Strength and elastic stability of cranes in aspect of new and old design standards

The current tendencies, connected with cranes design and the wide range of European Standardization, concerning steel construction of load – carrying structure lead to the construction of cranes (on the basis of new and more accurate calculation methods), which are lighter [1, 2] but which have lower safety margin of strength [3-5]. We can observe the development of international technical standardization, assume that the development in the domain of calculations and manufacture eliminate some dangers generated in the past. Such a philosophy was presented by the authors of new European Standards of cranes design. In this study the FEM analysis of stability [6-8] and strength of load – carrying cranes structures, designed according to Polish Standards (PN) was carried out. The analysis was compared to the results of the same analysis according to European Standards EN 13001. The analysis and carrying out of parametric geometrical models as a basis for FEM, were preceded by parameterization of real cranes geometrical and material constructional features according to its documentation (Fig. 1).


Introduction
The current tendencies, connected with cranes design and the wide range of European Standardization, concerning steel construction of load -carrying structure lead to the construction of cranes (on the basis of new and more accurate calculation methods), which are lighter [1,2] but which have lower safety margin of strength [3][4][5].We can observe the development of international technical standardization, assume that the development in the domain of calculations and manufacture eliminate some dangers generated in the past.Such a philosophy was presented by the authors of new European Standards of cranes design.
In this study the FEM analysis of stability [6][7][8] and strength of load -carrying cranes structures, designed according to Polish Standards (PN) was carried out.The analysis was compared to the results of the same analysis according to European Standards EN 13001.
The analysis and carrying out of parametric geometrical models as a basis for FEM, were preceded by parameterization of real cranes geometrical and material constructional features according to its documentation (Fig. 1).
Fig. 1 General view of analysis process

Standardization in cranes design
At the time when design standards from eighties were obligatory [9,10] the safety margins (reserve of stability and strength) were bigger.That caused that the designed and produced cranes according to this standards were heavier.Detailed standards provisions with ready formulas facilitated calculations of loads in the typical cases, but in other cases did not indicate the clear calculations models [11][12][13][14][15][16].There were paradoxes in design process like very high loads assuming in some construc-tional details (much higher than it really was), only for not to cause stability loss of some low strength and less important elements.
The collection of new European standards of cranes design [17][18][19] listed different kinds of loads and proof conditions in comparison with the old standards.The loads acting on a crane are divided into the categories of regular, occasional and exceptional which shall be considered in proof against failure by uncontrolled movement, yielding, elastic instability and, where applicable, against fatigue.
Estimation of influences of new European cranes design standards on the reduction of cranes load-carrying structures mass, will be possible only after the collection of numerous number of experiences.That is the reason why from the parameter base of overhead travelling cranes with box girder [20] those with 5, 8, 12.5, 20, 35, 40 and 50 t load capacity were chosen for strength and stability calculations.

Analysis methodology and models preparation
The constructional features parameterisation was made on series of overhead travelling cranes, which are the dominant class of cranes used in mechanical handling.After analyzing of about 1000 cranes, more than 150 of them (designed and carried out in 1970-2005) were chosen as the representative ones.Table 1 shows basic parameters of analysed 20t hosting capacity cranes.The parameters which characterize box girder overhead travelling crane were divided into 12 groups described in detail in [20].The analysed cranes characterise 6 forms of box girders, that depend on quantity of membranes and stiffeners (Fig. 2).
To simplify usage of parameter base and faster preparation of geometrical models a software called USPN was created (Fig. 3).It was a combination of MS Excel (Visual Basic) and Solid Edge software, which allowed the prepared for FEM calculations CAD models in only few seconds receive.For such a big base of parameters and research objects USPN was very helpful.All procedures that allow automatic generation of geometrical models were collected in this software.The application generates a 3D shell geometrical model of load-carrying crane structure parameterized in data base (MS Excel).Such a model was directly imported to FEM pre-processor (Altair Hypermesh) were finite elements model with proper boundary conditions was build.For creation of FEM model CTRIA3, CQUAD4, CHEXA, RBE2, CBAR elements and MSC,NASTRAN as the solver were used [21].

