EN 13001-2:2014
(Main)Crane safety - General design - Part 2: Load actions
Crane safety - General design - Part 2: Load actions
This European Standard specifies load actions to be used together with the standard EN 13001 1 and EN 13001 3, and as such they specify conditions and requirements on design to prevent mechanical hazards of cranes, and a method of verification of those requirements.
NOTE Specific requirements for particular types of crane are given in the appropriate European Standard for the particular crane type.
The following is a list of significant hazardous situations and hazardous events that could result in risks to persons during normal use and foreseeable misuse. Clause 4 of this standard is necessary to reduce or eliminate the risks associated with the following hazards:
a) Instability of the crane or its parts (tilting).
b) Exceeding the limits of strength (yield, ultimate, fatigue).
c) Elastic instability of the crane or its parts (buckling, bulging).
d) Exceeding temperature limits of material or components.
e) Exceeding the deformation limits.
This document is not applicable to cranes that are manufactured before the date of its publication as EN.
Kransicherheit - Konstruktion allgemein - Teil 2: Lasteinwirkungen
Diese Europäische Norm legt die Lasteinwirkungen fest, sie ist zusammen mit EN 13001 1 und EN 13001 3 anzuwenden und spezifiziert die Bedingungen und Anforderungen zur Vermeidung von mechanischen Gefährdungen bei Kranen sowie eine Methode der Überprüfung dieser Anforderungen.
ANMERKUNG Besondere Anforderungen für spezielle Krantypen sind in der zutreffenden Europäischen Norm für den speziellen Krantyp angegeben.
Im Folgenden ist eine Auflistung von signifikanten Gefährdungssituationen und Gefährdungsereignissen gegeben, die Risiken für Personen während des normalen Gebrauchs und vorhersehbarem Missbrauch (des Krans) zur Folge haben könnten. Abschnitt 4 dieser Norm wird zur Reduzierung oder Eliminierung der mit den folgenden Gefährdungen verbundenen Risiken benötigt:
a) Instabilität des Krans oder seiner Teile (Kippen);
b) Überschreitung der Festigkeitsgrenzwerte (Fließgrenze, Bruch-, Ermüdungsfestigkeit);
c) elastische Instabilität des Krans oder seiner Teile (Knicken, Ausbeulen);
d) Überschreitung von Temperaturgrenzwerten des Werkstoffs oder der Komponenten;
e) Überschreitung der Verformungsgrenzwerte.
Diese Europäische Norm gilt für Krane, die nach dem Datum der Veröffentlichung dieser Norm als Europäische Norm hergestellt werden.
Sécurité des appareils de levage à charge suspendue - Conception générale - Partie 2: Charges
La présente Norme européenne spécifie les actions de charge devant être utilisées conjointement avec l'EN 13001 1 et l'EN 13001 3, et dans ce cadre, elles spécifient les conditions et prescriptions de conception visant à prévenir les dangers mécaniques liés aux appareils de levage à charge suspendue, et elle fournit une méthode de vérification de ces prescriptions.
NOTE Des prescriptions spécifiques pour des types particuliers d’appareil de levage à charge suspendue sont données dans la Norme européenne appropriée au type particulier d’appareil de levage à charge suspendue.
La liste suivante spécifie les situations et les événements dangereux significatifs susceptibles d’entraîner des risques pour les personnes lors d’une utilisation normale et d’une mauvaise utilisation prévisible. L’Article 4 de la présente norme est nécessaire pour réduire ou éliminer les risques associés aux phénomènes dangereux suivants :
a) Instabilité de l’appareil de levage à charge suspendue ou de ses éléments (basculement).
b) Dépassement des limites de résistance (élasticité, rupture, fatigue).
c) Instabilité élastique de l’appareil de levage ou de ses éléments (flambage, voilement).
d) Dépassement des limites de température du matériau ou des composants.
e) Dépassement des limites de déformation.
Le présent document n'est pas applicable aux appareils de levage à charge suspendue qui ont été fabriqués avant sa date de publication comme EN.
