# suspension bridge parabola equation

So the weight is equal to. This is a picture of the master mechanic E.F. Farrington traveling the length of the newly installed cable of the Brooklyn Bridge. How does the altered Extra Attack feature of the Bladesinger (Tasha's Cauldron version) interact with Fighter's additional Extra Attacks? However, we will provide a brief summary and description of parabolas below before explaining its applications to suspension bridges. I would be interested in knowing the equation of the main cable to calculate the length of the secondary cables (the vertical ones). How would sailing be affected if seas had actually dangerous large animals? The total distance between both bridge support is. By "sag", do you mean the height of the parabola? Since the cable forms a parabola its equation is $y = a x^2 + b x + c$ for some numbers $a, b$ and $c.$ Since you know $(0, 10)$ is on the graph of the parabola you have $10 = a \times 0^2 + b \times 0 + c$ you know that $c = 10.$ http://mathcentral.uregina.ca/beyond/articles/Architecture/Bridges.html, http://whistleralley.com/hanging/hanging.htm, http://news.sciencemag.org/sciencenow/2010/01/14-02.html, http://carondelet.net/Family/Math/03210/page4.htm. The variable in a relation who’s value depends on the value of the independent variable is called what? To find the height of main cable at left bridge support put x=0. Click here to see ALL problems on Finance. From the previous sections, we explained the forces active in the bridge: tension and compression. The parabolic curves of the suspension cable are not created by gravity alone, but also by other forces: compression and tension acting on it. This is a force coming from the right that corresponds to the direction of the suspension cable. @CarlWitthoft If the deck weight is far larger than the weight of the cable, then the parabola is a better fit; I explore the transition. Is a Circle of Stars Druid's Chalice form affected by Grave Cleric's Circle of Mortality? Apparently the cable is in higher tension when the tower is lower? 3. If the speed of an electromagnetic wave is 100,000 cm/s and its wavelength is 100 cm, what is its frequency? Device category between router and firewall (subnetting but nothing more). At the middle of the bridge, , which defines the most efficient use of the suspension cable. I'm reading the derivation of the equation of the hanging catenary from Wikipedia: In the same article the parabolic equation governing the shape of the main cable of a suspension bridge is discussed, and its equation is obtained as following: Here $w$ is the density of the deck and $T_{0}$ is the horizontal tension on the cable at lowest point. Making statements based on opinion; back them up with references or personal experience. Differential equation of the vertical displacement of a cable. Which sentence from the section "the halloween storm" best summarizes its main idea? How do I use zsh to pipe results from one command to another (while in a loop)? Engineering Stack Exchange is a question and answer site for professionals and students of engineering. Question 1100161: Suspension Bridge. To get more in-depth and more into calculus (of which I do not yet have an understanding), go to Hanging with Galileo , a comprehensive webpage that compares the equations of the catenary (a hyperbolic cosine) and the parabola in relation to a suspension bridge. The profile of the cable of a real suspension bridge with the same span and sag lies between the two curves. example: burning... View a few ads and unblock the answer on the site. Have tunnel boring machines been mass produced? Which of the following sentences is written correctly? “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. If the deductive reasoning is not enough for you, there is another way to prove that the curve of the cable in a suspension bridge is a parabola. Note: That this is not a vector quantity, but rather a magnitude quantity. 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 on-land. This page was last edited on 3 June 2013, at 14:21. Also the weight of the suspension cable is negligible compared to that of the deck, but it is also supporting the weight of the deck. When you were first introduced to parabolas, you learned that the quadratic equation, is its algebraic representation (where and are the coordinates of the vertex and and are the coordinates of an arbitrary point on the parabola. This is also another conceptual reason why the suspension cables hang in a parabolic curve. Rephrasing the cable problem as the ‘suspension bridge problem’ we need to solve a two-component non-linear equation … Question sent to expert. Some basic differential calculus is needed to derive an equation for the suspension cables, which gives us a parabolic equation. Since the cable forms a parabola its equation is $y = a x^2 + b x + c$ for some numbers $a, b$ and $c.$, Since you know $(0, 10)$ is on the graph of the parabola you have $10 = a \times 0^2 + b \times 0 + c$ you know that $c = 10.$, You also know that $(100,40)$ and $(-100, 40)$ are on the graph so substitution gives you two equations to solve for $a$ and $b.$.