:1 f . - .ur u 2 .vfifim :,77. . . ;. . I ~ . L |\I \. u , A I u. u 0 OD 3&6. WWQJ... ”WNW... , . .. . . .4109... RM”: 5 . :14. ‘ L . ‘ . ‘ ‘15:; L.\' \‘v' ,\ B,“ ‘4. a“ .u u, - . A ' ' It- ' ' “‘0‘ “ii lrl‘.‘v.:i;[;".. 3" "'53"; “7" *‘U-‘f‘krp. ft i’ 1 W J: .‘ MUM ‘5’ 1' " x ‘ .'."'“" l 34’: . Whig“. .. ébrv... .Whfl“.;.nun{>nv . . .5. . a .. wfifimbnrnurmuwmn. AR“. . .. Huh-VJ. 6. ”Banana 00.3w. . , flhfimfimfiflqflwfifiwk. L ..I ..¢n.-.IHHM.PVJWWPU.CM~V.P .. cwfiEfiufl. v‘. '- {I c . A .... nib}... . .. «alwwmwwmidh pasture: 9....» . . :fivfl' . c '0‘ . u 0" a Q an: RN .\I‘ a ;rv r 3‘1 l..‘o[..vbt hut. 4 Iii...le {I “L3. . '01. N‘Jll‘ I alwolchflf ., . If). p ”5.10 U I V n‘ 4 . . . limwhof. .Q..u1.....d._., 3.1.1... 4 O . ‘l \p) . it’ll.) IIIUIO . nircor.\&3t.v.” ..“. r t n y? I I“... VVIOv’UV 401965;th b ,i I. Ivb?ttublU0.II-vnnck>‘. \P.) L5; 0 .‘I-olbb o . u v u v ll? 1 . ‘tu 1' I 3h {D - . b . ‘ V» O ., (It! 1.. buns utknl I??-x:?. (ISLICH’I lle. .znts‘hu: \‘I littltlv 0b.~xv.cvb ”nfifluwmr! ta gamma. .ll -4 . . I. Z. ‘ I .n 1| 1 r0 . ‘ . , 5.3.5.1...‘K. - , .. . Noah: . . . M. . i ‘ . wihyuh! 3|]. {Mum ' m: J m ' ii C 't ‘1 ‘.~;.d '1'." Uiihflfi’i. .L “HRH.“HI‘)‘ ‘ n .9" I .A..' I mm. 1.5;; . H V n L” f'iémnéi {5 t | Illllllmllllllflllllli L “flew“ 3 1293 009898408 llBRARY Michigan State University This is to certify that the thesis entitled THE EFFECT OF TRANSIENT VIBRATION ON THE TOP-TO-BOTTOM COMPRESSIVE STRENGTH OF UNITIZED CORRUGATED SHIPPING CONTAINERS presented by ALAN ROBERT ADAMS has been accepted towards fulfillment of the requirements for ”5/5” C4 (SE/u Z7 Bruce Harte Major professor Date October 27, I987 0-7639 MSU is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES “ RETURNING MATERIALS: Place in book drop to remove this checkout from your record. _FINES will be charged if book is returned after the date stamped below. ~ :6."- at“ “A“ ‘ 2 {lg v... THE EFFECT OF TRANSIENT VIBRATION ON THE TOP-TO-BOTTOM COMPRESSIVE STRENGTH OF UNITIZED CORRUGATED SHIPPING CONTAINERS By, Alan Robert Adams A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE School of Packaging 1987 ABSTRACT THE EFFECT OF TRANSIENT VIBRATION ON THE TOP-TO-BOTTOM COMPRESSIVE STRENGTH OF UNITIZED CORRUGATED SHIPPING CONTAINERS By Alan Robert Adams The top—to-bottom compressive strength of corrugated shipping containers which had been subjected to a simulated transportation vibration environment was compared to the top-to-bottom compressive strength of non-vibrated boxes. The study was conducted on two sets of R80 boxes of different dimensions. The containers were conditioned according to ASTM test standard D 695, and vibrated in compliance with ASTM test standard D 999. The compressive strengths of the boxes were determined according to ASTM test standard D 642. Moisture content of the box material was also determined as outlined in ASTM test standard D 644. The mean top-to-bottom compressive strength of those boxes which did not fail in a simulated transient vibration environment was greater than the mean top-to-bottom compressive strength of non-vibrated boxes. The load at which failure occurred in the simulated transient environment was approximately one-third the value of the non-vibrated box top to bottom mean compressive strength. A simple mathematical model was devised to explain the phenomenon and predict the maximum strength expected from an RSC box. DEDICATION This thesis is dedicated to my parents, Robert G. Adams and Rosalyn B. Adams, whose patience and support made this accomplishment possible. iv ACKNOWLEDGEMENTS I would like to thank my major advisor Dr. B.R. Harte for his support and guidance through the graduate program. I would also like to express my gratitude to the members of my graduate committee, Dr. R. Brandenburg, Dr. S.E.M. Selke, Mr. D.E. Young. The assistance I received from, Dr. J. Gill with statistical design, Dr. J.W. Goff for package instrumentation, and Dr. G.J. Burgess in mathematical modeling, is also appreciated. I am also indebted to the following companies for donating Itesting materials, Dow Chemical, Midland MI, Pillsbury, Minneapolis MN, and Lever Brothers, New York NY. TABLE OF CONTENTS Page LIST OF TABLES ........................................ viii LIST OF FIGURES ....................................... ix INTRODUCTION .......................................... 1 LITERATURE REVIEW ..................................... 4 COMPRESSIVE STRENGTH ............................. 4 EFFECTS OF VIBRATION ............................. 5 CORRECTION FACTORS ............................... 6 TRANSPORTATION ENVIORNMENT ....................... 7 TEST METHODS ..................................... 7 PREDICTING RESONANCE ............................. 7 ESTABLISHED TEST METODS .......................... 8 EXPERIMENTAL, MATERIALS AND PROCEDURES ................ 11 SAMPLE CONTAINERS ................................ 11 CONDITIONING ..................................... 13 TESTING PROCEDURE ................................ 14 TESTING SEQUENCE ................................. 14 COMPRESSION TESTING .............................. 14 VIBRATION TESTING ................................ 16 MOISTURE CONTENT ................................. 16 RESULTS AND DISCUSSION ................................ 18 BOX No.1 OBTAINED FROM THE LEVER BROS. CO ........ 18 BOX No.2 OBTAINED FROM THE PILLSBURY OO .......... 21 BOX No.3 OBTAINED FROM THE PILLSBURY OO .......... 28 vi DETERMINATION or THE "A" VALUE FOR BOX No.2 ...... DETERMINATION OF THE “A" VALUE FOR BOX No.3 ...... SUMMARY ............................................... APPENDIX 1 ............................................ APPENDIX 2 ................................ . ............ APPENDIX 3 ............................................ LIST OF REFERENCES .................................... vii 37 38 4o 42 43 44 so Table 1. 2. 3 4 5. 6 7 8 9 10. 11. 12. 13. l4. 15. 16. 17. 18. 19. 29. 21. LIST OF TABLES Page Compressive Strength of Box No. 1...; ........... 19 Compressive Strength of Box No. 2 ............... 25 Compressive Strength of Box No. 3 ............... 29 Determining the "a" value ....................... 3? Determining the "a“ value ....................... 38 Moisture Content of Box No. 2 ................... 44 Moisture Content of Box No. 2 ................... 45 Moisture Content of Box No. 2 ................... 46 Moisture Content of Box No. 2 .................... 47 Moisture Content of Box No. 2 ................... 48 Moisture Content of Box No. 2 ................... 49 Moisture Content of Box No. 2 ................... 50 Moisture Content of Box No. 2 ................... 