Catenary lighting canopy -- Working out reactions at columns

[Alex999]

Hi guys, first time poster so play nice :)

Outline of problem:

The situation I have is that there are 4 supporting columns. These columns support support a wire and this wire is then used to hang wires which support festive lights. (see diagram below)

What I'm looking for as an end point is to be able to say what are the forces going onto the columns

I'm not looking for a numerical answer as such, hence i haven't provided any figures, I'm just looking for the right way to think about it and then I can put numbers to it later.

equations:

n/a

attempted solution:


The way I'm thinking of it initially is the middle wires are effectively catenary systems (as the lights are placed at regular and relatively close intervals and I can therefore approximate it as the wire having a self weight that includes the lights) and therefore I can specify a vertical and horizontal force at each point where these inner wires connect to the outer wires.

However I'm hitting a bit of a mental block when it comes to thinking about the outer wires which connect to the columns and how I would go about it. I remember doing the simpler tension problems (weight hung between two wires) when I did mechanics and was wondering whether this would be the path to take... but like I've said I'm in abit of a muddle thinking about it and could use some guidance.

 

[SteamKing]

From the standpoint of static equilibrium, the four corner posts must support the weight of all the wires and the lights attached. Depending on the amount of sag in the wires connecting the columns, there will be additional horizontal loads imposed on the free ends of these members, which will tend to draw them together.

A wire supported at both ends and carrying a uniformly distributed weight along its length has a shape which is called a catenary. One can analyze the statics of such structures as described in this article:

https://en.wikipedia.org/wiki/Catenary

When the loads are no longer uniformly applied, the analysis becomes more complex, and the shape changes from a catenary to something more parabolic.

Beyond this, analysis would require that you look at specific cases, where you know the properties of the wire, the arrangement and properties of the lights, etc.