‘4 ”.5?“ a 2:04 o 2.: .9... tin! ,. l . SE... 1.5... .4.~.\.......z:..¢... “win . «.39.» swan innin- ‘zz‘. I . 4 .1‘ L1. ‘41.... .8" .17}. . 9....9hxaV .2... , . 5.1.. ..........3s.. 4 .«An .Fnh "a. 22. s..- 1l1$ss..i£..... . zapzliialiiunau? x3359... rapist: . .. 355......»Suiikil. 2,. .21..l.t!.-..... v.14; 3879.“ IIIIIIIIIIIIIIIIIIIIIIIIIIIII 31100293 LIBRARY Michigan State University This is to certify that the thesis entitled EXAMINATION OF INSTRUMENTED SHIPPING BOX TO EVALUATE DYNAMIC COMPRESSION FORCE DURING TRANSPORTATION VIBRATION presented by David A1an Leinberger has been accepted towards fulfillment of the requirements for M. S. degree inSchool of Packaging Mflé r6 Major profe% Date Mr/fé’ / / 0.7639 MS U is an Affirmative Action/Equal Opportunity Institution PLACE iN RETURN BOX to remove We checkout from your record. TO AVOID FINES return on or before date duo. DATE DUE DATE DUE DATE DUE L l—Tll l MSU to An Affirmative Action/Equal Opportunity institution cmmut EXAMINATION OF INSTRUMENTED SHIPPING BOX TO EVALUATE DYNAMIC COMPRESSION FORCE DURING TRANSPORTATION VIBRATION By David Alan Leinberger A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1993 Paul Singh, Ph.D. ABSTRACT EXAMINATION OF INSTRUMENTED SHIPPING BOX TO EVALUATE DYNAMIC COMPRESSION FORCE DURING TRANSPORTATION VIBRATION By David Alan Leinberger For years, packaging engineers have designed corrugated fiberboard containers to provide stacking strength to support the static load of the boxes stacked on top. Even with safety factors used to account for loss in strength due to humidity, temperature, creep, stacking pattern variations, etc., corrugated boxes still fail. One unknown variable has been the variation in compression force experienced by boxes when they are vibrated during transportation. A self-contained compression recorder was built, and proven to accurately measure dynamic force during vibration. This system was used in simulated transportation environments with varying loads using five different random vibration spectra. The maximum compression occurs to the bottom box in a stack. In simulated vibration tests, 99.5% of the force readings were below 1.2 to 5.2 times the weight of the static load. The maximum measured force was about 9.5 times the weight of the static load. Copyright by David Alan Leinberger 1993 In memory of my late mother, Joan Leinberger, whose love and support continue to inspire me beyond words. ACKNOWLEDGMENTS I would like express my sincere thanks to the members of my graduate committee, Dr. 5. Paul Singh, Dr. Gary Burgess, and Dr. Galen Brown. Thanks to Dennis Young, Dale Root and especially Chuck Pierce at Lansmont as well as Mike Bogar and Bill Vertner at Tektronix for the use of their testing equipment. Thanks to Bernard Fehr for his assistance with electronics and software. Thanks to A1 V055 and Mark Kerr at IBM for sharing their knowledge and advice. I would also like to thank the Consortium of Distribution Packaging for the funding which made this research possible. Finally, I am especially thankful to my father, Ken Leinberger, and my sister and brother-in-law, Kelly and Mark Allison for their guidance and support. TABLE OF CON TENTS List of Tables ................................................................................... List of Figures ................................................................................. List of Abbreviations ..................................................................... 1.0 Introduction ........................................................................ 2.0 The Data Acquisition System ........................................... 2.1 Accuracy of ISB ...................................................... 3.0 Experimental Design ......................................................... 4.0 Data and Results ................................................................ 5.0 Summary and Conclusions .............................................. 6.0 Recommendations ............................................................. List of References ........................................................................... Appendix A Calculating Force Using F = m(1+A) ............. Appendix 5 Complete Data for Composite Truck Spectrum, Level 1 ............................................. iii 18 32 45 47 SO LIST OF TABLES Table I 2 3 4. 5 6 7 Calculated vs. Measured Peak Force Using Lead Weights ........... Calculated vs. Measured Peak Force Using Boxes ......................... Data: Truck Composite Spectrum, Assurance Level 1 (ASTM).... Data: Truck Composite Spectrum, Assurance Level 2 (ASTM).... Data: Rail Composite Spectrum, Assurance Level 1 (ASTM) ....... Data: Inter-modal Spectrum (AAR) .................................................. Data: Truck Composite Spectrum, (Singh and Marcondes) .......... B-l. Complete Data: Truck Composite Spectrum, Assurance Level 1. iv Page 17 17 38 4O 42 50 LIST OF FIGURES Figure Page 1. Drawing of Instrumented Shipping Box (ISB) ............................... 5 2. Accuracy: Static Load = 0 lb .............................................................. 8 3. Accuracy: Static Load = 3251b .......................................................... 9 4. Example of Maximum Sampling Error ........................................... 11 5. Force vs. Deflection Curve for One Shear Beam ............................ 13 6. Comparison of Accuracy Before and After Random Vibration. 15 7. ISB Location Test ................................................................................ 19 8. PSD: Truck Composite Spectrum, Assurance Level 1 (ASTM)... 20 9. PSD: Truck Composite Spectrum, Assurance Level 2 (ASTM)... 21 10. PSD: Rail Composite Spectrum, Assurance Level 1 (ASTM) ....... 22 11. PSD: Inter-modal Spectrum, (Assoc. of American Railroads) ..... 23 12. PSD: Truck Composite Spectrum, (Singh and Marcondes) ......... 24 13. Drawing of Test Setup for Resonance Searches ............................. 26 14. Resonance Search for 109 lb Load .................................................... 27 15. Resonance Search for 2171b Load .................................................... 28 16. Resonance Search for 325 lb Load .................................................... 29 17. Resonance Search for 426 lb Load .................................................... 30 18 . Simulated Shipping Test Setup ....................................................... 31 19. Dynamic Force: Truck Composite Spectrum, Level 1 (ASTM).. 33 LIST OF FIGURES (cont) Figure Page 20. Dynamic Force: Truck Composite Spectrum, Level 2 (ASTM).. 35 21. Dynamic Force: Rail Composite Spectrum, Level 1 (ASTM) ...... 37 22. Dynamic Force: Inter-modal Spectrum (AAR) ............................. 39 23. Dynamic Force: Truck Spectrum, (Singh and Marcondes) ......... 41 A-1. Force Transducer Test Setup ........................................................... 48 A-2. Calculated vs. Measured Force Using Transducer ...................... 