #2 Comparison of the maximum forces shows that specimen #2 did not reach the desired strength level. In fact, the low strains measured in the bar can be interpreted as an indication that the bars are slipping in the concrete. CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 89 6.2.3 Three Dimensional Distribution to Anchors During testing, LVDT 3 was placed near the plate edge on specimen #2 (recall Figure 3.15). The plate uplift at this location could then be compared to the uplift measured by LVDT 4, along the centerline of the beam. However, the extensive plate uplift observed during test 2 precludes a comparison of three dimensional distibution to the anchors. This is because the majority of plate displacement is due to bar slippage, and thus cannot be interpreted as distribution of strains to the various anchors. 6.2.4 Finite Element Model Stress Contours The stress contours obtained from the FE analysis of specimen #2 has led to results very similar to that of specimen #2. The stress contour plots for specimen #2 have been included for completeness. It is interesting to note the plate x-plane stress, Sx, for specimen #2. Figure 6.15 contains the legend stating the maximum tensile stress as being 304 MPa. Recall that for specimen #1, the maximum plate bending stress was determined to be 414 MPa (Recall Figures 6.7 & 6.8). This is interesting because the second specimen is under a higher force. The lower plate stress can be explained by the fact that the cantilever length of the plate is decreased due to the increased diameter of the pipe (from d>324 to <b406). CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 90 OCT 27, 1995 11:05:44 . , -306.216 -238.394 ' I -170 RVI I -102.748 I -34.926 1 32.897 2 100.719 • 168.542 \ 236.364 1 304.187 OCT 27, 1995 11:01:04 I , -364.463 \=={ -289 .163 msM -213.863 §§§§ -138.563 S K -63 .264 jg—j 12 .036 j j j j 87 .336 • • III: t i l -1 313.236 Figure 6.16 - Stress contour Sy (back view) CHAPTER 6 - COMPARISON BETWEEN ANALYTICAL & EXPERIMENTAL WORK 91 OCT 27, 1995 10:59:02 I 1 -612.542 \===\ -496 .154 m -Ui.ivt j=8S^ -146.988 L 1 434.956 Z A Figure 6.17 - Stress contour Sz OCT 27, 1995 11:00:10 -612.542 -496.154 -379.765 -263.376 -146.988 -30.599 85 .79 202.178 318.567 Figure 6.18 - Stress contour Sz (back view) CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 92 7.0 DISCUSSION OF DEFORMED BAR SLIPPA GE Because the deformed bar anchors slipped and caused undesireable embedded plate anchorage behaviour, the question of bond strength and design philosophy must be addressed. This chapter describes the most significant factors influencing bond strength, and then focuses on the ones which affected the tests. There will then be a progression from present assumptions to more reasonable assumptions regarding deformed bar behaviour. If the Nelson D2L bars are used in future designs, these new assumptions could lead to a more reliable connection. 7.1 PARAMETERS INFLUENCING BOND STRENGTH The behaviour of the two specimens points to deformed bar slippage as an area of primary concern. Several parameters have been identified as having a significant effect on the bond strength between steel bars and concrete. Bond strength is typically most affected by the concrete compressive strength and the type of deformation on the steel bar. Furthermore, the bond strength under monotonic load (one way pull out tests) is significantly higher than for reversed cyclic loading. 7.1.1 Concrete Strength It is widely accepted that bond strength is directly related to concrete compressive strength. The most common relationship is that bond strength increases with the square root of f c. For example, a 45 MPa mix should give higher bond strengths than a 30 MPa mix by a factor of (45)5/(30)5 = 1.22. In the modular bridge program, 45 MPa concrete is used in an effort to reduce the necessary length of the anchorage bars. CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 93 7.1.2 Monotonic versus Reversed Cyclic Loading Reversed cyclic loading at large stress levels tends to lead to bond deterioration in subsequent load cycles. Monotonic load tests tend to generate higher bond stresses because of the lack of this progressive bond destruction. Many reversed cyclic loading tests have seen bond strengths reduced by 50% compared to the monotonic case1. Therefore, reversed cyclic loading applications should require greater embedment lengths than suggested by monotonic tests. 7.1.3 Steel Bar Deformations Extensive research has been performed by numerous authorities on the effects of bar deformations on bond strength. The bond strength of smooth bars have been compared to that of conventional reinforcing in many of these tests. For 30 MPa concrete, Table 7.1 shows the range of average bond strength found in some literature. Smooth Bars Deformed Wire Conventional Reinforcing Bond Strength, x 0.82 to 2.7 MPa ????? MPa 5.2 to 7.0 MPa Table 7.1 - Data obtained from literature on bond strength In Figure 7.1, the bar on the top is the bar used in the present specimen (Nelson Catalogue, D2L bar), whereas the bottom bar is a typical reinforcing bar. Ribbed deformations provide an area for compressive reactions to form and resist slip. The Nelson deformed bar has the form of slight dimples rather than significant ribs. i Ismail & Jirsa, "Bond Deterioration in Reinforced Concrete Subject to Low Cycle Loads", ACI Journal, June 1972 CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 94 Figure 7.1 - Deformed bars (Nelson bar on top, conventional bar on bottom) 7.2 EXPLANATION FOR BAR SLIPPAGE This section explains why the majority of the Nelson deformed bars failed by slipping rather than the desired bar fracture. The Nelson Catalogue specifies that the bars are made from deformed wire (see Figure 7.1). The catalogue's basis for the equations is the ACI code. The catalogue's embedment lengths are correctly tabulated assuming the bars possess a yield strength of 483 MPa (70 ksi). However, the bars were much stronger than the catalogue states. In addition, cyclic loading presumably further reduced the strength of the connection. CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 95 7.2.1 Actual Stress Strain Relationship The reason for bar slippage could be explained by the fact that the bars are substantially stronger than the catalogue guaranteed minimum strengths. While the catalogue bases embedment lengths on a yield strength of 483 MPa, simple tensile tests suggest that the bars have an ultimate strength of « 750 MPa. Figure 7.2 displays the results of the tensile tests that were performed at the structural laboratory of the University of B.C. Although the ACI code has conservatism built into embedment length formulae, the ratio of 750/483 presents a factor of 1.55. It is difficult to determine if the code is conservative enough to allow for this degree of steel overstrength. As was the case with the pipe pile, the anchorage bar manufacturer apparently assumes that, "stronger is better". However, stronger bars could lead to bond failure rather than the desired bar yielding. 8 0 0 7 0 0 6 0 0 Idealized behaviour with excellent ductility beyond 10 times yield strain o o 5 1 0 1 5 Thousands Microstrain Figure 7.2 - Idealized and actual stress-strain curves for 1 5 M - D2L Anchors CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 96 7.2.2 Reversed Cyclic Loading The higher than anticipated strengths were not the only reason for deformed bar slippage. After reviewing the strain gauge data, it can be said with reasonable confidence that cyclic loading reduced the bond strength of the deformed anchors. As was stated previously, the specified concrete strength used for the specimen was 45 MPa, and the Nelson Catalogue length was correctly tabulated using the ACI formulae as follows (changed to metric for convenience): L c o d e = 0.36*db*fy/(rc)05*(2-414/fy)= 0.36* 16*483/(45)° 5*(2-414/483)= 474 mm [ACI 12.2.3] However, the 15M-D2L anchors welded to the plate were 600 mm long, rather than the catalogue recommended length of 474 mm. The catalogue value of 474 mm should lead to achieving a stress in the bar of 483 Mpa. Therefore, a reverse calculation determines the stress that the 600 mm long bar can achieve: Lactuai = 600 mm = 0.36*16*f a c hi e v e b, e/(45)°- 5*(2-414/f a c h i e v a b l e) — » fachievabie = 556 MPa The strain gauges were monitoring two bars which slipped in the concrete. The maximum observed strain in bar R6C3 was 2200 microstrains (recall Tables 4.2 & 6.2). This corresponds to a bar stress of 2200* 10"6 * 200,000 = 440 MPa. This is much lower than the presumably attainable stress of 556 MPa previously calculated. It was shown in Section 7.1.2 that other research projects have discovered that the bond strength for conventional reinforcing steel was reduced by 50 % due to reversed cyclic loading. It appears that the embedment lengths quoted in the Nelson Catalogue are not intended for reverse cyclic loading. The high strength of the bars and the effects of cyclic loading are the most likely reasons for slippage of the deformed anchors. These factors most likely cause the inconsistencies with the minimum embedment lengths presented in the Nelson Catalogue. Also, considering these factors could lead to a more reliable design. The implementation of these factors is shown in the following section. CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 97 7.3 PROGRESSION OF DESIGN APPROACHES FOR D2L ANCHORS The Nelson catalogue states that the tabulated embedment lengths allow the bars to reach a stress of 483 MPa. However, design of moment connections is based on ductility and load redistribution. In fact, moment connections depend on ductility for both seismic and non-seismic applications. This section outlines a progression of assumptions which lead up to the most reasonable design assumptions. The design assumptions are based on data obtained throughout testing, and should also allow for a reliable connection to be designed using the D2L anchors. 7.3.1 Present Approach Based on Specified Yield Stress With Large Ductility In the case of the current MoTH design approach for the moment resistance of the embedded plate anchorage, several rows of bars were assumed to be yielding at the same time. Figure 7.3 shows how the yield stress in the bars is assumed to be 483 MPa, which was the specified yield stress. Another assumption key to the design philosophy was with regards to the ductility of the steel bars. Although the present design assumes that the bars can reach ten times the yield strain, the bars can only reach about 3.5 times the yield strain (recall Figure 7.2). This is due to the fact that the bars are cold rolled, and therefore do not possess large ductility. Note that this approach also assumes that the bars will not slip in the concrete, because they are assumed to be long enough to fail in tension. i Cy = 483 MPa i 0"row5 0"row4 ^ " ^ ^ ^ 1 1 rr CJr0w2 C>row3 ^ — C>rowl ^afc Figure 7.3 - Stress distribution based on specified yield stress and large ductility CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 98 7.3.2 Anchorage Strength Based on Actua l Steel Properties A more correct prediction of the anchorage strength would be to use the actual stress-strain relationship. That is, use the actual strength of 750 MPa, along with the moderate ductility level of 3.5 times the yield strain at failure. Figure 7.4 shows this revised approach. The ultimate strength obtained from these assumptions is almost identical to that obtained using the previous assumptions of lower strength bars with higher ductility. This is because the higher strength bars would give each row a higher stress to attain. However, the lower ductility limits the number of rows which could yield prior to the outer row reaching the failure strain. Note that the previous assumptions could allow three rows to yield (recall Figure 7.3), but the actual steel properties limit the connection to only two rows of bars yielding (Figure 7.4). This approach also assumes that the bars are long enough such that the bars fail in tension prior to slipping. CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 99 7.3.3 Anchorage Strength Considering Bond Failure The next step to improve predicting the strength of the anchorage would be to limit the moment capacity by potential bar slippage. Figure 7.5 shows the stress distribution which is governed by the outermost row of bars slipping. The presumed basis for this design approach is as follows: if the minimum recommended catalogue embedment length is provided, the bars could slip at a bar stress as low as 483 MPa. However, as was previously discussed in Section 7.2.2, a slightly longer bar was used. This would then change the bar slippage stress from 483 MPa to approximately 556 MPa. This design approach would assume that the bars have an ultimate strength of 750 MPa. i o y * 556 MPa 0"row5 0*r0W4 | | ^ - .