• Steel and Composite Structures
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• 제7권6호
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• pp.441-456
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• 2007

In literature for thin-walled sections with L, [, +, I, and ${\Box}$- shapes the approximate torsion equations for stiffness are used which were proposed by Bach (Hsu 1984), p.30. New formulae for torsional stiffness of bars with L, [, +, I, and ${\Box}$ cross section valid not only for thin-walled sections are presented in this paper. These formulae are obtained by appropriate polynomial approximation of stiffness results obtained by means of method of fundamental solutions. On the base of obtained results the validity of Bach's formulae are verified when cross section is not thin-walled.

• Steel and Composite Structures
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• 제3권4호
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• pp.261-275
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• 2003

Truss members built-up with double angles back-to-back have monosymmetric cross-section and twisting always accompanies flexion upon the onset of buckling about the axis of symmetry. Approximate formulae for calculating the buckling capacity are presented in this paper for routine design purpose. For a member susceptible only to flexural buckling, its optimal cross-section should consist of slender plate elements so as to get larger radius of gyration. But, occurrence of twisting changes the situation owing to the weakness of thin plates in resisting torsion. Criteria for limiting the leg slenderness are discussed herein. Truss web members in compression are usually considered as hinged at both ends for out-of-plane buckling. In case one (or both) end of member is not supported laterally by bracing member, its adjoining members have to provide an elastic support of adequate stiffness in order not to underdesign the member. The stiffness provided by either compression or tension chords in different cases is analyzed, and the effect of initial crookedness of compression chord is taken into account. Formulae are presented to compute the required stiffness of chord member and to determine the effective length factor for inadequately constrained compressive diagonals.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.39-51
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• 2001

This paper shows how boundary element method can be used to calculate torsion geometrical stiffness of cross-sections of various beams and airfoil profiles. Using the BEM direct formulation, the technique for determining bending and torsional geometrical characteristics of arbitrary multiply connected cross-sections is presented. The application limits of several well-known formulae on some test problems have been demonstrated and discused.

• Journal of Advanced Marine Engineering and Technology
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• 제5권1호
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• pp.34-51
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• 1981

Lately, due to increasing engine output by high supercharging, heavy crankshaft and propeller mass, as well as long strokes attended with the reduced crankshaft axial stiffness, the critical crankshaft axial vibration has frequently appeared in maneuvering range of the engine. Some investigators have developed calculating methods of natural frequencies and resonant amplitudes for crankshaft axial vibrations. But their reliabilities are uncertain as the estimated crankshaft axial stiffness are incorrect. The calculating procedure of these natural frequencies is practically analogous to the classical calculation of torsional vibration frequencies, except for an important difference due to the relationship of the axial stiffness of a crank and the angle between the crank and other, especially the adjacent, cranks. In this paper, 6 calculation formulae of crankshaft axial stiffness already published and a theoretically- developed one by authors are checked by comparing their calculating results with those measured values of one model crankshafat and three full-scale actual crankshafts. Also, the calculating methods of the crankshaft axial free vibration are investigated and their computer programs are developed. Finally, those developed computer programs are applied to calculating one model crankshaft and two full-scale actual crankshafts of ship's propulsion engines and their calculated results are compared with those measured values.