Anchorage Strength and Behavior of Headed Bars in-ACI

ACI Structural Journal/September-October 2009 579

ACI Structural Journal, V. 106, No. 5, September-October 2009.MS No. S-2007-003.R4 received May 16, 2008, and reviewed under Institute publication

policies. Copyright © 2009, American Concrete Institute. All rights reserved, including themaking of copies unless permission is obtained from the copyright proprietors. Pertinentdiscussion including author’s closure, if any, will be published in the July-August 2010ACI Structural Journal if the discussion is received by March 1, 2010.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Thirty exterior beam-column joint specimens without transversereinforcement were tested to measure anchorage strength withrespect to anchorage configuration and embedment length. Theanchorage behavior of bars terminated with a head and with a90-degree hook is investigated and compared with each other andexisting models. It is found that existing models based on idealizedfailure modes do not properly predict the concrete contribution toanchorage strength of headed bars terminated in exterior joints. Anew model that accounts for head bearing and bond capacity ofthe anchored bars is proposed and calibrated using statisticalanalysis of the experimental results. The model conservativelyestimates the anchorage strength of the headed bars terminatedwithin exterior beam-column joints with sufficient side cover.Features of the new model are compared with the existing models.

Keywords: anchorage; bar(s); beam-column joint; bearing; bond;CCT node.

INTRODUCTIONHeaded bars, as shown in Fig. 1, provide an alternative to

hooked bars and assist in alleviating steel congestion.1-3

Previous research on headed bars may be divided into twocategories: performance of headed bars in realistic structuralsystems, and investigation of the mechanics of the headedbars under idealized conditions.

Previous structural system studies include a number ofbeam-column joint investigations,3-5 where headed barswere used for longitudinal reinforcement, and slab-columnjoint investigations,6,7 where headed bars were used forshear reinforcement. The reliability and applicability of theheaded bars were validated in these studies and, consequently,guidelines on the use of headed bars were introduced inACI 352R-028 and ACI 421.1R-08.9 These guidelines provideguidance on general application of bars but do not provide directestimates for the anchorage strength of headed bars.

To assist in the development of models on anchoragestrength, previous studies on headed bars under idealizedconditions examined headed bar failures, such as side-faceblowout10-13 and concrete breakout10 modes. These studiesconsisted of idealized evaluations where headed bars werepulled from concrete blocks.

Headed bar anchorages are commonly used in areas wheredevelopment hooks or traditional reinforcement developmentlengths cannot be achieved. A number of standard config-urations are shown in Fig. 2. The anchorage mechanism ofheaded bars is typically modeled according to strut-and-tieconcepts with the bar head region classified as a compression-compression-tension (CCT) node. These nodes are furtherclassified as either surface CCT nodes or interior CCTnodes, depending on the location of headed bars.

The surface CCT node may be formed at a support or at aconcentrated load point such as dapped-end beam or corbel.The interior CCT node is formed inside a member such as an

Title no. 106-S53

Anchorage Strength and Behavior of Headed Bars in Exterior Beam-Column Jointsby Sung-Chul Chun, Bohwan Oh, Sung-Ho Lee, and Clay J. Naito

Fig. 1—Headed bars and hooked bars (No. 8, No. 11, andNo. 18).

Fig. 2—Examples of headed bars developed in surface CCTnodes and interior CCT nodes.

ACI Structural Journal/September-October 2009580

exterior or corner beam-column joint and hanging headedbars in a deep beam. The surface CCT node differs from theinterior CCT node in three ways. First, the strength of thesurface CCT node is typically higher than that of the interiorCCT node due to the surface bearing plate, which providestransverse deformation restraint to the node concrete.Second, the dimension of the surface CCT node is determinedby the size of the bearing plate, whereas the dimension of theinterior CCT node is determined from internal stress fields.

Third, the bond outside a nodal zone or an extended nodalzone is easily lost at ultimate state in the surface CCT nodedue to cracks near the nodal zone.13

An exterior beam-column joint is an ideal application forheaded bars due to the high level of reinforcement congestionthat occurs. In this application, the variation of bond strengthalong the bar and the anchorage strength are dependent notonly on the materials but also on the geometry of the reinforcingbar and the state of stress in the beam-column connection. Inthis paper, idealized exterior beam-column joint tests wereconducted to evaluate the concrete contribution to theanchorage strength of headed bars.

Failure modes regarding headed bar anchorage in an exteriorbeam-column joint can be classified as shown in Fig. 3. Allfailure modes are induced as a result of the tensile force onthe anchored headed bar. Side-face blowout failure occurswhen inadequate side cover is provided. This can be alleviatedwhen proper side cover is provided.8 Concrete breakout mayoccur when an effective beam depth is greater than 1.5 timesan embedment length.14 This case is rare due to the typicalrelative depths used for beams and columns as well as thehigher strength and stiffness provided by most columns. Apullout mode of failure can occur if the net head area is lessthan 4 times the bar cross-sectional area. The pullout capacityof headed bars can be calculated using Section D.5.3 ofACI 318-08.15 When proper embedment and head geometryis used, a joint shear failure mode governs the response of theexterior beam-column joint. In this paper, the anchoragestrength of headed bars under a joint shear failure mode isinvestigated through experiments and a new model to predictthe strength is proposed.

RESEARCH SIGNIFICANCEThe research examines 30 specimens simulating exterior

beam-column joints with headed or hooked beam reinforcementanchorage. To investigate the concrete contribution to theanchorage strength, transverse reinforcement was not placedin the joints. The specimens were designed to reflect thecharacteristics and boundary conditions of an interior CCTnode typical of an exterior beam-column joint. Theanchorage strength of the headed bars was found to consistof a combination of head bearing and bond. Based on theseresults, a new comprehensive model is developed that allowsfor accurate prediction of the anchorage capacity of the headedbars terminated within the exterior beam-column joints.

TEST PROGRAMAn experimental program was developed to investigate

anchorage behavior of headed bars. The test matrix is shownin Table 1 and details of the specimens are presented inFig. 4. The test setup examines the anchorage of longitudinalbeam reinforcement in an exterior beam-column joint usingheaded reinforcement. The specimens were tested with thecolumn in a horizontal position, as shown in Fig. 5. Thedemands generated from beam flexure were idealized byapplying a compression/tension force couple to the face ofthe column. The force couple was monotonically increaseduntil failure. The compressive force was applied to a bearingplate across the full width of the column. The tension forcewas applied through high-strength loading bars attached tothe anchored headed and hooked bars. No column axial loadwas applied, as tests have shown that including axial loadtends to improve joint behavior.16 A length of column wasincluded to minimize boundary effects and to generate a

ACI member Sung-Chul Chun is a Principal Researcher at Daewoo Institute ofConstruction Technology (DICT), Suwon, Korea. He received his BS, MS, and PhDfrom Seoul National University in 1994, 1996, and 2007, respectively. His researchinterests include steel anchorage to concrete, composite structures, and rehabilitationof reinforced concrete structures.

