Defining Bimetallic Conductors
Table of Contents
Defining unimetallic cables
To define a unimetallic cable, only the k1 polynomial and the final modulus for the outer material needs to be specified and these will all have the same values for e.g.
Defining Bimetallic cables
To define the mechanical properties of a conductor, first click on the “Elasticity” column in the conductor library which will open a “cable editor” popup. In this, you are able to define the stress strain curve and thermal expansion coefficient for each individual material in the cable. Each cable can have a maximum of two materials:
Bimetallic cables will have both inner and outer
Unimetallic cables will have just outer specified
Cable coefficients
Each material’s stress-strain curve is defined by five coefficients: k0, k1, k2, k3, k4
that define the 4th order polynomial representing (non)linear relationship between strain and normal axial stress in loading conditions. The stress-strain polynomial is given as:
Where the coefficients within the cable editor are given as:
The editor will produce a graph of the coefficients for visualisation of the polynomial:
In a bimetallic conductor, these stress strain curves are scaled by the relative surface area of each of the materials, such that summing them is accurate.
Final Modulus
A “Final Modulus” for the inner (if relevant) and outer material must be specified. This is a modulus of elasticity of the linear elastic ‘curve’ used in both unloading conditions (e.g. to calculate the permanent strain in a cable from a known point on the loading curve) and in static analysis calculations.
The value of it will often be similar in magnitude to the k1 polynomial of the material.
Thermal expansion
The thermal expansion coefficient is a value of how much the material will expand based on a temperature increase of 1 degrees Celsius (or Fahrenheit - based on design settings). The thermal strain of a material is calculated from its thermal expansion coefficient and the temperature difference between the current environmental simulation and the initial stringing conditions. This is done on a per-material basis and the materials are then combined to determine an overall thermal strain.
Bundles
Both unimetallic and bimetallic cables can be used in a bundle. Bundles are simulated as a collection of materials from all the individual cables rather than being simulated separately - for example: permanent strains, thermal offsets, and loading curves are calculated for each load bearing material in the bundle individually, and then combined into an overall curve that determines the overall behavior of the bundled cable. Cables in the bundle specified as non load-bearing add wind + mass loads to the cable without changing the material curves.
We sum the curves due to the “parallel spring model” in which load bearing cables are deemed as parallel springs geometrically constrained at the ends such that length of each spring is equal. Corollary to this is that forces at the endpoints are the sum of individual forces in each spring. This allows us to sum individual stress strain curves to get an equivalent stress strain curve.
See picture below of parallel spring model, and of curve sum:
Bird-caging
Bird-caging is when one of the materials in the cable can’t sustain compressive loads and instead buckles outwards. In the case of a stranded cable this can somewhat resemble the shape of a bird-cage. The derived piecewise Stress strain curve of bird-caging materials have a first piece that is a polynomial with all 0 coefficients. Bird-caging behaviour is specified on per material basis, and it is up to user to decide whether the material with the smaller thermal expansion coefficient (usually inner material) can birdcage in cold environments.
Bird-caging is specified by ticking the checkbox on either inner or outer cables
Effect of outer material compression on cable behaviour
In general, when the material with a larger thermal expansion coefficient does not birdcage but can sustain compression then in hot environments onset of compressive stresses in those materials oppose the tensile stresses in material with lower thermal expansion, effectively reducing both cable tension and its effective stiffness, resulting in additional sag.