^^Orow3 0"r0w2 0"rowl ^afc Figure 7.5 - Stress distribution based on actual steel strength and bond failure CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 100 7.3.4 Anchorage Strength Considering Effects of Cyclic Loading The only difference between this design approach and the previous one is the inclusion of cyclic loading effects. Literature as well as strain gauge data from this test shows that bond degradation will occur with repeated loading. In fact, it is thought that the effects of cyclic loading severely reduced the strength of the connection. Figure 7.6 shows how the maximum stress in the bar is limited by de-bonding from the concrete. The value of 440 MPa was previously shown to be calculated using the maximum strain gauge reading. i G y « 440 MPa r ^row5 *^*^^>*Grow4 1 1 - ^ O r o w S a r o „2 a r o w l ^afc Figure 7.6 - Actual failure based on actual steel strength, bond failure and cyclic loading 7.4 CHANGES TO THE ANCHORAGE SYSTEM The actual failure mode observed in the second test was one of bar slippage. The best method of predicting this failure is the approach graphically illustrated by Figure 7.6. However, in order to design for a ductile failure mode, bar slippage must be precluded. CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 101 7.4.1 Continue to use Nelson D2L Anchors If Nelson D2L bars were to be used in future designs, one should specify substantially longer bars than those listed in the Nelson catalogue. This should alleviate concerns regarding bar pull-out due to bar overstrength as well as reversed cyclic loading. The additional length should be based on the results of additional studies performed with different lengths of bars, bar diameters and concrete strengths. Nevertheless, this research has shown that two multiplication factors should be applied to the Nelson catalogue values. First, the overstrength of the bars should be accounted for by changing the yield strength in the ACI code from 483 MPa to 750 MPa (the formulae have been changed to metric units for consistency): Licode = 0.36*db*fy/(rc)05 * (2-414/fy)= .36*16*750/(45)° 5 *(2-414/750)= 933 mm [ACI 12.2.3] Second, a factor to account for bond degradation under cyclic loading could be expressed as the achievable bar stress divided by the maximum observed bar stress. Recall from Section 7.2.2 that whenever the catalogue embedment length is used, the achievable bar stress was defined as 483 MPa: except that in this case a longer bar was used. The achievable bar stress was determined to be 556 MPa. It is conceivable that if the bar length used was the catalogue length, such that the achievable bar stress was 483 MPa, then the maximum observed bar stress would have been less than 440 MPa. Therefore, the factor might be the same as presented below: Lcyclic = 0"achievable/0"test result = 556/440 = 1.26 In the case of this test, the new development length could be expressed as: Lrevised = I^ code * LcyCiic = 933 mm * 1.26 = 1176 mm Because the revised development length is longer than the cap beam is deep, the only conceivable solution for the D2L bars would be to weld end plates on the end of the bars. One could also consider using hooked end bars. CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 102 7.4.2 Use Conventional Reinforcing Steel Possibly the most reliable connection which could be proposed is one which uses conventional reinforcing steel instead of the Nelson D2L bars. Conventional reinforcing steel has more substantial deformations than the D2L bars (recall Figure 7.1). This should aid in increasing the bond strength between the concrete and steel. Also, the material properties of conventional rebar (Grade 400) are more favourable for applications in moment connections. This is due to the more definite yield plateau and high level of ductility. The assumption of ten times the yield strain can be used for conventional rebar, whereas the D2L bars can only confidently reach 3.5 times the yield strain. Also, the bond characteristics for conventional rebar has been the subject of extensive research, and vast literature is available on it's applicability in seismic applications. The present MoTH assumptions are actually more valid for the conventional rebar, because they include high ductility and failure by bar fracture. Figure 7.7 shows the corresponding stress distribution. Caution should be exercised in order to ensure that the proper reinforcing steel is specified. A weldable grade must be used, otherwise manual welding of the bars could lead to poor quality welds. J a y = 400 MPa r ^row5 O~row4 ^ S ^ ^ > ^ | | a r o w 3 C»rowl \ S a f e Figure 7.7 - Stress distribution using conventional reinforcing steel CHAPTER 7 - DISCUSSION OF DEFORMED BAR SLIPPAGE 103 The use of the 400 MPa rebar rather than the 483 MPa D2L bars will not lead to a larger connection. The D2L bars were previously limited to smaller diameters, because the development length was short enough to fit in the depth of the cap beam. Now because the conventional rebar requires a shorter development length, a larger diameter can be used which will still have a length short enough to fit in the depth of the cap beam. Table 7.2 illustrates the development length concept by comparing a 15M-D2L bar and a 20M-Conventional Rebar. Development Length 15M-D2L in 45 MPa Concrete (Nelson Catalogue) 474 mm 15M-D2L in 45 MPa Concrete (Revisions Based On Test Results, Recall Section 7.5.1) 1176 mm 20M-Conventional Grade 400 Rebar in 30 MPa Concrete 450 mm Table 7.2 - Development length comparison for D2L bars and conventional rebar One additional advantage of using the conventional reinforcing steel is also indicated by Table 7.2. The present design using the D2L bars incorporates 45 MPa concrete in order to reduce the development length of the anchorage bars. High strength concrete reduces the development length, but it does not increase the moment resistance of the connection. Note the reduced strength of concrete for the conventional rebar. The development length for the rebar is the same for any concrete strength above 30 MPa. Therefore, if conventional rebar was considered as an alternative to the D2L bars, a lower strength concrete could be specified without sacrificing moment resistance. CHAPTER 8 - COMPUTERIZED DESIGN AID 104 8.0 COMPUTERIZED DESIGN AID Through the course of this research, numerous designs of various anchorage configurations have been made. A multitude of variables existed. Primary variables included the concrete beam size, pipe size and anchorage layout. Designing with all these considerations in mind can prove to be time consuming if one does not make an accurate initial guess: the process of arriving at an efficient design is an iterative process. A computerized approach would prove useful in speeding up the design of the connection. Furthermore, the findings of the finite element modelling and the research could be implemented into the computer program. This would allow for the most accurate predictions of the connection behaviour. Also, designs specifying the Nelson D2L bars or conventional reinforcing steel could be used. 8.1 PROGRAM BASICS A computer design aid called "ANCHOR" has been developed in a spreadsheet environment. The spreadsheet program, Lotus 123 Release 4 for Windows has been used as the host. The strength of the program lies in the ease of data manipulation for rapid changes to design. The program is not a "black box" where equations and the design process are unseen. Instead, ANCHOR has all of it's equations visible to the user, such that the theory is clearly interpreted. Finally, code references and helpful comments are included so that the basis of the equations is readily understood. Assuming the user has a basic understanding of spreadsheets, this chapter presents enough information to use the program. In addition, Appendices D, E, F, G and H present extensive calculations printed directly from ANCHOR. CHAPTER 8 - COMPUTERIZED DESIGN AID 105 8.1.1 Worksheets ANCHOR consists of one file which can be opened in Lotus for Windows. Within this file, there is a series of worksheets. Each worksheet relates to a specific element of the connection. For example, one sheet may contain information and calculations for the steel pipe, while the concrete beam design is on a separate worksheet. Figure 8.1 shows the spreadsheet and the series of worksheets involved in the program. The sheet the program is presently in is the main directory. This is indicated by the light gray background to the "MAIN" portfolio. All the other portfolios are in a dark grey background, and have an arrow pointing to them. The sheets which can be accessed by clicking them with the mouse button include: Mp[PIPE], Vr[BEAM], Mr [BEAM], Mr[ANCH], My [PL ATE], and SUMMARY. S " ~^ " ~~ " " lotur. 1-2-3 Release 4 - |ACONin.WM] ; ^ im File Edit View Style Tools Range Window Help MAIN sMffl$SM&fflimM £ B sci p nr n 4 + 4 4 3 ; Q a 4 i B | 7 U L N » l 4 m m __B Q J \ l r 3 | o | B N . i l i i ,X j New Sheet TO GET STARTED ON DESIGN MODIFICATIONS. SIMPLY CLICK ON ANY OF THE PORTFOLIOS LISTED ABOVE (IT IS RECOMMENDED THAT YOU START FROM THE LEFT) i .in _1L_-. 12.. mm Lisf: mm i / IB m 1 T Z ANCHOR mt Connection Design For The Modular Bridge Progrmn 24 mssf 34-WELCOME TO THE SPREADSHEET DESIGN TOOL WHICH ALLOWS FOR QUICK AND SIMPLE MODIFICATIONS TO THE DESIGN OF CONNECTIONS BETWEEN STEEL PIPE PEES AND PRECAST CONCRETE BEAMS USED IN THE MODULAR BRIDGE PROGRAM . t e ' i f e . J i JAsaL Figure 8.1 - MAIN directory in ANCHOR spreadsheet CHAPTER 8 - COMPUTERIZED DESIGN AID 106 8.1.2 Input and Output ANCHOR consists of a series of input values and subsequent calculations. A typical worksheet is presented in Figure 8.2. This specific worksheet deals with the calculation of the plastic moment capacity of the given cross section. mm Lotus 1-2-3 Release 4-[ACON1B.WK4] -"^f Eile Edit yiew Style Iools flange Window Help DAI IF D C "ft" MflBEAM D ' VJ| New'Sheet \ 1 5 S'lMOMENiT CAPACITYOF PIPE COLUMN WATERmt.'PRQPBFttlBS fy p h p p « p p « t t e n i > a i ^ < a ^ r t » i i » 1 p i a « ^ c a p a ^ i 5 e » l a n » : 6 p_• 'k p h c w e r = imlmlmum O M e w t e n g t h factoriitaf pp* y h i d rbenqth j» ! _ 310 ....„_. 1 23 ; ICROSS SECTIONAL BBOMETRY s| it p pt» thbknew 12.7 pbe outside diameter 4 0 6 i 'PLASTXi SECT.'Ofll MODULUS AND CHECH FOR COMPACT SECTION \ IT H'& igi-CH E CKINfi! p « T S j j j f e S | ^ T O N ? « :«:COM PAC TONE J<input< j_ ]<input< ^ j<input<_: <jnput< |mm !<input< mm"3 i<oab< <cab< .ilL§5L % \SFECIFi£.a MOMENT CAPACITY {PLASTIC) 24 If Kfa j^oe i= iphJpifs^lyflips'-Z/oim'le+Oi 25 1.; 26 I H H . t £09 AasEassJL.J. J»_1.'