- -- ---- -

I,

ANALYTICAL STRENGTH

ASSESSMENT

5t h Edition

VDMA Verlag

I IForschungskuratorium II

Maschinenbau

FKM-Guideline

ANALYTICAL STRENGTH ASSESSMENT

OF COMPONENTS

IN MECHANICAL ENGINEERING

5th, revised edition, 2003, English Version

Translation by E. Haibach

Title of the original German Version:

RECHNERISCHER FESTIGKEITSNACHWEIS

FUR MASCHINENBAUTEILE

5., iiberarbeitete Ausgabe, 2003

Editor:

Forschungskuratorium Maschinenbau (FKM)Postfach 71 0864, D - 60498 Frankfurt / Main

Phone *49 - 69 - 6603 - 1345

(c) 2003

byVDMA Verlag GmbH

Lyoner StraBe 18

60528 Frankfurt am Main

www.vdma-verlag.de

All rights reserved

AIle Rechte, insbesondere das Recht

der Vervielfaltigung und Verbreitung

sowie der Ubersetzung vorbehalten.

Kein Teil des Werkes darfin irgend­

einer Form (Druck, Fotokopie,

Mikrofilm oder anderes Verfahren) ohne

schriftliche Genehmigung des Verlages

reproduziert oder unter Verwendung

elektronischer Systeme gespeichert,

verarbeitet, vervielfaltigt oder

verbreitet werden.

ISBN 3-8163-0425-7

3

This FKM-Guideline was elaborated under contract between

Forschungskuratorium Maschinenbau e.V. (FKM), Frankfurt / Main, and

IMA Materialforschung und Anwendungstechnik Gmhfl, Dresden,

as contractor in charge,

by

Dr.-Ing. Bernd Hanel,

IMA Materialforschung und Anwendungstechnik GmbH, Dresden,

Prof. Dr.-Ing. Erwin Haibach,

Wiesbaden,

Prof. Dr.-Ing. TimID Seeger,

Technische Hochschule Darmstadt, Fachgebiet Werkstoffmechanik,

Dipl.-Ing. Gert Wlrthgen,

IMA Materialforschung und Anwendungstechnik GmbH, Dresden,

Prof. Dr.-Ing. Harald Zenner,

Technische Universitat Clausthal, Institut fur

Maschinelle Anlagentechnik und Betriebsfestigkeit,

and it was discussed among experts from industry and research institutes

in the FKM expert group "Strength of components" .

Financial grants were obtained from the "Bundesministerium fUr Wirtschaft (BMWi, Bonn)" through

the "Arbeitsgemeinschaft industrieller Forschungsvereinigungen 'Otto von Guericke ' e.V. (AiF,

K6ln)" under contract AiF-No. D-156 and B-9434. The "Forschungskuratorium Maschinenbau e.V."

gratefully acknowledges the financial support from BMWi and AiF and the contributions by the experts

involved.

Terms of liability

The FKM-Guideline is intended to conform with the state of the art. It has been

prepared with the necessary care. The user is expected to decide, whether the

guideline meets his particular requirements, and to observe appropriate care in

its application. Neither the publisher nor the editor, the involved experts, or the

translator shall be liable to the purchaser or any other person or entity with

respect to any liability, loss, or damage caused or alleged to have been caused

directly or indirectly by this guideline.

Preface to the English Version of

the 5th

Edition.

For engineers concerned with construction and

calculation in mechanical engineering or in related fields

of industry the FKM-Guideline for analytical strength

assessment is available since 1994. This guideline was

elaborated by an expert group "Strength of components"

of the "Forschungskuratorium Maschinenbau (FKM),

Frankfurt/Main," with financial support by the

Bundesministerium fur Wirtschaft (BMWi), by the

"Arbeitsgemeinschaft industrieller Forschungsvereini­

gungen 'Otto von Guericke" and by the "Forschungs­

kuratorium Maschinenbau.

Based on former TGL standards and on the former

guideline VDI 2226, and referring to more recent

sources it was developed to the current state of

knowledge.

