Box Compression Analysis of World-Wide Data Spanning 46 Years
Keywords:Box compression, strength, model, bending stiffness, ECT, BCT, buckling
AbstractThe state of the art among most industry citations of box compression estimation is the equation by McKee developed in 1963. Because of limitations in computing tools at the time the McKee equation was developed, the equation is a simplification, with many constraints, of a more general relationship. By applying the results of sophisticated finite element modeling, in this current study we derive a more general box compression formula that preserves the underlying theory of the McKee equation but removes the constraints. This formula is solvable with modern spreadsheet software, and we present an implementation method and example outputs as we relax or impose the various constraints. We analyze data obtained from multiple literature sources containing the traditional McKee equation inputs. We quantify the disparity between the McKee equation and the various sources of data and present an improved model for single-wall box-compression strength. The model attaches physical meaning to what were previously only fitting parameters, and it can serve as a tool for additional explorations in box optimization.
Angell, B. S., and P. R. Paslay. 1959. Prediction of shorttime static compressive strength of corrugated containers. Tappi J.42(6):194A-199A.nAmerican Society for Testing and Materials (ASTM). 1999. Standard practice for conducting an interlaboratory study to determine the precision of a test method. ASTM E 691. American Society for Testing and Materials, West Conshohocken, PA.nAmerican Society for Testing and Materials (ASTM)., 2003. Standard test method for determining compressive resistance of shipping containers, components, and unit loads. ASTM D 642. American Society for Testing and Materials, West Conshohocken, PA.nBatelka, J. J., and C. N. Smith. 1993. Package compression model. IPST Project 3746, final report. Institute of Paper Science and Technology, Georgia Institute of Technology, Atlanta, GA.nBormett, D. W., D. J. Fahey, and J. F. Laundrie. 1981. Use of oak in linerboard. Res. Pap. RP-FPL-410. USDA, Forest Serv., Forest Prod. Lab., Madison, WI.nBrodeur, P. H., I. M. Hutten, and J. L. Jonakin. 1997. MD and CD properties of linerboard components and the resulting box compressive strength. Tappi J.80(10):27-35.nBuchanan, J. S., J. Draper, and G. W. Teague. 1964. Combined board characteristics that determine box performance. Paperboard Packaging, September:74-85.nCarlson, T. A. 1941. Factors affecting the compressive strength of fibre boxes. Fibre Containers26(3):28-35.nChallas, J., M. Schaepe, and C. N. Smith. 1994. Predicting package compression strength geometry effect. IPST Project 3806, final report. Institute of Paper Science and Technology, Georgia Institute of Technology, Atlanta, GA.nCollaborative Testing Services. 2004. Analysis 301, reports for cycles 201, 203, 205, 207, 209, 211, and 213. Collaborative Testing Services, Inc., Sterling, VA. http://www.collaborativetesting.com/paper/current_report.html'>http://www.collaborativetesting.com/paper/current_report.htmlnFahey, D. J., and D. W. Bormett. 1982. Recycled fibers in corrugated fiberboard containers. Tappi J.65(10):107-110.nFourdrinier Kraft Board Institute. 1953. Testing compression reports 39 and 41. Institute of Paper Chemistry, Appleton, WI.nFrank, B. 2004. Caliper or weighted caliper for evaluating boxes. Corrugating International, October:3-8.nGartaganis, P. A. 1975. Strength properties of corrugated containers. Tappi J.58(11)nHahn, E. K., A. de Ruvo, B. S. Westerlind, and L. A. Carlsson. 1992. Compressive strength of edge-loaded corrugated board panels. Exper. Mech., September:259-265.nHartikainen, K. 1989. CAB—Computer aided box optimization, F.E.F.C.O. In Proc. 5th FEFCO Technical Seminar, Nice, France.nIPC. 1967. The effect of distribution of stiffness between components on the compressive performance of corrugated boxes. Testing compression report 85, Project 2695-3. Institute of Paper Chemistry. Appleton, WI: Pp. 1-52.nJohnson, M. J., Jr., and T. J. Urbanik. 