7327x

2019-12-03

Method of Determining the Allowable Deformation of Crane Runway Girders

This article describes the different options for determining the allowable deformation of crane runway girders. Since multi-span beams and flexible lateral supports (sway bracing) are used in practice, this article will show how to select the correct method.

General

In addition to the ultimate limit state design, the serviceability limit state design is of particular importance for crane runway girders. Compliance with the deformation limit values is important not only for the serviceability, but also for the reduction of wear. Thus, large horizontal deformations can lead to increased skewing of the crane and thus cause increased wear of the tracking means. Vertical deformations must also be avoided to the greatest possible extent in order to avoid excessive vibration of the crane during operation. Finally, it is also necessary to limit the inclination (slope) of the crane runway girder, because otherwise the crane will not be able to move under full load.

Method 1: Deformation Related to an Undeformed System

Method 1 can be used for single-span beams with fixed and rigid supports.

The following boundary conditions apply:

δ_{y, z} < \frac{L}{X} oder δ_{y, z} < 25 mm

Formula 1

The deformation is determined as follows:

δ_{y, z} = |\frac{U_{c} - U_{L} - (U_{R} - U_{L}) \cdot x}{L}| < \frac{L}{X}

Formula 2

U_c... Deformation of the cross-section
U_L... Deformation of the left support
U_R... Deformation of the right support
x ... Coordinate of the cross-section in the local axis system
L ... Distance of supports

The following applies:

U_{c} \neq 0, U_{L} = 0, U_{R} = 0

Formula 3

Maximum Vertical Deformation of Crane Runway Girder with Rigid Supports

Method 2: Deformation Related to a Deformed System

If you define spring constants for the supports to consider flexible supports, you can use Method 2 under Details. Example File 2, which you can download below this article, contains defined springs for the vertical supports. Figure 02 shows the difference between Method 1 and Method 2.

The following boundary conditions apply:

δ_{y, z} < \frac{L}{X} oder δ_{y, z} < 25 mm

Formula 1

The deformation is determined as follows:

δ_{y, z} = |\frac{U_{c} - U_{L} - (U_{R} - U_{L}) \cdot x}{L}| < \frac{L}{X}

Formula 2

The following applies:

U_{c} \neq 0, U_{L} \neq 0, U_{R} \neq 0

Formula 4

The spring stiffnesses of the supports should have similarly large values when using this method.

Comparing Results According to Method 1 and Method 2

Method 3: Deformation Related to the Inflection Points of the Deformed System

This method is used for continuous beams. Compared to a single-span beam, it does not make sense to use the distance between the supports to determine the allowable deformation for multi-span beams. This can lead to conservative, uneconomical results. In order to determine the governing length, the inflection points of the bending line are determined in Method 3.

The following condition is applied:

ω'' = - \frac{M_{y}}{E \cdot I_{y}}

Formula 5

At the inflection points:

ω'' = 0

Formula 6

The deformation is determined as follows:

δ_{y, z} = |\frac{U_{c} - U_{Li} - (U_{Ri} - U_{Li}) \cdot x}{L}| < \frac{L}{X}

Formula 7

U_c... Deformation of the cross-section
U_Li... Deformation of the left inflection point
U_Ri... Deformation of the right inflection point
x ... Coordinate of the cross-section in the local axis system
L ... Distance between the left and right inflection points

Another advantage of this method is that the supports can also have different spring stiffnesses.

Comparing Results According to Method 1 and Method 3

Crane Runway Girder with Cantilevers

For cantilevers, the bending line is similar to the half-inverted bending line of a single-span beam. Therefore, the following calculation is performed for Method 1:

δ_{y, z} = |U_{c}| < 2 \cdot \frac{L}{X}

Formula 8

If Method 3 is activated, the limit deformation of a cantilever is checked by rotating the cantilever on the support around the local y-axis.

