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UBC Theses and Dissertations

Experimental investigations of anchorage capacity of precast concrete bridge barrier for Performance… Ngan, Caroline Lai Yung 2008

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EXPERIMENTAL INVESTIGATIONS OF ANCHORAGE CAPACITY OF PRECAST CONCRETE BRIDGE BARRIER FOR PERFORMANCE LEVEL 2  by  CAROLINE LAI YUNG NGAN B.A.Sc., University of British Columbia, 2006   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  The Faculty of Graduate Studies (Civil Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2008  © Caroline Lai Yung Ngan, 2008    ii Abstract In the last twenty years, the design requirements of bridge barriers have changed with the aim of improving the safety of commuters on the bridge. A majority of precast concrete bridge barriers (PCBB) on highway bridges in British Columbia were designed and installed in accordance with the 1988 Canadian Highway Bridge Design Code (CHBDC).  To ensure that these barriers comply with the current code requirements, research and testing were deemed obligatory.  In particular, the anchorage capacity of the parapet under the CHBDC design load warrants verification.  A finite element model of the barrier was developed in ANSYS to study its structural response. Static testing of a set of barriers was carried out at the University of British Columbia to better understand the behaviour of the barrier.  The experimental results were used to calibrate and verify the finite element model.  Through the finite element model and experimental results, a simpler model has been developed in a formatted spreadsheet environment to allow better estimates of the anchorage capacity of different barrier designs. The model was scaled to a wider use for practicing engineers so to ease and improve the design of anchorages of precast concrete bridge barrier under Performance Level 2 loading in accordance with the Canadian Highway Bridge Design Code.    iii Table of Content Abstract ........................................................................................................................................... ii Table of Content ............................................................................................................................ iii List of Tables .................................................................................................................................. v List of Figures ................................................................................................................................ vi Acknowledgements...................................................................................................................... viii 1 Objective ................................................................................................................................. 1 1.1 Phase I............................................................................................................................. 1 1.2 Phase II............................................................................................................................ 2 2 Introduction............................................................................................................................. 3 3 Literature review and research................................................................................................ 5 3.1 Applicable codes............................................................................................................. 5 3.2 Review of CHBDC ......................................................................................................... 5 3.3 Traffic barrier requirement in CHBDC........................................................................... 6 3.3.1 Performance level ................................................................................................... 6 3.3.2 Crash test requirement ............................................................................................ 8 3.3.3 Anchorages ............................................................................................................. 9 3.4 Barrier testing in the United States ............................................................................... 10 4 Determination of barrier behaviour using finite element methods ....................................... 12 5 Capacity estimates using formatted spreadsheet................................................................... 16 5.1 Optimum performance level ......................................................................................... 16 5.1.1 Reference tables .................................................................................................... 16 5.1.2 Optimum performance level calculation............................................................... 20 5.2 Barrier capacity............................................................................................................. 22 5.2.1 Fundamentals and assumption .............................................................................. 22 5.2.2 Barrier capacity calculation .................................................................................. 27 6 Experimental testing ............................................................................................................. 32 6.1 Test specimen and experimental setup ......................................................................... 32 6.2 Loading requirements ................................................................................................... 35 6.3 Loading apparatus......................................................................................................... 36 6.4 Sensor arrangement....................................................................................................... 37 6.5 Projected failure modes................................................................................................. 40 7 Test results ............................................................................................................................ 41 7.1 Observations during test #1 .......................................................................................... 41 7.2 Observations during test #2 .......................................................................................... 47 7.3 Observations during test #3 .......................................................................................... 48 7.4 Acquired data ................................................................................................................ 51 7.5 Discussion of test results............................................................................................... 56    iv 8 Correlation with spreadsheet calculations ............................................................................ 58 9 Conclusions........................................................................................................................... 59 References..................................................................................................................................... 61 Appendix A – Stiffener design ..................................................................................................... 62 Appendix B – Design program ..................................................................................................... 65      v List of Tables Table 1 – Traffic barrier loads, from Figure 3.8.8.1, CAN/CSA-S6-06........................................10 Table 2 – Loads on traffic barriers (CHBDC Table 3.8.8.1) .........................................................16 Table 3 – Highway Type Factor, Kh, table (CHBDC Table 12.1).................................................17 Table 4 – Highway Curvature Factor, Kc (CHBDC Table 12.2) ...................................................17 Table 5 – Highway Grade Factor, Kg (CHBDC Table 12.3) .........................................................18 Table 6 – Superstructure Height Factor, Ks (CHBDC Table 12.4) ...............................................18 Table 7 – Optimum performance levels – Barrier clearance less than or equal to 2.25 m (CHBDC Table 12.5) .....................................................................................................................19 Table 8 – Optimum performance levels – Barrier clearance greater than 2.25 m and less than or equal to 3.75 m  (CHBDC Table 12.6) ..........................................................................................19 Table 9 – Optimum performance levels – Barrier clearance greater than 3.75 m (CHBDC Table 12.7) ...............................................................................................................................................20 Table 10 – Barrier capacity estimated from estimated yield lines.................................................31 Table 11 – Physical parameters of test set up ................................................................................33 Table 12 – Application of Forces in accordance with CHBDC.....................................................35 Table 13 – Summary of Results.....................................................................................................56      vi List of Figures Figure 1 – Application of design loads to traffic barriers, from CAN/CSA-S6-06 Figure 12.5.2.49 Figure 2 – Isometric view of the PCBB with fixed support along edge and anchor location .......12 Figure 3 – Isometric view of the stress distribution of the PCBB when it is loaded in the end (top) and loaded in the middle (bottom). .......................................................................................13 Figure 4 – Contour of x-component of displacement of PCBB (horizontal displacement)...........14 Figure 5 – Contour of y-component of displacement of (vertical displacement) ..........................14 Figure 6 – Contour of displacement vector sum of the PCBB ......................................................15 Figure 7 – Screen capture of design program ................................................................................22 Figure 8 – Assumed yield line pattern for interior (left figure) and end (right figure) of barrier..23 Figure 9 – Original and deformed positions of the top of the barrier wall ....................................24 Figure 10 – Plastic hinge mechanism for top beam.......................................................................25 Figure 11 – Internal work by barrier wall ......................................................................................26 Figure 12 – Flexural resistance of concrete barrier .......................................................................28 Figure 13 – Screen capture of barrier capacity calculation in design spreadsheet ........................30 Figure 14 – Drawing of precast concrete bridge barrier as provided by Rapid-Span Precast Ltd.32 Figure 15 – Precast Concrete Bridge Barrier provide by Rapid-Span Precast Ltd........................32 Figure 16 – Schematic of experimental setup................................................................................34 Figure 17 – Anchor bolt detail .......................................................................................................34 Figure 18 – Loads and location in isometric view.........................................................................36 Figure 19 – Schematic of the setup of the transverse loading system with the hydraulic ram, elevation view ................................................................................................................................37 Figure 20 – Locations of LVDTs for test #1 (transverse load applied at the right end of the barrier)............................................................................................................................................38 Figure 21 – Locations of LVDTs for test #2 (transverse load applied at the left end of the barrier)38 Figure 22 – Locations of LVDTs for test #3 (the transverse load applied at the center of the barrier)............................................................................................................................................38 Figure 23 – Setup of the transverse load system for test #1 ..........................................................39 Figure 24 – Setup of the transverse load system for test #2 ..........................................................39 Figure 25 – Setup of the transverse load system for test #3 ..........................................................40 Figure 26 – First crack at anchor #3  (not marked but visible as diagonally fine line from top of the block-out to lower right hand) .................................................................................................42 Figure 27 – Crack developed at the back of the barrier .................................................................42 Figure 28 – Cracks as developed at about 45 degrees to longitudinal axis ...................................43 Figure 29 – Barrier at final failure .................................................................................................44 Figure 30 – Close up of the failed barrier at anchor #2 .................................................................44 Figure 31 – Failure of anchor #1 of the barrier..............................................................................45 Figure 32 – Side view of the base of the failed barrier..................................................................45    vii Figure 33 – Full side view of the base of the failed barrier ...........................................................46 Figure 34 – Torsional failure of the barrier looking from the back ...............................................46 Figure 35 – Diagonal cracks developed during test #2..................................................................47 Figure 36 – Failure of barrier by anchor pull out...........................................................................47 Figure 37 – View of modified load beam (schematic and photo of split load beam)....................48 Figure 38 – First crack developed during test #3 on rear side of barrier .......................................49 Figure 39 – Diagonal cracks initiated by anchor block-outs, right of the center...........................49 Figure 40 – Diagonal cracks initiated by anchor block-outs, left of the center .............................50 Figure 41 – Cracks at the back of the barrier.................................................................................50 Figure 42 – Displacement vs. loading for LVDT1, LVDT2, LVDT4 and LVDT6 for test #1 .....51 Figure 43 – Displacement vs. loading for jack, LVDT 3, LVDT 5 for test #1..............................52 Figure 44 – Plots of Displacement vs. Force for LVDT1, LVDT2, LVDT4 and LVDT6 for TEST #2....................................................................................................................................................53 Figure 45 – Displacement vs. force for LVDT3, LVDT5 and hydraulic jack for test #2..............53 Figure 46 – Displacement vs. force for LVDT 1, LVDT 3, LVDT 5, and hydraulic jack for test #3, raw data....................................................................................................................................54 Figure 47 – Displacement vs. force for LVDT 2, LVDT 4, LVDT 6 for test #3, raw data...........54 Figure 48 – Displacement vs. force for LVDT 1, LVDT 3, LVDT 3, and Jack for test #3, smoothened ....................................................................................................................................55 Figure 49 – Displacement vs. force for LVDT 2, LVDT 4, LVDT 6 for test #3, smoothened .....55     viii Acknowledgements I would like to express my sincere gratitude to my research supervisor, Prof. Dr.-Ing. S.F. Stiemer at the University of British Columbia, for his guidance and wisdom throughout the study period.  I wish to extend my thanks to the Civil Engineering Department at UBC, especially the solid contribution of our technicians who made the experimental investigation a full success.  In particular, Doug Smith, John Wong, and Felix Yao need to be mentioned.  I would also like to gratefully acknowledge the industrial contribution from Rapid Span and Empire Dynamic Structures.  The donation of the test specimen by Rapid Span and the expert advice by Paul King, Engineering Manager, are gratefully acknowledged.  David Halliday, Vice- President of Empire Dynamic Structures, provided us with the steel base for our test setup that enabled us to keep in the limits of our budget and time constraint. Lorna Longmuir, shipping and receiving from the same company, helped us in matters of transportation of the test specimen from Armstrong and the steel base from Port Coquitlam.  Kevin Baskin, Bridge Engineer at the Ministry of Transportation of British Columbia, guided us in all matters of the experimental investigations with his extensive expertise and most valuable advice.  A number of undergraduate and graduate students worked in a team on this project: Bo Jin, Franklin Wang, Ghazale Heydari, Pranita Singh, Rozita Kohan, Victor Ke, and Yi Gao.  I want to thank them for all their help and contribution.   1 1 OBJECTIVE The objective of the research and testing resulting in this report is as follows: Research and testing of the precast concrete bridge barriers (PCBB) shall result in developing and testing anchorages that meet the requirements for Performance Level 2 barrier systems as given by the current Canadian Highway Bridge Design Code (CHBDC). 1.1 Phase I The first phase of the project consisted of literature review of the applicable codes for the design of PCBB, the precursor to the codes, and the comparison of common barriers and superstructures with other jurisdictions.  This was completed and reported by K. Bleitgen and S.F. Stiemer in “Developing and Testing of Precast Concrete Bridge Barrier Anchorages to meet the requirements for PL-2 Barrier Systems of the Canadian Highway Bridge Design Code” (2006). The report included: 1. Review Canadian Highway Bridge Design Code (CHBDC) requirements for PCBB 2. Literature review of background to CHBDC requirements for bridge barriers and other information available regarding PCBB and barrier testing 3. Review the effect of inter-connection between adjacent precast concrete barriers 4. Compare British Columbia Ministry of Transportation (BC MoT) anchorage details for PCBB to details used by other jurisdictions/suppliers 5. Review the effect of bridge type on anchorage capacity: a. Barrier anchored to concrete slab b. Barrier anchored to box girder flange 6. Carry out site visits to existing bridges to examine the MoT precast concrete bolt down barrier system in service 7. Carry out site visits to fabrication plants where the PCBB are fabricated and liaise with the fabricators regarding fabrication issues     2 1.2 Phase II The second phase of the research project consists of the development of design program to predict barrier capacities as well as the testing of a set of PCBB as calibration tool for the design program.  The scope of the second phase includes: 1. Experimental testing of a set of PCBBs under static loading 2. Develop a design program to predict the barrier capacities according to the CHBDC requirements.  Two programming environment explored are: a. FEM (ANSYS) analysis based on first principles b. Formatted spreadsheet (EXCEL) based on yield lines 3. Correlate test results with analysis 4. Calibrate design program for use in the engineering community This report describes the design program developed and the static load test done at the University of British Columbia.      3 2 INTRODUCTION The purpose of a concrete barrier is to redirect vehicle in a controlled manner in the event of a collision. The vehicle shall not over turn or rebound across traffic lanes. The barrier shall have sufficient strength to survive the initial impact of the collision and to remain effective in redirecting the vehicle.  To meet the design criteria, the barrier must satisfy both geometric and strength requirements. The geometric conditions will influence the redirection of the vehicle and whether it will be controlled or not. This control must be provided for the complete mix of traffic from the largest trucks to the smallest automobiles. Geometric shapes and profiles of barriers that can control collisions have been developed over the years and have been proven by crash testing. Any variation from the proven geometry may involve risk and is not recommended. Barrier design provisions established in codes are constantly updated in order to improve the performance of barriers to help restrain errant vehicles from leaving the roadway or pedestrians from leaving the sidewalk. Considerable amounts of research and development of new structural systems are being carried out. However, there are still many barrier design requirements that remain challenging. The majority of precast concrete bridge barriers (PCBB) on BC highway bridges were designed in accordance with the Canadian Highway Bridge Design Code (CHBDC) from 1988 (K. Bleitgen and S.F. Stiemer, 2005).  Due to the continual updates in design provisions aiming to improve the safety of commuters on the bridge, the basics of the barrier design requirements have changed dramatically from the 1988 code to the present 2006 code.  To ensure that current barriers on BC highway bridges comply with the current code requirements, research and testing were deemed obligatory.  In particular, the anchorage capacity of the PCBB under specified CHBDC design loads necessitates verification. The objectives of the project are to verify that current precast concrete bridge barriers (PCBB) on BC highway bridges comply with the 2006 Canadian Highway Bridge Design Code (CHBDC) under Performance Level 2 loading, and to develop a relatively easy to use model for designing the anchorage of PCBB.  Two proposed approaches to problem solution are to use Finite Element Analysis program (ANSYS) based on first principles and formatted spreadsheets   4 (EXCEL) based on yield lines.  As a calibration tool for the FE model as well as to gain understanding of the failure mechanism of the barrier, a series of static load testing of the barriers were performed.    5 3 LITERATURE REVIEW AND RESEARCH 3.1 Applicable codes In Canada, the national code that provides provision in the design, evaluation, and structural rehabilitation design of fixed and movable highway bridges is the Canadian Highway Bridge Design Code (CHBDC) CAN/CSA-S6-06 prepared by the Canadian Standards Association (CSA). In section 12 of the CHBDC, the requirement for the design of bridge barriers is outlined. In addition, each province or territory may have supplementary specifications and standards establishing detailed requirements, consistent with current nationwide practices, which apply to common highway bridges.  In British Columbia, BC Ministry of Transportation (BC MoT) published the “Standard Specifications for Highway Construction” and “Design Standards, Bridge Standards and Procedures” to provide further provisions governing the design of highway bridge components in the province. Besides the national and provincial codes, there are also references made to relevant literature from other jurisdictions.  For instance, concerning crash test requirements, the Canadian Highway Bridge Design Code refers to the American Association of State Highway and Transportation Officials (AASHTO)’s Guide Specifications of Bridge Railings.  This guide made further reference to the National Cooperative Highway Research Program (NCHRP), Report 350: Recommended Procedures for the Safety Performance Evaluation of Highway Features. 3.2 Review of CHBDC The Canadian Highway Bridge Design Code CAN/CSA-S-06 is prepared by the Canadian Standards Association (CSA) for highway bridge design in Canada and the latest version was published in 2006.  