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ANCHOR EMBEDMENT REQUIREMENTS FOR SIGNAL/SIGN STRUCTURES By KATHLEEN M. HALCOVAGE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2007 2007 Kathleen M. Halcovage To my family, for your constant love and support throughout my life. To my parents, Barbara and George, your dedication to providing me with the best education available has been a pivotal part of my success. To my siblings, Barbara, George, Sarah, and Christopher, you have always encouraged me and challenged me to be the very best that I can be. To my niece and nephew, Grace and Aidan, you light up my life and always remind me of what is important in life. ACKNOWLEDGMENTS I thank my advisor, Dr. Ronald A. Cook, for his guidance throughout the course of my research and tenure at the University of Florida, the Florida Department of Transportation Structures Research Center Staff for their hard work in building my test apparatus and orchestrating the testing of the specimen, and my supervisory committee for their assistance in the preparation of this thesis. I also thank my family for their constant support and encouragement. TABLE OF CONTENTS page A CK N O W LED G M EN T S ................................................................. ........... ............. ..... LIST OF TABLES .............. ......... ...................................................7 LIST OF FIGURES .................................. .. ..... ..... ................. .8 A B S T R A C T ............ ................... ............................................................ 1 1 CHAPTER 1 INTRODUCTION ............... .......................................................... 13 2 B A CK G R O U N D .......................................... ................ ......................... .... 15 2.1 Literature Review ................................... .. ........... .. ............15 2.2 Site Investigation .................................................................... 19 2.3 A applicable C ode Provisions ........................................... ....................................... 19 2.3.1 Cracking and Threshold Torsion............................................................ .......... 20 2.3.2 N ominal Torsional Strength ...........................................................................22 2.3.3 C om bined Shear and T orsion ..................................................................... .. ....23 2.3.4 ACI Concrete Breakout Strength for Anchors ................................................. 24 2.3.5 Alternate Concrete Breakout Strength Provisions.................... ...............26 2.3.6 ACI 31805 vs. AASHTO LRFD Bridge Design Specifications........................28 3 DEVELOPMENT OF EXPERIMENTAL PROGRAM ................................. ...............33 3.1 D description of T est A pparatu s ............................................. ......... ..............................33 3.2 Shaft D design .............. ................................. ................. ............... 34 3.2.1 Torsion D design .................... .. .............. .... ........... 34 3.2.2 Longitudinal and Transverse Reinforcement ............................... ................ 35 3 .2 .3 F lex u re ....................................................................................3 5 3.3 A nchor D design ....................................................................................................... ..... 36 3.3.1 D iam eter of A nchor B olts ...................................................................................36 3.3.2 Concrete Breakout Strength of Anchor in Shear Parallel to a Free Edge ..............37 3.3.3 Development Length of the Bolts............... .................................. ...................39 3.4 Steel Pipe A apparatus D design ................................................. ............................... 39 3.5 Concrete Block D design ..................................................... ........ .. ............ 41 3.6 C om bined Shear and T orsion ........................................ ............................................42 3 .7 O v erv iew .......................................................................... 4 2 4 IMPLEMENTATION OF TESTING PROGRAM.....................................................51 4.1 M materials ...................................................... 51 4.1.1 Concrete Strength ..................................... ....... .............. ... .......... 51 4.1.2 Bolt Strength....................................... ..... .......... 51 4.1.3 Carbon Fiber Reinforced Polymer Wrap....................................................51 4.2 Instrum entation ..................... .......... ......... ............ ............ 53 4.2.1 Linear Variable Displacement Transducers ................................. ............... 53 4 .2 .2 Strain G ages.................................................................................... ........ .. ... 54 5 T E ST R E SU L T S ................................................................60 5 .1 In itia l T e st .................................................................................................................. 6 0 5.1.1 Behavior of Specimen During Testing ...................................... ...............60 5.1.2 Behavior of Strain Gages During Testing ..........................................................61 5.1.3 Sum m ary of Initial Test Results ................................................................. 62 5.2 CFR P R etrofit Test .................. .................. .. .... .. ................ ............. ........ 62 5.2.1 Behavior of Specimen with CFRP Wrap During Testing ....................................63 5.2.3 Behavior of Strain Gages During Testing ................................... .................64 5.2.4 Sum m ary of Test R esults............ ......................................... ............... 64 6 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS .............................75 APPENDIX A TEST APPARATUS DRAWINGS......................................................... ...............77 B DESIGN CALCULATION S ....................................................... ......... ......82 C IN IT IA L T E ST D A T A ................................................................................... ............ 108 D R E TR O FIT TE ST D A TA ................................................................................. ........... 115 L IST O F R E F E R E N C E S ..................................................................................... ..................122 B IO G R A PH IC A L SK E T C H ......................................................................... .. ...................... 124 6 LIST OF TABLES Table page 3 1 F field dim en sion s .................................................................................................... 50 32 Sum m ary of design calculations ......................................................... 50 LIST OF FIGURES Figure page 11 Failed cantilever sign structure ........................................................................... ...... 14 21 Cantilever sign structure at Exit 79 on Interstate 4 in Orlando.......................................29 22 N ew foundation installed at the site ...................................................................... 29 23 Failed foundation during postfailure excavation...........................................................30 24 Concrete breakout of an anchor caused by shear directed parallel to the edge for a circular foundation ............... ................. .............. ................ ......... 30 25 Concrete breakout failure for an anchor loaded in shear............................................31 26 Determination of Avco based on the 35 failure cone ...................................................31 27 Shear load oriented (a) perpendicular to the edge and (b) parallel to the edge .................32 31 Schem atic of test apparatus........................................................................................... 44 32 Front elevation of test apparatus .......................................................................... ....... 44 33 P lan view of test apparatus s .................................................................. ...... .................. 45 34 Side elevation of test apparatus....................................................................... 45 35 Lever arm for the calculation of bolt flexure.................................................................. 46 36 Adjusted cover based on a single anchor and 350 failure cone.......................................46 37 Development of the projected failure area for the group of anchors around a circular fou n d action .................................................................................4 7 38 Two anchor arrangement displays the minimum spacing such that no overlap of the failure cones occurs............ ..................................... .... 47 39 O overlap of failure cones.............................................................................. ............ 47 310 The contribution of the "legs" of the failure cone to AV, along a straight edge decreases as the number of bolts increases.................................................... ............. 48 311 Overlap of failure cones for a circular foundation........... ................................ 48 312 A ssem bled test specim en ............................................................ ............... 49 313 Shaft with pipe apparatus attached prior to instrumentation being attached ...................49 41 Method for the determination of the tension, TCFRP, that must be resisted by the C FR P w rap ................ .... ........ ............... .............................55 42 Instrum entation layout on the base plate ........................................ ....................... 56 43 Instrum entation layout on face of shaft ........................................ ......................... 56 44 Instrumentation layout on rear of shaft/face of concrete block ......................................57 45 Instrumentation layout of pipe at load location ...... ........ ..........................................57 46 Location of LVDTs D1V, D4, and D7 on the test specimen .........................................58 47 Strain gage layout on base plate............................................... .............................. 58 48 Strain gage on base plate of test specim en............................................ .. ................59 51 Initial cracks on face of shaft ....................................................................... 66 52 Initial cracks on face and side of shaft (alternate view of Figure 51) ............................66 53 Face of test specimen after testing exhibits cracks between the bolts along with the characteristic concrete breakout cracks ........................................ ......................... 67 54 Crack pattern on face of shaft after testing depicts characteristic concrete breakout failure cracks ................ ..................................... ............................67 55 Applied Torsion vs. Plate Rotation Plot Initial Test............................................. 68 56 Applied Torsion vs. Bolt Strain Plots for each bolt at the appropriate location on the base plate with Applied Torsion vs. Plate Rotation plot in center (full size plots in A pp en dix C ) .............................................................................. 69 57 Bolt Strain Comparison Plot for Initial Test exhibits the redistribution of the load coinciding w ith crack form ations............................................................ .....................70 58 Shaft with the CFRP wrap applied prior to testing ............................... ...................70 59 Applied Torsion vs. Plate Rotation Plot Retrofit Test................... ........................... 71 510 Shaft exhibiting characteristic torsion cracks from face to base of shaft ........................71 511 Applied Torsion vs. Bolt Strain plots for the Retrofit Test at the appropriate bolt location around the base plate with Applied Torsion vs. Plate Rotation plot in center (full size plots in A appendix D )................................................. .............................. 72 512 Bolt bearing on the bottom of the base plate during loading ....................................73 513 Bolt Strain Comparison plot for the retrofit test exhibits slope changes at milestone lo a d s ..............................................................................................7 3 514 Face of shaft after test illustrates yielding of bolts, concrete breakout cracks around the perimeter, and torsion cracks in the center. ..................................... ............... 