The limit condition is as follows:

φ_{y} < \frac{1}{200}

Formula 9

Result cantilever of Example File 4 with Method 1:

δ_{z} = |7.618 mm| < 2 \cdot \frac{2.000}{600}

δ_{z} = |7.618 mm| < 6.667 not met

In other words :

\frac{7.618}{2 \cdot 2.000} = 525 > 600

Formula 10

Result cantilever of Example File 4 with Method 3:

φ_{y} = 4.258 mrad = 0.004258 rad < \frac{1}{200} rad

0.004258 < 0.005 true

\frac{0.004258}{0.005} = 0.851 < 1

Formula 11

You can see that the allowable deformation according to Method 1 for the cantilever has not been met. However, the German National Annex to EN 1993-6 specifies

δ_{y, z} < \frac{L}{500} and δ_{y, z} \leq 25 mm

Formula 12

for the allowable vertical deformation according to Table 7.2 row a).

Summary

To ensure the correct functioning of a crane system, deformations and displacements must be limited. As a result, the wear is also limited. If the limit conditions of the serviceability limit state design are met, it is usually unnecessary to carry out a separate vibration design for the crane runway girder.

Author

Mr. Flori is the customer support team leader and provides technical support for customers of Dlubal Software.

Links

Structural Analysis and Design Software for Cranes and Craneways

References

Seeßelberg, C.: Kranbahnen - Bemessung und konstruktive Gestaltung nach Eurocode, 4. Auflage. Berlin: Beuth, 2014

Downloads

Model 1 of Technical Article | CRANEWAY 8 file

1.16 MB

Model 2 of Technical Article | CRANEWAY 8 file

1.16 MB

Model 3 of Technical Article | CRANEWAY 8 file

1.62 MB

Model 4 of Technical Article | CRANEWAY 8 file

1.93 MB

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Knowledge Base

KB 001612 | Method of Determining Allowable Deformation of Crane Runway Girders

Length: 00:00:30 min

FAQ

[EN] FAQ 004874 | Is it possible to design intermittent welds in the CRANEWAY add-on module?

Length: 00:00:28 min

FAQ

[EN] FAQ 004693 | Is it necessary to enter the loads of a crane for each axle or wheel in the table of ...

Length: 00:00:37 min

FAQ

[EN] FAQ 004652 | Is it possible to design a crane runway girder without stiffeners on supports in CRANEWAY?

Length: 00:00:51 min

FAQ

FAQ 004115 | How can I obtain internal forces, calculated in CRANEWAY, for a special x-location?

Length: 00:00:55 min

FAQ

[EN] FAQ 003064 | Where can I enter distances of crane axes?

Length: 00:00:24 min

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[EN] FAQ 003324 | How do I change the preset partial factors in CRANEWAY?

Length: 00:00:37 min

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Knowledge Base Articles

For crane runways with large spans, the horizontal load from skewing is often relevant for the design. This article describes the origin of these forces and the correct input in CRANEWAY. The practical implementation and the theoretical background are discussed.

In CRANEWAY, the action of a rail as "statically effective" or "statically ineffective" is defined under "Rail‑Flange Connection" in the Details dialog box. This setting controls the calculation of the load introduction length according to EN 1993-6, Tab. 5.1.

Consideration of Minimum Distance Between Two Cranes

In the event of converting or extending a hall, the building owner may want to add a second or third crane to an existing crane runway. Since the original design usually does not consider other cranes, a common solution is to design a minimum distance between the cranes. This is done via the crane technology settings.

Product Features

Craneway and weld stress analysis
Craneways and weld fatigue design
Deformation,
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 (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 listed above, you can also define a specific NA, applying user-defined limit values and parameters.

All results are arranged in result windows sorted by different topics. The design values are illustrated in the corresponding cross-section graphic. The design details cover all intermediate values.

General Stress Analysis

CRANEWAY performs the general stress analysis of a craneway girder by calculating the existing stresses and comparing them with the limit normal, limit shear, and limit equivalent stresses. Welds are also subjected to the general stress analysis with regard to parallel and vertical shear stresses and their superposition.