51‘ Moisture Content of Box No. 2 ................... 52 Moisture Content of Box No. 2 ................... 53 Moisture Content of Box No. 3 ................... 54 Moisture Content of Box No. 3 ................... 55 Moisture Content of Box No. 3 ................... 56 Moisture Content of Box No. 3 ................... 5? Moisture Content of Box No. 3 ................... 58 Moisture Content of Box No. 3 ................... 59 viii LIST OF FIGURES Table Page 1. A Typical RSC ................................... 12 2. Yield point on force-deflection curve ........... 15 3. Two sides of the box folding in rather than all four sides buckling together ............... 22 4. Typical "U" shaped pattern on the side of a corrugated box during compression .............. 23 5. Empty bottom box with box cap in place .......... 24 6. Top view of corrugated box showing ethafoam and concrete brick placement ........................ 27 7. Wood frame with removable lead weights ......... 30 8. 8.5 X increase in top—to-bottom compressive strength, Box No. 2 ............................. 33 9. 7.8 x increase in top-to-bottom compressive strength, Box No. 3 ............................. 34' 10. Four corners of a box acting as individual springs ......................................... 32 11. Rectangular plate supported on corners with a single concentrated force P in the exact center. 42 ix WIDE It is generally accepted that a package has three main functions: (1) to contain and protect, (2) to provide some utility, and (3) to communicate. If one of the three functions is deficient the package is considered to have failed. In the transportation environment a package is subjected to the dynamic forces of vibration which could cause package failure. Very little research has been published on the effect of vibration on the ability of a package to fulfill these functions. A tour through a typical warehouse will show that one of the most common packaging systems is the corrugated box. Observing a stack of boxes demonstrates that the bottom box is usually in the worst physical condition of the stack, with boxes at the top being in a less damaged state. When the boxe’s physical condition is severe enough, it will collapse, thus failing to contain, protect, and to communicate. The determination of box top-to-bottom compressive strength is a common test procedure used to evaluate shipping containers. This test works satisfactorily for static loads, but the procedure is inadequate for dynamic testing. Under normal, established testing procedures boxes are first preconditioned, conditioned, and lastly compression- tested empty with no correlation to dynamic environment testing. If dynamic testing is done, it is to determine if the package will survive a vibration resonance test for a set period of time. The actual strength of the container following repetitive shocks at resonance frequency may change from its non-vibrated state. A reduction in top-to-bottom compressive strength may occur due to the dynamic vibration environment. If this occurs, a factor of some kind may be necessary to correct box top-to-bottom compressive strength to compensate for the loss due to vibration. If the factor is too low, a weak box results and damage occurs, or overpackaging could occur if the factor is too high. Either way results in an economic loss. A significant cost savings could result if an approximate value could be determined that would predict the strength reduction due to transient vibration. Typically factors used to correct box top-to-bottom compressive strength have been developed based on experience, rules of thumb, or trial and error. These methods are inaccurate and inadequate in today’s cost- competitive marketplace. QBJEQII¥E$_QE_§IQDX This study was conducted: 1. To evaluate the change in top-to-bottom compression strength of corrugated shipping containers as a function of vibration. 2. To test different container systems to see if general top-to-bottom compressive strength patterns exist for corrugated shipping containers. Systems tested will be varied according to size, number of boxes in the stack, weights in boxes, and types of dunnage. QQMERESSI!E_SIBENGIH Godshall in (1985) stated that the "corrugated container industry has been making board specifications that have little if any correlation with compression properties. These specifications are those set by the carrier classifications boards which, in the absence of other standards for grade classifications, have become the defacto standards for grade classification of corrugated fiberboard. The corrugating industry in the United States has continued to manufacture corrugated fiberboard using bursting strength and basis weight specifications, as set forth by the carrier industries, because it has been to their economic advantage to support these specifications. They have ignored the findings of the research community and the needs of shippers for compression strength. However, corrugated users are becoming more knowledgeable about the performance requirements of the transportation environment and are making stronger demands on their suppliers to meet their needs for greater box compressive strength.” Uniform Freight Classification Rule 41 (1978) and National Motor Freight Classification Item 222 (1978) require that single wall, corrugated fiberboard containers have a minimum bursting strength ranging from 125 psi. to 350 psi., with a required minimum combined weight of facings ranging from 52 lbs. to 180 lbs. allowing for a contents 4 5 weight of 20 lbs. to 129 lbs. No mention is made of compressive strength in the standards. McKee, Gender and Wachutta (1963) devised a formula to determine top—to-bottom compression strength of corrugated boxes. The expression is as follows: 0.5378 0.4924 Top-to-bottom compression = 5.8745 Pm h z where Pm = column crush in lb/inch; h = caliper of board in inches, and z = box perimeter (2L + 2") in inches. This formula applies only to standard conditions, 73 degrees F (23 degrees C), 5OX R.H.. There is no parameter to account for vibrational effects. W Godshall (1968) reported that "failure (boxes which collapsed on a vibration table during testing) of containers appears to be due primarily to simple dynamic overloading (load on the top of the box was too great), and to dynamic overloading resulting from resonant amplification of vibrational input. Fatigue had no apparent effect on the top-to-bottom compressive strength of corrugated containers." Goff (1974) reported on performance. standards for parcel post packages, and concluded that vibration was shown to be of little