SHAPE FINDING

Let us start off with the shape finding of a simple, rectangular planned, crossed arches. The structure would be something that could hold the arc shape like a curved pipe. The fabric would then be hypothetically stretched over the arches and pinned along the edges.

  • STEP 1: Find the heights along the arc.
  • STEP 2: Solve equilibrium equations for locations of interior points.




    • EXAMPLE:
    Find the elevation of the 4 interior
    points shown in the figure to the right.
    Assume the horizontal component of each
    cable force is 1000 lbs.





    SOLUTION:

    We know that the crossed arches are arcs and based on the goemetric properties we are able to find the height at any point along the arc.

    x^2 + y^2 = R^2
    theta/2 = arctan 5/(44.72/2) = 12.604°
    theta = 25.209 ........... R*sin theta = 44.721/2
    R = 52.499 ................ R*cos theta = 47.499




    Now, because of symmetry, we have an axonometric of one eighth the cable net.



    The vertical component "V" is to the change in the "Z" direction as the horizontal component "H" is to the change in the "X" direction.

    V/H = delta Z/delta X

    V = H*deta Z/deta X


    Using vertical equilibrium:

    Rewriting: 

    -6 Z1 +   Z2        = -22.872

   Z1 - 6 Z2 + 4 Z3 = 0

 2 Z2 - 6 Z3        = -10.196

    Substitute in for Z2 and solve.
    Solution:
    Z1 = 4.203'
    Z2 = 2.350'
    Z3 = 2.474'


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