Wednesday, March 27, 2013
Monday, March 25, 2013
Thursday, March 21, 2013
Tuesday, March 19, 2013
Wednesday, March 6, 2013
So, today I began to write the VERY rough draft of my paper. I have an outline, and have begunt to fill in the research I have found for each topic. Right now the big challenge is figuring out the organization. I did some additional research/data gathering for the development of cable-stayed bridges. Right now I have around 15 pages of notes on the structure of bridges to condense. Goody. Here is what I found today (note- these are just copied and pasted from source material. not rewritten or condensed yet). I also have also continued to develop my outline by breaking down each of my topics into smaller areas and adding sources for each.
Development of the
Cable Stayed Bridge
Cable Stay type bridges have been around a lot longer than a
lot of people think and
can be traced back more than four centuries.
Many early bridges using cable stays incorporated both cable
stays and suspension
cables. One very famous example of this is the Brooklyn
Bridge in New York City, which
was completed in 1883.
In recent years, starting around the 1970s, cable stay
bridges have become increasingly
popular, as improvements in materials and technology have
resulted in cable stays
bridges becoming a fast and economical way to cross medium to
long spans (300 to
over 3000 feet).
Cable stays also have the advantage of being able to easily
incorporate extra towers, creating multi-span bridges which can be
several miles in length.
The concept of bridging long spans by suspended ropes or
chains anchored to a mast is
well known since ancient times. However, the system of
inclined cables was adopted in
combination with suspended cables for the first time in
Brooklyn Bridge, USA in 1932.
Cable stayed bridges have come a long way from the plump deck
girders of the
Stroemsund Bridge (1954) in Sweden, and find wide
applications all over the world
because of economy and elegant appearance. They are
considered generally economical
for spans of about 100 – 500 m; however, larger spans are not
uncommon. Because of
the aesthetics, they are adopted to short span and pedestrian
bridges as well.
Several fascinating and spectacular bridges have been
designed and built in the last few
decades than at any other comparable time in the annals of
civilisation (Rao 2003, and
Sakran 2010). A note worthy development in bridges is that of
cable stayed structures,
widely adopted all over the world since the 1960s because of
their elegance as well as
economy (Wittfoht 1984). Traditional suspension bridges
evolved into cable stayed
bridges that eliminated the need for strong anchorages of the
suspension cables thereby
reducing the impact on environment. Cable stayed bridges are
generally considered
advantageous for spans of about 100 – 500 m; however, larger
spans over 1 000 m are
not uncommon. Further, because of the elegant appearance, the
system is adopted to
spans less than 100 m, and to pedestrian bridges.
Another development in cable stayed bridges is the extradosed
system with short
pylon height, developed in the 1990s to combine the
advantages of the prestressing with
those of cable stays (Virlogeux 2002, and Sakran 2010).
Conventional cable stayed
bridges require high pylons (generally, span / 5) to support
the long span girders, leading
to large inclination of cables with the bridge axis (about
30° to 80°). The large
inclination of the cables results in significant variations
in the cable tension due to deck
deformations under live load (Walther 1988, and Gottemoeller
2004). Extradosed bridges
with short pylon heights (generally span / 10) have cables of
small inclination with bridge
axis (less than 30o), consequently low variation in cable
stresses.
However, cable stayed bridges are not built in Caribbean so
far despite their
elegance, economy and structural advantages. Wind and seismic
forces are significant in
Caribbean; cable stayed bridges would be advantageous because
of their better
performance under wind and seismic forces than other
conventional bridge systems.
AIM OF CABLE SUPPORTS IS TO REDUCE DEFLECTIONS AND FORCES ON
THE GIRDER
Stay cables carry
most of the vertical loads on the deck, usually about 85 – 95
percent. The
vertical component of the cable force supports the girders, and reduces
bending stresses,
while the horizontal component provides longitudinal prestress. Both
these effects
reduce forces and deflections in the girders.
Initially box
girder sections were adopted for torsional and lateral rigidity of the
deck, but flexible
deck systems with two longitudinal girders interconnected with cross
girders were
adopted successfully (Wittfoht 1984, and Virlogeoux 2002).