Analysis results
Strength analysis of load-carrying crane structures was carried out by calculating von Misses stress in the middle of cranes span -middle of girder was the position of hoisting winch and load (Figs. 5 and 6).Girder is the heaviest element in cranes structure, therefore decreasing its mass is more favourable than mass decreasing of other constructional details.In analysis there was stress from load combinations according to up today used polish standards [2,3] and new European standards calculated [4][5][6].On the basis of received von Misses stresses a special W factor was calculated (separately for polish standards -W PN (1) and European standards W EN (2)) that could be understood as the proof of static strength degree of load-carrying crane struc-    Proof of elastic stability of crane elements was also made with use of FEM in case as buckling of plate fields subjected to compressive and shear stresses.The analysis was made for girders webs loaded in the middle of cranes span with maximal force coming out of hoisting capacity.The results are shown in the form of dimensionless factor λ, which is a multiplier of characteristic loads f i -calculated from loads combinations to get critical buckling load Factor λ shows de facto "reserve" of elastic stability of load-carrying crane structure, in relation to the required value, coming out of position and loads value.An example of displacement for local stability loss -buckling of girders web is shown in Fig. 11 and factor λ values frequency for all cranes being under consideration is shown in Fig. 12.Additionally, as a completion of strength and stability analysis, the calculations for 10 first natural frequencies and deflection of crane structures were made.The third natural frequency was recognized as the most important one (an example is shown in Fig. 13 and values for 20 t hoisting capacity cranes in Table 2).

Conclusions
Analyzing the values of calculated von Misses stresses and W factors, we can observe that for majority of cranes W EN factor value does not exceed 0.5.For the cranes with Q = 5-10 t hoisting capacity its average value is W EN = 0.37 and increases constantly together with hoisting capacity of the crane to W EN = 0.40 for the cranes with Q < 20 t, W EN = 0.50 for Q < 40 t and W EN = 0.55 for the other, W EN values are less from W PN in most cases.Average difference of both factors is not large and amount about 3%.
Especially for cranes with small hoisting capacity not big value of W factor could hint about overdimensioning of the structure.Of course other kind of designs proofs (especially proof of fatigue strength and proof for welded connections) are very important and it cannot be omitted, but only little girders mass decreasing could "slim" the whole load-carrying structure.Moreover, no girder form neither cranes span has an influence on factor W value.
The proof of elastic stability is made to prove that ideally straight structural members or components will not lose their stability due to lateral deformations caused solely by compressive forces or compressive stresses.This proof is retained for all structures being under consideration.The biggest values of λ factor were observed for girders types 0pp + 0k and 1pp + 0k, so those without longitudinal stiffeners.An influence of small cranes span for this girders types is significant this time.For the most common occurring girders types 1pp + 1k and 2pp + 1k, average value of λ factor becomes 2.03 and 2.66.
In comparison to proof of static strength degree (factor W), the values of factor λ becomes much higher, It shows that elastic stability reserve of load-carrying cranes structures is big.That makes potentially decreasing of the structure mass possible, through lower number of elements that do not have a special influence on strength (longitudi-

STRENGTH AND ELASTIC STABILITY OF CRANES IN ASPECT OF NEW AND OLD DESIGN STANDARDS S u m m a r y
In this study the analysis of elastic stability and strength of load -carrying cranes structures, designed according to Polish Standards were carried out.The analysis was compared to the results of the same analysis according to European Standards EN 13001.The analyzed cranes characterize 6 forms of girders, depending on quantity of membranes and stiffeners.Geometrical models were created with UNSP -software carried out for better use of geometrical features base.As the FEM solver the MSC,NASTRAN was used.The elements for creation of FEM model were CTRIA3, CQUAD4, CHEXA, RBE2, CBAR.The stability and strength analysis was carried out for the case of load with hoisting capacity and hoisting winch position in the middle of a span.The results were presented in the form of dimensionless factors W and λ.

Fig. 3
Fig. 3 Numerical research block diagram Forces coming out from proper loads combinations were simulated as concentrated (acting on node) or as pressure.The models were supported in wheels axes.An example of crane load-carrying structure FEM model is shown in Fig. 4.

Fig. 4 FEM
Fig. 4 FEM model of load-carrying crane structure with Q = 5 t and L = 30 m (girder 2pp + 1k with hidden web)

Fig. 5
Fig. 5 Von Misses stress values for load-carrying crane structure with Q = 20 t and L = 21.8 m at A1 load combinations is limit design stress, MPa and σ is von Misses stress, MPa value for load combinations according to polish σ PN or European standards σ EN .The factor W can assume values between 0 an 1.The values closer to 0 mean little proof of static strength degree of load-carrying crane structure -big overdimensioning of crane mass, however the values closer to 1 mean high proof of static strength degree of load-carrying crane structure -small overdimensioning of the crane mass.In both cases extreme values are undesirable.Comparison of W factors calculated from load combinations according to polish W PN and European W EN standards are shown in Figs.7-10 (for selected hoisting capacities) and Table2(for cranes with 20 t hoisting capacity).

Fig. 7 FactorFig. 8 Factor
Fig. 7 Factor W values for cranes with Q = 5 t and Q = 8 t load capacities

Fig. 10 Factor
Fig. 10 Factor W values for cranes with Q = 35 t, Q = 40 t and Q = 50 t load capacities

Table 2
nal or transverse stiffenings) or the application of other girders type.