49 vi r< LIST OF ABBREVIATIONS Peak Acceleration Actual Peak Compression Force Measured Peak Compression Force Percent Error Force Sampling Frequency Vibration Frequency Acceleration Due to Gravity = 386.4 in/sec2 Spring Constant Equivalent Spring Constant Mass Absolute Magnification Factor Time Time Increment Between Samples = 1 / Fs Period of Vibration = 1/Fv Weight Amplitude at Any Instant of Time vii 1.0 INTRODUCTION The purpose of this study was to develop the methodology, equipment, and hardware necessary to measure dynamic compression forces experienced by packages during transportation. Various studies have examined the effect of static compression on packages during warehouse storage conditions. For example, the stacking pattern has a great effect on compression strength. Misalignment of boxes can reduce stacking strength by 50%. Even perfectly aligned, 3-box high column stacks show a 23% reduction in compression strength (Kellicutt, 1963). The effect of creep during long term storage has been shown to reduce compression strength. In a study by Moody and Skidmore (1966), containers were found to retain only 55% of their original yield force after three months of storage. Temperature and humidity affect the final box compression strength. As the cellulose in the corrugated fiberboard absorbs moisture, the compression strength decreases. The moisture content of the board is in turn affected by the temperature (Laufenberg, 1992). Recycled fiber content has also been shown to reduce compression strength to corrugated boxes. In a study using 100% recycled fibers, repeated recycling caused a 25% decline in top-to-bottom compression strength of containers (Koning and Godshall, 1975). 2 A recent trend toward high-performance corrugated has added yet another variable in compression strength. Cyclic conditions of temperature and humidity have been shown to have a greater negative effect on fiberboard made from fiber-efficient liner board than standard fiberboard. However, both fiberboards performed similarly under non-cyclic environments (Boonyasarn, 1990). On the basis of these factors, packages are designed to withstand a maximum compression load produced by the static load on top. However, this approach does not consider the dynamic compression forces experienced during transportation. This study aimed at developing a instrumented shipping box (ISB) capable of measuring the compressive force experienced by the bottom package during transportation. This system was then used in a lab along with an electrohydraulic vibration table to simulate different transportation environments. The dynamic compressive forces were measured and analyzed for four different stacked package column weights. Five different transit vibration levels were investigated simulating truck, rail, and inter-modal shipments using random vibration power density spectrums. With increasing public pressure to reduce the amount of packaging, it is essential to know what role each of these factors plays in the overall strength of a corrugated container. The objectives of this study were: 1. To develop a data acquisition system to measure dynamic compression forces of stacked corrugated boxes. 2. To measure dynamic compression forces on boxes during random vibration in laboratory simulated transportation tests. 2.0 THE DATA ACQUISITION SYSTEM The ISB consisted of a rigid outer casing constructed of reinforced plywood capable of withstanding 5000 pound compression load. The instrument measured 16 in (length) x 13 in (width) x 10in (height) and was designed to fit one ninth of a standard GMA pallet. The instrument weighed 45 lb. The major components of the instrument include: A) B) C) D) E) One, 8-bit controller style microprocessor containing 64K of non- volatile static RAM, a real-time clock/ calendar, both a synchronous and asynchronous serial port, and a lithium backup battery. Four, 8-Megabit dynamic RAM storage (mass storage) memory banks. These memory devices used synchronous serial to communicate with the microprocessor. Two, 8-channel multiplexed 12-bit analog to digital converters (A/ D). The A / D used synchronous serial to communicate with the microprocessor. Four, 0 to 5000 lb shear beam style load cells. These load cells were temperature compensated from 0° to 150° F providing 3 mV/ V signal at full output and used 350 9 bridge resistance. Four, instrumentation amplifiers to process the signal from the shear beams. G) K) L) 4 One, 0 to i 50 g monolithic capacitive accelerometer. The sensitivity was approximately 20 mV/ g with a frequency response from 0 Hz to 500 Hz (3 dB down). The range of the accelerometer was limited to 1:20 g's. Two, 4 amp/ hour 6 V lead acid, gel type batteries. A hexadecimal rotary input switch to control the mode of operation. Two push button switches to increment, decrement or start the functions of a given mode. An R5232 serial port (9600 baud) to send or receive information from a personal computer. Three power supplies, one 5 V power supply for the digital circuitry, one 8 V power supply for the analog circuitry, and one precision 5 V power supply for the A / D. A crowbar is used to protect the circuitry against over voltage. A built in battery charger for the gel batteries. The batteries could be recharged in approximately 5 hours. A two color LED indicated the unit was charging. The instrument could run for about 20 hours on a full charge. A 16x2 full alpha-numeric liquid crystal display (LCD) was included to provide information to the user. The four load cells were placed at each corner of the box's lid. The lid was undercut so that it could float free of the box sides and was supported by the load cells (Figure 1). With this configuration, the forces acting on individual corners could be measured (0 to 5000 lb) as well as the sum of the forces on the entire lid (0 to 20,000 lb). The box was constructed of 5 / 8 in. plywood with a 3/ 4 in. plywood lid. The load cells were supported on an internal steel box-type Top Cover vo99eeeoee90999999oee.oeeeeeoeoooeveooooevoee 2...... .9. A .92.... .9.9292929.029.929.9. .9. .9.9.9.’.’. .‘.’.’.’.'2’.°....x’x’.....°.‘ 0.01 ,. _ _ _ _ _ _ :2: Shear Beam Load Cel | 3.: ~ ‘ ~ ~ \\‘ f. {02 k \ \ k \ \ no . e r 7 V v D 0 a; I 3" 4", I' I Q t: _ 1.4. 14 A; _ Metal Frame 0 ' O ::::|99... -/_ PQQOOO... //-/-l ¢.4::: ’ 51;: “7’”? 33931.1 .~E3§ WOOd BOX '0 'D O O O 0‘ D ” 0.0.0, 9 D 0.0, f".- ’3‘1’3’. 0°: ’: 0‘0. ’0’. 'e’o'e'e’e. DO. :0»... 0‘ v 00” 0 00’s,. q o o 9’ 0 6’0 0 e 4’ I e ’9 ’9’ 0’0 9’1 '9’ ’e'e" .0 9‘ 5’9”.” ’0 ww': :o’oxév’: arm»: £541 2 :1 ti: {1.2.3 : ° ° .. . ... ...........................¢3t¢¢3£ - 0.0 Figure 1. Drawing of Instrumented Shipping Box (ISB) 6 frame that provided rigid support and overload protection. The lid could be removed and replaced by a smaller platform to test the accuracy of a given load cell. The microprocessor used an 11.0592 MHz crystal resulting in a machine cycle time of 1.1 us. This crystal frequency provided the highest processor speed and allowed the development of special timing for the asynchronous serial port. The real-time clock calendar provided a means of time and date stamping test data. The lithium backup battery provided for the retention of microprocessor programs and data without the need for EPROM or EEPROM type memory. The bulk of the test data was stored in the mass storage devices. A means of testing the mass storage for stuck bits was included. The LCD provided an independent means of viewing the load cell weights, box temperature, battery charge, and the 1 amount of filled memory. The two A/Ds provided a total of sixteen channels of 12-bit data acquisition. One A/ D provided information from the four shear beams, monitored the analog voltage supply, 12 V battery pack, and two thermometers (shear beam and ambient temperatures). The second A/ D provided information from the single-axis accelerometer and allowed for further expansion. Due to the amount of time required to access the A / D5 and save the data into mass storage, the maximum sampling rate was 200 Hz. For convenience and due to differing testing criteria, the sampling rate could be set from 0.1 Hz to 200 Hz. Reading and saving data from one channel of A / D required approximately 0.275 ms. To achieve the most "instantaneous" reading of the A / D channels, they were read in bursts at the beginning of a sampling cycle and saved to the microprocessor. After reading all channels, the data was sent from the microprocessor to mass storage. Using a 200 Hz sampling rate, the mass storage was filled in approximately 21 minutes. 