considerations for design of concrete structures subjected to fatigue loading

increase in the allowable stress range for prestressing steel from 0.04 fpu to 215R-2 Keywords: beams supports; compressive strength; concrete pavements: cracking frac- 2.2-Reinforcing

ACI 215R-74

(Revised 1992/Reapproved 1997)

Considerations for Design of Concrete Structures

Subjected to Fatigue Loading

John M Hanson Chairman Paul W Abeles John D Antrim Earl I Brown, II John N Cernica Carl E Ekberg, Jr.*

Neil M Hawkins Hubert K Hiisdorf

Craig A Ballinger Secretary Cornie L Hulsbos Don A Linger Edmund P Segner, Jr.

Surendra P Shah Laurence E Svab William J Venuti

* Chairman of ACI Committee 215 at the time preparation of this report was begun.

Committee members voting on the 1992 revisions:

David W Johnston Chairman

M Arockiasamy P.N Balaguru Mark D Bowman John N Cernica Luis F Estenssoro John M Hanson Neil M Hawkins Thomas T.C Hsu

Craig A Ballinger Secretary

Ti Huang Lambit Kald Michael E Kreger Basile G Rabbat Raymond S Rollings Surendra P Shah Luc R Taerwe William J Venuti

This report presents information that is intended to aid the practicing engineer

confronted with consideration of repeated loading on concrete structures

Investi-1.1-Objective and scope

gations of the fatigue properties of component materiak+oncrete, reinforcing l.2-Definitions

bars, welded reinforcing mats, and prestressing tendons-are reviewed Applica- 1.3-Standards cited in this report

tion of this information to predicting the fatigue life of beams and pavements is

discussed A significant change in Section 3.1.2 of the 1992 revisions is the Chapter 2-Fatigue properties of component materials, pg.

increase in the allowable stress range for prestressing steel from 0.04 fpu to 215R-2

Keywords: beams (supports); compressive strength; concrete pavements: cracking (frac- 2.2-Reinforcing bars

turing); dynamic loads; fatigue (materials); impact; loads (Forces); microcracking; plain 2.3-Welded wire fabric and bar mats

concrete; prestressed concrete; prestressing steel; reinforcedconcrete: reinforcingsteels; 2.4-Prestressing tendons

specifications; static loads: strains; stresses; structural design; tensile strength; welded

wire fabric; welding; yield strength.

CONTENTS

Chapter 3-Fatigue of beams and pavements, pg 215R-15

3.1-Beams 3.2-Pavements

Chapter l-Introduction, pg 215R-2

ACI Committee Reports, Guides, Standard Practices, and

Commentaries are intended for guidance in designing,

plan-ning, executing, or inspecting construction and in preparing

specifications Reference to these documents shall not be

made in the Project Documents If items found in these

doc-uments are desired to be part of the Project Docdoc-uments they

should be phrased in mandatory language and incorporated

into the Project Documents.

2 1 5R-1

Notation, pg 215R-19 References, pg 215R-19 Appendix, pg 215R-23

ACI 215R-74 (Revised 1992) became effective Nov 1, 1992.

Copyright 0 1992, American Concrete Institute.

All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by any electronic or mechanical device, printed or written or oral, or recording for sound or visual repro- duction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.

215R-2 ACI COMMITTEE REPORT

CHAPTER l-INTRODUCTION

In recent years, considerable interest has developed in the

fatigue strength of concrete members There are several

rea-sons for this interest First, the widespread adoption of

ulti-mate strength design procedures and the use of higher

strength materials require that structural concrete members

perform satisfactorily under high stress levels Hence there is

concern about the effects of repeated loads on, for example,

crane beams and bridge slabs

Second, new or different uses are being made of concrete

fatigue; however, this report does not specifically deal withthese types of loadings

1.3-Standards cited in this report

The standards and specifications referred to in this ment are listed below with their serial designation, includingyear of adoption or revision These standards are the latesteffort at the time this document was revised Since some ofthe standards are revised frequently, although generally only

docu-in mdocu-inor details, the user of this document may wish to checkdirectly with the committee if it is correct to refer to themembers or systems, such as prestressed concrete railroad latest revision

