Several mechanisms contribute in a complex way to the bond resistance. For small bond stresses bond can be achieved by adhesion. When the bond stress #b increases, the shear-key effect from the ribs will be more important and the adhesion is eventually broken. The shear stress along the interface results in inclined principal tensile and principal compressive stresses in the surrounding concrete. When the principal tensile stress reaches the tensile strength of concrete, inclined cracks form near the tips of the ribs and the bond resistance depends mainly on the action of inclined compressive struts originating from the ribs, see Fig. 7-16.
concrete favourable compression $c $c Fs
compressive principal stresses failure zone
tensile principal stresses
failure area
Fs
$s
Fig. 7-16: The bond mechanism along ribbed anchor bars results in inclined cracks and inclined compressive forces. The longitudinal component corresponds to the bond stress and the transverse component must be balanced by the surrounding concrete
To keep equilibrium these inclined compressive struts, which act outwards in all radial directions, must be balanced by tensile stresses. These tensile stresses appear in rings around the anchored bar.
When the anchor bar is placed in well-confined concrete, these ring stresses can be resisted by the surrounding concrete and either a pullout failure or rupture of the steel bar will finally result.
According to the CEB-FIP Model Code 90 the anchorage conditions can be considered as confined when the concrete cover is at least 5 times the bar diameter and the spacing between adjacent anchored bars is at least 10 bar diameters. Confined conditions can also be achieved by transverse reinforcement with a total area, across the critical splitting plane, of at least one time the total area of all bars anchored in the same section, or by a transverse pressure that is at least 7,5 MPa.
However, when the concrete cover is small the ring stress might cause the concrete cover to crack and splitting cracks develop through the concrete cover along the bar, see Fig. 7-17. The effect of inclined compressive struts is the same as that of a radial pressure to the surrounding concrete originating form the anchored bar. It is obvious that in case of small concrete covers the resistance to such a pressure is small and the concrete might crack.
("
("
Fig. 7-17: The inclined compressive stresses must be balanced by tangential tensile stresses in the surrounding concrete, according to Tepfers (1973)
This type of longitudinal splitting cracks may result in a sudden brittle type of splitting failure where the concrete cover along the anchorage length splits away, as shown in Fig. 7-9 a. The risk of such brittle splitting failures increases when the anchor bar is located with a small concrete cover especially near a corner, when there is small spacing between adjacent bars and no or small amounts of transverse reinforcement. According to recent test results the tendency for brittle splitting failures is more pronounced in high strength concrete, since the ability for favourable stress redistribution will be smaller when the concrete strength increases %fib (2000b) .
However, if the anchorage zone is confined by stirrups a new state of equilibrium can exist also after occurrence of longitudinal splitting cracks, since the anchorage zone is kept together and the transverse bars are able to resist tangential tensile stresses across the cracks. In that case brittle splitting failures can be avoided and the anchorage capacity will be governed by pullout failure. However, in this case the pullout failure develops in split concrete (with longitudinal cracks) where the pullout resistance is smaller than in well-confined concrete.
Fig. 7-18 shows a typical crack pattern from a pullout test of a 16 mm anchor bar with a small concrete cover c = 16 mm (or c = 1,0)!), from Engström et al. (1998). The anchorage length was 290
mm, the concrete compressive strength was about 20 – 25 MPa, the bar was placed in a mid position in a wide specimen and the specimen was provided with 4 stirrups !6 mm with constant spacing within the anchorage length and enclosing the anchored bar.
A longitudinal splitting crack appeared rather early during the test, but the tensile force could still be increased. The crack propagated successively when the tensile force continued to increase. Transverse cracks appeared one by one in a ‘fishbone’ pattern. Due to the confinement from the surrounding concrete in the wide specimen and the transverse stirrups, it was possible to reach the same anchorage capacity as in the comparable tests (N290) in well confined concrete, see Fig. 7-14. Accordingly, the pullout resistance in split concrete was in this case the same as in well-confined concrete without cracks. However, the residual capacity after the peak was smaller in the test with splitting cracks.