7 To calibrate the ISB, each load cell was calibrated from 0 to 330 lb. Weight was added tc one load cell at a time in increments of approximately 55 lb. The voltage output versus load was plotted for the load cell. All of the load cells produced a linear calibration graph. The slope of the line was used as a conversion from voltage output to weight. The cover was then placed on the ISB and all four cells were tested together from 0 to 825 lb to verify these conversions for the entire ISB. The ISB consistently read the known weight. The ISB was periodically tested against these known weights to verify its accuracy. However no significant deviation was observed. 2.1 ACCURACY OF ISB Due to limitations of the load cells and the A/ D conversion, the smallest discernible increment for any load cell was approximately 1.2 lb For this reason, the entire ISB was limited to an accuracy of 1:48 (or 5) lb. To verify the 158's accuracy, it was allowed to record continuously for 5 minutes. First it was tested with no weight. The sampling rate was set at 200 Hz, producing 60,000 readings. The results are listed in Figure 2. The mean weight was 0 lb with a standard deviation 1.6 lb All but four readings fell within the expected :1: 5 lb accuracy, or 99.993%. This test was then repeated with a 327 lb static load. The results are given in Figure 3. The mean weight was 3271b with a standard deviation of 2.1 lb. All but 556 readings fell within the :i: 5 lb accuracy, or 99.073%. Since the ISB was limited to a maximum sampling rate of 200 Hz, it would not necessarily capture the peak compression force for every wave. The maximum possible error occurs when two readings are evenly distributed on 20000 18000 16000 14000 12000 10000 8000 Number of Readings 6000 4000 - 2000 NCO“) III Figure 2. VC‘ONFOFNC‘OVLD‘DBw Force Recorded by ISB (lb) Accuracy: Static load = 0 lb mmm mmm can mmm mmm me omm mmm mmm hwm mmm mmm vmm mmm «No pmm own mpm m—m firm 14000 12000 10000 8000 6000 mmfiwmmm .«0 59:52 325 lb Force Recorded by ISB (lb) Accuracy: Static Load Figure 3. 10 either side of the peak compression (Figure 4). Sinusoidal motion is represented mathematically by the equation: Y = A - sin( 27r- At) [24] Where: Y = amplitude at any instant of time A = peak acceleration At = time increment T = time period of oscillation t = time The peak amplitude occurs when t = T/ 4 and the maximum peak measurement error occurs when t = T/ 4 :i: At / 2. At this time, the measured compression load, Cm, will be: 27: T At C = A- ' —— ——-— 2-2 m sml: T (4 2 H [ ] or Cm = A- cos(£TA-,—t) [2-3] Therefore, the maximum percentage error, %E, for any measured value of compression is: %E = 100(Afm) [2-4] 01' %E = 100 [1-cos(fl?FSV-)] [2—5] Where: Fs = sampling frequency Fv = vibration frequency Compression Force Actual Peak Compression Force (Ca) Azasured Peak Compression Force (Cm) Figure 4. Time Example of Maximum Sampling Error 12 The vibration frequency for which the maximum error for any sample exceeds 5% when using a sampling rate of 200 Hz: 200 -arccos (1 — —5— EV = 100) = 20.2Hz [2-6] 7! Therefore, for any individual reading, the maximum possible error in the measured compression force exceeds 5% for vibrations above 20.2 Hz. There also was some degree of error caused by the shear beam's natural frequency. To determine the shear beam's natural frequency, a force versus deflection curve was established. Weight was added in increments while measuring the deflection using feeler gauges. The slope of the line produced the spring constant for one load cell: K=768 lb/ .011 in = 69818 lb/ in (Figure 5). Since there are four load cells, the spring constant for the entire box was: Keq = 4 x 69818 = 279,272 1b/ in. The cover weighed 5.7 lb and each shear beam weighed 2.5 lb. From this, the ISB's natural frequency was calculated: Fn = 3— &5 = 417 Hz [2-7] ZIT W Where: W = 5.7 + 4(2.5) = 15.7 lb g= 386.4 in /sec2 The ISB's natural frequency was used to determine the frequency of vibration which exceeds the maximum error of 5% or |M| > 1.05: IM : ———1 [2‘8] 1.05 = W [2-9] Deflection (in) 13 0.016 ~- 0.014 0.012 0.01 0.008 0.006 0.004 0.002 o : - I ‘- - 0 200 400 600 800 Force(lb) Figure 5. Force vs. Deflection Curve for One Shear Beam 14 The error exceeds 5% for vibrations above 91 Hz. Since the natural frequencies of the loads used in this study were below 15 Hz, the error induced by the ISB's natural frequency was negligible. The ISB was also tested to verify its ability to record accurately before and after a 5 minute period of random vibration. To do this, the ISB was placed on the vibration table and loaded with 4381b. This load exceeded the highest load used during this study. The sampling rate was set at 200 Hz. The ISB was allowed to record for 30 seconds to develop a baseline for comparison. Then random vibration was performed for 5 minutes using Truck Composite Spectrum, assurance level 1 (ASTM). This represented the most severe random vibration spectrum used in this study. The ISB was allowed to continue recording for another 30 seconds after random vibration was stopped. A comparison of the recordings before and after vibration is given in Figure 6. The mean before vibration was 4381b with a standard deviation 1.6 lb. After vibration, the mean was 440 lb with a standard deviation 1.8 lb. Both readings fell within the expected accuracy of i5%. Therefore, the ISB accuracy was not significantly affected by the bouncing experienced during random vibration. All of the experiments up to this point tested the ISB's ability to measure static forces. The next experiment focused on the ISB's ability to accurately measure dynamic forces experienced during vibration. Force can be measured directly using transducers or load cells, like the ISB, or can be calculated from a known mass and a measured acceleration using Newton's second law applied to the load on top of the ISB: Force = Mass x (1 + Acceleration at the Center of the Mass) [2-10] See Appendix A for more information. Two different tests were performed using different loads and accelerations: lead weights strapped together weighing 226 lb using an acceleration of 0.25 g. The second test incorporated a stack of four 15 1800 1600 ~' 1400 I .Betore (I) 00 on | @1000 Je- g I “-0 O H G —H E 800 11 z i 600 * . — 400 —— 200 — '1 Fair 01 '— FNMVIOCDNmmov-NOOVIDCON MGMMGQMMQVVVVVVV’V V'VV’VV'VVVVV’VVVV’V’VV Force Recorded by ISB (1b) Figure 6. Comparison of Accuracy Before and After Random Vibration 16 concrete filled boxes weighing 217 lb using 0.5 g acceleration. The 0.5 g acceleration caused the boxes to separate and "bounce" during the test. The loads were stacked on top of the ISB and vibrated using sinusoidal vibration. An accelerometer was placed in the center of the load to monitor acceleration. One minute samples were taken at a sampling rate of 200 Hz. Measurements were taken for frequencies below, near, and above the load natural frequencies. The results using the lead weights verify the ISB measured dynamic compression within the expected range of accuracy, :t 5% (Table 1). Either direct measurement of force or calculation of force using Newton's second law could be used to quantify dynamic compression force in this example. However in