FEDERATION EUROPEENNE DE LA MANUTENTION

SECTION I

HEAVY LIFTING APPLIANCES

F.E.M.

1.001 3rd EDITION

REVISED 1998.10.01

RULES FOR THE DESIGN OF

HOISTING APPLIANCES

B O O K L E T 1

OBJECT AND SCOPE

The total 3rd Edition revised comprises booklets 1 to 5 and 7 to 9 Copyright by FEM Section I

Also available in French and German

Booklet 1

OBJECT AND SCOPE

1.1. PREFACE.............................................................................................................................. 2

1.2. INTRODUCTION ................................................................................................................... 3

1.3. OBJECT OF THE RULES ..................................................................................................... 5

1.4 SCOPE .................................................................................................................................. 6

LIST OF SYMBOLS AND NOTATIONS .......................................................................................... 7

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1.1. PREFACE

The Rules for the Design of Hoisting Appliances set up by the Technical Committee of the Section Iof the F.E.M., which have been published so far in two Editions, the first one in 1962 and thesecond in 1970, have been increasingly widely used in many countries all over the world.

Taking accourt of this enlarged audience, Section I of the FEM decided to change the format ofthese Design Rules and to facilitate updating by abandoning the single volume form and dividingthe work into a number of separate booklets as follows :

Booklet 1 - Object and Scope

Booklet 2 - Classification and loading on structures and mechanisms

Booklet 3 - Calculating the stresses in the structure

Booklet 4 - Checking for fatigue and choice of mechanism components

Booklet 5 - Electrical equipment

Booklet 6 - Stability and safety against movement by the wind

Booklet 7 - Safety rules

Booklet 8 - Test loads and tolerances

Although not directly a part of these Design Rules, the opportunity is taken to draw attention to thenew Terminology of Section I.

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1.2. INTRODUCTION

To facilitate the use of these Rules by the purchasers, manufacturers and safety organizationsconcerned, it is necessary to give some explanation in regard to the two following questions.

1. How should these Rules be applied in practice to the different types of appliance whoseconstruction they cover ?

2. How should a purchaser use these Rules to define this requirements in relation to anappliance which he desires to order and what conditions should he specify in this enquiry toensure that the manufacturers can submit a proposal in accordance with tris requirements ?

1. It is necessary first to recognize the great variety of appliances covered by the Design Rules. Itis obvious that a crane having very high speeds and a rapid working cycle is not designed in thesame manner as a small overhead crane for infrequent duty. For such a machine there can beno question of making all the verifications which would appear to be required, from readingthrough the Rules, because one would clearly finish with a volume of calculations which wouldbe totally out of proportion to the objective in view. The manufacturer must therefore decide ineach particular case which parts of the machine, which he is designing, should be analysed andthose for which calculation is unnecessary, not because he must accept that the results for thelatter would not be in accordance with the requirements of the Rules, but because on thecontrary he is certain in advance that the calculations for the latter would only confirm afavourable outcome. This may be because a standard compornent is being used which hasbeen verified once and for all or because it has been established that some of the verificationsimposed by the Rules cannot in certain cases have an unfavourable result and therefore serveno purpose.

If one takes, for exemple, the fatigue calculations, it is very easy to see that certain verificationsare unnecessary for appliances of light or moderate duty because they always lead to theconclusions that the most unfavourable cases are those resulting from checking safety inrelation to the elastic limit.

These considerations show that calculations made in accordance with the Rules can take a verydifferent form according to the type of appliance which is being considered, and may in the caseof a simple machine or a machine embodying standard components be in the form of a briefsummary without prejudicing the compliance of the machine with the principles set out by theDesign Rules.

2. As far as the second question is concerned, some explanation is first desirable for thepurchaser, who may be somewhat bewildered by the extent of the document and confusedwhen faced with the variety of choice which it presents, a variety which is, however, necessary ifone wishes to take account of the great diversity of problems to be resolved.

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In fact, the only important matter for the purchaser is to define the duty which he expects from hisappliance and if possible to give some indication of the duty of the various motions.

As regards the service to be performed by the appliance, two factors must be specified, i.e. :

- the class of utilization, as defined in 2.1.2.2 ;

- the load spectrum, as defined in 2.1.2.3.

In order to arrive at the number of hoisting cycles determining the class of utilization, the purchasermay, for instance, find the product of :

- the number of hoisting cycles which the appliance will have to average each day on which it isused ;

- the average number of days of use per year ;

- the number of years after which the appliance may be considered as having to be replaced.

Similarly, the load spectrum may be calculated by means of the simplified formula set out in theabove mentioned paragraph.

In neither case do the calculations call for a high degree of accuracy, being more in the nature ofestimates than of precise calculations. Moreover, the numbers of hoisting cycles determining theclasses of utilization do not constitute guaranteed values : they are merely guide values, serving asa basis for the fatigue calculations and corresponding to an average life which can be expectedwith a reasonable degree of safety, provided the appliance, designed in accordance with thepresent design rules, is used under the conditions specified by the customer in his call for tenderand also that it is operated and maintained regularly in compliance with the manufacturer'sinstructions.

If he is unable to determine the class of utilization and the load spectrum, the purchaser mayconfine himself to stating the group in which the appliance is to be classified. A guide as to thechoice of group is provided by Table 2.1.2.5., which is not binding but gives simple exempleswhich, by way of comparison, may facilitate selection.

In the case of mecanisms, the following should also be specified :

- the class of utilization, as specified in 2.1.3.2. :

- the load spectrum, as defined in 2.1.3.3. :

the same observation apply as were made concerning the appliance as a whole.

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The tables in Appendix A.2.1.1. may be used to facilitate determination of the class of utilization.On the basis of the class of utilization of the appliance, they make it possible to determine a totalnumber of working hours for the mechanism, according to the average duration of a working cycleand the ratio between the operating time of the mechanism and the duration of the complete cycle.

Table T.2.1.3.5. may be used as a guide by a purchaser wishing simply to choose a group for eachof the mechanisms with which the appliance he wants to order is to be fitted.

As a general rule, the purchaser has no other information to supply in connection with the design ofthe appliance, except in certain cases :

- the area of hoisted loads presented to the wind, if this area is larger than those defined in2.2.4.1.2. ;

- the value of the out-of-service wind, where local conditions are considered to necessitatedesign for an out-of-service wind greater than that defined in 2.2.4.1.2.

1.3. OBJECT OF THE RULES

The purpose of these rules is to determine the loads and combinations of loads which must betaken into account when designing hoisting appliances, and also to establish the strength andstability conditions to be observed for the various load combinations.

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1.4 SCOPE

The Rules apply to the design of lifting appliances or parts of lifting appliances which appear in theillustrated terminology for cranes and heavy lifting appliances of Section I of the FEM.

Appliances not covered by Section I

1) Lifting appliances included in Section V, for exemple :

- mobile jib cranes on pneumatic or solid rubber tyres, crawler tracks, lorries, trailers andbrackets.

2) Lifting equipment which according to the internal regulations of FEM, are included in Section IX,that is to say :

- various items of series lifting equipment,

- electric hoists,

- pneumatic hoists,

- accessories for lifting,

- hand operated chain blocks,

- elevating platforms, work platforms, dock levellers,

- winches,

- jacks, tripods, combined apparatus for pulling and lifting,

- stacker cranes.

For series lifting equipment, those chapters of the Design Rules of Section I which have beenaccepted by Section IX should be used.

These rules comprise eight booklets. In addition some booklets contain appendices which givefurther information on the method of application.

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LIST OF SYMBOLS AND NOTATIONS

Symbol Unit Dsignation Paragraphe

A m2 Area exposed to wind 2.2.4.1.

A - Combined influence of residual tensile stresses with dead weightstresses 3.1

A1 A8 - Crane groups 2.1.2

Ae m2 Enveloped area of lattice 2.2.4.1.4

a mm Wheelbase of crane :Dimension of lattice in wind load calculation :Length of strip of plate in buckling calculation :Size of fillet weld in notch case 2.33

2.2.2.32.2.4.1.4A-3.4T.A.3.6.-2.33

a m/s2 Acceleration 5.8.3.1

B - Influence of thickness of structural member 3.1.1.2

B mm Width of lattice in wind load calculation 2.2.4.1.4

B0 B10 - Classes of utilization of structural members 2.1.4.2

b mm Breadth of section across wind front :Largest dimension of rectangular steel section :Length of plate in buckling calculation :Useful width of rail in wheel calculation

2.2.4.1.43.1.1.2A-3.44.2.4.1

C - Influence of cold :Coefficient used to calculate the tightening torque of bolts :Selection coefficient for choice of running steel wire ropes

3.1.1.3A-3.2.2.2.2.34.2.2.1.3.1

Cf - Shape coefficient in wind load calculation 2 2.4.1.4

c, c' - Factors characterising the slope of Whler curves 4.1.3.5

c1, c1max - Rotation speed coefficients for wheel calculation 4.2.4.1

c2, c2max - Group coefficient for wheel calculation 4.2.4.1

cos - Power factor 5.2.3.3.2

D - Symbol used in plate inspection for lamination defects T.A.3.6

D m Section diameter in shape factor determination 2.2.4.1.4

D mm Rope winding diameter :Wheel diameter :Shaft diameter in fatigue verification of mechanism parts .

