EVALUATTON OF SOME EXISTING EMPIRICAL EQUATIONS FOR TOP‘TO-‘BOTTOM COMPRESSTON STRENGTH 0F CORRUGATED FlBREB-OARD BOXES THESIS FOR THE DEGREE OF M. s. MICHIGAN sure UNIVERSITY SALUSTIANO S. MIRASOL. JR. {966 THESIS '7 4’ v: "3» ya '01 a. “*2, mmmuummnmmmm L ' ‘ .J t 1293 00989 8390 A.” UKMVCK‘E-Ifiy fl- : 1 4 a; z:=-:.=;s;§rmmng EVALUATION OF SOME EXISTING EMPIRICAL EQUATIONS FOR TOP-TO-BOTTOM COMPRESSION STRENGTH OF CORRUGATED FIBREBOARD BOXES BY ’1' I" Salustiano S; Mirasol, Jr. AN ABSTRACT Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Fbrest Products 1966 ABSTRACT EVALUATION OF SOME EXISTING EMPIRICAL EQUATIONS FOR TOP-TO-BOTTOM COMPRESSION STRENGTH OF CORRUGATED PIBREBOARD BOXES By Salustiano S. Mirasol, Jr. The topoto-bottom compression test of corrugated fibreboard container is widely used to evaluate the performance of boxes subjected to stacking load. It often discloses from the nature of the failures and the capacity to withstand loading. deficiencies in design, construction. or fabrication. 0n the basis of the engineering properties of the components and the box dimensions. quite a number of empirical equations have been developed to estimate the top-to-bottom compression strength of a corrugated fibre- board box. Four empirical equations which the author believes have made distinct and valuable advances in the determination of compression strength of boxes were evaluated. The equations involved are those of Kellicutt and Landt: Maltenfort; McKee. Gander’and Wachuta. McKee, Gander and Wachuta formulated two interrelated equations which were evaluated in this study. Salustiano S. Mirasol. Jr. The experiment was designed for a 200 1b. single wall and belute construction corrugated fibreboard. All the test board blank sheets and the components of the board used throughout the study came from the same roll of liners and corrugating medium and were produced in a single production run on one corrugating machine. The study involved the making of 900 boxes of 225 sizes in a sample making equipment. The box sizes were such that the dimensions were all dependent on three parameters, namely, depth to perimeter ratio, perimeter, and length to width ratio. With the manner in which the dimensions of the boxes were determined, an analysis was undertaken with respect to individual parameters in addition to the primary objective of the experiment. The test procedures employed satisfied either the TAPPI Standards or the ASTM Standards in the preparation of test samples and the actual testing. Due to unavailability of standard test procedure for the determination of the Column Crush Test, the author devised a method which to him seemed satisfactory. On the other hand. the Concora Liner Test value for the test board was not determined because a special fixture needed for the test was not available. However. on account of the linear nature of the equation, further evaluation was still undertaken. Salustiano S. Mirasol, Jr. Based on the data compiled from the actual testing of fibreboard components, corrugated fibreboards and 830 boxes made of a single wall C-flute, 200 lb test board, the major findings of the study are: 1. Except for the haltenfort Empirical Enuation, theoretical values for top-to-bottom compression strength are all low. If the Concora Liner Test result on the liners used would fall within the range 28.3 lb. to “5.6 1b.. the equation by Maltenfort would equal the test result values on certain range. 2. The empirical equation of Kellioutt and.£andt as well as Maltenfort's are closely correlated although the increment could not be determined. Similarly. the two equations of McKee, Gander and Wachuta are highly correlated. 3. Varying the length to width ratio changes slightly the compressive strength. Boxes with L/U - 1.25 and L/H a 1.50 give higher compressive strength than square boxes. 0n boxes with L/w - 1.75 and L/H a 2.00 the resultant compressive strengths are lower than on a box with an L/w a 1.00 or a square box. Dr. James w. Goff Adviser EVALUATION OFLSOME EXISTING EMPIRICAL EQUATIONS FOR TOPbTO-BOTTOM COMPRESSION STRENGTH OF CORRUGATED FIBREBOARD BOXES By Salustiano S. Mirasol, Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Forest Products 1966 ACKNOWLEDGEMENTS The author takes this opportunity to thank those individuals whose assistance, encouragement and cooperation made this thesis meaningful. A special thank you is extended to Dr. James W. Goff for the many helpful discussions and suggestions during the course of this study, and for guiding the graduate program. The author wishes to thank Dr. Charles M. Stine, Dr. Hugh E. Lockhart and Dr. William A. Bradley for their invaluable help. The author is deeply grateful to West Virginia Pulp and Paper Company, Hinde and Dauch Division of Sandusky, Ohio, for the use of the facilities of their Technical Center Division Laboratory, for the materials used and the cooperation of its staff in the completion of the test study. The author is grateful to his wife, Nora, for her assistance and encouragement. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS ................................. LIST OF TABLES ................................... LIST OF FIGURES .................................. APPENDIX LIST .................................... INTRODUCTION ..................................... DEVELOPMENT OF CORRUGATED FIBREBOARD BOX ......... TECHNICALJADVANCEMENT ............................ EMPIRICAL EQUATIONS .............................. Kellicutt and Landt .......................... Maltenfort ................................... McKee, Gander and wachuta .................... DESIGN OF EXPERIMENT ............................. TEST METHODS ..................................... Material Test ................................ RSC Box Compression Test ..................... RESULTS.AND DISCUSSION ........................... CONCLUSIONS ...................................... BIBLIOGRAPHY ..................................... APPENDIX .OOOOOOOCOOOOOOO0.0.0.000...0.00.00.00.00 111 Page 11 iv vi 11 11 13 1a 19 21 22 26 28 50 52 55 Table LIST OF TABLES Actual and theoretical compression strengths for different IDX perimeters eeoeeeeeeeeeoeeceoo The compressive load difference in pounds between the average experimental results and the theoretical computed values oeeeooeeeoeeoeee Average compression strength in pounds for different perimeters with depth to perimeter ratio constant based on 20 samples ............. Average compression strength in pounds per inch perimeter for different perimeters with depth to perimeter ratio constant based on 20 samples ... Average compression strength in pounds for different perimeters with length to width ratio constant based on 28-32 samples eeeeeeccceeeecee Average compression strength in pounds per inch perimeter for different perimeters with length to width ratio constant based on 28-32 samples.. iv Page 29 30 36 38 “3 “5 Figure 10 11 12 13 14 LIST OF FIGURES Nomenclature of a regular slotted container .... 6011111111 Crush Test eoeeeeeeeeececeeeeeceoeccceeee variation of average compressive load in pounds with perimeter in inches for observed and theoretical values ceeecceceeeeeeeeeeeceoceeeoce variation of average observed compressive load in pounds with theoretical values ................. variation of average compression load in pounds with depth to perimeter ratio for specific perimeter eeeeeeeeeeoeoeceeeeeeeeeeeeceeeeoeeoee variation of average compression load in pounds per inch perimeter with depth to perimeter ratio for specific perimeter eeeoeeeceeeeceoeece variation of average compression load in pounds with height in inches for specific perimeter ... variation of average compression load in pounds per inch perimeter with perimeter in inches for specific depth to perimeter ratio .............. variation of average compression load in pounds with perimeter in inches for specific length to Width ratio eeesoeeeeeeeeeeeeeeeeeeceeeeoeeeeoee variation of average compression load in pounds per inch perimeter with perimeter in inches for SpeCIfic length 130 Width ratio eeeeoeeooeeooeeeo Relatively short height corrugated box buckling under load ececeeeeeeeeeeeoeeeeoecosees Relatively medium height corrugated box buckling under load coeeeceececeeeeeeeeeoceceecc Relatively tall corrugated box buckling under load ...O.......O.......OOOOOOOOOOOOOOOOOC...... Typical corrugated box with its side panels numbered. for reference oeeeoceeeeeooeeeeeeeeococ Page 6 25 31 32 37 39 no #2 Ah #6 #8 #8 49 “9 :3 <3 tr > APPENDIX LIST Test Materials .......................... Box Sizes ............................... Column Crush Test Results ............... Average Compressive Load on Four Samples in Pounds ............................... Average Compressive Load on Four Samples in Pounds Per Inch Perimeter ............ Computed Values Using the Maltenfort Enuation: P - 5.8L + 12W - 2.1D + 350 + 605 (CLT‘O) eeeceeeeeoooeeeoeeeeeecoeee vi Page 56 58 70 71 73 75 INTRODUCTION The top-to-bottom compression test of empty boxes is perhaps one of the most commonly used today for evaluat- ing the performance of corrugated fibreboard containers. The test is used to determine the ability of different boxes to withstand stacking lead. Furthermore, it often discloses from the nature of the failures and the capacity to carry load, deficiencies in design, construction or fabrication, which are of vital information to the manufac- turer. During the past two decades, quite a number of empi- rical equations have been developed to estimate the top-to- bottom.compression strength of a corrugated fibreboard box on the basis of the engineering properties of the com» ponents and the box dimensions. The parameters involved maybe one or more of the following: box perimeter; Young's modulus of elasticity (E); flexural stiffness; transverse shear stiffness; short column crush test; ring crush test (liners and medium); Concora Liner Test (CLT); caliper; basis weight; and flute type. Four empirical equations which the author believes have made distinct and valuable advances in the determina- tion of compression strength of boxes will be the equations to be evaluated. The fifth equation by Ranger (1)* which also deserves equal merit will not be included because a parameter which was based on experimental data introduce doubts at the start, due to the use of a different conditioning standard prior to testing. The test materials were conditioned at 68°F and 65% relative humidity for '48 hours before testing which would be outside of the allowable limits for condi- tioning set by TAPPI (TAPPI Standard Th02-m-h9 for condi- tioningt 73 3 3.5°P temperature and 50 t 2% relative humidity). The equations involved are those of Kellicutt and Landtg haltenfort; and McKee, Gander*and Wachuaa. Melee, et a1 formulated two interrelated equations which will be evaluated in this study. With the required parameter values determined (except the Concora Liner Test which was not included due to unavailability of test fixtures) to satisfy the empirical equations, the compression strengths are computed. Correlation.is then made with the actual com- pression test values of boxes. Aside from correlating the theoretical values for compression strength with actual results, an analysis will be made on the tested corrugated boxes on the basis of variations in perimeter, depth to perimeter ratio, and length to width ratio. This analysis is brought about by * Reference listed in the bibliography. choosing box sizes which follow a pre-determined set of parameters. With no set standard for determining the short column crush test (sometimes called edgewise compression strength) of corrugated fibreboard as of this writing, the author devised a method which to him seemed very satisfactory. The full detail of the method is included in the section on test methods. The entire evaluation is based on 200 lb. single wall test board with only one type of flute, Cnflute. All the corrugated fibreboard.bdanks on this study were made cans single production run which used the same liners and medium throughout, sufficient to make 900 boxes of 225 sizes. DEVELOPMENT or CORRUGATED FIBREBOARD Box (2)* The first appearance of a corrugated form of some relationship to the present corrugated box is believed to have appeared in England. On July 7, 1856, a patent was granted to Edward Charles Healey and Eward Ellis Allen covering the fluting of paper or other materials to be used as a cushioning or lining for the sweat bands of hats. At that time it is believed that corrugating was achieved by first wetting the material and then passing it between a heated pair of corrugated or embossed rollers or between a heated pair of corrugated dies. Although this invention had cushioning as its primary function, it is not given a great deal of direct credit on the eventual development of corrugated boxes because little or'no progress was made with the idea towards the packaging field. The breakthrough was on December 19, 1871 when the first real patent for corrugated material that is directly traceable to the present corrugated boxes was granted to an American,.Albert L. Jones for an ”improvement in paper for packing”. A portion of Mr. Jones' claims were: ”The subject of this invention is to provide means for securely packing vials and bottles with a single “Material for this topic was taken from the book “Paperboard and Paperboard Containers..A History.” by H. J. Bettendorf. thickness of the packing material between the surface of the article packed: and it consists in paper, card- board, or other suitable material, which is corrugated, crimped, or bossed, so as to present an elastic surflace .......instead of wrapping the vials or bottles with the corrugated material, the latter may be made into packing-boxes e e e e "e Rights to Jones' patent apparently were obtained by Henry D. Norris, who started making the corrugated material for packing glass bottles. In the meantime, in 187h, Oliver Long obtained a patent on lined corrugated fibreboard (single face and double face) for packing purposes, a vast improvement to the original corrugated material alone. The use of the unlined materials replaced straw, sawdust and excelsior in packing glass bottles and glass lamp chimneys in wooden boxes and barrels. With the invention of lined corrugated fibreboard, boxes were made for express shipments and then as freight shipping containers. Corrugated fibreboard arose as a cushioning material and then became a large shipping container due to the savings in freight and handling costs. The corrugated con- tainer, originally designed for light express shipments, had in the meantime been developed and most of the present day styles were available. Notably there was the so-called regular slotted container shown in Figure 1, a box made of one blank, scored so as to form the four side panels of the box, joined with tape or stitches to form.a tube, slotted in from both ends of the tube to form closure flaps, and scored around the tube to permit the flaps to close. Inner Flaps Outer Flaps Manufacturer' Joint Taped val L'" H Length W K L LIV ,/ = Width \/ D = Depth Regular Slotted Container (RSC) 2 The dimensions given are the inside dimensions of the box. 7T h) t1 , + TU 53 L W+D I ------'== i: 5 5 U I I 5 .:== : I l I l I I I I I I I I L fl F—m—«F—‘F— +- 1% Blank Size of R80 Box "A" Scores = horizontal dotted lines "B" Scores = vertical dotted lines Perimeter = Z = 2L + 2W % r”; I Figure 1 Nomenclature This type of container is characteristic of 90% of shipping containers made today. The RSC boxes were very attractive to the cereal manufacturers because they were delivered collapsed ready to be set up as boxes and they were compatible with the cartons of cereals on account of its lightness, smoothness and printability. The demand for corrugated shipping boxes grow fast due to the extended use of these boxes into many lines of products other than for cereal food products. Corrugated fibreboard containers provide strong. resilient, and lightweight packaging at low cost. TECHNICAL ADVANCEMENT The first recorded laboratory tests for the improve- ment of shipping containers were made in 1905 by the Forest Service (3) in cooperation with Purdue University. The purpose of these tests was to determine the merits of different kinds of wood as box material. Corrugated fibre- board material was excluded from the tests due to its limited use on cereals alone on a special permit from the Official Classification Committee during that