The requirements for the design of barriers are specified in Section 12. Barriers are divided into four different types based on their function: • Traffic barrier, • Pedestrian barrier, • Bicycle barrier, and • Combination barrier.   6 In the appraisal of a barrier, there exist general factors beyond the basic strength requirements. These factors are durability, ease of repair, snow accumulation on and snow removal from deck, visibility through or over barrier, deck drainage, future wearing surfaces, and aesthetics. Damaged barriers need to be repaired quickly with minimal disruption to traffic. Traffic barriers should be designed with features such as anchorages that are unlikely to be damaged or cause damage to the bridge deck during an accident and modular construction using prefabricated sections that allow damaged sections to be repaired quickly. 3.3 Traffic barrier requirement in CHBDC Of concern to this project is traffic type barrier.  Traffic barriers are to be provided on both sides of highway bridges to delineate the superstructure edge and thus reducing the consequences of vehicles leaving the roadway upon the occurrence of an accident (CAN/CSA-S6-06).  Crash tests are used to determine barrier adequacy in reducing the consequences of vehicles leaving the roadway.  The adequacy of a traffic barrier in reducing the consequences of a vehicle leaving the roadway is based on the level of protection provided to the occupants of the vehicle, to other vehicles on the roadway and to people and property beneath the bridge. This protection is provided by various ways:  by retaining the vehicle and its cargo on the bridge, by smoothly redirecting the vehicle away from the barrier, and by limiting the rebound of the vehicle back into traffic. 3.3.1 Performance level The requirement for traffic barrier is dependent on the site as well as on the expected frequency and consequences of vehicle accidents at the site.  This procedure assumes that the frequencies and consequences of vehicle accidents at bridge sites are a function of the percentage of trucks, design speed, highway type, curvatures, grades, and superstructure height. The ranking system used in CHBDC to determine the bridge site condition is categorized into three levels: Performance Level 1 (PL-1): The performance level for traffic barriers on bridges where the expected frequency and consequences of vehicles leaving the roadway are similar to that expected on low traffic volume roads.   7 Performance Level 2 (PL-2): The performance level for traffic barriers on bridges where the expected frequency and consequences of vehicles leaving the roadway are similar to that expected on high to moderate traffic volume highways. Performance Level 3 (PL-3): The performance level for traffic barriers on bridges where the expected frequency and consequences of vehicles leaving the roadway are similar to that expected on high traffic volume highways with high percentage of trucks. The optimum performance levels for a site is determined based on the Barrier Exposure Index (Be), percentage of trucks, design speed, and barrier clearance.  The barrier exposure index is defined as: Be = (AADT1) Kh Kc Kg Ks /1000 where: AADT1 ≤ 10,000 vehicles per day per traffic lane per vehicle speeds 80km/h or greater Kh = highway type factor, see CHBDC CAN/CSA-S6-06, Table 12.5.2.1.2 (a) Kc = highway curvature factor, see CHBDC CAN/CSA-S6-06, Table 12.5.2.1.2 (b) Kg = highway grade factor, see CHBDC CAN/CSA-S6-06, Table 12.5.2.1.2 (c) Ks = superstructure height factor, see CHBDC CAN/CSA-S6-06, Table 12.5.2.1.2 (d) With the design speed, the percentage of trucks, and the barrier exposure index, the performance level can be determined from reading the corresponding values in the tables given in CHBDC CAN/CSA-S6-06 Section 12.5.2.1.3. There are three different tables to cover various barrier clearances: • Table 12.5.2.1.3 (a) for Barrier Clearance ≤ 2.25m • Table 12.5.2.1.3 (b) for 2.25m < Barrier Clearance ≤ 3.75m • Table 12.5.2.1.3 (c) for Barrier Clearance > 3.75m Based on the performance level (PL), the CHBDC specifies the longitudinal, transverse, and vertical load a barrier satisfying this PL would need to withstand.  There is also a minimum barrier height requirement based on the PL and can be determined using Table 12.5.2.2. The   8 minimum barrier heights for PL 1, 2, and 3 traffic barriers are 0.68 m, 0.80 m, and 1.05 m respectively. Traffic barrier height requirements are intended to prevent impacting vehicles from vaulting or rolling over a barrier. The higher the center of gravity of the impacting vehicle, the greater the required traffic barrier height is needed to contain it. Alternative performance levels, as mentioned in Section 12.5.2.1.1 in CHBDC CAN/CSA-S6-06, have to be approved by the Regularity Authority for the bridge and defined by specifying their crash test requirements. These levels shall be considered along with Performance Level 1, 2, or 3 when determining the optimum performance level. The optimal level of traffic barrier performance at a bridge site is assumed to be the level giving the least costs, where costs include the cost of supplying and maintaining a traffic barrier and the cost of accidents expected with the use of the traffic barrier.  The assumed accident rates, accident severities, and traffic barrier costs used by a computer-based Benefit-Cost Analysis Program (BCAP) in determining optimal levels of traffic barrier performance, as well as the engineering judgment used to adjust these optimal levels for use in the codes are outlined in AASHTO (1989). 3.3.2 Crash test requirement In Section 12.5.2.3 of the CHBDC, it is specified that, with the defined performance level, the crash test requirements should be in accordance with the crash test requirements of AASHTO Guide Specifications for Bridge Railing. Those crash test requirements shall be satisfied along the entire length of a traffic barrier, including at any changes in barrier type, shape, alignment, or strength that may affect the barrier performance. Alternative performance levels shall meet the crash test requirements of the optimum performance level or of a more severe performance level as considered. The specifics of the crash test are outlined in the National Cooperative Highway Research Program (NCHRP) Report 350: Recommended Procedures for the Safety Performance Evaluation of Highway Features.  The crash test requirements for barrier Test Levels 2, 4, and 5 of NCHRP Report 350 shall be taken as meeting the crash test requirements for Performance Level 1, 2, and 3 respectively.   9 According to Section 12.5.2.3.4 in CHBDC, any changes in details affecting the geometry, strength, or behaviour of the traffic barrier or traffic barrier transition that meets the aforementioned requirements can be demonstrated to not adversely affect barrier-vehicle interaction. 3.3.3 Anchorages The performance of the traffic barrier anchorage during crash testing is the basis for its capability. The anchorage is considered to be acceptable if no significant damage occurs in the anchorage or deck during crash testing. If crash test results for the anchorages are not available, the anchorage and deck shall be designed to resist the maximum bending, shear and punching loads that can be transmitted to them by the traffic barrier. The loads should be applied as in Figure 1.  Figure 1 – Application of design loads to traffic barriers, from CAN/CSA-S6-06 Figure 12.5.2.4    10 However, the loads have to be greater than those resulting from the loads defined in Section 3.8.8 of the CHBDC (Barrier Loads). The transverse, longitudinal, and vertical loads should be applied simultaneously and are specified as shown in Table 1. Table 1 – Traffic barrier loads, from Figure 3.8.8.1, CAN/CSA-S6-06  3.4 Barrier testing in the United States Previously, many jurisdictions have performed tests on concrete road barriers. The Center for Transportation Research (CTR) at the University of Texas at Austin, sponsored by Texas Transportation Institute (TTI), performed the pendulum test and equivalent static test for the T203 and T501 barriers with mechanical anchors.  It has been reported in the “Design of Retrofit Vehicular Barriers Using Mechanical Anchors” (FHWA/TX-07/0-4823-1).  TTI also performed both crash test and static test with full-scale Jersey safety shaped barrier, as documented in “Testing and Evaluation of The Florida Jersey Safety Shaped Bridge Rail” (FHWA/TX-04/9- 9132-1). A series of three crash tests complying with NCHRP Report 350 Test Level 4 were performed followed by a series of static testing.  The three tested locations of the barrier are right end, middle, and left end (with neighbour barrier). The estimated capacities from the yield line analysis are 185 kN at the end and 276 kN in the middle.  The maximum loads resulting from the three tests were 201 kN, 156 kN, and 325 kN for the left end, right end, and centre, respectively.  The deflection in all cases ranges from 9 to 12.7 mm.  For the CTR research for T203 and T501 with mechanical anchors, each type of barrier was tested dynamically and statically.  The T203 barrier exhibited a dynamic capacity of 271 kN and a static capacity of 267 kN.  For the T501 barrier, the dynamic capacity is 287 kN and the static capacity is 258 kN. It can be concluded from the test results that the static analysis using yield line theory provides good estimates of failure loads. Dynamic crash testing may not be necessary in the future for certifying the actual barrier capacities. In addition, dynamic effects such as strain rates do not   11 play a role in the relatively slow loading of the barrier. A concrete barrier does not require large displacements to achieve its maximum capacity; therefore inertia effects are not critical. The static testing is a more accurate and reproducible way of assessing barrier behaviour and ultimate capacity. In addition, knowledge gained by these tests is easily implemented into the design experience. It allows for separating the highly variable effects of the crash object from the real barrier capacity.   12 4 DETERMINATION OF BARRIER BEHAVIOUR USING FINITE ELEMENT METHODS To better understand the behaviour of the precast concrete bridge barrier (PCBB) under service load, a finite element model was created using ANSYS. This software is a general purpose finite element modeling package for numerically solving a wide variety of mechanical problems including static and dynamic structural analysis (both linear and non-linear). The PCBB to be tested was modeled in its entirety using SOLID95 elements. SOLID95 is a 3-D 20-Node structural solid having three degrees of freedom (DOF) per node. The isometric view of the model with the meshed elements is shown in Figure 2.  Figure 2 – Isometric view of the PCBB with fixed support along edge and anchor location  The length of the barrier is 5792 mm with 7 anchors spaced at approximately 865 mm. The barrier had fixed support along the back edge and at each anchor location. A total force of 100kN is distributed across 1050mm (as specified in CHBDC for Performance Level 2 Traffic Barrier) at 765 mm above the base. Since the location along the barrier to apply the force has not been specified in the code, two cases were considered: loading in the end, and loading in the middle of the barrier.  A static analysis was performed on the model and the resulting equivalent stress   13 distribution contours for the two cases are shown in Figure 3.  Stress concentrations occurred as expected in the vicinity of the anchorages.   Figure 3 – Isometric view of the stress distribution of the PCBB when it is loaded in the end (top) and loaded in the middle (bottom). As shown in Figure 3, the maximum stress (SEQV) and deflection (DMX) are higher when the load is applied to the end of the barrier compared to when the load is applied in the middle of the barrier.  This indicates that loading at the end of the barrier will result in the worst case scenario.   14 The deflection of the barrier in x-, y-direction and displacement vector sum is presented in Figure 4, Figure 5, and Figure 6 for the case when load is applied at the end.  