University of Ghana http://ugspace.ug.edu.gh DESIGN OF LIGHTER WEIGHT CONCRETE ELECTRICITY POLES AS AN ALTERNATIVE FOR POWER DISTRIBUTION IN SUPPORT OF GHANA’S NUCLEAR POWER PLANT PROGRAMME CATHERINE LADZE BOYETEY DEPARTMENT OF NUCLEAR ENGINEERING SCHOOL OF NUCLEAR AND ALLIED SCIENCES UNIVERSITY OF GHANA MPHIL 2021 University of Ghana http://ugspace.ug.edu.gh DESIGN OF LIGHTER WEIGHT CONCRETE ELECTRICITY POLES AS AN ALTERNATIVE FOR POWER DISTRIBUTION IN SUPPORT OF GHANA’S NUCLEAR POWER PLANT PROGRAMME A thesis submitted to the: DEPARTMENT OF NUCLEAR ENGINEERING SCHOOL OF NUCLEAR AND ALLIED SCIENCES UNIVERSITY OF GHANA By BOYETEY CATHERINE LADZE (10705310) In partial fulfilment of the requirements for the degree of MASTER OF PHILOSOPHY In NUCLEAR ENGINEERING JULY 2021 University of Ghana http://ugspace.ug.edu.gh DECLARATION I hereby declare that with the exception of references to other people’s work which have been duly acknowledged, this compilation is the result of my own research work and no part of it has been presented for another degree in this University or elsewhere. …………………………………… Date……………………………. CATHERINE LADZE BOYETEY (Candidate) I hereby declare that the preparation of this project was supervised in accordance with the guidelines of the supervision of Thesis work laid down by University of Ghana. …………………………………………… ……………………………………... Dr NII K. ALLOTEY Dr E.K. BOAFO (PRINCIPAL SUPERVISOR) (Co-SUPERVISOR) Date…………………… Date…………………… i University of Ghana http://ugspace.ug.edu.gh ABSTRACT Electricity is an essential commodity or utility for individuals and nations alike. With the advancement of technology, access to electrical power is paramount to the economic development of a country. The World Bank ranked electricity as the second most important constraint to business activities in the country. It estimated that Ghana lost about 1.8 per cent of GDP during the 2007 power crisis. Key elements of the electricity distribution network in Ghana are the electricity poles, conductors, transformers and insulators. The primary materials used for the construction of poles are timber, concrete and steel with timber being the most common due to its relatively low cost and availability. Timber, however, is plagued by varied agents of destruction which include termite and fungal action, as well as destruction by outbreaks of fire. Concrete poles though unaffected by these destructive elements, tend to be quite heavy. This poses a unique problem for the transport and management of such poles. This study is focused on improving the design of the concrete poles such that they are lighter than the previously used concrete poles while ensuring strength and stability. A proposed model of a tapered pole with a rectangular cross-section was designed according to guidelines stated in the EUROCODES design manual and analysed in ETABS 2016. From the analysis results, the pole design was found to have successfully passed all design requirements with a weight of 450kg and 575kg for the 9 meter and 11-meter pole respectively. Though these pole designs are not as light as timber poles, they are about half the weight of previously used concrete poles. This study could enhance the electricity distribution infrastructure in Ghana. In anticipation of the introduction of nuclear power into the energy generation mix of the country, the lighter ii University of Ghana http://ugspace.ug.edu.gh weight reinforced concrete poles designed in this study could be utilised to increase the accessibility of electricity to the end-user. iii University of Ghana http://ugspace.ug.edu.gh ACKNOWLEDGEMENT First, I will like to thank God Almighty for the grace and mercy shown me in this degree’s pursuance. I thank my parents and sisters for the unending support they have given me over the years that brought me this far. My profound gratitude goes to my supervisors, Dr Nii Kwashie Allotey and Dr Emmanuel Boafo, for their patience, guidance, and support, which made this thesis a success. I would also like to appreciate the following people for their assistance in various forms towards the completion of this study: Dr Seth K. Debrah, Dr. Emmanuel Maurice Aurthur, Dr. Ameyaw Ing. Brownson Ateko, Kojo Asare Amankrah, Kwaku Amoa Buahin, David Diop Frimpong, Ethna Adzokpa and Caleb Wiredu. Finally, I would like to thank all my friends and loved ones. I couldn’t have done it without you. iv University of Ghana http://ugspace.ug.edu.gh TABLE OF CONTENTS DECLARATION ................................................................................................................. i ABSTRACT ........................................................................................................................ ii ACKNOWLEDGEMENT ................................................................................................. iv Table of Contents ................................................................................................................ v List of Figures .................................................................................................................. viii List of Tables ...................................................................................................................... x 1 CHAPTER ONE: INTRODUCTION ......................................................................... 1 1.1 Background and Context ...................................................................................... 1 1.1.1 The current state of the distribution network in Ghana ................................ 3 1.2 Problem Statement ............................................................................................... 4 1.3 Research Objectives ............................................................................................. 5 1.4 Relevance and Importance of the Research ......................................................... 6 1.5 Outline of the Thesis ............................................................................................ 8 2 CHAPTER TWO: LITERATURE REVIEW.............................................................. 9 2.1 Introduction .......................................................................................................... 9 2.1.1 Electrical Power Distribution ........................................................................ 9 2.1.2 History and Evolution of Electricity Poles ................................................... 9 2.2 Types of Electricity Distribution Poles .............................................................. 10 2.2.1 Wooden Electric Pole ................................................................................. 11 v University of Ghana http://ugspace.ug.edu.gh 2.2.2 Concrete poles ............................................................................................. 16 2.3 Structural Design ................................................................................................ 17 2.3.1 Limit State Design ...................................................................................... 18 2.3.2 Analysis and design .................................................................................... 19 2.3.3 Load Considerations ................................................................................... 21 2.3.4 Material Design ........................................................................................... 22 2.3.5 Finite Element Method ............................................................................... 26 2.3.6 Computational Modelling Using Finite Element Method .......................... 27 3 CHAPTER THREE: METHODOLOGY .................................................................. 30 3.1 Introduction ........................................................................................................ 30 3.2 Collection of Data and Acquisition of Design Tools and standards .................. 31 3.3 Modelling and Simulation .................................................................................. 32 3.3.1 Initial Pole Design Proposal........................................................................ 33 3.3.2 Model Creation ........................................................................................... 34 3.3.3 Boundary conditions ................................................................................... 36 3.3.4 Load Definition and Calculation ................................................................. 36 3.4 Post-processing................................................................................................... 45 4 CHAPTER FOUR: RESULTS AND DISCUSSION ................................................ 46 4.1 Moment Distribution .......................................................................................... 46 4.2 Pole Structure Displacement .............................................................................. 48 vi University of Ghana http://ugspace.ug.edu.gh 4.3 Interaction Diagram for Pole Structure .............................................................. 50 4.4 Design Summary ................................................................................................ 53 5 CHAPTER FIVE: CONCLUSION AND RECOMMENDATION .......................... 55 5.1 Conclusion .......................................................................................................... 55 5.2 Recommendation ................................................................................................ 56 REFERENCES ................................................................................................................. 57 APPENDIX A ................................................................................................................... 63 APPENDIX B ................................................................................................................... 80 vii University of Ghana http://ugspace.ug.edu.gh LIST OF FIGURES Figure 1.1: Electric-Power-Generation-Transmission-and-Distribution-Network-in-Ghana (Nunoo & Attachie, 2011) .................................................................................................. 1 Figure 1.2:High tension pole with mounted transformer .................................................... 4 Figure 2.1: types of trees considered for the production of timber poles ......................... 12 Figure 2.2: Deterioration of timber pole due to ant and termite infestation ..................... 14 Figure 2.3: Mix proportion relationships .......................................................................... 22 Figure 2.4: Strength gain curve of concrete ...................................................................... 23 Figure 2.5: Cover to reinforcement ................................................................................... 26 Figure 2.6: Complete procedure for finite element method (Kolgiri, 2009) .................... 27 Figure 3.1: flow chart of how the study was carried out .................................................. 30 Figure 3.2: Initial pole designs proposed .......................................................................... 33 Figure 3.3: Free body diagram for tapered pole design drawn in AutoCAD ................... 35 Figure 3.4: Material definition for concrete and steel in ETABS 2016 ............................ 35 Figure 3.5: Wind velocity at 10m height for Ghana (Badger et al., n.d.) ......................... 38 Figure 3.6: Wind forces on conductors – General case (En 50341-1 – Overhead Electrical Lines Exceeding AC 1 KV – Part 1: General Requirements – Common Specifications, 2012) ................................................................................................................................. 43 Figure 4.1: a. Moment distribution for 9meter pole with pinned support ......................... 46 Figure 4.2 a. Moment distribution for 11meter pole with pinned support ........................ 47 Figure 4.3: a. Un-guyed displacement graph, 9meter pole b. Un-guyed displacement graph, 11meter pole .......................................................................................................... 48 viii University of Ghana http://ugspace.ug.edu.gh Figure 4.4: a. Guyed displacement graph – 9meter pole b. Guyed displacement graph – 11meter pole 49 Figure 4.5: Axially loaded column with both uniaxial and biaxial loading ...................... 50 Figure 4.6 Interaction diagram for combined bending and axial load .............................. 51 Figure 4.7: PMM interaction diagram for 9meter pole provided by ETABS 2016 .......... 52 Figure 4.8: PMM interaction diagram for 9meter pole provided by ETABS 2016 .......... 52 Figure B.1: Terrain images for Terrain types 0, III and IV .............................................. 82 ix University of Ghana http://ugspace.ug.edu.gh LIST OF TABLES Table 2-1: Concrete strength classes for C20/25 to C35/45 (British Standards Institution, 2008) ................................................................................................................................. 24 Table 3-1: Initial electricity pole design dimensions ........................................................ 34 Table 3-2: Wind load calculation output .......................................................................... 