IB Math Internal Assessment
Beijing No.55 International School
Name: Justine Tay
Class: 11(3)
TABLE OF CONTENTS
Abstract
Acknowledgements
Topic
Introduction
Images of Golden Gate Bridge
Types of formula to parabola:
Worked example
Worked example 2
Proof
Conclusion
Abstract:
The main focus and the finality of this Internal Assessment will be on the mathematical term, parabola. Parabola is any point that has an equal curve distance to a fixed point and a straight line. Occurs in many uses in the industry and faced in our daily lives.
Acknowledgement:
Sincere gratefulness for Ms. Zhang for being my Mathematics Internal Assessment supervisor. Guidance and care through this essay report. Thankful.
Topic:
Proof
…show more content…
Suspension bridges are able to work efficiently because of their cables, which are interesting from a mathematical perspective.
Since the bridge’s deck spans a long distance, it must be very heavy in weight by its own, not to mention all the weight of the heavy load of traffic that it must carry. Because of all this weight, this results in two active forces: compression and tension. The cable’s parabolic shape results in order for it to effectively address these forces acting upon the bridge. For instance, the deck sags from all the weight of the traffic because of compression forces, which travels upwards the cables. The cables then transfer those compression forces downwards the vertical towers, down into the foundations buried deep within the earth. However, the cables receive the brunt of the tension forces, as they are supporting the bridge’s weight and its load of traffic, being stretched by the anchors' ends
A simple beam bridge that is flat across and supported at the two ends. A longer beam bridge can be held up along the middle by piers standing in the river. The weight of the bridge itself, plus the load that it carries, plus gravity are the downward forces are spread evenly across the length of the bridge. The upwards forces that hold the bridge up come from the piers. The Confederation Bridge in Canada is a famous beam bridge.
When bridges are poorly constructed, they may fail due to load they carry, collision by derailed trains or even by vehicles that lose control leading to catastrophic incidences. However, if bridges are well-constructed, the chances or injury are greatly minimized in the event of an accident. Discussed in the subsections are the requirements of AS 5100 standards in relation to cable-stayed bridges and include design requirements for bridges, bridge aesthetics, bridge functional requirements, bridge component design requirements and bridge construction
In this section, students are taught how to relieve their stress and perform better during assignments and homework. Tips and tricks are given to students for studying and improving their actual testing performance. This section is also designed to help first time math students at the University of Phoenix to get a good understanding of their upcoming math course(s). All aspects of the classroom and what to expect will be
Compression is the force pressing a material and compacting it and acts on the towers of a suspension bridge, this force is created from the weight of the towers and the load on the bridge. Compression forces will also act on the surface of the bridge deck as when a load is applied it will have some flexibility and bend, it will then travel up the cables, ropes or chains to transfer the compression forces to the towers. The towers then dissipate the compression directly into the earth. (Bagga 2014).
Initially, suspension bridges before 1940 were made of piers, towers, wires, anchorages, and roadways. Piers were the main foundation for the suspension bridges. There usually were two of them, which were made out of cement and were entrenched in ground underneath the body of water that the bridge was spanned across. Towers were built on top of the piers to provide a means of connection for the roadways and wires. Wires were connected to the towers, roadways, and anchorages to provide tension support for the weight of the bridge. The anchorages were large cement platforms that were planted into the ground on either side of the land so that the wires could be connected to it. Lastly, the roadways were the main point of the suspension bridge. They usually were wide enough to provide four lanes of traffic and stretched from one side of the bridge to the other. This was the basic design of the suspension bridges
You have selected a course unlike any other math course. The purpose of this Summer Assignment is to:
Calculations were performed to determine the effectiveness of the design of the platform. Allowing for a safety factor of 1.5 times the design weight of 10kg and considering the bridge must not be overdesigned; plans were made for the bridge to fail at 25kg, 2.5 times that of the design weight. According to the calculations, the bridge would hold a load of over 15kg and experience failure at 20kg in the members. These calculations were later disproven in the testing, breaking 8kg earlier than expected, due to unforseen errors. An analysis of the bridge design and calculations has been included at the end of this report.