Figure 4 – Contour of x-component of displacement of PCBB (horizontal displacement)   Figure 5 – Contour of y-component of displacement of (vertical displacement)    15  Figure 6 – Contour of displacement vector sum of the PCBB As can be seen from the contour plots, when the barrier was loaded at one end, there were minimal deflection and stresses at the other end of the barrier. Also, the maximum displacement should occur at the corner of application of load.   16 5 CAPACITY ESTIMATES USING FORMATTED SPREADSHEET A design program was developed to identify the design loads and compute the capacity of the barrier following the methods from the American Association of State Highway and Transportation Officials (AASHTO) Bridge Design Specifications using yield lines.  The program is implemented in Microsoft Excel using macros developed to create a formatted spreadsheet (previously developed by Dr. S.F. Stiemer and former graduate students).  This section outlines the basis for the formulation of the two major calculations (performance level and barrier capacity) in the spreadsheet. 5.1 Optimum performance level 5.1.1 Reference tables The goal of the interactive spreadsheet is to allow for calculation of barrier requirement and capacity without re-visiting all the various codes. In order to facilitate this, the applicable tables from the Canadian Highway Bridge Design Code are incorporated into the spreadsheet as references. The tables included are: • Loads on traffic barriers (Table 3.8.8.1 CHBDC) • Highway Type Factors, Kh (Table 12.1 CHBDC) • Highway Curvature Factors, Kc (Table 12.2 CHBDC) • Highway Grade Factors, Kg (Table 12.3 CHBDC) • Superstructure Height Factors, Ks (Table 12.4 CHBDC) • Optimum performance levels (Table 12.5 – 12.7 CHBDC) The following shows the screen capture of the tables created in the design program as reference. Table 2 – Loads on traffic barriers (CHBDC Table 3.8.8.1)    17  Table 3 – Highway Type Factor, Kh, table (CHBDC Table 12.1)                  Table 4 – Highway Curvature Factor, Kc (CHBDC Table 12.2)         18 Table 5 – Highway Grade Factor, Kg (CHBDC Table 12.3)         Table 6 – Superstructure Height Factor, Ks (CHBDC Table 12.4)    19 Table 7 – Optimum performance levels – Barrier clearance less than or equal to 2.25 m  (CHBDC Table 12.5)  Table 8 – Optimum performance levels – Barrier clearance greater than 2.25 m and less than or equal to 3.75 m  (CHBDC Table 12.6)       20  Table 9 – Optimum performance levels – Barrier clearance greater than 3.75 m (CHBDC Table 12.7)  5.1.2 Optimum performance level calculation The strength requirements for barriers depend on the conditions of the highway. For given traffic conditions, performance level for the barrier can be selected and the requirement of the barrier satisfying that level defined. The first section of the spreadsheet calculates the required performance level and barrier collision force given user inputs such as: • Average Annual Daily Traffic for the first year after construction • Design Speed • Highway Type • Radius of Curve • Position of Barrier (inside/outside of curve)   21 • Highway Grade • Superstructure Height Above Ground or Water Surface • Usage of Land (High/low occupancy) • Water Depth beneath bridge (deep/shallow) • Truck Percentage, and • Barrier Clearance. According to the CHBDC, the optimum performance level can be found in Table 12.5 – 12.7 knowing the exposure index (Be), percentage of trucks, design speed, and barrier clearance. The percentage of trucks, design speed, and barrier clearance are user input values whereas the barrier exposure index is calculated as: [1] Be = (AADT1) Kh Kc Kg Ks / 1000 where AADT1 =  Average Annual Daily Traffic for the first year after construction Kh  =  Highway Type Factors (Table 12.1 CHBDC) Kc  =  Highway Curvature Factors (Table 12.2 CHBDC) Kg  =  Highway Grade Factors (Table 12.3 CHBDC) Ks  =  Superstructure Height Factors (Table 12.4 CHDBC) All the applicable tables are incorporated into the spreadsheet.  The programme utilizes the “look-up” function to obtain values for the Kh, Kc, Kg, Ks factors from the reference tables listed in Section 5.1.1 based on user input for the bridge site conditions. The highway type factor, Kh, depends on the type of highway (one/two way, divided/undivided) and the design speed.  It ranges from 1.00 to 2.00.  The highway curvature factor, Kc depends on the radius of curvature (<= 300m to >= 600 m) and whether the barrier is on the outside or inside of the curve.  It has values from 1.00 to 4.00.  The highway grade factor, Kg, depends on the grade (>= -2 to <= -6) and has values ranging from 1.00 to 2.00.  The superstructure height factor, Ks, is a function of   22 the superstructure height above ground or water surface and whether it is high or low occupant land use.  It ranges from 0.7 to 2.85. After all the factors are extracted and the exposure index calculated, the resulting performance level will be determined, along with the collision force requirement on the traffic barrier.  These results are also shown graphically at the top left corner of the spreadsheet (see Figure 7).  Figure 7 – Screen capture of design program 5.2 Barrier capacity 5.2.1 Fundamentals and assumption The capacity of the precast concrete bridge barrier is estimated based on the formation of yield lines at limit state.  The yield-line method is a procedure where the slab is assumed to behave inelastically and exhibits adequate ductility to sustain the applied load until the slab reaches a plastic collapse mechanism.  This assumption is realistic because the reinforcement proportionality required by AASHTO results in an under-reinforced ductile system.  The slab is assumed to collapse at a certain ultimate load through a system of plastic hinges called yield lines.  The yield lines form a pattern in the slab creating the mechanism.  The ultimate load can Calculation for performance level User input for bridge condition Display diagram for the performance level in question and barrier design parameters definitions   23 be determined by using the equilibrium approach or the energy approach.  The energy approach is an upper-bound approach, which means that the ultimate load established with the method is either equal to or greater than the actual.  The fundamentals and the primary assumptions of the yield line theory are as follows (Ghali and Neville, 1989): • In the mechanism, the bending moment per unit length along all yield lines is constant and equal to the moment capacity of the section. • The slab parts (area between yield lines) rotate as rigid bodies along the supported edges. • The elastic deformations are considered small relative to the deformation occurring in the yield lines. • The yield lines on the sides of two adjacent slab parts pass through the point of intersection of their axes of rotation. The lateral load carrying capacity of a uniform thickness solid concrete barrier was analyzed by Hirsh (1978).  The expressions developed for the strength of the barrier are based on the formation of yield lines at the limit state.  The assumed yield line pattern caused by a truck collision that produces a force, Ft, which is distributed over a length Lt, is shown below.  Figure 8 – Assumed yield line pattern for interior (left figure) and end (right figure) of barrier For an assumed yield line pattern that is consistent with the geometry and boundary conditions of a wall or slab, a solution is obtained by equating the external work due to the applied loads to the internal work delivered by the resisting plastic moments along the yield lines. The applied load determined by this method is either equal to or greater than the actual load; that is, it is non- conservative.  The angle of the inclined yield lines can be expressed in terms of the critical   24 length Lc.  The applied force Ft is then minimized with respect to Lc to get the least value of this upper bound solution. The original and deformed positions of the top of the wall are shown in Figure 9.  Figure 9 – Original and deformed positions of the top of the barrier wall The shaded area represents the integral of the deformations through which the uniformly distributed load wt = Ft /Lt acts.  For a virtual displacement δ, the displacement x is:  and the shaded area becomes Area = . Thus, the external work W done by wt is: . The internal work along the yield lines is the sum of the products of the yield moments and the rotations through which they act.  The segments of the wall are assumed to be rigid so that all of the rotation is concentrated at the yield lines.  At the top of the wall (as shown in Figure 10), the rotation, θ, of the wall segments for small deformations is:   25 .  Figure 10 – Plastic hinge mechanism for top beam The barrier can be analyzed by separating it into a beam at the top and a uniform thickness wall below.  At the limit state, the top beam will develop plastic moments Mb equal to its nominal bending strength Mn and form a mechanism as shown in Figure 10.  Assuming that the negative and positive plastic moment strengths are equal, the internal work Ub down by the top beam is . The wall portion of the barrier will generally be reinforced with steel in both the horizontal and vertical directions.  The horizontal reinforcement in the wall develops moment resistance Mw per unit length about a vertical axis.  The vertical reinforcement in the wall develops a cantilever moment resistance Mc per unit length about a horizontal axis.  These two components of moment will combine to develop a moment resistance Mα about the inclined yield line as shown in Figure 11.   26  Figure 11 – Internal work by barrier wall If we assume that the positive and negative bending resistance Mw about the vertical axis are equal, and we realize that the projection on the horizontal plane of the rotation about the inclined yield line is θ, the internal work Uw done by the wall moment MwH is: . The projection on the vertical plane of the rotation about the incline yield line is δ/H, and the internal work Uc done by the cantilever moment McLc is: . Given that: ,   27 we can substitute external work and internal work and get: . This expression depends on the critical length Lc that determines the inclination of α of the negative moment yield lines in the wall.  The value for Lc that minimizes Ft can be determined by differentiating equation for Ft with respect to Lc and setting the result equal to zero.  That is, . This minimization results in a quadratic equation that can be solved explicitly to give . When this value of Lc is used in the equation for Ft, we get the minimum transverse force Ft.  The minimum transverse force represents the nominal transverse resistance of the barrier. That is:  where Rw is the nominal railing resistance to transverse load.  By rearranging equation for Ft, we can write: . 5.2.2 Barrier capacity calculation The barrier capacity calculation implemented in the spreadsheet program used the yield line theory as outlined in the previous section.  It includes only the ultimate flexural capacity of the concrete component and is based on the assumptions that:   28 • the yield line failure pattern occurs within the parapet only and does not extend into the deck • sufficient longitudinal length of parapet exists to result in the yield line failure pattern • negative and positive resisting moments in the barrier body are equal The resisting moment along the yield lines is a resultant of the moment resistance about the vertical axis from the longitudinal reinforcement (Mw) and the moment resistance about the horizontal axis from the transverse reinforcement (Mc) as shown in Figure 12.  Figure 12 – Flexural resistance of concrete barrier With some algebraic manipulation based on the principle of virtual work, the critical wall length over which the yield line mechanism occurs, Lc, can be taken as:   within a wall segment. The nominal railing resistance to transverse load, Rw within a wall segment, can be calculated as:   29 .  