BS EN 13001-3-6:2018
BSI Standards Publication
Cranes - General design Part 3-6: Limit states and proof of competence of machinery - Hydraulic cylinders
BS EN 13001-3-6:2018
BRITISH STANDARD
National foreword This British Standard is the UK implementation of EN 13001-3-6:2018. The UK participation in its preparation was entrusted to Technical Committee MHE/3/1, Crane design. A list of organizations represented on this committee can be obtained on represented request to its secretary. secretar y. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. © The British Standards Institution 2018 Published by BSI Standards Limited 2018 ISBN 978 0 580 89957 7 ICS 23.100.20; 53.020.20 Compliance with a British Standard c annot confer immunity from Compliance legal obligations.
This British Standard was published under the authority of the Standards Policy and Strategy Committee on 31 March 2018. Amendments/corrigenda issued since si nce publication
Date
Text af fected
STANDARD ANDARD EUROPEAN ST
EN 13001-3-6
NORME EUROPÉENNE EUROPÄISCHE NORM
February 2018
ICS 23.100.20; 53.020.20
English Version
Cranes - General design - Part 3-6: Limit states and proof of competence of machinery - Hydraulic cylinders Appareils de levage à charge suspendue su spendue - Conception générale - Partie 3-6 : États limites et vériication d'aptitude des éléments
Krane - Konstruktion allgemein - Teil 3-6: Grenzzustände und Sicherheitsnachweis von Maschinenbauteilen - Hydraulikzylinder
de mécanismes - Vérins hydrauliques This European Standard was approved by CEN on 13 November 2017. 2017. CEN members are bound to comply with the t he CEN/CENELEC CEN/CENELEC Internal Regulations Regulat ions which stipulate the conditions condit ions 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 st andards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member. This European Standard exi sts in three of icial versions (English, French, German). A version version in any other language made by translation under the responsibility of a CEN member into its own language and noti ied to the CEN-CENELEC Management Centre Centre has the same statu s as the oficial versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Fin land, Former Yugoslav Republic Republic of Macedonia, France, Germany, Greece, Hungar y, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES EUROP ÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2 0 18 C E N
All rights of exploitation in any form and by any means reserved worldwide for CEN national Members
Ref . No. EN 13001-3-6:2018: E
BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
European foreword This document (EN 13001-3-6:2018) has been prepared by Technical Committee CEN/TC 147 “Cranes
— 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 August 2018, and conlicting national standards shall
be withdrawn at the latest by August 2018. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN shall not be held responsible for identifying any or all such patent rights. 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. According to the CEN-CENELEC Internal Regulations, the national standards organisations of the following follo wing countries are bound to implement 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, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
Introduction This European Standard has been prepared to be a harmonized standard to provide one means for the mechanical design and theoretical veriication of cranes to conform with the essential health and
safety requirements of the Machinery Directive, as amended. This standard st andard also establishes interfaces interfaces between the user (purchaser) 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 EN ISO 12100:2010. The machinery concerned and the extent to which hazards, hazardous situations and events are covered cover ed are indicated in the t he scope of this standard. st andard. 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.
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Contents
Page
European foreword .............................................................................................................................................................................................................. 2 Introduction. ................................................................................................................................................................................................................................ 3 European foreword .............................................................................................................................................................................................................. 6 Introduction. ................................................................................................................................................................................................................................ 7 1
Scope ................................................................................................................................................................................................................................. 8
2
Normative reference referencess ...................................................................................................................................................................................... 8
3
Terms, deinitions and symbols ............................................................................................................................................................ 9 3.1 Terms and deiniti deinitions ons ....................................................................................................................................................................... 9 3.2 Symbols an abbreviations ............................................................................................................................................................. 9 3.3 Terminology ........................................................................................................................................................................................... 11
4
General. ........................................................................................................................................................................................................................ 12 4.1 Documentation .................................................................................................................................................................................... 12 4.2 Materials for hydraulic cylinders ......................................................................................................................................... 13 4.2.1 General requirements. .............................................................................................................................................. 13 4.2.2 Grades and qualities .................................................................................................................................................. 14
5
Proof of static strength. ...............................................................................................................................................................................14 5.1 General ........................................................................................................................................................................................................ 14 5.2 Limit design stresses ...................................................................................................................................................................... 15 5.2.1 General................................................................................................................................................................................... 15 5.2.2 Limit design stress in structural members ............................................................................................ 16 5.2.3 Limit design stresses in welded connections ....................................................................................... 17 5.3 Linear stress analysis ..................................................................................................................................................................... 17 5.3.1 General................................................................................................................................................................................... 17 5.3.2 Typical load cases and boundary conditions ....................................................................................... 17 5.3.3 Cylinder tube .................................................................................................................................................................... 18 5.3.4 Cylinder bottom ............................................................................................................................................................. 20 5.3.5 Piston rod welds ............................................................................................................................................................ 21 5.3.6 Cylinder head ................................................................................................................................................................... 21 5.3.7 Cylinder tube and piston rod threads ......................................................................................................... 21 5.3.8 Thread undercuts and locking wire grooves ........................................................................................ 22 5.3.9 Oil connector welds .................................................................................................................................................... 23 5.3.10 Connecting interfaces to crane structure ................................................................................................ 23
5.4
5.5
6
Nonlinear stress analysis ............................................................................................................................................................ 23 5.4.1 General................................................................................................................................................................................... 23 5.4.2 Standard cylinder with end moments ........................................................................................................ 24 5.4.3 Support leg ......................................................................................................................................................................... 24 Execution of the proof .................................................................................................................................................................... .................................................................................................................................................................... 25 5.5.1 Proof for load bearing components .............................................................................................................. 25 5.5.2 Proof for bolted connections .............................................................................................................................. 25 5.5.3 Proof for welded connections ............................................................................................................................ 25
Proof of fatigue strength. ...........................................................................................................................................................................25 6.1 General ........................................................................................................................................................................................................ 25 6.2 Stress histories ..................................................................................................................................................................................... 26 6.3 Execution of the proof .................................................................................................................................................................... .................................................................................................................................................................... 27 6.4 Limit design stress range ............................................................................................................................................................ 27 6.5 Details for consideration ............................................................................................................................................................. 28 6.5.1 General................................................................................................................................................................................... 28
6.5.2 6.5.3 6.5.4
6.5.5 4
...................................................................................................................................................................... 28 Bottom weld...................................................................................................................................................................... Notch stress at oil connectors ........................................................................................................................... 30 Cylinder head ................................................................................................................................................................... 31 Piston rod ............................................................................................................................................................................ 33
BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
6.5.6 6.5.7
6.5.8 7
Cylinder head bolts ..................................................................................................................................................... 35 Cylinder head lange weld .................................................................................................................................... 35 Mechanical interfaces ............................................................................................................................................... 37
Proof of elastic stability ............................................................................................................................................................................. 37 7.1 General ........................................................................................................................................................................................................ 37 7.2 Critical buckling load ...................................................................................................................................................................... 38 7.3 Limit compressive design force ............................................................................................................................................. 39
7.4 Execution of the proof . ................................................................................................................................................................... 40 Annex A (informative) Critical buckling load for common buckling cases................................................................41 Annex B (informative) Second order analysis of two important cases ..........................................................................45 Annex C (informative) Shell section forces and moments for cylinder bottom ....................................................48 Annex D (informative) Fatigue analysis of bottom weld for more complex cases ..............................................51 Annex E (informative) Selection of a suitable set of crane standards for a given application............... ...............54 Annex ZA (informative) Relationship between this European Standard and the essential requirements of Directive 2006/42/EC aimed to be cover covered ed ............................................................................56 Bibliography ............................................................................................................................................................................................................................. 57
© ISO ISO pub-date year – All rights reserve reserved d
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
European foreword This document (EN 13001-3-6:2018) has been prepared by Technical Committee CEN/TC 147 “Cranes
— 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 August 2018, and conlicting national standards shall
be withdrawn at the latest by August 2018. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN shall not be held responsible for identifying any or all such patent rights. 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. According to the CEN-CENELEC Internal Regulations, the national standards organisations of the following follo wing countries are bound to implement 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, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
Introduction This European Standard has been prepared to be a harmonized standard to provide one means for the mechanical design and theoretical veriication of cranes to conform with the essential health and
safety requirements of the Machinery Directive, as amended. This standard st andard also establishes interfaces interfaces between the user (purchaser) 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 EN ISO 12100:2010. The machinery concerned and the extent to which hazards, hazardous situations and events are covered cover ed are indicated in the t he scope of this standard. st andard. 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.