the second experiment, Newton's second law no longer applied since the boxes separated during vibration (Table 2). Separation or "bouncing" changed the center of mass in this experiment and precluded the use of Newton's second law. To use Newton's law, an accelerometer must be placed at the center of each box, since each box moves independently. Most of the random spectra used in this study caused the boxes to "bounce". Therefore, the dynamic compression forces exerted by a column of boxes were measured directly using the ISB for the rest of this study. In summary, the compression ISB's accuracy was determined by the smallest increment of measurement, the sampling rate, the ISB's natural frequency, and the frequency of the vibration. Since a sampling rate of 200 Hz was used throughout this study, the maximum error was 5% of the top load 21:5 1b, for vibration frequencies under 20 Hz. 17 Table 1. Calculated vs. Measured Peak Force Using Lead Weights Table Acceleration (g's) 0.25 Load Natural Frequency (Hz) 32.4 Load Weight (1b) 226 Vibration Measured Calculated Measured Difference Between Frequency (Hz) Peak Peak Force (lb) Peak Force Calculated and Acceleration at F=m(1+A) From ISB (lb) Measured Peak Load Center (g's) 5.6 0.25 283 269 4.78% 125 0.3 294 308 4.83% 53.4 0.3 294 307 4.36% 90.6 0.125 254 244 -4.11% Table 2. Calculated vs. Measured Peak Force Using Boxes Table Acceleration (g's) 0.5 (Boxes were bouncing) Load Natural Frequency (Hz) 1 1 Load Weight (lb) 217 Vibration Measured Calculated Measured Peak Difference Frequency Peak Peak Force (lb) Force From ISB Between (Hz) Acceleration F=m(1+A) (lb) Calculated and at Load Measured Peak Center (g's) 7.5 0.85 401.45 521.00 29.78% 10.6 1.3 499.10 514.00 2.99% 17 0.5 325.50 286.00 -12.14% 23 0.175 254.98 246.00 -3.52% Spg 3.0 EXPERIMENTAL DESIGN The first step was to determine where the maximum dynamic compression force occurs in a stack of boxes. To accomplish this, the ISB was placed on the bottom, middle and top of a stack of four boxes during five minute tests using random vibration. Truck Composite Spectrum, Assurance Level 1 (ASTM), was used as the random vibration spectrum. The results are summarized in Figure 7. The test showed that the maximum compression force occurred to the bottom box during transportation. For the rest of this study, dynamic compression force was measured at the bottom of the stack, since the bottom represents the worst case during shipment. The next step was to measure dynamic compression forces exerted on packages during simulated shipping environments. Five different random vibration spectrums were used in this study. They include: - Truck Composite Spectrum, Assurance Level 1 (ASTM, 1992) (Figure 8) - Truck Composite Spectrum, Assurance Level 2 (ASTM, 1992) (Figure 9) - Rail Composite Spectrum, Assurance Level 1 (ASTM, 1992) (Figure 10) - Inter-modal spectrum, (Association of American Railroads, 1992) (Figure 11) - Truck Composite Spectrum, (Singh and Marcondes, 1992) (Figure 12) The PSD's show the vibration level along a spectrum of frequencies. These spectra define the random vibration tests. 18 Peak Dynamic Compression force (lb) 19 1400 1200 1000 800 600 400 200 0 -1 Top Middle Bottom Location of ISB in Stack Figure 7 ISB Location Test 2O OJ. (L01 1 \ N E CD x L5 {2' m an (1001 0.0001 0.00001 ; ; .' 1 10 100 1000 Frequency (Hz) Figure 8. PSD: Truck Composite Spectrum, Assurance Level 1 (ASTM) 21 1 0.1 0.01 - N E 8% U 5% 94 0.001 0.0001 1 0.00001 ; : : 1 10 100 1000 Frequency (Hz) Figure 9. PSD: Truck Composite Spectrum, Assurance Level 2 (ASTM) 0.1 0.01 PSD: GxG/Hz f \ 0.0001 0.00001 , : : 1 1 10 100 1000 Frequency (Hz) Figure 10. PSD: Rail Composite Spectrum, Assurance Level 1 (ASTM) 0.1 0.01 0.001 - PSD: G x G/Hz 0.0001 0.00001 k_. 0.000001 : : 1 1 0 100 1000 Frequency (Hz) -h Figure 11. PSD: Inter-modal Spectrum, (Assoc. of American Railroads) 24 0.1 0.01 a x 0.001 - 1 A O 53 9.. 0.0001 0.00001 0.000001 : 1' 1 10 100 Frequency (Hz) Figure 12. PSD: Truck Composite Spectrum, (Singh and Marcondes) 25 Corrugated boxes containing concrete blocks cushioned with polyethylene foam, were used to simulate a packaged product. Four different loads were used in this study. A rigid wood interface was constructed so that an accelerometer could be located at the stack's mass center (Figure 13). Resonance searches were performed on all four loads using sinusoidal vibration at 0.5 g's constant acceleration and are included in Figure 14 to 17 as graphs of transmissibility versus vibration frequency. These graphs define the natural frequency of the four different stacks of boxes. The loads used include: 1) 109 lb, 2 boxes, natural frequency ~ 12 Hz 2) 217 lb, 4 boxes, natural frequency ~ 10 Hz 3) 325 lb, 6 boxes, natural frequency ~ 8 Hz 4) 426 lb, 8 boxes, natural frequency ~ 6 Hz Dynamic Compression forces were measured for the four loads using all five random spectra according to the following procedure: 1. 99°N9‘9‘PPJN 10. Zero the ISB with no weight on it. Stack the appropriate load on tOp. Install a retaining fence around the stack (Figure 18). Start vibration table. Wait for vibration table to ramp up to full power. Start recording with ISB. Record for 5 minutes. St0p recording with ISB. Stop vibration table. Download data to personal computer. This procedure provided a uniform means to collect the data from the five simulated shipping tests being evaluated. 26 ”///////. Figure 13. Drawing of Test Setup for Resonance Searches Transmissibility 27 100 10 J/ ,M 1 A?” \ -0- \ _.__ \ \ I _ l I 0.1 1 10 Frequency (Hz) Figure 14. Resonance Search for 1091b Load Transmissibility 28 10 -l #% 0.1 1 10 Frequency (Hz) Figure 15. Resonance Search for 217 lb Load 100 Transmissibility 10 -L 0.1 29 Figure 16. \ / / / \ _. \ \ l V l 1 0 Frequency (Hz) Resonance Search for 325 lb Load 100 Transmissibility 10 —L 0.1 30 Figure 17. \ / / h I J \ \ ___ \ l V “1. \V '2 \ 1 0 1 0 0 Frequency (Hz) Resonance Search for 426 lb Load 31 Retaining Fence / Concrete Filled Boxes Instrumented Shipping Box \ll \:><:\—————-Vlbrotlon Tobie Figure 18. Simulated Shipping Test Setup 4.0 DATA AND RESULTS The data was analyzed and the dynamic compression force values were established as a percentage of the static load. These were then plotted as a cumulative percentage of occurrence. The results of these tests were summarized in Figures 19 to 23. A complete distribution of the dynamic force readings was included as an example for the 109 lb load, vibrated using Truck Composite Spectrum, Assurance Level 1 (ASTM) (Table B-1). Since a complete distribution contained 60,000 measurements for each of the 20 tests, the data was condensed into a table format showing the dynamic force / static load versus cumulative occurrence. The lowest and highest readings for each test were also included in these tables (Table 3 to Table 7). The shape of the graphs indicated a normal distribution of the force measurements. Approximately 50% of the measurements fell above the static load and 50% below. The normal distribution of the force measurements was consistent with the normal distribution of acceleration produced by random vibration. The ISB reported some negative force values in most of the tests. This was true for all the spectra except inter-modal. One possible explanation is that when the vibration table produced enough acceleration to cause the entire load to lift off the ISB, the lid on the ISB also lifted. When this occurred, the measured force dropped below the level previously set as 0 lb. Also when this happened, the 32 33 600.0% +Static Load: ' 0 500.0/. 