Design for serviceability of prestressed concrete - Concrete Structures: Stresses and Deformations - page 413

For a chosen value of β D , the permanent stress is (Equations (12.7) and

(12.11) ):

σ perm = σ q [1 − β D (1 + I/ ( 8 α q Af 0 y )] (12.12)

12.5 Examples of design of prestress level
in bridges
Figures 12.2(a) and 12.2(b) represent cross-sections of bridges that will be
used in design examples and in parametric studies. The thickness h will
be varied as well as the span to thickness ratio l / h .

Example 12.1 Bridges continuous over three spans
Consider a bridge deck having a constant cross-section shown in Fig.
12.2(a), continuous over three spans 0.7 l , l and 0.7 l , with l = 60 m and

h = 3 m. The cross-sectional area properties are: A = 7.25 m 2 ; I =

9.51 m 4 ; the y coordinate of the top- -1.168 m. In addition to

its self-weight (24 kN-m 3 ), the deck carries a sustained dead load of
32.5 kN-m. Thus, the total permanent load is: q

fi bre is y =

= 32.5 + 24 (7.25) =

206.5 kN-m. Assume a parabolic tendon pro fi le (Fig. 12.3) with f 0 =

h β D and the required

mean prestressing force, P m such that the permanent stress at top

− 0.1 m. Determine the balanced de fl ection factor

fi bre

over the two interior supports equal the allowable stress, σ allowable =

− 2MPa.

For a continuous beam of the speci ed spans, the bending moment

over the two interior supports is (by elastic analysis):

fi

0.0763 ql 2 ; thus

M q = − α q = − 0.0763

α q can be more accurately calculated by considering the
fact that over a short distance over the supports, the actual pro

The value

fi le of

the tendon should be convex to avoid sudden change in direction.
The hypothetical stress value at top

fi bre if q were applied without

prestressing (Equation (12.9) ):

0.0763 (206.5 × 10 3 ) (60) 2 (

− 1.168)

9.51

σ q = − = 6.97 MPa

The balanced de fl ection factor is (Equation (12.8) ):