Monday, December 10, 2012
12/10/12 at 4:09
Today I began planning out my presentation, which I will present on Friday. Lots'o physics and math. You're welcome.
Thursday, December 6, 2012
I'm still working on getting through that one document. It's been difficult, as I have had to stop to look up many of the terms, which lead to other research. Basically, I have an armada of links to sort through. Here are my notes from today:
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
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
Tuesday, December 4, 2012
Today, I continued to collect information for my Thesis project. Specifically, I am still trying to understand the basic mechanics of a cable-stayed bridge so that I can apply them to the Margaret Hunt Hill Bridge. Copied from my notes for today:
Dead loads are static forces that are relatively constant for an extended time. They can be in tension or compression. The term can refer to a laboratory test method or to the normal usage of a material or structure. including the weight of the structure itself
Live loads are usually unstable or moving loads. These dynamic loads may involve considerations such as impact, momentum, vibration, slosh dynamics of fluids, etc. An impact load is one whose time of application on a material is less than one-third of the natural frequency of vibration of that material.
Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain in the elastic (initial, linear) portion of the stress-strain curve:
where
Linear
versus non-linear
For many materials, Young's modulus is essentially constant over a range of strains. Such materials are called linear, and are said to obey Hooke's law. Examples of linear materials are steel, carbon fiber and glass. Non-linear materials include rubber and soils, except under very small strains.
https://engineering.purdue.edu/~ahvarma/CE%20579/CE579_Half_course_summary.ppt.
– explains stability and buckling
P(cr) = critical load
P(cr) = critical load
n Bifurcation means the splitting of a main body into two
parts.
Energy approach – consists of writing the equation expressing the complete potential energy of the system. Analyzing this total potential energy to establish equilibrium and examine stability of the equilibrium state.
Energy approach – consists of writing the equation expressing the complete potential energy of the system. Analyzing this total potential energy to establish equilibrium and examine stability of the equilibrium state.
Energy method – slide 37
Harp, radial, fan,
Figure 19.7, or other cable configurations have all been used. However,
except
in very long span
structures, cable configuration does not have a major effect on the behavior of
the bridge.
the bridge.
A
fan-type cable arrangement can also be very attractive, especially for a
single-plane cable system.
Because
the cable slopes are steeper, the axial force in the girder, which is an
accumulation of all
horizontal
components of cable forces, is smaller. This feature is advantageous for
longer-span
bridges where compression in the girder may control the design.
A
harp-type cable arrangement offers a very clean and delicate appearance because
an array of
parallel cables will always appear parallel irrespective of the
viewing angle. It also allows an earlier start of girder construction because
the cable anchorages in the tower begin at a lower elevation.
A
radial arrangement of cables with all cables anchored at a common point at the
tower is quite
efficient. However, a good detail is difficult to achieve. Unless
it is well treated, it may look clumsy
Cables
Cables are the most important elements of a cable-stayed bridge.
They carry the load of the girder
and transfer it to the tower and the back-stay cable anchorage.
The cables in a cable-stayed bridge are all inclined, Figure 19.10. The actual stiffness of an inclined
cable varies with the inclination angle, a,
the total cable weight, G, and the cable tension force, T where E and A are Young’s modulus and the cross-sectional area of the cable.
And if the cable tension T changes from T 1 to T2, the equivalent cable stiffness will be
19.3 and 19.4
In
most cases, the cables are tensioned to about 40% of their ultimate strength
under permanent
load
condition. Under this kind of tension, the effective cable stiffness approaches
the actual values,
except
for very long cables. However, the tension in the cables may be quite low
during some
construction stages so that their effectiveness must be
properly considered.
A safety factor of 2.2 is usually recommended for cables. This
results in an allowable stress of
45% of the guaranteed ultimate tensile strength (GUTS) under dead
and live loads [9]. It is prudent
to note that the allowable stress of a cable must consider many
factors, the most important being
the strength of the anchorage assemblage that is the weakest point
in a cable with respect to capacity
and fatigue behavior.
Dead and live loads: http://www.britannica.com/EBchecked/topic/79272/bridge/72038/Live-load-and-dead-load
In order to carry traffic, the structure must have
some weight, and on short spans this dead load weight is usually less than the
live loads. On longer spans, however, the dead load is greater than live loads,
and, as spans get longer, it becomes more important to design forms that
minimize dead load.
Dead loads are static forces that are relatively constant for an extended time. They can be in tension or compression. The term can refer to a laboratory test method or to the normal usage of a material or structure. including the weight of the structure itself
Live loads are usually unstable or moving loads. These dynamic loads may involve considerations such as impact, momentum, vibration, slosh dynamics of fluids, etc. An impact load is one whose time of application on a material is less than one-third of the natural frequency of vibration of that material.