ties and continuously reinforced concrete pavements These

uses of concrete demand a high performance product with an ACI 301-89

assured fatigue strength

Third, there is new recognition of the effects of repeated ACI 318-89

loading on a member, even if repeated loading does not

cause a fatigue failure Repeated loading may lead to inclined ASTM A 416-90

cracking in prestressed beams at lower than expected loads,

or repeated loading may cause cracking in component

mater-ials of a member that alters the static load carrying char- ASTM A 421-90

acteristics

This report is intended to provide information that will

serve as a guide for design for concrete structures subjected

to fatigue loading ASTM 722-90

However, this report does not contain the type of detailed

design procedures sometimes found in guides

Chapter 2 presents information on the fatigue strength of AWS Dl.4-79

concrete and reinforcing materials This information has been

obtained from reviews of experimental investigations reported

in technical literature or from unpublished data made

avail-able to the committee The principal aim has been to

sum-marize information on factors influencing fatigue strength

that are of concern to practicing engineers

Chapter 3 considers the application of information on

concrete and reinforcing materials to beams and pavements

Provisions suitable for inclusion in a design specification are

recommended

An Appendix to this report contains extracts from current

specifications that are concerned with fatigue

1.2-Definitions

It is important to carefully distinguish between static,

dynamic, fatigue, and impact loadings Truly static loading, or

sustained loading, remains constant with time Nevertheless,

a load which increases slowly is often called static loading;

the maximum load capacity under such conditions is referred

to as static strength

Dynamic loading varies with time in any arbitrary manner

Fatigue and impact loadings are special cases of dynamic

loading A fatigue loading consists of a sequence of load

repetitions that may cause a fatigue failure in about 100 or

more cycles

Very high level repeated loadings due to earthquakes or

other catastrophic events may cause failures in less than 100

cycles These failures are sometimes referred to as low-cycle

Specifications for Structural Concrete forBuildings

Building Code Requirements for forced Concrete

Rein-Standard Specification for Uncoated SevenWire Stress Relieved Steel Strand for Pre-stressed Concrete

Standard Specification for Uncoated StressRelieved Steel Wire for Prestressed Con-crete

Standard Specification for Deformed andPlain Billet Steel Bars for Concrete Rein-forcement

Standard Specification for Uncoated HighStrength Steel Bar for Prestressing Con-crete

StructuralWelding Code-Reinforcing Steel

CHAPTER 2-FATIGUE PROPERTIES

OF COMPONENT MATERIALS

The fatigue properties of concrete, reinforcing bars, andprestressing tendons are described in this section Much ofthis information is presented in the form of diagrams and al-gebraic relationships that can be utilized for design However,

it is emphasized that this information is based on the results

of tests conducted on different types of specimens subjected

to various loading conditions Therefore, caution should beexercised in applying the information presented in this report

2.1-Plain concrete*

2.1.1 General-Plain concrete, when subjected to repeated

loads, may exhibit excessive cracking and may eventually failafter a sufficient number of load repetitions, even if the maxi-mum load is less than the static strength of a similar speci-men The fatigue strength of concrete is defined as a fraction

of the static strength that it can support repeatedly for agiven number of cycles Fatigue strength is influenced byrange of loading, rate of loading, eccentricity of loading, loadhistory, material properties, and environmental conditions

* Dr Surendra P Shah section of the report.

was the chairman of the subcommittee that prepared this

FATIGUE LOADING DESIGN CONSIDERATIONS 215R-3

Fig l-Fatigue strength of plain concrete beams

Fatigue is a process of progressive permanent internal

structural change in a material subjected to repetitive

stresses These changes may be damaging and result in

pro-gressive growth of cracks and complete fracture if the stress

repetitions are sufficiently large.1,2 Fatigue fracture of

concrete is characterized by considerably larger strains and

microcracking as compared to fracture of concrete under

static loading.3,44Fatigue strength of concrete for a life of ten

million cycles-for compression, tension, or flexure-is

roughly about 55 percent of static strength

2.1.2 Range of stress -Theeffect of range of stress may be

illustrated by the stress-fatigue life curves, commonly referred

to as S-N curves, shown in Fig 1 These curves were

devel-oped from tests on 6 x 6 in (152 x 152 mm) plain concrete

beams5 loaded at the third points of a 60 in (1.52 m) span

The tests were conducted at the rate of 450 cycles per min

This concrete mix with a water-cement ratio of 0.52 by weight

provided an average compressive strength of 5000 psi (34.5

MPa) in 28 days The age of the specimens at the time of

testing ranged from 150 to 300 days

In Fig 1, the ordinate is the ratio of the maximum stress,

Sm a x to the static strength In this case, Smax is the computed

flexural tensile stress, and the static strength is the modulus

of rupture stress, f, The abscissa is the number of cycles to

failure, plotted on a logarithmic scale

Curves a and c indicate that the fatigue strength of

con-crete decreases with increasing number of cycles It may be

observed that the S-N curves for concrete are approximately

linear between 102 and 107 cycles This indicates that

con-crete does not exhibit an endurance limit up to 10 million

cycles In other words, there is no limiting value of stress

below which the fatigue life will be infinite

The influence of load range can be seen from comparison

of Curves a and c in Fig 1 The curves were obtained from

tests with loads ranging between a maximum and a minimum

which was equal to 75 and 15 percent of the maximum,

re-spectively It is evident that a decrease of the range between

maximum and minimum load results in increased fatigue

strength for a given number of cycles When the minimum

and maximum loads are equal, the strength of the specimen

corresponds to the static strength of concrete determinedunder otherwise similar conditions