109 lb + Static Load: 217 lb 400.0% +Static Load: g5 325 lb 11 '5 g —.—' Static Load: L -‘ 300.0% 426 lb 2 1 E U) 2 200.0% 0 .J 2 E G i a 100.0% 0.0% '/./ -100.0% 0.0% 20.0% 40.0% 60.0% 80.0% 99.50% Cumulative Occurrence Figure 19. Dynamic Force: Truck Composite Spectra, Level 1 (ASTM) Table 3. Data: Truck Composite Spectrum, Assurance Level 1 (ASTM) Dynamic Load / Static Load (%) .' Y.- \" .bl'l. '3‘ - Cumulative Static Load: Static Load: Static Load: Static Load: Occurrence 109 lb 217 lb 3251b 426 lb 0.5% -9.2% -4.6% -4.6% -0.2% 10.0% -2.8% 5.1 % 13.5% 23.7% 20.0% 6.4% 25.8% 34.1% 42.3% 30.0% 24.0% 46.1 % 51.6% 58.5% 40.0% 46.2% 65.0% 68.6% 75.1 % 50.0% 72.0% 85.0% 86.1% 92.3% 60.0% 100.6% 107.8% 105.1% 111.0% 70.0% 134.0% 133.2% 128.5% 132.2% 80.0% 178.2% 165.0% 157.4% 158.0% 90.0% 251.2% 211.5% 198.9% 193.4% 95.0% 316.8% 251.2% 235.8% 220.2% 99.5% 520.8% 359.5% 317.3% 277.0% Lowest reading: -36.1 % ~11.1 % -15.4% -6.3% Highest reading: 957.5% 583.0% 407.6% 336.2% 35 400.0% 350.0% —'— Static Load: 109 lb SOC-0% + Static Load: 217 lb 3? 250.0% +Static Load: v 325 lb 3 3 —0—Static Load: .2 200.0% 426 lb 5 U) 1, 150.0% a o _l .2 5 100.0% C > a 50.0% 0.0% -50.0°/o 0.0% 20.0% 40.0% 60.0% 80.0% 99.50% Cumulative Occurrence Figure 20. Dynamic Force: Truck Composite Spectra, Level 2 (ASTM) Table 4. Data: Truck Composite Spectrum, Assurance Level 2 (ASTM) Dynamic Load / Static Load (%) Cumulative Static Load: Static Load: Static Load: Static Load: Occurrence 109 lb 217 lb 3251b 426 lb 0.5% -21.2% -2.3% 1.2% 3.8% 10.0% -4.6% 23.0% 31.1% 35.7% 20.0% 10.1% 41.9% 49.4% 51.6% 30.0% 30.3% 58.0% 63.9% 65.0% 40.0% 48.8% 73.3% 78.1 % 77.9% 50.0% 70.9% 88.9% 92.8% 91.5% 60.0% 93.9% 106.9% 108.5% 106.1% 70.0% 120.6% 128.6% 127.0% 122.5% 80.0% 158.3% 155.3% 148.5% 142.0% 90.0% 221.7% 194.5% 180.4% 170.0% 95.0% 259.6% 228.1 % 206.6% 193.4% 99.5% 390.4% 316.1 % 272.1 % 246.2% Lowest reading: -30.4% -5.5% -2.2% -4.9% Highest reading: 593.0% 488.9% 355.4% 297.9% 250.0% 200.0% 150.0% 100.0% Dynamic Load I Static Load (%) 50.0% 0.0% Figure 21. 37 —'— Static Load: 109 lb + Static Load: 217 lb —*'— Static Load: 325 lb i —.— Static Load: 426 lb I 0.0% 20.0% 40.0% 60.0% Cumulative Occurrence 80.0% 99.50% Dynamic Force: Rail Composite Spectra, Level 1 (ASTM) 38 Table 5. Data: Rail Composite Spectrum, Assurance Level 1 (ASTM) Dynamic Load / Static Load (%) Cumulative Static Load: Static Load: Static Load: Static Load: Occurrence 109 lb 217 lb 3251b 426 lb 0.5% 6.0% 21.6% 27.7% 35.9% 10.0% 42.4% 52.5% 55.6% 57.9% 20.0% 58.0% 66.4% 67.9% 67.8% 30.0% 71.8% 77.0% 77.5% 75.0% 40.0% 82.8% 87.0% 85.8% 82.3% 50.0% 93.9% 96.0% 94.1 % 88.8% 60.0% 105.9% 106.3% 103.0% 96.0% 70.0% 118.8% 117.7% 112.5% 103.7% 80.0% 135.6% 131.5% 124.5% 112.7% 90.0% 159.3% 150.2% 141.1 % 125.9% 95.0% 180.5% 167.0% 155.0% 136.6% 99.5% 238.5% 210.6% 191.2% 173.9% Lowest reading -11.1% -0.9% 7.1 % 13.2% Highest reading 320.4% 270.5% 254.8% 21 1.3% Dynamic Load 1 Static Load (%) 39 130.0% I —'_ Static Load: 120.00/0 -— 109 |b ._ Static Load: / 217 lb 110 0°/ __ "*— Static Load: / ° o 325 lb / '—’— Static Load: 426 lb 100.0% I I g / / l/ / 90.0% - 80.0% ' 70.0% . 0.0% 20.0% 40.0% 60.0% 80.0% Cumulative Occurrence Figure 22. Dynamic Force: Inter-modal Spectrum (AAR) 99.50% Table 6. Cumulative Occurrence 0.5% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 95.0% 99.5% Lowest reading Highest Reading Data: Inter-modal Spectrum (AAR) Dynamic Load/ Static Load (%) Static Load: Static Load: Static Load: Static Load: 109 lb 81.0% 90.0% 94.0% 95.5% 97.9% 99.5% 101.2% 103.6% 106.0% 109.5% 1 12.5% 119.8% 71.20% 148.30% 217 lb 325 lb 426 lb 81.0% 90.0% 94.0% 96.0% 98.0% 99.9% 101.6% 103.2% 105.7% 109.4% 111.9% 119.8% 70.70% 132.30% 77.2% 87.6% 91.6% 94.4% 96.5% 98.7% 101.1 % 103.3% 106.4% 110.4% ' 113.7% 122.2% 69.50% 131.60% 79.6% 90.1 % 93.2% 96.0% 98.1 % 100.2% 102.3% 104.6% 107.2% 111.2% 1 14.2% 123.0% 71.80% 135.50% 41 300.0% 250.0% i + Static Load: 109 lb + Static Load: :5 200.0% 217 lb V D 1, +Static Load: § 325 lb é —‘— Static Load: II a 150.0% 426 lb 'o / Q o _l 2 E 100.0% C > o 50.0% / 0.0% . 0.0% 20.0% 40.0% 60.0% 80.0% 99.50% Cumulative Occurrence Figure 23. Dynamic Force: Truck Spectrum (Singh and Marcondes) 42 Table 7. Data: Truck Composite Spectrum, (Singh and Marcondes) Dynamic Load/ Static Load (%) Cumulative Static Load: Static Load: Static Load: Static Load: Occurrence 1091b 217 lb 325 lb 426 lb 0.5% 9.2% 30.4% 47.7% 52.3% 10.0% 42.0% 62.0% 71.0% 69.0% 20.0% 59.0% 74.0% 81.0% 77.0% 30.0% 73.0% 83.0% 88.0% 83.0% 40.0% 87.0% 92.0% 94.0% 89.0% 50.0% 99.0% 100.0% 94.0% 94.0% 60.0% 114.0% 109.0% 106.0% 100.0% 70.0% 129.0% 119.0% 113.0% 105.0% 80.0% 149.0% 130.0% 121.0% 113.0% 90.0% 176.0% 146.0% 132.0% 123.0% 95.0% 202.0% 160.0% 141.0% 132.0% 99.5% 265.2% 193.6% 163.9% 163.4% Lowest reading -10.1% 10.1% 28.9% 34.7% Highest reading 365.6% 245.2% 189.7% 190.8% 43 momentum of the shear beams may have caused them to flex upward further exaggerating these negative measurements. In tests where the acceleration level was equal at the load natural frequencies, the dynamic load/ static load ratio was consistently greatest for the 109 1b, 2 box load and smallest for the 426 lb, 8 box load. This trend was seen in tests using both Truck Composite Spectra (ASTM), (Figures 19 and 20), as well as using Rail Composite Spectrum (ASTM), (Figure 21). This trend suggests that as the number of boxes increased, more energy was absorbed by the stack, lowering the dynamic load/ static load ratio. In the inter-modal test, the random vibration level was not evenly distributed across the natural frequencies of the test loads. In this test, the 426 lb, load with a natural frequency = 6 Hz, experienced the highest vibration level, while the 109 lb load, natural frequency = 12 Hz, experienced the lowest. The graph (Figure 22) shows that the heavier, lower natural frequency loads produced a higher dynamic force/ static force ratio than the lighter, higher natural frequency loads. Clearly, the frequency content of the random vibration affected the dynamic compression force measured by the ISB under different loads. 5.0 CONCLUSIONS On the basis of this study, the following conclusions were made: The instrumented shipping box is capable of measuring dynamic compression forces exerted on packages during simulated shipping tests in stacked configurations. Dynamic compression force can be calculated from a known mass and a measured acceleration using the equation: Dynamic Compression Force = Mass x (1 + Acceleration at mass center) only for loads that remain in contact during vibration. The maximum compression force in a stack of boxes occurs to the bottom box. Using simulated shipping environments, 99.5% of the measured forces were below a range of 1.2 to 5.2 times the static load. The maximum dynamic compression force measured was about 9.5 times the static load when using the Truck Composite Spectrum, assurance level 1 (ASTM). Lighter loads containing fewer boxes produced higher dynamic load/ static load ratios than heavier loads made up of more boxes. 6.0 RECOWENDATIONS The major limitation to the ISB's accuracy was determined by its sampling rate. Therefore, an increase in the sampling rate would decrease the maximum error threshold, below 5% and allow for more accurate measurements above the present 20 Hz vibration limit. This study used random vibration to represent the shipping environment. For this reason, the actual amplitude and frequency of vibration was unknown at any instant of time. Similar tests could incorporate a real time vibration controller reproducing previously recorded shipments. Alternatively, the ISB could be placed in a truck during shipments. However, the reproducibility of these shipments would be limited. Lastly, the movement of boxes on top of the ISB during vibration needs further study. This study indicates that the boxes in a stack may not be accurately described as a single mass. A time history of dynamic compression along with the acceleration at the center of mass of each box may provide a better understanding. A high speed camera may also provide insight. 