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1
Scope
This European Standard is to be used together with EN 13001-1, EN 13001-2 and EN 13001-3-1 as well as pertinent crane type product EN standards, and as such they specify general conditions, requirements and methods to, by design and theoretical veriication, prevent mechanical hazards of
hydraulic cylinders that are part hydraulic par t of the load carrying structures s tructures of cranes. Hydraulic piping, piping, hoses and connectors used with the cylinders, as well as cylinders made from other material than carbon steel, are not within the scope of this standard. st andard. The following are signiicant hazardous situations and hazardous events that could result in risks to persons during intended use and reasonably foreseeable misuse. Clauses 4 to 7 of this standard are
necessary to reduce or eliminate risks associated with the following hazards: a)
exceeding the limits of of streng strength th (y (yield, ield, ultimate, fatigue); fatigue);
b)
elastic inst instability ability (co (column lumn buckling).
NOTE
2
EN 1300113001-3-6 3-6 deals only with the limit stat statee method in accordance with EN 1300113001-1. 1.
Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest lat est edition edit ion of the referenced document (including (including any amendments) applies.
EN 10083-2:2006, Steels for quenching and tempering — Part 2: Technical delivery conditions for non alloy steels
EN 10210-2:2006, Hot inished structural hollow sections of non-alloy and ine grain steels — Part 2: Tolerances, dimensions and sectional properties propert ies
EN 10216-3:2013, Seamless steel tubes for pressure purposes — Technical delivery conditions — Part 3: Alloy ine grain steel tubes
EN 10277-2:2008, Bright steel products — Technical delivery conditions — Part 2: Steels for general engineering purposes
EN 10305-1:2016, Steel tubes for precision applications — Technical Technical delivery conditions — Part 1: Seamless cold drawn tubes
EN cold10305-2:2016, drawn tubes Steel tubes for precision applications — Technical delivery conditions — Part 2: Welded EN 1300113001-1, 1, Cranes — General design — Part 1: General principles and requirements requirements EN 13001-2, Crane safety — General design — Part 2: Load actions EN 13001-313001-3-1, 1, Cranes — General Design — Part 3-1: 3-1: Limit States and proof competence of steel struct structure ure EN 13445-2:2014, Unired pressure vessels — Part 2: Materials EN ISO 148-1:2016, Metallic materials — Charpy pendulum impact test — Part 1: Test method (ISO 148-1:2016) Welding ing — Fusion-welded joints in steel, s teel, nickel, titaniu t itanium m and their alloys (beam welding EN ISO 5817:2014, Weld excluded) — Quality Quality levels for imperfections imperfect ions ( ISO ISO 5817:2014 )
EN ISO 8492:2013, Metallic materials — Tube — Flattening test ( ISO ISO 8492:2013 )
EN ISO 12100:2010, Safety of machinery — General principles for design — Risk assessment and risk reduction ( ISO ISO 12100:2010 )
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general-purpose metric screw threads — Basic Bas ic dimensions ISO 724:1 724:1993, 993, ISO general-purpose
3 3.1
Terms, deinitions and symbols Terms and deinitions
For the purposes of this thi s document, the terms and deinitions dei nitions given g iven in EN ISO 12100:201 12100:2010 0 apply. apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses: — IEC Elect Electropedia: ropedia: available at http://www.electropedia.org/ — ISO Online browsing platform: available available at http://www.iso.org/obp 3.2
Symbols an abbreviations
The essential symbols and abbreviations are given in Table 1. 1. Table 1 — Symbols and abbreviations Sy mbols A% A%
Percentage elongation at fracture
a Ai, B i, C i, Di
Weld throat thickness Constants Stress area Piston diameter Rod diameter Diameter of axles Pressure affected diameter Weld diameter Modulus of elasticity Compressive force Compressive force Finite Elements Limit design stress Limit design stress, normal Limit design stress, shear Lateral force External design force Ultimate strength Limit design weld stress Yield strength thickness of the cylinder bottom Moment of inertia, generic Moment of inertia of the tube Moment of inertia of the rod Overall length of the cylinder
A s A D d D a,i D p D w E F F A A FE f Rd f f Rdσ f f Rdτ f F S F Sd f u f f w,Rd f f y f h I I 1 I 2 L L 1 L 2 m
Descript ion
Length of the cylinder tube Length of the c ylinder rod Slope of the log Δ σ – log N curve
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M 0 MB N N k N Rd N Sd p p i1 p i2 p
r r
Maximum pressure in piston side chamber Maximum pressure in rod side chamber Outer pressure Design pressure Middle radius of the tube (R = Ri + t /2) /2) Inner radius of the tube Inner radius of the tube Outer radius of the tube Outer radius of the piston rod
s 3 s
Stress history h istory parameter (see EN 13001-3-1 13001-3-1))
p o p p Sd p R r i R i r o
T 0
Wall thickness of the tube Shell section transverse force, acting at the intersection between tube and bottom
x, x, y α
Longitudinal and lateral coordinates Angular misalignment, radians
γ m
General resistance factor (γ m = 1,1, see EN 13001-2)
γ mf
Fatigue strength speciic resistance factor (see EN 13001-3-1)
γ R
Total resistance resist ance factor ( γ R = γ m · γ s)
γ s
Speciic resistance factor
Δσ Δσ c
Stress range Bending stress range in the tube Characteristic fatigue strength
Δσ m
Membrane stress range in the tube (axial)
Δσ Rd Rd
μ μ i
Limit design stress range Design stress range Design pressure range on piston side Maximum displaceme displacement nt Reduction factor for buckling Slenderness Friction parameters Friction factors
ν
Poisson’ss ratio Poisson’ rat io (ν = 0,3 for steel)
t
Δσ b
Δσ Sd Sd Δ pSd δ max κ λ λ λ λ i
σ a σ b σ r σ Sd
Axial stress st ress in the tube Lower extreme value of a stress range Radial stress in the tube Design stress, normal
σ t
Tangential stress in the tube (hoop stress)
σ u
Upper extreme value of a stress range
σ w,Sd τ Sd τ w,Sd
10
Shell section bending moment, acting at the intersection between tube and bottom Bending moment Compressive force Critical buckling load Limit compressive design force Compressive design force
Weld design stress, normal Design stress, shear Weld design stress, shear
BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
3.3
Terminology
Terms which are used in this European Standard for the main parts of hydraulic cylinder are indicated in Figure 1 to 1 to Figure 3. 3.
Key
1 2 3 4
5 6 7 8 9 10 11 12 13
bushing rod head cylinder head oil connector piston rod cylinder tube spacer piston nut cylinder bottom grease nipple piston sid idee chamber rod side chamber Figure 1 — Complete cylinder
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Key
1 2 3
wiper O-ring secondary se seal
4
guide ring (2 × )
5 6 7
primary seal backup ring O-ring Figure 2 — Cylinder head
Key
1 2 3
seal pressure element guide ring (2 × )
Figure 3 — Piston
The igures above show some speciic design features in order to exemplify the terminology. Other
designs may be used. 4 4.1
General Documentation
The documentation of the proof of competence shall include: — design assumpt assumptions ions including calculat calculation ion models; — applicable loads and load combinations; — materia materiall grades and qualities; — weld quality qualit y levels, in accorda accordance nce with EN ISO 5817 5817:201 :2014 4 and EN 13001-313001-3-1; 1; 12
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— relevant limit stat states; es; — result resultss of the proof of competence calculation, and test testss when applicable. 4.2
Materials for hydr hydraulic aulic cylinders
4.2.1
General requirements
The materials for tubes and rods that are subjected to internal pressure shall fulil the following
requirements: — The impact toughness in the transversal direction direc tion shall be teste tested d in accordance with EN ISO 148148-1 1
and shall meet the requirements stated in EN 13001-3-1. Samples shall be cut out in the transversal direction and prepared such that the axis of the notch is perpendicular to the surface of the tube. t ube.
