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

### Technical Article

001519 05/16/2018
For suspension cranes, the bottom chord of the runway girder is subjected to local flange bending due to the wheel loads in addition to the main load bearing capacity. The bottom chord behaves like a slab due to these local bending stresses and has a biaxial stress condition [1].

#### 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

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:

${\mathrm\sigma}_{\mathrm v,\mathrm{Ed},\mathrm{ser}}\;=\;\sqrt{\mathrm\sigma_{\mathrm{Σx},\mathrm{Ed},\mathrm{ser}}^2\;+\;\mathrm\sigma_{\mathrm{Σy},\mathrm{Ed},\mathrm{ser}}^2\;-\;{\mathrm\sigma}_{\mathrm{Σx},\mathrm{Ed},\mathrm{ser}}\;\cdot\;{\mathrm\sigma}_{\mathrm{Σy},\mathrm{Ed},\mathrm{ser}}\;+\;3\;\cdot\;\mathrm\tau_{\mathrm{Ed},\mathrm{ser}}^2}\;\leq\;\frac{{\mathrm f}_\mathrm y}{{\mathrm\gamma}_{\mathrm m,\mathrm{ser}}}$

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.

#### Reference

 [1] Seeßelberg, C.: Kranbahnen: Bemessung und konstruktive Gestaltung nach Eurocode, 5th edition. Berlin: Bauwerk, 2016 [2] Eurocode 3: Design of steel structures - Part 6: Crane supporting structures; EN 1993-6:2007 + AC:2009 [3] Petersen, C.: Stahlbau, 4th edition. Wiesbaden: Springer Vieweg, 2013