2 Bond Behavior of Embedded Reinforcing Steel Bars3 for Varying Levels of Transversal Pressure1234
4 Hamdy M. Afefy1 and El-Tony M. El-Tony2
5 Abstract: Because of columns loads, reinforced5 concrete (RC) continuous beams in skeleton structures are subjected to transverse com-6 pressive stress at support locations. Such lateral pressure can enhance the bond between the main top reinforcing bars and the surrounding7 concrete because of the confinement effect. Thus, the development length can be reasonably decreased compared to the case of no lateral8 pressure. However, different codes of practice, such as the Egyptian code standard ECP 203-2007 and the American Concrete Institute (ACI)9 code standard ACI 318-116 , stipulate increasing the reinforcement location factor for upper reinforcement implemented in the calculation of
21 Bond is the major structural property of reinforced concrete (RC),22 accountable for the transmission of forces between concrete and23 reinforcing bars, thus ensuring strain compatibility and composite24 action. In addition, inadequate bond strength can result in a signifi-25 cant decrease in the ultimate capacity and stiffness of the structure26 when subjected to different loading conditions (Chao et al. 2009).27 Bond is considered to be a result of three different mechanisms:28 chemical adhesion, friction, and mechanical interlocking between29 the ribs of the reinforcing bars and the concrete in the case of de-30 formed steel bars. Smooth plain bars depend on chemical adhesion31 and friction only, whereas deformed bars develop their bond32 resistance mainly from the mechanical interlocking between the33 ribs and the surrounding concrete. The classical concept of bond34 is that forces act parallel to the interface between the bar and35 the concrete and that bond failures are caused by exceeding the36 ultimate bond strength, resulting in pull-out of the bar. This concept37 accurately explains the bond behavior of plain smooth bars in con-38 crete, but does not explain the bond behavior of deformed bars. In39 the latter case, it is generally accepted that bond forces radiate into40 the surrounding concrete at some inclination from the bonding sur-41 face of the bar, with a risk of spalling of the concrete cover.
42Research on bond behavior indicates that bond strength is gov-43erned by factors such as the strength of the concrete, the thickness44of the concrete surrounding the reinforcing bar, the confinement of45the concrete due to transverse reinforcement, and bar geometry46(Atorod et al. 1993; Yerlici and Ozturan 2000; Valcuende and Parra472009; Arel and Yazici 2012). Ferguson and Breen (1965) showed48that the volume of the stirrups can affect the splice strength of49reinforcing bars. Jeanty et al. (1988) concluded that, for beams with50and without transverse reinforcement crossing the plane of split-51ting, the top bar factor is 1.22, which means that the required52lap splice length must be increased by 22% for spliced top tension53bars. Furthermore, the presence of transverse reinforcement across54the plane of potential splitting significantly reduces the required55development length for both bottom-cast and top-cast bars. Xu56et al. (2014) recently showed that the residual and ultimate bond57strength of plain round bars increases with increases in average58lateral pressure.59When RC structures are analyzed, complete bond between the60reinforcement and the concrete is perhaps the most common61assumption. This assumption is used in almost all hand calculations62in ultimate limit-state analysis. In finite-element analyses also, this63is a rather frequent assumption; it is often sufficient for the level of64modeling desired especially when the overall behavior of a larger65structure is examined. However, for more detailed analyses of66smaller parts of a structure, particularly if one is interested in fol-67lowing crack development more thoroughly, the bond mechanism68needs to be taken into account. The usual way to do this is to em-69ploy the bond-versus-slip relationship as input.70Several researchers examined the bond mechanism and sug-71gested various bond-versus-slip relationships to be used in analy-72ses. For example, Tassios (1979) and Eligehausen et al. (1983)73included both monotonic and cyclic loading. However, for more74detailed analyses of the behavior of parts of a structural member
1Associate Professor, Dept. of Structural Engineering, Faculty of Engi-neering, Tanta Univ., Tanta, Egypt (corresponding author). E-mail:[email protected]
2Associate Professor, Dept. of Structural Engineering, Faculty ofEngineering, Alexandria Univ., Alexandria, Egypt.
