flexural anchorage behavior in diagonally cracked girders

ACI Structural Journal/March-April 2013 263

Title no. 110-S23

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 110, No. 2, March-April 2013.MS No. S-2011-116 received May 2, 2011, and reviewed under Institute publication

policies. Copyright © 2013, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the January-February 2014 ACI Structural Journal if the discussion is received by September 1, 2013.

Flexural Anchorage Behavior in Diagonally Cracked Girders: Experimentby Mary Ann T. Triska, Joshua K. Goodall, and Christopher Higgins

When load-rating the large number of diagonally cracked reinforced concrete (RC) deck-girder bridges constructed during the 1950s, the modern AASHTO LRFD check of flexural tension reinforcement anchorage can limit member ratings. The rating check compares the tensile demand in the reinforcing bar to the available tensile force at the section of interest. Among other parameters, the tensile demand is controlled by the diagonal crack angle at the section. The crack angles noted in inspections are generally flatter than those in the provisions and engineers are uncertain as to the inputs. The available tensile force in the flex-ural steel depends on the embedded reinforcing length; however, information is limited regarding bond stress developed with larger-diameter bars for full-size specimens. This research produced new flexural anchorage data in diagonally cracked girders that will help bridge engineers evaluate older concrete bridges. The results showed that the available bond strengths are higher than presently prescribed in ACI 318.

Keywords: anchorage; bond stress; bridges; full-scale testing; reinforced concrete; shear.

INTRODUCTIONMany conventionally reinforced concrete (RC) deck-

girder bridges from the 1950s remain in the national inven-tory and are reaching the end of their originally intended design life. Field inspections in Oregon revealed that these bridges commonly exhibit diagonal cracks in the high-shear regions of the girders and bent caps. Design specifications between 1944 and 1965 limited the concrete working shear stress at service load levels and stirrups were provided where needed to carry residual demands. Following the collapse of two Air Force base warehouses in Ohio and Georgia in 1955 and 1956,1 additional research on the shear behavior of RC members was conducted. It was then recognized that the specified concrete shear-stress contribution was too liberal and was reduced in subsequent editions of the ACI 318 spec-ification beginning in 1963.2 This change increased the required amount of transverse reinforcing steel from earlier designs. During the same time period, research to determine the bond strength of deformed reinforcing bars increased the allowable bond stress in the 1953 AASHTO Specification, thereby reducing anchorage requirements.3 The newly emer-gent deformed bars meeting ASTM A305-50T4 were used to provide anchorage in locations that would previously have required flexural bars to be bent across the web or terminate with a hook.

Historic design factors, such as overestimation of the concrete contribution to shear resistance and the practice of terminating flexural steel without special detailing, as well as increased loads present today, may contribute to the insuf-ficient capacity of RC bridge elements when assessed using modern design provisions. Of particular interest in this study is the behavior and strength of flexural steel reinforcement

anchorages interacting with diagonal cracks in the evalua-tion of vintage RC bridges. The modern AASHTO LRFD check of the flexural steel anchorage compares the tensile demand in the reinforcing bars induced by the applied load, including the additional demand due to diagonal cracking, to the available tensile capacity.5 From AASHTO LRFD Eq. 5.8.3.5-1, tensile force demand is controlled by the load-induced moment and shear, the number of stirrups, and the diagonal crack angle at the section of interest. The available tensile capacity in the flexural steel depends on the bar size, placement, material properties of the steel and concrete, and the embedded length. However, little information is currently available regarding bond stresses developed with larger-diameter bars in full-size elements when diagonal cracks are present. Applying these modern design provisions for evalu-ation of existing flexural details can often result in the girder rating being controlled by the flexural steel anchorage.

Flexural reinforcement bond anchorage requirements in the AASHTO and ACI 318 specifications have evolved over time to reflect the latest experimental research, behavior theories, analysis methods, and service perfor-mance. ASTM A305-50T4 deformed reinforcing bars were standardized in the late 1940s due in part to the numerous pullout tests conducted by Clark6 to characterize the bond behavior of deformed reinforcement. His work also contributed to the AASHTO 19533 requirement of limiting permissible applied bond stress to the minimum of 0.10fc′ or 350 psi (2.41 MPa), where fc′ is the compressive strength of concrete (psi). Further work by Mains7 demonstrated that bond stress varies along the length of deformed reinforcing bars, peaking at values much higher than the average value permitted by the design specifications of the time. Thus, by 1973, AASHTO permitted allowable bond stresses of 4.8√fc′/db not to exceed 500 psi (3.45 MPa), where db is the bar diameter (in.).8 However, ACI 318-632 permitted higher bond stresses of 9.5√fc′/db not to exceed 800 psi (5.52 MPa).2

The development length approach ld was introduced in ACI 318-71.9 Based on the bond stress specified in ACI 318-632 and assuming that the steel develops to 125% of the yield stress, development length was defined as

0.04 b yd

c

A fl

f=

′ (1)9

264 ACI Structural Journal/March-April 2013

Mary Ann T. Triska is a PhD Student at Oregon State University, Corvallis, OR. She received her BS from the University of Portland, Portland, OR, and her MS from Oregon State University. Her research interests include evaluation, rehabilitation, and sustainable design of infrastructure.

Joshua K. Goodall is a Structural Designer at HW Lochner, Inc., Salem, OR. He received his BS and MS from Oregon State University. His research interests include analysis and evaluation of bridges and structures.