consequence as a cause of damage in the parcel post system. Damage (boxes collapsing under load) could only be produced in the laboratory under very severe input conditions using very poorly constructed packages. When the load was sufficient to cause damage, all similar packages tested under this load were damaged. Guins (1975) found that an 8:1 amplification of the forcing vibration occurs during resonance, which induces bouncing in a stack of boxes. The acceleration value of the bouncing dynamic load will be 2-4 times the value of the static load. Therefore the dynamic load should only be 25 to 50 percent of the static load value. CQRREQIIQN.EA§IQBS Hanlon (1984) reports that a common rule of thumb for long-term storage is to use one—fourth of the compressive strength of a corrugated box as a safe load. He states that a more accurate method would be to calculate the fatigue factor for the length of time the material is expected to remain in storage. Factors are discussed for humidity and fatigue, but no reference is made to dynamic loading. In the American Society for Testing and Materials standard (D 4189-82), the ability of a package to withstand the compressive loads that occur during vehicle transport or warehousing is considered an integral part of performance testing. Factors suggested range from 8.9 to 3.9 depending on which assurance level is desired (8.0 being the highest assurance level for extremely fragile products). The top- to-bottom compressive strength is divided by the factor for the estimated true value. Young (1988) suggests that a factor of 3 to 8 be used to account for hazards in the transportation environment. IBANSEQBIAIIQN_EN¥IRQNMENI Forest Products Laboratory (Report 22) describes vibration levels using a power spectral density envelope curve for typical trucks and railcars. Acceleration values in the envelope curves are considered typical of most vehicles if the occasional high peaks, not considered representative of continuous vibration, are excluded. For trucks 3 he to 20 HE is considered an average range at approximately 0.5 g’s; for railcars the same frequencies have an average acceleration of 0.2 g’s. W W Godshall (1973) attempted to predict resonant frequencies using spring factors obtained by repeated cyclic loading in a universal testing machine. The predicted resonant frequencies were all lower than the experimentally determined resonant frequencies; averaging only 81 percent of the actual values. He concluded that this was prdbably due to differences between static and dynamic spring factors and, for accuracy, an actual vibration transmissibility test should be used for precise determination of resonant frequencies. Harris (1978) explained the jump phenomenon for a softening spring system (corrugated boxes are softening springs). "When the system is initially vibrated at a frequency higher than the natural frequency, followed by a 8 decrease in frequency (continuously at a slow rate) the amplitude of the vibration increases, up to a point (this is resonance). In particular, at the point of vertical tangency of the response curve, a slight decrease in frequency requires that the system perform in an unusual manner; i.e., that it "jump“ down in amplitude to the lower branch of the response curve“ (this is not a smooth gradual decrease in amplitude). If the stack of boxes is initially vibrated from a lower frequency and gradually increased it will not have the same natural frequency. There is a portion of the response curve which is "unattainable". This is important to recognize in designing an experiment for determining resonance so that all samples are tested at the same natural frequency. Kusza and Young (1974) discussed the vibration response of packages stacked in a column. They concluded that the greater the number of boxes in a stack, the lower the effective natural frequency of the stack. In this situation the oscillation of the top box was most severe. For this thesis the top box will be monitored to determine the natural frequency for the stack of boxes. W The American Society for Testing and Materials standard (D 685-73) includes conditioning of paper products and lists two steps in the conditioning process for knocked down shipping containers. First the samples must be 9 preconditioned in an atmosphere of 10 to 35 X relative humidity at a temperature of 22 to 40 degrees C for a period of 5 to 10 hours. The second step is to condition in an atmosphere of 50.0 i 2.0 X R.H.and 23.0 i 1.0 degrees C. for 5 to 8 hours. The American Society for Testing and Materials standard (D 4169), which covers vibration performance testing, requires that for the highest assurance level, .5 g’s and a dwell of 15 minutes for truck transport and .25 g’s with a dwell of 15 minutes for rail transport be used. The American Society for Testing and Materials standard (D 999-75) Method C, the unitized load or vertical stack resonance test, covers the effects of resonance in multiple- unit stacked loads, and recommends that if dwell time is not specified by other relevant ASTM test standards a dwell of 15 minutes be used. The American Society for Testing and Materials standard (D 642-76) is the Standard Method of Compression Testing for Shipping Containers. The method suggests testing containers without contents, sealing the box to avoid distortions that may affect its load-bearing ability, and applying a preload of 50 lb force with the load being applied at a rate of .5 1 0.1 in./min.. In American Society for Testing and Materials standard (D 844-55) determination of the moisture content of paper products by oven drying is covered. The method requires the sample to be weighed, dried for 2 hours at 105 i 3 l0 degrees C then cooled in a desiccator for a period of one hour and reweighed. The percent moisture is determined by taking the difference in weight and dividing by the initial weight then multiplying by 100. W W Three sets of regular slotted containers (R.S.C.) were used in this study (figure No. 1). B I 1 5 IE' I' Corrugation - C flute, double faced. Dimensions 18 1/4“ x 11 1/4“ x 11 3/4“ (L x W x D) Bursting Test - 200 lbs. per square inch. Minimum Combined Weight Facings - 84 lbs per 1000 square feet. Size Limit - 75 inches. Gross Weight Limit - 65 lbs. Manufactured by Container Corporation of America for Lever Brothers Company. B I 2 S 'EI I' Corrugation - C flute, double faced. Dimensions 19 1/2” x 10 1/4” x 7 1/4" (L x W x D) Bursting Test - 200 lbs. per square inch. Minimum Combined Weight Facings - 84 lbs per 1000 square feet. Size Limit - 75 inches. Gross Weight Limit - 65 lbs. Manufactured by Owens Illinois - Forest Products Division for the Pillsbury Company. 