74 515 Torsion cracks along length of the shaft after the test .....................................................74 Ai Dimensioned front elevation drawing of test apparatus ............... ...... ......... 77 A2 Dim ensioned plan drawing test apparatus ........................................ ...... ............... 78 A3 Dimensioned side elevation drawing of test apparatus.................................................79 A4 Dim ensioned pipe apparatus drawing ..................................................... .... ........... 80 A5 Dim ensioned channel tiedown drawing ........................................ ....................... 81 C1 Applied Torsion vs. Rotation Plot .............................................................................108 C2 Bolt Strain Comparison Plot ........................................................................ 108 C3 Applied Torsion vs. Strain Plots for each bolt location............................109 D A applied Torsion vs. R rotation Plot .................................................................................115 D 2 B olt Strain C om prison Plot ............................................................................ ............ 115 D3 Applied Torsion vs. Strain Plots for each bolt location............................116 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering ANCHOR EMBEDMENT REQUIREMENTS FOR SIGNAL/SIGN STRUCTURES By Kathleen M. Halcovage May 2007 Chair: Ronald A. Cook Major: Civil Engineering During the 2004 hurricane season, several anchor embedment failures of the foundations of cantilever sign structures occurred. The purpose of this research program was to determine the cause of the failure of those foundations. After a thorough literature review, in conjunction with site investigation, and testing, it was determined that the failure originated from the shear load on the anchors directed parallel to the edge of the foundation. The shear load resulted from the torsion loading on the anchor group that occurred during the hurricane. Investigation of this failure mode, based on the ACI 31805 Appendix D provisions for concrete breakout of anchors, indicated that this is a failure mode not considered in the current design procedures for these types of foundations. Furthermore, it was determined that it very well describes the type of failure noted in the field investigation. A test specimen was designed to preclude other possible failure modes not exhibited in the field (e.g. steel failure of the anchors, bending of the anchors, and torsional failure of the foundation). The results of the testing indicated the failure of the foundations was caused by concrete breakout due to shear on the anchors directed parallel to the free edge of the foundation. The test specimen failed at the torsion predicted by the ACI 31805 Appendix D provisions based on the expected mean strength of the anchors for concrete breakout with shear directed parallel to the free edge. Additionally, the cracks that formed were the same type as those noted in the field investigation, and matched the expected pattern for concrete breakout failure. After failure, additional testing was performed to determine a viable repair/retrofit option. The repair/retrofit option used a carbon fiber reinforced polymer (CFRP) wrap around the top of the foundation. The results of this testing indicated that this repair/retrofit technique strengthens the foundation such that it not only meets its initial capacity for concrete breakout, but, also, can exceed this capacity. The results of this test led to the development of guidelines for the evaluation and repair/retrofit of existing foundations. CHAPTER 1 INTRODUCTION During the 2004 hurricane season, the failure of foundations of cantilever sign structures occurred along Florida highways (Figure 11). These failures necessitated a review of the current design and construction procedures for the foundations of cantilever sign structures. The main objective of this research program was twofold: to determine the cause of the failure of the cantilever sign structures; and, to propose a retrofit option for the foundation. In order to fulfill this objective, a thorough literature review, site investigation of a failed foundation, and experimental program were conducted. The findings of the literature review and site investigation were used to develop the experimental program. The findings of the experimental program were applied in the development of the retrofit guidelines. Furthermore, this project tested whether or not the ACI 31805, ACI (2005), Appendix D provisions for anchorage to concrete are applicable for circular foundations. Figure 11. Failed cantilever sign structure CHAPTER 2 BACKGROUND While there have not been published reports detailing failures of sign structure foundations, such as those being investigated in this study, information on the behavior of anchor installations under various load conditions was found. The main subjects of much of the literature were the effects of fatigue and wind load on overhead sign structures. Additionally, there have been studies conducted on the failure modes of anchor installations, but these findings were not based on circular foundations. In later sections, one of these anchorage failure modes will be introduced for application in this research program. This chapter presents the findings of the literature review, the conclusions drawn based on a site investigation of a failed foundation, and applicable design equations for the determination of the failure mode. The information presented in the chapter served as the base upon which the experimental program was developed. 2.1 Literature Review Keshavarzian (2003) explores the wind design requirements and safety factors for utility poles and antenna monopoles from various specification manuals. It was found that the procedure outlined in ASCE (1991), ASCE 74 Guidelines for Electrical Transmission Line Structural Loading, resulted in the smallest factor of safety for the design. AASHTO (2001), Standard Specificationsfor Structural Supportsfor Highway Signs, Luminaires and Traffic Signals, was used as a part of the comparison for the design of the antenna monopole. The design from this specification was compared to that from ASCE (2000), ASCE 798Minimum Design Loadsfor Buildings and Other Structures; TIA/EIA (1996), Structural Standards for Steel Antenna Towers andAntenna Supporting Structures; and, ASCE 74. The wind forces at the base were the same for ASCE 74, AASHTO, and ASCE 798. The forces using TIA/EIA were higher because it requires that a 1.69 gust response factor be applied to the design. Therefore, the pole designed using TIA/EIA would have between 30 and 40 percent extra capacity. ASCE 798 and AASHTO resulted in the same margin of safety. The paper did not include findings that were completely relative to this project, but it provided additional sources for design of structures for comparative purposes. Keshavarzian and Priebe (2002) compares the design standards specified in ASCE (2000), ASCE 798, and IEEE (1997), NESC NationalElectrical Safety Code. The NESC does not require that utility poles measuring less than 60 feet in height be designed for extreme wind conditions. Short utility poles were designed to satisfy NESC specifications (i.e. without extreme wind conditions). The poles were then evaluated according to the ASCE 798 wind load requirements. It was found that the poles did not meet the ASCE 798 requirements. Therefore, it was recommended that the exclusion for short utility poles in the NESC be reevaluated. The paper also mentioned AASHTO (1994), Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals. It outlined that in the AASHTO specification, support structures exceeding 50 feet and overhead sign structures must be designed for a 50year mean recurrence interval, or extreme wind loading condition. MacGregor and Ghoneim (1995) presents the background information for the formulation of the thinwalled tube space truss analogy design method for torsion that was first adopted into ACI (1995), ACI 31895. The design methodology was adopted because it was simpler to use than the previous method and was equally accurate. The basis for the derivation of the new method was based on tests that were conducted in Switzerland. Both solid and hollow beams were tested during that research. In comparing the data from both tests, it was discovered that after cracking the concrete in the center had little effect on the torsional strength of the beam. Therefore, the center of the crosssection could be ignored, and the beam could be idealized as a hollow tube. A space truss was formed by longitudinal bars in the corners, the vertical closed stirrups, and compression diagonals. The compression diagonals were spiraled around the member and extended between the torsion cracks. The paper also explained the shear stresses created by torsion on the member. In addition to the derivation of the equations for torsion and shear, the authors discussed the limits for when torsion should be considered and the requirements for minimal torsional reinforcement. The tests, conducted on both reinforced and prestressed concrete beams, showed that there was acceptable agreement between the predicted strengths, as determined by the derived equations, and the test results. This agreement was comparable to the design equations from the ACI Code. In addition to these papers, other reports reviewed include Lee and Breen (1966), Jirsa et al. (1984), Hasselwander et al. (1977), and Breen (1964). These four studies focused on important information regarding anchor bolt installations. Other reports that were examined for relevance were from the National Cooperative Highway Research Program (NCHRP). These are: Fouad et al. (1998), NCHRP Report 411; Kaczinski et al. (1998), NCHRP Report 412; and, Fouad et al. (2003), NCHRP Report 494. Fouad et al. (2003) details the findings of NCHRP Project 1710(2). The authors stated that AASHTO (2001) does not detail design requirements for anchorage to concrete. The ACI anchor bolt design procedure was also reviewed. Based on their findings, they developed a simplified design procedure. This procedure was based on the assumptions that the anchor bolts are hooked or headed, both longitudinal steel and hoop steel are present in the foundation, the anchor bolts are cast inside of the reinforcement, the reinforcement is uncoated, and, in the case of hooked bolts, the length of the hook is at least 4.5 times the anchor bolt diameter. If these assumptions did not apply, then the simplified procedure was invalid. The anchor bolt diameter was determined based on the tensile force on the bolt, and the required length was based on fully developing the longitudinal reinforcement between the embedded head of the anchor. The authors further stated that shear loads were assumed to be negligible, and concrete breakout and concrete side face blowout were controlled by adequate longitudinal and hoop steel. The design procedure was developed based on tensile loading, and did not address the shear load on the anchors directed parallel to the edge resulting from torsion. Additionally, the authors presented the frequency of use of different foundation types by the state Departments of Transportation, expressed in percentages of states reporting use. According to the survey the most common foundation type used for overhead cantilever structures was reinforced castinplace drilled shafts (67100%) followed by spread footings (34 66%) and steel screwin foundations (133%). None of the states reported the use of directly embedded poles or unreinforced castinplace drilled shafts. ASCE (2006), ASCE/SEI 4805, entitled Design of Steel Transmission Pole Structures was obtained to gather information on the foundation design for transmission poles structures. The intent was to determine whether or not the design of such foundations was relevant to the evaluation of the foundations under examination in this research. In 9.0 of the standard, the provisions for the structural members and connections used in foundations was presented. Early in the section, the standard stated that the information in the section was not meant to be a foundation design guide. The proper design of the foundation must be ensured by the owner based on geotechnical principles. The section commented on the design of the anchor bolts. The standard focused on the structural stability of the bolts in the foundation; it looked at bolts in tension, bolts in shear, bolts in combined tension and shear, and the development length of such bolts. The standard did not present provisions for failure of the concrete. 