The results of fatigue tests usually exhibit substantiallylarger scatter than static tests This inherent statistical nature

of fatigue test results can best be accounted for by applyingprobabilistic procedures: for a given maximum load, minimumload, and number of cycles, the probability of failure can beestimated from the test results By repeating this for severalnumbers of cycles, a relationship between probability of fail-ure and number of cycles until failure at a given level of

maximum load can be obtained From such relationships, S-N

curves for various probabilities of failure can be plotted.Curves a and c in Fig 1 are averages representing 50 percent

probability of failure Curve d represents 5 percent ity of failure, while Curve bcorresponds to an 80 percentchance of failure

probabil-The usual fatigue curve is that shown for a probability offailure of 50 percent However, design may be based on alower probability of failure

Design for fatigue may be facilitated by use of a modifiedGoodman diagram, as illustrated in Fig 2 This diagram isbased on the observation that the fatigue strength of plainconcrete is essentially the same whether the mode of loading

is tension, compression, or flexure The diagram alsoincorporates the influence of range of loading For a zerominimum stress level, the maximum stress level the concretecan support for one million cycles without failure is takenconservatively as 50 percent of the static strength As theminimum stress level is increased, the stress range that theconcrete can support decreases The linear decrease of stressrange with increasing minimum stress has been observed, atleast approximately, by many investigators

From Fig 2, the maximum stress in tension, compression,

or flexure that concrete can withstand for one million titions and for a given minimum stress can be determined.For example, consider a structural element to be designed forone million repetitions If the minimum stress is 15 percent

repe-of the static ultimate strength, then the maximum load thatwill cause fatigue failure is about 57 percent of static ultimateload

loo -“’

Fig.g2-Fatigue sionor flexure

compres-215R-4 ACI COMMITTEE REPORT

0.6 -

aen-1

O- I I III I I III I

Cycles to Failure,N

Fig 3-Influence of stress gradient

2.1.3 Load history-Most laboratory fatigue data are

ideal-ized, since in these tests the loads alternated between

con-stant minimum and maximum values Concrete in structural

members may be subjected to randomly varying loads

Cur-rently, no data are available6

showing the effect of randomloading on fatigue behavior of concrete Effects of different

values of maximum stress can be approximately, although not

always conservatively, estimated from constant stress fatigue

tests by using the Miner hypothesis.7 According to this rule,

failure occurs if Z(n,/N,) = 1, where n, is the number of

cycles applied at a particular stress condition, and NI is the

number of cycles which will cause fatigue failure at that same

stress condition

The effect of rest periods and sustained loading on the

fatigue behavior of concrete is not sufficiently explored

Lab-oratory tests have shown that rest periods and sustained

loading between repeated load cycles tends to increase the

fatigue strength of concrete.5 In these tests, the specimens

were subjected to relatively low levels of sustained stress If

the sustained stress level is above about 75 percent of the

static strength, then sustained loading may have detrimental

effects on fatigue life.3 This contradictory effect of creep

loading may be explained from test results which show that

low levels of sustained stress increase the static strength,

whereas high levels of sustained stress resulted in increased

microcracking and failure in some cases

2.1.4 Rate of loading-Several investigations indicate that

variations of the frequency of loading between 70 and 900

cycles per minute have little effect on fatigue strength

pro-vided the maximum stress level is less than about 75 percent

of the static strength.8 For higher stress levels, a significant

influence of rate of loading has been observed.9 Under such

conditions, creep effects become more important, leading to

a reduction in fatigue strength with decreasing rate of

loading

2.1.5 Material properties-The fatigue strength for a life of

10 million cycles of load and a probability of failure of 50percent, regardless of whether the specimen is loaded in com-pression, tension, or flexure, is approximately 55 percent ofthe static ultimate strength Furthermore, the fatigue strength

of mortar and concrete are about the same when expressed

as a percentage of their corresponding ultimate staticstrength.10’ Many variables such as cement content, water-cement ratio, curing conditions, age at loading, amount ofentrained air, and type of aggregates that affect staticultimate strength also influence fatigue strength in a similarproportionate manner.ll

