ISO 23778:2022

Proof of competence of hydraulic cylinders in crane applications

This document applies to hydraulic cylinders that are part of the load carrying structure of cranes. It is intended to be used together with the ISO 8686 series and ISO 20332, and as such they specify general conditions, requirements and methods to prevent mechanical hazards of hydraulic cylinders, by design and theoretical verification. This document does not apply to hydraulic piping, hoses, connectors and valves used with the cylinders, or cylinders made from other material than (carbon) steel.

Vérification d’aptitude des vérins hydrauliques pour appareils de levage

General Information

• Status: Published
• Publication Date: 14-Sep-2022
• ICS: 53.020.20 - Cranes
• Technical Committee: ISO/TC 96/SC 10 - Design principles and requirements
• Drafting Committee: ISO/TC 96/SC 10/WG 1 - Panel of technical experts
• Current Stage: 6060 - International Standard published
• Start Date: 15-Sep-2022
• Due Date: 08-Dec-2022
• Completion Date: 15-Sep-2022

Relations

• Consolidated By: ISO/TS 7552-2:2024 - Molecular in vitro diagnostic examinations - Specifications for pre-examination processes for circulating tumour cells (CTCs) in venous whole blood - Part 2: Isolated DNA
• Effective Date: 12-Nov-2022

Overview

ISO 23778:2022 - Proof of competence of hydraulic cylinders in crane applications - specifies design and theoretical verification methods to prevent mechanical hazards of hydraulic cylinders that form part of the load‑carrying structure of cranes. It is intended to be used together with the ISO 8686 series (crane loads) and ISO 20332 (proof of competence of steel structures). The standard covers documentation, materials (carbon steel), and analytical methods to demonstrate static strength, fatigue strength, and elastic stability of cylinder components and connections.

Note: ISO 23778:2022 does not apply to hydraulic piping, hoses, connectors, valves, or cylinders made from non‑(carbon) steel materials.

Key topics and technical requirements

• Scope & exclusions: Applies to hydraulic cylinders integrated into crane load paths; excludes external hydraulic components and non‑carbon steel cylinders.
• Documentation: Requires complete design assumptions, calculation models and evidence supporting the proof of competence.
• Materials: General requirements for materials and specified grades/qualities for (carbon) steel cylinder components.
• Proof of static strength: Limit design stresses, linear and nonlinear stress analysis methods, and checks for tube, bottom, piston rod welds, threads and connecting interfaces.
• Proof of fatigue strength: Definition of stress histories, execution of fatigue proofs, limit design stress ranges and detail treatment for bottom welds, oil connector notches, cylinder heads, rods and fasteners.
• Proof of elastic stability: Critical buckling load determination, limit compressive design force, and execution guidelines for stability verification.
• Connections & welds: Specific attention to welded and bolted connections, weld throat thickness, weld quality levels and stress concentration details.
• Analytical tools: Use of finite element analysis (FE), linear/nonlinear analysis and referenced symbols and parameters for consistent calculations.
• Annexes: Informative annexes cover common buckling cases, second‑order analyses, shell section forces at the bottom, and advanced fatigue analyses.

Practical applications and users

ISO 23778:2022 is practical for:

• Crane designers and structural engineers performing design verification of hydraulic cylinders.
• OEMs and component manufacturers developing load‑bearing hydraulic cylinders for cranes.
• Certification bodies and conformity assessors evaluating mechanical safety and compliance.
• Maintenance engineers and safety inspectors assessing remaining life, fatigue risks and structural integrity.
• R&D and testing teams using FEA for component optimization and risk reduction.

Using ISO 23778 helps ensure reliable design verification, harmonized calculations, stronger safety cases, and alignment with crane load principles (ISO 8686) and steel structure proofs (ISO 20332).

