IllllllllllllllllIllllllllllllllllllllllllllllllll|l|ll||lll|l 301834 5961 LIBRARY Michigan State University This is to certify that the thesis entitled PREDICTION OF BENDING STRENGTH OF LONG CORRUGATED BOXES presented by ORANIS PANYARJUN has been accepted towards fulfillment of the requirements for MASTER degree in PACKAGING Date AUGUST 20. 1998 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 1M WWpGS-nfl PREDICTION OF BENDING STRENGTH OF LONG CORRUGTAED BOXES BY ORANIS PANYARJUN .A THESIS Submitted to Michigan State University In partial fulfillment of the requirements For the degree of MASTER OF SCIENCE School of Packaging 1998 ABSTRACT PREDICTION OF BENDING STRENGTH OF LONG CORRUGATED BOXES BY Oranis Panyarjun This study investigated the strength of long corrugated boxes in bending and determined the cause of box failure to predict any other boxes in the same situation. Five panel folder style boxes with different cross sectional shapes, flute directions, lengths, and orientations in the compression test were tested. by a Pallet Load Compression Tester with a fixed platen. In addition, the box compression strength predicted by the Mckee formula was compared to the actual box compression strength. Comparing the actual experimental result and the formula result, both results are close together even though the box dimensions, flute directions, cross section shapes, and lengths are very different. This study can conclude that the failure of corrugated boxes is a local failure not a system failure like other engineering beams made from concrete or metal. The bending strength depends on the Edge Crush Test and. the jposition and length over which the compressive force is applied. TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES 1.0 INTRODUCTION 1 . 1 Market 1.2 Styles, Shapes, and Sizes 1.3 The scope of the research 1.4 Thesis Objectives 2.0 LITERATURE REVIEW 2.1 Box Compression Strength Box perimeter Bending Stiffness and Thickness Board propertieszECT 2.2 .McKee Formula and Engineering Beam Theory 3.0 MATERIALS AND METHODS 3.1 Test materials 3.2 Compression Test Machine 3.3 Conditioning 3.4 Test Methods 4.0 RESULTS AND DISCUSSION 4.1 Box compression strength of each group (Triangular, Square, and Rectangular) 4.2 The Effects of dimension, flute direction, and cross sectional shape 4.3 Correlation between experiment and Calculation 4.4 Formula Result for triangle cross sectional Shape 4.5 Analysis of failure 4.6 Error analysis 5.0 CONCLUSIONS AND FUTURE STUDY BIBLIOGRAPHY m 43 43 49 49 49 52 52 60 64 65 68 74 76 78 LIST OF TABLES Table 1 Four standard flute sizes 2 Square Cross Section Results 3 Rectangular Cross Section Results 4 Triangular Cross Section Results 5 Right Isosceles Triangular Cross Section results 6 Comparison between compressive force from formula and actual compressive force from the experiment Page 33 52 53 55 56 61 LIST OF FIGURES Figure Page 1 Regular Slotted Container 2 2 Full-Telescope Design-Style Box 4 3 One-piece folder 5 4 Five-panel folder 6 5 Double-Slide Box 8 6 Bliss Box 9 7 Self-erecting Box 11 8 The proportions of a box 12 9 Box dimensions 14 10 Bending of long boxes 17 11 ‘Various packages in a vehicle 18 12 Total product cost 21 13 Defommation and Bulging 24 14 Distributed and Concentrated Forces 27 15 Flute direction effect on stiffness 29 16 Single, Double, and Triple wall board 31 17 Test set up for measuring edge crush resistance 35 18 Stressvariation: compression on top and tension on bottom 37 19 Measuring ECT perpendicular and along the flutes. 38 Figure 20 Factors related to Beam Formula 21 Category no.1 22 Category no.2 23 Category no.3 24 Category no.4 25 Compression Test Machine 26 Force vs deflection for a box with triangular cross section 27 Force vs deflection for a box with square cross section 28 Force vs deflection for a box with rectangular cross section 29 Loading of boxes with Triangular cross sectional shapes 30 Example for Graph of Group A.and B 31 Example for Graph of Group C, E and G 32 Example for Graph of Group D, F and H 33 Orientation of wood block and local failure 34 Bulging and Tipping causing experiment error vi Page 41 45 46 47 48 50 57 58 59 66 69 70 71 73 75 1 . 0 INTRODUCTION 1.1 MARKET For more than 90% of industrial and consumer goods shipments, corrugated containers have been used (Fiedler, 1995). There is high tendency to increase the use of corrugated boxes. It is evident from the Freedonia Group Inc. study concerning a detailed analysis of corrugated and paperboard box sectors in the USA (Anon,1997) that by the year 2000, the total US shipments of corrugated and paperboard boxes will be 37m tons with an annual growth rate of 3.5% due to technological developments being driven into nontraditional markets and more paper boxes used for increased production of durable and nondurable goods (Anon, 1997) . 1.2 STYLES, SHAPES, AND SIZES 0F CORRUGATED BOXES 1. Slotted styles To make slotted box style, one piece of corrugated fiberboard is scored and slotted to fold into a box. At a joint, one side panel and one and panel are brought together by glue, tape, or stitching. The most common style of corrugated box for most products is the RSC (Regular Slotted Container) (Figure 1) where all flaps are the same Figure 1. Regular Slotted Container depth. This style is the most economic design having the least production waste (Fibre box handbook, 1991). 2. Telescope boxes This style is composed of two or more parts. One piece can be the separate top or cover and the other piece can be the body. The cover slides onto the body. For example, one type of this style which causes the least manufacturing waste is the FTD (Full-Telescope Design-Style Box) (Figure 2). Due to the same depth of the cover and the body, the extra thickness of board on all sides and and panels will provide higher compression strengths for stacking performance of fragile products. 