Prestressing for continuous beams - The Design of Prestressed Concrete Bridges - page 168

150 kN respectively. Thus for a prestress force of 22 MN, we would need 220 of the
13 mm strand, and 147 of the larger size.
We will adopt 9 tendons of 12 No 13 mm strands in each web, although this falls
marginally short of the required 220 strand, providing 21.6 MN of force. However,
there is no point in seeking too much precision, as the working prestress force per
strand will only be fi nalised once a calculation of prestress losses has been carried out.
The following calculations will be carried out with P = 22 MN.
These tendons may be arranged in a variety of ways. Two possibilities will be
illustrated:
a) The tendons are all located inside the web reinforcement, Figure 6.19 (a). This
arrangement is simpler to build, but it would not be possible to achieve the
eccentricity adopted in the calculation. The prestress sizing exercise would need
to be redone, and a greater prestress force adopted.
b) The tendons are located partially outside the web reinforcement, Figure 6.19 (b).
This arrangement allows the designer to maximise the prestress eccentricity and
has generally been adopted by the author in his practice. It requires more careful
design and detailing, but is more economical.
The tendon arrangements shown are based on UK practice where they are spaced at
two times their internal duct diameters.
6.16.6 Plotting the cable zone
With the assumed P and M p , and with design sections at tenth points of each span,
the upper and lower limits of the cable zone may be plotted, using the techniques
explained in 5.14 . It will initially be assumed that the limiting stresses are zero on both
extreme fi bres.
For instance, at section 1.4:
P = 22 MN
M p = +5.2 MNm
M max = +31.1 MNm
M min = +14.4 MNm.
Then, under the maximum moment the centre of pressure must not rise above the
top of the kern, while under minimum moment it must not fall below the bottom of
the kern. Consequently the upper limit of the cable zone is plotted down from the top
of the kern by a distance ( M max + M p )/ P = (+31.1 + 5.2) /22 = 1.65 m, and the lower
limit of the zone is plotted down from the bottom of the kern by ( M min + M p )/ P =
(+14.4 + 5.2)/22 = 0.891 m. The sign convention is that sagging moments are
positive, and positive dimensions are plotted down from the relative kern limit.
For section 2.0:
P = 22 MN
M p = +13 MNm
M max = -25.5 MNm
M min = - 44.7 MNm.