Key
1 sample sample cut out in long longitudin itudinal al directio direction n 2 sampl samplee cut out out in transv transversa ersall direction direction Figure 4 — Sample for impact toughness testing
— If the materia materiall thickness or tube dimensions do not allow samples to be cut out, the tube materia materiall shall pass a lattening test in accordance with EN ISO 8492. For welded tubes two test are required,
one with the weld aligned with the press direction and one where the weld is placed 90 degrees from the press direction. The tube section shall be lattened down to a height H given given by:
where Do is the outer diameter of the tube; t is is the t he wall thickness of the tube.
Material used in other parts shall meet the requirements stated in EN 13001-3-1.
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4.2.2
Grades and qualities
European Standards specify materials and speciic values. This standard gives a preferred selection.
Steels in accordance with the following European Standards shall be used as tube material: — EN 10083-2; — EN 1021 10210-2; 0-2; — EN 1021 10216-3; 6-3; — EN 10277-2; — EN 1030510305-1; 1; — EN 10305-2; — EN 13445-2.
Alternatively, other steel grades and qualities than those listed in this clause may be used as tube material provided that they comply with the following requirements: — the design value of f y is limited to f u/1,1 for materials with f u /f y < 1,1; — the percentage elongation at fract fracture ure A % ≥ 14 % on a gauge length
(where S 0 is the
original cross-sectional area);
Grades and qualities of materials used in other parts of cylinders or mounting interfaces of cylinders shall be selected in accordance with EN 13001-3-1. 5
Proof of static strength
5.1 General
A proof of static strength by calculation is intended to prevent excessive deformations due to yielding of the material, elastic instability and fracture of structural members or connections. Dynamic factors given in EN 13001-2 or relevant product standards are used to produce equivalent static loads to simulate dynamic effects. Also, load increasing effects due to deformation shall be considered. The use of the theory of plasticity for calculation of ultimate load bearing capacity is not considered acceptable accep table within the terms of this standard. The proof shall be carried out for structural struct ural members and connections while taking into account the most unfavourable load effects from the load combinations A, B or C in accordance with EN 13001-2 or relevant product standards. The cylinders are either active or passive. Active cylinders are moving and thereby increasing the potential energy of the crane. Passive cylinders are either not moving or moving thereby decreasing the potential energy of the crane. As the forces applied to the cylinder by the crane structure are computed in accordance with with EN E N 13001-2, 13001-2, they they are are already increased by the partial safety safet y factors γ p and relevant dynamic factors. Formulae (1 (1)) and (2) give design pressures pSd caused by forces acting on the cylinder from the crane structure. In addition, additional pressures pSde caused by internal phenomena in the hydraulic circuit shall be considered and added to the design pressures pSd . Such internally generated pressures can be caused e.g. by regenerative connections, pressure drop in return lines or cushioning. In case a cylinder is intended to be tested as a component at higher pressure than the design pressure pSd , this load case shall also be taken into account in the proof of static st atic strength, and in which case the test pressure shall be multiplied multiplied by a partial partia l safety factor γ p equal to 1,05. pSd in the piston side chamber or in the rod side chamber shall be computed from The designforce pressure the design F Sd η due to friction. frict ion. Sd taking into account the force direction and the cylinder eficiency
An eficiency factor Ψ is used to handle the effect of cylinder friction. For active cylinders Ψ has the value of 1 /η and for passive cylinders Ψ has the value ofη. 14
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For the piston side chamber, the design pressure is given by:
(1)) (1
where Sd is the external F Sd ex ternal design force; D is the piston diameter.
Ψ is set to η for passive cylinders and to 1/η for active cylinde c ylinders. rs.
For the rod side chamber the design pressure is given by:
(2)
where F Sd ex ternal design force; Sd is the external D is the t he piston diameter; d is is the t he rod diameter;
Ψ is set to η for passive cylinders and to 1/η for active cylinders; pSde is additional pressure caused by internal phenomena.
Unless justiied information for the value of η is used, the value 1,1 shall be assigned to Ψ.
This standard is based on nominal stresses, i.e. stresses calculated using traditional elastic strength of materials theory which in general neglect localized stress non-uniformities. When more accurate alternative methods of stress calculation are used, such as inite element analysis, using those stresses
for the proof given in this standard may yield y ield inordinately inordinately conservative conservative results. 5.2
Limit design stresses
5.2.1
General
The limit design stresses shall be calculated from:
(3)
where f k is the characteristic values (or nominal value); γ R is the total resistance factor
;
γ m is the general resistance factor
(see EN 13001-2);
γ s is the speciic resistance factor applicable to speciic structural components as given in the
clauses below below.. NOTE
is equiva equivalent lent to
in EN 13001 13001-1. -1.
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5.2.2
Limit design stress in structural members
The limit design stress f Rd struct ural members, members, shall be calculated from: Rd, used for the design of structural
(4)) (4
(5)
with where f y is the minimum value va lue of the yield stress of the material; γ sm t he speciic resistance factor for material. sm is the
for steels according to standards listed in 4.2.2; for other steels. For tensile stresses perpendicular per pendicular to the plane of rolling (see Figure 5), the material shall sha ll be suitable for carrying perpendicular loads and be free of lamellar defects. EN 13001-3-1 speciies the values of γ sm sm
for material loaded perpendicular to the rolling plane.
Example from cylinder cyli nder tube bottom, where plate steel is used (eye is welded). welded). The igure igur e shows a tensile
load perpendicular to plane of rolling where:
Key
1 is th thee pla plane ne of rol rolli ling ng 2 is the dir direct ection ion of str stress ess/lo /load ad Figure 5 — Tensile load perpendicular to plane of rolling
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5.2.3
Limit design stresses in welded connections
The limit design weld stress f w,Rd w,Rd used for the design of a welded connection shall be in accordance with EN 13001-3-1. 5.3 5.3.1
Linear stress analysis General
5.3 comprises 5.3 comprises typical ty pical details for consideration consideration that are relevant for the proof of static st atic strength. Details that are only relevant for fatigue analysis (e.g. shell bending of tube) are not dealt with in 5.3 5.3.. In cases or conditions not covered here, other recognized sources or static pressure/force testing shall be used. 5.3.2
Typical load cases and boundary conditions
Before executing calculations, boundary conditions and loading shall be investigated. Typical conditions to be determined are: — external forces and directions; — type of cylinder; — cylinder tube and rod mounting to the machine; — forces/ forces/stress stresses es due to thread pre-tight pre-tightening; ening; — direction of gravity. Different load cases shall be considered when calculating static strength for cylinders. Typical load cases are shown in Figure 6 to 6 to Figure 10 here 10 here below.
Figure 6 — Pushing cylinder with suppo s upported rted bottom
Figure 7 — Pushing cylinder, lange mounted with unsupported bottom
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Figure 8 — Pulling cylinder or pushing cylinder with pressurized rod chamber
Figure 9 — Pushing cylinder at end of stroke
Figure 10 — Pulling cylinder at end of stroke
The worst load condition or combination shall be used when calculating stresses σSd or σw,Sd for a feature. 5.3.3
Cylinder tube
Cylinder tube stresses shall be computed from three components. For calculation of each component, forces and pressures shall be determined in accordance with 5.3.2 5.3.2..
