Rawlins 1999

602 1EEE Transactions on Power Delivery, Vol. 14, NO.2, April 1999 Some Effects of Mill Practice on the Stress Strain Behavior of ACSR Charles B. Rawlins, Fellow, IEEE Alcoa Fujikura Ltd. Brentwood. TN 37027 Abstract: In recen. years, operating temperatures of mill practices was studied, and it was concluded that overhead lines have risen. Tests have indicated that variations in those practices may explain the deviant sags. conventional sag tension calculations may underestimate Two mill effects seem to stand out. One is associated sags that occur at The higher temperatures in ACSR with the presence of tensile stress in the aluminum part of (aluminum cable steel reinforced) spans. Search for the ACSR, as it is placed on the reel. The other arises Erom source of the disparities has identified two effects associated variations in lengths of lay, permitted under ASTM with the manner in which conductors are manufactured. standards [71. One effect involves residual stresses, resulting from stranding practice, in the finished conductor. The other is 11. BUILT-IN STRESS IN ALUMINUM OF ACSR caused by the ability of the aluminum part of ACSR to bear axial compression. Analysis of these effects appears to In looking for the sources of the problem, we focussed explain the cllsparity in at least one of the test programs that on EPRI's high temperature sag runs on Hawk ACSR, in revealed it. their 95.5 m (310 foot) indoor span [5], because those runs showed the largest deviations. In fact, there were clues in Keywords: Sag, tension, conductor, temperature, residual, that data pointing toward the effects we identified. One of stress, compression, modulus, lay. these clues came from strain measurements made as the conductor sample was being prestretched. I. INTRODUCTION The plan of test involved prestretchmg the sample to simulate 10 years of creep at 18% of conductor rated Procedures for calculating sags and tensions in strength. The prestretching routine called for applying a overhead lines employing ACSR were originally described in tension of 45.8 kN (10300 lbf) for 20 minutes. EPRI's span the Alcoa Graphic Method [l]. Although most such supports could not manage thls tension, so the procedure was calculations are now performed by computer, the procedures carried out with the sample strung out on the floor of the lab. used even today are essentially the same. The length of the sample was measured before, during and These procedures incorporate several assumptions and after application of the tension, the before and after approximations wluch were shown to cause little error under measurements being made under 4.45 kN (1000 lbf) load, conditions applicable during most of the era when ACSR has which is about 15.86 MPa (2300 psi) stress for Hawk. The been employed. However, in recent years operating measurements showed that the sample deviated from temperatures for overhead lines have increased, and two test expected behavior, even during the prestretch. In particular, programs, aimed at investigating effects of this increase, the amount of set taken by the sample was about 60% greater have revealed disparities between measured sags and those than expected. predicted by conventional sag tension calculations. The Fig. 1 shows how the expected set is determined. The disparities are associated with high conductor temperatures. figure is based on Alcoa's Stress Strain Chart 1-782, which One program was carried out by Ontario Hydro [2,3], and is applicable to Hawk ACSR. The initial 1-hour aluminum, the other by EPRI [5J . steel and composite curves are shown. Now, after 20 Alcoa Fujikura Ltd. commissioned the investigation minutes at 45.8 kN (10300 lbf) tension, which is 163.1 MPa reported here to identify the sources of these disparites. (23656 psi), the total measured strain was 0.264%, relative Among other possible sources, the influence of cable to the strain at 15.86 MPa (2300 psi). Thus, the final composite curve and the final steel curve should have had PE-325-PWRD-0-12-1997 A paper recommended and approved by the positions shown in the figure. Thus, the permanent set at the IEEE Transmission and Distribution Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Power 15.86 MPa should have be 0.036% as indicated. However, Delivery. Manuscript submitted July 1, 1997; made available for printing the measured set was actually 0.059% [ 5 ] . December 12,1997. The best way to explain this difference is to say that the initial composite curve should have been further to the left. That would occur if the aluminum had been under tension as the sample was taken from the reel, that is, if the cable had 0885-8977/99/$10.00 0 1997 IEEE 603 25000 aluminum portion, and corresponding compression in the steel. Built-in stress is characteristic of two-pass stranding. 20000 It happens that essentially all multilayer ACSR manufactured in the US before WWII was stranded in one .- pass. This was also the period when stress strain curves for % 15000 the standard strandings were established. At that time, a 3 stress-free conductor was considered normal and desirable, 8 VI 10000 and standard stress strain curves were constructed assuming that condition. That assumption became the default industry 5000 standard, and appears to be even to this day. After WWII, and especially after 1950, two-pass 0 1 stranding came increasingly into use because it afforded 0 005 01 015 0.2 025 03 035 some cost savings in manufacture. Even though two-pass Strain - percent ACSR was often visibly not stress-free, stress strain curves were still constructed on the stress-free assumption. This Fig. 1 Analysis of expected prestretch of Hawk ACSR was justified on the basis that calculations showed stringing tensions to be relatively insensitive to built-in stress. come off the strander with built-in stress. In order to However, it is likely that the calculations did not consider investigate this, we shifted the initial aluminum and steel the high operating temperatures that are of current interest. curves in the strain direction such as to simulate built-in Thus it appears that built-in stress has acquired importance stress, and then adjusted these shifts to make the permanent because of a change in line design environment: set come out to the measured value. significantly increased operating temperatures. With these shifts, the built-in aluminum virtual' stress We note in passing that the stringing properties of - the stress when the steel has no tension - turned out to be conductors can also be influenced by built-in stresses [6]. 9.6 MPa (1400 psi). This value is not veIy sensitive to the It is often possible to surmise the amount of built-in exact value of the prestress tension or duration, because the stress from measured stress strain curves, and we have operating point after the prestress is removed is on the steel reviewed a large number of such curves from our files. The final curve. We conclude that the cable used in the test was procedure requires that the so-called "slack aluminum" leg of stranded and put on the reel with built-in aluminum stress of the final stress strain curve be well defined, and that there be at least 9.6 MPa (1400 psi) virtual, or over I 1 MPa (1600 a separate repeated stress strain test of the steel core alone. psi) actual. Some of the original built-in stress may have The procedure entails estimating the initial conductor strain been lost to stress relaxation on the reel, before the sample at which the stress in the steel core is zero. was taken from it. Fig. 2 illustrates how this is done. It shows the Where does this stress come from, and why is it not repeated composite stress strain curve of a sample of Condor reflected in standard stress strain curves such as Fig. l? The ACSR. The slack aluminum leg of the final composite curve stress in the aluminum part of multilayer ACSR is caused by intercepts zero stress at a strain of a little less than 0.001. If bralung tension on the aluminum wires as they are pulled the aluminum is assumed to be free of stress in this leg, the from their spools in the strander to form the cable, plus final stress in the steel is zero at that strain. However, a friction experienced as they move to and through the closing separate test of the steel core alone showed that the core die. When both aluminum and steel strands are stranded at underwent a plastic strain of 0.0005, from initial to final. the same time - "one-pass stranding," - and the spool brakes Thus, the steel was under zero stress initiaf at a little less are properly set, all strands emerge from the last closing &e than 0.0005 strain. Then the initial composite stress was with about the same strain. The conductor then leaves the 40000 1 strander capstan largely stress-free. However, when the core 35000 is stranded in a separate operation, usually in a tubular '$ 30000 strander, and then fed into another machine to apply the - aluminum - "two-pass stranding," the steel comes through with negligible stress at the last closing die, and when the finished conductor leaves the capstan there is tension in the 'Virtual stress in the aluminum (or steel) is the tension in o 0.001 o.ooz 0.003 0.004 0.005 0.006 the aluminum (or steel) component of ACSR divided by total Strain conductor area. Thus, the sum of the aluminum and steel virtual stresses equals the average stress on the total Fig. 2 Repeated stress strain test - Condor ACSR conductor area. 604 entirely on the aluminum at this strain. From Fig. 2, this 111. COMPRESSION MODULUS OF AL- PART stress was about 34 Ml’a (5000 psi). Therefore, the built-in OF ACSR aluminum virtual stress was about 5000 psi. As shown below in Section 111, there can be Conventional sag tension technology considers that the compressive stress on the aluminum in the slack aluminum aluminum portion of ACSR does not sustain siwlcant leg of the final curve, and this can introduce an error in the compressive stress in the slack aluminum leg of the final procedure, because the intercept at 0.001 strain in Fig. 2 stress strain curve. Instead, it is assumed that the aluminum would then not represent a stress-free condition. The error layers expand to larger diameter, becoming loose, in order can be avoided by replacing this slack aluminum leg with the to absorb any excess strand length as the conductor becomes final virtual modulus of the steel core, anchored to the knee shorter. True enough, when they are compressed t h s way, point of the final composite curve. In the case of Fig. 2, this the strands can function as compression springs, and thus yielded built-in virtual aluminum stress of 25 MPa (3600 take on some compressive force and stress. The appropriate psi). spring constants can be calculated, and from them an The built-in stress values obtained, before and after effective compression modulus can be determined. The WWII, reflect the shift from one- to two-pass stranding. Out required expressions are given in Appendix 1. These moduli of thirty-nine tests of multilayer ACSR before the war, where turn out to be much smaller than the tensile modulus: about the data permitted its estimation, only two showed 965 MPa (140,000 psi) versus around 55 GPa (8,000,000 sigruficant built-in stress. Post-war, of W - t w o such tests, psi) for the aluminum part of the 26/7 stranding of ACSR, twenty showed built-in stress. for example, so they seem small enough to neglect. It was possible to analyze stress strain data reported by Nigol and Barrett, at Ontario Hydro, however, found Ontario Hydro in its CEA-funded project in the same larger compression stresses in their stress strain tests [2] manner [ 3 ] . Of eight tests, all showed built-in stress. It was than would be explained by compression of the free strands. also possible to determine the built-in stresses for the other They pointed out that the inner and outer aluminum layers conductors tested by EPRI [ 5 ] , using the procedure of Fig. 1. could interfere with each other as they tried to expand during Four of the six conductors tested demonstrated built-in compression. stress. The others, both 18/1 strandings, were probably We have analyzed the mechanisms involved in this stranded in one pass. The distribution of actual - not virtual - interference, and developed a method for calculating the built-in stresses from these three sources is shown in Fig. 3. increase in effective compression modulus that results from It is evident that there is considerable variation in the it. The required equations are derived in Appendix 2. estimated values, with the mean somewhere between 14 and Interestingly, interference does not occur if the outer two 17 MPa (2000 and 2500 psi). A number of factors may layers conform to ASTM preferred lays, and any other contribute to this variation, some due to mill practices and aluminum layers have lays near the middle of the permitted controls, some to differences in strand sizes or stranding, range. Thus, many ACSR production lots do not experience some to where and when samples were taken, and some interlayer interference, and the effective compression related to accuracy in stress strain testing. Because of the modulus remains small. limited amount of data available, and the large amount that When the outer layer lay deviates on the short side would be required to do it, it seems unlikely that these effects from preferred, and/or the inner layers deviate on the long can feasibly be sorted out and evaluated separately in the side, interference occurs and the compression modulus foreseeable future. becomes more significant. The larger these deviations, the 9 , I larger the compression modulus becomes, and the maximum 8 PRI Report [ 4 ] * * deviations permitted by ASTM [7] can result in large enough C E A R e p o r t [Z] compression moduli to influence sags. For the 26/7 3 6 stranding, if the outer layer has the shortest permitted lay 10 5 and the inner layer has the longest, then the calculated $ 4 increase in the compression modulus is 4.8 GPa (700,000 $ 3 psi), for a total of 5.8 GPa (840,000 psi), or 10% of the 2 aluminum tensile modulus. More sigmficantly, the virtual 1 aluminum compression modulus can be as much as 4.96 GPa 0 (720,000 psi), compared with the virtual steel modulus of 0 1000 2000 3000 4000 5000 about 28 GPa (4,000,000 psi), or about 18% of it. Built-in stress - psi The way this change in modulus comes into play is Fig. 3 Distribution of built-in aluminum stress in multilayer illustrated in Fig. 4. The aluminum curves are idenbfied as ACSR. (*) There were 32 additional cases where built-in 2A for initial and 3A for final. When the compression stress was about zero. (**) There were two additional cases, modulus is negligible, the final curve goes to the abscissa at involving 18/1 strandmg, where stress was about zero. 605 enough defined to permit the estimation. Although there are 25000 several "sports," the correlation is generally good. 20000 IV. EFFECTS OF BUILT-INSTRESS AND 15000 COMPRESSION MODULUS IN EPRI'S TEST OF HAWK v) a ; 10000 Space does not permit a detailed discussion of the P manner in which these effects influence predicted sags. 5000 However, the general effect of built-in stress is to shorten the slack aluminum leg of the final stress strain curve. Now, in 0 any given sag tension problem for ACSR, there is a A temperature below which the aluminum is not slack under '4 -5000 ' 0 0.05 0.1 0.15 0.2 0.25 03 0.35 I final conditions, and above which it is. Shortening the slack aluminum leg raises this transition temperature. Strain - percent Finite aluminum compression modulus has no effect below the transition temperature. Above that temperature, Fig. 4 Effect of Aluminum Compression Modulus on the increased slope of the slack aluminum leg results in stress strain behavior. A = composite final modulus in increased sag. slack aluminum leg. How did these effects influence the results of EPRI's test on Hawk? Fig. 6 shows the results of the EPRI tests. about 0.125% strain, and is assumed to be zero, following After the sample was prestressed to take out the creep, it was the strain axis, for lower strains. Finite compression lifted into the test span and pulled to tension at 24°C. The modulus swings that leg down, where it is labeled temperature was then raised to 45OC, and then increased "Aluminum compression". When this happens, the final again in steps, up to 150°C. Then it was brought down to composite curve is the sum of h s segment and the steel 65OC, and then stepped up to 150°C two more times from final, shown in Fig. 4 by the dotted line A . Thus, when the 65. The uppermost curve is the sag directly measured in the compression modulus of the aluminum is significant, we span, using a transducer, averaged for the three temperature expect that the slack aluminum leg will have a slope greater cycles. than the final steel modulus (3s of Fig. 4), and that does Now, the tension itself was also measured during this indeed occur in measured stress strain test data. procedure, and the second uppermost curve shows the sags This Merence between the steel modulus and the slope that would be calculated from the measured tensions. There of the slack aluminum leg can be used to estimate actual is evidently some disparity here, and since the span in wluch compression modulus from measured stress-strain data. Fig. sag was measured included about 1 m (3 feet) of hardware at 5 shows the correlation between these "measured" values and each end, the sag derived from measured tension seems the the moduli calculated from App. 1 and App. 2 for a number more credible. of data sets, in which the slack aluminum leg was clearly The next-to-lowest curve shows the predicted sags, based on conventional sag tension technology. These 500000 calculations assumed 10 years of creep at 18% tension. The I difference between this curve and the curves based on 9 680000 measurement represents the disparity between measurement 3 400000 4 - s cl 0 + Stranding and prediction referred to in the Introduction. Fig. 6 shows the impact of several things upon .3 300000 predicted sags. To begin with, the lowest curve assumes that S. + x E 0 26/7 the conductor was brought to tension at the tension actually U O O A 3017 measured at 45' C, since that is where EPRI's tabulated data 3 200000 + Q on tension started. > 8 0 -0 + O O 0 4517 The third curve up shows the change in predicted sags, ! 