Investigation of the Dynamic Loads on Tower Cranes duringSlewing Operations

Manuel Stölzner1, Michael Kleeberger1, Marcel Moll1 and Johannes Fottner11Chair of Materials Handling, Material Flow, Logistics, Technical University of Munich,

Boltzmannstr. 15, 85748 Garching, Germany{manuel.stoelzner, michael.kleeberger, marcel.moll, j.fottner}@tum.de

Keywords: Tower Cranes, Static and Dynamic Analysis, Finite Element Method, Vibration Model, Dynamic Factors.

Abstract: For decades, tower cranes have been the most important hoisting device used in building construction. In orderto avoid security risks at the construction site, it is essential to analyse the dynamic behaviour of these cranesduring the work process as the crane motions cause dynamic forces on the supporting structure. Accordingto the current standards, stress calculations for tower cranes are carried out based on static approaches. Thestandards stipulate the use of special dynamic factors in the static calculation to estimate the dynamic loads.This article analyses the dynamic behaviour of a tower crane during the important work process of slewing.The results of the approach according to the standards are compared with the results of the nonlinear dynamicfinite element calculation. In addition, a newly developed vibration model based on a two-mass model willbe presented in this paper. The model helps to estimate the dynamic loads more accurately than the methodscurrently used. However, the computation time required to perform the stress calculation is only slightlyincreased.

1 INTRODUCTION

Tower cranes are very versatile and widely used.A range of tower cranes is available extending fromsmall cranes, often used for the construction of de-tached houses, to large tower cranes with specialclimbing facilities for the construction of high-risebuildings. Their field of application currently in-cludes a hoisting capacity of about 100 metric tonnes,and a hoisting height of more than 100 metres. Inorder to meet the different requirements on construc-tion sites, most tower cranes are designed modularly,which enables a large number of boom configurations.The fundamental motions of tower cranes are slewing,hoisting and they also allow either a luffing motion orload travel. During operation, crane motions causedynamic forces on the hoist load and on the crane’sstructure. In order to guarantee the safety of cranes,exact calculations of the boom system are absolutelyessential throughout the developing process. Conse-quently, one main objective of the stress calculation isto reproduce the system’s dynamic behaviour as real-istically as possible.According to the current international standardISO 8686 and the European standards EN 13001and EN 14439, static approaches are used to perform

stress calculations for tower cranes. In order to con-sider the dynamic effects during the working process,rigid body approaches are used and special dynamicfactors are defined. These factors are either based onthe experience of the crane manufacturers or alterna-tively they are selected from tables in the standards.In this publication, the approaches in the internationalstandard are evaluated by comparing the calculationresults with the results of other calculation methods.Some scientific studies on tower cranes are alreadyavailable in the literature. However, recent publica-tions often deal with questions of control engineeringto reduce the effects of load swing, e.g. (Le et al.,2013; Blajer and Kołodziejczyk, 2011; Doçi et al.,2016). In almost all cases, models with rigid or sim-ple elastic bodies are used. Although these simplifiedmodelling approaches help to solve control engineer-ing problems, they are not adequate for investigat-ing the dynamic effects on the structure in the stresscalculation.Only a few publications exist that deal with the dy-namic behaviour of tower cranes taking into accountelastic deformation, or that evaluate the approachesin the standard. Some papers (Ju and Choo, 2005; Juet al., 2006) focus on frequency investigations for dif-ferent applications. An earlier research project has al-

