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Abstract

The present paper addresses how the commonly used Hertz formulas for contact stresses underestimate the actual stresses seen in practice due to temperature differentials, misalignments and other contruction-related defects. First, two failure cases of Swedish bridge roller bearings are analyzed and discussed; then, a detailed finite element (FE) model is used to investigate the accuracy of the traditional roller bearing design rules in view of issues such as abutment and girder deformability, misalignment imperfections and material nonlinearity. The bearing capacity of the studied rollers as provided by the manufacturer is used as reference. A rigorous FE model that accurately models girder, roller assembly and abutment provides the necessary information for the assessment of the related contact stresses, which were traditionally calculated by means of the Hertz analytical formulas. Numerical results first establish that roller bearings develop contact stress concentrations at the outer edges of the cylindrical drums. Second, it is established that the contact stresses are very sensitive to misalignment imperfections between the bridge girder and the abutment. Last, it is shown that the roller bearings develop inelastic deformation at relatively low loads in relation to the design load. These reasons, combined with the unlikelihood for roller bearings to shake-down, constitute the basis of the observed roller bearing failures.

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... Li [4] and P. Wang [5] used the fault diagnosis technology to give the correct judgment to the various failure symptoms of the axle box bearing, and extended the service life of the bearing. E.K. Koltsakis [6] set the contact stress model of bearing, improved the reliability of the bearing by the observation of the influence of the contact stress and the secondary surface stress on the bearing. All of the above studies were analyzed just on the bearings without considering the reliability of the axle box bearing system. ...
Article
The historic Port Weir Bridge over the Nidau‐Büren Canal in the Canton of Bern, Switzerland, was inaugurated in 1938. This multi‐purpose structure serves as an important road bridge, a mechanised weir, a lock for canal boats, as well as a hydroelectric power station. During inspections in 2018, severe concrete damage and reinforcement corrosion were observed on this protected structure. Immediate temporary reinforcement measures were required as the conformity factors for structural safety at numerous locations were significantly below the minimum requirements. A project specific traffic load model allowed the temporary strengthening works to be limited to a few critical elements, thereby allowing the bridge to be reopened for heavy traffic in 2019 and then fully rehabilitated between 2020 and 2022. The renovation project involved an innovative reinforced UHPFRC strengthening of the existing T‐beam superstructure and a widening of the deck to bring the lane widths up to modern standards. This paper outlines the safety measures and the UHPFRC strengthening concepts applied, as well as some of the key construction challenges associated with maintaining road traffic on the bridge and traffic in the canal lock below the bridge during the construction works. Additionally, the UHPFRC strengthening concept is demonstrated by means of a design example.
Article
The paper is aimed at finding the likely failure mechanism of a bridge roller bearing made of high strength martensitic stainless steel. Spectroscopy and stress analysis of the roller indicated that an initial radial surface crack, found at an end face of the roller and close to the contact region, was induced by stress corrosion cracking (SCC). The initial crack subsequently changed shape and increased in size under growth through fatigue and finally formed a quarter-circle radial crack centred on the end face corner of the roller. Numerically computed stress intensity factors for the final crack showed that crack loading was predominantly in Mode II. For a crack size as observed on the fracture surface, the maximum service load, as specified by the manufacturer, enhanced by a certain roller bearing misalignment effect, was sufficient for failure through fracture.
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With the innovation of elastomeric bearings in the mid-1950s steel bearings lost their interest and significance both in research and development and subsequently even in application. Steel bearings were gradually abandoned in bridges, followed by the technical literature and design standards. However, a great number of steel bearings remain today in service world-wide and will pose their particular challenges in the future. To the author’s knowledge, just in Sweden, high strength stainless steel bearings still exist in no less than some 650 bridges. In recent years, a large number of such bearings have failed with an alarmingly high frequency in Sweden during a period of six to twenty years after installation making them a serious maintenance cost issue.
Article
In this work, the finite element method is employed to gain an understanding of the behaviour of a cracked bridge roller bearing in service. The cracked roller is considered as a two-dimensional edge-cracked disk subjected to a radial compressive line load. The crack parameters KI and KII are calculated for the relevant load configuration and angle of disk rotation. The calculated data are also used to check the accuracy of approximate SIF solutions reported earlier (Schindler, 1990; Schindler and Morf, 1994). For plain Mode I loading very good agreement is found between the obtained results and data presented in Schindler and Morf (1994).