Figure 11 — Stresses in cylinder tube 18
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The tangential stress (hoop stress) is given by:
(6)) (6
For cylindrical shells such as tubes or hollow rods that are also loaded by an outer pressure, the combination of inner and outer pressure that gives the largest absolute value of the tangential (hoop)
stress shall be used. Maximum radial stress magnitude magnit ude in the tube occurs at the inner radius r i or the at the outer radius r o and is given by: or
(7)
For the cylinder arrangement shown in Figure 6, 6, maximum axial axia l stress in the tube is given by:
(8)
For the cylinder arrangements shown in Figure 8 8 and Figure 10, 10, maximum axial stress in the tube is given by:
(9)
For the cylinder arrangement shown in Figure 7 7 and Figure 9, 9, maximum axial stress in the tube is given by:
(10)
where r is is an arbitrary radius of the tube; r i is the inner radius of the tube; r o is the outer radius of the tube; r r is the outer radius of the piston rod; pi is the inner pressure; pi1 is the inner maximum pressure in piston side chamber; pi2 is the inner maximum pressure in rod side chamber; po is the outer pressure; M b is any bending moment acting act ing on the cylinder c ylinder tube (e.g. dead weight).
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The von Mises equivalent stress shall be computed for the location having the most severe stress as: 5.3.4 5.3.4.1
(11)
Cylinder bottom Bottom plate
The stress in an unsupported bottom plate, in a cylinder with the ratio outer diameter to inner diameter in the range 1,07 to 1,24, shall be calculated as:
(12)
where pi is the inner pressure; D is the inner diameter; t is is the t he tube thickness; h is the bottom thickness.
Figure 12 — Stresses in unsupported cylinder bottom 5.3.4.2
Bottom weld
Bottom welds shall be calculated for different load cases in accordance with 5.3.2 5.3.2..
Figure 13 — Bottom weld
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7 and The bottom weld is loaded by the axial force in the tube, caused by internal pressure ( Figure 7 Figure 8) or by pushing cylinder coming to end of stroke (Figure 9).
(13)
where is the design axial force acting in the tube; F Sdt Sdt is a is the effective thickness of the weld; R is the middle radius of the weld. 5.3.5
Piston rod welds
Piston rod welds shall be calculated for different load cases according to 5.3.2 5.3.2,, in the same way as the calculation of bottom wel welds. ds.
(14)
where F Sdw t he maximum design force acting in the rod; Sdw is the a is the effective thickness of the weld; R is the middle radius of the weld. 5.3.6
Cylinder head
Depending on the design, the cylinder c ylinder head has a governing stress area Ac, which is the smallest area that carries the axial load. Axial force can be caused by internal pressure, external force or pre-tightening. The stresses in the cylinder head shall be calculated for the different load cases in accordance with 5.3.2.. The design stress shall be computed as: 5.3.2
(15)
where F Sdh ma ximum axial design force acting on the head; Sdh is the maximum Ac is the critical stress area for the axial force holding the cylinder head. 5.3.7
Cylinder tube and piston rod threads
Stresses in cylinder tube threads and piston rod threads shall be calculated for the different load cases in accordance with 5.3.2 5.3.2.. The design stress shall be computed as:
(16)
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(17)
where F Sdr Sdr is the maximum design force acting on the cylinder head or the piston rod head; As is the stress st ress area of the threaded t hreaded cylinder cyli nder tube or piston piston rod (equivalent to stress area ar ea of bolt or nut); nut); L is the t he effective thread length, maximum max imum 0,9 · d 2; d 2 is the pitch diameter of the thread in accordance to ISO 724.
It should be considered that the tube diameter can increase due to the internal pressure and thus decrease the shear area in Formula (17). 5.3.8
Thread undercuts and locking wire groov grooves es
Stresses in thread undercuts or locking wire grooves shall be calculated for the different load cases in accordance with 5.3.2 5.3.2.. The design stress shall be computed as:
(18)
where F Sdu t he maximum design force acting at the undercut; Sdu is the
cr itical stress area at the undercut or locking wire groove. Ac is the critical
Figure 14 — Undercuts at thread run out
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5.3.9
Oil connector welds
This clause considers oil connectors welded to the tube. The design stress σw,Sd shall be computed as:
(19)
with
(20)
(21)
and
where pSd is the design pressure for chamber side; Dp is the pressure affected diameter; a is the effective thickness of the weld; Dw is the effective weld diameter.
Figure 15 — Welded oil connector
5.3.10 Connecting interfaces interfaces to to crane crane structure structure
The design stresses in parts connecting the cylinder to the crane structure shall be calculated in accordance with w ith EN 13001-313001-3-1. 1. 5.4 5.4.1
Nonlinear stress analysis General
Nonlinear stress analysis takes into account the force balance in the deformed shape of the cylinder and can be governing when the compressive force acts together with bending moment or lateral force, or due to the angular misalignment α between rod and tube caused by the play at the guide rings. Nonlinear stress analysis may be omitted if lateral forces and bending moments are negligible, and if the maximum displacement δ max max due to the angular misalignment α is smaller than L/600, where L is the overall length of the cylinder. If the misalignment is unknown, δ max max shall be set to L/300. The omission of a second order analysis shall be justiied.
In particular the t he cases described in 5.4.2 and 5.4.3 might require nonlinear stress analysis. The nonlinear stress analyses may either be made with FE-analysis or by the analytical equations given in Annex B. B.
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5.4.2
Standard cylinder with end moments
Standard cylinder with the same coniguration as in buckling case D (see 7.2), loaded by a compressive force F and and by moments M 1 and M 2 caused by axle frictions acting at the bushings at the cylinder’s ends, and with an angular misalignment α between between the cylinder tube and the piston rod caused by play at
guide rings, see Figure 16. 16.
Figure 16 — Cylinder with end moments from axle f rictions and angular misalignment misalig nment
5.4.3
Support leg
Support leg cylinder loaded by a compressive force F A and by a lateral force F S, and with an angular misalignment α between between the cylinder cyli nder tube and the piston rod caused by play at guide rings, ring s, see Figure 17. 17.
Figure 17 — Support leg cylinder with lateral force and angular misalignment
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5.5
Execution of the proof
5.5.1
Proof for load bearing components
For the load bearing components (e.g. tube, rod, lugs) it shall be proven that: and
(22)
where σSd is the design normal stress or the von Mises equivalent stress; τSd is the t he design shear shear stress; f Rdσ t he corresponding corresponding limit design stresses st resses in accordance accordance with 5.2.2 5.2.2.. Rdσ, f Rdτ Rdτ are the 5.5.2
Proof for bolted connections
Bolted connections shall be proofed in accordance with EN 13001-3-1. 5.5.3
Proof for welded connections
For the weld it shall be proven that:
(23)
where σw,Sd is the design weld stress; f w,Rd w,Rd is the limit design weld stress in accordance with EN 13001-3-1.
6
Proof of fatigue strength
6.1 General
The proof of fatigue strength is intended to prevent risk of failure due to formation and propagation of critical cracks in load carrying carry ing part of a hydraulic cylinder cylinder under cyclic loading. loading. For the execution of the proof of fatigue strength, the cumulative damages caused by variable stress cycles shall be calculated. In this European Standard, Palmgren-Miner’s rule of cumulative damage is relected relec ted by use of the t he stress hist history ory parameters paramet ers (see EN 13001 13001-3-3-1 1). The fatigue strength speciic resistance factor γ mf is as deined in EN 13001-3-1. mf is
The limit design stress of a constructional detail is characterized by the value of the characteristic fatigue fatig ue streng strength th , which represents the fatig fatigue ue streng strength th at 2· 2·10 106 cycles under constant stress range loading and with a probability probability of survival sur vival equal to P S 97,7 % (see EN 13001-3-1). -values depend on the quality level of the weld. Quality levels shall be in accordance with EN ISO 5817:2014, Annex C.
Fatigue test testing ing may be used to establi establish sh -values for detai details ls deviat deviating ing from those given here below below,, or to prove higher -values than those given here. Such fatig fatigue ue test testing ing shall be done in accordance with EN 13001-3-1.
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6.2
Stress histories
The stress history is a numerical presentation of all stress variations that are signiicant for fatigue.
Stress histories shall be determined either through stress calculations or measurements, in both cases simulating the loading imposed on the cylinder. For the proof of fatigue strength, stress histories are expressed as single-parameter representations of frequencies of occurrence of stress ranges by using methods such as the hysteresis counting method (Rain low or Reservoir method) with the inluence of mean stress neglected. Each of the stress ranges is suficiently described by its upper and lower extreme value.
