Splice Strength of Conventional and High Relative Rib Area Bars in Normal and High-Strength Concrete

Transcription

1 ACI STRUCTURAL JOURNAL Title no. 97-S65 TECHNICAL PAPER Splie Strength o Conventional and High Relative Rib Area Bars in Normal and High-Strength Conrete by Jun Zuo and David Darwin The eets o onrete strength, oarse aggregate quantity and type, and reinoring bar geometry on splie strength are evaluated. Results or 6 splie speimens with reinoring bars with relative rib areas (ratio o projeted rib area normal to bar axis to the produt o the nominal bar perimeter and the enter-to-enter rib spaing) ranging rom to 0.11, onrete strengths ranging rom 250 to 15,650 psi (29 to 108 MPa), and quantities o limestone and basalt oarse aggregate ranging rom 1586 to 1908 lb/yd 3 (91 to 1132 kg/m 3 ) are reported. The results are ombined with the ACI Committee 08 database to develop design equations or development and splie length, whih are then ompared with the design riteria in ACI For splies not oniney transverse reinorement, the 1/ power o ompressive strength best haraterizes the eet o onrete strength on splie strength. 3/ haraterizes the eet o onrete strength on the additional splie strength providey transverse reinorement. The splie strength o bars oniney transverse reinorement inreases with an inrease in relative rib area anar diameter. The use o stronger oarse aggregate results in an inrease in splie strength or bars both with and without onining reinorement. For splies oniney transverse reinorement, the higher the quantity o oarse aggregate, the greater the ontribution o transverse reinorement to splie strength. The expressions haraterizing the splie strength o reinoring bars aurately represent the development/splie strength o bottom-ast unoatears as a untion o member geometry, onrete strength, relative rib area, bar size, and oninement, providey both onrete and transverse reinorement. The new design expressions are superior to the design riteria in ACI in terms o both saety and eonomy. The riteria in ACI or developears and Class A splies are unonservative or No. 6 (No. 19) and smaller bars. Keywords: bond; deormed reinorement; splie; stirrup; tie. INTRODUCTION Conrete properties have a signiiant eet on the bond strength between reinoring bars and onrete. Azizinamini et al. (1993, 1995) studied the eet o high onrete strength on bond using beam splie tests. The test results indiated that the average bond stress at ailure, normalized with respet to the square root o onrete ompressive strength, dereases with an inrease in ompressive strength. The rate o derease beomes more pronouned as the splie length inreases. Azizinamini et al. noted that the bearing apaity o onrete (related to ) inreases more rapidly than tensile strength (related to ) as ompressive strength inreases. For high-strength onrete, the higher bearing apaity prevents rushing o the onrete in ront o the bar ribs (as ours or normal strength onrete), whih redues loal slip. They onluded that, beause o the redued slip, ewer ribs transer loaetween the steel and the onrete, whih inreases the loal tensile stresses and initiates a splitting ailure in the onrete prior to ahieving a uniorm distribution o the bond ore. Beause o the brittle nature o these ailures, they reommended that a minimum quantity o stirrups be used or bars splied or developed in high-strength onrete. Esahani and Rangan (1996) investigated the inluene o onrete strength on bond using both beam-end and splie tests. No onining transverse reinorement was used. They observed that the extent o onrete rushing in ront o ribs varied depending on onrete strength. As onrete strength inreased, the degree o rushing dereased, with no onrete rushing observed or greater than 11,000 psi (75 MPa). In ontrast to Azizinamini et al. (1993, 1995), they ound that the average bond stress at ailure, normalized with respet to the, was higher or high-strength onrete than or normal strength onrete. In work that preeded the urrent eort, Darwin et al. (1996a) noted that, or normal strength onretes, higherstrength oarse aggregates an inrease the ontribution o transverse reinorement to bond strength by up to 5%. The sope o that study did not over the eet o aggregate properties on bond in members without transverse reinorement or the eet o aggregate quantity. This paper desribes the ontinuation o a study to improve the development harateristis o reinoring steel by aurately haraterizing the development and splie behavior o urrent reinoring bars and modiying the deormation harateristis o bars to obtain improveond strength. Earlier work in the study (Darwin and Graham 1993; Darwin et al. 1996a, 1996b) established that an inrease in the relative rib area o reinoring bars R r (ratio o projeted rib area normal to bar axis to the produt o the nominal bar perimeter and the enter-to-enter rib spaing) inreases the bond strength between reinoring steel and onrete or bars onined by transverse reinorement. The earlier work also demonstrated that an inrease in R r inreases the bond strength o epoxy-oated reinorement, both with and without onining steel. RESEARCH SIGNIFICANCE The prinipal goals o the work reported in this paper are to gain a better understanding o the eet o onrete properties on bond strength, to better understand the behavior o high relative rib area bars over the ull range o onrete strengths now used in pratie, and to develop a design expression that aurately represents the bond strength o reinoring bars as a untion o the geometri and material properties o the onrete member and the reinoring bars. ACI Strutural Journal, V. 97, No., July-August MS No reeived August 2, 1999, and reviewed under Institute publiation poliies. Copyright 2000, Amerian Conrete Institute. All rights reserved, inluding the making o opies unless permission is obtained rom the opyright proprietors. Pertinent disussion will be published in the May-June 2001 ACI Strutural Journal i reeivey January 1, ACI Strutural Journal/July-August 2000