The FKM-Guideline

- is applicable in mechanical engineering and in related

fields of industry,

- allows the analytical strength assessment for rod­

shaped (lD), for shell-shaped (2D) and for block-shaped

(3D) components under consideration of all relevant

influences,

- describes the assessment of the static strength and of

the fatigue strength, the latter according to an assessment

of the fatigue limit, of the constant amplitude fatigue

strength, or of the variable amplitude fatigue strength

according to the service stress conditions,

- is valid for components from steel, cast steel, or cast

iron materials at temperatures from -40°C to 500 °C, as

well as for components from aluminum alloys and cast

aluminum alloys at temperatures from -40°C to 200 °C,

- is applicable for components produced with or without

machining, or by welding,

- allows an assessment in considering nominal stresses as

well as local elastic stresses derived from finite element

or boundary element analyses, from theoretical

mechanics solutions, or from measurements.

A uniformly structured calculation procedure applies to

all of these cases of application. The calculation

procedure is almost completely predetermined. The user

has to make some decisions only.

The FKM-Guideline is a commented algorithm,

consisting of statements, formulae, and tables. Most of

the included figures have an explanatory function only.

4

Textual declarations are given where appropriate to

ensure a reliable application.

Its content complies with the state of knowledge to an

extend that may be presented in a guideline and it

enables quite comprehensive possibilities of calculation.

The employed symbols are adapted to the extended

requirements of notation. The presented calculation

procedure is complemented by explanatory examples.

Practically the described procedure of strength

assessment should be realized by means of a suitable

computer program. Presently available are the PC

computer programs "RIFESTPLUS" (applicable for a

calculation using elastically determined local stresses, in

particular with shell-shaped (2D) or block-shaped (3D)

components) and "WELLE" (applicable for a calculation

using nominal stresses as it is appropriate in the

frequently arising case of axles or shafts with gears etc).

The preceding editions of the FKM-Guideline observed

a remarkably great interest from which the need of an up

to date guideline for analytical strength analyses

becomes apparent. Moreover the interest of users was

confirmed by the well attended VDI conferences on

"Computational Strength Analysis of Metallic

Components", that were organized for presentation of

the FKM-Guideline at Fulda in 1995, 1998 and 2002.

The contents-related changes introduced with the third

edition from 1998 were mainly concerned with the

consideration of stainless steel and of forging steel, with

the technological size factor, with the section factor for

assessing the static strength, with the fatigue limit of

grey cast iron and of malleable cast iron, with additional

fatigue classes of welded structural details and with the

local stress analysis for welded components, with the

specification of an estimated damage sum smaller than

one for the assessment of the variable amplitude fatigue

strength, with the assessment of multiaxial stresses, and

with the experimental determination of component

strength values.

An essential formal change in the third edition was a

new textual structure providing four main chapters, that

describe the assessment of the static strength or of the

fatigue strength with either nominal stresses or local

stresses, respectively. For ease of application each of

these chapters gives a complete description of the

particular calculation procedure, although this results in

repetitions of the same or almost the same parts of text in

the corresponding sections.

The major change in the forth edition from 2002 is the

possibility of considering structural components made

from aluminum alloys or cast aluminum alloys by

applying the same calculation procedure that was

developed for components from steel, cast steel and cast

iron materials so far.

The decisions necessary to include aluminum materials

were derived from literature evaluations. It had to be

recognized, however, that some of the relevant factors of

influence were not yet examined with the desirable

clearness or that available results could not be evaluated

objectively due to large scatter. In these cases the

decision was based on a careful consideration of

substantial relations.

Concerning an analytical strength assessment ofcomponents from aluminum alloys or from castaluminum alloys this guideline is delivered to thetechnical community by supposing that for the timebeing it will be applied with appropriate caution andwith particular reference to existing experience so

far.

The involved research institutes and the "Forschungs­kuratorium Maschinenbau (FKM)" will appreciate any

reports on practical experience as well as any proposalsfor improvement.