2.2 Site Investigation A site investigation was conducted at the site of one failed overhead cantilever signal/sign structure located at Exit 79 on Interstate 4 in Orlando (Figure 21). Figure 22 is the newly installed foundation at the site. The failed foundation had the same anchor and spacing specifications as the new foundation. This site visit coincided with the excavation of the failed anchor embedment. During the course of the excavation the following information was collected: * The anchor bolts themselves did not fail. Rather, they were leaning in the foundation, which was indicative of a torsional load on the foundation. While the integrity of the anchor bolts held up during the wind loading, the concrete between the bolts and the surface of the foundation was cracked extensively (Figure 23). The concrete was gravelized between the anchors and the hoop steel. It should be noted that upon the removal and study of one anchor bolt, it was evident that there was no deformation of the bolt itself. * The hoop steel did not start at the top of the foundation. It started approximately 15 in. (381 mm) into the foundation. * The concrete was not evenly dispersed around the foundation. The hoop steel was exposed at approximately three to four feet below grade. On the opposite side of the foundation there was excess concrete. It was assumed that during the construction of the foundation, there was soil failure allowing a portion of the side wall to displace the concrete. 2.3 Applicable Code Provisions The initial failure mode that was focused on in the background review was torsion. However, based on the results of the site investigation, it was determined that the most likely cause of failure was concrete breakout of an anchor (Figure 24). The equations for torsion are presented in this section as they were used during the design of the experimental program to prove that the concrete breakout failure will occur before the torsional failure. 2.3.1 Cracking and Threshold Torsion Torsion is the force resulting from an applied torque. In a circular section, such as the foundation under review, the resulting torsion is oriented perpendicular to the radius or tangent to the edge. ACI (2005), ACI 31805, details the equation for the cracking torsion of a nonprestressed member. In R11.6.1, the equation for the cracking torsion, Tcr, is given (Equation 21). The equation was developed by assuming that the concrete will crack at a stress of 4\/f'c. (A 2 T 4 = 4 (21) Where Tcr = cracking torsion (lb.in.) f'c = specified compressive strength of the concrete (psi) Acp = area enclosed by the outside perimeter of the concrete crosssection (in.2) = 7r2, for a circular section with radius r (in.) epp = outside perimeter of the concrete crosssection (in.) = 27r, for a circular section with radius r (in.) This equation, when applied to a circular section, results in an equivalent value when compared to the basic equation (Equation 22) for torsion noted in Roark and Young (1975). The equality is a result of taking the shear stress as 4ff'c. T = (22) 2 Where T = torsional moment (lb.in.) r = shear stress, 4/f'c, (psi) r = radius of concrete crosssection (in.) ACI 31805 11.6.1 (a) provides the threshold torsion for a nonprestressed member (Equation 23). This is taken as onequarter of the cracking torsion. If the factored ultimate torsional moment, T, exceeds this threshold torsion, then the effect of torsion on the member must be considered in the design. T = AC (23) Where 0 = strength reduction factor AASHTO (2004), AASHTO LRFD Bridge Design Specifications, also presents equations for cracking torsion (Equation 24) and threshold torsion (Equation 25). Equation 24 corresponds with the AASHTO (2004) equation for cracking torsion with the exception of the components of the equation related to prestressing. That portion of the equation was omitted since the foundation was not prestressed. It must be noted that these equations are the same as the ACI 31805 equations. A2 TC= 0.125 cp (24) Pc Where Tcr = torsional cracking moment (kipin.) Acp = total area enclosed by outside perimeter of the concrete crosssection (in.2) pc = the length of the outside perimeter of the concrete section (in.) AASHTO (2004) also specifies the same provision as ACI 31805 regarding the threshold torsion. In 5.8.2.1, it characterizes the threshold torsion as onequarter of the cracking torsion multiplied by the reduction factor. Equation 25 corresponds with the threshold torsion portion of AASHTO (2004) equation. T = 0.250T1r (25) The above referenced equations considered the properties and dimensions of the concrete. They did not take into consideration the added strength provided by the presence of reinforcement in the member. For the purposes of this research, it was important to consider the impact of the reinforcement on the strength of the concrete shaft. 2.3.2 Nominal Torsional Strength ACI 31805 11.6.3.5 states that if the ultimate factored design torsion exceeds the threshold torsion, then the design of the section must be based on the nominal torsional strength. The nominal torsional strength (Equation 26) takes into account the contribution of the reinforcement in the shaft. T, = 2AAf cotO (26) s Where T, = nominal torsional moment strength (in.lb.) Ao = gross area enclosed by shear flow path (in.2) A, = area of one leg of a closed stirrup resisting torsion with spacing s (in.2) fyt = specified yield strengthfy of transverse reinforcement (psi) s = centertocenter spacing of transverse reinforcement (in.) 0 = angle between axis of strut, compression diagonal, or compression field and the tension chord of the member The angle, 0, is taken as 45, if the member under consideration is nonprestressed. This equation, rather than taking into account the properties of the concrete, takes into account the properties of the reinforcement in the member. These inputs include the area enclosed by the reinforcement, the area of the reinforcement, the yield strength of the reinforcement, and the spacing of the reinforcement. For the purpose of this research, the reinforcement under consideration was the hoop steel. AASHTO (2004) also outlines provisions for the nominal torsional resistance in 5.8.3.6.2. Equation 27 is the same equation that ACI 31805 presents. The only difference is in the presentation of the equations. The variables are represented by different notation. 2AoAfy cot0 Tn = (27) s Where T, = nominal torsional moment (kipin.) Ao = area enclosed by the shear flow path, including any area of holes therein (in.2) At = area of one leg of closed transverse torsion reinforcement (in.2) 0 = angle of crack As the above referenced equation evidences, the ACI 31805 and the AASHTO (2004) provisions for nominal torsional strength are the same. Based on the code provisions, the nominal torsional strength represents the torsional strength of the crosssection. 2.3.3 Combined Shear and Torsion Another area that had to be considered in this research was the effect of combined shear and torsion. Both ACI 31805 and AASHTO (2004) outline equations for the combined shear and torsion. Since the foundation had a shear load applied to it, it had to be determined whether or not the shear load was large enough to necessitate consideration. The ACI 31805 equation (Equation 28) and the AASHTO (2004) equation (Equation 29) are presented hereafter. The ACI 31805 equation is located in 11.6.3.1 of ACI 31805, and the AASHTO (2004) equation is presented in 5.8.3.6.2 of that specification. The ACI 31805 equation is presented with V, substituted on the lefthand side. V < Vu + 1p7Ah (28) b" d 1 .7A2 h Where V, = factored shear force at section (lb.) bwd = area of section resisting shear, taken as Aoh (in.2) T, = factored torsional moment at section (in.lb.) ph = perimeter of centerline of outermost closed transverse torsional reinforcement (in.) Aoh = area enclosed by centerline of the outermost closed transverse torsional reinforcement (in.2) The AASHTO (2004) equation that is presented (Equation 29) is intended for the calculation of the factored shear force. For the purpose of this project, the righthand side of the equation was considered. V V = V (.92Ao (29) Where V, = factored shear force (kip) ph = perimeter of the centerline of the closed transverse reinforcement (in.) T, = factored torsional moment (kipin.) The determination of whether or not shear had to be considered was made based on a comparison of the magnitudes of the coefficients of these terms. This is investigated further in Chapter 3. 2.3.4 ACI Concrete Breakout Strength for Anchors In ACI 31805 Appendix D, the concrete breakout strength is defined as, "the strength corresponding to a volume of concrete surrounding the anchor or group of anchors separating from the member." A concrete breakout failure can result from either an applied tension or an applied shear. In this report, the concrete breakout strength of an anchor in shear, D.6.2, will be studied. The breakout strength for one anchor loaded by a shear force directed perpendicular to a free edge (Figure 25) is given in Equation 210. Vb = 7 f(c)5 (210) Where Vb = basic concrete breakout strength in shear of a single anchor in cracked concrete (lb.) Se = load bearing length of anchor for shear (in.) do = outside diameter of anchor (in.) ca, = distance from the center of an anchor shaft to the edge of concrete in one direction; taken in the direction of the applied shear (in.) The term te is limited to 8do according to D.6.2.2. The equations in ACI 31805 were developed based on a 5% fractile and with the strength in uncracked concrete equal to 1.4 times the strength in cracked concrete. The mean concrete breakout strength in uncracked concrete is provided in Fuchs et al. (1995) and given in Equation 211. Vb =13 d, J(c1)15 (211) For a group of anchors, Equation 212 applies. This equation is the nominal concrete breakout strength for a group of anchors loaded perpendicular to the edge in shear. A, Vcbg V= ,Vec,v Ved,V c Vb (212) Where Vcbg = nominal concrete breakout strength in shear of a group of anchors (lb.) Av = projected concrete failure area of a single anchor or group of anchors, for calculation of strength in shear (in.2) Avco = projected concrete failure area of a single anchor, for calculation of strength in shear, if not limited by corner influences, spacing, or member thickness (in.2) = 4.5(ca1)2, based on a 350 failure cone (Figure 26) fe, v = factor used to modify shear strength of anchors based on eccentricity of applied loads, ACI 31805 D.6.2.5 qed, v = factor used to modify shear strength of anchors based on proximity to edges of concrete member, ACI 31805 D.6.2.6 qci,v = factor used to modify shear strength of anchors based on presence or absence of cracks in concrete and presence or absence of supplementary reinforcement, ACI 31805 D.6.2.7, accounted for in Equation 211 The resultant breakout strength is for a shear load directed perpendicular to the edge of the concrete. Therefore, an adjustment had to be made to account for the shear load acting parallel to the edge since this was the type of loading that resulted from the torsion on the anchor group. In D.5.2. l(c) a multiplication factor of two is prescribed to convert the value to a shear directed parallel to the edge (Figure 27). Fuchs et al. (1995) notes that the multiplier is based on tests, which indicated that the shear load that can be resisted when applied parallel to the edge is approximately two times a shear load applied perpendicular to the edge. In order to convert the breakout strength to a torsion, the dimensions of the test specimen were considered to calculate what was called the nominal torsional moment based on the concrete breakout strength, Tn,breakout. 