ACI member Bohwan Oh is a Research Fellow at DICT. He received his BS from YonseiUniversity, Korea, and MS and PhD from Lehigh University, Bethlehem, PA. Hisresearch interests include modeling of concrete behavior and high-rise building systems.

Sung-Ho Lee is a Senior Researcher at DICT. He received BS and MS from KoreaUniversity in 2000 and 2002, respectively. His research interests include steelanchorage to concrete and behavior of beam-column joints.

Clay J. Naito is an Associate Professor of structural engineering at Lehigh University. Hereceived his BS in 1993 from the University of Hawaii and MS and PhD from theUniversity of California-Berkeley, Berkeley, CA. His research interests includepredictive modeling and experimental validation of reinforced and prestressedconcrete structures subjected to extreme events.

Fig. 3—Failure modes regarding headed bar anchorage inexterior beam-column joint.


typical ratio of column shear and flexure on the joint. Thetesting condition generates flexural forces within the columnand mimics the clamping demands generated by the column.Thirty full-scale specimens were tested. The test specimenswere similar to those by Marques and Jirsa17 from whichACI 318 code provisions15 for hooked bars were derived.The specimens of Marques and Jirsa were tested in a verticalposition and axial loads were applied.

The specimens were designed to fail the anchorage. Theembedment length le was varied from 8.4db to 15.5db forNo. 18 specimens and from 6.3db to 10.4db for No. 11 specimensand No. 8 specimens, where db denotes a bar diameter. Thelargest embedment length tested is approximately 75% ofthe development length of hooked bars (ldh) required inACI 352R-028 (for Type 1 connections) and ACI 318-0815

without modification factors. The anchorage of a singlelongitudinal bar was examined to avoid interference ofmulti-bar effects. No transverse reinforcement was includedto minimize potential confining enhancements to theanchorage. All specimen detailing and testing configurationdecisions were made to provide a lower-bound (conservative)estimate of capacity.

The specimens were designed in accordance withACI 352R-028 except for the provisions regarding transversereinforcement in the joint and the embedment length of aheaded bar. Main test variables include embedment lengthand bar diameter. Three bar diameters (25, 36, and 57 mm[No. 8, No. 11, and No. 18]) were chosen, which represent arange of bars used for beam reinforcement. The width of thespecimen is 6 times the headed bar diameter (6db). The clearside cover of 2.5db for a beam bar in an exterior joint is acommon case, providing that the diameters of column barsand hoops are equal to 1db and 0.5db, respectively. Side-faceblowout failure is precluded with the clear side cover of2.5db. For comparison, two specimens with hooked barswere tested for each headed bar diameter examined. Theembedment lengths for the hooked bar specimens werechosen to be equal to the longest and shortest embedmentlengths of headed bars for each diameter.

Material properties of the bars are in conformance withASTM A61518 Grade 60 (Grade 420 in SI units) and thedesign compressive strength of concrete at an age of 28 daysis 24 MPa (3480 psi). The low concrete strength wasintentionally chosen to produce anchorage failure prior to

the yielding of the headed bar. As-built material propertiesof specimens are summarized in Table 1.

A new screw-on headed bar system was used and the headwas attached to the bar end using a parallel-threaded connection.The threads are formed by cold-rolling the bar with a press andthe sectional area of the thread is not reduced. The head shapeis circular with a net head area Anh, equal to 4 times of the bararea Ab in accordance with the studies by Wallace.1,3 Theheaded bars for the tests are shown in Fig. 1 and the headdimensions refer to Hong et al.19

Strain gauges were used on the bar surface to assess thestrain distribution over the embedded length. The strain

Table 1—Test matrix

Specimen ID*le

†, mm (in.) Column bars N‡

Details of specimens,§

mm (in.), MPa (ksi)

No. 18-H-0.9L 908 (35.7) Four No. 11 1 B = 350 (13.8);a = 105 (4.1);l = 6708 (264.1);ln = 5748 (226.3);Dc = d = 958 (37.7);Hoop = No. 5 at 480 (18.9);fc′ = 24.2 (3.51); andfy = 447.7 (64.92).

No. 18-M-0.9L 888 (35.0) Four No. 11 2

No. 18-M-0.7L 684 (26.9) Four No. 11 2

No. 18-M-0.7L-2R 684 (26.9) Eight No. 11 2

No. 18-M-0.5L 479 (18.9) Four No. 11 2

No. 18-H-0.5L 499 (19.6) Four No. 11 1


No. 11-M-0.9L 372 (14.6) Four No. 8 2

No. 11-M-0.7L 295 (11.6) Four No. 8 2

No. 11-M-0.7L-2R 295 (11.6) Four No. 11 2

No. 11-M-0.5L 217 (8.5) Four No. 8 2

No. 11-H-0.5L 229 (9.0) Four No. 8 1


No. 8-M-0.9L 264 (10.4) Four No. 6 2

No. 8-M-0.7L 212 (8.3) Four No. 6 2

No. 8-M-0.7L-2R 212 (8.3) Four No. 8 2

No. 8-M-0.5L 161 (6.3) Four No. 6 2

No. 8-H-0.5L 170 (6.7) Four No. 6 1

*No. 1-2-3L-4R: 1 bar designation number; 2 H-hooked bar, M-headedbar; 3 embedment length to column depth ratio; 4 “2R” denotes that thespecimen was reinforced with twice the normal column reinforcements.†le = embedment length.‡N = number of specimens.§Refer to Fig. 4.

Fig. 4—Details of specimens. (Note: 1 mm = 0.0394 in.)


gauges were spaced at 3db with the first gauge applied at 1dbfrom the face of the head. For the No. 18 specimens, twostrain gauges were affixed at each measurement point onboth sides of the bar, and the results were averaged. Thisminimized the contribution of any localized bar flexure tothe strain. For the hooked bars, the strain gauges wereaffixed on the straight portion but were not installed on thehook. Slip was measured at the head of the headed bars andat the beginning of the hook bend, as shown in Fig. 4. Loadwas applied to the bars at a rate of 5 MPa/min (725 psi/min)under load control. The tests were terminated when theapplied load decreased to 85% of the maximum load.

TEST RESULTSMode of failure and cracking behavior

For all specimens, cracks initiated at the face of thecolumn around the anchored bar (indicated as 1 in Fig. 6).