Varnost žerjava - Konstrukcija, splošno - 2. del: Učinki obremenitev
Standard EN 13001-2 določa ukrepe za obremenitve, ki jih je treba uporabiti skupaj s standardoma EN 13001-1 in EN 13001-3. Ti standardi določajo pogoje in zahteve za načrtovanje žerjavov z namenom preprečevanja mehanskih nevarnosti žerjavov ter podajajo metodo za preverjanje izpolnjevanja teh zahtev. OPOMBA Posebne zahteve za posamezne vrste žerjavov so navedene v ustreznem evropskem standardu za posamezne vrste žerjavov. Spodaj je naveden seznam pomembnih nevarnih razmer in dogodkov, zaradi katerih bi lahko prišlo do ogroženosti oseb med običajno uporabo in predvideno nepravilno uporabo. Točka 4 v tem standardu je potrebna za omejitev ali odpravo tveganj, povezanih z naslednjimi nevarnostmi: a) Nestabilnost žerjava ali njegovih delov (naklon). b) Prekoračitev mej trdnosti (meja prožnosti, končna meja, meja utrujanja). c) Elastična nestabilnost žerjava ali njegovih delov (uklon, izbočenost). d) Prekoračitev temperaturnih omejitev materiala ali sestavnih delov. e) Prekoračitev mej deformacije. Ta dokument se ne uporablja za žerjave, ki so bili izdelani, preden je bil objavljen kot standard EN.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-oktober-2014
Nadomešča:
SIST EN 13001-2:2011
SIST EN 13001-2:2011/AC:2012
Varnost žerjava - Konstrukcija, splošno - 2. del: Učinki obremenitev
Crane safety - General design - Part 2: Load actions
Kransicherheit - Konstruktion allgemein - Teil 2: Lasteinwirkungen
Sécurité des appareils de levage à charge suspendue - Conception générale - Partie 2:
Effets de charge
Ta slovenski standard je istoveten z: EN 13001-2:2014
ICS:
53.020.20 Dvigala Cranes
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EUROPEAN STANDARD
EN 13001-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2014
ICS 53.020.20 Supersedes EN 13001-2:2011
English Version
Crane safety - General design - Part 2: Load actions
Sécurité des appareils de levage à charge suspendue - Kransicherheit - Konstruktion allgemein - Teil 2:
Conception générale - Partie 2: Charges Lasteinwirkungen
This European Standard was approved by CEN on 14 June 2014.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2014 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13001-2:2014 E
worldwide for CEN national Members.
Contents Page
Foreword .3
Introduction .4
1 Scope .5
2 Normative references .5
3 Terms, definitions, symbols and abbreviations .5
3.1 Terms and definitions .5
3.2 Symbols and abbreviations .6
4 Safety requirements and/or measures . 10
4.1 General . 10
4.2 Loads . 10
4.2.1 General . 10
4.2.2 Regular loads . 11
4.2.3 Occasional loads . 18
4.2.4 Exceptional loads . 25
4.3 Load combinations . 33
4.3.1 General . 33
4.3.2 High risk situations. 34
4.3.3 Favourable and unfavourable masses . 34
4.3.4 Partial safety factors for the mass of the crane . 35
4.3.5 Partial safety factors to be applied to loads determined by displacements . 36
4.3.6 Load combinations for the proof of competence . 37
4.3.7 The proof of crane stability . 40
Annex A (informative) Aerodynamic coefficients . 42
A.1 General . 42
A.2 Individual members . 45
A.3 Plane and spatial lattice structure members . 51
A.4 Structural members in multiple arrangement . 53
Annex B (informative) Illustration of the types of hoist drives . 55
Annex C (informative) Calculation of load factor for indirect lifting force limiter . 58
Annex D (informative) Guidance on selection of the risk coefficient . 60
Annex E (informative) Selection of a suitable set of crane standards for a given application . 62
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of EU Directive 2006/42/EC . 63
Bibliography . 64
Foreword
This document (EN 13001-2:2014) has been prepared by Technical Committee CEN/TC 147 “Crane —
Safety”, the secretariat of which is held by BSI.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by February 2015 and conflicting national standards shall be withdrawn
at the latest by February 2015.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN 13001-2:2011.