2.3.5 Alternate Concrete Breakout Strength Provisions In the book Anchorage in Concrete Construction, Eligehausen et al. (2006), the authors presented a series of equations for the determination of the concrete strength based on a concrete edge failure. These equations are presented in Chapter 4, 4.1.2.4 of the text. Equation 213 is the average concrete breakout strength of a single anchor loaded in shear. It must be noted that this equation is for uncracked concrete. Vc =3.0 do fc c0 (213) 0 e c200 al Where oV,c = concrete failure load of a nearedge shear loaded anchor (N) do = outside diameter of anchor (mm) te = effective load transfer length (mm) fcc200oo = specified concrete compressive strength based on cube tests (N/mm2) S1.i18f'c ca, = edge distance, measured from the longitudinal axis of the anchor (mm) a =0.1 e \a S = 0.1. do C al As was the case for the ACI 31805 equations, the term te is limited to 8do. Equation 214 accounts for the group effect of the anchors loaded concentrically. The authors stated that cases where more than two anchors are present have not been extensively studied. They did, however, state that the equation should be applicable as long as there is no slip between the anchor and the base plate. AV A V~ (214) Where Av = projected area of failure surface for the anchorage as defined by the overlap of individual idealized failure surfaces of adjacent anchors (mm2) Avco = projected area of the fully developed failure surface for a single anchor idealized as a halfpyramid with height ca1 and base lengths 1.5ca1 and 3ca1 (mm2) ACI 31805 specifies that, in order to convert the failure shear directed perpendicular to the edge to the shear directed parallel to the edge, a multiplier of two be applied to the resultant load. The provisions outlined in this text take a more indepth approach to determining this multiplier. The method for calculating this multiplier is detailed in 4.1.2.5 of Eligehausen et al. (2006). The authors stated that, based on previous research, the concrete edge breakout capacity for loading parallel to an edge is approximately two times the capacity for loading perpendicular to the edge if the edge distance is constant. The authors further moved to outline equations to calculate the multiplier based on the angle of loading. The first equation (Equation 215) that is presented in the text is a generalized approach for calculating the multiplier when the angle of loading is between 550 and 900 of the axis perpendicular to the edge. For loading parallel to the edge the angle is classified as 900 (Figure 27). 1 =aV = .(215) cosa + 0.5sina Where Wa,v = factor to account for the angle between the shear load applied and the direction perpendicular to the free edge of the concrete member a = angle of the shear load with respect to the perpendicular load This equation results in a factor of two for loading parallel to the edge. Equation 216 provides the concrete breakout strength for shear directed parallel to the edge using qfa,v. VUyC = Va'V *.Vu,c (216) Where Vuc,a= concrete failure load for shear directed parallel to an edge based on qa,v (N) An alternate equation for calculating this factor is also presented in the Eligehausen et al. (2006) text. This equation is only valid for loading parallel to the edge. This equation is based on research proposing that the multiplier to calculate the concrete breakout capacity for loading parallel to the edge based on the capacity for loading perpendicular to the edge is not constant. Rather, it suggested that it is based on the concrete pressure generated by the anchor. The base equation for the application of this factor is Equation 217. Suc, parallel = parallel V ,c (217) Where V ,= concrete failure load in the case of shear parallel to the edge (N) parallel = factor to account for shear parallel to the edge Vu,c = concrete failure load in the case of shear perpendicular to the edge (N) Equation 218 is used for the determination of the conversion factor parallel. =' parallel = 4 k n' cc (218) Where k4 = 1.0 for fastenings without hole clearance 0.75 for fastenings with hole clearance n = number of anchors loaded in shear fcc = specified compressive strength of the concrete (N/mm2) conversion tof'c as specified for Equation 213 The results of Equation 213 through Equation 218 are presented alongside the ACI 318 05 equation results in Chapter 3. These are presented for comparative purposes only. 2.3.6 ACI 31805 vs. AASHTO LRFD Bridge Design Specifications In Sections 2.3.1 through 2.3.3, both the applicable design equations in ACI 31805 and AASHTO (2004) were presented. As was shown, the ACI and AASHTO equations were the same. Additionally, the provisions for the concrete breakout failure capacity are only provided in ACI 31805. AASHTO does not provide design guidelines for this failure. Therefore, the ACI 31805 equations were used throughout the course of this research program. Figure 21. Cantilever sign structure at Exit 79 on Interstate 4 in Orlando Figure 22. New foundation installed at the site Figure 23. Failed foundation during postfailure excavation Figure 24. Concrete breakout of an anchor caused by shear directed parallel to the edge for a circular foundation Vb .. .. . . ... . : : :. : : : : : : : . . . . . . . . . . '. . . . . . . . . ............................... . . . . a . . . . . . . Figure 25. Concrete breakout failure for an anchor loaded in shear . .. . .. . . . . .'." ".'.'.'.'.'.'." .'.'.'.'.'.'.'.'.'.'." .'.'.'.'.'.'.'.'.'.'." .'.'.'.'.'.'.'.'.'.'." .'.'.'.'.'.'.'.'.'". .'.'.'.'.'.'.'.'.'.'." . .... . . .. . . ... . . .. . . .... . . .. . . . .... .. . .. . . .... ... . .. 1.5cal A vco=. 5cal 2(1.5cal) =4.5(al)2 Figure 26. Determination ofAvco based on the 35 failure cone .............................. .............................. .............................. .............................. .............................. .............................. .............................. .............................. .............................. .............................. .............................. .............................. .............................. . . . . . . ........... .............................. .............. ............... .............................. .............. ............... ............... .............. .............. ............... .............................. .............. ............... . . . . . . . . .............. 0 . . ...... ............. ::::::::::::::::::::::: ... ...Perpendicular . . .. . .. .. . . A.i . .4. ..:. . .I ... Figure 27. Shear load oriented (a) perpendicular to the edge and (b) parallel to the edge ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ ............. . . . . . . . ............. ............... ............... ............... ................ ............. .. ............... ............... ............................... . . . . . . . . . ............................... . . . . . . .......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................ ................................ ................................ ................................ ................................ ................................ ................................ ................................ CHAPTER 3 DEVELOPMENT OF EXPERIMENTAL PROGRAM After a thorough background investigation, it was determined that the most likely cause of the failure was the concrete breakout of an anchor loaded by a shear force directed parallel to a free edge. The shear force on the individual anchors was caused by torsion applied to the bolt group from the sign post. Based on this determination, an experimental program was formulated to determine if this was in fact the failure mode of the foundation. Therefore, it was of the utmost importance to design the test apparatus to preclude other failure modes. This chapter focuses on the development of the experimental program. 3.1 Description of Test Apparatus The test apparatus was designed such that the field conditions could be closely modeled for testing at the Florida Department of Transportation (FDOT) Structures Research Center. A schematic of the test apparatus is shown in Figure 31. The test apparatus consisted of: * A 30" (762 mm) diameter concrete shaft that extended 3'0" (914 mm) outward from the concrete block * Twelve 37" (940 mm), 1.5" (38.1 mm) diameter F1554 Grade 105 anchor bolts embedded into the concrete around a 20" (508 mm) diameter * A 16" (406 mm) diameter steel pipe assembly welded to a 24" (610 mm) diameter, 1" (25.4 mm) thick steel base plate with holes drilled for the anchor bolts to provide the connection between the bolts and pipe assembly * A 6'0" x 10'0" x 2'6" (1830 mm x 3050 mm x 762 mm) reinforced concrete block to provide a fixed support at the base of the shaft * Two assemblies of C 12x30 steel channels and plates to attach the block to the floor The base for the design of the various components of the test apparatus was one half of the size of the failed foundation investigated during the site visit. The dimensions of the field foundation are presented in Table 31. From that point, the elements of the test apparatus were designed to preclude all failure modes other than the concrete breakout failure of the anchors. Information pertaining to the design of the components of the apparatus is presented in the following sections. Figures 32 through 34 are drawings of the test apparatus. For large scale dimensioned drawings, reference Appendix A. Complete design calculations are located in Appendix B. 3.2 Shaft Design The starting point for the design of the concrete shaft was based on developing a test specimen approximately one half of the size of the foundation that was investigated during the site visit. From there, the various components of the shaft were designed the meet the ACI 318 05 requirements, and to prevent failure before the concrete breakout strength was reached and exceeded. All of the strengths were calculated using a concrete strength of 5500 psi (37.9 MPa), which was the strength indicated on the FDOT standard drawings. 3.2.1 Torsion Design The basic threshold torsional strength of the shaft, 24.6 kipft (33.4 kNm) was calculated using the ACI 31805 torsional strength equation (Equation 23). This strength, however, did not take into account the reinforcement in the shaft. Therefore, it was assumed that the threshold torsion would be exceeded. As a result, the torsional strength of the shaft was based on the nominal torsional strength. In order to calculate the torsional strength that the shaft would exhibit during testing, the ACI nominal torsional strength equation was applied. Before the strength was calculated, the minimum requirements for the shaft reinforcement were followed as outlined in ACI 31805 7.10.5.6 and 11.6.5.1. The nominal torsional strength (Equation 26) was then calculated for the specimen. This value, 253 kipft (343 kNm), was compared to the concrete breakout strength. The spacing of the hoop steel in the shaft was altered until the nominal torsional strength exceeded the concrete breakout strength. Hence, if the concrete breakout failure was the correct failure mode, it would occur before the torsional capacity of the shaft was exceeded during testing. 3.2.2 Longitudinal and Transverse Reinforcement As was outlined in the previous section, the required amount of hoop steel to meet the ACI 31805 specifications was determined using guidelines from Chapters 7 and 11 in the code. The resultant hoop steel layout was twentyfour #4 bars spaced evenly around a 27 in. (686 mm) diameter circle. The transverse hoops were comprised of #3 bars at 2.5 in. (635 mm) totaling fourteen #3 bar hoops. The required splice for the #3 bar was 12 in. (305 mm), and the development length required for the #4 bar into the concrete block was 8 in. (203 mm) with a 6 in. (152 mm) hook. In the test setup, the #4 bars extended 27 in. (686 mm) into the block, which exceeded the required length. This length was used for simplicity in design and construction of the test setup. The #4 bars were tied into one of the cages of reinforcement in the concrete block. 3.2.3 Flexure Due to the eccentric loading of the bolts, the flexural capacity of the shaft had to be calculated. It had to be determined that the shaft would not fail in flexure under the load applied during testing. The flexural reinforcement in the shaft was the longitudinal reinforcement, the #4 bars. The first step to determine the capacity was to assume the number of bars that would have yielded at the time of failure. From that point, the neutral axis of the shaft was located following the ACI 31805 concrete stress block methodology presented in Chapter 10 of the code. It was then checked if the number of bars that had yielded was a good assumption. Once this was verified, the nominal moment capacity of the shaft was calculated, and, then, compared to the maximum flexural moment based on the concrete breakout capacity. The flexural capacity of the shaft, 262 kipft (355 kNm), exceeded the maximum flexural moment on the shaft, 60.6 kipft (95.2 kNm). 3.3 Anchor Design 3.3.1 Diameter of Anchor Bolts The starting point for the diameter of the F1554 Grade 105 anchor bolts to be used in the test apparatus was based on half the diameter of those in the field specimen. The size determined using that methodology was 1 in. (25.4 mm). Once the concrete breakout strength capacity of the anchors was determined, the corresponding shear load on each of the bolts was calculated. The anchor bolt diameter had to be increased to 1.5 in. (38.1 mm) in order to ensure that the bolts would not experience steel failure in flexure or shear. The maximum flexure on the bolts was calculated by taking the maximum shear applied to each bolt and calculating the corresponding maximum flexural moment (Figure 35). The lever arm (Equation 31) for the calculation of the capacity was defined in Eligehausen et al. (2006) Section 4.1.2.2 b. S= e1 +a3 (31) Where: / = lever arm for the shear load (in.) el = distance between the shear load and surface of concrete (in.) a3 = 0.5do, without presence of a nut on surface of concrete, Figure 35 (in.) 0, with a nut on surface of concrete The base plate was restrained against rotation, and translation was only possible in the direction of the applied shear load. The maximum applied moment for each bolt was calculated based on these support conditions and the lever arm calculation. Full fixity occurred a distance a3 into the shaft. Using the section modulus of the bolts, the stress was then calculated and compared to the yield strength of the bolts, 105 ksi (724 MPa). The shear strength of the bolts was calculated using the provisions in Appendix D of ACI 31805. In both cases it was determined that the bolts had sufficient strength. 