These cracks are thought to occur due to bond loss. The cracksthen propagated toward the head or the hook along the bar. Inspecimens with an embedment length of 90% of the columndepth, bond cracks along the column bars and flexural cracksin columns formed as 2 and 3 in Fig. 6(a) and (b). In somespecimens, diagonal cracks near column face occurred as 4 inFig. 6 due to a combination of shear stresses developed fromloaded bar and column bar. After the cracks along the anchoredbar reached the vicinity of the head or hook, diagonal cracksformed from the head or hook toward the compressive zone ofthe virtual beam (5 in Fig. 6). In specimens with a shallowembedment length of 50% of column depth, cracks 3 and 4did not occur and, instead, a cone-shaped concrete breakoutfailure was observed, as shown in Fig. 6(c).

After diagonal crack 5 formed, two failure modes wereobserved: concrete breakout and joint shear. Specimens with

Fig. 5—Test setup. (Note: units are in mm [in.].)

Fig. 6—Crack patterns after failure (grids are spaced at 100 mm [3.94 in.]).


embedment length of 50% of column depth showed diagonalcracks radiating from both sides of the head (7 in Fig. 6(c)).The anchorage force decreased as a breakout cone formedand separated. This type of failure is referred to as a concretebreakout failure, as shown in Fig. 7(a). The other specimensfailed immediately after the diagonal crack 5 occurred(Fig. 6(b) and (e)) as shown in Fig. 7(c) or after the diagonalcrack 5 extended to the other column side (Fig. 6(f)), asshown in Fig. 7(b). This failure is a joint shear failure. Unlikespecimens with headed bars (denoted as headed specimenhereafter), the specimens with hooked bars (denoted ashooked specimen hereafter) did not fail immediately whenthe diagonal crack 5 formed. This is attributed to the orien-tation of the hook that crossed the primary diagonal crack 5.Additional cracks (6 in Fig. 6(a) and (d)) formed across thehook and tail with additional loading.

Both failure modes occurred in a brittle sudden mannerbecause no transverse reinforcement was provided in thejoints. The bar force at the occurrence of diagonal cracking(Pcr) and maximum anchorage capacity (Pm) are reported inTable 2.

Slip of heads and hooksMeasured force versus slip relationships for all specimens

except No. 11-M-0.5L-(2) and No. 8-M-0.9L-(1) arepresented in Fig. 8. Specimens having equivalent embedmentlength are plotted together.

Specimens with embedment length of 90% of columndepth—The initial cracks along the anchored bar (marked as� in Fig. 8) of the specimens having equivalent embedmentlength occurred at similar loads. The load at initial verticalcrack occurrence are lower than the flexural cracking loadsof the columns (409, 117, and 64 kN [91.1, 26.3, and 14.4 kips]for No. 18 series, No. 11 series, and No. 8 series, respectively).Therefore, the vertical cracks are considered to be initiated bybond loss. The diagonal cracking (marked as � in Fig. 8 and5 in Fig. 6) loads of the specimens having equivalentembedment length are also similar. After diagonal cracking,the load of the headed specimens rapidly decreased, buthooked specimens resisted additional load. The additionalload of hooked specimens is attributed to the hook crossingthe primary diagonal crack. The maximum loads for hookedspecimens are greater than those for headed specimens by

Fig. 7—Observed failure modes: (a) cone-shaped concrete breakout failure of 0.5L specimens;(b) joint shear failure with extended diagonal cracks of 0.7L specimens; and (c) joint shearfailure of 0.9L specimens.

Fig. 8—Bar force-head and hook slip (Note: �: at initial cracking; �: at diagonal cracking; •: at maximum load; solid markfor headed specimens; and void mark for hooked specimens.)


20.9%, 40.0%, and 19.1% for No. 18 series, No. 11 series,and No. 8 series, respectively.

The slip of all headed specimens (including specimenswith embedment length of 70% and 50% of column depth) atdiagonal cracking loads are less than 0.3 mm (0.012 in.), andfor most specimens, the slip is less than 0.2 mm (0.008 in.).The slip of hooked specimens at diagonal cracking loads arealso small (from 0.17 to 0.69 mm [0.007 to 0.027 in.]) butgreater than those of headed specimens, especially forNo. 18-H-0.9L and No. 18-H-0.5L. Due to the bendradius on the hooked bar, the straight segment of the hookedbar is shorter than the headed bar for the same embedment.As a result, the hook provides a greater proportion of theanchorage strength for the hooked bar than the head does forthe headed bar anchorage. The concrete inside hook radiusmay have crushed, resulting in slip at the face of the joint.20

After diagonal cracking, the slip rapidly increased for allhooked specimens. For No. 18-H-0.9L, No. 11-H-0.9L, andNo. 8-H-0.9L, the slip at maximum load was 1.30, 1.03, and3.14 mm (0.05, 0.04, and 0.12 in.), respectively. Generally, theslip induces a significant pinching effect on the load-deformation behavior of a beam-column joint undercyclic loading. This behavior reduces the energy resistance

of the connection and, thus, the slip should be limited untilthe design strength is developed. CEB-FIP MC9021 specifiesthat the slip for headed bars between the bar and the concreteat the loaded end shall not exceed 0.5 mm (0.02 in.) under 95%of the ultimate force. Because the slip in Fig. 8 was measuredbetween the hook (or the head) and the concrete at the rear ofthe joint, the slip relative to the face of the joint will begreater than the measured slip due to the additional elongationof the bar in the joint. Because the slip at the face of the jointexceeds 0.5 mm (0.02 in.), the additional strength after diagonalcracking should be ignored for safety of the overall structure.

Specimens with embedment length of 70% of columndepth—Graphs of Fig. 8(b), (e), and (h) show comparisonsof force versus slip relationships of specimens having heavycolumn reinforcement with those of specimens having normalcolumn reinforcement. The normal column reinforcementwas determined in accordance with ACI 352R-028 and thecolumns of specimens having “2R” in their identificationswere reinforced with twice the normal column reinforcements(refer to Table 1). These specimens were tested to investigatethe influence of the amount of column reinforcement on theanchorage capacity.