40 Table 3-3: Values of wind force action on tapered and circular pole as well as on conductors ......................................................................................................................... 44 Table 4-1: Final Pole design dimensions .......................................................................... 53 Table 4-2: Comparison between previously used concrete poles and the lighter weight concrete pole design .......................................................................................................... 54 Table 4-3: .......................................................................................................................... 54 Table A-0-1: Wind force action on conductors for 9meter poles at Terrain IV ............... 64 Table A-0-2: Wind force action on conductors for 9meter poles at Terrain III ............... 66 Table A-0-3: Wind force action on conductors for 9meter poles at Terrain 0 ................. 67 Table A-0-4: Wind force action on conductors for 11meter poles at Terrain IV ............. 68 Table 0-5: Wind force action on conductors for 11meter poles at Terrain III .................. 69 TableA-0-6: Wind force action on conductors for 11meter poles at Terrain 0 ................ 70 Table 0-7: Wind force action on poles for 9meter poles at Terrain IV ............................. 71 TableA-0-8: Wind force action on poles for 9meter poles at Terrain III .......................... 72 Table A-0-9: Wind force action on poles for 9meter poles at Terrain 0 ........................... 73 Table A-0-10: Wind force action on poles for 11meter poles at Terrain IV .................... 75 Table 0-11: Wind force action on poles for 11meter poles at Terrain III ......................... 76 Table A-0-12: Wind force action on poles for 11meter poles at Terrain 0 ....................... 77 x University of Ghana http://ugspace.ug.edu.gh Table B-1: Terrain type description .................................................................................. 81 Table B-3:Exposure classes related to environmental conditions in accordance with EN 206-1(British Standards Institution, 2008) ....................................................................... 84 Table B-4: Minimum concrete cover(British Standards Institution, 2008) ...................... 88 xi University of Ghana http://ugspace.ug.edu.gh 1 CHAPTER ONE: INTRODUCTION 1.1 BACKGROUND AND CONTEXT Electricity is an essential commodity or utility for individuals and nations alike. With the advancement of technology, access to electrical power is paramount to the economic development of a country. The World Bank ranked electricity as the second most important constraint to business activities in the country. It estimated that Ghana lost about 1.8 per cent of GDP during the 2007 power crisis (Mathrani et al., 2013). An added advantage of a reliable power supply system is that the comfort of individuals is ensured. Generally, electricity goes through a three-step process before it arrives at the end-user for consumption. First, power is produced from generators. Second, the electric power is transported over the transmission network to the bulk load distribution substations. Finally, power is delivered to the individual customer sites using distribution lines. Figure 1.1: Electric-Power-Generation-Transmission-and-Distribution-Network-in- Ghana (Nunoo & Attachie, 2011) Presently, electrical power in Ghana is generated through Hydro and thermal power plants. Over the past decade, Ghana’s power sector has been plagued with power supply 1 University of Ghana http://ugspace.ug.edu.gh challenges, resulting in a considerable impact on the country’s economic situation. To offset the power crisis, policies have been made to harness nuclear energy. Nuclear energy will serve as a base-load power supply to offset energy crises experienced recently in the country (Bokpe, 2019). A system of electrical wires and cables transmit electrical power from the source of generation to consumers. These lines may be overhead as used in Ghana or sometimes laid underground, as is the case in most European countries (House et al., 2003). There are two stages of transporting electricity: • The transmission of electricity from the source/power plant to a substation. • The distribution of electricity - transports power from the substation to consumers. The transmission and distribution lines network make up what is commonly referred to as “the grid.” Ghana has an extensive transmission system that covers all the regions of the country. High-voltage transmission network connects generation sites in Akosombo, Aboadze, Takoradi, Kpong and Tema to various load centres around the country. The network features over 4,000 km of high-voltage electric transmission lines that connect to over 40 substations. Substations on the transmission system receive power at higher voltages and lower them to lesser volts to feed the distribution systems. (Kuenyehia et al., 2019) The distribution system is a network of low-voltage distribution lines generally considered to begin at the bulk power distribution substation. GRIDCo then delivers electricity to wholesale power buyers and then to the retail consumer’s meter. At key locations, voltage is lowered by transformers to meet consumer needs. The distribution network consists of 2 University of Ghana http://ugspace.ug.edu.gh electric poles, transformers, conductors and insulators. Timber, concrete as well as metal (steel) are materials used for electric poles with timber being the most common. Timber is the material of choice because of its low cost of production as well as availability. 1.1.1 The current state of the distribution network in Ghana The distribution network in Ghana currently, predominantly makes use of timber poles with a few sightings of concrete and steel poles. The Electricity Company of Ghana (ECG) is venturing into the use of other materials apart from timber as the mainstay for the distribution poles. The Northern Electricity Distribution Company (NEDCO) has also given out a contract for the production of concrete poles. This presupposes that timber as the preferred material used for the production of distribution poles may be phasing out. The conductors of choice are120 mm2 All Aluminium Alloy Conductors (AAAC). The distribution network is grouped into two categories, the high-tension poles and the low- tension poles. The high-tension poles are characterised by longer and thicker poles, usually 11meter poles with three conductors attached at the pole, as shown in Figure 1.2. The longest span between high tension poles are 100 meters, and the shortest is 80 meters. There are some assemblies of high-tension poles that have a transformer mounted on the pole while others have a transformer placed close by. Low tension poles are comparatively shorter and thinner, usually 9meter in length and have four conductors attached to it. The distance between low tension poles may span up to 50 meters. 3 University of Ghana http://ugspace.ug.edu.gh Figure 1.2:High tension pole with mounted transformer 1.2 PROBLEM STATEMENT A study undertaken by the Governments of Ghana and the United States concluded that “inadequate and unreliable” power supply is one of three major constraints to future economic growth. The Institute of Statistical, Social and Economic Research (ISSER) at the University of Ghana estimated in a 2014 study that Ghana, on the average, lost production worth about US $2.1 million per day (2% of GDP) through the power crisis(“Institute of Statistical, Social and Ecconomical Research (ISSER) Annual Report,” 2015). There are a host of challenges faced in the generation, transmission and distribution of power. This research deals with some of the challenges with the distribution network, specifically, the challenges associated with electric distribution poles. As stated early on, Ghana makes use of three materials for electric distribution poles, timber, concrete and metal, timber being the most common. 4 University of Ghana http://ugspace.ug.edu.gh Timber is treated to prevent deterioration by natural elements. However, despite treatments, the timber still is subject to deterioration and decay at varying levels due to fungal and termite attacks. (Yang Yu, Jianchun Li, Ning Yan, Ulrike Dackermann, Bijan Samali, 2016). Another issue that has plagued the use of timber electric poles is how easily it burns. In Ghana, bush burning is a common practice for farmers at the turn of planting seasons and has quickly become the bane of timber poles. According to two news articles from 2017 and February 2019, a total of 228 high-tension poles and 48 low-tension poles have been lost to bush fires, which cost the government of Ghana over 200,000 Ghana cedis to replace (Asiedu-Addo, 2017; Saeed, 2019). Also, a pole fire can be ignited by sparks that may occur as a result of damaged or faulty wires or insulators that allow leakage of current into the wooden pole. (Lunuwilage, 2013) Timber has been the material of choice for electric poles due to low cost of production as well as availability. However, in recent times, there has been a decline in the Ghana timber industry. Hence, there is a need to import timber to replace destroyed poles and erect new ones to achieve 100 per cent power access in Ghana (Adaam, 2014). Importing timber to be used for poles considerably increases the cost of production. This research focuses on improving the design of concrete poles such that the inherent strength and stability of the pole is equal to or better than the timber poles while eradicating the problem of using timber. 1.3 RESEARCH OBJECTIVES The overall objective of this study is to design a lighter weight reinforced concrete distribution pole as an alternative to existing timber electric poles in Ghana. This would 5 University of Ghana http://ugspace.ug.edu.gh result in the improvement of the electricity distribution infrastructure in Ghana. The following tasks aided in achieving this goal. • Determine the overall wind force applied to the distribution pole. • Model and simulate an FE model of the proposed concrete pole with the use of a mechanical tool. • Determine the capacity of the proposed pole structure. • Assess the stability of the proposed pole structure • Based on the moment distribution, select the type of support system. 1.4 RELEVANCE AND IMPORTANCE OF THE RESEARCH Electricity is one of the essential utilities in a country and a major determinant of the economic prosperity of the country. It plays a significant role in industries such as healthcare, education, just to mention a few. On an individual level as well, the use of electrical gadgets have made the execution of daily tasks easier and hence improves the quality of life(Kumi, 2017). As of the year 2018, Ghana could boast of an 82.3% electricity access, one of the highest in Sub-Saharan Africa (Ghana Energy Situation - Energypedia.Info, n.d.) with plans to make it a hundred per cent by the year 2020. To achieve this, it is required that generation, transmission and distribution of power are reliable and stable. Generation of electricity in Ghana is achieved primarily from the hydropower plant at Akosombo as well as from thermal power plants. The overall installed capacity of all generation plants add up to 4399 MW; however, 2400 MW of electric power is produced. Changing hydrological conditions, inadequate fuel supply, as well as run-down 6 University of Ghana http://ugspace.ug.edu.gh infrastructure, have caused the plants to generate below their capacity. (Africa & Support, 2016). In view of this, there is a national policy for Ghana to include nuclear power in her energy generation mix. Nuclear power has proven to be a more reliable source and can serve as the base-load for electric power generation. With the likely introduction of nuclear power, the reliability and stability desired on the generation leg of power production will be largely dealt with. However, from the perspective of the end-user, until electricity is accessible, solving the problems associated with generation does not solve their problem. This brings to light the issues associated with the transmission and distribution of power. Electricity distribution poles are predominantly constructed with timber and a few others with concrete. As mentioned earlier, timber is susceptible to burning and decay while the concrete poles are so old most have deteriorated beyond repair. If Ghana is to achieve 100 per cent electricity access, and for the end user to enjoy the full benefits of a stable and reliable power generation, investigations should be conducted into the use of other materials for electricity pole construction thereby making this study relevant. The outcome of the research will be the development of a more stable alternative to the timber poles, made of lighter weight concrete. This will be designed to have a longer life span and strength as well as eradicate the problem of decay and burning associated with timber and hence generally improve the electricity distribution infrastructure in Ghana. The key contribution of this study is the design of normal weight concrete to produce relatively light electricity poles in Ghana. Over the years, there have been numerous 7 University of Ghana http://ugspace.ug.edu.gh research studies as well as experimental work conducted in the use of alternative materials for the construction of electricity poles. In this study, the choice of material investigated was informed by the ease of production of normal weight concrete in Ghana without the need for specialised skills. Also, materials for reinforced normal weight concrete are locally available and comparatively cheaper than other materials. 