2.1.6 Stress gradient-Stress gradient has been shown to fluence the fatigue strength of concrete Results of test12 on

in-4 x 6 x 12 in (102 x 152 x 305 mm) concrete prisms under peated compressive stresses and three different straingradients are shown in Fig 3 The prisms had a compressivestrength of about 6000 psi (41.4 MPa) They were tested at

re-a rre-ate of 500 cpm re-at re-ages vre-arying between 47 re-and 77 dre-ays

For one case, marked e = 0, the load was applied

concen-trically, producing uniform strain throughout the cross tion To simulate the compression zone of a beam, load was

sec-applied eccentrically in the other two cases, marked e = % in (8.5 mm) and e = 1 in (25.4 mm) The loads were applied

such that during the first cycle of fatigue loading the mum strain at the extreme fiber was the same for all threesets of specimens For the two eccentrically loaded cases, theminimum strain was zero and half the maximum strain, re-

maxi-spectively The stress level, S, was defined as the ratio of the

extreme fiber stress to the static compressive strength f,‘ Theextreme fiber stress in eccentrically loaded specimens was de-termined from static stress strain relationships and the maxi-mum strain at the extreme fiber as observed during the firstcycle of fatigue loading

From the mean S-N curves shown in Fig 3, it can be seen

that the fatigue strength of eccentric specimens is 15 to 18percent higher than that for uniformly stressed specimens for

a fatigue life of 40,000 to l,OOO,OOO cycles These results are

in accord with the results of static tests where it was shownthat the strain gradient retards internal microcrack growth.13

For the purpose of design of flexural members limited byconcrete fatigue in compression, it is safe to assume thatfatigue strength of concrete with a stress gradient is the same

as that of uniformly stressed specimens

2.1.7 Mechanism of fatigue fracture-Considerable research

is being done to study the nature of fatigue failure in crete 1-4,14-17

con-Researchers have measured surface strains,changes in pulse velocity, internal microcracking and surfacecracking to understand the phenomenon of fracture It hasbeen observed that fatigue failure is due to progressive inter-nal microcracking As a result, large increase in both the lon-gitudinal and transverse strains and decrease in pulse velocityhave been reported preceding fatigue failure External surfacecracking has been observed on test specimens long beforeactual failure

Progressive damage under fatigue loading is also indicated

by reduction of the slope of the compressive stress-straincurve with an increasing number of cycles In addition to in-

FATIGUE LOADING DESIGN CONSIDERATIONS 21 5R-5

S t r a i n x 106

Fig 4-Effect of repeated load on concrete strain

Fig 5-Fatigue fracture of a reinforcing bar

ternal microcracking, fatigue loading is also likely to cause

changes in the pore structure of the hardened cement paste

Creep effects must also be considered They become more

significant as the rate of loading decreases

2.1.8 Concrete strain-Similar to the behavior of concrete

under sustained loads, the strain of concrete during repeated

loading increases substantially beyond the value observed

after the first load application,2 as shown in Fig 4 The strain

at fatigue failure is likely to be higher if the maximum stress

is lower

2.2-Reinforcing bars*

2.2.1 General-Fatigue of steel reinforcing bars has not

been a significant factor in their application as reinforcement

in concrete structures However, the trend in concrete

struc-tures toward use of ultimate strength design procedures and

higher yield strength reinforcement makes fatigue of

rein-forcing bars of more concern to designers It is noteworthy,

though, that the lowest stress range known to have caused a

fatigue failure of a straight hot-rolled deformed bar

em-bedded in a concrete beam is 21 ksi (145 MPa) This failure

occurred after 1,250,000 cycles of loading on a beam

con-taining a #ll, Grade 60 test bar, when the minimum stress

level was 17.5 ksi (121 MPa).26

A typical fatigue fracture of a reinforcing bar is shown inFig 5 This is also a #ll, Grade 60 bar which at one timewas embedded in a concrete beam that was subjected to re-peated loads until the bar failed In this figure, the orien-tation of the bar is the same as it was in the beam; thebottom of the bar was adjacent to the extreme tensile fibers

in the beam The smoother zone, with the dull, rubbed pearance, is the fatigue crack The remaining zone of morejagged surface texture is the part that finally fractured intension after the growing fatigue crack weakened the bar It

ap-is noteworthy that the fatigue crack did not start from thebottom of the bar Rather it started along the side of the bar,

at the base of one of the transverse lugs This is a commoncharacteristic of most bar fatigue fractures

Quite a number of laboratory investigations of the fatiguestrength of reinforcing bars have been re

years from the United States,18-26 Canada, !?

