112. DETAILING AT ANCHORAGE

The anchorage zone of prestressing tendons must be specially designed so that the prestressing forces are
transferred to the structure in complete safety and tensioning can be undertaken without any difficulty
whatsoever.

The data sheets pertaining to anchorages and detailing contain the information and recommendations res-
pective to each type, notably:
• the dimensions;
• the minimum distances permissible between anchorage axes and between these axes and the closest
concrete face;
• the clearance to be provided behind each anchorage for the installation of the tensioning jack;
• the primary helical or cross-wise bursting reinforcement.

112.1 Concrete strength

The consultant must specify the minimum strength required of the concrete in the anchorage zone to allow for
tensioning, taking into account the cover conditions and the grouping or spacing between anchorages. The
required strength, f

c min.

given in the technical characteristics and specifications of anchorages (section 120),

varies according to the different classes of concrete. This information only concerns local actions. The consul-
tant must also consider the general equilibrium. This strength is considered to be reached when it is in ac-
cordance with the average of the results of trials performed on at least 3 test cylinders or cubes, sampled
from one of the mixes poured in the anchorage zone.

Reminder: relationship between the values of compressive strength, resulting from test cubes and those ob-
tained from test cylinders, according to the Beton-Kalender:
• Tests according to the BRD German standard, on test cubes: 200 x 200 mm:
Compressive strength:

b

w

• Tests according to the CEB-FIP Recommendations, on test cylinders: 15 x 30 cm:
Compressive strength: f

c

For B 15 and B < 15 concrete:

b

w

= 1.25 f

c

f

c

= 0.80

b

w20

= 0.76

b

w15

For B 25 and B > 25 concrete:

b

w

= 1.18 f

c

f

c

= 0.85

b

w20

= 0.81

b

w15

For the same concrete, the strength values measured on cubes are therefore always greater than those ob-
tained on cylinders.

Furthermore, the consultant must specify the tendon tensioning sequence; this choice is important, since it can
influence the strength required for each stressing phase.

112.2 Lateral cover and anchorage distances

In order to prevent excessive stress concentrations in the concrete, the anchorages must be installed at a suf-
ficient distance to the concrete edges and/or to the other anchorages.

These distances are specified in the data sheets.

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112. DETAILING AT ANCHORAGE

112.3 Design principle of reinforcement

It is generally considered that a stress distribution is only deemed to be in compliance with Navier’s as-
sumption at a distance of about the depth of the considered member from the anchorages.

The zone running between the anchorages and the stress distribution section complying with Navier’s as-
sumption, is commonly known as the anchorage zone or prestressing dispersion zone.

Considering the considerable action effects occurring in this area, especially during tensioning operations,
special attention should be paid to this structural part, during the design as well as construction, in particu-
lar with regard to the anchorages’ arrangement, their cover and spacing, the reinforcement and concrete
casting around the anchorages.

For the analysis of the dispersion zone, one traditionally differentiates the first stress regularisation zone and
the general equilibrium zone. Two types of reinforcement, behind the anchorages, can also be distinguished:
• the primary bursting reinforcement, meant to withstand the bursting forces developed immediately behind
the anchorages, in the first regularisation zone;
• the general equilibrium reinforcement, which ensures the transmission of prestressing forces from the an-
chorages up to the zone where stresses are distributed according to Navier’s assumption.

112.31 Primary bursting reinforcement

A typical primary bursting reinforcement is given
in the data sheets for each anchorage. This takes
the form of helical or cross-wise hoops. These
have been justified by tests carried out on isolated
blocks including a centred anchorage (onto which
a compressive force is exerted) and reinforcement
pertaining to the first regularisation zone.

Therefore, the bursting reinforcement drawn on the
data sheets concerns isolated anchorages.

This does not mean that the designer need not
provide connecting reinforcement between an-
chorages. Difficulties during the installation of
reinforcement and the pouring of concrete may
occur if the anchorages are too close from each
other (see fig. 11), and also for this reason it is
important to observe the minimum distances bet-
ween anchorage axes.

112.32 General reinforcement

The reinforcement necessary to the general equilibrium depends on the shape and dimensions of the end
element, the distribution of anchorages, the inclination of the tendons in comparison to the concrete face,
etc… The design of the necessary reinforcement is carried out by means of internal equilibrium calcula-
tions, examples of which are given below. More detailed methods for the determination of reinforcement
are available in the technical literature.

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Fig. 11

helical or cross-wise hoop

continuity stirrups

112. DETAILING AT ANCHORAGE

D

ETERMINATION OF FORCES IN THE GENERAL REGULARISATION ZONE

The stress regularisation zone is considered to be
as long as the member depth, i.e. at a distance
from the anchorages equal to the member depth,
the stresses follow Navier’s assumption.
Let BC be a section in this regularisation zone (see
fig. 12). The equilibrium of the solid A B C D al-
lows the determination of the forces on section
B C:
Axial load