3.3.2 Concrete Breakout Strength of Anchor in Shear Parallel to a Free Edge The breakout strength provisions outlined in ACI 31805 Appendix D and the breakout provisions introduced in Eligehausen et al. (2006) were applied to the design of the shaft. Equation 211, from ACI 31805, was used as the primary equation for the calculation of the breakout strength. In order to apply the ACI provisions to the circular foundation a section of the concrete was ignored (Figure 36). If the full cover, c, was used in the calculation, the failure region would have included area outside of the circle. Rather than extending beyond the edge of the concrete, the 35 degree failure cone (Figure 26) was extended to the edge of the shaft as shown in Figure 36. Equation 32 was developed to determine the adjusted cover, cal. r2 +3.25(r2 r 2)r a = (32) 3.25 Where rb = radius measured from the centerline of the bolt to the center of the foundation (in.) (Figure 36) r = radius of circular foundation (in.) As presented in Section 2.3.4, the projected concrete failure area for a single anchor, Avco, is equivalent to 4.5(ca1)2. Figure 37 illustrates the development of the projected concrete failure area for a group of anchors, Avc, as a function of the number of bolts, n, the radius of the shaft, r, and the adjusted cover. The resultant concrete breakout strength using the adjusted cover approach was conservative relative to assuming the full cover. Equation 33 and Equation 34 are used to calculate the concrete breakout torsion, Tn,breakout, and are based on the ACI provisions for shear parallel to the free edge. For A_ < sin' 1 5c A~ ) ],breakout = 2 AVC Vb rb (33) AVco For A > sin 1.5cal (i.e. no overlap of failure cones) ] =,breakout = 2 n Vb .rb (34) Where A = angle of circular sector for each bolt (deg) (Figure 37) ca, = adjusted cover (in.) (Equation 32) rb = radius measured from the centerline of the bolt to the center of the foundation (in.) (Figure 36) Avc = projected concrete failure area of a group of anchors (in.2) (Figure 37) A, = projected concrete failure area of a single anchor (in.2) (Figure 36) Vb = concrete breakout strength in shear for a single anchor calculated using Equation 2 11 with ca, as calculated in Equation 32 (lb.) n = number of bolts Using Equation 33, the ACI concrete breakout torsion for the test specimen was determined to be 182 kipft (247 kNm), which was less than the nominal torsional capacity. During the analysis of the design equations, an issue arose regarding the calculation of the Eligehausen et al. (2006) factor Vparallel. The result of Equation 218 was 4.06 compared to the ACI 31805 factor and qa,v of 2.0. This prompted an investigation of the application of the multiplier to the circular foundation in this research program. The majority of the tests for the determination of Vu,c (Equation 214) were for groups of two bolts. Therefore, it was investigated how the Avc/Avo term is affected by the spacing between the bolts and the number of bolts. Figure 38 shows that for spacing, s, of 3. Oca or greater there is no overlap of the breakout cones. In those cases the strength is the sum of the single anchor strengths. Figure 39 illustrates the overlap of the breakout cones. The Avc/Avoc term is used to calculate the breakout strength for the case where the failure cones overlap. Av/Avco can be normalized by dividing by the number of bolts. An increase in the number of bolts at the same spacing along a straight edge leads to a reduction in the normalized A V/AVco term. This reduction is illustrated in Figure 310. The contribution of the failure cone outstanding "legs" at the ends of the group area, Ave, decreases as the number of bolts increases. For a circular foundation, with s<3. Ocal, there is a constant overlap of the failure cones with no outstanding "legs" (Figure 311). The equivalent number of bolts along a straight edge is taken as infinity in order to represent a circular foundation (i.e. no outstanding "legs"). Therefore, the normalized Avc/Avco term for this case was calculated for an infinite number of bolts at the prescribed spacing for the foundation. To convert these ratios into a multiplier for WVparallel, the ratio of the normalized A vc/Avco for an infinite number of bolts to the normalized term for two bolts was calculated. That multiplier, 0.52, was applied to the parallel term resulting in an adjusted parallel of 2.1. This resulting value agreed with the ACI 31805 factor and the Eligehausen et al. (2006) factor qaW,vof 2.0. The resultant concrete breakout torsions, based on the Eligehausen et al. (2006) concrete breakout strength (Equation 213), were 167 kipft (227 kNm) using parallel of 2.1 in Equation 217, and 159 kipft (216 kNm) using Ia,Tv of 2.0 in Equation 216. These torsions were calculated using the same moment arm, rb, used in Equation 33 and Equation 34. These results and the results of the other calculations are summarized in Table 32. 3.3.3 Development Length of the Bolts Another key aspect of the shaft design was to ensure that the anchor bolts were fully developed. In order to meet the code requirements, the splice length between the #4 bars and anchor bolts was calculated using the development length equations presented in ACI 31805 Chapter 12. The bolts needed overlap the #4 bars across 26.7 in. (678 mm), and in the test setup the overlap was 29 in. (737 mm). Therefore, this requirement was met. 3.4 Steel Pipe Apparatus Design The components of the steel pipe apparatus included the pipe, which was loaded during testing, and the base plate. The pipe design was based on the interaction between torsion, flexure, and shear as presented in AISC (2001), LRFD Manual of Steel ConstructionLRFD Specification for Steel Hollow Structural Sections. Each of the individual capacities was calculated for various pipe diameters and thicknesses. The individual strengths were compared to the projected failure loads for testing, the concrete breakout failure loads. In addition to verifying that the capacity of the pipe exceeded those loads, the interaction of the three capacities was verified. The purpose was to check that the sum of the squares of the ultimate loads divided by the capacities was less than one. Based on this analysis, it was concluded that an HSS 16.000 x 0.500 pipe would provide sufficient strength. In order to load the pipe, it needed to have a ninety degree bend in it. This was achieved by welding two portions of pipe cut on fortyfive degree angles to a steel plate. The weld size for this connection was determined such that the effective throat thickness would equal the thickness of the pipe, which was 0.50 in. (12.7 mm). The factors included in the design of the base plate were the diameter of the pipe, required weld size, bolt hole diameter, and the required distance between the edge of the bolt hole and the edge of the plate. The required width of the weld between the base plate and the pipe was calculated such that the applied torsion could be transferred to the plate without failing the weld. From that point, the bolt hole location diameter had to be checked to ensure that there was sufficient clearance between the weld and the nuts. It was important that the nuts could be fully tightened on the base plate. A 0.25 in. (6.35 mm) oversize was specified for the bolt hole diameter. This oversize was based on the standard oversize used in the field. Beyond that point, it was ensured that there would be sufficient cover distance between the bolt hole and the edge of the plate. The design of the components of the steel pipe apparatus was crucial because these pieces had to operate efficiently in order to correctly apply load to the bolts. If the apparatus were to fail during testing, the objective of the research could not be achieved. The weight of the pipe apparatus was calculated in order to normalize the load during testing. The load applied to the anchorage would be the load cell reading less the weight of the pipe apparatus. 3.5 Concrete Block Design The design of the concrete block was based on several key factors to ensure that it served its purpose as a fixed support at the base of the shaft. The amount of reinforcement required was based on a strutandtie model of the block as outlined in ACI 31805 Appendix A and, as an alternate approach, beam theory to check the shear strength and flexural strength of the block. For the flexural capacity calculations, the ACI 31805 concrete stress block provisions were utilized. Based on the results of both approaches, it was determined that 3 #8 bars, each with a 12 in. (305 mm) hook on both ends, spaced across the top and the bottom of the block were required. Additionally, two cages of #4 bars were placed in the block on the front and back faces meeting the appropriate cover requirements to serve as supplementary reinforcement. The purpose of reinforcing the block was to ensure structural stability of the block throughout the testing process. Two channel apparatuses were also designed in order to tie the block to the floor of the laboratory in order to resist overturning. The loads that had to be resisted by each tiedown were calculated such that the floor capacity of 100 kips (445 kN) per tiedown would not be exceeded. The channels were designed in accordance with the provisions set forth in AISC (2001). The welds between the channels and steel plates had to be sufficiently designed such that the channels would act as a single unit thereby transferring load from the plates through the channels. Also, the channels were spaced far enough apart to fit 1.5 in. (38.1 mm) bolts between the channels. A 0.25 in. (6.35 mm) oversize was specified for the spacing of the channels and the holes in the steel plates. The construction drawings for the channels are located in Appendix A. In addition to assuring that the concrete block system had sufficient capacity to resist the applied load, the bearing strength of the concrete had to be calculated. This was done in order to verify that the concrete would not fail in the region that was in contact with the steel channels. The bearing strength was found to be sufficient. As a result, it was concluded that the concrete block system would efficiently serve as a fixed connection, and under the loading conditions it would not prematurely fail. 3.6 Combined Shear and Torsion As was presented in Chapter 2, a calculation had to be carried out to ensure that shear need not be considered in the design. Rather than inputting the values for the ultimate shear and ultimate torsion into Equation 28, the coefficients of these terms were calculated. The base for doing so was to input the torsion as a function of the shear. For the test specimen, the ultimate torsion, T,, was taken as the moment arm multiplied by the ultimate shear, Vu. The moment arm for the load was 9 ft. (2740 mm). As an alternate approach, the actual concrete breakout strength and the corresponding shear could have been inputted into the equation rather than the generic variables. The result of the calculation to determine the coefficients was that the coefficient for the shear term was 1 compared to a coefficient of 88 for the torsion term. This calculation sufficiently verified that the shear contribution could be ignored in design. 3.7 Overview The previous sections detailed the design of the various components of the experimental program. It was of the utmost important to verify that the apparatuses not pertaining to the foundation failure would not fail during testing (i.e. concrete block system and pipe apparatus). Furthermore, all other foundation failure modes had to be precluded in the design. This ensured that if the concrete breakout failure in shear was the failure mode it would be observed during testing. Figure 312 and Figure 313 show the fully assembled test specimen at the Florida Department of Transportation Structures Research Center. CONCRETE BLOCK SHAFT BASE PLATE PIPE ASSEMBLY hL I I LOAD LOCATION Figure 31. Schematic of test apparatus Figure 32. Front elevation of test apparatus Figure 33. Plan view of test apparatus Figure 34. Side elevation of test apparatus Leveling Nut Figure 35. Lever arm for the calculation of bolt flexure Figure 36. Adjusted cover based on a single anchor and 350 failure cone chord = 2r sin  r^sin \ /,..2 Figure 37. Development of the projected failure area for the group of anchors around a circular foundation 1.5ca, 1.5ca, 1..5c 1.5c Cal s=3. 