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001519

2018-05-16

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

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 must 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:

F_{f, Rd} = \frac{l_{eff} \cdot t_{f}^{2} \cdot \frac{f_{y}}{γ_{M 0}}}{4 \cdot m} \cdot [1 - {(\frac{σ_{f, Ed}}{\frac{f_{y}}{γ_{M 0}}})}^{2}]

Formula 1

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

Loading Lower Flange by Wheel Loads

The following condition must be met:
F_z,Ed ≤ F_f,Rd

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

Influencing Parameters for Calculating Effective Length According to [2], Tab. 6.2

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 the wheel loads in the structural analysis.

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

Local Stresses in the 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 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:

σ_{ox, Ed, ser, i} = c_{x, i} \cdot \frac{F_{z, Ed}}{t_{f}^{2}}

Formula 2

Transversal direction of the beam:

σ_{oy, Ed, ser, i} = c_{y, i} \cdot \frac{F_{z, Ed}}{t_{f}^{2}}

Formula 3

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

μ = \frac{2 \cdot n}{(b - t_{w})}

Formula 4

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 cases 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:

σ_{v, Ed, ser} = \sqrt{{(σ_{x, Ed, ser})}^{2} + {(σ_{y, Ed, ser})}^{2} - (σ_{x, Ed, ser}) (σ_{y, Ed, ser}) + 3 {(τ_{Ed, ser})}^{2}} \leq \frac{f_{y}}{γ_{M, s e r}}

Formula 5

where

σ_{Σx, Ed, ser} = σ_{x, Ed, ser} + 0, 75 \cdot σ_{ox, Ed, ser}

Formula 6

σ_{Σy, Ed, ser} = 0.75 \cdot σ_{oy, Ed, ser}

Formula 7

Summary

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

Literature

[1]	Seeßelberg, C.: Kranbahnen: Bemessung und konstruktive Gestaltung nach Eurocode, 5th ed. 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 ed. Wiesbaden: Springer Vieweg, 2013

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