a»; ,5: .vg an" _ :9. in; TV 3’ w .3- p ‘3 M" ' ‘1‘“ " 5’?“" (9‘23"? , . 3 .bf ,A‘IN1‘?.- k} {'19. \r\;’ 3.9;. {J 0.95;: r. jig/s amid} :fi'x. 5'1 “x; "ix. ’_ 2‘ ‘ ‘1’ _z.“ a g' x. \ , :1. “1313.3 Liil‘éi“; ‘5 ‘3 I“. if 5%.! a$¢tu3£ "xx-emu ($5.6: n ”.35.; ‘4'- Oil ll ": Eusizagi Q mm LIBRARY 27W Egg-NIL“ m 2 199:5. THE TOP TO BOTTOM COMPRESSION STRENGTH OF A CORRUGATED CONTAINER AS A FUNCTION OF FLUTE SIZE AND RELATIVE HUMIDITY DETERMINED BY A DEAD LOAD BY Robert George Bjornseth A THESIS Submitted to the College of Agriculture Michigan State university of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Forest Products School of Packaging 1959 11 AN ABSTRACT This investigation was made to determine the ef- fect of relative humidity, flute size and load on the compression strength of corrugated containers. In add— ition, a new test procedure was used to evaluate the previously mentioned variables. The variables consisted of four relative humidi- ties (30%, 50%, 70%, 90%), three flute sizes (A, B, a), and varying loads. All tests were controlled within the conditions specified by the listed references. The test results showed that relative humidities 70% and 90% effected the strength of a corrugated con- tainer. O flute board seemed to provide the stronger board for container construction. 111 ACKNOWLEDGMENTS The author wishes to extend his sincere appreci— ation to Dr. H.J. Raphael and Dr. J.W. Goff for their extremely helpful guidance and assistance during the course of this study. Thanks are also due to Dr. W.D. Baten for his valuable assistance in the statistical interpretation of this study. Mr. William Jones and The Twin Cities Container Corporation also deserve thanks for their generosity in supplying the box blanks for this study. iv TABLE OF CONTENTS Page An Abstract ........................................ 11 Acknowledgements ................................... iii List of Tables ..................................... v List of Figures .................................... vii I. Introduction ................................. 1 II. Experimental Procedure ....................... 6 III. Analysis of Data ............................. 15 IV. Conclusions .................................. 39 V. Suggestions for Further work ................. 41 L13: Of ROfCI'CDCCU oeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee "‘2 I; 9 Table I. II. III. IV. V. VII. VIII. II. I. XII. XIII. LIST OF TABLES Static Compression Results, Load-Deflection - Flute A, Relative Humidity 30% ................ Static Compression Results, Load—Deflection - Flute B, Relative Humidity 30% ................ Static Compression Results, Load-Deflection.- Flute 0, Relative Humidity'30% ................ Static Compression Results, Load—Deflection - Flute A, Relative Humidity 50% ................ Static Compression Results, Load—Deflection.- Flute B, Relative Humidity 50% ................ Static Compression Results, Load—Deflection — Flut. C, RllatiV. Humidity 50% eeeeeeeeeeeeeeee Static Compression Results, Load-Deflection«-« Flut. ‘, Relativ. Hmidity 70% eeeeeeeeeeeeeeee Static Compression Results, Load-Deflection - Flute B, Relative Humidity 70% ................ Static Compression Results, Load-Deflection - Flute 0, Relative Humidity 70% ................ Static Compression Results, Load—Deflection - FIUt. A, RClativ. Humidity 90% .eeeeeeeeeeeeeee Static Compression Results, Load-Deflection.- Flute B, Relative Humidity 90% ................ Static Compression Results, Load-Deflection - Flut. O, Relativ. HWidity 90% eeeeeeeeeeeeeeee Summary of Test Results, Deflection, With Averages - Flute Size A,B, and C,_Relative Humidities 30% and 50%, Loads at 400 lbs, 450 lbs, 500 lbs, 525 lbs, 550 lbs .,.......... Page 17 18 19 2O 21 22 23 24 25 26 27 2S 29 (“I Table XIV. XVII. XVIII. LIST OF TABLES Summary of Test Results, Deflection, With AV- erages - Flute Size A,B, and o, 70% Relative Humidity, Loads at #00 lbs, 450 lbs, 500 lbs, 525 lbs OOOCCOCOOOOOOOIO0.00.00.00.00.0.0.0.... Summary of Test Results, Deflection, With Av- erages - Flute Size A,B, and c, 90% Relative Humidity, Loads at 250 lbs, 300 lbs, 350 lbs, 400 1b8 .00...0....OOOOOOOOCOOOOOOOOCO0.0000... Analysis of Variance for 30% and 50% Relative Humidity, All LOB-d8 eeeeeeeeeeeeeeeeeeeeeeeeeee Analysis of Variance for 70% Relative Humidity, A11 Flut. 81208, All LOB-d5 eeeeeeeeeeeeeeeeeeee Analysis of Variance for 90% Relative HUmidity, All Flux. 812.8, All Loada eeeeeeeeeeeeeeeeeeee vi Page 30 31 34 38 115T OF FIGURES Figure l. Baldwin~Emery SR—l. — Testing Machine (Model FGT) 2. Baldwin Stress-Strain Recorder (Mbdel MAlB) vii Page 10 ll I. INTRODUCTION he