/ DASIC DESIGN DATA ECR THE USE OF EIEERECARD IN SHIPPING CONTAINERS November 19<51 No. D1911 UNITED STATES DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY Madison 5, Wisconsin In Cooperation with the University of Wisconsin L OF FOKSM LISRARY Digitized by the Internet Archive in 2013 http://archive.org/details/bandatafOOfore K. Q. K: Forest Pre U. S Since corrugf . i amp nsion in their use Salient advantage: 3 f packing and un{ i pping container But has b< for relating the properties of component paperboaj ip board and to the finished box Although /aluating container strength and s< al design, much more needs to be done A basic study of fiberboard shipping initiated at the U. S. Forest Products Laboratory before World War ] Lnued for several of the war years. This early work r In methods for evaluating the properties of paperboard a? rboard as engineering materials, which showed that the sti sheets can be correlated with those o- (2, 3, k, 5, 6, 12, 15, lk)l These conclusions s i • premise fiber contain them- selves to scientif: and it was that basic design criteria could be developed similar to | oped for boxes made from wood. " \ ± n COO p. tion with thi od anci for the Armed For" with T lc objective -This paper rep Fo assign r 360 in 1 : us ions conta not -Maintain- y of w This article discusses procedures for such scientific analysis and gives some basic design criteria obtained since the study was resumed. Tests and Procedures Several forms of material and test methods were used in this investigation: (l) component paperboard sheets were subjected to ring-crush, modified ring- crush, and strip-column tests; (2) built-up corrugated boards were given bending, shear, and flexural-shear tests; (3) fiberboard structures consisting of four panels representing a box without top or bottom were given compression tests; and (h) conventional slotted boxes were given compression tests and tested in a revolving drum with can-type loads. Material, Method of Construction, and Size of Tubes and Boxes Material . --All of the tubes and boxes tested were made of double-faced corru- gated fiberboard. Some of the A- and B-flute board was made on the Laboratory's corrugator and was of balanced construction, having the same basis weight of jute or kraft for both liners in combination with several different corrugating mediums. The liners, which were in thicknesses of either 0.009, O.OlP^ or 0,030 inch, were combined with either straw, kraft, pinewood, chemfiDre, chestnut, or aspen corrugating mediums. Other boards and boxes included A-, B- , and C-flute fabricated in commercial corrugated box factories. Not all of these boards were of balanced construc- tion, although all were made of paperboard component materials being used commercially. Some of the boxes were made at the Laboratory from V3c and W6c boards produced commercially . Other V3c boxes tested were actually made by a commercial fabricator. Samples of the component materials of all the bdards were also tested. Method of constructing tubes and boxes . --The blank from which each tube was made was cut to the proper size, with the corrugations either perpendicular or parallel to the height dimension, with a sharp power saw. This procedure was employed to secure square top and bottom edges, and to eliminate the damage due to crushing and tearing" of the liners and corrugations along the edges, which result when a shearing blade is used for cutting. The joint was made by over- lapping one side par 1 over the edge of the side panel on the opposite end of the blank the thickness of the fiberboard- Cloth-backed tape 3 inches wide was applied to the inside and outside surfaces of the joint to overlap each panel about l-l/2 inches . The boxes made and tested were the regular slotted type and had manufacturers joints fabricated by stitching, tape, or glue. The top and bottom flaps were sealed with adhesive Sizes of tubes and boxes tested , --Tubes made of Laboratory boards were made in a variety of sizes from 2 inches square to 35 inches square,. The height of the tube varied from 2 inches up to kQ inches . Bept. No. D1911 -2- The tubes and boxes made from com Eily square, but oblong cross two or three times the width dimension. 1 boxes are included within a range of eights of the tube 8 and boxes were Component Paperboard Te s Modified ring-crush tes' developed at the Laboratory, was emploj pro- portional limit, stress at maximum load .ners and corrugating mediums. A number of layers of the pa] rolled into the form of a hollow cylinder, usii . ag the outside lap and of providing f La > machine. Two optical strain gages were a pression over a definite gage h on ea o oppc I tie specimen, reliable data were o! i for \ gs of the applied load. Sp^ prepared so lied parallel to either the "with-nu the paperboard . Ring-crush test .--Eing-c - test.ing 1/2- by 6- inch strips supported on the i of several removable islands . The isla according to the thickness of the sp roived tests of strips, 3/8 by 6 1 form pressure In both techniqi that yielded a single valu' of ma S trip-column test .,- -A strip long that was held straight b^ [de a column l/l6 inch high. As v ilue of maximum load was obtained as a - g machine , Tests of Built-up Boa Bending tests .