4.2.3.14.2.4.1A-4.1.3

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Dt mm Diameter of bolt holes 3.2.2.2.1

d mm Depth of section parallel to wind direction in wind load calculation :Nominal diameter of bolt :Nominal diameter of rope :Shaft diameter in fatigue verification of mechanism parts

2.2.4.1.4A-3.2 .2 .2 .34.2.2.1.3A-4.1.3

d2 mm Bolt diameter at thread root 3.2.2.2.1

dc - Number of completed starts per hour 5.8.1.4

di - Number of impulses or incomplete starts per hour 5.8.1.4

dmin mm Minimum rope diameter A-4.2.2

dt mm Nominal bolt diameter 3.2.2.2.1

E N/mm2 Elastic modulus of steel A-3.4

E1 E8 - Groups of components 2.1.4.1

ED % Duty factor 5.8.1.4

e mm Thickness of strip of plate in buckling calculation :Thickness of plate in welded joints

A-3.4T.A-3.6-2.31

e1, e2 mm Plate thicknesses in welded joints A-3.4

F N Wind force :Horizontal force during acceleration :Tensile load in bolts :Compressive force on member in crippling calculation

2.2.4.1.2A-2.2.33.2.2.2.2A-3.3

F0 N Minimum breaking load of rope 4.2.2.1.2

F1 N Permissible working load on bolts 3.2.2.2.1

Fc N Projection of rope load on the x axis during travelling A-2.2.3

Fcm N Inertia force due to the load during travelling A-2.2.3

Fcmax N Maximum value of Fc A-2.2.3

f - Fill factor of rope 4.2.2.1.3

fcy Number of electrical brakings 5.8.1.4

g m/s2 Acceleration due to gravity. according to ISO 9.80665 m/S2 A-2.2.3

H - Coefficient depending on group for choice of rope drums andpulleys 4.2.3.1.1

I kgm2 Moment of inertia of mass in slewing motion A-2.2.3.-3

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I1, I2 mm4 Moment of inertia of stiffeners A-3.4

ID A Starting current of motor 5.2.3.3.2

IN A Nominal current of motor 5.2.3.3.1

Itot A Sum of currents IA and IN 5.2.3.3.2

IZ mm4 Moment of inertia of stiffeners A-3.4

Ii kgm2 Moment of inertia of mass of a part in rotation A-2.2.3

Im kgm2 Moment of inertia of mass of all parts in rotation A-2.2.3.-2.1

JM kgm2 Moment of inertia of mass of motor and brake 5.8.1.4

j - Group number in component groups E1 to E8 4.1.3.6

j0 m/s2 Acceleration in horizontal motions A-2.2.3.-2.2

jm m/s2 Average acceleration/deceleration in horizontal motions A - 2.2.3

K - Empirical coefficient for determining minimum breaking strength ofrope 4.2.2.1.3

K0 K4 - Stress concentration classes for welded parts A-3.6

K2 - Coefficient for calculating force in the direction of the wind forlattice girders and towers 2.2.4.1.4.4

KL N/mm2 Pressure of wheel on rail 4.2.4.2

Km - Mn med / M max 4.2.1.2

k - Spinning loss coefficient 4.2.2.1.3

kc - Corrosion coefficient in fatigue verification of mechanism parts A-4.1.3

kd - Size coefficient in fatigue verification of mechanism parts A-4.1.3

km - Spectrum coefficient for mechanisms 2.1.3.3

kp - Spectrum coefficient for cranes 2.1.2.3

ks - Shape coefficient in fatigue verification of mechanism parts 4.1.3.3

ksp - Spectrum coefficient for components 2.1.4.3

ksp - Spectrum coefficient for mechanism parts 4.1.3.5

ku - Surface finish (machining) coefficient in fatigue verification ofmechanism parts 4.1.3.3

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K K - Buckling coefficients used in buckling calculations A-3.4

L N Maximum permissible lifting force 5.8.2.1

L1 L4 - Spectrum classes for mechanisms 2.1.3.3

l m Length of suspension/length of load pendulum A-2.2.3.-2

l m Equivalent length of fine 5.2.3.3.2

l m Length of members in wind force calculations :Overall width or rail head

2.2.4.1.4.14.2.4.1.2

lk m Length of parts tightened in bolted joints 3.2.2.2.1

M N.m External moment in bolted joints 3.2.2.2.2

M1 M8 - Mechanism groups ; 2.1.3.1

M1,M2, M3 - Motor torques required during a cycle of operations 5.8.1.3.1

MF N.m Braking torque of motor 5.8.2.1

MNmax N.m Maximum running torque required to lift the load 5.8.2.1

Ma N.m Torque required to tighten bolts A-3.2.2.2.2.3

MF N.m Bending moment in member in crippling calculation A-3.3

Mmax N.m Maximum value of motor torque 5.8.2.1

Mmed N.m Mean value of torque M during motor running time fiT 5.8.2.1

Mmin N.m Minimum motor torque during starting 5.8.2.1

m - Number of friction surfaces in bolted joints 3.2.2.2.2

m kg Equivalent mass for calculating loads due to horizontal motions :Total mass of crane

A-2.2.3.-1A-2.2.3.-2

m0 kg Mass of crane without load A-2.2 .3.-1

ml kg Mass of the load A-2.2 .3.-1

mL kg Mass of the hook load 5.8 .3.1

me kg Equivalent mass in calculation of loads due to horizontal motion A-2.2.3.-2.1

m kg Load 2.1.2.3

mlmax kg Safe working load 2.1.2.3

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N - Number of hoisting cycles A-2.1.1

N N Force perpendicular to joint plane in bolted joints 3.2.2.2.2

NG - Ordinary quality in welding 3-57 $$$$$

NM N Tensile force due to external moment in bolted joints 3.2.2.2.2

n - Number of hoisting cycles :Number of stress cycles

2.1.2.34.1.3.5

n min-1 Nominal rotation speed of motors in rpm 5.8.1.4

nmax - Number of hoisting cycles determining the total duration of use 2.1.2.3

P N Load on wheel 4.2.4.2

P1 P4 - Spectrum classes for components 2.1.4.3

P10, P100 - Symbols indicating welding tests T.A-3.6

PL N/mm2 Limiting pressure in wheel calculation 4.2.4.1

PN W Nominal power of motor 5.8.1.4

PNmax W Maximum power requirement of motor 5.8.2.1

Pmoy I, II N Mean load on wheel in loading cases I and II 4.2.4.1

Pmoy III N Mean load on wheel in loading case III 4.2.4.1

Pmin I, II, III N Minimum load on wheel in loading cases I, II and III 4.2.4.1

Pmax I, II,III N Maximum load on wheel in loading cases I, II and III 4.2.4.1

Pmed kW Equivalent mean power 5.8.1.3.2

p mm Span of crane 2.2.3.3

pa mm Pitch of thread 3.2.2.2.1

Q1 Q4 - Spectrum classes for cranes 2.1.2.3

q - Correction factor for shape coefficient ks A-4.1.3

q N/mm2 Dynamic pressure of the wind 2.2.4.1.1

R0 N/mm2 Minimum ultimate tensile strength of the wire of a rope 4.2.2.1.3

RE N/mm2 Apparent elastic limit E according to ISO 3800/1 3.2.2.2.1

r - Number of levers of loading :Ratio of stresses for large deformations

2.1.3.33.5

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r mm Radius of cylindrical shells in buckling calculations :Radius of rope groove :Radius of rail head :Blending radius

A-3.44.2.3.24.2.4.1.2A-4.1.3

r /km Ohmic resistance per unit length 5.3.2

S N Stress :Maximum tensile force in rope

2.1.3.3 4.2.2.1.1.2

S m2 Area of all members of lattice girders and towers 2.2.4.1.4.4

S mm2 Cross sectional area of conductor 5.2.3.3.2

S1 mm Bearing diameter under bolt head 3.2.2.2.1

SG N Load due to dead weight. constant load . 2.2.1 & 3.5

SH N Load due to horizontal motions 2.2.3

SL N Load due to working load 2.2.1

SM N Load due to torques 2.5

SMmoy N Mean type M load in bearing calculation 4.2.1.2

SMmin N Minimum type M load in bearing calculation 4.2.1.2

SMmax I N Maximum type M load in load case I 2.6.1.1

SMmax II N Maximum type M load in load case II 2.6.2.1

SMmax III N Maximum type M load in load case III 2.6.3.1

SMA N Load due to acceleration or braking 2.5.1

SMCmax N Load due to maximum motor torque 2.6.4.3

SMF N Load due to frictional forces 2.5.1

SMG N Load due to vertical displacement of moveable parts of a liftingappliance. excluding the working load 2.5.1

SML N Load due to vertical displacement of the working load 2.5.1

SMW N Load due to the effect of limiting wind for appliance in service2.5.1

SMW 8 N Load due to wind effect for q - 80 N/mm2 2.6.2.1

SMW 25 N Load due to wind effect for q - 250 N/m2 2.6.2.1

SR N Load due to forces not reacted by torques 2.5

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SRmax I N Maximum type R load in loading case I 2.6.1.1

SRmax II N Maximum type R load in loading case II 2.6.2.1

SRmax III N Maximum type R load in loading case III 2.6.3.1

SRmin N Minimum type R load in bearing calculation 4.2.1.3

SRmoy N Mean type R load in bearing calculation 4.2.1.3

SRA N Load due to accelerations/decelerations 2.5.2

SRG N Load due to self weight of crane parts 2.5.2

SRL N Load due to working load 2.5.2

SRW N Load due to wind 2.5.2

SRWmax N Load due to out of service wind 2.5.2

SRW25 N Wind load for q - 250 N/m2 2.6.2.2

ST N Load due to buffer effect 2.3.3

SV N Variable load when calculating structural members subject to largedeformations 3.5

SW N Load due to in service wind 2.3.2

SWmax N Load due to out of service wind 2.3.3

Sb mm2 Root sectional area of bolt 3.2.2.2.1

Seq mm2 Equivalent sectional area of tightened bolt 3.2.2.2.1

Sp mm2 Area of members of lattice girders and towers 2.2.4.1.4.4

s m Span of lifting appliance :Rail centres of crab :Distance between travel rails of lifting appliance

8.2.2.18.2.2.48.2.3

T h Total duration of use of lifting appliance 2.1.3.3

T J Total kinetic energy in luffing motion A-2.2.3.-4

T C Ambient temperature at place of erection 3.1.1.3

T N Force parallel to joint plane in bolted joint3.2.2.2.2

T s Duration of cycle 5.8.1.4

T0 T9 - Classes of utilization of mechanisms 2.1.3.2

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T1 s Period of oscillation A-2.2.3.-2