3. Folder This style of corrugated boxes is made of one or more pieces of fiberboard folds around a product. For example, a 1PF (one-piece folder) (Figure 3) uses one jpiece of a corrugated board which is scored to form the sides and ends, and extensions of the side flaps to be the top. Another example, a five-panel folder (FPF) (Figure 4) is composed of five panels which are slotted and scored. The fifth panel is the closing flap covering a side panel. Both ends of the box with several thickness protect long articles of small diameter from.environmenta1 damage or the \ Figure 2. Full-Telescope Design-Style Box box from penetration by these long articles (Fibre box handbook, 1991). 4. Slide-type boxes A tube or shell is folded from two or more rectangular, scored pieces of board. To serve a packaging function, each piece slides into or onto each other. It is very easy to close or open the box. For instant, DS (Double-slide Box) (Figure 5) is two shells from two pieces of board sliding onto each other. The two thicknesses of four sidewalls provide stacking strength (Fibre box handbook, 1991). 5. Rigid boxes A rigid box style consists of three pieces of fiberboard. Two identical end panels have flaps to attach to a body which is made from one piece of the fiberboard folding to form the two side panels. An example of this corrugated box style is No.2 Bliss Box (Figure 6) which is made from one scored piece forming to be the body and two and pieces with four flaps providing good stacking strength. Seams are formed on the body panels (Fibre box handbook, 1991). Ill“" “--I Figure 5. Double-Slide Box Figure 6. Bliss Box 6. Self-erectingiboxes The style is used for boxes which don’t contain heavy products. It is unnecessary to use automatic set-up equipment. For self-erecting boxes (Figure 7), two pairs of adjacent bottom flaps slide together and act like a bottom joint while four panels of top flaps are the same as a regular slotted container (Fibre box handbook, 1991). Shapes of corrugated boxes The shape of a corrugated box is important since it determines the amount of board used to make it and affects the overall stability. The shape of the box is defined by the ratio by the length of the longest side divided by the shortest side and by the ratio of the intermediate side to the shortest side. The ratios, L/W and D/W, where L = Box Length, W = Box Width and D = Box Depth would specify the proportions of the box as in Figure 8 (P.G. Wright, 1988) . 10 End Proportions D/W A 1 FjTall square based box 2 ‘ Narrow squared sided box K 3 f<>l Tawgz‘::uare ended box K/ Cubic 4” 1 2 3 L/W Figure 8. The proportions of a box 12 Sizes of corrugated boxes In the fiberboard box industry, the manufacturer states inside box dimensions in the order of length, width and depth inside. Length, width, and depth are based on which a panel side is the opening. Even though two boxes have the same size, it doesn’t mean that they have the same dimensions as well (Figure 9). According to the opening, the longer dimension is the length and the smaller side is the width. The depth is determined by the distance perpendicular to the innermost surface of opening (Muldoon, 1984) . 13 Figure 9. Box dimensions 14 1 .3 THE SCOPE OF THE RESEARCH These corrugated shipping containers have to fully protect the product inside until they reach the consumers. Proper shipping containers have the capability to withstand the distribution environment: manual handling, utilized handling, truck transportation, and railcar transportation. Another factor is storage conditions. A wide range of humidities and temperatures is found during shipping these packages from the East to western mountain states (Forehand, 1995) . A loss of about 50% of a corrugated container’s stack strength can come from a change in relative humidity. Water, contamination, and infestation can also affect goods inside (UPS, 1971). Forces causing distribution damage against these packages can be classified into four types - Shock, Vibration, Compression, and Climate hazards (Forehand, 1995) . Long corrugated boxes whose the style is FPF are used for long and narrow products such as curtain rails, window frames, chair parts, desk, and shelf components, fishing gears, golf clubs. With a ratio of base proportions and end proportions of 3:1, the long square ended shapes will cause difficulty in handling, both manually and by mechanical equipment, being prone to straddle and jam on corners and rolling about its long axis (P.G.Wright, 1988). When long 15 FPF corrugated boxes are sent into trains or trucks, they are very hard to pass through their standard doors without damage. Convolute wound tubes perform the same function but are not considered. for this research even though their strength is higher than corrugated boxes. This is because the adhesive between paper layers makes recycling difficult and the higher cost of distribution and storage due to circular cross section shape makes them too expensive. Many shipping companies encounter problems with using long corrugated boxes due to the length of the box. For the United Parcel Service System, two levels of handling are hand sorting from conventional conveyor belts and high - speed mechanical and electronic sorting equipment used. The problem which often occurs during sorting by conveyors is that the long corrugated box ends up supporting other boxes like a bridge: the ends are supported either by chutes, conveyers, or other boxes, and the middle is loaded by other packages as shown in Figure 10. Another problem is that various packages -heavy and light with many styles and shapes of containers and types of products - are loaded together in a single vehicle (Figure 11) (UPS, 1971), which also loads long boxes as in FigurelO. l6 Figure 10. Bending of long boxes Figure 11. Various packages in a vehicle 18 1.4 THESIS OBJECTIVES The problem. with bending of long corrugated. boxes during transporting concerns the United Parcel Service and Federal Express, which need to know how strong these boxes are likely to be before they have to transport these packages to their customers. This jpoint relates to the economics of the total business. UPS and Federal Express lose money due to the overpackaging costs to make sure that the packages ordered are able to protect the products inside and due to physical damage costs as a result of underpackaging. From. ‘UPS damage claims information, consumers believe that the cause of damage comes from handling rather than inadequate packaging (UPS, 1971). Figure 12 shows the total cost of delivering the product including packaging costs and damage costs. The higher the packaging cost, the lower the damage cost. The minimum point of the total cost is the cost optimization of the system (Forehand, 1995). The objectives of the thesis research are as follows: 1” To find the strength of long corrugated boxes in bending. l9 2. To study the process of the compression testing, data collecting and analyzing as well as predicting bending strength of long corrugated boxes. 