--The b< ■ placed across two ro! edg he load was app wooden bearing head. Si igs of load ai Ken from the dial of the testing machine a' -d at the middle of the spar either parallel or perpe She ar tests. --By giiing a strip fastening a dial gage to k and the relative displaceme; two fa simultaneously with inert pression or tension in a on the flutes either parallel or Kept. No. D1911 Flexural- shear tests , --By using a test specimen of built-up board in the form of a square flat plate and applying equal loads at the four corners and measuring the mean deflection of the plate, the flexural shearing moduli were determined. The flexural shearing was accomplished by applying the load downward to two diagonally opposite corners of the plate and upward to the other two. The mean deflection of four points on the diagonals equally distant from the center was read simultaneously with increments of load. The experimental procedure was to plot a load-deflection curve , and from its shape the shear moduli were determined. Compression Tests of Tubes and Boxes To determine the relationships of size, shape of cross section, and height involved in the bending and crushing of the side walls, compression tests were made of tubes and boxes. The tests were made in a universal testing machine that had a mechanism for making an autographic load-compression curve of each test. Before test, the tubes and boxes were conditioned in a controlled atmosphere The direction of the flutes in the side walls of the tubes and boxes was either vertical (parallel to the direction of the applied load) or horizontal (perpendicular to the applied load) . Drum tests of loaded boxes . --A number of drum tests were made of various kinds of boxes. They included boards of A-, B-, and C-flute construction with either jute or kraft liners. The boxes had can-type loads and the plus weight of contents was approximately 1 pound for each inch of length plus depth/ width. Failure was considered complete when the contents spilled from the box during the drum test . Discussion of Ee suits It was apparent in the initial studies at the Laboratory that the strength properties of corrugated fiberboard and the component paperboard materials could be obtained from tests designed to yield engineering information. In the early tests, the modulus of elasticity of paperboards, as determined by a tension test, was fo\_nd to correlate with engineering data from column, bending, and shear te.sts of the built-up corrugated board. It was desired also to determine if a similar correlation could be obtained for compressive stresses. One of the more precise tests was the modified ring-crush test which has previously been described It was found to be useful in correlating the maximum crushing loads of fiberboard tubes with the maximum crushing strength of paperboard. Its principal use in this study, however, was to evaluate simpler tests, such as ring-crush and strip-column tests, both of which are considered suitable for use by industry. Evolution of a Design Formula One of the main objectives of the investigation was to develop a method of expressing the crushing strength of a corrugated fiberboard box using Kept. No. D1911 -k- information obtained from a simple test of the component paperboard sheets. In the development, the tube was used as the intermediate link between tests of the components and of the box Before a start could be made toward the consolidation of the mathematical relationships involved in the bending and crushing of the thin plates repre- senting the four walls of a fiberboard tube, some assumptions had to be made. Paperboard being nonisotropic it was recognized that a formula applica- ble to fiberboard with the machine direction parallel to the applied load might not be applicable to fiberboard with the load applied perpendicular to the machine direction of the paperboard It was also recognized that Four- drinier paperboard exhibited less difference in strength properties with and across the machine direction of the paperboard than did the jute or cylinder boards With the recognized characteristics as a guide, it was felt that a basic formula could be evolved from data developed at the Forest Products Laboratory for applying the thin plate theory of mechanics to the design of panels of plywood. The plywood is also a nonisotropic material In using these data, the orientation of panel dimensions and selection of axes of ref- erence were as shown in figure 1. This figure represents one of the four faces of a tube Notations used in the various mathematical expressions are explained in the section of this report designated "Notations," and a few of the notations are repeated in the text„ It was found in tests of plywood panels (11) that the stress at which buckling occurred was about equal to the proportional limit of the material, this being about two-thirds of the ultimate compressive strength. From a logarith- mic plotting of plywood plates in compression in which the ratio of P (average stress at failure) to P u (ultimate compressive strength of the material) was plotted as the ordinate - and the ratio of P cr (observed critical stress) to P u as the abscissa, the slope of the curve deslgna + ed as m was found to be one~ third and a good approximation of the data was given by the equation: p u ~ V p u u The problem was to find what relationships would apply in corrugated fiber- board and determine a value of m, the slope of the buckling curve of thin plates , It was found— that P crs (critical stress with shear included) = ^ H A By substituting the above expression in the equation for plywood, the basic formula is obtained, -j— —Explanation of the terms of this and subsequent mathematical expressions will be found in the Notations at end of this article. Kept, No. D1911 -5- p 1-m P = - -P- n 2 1 m (— + -) V H A' Before the proper tests of component sheets and tests of built-up corrugated board had been developed to yield the necessary information, the determina- tion of the unknown quantities of the formula was made from plottings of cubical tubes -- each tube representing four square panels. By the use of bending and shear tests of