Design for serviceability of prestressed concrete - Concrete Structures: Stresses and Deformations - page 408

12.2 Permanent state
Durability of concrete structures is closely linked to their serviceability in the
permanent state. This is de

ned here as the state of the structures subjected to
sustained loads such as the prestressing, the self-weight and the superimposed
dead loads and the quasi-permanent live loads. A prestressed structure may
be designed such that cracks occur only under the e

fi

ect of exceptional live
load combined with temperature variation. Such cracks open and close in
each cycle that the loads are applied. However, cyclic loading of cracked
structures produces residual opening of cracks and residual de

ff

fl ections which

are discussed in this chapter. Some bridges exhibit increasing de ections after

several decades in service. This is attributed partly to the irreversible curva-
ture which adds to the de

fl

fl ections due to the e ff ects of creep, shrinkage and

relaxation.
The approach adopted in this chapter to achieve satisfactory serviceability
is to limit the tensile stress in the permanent state to a speci fi ed value. This

can be achieved by designing the prestressing such that its e ect combined

with the sustained loads produce stress in concrete not exceeding the speci

ff

ed
value. In the permanent state the structure has no or only limited cracks; thus
any elastic analysis ignoring cracking is considered adequate to calculate the
stress in concrete due to the sustained loads and the prestressing combined.
In addition to the prestressing, the structure should have non-prestressed
reinforcement, the design of which is discussed below.

fi

12.3 Balanced deflection factor
The balanced de fl ection factor β D is de fi ned as the ratio between the

elastic de ections at mid-span due to prestressing and due to sustained

quasi-permanent loads:

fl

D ( P m )
D ( q )

β D = − (12.1)

where D ( P m ) is the de fl ection at mid-span due to prestressing. In the calcula-

tion of this de ection the prestressing force in a tendon is taken equal to the

mean of the initial prestressing force excluding friction loss and the force
remaining after losses due to creep and shrinkage of concrete and relaxation
of prestressed steel. D ( q ) is the elastic (immediate) de

fl

fl ection at mid-span due

to permanent and quasi-permanent load.
A parabolic tendon having constant prestressing force exerts on a prismatic
concrete member a uniform upward load. If, in addition, the permanent load
is uniform downward, the balanced de β D is the same as the

well-known balancing load factor, which is equal to minus the ratio of
the intensities of the upward and the downward loads. However, use of the

fl ection factor,