orted in recentand Japan.35-39

7;28 Europe,29-34

In most of these investigations, the ship between stress range, S,, and fatigue life, N, was deter-mined by a series of repeated load tests on bars which wereeither embedded in concrete or tested in air

relation-There is contradiction in the technical literature as towhether a bar has the same fatigue strength when tested inair or embedded in a concrete beam In an investigation31 ofhot-rolled cold-twisted bars, it was found that bars embedded

in beams had a greater fatigue strength than when tested inair However, in another investigation,29 the opposite conclu-sion was reached More recent Studies28,32 indicate that thereshould be little difference in the fatigue strength of bars inair and embedded bars if the height and shape of the trans-verse lugs are adequate to provide good bond between thesteel and concrete

The influence of friction between a reinforcing bar andconcrete in the vicinity of a crack has also been considered.32

In laboratory tests, an increase in temperature is frequentlyobserved at the location where the fatigue failure occurs.However, rates of loading up to several thousand cycles perminute and temperatures up to several hundred degrees Care normally not considered to have a significant effect onfatigue strength.400In a statistical analysis41 of an inves-tigation of reinforcing bars,266differences in fatigue strengthdue to rates of loading of 250 and 500 cycles per minute werenot significant

It is therefore believed that most of the data reported ininvestigations in North America and abroad is directly com-parable, even though it may have been obtained under quitedifferent testing conditions

A number of S,-N curves obtained from tests on concretebeams containing straight deformed bars made in NorthAmerica18,21,24-28

are shown in Fig 6 These curves are forbars varying in size from #5 to #ll, with minimum stresslevels ranging from -0.10 to 0.43 of the tensile yield strength

215R-6 ACI COMMITTEE REPORT

Cycles to Failure, N, millions

Fig 6-Stress range-fatigue life curves for reinforcing bars

6, they include the highest and lowest fatigue strength The

varying characteristics of these curves suggest that there are

many variables in addition to stress range that influence the

fatigue strength of deformed reinforcing bars

Most of the curves in Fig 6 show a transition from a

steeper to a flatter slope in the vicinity of one million cycles,

indicating that reinforcing bars exhibit a practical fatigue

limit Fatigue strengths associated with the steeper or flatter

part of the S,-N curves will be referred to as being in the

finite life or long life region, respectively Because of the lack

of sufficient data in the long life region, it is noted that many

of the S,-N curves in this region are conjectural

The fatigue strength of the steel in reinforcing bars

de-pends upon chemical composition, microstructure, inclusions,

and other variables.40 0However, it has been shown26,28 that

the fatigue strength of reinforcing bars may be only one-half

of the fatigue strength of coupons machined from samples of

the bars In addition, reinforcing bar specifications are based

on physical characteristics Consequently, the variables related

to the steel composition are of limited concern to practicing

structural engineers The variables related to the physical

characteristics and use of the reinforcing bars are of greater

concern The main variables that have been considered in the

technical literature are:

Each of these is discussed in the following sections

2.2.2 Minimum stress-In several investigations,18,21,29 it has

been reported that the fatigue strength of reinforcing bars is

relatively insensitive to the minimum stress level However,

in two recent investigations,26,28 it was concluded that

mini-mum stress level does influence fatigue strength to the extent

approximately indicated by a modified Goodman diagramwith a straight line envelope This indicates that fatiguestrength decreases with increasing minimum stress level inproportion to the ratio of the change in the minimum stresslevel to the tensile strength of the reinforcing bars

2.2.3 Bar size and type of beam-These two factors are lated because bars embedded in concrete beams have a stressgradient across the bar In design, it is only the stress at themidfibers of the bar that is generally considered Large bars

re-in shallow beams or slabs may have a significantly higherstress at the extreme rather than the midfibers of the bar.The effect of bar size is examined in Table 1 using datafrom three investigations 28y32P36 Since #8 bars or their equi-valent were tested in each of these investigations, the fatiguestrength of other bar sizes was expressed as a ratio relative tothe fatigue strength of the #8 bars For each comparison, thebars were made by the same manufacturer, and they alsowere tested at the same minimum stress level The fatiguestrength is the stress range causing failure at 2 million ormore cycles

The tests reported in Reference 32 were on bars subjected

to axial tension Therefore, there was no effect of straingradient in this data, yet the fatigue strength of the #5 barswas about 8 percent greater than that of the #8 bars.Tests in Reference 28 were on bars in concrete beams.The strain gradients in these beams resulted in stresses at theextreme fibers for the different size bars that were about thesame Still, an effect of bar size was found that was of aboutthe same order of magnitude

In the tests in Reference 36 the strain gradient was greateracross the #8 bars than the #6 bars Therefore, part of thedifference in fatigue strength should be attributed to thehigher stress at the extreme fibers of the #8 bars However,the differences, compared to the other test results, are aboutthe same