N = O

Shear force

V = F – X

Bending moment

M = F (y – d) – Xe

These forces vary according to the ordinate y of the chosen section and the most unfavourable section must
therefore be found. One should in particular check the section at the tendon level, since it may obviously be
a critical section. However, this is not always the case, as shown by the following examples:
• Case A (see fig. 13):
Section B C
Shear force X = – 0.30 F therefore V = F – 0.30 F = 0.70 F
Moment in section B C : M = – 0.30 F . 0.30/2 = – 0.045 F
Section E F
Shear force in section E F (symmetry axis of the
element): V = 0
Moment in section E F:
M = F (0.70 – 0.50) = 0.20 F
Section B C is the most affected by shear force and
section E F the most affected by the bending moment.
• Case B (see fig. 14):
Section B C
Shear force: X = – 0.80 F therefore V = F – 0.80 F = 0.20 F
Moment M = 0.80 F . 0.40 = – 0.32 F
Section E F
Shear force: V = 0
Moment M = 0.20 F – 0.50 F = – 0.30 F
Section B C is then the most affected by the ben-
ding moment and shear force.
• Case C, tendons inclined over the member axis
(see fig. 15):
Here again, the length of the regularisation zone
is considered to be equal to the member depth.
However, one must now take into account the
shear forces at the member end.
The following forces and moment are exerted on
section B C :
• Axial load

N = Q – Y

• Shear force

V = F – X

• Bending moment

M = F (y – d) – Xe – (Q + Y) . a

2

The axial load can be a compressive or a tensile
force, depending on the position of section B C.

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Fig. 12

Fig. 13

Fig. 14

A

B

d

y

e

a

F

D

X

C

M

V

t

x

s

x

s

x

a

S

BC

t

x

= V

S

CD

s

x

= X

A

B

E

F

30

30

70

70

F

D

C

F

tendon axis

a = 200 cm

a = 200 cm

A

B

E

F

80

80

20
20

F

D

C

F

tendon axis

a = 200 cm

a = 200 cm

112. DETAILING AT ANCHORAGE

The maximum forces are to be found on inclined
planes. The planes passing through the tendon
axes must be especially checked since cracks are
more likely to occur there.

N

ECESSARY REINFORCEMENT IN THE REGULARISATION ZONE

The forces determined above, increased following
the different codes, must be dealt with using rein-
forcing bars.
According to the moment direction, the reinforce-
ment determined is distributed over a length of
a/4 if it has to be installed near the anchorages,
otherwise over a length of a/2.
In both the cases studied above, the reinforcement must be installed in accordance with the diagrams
below: fig. 16 for case A and fig. 17 for case B.
Having determined the bending reinforcement, the shear strength can be easily checked using the following
rule:
• if the bending reinforcement is sufficient to with-
stand the shear force, no reinforcing bar need be
added;
• if the bending reinforcement is not sufficient to
withstand the shear force, reinforcing bars must be
added so that the total section may globally with-
stand the shear force.

112.33 Other types of bursting reinforcement

E

MBEDDED ANCHORAGES

When a dead-end anchorage is embedded in
concrete, compressive strains develop under the
anchorage during tensioning and tensile stresses
occur behind the anchorage.
To prevent cracks, it is necessary to provide reinforcing bars, parallel to the tendons, to ensure the cohesion of the concrete
(see fig. 18). In order to prevent any disorder, these bars must bear about 20 % to 30 % of the anchoring force.

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Fig. 15

Fig. 16

Fig. 18

y

d

e

Q

A

C

t

y

s

x

D

X

a

a

F

B

N V M

t

x

s

y

S

CD

s

x

= X

S

CD

t

y

= Y

S

BC

t

x

= V

Fig. 17

a/4

a

a/2

a/2

L = 200 à 250 cm

112. DETAILING AT ANCHORAGE

E

ND ANCHORAGES

It is absolutely necessary to bind the anchorages
near the concrete edges, using reinforcing bars
fastening the anchorage to the member core (see
fig. 19).

A

NCHORAGES IN WEB ENLARGEMENTS

Such an anchorage induces the following forces:
• a tensile force in the part of the web located be-
hind the anchorage. This is the same force as in
the case of the embedded anchorage;
• moments in the web due to the tendon eccentri-
city;
• shear between the web and the anchorage
block.

To withstand these forces, longitudinal reinforcing
bars must be provided in the web as well as conti-
nuity reinforcement in front of the anchorage, to pre-
vent the occurrence of cracks in the web at the level
of the enlargement (see fig. 20).

Lastly, in the curved part of the tendon, the off-balance thrusts must be opposed.

These thrusts are withstood by stirrups that extend considerably from the curved part determined by the de-
sign, due to site tolerances which may significantly alter the position of the curved zone.

112.34 Surface reinforcement

The purpose of this reinforcement is to prevent scaling of the concrete edges or the onset of cracks arising
from re-entrant angles or notches. It is preferably installed with the minimum cover, i.e. 30 to 50 mm, be-
hind the anchorage. It is usually part of the general reinforcement of the member considered.

112.35 Summary of reinforcement necessary at anchorage

The indications given above permit the design of the reinforcement necessary in the general equilibrium
zone, to be combined with the primary binding reinforcement.

It is also necessary to take into account surface reinforcing bars as well as special effects (eccentricity, blockouts,
etc…), where these occur.

All reinforcement to be provided in the anchorage zones must be shown on the construction drawings of the
structure.

112.36 Clearance at anchorage

For each anchorage, clearance must be provided behind each tendon extremity, in order to facilitate the ins-
tallation of the block and jaws and the operation of the tensioning jack. One must also take account of the
protective concrete cover of the tendons extremities after tensioning and the possible fitting of a temporary or
permanent casing.

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Fig. 19

Fig. 20

flexural and tensile

reinforcement

continuity reinforcement

curvature reinforcement