Problem Along With the tremendous increase in use of the corrugated fibreboard shipping containers, has come the problem of toppling of columns of containers during stor- age. This may be due, in part, to the atmosphere sur- rounding the boxes, overloading of the containers, types of board used in the container or a combination of these factors. Objectives The objectives of this study were to determine the effects of humidity and flute size on the top-load com- pression strength of a corrugated container and to pos— sibly find a more realistic compression test for corru- gated containers. A test that would: I.) more closely approximate the conditions of long duration dead loads; 2.) not reguire a large number of samples; 3.) be easy to analyze statistically. The standard ASTM compression test requires that the load be applied with a continuous motion of the mov- able head of the testing machine, at a speed of 0.5 in. per min., until failure and maximum load or either has been reached (1). This static loading of the container does not take into account the effects of creep or fatigue encountered in compressive loads of longer duration, such as occur in warehouse stacking (3). The test pro- cedure developed for this study, was designed to include the effect of fatigue that occurs over a long period of time. Fatigue of this type, is defined as stress vari- ations that occur continuously over a relatively long period of time (5). For the purposes of this study, it can be pictured as a ratio of a load to the strength of the container. As time passes, this ratio will in- crease. In other words, the effect of time and load de- creases the strength of the container and therefore this effect will increase with a longer period of time. In many cases, the fatigue strength of a container is less than the dynamic yield strength. It can.be assumed, that the omission of the effect of fatigue will give a somewhat false impression of the corrugated container. The test method used in this study is original, in- corporating a series of dead loads which are applied to a corrugated container for a specified length of time. The data that is obtained from such a test is simply the deflection, at a dead load, over a specified period of time. Dividing the deflection by the time, produces a value in inches per minute. Therefore, for a specified load, flute size and humidity, a rate of deflection is obtained. This can.be used as the criteria for judging the strength of the corrugated container. In other words, a high rate of deflection would indicate a coup tainer of low compression strength and a low rate of deflection would show a high compression strength. Previous Work A study was made, at the Forest Products Laboratory, to determine the safe stacking life of corrugated conp tainers. This study involved a dead load, various con— trolled atmospheres and two different kinds of corru- gated board. The load was applied by using weights and was left until the container failed. The following is quoted from this study: “The behavior of the corrugated boxes subjected to various dead loads appeared to follow a general pattern that may be described by the reactions during three dis- tinct periods of time. The first period, in Which there was a rapid compression of the boxes, resulted from the initial application of the load and started the instant the load contacted the box. Some of the rapid compres- sion can be attributed to flattening of the rounded por- tion of the score along the horizontal edges of the box, together with a general leveling of the surfaces. The rapid compression continued but at a decreasing rate, for a comparatively short period of a few seconds to l to 2 hours, with a rather abrupt transition into the second period. The compression during the second period continued at a uniform but much slower rate. It had been observed that when in the third period the rate of com- pression again increased, failure was imminent and oc- curred as compression in creased more and more rapidily'(3). Although the last two periods of reaction were ex-* perienced in this experiment, the first period was not noticed. It probably occurred while attaining the in, itlal load and hence was not detected. Two significant conclusions came out of the study made by the Forest Products Laboratory. These were: 1.) for the conditions considered in the study, increases of moisture content reduced the time a box could sustain a dead load, and for it to remain in a stack for a spe— cific period would necessitate a reduction in the mag- nitude of the dead load; 2.) the influence of moisture content on the compressive strength of