Table l-Effect of bar size

Fatigue strength relative to Tests

Gr:*de fatigue strength of No 8 barsreported

in I bar I No 5 I INo 6 No 8 I No 1 0 Reference 28

,~~~~~

-FATIGUE LOADING DESIGN CONSIDERATIONS 215R-7

In another investigation26,411where both bar size and type

of beam were controlled variables, the former was found to

be significant and the latter was not significant This

inves-tigation included bars of 5 different sizes-#5, 6, 8, 10, and

ll-made by a major United States manufacturer These bars

were embedded in rectangular or T-shaped concrete beams

having effective depths of 6, 10, or 18 in (152, 254, or 457

mm) In this investigation, the fatigue life of #8, Grade 60

bars subjected to a stress range of 36 ksi (248 MPa) imposed

on a minimum stress of 6 ksi (41.4 MPa) was 400,000 cycles

Under identical stress conditions, the fatigue life of the #5,

6, 10, and 11 bars were found to be 1.22, 1.30, 0.76, and 0.85

times the life of the #8 bars, respectively This trend is the

same as that for the data shown in Table 1 The irregular

var-iation was attributed to differences in surface geometry

2.2.4 Geometry of deformations-Deformations on

rein-forcing bars provide the means of obtaining good bond

be-tween the steel and the concrete However, these same

defor-mations produce stress concentrations at their base, or at

points where a deformation20,21,23 intersects another

defor-mation or a longitudinal rib These points of stress

concen-trations are where the fatigue fractures are observed to

initiate

Any evaluation of the influence of the shape of the

deformations on fatigue properties of the bar must recognize

that the rolling technique and the cutting of the rolls

nec-essarily requires specific limitations and variations in the

pattern This applies to the height of the deformations, the

slopes on the walls of the deformations, and also to the fillets

at the base of the deformations

An analytical study42 has shown that stress concentration

of an external notch on an axially loaded bar may be

appreci-able This study indicated that the width, height, angle of rise,

and base radius of a protruding deformation affect the

mag-nitude of the stress concentration It would appear that many

reinforcing bar lugs may have stress concentration factors of

1.5 to 2.0

Tests on bars having a base radius varying from about 0.1

to 10 times the height of the deformation have been

re-ported.25,26,28,36 These tests indicate that when the base radius

is increased from 0.1 to about 1 to 2 times the height of the

deformation, fatigue strength is increased appreciably An

increase in base radius beyond 1 to 2 times the height of the

deformation does not show much effect on fatigue strength

However, Japanese tests366have shown that lugs with radii

larger than 2 to 5 times the height of the deformation have

reduced bond capacity

Tests have indicated30,31,39 that decreasing the angle of

in-clination of the sides of the deformations with respect to the

longitudinal axis increases the fatigue strength of a

rein-forcing bar This increase occurs for bars with lugs havin

abrupt changes in slope at their bases It has been noted4Q

that the base radius should be determined in a plane through

the longitudinal axis of the bar, since this is the direction of

the applied stress The base radius determined in this plane

will be substantially larger than a base radius determined in

a plane perpendicular to a sharply inclined lug

In two experimental investigation,23,34 it was found that

the condition of the rolls, whether new or worn, had littleeffect on fatigue strength However, a conflicting opinion hasbeen ex

‘:ressed in Reference 32.

Tests 2 also show a substantial effect on the fatigue tance of reinforcing bars due to brand marks The brandmarks cover the identification of the bar as to size, type ofsteel (billet, rail, or axle), mill that rolled the steel, and yieldstrength (Grade 40, 60, or 75).44 The stress concentration at

resis-a bresis-ar mresis-ark is similresis-ar to thresis-at cresis-aused by bresis-ar deformresis-ations

It has also been demonstrated24 that the fatigue strength

of a reinforcing bar may be influenced by the orientation ofthe longitudinal ribs In that study, an increased fatigue lifewas obtained when the longitudinal ribs were oriented in ahorizontal position rather than a vertical position This phe-nomenon is apparently associated with the location at whichthe fatigue crack initiates In other words, if there is aparticular location on the surface of a bar which is morecritical for fatigue than other locations, then the positioning

of that location in the beam will influence the fatiguestrength

2.2.5 Yield and tensile strength -In three

investiga-tions 921,27,28the fatigue strength of different grades44 of barsmade by the same North American manufacturer were com-pared The results of these comparisons, all of which are inthe long life region of fatigue life, are shown by the bargraphs in Fig 7 It was concluded in References 21 and 28that the fatigue strength of the bars was relatively insensitive

to their yield or tensile strength References 21 and 28 clude 157 and 72 tests, respectively Reference 27, whichincludes 19 tests, indicated that fatigue strength may be pre-dicted for grade of steel as a function of the stress range

