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16 2.1 Research Approach The focus of the experimental phase of this study was on the use of ASTM A1035 (2009) reinforcing steel since it cap- tures both behavioral aspects of interest (i.e., it has a very high strength and no discernable yield plateau). The project identiï¬ed aspects of reinforced-concrete design and of the AASHTO LRFD speciï¬cations that may be affected by the use of high-strength reinforcing steel. Design issues were priori- tized and an integrated experimental and analytical program was designed to develop the data required to permit the inte- gration of high-strength reinforcement into the LRFD speci- ï¬cations. This program included parametric, experimental, and analytical studies in addition to a number of âproof testsâ intended to validate existing LRFD provisions when applied to higher strength reinforcing steel. Table 3 provides a sum- mary of the primary aspects addressed in this study and the approach by which they were addressed. Subsequent sections of this chapter discuss each experimental and/or analytical program in turn. 2.2 Mechanical Properties of Reinforcing Steel Table 4 provides a summary of all reinforcing bar grades and sizes tested as part of this study. Batch numbers are underlined and the specimens in which each batch was uti- lized are also indicated. Appendix A provides summaries of all tests conducted and axial stress-strain curves obtained from all bars tested. All tension tests were conducted in compliance with ASTM E8 and were conducted on full bar sections (not machined coupons). As reported in Appendix A, A1035 bars and A496 and A82 wire exhibit no discernable yield plateau. A615 and A706 exhibit clearly deï¬ned yield plateaus and A955 stainless steel grades exhibit a clear âabrupt change of stiffness,â but no deï¬ned plateau. 2.2.1 ASTM A1035 Reinforcing Steel The data obtained for A1035 bars in this study are gener- ally consistent with those reported by others as summarized in Section 1.3.2. That is â¢ Values of yield ( fy) and ultimate ( fu) strengths were consis- tent from batch to batch and bar size to bar size. The average ultimate strength was fu = 163 ksi having a COV of only 3.9% across all specimens. The average rupture strain exceeded 0.10 and had a COV of 28%. â¢ The use of the ASTM A1035-prescribed 0.2% offset method for establishing yield strength results in an average yield strength, fy = 129 ksi (COV = 4.6%). Stress corresponding to a strain of 0.007 resulted in the most consistent (COV = 4.0%) value of yield strength, fy = 133 ksi. â¢ Yield and ultimate strength values remained essentially unaffected by bar size. â¢ Regardless of the manner by which yield stress was deter- mined, the condition fu > 1.25fy was satisï¬ed in all cases. â¢ Calculated values of modulus of elasticity, Es, determined as secant modulus at 60 ksi were very consistent, averaging 28,137 ksi (COV = 7.1%). â¢ All bars tested exhibited linear behavior through stress levels of at least 70 ksi. A Ramberg-Osgood (R-O) function was established for each batch of reinforcing steel that was used in a number of subsequent analyses reported in this work. The R-O function is given in Equation 7 (Ramberg and Osgood 1943). The parameters, A, B, and C, established using a nominal value of Es = 29,000 ksi are given in Appendix A. The general form of the resulting R-O curve is shown in Figure 3. f A A B f C C pu= + â +( )â¡â£ â¤â¦ â§ â¨âª â©âª â« â¬âª ââª â¤29 000 1 1 1 , Îµ Îµ ksi (Eq. 7)( ) C H A P T E R 2 Research Program and Findings
17 Experimental Aspect of Study Parametric Proof Tests Analytical Notes Mechanical properties of reinforcing steel X 47 batches including 8 steel grades and 13 bar sizes tested Flexural reinforcement X X 6 large-scale beam tests and extensive parametric analysis Fatigue X 2 large-scale beam proof tests Shear reinforcement X 5 large-scale beam tests and 4 AASHTO Type I girders Shear friction behavior X 8 full-scale proof tests Compression members X Extensive analytical study Bond and development X 18 full-scale proof tests Deflections X Crack widths Considered with flexure X Integration of flexural data into extensive parametric studies Table 3. Research approaches taken with respect to various aspects of this study. ASTM Designation Bar Size Batch Number and Test Specimen Use A1035 #3 1: SR1 to SR5; P1035-3A 1B: P1035-3B 2: Type I-4 3: Type I-1 to 1-3* A1035 #4 1: all H; P1035-4A 1B: P1035-4B A1035 #5 1: F1; F3; D5-1; D5-2; all H; all fatigue 2: F4; F6; D5-3; D5-4 A1035 #6 1: F2 2: F5 A1035 #8 1: D8-1; D8-2; SR1 to SR4; all H 2: D8-3; D8-4; SR5 A615 #3 1: D5-1; D5-2, D8-1, D8-2 2: D5-3; D5-4; D8-3; D8-4 3: all P615 4: all H; all fatigue A615 #4 1: F1 to F3; SR1 to SR4 2: F4-F6 3: Type I-1 to Type I-3 4: Type I-4 5: all P615 A706 #4 1: tension tests only 2: tension tests only A706 #6 1: tension tests only 2: tension tests only A706 #8 1: tension tests only 2: tension tests only A496 D4 1: tension tests only A496 D8 1: tension tests only A496 D12 1: tension tests only A496 D20 1: tension tests only A496 D31 1: tension tests only A82 W4 1: tension tests only A82 W8 1: tension tests only A82 W12 1: tension tests only A955 (316) #4 1: tension tests only A955 (316) #6 1: tension tests only 2: tension tests only A955 (316) #8 1: tension tests only A955 (2205) #4 1: tension tests only 2: tension tests only A955 (2205) #6 1: tension tests only 2: tension tests only A955 (2205) #8 1: tension tests only A955 (N32) #4 1: tension tests only A955 (N32) #6 1: tension tests only A955 (N32) #8 1: tension tests only Notes: *No test data are available for A1035 #3 batch 3 bars; no additional samples accompanied the bar order. Test specimen labels: D5-1, D5-2, D5-3, D5-4, D8-1, D8-2, D8-3, and D8-4: beam splice specimens; H: hooked specimens; F1, F2, F3, F4, F5, and F6: flexural specimens; P615, P1035-4A, P1035-4B: shear friction specimens; SR1, SR2, SR3, SR4, SR5: reinforced-concrete shear specimens; Type I-1, Type I-2, Type I-3, and Type I-4: AASHTO Type I girder shear specimens. Table 4. Reinforcing steel tested in this study and its use in specimens.
18 A critical objective of the present work is to identify an appropriate steel strength and/or behavior model to ade- quately capture the behavior of high-strength reinforcing steel while respecting the tenets of design and the needs of the designer. As will be described throughout this report, a value of yield strength, fy, not exceeding 100 ksi was found to be permissible without requiring signiï¬cant changes to the LRFD speciï¬cations or, more critically, to the design philos- ophy and methodology prescribed therein. Some limita- tions to this increase in permissible yield strength were identiï¬ed and also are discussed. Based on the stress-strain diagrams obtained as part of the reported project and all pre- vious studies, A1035 reinforcing steel easily meets a yield value of 100 ksi using the 0.2% offset method or for the âstress at a strainâ method for strains exceeding 0.004. All available test data exhibit nonlinear behavior at stresses greater than 70 ksi. Thus, it is felt that assumptions of a linear stress-strain relationship made for calculating service load displacements and crack width are likely adequate since service load stresses are traditionally taken as fs = 0.60fy. However, deï¬ection or serviceability considerations at loads greater than this must account for the nonlinear nature of the reinforcement at high stresses. Post-yield behavior, particularly when employing a plastic design methodology, will also be affected by both the lack of a well-deï¬ned yield plateau and the nonlinear post yield behavior. This behavior is most critical in seismic applica- tions, which are beyond the scope of the present work. 2.3 Flexural Reinforcement Flexural behavior and design of members reinforced with A1035 reinforcement and other grades of reinforcing bars that do not exhibit well-defined yield plateaus were examined analytically and experimentally. Different aspects of this component of the research are presented in this section. 2.3.1 Flexural Resistance The nominal moment capacity (Mn) for non-prestressed members is commonly calculated by assuming a constant yield stress for the steel. For bars without a well-deï¬ned yield plateau, several approaches may be used to deï¬ne the yield stress. In order to examine these methods, parametric stud- ies were performed to assess the ï¬exural resistance of mem- bers reinforced with various grades of steel reinforcement that do not have a well-deï¬ned yield plateau. The moment capacity was calculated by a number of methods ranging from simple design-oriented procedures to complex ï¬ber analysis. In ï¬ber analysis, a cross section is divided into layers (ï¬bers). The cross sectional and material properties for each layer are deï¬ned, and strain compatibility between the layers is enforced. Realistic complete stress-strain relationships for concrete and steel layers are employed as opposed to simpliï¬ed relation- ships typically used in the strain compatibility method. There- fore, complex analyses can be performed by ï¬ber analysis technique. Comparing the results from the range of models made it possible to evaluate whether approximate methods are appropriate for members reinforced with reinforcing bars with no clear yield plateau and what material properties to use in these cases. 188.8.131.52 Members and Parameters Sections modeled were deck slabs, rectangular beams, and T-beams with varying steel types, amounts of steel, and con- crete compressive strengths. The variables considered are summarized in Table 5. A total of 286 cases were examined. Three different amounts of tensile reinforcement were incor- porated in the rectangular beams. A maximum area of steel, As,max was determined based on the minimum steel strain of 0.004 imposed by ACI 318-08 (ACI 2008). A minimum area of steel, As,min, was established to satisfy AASHTO Â§184.108.40.206.2 (i.e., to ensure that the ï¬exural resistance with As,min is at least 1.2Mcr, where Mcr is the cracking moment of the section). The average of As,min and As,max also was considered. Rectangular beams with As,min are in the tension-controlled region. Rec- tangular beams reinforced with As,max have the lowest steel strains allowed by ACI 318-08. The average of As,min and As,max results in cross sections with strains between these limits. Because of the additional compression strength provided by the ï¬anges of the T-beams, the calculated amount of steel required to provide As,max (i.e., to ensure a minimum strain of 0.004) was found to be excessive and impractical. Therefore, the values of As,max determined for the rectangular beams were provided in the corresponding T-beams. Nonetheless, the selected values of As,max resulted in members that fell well into the tension-controlled region. Providing more steel to obtain members in the transition region was impractical; hence, only Figure 3. Ramberg-Osgood Curve and definition of parameters.
one amount of reinforcement was used for the T-beams. The amount of steel provided in the slabs was determined based on spacing limitations prescribed in AASHTO LRFD Bridge Design Specifications, Â§220.127.116.11, Â§18.104.22.168, and Â§5.10.8 (AASHTO 2004). 22.214.171.124 Capacity Calculation Procedures The nominal moment capacity of each section was calcu- lated both by a strain compatibility procedure using different methods for modeling the steel stress-strain relationships and a ï¬ber analysis procedure. A commercial computer program XTRACT (2007) was used to perform the ï¬ber analyses. The concrete was modeled using the unconï¬ned concrete model proposed by Razvi and Saatcioglu (1999). The measured stress-strain data (refer to Appendix A) for each type of rein- forcing steel were input directly into the XTRACT program. By using the experimentally obtained data, a more accurate capacity can be determined. Moment-curvature analyses were run in which the concrete strain was limited to 0.003, the level of strain used in the strain compatibility analyses. The results from ï¬ber analyses are deemed to predict the most accurate ï¬exural capacity. An Excel program (Shahrooz 2010) was used to compute ï¬exural capacities based on strain compatibility analysis. The constitutive relationship of the reinforcing bars was modeled (1) as elastic-perfectly plastic with the yield point obtained by the 0.2% offset method and the stress at both strain = 0.0035 and strain = 0.005; and (2) by the Ramberg-Osgood (1943) function determined to best ï¬t the experimentally obtained data. The analyses utilized data from the measured stress- strain relationships of 102 samples of A706, A496 and A82, A955, and A1035 reinforcing bars. The measured relation- ships are presented in Appendix A. Table 6 summarizes the yield strengths obtained from each method. An equivalent stress block for high-strength concrete, developed as part of NCHRP 12-64 (Rizkalla et al. 2007), was used to compute the concrete contribution to section behav- ior. Additional information is provided in Appendix B and Ward (2009). 126.96.36.199 Results The moment capacity for each section computed based on the aforementioned methods was normalized with the corre- sponding capacity calculated from the ï¬ber analyses. Table 7 summarizes the results of the strain compatibility analyses conducted using the Ramberg-Osgood function for the rec- tangular beams, T-beams, and slabs for all of the steel types and the selected concrete strengths considered. The com- puted capacities are below or nearly equal to those calculated based on ï¬ber analysis (i.e., the ratios are close to, or slightly less than, unity). The exceptional estimates of the expected capacity based on the Ramberg-Osgood function in conjunc- tion with strain compatibility analysis should be expected since this function closely replicates the measured stress-strain curves that were used in the ï¬ber analyses. Additionally, the good correlation suggests that well-established procedures can be used to calculate the ï¬exural capacity of members rein- forced with bars that do not have a well-deï¬ned yield plateau so long as the stress-strain relationship is modeled accurately. In spite of its success, the use of Ramberg-Osgood func- tions is not appropriate for routine design. Most designers are familiar with using a single value of reinforcing bar yield, fy. For this reason, further strain compatibility analyses were carried out using the yield strength values given in Table 6. The results are summarized in Table 8. For the beams having 5 ksi concrete, the ratios from any of the values of yield strength are less than unity (i.e., the ï¬exural strength can be conservatively computed based on any of three methods used to establish the yield strength). The same conclusion cannot be drawn for the beams with 10 and 15 ksi concrete. For a Table 5. Variables for parametric studies. Parameter Deck Slab Rectangular Beam T-Beam Dimensions 7 in. and 10 in. thick 12 in.Ã16 in., 12 in.Ã28 in., 12in.Ã36 in., 16 in.Ã28 in., 16 in.Ã36 in., and 16 in.Ã 40 in. 12 in.Ã28 in., 12 in.Ã36 in., 16 in.Ã36 in., and 16 in.Ã 40 in. with 96 in. effective flange width and 7 in. flange thickness Concrete Strength, fâc 5 ksi 5, 10, and 15 ksi Reinforcement Grades A706, A496 & A82, A955 (3 grades), and A1035 Bar Sizes #4, #5, and #6 #6 for 12 in.-wide beams; and #8 for 16 in.-wide beams. All beams are assumed to have #4 stirrups with 2 in. of clear cover. Tension Reinforcement Based on AASHTO spacing limitations As,min, As,max, 0.5(As,min+As,max) As,max from corresponding rectangular beams Table 6. Average and standard deviations of fy (ksi). Method for Establishing the Yield Strength 0.2% Offset Method Strain @ 0.005 Strain @ 0.0035Bar Avg. (ksi) Std. Dev. (ksi) Avg. (ksi) Std. Dev. (ksi) Avg. (ksi) Std. Dev. (ksi) A496 & A82 93 6.02 93 5.71 88 5.95 A706 68 3.30 68 3.83 67 3.05 A995 78 5.21 78 5.21 72 3.53 A1035 127 7.25 115 4.59 93 4.01 19