corrugated fibre- board boxes was found to be about the same for the dif— ferent kinds of board included in this study. These two conclusions and the three reaction.per— iods seem to be the only basis for comparing the results of the procedure used in the present study with those obtained by the standard test methods. Of course, this will not show Which is a better compression test, if there is a better test, but it should give enough information to make a comparison of the two. II. EXPERIMENTAL PROCEDURE Sample Containers .Elile The container size was held constant at 10“ x S“ x 8'. The reason for using a container of this size was to assimilate a size structure that is prac- tical. A corrugated container with a depth less than eight inches shows a high structural strength and there- fore the differences between the tested variables would be less (u). Other reasons, were to facilitate use of the testing machine, the humidity cabinet and also the a— vailable gluing blocks. Material. The corrugated containers were made from double-face 200 pound test bcxard, with the board varying in flute size. The A and B flute board was obtained from Twin Cities Container Corporation and the C flute from the M. S. U. Packaging Laboratory. The manufacturers joint was taped using a four inch fibreglass reinforced kraft tape. A casein adhesive was used for sealing the top and bottom flaps. The material makeup was the same for all types of board tested. This board was 42* — 264+ - hat. Preparation The corrugated containers were sealed in accor- dance with the method described in the ASTM standards. The face of the box was sealed as follows: A'board similiar in size to that used for the first closure was suspended in the opening of the box. A carriage bolt was then placed so that it extended upward through the center of the board. Next, the short or inner flaps' were flexed first outward and then inward, and finally brought to rest on the board and given a coating of glue. Then the longer or outer flaps were flexed outward and inward and brought to rest on the glued surfaces. Pres- sure was applied by slipping a second board down over the bolt, and tightening the nut to draw the two boards together, thus holding the glued joint until it set (1). The A and B flute container blanks were cut by the supplying company. The C flute container blanks were made on the department sample table using the normal sample making procedure.. The style of the container was of the regular slotted type. 1551 Method. Desigg. A total of 36 corrugated containers were tested. The tests were run in four series. Each series consisted of nine test containers, conditioned at a particular relative humidity. The nine samples consis— ted of three containers each of A, B and C flute board. The four series consisted of nine samples at 30%, 50%, 70% and 90% relative humidities respectively. Humidity_Control. The relative humidities of 30%, 70% and 90% were obtained by using the Blue - n Counter Flow Relative Humidity Cabinet (Model OP77OH) in the Forest Products building which is located about a block away from the testing apparatus. Because of this, the test specimen had to be placed in a polyethylene bag to preserve the desired humidity. The sample was also tested in the polyethylene bag so as to insure a con- stant humidity over the period of time required for the test. The polyethylene bag was conditioned along with the test specimens. The Packaging Laboratory condi- tioning room was used for the tests at standard condi- tions (50% relative humidity and 73° 7). The specimens were placed on a fluted piece of corrugated board so they would be properly conditioned. The four humidities were controlled within.plus or minus two percent. The length of time that the speci- mens were exposed was approximately 20 hours. Transfer 2; Samples. Each sample was taken from the humidity cabinet and placed in a pre-conditioned polyethylene bag. The seal on the bag was made by twis- ting and doubling over the polyethylene and securing with a rubber band. The enclosed sample was then moved to the compression testing machine. The approximate time of transfer was about two minutes. The time of transfer plus the time required to run the tests was approximately 45 minutes. All the testing was done in a room conditioned at 50% relative humidity and 73°F. Therefore, the outside conditions for testing were al- ways 50% relative humidity. However, the outside conp ditions during the time of transfer varied from 30% to 95% relative humidity. It Would seem that this would be sufficient time for the sample to gain or lose mois- sture. A weight check was made on three samples fromieach series. The results showed there was not a significant loss or gain of moisture. Compression Tests. The apparatus used for the dead load compression tests was the Baldwin - Emery SR-lt Testing Machine (Model FGT) and the attached stress - strain recorder which is shown in Figures 1 and 2. As stated previously, the tests were run in four series, with each series containing nine samples. The nine samples were run.in succession until completionwof the series. 