Simple mathematical buoyancy functions with application to calculation of shear forces and longitudinal bending moments for ships in arbitrary trimmed conditions 1

Abstract

The present paper deals with some fundamental, mathematically describable properties of the hull displacement distribution, which don’t seem to have been treated previously in ship technical literature.

The practical application is chiefly aimed at the calculation of still water shear forces and bending moments in ships of full form with long parallel middle body, in arbitrary trim conditions.

In order that the computing method may be used in the most efficient way, the hydrostatic curves should be supplemented with the following coefficients:

Prismatic coefficient, φ.

Position of the half-section, h according to eq. (10).

Shift of the half-section, in terms of the shift of the centre of buoyancy, at a small change of trim, ${\mathit{\zeta }}_{\mathrm{H}}\mathrm{/}{\mathit{\zeta }}_{\mathrm{B}}$ according to eq. (18a).

The buoyancy double-moment factor at the half-section, i.e. the minimum value ${\mathit{\mu }}_{\mathrm{O}}$ .

All these coefficients can easily be computed together with the usual hydrostatic data, and they are sufficient for an exact calculation of the shear forces and bending moments within the parallel middle body. To make an application of the method possible also at an early stage of the design, one chapter of the paper deals with calculation of approximate values of the relevant hydrostatic data.

In an appendix (App. III) the possibilities are discussed of estimating also the wave induced bending moments and shear forces, in order that the total load distribution on the hull may be determined.