### 1. Introduction

### 2. Notations

### 3. Types of Stresses

### 3.1 Nominal Stress

### 3.2 Effective Notch Stress

### 3.3 Hot-spot Stress

#### 3.3.1 Type a hot-spot stress

#### 3.3.2 Type b hot-spot stress

### 4. Basic Design S-N Curves

### 4.1 Basic Design S-N Curves of DNV GL

*s*

_{log}

*is 0.2 for weld joints of non-tubular and tubular members under an in-air environment (IA), a seawater environment with cathodic protection (CP), and a free corrosion environment (FC). In the case of high-strength steel with a yield strength exceeding 500 MPa,*

_{N}*s*

_{log}

*is 0.162.*

_{N}### 4.2 Basic Design S-N Curves of ABS

*N*be the number of cycles to fatigue failure. The basic design S-N curves corresponding to the cases where the number of failure cycles are smaller and larger than N

_{Q}*are expressed as Eqs. (7) and (8), respectively.*

_{Q}*N*in DNV GL, which is denoted as

*s*, is constant regardless of the SDCs, but those in ABS, log σ, vary with the SDCs, which were copied from Almar-Næss (1985) and BS.

_{log N}### 4.3 Basic Design S-N Curves of BS

*m*) and intercept (log

*C*), as shown in Eq. (9). Table 8 lists the

_{d}*d*value according to the probability of failure. For example, if the probability of failure is 2.3%;

*d*equals 2.0 and

*C*corresponding to this

_{d}*d*becomes

*C*.

_{2}*d*was assumed to equal 2.0 for the BS S-N curves. Tables 9, -11 list the material constants for the three environments (the IA, CP, and FC). In Table 9,

*S*

*is the fatigue limit at 10 million cycles except for the S1 and S2 grades. Therefore, the IA environment S-N curves show an infinite life after 10 million cycles. BS also presents the S1 and S2 grades under shear stress conditions. S1 is used if fatigue cracking occurs in the weld toes, while the S2 is used for weld throats.*

_{OC}*S*,

_{rt}*S*, and

_{OC}*S*) are the slope change points, where the

_{O}_{V}*S*is listed in Table 10. The

_{rt}*S*and

_{OC}*S*are the fatigue strengths corresponding to 10 million and 50 million cycles, respectively. The S-N curves in the CP and FC environments cannot be applied to the cases under shear stresses.

_{OV}*S*corresponding to 50 million cycles. A bilinear S-N curve can be applied to variable loading conditions because the variable stress may sometimes exceed the fatigue limit, even though the average stress is less than the fatigue limit. For example, assuming that the second slope is 5 (

_{OV}*m*=5), the S-N curve can be obtained, as shown in Fig. 6(b).

### 4.4 Basic Design S-N Curves of IIW

*C*using equation (11) and substituting it into Eq. (10).

*m*=22.0. The basic design S-N curves for the shear stress application can be considered to be single sloped because they have a fatigue limit of 100 million cycles.

- Out of the 83 SDCs in the IIW code, select a reference structure detail, which should be most similar to the target.

- Derive two hot-spot stresses through finite element analyses for two structural details:

*σ*and_{hs,ref}*σ*corresponding to the reference structural detail and target one._{hs,assess}- Derive a new FAT (

*FAT*) based on the ratio of the hot-spot stresses using Eq. (13)._{assess}-To construct a new basic design S-N curve using the

*FAT*._{assess}

*m*=3.0).

### 4.5 Basic Design S-N Curves of EC3

*. EC3 determines the SDC based on Δσ*

_{C}*. For intervals less than 5 million cycles, the slope is 3.0. The fatigue strength at 5 million cycles is defined as Δσ*

_{C}*. The slope from 5 million cycles to 100 million cycles is 5.0. The fatigue strength at 100 million cycles is defined as Δσ*

_{D}*, which is the fatigue limit.*

_{L}### 5. Comparison between Codes

### 5.1 Comparison of Nominal SDCs

### 5.2 Comparison of the Probabilities of Failure

*d*= 2.0, the S-N curves of BS also have the same probability of failure as DNV GL and ABS. On the other hand, IIW and EC3 provide the S-N curves with a 5% probability of failure (refer to Table 15).