Normally in reinforced concrete structures, the main reinforcement is anchored in regions where the concrete cover is as small as possible with regard to minimum requirements. The design rules for anchorage regions assume that the anchorage capacity is governed by splitting cracks. However, in precast concrete structures anchor bars are often placed with considerable concrete covers far away from corners. In such cases the anchorage is often provided in regions, which can be considered as
‘well confined’. Confined conditions can be achieved either by a thick concrete cover, great amounts of transverse stirrups or a transverse pressure
Fig. 7-18: Typical crack pattern from pullout test of an anchor bar placed in a mid position of a wide specimen but with a small concrete cover, according to Engström et al. (1998)
It is stated in CEB-FIP Model Code 1990 that anchorage regions should always fulfil minimum rules with regard to concrete cover and transverse stirrups. Hence, the concrete cover should be at least one bar diameter, and in beams the transverse reinforcement in anchorage regions should have a total area, across the critical splitting plane, of at least one quarter of the cross-sectional area of one anchored bar. In slabs no transverse reinforcement is required. This can be motivated by the fact that in slabs the spacing between bars is normally greater than in beams and almost all of the bars are placed far away from corner regions.
The local relationship between bond stress and slip has been studied experimentally in pullout tests with short embedment lengths, for instance according to the principle shown in Fig. 7-19. In this type of test the bond stress will be rather uniformly distributed along the bonded length la since this is very
short. Since the bonded length is placed in the interior part of the test specimen, boundary effects are prevented and the anchorage conditions can be considered as confined.
For a certain applied tensile force the (average) bond stress is calculated as
a b l N ) *! + # (7-1)
The slip s is assumed to be equal to the measured relative displacement a between the
reinforcement bar and the end face of the concrete specimen. Fig. 7-20 a shows some typical examples of relationships between bond stress and slip obtained from pullout tests of ribbed bars with short embedment length in confined concrete, according to Soroushian and Choi (1989). The typical bond behaviour and the bond mechanisms involved are explained in Fig. 7-20 b.
x 200 mm l = 3b ! b 200 Cube Embedment length Plastic tube for debonding
cube 200 , 200 mm
##b
embedment lnegth la= 3!
plastic tube for debonding
Fig. 7-19: Example of pullout test with short embedment length, according to Losberg and Olsson (1979)
# [MPa] 16 12 8 4 0 0 5 10 [mm] # [MPa] adhesion [mm] s frictional phase shear-keys crushed or sheared off cracking softening s a) b)
Fig. 7-20: Relationship between bond stress and slip for ribbed bars in confined concrete, a) examples of relationships obtained from pullout tests with short embedment length,%Soroushian and Choi (1989) , b) typical bond behaviour and mechanisms
It should be noted that the relationship between bond stress and slip refers to the local condition. Along an anchor bar the bond stress is normally not uniformly distributed and various sections have developed different slips. However, if the bond conditions are the same for all sections along the bar, all sections will have the same relationship between the bond stress and the local slip, i.e. the total slip developed in that section.
In pullout tests with a short embedment length in well confined concrete the bar is strong in relation to the total bond resistance. Accordingly, a pullout failure caused by shear failure along the tips of the ribs will limit the capacity and occur when the steel stress still is small. The corresponding bond-stress slip relation can be regarded as a virgin curve, which is an upper limit for the bond behaviour that is obtainable in real applications. The total bond resistance increases with the anchorage length. Hence, if the total bond resistance exceeds the yielding capacity of the bar, the bar will start to yield at the loaded end before the maximum bond stress according to the virgin curve is reached. As it was shown by Engström (1992) yielding of the bar results in a drastic decrease of the bond stress for further imposed slip, see Fig. 7-21 a. In cases where the concrete cover is small, longitudinal cracks will occur due to the effect of the radial compressive stresses before the maximum bond stress according to the virgin curve is reached. The maximum bond stress will then be determined by the formation of longitudinal splitting cracks, see Fig. 7-21 b. The post peak behaviour depends on the actual confinement. With little confinement the crack formation might result in a sudden splitting failure of the whole anchorage region. With more transverse stirrups, for example, it
may be possible to achieve a new equilibrium in the cracked concrete. Bond stresses can redistribute along the anchorage length and a stable post-peak behaviour can be achieved where the residual bond stress depends on the actual confinement.
Bond Slip Pullout failure in confined concrete ‘virgin curve’ in case of no yielding yielding is reached
reduced bond after yielding is reached
Bond
Slip No yielding of steel
‘virgin curve’
in case of pullout failure in confined concrete
splitting of concrete cover
splitting induced pullout failures, various amounts of confinement splitting failure a) b)
Fig. 7-21: Typical relationships between bond stress and slip, virgin curve valid for anchorage in well confined concrete (dotted curve), a) influence of yielding of the bar, b) influence of longitudinal splitting and various amounts of transverse reinforcement
On basis of results from pullout tests with short embedment length, a schematic local relationship between bond stress and slip is proposed in CEB-FIP Model Code 1990, see Fig. 7-22. This relationship can be used as in-put data in calculations where the local bond slip behaviour needs to be considered. The relationship in the Model Code is valid for normal strength concrete. For high strength concrete reference is made to fib (2000b).