2 ACI member Jun Zuo is a strutural engineer with Construtive Engineering Design, Kansas City, Mo. He reeived a BS in arhitetural engineering rom Tongji University, China, and an MS and PhD in ivil engineering rom the University o Kansas, Lawrene, Kan. David Darwin, FACI, is the Deane E. Akers Proessor o Civil Engineering and Diretor o the Strutural Engineering and Materials Laboratory at the University o Kansas. He is a past member o the Board o Diretion and the Tehnial Ativities Committee and is past-president o the Kansas Chapter o ACI. He is also past-hairman o the Publiations Committee and the Conrete Researh Counil, and a member and past-hairman o ACI Committee 22, Craking. He hairs the TAC Tehnology Transer Committee and ACI Committee 08, Bond and Development o Reinorement, and serves on ACI Committees 6, Frature Mehanis, and Joint ACI-ASCE Committees 5, Shear and Torsion; and 7, Finite Element Analysis o Reinored Conrete Strutures. He is a reipient o the Arthur R. Anderson and ACI Strutural Researh Awards. Only unoated reinorement is overed. The researh is signiiant beause it demonstrates that onrete strength has a muh greater eet on the additional splie strength provided by transverse reinorement than it does on the splie strength o bars not oniney transverse reinorement. The paper also demonstrates that inreases in aggregate strength and quantity result in higher splie strengths. Design expressions developeased on analyses o the test results and a large international database represent splie/ development length as a untion o onrete strength, relative rib area, bar size, and oninement providey both onrete and transverse reinorement. O major signiiane is the observation that the design riteria in ACI or developears and Class A splies are unonservative or No. 6 (No. 19) and smaller bars. Full details o the study are presentey Zuo and Darwin (1998). EXPERIMENTAL PROGRAM The test program onsisted o 6 beam splie speimens ontaining unoated, bottom-ast bars; 1 speimens had splies that were oniney stirrups, and 23 speimens had splies that were not oniney stirrups. Ten deormation patterns were evaluated. Reinoring bars ranged in size rom No. 5 to 11 (No. 16 to 36), with relative rib areas ranging rom 0.69 to Normal and high-strength onretes were manuatured with both limestone anasalt oarse aggregates. Conrete strengths ranged rom,250 to 15,650 psi (29 to 108 MPa). Test speimens The splie speimens (Fig. 1) were 16 t (.9 m) long, with nominal widths o 12 or 18 in. (305 or 60 mm) and a nominal depth o 15.5 or 16 in. (395 or 05 mm). Splie lengths ranged rom 16 to 0 in. (05 to 1020 mm). The beams ontained two or three spliears (Fig. 1(a)) loated in the onstant moment region o simply supported test speimens. The beams were tested in an inverted position (Fig. 1(b)). Atual member dimensions are given in Table 1. ACI Strutural Journal/July-August 2000 Fig. 1 Beam splie speimens: (a) beam oniguration as ast; and (b) test setup (Note: 1 in. = 25. mm; 1 t = 305 mm). Materials Reinoring steel The reinoring bars met the requirements o ASTM A 615. Ten deormation patterns were evaluated, inluding our onventional patterns, designated 8C0A, 8N0, 11N0, and 11B0, and six experimental patterns, designated 5C3, 8C1, 8F1, 8N1, 8N3, and 11F3 (reer to Darwin et al. (1996a) or photographs o the deormation patterns). In the bar designations, the irst number o the designation (one or two digits) is the bar size (ustomary units); the middle letter identiies the manuaturer; the trailing number identiies the deormation pattern; and a last letter is used i bars with the same deormation pattern were produed rom dierent heats o steel. The relative rib areas range rom to or the onventional bars and rom to 0.11 or high R r bars. The reinoring bars used as transverse reinorement also met the requirements o ASTM A 615. Bar properties are given in Table 2. Conrete Six onrete mixtures were used to study the eets o onrete strength and type and quantity o oarse aggregate on splie strength. The mixtures are designated as NNL, NHL, HNL, HHL, NNB, and HHB, in whih the irst letter indiates the onrete strength, N = normal strength ( < 8000 psi [55 MPa]), and H = high strength ( 8000 psi [55 MPa]); the seond letter indiates the quantity o oarse aggregate, N = normal (1586 to 1661 lb/yd 3 [91 to 985 kg/m 3 ]), and H = high (1803 to 1908 lb/yd 3 [1070 to 1132 kg/m 3 ]); and the last letter indiates the type o oarse aggregate, L = limestone, and B = basalt. The limestone and basalt have ompressive strengths o approximately 15,000 and 50,000 psi (103 and 35 MPa), respetively. Conrete strengths ranged rom 250 to 6300 psi (29.3 to 3. MPa) or normal-strength onrete, and rom 8370 to 15,650 psi (57.7 to MPa) or high-strength onrete. Compressive strength was determineased on the average o at least three 6 x 12 in. (150 x 300 mm) ylinders or strengths lower than 12,500 psi (86 MPa) and at least three x 8 in. (100 x 200 mm) ylinders or higher-strength onrete. Test ages ranged rom 7 to 135 days. Mixture proportions and onrete properties are summarized in Table A.1 o Appendix A. * Test proedure The splie speimens were tested as shown in Fig. 1(b). Loads were applied at the ends o the antilevered regions. * The Appendix is available in xerographi or similar orm rom ACI headquarters, where it will be kept permanently on ile, at a harge equal to the ost o reprodution plus handling at the time o request. 631