Ta N Permissible load per bolt which can be transmitted by friction3.2.2.2.2

Tc C Test temperature for impact test 3.1.3

Ti h Total duration of use of mechanism A-2.1.1

Tm s Mean duration of acceleration or deceleration A-2.2.3-2

t s Time when calculating loads due to horizontal motionA-2.2.3.-2.1

t mm Thickness of structural member when choosing steel quality :Thickness of cylindrical shell wall in buckling analysis :Thickness of web of trolley rail girder

3.1.1.2

A-3.48.2.2.7

t1, t2...ti, tr

s Duration of different levers of loading 2.1.3.3

t1, t2, t3 s Duration of action of couples M1, M2 and M3 5.8.1.3.1

t* mm Ideal section thickness when choosing steel quality 3.1.1.2

td s Duration of deceleration when calculating loads due to horizontalmotion 2.2

tmc s Average duration of a hoisting cycle A-2.1.1

U0 U9 - Classes of utilization of lifting appliances 2.1.2.2

u V Permissible voltage drop 5.3.2

VL m/s Hoisting speed : 2.2.2.1.15.8.2 .1

Vs m/s Theoretical wind speed 2.2.4.1.1

Vt m/s Nominal travel speed of appliance 2.2.3.4.1

v m/s Steady horizontal speed of point of suspension of load A-2.2.3.-2

v mm Distance of extreme fibre from centre of gravity of section incrippling calculation A-3.3

v m/s Travel speed 5.8.3.1

W0, W1, W2 - Notch cases of unwelded members A-3.6

Wi s-1 Angular velocity of a mechanism part about its centre of rotation

when calculating loads dueto horizontal motion A-2.2.3

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x /km Reactance per unit length 5.3.2

x m Coordinate of point of suspension of hoist rope along an axisparallel to the direction of travel 2.1

x1 m Coordinate of position of centre of gravity of suspended load alongan axis having the same direction. sense and origin as the axis ofx 2.1

ZA - Assessing coefficient for influence A 3.1.1.1

ZB - Assessing coefficient for influence B 3.1.1.2

ZC - Assessing coefficient for influence C 3.1.1.3

Zp - Minimum practical factor of safety for choice of steel wire ropes4.2.2.1

z m Coordinate expressing horizontal displacement of load relative tocrane A-2.2.3.-2.1

zd m Displacement of load during travel motion of craneA-2.2.3.-2.2

zm m Displacement of load during travel motion of craneA-2.2.3.-2.2

- Ratio of sides of panel in buckling calculation T.A-3.4.1

i - Ratio of duration of use of mechanism during a hoisting cycle toaverage duration of cycle A-2.1.1

m Angle of inclination of rope during acceleration of craneA-2.2.3.-2.1

- Time coefficient relating to acceleration of craneA-2.2.3

crit - Critical value of A-2.2.3.-2.2

c - Amplifying coefficient of loading depending on crane group2.3

m - Amplifying coefficient of loading depending on mechanism group2.6

l1 mm Shortening of joined elements under the tightening force in boltedjoints 3.2.2.2.1

l2 mm Extension of bolt under tightening force 3.2.2.2.1

s mm Divergence in span of crane :Divergence in crane rail centres

8.2.2.18.2.3

b - Elastic coefficient of bolted joints 3.2.2.2.1

- Shielding coefficient in calculation of wind force :Poisson's ratio :Overall efficiency of mechanism

2.2.4.1.4.2A-3.45.8.3.1

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Angle of wind relative to longitudinal axis of member 2.2.4.1.4.4

, , - Safety coefficients applying to bolted joints 3.2.2.2.1

- Ratio of the extreme stress values in fatigue calculation3.6

m/mm2Electric conductivity 5.2.3.3.2

x, y, xy - Ratio of extreme individual stresses x, y , xy in fatiguecalculation A-3.6

- Coefficient applied to horizontal forces in travel motions :Slenderness of column in crippling calculation

2.2.3.3A-3.3

- Mass constant in calculation of loads due to acceleration ofhorizontal motion :Coefficient of friction in threads :Coefficient of friction of contact surfaces in bolted joints

A-2.2.3.-23.2.2.2.13.2.2.2.2.-3

- Safety coefficient for critical stresses in structural members 3.Intro]

- Dead weight coefficient in calculation of structural memberssubjected to significant deformation 3.5

E - Safety coefficient for calculation of structural members dependingon case of loading 3.2.1.1

R - Safety coefficient for calculation of mechanism parts depending oncase of loading 4.1.1.1

T - = E , safety coefficient for calculation of bolted joints depending oncase of loading 3.2.2.2.2

V - Safety coefficient for buckling 3.4

K - Safety coefficient for verification of fatigue strength of mechanismparts 4.1.3.7

- Experimentally determined coefficient depending on crane type forcalculating dynamic coefficient 2.2.2.1.1

- Reducing coefficient applied to critical stresses in bucklingcalculation A-3.4

1 - Coefficient used to determine the dynamic test load 2.3.3

2 - Coefficient used to determine the static test load 2.3.3

N/mm2 Calculated stress in structures in general 3.2.1.1

0 N/mm2 Tensile stress for =0 in calculation of fatigue strength

A-3.6

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1 N/mm2 Working stress in the root section of bolts 3.2.2.1

1 N/mm2 Equivalent stresses permissible for bolts 3.2.2.1

+1 N/mm2 Permissible tensile stress for =+1 in fatigue calculation

A-3.6A N/mm

2 Amplitude of the permissible maximum stress in bolts for fatiguecalculations 3.2.2.1

E N/mm2 Apparent elastic limit of steel 3.2.2.1

G N/mm2 Tensile stress due to permanent load :

Stress due to dead weight3.1.1.13.5

R N/mm2 Ultimate tensile strength 3.2.2.1

ER N/mm2 The EULER Stress A-3.4

V N/mm2 Stress due to variable loads 3.5

a N/mm2 Permissible tensile stress for structural members :

Permissible stress for mechanism parts3.1.1.14.1.1.1

af N/mm2 Permissible normal stress for verification of fatigue strength of

mechanism parts 4.1.3.7

b N/mm2 Initial stress in calculating bolted joints 3.2.2.2.1

bw N/mm2 Endurance limit of materials of mechanism parts under alternating

bending 4.1.3.2

c N/mm2 Permissible fatigue strength in compression for structural members

:Calculated compressive stress for mechanism parts

A-3.64.1.1.3

cg N/mm2 Compression stress in wheel and rail 4.2.4.2

cp N/mm2 Equivalent stress used in calculating structural members 3.2.1.3

cr N/mm2 Critical stress used in calculating structural members subjected to

large deformations 3.5

vcr N/mm2 Critical buckling stress A-3.4

vcr.c N/mm2 Critical comparison stress used in buckling calculation A-3.4

d N/mm2 Endurance limit of materials of mechanism parts 4.1.3.4

f N/mm2 Calculated bending stress in mechanism parts 4.1.1.3

vi N/mm2 Ideal buckling stress for thin walled circular cylinders A-3.4

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inf N/mm2 Lower stress in determination of stress spectrum 2.1.4.3

k N/mm2 Fatigue strength of mechanism parts 4.1.3.6

kx N/mm2 Fatigue strength for normal stresses in the x direction 4.1.3.7

ky N/mm2 Fatigue strength for normal stresses in the y direction 4.1.3.7

m N/mm2 Arithmetic mean of all upper and lower stresses during the total

duration of use :Permissible stress in conformity tests to ISO 3600/1

2.1.4.33.2.2.2.1

max N/mm2 Maximum stress in fatigue calculation for structural members 3.6

min N/mm2 Minimum stress in fatigue calculation for structural members 3.6.4

n N/mm2 Bearing pressure in riveted joints 3.2.2.1

p N/mm2 Theoretical tensile stress in bolt due to tightening 3.2.2.2.1

sup N/mm2 Upper stress in determination of stress spectrum 2.1.4.3

sup max N/mm2 Maximum upper stress in determination fo stress spectrum 2.1.4.3

sup min N/mm2 Minimum upper stress in determination of stress spectrum 2.1.4.3

t N/mm2 Permissible tensile stress in fatigue verification of structural

members :Calculated tensile stress in mechanism parts :Tensile stress in rope

A-3.64.1.1.3A-4.2.2

v N/mm2 Reduced buckling stress of thin walled circular cylinders A-3.4

w N/mm2 Permissible stress in alternating tension/compression in fatigue

verification of mechanism parts A-3.6

wk N/mm2 Permissible alternating stress in fatigue verification of mechanism

parts 4.1.1.3

x N/mm2 Normal stress in the x direction when calculating structural

members 3.2.1.3

xa N/mm2 Permissible stress in fatigue verification of structural members A-3.6

x max N/mm2 Maximum stress in fatigue verification of structural members A-3.6

x min N/mm2 Minimum stress in fatigue verification of structural members A-3.6

y N/mm2 Normal stress in the y direction when calculating structural

members 3.2.1.3

ya N/mm2 Permissible stress in fatigue verification of structural members A-3.6

1 - 19

y max N/mm2 Maximum stress in fatigue verification of structural members

A-3.6y min N/mm

2 Minimum stress in fatigue verification of structural members A-3.6

N/mm2 Shear stress in general :Calculated shear stress for mechanism parts

3.2.1.34.1.1.3

a N/mm2 Permissible shear stress when calculating structural members 3.2.1.2

af N/mm2 Permissible shear stress in fatigue verification of mechanism parts 4.1.3.7

b N/mm2 Torsional stress in bolts due to tightening 3.2.2.2.1

vcr N/mm2 Critical buckling shear stress A-3.4

d N/mm2 Endurance limit of materials of mechanism parts 4.1.3.4

k N/mm2 Fatigue strength of mechanism parts 4.1.3.6

max N/mm2 Maximum shear stress in fatigue verification of mechanism parts 3.6.4

min N/mm2 Minimum shear stress in fatigue verification of mechanism parts 3.6.4

w N/mm2 Endurance limit under alternating shear of materials of mechanism

parts 4.1.3.2

wk N/mm2 Endurance limit under alternating shear in fatigue verification of

mechanism parts 4.1.3.3

xy N/mm2 Shear stress when calculating structural members 3.2.1.3

xya N/mm2 Permissible shear stress in fatigue verification of structural

members A-3.6

xy max N/mm2 Maximum shear stress in fatigue verification of structural members A-3.6

xy min N/mm2 Minimum shear stress in fatigue verification of structural members A-3.6

, - Slope of Whler curve 4.1.3.5

- Dynamic coefficient for hoist motion :Ratio of stresses at plate edges in buckling calculation

2.2 .2.1.13.4

h - Dynamic coefficient when calculating loads due to acceleration ofhorizontal motions A-2.2.3.-2

- Tolerance factor in bolted joints 3.2.2.2.1

- Crippling coefficient 3.3

s-1 Angular velocity of shaft when calculating loads due to horizontal

1 - 20

motion A-2.2.3.-3

1, 2, r s-1 Frequencies of oscillation during load swing A-2.2.3.-2.2

m s-1 Angular velocity of motor A-2.2.3.-2.1

FEDERATION EUROPEENNE DE LA MANUTENTION

SECTION I

HEAVY LIFTING APPLIANCES

F.E.M.