20 Total cost Cost optimization Damage Costs Package Costs Low Rate of Damage High Figure 12. Total product cost 21 2.0 LITERATURE REVIEW 2.1 BOX COMPRESSION STRENGTH Box compression strength is the resistance of a corrugated box to a uniformly applied compressive force. In the case of stacking for storage and distribution, top-to- bottom compression strength is the most significant issue while end-to-end and side-to-side compression also may be of interest in particular applications (Fibre box handbook, 1991) . More compression resistance results in greater stacking heights in stores and during transportation and is a good measure of overall robustness and rough handling resistance of the box (P.G. Wright, 1988). In the future, the tendency to improve the performance of corrugated boxes to achieve higher stacking to get the maximum amount of product in a given space, longer holding in the warehouse, and being subjected to unforgiving automated handling is on the development of raw materials, design, and manufacturing control without increasing its basis weight (Cox, 1988). When the corrugated box is placed under a top-to- bottom compression load, only its four vertical side panels excluding its flaps would support this force. After the load exceeds the limit of strength of the four corners where the four panels are joined together, failure begins 22 at a horizontal crease running across the panels in an arch shape from one vertical corner to the other and then the panels began to deform and.bulge sideways in Figure 13 (Cox, 1988 and P.G.‘Wright, 1988). Since the shipping' container' encounters ‘various environmental and handling hazards related to compression during transporting by trucks or trains, Rule 41 of the Uniform. Freight Classification (UFC) and Items 222 of National Motor Freight Classification (Fibre box handbook, 1991) have been used as the standard classifications for fiber boxes. They are in the form of articles that have similar transportation characteristics (value, density, fragility, and. potential for damaging other freight or carrier’s equipment) grouped together into classes (Fiber box Handbook Supplement, 1991 and Maltenfort, 1988) . Both carrier rules for corrugated construction can help carriers determine specific boards given the product weight, and the box size (Saroka, 1995). Rule 41 and Items 222 no longer serve as the only regulation indicating a box’ s ability to meet today’ 3 performance needs. Performance criteria instead of shipping regulation influences the box specification (Cox, 1988). Instead of using the burst test or Mullen test in order to indicate a board’s resistance to rupture and relate to the board’s tensile properties, it is 23 Figure 13. Deformation and Bulging 24 more suitable to choose Edge Crush Test (ECT) for grading corrugated board since calculated ECT is associated with the prediction of compression strength of a container against failure from stacking (Saroka, 1995). To test the shipping container using the compression tester, the box is placed between two large platens, one of which can exert pressure. An even force is exerted against the package until failure is reached. Most equipment is calibrated to provide a reading in pounds of pressure exerted. This is likely to simulate the stresses and strains encountered in storage, warehousing, palletizing, and feeder loading (U.P.S, 1971) . The test procedures of compression tests are described in: 1. ASTM D 642, Compression Test for Shipping Containers (ASTM standard, 1994). 2. ASTM D 4577, Compression Testing of Shipping Containers Under Constant Load (ASTM standard, 1994). The various significant factors that affect box compression strength are the properties of corrugated board-edgewise compression resistance, .bending stiffness, as well as its thickness, the types of corrugated boards- flutes, corrugated. medium. and liner, and also the box perimeter which will be discussed below (Bean, 1996) . 25 Box Perimeter Compression strength relates to the dimensions of the boxes . Compared to RSC corrugated containers, the type of load against long FPF corrugated containers is different. Forces which act over a large area of RSC boxes are distributed. It may be either uniform or not while for long FPF boxes, forces act at a single point on the containers (Figure 14) (Slaby and Tyson, 1969) . The more the base circumference of the box, the more the compression strength. If the ratio of base length to width is 1, the compression strength is a maximum for a given perimeter and if the depth of the boxes increases, the compression strength will decrease until 30% of the perimeter is reached (Domowicz, Subicki, and Rzezniczak, 1978). 