Christopher Higgins is a Professor of structural engineering in the School of Civil and Construction Engineering at Oregon State University. He received his BS from Marquette University, Milwaukee, WI; his MS from the University of Texas at Austin, Austin, TX; and his PhD from Lehigh University, Bethlehem, PA. His research interests include evaluation and rehabilitation of bridges.

where Ab is the area of the developing bar (in.2). Orangun et al.10 took the results from 11 separate test programs that demonstrate the influence of clear cover, reinforcement spacing, and transverse confinement on bond strength to develop the following empirical equation to more accu-rately determine the minimum development length of Grade 60 (Grade 420) reinforcement

10,200

1 2.5

bd

c trb

dl

Cf Kd

=

+ + f′

(2)10

where C is taken as the lesser of the clear cover or half the clear spacing and C/db ≤ 2.5; and the capacity reduction factor f is 0.8. Lastly, the transverse reinforcement term is defined as

= ≤ 2.5600

tr yttr

b

A fK

sd (3)10

where Atr is the area of transverse reinforcement (in.2); fyt is the yield stress of the transverse reinforcement; and s is trans-verse reinforcement spacing (in.). A comparison of Eq. (1) and (2) showed that ACI 318-719 provisions could be under- or unnecessarily conservative depending on cover and trans-verse reinforcement.10 Thus, a refined form of Eq. (2) was adopted by ACI 318 and is still used in the current version of the design code, ACI 318-11.11

Twenty years later, Darwin et al.12 further refined the work of Orangun et al.10 with more recent experimental test results, which included data for high-strength steel and concrete specimens. Although never adopted, the proposed design equation shown as follows demonstrated that the ACI 318-9513 design equations overestimated development and lap splice lengths

1/4 2130 0.1 0.9

80.2

y M

mcd

b tr

b

f ccfl

d c Kd

− + f ′

= +

(4)12

where fy is longitudinal steel yield strength (psi); and f is a factor of safety taken as 0.9. The term c, taking into account concrete cover, is determined as

( ) = + +

0.5 0.1 0.9Mm b

m

cc c d

c (5)12

where cm and cM are the minimum and maximum values of cb or cs; cb is the bottom cover (in.); and cs is the minimum of one-half of the clear spacing between bars (in.) or one-quarter of the side cover of the reinforcing bars (in.). Lastly, the transverse reinforcement index is defined as

=34.5 d tr

tr

t AK

sn (6)12

where td = (0.72db + 0.28) represents the effect of bar size on the confining steel force; and n is the number of bars being developed.

The majority of the test results used to develop Eq. (2) and (4) were obtained by testing small concrete specimens with small-diameter reinforcing bars with the exception of Clark.6 In recent years, Abrishami and Mitchell14 have tested larger bars, but there is still a lack of information about the larger reinforcing bars common in bridge construc-tion. Among other parameters, bond strength depends on mechanical interlock between the concrete and the lugs of the deformed reinforcing bars. Because the dimensions and location of the lugs on the reinforcement vary with bar size, the aggregate in the concrete may become trapped between lugs on larger bar, but not on smaller bar. This condition influences the bond strength for larger bars. Therefore, to improve evaluation and rating methods of older RC bridge structures, the behavior of the RC bridge girders containing vintage flexural cutoff details in the presence of diagonal cracks was studied in the laboratory. Realistic vintage speci-mens were constructed, instrumented, and tested to failure. The instrumentation plan focused on measuring the bond stresses along the bars adjacent to a diagonal crack and along the embedment length of the bars past the diagonal crack.

RESEARCH SIGNIFICANCEMany older and cracked RC bridges are in the inven-

tory. Some agencies are applying AASHTO specifications to check flexural anchorages at diagonal cracks. The use of prescribed development lengths to evaluate existing details may limit the bridge rating in many cases. Relatively little information is available for large-size bars in diagonally cracked girders. The research provides new data for inspec-tion and evaluation of bond and anchorage in shear-domi-nant regions of existing bridges. This will help bridge-rating engineers efficiently identify potential issues and prioritize use of limited resources for repair or replacement of truly deficient bridges.

EXPERIMENTAL PROGRAMTest specimens

Twelve specimens were used to characterize the perfor-mance of large size 1950s vintage RC deck girders with diagonal cracks intersecting flexural reinforcing steel near cutoff locations. Specimens were designed at full scale with typical reinforcing details and materials to represent mid-twentieth-century design and construction practice. Specimen proportions were based on the review of struc-tural design drawings from over 442 RC bridges constructed in the 1950s.15 For this era, the typical specified concrete


strength was 3300 psi (21 MPa)15 and the reinforcing steel was intermediate-grade ASTM A305-50T.4

Intermediate-grade steel is not readily available for larger bar sizes typical of flexural steel. Therefore, ASTM A706/A706M16 Grade 60 (Grade 420) steel was used for flexural reinforcing bars. ASTM A615/A615M17 Grade 40 (Grade 280) steel was used for the stirrups. The use of Grade 60 (Grade 420) steel requires higher bond stresses over the same embed-ment length to achieve yield. Thus, specimen bond demands are higher than that required in a member with lower-yield material. Also, the flexural steel area is roughly 66% of an equivalent beam using intermediate-grade steel. This produces smaller dowel force contributions in the speci-mens compared to a member with lower yield materials. It is worth noting that, based on review of the ASTM defor-mation requirements, present-day reinforcing bars have iden-tical requirements to those first implemented in 1950.4 Thus, the mechanical bond for the test specimens can be directly compared to those used in the field.