75 where the bond mechanism plays a crucial role, a more refined76 model is needed, mainly for analyses of anchorage regions such77 as splices and anchorage of the reinforcement at the end supports.78 A requirement of this type of model is that the bond mechanism be79 described in such a way that the bond versus slip achieved in a80 structure is a result of the analysis rather than the input. Another81 requirement is that the model include not only the bond stresses but82 also the splitting stresses that result from the anchorage. Gylltoft’s83 (1983) proposed model includes the effect of normal stresses,84 which allows an outer pressure to increase the capacity. However,85 it does not include any active normal splitting stresses that result86 from the anchorage, and bond versus slip is used for the input.87 Some models, such as that developed by Mainz (1993), include88 active splitting stresses but still use a form of bond versus slip as89 input. Reinhardt et al. (1984) modeled the bond mechanism in a90 more detailed way, including the ribs of the reinforcement in the91 geometrical model. The models by Uijl and Bigaj (1996) and92 Cox (1994) include splitting stress, where bond stress is also related93 to radial deformation between the reinforcement bar and the con-94 crete. Furthermore, to improve description of bond behavior in95 numerical simulation, new zero-thickness joint elements were de-96 veloped and introduced at the interface between the steel reinforce-97 ment and the concrete to allow use of a nonlinear law (Monti et al.98 1997; Lowes et al. 2004; Dominguez et al. 2005; Monti et al. 1997;99 Richard et al. 2010; Ibrahimbegovic et al. 2010; Casanova et al. 2012).
100 For continuous beams in RC skeleton structures, the upper ten-101 sile reinforcements are subjected to high lateral compressive stress102 at the beam-column connection, especially at lower floors in multi-103 story buildings under gravity loading. This effect has a great influ-104 ence on bond strength in this region. Accordingly, the effect of105 lateral pressure on reinforcement has to be considered in the cal-106 culation of development length in this region, which can affect the107 top bar factor as stipulated by ECP 203-2007 (ECP 2007) and ACI108 318-11 (ACI 2011). Both codes introduce a top bar factor of 1.3 for109 calculating the development length of the upper bar reinforcement110 where the substrate concrete is greater than 300 mm to account111 for freshly placed concrete. On the other hand, CEB-FIP 2010112 (CEB-FIP 2010) allows increasing the design bond strength of113 the main reinforcing bar when the bar is subjected to transverse114 compression. However, it limits the maximum contribution of the115 transverse compression to 40% of its value when the influences of116 passive confinement from the concrete cover and transverse117 reinforcement are in excess of their respective permissible minima.118 The main target of the current study was to experimentally in-119 vestigate how transverse pressure on reinforcement affects develop-120 ment length calculations, and to illustrate the discrepancies in121 bond length calculations stipulated by ECP 203-2007, ACI122 408R-03, and CEB-FIP 2010 in considering such effect.123 To study how transverse pressure on reinforcement affects the124 bond characteristics of the main top reinforcement of continuous
125beams near the beam-column connection, the RC column was si-126mulated by a short column subjected to varying axial capacity from127zero (final floor case) to 40% of the nominal capacity of the column128cross section. This relatively moderate axial capacity was chosen to129comply with the limitation of CEB-FIP 2010 and to account for the130upper floors, where the acting column loads are relatively small131compared to those of the lower floors. The main reinforcement132of the beam was represented by a steel reinforcing bar embedded133in the RC column and extended outside it by a length approxi-134mately three times the column side to accommodate the set-up135required for the pull-out process. Three bar diameters were consid-136ered, 10, 12, and 16 mm, for both deformed and smooth plain137bars
138Experimental Program
139Test Specimens