0c1a Figure 38. Two anchor arrangement displays the minimum spacing such that no overlap of the failure cones occurs Figure 39. Overlap of failure cones II r H "Leg"_ "Leg" A Vc Leg" "Leg" Figure 310. The contribution of the "legs" of the failure cone to Avc along a straight edge decreases as the number of bolts increases Figure 311. Overlap of failure cones for a circular foundation Figure 312. Assembled test specimen Figure 313. Shaft with pipe apparatus attached prior to instrumentation being attached Table 31. Field dimensions Component Field Dimension Shaft Diameter 60 in. Hoop Steel Diameter 46 in Hoop Steel Size #5 Longitudinal Steel #9 Size Anchor Bolt Diameter 2 in. Anchor Embedment 55 in. Bolt Spacing 36 in. Diameter Base Plate Diameter 42 in. Base Plate Thickness 11/ in. Table 32. Summary of design calculations Component Design Type Shaft Cracking Torsion Basic Torsion Threshold Torsion Nominal Torsion Anchor ACI Concrete Breakout Eligehausen et al. Concrete Breakout Eligehausen et al. Concrete Breakout Bolt Flexure Bolt Shear Equation Reference (21) (22) (23) (24) (212) (216) (217) Result 131 kipft 131 kipft 24.6 kipft 253 kipft 182 kipft 159 kipft 167 kipft 253 kipft 1756 kipft CHAPTER 4 IMPLEMENTATION OF TESTING PROGRAM In order to proceed with testing the specimen presented in Chapter 3, important considerations had to be made. The first area under consideration was the concrete strength. It was important to determine this to calculate the predicted failure mode prior to testing. Also, the flexural and shear strengths of the bolts were calculated using the specified yield strength. The other area that was of key importance was the instrumentation. The instrumentation was required to produce meaningful data during testing. The other section of this chapter is on the carbon fiber reinforced polymer (CFRP) wrap used in the retrofit test. 4.1 Materials 4.1.1 Concrete Strength As it was stated in Chapter 3, the initial calculations for the design of the test setup were carried out on the assumption of a concrete strength of 5500 psi (37.9 MPa). The concrete breakout strength was recalculated based on the concrete strength at the time of testing. On the date of the test, the concrete strength was 6230 psi (43 MPa). This strength was calculated based on the average of three 6 in. (152 mm) x 12 in. (305 mm) cylinder tests. 4.1.2 Bolt Strength The yield strength of the F1554 Grade 105 anchor bolts was assumed to be 105 ksi (723.95 MPa). This was used to calculate the flexural strength and shear strength of the bolts. 4.1.3 Carbon Fiber Reinforced Polymer Wrap The first test was considered concluded after significant cracking and when the test specimen stopped picking up additional load. The loading was ceased before the specimen completely collapsed. The reason for doing so was to enable a second test to be performed on the specimen after it was retrofitted with a carbon fiber reinforced polymer (CFRP) wrap. The second test verified whether the CFRP wrap was an acceptable means to retrofit the failed foundation. The amount of CFRP that was applied to the shaft was determined by calculating the amount of CFRP required to bring the shaft back to its initial concrete breakout strength. The CFRP wrap that was used for the retrofit was SikaWrap Hex 230C. The properties of the wrap were obtained and the ultimate tensile strength was used to calculate the required amount that needed to be applied. The property specifications for the SikaWrap were based on the mean strength minus 2 standard deviations. ACI (2002), ACI 440.R02, 3.3.1 specifies that the nominal strength to be used for design be based on the mean strength less 3 standard deviations. Therefore, the design strength provided by Sika was adjusted to ensure that the design met the ACI specifications. The method for calculating the amount of CFRP required was to convert the torsion to a shear load per bolt. The shear load, which was directed parallel to the edge, had to be adjusted to such that it was directed perpendicular to the edge. In order to do this, the ACI multiplier of 2 was divided from the load. That load per bolt directed perpendicular to the edge was converted to a pressure around the circumference of the shaft. The equivalent tension that had to be resisted by the CFRP wrap was then calculated, and the amount of CFRP to provide that tensile strength was determined. Figure 41 illustrates this method. Two layers of the wrap were prescribed to meet the ACI concrete breakout strength based on assuming that the full 12 in. (305mm) width of the CFRP wrap would not be effective. Rather, it was assumed that the depth of the concrete breakout failure cone based on the cover, 1.5cover, was the effective width, 7.5 in. (191 mm). Three layers of the CFRP wrap were applied to the specimen. The addition of the extra layer exceeded the required strength, so it was deemed acceptable. Once the wrap was set, the retrofit test was carried out. Calculations for the design of the CFRP wrap layout are located in Appendix B. 4.2 Instrumentation 4.2.1 Linear Variable Displacement Transducers Linear Variable Displacement Transducers (LVDTs) were placed at the location of the load cell, and at various points along the shaft and base plate. A total often LVDTs were utilized in the project. Figure 42 is a schematic of the layout of the LVDTs on the base plate. Figure 43 and Figure 44 show the location of the LVDTs on the shaft, and Figure 45 shows the LVDT at the load location. The denotation for each of the LVDTs is also on the drawings. These identification codes were used to denote the LVDTs during testing. The purpose of the LVDTs along the shaft and base plate was to allow for the rotation of the base plate to be measured during the testing. The LVDTs at the front and back of the shaft were to allow for the rotation to be measured relative to the rotation of the shaft. The intent in the project was such that the shaft would not rotate; only the base plate would rotate as the bolts were loaded. The horizontal LVDT on the base plate was intended to indicate if there was any horizontal movement of the base plate. The rotation of the base plate was calculated using Equation 41. RDi +Dz} (41) R = tan (41) D gage Where R = base plate rotation (rad) D1v = displacement of LVDT D1V (in.) Ds = displacement of LVDT D3 (in.) Dgage = distance between LVDTs D1V and D3 (in.) Once the test apparatus was assembled, the distance Dgage was measured. This distance was 26.31 in. (668 mm). Figure 46 shows LVDTs D1V and D4 on the test specimen. 4.2.2 Strain Gages Strain gages were attached to the base plate on the outer surface adjacent to the bolt holes in order to determine how may bolts were actively transferring load given the 1.75 in. (44.5 mm) holes for the 1.5 in. (38.1 mm) anchors. In applying the ACI 31805 equation for concrete breakout strength of an anchor in shear directed parallel to an edge (Equation 212) it was of key importance to know how many bolts were carrying the load. For instance, if two bolts were carrying the load, the concrete would fail at a lower load than if all twelve bolts were carrying the load. In addition to showing the placement of the LVDTs, Figure 42 also details the location of the strain gages on the base plate. Figure 47 shows the denotation of the strain gages relative to the bolt number, and Figure 48 shows a strain gage on the base plate of the test specimen. Note that the bolt numbering starts at one at the top of the plate and increases as you move clockwise around the base plate. Divide by 2 J T TCFRP c ^FRP \ Figure 41. Method for the determination of the tension, TCFRP, that must be resisted by the CFRP wrap Strain Figure 42. Instrumentation layout on the base plate D6 Figure 43. Instrumentation layout on face of shaft I Figure 44. Instrumentation layout on rear of shaft/face of concrete block I D1 Figure 45. Instrumentation layout of pipe at load location Figure 46. Location of LVDTs D1V, D4, and D7 on the test specimen Bolt 1 / Figure 47. Strain gage layout on base plate Figure 48. Strain gage on base plate of test specimen Figure 48. Strain gage on base plate of test specimen CHAPTER 5 TEST RESULTS Two tests were performed on the test specimen. The initial test was conducted to determine whether the concrete breakout failure was the failure mode demonstrated in the field. The verification of this was based on the crack pattern and the failure load recorded. If the failure torsion was the concrete breakout failure torsion, then the hypothesized failure mode would be verified. The retrofit test was performed on the same test specimen. This test was completed to establish whether a CFRP wrap was an acceptable retrofit for the foundation. 5.1 Initial Test 5.1.1 Behavior of Specimen During Testing The initial test on the foundation was carried out on 31 August 2006 at the Florida Department of Transportation Structures Research Center. The test specimen was gradually loaded during the testing. Throughout the test, the formation of cracks on the surface of the concrete was monitored (Figures 51 and 52). At 90 kipft (122 kNm), the first cracks began to form. When 108 kipft (146 kNm) was reached, it was observed that the cracks were not extending further down the length of the shaft. Those cracks that had formed began to slightly widen. These cracks, Figure 51, were characteristic of those that form during the concrete breakout failure. At 148 kipft (201 kNm), cracks spanning between the bolts had formed (Figure 53). The foundation continued to be loaded until the specimen stopped taking on more load. The torsion load peaked at 200 kipft (271 kNm). Loading ceased and was released when the applied torsion fell to 190 kipft (258 kNm). The predicted concrete breakout capacity of the shaft at the time of testing was calculated as 193 kipft (262 kNm) (Equation 33). At failure, the foundation displayed the characteristic cracks that one would see in a concrete breakout failure (Figure 54). As intended, the bolts did not yield, and the shaft did not fail in torsion. Data was reduced to formulate applied torsion versus plate rotation and applied torsion versus bolt strain plots. The Applied Torsion vs. Plate Rotation plot (Figure 55) shows that the bolts ceased taking on additional load after the noted concrete breakout failure due to the shear parallel to the edge resulting from the applied torsion. It also exhibits slope changes at the loads where crack development started or the existing cracks were altered. The first slope change at 108 kipft (146 kNm) coincided with the widening of the characteristic diagonal cracks on the front face of the shaft. The second change occurred at 148 kipft (201 kNm) corresponding with the formation of cracks between the bolts. 