Article
Full-text available
Tempering of alloy steels in the temperature range of 400–600 °C causes temper embrittlement i.e. decrease in notch toughness of the material and the nil ductility temperature is raised to room temperature and above. The fracture in temper-embrittled steel is intergranular and propagates along prior austenitic grain boundaries. The embrittlement occurs only in the presence of specific impurities, e.g. P, Sn, Sb and As. These elements have been shown to segregate along prior austenite grain boundaries during tempering. Similar type of temper embrittlement can occur in martensitic stainless steel (SS) if tempered in the temperature range of 450–600 °C. This paper reports a case of failure of components made from martensitic SS 420 due to temper embrittlement. These components were subjected to a temperature of 120 °C in the initial stages of service and had shown brittle fractures. Scanning electron microscopic examination of the fracture surface of both the components showed intergranular fracture. The microstructures of the failed components confirmed that the materials were in hardened and tempered condition. In addition, the microstructure revealed both intergranular corrosion (IGC) and intergranular cracking. The electron backscatter diffraction study also showed retained austenite in the first component’s material. The material undergoing IGC might be related to a wrong heat-treatment during fabrication and subsequent pickling procedures. To confirm this, a sample each from both the components was exposed to 5% nitric acid solution at 25 °C. the results showed very high corrosion rate and the attack was intergranular in nature. The failure of both the components was concluded to be due to wrong tempering treatment in the temperature range of 450–600 °C that cause grain boundaries to become susceptible to embrittlement and corrosion.
Article
Full-text available
Abstract: This chapter surveys mathematical methods and principal results in the mechanics of fracture. Primary emphasis is placed on the analysis of crack extension as treated through methods of continuum mechanics. Section II begins with relevant concepts and basic equations from the mechanics of solids, including a survey of elasticity and plasticity, and of associated mathematical methods for boundary value problems, such as analytic function theory. Energy comparison methods and the related path-independent energy integral are introduced in this section; these novel methods of analysis prove to be widely applicable for subsequently treated notch and crack problems. Section III deals with the application of linear elasticity to fracture. Several two-dimensional crack, problems are solved and approximate methods are presented for determination of stress-intensity factors with more complicated geometries. Theories of elastic-brittle fracture are reviewed and the equivalence of Griffith energy balance and cohesive forces approaches is demonstrated. In addition, dynamic running crack problems, energy rate computations, and stress concentrations at smooth-ended notches are discussed. Section IV, the longest section, deals with the elastic-plastic and fully plastic analysis of fracture. Here, the small-scale yielding approximation, for which elastic stress-intensity factors govern near tip deformation fields, is presented. Elastic-plastic crack problems in plane strain and plane stress are discussed; while these results are necessarily approximate, further insight is provided by treatment of the simpler antiplane strain case. The incremental and path-dependent nature of plastic stress-strain relations is shown to lead to a view of fracture as an instability point in a process of continuing crack advance under increasing load. Additional topics in this section include plastic strain concentrations at smooth ended notches, limit analysis of notched bodies, and a brief treatment of separation mechanisms in ductile materials.
Book
Full-text available
This application-oriented book introduces the associations between contact mechanics and friction and with it offers a deeper understanding of tribology. It deals with the associated phenomena of contact, adhesion, capillary forces, friction, lubrication, and wear from one consistent viewpoint. The author goes into (1) methods of rough estimation of tribological quantities, (2) methods for analytical calculations which attempt to minimize the necessary complexity, (3) the crossover into numerical simulation methods. With these methods the author conveys a consistent view of tribological processes in various scales of magnitude (from nanotribology to earthquake research). Also, system dynamic aspects of tribological systems, such as squeal and its suppression as well as other types of instabilities and spatial patterns are investigated. This book contains problems and worked solutions for individual chapters in which the reader can apply the theory to practical situations and deepen the understanding of the material. © Springer-Verlag Berlin Heidelberg 2010. All rights are reserved.
