Cables continued
Over
the years, many new cable systems have been successfully used. Parallel wire
cables with
Hi-Am
sockets were first employed in 1969 on the Schumacher Bridge in Mannheim,
Germany.
Since
then, the fabrication technique has been improved and this type cable is still
one of the best
cables
commercially available today. A Hi-Am socket has a conical steel shell. The
wires are parallel
for
the entire length of the cable. Each wire is anchored to a plate at the end of
the socket by a
button
head. The space in the socket is then filled with epoxy mixed with zinc and
small steel balls.
The
Hi-Am parallel wire cables are prefabricated to exact length in the yard and
transported to
the
site in coils. Because the wires are parallel and therefore all of equal
length, the cable may
sometimes
experience difficulty in coiling. This difficulty can be overcome by twisting
the cable
during
the coiling process. To avoid this problem altogether, the cables can be
fabricated with a
long lay. However, the long lay may cause a very short cable to
twist during stressing.
http://navyaviation.tpub.com/14018/css/14018_142.htm
- explains lay lengths
Threadbar tendons were used for some stay cables. The first one was for the Hoechst Bridge over the
Threadbar tendons were used for some stay cables. The first one was for the Hoechst Bridge over the
Main
River in Germany. The Penang Bridge and the Dames Point Bridge also have bar
cables. They all
have
a steel pipe with cement grout as corrosion protection. Their performance has
been excellent.
The
most popular type of cable nowadays uses seven-wire strands. These strands,
originally
developed
for prestressed concrete applications, offer good workability and economy. They
can
either
be shop-fabricated or site-fabricated. In most cases, corrosion protection is
provided by a
high-density
polyethylene pipe filled with cement grout. The technique of installation has
progressed
to
a point where a pair of cables can be erected at the site in 1 day.
In
search of better corrosion protection, especially during the construction stage
before the cables
have
been grouted, various alternatives, such as epoxy coating, galvanization, wax
and grease have
all
been proposed and used. Proper coating of strands must completely fill the
voids between the
wires
with corrosion inhibitor. This requires the wires to be loosened before the
coating process
takes
place and then retwisted into the strand configuration.
In
addition to epoxy, grease, or galvanization, the strands may be individually
sheathed. A
sheathed
galvanized strand may have wax or grease inside the sheathing. All three types
of additional
protection
appear to be acceptable and should perform well. However, a long-term
performance
record
is not yet available.
The most important element in a cable is the anchorage. In this
respect, the Hi-Am socket has
an excellent performance record. Strand cables with bonded
sockets, similar to the Hi-Am socket,
have also performed very well. In a recently introduced unbonded
anchorage, all strands are being
held in place only by wedges. Tests have confirmed that these
anchorages meet the design requirements.
But unbonded strand wedges are delicate structural elements and
are susceptible to construction
deviations. Care must be exercised in the design, fabrication, and
installation if such an
anchorage is to be used in a cable-stayed bridge. The advantage of
an unbonded cable system is
that the cable, or individual strands, can be replaced relatively
easily.
Cable anchorage tests have shown that, in a bonded anchor, less
than half of the cyclic stress is
transferred to the wedges. The rest is dissipated through the
filling and into the anchorage directly
by bond. This is advantageous with respect to fatigue and
overloading.
The Post Tensioning Institute’s “Recommendations for Stay Cable
Design and Testing,” [9] was
published in 1986. This is the first uniformly recognized criteria
for the design of cables. In conjunction
with the American Society of Civil Engineers’ “Guidelines for the
Design of Cable-Stayed
Bridges” [10], they give engineers a much-needed base to start
their design.
GIRDER
-just read whole
section. Not much I can pull out of it.
TOWER
-most aesthetic
aspect
-clean and simple preferable
-clean and simple preferable
Figure 19.15
Although
early cable-stayed bridges all have steel towers, most recent constructions
have concrete
towers.
Because the tower is a compression member, concrete is the logical choice
except under
special
conditions such as in high earthquake areas.
Cables
are anchored at the upper part of the tower. There are generally three concepts
for cable
anchorages at the tower: crisscrossing, dead-ended, and saddle.