10 Figure l Ealdwin—Emery SR~A « Testing Machine (Model FGT) Figure 2 Baldwin Stress—Strain Recorder (Model HUB) 12 The machine settings, used for these tests, are as follows: Load Range..........1000 lbs. Upper Limit..e95% Lower Limit...-10% Platen Speed........0.008 to 0.8 in./min. Deflectometer x Magnifier...200:magnification Recorder Range..........half range Rate of Loading.........50 lbs./min. Platen Stops..........l in. and 12 in. The sample was placed between the two auxiliary wooden platens and a load was applied at a rate of 50 pounds per minute until 400 pounds was reached. The rate of loading was determined by a load pacer built inithe compression.machine. When 400 pounds was reached, the: recorder pen was engaged and the load was held at #00 pounds for a period of 5 minutes. The timing was done by manual operation of the speed control. The manual. operation of the testing machine required varying the speed of the machine so that a load could be held as the deflection per minute of the sample varied. The load was held within plus or minus 2 pounds which is a onc-half percent error at #00 pounds. At the end of the five minute interval, the load was increased to #50 pounds and again held for five minutes. This procedure 13 was repeated by adding increments of 50 pounds until a 500 pound load was reached. Then.25 pound increments were used until the sample failed. However, for the higher relative humidities the range of dead loads had to be changed to facilitate the use of the defecto- meter. For example, at 90% relative humidity the loads started at 200 lbs. and not at 400 lbs. If the sample failed before the five minute interval was completed, the failure was indicated on the load dial and the stop- watch was stopped, noting the elapsed time. From this an inches per minute deflection can be calculated for the failure point. After testing, the sample was coded for flute size, humidity and replication. For example, A-90—2 would mean the second A flute container tested at 90% relative humidity. The test procedure just described was not based on the failure of the container. Rather, it was based on a rate of deflection at a given load. By using this method, it was hoped that a more definite picture of the effect of compression on a corrugated container could be obtained. A series of 9 containers, similiar to the ones used in this experiment, were also tested by the Standard ASTM Compression.Method. The failure 14 point of these containers varied as much as 250 pounds using the ASTM test. The variations, resulting from the test method developed for the present study, ranged from a maximum of 75 lbs. to zero at failure. This certainly doesn't mean that one test is better than the other as the number of samples tested using the ASTM method was not statistically large enough. However, this may be indicative of further work in comparing the two methods. Using the new method allows one to Obtain a signi- ficant amount of data from a relatively small number of test samples and this data easily lends itself to statis- tical interpretation. However, the time required for testing is quite lengthy and the machine must be conp tinually watched so as to hold the load. It was also necessary to alter the speed control so that the move- able platen could be stopped using this control; this was necessary to hold the load. 15 III. ANALYSIS OF DATA Dead Load Compression Test Results Tables I thru XII show the results in deflection per minute of the various static loads. Also noted, is the static load at which the container failed. Of course, not all the specimens will show a failure load simply because the load at failure occurred above the range that was used for the statistical analysis. Where the load at failure was below the maximum value in the analysis range, a maximum deflection value was entered in the table for this sample. It can be assumed that after failure the deflection of the conp tainer is infinite. Therefore, if the deflection value obtained at failure is used, it represents the minimum deflection value at the load in question. For example, the static loads used for statistical analysis ranged from 400 