Concrete was provided by a local ready mix company. The concrete mixture was designed to produce compres-sive strength in the range of 4000 psi (27.6 MPa) to

account for in-place strength increase above the speci-fied strength 3300 psi (22.8 MPa). Based on limited core samples available for the bridge population considered (47 samples),18 the in-place concrete strengths are quite vari-able, but in-place strength was generally higher than speci-fied and have likely increased over time. Given these consid-erations, the target mixture strength reasonably emulates concrete in vintage RC bridges. The day-of-test material properties are reported in Table 1. Testing procedures to determine concrete compressive strength, concrete tensile strength, and steel yield stress were performed in accordance with ASTM C39/C39M,19 ASTM C496/C496M,20 and ASTM E8/E8M,21 respectively. No corrosion or other degra-dation was investigated, as the bridge population considered in this study does not show signs of corrosion or other envi-ronmental distress.

All of the test specimens were 26 ft (7.92 m) long, with 14 x 42 in. (356 x 1067 mm) stems, and a 36 x 6 in. (914 x 152 mm) deck. The stirrup spacing, number of flex-ural bars, location of flexural bar cutoff, span length and preformed crack orientation, and distance from the loading point were systematically varied, as summarized in Table 2. Six specimens were used to test the positive-moment bending region, where the deck portion is in flexural compres-sion (designated as T) and six specimens investigated the negative-moment region, where the deck is in flexural tension (designated as inverted-T or IT). Depending on the configuration of the specimen (T or IT), the flexural steel was arranged in one or two layers, as shown in typical cross sections in Fig. 1 and in elevation in Fig. 2. All specimens were tested to failure. Each specimen was instrumented to monitor midspan displacement, support settlement, local crack motion, and strain in the stirrups. Eight of the speci-mens (four Ts and four ITs) were instrumented to measure strain and slip of the flexural cutoff bars to quantify bond stress and determine tensile demand, as shown in Fig. 2. Flexural strain gauges were placed on the extreme tension face periodically between the end of the cutoff and the inter-section of the preformed crack. T- and IT-specimens had three and four flexural strain gauges, respectively, as shown in Fig. 1. Figure 3 illustrates the specimen naming conven-tion used in this study.

Table 1—Material properties

Specimen IDfc′, psi (MPa)

fct, psi (MPa)

fy, psi (MPa)

fyv, psi (MPa)

T.45.Ld3.(4).10 3165 (21.8) 284 (1.96)

71.7 (494.3)

53.5 (368.8)

T.45.Ld3.(5).10 3302 (22.8) 272 (1.88)

T.60.Ld3.(5).10 3417 (23.6) 263 (1.81)

T.NA.Ld3.(5).10 3538 (24.4) 282 (1.94)

IT.45.Ld2.(6).12 3918 (27.0) 332 (2.29)

IT.60.Ld2.(6).12 3862 (26.6) 246 (1.70)

IT.45.Ld2.(5).10 3603 (24.8) 240 (1.65)

IT.60.Ld2.(5).10 3664 (25.3) 261 (1.80)

IT.NA.NA.(6).10 3360 (23.2) 364 (2.51) 75.8 (523)

50.7 (349.6)

IT.NA.NA.(6).12 3290 (22.7) 364 (2.51) 75.8 (523)

T.NA.NA.(6).12 4570 (31.5) 391 (2.69) 74.9 (516)

T.NA.Ld2.(5).12 4725 (32.6) 391 (2.69) 74.9 (516)

Table 2—Variable parameters for each specimen

Specimen ID Span, ft (m) s, in. (mm)

No. bars of flexuralCutoff location from support,

in. (cm)Preformed crack angle,

degreesHook Straight Cutoff

T.45.Ld3.(4).10 24.0 (7.32) 10 (254) 2 0 2 66.2 (168) 45

T.45.Ld3.(5).10 24.0 (7.32) 10 (254) 2 1 2 66.2 (168) 45

T.60.Ld3.(5).10 24.0 (7.32) 10 (254) 2 1 2 66.2 (168) 60

T.NA.Ld3.(5).10 24.0 (7.32) 10 (254) 2 1 2 66.2 (168) None

IT.45.Ld2.(6).12 21.6 (6.58) 12 (305) 2 2 2 40.0 (102) 45

IT.60.Ld2.(6).12 21.6 (6.58) 12 (305) 2 2 2 60.0 (152) 60

IT.45.Ld2.(5).10 21.6 (6.58) 10 (254) 2 1 2 40.0 (102) 45

IT.60.Ld2.(5).10 21.6 (6.58) 10 (254) 2 1 2 40.0 (102) 60

IT.NA.NA.(6).10 24.0 (7.32) 10 (254) 3 3 0 —

NoneIT.NA.NA.(6).12 24.0 (7.32) 12 (305) 0 6 0 —

T.NA.NA.(6).12 24.0 (7.32) 12 (305) 0 6 0 —

T.NA.Ld2.(5).12 24.0 (7.32) 12 (305) 0 3 2 60.0 (152)


A preformed diagonal “crack” was cast in seven of the specimens (three Ts and four ITs) using a 1/16 in. (1.59 mm) thick polycarbonate sheet to investigate the influence of existing diagonal cracking on bond anchorage behavior. Two crack angles were considered: 45 and 60 degrees (more typical of field-observed service-level crack angles). The preformed crack originated at the flexural reinforcement and

Fig. 1—Typical cross sections of: (a) T-beam; and (b) IT-beam specimens.

Fig. 2—Typical elevations of (top) specimens not instrumented for cutoff bar slip and (bottom) specimens instrumented for cutoff bar slip.

Fig. 3—Specimen naming convention.


terminated at the theoretical compression zone depth (using ACI 318-11 Chapter 10 analysis methods)11 and was coinci-dent with the edge of the loading plate. Laterally, the poly-carbonate sheet extended between the stirrup legs. Crack thickness was typical of a relatively wide diagonal crack identified during inspection of vintage bridges.15 To induce failure near the detail considered, the opposite half of the beam contained stirrups spaced at 6 in. (152 mm) and two hooked flexural bars extending past the support.