100000 we0 0 5417 relative to the lowest curve, caused by taking the 9.6 MPa 9 Bo +54/19 (1400 psi) virtual built-in aluminum stress into account. A A This is clearly a significant change. 0 It was not possible to calculate the predicted 0 100000 200000 300000 400000 compression modulus of the aluminum, because the lengths Calculated Virtual Compression Modulus psi of lay in EPRI's test samples were not measured. However, Fig. 5 Correlation of measured and calculated aluminum we surmised a value for this modulus, based upon the virtual compression modulus - Multilayer ACSR difference in slopes between the calculated and measured 606 ni = number of strands in ith layer 8 P = total tension or compression load in aluminum part of ACSR I R = radius of strand helix (radius from conductor to strand axis) 6 T = tension (or compression) force in one strand of ith * layer, along the strand axis. c 35 Y = interlayer pressure per unit length of strand 0 v) a = lay angle of strand helix at strand axis 4 Aa = radial expansion of aluminum portion as a unit E = conductor axial strain 3 E , = conductor strain during unloading after aluminum 2 goes slack 20 40 60 KO 100 120 140 160 e = T/2-a Temperature -T G = polar moment of inertia of strand area K = curvature of strand due to helicity = sin2a/R - - 0 - . Measured in test span +Based on measured tension in test span X = lay length +Calculated with SAGT U = Poissonratio +Corrected to acbil initial 4593 tension +Corrected for above and 1400 psi built-in stress -Corrected for above and aluminum compression modulus +Corrected for above and effect of temperature on elastic moduli Fig. 6 Predicted and measured sags in EPRI 3 10 foot span of Hawk ACSR Fig. 7 Definition of helix dimensions curves, the bottom two and top two, respectively, visible in Fig. 6. Increased compression modulus increases this slope, VI. REFERENCES and we found that we could eliminate the difference in slopes by assuming that the outer layer was at ASTM preferred, and A. C. S. R. Graphic Method for Sag-Tension the inner layer was at the maximum permitted lay. That led Calculations, Aluminum Co. of America, Pittsburgh, to the middle curve, identified by the black squares. PA, 1927. Finally, and this is not a mill effect, we followed a 0. Nigol and J. S. Barrett, "Characteristics of ACSR suggestion of Seppa [S] and took into account the effect of Conductors at High Temperatures and Stresses," IEEE temperature on the elastic moduli of aluminum and steel. Trans. on Power Apparatus and Systems, Vol. PAS- That led to the thud highest curve, identified by circles. 100, No. 2, February 1981, pp 485-492. This last curve agrees rather well with the sags based 0. Nigol and J. S. Barrett, "Development of an upon the measured tensions. In fact, the agreement may be Accurate Model of ACSR Conductors for Calculating better than indicated, since the measured temperatures were Sags at High Temperatures," Ontario Hydro Research of the outer layer strands; the average temperature over the Division, CEA Contract No. 78-93, Part 111, March conductor cross section would have been higher (91. On 1982. that basis, we feel that the effects of built-in stresses and Ibid, Part I, March 1980. finite aluminum compression modulus largely account for Dale Crane, "Conductor Sag and Tension the disparity turned up by the EPRI test. Our conclusion is Measurements at High Temperatures," TLMRC, EPRl, that provision for taking these mill effects into account in RP1717-51fl85, May 1993. sag tension calculations is appropriate. E. Brandt, "Ermittlung des Verlegeverhaltens von Freileitungseilen," Energiewirtschaftliche Tagesfragen, V. NOMENCLATURE 23, (1/2): 10-19, 1973. ASTM Standard B232, Standards on Metallic A, = total aluminum area Electrical Conductors, American Society for Testing 'Ai= area of strand in ith layer and Materials, Philadelphia, 1992. d = strand diameter Tapani Seppa, 1996, Personal communication. D = outside diameter of strand layer D. A. Douglas, "Radial and Axial Temperature E = Young's modulus Gradients in Bare Stranded Conductor," IEEE Trans., G = shear modulus Vol. PWRD-1, NO. 2, April 1986, pp 1-15. I = area moment of inertia of strand [ 101 A. E. H. Love, A Treatise on the Mathematical Theory I = length of wire in one lay length of Elasticity, New York: Dover, 1944, $271, Eq. (42). 607 VII. BIOGRAPHY F - 36 sin 6 _--. Charles B. Rawlins (M'61 SM'79 F'81) was born in Sh n2d2 64 Annapolis, Md. on July 4, 1928. He graduated from Johns Hopkins University, Baltimore, Md. with B. E. degree, and received his M. S . from Clarkson College of Technology in 1965. He joined Alcoa Laboratories in 1949, and specialized - 9nd'EsinO . - - 16 n2 (;I: + sin20 ) in overhead conductor dynamics throughout his career. He conducted research in aeolian vibration, galloping and wake- The spring constant per unit area of strand, that is, its induced oscillation of overhead conductors, fatigue and apparent Young's Modulus, is, aerodynamic characteristics of conductors, and other related areas. He is the author of a number of papers and articles, and co-author of the EPRI Transmission Line Reference E e f f= - 4 .- F r d 2 Sh 9. - 4 (- cos26 + sin20) . l+u n2 E sine Book, Wind-Induced Conductor Motions. He holds nine patents. Recall that 8 =7r/2-a, where cy is the angle Mr. Rawlins is a member and past between the helix axis and the strand axis. The factor, chairman of the Working Group on Conductor Dynamics of the Subcommittee on Towers, Poles and Conductors. He is a member of CIGRE is nearly constant for practical values of a. Taking Y = 1/3, and is U.S. Member of Working Group 22-11, "Mechanical Behavior of Conductors and Fittings." He is a a [ 5" I 10" I 1.5" member of ASME and Sigma Xi. Factor 1 2.237 1 2.199 1 2.137 APPENDIX 1 Thus, to a good approximation, COMPRESSION MODULUS OF FREE STRAND LAYER (Al.l) When the aluminum layers of an ACSR go slack, following a tension loading that leaves permanent set in There is actually some additional compliance of the them, they are able to sustain some compressive load because strand that results from the compressive stress on it. It can they act as helical compression springs. The stiffness, or be shown that when this compliance is taken into account, spring constant for a helical strand can be calculated from the effective modulus then becomes, Love [lo]. Love's equations actually give the axial force, F , 1 and torque, K , that result from axial deflection 6h and Eeff = 1 (A1.2) torsional deflection 6x. Since we are not interested in the change in torque, and are assuming that the conductor does not twist, we need only the part that gives, 1 I l 7 U -- n2 1 (A1.3) N 1 1 1 + F = -(G9. cos20 E1 . sin26)Sh 1R2 -+EGG E+& For a 6 strand layer with a = 15", this changes E,ff from where 1 is the length of wire in the spring, GO is the 611,111 psi to 572,304 psi, a reduction of 6.35%. The torsional rigidity of the strand or wire, E1 is its flexural effect diminishes as the number of strands increases. For 12 rigidity and 6 is 7 ~ / 2- a. For round wire, strands, with a = 15", the reduction is 1.7%. APPENDIX 2 INTERFEWNCE MODULUS OF ALUMINUM LAYERS Thus, Consider an ACSR that has been subjected to some rr d4 -+ sin28 . E . - initial loading, following which the load is reduced. The - 1R2 l + u ) 64 unloading will follow the final stress-strain curve, and at some point the tension in the aluminum portion will go to Now, per unit length of conductor, 1 = l/sin8. zero. Since the aluminum will have experienced some Furthermore, in a well packed strand layer, R = nd/6. plastic deformation, while the steel will have experienced Thus, the spring constant for a strand becomes, 608 little if any, the steel will still be under tension when the Lay length X will change, however, because of E,, and the aluminum "goes slack." rate at which R varies with X is, As the conductor tension is reduced further, the aluminum 1 layers will tend to expand away from the core and become 2n.tan a loose. The rates at which the indwidual aluminum layers expand will usually be different, due to differences in the But the conductor strain is E , = , so dX = E,, and layer diameters and the lay angles of the strands. A shallow the radial expansion of the layer is, lay angle or large lay ratio will cause more rapid radial expansion than a large lay angle or short lay ratio. Because of this, there are conditions where an inner layer will expand radially more rapidly than the layer above it, and there will Note that E , is negative, so A R is positive. Now, if the be interference between them. When that happens, the outside diameter of the layer is D and strand diameter is d , layers must press against and strain against each other, and then one effect of this is a net compressive stress developing in the pair of layers taken as a unit. If there are more than two a,(D-d) aluminum layers, then three or more layers may lock tan Q = 7 together in thw manner, dependmg upon their relative rates of radial expansion following unloading of the conductor But in a well-packed strand layer, D - d = "d 3 , so past the "slack aluminum" point. The effect of this net compressive stress is to extend the A R = -n.d. 6. tanz a final stress-strain curve for the aluminum into the negative stress range, rather than simply having it stop at zero stress If we identify the individual layers by the subscript, as is generally assumed. In that range, the effective i = 1 , 2 , 3 ,..., then aluminum modulus is different from that in the positive stress range, being determined by the degree to which the various layers interfere with each others' expansion. We can calculate t h s negative-stress leg of the final aluminum curve These A& are generally different, even though all layers by analyzing that interference. experience the same conductor strain, E , . The next step in We will focus on what happens as conductor elongation our analysis is to force all interfering layers to share the is reduced, below the point where the aluminum goes slack same radial deflection, A,. This will require adational (the intersection of curves 3As and 3s in Fig. 4.). Assume deflections, 6R, , such that, that all aluminum layers go slack simultaneously, although this is probably only approximately true. We will begin the analysis by determining how rapidly each layer would expand radially, during ~s further reduction in elongation, for all interfering layers. In reality, these additional in the absence of interference. Then we will determine how deflections take place simultaneously with the A& , but it is much each layer must be deflected radially from its free convenient for us to treat them as though they took place expansion position in order to eliminate the interference, and sequentially. Thus, we have treated the A& as though they yet leave the locked-together set of interfering layers in took place without change in strand tension, letting that mechanical equilibrium. These individual deflections will remain zero. The layers expanded without restraining each require strains in the strands of the layers in question, and other. Now we will treat the S R , as occurring in the absence those strains will determine the layer tensions. The sum of of additional conductor strain, as we force the layers to the these tensions is the tension in the aluminum, and that may position where they are in contact, but do not interpenetrate. be used to calculate an overall average aluminum stress. The If the conductor elongation is indeed held constant during ratio of this stress to the conductor strain that provoked the h s second step, then so is lay length, A, so the rate of interference between layers is the aluminum modulus in the change of helix radius with respect to wire length is, negative stress range. - aR =1.A= _1 . - 1 - - 1 Let the decreasing conductor strain that follows the point where the aluminum goes slack be E , Now the length of ai 2n 2.- 2a &$ - 2n.sin a strand in one lay length is, Thus, S R = L . & 2n.sma 1 1=JX2+4r2.R2, SO R=F Jzzl;;z But, sin a = 7 P(D-d) 1 = F ( D - d ) . Also, D - d = SO, , If there is no interference between layers when E,, occurs, the strand will experience negligible stress, so 1 will be constant. W.3) 609 This gives the radial deflection of the layer as a function of Equation (A2.1) may be substituted into (A2.2), to the longitudinal strain of the wire of the strands, dZ/l. We eliminate the AR, thus: will take the source of d l / l to be a change in strand tension, Ti,and this tension arises because the interfering layers (A2.7) press against each other. E the area of a strand in the ith layer is Ai, then providing as many equations as there are interfering layers. These equations, with (A2.6) form a set of simultaneous so that equations that maybe solved for A, and the SR, as unknowns. The tension required to cause deflection 6% is thus, For compactness, define (A2.4) %e. sin3ai . tan ai = Ci = 44 47% . sin3ai . tanai (A2.8) Now, strand tension ordinarily results in a binding and pressure from the layer in question upon the layer below. In the present case, however, the inner layer(s) of the interfering group of layers will be in compression, so they Then these equations can be written in matrix form. For will exert a pressure outward to meet the inward pressures illustration we will assume three interfering layers. Thus, from above. Within the group of layers that is expanding as o o -11 1 {5 ) a unit, the radial forces from the various layers must be in r i equilibrium; they must add up to zero, since the group is out of contact with layers below and above. We need to relate 0 0 01 01 -1 -1 . *a = E,' { $} (A2.10) these interlayer forces to the strand tensions, Ti. Let the radial force acting between the layers be Y per unit strand length for each strand in the layer. Now it can be T h s may be written even more compactly as, shown that Y = K . T , where T is the tension (or compression) in the strand along its axis, and K is the C.s=E,.B (A2.11) curvature of the strand. For a helix, K = sin2a/R. The total inward radial force from a layer, per unit length along where C is the square matrix, B is the column vector, { B1 the c o n p c f o r is thus, BZ E$ O}T, and 6 is the column vector, {SRI 6R2 6R3 A,) ' Then, S = E,. C-' . B (A2.12) where C-' is the matrix inverse of C. Now, from (A2.4), the tension per strand in the ith layer is, The cos cy in the denominator occurs because we are now working per unit length of conductor, instead of strand. These interlayer radial forces must add up to zero, so 6. . Ti = 0 i Substituing (A2.4) into (A2.5), 6. % ' . =O i The component of Ti in the direction of the conductor axis is Ti. cos ai , so the contribution of that layer to conductor tension is, niTi . cos ai = niHi . cos ai . SR, This gives one equation relating the SR, as unknowns. All other parameters in (A2.6) are defined by the conductor Thus, the total tension in the group of interfering layers is, structure. The equation imposes balance of radial forces within the interfering group of layers. P= i niHi . cos ai . 