For end of wall or at joint, the critical wall length is:      with: Ft = transverse force specified by code H = height of wall Lc = critical length of yield line failure pattern Lt = longitudinal length of distribution of impact force Ft Mb = additional flexural resistance of beam in addition to Mw, if any, at top of wall Mc  = flexural resistance of cantilevered walls about an axis parallel to the longitudinal axis of the bridge Mw = flexural resistance of the wall about its vertical axis Rw = total transverse resistance of the railing  To calculate the capacity of the parapet, the program requires the following user inputs: • Moment strength of Beam (if any), • Height of Barrier Body (Wall) • Steel Yield Strength • Concrete Compressive Strength   30 • Horizontal Reinforcement Size • Vertical Reinforcement Size • Effective Concrete Depth to reinforcement • Horizontal Reinforcement Spacing • Vertical Reinforcement Spacing • Resistance Factor for Extreme Event Limit State (=1) The spreadsheet calculates first the moment strength about vertical axis and horizontal axis of the interior region.  These are a function of the longitudinal and transverse reinforcement, respectively.  The capacity of the barrier is then calculated and is compared to the collision force requirement for the site’s performance level and indicates if the barrier design is adequate.  The same procedure is repeated for the end region of the barrier.  Figure 13 is a screen capture of the calculation section for the barrier capacity estimation.  Figure 13 – Screen capture of barrier capacity calculation in design spreadsheet Moment strength about vertical axis (interior and end) Moment strength about horizontal axis (interior) Capacity and check (interior) Moment strength about horizontal axis (end) Capacity and check (end)   31 The calculated values for the barrier to be experimentally tested are summarized in Table 10. Table 10 – Barrier capacity estimated from estimated yield lines  Barrier Capacity Interior Region 531 kN End Region 279 kN   32 6 EXPERIMENTAL TESTING 6.1 Test specimen and experimental setup Two barriers were provided by Rapid-Span Precast Ltd., Armstrong B.C, for static testing. The barriers are designed in accordance with BC Ministry of Transportation specifications.  Figure 14 and Figure 15  are the drawing and photo of the barrier provided by Rapid-Span Precast Ltd.  Figure 14 – Drawing of precast concrete bridge barrier as provided by Rapid-Span Precast Ltd.  Figure 15 – Precast Concrete Bridge Barrier provide by Rapid-Span Precast Ltd.   33 The precast concrete is in accordance with CAN/CSA-A23.1 with minimum compressive strength of 35 MPa at 28 days. The barrier is 5792 mm in length by 910 mm in height. It contains 7 blockouts for the installation of anchor bolts at about 860 mm spacing. At each location of blockout, a HSS 60x4.8, 135mm long bolt sleeve was cast into the concrete. To prevent the bolt sleeve from breaking out in case of maximum loading, the HSS is connected to a WT 155x19.5 steel plate.  The bolt sleeve is to be filled with non-shrink grout of 30MPa after the anchor has been fastened to the bridge deck.  The concrete barrier has even distribution of longitudinal and transverse reinforcement.  There are 6-10M longitudinal bars along the rear face of the barrier and 4-15M bars along the front face of the barrier.  The top portion of the barrier contains 40- 15M vertical reinforcement bars spaced at 136 mm.  The bottom portion of the barrier contains 40-10M vertical reinforcement bars spaced at 136 mm (see Figure 14).  Table 11 summarizes the physical parameters of the specimen. Table 11 – Physical parameters of test set up Parameter Value Barrier Height 910 mm Barrier Length 5792 mm Concrete Strength of Barrier 35 MPa Grout Strength 30 MPa No. of Anchor Bolts 7 Anchor Bolt Diameter 25 mm Anchor Bolt Spacing ~ 860 mm Bolt sleeve used HSS 60x4.8, 135mm long Longitudinal Reinforcement 6 – 10M @ approx. 149mm (rear face) 4 – 15M @ approx 245mm (front face) Transverse Reinforcement Top:       40 – 15M @ approx. 136 mm Bottom: 40 – 10M @ approx. 136 mm  The barrier needed to be fastened to concrete slab floor of the lab to simulate the action of the bridge deck. As the floor slab hold-down grid had different spacing from the barrier anchor bolts, an I-shape steel base beam was designed to act as the connector. A C-channel was stitch-welded to the upper flange of the I-beam to provide a flat support. Transverse stiffeners were also added   34 to both sides of the base beam to improve the torsional resistance of the base (calculations for the design and check of stiffener are attached in the Appendix). A schematic of the setup can be found in Figure 16.    Figure 16 – Schematic of experimental setup Nine 52 mm diameter holes at 900 mm spacing were drilled for securing the steel base onto the floor slab. Seven 25 mm diameter holes coinciding with the barrier anchors were drilled on the upper flange to attach the barrier onto the base. The anchor bolts used comply with CSA Specification CAN3-G40.21-M Grade 400W and the plate washer was of grade 300W. Figure 17 shows a detail of the bolt system. Once the anchor bolt is secured between the barrier and the base, the bolt sleeve in the barrier were filled with non-shrink grout.  Figure 17 – Anchor bolt detail   35 In the field, all steel parts, such as bolts, nuts, and washers, should be galvanized after fabrication, before installation for corrosion protection. This is not necessarily a requirement for the experimental test. 6.2 Loading requirements The goal of this project is to comply with specifications in the CHBDC for barrier design, which is performed in a way of static analysis. The results of barrier testing by TTI showed the static force capacity of a barrier that passed NCHRP Report 350 test designation 4-11 and 4-12. When following TTI’s findings, one must conclude that the static testing is an economical and adequate method for a realistic barrier capacity evaluation. According to the CHBDC, a barrier satisfying Performance Level 2 needs to meet the specified loading requirement summarized in Table 12.  Table 12 – Application of Forces in accordance with CHBDC  Forces Height of Application Spread of Load Transverse Load 100 kN 765 mm from base 1050 mm Vertical Load  30 kN Top of barrier 5500 mm Longitudinal Load 30 kN 765 mm from base 1050 mm  Figure 18 shows a schematic of the transverse, vertical and longitudinal loads.    36  Figure 18 – Loads and location in isometric view The effect of the vertical and longitudinal loads in regard to the failure mode and capacity of the parapet can be deemed to be negligible. Therefore, in the experiment, the barrier will be subjected to a 100 kN transverse load only that is applied uniformly over a length of 1050 mm at 765mm above the base of the barrier. The code states that the transverse load can be applied at any location along the barrier. Based on analysis and common engineering judgement it is apparent that the worst loading case exists when the load is applied at the end of the barrier. This gave us the opportunity to test one of the available specimen twice (at each end, test #1 and test #2) and the second specimen in the centre of the barrier (test #3). 6.3 Loading apparatus The transverse load is applied by a hydraulic ram with integrated load cell attached to a pillar, and distributed longitudinally by a 1050 mm long spreader beam. To ensure that the load is applied evenly onto the sloped face of the barrier, a wedge shaped piece of timber is placed between spreader beam and barrier. This also eliminated any possible local stress concentrations   37 from imperfections of the surfaces in contact. Figure 19 illustrates the transverse load application system schematically.  Figure 19 – Schematic of the setup of the transverse loading system with the hydraulic ram, elevation view 6.4 Sensor arrangement Six linear variable differential transformers (LVDTs) are used to measure the horizontal displacement of the barrier at various locations. For test #1, the locations of measurement were at the top and bottom of the barrier aligned with the first and second anchors at the edge of application of force. Two sensors were placed at the top and bottom at the position of the anchor at the far end. For test #2, the LVDTs were at the top and bottom of the barrier aligning with the first, second, and third anchors at the edge of application of force. For test #3 where the load is applied in the center, the LVDTs were located at the top and bottom of the barrier aligning with the middle three anchors. The following three figures show the schematic of the locations of LVDTs for each test.    38  Figure 20 – Locations of LVDTs for test #1 (transverse load applied at the right end of the barrier).   Figure 21 – Locations of LVDTs for test #2 (transverse load applied at the left end of the barrier)  Figure 22 – Locations of LVDTs for test #3 (the transverse load applied at the center of the barrier) The actual setup of the experiment for each loading case is shown in the following figures.   39  Figure 23 – Setup of the transverse load system for test #1    Figure 24 – Setup of the transverse load system for test #2   40   Figure 25 – Setup of the transverse load system for test #3 6.5 Projected failure modes The possible failure modes of the anchor assembly were identified prior to the testing. A number of limit states were checked numerically: • Tension failure of o Bolt in tension o Concrete breakout (spalling) o Pullout in tension • Shear failure of o Bolt in shear o Concrete block shear breakout In addition, the capacity of the barrier was estimated using yield lines approach as described in the American Association of State Highway and Transportation Officials (AASHTO) Bridge Design Specifications as summarized in Chapter 5.   41 7 TEST RESULTS 7.1 Observations during test #1 The hydraulic ram used to apply the transverse load was displacement controlled, which is a safety measure for test specimen that can fail in a brittle mode. It had a maximum stroke length of +/- 76.2 mm. The barrier was initially loaded at a rate of 3 mm/20 min. The application speed was increased to 15.24 mm/20 min. While the barrier was loaded, the displacement of the load cylinder (jack displacement) and associated force were monitored visually on a screen. This visual inspection permitted easy control of the test situation. Once the gaps between the load cylinder and the barrier were closed the load deflection curves developed as expected. A number of readings of the LVDTs were concurrently monitored. For a while, a linear relationship was observed between load and deformation, indicating elastic deformation of the barrier. The first crack was spotted developing diagonally from anchor #3, counting from the loading end (Figure 26).  This was followed by a crack through anchor #4, and then through anchor #2. Relatively small cracks quickly emerged parallel to each other in between anchors.  There were also diagonal cracks developed on the back side of the barrier through the lifting hole above anchor #2.  Figure 26, Figure 27, and Figure 28 are photo depicting the cracks.  White-wash coat was applied to the barrier for easier spotting of cracks.    42  Figure 26 – First crack at anchor #3 (not marked but visible as diagonally fine line from top of the block-out to lower right hand)  Figure 27 – Crack developed at the back of the barrier (blue marker line is drawn to the right of the actual crack) Anchor #3   43  Figure 28 – Cracks as developed at about 45 degrees to longitudinal axis An elastic relationship between force and displacement was sustained to about 140 kN. Consecutively the displacement increased at a faster rate than the force, indicating some nonlinear, maybe plastic, deformation of the barrier. More cracks appeared. Cracks through anchor #2 and #3 were getting noticeably wide. Finally the barrier reached a maximum load of 250 kN when it had a significant decline in strength. The first mode of failure seemed to be a torsional failure of the barrier. At this time, the maximum displacement at the top right corner of the barrier was about 80 mm. Loading on the barrier continues and the parapet recovered its strength.  