4. Deriving a linear heavy cable equation

Questions and discussion for this lecture live here. Fire away by hitting Reply below :fire:

Hi Dr. Sean

  • Catenary shape and fanicular form are the same?
  • Does the analytical solution nearly represent the shape of real catenary form finding (I mean from experiment)?

Hi,
Yes - since our analysis progressively eliminates the contribution from any members in compression - the resulting structure will be tension-only.

The analytical solution should approximate an experimental solution, although one must allow for all of the usual discrepancies between analytical and experimental solutions - one that comes to mind will be the assumption of completely frictionless joints - this is difficult to represent in practice. But, generally speaking, the our analytical solution should be a good approximation.

Seán

In my case it is not quite clear why the negative dy/dx. Is it related on how is theta is measured?

Hey @Mauricio
The negative sign accounts for the fact that the vertical coordinate is positive downwards and in our setup of the problem, the vertical position of the right side of the cable segment is above the left side. So, for the tan of theta to be equated to dy/dz, we add the negative sign, accounting for the fact that dy is negative.
S