MOMENT OF INERTIA OF SECTION AT FRAME M.

Assumed neutral axis 26.5' above base.

Actual neutral axis=26131.28' above assumed neutral axis 27.78' above base line.

Moment of inertia about correct neutral axis=2(810,320 +7,577 — 3,341)

1,629,112 Ft.2 Sq. In.

NOTE. Rivets neglected both in compression and tension.

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MOMENT OF INERTIA OF SECTION AT FRAME N.

Assumed neutral axis = 26.5' above base.

7,577

7,359

Actual neutral axis= =1318.65' below assumed neutral axis= 25.85' above base line.

Moment of inertia about correct neutral axis= 2 (684,025 +7,359-806, =1,381,156 Ft.2 Sq. In.

Curve of Load.

The curve of loads is obtained by measuring the difference between the curves of weight and buoyancy at the various ordinates and spotting off the excess buoyancy above the base; and the excess weight below their points of intersection with this line will show the waterborne sections, which for calculating purposes are taken as the points of support.

Curve of Shearing Stresses.

This curve is calculated from the foregoing curve of load by *aking its area at various ordinates measured from forward aft and plotting these areas off above or below the base line as in the case of the curve of loads, observing that the greatest stresses will be opposite the points of support (or waterborne sections). A curve run through the foregoing spots will show the shearing stresses graphically.

Curve of Bending Moments.

As the bending moment at any section in the length of a ship is equal to the algebraic sum of the shearing stresses in relation to either end, it is evident that a curve of bending moments may be obtained from these stresses and plotted off as was done for the shearing curve from the curve of loads, observing that the maximum and minimum bending moments will be coincident with the points of support.

To apply similar curves and the data constituting them to the determination of the stresses experienced by a ship amongst waves, it is usual to take the two extreme bending moments to which a vessel is subjected, viz.: (1) hogging on the crest of a wave, and (2) sagging in the trough, and to construct a trochoid wave of such form as will give the same displacement of immersed body (in both cases) as obtained in smooth water. The curves are then calculated as explained in the foregoing, taking the height of wave as being of the length.

The subjoined table shows a specimen calculation of the moment of inertia of the sections, observing that although the rivets in this case are neglected for compression, it would probably be somewhat more accurate to include them.

Unless in exceptional cases it will be found sufficiently approximative for comparative purposes to multiply the displacement of the proposed vessel by one-thirtieth to one thirty-fifth of the length when the product will equal the maximum bending moment, as