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