built-up board, together with the modified ring- crush test of component sheets, it was possible to make these determinations without testing the tubes Determination of m To determine the exponent "m," which would adequately describe the shape of a curve representing compression failures of cubical tubes of various sizes, the following method was employed: From a plotting of cubical tubes, in which the maximum loads, in pounds per inch of panel width, in compression were plotted against size of cube, three points were selected for use. Two of the points selected were representative of the extremities of that portion of the curve in which failure of the tube occurs by buckling The third point selected was midway between the other two. The points were designated as a a P a ; a^ P^; and a c P c , and selected such that P^ =j/' P a P c . The points selected for the original determination of m are designated on a typical plot representing compression failures of cubical tubes (fig. 2). Substituting the values of these points in the basic formula, three equations were obtained. These equations were simultaneously solved for m and H. A P, a m = log a b 2 + H A A 2 2 k H = a a a c ~ a b A 2a b 2 - a a 2 - a c 2 The value of the exponent used in the initial calculations was determined as 335- The value, 0.272, was used for calculations involving loads applied perpendicular to the flutes Kept. No. D1911 -6- Because it had been seen by trial calculations that slight differences in the value of m did not appreciably change the total calculated tube load, it became apparent that average values of m could be used and thus eliminate the necessity of making determinations of m for each specific board in future calculations Based on the determinations involving several boards, the average values of m were found to be O.376 and 253 for tubes with the load applied parallel and perpendicular to the flutes, respectively, However, the values 1/3 and l/k were chosen to simplify calculations. Determination of A, Transverse Shear Stiffness Factor of a Panel (8 Equation 17, A = h A*yz + Mxz b 2 2 2 n c a The integer "n" (number of half waves that a panel shapes itself into under ,2 2 2 stress) is so chosen to make the sum of Dt E + D c n a a minimum. The 1 2 2 2 ? n c a c -^ values of shear moduli were determined independently by shear tests of built- up board, using the formula M P cos 9 £ WL d ' where M = shear modulus P = shear load of a built-up board at 0.001- inch displacement of faces, pounds = the angle of plane of specimen surface with the plane of loading platens, used as 90° W = width of specimen, inches L = length of specimen, inches c = thickness of core, inches d = displacement of faces, used as OcOOl inch With the shear modulus known, A can be determined from the formula Determination of H, the Bending Stiffness Factor of a Panel From the plotting of cubical tubes, 5 was known, and with the solution of A A ~TT in the preceding paragraphs, H could be determined by the relationship H = — A, "" A Rept„ No. D1911 -7- As an alternate method, H can be determined from EI, determined by bending tests or column tests of built-up board, by the following equation (8, Equation 19) : o -k 2 2 2 H =ji d D, — E — + D - — — + 2K 1 n2 a 2 2 b 2 in which (10, Equations 63 and 83) D 1 or D 2 = E = m modulus of elasticity of corrugating material in the across- machine direction cross section area per inch of width = ^ c " ^' E(K-j_ l£) , Sk where k = if 2 (c - t) 2 US 2 +Tr 2 (c - t) 2 and E(K, tf) = an elliptic integral determined from tables when K 1 p • , _ is known Determination of Pp from Curve Data of Cubical Tubes Before the modified ring-crush test was used, the proportional limit of built-up corrugated board was determined from plottings of cubical tubes The method described under "Determination of m" was used, solving the three simultaneous equations for the proportional limit value P _£ HP, 1-m m = P 1 m <*a 2 ♦ f) - ? b m (a b 2 + ?) , Pft - ^ A A The value of H being known, and the values of m and — being determined by use ~~ A of the simultaneous equations, the value of P p can be computed by use of any one of these expressions. Repto No. D1911 -9- Determination of P-p from Modified Ring-crush Test By use of the modified ring-crush test of paperboards, the values of proportional limit, maximum crushing strength, and modulus of elasticity in compression are obtained. From this information, the P p of the built- up fiberboard can be calculated by: P = P (h - c)a + P„ r aa t c P pf P c Reasonably accurate predictions of crushing strength of tubes were obtained with the use of the basic formula. The calculations and manipulations involving values from tests of both paperboard and the built-up corrugated board, however, were deemed too complicated for practical use. As a result ^ simplification of the procedure of making predictions of compressive strength was started, It was apparent that the first step in simplification was one of finding a simple test of the component paperboard sheets. Secondly, it appeared advisable to eliminate, if possible, the tests of built-up board involved in the procedure A search was started for a simple test of the components, the resulting values of which could be combined in the proper proportion to provide an index for the compressive strength of the built-up board* A significant finding at this stage of the development provided the basis for considerable progress in simplification. It was found that the combined ring-crush value designated P x (pounds per inch) of different boards corresponded to the compressive - strength of a specific size of cubical tube when the crushing load was applied parallel to the flutes and to another size when the crushing load was applied perpendicular to the flutes „ The two values were found to be constant (designated a x 2 values) for tubes made of various combinations of materials,, A different a x 2 value was found, however, for A-, B-, and C-flute construction- Prom actual tests of tubes made from a variety of boards, these values were determined to be 8,36, 5. 