Civil Engineering Reference
In-Depth Information
clear that this shortening will have a much greater effect on the fl atter catenary. Thus
the tension in a catenary that is too fl at would rise uncontrollably when it shortens,
leading to cracking of the concrete or the opening of construction joints.
The slope at the ends of a parabola may be expressed as 4 s/c. For a sag of 1/45,
this gives an end slope of 1/11.25 at mean temperature and under dead loads. This
gradient may confl ict with regulations for use of the bridge by people in wheelchairs,
which may be defi ned as a gradient not exceeding 1/20. At North Woolwich (
18.5.5
)
this was the specifi ed limiting gradient, and it was achieved by locally surcharging the
deck. However, this solution is only applicable to short spans, where the thickness of
surcharge remains only a few centimetres. A parabola with an end slope of 1/20 would
have a sag of only 1/80, which is not compatible with a concrete stressed ribbon that
would not be substantially cracked in cold weather.
Unlike a steel cable, the concrete catenary has a signifi cant bending stiffness. At
abutments and over piers, where the variations in sag cause changes to the curvature
of the ribbon, local bending moments are created that are too large to be carried by
the thin slab, making it necessary to thicken the deck locally with haunches. However,
the haunches increase the local stiffness of the slab, increasing the bending moments.
Consequently, they must be as shallow and as short as possible, and should have a
thickness that varies parabolically rather than linearly, to match closely the shape of
the bending moment diagram and to minimise their stiffening effect, Figure 18.27.
It is not desirable to design these haunches to the normal rules of fully prestressed
concrete, as this leads to excessive compressions in the deck, increasing the creep
shortening. A partially prestressed solution should be adopted. Under normal service
loads and at normal temperatures the deck should be uncracked, while under the effect
of extreme temperatures the deck should not be decompressed by the direct tension,
while the bending moments are carried in reinforced concrete action.
Concentrated live loads on the deck also create local curvature as it tries to behave
like a cable, adjusting its gradient either side of the load. Consequently local sagging
bending moments are generated beneath the load. If the stressed ribbon is only carrying
pedestrians, moments will be negligibly small. However if it carries vehicles, such local
moments may become signifi cant.
As all the bending moments on the deck are caused by imposed changes in curvature,
it is very important to use in the calculations an elastic modulus for the concrete that is
relevant to the duration of the load; dead loads, shrinkage and creep call for the lowest
modulus, seasonal temperature changes a higher modulus, daily temperature changes
higher yet and live loads the normal short-term value. The cracked inertia should
be used in the calculations in areas of high bending moment. Lightweight concrete
that has a lower modulus than dense concrete should have a role in stressed ribbon
bridges.
18.5.3 Intermediate pier crossheads
The design of intermediate pier crossheads further illuminates the particular
characteristics of concrete stressed ribbon bridges. Consider the crosshead shown in
Figure 18.25 (a), where the deck is carried by a pier consisting of a single central
column. The deck slab cantilevers either side of the column. If the deck had consisted
