Cranes - General design - Part 1: General principles and requirements

This European Standard specifies general conditions, requirements and methods to prevent mechanical hazards of cranes by design and theoretical verification. Note: Specific requirements for particular types of crane are given in the appropriate European Standard for the particular crane type. The following is a list of significant hazardous situations and hazardous events that could result in risks to persons during normal use and foreseeable misuse. Clause 4 of this standard is necessary to reduce or eliminate the risks associated with those hazards: a) rigid body instability of the crane or its parts.

Krane - Konstruktion allgemein - Teil 1: Allgemeine Prinzipien und Anforderungen

Diese Europäische Norm ist zusammen mit Teil 2 und Teil 3 anzuwenden und spezifiziert allgemeine Bedingungen, Anforderungen und Methoden zur Vermeidung von Gefahren bei Kranen durch die Konstruktion und theoretische Überprüfung. Teil 3 befindet sich in der Vorentwurfsphase; die Verwendung der Teile 1 und 2 setzt nicht die Veröffentlichung von Teil 3 voraus.
ANMERKUNG Besondere Anforderungen für spezielle Krantypen sind in der zugehörigen Europäischen Norm für den speziellen Krantyp angegeben.
Im Folgenden ist eine Auflistung von wichtigen gefährlichen Situationen und gefährlichen Ereignissen gegeben, die Risiken für Personen während des normalen Gebrauchs (des Krans) und vorhersehbarem Missbrauch zur Folge haben könnten. Abschnitt 4 dieser Norm ist erforderlich, um mit folgenden Gefahren verbundene Risiken zu reduzieren oder zu eliminieren:
a)   Starrkörperinstabilität des Krans oder seiner Teile (Kippen, Abtreiben);
b)   Überschreitung der Festigkeitsgrenzwerte (Fließen, Bruch, Ermüdung);
c)   Elastische Instabilität des Krans oder seiner Teile (Knicken, Beulen);
d)   Überschreitung von Temperaturgrenzwerten des Werkstoffs oder der Komponenten;
e)   Überschreitung von Verformungsgrenzen.
Diese Europäische Norm gilt für Krane, die nach dem Datum der Genehmigung dieser Norm durch CEN hergestellt werden und dient als Referenzgrundlage für die Europäischen Normen für spezielle Krantypen.

Appareils de levage a charge suspendue - Conception générale - Partie 1: Principes généraux et prescriptions

La présente norme européenne spécifie les conditions, prescriptions et méthodes générales afin d'éviter les risques mécaniques dus aux grues, en utilisant la conception et la vérification. NOTE: Les prescriptions spécifiques relatives aux types particuliers de grues sont données dans la norme européenne appropriée au type particulier de grue.

Varnost dvigala (žerjava) – Konstrukcija, splošno – 1. del: Splošna načela in zahteve

General Information

Status
Withdrawn
Publication Date
28-Feb-2005
Withdrawal Date
14-Apr-2009
Current Stage
9900 - Withdrawal (Adopted Project)
Start Date
15-Apr-2009
Due Date
08-May-2009
Completion Date
15-Apr-2009

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SLOVENSKI STANDARD
SIST EN 13001-1:2005
01-marec-2005
9DUQRVWGYLJDOD åHUMDYD ±.RQVWUXNFLMDVSORãQR±GHO6SORãQDQDþHODLQ
]DKWHYH
Cranes - General design - Part 1: General principles and requirements
Krane - Konstruktion allgemein - Teil 1: Allgemeine Prinzipien und Anforderungen
Appareils de levage a charge suspendue - Conception générale - Partie 1: Principes
généraux et prescriptions
Ta slovenski standard je istoveten z: EN 13001-1:2004
ICS:
53.020.20 Dvigala Cranes
SIST EN 13001-1:2005 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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EUROPEAN STANDARD
EN 13001-1
NORME EUROPÉENNE
EUROPÄISCHE NORM
December 2004
ICS 53.020.20
English version
Crane safety - General design - Part 1: General principles and
requirements
Sécurité des appareils de levage à charge suspendue - Krane - Konstruktion allgemein - Teil 1: Allgemeine
Conception générale - Partie 1: Principes généraux et Prinzipien und Anforderungen
prescriptions
This European Standard was approved by CEN on 2 March 2004.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2004 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN 13001-1:2004: E
worldwide for CEN national Members.