Table 2—Test results

Specimen IDDiagonal cracking load Pcr , kN (kips)

Maximum load Pm, kN (kips)

Bond strength Pb-e, kN (kips)

Bearing strength Ph-e, kN (kips) Pb-e /Pcr Ph-e /Pcr

Proposed model Failuremode*Pcal, kN (kips) Pcr/Pcal

No. 18-H-0.9L 760.7 (171.0) 843.3 (189.6) NA NA NA NA — — JS

No. 18-M-0.9L-(1) 701.3 (157.7) 701.3 (157.7) 298.3 (64.5) 414.3 (93.1) 0.41 0.59739.5 (166.2)

0.95 JS

No. 18-M-0.9L-(2) 693.2 (155.8) 693.2 (155.8) 298.3 (67.1) 394.9 (88.8) 0.43 0.57 0.94 JS

No. 18-M-0.7L-(1) 434.4 (97.6) 434.4 (97.6) 292.1 (65.7) 142.3 (32.0) 0.67 0.33501.2 (112.7)

0.87 JS

No. 18-M-0.7L-(2) 444.2 (99.8) 444.2 (99.8) 266.8 (60.0) 177.4 (40.0) 0.60 0.40 0.89 JS

No. 18-M-0.7L-2R-(1) 491.8 (110.6) 491.8 (110.6) 233.5 (52.5) 258.3 (58.1) 0.47 0.53501.2 (112.7)

0.98 JS

No. 18-M-0.7L-2R-(2) 515.3 (115.8) 515.3 (115.8) 316.6 (71.2) 198.7 (44.7) 0.61 0.39 1.03 JS

No. 18-M-0.5L-(1) 309.4 (69.6) 309.4 (69.6) 164.7 (37.0) 144.7 (32.5) 0.53 0.47262.9 (59.1)

1.18 CB

No. 18-M-0.5L-(2) 309.0 (69.5) 309.0 (69.5) 171.3 (38.5) 137.8 (31.0) 0.55 0.45 1.18 CB

No. 18-H-0.5L 284.2 (63.9) 307.1 (69.0) NA NA NA NA — — CB

No. 11-H-0.9L 217.0 (48.8) 322.8 (72.6) NA NA NA NA — — JS

No. 11-M-0.9L-(1) 228.8 (51.4) 228.8 (51.4) 106.8 (24.0) 122.0 (27.4) 0.47 0.53221.5 (49.8)

1.03 JS

No. 11-M-0.9L-(2) 212.1 (47.7) 233.0 (52.4) NA NA NA NA 0.96 JS

No. 11-M-0.7L-(1) 192.5 (43.3) 192.5 (43.3) 81.5 (18.3) 111.0 (25.0) 0.42 0.58151.5 (34.1)

1.27 JS

No. 11-M-0.7L-(2) 169.7 (38.2) 185.0 (41.6) NA NA NA NA 1.12 JS

No. 11-M-0.7L-2R-(1) 197.8 (44.5) 262.7 (59.1) NA NA NA NA151.5 (34.1)

1.31 JS

No. 11-M-0.7L-2R-(2) 187.3 (42.1) 227.1 (51.1) 106.9 (24.0) 80.4 (18.1) 0.57 0.43 1.24 JS

No. 11-M-0.5L-(1) 116.8 (26.3) 194.2 (43.7) 47.8 (10.8) 69.0 (15.5) 0.41 0.5980.5 (18.1)

1.45 CB

No. 11-M-0.5L-(2) 121.7 (27.4) 152.7 (34.3) 56.4 (12.7) 65.5 (14.7) 0.46 0.54 1.51 CB

No. 11-H-0.5L 106.1 (23.8) 127.7 (28.7) NA NA NA NA — — CB

No. 8-H-0.9L 113.6 (25.5) 149.5 (33.6) NA NA NA NA — — JS

No. 8-M-0.9L-(1) 123.7 (27.8) 123.7 (27.9) NA NA NA NA108.2 (24.3)

1.14 JS

No. 8-M-0.9L-(2) 122.7 (27.6) 127.3 (28.6) NA NA NA NA 1.13 JS

No. 8-M-0.7L-(1) 93.7 (21.1) 122.1 (27.4) NA NA NA NA75.0 (16.8)

1.25 JS

No. 8-M-0.7L-(2) 91.1 (20.5) 126.6 (28.5) NA NA NA NA 1.21 JS

No. 8-M-0.7L-2R-(1) 88.8 (20.0) 141.6 (31.8) 40.4 (9.1) 48.3 (10.9) 0.46 0.5475.0 (16.8)

1.18 JS

No. 8-M-0.7L-2R-(2) 90.4 (20.3) 144.9 (32.6) 31.5 (7.1) 58.9 (13.3) 0.35 0.65 1.21 JS

No. 8-M-0.5L-(1) 59.4 (13.4) 73.1 (16.4) NA NA NA NA42.4 (9.5)

1.40 CB

No. 8-M-0.5L-(2) 56.1 (12.6) 94.0 (21.1) NA NA NA NA 1.32 CB

No. 8-H-0.5L 67.2 (15.1) 80.3 (18.1) NA NA NA NA — — CB

Average 0.49 0.51 Average 1.16

COV 15%*JS: Joint shear failure, CB: concrete breakout failure.


There is no significant difference in behavior between thespecimens until diagonal cracking occurs. At diagonalcracking, the average strengths of the two duplicate specimenswith heavy column reinforcement were greater than thosewith normal column reinforcements by 14.6% and 6.3% forNo. 18 specimens and No. 11 specimens, respectively. Theaverage strength of two No. 8-M-0.7L-2R specimens,however, was less than the average load of two No. 8-M-0.7Lspecimens by 3.0% at diagonal cracking. The diagonal crackoccurred due to failure of the compressive strut from thebearing head to the compressive zone of the idealized beam,as illustrated in the strut-and-tie model of Fig. 2(b). Because thecolumn is elastic prior to diagonal cracking, the shear strengthwas not affected by the amount of column reinforcement.Consequently, there was little difference in diagonalcracking loads with variations on the amount of columnreinforcement for No. 11 and No. 8 specimens. The columnreinforcement of No. 18-M-0.7L-2R, however, was placedin double layers, whereas that of No. 18-M-0.7L was in singlelayer as shown in Fig. 4 and Table 1. If the joints are modeledby a strut-and-tie model, the widths of the longitudinal ties ofNo. 18-M-0.7L-2R are greater than the widths of the ties ofNo. 18-M-0.7L. The width of the diagonal strut of No.18-M-0.7L-2R is greater than that of No. 18-M-0.7L and, there-fore, the strut capacity of No. 18-M-0.7L-2R is enhanced.

After diagonal cracking, No. 18 specimens immediatelylost load-carrying ability. The loads of No. 11 and No. 8specimens increased after a marginal decrease due to diagonalcracking. These specimens reached maximum loads when theextended diagonal crack (crack 8 of Fig. 6(f)) occurred. Themaximum loads of specimens with heavy column reinforcementare higher than those with normal column reinforcement by29.7% and 15.2% for No. 11 and No. 8 specimens, respectively.The column reinforcements were located across the extendeddiagonal crack. As more column reinforcement wasprovided, the formation of the extended diagonal crack wasdelayed. Therefore, the specimens with heavy column rein-forcement could resist higher load than the specimens withnormal column reinforcement. The measured slip of thespecimens, which exceeded the cracking load, is greater thanthe allowable value of 0.5 mm (0.02 in.). As mentionedpreviously, the additional strength after diagonal crackingshould be ignored for safety of the overall structure.