1.001 3rd EDITION

REVISED 1998.10.01

RULES FOR THE DESIGN OF

HOISTING APPLIANCES

B O O K L E T 2

CLASSIFICATION AND LOADING ON STRUCTURES AND MECHANISMS

The total 3rd Edition revised comprises booklets 1 to 5 and 7 to 9 Copyright by FEM Section I

Also available in French and German

Booklet 2

CLASSIFICATION AND LOADING

ON STRUCTURES AND MECHANISMS

2.1 GROUP CLASSIFICATION OF HOISTING APPLIANCES AND THEIR COMPONENT PARTS.......................................................................................................................................................................4

2.1.1. GENERAL PLAN OF CLASSIFICATION .................................................................................4

2.1.2. CLASSIFICATION OF HOISTING APPLIANCES AS A WHOLE..........................................42.1.2.1. CLASSIFICATION SYSTEM ...................................................................................................... 42.1.2.2. CLASSES OF UTILIZATION...................................................................................................... 42.1.2.3. LOAD SPECTRUM .................................................................................................................... 52.1.2.4. GROUP CLASSIFICATION OF HOISTING APPLIANCES............................................................ 72.1.2.5. GUIDANCE ON GROUP CLASSIFICATION OF AN APPLIANCE................................................. 7

2.1.3. CLASSIFICATION OF INDIVIDUAL MECHANISMS AS A WHOLE .....................................72.1.3.1. CLASSIFICATION SYSTEM ...................................................................................................... 72.1.3.2. CLASSES OF UTILIZATION...................................................................................................... 92.1.3.3. LOADING SPECTRUM............................................................................................................... 92.1.3.4. GROUP CLASSIFICATION OF INDIVIDUAL MECHANISMS AS A WHOLE............................... 102.1.3.5. GUIDANCE FOR GROUP CLASSIFICATION OF INDIVIDUAL MECHANISMS AS A WHOLE .... 10

2.1.4. CLASSIFICATION OF COMPONENTS .................................................................................122.1.4.1. CLASSIFICATION SYSTEM .................................................................................................... 122.1.4.2. CLASSES OF UTILIZATION.................................................................................................... 122.1.4.3. STRESS SPECTRUM............................................................................................................... 132.1.4.4. GROUP CLASSIFICATION OF COMPONENTS ........................................................................ 14

2 - 2

2.2. LOADS ENTERING INTO THE DESIGN OF STRUCTURES ..........................................................15

2.2.1. PRINCIPAL LOADS...................................................................................................................15

2.2.2. LOADS DUE TO VERTICAL MOTIONS..................................................................................162.2.2.1. LOADS DUE TO HOISTING OF THE WORKING LOAD............................................................. 16

2.2.2.1.1. VALUES OF THE DYNAMIC COEFFICIENT ................................................................... 162.2.2.2. LOADS DUE TO ACCELERATION (OR DECELERATION) OF THE HOISTING MOTION AND TOVERTICAL SHOCK LOADINGS WHEN TRAVELLING ALONG RAIL TRACKS ...................................... 172.2.2.3. SPECIAL CASE........................................................................................................................ 17

2.2.3. LOADS DUE TO HORIZONTAL MOTIONS SH......................................................................192.2.3.1. HORIZONTAL EFFECTS DUE TO ACCELERATION (OR DECELERATION)........................ 19

2.2.3.1.1. TRAVERSE AND TRAVEL MOTIONS................................................................................ 192.2.3.1.2. SLEWING AND LUFFING (DERRICKING) MOTIONS ......................................................... 20

2.2.3.2. EFFECTS OF CENTRIFUGAL FORCE....................................................................................... 202.2.3.3. TRANSVERSE REACTIONS DUE TO ROLLING ACTION.......................................................... 212.2.3.4. BUFFER EFFECTS ST............................................................................................................... 21

2.2.3.4.1. BUFFER EFFECTS ON THE STRUCTURE ........................................................................ 212.2.3.4.2. BUFFER EFFECTS ON THE SUSPENDED LOAD ............................................................. 22

2.2.4. LOADS DUE TO CLIMATIC EFFECTS...................................................................................222.2.4.1 WIND ACTION........................................................................................................................... 22

2.2.4.1.1. WIND PRESSURE......................................................................................................... 222.2.4.1.2. DESIGN WIND CONDITIONS ............................................................................................ 23

2.2.4.1.2.1. In-service wind ................................................................................................................ 232.2.4.1.2.2. Wind out of service .......................................................................................................... 24

2.2.4.1.3. WIND LOAD CALCULATIONS........................................................................................... 252.2.4.1.4. SHAPE COEFFICIENTS.................................................................................................... 25

2.2.4.1.4.1. Individual members, frames, etc. ........................................................................................ 252.2.4.1.4.2. Multiple frames of members : shielding factors...................................................................... 282.2.4.1.4.3. Lattice towers.................................................................................................................. 292.2.4.1.4.4. Parts inclined in relation to the wind direction ....................................................................... 29

2.2.4.2. SNOW LOAD........................................................................................................................... 302.2.4.3. TEMPERATURE VARIATIONS.................................................................................................. 30

2.2.5 MISCELLANEOUS LOADS.......................................................................................................302.2.5.1. LOADS CARRIED BY PLATFORMS......................................................................................... 30

2.3. CASES OF LOADING ........................................................................................................................31

2.3.1. CASE I : APPLIANCE WORKING WITHOUT WIND.............................................................31

2.3.2. CASE II : APPLIANCE WORKING WITH WIND ....................................................................31

2.3.3. CASE III : APPLIANCE SUBJECTED TO EXCEPTIONAL LOADINGS .............................32

2.3.4. CHOOSING THE AMPLIFYING COEFFICIENT C ...............................................................33

2.4. SEISMIC EFFECTS ............................................................................................................................33

2.5. LOADS ENTERING INTO THE DESIGN OF MECHANISMS..........................................................34

2.5.1. TYPE SM LOADS........................................................................................................................34

2.5.2. TYPE SR LOADS........................................................................................................................34

2 - 3

2.6. CASES OF LOADING ........................................................................................................................35

2.6.1. CASE I - NORMAL SERVICE WITHOUT WIND....................................................................352.6.1.1. TYPE SM LOADS..................................................................................................................... 352.6.1.2. TYPE SR LOADS ..................................................................................................................... 35

2.6.2. CASE II - NORMAL SERVICE WITH WIND ...........................................................................362.6.2.1. TYPE SM LOADS..................................................................................................................... 362.6.2.2. TYPE SR LOADS ..................................................................................................................... 36

2.6.3. CASE III - EXCEPTIONAL LOADS ..........................................................................................372.6.3.1. TYPE SM LOADS..................................................................................................................... 372.6.3.2. TYPE SR LOADS ..................................................................................................................... 37

2.6.4. APPLICATION OF THE ABOVE CONSIDERATIONS FOR CALCULATING SM ..............372.6.4.1. HOISTING MOTIONS................................................................................................................ 382.6.4.2. HORIZONTAL MOTIONS.......................................................................................................... 382.6.4.3. COMBINED MOTIONS .............................................................................................................. 39

.....................................................................................................................................................................39

APPENDIX..................................................................................................................................................40

A.2.1.1. - HARMONISATION OF THE CLASSES OF UTILIZATION OF APPLIANCES ANDMECHANISMS.......................................................................................................................................40

A.2.2.3. - CALCULATION OF LOADS DUE TO ACCELERATIONS OF HORIZONTAL MOTIONS.................................................................................................................................................................45

2 - 4

2.1 GROUP CLASSIFICATION OF HOISTING APPLIANCESAND THEIR COMPONENT PARTS

2.1.1. GENERAL PLAN OF CLASSIFICATION

In the design of a hoisting appliance and its component parts, account must be taken of the dutywhich they will be required to perform during their duration of use ; for this purpose groupclassification is employed of :

- the appliance as a whole ;

- the individual mechanisms as a whole ;

- the structural and mechanical components.

This classification is based on two criteria, namely :

- the total duration of use of the item considered ;

- the hook load, loading or stress spectra to which the item is subjected.

2.1.2. CLASSIFICATION OF HOISTING APPLIANCES AS A WHOLE

2.1.2.1. CLASSIFICATION SYSTEM

Appliances as a whole are classified in eight groups, designated by the symbol A1, A2, ..., A8respectively (see section 2.1.2.4.), on the basis of ten classes of utilization and four load spectra.

2.1.2.2. CLASSES OF UTILIZATION

By duration of use of a hoisting appliance is meant the number of hoisting cycles which theappliance performs. A hoisting cycle is the entire sequence of operations commencing when aload is hoisted and ending at the moment when the appliance is ready to hoist the next load.

The total duration of use is a computed duration of use, considered as a guide value,commencing when the appliance is put into service and ending when it is finally taken out ofservice.