Further improvements may also be expected from

ongoing research projects concerning the procedure ofstatic strength assessment using local elastic stresses,

Chapter 3, and the fatigue assessment of extremely sharp

notches.

Last not least the fifth edition of the FKM-Guideline is a

revision of the forth edition with several necessary,

mainly formal amendments being introduced. It is

presented in both a German version and an English

version with the expectation that it might observe similar

attention as the preceding editions on a broadened

international basis of application.

5

Notes of the translator

This English translation is intended to keep as close as

possible to the original German version, but by using a

common vocabulary and simple sentences. If the given

translation is different from a literal one, the technical

meaning of the sentence and/or of the paragraph ismaintained, however.

The translation observes an almost identical structure ofthe headlines, of the chapters, of the paragraphs and of

the sentences, and even of the numbering of the pages.

Also the tables and the figures as well as their numberingand headlines are adapted as they are, while only the

verbal terms have been translated.

In particular the original German notation of themathematical symbols, indices and formulas, as wellas their numbering, has not been modified in order toinsure identity with the German original in thisrespect.

The applier of this guideline is kindly asked to acceptthe more or less unusual kind of notation which isdue to the need of clearly distinguishing between agreat number of variables.

In particular the applier is pointed to the speciality,that a comma ( , ) is used with numerical valuesinstead of a decimal point ( . ), hence 1,5 equals 1.5for example. .

For updates and amendments see

www.fkm-guideline.de

6

References

/1/ TGL 19 340 (1983). Ermiidungsfestigkeit, Dauerfestigkeit der Maschinenbauteile.

/2/ TGL 19 341 (1988). Festigkeitsnachweis fiir Bauteile aus Eisengusswerkstoffen.

/3/ TGL 19 333 (1979). Schwingfestigkeit, Zeitfestigkeit von Achsen und Wellen.

/4/ TGL 19 350 (1986). Ermiidungsfestigkeit, Betriebsfestigkeit der Maschinenbauteile.

/5/ TGL 19 352 (Entwurf 1988). Aufstellung und Uberlagerung von Beanspruchungskollektiven.

/6/ Richtlinie VDI 2226 (1965). Empfehlung fiir die Festigkeitsberechnung metallischer Bauteile.

/7/ DIN 18 800 Teil 1 (1990). Stahlbauten, Bemessung und Konstruktion.

/8/ DIN ENV 1993 (1993). Bemessung und Konstruktion von Stahlbauten, Teil1-1:

Allgemeine Bemessungsregeln, ... (Eurocode 3).

/9/ Hobbacher, A.: Fatigue design of welded joints and components. Recommendations of the Joint Working

Group XIII-XV, XIII-1539-96 / XV-845-96. Abbington Publishing, Abbington Hall, Abbington,

Cambridge CB1 6AH, England, 19996

/10/ Haibach, E.: Betriebsfestigkeits - Verfahren und Daten zur Bauteilberechnung, 2.Aufl.

Berlin und Heidelberg, Springer-Verlag, 2002, ISBN 3-540-43142-X.

/11/ Radaj, D.: Ermiidungsfestigkeit. Grundlage fur Leichtbau, Maschinenbau und Stahlbau.

Berlin und Heidelberg: Springer-Verlag, 2003, ISBN 3-540-44063-1.

/12/ FKM-Forschungsheft 241 (1999). Rechnerischer Festigkeitsnachweis fiir Bauteile aus Alumininiumwerkstoff.

/13/ FKM-Forschungsheft 230 (1998). Randschichthartung.

/14/ FKM-Forschungsheft 227 (1997). Lebensdauervorhersage II.

/15/ FKM-Forschungsheft 221-2 (1997). Mehrachsige und zusammengesetzte Beanspruchungen.

/16/ FKM-Forschungsheft 221 (1996). Wechselfestigkeit von Flachproben aus Grauguss.

/17/ FKM-Forschungsheft 183-2 (1994). Rechnerischer Festigkeitsnachweis fur Maschinenbauteile, Richtlinie. *1

/18/ FKM-Forschungsheft 183-1 (1994). Rechnerischer Festigkeitsnachweis fiir Maschinenbauteile, Kommentare.

