x d«meon circumference ■ 2irr Fig. 5.4. Thin tube with longitudinal split.

where k\ and k2 for thin-walled tubes are usually equal to

It should be noted here that the presence of even a very small cut or gap in a thin-walled tube produces a torsional stiffness (torque per unit angle of twist) very much smaller than that for a complete tube of the same dimensions.

5.5. Other solid (non-tubular) shafts

Table 5.2 (see p. 146) indicates the relevant formulae for maximum shear stress and angle of twist of other standard non-circular sections which may be encountered in practice.

Approximate angles of twist for other solid cross-sections may be obtained by the substitution of an elliptical cross-section of the same area A and the same polar second moment of area J. The relevant equation for the elliptical section in Table 5.2 may then be applied.

Alternatively, a very powerful procedure which applies for all solid sections, however irregular in shape, utilises a so-called "inscribed circle" procedure described in detail by Roark^. The procedure is equally applicable to thick-walled standard T,I and channel sections and is outlined briefly below:

Inscribed circle procedure

Roark shows that the maximum shear stress which is set up when any solid section is subjected to torque occurs at, or very near to, one of the points where the largest circle which

R.J. Roark and W.C. Young, Formulas for Stress & Strain, 5th edn. McGraw-Hill, Kogakusha.

d«meon circumference ■ 2irr Fig. 5.4. Thin tube with longitudinal split.


Maximum shear stress

Angle of twist per unit length



16 T jzb2h at end of minor axis XX

where J = —Ibh3 + hb* I and A is the area of cross-section = irbh/4 64

Equiloterol triangle

Equiloterol triangle

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