J. Cairns · Bond and anchorage of embedded steel reinforcement in fib Model Code 2010
700
Bar stress (MPa)
600 500 Eq.3
400
Grade 400 300
Grade 500
200
Grade 600 Grade 700
100 0 0
20
40 Bond length lb,0 /φ
60
80
Fig. 4. Mean bond stress for various reinforcement grades
Table 2. Factor η4 for steel grade
datum, and introduces a new factor η4, Table 2, into the expression for basic design bond strength fbd,0 to adjust bond strength for other reinforcement grades.
is substantially unchanged within the limits imposed by MC90. The wider range of results in the new test database has, however, allowed limiting values imposed by MC90 to be relaxed somewhat in fib Model Code 2010. Bond strength is also influenced by the clear spacing between bars, cs in Fig. 2, and this can be significant, particularly for slabs. This influence is now recognized in fib Model Code 2010 through the inclusion of a term cmax/cmin in factor α2.
3
3.3
fyk (MPa) η4
400 1.2
500 1.0
600 0.85
700 0.75
800 0.68
Design anchorage length of straight bars in tension
Basic bond strength for benchmark conditions of confinement may be modified to take account of minimum cover, bar spacing, transverse reinforcement and confining pressure in excess of their respective minima – according to Eq. 6.1-21 of fib Model Code 2010, reproduced here as Eq. (9), which represents a tri-linear relationship in which fbd = (α2+α3) fbd,0 – 2ptr < 2.0 fbd,0 – 0.4ptr < 1.5/γ⎯f c√ ck
(9)
where α2 and α3 represent the confinement provided by concrete around the bars and by secondary reinforcement respectively and ptr is the average compressive stress on the section acting perpendicular to the bar axes of the bars. Note that compressive stress is taken to be negative; transverse compression hence increases bond strength fbd.
3.2
Confinement by concrete cover and transverse reinforcement
The beneficial influence of secondary reinforcement and increasing concrete cover on bond strength has been recognized for many years, and was included in MC90. Coefficients for minimum cover and transverse reinforcement were combined factorially in MC90, but it was considered more rational for contributions from these components to be summed, as in Eq. (3). Although the format of the expressions for the contributions of minimum cover and secondary reinforcement have changed in fib Model Code 2010, the net influence of minimum cover and transverse reinforcement on bond strength, each taken individually,
Transverse pressure
The effect of transverse compression on bond is two-fold: it retards the onset of splitting failure and increases the frictional force at the bar/concrete interface. The first of these mechanisms dominates in situations with low confinement by concrete cover and secondary reinforcement when splitting failure would otherwise occur, with frictional enhancement taking over at higher pressures once the splitting failure mode is suppressed. “Higher” confining pressures may be taken as those that exceed the tensile strength of the concrete. Much of the available data comes from tests with high unidirectional lateral stresses, where bond failure took place either by pullout, or in a splitting mode where the splitting crack ran parallel to the direction of the applied lateral stress, and relate to conditions where confinement was already relatively high, even without applying transverse pressure. The factor α5 in MC90 appears to have been derived for this condition and correlates fairly well with results in such stress environments. However, it underestimates the enhancement in strength where confinement from cover and transverse reinforcement is low, and fib Model Code 2010 includes a tri-linear relationship to represent the enhancement in bond due to transverse pressure, Eq. (9) and Fig. 5. A parametric investigation of representative simply supported beams has found that if anchorage demand at an end support or an equivalent situation is high, Figs. 6a and 6b, transverse compression will be sufficient to position the stress environment on the intermediate segment of Fig. 6, but that in other circumstances end anchorage capacity will not be critical. The intermediate segment of
Structural Concrete (2015), No. 1
49