II p ,l \ \ 1 l '1 t; H M. ‘ al N W "H M M W I t \ N l N 1 ‘ 'F’HE EFFECT Q?" TEMfiRATURE AND MECHANICAL PfiQPERT'éES 0N FARM FENCE PERFORMANCE Thesis for flu Deg-me a? M. 5. MICHIGAN STATE UNEVERSUY Jack D. Wilson 1958 Mae-.333 vii. 41A.” . 01' r l4... w? .r*~ ~ (1" J :23: tne me 3h () Tie in :r‘en’ g .I.. NM V‘y“ D . .' .3" ":8 an ‘ uic-n;_4t .9. I ' ' ..;3 -n :r.e 11 n. . 3‘ ’ _l'~. ‘E var: ., - n "\ »--.-.s Jet;- J .JH.DY “- we , . :v~‘v ‘-.'.“vf a”; u. ’ \- “fl“ 7:; ’ ‘u f‘ V VJ I :h.. “‘e-aDA- .. ~.: ‘ "v .’ .f‘ 1 . -9” ‘..--‘.‘:'~ ‘ 'b‘ Ah’: “\4 .' .,' 38., a .. a“: \D " U1.wt., {3‘ L 2 JACK D. WILSON ABSTRACT The objectives of this investigation were: (1) to test the mechanical properties of wire from woven wire fence with special consideration for the tension curve, (2) to determine an accurate and suitable method for measuring the load in the individual wires of a fence, (3) to determine magnitudes of load changes due to temperature variation. A review of literature was made. It was found that the load in fence may be increased by as much as 50 per cent due to temperature variation. Much of this load increase was due to the barbed wires which have no tension curves. It was also found that tension curves are not nearly elastic as they are thought to be. The investigation on the mechanical properties was conducted in the Materials Testing Laboratory of the Applied Nbchanics Department. Tension curves were the main object cfi‘interest. The specimens used in the tests were 16 inches hilength and included two tension curves. The strain gage used to measure the elongation in the wire was a mechanical one with a 10 inch gage length. The strain gage was fastened totmm specimen to include the two tension curves. Load was zunflied with a Baldwin-Emery SR~4 Testing Machine. A means of measuring the load in the individual wires was needed and a load transducer composed of a metal link with two 53-4 A-l8 gages bonded to it, was developed to meet this need. A switching mechanism was developed to LU JACK D. WILSON ABSTPACT handle the ten transducers at one time. This switching mechanism consisted of two low resistance intercom switch 5 I: boxes used in conjunction with two toggle switches. reference transducer was used as a means of accounting for zero shift of the transducers, due to unhooking and rehooking of the leads to the strainmeter. Field tests were conducted on a 2: rod length of fence. The end arrangements were single span with a 8.25 feet compression member and two nine gauge wires as the tension member. The end posts were set 3.5 feet deep in concrete. Stretching was done with a winch of a Dodge Power Wagon. Four tests were conducted, the first three on 1347—6-11 type fence, and the last one on 939-6-11 type fence. The greatest extreme in temperature was encountered on the fourth test when the high was 59 degrees F and the low was 5 degrees F. This temperature drop to 5 degrees F produced a load increase of 3M2 pounds over the lowest measured load of December 31. The results of the field tests showed there was a general downward trend in the load over a period of time and this was due to horizontal movement of the end post and temperature variation. The temperature variation produced a saw-tooth effect in the load. The laboratory investigation of the mechanical prop- erties of the wire showed that, as the load increased the u JACK D. WILSON ABSTRACT efficiency or the ability of the wire to return to its original shape, decreased. The wire specimens showed "yielding" at loads much lower than the yield loads of the material in the wire, which is due to the combined state of stress in the tension curves. Recommended tightening loads are high and use up much of the elastic potential of the wire. These high recommended tightening loads also require strong end post arrangements to insure freedom from failure. THE EFFECT OF TEMPERATURE AND MECHANICAL PROPERTIES ON FARM FENCE PERFORMANCE by Jack D. Wilson A THESIS Submitted to Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1958 {fv;;i~€§?/ 96"th7 TABLE OF CONTENTS ACKNOWLEDGMENTS. . . . . . . . . . . . . LIST OF FIGURES. . . . . . . . . . . . INTRODUCTION. OBJECTIVES REVIEW OF LITERATURE . Properties of Tension Curves Effect of Temperature on Woven Wire Fence Bonded Wire Strain Gages and Their Applications Recommended Tightening Loads Linear Expansion Horizontal Movement of End Posts PRELIMINARY INVESTIGATIONS Mechanical Properties of the Wire. Procedure and considerations made on tension curve recovery tests. . . . . . . Results of tension curve recovery tests Results of reload curve tests. . . . . . A hypothetical correlation between recovery properties of wire and recommended tightening loads. . . . . . . . . . . . - A hypothetical correlation between transverse loads and known properties of the wire. Instrumentation Methodology. Procedure for testing SR- 4 gages bonded directly on wire . . . . Results. . . . . Page ii [—4 KOWCDflNth-P‘w l2 19 24 26 27 29 29 iv Page Procedure in developing load transducers . . 30 Results. . . . . . . . . . . . 3O Considerations and results in instrumentation of load transducers . . . . . . . . . 32 FIELD TESTING . . . . . . . . . . . . . . 38 Apparatus. . . . . . . . . . . . . . 38 Test No. l . . . . . . . . . . . . . 39 Results . . . . . . . . . . . . . AO Test No. 2 . . . . . . . . . . . . . AO Results . . . . . . . . . . . . . AO Test No. 3 . . . . . . . . . . . . . Al Results . . . . . . . . . . . . . A3 Test No. A . . . . . . . . . . . . . A3 Results . . . . . . . . . . . . . A3 General Results of Field Testing . . . . . . A5 CONCLUSIONS . . . . . . . . . . . . . . . 51 RECOMMENDATIONS FOR FURTHER STUDY. . . . . . . . 52 BIBLIOGRAPHY. . . . . . . . . . . . . . . 53 ACKNOWLEDGMENTS The author wishes to express his appreciation for the valuable guidance and assistance received from Dr. James S. Boyd. He sincerely thanks Dr. John T. McCall of the Applied Mechanics Department for his valuable assistance. 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 of the Department of Agricultural Engineering for their efforts in arranging for the research assistantship. He also wishes to thank Republic Steel and U. S. Steel for their making available the funds under which this research was conducted. Appreciation is extended to Robert A. Aldrich, James L. Butler, Philip J. Mielock, James B. Cawood and Dr. William Baten, Agricultural Experiment Station Statistician, and all others who provided valuable aid. Lg. LIST OF FIGURES Figure Page 1. Method for measuring efficiency of recovery curves. . . . . . . . . . . . . ll 2. Recovery curves for nine gauge Brand A . . . l3 3. Recovery curves for nine gauge Brand B . . . 1A A. Recovery curves for nine gauge Brand C . . . 15 5. Recovery curves for 11 gauge Brand A . . . . l6 6. Recovery curves for 11 gauge Brand B . . . . 