(24)
where is the upper extreme value of a stress range; is the lower extreme value of a stress range; is the stress range. Stress history parameter s3 is calculated as follows, based on a one-parameter presentation of stress histories during the design life of the cylinder:
(25)
where
(26)
(27)
where ν is the relative total number of occurrences of stress ranges; k 3 is the stress st ress spectrum factor dependant on m;
is the stress st ress range i; is the t he design stress range; ni is the number of occurrences of stress range i;
is the total number of occurrences of stress ranges during the design life of the cylinder; is the reference number of cycles. Depending on which part of a cylinder that is considered, the stress range is proportional to either the external force range or the pressure range in either chamber. Therefore, the stress ranges in Formula (26) can (26) can be substituted with the corresponding force ranges F Δ or or pressure ranges pΔ.
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In general, the stress history parameter s3 has different values for different parts of a cylinder. These values are related to the duty and decisively depend on one of: — number of working cycles and exter external nal force spect spectrum; rum; — number of pressure pressure cycles and related pressure spect spectrum rum in piston side chamber; — number of pressure pressure cycles and related pressure spect spectrum rum in rod side chamber; For thermally stress relieved or non-welded components, the compressive portion of the stress range may be reduced to 60 %. Different parts of cylinders may be arranged into classes S of the stress history parameter sm. The Table 2. Table 2. When a class S is is referred to in the proof classiication is based upon m = 3 and is speciied in of fatigue strength for a cylinder part, the value of the stress history parameter s3 shall be taken in accordance with the Table 2. 2. Proof of competence for fatigue may be omitted when the value of the stress history parameter s3 is lower than 0,001. Table 2 — Classes S of of stress history parameter s3 Class
S 02 02
0,002
s3
S 01 01
0,004
S 0
0,008
S 1
0,016
S 2
0,032
S 3
0,063
S 4
0,125
S 5
0,25
S 6 S 7 S 8 S 9
0,5
1,0
2, 0
4,0
When a single stress history class S is is used to characterize a cylinder, the most severe class occurring within the t he cylinder shall shall be used. 6.3
Execution of the proof
For the detail under consideration it shall be proven that:
(28)
(29)
where is the design stresses range (the same as in 6.2);
max σ, min σ are the extreme values of design stresses (compression stresses with negative sign); is the t he limit design stress range. 6.4
Limit design stress range
The limit design stress range is given g iven by:
(30)
where t he limit design stress range; ΔσRd is the Δσc is the characteristic fatigue strength; γ mf is the fatigue strength speciic resistance factor (see EN 13001-3-1); mf is
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s3 is the stress history parameter; m is the t he slope of the logσΔ — log N -curve. -curve.
For the case of m > 3, Formula (30) is (30) is a conservative simpliication. With knowledge of the actual stress spectrum, a more detailed calculation may be done in accordance with EN 13001-3-1. 6.5 6.5.1
Details for consideration General
This chapter deals with details where fatigue might occur and that can be relevant for the cylinder under consideration. The characteristic fatigue strengths are given for commonly used designs. For other details or for deviating conditions, other recognized sources or fatigue testing should be used. 6.5.2
Bottom weld
The cylinder bottom can either be supported or unsupported, see Figure 18. 18. The bottom weld also transfers the axial load in the t he unsupported unsupported case.
Figure 18 — Cylinder bottom, supported (upper) and unsupported (lower)
x between For the and purpose of stress relieving thethe bottom may be a distance bottom the weld, see Figure 19. In 19. case without wweld, ithoutthere stress relieving, the distance x is is setthe to cylinder zero.
Figure 19 — Bottom weld
The shell section transverse force T 0 and the shell section bending moment M 0 act at the intersection between the cylinder tube and the bottom (see Annex C). For the basic case of a bottom with constant thickness, there are two sets of equations for T 0 and M 0 de depending pending on whethe whetherr the bottom the bottom is assumed to be supported by a constant pressure or unsupported. Formulae (31) and (32) give T 0 and M 0 for cylinders with supported bottom, whereas Formulae (35) and (36) give T 0 and M 0 for cylinders with unsupported bottom. 28
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For supported cylinder bottom, the shell section transverse force T 0 and the shell section bending moment M 0 are given by:
(31)
(32)
For cylinders where the stiffness of the bottom is much higher than the stiffness of the tube, i.e. h ≫t , Formulae (31) and (32) may be well approximated by Formulae (33) and (34). As the approximated equations yield conservative results at x = = 0 when h ≥ t , they may also be used in that t t hat case.
(33)
(34)
For unsupported cylinder bottom, the shell section transverse force T 0 and the shell section bending moment M 0 are given by:
(35)
(36)
where
Ri is the inner radius of the tube; R is the middle radius of the tube (i.e. R = Ri + t /2); /2); t is is the t he wall thickness of the tube; h is the thickness t hickness of the cylinder bottom; bottom;
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ν is Poisson’ Poisson’ss ratio rat ioν( = 0,3 for steel);
Δ pSd is the design pressure range on piston side.
For some more complex cases, T 0 and M 0 can be obtained by solving the equation systems given in Annex D. D. from the t he cylinder bottom bottom is given g iven by: The bending stress range Δ σb( x ) at the distance x from
(37)
where the plus sign denotes the inside of the tube and the minus sign denotes the outside of the tube. The membrane stress range Δσm depends on the bottom support and is given by:
Supported Suppo rted bottom:
(38)
Unsupported Unsup ported bottom: The total stress range ΔσSd at the weld location x shall, for the outside of the cylinder tube, be
computed as:
(39)
shall, for the inside of the cylinder tube, be computed as: The total stress range Δ σSd at the weld location x shall,
(40)
The following following characteristic fatigue strengths with w ith m = 3 shall be used: Outside tube, weld toe in quality C: Δσc = 100 MPa; Outside tube, weld toe in quality B: Δσc = 112 MPa; Inside tube, weld root: Δσc = 71 MPa. The design stress range ΔσSd may additionally be computed using a FE-analysis model for increased
accuracy by applying one of the methods described in [1 [1] and [3 [3]. 6.5.3
Notch stress at oil connectors
This clause deals with oil connector welded with all around illet weld in quality C. The design stress range ΔσSd is based on the pressure range at the oil connector’s cylinder end and shall be computed as:
(41)
where Δ pSd is the design pressure range for that cylinder end; 30
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D is the t he piston diameter; t is is the t he thickness of the cylinder tube.
Figure 20 — Oil connector on piston side
The characteristic fatigue strength Δ σc = 80 MPa with m = 3 shall be used.
The same calculation method shall be used for oil connectors both on piston side and rod side. 6.5.4 6.5.4.1
Cylinder head General
The design stress range Δ σSd is based on the force range F Δ resulting from the rod side’s pressure range. The force range Δ F shall shall be computed as:
(42)
where Δ pSd is the design pressure range on rod side; D is the t he piston diameter;
is the rod diameter. d is 6.5.4.2
Tube thread
This clause deals with end of cylinder tube with machined threads. The design stress range Δ σSd shall
be computed as:
(43)
where Δ F Sd Sd is the design force range acting on the cylinder head; As is the t he stress area of the threaded tube.
Figure 21 — Tube thread
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The characteristic fatigue strength (in MPa) for m = 3 shall be computed as:
(44)
where d s is the stress diameter for inner thread and inner diameter for outer thread; Ds is the outer diameter for inner thread and stress diameter for outer thread. 6.5.4.3
Tube thread undercut
This clause deals with half circular undercut at end of cylinder tube threads. The design stress range ΔσSd shall be computed as:
(45)
where Sd is the design force range acting on the top nut; ΔF Sd A is the smallest stress st ress area of tube at the undercut.
Figure 22 — Undercut for tube thread
The characteristic fatigue strength (in MPa) for m = 5 shall be computed as:
(46)
where f y is the yield strength in MPa. Formula (46) requires that the bottom radius of the undercut is at least 35 % of the undercut depth. 6.5.4.4
Locking wire groov groove e
This clause deals with stress concentration at locking wire groove. The design stress range Δ σSd is
based on nominal stress at remaining area, and shall be computed as:
(47)
where ΔF Sd Sd is the design force range acting on the top nut; A is the smallest stress st ress area of the tube at the groove.