6 R , (A2.15) 610 Define the row vector, F = {nlHlcos a1 ~2H2cosa 2 n3H3cos cy3 ... 0) Then P is given by a quadratic form: P = E , . F . C-l . B (A2.16) Let the total aluminum area be A. Then the effective aluminum modulus in the negative stress region is, Note that E, is defined on the aluminum area, rather than the total conductor area, so it must be multiplied by Ha before being used in sag-tension calculations. In this analysis, we have neglected the effects of the changes in bending moment and torque that occur as a strand deflects. These effects are generally small, but may be provided for by multiplying the Ciof (A2.8)by the factor, Cautions This analysis assumes that the magnitude of A, is small compared to the layer radii. In addition, it is assumed that the the expansion of the aluminum does not become localized, forming a birdcage. Rather, the looseness of the aluminum is taken to be d o r m along the conductor. There is evidence from Nigol et a1 that, at least at high conductor temperatures, the buckling of the aluminum may concentrate into localized birdcages. In that case, the effective value of E, is reduced. Finally, it is assumed that the normal compliance at interlayer contacts is negligible. 61 1 Discussion J. Stephen Barrett (Ontario Hydro, Toronto, Canada): The paper presents built-in stress as a new explanation for excess high-temperature sags of ACSR. As the result of an incorrect D. Douglass and J. B. Roche: assumption in the analysis and the ignoring of experimental As existing transmission lines are operated at increasingly high temperatures, results that refute that assumption, the importance of built-in the correct calculation of sag at high temperature becomes more important. This is particularly true on older lines which may be required to carry electrical loads stress has been overestimated at the expense of an existing approaching their thermal limit under ‘emergency” loadings. Maintenanceof the explanation, namely, compressive stress in the aluminum public safety is directly dependent on our ability to calculate high temperature wires. sags. Mr. Rawlin’s paper seems to concludedthat our ability to do this is in doubt. In Appendix 2, the explanation of compressive stresses above the birdcaging temperature reads as though it is being We have several questions on this important topic: given for the first time. The essentials of the explanation were 1. Is Mr. Rawlins able to site additional experimental evidence for his given in 1981 [l], including reference to an equation theories of residual compressive stress in aluminum due to ”two pass‘ stranding practices and compressive stress due to certain lay length describing the dependence of radial displacement on lay angle combinations other than the tests in the 300 fl indoor span? and change of axial strain (equivalent to the author’s A2.1). 2. Why does Mr. Rawlins suspect that the aluminum final curve changes At the 1997 IEEE Winter Meeting, as a guest of the Working slope exactly at the point where the virtual aluminum stress is zero? Group “Thermal Aspects of Overhead Conductor”, I made a Could this slope change not occur for negative or positivealuminum stress? presentation entitled “Deviant Behaviour of Conductors”. A prominent part of the presentation was the description of “A 3. It seems to the discussors that flaws and certain experimentalerrors in the experimental procedures used in both the 300 ft span testing and in Detailed Mechanical Model of Helically-Stranded the derivation of the Alma Stress-strain Chart 1-782 may explain the Conductor”, developed in 1989, in which each layer of a observed differences in calculated and experimental data. conductor is described by a matrix involving the stretch, bend a) On what is the stress-strain curve based? Variations between stress-strain tests on the same run of conductor are not and twist of individual wires. Among the predictions of the insignificant. Is this curve based on a single test? .on the average model are: compressive stresses leading to excess high- of a series? b) We believe that compressiveend fittings were used in the 300 fl temperature sag; different stresses in each layer; and, for EPRl tests In this relatively short span, could not relative length tension strung conductors, high stress in the penultimate layer changes in aluminum and steel produced the same sorts of variation noted in the paper? Would this not be a much simpler and anomalous high-temperature behaviour. The boundary explanation than ”built-in aluminum stress from two-pass conditions for the particular type of birdcaging of interest stranding” 4. Finally, it seems to the discussors that the variations noted in this paper were stated to be that the two a l u ” layers move together, yield higher sags than those calculated for high steel content ACSR (26/7, and that their radial forces balance. At the presentation of my 300,30/19,etc.) but less that the sags calculated by the assumptionthat detailed model, I stated that it mostly confirmed the the effective thermal elongation coefficient is independentof conductor temperature. By our own calculations it appears that this sag error could assumptions of sag-tension program STESS [2], based on the be as much as 10% for a 1000 ft span at 100°C (see figure). Since the original proposal of Olaf Nigol: namely that, as the author’s hypotheses do not seem readily convertible to a practical calculation method (how could you know the manufacturingdetails for the temperature rises, the net aluminum stress passes through zero conductor in a 50 year old line?), is there any alternative to using the and becomes compressive, while the sag increases at the same effective thermal elongation coefficient at all temperatures? same rate as before. When the “birdcaging temperature” is reached, the compressive stress reaches its limiting value, the aluminum wires begin to move radially outwards (birdcage), Increase In Final Sag with Temperaturefor Mallard ACSR in 1161 ft Ruling Span and the sag-temperature graph changes slope. In my presentation, I stated that the only discrepancy was that the detailed model predicts that the compressive stress continues Assumingthat the CTE does not to increase above the birdcaging temperature, but at a much *r, - lesser rate. Overheads of the talk were mailed to members of .3= Error 37 -~ the Working Group by the chairman. Some people have a strong intuitive feeling that, as the -- 5 35 aluminum stress changes from tensile to compressive, the H 33 elastic modulus ought to change as well. This is not the case. I -- Assuming that the CTE changes with condudor temperature as modeled 31 -~ by SAG10 program using Chart 1- In a two-aluminum-layer ACSR with unfavourable lay 75? lengths, the net aluminum stress is compressive below the birdcaging temperature. The inner layer is in compression 25 27-20? 30 80 130 180 while the outer layer is in tension. At the same time, the outer layer presses radially inwards harder than the inner layer presses outwards. As a result, the inner layer is pressed - Conductor Temperature deg F against the steel core and no birdcaging takes place. Therefore, as the net aluminum stress changes from tensile to Manuscript received June 10, 1998. compressive, there is no change of elastic modulus, just as 612 there is no change of elastic modulus when a coil spring goes Traditional from tension to compression. As the temperature increases towards the birdcaging temperature, the tension on the outer layer drops, as does its inward radial force. The axial Aluminu compression on the inner layer increases, as does its outward radial force. At and above the birdcaging temperature, the radial forces balance. As the temperature continues to rise, .___ the aluminum wires move radially outwards. This new degree of freedom results in a different elastic modulus for the Strain aluminum. There are therefore two compressive moduli: one below the birdcaging temperature, equal to the tensile modulus; and one above the birdcaging temperature, which 1 would propose calling the “birdcaging modulus” (rather than “the compressive modulus” as in the paper). The aluminum stress phenomena that occur with rising temperature near the “shoulder” of the sag-temperature graph (Fig. 6 of the paper) are very similar to those that occur with decreasing tension near the “knee” of a stress-strain curve (Fig. 2 of the paper). Specifically, the aluminum wires can be in net compression above the knee of the stress-strain curve, as in Fig. 9 of [11. Strain The inner aluminum layer has a smaller lay angle than the outer layer. My detailed model shows that this results in a higher elastic modulus and higher stress on the inner layer Barrett / under most conditions. This, in turn, results in larger permanent elongation of the inner layer during prestress or creep. The inner layer therefore normally “goes slack” before the outer layer upon approaching birdcaging situations. The paper makes the incorrect initial assumption that “all aluminum layers go slack simultaneously” at the birdcaging temperature and at the “knee” of stress-strain curves. As a result of this incorrect assumption and the ignoring of permanent elongation in the paper’s analysis, compressive stresses below the birdcaging temperature and above the Rawlins “knee” of stress-strain curves are erroneously eliminated. The incorrect initial assumption of zero stress at the knee leads to the false conclusion that the final steel curve must be “anchored to the knee of the composite curve”. This conclusion is used as the basis of an incorrect procedure for deriving the “built-in” stresses of Fig. 3, which are then used to explain the excess sags that would have been explained by the compressive stresses that were erroneously eliminated. The new issue presented in the paper is the significance of Fig. 1: Various Models of Aluminum Stress. built-in stresses. Experimentally, this boils down to a question of where the final steel stress-strain curve ought to be positioned with respect to the composite stress-strain curve. The analysis of the EPRI tests on Hawk conductor is References [2-41 of the paper describe several stress- strain biased towards emphasizing built-in stresses. The increase of tests where the aluminum wires were cut after the tests were “set” in Fig. 1 is attributed to the extra permanent elongation completed, thus relieving the tension on the steel cores and caused by higher tensile aluminum stress. The extra “set” allowing them to shorten to their unstressed lengths. This after prestress has previously been attributed to compressive provides an indication of where the final steel curve ought to stress. If the aluminum wires are cut, this extra “set” vanishes be placed. In several cases, the shortening of the conductor [2-41. The analysis of the stress-strain curve of Fig. 2 is upon cutting the aluminum wires is dramatically large, making similarly biased. By using the incorrect procedure of it obvious that the final steel curve cannot possibly be “anchoring the final steel curve to the knee of the composite “anchored to the knee of the composite curve”. Both theory curve”, it is likely that built-in stress has been overestimated at and the weight of experimental evidence are against the the expense of compressive stress. Figure 6 shows that the paper’s method of determining built-in stresses. bulk of the excess sag has accumulated below the birdcaging 613 temperature. All of this portion has been attributed to built-in Mr Rawlins cites this important source of error and stress as a result of the incorrect initial assumption. inconsistency as well as the range of lay factors that are As things stand, there is very little evidence of built-in acceptable and the selection of which will certainly have an stresses. One possible way to obtain direct evidence of built- effect on many performance specifics. in stress is to apply bolted clamps to new conductor samples These are but two of a number of adjustments or changes upon removing them from the reel [l]. After laying the that result in every batch of ACSR being slightly different from another and the reason that experienced line engineers conductor out straight, both ends can be cut flush and the ensure that line elements, such as quad bundles, are clamps removed. The built-in stress can then be computed constructed of four strandings all from the same batch. from the amount that the steel core protrudes beyond the aluminum. For a 100 m sample of Hawk conductor, the 11 Our first search into the unpredictable performance of ACSR MPa (1600 psi) of built-in stress suggested in the paper would came with trying to understand the data that were the basis produce over 50 mm of steel protrusion. for the CIGRE Predictor equations for estimating future Fig. 1 illustrates the various models of aluminum stress creep of a suspended ACSR. The predictor equations that have been proposed. The traditional model has neither contained coefficients associated with the several compressive stress nor built-in stress. The Nigol model has parameters that influenced creep and we expected to see compressive stress that reaches a fixed limiting value. The these coefficients varying in some sort of progression as the Barrett model confirms the existence of compressive stresses strandings changed in steel content or layers of aluminum. The coefficients jumped back and forth in an unseemly above the knee, depending on lay lengths, and predicts that manner and comprehension came only after realization that the compressive stress continues to increase in magnitude the data came from creep studies done in a number of below the knee, but at a low rate. The Rawlins model countries, each study making use of standard strandings but eliminates the important compressive stress above the knee with different variations in strand tensions and lay factors and replaces it with a large built-in tensile stress. For the and so forth. same conductor tension, the extra aluminum stress produces more permanent elongation than the other models. The author‘s mathematical analysis is contained in two appendices and appears to be very precise as it includes secondary effects usually omitted in more casual REFERENCES approaches to the subject. Considerations of Poisson’s ratio indicate a very great precision but we question whether this Nigol and J.S. Barrett, “Characteristics of ACSR level of precision is justified in view of the fact that the size Conductors at High Temperatures and Stresses”, IEEE or diameter of the individual wires can vary throughout the Transactions on Power Apparatus and Systems, Vol. makeup of the total stranding. Fabricators draw the PAS-100, No. 2, February 1981, pp 485-493. aluminum wires through dies that start out slightly undersize Barrett, S.Dutta and 0. Nigol, “A New Computer Model and continue until wear increases the diameter to a larger of ACSR Conductors”, IEEE Transactions on Power than nominal limit that would also see too much metal being Apparatus and Systems, Vol. PAS-102, No. 3, March put into the conductor. We suggest that the variations in 1983, pp 614-621. strand diameter, which could conceivably all balance out but which could also at times work against best interests, will Manuscript received February 12, 1998. approach and maybe swamp the Poisson effect on diameters. A stress of 9.6MPa (14OOpsi) would induce a change of transverse strain of about 0.004% while the permitted range of die diameters could approach or exceed H. BRIAN WHITE, Consultant 21.O% Hudson, Quebec, Canada : One major influence on high temperature performance This is an interesting and useful contribution to the quickly appears to have been overlooked by the author and that is growing assemblage of papers that relate to the potential the influence of the temperature at which the conductor was problems of operating ACSRs at higher than normal stranded. ACSR can be put together at plants where the temperatures. The author focuses on mill practices that he winter shop temperatures can be at 2OoC or lower while at believes contribute to higher than expected sags or at least other locations, summer shop temperatures possibly to uncertainty as to what is happening. approach 40OC. Marrying aluminum and steel at these two temperatures, or at somewhere in between, will result in This concentration on mill practices reminds us of our own conductors with significantly different properties as related few years spent as a conductor designer or specialist and to creep and specially high temperature performance where we remember well the setting up in the plant for a new