5.1.2 Behavior of Strain Gages During Testing Figure 56 displays the Applied Torsion vs. Bolt Strain plots for each bolt relative to its location on the foundation. Recall that the term bolt strain refers the measurement of the strain in the base plate at the bolt location. The strain was a result of the bolt carrying load. The first line on the plots in Figure 56 is 50 kipft (67.8 kNm). At this level, all of the bolts were carrying load with the exception of bolts one, six, and eight. At the next level, 100 kipft (136 kNm) bolt one picked up load, but bolts six and eight remained inactive. It must be noted that, at 108 kipft (138 kNm), which was the first slope change on the Applied Torsion vs. Plate Rotation Plot, a redistribution of the loading occurred. This redistribution is illustrated in Figure 57. As the cracks widened, those bolts that were transferring the majority of the load were able to move more freely, and, therefore, the other bolts became more active in transferring the load to the foundation. A similar redistribution to a lesser degree occurred at approximately 148 kipft (201 kNm), which coincided with the first observation of cracks between the bolts. As the various plots illustrate, some of the strain gages recorded negative strains, while others recorded positive strains. This was most likely due to the bearing location of the bolt on the base plate. Although this occurred, the relative strain readings were considered acceptable. To further explore this phenomenon, strain gages were placed on the bottom of the base plate in addition to those on the top for the second test. 5.1.3 Summary of Initial Test Results The results of this test indicated that the concrete breakout failure was the failure mode observed in the site investigation. The characteristic cracks and the structural integrity of the bolts in the failed foundations, as observed during the site investigation, was the first step to arriving at this failure mode. The percent difference between the failure torsion and the predicted failure torsion (Equation 33) was 3.6%. Therefore, it was concluded that the foundation failed at the failure torsion for the predicted failure mode. These results indicated that the design methodology for cantilever sign foundations should include the concrete breakout failure due to shear directed parallel to an edge resulting from torsional loading. All plots for the first test are located in Appendix C. 5.2 CFRP Retrofit Test After the results of the first test were reviewed, the need for a method to strengthen existing foundations became apparent. Since the concrete breakout failure had not been considered in the design of the cantilever sign structure foundations, a system had to be put in place to evaluate whether or not those existing foundations would be susceptible to failure. One economical method of retrofitting the existing foundations is the use of Carbon Fiber Reinforced Polymer (CFRP) wraps. Recall that, at the conclusion of the first test, the bolts had not yielded, and the concrete was still intact. This enabled a second test on the failed foundation to be carried out. The key focus of this second test was to determine if the foundation could reach its initial concrete breakout strength again. The foundation was retrofitted with three layers of 12 in. (305 mm) wide SikaWrap Hex 230C (Figure 58). This amount of CFRP exceeded the amount required to attain the concrete breakout strength, 193 kipft (262 kNm). The torsional strength of the shaft with the CFRP wrap was calculated. The resultant strength based on the effective width, Section 4.1.3, of 1.5cover, or 7.5 in. (191 mm), was 229 kipft (310 kNm). Since that effective depth was an assumption for design, the strength based on the full width, 12 in. (305 mm), of the wrap, 367 kipft (498 kNm), was also calculated for reference. 5.2.1 Behavior of Specimen with CFRP Wrap During Testing The second test was conducted on 13 September 2006. For this test, the concrete strength was not required to be known, since the concrete had already failed. The containment provided by the CFRP wrap, along with the anchor bolts, was the source of the strength of the foundation. As the purpose of the second test was to learn how much load the foundation could take, and if that load met or exceeded the concrete breakout strength, the load was not held for prolonged periods at regular intervals during the test. Figure 59 is the Applied Torsion vs. Plate Rotation plot for the second test. The foundation was closely monitored for crack formation along the shaft, propagation of existing cracks, and failure of the CFRP wrap. The strength of the foundation exceeded the predicted concrete breakout strength of 193 kipft (262 kNm). It was not until the loading reached 257 kipft (348 kNm) that the first pops of the carbon fibers were heard. At that torsion load, the strength of the CFRP wrap based on the effective depth, 229 kipft (310 kNm), was exceeded. Therefore, the effective depth of the wrap was a conservative assumption. At approximately 288 kipft (390 kNm) more pops were heard. However, the carbon fiber did not fail. During the course of the test, characteristic torsion cracks began to form along the shaft (Figure 510) and propagated to the base of the shaft. This occurred because the ACI 318 05 nominal torsional strength (Equation 26) of 253 kipft (343 kNm) was exceeded. Although these cracks had formed, the foundation still had not failed. Another phenomenon that occurred was the yielding of the bolts. According to the calculations for the yield strength of the bolts, the bolts yielded at approximately 253 kipft (343 kNm) of applied torsion. The strength was determined using the same methodology outlined in Section 3.3.1. This was the within the range in which the yielding was observed (Figure 59). The bolts were yielding, but they did not reach their ultimate strength. The test abruptly concluded when the concrete block shifted out of place, causing the load cell to be dislodged from its location on the pipe. This occurred at 323 kipft (438 kNm). 5.2.3 Behavior of Strain Gages During Testing For the retrofit test, strain gages were placed on the top and bottom of the base plate. Figure 511 shows each of the Applied Torsion vs. Bolt Strain plots at the appropriate bolt locations. Note that as the loading increased, the bottom strain gages began to behave similarly for all of the bolts. The strain was increasing at a higher rate. This illustrated that as the bolts picked up load and began to bend, they were primarily in contact with the bottom of the base plate (Figure 512). The strains recorded by the bottom gages indicate that all of the bolts became active during the test. Similar to the behavior of the bolts throughout the initial test, Figure 513 illustrates the changes in the bolt strain data for the top gages corresponding with milestone loads during the test. 5.2.4 Summary of Test Results Upon removal of the pipe apparatus, the crack pattern illustrated the concrete breakout failure, and torsional cracks in the center of the shaft verified that the torsional capacity was exceeded during testing (Figure 514). Figure 515 details the characteristic torsion cracks on the side of the shaft after testing. The test proved that the CFRP wrap was an acceptable method for retrofitting the foundation. It exceeded the concrete breakout strength. The success of this retrofit test led to the development of guidelines for the evaluation of existing foundations and the guidelines for the retrofit of those foundations in need of repair. All plots for the retrofit test are located in Appendix D. Figure 51. Initial cracks on face of shaft f7 / em & it I I t4 'tt A\4a6 Figure 52. Initial cracks on face and side of shaft (alternate view of Figure 51) Figure 53. Face of test specimen after testing exhibits cracks between the bolts along with the characteristic concrete breakout cracks Figure 54. Crack pattern on face of shaft after testing depicts characteristic concrete breakout failure cracks 250 200 S150 o E 100 B. 50 0 Figure 55. Applied Torsion vs. Plate Rotation Plot Initial Test 68 Peak Applied Torsion Crack Formation Between Bolts Cracks Begin to Widen 0 0.5 1 1.5 2 2.5 3 Rotation (deg) Figure 56. Applied Torsion vs. Bolt Strain Plots for each bolt at the appropriate location on the base plate with Applied Torsion vs. Plate Rotation plot in center (full size plots in Appendix C) 200 Crack Formation Between Bolts S150,, .7. .. .  100 / Cracks Begin to Widen 50 ' 0 750 600 450 300 150 0 150 300 450 600 750 Microstrain Figure 57. Bolt Strain Comparison Plot for Initial Test exhibits the redistribution of the load coinciding with crack formations Figure 58. Shaft with the CFRP wrap applied prior to testing 350 300 S250 S200 150 100 50 0.5 1 1.5 2 2.5 Rotation (deg) Figure 59. Applied Torsion vs. Plate Rotation Plot Retrofit Test Figure 510. Shaft exhibiting characteristic torsion cracks from face to base of shaft 4.5 5 I 4I I I I I 10 I I .... A ....7 ......A..... Figure 511. Applied Torsion vs. Bolt Strain plots for the Retrofit Test at the appropriate bolt location around the base plate with Applied Torsion vs. Plate Rotation plot in center (full size plots in Appendix D) I Ell Base Plate Bearing Location Figure 512. Bolt bearing on the bottom of the base plate during loading 350 300 250 ". S200 a 150 100 50 0 1100 825 550 275 0 275 550 825 1100 Microstrain Figure 513. Bolt Strain Comparison plot for the retrofit test exhibits slope changes at milestone loads Bolts Yielded ACI Concrete Breakout Strength ________^ H ^ ^ / ____ ^y^ Figure 514. Face of shaft after test illustrates yielding of bolts, concrete breakout cracks around the perimeter, and torsion cracks in the center. Figure 515. Torsion cracks along length of the shaft after the test CHAPTER 6 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS The purpose of this research program was to determine the cause of the failure of foundations of cantilever sign structures during the 2004 hurricane season. After a thorough literature review, in conjunction with the site investigation, and testing, it was determined that the foundations failed as a result of an applied torsion which caused a concrete breakout failure due to shear directed parallel to the edge on the anchors. This anchorage failure is detailed in ACI 31805 Appendix D. Previous to this experimental research, this failure mode was not considered in the design of the cantilever sign foundations. Cantilever sign foundations need to be designed for shear parallel to the edge on the anchor resulting from torsion. Test results indicate that the failure of the foundations was caused by concrete breakout due to shear directed parallel to the edge on the anchors. The test specimen failed at the torsion predicted by the ACI 31805 Appendix D design equations. Additionally, the crack pattern matched the crack pattern exhibited in the field, and both foundations emulated the characteristic crack pattern of the shear directed parallel to an edge for concrete breakout failure. It is recommended that future tests be performed on circular foundations to further investigate the concrete breakout failure for a shear load directed both parallel and perpendicular to an edge. Additional testing was performed to determine an acceptable retrofit option. It was determined that applying a CFRP wrap to the foundation strengthens the foundation such that it not only meets its initial concrete breakout capacity, but, also, exceeds the capacity. The results of this test led to the development of guidelines for the evaluation and repair of existing foundations. The guidelines were based on the following: S Using either the torsional load from the design or, if not available, using the ACI nominal torsional strength (ACI 31805 11.6.3.6), determine the torsional capacity of the foundation. * Calculate the concrete breakout strength in accordance with ACI Appendix D. * If the concrete breakout strength is less than the maximum of the nominal torsional strength and design torsion, then the foundation is susceptible to failure. * The amount of the SikaWrap 230C required is calculated using the maximum of the nominal torsional strength and the design torsion. The amount required is given in layers of the CFRP wrap. These guidelines were submitted to the Florida Department of Transportation. The guidelines will be used to evaluate and, if necessary, repair the existing foundations. It is critical that such foundations be evaluated in order to determine the susceptibility to this type of failure. The proper use of the findings of this research program will allow for future prevention of the failures exhibited during the 2004 hurricane season. APPENDIX A TEST APPARATUS DRAWINGS e 1]n__ 1IFel 2 2[2_I_ ' Sr 9. E  . . .  t  S em " /   tI v __ ,__/ _ = ~ a*~ 1 I, c: i' Qr4 __ is F I Ct C)n C g e B3 e C) C Ct3 C) S~ 64 I"I    ..  . .. ', . . ..   n. ,.,._ I 4 '0 S  a: e SC .<. ,& Sb S P Ii Q) igA 4 K 3 u r eL ~c16; fff Pld 9 Bsd w8 ~C~~el r 4 ~1 APPENDIX B DESIGN CALCULATIONS Design of Test Program Input Shaft d := 30in Diameter of the Shaft f := 5500psi Concrete Strength Hoop Steel BarSize Hoop := 3 Hoop Steel Size sh:= 2.5in Spacing of Hoop Steel ft = 60ksi Yield Strength of Hoop Steel dh:= 27n Hoop Steel Diameter Bar Size Long:= 4 Longitudinal Steel Size torsion = 075 ACI 31805 9.2.3.2 Moment Arm:= 9f1 ORIGIN 1 Bolts do:= 15in Diameter of the Bolt db:= 20in CenterCenter Diameter of Bolts boltt= 105ki No Bolts:= 12 Number of Bolts CFRP Properties tC. := 0.u5]h in Thickness of \\rap fn CtRI := 91lksi Tensile Strength of CFRP w cF I, := 12in Width of CFRP Sheet For the Hield model, FI554 Grade 55 Anchor Bolls were used. tboltfield:= 55ksi Failure Equations Torsion Cracking Torsion Acp := Pp 2 cp 2 2 c ..ACcp Ter: 4 .psl  Psi Pep) Basic Torsion T: 4 Ipsi psi (ds3 Tbasic 2 Threshold Torsion \Cp =p l. I 2n lcr = 131 nI L kp. Li Th.I, 11 'I kLpIi Tthreshold = @torsion psl Spsi t Pcp) Nominal Torsional StrengthPcp Nominal Torsional Strength I l.2cshold = 2 7 k!prt Ao: .(dh 2)2 Area enclosed by hoop steel At:= I.[(Bar Size Hoopin + 8) 2]2 Area of hoop steel S: 45 ACI3180511.6.3.6 (a) Grad: 0. 