00, and 6.10 for A- , B- , and C-f lutes, respectively, when the crushing load was applied parallel to the flutes. With the establishment of this relationship the final step in the evolution, that of relating the tube to the finished box, could be started. Relationship of Static Tube and Box Loads It has been pointed out that the static compressive strength of tubes represents optimum that may be obtained with any given corrugated board, and it follows that these optimum compressive loads will not be attained in corresponding corrugated fiber boxes because of various factors that enter into their manufac- ture and use. Hence, in order to use for design purposes the formula which had been developed for the tube, it was necessary to establish the relationship between the tube and box. Bept. No. D19H -10- To determine the relationship of the crushing strength of fiberboard tubes to the top-to-bottom crushing strength of the finished fiberboard box, comparisons of tube and box loads for corresponding sizes were made From the comparisons, which included those with square and oblong cross sections in various heights, it was observed that the relationship was fairly constant up to certain limits. For instance, for tube loads up to about 1,500 pounds, the box loads were approximately 7 of the corresponding tube loads For tube loads greater than 1,500 pounds the ratio of box loads to tube loads was no longer constant but decreased with an increase in tube load it was observed that the tube loads continued to increase beyond the 1,500-pound value while the corresponding box loads did not change appreciably In general, the maximum load that tubes of a given cross section will with- stand decreases with an increase in height from 2 inches up to 12 or l6 inches, depending upon the kind of material from w] Lt was made A further increase in height had iit + Ie influence on its resistance to crushing This can be explained by the fact +hat the lower I of length, that is, the 12-, Ik-, or l6-inch length, represents the wave length into which any particular combination of material would shape itself under stress and that the greater lengths were merely multiples of this wave leng\ Increases in compression strength did not occur, however, with decreases in height of boxes . This can be accounted for, at least in part, by the end condition of the side panels of the box. D.. he horizontal score, wmch has been found to be one of the weaker poir a box, rolling and bending takes place along the score, usually resulting in premature buckling As a result, the higher loads are not attained by the shorter panels as th^y are with a tube where normal buckling occurs. Although some differences in Loads were attained for boxes of various heights, for practical purposes, the box "Loads have been considered the same for a specific cross section regardless of heigh* Application of Formula t o Box It was found that the ratio of box load to box factor) for various cross sections with heights 12 laches and gre reasonably constant. For heights less than 12 inches , however, there was considerable divergence between the box and tube loads This was due to increases in tube loads for decreasing heights while the box Loads remained about constant *nroughout the range Therefore, to eliminate this divergence by deriving a box factor that would apply regardless ihe shape of the box, it wa3 necessary to relate the box to a tube hav-i \g an. ab ratio ( width of pane I n of I 5 or less. Al- ' height of panel though it was found 1 'hat a single box factor could be used for a specific flute, the same factor could not be used for all three flutes Hence, box factors were determined for A , B^ , and C-flute boxes Further, it was found that the box factor provided a means for adjusting box loads for the specific kinds of body joints. Some tentative box factors whi^h have been determined are included in table 1, Eept- No D1911 LI Table l c --Tentative box factors for A-, B- , and C-fluite boxes Source of : Type of : Box factors (j) for boxes boxes : manufacturer's: with flutes vertical in : joint . side wallai Flute A : B Laboratory made : Taped : 0.717 : 0,752 : O.717 from commercial : Stapled : , „ * . . . . . <» : »622 :...„. material Commercially : Taped : 677 : .597 : "667 made : Stapled 1 , „ „ . « . » . » : „564 : . , „ , —Box factors for boxes with flutes horizontal in side walls have not been determined. As a result of the establishment of a x p values and box factors > the design formula for calculating the top-to-bottom compressive strength of the finished corrugated fiberbcard box with flutes vertical in side walls now becomes; 1/3 ZJ in which P = total compressive strength of box in pounds P x = composite ring-crush load of built-up board (pounds per inch) ('P-rl single face + P r /> double back + ax P rc ) a p = either 8„3o7 5-00, or 6,10 for A-,, B-, or C-f lute , respectively Z = perimeter of box in inches J = box facto Alinement Char*- ? To simplify use of the formula , alinement charts for calculating the strength of A- , B- , or C -flute boxes have been constructed (figs, 3? ^> and 5)° To use the alinement charts, determine the combined ring-crush strength of the single- face liner (S„FoL„)> the double-back liner (D.B.I.)