Stress-Strain Creep and Temperature Dependency of ADSS Sag An

Stress-Strain, Creep, and Temperature Dependency of ADSS (All Dielectric Self Supporting) Cable’s Sag & Tension Calculation Cristian Militaru Alcoa Fujikura Ltd., Spartanburg, SC Abstract It has been common in the industry to calculate sag & tension charts for ADSS cables without taking into consideration the influence of creep, coefficient of thermal expansion (CTE). and the difference between the initial and final modulus. In some applications where the sag and tension performance of the cable is not critical. the presentation of data in this manner is appropriate. However, the great majority of applications require very exact determination of sag and tension, and the influence of  the above factors is important. There is also confusion between the “final state” (after creep) and the ‘loading condition” (wind+ice). which are 2 different cases. Following thorough and repeated stress-strain and creep tests, this paper will show that ADSS cable has both an “initial state” and a “final state”, each state having an ‘unloaded” (bare cable) and a “loaded” (ice and/or wind) case with resulting sag 8 tension charts as a function of  creep and CTE. Additionally, the results of this work were compared and validated by common industry sag &tension software, including Sag10 and PLS-CADD.

Fig.1

Catenary Curve Analytic Method

+

Catenary Curve Analytic Method

(1 I), followed by:

l + y

Fig.1 presents an ADSS cable element under the extrinsic (wind and ice) stresses and intrinsic (cable weight) stresses, with a length, On the curve y(x), given by the

which has as solution: (13) integrating rel.(13) results:

=

formula:

(14);for x=0 results: (1); yields:

=

(2) (16),so:

 Also,the equilibrium equations results in: =H 

(3);

k,

=  

=  

0 (17).

w 

resulting the catenary curve

(4)

considering rel. (2). the derivative of  rel. (4) yields: dV 

dl 

-=

(5); also, the slope in any

w -

point of the catenary curve is defined as the first derivative of the function of the curve:

dV 

 H 

and (8) results:

(7) and:

=

y = w . integrating rel.

(8) using rel. (5)

(9) , and then:

(10),

=

(20). a In Fig.2 the designations are: S= span length half span length (assuming level supports) D= sag at mid-span H= tension at the lowest point on the catenary (horizontal tension) - only for level span case, it is in the center of the span T= tension in cable at structure (maximum tension) P= average tension in cable L/2=arc L/2=arc length of half-span I= arc length from origin to point where coordinates are (x,y)

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Loading I Curve

Resultant weight:

[lbs/ft]

Type

cross Sectional area:A [in21

B

0.277

0.6447

H

1.615

0.6447

S=1400 [ft] Stress [psi]

Stress-Strain Tests

Tensions Limits: a) Maximum tension at Oo F under heavy loading not to exceed 51.35% RBS: MWT=51.35%RBS [Ibs]. I

I

Note: (max. working tension) was selected less than MRCL, in order for this ADSS cable to cope with limit c) presented below. b) initial tension (when installed) at 600F w/o ice or wind (“bare” cable) not to exceed 35% RBS: T  

c)

This catenary table is transformed in a Preliminary SagTension Graph, in Fig.4. This graph has 2 ‘y” axes: left side: stress [psi], and B-bare cable: H-heavy load. and right side: sag: D [ft]. Also, it has 2 ‘x” axes, strain. [%] (arc elongation in percent of span) and temperature, 8

= 35%RBS

Stress-strain tests on ADSS cable performed in the lab show (see Fig.3) that they tit a straight line, characterized by a polynomial function of  degree, whereas metallic cables (conductors. OPT-GW, etc.) are characterized by a polynomial function of the degree (5 coefficients). From ail the tests performed, results show, that differences exist between the initial modulus. E (slope of the “charge” curve) and the final modulus, E f (slope of the “discharge” curve) and their values depend upon the ADSS cable design. There is also a permanent stretch, (also referred to as “set"), at the “discharge” , which depends on the ADSS design. Creep

Final tension at 600F w/o ice or wind (“bare” cable) not to exceed 25% RBS:

Guide to Columns: 1 and 2 are the same for any span, any material. 3,4,5,6 are the same, for the same span for any material: ACSR, AAC, EHS, ADSS, etc. 7 and 8 are different, from one material to another  (ACSR, AAC, EHS, ADSS, etc.)

