3 Hot Spot Stress for Details Different From Web-Stiffened Cruciform Joints

3.1 Welded details

3.1.1

For hot spot type ‘a’, the structural hot spot stress, σ_HS, is calculated from a finite element analysis with t_n50 × t_n50 mesh density and is obtained by the following formula:

σ_HS = 1.12 ⋅ σ

where:

σ : Surface principal stress, in N/mm², read out at a distance t_n50/2 away from the intersection line.

t_n50 : Plate net thickness, in mm, in way of the weld toe.

At structural details where the hot spot type ‘a’ is classified as a web-stiffened cruciform joint, the stress read out procedure of [4.2] is to be applied.

For hot spot type ‘b’, the stress distribution is not dependent on the plate thickness; the structural hot spot stress, σ_HS, is derived from a finite element analysis with mesh density 10×10 mm and is obtained by the following formula:

σ_HS = 1.12 ⋅ σ

where:

σ : Surface principal stress, in N/mm², read out at an absolute distance from the intersection line of 5 mm.

3.1.2 Stress read out methods

Depending on the element type, one of the following stress read out method is to be used:

With 4-node shell element:
- Element surface stress components at the centre points are linearly extrapolated to the line A-A as shown in Figure 15 to determine the stress components for load case ‘i1’ and ‘i2’ at the stress read out point located at a distance t_n50/2 from the intersection line for type 'a' hot spot. Two principal hot spot stress ranges are determined at the stress read out point from the stress components tensor differences (between load case ‘i1’ and ‘i2’) calculated from each side (side L, side R) of line A-A. The angle θ between the direction x of the element co-ordinate system and the principal direction pX of the principal hot spot stress range co-ordinate system has to be determined.
• With 8-node shell element:
- With a t_n50 × t_n50 element mesh using 8-node element type, the element mid-side node is located on the line A-A at a distance t_n50/2 for type 'a' hot spots. This node coincides with the stress read out point. The element surface stress components for load case ‘i1’ and ‘i2’ can be used directly without extrapolation within each adjacent element located on each side (side L, side R) of the line A-A as illustrated in Figure 16. Two principal hot spot stress ranges are determined at the stress read out point from the stress components tensor difference (between load case ‘i1’ and ‘i2’) calculated from each side of line A-A. The angle θ between the direction x of the element coordinate system and the principal direction pX of the principal hot spot stress range coordinate system has to be determined.

For fatigue assessment of type ‘b’ hot spots, a beam element is to be used to obtain the fatigue stress range. The stress range is to be based on axial and bending stress in the beam element. The beam element is to have the same depth as the connecting plate thickness while the in-plane width is negligible.

Figure 15 : Determination of stress read out points and hot spot stress for 4-node element

Figure 16 : Determination of stress read out points and hot spot stress for 8-node element

3.1.3

The above read out procedure is based on element surface stresses. Generally, in FE software the element stresses are calculated at the Gaussian integration points located inside the element. Depending on the element type implemented in the FE software, it may be necessary to perform several interpolations in order to determine the actual stress at the considered stress read out point at the surface of the element mid-point or element edge.

3.2 Base material

3.2.1 For fatigue assessment at a free plate edge, a beam element is to be used to obtain the fatigue stress range. The beam element is to have the same depth as the connecting plate thickness while the in-plane width should be negligible.

3.3 Bent hopper knuckle

3.3.1 The hot spot stress at the inner bottom/hopper sloping plate in transverse and longitudinal directions (i.e. hot spots 1, 2 and 3 defined in Ch 9, Sec 2, Table 5) of a bent hopper knuckle is to be taken as the surface principal stress read out from a point shifted away from the intersection line between the considered member and abutting member by the weld leg length.

The hot spot stress, in N/mm², is obtained by the following formula:

σ_HS = σ_shift

where:

σ_shift : Surface principal stress, in N/mm², at the shifted read out position as defined in [4.2.1] and taken as:

σ_shift = σ_membrane (x_shift) + σ_bending (x_shift)

σ_bending (x_shift): Bending stress, in N/mm², at x_shift position.

σ_membrane(x_shift): Membrane stress at x_shift position, in N/mm².

3.3.2

The procedure for calculation of hot spot stress at flange such as inner bottom /hopper sloping plate is the same that for web-stiffened cruciform joints as described in [4.2.1]. The procedure that applies for hot spots on the ballast tank side of the inner bottom/hopper plate in way of a bent hopper knuckle is in principle the same as that applied on the cargo tank side of the inner bottom plate for welded knuckle in Figure 18 and Figure 19. The intersection line is taken at the mid-thickness of the joint assuming median alignment. The plate angle correction factor and the reduction of bending stress as applied for a web-stiffened cruciform joint in [4.2.2] are not to be applied for the bent hopper knuckle type.

3.3.3

The stress at hot spots located in way of the web such as transverse web and side girder (i.e. hot spots 4, 5 and 6 defined in Ch 9, Sec 2, Table 5) at a bent hopper knuckle type is to be derived as described for web-stiffened cruciform joints in [4.3.1].