_'.I9.2S*J Figure 8.2 - Calculation sheet for plastic moment of pipe The user must input values for the parameters with "<input< " as the entry in column H. When this is encountered, the user should enter the appropriate value in column F. A description of the input parameter is given in column D, and it is symbolically represented in column B. The computer automatically updates the calculations when data is changed. These computed values are denoted by "<calc<" in column H. The formula by which the value in column F is calculated is given in column D, and column B contains the calculations symbolic title. CHAPTER 8 - COMPUTERIZED DESIGN AID 107 8.1.3 Checks In the spreadsheet, there are a series of checks to ensure that the design is adequate. For example, the computer checks to ensure that the steel pipe is a compact section. If the pipe is a compact section, the result will be an "OK" in the calculation box. If the section is not a compact one, then the calculation box will show a "NG", representing "not good". These checks are shaded for easy identification. This is shown by the previous Figure 8.2. The check being made is given in row 19, column D. The result of the check (OK or NG) is placed in column F. Note the reference to the code equation is given in column I. 8.1.4 Interactive Buttons One additional feature of ANCHOR is the use of interactive buttons. Clicking on these buttons with a mouse allows the user to perform simple tasks which otherwise could become tedious. Figure 8.3 shows two applications of the interactive button. The button near the top of the worksheet contains the text, "PRINT MR[BEAM] PAGE". If the user clicks on this button, the entire worksheet that is presently employed will be highlighted in preparation for printing. The button near the bottom of the screen say, "YOU MUST CLICK HERE ON THIS BUTTON TO SOLVE FOR THE NEUTRAL AXIS "C". Activating this button tells the computer to reach a solution for the moment resistance of the concrete beam. That is, the computer iterates until the tensile forces in the steel equals the compressive forces in the concrete and steel. If some data is altered, this button must be activated in order for the computer to arrive at a solution satisfying equilibrium. This button saves time because otherwise the user would need to rigorously enter neutral axis values until equilibrium was satisfied. CHAPTER 8 - COMPUTERIZED DESIGN AID 108 Lotus 1-2T3 Release A -|AC0N1B.WK4]i35Sr Eile Edit View Style Iools flange WJndow H,elp ^ I S E I ''ills Sheet iQuck Reference Tabteof CWM Mtc<lonalaiea» «w»1eclicl^<qDlna ba» 10 mm d B m e t e r tare _n_L. 3-9?-m.m-?.. l i s mm dameter tiara j= I 2(5 mm"2 2Q mm dimeter bare 300irnm*2 25 mm diameter bars B....11 j . i...j^?JJm.mJ^[T!^^f..^.re... 9 ,M : i mmjjismeter bars 10 S > 4^5 mm diameter bare 711'I i£ 13'" frYpMENT CAPACITY OF CONCRETE BEAM "14.. SCO mmA2 7COjmmA2 15COimm*2 2SCOimm'12 15 atfe?I§3/iltte35ESfiIfe§l.. .16. . alpha f j a j p t e f a r ^ ^ ^ ^ l n g i t u H n ^ « t i e n g i h ]7. Ej Young's modulus for re inf. steei ... : t i ; .... 0.85! F nSSSSSin>a~ 19 i { c r o s s $&TIOMAL GEOMETRY ....21 . «12 p j d a p t h fe m i d d l e bnafcidlnal w i n f o t o i n a h a w 22 ? f «t3 ( dep th to b o t t o m l o n g i t u d i n a l w r n f o j o i n g h a w 23 g>>«.. 24 » l A » t 2 25 26 m = I aojmin ; I li^insr^ = ( "~ 670jmm p ! t o t a l a > B » o f top l o n g i t u d i n a l h a w ! 4200 Im m 2^ '= tola1 a^cao7rrd~dk: brgtud :-ial ba r^ ^ 8COJmm*2 = tota a-ea of bottom bngrtud nal bore - _ 42uJJmm*2 • CL Ml 1STr LCH HERE CM TM* EHrCMTI SL'L 'C F^ThE tlEHTP.Hi <input< I <input<J_ <input< <tnpjirt< <jnput<_ <]nput<_ 'Automatic JAnal i 1 2 1 1 1 / 2 3 ^ 1 1 2 2 W J L T D ..lass*! Figure 8.3 - Print and iterate simplified by interactive buttons 8.1.5 Quick Reference Tables A quick reference table is shown in Figure 8.3. The table is immediately below the "PRINT MR[BEAM] PAGE" button. This table is simply included for conveniences. In this case, it gives the area of standard reinforcing steel. Another quick reference table is contained in the worksheet pertaining to the calculation of the moment resistance of the anchorage, Mr[ANCH]. The table gives area of conventional reinforcing steel, as well as areas of Nelson D2L bars presently used in design of the connection. CHAPTER 8 - COMPUTERIZED DESIGN AID 109 8.2 PROGRAM COMPONENTS Due to capacity design criteria, the plastic moment of the pipe is required to be the "weakest link" in the connection. Once the plastic moment capacity of the pile is known, the concrete beam and embedded plate anchorage can be designed. The beam and anchorage need to be stronger than the pipe by the user prescribed overstrength factor, $0. To divide these calculations into "bit size" tasks, the spreadsheet has been compartmentalized. That is, there are several worksheets within the file of ANCHOR. wk4. The options are shown in Figure 8.4, as they are shown on the actual spreadsheet. Z j 4 ; 5 \ _ £ _ J L _ J TO GET STARTED OM DESIGN MODIFICATIONS, SIMPLY CLICK OM AMY OF THE PORTFOLIOS LISTED ABOVE (IT IS EECOMMEMDED THAT YOU START FROM THE LEFT) Figure 8.4 - Various worksheets available in ANCHOR 8.2.1 Steel Pipe, Mp[PD?E] The worksheet pertaining to the steel pipe leads to the calculation of it's plastic moment capacity. The input parameters include the specified yield stress, overstrength factor, pipe diameter and wall thickness. For these values, the computer calculates the plastic moment capacity of the pipe. CHAPTER 8 - COMPUTERIZED DESIGN AID 110 8.2.2 Concrete Beam, V r [ B E A M ] , M r [ B E A M ] The concrete beam has two relevant calculations. First, the shear resistance of the beam has it's own worksheet. Here, depth and width of the beam are specified in addition to stirrup size and spacing. Second, the moment resistance of the concrete beam is computed on a separate worksheet. This sheet contains information about the longitudinal reinforcing steel. Furthermore, it uses information entered in shear resistance worksheet. For this reason, re-entering data in the shear resistance sheet requires that the user return to the moment resistance sheet. The user must re-click the iteration button for solving the neutral axis if information above it is changed. 8.2.3 Embedded Plate Anchorage, M r [ A N C H ] This worksheet computes the moment resistance of the embedded plate anchorage layout. The user specifies the location of the rows widthwise and lengthwise. The user also dictates whether the steel bars are the Nelson D2L bars, or conventional reinforcing steel. Once the necessary information is given, the computer readily generates the layout of the anchors, such that any accidental errors in the input can be observed (Figure 8.5). CHAPTER 8 - COMPUTERIZED DESIGN AID 111 Lotus 1-2-3 Release 4 : |AC0N1D.WM] File Edit yiew Style Iools fiange Window Help - - • J - J — EA40 j^S) i If B TT 4 -.j^i.Now Sheet 44 S: 48 . « >. 50.4 51 ? 52 53 i 54 * 55 I 56 i 57-4 58 1 59 * bO . bl f j .62 t i 63 t 64 _ 65 p e m EMBEDDED PLATE LAYOUT soo I 100 600 g. fi. 500 x I *M UJ § 3O0 200 100 Ol • * * I I , , 0 100 200 PLATE LENGTH [IT, 300 *oo 500 eoo TOO It] (measured along the beam'? kngth] a jAnal I 12j11/23/^11 29AWJ irxnj 3 • if Figure 8.5 - Embedded plate layout generated by computer 8.2.4 Plate Y ie ld ing A t Pipe Edge, M y [ P L A T E ] The program also attempts to calculate whether plate yielding at the pipe edge will occur. There are many assumptions surrounding this calculation, and they are stated within the computer program itself. Two different approaches are used, and both have their merits. 8.2.5 Summary Sheet, S U M M A R Y The summary sheet is the final sheet in the program. It has been selected as a means of highlighting the most important design features. It also serves as a good comparison between the moment resistance of the steel pipe, concrete beam and anchorage. If the factor of safety in the summary sheet does not exceed the overstrength factor, the connection needs to be redesigned. CHAPTER 9 - ALTERNATIVE CONNECTIONS 112 9.0 ALTERNATIVE CONNECTIONS The most disturbing characteristic of the present connection is the slippage of the deformed bar anchors. Confidence in the overhead weld between the pipe and the embedded plate remains a concern. This chapter suggests alternative concepts which may be considered to address these issues. Some ideas may be considered simple, and may not need further testing to verify their appropriateness. Other concepts could at first seem disputable, but with future testing they could prove to be the most effective solution. Some of the proposals will be discussed only briefly as they have already been explored in some detail earlier in the report. 9.1 CHANGES TO THE STEEL PIPE AND OVERHEAD WELD The failure of the connection must consistently occur in the pipe. The Northridge earthquake presented numerous examples of weld failures in buildings which were though to be adequately designed. The modular bridge program involves a crucial full strength weld. It would be desireable to maintain a high degree of confidence in the weld. Two approaches could be used. First, increase the cross sectional area of the weld. Second, decrease the cross sectional area of the pipe. Although these approaches reach the same goal, it will be shown that they can be achieved in different ways. CHAPTER 9 - ALTERNATIVE CONNECTIONS 113 9.1.1 Steel Pipe Collar The addition of the steel pipe collar to the pile is presently used by MoTH in the design and construction of the modular bridges. It has been included in this section for completeness, as well as to show how different design philosophies aim to yield the same result. Figure 9.1 shows how the pipe collar would be implemented. It's main purpose is to increase the cross sectional area of the weld, thus decreasing the stress in the weld at the point of plastic hinging in the pile: it is used strictly to reduce the likelihood of weld failure. The addition of the pipe collar lowers the plastic hinge location, and therefore could increase the moment demand on the anchorage. The main benefit of the connection is the simplicity of the concept. In addition, the bridge inspectors have commented on the apparent ease of installation. Also, because of the simplicity of the concept, it could be readily adopted without testing. One of it's setbacks is the fact that it more than doubles the amount of overhead welding necessary to complete the connection. Also, it does not address concerns regarding the embedded plate anchorage problems. EMBEDDED P L A T E AND CONCRETE BEAM ABEiVE \ AND C O L L A R / CP FDR P I L E 300 P I L E H A L F S E C T I O N TO FIT P I L E P R O F I L E PIPE P I L E E L E V A T I O N Figure 9.1 - Pipe collar concept CHAPTER 9 - ALTERNATIVE CONNECTIONS 114 9.1.2 Stiffeners Added to Connect ion Using steel plate stiffeners in the connection could serve two purposes. First, it would increase the cross sectional area of the weld. This would reduce the likelihood of weld failure. Second, it could allow for the use of a thinner embedded plate. This is because of the ability of the stiffener plates to stiffen the embedded plate, thus uniformly distributing the strains to the anchors. Figure 9.2 shows how the connection with stiffeners might look. The possible questions surrounding the connection are numerous. The stress concentrations introduced by stiffener plates would require analysis, possibly in addition to some physical testing. Also, installing the stiffeners in the overhead position could be tedious, especially of the geometry of the bridge introduces non-square angles between the pipe and plate. Once again, this approach does not address the concerns of the embedded plate anchorage. ELEVATION Figure 9.2 - Stiffener plate concept CHAPTER 9 - ALTERNATIVE CONNECTIONS 115 9.1.3 Holes Put into Pipe The most unique solution would be to place holes in the plastic hinge region of the pipe. The result of this strange operation would be to reduce the plastic hinge capacity of the pipe, but the effects would be far reaching. First, the area of the overhead would remain unchanged, but the area of the pipe would be decreased. This would reduce the stress in the weld, decreasing the likelihood of weld failure. Second, the reduced plastic moment capacity would limit the demands on the embedded plate anchorage. Therefore, the present Nelson D2L bars could still be used because the stresses in the connection would be substantially reduced. This could also lead to a thinner embedded plate. This is the only solution pipe modification which will also alleviate concerns with regards to the anchorage system. The main problem with this connection is the fact that it is unproven: stability of the irregular section is questionable. The holes should not lead to additional problems with corrosion, because the presently used pipe collar installation process also leads to holes being placed in the pipes (Recall Figure 2.7). BEAM WIDTH CRClSS SECTION Figure 9.3 - Holes in pipe concept CHAPTER 9 - ALTERNATIVE CONNECTIONS 116 9.2 CHANGES TO THE ANCHORAGE It has been shown throughout this report that deformed bar slippage led to unsatisfactory behaviour of the anchorage system. Unless the moment capacity of the pile is reduced, this issue should be addressed. This chapter reiterates solutions which were discussed earlier in this report. They have been included in this section for completeness, and they will be briefly revisited. 