TN295 No. 9255 HKsSS 4y .*»•• "^ 6* ° aV^ •V/Wf' cP°^ •* SCOTS' «\>"^ oW«ZW« e>^„. -»*elfi^^ r o «V^. „fc2? .F^ °q, ^T*\o° V v ,•«••- ""it v. Tvi* .A *oF • ** v % * * A •4» •A v ' A* ^ ^9 S j>^ ^ *« :. -z £ °^ ^o< ^ - - ■- V ^•— A* ^A* *£m2>s. ** m a %.»«• ♦ T ^o 4 * 3,0-^. ro° v ^ •• •/ %. • • 1 1 - A> V .»i"»-. 'c^ a0 v , %^^\^ V*^\^ %.^r^^ V v^ "*7*T! BUREAU OF MINES V/t / INFORMATION CIRCULAR/1990 Baseline Tensile Testing at the Wire Rope Research Laboratory By William M. McKewan and Anthony J. Miscoe (801 \ YEARS g %U OF ^ U.S. BUREAU OF MINES 1910-1990 THE MINERALS SOURCE Mission: As the Nation's principal conservation agency, the Department of the Interior has respon- sibility for most of our nationally-owned public lands and natural and cultural resources. This includes fostering wise use of our land and water resources, protecting our fish and wildlife, pre- serving the environmental and cultural values of our national parks and historical places, and pro- viding for the enjoyment of life through outdoor recreation. The Department assesses our energy and mineral resources and works to assure that their development is in the best interests of all our people. The Department also promotes the goals of the Take Pride in America campaign by encouraging stewardshipandcitizen responsibil- ity for the public lands and promoting citizen par- ticipation in their care. The Department also has a major responsibility for American Indian reser- vation communities and for people who live in Island Territories under U.S. Administration. Information Circular 9255 M Baseline Tensile Testing at the Wire Rope Research Laboratory By William M. McKewan and Anthony J. Miscoe UNITED STATES DEPARTMENT OF THE INTERIOR Manuel Lujan, Jr., Secretary BUREAU OF MINES T S Ary, Director Library of Congress Cataloging in Publication Data: McKewan, William M. Baseline tensile testing at the Wire Rope Research Laboratory / by William M. McKewan and Anthony J. Miscoe. p. cm. - (Information circular / Bureau of Mines; 9255) Includes bibliographical references p. 23. Supt. of Docs, no.: 128.27:9255. 1. Mine hoisting-Equipment and supplies-Testing. 2. Wire rope-Fatigue- Testing. 3. Fatigue testing machines. I. Miscoe, Anthony J. II. Title. III. Series: Information circular (United States. Bureau of Mines); 9255. TN295.U4 [TN339] 622 s-dc20 [622'.6] 89-600355 CIP CONTENTS Page Abstract 1 Introduction 2 Equipment description 2 Experimental design 4 Experimental procedure 5 Experimental results 5 Typical results 5 Summary of normal breaks 7 Construction stretch 12 Breaking load versus gauge length 13 Breaking load versus reel position 13 Effects of stroke rate on results 15 Effect of gauge length on modulus of elasticity 15 Comparison of zinc and epoxy socketing 21 Torque calculations 22 Summary 23 References 23 ILLUSTRATIONS 1. Tensile and axial fatigue testing machine 3 2. Typical test data, rope D 8 3. Typical test data, rope B 9 4. Stress versus strain, rope B 13 5. Effect of prestretching on rope samples, rope B 13 6. Breaking load versus sample length 14 7. Effect of sample position on reel 15 8. Effect of log stroke rate, rope G 15 9. Modulus versus gauge length for various ropes 16 10. Elongation versus gauge length at 100,000-psi stress for various ropes 20 11. Elongation correction for stretch of socket filler versus load 21 12. Breaking strength and elongation versus gauge length for epoxy and zinc terminations 21 13. Modulus versus gauge length for epoxy and zinc terminations 22 TABLES 1. Tensile and axial fatigue testing machine specifications 3 2. Characteristics of wire ropes used in tests 4 3. Typical baseline test on wire rope D 6 4. Typical baseline test on wire rope B 7 5. Summary of test series on rope A 10 6. Summary of test series on rope B 10 7. Summary of test series on rope C 10 8. Summary of test series on rope D 11 9. Summary of test series on rope E 11 10. Summary of test series on rope F 11 11. Effect of stroke rate, rope G test series 12 12. Test series on zinc-filled sockets, rope H 12 13. Baseline tensile test summary 12 14. Effect of sample length on modulus and elongation at 100,000-psi stress for rope A 17 15. Effect of sample length on modulus and elongation at 100,000-psi stress for rope B 18 16. Effect of sample length on modulus and elongation at 100,000-psi stress for rope C 18 17. Effect of sample length on modulus and elongation at 100,000-psi stress for rope D 18 18. Effect of sample length on modulus and elongation at 100,000-psi stress for rope E 18 19. Effect of sample length on modulus and elongation at 100,000-psi stress for rope F 19 20. Effect of sample length on modulus and elongation at 100,000-psi stress for rope H 19 TABLES - Continued Page 21. Elongation correction versus rope diameter at 100,000-psi stress 22. Calculation of Gibson's torque constant 21 23 UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT ft foot lbf-ft/kip pound (force) foot per kip ft/min foot per minute m meter gpm gallon per minute min minute hp horsepower mm millimeter in inch pet percent in/min inch per minute pet in/in percent inch per inch kip/in 2 kip per square inch psi pound (force) per square inch lb pound s second lbf-ft pound (force) foot BASELINE TENSILE TESTING AT THE WIRE ROPE LABORATORY By William M. McKewan 1 and Anthony J. Miscoe 2 ABSTRACT The U.S. Bureau of Mines has established a wire rope research laboratory to examine the factors that affect the life of wire rope. Ropes of sizes ranging from 3/4 to 2 in. in diameter and from 2 to 35 ft in length were tested to determine their breaking strength, elongation, and torque. This was done to characterize the test equipment on ropes used in mine hoisting systems. Metallurgist. Supervisory physical scientist. Pittsburgh Research Center, U.S. Bureau of Mines, Pittsburgh, PA. INTRODUCTION The U.S. Bureau of Mines hoisting systems develop- ment project is an effort to improve the safety and efficiency of mine hoisting systems. A major part of this effort involves the study of the degradation of wire rope during its service life. Some 500 hoists are used in the United States, and in most of them, the cages for personnel and the skips for product are raised and lowered by a single wire rope. Cages may hold as many as 100 people, and shafts are as deep as 7,000 ft. Skips have fallen in this country, with accidents to nearby personnel and damage to the hoisting system. The accidents resulting from retrieving the rope, repairing, and putting the shaft back into service are significant. No cages have fallen in the United States, but the probability of such occurrences will escalate in the future because mining deeper reserves will require longer ropes and higher hoisting speeds. Lower safety factors will be used since regulations state that the safety factor can be reduced from 7 to 4 as shaft depth increases from to 4,000 ft and more. The fact that cages have fallen in foreign countries confirms that this research is not only desirable but necessary. While the technology of fabricating wire ropes has achieved a high degree of sophistication, the quantitative understanding of the degradation of the rope during