It reached a second peak after which it finally broke off almost completely showing a combination of torsional and anchorage breakout (of anchor #2) failure modes. Some pictures of the failed barrier follow.  Anchor #2   44  Figure 29 – Barrier at final failure   Figure 30 – Close up of the failed barrier at anchor #2    45  Figure 31 – Failure of anchor #1 of the barrier   Figure 32 – Side view of the base of the failed barrier   46  Figure 33 – Full side view of the base of the failed barrier   Figure 34 – Torsional failure of the barrier looking from the back   47 7.2 Observations during test #2 The unloaded end (left end) of the barrier was tested in test #2. Similar setup and procedures were used.  The barrier was loaded at a rate of 76.2 mm/20 min. The first crack was spotted at a load of 122 kN which developed diagonally at approximately 45 degrees beneath the third anchor bolt from the loading end. Similar cracks and failure modes were observed for the left end of the barrier (Figure 35 and Figure 36). The peak load reached in test #2 is 293 kN.  Figure 35 – Diagonal cracks developed during test #2   Figure 36 – Failure of barrier by anchor pull out   48 7.3 Observations during test #3 The third test involved transverse loading in the centre of the barrier. In order to simulate the estimated yield line failure mode, the 1050 mm long spreader beam was constructed in two pieces with hinges to allow for rotation when a failure of the barrier would occur as assumed in the code.  Figure 37 shows the schematic and photo of the loading beam set up for test #3.  Figure 37 – View of modified load beam (schematic and photo of split load beam) to accommodate possible crack development in centre  The initial loading rate during this test was 76.2 mm/20 min, similar loading rate as that used in test #2. The first crack was noticed at a load of approximately 184 kN which developed transversely through the back of the barrier centre (Figure 38). Further cracks developed diagonally starting from the anchor block-outs to the left (Figure 39). The cracks met at the block-out for the middle anchor, which formed a “V” shaped, resembling that failure mode estimated by the yield line. No anchorage break-out was detected. The barrier had reached its failure capacity by developing extensive cracks. Consecutively the load resisting mechanism changed from flexural to tensile action as provided by the steel reinforcement. The maximum load reached for test #3 was 460 kN.   49  Figure 38 – First crack developed during test #3 on rear side of barrier   Figure 39 – Diagonal cracks initiated by anchor block-outs, right of the center (blue lines indicate the general orientation of the cracks)  Back of barrier First crack   50  Figure 40 – Diagonal cracks initiated by anchor block-outs, left of the center   Figure 41 – Cracks at the back of the barrier 3 main cracks   51 7.4 Acquired data A computer controlled data acquisition system was used to record the time histories of displacements and loading. The following graphs show the displacement of all the LVDTs vs. loading. Effects caused by any slippages between anchor bolts and associated anchor holes in the base beam and strong floor have been eliminated. Figure 42 and Figure 43 are the results from test #1. LVDT 2, 4, and 6 were located at the bottom of the barrier and LVDT 1, 3, and 5 were located at the top of the barrier (see Figure 20). Since the top of the barrier near the application of load (jack, LVDT 3 and 5) underwent significantly more deformation than the rest of the measured locations, they were plotted to a different scale.  Figure 42 – Displacement vs. loading for LVDT1, LVDT2, LVDT4 and LVDT6 for test #1   52  Figure 43 – Displacement vs. loading for jack, LVDT 3, LVDT 5 for test #1 As one can see, LVDT #3 and #5 recorded the most deformation, namely at the top left corner of the barrier above anchor #1 and anchor #2. The maximum load observed was 250 kN, after which there is a significant decrease in force. At that time, the maximum horizontal displacement was approximately 77 mm (LVDT 5).  After the barrier recovered, a further extension of the load cylinder showed a recovery of the barrier to a second peak of about 240 kN until complete break- out of the barrier occurred.  The maximum displacement measured was 125 mm. As expected, minimal displacements were observed in LVDT 1 and 2 positioned at the far end of the barrier. For the LVDTs near to the application of force (LVDT #3, 4, 5, 6), linear relationship were observed up to approximately 140 kN. After that point, larger deformations were observed with respect to the rate of increasing load. Figure 44 and Figure 45 show similar graphs for test #2. Similar LVDT arrangements were used; LVDT #5 and #3 were at the top of the barrier directly above the anchors in proximity of the load; LVDT #6 and #4 were at the bottom of the barrier corresponding longitudinally with #5 and #3; LVDT #1 and #2 were the top and bottom of the barrier aligned with the third anchor from the location of applied force (refer to Figure 21 for schematic of locations of LVDTs for test #2). The graphs show very similar characteristics as they were observed for test #1 up to the peak load. During test #2, the recovery leading to a second, lower peak value was recorded by the jack, while the recording of the other LVDTs were stopped after to reaching the first and   53 governing the peak load.  Again, the maximum displacement was recorded by LVDT 5 (about 92 mm).  Figure 44 – Plots of Displacement vs. Force for LVDT1, LVDT2, LVDT4 and LVDT6 for TEST #2  Figure 45 – Displacement vs. force for LVDT3, LVDT5 and hydraulic jack for test #2 Similarly for test #3, loading in the center of the barrier, force and displacement charts were plotted and are presented in Figure 46 through Figure 49. LVDT 1, 3, and 5 are located at the top   54 of the barrier aligning with the middle three anchors, counting from right to left. LVDT 2, 4, and 6 are located at the bottom of the barrier (please refer to Figure 22 for LVDT location diagram).  Figure 46 – Displacement vs. force for LVDT 1, LVDT 3, LVDT 5, and hydraulic jack for test #3, raw data   Figure 47 – Displacement vs. force for LVDT 2, LVDT 4, LVDT 6 for test #3, raw data    55  Figure 48 – Displacement vs. force for LVDT 1, LVDT 3, LVDT 3, and Jack for test #3, smoothened  Figure 49 – Displacement vs. force for LVDT 2, LVDT 4, LVDT 6 for test #3, smoothened  Once again, the top of the barrier (LVDT 1, 3, and 5) underwent more deformation than the bottom of the barrier (LVDT 2, 4, and 6). In this case, the maximum load reached was approximately 460 kN, significantly higher than when the load was applied at the ends of the barrier.  The maximum horizontal displacement measured at peak load was 72 mm (LVDT 5). Table 13 summarizes key results from all the tests.   56 Table 13 – Summary of Results  Test #1 (right end) Test #2 (left end) Test #3 (middle) Test date Oct 25, 2007 Nov 5, 2007 Dec 20, 2007 Loading location Right end of Barrier Left end of Barrier Center of Barrier Loading rate 15.24mm/20min 76.2mm/20min 76.2mm/20min First cracking appears at ~120 kN 122 kN 184 kN Predicted capacity from yield line theory* 279 kN 279 kN 531 kN Predicted capacity from actual yield lines 253 kN 253 kN 491 kN Failure occurred at (maximum load capacity) 250 kN 293 kN 493 kN Maximum displacement of top LVDT @ peak load 77 mm (LVDT 5, above 1st anchor from load) 92 mm (LVDT 5, above 1st anchor from load) 72 mm (LVDT 3, above middle anchor) Displacement of adjacent top LVDT @ peak load 62 mm (LVDT 3, above 2nd anchor from load) 78 mm (LVDT 3, above 2nd anchor from load) 69/71 mm (LVDT 1/5 adjacent to middle LVDT) Maximum displacement of bottom LVDT @ peak load 19 mm (LVDT 6, below 1st anchor from load) 28 mm (LVDT 6, below 1st anchor from load) 19 mm  (LVDT 4, below middle anchor) Displacement of adjacent bottom LVDT  14 mm (LVDT 4, below 2nd anchor from load) 19 mm (LVDT 4, below 2nd anchor from load) 14/17 mm (LVDT 2/6 adjacent to middle LVDT) *The capacity of a given barrier was estimated based on the yield line analysis as outlined in the American Association of State Highway and Transportation Officials (AASHTO) Bridge Specifications. 7.5 Discussion of test results The maximum load capacities of the barriers are 250 kN and 293 kN at the end, and 493 kN at the interior region.  This successfully proved that the precast concrete bridge barriers designed   57 according to the 1988 CHBDC comply with today’s required code.  The anchorage of the tested versions of the parapet is sufficient as failure occurs in the barrier body first. From the test results, it can be concluded that the capacity of the barrier is much higher when the impact load is applied at the middle of the barrier than if the load is applied at the ends of the barrier. This is as expected because the dominating failure mode was flexure and loading at the center of the barrier allows for the complete yield lines to developed (V shaped) whereas loading at the ends would only develop one diagonal yield line (parallel diagonal cracks).  This fact leads immediately to the recommendation, that all barriers should form a linked chain, in order to utilize the ultimate capacity of the barrier. This requires good connections between the barriers and a special treatment of the first and last member of this chain. After the concrete cracked in the barrier, the tensile force is quickly transferred to the reinforcement and to the anchor. When loading at the middle of the barrier, the load is resisted by three anchors, causing it to be less susceptible to anchorage pull out. However, when the barrier is impacted at the free ends, only the first two anchors was effective in resisting the tensile force and the barrier failed in anchorage pull out. During the experiment, it was observed that a large amount of the cracks initiated from and developed through the anchor block-outs as well the lifting holes. These crack patterns suggested that the anchor block-outs and the lifting holes presented weak links in the barrier. Special attention is required for detailing of those areas. In particular, the block-outs for the anchor bolt detail needs careful attention not to initiate premature crack formation. The actual capacity of the barrier was slightly less than that predicted from spreadsheet’s yield line analysis. Nonetheless, the barriers as tested sustained more than 2.5 times at the end and 5 times at the interior of the required 100 kN load as per the current Canadian Highway Bridge Design Code for Performance Level 2 traffic barrier. The results from these experiments can be used to further improve the yield line estimates as stated in AASHTO and to use as a calibration tool to develop an easy to use model to design and predict the capacity of precast concrete bridge barriers.   58 8 CORRELATION WITH SPREADSHEET CALCULATIONS By comparing the calculated results with the experimental results, it was found that the assumed yield lines provided a relatively good estimates of the capacity of the barrier at the end region (279 kN predicted vs. 250 kN and 293 kN measured for tests #1 and #2), as well as for the interior region (531 kN predicted vs. 493 kN measured for test #3). The discrepancy can be attributed to the fact that the yield line approach includes only the ultimate flexural capacity of the concrete component.  