period. In 1910, the Forest Products Laboratory was esta- blished at Madison, Wisconsin (3). The Laboratory's objective in connection with shipping containers was to develop fundamental principles of design and relationships of the various details necessary to produce containers that are balanced in strength. Although actual testing of corru- gated fibreboard containers at the Forest Products Laboratory started even before world War I, and in spite of the develop- ment of the hexagonal testing drum, thorough study on the scientific design of fibreboard boxes started only in the early thirties. The early manufacturers and users were apparently concerned on how the corrugated boxes could withstand rough handling. They resorted to such tests as dropping the box off the tailgate of a truck, bouncing it down a flight of stairs, sliding it down a chute or actually shipping and then checking at the point of destination. With emphasis on rough handling, the revolving drum became a widely used test for determining corrugated box performance. In the late thirties, universal acceptance was achieved in the use of corrugated fibreboard boxes as shipping containers which provided adequate protection to its content. For this reason, increased consideration was given to the strength of the corrugated boxes. An extensive evaluation was made by McCready and Katz (A) on the corru- gated fibreboard as an engineering material in connection with a study of adhesive on the strength of corrugated fibreboard. They may be the first to formulate an empirical equation for compression strength as a function of modulus of elasticity based on the thin plate theory of mechanics. At about the same period, Carlson (5,6) published his findings on some factors that would affect the determi- nation of engineering properties' values for corrugated fibreboard as well as the significance of these factors to the compressive strength of the box made of the same material. In 19A3, Little (7) developed an equation for box compression strength based on the engineering column strength formula by Rankine. The assumption was that corrugated fibreboard is uniform in its properties and that the same laws could be applied to it which govern other elastic materials. 10 From 1951 to the present, several attempts were made to formulate empirical equations which could predict the compressive strength of the corrugated fibreboard box. At this point, four of those empirical equations will be discussed in more detail and from thereon, actual evaluation would be made. EMPIRICAL EQUATIONS Using the principles of engineering mechanics and statistics, simplified formulae were developed relating top-to-bottom compression strength of boxes with its combined corrugated fibreboard properties, component properties that comprise the fibreboard, and box dimen- sions. The empirical equations that are involved will be discussed according to their chronological order of publication and not due to preference. I. Kellicutt and Landt's (8) Empirical Equation 1/3 «may- a m P' (rsf+rdf+ar (Z/h) cm) Where: P - total box compressive strength in lbs. r8f - ring crush of single face liner in cross machine direction, lb/in. rd: - ring crush of double face liner in cross machine direction, lb/in. rcm - ring crush of corrugated medium in cross machine direction, lb/in. a: a take-up factor of corrugating medium: A-flute --- 1.523 B-flute --- 1.361 C-flute -- 1.”?7 11 12 K - Constant: A-flute --- 8.36 B-flute --- 5.00 Coflute --- 6.10 Z - box perimeter, in. J u box factors (for laboratory made and taped) A-flute -~- 0.71? B-flute --« 0.752 C-flute c-e 0.717 The empirical equation (I) in the preceding page evolved from the basic formula developed at the Forest Product Laboratory, 0.3. Department of Agriculture, for the design of plywood panels by applying the thin plate theory of mechanics. Fibreboard being a nonisotropio material is comparable to plywood. The main objective was to develop a method of expressing the compressive strength of a corrugated fibreboard box using test data obtained from simple tests on the components of the fibreboard. In the development a tube made of corrugated fibreboard consisting of four panels representing a box without top and bottom was used as the intermediate link between tests of the fibreboard components and of the box. In the equation, three constants are involved. First, the take-up factor,‘2:, which is actually a corruga- ted fibreboard trade constant corresponding to the length in feet of the corrugating medium that comprises a foot of corrugated fibreboard, and it differs for every type of flute used. Secondly, the constant K is defined as the ratio 13 of the combined ring crush value on the cross machine direction in pounds per inch (liners and medium) and the compressive strength of a specific size of cubical tube with the vertical crushing load parallel to the flute. Different values were determined for each specific flute construction. Finally, box factor, J, is the ratio of box compressive load to tube compressive load for various cross sections with height 12 inches and greater found to be reasonably constant. On heights less than 12 inches, consi- derable divergence between the box and tube loads existed. Specific box factor applies to a type of flute and the kind of Joint used in the manufacturer's Joint. II. Maltenfort's (9) Empirical Equation P =- 5.8L 4» 12w - 2.11) + K + k(CLT-0) (11) Where: P a total box compressive strength in lbs. L - box length, in. w - box width, in. D - box height, in. K - Constanta A-flute --- 365 B-flute --- 212 C-flute -~- 350 k - Constant: A-flute --- 6.5 B-flute --- 5.“ C-flute ..- 6.5 1h CLToo = average Concora Liner Test - across machine direction of single face and double face liners, 1“ lbs e The empirical equation was developed by applying linear regression analysis, a statistical method, on series of test data for top-to-bottom compression strength of single wall corrugated fibreboard boxes. On the basis that the relationship of dimensions to compressive strength is linear, an equation was formulated using the dimensions and liners strength without regard for the corrugating medium. The equation (II) in the preceding page is actually a simplified form of: P a 4.45(2L + 2w) - 3.1(L1- W) - 2.1D + K + k(CLT-0). The constants, with the values in the quantity (2L + 2H) excluded, were the values determined using statis- tical method. Concora.Idner Test (0LT) is a straight crush test on.a 6 inches by i inch strip of liner instead of a ring crush. The advantages over the ring crush test as claimed are: (a) on heavy liner grades, damage resulting in trying to form a ring is avoided; (b) it avoids the effect on the strength of the material by the circular configuration of the test specimen; (c) a straight crush test corresponds with the kind of loading experienced by liners on box compression testing. 15 III. McKee, Gander and Hachuta's (10) First Empirical Equation when D/Z a 1/7. . ---- 0.2 u o.u 2 P . 2.028 Pho 746 (1/5 5 z 9 ny ) (III) Where: P a total box compressive strength in lbs. Pb - edgewise compressive strength of plate material, lb/in. 01 a flexural stiffness of combined board in machine direction per unit width, lb-in. 0y - flexural stiffness of combined board in cross- machine direction per unit width, lb-in. Z a box perimeter, inch. The empirical equation is based on the assumption which relates the ultimate compressive strength of a plate to the instability load and the edgewise compression strength of the material of the plate by means of a power function. Basic Equation: b Pa/Pcr ' C (Pm/Per) or b 1-b P = c P P (a) 2 El 01‘ 16 Where: Pz . ultimate strength of the plate per unit width, lb/in. Per . instability load, lb/in. C, b C Constants From the theory of buckling of initially flat plates, Per - 12 kcr Vfi;‘fi;'/w (‘0) Where: kcr a buckling coefficient (Hz/12) [( lea/n2 ) + (112/1.2 ) 4» 2K] '1 I W143?) (n/m n a number of halfwaves in buckled panel in the direction of load n . 1. 11' W11?!) s r :3 WITH? K =- a plate parameter dependent on mechanical properties and cross-section geometry of the combined fibreboard, dimensionless. w - width, inch. D I depth, inch. By approximation, K a 0.5, 4ybifig. a 7/6, W ' Z/h. Enuation (b) then becomes «waves 196132 ,, 9,322 °r 22 921222 196132 17 Where: n =- 1. 