service is at a very low level. A wire rope is really a mechanical system having a very complex geometry. It is actually a multilayer spring with internal damping. When a loaded wire rope is bent around a sheave to change its direction, the mechanics become even more complicated since transverse forces are introduced. In addition to the internal wear caused by the wires sliding on each other, external wear is caused by rubbing and sliding in the sheave. Adding to the problem are the dynamics of ropes up to a mile long and ropes traveling at speeds up to 2,850 ft/min, accelerating and decelerating with attached loads on imperfectly aligned guides. Also to be considered are the mine shaft environmental conditions of abrasive dirt and acid or alkaline moisture. Consequently, mine- hoist ropes endure great punishment. Analysis of the effects of these factors on the deterioration of a wire rope therefore requires an extensive research program and data generation with high precision. The Wire Rope Research Laboratory (WRRL) was es- tablished by the Bureau to examine the factors that affect wire rope strength, and ultimately, its useful life. At present, hoist ropes in mines are inspected both visually and by nondestructive sensors. A judgment is made, based on the observations and experience of the observer, as to whether the rope meets the retirement criteria of the U.S. Mine Safety and Health Administration (MSHA) (if and should be retired from service. At some mines, ropes are retired after a certain period of time has occurred or a given amount of tonnage has been lifted. The purpose of the WRRL is to provide accurate data to determine the effects of variables on the reduction of the strength of wire rope during its service life so that judgment becomes less of a factor. The best way to measure the deterioration of strength in a wire rope is to measure its ultimate or breaking strength, but this obviously cannot be done while the rope is in service. At the WRRL, ropes will be deteriorated by a bending fatigue machine of unique design, containing three sheaves that will exercise a 1,000-ft length of rope to produce nine different levels of fatigue at a predetermined tensile load and travel speed. Visual inspection and non- destructive testing (NDT) profiles will be made periodi- cally as the rope is cycled. After some time, broken wires and other indications of wear will determine that the rope be removed. Sections of special interest will be cut out, then further subdivided for detailed examination. The ex- amination will consist of four analyses (in addition to the NDT profile): wire-by- wire examination for correlation with the NDT profiles, single-wire torsion tests, metallo- graphic examination, and tensile strength measurements. The primary objectives of the baseline testing program covered in this report were to determine (1) the operating characteristics of the tensile machine, (2) the precision of data produced by the tensile machine, and (3) the proper- ties of the wire rope samples used during tensile testing. EQUIPMENT DESCRIPTION Although the tensile machine was designed primarily for tensile strength tests on wire rope specimens in support of bending fatigue research, it also has the versatility to test fatigue under cyclic axial force. The main application of this tensile machine will be to measure breaking strengths, elongations, and torques of new ropes for comparison with measurements made after the ropes have been degraded on the bending fatigue machine. These measurements will provide quantitative data to establish the effects of service conditions on the life of wire ropes. New and used ropes from mine hoists, obtained through cooperative agreements with mining companies, will also be tested to assess the effects of real-life use. The ma- chine is shown in figure 1. System specifications are listed in table 1. Italic numbers in parentheses refer to items in the list of references at the end of this report. '///////""""■ Figure 1. -Tensile and axial fatigue testing machine. Table 1, -Tensile and axial fatigue testing machine specifications Description Specification Maximum rope tension lb . . 800.000 Maximum rope diameter in . . 2-1/2 Specimen length ft . . 2-33 Maximum actuator speed in/min . . 16 Hydraulic system: Row rate gpm . . 70 Pressure psi . . 3.000 Drive motor hp . . 125 The machine is essentially a hydraulically actuated ten- sile testing machine in a horizontal position rather than the usual vertical position to reduce vertical height re- quirements and for ease of access. It is composed of three elements operating in conjunction: the load frame, the electrical console, and hydraulic power supply. The load frame contains the hvdraulic crosshead locks. The locks sustain full rated load in either direction with zero slippage and zero backlash. Safety containers for the specimen are provided for operator protection during testing. Functionally, the test machine is a closed-loop servohy- draulic system in which high-pressure hydraulic fluid under the precise control of a servovalve is provided to the hy- draulic actuator, which applies the load to the specimen. To accomplish this, the system controller accepts externally generated electrical control and feedback signals from the transducer. These signals are compared to detect any error, and the resulting signal is used to control the servo- valve. Several operating variables can be selected as con- trol parameters by choosing the appropriate transducer for the feedback signal. The controllable parameters are displacement of the actuator, load applied to the specimen, and torque generated by the wire rope specimen as an ax- ial load is applied. The electronic control console contains all the necessary components for servocontrol, hydraulic power control, sig- nal conditioning, test parameter readout, and interlock functions. It also contains a digital computer and the nec- essary interfaces to record, manipulate, and plot the testing data. The factors examined in the baseline series were 1. The precision of the data generated by the system for ultimate strength, elongation, and torque. 2. The effectiveness of resin sockets to withstand rope ultimate-strength loads and comparison of resin sockets with zinc (spelter) sockets. 