On the Exact Solution of Non-Uniform Torsion for Beams with Axial Symmetric Cross-Section
In the traditional theory of non-uniform torsion the axial displacement field is expressed as the product of the unit twist angle and the warping function. The first one, variable along the beam axis, is obtained by a global congruence condition; the second one, instead, defined over the cross-section, is determined by solving a Neumann problem associated to the Laplace equation, as well as for the uniform torsion problem. So, as in the classical theory the warping function doesn’t punctually satisfy the first indefinite equilibrium equation, the principal aim of this work is to develop a new theory for non-uniform torsion of beams with axial symmetric cross-section, fully restrained on both ends and loaded by a constant torque, that permits to punctually satisfy the previous equation, by means of a trigonometric expansion of the axial displacement and unit twist angle functions. Furthermore, as the classical theory is generally applied with good results to the global and local analysis of ship structures, two beams having the first one an open profile, the second one a closed section, have been analyzed, in order to compare the two theories. Keywords—Non-uniform torsion, Axial symmetric cross-section, Fourier series, Helmholtz equation, FE method.
Incidence of Load Combination Methods on Time-Variant Oil Tanker Reliability in Intact Conditions
Abstract Reliability analysis of an oil tanker in intact conditions is performed to investigate the incidence of load combination methods on hull girder sagging/hogging time-variant failure probability. Particularly, Turkstra rule, Ferry Borges and Castanheta method and Poisson square wave model are applied to evaluate the statistical distribution of bending moment, with reference to both one voyage and 1-year period. Statistical properties of time-variant ultimate strength are determined by Monte Carlo simulation, up to 25-year ship lifetime; bending capacity is determined by means of a modified incremental-iterative method, to account for corrosion wastage of structural members contributing to hull girder strength, welding residual stresses and material properties randomness. After determining the still water load combination factors, based on statistical properties of still water, wave and total vertical bending moments, with reference to 1-year time interval, reliability analysis is performed by Monte Carlo simulation, based on limit state formulations relative to different load combination methods. Finally, the VLCC double hull oil tanker, benchmarked in the 2012 ISSC report, is assumed as a reference ship and obtained results are fully discussed.
LXXXIV. The axis of distortion of a twisted elastic prism
Summary Duncan, Ellis and Scruton (1933) have shown that if an elastic cantilever is twisted, the displacement of its tip relative to its support consists of a rotation about the flexural centre of its cross-section. In this paper is considered the distortion of a twisted prism without reference to its support, and it is found that the axis of distortion of such a prism is in general quite different from the axis of displacement found by Duncan, Ellis and Scruton—an effect that has been previously noticed by Cullimore (1949). General expressions are derived for the determination of the axis of distortion, and its effect on practical cantilevers subjected to finite twisting is estimated. Experiments designed to test the analysis are described, and their results are found to confirm it satisfactorily.