Fatigue Design

Fatigue design is performed for up to three cranes operating at the same time, based on the nominal stress concept according to EN 1993-1-9. In the case of fatigue design according to DIN 4132, a stress curve of crane passages is recorded for each stress point and evaluated according to the Rainflow method.

Buckling Analysis

Buckling analysis considers the local introduction of wheel loads according to the EN 1993-6 or DIN 18800-3 standards.

Deformation,

Deformation analysis is performed separately for the vertical and horizontal directions. The available related displacements are compared to the allowable values. You can specify the allowable deformation ratios individually in the calculation parameters.

Lateral-torsional buckling analysis

The lateral-torsional buckling analysis is performed in accordance with the second-order analysis for torsional buckling considering imperfections. The general stress analysis has to be fulfilled with the critical load factor greater than 1.00. As a result, CRANEWAY displays the corresponding critical load factor for all load combinations of the stress analysis.

Support forces

The program determines all support forces on the basis of the characteristic loads, including dynamic factors.

Detailed Settings for Crane Runway Calculation

During the calculation, crane loads are generated in predefined distances as load cases of the crane runway. The load increment for cranes moving across the crane runway can be set individually.

The program analyzes all combinations of the respective limit states (ULS, fatigue, deformation, and support forces) for each crane position. In addition, there are comprehensive setting options for specification of the FE calculation, such as length of finite elements or break-off criteria.

The internal forces of a crane runway girder are calculated on an imperfect structural model according to the second-order analysis for torsional buckling.

Geometry, material, cross-section, action, and imperfection data are entered in clearly arranged input windows:

Geometry

Quick and convenient data input
Definition of support conditions based on various support types (hinged, hinged movable, rigid, and user-defined, as well as lateral on upper or bottom flange)
Optional specification of warping restraint
Variable arrangement of rigid and deformable support stiffeners
Possibility to insert hinges

CRANEWAY Cross-Sections

I-shaped rolled cross-sections (I, IPE, IPEa, IPEo, IPEv, HE-B, HE-A, HE-AA, HL, HE-M, HE, HD, HP, IPB-S, IPB-SB, W, UB, UC, and other cross-sections according to AISC, ARBED, British Steel, Gost, TU, JIS, YB, GB, and others) combinable with section stiffener on the upper flange (angles or channels) as well as rail (SA, SF) or splice with user-defined dimensions
Unsymmetrical I-sections (type IU) also combinable with stiffeners on the upper flange as well as with rail or splice

Actions

It is possible to consider the actions of up to three simultaneously operated cranes. You can simply select a standard crane from the library. You can also enter data manually:

Number of cranes and crane axles (maximum of 20 axles per crane), center distances, position of crane buffers
Classification in damage classes with editable dynamic factors according to EN 1993-6, and in lifting classes and exposure categories according to DIN 4132
Vertical and horizontal wheel loads from self-weight, hoist load, mass forces from drive, as well as loads from skewing
Axial loading in driving direction as well as buffer forces with user-defined eccentricities
Permanent and variable secondary loads with user-defined eccentricities

Imperfections

The imperfection load applies in compliance with the first natural vibration mode - either identically for all load combinations to be designed, or individually for each load combination, as mode shapes may vary depending on the load.
Convenient tools available for scaling the mode shapes (rise determination of inclination and precamber).

Frequently Asked Questions (FAQ)

How can I obtain internal forces, calculated in CRANEWAY, for a special x-location?

Is it possible to design intermittent welds in the CRANEWAY add-on module?

Is it necessary to enter the loads of a crane for each axle or wheel in the table of crane loads in Window 1.4?

Is it possible to design a crane runway girder without stiffeners on supports in CRANEWAY?

Where can I enter distances of crane axes?

How do I change the preset partial factors in CRANEWAY?

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