11 12 r .L mLJGH .u ”mm W; HOUHQE H. < I; Duds. > 92095») \/ ( Hadep 1 U l3 E I 3 S 'E' l' Corrugation - B flute, double faced. Dimensions 15 1/4“ x 6 1/4” x 4 1/2" (L x W x D) Bursting Test - 125 lbs. per square inch. Minimum Combined Weight Facings - 52 lbs. per 1000 Square Feet. Size Limit - 40 inches. Gross Weight Limit - 20 lbs. Manufactured by Weyerhaeuser Company for the Pillsbury Company. CONDITIONING Boxes were received knocked-down from Lever Brothers and Pillsbury. A glued manufacture’s joint (glued by the corrugated box manufacture’) was used on all boxes. Containers were first prebroke’ and set up unsealed without bending flaps to allow for air circulation. The boxes were then preconditioned at 74 degrees F, and 30% R.H., for 24 hours, and, then, finally conditioned at 72 degrees F, at 50 i 2% R.H., for 8 hours, in accordance with ASTM D 885 - 73. Temperature and relative humidity conditions were monitored using a Bendix recording Hygro-thermograph (model 594). The Hygro-thermograph was calibrated with a Bendix Psychron Psychrometer (model 566). After conditioning, empty containers were sealed top and bottom as outlined in ASTM Standard D 642 with 3M brand (3M - Minneapolis, MN) plastic sealing tape. l4 TESTIN§_EEQQEDQEE W Because all of the testing could not be performed during the same test-run, testing was divided into groups to avoid the combined effects of different moisture contents, different temperatures, and machine setup variability. For each test run one group of boxes was tested. One test group contains two boxes for each treatment performed; a treatment is each of the five different top loads and one control. Thus twelve boxes were tested during each run. Twenty samples for each treatment were needed (Gill 1986, see Appendix 2). Six treatments with twenty samples resulted in one hundred twenty boxes tested for each box size. WW Compression strengths of all the samples were evaluated using a Instron Universal Testing Machine Model TTC 2344642. A free floating platen apparatus was designed for this experiment and is discussed in Appendix 1. Crosshead speed used was 0.5 inches per minute, as recommended in ASTM D 842-76 with the chart paper speed set at 5 inches per minute. Compressive strength was considered to be the yield point; the highest point on the force- deflection curve (figure 2). The compressive strength for each treatment category is reported as the average of twenty samples. 15 Yield point. Force DeFIécLIon Yield point on Force- deFIecLlon curve. Figure 2. 16 H'] Ii I |° All vibration testing was performed using an MTS 840 Electra—hydraulic vibration test system. Samples were tested at 0.5 g’s during resonance for 15 minutes as described in ASTM D 4189, for the highest assurance level for the worst ride in truck transportation. Resonance determination was calculated using a Hewllet-Packard X-Y plotter model 7034A, and a Kistler accelerometer model 815A5. The accelerometer was mounted in one of the boxes containing a load and placed on the top of the stack. "G” levels experienced in the package were plotted as a function of table frequency. Resonance was considered to be at the frequency where the package encountered the highest g level. The starting frequency of the vibration table was a lower frequency than the stack resonance frequency and was increased to the natural frequency of the stack to avoid a change in resonance frequency due to the ”jump" phenomenon (Harris 1976). Wheat Determination of moisture content was performed on containers that were tested for compression strength. One box flap was cut off each box tested. The procedure followed was ASTM D 644 with one exception. Weighing containers are recommended when transporting samples from storage and testing location to avoid changes in moisture content due to differing atmospheres. These containers were not used because test samples were in the same conditioned l7 atmosphere room during testing, and during moisture content determination. Samples were weighed, placed in a drying oven at 100 i 3 degrees C for two hours, cooled for one hour in a dessicator, and then reweighed. Percent moisture was calculated for wet basis percent moisture by using the difference between the initial and final weights divided by the initial weight multiplied by 100. RESHLIS_AND_DISQQSSIQN Two hundred eighty seven corrugated shipping containers were tested to determine if a change in compressive strength would result from transient vibration. All testing was done at 23 degrees C, 50% R.H.. Moisture content determination was performed for each test day. Bax—NQL_I_Qhfinin§d_129m_§h£.L!!§I_BIQSL_QQL Table one contains the results for this box at the various loads. For this test a stack of five boxes was chosen. The top four boxes contained evenly distributed weights. The bottom box was empty and supported the lead. A stack, five boxes high was chosen because a typical truck trailer 40 feet long by 8 feet wide has 46080 square inches of floor space. If 90% space utilization is achieved there is 41472 square inches of usable space. Divided usable space by area per box of 205 square inches to calculate 202 boxes per layer. Normal truck trailers are capable of carrying 40,000 lbs. divided by 202 boxes per layer there would be 198 lbs per box if only one layer per truck is used. 198 lbs. per box is more weight than allowed by Uniform Freight Classification Rule 41 (1978). Rule 41 specifies a maximum allowable weight of 65 lbs. per container for 200 lbs test C—flute corrugated fiberboard. A range of 18 to 50 lbs per box was chosen to stay within the linnits of Rule 41. Divide the lightest load 72 lbs. by 18 113:3. per box calculates 4 boxes are required to contain the 18 l9 13:212.]. Wu Compression Strength (lbs) vigggged 72 lb 88 lb 104 lb 112 lb Box load load load load 1. 800 . 820 720 600 740 2. 800 720 760 700 720 3. 880 720 780 680 680 4. 820 800 700 860 740 5. 840 780 760 720 680 6. 820 900 800 700 640 7. 740 720 760 800 620 8. 720 720 720 880 720 9. 820 880 860 520 780 10. 