Thus, fbpt includes the favourable effect of "push-in" at release. This is the "bond situation" to which MC90 refers in the definition of am when the stress decreases at release there is transverse expansion of the tendons, giving a kind of "wedge" effect. Furthermore, fbpt is here a mean value of the bond strength, not a lower limit as in MC90 (the upper limit corresponds to a9 _ 0,5 for the transmission length). See for upper and lower design values. Transmission length

The basic value of the transmission length is lpt _ a1a2 ^ api/fbpt where a1 _ 1,0 for gradual release, 1,25 for sudden release (same as a8 in MC90) a2 _ 0,25 for circular tendons, 0,19 for 7-wire strands (cf. MC90: 7/36 « 0,19) api stress in tendon just after release (same as MC90) Normally a short transmission length gives higher transverse stresses in the concrete at release (spalling, splitting and bursting stresses in the terminology of MC90), whereas a long transmission length is more critical for ULS with regard to shear, bending moment etc. Furthermore, there is an uncertainty in the calculated value. Therefore, the more unfavourable of the following two values should be used as a design value, depending on the design situation: lpt1 _ 0,8 lpt lpt2 _ 1,2 lpt

The factors 0,8 and 1,2 are the same as in the ENV, (4). The corresponding factor in MC90 is a9 with the values 0,5 and 1,0. With the mean value of this factor included elsewhere, see, comparable values of a9 would be 0,67 and 1,33. Anchorage in ULS Bond strength

The bond strength for anchorage of stresses above prestress is fbpd = %2 fctd where r|p2 takes into account the type of tendon and the bond situation at anchorage ("pull-out") = 1,4 for indented wires = 1,2 for 7-wire strands |1 same as above fctd = fctk,0,05 / ye, design value of concrete tensile strength rp2 has the same values as rp1 in MC90. and there is no favourable effect of "push-in". Instead the bond situation at anchorage is characterized by "pull-out", where the tendons "shrink" in the transverse direction when the stress increases.

For fctd there is a limitation to the value valid for C55. The reason is that the linear relationship between fbpd and fctd cannot be expected to be valid for higher concrete strengths. This is due to an increasing brittleness, which results in a more uneven distribution of the bond stress. The average bond strength will normally increase also above C55, although not in proportion to the tensile strength. This may be taken into account, but requires a special verification. Anchorage length

The anchorage length is based on the upper design value of the transmission length and the increase of stress above the remaining prestress, with bond strength according to

lbpd = lpt2 + a,2 ^ (Opd - CTp«) / fbpd where lpt2 the upper design value of the transmission length (see

apd tendon stress to be anchored (same as in MC90)

ap~ the remaining prestress (after all losses; same as in MC90) Numerical comparisons Transmission length Effect of concrete strength

The transmission length according to EN, MC90 and ENV is shown in figure 8.1 as a function of the concrete strength. The figure covers indented wires and strands, different bond conditions and the way of release. The lower design value of the transmission length is shown. The straight line representing the ENV is the same in all 6 diagrams, since the ENV does not make any difference between strands and indented wires, nor does it take into account bond conditions, nor the way of release (at least does not tell how to do it). The EN and MC90, on the other hand, do take these parameters into account.

Due to this the comparison gives very different results. For example, for strands released gradually and in good bond conditions, the ENV is extremely conservative compared to the EN and MC90, whereas for indented wires released suddenly and in bad bond conditions, the ENV is by far on the unsafe side. Effect of initial prestress

Figure 2 shows the transmission length as a function of the initial prestress. The most notable difference in this case is that the ENV does not take into account the magnitude of the initial prestress at all (at least it is not explained how to do), whereas according to the EN and MC90 the transmission length is directly proportional to the prestress.

The comment to figure 8.1 in the third paragraph of applies also to figure 8.2. Anchorage length

In figure 8.3 the total anchorage length in ULS is shown as a function of the stress to be anchored. Like for the transmission length, the ENV is conservative for gradually released strands in good bond conditions, and far on the unsafe side for wires in bad bond conditions, particularly if released suddenly.

lu tie h ted wires

7-wire sir and s

Good bond conditions

Graduai release lu tie h ted wires


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