Civil Engineering Reference
In-Depth Information
hand, Benaim's Sungai Dinding Bridge in Malaysia, Figure 17.16, which had a slender
steel composite deck, and Maillart's Salginatobel Bridge, Figure 1.18, are examples of
bridges where the arch ring has been designed to carry most of the bending moments.
It is also possible to design the bridge such that the bending moments are shared more
or less equally.
For long-span bridges, such as the Krk Bridge, Figure 17.19, the arch needs to be
deep to resist buckling and it naturally carries the bending moments. When the deck
consists of a series of statically determinate spans, it clearly cannot relieve the arch of
any bending moment.
17.7.3 Effect of shortening of the arch and spreading of the abutments
Reinforced concrete arches must be designed to resist the effects of shortening of
the arch ring due to elastic and creep deformations under compression, concrete
shrinkage and temperature drop. These effects cause the crown to drop and induce
sagging bending moments at mid-span and hogging moments at the springings of a
monolithic arch. Spreading of the abutments as a response to the thrust causes bending
moments similar to those due to arch shortening. The thicker and stiffer the arch, the
greater these moments will be. Consequently, it is important to keep the arch as thin as
possible, compatible with stability and with the strength necessary to carry the bending
moments due to point loads.
Reinforced concrete arches generally have a span/rise ratio of between 4 and 8.
However arches with a rise of span/10 or even fl atter can be designed. The fl atter the
arch, the greater the effects of shortening will be. This may be easily understood by the
fact that the length of an arch with a rise of 1/5 is about 10 per cent greater than the
span, while for a rise of 1/10, it is only 2.6 per cent greater.
The arch shortening/spreading of foundations are imposed deformations that can
cause cracking, but in most cases cannot cause collapse. However, these actions change
the geometry of the arch, and so induce second order effects. For arches with a span/
rise ratio of about 8 or less, these second order effects are not signifi cant. However,
for very fl at arches, the changes in geometry may be signifi cant, increasing the bending
moments in the arch and even threatening its survival.
17.7.4 Instability of arches
As arches are in compression, they must be checked against buckling instability.
Generally, when the bridge has been designed so that the bending moments are
carried by the arch, a thickness in the plane of the arch of span/60 at the crown is
likely to provide a satisfactory factor of safety as the arch shape inhibits in-plane
buckling. When the bending moments are carried by the deck, the arch thickness is
governed by criteria other than general buckling, such as compressive stress, bending
moments, local buckling between points of liaison with the deck or stability during
construction.
Buckling perpendicular to the arch plane is similar to conventional strut behaviour,
and the arch rib should be checked and reinforced as a strut as a fi rst approximation.
However, due to the curvature of the arch, its torsional strength is mobilised in any
lateral defl ection. A slenderness of 1/30 for an arch fi xed in the plane of buckling,
and 1/20 for a pinned structure are likely to be satisfactory, although more slender