Tests

 According to the ADSS cable draft standard, IEEE P12221, the creep test must be performed at a constant tension equal to 50%. MRCL for 1000 hours at room temperature of  F. in general, for ADSS cables. therefore the test is done at T=[%MIN/2...%MAX/2] RBS=ct. (see Fig.3). Considering a ‘nominal” value of MRCL=50% RBS, the ‘default” constant tension for the test would be: RBS. The creep test on the cable design analyzed was performed at a constant tension: RBS, because for  this cable: RBS. The values ware recorded after every hour (see Fig.8”CreepTest, Polynomial Curve” and Fig.G-"Creep Test: Logarithmic Curve”). The strain after 1 hour, defined as ‘initial creep”, was 42.89 [pin/in].  After 1000 hours (41.8 days) the strain was 314.10 So the recorded creep during the test, defined as strain at 1000 [h] minus strain at 1 [h], is The extrapolated value after 87380 hours (10 years, 364 days/year) was 1142.69 [pin/in]. Therefore, the “IO years creep”, which is defined as strain at 87380 [h] minus strain at 1 [h]. was 1100 Other creep tests performed on other ADSS cable designs showed ‘IO years creep” values in the same range. The curves on the stress-strain and tension-strain graphs are identical. The only difference is that on the ordinates (y) axis, when going from tension [ibs] to stress [psi], there is a division by the cross-sectional area of the cable, A The values on the strain (x) axis remain the same. For the stress-strain graph (Fig.3) at a tension (stress) equal with the value for which the creep test was performed, MRCL MRCL/A), a parallel to the x axis intersects the initial modulus” curve in a point of abscise, MRCL, and from that point, going horizontally. adding the ‘IO years creep value of 0.11 is obtained the point on the ‘IO years creep” curve corresponding to that tension for which the creep test was performed. Drawing a line from the origin through that point gives the slope (the modulus) for the “IO years creep”, E Always,

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Anql e: Sl ope: t on Modul us:

>t on

d >ton

Ei > ( 10

Fig. 3

-

General Stress-Strain Chart for an ADSS cable

Fig. 4

608

-

Preliminary Sag-Tension Graph for an ADSS cable

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CREEP:

vs. TIME: t (FITTED LINE)

100

1000

TIME:t

10000

100000

hours

Fig. 5- Creep test for a particular ADSS cable : Polynomial Curve log

= 0.2889

TIME: t [ hours ] LOG

log42.69

87360 h (10 yn)

1 year=364 days

Fig. 6 - Creep test for a particular ADSS cable : Logarithmic Curve International Wire & Cable Symposium Proceedings 1999

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for any ADSS design, the relation between the 3 moduli is

Coefficient of Thermal Expansion The values for CTE (designated here as a) were determined by the individual material properties in a mixture formula: a =

(39)

where

Ei are

the CTE, cross-sectional area and modulus of each one of  the elements in the ADSS construction respectively. For  the great majority of ADSS cable designs, the influence of  CTE is smaller than that of creep. Designs with a low number of aramid yarn ends (typically for short spans) will yield larger differences in sags due to temperature than designs with a high number of aramid yam ends. This is due to the fact that the aramid yarn is the only element with a negative a , while the rest of the elements have a positive a. To appreciate the impact of the contribution of aramid yam to the ADSS CTE, designs with low number of aramid yam ends have a CTE typically in the range which is relatively close to aluminum, to and sometimes larger than steel, The CTE for cables with higher  numbers of aramid ends are often 100 to 1000 times smaller, to and so, for those designs, the influence of CTE on sag is negligible.

