Self-supporting steel lattice structures are most often used in various civil engineering applications to support the transmission lines that distribute electricity. The National Grid main transmission network has approximately 22,000 self-supporting lattice transmission towers located throughout England and Wales. In recent times, there has been a significant increase in the demand for power and many of the National Grid lattice transmission towers are required to support heavy loads. Global climate change which causes conditions such as extreme winds and heavy ice impose additional loads. The failure of one tower can rapidly propagate and lead to severe damage along the entire power line thus the subsequent repair or replacement costs can be astronomical. All of these facts indicate that find an economical and efficient upgrade to current tower designs is required in order to carry the heavier loading. Hence, this project is aimed at developing an economical and efficient scheme to upgrade lattice transmission towers. A finite element model of a transmission tower was developed using ANSYS commercial software with 3D trusses. A structural analysis was performed to determine the deformation and stresses in the tower under the anticipated cable and wind loads. The individual members of the transmission tower have their own deformation and stress properties. Based on analysis results, an appropriate tower strength improvement was developed and an essential modification was made to the existing tower design to reduce deformation and stress. The modified transmission tower model is compared to the upgrade tower models of other authors.
Chapter 1
INTRODUCTION
1.1 General
Steel lattice structures are used in many civil engineering applications. A lattice structure is a form of members and connections which act together to withstand an applied load. Typical lattice structures include roofing structures, grids and transmission towers, among others. Lattice structures are suited for situations requiring a low weight, high wind resistance, an economical use of materials and easy construction. For these reasons, steel lattice transmission towers are most commonly used to support and transmit electricity. The National Grid main transmission network has approximately 22,000 self-supporting lattice steel towers located throughout England and Wales. Because one lattice transmission tower design can be used for hundreds of towers in a transmission line, it is essential to find an economical and efficient design. A typical tower has a square base with a similar bracing system on all faces. A 50 m-high transmission tower supports wires that usually have a spacing of between 300 m to 450 m. Most transmission towers are constructed with angle section members that are eccentrically connected, therefore transmission towers are one of the most difficult forms of structure to analyse. As a result, various computer programmes that analyse transmission towers are used to make different assumptions in order to simplify the computations.
1.2 Literature Review
A transmission tower is analysed as a space truss structure. A space truss structure is normally defined as a form of structure where the elements and nodes extend three-dimensionally. Space trusses consist of two forces, i.e. the members are pin-jointed at the ends and the loads apply on the joints so that the members are either stretched or compressed but not rotated. The truss elements are connected at the node and form a triangular loop, and the formed loops are gathered together to form the entire frame. The nodes have six degrees of freedom which comprise three in translation and three in rotation. The translation movements occur in x, y and z directions while rotation takes place perpendicular to the three axes.
In Structural Modelling, several authors have contributed with theoretical and experimental investigations to access the best modelling strategy for steel transmission and telecommunication towers. Albermani and Kitipornchai 1993 and 2003; El- Ghazaly and Al-Khaiat 1995; Madugula and Wahba 1998; Kahla 1994 and 2000 and many more research's contribute their work.
Kahla 1994 numerically modelled the dynamical effects present in guyed steel towers including the cable galloping effects. Later the same author, Kahla 2000, dynamically modelled the rupture of a cable present in guyed steel towers. The analysis indicated that the guyed steel towers cable rupture, disregarding the wind actions and it was one of the most severe critical load hypotheses for the investigated structures. Wahba et al 1998, considered the dynamical nature of the load acting in guyed steel towers like wind, earthquakes and cable gallop. The finite element method was used to model the tower bars as 3D truss and 3D beam elements obtaining the structural models dynamical characteristics. In a subsequent phase these results were compared to experiments. Wahba et al 1998 research paper also described the results of experiments made to identify the main parameters that influence the guyed steel towers natural frequencies, as well as, there and associated vibration modes. Ghazalyt and Khaiatz 1995, evaluated telecommunication guyed steel tower designs based on discussions of the various non-linear aspects involved on their numerical modelling. This paper also contemplated the development and comparisons of the results of a 3D model for a 600 meter height guyed steel tower. Wahba et al 1998, performed an investigation of the numerical models used in telecommunication guyed steel towers. The authors stressed the relevance of considering the non-linear effects present even at service load levels. In a subsequent paper, Madugula and Wahba 1998, described two different finite element models for the dynamical simulation of guyed steel towers. This paper also contemplated an experimental modal analysis of reduced-scale guyed steel towers models that produced results in consonance with the developed numerical models. Albermani and Kitipornchai 2003, used the finite element method by means of a geometrical and physical non-linear analysis to simulate the structural response of telecommunication and transmission steel towers. Their investigation is on the possibility of strengthening steel truss towers from a restructure and rearrangement of their bracing systems. The adopted solution consisted on the addition of axially rigid systems to intermediate transverse planes of the tower panels. The main purpose of the adopted modelling strategies was to investigate the structural behaviour of the guyed steel towers, preventing the occurrence of spurious structural mechanisms that could lead to uneconomic or unsafe structure.