run the positioning of the knee is so dependent on the initial of ACSR, a setting up process needed every time the sharing of the load between the aluminum and the steel. strander was switched from one stranding to another. The foreman had his 2” x 4” with which he struck the strands as Our objective with these comments is not to introduce more they left the spool, tuning the brakes and thus the tensions complications into an already complex subject but to to suit his feel, without benefit of a tuning fork. possibly moderate several of the current studies that appear 614 to be going beyond the accuracy permitted by factors of Built-in Stress in Aluminum which we have little corltrol or knowledge. We may know the temperature at which the line was first sagged, or failing that, we can make a precise survey of It is possible that an ACSR conductor will have existing sags and insulator offsets to try to rationalize what some built-in stresses. The author believes that the will happen in the future. However failure t o know the two-pass stranding is the cause of these built-in temperature at which the conductor was made will in itself confound attempts to be precise about future performance at stresses. While we agree that the manufacturing high temperatures as will lack of knowledge about all past process will have some influence on the stress strain experiences of load, time and temperature,(creep history), behavior of ACSR, we do not know whether we as well as the mill problems that the author discusses. have sufficient data to confirm that the two-pass We see two approaches to this overall problem and the first stranding is the only cause of these built-in stresses. that comes to mind is to try to better define the scope or For example, different temperatures in steel and scale of these never to be known inputs and influences on sags and thus permit the setting of necessary but sufficient aluminum at the time of manufacturing can also buffers. create built-in stresses in an ACSR conductor. To verify whether there is any built-in tensile stress in The second step is based on the realization that the major an ACSR conductor, we can install two tight clamps influence on not knowing where the conductor is during high temperature operation is lack of precise knowledge of the on a piece of long conductor, then cut the weather conditions out and along the line and thus the need conductor into a short conductor sample with two for devices that can monitor the conductor position, at least clamps at both ends. If we release the clamp at one at the most sensitive or critical spans. end, naturally, you will see the steel core comes out This paper is an excellent exposure of two of the significant if there were tension stresses in the aluminum inputs to the problem and while we must relegate to others strands. However, people have seen both cases in an appraisal of the mathematical support material, it is apparent that the overall subject has now been exposed to which the steel core either come out or retract in, examination under a new light. and certainly, the two-pass stranding method will not explain why the steel core retracts in. Manuscript received February 13, 1998. The paper concluded that the referenced Hawk conductor had a 1400 psi tension stress in it. To determine built-in stresses, one really needs to study L. Shan (EPRI, 100 Research Dr., Haslet, TX 76052): the stress strain curves of the conductor under The paper presents the author’s view on the stress investigation. It is known that for the same type of strain behavior of ACSR operated at high conductor the stress strain curves obtained from temperatures. Many good points have been made various tests will vary. Sometimes, the difference throughout this paper. Specifically, from a conductor to another can be quite large. The stress strain curves used by the traditional sag 1. there can be compressive stress on the tension methods are actually the averages curves aluminum in the slack leg of the stress strain combined from many stress strain tests. The stress curves. strain test was not performed for the Hawk 2. the compression modulus of aluminum part of conductor used in the EPRI test. Since we do not ACSR is not zero. have the stress strain curves for the Hawk test 3. there may be some built-in stresses in ACSR conductor, we really can not tell how much the conductor built-in tensile stress in aluminum strands was. 4. it is appropriate to take some of the above Additionally, the compressive stress on the effects into account in sag tension calculation aluminum in the slack leg of the stress strain curves also changes the permanent set which was used by The behavior of ACSR at high temperature is the author to estimate the magnitude of built-in complicated, and there are many issues that need to stress. Aluminum Association specifies a smaller of be further explored and explained before sound 8% RTS or 1000 lb tension to take out the initial conclusions can be made with regard to effects of slack in the conductor before a test. It has been mill practice on the stress strain behavior of ACSR. observed that oftentimes 8% RTS or 1000 lb initial 615 tension may still leave some initial slack in the Associated Hardware Impacts During High conductor before the test data is recorded. This also Temperature Operations - Issues and Problems,” changes the permanent set. Final Report, EPRI TR-109044, Electric Power Research Institute, Palo Alto, California, Compression in Aluminum December 1997. Manuscript received February 18, 1998. The author made an attempt to estimate the compression modulus of aluminum part of ACSR. However, the net effect of the compression modulus Yakov Motlis (Ontario Hydro, Toronto, Canada): The author in aluminum appears small as shown in Fig. 6 . To should be commended for recognizing in this paper the our knowledge, it is also possible the friction existence of compressive stress in aluminum layers of ACSR between strands will have some influence on the conductors at high operating temperatures that wasignored by some people in the industry since publication [l] 17 years ago. compression modulus of aluminum strands. It will Fig. 1 contains a label stating, “Chart 1-782 with no built- be interesting to know the actual compression in aluminum stress”. Curve fits to this chart, used in the modulus value used in Fig.6. In general, we believe ALCOA sag-tension program, however, indicate that the compression in aluminum plays an important the virtual aluminum stress at the origin is -6.1 MPa (-883 psi), corresponding to an actual stress of -7.1 MPa (-1 027 psi). part in changing the behavior of ACSR conductors This is not negligible in comparison to the 11 MPa “built-in” operated at high temperature. STESS (a program by stress proposed in the paper. The shift of the composite curve CEA and Ontario Hydro) uses an empirical towards the right can be seen in Fig. 1 of the paper. The compression limit (typically, 10 mpa) approach to aluminum curve intersects the strain axis at 0.015% and the include the effect of compression in aluminum to steel curve intersects at 0.0006%. The difference of 0.0144% is “slack”, where approximately one third may be attributed to improve high temperature sag calculation. the thermal effect of testing at 75°F and the remainder is probably the result of sample preparation, and ought to have High TemDerature Effects been removed ffom the design curves. The conductor described by Chart 1-782 would have to be cooled from the test temperature of 24°C (75°F) to 11°C (52.5”F) in order to Traditionally, stress strain and creep tests were produce a stress-fiee state. The result of this aluminum conducted at room temperature. Selected stress “slack” is to underestimate the expected permanent set caused strain tests may need to be conducted at high by prestressing. temperature to reveal some of the problems related Regarding the actual testing of the “Hawk” conductor [2], the paper does not mention clearly that the conductor sample to the ACSR sag prediction at elevated was cut and crimped at 24°C (75°F) and prestressed for 20 temperatures. minutes at 32” (89°F). Judging by the location of the composite curve in Fig. 1, the temperature appears to be close Concluding Remarks to the chart-test temperature (coincidentally also 24°C (75”F), rather than the actual prestress temperature. The remainder of our analysis is based on sag-tension The author made a sincere effort to explore issues program STESS [3] using curves the same as ALCOA Chart related to the stress strain behavior of ACSR. 1-782, except that the slack in the design curve is zero at room However, at the end of the presentation, the author temperature. In STESS, built-in tensile aluminum stresses can indicated that he will use several approaches be modeled by specifying a negative value of slack in the outlined in the paper to modi@ the sag-tension loading file. Based on the information provided in [2] for a 94.488 m computer programs for use by practitioners. Based (3 10 fi.) test span, our analysis of the sag-temperature test on on the information provided by several discussers ‘&Hawk”conductor was performed using Version 3 of sag- during the paper session and this discussion, our tension program STESS, which employs temperature- opinion is that it is inappropriate to make these dependent elastic moduli. The chronological conductor loading history given in the paper was modeled by the changes in the current sag-tension programs at this following load file: time because the author does not have the necessary pieces of experimental data to support such scow -1 1 MPa (-1600 psi) changes. SLACK -0.000045 strain units TEMP 23.888”C (75°F) References TEN 4.448 kN (1000 Ib) [cut & crimp] (11 L. Shan and D. Douglas, “Conductor and TEMP 3 1.667”C (89°F) 616 TEN 45.8 kN (10,300 lb), 20 min. [prestress] Although built-in stresses would escape from short test TEMP 23.888’C (75‘F) samples unless special precautions were taken, most of the SAG 0.79 m (2.6 ft.) [sag in] stress would remain in conductors in the field, because of the TRUN 20°C to 150°C in steps of 5C” cumulative fiction of the large lengths involved. Ifbuilt-in stress had the importance given to it in the paper, this would The compressive stress of -1 1 MPa (-1600 psi) is of the mean that the stress-strain infomation provided by conductor same magnitude as the built-in tensile stress assumed in the manufacturers would significantly underestimate the post-war paper. The aluminum slack of -0.000045 strain units with aluminum stresses. An expected consequence of using this respect to the steel cwve at 20°C (68°F) is based on the supposedly incorrect information might be an increase o f assumption that the conductor was in a neutral stress state at fatigue failures after 1950, due to aeolian vibration. The above the cut 62 Crimp temperature of 23.89”C (75°F). mentioned three runs of STESS also demonstrated that for a The testing temperature of 75°F is 7°F (39°C) above case with built-in stress the stress in aluminum at 20°C is room temperature. Thf: difference between the steel and larger than for two other cases, e.g. the base case and with aluminum thermal expansion coefficients is 0.0000115 per compressive stress in aluminum , that may raise a concern (“C) that results in: (-3.9 x 0.00001 15 =0.000045). about an increased risk of conductor fatigue. For the sag-temperature run, the sag was specified to be The large built-in stresses proposed in the paper might 0.79 m (2.6 a.) at 23.89”C (75°F) to match the low- lead one to expect that the permanent elongation of post-war temperature conditions in Fig. 6-24 of [2]. The sag- conductors ought to be larger than those of pre-war temperature run indicated that the computed sag was within conductors. During the development of STESS, many stress- 30 mm (1.2 in.) of the measured values over the whole strain tests were undertaken. After carefully comparing the temperature range of the test. This demonstrates that, for a initial composite curves with pre-war design curves, it was prestressed conductor, the effect of 11 MPa (1600 psi) built-in concluded that there were no systematic differences in stress is approximately the same as of -11 MPa compressive permanent elongation. The curves used by STESS, like those stress. For a conductor that is strung normally, however, of other familiar sag-tension programs, are therefore based on without a prestress, the effects are not the same. Three runs of the pre-war curves. computer program SWSS were done to model built-in stress In our field and testing experience, conductor on the reel of 11 MPa given in the paper (by specifying slack of often anives with the steel core retracted inside the aluminum -0.000573); compression in aluminum (by specifying by approximately 10 to 20 mm. According to this paper, one -1 1 m a ) ; and a base case without built-in stress and without would expect the steel to protrude, but this seems to be a rare compression,just as a regular sagtension program. The results occurrence. confirm that built-in stress would lead to excess creep so that there would be excess sag at both low and high temperatures. REFERENCES Compressive stress, on the other hand, results in excess sag only at high temperatures. 0. Nigol and J.S. Barrett, “Characteristics of ACSR [l] Ref. [l] describes the use of bolted clamps when Conductors at High Temperatures and Stresses”, preparing a conductor for stress-strain tests. This is to ensure IEEE Transactions on Power Apparatus and Systems, that the conductor, when tested, is in the same state in which it Vol. PAS-100, No. 2, February 1981, pp 485-493. was manufactured. Without such precautions, the intemal [2] Dale Crane, “Conductor Sag and Tension friction in a short conductor sample is not adequate to preserve Measurements at High Temperatures”, Report the stress state, including any “built-in” stresses that might TLMRC-92-T-3 RP1717-51E85 of the EPRl have been produced during manufacture. The same technique Transmission Line Mechanical Research Institute, is now prescribed in an Appendix to the Canadian Standard May 1993. [4] for ACSR conductors. [3] J.S. Barrett, S. Dutta and 0. Nigol, “A New The report [2] on the “Hawk” test describes the sample Computer Model of ACSR Conductors”, IEEE preparation in detail: “Each conductor was carefilly unrolled, Transactions on Power Apparatus and Systems, Vol. identified and inspected for defects such as birdcaging, PAS-102, NO. 3, March 1983, pp 614-621. unraveling, scarring, etc. The conductors were coiled on [4] CAN/CSA-C49.1-M87, “Round Wire Concentric spools and stored on end prior to testing”. “To install the Lay, Overhead Electrical Conductors” Canadian dead ends, a smooth cut was made with the conductor laid out Standards Association. straight; the conductor was then marked f o r the dead end and trimmed”. “Ajier one dead end was crimped on, the Manuscript received February 10, 1998 conductors were stretched out and laid straight with approximately 1000 Ih tension and marked at the C U I length”. No special procedures for maintaining the conductor’s stress T. 0. Seppa (The Valley Group Inc., Ridgefield, CT): The state are mentioned. It therefore appears reasonable to assume remarkable quality of this report is that it shows that seemingly “old” that, even if built-in stresses of the magnitudes discussed in the data can be re-evaluated to present new insights. A large part of the paper had been imparted to the conductor during manufacture, data has been available for several decades, but has not been critically evaluated because there seems to be no need for it, because most of these stresses would be released. On the other hand, transmission line were seldom, if ever, operated in the temperature the thermal strains of the 75°F cut & crimp temperature would region where the compressive forces became relevant. Today, when be locked in. many lines are operated regularly above lOO”C, the significant 617 differences between measured and predicted sags have become very The magnitude of the errors resulting from such practices can be evident. * significant. Consider, for example, a case of a 1000 ft.