180 2AoAtf ot T, torsion: "t( rad) sh A 5712 56 i A i II In rd l 7 In ls,.UU= '5 kiptt Combined Shear and Torsion T,(Vu) := V.Moment Armkip If V := 1kip T( Coefficient Shear:= Coefficient Torsion : Ah:= Ao Aoh = 572.56 in" p11:= ndh Ph = 84.82 in V) := Vu.Moment_Arm SVu , kip Aoh in2 Tu(Vu) Ph2 kipin in 2 1.7 _ 1 A "2J Coefficient Torsion CofficientShear88.58 Cocfficient Shcar The coefficient for the torsion term is 88 times that of the shear term. Therefore. shear need not be considered. Concrete Breakout Strength dsdb cover : Bolt Cover 2 c db 2 ds 2 Q) Cdb 2 + 3.25   cal: 3.25 C I 3 s5 in Cover for the calculation of the anchor ritcmLthi = 2r sin  2 hord 3600 r A  TZ 360 A: deg No Bolts A = 30 deg n chord 1.5c, chord_group:= 2sinI chord_group = 7.76 in Amiingroup:= 2asin . Amingroup = 45.24 deg If A is greater than Anoup then there is no group effect AVc:= NoBoltschord_group1.5Cal C i r = 111 A\'c 53 AVo: 4.5cal A co o 5 u `J Effect:= "Group Effect Analysis is Valid" if A < Amin group "Analysis Invalid" if A> Am group Check_Group_Effect = "Group Effect Analysis is Valid" ACI 318051).6.2 1c:= 8do Vb :=2 5P 15 Vb. 13i .a lbf [do) in ,j psi In i I ycV: 1.4 Vb = 13.5 kip ACI 31805 D.6.2.7 1.0 for cracked concrete with no supplcmenutal rcinlforctmcut or reinforcement smaller than a No. 4 bar 1.2 for cracked concrete with edge reinforcement of a No.4 bar or greater 1.4 for uncracked concrete or with edge reinforcement of a No.4 bar or greater enclosed within stirrups spaced no more than 4 in. apart WecV: 1.0 ACT 31805D.625 edV : 1.0 ACI 31805 D.626 All anchors are loaded in shear in the same direction Ave AVc Vebg : 'cV.4\''edV"b \VLcI Vcbg parallel: 2"Vcbg Tn breakoutACI: Vebg_parallel*(db 2) Vcbg = 109.01 kip Vcbg_parallel = 218.03 kip Tn breakout ACI = 81.69kip.fi CheckGroup Eligehausen et al. (2006) Concrete Breakout Provision fcc200 := 1.18f IXI i the conm\eI)ion factor between die cylinder test and cube rest do 0.5 rmm a := 0.1  cal mm 0.5 0. p : 0.1. a cal mM p P1.5 Va,, 3 cc200 cal 5 umm mm N mm Avc Vuc : V'uc AVco \,*S2.'6 N \' = 1 t LIp uV = 4 2'1.1 27 N L '. tI p a := 90 S 180 1 V: cos( av) + 0.5 sin(V) Vue V:= VucdI aV Parallel := 4*k4" [ mdo cc 200 NoBolts fcc200 mmy NN 2 mm Vuc N jc ~ IYI S Lip k := 0.75 ' pa:iIllel Equation 218 was based on tests with two bolts with a straight edge. Therefore, the applicability of the equation comes into question when there are more than two bolts being loaded. The following analysis will determine the ratio of V/, for 2 bolts and V, for arrangements of 2 or more bolts. Step 1: For 2 bolt arrangements, calculate Vc as a function of spacings, and V'c. The spacing will be taken as a function of the cover A, will be the area of the group of anchors for a unit depth Ao will be the area of a single anchor for a unit depth '4'ctV  cover cover = 5 in Sb:= T.db + No_Bolts Sb = 5.24 in Ao(c) := 1.52c Ao(c) > 3.0c This value does not change as a result of changing the spacing. The generic variable for the cover is c. L5ca I 1.5c1 I 1.Sca1 I 1.5c1a s=3. 0ca For the case where s>=3.0cal, there is no overlap. 3.0c 1.5c s(c) := 1.0c 0.5c 0.c For n:= 2 Av(c, s,n) Ao(c).n Av(c,s,n) := 2(1.5.c) + s(c)(n 1) n is the number of bolts A(c,s,n) > 30deg(c,function,2) 0.75 The ratios are normalized by factoring out the number of bolts 0.67 under consideration such that the 0.58 result may be compared to the 0.5 J ratio for 2 or more bolts. For a circular foundation,n is considered equal to infinity because the bolts are continuous; there is no end as there is for a straight edge n:= 1.1020 AV c,s,n) Ao(c).n For n= infinity 0.5 0.33 0.17 0 0 Therefore, to calculate the reduction factor for the parallel conversion multiplier, the ratio of the Ae!/Ago terms for 2 bolts and an infinite number of bolts will be calculated considering the proper ratio ofs/c. For the foundation under invesitgationpz is equal to infinity sb = 1.05 cover sb sratiotest(c):= c cover Av(c, sratio test, n) Group Multiplier Infinity:= Ao( Ao(c)n Group Multiplier 2 Bolts : AV(c, sratio test, 2) Ao(c).2 Group_I Millriphlr_ruliiur 0 35 ( rIup 1_Multilier_ iIfi niry Groi.p Mulltiphei 2 Boll' Group Multiplier Infnity Reduction s bolt Group Multiplier 2 Bolts Vparallelnew:= V parallel'Wreduction s bolt Vucparallel := parallel newVuc Tn breakoutaV := VucaV(db + 2) Tn breakout parallel := Vucparallel'(db 2) G roupl ulitiplhcr 2 Boll' 11 t'redJiiclnj 1oll = IIe'l k'pl.illel_ne = 2 1 'tipara.llel = 893,' 0 N 'ucpaiaallel 2111" 4 I l'i ca lL III(.IV [1 hi eakr'ur i:par:ilIel lb ~ Lip Ii I 1 kipll Summary of Failure Equations Tr = 131.06kip.ft Tbasic = 131.06 kipl f Tthreshold = 24.57 kip. fi Tntorsion = 252.95 kipft Tn breakout ACI= 181.69 kipft Tnbreakout ctV = 159.4kip.ft According to ACI 31805 11.6.3.5, assuring the ultimate torsion exceeds the threshold torsion, the nominal torsional capacity is taken as the strcngth of the section. Tn breakout wpurullc = 167.48kip.ft For the design of the various components of the test specimen, the ACI Concrete Breakout Strength will be the maximum moment as it is the predicted failure mode. (breakout ACi Mmax := Tnbreakout ACI Mmax = 181.69 kip ft Vmax:= 1ima + Moment Arm Vmax= 20.19kip Failure Load Tn torsion 252.95 kip.ft Shaft Design Mmax shaft: Vmax36in Mmax shaft 60.56kip.ft BarSizeHoop = 3 Bar SizeLong 4 sh 2.5 in := 60ksi t 60ksi dh 27in Required splice for #3 bars ACI 31805 12.2.2 & trWf e (Bar Size Hoop RequiredSpliceHoop := * *\ Size inp ec 25. .psi Spsi Required splice between #4 bars and anchor bolts s:= 0.8 Use the simplification for the (%+KtI)/db term .3 bolt field VtyWe*ys' ( Id: No d 40 rfc cb Ktr term Spsi Note: The yi psi determine th the field for Development length of #4 bars ACI 31805 12.5 0.02 . &e Bar Size Long ~ ldh:=  Pm Fpsi RequiredSplihe_ loop 1 2 14 in cb Ktr term: 2.5 ACI31805 12.2.3 Id 2 'im eld Nti cngth in the field was used to e splice length to replicate the embedment in the test setup. s% Ir1 jij Hook Length= 12Bar Size Long 8 yt: 1.0 Ye: 1.0 k : 1.0 Hook Length t in Flexural Capacity of Shaft Calculated using to ACI Stress Block Bar Size Longm + 8 R := ds 2 R = I u AIng_ steel:= r Size Longin S= 60 ksi number of bars:= 24 numberbars_yieldedAlong steer fy Ac := 0.85fc Acircseg(h) := R2acos{R (R h). 2Rh h A h:= n,.. \cr,,egilh.h,0in,15m) i 0 reel = 2 i " Ac 12 '1 ui i = .3 .3'i P (f): 0.85 0.65 0.85 if f < 4000.psi if f > 8000psi 0.05f 4000psi 1000p0.05si 1000psi 7 ACI 10.2.7.3 h c:= c = 4.2!. W p c y:= .002 = 2Sini .003 The assumption was correct! 9.2502inAl,,;_stee1l2 + 12.0237 in .A\lilgsteel2 + 15in.Along_steel2 ... + 17.9763 inAlong_steel2 + 20.7 N I.All,,g _steer2 + 23.1314inAlong_steer2 ... +25.0189mAlo,,nI steer2 + 26.1677 nAloi_ steer2 + 26.5inAlong steel bars Alo 17Alongsteel Oflexure:= 90 Mn Shaft:= flexure nuIberbars_yieldedAlot, g steerfy dbars ) Check Flexure Shaft : "Sufficient Strength" if Mn Shaft > Mmax shaft "Insufficient Strength" if Mn Shaft < Mmax shaft Check_FI excre_Sh.jll = "Siil'litenl SIrelngil" n Sh.i = 262.2. p f l ( I ( Ic I dbars 19.13 in Anchor Design Check Bolt Flexure and Shear Mmax Vmax anchor : No Bolts 2 Vmax anchor 18.17 kip fbolt:= Mmax anchor bolt uta: min(l .9_bollt125ki) max anchor: Vmax anchor" Mmax anchor 24.98 kip.in bolt= 75.4ksi Ase bk futa 125 ksi Vbol : .5do I 2m 2 do 4 Sbolt 0.33 in3 t:= 1.405in2 Ase bolt'uta CheckBolt Flexure : "Sufficient Strengll" if fbol < f bolt "Insufficient Strcllglh" if fbol> y bolt Check_Bolt_Flexure = "Sufficient Strength" Check Bolt Shear: "Sufficient Strenth" if Vbolt Vmaxanchor "Insufficient Strength" if Vbolt < Vax anchor Check_Bolt_Shear = "Sufficient Strength" Calculate the load that will cause the bolts to yield fy boltSboltdbNo Bolts Mbolt yicld 0.5do + 2in Mboltield = 253.02 kipft Pboltyield:= Mbolt yield : Moment_Arm Pboltyield = 28.11 kip Pipe Apparatus Design Based on AISC LRFD Manual of Steel Construction LRFD Specificationfor Steel Hollow Structural Sections Pipe PropertiesHSS 16.000 x 0.500 tppe: 0.465 Apipe: 22.7i2 D t : 34.4 Wpipe: 82.8  4 3 ,3 pipe : 685 i Spipe: 85.7in rpipe : 5.49in Zpipe : 112m3 Dpipe: 16in Jpipe : 1370in Cpipe : 1713i Design of Short Section Applied Shear, Torsion, and Flexure LShortPipe : 15in Vma 20.19 p Nlm 15I., ki p i'lorsion MFlexure : VmaxLShort Pipe Design Flexural Strength b:= 0.90 pipe := Dt kpApipe 49.3 MdShortPipe:= ip pipe CheckFlexureShortPipe := (heck Flexire Design Shear Sirength v:= 0.9 F 1.60E 0.78E' Fcr := max , 5 3 5 3 LShort_Pipe D t 4 D t2 D F "pipe Fcr:= mm(0.6.Fyipei,Fcr) Vd Short Pipe:= vFcr Apipe + 2 Fy :ipe: 42ksi Fupipe 58ksi E:= 29000ksi Nie leie 25 23 1,p fi kpJipe:= 0.0714E + Fyjipe Spipe 34.4 pipe > Xpipe, tbFypipe"Zpipe, "Equation Invalid") Md_nhoPrt_Plpc 352.8 kip h "Sufficient Sure ,gh" if Md Short Pipe > MFlexure "Insufficient Strength" if MdShort Pipe <1 le]..me _Sholrt_Pilie = "S efficient S. ctimlh" Fr = 575.22 ksi i = 2 2 ksi V1 Mhorl Pipe = 257 V2 jp Check Shear Short Pipe := "Sufficient Strength" if VdShort Pipe > Vmax "Insufficient Strength" if V ShortPipe _heckSheaiShorl_Pipe = 'Sull'ilenti Strenglh" Design Torsional Strength T:= 0.90 Tdpipe: TFcrCpipe Idjupc 3I 1 krpi Check Torsion Short Pipe : "Sufficient Srienliiil" if Tdipe > Mmax "Insufficient Strength" if Tdpipe < Mmax tlieck Tor'i 'ii Shirt Pipe "Sitticienir St ieliLh" Check Interaction SMFlexure Vmax Interaction Short Pipe MF:exure + Vmax Md Short PipeJ VdShort Pipe Mmax Tdpipe Interaction Short Pipe 0.48 Check Interaction Short Pipe : "Sufficient Sriei"llg' if Interaction Short Pipe < 1 "Insufficient Cerniitli' if InteractionShort Pipe > 1 'hec'k_h.eia ion__ hIrlin_Pti [ "Sutli.'litIl Suie pii" Design of Long Section Applied Shear and Flexure LLongPipe: 9ft \Va li19 1)p M11 m l1l 6'J klp Design Flexural Strength Md Long Pipe iflpjipe > pipe b.Fylipe.Zpipe'"Equation Invalid") M duonieip nIie:up p i f 1 L n 1 M 1 I 1 ,' ~ e 3 2S kip). h Check Flexure Long Pipe : "Sufficient sieLI1" if MdLong Pipe > M ax "Insufficient Strength" if MdLong Pipe < Mmax ( heck Flexire I iue Pipe "Sllticient SNtlentlih" Design Shear Strenglth Vd Long Pipe := vFcrApipe 2 Check Shear Long Pipe : VI I on, Pipe 5' 4' kip "Sufficient Strength" if Vd LongPipe > Vmax "Insufficient Strength" if VdLongPipe < Vmax Check Slie: I [ onp Pipe "Silicient Stlie1rli'" Check Interaction /2 Mm 1 Vnax Interaction LongPipe :=  + max Md Long_Pipe VdLong_Pipe Interaction Long Pipe = 0.52 Check Interaction Long Pipe : "Sufficient Sircnilh" if Interaction Long Pipe < 1 "Insufficient Sircngili" if Interaction Long_Pipe> 1 Check_Interaction_Long_Pipe = "Sufficient Strength" Weight of Pipe Apparatus lbf 24m 2 lbf Wipe app := W peLShort Pipe + WpipeLLong ipe + 490 n2 lin + 26in20in0.5in490 Base Plate \\ eld Plate Wpipeapp = 1.05 kip This weight must be subtracted from the applied load to account for overcoming the weight oftlle pipe before the bolts were loaded. Will be used to normalize the test results Concrete Block Design Reinforcement Two different methods were employed to check the reinforcement in the block: A) StrutandTie Model B) Beam Theory R K .4' A) Design by StrutandTie Model ACI 31805 Appendix A Mmax = 181.69 kipft Mmax d:= 6ft+ 8in R:= d R = 27.25 kip NODE A 9 := ata  6 = d~ft) R T C sin(O) T:= C.cos(0) 0.64 C = 45.42 kip T 36.34kip R C Check Reinforcement NoBarsBlockReinforcement := 3 BlockReinforcement Bar No := 8 fyBlock Reinforcement : 60ksi (Block Reinforcement Bar No 8N 2 ABlock Reinforcement:" No Bars Block Reinforcement.. BlckReinfrceent Bar No22 \BII, R LIIlOrLCCIILt ll U 2 _r? L CheckReinforcement_A := "Sufficient iieigtl" if (ABlock Reinforcementt Block Reinforcement) > T "Insufficient rleilr'h" if ABlockReinforcement.y_BlockReinforcement < T li'hel. ReinriloiccIlnent \ B) Beam Theory R II SIi I II II II Ii II Ii II Ii II II II I I II I I I I I i I I I I I ,II I I I I I I I I I I Vblo M Y ' :I , I ' I4 3'o" 4'9" Vblock : R \block 2:.25 'ip M : R.(3ft+ 4in) 121 " tlml'l e'llli ,iret'l li" M "90.&1 Ip.ft Check Shear Check Shear B := "Sufficient Strength" if ABlock Reinforcementf Block_ RCIIfi.[L !It) > Vblock "Insufficient "IieC1lh" if ABlockReinforcement _BlockReiforcement < Vblock ( ]ick Sihear B = "Su'iiicinl Sircength" Check Flexure i b d A,  *** 0.85s, b := 30in h:= 6ft d:= 5.5ft Locate the neutral axis, c, such that (C T) T:= ABlockReinforcement BlockementBlo Reinforment T 141.37 kip CT(a):= C(a) T a:= root(CT(a),a,0,h) C(a) : 0.85fcba . = I 1ll 11 1P(fc) := 0.85 0.65 0.85 p (fc)= 0.78 a c :=  if fc <4000psi if fc> 8000psi  0.5fc 4000psi) ( 1000psi j ACI 10.2.7.1 Calculate the nominal moment capacity, M1 Capacity Reduction Factor Mn Block:= T'( 2 ACI 9.3.2, ACI 10.3.4, ACI 10.9.3 1 BI U k = "I 'Lp II CheckFlexure_B := "Sufficient Strength" if Mn Block > M "Insufficient Strength" if Min Block < M Check FILcirc B "SliIt'iciclt Sircenrll" ACI 10.2.7.3 . = I oI C 10.1 1 a1 Required Hook Length for a #8 Bar ookNo8 : 12.(Block Reinforcement BarNoin ACI R12.5  8 Summary of Concrete Block Design Reinforcement Block Reinforcement Bar No = 8 NoBars_BlockReinforcement = 3 3 bars on top and bottom Check_Reinforcement_A = "Sufficient Strength" Check_Shear_B = "Sufficient Stiength" Check_FlexureB = "Sufficient Strength" Hook No 8 = 12in 