1r D/Z 5 31/2714 n =- 2, 1: 31/5711» é 3V6"/1u n - 1'. 1r BVITFn/iu 5 amt'm/m Denoting the modified buckling coefficient within the bracket as k in equation (c) and substituting in equation (a), then multiplying by Z to obtain the total compression load, the resulting equation is: 2-21; ---)1-‘0 ZZb-i 1-b P =- C (hm tJ( VDx DID?) , K (d) The modified buckling coefficient is assumed to be K1") .- K2“, and being a constant, equation (d) is further simplified into: P :- aPm b(V'D:D;.) 1.13 2213.1 (e) The experimental constants g and b of the simplified box formula were determined by a logarithmic plotting of the load ratios [-..Elé-.. q vs. My:1):.E’lhafim:l of actual ..-- m- 2 V511), /z Vfixny /z test results wherein a straight line was fitted by the method of least squares which gave values for a :- 2.028 and b :- O.7(+6, thus the empirical equation. 18 IV. McKee, Gander and wachuta's (10) Second Empirical Equation when D/Z a 1/7. . . . 2 O 706 no 508 20 49 (IV) P " 508?“ Pm Where: h a combined fibreboard caliper, inch. The empirical equation was actually derived from the first equation of the same authors. 0n the basis that corre- lation of composite flexural stiffness, edgewise compression strength, and combined fibreboard caliper existed, equation 0. 46 ---- 0.2 b 0.492 P a 2.028 Rm 7 (W/fixpy ) 5 Z was further simpli- fied. Designating the ordinate as map; in lb—in. and the abscissa, the product of edgewise compression strength, multiplied by caliper squared (Eh ha) in lb-in., test data were plotted. Fitting a line on the points plotted, a corre- lation was achieved which gave the relation, W/fiifig- - 66.1 (Eh h?) and by substituting this relation in equation (III). gives the empirical equation (IV). DESIGN OF EXPERIMENT The experiment was designed for a 200 lb. single wall and C-flute construction corrugated test board.* All the corrugated fibreboard blank sheets and the components of the board used throughout the study came from the same roll of liners and corrugating medium.and were produced in.a single production run on one corrugating machine. At the start of production, quality checks were done on the test board before getting the set of blanks needed. With the evaluation of the empirical equations as the primary objective on the basis of actual.test results on top-to-bottom compression strength of 380 boxes, diffe- rent sizes were considered. The box sizesfl were such that the dimensions were all dependent on three parameters, namely, depth to perimeter ratio (DMZ), perimeter (Z), and length to width ratio (L/W). The parameter values involved are: Perimeter We 4.1223322). W .08 N 30 1.00 '2“ 38 1.50 .32 * See.Appendix.A for test material description ** See Appendix B 19 20 Am as 1.75 2:: as 2.00 .70 56 The D/Z - .08 was not used in combination with peri~ meters 30 inches, 3h inches, and 38 inches on account of the very low resultant box depth (range: 2-13/32” - 3-1/32”) Which was not practical especially with the presence of flaps. In spite of the combinations being reduced by 15, there were still 225 combinations and thus sizes. With four samples for each size, the total number of boxes tested was 900. All of these boxes tested were made individually in the laboratory on a sample maker equipment. With the manner in which the dimensions of the boxes were determined, an analysis will be undertaken with respect to individual parameters in addition to the primary objective of the experiment. TEST METHODS Tests on the fibreboard components and the combined board were performed under controlled conditions of tempe- rature and humidity, and the test pieces were made after the sample materials had been adequately exposed to test conditions. Similarly, the 380 test boxes were compression tested in the same controlled conditions although the actual box making was done under ordinary room conditions. All the sample materials and test boxes underwent preconditioning format least 2n hours at 100°? temperature (TAPPI Standard Tues-mugs not to exceed 1uo°s). After preconditioning they were then transferred into the conditioning room where the temperature is controlled at 72°F‘and relative humidity at 50% (TAPPI Standard ThOZ-m-hQ for conditioning: Tempera- ture - 73 3 3.5°F, Relative Humidity - 50 3 2% and for not less than 2h hours). The purpose of preconditioning the boxes is to approach the moisture content at equilibrium under standard conditions from a drier state. The moisture content, if necessary, is reduced to less than half the value under standard conditions during preconditioning, then raised to standard conditions in the controlled room. With the above standard conditions satisfied, the basis weights and calipers for corrugated fibreboard and its components were determined by using the TAPPI Standard 21 22 Tflio-mphS and TAPPI Standard Thii-m-hh, respectively. t a est Bing Crush Test - (ASTM Designation: D1160 - 60) Test specimens are cut 6 inches long and i inch wide. Since cross machine ring crush values for liners and medium are required, the machine direction of the specimens should be lengthwise. Each test specimen is inserted in the specimen holder’and positioned at the center between the two platens of the compression tester. The maximum load required to collapse the specimen is the desired value. A minimum of ten specimens for each principal direction of the fibreboard is recommended. The compression tester used on this particular test is an H & D Crush Tester. Concora Liner Test (9) The same test specimens for the ring crush test are used in this determination. The only difference lies on the configuration of the specimen when placed between the platens. The 0LT specimen is straight instead of in the form of a ring and thus, a special jig consisting of a platen and sample holder had to be fitted on.an H e D Crush Tester. Due to unavailability of a fixture, the CLT-O value will be excluded but the empirical equation will still be evaluated on account of the linear nature of the equation. 23 Static Bending Test Six 13 inches by 2 inches specimens with the corru- gations parallel to the length and six 13 inches by 3 inches with corrugations perpendicular to the length were clean cut with extra care in order not to damage the flutes. On each set, three specimens were tested with the load applied to the single face and the other three to the double face. The set-up is such that the board specimen is sup- ported near its ends by two i inch wooden dowels 12 inches apart with an overhang of i inch on both ends. Two points loading was used with the points spaced 0 inches apart. The rate of loading was 0.05 inch per minute while the center deflection of the beam was measured in 0.001 inch. Simultaneous readings were made at intervals of 0.2 pound until failure occurred. Tests were performed on a Baldwin- Emery SB-h testing machine. With the data on load and corresponding deflection plotted, the slope of the curve at the origin was determined and this would correspond to the load deflection ratio, “5;. Using the equation, EI - «fig-91%;- for two point loading (11) and with the slope and the length L.of'the beam between supports known, the flexural stiffness was computed. To obtain the value of flexural stiffness per inch width, the computed E1 is divided by the width in inches of the tested specimen. 1 l l I]- 2h Column Crush Test The column crush test was utilized to measure the structural resistance of corrugated fibreboards when loaded as columns. On this specific test, no standard as yet has been set by either the American Society for Testing Mateo rials (ASTM) or the Technical Association of Pulp and Paper Industry (TAPPI). It is for this reason that the author devised his method of testing. In the design of the method, difficulties in the preparation of the specimens, the propping of the specimen perpendicular to the platens of the compression tester, and the distribution of compressive load on the specimen edges were considered. H The procedure is to clean out rectangular specimens of 1 inch long and 3/4 inch wide with the flute parallel to the width without damaging the flutes. A number of specimens are placed side by side and s i inch strip of tape with its adhesive facing outward is used as a loose band Just to gather them together, in such a way that specimens would slip if it were free to do so. This is illustrated in Figure 2(a). The choice of the specimen size was based on earlier'trials, and the convenience that an inch length gives in the determination of the edgewise compression strength per inch width is realized by merely dividing the total compressive load by the number of speci- mens used. The number of specimens needed in a sample is (a) ' 1" Strip Tape —«. 