45 LIST OF REFERENCES LIST OF REFERENCES AST'M. 1992a. "Standard Practice for Performance Testing of Shipping Containers and Systems." ASTM Standard D 4169 - 92a. "Study of the Shock and Vibration Environment in Boxcars." Association of American Railroads. Report #DP7-92, Washington, DC, November, 1992 Brandenburg, R.K. and Lee, 1.]. "Fundamentals of Packaging Dynamics." MT‘S Systems Corporation. Minneapolis, Minnesota, 1990. Boonyasam, A. "The Effect of Cyclic Environments on the Compression Strength of Boxes Made from High-Performance (Fiber-Efficient) Corrugated Fiberboards." 1990. Kellicutt, K.Q. "Effect of Contents and Load Bearing Surface on Compressive Strength and Stacking Life on Corrugated Containers." 1963. Koning, I.W. and Godshall, W.D. "Effect of Repeated Recycling of Fiber on Corrugated Container Strength", Paperboard Packaging, December 1975, pp. 37-40. Laufenberg, T.L. "Cyclic Humidity Effect on Paperboard Packaging." Forest Products Lab, Madison, Wisconsin, September 1992 Moody, RC, and Skidmore, K.E., 1966. " How Dead Load Downward Creep Influences Corrugated Box Design." Singh, SP. and Marcondes, I. "Vibration Levels in Commercial Truck Shipments as a Function of Suspension and Payload," Journal of Testing And Evaluation, Vol. 20, No. 6, November 1992. APPENDICES APPENDIX A Calculating Force Using F = m(1+A) To verify that Newton's law was being applied correctly, a force transducer was securely fastened to a small vibration table. On top of the transducer was a mass, glued to a 2 in. thick piece of polyurethane foam (Figure A-1). This created a spring mass system with a natural frequency of 21 Hz. Since the mass and foam were glued together, there was no separation or "bouncing" even when the acceleration exceeded 1 g. An accelerometer was mounted close to the mass center and fed to an oscilloscope. The transducer was also connected to the oscilloscope. The acceleration and compression force were recorded at various frequencies with the vibration table running at a constant acceleration of 0.5 g's. The results are shown in Figure A-2. This graph clearly shows that Newton's law was being applied correctly and dynamic force could be calculated from a measured acceleration. 47 O O 010% Oscilloscope Accelerometer ‘ Mass Foam Force Transducer _=_ r j \\\\r_r/<:;\T“~————-Vibration Table "_ or )— 1—4 Figure A-l. Force Transducer Test Setup Compression Force (lb) 3.5 2.5 1.5 0.5 49 A 9 A Calculated Force (lb) A . 9 Measured Force (lb) 0. g 8 _ I A ' o o ‘ A o _. A A o l l l l l M] I I I I I I 0 1 0 2 0 3 0 4 0 5 0 6 0 Frequency of Vibration (Hz) Figure A-2. Calculated vs. Measured Force Transducer APPENDIX B Table B-1 Complete Data for Composite Truck Spectrum, Level 1 Load: 109 lb Load: 217 lb Load: 325 lb Load: 426 lb Dynamic Number Dynamic Number Dynamic Number Dynamic Number Force of Force of Force of Force of (lb) Readings (1b) Readings (lb) Readings (1b) Readings ~39 1 ~24 1 ~50 1 ~27 1 ~29 2 ~22 4 -29 1 ~18 1 ~23 2 ~21 3 ~28 2 ~13 1 ~22 2 ~19 1 ~27 2 ~12 1 ~21 2 ~18 3 ~26 1 ~11 1 ~20 1 ~17 6 -24 1 ~10 1 ~19 1 ~16 5 ~23 5 ~9 1 ~18 3 ~15 16 ~22 5 -7 14 ~17 6 ~13 34 ~21 7 -6 16 ~16 14 ~12 58 ~20 16 -5 29 ~15 15 ~11 89 ~18 21 -4 50 ~14 1 ~10 131 ~17 30 -3 11 ~13 27 -9 207 ~16 74 -2 62 ~12 39 -8 1 ~15 185 -1 133 ~11 60 ~7 347 ~13 269 0 194 ~10 89 -6 682 ~12 295 1 157 -9 171 -5 814 ~11 277 2 134 -8 6 -4 672 ~10 272 4 104 ~7 331 -3 1 -9 265 5 9O -6 890 -2 518 ~7 210 6 58 -5 1806 -1 368 -6 145 7 69 -4 2383 0 243 -5 126 8 60 -3 4 1 248 ~4 135 9 4 50 I 1 H N :gxoooxioxme-wrov-ao NHHHHHHHH OOWVO‘U‘IfiiWN 013383513 8&3888gk’18 1371 1112 628 613 511 487 445 108 362 408 397 429 400 24 401 431 386 336 318 55 359 378 313 82 244 303 301 310 301 17 303 298 HH Hoxoooxioxcneoaro Nt—IHHr—IHt—IHH O\OQ\]O\UIJ>OJN 019385.52 0303 OJ QWWOJNNNN Table B-1 (cont) 212 198 166 126 184 196 182 201 157 149 177 170 145 20 183 152 167 137 107 162 159 182 140 182 151 135 173 114 49 156 51 zgomummewnwogbds NHHHl—sl—ti—ni—ii—s OGCDVO‘UIIFOON bifiifilt’afl (.003me NM WNHOOgVO\ 68 52 118 102 118 97 90 90 80 74 72 87 81 107 15 71 97 95 91 97 89 61 21 97 90 94 96 71 85 10 11 12 13 15 16 17 18 19 20 REUBB 26 27 29 30 31 32 33 35 37 38 39 4O 41 42 43 45 47 52 59 61 52 62 60 49 6O 296 192 93 310 319 316 50 252 309 253 246 280 275 298 305 139 156 266 270 250 47 211 242 178 73 273 274 247 232 109 156 Table B-1 (cont) 148 144 143 19 140 142 152 142 155 10 157 160 160 176 87 79 170 153 167 160 13 156 168 146 154 135 43 189 179 161 148 42 109 169 180 151 177 52 SSSSSESSBSSSK 81 93 93 87 92 109 58 110 79 101 98 101 100 94 110 74 97 103 92 93 81 96 113 102 110 89 98 98 127 53 Table B-1 (cont) 72 229 76 15 71 32 85 92 73 229 77 169 72 103 86 76 74 252 78 168 73 115 87 12 75 247 79 159 74 112 88 61 76 51 80 162 75 106 89 71 77 210 81 104 76 17 90 78 78 203 82 58 77 74 91 67 79 279 83 184 78 110 92 76 80 248 84 184 79 104 93 3 81 154 85 186 80 103 94 69 82 103 86 175 81 124 95 74 83 217 87 32 82 7 96 83 84 267 88 136 83 115 97 7O 85 212 89 175 84 103 98 43 86 236 90 142 85 114 99 35 87 90 91 192 86 111 100 71 88 162 92 157 87 61 101 83 89 210 93 23 88 66 102 75 90 243 94 161 89 109 103 76 91 240 95 147 90 124 104 3 92 201 96 159 91 116 105 73 93 66 97 167 92 112 106 93 94 216 98 97 93 4 107 70 95 283 99 95 94 115 108 88 96 211 100 193 95 114 109 76 97 235 101 167 96 120 110 17 98 131 102 162 97 123 111 88 99 125 103 171 98 96 112 87 100 233 104 22 99 16 113 84 101 231 105 160 100 126 114 66 102 191 106 172 101 132 115 18 103 233 107 161 102 117 116 63 104 66 108 180 103 121 117 85 105 196 109 124 104 21 118 95 106 203 110 45 105 95 119 101 107 212 111 149 106 119 120 90 108 221 112 154 107 131 121 4 54 Table B-1 (cont.) 109 145 113 182 108 125 122 81 110 74 114 187 109 109 123 91 111 197 115 65 110 9 124 86 112 213 116 118 111 131 125 80 113 208 117 172 112 116 126 63 114 208 118 177 113 129 127 28 115 94 119 158 114 130 128 95 116 138 120 178 115 70 129 78 117 206 121 35 116 60 130 95 118 226 122 174 117 137 131 81 119 199 123 197 118 112 132 12 120 166 124 169 119 121 133 64 121 58 125 183 120 116 134 108 122 190 126 95 121 5 135 89 123 222 127 65 122 95 136 105 124 214 128 173 123 120 137 90 125 212 129 177 124 108 138 6 126 131 130 180 125 119 139 95 127 101 131 160 126 111 140 83 128 175 132 53 127 17 141 109 129 185 133 109 128 116 142 85 130 213 134 188 129 123 143 35 131 182 135 166 130 132 144 58 132 80 136 164 131 133 145 92 133 133 137 136 132 54 146 92 134 197 138 41 133 78 147 100 135 196 139 170 134 130 148 94 136 I69 140 194 135 118 149 16 137 152 141 171 136 134 150 69 138 71 142 161 137 127 151 100 139 153 143 89 138 10 152 91 140 185 144 87 139 139 153 100 141 174 145 143 140 118 154 68 142 173 146 163 141 157 155 19 143 96 147 175 142 114 156 98 144 106 148 147 143 104 157 84 145 180 149 35 144 33 158 104 55 Thflflefhl(tont) 146 190 150 151 145 137 159 96 147 194 151 151 146 120 160 14 148 143 152 155 147 116 161 68 149 68 153 163 148 145 162 110 150 123 154 124 149 33 163 111 151 163 155 50 150 121 164 104 152 191 156 178 151 131 165 88 153 191 157 157 152 146 166 15 154 108 158 177 153 143 167 113 155 69 159 166 154 122 168 