26 Figure 14. Distributed and Concentrated Forces 27 Board Properties : Bending Stiffness and Thickness From a study of the compression strength of corrugated fiberboard boxes at the Finnish Pulp and Paper Research Institute (Toroi and Kainulainen, 1986) , with a lack of reliable measuring instruments, nobody usually knows the bending stiffness of corrugated board in practice. However, the theory of multilayered structures is able to predict the basic factors affecting the bending stiffness. The theory has concluded that the major factor related to the bending stiffness of corrugated board is the thickness, which is based on the flute profile, and how well the initial flute height has performed after conversion. Flexural stiffness of corrugated board is another factor which is important to a box’s top-to-bottom compressive strength. The stiffness of the individual linerboard and medium components influences flexural stiffness of corrugated board. If the caliper of the board component increases, a box’s flexural stiffness can be improved (Cox, 1988) . It can also depend on the direction of the flutes. In a direction along the flutes, the stiffness of corrugated board is greater than that in a cross direction (against flutes) (Figure 15). 28 Figure 15. Flute direction effect on stiffness 29 Figure 16 shows how corrugated board is composed of a corrugated mediwm sandwiched between two liners or facings for singlewall. For doublewall board, it is composed of two fluted medium plies and three linerboard plies while triplewall board combines three fluted medium plies and five linerboard plies (Saroka, 1995) . The purpose of the medium is to separate the facings, stop them from sliding relative to another and prohibit them from localized bucking. The medium acts like a low density core which makes corrugated boards strong and lightweight. The higher the quality of board, the higher the quality of paper used and process in corrugating production (P.G. wright, 1991). Singlewall is used for shipping containers primarily, partitions, cushions, pads, and display stands while with its high stacking strength, doublewall board is used for heavy or bulky products such as machinery, appliances, or furniture. Large and very heavy products are mostly contained in corrugated boxes with board materials with triplewall types. Moreover, instead of using wood, triplewall board is used to construct large bulk bins and boxes. 30 A/M /\/\/W /\/\/\/\/< / \ /\/\/\/\/\ /\/\/\/\/§’ Figure 16. Single, Double, and Triple wall board 31 Corrugated boards are classified into four standard flute sizes - A, B, C, E - flute (Table 1). The size of the teeth in the meshed corrugating roll designates the flute sizes (Muldoon, 1984). The largest flute is A" followed by C, B, and E-flute. The larger the flutes, the greater the stacking strength as well as compression strength but the smaller the puncture resistance (Saroka, 1995). As a result of properties of the component boards and the structural parameters of the combined board affecting the box compression resistance of a given box, the study of compression strength of corrugated fiberboard boxes at the Finnish Pulp and Paper Research Institute continues to estimate the box compression strength by the basis weight of linerboards and fluting in order to evaluate the optimum design of alternative corrugated boards. 32 Table 1. Four standard flute sizes Type Flutes per linear Approximate height foot .A-flute 35 i 3 3/16-inch B-flute 50 i 3 3/32-inch C-flute 42 i 3 9/64-inch E-flute 94 i 4 3/64-inch 33 Board properties : Edge Crush Test The edge crush resistance of the corrugated board is the strength property most widely used to predict whole box compression strength. Figure 17 shows the test set up for measuring edge crush resistance. There are two reasons for using ECT to predict box strength. The first is that the edge crush strength measures the necessary force to collapse a short vertical sample of corrugated board and therefore simulates box compression. The second is that it appears in the McKee formula (section 2.2) . Testing for ECT must be done carefully since the result is very much influenced by the cutting accuracy of the specimen cutter, the type of instrument used and so on. Until recently, test pieces have been sawn from the corrugated board, or cut by hand with a simple knife. Rough or uneven edges have then given slightly lower ECT-values coupled with big variations in the results. Waxing of the edges gives higher results, but it also makes this testing method more complicated. Current practice requires the use of a special two bladed precision cutter (The Billerud cutter) which provides a rapid and reproducible test result (P.G.Wright, 1988) . 34 Figure 17. Test set up for measuring edge crush resistance a) along flutes b) against flutes 35 The ECT has been used as an index for estimation of the stackability of boxes stored on pallets in warehouse. The higher the edgewise compression resistance, the better the stacking properties of the boxes (Thielert, 1986). The ECT is related to both the stacking strength and the overall transportation performance of a corrugated board box (Markstrom, 1988). From engineering principles applied to beams, a long corrugated box acts like a beam which develops stresses from bending. There are some differences between normal compression of general boxes and bending. Long boxes encounter compression on top, and tension on bottom (Figure 18) . In short beams, shearing stresses play an important role while bending stresses are the significant factor in long beams. Between the two supports, a load at the center produces bending at all points in the beam and the beam curves downward between two supports. There are two directions of stresses in long beams. First, the vertical stress results from the load of product weight. Second, the horizontal stress comes from resistance to curving of long fiber boxes. Thus, both directions of a corrugated board - perpendicular and along with flutes are measured for ECT (Figure 19) (Slaby, and Tyson, 1969). 36 Figfure 18. Stress variation: compression on top and tension on bottom 37 Figure 19. Measuring ECT perpendicular and along the flutes. 38 2 . 