Sag-Tension Charts The well known general equation of change of state: (40)

shows- that the change in slack Is only equal to the change In elastic elongatlon + change In thermal elongation, and does not include the change In plastic elongation (the creep). Therefore, the above relation is true only if the 2 states of the cable are in the same stage, initial or final. When viewing sag charts (Fig.1 1 & Fig.12). this equation will allow a user to go only vertically from one case to another case, but it will not allow him to go horizontally (same temperature, same loading conditions, from initial stage to final stage) due to the influence of  creep. A simplistic way of solving this issue which is still used in some European countries is the following: the creep influence is considered to be equivalent with an “off-set temperature”, g iven by the ratio (conductor IO yrs. creep-initial elongation)/ CTE. But this is not an exact method, because it only calculates an INITIAL sag&tension chart, with the FINAL sag&tension chart being identical with the initial chart, the only thing is that the Initial chart,

is moved to align It with the new corresponding temperature. Therefore, the final sag at temperature ‘8” is equal with the initial sag at temperature The most accurate and exact solution is the graphic method. In this method, which was developed by 3 , the stressstrain graph (Fig.3) of the ADSS cable is superimposed on the ADSS preliminary sag-tension graph (Fig.4), so their  abscissas coincide and the whole system of curves from Fig.3 are translated to the left, parallel with the “x” axis. up until the initial curve. noted “2”, in Fig. 3 (and also in 610

Fig.7) intersects the curve H on the index mark=11300 psi (tension limit a]) the imposed maximum tension at under heavy load. For purposes of this paper, a MWT of 51%RBS was imposed. This MWT, which is less than the cable’s MRCL of 56%RBS, was used to be sure that neither tension limits b] or c] will be exceeded. Therefore, tension limit a] is the governing condition. The superimposed graphs then appear in Fig.7. The resultant initial sag at under heavy loading (54.10 ft.) is found vertically above point a] on curve D. The initial tension at bare cable=8750 psi (4352 Ibs) is found at the intersection of curve 2 with curve B, and the corresponding sag (15.59 ft) is on curve D. The final stress-strain curve 3a. which is the curve after loading to the maximum tension (MWT=51%RBS). at OOF, is drawn from point a], which is the intersection point of curves 2 and H, parallel to curve 3, which is the final stress-strain curve afler loading to MRCL=56%RBS, at Now, the final tension at after heavy loading =6440 psi (4151 Ibs) is found where curve 3a intersects curve B. The corresponding sag (18.35 fl) is found vertically on curve D. The next operation is to determine whether the final sag after IO years creep at will exceed the final sag after  heavy loading at Before moving the stress-strain graph from its present position, the location of  on its temperature scale is marked on Fig.7 as reference point R. The temperature off-set to the right at (Fig.7) in %strain is equal to (41) where is the ADSS CTE. Therefore, the stress-strain graph is moved to the right with 0.01992 [%I (Fig.7) until on the temperature scale coincides with reference point R (Fig.8). The initial tension at psi (4210 Ibs) is found at the intersection of curve 2 with curve B, and the corresponding sag (18.1 lft) is found vertically on curve D (Fig.8). The final stress-strain curve 3 b. under heavy loading, after creep for IO years at 800F. is drawn from the intersection point of curves 4 and parallel to curve 3. The final tension at 800F after creep for  IO years=5500 psi (3548 Ibs) is located at the intersection of curve 3b (or curve 4) with curve B . The corresponding sag (19.13 ft) is found vertically on curve D (Fig.8). Since the final sag at 600F after creep for 10 years=19.13 ft

(Fig.8) exceeds the flnal sag at after heavy loading=16.35 ft (Fig.7), creep is the governing case. For this case, users of Sag10 will see the flag, “CREEP IS  A FACTOR”. SAG10 will print only the final chart afler  creep (not the final chart afler heavy load). Users of  PLSCADD will see the same results in the chart called “FINAL  AFTER CREEP” (see Fig.1 1 & Fig. 12). The final sag and tension at must now be corrected using the revised stress-strain curve. For this purpose, the temperature axis will have an off-set of 0.01992 [%] to the lefl (Fig.8) to provide the values at Therefore, the stress-strain graph is moved to left (Fig.8) until on the temperature scale coincides with reference point R (Fig.9). The corrected final tension at bare cable, (after creep for  10 years at psi (3887 Ibs) is found at the intersection between curves 3b and B. The corresponding final sag (18.40 ft.) is found vertically on curve D. The final tension at under heavy loading, (after 10 years creep at psi (7027 Ibs) is found at the intersection between curves 3b and H. It’s corresponding resultant final sag (58.07 fl) it’s on curve D (Fig.9). When