On the basis of the total duration of use, we have ten classes of utilization, designated by thesymbol U0, U1, ..., U9. They are defined in table T.2.1.2.2.

2 - 5

Table T.2.1.2.2. - Classes of utilization

SymbolTotal duration of use

(number nmax of hoisting cycles)U0U1U2U3U4U5U6U7U8U9

16 00032 00063 000

125 000250 000500 000

1 000 0002 000 0004 000 000

50

Rolled sections [ ]

Rectangular hollowsections up to356 mm square

and 254 x 457 mmrectangular

1,15

1,4

1,05

1,15

1,45

1,05

1,3

1,5

1,2

1,4

1,55

1,3

1,45

1,55

1,4

1,5

1,55

1,5

1,6

1,6

1,6

Other sections 1,30 1,35 1,60 1,65 1,70 1,80 1,80Individualmembers

Circular sections where :

D.Vs < 6 m2/sD.Vs 6 m2/s

0,600,60

0,700,65

0,800,70

0,850,70

0,900,75

0,900,80

0,900,80

Rectangularhollow sectionsover 356 mmsquare and254 x 457 mmrectangular

Wind

b/d21

0,50,25

1,551,401,00,80

1,751,551,200,90

1,951,751,300,90

2,101,851,351,0

2,201,901,401,0

Flat-sided sections 1,70Singlelatticeframes

Circular sections where :

D.Vs < 6 m2/sD.Vs 6 m2/s

1,100.80

Machineryhousesetc.

Rectangular cladstructures on groundor solid base

1,10

(1) See figure 2.2.4.1.4.1.

b

d

2 - 28

(I) Aerodynamic slenderness :( length of member ) / ( breadth of section across wind front ) = l/b * or l/D *

* In lattice construction the lengths of individual members are taken between the centres ofadjacent node points. See diagram below

(II) Solidity ratio : (area of solid parts) / (enclosed area) = A /Ae = 1n [(li . bi)/(L . B)]

(III) Spacing ratio :(distance between facing sides) / (breadth of members across wind front ) = a/b or a/B

for "a" take the smallest possible value in the geometry of the exposed face.

(IV) Section ratio :(breadth of section across wind front) / (depth of section parallel to wind flow)= b/d

Figure 2.2.4.1.4.1. - Definitions : Aerodynamic Slenderness, Solidity Ratio,Spacing Ratio, and Section Ratio

2 - 29

2.2.4.1.4.2. Multiple frames of members : shielding factors

Where parallel frames or members are positioned so that shielding takes place, the wind loadson the windward frame or member and on the unsheltered parts of those behind it are calculatedusing the appropriate shape coefficients. The wind load on the sheltered parts is multiplied by ashielding factor given in table T.2.2.4.1.4.2. Values of vary with the solidity and spacing ratiosas defined in figure 2.2.4.1.4.1.

Table T.2.2.4.1.4.2. - Shielding coefficients

Spacing ratio Solidity ratio A/Aea/b 0,1 0,2 0,3 0,4 0,5 0,60,51,02,04,05,06,0

0,750,920,951,01,01,0

0,400,750,800,880,951,0

0,320,590,630,760,881,0

0,210,430,500,660,811,0

0,150,250,330,550,751,0

0,100,100,200,450,681,0

Where a number of identical frames or members are spaced equidistantly behind each other insuch a way that each frame shields those behind it, the shielding effect is assumed to increaseup to the ninth frame and to remain constant thereafter.The wind loads are calculated as follows :

On the 1st. frame F1 = A.q.Cf in N

On the 2nd. frame F2 = .A.q.Cf in N

On the n.th frame Fn = (n-1).A.q.Cf(where n is from 3 to 8) in N

On the 9th and subsequent F9 = 8.A.q.Cf in Nframes

The total wind load is thus :

Where there are up to 9 frames Ftotal = [1 + + 2 + 3 + .... + (n-1)].A.q.Cf= [(1 - n) / (1 - )].A.q.Cf in N

Where there are more than Ftotal = [1 + + 2 + 3 + .... + n8 + ( - 9)8].A.q.Cf9 frames = [(1 - 9) / (1 - ) + (n - 9) 8].A.q.Cf in N

Note - The term x used in the above formula is assumed to have a longer limit of 0.10. It is takenas 0.10 whenever x < 0.10.

2 - 30

2.2.4.1.4.3. Lattice towers

In calculating the "face-on" wind load on square towers, in the absence of a detailed calculation,the solid area of the windward face is multiplied by the following overall force coefficient :For towers composed of flat sided sections 1,7 (1 + )For towers composed of circular sections

where D.Vs < 6 m2/s 1,1 (1 + )

where D.Vs 6 m2/s 1,4

The value of is taken from table 2.2.4.1.4.2. for a/b = 1 according to the solidity ratio of thewindward face.

The maximum wind load on a square tower occurs when the wind blows on to a corner. In theabsence of a detailed calculation, this load can be considered as 1.2 times that developed with"face-on" wind on one side.

2.2.4.1.4.4. Parts inclined in relation to the wind direction

Individual members. frames, etc.

Where the wind blows at an angle to the longitudinal axis of a member or to the surface of aframe, the wind load in the direction of the wind is obtained from :

F = A.q.Cf sin2 in N

where F, A, q and Cf are as defined in 2.2.4.1.3.and is the angle of the wind ( < 90) to the longitudinal axis or face.

Lattice trusses and towers

Where the wind blows at an angle to the longitudinal axis of a lattice truss or tower, the wind loadin the direction of the wind is obtained from :

F = A.q.Cf.K2 in Nwhere :F, A, q and Cf are as defined in 2.2.4.1.3. and K2 = / [50 (1,7 - Sp/S)]which cannot be less than 0,35 or greater than 1.

is the angle of the wind in degrees ( < 90) to the longitudinal axis of the truss or tower.

Sp is the area in m2 of the bracing members of the truss or tower projected on to its windward

plane.

S is the area in m2 of all (bracing and main) members of the truss or tower projected on to itswindward plane.

The value of K2 is assumed to have lower and upper limits of 0.35 and 1.0 respectively. It is takenas 0.35 whenever the calculated value < 0.35 and as 1.0 whenever the calculated value > 1.0.

2 - 31

2.2.4.2. SNOW LOAD

Snow loads shall be neglected in the design calculations for overhead travelling cranes, bridgecranes and jib cranes.

2.2.4.3. TEMPERATURE VARIATIONS

Stresses due to temperature variations shall be considered only in special cases such as whenmembers are not free to expand.

In such cases, the maximum temperature fluctuation shall be taken to be :- 20 C to + 45 C.

2.2.5 MISCELLANEOUS LOADS

2.2.5.1. LOADS CARRIED BY PLATFORMS

Access gangways, driver 's cabine and platforms shall be designed to carry the followingconcentrated loads :

3000 N for maintenance gangways and platforms where materials may be placed,

1500 N for gangways and platforms intended only for access of personnel,

300 N as the horizontal force which may be exerted on handrails and toe-guards.

These loads are not to be used in the calculations for girders.

2 - 32

2.3. CASES OF LOADING

Three different cases of loading are to be considered for the purpose of the calculations :

- the working case without wind,

- the working case with limiting working wind,

- the case of exceptional loadings.

Having determined the various loads in accordance with section 2.2, account is taken of a certainprobability of exceeding the calculated stress, which results from imperfect methods ofcalculation and unforeseen contingencies, by applying an amplifying coefficient C, which variesaccording to the group classification of the appliance.

The values of this coefficient C are indicated in clause 2.3.4.

2.3.1. CASE I : APPLIANCE WORKING WITHOUT WIND

The following shall be taken into consideration : the static loads due to the dead weight SG, theloads due to the working load SL multiplied by the dynamic coefficient , and the two mostunfavourable horizontal effects SH among those defined in clause 2.2.3., excluding buffer forces.

All these loads must then be multiplied by the amplifying coefficient C specified in clause 2.3.4.,viz :

C (SG + SL + SH)

In cases where travel motion takes place only for positioning the appliance and is not normallyused for moving loads the effect of this motion shall not be combined with another horizontalmotion. This is the case for example with a dockside crane which, once it has been positioned,handles a series of loads at a fixed point.

2.3.2. CASE II : APPLIANCE WORKING WITH WIND

The loads of case I are taken to which are added the effects of the limiting working wind SWdefined under 2.2.4.1.2.1. (table T.2.2.4.1.2.1.) and, where, applicable the load due totemperature variation, viz :

C (SG + SL + SH) + SW

Note - The dynamic effects of acceleration and retardation do not have the same values in case IIas in case I, for when a wind is blowing the accelerating or braking times are not the same aswhen still conditions prevail.

2 - 33

2.3.3. CASE III : APPLIANCE SUBJECTED TO EXCEPTIONAL LOADINGS

Exceptional loadings occur in the following cases :

- appliance out of service with maximum wind- appliance working and subjected to a buffer effect- appliance undergoing the tests indicated in booklet 8.

The highest of the following combinations shall be considered :

a) The loads SG due to the dead weight, plus the load Sw max due to the maximum wind asmentioned under clause 2.2.4.1.2.2. (including the reactions of the anchorages)

b) the loads SG due to the dead weight and SL due to the working load plus the greatest buffereffect ST as envisaged in clause 2.2.3.4.

c) the loads SG due to the dead weight plus the highest of the two loads 1 SL and 2 SL ; 1and 2 being the coefficients by which the safe working load is multiplied for the dynamictest (1) and for the static test (2) as in clauses 8.1.1. and 8.1.2.

These three cases are expressed by the formulae :a) SG + Sw maxb) SG + SL + ST

9

c) SG + 1 SL or SG + 2 SL

Note 1 - It should be noted that the checks under (c) are only to be made in cases where theworking load, when assumed to act alone, produces stresses opposed in direction to thosecaused by the dead weight up to the point at which the static test load does not exceed 1,5 timesthe safe working load.

Note 2 - When using decelerating devices in advance of buffer impact under the conditionsmentioned in clause 2.2.3.4.1. ST will be taken to be the highest load resulting either from theretardation previously caused by the decelerating device or from that finally caused by the buffer.