3 Table 1 Splie speimen properties and test results Speimen no. and onrete * Bar designation n l s, in. b, in. h, in., in. so, in. si, in. b, in. d, in., psi N d s, in. yt, ksi P, kips M u, k-in. s, ksi 19.1 NNL 8N NNL 8N NNL 11F NNL 11F NNL 8N NNL 8N NNL 8N NNL 8N a.1 HHL 8N a. HHL 8N a.5 HHL 8N a.6 HHL 8N b.1 HHL 8N b.3 HHL 8N b.5 HHL 11F NNL 8N NNL 5C NNL 8N NNL 8N HHL 8N HHL 8N HHL 8N HHL 11F , HHL 11F , HHL 11F , HHB 8N , HHB 8N , HHB 8N , HHB 11F , HHB 11F , HHB 11F , HHB 8N , HHB 8N , HHB 8C0A , HHB 11F , HHB 11B , HHB 11F , HHB 11B , NHL 8C0A NHL 8N NHL 8C0A NHL 8C0A NHL 8C0A NNL 8F NNL 8C0A NHL 8C0A NNL 8F NNL 8C0A HHB 8C , HHB 8N , HHB 8C , HHB 11F , HHB 11N , * Speimen and onrete: G.P-SQA = group number (19 to 3); P = asting order in group (1 to 6); S = strength (N = normal, H = high); Q = aggregate quantity (N = normal, H = high); and A = aggregate type (L = limestone, B = basalt). Bar stress omputed using moment-urvature method i M u does not exeed moment apaity rom moment-urvature analysis; otherwise, s omputed using ultimate strength method; M u and s inlude eets o beam sel-weight and loading system. Note: N = number o stirrups; d s = stirrup diameter; yt = stirrup yield strength; 1 in. = 25. mm; 1 psi = 6.89 kpa; 1 ksi = 6.89 MPa; 1 kip =.5 kn; and 1 k-in. = kn-m. 632 ACI Strutural Journal/July-August 2000

4 Table 1 (ont.) Splie speimen properties and test results Speimen no. and onrete * Bar designation n l s, in. b, in. h, in., in. so, in. si, in. b, in. d, in., psi N d s, in. yt, ksi P, kips M u, k-in. s, ksi 0.5 HHB 8N , HHL 8N , HHL 8N , HHL 8N , HHL 8N , HHL 8C0A , HNL 8N , HNL 8N , HNL 8N , HNL 8N , HNL 8N , HNL 8N , * Speimen and onrete: G.P-SQA = group number (19 to 3); P = asting order in group (1 to 6); S = strength (N = normal, H = high); Q = aggregate quantity (N = normal, H = high); and A = aggregate type (L = limestone, B = basalt). Bar stress omputed using moment-urvature method i M u does not exeed moment apaity rom moment-urvature analysis; otherwise, s omputed using ultimate strength method; M u and s inlude eets o beam sel-weight and loading system. Note: N = number o stirrups; d s = stirrup diameter; yt = stirrup yield strength; 1 in. = 25. mm; 1 psi = 6.89 kpa; 1 ksi = 6.89 MPa; 1 kip =.5 kn; and 1 k-in. = kn-m. Table 2 Properties o reinoring bars Rib height Bar designation * Yield strength, ksi Nominal diameter, in. Weight, lb/t % light or heavy Rib spaing, in. ASTM, in. Average, in. Relative rib area 5C %L C0A %L N %L C %L F %L N %H N %H N %L B %L F %L * Bar designation: No. AAB, No. = bar size (No. 5, No. 8, or No. 11); AA = bar manuaturer and deormation pattern; B0 = onventional Birmingham Steel bars; C0 = onventional Chapparal Steel bars; C1, C3 = new Chapparal Steel bars; N0 = onventional North Star Steel bars; F1, F3 = new Florida Steel bars; N1, N3 = new North Star Steel bars; B = letter used i bar had same deormation pattern as reportey Darwin et al. (1996a), but were produed rom dierent steel heat. Average rib height between longitudinal ribs. Note: 1 in. = 25. mm; 1 ksi = 6.89 MPa; 1 lb/t = 1.9 kg/m; and 1 mil = mm. Beams were loaded ontinuously at a rate o approximately 3 kips (13.3 kn) per min until ailure, with tests lasting 15 to 20 min. SPECIMEN BEHAVIOR AND ANALYSIS OF TEST RESULTS Results and observations Moments and maximum bar stresses in the splies at ailure are given in Table 1. The eets o beam sel-weight and the weight o the loading system are inluded. Bar stresses are alulated using moment-urvature or ultimate strength methods, as indiated in Table 1 and desribed in Appendix B. * Most o the speimens ailey splitting at the tension ae within the splie region. For members ast with normal strength onrete, beams with splies that were not onined by transverse stirrups ailed suddenly, with a quik drop in load ater the peak. Beams with splies oniney stirrups exhibited a more dutile behavior, with a slow drop in load ater the peak. For members ast with high-strength onrete, similar dierenes were observeetween members without * The Appendix is available in xerographi or similar orm rom ACI headquarters, where it will be kept permanently on ile, at a harge equal to the ost o reprodution plus handling at the time o request. and with stirrups. The high-strength onrete beams ailed in a more brittle manner than the normal-strength onrete beams. The extent o onrete damage at the steel-onrete interae depended on the onrete strength anar deormation pattern. Damage was more extensive near the disontinuous ends o splies. For normal strength onrete, damage was similar to that observey Darwin et al. (1996a) or onventional bars, the onrete rusheetween the bar ribs, while or high R r bars, the onrete both rushed and sheared. In general, the greater the oninement providey transverse reinorement, the greater the damage at the interae near the disontinuous ends o the spliears. For high-strength onrete speimens without stirrups in the splie region, the interae showed little or no onrete damage. For bars oniney stirrups, onrete damage at the interae was similar to that observed in normal strength onrete beams, but the damage ourred over a longer region, up to 3/ o the splie length. In mathed pairs o speimens ontaining onventional and high relative rib area bars oniney stirrups, the high relative rib area bars produed higher splie strengths. ACI Strutural Journal/July-August

5 Table 3 Eet o onrete properties on splie strength o splies not oniney transverse reinorement Number o Test-predition ratio Conrete * tests Maximum Minimum Average NNL NHL HHL NNB HHB * Conrete designation: SQA: S = strength (N = normal, H = high); Q = aggregate quantity (N = normal, H = high); and A = aggregate type (L = limestone, B = basalt). Test-predited splie strength ratio; test strength = A b s / 1/, determined rom test results; predited strength determined using Eq. (1); and predited strengths or individual speimens presented in Table A.5 o Appendix A. Evaluation o test results In previous work on high R r bars, Darwin et al. (1996a) observed that the type o oarse aggregate signiiantly aets splie strength or bars that are oniney stirrups. That study did not address the eet o oarse aggregate type on the splie strength o bars not oniney transverse reinorement nor the eet o oarse aggregate