2 MCKEE FORMULA AND ENGINEERING BEAM THEORY At the Institute of Paper Chemistry, Appleton, Wisconsin, R.C. .MeKee, J:W. Gander, and J.R. Wachuta (Guins , 1 97 5) developed the top- to -bottom compres sion strength formula for corrugated boxes. Box compression strength can be predicted using McKee’ 3 equation as follows; cs = 5.87 * ECT *(z * it)“2 Where CS = top-to-bottom compression strength, in lbs. ECT = Edge crush test, in lbs/in Z = Box perimeter (2L+2W), in inches Board thickness, in inches This equation is practical for normal slotted style boxes where failure is jprimarily’ due to crushing. It. is not feasible to use this equation for long corrugated boxes since the longer length of these boxes causes the method of loading to be one of bending. So length is another factor related to predicting the strength of long corrugated boxes, in addition to the completely different state of stress created by bending. 39 Beam‘Formula In Figure 20, a long corrugated box should fail when the stress created by bending reaches a critical level related to the ECT: Stress = (force/width)/thickness = ECT/T- - - -(1) T = board thickness The bending moment for a long corrugated box loaded by force F at its center is IMoment = (F/2) x (L/2) - - - -(2) From the flexure formula (Slaby and Tyson, 1969); s = M c - - - -(3) I S = Stress M = Moment c = half of cross sectional height I = Moment of Inertia of cross section The moment of Inertia for a solid rectangle cross section is; I = w.H3/12 ----(4) Since the corrugated box is not a solid beam, the moment of inertia is I = w.n3/12- (W-2T)(H-2T)3/ 12 I H2T(H+3W)/6 ----(5) 4O T H-2T F/2 ' 4 I I H 172 I w-2'r l I I Vi 4> Figure 20. Factors related to beam formula 41 Substituting into equation (3) gives; ECT = (FL/4) (II/2) - - - ‘(61 '1' H7 T (mam/6 Solving for F gives the force required to make it fail F = 4. ECT .H(H+3W) - - - -(7) 3L When comparing the calculated force and the actual force from the experiment in Table 6 of Chapter 4, it can be concluded that this formula is useless in predicting the maximum compression load. Due to the variation in corrugated board performance and atmospheric conditions, corrugated board can not been considered an engineering material with unifomm properties. Thus, the previous engineering theories can not be used in the process of determining the maximum compression strength. Moreover, the structure of the long corrugated board is not solid like other engineering material such as concrete so the moment of inertia calculated is improper to substitute in this formula (Guins,1975). Buckling also plays an important role. 42 3.0 MATERIALS AND METHODS 3.1 TEST MATERIALS The fiberboard material used in this study was single- wall C-flute with an approximate height of of 0.361 cm, 130 i 10 of flutes per meter, and a take-up factor of 1.43. Five panel folder style boxes were used. for this experiment. Long corrugated boxes were divided into four categories according to the shape of the cross section. Thus, four different types of corrugated containers were constructed as follows; 21.2322gory no. 1 : 14 boxes with square cross section(Group A., B will be described in statistical analysis in the next chapter). (Figure 21) 3 lengths of long corrugated boxes; 31.25", 21”, 12". 2 flute directions; perpendicular and parallel to the length. 2 orientations in the compression test; vertical and horizontal direction. 1 size of cross section; (6.10” x 6.10”). 2.§E£ggory no. 2 : 12 boxes with rectangular cross section (Group C, D, E, F, G, H will be described in statistical analysis in the next chapter). (Figure 22) 3 lengths; 31.25", 21", 12” 43 2 flute directions; perpendicular and parallel to the length. 2 orientations in the compression test; vertical and horizontal direction. 3 sizes of cross section; (12.2"x6.10”),(12.2"x9.06"),(15.0"x6.10”). . Category no.3 :8 boxes with regular triangular cross section( A, B, E, F, H, I, L, M )(Figure 23) 3 lengths of long corrugated boxes; 31", 26”, 24". 2 flute directions; perpendicular and parallel to the length. 1 orientation in the compression test. 2 sizes of cross section;(6"x6”x6”), (9”x9"x9"). . Category no.4 :6 boxes with right isosceles triangle cross section ( Group C,D,G,J,K,N) (Figure 24). 2 lengths of long corrugated boxes; 26", 21”. 2 flute directions; perpendicular and.parallel to the length. 1 orientation in the compression test. 2 sizes of cross section; (6”x6”x8.485"),(9”x9"x12.728"). 44 Cross Sectional Shape x \\ :\ a s. \ Figure 21. Category no. 1 Cross Sectional Shape Ex 3/2x [:lx 2x 3X 2x Figure 22. Category no. 2 46 3.2 COMPRESSION TEST MACHINE All boxes were tested. using a Lansmont 122-30 K Pallet Load Compression tester with a fixed platen as shown in figure 25. The test was conducted in accordance with ASTM D-642 at a load speed of 0.5 inch/min. Compressive force (lbs.) versus deflection (inch) was recorded in a graph format . 3.3 CONDITIONING Conforming to ASTM D-642, the boxes were conditioned at standard condition of 73 °F and 50% Relative Humidity for at least 24 hours before testing. 3.4 TEST METHODS ASTM D642 - 90 is the standard test method for determining the Compression Resistance of Shipping Containers, components and unit loads. For this experiment, the application of a fixed platen compression tester is recommended by this standard. A 10 lb. “preload” was arbitrarily applied in order to set the reference point for zero deflection, to ensure definite contact between the sample and platen before the test procedure started. Shipping containers for this experiment were tested empty. 49 Wood Block 1e Figure 25. Compression Test Machine 50 The procedure measures the ability of the container to resist external compressive loads applied to its faces. The test recommends compressing the box to failure and recording of the maximum. applied load (lbs.) and the deflection (inch) compared to the pre-loaded configuration. This research is concerned with only the compression strength (lbs.) as an indicator of box failure. 