THS. THE FINES“? OF THE TENSEGN CURVE GM FARM. «LBENCE FEMC'RMANCE Tim‘s—Es h! Hm Dawes a? 52%.. S. it‘aECHE‘fEAN ST’A’E‘E UMVERSETY .35:sz W. Thmw HIM 54kt}: LIBRARY Michigan State University r—v This is to certify that the thesis entitled The Effects of the Tension Curve on Farm Fence Performance presented by James W. Throop has been accepted towards fulfillment of the requirements for Jim—degree inmmral Engineering : //"‘ _\ .’ ‘ // ;,/, ,/I/) '7 . / ’fl , ' 1" )4 J11 Ir/ fi/‘TS/M ’ ’76 C/ [/ Major professor/ 1 / L/ / ‘t. Date November 15, 1962 0.169 THE EFFECTS OF THE TENSION CURVE -ON FARM FENCE PERFORMANCE by James W. Throbp AN ABS TRACT Submitted to the Colleges of Agriculture and Engineering of Michigan State UniVersity of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN AGRICULTURAL ENGINEERING Department of Agricultural Engineering 1962 . I, j / .l 7 // 1/ _/7 APPr°Y°d LéZZE7z6z/fié£;Zjieajfé;/ JAMES W. THROOP ABSTRACT Little factual information is available about farm. fencing. Pr0per design of end and corner assemblies re- quire‘knowledge of the magnitude of the load imposed by i the woven wire. .Properties of fence wire which could affect fence performance were investigated. PrOperties of the tension curve when subjected to axial loads were investigated. A reduction in height with cyclic loading to a 300 pound maximum.gave an average height reduction of 21.05%. A two year study of an experi- mental fence produced evidence that the tension curve ' height does not decrease with time, but increases and de- creases with changes in fence temperature. Tests were conducted to determine the elastic slope of the load-strain diagram.at various maximum.loadings, and from.this information Tension-Temperature constants were calculated which can be used to predict the changes in fence tension due to temperature changes. Strain energy~relationships were used to evaluate tension curve designs and experimental evaluation of four new designs were made. Several devices to measure fence tension were evaluated.' All were satisfactory in laboratory teats but not suited to practical field application. THE EFFECTS OF THE TENSION CURVE ON.FARE FENCE PERFORMANCE by James W. Throap A THESIS . Submitted to the Colleges of Agriculture and Engineering of Hichigan State University of Agriculture and Applied Science ,in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN AGRICULTURAL ENGINEERING Department of Agricultural Engineering 1962 ACKNOWLEDGMENTS The author wishes to express his appreciation for the valuable guidance and assistance from.Dr. James S. Boyd. He sincerely thanks Dr. Clement A. Tatro of the Applied Mechanics Department for his valuable assistance and suggestions. The use of the facilities of the Applied Mechanics Department was greatly appreciated by the author. The author wishes to express his appreciation to Dr. Arthur W. Farrall, Head of the Department of Agricultural Engineering, and to Dr. Merle L. Esmay, Graduate Advisor for the Agricultural Engineering Department for their efforts in arranging for the research assistantship. He also wishes to thank the United States Steel Company for making available the funds under Which this research was conducted. ii TABLE OF CONTENTS Page INTRODUCTION......................................... .1 OBJECTIVES........................................... REVIEW OF LITERATURE................................. Properties of Fence Wire........................ Age Hardening...'....ooo......................... comm-F: Properties of The TEnsion Curve................. Stress Relaxation............................... 10 Strain Energy Theory............................ 11 Effects of Temperature on Fence................. 12 PRELIMINARY INVESTIGATION............................ 13 Stress Relaxation in Fence Wire................. 13 INVESTIGATION OF PROPERTIES OF THE TENSION CURVE..... 16 Reduction in Height of Tension Curves........... 17 Reduction in Height With Cyclic Loading......... 17 Time and Temperature Effect on The Tension Curve l9 Elongation of Tension Curves.................... 21 Mechanics of The Tension Curve.................. 2h Investigation of New Tension Curve Designs...... 32 Theoretical Correlation Between Temperature Changes and FenCe Tension.a................ h2 METHODS OF DETERMINING FENCE TENSION................. E6 CONCLUSIONS.......................................... so RECOMMENDATIONS FOR FURTHER STUDIES.................. 52 BIBLIOGRAPHY......................................... S3 GLOSSARY............................................. 