1.5 OUTLINE OF THE THESIS The thesis is divided into five chapters and is organised as per the detail given below: Chapter 1: Presents a brief introduction to the topic of study. Chapter 2: Presents a review of literature on topics relevant to this study. Chapter 3: Presents the method employed to achieve the objective of this study. Chapter 4: Presents a discussion on the results obtained. Chapter 5: Presents conclusions of the study and recommendations for future studies. 8 University of Ghana http://ugspace.ug.edu.gh 2 CHAPTER TWO: LITERATURE REVIEW 2.1 INTRODUCTION This chapter presents a brief overview of the current distribution network in Ghana. It outlines the types of electricity poles and focuses on the design of concrete poles. 2.1.1 Electrical Power Distribution Electric power distribution is the delivery of electricity from high-voltage transmission circuits to the end-user. Primary distribution lines are “medium-voltage” circuits, normally thought of as 600 V to 35 kV. At a distribution substation, a transformer takes the incoming transmission-level voltage (35 to 230 kV) and steps it down to several distribution primary circuits, which fan out from the substation. Close to each end user, a distribution transformer takes the primary-distribution voltage and steps it down to a low-voltage secondary circuit (commonly 120/240 V; other utilisation voltages are used as well). From the distribution transformer, the secondary distribution circuits connect to the end user where the connection is made at the service entrance. The distribution network can be underground or mounted on poles. Over the years due to technological advancement, different material such as steel, timber, concrete and fibreglass have been investigated and used for poles. 2.1.2 History and Evolution of Electricity Poles The first of utility poles were erected in the 19th century to carry telegraph wires. In 1843, Samuel Morse wanted to connect Baltimore, Maryland and Washington DC with a telegraph line. He had perfected the telegraph, a technology in which the government showed interest and awarded him the contract to construct the telegraph line. He initially 9 University of Ghana http://ugspace.ug.edu.gh buried the line underground but found so many problems with the line and was forced to dig it up. With time running out and funds running low, he with his team came up with a plan to hang the line on posts, to be exact, chestnut posts 20 to 30 feet in height. This plan worked successfully and in I844, the first telegraph was transmitted. Though the wooden poles were used because of time and financial constraints, however, they quickly caught on because it was cheaper and chestnut was abundant. By the turn of the 20th century, the chestnut poles carried telegraph, telephone and electrical lines. The poles were outfitted with insulators so they could safely carry electrical lines. Overtime, the use of chestnut wood phased out and other species of wood were introduced. (Mulqueen, 2017; Utility Poles - Aged Woods, Inc., 2017) Due to technological advancements, materials such as steel fibreglass and concrete have been introduced to be used as electrical/utility poles. Timber poles however continue to dominate mainly because of the low cost of production.(Adaam, 2014) 2.2 TYPES OF ELECTRICITY DISTRIBUTION POLES There are various types of poles being used today. The type of pole is selected based on a combination of factors, the most common of which are the: • mechanical strength • weight – preferably, the pole should be lighter weight without having an impact on its mechanical strength • Cost impact of such construction, including the maintenance cost In the world today, there are different types of materials being used for the construction of poles. The most common materials in use are: 10 University of Ghana http://ugspace.ug.edu.gh 1. Wooden Electric Pole 2. Concrete Electric Pole 3. Steel Tubular Electric Pole Recently, studies are being conducted on the use of composite materials as well as other materials such as fibre glass for electricity distribution poles but this research will concentrate on normal weight concrete as the material of choice. 2.2.1 Wooden Electric Pole As stated earlier, wood was the material to be used for the first poles. In the beginning, these wooden poles were used for 400- and 200-volts low tension lines, 11 kilovolt high tension lines and on occasion 33 kilovolt lines. Wood selected for use as electric poles should meet the necessary strength requirements. With these requirements of utility poles in mind, trees selected for use should possess the following. The main trunk of the tree should be: • 30 to 60 feet high and be string-line straight (Figure 2.1), however in some cases, it may be impossible to get straight wood for such lengths hence a small degree of curvature is acceptable. Alternatively, two short length poles can be joint together to achieve the length requirements. • free of major stem defects (cankers, cat-faces, rot) • have minimal taper • be largely free of branch knots • have a small juvenile core 11 University of Ghana http://ugspace.ug.edu.gh • Meet specific height and diameter requirements. Figure 2.1: types of trees considered for the production of timber poles Based on the above stated requirements, there are some species of wood that are deemed acceptable for use as distribution poles. Initially, species such as chestnut and cedar were used because they are naturally resistant to rot and decay. However, with the decline of cedar and the fungal problems associated with chestnut, other species of wood have been introduced. Some common ones include: • Southern Yellow Pine • Douglas Fir • Western Larch • Lodgepole pine • Western Red Cedar • Ponderosa Pine • Jack Pine 12 University of Ghana http://ugspace.ug.edu.gh 2.2.1.1 Causes of Deterioration Wood poles are continually exposed to biotic and abiotic factors. (Gezer et al., 2015) Examples of abiotic factors are weathering and burning. Weathering is the erosion of wood surface due to the combined action of wind, rain, changing temperatures and exposure to sunlight.(Graham, 1960; Shupe et al., 2008) This causes roughening of the surface, checking, splitting and wood cell erosion. In some areas where bush fires are rampant, there are issues of wood poles being burnt. The biotic factors include attack by plants, insects, and animals that utilise wood both for food and for shelter, some of which are: • Decay fungi: Decay utilise starches, cellulose, and lignin of complex plants, in this case the cell walls in wood to produce food causing changes in appearance, that is colour and luster, as well as compromising the strength.(Graham, 1960) • Termites: Termites feed on cellulose which is abundant in wood material. (Graham, 1960) • Carpenter Ants: Carpenter ants bore holes in wood material to be used as places for shelter and nesting purposes, (Shupe et al., 2008) • Beetles: They feed on the wood when they hatch, creating tunnels in the process. Once the larvae have developed into adults, they emerge from the wood leaving behind holes in the wood surface.(Shupe et al., 2008; Wood Boring Insects and Beetles | Western Exterminator, n.d.) 13 University of Ghana http://ugspace.ug.edu.gh Figure 2.2: Deterioration of timber pole due to ant and termite infestation Deterioration can however be retarded by treating the wood with preservatives, hence increasing the life expectancy of the wood pole. Initially 15 to 20 years of service was expected, today wood poles have been seen to last up to 50 years. (Graham, 1960) 2.2.1.2 Wood Preservation Wood preservation is the injection of chemicals into wood through the process of pressure or thermal impregnation to provide effective long-term resistance to attack by fungi, bacteria, insects, and marine borers. (Neulicht & Shular, 1999) A few trees like cedar, chestnut and redwood have a heartwood with naturally occurring chemicals that make them resistant to rot and decay and organisms that destroy the wood, but other species of wood have to be injected with chemicals to achieve that resilience to rot and decay. These chemicals also serve to protect against weathering and fire damage. (Graham, 1960) 14 University of Ghana http://ugspace.ug.edu.gh Preservatives are mainly classified into two groups, the tar oil/ oil-soluble preservatives and the water-soluble preservatives. (Shupe et al., 2008) There are others such as organic solvent-borne preservatives and emulsions/micro-emulsions (Mai & Militz, 2007), however the above mentioned are the widely used. Oil-soluble preservatives such as creosote and pentachlorophenol are the most common for the treatment of wood for poles. An additional benefit is that these preservatives provide protection against weathering and hence dimensional stability by reducing water absorption. (Graham, 1960) 2.2.1.3 Durability of Wooden Poles According to Gezer et al.,(2015), on their research work on inspection of wooden poles in Artvin, Turkey, they found that, the reasons for the short service life of utility poles were 1. the decay due to fungi, 2. insect infestation, 3. inadequate impregnation, 4. insufficient preservative penetration depth, 5. the deep cracks and splits, 6. poor quality control, 7. no inspection and lack of remedial treatments. The above led them to conclude on the importance of increasing the service life of wood poles because of: 1. the costs associated with their replacement 2. environmental concerns, out of service poles are considered hazardous wastes which must be adequately disposed of or recycled. 15 University of Ghana http://ugspace.ug.edu.gh Taking a cue from this research, instead of looking at prolonging the service life of the wood pole, this research thesis, explores the idea of using an alternative material, specifically normal weight concrete to achieve the same goal. 2.2.2 Concrete poles Concrete is a composite material that is comprised of water, fine and coarse aggregates and cementitious material. Chemical additives may be added to achieve desired properties of the concrete mix for a specific use. Concrete has been found to have high compressive strength however has a low tensile strength equivalent to about 10% of its compressive strength and hence considered a quasi- brittle material. To rectify this problem, concrete structures are designed with steel bars which serve as a reinforcement of tensile strength and protection against a brittle failure.(Słowik, 2019) Concrete is one of the most widely used materials in the construction industry across the world due to the economy of its use, durability as well as the ease of manufacturing. Concrete having the ability to be cast into any desired form or shape is also an added advantage of concrete as a construction material. (Durocrete Engineering Services Pvt. Ltd, 2000). Concrete poles have been in use since the early 1900s, but gained popularity when the use of creosote (the most common wood preservative) proved to have negative effects on the environment(“A Wide Creosote Ban Is Proposed by E.P.A.,” 1984; Angeling, 2017). Studies have shown that concrete poles are durable, require low maintenance and have a 16 University of Ghana http://ugspace.ug.edu.gh life span of more than 80 years (Angeling, 2017). The initial cost of erecting concrete poles are higher than wooden pole, however the long term cost effect is lower due to lower maintenance cost. Normal concrete is a relatively heavy material weighing between 2240 to 2450 kg/m3. This increases the cost of transportation and hence the overall cost of production of concrete poles. During the twentieth century, numerous experiments have been conducted to reduce the weight of concrete whilst retaining the other properties. The result of these experiments was lightweight concrete with a density of 300–2000 kg/m3, with a practical range of 500– 1850 kg/m3 (Guo, 2014; Hedjazi, 2016). It has been found that the use of lightweight concrete reduces the overall weight of the structure by 20 to 40%.(Guo, 2014). 2.3 STRUCTURAL DESIGN According to Mrema, 2011, “Structural design is the methodical investigation of the stability, strength and rigidity of structures.” The objective in structural analysis and design is to produce a structure, in this case the electricity pole, which can resist applied loads without failure during its intended life. The principal purpose of a structure is to transmit or support loads. If actual loads applied exceed the design specifications, the structure will probably fail to perform its intended function, with possible serious consequences. Electricity distribution poles are designed to withstand loads generated from weather- related events, construction and maintenance events and must provide failure containment to minimise damage from catastrophic events. The characteristic design loads depend on the structure location, that is, the geography, topography and elevation of the location.