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.

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:

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

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

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

• : the vectorial sum of the forces acting on the body equals zero. This translates to

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;

• : the sum of the moments (about an arbitrary point) of all forces equals zero.

https://docs.google.com/viewer?a=v&q=cache:nY1veEFtgDUJ:www.fao.org/docrep/015/i2433e/i2433e03.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESgRTASZGysKGiZQHuhddZ0bAfG3IOBLSrFlcDfHTUEMJoISvRFKcycgQf0K7_02yXcN3j_Ixkg8fnQMMZvJtBn0A9wk1Zf_imr3MtSXYkwydq8p7c_EIkGAiqAutAzpFDy2wke1&sig=AHIEtbTqNdaBECHp6hqu1TEvsC6NKN6lAA – force balancing, READ NEXT

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://www.public.iastate.edu/~fanous/ce332/influence/homepage.html - INFLUENCE LINES

http://people.virginia.edu/~pjm8f/engr162/beam/shear_force_and_bending_moment.htm - SHEAR FORCE

http://kma.go.ke/ama/presentations/Lecture14.pdf - SHEAR FORCE LECTURE

http://www.codecogs.com/reference/engineering/materials/shear_force_and_bending_moment.php - ALSO SHEARING FORCE

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:

https://engineering.purdue.edu/~ahvarma/CE%20579/CE579_Half_course_summary.ppt. – explains stability and buckling
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 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.

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]

Tension Members

www.ce.sc.edu/.../rizos/.../Members%20in%20Tension%20-%20I.ppt

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.

Book to buy - don't buy, can see it all in the preview

Cable Stayed, Supported And Suspension Bridges

By P. Dayaratnam


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:

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

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

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.

Today I worked on my A&M Honors application, submitted my USC application, and will go to an interview at the Perot Museum.

Today I organized a meeting with the Perot museum to do an interview for a possible volunteer/internship position, and I worked on a scholarship essay.

Today I worked on my USC and A&M Honors applications, which are due by Dec. 1. We all discussed Mary Barclay's blackness, and filled her with the appropriate ammount of shame.

Today I worked on finishing my annotated bibliography.

Today I worked on my college applications (A&M Honors).

Today I visited the Trinity Trust Foundation to talk with them about my project. I was able to watch a video on the construction of the bridge as well as a video on the architect, Calatrava.

Today I worked on my USC and A&M Honors applications. I continued talking with the Trinity Trust Program about a visit.

I completed and submitted my Cal Poly Application today.

I completed and submitted my U Michigan application today. 3 down, 7 to go.

Today I worked on my application to the Coca Cola Scholars Foundation scholarship, and sorted out required documents and deadlines for my transcripts.

Today I continued to work on the college apps due. Nov. 1. So far I have submitted Georgia Tech and U Illinois, and I am working on U Michigan, UT Austin, and A & M.

Today I worked on college essays and got them reviewed by peers. The Nov. 1 deadline is close and I have yet to hear back from the Trinity Trust, so thesis work is temporarily stalled.

Today I went over essays and short answer responses for my over abundant college applications. Thank goodness for my fantastic personality.

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.

Today I worked mostly on SAT prep for my subject tests tomorrow. Wish me luck. I have been reading a document on the bridge sent to me by my mentor.

Today I began to read a document on the Hunt Hill Bridge given to me by mentor.

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.

Today I validated my transcript, and reviewed the presentation guidlines for my thesis presentation. I emailed with my possible mentor about documents to review and possiby other experts in the field to talk to.

Today I contacted my possible mentor, and contacted the office of admissions of U Illinois @ Urbana-Champaign.

Today I did some research on the designer of the Hunt Hill Bridge, and continued to work on scholarship and college applications.

Today I continued to work on my common app, as well as applications for individual colleges. I researched honors programs and their available scholarships.

Today I continued to fill out my common app, as well as researched some other possible colleges.

Today I updated my resume, compiled a final list of colleges, and started the common app. I also worked on a continuing list of scholarships.

Yesterday I did not work on my thesis, but I did set up my cappex account to help with my college process and compiled a list of scholarship opportunities.

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.