20 limited number of cases (given in Table 9) involving relatively large longitudinal reinforcement ratios (Ïg), the strength ratio exceeds unity if the capacity is based on an idealized elastic- perfectly plastic stress-strain relationship with the yield strength taken as the stress at a strain of 0.005 or determined based on the 0.2% offset method. That is, the yield strengths based on these two methods may result in slightly unconser- vative estimates of the expected capacity in cases with large reinforcement ratios and high-strength concrete. The aforementioned behavior can be understood with ref- erence to Figure 4, which depicts a measured stress-strain curve for an A706 bar along with the idealized elastic-perfectly plastic model based on the yield strength taken as the value determined from the 0.2% offset method and the stress at strain equal to 0.005. Note that in this case, these two methods result in the same values of yield strength. Between points âaâ and âbâ (see Figure 4) the elastic-perfectly plastic model deviates from the measured stress-strain diagram. The stresses based on this model exceed the actual values. For strains below point âaâ and strains above âb,â the stresses from the idealized model are equal to, or less than, the measured values. As the rein- forcement ratio increases (i.e., as the amount of longitudinal steel becomes larger), the strain in the reinforcing bars at any given applied moment will become less. For the cases involv- ing the large reinforcement ratios shown in Table 9, the steel strains fall between points âaâ and âbâ when the extreme con- crete compressive stress of 0.003 is reached. Thus, the higher yield strength from the elastic-perfectly plastic model over- estimates the actual ï¬exural capacity. In the case of T-beams and slabs, any of the aforemen- tioned methods for establishing the yield strength result in acceptable, conservative ï¬exural capacities. As is evident from Table 10, the ratios of the ï¬exural capacity based on simple elastic-perfectly plastic models to the corresponding values from ï¬ber analysis are less than one. The trend of data is expected, as the longitudinal strain in a T-beam will be higher than that in an equivalent rectangular beam because of the addi- tional compressive force that can be developed in the ï¬ange. The smaller depths of the slabs will also increase the strain in the longitudinal bars. In both these cases, the larger strains will correspond to cases beyond the strain at point âbâ in Fig- ure 4, where the elastic-plastic assumption underestimates the real stress developed in the steel. 188.8.131.52 Summary and Recommendations Considering the presented results, the use of Ramberg- Osgood functions for deï¬ning the stress-strain characteristics of reinforcing bars without a well-deï¬ned yield plateau will produce the most accurate estimate of the actual ï¬exural Table 7. Ratios of flexural capacity determined from Ramberg-Osgood strain compatibility analysis to that determined from fiber model. Section Average Minimum Maximum Standard Deviation Rectangular 0.944 0.835 0.999 0.037 T-beam 0.962 0.925 0.999 0.017 Slab 0.875 0.668 0.955 0.107 Note: Ratio less than 1 is conservative. Table 8. Ratios of rectangular beam flexural capacity calculated from elastic-plastic analyses to that from fiber model. Yield Point f'c (ksi) Average Minimum Maximum StandardDeviation 5 0.820 0.578 0.958 0.094 10 0.815 0.603 0.964 0.100 @ Strain = 0.0035 15 0.825 0.596 0.991 0.108 5 0.884 0.727 0.977 0.070 10 0.880 0.652 1.014 0.084 @ Strain = 0.005 15 0.891 0.688 1.072 0.092 5 0.909 0.789 0.966 0.057 10 0.884 0.756 0.971 0.075 0.2% offset 15 0.890 0.749 1.007 0.092 Note: Ratio less than 1 is conservative. Table 9. Cases where elastic- plastic analysis overestimated flexural capacity. Steel Type f'c (ksi) Ïg Ratio 10 3.84% 1.014 15 3.67% 1.006 15 3.67% 1.005 15 4.06% 1.022 15 4.11% 1.023 15 2.88% 1.072 A706 15 4.07% 1.023 A995 15 3.43% 1.020 A1035 15 2.65% 1.007
capacity. The use of the strain compatibility approach assum- ing an elastic-perfectly plastic steel stress-strain relationship having a yield stress deï¬ned at either a strain of 0.0035 or 0.005 ensures that the ï¬exural capacity is computed conserva- tively and reliably for the range of reinforcement ratios and concrete compressive strengths encountered in practice. How- ever, for beams with reinforcement ratios exceeding 2.65%, the deï¬nition of the yield stress at a strain of 0.0035 is more appropriate. The latter approach is consistent with the currently prescribed ACI 318 (ACI 2008) approach. The use of the stress at 0.0035 strain effectively ensures that the steel strain under the design condition is beyond point âbâ shown in Figure 4. (Recall that this condition is enforced in the design approach through the deï¬nition of Asmax as the steel content that allows a steel strain of 0.004 to be achieved.) 2.3.2 Tension-Controlled and Compression-Controlled Strain Limits for High-Strength ASTM A1035 Reinforcing Bars 184.108.40.206 Fundamental Concepts The current steel strain limits of 0.005 deï¬ning the lower bound of tension-controlled behavior and 0.002 or less deï¬n- ing compression-controlled behavior are based on having an adequate change in steel strain from service load to nominal strength. Nonetheless, the strain limits have been calibrated based on the expected performance of ï¬exural members rein- forced with Grade 60 longitudinal bars. Considering that A1035 bars could be subjected to larger service level strains and have different stress-strain relationships, the strain lim- its deï¬ning tension-controlled and compression-controlled behaviors need to be reevaluated. 220.127.116.11 Development The curvature ductility of sections reinforced with A615 Grade 60 reinforcement was computed for the following cases: concrete compressive strength from 4 to 15 ksi in 1-ksi increments; tension longitudinal reinforcement (Ï) from 0.1% to 6.1% in 0.06% increments; compression longitudi- nal reinforcement (Ïâ²) taken as 0, 0.5Ï, and Ï; and ratio of the effective depth of the compression longitudinal bars to the effective depth of the tensile longitudinal bars (dâ²/d) equal to 0 or 0.1. The stress-strain relationship of Grade 60 was modeled as elastic-perfectly plastic. For the same cases, the curvature ductility was recomputed by using A1035 Figure 4. Typical measured stress-strain diagram and elastic-perfectly plastic model. Table 10. Ratios of T-beam and slab flexural capacity calculated from elastic-plastic analyses to that from fiber model. T-Beams Yield Point Average Minimum Maximum StandardDeviation @ Strain =0.0035 0.741 0.571 0.859 0.091 @ Strain =0.005 0.795 0.659 0.890 0.069 0.2% offset 0.748 0.718 0.764 0.019 Deck Slabs Yield Point Average Minimum Maximum StandardDeviation @ Strain =0.0035 0.828 0.609 0.953 0.115 @ Strain =0.005 0.854 0.638 0.971 0.113 0.2% offset 0.909 0.839 0.951 0.043 Note: Ratio less than 1 is conservative. 21
22 Grade 100 reinforcement. An equation proposed by Mast (2006) was used to characterize the material properties of A1035 reinforcement. Details of the formulation are pro- vided in Appendix C. The relationship between the strain levels for A615 and A1035 reinforcing bars is illustrated in Figure 5 for one of the cases considered. For this example, a singly reinforced mem- ber having f â²c = 4 ksi, the strain in the A1035 bars needs to be 0.00793 in order to achieve the same implied ductility of the same tension-controlled member reinforced with A615 bars. The complete set of results is shown in Figure 6. As expected, the addition of compression bars (i.e., Ïâ²> 0) increases the strain in the tension reinforcement, which improves the duc- tility. As the concrete compressive strength increases, the ten- sion reinforcement strain drops, which is an indication of reduced ductility. 18.104.22.168 Recommendations Based on the results shown in Figure 6, the following strain limits are recommended to deï¬ne tension-controlled and compression-controlled members that use reinforcement with fy = 100 ksi in cases where the service load stresses are lim- ited to 60 ksi. Linear interpolation may be used for fy between Figure 5. Example for f â²c 4 ksi, â² 0, dâ²/d 0, target t 0.005 in ASTM A615. Figure 6. Equivalent strains for tension-controlled and compression-controlled members reinforced with ASTM A1035.
60 and 100 ksi for the compression-controlled limit, and 75 to 100 ksi for the tension-controlled limit. Tension Controlled: Îµt â¥ 0.008 Compression Controlled: Îµt â¤ 0.004 Where Îµt is the strain in tensile strain in the extreme longi- tudinal reinforcement. These limits are nearly identical to those recommended by Mast et al. (2008), that is, 0.004 and 0.009. It must be recognized that selecting a different value of fy or fs results in different calibrations. 2.3.3 Moment Redistribution AASHTO Â§22.214.171.124 allows redistribution of negative moments at the internal supports of continuous reinforced-concrete beams. Redistribution is allowed only when the strain in the extreme longitudinal reinforcement (Îµt) is equal to, or greater than, 0.0075. This strain limit of 0.0075 is derived in Mast (1992) and can be traced to cases for which the provided area of steel is approximately one-half of that corresponding to bal- anced failure (see Appendix C). As derived in Appendix C, for such cases the value of Îµt is 0.003 + 2Îµy. For Grade 60 reinforce- ment, the yield strain (Îµy) is 0.0021; hence, Îµt becomes 0.0072. This strain is essentially the same as 0.0075, which is the strain beyond which moment redistribution is permitted. In the case of A1035 reinforcement, the yield strain is higher than that for Grade 60 reinforcement. As discussed in Appendix C, Mastâs Equation provides a very good lower- bound estimate of A1035 stress-strain relationship. Mastâs Equation is as follows: Based on Mastâs Equation, the strain at 100 ksi is 0.0043. Using this strain as the yield strain (Îµy), the value of Îµt becomes 0.0115 (Îµt = 0.003 + 2Îµy = 0.003 + 2(0.0043) = 0.0115) or approx- imately 0.012. Therefore, 0.012 is proposed as the strain limit for which moment redistribution is allowed for members reinforced with A1035 reinforcement. if fs s s Îµ Îµ > = â + 0 00241 170 0 43 0 00188 . . . if f Es s s sÎµ Îµâ¤ =0 00241. According to current AASHTO speciï¬cations, strain in the extreme tension reinforcement (Îµt) must exceed 0.0075 in order to be able to redistribute moments. This strain is 1.5 times the current strain limit of 0.005 that deï¬nes tension controlled. The proposed strain limit of 0.012 is also 1.5 times the pro- posed tension-controlled strain limit of 0.008. 2.3.4 Experimental Evaluation To better understand the behavior and capacity of flexural members reinforced with A1035 bars and evaluate the aforementioned strain limits for tension-controlled and compression-controlled sections, six specimens were designed, fabricated, and tested. Appendix D provides detailed informa- tion regarding the experimental program as well as a complete record of the test data. 126.96.36.199 Test Specimens and Experimental Program The test specimens, which were 12 in. wide by 16 in. deep ï¬exural members with nominal 10-ksi and 15-ksi concrete and A1035 longitudinal bars, were designed, fabricated, and tested. To prevent the possibility of shear failure, #4 Grade 60 A615 stirrups were provided throughout the span. For both concrete strengths, the specimens were designed based on the following strain targets: (1) tension-controlled strain limit of 0.008; (2) 0.006, which is in the transition region between tension controlled and compression controlled, and (3) above 0.010 to examine crack widths in beams with low reinforce- ment ratio. The specimen details and material properties of the longitudinal bars are summarized in Tables 11 and 12, respectively. The specimens were tested over a 20-ft simple span in a four-point loading arrangement having a constant moment region of 3.5 ft. The specimens were instrumented to capture the load, deï¬ection, and steel and concrete strains. 188.8.131.52. Results and Discussions Ductility. One of the concerns when using high-strength reinforcing bars such as A1035 is related to the reduced ductility resulting from the use of larger yield stresses and 23 Table 11. Flexural specimens. Reinforcement (A1035) fâc (ksi) Specimen ID Layer 1 Layer 2 Design Measured Target Îµt Comment F1 4 #5 2 #5 10 12.9 0.0080 Tension controlled F2 4 #6 2 #6 10 12.9 0.0060 Transition F3 4 #5 ---- 10 12.9 0.0115 Tension controlled, small Ï F4 4 #5 4 #5 15 16.5 0.0080 Tension controlled F5 4 #6 4 #6 15 16.3 0.0060 Transition F6 4 #5 2 #5 15 16.9 0.0103 Tension controlled, small Ï
24 states, which can conveniently be accomplished by evaluating the load-deï¬ection response. The analytical load-deï¬ections were obtained by using a computer program called Response 2000 (Bentz 2000). Modeling of the specimens is discussed in Appendix D. The measured and predicted load-deï¬ection responses for specimens F1 and F4, which are deemed to rep- resent members that will likely be encountered in practice, are compared in Figure 10. For specimen F1, which was cast with nominal 10-ksi concrete, the analytical load-deï¬ection response is remarkably close to its experimental counterpart. In contrast, the computed load-deï¬ection for the specimen cast with nominal 15-ksi concrete (i.e., specimen F4) exhibits a higher stiffness than the experimental data. This difference is attributed to overestimation of aggregate interlock in the matrix of 15-ksi concrete. Considering the challenges of modeling high-strength concrete, the shown load-deï¬ection response for specimen F4 is adequate. The results shown in Figure 10 suggest that well-established techniques are appli- cable to members reinforced with A1035 high-strength lon- gitudinal bars, and stiffness of such members can adequately be computed. Strain Level. The average strain from strain gages bonded to the longitudinal bars at midspan is plotted versus the applied load in Figure 11. For each specimen, the target design strain (Îµt in Table 11) is also plotted. The measured strains Table 12. Measured properties of A1035 longitudinal reinforcement. Yield Strength (ksi) Bar Size Specimens Rupture Strain Calculated Modulus of Elasticity (ksi) Ultimate Strength (ksi) @ Strain = 0.0035 @ Strain = 0.0050 0.2% Offset #5 F1, F2, F3 0.103 26074 164.1 89.2 112.5 130.2 #5 F4, F5, F6 0.137 27280 164.9 92.9 115.0 129.2 #6 F1, F2, F3 0.103 29001 161.3 91.1 111.7 121.8 #6 F4, F5, F5 0.145 27711 165.3 94.1 117.9 134.4 Figure 7. Cracking patterns in Specimen F4 prior to failure. Table 13. Maximum midspan deflection. Specimen Deflection F1 L/44 F2 L/48 F3 L/39 F4 L/38 F5 L/47 F6 L/29 the subsequent greater utilization of the concrete capacity. The midspan deï¬ection (expressed in terms of span length, L = 20 ft) corresponding to the maximum is tabulated in Table 13. The deï¬ections at ultimate are clearly large. All of the specimens exhibited a well-distributed crack pattern. Well before failure, noticeable crack opening and curvature of the beams were noticed (Figure 7). Prior to failure, the beams exhibited visual warning signs of distress (see Figure 8). The large deï¬ections and visual warning signs of distress before fail- ure attest to the ductility of the specimens. Overall Response and Capacity. The measured load- deï¬ection relationships are plotted in Figure 9. As discussed above, the specimens exhibit large deï¬ections prior to failure. The expected capacities were computed based on standard strain compatibility analyses in which the stress-strain rela- tionship of A1035 longitudinal bars was modeled (1) as being elastic-perfectly plastic having a yield strength (fy) equal to 100 ksi, which approximately corresponds to the stress at strain of 0.004; (2) by an equation proposed by Mast (1992); and (3) by the Ramberg-Osgood function describing the measured stress-strain behavior. The ratios of observed-to- predicted behavior are given in Table 14. All of the specimens reached and exceeded their predicted capacities. Reï¬ective of the previously described analytical work, the predictions made using the Ramberg-Osgood representation of the steel behavior are remarkably close to the experimentally observed behavior while those made using the fy = 100 ksi assumption are quite conservative. The capacities based on Mastâs Equa- tion are reasonably close to the measured values. In addition to being able to accurately predict the capacity of members reinforced with high-strength A1035 reinforcing bars, it is equally important to examine whether established modeling procedures can capture the stiffness at various limit