International Wire & Cable Symposium Proceedings 1999

Fig. 7 - First Trial check of tension limits, for 

Fig. 8- Second Trial, to check effect of 10 years creep, at

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Fig. 10- Final Trial. for 

612

after adjustment for 10 years creep

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correction

determining temperatures for calculation of sag and tension performance, the maximum temperature of the  ADSS cable should be the maximum ambient temperature plus the heat absorbed by the cable. A reasonable assumption is Electrical conductors can reach higher values. i.e. or  due to the continuous current rating of the conductor, which does not exist for ADSS cables. Thus. for  the temperature off-set to the right (Fig.9) to get values at in %strain is : Therefore, the stress-strain graph is moved to the right with this value (Fig.9) until on the temperature scale coincide with reference point R (Fig.10). The initial tension at psi (4069 Ibs) is found at the intersection of  curve 2 with curve B, and corresponding sag (16.67 ft) is on curve D. The final tension at (after creep for 10 years at psi (3407 Ibs) is found at the intersection of  curve 3b (or 4) and curve B, and corresponding sag (19.91 ft) is on curve D (Fig.10). Conclusions Using this ADSS cable characteristics as input data, the output in SAG10 is presented in Fig.11, while the output screen for PLS-CADD is presented in Fig.12. As can be noticed. the graphical method presented above produces very similar results in these two programs, as well as in other sag and tension programs on the market. As a note, for different ADSS designs and different span and loading conditions, there can be many situations when the permanent elongation after heavy loading (due to the stretch of the cable, p) is larger than the elongation after 10 years creep. In these cases, for  users of the SAG10 program, the flag “CREEP IS NOT A FACTOR” is shown, and the final sag printed is the sag after heavy load (no more after IO years creep). Users of PLS-CADD will see the same result in the chart called “FINAL AFTER LOAD”. The influence of creep on ADSS cable sags is different from one design to another. As an example, the difference between the final and initial sag can range from 0.5 ft up to 1.2 fl in a span range of 200-600 fl, and from 1.5 ft. up to 2.5 fl in a span range of 600-1400 fl, under NESC Heavy loading. For spans over 1600 ft the differences can be 3-3.5 ft. For spans under NESC Light or Medium loadings, the creep influence results in sag differences less than the numbers listed above. The influence of the coefficient of thermal expansion of the ADSS cables is smaller than that of creep: as an example, changes in sag due to temperatures ranging from -2OoF to would yield 0.5 ft up to 1.75 fl for low aramid yarn counts applications, and becomes negligible (0.01 ft) for those designs with maximum numbers of aramid yarns.

References 1.

IEEE 1222P- Standard for All Dielectric Self-Supporting Fiber  Optic Cable (ADSS) for use on Overhead Utility Lines - Draft,  April 1995  Aluminum Electrical Conductor Handbook. chapter 5- third 2. edition, 1989 3 .  Alcoa Handbook, Section 8:“Graphic Method for Sag Tension Calculation for ASCR and Other  Conductors”-1970

Fig.12

-

PLS-CADD Output for this ADSS design

received MS degree (1980-1985) and Ph.D. degree (1990-1995) in Electrical Power Engineering from Polytechnic University of Bucharest, Romania. He worked for 11 years as a Transmission Design & Consultant Engineer in the power  utility industry in Europe, Middle East and SouthEast Asia. Since 1996 he has been employed with Alcoa Fujikura Ltd., USA, as a Development Engineer in the OPT-GW 8 ADSS cable and hardware department. Mailing Address: Alcoa Fujikura Ltd. P.O.Box 3127, Spartanburg, SC 29304-3127. Mr. Cristian Militaru

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