4: With its Adhesive Facing Outward A set of five specimens in a sample loosely banded by a tape with its adhesive facing outward (not touching the samples) ready for compression test. (b) Load Direction Platen ‘A v‘ [/7 Sample 9;" Thick / Foam / \ \ i 3 A sample (five specimens with its flutes.vertical) with foams on its bearing surface in-between platens of a compression tester. Figure 2 Column Crush Test 26 arbitrarily determined. As a guide, the corrugated fibreboard caliper multiplied by the number of specimens should be approximately or slightly less than an inch. This would give a loading area which is almost a square. To counteract the difficulty in the distribution of the bearing load due to the nature of the material tested, two i inch thick foam out 1% inches by 1% inches are placed on the bearing areas as shown in Figure 2(b). This would also minimize the effect of the slight irregularities which exist when the specimens are cut to their specified size. The results of the column crush test using the proposed method are shown in Appendix C. S m sea est TAPPI Standard method TBOh-m-bs specifies glued flaps on compression testing of corrugated shipping containers. Any other method of sealing the flaps is also satisfactory provided the method followed does not leave anything inside the box which would influence the compression test. With the above condition imposed, the 830 test boxes were made with a provision to facilitate the stapling of the flaps. This is to prevent the bracing action brought 27 about by the lowering of the flaps during compression when the wider panels break inward. During the box making, the flaps were made narrow so that upon closure an access hole is available for the stapler to clinch with four staples the inner'and outer flaps together. The compression testing of all the 350 test boxes was performed on the Tinius-Olsen Compression Tester at a platen speed of 0.5 inch per minute and with fixed platen. (TAPPI Standard Taou.m-u5 on platen speed 8 0.5 t 0.25 inch per minute with either fixed or floating platen.) RESULTS AND DISCUSSION All the data necessary to satisfy the objectives of the experiment had been compiled. These would take the form of tables, figures and graphs. In the succeeding discussion, the equations will not be referred to by their author's names but rather by the Roman numbers designated to each specific equation. at ca uat o s In evaluating the four empirical equations considered in this study, two tables, 1 and 2, and two graphs, Figures 3 and h, were utilized. On Table 1, computed values based on the empirical equations (except Maltenfort's equation wherein no definite conclusion could be formulated in the absence of the Concora Liner Test) were found to be low. The variations are shown on Table 2 which gives the trend as to how close the computed compressive values are to the experimental values. Since Enuation (II) does not have the 6.5 (CLT-O) value which is a constant and with the variations given on Table 2, the range of values that CLT-O would have to limit the variation to a minimum was computed. The CLT-O value for the component materials used in the experiment should be within the range: 28.3 to “5.6. If the value 28 9 2 ..m Nausea“: com .moakem amen some no." usedmcoaav uo pom chance on» no smokers I o «we who Aoaaqov mum Ham AOIEAOV mm“ :mm Aonaqoa nan awn Aotaaov name» 03 no omeno>< I so mumou 0.3 Mo ommhod; I s m am: a r em sam.m a m a e ~m:.o mom.o esa.o nuance: use. Hoodoo .oeMoz .>H h N E . mm: as: N uLnanxr a mac N u m Noe.o mea.o masses: use Mousse .oowoz .HHH no.9aov no.9aov fireman m.e+oo:m “$7.03“ “6.03: “$1.03: “6&3: 3353 n6 + own + ma.~ u 3m“ + Am.“ a a successes: .HH use ans new moo own «on .:\N. n\H . Assad + use + .63 ... a pecan one susodaaos .H ..mem ..omw ..mea .moa .Nme come some smog .nlqma. .muw .ma. .maw. Inqduunnnnuqmai nsmdmmmmmummmJumqqmauunuu .en a N .m: u a .me u s .mn a N .e« I a .om I N no.“ m Hon m n no.“ no.“ m no.“ a n no.“ m duo ear... .0), K. . sauna, om e..ume .au‘ zoo o-en - use .mspod. v 0.9“: 30 Table 2. The Compressivo load Difference in Pounds Between the §eoe _uenta_ Res _ts and the Theo_et ca_ e-m-uted alues ...—.-..“ I II III IV Kellicutt & McKee,Gander McKee,Gander Egg, Lang; Ma Na ta a h ta 30 88 184* 181 193 3b 96 200* 183 196 38 9a 205* 175 189 h2 138 2h7* 209 22“ #8 163 280* 229 245 56 176 296* 230 2a? ' — These figures would vary if CLT—O value was available. Thus, the figures would assume lower'values and/or negative values if the computed compressive load with CLTbO value included exceed that of the actual test values. m maswam mononH ad nepeaanom at s. a s s a nuance: use Mousse .moMoz >H||l X masses: use .3335 £832 HHHII D encased»: HHII¢ panda ens specifies HI: 4 Ben sums HespoH % \ \ \opm »u am pm .mmMoz ... HHH w. 1 \x \ 000 b“ PROHdeHdz I. HH m \ x xx 00m Du PPSOHHH0M I H 5000 \\ \\ \ cm: n 2550 HeoeH we. . \ \x a nu an \a xv mxeamad .m .\ .\. \ 1. \\ s \\ UL \\ \.\ \ U mu .\ . x. m o .oo o a Izzl 4 D\ x\ Q .n p M 2 HHH M pertussis: .. Hailb s peseq was 33323 n all. 4 A 68 33 determined falls near the lower limit, it would approach the first three low perimeters but would still give a low value on the remaining perimeters. Similarly, if CLT-O value is near the upper limit of the range it would satisfy the higher perimeters considered. However, it would have in turn a high compression value exceeding the actual compression test value for the low perimeters. At this point, it is worth mentioning that the constant shown in Table 1 which has been determined for Equation (II) is an average, using an entire range of depth, length, and width variations for each set of perimeter used: Upon analyzing Figures 3 and a. distinct patterns are noted. It appears correlations among the equations are in pairs. Equations (I) and (II) are highly correlated through- out the entire range of perimeters. The difference could not be determined for the reason mentioned earlier. Similarly, Equations (III) and (IV) are highly correlated on the perimeters considered with slightly lower values for Equation (IV). The two equations differ only by 12-16 pounds on the entire range. The plotted test data in Figure 3, on the other hand, seemed to show some slight correlation on the first three lower perimeters but abruptly changed its pattern in the * See Appendix F. 3“ remaining perimeters. The pattern is a widening of the gap with respect to the theoretical curves. Figure 4 shows how close the correlation between an ideal curve and the theore- tical-actual curves are. By approximating the slope of the curves and comparing with the ideal curve, inferences could be made that Equations (III) and (IV) are more closely correlated with respect to the overall range of perimeters than Equations (1) and (II) without regard to the variation constants. The constants could be easily altered without difficulty to bring the theoretical value to that of the actual test values. A general trend exists on all the equations in that as the perimeter is increased, the theoretical values decreased when actual test values increased more rapidly. W A general knowledge could be restated that as the box perimeter is increased, top-to-bottom compressive strength correspondingly increases. As to the resultant increase, many attempts have been made but no conclusive evidence have been published so far. The succeeding discussion will not pinpoint the relationship but rather would analyze the effects on the compressive strength of the corrugated box when one parameter is varied while the other parameters are held constant. 