Cutoff bar lengths were determined using ACI 318-1111 minimum development lengths. Using design mate-rial properties of 3300 psi (22.8 MPa) concrete and 68.5 ksi (472 MPa) steel, a No. 11 (36M) reinforcing bar has a minimum development length of 60 in. (152 cm) for an IT beam and 61.1 in. (155 cm) for a T-beam. In the specimens without preformed cracks (except T.NA.Ld3.(5).12), minimum development lengths were provided per ACI 318-11.11 In specimens with preformed cracks, prelim-inary analysis showed that the use of full development lengths past the preformed crack would not likely result in anchorage failure. Therefore, the embedment length of the IT-beam specimens IT.45.Ld2.(6).12, IT60.Ld2.(6).12, and IT.45.Ld2.(5).10 was taken as 30 in. (76.2 cm) or one-half the specified minimum design development length. The embedment length of the T-beam specimens was 20.4 in. (51.7 cm) or approximately one-third the minimum design development length.

Test procedure and loading schemeA reaction frame anchored on a strong floor was used to

apply a four-point loading using a 500 kip (224 kN) servo-hydraulic load-controlled actuator. The specimens were tested at span lengths between the centerline of the support, as reported in Table 2. A steel spreader beam distributed the actuator force through two 2 in. (51 mm) diameter rollers to two 4 in. (102 mm) wide plates spaced 24 in. (610 mm) apart. Similarly, the end support reactions were distributed via 4 in. (102 mm) wide plates resting on captive rollers. All loading plates were leveled and grouted using high-strength grout. Load was applied cyclically without reversal with increasing incremental steps of load: 25 kips (111 kN) up to a load of 100 kips (445 kN) and steps of 50 kips (22 kN) thereafter until failure. The loading rate was pseudostatic,

applied at 1 kip/s (4.45 kN/s). Upon reaching the target load step, the load was reduced from the maximum by 25 kips (111 kN) so cracking could be identified and recorded while minimizing creep effects while the load was held. Additional details and photographs of the experimental setup and speci-mens is available online.22,23

EXPERIMENTAL RESULTSBased on the observed crack patterns, cutoff reinforcing

bar slippage, and load-midspan displacement behavior at failure, four of the T-beam specimens exhibited pullout anchorage failures and two failed in shear-compression, as noted in Table 3. Two of the IT-beam specimens failed in shear-compression and four failed in splitting anchorage, as reported in Table 3. For this work, a shear-compression failure was classified as yielding of the stirrups and crushing of the concrete compression zone. A shear anchorage failure was determined to occur when the cutoff bars exhibited slip of 0.05 in. (1.27 mm) or greater prior to the concrete crushing in the compression zone. The observed pullout anchorage failures were ductile and exhibited signs of distress prior to failure, including characteristic cracking near the ends of the cutoff bars and permanent slip of the cutoff bars in excess of 0.05 in. (1.27 mm).

The applied shear at failure, observed failure and as-built preformed diagonal crack angles, and midspan displacement at failure are reported in Table 3. Shear forces reported in Table 3 include the applied shear on the specimen from the actuator VAPP, the shear force from the portion of the beam’s self-weight acting at the failure plane VDL, and the sum of these as the total shear force VEXP. Using a unit weight of RC of 150 lb/ft3 (23.6 kN/m3), VDL was estimated by computing the weight of concrete acting on the diagonally cracked failure plane.

The load-deformation responses of all specimens are shown in Fig. 4. Midspan and support displacements were recorded for both sides of each specimen for a total of six measurements. The deformations reported in Fig. 4 are the average of the two midspan measurements and after removing the measured rigid-body displacements that take place at the supports. T-beam specimens exhibiting anchorage failure were able to sustain the applied load as deformations increased rapidly. The apparent ductility was

Table 3—Summary of specimen condition at failure

Specimen ID VAPP, kips (kN) VDL, kips (kN) VEXP, kips (kN)Failure crack angle,

degrees Failure typeMidspan deflection, in.

(mm)

T.45.Ld3.(4).10 111.9 (498) 2.9 (12.9) 114.8 (511) 36.0

Pullout anchorage

1.44 (36.6)

T.45.Ld3.(5).10 148.6 (661) 3.1 (13.8) 151.7 (675) 33.0 2.57 (65.3)

T.60.Ld3.(5).10 154.0 (685) 3.7 (16.4) 157.7 (701) 49.0 1.70 (43.2)

T.NA.Ld3.(5).10 154.4 (687) 3.0 (13.3) 157.4 (700) 35.0 1.73 (43.9)

IT.45.Ld2.(6).12 225.0 (1001) 3.4 (15.1) 228.4 (1016) 32.0Shear compression

0.97 (24.6)

IT.60.Ld2.(6).12 175.2 (779) 7.6 (33.8) 182.8 (813) 60.0 0.69 (17.5)

IT.45.Ld2.(5).10 179.1 (797) 4.8 (21.4) 183.9 (818) 44.0

Shear anchorage

0.98 (24.9)

IT.60.Ld2.(5).10 182.6 (812) 4.8 (21.4) 187.4 (834) 45.0 1.05 (26.7)

IT.NA.NA.(6).10 200.7 (893) 4.6 (20.5) 205.3 (913) 32.0 1.20 (20.5)

IT.NA.NA.(6).12 179.2 (797) 4.6 (20.5) 183.8 (818) 29.0 1.24 (31.5)

T.NA.NA.(6).12 180.7 (804) 3.2 (14.2) 183.9 (818) 55.0Shear compression

1.02 (25.9)

