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