17 7. Recovery curves for 11 gauge Brand C . . . . l8 8. Characteristic reload-recovery curves for nine gauge Brand B . . . . . . . . . . 2O 9. Characteristic reload-recovery curves for nine gauge Brand C . . . . . . . . . . 21 IO. Characteristic reload-recovery curves for 11 gauge Brand A . . . . . . . . . . 22 ll. Characteristic reload-recovery curves for 11 gauge Brand B . . . . . . . . . . 23 12. Variation in size of tension curves from same roll of fence . . . . . . . . . . 31 13. Load transducer (tension link) . . . . . . 31 1A. Comparison of actual and computed loads on no. 2 tension link. . . . . . . . . 33 15. Wiring diagram of strainmeter and switching unit 3A 16. Switching unit with strainmeter. . . . . . 35 1?. Switching unit in use . . . . . . . . . 35 18. Load and temperature vs. time in a 20 rod length of lOA7-6—ll fence, second test . . A2 vi Figure Page 19. Load and temperature vs. time in a 20 rod length of lOA7-6-ll fence, third test . . AA 20. Load and temperature vs. time in a 20 rod length of 939-6-11 fence, fourth test . . A6 21. Load as a function of temperature and time in a 20 rod length of fence, third test. . . A9 INTRODUCTION Farm fence being a passive, inactive part of the farm operation is probably the most neglected item on the American farm today. The farmer fails to realize the im- portance and value of fence. If the value could be measured in dollars and cents, farmers would realize the importance of good fence. An average farm of 160 acres might have lOAO rods of fence. Using a conservative value of $2.50 per rod as replacement cost the total value of the fence would be $2,600.00. Most of the cause for the widespread disrepair of farm fence can be attributed to faulty construction, including the following: 1. Improper selection of materials, 2. Stretching the fence too tightly or too loosely, 3. Improper construction of end and corner post arrangements. Since according to Giese and Henderson (A), fence failure is almost always a result of corner post failure, "overdesigning" of the corner post has been adopted as a means of assuring a lasting corner post arrangement and corresponding longer lasting fence. Practices which can be classified as overdesign are; using a large amount of concrete to set the posts and anchoring the corner posts with cables. Generally, these are time consuming methods of constructing a fence. Woven wire fence is designed with tension curves in the horizontal line wires. These curves spaced every six inches are designed to act like springs, keeping the fence taut and abSorbing two possible changes in load conditions: 1. Internal loads due to temperature change, 2. External loads, such as transverse loads applied by livestock running into or leaning against the fence. Tests have proven that tension curves, their elastic range being small, do not act like springs, and show little ability to spring back to their original shape after a load increase and decrease has taken place. Fence manufacturers and fence builders use a general rule "that fence is under the proper tightening load when one-half the tension curves are removed." This is imprac- tical as the amount of load to pull out one-half the tension curve varies due to temperature and size of the tension curve. Tests have proved that loads on woven wire fence will decrease and increase with corresponding increases and decreases in temperature. They were conducted however by measuring the total load increase in the fence so the action on the individual wires when subjected to these temperature variations, is unknown._ OBJECTIVES To determine an accurate and suitable method for measuring the load in the individual wires of a fence. To determine magnitudes of load changes due to temperature variation. To test the properties of the wire in the fence with special consideration for the tension curves. REVIEW OF LITERATURE The review of literature was made in six parts: 1. Properties of tension curves Effect of temperature on woven wire fence Bonded wire strain gages and their applications 2 3 A. Recommended tightening loads 5 Linear expansion 6 . Horizontal movement of end posts Prgperties of Tension Curves Carlson (1) observed that tension curve efficiency or the ability of the tension curve to spring back to its original shape after a load is applied and subsequently released, increases as the wire size decreases. The load necessary to reduce the tension curve by one-half on a nine gauge wire is much greater than that to reduce the tension curve by one-half on a smaller 12.5 gauge wire. Tests conducted by Giese and Henderson (A) and also by Carlson (1) indicate the more the tension curve is pulled out, the less efficient it becomes. Giese and Henderson (A) also observed, that higher tension curves require less load to produce half reduction in height than shallower curves. 5 According to Schueler (13) the size and shape of the tension curves varies considerably, even in the same roll of fence. Figure 12 shows tension curves taken from the same roll of a commercial fence. (See Figure 12, page 31.) In their summary Giese and Henderson (A) gave a general statement concerning tension curves. They wrote; The tension curve in woven wire fencing is beneficial in helping to maintain a taut condition but is not entirely effective because the elastic range is small. The manufacturers recommendation to half remove the tension curve is not sufficiently specific, is not equally applicable to summer and winter stretching and is likely to give variable results because of differences in shape and size of tension curves. Effect of Temperature on Woven Wire Fence Giese and Strong (5) in their tests concluded, "that the total load on a fence end varies with the stretch and may be increased 50 per cent or more with varying temper- ature conditions;" A great deal of this load increase is due to the barbed wire or wires above the woven wire. They obtained the following results on a double span end fence. On December 17 at a temperature of 61 degrees F, the load was approximately 1800 pounds while on January 2 the tem- perature was -A degrees F and the load increased to 2600 pounds. Giese and Henderson (A) using a coefficient of thermal expansion for steel (annealed) of 6.1 x 10"6 per degree F made the following computations. The decrease in a AOO foot length of fence with a drop in temperature of 80 degrees 2.4; .041!“ "C ,2 ~n "i .CQ @er N V . *1 .H 4,... ‘ACSEuuedUI ' é Size temper . : F‘ ""1?“ van " V‘h-V.'A‘E U .._- ‘ . 1 ‘- h-tie (11:51 a 131.: incre “A“ “ -.- H- o".benfv‘°i U l l P‘~G .':* u N .