Related standards

• ISO 8686 series - Cranes: design principles for loads and load combinations
• ISO 20332:2016 - Cranes: proof of competence of steel structures
• ISO 12100 - Safety of machinery: risk assessment and reduction
• Referenced material and testing standards (e.g., ISO 148‑1, ISO 5817) for material and weld quality requirements

Keywords: ISO 23778:2022, hydraulic cylinders, crane applications, proof of competence, static strength, fatigue strength, elastic stability, crane safety, ISO 8686, ISO 20332.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 23778
First edition
2022-09
Proof of competence of hydraulic
cylinders in crane applications
Vérification d’aptitude des vérins hydrauliques pour appareils de
levage
Reference number
© ISO 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 General . 3
5.1 Documentation . 3
5.2 Materials for hydraulic cylinders . 5
5.2.1 General requirements . 5
5.2.2 Grades and qualities . 6
6 Proof of static strength .7
6.1 General . 7
6.2 Limit design stresses . 8
6.2.1 General . 8
6.2.2 Limit design stress in structural members . 8
6.2.3 Limit design stresses in welded connections . 9
6.3 Linear stress analysis . 9
6.3.1 General . 9
6.3.2 Typical cylinder arrangements. 9
6.3.3 Cylinder tube. 11
6.3.4 Cylinder bottom .13
6.3.5 Piston rod welds . 14
6.3.6 Cylinder tube and piston rod threads . 14
6.3.7 Thread undercuts and locking wire grooves . 14
6.3.8 Oil connector welds . 15
6.3.9 Connecting interfaces to crane structure . 16
6.4 Nonlinear stress analysis . 16
6.4.1 General . 16
6.4.2 Standard cylinder with end moments . 16
6.4.3 Support leg . 16
6.5 Execution of the proof . 17
6.5.1 Proof for load bearing components . 17
6.5.2 Proof for bolted connections . 17
6.5.3 Proof for welded connections . 18
7 Proof of fatigue strength .18
7.1 General . 18
7.2 Stress histories . 18
7.3 Execution of the proof . 20
7.4 Limit design stress range . 20
7.5 Details for consideration .20
7.5.1 General .20
7.5.2 Bottom weld . 20
7.5.3 Notch stress at oil connectors . 23
7.5.4 Cylinder head . 24
7.5.5 Piston rod . 26
7.5.6 Cylinder head bolts .28
7.5.7 Cylinder head flange weld .28
7.5.8 Mechanical interfaces . 30
8 Proof of elastic stability .30
8.1 General .30
8.2 Critical buckling load .30
8.3 Limit compressive design force . 32
iii
8.4 Execution of the proof . 33
Annex A (informative) Critical buckling load for common buckling cases .34
Annex B (informative) Second order analysis of two important cases.38
Annex C (informative) Shell section forces and moments for cylinder bottom .41
Annex D (informative) Fatigue analysis of bottom weld for more complex cases . 44
Bibliography .47
iv
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
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ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 96, Cranes, Subcommittee SC 10, Design
principles and requirements.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
v
INTERNATIONAL STANDARD ISO 23778:2022(E)
Proof of competence of hydraulic cylinders in crane
applications
1 Scope
This document applies to hydraulic cylinders that are part of the load carrying structure of cranes. It is
intended to be used together with the ISO 8686 series and ISO 20332, and as such they specify general
conditions, requirements and methods to prevent mechanical hazards of hydraulic cylinders, by design
and theoretical verification.
This document does not apply to hydraulic piping, hoses, connectors and valves used with the cylinders,
or cylinders made from other material than (carbon) steel.
2 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 edition of the referenced document (including any amendments) applies.
ISO 148-1, Metallic materials — Charpy pendulum impact test — Part 1: Test method
ISO 683-1, Heat-treatable steels, alloy steels and free-cutting steels — Part 1: Non-alloy steels for quenching
and tempering·
ISO 683-2, Heat-treatable steels, alloy steels and free-cutting steels — Part 2: Alloy steels for quenching and
tempering
ISO 724, ISO general-purpose metric screw threads — Basic dimensions
ISO 5817:2014, Welding — Fusion-welded joints in steel, nickel, titanium and their alloys (beam welding
excluded) — Quality levels for imperfections