51 4.0 RESULTS AND DISCUSSION 4.1 BOX COMPRESSION STRENGTH OF EACH GROUP Force VS deflection curves were generated using the Compression Test Machine in Figure 25. Sample curves for the three groups: triangular, square, and rectangular cross section shapes are shown in Figures 26, 27 through 28, respectivelyu The results are shown in Table 2 through Table 5. Table 2. Square Cross Section Results (category no.1) Sample Dimension Support Flute ECT Compression No. LxWxH Space, 8 Direction (lbs per strength (inch) (inch) inch) (lbseinches) A1 38.5x6.10x6.10 31.25 L 38.04 83.1 @0.59 A2 38.5x6.10x6.10 31.25 L 36.44 95.0 @0.46 A3 28.0x6.10x6.10 21 V L 29.07 79.7 @0.80 A4 28.0x6.10x6.10 21 L 30.15 78 @0.52 A5 19.00x6.10x6.10 12 L 30.99 79.0 @0.3 A6 19.00x6.10x6.10 12 L 30.55 100 80.75 Bl 38.5x6.10x6.10 31.25 W 11.11 69.1 80.36 BZ 38.5x6.10x6.10 31.25 W 11.01 81.3 @0.31 33* ‘ 28.0x6.10x6.10 21 w 10.71 77.4 @0.74 B4 28.0x6.10x6.10 21 W 10.44 117.7 («30.39 BS 19.00x6.10x6.10 12 W 9.35 92 @0.6 B6 19.00x6.10x6.10 12 W 9.81 170 @0.5 52 Table 3.Rectangular Cross Section Results (Category No. 2) Sample Dimension Support Flute ECT Compression No . LxWxH Space , Direction (lbs per Strength (inch) 8 inch) (lbs@ inches) (inch) c1 38.25x12.20x6.10 31.25 L 31.59 88.8 80.72 02 38.25x6.10x12.20 31.25 L 31.84 84.6 80.46 c3 28.00x12.20x6.10 21 L 29.35 72.6 80.48 c4 28.00x6.10x12.20 21 L 30.37 100.3 @0.83 c5 19.00x12.20x6.10 12 L 31.39 91.3 80.85 C6 19.00x6.10x12.20 12 L 28.82 70.1 @0.83 D1 38.25x12.20x6.10 31.25 ‘w 10.99 88.8 80.34 02 38.25x6.10x12.20 31.25 W' 8.94 116.3 80.46 03 28.00x12.20x6.10 21 'w 10.24 106.9 @0.44 D4 28.00x6.10x12.20 21 'w 10.26 115.2 80.45 05 19.00x12.20x6.10 12 W' 10.99 116.6 80.47 D6 19.00x6.10x12.20 12 ‘w 9.46 90 80.55 31 38.25x12.20x9.06 31.25 L 29.6 74 80.40 32 38.25x9.06x12.20 31.25 L 29.76 109 81.47 E3 28.00x12.20x9.06 21 L 29.66 87.3 81.03 * n4 28.00x9.06x12.20 21 L 30.46 105.9 80.79 E5 19.00x12.20x6.10 12 L 32.16 71.7 80.32 E6 19.00x9.06x12.20 12 L 29.44 96.5 81.18 53 Sample Dimension Support Flute ECT Compression No. waxH Space, Direction. (lbs per Strength (inch) 8 inch) (lbseinches) (inch) F1 38.25x12.20x9.06 31.25 L 29.6 102.4 @0.46 F2 38.25x9.06x12.20 31.25 L 29.76 118.9 80.69 F3 28.00x12.20x9.06 21 L 29.66 104.4 90.46 F4 28.00x9.06x12.20 21 L 30.46 114 @0.45 F5 19.00x12.20x6.10 12 L 32.16 104.380.54 F6 19.00x9.06x12.20 12 L 29.44 123.280.70 Gl 38.25x15.00x6.10 31.25 'W 9.86 53.7@0.77 G2 38.25x6.10x15.00 31.25 ‘W 10.25 105.401.18 G3 28.00x15.00x6.10 21 'W 9.04 98.2@l.24 G4 28.00x6.10x15.00 21 ‘W 9.25 83.8@0.98 G5 19.00x15.00x6.10 12 'W 9.77 75.3@1.18 G6 l9.00x6.10x15.00 12 W’ 30.87 89.761.20 H1 38.25x15.00x6.10 31.25 L 9.77 101.3@0.52 HZ 38.25x6.10x15.00 31.25 L 9.49 111.390.43 H3 28.00x15.00x6.10 21 L 9.66 111.9@0.45 H4 28.00x6.10x15.00 21 L 8.75 116.7@0.45 H5 l9.00x15.00x6.10 12 L 11.16 132.9@0.67 H6 19.00x6.10x15.00 12 L 10.45 ll7.4@0.41 54 Table 4. - Triangular Cross Section Results (category no.3) Sample Width 1 Width 2 Width 3 Span Edge Crush Compression (inch) (inch) (inch) (inch) Test Strength (lbs per (lbseinches) inch) A 6 6 A 6 31 30.35 35.1 80.72 H B 9 9 9 26 ' 5 30.35 162.8 80.1.12 .. E 6 6 6 24 30.35 ' 31.2 @0.52 F 9 9 9 24 30.35 82.3 91.28 H 9 9 9 31 10.10 39.1 @0.26 I 6 6 6 31 10.10 78.5 @0.52 L 9 9 9 ’ 24 10.10 48.4 80.47 M 7 6 6 9' H i 24 1 10.10 30.180.73 ‘Width 1 = Width 2 =‘Width 3 55 Table 5. Right Isosceles Triangular Cross Section Results (category no.4) Sample Width 1 Width Width 3 Span Edge Crush Compression (inch) 2 (inch) (inch) Test Strength (inch) (lbs per (lbseinches) inch) C 6 6 8.485 26 30.35 33.9 @0.40 D 9 9 12.728 26 30.35 51.7 80.72 G 6 6 8.485 21 30.35 21.7 90.23 J 9 9 8.485 26 10.10 34.6 80.27 K 6 6 12.728 26 10.10 81.5 90.61 N 9 9 8.485 21 10.10 70.5 80.58 ‘Width 1 = Width 2 ‘Width 3 = (Width 1 or Width 2) x V 2 56 Force (Lbs) 80 70 60 50 40 30 20 10 0 1.4 b' I Deflection (inches) Figure 26. Force vs deflection for a box with triangular cross section 57 Force (Lbs) A 80 70 60 50 40 30 20 10 0 1.4 i rfir Deflection (inches) Figure 27. Force vs deflection for a box with square cross section 58 Force (Lbs) A 80 70 60 50 40 30 20 10 0 1.4 : » Deflection (inches) Figure 28. Force vs deflection for a box with rectangular cross section 59 4.2 THE EFFECTS OF DIMENSION, FLUTE DIRECTION, AND CROSS SECTIONAL SHAPE The compression strength results in Table 2 through 5 were fitted to an equation of the form; r=x* s'Wrw‘WrHes'rzzc'rdl ----(8) Where F is compression strength, K is a constant, S is the span (inches) between supports, 'W is the width (inches), H is the height (inches), and ECT is the edge crush test (lbs./in) in the direction of the length. Increasing the width, edge crush test, and height of boxes is expected. to increase compression. strength. .A. shorter span should also increase compression strength and so b, c and d.are expected to be positive, and a is negative. The results of the fit were as follows; a = 0.05, b = -0.05, c = 0.16, and d = 0.33. R-Square of the formula for these boxes was about 37 - 44 %. For horizontal flutes, CS = 18 S 0.05 W -0.05 H 0.16 ECT 0.33 _ _ _ _( 9 ) or cs 5 18 (a x ECT 2) 1" For vertical flutes, CS 5 20% higher than with horizontal flutes In groups of package samples with square and rectangular cross sectional shapes, almost all boxes with vertical flutes running against the length were able to 60 resist higher compression loads than those with horizontal flutes along the length of the box. The flutes in the vertical direction acted like columns, which take compressive load, better, and the flutes running in the horizontal direction were easy to fold or collapse. Thus, the vertical columns are stronger than the horizontal flutes. Table 6 shows the comparison between the actual compression strength results in Table 2 and. 3 and the strength predicted by equation ( 8 ). Table 6. Comparison between compressive force from formula and actual compressive force from experiment. Sanmle Dimension Support Flute ECT Compressive Actual No. LxWxH Space, Direction (lbs Force from Compression (inch) 8 per Formula Force (inch) inch) (lbse inches) Al 38.5x6.10x 31.25 L 38.04 56.56 83.1 @0.59 6.10 A2 38.5x6.10x 31.25 L 36.44 55.77 95.0 @0.46 6.10 A3 28.0x6.10x 21 L 29.07 75.89 79.7 80.80 6.10 A4 28.0x6.10x 21 L 30.15 75.89 78.0 @0.52 6.10 A5 19.00x6.10 12 L 30.99 75.89 79.0 (90.3 x6.10 A6 19.00x6.10 12 L 30.55 75.89 100 @0.75 x6.10 Bl 38.5x6.10x 31.25 w 11.11 91.06 69.1 80.36 6.10 32 38.5x6.10x 31.25 W 11.01 91.06 81.3 @0.31 6.10 BB 28.0x6.10x 21 W 10.71 91.06 