3. The effect of actuator speed on generated data. 4. The effect of sample length on generated data. 5. Variation of generated data along the length on a single reel of rope. EXPERIMENTAL DESIGN There are a number of factors that can be determined during the tensile testing of wire rope. Some are measured directly, such as breaking load, and some are calculated, such as modulus of elasticity. Before a test is conducted, certain physical measurements are made on the rope. These are (1) gauge length, the rope length between the sockets, (2) rope diameter, and (3) lay length. From the diameter and the rope construction, the metallic area can be calculated. During the course of the program the operational char- acteristics of the machine were determined. The measure- ments made during testing were (1) the displacement of the actuator rod, or the stroke, (2) the load applied to the specimen, and (3) the torque generated by the specimen as an axial load is applied. The sensors for these measure- ments were calibrated by the machine manufacturer. Bureau researchers wanted to gain as much information as possible from the testing, both about the tensile machine and about the different samples of rope. It was known in advance that the manufacturer's catalog does not provide any detailed information about a rope. Manufacturers are required only to meet a minimum strength, nothing else; they are not required to give data on the actual breaking strength, the elongation, the chemical composition, or the microscopic structure of the rope. Therefore, the experimental work was designed to gain maximum data from as few tests as possible. Originally, 10 tests were scheduled for each rope series. The characteristics of the ropes chosen for each series are shown in table 2. Samples were cut to the following lengths: 5, 10, 15, 20, and 35 ft. Two samples were taken of each. The 10 samples were cut from the reel in random order. From a procedure of this nature, the precision of the testing could be calculated. In addition, the effects of sample size on the results and the uniformity of the rope on the reel could be determined. Later, it was decided to add 2-ft samples to the test program to increase the range of the data and to substitute 30-ft samples for the 35-ft samples to allow for the larger elongations. Table 2.-Characteristics of wire ropes used in tests Rope (All ropes were fiber core, improved plow steel, set in socket with epoxy resin, and tested at 1-in/min stroke rate, unless otherwise noted) Diam, in Description Strength, 1 Samples kips tested 83.6 10 184.0 12 129.2 10 47.6 10 310.0 11 320.0 13 129.2 9 184.0 5 1 1-1/2 1-1/4 3/4 1-7/8 2 1-1/4 1-1/2 6 x 25 filler wire, 6-in right regular lay ... . 6x19 Seale, 10-in right Lang lay 6 x 25 filler wire, 8-in right Lang lay 6x19 Seale, 5.25-in right Lang lay 6 x 25 filler wire, 12.75-in right Lang lay . . 6 x 25 filler wire, 13.125-in right regular lay 6 x 25 filler wire, 8-in right regular lay ... . 6x19 Seale, 10-in right Lang lay 'Catalog. 2 Tested at stroke rates of 0.0625, 0.125, 1, 8, and 16 in/min. 3 2nc-filled socket. EXPERIMENTAL PROCEDURE Enough rope was cut to allow for the amount that would be in the sockets. The ends were seized, broomed, and cleaned. The brooms were cleaned in a vented tank of trichloroethane and then washed with steam and detergent to remove any residual matter. The brooms were then closed, inserted into the sockets and set in an epoxy resin. With this procedure, there was no problem with the brooms pulling out of the sockets. After curing for about an hour, the samples were ready for testing. One series of samples was made commercially with zinc- filled sockets, using rope from a reel that had been previously tested, to compare the results obtained with zinc and epoxy sockets. The samples were placed in the tensile machine, and the testing was begun. Initially a prestretch load of about 5 to 10 kips was placed on the rope, and the stroke was set at zero. This procedure led to an S-shaped curve during the elastic portion of the test, because of the construction stretch that exists in new rope. During the second series of samples, a prestretch load equal to 20 pet of the breaking strength was placed on the sample for 10 min or until the rope stopped elongating. This load was then removed, and the test was conducted as before. This pro- cedure eliminated construction stretch and the S-shaped curves. The 20-pct prestretch load was used for all of the remaining tests. Construction stretch and the S-curves are discussed later in this report. The following measurements were made during the testing as a function of time: (1) load in kips, (2) stroke in inches, (3) torque in kip-inches. From these measure- ments the other factors can be calculated, such as stress, strain, and elongation. The "Wire Rope Users Manual" (2) gives certain speci- fications for determining breaking strengths of wire ropes: The breaking strength is the ultimate load registered on a wire rope sample during a tension test.... All discussion of strength is predicated on the assumption of there being a gradually applied load that will not exceed one inch per minute.... A minimum acceptance strength, 2-1/2% lower than the published nominal breaking strengths, was established as the industry tolerance.... The sample's length must not be less than 3 ft (0.91 m) between sockets for ropes with diameters of from 1/8 inch (3.2 mm) through 3 inches (77 mm); on ropes with larger (over 3 inches) diameters, the clear length must be a least 20 times the rope diameter. The test is considered valid only if failure occurs 2 inches (51 mm) or more from either of the sockets, or from the holding mechanism. The "Wire Rope Users Manual" specifications were fol- lowed for most of the testing. The exceptions were (1) a few 2-ft samples were tested to aid in the determination of modulus of elasticity, and (2) a series of tests were run over a range of stroke rates to determine the effect of this variable. EXPERIMENTAL RESULTS TYPICAL RESULTS There were eight series of rope samples run during the baseline testing. Of these samples, only the 80 samples that broke more than the standard two in from the sockets were used for the determination of breaking strength. However, samples that broke near the sockets could be used for calculation of modulus of elasticity and yield because these data are accumulated prior to the breaking point and are independent of behavior in the plastic region near the breaking point. The data from two tests are shown in tables 3 and 4. The stroke in inches is shown to be a function of time in seconds since the stroke was set at 1 in/min. This can be seen easily by comparing the stroke data with the time at 60-s intervals. The load in kips and the torque in kip- inches were measured by the machine at the designated time intervals. The torque in pound (force) feet was calculated from the torque in kip-inches. The elongation in inches was determined from the stroke, using a com- pliance factor determined by the machine configuration and the socket diameter. This factor multiplied by the load is subtracted from the stroke to give the elongation. The compliance factor takes care of any tension or compression in the machine parts, the grips, and the sockets. This is a significant correction as can be seen by comparing stroke with elongation. The stress in kips per square inch is calculated by dividing the load by the rope metallic area. The strain in percent inch per inch is calculated by dividing the elongation by the rope gauge length in inches and multiplying by 100. From the data in tables 3 and 4, the curves in fig- ures 2 and 3, respectively, were plotted. From every run made during the baseline testing, a table was generated and three curves were plotted. Table 3.-Typical baseline test on wire rope D Time, s Stress. kip/in Strain, pet in/in Torque, Ibf-ft Load, kips Elongation, in Stroke, in 1.5 . . 12.0 . 24.0 . 36.0 . 48.0 . 60.0 . 72.0 . 84.0 . 96.0 . 