T.NA.Ld2.(5).12 156.0 (694) 2.9 (12.9) 158.9 (707) 45.0 1.12 (28.4)


not due to reinforcing steel yielding at midspan as with a flex-ural failure but, rather, the ductility was due to the residual bond stress created by the cutoff bars as they slipped signifi-cantly. For the T-beam specimens instrumented to measure cutoff bar slip, at low loads, the permanent slip of the cutoff bars was less than 0.01 in. (0.25 mm). However, at failure, as much as 0.50 in. (12.7 mm) (the limit of the instrumenta-tion) of slip was measured while load increased only moder-ately, as shown in Fig. 5. The two IT-beams, which failed in shear-compression, had a stiffer load-deformation response than the four IT-beams, which failed in shear-anchorage, as shown in Fig. 4. The load-cutoff bar-slip responses of the

IT-beams instrumented to measure cutoff bar slip are shown in Fig. 6. Specimens IT.45.Ld2.(6).12 and IT.60.Ld2.(6).12, which failed in shear compression, had relatively little slip of the cutoff bars and no permanent slip. In contrast, Speci-mens IT.45.Ld2.(5).10 and IT.60.Ld2.(5).10, which failed in shear anchorage, exhibited permanent slip following the load steps just prior to failure.

For the specimens failing in anchorage, characteristic flexural reinforcing bar slip-induced cracking was observed. Starting at the 100 kip (445 kN) load cycle, cracks along the anchorage zone of the cutoff bars initiated in the T-beam specimens, as shown in Fig. 7(a). These cracks were charac-

Fig. 4—Load-midspan displacement response of specimens.


terized by periodic vertical cracks extending from the loca-tion of the cutoff bar to the bottom soffit of the beam stem. The vertical cracks were connected by primary horizontal cracks at the level of the cutoff bar. As the applied load increased, the extent and density of the cracking increased. At failure, as the cutoff bars slipped, new diagonal-tension cracks formed while some of the existing service-level diag-onal cracks propagated. All of the additional diagonal-tension cracks were more vertical than the widest service level crack and were located closer to midspan. Additionally, Speci-mens T.NA.NA.(6).12 and T.NA.Ld2.(5).12 both observed to fail in shear-compression, exhibiting anchorage cracking near the support and the cutoff locations, respectively.

IT-beam specimens failing in shear anchorage demonstrated similar chevron cracking located at the flange of each spec-imen beginning at the 150 kip (667 kN) load cycle, as shown in Fig. 7(b). This type of slip-induced cracking was clearly evident on both the bottom and top flange surfaces along the length of the developing flexural reinforcement. Also, at failure, large horizontal splitting cracks were present that originated at the cutoff location and extending along the full length of the cutoff bar to the location of the diagonal failure crack. This is in contrast to the shear-compression failures, which were characterized by ruptured stirrups without hori-zontal anchorage cracking. The appearance of these chevron cracks occurs just prior to failure for the IT-specimens

Fig. 5—Load-cutoff bar-slip response for select instrumented T-beam specimens.

Fig. 6—Load-cutoff bar-slip response for select instrumented IT-beam specimens.

Fig. 7—Typical anchorage cracking caused by slip of cutoff bars in: (a) T-beam specimens; and (b) IT-beam specimens.


Table 4—Summary of peak and average bond strength in cutoff and anchored bars

Specimen ID Failure mode

Cutoff bars Anchored bars

Bar Mean µavg, psi (MPa) Peak µavg, ksi (MPa) Mean µavg, ksi (MPa)

T.45.Ld3.(4).10

Pullout anchorage

1 560 (3.86) 1149 (7.92)280 (1.93)

2 732 (5.05) 1748 (12.05)

T.45.Ld3.(5).101 1098 (7.57) 2818 (19.43)

287 (1.98)2 834 (5.75) 1964 (9.31)

T.60.Ld3.(5).101 745 (5.14) 887 (6.12)

271 (1.87)2 866 (5.97) 930 (6.41)

T.NA.Ld3.(5).10 1 1120 (7.72) 1250 (8.62) 298 (2.05)

Average T-beam 851 (5.87) 1535 (10.58) 284 (1.96)

IT.45.Ld2.(6).12Shear compression

1 405 (2.79) 977 (6.74) 345 (2.38)

IT.60.Ld2.(6).12 1 459 (3.16) 957 (6.60) 374 (2.58)

IT.45.Ld2.(5).10Shear anchorage

1 648 (4.47) 2165 (14.93) 396 (2.73)

IT.60.Ld2.(5).10 1 634 (4.37) 2013 (13.88) 396 (2.73)

Average IT-beam (shear anchorage) 641 (4.42) 2090 (14.40) 396 (2.73)

and early on for the T-specimens. These cracks should be identifiable in field conditions and should be noted by bridge inspection teams.

Of the seven specimens with preformed cracks, only two specimens (IT.60.Ld2.(6).12 and IT.45.Ld2.(5).10) failed at the preformed crack location, as reported in Table 3. In both cases, the reason for failure at the preformed crack is not related directly to the preformed crack, but rather to other design parameters. In the case of Specimen IT.60.Ld2.(6).12, the preformed crack height termination at the bottom of the compression zone was based on an assumed yield strength for the flexural steel in specimen design that was lower than that provided in fabri-cation (68.5 versus 71.7 ksi [472 versus 494 MPa]). The embedment length provided, although fractional to that prescribed by ACI 318, allowed the cutoff bars to develop their full yield strength. Therefore, the concrete compres-sion zone in the specimen was smaller than required and the specimen failed in shear compression.

