Seth, B. R.
(1934)
*Torsion of beams whose cross-section is a regular polygon of n sides*
Mathematical Proceedings of the Cambridge Philosophical Society, 30
(2).
pp. 139-149.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0305004100016558

## Abstract

E. Trefftz has discussed the problem of the torsion of a beam whose cross-section is bounded by a polygon with the help of the Schwarz-Christoffel transformation given by
dw/dt=A(t-ξ_{1})^{a1/π} (t-ξ_{2})^{a2/π}...(t-ξ_{n})^{an/π}, (1)
where a1, a2, …, an are external angles of the polygon in the w-plane, and ξ1, ξ2, …, ξn are the points on the real ξ-axis in the t-plane that correspond to the angular points of the polygon in the w-plane. In the case of regular polygons a further transformation of the upper half of the t-plane into the interior of a circle in the z-plane with the help of the transformation
Z=i-t/i+t (2)
greatly simplifies the problem, and some definite results can be obtained.

Item Type: | Article |
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Deposited On: | 22 Nov 2011 13:01 |

Last Modified: | 22 Nov 2011 13:01 |

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