ready investigated the dynamic loads of tower craneswhen hoisting grounded loads (Maier, 2000). For thecrane analysed, this research project showed that thedynamic factor for hoisting, according to EN 13001,describes the loads more accurately than the specifica-tions in the standard DIN 15018, which is now obso-lete. However, this work provides no comparison withthe standards for crane movements involving majordisplacement of the supporting structure, such as theprocess of luffing or slewing.Since the standards for mobile cranes use similar ap-proaches for the design, the applicability of the dy-namic factors has been evaluated in some publicationson mobile cranes, such as (Kleeberger et al., 2014;Stölzner et al., 2018; Stölzner et al., 2019). Thesearticles have shown that the simplified approaches ofthe calculation methods currently used are often inap-propriate for reproducing the true dynamic effects onmobile cranes. As it can be assumed that the calcula-tion approaches of the standards have similar deficitsfor tower cranes as for mobile cranes, the dynamicbehaviour of tower cranes is analysed in more detailbelow. Since the publications mentioned above showthat the greatest inaccuracies occur in the calculationof slewing processes, this article focuses on the dy-namic loads on tower cranes during slewing.The nonlinear dynamic finite element method cancharacterise the dynamic effects on cranes very accu-rately. In this article, the results calculated using theapproach from the international standard ISO 8686are evaluated by means of a comparison with the re-sults of the nonlinear dynamic finite element calcula-tion, as this method can be considered reliable.Although the dynamic finite element method allowsexact and reliable calculations, it is very rarely usedby crane manufacturers. The main disadvantage ofthis calculation method is the increased computing ef-fort compared to a static calculation. There is alsono reasonable way to consider the standards’ partialsafety factors in a dynamic calculation.Alternatively, the standards permit the use of othermethods to calculate the dynamic factors. In orderto achieve a more accurate calculation of the dynamicbehaviour of tower cranes without a disproportionateincrease in computing time, a special vibration modelis presented in this publication. This new method al-lows the dynamic factors for the slewing process tobe calculated in a more precise way than the currentmethods. The applicability of the vibration model andthe calculation standard is shown for a tower cranewith different loads and load positions. In order toassess the accuracy of the model and the standard,several angular velocities and angular accelerations ofthe tower crane are taken into account.

2 STATE of the ART

The international standard ISO 8686-1(ISO 8686-1, 2012) defines general rules for thestress calculation of cranes. With regard to the loadassumptions, the general European standard forcrane calculation EN 13001-2 (EN 13001-2, 2014)is mostly identical to the international one. Thedesign principles for loads and load combinationsof tower cranes are specified in the product-specificinternational standard ISO 8686-3 (ISO 8686-3,2018) and in the European standard EN 14439(EN 14439, 2010).In the standards, the approach for consideringdynamic loads is based on a rigid body kineticanalysis and uses quasi-static calculation methods.In order to take the effect of the dynamic forcesinto consideration, the use of dynamic factors issuggested. However, the standard ISO 8686-3 alsoallows other values to be used for dynamic factors“when determined by recognized theoretical analysisor practical tests” (ISO 8686-3, 2018). The nonlineardynamic finite element calculation and the vibrationmodel presented here (see Section 3) both belongto the accepted theoretical methods of analysismentioned above.To carry out the stress calculation of tower cranes,the version of the European standard EN 14439 thatis currently valid refers to the now-obsolete standardDIN 15018 (DIN 15018, 1984) and the guidelineFEM 1.001 (FEM 1.001, 1998). The internationalstandard provides fixed values for the dynamicfactors, whereas the guideline FEM 1.001 definesanother method of describing dynamic loads duringthe horizontal movements of tower cranes. Thisguideline proposes an approach based on a two-degree-of-freedom model, which allows the factorsto be calculated depending on the crane configuration(see Section 2.2).In addition to the dynamic factors, both the interna-tional and the European standards prescribe the useof partial safety factors in order to compensate foruncertainties in the load assumptions. Since the aimof this publication is not to evaluate safety factorsbut to assess the quasi-static loads from the vibrationmodel and the calculation standards, no safety factorsare used. Nevertheless, the partial safety factors canbe considered in the same way as prescribed in thestandards when this vibration model is used.

2.1 ISO 8686

The standard ISO 8686-3 “gives specific require-ments and values for factors to be used at the struc-tural calculation” (ISO 8686-3, 2018) of tower cranes.The current draft of the product-specific Europeantower crane standard EN 14439 (prEN 14439, 2018)corresponds to the approaches of this standard.Based on ISO 8686-1, the loads are classified as regu-lar loads, occasional loads and exceptional loads. Theoccasional loads include all forces caused by skewingor loads due to climatic and environmental influencessuch as loads from wind, snow or temperature varia-tion. Exceptional loads are test loads and other loadsthat occur very rarely during regular crane operations,for instance loads caused by emergency off or loadsdue to unintentional loss of the hoist load. Amongregular loads are the forces caused by “acceleration ofall crane drives including hoist drives” (ISO 8686-1,2012). The dynamic loads resulting from slewing op-erations fall into this category of forces.According to ISO 8686, the forces applied on thestructure during acceleration and deceleration are cal-culated with rigid-body models. The calculation in-cludes both centrifugal forces and inertial forces.Since a rigid-body analysis does not reflect the elasticeffects, the changes in the forces are multiplied by adynamic factor. To estimate the dynamic loads, thedynamic factor Φ5 is defined and some default valuesof this factor are proposed in the standard. To con-sider the inertia forces, the general rules in the stan-dard ISO 8686-1 provide a range between 1 and 2 forthis factor. The product-specific part ISO 8686-3 de-fines a factor of Φ5 = 1.5. The centrifugal forces areconsidered by a factor of Φ5 = 1.In addition to the proof of strength, ISO 8686-3 alsorequires a proof of fatigue. As the aim of this article isnot to analyse fatigue, but rather to evaluate and im-prove the underlying load assumptions, the proof offatigue is not considered.

