Design for serviceability of prestressed concrete - Concrete Structures: Stresses and Deformations - page 409

balanced de fl ection factor is preferred here because it applies with any tendon

pro le and with members having variable depth.

The signi

fi

ection factor is explained by Fig. 12.1,
which depicts the strain distribution in a section of members having

fi cance of the balanced de fl

β D = 0

and 1. In the former the strain at the centroid, ε O = 0 and the curvature, ψ ≠ 0;

in the latter ε O ≠ 0 and ψ = 0. We recognize that with β D = 0, the member is

non-prestressed and with β D = 1, the prestressing is just su cient to eliminate

the de ection.

In determining

fl

ection is calculated using the
cross-sectional area properties of gross concrete sections and an estimated
reduction of the prestressing forces to account for the time-dependent losses
due to creep, shrinkage and relaxation. Because the analysis is concerned with
the behaviour of the structure during its service life, it is suggested that the
prestressing force used in calculating

β D by Equation (12.1), the de fl

β D be the average of the values before

and after the time-dependent losses.

12.4 Design of prestressing level
In the design of a prestressed structure the level of prestressing, expressed by
the balanced de

β D , can be a means of controlling cracks in
service condition. For this purpose the structure can be designed such that the
stress at a speci

fl ection factor

fi ed fi bre due to prestressing combined with sustained quasi-

permanent loads, σ perm satisfy the condition:

σ perm σ allowable (12.2)

where σ allowable is an allowable stress value depending upon the width of cracks

that can be tolerated and the amount of non-prestressed reinforcement that is

Figure 12.1 Strain distribution in a cross-section of members having the balanced
deflection factors D = 0 and 1.