700 600 mean 804.4 762.2 758.0 651.1 892.0 Std. 48.8 68.9 49.7 64.9 58.3 dev. 20 load and one empty box on the bottom for a total stack of five boxes. The stack height should not be any taller than a truck door which is typically eight feet, the height for five boxes high is 4.9 feet. Non-vibrated average compressive strength for this box was 804 lb. As the top load was increased for each test run the compressive strength decreased from 762 lbs per box for a 72 lb. top load to 692 lbs. per box for a 112 lb top load. The standard deviation for the 72 lb. top load, which had the greatest variance, was within nine percent of the non- vibrated new box compressive strength. A possible conclusion would be that with an increase in top load the strength of a box will decrease. However several potential variables need to be considered. Vibration testing for this set of boxes was done on a weight by day basis; for example all of the 72 lb load tests were done on the same day. Machine setup, testing room atmospheres, test technician error are all factors that could change on a day-to-day basis. No provision was made to account for these variables. One way of investigating the changing test conditioning atmospheres would be to determine moisture content of the boxes. A change in moisture content possibly indicates that there was a change in the procedure or conditioning of the samples that could have skewed the results. At loads higher than 112 lbs the boxes failed. However, this failure was not typical of failure patterns in 21 the distribution environment. The boxes were crushed on two sides with the remaining sides still intact (figure 3). Observations in several warehouses demonstrated that typically a box will fail due to panels caving-in or out with development of a U shaped pattern (figure 4). This U shaped pattern is the same pattern that will occur in a typical compression test. In order to duplicate the same U shaped pattern during testing, a box cap was placed over the empty bottom box (figure 5) for the remaining sets of boxes. Placement of this cap over the top of the bottom box distributed the load over the entire box top surface and when failure occurred the same U shaped pattern resulted. B9x_NQL_Z_QhInin2d_129m_Ih§_Eillfihn£¥_§QL In table 2 are presented the results for box No. 2 tested under the various loads. Loading values were determined by a trial test. For test loadings over 215 lbs. the sample container was crushed in every trial. The loading was then decreased by 4 percent per loading to a load that was 21 percent of the non-vibrated box compressive strength. A loading of 21 percent of the non-vibrated box compressive strength is under the recommended safe limit of 25 percent as recommended by Hanlon (1984). For this test the boxes were tested in groups as discussed previously. Rule 41, Uniform Freight Classification (1978) allows a maximum load of 65 lbs. per box for 200 1b test C-flute corrugated fiberboard. Loads 22 .m ijmdu Lmiymmoy QCHHJUJD mmUHm Ljou HHU COLD LmLDUL CH OCHUHOQ XOD min m0 mmflem 03F I] “fir—”3150 x03 JAQEU Cm 23 Typical 'U' shaped pattern on the side 0F a corrugated box during compression. Irlgurerlh 24 31:: c: I::II::J do: E (VI bretion Table! Emptg bottom box with box cap in place Figure 5. 25 TabIILZ W Compression Strength (lbs) _____* denotes failure of viggzged 125 lb 148 lb 188 lb 191 lb 215 lb __.__BQx load__.___19ad load______lQad load 1. 550 820 810 840 t 685 2. 610 480 620 610 590 3. 560 610 880 620 630 670 4. 580 800V 640 630 660 _____ 5. 640 620 670 650 880 _____ 8. 550 640 620 670 670 _____ 7. 590 880 630 620 670 _____ 8. 620 570 650 650 _____ _____ 9. 570 840 820 850 ‘10. 610 640 850 590 690 660 11. 540 590 880 660 700 _____ 12. 600 680 620 880 660 13. 620 830 650 860 660 14. 580 820 p 680 670 650 630 15. 600 840 870 610 870 16. 570 830 700 870 700 830 17. 820 890 680 850 _____ 640 18. 540 610 850 880 _____ 19. 580 810 820 610 680 _____ ZQL__§221 620_, 660 _egg 519 ..... mean 586 820 847 641 _____ _____ Std. dev. 28.4 42.2 23.5 24.8 container 26 ranging from 21 lbs. to 36 lbs. were used to stay within limits of the rule. Six boxes containing 21 lbs each were used for a stack loading of 125 lbs. A box cap was placed over the empty bottom box supporting the load, bringing the total number of boxes in the stack to seven. Seven boxes have a height of 4 feet which is under the truck trailer door limit of 8 feet. Concrete bricks were used as weights in the boxes with 9 1b density ethafoam as dunnage. To change weights in the boxes, bricks were added to and subtracted from each box as shown in figure 6. When a brick was removed a brick made of ethafoam replaced it, always positioned to keep the load evenly distributed. There was no resonance frequency interference between the brick, the ethafoam, and the stack, because both the brick and the ethafoam were determined to have a considerably higher resonance than the stack. As shown in table 2 the boxes did not decrease in strength but increased. The first three loads resulted in a significant increase in strength compared to the non- vibrated box strength (Dunnett statistical test at 85 percent power (percent power is similar to confidence level) (Gill, Appendix 2)). Since the results from box No. 1 and No. 2 were different, it was decided to try a third test on a different container. The test was designed with a different size box, numbers of containers in the stack, and system for loading with weights. 27 Concrete Bricks EthaFaam Bricks Concrete Bricks EthaFoam Bricks EthaFaam Dunnage Concrete Bricks EthaFoam Dunnage EthaFoam Bricks EthaFoam Dunnage Concrete Bricks EthaFoam Bricks i Top view oF corrugated box showing ethaFoam and concrete brick placement. Figure 6. 28 E N a Q]! . I E II 2.1] l C In Table 3 are shown the results for the third box with the various loadings. For this test B flute corrugated board was used instead of C flute, the box was approximately one-half the height dimension of the previous box, and eleven boxes were chosen for the stack height with ten boxes containing weights, the box cap, and the empty box on the bottom. The dimensions of the third box were too small to permit use of bricks for the load so lead weights were used. One and one-half pound weights were added and removed from a wooden frame placed in the corrugated box (figure 7). The wooden framework was necessary because there was no other dunnage used to fill the corrugated container. The resonance frequency of the wooden frame and bricks was checked and found to be higher than the resonance of the stack. Using the Dunnett t-test, the compressive strength of the non-vibrated boxes and the 75 lb. loaded boxes were found to be significantly different at 85 percent power. level. 85 percent power level was chosen so not to vary from the previous power levels. It is not obvious from table 3 that the compressive strengths of the non-vibrated boxes were found not to be significantly different than the 80 and 90 lbs. loaded boxes. Boxes loaded to approximately one third the non-vibrated compressive strength had a failure rate of thirty percent. Several factors may be of importance. In the second set of boxes, non—vibrated box 29 Iahle.