‘4. ball 4*“ nd‘ :v...n P's,“ c nihe Li“ L, s,“° . ‘Vduv . § ‘ ‘ “M m uit‘i‘ei‘l ~;T)E T r . .he _ h fi. ‘ " :9 Lilfislgt: F to -20 degrees F is 3.12 inches. Assuming fixed ends for the wire, a nine gauge wire with no tension curves stretched to 380 pounds at 80 degrees F, would experience a load increase to 530 pounds for the,temperature drop to -20 degrees F, a permanent stretching of the wire and subsequently a drop in load to 260 pounds when the tem- perature again reached 80 degrees F. The barbed wire under the recommended load of 250 pounds, and under the same temperature conditions would increase to 330 pounds, dropping to approximately 185 pounds. The number nine wire with the tension curves, under a 380 pound load would increase to 395 pounds dropping to 285 pounds. Ap- parently the tension curve absorbed the load increase but did not keep the wire taut for an increase in temper- ature and subsequent decrease back to the original temper- ature. Bonded Wire Strain Gages and Their Applications The SR-A strain gage is a bonded wire strain gage. It consists of a grid or pattern of very small diameter wire cemented between two pieces of thin paper which acts as a base. The wire grid has the property of linear variation of electrical resistance with strain. In order to measure strain in some specimen, one or more of these strain gages are bonded to the surface of the specimen. Next the gage is connected to an electrical ?I iii- instrument which will measure small changes in resistance, such as a Wheatstone Bridge. If proper procedures of bonding and operation are used the expected accuracy of the gages will be as low as three per cent. The duco type SR-A gage is one where the wire is sup- ported by a thin paper base impregnated with nitrocellulose. The duco gage is best adapted to temperatures of less than 150 degrees F. It is also more adaptable to bonding on small curved surfaces since the base is pliable. Recommended Tightening Loads Reynolds (12) gave 250 pounds as the load necessary to pull out one-half the tension curve in a 12.5 gauge wire. Giese and Henderson (A) found values of A21 pounds for nine gauge and 37A pounds for 11 gauge wire as the loads necessary to reduce the height of the tension curve by one-half. As was mentioned earlier, 250 pounds is the recommended stretching load for barbwire. Using these values for 10A7—6-ll woven wire topped with one strand of barbed wire, the total recommended stretching load would be A076 pounds. This presentseadesign problem for fence end corner constructions. Linear Expansion With a few exceptions the dimensions of all substances vary directly as the temperature of the substance varies. If a specimen is wire, the change in length is important. . ‘ i :P‘“"‘ z__.L | ' A. ...-; " nafl‘,‘ a: '1 i ‘ Vw‘ ""b 212': is z ‘1 urea!" H e .- QJ‘JAV’ u. I {flap-‘2 A‘QI‘ sv'V.---J. 21ml -. A?" A? .st‘L—v-A J " n ,‘f‘lfiflv‘3-Q, *- n “‘A'V. U FA A ”en I 4*" y ; DU“, V‘ N ‘dt- -..:i v f": fi‘v Hwy . h \uv“;t::qe 8 It has been found experimentally that the increase in” length.£fl_ is proportional to the original length L-o and very nearly proportional to the change in temperature Ak-r . That is AL=<>¢ Lo ATwhere ad is a proportionality con- stant, different for different materials and is called the coefficient of linear expansion. Horizontal Movement of End Posts Giese and Henderson (A) conducted tests concerning the horizontal movement of single and double span end post arrangements with various levels of load. They concluded, 50 per cent of the horizontal movement of both ends came during loading or within 2A hours of loading. They also observed, "horizontal movement of the end post is the largest factor contributing to the reduction in fence loads prior to complete failure." The load on both ends tested, dropped approximately 20 per cent during the first 2A hours and approximately A0 per cent during the first month. The end posts were in holes bored to size and no concrete was used in the end post arrangements. PRELIMINARY INVESTIGATIONS There were two considerations in the preliminary investigation. First a laboratory investigation was under- taken, to gain some knowledge about the mechanical proper- ties of the wire in woven wire fence. The tension curve was given prime consideration in this investigation. Although numerous tests have been carried out on tension curves, in each case the height of the tension curve was used as a measure of the properties making it very difficult to correlate these results with the linear properties in which we are interested. The second part of the preliminary investigation was concerned with developing a method of measuring the load in the individual wires of a fence. Mechanical Properties of the Wire The objectives of the laboratory testing of the mechanical properties of various brands of wire were: 1. To try to relate some of the recommended practices of erecting farm fence with known physical properties of the wire, 2. To be able to analyze more thoroughly the experi- mental data from the field testing. Procedure and considerations made on tension curve recovery tests. Three brands of wire were tested for the ( 10 recovery properties of the tension curves. The testing procedure was conducted in the following manner. The specimen in each case was a 16 inch length of line wire including two tension curves. A mechanical Tinius Olsen Strain Gage of 10 inch gage length was fastened to the _specimen to include the two tension curves. The load was applied by means of a Baldwin-Emery SR-A TEsting Machine. The load was applied in increments of 50 pounds and at the end of each increment the load was backed off to "zero" load. During the return to zero load from each position, elongation readings were taken at convenient intervals. From the zero load position, a higher load was applied and the process was repeated again. Two considerations were made in analyzing the recovery curve data. The first consideration was the elongation in the wire and it was assumed that permanent elongation dueI to loading could be attributed to the straightening out of the tension curves and therefore plastic deformation in'the straight portion of the wire was negligible. The second consideration was that each curve, of the two curves included in the ten inch gage length, contributed one-half of the total permanent elongation due to loading. This assumption wasbased on the fact that tension curves in series require the same load to reduce the height of all the curves by a specified amount as the load required to reduce the height of one curve by the same amount. 