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Figure 23 — Locking wire groove
The characteristic fatigue strength (in MPa) for m = 5 shall be computed as:
(48)
where f y is the yield strength in MPa.
Formula (48) requires that the bottom radius of the undercut is at least 35 % of the undercut depth. 6.5.5 6.5.5.1
Piston rod General
The design stress range ΔσSd where the piston rod head and the piston are connected to the piston rod acting on the piston rod. is based on the force range Δ F acting 6.5.5.2
Piston rod threads
This clause deals with end of piston rod with machined threads. The design stress ranges Δ σSd at the
threads on the piston rod shall be computed as:
(49)
where Δ F Sd Sd is the design force range acting on the piston rod thread; As is the t he stress area of the threaded piston rod.
Figure 24 — Threads on piston rod
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The characteristic fatigue strength (in MPa) for m = 3 shall be computed as:
(50)
where d s is the stress diameter for inner thread and inner diameter for outer thread; Ds is the outer diameter for inner thread and stress diameter for outer thread. 6.5.5.3
Piston rod thread undercuts
This clause deals with undercut at end of piston rod threads. The design stress range Δ σSd shall be
computed as:
(51)
where Sd is the design force range acting on the piston rod; ΔF Sd A is the smallest stress st ress area of the piston rod at the undercut.
The characteristic fatigue strength for m = 5 shall be computed as (in MPa):
(52)
where f y is the yield strength in MPa.
Formula (52) requires that the bottom radius of the undercut is at least 35 % of the undercut depth. 6.5.5.4
Piston rod welds
This clause deals with piston welded to rod with illet weld, groove weld or friction weld.
Figure 25 — Piston rod welds, illet weld (left) and groove weld (right)
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The design stress ranges ΔσSd at the welds on the piston rod shall be computed as:
(53)
where Sd is the design force range acting on the piston rod; Δ F Sd A is the cross section area of the weld (rod area in case of friction weld).
The following following characteristic fatigue strengths Δσc with m = 3 shall be used: — Fillet weld in quality C Δσc = 45 MPa; — Fillet weld in quality B Δσc = 50 MPa; — Groove weld in quality C Δσc = 63 MPa; — Groove weld in quality B Δσc = 71 MPa; — Friction weld in quality C Δ σc = 80 MPa; — Friction weld in quality B Δσc = 90 MPa. 6.5.6
Cylinder head bolts
The fatigue strength of the cylinder head bolts shall be assessed in accordance with EN 13001-3-1. 6.5.7 6.5.7.1
Cylinder head lange weld General
This clause deals with lange at end of cylinder tube welded to tube with groove or illet weld.
Figure 26 — Cylinder head lange welds, illet weld (left) and groove weld (right)
A lange weld of a pulling cylinder is subjected to axial shell bending stress from the internal pressure, whereas the lange weld of a pushing cylinder is subjected to axial membrane stress from the axial load at end of stroke. The lange weld of a pulling cylinder shall in addition to axial stress also be assessed for tangential (hoop) stress. At least quality C shall be used for the lange weld.
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6.5.7.2
Pulling cylinder cylinder,, axial stress
With the conservative assumption that the lange is rigid, the shell section transverse force T 0 and the shell section bending moment M 0 acting at the end of the tube are given by:
(54)
(55)
where
Ri is the inner radius of the tube; R is the middle radius of the tube (i.e. R = Ri + t /2); /2); t is is the t he wall thickness of the tube; ν is Poisson’ Poisson’ss ratio rat io (ν = 0,3 for steel); st eel);
Δ pSd is the design pressure range on rod side.
into the cylindrical part is given by: The bending stress range Δ σb( x ) at the distance x into
(56)
The membrane stress range Δσm is given by:
(57)
where Ri is the inner radius of the tube; r o is the outer radius of the rod; R is the middle radius of the tube (i.e. R = Ri + t /2); /2); t is is the t he wall thickness of the tube;
Δ pSd is the design pressure range on piston side. The total design stress range Δ σSd( x ) at the weld location x shall shall be computed as:
The characteristic fatigue strength Δ σc = 100 MPa with m = 3 shall be used.
(58)
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The design stress range ΔσSd may additionally be computed using a FEM model for increased accuracy
by applying one of the methods described in [1 [1] and [3 [3]. 6.5.7.3
Pushing cylinder cylinder,, axial stress at end of stroke
The axial design stress range ΔσSd at the lange weld shall be calculated as:
(59)
where Ri is the inner radius of the tube; R is the middle radius of the tube (i.e. R = Ri + t /2); /2); t is is the t he wall thickness of the tube;
Δ pSd is the design pressure range on piston side. The characteristic fatigue strength Δ σc = 100 MPa with m = 3 shall be used. 6.5.7.4
Pushing and pulling cylinder cylinder,, axial stress
For cylinders that are both pulling and pushing, and when w hen both modes modes require require to to be considered in the fatigue assessment, the axial stress ranges Δ σSd from Formulae (58) and (59) may, as a conservative assumption, be added and the sum be taken as an effective design stress range Δ σSd . A more precise analysis requires knowledge knowledge of the actual act ual stress range spectrum spect rum at the t he weld. weld. 6.5.7.5
Pulling cylinder cylinder,, tangential stress
The tangential design stress range ΔσSd at the lange weld shall be calculated as:
(60)
where R is the middle radius of the tube; t is is the t he wall thickness of the tube;
Δ pSd is the design pressure range on rod side. The characteristic fatigue strength Δσc = 180 MPa for weld quality B and σΔc = 140 MPa for weld quality C and with m = 3 shall be used. 6.5.8
Mechanical interfaces
The fatigue strength of the mechanical interfaces between the hydraulic cylinder and the rest of the crane structure shall be assessed in accordance with EN 13001-3-1. 7
Proof of elastic stability
7.1 General
The proof of elastic stability is made to prove that ideally straight cylinde c ylinders rs will not lose their stability due to lateral deformation caused solely by compressive forces or compressive stresses. Deformations
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due to compressive forces or compressive stresses in combination with bending moments caused by external forces or by initial geometric imperfections shall be assessed by the theory of second order (5.4 5.4 Nonlinear stress analysis) as part of proof of static strength. This chapter covers buckling of
complete cylinders and internal buckling of piston rods. 7.2
Critical buckling load
The critical buckling load N kin iscompression the smallest and bifurcation load according to elastic FTable or cylinders cylin dersa having only one part loaded with constant cross section, N k is theory. given inFor 3 for 3 for selection of boundary conditions, also known as Euler’s buckling cases. Table 3 — Critical buckling load N k for Euler’s buckling cases k for Euler c ase no
1
2
3
4
5
Boundary condi-
tions
N k
E is is the modulus of elasticity I is is the moment of inertia of the member in the plane of the igures L is the length of the member
For other boundary conditions or for cylinders consisting of several parts i that are loaded in compression and with different cross sections, N k may be computed from the differential equation, or system of differential equations, of the elastic delection curve in its deformed state, which has the
general solution: where x is is the longitudinal coordinate; y is is the lateral coordinate in the weakest direction of the member; E is is the t he modulus modulus of elasticity; i is an index running over the number of cylinder parts that are loaded in compressioni ≥ ( 1);
(61)
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I i is the moment of inertia of part i in the weakest direction of the member; N is is the compressive force; Ai, Bi, C i, Di are constants to be found by applying appropriate boundary conditions.
