Cranes - UC3M

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CRANES I

Mechanical Engineering DepartmentCarlos III University

CRANES

TRANSPORTATION

CRANES I

INTRODUCTION

• Crane: device used to lift or lower materials in the vertical direction and to

move them horizontally while being

hanged.

• UNE 58-104-87. Part 1. Types of transport

elevators:

– According to design.

– According to movement possibilities.

– According to device control.

– According to orientation possibilities.

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INTRODUCTION

• The dynamic structural calculation allows to determine the

stress of the elevator during its operation.

• Phases:

1. Find the external forces and their combination, that act on the

structure.

2. Displacement, stress and reaction calculation of each of the

components applying the adequate calculation process.

3. Verification of the obtained values of elasticity, resistance and

stability.

Nowadays: Finite element programs are used

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• Loads to be considered:

– Principal loads acting on the structure for the motionless elevator. The worst

loads are:

• Normal operation load: service load + accessories

• Self weight: crane components weight (set aside operation load)

– Loads due to vertical movements:

• Accelerations or decelerations

• Vertical impacts due to the rollers

– Loads due to horizontal movements:

• Accelerations or decelerations

• Centrifugal force

• Lateral effects due to rolling

• Impact effects

– Loads due to changes in climate:

• Wind, snow and temperature effects

– Various loads:

• Dimensioning of rails and aisles

INTRODUCTION

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STRUCTURAL CALCULATION: CASE I

• CASE I: Without wind:– The next loads are considered: static due to self weight SG, forces

due to service load SL multiplied by the dynamic coefficient ψand the two most unfavourable horizontal effects SH, set aside

impact effects, multiplied by an increase factor γc:

( )c G L Hγ S +ψS +S

– Increasing factor γc [UNE 58132-2] : Depends on the elevator classification group

1,201,171,141,111,081,051,021,00γc

A8A7A6A5A4A3A2A1Elevator

group

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• Dynamic coefficient ψψψψ: takes into account– The service load lifting.

– The accelerations and decelerations in the lifting process.

– The vertical impacts due to the rolling in the track.

( )c G L Hψγ S + S +S

LΨ=1+ξV

VL is the lift speed in m/s

ξ is an experimental coefficient obtained by carrying out several tests in different elevators

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Bridge and gantry crane

Jib crane

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STRUCTURAL CALCULATION: TOWER CRANE

It is important to know the

maximum load depending on the

position: its values are usually

specified in points A and B

Pi=Q+Pc

(load+trolley)

G: crane weight

Gc: counterweight weight

Jib

Mast

Jib pendants Jib pendants

Counterweight jib

Cat head

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Above structure

( )

( )

B1

c2

ψ PT =

sen β

GT =

sen α

⋅

2 2

Tσ = σ +3τ

Traction forces in the jib ties

( )

( )

B1

c2

PT =

sen β

GT =

sen α

The jib pendants are subject to

traction, while the cat head is

subjected to compression, flexure

and shear

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1

22

2

Tσ =

A

Tσ =

A

Forces in the cat head are:

( ) ( )( ) ( )

1 2

1 2

V=T sen β +T sen α

H=T cos β -T cos α

M=H h

⋅ ⋅

⋅ ⋅⋅

c

p

f

pf

z

Vσ =

A

Mσ =

W

H mτ=b I

⋅⋅

Von Misses

2 2

T f cσ = (σ σ ) +3τ+

m: first moment of the

principal area

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Above structure

pl,f A 3

pl,c A

M =ψ P L

V =ψ P

⋅ ⋅

⋅

The jib is subjected to flexure and

shear forces:

pl,f A 3

pl,c A

M =P L

V =P

⋅A 3

f

pf

A

z

ψ P Lσ =

W

ψ P m=

b Iτ

⋅ ⋅

⋅ ⋅⋅

2 2

T fσ = σ +3τ

Von Misses

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Mast

f B 1 c 2

c B c

M =P L G L G e

V =P G G

⋅ − ⋅ + ⋅+ +

The mast is subjected to flexure and

compression forces

B 1 c 2f

mf

B cc

m

ψ P L G L G eσ =

W

ψ P G Gσ =

A

⋅ ⋅ − ⋅ + ⋅

⋅ + +

f B 1 c 2

c B c

M =ψ P L G L G e

V =ψ P G G

⋅ ⋅ − ⋅ + ⋅⋅ + +

T f Cσ =σ σ+

MfVce LL2

L1=L+e

Jib tie Jib tie

Jib

Cat head

Counterweight jib

Tower

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• Loads due to horizontal movements:– Accelerations and decelerations due to translations

movements of the crane

– Acceleration or decelerations due to movements of the

load

– Centrifugal force

– Lateral effects due to rolling (loads due to obliquity)

