Longitudinal stresses Static loading If the ship is considered floating in still water, two different forces will be acting upon it along its length. The weight of the ship and its contents will be acting vertically downwards. The buoyancy or vertical component of hydrostatic pressure will be acting upwards In total, the two forces exactly equal and balance one another such that the ship floats at some particular draught. The centre of the buoyancy force and the centre of the weight will be vertically in line. However, at particular points along the ship's length the net effect may be an access of buoyancy or an excess of weight. This net effect produces a loading of the structure, as with a beam. This loading results in shearing forces and bending moments being set up in the ship's structure which tend to bend it The static forces acting on a ships structure are shown in Figure 2(a). This distribution of weight and buoyancy will also result in a variation of load, shear forces and bending moments along the length of the ship, as shown in Figure 2(b)-(d ). Depending upon the direction in which the bending moment acts, the ship will bend in a longitudinal vertical plane. The bending moment is known as the still water bending moment(SWBM). Special terms are used to describe the two extreme cases: where the buoyancy amidships exceeds the weight, the ship is said to"hog, and this condition is shown in Figure 3, where the weight amidships exceeds the buoyancy, the ship is said to"sag" and this condition is shown in Figure 4 Excess of buoyancy Fig 3 Hogging condition Fig. 4 Sagging condition Dynamic loading If the ship is now considered to be moving among waves, the distribution of weight will be the same. The distribution of buoyancy, however, will vary as a result of the waves. The movement of ship will also introduce dynamic forces The traditional approach to solving this problem is to convert this dynamic situation into an equivalent static one. To do this, the ship is assumed to be balanced on a static wave of trochoidal form and length equal to the ship The profile of a wave at sea is considered to be a trochoid. This gives waves where the crests are sharper than the hroughts. The wave crest is considered initially at midships and then at the ends of the ship The maximum hogging and sagging moments will thus occur in the structure for the particular loaded condition considered,as shown in Figure 5 Still water Wave trough amidships Wave crest amidshipsLongitudinal stresses Static loading If the ship is considered floating in still water, two different forces will be acting upon it along its length. The weight of the ship and its contents will be acting vertically downwards. The buoyancy or vertical component of hydrostatic pressure will be acting upwards .In total, the two forces exactly equal and balance one another such that the ship floats at some particular draught. The centre of the buoyancy force and the centre of the weight will be vertically in line. However, at particular points along the ship’s length the net effect may be an access of buoyancy or an excess of weight. This net effect produces a loading of the structure, as with a beam. This loading results in shearing forces and bending moments being set up in the ship’s structure which tend to bend it. The static forces acting on a ship’s structure are shown in Figure 2(a). This distribution of weight and buoyancy will also result in a variation of load, shear forces and bending moments along the length of the ship, as shown in Figure 2(b)-(d). Depending upon the direction in which the bending moment acts, the ship will bend in a longitudinal vertical plane. The bending moment is known as the still water bending moment (SWBM). Special terms are used to describe the two extreme cases: where the buoyancy amidships exceeds the weight, the ship is said to “hog”, and this condition is shown in Figure 3, where the weight amidships exceeds the buoyancy, the ship is said to “sag”, and this condition is shown in Figure 4. Excess of buoyancy Fig. 3 Hogging condition Fig. 4 Sagging condition Dynamic loading If the ship is now considered to be moving among waves, the distribution of weight will be the same. The distribution of buoyancy, however, will vary as a result of the waves. The movement of ship will also introduce dynamic forces. The traditional approach to solving this problem is to convert this dynamic situation into an equivalent static one. To do this, the ship is assumed to be balanced on a static wave of trochoidal form and length equal to the ship. The profile of a wave at sea is considered to be a trochoid. This gives waves where the crests are sharper than the throughts. The wave crest is considered initially at midships and then at the ends of the ship. The maximum hogging and sagging moments will thus occur in the structure for the particular loaded condition considered, as shown in Figure 5. Still water Wave trough amidships Wave crest amidships Excess of weight