Design for serviceability of prestressed concrete - Concrete Structures: Stresses and Deformations - page 416

A = 6.00 m 2 ; I = 5.10 m 4 . Repetition of the above calculation using this

data gives:

σ q = 34.05 MPa

β D = 0.85

P m = 23 300 kN

Example 12.3: Effects of variation of span to thickness ratio on β D
For the closed bridge cross-section shown in Fig. 12.2(a), determine the
value of β D required for an allowable stress, above the interior supports,

σ allowable 2 MPa. Assume that the bridge deck is continuous over three

spans of lengths: 0.7 l , l and 0.7 l . Consider l

= −

= 30, 60 and 90 m and l / h

= 20, 25 and 30. In all cases use f 0 = h − 0.1 m and q = self-weight plus

32.5 kN/m; speci c weight of concrete 24 kN-m 3 .

Calculations similar to Example 12.1 give the results in Table 12.2
which indicate that

fi

β D varies between 0.94 and 0.69; the lower value is
approached with the increase in l or in l . The values of the mean
prestress force P m for each case are also given in the same table.

Table 12.2 Variation of the required balanced deflection factor D with the span l
and span to thickness ratio l /h. Bridge deck with spans 0.7 l , l and 0.7 l ;
closed cross-section (Fig. 12.2a); sustained load q = self-weight plus
32.5 kN-m; allowable permanent stress at top fibre above interior sup-
ports, allowable = − 2 MPa

l /h l = 30 l = 60 m l = 90 m

P m (kN) P m (kN) P m (kN) D D D

20 0.94 12 800 0.79 25 400 0.75 41 600

25 0.87 14 500 0.73 27 500 0.71 45 500

30 0.83 16 400 0.72 31 100 0.69 49 700

12.6 Transient stresses
The transient stress in concrete, caused by variable actions such as live

load and temperature variation when added to the sustained stress

∆ σ

σ perm
can produce irreversible opening of cracks and irreversible deformations.
The values of

∆ σ and σ perm will be used below (Section 12.9) to give the