(Dagher, 2006) 17 University of Ghana http://ugspace.ug.edu.gh 2.3.1 Limit State Design Designing an engineering structure should ensure that: • under the worst loadings the structure will be safe • during normal working conditions, deformation of the members do not diminish the appearance, durability or performance of the structure. Three basic methods using factors of safety are used to achieve safe, workable structures have been developed; • The permissible stress method: ultimate strengths of the materials are divided by a factor of safety to provide design stresses usually within the elastic range. • The load factor method: working loads are multiplied by a factor of safety. • The limit state method: working loads are multiplied by partial factors of safety. Also the materials’ ultimate strengths are divided partial factors of safety. Though the permissible stress method has proved to be a simple and useful method, it does have some serious inconsistencies. It is based on an elastic stress distribution hence cannot be applied to semi-plastic materials like concrete. Neither is it suited to non-proportional load deformations as in slender columns.(Mosley et al., 2012) Ultimate strength of the materials are used in the load factor method calculations. The method does not apply factors of safety to material stresses, and does not take into account the variability of the materials. Also, it cannot be used for deflections calculations or cracking at working loads. The limit state method of design overcomes the disadvantages of the previous methods by the application of partial factors of safety, both to the loads and to the material strengths. 18 University of Ghana http://ugspace.ug.edu.gh The magnitude of the factors is varied so they may be used either with the plastic conditions in the ultimate state or with the more elastic stress range at working loads. The two types of limit state are the ultimate limit state and the serviceability limit state. 1. Ultimate Limit State (ULS): This limit state is concerned with the safety of the people and of the structure. This requires that the whole structure or its elements should not collapse, overturn or buckle when subjected to the design loads. 2. Serviceability Limit State (SLS): This limit state is concerned with: • Comfort of the occupants • Appearance of the structure. The structure should not become unfit for use due to excessive deflection or cracking. The normal practice is to design for the ultimate limit state for reinforced concrete structures is to check for serviceability and take all necessary precautions to ensure durability.(Bhatt et al., 2017; Mosley et al., 2012) 2.3.2 Analysis and design The complete analysis of a load-carrying structural member by the method of equilibrium involves consideration of three conditions relating to specific laws of forces. The laws of material deformation, and geometric compatibility. These basic principles of analysis are as follows: 1. Equilibrium Conditions: Equations of the equilibrium of forces must be satisfied throughout the structural member. 2. Material Behavior: The stress–strain otherwise force-deformation relations (for example, Hooke's law) must apply. 19 University of Ghana http://ugspace.ug.edu.gh 3. Geometry of Deformation: Compatibility conditions of deformations must be satisfied, that is, the deformed portion of each member must fit together An alternative to the equilibrium methods is the use of energy methods. The aspect of both the equilibrium and the energy approaches is twofold. These methods can provide solutions of acceptable accuracy The process by which science and engineering techniques are applied to a structure or system to allow its realization is engineering design. The objective of a structural design includes finding suitable materials, dimensions, and shapes of the members of a structure in order to support prescribed loads without failure. A good design satisfies the following requirements; • Performance • Cost • safety requirements. For a design problem with numerous choices, the designer may make decisions on the basis of experience. Design decisions, like the choice of the values of safety factors and material properties, are significant in the preliminary design process. The following is the design procedure for a structural member: 1. Evaluate the most likely modes of failure of the member. 2. Determine the expressions relating applied loading, eg. to stress, strain. 3. Determine the maximum usable value of stress, strain, or energy 20 University of Ghana http://ugspace.ug.edu.gh 4. Select a design factor of safety. This is to account for uncertainties in a number of aspects of the design. The factor of safety is expressed as: The factor of safety should be greater than 1.0 for failure to be circumvented. The value 1.5 or greater is usually selected as a factor of safety, based on the experience and judgment of the designer.(Ugural & Fenster, 2016) 2.3.3 Load Considerations In structural design, forces and moments applied to a structure is termed loads. These may be applied externally (surface loads), or within the structure (body loads). Loads are described as either static or dynamic. Static loads are of constant magnitude, direction, and location, independent of time. Dynamic loads however change with time, some examples are: • Live loads’’ from occupant activity, • wind loads, • seismic (earthquake) Dynamic loads are grouped into two categories:(Jenkins & Khanna, 2005) 1. Steady-state loads - loads that maintain the same character (frequency, amplitude, etc.) over the long term. 21 University of Ghana http://ugspace.ug.edu.gh 2. Transient loads are loads that change their character (e.g., they may decay) with time. 2.3.4 Material Design There are numerous properties of concrete such as durability, porosity among others which are considered very important. However, the strength of the concrete is usually considered to be the most valuable property. The strength of concrete is directly related to the structure of the cement paste (water: cement ratio) and hence gives an overall image of the concrete quality.(Neville & Brooks, 2010) Figure 2.3: Mix proportion relationships The strength of concrete may be defined as the compressive strength of hardened concrete at an age of 28 days. As can be seen in Figure 2.3 beyond 28 days there are very small increments in the strength and does not change much from what is recorded on day 28. 22 University of Ghana http://ugspace.ug.edu.gh Figure 2.4: Strength gain curve of concrete The compressive strength of concrete is categorised into different strength classes, which are based on the characteristic (5%) cylinder strength or the characteristic cube strength. The highest recommended value for the compressive strength of concrete is C90/105. From Figure 2.4, it can be seen that as compressive strength increases, the water cement ratio (wcr) decreases hence affecting other properties of concrete. (Angeling, 2017) Strength and strain properties for strength concrete classes C20/25 – C35/45 (normal strength concrete), according to EN 1992 (British Standards Institution, 2008), can be found in Table 2-1 23 University of Ghana http://ugspace.ug.edu.gh Table 2-1: Concrete strength classes for C20/25 to C35/45 (British Standards Institution, 2008) Stregnth fctk,0.05 fctk,0.95 Class/ fck, MPa fck,cubeMPa fcm Mpa fctm Mpa Ecm GPa Mpa Mpa Property C20/25 20 25 28 2.2 1.5 2.9 30 C25/30 25 30 33 2.6 1.8 3.3 31 C30/37 30 37 38 2.9 2.0 3.8 33 C35/45 35 45 43 3.2 2.2 4.2 34 𝑓𝑐𝑘: the cylindrical compression strength 𝑓𝑐𝑘.𝑐𝑢𝑏𝑒: cubical compression strength. Other values given in the table are the 𝑓𝑐𝑚: mean value for cylindrical compression strength, 𝑓𝑐𝑡𝑘0.05: the lower characteristic tensile strength 𝑓𝑐𝑡𝑘0.95: an upper characteristic tensile strength 𝑓𝑡𝑚: the mean tensile strength 𝑓𝑐𝑚: at maximum stress; 𝐸𝑐𝑚: mean value for the modulus of elasticity Concrete as a material has a significantly low tensile strength. Reinforced cement concrete (RCC), a composite material was introduced to overcome the low tensile strength of concrete. The reinforcement which are steel bars transfer tensile forces after cracking in the tensile areas. (Angeling, 2017) 24 University of Ghana http://ugspace.ug.edu.gh Reinforcement or steel bars are categorised as high yield bars and mild steel bars. Both types of bars are ribbed to enhance the bond between the bar and the concrete. Reinforcement bars are susceptible to corrosion when exposed to the atmosphere. To cater for this, a distance between the surface of the reinforcement bar (including links and stirrups and surface reinforcement where relevant) and the surface the concrete is provided. This is called concrete cover or cover to reinforcement.(British Standards Institution, 2008) The cover provided is defined in EUROCODE 2 as a minimum cover, cmin plus an allowance in design for deviation, Δcdev. cnom = cmin + Δcdev The minimum cover specified is dependent on the exposure conditions and environmental factors. EUROCODE 2 defines different exposure conditions and the minimum cover to be provided. See Tables B-2 and B-3 in Appendix B Besides corrosion protection, minimum concrete cover is provided in order to ensure: - the safe transmission of bond forces - an adequate fire resistance (British Standards Institution, 2008) 25 University of Ghana http://ugspace.ug.edu.gh Figure 2.5: Cover to reinforcement 2.3.5 Finite Element Method Engineering problems are generally physical representations of mathematical models. These mathematical models are sets of differential equations derived from applying fundamental laws of nature to a system(Moaveni, 1999). There are numerous methods for solving these mathematical models of which the finite element method is one. Finite Element Method (FEM) is a computational technique used to obtain approximate solutions of boundary value problems in engineering (Hutton, 2004). Simply, it is a method used to solve a complicated problem by replacing it with a simple problem. (Rao, 2011). The method is based on dividing the problem domain into several small elements known as domain discretisation, which are analysed by applying known physical laws to each of them.(Amankrah, 2015; Liu & Quek, 2013) The behaviour of each sub-domain, shaped by nodes and elements, is approached by using piecewise linear functions to represent the continuous function of an unknown field variable. The unknown represents discrete values of the field variable at the nodes. 26 University of Ghana http://ugspace.ug.edu.gh Appropriate principles are then used to develop equations for the elements which are then combined in a system of linear algebraic simultaneous equations which represent the system. These equations are solved to return the necessary field variable (Liu & Quek, 2013). Figure 2-6 below shows the finite element process. Figure 2.6: Complete procedure for finite element method (Kolgiri, 2009) 2.3.6 Computational Modelling Using Finite Element Method The behaviour of a physical phenomenon in a system depends upon the geometry of the system, the material properties and the initial and boundary conditions. The procedure of computational modelling using FEM broadly consists of four steps: • Modelling of the geometry • Meshing (discretisation) • Specification of material property 27 University of Ghana http://ugspace.ug.edu.gh • Specification of boundary and loading conditions 2.3.6.1 Modelling of the geometry There are numerous ways to model a geometry in in an analysis software or a simulator. Many simulators are coded with the option of modelling the geometry in the software. Otherwise, provision is made to import the geometry file from Computer Aided Design software like AutoCAD and SOLIDWORKS. 2.3.6.2 Meshing The process of discretising the geometry into small units called elements is referred to as meshing. Scientific theories are needed to discretise the geometry. The theories differ for every problem and provide the equations that govern the analysis to be run by the simulator. Mesh generation is an important task in pre-processing and can be tricky to produce a credible mesh especially for complex problems. The geometry and the displacement distribution of a real structure varies continuously. When using finite element to model the structure, the discretised structure cannot be fully matched with real model which causes errors. These errors can be reduced using smaller element or what is referred to a finer mesh (Neupane, 2014). For a mesh to be considered credible, the domain should be properly divided into elements of specific shapes. Triangles and quadrilaterals are used in 2D geometries while tetrahedrons and hexahedrons in 3D geometries. (Liu & Quek, 2013) 2.3.6.3 Material properties Engineering systems usually consist of multiple components. Each of these components may be of the same material or different materials. In some situations, there may be 28 University of Ghana http://ugspace.ug.edu.gh multiple materials within a single component as is the case of a composite material. Properties of materials can be defined for a group of elements or individual elements if required. The FEM can therefore work conveniently for systems with multiple materials, which is a significant advantage. For different phenomena or physics to be simulated, different sets of material properties are required, for instance, Young’s modulus and shear modulus are material properties that need to be specified for the stress analysis of solids and structures. ( Liu & Quek, 2013) 2.3.6.4 Boundary, initial, and loading conditions Boundary, initial, and loading conditions play a decisive role in the simulation. Conditions can be specified either to the geometrical identities (points, lines or curves, surfaces, and solids) or to the mesh identities (nodes, elements, element edges, element surfaces). The boundary, initial, and loading conditions differ for each problem (Liu & Quek, 2013). 