The critical buckling load N k is found as the smallest positive value N that that satisiesFormula Formula (61), or system of Formulae (61), when solved with the appropriate boundary conditions applied. Equations for 4 are given in Annex A. the most common cylinder cases A tousing G shown in Table analysis A . Alternatively, the critical buckling load N kbuckling may be calculated FE buckling [2]. [2 Table 4 — Common buckling cases for hydraulic cylinders
A
Regular Euler 1 case
B
C
As Euler 1 Regular case, but with Euler 2 case two different dif ferent cross-sections
D
E
As Euler 2 Two coupled case, but with Euler 2 cases two different dif ferent cross-sections
F
An Euler 2 case that is coupled with a rotational
G
Regular Euler 3 case
spring
For the case when the rod buckles internally inside the cylinder tube, the critical buckling load N k shall be calculated by using the appropriate Euler case from Table 3. 3. However, a critical buckling load N k resulting in a design compressive force N Sd Sd that exceeds the limit design compressive force N Rd Rd may be acceptable if a second order calculation in accordance with 5.4 shows that the design stress does not exceed the limit design stress. 7.3
Limit compressiv compressive e design force
The limit compressing design force N Rd,i Rd,i for a cylinder part i is computed from the critical buckling load by: where
(62)
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κ i is a reduction factor for the evaluated cylinder part i; f yk,i y ield d stress of the t he evaluated cylinder cylinder part i; yk,i is characteristic yiel Ai is the t he cross section area of the evaluated cylinder cylinder part i; γ m is the general resistance factor, γ m = 1,1 (see EN 13001-2).
The reduction factor κ i is computed from the slenderness λi, which is given by:
(63)
where N k is the critical buckling load in accordance with 7.2 .2..
Depending on the value of λi, the reduction factor κ i is given by:
(64)
Rd is taken Rd,i of all parts i: The overall limit compressing design force N Rd t aken as the minimum value N Rd,i
(65)
If there is more than one cylinder part loaded in compression, additionally the following condition shall apply to each cylinder part i: 7.4
(66)
Execution of the proof
For the member under consideration, it shall be proven that: where N Sd Sd is the design value of the compressive force; N Rd .3.. Rd is the limit design compressive force according to 7.3
(67)
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Annex A (informative) Critical buckling load for common buckling cases
A.1
General
Depending on different mounting conditions, the common buckling cases shown in Figure A.1 A.1 can be found. A. Regular Euler 1 case (see 7.2 .2,, Table 2).
B. As Euler 1 case, but with two t wo different cross-sections. cross-sections. C. Regular Euler 2 case (see 7.2 .2,, Table 2).
D. As Euler 2 case, but with w ith two t wo different cross-sections. cross-sections. E. Two coupled Euler 2 cases. F. An Euler 2 case that is coupled with a rotational spring. G. Regular Euler 3 case (see 7.2 .2,, Table 2).
A
B
C
D
E
F
G
Figure A.1 — Common buckling cases for hydraulic cylinders
The criticaltobuckling loads N kequation loads for buckling A to are obtained by applying conditions the differential or acases system ofGdifferential equations givenappropriate in 7.2 .2.. Theboundary following part of this annex provides the relevant equations that yield the critical buckling loads N k for buckling A.2 to A.8 ), where: cases A to G (Figures A.2 to
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N is is the compressive force; L1 is the effective effec tive buckling length length of the t he cylinder tube; tube; L2 is the effective effect ive buckling length length of the t he piston rod; I 1 is the moment of inertia of the cylinder tube; I 2 is the moment of inertia of the piston rod; is the elastic modulus of steel; E is
and where:
A.2
Buckling case A
Figure A.2 — Buckling case A (regular Euler 1 case)
Regular Euler 1 case:
A.3
(A.1)
Buckling case B
Figure A.3 — Buckling case B (as Euler 1 case, but with two different cross-sections) N k is given by the smallest positive root N of: of:
(A.2)
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
A.4
Buckling case C
Figure A.4 — Buckling case C (regular Euler Euler 2 case)
Regular Euler 2 case:
A.5
(A.3)
Buckling case D
Figure A.5 A. 5 — Buckling case c ase D (as Euler 2 case, but with two different cross-sections) cross-sections) N k is given by the smallest positive root N of: of:
A.6
(A.4)
Buckling case E
Figure A.6 — Buckling case E (two coupled Euler 2 cases) N k is given by the smallest positive root N of: of:
(A.5)
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
A.7
Buckling case F
Figure A.7 — Buckling case F (Euler 2 case coupled with a rotational spring) N k is given by the smallest positive root N of: of:
(A.6)
where the end support stiffness k r of the rod provided by the cylinder tube is given by:
A.8
Buckling case G
Figure A.8 — Buckling case G (regular Euler 3 case)
Regular Euler 3 case:
(A.7)
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Annex B (informative) Second order analysis of two important cases
B.1
Compressed cylinder with end moments and angular misalignment
This clause deals with the case described in 5.4.2 and shown in Figure 16. 16.
Figure B.1 — Compressed cylinder with end moments moments and angular ang ular misalignment
are bending moments from axles, where λi depend on axle diameters Da,i and frictions μi as:
(B.1)
with i = 1 for the tube and i = 2 for the rod. A negative value of λi is used for an axle a xle that is rotating in the favourable favourable direction. There can also be an angular misalignment misa lignment α between between the cylinder tube and the piston rod. The two constants A and B are found by solving the equation system formed by (B.2) and (B.3):
(B.2)
(B.3)
where
with i = 1 for the tube and i = 2 for the rod. Once the constants A and B are known, the bending moments MBi and lateral displacements y i are given by these pairs of equations:
(B.4) (B.5)
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
(B.6)
(B.7)
where
B.2
Compressed cylinder with lateral end force and angular misalignment
This clause deals with the case described in 5.4.3 and shown in Figure 17. 17.
Figure B.2 — Compressed Compressed cylinder with lateral end force and angular misalignment misalig nment
There can also be an angular misalignment α between between the cylinder tube and the piston rod. The two constants const ants A and B are found by by solving the equation system syst em formed by Formulae (B.8) and (B.8) and (B.9):
(B.8)
(B.9)
where
with i = 1 for the tube and i = 2 for the rod. Once the constants A and B are known, the bending moments MBi and lateral displacements y i are given by these pairs of equations:
(B.10)
(B.11)
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(B.12)
(B.13)
where
B.3
Axial stresses for cases in B.1 B.1 and and B.2
Once the b Once the bendi ending ng moments in the tube MB1( x ) and in the rod MB2( x ) have been computed in accordance with B.1 with B.1 or orB.2 B.2,, the corresponding values for the axial stresses σa( x ) are given by the following equations: equat ions: For the tube:
(B.14)
where R1 is the outer radius of the tube; I 1 is the moment of inertia of the tube.
For the rod: where R2 is the outer radius of the rod; I 2 is the moment of inertia of the rod; F A is the compressive axial force; A2 is the cross section area of the rod.
Having found the extreme values of σa, the effective effect ive stresses are given by Formula (11 (11)).
(B.15)
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Annex C (informative) Shell section forces and moments for cylinder bottom
The shell section internal transverse force T 0 and the internal shell section bending moment M 0 described in 6.5.2 6.5.2 act at the intersection between the cylinder tube and the bottom. By combining equations for displacement due to internal pressure and due to internal forces at the intersection between bottom and tube, and by setting those displacements equal at the intersection, two equation systems for T 0 and M 0 are derived, depending on whether the bottom is assumed to be supported by a constant pressure or unsupported.
Key
upper par upper part: t: lower low er part: part:
displacem displa cement entss due to int intern ernal al pre pressu ssure re displa dis placem cement entss due to inter internal nal for forces ces at the the inters intersect ection ion
Figure C.1 — Deformations of tube and bottom due to pressure and internal forces
Compatibility Compa tibility at the t he intersection between between bottom and tube gives these two t wo equations: equations:
(C.1)
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(C.2)
For bottom supported by constant pressure, additionally α p = 0 applies. The deformations in Formulae (C.1) and (C.2) can be replaced replaced by these quantifying quantify ing expressions: expressions:
(supported (sup ported bottom)
(C.3)
(unsupported (unsup ported bottom)
(C.4)
(C.5)
(C.6)
(C.7)
(C.8)
(C.9)
where
Ri is the inner radius of the tube; R is the middle radius of the tube (i.e. R = Ri + t /2); /2); t is is the t he wall thickness of the tube; h is the thickness t hickness of the cylinder bottom; bottom; ν is Poisson's ratioν( = 0,3 for steel);
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
E is is the elastic modulus;
Δ pSd is the design pressure range on piston side.
t he following equation equation systems. Formulae (C.3) to (C.9) inserted into Formulae (C.1) and (C.2) gives the For supported bottom:
(C.10)
Simplifying the equation system (C.10), it becomes:
(C.11)
where Solving (C.11) for T 0 and M 0 and simplifying yields Formulae (31) and (32) for cylinders with
supported bottom.