(305 m) span of ACSR 26/7 Drake in a heavy loading area. According to the There are several other important effects to be considered, in addition graphic method, the kneepoint is 67°C and the expected sag is at to the mill effects described by the author, when the realistic error 100°C is 30.5 ft. (9.3 m). Assume that the conductor is operated at range of calculated vs. actual sags are considered. They include: 100°C and that the actual kneepoint is 95°C. The resulting actual sag is 31.7 ft (9.7 m). It would be of interest to have the author’s 1 . The manufacturing temperature of the conductor. The Aluminum comments on the magnitude of high temperature buffers which he Association stress strain curves assume a manufacturing temperature would recommend. of approximately 20°C. If the conductor is manufactured at a higher or lower temperature, the “kneepoint” of the sag-temperature graph We would like the author’s comments on the error sources Of the (e.g. Fig 6 of the report) is shifted by an equal amount. EPRI data [5], which he has used as a base reference. The currentkemperature data in the Hawk tests raises substantial What further aggravates the situation is that sometimes the steel core questions. For example, a current of 783 A results in conductor is brought in from an outdoor warehouse, while the aluminum wires temperatures of 160-144°C (average 150). IEEE method of on the bobbins are at the factory temperature. Such lack of calculation shows that even for zero wind speed and a IOW emissivity temperature control can further aggravate the uncertainty of the of 0.4, the conductor temperature should not exceed 135°C. kneepoint temperature. Combined, the manufacturing temperature effects can cause an uncertainty of up to k15”c compared to the [I] J. F. Minambres et al: “Radial Temperature Distribution in assumed kneepoint temperature. ACSR Conductors Apllying Finite Elements” IEEE PE-029-PWRD- 0-1 1-1997, IEEE WPM 1998, Tampa, FL. 2. The author’s treatment assumes that the manufacturing control of the wire tensions is perfect (each wire has the same tension). This is a [2] Tapani 0. Seppa: “Accurate Ampacity Determination’ rather idealized assumption. IVO in Finland conducted a number of Teperature-Sag Model for Operational Real Time Ratings” IEEE tests with 26/7 and 54/7 conductors in 1965-1972, in which strain Transact. on Power Deltvety, Vol. 10, NO. 3, July 1995, pp. l46C- gages were mounted on a number of outside strands in tests spans of 1470. 40 m to 360 m length. The tests indicated that at stress levels of 30- 60 N/mmz the individual wire stresses typically varied +5 N/mm2. Manuscript received February 13, 1998. An indirect indication of the difference in wire tensions is the temperature range of the curved part of Figure 6. Although some portion of this data may be caused by temperature differences T. Okumura and K. Fujii (Sumitomo Electric Ind., Ltd., Osaka, between the core and the surface of the conductor (see 3. below), the Japan): We are very much impressed by the analytical approach temperature range of the curved part is too large to be explained given by Mr. Rawlins. In Japan we have not attempted this kind of solely by the temperature gradient. Note also that the tightest wire in investigation, though we have been using heat resistant aluminum each layer will act as a “baling wire” restraining the outward alloy conductor steel reinforced operated at high temperature for expansion of the layer below it. more than 30 years as the conductor for trunk lines. Referring to our experiences during this time, I would like to give the following 3. The author assumes that the conductor is isothermal. At high comments: current densities, this is not true, as shown by the report [l], which indicates temperature differences in excess of 10°C. Temperature 1 . The first one is concerning the relaxation of stress in aluminum differences between the core and the surface of the conductor will strands during the stranding process. As is well known, a stranded increase the shift of the kneepoint. conductor is driven to its shipping reel by the capstan of the stranding machine. Considering the size of driving wheel of the Experimental data collected by tension monitoring systems [2] in capstan (usually 1.2 to 1.5 m diameter), we can conclude that an actual field installations seems to show that the difference between aluminum strand of the conductor in the capstan strained up to the assumed and actual kneepoint is typically 20-35OC for two aluminum plastic deformation region, taking account of the slip movement layer and 30-40”C for three aluminum layer ACSR conductors. between each strands. Because the binding force of the outside Although a part of the shift is probably caused by missapplied layer on the inner layer or those in the inner layer itself, limit loading assumptions (very few lines see the assumed maximum ice or slipping movements of strands through friction between layers. wind loads), it appears evident that the sag deviations discussed by Therefore, some degree of the relaxation of stress due to the the author are real and common in operating transmission lines. plastic deformation should be expected. 2. The second is the similar effect given by the stringing sheaves in Another observation of interest from sites with tension monitors is paying out operation. As for this effect, measured data is available that conductor installed at the same time may not have the same in the report of the Society of Electrical Cooperative Research of properties, especially regarding the kneepoint temperatures. At one Japan as shown in the attached figure 1 . This figure shows that the site a tension monitoring system monitoring two ruling span sections more the product of contact force of sheave times the number of of ACSR Drake with close to the same RS lengths indictaes passed sheave becomes, the more the permanent elongation of kneepoints of 90 and 105”C, respectively, with a calculated kneepoint conductor paid out becomes. This permanent elongation is of 6 5 7 5 ° C . At another site a similar monitor indicates for ACSR thought to be caused first by the reduction of the lay diameter due Cardinal kneepoint temperatures of 120°C and 140”C, respectively, to nicking of aluminum strands, which results in the reduction of with a calculated kneepoint temperature of 80-95°C. Possible stress in aluminum strands. The second effect is the similar explanations include difference in historical loading and different permanent deformation observed in capstan of the stranding “workout” of conductor during stringing. It would be of interest to machine. In case of the sheaves, this effect is more likely due to have the authors comments. their shorter diameter. 3. Due to the relaxation effects on the aluminum strands, there is no Today, some engineers advocate reducing the clearance buffers substantial amount of remaining stress in the aluminum part of because they believe that sags can be calculated to the nearest inch. conductors installed in transmission line. Therefore we can utilize 618 8 1) CONVENTIONAL 7 2)COUNTING SHIFT OF ?-.. c 6 0) = 5 z m 4 ~ Temperature where the stress 3 o l aluminum par1 becomes Zero 2 20 40 60 80 100 120 140 160 n. 01 Temperature (degree C) IO0 1000 10000 100000 0 Fig.2 Sag-Tension Relatlonship __ Fig.1 Measured Permanent Elongation of r ! Considering shift of tension ZNoconTdering shlft of tension -e ~ I the Conductor Passing Sheaves +Measured in test span Data shown in Fig 6 of where, -e Based on measured tension in test span +Calculated -___ with SAGT ~ ~~ 2Tsinq k - 2 n' =- m(R+rh [2TsinP2 ) .+ m(R n' :number of stands contacting sheaves (R+r)@ n' = __. P Workmg Tension 6 :contacting angle (rad) m :number of strands P :lay length P l N P , -=- m NZ;F E,',, N :number of layer R :radius of sheave (mm) r :radius of conductor (mm) T :conductortension (kg) Elongation anti-vibration dampers without accidents which are designed not to take account of remaining stress as Mr. Rawlins pointed out. The last is concerning the calculation method itself. As was discussed in the CIGRE SENDAI colloquium last October, Japanese transmission lines are designed by a very simple sag- tension calculation method. We use for instance, constant Young's modulus value of a conductor which is calculated from the modulus and the cross sectional area of each component material. ZTACIR 240 mni And the value is very close to the final modulus value used in the calculation method of U.S.. In Fig. 2, I plotted the sag values calculated by our method with an initial sagging condition of ACSR Hawk with 2.6ft sag at 25°C in 3 10 ft span. Further, I gave the calculated results with the same condition taking account of the tension shift from aluminum part to steel core. In this checking calculation, we are dealing with the tension decreasing process, therefore we can apply Young's modulus of final value which is almost equal to that used in our calculation. A simple introduction of the concept of our calculation method taking account of the tension shift is given in Fig. 3. Our calculation results meet the measured values well taking 0 50 100 150 200 250 300 account of the effects of fittings at both end of the test span as Mr. Conductor Temperature ("C) Rawlins pointed out. When we compare two curves (our calculation and the measured value in test span in the paper), we Fig.4 Companson of Measured Sag and Calculated Sag can find that the difference of the critical temperature value where the stress in the aluminum part becomes zero is around 8°C and At the same time, in Fig. 4 we show the comparison of calculated that the derived from ours is higher. It is our belief that this sag and measured sag of high temperature conductors at our 112m difference is caused by the pre-tensioning if the tested conductor test span. The conductors are 240 mm'ZTACIR and 240 mmz was attached with clamps at both ends before sagging, or that the TACSR which were strung in parallel. The sag of both conductors manufacturing temperature of the conductor is 8 degrees lower was the same at initial conditions (Initial tension of ZTACIR is than our assumed temperature which is 15°C with no remaining 20% U.T.S.). Then the temperature of ZTACIR and TACSR was stress in the aluminum strands as is shown in the attached paper. raised by current flow. The relation of conductor temperature and 619 sag was measured. In this case both conductors were not Program and the majority of the stress-strain charts that were pretensioned. Therefore the measured values well coincide with provided by Alcoa. the calculated results as shown in Fig. 4. In Japan high temperature conductors were used in large scale for the first time around 30 years ago. And in the investigation stage Two items not covered in the paper are: prior to it, the discrepancy of sag values between measured ones 1) Alcoa's stress-strain curves are based upon aluminum and those calculated by the conventional method was observed. strands produced from "hot-rolled" redraw rods. while Then we developed our new calculation method and have most conductor produced today is drawn from cast (or conducted several tests to fix the detail condition for the line Properzi) redraw rods; and design with sufficient engineering accuracy. Currently, in Japan it 2) The effects of elevated temperature creep of the aluminum is believed that our method can be used to design the line of high temperature conductors with more than twenty years operation strands. experience. Stress Strain Curves At AEP. we recognized the apparent Manuscript received February 13, 1998. inconsistency of installing conductor made from cast rods with data based upon rolled rods. and studied the problem. I R 0. Kluge, Member,IEEE contacted Wyland Howitt (now retired from Alcoa). Bill WisconsinPower and Light Co. Howington (then with Noranda) and others, and was advised Madison WI 53701 : that: In actual installations, the behavior of mechanical systemsoften deviate from what a. The stress-strain curves provided by the vendors were is intuitivelyexpected. To account for these unknowns, designershave learned to "conservative." based upon numerous tests. Since use empirical formulasand safety margins to protect the public from uncertainties clearance is of the most concern, this was interpreted to in their design. Obviously, designerwould like to understandthese behaviors so mean that for a given stringing sag. the provided stress- that they can be certain their installationsare safe and not overly conservative. strain data would provide the masimum increase in sag to Sinceother researchers have raised suspicionregardingthe unexpected elongation the final condition. of conductorsunder high temperatures'2, I would like to join with my colleagues b. There are significant variations in stress-strain data for to thank Mr. Rawlins for the insight he has providedto understandwhy conductorsdo not always behave at high temperatures, as had previously been both "cast" and "rolled" rods. and individual tests could thought. In this paper, Mr. Rawlins identifiestwo mill practices that, at least produce stress-strain charts for "cast" rods that looked like partidy, explain this behavior. With this knowledge and, ifthe mill practices are those for "rolled" rods. and visa-versa. known for a specificconductor, designers can now predict the sag at high temperaturesmore precisely. Based upon these comments. we then looked at the impact of installing conductor made from cast rods with sag data based However, as Mr. Rawlins also points out, transmission engineersand especially upon rolled rods. operators, who are dealing with older, existing installations, do not normally know how the conductor was stranded at the factory, and, therefore, are still unable to calculate the exact sag of the conductor at high temperature. Since this is the At AEP, our design tensions are set at the "Final" norm, designers must stiU use assumptionsand safety factors. To provide greater condition, as opposed to the "Initial" condition used by many confidence for the designer that hisher sag calculationis reasonable, I have the following two questions for Mr. Rawlins. other utilities. When we.compare sag and tension runs based upon "rolled" and "cast" rods for a conductor size, the 1) What is the normal range for the "built-in" (pretension) of the aluminum "Final" sags and tensions are the same for both types. but the strandswhen the conductor is manufactured by the two-pass method? Do you feel the distributionshown in Fig. 3 of your paper is representativeof the "Initial" (or stringing) sags are less for the conductors made industry practice? from "rolled" rods. If we install the conductor made from "cast" rods using data that is based upon "rolled" rods. the 2) To explain EPRI's test results, you had to assume that the lay of the inner aluminum strands was longer than the lay of the outer stands. Is this normal final sags are also smaller by about the same magnitude mill practice? If the steel core is prestranded and the aluminumis stranded in a (ignoring elevated temperature creep). This provides second pass, would not all the aluminumstrands normally have the same lay increased ground clearance but also results in a small length? What is the likelihood that the inner aluminumlay is longer than the outer such that aluminumcompressioncan occur? Is there mill data to provide increase in the Final Tensions at 6O"F (4%. used for a distribution of lay lengths for aluminum strands at different layers? vibration studies) and weather loadings (-2.5%. used for References: structure design and selection). but these are deemed to be minor increases and within acceptable limits. (1) 0.Mgol and J. S.Barrett, "Characteristicsof ACSR Conductors at High Temperatures and Srzesses," IEFE Transactions, Vol.PAS-100, N0.2, February 1981. pp485-492. Effects of Elevated Temoerature CreeD In the early 1970s. (2) Dale Crane, &.al., "Conductor Sag and Tension Measurementsat High John Harvey and Bob Larson of Alcoa published papers on Temperatures," TLMRC, EFW, RP1717-511T85, May 1993. how to predict and include elevated temperature creep in sag Manuscript received February 13, 1998. calculations. Creep is a Function of time. temperature and tension: elevated temperature creep is defined as' occumng when the conductor operating temperature is above 167°F (75°C). B. Freimark (American Electric Power, Columbus. OH); I appreciate learning of these mill practices that affect the In discussions with John Harvey (shortly before his conductor's "mechanical" propenies. AEP presently uses a retirement) it was agrccd that for ACSR conductors. the modified licensed version of the Alcoa Sag & Tension amount of additional creep due to cxposure to elevated 620 temperatures was limited. as the creep ceased once all of the approaches or passes through zero stress. Once this has occurred, the tension was transferred to the steel. conventional model assumes the aluminum load remains at zero with a zero modulus of elasticity and all load is carried by the steel core. This location on the stress strain curves has been referred to as the We studied the effects of elevated temperature creep composite