( )c L HGγ S +ψ +SS

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• Accelerations or decelerations of movements :– Accelerations/decelerations due to translation movements

of the crane

– The acceleration/deceleration value depends on:• The desired speed

• Time to accelerate/decelerate

• Usage of the elevator


aH = V

g⋅

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0,0642,500,16

0,0783,200,25

0,162,500,0984,100,40

0,193,200,125,200,63

0,333,000,254,000,156,601,00

0,433,700,325,000,198,301,60

0,474,200,355,600,229,102,00

0,524,800,396,302,50

0,585,400,447,103,15

0,676,000,508,004,00

Acceleration

[m/s2]

Time to

accelerate

[s]

Acceleration

[m/s2]

Time to

accelerate

[s]

Acceleration

[m/s2]

Time to

accelerate

[s]

(c)

High speed with great

accelerations

(b)

Medium and high speeds (usual

applications)

(a)

Low and medium speed with

large travellingDesired

speed [m/s]

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• Accelerations or decelerations of the load movement:– Inertia force of the load (with weight W):

– Rotational movement:


T=Jα

WaF= =ma

g

T: Inertia moment

J: Inertia polar moment =

α: Angular acceleration

2

i im d∑

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2

i ie 2

m dm =

D∑

eF=m a⋅

a=α D⋅

Inertia forces due to rotation:

Equivalent mass Tangencial acceleration

2

i im dF=

Dα ⋅∑

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• Loads due to obliquity:– Tangential forces between the wheels and the rail track.

– Guide forces.

• A simple translation mechanical model is needed:– n pairs of wheels in line.

– p coupled pairs.


Fixed/Fixed(F/F)

Fixed/Mobile(F/M)

Coupled (C) Individual (I)

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• Loads due to centrifugal forces:– Effects of the cable inclination


2

c

WR πnF =

g 30

W: Load

R: Radius

n: Rotating speed

g: gravity acceleration

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STRUCTURAL CALCULATION: CASE II

• CASE II: Normal operation with service limitwind– To the loads considered in CASE I it is added the

effect of service limit wind Sw and, if needed, theload due to variation in temperature:

– Overloading due to snow is not considered.

( )c G L H wγ S +ψS +S S+

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• Wind effect


•A is the net surface, in m2, of the considered element, that is, the solid surface

projection over a perpendicular plane in the wind direction.

•Cf is a shape factor, in the wind direction, for the considered element.

•p is the wind pressure, in kN/m2, and it is calculated by means of the following

equation:

where vs is the calculated wind speed in m/s

fF=A p C⋅ ⋅

-3 2

sp 0,613 10 v [kPa]= ⋅ ⋅

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1,1Square structures filled (air cannot flow

beneath the structure)

Machine

room, etc

1,2

0,8

Circular metal sections

in which Dvs < 6 m2/s

in which Dvs ≥ 6 m2/s

1,7Flat side metal section

Simple

lattice work

2,2

1,9

1,4

1,0

2,1

1,85

1,35

1,0

1,95

1,75

1,3

0,9

1,75

1,55

1,2

0,9

1,55

1,40

1,0

0,8

b/d

≥21

0,5

0,25

Square metal sections of more than

350 mm side and rectangular of more

than 250 mm x 450 mm

1,1

0,8

1,0

0,75

0,95

0,70

0,90

0,70

0,80

0,65

0,75

0,60

Circular metal sections

in which Dvs < 6 m2/s

in which Dvs ≥ 6 m2/s

1,91,71,651,61,351,3Metal section in L, in U and flat plates

Simple

elements

50403020105

Aerodynamic drag coefficientl/b or l/DDescriptionType

Cf: Shape factor [UNE 58-113-85]