For unsupported bottom:
(C.12)
Simplifying the equation system (C.12), it becomes:
(C.13)
where Solving (C.13) for T 0 and M 0 and simplifying yields Formulae (35) and (36) for cylinders with unsupported bottom.
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Annex D (informative) Fatigue analysis of bottom weld for more complex cases
This annex deals with cases that are more complex than the basic cases described in 6.5.2 6.5.2.. More generally the compatibility equations for the junction point (J) between bottom and tube can be written
in the form:
(D.1)
(D.2)
where is the radial displacement of the tube due to the internal pressure p; is the radial displacement of the tube due to internal forces; is the radial displacement of the bottom’s outer rim; is the distance between the bottom’s neutral axis and the junction point; (J);
is the slope of the tube due to internal forces; is the bottom’s slope due to the internal pressure p; is the bottom’s slope due to the boundary reaction on the bottom; is the bottom’s slope due to internal forces.
Figure D.1 — Deformations due to internal constraining reactions
Undercut groove at bottom edge An inner undercut groove between bottom and tube changes the bending moment acting on the bottom, so that the distance e between J and the bottom neutral axis becomes less thanh/2.
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For this case the total moment acting on the bottom, M b, is given by
(D.3)
Boundary forces on supported bottom other ot her than constant pressure: In 6.5.2 6.5.2 the the supported cylinder bottom it is assumed that a constant pressure q equal to the internal pressure p acts on the outside wall of the bottom, which gives . Other boundary conditions are possible, e.g. bottom supported by one or more welded lugs. These cases can be approximated by one of the following boundary conditions: 1) Force Q concentrated at the centre of the bottomFigure ( D.2, left);
Figure D.2, right); 2) Force Q applied along an annular line with radius b (
where
Figure D.2 — Boundary forces on supported bottom other than constant pressure
Equation systems to solve for T 0 and M 0 T 0 and M 0 can be found for some important cases with undercut grove by solving these equation
systems here below.
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Unsupported Unsuppo rted bottom bot tom with under undercut cut groove:
(D.3)
Supported Suppo rted bottom bot tom with under undercut cut groove:
(D.4)
where
for bottom supported by a constant pressure;
for bott bottom om supported by a concentrated load at the centre;
for bott bottom om supported by an annular line load at radius b;
Ri is the inner radius of the tube; R is the middle radius of the tube (i.e. R = Ri + t /2); /2);
is the t he wall thickness of the tube; t is h is the thickness t hickness of the cylinder bottom; bottom; b is the radius of the annular line where the force acts; e is the distance between the bottom’s neutral axis and the junction point; ν is Poisson’ Poisson’ss ratioν( = 0,3 for steel); ste el); ΔpS d is the design pressure range on piston side.
BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
Annex E (informative) Selection of a suitable set of crane standards for a given application
Is there a product standard in the following list that suits the application?
EN 12999 EN 13000 EN 14439 EN 14985
EN 15011 EN 13 1385 8522-1 1 EN 138 385 52-2 EN 14492-1 EN 14492-2
EN 13157 EN 13155 EN 14238
Cranes — Loader cranes Cranes — Mobile cranes Cranes — Safety — Tower cranes Cranes — Slewing jib cranes Cranes — Bridge and gantry cranes Cran Cr anes es — Off Offsh shor oree cran cranes es — Pa Part rt 1: 1: Gen Gener eral al purp purpos osee offs offsho hore re cr cran anes es Cran Cr anes es — Off Offsh shor oree cra cran nes — Par Partt 2: 2: Fl Floa oati ting ng cr cran anes es Cranes — Power driven winches and hoists — Part 1: Power driven winches Cranes — Power driven winches and hoists — Part 2: Power driven hoists Cranes — Safety — Hand powered cranes Cranes — Safety — Non-ixed load lifting attachments
Cranes — Manually controlled load manipulating devices Y ES NO
Use it directly, plus the standards
that are referred to
Use the following:
EN 13 1300 001 1-1 EN 130 300 01-2
Craness — Gen Crane Gener eral al de desig sign n — Part 1: Ge Gene neral ral pri princ ncip iple less an and d req requir uirem emen ents ts Cran Cr anes es — Ge Gen ner eral al des esig ign n — Pa Part rt 2: Loa Load d acti actioons
EN 13001-3-1
Cranes — General Design — Part 3–1: Limit States and proof competence of steel
EN 13001-313 001-3-2 2
structure Cranes — General design — Part 3–2: Limit states and proof of competence of wire ropes in reeving systems
EN 13001-3-3 EN 13001 13001-3-4 -3-4
EN 13001-3-5 EN 13001-3-6 EN 13135 EN 13557 EN 120771 2077-2 2 EN 13586 EN 14502-1
Cranes — General design — Part 3–3: Limit states s tates and a nd proof of competence of of wheel/
rail contacts Cranes — General design — Part 3–4: Limit states and proof of competence of ma -
chinery — Bearings Cranes — General design — Part 3–5: Limit states and proof of competence of forged hooks Cranes — General design — Part 3–6: Limit states and proof of competence of machinery — Hydraulic cylinders Cranes — Safety — Design - Requirements for equipment Cranes — Controls and control stations Cranes safety - Requirements Requirements for health and safety safet y — Part 2: Limiting and indicating devices Cranes — Access Cranes — Equipment for the lifting of persons — Part 1: Suspended baskets
53
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EN 14502-2 EN 12644-1 EN 12644-2
Cranes — Equipment for the lifting of persons — Part 2: Elevating control stations Cranes — Information Information for use and testing — Part 1: Instructions Cranes — Information for use and testing — Part 2: Marking
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Annex ZA (informative) Relationship between between this European Standard and the essential requirements of Directive 2006/42/EC aimed to be covered
This European Standard has been prepared under a Commission’s standardization request “M/396” to provide one voluntary means of conforming to essential requirements of Directive 2006/42/
EC Machinery. Once this standard is cited in the Oficial Journal of the European Union under that Directive 2006/42/
EC, compliance with the normative clauses of this standard given in Table ZA.1 ZA.1 confers, within the limits of the scope of this standard, a presumption of conformity with the corresponding essential requirements of that Directive 2006/42/EC, and associated EFTA regulations. Table ZA.1 — Correspondence between this European Standard and Annex I of Directive 2006/42/EC Essentialtive Requirements 2006/42/ECof Direc-
Clause(s)/subclause(s) of this EN
Requirements given in Annex I, ClausClauses 4, 5, 6 and 7 es 1.3.2 and 4.1.2.3
WARNING 1
Remarks/Notes
all requirements are covered
Presumption Presump tion of conformit y stays valid only as long as a reference to this Europea European n Standa Standard rd
is maintained in the list published in the Oficial Journal of the European Union. Users of this standard should consult frequently the latest list published in the Oficial Journal of the European Union. WARNING 2
this standard.
Other Union legislat legislation ion may be applicable applicable to the product(s) product(s) fall falling ing within the scope scope of
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BS EN 13001-3-6:2018 EN 13001-3-6:2018 (E)
Bibliography [1]
N E., F W., M S. J. Fatigue analysis ana lysis of welded components; components; Designer’s guide to the structural hot-spot stress approach, September 2006
[2] [3]
Klaus-Jürgen Finite Element Procedures, June 19 1995 95 B H A. IIW International Inter national Institute Inst itute of Welding. Welding. IIW-182 IIW-1823-07 3-07 ex XIII-215 XIII-2151r4-07 1r4-07/XV/XV1254r4-07: 1254r 4-07: Recommendations Recommendations for fatigue fat igue design of welded joints and components, December 2008
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