An undergraduate level experiment involving the nonlinear mechanics of deformable bodies is described. The phenomenon of interest is the large elastic sideways deflection of a column under compressive loading. The experimental arrangement and the measurement’s simple equipment are usually found in undergraduate laboratories. The analysis is more involved because the use of nonelementary functions is required. To circumvent this difficulty, the analysis can be done with a spreadsheet or a data analysis program that has been preprogrammed to compute the required integrals.

Topics
Data analysis, Laboratories
1.
Stephen P. Timoshenko, History of Strength of Materials (Dover, New York, 1983), pp. 28–40.
2.
G. Wayne Brown, Basic Statics and Stress Analysis (McGraw–Hill Ryerson, Toronto, 1985), pp. 610–632.
3.
John F. Knott, Fundamentals of Fracture Mechanics (Butterworths, London, 1973), pp. 1–2.
4.
Augustus E. H. Love, A Treatise on The Mathematical Theory of Elasticity, 4th ed. (Dover, New York, 1944), pp. 399–413.
5.
Stephen P. Timoshenko and James M. Gere, Theory of Elastic Stability, 2nd ed. (McGraw-Hill Kogakusha, Tokyo, 1961), pp. 76–82.
6.
Reference 1, p. 255.
7.
Arnold Sommerfeld, Mechanics (Academic, New York, 1952), pp. 87–90.
8.
Th.
Höpfl
,
D.
Sander
, and
J.
Kirschner
, “
Demonstration of different bending profiles of a cantilever caused by a torque or a force
,”
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Milton Abramowitz and Irene A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards, 1964), pp. 591–592 and 〈www.convertit.com〉.
10.
The numerical evaluations and plots were made by using a graphing program, KaleidaGraph, which has tools similar to a spreadsheet. Synergy Software, 2457 Perkiomen Avenue, Reading, PA 19606-2049, 〈www.kaleidagraph.com〉.
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© 2004 American Association of Physics Teachers.
2004
American Association of Physics Teachers
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