13.5Fatigue Assessment

13.5.2.1

The maximum (absolute) value of the normal and shear stresses shall never exceed the elastic limit $\left(f_{y}, \tau_{y}\right)$ for the material under cyclic loading.

13.5.2.2

The maximum stress range shall not exceed $1.5 f_{y}$ for normal stresses and $1.5 f_{y} / \sqrt{3}$ for the shear stresses under any circumstance.

13.5.2.3 Constant stress range

The actual normal and shear stress range $f$ and $\tau$ at a point of the structure subjected to $N_{\mathrm{sc}}$ cycles in life shall satisfy.

$f \leq f_{\mathrm{fd}}=\mu_{r} f_{\mathrm{f}} / \gamma_{\mathrm{mft}}$

$\tau \leq \tau_{\mathrm{fd}}=\mu_{r} \tau_{\mathrm{f}} / \gamma_{\mathrm{mft}}$

where

• $\mu_{r}=$ correction factor (see 13.2.1),

• $\begin{aligned} \gamma_{\mathrm{mf}} & =\text { partial safety factor against fatigue failure } \\ & \text { given in Table 25, and }\end{aligned}$

• $f_{\mathrm{f}}, \tau_{\mathrm{f}}=$ normal and shear fatigue strength ranges for the actual life cycle, $N_{\mathrm{SC}}$, obtained from 13.4.

13.5.2.4 Variable stress range

Fatigue assessment at any point in a structure, wherein variable stress ranges $f_{\mathrm{fi}}$ or $\tau_{\mathrm{fi}}$ for $n_{i}$ number of cycles $(i=1$ to $r$) are encountered, shall satisfy the following:

a) For normal stress ($f$)

Figure description:

Uncorrected Fatigue Strength Design Chart

Uncorrected Fatigue Strength vs Number of Stress Cycles

Legend

• Detail category 100 — color: black; symbol: solid line
• Detail category 80 — color: black; symbol: solid line

Annotations

• Stress range corresponding to $2 \times 10^6$ cycles (vertical_line - position: x = 2e6)
• Detail category (\zeta_{rn} (text_label - position: pointing to intersection points at 2e6 and 5e6 cycles))
• $d_s = 5$ (text_label - position: between the two lines near x = 2e7, indicating slope exponent)
• 100 (text_label - position: x = 2e6, y = 100)
• 80 (text_label - position: x = 2e6, y = 80)
• 83 (text_label - position: x = 5e6, y = 83)
• 67 (text_label - position: x = 5e6, y = 67)

FIG. 23 S-N CURVE FOR SHEAR STRESS

$\frac{\sum_{i=1}^{r_{s}} n_{i} f_{i}^{3}}{5 \times 10^{6}\left(\mu f_{\mathrm{fn}} / \gamma_{\mathrm{mft}}\right)^{3}}+\frac{\sum_{j=\gamma_{s}}^{r} n_{j} f_{j}^{5}}{5 \times 10^{6}\left(\mu f_{\mathrm{fn}} / \gamma_{\mathrm{mft}}\right)^{5}} \leq 1.0$

b) For shear stresses (τ)

$\sum_{i=1}^{r} n_{i} \tau_{\mathrm{fi}}^{5} \leq 5 \times 10^{6}\left(\mu \tau_{\mathrm{fn}} / \gamma_{\mathrm{mft}}\right)^{5}$

where $\gamma_{5}$ is the summation upper limit of all the normal stress ranges $\left(f_{i}\right)$ having magnitude lesser than $\left(\mu_{\mathrm{c}} f_{\mathrm{fn}} / \gamma_{\mathrm{mft}}\right)$ for that detail and the lower limit of all the normal stress ranges $\left(f_{j}\right)$ having magnitude greater than $\left(\mu_{\mathrm{c}} f_{\mathrm{fn}} / \gamma_{\mathrm{mft}}\right)$ for the detail. In the above summation all normal stress ranges, $f_{i}$, and $\tau_{\mathrm{i}}$ having magnitude less than $0.55 \mu_{\mathrm{c}} f_{\mathrm{fn}}$, and $0.55 \mu_{\mathrm{c}} \tau_{\mathrm{fn}}$ may be disregarded.