9 Loadings resulting from the working load are taken into account but the effects of load swingresulting from the stock are neglected because this swing only loads the structure when theother effects have been practically absorbed. This comment does not apply to rigidly guide loadswhich cannot swing.

2 - 34

2.3.4. CHOOSING THE AMPLIFYING COEFFICIENT C

The value of the amplifying coefficient c depends upon the group classification of the appliance.Table T.2.3.4. - Values of amplifying coefficient C

Appliancegroup A1 A2 A3 A4 A5 A6 A7 A8

c 1,00 1,02 1,05 1,08 1,11 1,14 1,17 1,20

2.4. SEISMIC EFFECTS

In general the structures of lifting appliances do not have to be checked for European seismiceffects.

However, if official regulations or particular specifications so prescribe, special rules orrecommendations can be applied in areas subject to earthquakes.

This requirement shall be advised to the supplier by the user of the installation who shall alsoprovide the corresponding seismic spectra.

2 - 35

2.5. LOADS ENTERING INTO THE DESIGN OF MECHANISMS

Mechanisms are subjected to two kinds of loading :

a) The loads, represented by the symbol SM, which are directly dependent upon the torquesexerted on the mechanisms by the motors or the brakes.

b) The loads, represented by the symbol SR, which are independent of motor or brake actionbut which are determined by the reactions which act upon the mechanical parts and whichare not balanced by a torque acting on the drive shafts 10.

2.5.1. TYPE SM LOADS

The loads of this type to be considered are :

a) SMG loads, corresponding to a vertical displacement of the centre of gravity of moving partsof the appliance other than the working load.

b) SML loads, corresponding to a vertical displacement of the working load as defined inclause 2.2. for structures.

c) SMF loads, corresponding to frictional forces which have not been allowed for in calculatingthe efficiency of the mechanism (see clause 4.2.6.1.1., booklet 4).

d) SMA loads, associated with acceleration (or braking) of the motion.

e) SMW loads, corresponding to the effect of the working wind assumed for the appliance.

2.5.2. TYPE SR LOADS

The loads of this type to be considered are :

a) SRG loads due to the weights of components which act on the part under consideration ;b) SRL loads due to the working load as defined in clause 2.2., for structures.c) SRA loads due to the accelerations or decelerations of the various motions of the

appliance or its parts, as calculated according to clause 2. 2.3.1. for structures, insofar asthe order of magnitude of these loads is not negligible compared to the SRG and SRL loads.

d) SRW loads due to the limiting working wind SW or to the maximum wind SW max (see clause2.2.4.1.), insofar as the order of magnitude of these loads is not negligible.

10 In a travel motion, for instance, the loads due to the vertical reaction on the rail wheels and thetransverse loads that stress the wheel axle but are not transmitted to the components of thedriving mechanism.

2 - 36

2.6. CASES OF LOADINGThree cases of loading are to be considered in the calculations :

Case I : Normal service without windCase II : Normal service with windCase III : Exceptional loadings.

A maximum load must be determined for each case of loading which serves as the basis for thecalculations.

Note - Clearly, case I and II are one and the same in the case of appliances which are notexposed to wind.

The various loadings being determined as indicated in paragraph 2.5., account is taken of acertain probability of exceeding the calculated stress, which results from imperfect methods ofcalculation and unforeseen contingencies, by applying an amplifying coefficient m depending onthe group in which the mechanism is classified. The values of this coefficient m are indicated intable T.2.6.

Table T.2.6. - Values of amplifying coefficient m

Mechanismgroup M1 M2 M3 M4 M5 M6 M7 M8

m 1,00 1,04 1,08 1,12 1,16 1,20 1,25 1,30

2.6.1. CASE I - NORMAL SERVICE WITHOUT WIND

2.6.1.1. TYPE SM LOADS

The maximum load SM max I of the SM type (see clause 2.5.) is determined by combining the loadsSMG, SML, SMF, and SMA defined in clause 2.5.1. which can be expressed by the relation :

SM max I = ( SMG + SML + SMF + SMA ) m

Note - It must be pointed out that it is not the combination of the maximum values of each of theterms in this relation that must be considered, but the value resulting from the most unfavourablecombination that could actually occur in practice.

2.6.1.2. TYPE SR LOADS

The maximum load SR max I of the SR type (see clause 2.5.) is determined by combining the loadsSRG, SRL, SRA, defined in clause 2.5.2. which can be expressed by the relation :

SR max I = ( SRG + SRL + SRA ) m

The note in clause 2.6.1.1. above applies here also.

2 - 37

2.6.2. CASE II - NORMAL SERVICE WITH WIND

2.6.2.1. TYPE SM LOADS

The maximum load SM max II of the SM type (see clause 2.5.) is determined by combining the loadsSMG, SML and SMF defined in clause 2.5.1. with one of the following two combinations :

a) the load SMA and the load SMW 8 corresponding to a 80 N/m2 wind.

b) the load SMW 25 corresponding to a 250 N/m2 wind.

The higher of the two values expressed by the relations set out below is taken :

SM max II = ( SMG + SML + SMF + SMA + SMW 8 ) mor

SM max II = ( SMG + SML + SMF + SMW 25 ) m

The note in clause 2.6.1.1. applies here also.

2.6.2.2. TYPE SR LOADS

The maximum load SR max II of the SR type (see clause 2.5.) is determined by combining the loadsSRG, SRL and SRA defined in clause 2.5.2. with SRW 25 which corresponds to a 250 N/m

2 wind, asexpressed by the relation :

SR max II = ( SRG + SRL + SRA + SRW 25 ) m

The note in clause 2.6.1.1. applies here also.

2 - 38

2.6.3. CASE III - EXCEPTIONAL LOADS

2.6.3.1. TYPE SM LOADS

The maximum load SM max III of the SM type defined under clause 2.5. is determined byconsidering the maximum load that the motor can actually transmit to the mechanism, allowingfor limitations due to practical operating conditions.

The values of SM max III are specified in clause 2.6.4.

2.6.3.2. TYPE SR LOADS

Since the consequences of an overload due to collision with a buffer or fouling are far lessserious for a mechanism than for the structure, the exceptional loading to be taken is that givenunder paragraph a) of clause 2.3.3. in the structures chapter.

This gives : SR max III = ( SRG + SRW max )

In cases where additional mooring or guying means are used to ensure immobility or stabilityunder maximum wind, the effect of these devices on the mechanism must be taken into accountwhere applicable.

2.6.4. APPLICATION OF THE ABOVE CONSIDERATIONS FOR CALCULATINGSM

The mechanisms of hoisting appliances perform one of the following functions :

- Purely vertical displacements of the centre of gravity of moving masses (e.g. hoistingmotions).

- Purely horizontal displacements in which the centre of gravity of the moving masses as awhole shifts horizontally (e.g. traverse, travel, slewing or counterbalanced luffing motions).

- Movements combining an elevation of the centre of gravity of the moving masses with ahorizontal displacement (e.g. non-counterbalanced luffing).

2 - 39

2.6.4.1. HOISTING MOTIONS

For type SM loads, the formula reduces to the following :

Case I and II : SM max I = ( SML + SMF ) m

In this case the load due to the hoisting acceleration is neglected because it is small comparedto SML.

Case III : SM max III = 1,6 ( SML + SMF )

Bearing in mind the general rules of clause 2.6.3.1., it is assumed that the maximum loads thatcan be transmitted to hoisting mechanisms are limited in practice to 1,6 times the SM max I load

11.

2.6.4.2. HORIZONTAL MOTIONS

Case I - The formula reduces to :

SM max I = ( SMF + SMA ) m

Case II - The higher of the following two values is taken :

SM max II = ( SMF + SMA + SMW 8 ) mor

SM max II = ( SMF + SMW 25 ) m

Case III - For SM max III the load corresponding to the maximum torque of the motor (or the brake)is taken unless operating conditions limit the torque actually transmitted, through wheel slip onthe rails, or through the use of suitable limiting means (e.g. hydraulic coupling, torque limiter,etc.). In this case the value actually transmitted must be taken 12.

11 In a hoisting motion it is impossible under normal working conditions to transmit to the mechanism loadsgreater than those due to the hoisting of the working load, as the effects of acceleration are negligible.A greater load could result only from mishandling (poor judgement of the load, etc.).On the basis of experience gained over many years of practice with widely differing hoistingappliances it is now accepted that a coefficient of 1,6 gives adequate safety. It must be stressedthat the use of excessively powerful motors should be avoided.12 Whereas in the case of hoisting motions the loads normally transmitted to the mechanism are limited by theload lifted, in horizontal motions the maximum torque of the motor can always be transmitted to themechanism if no mechanical limitation exists. This is why a different way of evaluating SM max III has beenspecified according to whether a hoist motion or other motion is being considered.

2 - 40

2.6.4.3. COMBINED MOTIONS

Case I and II :For cases I and II, the load SM max II

13 is determined by applying the general formula defined inclauses 2.6.1.1. and 2.6.2.1.

Case III :The load caused by applying the maximum motor torque SMC max III can be taken for the maximumvalue SM max III This often unduly high value is always acceptable since it enhances safety.

It must be used when the power involved for raising the centres of gravity of the moving massesis negligible compared to the power needed to overcome accelerations or wind effects.

Conversely, when the effect of the accelerations or the wind is negligible in comparison with theeffect of displacing the centres of gravity of the moving masses vertically, this value is too highand SM max III can be calculated from the formula :

SM max III = 1,6 SM max II

Between these two limiting values, each individual case should be examined according to themotor chosen, the method of starting and the relative magnitudes of the loads due to inertia andwind effects on the one hand and those due to raising of the centres of gravity on the other.

Without exception, when operating conditions limit the torque actually transmitted to themechanism (see clause 2.6.4.2.), this limiting torque will be taken as the value of SMC max if it isless than the values defined above.

.

13 or SM max I in the case of appliances not subjected to wind.