ISO 8492, Metallic materials — Tube — Flattening test
ISO 8686 (all parts), Cranes — Design principles for loads and load combinations
ISO 12100, Safety of machinery — General principles for design — Risk assessment and risk reduction
ISO 20332:2016, Cranes — Proof of competence of steel structures
EN 10277:2018, Bright steel products — Technical delivery conditions — Part 2: Steels for general
engineering purposes
EN 10297-1, Seamless circular steel tubes for mechanical and general engineering purposes — Technical
delivery conditions — Part 1: Non-alloy and alloy steel tubes
EN 10305-1, Steel tubes for precision applications — Technical delivery conditions — Part 1: Seamless cold
drawn tubes
EN 10305-2, Steel tubes for precision applications — Technical delivery conditions — Part 2: Welded cold
drawn tubes
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 12100 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Symbols
For the purposes of this document, the symbols given in Table 1 apply.
Table 1 — Symbols
Symbols Description
A% Percentage elongation at fracture
a Weld throat thickness
A , B , C , D Constants
i i i i
A Stress area
s
D Piston diameter
d Rod diameter
D Axles diameter
a,i
D Pressure affected diameter
p
D Weld diameter
w
E Modulus of elasticity
F Compressive force
F Compressive force
A
FE Finite elements
f Limit design stress
Rd
f Limit design stress, normal
Rdσ
f Limit design stress, shear
Rdτ
F Lateral force
S
F External compressive design force
Sd
f Limit design weld stress
w,Rd
f Yield strength
y
h thickness of the cylinder bottom
I Moment of inertia, generic
I Moment of inertia of the tube
I Moment of inertia of the rod
L Overall length of the cylinder
L Length of the cylinder tube
L Length of the piston rod
m Slope of the log Δσ − log N curve
M Shell section bending moment, acting at the intersection between tube and bottom
M Bending moment
b
N Compressive force
N Critical buckling load
k
N Limit compressive design force
Rd
p Maximum pressure in piston side chamber
i1
p Maximum pressure in rod side chamber
i2
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbols Description
p Outer pressure
o
p Design pressure
Sd
R Middle radius of the tube (R = r + t/2)
i
r Inner radius of the tube
i
r Outer radius of the tube
o
r Outer radius of the piston rod
r
s Stress history parameter (see ISO 20332)
t Wall thickness of the tube
T Shell section transverse force, acting at the intersection between tube and bottom
x, y Longitudinal and lateral coordinates
α Angular misalignment, radians
γ General resistance factor (γ = 1,1, see ISO 8686-1)
m m
γ Fatigue strength specific resistance factor (see ISO 20332)
mf
γ Total resistance factor (γ = γ × γ )
R R m s
γ Specific resistance factor
s
Δσ Stress range
Δσ Bending stress range in the tube
b
Δσ Characteristic fatigue strength
c
Δσ Membrane stress range in the tube (axial)
m
Δσ Limit design stress range
Rd
Δσ Design stress range
Sd
Δp Design pressure range on piston side
Sd
δ Maximum displacement
max
κ Reduction factor for buckling
λ Slenderness
λ Friction parameters
i
μ Friction factors
i
ν Poisson’s ratio (ν = 0,3 for steel)
σ Axial stress in the tube
a
σ Lower extreme value of a stress range
b
σ Radial stress in the tube
r
σ Design stress, normal
Sd
σ Design weld stress, normal
w,Sd
σ Tangential stress in the tube (hoop stress)
t
σ Upper extreme value of a stress range
u
τ Design stress, shear
Sd
τ Design weld stress, shear
w,Sd
5 General
5.1 Documentation
The documentation of the proof of competence shall include:
— design assumptions including calculation models;
— applicable loads and load combinations;
— material grades and qualities;
— weld quality levels, in accordance with ISO 5817 and ISO 20332;
— relevant limit states;
— results of the proof of competence calculation, and tests when applicable.
The main parts of hydraulic cylinder are indicated in Figure 1 to Figure 3.
Key
1 bushing 8 piston
2 rod head 9 nut
3 cylinder head 10 cylinder bottom
4 oil connector 11 grease nipple
5 piston rod 12 piston side chamber
6 cylinder tube 13 rod side chamber
7 spacer
Figure 1 — Complete cylinder
Key
1 wiper
2 O-ring
3 secondary seal
4 guide ring (2 ×)
5 primary seal
6 backup ring
7 O-ring
Figure 2 — Cylinder head
Key
1 seal
2 pressure element
3 guide ring (2 ×)
