1. 4. Local strength calculation

2. Response patterns of typical ship structures
Primary, secondary and tertiary structure

3. 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) .

4. 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 .

5. 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.

6. 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.

7. 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

9. Computational models for typical ship grillages
Bulkhead
Girder
Floor
Side
Strength computational model of a bottom grillage

10. 4.2 Tertiary structural response
A longitudinal at bottom
Strength computational model

11. A longitudinal at deck
Strength computational model:
Buckling (stability) computational model:

12. 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> )

13. A bottom shell in longitudinal framing system
Strength computational model: 4 a b
Stress at center along longitudinal direction (a/b> )

14. 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> )

15. 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)

16. 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)

17. Strength computational load
1、Bottom Structure load
Including: Bottom shell, longitudinal at bottom, grillage at bottom
the computational load

18. 2、Broadside Structure load

19. 3、Deck Structure load

21. 4、 Bulkhead Structure load

22. 4.3 Shear lag and effective breadth
Loading and resulting strain in flanges of simple beam

23. 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.

24. 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.

25. 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

26. 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,

27. The quantity is called the plate effectiveness.

28. 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

29. 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

30. 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.

31. 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.

32. 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

33. Bucking requirement for a panel
Bucking requirement for a longitudinal

34. Design analysis of the plating

35. 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

36. 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.

37. Design analysis of the longitudinal

39. 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.