Civil Engineering Reference
In-Depth Information
are carried out. It will be seen that the outer limits of the cable zone at positions of
maximum and minimum moment are often defi ned by the limiting eccentricity.
The upper and lower limits of the cable zone should be plotted at every tenth point
along the spans, giving a zone of the general shape shown in Figure 6.5.
As described for the statically determinate beam, the cable zone will be very narrow
at design sections which determine the prestress force, generally supports and mid-
span, and wider in between. The prestress centroid must lie between the two limits
defi ned by this cable zone.
However, the position of this cable zone within the depth of the beam is dependent
on the value of
M
p
chosen, and the designer is not sure whether this
M
p
is in fact
achievable. This may be checked by calculating the
M
p
that results from a cable profi le
placed fi rstly along the top of the zone, and then from a profi le placed along the
bottom of the zone. If these two profi les give rise to values of
M
p
that bracket those
chosen, then it is clear that there exists a cable profi le between the two limits that
will give rise to parasitic moments equal to those chosen. The designer then has to
place the cable centroid within the cable zone so that he achieves the desired parasitic
moments, using the techniques described in
6.20
.
6.17 Prestress scheme 2
Scheme 1 involves 9 tendons in each web, extending over the full length of the deck.
Although it is possible to use tendons of 152 m length, the friction losses are likely
to make the option uneconomical. It would be necessary either to couple tendons or
to overlap them to reduce the maximum length. An alternative scheme would be as
shown in Figure 6.21 (a). Here half the tendons are overlapped over piers 2.0 and 4.0,
where the design was the tightest, and where the
M
p
required was rather close to the
maximum that is likely to be achievable. The new arrangement provides 8 tendons per
web, yielding a total of 19.2 MN at sections 1.4, 2.5, 3.0, 3.5 and 4.6, and 12 tendons
yielding 28.8 MN at sections 2.0 and 4.0. Furthermore, assuming that the anchorage
points of the cables that are stopped off are 5 m either side of the penultimate piers,
the total length of prestressing tendon has been reduced by some 5 per cent.
The equations of
6.16.1
may be used to discover the acceptable ranges of
M
p
with
the newly defi ned forces.
•
•
•
•
From equation 1,
M
p
at section 1.4 must not exceed 1.44 MNm
From equation 2,
M
p
at section 2.0 must not be less than 3.14 MNm
From equation 4,
M
p
at section 2.5 must not exceed 9.24 MNm
From equation 6,
M
p
at section 3.0 must not be less than 12.69 MNm
Thus a scheme with
M
p
of 3.5 MNm at section 2.0 and 12.7 MNm at section 3.0,
yielding 1.4 MNm at section 1.4 and 8.1 MNm at section 2.5, satisfi es all criteria,
although the
M
p
required at section 3.0 is almost as large as that previously found at
pier 2.0, Figure 6.21 (b).
These two examples illustrate how the basic equations allow the designer to refi ne
his prestressing scheme, and defi ne the parasitic moments that are required to make
it work.