Figure 3 — Piston
Figures 1 to 3 show some typical design features. Other designs may be used.
5.2 Materials for hydraulic cylinders
5.2.1 General requirements
The materials for load carrying cylinder tubes and piston rods shall fulfil the following requirements:
— The impact toughness in the transversal direction shall be tested in accordance with ISO 148-1
and shall meet the requirements stated in ISO 20332. Samples shall be cut out in the longitudinal
direction. For cylinder tubes and pressurized piston rods, samples shall also be cut out in the
transversal direction. The samples shall be prepared such that the axis of the notch is perpendicular
to the surface of the tube.
Key
1 sample cut out in longitudinal direction
2 sample cut out in transversal direction
Figure 4 — Sample for impact toughness testing
— If the material thickness does not allow samples to be cut out in the transversal direction, the tube
material shall pass a flattening test in accordance with ISO 8492. For welded tubes, two tests are
required; one with the weld aligned with the press direction and one where the weld is placed 90°
from the press direction, see Figure 4. The tube section shall be flattened down to a height H given
by:
10, 7⋅t
H =
t
C +
D
o
where
C is a factor that depends on the yield strength of the material,
C is 0,07 for f ≤ 400 MPa and C is 0,05 for f > 400 MPa;
y y
D is the outer diameter of the tube;
o
t is the wall thickness of the tube.
Material used in other parts shall meet the requirements specified in ISO 20332.
5.2.2 Grades and qualities
Steels in accordance with the following standards shall preferably be used as material for cylinder
tubes and piston rods:
— ISO 683-1;
— ISO 683-2;
— EN 10277:2018;
— EN 10297-1:
— EN 10305-1;
— EN 10305-2.
Alternatively, other steel grades and qualities than those listed in this subclause may be used as
material for cylinder tubes and piston rods, provided that the following conditions apply:
— the design value of f is limited to f /1,1 for materials with f /f < 1,1;
y u u y
— the percentage elongation at fracture A % ≥ 14 % on a gauge length LS=×56, 5 (where S is the
00 0
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 ISO 20332.
6 Proof of static strength
6.1 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 the relevant part of ISO 8686 are used to produce equivalent static loads to simulate dynamic
effects. Also, load increasing effects due to deformation shall be considered. The theory of plasticity
for calculation of ultimate load bearing capacity is not considered acceptable for the purposes of this
document. The proof shall be carried out for structural members and connections while taking into
account the most unfavourable load effects from the load combinations A, B or C in accordance with the
relevant part of ISO 8686 or relevant product standards.
This document considers only nominal stresses, i.e. those calculated using traditional elastic strength
of materials theory; localized stress concentration effects are excluded. When alternative methods of
stress calculation are used such as finite element analysis, using those stresses directly for the proof
given in this document can yield inordinately conservative results as the given limit states are intended
to be used in conjunction with nominal stresses.
Cylinder actions are either active or passive. The action is active when the force from the cylinder exerts
a positive work on the crane structure, elsewise the action is passive.
As the forces applied to the cylinder by the crane structure are computed in accordance with ISO 8686,
they are already increased by the partial safety factors γ and relevant dynamic factors. Formula (1)
p
and Formula (2) give design pressures p caused by forces acting on the cylinder from the crane
Sd
structure. In addition, additional pressures p caused by internal phenomena in the hydraulic circuit
Sde
shall be considered and added to the design pressures p . Such internally generated pressures can be
Sd
caused, for example, 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
p , this load case shall also be taken into account in the proof of static strength, and in which case the
Sd
test pressure shall be multiplied by a partial safety factor γ equal to 1,05.
