1、National SteelBridge AllianceA Fatigue PrimerforStructural EngineersbyJohn W. FisherGeoffrey L. KulakIan F. C. SmithA Note of CautionAll data, specifications, suggested practices, anddrawings presented herein, are based on the bestavailable information and delineated in accordancewith recognized pro
2、fessional engineering principlesand practices, and are published for general informa-tion only. Procedures and products, suggested or dis-cussed, should not be used without first securing com-petent advice respecting their suitability for any givenapplication.Publication of the material herein is no
3、t to be con-strued as a warranty on the part of the National SteelBridge Alliance or that of any person named herein that these data and suggested practices are suitablefor any general or particular use, or of freedom frominfringement on any patent or patents. Further, anyuse of these data or sugges
4、ted practices can only bemade with the understanding that the National SteelBridge Alliance makes no warranty of any kindrespecting such use and the user assumes all liabilityarising therefrom.Copyright 1998, National Steel Bridge Alliance May 1998A FATIGUE PRIMER for STRUCTURAL ENGINEERS by John W.
5、 Fisher Lehigh University Bethlehem, Pennsylvania, USA Geoffrey L. Kulak University of Alberta Edmonton, Alberta, Canada Ian F.C. Smith Swiss Federal Institute of Technology Lausanne, Switzerland ii ACKNOWLEDGMENTS AND DISCLAIMER Several US state highway departments and highway design firms or consu
6、ltants supplied information on various bridge structures reported in this document. These include transportation departments in the States of Connecticut, Maryland, Massachusetts, Minnesota, Ohio, Pennsylvania, South Dakota, Virginia, and West Virginia and the firms DeLeuw Cather and Company, Fay, S
7、pofford and Thorndike Inc., Greiner Engineering Sciences, Kozel Engineering Company, Modjeski and Masters Inc., and Wiss Janney Elstner Associates Inc. Their contributions are noted with thanks. The document was proofread with great care by Jeffrey DiBattista, Graduate Student at the University of A
8、lberta and helpful comments were provided on the technical content by Prof. Gilbert Grondin, also of the University of Alberta. Jeffrey DiBattista did many of the calculations associated with the example presented in Chapter 5. The contributions of Manfred Hirt, Professor of Steel Construction and D
9、irector of ICOM, Swiss Federal Institute of Technology, Lausanne, are gratefully recognized. Professor Hirt is the co-author of a principal source document (Reference 1). Figure 4 is taken from Hirt, M.A. “Anwendung der Bruchmechanik fr die Ermittlung des Ermedungsverhaltens geschweisster Konstrukti
10、onen,“ Bauingenieur, 57 (1982), and is used with his permission. The authors also thank Dr. Peter Kunz, formerly at ICOM, for his help with the preparation of Example 7. The authors have taken care to ensure that the material presented is accurate. However, it must be understood that persons using t
11、he material assume all liability arising from such use. Notification of errors and omissions and suggestions for improvements are welcome. No part of this publication may be reproduced or distributed in any form or by any means without the prior written permission of the authors. iii TABLE OF CONTEN
12、TS 1 Introduction 1 2 Basic Fracture Mechanics Concepts 2.1 How to Account for a Crack 2 2.2 Fracture Limit State .6 2.3 Fatigue Limit State 8 2.4 Fracture Mechanics Used as a Qualitative Design Tool .11 3 Fatigue Strength Analysis 3.1 Introduction and Historical Background .16 3.2 Sources of Flaws
13、in Fabricated Steel Structures .18 3.3 Basis for Design Rules .22 3.4 Design Rules Given by the AASHTO Specification.25 3.5 Fracture Mechanics Analysis of Fatigue.29 4 Fatigue Assessment Procedures for Variable Stress Ranges 4.1 Cumulative Fatigue Damage .34 4.2 Analysis of Stress Histories.40 4.3 F
14、atigue Limits47 5 Fatigue Design According to the American Association of State Highway and Transportation Officials Specification (AASHTO) 5.1 Introduction .51 5.2 Redundancy and Toughness51 5.3 Fatigue Design in the AASHTO Specification .54 5.3.1 Fatigue Load and Frequency .54 5.3.2 Fatigue Resist
15、ance.56 5.4 Summary of AASHTO Requirements.58 5.5 Design Example 59 iv 6 Distortion-Inducted Fatigue Cracking 6.1 Introduction .73 6.2 Examples of Distortion-Induced Cracking73 6.3 Further Examples of Distortion-Induced Cracking.76 6.3.1 Web Gaps in Multiple Girder and Girder Floor Beam Bridges 76 6
16、.3.2 Web Gaps in Box Girder Bridges79 6.3.3 Long Span Structures 81 6.3.4 Coped Beam Connections .82 6.3.5 Connections for Lateral Bracing .83 6.3.6 Other Examples .83 6.4 AASHTO Specification Requirements Relating to Distortion-Induced Fatigue .84 6.5 Design Examples.85 6.6 Summary87 7 Inspection a
17、nd Repair of Fatigue Cracks 7.1 Introduction .88 7.2 Protocol for Fatigue Crack Investigation 88 7.3 Identifying the Causes of Cracking.89 7.4 Cracking at Low Fatigue Strength Details 90 7.5 Methods for Inspection of Fatigue Cracking.95 7.6 Repair of Fatigue-Cracked Members 97 7.7 Avoiding Future Cr