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Wind

Element length 1 1Aerodynamic coefficient= or

Section height facing wind b D=

Section height facing wind bSection proportion=

Section width parallel to wind d=

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0,5028,5Dock cranes that should continue

operation in case of strong wind

0,2520Every normal crane installed in exteriors

0,12514

Cranes which can be protected against

wind and designed exclusively for light

wind (for example, low height cranes

with an easily folding jib to the ground)

Wind pressurekPa/m2

Wind speedm/s

Type of crane

Speeds and pressures of service wind [UNE 58-113-85]

-3 2

sp 0,613 10 v [kPa]= ⋅ ⋅

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• Snow overloading:– It is not considered

• Temperature effect:– Only when the elements cannot freely expand

– Temperature limit -20 ºC + 45 ºC


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STRUCTURAL CALCULATION: CASE III

• CASE III: Elevator subjected to exceptional loads

a) Elevator out of service subjected to maximum wind.

b) Elevator in service subject to impact.

c) Elevator subjected to static and dynamic tests.

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STABILITY

m m b bW d W d W d> +

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STABILITY

( )m m f o f b b rW d W d d W d Wd+ − > +

Wm

Rotation axis

CRANES I

f

QM =- L

2⋅

c c

QG d=G e+(P ) L

2⋅ ⋅ + ⋅

f

QM = L

2⋅

COUNTERWEIGHT CALCULATION

f c i cM =(P Q ) L+G e-G d+ ⋅ ⋅ ⋅

It is usually calculated so that it counteracts the half

of the material moment and the jib moment

P=Qi+Pc(Load+hoist)

Moment:

Without load: Qi=0

With load: Qi=Q

With this type of counterweight the mast, with and without

load, has a uniform solicitation in a favourable way

Most unfavourable

situations:

f c i c i

Q QM =(P Q ) L+G e- G e+(P ) L Q L

2 2

+ ⋅ ⋅ ⋅ + ⋅ = − ⋅

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It is used by manufacturers and clients so that a specific elevator operates within

certain required service conditions.

CLASSIFICATION

Crane and elevators classification allows to establish the design of the structure and of the mechanisms

Elevator classification Mechanism classification

It gives the manufacturer

information of how to design and

verify the elevator so that it has

the desired service life for the

operation service conditions

Used by the client and the

manufacturer to achieve a

fixed elevators service

conditions

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CLASSIFICATION OF THE EQUIPMENT

• The total number of manoeuvre cycles is the sum of all of the cycles carried out during the elevator life.

• The user expects that the elevator’s manoeuvre number of cycles is achieved during its life.

• The total number of manoeuvre cycles has a relationship with the usage factor:

– The manoeuvre spectrum has been conveniently divided in 10 usage classes.

CLASSIFICATION OF THE EQUIPMENT (standard 58-112-91/1)

Number of cycles of a manoeuvre Load spectrum coefficient

A manoeuvre cycle begins when the load is prepared to be lifted and finishes when the elevator is prepared to lift the next load

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CLASSIFICATION OF THE EQUIPMENT: TOTAL NUMBER OF CYCLES

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CLASSIFICATION OF THE EQUIPMENT

• Depending on the available information of the number and weight of the loads to be lifted during the elevator life:

– Lack of indications: manufacturer and client have to achieve an agreement.

– If the information is available: the load spectrum coefficient of the elevator can be calculated.

CLASSIFICACIÓN OF THE EQUIPMENT (standard 58-112-91/1)

Number of cycles of a manoeuvre Load spectrum coefficient

The load condition is the number of times a load is lifted, which is suitable to the elevator capacity

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CLASSIFICATION OF THE EQUIPMENT : LOAD LEVEL

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i ip

T max

C PK =

C P

∑

Ci is the mean number of cycles of manoeuvre for each different load level.

CT is the total of the individual cycles for every load level.

Pi are the values of the individual loads characteristic of the equipment service operation.

Pmax is the maximum load that the equipment is authorized to lift (safe working load).