29 University of Ghana http://ugspace.ug.edu.gh 3 CHAPTER THREE: METHODOLOGY 3.1 INTRODUCTION The method applied in the design and analysis of the distribution pole is presented in Figure 3.1. A description of the various components of the methodology is provided in sections of this chapter. Collection of Data • ETABS and acquisition of • Collect data • Initial design Analysis Tool and on existing proposal Standards concrete • Model creation poles o Material and size definition Modelling and • Apply boundary Simulation conditions • Loa definition and calculation Failure of • Solve Post Processing design – Redesign Success of design - Analysis of data • Stress • Strain • Displacement Figure 3.1: flow chart of how the study was carried out 30 University of Ghana http://ugspace.ug.edu.gh 3.2 COLLECTION OF DATA AND ACQUISITION OF DESIGN TOOLS AND STANDARDS Relevant data were collected from some institutions throughout the course of the study. Electricity Company of Ghana (E.C.G.) The Electricity Company of Ghana provided information on the design specifications they use for the existing timber poles. E.C.G. also provided information on the costs and problems associated with the use of timber poles. Data provided include structural design report of steel concrete and timber poles, which captured input parameters such as cross- sectional dimensions and material specifications. African Concrete Products (A.C.P.), CK Engineering and Construction Limited Design reports of the concrete poles previously used in Ghana were obtained from A.C.P. CK Engineering and Construction Limited also provided reports on prestressed spun concrete poles. The information provided included material specification as well as pole dimensions. Bye Ways Company Limited An interview was conducted with the production manager of the company. The production process involved in the production of timber poles, from the procurement of the wood, through the preparation and preservation of the pole Acquisition of design tools and standards ETABS 2016 from CSI was obtained and utilised for modelling and simulation of the pole structure. EUROCODE design manuals were also used as a guide for the pole design. 31 University of Ghana http://ugspace.ug.edu.gh • EN 50341-1 : Overhead electrical lines exceeding AC 1 kV - Part 1: General requirements - Common specifications (En 50341-1 - Overhead Electrical Lines Exceeding AC 1 KV - Part 1: General Requirements - Common Specifications, 2012) • BS EN1991-1-4: Actions on structures — Part 1-4: General actions — Wind actions (BSI, 2010) • BS EN 019921-1: Design of concrete structures —Part 1-1: General rules and rules for buildings(British Standards Institution, 2008) • BS EN 13369:2004 : Common rules for precast concrete products (British Standards Institution, 2007) • BS EN 12843:2004 : Precast concrete products – Masts and Poles (British Standards Institution, 2004) 3.3 MODELLING AND SIMULATION This portion of the work was completed using ETABS 2016 from CSI. To accomplish the design in ETABS, the following steps were required: • Initial design proposal ▪ Model creation • Material and size definition • Apply boundary conditions • Load definition and calculation • Solve the problem 32 University of Ghana http://ugspace.ug.edu.gh The pole structure in this study was designed assuming the worst-case scenario. Hence a pole located at either the beginning or the end of a line network was considered. 3.3.1 Initial Pole Design Proposal The proposed designs for the pole structure, as shown in Figure 3.2 were: • a tapered structure with a rectangular cross-section • a cylindrical pole Figure 3.2: Initial pole designs proposed These designs were proposed based on some considerations. The first consideration was the objective of this study, to design a light concrete pole with normal weight concrete. The size of the pole was reduced as much as possible to achieve a relatively light structure as compared to the previous concrete poles that were being used in Ghana. The second consideration was the minimum cover to reinforcement that should be provided, as stated by BS EN1992-1-1 and BS EN12843. 33 University of Ghana http://ugspace.ug.edu.gh Based on the considerations stated above, the dimensions for the initial pole designs proposed were: Table 3-1: Initial electricity pole design dimensions Tapered Pole Circular Pole 9m 11m 9m 11m Top 150x 150 150 x 150 150 150 Butt 250 x 150 250 x 150 150 150 NB: All dimensions are in millimetres (mm) unless otherwise specified The weight of the circular pole structure was found to be relatively high (almost the same as the weight of previous concrete poles); hence, only the tapered poles were considered for this study. 3.3.2 Model Creation A free body diagram (Figure 3.3) for each structure was drawn in AutoCAD and then imported into ETABS 2016 after which the structural and material properties were assigned to the model. The material used for the pole structure was concrete of strength class C25/30 as specified BS EN 13369 and for the reinforcement bars, high yield steel (fy = 500). The properties of this material is specified in the software (Figure 3.4) and are be applied as needed during the analysis. 34 University of Ghana http://ugspace.ug.edu.gh Figure 3.3: Free body diagram for tapered pole design drawn in AutoCAD Figure 3.4: Material definition for concrete and steel in ETABS 2016 35 University of Ghana http://ugspace.ug.edu.gh 3.3.3 Boundary conditions The next step was to apply the boundary conditions, that is, determine the type of supports for the pole structure. Two support scenarios were considered: • A fixed support • A pinned support Pinned supports are able to resist both horizontal and vertical forces but allow rotation. Fixed supports however is rigid and can resist moments as well as vertical and horizontal forces. 3.3.4 Load Definition and Calculation The final step before simulation was the application of loads cases, as described below, onto the model. With the exception of the self-weight of the pole and maintenance loads, all other loads were applied as lateral point loads at the top pole. The imposed loads were applied to the face of the structure and the wind loads to the side of it. The self-weight of the pole and maintenance loads were applied as axial loads. The pole is subjected to two types of loading: • Direct loading which comprises of - Dead Loads - Maintenance loads, taken to be 0.75 kN/m2 - Wind loads • Imposed Loads - loads generated from the conductors and fixtures attached to the pole. 36 University of Ghana http://ugspace.ug.edu.gh The dead loads, otherwise called the self-weight of the structure can be calculated by multiplying the volume of the structure and the unit weight of the material used to construct the structure. For this design, however, the self-weight of the pole structure was calculated in the software using the dimensions assigned to the structure and the property of the material assigned. 3.3.4.1 Wind loads The wind loads were calculated using the guidelines provided by BS EN1991-1-4 Wind Velocity Pressure Wind actions fluctuate and act directly as pressures on the external surfaces of enclosed structures. Pressures act on areas of the surface of the structure resulting in forces normal to the surface of the structure or of individual cladding components.(BSI, 2010) The wind loads are calculated based on EUROCODE 1991 – 1- 4 – Actions on Structures. The first step to calculating the wind loads is to obtain the wind velocities. This information was obtained from the Global Wind Atlas based on the previous regional demarcations in Ghana, that is, the ten regions in Ghana. The wind velocities obtained were at an altitude of 10 m as shown in Figure 3.5. 37 University of Ghana http://ugspace.ug.edu.gh Figure 3.5: Wind velocity at 10m height for Ghana (Badger et al., n.d.) The wind velocities obtained were corrected using correctional factors as provided by BS EN1991 – 1- 4 – Actions on Structures. The correctional factors are applied using the equations below. 𝑣𝑏 = 𝑐𝑑𝑖𝑟 ∗ 𝑐𝑠𝑒𝑎𝑠𝑜𝑛 ∗ 𝑣𝑏,0 3.1 where: vb = basic wind velocity vb,0 = value of the basic wind velocity cdir = directional factor, taken to be 1.0 cseason = season factor, taken to be 1.0 𝑣𝑚(𝑧) = 𝑐𝑟(𝑧) ∗ 𝑐𝑜(𝑧) ∗ 𝑣𝑏 3.2 vm(z) = mean wind velocity at height z co(z) = orography factor, taken as 1.0 cr(z) = roughness factor 38 University of Ghana http://ugspace.ug.edu.gh The Roughness factor cr(z) is determined by the terrain of the location of the structure. EN BS1991 – 1- 4 – Actions on Structures provides terrain categories and parameters to be used for the wind load calculations. Three terrain categories were used for this study, terrain categories 0, III and IV. See Appendix B for the table and images. cr(z) is given by: 𝑧 𝑐𝑟(𝑧) = 𝑘𝑟 ∗ ln ( ) for 𝑧𝑚𝑖𝑛 ≤ 𝑧 ≤ 𝑧𝑚𝑎𝑥 3.3 𝑧0 𝑐𝑟(𝑧) = 𝑐𝑟(𝑧𝑚𝑖𝑛) for 𝑧 ≤ 𝑧𝑚𝑖𝑛 3.4 where: z0 = roughness length kr = terrain factor depending on the roughness length z0 calculated using: 0.07 𝑧 0𝑘𝑟 = 0.19 ∗ ( ) 3.5 𝑧0,𝐼𝐼 where: z0,II = 0.05 m (terrain category II, Table B-1 Appendix B) zmin is the minimum height zmax is to be taken as 200 m The next step in the process is to compute the wind velocity pressure (𝑞𝑝(𝑧)), given by the equation: 1 𝑞𝑝(𝑧) = [1 + 7 ∗ 𝐼𝑣(𝑧) ] ∗ ∗ ρ ∗ 𝑣 2 2 𝑚 (𝑧) 3.6 where: ρ = air density, to be taken as 1.25 kg/m3 Iv(z) = wind turbulence intensity calculated using the equation below. 39 University of Ghana http://ugspace.ug.edu.gh 𝑘 I 𝑖 𝑣(𝑧) = 𝑧 for 𝑐0(𝑧)∗ ln( ) 3.7 𝑧0 𝐼𝑣(𝑧) = 𝐼𝑣(𝑧𝑚𝑖𝑛) for 𝑧 ≤ 𝑧𝑚𝑖𝑛 3.8 where: ki = turbulence factor. The recommended value for ki is 1.0. Table 3-2: Wind load calculation output Region vb,0 vb vm Iv qp Ashanti 3.02 3.0502 1.645772 0.434294 6.839233 Brong Ahafo 3.02 3.0502 1.645772 0.434294 6.839233 Central 3.35 3.3835 1.825608 0.434294 8.415562 Eastern 4.05 4.0905 2.207079 0.434294 12.29996 Greater Accra 4.14 4.1814 2.256125 0.434294 12.85269 Northern 2.93 2.9593 1.596726 0.434294 6.437671 Upper East 3.11 3.1411 1.694818 0.434294 7.252943 Upper West 3.05 3.0805 1.662121 0.434294 6.975787 Volta 3.46 3.4946 1.885554 0.434294 8.977299 Western 2.79 2.8179 1.520432 0.434294 5.837164 Wind Force on Pole The final step of the wind load calculation is to use the velocity pressure calculated above to compute the wind force (Fw). For this step, the geometry or the shape of the structure to be designed is considered. In some cases, the material to be used is also considered. The equation used to compute the wind force is given by: 40 University of Ghana http://ugspace.ug.edu.gh 𝐹𝑤 = 𝑐𝑠𝑐𝑑 ∗ 𝑐𝑓 ∗ 𝑞𝑝(𝑧) ∗ 𝐴𝑟𝑒𝑓 3.9 where: cscd = structural factor which is taken to be 1.0 Aref = reference area and should be determined by the expression 𝐴𝑟𝑒𝑓 = 𝑙 ∗ 𝑏 cf = force coefficient for structural elements The force coefficient differs from one structural element to another depending on the geometry of the element. For this research, the structural coefficients considered were structural elements with rectangular sections and cylindrical structural elements. Structural elements with rectangular cross-sections The force coefficient cf for rectangular cross-sections is given by: 𝑐𝑓 = 𝑐𝑓,0 ∗ 𝜓𝑟 ∗ 𝜓𝜆 3.10 and that of cylindrical elements is given by: 𝑐𝑓 = 𝑐𝑓,0 ∗ 𝜓𝜆 3.11 where: cf,0 = force coefficient of rectangular sections with sharp corners and cylinders without free- end flow ψr = reduction factor for square sections with rounded corners. ψr = 1 ψλ = end-effect factor for elements with free-end flow The end factor is a function of the slenderness ratio λ. The value of λ is determined from Figure B-2 in Appendix B. The end factor is subsequently read from the graphs provided in BS EN1991 – 1- 4 – Actions on Structures as shown in Figures B-3 in Appendix B. 41 University of Ghana http://ugspace.ug.edu.gh Imposed loads The imposed loads considered for this design were the loads generated from the conductors and fixtures attached to the pole. Fixtures, such as insulators and cross-arms were assumed to generate a force of 1.0kN as provided by BS EN50341 For the conductors, two load cases were considered, that is: • The self-weight of the conductor • The force generated due to wind action on the conductor In Ghana, 120mm2 All Aluminium Alloy Conductors (AAAC) are used for electricity distribution. The conductor spans a distance of up to 100 meters for high tension distribution and up to 50 meters for low tension distribution. The dimensions of the conductor provided in BS EN50183 are as follows Area = 118.9 mm2 Diameter = 14.0 mm Mass (per unit length) = 324.5 kg/km The self-weight of the conductor was computed using the mass of the conductor and a span of 100 and 50 meters for high tension and low-tension distribution, respectively. The force generated due to wind action was calculated according to EN 50341-1. The force generated is dependent on the arrangement of the distribution poles as well as the angle at which the wind hits the conductor as illustrated in Figure 3.6. 