A hull is supported in water by the buoyant force of the water that it displaces. The upward buoyant forces acting on the length of the hull equal the downward gravity forces acting throughout the length of the hull. The buoyant and gravity forces are equal and are concentrated at the center of buoyancy and the center of gravity. Individual buoyancy forces are proportional to the cross-sectional area of the submerged hull at the point at which they are measured, and the individual gravity forces are measured by the weight of cargo, machinery, equipment, etc., at a point along the hull. When the individual buoyancy and gravity forces are plotted as ordinates from the same baseline that represents the ship's length, two curves are developed, a buoyancy curve and a weight curve.
The load curve is formed by plotting the differences between weight and buoyancy at individual points along the length of the ship. The load curve crosses the baseline when weight equals buoyancy.
When the load curve is above the baseline, weight is greater than buoyancy, and it is less than buoyancy when the curve is below the line. Since total weight equals total buoyancy, the area of the load curve above the line equals the area below.
When unequal loading is indicated by the load curve, shearing forces and bending moments will be set up in the vessel. The shearing curve is developed by integrating the load curve, a process which calculates the area under the curve. When the shearing curve is integrated the process produces the bending moment curve. Representative curves of shearing force, developed from the above load curve, and bending moment, developed from the shearing force curve.
ABS presents formulae for the calculation of shear stresses caused by loading and wave actions.
Longitudinal strength work sheets are provided to the vessel to help calculations of stress numerals for the various weights added to the light ship displacement. Each added weight (cargo, bunkers, and other variables carried in specified locations), when multiplied by a factor provided a designer, will give a number known as the stress numeral, sometimes a positive number, sometimes a negative one. The algebraic sum of the calculated stress numerals and the stress numerals provided for the light ship equals the net stress numeral. Stress numeral = (actual bending moment/allowable bending moment) x 100.
Since the actual bending moment must be less than the allowable bending moment, the stress numeral must be less than 100. If it is greater than 100 the ship is improperly loaded and there is a probability that the ship will break due to excessive bending moments.
Maximum bending moments happen in the vicinity of amidships. At this location the shear force is zero, and from this location forward and aft the moment arms of the shear force are maximum.
The computer is now used in figureing this out, it helps in the calculation and is faster.