quantity. Darwin et al. (1996b) ound that the 1/ power o the onrete ompressive strength haraterizes the eet o onrete strength on splie strength or bars both onined and not oniney transverse reinorement. The earlier studies (Darwin et al., 1996a) also showed that the additional strength providey onining steel T s, normalized with respet to 1/, is a untion o the eetive transverse reinorement NA tr /n, in whih N is the number o transverse stirrups or ties in the splie region, A tr is the area o eah stirrup or tie rossing the potential plane o splitting adjaent to the reinoring bars being developed or splied, and n is the number o reinoring bars being developed or splied along the plane o splitting. The yield strength o the transverse reinorement was ound to have no measurable eet on T s (Maeda et al. 1991; Sakurada et al. 1993; Azizinamini et al. 1995; and Darwin et al. 1996a, 1996b). The database usey Darwin et al., however, inluded only a small number o speimens made with high-strength onrete. Thus, with more data available on high-strength onrete speimens, the question arises as to whether or not the 1/ power o is still appropriate or haraterizing the ontribution o onrete strength to bond. For the evaluations that ollow, the urrent results are ombined with those reportey Choi et al. (1991), Hester et al. (1993), and Darwin et al. (1996a) on splie speimens similar to the urrent NNL onrete speimens (normal strength onrete with a normal quantity o limestone oarse aggregate). Speimens 8.3 and 10.5 testey Darwin et al. (1996a) ontained NNB onrete (B = Basalt). The previous test results are summarized in Tables A.2, A.3, and A. o Appendix A. * Strength evaluations are based on the assumption that the total ore in a bar at splie ailure T b equals the sum o a onrete ontribution T and a transverse reinorement (steel) ontribution T s, T b = T + T s. Conrete ontribution T Using proedures desribey Darwin et al. (1996b) and a database onsisting o 171 speimens ontaining developed or spliears not oniney transverse reinorement (Chinn 1955; Chamberlin 1956, 1958; Ferguson and Breen 1965; Thompson et al. 1975; Zekany et al. 1981; Choi et al. 1991; Hester et al. 1993; Rezanso et al. 1993; Azizinamini et al. 1993; Hatield et al. 1996; Darwin et al. 1996a; Zuo and Darwin 1998) with onrete strengths ranging rom 2610 to 15,650 psi (18.0 to MPa), the ultimate bond ore or bars not oniney transverse reinorement T an be expressed as (Zuo and Darwin 1998) T A b = s = [ 59.8 l d ( min ) A b ] 0.1 max min where A b = single spliear area, in. 2 ; s = bar stress at ailure, psi; = onrete ompressive strength, psi; 1/, psi l d = splie or development length, in.; min, max = minimum or maximum value o s, or b ( max / min < 3.5), in.; s = min ( si in., so ) in.; si = 1/2 o lear spaing between bars, in.; so, b = side or bottom over o reinoring bars, in.; and = bar diameter, in. This expression diers somewhat rom that obtained in the earlier studies (Darwin et al. 1996a, 1996b) in that the oeiient or l d has dereased rom 63 to 59.8 and the oeiient or A b has inreased rom 2130 to As beore, 1/ best represents the eet o ompressive strength bond strength. The database used to establish Eq. (1) inludes an additional 38 beams, ompared to that usey Darwin et al. (1996b), and an inrease rom 7 to 19% in the portion o the tests representing high-strength onrete ( > 8000 psi [55 MPa]). A omparison o the test and predited strengths or the beams used to establish Eq. (1) is presented in Table A.5 o Appendix A *. The mean test-predition ratio is 1.00, with a oeiient o variation (COV) o 0.10, ompared to 1.00 and obtainey Darwin et al. (1996b) or the smaller database. Test-predition ratios based on Eq. (1) are used to evaluate the eets o onrete properties on splie strength. Eets o onrete properties on splies without transverse reinorement Speimens without stirrups within the splie region inlude 35 ontaining NNL onrete (nine rom the urrent study, 12 rom Darwin et al. [1996a], eight rom Choi et al. [1991], and seven rom Hester et al. [1993]), two ontaining NNB onrete (Darwin et al. 1996a), six ontaining NHL onrete, our ontaining HHL onrete, and nine ontaining HHB onrete. Eet o oarse aggregate Table 3 summarizes the range and mean o the test-predition ratios or the splies not onined by stirrups. The results show no measurable dierene in the test-predition ratios or onrete ontaining the same type o oarse aggregate, regardless o oarse aggregate ontent or onrete strength, but do show a dierene based on the type o oarse aggregate. The average test-predition ratios range rom 0.96 to 1.01 or the onretes ontaining limestone, ompared with 1.10 and 1.13 or the onretes ontaining basalt. This observation an be explaineased on studies by Kozul and Darwin (1997) and Barham and Darwin (1999), using the same oarse aggregates, whih show that onretes ontaining basalt yield only slightly higher lexural * The Appendix is available in xerographi or similar orm rom ACI headquarters, where it will be kept permanantly on ile, at a harge equal to the ost o reprodution plus handling at the time o request. (1) 63 ACI Strutural Journal/July-August 2000

