4. Local strength calculation
Response patterns of typical ship structures Primary, secondary and tertiary structure
Secondary response comprises the stress and deflection of a single panel of stiffened plating, e.g., the panel of bottom structure contained between two adjacent transverse bulkheads. The loading of the panel is normal to its plane and the boundaries of the secondary panel are usually formed by other secondary panels (side shell and bulkheads) .
Tertiary response describes the out-of-plane deflection and associated stress of an individual panel of plating. The loading is normal to the panel, and its boundaries are formed by the stiffeners of the secondary panel of which it is a part .
4.1 Secondary structural response Orthotropic plate theory Orthotropic plate theory refers to the theory of bending of plates having different flexural rigidities in the two orthogonal directions. In applying this theory to panels having discrete stiffeners we idealize the structure by assuming that the structural properties of the stiffeners may be approximated by their average values, which are assumed to be distributed uniformly over the width or length of the plate.
Beam-on-elastic-foundation theory The beam on elastic foundation solution is suitable for a panel in which the stiffeners are uniform and closely spaced in one direction and more sparse in the other. One of the latter members may be thought of as an individual beam having an elastic support at its point of intersection with each of the closely-spaced orthogonal beams.
Grillage theory In the grillage method, each stiffener in the two orthogonal sets of members is represented as a simple beam. The finite element method
Computational models for typical ship grillages Bulkhead Girder Floor Side Strength computational model of a bottom grillage
4.2 Tertiary structural response A longitudinal at bottom Strength computational model
A longitudinal at deck Strength computational model: Buckling (stability) computational model:
A bottom shell in longitudinal framing system Strength computational model: 4 a b Stress at mid-length of short side along longitudinal direction (a/b>1.5-2.0)
A bottom shell in longitudinal framing system Strength computational model: 4 a b Stress at center along longitudinal direction (a/b>1.5-2.0)
A bottom shell in longitudinal framing system Strength computational model: 4 a b Stress at mid-length of long side along transverse direction (a/b>1.5-2.0)
transverse framing system A bottom shell in transverse framing system Strength computational model: 4 a b Stress at mid-length of long side along longitudinal direction (b/a>2.0)
A bottom shell in transverse framing system 4 a b A bottom shell in transverse framing system Strength computational model: Stress at center along longitudinal direction (b/a>2.0)
Strength computational load 1、Bottom Structure load Including: Bottom shell, longitudinal at bottom, grillage at bottom the computational load
2、Broadside Structure load
3、Deck Structure load
4、 Bulkhead Structure load
4.3 Shear lag and effective breadth Loading and resulting strain in flanges of simple beam
An important effect of this edge shear loading of a plate member is a resulting nonlinear variation of the longitudinal stress distribution. This is in contrast to the uniform stress distribution predicted in the beam flanges by the elementary beam equation.
In many practical cases, the departure from the value predicted by the elementary beam equation will be small. But in certain combinations of loading and structural geometry, the effect referred to by the term shear lag must be taken into consideration if an accurate estimate of the maximum stress in the member is to be made.
Deck longitudinal stress, illustrating the effect of shear lag The effect of shear lag in a ship is to cause the stress distribution in the deck, for example, to depart from the constant value predicted by the elementary beam equation. A typical distribution of the longitudinal deck stress in a ship subject to a vertical sagging load is sketched in the following figure. Deck longitudinal stress, illustrating the effect of shear lag
The effective breadth, , is defined as the breadth of plate that, if stressed uniformly at the level across its width, would sustain the same total load in the x-direction as the non-uniformly stressed plate. Hence,
The quantity is called the plate effectiveness.
Strength requirement for a panel Design analysis of the bottom shell in transverse framing system Strength requirement for a panel Stability requirement for a panel Pressure satisfying both the requirements of strength and buckling
H satisfying the requirements of both strength and buckling 220 240 300 350 400 H, m 12.9 15.4 24.0 32.6 42.6 b/t 37 35 32 29 27 6.4 7.7 12.0 16.3 21.3 52 49 45 41 38 H satisfying the requirements of both strength and buckling b/t satisfying the requirement of buckling only
Conclusions: If the buckling load is required to reach yielding strength, the computed H is much higher than real value of H for most real ships and the value of b/t is quite small as well. For this case, the structure design is NOT reasonable. If the buckling load is designed to reach the half yielding strength, the use of low strength steel ( ) is Okay only.
Conclusions: 3) Reduction computation has to be considered to determine the plating thickness due to the poor stability performance of the bottom shell in transverse frame system.
Strength requirement for a panel Design analysis of the bottom shell and the longitudinal at bottom in longitudinal framing system Strength requirement for a panel Strength requirement for a longitudinal
Bucking requirement for a panel Bucking requirement for a longitudinal
Design analysis of the plating
H satisfying the requirements of both strength and buckling 220 240 300 350 400 H, m 5.9 7.0 10.9 14.9 19.4 b/t 60 58 52 48 45 2.9 3.5 5.4 7.4 9.7 85 82 74 68 64 H satisfying the requirements of both strength and buckling b/t satisfying the requirement of buckling only
Conclusions: For high strength steel ( ), the size of plating is controlled by the requirement of buckling. For low strength steel ( ), the size of plating is controlled by the requirement of strength.
Design analysis of the longitudinal
The size of the longitudinal at deck is controlled by the stability requirement. The size of the longitudinal at bottom is controlled by the strength requirement.