18、acking Problems.100 8 Special Topics 8.1 Bolted or Riveted Members 102 8.1.1 Bolted Members 102 8.1.2 Threaded Rods.106 8.1.3 Riveted Connections108v 8.2 Environmental Effects; Use of Weathering Steel110 8.3 Combined Stresses 114 8.4 Effect of Size on Fatigue Life .115 8.5 Role of Residual Stress115
19、 8.6 Quantitative Design Using Fracture Mechanics121 REFERENCES 124 INDEX 128 1 Chapter 1. Introduction Fatigue in metals is the process of initiation and growth of cracks under the action of repetitive load. If crack growth is allowed to go on long enough, failure of the member can result when the
20、uncracked cross-section is sufficiently reduced such that the part can no longer carry the internal forces. This process can take place at stress levels (calculated on the initial cross-section) that are substantially less than those associated with failure under static loading conditions. The usual
21、 condition that produces fatigue cracking is the application of a large number of load cycles. Consequently, the types of civil engineering applications that are susceptible to fatigue cracking include structures such as bridges, crane support structures, stacks and masts, and offshore structures. T
22、he first approach in the design and execution of structures is to avoid details that might be prone to cracking, and then to inspect the structure for cracks, both during fabrication and later in its life. However, it is inevitable that cracks or crack-like discontinuities will be present in fabrica
23、ted steel elements, and it is the responsibility of the engineer to consider the consequences in terms of brittle fracture and in terms of fatigue. The fatigue behavior of a fabricated steel engineering structure is significantly affected by the presence of pre-existing cracks or crack-like disconti
24、nuities. Among other things, it means that there is little or no time during the life of the structure that is taken up with “initiating“ cracks. Probably the most common civil engineering structures that must be examined for fatigue are bridges. In North America and elsewhere, early steel bridge st
25、ructures were fabricated using mechanical fasteners, first rivets and later high-strength bolts. In these cases, initial imperfections are relatively small. In addition, loading and load frequency were also low by todays standards. Consequently, fatigue cracking in these early structures was infrequ
26、ent. In the 1950s welding began to be used as the most common method for fabrication. This had two principal effects related to fatigue. First, welding introduces a more severe initial crack situation than does bolting or riveting. Second, the continuity inherent in welded construction means that it
27、 is possible for a crack in one element to propagate unimpeded into an adjoining element. Design rules at this period of time had been developed from a limited experimental base and the mechanism of fatigue crack growth was not well understood. Furthermore, most of the experimental results came from
28、 small-scale specimens. This is now known to be a 2 limitation in evaluating fatigue strength: reliance on small-scale specimens can result in overestimates of fatigue strength. During the 1970s and 1980s there were many examples of fatigue crack growth from welded details now known to be susceptibl
29、e to this phenomenon. Research revealed that the type of cracking observed in practice was in agreement with laboratory test results and supportable by theoretical predictions. Experience in the 1970s also exposed an unexpected source of fatigue cracking, that from distortions. This is also a phenom
30、enon related largely to welded structures. The purpose of this publication is to provide the student and the practicing engineer with the background required to understand and use the design rules for fatigue strength that are currently a standard part of design codes for fabricated steel structures
31、. The approach adopted establishes the basis for the problem in terms of fracture mechanics, that is, an analytical tool that accounts for the presence of a crack in a structure 1. The focus is then directed specifically upon the issue of fatigue. It is intended that fundamentals are presented in a
32、general way, but applications will refer to the specification for the design of steel bridges prepared by the American Association of State Highway and Transportation Officials (AASHTO) 2. This specification is widely used in the United States, and the governing Canadian specification is nearly iden
33、tical to it. 3 Chapter 2. Basic Fracture Mechanics Concepts Use of the fracture mechanics method of analysis is relatively recent. Originally advanced to explain the rupture of glass specimens 3, its introduction into the field of structural engineering practice started when it was used in the 1940s