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EN 13001-1:2004 (E)
Contents
Page
Foreword . 3
Introduction . 4
1 Scope. 4
2 Normative references. 4
3 Terms, definitions, symbols and abbreviations. 5
3.1 Terms and definitions . 5
3.2 Symbols and abbreviations . 5
4 Safety requirements and/or measures . 8
4.1 General . 8
4.2 Proof calculation. 8
4.2.1 General principles. 8
4.2.2 Models of cranes and loads .10
4.2.3 Simulation of load actions .10
4.2.4 Load combinations and load effects.11
4.2.5 Limit states .11
4.2.6 Proof of competence.11
4.2.7 Methods for the proof of competence.12
4.3 Classification .14
4.3.1 General .14
4.3.2 Total numbers of working cycles.15
4.3.3 Average linear or angular displacements.15
4.3.4 Frequencies of loads .17
4.3.5 Positioning of loads.18
4.4 Stress histories.19
4.4.1 General .19
4.4.2 Frequencies of stress cycles .20
4.4.3 Transformation of the identified stress cycles into cycles with constant mean
stress or constant stress ratio.21
4.4.4 Classification of stress histories.23
Annex A (informative) Selection of a suitable set of crane standards for a given
application .26
Annex ZA (informative) Relationship between this European Standard and the Essential
Requirements of EU Directive 98/37/EC.27
Bibliography .28
2

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EN 13001-1:2004 (E)
Foreword
This document (EN 13001-1:2004) 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 June 2005, and conflicting national
standards shall be withdrawn at the latest by June 2005.
According to the CEN/CENELEC Internal Regulations, the national standards organisations of the
following countries are bound to implement this European Standard: Austria, Belgium, Czech Cyprus,
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia,
Spain, Sweden, Switzerland and the United Kingdom.
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 EC Directive 98/37.
For relationship with EC Directive 98/37, see informative annex ZA, which is an integral part of this
document.
Annex A is informative.
This European Standard is one Part of EN 13001. The other parts are as follows:
Part 1: General Principles and requirements
Part 2: Load actions
Part 3.1: Limit states and proof of competence of steel structures
Part 3.2: Limit states and proof of competence of rope reeving components
Part 3.3: Limit states and proof of competence of wheel/rail contacts
Part 3.4: Limit states and proof of competence of machinery
3

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EN 13001-1:2004 (E)
Introduction
This European Standard has been prepared to be a harmonized standard to provide one means for
the mechanical design and theoretical verification of cranes to conform with the essential health and
safety requirements of the Machinery Directive, as amended. This standard also establishes
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 1070.
The machinery concerned and the extent to which hazards are covered are indicated in the scope of
this standard.
When provisions of this type C standard are different from those, which are stated in type A or B
standards, the provisions of this type C standard take precedence over the provisions of the other
standards, for machines that have been designed and built according to the provisions of this type C
standard.
1 Scope
This European Standard is to be used together with Part 2 and Part 3, and as such, they specify
general conditions, requirements and methods to prevent mechanical hazards of cranes by design
and theoretical verification. Part 3 is only at pre-drafting stage; the use of Parts 1 and 2 is not
conditional to the publication of Part 3.
NOTE Specific requirements for particular types of crane are given in the appropriate European
Standard for the particular crane type.
The following is a list of significant hazardous situations and hazardous events that could result in
risks to persons during normal use and foreseeable misuse. Clause 4 of this standard is necessary to
reduce or eliminate the risks associated with the following hazards:
a) rigid body instability of the crane or its parts (tilting, shifting);
b) exceeding the limits of strength (yield, ultimate, fatigue);
c) elastic instability of the crane or its parts (buckling, bulging);
d) exceeding temperature limits of material or components;
e) exceeding the deformation limits.
This European Standard is applicable to cranes which are manufactured after the date of approval by
CEN of this standard and serves as reference base for the European Standards for particular crane
types.
2 Normative references
This European Standard incorporates, by dated or undated reference, provisions from other
publications. These normative references are cited at the appropriate places in the text and the
publications are listed hereafter. For dated references, subsequent amendments to or revisions of any
4

