Buckling of Axially Loaded, Long Rectangular Paperboard Plates

Authors

  • Millard W. Johnson, Jr
  • Thomas J. Urbanik

Keywords:

Plates, elastic stability, buckling, corrugated fiberboard, paper, material failure, edgewise compression

Abstract

This study examines the elastic buckling of long rectangular plates made of paper and subjected to compressive axial loading. The model is appropriate for the facing and flute components of corrugated fiberboard. A dimensionless stiffness, S, and mean Poisson's ratio, v, characterize the dimensions of the plate and the nonlinear orthotropic stress-strain relation of paper. The dimensionless buckling stress σ depends on S, v, and the plate edge condition, which can be fixed or simply supported. An examination of σ versus S predicts the stiffness needed to prevent elastic buckling and shows how the significance of edge restraint and material nonlinearity vary with S. An iterative solution is given for doing the analysis. Comparing the results obtained assuming fixed edges to those obtained assuming simply supported edges explains how fiberboard strength may vary due to component variations. Comparing the results obtained for nonlinear materials to those obtained for linear materials explains why fiberboard edgewise compressive strength cannot be accurately predicted from only the components' strengths.

References

Johnson, M. W., Jr., and T. J. Urbanik. 1984. A nonlinear theory for elastic plates with application to characterizing paper properties. J. Appl. Mech. 51:146-152.nJohnson, M. W., Jr., T. J. Urbanik., and W. E. Denniston. 1979. Optimum fiber distribution in singlewall corrugated fiberboard. USDA Forest Serv. Res. Pap. FPL 348, Forest Prod. Lab., Madison, WI.nRosenthal, M. R. 1977. Effective thickness of paper: Appraisal and further development. USDA Forest Serv. Res. Pap. FPL 287, Forest Prod. Lab., Madison, WI.nSetterholm, V. C. 1974. A new concept in paper thickness measurement. Tappi 57(3):164.nUrisanik, T. J. 1981. Effect of paperboard stress-strain characteristics on strength of singlewall corrugated fiberboard: A theoretical approach. USDA Forest Serv. Res. Pap. FPL 401, Forest Prod. Lab., Madison, WI.n

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Published

2007-06-28

Issue

Number 2 / April 1987

Section

Research Contributions

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