Specimens IT.45.Ld2.(5).10 and IT.60.Ld2.(5).10 had the same reinforcement details. The only significant differ-ence between the specimens was the preformed crack angle. However, both failed at approximately the same crack angle and location at essentially the same load, as seen in Table 3. Therefore, for Specimen IT.45.Ld2.(5).10, the failure along the preformed crack was not related to the loss of aggregate interlock but rather to the fact that the preformed crack was located coincident to where the specimen would have failed without the preformed crack. These findings indicate that the contribution of aggregate interlock to shear strength for large girders with these reinforcing details may be insignificant.

The mean average and peak average bond stress values for the specimens with flexural stain data are reported in Table 4. The average bond stress µavg over an incremental segment of reinforcement was calculated at each instrumen-tation point as

Dm =

4s b

avgem

f dl

(7)

where Dfs is the change in reinforcement stress over the length of the segment, which may not exceed fy; and lem is the embedment length. The mean µavg was taken as the mean µavg of all the strain gauges between the end of the cutoff bars and the preformed crack. The peak µavg was taken as the maximum µavg value along the cutoff bars. For the IT-beam specimens, the peak µavg occurred coincident with failure. For the T-beam specimens, the peak values occur prior to failure. Mean µavg in Specimens IT.45.Ld2.(5).10 and IT.60.Ld2.(5).10 (both shear-anchorage failures) were much higher than the mean µavg calculated for Specimens IT.45.Ld2.(6).12 and IT.60.Ld2.(6).12 (both shear-compression failures), as noted in Table 4. For IT-specimens, the mean µavg in the well-anchored bars were similar. The peak µavg for the specimens that failed in shear-anchorage provide an estimate for the µavg that produced splitting failures in the deck.

To analyze the difference in demand between the anchored bars and the cutoff bars, a tensile ratio Tratio was considered as tensile force on the cutoff bars Tcutoff at a given instru-mented location compared to the tensile force on the corre-sponding average, well-anchored bar Tanchored

= cutoffratio

anchored

TT

T (8)

The Tratio was calculated at all locations where strain gauges were placed on all reinforcing steel in the region between the preformed crack and the end of the cutoff bar. A linear regression of the one-sided, 97.5% lower-confi-dence limit for the data from the T- and IT-beam tests was computed where the R2 correlations from each beam config-uration were 0.8054 and 0.9854, respectively. From the regression lines, the maximum tensile forces T97.5CL(T) and T97.5CL(IT) for the cutoff bar in T- and IT-beams, respectively, were computed as

97.5 ( )0.0230

CL T em s yT l A f= (9)


97.5 ( )0.0216

CL IT em s yT l A f= (10)

where lem is the reinforcing bar embedment length (in.); As is the bar area (in.2); and fy is the steel yield stress (ksi). Equa-tions (9) and (10) must be limited by the full yield strength to indicate that the bar is fully developed. Additionally, Eq. (9) and (10) may be converted to a maximum permis-sible average bond stress mavg(T) and mavg(IT) in psi by

( ) 5.74avg T y bf dm = (11)

m =( ) 5.40avg IT y bf d (12)

where fy is the reinforcing steel yield stress (ksi); and db is bar diameter (in.). Using the measured material properties, the 97.5% lower-confidence limit average bond stress and development lengths for the T- and IT-beams were each calculated as 581 and 545 psi (4.01 and 3.76 MPa), respec-tively, and 43.3 and 46.3 in. (109 and 119 cm), respectively.

Using actual material properties (fy = 71.7 ksi [494.3 MPa] and approximate average fc′ = 3500 ksi [24.1 MPa] for speci-mens with known bond stresses and that failed in anchorage) of the specimens to determine the 97.5% lower-confidence limit, the development lengths and bond stress were calculated using the methods found in ACI 318-11,11 Chapter 12 (two methods); AASHTO LRFD5; Orangun et al.10; and Darwin et al.12 As summarized in Table 5, all of these values were also compared to bond stress values for larger bars, as reported by Clark6 and Mains.7 As shown in Table 5, the design specifications were highly conservative when compared to experimentally measured results. However, measured bond stress values were within the limits reported by others in the literature. Darwin et al.’s12 Eq. (4) predicted the measured average bond stresses of the specimens quite well, as seen in Table 5. Of the design specification procedures considered, the more detailed ACI 318-1111 procedure better reflected the experimentally measured response, although it remained conservative. From these results, it is likely that analysis of existing bridge members based on prescribed design devel-opment lengths will under-predict the available maximum average bond strength and, therefore, more likely predict shear-anchorage failures that may in fact be controlled by alternative failure mechanisms.

AASHTO LRFD defines the tensile demand Tdemand of the flexural reinforcement as

( 0.5 )cot

AASHTO LRFD 5.8.3.5-1 (modified)

udemand u s

v

MT V V

d= + − q

(13)5

where Mu is the moment demand taken where the crack crosses the flexural steel; dv is the effective shear depth defined by AASHTO LRFD; Vu is the factored shear demand; Vs is the tensile force carried by the stirrups; and q is the diagonal crack angle. The tensile force the reinforce-ment actually resists, Tresistive, was calculated from the steel strain es as

= e <resistive s s s s yT A E A f (14)

Table 5—Comparison of literature, design specification, and experimental development lengths

MethodDevelopment

length, in. (cm)mavg, psi (MPa)

Mains7 42 (107) 613 (4.23)

Orangun et al.10 (f = 1.0) 43 (109) 594 (4.10)

Experimental T-beam, 97.5 CL 44 (112) 581 (4.01)

Experimental IT-beam, 97.5 CL 47 (119) 545 (3.76)

Darwin et al.12 (f = 1.0) 50 (127) 510 (3.52)

Orangun et al.10 (f = 0.8) 53 (135) 475 (3.28)