25 Figure 8. Crack patterns and curvature in Specimen F4 immediately prior to failure. Table 14. Ratio of measured to computed capacities. Method Specimen fy = 100 ksi Mast Eq. Ramberg-Osgood F1 1.47 1.12 1.07 F2 1.31 1.11 1.08 F3 1.54 1.08 1.01 F4 1.37 1.08 1.02 F5 1.35 1.19 1.14 F6 1.44 1.06 0.991 Figure 9. Loadâmidspan deflection. (a) Specimens F1, F2, F3 (b) Specimens F4, F5, and F6 Figure 10. Measured and computed load-deflection relationships. clearly demonstrate that the specimens reached and exceeded the target strains. Two strain gages were bonded to the concrete surface at the midspan (i.e., in the constant moment region) to measure the compressive strain. The average strain was used to assess the performance of the specimens. The ratio of the peak strain to the target design strain is summarized in Table 15. The specimens developed a strain of at least 1.9 times larger than their target values prior to failure. At failure, the con- crete strain (tabulated in Table 15) ranged from 0.0025 to 0.0039 with an average value of 0.0033. The selection of a maximum concrete strain of 0.003 in a compatibility analysis of members reinforced with high-strength A1035 is rational. 2.3.5 Summary and Recommendations Considering the magnitudes of the strains in the longitu- dinal bars and concrete, the specimens performed adequately and met the design objective. The proposed strain limits of Îµt = 0.008 or higher for tension-controlled behavior and Îµt = 0.004 for compression-controlled are appropriate. Moreover, well-established strain compatibility analysis techniques can
26 effectively and reliably be used to determine ï¬exural capacity of members with A1035 longitudinal reinforcement. Members reinforced with high-strength ASTM A1035 bars exhibit ade- quate ductility and do not suggest any unexpected response characteristics. 2.4 Fatigue Performance of High-Strength Reinforcing Steel Fatigue is a process of progressive structural change in a material subjected to transient loads, stresses or strains. Fatigue strength is deï¬ned as the maximum transient stress range (S) that may be repeated without causing failure for a speciï¬ed Table 15. Ratio of peak strain to target strain and maximum concrete strain. Peak Strain/ Peak Concrete Specimen Target Strain Strain F1 2.46 0.0025 F2 2.07 0.0027 F3 3.14 0.0034 F4 3.68 0.0038 F5 1.92 0.0039 F6 3.24 0.0033 Figure 11. Load-midspan steel strain. (a) Specimens F1, F2, F3 (b) Specimens F4, F5, F6
number of loading cycles (N). The stress range is deï¬ned as the algebraic difference between the maximum and the min- imum stress in a stress cycle: S = fmax â fmin (i.e., the transient stress). Most ferrous materials exhibit an âendurance limitâ or âfatigue limitâ below which failure does not occur for an unlimited number of cycles, N. In general, the concrete mate- rial fatigue performance exceeds that of the steel and is not considered in design (Neville 1975). The AASHTO (2007) limit for fatigue-induced stress in mild steel reinforcement is based on the outcome of NCHRP Project 4-7 as reported by Helgason et al. (1976). The maxi- mum permitted stress range ( ff) in straight reinforcement resulting from the fatigue load combination is given in AASHTO LRFD (2007) Â§184.108.40.206 as follows: Where: fmin = algebraic minimum stress level (compression is neg- ative) and r/h = ratio of base radius to height of rolled-on transverse deformations; 0.3 may be used in the absence of actual values. Recent revisions to AASHTO LRFD Â§220.127.116.11 simply incor- porate the default r/h ratio as follows: The AASHTO-prescribed relationship is shown (see Appendix E) to represent the lower-bound results of many fatigue studies considering a range of bar sizes and is reported applicable for Grades 40, 60, and 75 ASTM A615 reinforcing bars (Corley et al. 1978). Corley et al. report that âA No. 11 Grade 60 bar fractured in fatigue after 1,250,000 cycles when subjected to a stress range of 21.3 ksi and a min- imum stress of 17.5 ksi tension. This is the lowest stress range at which a fatigue fracture has been obtained in an undisturbed North American produced reinforcing barâ [emphasis added]. The fmin term is appropriate where fmin is positive (i.e., ten- sion, the usual case) but appears to be âcalibratedâ to result in the same stress values as were used for working stress design using Grade 40 steel. Finally, bar size is not consid- ered in the AASHTO-prescribed limit, although it is well established that larger bar sizes typically have lower fatigue limits (Tilly and Moss 1982). 2.4.1 AASHTO Fatigue Equation and Design with High-Strength Steel The use of high-strength reinforcement may permit a reduction of the total area of steel required for ï¬exural resis- f ff â¤ â ( )24 0 33. min ksi units (Eq. 9) f f r hf â¤ â + ( ) ( )21 0 33 8. min ksi units (Eq. 8) tance. The resulting larger transient stresses in the steel may adversely affect fatigue performance of the member. Speciï¬- cally, if designed efï¬ciently, both the minimum and maxi- mum stresses will increase coincident with the value of fy used in design. However, the maximum stress may be increased to a greater degree, resulting in a larger stress range under tran- sient loads. For example, the value of fmin will generally be on the order of 0.20fy. For Grade 60 A615 steel, the present AASHTO requirement (Equation 9) results in a fatigue limit of 20 ksi. Applying the same equation to steel having a yield strength of 120 ksi, for instance, results in the unnecessary (and unwarranted) reduction of the permitted fatigue stress to 16 ksi. The lower fatigue limit implies that the higher strength material has reduced fatigue performance, which is contrary to all available data (Appendix E). The counterintu- itive outcome, in terms of design, is that more of the higher strength steel is required to carry the same transient loads. Although some data suggest an improved fatigue limit for higher strength bars (DeJong et al. 2006) may be permissible, there are insufï¬cient data at this time to make any recom- mendation in the direction of changing the AASHTO fatigue limit (Equation 9) and/or making the fatigue limit a function of yield (or tensile) capacity. Nonetheless, the impact of applying Equation 9 to higher strength reinforcing steel is that fmin may be increased by taking advantage of the higher strength steel, but the increase results in an unwarranted reduction in the fatigue limit. It is, therefore, proposed to normalize fmin by the yield stress, fy. Calibrating this equation so that there is no effect for Grade 60 reinforcement, one arrives at the following: While still conservative, this equation recognizes that fatigue behavior of ferrous metals is largely unaffected by the yield strength of the material itself; thus, the baseline endurance limit of 24 ksi is unchanged. 2.4.2 Effect of High-Strength Steel on the AASHTO Fatigue Provisions In order to understand the role of fatigue in the design of reinforced-concrete ï¬exural members, the following approach was taken. A simply supported beam having length L was considered. Nominal moments are determined at the midspan using the following loads: DL = dead load (self weight). This value is determined for a range of values of DL/LLlane. LLlane = speciï¬ed lane load = 0.64 k/ft (AASHTO LRFD Â§18.104.22.168.4). f f ff yâ¤ â ( ) ( )24 0 20. min ksi units (Eq. 10) 27
28 LLtruck = greatest effect of design tandem (Â§22.214.171.124.3) and design truck (Â§126.96.36.199.2). For truck on simple span, the minimum 32-kip axle spacing of 14 ft is used. LLfatigue = effect of single design truck having 32-kip axle spacing of 30 ft (Â§188.8.131.52.1). It is recognized that the maximum moment does not occur exactly at the midspan; however, the error in making this assumption is quite small and becomes proportionally smaller as the span length increases (Barker and Puckett 2007). From these moments, the STRENGTH I and FATIGUE design moments are determined (Â§3.4.1) as follows: Where the 1.33 and 1.15 factors are for impact loading (IM) (Â§184.108.40.206). In order to normalize for distribution, multiple lanes, etc., it is assumed that the STRENGTH design is optimized; therefore, the stress in the primary reinforcing steel under STRENGTH conditions is Ïfy = 0.9fy regardless of bridge geometry. If this is the case, the reinforcing stress associated with the FATIGUE load is as follows: Similarly, the minimum sustained load will result in a rein- forcing stress of The stress in the reinforcing steel under FATIGUE condi- tions is then normalized by the allowable stress [according to f f DL STRENGTHymin .= Ã( )0 9 f f FATIGUE STRENGTHf y= Ã( )0 9. FATIGUE LLfatigue= Ã( )0 75 1 15. . STRENGTH DL LL LLlane tru= + + Ã( )1 25 1 75 1 75 1 33. . . . ck AASHTO Equation 220.127.116.11-1 (Equation 9, above)] to deter- mine the ratio of transient (FATIGUE) stress to the calculated fatigue stress limit. The results from this approach are shown in Figure 12 for simple spans L = 10 to 160 ft and DL/LLlane = 0.5, 1, 2, and 4. In this plot, the vertical axis reports the ratio ff /[24 â 20( fmin/ fy)]. Based on this approach, it is not expected that the fatigue limits of Â§18.104.22.168 will affect design using fy = 60 ksi over the range considered since the ratio of stress range/fatigue limit is less than unity for all cases. The effects of using fy = 100 ksi in this simpliï¬ed scenario include an expected increase in fmin and ff equal to the ratio of yield strengths = 100/60 = 1.67. As seen in Figure 12, however, the calculated stress range remains below the fatigue limit given by Equation 22.214.171.124-1 for all but spans shorter than 20 ft hav- ing fy = 100 ksi. The effect of continuing to use the extant ver- sion of Equation 126.96.36.199-1: fr â¤ 24 â 0.33fmin, is relatively negligible, shifting the 100 ksi curves upward by less than 5% in the scenario presented. Thus, despite the inherent conservativeness of the AASHTO LRFD 188.8.131.52 fatigue provisions, it is not believed that these will impact most rational designs for values of fy up to 100 ksi. It has been shown that increasing the usable yield strength of steel decreases the margin of safety against fatigue. Only in the shortest of spans, where vehicular loads dominate behavior would the âfatigue checkâ fail and additional steel be required. 2.4.3 Fatigue of Slabs (AASHTO LRFD Section 9) Slabs, being shallower and having a proportionally greater LL/DL ratio, may be considered to be more fatigue sensi- tive than the generic conditions described above. However, Figure 12. Transient stress-to-fatigue limit ratio for simple span bridges.
AASHTO LRFD Â§9.5.3 excludes concrete deck slabs from being investigated for fatigue. AASHTO justiï¬es this exclusion based on results reported by de V Batchelor et al. (1978). It has been shown that slabs resist applied loads primarily through internal arch action (AASHTO Â§9.7.1) and that the nominal steel required is primarily to resist local ï¬exural effects (punching) and to provide conï¬nement such that the arching action may be developed (Fang 1985 and Holowka et al. 1980). 2.4.4 Fatigue Test Specimens 184.108.40.206 Fatigue Specimen Details Specimen details were selected to correspond to the details of ï¬exural specimen F3 (see Section 2.3.4 and Appendix D). Two beams 16 in. deep by 12 in. wide having four #5 A1035 longitudinal bars and #3 A 615 stirrups spaced at 9 in. along the entire length of the beam were cast with 10 ksi concrete. The beams were 18.5 ft long and were tested in midpoint ï¬ex- ure over a span of 16.5 ft. Four-inch-wide neoprene supports were used; therefore, the face-to-face dimension of the span is 16 ft-2 in. The fatigue test beams had the same shear span details as ï¬exural specimen F3 but were not provided with a constant moment region. This difference is due to the nature of large-scale fatigue testing and the difï¬culties in providing accurate and safe four-point bending conditions. The meas- ured material properties of the steel reinforcement are given in Appendix A. In summary, fy = 130 ksi (based on 0.2% offset method), and the measured concrete compressive strength was 9.71 ksi. Cyclic testing was carried out at a fre- quency of 1.2 Hz. At regular intervals, the frequency was reduced to 0.003 Hz (1 cycle in 5 minutes) and a fully instru- mented cycle was carried out. 220.127.116.11 Fatigue Test Protocol Details of how the fatigue test protocol was established are provided in Appendix E. The protocol adopted involved test- ing the ï¬rst beam at a stress range (in the primary #5 A1035 reinforcing bars) of 32 ksi. The justiï¬cation being that if the beam withstands 2 million cycles at stress greater than the theoretical endurance limit (for N = 2,000,000) of 28 ksi (see Appendix E), it has de facto exceeded the current AASHTO requirements and thus represents a proof test with good con- ï¬dence. Since the ï¬rst beam successfully resisted 2 million cycles, the second beam was tested at a greater stress range, 46 ksi, to provide a second data point along the S-N curve. All test control is based on reinforcing bar stress measured using strain gages. Four strain gages were used in each specimen: one mounted on each A1035 bar. Gages on bars 1 and 3 were located 8 in. to the left of the midspan loading point and those on bars 2 and 4 were located 8 in. to the right. 18.104.22.168 Results of Fatigue Test 1 Fatigue Test 1 was conducted between 3/10/2009 and 3/31/2009. The applied load at midspan was cycled between 7 and 17 kips at a rate of 1.2 Hz for 2 million cycles. The mea- sured stress range in the A1035 longitudinal steel was 31.1 ksi in the initial test cycles. Strain gages were lost during the ï¬rst 100,000 cycles (loss of gages due to fatigue loading is expected). Due to the nature of fatigue damage, however, the stress range will increase marginally throughout the test (Neville 1975 and Harries et al. 2006). Moreover, equipment malfunc- tion during a few initial cycles resulted in unintentional load- ing of Fatigue Test 1 beyond 30 kips. These higher stress range cycles had little impact on the beam behavior beyond causing additional cracks. During fatigue cycling, no notable degradation in beam stiffness was observed. A small drift in absolute displacements was observed; the drift is attributable to degradation of the neoprene pads and âshakedownâ of the test frame. Nonethe- less, the differential displacement, measured between 7 and 17 kips applied load, remained essentially constant. Figure 13 shows both the deï¬ection (left axis) and secant stiffness mea- sured between applied loads of 7 and 17 kips (right axis) cycle histories for Fatigue Test 1. Crack width measurements both during fatigue cycling and following the fatigue test during a monotonic load cycle to 46 kips (capacity of actuator used) were remarkably consistent and conï¬rmed the measured and analytically calculated bar stresses (Soltani 2010). Fatigue Test 1 behaved very well. The results indicate that the A1035 bars can maintain 2 million cycles at 31 ksi with little or no apparent damage. 22.214.171.124 Results of Fatigue Test 2 Fatigue Test 2 was conducted between 4/14/2009 and 4/16/2009. The applied load at midspan was cycled between 7 and 25 kips at a rate of 1.2 Hz. The measured stress range in the A1035 longitudinal steel was 45.5 ksi in the initial test cycles. One of the four reinforcing bars (a corner bar) experienced a fatigue failure at N = 155,005. The final meas- ured cycle was N = 100,000. As shown in Figure 14, the deflections were increasing with a rising number of cycles although the differential displacement (between 7 and 25 kips) remained relatively constant. The secant stiffness (also measured between 7 and 25 kips) demonstrated some decay in the initial 100,000 cycles. The final data points at N = 155,005 in Figure 14 were obtained from a single cycle following fatigue failure and clearly indicate the effect of the loss of one of the four primary reinforcing bars. Figure 15 shows the ruptured bar following testing (and removal of cover concrete). The bar failed at the location near a stirrup which is typical of such fatigue failures because of fretting 29
30 effects at the transverse bar locations. Figure 15(c) shows the fracture surface of the bar, which is clearly indicative of a fatigue failure. The failure of a bar at N = 155,005 under S = 45.5 ksi is very close to the prediction, which is thought to be conservative. Therefore, an investigation of the fatigue failure surface using scanning electron microscopy (SEM) was conducted (see Appendix E). The SEM revealed aluminum (Al) inclusions in the fracture surface and a signiï¬cant silicon (Si) inclusion at the edge of the bar section, which is thought to have served as a crack initiator. 2.4.5 Summary of Fatigue Tests and Conclusions The adopted S-N relationship described in Appendix E and the two S-N pairs from the tests conducted are shown in Figure 16. Since both S-N pairs fall to the right of the S-N Figure 13. Cumulative damage curves for Fatigue Test 1. Figure 14. Cumulative damage curves for Fatigue Test 2 (fatigue failure occurred prior to obtaining the final data point).