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EN 13001-1:2004 (E)
of these publications apply to this European Standard only when incorporated in it by amendment or
revision. For undated references the latest edition of the publication referred to applies (including
amendments).
EN ISO 12100-1:2003, Safety of machinery — Basic concepts, general principles for design — Part 1:
Basic terminology, methodology (ISO 12100-1:2003).
EN ISO 12100-2:2003, Safety of machinery — Basic concepts, general principles for design — Part 2:
Technical principles and specifications(ISO 12100-2:2003).
EN 1070:1998, Safety of machinery — Terminology.
EN 1990-1:2002, Eurocode – Basic of structural design.
EN 13001-2, Cranes — General design — Part 2: Load actions.
ISO 4306-1:1990, Cranes — Vocabulary — Part 1: General.
3 Terms, definitions, symbols and abbreviations
3.1 Terms and definitions
For the purposes of this European Standard, the terms and definitions given in EN 1070:1998,
EN 1990-1 :2002 and clause 6 of ISO 4306-1 :1990 apply.
3.2 Symbols and abbreviations
For the purposes of this European Standard, the symbols and abbreviations given in Table 1 apply.
Table 1 — Symbols and abbreviations
Symbols,
Description
abbreviations
Allowable (admissible) stress
adms
C Total number of working cycles
C Number of working cycles where a load i is handled
i
C Number of working cycles of task r
r
D
Classes of average displacements X
D to D
lin0 lin9 Classes of average linear displacement X
lin
D to D
ang 0 ang5 Classes of average angular displacement X ang
f Characteristic loads
i
F
Combined loads from load combination j (limit state method)
j
Combined loads from load combination j (allowable stress method)
F j
k Stress spectrum factor
5

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EN 13001-1:2004 (E)
Table 1 (continued)
Symbols,
Description
abbreviations
kQ Load spectrum factor
kQ Load spectrum factor for task r
r
Limit in damage calculation
limD
lims Limit design stress
m Inverse slope of the log s /log N curve
a
ˆ Total number of stress cycles
n
n
Number of stress cycles of class ij
ij
(r)
n Number of stress cycles of class ij occurring each time task r is carried out
ij
n ,n
Service frequency of position i or j
ri rj
n ( R or s ) Number of stress cycles with stress amplitude s ( R or s )
m a m
Number of stress cycles with amplitude s ( R or s )
n ( R or s )
a,i m
i m
Number of stress cycles to failure by fatigue
N
N
Number of cycles at reference point
D
p
Average number of accelerations
Classes of average numbers of accelerations p
to
P , P P
0 3
Classes of load spectrum factors kQ
to
Q Q
0 5
Q
Maximum value of Q for all tasks r
r
Q Magnitude of load i
i
Maximum load for task r
Q
r
R Characteristic resistance of material, connection or component
d
Stress ratio
R
s
Stress history parameter
S , S , to S Classes of stress history parameters s
0 9
S Load effect in section k of a member (limit state method)
k
Load effect in section k of a member (allowable stress method)
S k
to Classes of total numbers of working cycles C
U ,U U
0 9
x , x
Displacement of the drive under consideration to serve position i or j
ri rj
6