59 111 LIST OF ILLUSTRATIONS Figure Page 1. United States Steel Standard Tension curve................................. 8 2. Stress Relaxation Curves for Fence Wire.... 1h ‘3. Reduction in Height of Tension Curves...... 18 h. Standard Tension Curve Load-Strain Diagram. 22 5. Load-Strain Characteristics for #9 Wire.... 25 6. Load-Strain Characteristics for #11 Wire... 26 7. Tensile Test of #9 Hard Temper Wire........ 28' 8. .Analysis of Tension Curves................. 30‘ 9. Etched Tension Curves...................... 3h 10. Wire Forming Die........................... 3h 11. Comparison of Load-Strain slopes for Spiral and Standard Tension Curves........... 36 12. -Possible Tension Curve Designs............. 37 13. Test of Curve Shown In Figure l2-b......... 39 1h. Load-Strain Diagram for Curve 12-c......... 11.0 15. Load-Strain Diagram for Rectangular Tension Curve................................. 16. Modified Rectangular Tension Curves........ A3 17. Comparison of Standard and Modified Rectangular Curves.............r......Ifli 18. ' Tension Curve Height Gauge................. h? 19. -Extensometer............................... h? 20. Extensometer............................... h9 21. Field Test of Extensometer................. M9 I it INTRODUCTION The erection and maintenance of woven wire fence is probably the most misunderstood operation on American farms. While the farmer has a very definite understanding of what he expects his fences to do for him, he has little real information to guide him.in the construction of a fence which will perform as he thinks it should. As a con- sequence of this lack of factual information, farm.fence construCtion practices vary widely from.region to region, and are almost uniformly mediocre in their results. This variation in construction practices has been brought into sharp focus by the problem of writing stand- ards for the erection of fences along the new divided high- "way systems being constructed by the various states. The ideal woven wire fence would be perfectly rigid, Icheap, never need repair, withstand the onslaughts of cattle, horses, hogs, and tractors without deforming or breaking the line posts, and not need a heavy, well anchored and post assembly. This is of course impossible. ' Several approaches to the problem of prOper fence construction have been taken.by various groups of investi- ‘gators. Giese and Henderson, for example, have observed that fence failure is usually accompanied by corner post 2 failure, and have deveIOped some excellent corner post con- structions to insure that this portion of the fence will be the last to fail. Unfortunately, these constructions are expensive and time consuming to install. .The advent of the mechanical fence building machine brought a need for a less expensive, yet durable and and corner construction which need not be overdesigned to in- sure that it would perform adequately under all conditions. To deveIOp a better corner design, it was necessary to know the magnitude of the loads imposed by the woven wire fence itself. A second problem, intensified by the use of the mech- anical fencer, was the tendency to overstretch the woven, wire.‘ Many farm tractors can develop enough drawbar pull to damage the woven wire fence. Some basis of design.and erection was desired which would predict the fence loads on the corner assembly, and which would serve as a guide in writing specifications and in_erecting fence. It was known that the cause of early corner post failure was excessive fence tension, but the causes of this tensiOn were not well defined. Giese and Strong indicated that the effects of, temperature might causean increase of 50% in the load imr posed by the fence. The work of Wilson provided quantita- tive data on the change in load with temperature. It seemed probable that some particular value of ini- tial tension would provide a minimum.change in load with temperature changes, and provide a margin of elasticity to 3 absorb loads caused by livestock. ‘It also seemed possible that some simple method of determining fence tension during erection might be deveIOped which could be used by farmers and other fence builders. 2. 