§ W4 Compression Strength (lbs) viggzted 60 lb 75 1b 90 lb 105 lb 120 lb Box load load______1gad load load 1. 380 340 370 310 370 _____* 2. 350 360 340 320 _____ _____ 3. 320 300 310 320 4. 280 300 330 280 390 380 5. 310 320 330 360 380 6. 310 330 350 330 I 350 330 7. 330 360 370 400 410 8. 380 380 420 410 410 9. 310 340 380 380 _____ 10. 280 320 360 330 350 _..__ 11. 270 300 380 340 260 _____ 12. 290 300 300 320 260 _____ 13. 280 330 290 370 320 _____ 14. 270 290 240 _____ _____ 15. 290 340 330 350 16. 300 360 320 340 330 400 17. 320 280 270 370 350 18. 300 300 310 320 400 330 19. 330 310 350 370 320 ____ 22...:20 382 3&2 312 ---------- mean 310 328 335 342 _____ _____ Std. dev. 33.2 28.4 41.7 33.3 * denotes failure of container 30 .N ijmum .mDLOHmB Unmfi mHflU>BEmL LJHB mEULL. UGO) flees...» 100) JIM SLUDLJJ POOH Loum3 U00+ Loam) 300* axons: no.4 s;a_os noon Axons) poeJ ENUQqu FMDCV‘ axons) $0.4 cl 1 aIIIPI |F%JWLflrT s fl .EOLIIIIIMIIIIII t00>§ L— 3l strength had a standard deviation of 3.3% of the mean compressive strength compared to the third set of boxes which had a standard deviation of 10.71% of the mean compressive strength. Included in the 90 lb load were two failures which were counted as zero. Percent moisture content was determined for each group of boxes (tables 6-21 in appendix 3). A box flap was cut off from each individual box, weighed, dried, and reweighed to determine the difference. This number was then divided by the original weight times 100, to obtain the percent moisture content. The mean moisture content for the second group of boxes was equal to 7.25% with a standard deviation of .19%. The third group of boxes had a mean of 8.89% with a standard deviation of .1%. In this study failure of the corrugated boxes was due to dynamic overloading, the weight of the load bouncing on the bottom container during resonance was too high. Most of the containers failed during the first four minutes of vibration. The top load at failure was one-third the mean value of the non-vibrated box top to bottom compressive strength. A factor of 3 should therefore be used when accounting for vibrational effects on corrugated box strength. If for Box No. 3, 90 lb. load, the two failures that occurred are not counted when calculating Dunnett’s t-test a significant statistical difference results. Graphing the Machine Compression Strength compared to Top load 32 demonstrates the corrugated boxes tested had an 8-10% increase in top to bottom compressive strength after subjection to vibration (figures 8 h 9). An explanation for this phenomenon is offered by Burgess (1987) where failure is due to a combination of side-wall buckling .and corner-crushing. The dominant influence on compression strength is corner rigidity since buckling of corrugated sides takes place at relatively low loads. The RSC can then be modeled as a system of 4 springs of different lengths, each of which fails when the compression reaches some critical value. The function of the sides is to maintain the springs in an upright position (figure 10). Four corners oF.a I1 box acting as indiv1dual 3 . 1’ springs. Figure ID When the floating platen begins to compress the RSC, it contracts only three of the 4 springs initially unless the four heights shown lie in a perfect plane. In this example “a" is equal to the distance' between the platens and the uncontracted spring when the platen firsts contracts the other three. "k" is equal to the spring constant of on: of the 4 identical corner springs. "x" is for compressions where the distance between the uncontracted spring and the 33 690 66... "GO" I N! COMPRICC I ”I STRENGTH I. b. e s u s .. s s .8 .9 P P 3: E! o It at 910 do do 110 2d 10? LORD-SECOND m 8.5 % increase in top-to-bottom compressive strength, Box No. 2 figure 8 34 370 H R 2904 ”ROME": COMPRICCIUE STRENGTH 11,-. u p E 3 0 2'0 «I: K it do i}. m TOP WAD-III" I03 7.8 % increase in top-to-bottom compressive strength, Box No. 3 figure 9 35 platen are different than the optimum distance “a". For compressions “x" greater than "a" the force/deflection relation is: F = (3k)x For compressions x less than a, the -platen has compressed three of the springs x and the fourth (x-a). So F = 3kx + k(x-a) = 4kx - ka Failure occurs when x is some critical value, say x , cr at which time the load F becomes the compression strength C; C = 4kx - ka or If there was a perfect RSC where a = 0, the compression strength would be as high as it would get: C = compression 0 strength when a = 0 Therefore, C = C - ka = C - (C + 4x )a and C'I'C =(1-a-l-4x) O or This states that the ratio of the compression strength with the out of planeness distance "a" to the compression strength for a perfect RSC (C , which is unknown) is l - a t 0 4x where x is the compression of the perfect RSC at cr or failure (which is also unknown). (Sample data was collected 36 for the box No. 2, see Table 4) Non-vibrated box (C,a) = (586, .086), Vibration sample (C,a) = (842, .016). now force fit these values into the above equation: 1). 586 + C l - .086 + 4x 0 cr 2). 642 + C = 1 - .016 + 4x 0 cr Solve simultaneously C = 655 lbs. and x = .2 inches. 0 cr For box No. 2 the compression strength and corresponding deflection of a perfect RSC would be 655 lbs. at approximately .2 inches. Therefore, C + 655 = 1 - a + .8 or C = 655 (l — 1.25a) Sample data for box No. 3 (see table 5), Non-vibrated box (C,a) = (310, .0485), Vibration sample (C,a) = (335, .008) force fit these values into the previous equation: 1). 310 t C = 1 - .0485 + 4x 0 cr 2).-335 + C = 1 — .008 + 4x 0 cr Solve simultaneously C = 340 lbs. and x = .14 0 cr inches. For box No. 3 the compression strength and corresponding deflection of a perfect RSC would be 340 lbs at approximately .14 inches. Therefore, C + 340 = 1 - a t .86 C = 340 (1 - 1.16a) 37 The "a" value is the sum of the height measurement of two opposite corners subtracted from the sum of the height measurement from the two remaining corners. A 20 lb. weight on a plywood board was placed on the end of the box, a ruler measured the distance between a table surface and bottom of the board. 1:.th Determining the "a" value for Box No. 2 test number 14. Measurements are clockwise around container in inches, two containers for each load were tested and averaged. Difference Non 7 31/64, 7 27/64, 7 31/64, 7 31/64 .0625 vibrated 7 33/64, 7 29/64, 7 33/64, 7 31/64 .110 box Total t 2 = .088 125 lb. 7 22/64, 7 22/64, 7 22/64. 