^ and the corrugating medium (CM,). For A-flute boxes apply the formula S.FoL, + D.B.L. + 1*523 x CM, using a tentative box factor of O-667 for commercially made boxes with taped manufacturer " 8 joints , Kept- No, D1911 -12- For B-flute boxes use S F.L. + D,B,L. + 1 36l x C M. with a tentative box factor for commercially-made boxes with taped joints being 0-597 an( i those with stapled joints, 56k For C-flute boxes use S.F.L + D-B.L + 1 477 x CM with a tentative box factor of 667 for boxes with taped joints. Then, using a straightedge, connect appropriate point A with box perimeter at point C With point B as a pivot, orient the straightedge with the box factor, point E and read the load on the compressive strength scale at point D Determinat ion of Stack.! ng Streng It has been known that corrugated fiberboara boxe lot be expected to support a stacking load equivalent to the lead attained by a compression test of the box in a testing machine But , although some large users of fiberboard containers have established their own stacking limits for boxes in storage ( l) , what has not been generally known is the portion of the compression test value the box can be expected to support for specific periods of time in various storage atmospheres To determine the information deemed necessary for establishing load limits for specific periods of storage, long-time loading + 3 made of several kinds of A- and B-flute boxes in severa] different atmospheres (7) ■ The results thus far obtained have indicated Lefined trends and relationships between the machine compressio] of boxes, the magnitude of the dead load of storage, a. , of loading, Compression Test s The top-to-bottom stat I ompression test value of '.tie finished container when empty was used as a basis for determining the amount of dead load to apply in the duratio- -of -load tests The dead loads were portions ranging from 55 "to 95 percent of this static compress: The static compression test values were determined by tests of similar boxes in the various atmospheres in which the duration-of- Loa ! les were to be conducted. Periods of R The behavior of corrugated fiberboard boxes subjected to various "dead loads" appeared to follow a general pattern as shown by bhe reactions during three distinct periods of time, The first period, in whi ..'as a rapid Rept, No D1911 -13- compression of the boxes 9 resulted from the initial application of the load, and started the instant the load contacted the box. Some of the rapid com- pression can be attributed to flattening of the rounded portion of the score along the horizontal edges of the box, together with a general leveling of the surfaces. The rapid compression continued, but at a decreasing rate for a comparatively short period of from a few seconds to 1 to 2 hours, with a rather abrupt transition into the second periodo The compression in the second period continued at a uniform but much slower rate. Compression in the third period increased more and more rapidly until failure occurred . The three periods described above were found to exist for all dead load durations whether for a few minutes or 30 days or more, the only significant difference being in the slope and length of the linear portion, period 2, of the result- ing curves c Generally, during the third period, failures were complete and included buckling and crashing of all four panels , The typical box had two of the four panels bowed in and the other two bowed out . Relation of Load to Duration When the dead loads represented a fairly large percentage of the compression test values, slight changes in the amount of dead load applied to a box changed the duration considerably. Loads that approached the static compressive strength of the box caused failures usually within minutes „ Dead loads which were about 60 percent of the static compressive strength extended the duration to about a month o An example of the relationship between the load and duration may be seen by the actual test results of four typical boxes included in the following tabulation: Ratio of dead load to static compressive Time to strength failure Static compressive strength of comparable box Actual dead load on box Pounds Pounds Percent Minutes 702 699 696 696 664 610 544 403 95 87 78 58 1.3 7*3 399^0 35-6 (days) Duration- of -load tests in which the dead loads approached the static compres- sive test value of the boxes are shown on the curve, figure 6, by the points in that portion of the curve marked A-B„ In the same figure the static com= pressive strength of the boxes representing the 100 percent level is shown at A-*- at a duration of about l-l/2 minutes. The curve of figure 6 may be used to determine the time to cause failure of any specific box regardless of size, magnitude of strength, and moisture con- tent of the fiberboard, when any specified amount of dead load is applied. The reason is that the curve, which is based on the ratio of the dead load to the static compressive strength, expresses a relationship which was found to apply Rept. No, D1911 ,14= for all materials and all moisture conditions studied. Knowing the ratio for a specific set of conditions figure 6 may be entered at the appropriate per- centage level and the point of entry projected horizontally to intersect the curve The duration, expressed as days, may he read on the opposite scale The straight line portion, B-C , of the curve in figure 6 shows that for each decrease of about 8 percentage points in the ratio of the dead load to the static compressive strength the duration of load to cause failure is increased about eight times It must be pointed out that the boxes included in this study had not been previously loaded or roughly handled before being used in the duration-of-load tests , A box which is damaged as a result