curve, it may be said that the specimen performance exceeded that predicted by the curve (i.e., for a given stress range, S, the fatigue life, N, was greater than predicted), although not by a significant degree. Both tests serve as proof tests of the AASHTO LRFD recommendations (Equation 9) and the proposed revision (Equation 10) that both limit the fatigue stress range to 24 ksi for the case of tension-tension fatigue (i.e., fmin > 0). The adoption of Equation 10 is recommended to address the unwarranted reduction in fatigue stress range that results from the use of the present AASHTO recommen- dation (Equation 9) in conjunction with high-strength rein- forcing steel. 31 Figure 15. Fatigue failure of single bar in Fatigue Test 2. (b) Fatigue Fracture of Bar 1 (c) Fracture Surface (a) Location of Bar Fracture (Beam is Inverted, Cover Has Been Removed) Figure 16. Predicted and experimental S-N data. 0 10 20 30 40 50 60 70 10000 100000 1000000 10000000 100000000 St re ss R an ge , S (k si) Cycles, N Equation E-2 fatigue test #1 fatigue test #2
32 2.5 Shear Reinforcement The use of A1035 steel as transverse reinforcement for ï¬ex- ural members was examined experimentally. The experimen- tal data from full-scale testing of reinforced and prestressed beams were augmented by the results from analytical studies. The performance of high-strength steel as shear reinforce- ment is evaluated in this section. 2.5.1 Shear Resistance Under current AASHTO LRFD Bridge Design Specifica- tions, the Sectional Design Model, which was derived from the Modified Compression-Field Theory (Vecchio and Collins, 1986), is prescribed for determining the required amount of shear reinforcement. The Sectional Design Model provides strain-based relationships to account for contributions from the concrete and the transverse rein- forcement to overall shear capacity. A value for the yield strength of the transverse steel is needed in order to apply the design equations in AASHTO LRFD (2007) Â§5.8.3. For design of the test specimens, a value of 100-ksi was selected as the âyield strengthâ of the A1035 steel. A com- plete synopsis of the design steps and equations is provided in Appendix F. 2.5.2 Experimental Evaluation A total of nine shear specimens were designed, fabricated, tested, and analyzed. The specimens consisted of ï¬ve rectan- gular reinforced-concrete beams and four AASHTO Type I prestressed girders. Of the nine specimens, all but one con- tained both high-strength (A1035) and A615 shear reinforce- ment. The primary goal was to evaluate the performance of high-strength steel as shear reinforcement in comparison to that of the commonly used A615 steel. Appendix F provides detailed information regarding the experimental program as well as a complete record of the test data. 126.96.36.199 Test Specimens and Experimental Program Specimen Details. The ï¬ve reinforced-concrete test beams (designated by SR_) were all 12 in. wide by 24 in. deep. The ï¬rst four of these specimens (SR1 through SR4) were designed based on a nominal concrete strength of 10 ksi and included #3 A1035 stirrups along with #4 A615 stirrups, placed in either half of the beam. Specimen SR5, however, was designed based on a 15 ksi nominal concrete strength and contained only #3 A1035 stirrups throughout the entire length of the beam. The spacing of stirrups in specimens SR1, SR4, and SR5 was governed by the amount required to resist a prescribed value of ultimate shear force. On the other hand, the maximum stirrup spacing currently allowed by AASHTO LRFD Bridge Design Specifications was used as the basis of design for specimens SR2 and SR3. For the specimens con- taining both types of transverse steel, the spacing and size of stirrups were selected such that the stirrup force as computed by would be nearly equal for the A615 and A1035 stirrups reinforcing in either half of the beam. The value of fy was taken as 100 ksi and 60 ksi for A1035 and A615 stirrups, respectively. All of the specimens were reinforced with #8 A1035 longitudinal bars to induce shear failure prior to reaching their ï¬exural capacities. Table 16 summarizes spec- imen details for the reinforced-concrete beams. The four prestressed AASHTO Type I girders (designated by SP_) had 7 in. deep by 48 in. wide composite slabs. All of the Type I girders were designed based on a nominal concrete strength of 10 ksi in the girder and 5 ksi in the slab. Each of these specimens had both #3 A1035 and #4 A615 stirrups along with 0.6-inch low-relaxation strands. The design of SP1 and SP3 was controlled by the amount of transverse rein- forcement required to resist an ultimate shear force. The shear capacities of these specimens were expected to be near their flexural capacities given the nature of the loading arrangement. Specimen SP2 used the maximum stirrup spac- ing currently allowed by AASHTO LRFD Bridge Design Spec- V A f d S s v y v = Table 16. Shear specimens (reinforced-concrete beams). Specimen Transverse f'c (ksi) Design ID Reinforcement Design Measured Criterion #4 A615 @ 9.5 in. SR1 #3 A1035 @ 8.5 in. 10 12.2 As Needed to Resist Vu #4 A615 @ 13 in. SR2 #3 A1035 @ 13 in. 10 12.9 Max. Allowed Spacing #4 A615 @ 13 in. SR3 #3 A1035 @ 13 in. 10 13.0 Max. Allowed Spacing #4 A615 @ 8.5 in. SR4 #3 A1035 @ 8 in. 10 13.1 As Needed to Resist Vu SR5 #3 A1035 @ 8.5 in. 15 16.9 As Needed to Resist Vu
ifications, and was expected to fail in shear. By selecting dif- ferent bar sizes and spacing in these three specimens, the amount of shear force provided by A615 and A1035 stirrups was kept nearly identical. Specimen SP4, on the other hand, was designed such that the A615 shear capacity exceeded the A1035 shear capacity in order to induce shear failure on the A1035 side. Table 17 summarizes specimen details. The mate- rial properties of transverse reinforcement are summarized in Table 18. Appendix A provides an in-depth discussion of material properties. Testing Program. Three different loading arrangements were selected to test the specimens. Specimens SR1, SR2, and SR5 were all 13.5 ft long and were tested over an 11-ft simple span in three-point bending. Specimens SR3 and SR4 were both 26 ft long and tested as a simply supported beam with a 6-ft overhang where the load was applied 1 ft from the tip of the overhang. Specimens SR3 and SR4 were tested in two phases such that one test isolated the loading to just one type of stirrup. The side of specimen SR3 reinforced with A1035 stirrups was tested ï¬rst. For specimen SR4, the side using A615 stirrups was tested ï¬rst. The side tested ï¬rst was not loaded to failure in order to be able to reposition the speci- men and load the other side. The prestressed specimens (SP1 to SP4) were all 30 ft long and tested over a 26.5-ft simple span in four-point bending with a constant moment region of 11 ft. For each test, specimens were instrumented to mea- sure load, deï¬ection, and both steel and concrete strains in given locations. 188.8.131.52 Results and Discussions The measured and observed responses are used to assess the performance of various specimens as described in the fol- lowing sections. 184.108.40.206.1 Observed Failure Modes. Both specimens SR1 and SR2 failed in shear on the side reinforced with #4 A615 stirrups. Figure 17 displays specimen SR2 after failure. In terms of strength, the failure on the portion of the beam using A615 transverse reinforcement suggests satisfactory perform- ance of the A1035 stirrups. The side of specimen SR3 with A1035 stirrups was loaded ï¬rst before testing the A615 side to failure. The failure load was higher than what was applied to the A1035 side; hence, no conclusion regarding performance of A1035 stirrups versus A615 stirrups can be drawn from specimen SR3. The order of testing of specimen SR4 was reversed from SR3; therefore, the A615 side was loaded short of failure. The failure on the A1035 side could be character- ized as ï¬exural. The observed failure mode was unexpected according to the computed capacities. Loading of specimen SR5 had to be stopped prior to failure after reaching the load- ing apparatusâ capacity, which was 20% larger than the best- predicted capacity (based on compression ï¬eld theory) and 33 Table 17. Shear specimens (AASHTO Type I girders). Specimen Transverse Girder f'c (ksi) Slab f'c (ksi) Design ID Reinforcement Design Measured Design Measured Criterion #4 A615 @ 8 in. SP1 #3 A1035 @ 7.5 in. 10 11.9 5 7.2 As Needed to Resist Vu #4 A615 @ 24 in. SP2 #3 A1035 @ 22 in. 10 12.4 5 9.9 Max. Allowed Spacing #4 A615 @ 11 in. SP3 #3 A1035 @ 10 in. 10 13.1 5 10.1 As Needed to Resist Vu #4 A615 @ 16 in. SP4 #3 A1035 @ 18 in. 10 10.5 5 6.3 Under-Designed A1035 Table 18. Measured properties of transverse reinforcement. Yield Strength (ksi) Stirrup Specimens RuptureStrain Calculated Modulus of Elasticity (ksi) Ultimate Strength (ksi) @ Strain = 0.0035 @ Strain = 0.0050 0.2% Offset #4 A615 SR1-SR4 n.r. 26934 100.7 62.6 64.2 63.5 #4 A615 SP1-SP3 n.r. 27596 105.4 86.3 88.2 88.2 #4 A615 SP4 n.r. 23945 105.0 83.4 92.9 90.2 #3 A1035 SR1-SR5 0.111 29800 156.0 95.0 112.0 130.0 #3 A1035 SP4 0.070 27740 164.1 93.0 117.2 131.9 Notes: There are no sample data for #3 A1035 stirrups used in SP1-SP3; n.r. = not reported.
34 67% larger than the capacity computed based on AASHTO equations. The behavior of specimens SR4 and SR5 suggests that the shear strength of members reinforced with A1035 appears to be appreciably larger than what is computed. Specimen SP1 was designed with the highest shear capac- ity and failed in a ï¬exural manner with no signs of excessive shear cracking. Specimen SP2, which had the least amount of shear reinforcement, failed in shear. The failure, which occurred on the A615 side, was quite brittle. Specimen SP3 had slightly larger stirrup spacing than SP1, and the com- puted capacities indicated a failure mode bordering ï¬exural and shear failure. Loading of this specimen was stopped after excessive ï¬exural cracks began to open at midspan. Specimen SP4 was designed after all the other shear specimens had been tested. In order to examine shear failure due to A1035 stir- rups, specimen SP4 was designed such that the capacity pro- vided by #4 A615 stirrups would be approximately 15% higher than that from #3 A1035 stirrups. This specimen expe- rienced shear failure on the side of the specimen with A1035 stirrups. Similar to specimen SR2, the failure was brittleâsee Figure 18. It should be noted that the failure load was 40% higher than the expected capacity based on a detailed analy- sis using compression-ï¬eld theory, and 75% larger than the capacity computed according to AASHTO provisions. The failure load was also 51% and 25% larger than the capacity of #4 A615 stirrups depending on whether AASHTO capacity or compression-ï¬eld theory is used. Capacity. Capacities were computed according to the Sectional Design Model in the AASHTO LRFD Speciï¬cations using as-built material properties. A program called Response 2000 (Bentz 2000), abbreviated as R2K in Table 19, also was used to compute the capacities. This program is a non-linear sectional analysis program for the analysis of reinforced- concrete elements subjected to shear based on the modiï¬ed compression-ï¬eld theory. As shown in Appendix F, load- deï¬ection responses from Response 2000 are reasonably close to the experimental results. A summary of the measured and computed capacities for the shear specimens is given in Table 19. This table also provides the ratios of measured capacities to the computed capacities. All of the specimens far exceeded the predicted capacities based on AASHTO. Even Response 2000 underestimates the shear capacities in most cases. The only specimen for which Response 2000 was found to be slightly unconservative was specimen SP1, which failed in a decidedly ï¬exural manner. The large ratios of measured to computed capacities have also been observed by others (Kuchma et al. 2005) and indicate the challenges of capturing shear behavior. The measured and computed capacities sug- gest adequate shear strength of A1035 stirrups designed based on current design equations in which stirrup yield strength is taken as 100 ksi. Shear Crack Patterns and Widths. One concern for using high-strength steel for stirrups is whether the high stress levels induced in the reinforcement may cause excessive crack- ing in the concrete resulting in degradation of the concrete component of shear resistance. Figure 19 displays the crack patterns for specimen SR4 corresponding to when the stress in A1035 stirrups was approximately 100 ksi. Crack patterns for the regions with A615 and A1035 stirrups were quite sim- ilar in terms of the load at which they formed and how they propagated. None of the test specimens exhibited an unusual behavior of A1035 stirrups in terms of crack formation and crack patterns. In addition to marking the diagonal cracks, their widths were measured at various load increments using a crack comparometer. Those increments correspond to approxi- mately 60% to 100% of the âyield strengthâ of the stirrups (fy =100 ksi for A1035). Below those increments, diagonal crack- ing was minimal or nonexistent. The loads at which diagonal cracks (i.e., shear cracks) could be measured are appreciably larger than service loads. The largest measured crack widths in the regions reinforced with #4 A615 and #3 A1035 stirrups are summarized in Table 20. In this table, the load increments are Figure 17. Failure mode of SR2 (A615 side). Figure 18. Failure mode of SP4 (A1035 side).
presented in terms of shear stress. The information in Table 20 is presented graphically in Figure 20. As expected, the shear crack widths exhibit a large scatter; however, the trends of the data indicate differences between A615 and A1035 stirrups. At lower levels of shear stress, the crack widths for the regions with A1035 stirrups are comparable in size to the crack widths for the regions using A615 stirrups. With an increase in shear stress, the cracks on the side reinforced with A1035 stirrups widened at a faster rate than the side with A615 stirrups. This trend should be anticipated because the A1035 stirrups were smaller than the A615 stirrups (#3 vs. #4). Despite these differences, it should be noted that the diag- onal cracks became measurable at shear stresses exceeding which is commonly used as concrete shear strength. At such stress levels, the magnitude of crack width is less of a concern because ensuing adequate load-carrying capacity is the main design objective. Moreover, the differences between the crack widths for regions with A615 and A1035 are rela- tively small. Strain Levels and Stirrup Forces. Even though the lon- gitudinal bars are all A1035 steel, the strains recorded on the two sides with A615 and A1035 stirrups should be equivalent if the stirrups are performing equally according to compression- ï¬eld theory. A representative load-longitudinal strain rela- tionship is shown in Figure 21; this ï¬gure is for specimen SR1. The longitudinal strains (measured by strain gages SG6 and 2 â²fc 35 Table 19. Measured and computed capacities. AASHTO Capacity R2K Capacity Measured/ Measured/ Specimen ID Stirrup Type Failure Mode Measured Capacity (kips) Computed (kips) Computed Computed (kips) Computed A615 Shear, 175 1.51 233 1.14 SR1 A1035 A615 side 26 175 1.51 233 1.14 A615 Shear, 147 1.55 190 1.20 SR2 A1035 A615 side 228 141 1.62 165 1.38 A615 Shear, 121 76 1.59 SR3 A1035 A615 side 114* 73 1.56 A615 Flexure, 117* 85 1.38 SR4 A1035 A1035 side 147 85 1.73 N/A (R2K cannot model these specimens that have overhangs.) SR5 A1035 N/A 300** 181 1.66 251 1.20 A615 199 1.22 244 0.99 SP1 A1035 Flexure 242 170 1.42 244 0.99 A615 Shear, 139 1.71 157 1.52 SP2 A1035 A615 side 238 130 1.83 149 1.60 A615 175 1.43 243 1.03 SP3 A1035 Flexure 250 154 1.62 239 1.05 A615 Shear, 153 1.51 188 1.23 SP4 A1035 A1035 side 231 132 1.75 164 1.41 Notes: * Loading was stopped prior to failure so the other side could be tested. ** Loading was stopped after reaching the actuatorâs capacity, which was 300 kips. Figure 19. Crack patterns of SR4. (a) A615 Side (b) A0135 Side
36 SG7) near the mid-span are exceptionally similar, and those measured near the quarter points are also good with a differ- ence of only a few hundred microstrain. The sudden jump in the strain readings around 145 kips on the A1035 side is attributed to formation of a crack near the strain gage, which led to continued differences between the strain values. All things considered, the longitudinal strain data again point toward similar behavior between the two types of steel used for the stirrups. In addition to placing strain gages on the longitudinal bars, strain gages also were bonded to the stirrups at the mid- depth. Using the measured stress-strain relationships of the #4 A615 and #3 A1035 steel (Appendix A), the strain readings can be converted into stirrup forces using which can then be used to analyze the performance of the stirrups. Figure 22 illustrates the variation of stirrup force as a func- tion of applied shear for specimen SR2. The two mirrored strain gage locations (refer to the inset) show nearly identi- cal results. The similarities of the stirrup forces suggest that the stirrups performed in accordance with the design objec- tive of developing nearly equal forces in #4 A615 and #3 A1035 stirrups. Yielding of A615 stirrups is evident from SG1 that was outside of the region influenced by the con- centrated load applied at the midspan and reactions. Between approximately 70 and 85 kips, the stirrup force remained essentially unchanged even though the applied shear force was increased by nearly 15 kips. In contrast, A1035 stirrups could continue to provide shear resistance after A615 stir- rups had yielded. The trend of data was generally similar for the other specimens, although formation of cracks near the strain gages occasionally affected the computed stirrup forces. V A f d S s v s v = Table 20. Maximum shear crack width. Maximum Crack Width in a Given Region (in.) Specimen ID Shear Stress ( fc') A615 Side A1035 Side 3.21 0.0098 0.0098 3.56 0.0118 0.0138 3.93 0.0157 0.0157 SR1 4.37 0.0217 0.0236 2.45 0.0157 0.0118 2.88 0.0256 0.0157 SR2 3.09 0.0276 0.0177 2.53 0.0118 0.0236 2.99 0.0157 0.0295 SR3 3.42 0.0236 0.0335 2.57 0.0138 0.0098 2.99 0.0197 0.0157 3.45 0.0217 0.0197 3.87 0.0236 0.0276 SR4 4.30 0.0315 0.0354 2.26 0.0098 2.69 0.0118 3.00 0.0157 SR5 3.28 N/A (This specimen only had A1035 stirrups.) 0.0177 SP1 **Cracks were too small to measure. 6.38 0.0118 0.0157 7.27 0.0157 0.0177 SP2 7.95 0.0256 0.0276 6.93 0.0079 0.0079 7.88 0.0098 0.0118 SP3 8.79 0.0118 0.0138 7.01 0.0059 0.0138 8.03 0.0098 0.0177 SP4 8.99 0.0118 0.0276 Shear stress = Shear force divided by bvdv. Figure 20. Maximum shear crack widthâshear stress.
220.127.116.11. Summary The current provisions, in which the yield strength of A1035 stirrups is taken as 100 ksi, were used to design reinforced- concrete and prestressed beams. These specimens performed well in terms of crack patterns, crack widths, and capacity. The experimental data do not suggest any unusual attributes insofar as using A1035 as shear reinforcement. 2.6 Shear Friction The shear-carrying mechanism present when shear is transferred across a concrete interface subject to Mode II (sliding mode) displacement is commonly known as aggre- gate interlock, interface shear transfer, or shear friction. The last of these terms will be used here. The interface on which shear acts is referred to as the shear or slip plane. A schematic representation of the shear friction mechanism is shown in Figure 23. The shear friction mechanism arises by virtue of the roughness of concrete crack interfaces. As a rough inter- face displaces in a shear mode (slipping, resulting in a defor- mation Î as shown in Figure 23), a âwedging actionâ develops forcing the crack to open in a direction perpendicular to the interface (crack width, w). This crack opening or âdilation of the shear crackâ engages the reinforcement (having area Avf) crossing the crack resulting in a âclampingâ force, Avf fs being generated. The clamping force attributed to the interface reinforcing steel, Avf fs, is engaged as the crack opens. Thus, 37 Figure 21. Comparison of longitudinal strains. Figure 22. Loadâaverage stirrup forces (Specimen SR2).