140Because the characteristics of the test specimens would affect141both measured bond stress and bond response [ACI 408R-03142(ACI 2003)], different configurations for the test specimens were143used to study the developed bond stress between the reinforcing144bars and the surrounding concrete. Fig. 1 is a schematic of the most145common configurations: pull-out, beam-end, beam anchorage, and146splice. Other specimens (e.g., wall) were used to study bond stress.147Ichinose et al. (2004) showed that pull-out specimens with a148smaller cover thickness exhibit a greater effect; however, this effect149can be reduced by a larger confinement provided either by the cover150concrete or the steel reinforcement. The experimental results of151Ichinose et al. (2004) confirmed that the size effect is mainly attrib-152utable to brittle splitting cracks and not to local crushing of concrete153in front of the bar ribs. Furthermore, according to ACI 408R-03,154with a large concrete cover and bar spacing, a pull-out failure is155possible whereas, with a smaller cover and bar spacing, a splitting156tensile failure is possible.157For the test specimens in this study, different configurations158from those specified by ACI 408R-03 were adopted to better re-159present the transverse lateral pressure of the column on the reinforc-160ing bar of the beam near the beam-column joint. In addition, the161size effect was deliberately sidestepped by choosing a larger con-162crete cover but with a practical value as used in RC members,163which also provided lateral steel reinforcement. A detailed descrip-164tion of the test specimen matrix follows.165The experimental program included 36 specimens divided into166six groups. Each group consisted of 6 specimens representing three167phases in which each test was typically conducted on 2 specimens168to increase confidence in the results. The first three groups repre-169sented plain smooth bars, with each group corresponding to one bar170diameter: 10 mm, 12 mm, or 16 mm. The remaining three groups
(a) (b) (c) (d)
F1:1 Fig. 1. Schematic of the test specimens considered by ACI 408R-03
171 were identical to the first three, but consisted of deformed bars. The172 three phases included in each group represented the level of axial173 load applied to the specimen column. These levels were 0Po,174 0.2Po, and 0.4Po, where Po was the nominal axial capacity of175 the column cross section that could be calculated from Eq. (1),176 as provided by ACI 318-11:
Po ¼ 0.85f 0cðAc − AsÞ þ Asfy ð1Þ
177 where f 0c = concrete cylinder strength (MPa); fy = yield stress
178 of the longitudinal bars (MPa); Ac = concrete cross-sectional area179 (mm2); and As = total cross-sectional area of the longitudinal180 bars (mm2).181 Table 1 summarizes the details of the test specimens. The typical182 specimen consisted of a short column and an extruded bar at the183 middle of the column height. The column cross section was184 120 mm wide by 250 mm long, and the overall height was 600 mm.185 The column dimensions were chosen to provide practical concrete186 cover parallel to the pull-out steel bar and to sidestep the effect of187 column buckling in both directions by either the axial load on the188 column or the lateral load provided by the pull-out bar. The column189 longitudinal reinforcement was four deformed bars of 12-mm190 diameter corresponding to a longitudinal reinforcement ratio of191 1.5%. The stirrups were made from smooth mild steel bars of192 8-mm diameter. Fig. 2 shows the concrete dimensions along with193 the reinforcement detailing for both the column and the embedded194 bar. The pull-out bars were embedded 250 mm into each concrete195 column and extended 20 mm from the free end to facilitate meas-196 uring the induced slip.197 All specimens were cast horizontally in wooden forms. Two198 days after casting, the standard cubes and the sides of the specimens199 were stripped from the molds and covered in wet Hessian until the200 seventh day, when the Hessian was removed and the specimens201 were allowed to air-dry until testing.
202 Material Properties
203 Normal-strength concrete was used in this study, with 35-MPa204 target cube strength—the average of three standard cubes of205 150-mm side length. The concrete mix contained a blend of Types206 I and II crushed pink limestone as the coarse aggregate; maximum207 aggregate size was 12 mm. The sand was supplied from a local208 plant near the site, and its fineness modulus was 2.7%. The volumes
209of limestone and sand in one cubic meter were 0.72 and 0.37,210respectively. The cement used was normal Portland cement211(Type I) with 4-kN=m3 cement content and a water-cement ratio212of 0.38. The actual cube strength was approximately 34 MPa,213and the corresponding cylinder strength was approximately21429 MPa. These values were used in all of the development length215calculations. The entire testing process lasted three continu-216ous days.217To determine the mechanical properties for the pull-out bars for218both plain smooth and deformed bars along with the longitudinal219bars of the short columns, tensile tests were performed on three220specimens for each bar size. The average values for the mechanical221properties of the plain and deformed bars are given in Tables 2222and 3, respectively. For the 8-mm mild steel bars used as stirrups223for the column, the mean tensile yield strength, ultimate strength,224and Young’s modulus were 250 MPa, 364 MPa, and 205 GPa,225respectively.