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EN 13001-1:2004 (E)
Table 1 (concluded)
Symbols,
Description
abbreviations
Average displacement during task r
x r
Average displacement
X
Average linear or angular displacement
X lin , X ang
Angles between horizontal line and lines of constant N in the s - s plane
a ,a
a m
1 2
a Relative number of working cycles for task r
r
Overall safety factor
g
f
Resistance coefficient
g
m
g Risk coefficient
n
g
Partial safety factor
p
g Reduced partial safety factor
p
m, m , m Rises of lines of constant N in the s -s -plane
1 2 a m
Relative total number of stress cycles
n
Stress amplitude
s
a
s (R or s ) Stress amplitude for constant stress ratio R or constant mean stress s
a m m
Maximum stress amplitude for constant stress ratio R or constant mean stress
ˆ
s (R or s )
m
a
s
m
Stress amplitude of range i
s
a,i
s (R or s ) Stress amplitude of range i for constant stress ratio or constant mean stress
a,i m
Lower extreme value of stress cycle
s
b
s Design stress in element l (limit state method)
l
s Design stress in element l (allowable stress method)
l
s
Stresses in element l resulting from S (limit state method)
1l k
s
Stresses in element l resulting from S (allowable stress method)
1l
k
s Stresses in element l arising from local effects (limit state method)
2l
s Stresses in element l arising from local effects (allowable stress method)
2l
Mean stress
s
m
Mean stress of range j
s
m,j
s Upper extreme value of stress cycle
u
Dynamic factors
f
i
7

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EN 13001-1:2004 (E)
4 Safety requirements and/or measures
4.1 General
Machinery shall conform to the safety requirements and/or measures of this clause. Hazards not
covered in EN 13001 may be covered by other general requirements for all types of cranes and/or by
specific requirements for particular types of cranes, as given in the EN standards listed in annex A. In
addition, the machine shall be designed according to the principles of ISO EN 12100-1 and
ISO EN 12100-2 for hazards relevant but not significant which are not dealt with by the above
mentioned standards.
4.2 Proof calculation
4.2.1 General principles
The objective of this calculation is to prove theoretically that a crane, taking into account the service
conditions agreed between the user, designer and/or manufacturer, as well as the states during
erection, dismantling and transport, has been designed in conformance to the safety requirements to
prevent mechanical hazards.
The proof of competence according to EN 13001 shall be carried out by using the general principles
and methods appropriate for this purpose and corresponding with the recognised state of the art in
crane design.
Alternatively, advanced and recognised theoretical or experimental methods may be used in general,
provided that they conform to the principles of this standard.
Hazards can occur if extreme values of load effects or their histories exceed the corresponding limit
states. To prevent these hazards with a margin of safety, it shall be shown that the calculated extreme
values of load effects from all loads acting simultaneously on a crane and multiplied with an adequate
partial safety coefficient, as well as the estimated histories of load effects, do not exceed their
corresponding limit states at any critical point of the crane. For this purpose the limit state method,
and where applicable the allowable stress method, is used in accordance with international and
European design codes.
The analysis of load actions from individual events or representative use of a crane (representative
load histories) is required to reflect realistic unfavourable operational conditions and sequences of
actions of the crane.
Figure 1 illustrates the general layout of a proof calculation for cranes.
8

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EN 13001-1:2004 (E)
Key
a) Models of crane and loads
b) Load actions
c) Limit states
d) Proof
Figure 1 — Layout of the proof calculation
9