Crisscrossing the cables at the tower is a good idea in a
technical sense. It is safe, simple, and
economical. The difficulty is in the geometry. To avoid creating
torsional moment in the tower
column, the cables from the main span and the side span should be
anchored in the tower in the
same plane, Figure 19.15. This, however, is physically impossible if they
crisscross each other. One
solution is to use double cables so that they can pass each other
in a symmetrical pattern as in the
case of the Hoechst Bridge. If A-shaped or inverted-Y-shaped
towers are used, the two planes of
cables can also be arranged in a symmetrical
pattern.
If the tower cross section is a box, the cables can be anchored at
the front and back wall of the
tower, Figure 19.16. Post-tensioning tendons are used to prestress the
walls to transfer the anchoring
forces from one end wall to the other. The tendons can be loop
tendons that wrap around three
side walls at a time or simple straight tendons in
each side wall independently.
As
an alternative, some bridges have the cables anchored to a steel member that
connects the
cables
from both sides of the tower. The steel member may be a beam or a box. It must
be connected
to
the concrete tower by shear studs or other means. This anchorage detail
simulates the function
of
the saddle. However, the cables at the opposite sides are independent cables.
The design must
therefore consider the loading condition when only one cable
exists. FIGURE 19.6
DESIGN
PERMANENT LOAD CONDITIONS –
A
cable-stayed bridge is a highly redundant, or statically indeterminate
structure. In the design of
such
a structure, the treatment of the permanent load condition is very important.
This load
condition
includes all structural dead load and superimposed dead load acting on the
structure, all
prestressing
effects as well as all secondary moments and forces. It is the load condition
when all
permanent loads act on the structure.
Because
the designer has the liberty to assign a desired value to every unknown in a statically
indeterminate
structure, the bending moments and forces under permanent load condition can be
determined
solely by the requirements of equilibrium, ΣH = 0,
Σ
V = 0,
and Σ M= 0. The stiffness
of
the structure has no effect in this calculation. There are an infinite number
of possible combinations
of
permanent load conditions for any cable-stayed bridge. The designer can select
the one
that is most advantageous for the design when other loads are
considered.
In statics, a structure is statically indeterminate (or hyperstatic)[1] when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure.
Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are
Σ H = 0: the sum of the horizontal components of the forces equals
zero;
Σ V = 0: the sum of the vertical components of forces equals zero;
Once
the permanent load condition is established by the designer, the construction
has to
reproduce
this final condition. Construction stage analysis, which checks the stresses
and stability
of
the structure in every construction stage, starts from this selected final
condition backwards.
However,
if the structure is of concrete or composite, creep and shrinkage effect must
be calculated
in
a forward calculation starting from the beginning of the construction. In such
cases, the calculation
is
a combination of forward and backward operations.
The construction stage analysis also provides the required
camber of the structure during construction.
LIVE LOAD
Live-load
stresses are mostly determined by evaluation of influence lines. However, the
stress at a
given
location in a cable-stayed bridge is usually a combination of several force
components. The
stress,
f,
of a point at the bottom flange, for example, can be expressed
as: 19.5
where
A is
the cross-sectional area, I is the moment of inertia, y is the distance from the neutral axis, and c is a stress influence coefficient due to
the cable force K anchored
at the vicinity. P is
the axial force and M is
the bending moment. The above equation can be rewritten as 19.6
where
the constants a1, a2, and a3 depend on the effective width, location of the point, and
other
global
and local geometric configurations. Under live load, the terms P, M, and K are individual influence lines. Thus, f is a combined influence line obtained by
adding up the three terms multiplied by the corresponding constants a1, a2, and a3, respectively.
In
lieu of the combined influence lines, some designs substitute
P, M,
and
K
with
extreme values,
i.e.,
maximum and minimum of each. Such a calculation is usually conservative but
fails to present
the
actual picture of the stress distribution in the structure.
http://kma.go.ke/ama/presentations/Lecture14.pdf
- SHEAR FORCE LECTURE
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