108.0 120.0 132.0 144.0 156.0 168.0 180.0 192.0 204.0 216.0 228.0 240.0 252.0 264.0 276.0 288.0 300.0 312.0 324.0 325.5 327.0 13.490 0.021 24.2 2.992 0.025 0.027 26.100 .167 47.6 5.789 .198 .203 44.382 .333 83.4 9.844 .397 .405 63.981 .497 121.1 14.191 .592 .603 82.926 .658 156.0 18.393 .784 .799 102.858 .826 194.4 22.814 .984 1.002 122.624 .990 229.3 27.198 1.179 1.201 140.906 1.154 262.3 31.253 1.374 1.399 157.534 1.317 293.3 34.941 1.568 1.596 171.740 1.480 319.6 38.092 1.763 1.793 183.693 1.651 340.9 40.743 1.967 1.999 193.602 1.817 358.3 42.941 2.164 2.198 201.533 1.982 372.5 44.700 2.361 2.396 208.030 2.146 385.0 46.141 2.556 2.593 213.206 2.313 391.6 47.289 2.756 2.793 217.556 2.481 399.3 48.254 2.956 2.994 220.694 2.646 402.8 48.950 3.152 3.191 223.665 2.815 407.6 49.609 3.354 3.393 226.032 2.979 409.7 50.134 3.549 3.589 227.687 3.145 411.9 50.501 3.747 3.787 229.504 3.313 414.8 50.904 3.947 3.987 230.771 3.482 417.5 51.185 4.147 4.188 232.146 3.651 416.3 51.490 4.349 4.390 232.809 3.814 416.3 51.637 4.543 4.584 233.855 3.983 416.0 51.869 4.745 4.786 234.238 4.148 415.0 51.954 4.941 4.982 234.842 4.319 415.8 52.088 5.145 5.186 235.063 4.483 413.8 52.137 5.341 5.382 235.176 4.507 413.8 52.162 5.369 5.410 235.063 4.527 414.0 52.137 5.393 5.434 From the plots of load versus elongation on fig- ures 24 and 3/4 and the data from the tables, the breaking strength and the breaking elongation can be determined. The breaking strength is defined as the maximum load that the rope attains. The breaking elongation is defined as the maximum elongation that the rope attains, which occurs when the rope breaks. The maximum load does not nec- essarily occur at the maximum elongation, as is shown in table 3. Figures 25 and 35 show plots of stress versus strain. The elastic region is the initial straight-line portion of the plot where stress is proportional to strain. The plastic region is the final part of the plot where the stress is no longer proportional to strain. The slope of the straight- line portion of a stress-strain curve is defined as the modulus of elasticity. It is equal to the stress divided by the strain and is in units of pounds per square inch. Because the stress-strain plots for many metals and for wire rope do not show a well-defined transition from elastic to plastic behavior, it is customary to define the yield stress by drawing a line parallel to the slope of the stress-strain plot and displaced 0.2 pet of the gauge length to the right. This line will intersect the curve in the plastic region. This point of intersection is defined as the yield stress. The strain at that point is the yield strain. Figures 2C and 3C show plots of torque versus load. As can be seen from the figures, torque is proportional to load almost to fracture. The slope of the torque-versus- load plot is called the Torque K. It has the units of pound (force) feet per kip. Table 4.-Typical baseline test on wire rope B Time, s Stress. kip/in Strain, pet in/in Torque, Ibf-ft Load, kips Elongation, in Stroke, in 1.5 .. 6.0 .. 12.0 . 18.0 . 24.0 . 30.0 . 36.0 . 42.0 . 48.0 . 54.0 . 60.0 . 66.0 . 72.0 . 78.0 . 84.0 . 90.0 . 96.0 . 102.0 108.0 114.0 120.0 126.0 132.0 138.0 144.0 150.0 156.0 162.0 168.0 174.0 180.0 186.0 192.0 198.0 204.0 207.0 13.051 0.041 188.3 11.578 0.024 0.031 25.607 .158 386.8 22.716 .092 .106 42.293 .315 647.6 37.518 .182 .206 55.289 .475 839.7 49.047 .275 .306 68.781 .635 1,045.8 61.016 .367 .406 83.099 .793 1,254.4 73.718 .459 .506 98.188 .946 1,478.3 87.103 .548 .603 112.892 1.108 1,694.6 100.147 .641 .705 126.713 1.262 1,895.6 112.408 .731 .802 139.875 1.421 2,088.9 124.084 .822 .901 152.155 1.588 2,267.0 134.978 .919 1.005 162.838 1.751 2,418.4 144.455 1.013 1.105 173.026 1.914 2,564.8 153.493 1.108 1.205 181.892 2.078 2,691.9 161.358 1.203 1.305 189.823 2.236 2,795.0 168.393 1.294 1.401 196.596 2.407 2,891.7 174.402 1.393 1.504 202.708 2.574 2,973.1 179.824 1.490 1.604 207.885 2.737 3,036.8 184.416 1.584 1.701 212.621 2.908 3,100.3 188.618 1.683 1.803 216.476 3.074 3,143.6 192.037 1.779 1.901 219.724 3.240 3,183.0 194.919 1.875 1.999 222.809 3.415 3,218.7 197.655 1.976 2.102 225.397 3.587 3,242.8 199.951 2.076 2.203 227.655 3.752 3,261.9 201.954 2.172 2.300 229.472 3.922 3,278.4 203.566 2.270 2.399 231.124 4.096 3,289.9 205.032 2.371 2.501 232.390 4.271 3,298.8 206.155 2.472 2.603 233.657 4.443 3,307.7 207.279 2.571 2.703 234.703 4.615 3,309.0 208.207 2.671 2.803 235.364 4.780 3,305.2 208.793 2.766 2.899 236.026 4.952 3,302.6 209.380 2.866 2.999 236.686 5.124 3,303.8 209.966 2.966 3.099 236.961 5.298 3,296.3 210.210 3.067 3.200 237.457 5.469 3,292.4 210.650 3.165 3.299 237.457 5.640 3,281.0 210.650 3.264 3.398 237.732 5.726 3,277.2 210.894 3.314 3.448 SUMMARY OF NORMAL BREAKS A normal break is defined as a break that occurs 2 in or more from the socket. Only data obtained with normal breaks were accepted for the measurement of breaking strength. The summaries of data for the eight series of rope tests are shown in tables 5 to 12. Also shown in the summary tables are the means, the standard deviations, and the percentage that the standard deviations are of the means. In table 13 the means, standard deviations, and the percent standard deviations of all of the ropes are shown for the breaking strength (load), the modulus of elasticity, the breaking stress, the yield stress, and the torque constant. It is apparent from examining the percent standard deviation columns that the precision is good for the measurement of load and torque. It is also apparent that any measurement involving elongation, such as modulus of elasticity, has poor precision, considering all of the data from a series. The measurement of stroke, elongation, and modulus of elasticity are discussed later. 240 7 ° D / □ D D D D D D D n 1 o o id / Yield, 191.9 kip/in Breaking stress, 2351 kip/in 2 / Modulus, 11.41 * I0 6 psi 2 3 4 5 ELONGATION, in KEY Y = 114.054827* X+ 8.310668 0.2-pct yield 2 3 STRAIN, pet in/in 20 30 40 LOAD, kips 50 60 Figure 2.-Typical test data, rope D. 240 200 240 160- 120 0.5 I dD dDooiddouj 1.0 1.5 2.0 2.5 ELONGATION, in 3.0 3.5 Yield, 182.3 kip/in* Breaking stress, 2377 kip/ in 2 Modulus, 8.90 « I0 6 ps. KEY •Y = 89.04544*X + 13.00276 0.2-pct yield 2 3 4 STRAIN, pet in/in 100 150 LOAD, kips 250 Figure 3.-Typical test data, rope B. 10 Table 5.-Summary of test series on rope A Sample length, ft 5.01 5.07 10.00 10.13 14.96 15.21 20.03 20.27 35.21 35.32 Mean .... SD Modulus of elasticity, 10 6 psi Break Yield Load, Elonga- Stress, Strain, Stress, kip/in Strain, kips tion, in kip/in 2 pet in/in pet in/in 92.06 2.78 228.00 4.62 188.00 2.41 92.38 2.61 228.80 4.28 183.70 2.03 92.04 5.04 288.00 4.20 183.90 2.03 91.09 5.07 225.60 4.18 191.90 2.44 89.50 6.84 221.70 3.81 185.20 2.30 91.09 7.76 225.60 4.21 186.90 2.27 91.16 9.82 225.80 4.09 182.30 1.93 91.04 9.76 225.50 4.01 187.30 2.19 90.06 16.48 223.10 3.90 185.50 2.14 90.96 16.93 225.30 3.99 183.90 1.96 91.14 NAp 225.74 4.13 185.86 2.17 .89 NAp 2.19 .23 2.78 .18 Torque K, Ibf-ft/kip Reel position, ft 8.48 9.29 9.50 8.89 9.43 9.49 9.77 9.59 9.87 9.90 9.42 .44 7.69 8.14 8.26 8.22 7.92 8.23 8.46 8.47 8.26 8.34 8.20 .24 2.9 251.0 116.8 226.5 13.7 240.0 264.4 132.7 203.0 39.7 NAp NAp SD . . pet 4.72 0.97 NAp 0.97 5.52 1.50 8.41 2.91 NAp NAp Not applicable. SD Standard deviation. Table 6.