79 156 158 160 63 155 5 169 107 157 146 161 117 156 115 170 112 158 155 162 152 157 139 171 46 159 132 163 174 158 144 172 51 160 77 164 179 159 99 173 105 161 93 165 121 160 61 174 97 162 180 166 41 161 63 175 96 163 173 167 144 162 148 176 109 164 161 168 167 163 112 177 18 165 136 169 166 164 133 178 81 166 67 170 135 165 139 179 114 167 119 171 91 166 14 180 108 168 154 I72 72 167 147 181 103 169 161 173 189 168 130 182 74 170 147 174 151 169 134 183 22 171 80 175 175 170 128 184 93 172 75 176 154 171 97 185 97 173 136 177 67 172 23 186 94 174 151 178 107 173 131 187 105 175 141 179 168 174 136 188 32 176 127 180 153 175 127 189 53 177 65 181 146 176 139 190 114 178 118 182 122 177 46 191 99 179 133 183 48 178 87 192 108 180 142 184 133 179 144 193 100 181 148 185 154 180 131 194 11 182 102 186 168 181 151 195 99 56 Table B~1 (cont.) 183 64 187 158 182 126 196 109 184 119 188 82 183 12 197 114 185 123 189 73 184 125 198 96 186 124 190 160 185 149 199 71 187 138 191 154 186 130 200 42 188 70 192 172 187 120 201 114 189 59 193 136 188 88 202 110 190 127 194 52 189 33 203 101 191 120 195 123 190 124 204 93 192 129 196 161 191 123 205 32 193 113 197 158 192 144 206 84 194 65 198 170 193 137 207 101 195 98 199 113 194 22 208 117 196 118 200 51 195 122 209 126 197 127 201 148 196 147 210 103 198 122 202 156 197 131 211 22 199 100 203 145 198 126 212 102 200 58 204 138 199 127 213 81 201 113 205 70 200 30 214 99 202 110 206 100 201 133 215 107 203 103 207 123 202 141 216 37 204 103 208 172 203 131 217 62 205 58 209 168 204 113 218 95 206 78 210 120 205 62 219 122 207 105 211 33 206 66 220 104 208 109 212 148 207 138 221 116 209 116 213 149 208 136 222 26 210 82 214 148 209 120 223 86 211 47 215 147 210 135 224 86 212 82 216 87 211 14 225 91 213 131 217 62 212 124 226 109 214 86 218 148 213 141 227 58 215 96 219 154 214 144 228 40 216 55 220 161 215 103 229 116 217 62 221 149 216 100 230 92 218 77 222 61 217 36 231 83 219 89 223 86 218 134 232 92 57 Table B-1 (cont.) 220 103 224 121 219 123 233 23 221 82 225 149 220 109 234 71 222 58 226 138 221 129 235 122 223 74 227 116 222 38 236 110 224 74 228 59 223 105 237 100 225 85 229 130 224 144 238 96 226 107 230 132 225 124 239 30 227 72 231 147 226 137 240 113 228 53 232 128 227 121 241 111 229 79 233 91 228 30 242 110 230 80 234 89 229 107 243 116 231 83 235 137 230 123 244 62 232 79 236 168 231 135 245 51 233 55 237 153 232 143 246 104 234 57 238 107 233 66 247 101 235 87 239 53 234 69 248 107 236 79 240 137 235 119 249 93 237 88 241 140 236 151 250 35 238 76 242 147 237 141 251 81 239 41 243 142 238 140 252 111 240 65 244 92 239 22 253 104 241 83 245 53 240 111 254 82 242 83 246 129 241 155 255 111 243 60 247 127 242 147 256 33 244 55 248 152 243 115 257 95 245 42 249 116 244 105 258 110 246 63 250 64 245 27 259 102 247 76 251 71 246 119 260 121 248 78 252 136 247 115 261 35 249 72 253 142 248 135 262 74 250 47 254 122 249 132 263 112 251 52 255 116 250 49 264 101 252 73 256 55 251 76 265 90 253 73 257 141 252 148 266 114 254 83 258 157 253 128 267 32 255 51 259 118 254 112 268 80 2.56 43 260 113 255 107 269 96 58 Table B-1 (cont.) 257 66 261 75 256 27 270 110 258 67 262 44 257 127 271 91 259 71 263 126 258 118 272 66 260 64 264 129 259 133 273 54 261 49 265 125 260 122 274 94 262 48 266 107 261 73 275 117 263 68 267 46 262 48 276 101 264 89 268 93 263 112 277 96 265 94 269 136 264 128 278 23 266 52 270 146 265 131 279 82 267 26 271 129 266 109 280 99 268 47 272 103 267 35 281 102 269 52 273 44 268 100 282 113 270 67 274 115 269 99 283 80 271 63 275 111 270 144 284 34 272 54 276 121 271 132 285 100 273 39 277 135 272 101 286 91 274 63 278 48 273 27 287 102 275 79 279 59 274 112 288 103 276 42 280 113 275 110 289 45 277 41 281 123 276 123 290 48 278 42 282 143 277 121 291 105 279 39 283 91 278 53 292 112 280 47 284 48 279 65 293 105 281 73 285 88 280 116 294 78 282 61 286 120 281 131 295 21 283 46 287 118 282 117 296 67 284 35 288 113 283 128 297 98 285 46 289 93 284 31 298 97 286 47 290 44 285 130 299 82 287 60 291 107 286 123 300 77 288 55 292 112 287 117 301 38 289 38 293 122 288 105 302 80 290 34 294 97 289 84 303 101 291 57 295 55 290 39 304 107 292 61 296 63 291 121 305 98 293 64 297 106 292 127 306 20 59 Table B-1 (cont.) 294 42 298 141 293 122 307 90 295 44 299 116 294 122 308 99 296 46 300 87 295 33 309 132 297 35 301 42 296 84 310 104 298 59 302 80 297 120 311 94 299 46 303 128 298 112 312 30 300 33 304 107 299 101 313 87 301 29 305 108 300 103 314 103 302 26 306 81 301 27 315 105 303 54 307 52 302 113 316 108 304 54 308 96 303 110 317 53 305 39 309 108 304 118 318 51 306 42 310 119 305 103 319 86 307 31 311 102 306 71 320 118 308 50 312 60 307 63 321 113 309 61 313 73 308 88 322 112 310 43 314 110 309 105 323 30 311 42 315 96 310 135 324 71 312 39 316 85 311 98 325 92 313 29 317 88 312 29 326 89 314 45 318 42 313 101 327 106 315 44 319 109 314 102 328 94 316 38 320 129 315 103 329 30 317 37 321 100 316 116 330 88 318 22 322 102 317 75 331 127 319 32 323 58 318 34 332 98 320 42 324 38 319 116 333 92 321 41 325 94 320 107 334 30 322 40 326 105 321 107 335 73 323 25 327 90 322 107 336 102 324 31 328 88 323 39 337 99 325 36 329 38 324 84 338 109 326 36 330 85 325 115 339 102 327 31 331 103 326 100 340 33 328 37 332 101 327 105 341 76 329 30 333 73 328 90 342 85 330 29 334 88 329 18 343 98 60 Table B~1 (cont.) 331 42 335 58 330 116 344 93 332 36 336 90 331 133 345 58 333 31 337 97 332 111 346 44 334 31 338 93 333 100 347 96 335 27 339 104 334 75 348 114 336 29 340 58 335 50 349 105 337 33 341 54 336 134 350 108 338 33 342 100 337 105 351 37 339 31 343 105 338 111 352 57 340 23 344 101 339 105 353 106 341 21 345 82 340 33 354 114 342 36 346 48 341 72 355 115 343 39 347 67 342 127 356 82 344 39 348 95 343 96 357 30 345 24 349 110 344 105 358 77 346 20 350 90 345 80 359 102 347 20 351 66 346 38 360 91 348 30 352 48 347 96 361 79 349 28 353 88 348 117 362 37 350 31 354 127 349 107 363 55 351 15 355 87 350 128 364 87 352 26 356 70 351 46 365 90 353 23 357 59 352 53 366 89 354 27 358 64 353 106 367 104 355 25 359 97 354 101 368 30 356 20 360 88 355 108 369 66 357 27 361 89 356 85 370 100 358 26 362 65 357 26 371 108 359 30 363 47 358 60 372 106 360 33 364 62 359 105 373 51 361 18 365 93 360 98 374 47 362 16 366 81 361 86 375 81 363 27 367 68 362 75 376 102 364 24 368 68 363 31 377 102 365 34 369 46 364 110 378 108 366 34 370 88 365 100 379 37 367 39 371 68 366 92 380 83 369 370 371 372 373 374 375 376 377 378 379 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 405 406 407 408 Table B-1 (cont.) 61 367 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 90 73 96 94 76 74 101 82 49 82 100 1 1 1 81 26 89 94 93 95 67 28 98 100 106 41 HSSS’S 33 93 381 382 383 387 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 81 112 97 41 7O 93 107 81 51 63 91 90 93 31 78 98 100 106 78 43 70 100 95 37 81 103 88383 92 89 101 405 407 408 410 411 412 413 414 415 416 417 418 419 420 421 423 424 425 426 427 428 429 430 431 432 433 434 435 437 438 439 441 12 19 17 11 13 16 19 12 14 19 12 15 16 13 17 16 15 12 10 18 19 15 13 15 18 14 16 13 13 18 15 10 410 41 1 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 437 438 439 440 441 442 443 445 Table B-1 (cont.) SSSSSSSSSBSH 62 405 407 410 41 1 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 99 76 47 103 101 71 75 30 68 92 81335 78 94 85 79 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 445 447 449 450 451 452 453 454 65 $83§$§33§8 96 NSNS 95 52 8:138 67 78 81 92 87 39 87 78 90 39 67 78 442 443 445 447 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 465 467 468 469 470 471 472 473 474 475 476 477 478 