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EN 13001-1:2004 (E)
4.2.2 Models of cranes and loads
For the calculation of the movements, inner forces (torques in gears, rope forces, etc.) and losses of
the crane or its parts, rigid body kinetic models are used.
The loads acting on this model are the motor torques and/or brake torques, which have to balance
any of the loads acting on the moved parts as losses, mass forces caused by gravity, movement of
the crane or parts thereof, and wind forces.
From this rigid body kinetic model of the crane and the load models, any variation of displacement,
speed, acceleration and/or inner forces as well as the corresponding instantaneous values of
acceleration and/or inner forces can be derived.
These variations, if calculated in conformity with the agreed service conditions, are the base for
estimating the histories of load effects (e. g. heat equivalents) and the stress histories. Since the
variations and instantaneous values of accelerations and inner forces calculated by using a rigid body
kinetic model only represent mean values of the real process, loads caused by sudden alterations of
these mean values shall be amplified by dynamic factors f to estimate their real values
i
(see EN 13001-2).
For cranes or crane configurations where all the loads from different drives acting simultaneously do
not affect each other because they are acting at right angles to each other (i.e. orthogonal), load
actions from drives can be considered independently. In cases where the loads from simultaneous
actions of different drives affect each other (dependent, non-orthogonal), this shall be taken into
account.
The calculation of nominal stresses in any mechanical and/or structural component of a crane or its
parts can commonly be based on appropriate elasto-static models, built up by beam or more
sophisticated elements, such as plane stress, plate or shell elements.
A nominal stress is a stress calculated in accordance with simple elastic strength of materials theory,
excluding local stress concentration effects.
4.2.3 Simulation of load actions
For the simulation of the time varying process of load actions on a crane or its parts, static equivalent
loads from independent events occuring during the intended use of a crane shall be applied to elasto-
static models, which correspond with the configuration and supporting conditions of the crane or its
parts under consideration.
NOTE In this context the term “load” or "load action" means any action or circumstance, which causes load
effects in the crane or its parts, for example: forces, intended and non intended displacements and/or
movements, temperature, wind pressure.
Static equivalent loads are given in EN 13001-2. These static equivalent loads are considered as
deterministic actions, which have been adjusted in such a way that they represent load actions during
the use of the crane from the actions or circumstances under consideration.
The limit state method (see 4.2.7.1) does take into account the probabilistic nature of the loads,
whereas the allowable stress method (see 4.2.7.2) does not.
If a different level of safety is required in some instance, a risk factor g may be agreed upon and
n
applied.
10

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EN 13001-1:2004 (E)
4.2.4 Load combinations and load effects
The loads shall be superimposed in such a way that the resulting load effects attain their
instantaneous extreme values for the considered situation of use. Such superimpositions are called
load combinations. Basic load combinations are given in EN 13001-2.
When establishing the load combinations, consideration shall be given to the use of the crane, taking
into account its control systems, its normative instructions for use, and any other inherent conditions,
where they relate to the specific aim of the proof of competence.
Magnitude, position and direction of all loads which act simultaneously in the sense of a load
combination, shall be chosen in such a way that extreme load effects occur in the component or
design detail under consideration. Consequently, in order to establish the extreme stresses in all the
design critical points, several loading events or crane configurations shall be studied within the same
load combination, e. g. different positions of a crab in a bridge or gantry crane.
The upper and lower extreme values of the load effects , in terms of inner forces or nominal stresses,
shall be used for a static proof calculation to avoid the hazards described in the scope. In combination
with the agreed service conditions and the kinematic properties of the crane or its parts, these values
limit the histories of inner forces or nominal stresses for the proof of fatigue strength.
For the proof of fatigue strength, the number and magnitude of significant stress cycles shall be
specified.
4.2.5 Limit states
For the purposes of this standard limit states are states of the crane, its components or materials
which, if exceeded, can result in the loss of the operational characteristics of the crane. There is a
distinction between ultimate limit states and serviceability limit states as follows:
a) Ultimate limit states, given by:
1) plastic deformations from the effect of nominal stresses or sliding of frictional connections;
2) failure of components or connections (e. g. static failure, failure by fatigue or formation of
critical cracks);
3) elastic instability of the crane or its parts (e. g. buckling, bulging);
4) rigid body instability of the crane or its parts (e. g. tilting, shifting).
b) Serviceability limit states, examples of which are:
1) deformations which impair the intended utilization of the crane (e. g. function of moving
components, clearances of parts);
2) vibrations that cause damage to the crane driver or cause damage to the crane structure or
restrict the ability to operate;
3) exceeding temperature limits (e. g. overheating of motors and brakes).
4.2.6 Proof of competence
The limit states applicable to the combination of material selection, manufacturing techniques and the
specified service conditions shall be stated in the proof of competence.
For the verification that the ultimate limit states are not exceeded, the following proofs shall be
established:
11