3. OBJECTIVES ' The objectives of this investigation were: To investigate properties of fence wire which could affect fence performance. To investigate the pr0perties of the tension curve un- der axial loads. To correlate these properties with the behavior of farm fence. To investigate methods of determining axial wire loads during fence construction. REVIEW OF LITERATURE Properties of Fence Wire In the investigation of the performance and properties of almost any mechanical device, one of the first consider- ' ations is usually the material from which the device is fab- ricated. The performance of woven wire fence is highly de- pendent on the material from which it is manufactured, which is steel wire. Since the cost of the finished product is of primary interest in such a highly competitive field, the steel must,be of a type which is economical to produce in large quantities. This in general limits the fence manufac- turer to the low carbon, silicon steels. Exceptions to this may occur when the fence manufacturer has access to higher carbon Steels which cannot be used for their original pur- pose due to incorrect analysis or production overruns. This investigation will be limited primarily to the low carbon, silicon steels. Observation Of the wire mill at a fence factory pro- duced the following information. Low carbon steels cannot be hardened by heat treatment, but are given higher physical prOperties by cold working processes. In the manufacture of wire, the reduction from.billet stock to wire stock is 6 performed hot, in a series of rolling stands, with the final product a heavy wire of about 1/2 inch diameter. This stock is then further reduced to the desired size by cold drawing, which leaves the wire very hard. If the in- creased hardness and tensile strength are not wanted, the wire is then annealed, usually as a part of the galvanizing process. Control of the-annealing process allows the pro- duction of wire of any desired temper, from dead soft to fully hard. Merchant wire products are usually classified as dead soft, quarter hard, half-hard, three-quarter hard, and hard. Bayer (10) lists the following approximate physical properties of various tempers of cold rolled Steel. Temper Tensile Strength.psi Elongatiqng% Hard ' 80,000 12,000 3% 2% Half Hard 6A,OOO 8,000 9% 5% Quarter Hard Sh,OOO 6,000. 20% 7% Soft h8,000 5,000 ; 30% 6% Dead Soft hh,OOO h,OOO 39% 6% In wire fence products, wire of various tempers, or hardnesses are used to meet the demands of various applic- ations. Wire used for brace wire is normally supplied in a softer temper than the wire used for line wires in woven wire fence. Stay wires for woven wire fence must also be ductile enough to withstand the wrapping operation without. fracture or tool wear. 7 A visit to a fence factory revealed one of the reasons for the wide variation in tension curves. The machines used at this factory were equipped with an eight station revolv- ing crimping head, so that every eighth curve on the Same wire was made by the same die. The other seven tension curves between were each made by a separate die, with the dies being replaced at random.as wear occurred. For each additional line wire, eight more dies were used, thus when making a ten strand fence, a total of eighty dies were used, no two of which were exactly alike. The standard tension curve dimensions of United States Steel Company are illustrated in Figure 1. This figure also illustrates the measurements for height of the tension curve and elongation of the tension curve. I The height of the tension curve has long been used as an estimate of the tension in the fence. The exact amount of reduction in height during stretching is someWhat con- troversial. Henderson (9), DeForest (h), and others (1) recommend removal of one-half of the height during. stretching. Neetzel (11) and Wilson (16) indicate that removal of one-fourth of the height of the tension curve is more nearly correct. CarlSon (2) conducted tests to deter- mine if an observer could tell When the height of the ten- sion curve had been reduced by one-half. The observers usually could not, and in some cases were in error by as much as h2%. ELONGATION —e—( f U.8.S. STANDARD TENSION CURVE FIGURE 1 9 Age Hardening Age hardening is another undesirable characteristic of low carbon steels used in fence wire. Grosvenor (7) states: Aging in iron and steel may result in an increase in strength and hardness, a loss of notch tough- ness and ductility and the reappearance of a sharply defined yield point in.a tensile stress strain curve after quench or cold working. Grosvenor (7) further indicates that the thorough deoxida- tion of the steel by use of a1uminum.or silicon can control the age hardening process. Davenport and Bain (3) indicate that the age hardening process can be controlled by aging at high (210°F) temperatures, and that the maximum age hard- ness obtained with 0.06% Carbon steel was at 70°F. Properties of the Tension Curve Woven wire has been produced with tension curves in 'the line wires for many years. These