final curve "knee", because of its shape and its importance on the clearances of AE:P lines, and in 1986 began to include on sags and tensions at elevated temperatures. Another key point its effects in the design of new lines and the review of older recognizes the strain location of the knee is always moved to the right lines for operation at elevated temperatures using estimating with built in aluminum stress. Hence, if an ACSR conductor is not formula. Between 1989 and 1994 we completed operated at temperatures where the conventional model predicts the modifications to our copy of the Alcoa Sag & Tension aluminum stress is zero, the effects discussed in this paper are essentially avoided and remain secondary in nature and effect. program to include the effects of elevated temperature creep using the fonnulas in the HarveyLarson papers and also the However, with the present climate in the industry to raise conductor 'Istop limit" noted above for ACSR conductors. At the operating temperatures to avoid capitol expenditures and maximize a temperatures and tensions that AEP designs its lines. the transmission line's utilization, the luxury of restricting operating "stop limit" for ACSR conductors generally controls the temperatures below the final curve knee may not be practical. adjusted "Final" sags. Additionally, may thousands of miles if transmission lines are presently operating without the detailed knowledge of built in stress levels and actual lay lengths used during conductor manufacture. Combined Effects As noted above, we install the conductor Therefore, how might a utility incorporate these effects into made from "cast" rods using data that is based upon "rolled" predicting clearances and hence determining maximum conductor rods. Thus the final sags are less (and the clearances operating temperatures which maximum line utilization and ensure a greater) if we ignore elevated temperature creep. When we safe and reliable facility? Would it be practical to determine upper include the effects of elevated temperature creep. the "Final" values for built in stress and aluminum compression modulus for various conductor designs, and use those values as nominal (and sags at the maximum operating temperature are the same for conservative) in sag tension calculations at elevated temperatures? Or conductors made from either "cast" or "rolled" rod when they would you recommend a more aggressive approach to actually are installed at the same "Initial" stringing sadtension. determine these values somehow and include them for any specific operating line? By including the effects of elevated temperature creep. I believe that we are adequately compensating for the Thank you for your paper and comments to my discussion. factors described by Mr. Rawlins that cause additional sags Manuscript received February 13, 1998. beyond those normally calculated. A. H. Peyrot (Power Line Systems, Inc., 918 University Bay Drive, Question for Mr. Rawlins: Since it would take a great effort Madison, WI 53705): Some measured sags at high temperature have to incorporate the mill praclices described in your paper in been reported to exceed what is predicted by conventional sag- the initial a n d final stress strain curves used in calculating tension programs. Such programs are computer implementations of final and initial (stringing) sags for any particular project. the graphical method. The author provides excellent explanations for what are your recoinmendations for the line designer? Is two possible contributions to the discrepancy. AEP's method of using " r o l l e d rod stress strain data and This reviewer would like to expand on the aluminum in compression including. the effects of clevaled temperature creep argument. Fig. 1 shows various assumptions that can be made reasonable? regarding the final stress-strain curve for the aluminum portion of an Manuscript received February 13, 1998. ACSR conductor at high temperature. The bilinear curve 0-Z-A assumes that the aluminum cannot carry compression. Curve P-Z-A assumes that it can carry some compression with a reduced J. L. Reding (Bonneville Power Administration): Complements to compression modulus. Some numerical values are suggested by the the author on a fine paper proposing and demonstrating some author. Line T-Z-A assumes that the aluminum can carry full secondary effects on the long accepted stress strain relationship in compression as if it were welded to the steel strands. This last ACSR conductors due to mill practices and tolerances during cable assumption is sometimes being used outside of North America. manufacture. Although the identified effects are secondary in nature, Reality is probably a version of the P-Z-A line, where P-Z is a curve they imply potentially significant impacts on conductor sags and rather than a straight line. Adding the aluminum and steel stress- tensions under high temperature operation. The primary reason for strain curves gives the three composite curves E-K-C, F-K-C and G- such impacts results from the mathematical models used to predict K-C. Using the graphical method, sags can be determined from the sags and tensions for conductors at elevated temperatures. The stresses calculated at the intersection points H, M, and L of the models extrapolate from room temperature stress strain tests to equilibrium curve with the three composite curves. The higher stress elevated temperatures using some key assumptions to bridge the point H corresponds to the underestimated sag reported by extrapolation from room temperature up to an elevated temperature conventional programs which assume no aluminum compression. The of interest. As pointed out by the author, and others, the two key lower stress points M and L correspond to the higher sags calculated assumptions are 1) the cable is tension balanced between the strands by assuming partial or full aluminum compression capability. and layers when placed on the shipping reel, and 2) the aluminum layers do not interact significantly once the aluminum stress has Fig. 2 shows sag calculations for the EPRI example described in the dropped to zero. An additional assumption I would offer is the steel paper. The calculations were done with the PLS-CADD line design and aluminum componenls act independently as elasticity members. program which has two options for modeling aluminum behavior, either full compression capability or none. The conductor was sagged A key point in the paper acknowledges these secondary effects do not to match the experimental sag of 2.6 ft at 25 degrees C after creep, become significant in the models until the aluminum component mine the same stress-strain data as the author and snecifving creen as 62 1 be entered by the program user or be part of an internal database covering typical situations. However, this analysis refinement may be excessive in view of other uncertainties which affect sag calculations (conductor manufacturing temperature, effect of temperature on modulus of elasticity, ruling span approximation, non-uniformity of temperature along the conductor or within its layers, etc.). In another approach, one could make use of sag calculations based on the two extreme assumptions of full or no aluminum compression, as was done for the example in Fig. 2. If the results from the two assumptions are significantly different, one should be concerned about the potential of underestimating sags using the traditional no compression method. In such cases, one could conservatively use the full compression results, or use some intermediate value. We are looking forward to seeing more experimental sag data from full scale span monitoring at high temperature to see how these data fit relative to the two suggested bounds. Manuscript received February 13, 1998. Fig. 1 Effect of aluminum compression Charles B. Rawlins: Because of the large number of discussions, and the overlap in their comments, I would like to organize my response by subject. rather than by individual I I I I I 8 I I discusser. This in no way minimizes my appreciation for the personal efforts and interest that went into their contributions. I appreciate them very much. Zero Aluminum Stress and the Knee Point Dr. Douglass and Mr. Roche ask why I suspect that the final aluminum curve changes slope exactly at the point where the aluminum stress is zero. I don't think it does. My view is that it does so f o r practical purposes, and I'll discuss the difference below under Alternate Hypotheses. The correspondence between zero aluminum stress and 2 1 t d S A G 2.6 FT 20 I 40 I 60 I 80 I loo I 120 ti 140 the knee point has been conventional wisdom for almost 70 years. The reason has to do with the way the aluminum layers accommodate longitudinal conductor strain. When a helical strand is pressed against the layer below, it can TEMPERATURE C respond to longitudinal strain only by stretching or contracting along its axis, because it is constrained against radial deflection. When it is not pressed against the layer Fig. 2 Calculated and measured sags below, the strand is free to change its helix radius, basically by changing its curvature, that is, by bending. The freedom that resulting from the conductor being held at 18 percent of its to bend greatly reduces the strand's longitudinal stiffness, ultimate strength for 10 years at 25 degrees C. because it can now act like a coil spring. Since it is the tension in the strand that binds it against the core, the Calculated sags ignoring aluminum compression are almost identical transition from radial constraint to radial freedom coincides to those shown by the author using SAGT. They provide a lower with zero strand tension, and that is where the change in bound of actual sags. The slope discontinuity at the transition stiffness occurs.. temperature of 45 degrees indicates that the aluminum loses tension It is true that a strand may be pressed against the layer at about that temperature. below by built-in bending stresses, similar to the way a Calculated sags assuming full compression capability are very good preformed armor rod presses against the conductor. However, matches to the test results up to 70 degrees C. Beyond that they these stresses in 1350H19 aluminum are only significant in provide an upper bound of measured sags. conductor made on planemy and tubular suanders, and only as far as the point where the conductor is engaged by the Given the theories and data presented in the paper, what can someone strander capstan. The repeated cycles of flexing and practically do to predict sags in critical high temperature situations? unflexing going over the bullwheels of the capstan largely One could make use of data on aluminum prestress and reduced relieve these bending stresses before the conductor goes on compression modulus, as described in the paper. This would require the reel. The do not play a significant role in determining the some trivial changes to existing sag-tension programs. The data could knee point. 622 It is also true that when more than one aluminum strand core contracted, showing it had been under tension when layer is present. there may be differences in the stresses the conductor tension was zero. among layers. That can influence the values of conductor The effect of this last observation is illustrated in Dr. strain where the total tension in the aluminum and the total Bamett's Fig. 1. The tail of the slack leg of the aluminum pressure on the core each reach zero. and make them unequal. final (the most clockwise point of each of the hca\-\.-curves) However, the difference behveen them is small in practical had to be displaced negatively. indicating comprcssion in the cases. and can be ignored in sag tension calculations. aluminum. That observation did not shed an! light on other parts of that leg to distinguish the cases in the last three Priority panels of the figure, hciwever. Dr. Barrett raises the question of priorih for the analysis Dr. Barrett and his colleagues found that they were able of Appendis 2 of the paper, and appears in the second to account for all three of these observations with one bold paragraph of his comments to claim priority for himself. I do hypothesis: dilation of the aluminum from the steel core does not agree. not occur until some critical level of compressive stress on the Dr. Barrett's 1981 explanation of "essentials" [2] was aluminum is breached - the delayed dilation hypothesis. Had sketchy and qualitative. Quantitatively, it went as far as they had access to a quantitative understanding of the (A2.1) of the paper and stopped. While he may have interaction between layers, as presented in Appendix 2 of the developed a quantitative analysis in 1989, he d d not disclose paper. they would more likely have focussed on the case its existence until the 1997 IEEE Winter Power Meeting. illustrated in the last panel of Dr. Barrett's figure. Parenthetically, I disclosed the existence of the analysis The delayed dilation hypothesis was bold, because there presented in the paper at the same meeting, one day earlier. was no real physical explanation for delayed dilation. There The description of Dr. Barrett's "mechanical model" in war a qualitative rationalization, however, involving effects of his talk cannot be construed as a "presentation" of a different lay angles in inner and outer layers. This quantitative analysis. Study of his overheads reveals merely a rationalization is covered in the third and fourth paragraphs single matrix equation, with undefined terms, apparently of Dr. Barrett's discussion, and his presentation there is the applicable to only a single strand layer. I am not aware of any clearest I have seen to date. I am not aware of any occasion, and Dr. Barrett refers to none, where the details of quantitative description of it, so I will try to provide one here. his model have been exposed to public scrutiny and comment. To the extent that my analysis agrees with Dr. Barrett's I reject his claim to priority. thinking, so do I. The question in point is: 'how much does zero net stress Alternate Hwotheses in the aluminum part of ACSR precede the loss of pressure on Much of Dr. Barrett's discussion pertains to the conflict the core, as strain is reduced after loading to a high tension? between the hypothesis that the aluminum part of ACSR begins to dilate from the core as soon as the net tension in it becomes negative, and the opposing hypothesis that dilation may be delayed until sigmficant compressive stress occurs. I prefer "dilation" to "birdcaging," because birdcaging is generally thought of as a localized, gross eqansion,of the aluminum @EEE Std. 524-1992], whereas the slack aluminum condition that concerns us here is a generahzed, basically-uniform, quite small radial expansion. I cleave to the former hypothesis, which is the traditional one, while Dr. Barrett and his colleagues cleave to the latter, which I prefer to call the "delayed dilation hypothesis.'' I suspect that their view of this area was influenced by the absence of a satisfactory quantitative analysis of layer interference while Ontario Hydro's investigation was in its early stages. At that time, the late seventies, they were Eo2 €12 Ec confronted in their test program with several anomalies in sag Conductor strain tension behavior of ACSR These included: 1. Unexpectedly large sags in outdoor span tests of Fig. 8 Stresses and strains in inner and outer layers conductors under heating. 2. Unexpectedly h g h knee point temperatures found in The situation is illustrated in Fig. 8, where we consider indoor laboratory measurements of -thermal expansion of an ACSR with two aluminum layers. The curve is the initial ACSR. stress strain curve for an aluminum strand. Now, if the 3. Clear evidence of significant compressive load in the conductor is strained to E,. the strands of the inner and outer aluminum part of ACSR at zero conductor tension, layers will also be strained. However, they will not be strained following loading to 70% UTS. When they cut the as much as the conductor. The arc length of a helix is greater aluminum strands, the abutting ends overlapped and the than that of its a.uis by the factor l/cosa. and onl! one 623 component. proportional to cos a. of the conductor's strain is The aqgjysis aboveignores effects of radial contraction directed along the strand's axis. Thus the strain experienced and expansion of the conductor as it is stretched and by a strand in a layer having lay angle a is only E, . COS?