Specimens with embedment length of 50% of columndepth—Unlike the specimens with deep embedment length,the loads carried by specimens with embedment length of50% of the column depth steadily increased after diagonalcracking until additional diagonal cracks, completing abreakout cone, were formed. The slip rapidly increased afterdiagonal cracking, such that additional strength after diagonalcracking should be ignored.

Bar stress distributionFigure 9 illustrates the stress distributions for the No. 18

specimens, which were calculated from the measured strainsand the stress-strain response of the coupon tests. Thehorizontal axis represents the location of strain gaugeswith an origin at the column face. Because the beamconcrete was not placed, the strains measured outside thejoint are equal to the strains at the column face.

Figure 9(a) shows the stress distributions of No. 18-H-0.9L(dashed lines) and No. 18-M-0.9L-(1) (solid lines). For theheaded specimen, the stress distributions at loads of 200 and400 kN (45 and 90 kips) show that most of the load is

resisted by bond. The slope of the line near the column faceat a load of 400 kN (90 kips) approached zero, which meansthe bond resistance near the column face is deteriorated.Bearing was evaluated from the bar strains at a distance of1db from the head face of headed bars and at the beginningof the hook bend. As load increases, head bearing starts todevelop. At a load of 600 kN (135 kips), the head bearingresists almost half of the load. For the hooked specimen, thestress distributions are similar to those of the headed specimenuntil the bar load of 600 kN (135 kips). At a load of 701 kN(158 kips), the slope of the line of the hooked specimenis flatter than that of the headed specimen, which meanssevere bond deterioration. Due to the shorter straightportion of the hooked specimen compared with theheaded specimen, most of the bar load is carried by thehook because the bond is deteriorated.

Fig. 9—Stress distribution along bar in No. 18 specimens.

586 ACI Structural Journal/September-October 2009

The stress distributions of No. 18-H-0.5L (dashed lines) andNo. 18-M-0.5L-(1) (solid lines) are presented in Fig. 9(b). Thedevelopment of head bearing and bond resistance of No.18-M-0.5L-(1) is similar to that of No. 18-M-0.9L-(1). For thehooked specimen (No. 18-H-0.5L), however, the bondresistance is lost earlier compared to No. 18-H-0.9L and No.18-M-0.5L-(1). At a load of 200 kN (45 kips), that is, twothirds of the maximum load, the dashed line is nearly flat,which denotes that the bond resistance is almost lost. Thebond loss of the hooked specimen is considered to beinduced by the shorter straight portion.

Head bearing and bond contribution toheaded bar anchorage strength

The contributions of head bearing and bond to the totalanchorage force were determined from the measured straindistributions. The head/hook anchorage contribution wasassumed to equal the stress at a distance of 1db from the headface of headed bars or at the beginning of the hook bend ofhooked bars. The bond contribution was determined bydeducting the bearing from the stress outside the joint.

The components of the anchorage force provided by bondand head (or hook) bearing are shown in Fig. 10. Loads atinitial cracking and diagonal cracking are marked in eachfigure. In hooked specimens, the increase of bond contributionbegins to slow down and even decrease on initial bond crackformation, and most of the bar force is carried by hookbearing at failure. This may induce concrete crushing insidethe hook radius. Because of this concrete crushing, slip of thehook was larger than that of the head at same load level, asshown in Fig. 8.

Even after the initial bond crack formed, bond resistancestill increased in headed specimens. Because the straightportion of the headed specimens is longer than that of thehooked specimens, bond resistance of the headed specimenswas always greater than that of the hooked specimens. Afterthe bond contribution reached its maximum value, thecontribution from bond remained relatively constant orslightly decreased while the head carried additional forcegain. At failure, approximately 60% of the bar force wascarried by head bearing and approximately 40% by bond forNo. 18-M-0.9L-(1), as shown in Fig. 10(a). In Table 2,contributions from the head bearing and the bond to the totalload at diagonal cracking of each specimen are summarized.

EXISTING MODELS FOR ANCHORAGE STRENGTH OF HEADED BARS

Models for predicting anchorage strength of headed barswere proposed by Thompson et al.,22 Bashandy,11 andDeVries.10 Thompson et al. conducted test programs of CCTnodes and lap splices. Several failure modes were mixed inthe tests. The specimens of the CCT node test failed by side-face blowout (laterally splitting), crushing of concrete, orrupture of nodal zone,13 and the specimens of the lap-splicetest failed by rupture of cover concrete.23 Thompson etal.’s22 model consists of two capacities induced by headbearing and bond. Section 12.6 for the development ofheaded bars is introduced in ACI 318-08 and it provides anequation to calculate the development length of a headed bar,which is based on the tests of Thompson. Bashandy tested 32simulated exterior beam-column joints and proposed a modelfrom 18 tests that failed by side-face blowout. DeVriesproposed two models for anchorage strength of headed barsdepending on the failure mode: concrete breakout or side-face blowout.

Section 12.6.2 of ACI 349-0614 stipulates that mechanicalanchorages shall be designed in accordance with Appendix D,which is a specification for anchor design and is based on theconcrete capacity design (CCD) method.24 ACI 349-0614 definesfive failure modes for anchors in tension: steel failure, concretebreakout, pullout, side-face blowout, and concrete splitting. Theanchorage strength is determined to be the lowest value amongthe strengths calculated from the failure modes.

From comparisons of test results with the existing models(refer to Table A in the Appendix), the existing models arenot suitable for predicting the concrete contribution of theanchorage strengths of the specimens in this researchbecause the failure modes on which the existing models arebased are different from the failure modes of this study.

PROPOSED MODEL FOR ANCHORAGE STRENGTH OF HEADED BAR

A strut-and-tie model for the anchorage of a headed bar inan exterior beam-column joint without transverse reinforcementwas developed using a smeared nodal zone and a fan by

Fig. 10—Bond and head bearing contribution to anchoragestrength of selected specimens.


authors.19 A new model is developed from the experimentalresults to predict the anchorage strength of the headed bar inan exterior beam-column joint. It is observed from the teststhat the anchorage strength of the headed bar is developedfrom a combination of head bearing and bond. Contributionof each component to the total anchorage strength is statisti-cally assessed from the measured data at the occurrence ofdiagonal cracking.