6 Fig. 2 Test-predition ratio versus onrete ompressive strength or splies not oniney transverse reinorement in onrete ontaining basalt and limestone oarse aggregates, using dummy variable analysis based on type o oarse aggregate (1 psi = 6.89 kpa). strengths but signiiantly higher rature energies (more than two times higher) than onrete o similar ompressive strength ontaining limestone or all ompressive strengths evaluated (2920 to 1,320 psi [20 to 99 MPa]). The higher rature energy providey the basalt results in an inreased resistane to rak propagation that delays splitting ailure and inreases splie strength. Eet o onrete strength Figure 2 ompares test-predition ratios to onrete strength or splie speimens ontaining limestone anasalt oarse aggregate. The best-it lines are based on a dummy variable regression analysis that limits the eet o the dierent number o tests arried out or normal and high-strength onrete with eah aggregate. The best-it lines are nearly horizontal, and the interept o the line or speimens ontaining basalt is approximately 15% greater than that or the speimens ontaining limestone. Beause the preditions used are based on Eq. (1), these observations illustrate that, on average or the speimens shown, 1/ provides an unbiased representation o the eet o onrete strength on bond and, as demonstrated in Table 3, stronger oarse aggregates produe higher splie strengths. A omparison o test/predition ratio versus or all 177 speimens used to develop Eq. (1) also produes a horizontal best-it line (Zuo and Darwin, 1998). In ontrast, i Eq. (1) is replaey an expression based on, the best-it lines (or both the data shown in Fig. 2 and the ull database) slope sharply down, indiating that suh a relationship progressively overpredits bond strength as inreases. Eets o onrete properties on splies with transverse reinorement To investigate the eets o onrete properties on the strength o splies oniney transverse reinorement, the additional bond ore due to oninement providey transverse reinorement T s is obtainey subtrating T (alulated using Eq. (1)) rom the experimentally determined total bond ore T b. Initially, omparisons o T s / 1/ with NA tr /n are used to evaluate the eet o onrete properties on T s or the speimens tested in this study, plus those testey Hester (1993) and Darwin et al. (1996a). Eet o oarse aggregate Figure 3 ompares T s / 1/ versus t r NA tr /n or No. 8 (No. 25) onventional bar splies in normal and high-strength onretes ontaining normal and high quantities o limestone oarse aggregate. The term t r = 9.6 R r (Darwin et al. 1996a) represents the observed Fig. 3 Inrease in bond ore T s normalized with respet to 1/ versus t r NA tr /n or No. 8 (No. 25) onventional bars in normal (N) and high-strength (H) onrete ontaining normal (N) quantities o limestone (L) oarse aggregate, showing ontributions to splie strength as untion o onrete strength and quantity o oarse aggregate (1 in. = 25. mm). Fig. Inrease in bond ore T s normalized with respet to 1/ versus NA tr /n or No. 8 (No. 25) onventional bars in normal (N) and high-strength (H) onrete ontaining normal (N) quantities o oarse aggregate, as aetey oarse aggregate type (basalt [B] or limestone [L]) and relative rib area (1 in. = 25. mm). eet o relative rib area on T s. Using t r as a parameter eliminates the eet o small dierenes in relative rib area (R r ranges rom to 0.085) rom the analysis. Figure 3 shows that T s / 1/ is higher or onretes ontaining high quantities o oarse aggregate (NHL and HHL) than or the onretes ontaining normal quantities (NNL and HNL), demonstrating that the quantity o oarse aggregate an have a measurable eet on T s. T s / 1/ is ompared with NA tr /n in Fig. or onventional and high R r No. 8 (No. 25) bars ast in normal strength onretes ontaining normal quantities o limestone anasalt oarse aggregate. Note that t r is not used as a parameter in this omparison. The igure shows that T s / 1/ is higher, the higher the relative rib area o the bar. The igure also shows that, or all bar patterns, T s / 1/ is higher or onrete ontaining basalt than or onrete ontaining limestone, mathing the earlier observations (Darwin et al. 1996a). Similar results are obtained in the urrent study or bars ast in high-strength onrete (Zuo and Darwin 1998). ACI Strutural Journal/July-August

7 Table Coeiients o determination r 2 or bestit lines o T s / versus NA tr /n or high relative rib area and onventional bars Bar designation * NSC HSC p = 1/ p = 1/2 p = 3/ p = 1 No. o tests 2 r Conventional No N F * Notation o bar designation is same as in Table 2. Normal strength onrete ontaining oarse aggregate; < 8000 psi. High-strength onrete ontaining limestone oarse aggregate; 8000 psi < 16,000 psi. Note: 1 psi = kpa. Table 5 C 1, C 2, t r, t d, and r 2 or dierent values o p p * C 1 C 2 t r t d r 2 1/ R r / R r / R r R r * Power o onrete ompressive strength used to normalize additional bond ore providey transverse reinorement T s. Coeiient o determination o best-it line. Fig. 5 Inrease in bond ore due to transverse reinorement T s normalized with respet to p versus NA tr /n or No. 8 (No. 25) high relative rib area bars (8N3): (a) p = 3/ ; and (b) p = 1/ (1 in. = 25. mm). Eet o onrete strength or urrent tests Figure 3 shows that, or onventional bars, T s / 1/ is higher or high-strength onrete than or normal strength onrete. Similar results are obtained or high R r bars (Zuo and Darwin 1998). These observations indiate that a power o greater than 1/ is needed to aurately haraterize the eet o onrete strength on T s. To apture what might be reerred to as the main behavior, powers p o equal to 1/, 1/2, 3/, and 1.0 were evaluated. To limit the number o variables, omparisons were initially made only or members ontaining limestone oarse aggregate. The test results or No. 8 and 11 (No. 25 and 36) high R r bars, 8N3 (R r = 0.119) and 11F3 (R r = 0.127), and No. 8 (No. 25) onventional bars were used or this purpose. For eah bar, T s normalized with respet to p is plotted versus NA tr /n, as illustrated or 8N3 bars and two values o p in Fig. 5a and 5b. The best-it lines or eah value o p are then determined. In general, the loser the oeiient o determination r 2 is to 1.0 or a best-it line, the better the orrelation between T s / p and NA tr /n, whih, in turn, indiates the better value o p to haraterize the eet o onrete strength on T s. The values o r 2 or the dierent values o p are summarized in Table. The results show that p = 3/ produes the highest r 2 or the high R r bars: r 2 = 0.92 or 8N3 bars, and r 2 = 0.66 or 11F3 bars. p = 1.0 produes the highest r 2 (0.71) or the onventional No. 8 (No. 25) bars. For all three bar patterns, p = 1/ produes the lowest r 2 values (0.76 or 8N3 bars, 0.57 or 11F3 bars, and 0.8 or onventional No. 8 [No. 25] bars). T s / p or 8N3 bars is plotted versus NA tr /n in Fig. 5(a) and (b) or p = 3/ and 1/, respetively. The igures show that when T s is normalized with respet to 3/, the data points or high-strength and normal strength onrete overlap, resulting in a higher value o r 2. When T s is normalized with respet to 1/, the normalizeond ores are higher or high-strength onrete than or normal strength onrete. Eet o onrete strength using database Overall, the best power o to haraterize the eet o onrete strength on T s involves onsideration o two other variables: bar diameter, and relative rib area R r. Following proedures usey Darwin et al. (1996a), an analysis was perormed (Zuo and Darwin 1998) with a database onsisting o 163 development and splie tests rom the U.S. and Canada (Mathey and Watstein 1961; Ferguson and Breen 1965; Thompson et al. 1975; Zekany et al. 1981; DeVries et al. 1991; Hester et al. 1993; Rezanso et al. 1991, 1993; Azizinamini 1995; Darwin et al. 1996a; and Zuo and Darwin 1998). The linear relationships produing the best math with the data or eah value o p are expressed as T s C p 1 ( t r t d ) NA tr = C n 2 The oeiients, C 1, C 2, t r, and t d, and the oeiients o determination r 2 are summarized in Table 5 or the our values o p. In eah ase, t r inreases linearly with relative rib area, and t d inreases linearly with bar diameter. r 2 is highest (0.860) or p = 1.0. r 2 (0.858) is just slightly lower or p = 3/. p = 1/ produes the lowest value o r 2 (0.786). As the next step, or eah value o p, Eq. (2) is ombined with Eq. (1) to obtain predited strengths. The predited strengths and test-predition ratios or the 163 speimens are summarized in Table A.6 o Appendix A. * The average o the test-predition * The Appendix is available in xerographi or similar orm rom ACI headquarters, where it will be kept permanantly on ile, at a harge equal to the ost o reprodution plus handling at the time o request. (2) 636 ACI Strutural Journal/July-August 2000

8 ratios is 1.0 or all our values o p. The least satter in the results, as indiatey the COV, is obtained or p = 1/2, or whih the COV = p = 3/ and p = 1/ provide COVs o and 0.122, respetively; while p = 1.0 has the highest COV (0.132). The values o COV relet the auray o the preditions or the overall database, while the values o r 2 relet the goodness o it between eah expression and the data. The best value o p or haraterizing the eet o onrete strength on T s should provide not only a low COV and a high r 2, but unbiased preditions or both normal and high-strength onrete. This means that, or the appropriate value o p, the best-it line o the test-predition ratio versus shoule horizontal. The best-it lines or the our values o p are plotted in Fig. 6(a). The igure shows that the slope o the lines dereases with an inrease in the value o the power o p. p = 3/ gives the smallest positive slope and a line that is nearly horizontal, while p = 1.0 gives a negative slope. Thus, o the our values o p, p = 3/ gives the least biased preditions o bond strength based on onrete strength. p = 1.0 overestimates bond strength or bars in high-strength onrete. The results in Fig. 6(a) suggest that the best value o p may be slightly higher than As another hek on the value o p and the auray o Eq. (1) and (2), an independent set o 33 splie speimens testey Kadoriku (199) was analyzed. For this series, ranged rom 3070 to 10,980 psi (21.2 to 75.7 MPa), and a single bar diameter o 19 mm was used. Beause R r was not reported, a value o R r = 0.78 (the mean value or No. 6 [19 mm] onventional bars [Darwin 1996b]) is used. The analysis (summarized in Table A.7 o Appendix A * ) indiates that p = 3/ provides the lowest COV (0.085) or the 33 speimens. The best-it lines or testpredition ratios using the our values o p are plotted versus in Fig. 6(b), and show the same harateristis as in Fig. 6(a): p = 3/ provides a nearly horizontal line, with the smallest positive slope, while p = 1.0 gives a negative slope. Thus, among the values o p evaluated, p = 3/ is the most appropriate or use in haraterizing the eet o onrete strength on T s. For simpliity and onveniene, p = 3/, (rather than a possibly more preise, slightly higher value) is seleted or the next step. DESIGN EXPRESSIONS To take ull advantage o the data available, the 33 tests by Kadoriku (199) are ombined with the initial 163 tests to obtain a best-it expression or the ontribution o transverse reinorement to splie strength T s 3 NA = 31.1 t r t tr d n with r 2 = Combining Eq. (1) with (3) gives an expression or total bond ore T b + A b = = s = T T s [ d ( min ) A b ] 0.1 max min (3) () Fig. 6 Best-it lines or test-predition ratios orresponding to powers o (p = 1/, 1/2, 3/, and 1.0), versus ompressive strength : (a) initial omparison; and (b) independent omparison or speimens testey Kadoriku (199) (1 psi = 6.89 kpa). A omparison o the test and predited strengths or the beams in the database in whih the bars are oniney transverse reinorement is presented in Table A.8 o Appendix A* and Fig. 7. The mean is 1.00, and the COV is (By way o omparison, Darwin et al. [1996b] obtained values o 1.01 and ) Dropping the interept 3.99 in Eq. (), substituting l d /s or N, where s = stirrup or tie spaing, and solving or development/splie length l d in terms o A b and, respetively, gives l d A b s (5) max min (5) = ( min ) 0.1 max t r t d A tr sn l d ---- s 1 min max min = K tr (6) NA t r t tr d n 1 2 * The Appendix is available in xerographi or similar orm rom ACI headquarters, where it will be kept permanantly on ile, at a harge equal to the ost o reprodution plus handling at the time o request. ACI Strutural Journal/July-August