7 21/64 .018 load 7 24/64, 7 20/64, 7 20/84, 7 21/64 .016 Total + 2 = .016 146 lb. 7 20/64, 7 21/84, 7 24/64, 7 23/64 .000 load 7 21/64, 7 20/64, 7 20/84, 7 22/84 .016 Total t 2 = .080 188 lb. 7 23/64, 7 20/64, 7 20/64, 7 21/64 .031 load 7 21/64, 7 22/84, 7 21/64, 7 20/64 .000 Total + 2 .016 38 D | . I' E II a u 1 : fin Bax N: 3 Another method was used to obtain "a" values for box No. 3. A vernier caliper accurate to 1/1000“ was used to measure the height of corners of the box. A statistically significant difference in strength existed between the non vibrated box and 75 lb. top load box and are the values presented. Inbl§_§ Determining the "a" value for Box No. 3 test number 2. Two sets of boxes were tested at the same time so there are four boxes per group. Measurements are in inches. difference New Box 4.965, 5.074, 4.983, 5.000 .148 4.990, 5.036, 5.038, 4.995 .005 4.995, 5.020, 5.015, 5.021 .031 5.040, 4.980, 4.995, 5.043 .012 Total t 4 = .0485 75 lb. 4.981, 4.952, 4.975, 4.990 .014 4.959, 4.960, 4.973, 4.971 .004 4.981, 4.955, 4.970, 4.973 .003 4.975, 4.961, 4.961, 4.965 .010 Total t 4 .008 39 This explanation states that if a box were perfectly square when manufactured it would have the greatest top to bottom compression strength. Boxes however are not perfectly square from the box manufacture. Some tolerances have to be allowed for the manufacturing process, but tighter the tolerances used when producing the corrugated box the higher the top to bottom compressive strength will be. SUMMARY Sets of different size corrugated boxes were tested to determine the effect of a simulated transient vibration environment on the mean top to bottom compressive strength. Moisture contents tests were performed on the sets of boxes and found to be similar. In summary: 1. Top to bottom mean compressive strength increased after subjection to vibration. This resulted in an 8 percent increase in top to bottom compressive strength In this study failure of the corrugated box was due to dynamic overloading. Containers failed in the first four minutes of testing on the vibration table with a top load of one-third the value of the non-vibrated box mean compressive strength. Higher tolerances followed during corrugated box manufacture will result in boxes having closer to equal box corner heights. Equal corner heights will increase top to bottom compression strength. A safety factor of 3 should be used for calculation of the maximum top load a box can withstand in a transient vibration environment. W 1. Environmental considerations: All testing was performed at standard conditions ASTM D 885-73, temperature and relative humidity were not evaluated. Testing should 40 41 be done to see if these same trends hold true in severe conditions. Pallet design and stacking patterns: What effect if any does the type of pallet used, and stacking pattern of boxes during vibration in transit have on the top to bottom compressive strength of corrugated shipping containers. Load: All boxes tested for compressive strength were empty; Does a load in the container during vibration affect the top to bottom compressive strength. Test Burgess theory (1987): Corrugated boxes increase in top to bottom compressive strength after subjection to vibrational input because the corners of the non- vibrated box being unequal in heights, compared to a vibrated box where the corners are closer to equal heights due to settling effect of vibrational input. APPENDICES 42 AHEEMDIX_1 From Den Hartog (1952) page 133 case 21. Illustration of problem. p Rectangular plate supported on corner. with a single concentrated Farce P in the b exact center. i J F—-'° —————fl Figure 11. 2 3 W = 6 (Pa t Et ) max a = 22", b = 28", b/a = 1.27 From page No.133 for b/a = 1.27, E = .153 Assume max force for platen = 1600 lbs. 6 2 Modulus of elasticity for aluminum = 9.9 - 10.3 x 10 lb/in Maximum deflection for .75" thick plate = 0.023990" One more consideration is weight of the platen. The weight should be less than the 50 lb pre-load required by ASTM Standard D 642 - 76 to account for slack in the platen mounting system. The density for aluminum is 188.5 lbs per cubic foot therefore .75" x 22” x 28" = 462 cubic inches t 1728 inches per cubic feet = 0.27 cubic feet x 168.5 = 45.5 lbs. 43 AEEENDIX_Z From Gill (1986) Nnmhe£_Q£_BQxafi_LQ_Iefih d = c + c J (r t 4) r = number of boxes 0 = expected standard deviation c = detectable change required d = 2.5 value given by Gill from OC curves 2.5 = 50 + 40 J (r + 4) r = 16 (plus 20% safety factor) = 20 boxes per treatment 93% Power E 1 . E X . Dunnett’s test t = (x - x ) t J (2(MS t r)) 1 2 e x = mean of control group 1 x = mean of treatment group 2 MS = Mean Squared Error e r = number per treatment value of t > 2.32 for positive test of difference value from Gill (1988) 85% power APPENDIX 3 44 W W Weight In Grams First test day No. Initial Wt. Final Wt. moisture % content 1. 6.1559 5.7398 6.76 2. 6.3936 5.9504 _6.93 3. 6.0375 5.6345 6.67 4. 6.0680 5.6574 6.77 5. 6.3323 5.8987 8.85 6. 6.1618 5.7445 6.77 7. 6.2212 5.7825 7.05 6. 6.1156 5.7027 6.75 9. 6.2726 5.8412 6.88 10. 6.0432 5.6377 6.71 Mean 6.81 Std Dev. 0.11 45 TehleJ WW Weight In Grams Second test day No. Initial Wt. Final Wt. Moisture % content 1. 6.1416 5.7046 7.12 2. 6.0721 5.6469 7.0 3. 6.0911 5.6537 7.18 4. 6.0821 5.6798 7.17 5. 6.2853 5.8481 6.96 6. 6.1684 5.7346 7.03 7. 6.1196 5.6781 7.21 8. 6.2441 5.7979 7.15 9. 6.1185 5.6796 7.17 10. 6.2281 5.7776 7.23 Mean 7.12 Std Dev. 0.09 46 TehleJ. WWW Weight In Grams Third test day No. Initial Wt. Final Wt. Moisture % content 1. 6.1790 5.7108 7.58 2. 6.2460 5.7909 7.29 3. 6.1415 5.6952 7.27 4. 6.1565 5.6835 7.68 5. 6.1241 5.6656 7.49 6. 6.2252 5.7732 7.26 7. 6.1513 5.6929 7.45 6. 6.1479 5.7129 7.08 9. 6.2053 5.7455 7.41 10. 6.0745 5.6394 7.16 Mean 7.37 Std Dev. 0.19 47 W W Weight In Grams Fourth test day No. Initial Wt. Final Wt. Moisture % , content 1. 6.1300 5.6834 7.29 2. ' 6.1407 5.6869 7.36 3. 6.0687 5.6298 7.23 4. 6.1530 5.7150 7.12 5. 6.2689 5.8138 7.26 6. 6.2378 5.7861 7.24 7. 6.0623 5.6233 7.24 8. 6.1907 5.7576 7.00 9. 6.2775 5.8174 7.33 10. 6.1005 5.6801 6.89 Mean 7.20 Std Dev. 0.15 48 Iahl£_lfl WW Weight In Grams Fifth test day No. Initial Wt. Final Wt. Moisture % content 1. 6.1129 5.6556 7.48 2. 6.2448 5.7748 7.53 3. 6.3554 5.8715 7.61 4. 6.1932 5.7231 7.59 5. 6.0529 5.3194’ 7.16 6. 6.0962 5.6443 7.44 7. 6.1564 5.7122 7.25 8. 6.2664 5.8031 7.39 9. 6.1949 5.7283 7.53 10. 6.3051 5.8404 7.37 Mean 7.44 Std Dev. 0.15 49 IahleJl WW Weight In Grams Sixth test day No. Initial Wt. Final Wt. Moisture % content 1. 6.2216 5.7643 7.35 2. 6.3299 5.6633 7.37 3. 6.2574 5.7932 7.42 4. 6.2546 5.7649 7.51 5. 6.2174 5.7543 7.45 6. 6.3344 5.8583 7.52 7. 6.2177 5.7526 7.29 8. 6.3072 5.8473 7.40 9. 