2.2 FEM 1.001

For the proof of strength, the European standardEN 14439 refers to the FEM guideline 1.001. Thisguideline distinguishes between dynamic forces dueto vertical and horizontal movements of the crane. Forthe horizontal movements, which include the slewingprocess, the guideline defines different dynamic fac-tors in the stress calculation related to the hoist loadand the supporting structure.In contrast to ISO 8686, the dynamic factor for thehoist load is calculated using a two-degree-of freedommodel of the crane (see Figure 1). In this model, m2 is

the mass of all translatory and rotary moving parts ofthe drive system and the supporting structure, reducedto the load suspension point, while m1 represents themass of the hoist load. The driving force F acts onm2. The stiffness k1 of the load pendulum is calcu-lated with the equation

k1 =m1 ·g

l, (1)

where g is the acceleration due to gravity and l is thelength of the pendulum.Defining the coordinate z = y− x leads to the equa-tions of motion

m1 · (ẍ+ z̈) = k1 · zm2 · ẍ = k1 · z−F.

(2)

Solving and evaluating these equations gives rise to adynamic factor by which to multiply the inertial forceon the hoist load.Furthermore, the FEM guideline prescribes a value of2 as the dynamic factor related to the supporting struc-ture. To determine this parameter, the square root ofthe square sum of the model’s two natural frequencies

ωa and ωb are calculated ωr =√

ω2a +ω2b and com-pared with the time for deceleration.

yx

k1m2 m1F

Figure 1: Model according to FEM 1.001.

When applied to the elastic lattice structures of towercranes with modern drive systems, this simplifiedmodel has two major disadvantages:

1. The elasticity of the supporting structure is notconsidered.

2. The controlled drives currently used for towercranes follow the accelerations and decelerationsspecified by the crane control very closely. Thus,the movement of the mass m2 is determined en-tirely by the crane control and the two-mass modelis consequently reduced to a one-mass model ofthe hoist load’s pendulum.

For these reasons, this simplified model cannot ac-curately represent the dynamic loads on tower cranesand the approach is consequently not adopted in thecurrent draft of EN 14439. Therefore, a modifiedtwo-mass model is presented in the following sectionin order to determine the dynamic loads during slew-ing with an increased accuracy.

3 VIBRATION MODEL

Figure 2 shows the modified vibration model forcalculating the dynamic factors. In comparison to

y1x2

k1k2m2 m1

xA(t)

Figure 2: Modified vibration model for calculating dynamicfactors of tower cranes.

Figure 1, an additional spring with the stiffness k2 isadded to describe the stiffness of the supporting struc-ture. Furthermore, the displacement xA(t) replacesthe driving force F . When the load case slewing iscalculated, xA(t) is proportional to the time course ofthe slewing angle of the crane slewing gear, which isdetermined by the crane control. The dynamic be-haviour of the supporting structure and the hoist loadcan thus be expressed by the equations of motion

m1 · (ẍ1 + ẍ2)+ k1 · x1 =−m1 · ẍA(t)m2 · ẍ2− k1 · x1 + k2 · x2 =−m2 · ẍA(t)