9.2.1 Longer Nelson D2L Deformed Bars Data from the two tests has questioned the validity of the embedment lengths presented in the Nelson catalogue for seismic applications. It is possible that in order to remain using the D2L bars, a much longer embedment length is required. Chapter 7 and section 7.4.1 in particular have dealt with this topic in great detail. 9.2.2 End Plates The addition of end bearing plates on the ends of the D2L bars is one possible solution. The weld to the end plate, and the end plate itself must be properly designed. The end plate must not pull out of the concrete, and must be strong enough to resist the force necessary to yield the bar. End plates could also be welded to smooth, hot-rolled bars. However, this would then involve the additional hand welding between the bar and the embedded plate. 9.2.3 Hooked Ends The D2L bars could also have hooked ends. This would aid in reducing the development length of the bars. Rather than using D2L bars, it may be more advisable to use hooked-end smooth hot-rolled bars, or even conventional reinforcing steel. CHAPTER 9 - ALTERNATIVE CONNECTIONS 117 9.2.3 Conventional Rebar Chapter 7, section 7.4.2, dealt specifically with the use of conventional reinforcing steel. The main benefits are predictable ductility and shorter development lengths. Also, there is an immense amount of literature on the bond between concrete and conventional reinforcing steel. The D2L bars have very little literature on bond characteristics, and confidence has not been increased by the findings of this research. Figure 9.4 is a decision tree indicating the various options which have been presented. Overhead welding reliability was an initial concern stated by MoTH. Although no sign of weld distress was observed, investigations of buildings following earthquakes have noted significant damage to welded connections. For this reason, it is still recommended that one of the techniques be included for increasing weld confidence. As this research has shown, there is reason for questioning the reliability of the current anchorage design. If holes are not placed in the pipe to reduce the plastic moment capacity, it is expected that changes should be made to the anchorage. These changes should encourage a more ductile and strong anchorage by avoiding bond failures. OVERHEAD WELD CONFIDENCE t HOLES IN PIPE PIPE COLLAR STIFFENER PLATES 1 CHANGES TO ANCHORAGE LONGER D2L BARS t END PLATES OR HOOKS (D2L, SMOOTH, OR CONVENTIONAL) CONVENTIONAL REBAR Figure 9.4 - Decision tree for possible changes to the connection CHAPTER 11 - SUMMARY 118 10.0 SUMMARY This chapter summarizes the findings of the research and makes recommendations for future designs. This research has investigated the behaviour of two full scale pile segments, and has made reasonable arguments as to why the connections behaved as they did. This paper has shown that the failure mode of the connection will ultimately determine the strength and ductility of the bridge. 10.1 CONCLUSIONS Two full scale, steel pile to concrete beam segments were tested under reversed cyclic loading. The pipe and beam were connected by a complete penetration weld between the pipe and an embedded plate which was cast in the beam. The embedded plate had anchorage bars welded to it. For both specimens, the desired failure mode was one of plastic hinging in the pile. Specimen #1 failed by plastic hinging in the pile. This was expected because the moment capacity of the pipe was much less than the predicted moment resistance of the anchorage. There were no signs of failure in the weld region. However, the test did show initial signs that the deformed bar anchors on the plate could be slipping. The connection exhibited both the desired strength and ductility (nA = 8:3). The results agreed closely with the two dimensional, non-linear theoretical model. The finite element model of the connection verified the need for a thick embedded plate to distribute strains to the plate anchorage. CHAPTER 11 - SUMMARY 119 Specimen #2 experienced embedded plate anchorage failure. This connection did not experience the desired strength due to the unexpected de-bonding of the anchorage bars. This deformed bar slippage also led to poor ductility (m = 2.2) and energy dissipation characteristics in the connection. Removal of the concrete from the specimen showed that of the 30 anchorage bars, 20 slipped, one weld was defective, and only nine failed in the desired bar fracture. The multitude of bars slipping can be attributed to the higher-than-anticipated yield strength of the bars, and the effects of reverse cyclic loading. The theory behind the embedment length in the Nelson catalogue is the length necessary to achieve a bar stress of 483 MPa under monotonic loads, and not the actual bar strength which is much larger. The piles and anchorage bars appear to be manufactured with no ceiling on their strength. Although they possess minimum strengths, there is apparently the philosophy that, "stronger is better". However, this is in conflict with the seismic design philosophy of ductility and capacity design. Excessive steel strengths in this research project have led to a violation of capacity design criteria. These material overstrengths have led to failures in regions of the connection where failure should not occur. The embedment lengths as stated in the Nelson catalogue should be questioned: their suitability particularly in cyclic loading applications is uncertain. The computerized design aid allows for rapid changes to the connection without consuming large amounts of time. Alternative connection details could prove to be an effective means of addressing the anchorage concerns. CHAPTER 11 - SUMMARY 120 10.2 RECOMMENDATIONS The following recommendations may help to improve the behaviour and reliability of the connection under seismic loading scenarios. • Increasing the pile overstrength factor should be considered in order to adhere to the principles of capacity design. • Consider changing the present pile specification from A252 Grade 2 (ay = 241 MPa) to A252 Grade 3 (rjt = 310 MPa). This should help avoid consistently being supplied the Grade 3 when Grade 2 is specified. Pipe manufacturers rarely supply pile grades lower than 310 MPa. • The pipe collar or equivalent detail should be used to maintain a high degree of confidence in the overhead weld. • If a moment connection design is attempted with the D2L anchor bars, the catalogue embedment lengths should be questioned. • The poor behaviour of the D2L anchorage bars necessitates corrective actions. A weldable conventional reinforcing steel or smooth bars with hooked ends or end plates may address this • A reasonably short (lengthwise) and thick embedded plate should be used to ensure that it does not yield at the pipe edge. A thicker plate also aids in distributing strains to the anchors. If an effective seismic design is to be developed, strength and ductility are basic concepts which need to be embraced. The failure mode is what often dictates the amount of strength and level of ductility in a given structure. In the case of this research, it has been shown that plastic hinging is an excellent way of attaining strength and high levels of ductility. However, this research has also exposed the fact that the slippage of the anchorage bars has led to a violation of fundamental seismic design principles. REFERENCES 121 R E F E R E N C E S Boyd (ed), "Brittle Fracture in Steel Structures", 1970 Cannon, "Flexible Baseplates: Effect of Plate Flexibility and Preload on Anchor Loading and Capacity", ACI Structural Journal, May-June 1992 Clark, "Bond of Concrete Reinforcing Bars", ACI Journal, November 1949 Clark, "Comparative Bond Efficiency of Deformed Concrete Reinforcing Bars", ACI Journal, December 1946 Collier, "Bond Characteristics of Commercial and Prepared Reinforcing Bars", ACI Journal, June 1947 Cook & Klingner, "Ductile Multiple-Anchor Steel-to-Concrete Connections", ASCE Structural Journal, June 1992 Eligehausen & Popov, "Behavior of Deformed Bars Anchored at Interior Joints Under Seismic Excitations", 4th Canadian Conference on Earthquake Engineering Fishburn, "Strength and Slip Under Load of Bent-Bar Anchorages and Straight Embedments in Haydite Concrete", ACI Journal, December 1947 Hawkins & Mitchell, "Seismic Response of Composite Shear Connectors", ASCE Structural Journal, September 1984 Ismail & Jirsa, "Bond Deterioration in Reinforced Concrete Subject to Low Cycle Loads", ACI Journal, June 1972 Johnston, "Guide to Stability Design Criteria for Metal Structures", 1976 Mains, "Measurement of the Distribution of Tensile and Bond Stresses Along Reinforcing Bars", ACI Journal, November 1951 Masubuchi, "Analysis of Welded Structures", 1980 Rehm & Eligehausen, "Bond of Ribbed Bars Under High Cycle Repeated Loads", ACI Journal, February 1979 Salmon & Johnson, "Steel Structures - Design & Behavior", 1971 Sherman, "Tests of Circular Steel Tubes in Bending", ASCE Structural Journal, November 1976 REFERENCES 122 Stanton, Anderson, Dolan & McCleary, "Moment Resistant Connections and Simple Connections" PCI Specially Funded Research & Development Program - Research Project No. 1/4, PCI, 1986 Stojadinovic & Thewalt, "Upgrading Bridge Outrigger Knee Joint Systems", EERC, June 1995 Vintzeleou & Tassios, "Behaviour of Dowels Under Cyclic Deformation", ACI Structural Journal, January 1987 Watstein, "Distribution of Bond Stress in Concrete Pull-Out Specimens", ACI Journal, May 1947 "Design of Highway Bridges", CAN/CSA-S6-88, 1990 "Seismic Design and Retrofit Manual for Highway Bridges", U.S. Department of Transportation, 1987 APPENDIX A - MATERIAL PROPERTIES 123 CONCRETE CYLINDERS POURING DATE: July 21, 1994 Slump = 95 mm Air Content = 5.2 % 3 Cylinders, 6"diameterx 12" long CRUSH TESTING DATE: August 25, 1994 COMPRESSIVE STRENGTHS Cylinder #1. Pult = 187 kip (ft' = 45 MPa) Cylinder #2. Pult = 220 kip (fc' = 54 MPa) Cylinder #3. Pult = 205 kip (ft'= 50 MPa) 52l) 78.14 I ANKIIS 1 Ff 0 m 3 1 3 i s > 51) ro ro oo co SHIX^HdO^d TVrHHlVN - V XION3ddV SHIItfHdCXHd TVmHlVW - V XIONSddV 931 sairandcrad TvraHivw - v xidNHddv APPENDIX B - WELDERS f ICKETS AND PROCEDURE SHEET 127 FIRM CERTIFIED TO CSA W47J 1 WELDER'S 1 EST RECORD JRAPPORT DE QUALiriCAtlON DE SOUDEUR 8 4 5 9 0 sm. iv 4 7 1 HOMME ' • J -SOC1AIIHS.NO 71R 7 f , 4 277 | N-PAS9 SOCIAtE / J " ° . / U H ^ ' ' I I S ^ n & u n HERMAN S T E U N E N B E R G • CLASSIFICATION CLASSriCAllON OnOAHZAllON OnOANISAtlON S O L I D ROCK S T E E 1 1 F A B R I C A T I N G rSSUKOAlE DATE DEMISSION T R A N S F E R A B L E 0 4 A 9 / P . ETHIAIIOMPAIE M l /) A / i r . / / • ' • • ' DAIEOEXnilAllOH " ' /J3 MO. DAY/JT1 vn /AH. MO DAY/JTT Yfl./AN. CATOHOr TO BE nEPniHIEO WITHOUT WTIIMEHAUtlrOHlZAIIOH S & S S X E F L A T / U O R L Z / V E R T / O V E R RgggSMAW E i E c i n o o E / r u E n METAL anour pA EiectnooE /onourDEMEiALOAtTonr 1 IIHCKHES3 I / n EfwssEim A ' " PROCEDURE HO HO DE MIOCEDUME INCH & N / A OVER • CWB SIGNATURE siaHArunE OE cwn *-**wt>CTi5 SIOWA'J SIOHATIjnE D/ 1 2 7 3 5 5 CANADIAN WELDING BUREAU BUREAU CANADIEN DE SOUDAGE 719 1.43 273 NORME W47 .1 SOCIAL INS. NO. N* D'ASS. SOCIALE N?MS!ETNIEUR BERT ST E UN EN BERG TYPE/LEVEL ,YP1— COMPANY T R A N S F E R A B L E CLASSIFICATION _ CLASSIFICATION O ORGANIZATION ORGANISATION S O L I D ISSUE DATE DATE DEMISSION ROCK S T E E L F A B R I C A T I N G 0 5 / 3 1 / 9 5 S S S O N 0 5 / 1 9 / 9 7 MO DAY/JR YR/AN. MO DAY/JR YR./AN. CARD NOT TO BE REPRINTED WITHOUT WRITTEN AUTHORIZATION CETTE CARTE NE PEUT ETRE REPRODUITE SANS UN6 AUTORISATION ECRITE WELDER IDENTIFICATION CARD CARTE D'IDENTITE DE SOUDEUR 1 2 7 3 5 5 V A L I D ONLY WHEN EMPLOYED BY A COMPANY C E R T I F I E D T o CSA W47.1 i t ^ B e F L A T / H O R I Z / VERT /OVER rSIi SMAW ELECTRODE/FILLER METAL GROUP j? A ELECTRODE/GROUPE DE METAL DAPPORTL 4 1 / 8 - I N C H & OVER PROCEOURE NO NO. DE PROCEDURE s s s i N / A M / A  I* / rt / CWB SIGNATURE ! 1 7 H C f o f f l S J l ^ T U R E SIGNATURE DU CWB SIGNATURE DU DETENTEUR APPENDIX B - WELDERS TICKETS AND PROCEDURE SHEET 128 <./»!«» .1 ' I . . • • • (Ulvlt loi i of I I I " Canadian Standard ! A t . . » c l a l l u n l 254 Morton St. Toronto, Out. M4S 1A9 Nu. ~ L'J Ha r . 