^. unstretched. These effects increase the separation Au and These strains for the inner and outer layers are shown in the decrease the final moduli of Fig. 8. Thus, they make E F more figure,where the subscripts I and 0,respectively, apply. The positive relative to ~ p That . is, they reduce (and generally stresses in the two layers at maximum load are therefore eliminate) the aluminum compressive stress at the knee point. and UO. Therefore, (C5) puts an upper limit on the magnitude of When the load is reduced, the stresses in the two layers compressive stress. follow their respective final moduli down, reaching zero I have evaluated (C5) using values of input parameters - stress at €12 and €02. These final moduli are E cos2al and based on stress strain data on typical 1350H19 aluminum - E cos2ao. Obviously, strands, and assuming combinations of lay angles within ASTM limits that cause the greatest compressive stress. For the 2617 stranding,the input parameters were: Now, the strains that occur on the initial loading produce I Ma... Tension-I I 50% RS I 70%RS 1 plastic deformation, as reflected in the fact that the slope of CC I 0.0027 I 0.0045 the initial curve is less than E in the vicinity of a1 and uo. If 01 - (DSi) U , I 17500 I 21000 we call this slope S,then the difference between a1 and a0 is, 3250000 1300000 S (psi) AU = SE, (cos2a1- COS~~O) (C2) E (psi) 1moO0 1o0ooooo These relations can be combined to obtain, €12 - €02 = Stranding 1811 2617 3017 45/7 5417 84/19 E jO%RSMa.x. -42 -48 -52 -62 -59 -54 70%RSMax. -74 -82 -84 -101 -96 -110 We are interested in the values of E where the net aluminum tension and net inward gripping force from the When the outer layer lay ratio was increased from its aluminum each reach zero. Under final conditions, the minimum of 10 to the preferred value of 11, CTAK was almost tensions in the aluminum layers in the direction of the halved in all cases shown in the table. conductor axis are given by, The compressive stresses &splayed in the table are PI = nrEAcos3ar (E - E 1 2 ) clearly quite small and are in my opinion small enough to ignore, even without the ameliorating effects of radial strains. This is why I consider that, for practical purposes, EP and E F Po = noEAcos3crg ( E - €02) (C3) are congruent. If I have read Dr. Barrett's description of the The inward pressure exerted by a helical strand due to its rationale behind the delayed dilation hypothesis correctly, I tension is equal to its tension times the inward curvature of agree with the principle, but the numbers I derive from it lead the helix, T - K per , unit length of strand. where to an entirely different view of its sigruficance. It is clearly K. = sin2a/R. Thus, the inward force by the entire layer per insignificant. conductor unit length is, The adoption of the delayed dilation hypothesis by Dr. Barrett and his colleagues is perplexing because there were F = - nT IC=- P IC clues in Ontario Hydro's test data that pointed elsewhere. For cosa cos2a example: Several of the tests presented in Fig. 3 of [2] displayed sin'-a . cos a small but clear differences between the final steel modulus = nEA (E -€2) R and the modulus of the slack aluminum leg of the composite final, similar to that illustrated in Fig. J of the This applies with appropriate subscripts to each layer. We paper. These differences can only be esplained by the can solve (C3) simultaneously for the value of E where presence of a compression modulus in the aluminum. + PI PO = 0; the result, E P , is the conductor strain where net Three of the four tests represented in Fig. 6 of [2] indicate aluminum tension vanishes. Similarly, we can solve for the E larger thermal expansion coefficients above the knee + where FI FO = 0; the result, E F . is the conductor strain points than that of steel. Thus, the aluminum had to be where the grip of the aluminum on the core vanishes. Then, active, with its stress varying as temperature increased, the stress in the aluminum at the knee point is. rather than being constant as then visualized by the delayed dilation hypothesis. The effect of stress upon steel's expansion coefficient is not sufficient to explain the where € A is the final aluminum modulus (true, not virtual). disparities. They can only be fully explained by also Aluminum compression occurs when e p > EF considering finite aluminum compression modulus. 624 In two of the four stress strain tests of Fig. 3 of 121, those In contrast, as described above, the delayed dilation on 2.18 cm and 2.81 cm diameter conductors, the hypothesis can account for only an insignificant change in hypothesized constant aluminum compressive stress is duminum compression stress and, by implication, in sag clearly absent, yet there was significant contraction of the tension behavior. Dr. Barrett refers to Fig. 9 of [2] as sample at zero tension when the aluminum layers were demonstrating sigxufbnt aluminum compression above the cut. In the other two tests, the steel core was evidently not knee of the final composite. This apparent evidence of reloaded to the previous maximum strain, thus permitting delayed dilation results entirely from arbitrarily placing the some residual elastic recovery in the core. origin of the steel initial w e at the origin of the composite NOW, the anomalies listed above that confronted Dr. initial, i. e., from assuming that built-in stress is zero. Barrett and his colleagues can be explained by the hvo mill Although in his discussion Dr. Barrett persists in effects dealt with in the paper. The third anomaly above is characterizing the congruence of the knee point with zero readily explained by compression modulus without resort to aluminum stress as incorrect, and is emphatic in asserting delayed dilation. If one accepts that the knee point of the final delayed dilation as the cause of knee point shifts, that composite w e coincides for practical purposes with zero hypothesis lacks an adequate quantitative rationale. It is a stress in the aluminum, then the compression stresses chimera. Built-in stress has a clear physical basis, and it surmised by Dr. Barrett from the shortening of his samples explains the shifts. when the aluminum was Cut can be used to deduce what the compression modulus was. It was simply the stress surmised Determination of Built-in Stress in EPRI's Test by Dr.Barrett divided by the change in strain spanned by the Drs. Douglass and Shan and Mr. Motlis raised questions slack aluminum leg. Ref. [3] presents nine tests in which the about the procedure used to determine built-in stress in aluminum cutting procedure was carried out. I have EPFU's Hawk sample, based on the prestretch data. calculated the virtual compression moduli indicated by the This procedure involved shifting the aluminum and steel shortening of the sample in each case, and find that the values initial curves shown in Fig. 1 to make the net strain k m the range from 330,000 to 590,000 psi. These are within the prestretch come out to 0.059% instead of 0.039%. That range found from Aicoak stress strain tests (see Fig. j), and required moving the aluminum initial to the left by are within the range that can occur with lay lengths permitted (coincidentally) 0.039% relative to the steel initial. Given the by ASTM, as calculated from Appendices 1 and 2. Thus, the aluminum initial virtual modulus of 58788 psi from Chart 1- delayed dilation hypothesis is not needed. 782, the shift introduced a positive increment of stress equal Unfortunately, data on the lay lengths actually present in to 2293 psi. However, as Mr. Motlis points out, Chart 1-782 the samples of [3], or any of Ontario Hydro's ACSR test incorporates 883 psi of slack in the aluminum. Thus, the net samples. is absent from their publications, so a correlation built-in virtual stress after the shift was 1410 psi, which I like that of Fig. 5 cannot be carried out. rounded to 1400 in the paper. The second anomaly, the shifted knee point temperatures The virtual aluminum compression modulus used in the in the thermal expansion tests, are readily explained by calculations was 5030 psi, of which 1375 was due to spring presence of built-in stress. Built-in stress, and compression effect (Appendix 1) and 3655 to interference (Appendix 2). stress due to delayed &lation, have about equal effects upon Is it proper to employ Chart 1-782. since it represents an knee point temperature, as confirmed by Mr. Moths in his average of several stress strain tests. and the sample in EPRI's discussion. The difference is that built-in stress is easy to test may have differed from the average? Note that in the explain, since it has a clear physical basis, while delayed above process the role of Chart 1-782 is limited. The initial dilation is not, since it lacks such a basis. composite is involved only up to 2300 psi. The steel initial The first anomaly. excess sags in spans under heating, and final are used, or, more narrowly. the initial steel up to can be explained in part by built-in stress and aluminum 2300 psi, and the set at 2300 after the strain increment of compression modulus. Presumably. the bdance of the 0.264%. This set, according to 1-782. is 0.0103%. The dsparity can be explained by r a d d thermal gradient in the average from a number of 7-strand steel cores is 0.0097, with conductor, as suggested by Dr. Barren. I haLe not tried to standard deviation 0.0042. Taking account of the departure explore that area. of 1-782 from the broader average, the shift of the aluminum There is solid evidence supporting the mill effects initial may have fallen short of the 0.059% measured set of described in the paper. First, those, who like Brian White the conductor by 0.0006%. However, if the EPFU sample was have spent time in cable mills, can testify to the use of one standard deviation off the average, the shift could have signiticant braking tensions, and 25 lbf or 100 N has been produced conductor set as much as f 0.0042% off of 0.059. quoted as typical. For a conductor such as Cardinal ACSR While this possible error is noticeable, it it leaves much of that force amounts to about 1800 psi. Second,the presence of the difference between the uncorrected conductor set,0.036%, aluminum compression modulus is indicated by various tests, and the measured 0.059% intact. The possible errors that both by Alma (see Fig. 5 of the paper) and by Ontario Hydro. could arise from deviations in the initial composite and steel Suitable quantitative analysis supports those indications, as curves below 2300 psi are also small. It would have been given in Appendices 1 and 2. Dr. Barrett misinterprets the desirable to use the measured characteristics of the reel of analysis of Fig. 1. "Set" is not an issue in this analysis. conductor the EPFU sample was taken from, but the credible Rather, built-in stress changes the point at which the errors from using Chart 1-782 still leave intact the conclusion aluminum reaches zero stress, namely, the knee point. that significant built-in stress was present, as well as a good 625 estimate of its magnitude. The results in Fig. 9 show even better agreement with the Mr. Motlis draws attention to the fact that the measured sags than Fig. 6. temperature where the sample was cut and crimped was 75OF, Dr. Shan remarks that compressive stress in the slack leg whereas the prestressing was canied out at 89OF. I neglected of Fig. 1 influences the apparent conductor set. When the to take that into account in determining the built-in stress aluminum initial is shifted to reflect built-in stress, the length using the above procedure, and it does make a difference. of this leg above 2300 psi becomes too short to cause a The amount of relative shift of the aluminum initial at 89°F significant effect from the aluminum compression modulus. needs to be O.Q5%, rather than 0.039% as given above. The imputed built-in stress increment becomes 2939 psi, leaving a Other Influences in the Test of Hawk net built-in stress of 2056 psi, which is more-nearly in line Sample preparation can certainly influence test results. with the other data of Fig. 3. The procedure used for the samples in the EPRI p r o e m would have permitted looseness in the samples near the ends, and led to at least some reduction of built-in stress in the sample. The above estimate of built-in stress based on the prestretch data would then apply to the sample, but not necessarily to the conductor on the reel. The estimated stress based on the prestretching the sample would still be the appropriate value to use in evaluating its sag behavior strung in the 3 10 foot test span. Use of compression fittings, not reverse pressed, can only introduce looseness into the sample. It cannot create, or e?cplain, built-in stress, as Messrs. Douglass and Roche's comment 3.b seems to suggest. Mr. Seppa points out that the radial temperature gradient would have been significant. citing [ l l ] . That reference 20 40 60 80 100 120 140 160 assumes 7.4 m/s of wind. The laboratory would have Temperature "c represented essentially still-air conditions. From [9], I estimate about 2.3"C core-to-surface difference at the - - o - .Measured sag masimum current used in the Han.k test, which would lead to -Sag based on measured tension about 300 psi o f additional alriniinum compressive stress. I +Cmected for all effects think this would have only a minor effect upon the sag at that +Effect of recovery only condition. +-Corrected to actual initio1 45°C tension Mr. Seppa suggests inconsistency in the data of (51 relative to the conductor temperature that 783 A should Fig. 9 Measured and Amended Predicted Sags produce. The data shows temperatures in the 160-144OC Amending the estimate of built-in stress changes the range, whereas the E E E method of calculation predicts not results shown in Fig. 6. The new overall w e for calculated more than 135OC. I think this apparent inconsistency results sag, accounting for actual initial 45OC tension, 2156 psi built- from the value of emissivity. 0.4, assumed by Mr. Seppa in stress, aluminum compression modulus and the effect of New conductor has emissivity in the 0.2 to 0.25 range, or temperature on elastic moduli. is shown in Fig. 9. 0.34 after 6 years storage [13). A value of 0.3 leads to an In the paper, I neglected to discuss the role of elastic IEEE method prediction of 147°C. recovery in the EPRI test procedure, or note that it was taken into account along with built-in stress and compression modulus in the results shown in Fig. 6. Elastic recovery is Influences on Built-in Stress Other than Spool Braking the shortening of the conductor sample between load cycles, Messrs. Seppa, Shan and White point out that the and is an expression of reverse creep. It gives rise to stress temperature in the mill and the temperature of the steel wire strain hysteresis loops such as can be seen in Fig. 2. The inventory influence the built-in stress found in the conductor EPRI samples were affected by this, since they were dropped when it reaches the reel. Mr. Okumura notes that the to zero tension after prestretching to move them into the test repeated flexing of the conductor going over the bullwheels of span. The precise amount of recovery experienced is the strander's capstan will cause the aluminum strands to seat - arguable. Recovery strain the width of the hysteresis loop - more intimately on the core, causing a reduction in the radii averaged 0.0076 f .0039% for 26/7 ACSR following the of the aluminum layers and a consequent reduction in built-in 50% RS loading cycle in 36 post-WWII tests. However: stress. The EPRI prestretch tension for Hawk was 52.8% Rs; These comments are well taken. I believe that the impact It was applied for only 20 minutes instead of 1 hour, of these effects is already incorporated in the data of Fig. 3, 9The time spent at zero tension was considerably greater in since all samples contributing to the distribution there were the EPFU procedure than occurs in stress strain tests. drawn from reels of finished conductor. Presumably, the I used 0.0076%. The effect of that adjustment alone is effects pointed out by Mr. Seppa relating to nonuniformity of indicated in Fig. 9. built-in stresses among strands would be also. 626 Other Evidence of Built-in Stress possible that one-pass ACSR is still being made in some The original clue t.o built-in stress was observation in mills. Protrusion would also be absent if the temperature at cable mills of protrusion of the steel core at the cut ends of the time of observation were d c i e n t l y above the mill cables on reels. Drs. Barrett and Shan, and Mr. Motlis, temperature when the conductor was stranded. comment on the absence of evidence of this or, at best, mixed Mr. Motlis suggests that comparison of pre- and post- evidence. Some discussion of the phenomenon is needed. W I initial composite curves should show greater Dr. Barren's assertion that the protrusion should