s1 s2 s3 f # #max s #b Bond stress Slip
Fig. 7-22: Schematic relationship between bond stress #b and local slip s according to CEB-FIP Model Code 1990
The idealised bond-slip relationship in Fig. 7-22 can be used for ribbed and smooth reinforcement bars with various anchorage conditions. For each case, appropriate values of the parameters #max,#f, s1,
The ascending branch of the relationship can be expressed by the function ( -- . / 00 1 2 # + # 1 s s max b (7-2)
For ribbed bars anchored in ‘confined’ concrete, the specified parameters are listed in Table 7-1. In this context, ‘confined’ concrete means that the bar should be embedded in concrete in such a way that it is possible to reach the pullout mode, where the concrete is sheared off along the steel to concrete interface without premature splitting failure.
Even in the case of confined concrete, the bond resistance can vary considerably depending on the local bond conditions. Of this reason the actual bond conditions are considered in the Model Code by classification into two categories ‘good bond conditions’ and ‘all other conditions’. The bond conditions can be considered as ‘good’ when the bar has an inclination of 453 - 903 to the horizontal during concreting, or when the bar has an inclination less than 453 to the horizontal and is placed either within a distance not more than 250 mm from the bottom or within a distance not more than 300 mm from the top of the concrete edge during concreting.
In precast structures the bond conditions of anchor bars are not always easy to define in these terms. It is then assumed that the two cases ‘good’ and ‘all other cases’ can be used as upper and lower estimates of the bond behaviour.
Bond conditions
Good All other cases
s1 1,0 mm
s2 3,0 mm
s3 free rib distance
( in eq. (7-2) 0,4
#max 2,5 fcc 1) 1,25 fcc 1)
#f 0,40#max
1)
fcc inserted in %MPa
Table 7-1: Parameters describing the idealised relationship, Fig. 7-22, between bond stress and local slip for ribbed bars in confined concrete, according to CEB-FIP Model Code 1990
For ribbed bars anchored in ‘unconfined’ concrete, the corresponding parameters are listed in Table 7-2. Unconfined concrete refers to the case when the failure is of the splitting type and the detailing corresponds to the minimum requirements of concrete cover and transverse confining reinforcement. For intermediate cases it is assumed that appropriate values of s1,s3 , #max and #f can be
found by linear interpolation between confined and unconfined concrete. If transverse reinforcement, with an area greater than the minimum, is present simultaneously with a transverse pressure, these two effects may be added.
The idealised bond stress-slip relationship defined for confined concrete corresponds to the virgin curve in Fig. 7-21. In the case of unconfined concrete, the bond stress-slip relation is modified by the parameters in Table 7-2 and the resulting bond-slip model simulates the effect of longitudinal splitting cracks shown in Fig. 7-21 b. As shown in the figure the bond-slip response is influenced by the actual amount of confining reinforcement. According to the CEB-FIP Model Code 90 this influence can be taken into account by linear interpolation between the models for confined and unconfined concrete.
However, the Model Code gives no information of how to consider the effect of yielding of the steel, which is shown in Fig. 7-21 a. Consequently, the bond-slip relationship according to Fig. 7-22 is only true as long as the tie bar remains in the elastic range.
Bond conditions
Good All other cases
s1 0,6 mm s2 0,6 mm s3 1,0 mm 2,5 mm ( in eq. (7-2) 0,4 #max 2,0 fcc 1) 1,0 fcc 1) #f 0,15#max 1) fcc inserted in %MPa
Table 7-2: Parameters describing the idealised relationship, Fig. 7-22, between bond stress and local slip for ribbed bars in unconfined concrete fulfilling minimum requirements of concrete cover and transverse confining reinforcement, according to CEB-FIP Model Code 1990
To simulate the bond-slip behaviour for smooth hot-rolled bars, it is proposed in the Model Code that the two intermediate stages of the idealised relationship in Fig. 7-22 should be removed, which means that s1 = s3. The specified parameters for this case are presented in Table 7-3. These parameters
are valid for anchorage in confined concrete as well as for unconfined concrete.
Bond conditions
Good All other cases
s1=s2=s3 0,1 mm
( in eq. (7-2) 0,5
#max=#f 0,3 fcc 1) 0,15 fcc 1)
1)
fccinserted in %MPa
Table 7-3: Parameters describing the idealised relationship, Fig. 7-22, between bond stress and local slip for smooth bars in confined or unconfined concrete, according to CEB-FIP Model Code 1990