Book
p>Bridge superstructures have to be designed to permit thermal and live load strains to occur without unintended restraints. Bridge bearings have to transfer forces from the superstructure to the substructure, allowing all movements in directions defined by the designer. The two functions -transfer the loads and allow movements only in the required directions for a long service time with little maintenance - are not so easy to fulfil. Differ­ent bearings for different purposes and requirements have been developed so, that the bridge designer can choose the most suitable bearing. By the movement of a bridge, gaps are necessary between superstructure and substructure. Expansion joints fill the gaps, allowing traffic loads tobe carried and allowing all expected displacements with low resistance. Ex­pansion joints should provide a smooth transition, avoid noise emission as far as possible and withstand all mechanical actions and chemical attacks (de-icing) for a long time. A simple exchange of all wearing parts and of the entire expansion joint should be possible. The present volume provides a comprehensive survey of arrangement, construction and installation of bearings and expansion joints for bridges including calculation of bearing reactions and movements, analysis and design, inspection and maintenance. A long list of references deals with the subjects but also with aspects in the vicinity of bearings and expansion joints. This book is aimed at both students and practising engineers, working in the field of bridge design, construction, analysis, inspection, maintenance and repair.
Book
Failure Analysis of Engineering Structures: Methodology and Case Histories is a collection of failure analysis reports, familiarizing readers with the practices, tools, and logic employed by experienced investigators in their search for causes and cures in the wake of serious failures. The collection consists of more than 50 reports, the majority of which document the service failure of an aircraft component or system. The reports follow a consistent format that includes a concise summary of the failure, background information, pertinent specifications, and an initial assessment based on visual examination. They also include a list of the testing procedures used, a discussion of the results, a conclusion, and recommendations. In addition to recording the lessons of history, the book provides an introduction to the methodology of failure analysis, describing common causes of failure, site access challenges, specimen collection, examination procedures, and advanced analytical techniques. It presents examples of failures due to design deficiencies, manufacturing defects, maintenance errors, and service abnormalities. It also addresses the issue of sabotage and various aspects of forensic analysis. For information on the print version, ISBN 978-0-87170-820-5, follow this link.
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Residual Stress Measurement and the Slitting Method provides complete coverage of the slitting method with new results in analysis, computation and estimation. It discusses different roles of residual stresses from the fracture mechanics perspective. Covering both near-surface and through-thickness residual stress measurements, the book serves as a reference tool for graduate students, researchers and practicing engineers. The authors include discussions on the general expressions for residual stresses acting on the site of a slit, the analysis based on fracture mechanics solutions and finite element computations, the estimations using continuous and piecewise functions with and without least squares fit, examples of residual stress measurement and error analysis, the measurement of stress intensity factors, and many more timely topics. With more than 130 figures, Residual Stress Measurement and the Slitting Method provides detailed formulations and examples of compliance functions, weighted least squares fit and convergence test in stress estimation, and computer programs to facilitate the implementation of the slitting method. This book is an invaluable reference for professionals and researchers in the field.
Article
The paper is aimed at finding the likely failure mechanism of a bridge roller bearing made of high strength martensitic stainless steel. Spectroscopy and stress analysis of the roller indicated that an initial radial surface crack, found at an end face of the roller and close to the contact region, was induced by stress corrosion cracking (SCC). The initial crack subsequently changed shape and increased in size under growth through fatigue and finally formed a quarter-circle radial crack centred on the end face corner of the roller. Numerically computed stress intensity factors for the final crack showed that crack loading was predominantly in Mode II. For a crack size as observed on the fracture surface, the maximum service load, as specified by the manufacturer, enhanced by a certain roller bearing misalignment effect, was sufficient for failure through fracture.
Chapter
Criteria of Failure Failure Modes Elastic Deformation and Yielding Fracture Mechanics and Unstable Crack Growth Fatigue Creep and Stress Rupture Fretting and Wear Corrosion and Stress Corrosion Failure Analysis and Retrospective Design References
Article
In this work, the finite element method is employed to gain an understanding of the behaviour of a cracked bridge roller bearing in service. The cracked roller is considered as a two-dimensional edge-cracked disk subjected to a radial compressive line load. The crack parameters KI and KII are calculated for the relevant load configuration and angle of disk rotation. The calculated data are also used to check the accuracy of approximate SIF solutions reported earlier (Schindler, 1990; Schindler and Morf, 1994). For plain Mode I loading very good agreement is found between the obtained results and data presented in Schindler and Morf (1994).