lbs. to 550 lbs. at 30% and 50% relative hu- midity. This would include static loads at 400, 450, 500, 525, and 550 pounds for each sample. Suppose the deflection readings went as follows: 400 lbs..........0.0010 in/min. 450 lbs..........0.0025 in/min. Failure 500 1bs..........0.00SO in/min. It can be seen that the container failed before 16 the desired static loads were reached. So that a sta- tistical analysis could be made, the following additions to the table were made: 400 lbs..........0.0010 in/min. 450 1bs..........o.0025 in/min. 500 1bs..........0.0080 in/min. 525 IbBOOOeeeQOQQOQOoso III/min. 550 lbs..........0.0080 in/min. In other words, the deflection after failure should be at the very least the deflection at failure. Tables XIII and IV give the average values for the three test variables. TABLE I Static Compression Results Load - Deflection 17 33— 3 run: A - HUIIDITT 3o 3 : : : : : g 3 Load ; 1301100131011 3 DOIIOGUIOD. : g 3 Applied : Units ’ ; In.[[in. : «3 3L“~ 32 .3 3 3 3 400 3 12 3 0.0012 3 3 3 450 3 1‘4- 3 0.0013; 3 3 Rep. 1 3 500 3 23 3 0.0023 3 3 3 525 3 2o 3 0.0020 3 3 3 550 3 25 3 0.0025 3 : t 400 : 20 a 0.0020 : : : n50 : 22 : 0.0022 : 3 Rep. 2 3 500 3 29 3 0.0029 3 : : 525 : 11 : 0.0011. : : : 550 : 17« : 0.0017 : 3 3 3 8 3 : : : : : : : hoo : 19 : 0.0019 : : : #50 e 11 : 0.0011. 3 : Rep. 3 : 500 : l3 : 0.0013 : : : 525 : 10 : 0.0010 : : : 55o : 13 : 0.0013 : ' Units in .0005 inch .II 1' 0‘ L .5 i b .0 I L, 0 d ‘ I: d Static:Compressionafiesults TABLE II 18 Load - Deflection f f rum: B - HUHIDITT 30 f f 5 Load 3 Deflection f Deflection E E Applied. E Units * E Ina/line 3 3 E #00 E 19 2 0.0019 3 : : 450 : 15 : 0.0015 : 3 R01). I. g 500 3 19 3 0.0019 g : : 525' : 25- : 0.0025 : 3 : 500 : 19 x 0.0019 g f 3 _:3_ 4. lg. : : : : : 400 3 11+ 3 0.0011: 3 3 z 450 3 12 3 0.0012 : : Rep. 2 z 500 3 1n : 0.001u : 3 : 525’ : 9 : 0.0009 : 3 : F-550 : 82 3 0.0098 3 3 t it i 3 z 2 #00 ; 18 3 0.0013 ; 3 3 450 : i0 : 0.03:8 : : Rsp. 3 500 g 0 g 0.0 g z z 550 3 6 3 0.0006 3 i J 2 2 ‘3 F Indicates failures Units in .0005 inch I C' 0 O 9‘ O " 0‘ I’ ‘ D V I J v 19 TABLE III; Static Compression Results Load - Deflection 3 3 FLUTE C - HUMIDITY 30 3 3 x . :1 : 3 3 3 3 E E Load E Deflection E Deflection E 3 : Appliti : Units . g In. /mne :- 3: 3 3 3. 3_ Q g #00: z 19 2 0.0019 E 3 Rep. 1 3 500 g l g 0. 001 :- 3 : 525 : 10 3 0.0010 g 3 3' 550 z 80 g 0. 0080 :_ i i i : 3, 3 3 3 3 3 : Hop. 2 3 500 : 24 : 0.002% : A i la a 1 g g #00 i 11 g 0.0011 g 3 . #50 E 10 . 0.0010 3 3 Rep. 3 E 500 E 13 E 0. 0013 3 , . 525 , 9 , 0.0009 , a 2 550 3 9 a 0.0009 E '3 Units in .0005 inch b 0 ve ‘ .l‘ v b I‘ f. (U L. 'U 0‘ eU 0‘ 0’ '1' ‘I '7 4‘ 0‘ l. i. U. 0' 9' '0 l‘ t‘ 0' 4' {V U U V 20 TABLE IV Static Compression Results 3 Load - Deflection f 5 FLUTE A - HUMIDITY 50 E 3 3 3 3 3 E E Load E Deflection E Deflection E : : : in 3 ; E #00 Q 12 § 0.0012 E : : #50 : 16 3 0.0016 E : R'p- 1 : 500 : 25 : 0-0025 : : : 525 : 27 : 0.0027 : 3 g 500 g 18 3 0.0018 3 A 3 3 3 A: E E #00 E 11 E 0.0011 E E : #50 E E 0.0009 E E E 525 E 33 E 0.003s E E E 500 E 26 E 0.0026 E E f #00 E 11 5 0.0011 5 E : 1+50 : l : 0. 00:2 3 . Rep. 3 : 500 . 2 : 0.00 : E E 525- : 16 E 0.0016 : E E 500 E 13 E 0.0018 E T Units in .0005 inch A . V v.4 ‘ D A A. l I. or 0‘ If I‘ en .11 6b O. I. rt 16 TABLE V Static Compression Results 21 Load - Deflection : f FLUTE B - HUMIDITY 50 f 3 3 3 3 : 3 3 Load 3 Deflection 3 Deflection 3 3 3 Applied 3 Units * 3 In./Min. 3 3 : #00 : 9. : 0.0009 : 3 3 #50 3 ll 3 0.0011 3 : Rep. 1 : 500 : 27 : 0.002 : 3 3 F..525 3 53 : 0.008 : : 3 500 : 3 0.0086 : 3, 3 3 3 3 3 3 3 3 3 3 3 #00 3 28 : 0.0028 : 3 : #50 : 15 : 0.0015 3 3 Rep. 2 3 500 : 66 : 0.0066 3 3 3 y..525 3 62 : 0.0182 : : 3 550 : : 0.0182 : j__ 3 23 3 3 3 3 #00 3 l# 3 0.00111} 3 3 : l+50 : 9 : 0-0009 : 3 Rep. 3 3 500 3 10 3 0.0010 3 3 3 525 3 11 3 0.0011 3 3 3 F-550 3 120 3 0.01#6 3 F Indicates failure T Units in .0005 inch a n TABLE VI Static Compression Results Load - Deflection FLUTE 0 - HUMIDITY 50 Load Applied Deflection Units * Deflection In./Min. #00 1350 500 525 550 10 10 11 7 12 0.0010 0.0010 0.0011 0.0007 0.0012 Rep. 1 #00 450 500 525 550 12 11 13 15 35 0.0012 0.0011 0.0013 0.0015 0.0035 Rep. 2 #00 #50 500 525 550 22 11 12 9 10 0.0022 0.0011 0.0012 0.0009 0.0010 3o 00 ee u u u .3 To u 00 00 ee eo-eo ee ee ee u co co "lee eo u u u ee 00 u re ee ee ee ee ee ee pa ee ee 00 00 ee e. ee ee e. co e. co ”(be ee 00 ee ee ee ee 00 Jeee ee ee eeeeee peee ee eeee ee eoeeeeee ee eo ee «no. 00 ee ee ”“00 ee eeeeee pe ee ee ee ee ee eepeuee ee 90 ee eoee eeee ee ee b .0 O. I. O. O. .0". O. .0 .0 .0 .0 u D. .0 O. .0 O. O. O. .0 .0 .0 O. .0 .0 .0 .0 * Units in .0005 inch TABLE VII Static Compression Results 23 Load - Deflection f f FEUTE A - HUMIDITY’ 70 f 3 3 3 3 3 i : Load ; Deflection : Deflection 3 3 3 3 3 3 E too 3 36 E 0.0036 2 3 : P- “.50 : 121]. 