-Summary of test series on rope B Sample Modulus of elasticity, 10 6 psi Break Yield Torque K, Ibf-ft/kip Reel length, ft Load, kips Elonga- Stress, tion, in kip/in 2 Strain, pet in/in Stress. Strain, kip/in pet in/in position, ft 4.81 . . 4.82 . . 4.82 . . 5.06 . . 9.64 . . 10.02 . 14.64 . 14.71 . 19.60 . 20.17 . 34.88 . 35.00 . Mean SD.. 7.84 8.90 8.63 8.11 10.51 10.35 10.95 11.00 11.04 11.33 11.76 12.07 10.21 1.46 210.60 210.90 210.60 207.80 207.80 209.10 208.20 207.70 207.70 208.20 207.40 207.70 208.64 1.31 3.68 3.31 3.42 3.34 5.49 6.76 9.93 8.74 12.56 12.00 19.06 19.49 NAp NAp 237.30 237.70 237.30 234.30 234.30 235.70 234.70 234.20 234.10 234.70 233.80 234.20 235.19 1.43 6.37 2.28 5.91 5.50 4.75 5.62 5.66 4.95 5.34 4.96 4.55 4.63 5.04 1.03 188.30 182.30 185.30 185.10 185.70 184.70 182.00 185.30 183.10 185.10 182.90 183.50 184.44 1.77 2.85 2.10 2.22 2.79 2.20 2.24 2.06 2.10 2.06 2.06 1.69 1.74 2.18 .35 16.27 16.28 16.28 16.31 16.61 16.39 16.52 16.54 16.56 16.53 16.60 16.46 16.45 .13 54.58 244.54 250.37 154.56 183.72 98.74 212.88 43.75 231.21 167.89 231.21 17.92 NAp NAp SD . . pet 14.27 0.63 NAp 0.61 20.43 0.96 15.90 0.81 NAp NAp Not applicable. SD Standard deviation. Table 7.-Summary of test series on rope C 4.76 . . 4.98 . . 9.69 . . 9.98 . . 14.90 . 14.98 . 19.80 . 19.94 . 35.36 . 35.39 . Mean SD.. Sample Modulus of elasticity, 10 6 psi Break Yield Torque K, Ibf-ft/kip Reel length, ft Load, kips Elonga- Stress, tion, in kip/in 2 Strain, pet in/in Stress. Strain, kip/in pet in/in position, ft 9.34 9.65 10.70 10.94 12.71 11.74 11.97 11.02 12.49 12.48 11.30 1.18 160.38 159.65 158.79 158.33 158.45 158.48 158.09 158.38 157.45 157.74 158.57 .87 2.69 2.76 4.46 4.56 6.75 6.39 8.79 9.39 15.39 15.79 NAp NAp 254.30 253.10 251 .70 251.00 251.20 251.24 250.60 251.10 249.60 250.10 251.39 1.39 4.72 4.61 3.84 3.86 3.78 3.55 3.70 4.09 3.63 3.72 3.95 .40 212.60 207.90 214.20 213.60 210.40 211.90 211.40 214.20 209.50 209.50 211.52 2.17 2.32 2.23 2.09 2.05 1.74 1.93 1.88 2.04 1.80 1.79 1.99 .19 14.07 13.92 14.04 14.05 14.21 14.35 14.18 14.26 14.20 14.11 14.14 .13 101.6 38.6 145.6 172.1 158.9 70.1 193.6 88.4 334.9 299.1 NAp NAp SD . . pet 10.46 0.55 NAp 0.55 10.25 1.03 9.74 0.88 NAp NAp Not applicable. SD Standard deviation. 11 Table 8.-Summary of test series on rope D Sample Modulus of elasticity, Break Yield Torque K, Ibf-ft/kip Reel length, Load, Elonga- Stress, Strain, Stress, kip/in Strain, position, ft 10 6 psi kips tion, in kip/in 2 pet in/in pet in/in ft 1.88 9.22 52.60 1.29 237.20 5.72 184.20 2.20 8.16 172.6 4.85 10.82 52.37 2.95 236.10 5.07 189.30 1.95 8.39 176.9 5.09 10.98 52.20 3.22 235.30 5.26 186.40 1.88 8.25 182.7 9.81 11.45 51.66 4.54 232.90 3.86 192.60 1.80 8.14 136.2 9.93 11.41 52.16 5.39 235.20 4.53 191.90 1.81 8.16 67.9 15.02 11.77 52.17 8.58 235.20 4.76 191.60 1.75 8.32 23.7 19.96 11.89 52.02 10.46 234.50 4.37 192.00 1.72 8.28 152.1 20.00 11.77 52.21 11.35 235.40 4.73 193.60 1.81 8.14 294.4 29.93 12.40 51.69 15.62 233.00 4.35 188.90 1.68 8.40 47.1 30.16 12.02 51.83 16.08 233.70 4.44 191.60 1.73 8.26 268.6 Mean 11.37 52.09 NAp 234.85 4.71 190.21 1.83 8.25 NAp SD .89 .30 NAp 1.35 .53 2.99 .IB .10 NAp SD . . pet 7.84 0.57 NAp 0.58 11.26 1.57 8.26 1.20 NAp NAp Not applicable SD Standard deviation. Table 9.-Summary of test series on rope E 1.96 2.00 4.88 4.91 9.87 9.93 14.90 14.97 19.82 20.01 29.96 Mean SD SD . . pet Sample Modulus of elasticity, 1 6 psi Break Yield Torque K, Ibf-ft/kip Reel length, ft Load, kips Elonga- Stress, tion, in kip/in 2 Strain, pet in/in Stress, Strain, kip/in pet in/in position, ft 6.34 6.83 9.25 9.72 10.76 10.49 10.99 11.77 12.62 12.34 12.59 10.34 2.16 20.93 338.80 338.60 331.70 334.00 329.00 330.70 329.90 327.60 328.90 326.80 328.30 331.30 4.16 1.26 1.34 1.42 2.74 2.80 5.16 5.08 7.96 7.74 10.25 10.10 14.78 NAp NAp NAp 238.80 238.60 233.70 235.30 231.80 233.00 232.40 230.80 231.80 230.30 231.30 233.44 2.95 1.26 5.72 5.92 4.68 4.76 4.33 4.29 4.54 4.31 4.31 4.21 4.11 4.65 .61 13.13 193.30 185.30 181.20 175.50 180.40 185.10 179.60 177.40 175.50 173.20 177.40 180.35 5.76 3.19 2.98 2.61 2.10 1.92 1.82 1.90 1.81 1.65 1.56 1.56 1.58 1.95 .46 23.40 19.13 19.53 20.01 19.90 20.44 20.30 20.51 20.31 20.65 20.71 20.54 20.18 .50 2.46 147.5 117.5 3.0 173.0 124.5 73.5 108.0 138.5 89.5 159.5 21.5 NAp NAp NAp NAp Not applicable. SD Standard deviation. Table 10.-Summary of test series on rope F Sample Modulus of elasticity, 10 6 psi Break Yield Torque K, Ibf-ft/kip Reel length, ft Load, kips Elonga- Stress, tion, in kip/in 2 Strain, pet in/in Stress, Strain, kip/in pet in/in position, ft 1.94 2.17 2.18 5.20 5.38 9.91 10.27 14.92 15.34 19.94 20.28 30.13 30.23 Mean SD SD . . pet 5.66 5.93 5.17 8.46 9.34 10.04 9.15 10.31 10.03 10.41 10.52 10.81 11.21 9.00 2.08 23.12 352.40 345.50 348.90 347.70 347.00 345.20 346.70 347.80 348.90 343.40 346.30 343.70 344.60 346.85 2.53 0.73 1.40 1.77 1.96 3.34 3.39 5.16 5.94 8.55 8.79 11.09 11.19 16.08 16.68 NAp NAp NAp 218.20 213.90 216.10 215.30 214.90 213.80 214.70 215.40 216.60 212.60 214.40 212.90 213.40 214.78 1.57 0.73 6.02 6.10 6.79 5.05 4.97 4.34 4.82 4.78 4.78 4.63 4.60 4.44 4.60 5.07 .75 14.77 165.70 167.90 160.80 164.20 157.30 162.50 167.10 163.20 166.60 164.70 164.30 162.90 159.40 163.58 3.07 1.88 3.02 2.79 2.69 2.10 1.82 1.80 1.99 1.80 1.87 1.72 1.73 1.66 1.59 2.04 .47 23.15 13.73 14.31 13.77 14.20 14.35 14.39 14.13 14.23 14.01 14.40 14.18 14.28 14.47 14.19 .23 1.62 209.97 38.25 35.08 42.92 3.08 217.07 11.75 230.65 120.09 249.24 120.09 162.42 93.92 NAp NAp NAp NAp Not applicable. SD Standard deviation. 12 Table 1 1 .-Effect of stroke rate, rope G test series Stroke, Sample length, ft Modulus of elasticity, Mpsi Break Yield Torque K, in/min Load, Kips Elonga- Stress, tion, in kip/in Strain, pet in/in Stress, Strain, kip/in pet in/in Ibf-ft/kip 0.0625 0.1250 1.0000 8.0000 16.0000 Mean SD SD pet . . NAp Not applicable. 15.08 15.05 15.10 15.07 15.07 15.07 15.08 15.08 15.06 NAp NAp NAp 12.16 12.17 12.20 12.49 12.56 12.57 12.83 13.08 13.19 12.58 .38 3.05 137.93 135.93 137.96 133.98 136.98 136.54 139.38 136.10 137.37 136.91 1.53 6.09 4.40 4.17 4.32 3.91 4.02 4.00 4.13 3.68 3.72 4.04 .25 1.12 218.70 215.50 218.70 212.40 217.00 216.50 221.00 215.80 217.80 217.04 2.44 1.12 2.43 2.31 2.38 2.16 2.22 2.21 2.28 2.03 2.06 2.23 .13 6.05 189.60 191.20 191.90 190.10 192.80 193.30 195.20 192.90 194.30 192.37 1.85 0.96 1.67 1.68 1.68 1.64 1.64 1.64 1.63 1.59 1.58 1.64 .04 2.19 9.53 9.56 9.33 9.49 9.36 9.58 9.59 9.52 9.51 9.50 .09 0.97 SD Standard deviation. Table 12.-Test series on zinc-filled sockets, rope H 5.08 10.11 20.12 20.15 30.21 Mean SD SD . . pet Sample Modulus of elasticity, 10 6 psi Break Yield Torque K, Ibf-ft/kip Reel length, ft Load, kips Elonga- Stress, tion, in kip/in 2 Strain, pet in/in Stress, Strain, kip/in pet in/in position, ft 8.59 10.90 11.30 11.89 12.07 10.95 1.40 12.78 210.20 207.80 208.10 205.70 206.40 207.64 1.74 0.84 3.60 5.83 11.92 10.50 17.81 NAp NAp NAp 237.00 234.20 234.60 231.90 232.60 234.06 1.98 0.85 5.90 4.80 4.94 4.34 4.91 4.98 .57 11.43 186.80 183.30 184.90 182.60 182.50 184.02 1.83 0.99 2.27 1.81 1.80 1.66 1.64 1.84 .25 13.88 16.42 16.52 16.55 16.50 16.73 16.54 .11 0.69 NAp NAp NAp NAp NAp NAp NAp NAp NAp Not applicable. SD Standard deviation. Table *3.