Chapter 2
Finite Element Method of Structural analysis
2.1 General
This chapter introduces the finite element method of structural analysis, with descriptions and formulations of elements typically used for modelling transmission towers. Nonlinear finite element techniques and load incrementing procedures are discussed in preparation for the sections
2.2 The Finite Element Method in Tower Analysis
The finite element method (FEM) is a mathematical procedure, most often computer aided, which is used to obtain approximate solutions to the governing equations of complex problems. In some cases, solutions to these problems cannot be obtained analytically. An analytical solution is a mathematical expression that can give an exact value of the field variable (displacement, temperature) at any location in the body. The finite element method, the field variable is approximated using interpolation functions pieced together between discrete points. Most practical engineering problems involve complicated geometry, material properties, or loading conditions, and therefore require a numerical solution procedure such as the finite element method. The finite element method can be considered as an extension or generalisation of the stiffness method (with reference to fixed structures) to two-dimensional and three- dimensional continuum problems, such as plates, shells and solid bodies. The finite element concepts used in continuum problems can be used to formulate the stiffness method of analysis treating the member of a framed structure as an element. Therefore, the element stiffness matrices derived for truss and beam elements using the stiffness method of analysis are identical to the stiffness matrices derived using finite element concepts. For each problem utilizing the Finite element method, several steps must be followed. The physical system must be discretized into smaller finite elements. The elements may be one-dimensional, two-dimensional, or three dimensional depending on the nature of the problem. For transmission towers, each angle member is usually modelled as a one-dimensional element, or line element, with one node at each end of the element. The unknown degrees of freedom, or the primary unknowns, are evaluated at these nodal points, an interpolation function must be selected which approximates the distribution of the unknown variable within an element. The function is expressed in terms of the nodal values of the element. For example, the unknowns quantity within a beam element (the transverse displacements) can he fully described once the degrees of freedom for each end node are known. The governing equations and constitutive relations are then defined. The element equations are formulated using the direct equilibrium method, energy methods, or the method of weighted residuals. For the two node line elements used in transmission towers, the direct equilibrium method is usually performed. The equation of equilibrium for each element can be written as: [k]•{d} = {f} (2.1a)
where [k] is the element stiffness matrix, {d} is the element displacement vector consisting of the unknown degrees of freedom, and {f} is the element nodal force vector. The equations for each element are assembled to obtain the global system of equations, and appropriate boundary conditions are applied. The assembled global system of equations can be written as
[K]•{q} = {F} (2.1b)
where [K] is the global stiffness matrix obtained by assembling all element stiffness matrices [k], {q} is the displacement vector consisting of the unknown global degrees of freedom, and {F} is the global force vector obtained by assembling all element force vectors {f}. The primary unknowns, {q}, are determined by solving the global system of equations, often by Gauss elimination, from which the secondary unknowns, such as element forces and moments, can be calculated.
The same steps are followed for any type of problem; the end result is always a matrix equation in the form of equation 2,1b. The same steps are followed for one- dimensional heat conduction, two-dimensional flow through porous media, or three-dimensional stress analysis. Because of its versatility, the finite element method has become the most popular computer analysis tool available to engineers today.
2.2.1 Truss Elements
Steel lattice transmission towers are often modelled as linear-elastic truss elements, since the angle members of the tower primarily resist axial loading with minimal bending resistance. The joints at the ends of truss members are idealized as frictionless pins, free to translate in any direction unless externally constrained by a specified boundary condition. In reality, however, the idealized pin connection seldom occurs. Truss elements are used in situations where the bending stresses are negligible compared to the axial stresses. If the angle members in a tower are modelled as truss elements, then they cannot resist lateral loading. Any wind load or dead load acting over the truss element must be distributed to the two connecting joints. It is standard practice to concentrate half of the self-weight of the member to each of the two joints the member connects. A problem with the truss element in modelling transmission towers is the possibility that a collapse mode may occur. Collapses modes are caused by out-plane instability at planar joints or by in-plane instability due to unstable subassemblies called mechanisms. A planar joint occurs when all the members terminating at one joint lie in the same plane, causing instability at the joint in the direction normal to the plane.
2.3 Nonlinear Finite Element Analysis
In the previous section it was assumed that the constitutive relations, used to derive the element equations, remained linear throughout the analysis. In some cases the stress-strain relationships do not obey the simple Linear elastic assumption, and the non- linearity of the material properties must be considered, In other problems the linear strain-displacement relationship cannot be used accurately due to large displacements and large strains altering the geometry of the elements, These types of problems are said to be geometrically non-linear. This section describes non-linear finite element problems that have only material non linearity; the assumption of small displacements and small strains is still made. In nonlinear problems, the stiffness matrix depends on the unknown quantity. A direct solution procedure is no longer possible, and an iterative solution scheme is required. For structural analysis problems, where the stiffness is a function of the displacements and the loading history, the tangential stiffness method is usually performed along with a load increment procedure. The nonlinear problem is essentially linearized over a small portion, or increment, of the total structural load.