The major changes in this revision are in 4.2.2.2, 4.2.3.4, 4.2.4.10, 4.3.2, 4.3.4 and 4.3.7. There are new
issues in 4.2.4.7, 4.2.4.8, Annex B, Annex C and Annex D.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association, and supports essential requirements of EU Directive(s).
For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of this document.
This European Standard is one Part of EN 13001. The other parts are as follows:
— Part 1: General principles and requirements
— Part 2: Load actions
— Part 3-1: Limit states and proof of competence of steel structures
— Part 3-2: Limit states and proof of competence of wire ropes in reeving systems
— Part 3-3: Limit states and proof of competence of wheel/rail contacts
— Part 3-4: Limit states and proof of competence of machinery
— Part 3-5: Limit states and proof of competence of forged hooks
For the relationship with other European Standards for cranes, see Annex E.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Introduction
This European Standard has been prepared to be a harmonized standard to provide one means for the
mechanical design and theoretical verification of cranes to conform to the essential health and safety
requirements of the Machinery Directive, as amended. This standard also establishes interfaces between the
user (purchaser) of the crane and the designer, as well as between the designer and the component
manufacturer, in order to form a basis for selecting cranes and components.
This European Standard is a type C standard as stated in the EN ISO 12100.
The machinery concerned and the extent to which hazards are covered are indicated in the scope of this
standard.
When provisions of this type C standard are different from those, which are stated in type A or B standards,
the provisions of this type C standard take precedence over the provisions of the other standards, for
machines that have been designed and built according to the provisions of this type C standard.
1 Scope
This European Standard specifies load actions to be used together with the standard EN 13001-1 and
EN 13001-3, and as such they specify conditions and requirements on design to prevent mechanical hazards
of cranes, and provides a method of verification of those requirements.
NOTE Specific requirements for particular types of crane are given in the appropriate European Standard for the
particular crane type.
The following is a list of significant hazardous situations and hazardous events that could result in risks to
persons during normal use and foreseeable misuse. Clause 4 of this standard is necessary to reduce or
eliminate the risks associated with the following hazards:
a) Instability of the crane or its parts (tilting).
b) Exceeding the limits of strength (yield, ultimate, fatigue).
c) Elastic instability of the crane or its parts (buckling, bulging).
d) Exceeding temperature limits of material or components.
e) Exceeding the deformation limits.
This document is not applicable to cranes that are manufactured before the date of its publication as EN.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
EN 1990, Eurocode - Basis of structural design
EN 13001-1, Cranes — General Design — Part 1: General principles and requirements
ISO 4306-1:2007, Cranes — Vocabulary — Part 1: General
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 1990, Clause 6 of ISO 4306-1:2007
and the following apply.
3.1.1
hoist load
sum of the masses lifted by the crane, taken as the maximum that the crane is designed to lift in the
configuration and operational conditions being considered
3.1.2
single failure proof system
force carrying arrangement of several components, arranged so that in case of a failure of any single
component in the arrangement, the capability to carry the force is not lost
3.2 Symbols and abbreviations
For the purposes of this document, the symbols and abbreviations given in Table 1 apply.
Table 1 — Symbols and abbreviations
Symbols,
Description
abbreviations
A1 to A4 Load combinations including regular loads
A
Characteristic area of a crane member
A Projection of the hoist load on a plane normal to the direction of the wind velocity
g
Area enclosed by the boundary of a lattice work member in the plane of its
A
c
characteristic height d
A Area of an individual crane member projected to the plane of the characteristic
j
height d
b Width of the rail head
h
b Characteristic width of a crane member
B1 to B5 Load combinations including regular and occasional loads
c
Spring constant
c , c , c , c Aerodynamic coefficients
o a oy oz
C1 to C11 Load combinations including regular, occasional and exceptional loads
CFF, CFM Coupled wheel pairs of system F/F or F/M
d
Characteristic dimension of a crane member
d , d
Distance between wheel pair i or n and the guide means
i n
e
Width of the gap of a rail
G
f Friction coefficient
f
Loads
i
f
natural frequency
q
f
Term used in calculating v(z)
rec
F Force in general
F, F , F
Wind loads
y z
ˆ
Maximum buffer force
F
F F
, Initial and final drive force
i f
ΔF Change of drive force
F , F , F , F
Tangential wheel forces
x1i x2i y1i y2i
F
Guide force
y
F , F
Vertical wheel forces
z1i z2i
...