of rough handling prior to storage would not be expected to sustain the same dead load for the same duration of ne as an undamaged box. Also, the length of time a box can be expected to sustain a dead load will be reduced as a result of increases in moisture con- tent of the fiberboard during storage „ This became apparent from the static compressive tes^ va.ues of boxes in various atmospheres Relation of Moisture Content of Fiber- board to Compressive St r ength The influence of moisture content on compressive strength of four lots of boxes made of different materials > are shown in the curves of figure 7- Here it is seen that the different curves have about the same slope, and for prac- ^ al purposes it would appear that an average slope represented by the broken line could be used. Using the representative broken line curve, a formula expressing the relationship of compressive strength of boxes to moisture con tent of the fiberboard was derived to facilitate the use of the data The formula was derived as follows; The broken - irve represents a box - ha+ has a compressive strength of 6 pounds at percent mois+uro contei (2) The s + rength of other boxes a T a.i moisture content values will be repre- sented by parallel lines in1 g X = at various compressive strengths, I This may be expressed by Y = bdo) 1 ^ » in which Y = compressive strength of box- pounds b = compressive strength at percent moisture cont m = average slope (determined to be -3»0l) x = moisture content^ ^For purposes of this equation,, moisture content mus + be expressed as a decimal , determined by dividing the weight of water by the oven-dry weight of fiberboard o Rept, No, D1911 15- (k) The compressive strength of a box at a specific moisture content may- be found by relating the box to one for which the compressive strength and moisture content are known, thus? P = P X (IP) 3 - 01 *i ~ 3.OIX0 (10) 2 in which P = compressive strength to be determined-pounds Pj_ = known compressive strength-pounds x-^ = moisture content for box having P-^ compressive strength x 2 = moisture content of box for which the compressive strength is to be determined5 3.01 = slope of curve For easier use of the relationship, an alinement chart was constructed from which the compressive strength of boxes at one moisture content can be readily interpreted in terms of another (fig. 8), To use the chart, connect points A and C, using a known compressive strength for a box at a specific moisture con- tent, with a straight edge- With point B as a pivot, orient the straight edge to the moisture content, point E, for which the corresponding compressive strength is desired, and read the load on the compress! ve-strength scale at point Do The example indicated by the lines on the chart shows that the compressive strength of 1,000 pounds for a box at 6 percent moisture content is reduced to ^30 pounds when the moisture content is increased to 18 percent . Comparison of Compressive Strength of Boxes wit n Eesistance to Kough Handling in the Bevolvir.g Drum Although it had been anticipated that general trends could be established, a close correlation between compressive strength and the results of rough-handling tests in the hexagonal drum was not expected „ Past experience had shown that the drum test is less precise than the compression test, and that test values vary more for boxes testec. in the drum than for those tested in the compression machine. Some relationship, however, was found to exist Generally, the boxes chat attained the greatest compressive loads also attained the greatest numbe _ of falls in the drum,, For example, the V3c boxes were stronger in compression than any of the boxes tested, and they attained about three times as many falls as the next best box. In comparing some W6c boxes, including 10 sizes and shapes, with similar V3c boxes, the following relation- ship was observed: the average compressive strength of the W6c boxes was 578 pounds and the average number of falls in the drum to cause failure was 170. For V3c boxes the values were 1,011 pounds and 570 falli Although more data are needed, it is felt that eventually it may be possible to obtain some general correlation between results of drum tests aad compression tests in considering performance standards for corrugated fiberboard boxes. Kept. No. D1911 -16- Hov Can BaBic Design Data Be Used i Ls intended that the information obtained in this study of fiberboard I the basic component paperboard sheets will be used: (i) To prepare tables and charts for design purposes and general specifica- tions applicable to various box sizes, load limits, and perhaps commodity classifications . (2) To develop design criteria that can be used by the box manufacturer in quality control operations as well as for design purposes to meet specific use requirements or standards „ The use of the basic information obtained in this study can best be illus- trated by the solution of a hypothetical problem, Let L1 be assumed that a regular slotted B-flute corrugated box having vertical flutes in the side walls is needed for a specific use, and the box must satisfy the following requirements: (1) The box must be 12 inches high and the perimeter is to be 82 inches . (2) The weight of the article and box is to be 40 pounds . (3) The box is to be constructed with a taped body joint „ (M The box with packaged article will be in storage 60 days before it reaches the consumer <> (5) The boxes will be piled seven high in the storage warehouses „ (6) Moisture content of the fiberboard during the storage period might be as high as 18 percent . The problem is one of seifecting the proper component paperboard sheets having the desired strength properties from