1/ 6'* con^.°ny S o l i d Rock Stee l Fabricat ing Co. . L t d . . M « £ ' 17780 Daley Road. Surrey. B . C . . V3T C H E C K TYPE OF • Manual (SMAWI • Submaroad Arc (SAW) WELDINGPROCESS • Flux Cora (FCAWI • Solid W i n 1GMAWI — CSA UW.'il - 3 B W / W T , UW/WT, Dailgnationi 50W/WT, ASTM A36, A53-B, AUtl , A500-A/B Wldg.Procadura SptclllcitlonNo. WPS - III ~ BA Applicable Standard!^ W /*7 . 1 fc W 5Q Welding CIBCUUCW \ t»n» i *— K^-^ v«_-- . Poiiiion Overhead ci.iiiiication g _ 7 Q i 8 ( b a 3 i c Elactroda (Wlra) E PFIEHE AT MINIMUM at par CSA W59 pa?Mura {Show Wilding Symbol with Oif Shut No. in Hill T SKETCH OF TYPICAL JOINT PREPARATION (Indict, limit, Q< Tol;>nc.z! TYPICAL PASS ANO ^ Y E F t S E O U E N C E C O M P L E T E JOINT PENETRATION G R O O V E D Back gougad to lound matal • Waldad onto trial backing D Waldad from oni tlda without backing • Waldad both tldat without back gouging D Waldad onto othar than tta*l backing G R O O V E W E L D P A R T I A L JOINT PENETRATION • Minimum at par CSA WB9 • Othtrl [tpaclfyl F I L L E T W E L D • Minimum at par CSA WB» JOINT TYPE at per CSA W69 • BUTT • T E E • C O R N E R • LAP • EDGE BUTT or FILLET Slia 1/4 5/16 3/8 1/2 IJL Slda No. .1,2,&3 Layar Numb* 3.4. P l « Numbar 1=1. 1-6 Elactrod* SUa Currant Polarity JAC/DCJ Re-vPrj HA. - l£L ExpUnnlon UpMahPri l - " W T O - 1 Q 7 7 • l l p r l a t P d r,P W T O - l Q n ? 17 13Q 130 1.3 Q 130 Automittt tr StmlAutemttk Electrical Stlckout Shielding an: l/hr. Wirt F*«d Speed VoKl Are Triral Sp«*d CWB Approval YfeWi* ProceAire Data 84 07 06 "•I- 'DMtion T Complnhi: Show $lgnmtuf* UBWetnf Suptnr APPENDIX C - NELSON SYSTEM PRODUCT AND EMBEDMENT CATALOGUE 129 l l ,o Nelson Sys tem ii WylP^I. <UU i U KM^Ufa ll liSM |C Clcl 1«J D2L • Deformed bar anchors Stock sizes Length D Stud Dli . I Length Pert No. 14" 021 12H" 101 064-835 H"02L 10H" 1014)64 536 V '021 W 101-064 537 H"02l I8S4" 101 064-539 H"02L 24H" 101 064 541 H"02L 12H" 101-064-762 D2L 18H" 101 064-765 IT 021 24*" 101-064-796 V 0 2 1 •24y,i" 101 064-923 H"D2L 30V.." 101-064-957 'A" 021 18 V.." 101 066 222 V," 021 24V.«" 101 066-170 V." 021 30Vu" 101-066-171 V," 02L 36Vi«" 101 066 172 • Physical properties of D2L anchors DUmtttr *» Nomlatl Ar«t ASTM D.ilgmtlon Aj ff Yield {• Lbi.(mln.) A i tj Temlw UMmht.) % H K H 005 011 0.19 ' 0.29 0-5 0-11 0-19 0-29 041 3.500 7.700 13.300 20.300 29.000 4.000 8.800 15.200 23.200 33.200 ~(t fum1 ' l W«IIU ttranglh llnesile) 80.000 p$i min. £S"2 MP*. fy r«hf tttvngtft 70.000 psi min. - y*?3 fllfc At ATM of ttud thank . U " Slud embedment length after weld CoM finished km ceibon steel pet ASTM A-108 C - 0 23mn. Mn-0.90m«. P - 0.040 m«. S-0.050 mai. Short form specification To Insure that certified Nelson products are used, the following specification Is suggested: "Concrete anchors shall be Nelson, flux filled deformed bar anchors, ,4ypeD2L, welded to plates as^fjownbii the drawings. iplStySfshall be made from ASTM A-108 cold worked, -deformed wire per ASTM A-496 and shall be welded per the manufacturers recommendation. io ' • Embedment properties of D2L anchors D 2 L tensile capacity in concrete — Pull out strength * 6 8 IO 12 14 EMBEDMENT (INCHES) •0 I J 14 EMBEDMENT (INCHESI 30 24 EMBEDMENT (INCHES) A P P E N D I X C - N E L S O N S Y S T E M PRODUCT A N D E M B E D M E N T C A T A L O G U E 130 Product and embedment data 12 t6 20 24 79 32 EMBEDMENT (INCHES) 80 KSI 12 16 20 24 . 26 32 36 40 Embedment (Inches) Not«: Embedment lengths are calculated from ACI Standard ACI-318, Section 12. including muMiptte* fo* bar* with yield strength in excess ol 60,000 psi. ACI minimum embedment length requirement is 12 Inches. The user may elect to use that portion of the graphs below 12" to estimate the embedment /tensile toed relationship where 12* minimum embedment is not possible. For Nght weight concrete use refer to ACI 318. Section 12.2.3. Use: The heavy horizontal black line indicates yield strength of the bar size used. For example, a 1/4 x 11" bar, after weld, will develop a minimum of 3,500 pounds in tensile when em-bedded in 3,000 psi normal weight concrete This is equivalent to the yield strength of the stud, at which point an irreversible deformation is beginning to occur. Nelson D2L anchors are also available on special order bent to the following shapes. DOUBLE BEND SINGLE BEND JHOOK 0 a Bend PjmeUt A5TU A-496 Menemjm bend test (fanctrs for hind or machint bent felormed wki material y f two Ornw stud d U m a * lor * • and under and to rkw Xui to ttormv. Minimum embedment length for D2L anchors in shear normal wt. concrete* 021 Diameter 3000 pil 4000 ptl 5000 ptl 6000 ptl "3 5 in. 3.0h. 3.0 in. 3.0 h. X 5.0 4.5 4.0 40 y, 7.0 6.0 55 50 X . 8.5 7.5 6.5 60 'A 10.5 9.0 7.5 7.5 'For Send lightweight Concrete muttipfy bf 1-18. AJ Lightweight Concrete multiply by 1.33. "After weld length. D2L shear capacity in concrete Deformed bar anchors embedded in concrete have shear capacities which may be conservatively calculated accor-ding to the formula used for headed anchors. An upper bound to shear capacity of 0.9 AsFs occurs as concrete strength exceeds 5,000 psi. Following are embedment length requirements and shear capacities for normal weight concrete. Appropriate spacing with regard to free edges and adequate distance between anchors should be maintained to reach full capacity. Good engineering practice dictates that safety factors appropriate to the connection usage should always be used. Shear capacity normal wt. concrete* D2L Dlatnetar 3000 p,l 4000 ptl 6000 ptl 6000 ptl 2.25 kips 2.85 bps 3.50 3.60 tipi X 4.80 6.25 7.60 7.92 Yi 8.50 10.80 13.20 13.68 X 13.00 16.50 20.10 20.88 Vt 18.69 21.70 24.38 26.80 "Reduction CoafHcienU for UM with concrete made with C-330 Aggregeft* Specified Connate Contpr estiva Stteagt* Ak Dry Unit W t of Concrete 90 95 100 108 110 115 120 <4.0 .73 .76 .78 .81 .83 .68 .88 5S0 .82 .85 .87 .91 .93 .96 .99 I APPENDIX D - CALCULATIONS FOR SPECIMEN #1 MOMENT CAPACITY OF PIPE PILE MATERIAL PROPERTIES fypipe = specified yield strength of pipe phipipe = performance factor of steel pipe (for capacity design =1) phiover = mimimum overstrength factor for pipe yield strength BASED ON MILL CERTIFICATE WITH Fyield = 410 MPa CROSS SECTIONAL GEOMETRY t = pipe thickness dia = pipe outside diameter 12.7 mm 324 mm <input< <input< <input< <input< <input< PLASTIC SECTION MODULUS AND CHECK FOR COMPACT SECTION Zform = diaA3/6*(l-(l-2*t/dia)A3) = 1231410 mmA3 <calc< = @il{dia/t>18000/fypipc,"NG","OK") = OK <calc< [7 THIS IS CHECKING THAT THE SECTION IS A COMPACT ONE THAT CAN DEVELOP THE FULL PLASTIC MOMENT SPECIFIED MOMENT CAPACITY (PLASTIC) • \Mppipe = phipipe*fypipe*Zform>le+06 = 382 kN*m <calc< \ NOTE: ALL REFERENCES ARETO CAN/CSA-S6-88 APPENDIX D - CALCULATIONS FOR SPECIMEN #1 132 ^HEAR CAPACITY OF CONCRETE BEAM MATERIAL PROPERTIES lambda = factor for light/normal weight concrete fyr = yield strength of reinforcing steel phibr = overall bridge performance factor fc' = compressive strength of concrete CROSS SECTIONAL GEOMETRY b = width of concrete beam h = total beam depth cover = minimum concrete cover to face of stirrups long = longitudinal bar diameter for main top & b< stirr = stirrup diameter Abst = Area of ONE LEG of steel stirrups s = spacing of steel stirrups ] 1.0 <input< 400.0 MPa <input< 0.85 <input< 45.0 MPa <input< 750.0 mm <input< 800.0 mm <input< 50.0 mm <input< bars = 30.0 mm <input< 15.0 mm <input< 200.0 mm <input< 225.0 mm <input< DEPTH TO BOTTOM LONGITUDINM STEEL d = h-covcr-stirr-long/2 = 720 mm <calc< CHECK MINIMUM REINFORCEMENT REQUIREMENTS Avmin = .35*b*s/fyr = 148 mmA2 <calc< [8.2.7.1.2] = @ilT2*Abst<Avmin,"NG","0K") = OK <calc< CALCULATION OF Vc(CONCRETE) & Vs(STEEL) CONTRIBUTIONS vb = (.07+10*Ast3/(b*d))»lambda*fc'A5 = 0.99 <calc< [8.6.6.2.1] vblow = ,08*lambda*fc'A.5 = 0.54 <calc< = @ifi>blow>vb,"NG","OK") = OK <calc< vbhigh = .19*lambda*fc'A.5 = 1.27 <calc< = @ifi;vbhigh<vb,"NG","OK") = OK <calc< Vc = vb*b*d/1000 = 535 kN <calc< [8.6.6.1.1] Vsl = 2*Abst*fyr*d/s/1000 = 512 kN <calc< [8.6.6.3.1] chkl = .33*b*d*lambda*fc'A.5/1000 = 1195 kN <calc< [8.6.6.3.4] smax = @if(Vsl>chkl,.25*d,.5*d) = 360 mm <calc< [8.6.6.3.4] = @if(smax<s,"NG","OK") = OK <calc< THIS KS CHECKING THAT MINIMUM STIRRUP SPACING IS NOT EXCEEDED Vs2 = .66*b*d*lambda*fc"\5/1000 = 2391 kN <calc< Vs = @min(Vsl,Vs2) = 512 kN <calc< [8.6.6.3.5] Vrl = Vc+Vs = 1047 kN <calc< [8.6.6.3.5] Vr2 = ,2*b*d*fc'/1000 4860 kN <calc< Vr = pliibr*@mm(Vrl,Vr2) = 890 kN <calc< [8.6.6.1.1] A P P E N D I X D - C A L C U L A T I O N S FOR SPECIMEN #1 133 [MOMENT CAPACITY OF CONCRETE BEAM MATERIAL PROPERTIES alpha = alpha factor for bending at ultimate strength Er = Young's modulus for reinf. steel CROSS SECTIONAL GEOMETRY stl = depth to top longitudinal reinforcing bars st2 = depth to middle longitudinal reinforcing bars st3 = depth to bottom longitudinal reinforcing bars Astl = total area of top longitudinal bars Ast2 = total area of middle longitudinal bars Ast3 = total area of bottom longitudinal bars ITERATION OF GUESSES FOR NEUTRAL AXIS c = LOCATION OF THE NEUTRAL AXIS (BY ITERATION) = 86.5 mm SOLVED BY COMPUTER CALCULATE BETA FACTOR AND MINIMUM REINFORCEMENT REQUIREMENTS beta = @if(fc'>55,.65,.85-(fc,-30)*.008) = 0.73 Asmin = 1.4*b*d/fyr = 1890 mmA2 = @if(Asmin>(Astl+Ast2+Ast3),"NG","OK") t = OK <calc< <calc< <calc< [8.6.2.1] [8.2.4.1] STRAINS IN BARS [ASSUMING A LINEAR DISTRIBUTION, PLANE SECTIONS REMAIN PLANE] estl = .003*(stl-c)/c = -0.0002 est2 = .003*(st2-c)/c = 0.01088 est3 = .003*(st3-c)/c = 0.02198 <calc< <calc< <calc< STRESES IN BARS fstl = @if(@abs(estl*Er)<r>T,estl*Er,@ifl;estl*Er<0,-fyr,fyr)) fst2 = @ilt@abs(est2*Er)<fyr,est2*Er,@if(est2*Er<0,-fyr,fyr)) fst3 = @ifi;@abs(est3*Er)<fyr>est3*Er,@if[est3*Er<0,-fyr,f>'r)) = @iltfst3<fyr,"NG","OK") WE WANT AN UNDER REINFORCED BEAM. THEREFORE, WE WANT THE BOTTOM REINFORCING STEEL TO YIELD, RATHER THAN HAVE CONCRETE CRUSHING AS TI IE FAILURE MODE -45 MPa 400 MPa 400 MPa = OK <calc< <calc< <calc< <calc< FORCES IN STEEL Tstl = fstl*Astl/1000 Tst2 = fst2*Ast2/1000 Tst3 = fst3*Ast3/1000 -189 kN 320 kN 1680 kN <calc< <calc< <calc< TOTAL FORCE IN STEEL AND CONCRETE (SHOULD BE EQUAL) Fsteel = Tstl+Tst2+Tst3 CConc = -alpha*fc'*beta*c*b/1000 DIFF = Fsteel+CConc = @IF(@ABS(DIFF)<l,"OK","NG") MUST ENSURE THAT Ceonc & Fsteel ABOVE ARE EQUAL IN ORDER TO ENSURE EQUILIBRIUM 1811 kN -1811 kN 0 kN = OK <calc< <calc< <calc< <calc< Mir = Cconc*(beta*c/2) M2r = Tstl*stl+Tst2*st2+Tst3*st3 -57170 = 1322489 <calc< <calc< MOMENT RESISTANCE OF BEAM \klrbeam = phibr*(Mlr+M2r)/1000 = IQ76 kN*m <cak< [theory] \ MOMENT RESISTANCE ACCORDING TO CODE Mrcode = phibr*(Ast3*fyr*(st3-beta*c/2))/le+06 = 983 kN*m <calc< [8.6.3.4.2] (this ignores the effects of middle and top reinforcing steel) <calc< (valid for values of Astl approx. = Ast3) 0.85 <input< 200000 MPa <input< 80 mm <input< 400 mm <input< 720 mm <input< 4200 mmA2 <input< 800 mmA2 <input< 4200 mmA2 <input< APPENDIX D - CALCULATIONS FOR SPECIMEN #1 134 IMOMENT CAPACITY OF PILE CAP EMBEDDED PLATE MATERIAL PROPERTIES fydef = yield strength of deformed bars 483 MPa <input< Edef = young's modulus for deformed bars = 200000 MPa <input< LOCATION OF DEFORMED BARS AND PLATE GEOMETRY set def(i) = 0 if there are more listings in this spreadsheet than there are rows of studs defl = space to center of first row of studs LENGTHWISE 37.5 mm <input< def2 = space to center of second row of studs LENGTHWISE 142.5 mm <input< deD = space to center of third row of studs LENGTHWISE 247.5 mm <input< def4 = space to center of fourth row of studs LENGTHWISE 352.5 mm <input< deft = space to center of fifth row of studs LENGTHWISE 457.5 mm <input< def6 = space to center of sixth row of studs LENGTHWISE • 562.5 mm <input< d e n = space to center of seventh row of studs LENGTHWISE 0 mm <input< def8 space to center of eighth row of studs LENGTHWISE 0 mm <input< widl = space to first column of studs WIDTHWISE 85 mm <input< wid2 = space to second column of studs WIDTHWISE 205 mm <input< wid3 = space to third column of studs WIDTHWISE 325 mm <input< wid4 = space to fourth column of studs WIDTHWISE 445 mm <input< wid5 = space to fifth column of studs WIDTHWISE 565 mm <input< wid6 = space to sixth column of studs WIDTHWISE 0 mm <input< diabar diameter of one single deformed bar 15 mm <input< Aem = Area of ONE SINGLE deformed bar 187 mmA2 <input< Iplate = length of embedded plate 600 mm <input< w = width of embedded plate 650 mm <input< EMBEDDED PLATE LAYOUT 700 500 100 i i • • _L • 1 • • - • I • j • • • • • I • " j I • • < • o ; e. 1 '"1 j J 4) • 1 • • 0 1— • i i • • 1 1 • • • ' 1 [ i 0 100 200 300 400 600 600 700 PLATE LENGTH [mm] (measured along the beam's length) 1TERA TION OF GUESSES FOR NEUTRAL AXIS SOLVED B cem = LOCATION OF NEUTRAL AXIS {BY ITERATION} 95.8 mm COMPUTE STRAINS IN BARS [ASSUMING A UNEAR DISTRIBUTION, PLANE SECTIONS REMAIN PLANE] edeflo = @if(defl=0,0,.003*(defl-cem)/ccm) -0.002 <calc< edcf2o = @if(def2=0,0,.003*(def2-cem)/cem) = 0.0015 <calc< edefJo = @if(def3=0>0,.003*(def3-cem)/cem) = 0.0048 <calc< edef4o = @if(def4=0,0,.003 *(def4-cem)/cem) 0.008 <calc< edefSo = @itTdef5=0,0,.003*(def5-cem)/cem) = 0.0113 <calc< edef6o = @if(def6=0,0,.003 •(def6-cem)/cem) = 0.0146 <calc< edef7o = @if(def7=0,0,.003*(def7-cem)/cem) 0 <calc< edefSo = @if(def8=0,0, 003*(def8-cem)/cem) 0 <calc< 1 APPENDIX D - CALCULATIONS FOR SPECIMEN #1 135 emax = @max(eden,edef2,edef3,edef4,edef5,edef6,edef7,edef8) = 0.0146 <calc< = @iitemax>10*rydef/Edef,"NG7'OK") ^ = GK <calc< THIS IS CI BECKING TO MAKE SURE 11IAT THE STRAINS DO NOT EXCEED 10 TIMES HIE YIELD STRAIN STRAINS IN BARS [USING INFORMATION REGARDING 3D DISTRIBUTION ALONG THE PLATE'S LENGTH] lfac = reduction factor along plate length el pipe c2edge e3edge edefl edef2 edef3 edef4 edef5 edef6 edef7 edefS .003*(dia/2+lplate/2-cem)/cem .003*(lplate-cem)/cem lfac*e2edge @ifrdefl>(lplate/2+dia/2): @ifi;del2>(lplate/2+dia/2), @iiTdef3>(lplatc/2+dia/2); @iftdef4>(lplate/2+dia/2). @ifl;def5>(lpIate/2+dia/2); @iRdef6>(lplate/2+dia/2); @if(def7>(lplate/2+dia/2), @ill;dcf8>(!plate/2+dia/2), elpipe+(defl-,elpipe+(def2-elpipe+(deD-elpipe+(def4-elpipe+(def5-elpipe+(dcf6-elpipe+(def7-elpipc+(def8-lplate/2-lplate/2-lplate/2-lplate/2-lplate/2-lplate/2-lplate/2-lplate/2-•dia/2)*(e3edge-•dia/2)*(e3cdge-dia/2)*(e3edge-dia/2)*(e3edge-dia/2)*(e3edge-dia/2)*(e3edge-dia/2)*(e3edge-dia/2)*(e3edge-•elpipe)/(lplate/2-•elpipe)/(Iplate/2-•elpipe)/(lplale/2-•elpipe)/(lplate/2-•elpipe)/(lplate/2-•elpipey(lplate/2-el'pipe)/(lplate/2-•elpipe)/(lplate/2-•dia/2),edcflo) •dia/2),edef2o) dia/2),edcf3o) dia/2),eder4o) dia/2),edef5o) •dia/2),edef6o) dia/2),edcf7o) dia/2),edef8o) STRAINS IN BARS [USING INFORMATION REGARDING 3D DISTRIBUTION ACROSS THE PLATE'S WIDTH] wfac = reduction factor across plate width edlwl edlw2 edlw3 edlw4 edlw5 edlu6 ed2wl ed2w2 ed2w3 ed2w4 ed2w5 ed2w6 ed3wl ed3w2 ed3w3 ed3w4 ed3w5 ed3w6 ed4wl ed4w2 ed4w3 ed4w4 ed4w5 ed4\v6 edSwl ed5w2 ed5w3 ed5w4 ed5w5 ed5w6 @i(lwidl=0,O,@'lTwidl<= @iflwid2=0,0,@iflwid2<= @iRwid3=0,0,@if(wid3<= @if(wid4=0,0,@ii'(wid4<= @ilTwid5=0,0,@if(wid5<= @if(wid6=0,0,@if(wid6<= @ifl>id l=0,0,@iil>id 1<= @in;wid2=0,0,@if(\vid2<= @iiTwid3=0,0,@iflwid3<= @ift>id4=0,0,@if(wid4<= @itlwid5=0,0>@iti;wid5<= @iil[wid6=0,0,@itlwid6<= @ifl;widl=0,0,@iftwidl<= @ift>id2=0,0,@'H>'id2<= @iltwid3=0,0,@il:(wid3<= @illwid4=0,0,@if(wid4<= @ifl>id5=0,0,@i»>id5<= @if(wid6=0,0,@itlwid6<= @iiIwidl=0,0,@ilTwdl<= @if(wid2=0,0>@iHwid2<= @if(wid3=0,0,@if(wid3<= @ifT,wid4=0,0,@>">id4<= @if(wid5=0,0,@in;wid5<= @iiTwid6=0,0,@ifl:wid6<= =w/2,edefl *(wid 1 *(( l-wfacy(w/2))+wfac),edefl "((w-wid 1)•((1 -wfac)/(w/2))+ :\v/2,eden*(wid2*((l-\vfac)/(sv/2))+\\fac),eden*((w-wid2)*((l-vvfac)/(\v/2))-i-:w/2,edefr(wid3*((l-\vfac)/(w/2))+wfac),eden*((w-wid3)*((l-wfac)/(w/2))+ :w/2,eden "(wid4"(( l-wfac)/(w/2))+wfac),edefl *((w-wid4)"(( l-wfac)/(w/2))+ :w/2,eden*(wid5*((l-\vfac)/(w/2))+\\fac),edefl*((w-wid5)*((l-wfac)/(\v/2))+ :w/2,edefl*(wid6*((l-wfac)/(w/2))+wfac),eden*((w-wid6)'((I-»fac)/(w/2))+ 'w/2,edef2*(wid 1 *(( l-\rfac)/(w/2))+wfac),edcl2*(( w-wid 1)*(( l-wfac)/(w/2))+ Av/2,edef2*(wid2*((l-wfac)/(w/2))+wfac),edef2*((w-wid2)*((l-wfacV(w/2))+ : :w/2,edef2*(wid3*((l-wfac)/(w/2))+wfac),edef2*((w-wid3)*((l-wfac)/(w/2))+ : Av/2,edet2*(wid4*(( l-wfac)/(\v/2))+\viac),edet2*((w-wid4)*(( l-wfac)/(w/2))+ :w/2,edef2*(wid5*(( l-wlac)/(w/2))+wfac),edel2*((w-wid5)*(( l-wfacV(w/2))+ w/2,edet2'(wid6,(( l-\vfac)/(w/2))+wt"ac),edet2*((w-wid6)'(( l-wfacV(w/2))+ \v/2,edeD*(widl*((l-\vfac)/(w/2))+wfac),edcf3 ,((w-widl)»((l-wfacy(w/2))+ : Av/2,edef3*(wid2*((l-wfac)/(w/2))+wfac),edef3,((w-wid2)*((l-wfacy(w/2))+ • :\v/2,edef3"(wid3"(( l-\vf'acy(w/2))+wfac),edeB"((w-wid3)*(( l-wfacy(w/2))+ ' w/2,edef3*(wid4*((l-Hfacy(w/2))+wfac),edeD*((w-wid4)*((l-wfacy(w/2))+ : w/2,edeD*(wid5*((l-wfac)/(w/2))+wfac),edef3,((\v-wid5)'((l-wfacy(w/2))+ •• w/2,edef3 *(wid6*(( 1 -wfacy(w/2))+»fac),edef3 *((w-wid6)*(( 1 -wfacy(w/2))+ •• w/2,edef4*(wid 1 •(( l-wfacy(w/2))+wfac),edef4"((w-wid 1)*(( l-wfacy(w/2))+ : w/2,edef4*(wid2*((l-wfacy(w/2))+wfac),edef4*((\v-wid2)*((l-wfac)/(w/2))+ : w/2,eder4*(wid3*((l-wlacy(w/2))+»fac),edef4 ,((w-wid3) ,((l-wfacy(w/2))+ = w/2,edef4*(wid4,((l-wfacy(w/2))+wfao.),edef4,((w-wid4)*((l-wfacy(w/2))+ : w/2,edef4*(wid5*((l-wfacy(w/2))+wfac),edet4*((w-wid5)*((l-wfacy(w/2))+ ; w/2,edef4'(wid6*((l-wfacy(w/2))+wfac),edef4*((w-wid6)*((l-wfacy(w/2))+ : @il^vidlH)A@iiTwidl<=w/2,edclV(widl*((^^ @iltwid2=0,0,@in;wid2<=\v/2,edel'5*(wid2*((l-wfacy(w/2))+wfac),edcf5*((w-wid2)*((l-wfacy(w/2))+ @ifl;wid3=0,0,@if(wid3<=w/2,edel'5*(wid3*((l-ttfacy(w/2))+wfac),edef5*((w-wid3)*((l-wfac)/(w/2))+ @itTwid4=0,0,@in;wid4<=w/2,edefi,(wid4,((l-wfacy(w/2))+wfac),edef5,((w-wid4)*((l-vvfacy(w/2))+ @il\wid5=0,0,@ifl;wid5<=w/2,edef5*(wid5*((l-wfacy(w/2))+wfac),edcf5*((w-wid5)*((l-wfacy(w/2))+ @iiTwid6=0,0,@if(wid6<=w/2>edef5*(wid6*((l-wfacy(w/2))+wfac),edef5'((w-wid6)*((l-wfacy(w/2))+ 1 <input< 0.0115 <calc< 0.0158 <calc< 0.0158 <calc< -0.002 <calc< 0.0015 <calc< 0.0048 <calc< 0.008 <calc< 0.0113 <calc< 0.0146 <calc< 0 <calc< 0 <calc< 1 <input< -0.002 <calc< -0.002 <calc< -0.002 <calc< -0.002 <calc< -0.002 <calc< 0 <calc< 0.0015 <calc< 0.0015 <calc< 0.0015 <calc< 0.0015 <calc< 0.0015 <calc< 0 <calc< 0.0048 <calc< 0.0048 <calc< 0.0048 <calc< 0.0048 <calc< 0.0048 <calc< 0 <calc< 0.008 <calc< 0.008 <calc< 0.008 <calc< 0.008 <calc< 0.008 <calc< 0 <calc< 0.0113 <calc< 0.0113 <calc< 0.0113 <calc< 0.0113 <calc< 0.0113 <calc< 0 <calc< APPENDIX D - CALCULATIONS FOR SPECIMEN #1 136 ed6wl ed6w2 ed6\v3 ed6\v4 ed6w5 ed6w6 ed7wl ed7w2 ed7w3 ed7w4 ed7w5 ed7w6 ed8wl ed8w2 ed8w3 ed8w4 ed8w5 ed8w6 @ii(widl=0,0,@ilTwi @iu>id2=0,0,@ift> @if(wid3=0,0,@if(wi @ift\vid4=0,0,@ift>: @if(wid5=0,0,@if(w @if(wid6=0,0,@iiiw: @il\widl=0,0,@in;wi @if(wid2=0,0,@ir(wi @if(wid3=0,0,@iHwi @if(wid4=0,0,@if(wi @ii\wid5=0,0,@in;wi @ilTwid6=0,0,@if(wi ©iflwid^O.O.lgilTw @if(wid2=0,0,@if(wi @if(wid3=0,0,@if(wi @if(wid4=0,0,@if(wi @if(wid5=0,0,@if(w @ifTwid6=0,0,@if(w d 1 <=w/2,edcf6*(wid 1 *(( 1 -wfacy(w/2))+wfac),edef6* d2<=w/2,edel"6»(wid2*(( 1 -wfac V(w/2))+wfac),edef6* d3<=w/2,edcf6*(wid3*((l-wfac)/(w/2))+«fac),edef6'* d4<=w/2,edcr6,(wid4*((l-Hfac)/(w/2))+wfac),edci'6* d5<=w/2,edcf6*(wid5*((l-»fac)/(w/2))+wrac),eder6* d6<=w/2,cdef6*(wid6*((l-wfacy(w/2))+wfac),edef6* id 1 <=w/2,edcf7*(wid 1 *(( 1 -wfacytw^J+wfacJ.eden*! d2<=w/2,edei7*(wid2*((l-wfac)/(w/2))+»fac),edef7' d3<=w/2,edef7*(wid3*((l-wfacy(w/2))+»fac),edef7' d4<=w/2,edef7*(wid4*(( 1 -wfacy(w/2))+wfac),edef7' d5<=w/2,cdel7*(wid5*«l-wfac)/(w/2))+wfac),eden d6<=w/2,edef7*(wid6*((l-»facy(w/2))+»fac))edef7' id K=w/2,edef8*(wid 1 *(( 1 • Id2<=w/2,cdei'8*(wid2*((l. id3<=w/2,cdef8*(wid3 •(( 1 • d4<=w/2,eder8,(wid4*(( 1-d5<=w/2,edcf8*(wid5*((l-d6<=w/2,edef8*(wid6*((l-wfac)/(W2))+wfac),edef8*i wfacy(w/2))+wfac),edef8*i wfacy(w/2))+wfac),edef8*i wfacy(w/2))+wfac),eder8 wfacy(w/2))+wfac),eder8*i \vfacy(w/2))+wfac),edef8 STRESSES IN BARS fdlwl fdlw2 fdlw3 fdlw4 fdlw5 fdlw6 fd2wl fd2w2 fd2w3 fd2w4 fd2w5 fd2»6 fd3wl fd3w2 fd3w3 fd3w4 fd3w5 fd3w6 fd4wl fd4w2 fd4w3 fd4w4 fd4w5 fd4w6 fd5wl fd5w2 fd5w3 fd5w4 fd5w5 fd5w6 fd6wl fd6w2 fd6w3 fd6w4 fd6w5 fd6w6 fd7wl fd7w2 fd7w3 fd7w4 fd7w5 fd7w6 @if(@abs(ed @if(@abs(ed @if(@abs(ed @if(@abs(ed @.if(@abs(ed @if(@abs(ed lwl*Edef)<fydef,ed lw2*Edef)<rydef,ed lw3*Edef)<fydef,ed hv4*Edef)<fydcf,ed lw5*Edef)<fydef,ed lw6*Edef)<fydefed lwl*Edef@if(edefl<0: lw2*Edef@if(edefl<0: lw3*Edef,@if(edcfl<0, lw4*Edef@if(edefl<0, lw5*Edef@if(edefl<0, hv6*Edef@if(eden<0, @if(@abs(ed2wl @if(@abs(ed2w2* @ilT.@abs(ed2w3 @if(@abs(ed2w4*: @if(@abs(ed2w5 @if(@abs(ed2w6 Edcf)<fydef,ed2wl Edef)<fydefed2w2 Edef)<fydefed2w3 Edcf)<fydef,ed2w4 Edcf)<fydef,ed2w5 Edef)<fydef,ed2w6 Edcf,@ •Edef,@i *Edef,@i *Edef,@i *Edef@i •Edef@i f(edef2<0, f(edef2<0, fCedeOO, r(edcf2<0, f(edel2<0, fTedef2<0, @ir(@abs(ed3wl*EdeO<fydef,cd3wltEdcf,@if(edci3<0, @if(@abs(ed3w2*EdeO<fjdef,ed3w2*Edcf,@ilXedcn<0, @if(@abs(ed3w3*EdeO<fydef,ed3w3*Edef,@if(cdeB<0, @ift@abs(ed3w4'*EdeO<fydcf,ed3w4*Edef,@if(edcf3<0, @if(@abs(ed3w5*Edef)<fydef,ed3w5*Edcf,@iRedcf3<0, @if(@abs(ed3w'6*Edet)<fydef,ed3w6*Edef@if(edef3<0, @if(@abs(ed4wl @if(@abs(ed4w2 @if(@abs(ed4w3 @if(@abs(ed4w4l @if(@abs(ed4w5 @if(@abs(ed4w6 *Edcf)<fydcf>ed4\vi *Edef)<fydefed4w2 *Edef)<fydefed4w3 *Edef)<fydefed4w4 •Edef)<fydef,ed4w5 *Edef)<fydef,ed4w6 •Edef@if(edef4<0, *Edef,@iftedcf4<0; •Edef,@if(edef4<0, *Edef,@ilTedef4<0, •Edef,@iftedef4<0, *Edef,@if(edef4<0, @if(@abs(ed5wl*Edef)<fydcf,ed5wl*Eder,@if(edel3<0, @if(@abs(cd5w2*Edef)<fydefed5w2*Edef@if(eder5<0, @if(@abs(ed5w3*EdeO<fydefed5w3*Edef,@ii{edef5<0, @if(@abs(ed5w4,Edci)<fydef,ed5w4'Edef,@if(edef5<0) @if(@abs(ed5w5*Edef)<fydef,ed5w5*Edef,@iiTedcf5<0, @i«@abs(cd5w6»EdeO<fydefed5w6*Edef@if(edcf5<0, -fydeffydef)) -fydeffydef)) -fydeffydef)) -fydeffydef)) -fydeffydef)) -fydeffydef)) •fydeffydef)) •fydeffydef)) •fydeffydef)) •fydef.fydef)) •fydeffydef)) •fydeffydef)) fydeffydef)) •fydeffydef)) fydeffydef)) •fydeffydef)) fydeffydef)) fydeffydef)) -fydeffydef)) -fydeffydef)) -fydeffydef)) -fydeffydef)) -fydeffydef)) -fydeffydef)) •fydeffy'def)) fydeffydef)) fydeffydef)) •fydeffydef)) fydeffydef)) fydeffydef)) @if(@abs(ed6w 1 •Edef)<fydefed6w 1 *Edef@if(edef6<0,-fydef fydef)) @if(@abs(ed6w2*EdeO<rydcf,ed6w2'Edef>@if(edcf6<0,-fydef,rydcf)) @if(@abs(ed6w3*EdeO<fydcf,ed6w3»Edef,@if(edef6<0,-fydef,fy'def)) @if(@abs(ed6w4*Edef)<fydef,ed6w4*Edef,@if(edef6<0,-fy'def,fydef)) @if(@abs(ed6w5*Edet)<fydef,ed6w5*Edef@if(edcf6<0,-f>def,fydeO) @if(@abs(ed6w64Edef)<fydef,ed6w6*Edcf,@if(eder6<0,-rydef fydef)) @if(@abs(ed7wl *EdeO<fydcfed7w 1 •Edef,@if(edef7<0,-rydef,fydeO) @if(@abs(ed7w2*EdeO<fydef,ed7w2*Edef,@ifl:edet7<0,-rydef,fydef)) @if(@abs(ed7w3'Edef)<fy'dcf,ed7w3*Edef@ill;cden<0,-fydef,rydef)) @iil@abs(ed7w4*EdeO<fydef,cd7w4*Edcf,@if(eden<0,-fydefrydeO) @if(@abs(ed7w5*EdeO<fydef,ed7w5,Edef,@i«:eden<0,-fydeffydef)) @if(@abs(ed7w6*Edef)<fydefed7w6*Edef,@if(edei7<0,-rydeffydef)) (w-wid 1 )*( l-wfac)/(w/2))+ = 0.0146 <calc< (w-wid2)*( (l-wfacy(w/2))+ = 0.0146 <calc< (w-vvid3)*( (l-wfacV(w/2))+ = 0.0146 <calc< (w-wid4)*( (l-wfacy<w/2))+ = 0.0146 <calc< (w-wid5)*( ;i-wfacy(w/2))+ = 0.0146 <calc< (w-wid6)*( (l-wfac)/(w/2))+ = 0 <calc< (w-wid 1)*( (l-wfacV(w/2))+ = 0 <calc< (w-wid2)*( (l-wfacy(w/2))+ = 0 <calc< (w-wid3)*( (l-wfacy(w/2))+ = 0 <calc< (w-wid4)*( (l-wfacy(w/2))+ = 0 <calc< (w-wid5)*( (l-wfaey(w/2))+ = 0 <colc< (w-wid6)*( ;i-wfacy(w/2))+ = 0 <calc< (w-wid 1)*( (l-wfacy(w/2))+ = 0 <calc< (w-wid2)*( (l-wfacy(w/2))+ = 0 <calc< (w-wid3)*( (l-wfacy(w/2))+ = 0 <calc< (w-wid4)*( (l-wfacy(w/2))+ = 0 <calc< (w-wid5)*( (l-wfacy(w/2))+ = 0 <calc< (w-\vid6)*( (l-wfacy(w/2))+ = 0 <calc< _ -365.1 <calc< = -365.1 <calc< = -365.1 <calc< = -365.1 <calc< = -365.1 <calc< = 0 <calc< = 292.56 <calc< 292.56 <calc< 292.56 <calc< = 292.56 <calc< - 292.56 <calc< • = 0 <calc< 483 <calc< 483 <calc< = 483 <calc< = 483 <calc< 483 <calc< 0 <calc< = 483 <calc< = 483 <calc< = 483 <calc< 483 <calc< = 483 <calc< = 0 <calc< = 483 <calc< = 483 <calc< = 483 <calc< 483 <calc< = 483 <calc< 0 <calc< 483 <calc< = 483 <calc< = 483 <calc< 483 <calc< = 483 <calc< = 0 <calc< 0 <calc< = 0 <calc< = 0 <calc< = 0 <calc< = 0 <calc< = 0 <calc< APPENDIX D - CALCULATIONS FOR SPECIMEN #1 137 fd8wl = @if^ @abs(ed8vvl*Edef)<fydef,ed8vvl*Edef,@if(edere<0,-fydef,rydeO) 0 <cale< fd8w2 = @ifI@abs(ed8w2*EdeO<rydef,ed8w2*Edef,@inedcf8<0,-fydef,fydef)) 0 <calc< fd8w3 @ift@abs(ed8w3*EdeO<rydef,ed8w3"Edef,@in;edef8<0>-fydef,rydef)) 0 <calc< fd8w4 = @ilI@abs(ed8w4*EdeO<fydef,ed8w4,Edef,@if(edere<0,-iydef,fydef)) 0 <calc< fd8w5 @ilT@abs(cd8w5*Edef)<ryder,ed8w5*Edef,@if(edere<0,-fydef,rydeO) 0 <calc< fd8»6 = @iil@abs(ed8\v6*EdeO<lydef,ed8w6*Edcf,@inedcre<0,-fydcr,lydcO) 0 <calc< FORCES IN STEEL Tdlwl fdlwl*Aem/1000 -68.28 kN <calc< Tdlw2 = fdlw2*Aem/1000 -68.28 kN <calc< Tdlw3 = fdlw3*Aem/1000 -68.28 kN <calc< Tdlw4 fdlw4*Aem/1000 -68.28 kN <calc< Tdlw5 = fdlw5*Aem/1000 -68.28 kN <calc< Tdlw6 = fdlw6*Aem/1000 0 kN <calc< Tdl = Td1w1+Td1w2+Tdlw3+Td1w4+Td1w5 +Td Kv6 -341.4 <calc< Td2wl = fd2wl*Aem/1000 = 54.709 <calc< Td2w2 = fd2w2*Aem/1000 = 54.709 <calc< Td2w3 fd2w3*Aem/1000 = 54.709 <calc< Td2w4 = fd2w4*Aem/1000 = 54.709 <calc< Td2w5 = fd2wS*Aern/1000 = 54.709 <calc< Td2w6 = fd2w6*Aem/1000 0 <calc< Td2 = Td2wl+Td2w2+Td2w3+Td2w4+Td2w5+Td2\v6 = 273.55 <calc< Td3wl = fd3wl*Aem/1000 = 90.321 <calc< Td3w2 = fd3\v2*Aem/1000 = 90.321 <calc< Td3w3 = fd3w3*Aem/1000 = 90.321 <calc< Td3w4 = fd3w4*Aem/1000 = 90.321 <calc< Td3w5 = fd3w5*Aem/1000 = 90.321 <calc< Td3w6 = fd3w6*Aem/1000 0 <calc< Td3 = Td3\vl+Td3\v2+Td3w3+Td3w4+Td3\v5+Td3vv6 = 451.61 <calc< Td4wl = fd4wl*Aem/1000 = 90.321 <calc< Td4w2 = fd4w2*Aem/1000 = 90.321 <calc< Td4w3 = fd4vv3*Aetn/1000 = 90.321 <calc< Td4w4 = fd4\v4*Aem/1000 = 90.321 <calc< Td4w5 = fd4w5*Aem/1000 = 90.321 <calc< Td4w6 = fd4w6*Aem/1000 0 <calc< Td4 = Td4wl+Td4w2+Td4w3+Td4w4+Td4w5+Td4w6 = 451.61 <calc< Td5wl = fd5wl»Aem/1000 = 90.321 <calc< Td5w2 = fd5w2*Aem/1000 = 90.321 <calc< Td5w3 = fd5w3*Aem/1000 = 90.321 <calc< Td5w4 = fd5w4*Aem'1000 = 90.321 <calc< Td5w5 = fd5w5*Aem/1000 = 90.321 <calc< Td5w6 = fdSwe^ Aem/lOOO 0 <calc< Td5 = Td5wl+Td5w2+Td5w3+Td5w4+Td5w5+Td5\v6 = 451.61 <calc< Td6wl = fd6wl*Aem/1000 = 90.321 <calc< Td6w2 = fd6w2*Aem/1000 = 90.321 <calc< Td6w3 fd6w3*Aem/1000 = 90.321 <calc< Td6w4 = fd6w4*Aem/1000 = 90.321 <calc< Td6w5 = fd6w5*Aem/1000 = 90.321 <calc< Td6w6 = fd6w6*Aem/1000 0 <calc< Td6 Td6wl+Td6w2+Td6w3+Td6w4+Td6\v5+Td6w6 = 451.61 <calc< Td7wl fd7wl*Aem/1000 0 <calc< Td7w2 = fd7w2,Aem/1000 0 <calc< Td7w3 = fd7w3*Aem/100O 0 <calc< Td7w4 = fd7w4*Aem/1000 o <calc< Td7w5 = fd7w5'Aem/1000 0 <calc< Td7w6 = fd7w6*Aem/1000 0 <calc< Td7 = Td7wl+Td7w2+Td7w3+Td7w4+Td7\v5+Td7w6 0 <calc< Td8wl = fd8wl*Aem/1000 0 <calc< Td8w2 = fd8w2*Aem/1000 0 <calc< Td8w3 = fd8w3*Aem/1000 0 <calc< Td8w4 = fd8w4*Aem/1000 0 <calc< Td8w5 = fd8w5*Aem/1000 0 <calc< Td8w6 = fdSwe'Aem/lOOO 0 <calc< Td8 = Td8wl+Td8w2+Td8w3+Td8w4+Td8w5+Td8w6 0 <calc< APPENDIX D - CALCULATIONS FOR SPECIMEN #1 138 TOTAL FORCE IN STEEL AND CONCRETE (SHOULD BE EQUAL) Cplate = -alpha*fc'*beta*cern*w/1000 Fdef = Tdl+Td2+Td3+Td4+Td5+Td6+Td7+Td8 Diffem = Fdef+Cplate = @ilT@abs(dinem)<l,"OK","NG") MUST ENSURETHAT Cplate & Fdef ABOVE ARE EQUAL IN ORDER TO ENSURE EQUILIBRIUM -1739 kN 1738.6 kN 0 kN Ok <calc< <calc< <calc< <calc< Mpll = Td8*def8+Td7*def7+Td6*def6+Td5*def5+Td4*def4 Mpl2 = Td3*def3+Td2*dcf2+Tdl*den+Cplate*beta*cem/2 619828 77163 <calc< <calc< MOMENT CAPACITY OF PILE CAP EMBEDDED PLA TE \Mrplate = phibr*(Mpll +Mpl2)/1000 592 kN'm <calc< FACTOR OF SAFETY FOR PLASTIC HINGE FORMATION FS - @niin(Afrplate/Mppipe.MrbeaniAfppipe) 1.55 <calc< = @if(FS<phiover,"NG","OK") THIS IS CHECKING TO ENSURE THAT PLASTIC IIINGE FORMATION IS THE MODE OF FAILURE. = OK <calc< APPENDIX D - CALCULATIONS FOR SPECIMEN #1 ICHECFC PLATE YIELDING AT ULTIMATE ANCHORAGE MOMENT MATERIAL PROPERTIES Fypl = yield strength of embedded plate CROSS SECTIONAL GEOMETRY tpl = thickness of embedded plate 350 MPa 50 mm CHECKING YIELD STRENGTH FOR EXCEEDENCE OF CODE LIMITATION OF330 MPa Fypla = @ittFypl>330,330,Fypl) = 330 MPa MOMENT RESISTANCE OF PLA TE |Mrpl <input< <tnput< <calc< phibr*l/6»\v»tplA2»Fypla/lE6 76 kN*m <calc< CASE A - TAKING MOMENT AT EDGE OF SHORT STRESS BLOCK [Presently suggested by MoTH] MfplI = -(Cplate*(beta*cem/2)+Fden*(beta*cem-den))/IE3 ; = 61 kN*m CASE B - TAKING MOMENT AT EDGE OF PIPE FOR LONG STRESS BLOCK lblock = (lplate-diaV2 = 138 mm Mfpl2 = -(-alpha*fc,*lbIock*w*(lblock/2)/lE3+Tdl*(lblock-den))/lE3 = 271 kN*m NEXT, COMPUTER DECIDES WHICH ONE OF A & B IS THE ACTUAL CASE, BY SEEING IF THE COMPRESSION BLOCK GOES PAST THE PIPE EDGE \Mfpl = @.if(beta*cem<tblockMfpTTMfpl2) 61 kN*m @ifIMrpl>Mfpl,"OK:","NG") = CMWXtm MUST ENSURE THAT THE PLATE IS STRONG ENOUGH SO THAT IT DOES NOT BEND DUE TO COMPRESSIVE REACTIONS IN THE CONCRETE <calc< <calc< <calc< <calc< <calc< NOTE THAT ALTHOUGH THE ABOVE ASSUMPTIONS SEEM RATHER CRUDE, THE DESIGN SHOULD BE CONSERVATIVE CONSIDERING THAT THE YIELDING OF THE PLATE HAS BEEN EVALUATED AT THE ULTIMATE ANCHORAGE MOMENT AND NOT THE PIPE PLASTIC MOMENT beta'cem Evaluate Bending^ Stress here Iplate dia lblock 4 + W alpha *fc' def(1) Evaluate Bending Stress here J mm C A S E A Fdef -def(1) C A S E B Fdef APPENDIX D - CALCULATIONS FOR SPECIMEN #1 NAME: MARK STEUNENBERG PROJECT: SPECIMEN #1 -324 DIA PIPE DATE: NOVEMBER 1995 S U M M A R Y OF DESIGN C A L C U L A T I O N S Width of concrete beam Height of concrete beam Area of Top longitudinal steel = Deptli to Top steel Area of Middle longitudinal steel Depth to Middle steel Area of Bottom longitudinal steel Depth to Bottom steel Diameter of steel stirrups = Spacing of stirrups Concrete compressive strength 750 mm 800 mm 4200 mmA2 80 mm 800 mmA2 400 mm 4200 mmA2 720 mm 15 mm 225 mm 45 MPa Diameter of deformed bar anchors = Yield strength of deformed bars Thickness of embedded plate = Width of embedded plate Deformed bars across width of beam = Length of embedded plate Deformed bars along length of beam Yield strength of embedded plate 15 mm 483 MPa 50 mm 650 mm 5 rows 600 mm 6 rows 350 MPa Pipe pile diameter Wall thickness of pipe Specified pipe strength = 324 mm 12.7 mm 310 MPa Shear Resistance ol Concrete Beam = 890 kN Moment Resistance of Concrete Beam 1076 kN*m I Moment Resistance of Anchorage Bars 592 kN*m 1 Plastic Moment of Pipe Pile (phi =1) 382 kN*m 1 MTNIMUM[Mr(beani). Mr(anchors)l/Mp(pipe) 1.55 I Overstrength Factor for Pipe Strength (Capacity Design) 1.32 | EMBEDDED PLATE LAYOUT PJ i _ j 1 1 • • i : : 1 _ © © ' © i * ; e o o i o o • • © ; _. j J i i ; I ! i ! _ • • j • ; • ; • • i — • r — • — j — — j — • -j—•>._;. -*> j • • • • 7 *) : : I j 1 H 1 1 1 1 1 i i i ' ' ' 1 i — ' 0 100 200 300 400 500 600 700 PLATE LENGTH [mm] (measured along the beam's length) APPENDIX E - CALCULATIONS FOR SPECIMEN #2 141 THE C O N C R E T E BEAM IS THE SAME AS FOR SPECIMEN #1. THUS, CALCULATIONS FOR THE BEAM AND EMBEDDED PLATE CAN BE FOUND IN APPENDIX D. F O M E N T C A P A C I T Y O F P I P E P I L E MATERIAL PROPERTIES fypipe = specified yield strength of pipe phipipe = performance factor of steel pipe (for capacity design =1) phiover = mimimum overstrength factor for pipe yield strength BASED ON MILL CERTIFICATE WITH Fyield = 338 MPa CROSS SECTIONAL GEOMETRY t = pipe thickness dia = pipe outside diameter 12.7 mm 406 mm <input< <input< <input< <input< <input< PLASTIC SECTION MODULUS AND CHECK FOR COMPACT SECTION Zform = diaA3/6*(l-(l-2*t/dia)A3) = 1965181 mmA3 <calc< = @il{dia/t>18000/lypipc,"NG","OK") = OK Mm <calc< [7.6.2] THIS IS CHECKING THAT THE SECTION IS A COMPACT ONE A THAT CAN DEVELOP THE FULL PLASTIC MOMENT SPECIFIED MOMENT CAPACITY (PLASTIC) \Mppipe = pliipipe*f\>pipe*Zfornti'Ie+06 ' = 474 kN*m <colc< | NOTE: ALL REFERENCES ARE TO CAN/CSA-S6-88 APPENDIX E - CALCULATIONS FOR SPECIMEN #2 142 NAME: MARK STEUNENBERG PROJECT: SPECIMEN #2 - 406 DIA PIPE DATE: NOVEMBER 1995 S U M M A R Y OF DESIGN C A L C U L A T I O N S Width of concrete beam = 750 mm Height of concrete beam = 800 mm Area of Top longitudinal steel = 4200 mmA2 Depth to Top steel 80 mm Area of Middle longitudinal steel = 800 mmA2 Depth to Middle steel 400 mm Area of Bottom longitudinal steel = 4200 mmA2 Depth to Bottom steel = 720 mm Diameter of steel stirrups = 15 mm Spacing of stirrups 225 mm Concrete compressive strength 45 MPa Diameter of deformed bar anchors = 15 mm Yield strength of deformed bars = 483 MPa Thickness of embedded plate = 50 mm Width of embedded plate 650 mm Deformed bars across width of beam = 5 rows Length of embedded plate 600 mm Deformed bars along length of beam = 6 rows Yield strength of embedded plate = 350 MPa Pipe pile diameter 406 mm Wall thickness of pipe = 12.7 mm Specified pipe strength = 241 MPa Shear Resistance of Concrete Beam = 890 kN Moment Resistance of Concrete Beam = 1076 kN*m Moment Resistance of Anchorage Bars = 592 kN*m Plastic Moment of Pipe Pile (phi = 1) = 474 kN*m MINlMUMfMr(beam), Mr(anchors)]/Mp(pipe) /1.25-Overstrength Factor for Pipe Strength (Capacity Design) ( 1.40 EMBEDDED PLATE LAYOUT 700 600 500 400 ~ 300 r -5 CL 200 100 j i i ! i m • i • • i I - l I 1 - • ! • I • • I • i • ! I - • i • i • • j • • e • • • • • i r ! I I | —• i — • | — — i - — • — i I I I ! • ' 1 • • • H 1 1 1 1 1 • l • < 1 1 0 100 200 300 400 500 600 700 PLATE LENGTH [mm] (measured along the beam's length) NOTE: VIOLATION OF CAPACITY DESIGN BECAUSE PIPE OVERSTRENGTH IS LARGER THAN CONNECTION FACTOR OF SAFETY APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 143 SOURCE CODE PROGRAM bending (input, output, datain, dataout); { FOR COMPUTING THE MOMENT CURVATURE RESPONSE OF A GIVEN } { EMBEDDED PLATE BY: MARK STEUNENBERG, 1995 } USES Crt; {must be present to use Clearscreen} VAR Input, Output : Text; {input & output files} dstrn, pstrn, pdif, dif : Real; {force & strain differences} maxnn, nn : Integer; {iteration counters} cl, kk : Integer; {condition & direction iterator} xl, x2, x3, fl, f2, f3, fl3 : Real; {linear interpolators} tol, kntol : Real; {tolerances} fcprime, fcrack, Ect, ecrack, ecprime : Real; {concrete properties} Area, datum : array [1.. 30] of Real; {input areas and distances} strain, calcforce : array [1.. 30] of Real; {iterating strains & forces} sumcalcforce, bend : Real; {summed force & moment} fy, Esteel : Real; {steel properties} A, B, C : Real; {Ramberg-Osgood coefficients} Ep, fpu : Real; {prestressing properties} datain, dataout : string[40]; {filenames} phi, kmphi : Real; {specified curvature} epinitial : array[1..30] of Real; {initial prestress} microepinitial : array[1..30] of Real; {initial prestress} factl, fact2, fact3, n, k : Real; {high strength concrete factors} fc, fp, fsteel : Real; {stresses} strn : Real; {iterative axial strain} Force, knForce : Real; {user defined force} mattype : array[1..30] of Integer; {material type code} nlayers : Integer; {number of layers} tsoption : Integer; {tension stiffening = ON/OFF} count 1 : Integer; {counter for various loops} PROCEDURE introduction; BEGIN Clrscr; {clears the screen} textcolor(lightgray); writeln; writelnC WELCOME TO'); WriteLn; textcolor(red); writelnC BBBBBBBB EEEEEEEEEE NN NN DDDDDD '); writeln(' BB BB EE NNN NN DD DD '); writelnC BB BB EE NNNN NN DD DD '); APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 144 writelnC BB BB EE NN NN NN DD DD '); textcolor(white); writelnC BB BB EE NN NN NN DD DD'); writelnC BBBBBBB EEEEEEEEEE NN NN NN DD DD'); writelnC BB BB EE NN NN NN DD DD •); textcolor(red); writelnC BB BB EE NN NN NN DD DD '); writelnC BB BB EE NNNN DD DD '); writelnC BB BB EE NN NNN DD DD '); writelnC BBBBBBBB EEEEEEEEEE NN NN DDDDDD '); writeln; textcolor(lightgray); writeln; WriteLn('*** This Program Determines the Moment in a Beam Column ***'); writeln('*** Given an Axial Load and Curvature ***')• WriteLn ('* * * By Mark Steunenberg, UBC Civil Engineering, 1995 ***'); writeln; writeln; END; PROCEDURE inputfile; {asking the user to define the input file} BEGIN textcolor(cyan); write('Please Enter the Input File (eg abc.xyz):'); readln(datain); textcolor(lightgray); assign (Input, datain); {this tells the data file to be ready} reset (Input); {for opening} END; PROCEDURE readfile; {reading from the input file} BEGIN readln(input, A, B, C); readln(input, fcprime); readln(input, fy, Esteel); readln(input, fpu, Ep); readln(input, nlayers); count 1 =1; WHILE count 1 <= nlayers DO BEGIN readln(input, mattype[countl],Area[countl],datum[countl],microepinitial[countl]); epinitial[countl] := microepinitial[countl]/1000; strain[countl] := 0; strn := 0; count 1 := count 1 + 1; END APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS END; PROCEDURE outputfile; BEGIN textcolor(cyan); write('Please Enter the Name of the Output File You Would Like to Create:'); readln(dataout); assign(output,dataout); rewrite(output); write('Please Enter The Axial Load Tolerance [kn]:'); Readln(kntol); tol :=kntol*1000; textcolor(lightgray); ClrScr; END; PROCEDURE gettsoption; BEGIN writeln; textcolor(cyan); write('Do You Want Tension Stiffening? (ON = l),(OFF = 0),(QUIT = 9 9 9 ) ; - ) ; readln(tsoption); textcolor(lightgray); END; PROCEDURE getforce; {asking the user to input a strain value} BEGIN