11 With the first consideration in mind a relationship between the experimental results and a one foot length of line wire can be made. There are two tension curves in every one foot length of line wire therefore since it was assumed in the ten inch gage length that the deformation was due only to the flattening out of the two tension curves, then results of the testing will apply in each case to a one foot length of wire. Efficiency of recovery for the various brands of wire was based on the ratio of the length which the specimen recovered upon reaching a no load condition, to the total increase in length of the specimen for that particular load increment. Efficiency would be measured in this manner since the important factor in actual field conditions is the ability of fence with tension curves, to return to zero elongation at a Specific load. Figure 1 shows how the efficiency was measured from the recovery curves. I. 004/ hr powvo’s EffiC/Cycj : _C_L_ b I l E Lorvsarl'oar /;Y f/Ych es Figure .7 12 Results of tension curve recovery tests. Since this testing was conducted in a cyclic manner of loading and un- loading there is a tendency for the yield point of the metal to be raised. This is due to a strain hardening effect in the material at the tension curve, which serves to improve the yield strength. Assuming a modulus of elasticity of 25 x 106 psi which was the value given by one of the companies for their wire, a tensile yield strength of 60,000 psi could be safely chosen since the wire is a cold drawn product. Using this as a criteria, the yield point for a 12.5 gauge wire would be A79 pounds, 650 pounds for an 11 gauge wire and 1060 pounds for a nine gauge wire. As the results showed there was permanent set in the wire at loads much lower than the yield point loads but the critical portion of the wire is not the straight portion but is rather the curved tension curves. These tension curves are subjected to a combined state of stress and it can be safely assumed that this is the reason for yielding of the specimen at loads below the tensile yield load of the material. In one respect tension curves act as stress raisers and in this respect fail to add to the favorable properties of the wire but nevertheless they do have a definite value in the favorable performance of the fence. Figures 2,3,A,5,6, and 7 show typical recovery curves for three brands of wire. The slope of the recovery curve is nearly constant for a particular size and brand of wire. 13 0.2m. a cam: 53% m .8.» ”3.3.5 auosoeom a 3de manic mono“: n“ ...o...3h:omu mmé o \\\ .8” .08. .oo» .1 8.... Spunod at p901 14 F..- ., E 933 m woman .mmsam m uom 35.56 Embouom a 0.3m: 353 3 83:36.03 mu.o o~.o no.0 o . L . l sooa \ m \. .08 n. \ T! a We m m. 9 .oon L.moe 15 one; o cnmnm .omsme m new mosuuo mucsooem .w enamdm wagon“ ca acaammaoau m~.o . o~.o P b \ i. 4T 00H com 000 00¢ '03fi03 “I P901 16 5.2... 4 398 .0923 .2 no.- ..»30 3:83 mono-nu 5 neuuewcoam m 9:62 F-i!: Lil I . 1.! "l’ I mo. 0 o x \ \\ .. ooa .08 .00» 1. 8.. wuma at up! 'l Iirl’a lll).l.!slvn .. .1... ul ll!.|l‘.'|..:l|. 1'7 on: a sauna {mums fl mom «330 326on b 9:53 canon“ 3 noun-baa: 3.5 3.0 no. a o i. 03.. oov MW “I 9.0! 18 910 o~.o. on: o 63.2.. {meme 3 non :38 Dopooom manna 5 33...?on no.0 9:5: .. OOH ~ .7 DON spunoa :2; pad: 1. co» a. s. 19 The efficiency of the tension curves decreases as the load increases in every case. This is a logical phenomena and gives a hint to the importance of initial stretching loads in fence. In general the efficiency of the various brands of wire was low at all loads. Efficiency ranged :flrom a high of 37 per cent at 100 pounds to a low of 12.5 jpei‘cent at 3A0 pounds. No attempt was made to rate the ei?ficiency of the brands of wire. There was no conclusive evidence of a relationship lxetween wire size and efficiency of the tension curves. bkaturally for the same load the smaller size wire elongated Inore than did the larger wire. Results of reload curve tests. After reaching the Zerm>load position in the recovery curve tests the load was Ifiun up again to the next higher increment of load (usually 550 pounds). These reload curves did not coincide with the IPecovery curves even though the rate of loading and unloading lNas constant. In general the reload curve showed a smaller (Elongation than did the unloading or recovery curve for the Same load. This property can be classified as mechanical Ilystersis in the wire. Figures 8, 9, 10, and 11 show the 3Peload and recovery curves for the three brands of wire tested. The different paths of the recovery and reload curves also could be attributed to the fact that although the elongation readings taken at load intervals were subjected 20 _......_1 F... l -A.-._ -~ 1.1., ”7 -.. ....._...—. -,,, 0.33 a 0:93 amuse 0 you meta huo>oooausa03m 03.230330 0 madman. 0053 a“ “33%”.on mH.o 0H.o no.0 0 TI . A P ill! 1‘ A \ \ \\\ \ soon x . \ \ M .1 com D. m. J O x x m p a. eaoaom .oo... \oom \ r!- ----::i- 15- ---...-!--I-L h." 26qu I 21 0.33 0 ~39; 93.5.0 0 net «023...... .32.... camsnuoanm adamfinepaanflfi 0 0.33m. «32: 3 US$33. who 3.0 no.0 0 . N nrOOH eonm .80.... 0250M 1. new huosooomll-l up A m: 7330 snnno : 22 (I .\.1 .I.¢Il|.. n!‘1.‘l"ll.l|l Ill: onus 4 wanna omauo-mm:wom wo>uau muouooomlvuoHna_ofiaufluouoanmdo .xHonsmwm manna" a“ :ofiuamnauu mm.o unannm mkmpoonm.llllzu.lllu .1 OCH 4 Com #00» ;00v “Pu“DJ “I P901 ”J 23 I'll. , [kr‘ ‘- r w .r _ __ i L ..‘ _ 1 i. r . C i . . . iL It'll naoo .. |. ‘-I'.||IIII'I.III . I : ll'lllilbt‘ll'uil .1F I, l' '1. mafia m ommnm omamc Ha Mom ao>uso muo>boqmrvaoflom oauonnmvoanmno ow.o a 0:03 3 3033.533 Ha annawm 1P \ \ mo.o. I - o \ :00.” 60m :oon unonoa eoo¢ mumpooom unIIIu . gem 9:01 apunoa u; 2A to a constant load rate, there was some time dependent elastic deformation which if taken into account, would cause the two curves to coincide. For instance, if the load were held constant at a certain level during the recovery tests, and was allowed to remain at that level for a period of time T1, then the elongation would decrease due to the time dependent, elastic after-effect. If during the “‘l Imeload period the load rate was stopped at the same load 813 the one during the recovery tests, then there would be i a. residual elongation during a period T2. Therefore, the J % ccbmbined effect of the time dependent elongation and con- J ‘tzraction in the reload and recovery tests respectively Mnould be for the two points at the same load to move closer tuogether at that load and possibly even coincide.' A hypothetical correlation between recovery properties 51: wire and recommended tightening loads. A 421 pound load fias been suggested as a proper tightening load on nine gauge VVire. Recovery curves were not run from this load on any C>f the three brands of wire tested so a conservative load c>f 325 pounds on Brand A wire will be used as the criteria <3f this analysis. An initial tightening load of 325 pounds would cause Efln elongation of .118 inches per foot or 6.49 feet in a 40 IWDd length of nine gauge wire. This increase in length can tNE attributed to the flattening out of the tension curves. Afisuming that the load could be returned to zero in the 25 fence there would be a permanent elongation of 5.225 feet in the wire. Of course in actual field conditions this decrease to zero load would not occur as long as the wire was secure in place, but it does ppint up the fact that a great deal of the elastic range of the wire is used up in the initial stretching of the fence. Brand B nine gauge wire under the same conditions of loading as described in the preceding paragraph would experience an initial elongation of 4.785 feet and a permanent elongation of 4.0158 feet upon return to zero load. Type C nine gauge wire would experience an initial elongation of 5.885 feet and a permanent elongation of 5.005 feet upon return to zero load. There is little difference between the final results for the three different brands of wire. A 325 pound load in nine gauge wire would produce a Stress of 18,400 psi which when related to 11 gauge wire Would mean a load of 200 pounds in the 11 gauge wire. For Brand A 11 gauge wire, an initial load of 200 EKands would produce an elongation of 5.83 feet in a 40 ,ITKi stretch.» There would be a permanent elongation of 4.4 feet in the wire upon return to zero load. In Brand B 11 gauge wire, an initial load of 200 pCHands would produce an elongation of 5.775 feet while there WC>uld be a permanent elongation of 4.685 feet upon return to zero load . 