38 the clamping force is passive in nature. The crack must open sufficiently to develop the âdesignâ clamping force, Avf fs. Loov and Patnaik (1994) conclude that a slip of Î = 0.02 in. is required to result in yield of conventional reinforcing steel having fy = 60 ksi. They additionally point out the inconsis- tency of limiting slip (a previous proposal by Hanson , for instance, suggested limited slip to Î = 0.005 in.) to a lower value since this may be insufï¬cient to generate fy in the inter- face reinforcement. Most critical to this discussion is the fact that only limited data are available for steel interface rein- forcement having a nominal yield capacity greater than 60 ksi. Kahn and Mitchell (2002) report a study where the actual yield stress of the interface reinforcing steel was either 70 or 83 ksi. In this study, they report signiï¬cantly increased scatter in shear friction prediction reliability when using the measured values of fy and conclude that fy should not be taken to exceed 60 ksi for design. Additionally, when normalized by concrete strength, the experimental results show no effect resulting from the different values of fy. The understanding of the shear friction resisting mechanism has evolved to recog- nize the complex nature of the crack interface behavior and to include the effects of aggregate and cement matrix proper- ties, dowel action of the interface reinforcement, and the localized effects of interface reinforcement within the inter- facial area (Walraven and Reinhardt 1981). Nonetheless, code approaches remain based on simple formulations derived from the work of Birkeland and Birkeland (1966). Considering only normal weight concrete and interface reinforcement oriented perpendicular to the interface, the pro- visions from AASHTO (2007) Â§5.8.4 to calculate the nominal shear friction capacity, Vni, are as follows: Where: Acv = area of concrete shear interface; Avf = area of interface shear reinforcement; Pc = permanent net compressive force across interface; V cA A f P V K f A V K A ni cv vf y c ni c cv ni cv = + +( ) â¤ â² â¤ Î¼ 1 2 (Eq. 11) fy = yield strength of interface shear reinforcement; fy â¤ 60 ksi; fcâ² = concrete compressive strength; Î¼ = âfriction factorâ (see below); c = âcohesion factorâ (see below); K1 = fraction of concrete strength available to resist inter- face shear (see below); and K2 = limiting interface shear resistance (see below). The factors Î¼, c, K1 and K2 are given based on the interface condition as follows: Interface condition c (ksi) Î¼ K1 K2 (ksi) Monolithically cast 0.400 1.4 0.25 1.50 Slabs on 1â4 in. amplitude 0.280 1.0 0.30 1.80 roughened surface Other on 1â4 in. amplitude 0.240 1.0 0.25 1.50 roughened surface Cast against surface with 0.075 0.6 0.20 0.80 no roughening The inclusion of the cAcv term in Equation 11 (which is reported to account for the effects of cohesion and aggregate interlock) requires that minimum interface reinforcement also be provided (Avf â¥ 0.05Acv/fy) since the design shear, Vu, could be less than cAcv, technically requiring no reinforce- ment across the interface. The parameters of Equation 11 are highly empirical and have been calibrated over a relatively narrow band of parameters; most signiï¬cantly, limited data exist for fy > 60 ksi. 2.6.1 Experimental Program An experimental study, intended as a series of proof tests of Equation 11 for shear interfaces having high-strength A1035 reinforcement was carried out. This test program is the only known study of shear friction behavior to include high- strength steel. Typical push-off specimens, having dimensions and details shown in Figure 24, were used in this study. This specimen geometry is commonly used for such tests. The applied load is concentric with the test interface, which is therefore effec- Figure 23. Shear friction analogy proposed by Birkeland and Birkeland (1966) (redrawn). w Î Avffs Avf Avffs Avffs AvffstanÏ V = AvffstanÏ Avffs V V Ï Ï N
tively subjected to only shear stress. The shear is resisted by the concrete along the test interface and the steel ties crossing the interface. For these tests, the interface was placed as a âcold jointâ with the concrete on one side placed and allowed to cure for 14 days prior to the placement of the other side of the interface. Prior to placing the second side of the interface, it was cleaned of laitance and roughened to create a surface condition with at least 1â4-in. amplitude. The interface was horizontal during concrete placement; thus, the interface may be thought of as representing the interface between a precast concrete girder and cast-in-place concrete deck. The interface steel reinforcement, therefore, represents the stirrup exten- sions or interface shear reinforcement along such a cold joint. The parameters measured during the experiments were mag- nitude of the shear load, displacement parallel to the shear interface, crack width perpendicular to the shear interface, and strain in the steel reinforcement across the test interface. The specimen designations and measured material pro- perties of the eight push-off specimens tested are shown in Table 21. Four types of duplicated specimens were tested. Spec- imen labels are preceded with âPâ (push-off); the numbers â615â or â1035â indicate the type of steel reinforcement used (ASTM A615 and A1035, respectively); the numbers â3â or â4â indicate the size of the interface steel reinforcement (#3 and #4, respectively); and the letters âAâ and âBâ are used to identify the duplicated specimens. All measured concrete and steel reinforcing bar material properties are reported in Table 21. Detailed material data are provided in Appendix A. The concrete used was a conventional 4000 psi mix having a w/c ratio of 0.44 and 1-in. maximum aggregate size. As noted in Table 21, the concrete strength on either side of the interface was 4220 psi and 6020 psi. For sub- sequent shear capacity calculations, the lower value is used. Two types of interface steel reinforcement were tested: ASTM A615 and A1035 with nominal yield strengths of 60 and 100 ksi, respectively. Two bar sizes of each steel type were tested: #3 and #4. All specimens had three double-legged ties crossing the interface; thus, the interface reinforcing ratios were 0.0041 and 0.0075 for the specimens having #3 and #4 ties, respectively. The instrumentation used in the experiments consisted of three strain gauges, one located on each of the interface ties approximately 3 in. from the interface, and eight linear variable displacement transducers (LVDTs) as shown in Figure 24. The strain gages were located away from the interface in order to improve their reliability and ensure that they were not dam- aged. Thus, the actual bar strain at the interface is expected to be greater than that measured by the gages since some of the bar stress is transmitted back into the concrete over this short development length. As the concrete is damaged during test- ing, the difference in strain between the interface and mea- surement location becomes less signiï¬cant. Testing consisted of the application of a monotonically increasing load to the top and bottom surfaces of the speci- mens until the ultimate shear capacity of the test interface was reached. The load was applied through a 10-in. diameter plate 39 Figure 24. Test specimen details and instrumentation. (a) Test Specimen (b) Instrumentation (c) Specimen Prior to Testing
40 at both the top and bottom of the specimens; a ball joint was used at the top to address small alignment discrepancies (none were observed in any test). A view of the test set-up is shown in Figure 24. The load was applied at a rate of approx- imately 5,000 lbs/min. Once the ultimate shear capacity was reached, loading was continued in displacement control until the specimen failed due to spalling or excessive deformation. Complete details of the experimental program are provided in Zeno (2009). 2.6.2 Experimental Results A summary of results for applied shear (V), shear displace- ment parallel to the interface (Î), crack width perpendicular to the interface (w), and interface steel reinforcement strain (Îµs) for each specimen is given in Table 21. For clarity, the gross section shear stress (Ï = V/Acv) and the apparent stress in the reinforcing steel ( fs = EsÎµs) also are reported. The shear- displacement (V-Î), shear-crack width (V-w), and shear- interface steel reinforcement strain (V-Îµs) plots of all specimens are shown in Figure 25. In general, duplicate instruments tracked each other very well; therefore, average values of Î, w, and Îµs are reported. Figure 26 shows examples of observed test behavior taken well after the ultimate load was achieved (displacements at ultimate load were too small to be seen in photographs). Two important shear load values were monitored during the push-off experiments: the load to cause the initial shear crack, referred to as the âcracking shear loadâ (Vcr); and the highest shear capacity obtained, referred to as the âultimate shear loadâ (Vu). After Vcr is attained, shear friction dominates the behavior of the loaded specimen until Vu is achieved. As described above, the shear friction mechanism arises from the roughness of the concrete interface and the clamping force by the interface reinforcement. After Vu is achieved, the specimen continues to deform with no further increase in capacity. The crack width increases, reducing the friction component, although theoretically increasing the clamping force. Addi- tionally, the roughness of the shear interface is reduced due to shearing off of the local asperities. 18.104.22.168 Shear Friction Behavior The experimental behavior illustrates that the shear fric- tion mechanism can be divided into three stages as follows: Stage 1: Pre-Cracked Behavior. Behavior at loads below the cracking shear load (Vcr) is very similar for all specimens. Table 21. Shear friction specimen details and experimental results. P615-3 P615-4 P1035-3 P1035-4 Specimen ID A B A B A B A B Interface Steel 6 #3 A615 6 #4 A615 6 #3 A1035 6 #4 A1035 Material Properties fcâ (psi) Cast #1: 6020 psi @ 28 days; 7120 psi @ 104 days (age at testing) Cast #2: 4220 psi @ 28 days; 5800 psi @ 90 days (age at testing) Avf (in2) 0.66 1.20 0.66 1.20 Acv (in2) 160.4 163.2 165.0 162.5 157.5 160.7 162.5 160.7 = Avf /Acv 0.0041 0.0040 0.0073 0.0074 0.0042 0.0041 0.0074 0.0075 fy (ksi) 67.3 61.5 130.0 126.0 140.0 131.3 fu (ksi) 103.0 102.3 156.0 157.6 174.0 172.3 u 0.153 0.206 - 0.111 - 0.071 Experimental Results at Cracking Shear Load Vcr (kips) 66.2 66.8 50.0 58.2 57.2 72.5 58.4 60.0 cr = Vcr /Acv (ksi) 0.41 0.41 0.30 0.36 0.36 0.45 0.36 0.37 cr (in.) 0.008 0.010 0.006 0.007 0.009 0.011 0.007 0.009 wcr (in.) <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 scr (Âµ ) 23 30 27 28 38 42 24 61 f scr = Es scr (ksi) 0.68 0.87 0.78 0.81 1.11 1.21 0.70 1.78 Experimental Results at Ultimate Shear Load Vu (kips) 112.5 96.5 114.5 129.0 90.0 105.0 135.7 113.5 u = Vu /Acv (ksi) 0.70 0.59 0.69 0.79 0.57 0.65 0.84 0.71 u (in.) 0.025 0.027 0.037 0.038 0.027 0.031 0.032 0.041 wu (in.) 0.008 0.007 0.009 0.008 0.007 0.008 0.008 0.010 su (Âµ ) 238 405 515 410 222 527 529 579 su = Es su (ksi) 6.92 11.74 14.93 11.90 6.44 15.29 15.35 16.79 Comparison with Equation 11 Vni (fy = 60 ksi) 78.1 78.8 111.3 111.0 77.4 78.2 110.8 110.6 Vu /Vni 1.44 1.23 1.03 1.16 1.16 1.35 1.25 1.03 Vni (measured fy) 82.9 83.6 113.1 112.8 122.7 121.7 201.6 196.1 Vu /Vni 1.36 1.15 1.01 1.14 0.73 0.87 0.69 0.58 Note: Shaded entries indicate that if the measured values of fy are used, Equation 11 becomes significantly unconservative when the higher strength A1035 bars are used.
It is characterized by a relatively linear relationship between the applied load (V) and shear displacement (Î), and negli- gible interface crack widths (w) and interface steel reinforce- ment strains (Îµs). Prior to cracking, applied load is resisted by concrete shear associated with the strength of the bond between the two surfaces that form the shear interface. The average value of cracking stress (Ïcr) for the cold-jointed spec- imens tested was found to be 380 psi and have a coefï¬cient of variation (COV) of 12%. This stress corresponds to a value of (psi), based on the lower concrete strength at the inter-5 â²fc face at the time of testing: fcâ² = 5800 psi. As should be expected, this value is largely unaffected by the steel reinforcement. The strain, and therefore stress, in the reinforcing steel at Vcr is negligibleâvarying only up to 61 Î¼Îµ in the present study. Hence, shear friction reinforcement does not signiï¬cantly con- tribute to the shear capacity of the interface up to the instant of cracking. The shear displacement at Vcr was less than 0.01 in. in all specimens. Stage 2: Post-Cracked Behavior. The post-cracked behavior from loads ranging from Vcr to Vu is characterized by a softening behavior, larger and visible interface crack widths, and higher interface steel reinforcement strains than in the pre-cracked stage. During the second stage, both Î and w exhibit a relatively linear relationship with the applied shear load. The shear friction mechanism is engaged in the second stage. The capacity of the now cracked interface to resist shear is primarily attributed to the friction that originates from the roughness of the two concrete surfaces that form the inter- face. The interface surfaces are tied together by the interface steel reinforcement. The ultimate shear capacity of those specimens having #4 bars was 760 psi, which is approximately 20% greater than those having #3 bars (630 psi). These values correspond to (psi) and (psi), respectively. Sig- nificantly, the ultimate capacity is unaffected by the grade of reinforcing steel, demonstrating the same average value (690 psi) for specimens having A615 and A1035 bars. Signiï¬cant variability of shear displacement (Î) values was observed ranging from 0.025 to 0.041 in. at Vu. Values of the crack width (w) at Vu show less variability, ranging from 0.007 to 0.010 in. In both cases, this variability appears to be related to the size of the interface steel reinforcement provided: the specimens with #3 bars have somewhat smaller values of Î and w than those with #4 bars. This observation is expected due to the greater capacity of the specimens having #4 bars and indicates that the apparent stiffness of the cracked speci- mens is unaffected by the bar size; thus, the greater the capac- ity, the greater the displacement. Average interface steel reinforcement strain values (Îµs) at Vu range between 222 and 579 Î¼Îµ. Associated with the greater capacity of the specimens having #4 bars, these specimens also exhibited greater bar strains at Vu. In general, the strains measured in the A1035 bars were marginally greater than those measured in the A615 bars. This observation is believed to be associated with the different bond characteristics of the bars used and is discussed further below. Because of the still low interface steel reinforcing strains, there is little active clamping force across the interface in this stage. Stage 3: Post-Ultimate Behavior. The behavior follow- ing achieving Vu is characterized by an increase in Î, w, and Îµs without any additional increase in applied loading. However, 8 â²fc10 â²fc 41 Figure 25. Test results. (b) V-w (a) V-Î (c) V- sÎµ
42 as seen in Figure 25, the behavior of the specimens with A615 interface steel reinforcement in this stage is different from that of the specimens with A1035 steel reinforcement. The specimens with A1035 steel reinforcement exhibit con- tinued load carrying capacity after the ultimate shear load is achieved, which can be seen as a plateau in the plots shown in Figure 25. The specimens with A615 steel reinforcement, on the other hand, demonstrate a more rapid degradation in post-ultimate load carrying capacity. Although this study is unable to determine the reasons for the different Stage 3 behavior, it is proposed that it may be attributed to the differ- ent bond characteristics of the bars used and is discussed fur- ther below. 22.214.171.124 Development of Clamping Force in Interface Steel In general, it can be seen that, as expected, the shear friction capacity of the specimens increased as the area of interface steel reinforcement increased. This increase is because the area of interface steel reinforcement is proportional to the clamp- ing force (i.e., fs = fsAs, where fs = ÎµsEs) and thus, the shear fric- tion capacity. On the other hand, it can be seen that the use of A1035 high-strength steel instead of A615 steel as interface reinforcement did not increase the shear friction capacity of the specimens signiï¬cantly. This trend is because, in all of the specimens, Vu was reached well before steel yielding occurred. In fact, as seen in Table 21, the stress in the interface steel rein- forcement is signiï¬cantly lower than its yield strength when the ultimate shear load is achieved. The slight increase in capacity of the specimens with A1035 interface reinforcement may be attributed to the enhanced bond characteristics of this steel (Sumpter 2007), because a better bond results in higher steel strains and increases the shear friction capacity of the interface. Although this study was not intended to investigate bond characteristics of the bars used and there was no discern- able difference in rib conï¬guration between the A615 and A1035 bars, the data do suggest marginally better bond char- acteristics of the A1035 bars in this instance (Zeno 2009). Based on the AASHTO design equation (Equation 11), it would be expected that the use of high-strength interface reinforcement would increase the shear friction capacity of the specimens. In fact, if the interface reinforcement had reached its yield strength during the experiments, it would be expected that specimens P615-4 and P1035-3, having similar nominal values of Avf fy, would have achieved similar shear friction capacities. However, the interface reinforcement did not yield. In fact, the P615-4 specimens had signiï¬cantly greater capacity than the P1035-3 specimens, even though the latter had high-strength interface reinforcement. These results illustrate that because the ultimate shear capacity is dominated by concrete behavior and is reached well before steel yielding occurs, the clamping force is a function of the steel modulus rather than the yield strength. Figure 26. Specimens following testing. (a) P615-3B at a slip exceeding 1in. ( can be seen as displaced horizontal lines representing interface reinforcement locations) (b) Distortion of the interface steel reinforcement of specimen P1035-3A following large slip and cover spalling Î