42 University of Ghana http://ugspace.ug.edu.gh Figure 3.6: Wind forces on conductors – General case (En 50341-1 - Overhead Electrical Lines Exceeding AC 1 KV - Part 1: General Requirements - Common Specifications, 2012) For this design, it was assumed that the poles are arranged in a straight line and also that the wind hits the conductor at a 90o angle hence the equation: 𝑄𝑤𝑐 = 𝑞𝑝(ℎ) ∗ 𝐺𝑐 ∗ 𝐶𝑐 ∗ 𝑑𝑐𝑜𝑠 2𝜙 ∗ 𝐿𝑚 3.12 where qp(h) = peak wind pressure h = height to be used for the conductor; Gc = structural factor for the conductor (also termed span factor); Cc = drag factor (or force coefficient) for the conductor which was taken to be 1 d = diameter of the conductor; φ = angle between wind direction and the longitudinal axis of the cross-arm defined in Figure 3-3 Lm = mean lengths of the two adjacent spans, L1 and L2 The structural factor Gc is given by: 43 University of Ghana http://ugspace.ug.edu.gh 1 + 2𝑘𝑝 𝐼 (ℎ) √𝐵2𝑣 + 𝑅2 𝐺𝑐 = 3.13 1 + 7𝐼𝑣(ℎ) where kp = peak factor defined as the ratio of the maximum value of the fluctuating part of the response to its standard deviation. Its recommended value is 3 Iv(h) = turbulence intensity R² is the resonance response factor, allowing for turbulence in resonance with the vibration mode. The recommended value for R² is 0 because resonance in the wind direction can be neglected for a line conductor. B² is the background factor, allowing for the lack of full correlation of the pressure on the span, and is given by: 1 𝐵2 = 3 𝐿𝑚 3.14 1 + 2 ∗ 𝐿(ℎ) L(h) = is the turbulent length scale (average size of gust in m) at the reference height, h of the conductors, given by the expression: ℎ 0.67+0.05ln (𝑧𝑜) 𝐿(ℎ) = 300 ( ) 3.15 200 Table 3-3: Values of wind force action on tapered and circular pole as well as on conductors Wind Load (kN) Pole height (m) Tapered Pole Circular Pole Conductor 9 0.061 0.018718 0.0091 11 0.078 0.031796 0.0184 44 University of Ghana http://ugspace.ug.edu.gh Also, safety factors were applied to load cases based on BS EN1992-1-1 3.4 POST-PROCESSING The initial design results were checked to establish the success or failure of the design. The initial sizes for the pole design was unsuccessful due to its inability to withstand the loads applied to it. Besides, the members were too small to contain the minimum required reinforcement bars safely. The pole size was varied until the design successfully passed all design requirements after which an analysis of the output data was carried out. 45 University of Ghana http://ugspace.ug.edu.gh 4 CHAPTER FOUR: RESULTS AND DISCUSSION 4.1 MOMENT DISTRIBUTION Bending moments are internal forces induced when an external force is applied to a structure. As the name implies, the induced force causes the structural member to bend or turn. It is known that a small external force can cause a large turning effect. The moment diagram is a pictorial description of how the moments are distributed throughout the structural member depending on the geometry of the member as well as the location and magnitude of the external forces. The type of support will also affect the moment distribution in a structural member. a b Figure 4.1: a. Moment distribution for 9meter pole with pinned support b. Moment distribution for 9meter pole with fixed supports 46 University of Ghana http://ugspace.ug.edu.gh a b Figure 4.2 a. Moment distribution for 11meter pole with pinned support b. Moment distribution for 11meter pole with fixed supports Figures 4-1 and 4-2 show the moment distribution for the 9- and 11-meter pole for respectively two support conditions; • Fixed support • Pinned support Figures 4-1a and 4-2a show the bending diagram for the pole with pinned supports. It can be seen that; the moments are distributed over the entire length of the pole with maximum 47 University of Ghana http://ugspace.ug.edu.gh moments being recorded at the top of the pole. Figures 4-1b and 4-2b show the bending moment diagram for fixed supports. The pole in this case behave like a cantilever where the applied forces at the unsupported end of the pole are carried to the supported end hence the maximum moment occurs at the pole supports. To construct a fixed support means that the foundation of the pole should be designed such that the pole can be fixed into it. However, such extreme lengths are taken in special cases when geotechnical reports indicate the soil at the location of the pole cannot support the pole. In Ghana, poles are pinned, hence for this study, the pole design was analysed with pinned supports. 4.2 POLE STRUCTURE DISPLACEMENT Displacement of the pole is the change in position of the pole about the supports as a result of applied loads. Figures 4.3a and 4.3b show the displacement graph for the 9- meter and 11-meter poles, respectively. a b Figure 4.3: a. Un-guyed displacement graph, 9meter pole b. Un-guyed displacement graph, 11meter pole 48 University of Ghana http://ugspace.ug.edu.gh The poles were designed to be light in weight. The weight reduction of the pole makes it more slender and hence increases the overall displacement of the pole. From the displacement graphs shown in Figure 4, the displacement in the 9 meter pole is significantly less than that of the 11 meter pole. This is attributed to the difference in length since all other parameters are the same. According to Angeling, 2017, decreasing length of the pole, while keeping all other parameters the same will decrease the displacements of the pole as is evident in the analysis results of the 9 meter and 11 meter poles. However, pole lengths are specific to their uses; hence a height reduction for this case is not possible. An alternative to this is the introduction of down guys. Per the analysis, it was realised that when the pole was guyed, the overall stability is increased; hence a reduction in the displacements as shown in Figures 4.4a and 4.4b. a b Figur e 4.4: a. Guyed displacement graph – 9meter pole b. Guyed displacement graph – 11meter pole 49 University of Ghana http://ugspace.ug.edu.gh 4.3 INTERACTION DIAGRAM FOR POLE STRUCTURE Assuming an axial load is applied directly at the centroid of the column, no moments will be induced in the column. In reality, however, taking into account accuracy and precision errors, an axial load will usually be applied some distance away from the centroid as shown in Figure 4.5. Figure 4.5: Axially loaded column with both uniaxial and biaxial loading This introduces an eccentricity that causes moments in either one (uniaxial) or two (biaxial) moments or bending in the column. With the induced moment, the capacity or ability of a column to carry an axial load is reduced. An interaction diagram is a visual representation of the combined loads (bending and Axial) that will cause a column to fail, a plot of axial loads against moment reactions as shown in figure 4.6. It investigates the capacity of the column to carry the different combinations of moment and axial loads. The curve is the failure plane. 50 University of Ghana http://ugspace.ug.edu.gh Figure 4.6 Interaction diagram for combined bending and axial load Suppose the axial load is greater than the moments. In that case, the column is described as brittle and characterised by a stocky structure, that is, a larger cross-section. This implies that the load combination (PMM ratio) for a brittle column will lie closer to the compression failure range shown in Figure 4-6. In the same way, when the moment reaction is greater, the column is described as ductile and characterised by a much slender column with longitudinal reinforcement to cater for the turning effect. The PMM ratio for a ductile column will lie closer to the tension failure range shown in Figure 4.6. That being said, the load combinations for both the 9 meter and 11-meter poles fell within the curve as shown in figures 4.7 and 4.8. This indicates that the distribution poles designed can withstand the loads applied to it. Also, the region the load combination (PMM ratio) falls on a point close to the tension failure range indicating that the pole will behave in a ductile manner. 51 University of Ghana http://ugspace.ug.edu.gh Figure 4.7: PMM interaction diagram for 9meter pole provided by ETABS 2016 Figure 4.8: PMM interaction diagram for 9meter pole provided by ETABS 2016 52 University of Ghana http://ugspace.ug.edu.gh 4.4 DESIGN SUMMARY After multiple variations of the pole size, the dimensions displayed on Table were used for the final design. Table 4-1: Final Pole design dimensions Tapered Pole 9 m 11 m Top(mm) 200x 100 200x 100 Butt(mm) 300 x 100 300 x 100 The forces applied were quite small hence stresses induced within the pole were equally minor as discussed in Section 4.3. Due to this, the minimum recommended area of reinforcement was calculated as one percent of the area of the pole. NB. The area referred to is the area of one leg of the pole which is 100 x 100. Per the minimum reinforcement required, 12 mm high yield reinforcement bars are provided in each leg of the pole with 8 mm tie rods. A cover to reinforcement of 25 mm was provided as required for this design according to BS EN12483. The weight of the designed poles was computed and compared to the weight of previously used concrete poles. It was found that by reducing the size of the pole, the weight of the pole is reduced significantly. Table 4-2 shows the percentage weight reduction. 53 University of Ghana http://ugspace.ug.edu.gh Table 4-2: Comparison between previously used concrete poles and the lighter weight concrete pole design Weight of pole (kg) Percentage weight Height of Pole Normal Lighter weight reduction (%) (m) Concrete concrete pole design pole 9 865 450 48.0 11 1078 575 46.7 Table 4-3: Geometry parameters of distribution pole with reinforcement requirements Min. Area of Area of Pole Volume Weight Embedment reinforcement reinforcement height(m) (m3) (kg) depth(m) (mm2) provided (mm2) 9 0.18 450 1.5 100 452.4 11 0.23 575 1.8 100 452.4 54 University of Ghana http://ugspace.ug.edu.gh 5 CHAPTER FIVE: CONCLUSION AND RECOMMENDATION 5.1 CONCLUSION The overall wind loads applied to the pole were a combination of the wind load acting on the conductor and the pole itself which were calculated using BS EN01991-1-4 action. The calculated loads along with the self-weight of the pole, the weight of the conductors and construction and maintenance loads were the overall load cases considered for the design analysis. A tapered structure with a rectangular cross section was modelled and analysed using finite element analysis. A free body diagram of the model was drawn in AutoCAD and the analysed in ETABS 2016. The analysis of this model was based on the stress strain and equilibrium equations with differing scenarios using pinned and fixed supports. An interaction diagram was generated for each pole. It showed that the load combination for each pole was within the capacity limits for the pole structure. This implies that the poles designed have the ability to withstand loads applied to it. The stability of the pole was also established by analyzing the displacement charts produced by ETABS 2016. It showed the maximum displacement suffered by each pole and the significant decrease in displacements when a down guy was introduced. From the analysis results, the pole design was found to have successfully passed all design requirements with a weight of 450kg and 575kg for the 9 meter and 11-meter pole respectively. Though these pole designs are not as light as timber poles, they are about half the weight of previously used concrete poles. This study could enhance the electricity distribution infrastructure in Ghana. 55 University of Ghana http://ugspace.ug.edu.gh Should these designs be implemented, they may prove to be more cost effective because; ▪ Materials are readily available in the local market ▪ Concrete poles generally require low maintenance ▪ No specialised skill set or machinery is required to construct the pole, thereby reducing the cost of production. Finally, in anticipation of the introduction of nuclear power into the energy generation mix of the country, should there be an overhaul of the distribution infrastructure, the lighter weight reinforced concrete poles designed in this study could be utilised to increase the accessibility of electricity to the end-user. 5.2 RECOMMENDATION For future work, it is recommended that the proposed pole designs be constructed and subjected to field and laboratory testing to validate the findings of this study. Secondly a comprehensive cost estimate analysis should be conducted to evaluate the cost benefits of using this lighter weight reinforced concrete pole design. 