-Baseline tensile test summary Rope series Breaking load Diam, in Mean, kips SD, kips SD, pet Modulus of elasticity Mean, SD^ STJ" pet Breaking stress Yield stress Torque K 10 6 psi 10 6 psi Mean SD, kip/in kip/in SD, pet Mean SD, kip/in kip/in 2 SD, pet Mean, Ibf-ft kip SD, Ibf- ft/kip SD, pet A B C D E F G H 1 1-1/2 1-1.4 3/4 1-7/8 2 1-1/4 1-1/2 91.14 208.64 158.57 52.09 331.30 346.85 136.91 207.64 0.89 1.31 .87 .30 4.16 2.53 1.53 1.74 0.97 .63 .55 .57 1.26 .73 1.12 .84 9.42 10.21 11.30 11.37 10.34 9.00 12.58 10.95 0.44 1.46 1.18 .89 2.16 2.08 .38 1.40 4.72 14.27 10.46 7.84 20.93 23.12 3.05 12.78 225.74 235.19 251.39 234.85 233.44 214.78 217.04 234.06 2.19 1.43 1.39 1.35 2.95 1.57 2.44 1.98 0.97 .61 .55 .58 1.26 .73 1.12 .85 185.86 184.44 211.52 190.21 180.35 163.58 192.37 184.02 2.78 1.77 2.17 2.99 5.76 3.07 1.85 1.83 1.50 .96 1.03 1.57 3.19 1.88 .96 .99 8.20 16.45 14.14 8.25 20.18 14.19 9.50 16.54 0.24 .13 .13 .10 .50 .23 .09 .11 2.91 .81 .81 1.20 2.46 1.62 .97 .69 SD Standard deviation. CONSTRUCTION STRETCH Wire rope stretches under load. This stretch comes from two sources, elastic and constructional. The elastic stretch is reversible, and the rope recovers to its original length when the load is removed. The construction stretch is not reversible. Construction stretch occurs in new rope and happens when a load is first applied. The wires and strands are first seated, then act in a constricting manner to compress the core permanently. Construction stretch is more pronounced in fiber-core ropes than in wire-rope- core or strand-core ropes. When a tensile test is made on a rope, and the con- struction stretch has not been removed, it adds to the 13 elongation on the rope during the initial loading. This will give an S-shaped stress-strain curve, with sometimes only a small central linear portion. An example is shown in figure 44. All of the rope A series and part of the rope B series were run in this manner, resulting in S-shaped curves. During the rope B series, it was decided to attempt to remove the construction stretch prior to the test. It was observed from examining the stress-strain curves that the linear portion began after the rope was loaded to about 20 pet of the breaking strength. Consequently, the ropes were loaded to 20 pet of the breaking strength and held for 10 min or until they stopped stretching. Then the load was removed, and the test was made under normal pro- cedures. The results are shown in figure 4B. This stress-strain plot does not have an S-curve and is linear from the beginning. For comparison, the curves 240 200 - 160 120 80 40 ,J a a a d oc Yield, 188 3 kip/irT f i Breaking stress, 2373 kip/in 2 / Modulus, 7.84* I0 6 psi KEY Y= 78.44I975*X- 19.60323 from figures 44 and 4B are plotted together in figure 5. All subsequent tests were made following this procedure for removing construction stretch. None of the following tests showed the S curves. BREAKING LOAD VERSUS GAUGE LENGTH Breaking load was plotted against gauge length to determine the effect of sample length on breaking load (fig. 6). The plots show a definite effect of length on breaking strength. The shorter samples have higher break- ing strengths than the longer samples. There seems to be little effect on samples of 15 ft and longer. However, the 2-ft samples have much higher strength. Even the 5- and 10-ft samples show higher strength. This is true for the 3/4-in-diameter samples as well as the 2-in-diameter samples. The reason for this phenomenon is not known. However, it can be hypothesized that shorter ropes with rigidly attached sockets form a more rigid structure in the test machine, thus exhibiting higher "system strength." BREAKING LOAD VERSUS REEL POSITION The samples were cut from the reel in a random order to determine whether any variations in properties existed along the length of the rope. When the variables were plotted against reel position, there was no correlation shown between any factor and the position on the reel. The most important variable in this respect is the breaking strength. Figure 7 shows two plots of breaking strength against reel position, for ropes B and D. As can be seen, there is no correlation. The results are the same for the other samples. 240 200- 160 i20 80 40 1 1 // 1 LoOODOlOaOCEDI B /V DDDQ - A°\ Ay Yield, 185 3 kip/in z P / Breaking stress, 237.3 kip/in 2 ~~ - . Jl Modulus, 8 63* I0 6 psi _ - // - f ' KEY - P/ ■ Y = 86.33028I*X +11.294128 - f / 0.2-pct yield ft '// " f/ - 1 1 1 I i I i I 2 3 4 5 6 7 STRAIN, pet in /in Figure 4. -Stress versus strain, rope B. A, 4.81 3-ft sample; B, 4.81 8-ft sample. 240 200 I 60 JC i, i , i ■ -1.4 -0.6 -0.2 0.2 0.6 LOG STROKE, in/min 1.0 1.4 Figure 8.-Effect of log stroke rate, rope G. A, Elongation; 8, modulus; C, breaking load. EFFECT OF GAUGE LENGTH ON MODULUS OF ELASTICITY When the data tables (tables 5-12) are examined, it becomes apparent that the columns involving strain measurements have high errors compared with the col- umns involving load or torque measurements. The modu- lus of elasticity, the breaking strain, and the yield strain all show these high errors. And yet, when samples of the same length are compared, the values are shown to be close to each other. Plots of modulus of elasticity, breaking strain, and yield strain against gauge length all show correlation, although not necessarily linear correla- tion. Figure 9 shows plots of modulus of elasticity versus gauge length for the various test ropes. These plots show 16 10.4 . 1 1 1 1 1 1 1 lo. - B ^__^. o - - nS*^ o 1 D / ~ : o/ \ - /d la Y = 0.l/(7.85005E-03 + 0.233202/X) J : 1 1 i _ j : F "i r Y = 0.l/(8.4877E-03*0.23029/X) J I I L 50 100 150 200 250 300 350 400 450 GAUGE LENGTH, in 50 100 150 200 250 300 350 400 450 500 GAUGE LENGTH, in Figure 9.-Modulus versus gauge length for various ropes. A, Rope A; B, rope B; C, rope C; D, rope D; E. rope E; F, rope F; G, rope H. 17 that the modulus of elasticity is lowest for the 2-ft samples and highest for the 30- and 35-ft samples, initially in- creasing rapidly in value with gauge length, then leveling off at the higher gauge lengths. The tensile machine does not measure gauge length directly. During the initial calibration of the machine, very precise measurements were made of the elongation and compression of the machine components over the full range of load capability. These components included the columns, heads, grips, pins, and sockets. The deflection data are contained in the data logging program. The pro- gram subtracts from the movement of the actuator the appropriate deflection at the sensed load for all of the involved components. The different grips and sockets for each rope size are included individually in the program. After pretest stretching, the load is removed, the gauge length is measured manually, and the actuator position is set to zero. Consequently, a very accurate and repro- ducible measurement is made of the change in distance between the socket ends during a run, which is