Head bearing contribution PheadAccording to the measured data, the head bearing stress is

proportional to the embedment length. The head bearingstress is determined by dividing the bar force (EsεbAb) by thenet head area (Anh), where Es denotes modulus of elasticityof headed bar, εb is measured strain at 1db from the head face,and Ab is headed bar area. Figure 11 shows the relationshipbetween normalized head bearing stress and normalizedembedment length. Because the strain gauges failed in somespecimens, the bearing strengths of nine specimens cannotbe determined, which are marked as “NA” in Table 2. InFig. 11, the x-axis represents the embedment length normal-ized by column depth Dc and the y-axis represents the stressdeveloped by head bearing normalized by effectivecompressive strength of concrete 0.85fc′ . The head bearingcannot be fully developed in the specimens with shallowembedment length. In the specimens with deep embedmentlength, however, the stress induced by the head bearing isgreater than 0.85fc′ .

The head bearing may be affected by the joint strut. Withdeep embedment length, the head is located in or behind thejoint strut and the head bearing can be fully developed. In thecase of shallow embedment length, the joint strut cannotconfine the head. Consequently, the head bearing is dependenton the normalized embedment length. For simplicity, a linearregression analysis is conducted and the following equationis derived.

Phead = [1 + 2.27(le – 0.7Dc)/Dc]0.85fc′Anh (1)

When the embedment length is 0.7Dc , the stress inducedby head bearing is equal to the effective compressivestrength of concrete. With shallow embedment length, thehead bearing capacity decreases linearly, and the headbearing capacity increases linearly with deep embedmentlength longer than 0.7Dc.

It is worth comparing Eq. (1) with Thompson’s model22

for head bearing capacity as follows

fs,head = n5%2fc′ (c/db) (2)

where fs,head is the anchorage bar strength provided by headbearing, n5% is a 5% fractile coefficient, c is a minimumcover dimension measured to bar center, Ψ (= 0.6 + 0.4(c2/c) ≤2.0) is a radial disturbance factor, and c2 is a minimum coverdimension measured in direction orthogonal to c.

By substituting 3, 4, 2, 0.7 for (c/db), (Anh/Ab), Ψ, n5%,respectively, into Eq. (2), Thompson’s model yields fs,head =16.8fc′ . Multiplying (Ab/Anh) to the fs,head yields 4.2fc′ of abearing stress acting on the concrete in front of the head. Themaximum strength from Eq. (1) with le ≈ Dc is1.93(0.85fc′ )Anh. Dividing the maximum value by Anh yieldsthe maximum bearing stress 1.6fc′ , which is approximately40% of Thompson’s model. The difference between the headbearing capacities calculated by Eq. (1) and (2) is due to thenode conditions of the tests on which each equation is based.As previously mentioned, the node strength of the surfaceCCT node is greater than that of the interior CCT node. Thehead bearing strength in the interior CCT node such asexterior beam-column joint may be determined by Eq. (1).

Bond contribution PbondThe bond stress is determined by dividing the measured

bond strength (Pb-e) by the bar diameter (φb) and the length(le – db), where the measured bond strength (Pb-e) is obtainedby subtracting the measured bearing strength (EsεbAb) fromthe bar load at the diagonal cracking. Traditionally, the bondstress is expressed in terms of . The bond stresses arescattered and had no relationship with the embedmentlength. The average of bond stresses for 15 specimens is0.504 (MPa) (6.07 [psi]) and is greater than thebond strength calculated from Section 12.2.2 of ACI 318-08.The directions of shear stresses on both interfaces betweenheaded bar and concrete in the interior CCT node are shownin Fig. 12(b). In the case of the surface CCT node, however,the directions of shear stresses on the interfaces of headedbar are opposite (Fig. 12(a)). Even though the bearing platedirectly confines the node concrete, the bond capacity may

Anh/AbΨ

fc′

fc′ fc′

Fig. 11—Relationship between normalized head bearingand normalized embedment.

Fig. 12—Shear stress distribution on headed bar.

588 ACI Structural Journal/September-October 2009

decrease in the surface CCT node due to the opposite directionof the shear stresses. The bond capacity of the headed barterminated within the exterior beam column joint may bedetermined by the following equation

Pbond = 0.504 φb(le – db) [MPa] (3)

= 6.07 φb(le – db) [psi]

where φb (= πdb) is a bar perimeter.

Proposed modelBy summing the bond and head bearing components, the

anchorage strength can be determined. The predicted valuescalculated from Eq. (1) and (3) are summarized in Table 2and Fig. 13 and compared to the test values for 24 specimens.Test results of six specimens failing in shear conducted byBashandy11 were also compared with the proposed model inTable 3 and Fig. 13. Figure 13 shows that the proposedmodel can predict the strengths without bias on four specimenseries. The average of ratios of tests to predictions is 1.16 andthe coefficient of variation is 0.15. It is found that a coefficientfor 5% fractile25 is 0.78 from statistical analysis. The final formof the proposed model is

(4)

= [MPa]

= [psi]

SUMMARY AND CONCLUSIONSAn experimental study was performed to assess the

anchorage capacity of the headed bar terminated within exteriorbeam-column joints without transverse reinforcement. Testswere conducted on 30 full-scale simplified specimens withbeam bars in diameters of 25, 36, and 57 mm (No. 8, No. 11,and No. 18) with both 90-degree hooked bar and headed baranchorages. Tensile load was directly applied to the bar and

fc′

fc′

P n5% Pbearing Pbond+( )=

0.78 1 2.27le 0.7Dc–

Dc

-----------------------+⎝ ⎠⎛ ⎞ 0.85fc′ Anh 0.504 fc′ φb le db–( )+

0.78 1 2.27le 0.7Dc–

Dc

-----------------------+⎝ ⎠⎛ ⎞ 0.85fc′ Anh 6.07 fc′ φb le db–( )+

the same amount of compressive load was applied to thecompressive zone of an idealized beam. A new modelpredicting anchorage strength of headed bars has beenproposed using statistical analysis of test results. Based onthe test results and statistical analysis, the followingconclusions were drawn:

1. The anchorage strength of headed bars consists of headbearing and bond. Initial anchorage is carried by bond. Asload increases in the bar, head bearing starts to develop.After bond contribution reaches its maximum value, bondresistance remains constant or slightly decreases. Theanchorage capacity of headed bars is provided by peak headbearing plus slightly reduced bond;

2. The head bearing strength contribution is proportionalto the embedment depth normalized by the column depth.Greater bearing strength is provided at greater embedmentdepths due to the confinement provided from the diagonalcompressive strut in the joint. When the embedment depth is0.7 times the column depth, the head bearing strength isequal to the effective compressive strength of concrete.From statistical analysis, a model is derived to predict headbearing strength as a function of a ratio of an embedmentlength to a column depth;

3. The measured bond strength per unit area has no relationshipwith embedment length. The mean bond strength of specimens isslightly higher than the bond strength calculated from Section12.2.2 of ACI 318-08. Considering the safety factor of provi-sions of the ACI 318 regarding development lengths, themeasured bond strengths are similar to bond strength determinedfrom ACI 318. The bond strength in the interior CCT node ishigher than that in the surface CCT node; and

4. The anchorage strength of the headed bars terminatedwithin exterior joint with sufficient side cover (greater than3db from the bar center) can be accurately predicted byEq. (4). The formulation predicts the strength based on acombination of head bearing and bond capacity. Failuremodes of headed bar anchorage are varied with givengeometric and material conditions and, therefore, a specificmodel complying with the given condition of the anchoragezone should be used rather than a general model for theanchorage strength of headed bars.