Furthermore, when the millennium bridge opened within the first weekend around 100,000 people had crossed the bridge. Due to such heavy traffic, this lead to something called resonance. Resonance is when the input vibrations frequency coincides with the natural frequency of the structure itself, causing large deflections to develop. The issue caused the bridge to undergo a swaying movement; hence led to its closure. After extensive research and analysis, it was found that the movement was caused by synchronized pedestrian footfall. To prevent this there were two options taken into account the lateral stiffening and the damping; both were used in order to increase the natural frequency of the structure so it did not match the footfall. In addition structures called fluid-viscous dampers and tuned mass dampers were installed to control both horizontal and vertical movements.
As Professor Farquharson’s studies progressed, modifications on the bridge continued. Tie-down cables were positioned on the bridge’s sides and wires were stretched diagonally across the bridge’s deck and main cables. Thus, the problem was believed to be solved. However, one of the reinforcing tie-down cables, placed only a month prior, snapped due to high speed winds on November 1. The date of this malfunction marks the start of a week-long series of unfortunate events ultimately leading to the bridge’s collapse on November 7.
Hello and I hope that everyone is ready to gear up on a new adventure of math. Here I'm again , attempting the class again, this time I am only taking one class. I drop the this class before after two weeks because I found to be overwhelming, due to me working two job and a fulltime student. As one of my favorite quote, " If you don't like something change it, if you can't change it, change your attitude ". (Maya Angelou). As you can see, I made the change, drop one job, and here I am again ready to succeed for excellence.
All are very effective and work well if built in the right conditions. The thing that separates these bridges from one another is that they all have different points of compression and tension. Tension is two forces of opposition that pull away from each other to keep it from being pulled together. If you imagine a rope in a game of tug-of-war, the rope has a lot of tension because it is being pulled apart, but the opposing force inside of the rope is trying to keep it together. The same can be applied to a bridge truss because the tension truss is opposing the compression truss by pulling the bridge apart. Tension also pulls the platform of the bridge by stretching it to keep the bridge from collapsing. Compression is two forces in opposition that push an object together to try to compress it. If you think of someone standing on a soda can, the soda can tries to resist being squished, but the weight of the person standing on the can still squashes it. This example can also pertain to the truss on a bridge. A compression truss opposes the tension truss by pulling the bridge together. Compression is also placed on the top of a truss and in its bases. The compression at the top of the bridge counteracts with the tension of the platform and balances out each force. The compression in its bases is from the weight of the platform and trusses. Bridge engineers calculate the tension and
Hecox (2011) says that the arch structure of the Tillman Bridge makes the canyon walls hold the weight of both vehicles and the bridge itself. In addition, the arch structure allows a better vision of the canyon for the drivers, which was a request of the population to the engineers of the project. In the other hand, according to Jones (2015), the truss structure of the new St. Anthony Bridge also was requested by the population because they wanted to keep a truss bridge in that place. The author also affirms that the St. Anthony Bridge is a truss, but the project team proposed adding a posttensioned concrete bottom chord to the steel truss in order to reinforce it. The project team made this choice because one bridge in Minnesota has collapsed in 2007, and the engineers wanted to lessen the fracture-critical issues to avoid a new catastrophe. In addition, this posttensioning approach wiil make the structure redundant for both resiliency and long-term durability. In conclusion, both bridge's structures were right chosen in order to provide safety and beauty in both
It is shaped in a way to transfer weight to the towers and anchors with its tension (O'Connor, 1971, p. 372). Cables are made of high strength wires spirally bound to form a rope (O'Connor, 1971, p. 372). Vertical cable suspenders that are fastened to the main cables hang the actual roadway. Stiffening girders and trusses are along the side of the bridge to distribute concentrated loads and help to keep the motion of the bridge at a minimum (Troitsky, 1994, p115).
The recent change in the national curriculum in mathematics, as well as having positive impacts, will also cause issues in teaching and learning mathematics. One of the
Superstructure bears the load that is being passed over the bridge and it transmits the forces caused by the same to substructure. Load received from the decking is transferred on to the substructure by Bearings. They also distribute the load evenly over the substructure material as it may not have sufficient strength to bear the superstructure load directly. Piers and Abutments are the vertical substructures which transfer the load to the earth in the foundation. Wing walls and returns are constructed as the extension of