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Zeszyty Naukowe 26(98) 99

Scientific Journals

Zeszyty Naukowe

Maritime University of Szczecin

Akademia Morska w Szczecinie

2011, 26(98) pp. 99–102 2011, 26(98) s. 99–102

Assessing the service life of operated steel load-carrying

structures of cranes on the basis of Eurocode 3

Ocena resursu eksploatowanych stalowych konstrukcji

nośnych dźwignic na podstawie Eurokodu 3

Włodzimierz Rosochacki

West Pomeranian University of Technology, Faculty of Maritime Technology

Zachodniopomorski Uniwersytet Technologiczny w Szczecinie, Wydział Techniki Morskiej 71-065 Szczecin, Al. Piastów 41, e-mail: wlodzimierz.rosochacki@zut.edu.pl

Key words: cranes, fatigue carrying capacity, Eurocode 3 Abstract

The article presents methodology of assessing the service life of steel load-carrying structures of cranes, tak-ing account of the approach presented in Eurocode 3. In the considered case, such assessment covers already operated structures. From criterion of assessment of fatigue carrying capacity, a condition has been derived, specifying the limit number of reloading cycles corresponding to exhaustion of the design operation period. Słowa kluczowe: dźwignice, nośność zmęczeniowa, Eurokod 3

Abstrakt

W artykule określono metodykę oceny resursu stalowych konstrukcji nośnych dźwignic z uwzględnieniem podejścia prezentowanego w Eurokodzie 3. Rozważono przypadek, w którym ocena taka obejmuje konstruk-cje już eksploatowane. Z kryterium oceny nośności zmęczeniowej wyprowadzono warunek określający gra-niczną liczbę cykli przeładunkowych, odpowiadającą wyczerpaniu projektowego okresu eksploatacji.

Introduction

Safety of cranes, their environment and, first of all, of persons operating them depends to a great extent on reliability of load-carrying structures. A typical requirement formulated in relation to elements of such structures is capability of correct performance of tasks without damages. Such ap-proach is presented, among other things, in papers [1, 2, 3, 4, 5] or in the already classic paper [6].

Issues of non-defectiveness of elements of crane structure normally cover two basic problems: determining resistance of such elements to actions of loads with extremely great values and actions of variable stresses. In case of the first of the mentioned issues, the determination normally covers the probability of occurrence of a preset number of cycles of changes in stresses without occurrence of damages being effect of stress of the

shear strength level [2, 3, 7]. In the second case, the forecast covers the probability of occurrence of a preset number of cycles of changes in stresses without occurrence of damages caused by the process of fatigue of material (the so-called cycle strength condition [1]) or the probability that such stress level which is identified with occurrence of fatigue damage will not occur during operation (the so-called stress strength condition). At this point, it is worth emphasizing, in accordance with [1], that 80–90% of cracks occurring during operation are of fatigue character.

Issues related to fatigue strength of steel structures have been widely presented, among others, in papers [8, 9, 10, 11, 12, 13, 14, 15, 16]. However, a physical theory able to describe quantitatively fatigue effects or a phenomenological theory including all mechanisms [17] could not be created.

Włodzimierz Rosochacki

100 Scientific Journals 26(98)

This paper raises the issues of assessment of fulfilling cycle strength condition for load-carrying crane structures taking account of the approach presented in Eurocode 3 [18]. In particular, consi-derations cover the case covering structures already partially undergoing the process of operation. The assessment is conducted taking account of calcu-lation spectrum and number of reloading cycles achieved until the time preceding such assessment.

Strength condition according to Eurocode 3

Standard [18] specifies methods of assessing and checking fatigue carrying capacity of elements, connections and nodes exposed to fatigue loads. The basis for introduction of these methods are results of fatigue tests of samples on a large scale which take account of impact of geometric and structural imperfections related to manufacturing of materials and workmanship (e.g. impact of welding tolerances and stresses has been considered). Methods of assessment specified in [18] are applied with a few exceptions, for all grades of construc-tion, stainless and hardly rusting steel. Fatigue strength, concerning scopes of stress variability, is determined by sets of S-N curves which correspond to fatigue categories. Each of these categories is expressed by normative fatigue strength, i.e. scope of stresses variability of fixed amplitude c

obtained for a given element (notch) and durability

Nc = 2106 of cycles. Approach to assessment of

fatigue carrying capacity, presented in the standard, is one of typical methods of dimensioning in high cycle perspective. Such methods are still successfully applied in contemporary design of load-carrying structures of cranes [1].

Checking carrying capacity

Assessing fatigue carrying capacity of elements (connections, nodes) of load-carrying structure of the crane according to [18], can be performed based on the determination of value of the so-called total damage D for the design operation period. This period, according to wording of [18], means the time in which the structure should operate safely – with acceptable probability of no destruction as a result of fatigue cracks. At this point, it should be emphasized that, as defined by the concerned standard, fatigue cracks appearing in the process of operation do not have to mean the end of operation of the structure.

