### NACA-TN-1344

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National Advisory Committee for Aeronautics, Technical Notes - Critical Stress of Thin-Walled Cylinders in Torsion

A theoretical solution is_given for the critical_stress of

thin-walled cylinders loaded in torsion} The results are presented

in terms of a few simple formulas and curves _which are applicable

to a wide range of cylinder dimensions from very short cylinders of

large radius to long cylinders of small radius. Theoretical

results are found to be in somewhat better agreement with experi—.

mental results than previous theoretical work for the same range

of cylinder dimensions.

For most practical purposes the solution to the problem of

the buckling of cylinders in torsion was given by DonneILin an

important contribution to shell theory published in 1933 (reference 1).

The present paper, which gives a solution to the same problenn

has two main objectives: first, to present a theoretical solution

of somewhat improved accuracy; second, to help complete a series

of papers treating the buckling strength ofcurved sheetfrom a

unified viewpoint based on a method .of analysis essentially

equivalent to that of Donnell but considerably simpler. (See,

for example,_references 2 and 3.)

The method of solution in the present'paper is that developed

in reference 3. The steps in the theoretical computations of the

critical stress are contained in the'appendix. The results are

given in the form of nondimensional curves and simple approximate

formulas which follow these curves closely in the usual range of

cylinder dimensions.

The values of ks for cylinders with either simply supported or

clamped edges are given in the form of logarithmic plots in

figure 1. The ordinate in this figure is the critical shear-

stress coefficient ks The abscissa is a curvature parameter Z

which is given directly by the theory and involves the dimensions

of the cylinder and Poisson s ratio.

For very short cylinders the value of the shear-stress coef-

ficient approaches the values for flat plates, 5.31!- when the edges

are simply supported and 8. 98 when the edges are clamped. As Z

increases ks also increases and the curves which defined 1:5

are given approximately by straight lines.

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