3 0.02 8 3 3 Rep. 1 3 500 3 3 0.0288 3 3 3 525 3 3 0.0288 3 3 3 3 L 3 . 3 ; i 000 i 22 ; 0.0022 ; 3 ‘ 3 11.50 3 27 g 0.002? 3 3 Rep. 2 3 500 3 S9 3 000059 3 3 f uoo f 313 3 0.00313 3 ‘ : 50 z 131 3 0.00131 : 3 Rep. 3 ; 2.. 00 ; an - 0.0300 ; f i 525 ; 3 0.0300 ; 1" Indicates failure 33- Units in .0005 inch TABLE VIII Static Compression Resul Load - Deflection ts 213 f f .PLUTE B - HUMIDITI' 70 f 3 3 3 3 3 ; ; Load ; Deflection.: Deflection.: : 3 Applied : Units * 3 In./Hin. ', 3 3 3 3 3 3 3 3 3 3 3 3 h00 3 19 3 0.0019 3 3 ' 3 r- 1350 3 28 3 0.0181 3 3 Rep. 1 3 500 3 3 030320 3 3 3 525 3 3 0.0320 3 3, L 32. .3 . i i h00 i 19 i 0.0019 i , Rep. 2 g 500 , 3 0.0320 3 3 3 525 3 4.. 0.0320 g L 2 2 0 _._3. i f 000 i 22 : 0.0022 3 3 ' I F- #50 . 1&1 . 0.0320 : . 8913k 3 I 500 Z 2 000320 3 ; g 525 g ; 0.0320 ; F Indicates failure 33 Units in .0005 inch 25 TABLE IX Static Compression.Results Deflection Load HUMIDITY 7O FBUTE O 00 00 00 00 00 In./Hin. Deflection Deflection Units * .m .m Applied fie ee ee ee ee 10 00 00 00 00 00 e, m. 0.0021 0.0080 0261 0. 0 sum 21 v0 00 00 00 00 00 w. 00 00 00 00 00 Rep. r..:.:..: 0.002h 0025 0.006; 0.010 0. 00 00 00 00 00 00 wnamw 13 I 00 0b .0 00 00 00 00 00 00 00 00 00 Rep. 00 00 00 0. 00 00 0.0017 0.00113 0.0023 0.00h6 00 00 00 00 00 00 . 3 e P 0 R 00 00 00 00 00 00 F Indicates failure 43 Units in .0005 inch 26 “21313 I Static Compression Results Load - Deflection : A“: : f : mm A - HUMIDITY 90 i 8 8 8 8 8 i ; Load i Deflection ; DeflectiOn ’ , : Applied , Unit: a . In./Hin. , 8 8 8 8 8 8 8 8 8 8 8 - a 250 z 21 3 8.0021 3 x : 300 : 19 x .0019 x : R°P° 1 : 35o : 30 : 0.0030 : 8 8 81.00 3 80 s 000080 8 _8__ 8 ' j J 1 n i. i ~ 1 333 z 33 i 3-3333 i 13°F. 2 350 80 020080 f 2 4 1L 9; ._ d i i 250 g 31 g 0.0031 g 3 n 3 300 z 32 3 0.0032 , 3 ep. 3 3 350 , 102 , 0.0102 : 3 g 1?- uoo ; 63 ; , 0.0630 ; *— F Indicates failure * Unite in .0005 inch 27 TABLE II Static Coulpreseion Reeulte Load - Deflection FLUTE‘B-HUMIDITY90 1 : z 73' a z : : : a : : : : z z : : x : : 3 Load : Deflection : Deflection a x : Applied : Unite * : In./Hin. : z : z : : : : : : 1 : x . : 250 : 25 : 0.0025 : : : 300 : 31 : - 0.0031 : : Repo 1 : P- 350 : A 119 : 0.0119 : x z 1100 : : 0.0119 : z a £1 1 _ 4- : z x : : : . z 250 g 21 : 0.0021 g : : 300 : 25 : 0.0025 x 3 Rep. 2 g F - 350 : 85 : 0.0212 3 8 3 1100 : : 0e0212 3 1. 1* 1 x a 1 1 1M .2 _ . _ _ 2 i i 250 g 22 ; 0.0022 g 3 g 300 : 19 3 0.0019 3 , ROP- 3 z 350 g 136 3 0.0186 : f 1“ Indicates failure * Units in .0005 inch TABLE XII Static Compression.Besu1te 28 Load - Deflection f f FDUTE c - HUMIDITY’ 90 i z : z : : : : z : : 3 3 Load 3 Deflection.3 Deflection.3 3 3 Applied 3 Units * 3 In./Hin. 3 s z : : , : : : 8 8 8 8 3 3 250 3 29 3 0.0029 g 3 3 300 3 82 3 0.0082 3 3 Rep. 1 3 r- 350 3 90 3 0.0187 3 3 . uoo . : 0.0187 3 31 0 L 1 _._ g f . i 250 f 27 g 0.002? f ; 3 300 : 26 , 0.0026 ; ; Rep. 2 ; 350 : 38 ; 0.0038 ; 3 ; P-u00 ; 78 : 0.0110 g 8 3 3 250 3 32 3 0.0032 3 z : 300 3 26‘ 3 0.0026 3 : Rep. 3 : 350 3 57 3 0.0057 3 i E P- 1300 i 60 : 0.0273 3 F’ Indicate: failure 4% Units in .0005 inch 29 TABLE XIII Summary Of Test Results Average Deflection In Inches/Minute 30% And 50% Relative Humidity 5. JLE’.£5 39.2 15.7 00 .0 .0 .0 .0 00 .0 .0 00 .0 00 00 00 00 00 00 Flute Size .0 00 00 00 00 00 00 .0 15.0 13.9 21 27.3 nu.5 .0 .0 .0 00 00 00 .0 0. Load 18.3 30.? co co co ee 00 ee.ee ee 30% m 00 .0 00 .0 00 00 00 .0 Humidity * Times 10"“ 30 DABLE XIV Sumnery of Test Results Average Deflection in Inches/Minute 7 0% Relative Humidity 00 .0 .0 .0 00 00 00 .0 er 60.).3 163.2 221.8 .0 .0 .0 00 00 00 00 00 .0 .0 .0 .0 .0 00 .0 .0 Flute Size 19 $ 2138:? v 8 . . . 3 2 123 eeeeeeeeeeeeeeee Load 00 00 .0 .0 00 0. .0 00 * Times 1044 31 TABLE IV Sumary 0f Test Results Average Deflection In Inches/HUnute 90¢ 3.1.1:“. Humidity : : z 139.3 : : Flute 3 3 3 8 8 B : 93 e3 8 g 3180 g 3 I g : z z 1111.5 : : : z z : : : _ : ; ; 250 ; 26.3 i g 1.0.4 g 350 3 106 e 8 : 3 3 hOO 3 299.0 3 : : z x : : z : 3* Times 10'“ 32 Techniques and procedures used in the statistical analysis are found in references (2), (7), and (8). Tables XVI thru XVIII show the results of the various analyses. Three separate analyses of variance were carried out on the test data. The original plan was to make an analysis by using a three-way classification that included all the test data. After reviewing the results, it was decided that the data at 70% and 90% relative humidity, were too large to analyse with the data