34、 to help explain the catastrophic failure of welded ship hulls. Currently, it is employed to assess the behavior of elements used in machinery, pipelines, automotive parts, spacecraft, turbine blades, and many other components. In this Chapter, basic concepts of the fracture mechanics approach are d
35、escribed in order to assist the reader in understanding the fatigue design rules. In addition, for those who might need to design at higher levels of sophistication, it will provide the basis for further reading and self-instruction. Only a summary of fracture mechanics concepts is given in this sec
36、tion. For simplicity, the discussion is limited to cases where the loads are applied at locations remote from the crack locations and normal to the crack surfaces, the so-called Mode 1 situation. (The different ways in which a crack can open, or modes, will be explained in Example 1). Excellent revi
37、ew articles provide more detailed information (for example, see Ref. 46) and several reference books are available 79. 2.1 How to Account for a Crack Five cases of a loaded plate containing a crack are shown in Fig. 1. It requires no knowledge of fracture mechanics to appreciate that cases 1 to 5 ar
38、e placed in order of increasing severity. Taking Case 1 as the basis for comparison, the following important Decreasing StrengthFigure 1 Five Different Cases of a Plate Containing a Crack1 234 54 fracture mechanics parameters can be identified: i) crack length (Case 2); ii) crack location (at edge o
39、f plate in Case 3); iii) effect of bending (Case 4); and iv) presence of a stress concentration (Case 5). Of course, the result of any of these parameters in weakening the plate will depend on the actual circumstances. The effect can be significant, however. For instance, the consequence of a sharp
40、stress concentration in combination with a crack (Case 5) could weaken a plate to less than one-half of its uncracked strength. A magnified view of the area around a crack tip in an infinitely wide plate is shown in Fig. 2. This resembles closely the conditions of Case 1 when the crack length is sma
41、ll compared with the plate width. When a remote stress, , is applied, the crack opens a certain distance, d, and the stress that this cross-sectional area would have carried is diverted to the uncracked area of the plate. This diversion creates a high concentration of stress in the vicinity of the c
42、rack tip. For an elastic material, theoretically this stress is infinite at the crack tip: in real materials, plastic zones are formed since the strain exceeds the ability of the material to behave elastically. This processwhereby i) an applied load causes a crack to open, ii) the crack opening reli
43、eves crack surfaces of stress, and iii) crack tip plastic straining is createdis the fundamental mechanism that weakens structures containing cracks or crack-like discontinuities. If plasticity is ignored, a description of the stress field near the crack tip can be obtained. Using special stress fun
44、ctions, a solution containing the coordinates r and is yyxyxxrxyaDetailCenterlineof crackFigure 2 A Crack in an Infinitely Wide PlateAASection A - A.crack surfacecrack tipcrack-tipplastic zonecrack frontd5 developed. For the particular case of = 0, that is, for the stress in the y-direction, the str
45、ess is yyar=2(1) provided that the crack length, a, is much larger than the distance from the crack tip, r. The numerator in Eq. (1) determines the gradient of the (theoretical) stresses as they rise to infinity when r approaches zero. This numerator is called the stress intensity factor, K. Thus: K
46、a= (2) The advantage of this model is that any combination of stress and crack length can be characterized by the single parameter K. Analytical solutions are available for other particular geometrical configurations and loading conditions; these are summarized in handbooks 10. However, many practic
47、al cases cannot be solved analytically. In such instances, the following expression is used to approximate K: KWY a = (3) where Y is an expression that corrects for plate and crack geometry and W corrects for non-uniform local stress fields caused by the presence of factors such as residual stresses
48、, stress concentrations, and stress gradients. Usually, such correction factors are determined using numerical methods. Here, also, solutions can be found in handbooks. Equation 1 is based on linear-elastic material behavior and cannot account for yielding at the crack tip. Furthermore, stress redis
49、tribution due to plasticity alters the stress field outside the crack tip plastic zone. Nevertheless, if this zone is small, say less than 2% of the plate thickness, of the crack length, and of the uncracked ligament, then the stress intensity factor (K) approach is satisfactory. These limitations are violated in many practical situations. For example, an elasticplastic analysis may be required when stress concentrations cause localized plasticity. The most common analyses either use a parameter named J, which is an expression of the change