2 - 41

APPENDIX

A.2.1.1. - HARMONISATION OF THE CLASSES OF UTILIZATION OFAPPLIANCES AND MECHANISMS

The present appendix sets out to demonstrate a method by which it is possible in many cases toderive the class of utilization of mechanisms from that of appliances as a whole and from certainparameters characterising the duty to be performed.

The starting point is the average duration tmc (in seconds) of a hoisting cycle as defined in clause2.1.2.2. This is therefore the time necessary to perform all the operations in such a cycle.

The total duration of use T of the appliance, expressed in hours, is then given by the relation :

T = N.tmc / 3600

Where N represents the number of hoisting cycles determining the class of utilization of theappliance.

Table T.A.2.1.1.1. gives the values of T for cycle durations of 30 - 480 s in accordance with theclass of utilization of the appliance. The number of hoisting cycles is the maximum number forthis class of utilization ; these values are, however, adjusted to 15 625, 31 250 and 62 500respectively for class U0, U1 and U2, in order to reduce the number of different values for T.

The next step is to determine for each mechanism the ratio i between the duration of use of themechanism during a hoisting cycle and the average duration tmc of the cycle.

Table T.A.2.1.1.2. gives the total durations of use Ti of the mechanism depending on the totalduration of use of the appliance, and for various conventional values of the ratio i . This tablealso shows the class of utilization of the mechanism. The various classes are represented bythe stepped areas.

It is thus sufficient to determine the class of utilization of the appliance by reference to tableT.2.1.2.2., the average duration of the hoisting cycle and the values of i in order to obtain theclasses of utilization of the mechanisms.

From the curves of the nomogram T.A.2.1.1.3. the classes of utilization for the mechanisms interms of these three parameters can be found directly.

2 - 42

Table T.A.2.1.1.1. - Total duration of use (T) of lifting appliances in hours

Averagedurationof a

Class of utilization of appliances

hoisting cycletmc (s)

U0 U1 U2 U3 U4 U5 U6 U7 U8 U9

30

45

60

75

90

120

150

180

240

300

360

420

480

130

195

260

325

390

520

650

780

1 040

1 300

1 565

1 825

2 085

260

390

520

650

780

1 040

1 300

1 565

2 085

2 605

3 125

3 645

4 165

520

780

1 040

1 300

1 565

2 085

2 605

3 125

4 165

5 210

6 250

7 290

8 335

1 040

1 565

2 085

2 605

3 125

4 165

5 210

6 250

8 335

10 415

12 500

14 585

16 665

2 085

3 125

4 165

5 210

6 250

8 335

10 415

12 500

16 665

20 835

25 000

29 165

33 335

4 165

6 250

8 335

10 415

12 500

16 665

20 835

25 000

33 335

41 665

50 000

58 335

66 665

8 335

12 500

16 665

20 835

25 000

33 335

41 665

50 000

66 665

83 335

100 000

116 665

133 335

16 665

25 000

33 335

41 665

50 000

66 665

83 335

100 000

133 335

166 665

200 000________> 200 000

> 200 000

33 335

50 000

66 665

83 335

100 000

133 335

166 665

200 000________> 200 000

> 200 000

> 200 000

> 33 335

> 50 000

> 66 665

> 83 335

> 100 000

> 133 335

> 166 665________> 200 000

2 - 43

Table T.A.2.1.1.2. - Total duration of use Ti (in hours) of mechanisms in terms of T and i

T Values of i Class ofutilization for

(h) 1,00 0,63 0,40 0,25 0,16 0,10 mechanism130 130 82 52 33 21 13195 195 123 78 49 31 20260 260 164 104 65 42 26325 325 205 130 81 52 33390 390 246 156 98 62 39520 520 328 208 130 83 52 T0650 650 410 260 163 104 65780 780 491 312 195 125 78

1 040 1 040 655 416 260 166 1041 300 1 300 819 520 325 208 1301 565 1 565 986 626 391 250 1571 825 1 825 1 150 730 456 292 1832 085 2 085 1 314 834 521 334 2092 605 2 605 1 641 1 042 651 417 261 T13 125 3 125 1 969 1 250 781 500 3133 645 3 645 2 296 1 458 911 583 3654 165 4 165 2 624 1 666 1 041 666 4175 210 5 210 3 282 2 084 1 303 834 521 T26 250 6 250 3 938 2 500 1 563 1 000 6257 290 7 290 4 593 2 916 1 823 1 166 7298 335 8 335 5 251 3 334 2 084 1 334 834

10 415 10 415 6 561 4 166 2 604 1 666 1 042 T312 500 12 500 7 875 5 000 3 125 2 000 1 25014 585 14 585 9 189 5 834 3 646 2 334 1 45916 665 16 665 10 499 6 666 4 166 2 666 1 66720 835 20 835 13 126 8 334 5 209 3 334 2 084 T425 000 25 000 15 750 10 000 6 250 4 000 2 50029 165 29 165 18 374 11 666 7 291 4 666 2 91733 335 33 335 21 001 13 334 8 334 5 334 3 33441 665 41 665 26 249 16 666 10 416 6 666 4 167 T550 000 50 000 31 500 20 000 12 500 8 000 5 00058 335 58 335 36 751 23 334 14 584 9 334 5 83466 665 66 665 41 999 26 666 16 666 10 666 6 66783 335 83 335 52 501 33 334 20 834 13 334 8 334 T6

100 000 100 000 63 000 40 000 25 000 16 000 10 000116 665 116 665 73 499 46 666 29 166 18 666 11 667133 335 133 335 84 001 53 334 33 334 21 334 13 334166 665 166 665 104 999 66 666 41 666 26 666 16 667 T7200 000 200 000 126 000 80 000 50 000 32 000 20 000

> 200 000 > 200 000 > 126 000 > 80 000 > 50 000 > 32 000 > 20 000T8

T9

2 - 44

Table T.A.2.1.1.3. - Classes of utilization for appliances and mechanisms

U - Class of utilization for appliances T - Class of utilization for mechanisms

2 - 45

EXAMPLE OF APPLICATION

Dockside cargo crane.

The class of utilization for the appliance will be U5.

A hoisting cycle comprises the following operations :

- hoisting of load ;- travelling ;- slewing ;- lowering ;- unhooking of load ;- hoisting empty ;- slewing ;- travelling ;- lowering empty ;- hooking on of new load.

The average time for completion of the cycle will be estimated at 150 s.

The ratios i will be estimated as follows :

- hoisting (hoisting and lowering) : i = 0.63

- slewing (2 directions) : i = 0.25

- travelling (do.) : i = 0.10

Table T.A.2.1.1.1. gives us for class U5 and tmc = 150 s :

T = 20 835 h

For the various mechanisms, table T.A.2.1.1.2. gives us, for T = 20 835 h, the following totaldurations Ti and classes of utilization :

- hoisting (i = 0.63) : Ti = 13 126 h T7

- slewing (i = 0.25) : Ti = 5 209 h T5

- travelling (i = 0.10) : Ti = 2 084 h T4

From the curves in table T.A.2.1.1.3. the same conclusions are drawn on the basis of theordinate tmc = 150 s (broken line).

2 - 46

A.2.2.3. - CALCULATION OF LOADS DUE TO ACCELERATIONS OFHORIZONTAL MOTIONS

PART 1 - METHOD

1. - BASIC DATA

Let

v be the steady horizontal velocity of the point of suspension of the load, either at the end ofthe acceleration period, or at the beginning of the braking period, according to whether anacceleration or a braking process is being considered, and

F an imaginary horizontal force in the same direction as v, applied at the point of suspensionof the load and producing the same effect on the motion under consideration as theaccelerating or decelerating torque applied by the motor or the brake.

2. - PROCEDURE

The different quantities set out below must be calculated in succession.

Equivalent mass (m)

The inertia of all moving parts other than the load, in the motion under consideration, is replacedby a single equivalent mass m assumed to be concentrated at the point of suspension of theload and given by the relation :

m = m0 + i [ ( Ii . wi2) / v2 ]Where :

m0 is the total mass of all elements, other than the load, undergoing the same pure linearmotion as the point of suspension of the load ;

Ii the moment of inertia of a part undergoing a rotation during the motion under consideration,this moment of inertia being considered about the axis of rotation, and

wi the angular velocity of the part referred to, about its axis of rotation, corresponding to thelinear velocity v of the point of suspension of the load.

The sum covers all parts in rotation (structure, mechanisms, motor) during the motionconsidered. However, in the case of mechanisms, the inertia of components other than thosedirectly coupled to the motor shaft can be ignored.

Mean acceleration or deceleration ( Jm ) :Jm = F / (m + m1 )

where m1 is the mass of the load.

2 - 47

Mean duration of acceleration or deceleration ( Tm ) :

Tm = v / Jm

Mean inertia forces :

The acceleration corresponding to the acceleration Jm at the point of suspension of the load iscalculated for each component part in motion. Multiplying this acceleration by the mass of thecomponent considered gives the mean inertia force it sustains.

In the particular case of the load itself, this force of inertia Fcm will be given by :

Fcm = m1 . Jm

Period of oscillation : Tl T1 = 2 . . ( l / g )0,5

l = the length of suspension of the load when it is in its uppermost position (values of l below2,00 m need not be taken into consideration) and,

g = the acceleration due to gravity.

Value of : = m1 / m

When the system driving the motion controls the acceleration and the deceleration andmaintains it at a constant value, is taken equal to 0 irrespective of the masses m and m1.

Value of : = Tm / T1

Value of h :

With the values obtained for and , the graph in figure A.2.2.1. is used to find the correspondingvalue h.

Inertia forces to be considered in the design of the structure :

The forces of inertia which take account of dynamic effects and which must therefore beconsidered in the structural calculations are obtained as follows :

- Inertia force due to the load : h . Fcm

- Inertia force on moving parts other than the load : twice the mean inertia forces.

3. - JUSTIFICATION

A justification of the method given above follows in part 2 of this appendix.