curves are spaced every six inches apart and are supposedly intended to act like springs, keeping the fence taut and absorbing changes in load due to the action of livestock or temperature. The tension curve is believed to have been invented as an aid. in estimating and controlling the tension in fence. In practice, the dimensions of the tension curve vary widely. .Schueler (13) indicates that the size and shapeof the tension curve varies considerably even in the same roll of fence. Wilson (16) also illustrates this variation. Giese and Henderson (5) list the following variations in height of factory tenSion curves: #9 gauge wire, 0.266 to 0.39h inches or 32.5%, #11 gauge wire, 0.200 to 0.236 inch or 18% variation. 10 The properties of the line wires which contain the tension curves, are of critical importance in maintaining a taut fence over a long period of time. For this reason the line wires must have high physical prOperties. This is usually done by limiting the annealing process, although _some manufacturers use a softer wire which work hardens dur- ing the fence stretching process. I Stress Relaxation One of the principal problems in erecting woven wire fence is maintaining sufficient tension in the fence to pre- vent it from.sagging over-long periods of time. This prob- lem is made even greater by the use of wire which is subject to the phenomena of stress relaxation. Stress relaxation is present to some extent in all metallic materials, and is exhibited to a marked degree by low carbon steels that have not been work hardened. An excellent example of stress relaxation is the inability of the brace wire used in fence corner construction to sustain a high initial load over a period of time. The initial loading of the brace wire will decrease rapidly at first, then more slowly until some min- imum.tension is sustained. Strom (15) found that this min- imum load for four #9 strands of brace wire was about 600 pounds, or 150 pounds per wire. Initial loads imposed on the four wires varied from.just above 600 pounds to more than 2100 pounds, and in each case the total load relaxed to about 600 pounds. 11 Load-strain diagrams for fence wire containing tension curves have been plotted by Giese and Henderson (5) Carlson (2), and Wilson (16). Giese recognized the value of these tests in.the following statement: The unloading curves are of much importance since they indicate by their SlOpe and position the elastic properties of the wire. The slope of the unloading curves gives the elasticity of the wire. The elongation at zero load is the permanent set or stretch resulting from.a particular load. GieSe and Henderson (5), Wilson (16), and Carlson (2), investigated the efficiency of recovery of the tension curve. Giese and Henderson found that increasing the elongation of the tension curve decreases the efficiency. Carlson found that tension curve efficiency is increased by decreasing wire diameters, and Wilson observed that the efficiency of the tension curve decreases as the load in- creases in every case. Wilson further stated that the critical portion of the wire is not the straight part but the tension curves, which act as stress raisers in the wire. Strain Energy:Theory Seeley and Smith (1h) state that the total elastic energy, U, stored in an object is equal to the integral of (it) 2as 2E1 Where: is the bending moment E 'is the modulus of elasticity is the moment of inertia of the section ds is the element of length taken along the neutral axis of the object. , 12 Effects of Temperature on Fence A'Giese and Henderson (5) observed that a temperature change of 70°F to 20°F gave an increase of apprOximately 50% in the fence tension. Wilson (16) concluded that temperature changes cause a general downward trend in the fence tension.' Giese and Henderson (5) quoted the coef- ficient of thermal expansion for steel as 6.1 x 10"6 per °F, as does Hausmann and Slack (8).. PRELIMINARY INVESTIGATION Stress Relaxation in Fence Wire Laboratory tests of fence wire were conducted to see if the wire used for line wires would behave in the same way as the brace wire tested by Strom.