(3)

with x1 = y1 − x2. The mass m1 again repre-sents the mass of the hoist load, the stiffness k1 isdefined by Eq. 1.The mass m2 and the stiffness k2 are determined bythe results of a frequency analysis of the crane’s finiteelement structure. Numerical investigations aboutmobile cranes have shown that the vibrations causedduring the slewing process of cranes contain only fewnatural frequencies (Stölzner et al., 2018). Duringthe process of slewing, tower cranes exhibit a similardynamic behaviour (see chapter 4.2). Consequently,only the first two lowest natural frequencies corre-sponding to the modeshapes, which are orthogonal tothe plane of the supporting structure, are decisive inanalysing the slewing process. ω1 is usually the low-est natural frequency of the crane structure at whichthe tip of the boom and the hoist load swing in phase,while ω2 is the lowest natural frequency at which thetip of the boom and the hoist load swing out of phase.The characteristic equation

det([

m1 m10 m2

]·λ2 +

[k1 0−k1 k2

])= 0, (4)

with λ21 =−ω21 and λ22 =−ω22 is used to calculate thevalues m2 and k2. The mass m2 and the stiffness k2are finally determined with the equations

m2 =−k21 ·m1(

k1−m1 ·ω21)·(k1−m1 ·ω22

) (5)k2 =−

k1 ·m1 ·ω21 ·ω22(k1−m1 ·ω21

)·(k1−m1 ·ω22

) . (6)The differential equations (3) of the two-mass modelcan easily be solved analytically. For that reason,no numerical methods are required for calculatingthe dynamic factor, and consequently the proposedmethod only needs slightly more computing time thanthe method proposed by the standard.The dynamic factor related to the hoist load and thesupporting structure are calculated with the solutionsx1(t) and x2(t) of Eq. 3 for the associated working cy-cle. The solution of the static displacement x1,m andx2,m for a constant averaged acceleration am of thedrive system results in the equations

x1,m =−m1 ·am

k1(7)

x2,m =−(m1 +m2) ·am

k2. (8)

The displacement solution x2(t) is proportional to thelateral deflection of the boom. As the maximum lat-eral deflection of the boom is again proportional to themaximum bending moment in the boom, the largestabsolute value of x2(t) at the point in time t = tmax is,therefore, relevant for calculating the dynamic factor.x1(tmax) is the corresponding value of the hoist load’slateral displacement. The new dynamic factors for thestatic stress calculation result from the quotient of thecalculated dynamic displacements x1(tmax), x2(tmax)and the static solutions x1,m and x2,m. The dynamicfactor applied on the supporting structure Φ5,s and thefactor for the hoist load Φ5,p are calculated with therelations

Φ5,s =x2(tmax)

x2,m(9)

Φ5,p =x1(tmax)

x1,m. (10)

Both dynamic factors refer to the inertial forces act-ing on the crane structure and the hoist load at theconstant mean accelerations am of the slewing drive.Based on the standard ISO 8686-3, the inertial forcesare still calculated with a rigid-body kinetic modelof the crane, and the dynamic behaviour is estimatedby applying the determined factors Φ5,s and Φ5,pon the inertia forces. To take the centrifugal forcesinto account, the factor of Φ5 = 1 recommended inISO 8686-3 is maintained.

The basic requirement of this vibration model is aconstant natural frequency during the slewing pro-cess, which is satisfied for both bottom slewing andtop slewing tower cranes. In the case of the bot-tom slewing tower cranes, the entire structure moves,which means that the stiffness, and thus also the nat-ural frequencies of the crane system, do not change.For top slewing tower cranes, the natural frequenciesalso remain constant, since the tower consists of arectangular cross-section and the moment of inertiais constant in all directions.

4 NUMERICAL ANALYSIS

According to ISO 4306-3 (ISO 4306-3, 2016), thecharacteristics of tower cranes can be classified asassembly, slewing level, type of boom and config-uration. In the following calculations, a stationary,top slewing crane with horizontal boom is analysed.The subsequent sections present the crane with itsanalysed parameters (see Section 4.1) and show thenumerical results using different calculation methods(see Section 4.2).