Darwin et al.12 (f = 0.9) 57 (145) 446 (3.08)

ACI 318-11 Complex Method11 64 (162) 400 (2.76)

Clark6 73 (185) 350 (2.41)

AASHTO LRFD5 75 (190) 338 (2.33)

ACI 318-11 Simple Method11 86 (218) 296 (2.04)

Table 6—Predicted and measured tensile demands at failure

Specimen IDAASHTO LRFD5

prediction, kips (kN)

Measured tensile force,

kips (kN)Bias TEXP/

TAASHTO

T.45.Ld3.(4).10 314.6 (1399) 297.2 (1322) 0.94

T.45.Ld3.(5).10 424.5 (1888) 400.3 (1780) 0.94

T.60.Ld3.(5).10 450.0 (2002) 422.7 (1880) 0.94

IT.45.Ld2.(6).12 638.7 (2841) 484.5 (2155) 0.76

IT.60.Ld2.(6).12 473.9 (2108) 461.4 (2053) 0.97

IT.45.Ld2.(5).10 446.6 (1986) 437.4 (1946) 0.98

IT.60.Ld2.(5).10 470.1 (2091) 461.0 (2051) 0.98

where Es is the modulus of elasticity of the flexural steel (ksi).At failure, the predicted AASHTO LRFD tensile demand

on the flexural reinforcing at the failure crack location using Eq. (13) was compared with the measured tension force in the flexural steel for all of the specimens with a preformed crack, as shown in Table 6. The failure crack was not neces-sarily the preformed crack, as noted in Table 3. In the analysis, the applied moment was taken at the intersection of the flexural steel and the failure diagonal crack. The Vs term was taken as the yield stress times the number of stir-rups crossing the actual failure diagonal crack, which was verified based on strain measurements at stirrup locations crossing the crack. The experimentally measured tensile force in the flexural bars was determined from strain gauges at or near the failure diagonal crack. The total net tension force at the preformed diagonal crack intersection was deter-mined by taking the sum of the tensile forces in each flexural bar. Using this approach, AASHTO LRFD predicted total (moment- and shear-induced) tensile demand and experi-mentally measured results, which were very close for all of the specimens except IT.45.Ld2.(6).12. All the other speci-mens failed at moderate-to-steep crack angles and in loca-tions with a dense array of strain gauges in the flexural bars. The low correlation between the experimental and AASHTO LRFD demands for Specimen IT.45.Ld2.(6).12 can be attrib-uted to failure occurring in a region with small numbers of


strain gauges with which to precisely determine the experi-mental tensile force in the flexural bars.

CONCLUSIONSThis research sought to provide bridge inspectors and

rating engineers with bond stress data representative of large reinforcing bars so they can better evaluate vintage RC deck-girder bridges containing diagonal cracks interacting with flexural reinforcing steel bar cutoffs. To meet this objective, 12 large-size specimens were designed and tested to failure. Based on the experimental results and comparisons with available bond and anchorage models and specifications, the following conclusions are presented:• The presence of a diagonal crack crossing the develop-

ment length of cutoff longitudinal bars does not neces-sarily control the specimen failure location.

• Location of the eventual failure crack depends on reinforcement detailing and load patterns, not the mere presence of diagonal cracks observed under service-level conditions.

• Large cracks without aggregate interlock were placed at locations with high shear demand and did not control failure. For the large-size specimens and details considered, this suggests that aggregate interlock does not contribute as substantially to shear strength as commonly presumed, if at all.

• Anchorage failures were observed in both T- and IT-beam specimens. T-beams exhibited ductile anchorage fail-ures due to the transverse confinement provided by the stirrups. In contrast, IT-beam specimens were nonduc-tile due to splitting of the deck.

• Under service-level loads, the preformed diagonal crack caused peak bond stresses in the flexural steel at the crack intersection. However, as load increases to failure and the eventual failure crack developed, the peak bond stresses shifted to the eventual failure crack.

• Tensile demand in the flexural steel at a diagonal crack location was well-predicted by AASHTO LRFD, Eq. (5.8.3.5-1), when the crack angle represents the in-place conditions.

• Rating engineers should check the anchorage demand with crack angles based on field data for existing diag-onal cracks for operating evaluations.

• Minimum design development length prescribed by AASHTO LRFD and ACI 318-11 are conservative when compared with the current experimental results, as well as bond stresses reported in the literature. Thus, use of design development lengths for evaluation of existing structures may produce ratings that are unnecessarily conservative and mistakenly identify anchorage failures.

• For rating cases where the application of design devel-opment lengths indicate anchorage deficiency, it is recommended that the minimum development length be calculated using Eq. (4) developed by Darwin et al.12 using f of 1.0 for bars anchored in the beam web where transverse steel is available in the anchorage zone and f of 0.9 for bars anchored in the deck.

• Bridge inspectors should look for the presence of chevron cracks similar to those shown in Fig. 7 that is associated with straight-bar terminations of the flexural reinforcing steel. Special attention should be given in negative-moment regions where cracking should be visible on the underside of the deck, as the onset of these cracks occurs very near the collapse load.

ACKNOWLEDGMENTSThis research was funded by the Oregon Department of Transportation

and overseen by research coordinator S. Soltesz. The findings and conclu-sions are those of the authors and do not necessarily reflect those of the project sponsors or the individuals acknowledged.