Chapter 3
Structural analysis of a full-scale transmission tower
3.1 Modelling
A full-scale lattice steel transmission tower is shown in Figure 3.1. This tower was originally tested at the Structural Engineering Research Centre in Chennai, India. The design is typically used in the National Grid transmission network located in England and Wales. The 50 m-high square tower is 18.5 m wide at the base and decreases to 5.5 m at the 28 m level. It comprises 1312 angle members and 502 connection nodes. These angle members do not include the joints that are only attached to the secondary members.
This transmission tower is designed with 31 different angle sizes, from L75x75x6 mm angles used in the transverse and longitudinal cross-bracing in the upper section of the tower to L150x150x20 angles used in the main legs of the bottom section of the tower. High tensile steel with a yield stress of 350 MPa is used for the leg members while mild steel is indicated for all other members. The tower loading condition shown in Figure 3.2 is one of several worst-case scenarios tested by the Chennai Structural Engineering Research Centre and the output from the test were used to verify the results of the ANSYS workbench programme.
3.2 Linear Finite Element Analysis
The tower is designed to support electrical transmission cables at the end of the six arms and the top of the tower, as well as wind loads that may distribute over the entire frame. The tower is constructed of angle shape steel (E=210 MPa, V=0.30). The base constraint is a simple support at all four bases. The effective weight of the cables at the end of the arms is variable, as shown in Figure. 3.1. In addition, the wind loads acting on the tower vary in x and y directions and reach levels high enough to distribute over the entire tower. The wind loads in the analysis of this tower do not include the secondary members or the joints that are only attached to the secondary members. The secondary members do not provide load resistance and their purpose is to reduce the unbraced length of the primary members. Maximum deflection occurs at the top of the tower and the value is very similar for both the test and the ANSYS programme. The analysis results show clearly that a failure occurred in the longitudinal face 'K' bracing in the second panel and the same failure occurred in the experiment. Compared with the failure load, the analysis model failed 7.5% higher than the experimental load. Overall, the discrepancy between the analysis and experimental result is very small, thus the developed model could represent the experimental transmission tower structure.
Experimental results
Finite element analysis results
Failure load 146 kN
Failed location at bottom panel
Failure member inverted 'k' bracing ( L100x100x8mm)
Failure load 157 kN
Failed location at bottom panel
Failure member inverted 'k' bracing (L100x100x8mm)
Table 3.1 Comparison of the experiment tests results and the finite element analysis
Conclusions
The analysis result failure load is 7.5% higher than the experimental result, thus the discrepancy is within the acceptable range; the failure location and failure member are similar in both the linear analysis and the experimental test. Based on these, it has been proved that the developed finite element model can represent the existing transmission tower structure.
Left view
Front view
50.76 m
4.76 m
10 m
8 m
28 m
15°
2°
5.5 mC:\Users\Ermias\AppData\Local\Temp\agptmp130\preview.pngC:\Users\Ermias\AppData\Local\Temp\agptmp130\preview.png
18.5m
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4OO kV tower Model
50.76 m square tower
18.5 wide at base and reduce to 5.5 m at 28 m level
502 Nodes and
1312 Elements
Top view
Figure 3.1 A full-scale lattice steel transmission tower model
Leg members
(High tensile steel of 350 Mpa yield stress) C:\Users\Ermias\AppData\Local\Temp\agptmp130\preview.png
(Mild steel of 250 Mpa yield stress)
Primary bracing
(Mild steel of 250 Mpa yield stress)
Secondary bracing
Figure 3.2: 440 kV Transmission tower Cross- Sections
Data source: - Rao, N.P., Knight, G.M.S., Lakshmanan, N. and Iyer, N.R. (2010) Investigation of transmission line tower failures. Engineering Failure Analysis, 17, pp. 1127-1141.
Finite element analysis
Figure 3.3: Load and support of the 400 kV type tower
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Figure 3.4: Finite element analysis results
Aims to complete
Improve the model.
Apply wind loads that distribute over the entire frame (using British Standards BS8100) and analyse the weather so that the tower can hold up in worst-case scenarios.
Next steps
Based on the analysis results, an appropriate tower strength improvement will be developed and an essential modification will be made to the existing tower design to reduce deformation and stress.
The modified transmission tower model will be compared to the upgrade tower models of other authors.
Why upgrade the tower
The failure of one tower can rapidly propagate and lead to severe damage along the entire power line. Thus the subsequent repair or replacement costs can be astronomical.
Increased demand for power and the fact that many of the National Grid lattice transmission towers are required to support heavy loads.
Because one lattice transmission tower can be used for hundreds of towers in a transmission line, it is important to find an economical and efficient design.
Global climate change, which causes conditions such as extreme winds and heavy ice, impose additional loads.
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