600
mm
250 mm
120
Pullout bar
stirrups 8 mm
2 12
2 12
250 mm
Welded plate
1000 mm
20 mm
F2:1Fig. 2. Concrete dimensions and reinforcement details of the typicalF2:2test specimen
Table 1. Test Matrix
T1:1 Group number Specimen Bar diameter (mm) Type of pulled-out steel bar Transverse load (kN) Number of specimens
T1:2 1 SP10-0.0 10 Plain bar 0 2T1:3 SP10-0.2 10 Plain bar 0.2Po (136 kN) 2T1:4 SP10-0.4 10 Plain bar 0.4Po (272 kN) 2T1:5 2 SP12-0.0 12 Plain bar 0Po 2T1:6 SP12-0.2 12 Plain bar 0.2Po (136 kN) 2T1:7 SP12-0.4 12 Plain bar 0.4Po (272 kN) 2T1:8 3 SP16-0.0 16 Plain bar 0Po 2T1:9 SP16-0.2 16 Plain bar 0.2Po (136 kN) 2
T1:10 SP16-0.4 16 Plain bar 0.4Po (272 kN) 2T1:11 4 SD10-0.0 10 Deformed bar 0Po 2T1:12 SD10-0.2 10 Deformed bar 0.2Po (136 kN) 2T1:13 SD10-0.4 10 Deformed bar 0.4Po (272 kN) 2T1:14 5 SD12-0.0 12 Deformed bar 0Po 2T1:15 SD12-0.2 12 Deformed bar 0.2Po (136 kN) 2T1:16 SD12-0.4 12 Deformed bar 0.4Po (272 kN) 2T1:17 6 SD16-0.0 16 Deformed bar 0Po 2T1:18 SD16-0.2 16 Deformed bar 0.2Po (136 kN) 2T1:19 SD16-0.4 16 Deformed bar 0.4Po (272 kN) 2
227 Fig. 3 shows the set-up of the tests. The column bottom end was228 supported on a rigid steel beam of the main testing frame; the top229 end was loaded by a load cell of 600-kN capacity to facilitate the230 different load levels. Steel caps were provided at both ends of the231 columns to distribute the column compression load at the upper end232 and to support the column lower end at the testing frame. A steel233 assembly was used for the pull-out test of the reinforcing bars,234 as shown in Fig. 3. The developed axial tensile load on the steel235 pull-out bars was measured by a load cell of 400-kN capacity. A236 linear variable displacement transducer (LVDT) of 100-mm meas-237 uring length was used to measure reinforcing bar slippage at the238 free end. In addition, a 100-mm Pi-gauge was mounted at the239 middle height of the column to measure the lateral tensile stress240 induced in the column. Load was applied to the reinforcing pull-241 out bar incrementally at an average rate of 3–5 kN=min. The load-242 ing continued until the specimen failed, either by yielding of the243 steel pull-out bar or by excessive slip between the bar and the244 concrete. After each loading step, the acting loads on both the245 column and the pull-out bar, the Pi-gauge reading, and the LVDT246 reading were recorded. An automatic data logger unit was used247 to record and store the data during the test for the load cells, the248 Pi-gauge, and the LVDT.
249Results and Discussion
250Assuming a uniform bond stress distribution over the embedded251length in concrete, the average bond stress between the reinforcing252bar and the surrounding concrete was calculated by Eq. (2):
τb ¼P
πdblbð2Þ
253where τb = bond stress (MPa); P = applied load (kN); db = bar254diameter (mm); and lb = bar embedded length (mm).255Table 4 summarizes the test results for all specimens.
256Failure Modes
257Two types of failure, pull-out and yielding, were observed in the258tests. Pull-out failure is due to the pull-out of the bar, whereas yield-259ing failure is due to the developed bond stress between the bar and260the surrounding concrete exceeding the yielding stress of the bar.261For the current study, all smooth plain bars exhibited pull-out262failure, as Table 4 shows. Even at a higher lateral pressure level263on the reinforcing bar, excessive slippage was recorded, with264further tensile loading on the reinforcing bar due to exhausted265chemical adhesion. Increasing the lateral pressure on the reinforc-266ing bar resulted in an increase in the frictional bond and consequent267enhancement of bond stress. The percentages of bond stress en-268hancement due to increased lateral pressures were 11 and 20 for269the 10-mm bars, 13 and 20 for the 12-mm bars, and 15 and 23270for the 16-mm bars, corresponding to 0.2Po and 0.4Po lateral271pressure, respectively, compared to the case of no lateral pressure272(0Po). The increased bar diameter resulted in increases in achieved273bond enhancement due to transverse pressure on the reinforcing274bar. For plain smooth bars, in all cases, no cracks or local failure275were observed, as shown in Fig. 4.276As for deformed bars, both modes of failures were observed.277For the 10-mm bar diameter, at all lateral pressure levels, yielding278failure occurred, in which the steel bar reached its maximum tensile279stress before reaching the ultimate bond stress. For both 12-mm and28016-mm bars, only pull-out failure occurred for the case of no lateral281pressure (0Po); in the case of 0.2Po and 0.4Po, yielding failure due282to the development of higher bond stresses was observed.