26 ' Brand C 11 gauge wire would experience an initial elongation of 5.225 feet for a 200 pound load and a per- nmnent elongation of 4.015 feet upon return to zero load. The previous analytical relationships between arbitrary loading and known recovery curve data, produces an interesting point. Suppose a 1047-6-11 standard fence, with top and bottom wires of nine gauge and the eight filler wires of 11 gauge is subjected to a 2250 pound load. This is the load resulting from combining 325 pound loads in the two nine gauge wires and 200 pound loads in the 11 gauge wires. The Inovement of the line wires relative to one another in the fence is fixed by the stay wires therefore, all the line ‘Wires in the fence would theoretically stretch the same Eunount when the 2250 pound load is placed on the fence. The results of the laboratory testing and corresponding Emnalytical evaluation has shown that if the load was dis- tributed as was assumed previously, the nine gauge wires 'Would elongate .66 feet more than would the 11 gauge wires. 'This would be impossible due to the relative fixed condition imposed by the stay wires. Therefore, the stress in the- 11 gauge wires would be greater than that in the nine gauge Wires and for all practical purposes the 11 gauge wires would ‘be carrying more than their share of the total load. 'A_hypothetical correlation between transverse loads Egld known properties of the wire. As was mentioned earlier . W13 IH'H ".'!.- “'I: 0.. 27 in the introduction, transverse loading imposes a critical test on the fence, particularly the end and corner post arrangement . The wire in the following analysis will be nine gauge Brand A wire. At some time T1, there is a load of 225 pounds on the wire. The wire is then subjected to momentary transverse loading at some time T2, and there is a corre- sponding increase in the load to 325 pounds. If the load (iropped off again to the original 225 pounds then the wire ‘would have suffered an elongation of .027 inches per foot cur for a 40 rod length of fence, 1.485 feet. This resultant «elongation would mean a definite sagging, permanent in ruature for the wire. The results in a fence subjected to tfliis same loading would be analogous to the results for a Single wire as shown above. 131§trumentation Methodology There were three possible methods of measuring loads ir1 individual wires. They were; 1. Mechanical strain gages mounted on the line wires, 2. SR-4 gages bonded directly to the line wires, 3. A load transducer, composed of SR-4 gages mounted on a metal link which would be fastened in the line wires. The use of mechanical gages as a means of measuring ldlads in wire was deemed undesirable for several reasons; 1. Cost would be prohibitive since ten gages would 28 be necessary at one time to measure the total load, 2. They are relatively bulky and subject to being bumped, in the field. Bonding SR-4 strain gages directly on the wire has txytkladvantages and disadvantages. The advantages are; 1. Speed of bonding when using a thermoplastic cement, Eras 2. Flexibility. ; ., The disadvantages are: é 1. In using a straing gage small enough to fit on t a wire there is a chance that this gage may be 1;"3 bonded to a spot on the wire where there is a discontinuity in the material and thus erroneous strains would be measured; 2. The heat necessary for the application of the gages with a thermoplastic cement, may have an injurious effect on the gages. The load transducer seemed to have good possibilities for measuring loads . Advantages are: l. The transducers can be checked for proper func- tioning prior to installation in the line wire; 2. They can be used more than one time if properly cared for. Disadvantages are: 1. They would be measuring loads in the transducer and not in the wire directly. 29 Procedure for testing SR-4 gages bonded directly qn wire. Two A-l8 SR-4 gages were bonded to the wire with IkaKhotinsky cement. A thermoplastic cement such as De- Kliotinsky was the only feasible method of bonding the gages tc> the wire directly, since under field conditions it would hue impractical to use the slow drying duco cement. The gxages were mounted opposite each other on the wire to eiliminate bending strains which would otherwise be picked up. Results.--The E value computed from the experimental Iwesults for Brand C nine gauge wire ranged from a high of 31..6 x 106 psi to a low of 25.5 x 106 ps. The average \nalue of E, from six tests on the same specimen was 29.91 x 106 psi. The load computed from experimental results and the kIlown load from the testing madiine agreed quite well al:though the computed load was lower in each case. On the Brand B wire, tests were not conclusive. The 6 El value was approximately 45 x 10 psi which is an unreason- ably high value. Mounting the gages directly on the wire was discon- tinued for various reasons, other than the ones already given as disadvantages; 1. DeKhotinsky cement tends to polymerize when left in warm air, ‘ 2. Under field conditions there would be a problem of trying to check the gages to insure no damage .«3 a. id.‘u-—.-lla.1 El 30 had been done during bonding, . 3. In bonding and molding the gage to the contour of the wire there is a good chance for injury to the gage and subsequent unreliable performance. Procedure in developing load transducers. The idea of'using tension links as load transducers in the line wires was first conceived by Lee (9). The load transducer is .,FQ fastened into the line wire. The load in the tension link and the load in the wire would be the same. Knowing E for a I... w.“ 'the link, A (area for the link) and E (the measured strain 111 the link), the value of P (load) can be computed using a modified version of Hookes law (P = eAE). The link itself vnas constructed as a metal strap with looped ends to :facilitate fastening the wire to it. A-l2 SR-4 gages were bonded to both sides of the metal link and the gages were Inooked in series in the same leg of the bridge, thus ‘elinunating bending. Figure 13 shows a tension link. Results.