Advertisement

Experimental Mechanics

, Volume 28, Issue 1, pp 70–76 | Cite as

An experiment for determining the Euler load by direct computation

  • G. A. Thurston
  • P. A. Stein
Article
  • 53 Downloads

Abstract

A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length; therefore, the experimental data allow a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.

Keywords

Experimental Data Mechanical Engineer Fluid Dynamics Direct Computation Rectangular Cross Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

A

parameter defined in eq (A9), approximately equal to the maximum tangent angle in deflected column

Ā

parameter defined in eq (A10), a measure of initial imperfection of unloaded column

EI

bending stiffness of composite column

h

thickness of columns with rectangular cross section

Jn(A)

Bessel function of the first kind of integer ordern and argument A

L

length of column

P

axial load on column

PE

Euler load on column

s

arc length

W

transverse deflection of loaded column ats=L/2

x, y

Cartesian coordinates; see Fig. 2

Δ

axial or end shortening of loaded column

εb

maximum bending strain at outer fiber

θ

angle between x axis and tangent to column

λ

nondimensional axial load

ζ

nondimensional arc length

L

lower load-shortening curve in Fig. 1 corresponding to curvature of deflected column of same sign as initial curvature

U

upper load-shortening curve in Fig. 1 corresponding to curvature of opposite sign to initial curvature

m

point at local minimum of upper load-shortening curve in Fig. 1 Bar over geometrical variables denotes undeformed shape of imperfect column.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Southwell, R.V., “On the Analysis of Experimental Observations in Problems of Elastic Stability,”Proc. Roy. Soc. London, Series A,135,601–616 (1932).MATHGoogle Scholar
  2. 2.
    Lundquist, E.E., “Generalized Analysis of Experimental Observations in Problems of Elastic Stability,” NACA TN 658 (1938).Google Scholar
  3. 3.
    Spencer, H.H. andWalker, A.C., “Critique of Southwell Plots with Proposals for Alternate Methods,”Experimental Mechanics,15,303–310 (1975).Google Scholar
  4. 4.
    Sweet, A.L., Genin, J. andMlakar, P.F., “Determination of Column-Buckling Criteria Using Vibratory Data,”Experimental Mechanics,17,385–391 (1977).CrossRefGoogle Scholar
  5. 5.
    Souza, M.A., Fok, W.C. andWalker, A.C., “Review of Experimental Techniques for Thin-walled Structures Liable to Buckling,”Part I,Experimental Techniques,7 (9),21–25,and (10),36-39 (1983).Google Scholar
  6. 6.
    Thurston, G.A., “Continuation of Newton's Method Through Bifurcation Points,”J. Appl. Mech.,36,Series E,425–430 (1969).MATHGoogle Scholar
  7. 7.
    Schmidt, R. andDaDeppo, D.A., “Discussion of ‘Continuation of Newton's Method Through Bifurcation Points’,”J. Appl. Mech.,37,Series E,247 (1970).Google Scholar
  8. 8.
    Thurston, G.A., “Author's Closure,”J. Appl. Mech.,37,Series E,247–248 (1970).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1988

Authors and Affiliations

  • G. A. Thurston
    • 1
  • P. A. Stein
    • 1
  1. 1.NASA Langley Research CenterHampton

Personalised recommendations