Table 2. Mechanical Properties of Smooth Plain Bars
283 In pull-out failure, concrete crushing in the vicinity of the284 pulled-out bar and concrete shearing between the ribs were285 observed. Fig. 5(a) shows the pull-out failure of specimen286 SD12-0.0, without lateral pressure, in which there was substantial287 failure of the concrete surrounding the bar at the loaded-end side.288 However, in the case of 0.4Po lateral pressure, shown in Fig. 5(c),289 there was no significant concrete failure, which indicated the ability290 of lateral pressure to maintain specimen integrity. That can be ex-291 plained with the aid of Figs. 6 and 7. Fig. 6 shows the typical stress292 distribution around the pull-out bar without lateral pressure, where293 lateral-ring tensile stresses were developed with further tensioning294 of the bar. These tensile stresses had their maximum magnitude295 at the concrete face of the loaded side, which corresponded to
296the expected higher failure zone. On the other hand, applying lat-297eral pressure counteracted the effect of tensile stress, as can be seen298in Fig. 7, and caused a smaller failure zone according to the level of299lateral pressure, as shown in Figs. 5(b and c). This led to switching300of the developed local cracks around the steel bar at the free end, as301shown in Fig. 5(d) compared to that shown in Fig. 5(e).
302Bond-Slip Behavior
303Fig. 8 shows a typical bond-slip relationship for both deformed bars304and plain smooth bars. For deformed bars, the bond mechanism305comprises three main components: chemical adhesion, friction,306and mechanical interlock between the bar ribs and the concrete.
F4:1 Fig. 4. Typical pull-out failure for plain bars
F5:1 Fig. 5. Typical failure pattern for deformed bars7
307 Initially, for very small values of bond stress (≤ 1.38 MPa) (Lutz308 and Gergely 1967; Gambarova and Karakoc 1982), chemical ad-309 hesion is the main resisting mechanism. If bond stress is increased,310 chemical adhesion is exhausted and replaced by the wedging action311 of the ribs. This wedging action leads to crushing in front of the ribs312 and secondary internal transverse (or radial) cracks (Goto 1971;313 Gerstle and Ingraffea 1990), and eventually to longitudinal cracks.314 Early concrete crushing in front of the ribs explains the nonlinearity315 of the ascending branch, as shown in Fig. 8. If inadequate confine-316 ment is provided, bond failure occurs as soon as the cracks spread317 through the concrete cover of the bar. With proper confinement,318 bond stress reaches a maximum of approximately one-third of319 the concrete cylinder strength, according to Gambarova and320 Karakoc (1982), before decreasing as the concrete between the ribs321 fails and frictional behavior ensues. For plain smooth bars, the322 frictional bond is the governing component, responsible for in-323 creasing bond stress after exhausting the chemical adhesion.324 Fig. 9 shows the relationships between bond stress and devel-325 oped slip for all 10-mm pull-out bars for both plain smooth and326 deformed bars. At low bond stress, all bars, either plain smooth327 or deformed, showed no slip until chemical adhesion was ex-328 hausted. Then frictional bond stress controlled the behavior of329 the plain smooth bars and mechanical interlocking controlled330 the behavior of the deformed bars. For plain bars, the frictional331 bond was enhanced as a result of lateral pressure, and this effect332 lessened with excessive bar slippage. As for deformed bars,333 mechanical interlocking increased with further loading, leading334 to reduced manifested bar slippage that continued until yielding335 failure occurred for all specimens. At failure, the recorded bar slip336 showed a decreased value due to increased lateral pressure for337 specimens SD10-0.2 and SD10-0.4, respectively, compared to that338 for specimen SD10-0.0.
