5 Stress Concentration Factors

5.1 Unsymmetrical stiffener

5.1.1 The stress concentration factor K_n for unsymmetrical flange of built-up and rolled angle stiffeners under lateral load, calculated at the web’s mid-thickness position, as shown in Figure 5, is to be taken as:

where:

for built-up profiles.

for rolled angle profiles.

b_g-n50 : Eccentricity of the stiffener equal to the distance from flange’s edge to web’s centreline, in mm, as shown in Figure 6.

b_f-n50 : Net breadth of flange, in mm, as shown in Figure 6.

t_f-n50 : Net flange thickness, in mm, as shown in Figure 6.

h_stf-n50 : Net stiffener height, including face plate, in mm, as shown in Figure 6.

t_w-n50 : Net web thickness, in mm, as shown in Figure 6.

h_w-n50 : Net web’s height stiffener, in mm, as shown in Figure 6.

t_p-n50 : Net thickness of attached plating, in mm, as shown in Figure 6.

ψ_Z : Coefficient given as:

Z_n50 : Net section modulus, in cm³, of stiffener with an attached plating breadth equal to the stiffener spacing.

Figure 5: Bending stress in stiffener with symmetrical and unsymmetrical flange

Figure 6 : Stiffener - net scantling

5.1.2 Bulb profiles

For bulb profiles K_n factor is to be calculated using the equivalent built-up profile as shown in Figure 7. The flange of the equivalent built-up profile is to have the same properties as the bulb flange, i.e. same cross sectional area and moment of inertia about the vertical axis and neutral axis position.

For HP bulb profiles, examples of the equivalent built up profile dimensions are listed in Table 3.

Figure 7 : Bulb profile and equivalent built-up profile

Table 3 : HP equivalent built-up profile dimensions

HP-bulb		Equivalent built-up flange in gross thickness
Height(mm)	Gross web thickness, t_w-gr (mm)	b_f(mm)	t_f-gr(mm)	b_g(mm)
200	9– 13	t_w-gr+24.5	22.9	(t_w-gr+0.9)/2
220	9– 13	t_w-gr+27.6	25.4	(t_w-gr+ 1.0)/2
240	10– 14	t_w-gr+ 30.3	28.0	(t_w-gr+1.1)/2
260	10– 14	t_w-gr+ 33.0	30.6	(t_w-gr+ 1.3)/2
280	10– 14	t_w-gr+ 35.4	33.3	(t_w-gr+ 1.4)/2
300	11– 16	t_w-gr+ 38.4	35.9	(t_w-gr+ 1.5)/2
320	11– 16	t_w-gr+ 41.0	38.5	(t_w-gr+ 1.6)/2
340	12– 17	t_w-gr+ 43.3	41.3	(t_w-gr+ 1.7)/2
370	13– 19	t_w-gr+47.5	45.2	(t_w-gr+ 1.9)/2
400	14– 19	t_w-gr+51.7	49.1	(t_w-gr+2.1)/2
430	15– 21	t_w-gr+ 55.8	53.1	(t_w-gr+2.3)/2

5.2 Longitudinal stiffener end connections

5.2.1 The stress concentration factors K_a and K_b are given in Table 4 for end connection of stiffeners subjected to axial and lateral loads. The values given in Table 4 for soft toe are valid provided the toe geometry complies with the requirements given in [5.2.5]. The stress concentration factor K_b given for lateral loads are to be used also for stress due to relative displacements.

5.2.2 Other connection types

When connection types other than those given in Table 4 are proposed, the fatigue strength for the proposed connection type is to be assessed either by performing a very fine mesh FE analysis as described in Ch 9, Sec 5 to obtain directly the hot spot stress, or by calculating the stress concentration factor using FE analysis according to [5.3].

5.2.3 Overlapped connection

Overlapped connection types for longitudinal stiffeners, i.e. attachments welded to the web of the longitudinals, are not to be used in the cargo hold region.

5.2.4 End stiffener without connection to web stiffener

Where the web stiffener is omitted or not connected to the longitudinal flange in way of:

Side shell below 1.1 T_sc.
Bottom.
Inner hull longitudinal bulkhead below 1.1 T_sc.
Hopper.
Topside tank sloping plating below 1.1 T_sc.
Inner bottom.

the following is required:

A complete collar as defined in Figure 8 (i.e. connection type ID 31 of Table 4), or,
A detail design for cut-outs as described in Ch 9, Sec 6, [2.1].

Equivalence to cut-outs given in Ch 9, Sec 6, [2.1]may be accepted provided it is assessed for fatigue by using comparative FE analysis which is based on hot spot stress around the cut-out in the web plate of the primary supporting member inclusive of the collar, as given in Ch 9, Sec 6, [2.2].

Figure 8 : Complete collar

5.2.5 Soft toe of web stiffener and backing bracket

The toe geometry end connection of web stiffener and backing bracket is to comply with the following:

θ ≤ 20

h_toe ≤ max (t_bkt-gr; 15)

where:

θ : Angle of the toe, in deg, as shown in Figure 9.

h_toe : Height of the toe, in mm, as shown in Figure 9.

t_bkt-gr : Gross thickness of the bracket, in mm.

5.2.6 Recommended detail designs

Recommended detail designs for longitudinal end connections with soft toes and backing brackets are given in Figure 9.