SLOVENSKI STANDARD
01-oktober-2014
1DGRPHãþD
SIST EN 13001-2:2011
SIST EN 13001-2:2011/AC:2012
9DUQRVWåHUMDYD.RQVWUXNFLMDVSORãQRGHO 8þLQNLREUHPHQLWHY
Crane safety - General design - Part 2: Load actions
Kransicherheit - Konstruktion allgemein - Teil 2: Lasteinwirkungen
Sécurité des appareils de levage à charge suspendue - Conception générale - Partie 2:
Effets de charge
Ta slovenski standard je istoveten z: EN 13001-2:2014
ICS:
53.020.20 Dvigala Cranes
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EUROPEAN STANDARD
EN 13001-2
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2014
ICS 53.020.20 Supersedes EN 13001-2:2011
English Version
Crane safety - General design - Part 2: Load actions
Sécurité des appareils de levage à charge suspendue - Kransicherheit - Konstruktion allgemein - Teil 2:
Conception générale - Partie 2: Charges Lasteinwirkungen
This European Standard was approved by CEN on 14 June 2014.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same
status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2014 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13001-2:2014 E
worldwide for CEN national Members.
Contents Page
Foreword .3
Introduction .4
1 Scope .5
2 Normative references .5
3 Terms, definitions, symbols and abbreviations .5
3.1 Terms and definitions .5
3.2 Symbols and abbreviations .6
4 Safety requirements and/or measures . 10
4.1 General . 10
4.2 Loads . 10
4.2.1 General . 10
4.2.2 Regular loads . 11
4.2.3 Occasional loads . 18
4.2.4 Exceptional loads . 25
4.3 Load combinations . 33
4.3.1 General . 33
4.3.2 High risk situations. 34
4.3.3 Favourable and unfavourable masses . 34
4.3.4 Partial safety factors for the mass of the crane . 35
4.3.5 Partial safety factors to be applied to loads determined by displacements . 36
4.3.6 Load combinations for the proof of competence . 37
4.3.7 The proof of crane stability . 40
Annex A (informative) Aerodynamic coefficients . 42
A.1 General . 42
A.2 Individual members . 45
A.3 Plane and spatial lattice structure members . 51
A.4 Structural members in multiple arrangement . 53
Annex B (informative) Illustration of the types of hoist drives . 55
Annex C (informative) Calculation of load factor for indirect lifting force limiter . 58
Annex D (informative) Guidance on selection of the risk coefficient . 60
Annex E (informative) Selection of a suitable set of crane standards for a given application . 62
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of EU Directive 2006/42/EC . 63
Bibliography . 64
Foreword
This document (EN 13001-2:2014) has been prepared by Technical Committee CEN/TC 147 “Crane —
Safety”, the secretariat of which is held by BSI.
This European Standard shall be given the status of a national standard, either by publication of an identical
text or by endorsement, at the latest by February 2015 and conflicting national standards shall be withdrawn
at the latest by February 2015.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN 13001-2:2011.
The major changes in this revision are in 4.2.2.2, 4.2.3.4, 4.2.4.10, 4.3.2, 4.3.4 and 4.3.7. There are new
issues in 4.2.4.7, 4.2.4.8, Annex B, Annex C and Annex D.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association, and supports essential requirements of EU Directive(s).
For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of this document.