(15). A coil of #9 wire was obtained from a wire mill. Individual strands 'of the wire were loaded in a Tinius Olsen Testing Machine tequipped with an extensometer. The extensometer was used to insure that the machine did not creep back and reduce the loading. Specimens were loaded to 100 pounds and the position of the machine locked. At the end of three min- utes, the load had decreased to thirty pounds. Additional specimens were loaded to h00 pounds and the machine locked. At the end of ten minutes, the lead had decreased to 120 pounds. At the time of the experiment, it was supposed that the wire was the Same as that used in the line wires of woven wire fence. It was later learned that the wire was of the same temper as brace wire. Figure 2 illustrates the time-load relationship for this test. Two different brands of line wire were tested in a Baldwin testing machine. This machine has a mechanical drive, rather than hydraulic as is the Olsen Machine, and can be positively locked. Eighteen inch long strands of #11 line wire, taken from a section of brand "A" fence, 13 m amnoHa amHa mazes mos neameo oneexaamm enamen mmeezH: leans a o m . . _ N H ,4 H O H -O> r-O "i we flmHB ”Odmm <.ozm=o onmzua ac umoaam 2H zouaopnum mazpom 2H ages 0:”. can 00.» Cum 00m Gem 0mm com and 00H 0: om." 00." On 00 _ _ _ p p . . P _ a p _ _ _ HEIGHT IN INCHE 8 Ohm . 1000. loan. loo“. . IoHv . none. 50¢. IO¢¢ . lone. 19 (5) cycles of loading to 100# and unload (2) cycles of loading to lh0# and unload (6) cycles of loading to 200# and unload (3) cycles of loading to 300# and unload Total of (16) cycles ' Before and after the test, the height of the tension curve was measured by means of a surface plate and a dial indica- tor. The following data was obtained. Height . Before Test After Test Reduction % Reduction .523 .uié .107 20.5 .522 .i20 _ .102 19.5 .555 .uzu .131 23.6 .530 ' .u22 .108 20.6 Average Reduction -- 21.05% Time and Temperature Effect on the Tension Curve Fences with no trace of the tension curve remaining are common. The question often arises as to whether the tension curves were removed during erection, or by the act- ion of livestock and climate on the fence. During the sump mer of 1960, a ho rod section of lane fence was erected on the beef farm of Michigan State University. In the fall of 1960, a number of tension curves were selected at random throughout the length of the fence and marked with red paint. A small checking fixture and a dial indicator were _used to measure the height of the tension curves. The curves were first measured in November of 1960, thereafter, 20 in January of 1961, and in July of 1962. Data from repre- sentative curves is presented below. 22325 ‘Nov.8,1960 Jan.l6,l96l Ju1y13,l962 29m 19°F ' . 39°F 77°F Wire Location #9 top .180 .178 .182 #11 filler .12h .116 .123 #9 bottom. .112 .105 .107 #9 top .177 .176 .192 #11 filler .150 .150 .158 #9 bottom .175 .178 .190 #9 top .1h7 .lha .1Sh #11 filler .th .12h .130 #9 bottom. .198 .192 .200 This fence was one of the first machine built fences, and was someWhat unevenly stretched during erection. The fence has been subject to the action of animals, weather, and farm.machinery for about two years. Some sections of the fence have had the stay wires ripped out-by tractor axles. The fence seems to have maintained its original tightness, and the data would seem to indicate that the differences in tension have somewhat equalized themselves. The tension curves definitely reflect the effects of changes in temperature on the fence tension, and have not decreased in height during a two year period. This experiment indic- 21 ates that the tension curves, even hough overstretched or unevenly stretched, do absorb strains due to climatic effects, and do tend to maintain fence tension, by expand- ing and contracting as necessary. Elongation of Tension Curves The elongation of the tension curve is of particular interest, for this preperty determines to a large extent the performance of the fence when subjected to various loads. Giese and Henderson (5) indicated that the slope of the unloading curve is of much importance, for this indicates the elasticity of the wire. The objective of this group of tests was to obtain insight into the behavior of the tension curve when subjected to repeated loading, to obtain data as to the elongation at various loads, and to measure the slope of the elastic and plastic portions of the loading and unloading diagrams. From.this data the specifications for a strain meter or extensometer could be obtained, and temperature-load charts projected. The results of these tests may be summarized as follows: Figure h illustrates a typical load-strain dia- gram. Strain is not unit strain in the usual sense, but is total strain for one tension curve. This diagram illus- trates the behavior of a tension curve during a series of increasing loads. Referring to the diagram at 0 strain and 0 load, as load is first applied to the newly formed curve, elastic deformation takes place. 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