339The same trend was observed for both 12- and 16-mm bars, as340shown in Figs. 10 and 11, respectively. However, an increase in bar341diameter resulted in higher bond stress and lower corresponding bar342slip, as reported in Table 4.
343Development Length of Steel Bars
344Because reinforcing bar bond stress is inversely proportional to de-345velopment length, increasing lateral pressure resulted in increased346bond stress. As a consequence, the corresponding development347length could be decreased. The obvious application of such a result348is decreasing the top bar factor stipulated by both ECP 203-2007349and ACI 318-11 for the main upper reinforcement of continuous350beams at the column region for skeleton structures because of351the lateral pressure of the column supports.352Values for the development length obtained for both smooth353plain and deformed bars were calculated based on experimental354results. These values were compared to development lengths355stipulated by ECP 203-2007, ACI 408R-03, and CEB-FIP 2010.356Development length is defined as the minimum length required357to completely develop the design tensile stress in the steel bars.358Using the design value of the tensile strength of the steel359bars as given in Tables 2 and 3, Eq. (2) can be rewritten as360follows:
τb ¼Abftπdbld
ð3Þ
T
Ring tension stresses
Boundary of expected
failure zone
F6:1 Fig. 6. Typical stress distribution for one-side pull-out test withoutF6:2 lateral pressure
T
Ring tension stresses
Uniform lateral pressure
Uniform lateral pressure
T
Resultant stresses
Boundary of expectedfailure zone according to
the level of lateral pressure
F7:1 Fig. 7. Typical stress distribution for one-side pull-out test with lateral pressure
Mechanical interlock
Shearing off Pull-off
Adh
esiv
e bo
ndSh
ear
bond
Bon
d
Slip
Deformed bar
Smooth plain bar
F8:1Fig. 8. Typical bond-slip relationship for pull-out failure
361where τb = average bond stress (MPa); ft = design tensile strength362of the steel bars (MPa); db = bar diameter (mm); Ab = bar cross-363sectional area (mm2); and ld = development length (mm).364From Eq. (3), the development length can be calculated as365in Eq. (4):
ld ¼Abftπdbτb
¼ dbft4τb
ð4Þ
366ACI 408R-03367According to ACI 408R-03, the development length of a steel bar368subjected to tensile force can be calculated using Eq. (5):
ld ¼12
25
fyffiffiffiffiffif 0c
p αβλdb ð5Þ
369where fy = design yield strength of the steel bar (MPa); f 0c = con-
370crete cylinder strength (MPa); α = reinforcement location factor371(1.3 for reinforcement placed so that more than 300 mm of372fresh concrete is cast below the development length or splice);373β = coating factor (1.0); λ = lightweight-concrete factor (1.0 for374normal-weight concrete); and db = bar diameter (mm).
375ECP 203-2007376Egyptian standard ECP 203-2007 stipulates Eq. (6) for calculating377the development length of a steel bar subjected to tensile force: 8
Ld ¼αβηðfyγsÞ4fbu
ϕ ð6Þ
378where Ld = development length (mm); α = correction factor for the379end bar condition (1 for a straight-ended bar); β = correction factor380for the surface condition of the steel bar (1 and 0.75 for smooth and381deformed bars, respectively); η = top bar factor (1.3 for reinforce-382ment placed so that more than 300 mm of fresh concrete is cast383below the development length); fy = steel yield strength (MPa);384γs = strength reduction factor for steel bar (1.15); ϕ = bar diameter385(mm); and fbu = ultimate bond stress (MPa).386According to Eq. (7),
fbu ¼ 0.3
ffiffiffiffiffiffiffifcuγc
sð7Þ
387where fbu = ultimate bond stress (MPa); fcu = concrete cube388strength (MPa); and γc = strength reduction factor (1.5).389Ultimate bond stress, according to ECP 203-2007, does not take390into account the surface of the reinforcing bar; that is, the allowable391bond stress for both smooth and deformed bars is the same. This392value is approximately 1.4 MPa for the current study, which ap-393proximately corresponds to the chemical adhesion part for both394smooth plain and deformed bars, as depicted in Figs 9–11. The395limiting value stipulated by ECP 203-2007 for plain smooth bars396is fairly good, but shows very conservative results for deformed397bars because it neglects the effect of both friction and mechanical398interlock between the bar ribs and the concrete. On the other hand,399as discussed later in this paper, CEB-FIP 2010 takes the bar surface400condition into account in the stipulated bond stress equation.