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Failure analysis of gear boxes was carried out by means of SEM, metallographic examination, mechanical properties testing and calculation. It was found that the failure is the fatigue fracture caused by fretting wear. The preventing measures were also suggested.
Article
A method is proposed for measurement of the hoop stress in an axisymmetric residual stress field in cylinders in which the axial stress is independent of the axial coordinate. The method involves measuring strains at the outside surface while an axial crack is cut progressively from the outside. Experimental results are presented for two short cylindrical rings cut from a long quenched cylinder. Good general agreement is obtained with X-ray and hole drilling measurements of residual stresses.
Article
This paper reports on the results of an experimental and analytical investigation on the mode I and mode II fracture mechanics behaviour of a high-strength steel. The aim was to identify the effect of crack tip geometry and loading system on the loading capacity of the material. Notched as well as pre-cracked single edge notched specimens were loaded in symmetric and anti-symmetric bending. The experimental results show that crack tip and loading parameters have a significant influence on the apparent critical fracture toughness values.The influence of a finite notch radius on the mode I and mode II fracture toughness is quantified by a J-integral analysis which indicates that for both loading systems crack initiation can be estimated by a local strain energy density criterion. A weight function analysis of the mode II loading shows that crack tip shielding due to contact between the crack faces becomes important if the distance from the first support roller to the crack plane is less than the thickness of the specimen. This result helps to explain the large scatter which is present in one of the experimental loading configurations.
Article
Martensitic stainless steels are widely used for their good mechanical properties and moderate corrosion resistance. However, the need for superior properties in specific applications (e.g. steam generators, mixer blades, etc.) led to wide researches on the performance improvement of these steels. Heat treatment was recommended as one of the best ways to this regard hence the effects of astenitizing temperature and time, and tempering temperature on the microstructure, mechanical and corrosion properties of AISI420 have been studied. In the current work the experimental results showed that the austeitizing temperature significantly affects mechanical properties. The increase of tempering temperature led to precipitation of M7C3 and secondary hardening in the range of 400–500°C. SEM micrographs of the fracture surfaces showed a mixed fracture mechanism (brittle and ductile) at 200°C and 700°C and brittle mechanism at 500°C. The Polarization curves were not significantly affected by the increment of austenitizing temperature.
Article
Since the use of steel, reinforced concrete and prestressed concrete as bridge building materials, structural bridge bearings had to be used. On the other hand the gap between bridge and abutment is bridged by means of expansion joints. The target of this paper is to give a very short state-of-the-art-report on bearings and expansion joints for bridges.
Article
A substantial fraction of the mysteries associated with crack extension might be eliminated if the description of fracture experiments could include some reasonable estimate of the stress conditions near the leading edge of a crack particularly at points of onset of rapid fracture and at points of fracture arrest. It is pointed out that for somewhat brittle tensile fractures in situations such that a generalized plane-stress or a plane-strain analysis is appropriate, the influence of the test configuration, loads, and crack length upon the stresses near an end of the crack may be expressed in terms of two parameters. One of these is an adjustable uniform stress parallel to the direction of a crack extension. It is shown that the other parameter, called the stress-intensity factor, is proportional to the square root of the force tending to cause crack extension. Both factors have a clear interpretation and field of usefulness in investigations of brittle-fracture mechanics.