in-4 0

0 Grade 4 0 6 0 75 4 0 6 0 7 5 40 75 40 75

Smln 0 Ify 0 3fy 0 Ify 0 3fy

M a n u f a c t u r e r A A B B

a) Data from Reference 21 , No.8 Bars

N q 2 million cycles

0 Grade 40 6075

S m m 025fy b) Data from Reference 27, No 5 Bars

‘r 20 ksi 0

N = 5 million cycles

Grade 40 60 75 4060 75 40 6075 40 60 75

S min 0 Ify 0 4fy 0 Ify 0 Ify Size N o 8 No 8 No 5 No 10

c) Data from Reference 28

Fig 7-Effect of grade of bar

ACI COMMITTEE REPORT

In another investigation26,41 on bars made by a major

United States manufacturer, the fatigue life of Grade 40,

Grade 60, and Grade 75 #8 bars, subjected to a stress range

of 36 ksi (248 MPa) imposed on a minimum stress of 6 ksi

(41.4 MPa), varied linearly in the ratio of 0.69 to 1.00 to 1.31,

respectively The ratio of 1.0 corresponds to a fatigue life of

400,000 cycles, and is therefore in the finite life region

Axial tension fatigue tests32 on unembedded reinforcing

bars made in Germany were carried out on four groups of

bars having yield strengths of 49, 53, 64, and 88 ksi (338,365,

441, and 607 MPa) All of the bars were rolled through the

same stand for elimination of variation in the deformed

sur-faces When tested with a minimum stress level of 8.5 ksi

(58.6 MPa), the stress ranges causing failure in two million

cycles were determined to be 28, 28,28, and 31 ksi (193, 193,

193, and 214 MPa), respective1 .

In a Japanese investigation,Z6 bars of the same size and

made by the same manufacturer but with yield strengths of

50, 57, and 70 ksi (345,393, and 483 MPa) were tested The

stress range causing failure in two million cycles was between

30 and 31.5 ksi (207 and 217 MPa) for all three groups of

bars

2.2.6 Bending-The effect of bends on fatigue strength of

bars has been considered in two investigation.21,29 In the

North American investigation,21 fatigue tests were carried out

on both straight and bent #8 deformed bars embedded in

concrete beams The bends were through an angle of 45 deg

around a pin of 6 in (152 mm) diameter The fatigue

strength of the bent bars was a little more than 50 percent

below the fatigue strength of the straight bars In one test, a

bent bar embedded in a reinforced concrete beam failed in

fatigue after sustaining 900,000 cycles of a stress range of 18

ksi (124 MPa) imposed on a minimum stress of 5.9 ksi (40.7

MPa) In another test, application of 1,025,000 cycles

pro-duced a failure when the stress range and minimum stress

were 16.4 ksi and 19.1 ksi (113 and 132 MPa), respectively

Tests29 have also been reported from Germany on both

plain and deformed hot-rolled bars bent through an angle of

45 deg However, these bars were bent around a pin having

a diameter of 10 in (254 mm) Compared to tests on straight

bars, the fatigue strength of the plain bars was reduced 29

percent by the bend, while the fatigue strength of the

de-formed bars was reduced 48 percent

2.2.7 Welding-In an investigation24 using Grade 40 and

Grade 60 reinforcement with the same deformation pattern,

it was found that the fatigue strength of bars with stirrups

attached by tack welding was about one-third less than bars

with stirrups attached by wire ties The results of the tests on

the Grade 60 reinforcement are shown in Fig 8 For both

grades of steel, the fatigue strength of the bars with tack

welding was about 20 ksi (138 MPa) at 5 million cycles All

of the fatigue cracks were initiated at the weld locations It

should be cautioned that tack welds that do not become a

part of permanent welds are prohibited by AWS D1.4109

un-less authorized by the Engineer Full penetration welds are

permitted by AWS D1.4

Investigations 19,22 have also been carried out to evaluate

the behavior of butt-welded reinforcing bars in reinforced

8 0

6 0

Stress Range

I

4 0.1

I 1.0

Cycles to Failure,N, millions

Stress Range

S, MPa

Fig 8-Effect of tack welding stirrups to Grade 60 bars

concrete beams In tests conducted at a minimum stress level

of 2 ksi (13.8 MPa) tension, the least stress range that duced a fatigue failure was 24 ksi (165 MPa) It was observedthat minimum stress level in the butt-welded joint was not asignificant factor affecting the fatigue strength of the beams

pro-2.3Welded wire fabric and bar mats*

Welded wire fabric may consist of smooth or deformedwires while bar mats usually consist of deformed bars Oftenfabric and bar mats are not used in structures subject to sig-nificant repeated loads because of concern that the weldedintersections will create significant stress concentrations Thisfeeling has been heightened by experience from abroad45 andthe relatively poor performance of smooth wire fabric in con-tinuously reinforced concrete pavements.46,47,48 In some cases,pavements reinforced with this fabric performed adequately

in service for 3 to 5 years Then several wide cracks occurred,necessitating extensive repairs While most of this crackingwas caused b