--First tests were run with a link (no. 1), ~11375" by . 1875“ in cross section. Although the test Prkoved successful, there was some question as to the sensi- tl‘vity of the tension link since the area of the link was gllite large compared to the area of the wire. For this reason, tension link no. 2 with a cross 8fiction of .125" by .125" was adopted as the one to be used 111 field tests. This was the smallest dimensions which 31 J. ‘ L . ’ ~ I. ., .‘fl _ .4 .r " \\ er" v-‘I - f_- ‘- ,- k -___ ‘-_,__,,,___‘__ r . w-‘N-t-u-r“ I 4.- -> - . ..- I J ,- .. _.-f " ‘ ‘_ fl 2 . r ' “‘M Figure 12 Variation in size of tension curves from same roll of fence I I! ‘. ’ L2; ' IW I ” ‘ WWII ” I I I I " ' "I" "----. , . 1 ----_ ‘ ----_ 7' “33%1/4'42343/4'éfixi'41 ’2'44 ‘4: 9’2 54:.) 5145/23: bfizi’; 3’44 M: “I.“ “CSTCOYT '2- 'IUPLI‘ Figure 13 Load transducer (tension link) 32 could be used with the SR-4 A—12 gages which have a minimum trim width of .125". Tests were run on the original tension link no. 2 and Figure 14 shows the relationship between the actual load applied by the testing machine and load computed using the modified Hookes law. Fourteen tension links were constructed in the same Inanner'as described for link no. 2. The links were checked by the prescribed methods to insure proper functioning and iE values were computed for each link as a further check. Considerations and results in instrumentation of load transducers. There were two problems remaining which had to be solved before tension links could be used in a field test. These were; 1. A multiple switching unit was needed to handle the ten tension links at one time, 2. A means of keeping track of the "zero" of the tension links from one set of readings to another was necessary. Two low resistance, intercom switch boxes were used 1n.conjunction with two toggle switches, as the multiple :switching system. This system had a capacity of handling 15 tension links at one time. Figure 15 is the schematic of the wiring while Figures 16 and 17 show the actual switching unit being used in the field. This system was tested before actual use in the field, to insure that strain readings would not vary appreciably due to switching. -RliTxn 3‘ . ‘5 ’- -' \ 1" "V. ~s w‘l . 33 und— aognoa «.9— no 233 633800 use :33 no sonny-930 «a 0.3m: eunuch 5 .33 . as»: corn 0% 8m bps 2.: . RI II ‘I Hanoi e338 spunoa at p301 pundmoo ‘II WW“ ..__. ....___._ e“... v“— loa. Denote Tension Links L a I 4 5 d w e 9 1g 11 12 13 1e 15 Strain-etc! c:l_ Figure 15: ”ring Diagram of Btu inmate:- and switching Unit 34 Figure 16 Switching unit with strainmeter g-.. I?‘ :77}? *M Figure I7 Switching unit in use 36 Since readings would be taken at intervals of one- half or more days apart it was impossible to leave the strainmeter hooked up out in the field. Consequently, since unhooking and rehooking the lead wires to the strainmeter causes a shift in the zero of the system, a method was needed to account for this shift in zero and adjust the values of the strain readings accordingly. A reference link was used to account for the zero each time. This reference link was identical to the tension link and was hooked into the switching unit also, but instead of being fastened in a line wire was taped to the fence and therefore was unstrained, due to load, each time a series of readings was taken on the fence, a reading was taken on the reference link. Since there was no strain in the reference link due to load, any change in strain from the previous series of readings was due to the change in hooking and unhooking of the lead wire. One lead of all the gages was a common lead and theother was hooked in the switching unit, and the lead to all the links through the switching unit was in effect a common lead, thus the assumption was made that the change in strain in the reference link was the same as that in the tension links due to unhooking and rehooking of the lead wires. For example, if the initial reading for the reference gage was 11,000 and at some later time after unhooking and rehooking of the lead wires was 11,050 then 50 would be 37, subtracted from all the readings of the tension links to compensate for zero shift. To account for any possible zero drift of the strain- meter itself, a reference setup was used. This reference setup is described in Perry and Lissner (10, pp. 170-174). In this case, two A-l2 SR-4 gages bonded on a piece of cold rolled steel, comprised the reference setup. FIELD TESTING Apparatus _ The initial requirement in the field testing phase was to construct two end post arrangements which would closely approximate fixed end conditions. The end arrange- ment was single span with a 8.25 feet horizontal compression ‘member and a diagonal tension member of two strands of nine gauge wire. The end posts were set 3.5 feet deep in con- crete, the concrete being 18 inches in diameter. The line ;posts were steel and were driven by means of a mechanical Ciriver. Line posts were spaced at one rod intervals. The thesting area was level thus eliminating many problems of (nonstruction of the fence itself. Initially a forty rod liength was deemed desirable but after the first test, the liength was shortened to 20 rods. Two angle irons were bolted to the ends of the fence ‘to facilitate fastening of the stretching mechanism and to ézive an even pull on the fence. Stretching of the fence -for'the first test was accomplished using two block and thickle type stretchers in conjunction with a dummy pull INDst arrangement but this proved unsatisfactory as to the amount of load that could be applied, so subsequent Stzretching was done with a winch of a Dodge Power Wagon. A- chain was fastened to the top and bottom of the angle 39 irons to get an even distribution of the pull of the winch, on the fence. A hydraulic dynamometer was connected between the chain and the winch cable to measure the initial stretching load. This method of stretching proved success- ful but is not recommended for use by farmers since lack of an instrument such as the dynamometer for measuring the load Inight cause too great a load to be applied with possible r_“ serious results. II The tension links were fastened into the fence before stretching was begun. Turnbuckles were used to facilitate . an even increment of length being added to the fence when E fl the tension links were added, since it was difficult to use éaxactly the same amount of wire in tieing the tension links iJito the fence. 'Test No. l The first test was conducted on a forty rod length of Ikence. Two block and tackle type stretchers were used. The INJll was made from two dummy pull post arrangements, one at Iihe halfway point (20 rods) and the other at the end of the fence. The fence used was Brand A 1047-6-11. No effort ‘Was made to record the initial load although this would be desirable, as it was later learned. During the cutting and iitapling of the wires to the corner posts, the second and tShird wires from the bottom slipped before they could be ‘Secured and this had a bearing on the final results as will be clarified later . 