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CLASSIFICATION OF THE EQUIPMENT : LOAD LEVEL

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CLASSIFICATION OF THE COMPLETE EQUIPMENT

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CLASSIFICATION OF THE COMPLETE EQUIPMENT

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CLASSIFICATION OF THE MECHANISM

• Maximum service duration can be computed by means of the mean daily service, in hours, of the number of working days per year and the number of the planned years of service.

• A mechanism is considered to be on service when it is on movement.

CLASSIFICACIÓN OF THE MECHANISMS (standard 58-112-91/1)

Usage of work equipment Mechanism load level

It is calculated for the planned service duration in hours

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CLASSIFICATION OF THE MECHANISM: USAGE

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CLASSIFICACIÓN OF THE MECHANISMS (standard 58-112-91/1)

Use of work equipment Loads applied to the mechanism

The load level is a feature that shows how much a mechanism is subjected toa maximum load, or only to low loads.

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i im

t max

t Pk =

T P

∑

ti is the mean service duration of the mechanism when subjected to individual loads.Tt iis the sum of the individual durations in all load level

Pi is the individual load level of the mechanism

Pmax is the maximum load applied to the mechanism

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CLASSIFICATION OF THE MECHANISM: APPLIED LOAD

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CLASSIFICATION

Crane with hook:

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CLASSIFICATION

Crane with hook: Usage class U5

Lift cylce

Load liftMovement of the loadRotationLoweringUnhook the loadUnloaded liftRotationMovement of the loadUnloaded liftTo hook a new load

tmc=150 s

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CLASSIFICATION

mcN tT [h]

3600

⋅=

Total length usage of the machine:

tmc= cycle mean length [s]N = Number of cycles

55 10 150T 20835 horas

3600

⋅ ⋅= ≈

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CLASSIFICATION

mechanismi

mc

t

tα =

For each of the mechanisms it is defined:

tmechanism= usage time of the mechanism during onecycle [s]tmc= mean duration of one cycle [s]

Load liftMovement of the loadRotationLoweringUnhook the loadUnloaded liftRotationMovement of the loadUnloaded loweringHook a new load

Lift mechanism

Slewing mechanism

Movement mechanism

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CLASSIFICATION

Lift mechanism

Slew mechanism Travelling mechanism

63%

10%25%




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CLASSIFICATION

Lift mechanism ααααi====0.63

Total duration of the mechanism in hours:

ΤΤΤΤi====13126 h Τ7Τ7Τ7Τ7

Slew mechanism ααααi====0.25


Travelling mechanism ααααi====0.10


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ENGINES

• Power calculation:

2e

G VP = [CV]

4500 η

⋅⋅

Lift movements

Travelling movementsPower

G1: self weight (trolley,span, etc.) [daN]

G2: load + accessories [daN]

V: speed [m/min]

η: mechanical efficiencyW: friction coefficient

7 for rolling bearing

20 for friction bearing

1 2t

(G +G ) W VP = [CV]

4500000 η

⋅ ⋅⋅

CRANES I

ENGINES

Torque needed to accelerate:

MA = Mw + Mb [daNm]

Starting torque = resistance torque + acceleration torque

22 21 21

(G +G ) dGD [daNm ]

η⋅=

2

1 1

b

a

GD nM [daNm]

375 t

⋅=

⋅∑t

w

1

716 PM [daNm]

n

⋅=

Masses moved linearly

Rotating mass2

2 2 221 2 2

1

nGD GD [daNm ]

n=

n1: engine speed in rpm

ΣGD12: inertia torque sum referred to engine axista: acceleration time:

Lift, cierre cuchara = 2 s

Trolley travelling or bridge crane, rotation = 4 s

Gantry travelling = 6 s

V: Mass lineal speed1

Vd [m]

π n=

⋅

The resistance torque only has to be taken into account for travelling engines

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ENGINES

CRANES I

ENGINES

Power needed to overcome wind resistance:

v v

S VP F [CV]

4500 η

⋅= ⋅⋅

Fv: wind pressure [daN/m2]

S: surface exposed to wind

To select travelling engine:

t v

w b

Engine power P +P [CV]

Max. motor toruque M +M [daNm]

≥

≥

To select lift engine:

e vEngine power P +P [CV]≥

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