amount extensions in the latter. That is a reasonable e,upectation, to 50 mm for a 100 m sample of Hawk with 1600 psi built-in judging from examination of composite curves with and stress assumes that there is no friction between the aluminum without the shifts to reflect built-in stress. As to actual data. part and the steel core. Actual protrusions are generally in the there were unfortunately enough differences in stress strain 0.1 to 0.2 inch range for conventional ACSR, and that is test procedures, before and after the war, that we could get because there is friction. The friction tends to trap the built-in large enough sample sizes only to compare the initial stresses by action similiu to the Chinese finger puzzle or the modulus values in the 30% to 50% RS load interval. For that Kellem grip. modulus, the average post-war value was 11% greater than This action is analogous to a ship's hawser wrapped the pre-war, contrary to e.upectation. I attribute t h s to around a bollard. Lf the hawser is allowed to slip slightly, looseness in the samples of the pre-war. one-pass conductors. friction with the bollard builds up the tension from the small level at the free end to the high strain at the ship end. The What Levels of Built-in Stress and Comuression Modulus buildup of tension is exponential along the hawser. growing Occw in Practice? at a rate that depends only upon the diameter of the bollard Fig. 3 contains all the information we have on built-in and its coefficient of friction with the hawser. It is not stress. The picture there needs to be qualfied in several difficult to apply the same analysis to the buildup of respects, however. aluminuni stress as the core begins to extrude from the As noted in the paper, some of the built-in stress will aluminum. For 26/7 ACSR and using the coefficient of decay through stress relaxation while the conductor sits on friction between 1350H19 aluminum and galvanized steel. the reel. strands, both in mill condition, the doubling distance is about Mr. Okumura points out that passage over bull wheels 3 feet. Thus, if a serving of tape at the cut end could initiate or sheaves stretches the aluminum and, judging from the data fiictional tension in the aluminum of, say, 0.5 lbf, that tension he presents, the effect can be quite sigruficant. A certain would grow to 600 Ibf with 10.2 doublings, or about 30.6 feet. amount of this occurs in the mill, and that part is already In Hawk ACSR 600 Ibf amounts to 1602 psi. If the reflected in Fig. 3. Further stretching occurs during stringing, aluminum and steel were flush before slipping commenced, however. My calculations using Mr. Okumura's formula and the relief of built-in stresses over that length. taking their data suggest that passage over as few as ten sheaves may e-xponential variation into account, would produce relative remove all built-in stress and, in fact, introduce some displacement between the cut ends of aluminum and steel of looseness. about 0.15 inches. Thus, protrusions of 0.15 inches are The values given in Fig. 3 are biased on the high side. consistent with built-in stress of 1600 psi. They are representative of the outside of the reel, since that is Note that the length over which slipping occurs, and the where stress strain samples are generally taken. That part is resulting protrusion, are not very sensitive to the initial from the end of the strander run, where the wire spools are frictional force. If that were 2 OZ. instead of 0.5 lbf, the nearly empty, and the brakes work against a short radius ann, region o f slip would be increased by two.doubling lengths to so the built-in stresses are largest. The average over the 36.6 feet, and the core p r o w i o n would increase to 0.19 length of the reel is probably around 2/3 of that on the inches. outside, so we think that the upper end of the distribution Obviously, these -e.uponentially growing frictional forces shown in Fig. 3 should probably be taken to be around 2500 can develop only if the aluminum can seat firmly on the core. psi, when referred to the reel average. That is the general case with conventional ACSR It is not All of these qualifications diminish estimated levels of the case with ACSWSD because of the gaps separating the built-in stress to be expected in completed lines. aluminum layers from each other and from the core. And, it Fig. 10 shows the combinations of lay ratios in a number may not be the case with ACSRfTW, since small gaps may of stress strain test samples of ACSR having two aluminum still occur. In the cases of ACSWSD and ACSRfIW, the layers. Several mills are represented. There appears to be a gaps have an additional effect, in that they let the core follow trend toward greater inner layer lay ratios, pre-war to post- a shorter path than the aluminum on the conductor reel, War. resulting in socalled "core deficit." When the conductor is pulled out, the core tends to draw in at the end. This tendency How Should Desimers Deal with these Mill Effects? is arrested in ACSWSD by installation of suitable fittings at Messrs.Kluge, Freimark, Reding, Seppa and White, the factory, but not for ACSWTW. I have seen side-by-side and Drs. Douglas, Peyrot and Shan raise questions on how samples of conventional ACSR and A C S W , with the core these effects should be dealt with. The answer rests in part protruding from the former about a tenth of an inch, but upon what their magnitudes are in practical cases. The paper slightly recessed for the TW. It may be that Mr. Motlis' presents results only for a laboratory span case. In order to observations of receded cores involved ACSRfTW. It is also put these effects in practical context, I have applied them to a 627 16 2 I 1 separate effects. The curve for their actual combined effect .- 0 I5 ASTM Lmits -4 I 1 I 4 s 0 4 falls below it, showing that the effects are not strictly additive. There is some interaction between them. Fig. 12 pertains to Hawk ACSR and shows the 3 2 -2 L F 14 13 -- -- O 1 I1 I .&/ 8 ASTM Preferred increments in final sag at 150°C that result from each of the mill effects separately, as functions of span length and NESC loading. ; I 0 -- IO 12 I o I I Maximum aluminum 11 -- O0 I Io Solidpointc a n post WWU I 10 * I - ' 1.4 2 8 9 10 11 12 13 Outer Layer Lav Ratio Fig. 10 Lay ratio combinations found in stress stram test samples of 2-layer ACSR 8 E 0.6 selection of realistic cases, employing a high level of built-in e stress, 3500 psi, and the combinations of lay ratio within ASTM limits such as to yield the largest aluminum compression modulus. Thus, I was looking at worst case 0.2 effects. Some of the results are shown in Figs. 11 and 12 and 600 800 1000 1200 1400 1600 1800 Table I below. - span Length feet Fig. 11 shows the final sags as a function of temperature for Hawk ACSR in a 1000 foot span under NESC Fig. 12 Increases in final sags from mill effects, Hawk ACSR Light Loading, with the two mill effects applied separately and together. Built-in stress shifts the knee point temperature Table I shows the sag increments for several sizes of up about 12°C. and displaces the arm above the knee point ACSR There are two groups of three conductors parallel to itself. Compression modulus alone changes the representing different size classes. Within each group there is slope of the arm above the knee point, but does not shift the a range of aluminum percentage. Although it is clear that knee point itself. Applied simultaneously, they shift the knee NESC loading, span length, size range and aluminum content point and change the slope above it. all have some influence on the increases in sag due to the mill effects, the overall picture is that built-in stress causes at most 36 about a foot of increased sag, while aluminum compression modulus may cause increments up to about 2 feet. 34 Table I B 32 Final 150°C Sag Increases - Feet e IESC Light Loading in 1000 foot Span 26 24 50 100 150 200 Temperature T ----t No cmection The increments in high temperature sag due to these e 3 5 0 0 psi built-in aluminum stress effects are clearly modest, especially taking into account that *Maximum aluminum compression modulus they are- based on worst-case assumptions. Given the +Built-in stress and compression modulus moderating effects bulleted above of relaxation on the reel, - - * - .Sum of separate effects strand setting going over bullwheels and sheaves. and spool Fig. 11 Hawk ACSR in 1000' span, NESC light loading build-down in the strander, it is arguable whether the residue from built-in stress amounts to as much as '/2 foot. Closer The top curve in Fig. 1 1 shows the effect of simply examination of effects of strand setting. described by Mr. superimposing the increments in sag that sprang from the Okumura, may further reduce that estimate.. 628 The indicated effects of aluminum compression modulus Full AI Compression and No Al COmPressiOn lines. are moderated by the fact that strander operators seldom work ~fmi11 effects =e taken into account. the range of at the extremes of the ASTM lay ratio limits. Simply uncertainty is defined by the questions, how much residual changing the outer layer lay ratio from the ASTM minimum built-in stress survives in the in-place conductor. and how of 10, used for the above calculations, to the preferred value much does the modulus of the slack a l d n u m leg of the final of 11 reduces calculatcd compression modulus by 30% to composite differ from the steel final modulus? The first 50%. The sag increments of Figs. 11 and 12 and Table I question influences displacement of the apex of the wedge of would be similarly redu:ed. Once the lays are fixed, however, doubt, and the second determines the wedge angle. the compression modulus is fixed for the life of the conductor. Addressed in this way. the range of doubt is greatly reduced. Relative to making practical use of information on these First, Prof. Peyrot's figure essentially assumes an infinite effects, we need to distinguish the design of new lines from upward shift of the kneepoint. Applying even the upper limit the assessment of existing ones. In both cases, the effects of Fig. 3 for built-in stress causes only a moderate shift. influence final sags at high temperatures. Second, even assuming the worst combination of permitted For new lines, the effects must be taken into account in lay ratios, the computed aluminum compression modulus the design and spotting of structures, and that means that leads to a wedge angle that is only a fraction of that resulting information on them inust be in hand at that point in the from the no-dilation approach. Compare the slopes in Fig. 9 design process. The picture here is different for built-in above with that of the Full Al Compression curve in Prof. stresses and compression modulus. Built-in stress is not a Peyrot's Fig. 2. Thus, the designer should benefit from controlled variable. True enough, strander operators do set assessing the mill effects by facing a much smaller range of the spool brakes, but that is done by feel or, as Mr. White has doubt that encompasses a shallower range of sags.. observed, by banging on the strands. I don't think that at As Mr. Kluge points out, transmission engineers and present anyone can predict what the built-in stress will be for operators normally do not know how their existing conductors any production run or even reel of conductor. The only way were made, and that makes it difficult to take mill effects into to determine it is to conduct a stress strain test on the finished account. Built-in stress acts by shifting the knee point conductor. These tests are expensive and, more importantly, temperature by a small and somewhat uncertain amount. the conductor will not have been made or probably even Once the line is placed in service, the knee point temperature ordered when the data is needed by the line designer. is shifted back by effects of creep and wind and ice loadings. Fortunately, as noted above, the practical effects of Whether the engineer can make a reasonable guess of the built-in stress are small, about 4 ! foot, so it would seem final result depends upon several uncertainties, among them: reasonable and prudent to take that value as a buffer, or to Whether the new conductor was well represented by the assume an upper limit of about 2500 psi and calculate the sag chart used in design; outcome. Engineering judgment might point to a smaller Whether initial sags were as intended; value than 2500 psi. What wind and ice loadings have occurred; Compression modulus effects are a different matter. Whether elevated temperature creep has occurred: Note that the lay ratios that lead to significant aluminum It seems likely, as suggested by Prof. Peyrot and Mr. Wlute, compression modulus also permit reduced mill costs. On the that the combined uncertainty would overshadow the residual other hand, they may cause increased structure heights and effect of built-in stress assumed to exist in the line when it costs, so there is an economic tradeoff to be evaluated. What was new. On that basis, trying to account for it in assessing makes this different from built-in stress effects is that the existing lines is probably not worth the effort. Operators have information needed to make that evaluation can be available a better chance of establishing knee point temperatures by on- before the tower designs are fixed. Lay length is a controlled line monitoring. mill variable within the ranges permitted by ASTM, and mill As pointed out in the discussion of Fig. 11. aluminum operators can calculate the effects of using the different lays compression modulus changes the slope of the sag- available on their machines upon production costs. The temperature curve above the knee point. Even though the lay designer can assess the impact of compression modulus on ratios in older conductors may not be known. it may be final sags and estimate the costs of the extra tower height thatworthwhile to establish a range of uncertainty for this slope if %vi11be required, if any temperatures well above the knee point are of concern. The In answer to Mr. Freimark. I don't have a good enough range of slope can be determined through calculation, feel for how the effects of rolled versus cast rod. and elevatedassuming the worst combination of lay ratios for one temperature creep play out, to take a position on whether they boundary and preferred lays for the other. could stand in for mill effects It is easy enough to calculate these effects that a stand-in should not be necessary Miscellaneous Messrs. Okumura, Peyrot. Shan, Douglass and Roche Responding to Mr. White's comments on Poisson's describe the concept of establishing for the designer a range Ratio, its role in Appendix I does not concern changes in of uncertainty, bounded on one side by the assumption that strand diameter, but rather the relationship between shear aluminum compression and built-in stress do not occur modulus and Young's Modulus, G = + E / ( lf v), as given (conventional sag tension practice), and on the other by the for example in $70,Eq. (24) of [ 101. assumption that dilation does not occur. This "wedge of Mr. M o t h suggests that the presence of built-in stress doubt" is well illustrated in Prof. Peyrot's Fig. 2 between the would impair the fatigue strength of conductors. Actually, 629 the fatigue strength of aluminum is relatively insensitive to REFERENCES the static component of stress, unlike steel. Data presented in [ 111 J. F. Mifiambres et al, "Radial Temperature Distribution Fig. 2-7 of (121 bears this out. in ACSR Conductors Applying Finite Elements," IEEE Mr. Seppa notes that nearby line sections installed at the Paper PE-029-PWRD-O-11-1997. same time have been found from tension monitor data to have 12) Transmission Line Reference Book, Wind-Znduced different kneepoint temperatures. One likely cause, alluded to Conductor Motion, Electric Power Research Institute, by h4r. Seppa, is described in Mr. Okumura's discussion: Palo Alto, CA. 1980. elongation of the aluminum during passage over sheaves. 131 W. S . Rigdon, H. E. House. R. J. Grosh and W. B. The variation of built-in stress from the beginning to the end Cottingham, "Emissivity of Weathered Conductors after of a strander run could also contribute. It is of interest that Service in Rural and Industrial Environments," AIEE the kneepoint shifts, from those predicted from sag tension Transactions on Power Apparatus and Systems, Vol. 81, calculations to those recorded by the tension monitors, are Pt. 111, February 1963, pp. 891-896. consistent with built-in stresses in the 2000 to 2300 psi range. Manuscript received June 12, 1998. 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