Fig. 13—Comparison between test results and predictedvalues. *Values in parentheses are calculated includingdata of Reference 11.

Table 3—Comparison of test results in Reference 11 and proposed model

Specimen ID

db,mm (in.)

fc′, MPa(ksi)

le,mm(in.)

Dc,mm(in.)

Anh,

mm2

(in.2)

Measured load P,

kN (kips)

Proposed model

Pcal,kN

(kips) Pcal /P

T1 35(1.4)

26.7 (3.87)

280 (11.0)

381 (15.0)

4494 (6.97)

227(51.0)

185.1 (41.6) 1.23

T2 35(1.4)

29.4 (4.26)

280 (11.0)

381 (15.0)

4494 (6.97)

222(49.9)

200.1 (45.0) 1.11

T3 35(1.4)

29.4 (4.26)

285 (11.2)

381 (15.0)

7094 (11.0)

232(52.2)

281.5 (63.3) 0.82

T4 25(1.0)

26.7 (3.87)

211 (8.3)

305 (12.0)

2690 (4.17)

94(21.1)

98.0 (22.0) 0.96

T5 35(1.4)

22.5 (3.26)

280 (11.0)

381 (15.0)

4494 (6.97)

167(37.5)

161.3 (36.3) 1.04

T31 35(1.4)

33.3 (4.83)

209 (8.2)

305 (12.0)

2838 (4.40)

173(38.9)

133.1 (29.9) 1.30

Average 1.08

Coefficient of variation 16%

Note: db is bar diameter, le is embedment length, Dc is depth of column (refer to Fig. 4), andAnh is net head area.


REFERENCES1. Wallace, J. W., “Headed Reinforcement: A Viable Option,” Concrete

International, V. 19, No. 12, Dec. 1997, pp. 47-53.2. Berner, D. E., and Hoff, G. C., “Headed Reinforcement in Disturbed

Strain Regions of Concrete Members,” Concrete International, V. 16, No. 1,Jan. 1994, pp. 48-52.

3. Wallace, J. W.; McConnell, S. W.; Gupta, P.; and Cote, P. A., “Use ofHeaded Reinforcement in Beam-Column Joints Subjected to EarthquakeLoads,” ACI Structural Journal, V. 95, No. 5, Sept.-Oct. 1998, pp. 590-606.

4. McConnell, S. W., and Wallace, J. W., “Use of T-Headed Bars inReinforced Concrete Knee-Joints Subjected to Cyclic Lateral Loading,”Report No. CU/CEE-94/10, Department of Civil Engineering, ClarksonUniversity, Potsdam, NY, 1994, 44 pp.

5. Chun, S. C., and Kim, D. Y., “Evaluation of Mechanical Anchorage ofReinforcement by Exterior Beam-Column Joint Experiments,” Proceedingsof 13th World Conference on Earthquake Engineering, Vancouver, BC,Canada, 2004. (CD-ROM)

6. Mokhtar, A. S.; Ghali, A.; and Dilger, W. H., “Stud Shear Reinforcementfor Flat Concrete Plates,” ACI JOURNAL, Proceedings V. 82, No. 5,Sept.-Oct. 1985, pp. 676-683.

7. Elgabry, A. A., and Ghali, A., “Tests on Concrete Slab-ColumnConnections with Stud Shear Reinforcement Subjected to Shear-Moment Transfer,” ACI Structural Journal, V. 84, No. 5, Sept.-Oct. 1987,pp. 433-442.

8. Joint ACI-ASCE Committee 352, “Recommendations for Design ofBeam-Column Connections in Monolithic Reinforced Concrete Structures(ACI 352R-02),” American Concrete Institute, Farmington Hills, MI, 2002,37 pp.

9. Joint ACI-ASCE Committee 421, “Guide to Shear Reinforcement forSlabs (ACI 421.1R-08),” American Concrete Institute, Farmington Hills,MI, 2008, 23 pp.

10. DeVries, R. A., “Anchorage of Headed Reinforcement in Concrete,”PhD dissertation, University of Texas at Austin, Austin, TX, 1996, 294 pp.

11. Bashandy, T. R., “Application of Headed Bars in ConcreteMembers,” PhD dissertation, University of Texas at Austin, Austin, TX,Dec. 1996, 302 pp.

12. Thompson, M. K., “The Anchorage Behavior of Headed Reinforcement

in CCT Nodes and Lap Splices,” PhD dissertation, University of Texas atAustin, Austin, TX, 2002, 502 pp.

13. Thompson, M. K.; Ziehl, M. J.; Jirsa, J. O.; and Breen, J. E.,“CCT Nodes Anchored by Headed Bars—Part 1: Behavior of Nodes,”ACI Structural Journal, V. 102, No. 6, Nov.-Dec. 2005, pp. 808-815.

14. ACI Committee 349, “Code Requirements for Nuclear Safety-Related Concrete Structures (ACI 349-06) and Commentary,” AmericanConcrete Institute, Farmington Hills, MI, 2006, 153 pp.

15. ACI Committee 318, “Building Code Requirements for StructuralConcrete (ACI 318-08) and Commentary,” American Concrete Institute,Farmington Hills, MI, 2008, 465 pp.

16. Meinheit, D. F., and Jirsa, J. O., “Shear Strength of R/C Beam-Column Connections,” Journal of the Structural Division, ASCE, V. 107,No. ST11, Nov. 1981, pp. 2227-2244.

17. Marques, J. L. G., and Jirsa, J. O., “A Study of Hooked Bar Anchor-ages in Beam-Column Joints,” ACI JOURNAL, Proceedings V. 72, No. 5,May 1975, pp. 198-209.

18. ASTM A615-06, “Standard Specification for Deformed and PlainCarbon Steel Bars for Concrete Reinforcement,” ASTM International,West Conshohocken, PA, 2006, 6 pp.