at 30% and 50% relative humidity. These extremes in values would produce a large error term which in turn would lead to a possible misinterpretation of the data if this error term were used as the basis for an F test. In addition, is the fact that due to the effect of humidity at 70% and 90% relative humidity the dead load had to be lower so as to facilitate the use of the recording devices. For example, the static load range at 90% in- cludes 250 lbs, 300 lbs, 350 lbs, and #00 lbs while the range at 30% and 50% starts at #00 lbs and ends at 550 lbs. Because of these obvious differences in humidities it can.be said that the detrimental effect of humidity" on a corrugated container is significantly greater at 90% relative humidity than at 70% relative humidity and 33 also significantly greater at 70% relative humidity than at 30% and 50%. The first analysis of variance was a three way classi- fication that included flute size (A, B and O), humidity (30% R. H. and 50% a. a.) and dead load (#00 lbs, #50 lbs, 500 lbs, 525 lbs, and 550 lbs) as the variables. The final analysis of this data showed the three-way inter- action of flute size 1 humidity x load to be signifi— cantly different from the error term. Also, there was no significant difference between the three-way inter— action and the three two-way interactions; humidity x flute size, humidity x laid, and flute size 1 load. This is an ideal situation because it enables one to test the averages of all the variables using an error term that is basic to each one. However, using the three-way in teraction mean square as the error term did not prove as ideal as was first expected. Testing the variables humidity, flute size, and load, using the three-way interaction, the F test showed no significance within the variables (8). Usually at this point, the problem is not pursued any further because of the non- significant F values. However, on examining the averages of the three deferent flutes, the two humidities and the five dead loads, it was found that there seemed to be an extreme average in each case. For example, the /‘l 34 XVI TABLE Analysis of Variance 30% Humidity and 50% Humidity All Loads All Flute Sizes 00 O. O. 9. O. C. Q. 0. O. O. C. O. O. Q. Q. C. O. O. O. O. O. Q. .0... Mean Square ee 0. 00 00 Sum of :Degrees of Squares: Freedom 9. O. O. I. 282/63 8 u. 9 7- 1 O 9 1.— 5 3 h». 2 h. 1 1 1 ee ee ee ee ee ee ee ee ee ee ee 90 ee ee ee ee ee ee ee ee 9 1 2 h? 2 nu. do do 0 do 6 ee ee ee ee ee ee e0 ee ee ma ee ee ee ee ee e0 ee ee ee ee g. n: ,o 9. n: my 7: so .i 7: .I. a; .l 7: 9. .l 7: 2 .4 do 0 2 O h... 1 O 2 3 9 1 do in... 5 9 1 9 1 1 3 eeeefieeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee d m X Av Av +v t u m u 1 O 1 F L .M P. e .n I o x Z L v. a. v. «I v. t S t t x .3 4L 4L ”M“ 4L 1 d C d C d I m m .m m m m m m m 0 1 O 1 I m... H F L H H a! H E ee ee ee ee ee ee ee ee ee mm ee ee ee ee ee ee ee ee ee ee 2.10 us, 60, .05) a A 35 averages for the flute sizes were: A = 18.63, B = 39.90, and O - 15.67. In this case, the extreme is the B flute average. As was nsntioned previously, the F test showed there was no difference between A, B, or G flutes. The averages seemed to indicate there was a significant dif- ference. It was decided to use an accepted test for significance that could be applied to the various aver- ages even though the F test showed no significance. A test developed by Mr. K. R. Nair was used (7). Using the appropriate tables and this test, it was found that there actually was a significant difference in flute size, but there was no difference in loads or humidi— ties. The second analysis of variance was a two-way classi- fication using the data at 70% relative humidity. The two effects or variables were flute size (A, B, and 0) and dead loads (400 lbs, 450 lbs, 500 lbs, and 525 lbs). The error mean square was not significantly different from the two-way interaction flute size 1 load. There— fore, the two were combined to form a new error term. This combined error mean square was used to test the main effects for significance. Both the flute size and the dead load showed significance. Therefore, the averages of each main effect or variable were tested 36 TABLE XVII Analysis of variance for 70% Humidity All Loads All Flute Sizes 0. O. 0. 0. O. O. C. O. O. O. O. O. O. O. O. O. O. O. F Score 0. O. O. 0. ea 118. n0. 5 O. C. O. 9. Freedom um of :Degrees of S Squares l3.l7** lh.l3*' 0 1.. 91 1 50 0 1 9m 0 O 5 5 8 do 1 O. I. O. O. 0. 0. O. O. O. O. 52 36.4 3 2 O. O. O. O. O. O. O. O. 0. 0. 59h. 1 1.. 51 552/ 52 .00.”... 