77.4 80.74 6.10 61 Sample Dimension Support Flute ECT’ Compressive Actual No. waxn Space, 3 Direction (lbs Force from Compression (inch) (inch) per Formula Force inch) (lbsflinches) B4 28.0x6.10x 21 ‘W 10.44 91.06 117.7 6.10 80.39 BS 19.00x6.lx 12 ‘W 9.35 91.06 92.0 6.10 @0.6 B6 l9.00x6.1x 12 W’ 9.81 91.06 170 6.10 80.5 C1 38.25x 31.25 L 31.59 75.89 88.8 12.20x6.l 80.72 C2 38.25x6.Lx 31.25 L 31.84 85.189 84.6 12.20 @0.46 C3 28.00x 21 L 29.35 75.89 72.6 12.20x6.1 @0.84 C4 28.00x6.1x 21 L 30.37 85.19 100.3 12.20 00.83 C5 19.00x 12 L 31.39 75.89 91.3 12.20x6.1 7 80.85 C6 l9.0x6.1x1 12 L 28.82 85.19 70.1 2.20 80.83 D1 38.25x 31.25 'W 10.99 91.07 88.8 12.20x6.l 20.34 D2 38.25x6.lx 31.25 W’ 8.94 102.23 116.3 12.20 @0.46 D3 28.00x 21 W 10.24 91.07 106.9 12.20x6.l @0.44 D4 28.0x6.1x1 21 'W 10.26 102.23 115.2 2.20 @0.45 D5 19.0x12.2x 12 'W 10.99 91.07 116.6 6.10 @0.47 D6 19.0x6.10x 12 ‘W 9.46 102.29 90.0 12.20 @0.55 El 38.25x 31.25 L 29.6 81.07 74.0 12.2x9.06 @0.44 E2 38.25x 31.25 L 29.76 85.19 109.0 9.06x12.2 01.47 E3 28.00x 21 L 29.66 81.07 87.3 12.2x9.06 81.03 E4 28.00x 21 L 30.46 85.19 105.9 9.06x12.2 80.79 62 Sample Dimension Support Flute ECT Compressive Actual No. L x W x H Space, S Direction (lbs force Compression (inch) (inch) per from formula Force inch) (lbs) E5 19.00x12.20 12 L 32.16 81.07 71.7 x6.10 €0.32 E6 19.00x9.06x 12 L 29.44 85.19 96.5 12.20 81.18 Fl 38.25x12.20 31.25 L 29.60 97.28 102.4 x9.06 @0.46 F2 38.25x9.06x 31.25 L 29.76 102.23 118.9 12.20 80.69 F3 28.00x12.20 21 L 29.66 97.28 104.4 x9.06 @0.46 F4 28.00x9.06x 21 L 30.46 102.23 114.0 12.20 @0.45 F5 19.00x12.20 12 L 32.16 97.28 104.3 x6.10 @0.54 F6 19.00x9.06x 12 L 29.44 102.23 123.2 12.20 80.70 G1 38.25x15.00 31.25 W’ 9.86 75.89 53.7 x6.10 @0.77 G2 38.25x6.10x 31.25 ‘W 10.25 88.17 105.4 15.00 01.18 G3 28.00x15.00 21 ‘W 9.04 75.89 98.2 x6.10 @1.24 G4 28.00x6.10x 21 W 9.25 88.17 83.8 15.00 80.98 G5 19.00x15.00 12 W“ 9.77 75.89 75.3 x6.10 @1.18 G6 19.00x6.10x 12 ‘W 30.87 88.17 89.7 15.00 61.20 H1 38.25x15.00 31.25 L 9.77 91.07 101.3 x6.10 f @0.52 HZ 38.25x6.10x 31.25 L 9.49 105.80 111.3 15.00 @0.43 H3 28.00x15.00 21 L 9.66 91.07 111.9 x6.10 @0.45 H4 28.00x6.10x 21 L 8.75 105.80 116.7 15.00 @0.45 H5 19.00x15.00 12 L 11.16 91.07 132.9 x6.10 @0.67 H6 19.00x6.10x 12 L 10.45 105.80 117.4 15.00 @0.41 63 4.3 CORRELATION BETWEEN EXPERIMENT AND CALCULATION Comparing the actual experimental result and the result predicted by the formula, both results are close together. After comparing all samples in all groups, it can be concluded that these actual data are not much ddfferent from. each other even though the box dimensions, flute directions, cross section shapes, and lengths are very different. Both the actual result and the result from the formula are between 70 - 120 lbs. The result shows that the box dimensions, flute directions, cross sectional shapes, and lengths are not major factors affecting box compression strength. ECT is the most influential factor. Reasoning that it is the edges of the box in contact with the wooden block that fail in the test, the compression strength should be the ECT times twice of the thickness of the wood block used (3 inches). For boxes with the flutes running perpendicular to the length, Edge Length x ECT = Compression Strength II 3 inches x 30 lbs / in _ 90 lbs In a normal compression test, the variation in compression strength is about i 20%. Thus, in this test, the actual compression force is expected to be about 90 lbs. i 9 lbs. This predicts the results in Table 6 very well. 64 4.4 FORMULA RESULT FOR TRIANGLE CROSS SECTIONAL SHAPE The above reasoning can also be used to evaluate bending strength of long boxes with triangle cross sectional shapes. In Figure 29, the compression strength F of a box with an equilateral triangle cross section should be related to the vector sum of the in-plane edge crush forces G as follows; 2 G * cos 30° = F 2 *' ( 30 lb/in x 1 H in.) * 0.866 = F 2 * ( 45 ) * 0.866 = F F = 78 lbs. The force can be anywhere between this value and half of it because the force could be supported by only one side. It is less likely for both sides of triangle to take the load equally at the same time. So the compressive force can be between 39 to 78 lbs. Again, it predicts the results in Table 4 very well. In case of right triangle, the force is put directly at the top of triangle beam. This compressive load is divided into two forces along both panels. 65 F/2 F/2 .'\. Figure 29. Loading of boxes with triangular cross section 66 For the boxes with right isosceles triangular cross section, the compressive force result is the same as those with equilateral triangle cross section. Thus, the same formula can predict both also. 67 4.5 ANALYSIS OF FAILURE The force VS deflection curves for rectangular and square cross sectional shapes can be divided into eight groups A, B, C, D, E, F, G, and H. For Groups A and B in Figure 30, the graphs are smooth. Group C, group E, group G in Figure 31 are the roughest curves with a lot of peaks. In Group D, F, and H (Figure 32) , all curves are much smoother than groups C, E, and G but rougher than groups A. and B. Groups C, E, and G consist of box samples with the flutes running along the box length. Non uniformity of corrugated board can cause the box to fail in steps. The various peaks in the force VS deflection curves could be the result of several local failures occurring in stages. This made compression strength very difficult to predict. From the actual compression strength of all kinds of samples, the values are so low. It indicates that damage can occur during sorting by UPS and Federal Express. 