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EN 13001-1:2004 (E)
a) proof of strength of members, connections and components:
1) under static and quasi-static loading;
2) under cyclic loading (fatigue);
b) proof of elastic stability of the crane and its parts;
c) proof of rigid body stability.
For the verification that the serviceability limit states are not exceeded, the following aspects shall be
considered, and a proof be established where appropriate:
a) proof of deformation;
b) vibration;
c) thermal performance.
4.2.7 Methods for the proof of competence
4.2.7.1 Limit state method
For a general description of the limit state method, see ISO 2394:1998, General principles on
reliability for structures. For all crane systems, the limit state method is applicable without any
restriction.
Individual characteristic loads f shall be calculated and amplified where necessary using the factors
i
f, multiplied by the appropriate partial safety factors g or reduced partial safety factors ? and
i p
p
combined into F according to the load combination under consideration. When agreed upon F shall
j j
also be multiplied by an appropriate risk coefficient g The result g ⋅F shall be used to determine the
n. n j
resulting load effects S , i.e. the inner forces in structural or mechanical components or the forces in
k
articulations and supports.
For proof that yielding and elastic instability will not occur, the nominal design stresses s due to the
1l
action of the loads on a particular component are calculated and combined with any stresses s
2l
resulting from local effects, calculated using the appropriate partial safety factors g and where agreed
p
upon the risk coefficient g .
n
The resulting design stress s shall be compared with the limit design stress lim s. It is derived from
l
the specific strength or characteristic resistance R of material, connection or component with at least
d
95 % probability of survival, divided by the resistance coefficient g = 1,10.
m
For the proof of rigid body stability it shall be shown that under the combined action of the loads
multiplied by their partial safety factors no rigid body movement occurs. All supports, where given
limits are exceeded, i.e. wheel/rail under tension or rope under compression, shall be neglected. This
means that in the sense of the elasto-static model, the corresponding restraints shall be set “inactive”.
The remaining positive and/or frictional support forces shall be sufficient to ensure the rigid body
stability.
A flow chart illustrating the limit state method for the proof calculation based on stresses is shown in
Figure 2. For the proof based on forces, moments, deflections the limit state method shall be applied
by analogy.
12

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EN 13001-1:2004 (E)
Key
f characteristic load i on the element component;
i
F combined load from load combination j including f- factors;
j
S load effects in section k of members or supporting parts, such as inner forces and moments, resulting from
k
load combination F ;
j
s stresses in the particular elementl as a result of load effects S ;
1l k
s stresses in the particular elementl arising from local effects;
2l
s resulting design stress in the particular element l;
l
R specified strength or characteristic resistance of the material, particular element or connection, such as the
d
stress corresponding to the yield point, limit of elastic stability or fatigue strength (limit states);
lim slimit design stress;
g partial safety factors applied to individual loads according to the load combination under consideration;
p
g risk coefficient, where applicable;
n
g resistance coefficient.
m
Figure 2 — Typical flow chart of the limit state method
4.2.7.2 Allowable stress method
For cranes of mass distribution class MDC1 (see EN 13001-2) with a linear relationship between load
actions and load effects, the allowable stress method is applicable for the proof of competence
calculation. The allowable stress method can also be used for portions of MDC2 systems that act in
the same manner as a linear MDC1 system. The allowable stress method is a special case of the limit
state method, where the partial safety factors are given the same value, which combined with the
resistance coefficient, forms an overall safety factor g . Because of its special character, the allowable
f
stress method is only reliable in specific cases.
Individual specified loads f shall be calculated and amplified where necessary using the factors f and
i i
shall be combined according to the load combinations under consideration. The combined load F
j
shall be used to determine the resulting load effects S , i. e. the inner forces in structural and
k
mechanical components or the forces in articulations and supports.
For proof that yielding and elastic instability do not occur, the nominal stress s due to the action of
1l
the load effects on a particular element or component shall be calculated and combined with any
stresses s resulting from local effects. The result
...

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