401CEB-FIP 2010402CEB-FIP 2010 implements Eq. (8) for calculating the design bond403length, lb, for reinforcing steel bars:
lb ¼ α4
σsd
4fbdϕ ð8Þ
0
1
2
3
4
5
6
0 0.5 1 1.5 2
Bon
d st
ress
, MPa
Slip, mm
SP10-0.0
SP10-0.2
SP10-0.4
SD10-0.0
SD10-0.2
SD10-0.4
F9:1 Fig. 9. Bond stress versus slip for all 10-mm pull-out bars (plainF9:2 smooth and deformed)
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6 7 8 9
Bon
d st
ress
, MPa
Slip, mm
SP12-0.0
SP12-0.2
SP12-0.4
SD12-0.0
SD12-0.2
SD12-0.4
F10:1 Fig. 10. Bond stress versus slip for all 12-mm pull-out bars (plainF10:2 smooth and deformed)
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9
Bon
d st
ress
, MPa
Slip, mm
SP16-0.0
SP16-0.2
SP16-0.4
SD16-0.0
SD16-0.2
SD16-0.4
F11:1 Fig. 11. Bond stress versus slip for all 16-mm pull-out bars (plainF11:2 smooth and deformed)
404 where α4 = function of the percentage of reinforcement lapped or405 anchored within 0.65lb from the center of the anchorage or lap406 length considered (0.85); σsd = design steel stress [yield stress407 (MPa)]; ϕ = bar diameter (mm); and fbd = design bond stress408 (MPa).409 According to Eq. (9),
410 where α2 = factor representing the influence of passive confine-411 ment from the concrete cover, c (1 for plain surface bars and, ac-412 cording to Eq. (10), >1 for ribbed surface bars because the413 minimum concrete cover, cmin, is always greater than the bar diam-414 eter). For the current study, α2 is taken as unity for both smooth and415 deformed bars:
α2 ¼�cmin
ϕ
�0.5�cmax
cmin
�0.15
ð10Þ
416 where α3 = factor representing the influence of passive confine-417 ment from transverse reinforcement (0 for the current study);418 fck = characteristic value of concrete strength; fb;0 = basic bond419 strength according to Eq. (11); and ptr = mean compression stress420 perpendicular to the potential splitting failure surface at the ultimate421 limit state.422 Where transverse compression perpendicular to the bar axis acts423 over a portion of the bond length, bond strength may be increased424 over that portion. Consequently, the corresponding bond length425 should be decreased. Obviously this effect is considered by426 CEB-FIP 2010; however, it should be considered by both ACI427 and ECP in bond length calculations for the top bars of continuous428 beams at the support locations in the case of multistory skeleton429 structures. For the current calculations, this effect was considered430 for both 0.2Po and 0.4Po lateral pressure on the reinforcing bar as431 shown in Eq. (11):
fb;0 ¼ η1η2η3η4ðfck=20Þ0.5
γcð11Þ
432 where η1 = coefficient for surface condition (0.9 and 1.8 for plain433 bars and ribbed bars, respectively); η2 = coefficient for the casting
434position of the bar during concreting (1 for good bond conditions);435η3 ¼ 1 for bar diameter <20 mm; η4 ¼ 1 for reinforcing bar436strength (500 MPa and 1.2 for reinforcing bar strength = 400 MPa);437and γc = partial safety factor for concrete material properties (1.5).