p
The design pressure p in the piston side chamber or in the rod side chamber shall be computed from
Sd
the design force F taking into account the force direction and the cylinder efficiency η due to friction.
Sd
An efficiency 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 of η.
For the piston side chamber, the design pressure is given by Formula (1):
4⋅F
Sd
p = ⋅Ψ (1)
Sd
π⋅D
where
F is the external design force;
Sd
D is the piston diameter;
Ψ is set to η for passive cylinders and to 1/η for active cylinders.
For the rod side chamber, the design pressure is given by Formula (2):
4⋅F
Sd
p = ⋅+Ψ p (2)
Sd Sde
π⋅−Dd
()
where
F is the external design force;
Sd
D is the piston diameter;
d is the rod diameter;
Ψ is set to η for passive cylinders and to 1/η for active cylinders;
p is additional pressure caused by internal phenomena (e.g. regeneration).
Sde
Unless justified value of the efficiency η is available and used, Ψ shall be assigned the value of 1,1 for
active cylinders and the value of 1,0 for passive cylinders.
6.2 Limit design stresses
6.2.1 General
The limit design stresses f shall be calculated from Formula (3):
Rd
ff= f ,γ (3)
()
Rd nk R
where
f is a general function as described in 6.2.2;
n
f is the characteristic values (or nominal value);
k
γ is the total resistance factor.
R
6.2.2 Limit design stress in structural members
The limit design stress f , used for the design of structural members, shall be calculated from
Rd
Formulae (4) and (5):
f
y
f = for normal stresses (4)
Rdσ
γ
Rm
f
y
f = for shear stresses (5)
Rdτ
γ ⋅ 3
Rm
with γγ= · γ
Rm msm
where
f is the minimum value of the yield stress of the material;
y
is the general resistance factor γ =11, (see ISO 8686-1);
γ
m
m
γ is the specific resistance factor for material in accordance with ISO 20332;
sm
γ = 0,95 is the basic value for material not loaded perpendicular to the rolling plane.
sm
For tensile stresses perpendicular to the plane of rolling (see Figure 5), the material shall be suitable for
carrying perpendicular loads and be free of lamellar defects. ISO 20332 specifies the values of γ for
sm
material loaded perpendicular to the rolling plane.
Figure 5 provides an example of a cylinder tube bottom where plate steel is used (eye is welded) and
shows a tensile load perpendicular to plane of rolling.
Key
1 plane of rolling
2 direction of stress/load
Figure 5 — Tensile load perpendicular to plane of rolling
6.2.3 Limit design stresses in welded connections
The limit design weld stress f used for the design of a welded connection shall be in accordance with
w,Rd
ISO 20332.
6.3 Linear stress analysis
6.3.1 General
Subclause 6.3 comprises typical details for consideration that may be relevant for the proof of static
strength. Details that are only relevant for fatigue analysis (e.g shell bending of tube) are not dealt
with in 6.3. For cases or conditions not covered here, other recognized sources or static pressure/force
testing may be used.
6.3.2 Typical cylinder arrangements
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/stresses due to thread pre-tightening;
— direction of gravity.
Different pressurized cylinder arrangements shall be considered when calculating static strength for
cylinders.
Typical pressurized cylinder arrangements are shown in Figure 6 to Figure 10.
Key
p pressure in piston side chamber
i1
Figure 6 — Pushing cylinder with supported bottom
Key
p pressure in piston side chamber
i1
Figure 7 — Pushing cylinder, flange mounted with unsupported bottom
Key
p pressure in piston side chamber
i1
p pressure in rod side chamber
i2
Figure 8 — Pulling cylinder or pushing cylinder with pressurized rod chamber
Key
p pressure in piston side chamber
i1
Figure 9 — Pushing cylinder at end of stroke
Key
p pressure in rod side chamber
i2
Figure 10 — Pulling cylinder at end of stroke
The worst load condition or combination shall be used when calculating stresses σ or σ for a
Sd w,Sd
feature.
6.3.3 Cylinder tube
Cylinder tube stresses, see Figure 11, shall be computed from three components. For calculation of each
component, forces and pressures shall be determined in accordance with 6.3.2.
Figure 11 — Stresses in cylinder tube
The tangential stress (hoop stress) is given by Formula (6):
2 2
r r
   