Young’s Modulus: Young's modulus, also
known as the tensile modulus, is a measure of the stiffness of
an elastic material and is a quantity used to
characterize materials. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's
law holds.[1] In solid
mechanics, the slope of the stress-strain curve at any point is called the tangent
modulus. The tangent modulus of the initial, linear portion of a
stress-strain curve is called Young's modulus. It can be experimentally
determined from the slope
of a stress-strain curve created during tensile
tests conducted on a sample of the material. In anisotropic
materials, Young's modulus may have different values depending on the direction
of the applied force with respect to the material's structure.
Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain in the elastic (initial, linear) portion of the stress-strain curve:
where
E is the Young's modulus (modulus of
elasticity)
F is the force exerted on an object under
tension;
A0 is the original cross-sectional area
through which the force is applied;
ΔL is the amount by which the length of the
object changes;
L0 is the original length of the object.
Linear
versus non-linear
For many materials, Young's modulus is essentially constant over a range of strains. Such materials are called linear, and are said to obey Hooke's law. Examples of linear materials are steel, carbon fiber and glass. Non-linear materials include rubber and soils, except under very small strains.
1.
Anchorage Assembly: [PPT]
www.ce.sc.edu/.../rizos/.../Members%20in%20Tension%20-%20I.ppt
Friday, November 30, 2012
As I have showcased irresponsibility and forgotten my flash drive, this post will serve for my notes today. At least it proves I was working. Check this out:
http://www.structuremag.org/article.aspx?articleid=768
Evolution of the Cable-stayed bridge
Construction technology and material science for bridges have been an important part of advancing cable stayed bridge technology. Material advancements introduced into bridge applications include self-consolidating concrete, stainless steel, higher strength concretes and composite fibers.
- Gives overview of 9 different cable-stayed bridges, both radial and parallel design. Bridges chosen for some design element they made use of.
Experience from these completed cable-stayed bridges has shown that the torsional rigidity of a closed cell box girder superstructure enhances structural response to wind loading during construction and eliminates the need for temporary stabilization attachments. Unique features such as precast delta frames and struts can expand the box girder to a system that allows the use of single pylons with a single plane of stays. This pre-fabrication and streamlined approach to long spans contributes to quicker construction. The cable-stayed system of continuous strands, with anchors only at deck level, creates easy access to the stays inside the box girder superstructure for both construction and future inspection. In addition to the economical use of cable-stayed bridges for spans of 600 feet to 1,500 feet and greater, the configurations offer an elegance that also addresses communities’ interests in creating exciting landmark bridges for the future.
http://freeit.free.fr/Bridge%20Engineering%20HandBook/ch19.pdf
THE MOST BEAUTIFUL LINK EVER.
Seriously. Explains everything about cable-stayed bridges, in different spans, from and engineer's bridge handbook. Will take a while to read though. Notes to follow:
contributes to the economy of a cable-stayed bridge.
quick link interjections, to explain other terms: Axial v. flexural stress
http://arch.umd.edu/Tech/Tech_III/Lectures/Flexure/Principles_of_Flexure.pdf
http://www.areforum.org/forums/showthread.php?132647-Axial-vs-Flexural-stress
as intermediate supports for the girder so that it could span a longer distance.
- look up global bending moment - http://web.aeromech.usyd.edu.au/AMME2301/Documents/mos/Chapter05.pdf
http://www.cee.lsu.edu/people/cai/J1998-Composite%20Girder%20Design%20of%20Cable-Stayed%20Bridges.pdf
modern cable-stayed bridges.
the bridge.
I only mangaged to get 1.5 sections into 7, but this hopefully will explain the basic mechanics of cable-stayed bridges so that I can apply them to the Margaret Hunt Hill Bridge.
http://www.structuremag.org/article.aspx?articleid=768
Evolution of the Cable-stayed bridge
Construction technology and material science for bridges have been an important part of advancing cable stayed bridge technology. Material advancements introduced into bridge applications include self-consolidating concrete, stainless steel, higher strength concretes and composite fibers.
- Gives overview of 9 different cable-stayed bridges, both radial and parallel design. Bridges chosen for some design element they made use of.
Experience from these completed cable-stayed bridges has shown that the torsional rigidity of a closed cell box girder superstructure enhances structural response to wind loading during construction and eliminates the need for temporary stabilization attachments. Unique features such as precast delta frames and struts can expand the box girder to a system that allows the use of single pylons with a single plane of stays. This pre-fabrication and streamlined approach to long spans contributes to quicker construction. The cable-stayed system of continuous strands, with anchors only at deck level, creates easy access to the stays inside the box girder superstructure for both construction and future inspection. In addition to the economical use of cable-stayed bridges for spans of 600 feet to 1,500 feet and greater, the configurations offer an elegance that also addresses communities’ interests in creating exciting landmark bridges for the future.