2 - 48

PART 2 - EXPLANATION OF THE METHOD

1. - STATEMENT OF THE PROBLEM

A hoisting appliance is a physical system consisting essentially of :

- concentrated masses (hook load, counterweights, ...) and distributed masses (girders,ropes, ...),

- elastic connections between these masses (girders, ropes, ...).

If such a system, originally in a state of equilibrium, is subjected to a varying load, it does nottend progressively towards a new state of equilibrium even if the new load applied is itselfconstant. On the contrary, it is set in a more or less complex oscillating motion about this newstate of equilibrium. During this motion, the various internal loads and stresses of the systemcan exceed sometimes to a marked extent - the values they would have assumed had thesystem been in static equilibrium under the influence of the new load.

Such a situation arises during acceleration or deceleration (braking) of a horizontal motion of ahoisting appliance. Thus if, starting from a position of rest, an appliance or part of an appliancebegins a motion of translation or rotation, the component parts of the system undergoaccelerations and are therefore subjected to inertia forces. Once a steady speed is attained, theacceleration ceases, the inertia forces disappear and the external load undergoes a newvariation.

The angle through which a rotating system turns (e.g. the rotating part of a crane) during the timefor which inertia forces are applied is generally relatively small. This being so, no appreciableerror will be involved if one assumes that each point in the system follows a straight path duringthis time. Since, moreover, there is no difference of principle between the treatment used forlinear motions and motions of rotation, in what follows the linear motion will be considered ingreater detail (chapter 2), whereas only a short note (chapter 3) will cover rotation.

2 - 49

2. - CALCULATING THE LOADS IN THE CASE OF A LINEAR MOTION

2.1. - GENERAL DATA

It is now proposed to examine the particular case of braking of the travel motion of a completeoverhead travelling crane when it is carrying a load suspended from its hoisting rope. Othercases encountered in practice can be dealt with in similar fashion.

Considering figure A.2.1. let :m1 be the mass of the suspended load,m the total mass of the overhead travelling crane including the crab (see note below

concerning the inertia of the motor and of the machinery driving the motion),x a coordinate defining the position of the crane along its track (more precisely, x represents

the coordinate of the point of suspension of the hoisting rope along an axis parallel to thedirection of travel),

x1 a coordinate defining the position of the centre of gravity of the suspended load along anaxis of the same direction, sense and origin as the axis of x ,

z = x1 - x a coordinate expressing the horizontal displacement of the load relative to the crane.

Let us assume that at the instant t = 0 the overhead travelling crane is moving in the positivesense of the x axis at a velocity v, and that the load is at rest relative to the crane.

( z = z' = 0, with : z' = dz / dt )

If the brake is applied to the travel mechanism at the instant t = 0, it will give rise from that instantto a horizontal braking force parallel to, but of opposite sense to, the x axis at each point where adriving wheel is in contact with its rail. To simplify masters, let us assume that the crab is locatedat mid-span of the main girders of the overhead travelling crane. It follows by symmetry that thetotal force at each rail is the same. Let us designate its projection on the x axis by F/2 (with F > 0),so that the total braking force acting on the system in motion 2 (crane plus load) is equal to F inabsolute value.

If the system were composed of rigidly interconnected masses, this would result in adeceleration of absolute value Jm given by the relation : Jm = F / ( m +m1 ) (2.1.1)

2 - 50

Figure A.2.1.

It must not be forgotten however that F originates in the braking torque applied to the travelmechanism which must not only brake the travel inertia of the crane and the load but also therotational inertia of the driving motor and the intervening machinery. Generally speaking, one canneglect the rotating inertia of all components other than those integral with the motor shaft. Inmany cases, however, the inertia of the latter must be taken into account and the relation (2.1.1.)holds good only provided that m incorporates an equivalent mass me given by the relation :

me . v2 = Im . m

2 (2.1.2.)where :

Im is the moment of inertia of all the components integral with the motor shaft (including themotor itself, of course) and

m the angular velocity of the motor corresponding to the travelling speed v of the crane.

Under the effect of the deceleration Jm, the suspension rope cannot retain its vertical position. Itsnew position of equilibrium is inclined to the vertical at an angle m given by the relation :

m = arctg( Jm / g ) (2.1.3.)

where g is the acceleration due to gravity. In this case the rope exerts a horizontal force on thecrane whose projection Fcm on the x axis is given by :

Fcm = m1 . Jm (2.1.4.)

2 - 51

In point of fact, the system is not rigid, the deceleration is not constant and is not therefore givenby (2.1.1.), the load and its suspension rope adopt an oscillating motion, and the horizontal forcedeveloped by the rope on the crane can assume values differing greatly from (2.1.4.).

By a similar reasoning, one may conclude that the deceleration of the system gives rise to inertiaforces which act on each component part of the crane and the crab, but that because of theelasticity of the girders the system will undergo an oscillating motion in the course of which thestresses will be subject to fluctuations which must be estimated.

The next two paragraphs deal in succession with the effect of the inertia forces on the load andon the girders.

2 - 52

2.2. - EFFECT OF INERTIA FORCES ON THE LOAD

In determining the motion which the load executes after the brake is applied, one can neglect themovement of the point of suspension due to girder flexibility in a horizontal plane. The amplitudeof this movement is, in fact, very small compared with the amplitude of swinging of the load.Calculations can therefore be carried out with the crane considered as a system which is notsubject to deformation.

The projection FC on the x axis of the force exerted by the rope on the crane is given by therelation :

FC= m1 . g [( x1 - x ) / l] = m1 . g . z / l (2.2.1)where l is the suspension length of the load. It will be noted that FC is proportional to thedisplacement z of the load with respect to its position of initial equilibrium, just as if it were anelastic restoring force.

The equations of motion can be written :

ml . x1 = m1 . g [( x1 - x ) / l] (2.2.2.)

m . x = m1 . g [( x1 - x ) / l] - F (2.2.3.)

while, assuming x = 0, for t = 0, the initial conditions are as follows :

for t = 0, x1 = x = 0 (2.2.4.)

x'1 = x' = v (2.2.5.)

z = x1 - x = 0 (2.2.6.)

z = x1 - x = 0 (2.2.7.)

Let :g / l = 1

2 (2.2.8.)

(m1 / m) . (g / l) = 22 (2.2.9.)

12 + 2

2 = r2 (2.2.10.)

F / m = J0 (2.2.11.)

Equations (2.2.2.) and (2.2.3.) then become :

x" + z" + 12 . z = 0 (2.2.12.)

x" - 22 . z = - J0 (2.2.13.)

whence

2 - 53

z + r2 . z = J0 (2.2.14.)

With the initial conditions of (2.2.4.) to (2.2.7.), the solution to these equations is given by :

z = ( J0 / r2 ) . [1 - cos( r . t)] (2.2.15.)

x' = v -[ ( 12./ r

2 ) . J0 . t ] - [ ( 22./ r

2 ) . ( J0 / r ) ] . sin(r . t) (2.2.16.)The complete expression for x is of no direct interest to us.

Let : J0 / r2 = zm (2.2.17.)

it can then be seen without difficulty that zm is the position of equilibrium that can be assumed bythe load during a constant deceleration of the crane equal to the value Jm defined by (2.1.1.), i.e.during the deceleration that would be obtained by applying the braking force F to the total mass(crane plus load) in motion, this mass being assumed to constitute a rigid system. The value z =zm defining the load displacement corresponds to the horizontal force Fcm, defined by (2.1.4.)exerted by the rope on the crane. Comparison between (2.2.1.), (2.2.15.) and (2.2.17.) thenshows that :

Fc = Fcm . [ 1 - cos(r . t) ] (2.2.18.)

If the deceleration period of the crane lasts for a time td such that :

r . td (2.2.19.)

it will be seen that Fc momentarily becomes twice Fcm, or in other words, that its maximum valueFc max is given by the relation :

Fc max = 2 . Fcm (2.2.20.)

If the condition (2.2.19.) is not satisfied, this means that the crane has stopped before the loadhas reached its maximum displacement z = 2 zm. However, after the crane stops, the load willusually continue to oscillate, so the rope will continue to exert a varying horizontal force on thecrane, and the maximum value which this can attain must be sought.

It is easy to verify that after the crane has stopped, the motion of the load is defined by theexpression :

z = zd . cos[ 1 . (t - td) ] + (zd / 1) . sin[ 1 . (t - td) ] (2.2.21.)

withzd = zm . [ 1 - cos(r . td) ] (2.2.22.)

z'd = r . zm . sin(r . td) (2.2.23.)

where td is the smallest positive value of t that makes the expression (2.2.16.) for x' equal to zero.

The maximum value Fc max assumed by Fc is then given by the relation :

2 - 54

Fc max = Fcm . { [ 1 - cos( r . td ) ]2 + ( r

2 / 12 ) . sin2( r . td ) }

0,5 (2.2.24.)

2 - 55

Generally speaking, we may take :

Fc max / Fcm = h (2.2.25.)

The determination of h is simplified by introducing the following quantifies :

Tm = v / Jm the time for which the slowing-down phase of the crane would last if thedeceleration were constant and the system in motion not subject to deformation.

T1 = 2 / 1 the period of oscillation of the pendulum system formed by the suspended load(crane stopped).

T1 = 2 . ( l / g )0,5

It can be verified without difficulty that h depends only on two non-dimensional parameters and defined by the ratios :

= m1 / m (2.2.26.)

= Tm / T1 (2.2.27.)

which can be obtained very easily. It will be noted that (2.2.16.) can be written :

x = v . { 1 - [ r . t + . sin( r . t ) ] / [ 2 . ( 1 + )0,5 ] } (2.2.28.)

and therefore :[ r . td + . sin( r . td ) ] / [ 2 . ( 1 + )0,5 ] = 1 (2.2.29.)

this equation makes it possible to determine the value of r . td to be introduced into (2.2.24.).

The graph in figure (2.2.1.) plots the values of h against for various values of . (The curve = 0 will be explained later in Chapter 5).

If < 1 (which is generally the case with overhead travelling crane travel motions, such as that inthe example dealt with), an analysis of the problem shows that h can in no case exceed 2. Thisvalue is reache