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The Quarterly Journal of Mechanics and Applied Mathematics 1954 7(3):287-298; doi:10.1093/qjmam/7.3.287
© 1954 by Oxford University Press
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TORSION OF A SEMI-INFINITE BODY AND A LARGE THICK PLATE

YI-YUAN YU {dagger}

( Washington University St. Louis )

Michell derived the equation for torsion of bars of varying circular cross-section. Using this equation, and by means of Fourier-Beesel series, Purser analysed the local effect near the ends of the bar due to an arbitrary distribution of torsional shearing forces over its terminal sections. A similar analysis is given in this paper for the torsional problem of a semi-infinite body and a large thick plate, which are essentially bars having very large radii. The Fourier-Bessel series is replaced by a Fourier-Bessel integral.

Stress and displacement components for the general cases are expressed in integral forms. These are then used to solve particular problems. In the first problem the torsional shearing force is distributed linearly within a circular area at the boundary of a semi-infinite body. The second problem consists of a semi-infinite body subjected to a concentrated torque at its boundary, which is considered as the limiting case of uniform shearing forces distributed over a finite circular area of the boundary. The similar problem for a large thick plate subjected to two equal and opposite concentrated torques on its surfaces is also discussed. Numerical results are given.


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