It was clear from the experiment that there are two possible failure mechanisms: torsion and anchor pull-out. From the failure diagrams as shown in Figure 30, it appears that the lifting holes represent a weak spot in the concrete wall. This affected the yield line pattern as estimated by AASHTO. In order to account for the effect of the lifting hole, the height of the wall needs to be an “effective wall height” which accounts for the 80 mm diameter holes. From the experimental observations, it was clear that there are two failure mechanisms possible: torsion and anchor pull out. However, the yield line approach only includes the ultimate flexural capacity of the concrete component. The anchorages are a major factor in the barrier strength and ought to be taken into consideration when calculating the moment strength of the wall about horizontal axis (Mc) of the bottom section of the barrier. For the top section of the barrier, the vertical reinforcement is effective in providing moment strength about the horizontal axis. However, at the bottom of the barrier, the vertical reinforcement is not anchored into the base and thus may not be able to provide the moment resistance as by the yield lines. Anchorage to the base is only provided by the anchor bolts. Therefore, for the moment strength of wall about horizontal axis (Mc) of the base section, the resistance should be calculated from the 25 mm diameter bolt spaced at 860 mm. The original calculations are updated to account for the actual yield lines and behaviour observed.  The calculated capacities based on the improved yield lines are 491 kN and 253 kN at the interior and end region of the barrier.   59 9 CONCLUSIONS Analysis and experimental investigations were conducted in order to study the behaviour and obtain the capacity of the Precast Concrete Bridge Barrier (PCBB) currently in use in British Columbia. The PCBB were designed in accordance with BC Ministry of Transportation’s standard. The loading specifications for design and static testing were based on the Canadian Highway Bridge Design Code for Performance Level 2 Traffic Barrier. The major findings are as follows: • The tests proved that the precast concrete bridge barriers in use on highway bridges, designed prior to the CHBDC comply with the current required code. • Anchorage of the tested versions of the PCBB is sufficient as failure occurs in barrier body first. Pull-out of anchor bolts will not occur • From the conducted tests as well as from the experimental investigations by TTI it can be concluded that static tests correlate well with crash tests (pendulum test). In fact, the static test can be deemed as the more accurate method of determining the barrier behaviour and ultimate capacity. This can be explained by the fact that dynamic effects such as strain rates do not play a role in the relatively slow loading of the barrier. A concrete barrier does not require large displacements to achieve its maximum capacity; therefore inertia effects are not critical. • The barrier test specimen failed in two different subsequent modes: torsion and pull out of anchorage from barrier. This leads to load maxima that were slightly less than estimated using Yield Line approach outlined in AASHTO. • A spreadsheet programme has been developed and calibrated for the design of precast concrete bridge barriers under Performance Level 2 loading in accordance with the Canadian Highway Bridge Design Code (CHBDC) and the American Association of State Highway and Transportation Officials (AASHTO) specifications. • Yield line theory as used in the spreadsheet design programme is adequate to predict the failure loads.   60 • The design programme can be easily modified to accommodate other PCBB barrier types and code updates. • An adjusted yield line analysis (with lines placed as observed in the experimental testing) gave a better correlation. • The CHBDC design method clearly creates highly conservative products. • Future design recommendations: o In order to utilize the ultimate of existing capacities, one should interconnect all barrier elements to a linked chain. A special treatment of the first and last member of this chain should be considered. o The block-outs for the anchor bolt detail needs careful attention not to initiate premature crack formation. o Lifting holes represent a weak spot in the concrete wall and ought to be considered in any computational predictions using yield line theory.    61  References  [1] AASHTO (2005). LRFD Bridge Design Specifications, 3rd ed., American Association of State Highway and Transportation Officials, Washington, DC.  [2] Alberson, D.C., et al. “Testing and Evaluation of The Florida Jersey Safety Shaped Bridge Rail”. Texas Transportation Institute, The Texas A&M University System, College Station, Texas, February 2004  [3] Bleitgen, K. and Stiemer, S.F. “Developing and Testing of Precast Concrete Bridge Barrier Anchorages to meet the Requirements for PL-2 Barrier Systems of the Canadian Highway Bridge Design Code”, internal report, University of British Columbia, December 18, 2006.  [4] Barker, R.M. and Puckett, J.A. Design of Highway Bridge: based on AASHTO LRFD Bridge Design Specifications. New York: John Wiley& Sons Inc. 1997.  [5] CAN/CSA-S6-06. Canadian Highway Bridge Design Code (CHBDC) A National Standard of Canada, November 2006, CSA International, Toronto, Ontario.  [6] CAN/CSA-S6-06. Commentary to the Canadian Highway Bridge Design Code, November, 2006, CSA International, Toronto, Ontario.  [7] Gao, Y. and Stiemer, S.F. “Loading and Design of Bridge Barriers according to Canadian Highway Bridge Design Code using Formatted Spreadsheets”, internal report, University of British Columbia, December 2007.  [8] Jin, B. and Stiemer, S.F. “Static Testing of Anchorage Capacity of Precast Concrete Bridge Barrier”, internal report, University of British Columbia, December 2007.  [9] Mitchell, G., et al. “Design of Retrofit Vehicular Barriers Using Mechanical Anchors”. Center for Transportation Research, The University of Texas at Austin, Austin, Texas. October 2006  [10] Williams, W.F., Buth, C.E., and Menges, W.L. “Repair/Retrofit Anchorage Designs for Bridge Rails”. Texas Transportation Institute, The Texas A&M University System, College Station, Texas. March 2007   62       Appendix A – Stiffener design   63     64   65       Appendix B – Design program  The Appendix contains images of the spreadsheets as developed for reference purpose only. Please ask for electronic files of the workable spreadsheets by e-mail from: sigi@civil.ubc.ca   66  PRO JEC T MoT SECTIO N 1  Reference  TITL E Barrier Loading and design check   DATE 12/09/0 7  C-CHBDC      FILE  PB.XLS   TIME 5:25 PM  A-AASHTO     DESCRIPTION  -Determination of barrier exposure index and find out optimum performance level -Design check precast concrete barrier's resistance to transverse load according to CHBDC -Follow yield line analysis method ASSUMPTION -The horizontal reinforcement consists no more than six bars on each face  -The bar size for vertical reinforcement is the same along the whole span -The barrier has no additional beam section at its top -The INPUT of barrier  is in accordance with MoT standard  precast barrier drawing          67                 68  INPUT   Average annual daily traffic for the first year after construction AADT 1 =   = 10000 []  Design Speed DS =   = 60 [km/h] 50/60/80/110   Highway Type T =   = type4 [] type1:one-way type2:two-way divided  type3:two- way undivided with five or more lanes type4:two-way undivided with four or fewer lanes   Radius of Curve R =   = 200 [m]  Position of Barrier(inside/outside of curve) in/out =   = inside   inside/outside   Highway grade G =   = -3 [%] -0.008333333   Superstructure Height above Ground or Water Surface Hs =   = 10 [m]  Usage of Land (high- occupancy/low-occupancy) U =   = high high/low   Water Depth beneath Bridge(deep/shallow) Dw =   = deep deep/shallow   Truck Percentage TP =   = 20 [%] 0/5/10/15/20/25/40   Barrier Clearance BCl =   = 2 [m]  Moment Strength of Beam, If Any, At Top of Wall Mb       0   Height of Wall H =   = 910 [mm]   69   Steel Yield Strength fy =   = 400 [MPa]  Concrete Compressive Strength f'c =   = 35 [MPa]  Bar Size for Horizontal Reinforcement (Front Face) S1 =   = 15M []  Bar Size for Horizontal Reinforcement (Rear Face) S2 =   = 10M []  Effective Concrete Depth (to corresponding bar)   (For Front Face Rebar) df1 =   = 143 [mm]     df2 =   = 169 [mm]     df3 =   = 214 [mm]     df4 =   = 316 [mm]     df5 =   = 0 [mm]     df6 =   = 0 [mm]   (For Rear Face Rebar) dr1 =   = 143 [mm]     dr2 =   = 158 [mm]     dr3 =   = 174 [mm]     dr4 =   = 190 [mm]     dr5 =   = 286 [mm]     dr6 =   = 316 [mm]  Bar Size for Vertical Reinforcement(top) S3 =   = 15M []  Bar Size for Vertical Reinforcement(bottom) S4       10M []  Space for Vertical Steel(Interior Region) Dint =   = 136 [mm]  Space for Vertical Steel(End Region) Dend =   = 136 [mm]   Height of Top Section of Ht =   = 557 [mm]   70 Wall  Height of Bottom Section of Wall Hb =   = 353 [mm]  Effective Concrete Depth (to corresponding bar)   (Top) dt1 =   = 159 [mm]   (Mid Top) dt2 =   = 207 [mm]   (Mid Bottom) db1 =   = 207 [mm]   (Bottom) db2 =   = 232 [mm]  The Resistance Factor for Extreme Event  Limit State Φ =   = 1 [] CALCU LATIO NS   DETERMINATION OF BARRIER EXPOSURE INDEX   Define Lookup Column Col1 = IF(in/out="outside",2,3) = 3  Define Lookup Column Col2 = IF(U="high",2,3)   3  Highway Type Factor Kh = IF(T="type4",LOOKUP(DS,Kh!C23:C27,Kh! D23:D27),LOOKUP(T,Kh!B19:B21,Kh!D19: D21)) = 1.3 []   C-Table12.1  Highway curvature factor Kc = IF(R>300,VLOOKUP(R,Kc,Col1),INDEX(K c,2,Col)) = 2 []   C-Table12.2  Highway grade factor Kg = LOOKUP(G,Kg!G5:G9,Kg!H5:H9) = 1.25 []   C-Table12.3  Superstructure height factor Ks = IF(Hs>5,VLOOKUP(Hs,Ks,Col2),INDEX(Ks ,2,Col2)) = 0.95 []   C-Table12.4  Barrier exposure index Be = (AADT1)KhKcKgKs/1000 = 30.875 []   C-12.4.3.2.3  DETERMINATION OF OPTIMUM PERFORMANCE LEVEL    71  Define index table with barrier clearance less than or equal to 2.25m BCl1 = LOOKUP(Be,OFFSET('Opt PL'!$J$5:$M$5,MIN(IF(('Opt PL'!$H$6:$H$40=DS)*('Opt PL'!$I$6:$I$40=TP),ROW('Opt PL'!$H$6:$H$40)-5)),),'Opt PL'!$J$5:$M$5)         C-Table12.5  Define index table with barrier clearance less than or equal to 3.75m BCl2 = LOOKUP(Be,OFFSET('Opt PL'!$J$50:$M$50,MIN(IF(('Opt PL'!$H$51:$H$85=DS)*('Opt PL'!$I$51:$I$85=TP),ROW('Opt PL'!$H$51:$H$85)-50)),),'Opt PL'!$J$50:$M$50)         C-Table12.6  Define index table with barrier clearance greater than 3.75m BCl3 LOOKUP(Be,OFFSET('Opt PL'!$J$95:$M$95,MIN(IF(('Opt PL'!$H$96:$H$130=DS)*('Opt PL'!$I$96:$I$130=TP),ROW('Opt PL'!$H$96:$H$130)-95)),),'Opt PL'!$J$95:$M$95)         C-Table12.7  Optimum Performance Level Opt PL = IF(BCl<=2.25,BCl1,IF(BCl<=3.75,BCl2,BCl 3)) = PL-2 []  DETERMINATION OF BARRIER LOADS  Transverse load Ft = LOOKUP(Opt PL,Load!B5:B7,Load!C5:C7) = 100 [kN]   C-Table3.8.8.1  Longitudinal  load Fl = LOOKUP(Opt PL,Load!B5:B7,Load!D5:D7) = 30 [kN]   C-Table3.8.8.1  Vertical load Fv = LOOKUP(Opt PL,Load!B5:B7,Load!E5:E8) = 30 [kN]   C-Table3.8.8.1  Longitudinal Length of Distribution of Impac Force Ft Lt = LOOKUP(Opt PL,Load!B5:B7,Load!F5:F8) = 1050 [mm]  C- Figure12.5.2 .4  Longitudinal distribution of vertical loads,Fv Lv   LOOKUP(Opt PL,Load!B5:B7,Load!G5:G8) = 5500 [mm] C- Figure12.5.2 .5   72  SHOW FIGURE  Define  figure index FI = IF(Opt PL="PL-1",1,IF(Opt PL="PL-2",2,3)) = 2  Determine Moment Strength about the Vertical axis MwH  Number of Rebars for Front Face nf = COUNTIF(G63:G68,">0") = 4  Number of Rebars for Rear Face nr = COUNTIF(G69:G74,">0") = 6  Area of Steel for Front Face(each bar) As1 = vlookup(S1,Rebar,4) = 200 [mm^2]  Area of Steel for Rear Face (each bar) As2 = vlookup(S2,Rebar,4) = 100 [mm^2]  Uniform Compression stress depth(Front Face) a1 = nf*As1*fy/(0.85*f'c*H) = 11.8  [mm]  Uniform Compression stress depth(Rear Face) a2 = nr*As2*fy/(0.85*f'c*H) = 8.9  [mm]  Moment Strength for Front Face Tension  ΦMnf = Φ*As1*fy*((df1+df2+df3+df4+df5+df6)-nf*a1/2) = 654687 82.0  [N-mm]  Moment Strength for Rear Face Tension  ΦMnr = Φ*As2*fy*((dr1+dr2+dr3+dr4+dr5+dr6)-nr*a2/2) = 496161 89.9  [N-mm]  Total Moment Strength about the Vertical axis MwH = (ΦMnf+ΦMnr)/2 = 575424 85.9  [N-mm] - Interior Region   Determine Moment Strength about the Horizontal axis Mcint  Area of Steel for Vertical Steel(top) As3int = vlookup(S3,Rebar,4)/Dint = 1.5 [mm^2/ mm]  Area of Steel for Vertical Steel(bottom) As4int = vlookup(S4,Rebar,4)/Dint = 0.7 [mm^2/ mm]  Uniform Compression stress depth(Vertical-top) a3int = As3int*fy/(0.85*f'c*1) = 19.8  [mm]   Uniform Compression a4int   As4int*fy/(0.85*f'c*1) = 9.9   73 stress depth(Vertical- bottom)  Moment Strength for Top Section Mctint = Φ*As3int*f'y*((dt1+dt2)/2-a3int/2) = 101831 .6  [N-mm]  Moment Strength for Bottom Section Mcbint   Φ*As4int*f'y*((db1+db2)/2-a4int/2) = 63105. 