/19/ FKM-Forschungsheft 180 (1994). Schweillverbindungen II.

/20/ FKM-Forschungsheft 143 (1989). Schweillverbindungen I.

/21/ FKM-Richtlinie Rechnerischer Festigkeitsnachweis fiir Maschinenbauteile,

3., vollstandig iiberarbeitete und erweiterte Ausgabe (1998).

/22/ FKM-Richtlinie Rechnerischer Festigkeitsnachweis fur Maschinenbauteile,

4., erweiterte Ausgabe (2002).

Related Conference Proceedings

Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Konstrukteure und Entwicklungsingenieure.

VDI Berichte 1227, Diisseldorf, VDI-Verlag, 1995.

Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Entwicklungsingenieure und Konstrukteure.

VDI Berichte 1442, Diisseldorf, VDI-Verlag, 1998.

Festigkeitsberechnung metallischer Bauteile, Empfehlungen fur Entwicklungsingenieure und Konstrukteure.

VDI Berichte 1698, Dusseldorf, VDI-Verlag, 2002.

Bauteillebensdauer Nachweiskonzepte. DVM-Bericht 800, Deutscher Verband fur Materialsforschung und

-prufung, Berlin 1997.

Betriebsfestigkeit - Neue Entwicklungen bei der Lebensdauerberechnung von Bauteilen. DVM-Bericht 802,

Deutscher Verband fur Materialsforschung und -prufung, Berlin 2003.

1 1'"and 2nd

Edition ofthe FKM-Guideline

7

Contents

Page 5 Appendices Page

0 General survey 5.1 Material tables. 131

0.1 Scope 9 5.2 Stress concentration factors 178

0.2 Technical background 5.3 Fatigue notch factors 187

0.3 Structure and elements 5.4 Fatigue classes (FAT) for welded

components of structural steel and of1 Assessment of the static strength aluminum alloys 195

using nominal stresses 5.5 Comments about the fatigue strength

1.0 General 19 of welded components 209

1.1 Characteristic stress values 5.6 Adjusting the stress ratio of a stress

1.2 Material properties 22 spectrum to agree with that of the S-N curve

1.3 Design parameters 30 and deriving a stepped spectrum 216

1.4 Component strength 33 5.7 Assessment using classes of utilization 218

1.5 Safety factors 34 5.8 Particular strength characteristics of

1.6 Assessment 36 surface hardened components 222

5.9 An improved method for computing the2 Assessment of the fatigue strength component fatigue limit in the case of

using nominal stresses synchronous multiaxial stresses 223

2.0 General 41 5.10 Approximate assessment of the fatigue

2.1 Parameters of the stress spectrum strength in the case of non-proportional

2.2 Material properties 47 multiaxial stresses 226

2.3 Design Parameters 50 5.11 Experimental determination of

2.4 Component strength 57 component strength values 227

2.5 Safety factors 68 5.12 Stress concentration factor for a substitute

2.6 Assessment 70 structure 230

3 Assessment of the static strength 6 Examplesusing local stresses

6.1 Shaft with shoulder 2313.0 General 73 6.2 Shaft with V-belt drive 2363.1 Characteristic stress values 6.3 Compressor flange made of grey3.2 Material properties 76 cast iron 2413.3 Design parameters 85 6.4 Welded notched component 2453.4 Component strength 89 6.5 Cantilever subject to two independent loads 2503.5 Safety factors 90 6.6 Component made of a wrought3.6 Assessment 93 aluminum alloy 256

4 Assessment of the fatigue strength 7 Symbols and basic formulasusing local stresses

7.1 Abbreviations 2594.0 General 97 7.2 Indices4.1 Parameters of the stress spectrum 7.3 Lower case characters4.2 Material properties 103 7.4 Upper case characters 2604.3 Design parameters 106 7.5 Greek alphabetic characters 2614.4 Component strength 113 7.6 Basic formulas 2624.5 Safety factors 1254.6 Assessment 127 8 Subject index 263

8