Article
In Deutschland wurden die nationalen Regelungen für Lager nach DIN 4141 und die darauf basierenden nationalen Zulassungen mittlerweile nahezu vollständig durch das Europäische Regelwerk DIN EN 1337 ersetzt. Diese Norm regelt die Anforderungen an die Bemessung, konstruktive Ausbildung, Herstellung, Transport, Einbau und Inspektion von Lagern im Bauwesen. Geregelt werden Elastomerlager, Rollenlager, Topflager, Kipplager, Kalotten‐ und Zylinderlager mit PTFE sowie Festhaltekonstruktionen und Führungslager. Moderne, hochfeste Gleitwerkstoffe, die außerhalb des Anwendungsbereiches der DIN EN 1337 liegen, können auf der Grundlage von europäischen Zulassungen (ETA) eingesetzt werden. Für die in Deutschland im Brückenbau am häufigsten zum Einsatz kommenden Lagertypen – Kalottenlager und Elastomerlager – werden die alten und neuen Regelungen hinsichtlich des Sicherheitsniveaus analysiert und bewertet sowie auf weitere Punkte hingewiesen, die im Rahmen der geplanten Überarbeitung der Normenreihe DIN EN 1337 nochmals kritisch hinterfragt werden müssen. Die bisherigen nationalen und derzeitigen europäischen Regelwerke gelten nur für Lager, die nicht durch Zugkräfte beansprucht werden. Obwohl die Vermeidung von Lagerzugkräften insbesondere im Brückenbau ein fundamentaler Konstruktionsgrundsatz ist, können in Sonderfällen Zugkräfte nicht vermieden werden. Da es für Zuglager keine normativen Vorgaben gibt, müssen an den speziellen Anwendungsfall angepasste Bemessungs‐ und Konstruktionsregeln erarbeitet werden. Anhand von Anwendungsbeispielen wird die besondere Problematik bei der Verwendung von Lagern unter Druck‐Zug‐Beanspruchungen erläutert. Structural bearings for bridges and buildings according to DIN EN 1337. In Germany the national design rules for bearings according to DIN 4141 and corresponding national approvals are meanwhile nearly completely replaced by the European Standard DIN EN 1337. This code specifies the requirements for design and manufacturing of structural bearings for bridges and buildings. DIN EN 1337 covers elastomeric bearings, roller bearings, pot bearings, rocker bearings and spherical and cylindrical PTFE bearings. Special applications, e.?g. applying modern sliding elements outside the scope of DIN EN 1337 which differ from the technical rules given in DIN EN 1337, can be used on the basis of European Technical Approvals (ETA). On this background for spherical bearings and elastomeric bearings the new rules are analyzed and assessed regarding the necessary safety requirements and also point to further items that should be inquired critically in the scope of revision of the DIN EN 1337. The old National Standards as well as the new European Standards are only valid for bearings without any uplift forces. Avoiding uplift forces is a fundamental design principle especially within the scope of bearings for bridges. However, in rare and worse cases it cannot be avoided that uplift forces occur. Under these conditions the rules in DIN 4141 and DIN EN 1337 for the design and the manufacture of bearings do not apply and modified design rules have to be developed. This is shown by means of two examples, where specially developed bearings for compression and uplift forces were designed.
Article
The renovation and widening project for the Golden Horn Bridge in Istanbul consisted of the construction of two new bridges and the repair of the existing bridge, erected in 1974. During a preliminary inspection of the concrete viaduct of the existing bridge, the cylinder of one of the roller bearings was found to have split in the longitudinal direction. After further investigation, it was found that the failure occurred due to fatigue and material problems. All the bridge bearings were therefore replaced because they were all of the same design. New pot-type bearings were installed in the steel bridge, and elastomeric bearings in the concrete viaduct. In total 16 bearings were replaced in the steel bridge and 20 in the concrete viaduct.
Article
The measurement of energy release rates using virtual crack extensions has been made using finite element techniques. An economic and accurate technique for calculating energy changes due to any number of virtual tip changes is presented. Mixed-mode situations can be dealt with by observing the direction of maximum energy release rate. Examples are given including various cracks in a plate in tension, a curving crack in a general two-dimensional shape, and a three-dimensional crack in a plate.
Article
In this paper an analytical expression for the energy release rate has been derived and put in a form suitable for a numerical analysis of an arbitrary 3-D crack configuration. The virtual crack extension method can most conveniently be used for such a derivation. This method was originally developed from finite element considerations and the resulting expressions were, therefore, based on the finite element matrix formulation [1-5]. In this paper the derivation of the energy release rate leads to an expression which is independent of any specific numerical procedure. The formulation is valid for general fracture behavior including nonplanar fracture and shear lips and applies to elastic materials as well as materials following the deformation theory of plasticity. The body force effect is also included. For 3-D fracture problems it is of advantage to use both an average and a local form of the energy release rate and definitions for both forms are suggested. For certain restrictions on the crack geometry it is shown that the energy release rate reduces to the 3-D form of the J-integral.