126.96.36.199 Components of Shear Friction The behavior described in the previous section is illus- trated in Figure 27, which shows the load-crack width (V-w) plots decomposed into their steel and concrete components for Specimens P615-3B and P1035-3B. Similar plots were developed for all specimens (Zeno 2009). In Figure 27, the steel clamping component of shear friction was calculated using the measured interface reinforcement strain (Îµs) to calculate the actual steel stress and assumes a friction factor, Î¼, equal to 1.0 (consistent with AASHTO provisions); thus, the steel clamping force component of the total shear fric- tion is Î¼Avf ÎµsEs. The concrete component was calculated by subtracting the steel component from the applied shear load: V â Î¼Avf ÎµsEs. Figure 27 also shows the calculated capac- ity for the specimens obtained using Equation 11 and mea- sured values of fy. From Figure 27 it can be seen that at its peak, the apparent concrete component greatly exceeds the nomi- nal concrete component (cAcv) and contributes to the major- ity of the shear friction capacity of the specimens. The corollary of this observation is that the steel component is significantly lower than the assumed design value (Î¼Avf fy) and reaches its peak value well after the shear friction capac- ity of the specimens is exceeded. As can be seen in Figure 27, steel yielding was observed in P615-3B but only after a crack opening of 0.09 in. while the steel in P1035-3B did not yield. The behavior of P1035-3B appears to achieve a âsteady stateâ (i.e., balance between the steel and concrete compo- nents after a crack opening of about 0.08 in.). Similar behav- ior was exhibited by all specimens having A1035 reinforcing (Zeno 2009). In all cases shown, the prescribed limits on shear friction capacity (K1f câ²Acv and K2Acv) are greater than the values of cAcv + Î¼Avf fy shown. Furthermore, it is acknowl- edged that the use of the empirical value Î¼ = 1 is arbitrary although supported by current codes and much previous research. The assumption of a Î¼ value is necessary to resolve the concrete component from an otherwise indeterminate equation. Different assumptions of Âµ will shift the curves in a linear manner. These ï¬ndings demonstrate that Equation 11 does not rep- resent the shear friction mechanism since it implies that the maximum concrete and steel components of the shear fric- tion occur simultaneously. In fact, as seen in Figure 27, the concrete component contributes to the majority of the shear friction capacity before the ultimate shear load is reached and then falls to a residual value while the steel component increases. However, the steel component never reaches its peak value, Î¼Avffy, before the ultimate shear load is reached. Nonetheless, empirically limiting the yield strength, fy, to 60 ksi in Equation 11 does provide safe design values. Values of the nominal design shear friction capacity (Vni) calculated from Equation 11 are given in Table 21. Provided the limitation fy < 60 ksi is imposed, Equation 11 gives conser- vative estimates of capacity. However, if the measured values of fy are used, Equation 11 becomes signiï¬cantly unconserva- tive when the higher strength A1035 bars are used (shaded entries). 2.6.3 Conclusions with Regard to Shear Friction The present AASHTO requirement for shear friction capac- ity (Equation 11) may be safely adopted for use with high- strength steel reinforcement and other steel not experiencing a well-deï¬ned yield plateau provided the value of fy used in the formulation is not taken greater than 60 ksi. This recommen- dation is the present requirement and no change to AASHTO LRFD Â§5.8.4 is required to accommodate high-strength steel. 2.7 Compression Members Analytical parametric studies were performed to examine behavior of columns reinforced with A1035 longitudinal and transverse reinforcement. The current AASHTO requirements 43 Figure 27. Components of shear friction behavior. (a) Specimen P615-3B (b) Specimen P1035-3B
for spacing of A1035 spirals were also examined and revisions have been recommended. 2.7.1 Column Capacity Parametric studies were conducted to determine whether columns reinforced with A1035 longitudinal and transverse reinforcement will reveal any unexpected results compared to columns reinforced with commonly used A615 steel. Other steel types (A706, A496, A82, and A955) were not initially included in the parametric studies in order to ï¬rst evaluate the results for A1035 reinforcement. 188.8.131.52 Details The parametric studies were performed by analyzing 270 cases with the variables shown in Table 22. For all cases, the amount of longitudinal steel for columns reinforced with ASTM A615 and ASTM A1035 bars was determined by using a target reinforcement ratio of 4% and 2%, respectively. Spac- ing for the transverse reinforcement was determined using AASHTO Â§5.10.6 and Â§184.108.40.206.1e. The column overall dimensions were arbitrarily selected to cover a wide range of practical column dimensions. The complete details of all 270 cases are provided in Appendix G. 220.127.116.11 Modeling A ï¬ber analysis program called XTRACT (Imbsen 2007) was used to perform detailed cross-sectional ï¬ber analyses. The stress-strain relationship for ASTM A615 reinforcement was based on an available model that replicates typical behav- ior of such bars. A user-deï¬ned material model, in which dis- crete strain and stress data points were input, was used to represent the stress-strain relationship of ASTM A1035. The strain and stress values for each data point were established from an appropriate Ramberg-Osgood function (Appendix A). The material behaviors of the unconï¬ned concrete shell and conï¬ned concrete core were based on the Razvi and Saatcioglu (1999) model that has been calibrated for concrete strengths up to 15 ksi. 18.104.22.168 Results Representative moment-curvature relationships and axial load-moment (P-M) interaction diagrams are shown in Fig- ures 28a and 28b, respectively, for a 24-inch diameter non- seismic, spirally reinforced column using #3, #4, and #5 spirals and 10-ksi concrete. The moment-curvature responses were generated for an axial load corresponding to 0.1f â²cAg where Ag is the column gross section area. The complete set of results is provided in Ward (2009). The variation in the moment-curvature diagrams is due to the differences in reinforcement ratios. The columns reinforced with A615 have more longitudinal bars and hence a greater stiffness. The reduced stiffness of columns with A1035 bars needs to be taken into account for design of bridges subjected to seis- mic loads. The different sizes of transverse steel do not sig- nificantly influence the moment-curvature relationships. This trend should be expected because the properties of concrete (confined and unconfined cores) do not apprecia- bly influence the response of members with small axial loads. Moreover, as discussed previously, the confined con- crete properties are not affected by the size of transverse bars. The axial load-moment interaction diagrams (see Fig- ure 28b) for columns with A615 and A1035 reinforcement vary primarily because of the larger amount of A615 longi- tudinal reinforcement. For a given type of steel (A615 or A1035), the size of transverse reinforcement does not affect the interaction diagrams. The aforementioned results and discussions do not suggest any unexpected responses when A1035 steel is used. In com- parison to A1035, the strengths and properties of other steel types (A706, A496, A82, and A955) are closer to the charac- teristics of A615. Since the responses of columns with A1035 steel do not suggest any unusual or unexpected trends, it was deemed unnecessary to perform similar parametric studies for A706, A496, A82, and A955. 44 Table 22. Variables for column parametric studies. Variable Value/Description Column Type Square tied columns designed and detailed for seismic loads; Circular spirally reinforced columns used in non-seismic regions; and Circular spirally reinforced columns for bridges subjected to seismic loads. Type of Reinforcement ASTM A615 with fy = 60 ksi and ASTM A1035 with fy = 120 ksi (for longitudinal and transverse bars) Column Size Square column dimension or diameter = 18, 24, 36, 48, 60 in. Transverse Reinforcement #3, #4, and #5 Concrete Strength fâc = 5, 10, 15 ksi
2.7.2 Spacing of Spiral Reinforcement For cases that are not controlled by seismic requirements, the volumetric ratio of spiral reinforcement must satisfy AASHTO Equation 22.214.171.124-1, that is Additionally, according to Â§126.96.36.199, the center-to-center spacing shall not exceed six times the diameter of the longitu- dinal bar or 6 in. From a practical point of view, the clear spacing of spirals cannot be less than 1 in. or 1.33 times the maximum size of the aggregate (AASHTO Â§188.8.131.52). The basis of AASHTO Equation 184.108.40.206-1 is to ensure that the axial load capacity of columns after spalling of the concrete cover is at least equal to the capacity before spalling. This provision Ïs g c c yh A A f f â¥ ââââ â â â â² 0 45 1. was reviewed to determine whether it accurately describes the conï¬ning ability of high-strength transverse steel. 220.127.116.11 Formulation The axial load before spalling of cover (Po) and the capacity after spalling of cover (Pâ²) can be computed from the follow- ing equations: Where: Ag = gross column area; As = area of longitudinal bar; fy = yield strength of longitudinal bars; P f A A A f P f A A A f o c g s s y cc c s s y = â² â( )+ â² = â² â( )+ 45 Figure 28. Representative responses. (a) Moment-Curvature Response (b) Axial Load-Moment Interaction
f â²c = unconï¬ned concrete strength; and f â²cc = conï¬ned concrete strength, which is a function of spacing of spiral(s). The provided spiral should be sufï¬cient such that Po and Pâ² are equal to each other, as follows: For a given concrete compressive strength, column size, cover, longitudinal reinforcement ratio, longitudinal bar size, spiral size, yield strength of spiral, and modulus of elasticity, iterate the value of the spiral spacing such that this equality is satisï¬ed. The Razvi and Saatcioglu (1999) model was used to compute f â²cc. Additional details, including the use of another conï¬ned concrete model, are provided in Appendix G. 18.104.22.168 Parametric Study Using the AASHTO provision and the aforementioned for- mulation, the required spiral spacing was computed for a num- ber of columns with the parameters listed in Table 23. All of the columns were reinforced with #9 longitudinal bars, and the longitudinal reinforcement ratio was set equal to 1.5%. The cover to the spiral was taken as 1.5 in. The aim of this study was to evaluate the spacing of high-strength spiral reinforcement. 22.214.171.124 Results and Discussions The calculated required spacings for a representative case are summarized in Table 24. The results for the other cases are provided in Appendix G. For a given concrete strength, the calculated spacing using any of the methods increases as the yield strength of the spiral increases. In terms of reduc- ing the spiral spacing in columns cast with high-strength con- crete, the use of larger, high-strength spirals is more efï¬cient. For a number of cases (shaded in Table 24), the calculated spacings exceed the maximum limit of 6 in. These cases involve columns using 5-ksi concrete. The calculated spacings in columns with a concrete strength of 15 ksi are below the maximum limit for all steel strengths. The trend of the computed spacings is expected. That is, as the column diameter becomes larger, the difference between the core and gross areas diminishes; hence, the ratio of axial load capacity before and after spalling of cover approaches â² â( ) = â² â( )f A A f A Ac g s cc c s 46 Table 23. Parameters for transverse spacing study. Variable Value/Description Concrete Compressive Strength* 5, 10, 15 ksi Spiral Yield Strength 60 ksi, 100 ksi, 120 ksi Column Diameter 18-80 in. (2-in. increments) Spiral Bar Size #3, #4, #5 Note: *The strain at peak stress ( co) was taken as 0.0025. Table 24a. Spacing of spiral (#4 Spiral, fyh 60 ksi). f'co =5 ksi f'co =10 ksi f'co =15 ksi D (in.) AASHTO ModelR-S AASHTO Model R-S AASHTO Model R-S 18 3.12 2.24 1.56 1.29 1.04 0.93 20 3.17 2.4 1.59 1.38 1.06 0.99 22 3.21 2.55 1.6 1.46 1.07 1.06 24 3.24 2.83 1.62 1.62 1.08 1.17 26 3.27 3.09 1.63 1.77 1.09 1.22 28 3.29 3.35 1.64 1.92 1.1 1.25 30 3.31 3.72 1.65 2.07 1.1 1.27 32 3.32 3.97 1.66 2.11 1.11 1.3 34 3.34 4.32 1.67 2.15 1.11 1.32 36 3.35 4.56 1.67 2.19 1.12 1.34 38 3.36 4.89 1.68 2.22 1.12 1.36 40 3.37 5.19 1.69 2.25 1.12 1.38 42 3.38 5.26 1.69 2.28 1.13 1.4 44 3.39 5.33 1.69 2.31 1.13 1.42 46 3.4 5.39 1.7 2.34 1.13 1.43 48 3.4 5.45 1.7 2.37 1.13 1.45 50 3.41 5.51 1.7 2.39 1.14 1.47 52 3.41 5.57 1.71 2.41 1.14 1.48 54 3.42 5.62 1.71 2.44 1.14 1.5 56 3.43 5.67 1.71 2.46 1.14 1.51 58 3.43 5.72 1.71 2.48 1.14 1.52 60 3.43 5.77 1.72 2.5 1.14 1.54 62 3.44 5.82 1.72 2.53 1.15 1.55 64 3.44 5.87 1.72 2.54 1.15 1.56 66 3.45 5.91 1.72 2.56 1.15 1.57 68 3.45 5.95 1.72 2.58 1.15 1.58 70 3.45 6 1.73 2.6 1.15 1.6 72 3.45 6.04 1.73 2.62 1.15 1.61 74 3.46 6.08 1.73 2.64 1.15 1.62 76 3.46 6.12 1.73 2.65 1.15 1.63 78 3.46 6.15 1.73 2.67 1.15 1.64 80 3.46 6.19 1.73 2.69 1.15 1.65 Notes: Shaded cells indicate where calculated spacings exceed the maximum limit of 6 in. The tabulated values of spacings are in inches. Method R-S is based on the confined model proposed by Razvi and Saatcioglu (1999 and 2002). unity and spirals can be placed at larger spacings. From a con- ï¬nement point of view, for an âinï¬nitelyâ large column, the spiral spacing is expected to become âinï¬nitely large.â The formulation presented in Section 126.96.36.199 accurately replicates this trend. The difference between the spacings based on cur- rent AASHTO requirements (Equation 188.8.131.52-1) and more rational methodology presented in Section 184.108.40.206 becomes more pronounced as the column diameter increases. Unfor- tunately, the available test data do not include test results for columns larger than 24 in. because of the large amount of axial force required to test such large columns. The level of axial load in most bridge columns is relatively small (on the order of 0.05f â²cAg) and is appreciably less than the axial load capacity. Therefore, the capacity after the loss of cover will be above the normal loads that typical bridge columns are expected to experience. This point is evident from Figure 29 in which the ratio of the axial load capacity (taken as 0.85f â²cAc, where f â²c = unconï¬ned concrete strength,
47 Table 24b. Spacing of spiral (#4 Spiral, fyh 100 ksi). f'co =5 ksi f'co =10 ksi f'co =15 ksi D (in.) AASHTO ModelR-S AASHTO Model R-S AASHTO Model R-S 18 5.21 3.15 2.6 1.81 1.74 1.31 20 5.29 3.38 2.64 1.94 1.76 1.4 22 5.35 3.59 2.67 2.06 1.78 1.48 24 5.4 3.97 2.7 2.28 1.8 1.64 26 5.44 4.35 2.72 2.49 1.81 1.8 28 5.48 4.72 2.74 2.7 1.83 1.95 30 5.51 5.23 2.76 3 1.84 2.12 32 5.54 5.58 2.77 3.2 1.85 2.16 34 5.56 6.07 2.78 3.48 1.85 2.2 36 5.58 6.41 2.79 3.65 1.86 2.24 38 5.6 6.88 2.8 3.7 1.87 2.27 40 5.62 7.33 2.81 3.75 1.87 2.3 42 5.63 7.78 2.82 3.8 1.88 2.33 44 5.65 8.21 2.82 3.85 1.88 2.36 46 5.66 8.64 2.83 3.9 1.89 2.39 48 5.67 9.07 2.84 3.94 1.89 2.42 50 5.68 9.19 2.84 3.99 1.89 2.45 52 5.69 9.28 2.85 4.02 1.9 2.47 54 5.7 9.37 2.85 4.06 1.9 2.49 56 5.71 9.45 2.85 4.1 1.9 2.52 58 5.72 9.54 2.86 4.14 1.91 2.54 60 5.72 9.62 2.86 4.17 1.91 2.56 62 5.73 9.7 2.87 4.21 1.91 2.58 64 5.74 9.78 2.87 4.24 1.91 2.6 66 5.74 9.85 2.87 4.27 1.91 2.62 68 5.75 9.92 2.87 4.31 1.92 2.64 70 5.75 9.99 2.88 4.33 1.92 2.66 72 5.76 10.06 2.88 4.37 1.92 2.68 74 5.76 10.13 2.88 4.39 1.92 2.7 76 5.77 10.19 2.88 4.42 1.92 2.71 78 5.77 10.26 2.89 4.45 1.92 2.73 80 5.77 10.32 2.89 4.48 1.92 2.75 Notes: Shaded cells indicate where calculated spacings exceed the maximum limit of 6 in. The tabulated values of spacings are in inches. Method R-S is based on the confined model proposed by Razvi and Saatcioglu (1999 and 2002). Table 24c. Spacing of spiral (#4 Spiral, fyh 120 ksi). f'co = 5 ksi f'co =10 ksi f'co =15 ksi D (in.) AASHTO ModelR-S AASHTO Model R-S AASHTO Model R-S 18 6.25 3.56 3.12 2.04 2.08 1.47 20 6.34 3.82 3.17 2.19 2.11 1.58 22 6.42 4.05 3.21 2.32 2.14 1.68 24 6.48 4.45 3.24 2.57 2.16 1.86 26 6.53 4.83 3.27 2.8 2.18 2.03 28 6.57 5.2 3.29 3.01 2.19 2.19 30 6.61 5.72 3.31 3.31 2.2 2.41 32 6.64 6.07 3.32 3.51 2.21 2.51 34 6.67 6.56 3.34 3.8 2.22 2.53 36 6.7 6.89 3.35 3.99 2.23 2.55 38 6.72 7.35 3.36 4.15 2.24 2.57 40 6.74 7.8 3.37 4.18 2.25 2.59 42 6.76 8.24 3.38 4.2 2.25 2.6 44 6.78 8.66 3.39 4.23 2.26 2.62 46 6.79 9.08 3.4 4.26 2.26 2.63 48 6.81 9.49 3.4 4.28 2.27 2.65 50 6.82 9.79 3.41 4.3 2.27 2.66 52 6.83 9.83 3.41 4.32 2.28 2.68 54 6.84 9.88 3.42 4.35 2.28 2.69 56 6.85 9.93 3.43 4.37 2.28 2.7 58 6.86 9.97 3.43 4.39 2.29 2.71 60 6.87 10.02 3.43 4.41 2.29 2.72 62 6.88 10.06 3.44 4.42 2.29 2.74 64 6.88 10.11 3.44 4.44 2.29 2.75 66 6.89 10.15 3.45 4.46 2.3 2.76 68 6.9 10.19 3.45 4.48 2.3 2.77 70 6.9 10.22 3.45 4.49 2.3 2.78 72 6.91 10.26 3.45 4.51 2.3 2.79 74 6.91 10.29 3.46 4.52 2.3 2.8 76 6.92 10.33 3.46 4.54 2.31 2.81 78 6.93 10.37 3.46 4.55 2.31 2.81 80 6.93 10.4 3.46 4.57 2.31 2.82 Notes: Shaded cells indicate where calculated spacings exceed the maximum limit of 6 in. The tabulated values of spacings are in inches. Method R-S is based on the confined model proposed by Razvi and Saatcioglu (1999 and 2002). Figure 29. Ratio of core axial load capacity to axial load demands.
