Results 1 to 3 of 3

Math Help - Quadratic Equations

  1. #1
    Newbie
    Joined
    Feb 2010
    From
    Near Chennai
    Posts
    20

    Thumbs up Quadratic Equations

    The lions gate bridge in vancouver BC, is a suspension bridge that spans 1516m. Large cables are attached to the tops of the towers, 50 m above the road. the road is suspended from the large cables with small vertical cables, the smallest one being 2m, find a quadratic equation to model the large cable shape.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by sureshrju View Post
    The lions gate bridge in vancouver BC, is a suspension bridge that spans 1516m. Large cables are attached to the tops of the towers, 50 m above the road. the road is suspended from the large cables with small vertical cables, the smallest one being 2m, find a quadratic equation to model the large cable shape.
    Maybe it's because I'm in Civil Engineering but this is a terrible question. There is no way to create a singular model to map the behavior of the cables for the entire span of the bridge. Well there is, but it certainly cannot be done with 1 quadratic function.

    There are 3 distinct parts: http://upload.wikimedia.org/wikipedi..._Vancouver.jpg

    So we will assume they are talking about the middle part (from left tower to right tower).

    If the cable is of constant density (which it is) then the positioning in the cable can be treated liked the deflection of a beam with a point load in the middle. Thus, the max deflection happens at Mid-Span and the height here is 2. Having said that, if the cables are held down via smaller wires the engineer could have positioned it differently, but this makes no sense because a symmetric structure will transfer the loads better (more evenly and efficiently) so we will say that this structure is symmetric.

    Treat this like a graph, so at the left we have the point (0,50) and on the right we have (1516,50). Of course, your analysis will depend on where you take your co-ordinate axis. You could take mid-span to be the origin whereas I am taking the left tower to be at the origin.

    Let us say

    F(x)=Ax^2 + bx + C

    F(0)=50=C

    F(x)=Ax^2 + bx + 50

    F(1516/2)=2=A(1516/2)^2 + b(1516/2) + 50

    And

    F(1516)=50=A(1516)^2 + b(1516) + 50

    Solve the 2 equations for the 2 unknowns.
    Last edited by AllanCuz; April 17th 2010 at 10:32 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,911
    Thanks
    774
    Hello, sureshrju!

    The description is not clear,
    but I can guess the design of the bridge.


    The Lion's Gate bridge in Vancouver, BC, is a suspension bridge that spans 1516m.
    Large cables are attached to the tops of the towers, 50 m above the road.
    The road is suspended from the large cables with small vertical cables, the smallest one being 2m.
    Find a quadratic equation to model the large cable shape.

    Place the bridge on coordinates axes with the center of the bridge at the Origin.

    Code:
                  :
          *       :       *(758,50)
          |       :       |
          |*      :      *|
          | *     :     * |
          |   *   :   *   |
          |       *       |
          |     (0,2)     |
          |       :       |
          |       :       |
      - - * - - - + - - - * - -
        -758      0      758
                  :

    The general form of this parabola is: . f(x) \:=\:ax^2 + c


    We have two point on the parabola: . (0,2),\;(758,50)

    f(0) = 2:\;\;0^2a + c \:=\:2 \quad\Rightarrow\quad c \;=\;2

    f(758,50):\;\;758^2a + 2 \:=\:50 \quad\Rightarrow\quad a \:=\:\frac{12}{143,\!641}


    Therefore, the equation is: . f(x) \;=\;\frac{12}{143,\!641}\,x^2 + 2

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quadratic Equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 16th 2010, 09:25 PM
  2. quadratic equations
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 14th 2010, 07:01 PM
  3. Quadratic Equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 15th 2010, 02:13 PM
  4. Replies: 1
    Last Post: June 12th 2008, 10:30 PM
  5. quadratic equations
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 18th 2008, 11:20 AM

Search Tags


/mathhelpforum @mathhelpforum