Analytical calculation model used when dimensioning timber poles used as overhead power line supports

Sammanfattning: Overhead power lines are more reliable and cost effective than underground cables when it comes to power transmission. The overhead power lines are often suspended above ground using timber pole supports. As the placement of each support depends upon topography amongst other things the conditions for most of the supports will be different and each pole can be viewed as a unique object. This requires that each support is dimensioned individually. The purpose of the project is to clarify how the dimensioning of a support should be performed. The main objective for the project is to develop an analytical model and simulation tool which can be used to dimension timber pole supports. Octave, a scientific programming language, is used for the simulation tool and to visualize the analytical model for the timber pole supports. The analytical model is validated by a finite element analysis, which is applied using the program ABAQUS/CAE. From the analytical model nomograms, which are diagrams that relate the parameters of the support, can be constructed. A nomogram is another tool that can be used when dimensioning timber supports. Many relevant design aspects are treated in the standard SS-EN 50341 and serves as the basis for the analytical calculation model. The supports can be divided into three main types; tangential supports, where the conductors continue straight at the support, angle supports, where the conductors make an angle at the support, and terminal supports, which are used at the endpoint of the conductors. Loads taken into account are: self-weight of components, wind, ice, conductor tension and maintenance. The loads are combined using a design equation which takes into account the probability of certain events occurring simultaneously using combination factors. Partial safety factors are also used to take into account possible deviations in loads, material or geometry. The failure modes of interest are rupture due to excessive bending loads and buckling due to excessive axial loads in the support legs. In the analytical calculations the timber is considered to be isotropic in accordance with the standard while the timber is modeled both as isotropic and orthotropic in the finite element analysis. The analytical model assumes that the cross-arm, which is the horizontal part of the support, only acts to distribute the load between the legs of the support without providing any extra stability by linking them together. In the finite element analysis the legs of the support are considered both individually and linked together by a cross-arm to test the validity of the assumption. To compare the results from the analytical model with finite element analysis one support of each type; tangential, angular and terminal is selected. An Octave script is written and applied to the selected supports to calculate their necessary dimensions. Based on the calculated dimensions 3D-models are created using PTC Creo Parametric 3.0 which then are imported into ABAQUS/CAE where the supports are subjected to finite element analysis. In addition to using the analytical model directly expressions that can be used to create nomograms for timber supports are also derived. Comparing results from FEM with the analytical model showed that the tangential and angular supports were over-dimensioned while the terminal supports were under-dimensioned in the analytical model. This means that a smaller dimension could be used for the tangential and angular supports. For the terminal support the analytical model needs to be altered so that failure will not occur. Changing the buckling mode for the terminal support in the analytical solution fixed the under-dimensioning issue. The finite element calculations where a cross-arm was used to link the legs of the support together showed no increased stability for buckling but showed lower bending stresses in the support legs. Using an orthotropic material model for the timber did not effect the calculations greatly as the properties in the length direction of the pole were significantly more important than the properties in the perpendicular directions. Dimensioning using nomograms is less accurate, as it only narrows the results down to a timber pole grade rather than a specific diameter. This decrease in accuracy is not cause for concern as the timber poles are ordered by grade and not a specific diameter. Using nomograms can give quick results when it comes to dimensioning.