56 University of Ghana http://ugspace.ug.edu.gh REFERENCES A Wide Creosote Ban is Proposed by E.P.A. (1984, August 16). The New York Times. https://www.nytimes.com/1984/08/16/garden/a-wide-creosote-ban-is-proposed-by- epa.html Adaam, I. (2014). Establishing Wood Pole Treatment Plant in Ghana [KARELIA UNIVERSITY OF APPLIED SCIENCES]. https://www.theseus.fi/bitstream/handle/10024/80097/Adaam_Isaac_2014_08_15.pd f?sequence=1&isAllowed=y Africa, & Support, P. A. (2016). Ghana Energy Sector Overview. April 2015. Amankrah, K. A. (2015). Finite Element Assessment of Precast Concrete Slab Using (Issue July). University of Ghana. Angeling, J. B. (2017). Weight reduction of concrete poles for the Swedish power line grid Using a Finite Element Model to optimize geometry in relation to Load requirements. Linnaeus University,Faculty of Technology. Asiedu-Addo, S. (2017). ECG spends over GH¢94,000 to replace burnt poles. Graphic Online. https://www.graphic.com.gh/news/general-news/ecg-spends-over-gh-94- 000-to-replace-burnt-poles.html Badger, J., Bauwens, I., Casso, P., Davis, N., Hahmann, A., Hansen, S. B. K., Hansen, Brian Ohrbeck Heathfield, D., Olsen, B. T., Knight, O. J., Lacave, O., Lizcano, G., Bosch i Mas, A., Mortensen, N. G., Onninen, M., & Potter Van Loon, Albertine Volker, P. (n.d.). Global Wind Atlas (3.0). Global Wind Atlas. Retrieved October 16, 57 University of Ghana http://ugspace.ug.edu.gh 2020, from https://globalwindatlas.info/area/Ghana Bhatt, P., MacGinley, T. J., & Choo, B. S. (2017). Reinforced concrete design to eurocode - Design Theory and Examples (4th ed.). Bokpe, S. J. (2019). Ghana’s nuclear source documents go to Cabinet this month. Graphic Online. https://www.graphic.com.gh/news/general-news/ghana-s-nuclear-source- documents-go-to-cabinet-this-month.html British Standards Institution. (2004). BS EN12843:2004 - Precast concrete products – Masts and poles. 3(November 2004), 1–8. British Standards Institution. (2007). BS EN13369:2004 - Common rules for precast concrete products (Issue October). British Standards Institution. (2008). BS EN1992-1-1:2004 – Design of concrete structures (Vols. 2-1–1). https://doi.org/10.1007/978-3-642-41714-6_51755 BSI. (2010). Bs En 1991-1-4:2005+a1:2010 (Vol. 3, Issue January). Dagher, H. J. (2006). Reliability-based design of utility pole structures. In Reliability- Based Design of Utility Pole Structures. https://doi.org/10.1061/9780784408452 Durocrete Engineering Services Pvt. Ltd. (2000). Durocrete Mix Design Manual. En 50341-1 - Overhead electrical lines exceeding AC 1 kV - Part 1: General requirements - Common specifications. (2012). Gezer, E. D., Temiz, A., & Yüksek, T. (2015). Inspection of Wooden Poles in Electrical Power Distribution Networks in Artvin , Turkey. Advances in Materials Science and Engineering, 2015, 11. http://dx.doi.org/10.1155/2015/659818 58 University of Ghana http://ugspace.ug.edu.gh Ghana Energy Situation - energypedia.info. (n.d.). Retrieved October 25, 2020, from https://energypedia.info/wiki/Ghana_Energy_Situation Graham, R. D. (1960). Causes and Prevention of Deterioration in Wood. Wood Pole Conference. Guo, Z. (2014). Chapter 4: Various Structural Concrete. In Principles of Reinforced Concrete. Hedjazi, S. (2016). Compressive Strength of Lightweight Concrete. Intech, 13. https://doi.org/http://dx.doi.org/10.5772/57353 House, H., Place, M., Kingdom, U., & Report, F. (2003). Overview of the Potential for Undergrounding the Electricity Networks in Europe. February, 1–49. Hutton, D. V. (2004). Fundamentals of Finite Element Analysis (O. Plant & L. K. Williams (Eds.)). MaGraw-Hill. Institute of Statistical, Social and Ecconomical Research (ISSER) Annual Report. (2015). In Institute of Statistical, Social and Ecconomical Research (ISSER). http://isser.edu.gh/images/Publication_files/ISSER ANNUAL REPORT 2014- 2015..pdf Jenkins, C., & Khanna, S. (2005). Mechanics and Materials. In Mechanics of Materials, A Modern Integration of Mechanics and Materials in Structural Design (1st ed., pp. 1– 28). Kolgiri, S. G. (2009). STATIC AND DYNAMIC ANALYSIS FOR ROTOR SHAFT OF ELECTRIC MOTOR. Walchand Institute of Technology/ Solapur University. 59 University of Ghana http://ugspace.ug.edu.gh Kuenyehia, K. (Kimathi & P. C. A., Odame, S. (Kimathi & P. C. A., & Arde-Acquah, P. (Kimathi & P. C. A. (2019). Electricity Regulation in Ghana. Lexology. https://www.lexology.com/library/detail.aspx?g=910beca2-f3bf-420f-8597- e7e3e6f53b38 Kumi, E. N. (2017). The Electricity Situation in Ghana: Challenges and Opportunities. CGD Policy Paper, September, 30. https://www.cgdev.org/ publication/electricity- situation-ghana-challenges-and-opportunities Liu, G. R., & Quek, S. S. (2013). The Finite Element Method: A Practical Course: Second Edition. In The Finite Element Method: A Practical Course: Second Edition (Second Edi). https://doi.org/10.1016/C2012-0-00779-X Lunuwilage, R. H. (2013). Study of Pole-top Fire Development in Power Distribution Networks (Issue October). University of Moratuwa, Sri Lanka. Mai, C., & Militz, H. (2007). Wood Preservatives. In U. Kues (Ed.), Wood production, wood technology and biotechnology impacts (pp. 259–271). http://univerlag.uni- goettingen.de Moaveni, S. (1999). Finite Element Analysis - Theory and Application with ANSYS. In B. Stenquist, C. Suraci, M. Horton, & A. Baker (Eds.), Minerals Engineering. Prentice - Hall Inc. https://doi.org/10.1016/s0892-6875(99)90030-4 Mosley, B., Bungey, J., & Hulse, R. (2012). Reinforced concrete design to Eurocode 2 (7th ed.). Palgrave Macmillan. https://doi.org/10.1680/edpfb.64553.193 60 University of Ghana http://ugspace.ug.edu.gh Mrema, G. C. (2011). Structural design. In Rural structures in the tropics: design and development (pp. 115–147). Rome, FAO. https://doi.org/10.1080/00038628.1965.9696133 Mulqueen, A. (Carlifonia P. U. C.-P. and P. D. (2017). A Natural History of the Wooden Utility Pole (Issue July). Neulicht, R., & Shular, J. (1999). Wood Preserving (Issue 4601). Neupane, D. (2014). Comparison of Some Fem Codes in Static Analysis [HAMK University]. https://www.theseus.fi/bitstream/handle/10024/87106/Neupane_Dilip.pdf?sequence =1 Neville, A. M., & Brooks, J. J. (2010). Concrete Technology (Second). Pearson Education Limit. Nunoo, S., & Attachie, J. C. (2011). A Methodology for the design of an electricity theft monitoring system. Journal of Theoretical and Applied Information Technology, 26(2), 112–117. Rao, S. S. (2011). The Finite Element Method in Engineering (Fifth). Butterworth– Heinemann. Saeed, S. S. (GNA). (2019). ECG loses GH¢120,000 in two months to bushfires. Ghana News Agency (GNA). https://www.ghananewsagency.org/social/ecg-loses-gh-120- 000-in-two-months-to-bushfires-145326 61 University of Ghana http://ugspace.ug.edu.gh Shupe, T. (Ph. D. L. F. P. D. C., Lebow, S. (Ph. D. U. F. P. L., & Ring, D. (Ph. D. D. of E. (2008). Causes and Control of Wood Decay , Degradation & Stain. Louisiana State University Agricultural Center, 1–28. https://doi.org/10.1128/AEM.00508-11 Słowik, M. (2019). The analysis of failure in concrete and reinforced concrete beams with different reinforcement ratio. Archive of Applied Mechanics, 89(5), 885–895. https://doi.org/10.1007/s00419-018-1476-5 Ugural, A. C., & Fenster, S. K. (2016). Advanced Mechanics of Materials and Applied Elasticity (5th ed.). Prentice Hall, Pearson Education, Inc. https://doi.org/10.1201/9781420057775 Utility poles - Aged Woods, Inc. (2017). https://www.agedwoods.com/utility-poles/ Wood Boring Insects and Beetles | Western Exterminator. (n.d.). Retrieved March 18, 2020, from https://www.westernexterminator.com/wood-boring-insects/ 62 University of Ghana http://ugspace.ug.edu.gh APPENDIX A LOAD CALCULATION TABLES AND SAMPLE CALCULATION OF A 9m POLE 63 University of Ghana http://ugspace.ug.edu.gh WIND FORCE ON CONDUCTORS Cc = 1 L2 = 50 Lm = 25 L1 = 0 P=1.25kg/m Lh = 28.63 9meter pole Table A-0-1: Wind force action on conductors for 9meter poles at Terrain IV Terrain IV: Zo=1 Region Vbmap Kr Cr Vm Iv Qp Lh Bsqr Gc Qw Ashanti 3.02 0.234329 0.47215 1.425893 0.496302 0.005685 31.43837 0.456036 0.672967 0.001339 Brong Ahafo 3.02 0.234329 0.47215 1.425893 0.496302 0.005685 31.43837 0.456036 0.672967 0.001339 Central 3.35 0.234329 0.47215 1.581702 0.496302 0.006996 31.43837 0.456036 0.672967 0.001648 Eastern 4.05 0.234329 0.47215 1.912207 0.496302 0.010225 31.43837 0.456036 0.672967 0.002408 Greater Accra 4.14 0.234329 0.47215 1.9547 0.496302 0.010684 31.43837 0.456036 0.672967 0.002517 64 University of Ghana http://ugspace.ug.edu.gh Terrain IV: Zo=1 Region Vbmap Kr Cr Vm Iv Qp Lh Bsqr Gc Qw Northern 2.93 0.234329 0.47215 1.383399 0.496302 0.005352 31.43837 0.456036 0.672967 0.001261 Upper East 3.11 0.234329 0.47215 1.468386 0.496302 0.006029 31.43837 0.456036 0.672967 0.00142 Upper West 3.05 0.234329 0.47215 1.440057 0.496302 0.005799 31.43837 0.456036 0.672967 0.001366 Volta 3.46 0.234329 0.47215 1.633638 0.496302 0.007463 31.43837 0.456036 0.672967 0.001758 Western 2.79 0.234329 0.47215 1.317298 0.496302 0.004852 31.43837 0.456036 0.672967 0.001143 0.002517 65 University of Ghana http://ugspace.ug.edu.gh Table A-0-2: Wind force action on conductors for 9meter poles at Terrain III Terrain III: Zo=0.3 Region Vbmap Kr Cr Vm Iv Qp Lh Bsqr Gc Qw Ashanti 3.02 0.215389 0.693312 2.093801 0.310667 0.008699 38.50183 0.506591 0.732897 0.002231 Brong Ahafo 3.02 0.215389 0.693312 2.093801 0.310667 0.008699 38.50183 0.506591 0.732897 0.002231 Central 3.35 0.215389 0.693312 2.322594 0.310667 0.010703 38.50183 0.506591 0.732897 0.002746 Eastern 4.05 0.215389 0.693312 2.807912 0.310667 0.015644 38.50183 0.506591 0.732897 0.004013 Greater Accra 4.14 0.215389 0.693312 2.87031 0.310667 0.016347 38.50183 0.506591 0.732897 0.004193 Northern 2.93 0.215389 0.693312 2.031403 0.310667 0.008188 38.50183 0.506591 0.732897 0.0021 Upper East 3.11 0.215389 0.693312 2.156199 0.310667 0.009225 38.50183 0.506591 0.732897 0.002366 Upper West 3.05 0.215389 0.693312 2.1146 0.310667 0.008872 38.50183 0.506591 0.732897 0.002276 Volta 3.46 0.215389 0.693312 2.398858 0.310667 0.011418 38.50183 0.506591 0.732897 0.002929 Western 2.79 0.215389 0.693312 1.934339 0.310667 0.007424 38.50183 0.506591 0.732897 0.001904 0.004193 66 University of Ghana http://ugspace.ug.edu.gh Table A-0-3: Wind force action on conductors for 9meter poles at Terrain 0 Terrain 0: Zo=0.003 Region Vbmap Kr Cr Vm Iv Qp Lh Bsqr Gc Qw Ashanti Brong Ahafo Central 3.35 0.156036 1.220831 4.089784 0.127811 0.019807 83.59127 0.690316 0.86408 0.00599 Eastern Greater Accra 4.14 0.156036 1.220831 5.054241 0.127811 0.03025 83.59127 0.690316 0.86408 0.009148 Northern Upper East Upper West Volta 3.46 0.156036 1.220831 4.224076 0.127811 0.021129 83.59127 0.690316 0.86408 0.00639 Western 2.79 0.156036 1.220831 3.406119 0.127811 0.013738 83.59127 0.690316 0.86408 0.004155 0.009148 67 University of Ghana http://ugspace.ug.edu.gh 11 meter Pole Table A-0-4: Wind force action on conductors for 11meter poles at Terrain IV Terrain IV: Zo=1 Region Vbmap Kr Cr Vm Iv Qp Lh Bsqr Gc Qw Ashanti 3.02 0.234329 0.522557 1.578121 0.448428 0.006443 38.39854 0.338616 0.619875 0.002795 Brong Ahafo 3.02 0.234329 0.522557 1.578121 0.448428 0.006443 38.39854 0.338616 0.619875 0.002795 Central 3.35 0.234329 0.522557 1.750565 0.448428 0.007927 38.39854 0.338616 0.619875 0.00344 Eastern 4.05 0.234329 0.522557 2.116354 0.448428 0.011586 38.39854 0.338616 0.619875 0.005028 Greater Accra 4.14 0.234329 0.522557 2.163384 0.448428 0.012107 38.39854 0.338616 0.619875 0.005253 Northern 2.93 0.234329 0.522557 1.531091 0.448428 0.006064 38.39854 0.338616 0.619875 0.002631 Upper East 3.11 0.234329 0.522557 1.625151 0.448428 0.006832 38.39854 0.338616 0.619875 0.002965 Upper West 3.05 0.234329 0.522557 1.593798 0.448428 0.006571 38.39854 0.338616 0.619875 0.002851 Volta 3.46 0.234329 0.522557 1.808046 0.448428 0.008457 38.39854 0.338616 0.619875 0.003669 Western 2.79 0.234329 0.522557 1.457933 0.448428 0.005499 38.39854 0.338616 0.619875 0.002386 0.005253 68 University of Ghana http://ugspace.ug.edu.gh Table 0-5: Wind force action on conductors for 11meter poles at Terrain III Terrain III: Zo=0.3 Region Vbmap Kr Cr Vm Iv Qp Lh Bsqr Gc Qw Ashanti 3.02 0.215389 0.739644 2.233726 0.291207 0.009475 46.18833 0.381129 0.684122 0.004538 Brong Ahafo 3.02 0.215389 0.739644 2.233726 0.291207 0.009475 46.18833 0.381129 0.684122 0.004538 Central 3.35 0.215389 0.739644 2.477808 0.291207 0.011659 46.18833 0.381129 0.684122 0.005583 Eastern 4.05 0.215389 0.739644 2.995559 0.291207 0.017041 46.18833 0.381129 0.684122 0.008161 Greater Accra 4.14 0.215389 0.739644 3.062127 0.291207 0.017806 46.18833 0.381129 0.684122 0.008527 Northern 2.93 0.215389 0.739644 2.167158 0.291207 0.008919 46.18833 0.381129 0.684122 0.004271 Upper East 3.11 0.215389 0.739644 2.300293 0.291207 0.010048 46.18833 0.381129 0.684122 0.004812 Upper West 3.05 0.215389 0.739644 2.255915 0.291207 0.009664 46.18833 0.381129 0.684122 0.004628 Volta 3.46 0.215389 0.739644 2.559169 0.291207 0.012437 46.18833 0.381129 0.684122 0.005956 Western 2.79 0.215389 0.739644 2.063607 0.291207 0.008087 46.18833 0.381129 0.684122 0.003873 0.008527 69 University of Ghana http://ugspace.ug.edu.gh TableA-0-6: Wind force action on conductors for 11meter poles at Terrain 0 Terrain 0: Zo=0.003 Region Vbmap Kr Cr Vm Iv Qp Lh Bsqr Gc Qw Ashanti Brong Ahafo Central 3.35 0.156036 1.254396 4.202227 0.124391 0.020647 93.61869 0.555209 0.831822 0.012022 Eastern Greater Accra 4.14 0.156036 1.254396 5.1932 0.124391 0.031533 93.61869 0.555209 0.831822 0.018361 Northern Upper East Upper West Volta 3.46 0.156036 1.254396 4.340211 0.124391 0.022025 93.61869 0.555209 0.831822 0.012825 Western 2.79 0.156036 1.254396 3.499765 0.124391 0.014321 93.61869 0.555209 0.831822 0.008339 0.018361 