which to fabricate the board for the b The solution to the problem will be made with the use of charts contained in this article as follows: (1) Boxes, each weighing 40 pounds, piled seven high will place a 240-pound deac'. load on the bottom box of each pile for a period of 60 days . (2) It may be seen from figure 6 that for storage involving 60 days the dea:i load must not exceed 56 percent of the top-to-bottom compressive strength of the box. Hence, the compressive strength of the box having 18 percent moisture content needs to be 430 pounds (240 pounds divided by O.56 = 430 pounds ) o Sept. No. D1911 ■ 17- (3) From figure 8., it may be seen that a box having a compressive strength of kJO pounds at 18 percent moisture content has a compressive strength of 760 pounds at 9-8 percent moisture content. (The latter condition was employed for development of design criteria presented in this study „) (k) It, may be seen from the solution drawn on figure k that a board having a combined ring-crush strength of 39 pouiJds per inch (across -machine direc- tion) is needed to satisfy the conditions involving the 82-inch perimeter box, 12 inches high, which has a compressive strength of j60 pounds when the moisture content is 9-8 percent From the partial inventory of paperboard stock included in the following tabulation the materials may be selected. It may be seen that liners Nos, 1 and 2 can be used with corrugating medium Noc L Also liner No, 3 could be used for both single-face and double-back with corrugated medium No= 2, but the resulting box would be stronger than necessary =. Therefore, a B- flutc board made from 47 -pound Fourdrinier kraft liners with chemfibre corrugating medium will be fabricated into a box that will meet the require- ments of "che problem, Inventory of Materials Material Basis weight Lb per 1,000 sq. "ft. Ring- crush strength across-machine direction L'bo "per in. Liners 1 Fourdrinier kraft 2 Fourdrinier kraft 3 High-density ferjift k Jute 5 J ite 6 Fourdrinier kraft 7 Fourdrinier Kraft 8 Jute Corrugating Mediums 47 15-78 ^7 15 -53 UQ 16.IC 52 10.3.3 52 9.6k ko 12.21 57 9.8.1 56 11.98 1 Chemfibre 28 5.97 2 Semichemical 26 7.22 3 Bogus 26 6.97 From the solution of the hypothetical problem it becomes apparent that the information contained in this article can be applied to the Inventory of any commercial manufacturer. The manufacturer, likewise } can design boxes to meet the requirements of his clientele on uhe basis of a simple ring-crush test of the paperboard sheets. Rept. No, D1911 -18- No tations The choice of axes and direction of applied load in relation to flutes are shown in figure 1< I a = width of panel, in inches. 2, <2 = ratio o. of corrugating medium when flat to length orrugal (A-flute = 1-523, B- flute = 1,3605, 3. a X 2 = averag; in inch es, of cubical tube corresponding to load P = a -A. height of paneJ 1 ties, thickness of o istance between liners) in inches, transverse shear s1 •• 3s factor of a panel, "true bending EL of a panel in a direction perpendicular to the applied load true bending EI of a panel in a direction parallel to the applied crushing :0a 1 moduJ js of elasticity of the core in a direction parallel to the flutes modulus of Lty of paperboard liners in a direction parallel -o I •' a>cis. modulus of elast i i1 y of paperboard liners in a direction para,.,-'., to the ST-axis, product of Lus of elasticity and moment of inertia of • Llt-u] gal I board, pro ; of • is of : Lasticity and moment of inertia of • om bending tests, per inch of width, in a dir illel or perpendicular to the direction of the fl i1 es . * upon P. 14, h = thickness in inches > of built-up corrugated board 15. H = bending stiffness factor of a panel. 16 J = box factor , ratio of box load to tube load - dependent upon tes and type of body joint. 17 K = flexura. shear stiffness factor l8, L = length of spa- in inches. 19 X-p = 1 - (Poisson 3 ra^io with the machine multiplied by Poisson s ratio across the machine direction of paperboard) Note: A" ;rage Poisson's ratio of two Fourdrinier kraft papertoards "with machine" - 328, average "across machine" = 219- Her (0.328 x 219) = 0.928^ 20 m = ar. exponent in the compression formula describing the slope of bu • for thin plates . 21 n = an integer (number of half waves into which the panel shapes j If under stress and is so chosen to make the quantity Dj k + Dp - 9_. a minimum) n 2 a 2 b 2 Rept No D191J -19- li b 5. c 6 A 7 D l 8 D 2 9. E c 10. E fx 11, E fy 12. EI 13 EI T P = maximum compressive load of a panel whose width is a, in pounds per inch of widths and whose height is b, in inches . Pp = compressive load at proportional limit of built-up corrugated fiberboard in pounds per inch of width . Note: This value may- be for flutes parallel or perpendicular to load, dependent upon P desired o 2k o Pp C = compressive proportional limit load in pounds per square inch in the with- or across-machine direction of corrugating material, dependent upon P . Note : When the load of a panel with flutes parallel to the load is to be calculated, then P X)C is regarded as in the across -machine direction of the corrugating, but when the load is applied perpendicular to the flutes this quantity is disregarded. 25 o Ppf = compressive proportional limit load in pounds per square inch, in the with- or across-machine direction of the liner material, dependent upon P 26c P u = ultimate compressive load of built-up board, in pounds per incho 27- P x = ring-crush load in pounds per inch of built-up board determined from summation of the loads of the liners and corrugating medium c 280 P r j^ = ring-crush load in pounds per inch of a l/2- by 6-inch strip of liner either with or across the machine direction, dependent upon P. 29 » P rc = ring-crush load in pounds per inch of a l/2- by 6- inch strip of corrugating medium in the across-machine direction „ 30 u S = half the distance, in inches, from crest of one corrugation to the next „ 31= t = thickness of corrugating material, in inches . 