# Design for the Lower Flange of Suspension Cranes According to DIN EN 1993-6

### Technical Article

#### Ultimate Limit State

It has to be verified that the wheel loads can be absorbed by the bottom chord. In [2], Chapter 6.7, Equation 6.2 the following formula is given:

${\mathrm{F}}_{\mathrm{f},\mathrm{Rd}}=\frac{{\mathrm{l}}_{\mathrm{eff}}\xb7{\mathrm{t}}_{\mathrm{f}}^{2}\xb7\frac{{\mathrm{f}}_{\mathrm{y}}}{{\mathrm{\gamma}}_{\mathrm{M}0}}}{4\xb7\mathrm{m}}\xb7\left[1-{\left(\frac{{\mathrm{\sigma}}_{\mathrm{f},\mathrm{Ed}}}{{\displaystyle \frac{{\mathrm{f}}_{\mathrm{y}}}{{\mathrm{\gamma}}_{\mathrm{M}0}}}}\right)}^{2}\right]$

where

l_{eff} = effective length according to [2], Table 6.2

m = lever arm of wheel load at the transition flange-web according to [2], Equation 6.3

σ_{f,Ed} = bending stress in the centroidal axis of the flange due to global loading

Image 01 - Loading of Lower Flange by Wheel Loads

The following condition has to be met:

F_{z,Ed} ≤ F_{f,Rd}

Particularly for the calculation of the effective length according to [2], Table 6.2, the location to design in the runway girder as well as the axle base of the wheel loads have to be considered.

#### Serviceability Limit State/Fatigue

For the design of suspension cranes in the serviceability limit state according to [2], it is necessary to determine the local bending stresses in the lower flange due to wheel loads according to [2], Chapter 5.8. The calculation of the necessary coefficients is carried out according to [2], Table 5.2. Furthermore, you have to superimpose the respective global stresses with the local stresses due to wheel loads in the structural analysis.

According to NCI (Germany) on Chapter 5.8 of EN 1993-6, it is allowed to reduce the local stresses to 75 % for this superposition. This design verifies the elastic behavior of the lower flange.

#### Local Stresses in Lower Flange

There are different methods to determine the local stresses in the lower flange which are also shown in [3]. In [2], the calculation according to the FEM guideline 9.341 "Local girder stresses" has been taken over. The stresses are calculated here at the local points 0, 1 and 2 as shown in Figure 01.

The stresses are taken from the following formulas:

Longitudinal direction of the beam:

${\mathrm{\sigma}}_{\mathrm{ox},\mathrm{Ed},\mathrm{ser},\mathrm{i}}={\mathrm{c}}_{\mathrm{x},\mathrm{i}}\xb7\frac{{\mathrm{F}}_{\mathrm{z},\mathrm{Ed}}}{{\mathrm{t}}_{\mathrm{f}}^{2}}$

Transversal direction of the beam:

${\mathrm{\sigma}}_{\mathrm{oy},\mathrm{Ed},\mathrm{ser},\mathrm{i}}={\mathrm{c}}_{\mathrm{y},\mathrm{i}}\xb7\frac{{\mathrm{F}}_{\mathrm{z},\mathrm{Ed}}}{{\mathrm{t}}_{\mathrm{f}}^{2}}$

where

cx,i and cy,i according to [2], Table 5.2

$\mathrm\mu\;=\;\frac{2\;\cdot\;\mathrm n}{\left(\mathrm b\;-\;{\mathrm t}_\mathrm w\right)}$ according to [2], Chapter 5.8 (4), Equation 5.7

It must be noted that the stresses of the individual wheels should be superpositioned in case of small axle bases xw ≤ 1,5 b (see Figure 02). See [2], Chapter 5.8 (8)

#### Superposition with Global Stresses

According to [2], Chapter 7.5, the local stresses in the longer flange have to be superimposed with the global stresses from the structural analysis:

${\mathrm{\sigma}}_{\mathrm{v},\mathrm{Ed},\mathrm{ser}}=\sqrt{{\mathrm{\sigma}}_{\mathrm{\Sigma x},\mathrm{Ed},\mathrm{ser}}^{2}{\mathrm{\sigma}}_{\mathrm{\Sigma y},\mathrm{Ed},\mathrm{ser}}^{2}-{\mathrm{\sigma}}_{\mathrm{\Sigma x},\mathrm{Ed},\mathrm{ser}}\xb7{\mathrm{\sigma}}_{\mathrm{\Sigma y},\mathrm{Ed},\mathrm{ser}}3\xb7{\mathrm{\tau}}_{\mathrm{Ed},\mathrm{ser}}^{2}}\le \frac{{\mathrm{f}}_{\mathrm{y}}}{{\mathrm{\gamma}}_{\mathrm{m},\mathrm{ser}}}$

${\mathrm{\sigma}}_{\mathrm{\Sigma x},\mathrm{Ed},\mathrm{ser}}={\mathrm{\sigma}}_{\mathrm{x},\mathrm{Ed},\mathrm{ser}}0.75\xb7{\mathrm{\sigma}}_{\mathrm{ox},\mathrm{Ed},\mathrm{ser}}$

${\mathrm{\sigma}}_{\mathrm{\Sigma y},\mathrm{Ed},\mathrm{ser}}=0.75\xb7{\mathrm{\sigma}}_{\mathrm{oy},\mathrm{Ed},\mathrm{ser}}$

#### Summary

Several factors have to be considered for the design of the lower flange. The designed location in the runway girder plays especially an important role for the determination of the effective length. Furthermore, the axle base of the wheels is important because the wheel loads and their local stresses may be superpositioned in case of small distances.

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When using interrupted welds between rail and flange, make sure that the applied weld length does not exceed the length of the rigid load application of the wheel load according to Equation 6.1 in [1].

- Craneway and weld stress analysis
- Craneways and weld fatigue design
- Deformation analysis
- Plate buckling analysis for wheel load introduction
- Stability analysis for lateral torsional buckling according to the second-order analysis of torsional buckling (1D FEA element)

For the design according to Eurocode 3 the following National Annexes are available:

- DIN EN 1993-6/NA:2010-12 (Germany)
- NBN EN 1993-6/ANB:2011-03 (Belgium)
- SFS EN 1993-6/NA:2010-03 (Finland)
- NF EN 1993-6/NA:2011-12 (France)
- UNI EN 1993-6/NA:2011-02 (Italy)
- LST EN 1993-6/NA:2010-12 (Lithuania)
- NEN EN 1993-6/NB:2012-05 (The Netherlands)
- NS EN 1993-6/NA:2010-01 (Norway)
- SS EN 1993-6/NA:2011-04 (Sweden)
- CSN EN 1993-6/NA:2010-03 (Czech Republic)
- BS EN 1993-6/NA:2009-11 (United Kingdom)

- CYS EN 1993-6/NA:2009-03 (Cyprus)

In addition to the National Annexes (NA) listed above, you can also define a specific NA, applying user-defined limit values and parameters.

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- I would like to use the CRANEWAY add-on module to design a suspension crane. Where are the design points 0, 1, and 2 for the stress analysis on the bottom flange and for the fatigue design?
- How can I introduce releases on the supports in the CRANEWAY program to prevent the effect of continuity?
- Where can I change the steel grade of a crane girder? Although I have set Steel St 37.2 in RSTAB, but S235 is only used for the calculation in CRANEWAY.
- Is it possible to manually adjust detail categories or a stress cycle of the detail categories?
- How is it possible to optimize the calculation time in CRANEWAY?

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