Reinforcement Strandfor Prestressed Structures Euro Code

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(4) Relaxation at temperatures of the structure over 20 °C will be higher than given in Figure 4.8. This may affect building structures in hot climates, power plants, etc. If necessary the producer should be asked to include relevant information in the certificate [see 3.3.2(2)].

(5) Short-term relaxation losses at a temperature of the structure exceeding 60 °C can be 2 to 3 times those at 20 °C. However, in general, heat curing, over a short period, may be considered to have no effect on long term relaxation results (see

Figure 4.8 — Relaxation losses after 1 000 h at 20 °C

Characteristic 1 fPk' tensile strength

Figure 4.8 — Relaxation losses after 1 000 h at 20 °C Susceptibility to stress corrosion (1) The provisions of apply. Temperature dependent behaviour See separate Part on Fire Resistance. Design of members in prestressed concrete General

P(1) This section relates to structures where prestress is provided by fully bonded internal tendons. P(2) The effects of prestressing to be considered include:

— minimum requirements for concrete classes (

— minimum requirements for prestressing units (

— determination of the relevant prestressing force (2.5.4)

— transfer of prestressing forces and anchorage zone design for pre-tensioned members (

— anchorage zones in post-tensioned members (

(3) The provisions of 2.5.4 should be applied in all calculations relating to the effects of prestress both in global and local analysis and in section design for the ultimate and serviceability limit states. Minimum strength class for prestressed concrete

(1) The minimum class for post-tensioned members is | C25/30 |, and for pre-tensioned members is | C30/37 |. Minimum number of prestressing units in isolated structural elements

P(1) Isolated prestressed concrete members shall contain in the pre-compressed tensile zone a minimum number of prestressing units in order to ensure that, with an adequate reliability, a failure of a certain number of bars, wires or tendons does not lead to a failure of the member.

(2) P(1) above applies to structural prestressed members in which no additional load-carrying capacity due to redistribution of internal forces and moments, transverse redistribution of loads or due to other measures (e.g. normal steel reinforcement) exists.

(3) The requirement of P(1) above may be considered to be met if the minimum number of bars, wires or tendons given in Table 4.6 is provided. Table 4.6 assumes equal diameters of all bars, wires or tendons.

(4) The requirement may also be assumed to be satisfied if at least one strand with seven or more wires (wire diameter T 4.0 mm) is provided in the isolated member.

(5) If the actual number of bars, wires or tendons in the isolated member is less than the values given in Table 4.6, adequate reliability against failure should be demonstrated.

Table 4.6 — Minimum number of bars, wires and tendons in the pre-compressed tensile zone of isolated members

Type of unit

Minimum number

Individual bars and wires


Bars and wires, forming a strand or a tendon


Tendons except strands (see para (4) above)

|3| Initial prestressing force

P(1) The initial prestressing force shall be determined in accordance with 2.5.4, which also lists relevant facto affecting loss of prestress.

P(2) The maximum force applied to a tendon Po (i.e. the force at the active end, immediately after stressing, x = 0, see shall not exceed Ap . oo,max, where:

Ap is the cross-sectional area of the tendon and oo,max is the maximum stress applied to the tendon

°o,max = | fpk or = |090|fp0.1k, whichever is the lesser (4.5)

P(3) The prestressing force applied to the concrete immediately after tensioning (post-tensioning) or after transfer (pre-tensioning), i.e. Pmo = ApBpmo, shall not exceed the lesser of the forces determined from:

Ap • Opmo = | 075| fpk • Ap, or |0M| fp 0.1 k • Ap (4.6)

where Bpmo is the stress in the tendon immediately after tensioning or transfer.

(4) For pre-tensioned members, Pmo, in P(3) above, is calculated from Equation (4.7) below:

where APc, and APu(x) are defined in and APir is the short-term relaxation loss.

(5) For post-tensioned members, Pmo is calculated from (4.8) below.

(6) Methods for evaluating APs1, APc, APir and APu(x) are given in

P(7) The minimum concrete strength required at the time of tensioning or stress transfer shall be indicated in technical approval documents for the prestressing system concerned. Where such documents do not exist, requirements concerning reliability and performance should be considered. (8) The limiting values of P(2) and P(3) above are generally valid; they may be modified, however, depending on a number of factors, e.g.:

— whether it is possible to replace a damaged tendon,

— the consequences of the fracture of a tendons, in particular, danger to human life.

— the stress levels in the concrete due to prestressing,

— the grade of steel and type of tendon used,

— whether or not the tendons are subsequently bonded,

— the time when the grout is injected into the ducts.

— the possibility of achieving the required prestressing force in

— the tendon by overstressing when unexpectedly high friction is met; in this exceptional case, the maximum initial force Po may be increased to | 0.95 | fp 0.1 k • Ap. Loss of prestress

P(1) Loss of prestress shall be calculated in accordance with the principles in

(2) An estimate is required of the effective prestress at various stages considered in the design, and hence an allowance has to be made for appropriate losses of prestress due to the different factors given in Whenever possible, these calculations should be based on experience or on experimental data relating to the materials and prestressing methods to be used. For a wide range of structures, and in the absence of such data, the general recommendations given in (5)-(11) may be used, in approximately estimating the total loss of prestress.

(3) It is recommended that the actual values of prestressing losses at tensioning should be checked by measuring the prestressing force transferred from one end of the tendon to the other.

(4) Immediate losses should be calculated in accordance with (5) to (8) below. Time dependent losses should be calculated in accordance with (9)-(10) below.

(5) Loss of prestress due to anchorage slip (APsl) should be determined from experience and technical approval documents relating to the prestressing system to be used.

(6) Calculation of the immediate loss of force in the tendons due to elastic deformation of the concrete (APc) may be based on the values of the modulus of elasticity of the concrete given in and on the values for the prestressing steel given in

For pre-tensioning, the loss of prestress should be calculated on a modular ratio basis, using the stress in the adjacent concrete.

For post-tensioning, a progressive loss occurs when tendons are not stressed simultaneously. Where greater accuracy is not required, this should be calculated on the basis of half the product of the modular ratio and the stress in the adjacent concrete averaged along the length of the tendons.

(7) The short-term relaxation loss (APir), which occurs in pre-tensioning between stressing the tendons and transferring the stress to the concrete, should be estimated using the data in

(8) The loss of prestress in post-tensioned tendons due to friction [APu(x)] may be estimated from:


u is the coefficient of friction between the tendons and their ducts e is the sum of the angular displacements over a distance x (irrespective of direction or sign) k is an unintentional angular displacement (per unit length) related to the profile of the tendons.

u depends on the surface characteristics of the tendons and the duct, on the presence of rust, on the elongation of the tendon and on the tendon profile. In the absence of more exact data, for tendons which fill about 50 % of the duct, the following values for u may be assumed, when using equation (4.9).

cold drawn wire 0.17

strand 0.19

deformed bar smooth round bar

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