6.1946 5.7457 7.25 10. 6.3068 5.8478 7.31 Mean 7.39 Std Dev. 0.09 50 Table_12 991W Weight In Grams Seventh test day No. Initial Wt. Final Wt. Moisture % content 1. 6.2768 5.6074 7.48 2. 6.3316 5.6724 7.25 3. 6.3736 5.9095 7.26 4. 6.1125 5.6735 7.18 5. 6.1399 5.6929 7.28 6. 6.1192 5.6661 7.40 7. 6.1349 5.6810 7.40~ 6. 6.3875 5.9212 ‘7.30 9. 6.3088 5.8478 7.31 10. 6.3906 5.9406 7.04 'Mean 7.29 Std Dev. 0.12 SI Tabled?! WW Weight In Grams Eighth test day Moisture % No. Initial Wt. Final Wt. content 1. 6.2253 5.7665 7.05 2. 6.1840 5.7541 6.95 3. 6.3022 5.8522 7.14 4. 6.1641 5.7149 7.29 5. 6.1782 5.7153) 7.43 6. 6.2712 5.7993 7.52 7. 6.2693 5.7675 7.69 8. 6.2703 5.6315 7.00 9. 6.2312 5.7733 7.35 10. 6.2626 5.6104 7.22 Mean 7.27 Std Dev. 0.24 52 151211.15 WW Weight In Grams Ninth test day No. Initial Wt. Final Wt. Moisture % content 1. 6.1355 5.6859 7.33 2. 6.2694 5.6136 7.27 3. 6.1659 5.7039 7.49 4. 6.3006 5.6324 7.43 5. 6.3033 5.6316 7.48 6. 6.2596 5.7907 7.49 7. 6.2146 5.7584 7.34 8. 6.2775 5.6059 7.51 9. 6.2415 5.7775 7.43 10. 6.3242 5.6528 7.45 Mean 7.42 Std Dev. 0.06 53 W W Weight In Grams Tenth test day No. Initial Wt. Final Wt. Moisture % content 1. 6.2993 5.8424 7.25 2. 6.1973 5.7519 7.19 3. 6.1646 5.7163 7.26 4. 6.1916 5.7467 7.19 5. 6.1295 5.7061 6.91 6. 6.1479 5.7031 7.23 7. 6.2031 5.7627 7.10 8. 6.0122 5.5963 6.92 9. 6.1042 5.6675 7.15 10. 6.1545 5.7105 7.21 Mean 7.14 Std Dev. 0.13 54 Tahle..16 WW3 Weight In Grams First and Second test groups No. Initial Wt. Final Wt. Moisture % content 1. 4.3002 4.0023 6.93 2. 4.4452 4.1492 6.66 3. 4.4096 4.1069 6.86 4. 4.3820 4.0808 6.87 5. 4.3686 4.0660 6.93 6. 4.4432 4.1326 6.99 7. 4.5551 4.2291 7.15 8. 4.3574 4.0621 6.78 9. 4.3978 4.0900 7.00 10. 4.4552 4.1458 6.95 Mean 6.91 Std Dev. 0.13 55 TehIe_Il 991W Weight In Grams Third test group No. Initial Wt. Final Wt. Moisture % content 1. 4.2356 3.9350 7.10 2. 4.3971 4.0834 7.13 3. 4.2861 4.0054 6.55 4. 4.3832 4.0827 6.86 5. 4.4756 4.1492 7.29 6. 4.4238 4.1086 7.13 7. 4.6602 4.3254 7.18 8. 4.3979 4.0868 7.07 9. 4.4505 .4'1346 7.10 10. 4.3907 4.0934 6.77 Mean 7.02 Std Dev. 0.22 56 W W Weight In Grams Fourth test group No. Initial Wt. Final Wt. Moisture % content ' 1. 4.4157 4 1145 6.82 2. 4.2548 3 9594 6.94 3. 4.3694 4.0666 6.93 4. 4.4056 4.0979 6.98 5. 4.1693 3.8845 6.83 6. 4.3089 4.0101 6.93 7. 4.4320 4 1345 6.71 6. 4.4208 4 1167 6.89 9. 4.3865 4.0817 6.95 10. 4.3077 4.0279 6.50 Mean 6.65 57 W W Weight In Grams Fifth test group No. Initial Wt. Final Wt. Moisture % content 1. 4.3424 4.0343 7.10 2. 4.3037 3.9925 7.23 3. 4.4565 4.1399 7.10 4. 4.6229 4.2838 7.34 5. 4.4502 4.1520 6.70 6. 4.4059 4.1076 6.77 7. 4.3851 4.0965 6.58 8. 4.2928 3.9895 7.07 9. 4.4159 4.1128 6.86 13. 4.4131 4.1137 3.34 Mean 6.96 Std Dev. 0.26 58 131113.20 WW Weight In Grams Sixth and Seventh test groups No. Initial Wt. Final Wt. Moisture % content 1. 4 2644 3.9837 6.58 2. 4 3132 4.0243 6.70 3. 4.2885 3.9981 6.77 4. 4.3850 4.1127 6.42 5. 4.4264 4.3205 error 6. 4.4164 4.1216 6.68 7. 4.5493 4.2597 6.37 8. 4.2701 3.9826 6.73 9. 4.4268 4.1186 6.96 10. 4.4213 4.1263 6.67 11. 4.2538 3.9611 6.68 12. 4.4619 4.1310 7.41 13. 4.3356 4.0236 7.19 14. 4.0007 4.0652 error 15. 4.3058 4.0185 6.67 16. 4.3442 4.0518 6.73 17. 4.3418 4.0462 6.81 18. 4.4174 4.1278 6.56 19. 4.3900 4.1061 6.47 20. 4‘3212 4.1086 6.56 Mean 6.73 Std Dev. 0.26 59 W Moistuze.§entent_ef_hex_fleu.fl H . II I G E' III Ni II I I II | I No. Initial Wt. Final Wt. Moisture % contents 1. 4.4436 4.1398 6.90 2. 4.4897 4.1673 7.18 3. 4.3529 4.0464 7.04 4. 4.5260‘ 4.2121 6.86 5. 4.3032 4.0001 7.04 6. 4.3437 4.0456 6.86 7. 4.4456 4.1447 6.77 8. 4.5013 4.1748 7.25 9. 4.2956 4.0059 ‘6.74 10. 4.3834 4.0767 6.57 11. 4.4282 4.1229 6.89 12. 4.3993 4.0896 7.04 13. 4.5393 4.2269 6.88 14. 4.3418 4.0382 6.99 15.‘ 4.4101 4.1033 6.96 16. 4.4028 4.1360 6.08 17. 4.4557 4.1504 6.85 18. 4.4099 4.1008 7.01 19. 4.4777 4.1585 7.13 _____ZQ- 4.3562 412064 6-23_.___. Mean 6.67, Std Dev. 0.29 LIST OF REFERENCES American Society for Testing and Materials. 1983. Standard Test Methods of Compression Test- for Shipping Containers. D642-76. American Society for Testing and Materials. 1982. Standard Test Methods for Moisture Content of Paper and Paperboard by Oven Drying. D 644—55. American Society for Testing and Materials. 1980. Standard Method of Conditioning Paper and Paper Products for Testing. D 685-73. American Society for Testing and Materials. 1981. Standard Test Methods for Vibration Testing of Shipping Containers. D 999—75. American Society for Testing and Materials. 1982. Standard Practice for Performance Testing of Shipping Containers and Systems. D 4169-82. Burgess. G. 1987. Private Communication. Michigan State University. School of Packaging. East Lansing, MI. Den Hartog, J.P. 1952. “Advanced Strength of Materials.” 1st. ed. McGraw-Hill Book Company, Inc. New York, New ' York. Gill, J.L. 1966. Private Communication. Michigan State University. Department of Dairy Science. East Lansing MI. Godshall, W.D. 1968. "Effects of Vertical Dynamic Loading on Corrugated Fiberboard Containers“, USDA Forest Service Research Paper. FPL 94. Godshall, W.D. 1973. "Vibration Transmissibility Characteristics of Corrugated Fiberboard", USDA Forest Service Research Paper. FPL 211. Godshall W.D. 1985. The Importance of Compression for Box Performance. presented at the Compression Symposium. Forest Products Laboratory, Madison, Wisconsin, October 1-3. Goff J.W. 1974. "Development of Performance Standards for Parcel Post Packages“, School of Packaging, Michigan State University, Project No. 3108 for U.S. Department of Commerce (NBS) Project No. 4-35711. Guins, S.G. 1975. Notes on Package Design. Published by Guins, Okemos, Michigan. 60 6T Hanlon, J.F. 1984 “Handbook of Package Engineering.” 2nd ed. McGraw-Hill Book Company. New York, New York. Harris, C.M. and Grade C.E. 1976 "Shock and Vibration Handbook“ 2nd ed. McGraw-Hill Book Company, New York, New York. Kusza,' T.J. and Young D.E. 1974. Testing. Package Development, November/December 1974, No 55. McKee, R.C., J.W. Grander, and J.R. Wachuta. 1963. Compression Strength Formula for Corrugated Boxes. The Institute of Paper Technology, Sept; National Motor Freight Classification 1978. Item 222, Fiber Box Handbook, Fiber Box Association, Chicago, Illinois 1979. Ostrem F.E. and Godshall W.D. 1979. An Assessment of the Common Carrier Shipping Environment, USDA Forest Service General Technical Report. FPL 22. Uniform Freight Classification 1978. 'Rule 41, Fibre Box Handbook, Fiber Box Association, Chicago, Illinois, 1979. Young, D.E. 1986. Private Communication. Michigan State University. School of Packaging. East Lansing, MI.