19. Hong, S.-G.; Chun, S.-C.; Lee, S.-H.; and Oh, B., “Strut-and-TieModel for Development of Headed Bars in Exterior Beam-Column Joint,”ACI Structural Journal, V. 104, No. 5, Sept.-Oct. 2007, pp. 590-600.

20. Ghali, A., and Dilger, W. H., “Anchoring with Double-HeadedStuds,” Concrete International, V. 20, No. 11, Nov. 1998, pp. 21-24.

21. Comité Euro-International du Béton, “CEB-FIP Model Code, 1990,”Thomas Telford, 437 pp.

22. Thompson, M. K.; Jirsa, J. O.; and Breen, J. E., “Behavior andCapacity of Headed Reinforcement,” ACI Structural Journal, V. 103,No. 4, July-Aug. 2006, pp. 522-530.

23. Thompson, M. K.; Ledesma, A.; Jirsa, J. O.; and Breen, J. E., “LapSplices Anchored by Headed Bars,” ACI Structural Journal, V. 103, No. 2,Mar.-Apr. 2006, pp. 271-279.

24. Fuchs, W.; Eligehausen, R.; and Breen, J. E., “Concrete CapacityDesign (CCD) Approach for Fastening to Concrete,” ACI StructuralJournal, V. 92, No. 1, Jan.-Feb. 1995, pp. 73-94.

25. Natrella, M. G., “Experimental Statistics,” National Bureau of StandardsHandbook 91, 1966.


Table A—Comparison of test values with predicted values

Specimen IDDiagonal cracking load Pcr, kN (kips)

Predicted strength by

Thompson Bashandy

DeVries

ACI 318-08 Proposed modelConcrete breakout Side-face blowout

(1)kN (kips) (1)/Pcr






No. 18-M-0.9L-(1) 701.3 (157.7) 1322.5(297.3)

1.89 126.5(28.4)

1.87 159.2(35.8)

0.23 619.6(139.3)

0.88 126.5(28.4)

0.18 739.5(166.2)

1.05

No. 18-M-0.9L-(2) 693.2 (155.8) 1.91 1.89 0.23 0.89 0.18 1.07

No. 18-M-0.7L-(1) 434.4 (97.6) 1267.8(285.0)

2.92 112.8(25.3)

2.28 141.4(31.8)

0.33 832.0(187.0)

1.97 112.8(25.3)

0.26 501.2(112.7)

1.15

No. 18-M-0.7L-(2) 444.2 (99.8) 2.85 2.23 0.32 1.87 0.25 1.13

No. 18-M-0.7L-2R-(1) 491.8 (110.6) 1267.8(285.0)

2.58 112.8(25.3)

2.02 141.4(31.8)

0.29 832.0(187.0)

1.69 112.8(25.3)

0.23 501.2(112.7)

1.02

No. 18-M-0.7L-2R-(2) 515.3 (115.8) 2.46 1.93 0.27 1.61 0.22 0.97

No. 18-M-0.5L-(1) 309.4 (69.6) 1,212.8(272.8)

3.92 97.1(21.8)

2.16 121.0(27.2)

0.39 997.6(224.3)

3.22 97.1(21.8)

0.31 262.9(59.1)

0.85

No. 18-M-0.5L-(2) 309.0 (69.5) 3.92 2.16 0.39 3.22 0.31 0.85

No. 11-M-0.9L-(1) 228.8 (51.4) 495.3(111.3)

2.17 53.3(12.0)

1.65 66.6(15.0)

0.29 256.9(57.8)

1.12 53.3(12.0)

0.23 221.5(49.8)

0.97

No. 11-M-0.9L-(2) 212.1 (47.7) 2.13 1.62 0.29 1.10 0.23 1.04

No. 11-M-0.7L-(1) 192.5 (43.3) 482.3(108.4)

2.51 48.4(10.9)

1.50 60.2(13.5)

0.31 284.5(64.0)

1.48 48.4(10.9)

0.25 151.5(34.1)

0.79

No. 11-M-0.7L-(2) 169.7 (38.2) 2.61 1.56 0.33 1.54 0.26 0.89

No. 11-M-0.7L-2R-(1) 197.8 (44.5) 482.3(108.4)

1.84 48.4(10.9)

1.10 60.2(13.5)

0.23 284.5(64.0)

1.08 48.4(10.9)

0.18 151.5(34.1)

0.77

No. 11-M-0.7L-2R-(2) 187.3 (42.1) 2.12 1.27 0.27 1.25 0.21 0.81

No. 11-M-0.5L-(1) 116.8 (26.3) 469.2(105.5)

2.42 42.9(9.7)

1.02 53.1(11.9)

0.27 284.5(64.0)

1.47 42.9(9.7)

0.22 80.5(18.1)

0.69

No. 11-M-0.5L-(2) 121.7 (27.4) 3.07 1.30 0.35 1.86 0.28 0.66

No. 8-M-0.9L-(1) 123.7 (27.8) 260.7(58.6)

2.11 33.0(7.4)

1.62 41.2(9.3)

0.33 141.0(31.7)

1.14 33.0(7.4)

0.27 108.2(24.3)

0.87

No. 8-M-0.9L-(2) 122.7 (27.6) 2.05 1.58 0.32 1.11 0.26 0.88

No. 8-M-0.7L-(1) 93.7 (21.1) 254.4(57.2)

2.08 30.2(6.8)

1.26 37.5(8.4)

0.31 152.3(34.2)

1.25 30.2(6.8)

0.25 75.0(16.8)

0.80

No. 8-M-0.7L-(2) 91.1 (20.5) 2.01 1.22 0.30 1.20 0.24 0.82

No. 8-M-0.7L-2R-(1) 88.8 (20.0) 254.4(57.2)

1.80 30.2(6.8)

1.09 37.5(8.4)

0.26 152.3(34.2)

1.08 30.2(6.8)

0.21 75.0(16.8)

0.84

No. 8-M-0.7L-2R-(2) 90.4 (20.3) 1.76 1.06 0.26 1.05 0.21 0.83

No. 8-M-0.5L-(1) 59.4 (13.4) 248.1(55.8)

3.39 27.1(6.1)

1.48 33.4(7.5)

0.46 152.3(34.2)

2.08 27.1(6.1)

0.37 42.4(9.5)

0.71

No. 8-M-0.5L-(2) 56.1 (12.6) 2.64 1.15 0.36 1.62 0.29 0.76

Average 2.46 0.31 1.53 0.25 0.88

COV 25% 18% 41% 18% 16%

APPENDIX

Documents

Anchorage Strength and Behavior of Headed Bars in-ACI