Spx

Aa pr is the variation of stress in the tendons due to creep, shrinkage and relaxation at location x, at time t.

is the estimated shrinkage strain, derived from the values in Table 3.4 for final shrinkage (see also 2.5.5 and Appendix 1).

is Es/Ecm is the modulus of elasticity for the prestressing steel, taken from 3.3.4.4. is the modulus of elasticity for the concrete (Table 3.2)

is the variation of stress in the tendons at section x due to relaxation. This may be derived from Figure 4.8, for a ratio of initial stress/characteristic tensile stress, (Bp/fpk) calculated from:

a cg a cpo

Ac cp

where Bpgo is the initial stress in the tendons due to prestress and permanent actions.

For simplification, and conservatively, the second term in equation (4.11) may be ignored. For normal buildings, Bp may be taken as 0.85 Bpgo.

is a creep coefficient, as defined in 2.5.5, (see also Appendix 1).

is the stress in the concrete adjacent to the tendons, due to self-weight and any other permanent actions the initial stress in the concrete adjacent to the tendons, due to prestress is the area of all the prestressing tendons at the level being considered. is the area of the concrete section. is the second moment of area of the concrete section.

is the distance between the centre of gravity of the concrete section and the tendons

In using Equation (4.10), an assumed value of total loss will be required initially, to permit the term %Bpr on the right hand side to be evaluated (this term depends on the level of final prestress). An iterative process is therefore necessary to solve and balance the two sides of Equation (4.10).

(10) The loss of prestress calculated in accordance with (9) above should be added to that determined by (5)-(8) above to assess the final prestress (Pmz). It is important to remember that these procedures are approximate, and may be adjusted to suit particular materials, stressing or design conditions.

(11) The design procedures to take account of the effects of prestress should be in accordance with 2.5.4.

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