nominally the gauge length for a solid sample. In the case of a socketed wire rope, the wire is not fastened rigidly to the socket end. The rope is broomed and cast with epoxy or zinc in the cone of the socket. Thus, the compressibility of the material in the socket becomes a variable. If an assumption is made that the broomed end of the rope can stretch and move to some degree out of the socket, then an explanation can be made for the high errors of the elongation measurements. There is some physical justification for this assumption. Markers placed on the socket ends with a pointer on the rope showed some movement of the rope end out of the socket when a load was applied. The rope end moved back into the socket when the load was removed. Further, the epoxy resin has a very low modulus of compression. Zinc has a higher modulus of compression, but it is still much lower than that of the high-carbon steel of which the wires are made. Consider the following. The broomed end in each socket moves out of the socket by an amount proportional to the load. Because the tensile machine measures the distance between the socket ends, it determines the sum of the lengths that each broom pulls out plus the elongation of the original length of rope measured between the sockets (the gauge length). The amounts that the broomed ends move out are independent of the gauge length of the sample. Consequently, the percentage error becomes less as the gauge length increases. It is possible to calculate this error if elongation at a constant load is plotted against gauge length for different sample lengths. For a solid rod, elongation would be directly proportional to gauge length within the elastic range. For a wire rope, elongation should still be directly proportional to gauge length, but with an intercept on the y-axis (elongation). The intercept represents the error caused by the broom pullout. This error is directly proportional to load while within the elastic region of the stress-strain plot. The values for elongation at a constant load cannot be taken directly from the data tables. If the B plots in fig- ures 2 and 3 are examined, it can be seen that the slopes for the stress-strain curves do not go through the origin of the coordinates, because of the preload put on the sample and the subsequent zeroing of the stroke. This can be al- lowed for by taking the slope of each stress-strain plot and mathematically forcing it through the origin. The slope of the stress-strain curve is the modulus of elasticity and is given in column 2 of the data tables (tables 5-11). Then, modulus = stress/strain, strain = stress/modulus, strain = elongation/gauge, and elongation = strain x gauge. (1) (2) (3) (4) Thus, it is possible to calculate elongation at a given strain, knowing the modulus of elasticity. These calcu- lations are shown for a given stress of 100,000 psi in tables 14-20. The given stress of 100,000 psi is approxi- mately at the midpoint of the elastic region of the stress- strain plot. As is demonstrated in the tables, strain is calculated from the modulus and the given stress using equation 2. Then, elongation is calculated from the strain and gauge using equation 4. Table 1 4.-Effect of sample length on modulus and elongation at 100,000-psi stress for rope A Sample Mod ulus of elasticity, 10 6 psi Strain, length, Calcu- Differ- Differ- Elonga- ft Actual lated ence ence, squared in/in tion, in 4.90 .. . 8.26 8.257 -0.003 0.00001 0.01211 0.712 5.01 . . . 8.48 8.293 -.187 .0349 .01179 .709 10.00 . . 9.50 9.195 -.305 .0931 .01053 1.263 10.13 . . 8.89 9.208 .318 .1010 .01125 1.367 14.96 . . 9.43 9.540 .110 .0122 .01060 1.904 15.14 . . 9.89 9.549 -.341 .1164 .01011 1.837 15.21 . . 9.49 9.552 .062 .0039 .01054 1.923 20.00 . . 9.57 9.726 .156 .0243 .01045 2.508 20.03 . . 9.77 9.727 -.043 .0019 .01024 2.460 20.27 . . 9.59 9.733 .143 .0205 .01043 2.536 35.08 . . 10.22 9.973 -.247 .0608 .00978 4.119 35.21 . . 9.87 9.975 .105 .0109 .01013 4.281 35.32 . . 9.90 9.976 .076 .0057 .01010 4.281 Mean . 9.45 NAp NAp NAp NAp NAp SS ... NAp NAp NAp .4856 NAp NAp Variatio n NAp NAp NAp .0405 NAp NAp SD ... .58 NAp NAp .2012 NAp NAp SD.. pet . 6.09 NAp NAp 2.1286 NAp NAp NAp N ot applicable. SD S tandard deviation. SS S urn of squares. NOTE.-fv lodulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). 18 Table 15.-Effect of sample length on modulus and elongation at 100,000-psi stress for rope B Table 17.-Effect of sample length on modulus and elongation at 100,000-psi stress for rope D Sample Modulus of elasticity, 10 6 psi Strain, Elonga- Sample length, Modulus of elasticity, 10 6 psi Strain, length, Calcu- Differ- Differ- Calcu- Differ- Differ- Elonga- ft Actual lated ence ence, squared in/in tion, in ft Actual lated ence ence, squared in/in tion, in 4.81 . . . 7.84 8.410 0.570 0.3252 0.01276 0.736 1.88 .. . 9.22 8.595 -0.625 0.3910 0.01085 0.245 4.82 . . . 8.90 8.416 -.484 .2341 .01124 .650 4.85 .. . 10.82 10.652 -.168 .0284 .00924 .538 4.82 . . . 8.63 8.416 -.214 .0457 .01159 .670 4.86 .. . . 10.82 10.655 -.165 .0272 .00924 .539 5.06 .. . 8.11 8.554 .444 .1970 .01233 .749 4.91 . . . 10.75 10.671 -.079 .0062 .00930 .548 9.64 .. . 10.51 10.136 -.374 .1400 .00951 1.101 5.09 .. . 10.98 10.728 -.252 .0634 .00911 .556 10.02 . . 10.35 10.215 -.135 .0182 .00966 1.162 9.81 . . . 11.45 11.535 .085 .0073 .00873 1.028 14.64 . . 10.95 10.896 -.054 .0029 .00913 1.604 9.93 . . . 11.41 11.546 .136 .0186 .00876 1.044 14.71 . . 11.00 10.904 -.096 .0093 .00909 1.605 15.01 . . 11.84 11.869 .029 .0008 .00845 1.521 19.60 . . 11.04 11.310 .270 .0730 .00906 2.130 15.02 . . 11.77 11.869 .099 .0098 .00850 1.531 20.17 . . 11.33 11.346 .016 .0003 .00883 2.136 19.96 . . 11.89 12.031 .141 .0200 .00841 2.014 34.88 . . 11.76 11.895 .135 .0181 .00850 3.559 20.00 . . 11.77 12.032 .262 .0688 .00850 2.039 35.00 . . 12.07 11.897 -.173 .0298 .00829 3.480 20.07 . . 12.19 12.034 -.156 .0243 .00820 1.976 Mean . 10.21 NAp NAp NAp NAp NAp 20.09 . . 11.86 12.035 .175 .0305 .00843 2.033 SS . . . NAp NAp NAp 1.0936 NAp NAp 29.88 . . 12.43 12.200 -.230 .0530 .00805 2.885 Variatio n NAp NAp NAp .0994 NAp NAp 29.93 . . 12.40 12.200 -.200 .0399 .00806 2.896 SD. . . 1.46 NAp NAp .3153 NAp NAp 30.16 . . 12.02 12.203 .183 .0335 .00832 3.011 SD.. Mean . 11.48 NAp NAp NAp NAp NAp SS .. . NAp NAp NAp .8226 NAp NAp pet . . 14.27 NAp NAp 3.0889 NAp NAp Variation NAp NAp NAp .0548 NAp NAp NAp N ot applicable. SD ... .81 NAp NAp .2342 NAp NAp SD S tandard deviation. SS S urn of squares. SD .. pet . . 7.09 NAp NAp 2.0406 NAp NAp NOTE.-K lodulus of elasticity = = 0.1/(9.68819E-03 + 0.142489/X). NAo N ot applicab e. Table 16.-Effect of sample length on modulus and elongation at 100,000-psi stress for rope C SD Standard deviation. SS Sum of squares. NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). Sample Modulus of elasticity, 10 6 psi Table 18.-Effect of sample length on modulus and length, Calcu- Differ- Differ- Strain, Elonga- elongation at 100,000-psi stress for rope E ft lated in/in squared Sample length, Modulus of elasticity, 10 6 psi Strain, 4.76 . . . 9.34 9.002 -0.338 0.1143 0.01071 0.612 Calcu- Differ- Differ- Elonga- 4.84 . . . 