NOTATIONAb = cross-sectional area of flexural reinforcement (in.2)Atr = cross-sectional area of transverse reinforcement (in.2)C = clear cover or half spacing (in.2)c = Darwin et al.12 cover constraintcb = bottom cover (in.)cM = maximum value of cb or cs (in.)cm = minimum value of cb or cs (in.)cs = half clear spacing (in.)db = reinforcing bar diameter (in.)dv = effective shear depth (in.)fc′ = compressive strength of concrete (psi)fct = tensile strength of concrete (psi)fy = yield stress of flexural reinforcing steel (psi)fyv = yield stress of transverse reinforcing steel (psi)Krt = transverse reinforcement indexld = reinforcing bar development length (in.)lem = reinforcing bar embedment length (in.)Mu = moment demand (kip-in.)s = stirrup spacing (in.)T97.5CL = 97.5% confidence limit maximum tensile force (kips)Tanchored = tensile force in well-anchored bar (kips)Tcutoff = tensile force in cutoff bar (kips)Tdemand = applied tensile demand (kips)Tratio = ratio comparing tensile force in cutoff bar to force in well-

anchored bar (kips)Tresistive = resistive tensile demand (kips)td = term representing effect of bar size on confining steel forceVAPP = applied shear from actuator (kips)VDL = applied shear from portion of self-weight acting at failure

plane (kips)VEXP = total applied shear (kips)Vs = shear force carried by stirrups (kips)Vu = shear demand (kips)Dfs = change in reinforcement stress over lem (psi)µavg = average bond stress (psi)q = diagonal crack angle (degrees)

REFERENCES1. Delatte, N. J., Beyond Failure: Forensic Case Studies for Civil Engi-

neers, American Society of Civil Engineers, Reston, VA, 2009, pp. 130-133.2. ACI Committee 318, “Building Code Requirements for Reinforced

Concrete (ACI 318-63),” American Concrete Institute, Farmington Hills, MI, 1963, pp. 76-77.

3. AASHTO, “Standard Specifications for Highway Bridges,” sixth edition, American Association of State and Highway Officials, Washington, DC, 1953, pp. 182, 238.

4. ASTM A305-50T, “Tentative Specifications for Minimum Require-ments for the Deformations of Deformed Steel Bars Concrete Reinforce-ment,” ASTM International, West Conshohocken, PA, 1950, pp. 218-220.

5. AASHTO, “AASHTO LRFD Bridge Design Specification,” third edition with 2005 interims, American Association of State Highway and Transportation Officials, Washington, DC, 2005, pp. 5-1:212.

6. Clark, A. P., “Bond of Concrete Reinforcing Bars,” ACI JOURNAL, Proceedings V. 46, No. 11, Nov. 1949, pp. 161-184.

7. Mains, R. M., “Measurement of the Distribution of Tensile and Bond Stresses along Reinforcing Bars,” ACI JOURNAL, Proceedings V. 48, No. 11, Nov. 1951, pp. 225-252.

8. AASHTO, “Standard Specifications for Highway Bridges,” Amer-ican Association of State and Highway Officials, Washington, DC, 1973, pp. 57-58, 93.

9. ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-71),” American Concrete Institute, Farmington Hills, MI, 1971, pp. 42-45.

10. Orangun, C. O.; Jirsa, J. O.; and Breen, J. E., “Re-Evaluation of Test Data on Development Length and Splices,” ACI JOURNAL, Proceedings V. 74, No. 3, Mar. 1977, pp. 114-122.

11. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp.


12. Darwin, D.; Zuo, J.; Tholen, M. L.; and Idun, E. K., “Development Length Criteria for Conventional and High Relative Rib Area Reinforcing Bars,” ACI Structural Journal, V. 93, No. 3, May-June 1996, pp. 347-359.

13. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-95) and Commentary,” American Concrete Institute, Farmington Hills, MI, 1995, 369 pp.

14. Abrishami, H., and Mitchell, D., “Analysis of Bond Stress Distri-butions in Pullout Specimens,” Journal of Structural Engineering, ASCE, V. 122, No. 3, May 1996, pp. 255-261.

15. Higgins, C.; Yim, S. C.; Miller, T. H.; Robelo, M. J.; and Potisuk, T., “Remaining Life of Reinforced Concrete Beams with Diagonal-Tension Cracks,” Report No. FHWA-OR-RD-04-12, Federal Highway Administra-tion, Washington, DC, 2004, 110 pp.

16. ASTM A706/A706M-09b, “Standard Specification for Low-Alloy Steel Deformed and Plain Bars for Concrete Reinforcement,” ASTM Inter-national, West Conshohocken, PA, 2009, 6 pp.

17. ASTM A615/A615M-09b, “Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement,” ASTM Interna-tional, West Conshohocken, PA, 2009, 6 pp.

18. Folkestad, J., “Carbonation of Mid-Twentieth Century Reinforced Concrete Bridges in Oregon,” BS thesis, Honors College, Oregon State University, Corvallis, OR, 2010, 83 pp.

19. ASTM C39/C39M-09, “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens,” ASTM International, West Conshohocken, PA, 2009, 7 pp.

20. ASTM C496/C496M-04e1, “Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens,” ASTM International, West Conshohocken, PA, 2004, 5 pp.

21. ASTM E8/E8M-09, “Standard Test Methods for Tension Testing of Metallic Materials,” ASTM International, West Conshohocken, PA, 2009, 27 pp.

22. Triska, M. A., “Flexural Steel Anchorage Performance at Diagonal Crack Locations,” MS thesis, Oregon State University, Corvallis, OR, 2010, http://scholarsarchive.library.oregonstate.edu. (last accessed Jan. 2, 2013)

23. Goodall, J. K., “Influence of Diagonal Cracks on Negative Moment Flexural Anchorage Performance in Reinforced Concrete Bridge Girders,” MS thesis, Oregon State University, Corvallis, OR, 2010, http://scholarsar-chive.library.oregonstate.edu. (last accessed Jan. 2, 2013)

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