1987. Buckling of axially loaded, long rectangular paperboard plates. Wood Fiber Sci.19(2):135-146.nKawabata, Y. 1997. New calculating method for compression strength of corrugated linerboard box—Concentrated on new Kellicutt equation. J. Korea Tappi29(4):73-85.nKellicut, K. Q., and E. F. Landt. 1951. Basic design data for use of fiberboard in shipping containers. Fibre Containers36(12):62-80.nKoning, J. W., Jr., and R. C. Moody. 1969. Effect of glue skips on compressive strength of corrugated fiberboard containers. Tappi J.52(10):1910-1915.nKoning, J. W., and W. D. Godshall. 1975. Repeated recycling of corrugated containers and its effect on strength properties. Tappi J.58(9):146-150.nLibove, C. L., and R. E. Hubka. 1951. Elastic constants for corrugated-core sandwich plates. National Advisory Committee for Aeronautics, Tech. Note 2289. NASA Center for Aerospace, Hanover, MD.nLittle, J. R. 1943. A theory of box compressive resistance in relation to the structural properties of corrugated paperboard. Paper Trade J.116(24):31-34.nLuo, S., J. C. Suhling, and T. L. Laufenberg. 1995. Bending and twisting tests for measurement of the stiffnesses of corrugated board. AMD-Vol. 209/MD Vol. 60, Mechan. Cellulosic Mat. ASME: 91-109.nMcKee, R. C., J. W. Gander, and J. R. Wachuta. 1963. Compression strength formula for corrugated boxes, Paperboard Packaging, August, 149-159.nMcKinlay, P. 1980. See footnote no. 2.nMiles, J. G. 1966. Compressive strength of corrugated containers: An interlaboratory study. Mater. Res. Standards, March:142-146.nSchrampfer, K. E., W. J. Whitsitt, and G. A. Baum. 1987. Combined board edge crush technology. IPC Project 2695-24 Progress Report 1. Institute of Paper Chemistry, Appleton, WI.nShick, P. E., and N. C. S. Chari. 1965. Top-to-bottom compression for double wall corrugated boxes. Tappi J.48(7): 423-430.nTAPPI. 2002a. Edgewise compressive strength of corrugated fiberboard. (Short column test). Tappi T811 om 02. TAPPI, Norcross, GA.nTAPPI. 2002b. Edgewise compressive strength of corrugated fiberboard using the clamp method. (Short column test). Tappi T839 om 02. TAPPI, Norcross, GA.nUrbanik, T. J. 1990. Forced vibration response of nonlinear top-loaded corrugated fiberboard containers. Pages 253-274, Vol. 1 In Proc., 61st Shock and Vibration Symposium, Pasadena, CA.nUrbanik, T. J., 1992. Effect of in-plane shear modulus of elasticity on buckling strength of paperboard plates. Wood Fiber Sci.24(4):381-384.nUrbanik, T. J., 1996. Review of buckling mode and geometry effects on postbuckling strength of corrugated containers. PVP- Vol. 343, Development, validation, and application of inelastic methods for structural analysis and design, ASME, pp. 85-94.nUrbanik, T. J., and E. P. Saliklis. 2003. Finite element corroboration of buckling phenomena observed in corrugated boxes. Wood Fiber Sci.35(3):322-333.nWolf, M. 1972. New equation helps pin down box specifications. Package Engineering, March:66-67.n
The copyright of an article published in Wood and Fiber Science is transferred to the Society of Wood Science and Technology (for U. S. Government employees: to the extent transferable), effective if and when the article is accepted for publication. This transfer grants the Society of Wood Science and Technology permission to republish all or any part of the article in any form, e.g., reprints for sale, microfiche, proceedings, etc. However, the authors reserve the following as set forth in the Copyright Law:
1. All proprietary rights other than copyright, such as patent rights.
2. The right to grant or refuse permission to third parties to republish all or part of the article or translations thereof. In the case of whole articles, such third parties must obtain Society of Wood Science and Technology written permission as well. However, the Society may grant rights with respect to Journal issues as a whole.
3. The right to use all or part of this article in future works of their own, such as lectures, press releases, reviews, text books, or reprint books.