Book to buy - don't buy, can see it all in the preview
Cable Stayed, Supported And Suspension Bridges
By P. Dayaratnamhttp://freeit.free.fr/Bridge%20Engineering%20HandBook/ch19.pdf
THE MOST BEAUTIFUL LINK EVER.
Seriously. Explains everything about cable-stayed bridges, in different spans, from and engineer's bridge handbook. Will take a while to read though. Notes to follow:
For spans up to about 1000 m, cable-stayed bridges are more economical.
A bridge carries mainly vertical loads acting on
the girder,
Figure 19.1. The stay cables provide intermediate supports for the girder so that it can
span a long distance. The basic structural form of a cable-stayed bridge is a series of overlapping
triangles comprising the pylon, or the tower, the cables, and the girder. All these members are under
predominantly axial forces, with the cables under tension and both the pylon and the girder under
compression. Axially loaded members are generally more efficient than flexural members. This
quick link interjections, to explain other terms: Axial v. flexural stress
http://arch.umd.edu/Tech/Tech_III/Lectures/Flexure/Principles_of_Flexure.pdf
http://www.areforum.org/forums/showthread.php?132647-Axial-vs-Flexural-stress
At the early stage, the idea of a cable-stayed bridge was to use cable suspension to replace the piers
as intermediate supports for the girder so that it could span a longer distance.
The bending moment in the girder under a specific load can be thought of as consisting of
a local component and a global component. The local bending moment between the cables is
proportional to the square of the spacing. The global bending moment of an elastically supported
girder is approximately - look up global bending moment - http://web.aeromech.usyd.edu.au/AMME2301/Documents/mos/Chapter05.pdf
http://www.cee.lsu.edu/people/cai/J1998-Composite%20Girder%20Design%20of%20Cable-Stayed%20Bridges.pdf
Considering that the function of the cables is to carry the loads on the bridge girder, which
remains the same, the total quantity of cables required for a bridge is practically the same independent
of the number of cables, or cable spacing,
Figure 19.4. But if the cable spacing is smaller, the
local bending moment of the girder between the cables is also smaller. A reduction of the local
bending moment allows the girder to be more flexible. A more flexible girder attracts in turn less
global moment. Consequently, a very flexible girder can be used with closely spaced cables in many
modern cable-stayed bridges.
Harp, radial, fan,
Figure 19.7, or other cable configurations have all been used. However, except
in very long span structures, cable configuration does not have a major effect on the behavior of
the bridge.
I only mangaged to get 1.5 sections into 7, but this hopefully will explain the basic mechanics of cable-stayed bridges so that I can apply them to the Margaret Hunt Hill Bridge.
Wednesday, November 28, 2012
Monday, November 26, 2012
Monday, November 19, 2012
Friday, November 9, 2012
Monday, November 5, 2012
Tuesday, October 30, 2012
Friday, October 26, 2012
Wednesday, October 24, 2012
Monday, October 22, 2012
Thursday, October 18, 2012
Tuesday, October 16, 2012
Today I contacted the Trinity Trust Project to set up a visit. This was recommended to me by my mentor and other advisors at City Hall. I hope to see models and other basic information about the bridge, as well as viewing two documentaries on the construction on the bridge they have at their office.
Friday, October 5, 2012
Wednesday, October 3, 2012
Monday, October 1, 2012
I believe that my presentation went moderately well, as far as getting the information across goes. I was incredibly nervous, so my delivery was rushed, and I looked at my note cards far to often. My transitions could have been smoother, but I didn't forget any large chunks of information. For next time, I will work on staying calm and knowing my presentation better, so it feels more natural.
Wednesday, September 19, 2012
Monday, September 17, 2012
Thursday, September 13, 2012
Friday, September 7, 2012
Wednesday, September 5, 2012
Friday, August 31, 2012
Thursday, August 30, 2012
Saturday, August 25, 2012
The Beginning
My name is Alia Eckardt, and I am currently a senior at TAG Magnet. This blog is dedicated to my senior thesis class, as well as to the progress of my college application process. Right now, my thesis project involves civil and/or structural engineering, my hopeful college major. I would like to look at the design and construction process of one particular structure in Dallas, possibly the Hunt Hill Bridge, as it would have significant coverage and documentation. I have met and talked with a possible mentor, a young civil engineer who works at a firm in Dallas, who has connections to a foundation that promotes women in science and technology. I was accepted into the Women in Engineering program at Cornell in the Fall, and hope to make more connections there.
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