Buoyancy curves Bending moment curves (a)----still water condition(b)---sagging condition(c)---hogging condition The total shear force and bending moment are thus obtained and these will include the still water bending moment considered previously. If actual loading conditions for the ship are considered which will make the above onditions worse, e.g. heavy loads amidships when the wave through is amidships, then the maximum bending moments in normal operating service can be found The ship's structure will thus be subjected to constantly fluctuating stresses resulting from these shear forces and bending moments as the waves move along the ship's length Stressing of the structure The bending of a ship causes stresses to be set up in the bottom shell plating and compressive stresses are set up in the decks. When the ship hogs, tensile stresses occur in the decks and compressive stresses in the bottom shell. This stressing, whether compressive or tensile, reduces in magnitude towards a position known as the neutral axis. The neutral axis in a ship is somewhere below half the depth and is in effect, a horizontal line drawn through ships section The fundamental bending equation for a beam is M_σ I Where M is the bending moment. I is the second moment of area of the section about its neutral axis, o is the stress at the outer fibres y is the distance from the neutral axis to the outer fibres This equation has been proved in full-scale tests to be applicable to the longitudinal bending of a ship. From the equation the expression is obtained for the stress in the material at some distance y from the neutral axis. the values m. i and y can be determined for the ship, and the resulting stresses in the deck and bottom shell can be found. The ratio l/y is nown as the section modulus, Z, when y is measured to the extreme edge of the section. The values are determined for the midship section, since the greatest moment will occur at or near midships(see Figure 2) The structural material included in the calculation for the second moment I will be all the longitudinal material which extends for a considerable proportion of the ship's length. This material will include side and bottom shell plating inner bottom plating(where fitted), centre girders and decks. The material forms what is known as the hull girder, whose dimensions are very large compared to its thickness Form "Merchant Ship Construction"by D.A. Taylor, 1980Buoyancy curves B Bending moment curves Fig.5 Dynamic loading of a ship’s structure (a)----still water condition (b)---sagging condition (c)---hogging condition The total shear force and bending moment are thus obtained and these will include the still water bending moment considered previously. If actual loading conditions for the ship are considered which will make the above conditions worse, e.g. heavy loads amidships when the wave through is amidships, then the maximum bending moments in normal operating service can be found. The ship’s structure will thus be subjected to constantly fluctuating stresses resulting from these shear forces and bending moments as the waves move along the ship’s length. Stressing of the structure The bending of a ship causes stresses to be set up in the bottom shell plating and compressive stresses are set up in the decks. When the ship hogs, tensile stresses occur in the decks and compressive stresses in the bottom shell. This stressing, whether compressive or tensile, reduces in magnitude towards a position known as the neutral axis. The neutral axis in a ship is somewhere below half the depth and is, in effect, a horizontal line drawn through ship’s section. The fundamental bending equation for a beam is y  = I M Where M is the bending moment, I is the second moment of area of the section about its neutral axis, σis the stress at the outer fibres, and у is the distance from the neutral axis to the outer fibres. This equation has been proved in full-scale tests to be applicable to the longitudinal bending of a ship. From the equation the expression y I M  = is obtained for the stress in the material at some distanceуfrom the neutral axis. The values M, I andуcan be determined for the ship, and the resulting stresses in the deck and bottom shell can be found. The ratio I/у is known as the section modulus, Z, whenуis measured to the extreme edge of the section. The Values are determined for the midship section, since the greatest moment will occur at or near midships (see Figure 2). The structural material included in the calculation for the second moment I will be all the longitudinal material which extends for a considerable proportion of the ship’s length. This material will include side and bottom shell plating, inner bottom plating (where fitted), centre girders and decks. The material forms what is known as the hull girder, whose dimensions are very large compared to its thickness. (Form “Merchant Ship Construction” by D.A. Taylor, 1980)