8.61 9.049 .439 .1929 .01161 .675 ft Actual lated ence ence, in/in tion, in 4.98 .. . 9.65 10.70 9.129 10.727 -.521 .027 .2710 .0007 .01036 .00935 .619 1.087 squared 9.69 . . . 1.96 .. . 6.34 6.219 -0.121 0.0146 0.01577 0.371 9.98 .. . 10.94 10.785 -.155 .0239 .00914 1.095 2.00 .. . 6.83 6.287 -.543 .2945 .01464 .351 14.98 . . 11.74 11.477 -.263 .0690 .00852 1.531 4.88 . . . 9.25 9.199 -.051 .0026 .01081 .633 19.80 . . 11.97 11.847 -.123 .0152 .00835 1.985 4.91 . . . 9.72 9.217 -.503 .2529 .01029 .606 19.94 . . 11.02 11.855 .835 .6973 .00907 2.171 9.87 . . . 10.76 10.985 .225 .0506 .00929 1.101 19.98 . . 11.95 11.857 -.093 .0086 .00837 2.006 9.93 . . . 10.49 10.998 .508 .2577 .00953 1.136 34.81 . . 12.26 12.381 .121 .0146 .00816 3.407 14.90 . . 10.99 11.737 .747 .5586 .00910 1.627 34.83 . . 12.25 12.381 .131 .0172 .00816 3.412 14.97 . . 11.77 11.745 -.025 .0006 .00850 1.526 34.95 . . 12.36 12.384 .024 .0006 .00809 3.393 19.82 . . 12.62 12.142 -.478 .2281 .00792 1.885 35.07 . . 12.64 12.386 -.254 .0645 .00791 3.329 20.01 . . 12.34 12.155 -.185 .0344 .00810 1.946 35.36 . . 12.49 12.392 -.098 .0096 .00801 3.397 29.85 . . 12.57 12.584 .014 .0002 .00796 2.850 35.39 . . 12.48 12.393 -.087 .0076 .00801 3.403 29.96 . . 12.59 12.588 -.002 5E-06 .00794 2.856 Mean . 11.36 NAp NAp NAp NAp NAp Mean . 10.52 NAp NAp NAp NAp NAp SS .. . NAp NAp NAp 1.5069 NAp NAp SS .. . NAp NAp NAp 1.6948 NAp NAp Variatio n NAp NAp NAp .1076 NAp NAp Variatio n NAp NAp NAp .1541 NAp NAp SD. .. 1.28 NAp NAp .3281 NAp NAp SD . .. 2.16 NAp NAp .3925 NAp NAp SD.. pet . . 11.27 NAp NAp 2.8880 NAp NAp SD .. pet . . 20.54 NAp NAp 3.7303 NAp NAp NAp N ot applicable. NAp N ot applicable. SD S tandard deviation. SD S tandard deviation. SS S jm of squares. SS S jm of squares. NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). 19 Table 19.-Effect of sample length on modulus and elongation at 100,000-psl stress for rope F Sample Modulus of elasticity, 10 6 psi Strain, length, Calcu- Differ- Differ- Elonga- ft Actual lated ence ence, squared in/in tion, in 1.94 .. . 5.66 5.441 -0.219 0.0481 0.01767 0.411 2.17 . . . 5.93 5.770 -.160 .0256 .01686 .439 2.18 . . . 5.17 5.783 .613 .3763 .01934 .506 5.20 .. . 8.46 8.211 -.249 .0618 .01182 .738 5.38 .. . 9.34 8.295 -1.045 .0910 .01071 .691 9.91 . . . 10.04 9.593 -.447 .1998 .00996 1.184 10.18 . . 8.81 9.641 .831 .6898 .01135 1.387 10.27 . . 9.15 9.656 .506 .2560 .01093 1.347 14.80 . . 10.89 10.220 -.670 .4484 .00918 1.631 14.92 . . 10.31 10.231 -.079 .0062 .00970 1.737 15.34 . . 10.03 10.268 .238 .0568 .00997 1.835 19.94 . . 10.41 10.582 .172 .0295 .00961 2.299 20.28 . . 10.52 12.600 .080 .0064 .00951 2.313 30.13 . . 10.81 12.959 .149 .0223 .00925 3.345 30.23 . . 11.21 12.962 -.248 .0616 .00892 3.236 Mean . 9.12 NAp NAp NAp NAp NAp SS . . . NAp NAp NAp 3.3796 NAp NAp Variatio n NAp NAp NAp .2414 NAp NAp SD... 1.99 NAp NAp .4913 NAp NAp SD .. pet . . 21.82 NAp NAp 5.3897 NAp NAp NAp Not applicable. SD Standard deviation. SS Sum of squares. NOTE.-Modulus of elasticity = 0.1/(9.68819E-03 + 0.142489/X). Table 20.-Effect of sample length on modulus and elongation at 100,000-psi stress for rope H Sample Modulus of elasticity, 10 6 psi Strain, length, Calcu- Differ- Differ- Elonga- ft Actual lated ence ence, squared in/in tion, in 2.06 .. . 6.12 5.787 -0.333 0.1106 0.01634 0.404 2.06 .. . 5.15 5.787 .637 .4062 .01942 .480 5.06 .. . 8.55 8.638 .088 .0077 .01170 .710 5.08 .. . 8.59 8.649 .059 .0035 .01164 .710 10.10 . . 10.38 10.391 .011 .0001 .00963 1.168 10.11 . . 10.90 10.394 -.506 .2564 .00917 1.113 20.12 . . 11.30 11.566 .266 .0705 .00885 2.137 20.15 . . 11.89 11.568 -.322 .1040 .00841 2.034 30.16 . . 11.90 12.021 .121 .0147 .00840 3.041 30.21 . . 12.07 12.023 -.047 .0022 .00829 3.003 Mean . 9.69 NAp NAp NAp NAp NAp SS ... NAp NAp NAp .9761 NAp NAp Variatio n NAp NAp NAp .1085 NAp NAp SD... 2.49 NAp NAp .3293 NAp NAp SD.. pet . . 25.71 NAp NAp 3.4004 NAp NAp NAp N ot applicable. SD S landard deviation. SS S jm of squares. NOTE.-N lodulus of elasticity = = 0.1/(9.68819E-03 + 0.142489/X). Plots of elongation versus gauge for the test ropes are shown in figure 10. As predicted, elongation is a linear function of gauge length with an intercept off the origin. The intercept is the sum of the amounts of the pullout of each broomed end at a stress of 100,000 psi. In plot A, which shows a plot for the rope A series samples, the equation of the slope is given as Y = 9.68819E-03 * X + 0.142489, (5) where Y = elongation, in, and X = gauge length, in. If the elongation (Y) is divided by the gauge length (X), the strain (S) is calculated as per equation 3. Equation 5 becomes where S = 9.68819E-03 + 0.142489/X, (6) S = strain, in/in. If the stress is divided by the strain (S), the modulus of elasticity (Mod) is calculated as per equation 1. Equa- tion 6 becomes Mod = 100,000/(9.68819E-03 + 0.142489/X), (7) where Mod = modulus of elasticity, psi. If equation 7 is divided by 1,000,000, the modulus of elasticity is converted from pounds per square inch to mil- lion pounds per square inch. Equation 7 then becomes Mod = 0.1/(9.68819E-03 + 0.142489/X). (8) Plots of modulus of elasticity in million pounds per square inch versus gauge length in inches are given in fig- ure 9 for all of the baseline test series. Also shown in the plots are the equations for the modulus of elasticity devel- oped as in equation 8. The curves shown were not deter- mined by curve fitting. These curves are derived from the elongation data for each series of tests and calculated as shown above in equations 5 through 8. The linearity of the elongation-versus-gauge-length plots and the positive intercepts prove the hypothesis that there is a constant error in elongation measurement that is pro- portional to load and independent of gauge length. r . r he fit of the data points to the calculated equations for modulus of elasticity on figure 9 is further proof of the hypothesis. The modulus of elasticity for rope A can be calculated using equation 8 and the gauge length data shown in ta- ble 14. The calculated values can be compared with the experimental values. The standard deviation for regression of the experimental data about the calculated curve is shown at the bottom of column 5 of table 14. This is much lower than the standard deviation for the experi- mental data (column 2), without considering the effects of gauge length. The same is true for the other series (tables 15-20). One way to determine strain accurately would be to mechanically mount an elongation measuring device such as the one developed by Versuchsgrube Tremonia (3). This procedure is generally undesirable because it would 20 Y = 7.96601 E- 03 *X* 0.082774 J I I I I I 1 1 F i i i i i \ is) s. 3" ^ f? CO -1 O 5" O ■h m D c > r- O o DO 3 m O -< m 3 S\ ^> Ok -A? 3 / 4fi(P^ "^ 5°* V \«V ^«y v**^/ v Z>'J> % 4,0* .«iif ♦U *•««>' »• A * ^ -J 1*°* ^ 4? »i^* > ^"5 ,**.*.• v " 5T ..Jitf* *> P, \/ .•* • "Pa a* *- "£*. a* ♦ f\ 'b^ ^V* • /\ : -W'° ****** : -? >bV Vw/ ° o A *^ f *\ ° ^^^^ °o, ^' :^^^: ^ 'II: W^ HECKMAN IXl BINDERY INC. |M| m, FEB 91 N. MANCHESTER, INDIANA 46962 V 4*'% ■° -^ait. o At^^.^% cP*-^«it% ^sXfc/* til' A.W ^i* • it , ^°%. <^. f«..„o A * A ^