The system of
inclined cables was adopted in combination
with suspended
cables for the first time in Brooklyn Bridge, New York, USA in 1883
(Wittfoht 1984).
However, the diagonal cables were added later to stiffen the suspension
bridge, possibly
because of the inferior quality wire in the main cables.
Early structures
The cable stayed
systems were developed by European bridge engineers, primarily
German engineers,
to obtain optimum structural performance from material like steel
which was in short
supply during the post war years. The structural system was
subsequently
adopted with advantage to steel - concrete composite and concrete
structures. In
particular, the cable stayed girder system is adopted extensively for
medium and long
spans.
Popularization of
Cable Stayed bridge helped by development of analytical software for engineers
The bridges have
slender appearance to create a dramatic silhouette, making the
minimum
intervention in the landscape. The stay cables supporting the longitudinal deck
girders render the
structure transparent and delicate, and provide numerous elegant
alternative
profiles for the structural system.
While the
structural system was confined mainly to Western Europe and United
States in the
1970s and 1980s, it found application all over the world in the past three
decades. Cable
stayed bridges were adopted widely in Asian countries as well, especially
in Japan and
China, followed by India and Vietnam. Most of the bridges with the longest
spans are located
in Asia, particularly in China and Japan (Table 1).
Spans in excess of
500 m are generally considered to be the prerogative of
suspended cable
systems. However, the spans of cable stayed bridges have increased
from 182.6 m of
Stroemsund Bridge to 1 088 m of Sutong Bridge, China (2008),
exceeding the 890
m main span of Tatara Bridge, Japan (1995).
The earlier
structures were of single – span cable stayed bridges, but multi-span
structures with
total length of a few kilometers are also adopted (Rio-Antirrio, Greece,
2004 and Millau
Viaduct, France and Spain, 2004). Hybrid systems with suspended
cables and stay
cables close to the pylons are developed for spans in excess of 2 000 m,
and may be
constructed in near future.
The tall pylons of
cable stayed bridges are utilised to span deep valleys for
economy, elegance
and to minimise environmental impact of the structure. The 343 m
high pylons of
Millau Viaduct are as tall as the Empire State Building, USA (380 m
high), and taller
than Eiffel Tower (300.5 m high).
NEXT Development:
combination suspension and cable stayed bridges
EXTRADOSED BRIDGES
A further
development in cable stayed bridges is the extradosed bridges with short pylons
(Figure 4). The
behaviour of extradosed bridges is closer to that of prestressed concrete
structures than
conventional cable stayed systems. Mathivat conceived the concept first
in the late 1980s,
but was not adopted till the 1990s. Later, other designers took advantage of
classifying the
supporting cables from short pylons as prestressing tendons instead of
cable stays and
obtained competitive designs; the economy resulted from the
specifications for
stay cables being more stringent than those for prestressing tendons.
The concept caught
on with other designers, particularly the French, Portuguese,
Japanese, and
Indian engineers, adopting the concepts widely (Sakran 2010).
Such bridges have
a low ratio of pylon height to main span of about 0.10 resulting
in a flat cable
profile (inclined at about 10° – 25° with the horizontal) leading to large
longitudinal
forces in the girders. The stress variation in cables is much smaller than that
in conventional
cable stayed bridges, which justifies the classification of the cables as
extradosed tendons
and not as stays. However, for simply supported spans longer than
about 200 m, the
stress variation in cables could be appreciable, and it would be desirable
to limit the
maximum stresses as per the specifications applicable to stays.
Because of the
small inclination, extradosed tendons carry only about 10 – 30
percent of the
vertical loads. However, the extradosed bridges are economical because of
the larger
permissible stresses; the maximum permissible tension in tendons is 60 percent
of the ultimate
strength of steel, compared to the corresponding value of 40 percent in
cable stays. Most
of the codes permit higher stresses in concrete in extradosed bridges
than in cable
stayed structures.
