Page 80 - Aircraft Stuctures for Engineering Student

Problems 65

Warping of
cross-section --

Fig. 3.10 Warping of a thin rectangular strip.

We should not close this chapter without mentioning alternative methods of
solution of the torsion problem. These in fact provide approximate solutions for
the wide range of problems for which exact solutions are not known. Examples of
this approach are the numerical finite difference method and the Rayleigh-Ritz
method based on energy principles5.

References

Wang, C. T., Applied Elasticity, McGraw-Hill Book Company, New York, 1953.
HetCnyi, M., Handbook of Experimental Stress Analysis, John Wiley and Sons, Inc., New
York, 1950.
Roark, R. J., Formulas for Stress and Strain, 4th edition, McGraw-Hill Book Company,
New York, 1965.
Handbook of Aeronautics, No. I, Structural Principles and Data, 4th edition. Published
under the authority of the Royal Aeronautical Society, The New Era Publishing Co.
Ltd., London, 1952.
Timoshenko, S. and Goodier, J. N., Theory of Elasticity, 2nd edition, McGraw-Hill Book
Company, New York, 1951.

Problems

P.3.1 Show that the stress function 4 = k(r2 - a2) is applicable to the solution
of a solid circular section bar of radius a. Determine the stress distribution in the
bar in terms of the applied torque, the rate of twist and the warping of the cross-
section.
Is it possible to use this stress function in the solution for a circular bar of hollow
section?