writeln; textcolor(cyan); Write ('Enter the Axial Load [kN] (Go Back To Tension Stiffening Option = 9 9 9 ) : ' ) ; Readln (knForce); textcolor(lightgray); Force := knForce* 1 0 0 0 ; END; PROCEDURE getphi; {asking the user to input a strain value} BEGIN writeln; textcolor(cyan); Write ('Enter the Curvature, phi [rad/km] (Go Back To Axial Load = 9 9 9 ) : ' ) ; Readln (kmphi); textcolor(lightgray); phi :=kmphi/l000000; END; APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 146 PROCEDURE steelstress; {computing the steel stress} BEGIN IF (Esteel*strain[countl] > fy) THEN {check for exceedence of + yield} fsteel := fy ELSE IF (Esteel*strain[countl] < -fy) THEN {check for exceedence of - yield} fsteel := -fy ELSE fsteel := Esteel*strain[countl]; {if steel is within yield limits} calcForce[countl] := fsteel*Area[countl] END; PROCEDURE prestress; {computing prestressing steel streses} BEGIN IF (epinitial[countl]+strain[countl]) = 0 THEN {give zero stress if strain = 0} fp := 0 ELSE IF (epinitial[countl]+strain[countl]) <= 0 THEN {use linear approximation for} BEGIN {negative stresses or program} fp := (epinitial[countl]+strain[countl])*Ep; {will crash} LF fp <= -fpu THEN {check for exceedance of - yield} fp := -fpu END ELSE IF ((epinitial[countl]+strain[countl]) <= 0.00000001) AND ((epinitial[countl]+strain[countl]) > 0) THEN fp := (epinitial[countl]+strain[countl])*Ep ELSE BEGIN fact2 := exp(C*ln(B*(epinitial[countl]+strain[countl]))); {non linear formula} fact3 := exp((l/C)*ln(l+fact2)); {Turbo can't raise} fp := (epinitial[countl]+strain[countl])*Ep*(A+(l-A)/fact3); {numbers to any power} IF fp > fpu THEN {thus the need to} fp := fpu {mess around with} END; {In and exponential} calcForce[countl] := fp*Area[countl] END; PROCEDURE calcproperties; BEGIN fcrack := 0.33*sqrt(fcprime); Ect := 5500*sqrt(fcprime); ecrack := fcrack/Ect; ecprime := -2*fcprime/Ect; END; APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 147 PROCEDURE conccompressive; {calculate compressive stresses} BEGIN {according to high strength concrete} n := 0.8+(fcprime/17); {formula} IF (strain[countl]/ecprime) < 1 THEN k:= 1 ELSE k := 0.67+(fcprime/62); IF strain[countl] = 0 THEN {stress = 0 if concrete stain = 0} fc :=0 ELSE {once again, it's a little} BEGIN {messy due to In and} factl := exp(n*k*ln(strain[countl]/ecprime)); {exponentials} fc := -fcprime*((n*strain[countl]/ecprime)/(n-l+factl)); END END; PROCEDURE tensionstiffened; {concrete stresses for tension stiffened} BEGIN LF (strain[countl] < 0) THEN {if strain negative call subroutine } conccompressive ELSE IF (strain[countl] > ecrack) THEN {if above cracking strain, then} fc := fcrack/(l+sqrt(500*strain[countl])) {use tension stiffening formula} ELSE fc := strain[countl]*Ect; {below cracking strain, use linear approx} END; PROCEDURE nottensionstiffened; {concrete stresses for non-tension-stiffened} BEGIN IF (strain[countl] <= 0) THEN {if strain negative call subroutine} conccompressive ELSE IF (strain[countl] > ecrack) THEN {if above cracking strain, no stress} fc := 0 ELSE fc := strain[countl]*Ect; {below cracking strain, use linear approx} END; PROCEDURE concstress; {this routine calls up the above subroutines} BEGIN {depending on tension stiffening} IF (mattype[countl] = 1) AND (tsoption = 1) THEN {material type 1 is tension stiffened} tensionstiffened {call subroutine} ELSE IF (mattype[countl] = 0) OR (tsoption = 0) THEN {material type 0 is not tension stiff.} nottensionstiffened; {call subroutine} calcForce[countl] := fc*Area[countl] END; APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 148 PROCEDURE showinput; {prints input file to screen and to output file} BEGIN Writeln (' * Summary of Input File *'); y^fJ^ J^ 'J* 'I' 'f* 'I' ^ t* *^ 'I' 'f^  'f' •'I* i^* 'I' 'I* 1^* ^ t* 'I* 'I* 'f^  si6 ^ 1* ')" writeln('CONCRETE ** fcprime = ',fcprime:5:1/ MPa'); writeln('STEEL ** Es = ', Esteel:5:l,' MPa ','fy = ',fy:5:l,' MPa'); writeln('PRESTRESSING ** Ep =Ep:5:l,'MPa ','fpu = ',fpu:5:l/MPa'); count 1 := 1; writelnCNumber of Layers = ',nlayers); writeln(*LAYER MAT# MATERIAL AREA [mmA2] YDATUM [mm] INITIAL MTLLISTRAIN'); WHILE count 1 <= nlayers DO BEGIN write(",countl:3,' ',mattype[countl],' '); IF mattype[countl] = 0 THEN writeln('rNO TS] CONCRETE ',Area[countl]:ll:l,datum[countl]:ll:l) ELSE IF mattype[countl] = 1 THEN writeln('[TS] CONCRETE ',Area[countl]:ll:l,datum[countl]:ll:l) ELSE IF mattype[countl] = 2 THEN writeln('STEEL ',Area[countl]:l l:l,datum[countl]:l 1:1) ELSE LF mattypefcountl] = 3 THEN BEGIN write('PRESTRESSING ',Area[countl]: 11: l,datum[countl]: 11:1); writeln(' ',microepinitial[count 1 ]: 11:1); END; count 1 := count 1 + 1; END; textcolor(cyan); write('PRESS ENTER TO CONTINUE WITH ANALYSIS'); textcolor(lightgray); readln; write ('*********************************************************')• writeln ('****************** * * * * *>y writeln(output,'START OF OUTPUT FLLE'); writeln(output); WriteLn (output,'*** This Program Determines the Moment in a Beam Column ***'); writeln (output,'*** Given an Axial Load and Curvature ***')• WriteLn (output,'*** By Mark Steunenberg, UBC Civil Engineering, 1995 ***'); writeln(output); writeln (output' ************************************>y Writeln (output,' * Summary of Input File *'); writeln (output' ************************************iy writeln(output,'CONCRETE ** fcprime = ',fcprime:5:1,' MPa'); APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 149 writeln(output,'STEEL ** Es = Esteel:5:l,' MPa \'fy = ',fy:5:l,' MPa'); writeln(output,'PRESTRESSrNG ** Ep = Ep:5:l,' MPa ','fpu - ',fpu:5:l,' MPa'); writeln(output); count 1 := 1; writeln(output,'Number of Layers = ',nlayers); writeln(output); writeln(output,'LAYER MAT# MATERIAL AREA [mmA2] YDATUM [mm] INITIAL MLLLISTRAIN'); WHILE count 1 <= nlayers DO BEGIN writ e(output,", count 1:3,' ',mattype[countl],' '); LF mattype[countl] = 0 THEN writeln(output,'[NO TS] CONCRETE '.Area[countl]:ll:l,datum[countl]:ll:l) ELSE IF mattype[countl] = 1 THEN writeln(output,'[TS] CONCRETE ',Area[countl]: 11:l,datum[countl]: 11:1) ELSE IF mattype[countl] = 2 THEN writeln(output,'STEEL ',Area[countl]: 11:1, datum [countl]: 11:1) ELSE IF mattype[countl] = 3 THEN BEGIN write(output, 'PRE STRE S SING ', Area[count 1 ]: 11:1 ,datum[count 1 ]: 11:1); writeln(output,' ',microepinitial[countl]: 11:1); END; countl := countl + 1; END; writeln(output,'** SPECIFIED AXIAL LOAD TOLERANCE = ',kntol:4:6,' kN'); write (output '***********************************^ writeln (output END; PROCEDURE Formom; BEGIN sumcalcforce := 0; bend := 0; countl := 1; WHILE countl <= nlayers DO BEGIN strain[countl] := strn - datum[countl]*phi; IF (mattype[countl] = 0) OR (mattype[countl] = 1) THEN concstress ELSE IF mattype[countl] = 2 THEN steelstress ELSE IF mattypejcountl] = 3 THEN prestress; sumcalcforce := sumcalcforce+calcforce[countl]; bend := calcforce[countl]*datum[countl]+bend; countl := count 1+1; END; END; APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS PROCEDURE thirty; BEGIN nn:=nn+l; IF nn > maxnn THEN BEGIN writelnC****** NO SOLUTION FOUND *****3'); BEND := 0.0; STRN := 0.0; Cl := 1; END END; PROCEDURE Iter; BEGIN C l := 0; dstrn := 0.00005; {set strain increment} maxnn := 250; {maximum iterations} tol := abs(tol); IF tol <= le-10 THEN {make sure tolerance is not zero} BEGIN Writeln('specified tolerance too small'); C l := 1; END; nn := 0; END; PROCEDURE Bound; {first try to bound the solution} BEGIN C1:=0; nn:=nn+l; IF nn >= maxnn THEN BEGIN WritelnC******* NO SOLUTION FOUND ********* i'); BEND := 0.0; STRN := 0.0; C l ~1 ; END; LF Cl o 1 THEN BEGIN FORMOM; PDIF := DIF; DIF := FORCE-sumcalcFORce; IF abs(dif) <= tol THEN {check tolerance just in case} C l := 1; APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS END; IF C l <> 1 THEN BEGIN IF sumcalcforce <= Force THEN (decide on direction to increment strain} kk:= 1 ELSE kk :=-l; IF nn = 1 THEN {if first iteration step} BEGIN Pstrn := strn; strn := strn+kk*dstrn; bound; END; END; IF Cl <> 1 THEN BEGIN IF (pdiPdif) < 0 THEN {twenty the solution is now bounded} BEGIN xl := pstrn; x2 := strn; fl := pdif; f2 := dif; END ELSE IF (pdif*dif) = 0 THEN {twentyone} BEGIN writelnC****** NO SOLUTION FOUND *****2'); BEND := 0.0; STRN := 0.0; Cl := 1; END ELSE IF (pdiPdif) > 0 THEN {twentytwo} BEGIN pstrn := strn; strn := strn+(kk*dstrn); bound; END; END; I F C l o i THEN thirty; LF Cl <> 1 THEN BEGIN {linearly interpolate for a new guess} x3 :=x2-((x2-xl)*f2/(f2-fl)); strn := x3; FORMOM; f3 := force - sumcalcforce; IF abs(£3) < tol THEN APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 152 Cl :=1; IF C l <> 1 THEN BEGIN A3 :=fl*f3; LF fl3 < 0 THEN BEGIN x2 := x3; f2 :=f3; END ELSE BEGIN xl := x3; fl :=f3; END; END; END; IF Cl <> 1 THEN thirty; END; BEGIN {this is the body of the main program} textcolor(lightgray); introduction; inputfile; outputfile; IF abs(tol) > le-10 THEN BEGIN readfile; calcproperties; showinput; gettsoption; WHILE tsoption <> 999 DO BEGIN IF tsoption = 1 THEN writeln(output,'TENSION STIFFENING OPTION IS NOW ** ON **') ELSE writeln(output,'TENSION STIFFENING OPTION IS NOW ** OFF **'); getforce; WHILE KNFORCE <> 999 DO BEGIN writeln(output,'** USER DEFINED AXIAL LOAD = ',KNFORCE:3:l,' kN ***); writeln(output,' CURVATURE [rad/km] MOMENT [kN*m]'); getphi; WHILE KMPHI <> 999 DO BEGIN iter; APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 153 IF Cl <> 1 THEN bound; WRITELNC AFTER ',NN,' ITERATIONS'); WRITELN('ERROR IN FORCE = ',(sumCALCFORCE-FORCE)/1000:5:5,' kN'); writeln('BENDING MOMENT = ',-bend/lE+06:5:l,' kN*m'); writeln(output, phi*le+06:10:2, -bend/le+06:25:l); getphi END; getforce; END; gettsoption; END; writeln; END ELSE writeln('******* SPECIFIED TOLERANCE IS TOO SMALL *******•); textcolor(lightgray); writeln(output,'** END OF OUTPUT FILE **'); close(input); close(output); END. • APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 154 INPUT FILE FOR PLATE IN SPECIMEN .025 118 10 RAMBERG OSGOOD COEFFICIENTS 50 fc 750 200000 fysteel, Esteel 1860 200000 fpu, Eprestressing 15 number of layers 0 65000 -250 0 the remaining lines are one per layer as follows: 0 65000 -150 0 material type, Area, Distance to Centroid, initial MLLLIstrain 0 65000-50 0 0 32500 50 0 material types: 0 32500 75 0 0 = non tension stiffened concrete 0 32500 125 0 1 = tension stiffened concrete 0 32500 175 0 2 = reinforcing steel 0 32500 225 0 3 = prestressing steel 0 32500 275 0 2 935 -262.5 0 2 935 -157.5 0 2 935 -52.5 0 2 935 52.5 0 2 935 157.5 0 2 935 262.5 0 NOTE: layers that are Not prestressed STILL NEED to have initial MILLIstrain = 0 IN OTHER WORDS: DO NOT LEAVE BLANK!!!! APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 155 OUTPUT FILE FOR PLATE IN SPECIMEN START OF OUTPUT FILE *** This Program Determines the Moment in a Beam Column *** *** Given an Axial Load and Curvature *** *** By Mark Steunenberg, UBC Civil Engineering, 1995 *** * Summary of Input File * CONCRETE ** fcprime = 50.0 MPa STEEL ** Es = 200000.0 MPa fy = 750.0 MPa PRESTRESSING ** Ep = 200000.0 MPa fpu = 1860.0 MPa Number of Layers =15 LAYER MAT# MATERIAL AREA [mmA2] YDATUM [mm] INITIAL MILLISTRAIN 1 0 [NO TS] CONCRETE 65000.0 -250.0 2 0 [NO TS] CONCRETE 65000.0 -150.0 3 0 [NO TS] CONCRETE 65000.0 -50.0 4 0 [NO TS] CONCRETE 32500.0 50.0 5 0 [NO TS] CONCRETE 32500.0 75.0 6 0 [NO TS] CONCRETE 32500.0 125.0 7 0 [NO TS] CONCRETE 32500.0 175.0 8 0 [NO TS] CONCRETE 32500.0 225.0 9 0 [NO TS] CONCRETE 32500.0 275.0 10 2 STEEL 935.0 -262.5 11 2 STEEL 935.0 -157.5 12 2 STEEL 935.0 -52.5 13 2 STEEL 935.0 52.5 14 2 STEEL . 935.0 •157.5 . 15 2 STEEL 935.0 262.5 ** SPECIFIED AXIAL LOAD TOLERANCE = 0.100000 kN ***************************************** ** TENSION STIFFENING OPTION IS NOW ** OFF ** ** USER DEFINED AXIAL LOAD = 0.0 kN ** APPENDIX F - SOURCE CODE FOR PROGRAM 'BEND' AND SAMPLE CALCULATIONS 156 CURVATURE [rad/km] MOMENT [kN*m] 0.00 0.0 1.00 81.0 2.00 162.0 3.00 240.0 4.00 320.0 5.00 400.0 6.00 479.9 7.00 559.6 8.00 639.2 9.00 716.8 10.00 761.6 11.00 806.1 12.00 845.1 13.00 867.2 14.00 889.1 15.00 910.7 16.00 932.1 17.00 950.7 18.00 959.8 19.00 968.7 20.00 977.6 21.00 986.2 22.00 991.4 23.00 998.6 24.00 1005.6 25.00 1012.4 26.00 1019.0 27.00 1025.4 28.00 1031.5 29.00 1033.1 30.00 1033.4 TENSION STIFFENING OPTION IS NOW ** OFF ** ** END OF OUTPUT FILE ** 

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