Though extradosed
bridges are considered to be economical for main spans in the
range of 80 – 150
m, they have been successfully adopted for much longer spans (Sakran
and Rao 2008). The
bridges over the Ibi and Kiso rivers in Japan have main spans of a
little over 270 m.
Behavior under
LOADS
The behaviour of
cable stayed bridges under static load was investigated along with the
influence of pylon
height (Sakran 2010). Four - lane cable stayed bridges with spans of
100 + 200 + 100 m,
and framed pylon with height varying from 20 – 60 m above the deck
slab level
subjected to Indian Roads Congress (IRC) loading were analysed.
The height of
pylons above the bridge deck level influenced the behaviour of
cable stayed
bridges significantly. Vertical deflections of the longitudinal girders
decreased with
increased pylon height, while the horizontal deflections of pylons
increased. The
bending moments in pylons decreased with pylon height, while the axial
force increased.
The material quantities required generally increased with pylon height,
and extradosed
system was found to be more economical than conventional cable stayed
bridges with tall
pylons for the spans investigated.
BEHAVIOUR UNDER
DYNAMIC LOADS
Cable stayed
bridges rest on a limited number of supports (abutments, and pylons), which
can absorb the
differential displacements during seismic action (Walther 1988).
Consequently,
earthquake tremors and wind forces have little effect on cable stayed
bridges. They
dissipate earthquake shock energy efficiently because of large deflections,
the deck
oscillations, and differential lengths of cables. The vertical component of
seismic loading is
taken up by pylons and stays. The deck being suspended at a multitude
of points, local
deformations are restrained from exceeding the elastic limits. However,
the response of
the structures to horizontal excitation may be critical (Desai et al 2006).
Structural systems
with varying pylon heights were investigated for the dynamic
behavior, and for
the influence of the pylon height for main spans of 100.0, 150.0, 200.0
and 250.0 m
(Sakran 2010). The pylon height (above the deck) to main span ratio was
varied from 0.10
to 0.30 in steps of 0.05, while the ratio of the side spans to the main span
was adopted as
0.50. Framed pylons with a height of 15.0 m above ground level up to the
bridge deck
surface were assumed in the analyses.
The seismic response
of cable stayed bridges subjected to the data of El Centro
(USA, 1940),
Himachal Pradesh (India, 1986) and Gujarat (India, 2001) earthquakes
based on time -
history acceleration and time - history velocity was investigated. The
investigations
indicated that the structures were not sensitive to seismic effects for the
parameters
considered. However, the response of structures with pylon height to span
ratio less than
0.18 reduced the seismic response significantly, and appeared to mark the
limit of extradosed
bridges.
The response of
flexible structures under wind forces may be of concern. Long
span structures
are prone to high wind loads and flutter. While wind loads may induce
excessive
stresses, flutter may induce excessive displacements.
Flutter is
self-induced vibration produced by a change in the wind force as a result
of structural
motion. However, only a few sectional shapes are sensitive to the condition
of wind induced
oscillations building up to large amplitudes. Flutter occurs in cable
supported bridges
because of the aerodynamic coupling of torsional and vertical motions.
Some suspension
bridges failed due to wind induced oscillations; Tacoma Narrows
Bridge being the
well documented classical case.
However, unlike
suspension bridges, flutter and wind load are not significant in
cable stayed
bridges. The varying lengths of stay cables dampen the oscillations. The
large difference
between the first mode of flexure (vertical vibrations) and torsional mode
precludes the
possibility of flutter and wind effects being critical. Flutter is generally
not
significant, if
the structural frequency in the torsional mode is more than 2.5 times that of
the first vertical
mode.
For the structures
investigated, the first few modes of vibrations were in the
vertical
direction; torsional vibrations occurred in the sixth or higher mode. The ratio
of
the first
frequency in torsional mode and that in the first mode in flexure was found to
be
generally more
than 2.5, which precludes the possibility of flutter.
The dynamic
response, and behavior of the structures under seismic conditions
indicated their
suitability to regions prone to earthquake and wind hazards.
Subscribe to:
Posts (Atom)