40 Results. The fence was erected on September 30 at a temperature of 70 degrees F. Early the next morning at a temperature of 49 degrees F, there was a 231.96 pound increase in load. The second and third wires from the bottom showed a decrease in load and this might be due to many variables; such as the original slipping of the wires through the staples and contraction and expansion of the tension member. It is felt that these inconsistent actions of the second and third wires are not important in the over-all picture of temperature versus load since the total results do show a consistent relationship between temper— ature and load. When the temperature rose to 62 degrees F on the Iafternoon of the same day the fence showed a total loss in load of 163.25 pounds. jgest No. 2 Test No. 2 was conducted on a twenty rod length of IBrand C 1047-6-11 fence. The dynamometer showed a load of 22700 pounds before the fence was fastened to the end post. lkfter fastening the fence to the end posts, during which ESome load was visibly lost, the tension links showed a total lxaad of 2080 pounds. The temperature at erection was 52 degrees F . Results. A temperature decrease of 18 degrees F pro- Ciuced a 72 pound increase in load the first day. Ten days 41 later at a temperature of 58 degrees F there was a total load of 1583.135 pounds in the fence. Thus the total de- crease in load in the fence for the ten day period was 496 gnaunds. This total decrease in load was due to a combin— aition of yielding and stretching of the wire and a small ruarizontal movement of the end posts through the soil. The following hypothetical analysis is approximate 111 the assumptions made but gives a characteristic des- cxriptive picture of what happens in the fence. Since the tnotal load initially is 2080 pounds, there would be a load (Jf 208 pounds in each wire assuming an equal distribution (bf the load throughout the fence. This would mean that the Ikence elongated 5.4166 feet during the initial stretching 34f the 11 gauge filler wires are used as the criteria of enlalysis. Figure 18 shows the load versus time and the temper- Etture versus time curve of the fence. Eggst No. 3 Test No. 3 was conducted using 1047-6-11 Brand C fence. 'The fence was erected on November 6 at a temperature of 45 Ciegrees F. The initial load from the dynamometer was 2800 IPOunds while the initial load from the tension links after tune fence had been fastened to the end posts, was 2549.158 INDunds. Again there was a drop in load which occurred ci‘uring cutting and fastening of the line wires to the end posts. 42 Mp“ taro in Degrees F once 30on .oonoh no gums com on a a“ as: 2: eunuch-mace use 2.3 2n enema mean 3 as: om - mm on em mm... pm $38 .. ma 8. w . 2 4 pm 8. .2 caoq .. OH on . l om unseen-male i am om. . 1. mm . an 2.1 n 01' Y ”mod n? 990'! 43 Results. A drop in temperature to 40 degrees F showed a load drop of 59.5 pounds. The largest load increase measured was from November 12 at a temperature of 54 degrees F to November 26 at a temperature of 32 degrees F. This load increase was 124.42 pounds. After being up for 38 clays and at the same approximate temperature (43 degrees F) as when it was erected, the fence showed a total load drop c>f 766.78 pounds. The slackening off of the load produced .a.definite observed slack in the fence. Figure 19 shows the load versus time and temperature 'versus time curve of the fence for the 38 day period. Eyest No. 4 The fourth test was conducted on a 939-6-11 Brand C fkence. The initial load according to the dynamometer was 11550 pounds. The bottom tension link gave inconsistent rwesults from the beginning of this test. 0n the next to the least readings taken, the reason for this inconsistency with tilis particular tension link was discovered to be an error 1I1 the switching procedure used and not due to a malfunc- txioning of the link itself. It was impossible to take into axzcount the error; thus the results give the load in eight VWires and not the total load of the nine wires. The test MTas begun on December 20 at a temperature of 59 degrees F. Results. This particular test included the greatest eX‘tremes in temperature. On January 3 the temperature 44 Temperature in Dog.“ I 6% 22“. £88 no same: can 8 a 3 as; .3 332.3% e5. 38 an 93»: uh!— 3 8:9 Io." omega on mm mm m Ma .2.- .. we as 5 :3 0L A oedema-92 .2" low on, .. Hm cm: on. 2-0! X waned at pad: 45 reached a low of 5 degrees F and the total load for that time was 1395 pounds which is an increase of 93 pounds over the initial load and an increase of 342.18 pounds over the lowest measured load on December 21. Figure 20 shows the load versus time and temperature versus time curves for the fourth test. (}eneral Results of Field Tests Two general observations were made in analyzing the ciata from the field testing. First, there was a general roperties of the soil. Generally, the temperature probably contributes to the load decrease in the following manner. The temperature fluctuates, causing the fence to contract and expand. These contractions and expansions produce corresponding load increases and decreases which are the saw-tooth effect of the data shown in Figures 17, 18, and 19. For instance, a temperature drop and corresponding load increase would cause 46 IF Tony-rattan in Degra- . II- . II I. I2: page 5.30m .ooaow;uo flwmtmemm cm a 5 as: .a» casuauqmin. an: 33 9m a: firewall l .38 5 on: Sale on ma mW km S l on e ens-.3939 on. ImII/ ow , 8 . om A. 2. l. 00 : oo 4. ,. 3 5A AVH .na 01 X ‘P‘mOd “I PM u? the fence to contract and be stretched. When the tempera- ture rose again the load in the fence would slacken off but as the recovery curves of the laboratory tests showed, there would be an added permanent elongation in the fence due to. the initial temperature drop and corresponding load increase. The added elongation would in effect reduce the load. Since this process is repeated again and again in the fence, the load would decrease with time. The horizontal movement of the end posts is a major factor in load drop in the fence, as was observed by Giese and Henderson (4), but the amount of horizontal movement is 21 function of temperature variation, initial load, proper- ‘ties of the soil, and fence end construction. High initial Zloads would cause a greater horizontal movement of the end I>ost initially and probably a larger drop in total load over 51 period of time. In other words, it would seem the higher IShe initial load the greater would be the percentage load Ctrop in the fence. Temperature variation would also seem the effect the amount of horizontal movement as the fluctu- Elting loads due to temperature changes would mean a cyclic 13ype of load bearing between the end