St. Venant's solution of the torsion problem applies only to cases where the cross-sections all warp in the same manner and by the same amount. This paper gives the solution for the cases where warping varies, either because there is a cross-section where there is a restraint on deformation or because the applied torque varies along the bar. The solution is restricted to small deflections such that the principle of superposition may be applied.
Get full access to this article
View all access options for this article.
References
1.
TimoshenkoS.1953 Collected Papers, ‘Theory of Bending, Torsion and Buckling of Thin-walled Members of Open Cross-section’ (McGraw-Hill, London and New York).
2.
ReissnerE.1955Oesterreichisches Ingenieur-Archiv, vol. 9, Nos. 2–3, ‘Torsion with Variable Twist’.
3.
GoodierJ. N.BartonM. V.1944J. appl. Mech., vol. 11, March, p. A-35, ‘Effects of Web Deformation the Torsion of I-beams’.
4.
NilesA. S.NewellJ. S.1954‘Airplane Structures’ (John Wiley, New York).
5.
WilliamsD.1960‘Theory of Aircraft Structures’ (Edward Arnold, London).
6.
SouthwellR. V.1956‘Relaxation Methods in Theoretical Physics’, vol. 2 (Oxford University Press, London.
7.
ShawF. S.1953‘Introduction to Relaxation Methods’ (Dover Publications, New York).
8.
de AllenD. N. G.ChittyL.PippardA. J. S.SevernR. T.1956Proc. Instn civ. Engrs, Lond., vol. 5, Part I, p. 198, ‘Experimental and Mathematical Analysis of Arch Dams’.
9.
FoxL.1949–50Phil. Trans. roy. Soc., A, vol. 242, p. 345, ‘Numerical Solution of Elliptic Differential Equations’.
10.
GillesD. C.1948Proc. roy. Soc., A, vol. 193, p. 407, ‘Use of Interlacing Nets’.
11.
LyseI.JohnstonB. G.1935Proc. Amer. Soc. civ. Engrs, vol. 61, p. 469, ‘Structural Beams in Torsion’.