0  [N-mm]  Average Moment Strength Aabout the Horizontal Axis Mcint = ((Mctint*Ht)+(Mcbend*Hb))/H = 86809. 1 [N- mm/m m]  Determine Critical Length of Wall Failure   Critical Length  of Wall Failure Lcint = Lt/2+((Lt/2)^2+8*H*(Mb+MwH)/Mcint)^(1/2) = 2783.6  [mm]   A13.3.1-2  Determine Nominal Resistance to Transverse Load   Nominal Resistance to Transverse Load Rwint = (2/(2*Lcint- Lt))*(8*Mb+8*MwH+Mcint*(Lcint^2)/H)/1000 = 531.1 [kN]   A13.3.1-1  Check Capacity of Resistance(Interior Region) Chk1 = if(Rwint>Ft,"OK","Check") = OK  Efficiency Eff = Rwint/Ft   531.1% -End Region   Determine Moment Strength about the Horizontal axis Mcend  Area of Steel for Vertical Steel(top) As3end = vlookup(S3,Rebar,4)/Dend = 1.5 [mm^2/ mm]   Area of Steel for Vertical Steel(bottom) As4end = vlookup(S4,Rebar,4)/Dend = 0.7 [mm^2/ mm]  Uniform Compression stress depth(Vertical-top) a3end = As3end*fy/(0.85*f'c*1) = 19.8  [mm]  Uniform Compression stress depth(Vertical- bottom) a4end   As4end*fy/(0.85*f'c*1)   9.9  [mm]   74  Moment Strength for Top Section Mctend = Φ*Asvend*f'y*((dt1+dt2)/2-a3end/2) = 101831 .6  [N-mm]  Moment Strength for Bottom Section Mcbend   Φ*Asvend*f'y*((db1+db2)/2-a4end/2) = 63105. 0  [N-mm]  Average Moment Strength Aabout the Horizontal Axis Mcend = ((Mctend*Ht)+(Mcbend*Hb))/H = 86809. 1 [N- mm/m m]  Determine Critical Length of Wall Failure   Critical Length  of Wall Failure Lcend = Lt/2+((Lt/2)^2+H*(Mb+MwH)/Mcend)^(1/2) = 1462.5  [mm]   A13.3.1-2  Determine Nominal Resistance to Transverse Load   Nominal Resistance to Transverse Load Rwend = (2/(2*Lcend- Lt))*(Mb+MwH+Mcend*(Lc^2)/H)/1000 = 279.0 [kN]   A13.3.1-1  Check Capacity of Resistance Chk2 = if(Rwend>Ft,"OK","Check") = OK  Efficiency Eff = Rwend/Ft   279.0%   Reference [1] Richard M. Barker and Jay A. Puckett , 1997, Design of Highway Bridge: based on AASHTO LRFD Bridge Design Specifications, John Wiley& Sons. INC., New York [2]Canadian Highway Bridge Design Code(CHBDC)-CAN/CSA-S6-06, November 2006, CSA International  [3] Commentary to the Canadian Highway Bridge Design Code -CAN/CSA-S6-06, November, 2006, CSA International [4] AASHTO (2005) . LRFD Bridge Design  Specifications, 3rd ed., American Association of State Highway and Transportation Officials, Washington, DC [5] S.F. Stiemer, Developing and Testing of Precast Concrete Bridge Barrier Anchorages to meet the Requirements for  PL-2 Barrier Systems of the Canadian Highway Bridge Design Code, University of British Columbia    75    PROJECT MoT SECTIO N 1 Refere nce   TITLE Barrier Loading and design check   DATE 12/09 /07 C- CHBD C     FILE  PB-modified.xls   TIME 5:08 PM A- AASH TO     DESCRIPTION  -Determination of barrier exposure index and find out optimum performance level -Design check precast concrete barrier's resistance to transverse load according to CHBDC -Follow yield line analysis method ASSUMPTION -The horizontal reinforcement consists no more than six bars on each face -The bar size for vertical reinforcement is the same along the whole span -The barrier has no additional beam section at its top -The INPUT of barrier  is in accordance with MoT standard  precast barrier drawing         76       77   INPUT   Average annual daily traffic for the first year after construction AA DT 1 =   = 10000 []   Design Speed DS =   = 60 [km/h] 50/60/80/1 10  Highway Type T =   = type4 [] type1:one- way type2:two- way divided type3:two- way undivided with five or more lanes type4:two- way undivided with four or fewer lanes    Radius of Curve R =   = 200 [m]   Position of Barrier(inside/outside of curve) in/ out =   = inside inside/out side   Highway grade G =   = -3 [%] -2/-2/-4/-5/-6'  Superstructure Height above Ground or Water Surface Hs =   = 10 [m]   78  Usage of Land (high- occupancy/low-occupancy) U =   = high   high/low  Water Depth beneath Bridge(deep/shallow) D w =   = deep  deep/shall ow    Truck Percentage TP =   = 20 [%] 0/5/10/15/20/25/40  Barrier Clearance BCl =   = 2 [m]  Moment Strength of Beam, If Any, At Top of Wall Mb       0   Height of Wall H =   = 910 [mm]   Steel Yield Strength fy =   = 400 [MPa ]  Concrete Compressive Strength f'c =   = 35 [MPa ]  Bar Size for Horizontal Reinforcement (Front Face) S1 =   = 15M []  Bar Size for Horizontal Reinforcement (Rear Face) S2 =   = 10M []  Effective Concrete Depth (to corresponding bar)    (For Front Face Rebar) df1 =   = 143 [mm]     df2 =   = 169 [mm]     df3 =   = 214 [mm]     df4 =   = 316 [mm]     df5 =   = 0 [mm]     df6 =   = 0 [mm]   (For Rear Face Rebar) dr1 =   = 143 [mm]     dr2 =   = 158 [mm]     dr3 =   = 174 [mm]     dr4 =   = 190 [mm]     dr5 =   = 286 [mm]   79     dr6 =   = 316 [mm]  Bar Size for Vertical Reinforcement(top) S3 =   = 15M []  Bar Size for Vertical Reinforcement(bottom) S4       25M []  Space for Vertical Steel(Top Region) Dint =   = 136 [mm]  Space for Vertical Steel(Bottom Region) De nd =   = 860 [mm]   Height of Top Section of Wall Ht =   = 557 [mm]  Height of Bottom Section of Wall Hb =   = 353 [mm]  Effective Concrete Depth (to corresponding bar)   (Top) dt1 =   = 159 [mm]   (Mid Top) dt2 =   = 207 [mm]   (Mid Bottom) db1 =   = 159 [mm]   (Bottom) db2 =   = 159 [mm]  The Resistance Factor for Extreme Event  Limit State Φ =   = 1 []   Modified Height H'     = 500 [mm]   Reduced Length L'       0.15 [m] CALCU LATIO NS    DETERMINATION OF BARRIER EXPOSURE INDEX    Define Lookup Column Col1 = IF(in/out="outside",2,3) = 3  Define Lookup Column Col2 = IF(U="high",2,3)   3  Highway Type Factor Kh = IF(T="type4",LOOKUP(DS,Kh!C23:C27,Kh!D23:D27),LOOKUP(T,Kh!B19:B21,K = 1.3 [] C- Table1    80 h!D19:D21)) 2.1  Highway curvature factor Kc = IF(R>300,VLOOKUP(R,Kc,Col1),INDEX(Kc,2,Col)) = 2 [] C- Table1 2.2   Highway grade factor Kg = LOOKUP(G,Kg!G5:G9,Kg!H5:H9) = 1.25 [] C- Table1 2.3  Superstructure height factor Ks = IF(Hs>5,VLOOKUP(Hs,Ks,Col2),INDEX(Ks,2,Col2)) = 0.95 [] C- Table1 2.4   Barrier exposure index Be = (AADT1)KhKcKgKs/1000 = 30.875 [] C- 12.4.3. 2.3  DETERMINATION OF OPTIMUM PERFORMANCE LEVEL    Define index table with barrier clearance less than or equal to 2.25m BC l1 = LOOKUP(Be,OFFSET('Opt PL'!$J$5:$M$5,MIN(IF(('Opt PL'!$H$6:$H$40=DS)*('Opt PL'!$I$6:$I$40=TP),ROW('Opt PL'!$H$6:$H$40)-5)),),'Opt PL'!$J$5:$M$5)  C- Table1 2.5   Define index table with barrier clearance less than or equal to 3.75m BC l2 = LOOKUP(Be,OFFSET('Opt PL'!$J$50:$M$50,MIN(IF(('Opt PL'!$H$51:$H$85=DS)*('Opt PL'!$I$51:$I$85=TP),ROW('Opt PL'!$H$51:$H$85)-50)),),'Opt PL'!$J$50:$M$50)  C- Table1 2.6   Define index table with barrier clearance greater than 3.75m BC l3 LOOKUP(Be,OFFSET('Opt PL'!$J$95:$M$95,MIN(IF(('Opt PL'!$H$96:$H$130=DS)*('Opt PL'!$I$96:$I$130=TP),ROW('Opt PL'!$H$96:$H$130)-95)),),'Opt PL'!$J$95:$M$95)  C- Table1 2.7    81  Optimum Performance Level Op t PL = IF(BCl<=2.25,BCl1,IF(BCl<=3.75,BCl2,B Cl3)) = PL-2 []   DETERMINATION OF BARRIER LOADS   Transverse load Ft = LOOKUP(Opt PL,Load!B5:B7,Load!C5:C7) = 100 [kN] C- Table3 .8.8.1  Longitudinal  load Fl = LOOKUP(Opt PL,Load!B5:B7,Load!D5:D7) = 30 [kN] C- Table3 .8.8.1  Vertical load Fv = LOOKUP(Opt PL,Load!B5:B7,Load!E5:E8) = 30 [kN] C- Table3 .8.8.1   Longitudinal Length of Distribution of Impac Force Ft Lt = LOOKUP(Opt PL,Load!B5:B7,Load!F5:F8) = 1050 [mm]  C- Figure 12.5.2. 4  Longitudinal distribution of vertical loads,Fv Lv  LOOKUP(Opt PL,Load!B5:B7,Load!G5:G8) = 5500 [mm] C- Figure 12.5.2. 5   SHOW FIGURE             770   Define  figure index FI = IF(Opt PL="PL-1",1,IF(Opt PL="PL-2",2,3)) = 2   Determine Moment Strength about the Vertical axis MwH  Number of Rebars for Front Face nf = COUNTIF(G63:G68,">0") = 4  Number of Rebars for Rear Face nr = COUNTIF(G69:G74,">0") = 6  Area of Steel for Front Face(each bar) As1 = vlookup(S1,Rebar,4) = 200 [mm^ 2]   Area of Steel for Rear Face (each bar) As2 = vlookup(S2,Rebar,4) = 100 [mm^ 2]   82  Uniform Compression stress depth(Front Face) a1 = nf*As1*fy/(0.85*f'c*H') = 14.0  [mm]  Uniform Compression stress depth(Rear Face) a2 = nr*As2*fy/(0.85*f'c*H') = 16.1  [mm]  Moment Strength for Front Face Tension Φ Mnf = Φ*As1*fy*((df1+df2+df3+df4+df5+df6)- nf*a1/2) = 65124 924.2 [N- mm]  Moment Strength for Rear Face Tension Φ Mnr = Φ*As2*fy*((dr1+dr2+dr3+dr4+dr5+dr6)- nr*a2/2) = 48743 865.5 [N- mm]  Total Moment Strength about the Vertical axis Mw H = (ΦMnf+ΦMnr)/2 = 56934 394.8 [N- mm] - Interio r Region   Determine Moment Strength about the Horizontal axis Mcint  Area of Steel for Vertical Steel(top) As3 int = vlookup(S3,Rebar,4)/Dint = 1.5 [mm^ 2/mm ]  Area of Steel for Vertical Steel(bottom) As4 int = vlookup(S4,Rebar,4)/Dint = 0.6 [mm^ 2/mm ]   Uniform Compression stress depth(Vertical-top) a3i nt = As3int*fy/(0.85*f'c*(1-L')) = 19.8  [mm]  Uniform Compression stress depth(Vertical-bottom) a4i nt   As4int*fy/(0.85*f'c*(1-L')') = 7.8  Moment Strength for Top Section Mct int = Φ*As3int*f'y*((dt1+dt2)/2-a3int/2) = 10183 1.6 [N- mm]  Moment Strength for Bottom Section Mc bint   Φ*As4int*f'y*((db1+db2)/2-a4int/2) = 36067. 8 [N- mm]  Average Moment Strength Aabout the Horizontal Axis Mci nt = ((Mctint*Ht)+(Mcbend*Hb))/H = 76321. 0 [N- mm/ mm]   Determine Critical Length of Wall Failure    83  Critical Length  of Wall Failure Lcin t = Lt/2+((Lt/2)^2+8*H*(Mb+MwH)/Mcint)^(1/2) = 2925.9  [mm] A13.3. 1-2  Determine Nominal Resistance to Transverse Load   Nominal Resistance to Transverse Load Rwi nt = (2/(2*Lcint- Lt))*(8*Mb+8*MwH+Mcint*(Lcint^2)/H)/1000 =  490.8 [kN] A13.3. 1-1  Check Capacity of Resistance(Interior Region) Ch k1 = if(Rwint>Ft,"OK","Check") = OK  Efficiency Eff = Rwint/Ft 490.8 %  -End Region   Determine Moment Strength about the Horizontal axis Mcend  Area of Steel for Vertical Steel(top) As3 end = vlookup(S3,Rebar,4)/Dend = 1.5 [mm^ 2/mm ]   Area of Steel for Vertical Steel(bottom) As4 end = vlookup(S4,Rebar,4)/Dend = 0.6 [mm^ 2/mm ]  Uniform Compression stress depth(Vertical-top) a3 end = As3end*fy/(0.85*f'c*(1-L')) = 19.8  [mm]  Uniform Compression stress depth(Vertical-bottom) a4 end   As4end*fy/(0.85*f'c*(1-L'))   7.8  [mm]  Moment Strength for Top Section Mct end = Φ*Asvend*f'y*((dt1+dt2)/2-a3end/2) = 10183 1.6 [N- mm]  Moment Strength for Bottom Section Mc ben d   Φ*Asvend*f'y*((db1+db2)/2-a4end/2) = 36067. 8 [N- mm]   Average Moment Strength Aabout the Horizontal Axis Mc end = ((Mctend*Ht)+(Mcbend*Hb))/H = 76321. 0 [N- mm/ mm]  Determine Critical Length of Wall Failure    84  Critical Length  of Wall Failure Lce nd = Lt/2+((Lt/2)^2+H*(Mb+MwH)/Mcend)^(1/2) = 1505.7  [mm] A13.3. 1-2  Determine Nominal Resistance to Transverse Load   Nominal Resistance to Transverse Load Rw end = (2/(2*Lcend- Lt))*(Mb+MwH+Mcend*(Lc^2)/H)/1000 =  252.6 [kN] A13.3. 1-1  Check Capacity of Resistance Ch k2 = if(Rwend>Ft,"OK","Check") = OK  Efficiency Eff = Rwend/Ft 252.6 %    Reference [1] Richard M. Barker and Jay A. Puckett , 1997, Design of Highway Bridge: based on AASHTO LRFD Bridge Design Specifications, John Wiley& Sons. INC., New York [2]          Canadian Highway Bridge Design Code(CHBDC)-CAN/CSA-S6-06, November 2006, CSA International [3] Commentary to the Canadian Highway Bridge Design Code -CAN/CSA-S6-06, November, 2006, CSA International  [4] AASHTO(2005) . LRFD Bridge Design  Specifications, 3rd ed., American Association of State Highway and Transportation Officials, Washington, DC [5] S.F. Stiemer, Developing and Testing of Precast Concrete Bridge Barrier Anchorages to meet the Requirements for  PL-2 Barrier Systems of the Canadian Highway Bridge Design Code, University of British Columbia   Note: For a yielding line pattern that is consistent with the geometry and boundary conditions, a solution is obtained by equating the external work due to the applied loads to the internal work done by the resisting moments along the yield lines. The applied load determined by this method is   85 either equal to or greater then the actual load, that is, it is non-conservative. 

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