35 Qggstant Parameter The given curves on Figures 5 and 7 were plotted based on the tabulated data on Table 3. Similarly, Figure 6 used the data on Table h. With the perimeters constant and with the depth to perimeter ratio varied, definite patterns were observed on Figure 6. These observed patterns support an earlier statement that the compressive strength increases with an increase in perimeter. The curves are such that the four lower perimeters are very unstable within the D/Z - 0.08 to D/Z a 0.32 and similarly, applies to Figure 7 on the height range of from 3-3/8 inches to 12 inches. The upper two perimeters have the same characteristics although the range of instability was reduced by one-half. The remaining portions of the curves taper down gradually but not at the same rate. This shows that no definite relationship exists as the perimeter is changed at a set interval with variable D/Z ratio and height. Figure 6 shows the effect of D/Z ratio with load per inch perimeter and with the perimeter constant. The curve is very much similar to Figure 5 but the arrangement now is in reverse; that is, as the perimeter is increased the load capacity per inch perimeter is reduced. 36 Table 3. Average Compression Strength in Pounds for Different Perimeters With Depth to Perimeter Ratio Constant gased on 20 Samples. D/Z 3o" 34" 38" 42" 48" 56" .68 T8 842 864 934 .16 684 734 749 780 814 869 .24 620 647 686 739 814 872 .32 662 690 733 762 822 880 .40 641 671 704 766 833 853 .48 652 672 686 723 810 866 .56 640 699 675 748 820 852 .70 653 660 679 743 784 818 m mammam oapmm ampmaanmm op spawn 37 A{we QMe QANe owe NMe {We mke maeHHT my tome //I \x / // ..OON. / \ / z/z . ,/ / V. //I \\\. /.// u I \II ./ Amy N ............. I-/- \\.\ ///, /Ai .omaxw ,I/ lllllllll \ 4/, my /. m /_ 1 /II/ a// m ,/ / some. U n. 0 e p T. .dmmu w. 0.. S zon u N Amy ....Nh H N mv ..mm H N 3 :08 ..me u N C .3 u N 3 :6mm 38 Table 4. Average Compression Strength in Pounds Per Inch Perimeter for Different Perimeters With Depth to Perimeter Ratio Constant Based on 20 Samples D/Z 3o" 34" 38" 42' 48" 56" .08 20.05 18.00 16.68 .16 22.80 21.59 19.71 18.57 16.96 15.52 .24 20.67 19.03 18.05 17.60 16.96 15.57 .32 22.07 20.29 19.29 18.14 17.13 15.71 .40 21.37 19.74 18.53 18.24 17.35 15.23 .48 21.73 19.77 18.05 17.21 16.88 15.46 .56 21.33 20.56 17.76 17.81 17.08 15.21 .70 21.77 19.41 17.87 17.69 16.33 14.61 39 w masmdm oapmm ampmaaaom op spawn S :Om zms =N¢ : mm ..#M :OM H II N H H II N N N N N N AAAAAA '— N Md' [no vvvvvv mm. mm. om. mm. em. 8.. B. 110 F limp ....m P rd 01 fl. °sqq up psoq uotsseadmoo GSBJGAV <5 cu 8 a xeqemtxeg qouI meg m oaswam monoeH ea pnwaem oMI mm mm am pm m, we \ I\. \\\\\\ ill// a =om n N I on o>aso 11/, x. .. Amw :w# H N I Amy obtnfio 1/ \ / / =N¢ H N I Alwv 050 I e / . zmn n N I an cease ./ .\. /, / ...—um H N I NV mad—D {I\ M a/ / =om u N . A.V obese \\-:/ A v x I! IIIIIIII (I \\ /’ / _ [I’ll] \\\\ / o z-.. / .4 I /. / III- . ./ -/ --.l--|--l.- 3/ ll/ll!’ i...\|\ \|.\||I /II /o -.III ........ ....--I. / / $7. / l/l A3 4008 ..omw +er aomm room aone °sqq ut psoq uotssexdmoo eSexeAv 41 Depth to Perimeter Ratio - Constant Figure 8 clearly shows that for D/Z <21/7, compressive strength would be relatively high, which is the case for D/Z - 0.08. The effects on the compressive strength upon varying the D/Z ratio is to vary more on lower perimeters, then gradually variation is decreased as the perimeter is increased. Length to Width Ratio - gogstagg Data on Tables 5 and 6 were used to plot the curves on Figures 9 and 10, respectively. Tests showed that varying the length to width ratio affected the compression load but not on a large scale. It was found that boxes tested with an L/W - 1.25 and L/W - 1.50 gave a higher compressive load than square boxes. Furthermore, boxes tested with an L/w s 1.75 and L/W a 2.00 presented values lower than an L/W a 1.00 would give. The BSC Box With the varied sizes of corrugated box tested, an observation was made with regards to the buckling characteristics of the vertical panels. Three distinct types of buckling were noticed. The first is a halfwave, as shown in Figure 11, which is characteristic of short depth boxes. This actually occurs Just before failure. Figures 12 and 13 42 mKOd'CUOCDKOO OHNMd‘d‘LfiN nnnnn "14'." §§§§§§\§ °° . cacacacacacacac: 80 l I I ' ' ' |I ' I ' I . I I I - ' : l . : l I : llll'l 4L$ 10400430 0 «hm \0 "e (U ‘bd. (1) 4pm 4-;- in / o "5% Sr :¥ : ; e = A e A A A 1 IL Y I I T V I II M N .— O 0\ CD I‘- \0 Ln d’ M (U N N N H H H H H H H xeiemtxeg use: 195 °sqq u: psoq uotssexdmoo eSsxeAv Perimeter in Inches Figure 8 43 Table 5. Average Compression Strength in Pounds for Different Perimeters with length to Width Ratio Constant gased on 28932 Samples, L/W 30" 34" 38” 42" 48“ 56" 1.00 660 688 711 761 822 861 1.25 656 692 710 780 847 891 1.50 648 694 714 784 825 888 1.75 658 678 681 759 812 844 2.00 629 657 694 730 794 856 44 mmli moaoaH ea Housmanmm m oaswam 1 Pm: 04 as. mm mm on. on. \ llllll 8N n {a \ .||-|| me; u {a . .\ ._ n OP " ._ n __Hj 000 .dmw 'sqq up psoq uotssexdmoo eSsxeAv 16mm x8m 45 Table 6. Average Compression Strength in Pounds Per Inch Perimeter for Different Perimeters With Length to Width fiatio Constant Basedwon 28~32 Samples. L/W 30' 34" 38” 42' 48' 56" 1.00 22.00 20.24 18.71 18.12 17.13 15.38 1.25 21.87 20.35 18.68 18.57 17.65 15.91 1.50 21.60 20.41 18.79 18.67 17.19 15.86 1.75 21.93 19.94 17.92 18.07 16.92 15.07 2.00 20.97 19.32 18.26 17.38 16.54 15.29 l (a i c: o: a: m xeiemtxsg qouI meg 1 a5 19. F ’Q'I TIT 46 (ifs? poof-notéssxdmog 50 42 Perimeter in Inches 38 f .41.] efisxenv Figure 10 4? illustrate two halfwave and three halfwave buckling, respectively, with the panels alternately buckling on each halfwave. No definite boundary could be determined but rather occurrence on some D/Z range are somewhat consistent. For the two and three halfwaves buckling, a stipulation that the panels should not be warped before testing does not necessarily have to be followed inasmuch as the side panels would still buckle as mentioned and therefore, would eliminate the effect of warping. As for the short depths, warped vertical panels would induce the direction of buckling. A further observation was made in that failures of the boxes tested occurred mostly in panel number 1, the wider vertical panel as shown in Figure 14. This may be due to the presence of the manufacturer's Joint which lessens the bearing capacity of the corner. All failures no matter what the height of the box may be (on boards without fabrication defects) always occur either on the bottom or on the top areas near the score line. The line of failure comes from the corners in contact with the platen, then forms a curve concave upwards for upper failure (convex upward for lower failure). This type of failure may be inwards or outwards depending upon the box configuration. #8 .cHSAHwH onoumn push noammoaa taco nouns .unozna moonwpmnfl mace so unwkpso maaaxosn Non copewsanoo pnwfimn agonm hac>apmamn d Ho nodpdunoo __ mnemam vac mo coapcmnaa .mnsaaaw caches amen noammmaaaoo amen: neat aroma me wnHHMosn Hop cmpmwznaoo pnwfimn anaema macbdudamn a Mo godpacaoo m. mnemam coca no .oapocndq 49 .mnsaacm mHonn pmdfi aoammcaaaoo Hound non: macaw ma mnHHMozp Mon ccpwwSHHoo Haw» aam>apeamn a do meandeaoo m_ onsmam uwoq no nouaocndn .mononmwmn you mnmnaza cmnwdwmc mum .pnaon m.an:pcmH sauce on» on noapcacn ad movam Heedpno> mp“ Spa: Hon cmpwwsnnoo Havana» d e. mnemaa CONCLUSIONS The conclusions are based on the data compiled from the actual testing of fibreboard components, corrugated fibreboards and R80 boxes made of a single wall C-flute, 200 lb. test board. The following conclusions are: . 1. Except for the Maltenfort Empirical Equation, theoretical values for top-tc-bottcm compression strength are all low. If the Concora liner Test result on the liners used would fall within the range 28.3 lbs. to 45.6 lbs., the equation by Maltenfcrt would equal the test result values on certain range. 2. The empirical equation of Kellicutt and Landt as well as Maltenfort's are closely correlated although the increment could not be determined. Similarly, the two equations of McKee, Gander and Nachuta are highly correlated. No correlation exists between the first two equations and the two latter equations. 0n the lower perimeters slight correlation exists between test results and the theoretical values but diverges on higher perimeters. 