Design for the Lower Flange of Suspension Cranes According to DIN EN 1993-6
Figure 01 - Loading of Lower Flange by Wheel Loads
![Figure 02 - Influence Parameters for the Calculation of the Effective Length According to [2], Tab. 6.2](/-/media/Images/website/pages/support-and-learning/support/knowledge-base/001519/02-en-png.png)
Figure 02 - Influence Parameters for the Calculation of the Effective Length According to [2], Tab. 6.2
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:
${\mathrm F}_{\mathrm f,\mathrm{Rd}}\;=\;\frac{{\mathrm l}_\mathrm{eff}\;\cdot\;\mathrm t_\mathrm f^2\;\cdot\;\frac{{\mathrm f}_\mathrm y}{{\mathrm\gamma}_{\mathrm M0}}}{4\;\cdot\;\mathrm m}\;\cdot\;\left[1\;-\;\left(\frac{{\mathrm\sigma}_{\mathrm f,\mathrm{Ed}}}{\displaystyle\frac{{\mathrm f}_\mathrm y}{{\mathrm\gamma}_{\mathrm M0}}}\right)^2\right]$
where
leff = 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
σf,Ed = bending stress in the centroidal axis of the flange due to global loading
Figure 01 - Loading of Lower Flange by Wheel Loads
The following condition has to be met:
Fz,Ed ≤ Ff,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.
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: ${\mathrm\sigma}_{\mathrm{ox},\mathrm{Ed},\mathrm{ser},\mathrm i}\;=\;{\mathrm c}_{\mathrm x,\mathrm i}\;\cdot\;\frac{{\mathrm F}_{\mathrm z,\mathrm{Ed}}}{\mathrm t_\mathrm f^2}$
Transversal direction of the beam: ${\mathrm\sigma}_{\mathrm{oy},\mathrm{Ed},\mathrm{ser},\mathrm i}\;=\;{\mathrm c}_{\mathrm y,\mathrm i}\;\cdot\;\frac{{\mathrm F}_{\mathrm z,\mathrm{Ed}}}{\mathrm t_\mathrm f^2}$
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:
${\mathrm\sigma}_{\mathrm v,\mathrm{Ed},\mathrm{ser}}\;=\;\sqrt{\mathrm\sigma_{\mathrm{Σx},\mathrm{Ed},\mathrm{ser}}^2\;+\;\mathrm\sigma_{\mathrm{Σy},\mathrm{Ed},\mathrm{ser}}^2\;-\;{\mathrm\sigma}_{\mathrm{Σx},\mathrm{Ed},\mathrm{ser}}\;-\;{\mathrm\sigma}_{\mathrm{Σy},\mathrm{Ed},\mathrm{ser}}\;+\;3\;\cdot\;{\mathrm\tau}_{\mathrm{Ed},\mathrm{ser}}}\;\leq\;\frac{{\mathrm f}_\mathrm y}{{\mathrm\gamma}_{\mathrm m,\mathrm{ser}}}$
where
${\mathrm\sigma}_{\mathrm{Σx},\mathrm{Ed},\mathrm{ser}}\;=\;{\mathrm\sigma}_{\mathrm x,\mathrm{Ed},\mathrm{ser}}\;+\;0.75\;\cdot\;{\mathrm\sigma}_{\mathrm{ox},\mathrm{Ed},\mathrm{ser}}$
${\mathrm\sigma}_{\mathrm{Σy},\mathrm{Ed},\mathrm{ser}}\;=\;0.75\;\cdot\;{\mathrm\sigma}_{\mathrm{oy},\mathrm{Ed},\mathrm{ser}}$
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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![Figure 02 - Influence Parameters for the Calculation of the Effective Length According to [2], Tab. 6.2](/-/media/Images/website/pages/support-and-learning/support/knowledge-base/001519/02-en-png.png?la=en&hash=78070663F19AF2999FFD8AB032E73AF639E29BE6){kind=link}