0 0 0 7.2 O 06 56 2 6 1 2 1 O. O. O. O. O. O. O. O. O. 0. d a C O z L .l 3 I 1 C C I a +. .M t O t u u r 0 l em 1 r T F F E 6083 O. O. O. O. 0 3 Combined Error: 182482 highly significant I. 37 using the studentized range table. It was found that there was a significant difference between 0 and A flute and 0 and B flute, but there was no difference between A and B flute. 0 flute was significantly lower and therefore, exhibited more strength according to this test. The dead loads also showed a difference with the loads 450 lbs, 500 lbs, and 550 lbs being greater than #00 lbs. These same loads showed no difference within themselves. The third analysis of variance was a two-way classi- fication using the data at 90% relative humidity. The two main effects or variables were flute size (A, B, and O) and dead loads (250 lbs, 300 lbs, 350 lbs, and 400 lbs). As in the analysis at 70% relative humidity, a combined error term was used. Using the combined error mean square as our error term, the F test showed the flute size to be nongsignificant. The dead load showed significance in that the dead load at 400 lbs was significantly larger than the loads at 250 lbs, 300 lbs, and 350 lbs. 38 TABLE XVIII Analysis of variance for 90% Humidity All Loads All Flute Sizes ee e0 0. 00 ee e0 00 e. e. e. 00 ee e. 00 ee 00 e0 e. F Score Mean Square 0. O. O. Q. Sum of :Degrees of Squares: Freedom Source of Variation ee ee ee e; O. O. O. 0. 3o 0 .- .v my 62 PHJ PHJ e e 09.. 1 ee ee ee ee 00 ee ee ee ee e1 25-4/2 8302 ”27.1 rhv IAU fill nu I411 1 ee ee ee ee ee ee ee ee ee ee 5236.4. 3 2 ee ee ee ee ee ee ee ee ee ee .IL 95/ Ph/ rhv GIL 2601 AV n81 fill n/_ «I— n/_ ni- Axv rhv MM” 0130 do .412 ee we ee ee ee ee ee ee ee ee . d a at nu Z L 4L 8 I 1. Cr atdto tuaur AV 1!. Av 1* “A TFLFE Combined Error: 350353 0. O. C. O. *‘ highly significant 39 IV. CONCLUSIONS The harmful effect of humidity on the compression strength of a corrugated container is significantly greater at 90% relative humidity than at 70% relative humidity and also significantly greater at 70% re— lative humidity than at 30% relative humidity and 50% relative humidity. There was not a significant difference between 30% relative humidity and 50% relative humidity. Therefore, at higher humidities, the stacking life of corrugated containers becomes considerably less. Containers of C flute construction statistically proved to be stronger than A and B flute containers when tested at 70% relative humidity. It also should be noted that the trend of the 0 flute averages show 0 flute construction to be stronger across all the tests. On the other band B flute construction was significantly weaker than A flute and C flute con- struction at 30%, 50%, and 70% relative humidities. As was expected, an increase in the dead load inp creased the rate of deflection. However, in a few instances, the box shows periods of reinforcement where the rate of deflection actually decreased with an increase in the dead load. 1+. 40 Due to the large error terms in the statistical anal- ysis, one set of variables showed non—significant differences when actually they were significant. This is due to the wide range of test values. Using a basis for evaluation previously mentioned, this test procedure seems to compare favorably with previous dead-load compression testing methods. V. SUGGESTIONS FOR FURTHER WORK Compare this test procedure with the ASTM.method by collating the stress - strain curves obtained from each method. This should show the difference between the effect of the dead load and the static load. Using the same variables and conditions, find a correlation between an actual long duration dead load test and the test procedure used in this study. in 2. 3. 42 LIST OF REFERENCES American Society for Testing Materials. ASTM Standards 23 Paper and Paper Productg and Shipping Containers. Philadelphia: American Society for Tziting Materials, 1955. Dixon, W.J. and Massey, F.J. introduction to Statistical Anal sis. New YorE: McGrawAHTIl Book 50., Inc., 1§57. Kellicutt, K.Q. and Landt, E.F. Safe Stacking Life of Corru ated_Boxes. Forest Products La oratory Tzcfinical Irticle. Maltenfort, G.G. ”Compression Strength of Corrugated Containers,“ Fibre Containers, V01 XLI, #7:#4 (July 1956). - Marin, J. and Sauer, J.A. Strength of Materials. New York: The Macmillan Company, l§5u. Mckee, R.C. and Gander, J.W. “To Load Compression,“ Tappi, Vol. #0, #1:57 (Jan. 1957 . , Nair, K.R. “The Distribution of the Extreme Deviate from the Sample Mean and its Studentized Form," Biometrika, Vol. 35, p. 126 (1947—48). London; University Press, 19u7. Snedecor, G.W. Statistical,Methods. Ames, Iowa: Iowa State College Press, 1 . RGQfii USE OE‘ELY -J U L- ----- 6-1886"... ’3. .~ ' . "inthat