9 Fig. 7 Experimental bond ore T b = A b s normalized with respet to 1/ versus predited bond strength, based on Eq. () (1 in. = 25 mm). in whih K tr = (0.52t r t d A tr /sn) 1/2, t r = 9.6R r , t d = , l d / 16, = ( min )(0.1 max / min + 0.9) and ( + K tr )/.0. max and min are deined ollowing Eq. (1). For onventional bars, the average value o R r is (Darwin et al. 1996a, 1996b), whih allows K tr to be expressed in a somewhat simpler and slightly onservative orm as K tr = (0.5t d A tr /sn) 1/2. The limits on l d / and ( + K tr )/ insure that a splitting ailure, rather than a pullout ailure, will govern bond strength (Darwin et al. 1996b; and Zuo and Darwin 1998). The inal step required to onvert Eq. (6) to a design expression involves the appliation o a strength redution φ ator. Using the LRFD approah desribey Darwin et al. (1998), a value o φ = 0.90 is obtained (Zuo and Darwin 1998), mathing the value alulatey Darwin et al. (1998) using a smaller database. Multiplying the right side o Eq. () by 0.9, setting s = y, and solving or l d / gives needed. The two equations are similar to the equations developed by Darwin et al. (1996b); the expressions dier in the values o the onstants in the numerator and denominator (2100 versus 1900 and 68 versus 72, respetively) and the deinition o K tr (Darwin et al. [1996b] used K tr = 35.5t r t d A tr / sn). In the earlier work, the 1/ power o was used to haraterize the eet o onrete strength on T s, based on a database that inluded only a small number o speimens ast with high-strength onrete. Beause the 1/ power o is the same as used to normalize T, the earlier K tr term is a untion only o bar size, relative rib area, and onining transverse reinorement. The two values o K tr are equal or = 660 psi (32 MPa). COMPARISON WITH ACI Equations (7) and (8) are generally similar in ormat to Eq. (12-1) in ACI , whih or bottom-ast, unoated bars in normalweight onrete is l ---- d y max min = K tr For design purposes, Eq. (7) an be onservatively simpliied by setting max / min = 1.0 and dropping the 0.25 term in the deinition o the eetive value o si (reer to Eq. (1)), whih gives l d ---- y Equations (7) and (8) may be applied or bottom-ast developed and spliears in normalweight onrete (Darwin et al. 1996b, 1998; and Zuo and Darwin 1998). Beause the database used to develop the expressions onsists o 90% splie speimens and 10% development length speimens, the 1.3 ator or Class B splies used in ACI is not = K tr (7) (8) l d y γ = K tr y in whih γ = 0.8 or No. 6 (No. 19) and smaller bars and = 1.0 or No. 7 (No. 22) and larger bars, K tr = A tr yt /(1500sn), yt = yield strength o transverse reinorement, is as deined or Eq. (8), and ( + K tr )/ 2.5. The appliation o Eq. (9) diers rom the appliation o Eq. (7) and (8) in three ways: 1) Eq. (9) distinguishes No. 6 (No. 19) and smaller bars rom larger bars using the γ term, leading to a 20% drop in development/splie length or the smaller bars; 2) the K tr term in Eq. (9) inludes the yield strength o the transverse reinorement yt, even though test results show that yt has no eet on bond strength; and 3) the development length l d alulated using Eq. (9) must be inreasey 30% or Class B splies (splies in whih the area o steel provided is less than two times the area o steel required or where more than 50% o the steel is splied). l d in Eq. (9) is used without modiiation or developears and Class A splies (splies or whih the area o reinorement provided is at least twie that requirey analysis and 1/2 or less o the total reinorement is splied). (9) 638 ACI Strutural Journal/July-August 2000

10 Fig. 8 Comparisons o test-predition ratio distributions using ACI , Eq. (7) and Eq. (8) or speimens ontaining: (a) No. 7 (No. 22) and larger bars; and (b) No. 6 (No. 19) and smaller bars without onining transverse reinorement. The relative eonomy and saety o the ACI riteria and those representey Eq. (7) and (8) an be obtainey omparing the strengths preditey the equations with test results in the database maintainey ACI Committee 08. Beause o the eet o R r on K tr (Eq. (7) and (8)), only tests o onventional reinorement are used or bars oniney transverse reinorement. The omparisons are presented in Tables A.9 and A.10 o Appendix A * and summarized in Table 6 and Fig. 8 and 9. The predited strengths do not inlude the 1.3 Class B splie length ator requirey ACI , and the omparisons or Eq. (7) and (8) are made using K tr = (0.5t d A tr /sn) 1/2. Comparisons are limited to test speimens with development/splie lengths 12 in. and, or bars onined by transverse reinorement, l d / 16. Separate results are presented or No. 7 (No. 22) and larger bars and No. 6 (No. 19) and smaller bars to show the eet o the γ ator. Overall, the omparisons with ACI 318 show greater satter and a signiiantly greater number o low test-predition ratios than those obtained with Eq. (7) or (8), espeially or No. 6 (No. 19) and smaller bars. Bars without transverse reinorement For No. 7 (No. 22) and larger bars without onining reinorement (Fig. 8(a)), the test-predition ratios range rom 0.6 to 2.37 or ACI 318, ompared with 0.85 to 1.5 * The Appendix is available in xerographi or similar orm rom ACI headquarters, where it will be kept permanantly on ile, at a harge equal to the ost o reprodution plus handling at the time o request. Fig. 9 Comparisons o test-predition ratio distributions using ACI , Eq. (7) and Eq. (8) or speimens ontaining: (a) No. 7 (No. 22) and larger bars; and (b) No. 6 (No. 19) and smaller bars with onining transverse reinorement. or Eq. (7), and 0.85 to 1.73 or Eq. (8). The average test-predition ratios are 1.22, 1.12, and 1.20, whih translates into slightly longer development and Class A splie lengths or ACI 318 than or Eq. (7) and (8). Beause o the 1.3 ator, Class B splie lengths are onsiderably longer or ACI 318. In terms o saety, not only are the lowest test-predition ratios muh lower or ACI 318, but 16% o the test-predition ratios are less than 1.0, ompared with 10 and 9% or Eq. (7) and (8), respetively. For No. 6 (No. 