Ac = core area) to the expected axial load demand (taken as 0.05f â²cAg, 0.10f â²cAg, or 0.20f â²cAg) is plotted for columns with diameters ranging from 8 in. to 96 in. with 2 in. of cover. For an 8-in. diameter, the loss of a 2-in. cover will signiï¬cantly reduce the available area (the core area is only 25% of the gross area for this rather small column). However, even for this small column, the axial load capacity of the core (taken simply as 0.85f â²cAc) is about 6% larger than an unrealistic axial load demand of 0.20f â²cAg. For more typical load demands and more realistic column sizes, the remaining capacity after the loss of cover will be sufï¬cient. 2.7.3 Summary and Conclusions ACI 318-08 allows the use of an equation identical to AASHTO Equation 220.127.116.11-1 for fyh up to 100 ksi. The references cited as the basis of allowing fyh = 100,000 ksi are those used as the basis of formulation presented in Section 18.104.22.168. In view of ACI 318-08 provisions, the results of the aforementioned para- metric study (Table 24), and the axial load capacity of the core relative to the expected axial load demands (Figure 29), it appears that the use of current AASHTO Equation 22.214.171.124-1 for fyh up to 100 ksi can be justiï¬ed for Seismic Zone 1. The exten- sion of this equation beyond 100 ksi is questionable at this time. 2.8 Bond and Anchorage 2.8.1 Splice Development AASHTO LRFD (2007) Â§126.96.36.199.1 prescribes the basic ten- sion development length of #11 bars and smaller, ldb, as follows: Where: Ab and db are the area and diameter of the bar being devel- oped; fcâ² is the concrete strength; and fy is the bar yield stress (i.e., the stress to be developed by the splice). Recent recommendations of NCHRP Project 12-60 (Ramirez and Russell 2008) are based on the ACI 318 (2008) requirements for basic tension development length with an additional factor, Î¨c = 1.2, applied when f câ² exceeds 10 ksi as follows: Where Î¨t and Î¨e are factors to account for âtop castâ bars and the use of epoxy-coated reinforcing steel (in this study both are taken as unity); Î» is a factor accounting for the use of lightweight concrete (also unity for this study). The term db y c t e c b tr b b f f c K d d= â² +( )( ) â ââ â â â 3 40 Î¨ Î¨ Î¨ Î» psi units (Eq. 13)( ) db b y c b y A f f d f= â² > ( )1 25 0 4. . ksi units (Eq. 12) (cb + Ktr)/db accounts for the beneï¬cial effects of transverse con- ï¬nement and has an upper limit of 2.5. For values of (cb + Ktr)/db less than 2.5, splitting failures are likely; for values greater than 2.5, pullout failures are likely. The latter cannot be affected by the addition of more conï¬ning reinforcement. The NCHRP 12-60 recommendations also differ from the ACI 318 formu- lation by removing the Î¨s factor, which reduces the develop- ment length (Î¨s = 0.8) for #6 bars and smaller. A comparison of development length calculations made using Equations 12 and 13 is presented in Figure 30. In this ï¬gure, calculated values for #8 bars are shown although all bar sizes exhibit similar trends. For the NCHRP 12-60 calculation (Equation 13), the value of (cb + Ktr)/db = 2.5 since this limit is typically obtained when conï¬nement is present. It is clear that the present AASHTO requirements are more conservative than those proposed by NCHRP 12-60. The latter is used in the present study and thus the experimental âproof testâ is conser- vative when compared to present AASHTO requirements. Although the current AASHTO requirement (Equation 12) does not address conï¬nement, it can be shown to result in development lengths comparable to those resulting from the ACI 408 (2003) requirements and to be more conservative than those resulting from the use of ACI 318 when typical levels of confinement are used. The AASHTO requirement may underestimate the development required in cases where no conï¬ning reinforcement is provided. However, as discussed in Chapter 1, conï¬ning reinforcement should always be used when developing or splicing ASTM A1035 or other high-strength reinforcing steel. 188.8.131.52 Splice Development Tests Eight spliced bar ï¬exural specimens, shown in Figure 31, were tested in four-point ï¬exure. Specimen labels begin with âDâ (for development) and indicate the bar size, followed by the specimen number. Each specimen had two tension bar 48 Figure 30. Comparison of development length calculations.
splices located entirely within the constant moment region of the test span. Two bar sizes were tested: #5 and #8. Nom- inal concrete strengths used for design were 10 and 15 ksi. The actual 28-day concrete strength was determined to be 12.9 and 15.4 ksi (see Appendix A). Measured steel reinforcing properties are given in Table 25 and details are provided in Appendix A. The splice lengths provided, summarized in Table 26, were obtained from Equation 13 to be sufï¬cient to develop bar stresses ( fy in Equation 13) of 100 and 125 ksi, respectively. The use of Equation 13 results in shorter develop- ment lengths than Equation 12 and is therefore less conserva- tive than Equation 12; thus, it was used in this study. 49 Figure 31. Splice development test specimen details. (a) #5 Specimens (D5-1, D5-2, D5-3, D5-4) (b) #8 Specimens (D8-1, D8-2, D8-3, D8-4) Table 25. Reinforcing steel properties. #3* #3â #4 #5 #8 ASTM grade A615 A615 A1035 A1035 A1035 fyâ¡ ksi 65.0 68.0 140.0 130.2 118.6 fu ksi 101 108.8 174.0 164.1 154.6 u 0.159 0.154 not reported 0.103 0.115 * Confining stirrups used in splice tests. â Confining ties used in hook anchorage tests labeled âDâ in Figure 33b and Table 27. â¡ Calculated using 0.2% offset method.
Strain gages were bonded on the bars immediately beyond their splice length from which the stress developed by each splice was determined using experimentally obtained stress- strain relationships (Appendix A). Conï¬nement reinforce- ment in the splice region (and along the entire span) consisted of #3 stirrups having a nominal yield capacity of 60 ksi spaced at 6 in. Based on the conï¬nement provided, a value of (cb + Ktr)/ db greater than 2.5 is calculated; thus, (cb+Ktr)/db = 2.5 for all specimens. 184.108.40.206 Splice Development Results All eight specimens developed their design bar stresses of 100 or 125 ksi exhibiting signiï¬cant reserve capacity (Table 26). Nonetheless, all specimens except for specimen D5-4 even- tually exhibited a failure of the splice rather than rupture of the spliced bars. The bars in specimen D5-4 ruptured. Fig- ure 32 shows the measured load-deï¬ection behavior of all specimens, and the predicted beam behaviors determined based on a Response 2000 (Bentz 2000) section analysis (see Appendix H) that assumes no splice is present. Since the splices did eventually slip, the full ductility of the sections was not achieved. Also shown on Figure 32 are the displacements at which the primary reinforcing steel achieved the design stresses of 100 and 125 ksi. Reasonable reserve capacity beyond these design values is achieved in all cases, particularly for the smaller #5 bars. The improved capacity of the smaller bars is accounted for in the ACI 318 version of Equation 13 by the Î¨s = 0.8. This factor has been removed from the NCHRP 12-60 version of Equation 13 and was not applied in the present work. Spliced beams exhibited good deï¬ection capacity, achiev- ing midspan deï¬ections on the order of L/55 at splice failure. Splice details focus on developing reinforcing bar strength; member ductility is achieved in practice through detailing such as staggering splice locations. The splice test series is intended as proof tests of the NCHRP 12-60 straight bar tension development length recommenda- tion given by Equation 13. These tests have clearly shown that this recommendation is adequate to develop up to 125 ksi in 15 ksi concrete. The present AASHTO requirements, given in Equation 12, are more conservative than those given by Equa- tion 13 (Figure 30). The AASHTO requirements would have resulted in development lengths 11% and 36% longer for 10 and 15 ksi concrete, respectively. In all cases, the 0.4dbfy limit to Equation 12 controls the development length. Thus, the pres- ent AASHTO requirements also have been demonstrated to be conservative through this test program. 2.8.2 Hook Anchorage AASHTO LRFD (2007) Â§220.127.116.11 provides geometric requirements for standard 90Â° or 180Â° hooked anchorages of deformed reinforcing bars in tension. The basic development length (lhb) of such standard hooked anchorages for bars hav- ing fy â¤60 ksi is as follows: Where: db = bar diameter in inches and fcâ² = concrete strength in ksi. For bars having a yield strength greater than 60 ksi, Equation 14 is modiï¬ed by the factor fy/60, effectively scaling the devel- opment length in an inverse manner with the bar capacity to be developed. Factors that increase the basic development length are prescribed for cases where lightweight aggregate (adjustment factor = 1.3) or epoxy-coated reinforcing steel (1.2) are used. These factors were not relevant in the present work and were taken as unity. For #11 bars and smaller, pro- vided with sufï¬cient concrete cover, the basic development length may be reduced as follows: 1. For side cover normal to the plane of the hook exceeding 2.5 in. and back cover to the 90Â° hook extension exceeding 2 in., the basic development length may be factored by 0.7. 2. For hooked bars enclosed by vertical or horizontal ties or stirrups having a spacing not exceeding 3db, the basic development length may be factored by 0.8. hb b c b d f d= â² â¥ â¥ ( )38 in ksi units (Eq. 14)8 6 0. . 50 Table 26. Splice development test results. Splice Length Design Bar Stress to be Developed; fy in Equation 13 Experimentally Observed Bar Stress DevelopedSpecimen Design c (ksi) Spliced Bars (in.) Stress(ksi) Strain Stress (ksi) Strain D5-1 10 2 #5 36db 22.5 100 0.0041 161 0.0261 D5-2 10 2 #5 45db 28.2 125 0.0063 160 0.0232 D5-3 15 2 #5 29db 18.4 100 0.0039 152 0.0135 D5-4 15 2 #5 37db 23.0 125 0.0060 163 0.0254 D8-1 10 2 #8 36db 36.0 100 0.0042 140 0.0126 D8-2 10 2 #8 45db 45.0 125 0.0074 152 0.0306 D8-3 15 2 #8 29db 29.0 100 0.0043 133 0.0096 D8-4 15 2 #8 37db 37.0 125 0.0070 139 0.0122 f'
Both factors may be applied simultaneously, resulting in a reduction factor of 0.56 for well-conï¬ned hook regions with sufï¬cient concrete cover. 18.104.22.168 Hook Anchorage Tests Eighteen ASTM A1035 hook anchorage specimens were tested. The specimen details shown in Figure 33b and Table 27 include two concrete strengths, nominally 5 and 10 ksi, and three bar sizes: #4, #5, and #8. The #4 bars were provided with standard 180Â° hooks and are intended to represent (1) the anchorage of stirrups in girder sections where the stirrups are also called upon to serve as interface reinforcement for a cast- in-place deck; or (2) the anchorage of primary reinforcing in cantilever slabs. The #5 and #8 bars were provided with stan- dard 90Â° hooks and are intended to represent anchorage of these bars where insufï¬cient length is provided to develop a straight bar. This condition may occur in starter bars for piers or abutments, wall piers, or in short ï¬exural members such as pier caps. Specimen labels begin with âHâ (for hook) and indi- cate the bar size followed by the specimen number; a trailing âNâ indicates that no conï¬ning reinforcement was provided. All hook development lengths were designed using Equa- tion 14 with all appropriate modiï¬cations. In all specimens, 51 Figure 32. Load-deflection behavior of splice test beams. Deflection at which the stress in the primary reinforcing achieves the intended design value is noted in each case. (a) Splice Specimens Having Nominal Concrete Strength, fcâ = 10 ksi (b) Splice Specimens Having Nominal Concrete Strength, fcâ = 15 ksi
the calculated value of lhb was modiï¬ed by the selected nom- inal values of fy, 100 or 125 ksi (see Table 27), using the factor fy/60. All specimens were provided with sufï¬cient cover to permit the 0.7 reduction factor to be applied. For all speci- mens having conï¬ning reinforcement (all but specimens in Table 27 ending in N), the conï¬nement was adequate to per- mit the 0.8 reduction factor to be applied. The objective of this limited test series was to serve as a series of proof tests: applying the existing AASHTO hooked bar development length requirements to the higher strength A1035 reinforcing steel. The measured material properties of the hooks and con- ï¬ning steel are given in Table 25. The measured 28-day con- crete strength for the specimens having nominal strengths of fcâ² = 5 and 10 ksi were 6.02 and 9.71 ksi, respectively. Strain gages were applied over the length of hooked embedment (see inset in Figure 35) to determine bar stresses. The test setup, shown in Figure 33a, was designed to replicate as closely as possible (without a full-scale element test) the stresses in the vicinity of a hook anchorage in ten- sion. The hydraulic ram places the bar in tension and the lever arm reaction to the right of the bar provides the equil- ibrating compression. In the setup used, the compression reaction is 1.2 times the bar tension, more than sufficient to provide the appropriate reaction force necessary to develop the hook. A short region of the hook was left unbonded as it entered the concrete block (achieved by wrapping the bar in foam pipe insulation) resulting in the development length beginning 3 in. below the concrete surface. The debonded region was provided to (1) mitigate the pullout of a cone of concrete at the concrete surface, which affects the develop- ment behavior and slip results; and (2) to provide additional concrete depth (h in Table 27) to mitigate the shear failure of a âconeâ of concrete anchored by the hook itself (this was nonetheless observed in Specimens H4-2 and H8-2, as dis- cussed below). Each bar was anchored using a bolted, in-line mechanical splice anchor with both sides of the splice anchor engaged. All bolts were fully torqued except for the lower two that were provided with only 1â3 and 2â3 of their recommended torque values, respectively. The reduced torque levels were intended (following the test of H5-1, see below) to mitigate failure associated with the stress raisers that this anchorage pro- duces. Although the anchorage performed ï¬awlessly in this arrangement, it is not the subject of this study, nor can any conclusions with respect to its performance be drawn. 22.214.171.124 Hook Anchorage Results The results in terms of bar stress achieved and the failure mode observed for all 18 specimens are shown in Table 27. All test specimens exceeded their design stresses of 100 or 125 ksi ( fy in Table 27). Indeed, most specimens achieved their ultimate 52 Table 27. Hook specimen details and test results. ID A* fc' fyâ lhdâ¡ h* D* s1* B* C* Ultimate Failure** bar size â hook angle ksi ksi in. in. in. in. bars in. ksi H4-1N #4 â 180o 5 100 10 16 none n.a. 4 #4 #3 @ 6 179 R H4-4N #4 â 180o 5 125 12 18 none n.a. 4 #4 #3 @ 6 177 R H4-1 #4 â 180o 5 100 8 14 5 #3 @ 1.5 1 4 #4 #3 @ 6 177 R H4-4 #4 â 180o 5 125 10 16 6 #3 @ 1.5 1 4 #4 #3 @ 6 177 R H4-2 #4 â 180o 10 100 6â â 12 3 #3 @ 1.5 1 4 #4 #3 @ 6 173 C/R H4-5 #4 â 180o 10 125 8 14 5 #3 @ 1.5 1 4 #4 #3 @ 6 176 R H5-1N #5â 90o 5 100 13 19 none n.a. 4 #5 #3 @ 6 168 R H5-4N #5 â 90o 5 125 16 22 none n.a. 4 #5 #3 @ 6 168 R H5-1 #5 â 90o 5 100 10 16 5 #3 @ 1.88 1.25 4 #5 #3 @ 6 160 RA H5-4 #5 â 90o 5 125 13 19 6 #3 @ 1.88 1.25 4 #5 #3 @ 6 168 R H5-2 #5 â 90o 10 100 8 14 4 #3 @ 1.88 1.25 4 #5 #3 @ 6 167 R H5-5 #5 â 90o 10 125 9 15 4 #3 @ 1.88 1.25 4 #5 #3 @ 6 168 R H8-1N #8 â 90o 5 100 20 26 none n.a. 4 #8 #3 @ 6 140 TS H8-4N #8 â 90o 5 125 25 31 none n.a. 4 #8 #3 @ 6 140 TS H8-1 #8 â 90o 5 100 16 22 5 #3 @ 3 2 4 #8 #3 @ 6 153 TS H8-4 #8 â 90o 5 125 20 26 6#3 @ 3 2 4 #8 #3 @ 6 138 TS H8-2 #8 â 90o 10 100 12 18 3 #3 @ 3 2 4 #8 #3 @ 6 162 C (no R) H8-5 #8 â 90o 10 125 15 21 4#3 @ 3 2 4 #8 #3 @ 6 166 R Notes: *See Figure 33b. â Design yield stress to be developed in Equation 14. â¡See Equation 14. **Failure mechanisms: R = bar rupture; RA = bar rupture affected by bar anchor; C = concrete shear failure; n.a. = not applicable; TS = test stopped prior to failure for safety considerationsâin this case, the maximum obtained bar stress is reported. â â Minimum development length.