70 University of Ghana http://ugspace.ug.edu.gh WIND FORCE ON POLE STRUCTURE Cf = 1.5 Lm = 50 ψ = 0.91 Ρ = 1.25kg/m λ = 70 Cf,o = 1.65 CsCd = 1 Lh = 28.63 9 meter pole Table 0-7: Wind force action on poles for 9meter poles at Terrain IV Terrain IV: Zo=1 Region Vbmap Kr Cr Vm Iv Qp Qw Ashanti 3.02 0.234329 0.47215 1.425893 0.496302 0.005685 0.011524 Brong Ahafo 3.02 0.234329 0.47215 1.425893 0.496302 0.005685 0.011524 Central 3.35 0.234329 0.47215 1.581702 0.496302 0.006996 0.014181 Eastern 4.05 0.234329 0.47215 1.912207 0.496302 0.010225 0.020726 71 University of Ghana http://ugspace.ug.edu.gh Terrain IV: Zo=1 Region Vbmap Kr Cr Vm Iv Qp Qw Greater Accra 4.14 0.234329 0.47215 1.9547 0.496302 0.010684 0.021657 Northern 2.93 0.234329 0.47215 1.383399 0.496302 0.005352 0.010848 Upper East 3.11 0.234329 0.47215 1.468386 0.496302 0.006029 0.012222 Upper West 3.05 0.234329 0.47215 1.440057 0.496302 0.005799 0.011755 Volta 3.46 0.234329 0.47215 1.633638 0.496302 0.007463 0.015127 Western 2.79 0.234329 0.47215 1.317298 0.496302 0.004852 0.009836 0.021657 TableA-0-8: Wind force action on poles for 9meter poles at Terrain III Terrain III: Zo=0.3 Region Vbmap Kr Cr Vm Iv Qp Qw Ashanti 3.02 0.215389 0.693312 2.093801 0.310667 0.008699 0.017632 Brong Ahafo 3.02 0.215389 0.693312 2.093801 0.310667 0.008699 0.017632 Central 3.35 0.215389 0.693312 2.322594 0.310667 0.010703 0.021696 72 University of Ghana http://ugspace.ug.edu.gh Terrain III: Zo=0.3 Region Vbmap Kr Cr Vm Iv Qp Qw Eastern 4.05 0.215389 0.693312 2.807912 0.310667 0.015644 0.031711 Greater Accra 4.14 0.215389 0.693312 2.87031 0.310667 0.016347 0.033136 Northern 2.93 0.215389 0.693312 2.031403 0.310667 0.008188 0.016597 Upper East 3.11 0.215389 0.693312 2.156199 0.310667 0.009225 0.018699 Upper West 3.05 0.215389 0.693312 2.1146 0.310667 0.008872 0.017984 Volta 3.46 0.215389 0.693312 2.398858 0.310667 0.011418 0.023144 Western 2.79 0.215389 0.693312 1.934339 0.310667 0.007424 0.015049 0.033136 Table A-0-9: Wind force action on poles for 9meter poles at Terrain 0 Terrain 0: Zo=0.003 Region Vbmap Kr Cr Vm Iv Qp Qw Ashanti Brong Ahafo 73 University of Ghana http://ugspace.ug.edu.gh Terrain 0: Zo=0.003 Region Vbmap Kr Cr Vm Iv Qp Qw Central 3.35 0.156036 1.220831 4.089784 0.127811 0.019807 0.040149 Eastern Greater Accra 4.14 0.156036 1.220831 5.054241 0.127811 0.03025 0.061318 Northern Upper East Upper West Volta 3.46 0.156036 1.220831 4.224076 0.127811 0.021129 0.042829 Western 2.79 0.156036 1.220831 3.406119 0.127811 0.013738 0.027848 0.061318 74 University of Ghana http://ugspace.ug.edu.gh 11 meter pole Table A-0-10: Wind force action on poles for 11meter poles at Terrain IV Terrain IV: Zo=1 Region Vbmap Kr Cr Vm Iv Qp Qw Ashanti 3.02 0.234329 0.522557 1.578121 0.448428 0.006443 0.011608 Brong Ahafo 3.02 0.234329 0.522557 1.578121 0.448428 0.006443 0.011608 Central 3.35 0.234329 0.522557 1.750565 0.448428 0.007927 0.014284 Eastern 4.05 0.234329 0.522557 2.116354 0.448428 0.011586 0.020877 Greater Accra 4.14 0.234329 0.522557 2.163384 0.448428 0.012107 0.021815 Northern 2.93 0.234329 0.522557 1.531091 0.448428 0.006064 0.010927 Upper East 3.11 0.234329 0.522557 1.625151 0.448428 0.006832 0.01231 Upper West 3.05 0.234329 0.522557 1.593798 0.448428 0.006571 0.01184 Volta 3.46 0.234329 0.522557 1.808046 0.448428 0.008457 0.015237 Western 2.79 0.234329 0.522557 1.457933 0.448428 0.005499 0.009907 0.021815 75 University of Ghana http://ugspace.ug.edu.gh Table 0-11: Wind force action on poles for 11meter poles at Terrain III Terrain III: Zo=0.3 Region Vbmap Kr Cr Vm Iv Qp Qw Ashanti 3.02 0.215389 0.739644 2.233726 0.291207 0.009475 0.017073 Brong Ahafo 3.02 0.215389 0.739644 2.233726 0.291207 0.009475 0.017073 Central 3.35 0.215389 0.739644 2.477808 0.291207 0.011659 0.021007 Eastern 4.05 0.215389 0.739644 2.995559 0.291207 0.017041 0.030704 Greater Accra 4.14 0.215389 0.739644 3.062127 0.291207 0.017806 0.032084 Northern 2.93 0.215389 0.739644 2.167158 0.291207 0.008919 0.01607 Upper East 3.11 0.215389 0.739644 2.300293 0.291207 0.010048 0.018105 Upper West 3.05 0.215389 0.739644 2.255915 0.291207 0.009664 0.017413 Volta 3.46 0.215389 0.739644 2.559169 0.291207 0.012437 0.02241 Western 2.79 0.215389 0.739644 2.063607 0.291207 0.008087 0.014571 0.032084 76 University of Ghana http://ugspace.ug.edu.gh Table A-0-12: Wind force action on poles for 11meter poles at Terrain 0 Terrain 0: Zo=0.003 Region Vbmap Kr Cr Vm Iv Qp Qw Ashanti Brong Ahafo Central 3.35 0.156036 1.254396 4.202227 0.124391 0.020647 0.037201 Eastern Greater Accra 4.14 0.156036 1.254396 5.1932 0.124391 0.031533 0.056816 Northern Upper East Upper West Volta 3.46 0.156036 1.254396 4.340211 0.124391 0.022025 0.039685 Western 2.79 0.156036 1.254396 3.499765 0.124391 0.014321 0.025803 0.056816 77 University of Ghana http://ugspace.ug.edu.gh SAMPLE CALCULATIONS – 9m Pole Typical ruling span: 50m Conductor: AAC 120 mm2, BS-EN50183 Code: Oak Diameter: 14 mm Data and calculation step by step Vb,0 = 4.14 m/s Basic wind velocity 3.1 cdir = 1 directional factor co = 1 orography factor zo = 0.003 m Roughness length: terrain category 0 cr = 1.22 roughness factor 3.3 Vm(h) = 5.0543 m/s Mean velocity 3.2 kr = 0.156 terrain factor 3.5 h = 6.6m ρ = 1.25 kg/m Density of air Iv (h) = 0.128 Wind turbulence intensity 3.7 qp (h) = 0.0302 kPa Peak wind pressure Wind Action on Conductor L1 = 50 m Adjacent pole lengths 78 University of Ghana http://ugspace.ug.edu.gh L2 = 0 m Lm= 25 m Mean Span L(h) = 85.59 m Turbulence length scale 3.15 B² = 0.690 Background factor 3.14 kp = 3 Peak Factor R² = 0 Resonance factor Gc = 0.864 Structural factor 3.13 φ = 0 Angle of incidence Cc = 1 Conductor drag factor Qwc = 0.0091 kN 3.12 Wind Action on Pole CsCd = 1 Structural factor Cf = 1.5 Pole drag factor/force coefficient 3.10 Aref = 1.35 Projected Area Fw = 0.061 kN 3.9 79 University of Ghana http://ugspace.ug.edu.gh APPENDIX B TABLES AND CHARTS FOR WIND LOAD CALCULATIONS - EUROCODE DESIGN MANUAL 80 University of Ghana http://ugspace.ug.edu.gh Table B-1: Terrain type description Terrain Description z0 ( zmin category m) (m) 0 Sea or coastal area exposed to the open sea 0.003 1 Lakes or flat and horizontal area with negligible I vegetation and 0.01 1 without obstacles Area with low vegetation such as grass and isolated obstacles II 0.05 2 (trees, buildings) with separations of at least 20 obstacle heights Area with regular cover of vegetation or buildings or with isolated III obstacles with separations of maximum 20 obstacle 0.3 5 heights (such as villages, suburban terrain, permanent forest) Area in which at least 15 % of the surface is covered IV with buildings 1 10 and their average height exceeds 15 m NOTE: The terrain categories are illustrated in A.1. 81 University of Ghana http://ugspace.ug.edu.gh Figure B.1: Terrain images for Terrain types 0, III and IV 82 University of Ghana http://ugspace.ug.edu.gh Figure B-2: Recommended values of λ for cylinders, polygonal sections, rectangular sections, sharp edged structural sections and lattice structures 83 University of Ghana http://ugspace.ug.edu.gh Figure B-3: Force coefficients for rectangular cross section Table B-2:Exposure classes related to environmental conditions in accordance with EN 206-1(British Standards Institution, 2008) Class Hydraulic engineering specific examples 1) designati Description of environment for the allocation of exposure classes on (for information) 1 No risk of corrosion or attack For concrete without reinforcement or embedded Unreinforced core concrete with zoned X0 metal: in environments building method where the concrete is not attacked. 2 Reinforcement corrosion, triggered by carbonisation XC1 dry or permanently wet Floors of lock chambers, economising basins or weirs, lock chamber walls below bottom 84 University of Ghana http://ugspace.ug.edu.gh Class Hydraulic engineering specific examples 1) designati Description of environment for the allocation of exposure classes on (for information) water, hydraulic filling and emptying systems Lock chamber walls in the area between XC2 wet, rarely dry bottom water and headwater (mutatis mutandis for economising basin walls) Surfaces not open to the weather (outside air, XC3 moderate humidity protected against precipitation) Freeboard of lock chamber or economising XC4 cyclic wet and dry basin walls, weir columns above low water, outside surfaces open to the weather, quays 3 Reinforcement corrosion caused by chloride, except for seawater Weir columns in the spray mist areas of road XD1 moderate humidity bridges XD2 wet, rarely dry Platforms of locks, traffic areas (e.g. port XD3 cyclic wet and dry areas), steps on weir columns 4 Reinforcement corrosion caused by chloride from seawater Exposed to airborne salt but XS1 not in direct contact with External components near the coast seawater Barrier floors, walls and foundation piles XS2 Permanently submerged below lowest known low-tide level tidal, splash Foundation piles, quays, moles and walls XS3 and spray zones above lowest known low-tide level 5 Frost with and without de-icing agents/seawater moderate water saturation Freeboard of economising basin walls, weir XF1 with fresh water, without de- columns above high water icing agents moderate water saturation Vertical components in spray water area and XF2 with seawater and/or de- components in direct spray mist areas of icing agents seawater 85 University of Ghana http://ugspace.ug.edu.gh Class Hydraulic engineering specific examples 1) designati Description of environment for the allocation of exposure classes on (for information) Lock chamber walls in the area between bottom water-1.0 m and headwater+1.0 m high water saturation with (applies mutatis mutandis to economising XF3 fresh water without de-icing basin walls), inlet and outlet areas of culverts agents between low water and high water, weir columns between low water and high water Vertical surfaces of seawater components such as foundation piles, quays and moles in high water saturation with fluctuating water level areas, horizontal XF4 seawater and/or de-icing surfaces affected by seawater, platforms of agents locks, traffic areas (e.g. port areas), steps on weir columns 6 Concrete corrosion through chemical attack slightly aggressive chemical XA1 environment moderately aggressive Concrete components which are in contact XA2 chemical environment and with seawater (underwater and fluctuating marine structures water level areas, spray water areas) Highly aggressive chemical XA3 environment 7 Concrete corrosion through wear stress Surfaces subject to stress from friction with ships (e.g. lock chamber walls above bottom water-1.0 m), components for energy XM1 moderate wear stress 2) conversion with wear from small-grain bed- load transport (e.g. due to construction measures such as bed-load catch basin), ice drift Weir backs and components for energy conversion (stilling basins, chute blocks) XM2 severe wear stress with wear from large-grain bed-load transport Components in mountain streams or bed-load XM3 very severe wear stress deflection tunnels 8 Concrete corrosion due to alkali silica reaction 86 University of Ghana http://ugspace.ug.edu.gh Class Hydraulic engineering specific examples 1) designati Description of environment for the allocation of exposure classes on (for information) Generally: Only for non-massive components Concrete which after normal (smallest component dimension ≤ 0.80 m). curing is not moist for an extended time and, after Internal components of hydraulic structures WO drying out, remains mostly that are not continuously exposed to a dry during use. relative air humidity of more than 80 % (e.g. interior spaces of steering stations). Generally: Always for massive components (smallest dimension > 0.80 m) regardless of humidity exposure. Concrete components of hydraulic structures Concrete that in use is exposed to weather or subject to temporary WF frequently wet or wet over or permanent water exposure in inland extended periods of time. waterways (e.g. entire height of lock chamber walls). Inner components of hydraulic structures subject to a relative air humidity of 80 % or more. Concrete components of hydraulic structures which come into contact with seawater Concrete, which, in addition (underwater and fluctuating water level to class WF wear, is exposed areas, spray water areas). WA to alkali frequently or for extended periods of time. Concrete components of hydraulic structures with de-icing salt exposure (e.g. subgrade areas of lock chamber walls). Concrete that is subject to Not relevant to hydraulic engineering. WS high dynamic wear and direct alkali charge. 1) These examples apply to the predominant stress factors during service life. Past experience suggests that different ambient conditions during construction or use (e.g. drainage) do not cause damage. 2) Lock chamber floors and filling systems not subject to bed-load transport wear are normally not subject to concrete corrosion due to hydroabrasion. 87 University of Ghana http://ugspace.ug.edu.gh Table B-3: Minimum concrete cover(British Standards Institution, 2008) Longitudinal steels Stirrups or spirals Ambient Exposure ≥ ≥ < C40/50 < C40/50 conditions classes C40/50 C40/50 C XC2/XC3 15 20 10 15 D XC4 15 20 10 15 E XD1/XS1 20 25 15 20 F XD2/XS2 25 30 20 25 88 University of Ghana http://ugspace.ug.edu.gh 89