This European Standard is one Part of EN 13001. The other parts are as follows:
— Part 1: General principles and requirements
— Part 2: Load actions
— Part 3-1: Limit states and proof of competence of steel structures
— Part 3-2: Limit states and proof of competence of wire ropes in reeving systems
— Part 3-3: Limit states and proof of competence of wheel/rail contacts
— Part 3-4: Limit states and proof of competence of machinery
— Part 3-5: Limit states and proof of competence of forged hooks
For the relationship with other European Standards for cranes, see Annex E.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech
Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,
Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
Introduction
This European Standard has been prepared to be a harmonized standard to provide one means for the
mechanical design and theoretical verification of cranes to conform to the essential health and safety
requirements of the Machinery Directive, as amended. This standard also establishes interfaces between the
user (purchaser) of the crane and the designer, as well as between the designer and the component
manufacturer, in order to form a basis for selecting cranes and components.
This European Standard is a type C standard as stated in the EN ISO 12100.
The machinery concerned and the extent to which hazards are covered are indicated in the scope of this
standard.
When provisions of this type C standard are different from those, which are stated in type A or B standards,
the provisions of this type C standard take precedence over the provisions of the other standards, for
machines that have been designed and built according to the provisions of this type C standard.
1 Scope
This European Standard specifies load actions to be used together with the standard EN 13001-1 and
EN 13001-3, and as such they specify conditions and requirements on design to prevent mechanical hazards
of cranes, and provides a method of verification of those requirements.
NOTE Specific requirements for particular types of crane are given in the appropriate European Standard for the
particular crane type.
The following is a list of significant hazardous situations and hazardous events that could result in risks to
persons during normal use and foreseeable misuse. Clause 4 of this standard is necessary to reduce or
eliminate the risks associated with the following hazards:
a) Instability of the crane or its parts (tilting).
b) Exceeding the limits of strength (yield, ultimate, fatigue).
c) Elastic instability of the crane or its parts (buckling, bulging).
d) Exceeding temperature limits of material or components.
e) Exceeding the deformation limits.
This document is not applicable to cranes that are manufactured before the date of its publication as EN.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
EN 1990, Eurocode - Basis of structural design
EN 13001-1, Cranes — General Design — Part 1: General principles and requirements
ISO 4306-1:2007, Cranes — Vocabulary — Part 1: General
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in EN 1990, Clause 6 of ISO 4306-1:2007
and the following apply.
3.1.1
hoist load
sum of the masses lifted by the crane, taken as the maximum that the crane is designed to lift in the
configuration and operational conditions being considered
3.1.2
single failure proof system
force carrying arrangement of several components, arranged so that in case of a failure of any single
component in the arrangement, the capability to carry the force is not lost
3.2 Symbols and abbreviations
For the purposes of this document, the symbols and abbreviations given in Table 1 apply.
Table 1 — Symbols and abbreviations
Symbols,
Description
abbreviations
A1 to A4 Load combinations including regular loads
A
Characteristic area of a crane member
A Projection of the hoist load on a plane normal to the direction of the wind velocity
g
Area enclosed by the boundary of a lattice work member in the plane of its
A
c
characteristic height d
A Area of an individual crane member projected to the plane of the characteristic
j
height d
b Width of the rail head
h
b Characteristic width of a crane member
B1 to B5 Load combinations including regular and occasional loads
c
Spring constant
c , c , c , c Aerodynamic coefficients
o a oy oz
C1 to C11 Load combinations including regular, occasional and exceptional loads
CFF, CFM Coupled wheel pairs of system F/F or F/M
d
Characteristic dimension of a crane member
d , d
Distance between wheel pair i or n and the guide means
i n
e
Width of the gap of a rail
G
f Friction coefficient
f
Loads
i
f
natural frequency
q
f
Term used in calculating v(z)
rec
F Force in general
F, F , F
Wind loads
y z
ˆ
Maximum buffer force
F
F F
, Initial and final drive force
i f
ΔF Change of drive force
F , F , F , F
Tangential wheel forces
x1i x2i y1i y2i
F
Guide force
y
F , F
Vertical wheel forces
z1i z2i
--------------------
...
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