68 Force (Lbs) .A 80 70 60 50 40 30 20 10 0 0.8 i I> Deflection (inches) Figure 30. Example for Graph of Group A and B 69 Force Lbs 80 70 60 50 40 30 20 10 A 0.8 i b Deflection (inches) Figure 31. Example for Graph of Group C, E and G 70 80 70 60 50 40 30 20 10 A Force Lbs | 0.8 l D Deflection (inches) Figure 32. Example for Graph of Group D, F and H 71 Comparing the results for the boxes with the flutes running parallel to one with the flutes running across the span, one with flutes running across higher deformation and bulging at the span’s center than ones with the flutes running along the length. Also testing package samples in Figure 33, two different positions of the wood block on the box surface created difference of damage. The wood block positioned in the vertical direction pressed test material surface more extremely than that positioned in horizontal direction. The cause of deforming and bulging of material depends on the load acting on and the surface area. The wood block for two different positions on the center of the sample used is the same so the weight of two situations is equal. The load applied on the surface was its weight. As the block placed in horizontal direction, the average load was distributed on the surface area of material, which contacted the area of the block. For placing the block in vertical direction, the more load was concentrated at the center of the long box so the intensity of damage occurred more than placing the block in horizontal direction. 72 Figure 33. Orientation of wood block and local failure 73 4.6 ERROR.ANALYSIS Errors came from many sources such as the test method, machine error, materials, and equipment condition. An important factor related to the test method which created lower compression force than it could be is bulging and tipping of both side walls as in Figure 34. Non uniform properties of the corrugated board also caused errors . The rough graphs were evidence that showed the uneven texture and properties of corrugated board. Another error came from the condition of box storage before testing. Controlling the storage room in which the boxes were placed was difficult because many students walked through. Several times of doors opening caused unstable room temperature and humidity. 74 ..a......#.. .0 e. O O .’ 6 e 0 e e . O . e O O . e o I . e e e e .0 O. . 0' O Figure 34. Bulging and Tipping causing experiment error 75 5.0 CONCLUSIONS AND FUTURE STUDY Unlike other engineering materials, paper is very weak and variable. A force applied to one point such as in the compression test here can cause the overall failure of the boxes. It is a local failure not a system failure like other engineering beams made from concrete or metal. The bending strength depends on the Edge Crush Test and the position and length over which the compressive force is applied. So from this experiment, it can be concluded that; 1. For a box with square and rectangle cross sectional shapes, the box fails when the maximum force is the ECT multiplied by the total edge length supporting the load. For a box with a triangular cross section shape, the compressive strength is the ECT multiplied by edge length and cosine 30°. The compression strength of boxes with vertical flutes is higher than that of boxes with horizontal flutes. The box dimensions, flute directions, and box spans don't affect the bending strength. 76 Future Study In order to use the simple predictions given here, the contact length between the load and the box must be known. In the controlled compression test, this contact length was related to the dimensions of the wooden block used. In real situations, this length will depend on the size of the boxes on top of the long corrugated box causing it to bend. So in order to use this prediction effectively, a study must be done to determine the various sizes and weights of boxes that pass through the UPS and Fed Ex sorting system. Simulating other support situations (not just two end supports) of boxes during transportation should be studied. For example, the box’s end is compressed by two boxes or both sides of the truck doors or airplane doors. It is likely for long boxes to be dropped during handling or transporting. Shock IMachine Testing can be applied for prediction of box failure due to dropping. 77 BIBLIOGRAPHY Anon. “Corrugated and Paperboard boxes.” Cleveland, OH, USA; Freedonia Group Inc, 1997. Bean, J. “Strong case for corrugated board." European Packaging Decision, edition 1, 1996, pp. 26-27. Cox, Jackie. “Do you boxes stand up to today’s treatment?." Americanpapermaker, vol 51, No.5, May 1988, pp.30- 32. Domowicz.A, Subicki K and Rzezniczak E. “Relation between the strength of corrugated boxes and their dimensions.” Przeglad.Papier, vol. 34, no. 3, Mar 1978, pp. 110-114. Kainulainen, Matti. and.Toroi, Martti. “Optimum composition of corrugated board with regard to the compression resistance of boxes.” Paper and Timber, vol 68, No.9, 1986, pp.666-668. Fiedler, Robert M; “Corrugated Shipping Containers and Performance," Distribution Packaging Technology. Institute of Packaging Professionals, Viginia, 1995. Forehand, Michael L. “Laboratory Simulation of distribution-Environment Hazards," Distribution Packaging Technology. Institute of Packaging Professionals, Viginia, 1995. Fibre Box.Association. Fibre Box Handbook, Fibre Box Association, Illinois, 1992. Guins, S.G. Notes on Package Desigg, S.G. Guins, 1975. Muldoon, Thomas J. “Industrial and Shipping Supplies.” The Packaging Encyclopedia, vol 29, No.4, 1984, pp. 183- 186. Soroka, walter. Fundamentals of Packagigg Technology, Institute of Packaging Professionals, Virginia, 1995. United Parcel Service. Packaging for the small parcel environment, United Parcel Service of America, Inc., 1971. 78 wright, P.G», McKinley, P.R. and Shaw, E.Y.N. Corrugated Fibreboard Boxes, Australian Paper Manufacturers, 1988. Slaby, Steve ML and Tyson, Herbert I. Statics and Introduction to Strength of Materials, Harcourt, Brace & World, Inc., 1969. Thewasano, S. Performance of Recycled Corrugated under various Temperatures and Humidities, MLS. Thesis, School of Packaging, Michigan State University, E.Lansing, 1989. Thielert, R. “Edgewise Compression Resistance and Static Load-Lifetime Relationship of Corrugated Board Samples." Tgppi Journal, pp. 77-80. Markstorm, H. Testing Methods and Instruments for Corrugated Board, (3m ed.) . Lorentzen & Wetre, ox4, S- 164 93 KISTA, Sweden. 79 "ICHIGRN STATE UNIV LIBRQRIES l I l I l ‘ . . . .1 l “. .1 31293018345961