4.1 Modelling

The calculation of the dynamic loads is based on acrane with a maximum hoisting capacity of 12 metrictonnes. In order to investigate the dynamic behaviourof different crane configurations, the evaluation com-prises different vertical and horizontal positions of thehoist load. To analyse the influence of the hoist load’svertical position, four different hoisting rope lengths(0.7 m, 5 m, 10 m, 46 m) are selected (see Figure 3).No damping is considered in the numerical calcula-tions because the objective of the investigations is to

0.7 m5 m

10 m

46 m5 m

75 m

Ê

Ë

Ì

Í

¬

®

¯

Figure 3: Modelling of the tower crane and analysed posi-tions of the hoist load.

assess the accuracy of different approaches for thestress calculations and not to analyse the influence ofdamping on the supporting structure.The finite element program NODYA, which was espe-cially developed for the crane calculation, is used tocarry out the calculations. The original focus of thissoftware was the dynamic and static stress calculationof mobile cranes, but it is also capable of calculat-ing the lattice boom structures of tower cranes (Maier,2000). It provides special features for the crane cal-culation such as a cable element and a superelement.The load cycle for analysing the dynamic effects in-cludes the phases acceleration, constant velocity anddeceleration. Linear time courses for the accelerationand velocity are assumed, choosing the same time foracceleration and deceleration (see Figure 4).The point in time tmax of the maximum lateral move-ment of the boom system is detected with a chosensimulation time of 60 s. To identify the maximumstress, the calculations are carried out with 11 dif-ferent time durations of constant velocity tB, rang-ing from 0 s to 20 s. Crane manufacturers often onlyconsider one acceleration phase, as the crane operatorshould commonly choose a convenient braking pointto achieve minimal vibration of the supporting struc-ture and the load. However, in the modelled processincluding the phase of deceleration, the influence ofthe crane operator is disregarded as this represents themore conservative load case.As described in Section 2.1, the loads calculated ac-cording to the international standard are mainly dom-inated by the inertia forces and, therefore, depend al-most entirely on the acceleration of the supportingstructure. To verify this approach and to show possi-ble dependencies of the dynamic loads on velocity oracceleration, different combinations of angular speedand angular acceleration are analysed in the calcula-tions (see Table 1). As the FEM guideline recom-mends an acceleration time between 5 s and 10 s, a

vam tB

vam

Acce-leration

Constant Velocity Dece-leration

t

am

0

−am

a(t), v(t)

a(t)

v(t)

Figure 4: Analysed time course of the angular accelerationand angular velocity of the slewing drive.

time close to this range is selected. In addition, it isensured that the drive torques do not exceed a valueof about 400 kNm.Table 1: Analysed combinations of angular velocity and ac-celerations.

ω in rads−1 ω̇ in rads−2 ω/ω̇ in s0.0105 0.0015 70.0105 0.0021 50.0105 0.0026 40.021 0.0021 100.021 0.003 70.0315 0.00263 120.042 0.0028 15

4.2 Results

The nonlinear dynamic finite element calculation isthe calculation method that can be considered themost realistic for cranes. For this reason, the resultsobtained from the calculation standard and the vi-bration model are evaluated by means of comparisonwith the results of the dynamic finite element calcula-tion.

4.2.1 Dynamic calculation and ISO 8686

Figure 5 shows an exemplary comparison betweenthe dynamic calculation and ISO 8686-3. The figureshows the time courses of the lateral deformation ofthe boom’s tip regarding 11 different times tB between0 s and 20 s. The maximum values depend stronglyon the point in time at which breaking is initiated andon the duration of the steady state time tB. However,it is not possible to standardise the most crucial timetB since the time courses change for different craneconfigurations and different angular velocities or ac-celerations. The results of the static calculation ac-cording to ISO 8686-3 are shown for a positive anda negative direction of slewing. In the crane configu-ration considered, the results of the static calculationare lower than the absolute maximum of the dynamiccalculation.Figure 6 shows the results of the lateral deformationof the crane’s boom tip for all load positions ¬-¯ andÊ-Í of Figure 3. The diagram shows the results forthe combination of velocity and acceleration at whichthe maximum lateral displacement of the boom tip oc-curs. When the angular velocities and accelerationsresulting in the maximum lateral displacement of thedynamic calculation are analysed, it is noticeable thatthe maximum always occurs at the highest consideredacceleration of 0.003 rads−2. This indicates that the

ISO 8686-3

ISO 8686-3

Dis

plac

emen

tin

m

0

1

2

3

1-

2-

3-

Time in s0 20 40 60

Figure 5: Time courses of the boom tip including dif-ferent times tB, ω = 0.0105 rads−1, ω̇ = 0.0026 rads−2,m1 = 12 t, length of hoisting rope: 10 m, horizontal loadposition: 5 m.

Dynamic calculationISO 8686-3

Dis

plac

emen

tin

m

0

1

2

3

4

5

Ê Ë Ì Í¬ ® ¯

Load positions according to Figure 3.