19) and smaller bars (Fig. 8(b)), the average test-predition ratios range rom 0.78 to 1.78 (mean = 1.22) or ACI 318, rom 0.96 to 1.1 (mean = 1.15) or Eq. (7), and rom 1.08 to 1.55 (mean = 1.27) or Eq. (8), indiating that, on average, ACI 318 development lengths are between the values or Eq. (7) and (8). In terms o saety, 32% o the test speimens have test-predition ratios less than 1.0 when evaluateased on ACI 318, ompared with 5 and 0% or Eq. (7) and (8), respetively. Bars with transverse reinorement For bars oniney transverse reinorement, the testpredition ratios or No. 7 (No. 22) and larger bars (Fig. 9(a)) range rom 0.85 to 2.19 (mean = 1.3) or ACI 318, rom 0.91 to 1.60 (mean = 1.18) or Eq. (7), and rom 0.9 to 1.9 (mean = 1.26) or Eq. (8). In this ase, ACI 318 requires greater average development lengths than Eq. (7) or (8). In terms o saety, 10% o the omparisons with ACI 318 have test-predition ratios below 1.0, versus 13 and 7% or Eq. (7) and (8), respetively. ACI Strutural Journal/July-August

11 Table 6 Test-predition ratios obtained with ACI (Eq. (9)) and proposed expressions (Eq. (7) and (8)) * No. 7 (No. 22) and larger bars No. 6 (No. 19) and smaller bars Beams without transverse reinorement Test-predition ratio Test ACI 318 Test Eq. (7) Test Eq. (8) Test ACI 318 Beams with transverse reinorement Test-predition ratio Test Eq. (7) Test Eq. (8) Maximum Minimum Average COV Beams with test-pred. < % 10% 9% 10% 13% 7% Maximum Minimum Average COV Beams with test-pred. < % 5% 0% 59% 3% 0% * For speimens with onventional reinorement in ACI Committee 08 database. Finally, or No. 6 (No. 19) and smaller bars with onining transverse reinorement (Fig. 9(b)), the test-predition ratios range rom 0.70 to 1.81 (mean = 1.00) or ACI 318, rom 0.9 to 1.61 (mean = 1.27) or Eq. (7), and rom 1.07 to 1.61 (mean = 1.35) or Eq. (8). The low average test-predition ratio or ACI 318 is not a sign o eonomy, but results rom the at that 59% o the test-predition ratios are less than 1.0. This ompares with 3 and 0% or Eq. (7) and (8), respetively. Saety and eonomy The high perentage o test-predition ratios less than 1.0 obtained with ACI or No. 6 bars and smaller raises signiiant onerns or the level o saety providey urrent design riteria or development/splie length, and demonstrates a lak o justiiation or using γ = 0.8 or smaller bars. The omparisons also illustrate that appliation o Eq. (7) and (8) not only produe, on average, somewhat shorter development lengths and signiiantly shorter splie lengths than Eq. (9), but that they provide a saety margin that is superior to that providey the riteria in ACI But why are there no ailures? The question arises as to why ailures have not ourred i the saety margin is as low as indiated in this analysis or No. 6 (No. 19) and smaller bars. There are several reasons. First, ACI requires that the development lengths alulated using Eq. (9) be inreased by 30% or Class B splies. The extra splie length more than makes up or using γ = 0.8. Seond, or developears and Class A splies, strutures are designed with load ators and apaity redution ators or lexure, axial load, and shear that provide protetion. Third, strutures rarely see the values o live load speiied in the statutory building odes. Happily, these ators help ushion the eets o the shorter development lengths or the smaller bars. The overall result is a smaller margin o saety or No. 6 (No. 19) and smaller bars than obtained or No. 7 (No. 22) and larger bars. Considering the large perentage o low test-predition ratios, it woule wise to use γ = 1.0 or all bar sizes. SUMMARY AND CONCLUSIONS Sixty-our splie speimens are used to investigate the eets o onrete properties on the splie strength o high relative rib area and onventional reinoring bars. Bar relative rib areas range rom to Conrete mixtures with strengths ranging rom 250 to 15,650 psi (29 to 108 MPa) and quantities o limestone anasalt oarse aggregate ranging rom 1586 to 1908 lb/yd 3 (91 to 1132 kg/m 3 ) are used. Test results rom this study are ombined with the results o previous studies. Development/splie design equations are developed or unoated reinoring bars based on a database inluding 196 speimens ontaining bars oniney transverse reinorement and 171 speimens ontaining bars not oniney transverse reinorement. The design equations aount or the eets o member geometry, bar size, relative rib area, oninement providey transverse reinorement, and onrete strength. A reliability-based strength redution φ ator is inorporated in the design expressions. The design expressions are then ompared with the development riteria in ACI using the ACI Committee 08 database. The ollowing onlusions are based on the test results and analyses presented in this paper: 1. Conrete with stronger oarse aggregate provides higher splie strength under all onditions o oninement; 2. For splies oniney transverse reinorement, the higher the quantity o oarse aggregate in the onrete, the greater the ontribution o transverse reinorement to splie strength; 3. For splies not oniney transverse reinorement, 1/ best haraterizes the eet o onrete strength on splie strength. 3/ haraterizes the eet o onrete strength on the additional splie strength providey transverse reinorement;. The splie strength o bars oniney transverse reinorement inreases with an inrease in relative rib area anar diameter; 5. The expressions haraterizing the splie strength o reinoring bars presented in this paper aurately represent the development/splie strength o bottom-ast unoated bars as a untion o member geometry, onrete strength, relative rib area, bar size, and oninement providey both onrete and transverse reinorement; and 6. The new design expressions are superior to the design riteria in ACI in terms o both saety and eonomy. The riteria in ACI or developears and Class A splies are unonservative or No. 6 (No. 19) and smaller bars. 60 ACI Strutural Journal/July-August 2000