Figure D commonly assumed as measure of fatigue damage. Fatigue carrying capacity is preserved when the condition is met:

1 

D (1)

Value of total damages (for nominal normal stresses  or shear stresses)  is determined in accordance with [18] from dependence:



 n i Ri Ei N n D (2) where:

nEi – number of cycles related to the scope of

stress variability Ff i (for shear stresses:

Ff i in band number i of calculation

spectrum);

Ff – partial coefficient for equivalent scopes of

stress variability; during operation [19] the following is defined Ff = 1;

NRi – durability (number of cycles) obtained on

the basis of calculation curve c / Mf – NR

or the scope of variability Ff i (or

relevant curve for shear stresses);

i, i – the scope of variability of nominal

stresses in band number i of spectrum; c, c – normative fatigue strength for Nc = 2106

cycles;

Nc = 2106 – number of cycles for which normative

fatigue strength is determined c (or c

in the case of determining value of damage for nominal shear stresses);

Mf – partial coefficient for fatigue strength c

(or c).

Characteristics of calculation spectrum used for calculations according to dependence (2) should be adequate to characteristics of load of the considered element (connection, node). Value of coefficient Mf

has been defined in [18], depending on consequences of a possible destruction and the method adopted when designing load-carrying structure of the crane (Tab. 1).

Table 1. Recommended values for partial factors for fatigue strength Mf [18]

Tabela 1. Zalecane wartości współczynnika częściowego dla wytrzymałości zmęczeniowej Mf [18]

Assessment method Consequence of failure Low consequence High consequence

Damage tolerant 1.00 1.15

Safe life 1.15 1.35

The issue of determining value of total damaging, based on example of nominal normal stresses, has been considered below. Assuming

i = 1 we obtain:



Ff



R m Mf c c N σγ γ σ N _  ₁  ₁        (3)

Assessing the service life of operated steel load-carrying structures of cranes on the basis of Eurocode 3 Zeszyty Naukowe 26(98) 101 and therefore:





m c Mf m Ff c σ γ γ σ N n D _         1 ₁ 1 (4) where:

n1 – number of cycles of stresses in band

number i of spectrum.

m – inclinatin of fatigue strength curve.

Value of damage D for the case when calcu-lation spectrum of stresses consists of i bands may be defined on the basis of (1) and (4):









                            m Ff n m c Mf c n m Ff m c Mf c γ σ σ γ N n ... γ σ σ γ N n D 1 ₁ (5)

Dependence (5) can be presented also in the following form:





m m Ff n m c Mf c n m Ff m c Mf c σ σ γ σ σ γ N n ... σ γ σ σ γ N n D max max max 1 1                                            (6) where:

max – maximum scope of nominal and normal stress variability in the designed operation period, specified for the considered structural node of the crane, according to elasticity theory without considering effects of swelling (for shear stresses respectively max).

Describing characteristics of calculation spectrum of scopes of stresses using coefficients:

i = ni / N, where: N 



n_i0ni andi = i / max

we obtain:

 

 









m m n n m m c Ff Mf c σ β α ... β α σ γ N N D max 1 1               (7)

Estimating the service life

Formula (7) creates – in case of partially worn out cranes – an interesting possibility to estimate the service life of their load-carrying structures by defining the number of reloading cycles Np the

crane may perform until exhaustion of the design operation period. An important point is identifi-cation of an element (connection, node) whose destruction excludes the crane from operation. The following considerations relate to such hypothetical place in the load-carrying structure.

Assuming that values of coefficients i and i

found in formula (7) are known and are determined sizes, and treating the number of reloading cycles N which may be performed by a selected element (connection, node) of the structure from the beginning of operation until the moment of exhaustion of the design operation period as identical with the number of changes in scopes of stresses, the condition (1) can be presented in the following form:

 

 



_{1 1}  





 _max



1        m m n n m m c Ff Mf c σ β α ... β α σ γ N N  (8) and further:

 

 

 







_m



m n n m m c c Ff Mf m β α ... β α N σ γ N σ               1 1 max 1  (9) Substituting:

 





 

 

_m





m n n m m c c Ff Mf _{N α β ... α β} σ γ A       _{1 1} we obtain: A N σ m         _max 1 (10)

The above dependence allows determining the limit number of cycles (assuming stresses in accordance with previous character of spectrum of loads), after reaching of which the designed operation period should be exhausted:

m gr _σ A N          max (11) From the above condition, knowing number of changes in stresses Nd performed by the crane until

the moment of assessment, the value can be determined Np:

d gr

p N N

N   (12)

i.e. the remaining number of cycles until exhaustion of the design operation period.

Włodzimierz Rosochacki

102 Scientific Journals 26(98)

Conclusions

In the presented approach to estimating the number of reloading cycles which may be performed by the crane from the moment of conducting such assessment until the moment of exhaustion of the design operation period, the condition of maintenance of fatigue carrying capacity specified in Eurocode 3 has been used.

Making of such forecast requires, among others, identification of spectrum of loads and determi-nation of the number of reloading cycles performed until the moment of assessment. This paper regards both characteristics as determined. This is, how-ever, a simplification, whose assumption in the calculation case being examined requires justifi-cation. It should be also emphasized that spectrum of loads accepted for calculations should be adequate to the analyzed structural node.

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Recenzent: dr hab. inż. Zbigniew Matuszak, prof. AM Akademia Morska w Szczecinie