438Comparison of Development Lengths: Experimental439Findings versus Standards
440Table 5 summarizes the calculated development lengths for both441smooth plain and deformed steel bars based on experimental re-442sults, and the development lengths obtained from the formulas443stipulated by ECP 203-2007, ACI 408R-03, and CEB-FIP 2010.444Comparisons of experimental and analytical results are also445provided.446The experimental results show that increasing lateral pressure447leads to a decrease in corresponding development length for both448smooth and deformed steel bars. However, the percentage increases449for deformed bars are lower than those for smooth bars, which may450be attributed to the mode of failure: the deformed bars under the451effect of lateral pressure experienced yielding failure whereas all452smooth bars exhibited pull-out failure. The application of 0.2Po453lateral pressure resulted in decreased development lengths by about45410, 12, and 13% for the 10, 12, and 16-mm smooth bars, respec-455tively. However, these decreases were smaller for the same bar456diameter of deformed bars: 3, 1.5, and 3.5%, respectively, for45710, 12, and 16-mm. In addition, development lengths from the ex-458perimental findings showed increases with increased bar diameter459for both smooth and deformed bars.460The calculated development lengths based on the equations461provided by CEB-FIP 2010 showed the same trend as in the ex-462perimental results. The percentage decreases were approximately46336 and 52, corresponding to lateral pressures of 0.2Po and 0.4Po,464respectively, for all smooth bar diameters. Similarly, the deformed465bars showed smaller decreases, approximately 22 and 36%, respec-466tively. This can be attributed to the fact that the enhancement of467bond stress by lateral pressure for smooth bars was more significant468than that for deformed bars. Both ECP 203-2007 and ACI 408R-03469showed the same development length for each bar diameter regard-470less of lateral pressure.471The most significant observation was that the development472length stipulated by ACI 408R-03 showed unconservative results
Table 5. Development Length Results9
T5:1 Groupnumber Specimen
Development lengthbased on experimental
data (mm) (3)
Development lengthaccording to ACI408R-03 (mm) (4)
Development lengthaccording to ECP203-2007 (mm) (5)
473 for all smooth bar diameters, whereas the development length stipu-474 lated by CEB-FIP 2010 showed unconservative results for smooth475 bars of diameters 10 and 12 mm. The development length stipu-476 lated by ECP 203-2007 showed the most conservative results of477 all. Indeed, smooth bars are no longer used in structural buildings478 as main reinforcing steel; this is a discrepancy that must be verified479 in detail in future studies.480 As for deformed bars, CEB-FIP 2010 showed more rational481 results compared to experimental findings whereas ECP 203-482 2007 showed much more conservative results, which should be483 reduced.
484 Conclusions
485 The current paper presents the test results of an experimental pro-486 gram undertaken to verify the effect of lateral pressure on reinforce-487 ment on the bond stress characteristics, bond-slip behavior, and488 development length calculations for such reinforcement. In addi-489 tion, comparisons of development lengths calculated based on490 ECP 203-2007, ACI 408R-03, and CEB-FIP 2010 are presented.491 Results for bar diameters for both smooth plain and deformed492 reinforcing bars, according to the considered lateral pressure levels,493 lead to the following conclusions:494 First, bond stress-slip behavior is significantly affected by the495 level of lateral pressure on the pull-out bar. In addition, the mode496 of failure can change from pull-out to yielding for deformed bars497 because of the effect of transverse lateral pressure on a portion of498 the development length.499 Second, development lengths calculated based on CEB-FIP500 2010 are in comprehensive agreement with experimental results501 for both smooth and deformed bars because an increase in lateral502 pressure over a portion of the embedded length of the steel bar re-503 sults in decreased development length. ECP 203-2007 and ACI504 408R-03 do not consider the effect of lateral pressure on bond505 stress. Furthermore, they stipulate increasing continuous beam506 development length in the vicinity of the supporting columns by507 increasing the top bar factor. Instead, these standards should508 stipulate decreasing development length because doing so has509 an advantageous effect on lateral pressure at the beam-column510 connection.511 Third, among the considered codes of practice, CEB-FIP 2010512 showed the most rational results and did not exaggerate develop-513 ment lengths for either smooth plain or deformed bars. It consid-514 ered the effect of lateral pressure on the reinforcing bar in the515 development length calculation, which resulted in a decrease in516 development length with an increase in lateral pressure on the517 reinforcing bar.518 Fourth, the ultimate bond stress stipulated by ECP 203-2007519 must be revised to consider reinforcing bar type. Currently, it520 presents an explicit equation for calculating bond stress for both521 smooth plain and deformed bars based on concrete compressive522 strength only. In addition, it must be changed to consider the effect523 of lateral pressure on reinforcement in the bond stress equation, as524 CEB-FIP 2010 does.
525 References
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