3. Varying the length to width ratio changes slightly the compressive strength. Boxes with L/w a 1.25 and L/W = 1.50 give higher compressive strength than square boxes. On boxes 50 51 with L/w = 1.75 and L/w = 2.00 the resultant compressive strengths are lower than on a box with an L/w = 1.00. BI BL IOGRA PHY 52 1. 3. h. 5. 6. 7. 8. BIBLIOGRAPHY Banger, A. E. 1960 The Compression Strength of Corrugated Fibreboard Cases and Sleeves. Paper Technology, vol. 1(5) 8 531-541. Bettendcrf’ He J. 1996 Paperboard and Paperboard Containers, A History. Board Products Publishing Co., Chicago, Illinois. Kellicutt, K. Q. 1959 F P L (Forest Products laboratory) Structural Design werk Rests on 50 Years Research. Package Engineering, vol. 9(2) 3 60-63. MCCready, Dc W. and D. L. Katz 1939 A Study of Corrugated Fibreboard - The Effect of Adhesive on the Strength of Corrugated Board. University of Michigan Engineering Research Bulletin No. 28 (1939;. Carlson, T. A. 19Q0 Bending Tests of Corrugated Board and Their Significance. Paper Trade Journal, vol. 110, NO. 8 3 123-1270 Carlson, T. A. 19b1 Some Factors Affecting the Compressive Strength of Fiber Boxes. Paper Trade Journal, Vbl. 112, No. 23, 35-38. Little, J. R. 19u3 A Theory of Box Compressive Resistance in Relation to the Structural Properties of Corrugated Paperboard. Paper Trade Journal, vol. 116, No. 2h, 31-3h. Kellicutt, K. Q. and E. F. Landt 1951 Basic Design Data for the Use of Fibreboard in Shipping Containers. U. S. Department of Agriculture, Forest Service, Forest Products Laboratory Bulletin D1911, 39 pp. 53 54 9. maltenfort, G. G. 1956 Compression Strength of Corrugated Containers- Parts I and II. Fibre Containers and Paper- board M1113. Vblc “1(7) 3 44,49,50,52,57, v01. “1(9) ' 60-62’67’68.72.7u’0 10. McKee, B. C., J. W. Gander’and J. B. wachuta 1963 Compression Strength Formula for Corrugated Boxes. Paperboard Packaging, Vol. 48(8) 8 149-159- 11. Marin, Jo and J. A. Bauer 1954 Strength of Materials. The Macmillan Company, New Ybrk. P. 151. 120 MCKee, Re C. and J. W. Gander 1957 Topgfioad Compression. TAPPI, vol. 40(1) x 57* . APPENDIX 55 APPENDIX A Test Materials Components of corrugated fibreboard Single Face Liner: Basis Height 8 45 lb/MSF Caliper a 0.0128 in. Mullen = 106 lb/sq.in. Ring Crush Test - MD a 14.41 lb/in width on = 10.13 lb/in width Double Face Liner: Basie Weight 2 44 lb/MSF Caliper = 0.0129 in. Mullen = 120 lb/sq.in. Ring Crush Test - MD = 14.48 lb/in width OD = 11.69 lb/in width Corrugating Medium: Basis Weight = 27 lb/MSF Caliper = 0.010 in. Mullen = 37.5 lb/sq.in. Ring Crush Test - MD a 6.30 lb/in width CD = 5.53 lb/in width 56 5? Combined corrugated fibreboard 200 lb. test board C-flute = 42 flutes/ft Basis Weight = 132 lb/MSF Caliper = 0.160 in. Mullen = 214 lb/sq.in. Flexural stiffness = 103 lb-in. (machine direction) Flexural stiffness = 47 lb-in. (cross-machine direction) Column Crush Test = 37.0 lb/in width APPENDIX B 58 Box Sizes Perimeter = 30" Code* D/Z L/W (i§.) (13.) (12.) 112 .16 1.00 7% 7t 4-13/16 122 .16 1.25 6-11/16 8-5/16 4-13/16 132 .16 1.50 6.0 9.0 4-13/16 142 .16 1.75 5-15/32 9-11/32 4-13/16 152 .16 2.00 5.0 10.0 4-13/16 113 .24 1.00 7% 7t 7-7/32 123 .24 1.25 6-11/16 8-5/16 7-7/32 133 .24 1.50 6.0 9.0 7-1/32 143 .24 1.75 5-15/32 9-11/32 7-7/32 153 .24 2.00 5.0 10.0 7-7/32 114 .32 1.00 75 74 9-5/8 124 .32 1.25 6-11/16 8-5/16 9-5/8 134 .32 1.50 6.0 9.0 9-5/8 144 .32 1.75 5-15/32 9-11/32 9-5/8 154 .32 2.00 5.0 10.0 9-5/8 115 .40 1.00 7% 7% 12 125 .40 1.25 6-11/16 8-5/16 12 135 .40 1.50 6.0 9.0 12 145 .40 1.75 5-15/32 9-11/32 12 155 .40 2.00 5.0 10.0 12 Perimeter =_30" 59 Code D/Z L/W (i§.) (12.) (13.) 116 .48 1.00 7% 7% 14-13/32 126 .48 1.25 6-11/16 8-5/16 14-13/32 136 .48 1.50 6.0 9.0 14-13/32 146 .48 1.75 5-15/32 9-17/32 14-13/32 156 .48 2.00 5.0 10.0 14-13/32 117 .56 1.00 7% 7% 16-13/16 127 .56 1.25 6-11/16 8-5/16 16-13/16 137 .56 1.50 6.0 9.0 16-13/16 147 .56 1.75 5-15/32 9-17/32 16-13/16 157 .56 2.00 5.0 10.0 16-13/16 118 .70 1.00 7% 75 21 128 .70 1.25 6-11/16 8-5/16 21 138 .70 1.50 6.0 9.0 21 148 .70 1.75 5—15/32 9-17/32 21 158 .70 2.00 5.0 10.0 21 Perimeter = 34" 212 .16 1.00 8% 8% 5-7/16 222 .16 1.25 7-9/16 9-7/16 5-7/16 232 .16 1.50 6-13/16 10-3/16 5-7/16 242 .16 1.75 6-3/16 10-13/16 5-7/16 252 .16 2.00 5-11/16 11-5/16 5-7/16 Perimeter =_34" 6O Code n/z L/w (13.) (13.) (12.) 213 .24 1.00 8% 8% 8-5/32 223 .24 1.25 7-9/16 9-7/16 8-5/32 233 .24 1.50 6-13/16 10-3/16 8-5/32 243 .24 1.75 6-3/16 10-13/16 8-5/32 253 .24 2.00 5-11/16 11-5/16 8-5/32 214 .32 1.00 8% 8% 10-7/8 224 .32 1.25 7-9/16 9-7/16 10-7/8 234 .32 1.50 6-13/16 10-3/16 10-7/8 244 .32 1.75 6-3/16 10-13/16 10-7/8 254 .32 2.00 5-11/16 11-5/16 10-7/8 215 .40 1.00 8% 8% 13-19/32 225 .40 1.25 7-9/16 9-7/16 13-19/32 235 .40 1.50 6-13/16 10-3/16 13-19/32 245 .40 1.75 6-3/16 10-13/16 13-19/32 255 .40 2.00 5-11/16 11-5/16 13-19/32 216 .48 1.00 8% 8% 16-5/16 226 .48 1.25 7-9/16 9-7/16 16-5/16 236 .48 1.50 6-13/16 10-3/16 16-5/16 246 .48 1.75 6-3/16 10-13/16 16-5/16 256 .48 2.00 5-11/16 11-5/16 16-5/16 Perimeter ;_34" 61 Code D/z L/w (12.) (12.) (12.) 217 .56 1.00 8% 8% 19-1/32 227 .56 1.25 7-9/16 9-7/16 19-1/32 237 .56 1.50 6-13/16 10-3/16 19-1/32 247 .56 1.75 6-3/16 10-13/16 19-1/32 257 .56 2.00 5-11/16 11-5/16 19-1/32 218 .70 1.00 8% 8% 23-13/16 228 .70 1.25 7-9/16 9-7/16 23-13/16 238 .70 1.50 6-13/16 10-3/16 23-13/16 248 .70 1.75 6-3/16 10-13/16 23-13/16 258 .70 2.00 5-11/16 11-5/16 23-13/16 Perimeter = 38" 312 .16 1.00 9% 9% 6-3/32 322 .16 1.25 8-7/16 10-9/16 6-3/32 332 .16 1.50 7-19/32 11-13/32 6-3/32 342 .16 1.75 6-29/32 12-3/32 6-3/32 352 .16 2.00 6-11/32 12-21/32 6-3/32 313 .24 1.00 92 9% 9-1/8 323 .24 1.25 8-7/16 10-9/16 9-1/8 333 .24 1.50 7-19/32 11-13/32 9-1/8 343 .24 1.75 6-29/32 12-3/32 9-1/8 353 .24 2.00 6-11/32 12-21/32 9-1/8 Perimeter = 38" 62 Code D/Z L/w (1g.) (13.) (12.) 314 .32 1.00 9% 9% 12-5/32 324 .32 1.25 8-7/16 10-9/16 12-5/32 334 .32 1.50 7-19/32 11-13/32 12-5/32 344 .32 1.75 6-29/32 12-3/32 12-5/32 354 .32 2.00 6-11/32 12-21/32 12-5/32 315 .40 1.00 9% 9% 15-7/32 325 .40 1.25 8-7/16 10-3/16 15-7/32 335 .40 1.50 7-19/32 11-13/32 15-7/32 345 .40 1.75 6-29/32 12-3/32 15-7/32 355 .40 2.00 6-11/32 12-21/32 15-7/32 316 .48 1.00 9% 95 18% 326 .48 1.25 8-7/16 10-9/16 185 336 .48 1.50 7-19/32 11-13/32 18% 346 .48 1.75 6-29/32 12-3/32 184 356 .48 2.00 6-11/32 12-21/32 18% 317 .56 1.00 9% 9% 21-9/32 327 .56 1.25 8-7/16 10-9/16 21-9/32 337 .56 1 .50 7-19/32 1 1 ~13/32 21 -9/32 347 .56 1 .75 629/32 12—3/32 21-9/32 357 .56 2.00 6-11/32 12-21/32 21—9/32 Perimeter_;m38" 63 Code n/z L/W (12.) (1%.) (13.) 318 .70 1.00 9% 9t 26-5/8 328 .70 1.25 8-7/16 10-9/16 26-5/8 338 .70 1.50 7-19/32 11-13/32 26-5/8 348 .70 1.75 6-29/32 12-3/32 26-5/8 358 .70 2.00 6-11/32 12-21/32 26-5/8 Perimeter = 42" 411 .08 1.00 103 103 3-3/8 421 .08 1.25 9-11/32 11-21/32 3-3/8 431 .08 1.50 8-13/32 12-19/32 3-3/8 441 .08 1.75 7-21/32 13-11/32 3-3/8 451 .08 2.00 7.0 14.0 3-3/8 412 .16 1.00 105 105 6-3/4 422 .16 1.25 9-11/32 11-21/32 6-3/4 432 .16 1.50 8-13/32 12-19/32 6-3/4 442 .16 1.75 7-21/32 13-11/32 6-3/4 452 .16 2.00 7.0 14.0 6-3/4 413 .24 1.00 104 103 10-3/32 423 .24 1.25 9-11/32 11-21/32 10-3/32 433 .24 1.50 8-13/32 12-19/32 10-3/32 443 .24 1.75 7-21/32 13-11/32 10-3/32 453 .24 2.00 7.0 14.0 10-3/32 Perime t3; = 42 " 64 Code D/z L/w (13.) (1%.) (13.) 414 .32 1.00 105 10% 13—7/16 424 .32 1.25 9-11/32 11-21/32 13-7/16 434 .32 1.50 8-13/32 12-19/32 13—7/16 444 .32 1.75 7-21/32 13-11/32 13-7/16 454 .32 2.00 7.0 14.0 13-7/16 415 .40 1.00 103 103 16-13/16 425 .40 1.25 9-11/32 11-21/32 16-13/16 435 .40 1.50 8-13/32 12-10/32 16-13/16 445 .40 1.75 7-21/32 13-11/32 16-13/16 455 .40 2.00 7.0 14.0 16-13/16 416 .48 1.00 105 105 20-5/32 426 .48 1.25 9-11/32 11-21/32 20-5/32 436 .48 1.50 8-13/32 12-19/32 20-5/32 446 .48 1.75 7-21/32 13-11/32 20-5/32 456 .48 2.00 7.0 14.0 20-5/32 417 .56 1.00 103 103 23-17/32 427 .56 1.25 9-11/32 11-21/32 23-17/32 437 .56 1.50 8-13/32 12-19/32 23-17/32 447 .56 1.75 7-21/32 13-11/32 23-17/32 457 .56 2.00 7.0 14.0 23-17/32 Perimeter = 42" 65 Code D/Z L/w (12.) (13.) (13.) 