32 o /* xz = shear modulus in a direction perpendicular to load„ 33- ^yz ~ shear modulus in a direction parallel to loadc 3^-o Z - perimeter of box, in inches „ Bept„ No„ D191.1 -20- LITERATURE CITED (1) BALKEMA, E. H. 1950, Quality Control of Corrugated Boxes . Buyers' Viewpoint Fibre Containers, Vol. 35; No. 6. (2) CARLSON, T. A. 1927c A new Test for Fiber Container Board: Its Significance and Relation to Other Tests University of Wisconsin, Master's Thesis . (3) 1939- A Study of Corrugated Fiberboard and Its Component Parts as Engineering Materials. Fibre Containers > Vol., 2k, No. 7« (k) 19^0 , Bending Tests of Corrugated Board and Their Significance.. Paper Trade Jour,, Vol- 110, No 6 8, Fibre Containers, Vol- 25, No, 3. (5) __ n 19^1 o Corrugated Board and Its Component Parts as Engineering Materials. American Management Association Proceedings . Ser. 128:23-29. (6) 19^1 Some Factors Affecting the Compressive Strength of Fiber Boxes, Paper Trade Jour v , Volo 112, No 23. (7) KELLICUTT^ K.. Q* and LANDT, E. F. 195-1- Safe Stacking Life of Corrugated Boxes. Fibre Containers, Volo 36, No. 9. (8) MARCH, H- W 19^8 „ Effects of Shear Deformation in the Core of a Flat Rectangular Sandwich Panel: 1 Buckling Under Compressive End Load. 2. Deflection Under Uniform Transverse Load Q U S„ Forest Products Laboratory Report No. 1583„ 29 p^, illus. (9) ___^ , KUENZ1, E. W., and KOMMERS, W. J. 19^2 Method of Measuring the Shearing Moduli in Wood. U. S. Forest Products Laboratory Report No, 1301, 8 p., illus „ (10) _ and SMITH, C B. 19^9 Flexural Rigidity of a Rectangular Strip of Sandwich Construction U„ S. Forest. Products Laboratory Report No. 1505, 19 p=, illus. (11) NORRIS, Co B 19^-7 • An analysis of the Compressive Strength of Honeycomb Cores for Sandwich Construction . N„A C,A. Tech„ Note 1251. Rept. No D1911 -21- (12) SEBORG, CO,, DOUGHTY, R, H., and BAIRD, P. K. 1933= Effect of Relative Humidity on the Moisture Content and Bursting Strength of Four Container Boards , Paper Trade Jour., Vol., 97, No. 15 . (13) SIMMONDS, P. A., HYTTINEN, AXEL, and SEBORG, CO. 19^<. Wet- strengthened Fiberboard from Reclaimed Fiber. Uo S„ Forest Products Laboratory Report No c RI469, 18 p., illus (Ik) SKIDMORE, K. E. and MYERS, EARL C. 19^+5° Tests of Solid Fiberboard Boxes Made of Wet -strengthened Reclaimed Material., U. S. Forest Products Laboratory Report No, RlVfO, 10 p.. illus. ADDITIONAL REFERENCES GRUNDY, A. V. 19^+0 . Improving the Quality of Corrugated Containers * Packing and Shipping, Vole, 67, No„ 3- 19^-0 o Engineering Aspects of Corrugated Container Purchasing. Fibre Containers, Vol. 2% No„ 7„ Rept. No. D19H -22- Figure 1«--A panel of fiberboard representing one of the four faces of a tube, showing orientation of dimensions, loads ^ and stresses, (ZM 88065 F) Rept„ No. D1911 LOAD - P Y-AXIS || ) f _J 1 i f «H U as CC? ft ri rH £3 d o rH CC3 rH o •H tf rQ fl 2 CtJ d -p Ch s ■ 0) O CO a d CO CD CO a CD rO rH •H t> d £ p fl d •H CD O H crj H CO d rH o •P Ctf "rH =H crj O rQ ce -P •H d A ctf B o d ^ s a V£ OJ « CD CO CO Repto No. D1911 Q cog < 1 ^3 D U _l h- 1 ) UJ n D> D L_ n U|- iu U Q o°- ^co _l huj hi _l cc _l < Q O < Q . i LJ • 2 '< LOAD TERMI BY co in 2_l i— LU CL LU OO Q U_ „*r o to (SQNnOd) H1QIM 13N\7d JO HDNI d3d QVOT IAJ D IAJ I X V IAI - d Figure 3* --Chart for determining the top-to-bottom compressive strength of A- flute corrugated fiberboard boxes when the flutes are verti- cal in the side walls. The resulting determinations will be for a box conditioned in the same atmosphere in /hich the ring- crush values were obtained „ (ZM 88067 F) Rept. No D1911 L-20 M 88067 F Figure 4, --Chart for determining the top-to-bottom compressive strength of B-flute corrugated fiberboard boxes when the flutes are verti- cal in the side walls., The resulting determinations will be for a box conditioned in the same atmosphere in which the ring crush values were obtained „ (ZM 88068 F) Kept NOo D1911 L- 20 7 M 88068 F Figure 5 ---Chart for determining the top-to-bottom compressive strength of C-flute corrugated fiberboard boxes when the flutes are verti- cal in the side walls. The resulting determinations will be for a box conditioned in the same atmosphere in which the ring- crush values were obtained . (ZM 88069 F) Sept. No. D1911 CO UJ CO X — U) r> Ol K UJ U a. CO o Q Z 2 rr 3 O CL Q — U. 2 CD 5 o u 80^ 70 ^ ■z. UJ ■z. 60 o CL 5 o _ <_> . o 50 o 2 T °° . CO h; o Wq: 40 30 20- ■150 140 130 •120 110 •100 90 80 -70 -60 50 -40 -30 en UJ X CJ cc LU h- LU a: UJ a. x o J_ L-20 Z M 88069 F -P u t3 a; -p o s nd C O O CO 0) K o ,o CO LU co q: LU uj ' . • O / • * l_ CD ,n Q > £ O < LU Q S O 1 — QC 1 — — ' f err / o 1 [I'll DF-LOAD FIBERBO; r ERENT US DEAD ► x-^ t/1 - a IO CM — = _o m O " o o CM m CD T u. o 7 ^ n ir _ • »/ ATI Of JGATE IN 1 H VAf e |ise : n -°8^ /—i - °E O o ( ; J J o • in m — : m — r<* — : to — . *> — bj i- ' 3 Z o / Z • « / • v * — "< o • o o / < / o =T - LU a. GO UJ T X o CD U. o CM UJ I- O o UJ cr 3 t- - O CO kD CM O O o_ O O O O O O O O IT) o o (SONDOd) S3X08 JO H19N3H1S 3AISS3ddlAJOO Figure 8 „ --Chart for converting top-to-bottom compressive strength of corrugated fiberboard boxes at one moisture content to strength at another moisture content „ (ZM 87365 F) Bept. Noo D1911 PIVOT CO Q Z> O a. i \- -z. LU cc t- co LU > CO CO LU cr o_ o o LU O o: LU Q. LU i o o LU c: J- co o 50^ ZM 97^65 r DIVERSITY OF FLORIDA llllllllllllllllllll 3 1262 08866 6200