Figure 9 : Detail design for soft toes and backing brackets

Table 4: Stress concentration factors

ID	Connection type ⁽²⁾⁽³⁾	Point ‘A’		Point ‘B’
ID	Connection type ⁽²⁾⁽³⁾	K_a	K_b	K_a	K_b
1^⁽¹⁾		1.28 for d≤150 1.36 for 150< d≤250 1.45 for d> 250	1.40 for d ≤150 1.50 for 150< d≤250 1.60 for d > 250	1.28 for d≤150 1.36 for 150< d≤250 1.45 for d> 250	1.60
2⁽¹⁾		1.28 for d≤150 1.36 for 150 < d≤250 1.45 for d> 250	1.40 for d ≤150 1.50 for 150 < d≤250 1.60 for d > 250	1.14 for d ≤150 1.24 for 150 < d≤250 1.34 for d> 250	1.27
3		1.28	1.34	1.52	1.67
4		1.28	1.34	1.34	1.34
5		1.28	1.34	1.28	1.34
6		1.52	1.67	1.34	1.34
7		1.52	1.67	1.52	1.67
8		1.52	1.67	1.52	1.67
9		1.52	1.67	1.28	1.34
10		1.52	1.67	1.52	1.67
11		1.28	1.34	1.52	1.67
12		1.52	1.67	1.28	1.34
13		1.52	1.67	1.52	1.67
14		1.52	1.67	1.34	1.34
15		1.52	1.67	1.52	1.67
16		1.52	1.67	1.28	1.34
17		1.28	1.34	1.52	1.67
18		1.28	1.34	1.34	1.34
19		1.28	1.34	1.28	1.34
20		1.28	1.34	1.52	1.67
21		1.28	1.34	1.52	1.67
22		1.28	1.34	1.34	1.34
23		1.28	1.34	1.28	1.34
24		1.28	1.34	1.52	1.67
25⁽¹⁾		1.28 for d≤150 1.36 for 150 < d≤250 1.45 for d > 250	1.40 ford ≤ 150 1.50 for 150 < d ≤ 250 1.60 ford > 250	1.14 for d ≤ 150 1.24 for 150 < d ≤ 250 1.34 for d> 250	1.25 for d ≤ 150 1.36 for 150 < d ≤ 250 1.47 for d > 250
26		1.28	1.34	1.34	1.47
27		1.52	1.67	1.34	1.47
28		1.52	1.67	1.34	1.47
29		1.28	1.34	1.34	1.47
30		1.28	1.34	1.34	1.47
31⁽⁴⁾		1.13	1.20	1.13	1.20
32⁽⁴⁾⁽⁵⁾ ⁽⁶⁾		1.13	1.14	N/A	N/A
⁽¹⁾ The attachment length d, in mm, is defined as the length of the welded attachment on the longitudinal stiffener flange without deduction of scallop. ⁽²⁾ Where the longitudinal stiffener is a flat bar and there is a web stiffener/bracket welded to the flat bar stiffener, the stress concentration factor listed in the table is to be multiplied by a factor of 1.12 when the thickness of attachment is thicker than the 0.7 times thickness of flat bar stiffener. This also applies to unsymmetrical profiles where there is less than 8 mm clearance between the edge of the stiffener flange and the attachment, e.g. bulb or angle profiles where the clearance of 8 mm cannot be achieved. ⁽³⁾ Designs with overlapped connection / attachments, see [5.2.3]. ⁽⁴⁾ ID.31 and 32 refer to details where web stiffeners are omitted or not connected to the longitudinal stiffener flange. See [5.2.4] ⁽⁵⁾ For connection type ID. 32 with no collar and/or web plate welded to the flange, the stress concentration factors provided in this table are to be used irrespective of slot configuration. ⁽⁶⁾ The fatigue assessment point ‘A’ is located at the connection between the stiffener web and the transverse web frame or lug plate.

5.3 Alternative design

5.3.1 Derivation of alternative stress concentration factors

Upon agreement by the Society, the geometrical stress concentration factors for alternative designs are to be calculated by a very fine mesh FE analysis according to the requirements given in Ch 9, Sec 5. Additional requirements for derivation of geometrical stress concentration factors for stiffener end connections using very fine mesh FE analysis are given below:

a) FE model extent: the FE model, as shown in Figure 10, is to cover at least four web frame spacings in the longitudinal stiffener direction with the detail to be considered located at the middle frame. The same type of end connection is to be modelled at all the web frames. In the transverse direction, the model may be limited to one stiffener spacing.

b) Load application: in general, two loading cases are to be considered:

Axial loading by enforced displacement applied to the model ends and
Lateral loading by unit pressure load applied to the shell plating.

c) Boundary conditions:

Symmetry conditions are applied along the longitudinal cut of the plate flange, along transverse and vertical cuts on web frames and on top of the web stiffener.
For lateral pressure loading: the model is to be fixed in all degrees of freedom at both forward and aft ends.
For axial loading: the model is to be fixed for displacement in the longitudinal direction at the aft end of the model while enforced axial displacement is applied at the forward end, or vice versa.

d) FE mesh density: At the location of the hot spots under consideration, the element size is to be in the order of the thickness of the stiffener flange or 10 mm depending on the type of stiffener. In the remaining part of the model, the element size is to be in the order of s/10, where s is the stiffener spacing.

Figure 10 : Fine mesh finite element model for derivation of geometrical stress concentration factor (example of stiffener with flange)

For the 2 loading cases specified above, the stress concentration factors are determined as follows:

For the axial loading case:
For the bending loading case:

σ_HSAx : Hot spot stress, in N/mm², determined at the stiffener flange for the axial load.

σ_NomAx : Nominal axial stress, in N/mm², calculated at the stiffener flange according to [3.1] for the axial load applied for the FE calculation.

σ_HSBd : Hot spot stress, in N/mm², determined at the stiffener flange for the unit pressure load.

σ_NomBd : Nominal bending stress, in N/mm², calculated at the stiffener flange according to [4.1] in way of the hot spot for the unit pressure load applied for the FE calculation.

The derivation of geometrical stress concentration factors for alternative designs is to be documented and provided to the Society.