# Fatigue Limit State Design of Rail Welds of Crane Girders According to EN 1993-6

### Technical Article

Based on the technical article about the ultimate limit state design of rail welds, the following explanation refers to the process of fatigue design of rail welds. In particular, this article explains in detail the effects of considering the eccentric wheel load of 1/4 of the rail head width.

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A fatigue design is generally only required for components of the crane runway that are exposed to stress changes due to vertical wheel loads ( [2] , Chapter 9.1 (3)). The corresponding note of the standard also states that stress changes due to side loads are usually negligible. However, these should be taken into account for the design of connections or for a high number of recurring acceleration and braking forces. This results in only vertical wheel loads, which according to [3] , Chap. 2.12.1 (7) with the corresponding dynamic factors.

Dynamic factors for modifying the vertical wheel loads:

φ _{fat, 1} = (1 + φ _{1} )/2

φ _{fat, 2} = (1 + φ _{2} )/2

#### Stresses due to wheel loads

In contrast to the ultimate limit state design, the stresses in the fatigue design refer to the angle legs of the weld. It is necessary to consider σ-stresses due to wheel load as well as local and global shear stresses due to shear force [4] , Chap. 5 (6).

Figure 01 - Weld Stresses in Fatigue Design

The special feature in the fatigue design of welds according to [2] is the consideration of the eccentric wheel load application of ¼ of the rail head width from a damage class of the crane of S3 ([2], Chapter 9.3.3 (1)). Thus, if the crane has a damage class ≥ S3 on the crane runway, the local stresses due to wheel loads on the upper flange including a portion of eccentric wheel load must be determined. [1] shows a simple engineering model for determining the increased wheel load.

Figure 02 - Increased Wheel Load in Case of Eccentric Wheel Load Application

For the calculation of shear stresses, the local shear stress according to [2], Chap. 5.7.2 (1) with 20% of the vertical stress from the wheel load. Furthermore, the global shear stresses from the shear force difference of a crossing ∆V have to be applied.

Figure 03 - Stress Calculation in Weld

Both for the calculation of the wheel load stresses and for the determination of the cross-section values, the worn rail height may be applied at 12.5% [2], chap. 5.6.2 (3). The effective load application length is calculated analogously to the procedure in the ultimate limit state design.

#### Limit state designs of fatigue

The fatigue design is performed with the stress ranges resulting from the structural analysis. Stress ranges from global stresses result as follows:

∆σ = σ _{max} - σ _{min}

∆τ = τ _{max} - τ _{min}

For local stresses, the stress ranges result for the corresponding maximum values because the minimum values are 0.

#### Damage equivalent stress range

The task is to transform a multi-level stress collective into a single-level collective with the same damage and to determine the resulting equivalent stress range in relation to 2 ∙ 10 ^{6} stress cycles.

Figure 04 - Multi-Level Stress Spectrum

Using the standardized Wöhler lines (slope m = 3 for longitudinal stresses and slope m = 5 for shear stresses) and the maximum numbers of working cycles, depending on the damage class of the crane according to [3], Table 2.11, the following formulas can be derived.

Calculation of the equivalent stress ranges:

$$\begin{array}{l}{\mathrm\sigma}_{\mathrm E,2}\;=\;\lbrack\frac1{2\;\cdot\;10^6}\;\cdot\;\mathrm\Sigma(\mathrm{Δσ}_\mathrm i^\mathrm m\;\cdot\;{\mathrm n}_\mathrm i)\rbrack^{1/\mathrm m}\\{\mathrm\tau}_{\mathrm E,2}\;=\;\lbrack\frac{\displaystyle1}{\displaystyle2\;\cdot\;10^6}\;\cdot\;\mathrm\Sigma(\mathrm{Δτ}_\mathrm i^\mathrm m\;\cdot\;{\mathrm n}_\mathrm i)\rbrack^{1/\mathrm m}\end{array}$$

The following graphic is displayed on the basis of the selected Wöhler line:

Figure 05 - Damage Equivalent Stress Range Within Used S-N Curve

Now, the final design can be performed by means of the design detail to be determined, in this case the weld, and the associated notch case (∆σ _{c} and ∆τ _{c} ). The construction details are shown in [4], Tab. 8.1 - 8.10, especially Table 8.10, which covers some details of the crane girder.

The partial safety factors depend on the planned inspection intervals and result from [4], Tab. 3.1 and [2], NA/Tab. NA.3:

$$\begin{array}{l}\frac{{\mathrm\gamma}_\mathrm{Ff}\;\cdot\;{\mathrm{Δσ}}_{\mathrm E,2}}{\displaystyle\frac{{\mathrm{Δσ}}_\mathrm c}{{\mathrm\gamma}_\mathrm{Mf}}}\;<\;1,00\\\frac{{\mathrm\gamma}_\mathrm{Ff}\;\cdot\;{\mathrm{Δτ}}_{\mathrm E,2}}{\displaystyle\frac{{\mathrm{Δτ}}_\mathrm c}{{\mathrm\gamma}_\mathrm{Mf}}}\;<\;1,00\end{array}$$

According to [4], chap. 5 (6) for the designs of the welds.

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