capacity ( fu in Table 25) as evident by a bar rupture failure in the exposed region of the barâdenoted by âRâ in Table 27. All ruptured bars exhibited signiï¬cant necking and elongation and were unaffected (except H5-1) by the bar anchorage or loading mechanism. Observed rupture stresses agree well with the pre- viously tested material properties (Table 25). Specimen H5-1 (the ï¬rst tested) exhibited a bar rupture affected by the installation of the splice anchor used to react the applied load (not actually part of the test). Nonetheless, this specimen still achieved a stress of 160 ksi. A change was made to the splice installation and this failure mode was mit- igated for all subsequent tests. Only two of the #8 specimens were tested to bar rupture; the remaining tests were stopped prior to failure at a stress of 140 ksi, which was still greater than the required proof load. The stoppage was done in the interest of laboratory safety (a rupturing #8 A1035 is a signif- icant projectile). In two specimens having very short devel- opment lengths, the ultimate failure was a shear âconeâ in the concrete (denoted by âCâ in Table 27). This failure mode (1) took place at loads that signiï¬cantly exceeded the required proof loads; (2) occurred at loads very close to those expected to cause bar rupture; and (3) is an artifact of the test specimen and would not be expected in real-world applications. Figure 34 shows an example of such a âCâ failure. Strain proï¬les demonstrate that the hooks are well devel- oped and transfer stress to the concrete through bond. Fig- ure 35 plots the bar strains with length along the #8 hooks (reported in units of bar diameters (db) for the sake of normalization). The uppermost data point on each curve (db = 0) is obtained from the clip gage mounted a few inches above the concrete specimen. The next data point (db = 3) is obtained from the strain gage located 3db into the concrete (see the right-hand inset in Figure 35). As would be expected, these ï¬rst two strains are similar since little development has yet been engaged. The next data point down is obtained from the strain gage located 5db from the hook bend and the ï¬nal data point is 5db around the bend on the hook itself. The strains at this ï¬nal location are all very small indicating that the hooked region is not being engaged in tension. The strain gages used were very small (0.25 in. overall length); their installation does not affect the bond stress development in any significant manner. The data in Figure 35 are given at stresses of 60 ksi (yield of mild steel), 100 ksi and 125 ksi (design values for this test), and 140 ksi (maximum value at which data are available for all specimens). The âslipâ of the hook also was measured using displacement transducers that measured the relative movement of the bar as it is âpulled outâ of the concrete. Since the slip measurement is obtained over a distance of exposed bar (about 5 in. in most tests), the reported slip is greater than the actual slip due to the elastic, and eventually inelastic, strain present over this un- bonded length. Figure 36a shows the slip recorded at stress lev- els of 60, 100, 125, and 140 ksi. The âultimateâ stress is the slip reported at the maximum stress obtained as given in Table 27. 53 Figure 33. Hook test setup and specimen details. Figure 34. Typical concrete shear failure (Specimen H8-2).
54 Figure 35. Strains along hook embedment at selected bar stresses. ldh 5db 3db 5db clip gage â0dbâ 3" debonded region concrete surface strain gage locations (a) #8 90o hook specimens (b) #5 90o hook specimens (c) #4 180o hook specimens
Figure 36b shows only the slip values reported at 125 ksi sorted against (1) concrete strength (5 or 10 ksi); (2) design bar stress (100 or 125 ksi); and (3) the presence of conï¬ning reinforce- ment (N specimens had no conï¬ning reinforcement). Conclusions drawn from Figures 35 and 36 include the following: 1. Through the proof loads (100 and 125 ksi), slip is limited and rarely exceeds 0.06 in. Indeed, through stresses of 140 ksi, slip rarely exceeds 0.09 in. and is not affected by bar size, concrete strength, development length, or the pres- ence of conï¬ning reinforcement. 2. Slip is not signiï¬cant until near the ultimate load (greater than 140 ksi). It is noted that in some cases, the large values of slip include the plastic deformation of the reinforcing bar in the gage length over which slip is measured. 3. Slip at 125 ksi is marginally (<0.01 in.) more pronounced for the 10 ksi concrete. This slight increase is attributed to the use of smaller aggregate (see Appendix A) and its effect on mechanical bond. 4. Slip at 125 ksi is unaffected by the development length pro- vided. Hence, there is reserve bond capacity beyond that implicitly assumed by the development length calculation. 5. The specimens having conï¬ning steel exhibited marginally (<0.02 in.) greater slip at 125 ksi than those that did not. This observation is counterintuitive although the difference is small and may be attributed to experimental scatter. The hook test series was intended as proof tests of the pres- ent AASHTO hook development requirements given by Equa- tion 14. These tests have shown that the present requirement is adequate to develop up to 125 ksi in 10 ksi concrete in cases where adequate cover and conï¬nementâbased on current design requirementsâare provided. 2.8.3 Summary and Conclusions The objective of this portion of the study was to evaluate existing AASHTO requirements in reference to the use of high-strength reinforcement (represented by ASTM A1035) with respect to issues of bar splice development and hooked bar anchorages. Spliced beam straight bar development tests and hooked anchorage pullout tests were performed as proof tests of the current AASHTO requirements as expressed by Equations 12 and 14. The small number of splice beam tests conducted augmented the extensive study by Seliem et al. (2009) and extended the available database to higher strength concrete. The results demonstrate that the present AASHTO require- ments for both straight bar tension development and hooked anchorage tension development may be extended to develop bar stresses of at least 125 ksi for concrete strengths up to 10 ksi provided adequate cover and conï¬nement are provided. In using higher strength steel, greater bar strain and slip will occur prior to development of the bar. The associated displacement of the bar lugs drives a longitudinal splitting failure beyond that where yield of conventional bars would occur; thus, conï¬ning reinforcement is critical in developing higher strength bars. The results of this study and previous work clearly indicate that conï¬ning reinforcement, designed in a manner consistent with current practice, should always be used when developing, splicing, or anchoring ASTM A1035 or other high-strength reinforcing steel. 2.9 Serviceability Considerations A fundamental issue in using A1035 or any other high- strength reinforcing steel is that the stress at service load ( fs; assumed to be on the order of 0.6fy) is expected to be greater 55 Figure 36. Slip of embedded hooks. (a) Slip at Different Stress Levels (b) Slip at 125 ksi
than with conventional Grade 60 steel. Consequently, the service load reinforcing strains are greater (i.e., Îµs = fs/Es). This larger strain affects deï¬ection and crack widths at service loads. In the following sections, discussion focuses on the behavior at loads corresponding to longitudinal reinforcing bar stresses of 36, 60, and 72 ksi, representing service load lev- els (i.e., 0.6fy) for steel having fy = 60, 100, and 120 ksi, respec- tively. At these service load stresses, the use of Es = 29000 ksi for all steel grades is acceptable (see Section 126.96.36.199) although experimentally determined R-O curves have nevertheless been used in all cases to calculate stress from measured rein- forcing bar strains. 2.9.1 Deflections of Flexural Members Table 28 summarizes the midspan deï¬ections of all ï¬exural beam specimens (F1 through F6) corresponding to longitu- dinal bar stresses of 36, 60, and 72 ksi. The experimentally measured deflections include any support settlement but do not include deï¬ection due to self-weight. Also shown in Table 28 are the deï¬ections calculated using both the Branson (Equation 1) and Bischoff (Equation 2) formulations (see Chapter 1) for effective moment of inertia (Ie). In calculating the applied moment (Ma in Equations 1 and 2), the self- weight of the beam is accounted for; thus, the effective moment of inertia is based on the appropriate cracked section for the load level considered. Where: P = total applied load in four-point bending (sum of two point loads); w = self weight of beam; L = length of simple span, 240 in. in all cases; a = length of shear span, 102 in. in all cases. In the formulations of effective moment of inertia (Equa- tions 1 and 2), the moment to cause cracking is calculated as 80% of the moment corresponding to modulus of rupture. Where: Ig = moment of inertia of gross concrete section, nominally 4096 in.4; y = neutral axis distance from the tensile face for gross concrete section, nominally 8 in. The use of the reduced value of Mcr accounts for cases where the applied moment (Ma) is only slightly less than the unre- strained Mcr (based on ) since factors such as shrinkage and temperature may still cause a section to crack over time (Scanlon and Bischoff 2008). 7 5. â²fc M f I y f I y cr c g c g = â²â ââ â â â = â² ( )0 80 7 5 6. . psi (Eq. 16) M Pa wL a = + 2 8 2 (Eq. 15) 56 Table 28. Comparison of experimental and calculated deflections at service load levels. Deflection Ma Experimental Branson Bischoff Beam and Bar Stress = As/bd (kip-in.) (in.) (in.) (in.) F1 @ 36 ksi 0.012 898 0.582 0.372 0.365 F1 @ 60 ksi 0.012 1318 1.145 0.600 0.590 F1 @ 72 ksi 0.012 1553 1.400 0.723 0.713 F2 @ 36 ksi 0.016 1038 0.527 0.318 0.312 F2 @ 60 ksi 0.016 1726 1.145 0.567 0.561 F2 @ 72 ksi 0.016 2084 1.450 0.695 0.690 F3 @ 36 ksi 0.007 645 0.527 0.269 0.288 F3 @ 60 ksi 0.007 900 0.855 0.478 0.482 F3 @ 72 ksi 0.007 1099 1.182 0.633 0.629 F4 @ 36 ksi 0.016 895 0.625 0.286 0.280 F4 @ 60 ksi 0.016 1405 1.146 0.501 0.492 F4 @ 72 ksi 0.016 1650 1.354 0.601 0.592 F5 @ 36 ksi 0.023 1313 0.688 0.330 0.326 F5 @ 60 ksi 0.023 2096 1.271 0.551 0.547 F5 @ 72 ksi 0.023 2517 1.583 0.669 0.666 F6 @ 36 ksi 0.012 569 0.458 0.156 0.166 F6 @ 60 ksi 0.012 1012 0.938 0.429 0.424 F6 @ 72 ksi 0.012 1242 1.229 0.561 0.552
In the calculation of deï¬ection, the self-weight is neglected since this component of the deï¬ection is also not included in the experimentally determined deï¬ections, against which com- parisons are made. For the beams considered, the deï¬ection associated with beam self-weight is approximately 19%, 11%, and 9% of the deï¬ections corresponding to applied load at bar stress levels of 36, 60, and 72 ksi, respectively. The midspan deï¬ections associated with the applied four-point bending are calculated as follows: The Branson and Bischoff formulations yield very similar results for the specimens tested. The correlation between the formulations is not as good for the lower reinforcing ratio of 0.007 (F3). This difference is consistent with the observa- tion that Bransonâs Equation underestimates short-term deflection for concrete members when the reinforcing ratio is less than approximately 1% (Bischoff 2005). Although both equations are suitable for calculating deflections, the Bischoff approach is based on fundamental mechanics and may therefore be applied for any type of elastic reinforcing material. The Branson formulation is empirical and cali- brated for mild steel. 2.9.2 Crack Widths Extensive crack width data were collected in the flexural test series (F1 to F6). To assess the effects of using higher strength steel, the crack widths corresponding to a variety of stresses in the reinforcing steel were determined and are plotted in Figure 37. Figure 37a provides the average crack Î = âââ ââ â â âââ ââ â â ââ â â â PL E I a L a Lc e 3 3 48 3 4 (Eq. 17) width measured at the height of the extreme tension steel from all cracks in the constant moment region. Figure 37b provides the maximum crack width measured in this region. The ratio of maximum to average measured crack widths for all specimens at all stress levels is 1.8, consistent with avail- able guidance for this ratio, which tends to range between 1.5 and 2.0 (CEB-FIP 1993). In all cases, the ratio of maximum to average crack width falls with increasing bar stress. At approximately 36 ksi, this ratio is 1.7, falling to 1.6 at 60 ksi and 1.5 at 72 ksi. The data shown in Figure 37 clearly show that at all consid- ered service load levels ( fs < 72 ksi), average crack widths are all below the present AASHTO de facto limits for Class 1 and Class 2 exposure (0.017 in. and 0.01275 in., respectively; see Section 188.8.131.52). Indeed, with the exception of beam F2, maximum crack widths also fall below the Class 1 threshold through bar stresses of 72 ksi. Crack width is largely unaf- fected by the reinforcing ratio within the range given. It is noted that all 12-in. wide beams had four bars (#5 or #6) in the lowermost layer; thus, crack control reinforcing would be considered excellent for these beams. Considering the mea- sured crack widths in this experimental study, it appears that the inherent conservativeness in existing equations allows present speciï¬cations to be extended to the anticipated higher service level stresses associated with the use of high-strength reinforcing steel. Using Equation 6 (as discussed in Chapter 1, this equation was derived from the present AASHTO LRFD provisions for crack control given in Equation 5), the expected crack width (w) for a given reinforcing bar strain (Îµs) is calculated. Figures 38a and 38b show the calculated crack width for both Class 1 and 2 exposure conditions, respectively, compared with measured average crack width from specimens F1 to F6. The generally 57 Figure 37. Measured crack widths with longitudinal bar reinforcing bar stress for flexural beams. (a) Average Crack Widths (b) Maximum Crack Widths
conservative nature of existing AASHTO crack control require- ments (Equation 5) is evident in Figure 38, supporting the dis- cussion in Section 184.108.40.206. 2.9.3 Summary and Conclusions The AASHTO LRFD specifications use the Branson for- mulation for computing an effective moment of inertia used to compute deflection. An alternative approach developed by Bischoff has been demonstrated to yield similar results and is based on fundamental mechanics, rather than being empirically calibrated as is Bransonâs Equation. Bischoffâ²s approach is also appropriate for any type of elastic reinforc- ing material. The average measured crack widths are below the present AASHTO de facto limits for Class 1 and Class 2 exposure. The inherent conservativeness in existing equations allows pres- ent speciï¬cations to be extended to the anticipated higher service level stresses associated with the use of high-strength reinforcing steel. 58 Figure 38. Measured versus calculated crack widths. (a) Class 1 Exposure; d = 1.00 (b) Class 2 Exposure; d = 0.75