Figure 6: Maximum lateral displacement of all analysedcrane systems, calculated with the dynamic calculation andaccording to ISO 8686-3. The maximum is always reachedwith ω = 0.021 rads−1 and ω̇ = 0.003 rads−2.

dynamic crane loads depend mainly on the angularacceleration and not on the angular velocity of thetower crane, which is analysed more precisely in Sec-tion 4.2.2. For all velocities and accelerations consid-ered, the calculation according to ISO 8686-3 resultsvalues that are too low for the dynamic loads. Fur-thermore, it is apparent that the differences betweenthe calculation according to the standard and the dy-namic finite element calculation occur for all investi-gated positions of the hoist load.

When we study the dependency of the maximum lat-eral displacement on the pendulum length, a decreas-ing crane load is obtained with increasing pendulumlength. For this reason, the requirement of the stan-dard, which prescribes a load position “at the top ofthe jib or immediately below the crab” (ISO 8686-1,2012) could be confirmed by these numerical tests.

4.2.2 Dynamic calculation and vibration model

Figure 7 shows a Fourier transformation of the dy-namic time course of the hoist load’s lateral displace-ment. In the frequency domain it becomes clear thatthe vibration is mainly dominated by two frequencies,which correspond to the first and the fourth naturalfrequency of the crane. Since other frequencies in-fluence the vibration signal only very slightly, the vi-bration can be simulated with the developed two massmodel.

Abs

olut

eva

lue

Four

ierc

oeffi

cien

tin

m

0

0.4

0.8

1.2

Frequency in Hz0 0.05 0.1 0.2 0.3

Figure 7: Fourier transformation of the hoist load’s lat-eral displacement, ω = 0.0105 rads−1, ω̇ = 0.0026 rads−2,tB =10 s, m1 = 2.5 t, length of hoisting rope: 46 m, horizon-tal load position: 75 m.

Figure 8 shows the time course of the lateral displace-ment of the hoist load’s suspension point for both thedynamic calculation and the vibration model. The vi-bration model reproduces the time course of the dy-namic finite element calculation with high accuracy.Both frequency and amplitude are reproduced almostexactly as the higher natural frequencies make no no-ticeable contribution to the vibration. For this rea-son, the use of only two natural frequencies in thevibration model shown leads to almost the exact re-construction of the nonlinear dynamic finite elementcalculation.

Dynamic calculationVibration model

Dis

plac

emen

tin

m

0

2

4

2-

4-

Time in s0 20 40 60

Figure 8: Time course of the hoist load’s suspension point,ω = 0.021 rads−1, ω̇ = 0.003 rads−2, tB = 14 s, m1 = 2.5 t,horizontal load position: 75 m.

Table 2 shows the dynamic factors related to the hoistload and the supporting structure according to theEqs. 9 and 10. The dynamic factors vary consider-ably, in part, when the different velocities and accel-erations are used. In all cases, the dynamic factor re-lated to the hoist load is higher than the factor for thesupporting structure, as an increased inertia force actson the hoist load due to the pendulum. Furthermore,a dependency of the dynamic factor on the angularacceleration of the crane can be derived, while thedependency on the angular velocity is considerablylower. In an earlier publication about mobile cranes, itwas already possible to determine dependency condi-tions for velocity and acceleration based on the break-ing time and the period of vibration (Kleeberger et al.,2014). Since the selected angular acceleration is rel-atively low in each case, the dependency on the an-gular acceleration is more significant in the presentedanalyses. The analysis of special working conditions,such as the load case emergency stop with its high ac-

Table 2: Dynamic factors calculated with the vibrationmodel, m1 = 2.5 t, length of hoisting rope: 5 m, load-liftingradius: 75 m.

