Design for serviceability of prestressed concrete - Concrete Structures: Stresses and Deformations - page 414

1 − ( − 2.0)/6.97

β D

1.168)]

= 0.79

1 + 9.51/[8( − 0.0763)(7.25)(2.9)( −

The absolute value of mean prestressing force should exceed
(Equation (12.11) ):

0.79 (206.5 × 10 3 )(60) 2
8(2.9)

P m = = 25 200 kN.

Table 12.1 gives the variation of β D for the same structure when the

allowable stress, 4.4 MPa. The same

table indicates the sensitivity of the permanent stress,

σ allowable is varied between + 2.4 and −

σ perm to the vari-
ation of the prestressing force. The table shows the typical result that
the absolute value of the sustained compressive stress drops rapidly
with the decrease of β D . In this example a change of β D from 1.0 to 0.6

varies σ perm from − 4.4 to 0.1 MPa. We recall that β D = 1.0 corresponds to

zero curvature (Fig. 12.1), or zero de fl ection. With β D = 0.6 the curva-

ture, the de ection and the cracking can be critical, particularly when

the transient stress due to live load and temperature,

fl

is high. Table
12.1 also demonstrates the typical result that the reserve compressive
stress

∆ σ

σ perm can be substantially eroded when the actual time-dependent
prestress loss is greater than estimated (e.g. when P m actual

= 0.9 P m ). This

can cause σ perm to become small compressive or even tensile, causing the

residual cracking and the residual de ection to be critical, after cyclic

application of exceptional live load and temperature variation.
The values on the last line of Table 12.1 are calculated for the open
cross-section shown in Fig. 12.2(b), with h

fl

= 3 m and area properties: A

= 6.00 m 2 ; I = 5.10 m 4 ; y t = − 0.813 m; q = 176.5 kN-m; other data are the

Table 12.1 Variation of the permanent stress, perm with the balanced deflection
factor D . The table also gives variation of the required D for a given
allowable stress, allowable . Three-span bridge of Example 12.1, Fig. 12.2(a)
and (b) with h = 3m

Balanced deflection factor, D 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Top fibre stress perm or allowable
(MPa); closed box section,
Fig. 12.2(a) 2.41 1.27 0.13 − 1.00 − 2.14 − 3.28 − 4.42

Top fibre stress perm or allowable
(MPa); open section, Fig. 12.2(b) 2.81 1.58 0.35 − 0.88 − 2.11 − 3.33 − 4.56