post and the soil. TQTus there might be a crushing action and breaking down of tdle soil around the base of the end post as the temperature 311d load varies thus permitting the end post to move. In 'tfle tests run, the load drop due to horizontal movement of tune end post could be safely assumed to be less than the 48 values given by Giese and Henderson (4) since the base of the post was set in concrete. Properties of the soil would affect horizontal move- xnent of the end posts but it was not taken into account for 'these tests. _Figures 17, 18, and 19 show the relationship between load and temperature. After the first couple of readings, d during which the load drop is most likely due to movement IIIi of the end posts and possibly a more even distribution of . v— the load throughout the fence, there was a "mirror" rela— tionship between the temperature-time curve and the load- I ‘ “Gigi? 1 I time curve. When the temperature rose, the total load decreased and as the temperature decreased the total load increased. Since the total load at any time is a function of time and temperature, a linear regression curve was run through the data using time x temperature on one coordinate axis and load on the other axis. The linear regression curve was run only on Test No. 3. The equation of the regression curve is y = 2524 - .550xz where y = load, x = time, and z = temperature. A linear curve seems illogical at first since at some high value of time x temperature the load would go to zero but the regression curve is defined only in the interval of the data taken and thus cannot be applied outside this interval. Figure 21 shows the regression curve. 49 3:. 9:5. .022 Mo news-q eom on a n« mega M.msoe no nofiuunsh a no eaoq fiwonswnh asaaqx_!:Bbuoana I83 8.: owe.” 8.2 2% 8% Se pen .3 .1 3 . 2 one . 2 can con l.m~ e 8 . an own _ _ . .3 l 1 new .«n R 3. e n “38.4.3” . 2’01 y spunDJ n1 pIOT 50 A three dimensional relationship (no. 1) of the form = b c _ 9355 . tn y ax 2 was found (y _ x‘3298 2.10404) and a ree dimensional relationship (no. 2) of the form y = a+bx+cz (y = 3677 - 26.438x - 20.4222) was fitted to the data. The standard error of estimation was 4.53 per cent for the linear curve used, while it was 6.34 per cent for the three dimensional relationship (no. 1) and 6.35 per cent for the three dimensional relationship (no. 2). Thus the linear curve fitted the data better. Actually the three variables of load, time, and tem- I ;h_ perature would constitute a regression plane if they were : J plotted on three coordinate axes where load, temperature, and time represent the three axes. 50 A non—linear curve (no. 1) of the form y = axbzC 9355 x.3298 2.10404 (no. 2) of the form y = a + bx + cz (y =3677 - 26. 438 x ) -20. 442 2 was fitted to the data. The standard error of estimation was found (y = ) and a non-linear curve was 4.53 per cent for the linear curve used, while it was 6.34 per cent for the non-linear regression curve (no. 1) and 6.35 per cent for the non-linear regression curve (no. 2), thus the first straight line fitted the data better. Actually the three variables of load, time, and tem- perature do not constitute a regression line but a regres- sion plane. The load (y), temperature (x), and time (2) represent three coordinate axes and thus for any one reading there is a value for each of the three variables. The three variables can be respresnted as a regression line on paper but we are actually looking at a side View of the three coordinate axes system, where the x and z axes coincide. The only method for separating the variables time and temperature would be to run a test holding the temperature constant. The load drop would thus be a time function only. CONCLUSIONS 1. The actual yield load for all brands of wire is lower than the theoretical yield loads and is due to a combined stress condition in the tension curve. The wire did not show a tendency to fail at the tenSion curve in. any of the series of tests. Page 12 2. The efficiency of the tension curves decreases as the load increases and there is no relationship between. wire size and tension curve efficiency. Page 19 3. Reload curves do not coincide with recovery curves which emphasizes even more thetnOn-elastic behavior of tension curves. Page 19 4. Recommended tightening loads use up much of the elastic potential of the tension curves, thus the feasibl- lity of using high stretching loads is questioned. Page 25 5. The smaller wires in a woven wire fence have a higher concentration of stress and thus carry more than their share of the load as compared to the top and bottom wires. Page 26 6. Strain gage, tension link transducers are adaptable to measuring loads in the individual wires. Pages 30-37 7. There is a general downward trend of the load due to temperature variation and movement of the end posts. The two cannot be separated except through controlled experiments. Page 45 RECOMMENDATIONS FOR FURTHER INVESTIGATIONS” 1. Develop a tractor mounted mechanism to erect the fence with a relatively small initial load. 2. Test the feasibility of mechanical driven steel posts (not line posts) as corner posts. 3. Measure the load at various positions along the fence to determine load distribution. IO. 11. 12. l3. l4. BIBLIOGRAPHY Carlson, T. Fence tension loops. Unpublished special problem for A.E. 411, A.E. Dept., M.S.U., 1956. Eckman, D. P. Industrial Instrumentation, 5th ed., Wiley and Sons Inc., New York, 1957. Fr Giese, H. Farm fence handbook, Agr. Ext. Bureau 8 1 Republic Steel Corp., 1938. = Giese, H. and Henderson, S. M. Farm fence end and , a corner design, Research Bull. 364, Ames Iowa, 1949. ‘ _4i Giese, H. and Strong, M. D. The construction of fence E_3 ends and corners, Agr. Eng. 21:131-134, 1949. Henderson, G. E. Planning farm fences, A Handbook, Southern Association of Agricultural Engineers and Vocational Agriculture, 1954. Jennings, B. A. Fence exposure tests, Agr. Eng. 25: 140-141, 1944. Kelly, M. A. R. Farm fence, U.S.D.A., Washington, Bull. 1832, 1940. Lee, L. D. Tension of wire fence under differences in temperature. Unpublished special problem for A.E. 411, A.E. Dept., M. S. U., 1957. Lissner, H. R. and Perry, c. c. The Strain Gage Primer, 1st ed, McGraw-Hill Book Co., New York, 1955. Miller, R. C. Engineering viewpoint on farm fencing, Agr. Eng. 16. 479, 1935. Reynolds, F. J. A demonstration of better fencing, ‘Agr. Eng., 19:121, 1938. Schueler, J. L. Engineering side of producing woven wire fencing, Agr. Eng., 15:391-393, 1934. Sears, F. w. and Zemansky, M. w. University Physics, 5th ed, Addison-Wesley Publishing Co., Inc., Cambridge, Mass. , 1953. 15. Strong, Maxton D. Tests on tension curves, Project 618, Ames Iowa, 1939. 16. Strong Corner, Tight Fence, Wallaces Farmer, 7:24, 1951. 17. Tight fence lasts longer,Ils.Hoards Dairyman, 80:196, 1935. . .ns, 1.“: CH} ”any"? L33. ’4“. , S w. R A R m. L V. n S R E W N U E T A” TIIIIIZ JlHllllfllllU