418 .70 1.00 104 105 29-13/32 428 .70 1.25 9-11/32 11-21/32 29-13/32 438 .70 1.50 8-13/32 12-19/32 29-13/32 448 .70 1.75 7-21/32 13-11/32 29-13/32 458 .70 2.00 7.0 14.0 29-13/32 Perimeter = 48" 511 .08 1.00 12 12 3-27/32 521 .08 1.25 10-21/32 13-11/32 3-27/32 531 .08 1.50 9-19/32 14-13/32 3-27/32 541 .08 1 .75 8-3/4 15:1: 3~27/32 551 .08 2.00 8.0 16.0 3-27/32 512 .16 1.00 12 12 7-11/16 522 .16 1.25 10-21/32 13-11/32 7-11/16 532 .16 1.50 9-19/32 14-13/32 7-11/16 542 .16 1.75 8-3/4 15%. 7-11/16 552 .16 2.00 8.0 16.0 7-11/16 513 .24 1.00 12 12 11-17/32 523 .24 1.25 10-21/32 13-11/32 11-17/32 533 .24 1.50 9-19/32 14-13/32 11-17/32 543 .24 1.75 8-3/4 154 11-17/32 553 .24 2.00 8.0 16.0 11-17/32 Perimeter = 48" 66 Code D/Z L/w (i:.) (12.) (12.) 514 .32 1.00 12 12 15-3/8 524 .32 1.25 10-21/32 13-11/32 15-3/8 534 .32 1.50 9-19/32 14-13/32 15-3/8 544 .32 1.75 8-3/4 15% 15-3/8 554 .32 2.00 8.0 16.0 15-3/8 515 .40 1.00 12 12 19-7/32 525 .40 1.25 10-21/32 13-11/32 19-7/32 535 .40 1.50 9-19/32 14-13/32 19-7/32 545 .40 1.75 8-3/4 15% 19-7/32 555 .40 2.00 8.0 16.0 19-7/32 516 .48 1.00 12 12 23-1/16 526 .48 1.25 10-21/32 13-11/32 23-1/16 536 .48 1.50 9-19/32 14-13/32 23-1/16 546 .48 1.75 8-3/4 151 23-1/16 556 .48 2.00 8.0 16.0 23-1/16 517 .56 1.00 12 12 26-29/32 527 .56 1.25 10-21/32 13-11/32 26-25/32 537 .56 1.50 9-19/32 14-13/32 26-29/32 547 .56 1.75 8-3/4 15% 26-29/32 557 .56 2.00 8.0 16.0 26-29/32 Perimeter = 43" 6? W * Code D/z L/w (1K.) (13.) (12.) 518 .70 1.00 12 12 33-5/8 528 .70 1.25 10-21/32 13-11/32 33-5/8 538 .70 1.50 9~19/32 14-13/32 33-5/8 548 .70 1.75 8-3/4 152 33-5/8 558 .70 2.00 8.0 16.0 33-5/8 Perimeter = 56" 611 .08 1.00 14 14 45 621 .08 1.25 12-15/32 15-17/32 4% 631 .08 1.50 11-7/32 16-25/32 45 641 .08 1.75 10-3/16 17-13/16 4% 651 .08 2.00 9-11/32 18-21/32 45 612 .16 1.00 14 14 8-31/32 622 .16 1.25 12-15/32 15-17/32 8-31/32 632 .16 1.50 11-7/32 16-25/32 8-31/32 642 .16 1.75 10-3/16 17-13/16 8-31/32 652 .16 2.00 9-11/32 18-21/32 8-31/32 613 .24 1.00 14 14 13-15/32 623 .24 1.25 12-15/32 15-17/32 13-15/32 633 .24 1.50 11-7/32 16-25/32 13-15/32 643 .24 1.75 10-3/16 17-13/16 13-15/32 653 .24 2.00 9-11/32 18-21/32 13-15/32 Perimeter : 56" 68 Code D/Z L/w (12.) (12.) (12.) 614 .32 1.00 14 14 17-15/16 624 .32 1.25 12-15/32 15-17/32 17-15/16 634 .32 1.50 11-7/32 16-25/32 17-15/16 644 .32 1.75 10-3/16 17-13/16 17-15/16 654 .32 2.00 9-11/32 18-21/32 17-15/16 615 .40 1.00 14 14 22-13/32 625 .40 1.25 12-15/32 15-17/32 22-13/32 635 .40 1.50 11-7/32 16-25/32 22-13/32 645 .40 1.75 10-3/16 17-13/16 22-13/32 655 .40 2.00 9-11/32 18-21/32 22-13/32 616 .48 1.00 14 14 26-7/8 626 .48 1.25 12-15/32 15-17/32 26-7/8 636 .48 1.50 11-7/32 16-25/32 26-7/8 646 .48 1.75 10-3/16 17-13/16 26-7/8 656 .48 2.00 9-11/32 18-21/32 26-7/8 617 .56 1.00 14 14 31-3/8 627 .55 1.25 12-15/32 15-17/32 31-3/8 637 .56 1.50 11-7/32 16-25/32 31-3/8 647 .56 1.75 10-3/16 17-13/16 31-3/8 657 .56 2.00 9-11/32 18-21/32 31-3/8 69 Perimeteg =_56" H w L D Code D/z L/w (in.) (in.) (in.) 618 .70 1.00 14 i4 39-7/32 628 .70 1.25 12-15/32 15-17/32 39-7/32 638 .70 1.50 11-7/32 16-25/32 39-7/32 648 .70 1.75 10-3/16 17-13/16 39-7/32 658 .70 2.00 9-11/32 18-21/32 39-7/32 * - code legend CODE LEGEND 1xx - Perimeter 30" xx1 - p/z - 0.08 2xx - Perimeter 34" xxz - D/Z - 0.16 3xx - Perimeter 38" xx3 - D/z - 0.24 4XX - Perimeter 42” XX4 - D/Z I 0.32 SXX - Perimeter 48” XX5 - D/Z ' 0.40 6xx - Perimeter 56' XX6 - D/Z - 0.48 xx7 - D/Z . 0.56 xxa - D/Z - 0.70 x1x - L/w - 1.00 xzx - L/w - 1.25 x3x - L/w . 1.50 x4x - L/u - 1.75 xsx - L/w - 2.00 A P PEN DIX C Column Crush Test Results on C-flute corrugated fibreboard: values based on 5 specimens per sample in pounds per inch width. 33.4 35.6 36.6 37.6 38.2 34.2 35.8 36.8 37.6 38.8 34.8 36.0 36.8 37.6 38.8 35.0 36.2 37.0 37.6 39.0 35.2 36.2 37.0 38.0 39.2 35.4 36.2 37.2 38.0 39.4 35.4 36.4 37.2 38.0 41.5 35.6 36.4 37.4 38.0 Average - 37.0 lbs./in. width 7O APPENDIX D Code* 1.00 1.25 1.50 1.75 2.00 12x 686 727 730 677 600 13X 583 606 630 656 625 14x 675 642 .642 678 672 15X 672 636 638 625 636 16X 669 666 616 659 650 17X 664 666 620 647 602 18X 669 652 660 667 619 22X 719 780 739 744 691 23X 642 642 655 666 633 24X 683 702 700 698 667 25X 694 686 663 664 650 26X 670 670 713 647 659 27x 760 703 710 678 642 28X 650 664 682 649 657 32x 800 702 820 725 700 3 X 608 685 713 712 711 34x 714 750 741 713 749 35x 767 746 699 628 682 36X 736 716 647 656 674 37x 690 672 672 684 657 38X 661 699 705 646 686 * See code legend on Appendix B 71 72 L/w L w L w L w L w Code 1.00 1.25 1.50 1.75 2.00 41x 841 836 859 861 812 42X 758 825 805 758 755 43x 684 772 800 722 717 44x 778 802 739 736 755 45X 784 763 794 749 743 46X 769 750 758 691 647 47X 731 753 754 795 698 48X 745 731 764 761 712 51X 836 835 853 874 894 52x 878 837 802 800 750 53x 803 863 810 827 770 54x 800 886 824 803 797 55x 850 825 825 850 900 56X 817 822 813 786 809 57X 828 855 864 797 755 58X 761 819 794 765 781 61x 953 965 936 822 995 62x 851 888 873 839 893 63X 872 908 885 883 815 64X 865 939 917 844 833 65x 867 850 872 849 830 66X 850 859 942 850 827 67x 832 885 877 844 825 68X 795 836 800 826 830 APPEHDIX E Average Compressive Load on Four Samples in Lbs. Per Inch Perimeter L/w L/w ”’L/w L/w L/w Code 1.00 1.25 1.50 1.75 2.00 12x 22.87 24.23 24.33 22.57 20.00 13x 19.43 20.20 21.00 21.87 20.83 14x 22.50 21.40 21.60 22.60 22.40 15x 22.40 21.20 21.27 20.83 21.20 16x 22.30 22.20 20.53 21.97 21.67 17x 22.13 22.20 20.67 21.57 20.07 18x 22.30 21.73 22.00 22.23 20.63 22x 21.15 22.94 21.74 21.88 20.32 23x 18.88 18.88 19.26 19.59 18.62 24x 20.09 20.65 20.59 20.53 19.62 25x 20.41 20.18 19.50 19.53 19.12 26X 19.71 19.71 20.97 19.03 19.38 27x 22.35 20.68 20.88 19.94 18.88 28X 19.12 19.53 20.06 19.09 19.32 32XL- 21.05 18.47 21.58 19.08 18.42 33x 16.00 18.03 18.76 18.74 18.71 34x 18.79 19.74 19.50 18.76 19.71 35x 20.18 19.63 18.40 16.73 17.95 36X 19.37 18.84 17.03 17.26 17.74 37x 18.16 17.68 17.68 18.00 17.29 38x 17.39 18.40 18.55 17.00 18.05 73 m 74 Code 1¥6g 1?ég 1fég “1?7g 2?6g 41X 20.02 19.91 20.45 20.50 19.33 42X 18.05 19.64 19.17 18.05 17.98 43X 16.29 18.38 19.05 17.19 17.07 44X 18.52 19.10 17.60 17.52 17.98 45X 18.67 18.17 18.90 17.83 17.69 46X 18.31 17.86 18.05 16.45 15.41 47X 17.41 18.17 17.95 18.93 16.62 48X 17.74 17.40 18.19 18.12 16.95 51X 17.42 18.02 17.77 18.21 18.63 52X 18.29 17.44 16.71 16.67 15.63 53X 16.73 17.98 16.88 17.23 16.04 54X 16.67 18.46 17.17 16.73 16.60 55X 17.71 17.19 17.19 17.71 18.75 56X 17.02 17.13 16.94 16.38 16.85 57X 17.25 17.81 18.00 16.60- 15.73 58X 15.85 17.05 16.54 15.94 16.27 61X 17.02 17.23 16.71 14.68 17.77 62X 15.20 15.86 15.59 14.98 15.95 63X 15.57 16.21 15.80 15.77 14.55 64X. 15.45 16.77 16.38 15.07 14.88 65X 15.48 15.18 15.57 15.16 14.82 66X 15.18 15.34 16.82 15.18 14.77 67X 14.86 15.80 15.66 15.07 14.73 68X 14.20 14.93 14.29 14.75 14.82 APPENDIX F Computed Values Using the Maltenfort Equation:= P : 5.8L + 128 - 2.1D + 350 + 6.5 (CLT-Ol.* L/W L/W L/W M11 M11 Code** 1.00 1.25 1.50 1.75 2.00 12X 473 478 483 486 489 13X 468 473 478 481 484 14X 463 468 473 476 479 15X 458 463 467 471 474 16X 453 458 463 466 469 17X 448 453 457 461 464 18X 439 444 449 452 455 Ave. 458 463 467 470 473 Overall Average = 466 22X 490 495 500 504 507 23X. 484 490 495 499 501 24X 479 484 489 493 496 25X 473 479 483 487 490 26X 467 423 478 481 485 27X 461 467 472 476 479 28X 451 457 462 466 469 Ave. 472 478 483 486 490 Overall Average = 482 32X 506 513 518 522 526 33X 500 507 512 516 520 34X 494 500 505 510 513 35X 487 494 499 503 517 36X 481 487 493 497 500 37X 474 481 486 491 494 38X 463 470 475 479 483 Ave. 486 493 498 503 506 Overall Average 2 497 * All the given figures exclude the 6.5 (CLT-O) value. ** See Appendix B for code legend. 75 76 W L/W L/w L/w L/w L/w Code 1.00 1.25 1.50 1.75 2.00 41X 530 537 543 547 552 42X 523 530 536 540 544 43X 514 521 527 532 535 44X 509 516 522 527 530 45X 505 509 515 519 523 46X 495 502 508 512 516 47X 488 495 500 505 509 48X 475 .482 488 493 497 Ave. 504 511 517 522 526 Overall Average = 516 51X 556 554 571 575 580 52X 547 556 552 568 572 53X 539 548 554 560 564 54X 531 540 545 551 555 SSX 523 532 538 544 543 55X 515 524 530 535 540 57X 507 515 522 527 532 58X 493 501 508 513 518 Ave. 527 535 541 547 551 Overall Average = 540 61X 590 599 607 613 619 62X 580 590 598 604 609 63X 571 580 588 595 600 644 552 571 579 585 590 65X 552 561 569 576 581 66x 543 552 560 566 572 07X 533 543 550 557 562 68x 517 526 534 541 546 Ave. 555 555 573 580 585 Overall Average = 572 llHllllflllllIll!”“1”leIIHHIHIWWWII"!!!llHl 009898390