Article
An experimental method is presented that enables stress intensity factors due to residual stress to be determined directly, without prior determination of the residual stress. The method is based on the crack compliance method, where a narrow cut is introduced progressively into the considered component, and the resulting strain change is measured by a strain gage. The required mathematical relations to determine stress intensity factors from strain measurements are established by means of some basic relations of linear elastic fracture mechanics. They are derived explicitly for two exemplary geometrical systems, which allowed for analytical treatment. Experimental data obtained in the case of a steel roller are presented and discussed.
Article
A method which can be used to obtain both tension and compression stress-strain curves from a single bend test was first proposed in 1910. Curiously, this apparently useful technique has been very little application since that time. For this reason, the present investigation was conducted to examine the merits and shortcomings of the test. Three materials which show different stress-strain curves in tension and compression, beryllium, cast iron and prestrained copper, were studied to test the versatility of the method. A special four-point bend fixture, designed to minimize loading errors, was designed for this study and is described. Generally, the stress-strain curves obtained from bending and conventional tests showed good agreement for strains less than about five percent. Finally, some advantages and disadvantages of the bending tests are pointed out.
Article
Fracture of 13 wt% chromium steel blades has been observed to occur in the intergranular mode in certain service failures. An attempt has been made in this study to identify the conditions in respect of material, loading and environment which may lead to intergranular fracture. Three different materials were subjected to varying heat treatments selected on the basis of fracture characteristics of as-received materials. It has been concluded that grain-boundary segregations of impurities and carbide precipitation, intergranular network of delta ferrite at prior austenitic grain boundaries, and a sufficient concentration of NaCl in conjunction with cyclic stress, promote intergranular fracture in a 13 wt% chromium steel.
Article
The article discusses the organization required at the start of an investigation of failure such as Apollo I disaster and to provide a methodology with some organizational tools. For many failure investigations, the failure is represented by a broken piece of hardware, such as a shaft failure. The International Space Station (ISS) has completed Phases I and II of its three-phase construction. Permanent human habitation has been in progress since 2 November 2000. Traveling at 17,500 mph, the Expedition Four crew orbits the earth every 90 min at an altitude of 220 miles. Failures can be individual parts, entire machines, or a process. Broken down further, they can be physical paper, or thinking/cultural in origin. In some cases, the reason things go wrong can be traced back to the culture of a company.
Article
The linear elastic, stiffness-derivative, finite element technique of Parks [ 1 ]is generalized to determine the ductile fracture parameter J from elastic-plastic finite element solutions. The method, based on energy comparison of two slightly different crack lengths, requires only one elastic-plastic finite element solution, and the altered crack configuration is obtained by changing nodal point positions. The technique is applied to finite element solutions for a deeply cracked, plane-strain bend specimen - a configuration for which J can be otherwise obtained - and the results are encouraging. The extension of the method to obtain arc-length-weighted J values in three-dimensional crack configurations is also proposed.
Article
We compare two methods for calculating the energy released during quasi-static crack advance. One method is based on a surface integral (line integral in two dimensions) expression for the energy release rate, whereas the other method is based on a volume (area) integral representation. A concise derivation of the volume (area) integral expression is given using a virtual-work-type identity for Eshelby's energy momentum tensor. The finite-element implementation of the volume (area) integral formulation corresponds to the virtual crack extension method. Within the context of this formulation, we outline a procedure for calculating pointwise values of the energy release rate along a three-dimensional crack front. For illustrative purposes, numerical examples are presented for a fully plastic, plane strain, edge-cracked panel subject to combined tension and bending.
Article
The present paper outlines a finite element method for calculating the energy release rate. The method is based on a continuum mechanics formulation of the virtual crack extension principle and can be used with linear elastic materials as well as materials following the deformation theory of plasticity. The formulation is easily incorporated into a finite element program, but can also conveniently be used as part of a post-processing program, which uses stress and displacement data from a finite element analysis to calculate the energy release rate. The present formulation can be used as a unified approach for 2-D and 3-D fracture problems and includes the effect of body forces and traction loading on the crack faces.