447 449 450 451 452 453 454 455 456 457 458 459 460 461 462 465 467 469 470 471 472 473 474 475 476 477 478 479 480 481 482 Table B-1 (cont.) 31 30 61 69 49 20 49 51 43 47 58 52 45 33 59 SKSSSSEBSSSSBESS 63 441 442 443 445 447 449 450 451 452 453 454 455 456 457 458 459 460 §§§§§§ 467 469 470 471 472 473 474 475 476 477 455 456 457 458 459 460 461 462 465 467 469 470 471 472 473 474 475 476 477 478 479 §§§§§§§§§ 489 490 491 85 82 74 32 71 92 76 59 60 83333 61 90 91 70 39 80 90 90 41 61 76 75 100 38383 76 82 53 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 507 508 510 511 512 513 514 515 NU1\IO\O\O\OJO\H:CDSO\\OO\\IU‘IO\\]U1":$\I#UIO\VZVS 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 51 1 512 513 514 515 516 517 518 519 Table B-1 (cont.) 47 41 39 8351528388333 53 388338 40 43 45 35 19 27 45 43 30 $1118.92 40 29 18 35 $5398 64 478 479 481 482 485 487 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 51 1 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 61 82 91 87 26 88813323 70 65 89 39 62 62 78 78 92 29 78 67 83838$SSEBE§ 74 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 541 542 543 545 547 549 550 551 552 thmmU'INOJthCflWNmrh-WHhm©WhhHm©VGthm©V©©VVOJm 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 545 547 549 550 551 552 553 554 555 556 Table B-1 (cont.) 30 13 833383 35 3333333 24 33351 37 16 16 30 24 29 20 24 10 18 32 24 20 18 65 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 541 542 543 545 547 549 550 551 49 51 8O 32 3838333 39 35 58 57 57 45 $333 73 38 27 53 62 55 35 50 62 50 53 45 27 50 74 529 530 531 532 533 534 535 536 537 538 539 541 542 543 545 547 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 565 74 69 39 76 78 8833333 81 31 67 74 52 39 57 61 82 90 50 50 67 74 881333 75 57 32 553 554 555 556 557 558 559 560 561 562 3333333 570 571 572 573 574 575 576 iii-OJNOJfihI-‘U'lNr-‘NvaerH-iNNOWNWWHfimWHt-‘VHNWWOJWWN 557 558 559 560 561 562 565 567 569 570 571 572 573 574 575 576 577 578 579 581 582 583 586 587 589 590 591 592 593 Table B-1 (cont.) 26 29 19 20 24 30 24 21 21 11 16 24 15 19 21 21 18 29 18 13 10 16 15 17 20 24 12 66 552 553 554 555 556 557 558 559 560 561 562 563 565 567 569 570 571 572 573 574 575 576 577 578 579 580 581 582 584 585 586 587 588 61 35 3O 61 59 3333 62 41 21 53 60 59 35 24 52 61 60 59 29 57 55 58 37 28 3382.“: 30 27 567 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 586 587 589 590 591 592 593 594 595 596 597 598 599 600 601 602 592 593 594 595 596 597 600 601 602 603 604 605 606 607 608 610 61 1 612 614 615 616 617 618 619 620 621 622 623 624 626 627 628 631 632 633 635 HHHHHHNNNHHHhCthNGIFNWUIOJBOJNNnFO-‘OJHNQOJNNVN 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 Table B-1 (cont.) 12 17 18 11 12 18 21 15 18 12 12 51338 15 16 20 13 14 16 11 16 19 18 17 13 19 12 11 17 20 67 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 61 1 612 613 614 615 616 617 618 619 620 621 622 623 624 625 39 59 39 27 msgasgaxs 49 33 38 45 49 27 24 41 43 29 8$$83538&&8 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 635 636 637 638 639 $8S$$ 637 638 639 641 642 643 647 649 650 652 654 655 657 658 659 661 662 665 667 668 670 672 674 675 676 679 681 685 688 691 HHI—IHt—INWHNrfiNNNHHWHHHWHHQHQNWNI—INQJt—tI—IHOJHN 631 632 633 635 637 639 641 642 643 645 647 649 650 651 652 653 654 655 656 657 658 659 660 §§§§§§ 667 Table B-1 (cont.) 11 11 11 12 16 11 15 11 11 14 10 16 12 10 12 10 oo 16 10 17 13 18 12 13 10 21 12 13 13 68 626 627 628 629 630 631 632 633 635 637 638 639 640 641 642 643 645 647 649 650 651 652 653 654 655 656 657 658 659 660 661 662 32 17 31 41 61 $8313 47 30 3388681888332133 24 39 47 42 19 21 27 32 30 27 19 48 641 642 645 647 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 667 669 670 671 672 673 674 675 676 69 Table B-1 (cont.) m%mawmnwa%m%wxummumwmmvumammnmwuwuwww 8 1.2 7 901.2345 78 01.23 5 7 01.23 mammwwmmmwwfimwwwwwwfiwwmmmmmmmmmmmnnnn mmmmwmnumwwwuymumuuwanwwmmummmwmmxuan 5 7 901. 3456 8 01.23 7 901.2345 78 mmafiwmaawmwwwwmamwwmwmmwwmwwwwwwwwwwm 9HWHE678NM9888W77M78586679W2396674586 901. 3456 8901.2 5 7 901.234.5678 1.23 wwwwmwwwmmwwwmwmmwwwmwwwwwwwwwwmmmmmm 112121112111111111.1311.21.11.11.11.11.11.21.111. 236701.235 1.234578 65781.2 7 57 5 345 wwwwmmmmmmmnnnnnnnmnmnnnnmmmmnnmwmwww 70 Table B-1 (cont.) awwwwa$wflflwmflwflmwwwwnfiflm%%mumflwmwfifimwfiflm 45678901. 4 67 9 1.23 5 7 901.23 5 7 90 nnnnnnnnmmnmnnmnmnmnmnmnmnnnnmmnmnmnn wwaM7BEWMEwMMMmmmnwwmmmflomfiw7mwnfiwmmfi 123 5 78 012345678901 4 67 90123 5 mmmmmmmmmmnnnnnnnnnnnnmmnmnnmnmnnnmnm 54565B9657696689835869444985B37157335 5 7 012345678901 4 67 90123 5 78901 mmmmmnnnnnnnnnnnnmmnmnnmnnnmnmnmnnnmn 21111111111112211111 82 0278023 7 055W wwmmmmwmmmmmmamm%wmm 71 Table B-1 (cont.) %mmmwuauaammumuwwwumannwuuammmwwmwamw mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm mmmnmumnwwmmmnwmwmwmuxmmmuuM%wwmnmnmm mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm 2912329657653324634723244513288366524 mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm 780 781 782 783 784 785 786 787 788 789 790 791 794 795 796 797 §§§§ 802 803 805 807 808 809 810 811 812 813 814 816 817 818 Table B-1 (cont.) SNNNWHNwammmeUI-hh NHNHNWNwNNHWVHmr-‘NIP-(fl 72 774 775 776 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 807 808 810 10 18 20 18 16 11 18 12 14 14 20 20 18 14 14 19 21 20 27 15 13 17 19 16 14 17 19 12 15 18 10 10 12 19 18 788 789 790 791 792 793 794 795 797 798 799 800 801 802 803 805 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 45 27 39 24 47 32 24 41 3888 30 37 42 27 42 41 “Sgififi 33 32 18 41 42 38 33 24 35 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 835 837 840 841 842 843 845 847 849 850 851 852 853 855 856 857 Table B-1 (cont.) WWHHHWHHWWHNHNHrhO-‘OJfiNmNt-‘HOJUF-\li-‘NOJVNNOJHD-‘N 73 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 835 837 838 839 840 841 842 843 845 847 825 826 827 828 829 830 831 832 833 835 837 838 839 840 841 842 843 845 847 849* 850 851 852 853 855 857 858 859 860 861 6183338 27 31 3531381” 27 39 47 19 33 32 43 21 21 43 39 39 31 20 31 15 32 20 29 870 871 873 876 877 879 885 891 892 893 894 895 900 910 911 912 913 914 915 916 918 920 921 922 923 Table B—1 (cont.) NHv—It=|I=|NNt—lt—lr—fit—fiv—IupHHNHHr—INHHWHNNWHNNNNOJHNHOJ 74 849 850 851 852 853 854 855 857 858 859 860 861 862 865 867 869 870 871 872 873 874 875 876 877 878 879 880 881 882 19 18 11 13 11 14 12 14 16 12 19 10 11 12 11 10 17 15 \l 14 18 16 13 11 10 15 10 870 871 872 873 874 875 876 877 878 879 880 §§§§§§ 887 889 890 891 892 893 894 895 896 897 898 'aifia’ts'a: 33813833838838 $888N88$B8$8383388588B838 925 928 936 939 941 943 944 949 952 953 956 957 958 960 961 962 965 970 974 978 979 982 983 985 990 1001 1012 1019 1022 1032 1034 1049 1051 1057 1069 1079 Table B-1 (cont.) HHO—lD—lD—‘HNHHHHHI—‘HHHNHHHHHHHHHHHWNHHHHHNH 75 885 887 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 c» \J.>.{3 E§xo w: cx~q E3 23¢» ~q axxo :3 w>:: 0\ 899 900 901 902 903 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 8888§388$883886§ 27 20 14 26 agammwmmaassmaa 1093 1109 1111 1139 1265 Table B-1 (cont.) p—Ig—Ip—Iy—SH 76 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 t—l H I—i D—lt—l H (”own-bu v—J HUI \JU'IQUJOCM v—t OJ mm0\\0\lmvfim\lhm 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 969 970 971 972 7 7 Table B-1 (cont.) 959 960 961 962 964 965 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 O‘WHWU'IO\\]\1\OIFth-uh\0r> r—I U'I \lmeVankVUIUIChO‘mO‘OU‘IVLfloWO‘N 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 14 14 12 17 19 21 18 14 17 21 10 17 12 17 12 16 19 11 14 16 26 10 16 15 12 \l 17 17 12 10 15 78 1kdfle1¥1 no n>