o
i
+1 +1
   
r r
   
σ ()rp=⋅ +⋅p (6)
ti o
2 2
r   r 
o i
−1 −1
   
r r
   
i o
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 in the tube occurs at the inner radius r or the at the outer radius r
i o
and is given by Formula (7):
σ =−p or σ =−p (7)
ri ro
For the cylinder arrangement shown in Figure 6, maximum axial stress in the tube is given by
Formula (8):
4⋅r
o
σ =⋅M (8)
ab
π⋅−rr
()
oi
For the cylinder arrangements shown in Figure 8 and Figure 10, maximum axial stress in the tube is
given by Formula (9):
pr⋅−r
()
ii2 r 4⋅r
o
σ = +⋅M (9)
a b
22 44
rr− π⋅−rr
()
oi oi
For the cylinder arrangement shown in Figure 7 and Figure 9, maximum axial stress in the tube is given
by:
pr⋅ 4⋅r
ii1 o
σ = +⋅M (10)
a b
22 44
rr− π⋅−rr
()
oi oi
where
r is an arbitrary radius of the tube;
r is the inner radius of the tube;
i
r is the outer radius of the tube;
o
r is the outer radius of the piston rod;
r
p is the inner pressure;
i
p is the inner maximum pressure in piston side chamber;
i1
p is the inner maximum pressure in rod side chamber;
i2
p is the outer pressure;
o
M is any bending moment acting on the cylinder tube (e.g. dead weight).
b
The von Mises equivalent stress shall be computed for the location having the most severe stress as:
σ = σσσ++−σσ −−σσ σσ (11)
Sd tr at at rr a
6.3.4 Cylinder bottom
6.3.4.1 Bottom plate
The stress in an unsupported bottom plate, see Figure 12, in a cylinder with the ratio outer diameter to
inner diameter in the range 1,07 to 1,24, shall be calculated as:
341 3 Dt+⋅2 D
  
