Beam Theory and Deflection

GHS uses simple beam theory in its Longitudinal Strength calculations. One of the limitations of this theory is that the cross section of the beam is assumed to remain constant throughout its length. This is not strictly true for most ship hulls, but it is presumed to be true over the mid length where the greatest bending moment occurs.

A further limitation imposed by GHS is that the deflection be close to parabolic in shape. This is reasonable for ship hulls where the ends are free and the deflection is small (relatively small deflection being a requirement of simple beam theory also).

Even discontinuities and singularities in the load curve are reduced to inflections and knuckles in the bending moment curve, and after the two additional integrations required to arrive at the deflection curve there are no remaining inflections. Therefore fitting a parabola to this curve is a reasonable approximation.

However a problem arises if there is a discontinuous section moment of inertia curve, since it will leave an inflection in the deflection curve. But more importantly, proper application of beam theory requires longitudinal continuity in the section properties. If there is a discontinuity the beam should be treated as two or more connected beams where the boundary conditions are matched at the intersections.

GHS treats the hull as one continuous beam.

As a partial protection against errors in the predicted deflection due to violation of beam theory limitations and the parabolic modeling of the deflection curve, GHS does not accept section moment of inertia curves where the slope changes sign more than once. This rules out jointed structures where joints are not as stiff as the structures they connect. In such cases, shear, bending moment and stress are valid insofar as they are not significantly modified by deflection.

You can always get stress results by giving the section modulus curve in the form where the section moment of inertia is not explicit.

A good source of beam theory background can be found at:
Link to Beam Theory discussion

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