ω ω̇ tB Φ5,s Φ5,pin rads−1 in rads−2 in s0.0105 0.0015 0 1.999 2.0170.0105 0.0021 2 1.889 1.9350.0105 0.0026 18 1.752 1.830.021 0.0021 12 1.889 1.9160.021 0.003 0 1.999 2.0170.0315 0.00263 12 1.717 1.7260.042 0.0028 18 1.526 1.578

celerations, would result in other dependencies. Over-all, it can be seen that the recommended value ofΦ5=1.5, which is specified in ISO 8686-3, cannot leadto satisfactory results in most cases. The value 1.5 isonly suitable for the longest acceleration time of 15 s.In Figure 9, the maximum lateral displacements ofthe boom’s tip resulting from the dynamic calcula-tion are compared with the quasi-static calculations.In order to investigate the quality of the load assump-tions derived from the vibration model with those ofISO 8686-3, the results of both methods are includedin the diagram. The quasi-static calculations usingthe vibration model are based on the dynamic fac-tors listed in Table 2. It is obvious that the dynamicfactors based on the vibration model allow a muchmore accurate representation of the dynamic calcula-tion than using the default factor of 1.5 which is spec-ified in the standard. The dynamic calculation can bereproduced with high accuracy for all angular veloci-ties and accelerations by using the calculated dynamicfactors. This clearly shows that the approach of thequasi-static calculation leads to precise results whenappropriate dynamic factors are used.

Dynamic calculationVibration modelISO 8686-3

Dis

plac

emen

tin

m

0

1

2

3

4

5

ω=

0.01

050

rad

s−1

ω̇=

0.00

150

rad

s−2

ω=

0.01

050

rad

s−1

ω̇=

0.00

210

rad

s−2

ω=

0.01

050

rad

s−1

ω̇=

0.00

260

rad

s−2

ω=

0.02

100

rad

s−1

ω̇=

0.00

210

rad

s−2

ω=

0.02

100

rad

s−1

ω̇=

0.00

300

rad

s−2

ω=

0.03

150

rad

s−1

ω̇=

0.00

263

rad

s−2

ω=

0.04

200

rad

s−1

ω̇=

0.00

280

rad

s−2

Figure 9: Maximum lateral displacement, m1 = 2.5 t,length of hoisting rope: 5 m, horizontal load position: 75 m.

5 CONCLUSION and OUTLOOK

In this paper, the dynamic loads on tower cranesduring the slewing operation were analysed. The ac-curacy of the standard ISO 8686-3 was evaluated bycomparing the results with the results of the nonlineardynamic finite element calculation. For the crane in-vestigated in this publication, the dynamic loads wereusually underestimated with the default dynamic fac-tor stipulated in the standard.In order to describe the dynamic behaviour of thetower crane during the slewing operation more ac-curately, a newly developed vibration model, basedon a two-degree-of-freedom system, was presented inthis article. With the help of this model, the elas-tic deformations of the supporting structure could beconsidered in the stress calculation. It was possi-ble to determine dynamic factors that allow a moreaccurate description of the dynamic loads on towercranes than the commonly used factors from the stan-dard. Concurrently, a similar computing time couldbe achieved, since the vibration model is based on ananalytical solution of the two-degree-of-freedom sys-tem. The comparisons included different angular ve-locities and accelerations of the driving system anddifferent positions of the hoist load to determine theinfluence of these parameters on the dynamic effects.By analysing typical working cycles, the risks and po-tentials of the current tower crane calculation duringthe slewing process could be shown. The knowledgeof the dynamic loads on tower cranes can provideinformation about the quality of the standard’s loadassumptions.To verify the statements on the dynamic propertiesand the applicability of the vibration model, system-atic comparisons including different types of cranesshould be carried out in the future. Furthermore, newmeasurements of currently used tower cranes are nec-essary to obtain further results regarding the accuracyof the modelled crane and the different calculationmethods. An important question also arises from theapplicability of the vibration model to different work-ing processes, such as hoisting or luffing.

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Kleeberger, M., Schneidler, S., and Günthner, W. A. (2014).Untersuchung der dynamischen Beanspruchungen beiGittermast-Fahrzeugkranen und Vergleich mit derquasistatischen Auslegung der Norm. In Tagungs-band 22. Kranfachtagung. Otto von Guericke Univer-sity Magdeburg.

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EN 14439 (2010). European Committee for Standardiza-tion: Cranes - Safety - Tower cranes.

FEM 1.001 (1998). Federation Europeenne de la Manu-tention (FEM): Rules for the design of hoisting ap-pliances.

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ISO 8686-1 (2012). International Organization for Stan-dardization: Cranes - Design principles for loads andload combinations - Part 1: General.

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Vienna University of Technology (Institute for Engi-neering Design and Product Development) togetherwith University of Belgrade (Faculty of MechanicalEngineering).