σ =⋅p −⋅ ⋅ (12)
Sd i  
 
350 7 D h
  
where
p is the inner pressure;
i
D is the inner diameter;
t is the tube thickness;
h is the bottom thickness.
Figure 12 — Stresses in unsupported cylinder bottom
6.3.4.2 Bottom weld
Bottom welds, see Figure 13, shall be calculated for different load cases in accordance with 6.3.2.
Figure 13 — Bottom weld
The bottom weld is loaded by the axial force in the tube, caused by internal pressure (see Figure 7 and
Figure 8) or by pushing cylinder coming to end of stroke (see Figure 9).
F
Sdt
σ = (13)
wS, d
2⋅⋅π Ra⋅
where
F is the design axial force acting in the tube;
Sdt
a is the effective throat thickness of the weld, see ISO 20332:2016, Annex C;
R is the middle radius of the weld.
6.3.5 Piston rod welds
Piston rod welds shall be calculated for different load cases according to 6.3.2, in the same way as the
calculation of bottom welds.
F
Sdw
σ = (14)
wS, d
2⋅⋅π Ra⋅
where
F is the maximum design force acting in the rod;
Sdw
a is the effective throat thickness of the weld, see ISO 20332:2016, Annex C;
R is the middle radius of the weld.
6.3.6 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 6.3.2. The design stress shall be computed as:
F
Sdr
σ = (15)
Sd
A
s
2⋅F
Sdr
τ = (16)
Sd
π⋅⋅Ld
where
F is the maximum design force acting on the cylinder head or the piston rod head;
Sdr
A is the stress area of the threaded cylinder tube or piston rod (equivalent to stress area of bolt
s
or nut);
L is the effective threaded length, maximum 0,9 ⋅ d ;
d is the pitch diameter of the thread in accordance with 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 (16).
6.3.7 Thread undercuts and locking wire grooves
Stresses in thread undercuts or locking wire grooves (see Figure 14) shall be calculated for the different
load cases in accordance with 6.3.2.
The design stress shall be computed as:
F
Sdu
σ = (17)
Sd
A
c
where
F is the maximum design force acting at the undercut;
Sdu
A is the critical stress area at the undercut or locking wire groove.
c
Figure 14 — Undercuts at thread run out
6.3.8 Oil connector welds
This subclause considers oil connectors welded to the tube (see Figure 15). The design stress σ shall
w,Sd
be computed as:
F
Sdo
σ = (18)
wS, d
A
with
AD=⋅π ⋅a (19)
w
and
pD⋅⋅π
Sd p
F = (20)
Sdo
where
p is the design pressure for chamber side;
Sd
D is the pressure affected diameter;
p
a is the effective throat thickness of the weld, see ISO 20332:2016, Annex C;
D is the effective weld diameter.
w
Figure 15 — Welded oil connector
6.3.9 Connecting interfaces to crane structure
The design stresses in parts connecting the cylinder to the crane structure shall be calculated in
accordance with ISO 20332.
6.4 Nonlinear stress analysis
6.4.1 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 due to the angular misalignment α is smaller than L/600, where L
max
is the overall length of the cylinder. If the misalignment is unknown, δ shall be set to L/300. The
max
omission of a second order analysis shall be justified.
In particular, the cases described in 6.4.2 and 6.4.3 may require nonlinear stress analysis. The nonlinear
stress analyses may either be made with FE-analysis or by the analytical formulae given in Annex B.
6.4.2 Standard cylinder with end moments
Figure 16 shows a standard cylinder with the same configuration as in buckling case D (see 8.2), loaded
by a compressive force F and by moments M and M caused by axle frictions acting at the bushings at
1 2
the cylinder’s ends, and with an angular misalignment α between the cylinder tube and the piston rod
caused by play at guide rings.
Figure 16 — Cylinder with end moments from axle frictions and angular misalignment
6.4.3 Support leg
Figure 17 shows a support leg cylinder loaded by a compressive force F and by a lateral force F , and
A S
with an angular misalignment α between the cylinder tube and the piston rod caused by play at guide
rings.
Figure 17 — Support leg cylinder with lateral force and angular misalignment
6.5 Execution of the proof
6.5.1 Proof for load bearing components
For the load bearing components (e.g. tube, rod, lugs) it shall be proven that:
σ ≤ f  and τ ≤ f (21)
Sd Rdσ Sd Rdτ
where
σ is the design normal stress or the von Mises equivalent stress;
Sd
τ is the design shear stress;
Sd
f , f are the corresponding limit design stresses in accordance with 6.2.2.
Rdσ Rdτ
6.5.2 Proof for bolted connections
Bolted connections shall be proofed in accordance with ISO 20332.
6.5.3 Proof for welded connections
For the weld it shall be proven that:
σ ≤ f (22)
wS,,dw Rd
where
σ is the design weld stress;
w,Sd
f is the limit design weld stress in accordance with ISO 20332.
w,Rd
7 Proof of fatigue strength
7.1 General
The proof of fatigue strength is intended to prevent risk of failure due to formation and propagation of
critical cracks in load carrying part of a hydraulic cylinder under cyclic loading.
For the execution of the proof of fatigue strength, the cumulative damages caused by variable stress
cycles shall be calculated. In this standard, Palmgren-Miner’s rule of cumulative damage is reflected by
use of the stress history parameters (see ISO 20332).
The fatigue strength specific resistance factor γ is as defined in ISO 20332.
mf
The limit design stress of a constructional detail is characterized by the value of the characteristic
fatigue strength Δσ , which represents the fatigue strength at 21⋅ 0 cycles under constant stress
c
range loading and with a probability of survival equal to P 97,7 % (see ISO 20332).
S
Δσ -values depend on the quality level of the weld. Quality levels shall be in accordance with
c
ISO 5817:2014, Annex C. Weld quality lower than weld quality class C shall not be used.
Fatigue testing may be used to establish Δσ -values for details deviating from those given here below,
c
or to prove higher Δσ -values than those given here. Such fatigue testing shall be done in accordance
c
with ISO 20332.
7.2 Stress histories
The stress history is a numerical presentation of all stress variations that are significant for fatigue.
Stress histories shall be determined either through stress calculations or measurements, in both cases
simulating the loading imposed on the cylinder. The classification of load cycles in the ISO 4301 series
can be used when estimating the number of relevant stress cycles.
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 flow or Reservoir method) with the influence of mean stress neglected.
Each of the stress ranges is sufficiently described by its upper and lower extreme value.
Δσσ=−σ (23)
ub
where
σ is the upper extreme value of a stress range;
u
σ is the lower extreme value of a stress range;
b
Δσ
is the stress range.
Stress history parameter s is calculated as follows, based on a one-parameter presentation of stress
histories during the design life of the cylinder:
sk=⋅ν (24)
where
Δσ n
 