Article
In an earlier paper it was suggested that a knowledge of the elastic-stress variation in the neighborhood of an angular corner of an infinite plate would perhaps be of value in analyzing the stress distribution at the base of a V-notch. As a part of a more general study, the specific case of a zero-angle notch, or crack, was carried out to supplement results obtained by other investigators. This paper includes remarks upon the antisymmetric, as well as symmetric, stress distribution, and the circumferential distribution of distortion strain-energy density. For the case of a symmetrical loading about the crack, it is shown that the energy density is not a maximum along the direction of the crack hut is one third higher at an angle ± cos^(-1) (1/3); i.e., approximately ±70 deg. It is shown that at the base of the crack in the direction of its prolongation, the principal stresses are equal, thus tending toward a state of (two-dimensional) hydrostatic tension. As the distance from the point of the crack increases, the distortion strain energy increases, suggesting the possibility of yielding ahead of the crack as well as ±70 deg to the sides. The maximum principal tension stress occurs on ±60 deg rays. For the antisymmetrical stress distribution the distortion strain energy is a relative maximum along the crack and 60 per cent lower ± 85 deg to the sides.
Article
A finite element technique for determination of elastic crack tip stress intensity factors is presented. The method, based on the energy release rate, requires no special crack tip elements. Further, the solution for only a single crack length is required, and the crack is â??advancedâ?? by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis. The promising straightforward extension of the method to general three-dimensional crack configurations is presented and contrasted with the practical impossibility of conventional energy methods.
Indian Railways Institute of Civil Engineering
  • S Ghansham
Lager im Bauwesen Ernst & Sohn: Berlin
  • T Block
  • W Kauschke
  • H Eggert
Block T, Kauschke W, Eggert H. Lager im Bauwesen Ernst & Sohn: Berlin, 2013.
Theory and Design of
  • P P Xanthakis
Xanthakis PP. Theory and Design of Bridges John Wiley & Sons, Inc., 1994.
Steel Bridge Design Handbook: Bearing Design
  • M Kaczinski
Kaczinski M. Steel Bridge Design Handbook: Bearing Design, Report No. FHWA-IF-12-052, vol. 15, Federal Highway Administration, 2012.
Bridge Bearings, Indian Railways Institute of Civil Engineering
  • S Ghansham
Ghansham S. Bridge Bearings, Indian Railways Institute of Civil Engineering, 2006.
Institution of Civil Engineers manual of bridge engineers
  • G Parke
  • N Hewson
Spannbeton Analyse von Bauwerksdaten, Schäden und Erhaltungskosten
  • G König
  • R Maurer
  • T Zichner
König G, Maurer R, Zichner T. Spannbeton Analyse von Bauwerksdaten, Schäden und Erhaltungskosten, Springer-Verlag: Berlin and Heidelberg, 1986.
6th world congress on joints, bearings and seismic systems for concrete structures
  • A Marioni
Marioni A. 6th world congress on joints, bearings and seismic systems for concrete structures. In The European Standard EN 1337 on Structural Bearings, Halifax, Canada, 17-21 September 2006.
Vorschlag für ein einheitliches Brückenlager
  • J Karig
Karig J. Vorschlag für ein einheitliches Brückenlager. Bautechnik 1923;1(357-60):416-33.
Online: urn:nbn:de:kobv:co1-opus-20692
  • V Wetzk
  • Brückenlager
Wetzk V. Brückenlager. 1850-1950. Dissertation. BTU Cottbus. Online: urn:nbn:de:kobv:co1-opus-20692, 21. 12; 2010.
I sprucken lagerrulle av stål till Ölandsbron. Stockholm: Statens Provningsanstalt
  • H G Linder
  • J Mårtensson
Linder HG, Mårtensson J. I sprucken lagerrulle av stål till Ölandsbron. Stockholm: Statens Provningsanstalt; 1977.
Schadens-und Sicherheitsanalysen an betriebsgeschädigten Stahlrollen von Brückenlagern
  • H J Schindler
  • U Morf
Schindler HJ, Morf U. Schadens-und Sicherheitsanalysen an betriebsgeschädigten Stahlrollen von Brückenlagern. In: Bundesamt für Strassenbau (Hrsg.): Forschungsauftrag 87/90 auf Antrag der Arbeitsgruppe Brückenforschung; 1995.