ii
k = ⋅ (25)
3 ∑
 

N
 
Δσ t
i
N
t
ν = (26)
N
ref
where
ν is the relative total number of occurrences of stress ranges;
k is the stress spectrum factor;
Δσ
is the stress range i;
i

is the maximum design stress range;
Δσ
n is the number of occurrences of stress range i;
i
is the total number of occurrences of stress ranges during the design life of the cylinder;
Nn=
t ∑ i
i
is the reference number of cycles.
N 2⋅10
ref
Depending on which part of a cylinder 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 be substituted with the corresponding force ranges ΔF or pressure ranges Δp.
In general, the stress history parameter s has different values for different parts of a cylinder. These
values are related to the duty and decisively depend on either:
— the number of working cycles and external force spectrum;
— the number of pressure cycles and related pressure spectrum in piston side chamber; or
— the number of pressure cycles and related pressure spectrum 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 s . The
m
classification is based upon m = 3 and is specified in Table 2. When a class S is referred to in the proof
of fatigue strength for a cylinder part, the value of the stress history parameter s shall be taken in
accordance with Table 2. Proof of competence for fatigue may be omitted when the value of the stress
history parameter s is lower than 0,001.
Table 2 — Classes S of stress history parameter s
Class S02 S01 S0 S1 S2 S3 S4 S5 S6 S7 S8 S9
s 0,002 0,004 0,008 0,016 0,032 0,063 0,125 0,25 0,5 1,0 2,0 4,0
When a single stress history class S is used to characterize a cylinder, the most severe class occurring
within the cylinder shall be used.
7.3 Execution of the proof
For the detail under consideration, it shall be proven that:
ΔΔσσ≤ (27)
Sd Rd
Δσσ=−maxminσ (28)
Sd
where
Δσ 
Sd
is the design stresses range (the same as Δσ in 7.2);
max σ, min σ are the extreme values of design stresses (compression stresses with negative sign);
Δσ
is the limit design stress range.
Rd
7.4 Limit design stress range
The limit design stress range is given by:
Δσ
c
Δσ = (29)
Rd
m
γ ⋅ s
mf 3
where
Δσ is the limit design stress range;
Rd
Δσ is the characteristic fatigue strength;
c
γ is the fatigue strength specific resistance factor (see ISO 20332);
mf
s is the stress history parameter;
m is the slope of the log Δσ − log N-curve.
For the case of m > 3, Formula (29) is a conservative simplification. With knowledge of the actual stress
spectrum, a more detailed calculation may be done in accordance with ISO 20332.
7.5 Details for consideration
7.5.1 General
This subclause deals with details where fatigue can 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.
7.5.2 Bottom weld
The cylinder bottom can either be supported or unsupported, see Figure 18. The bottom weld also
transfers the axial load in the unsupported case.
Figure 18 — Cylinder bottom, supported (upper) and unsupported (lower)
For the purpose of stress relieving the
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