Y inadequate detailing of splices, field studies inConnecticut4

have revealed failures at the welds in a cant number of instances

signifi-Any assessment of welded wire fabric or bar mats basedprimarily on their performance in pavements is unrealistic Inany given length of pavement, wide variations are possible inthe stress spectrum for the reinforcement The average stresslevel in the reinforcement is strongly dependent on the pave-ment’s age, its thermal and moisture history, and the longi-tudinal restraint offered by the subgrade The stress range inthe reinforcement caused by the traffic depends on the sup-port offered by the subgrade as well as the magnitude of theloading

Several recent investigations have examined the fatiguecharacteristics of fabric and bar mats in air.45,48,49 For smoothwire fabric45,499the disturbance due to the welded intersectiondominated over all other influences, so that failures wereconfined to the heat affected zone of the weld For bar mats,the disturbance due to the welded intersection dominatedonly if the stress concentration caused by the intersection wasgreater than the concentration caused by the deformation.The available evidence does not indicate that these effects

* Dr Neil M Hawkins prepared this section of the report.

FATIGUE LOADING DESIGN CONSIDERATIONS 215R-9

Stress

Sr ,ksi

- 276 Stress Range

S, MPa

Fig 9-Median S,-N curves for welded reinforcing mats

are additive

Results for “cross-weld” tests conducted in air are

summarized in Fig 9 In the German investigation45 15 tests

were made on a smooth wire fabric consisting of 0.236 in (6

mm) diameter wires welded to 0.315 in (8 mm) diameter

wires

In one American investigation49 59 “cross-weld” tests were

made on a 2 x 2-6 x 6 (0.263 in or 6.7 mm diameter) smooth

wire fabric, and in the other investigation48 22 “cross-weld”

tests and 30 between weld tests were made on #5 Grade 60

deformed bars with #3 deformed bars welded to them

The University of Washington49 investigation was intended

to provide a statistically analyzable set of test data for three

stress ranges It was observed that when the penetration

across the weld was less than one-tenth of the diameter of

the wire, there was incomplete fusion of the wires and the

formation of a cold joint For a greater penetration, the

molten metal squirted into the intersection between the wires

causing a marked stress concentration so that the fatigue life

for a hot joint was about half that for a cold joint The result

shown in Fig 9 is the median fatigue life value for the

pene-tration considered as a random variable In those tests the

fatigue life values for a given stress range and a 95 percent

probability of survival exceeded the life values obtained in

tests on high yield deformed bars.25 In the tests48 on the bar

mats it was found that the welded intersection reduced the

fatigue life for a given range by about 50 percent throughout

the short life stress range

Tests on slabs reinforced with smooth wire mats have been

reported in References 49 and 50 The results are

summar-ized in Fig 10, where it is apparent that there is reasonable

correlation between the two sets of data In the Illinois test,50

the 12 in (305 mm) wide, 60 in (1.52 m) long slabs were

re-inforced with #0 gage wires longitudinally with #8 gage wires

welded to them at 6 or 12 in (152 or 305 mm) spacings

In the University of Washington tests,49 the 54 in (1.37 m)

square slabs were reinforced with two layers of the same 2 x

2-6 x 6 fabric as that tested in air In the slab tests, it was

observed that there was a rapid deterioration of the bond

be-tween the smooth wires and the concrete under cyclic

load-ing, so that after 104 cycles of loading, all anchorage was

pro-vided primarily by the cross wires Fatigue life values for

frac-ture of the first wire in those slabs could be predicted using

6 0 t

Fig IO-A’,-N curves for slabs containing mats

the results for the wire tested in air and a deterministicassessment of the appropriate probability based on the num-ber of approximately equally stressed welds in the slab Theappropriate probability level for these slabs was about 98percent, indicating a need for a design approach for weldedreinforcing mats based on a probability of survival greaterthan the 95 percent commonly accepted for reinforcing barsand concrete

The fatigue life values for collapse were about doublethose for fracture of the first wire The values for collapsecould be predicted from the results of the tests conducted inair using a deterministic procedure for assessment of the ap-propriate probability level and Miner’s theory7

to predictcumulative damage effects

A comparison of the S-N curves for wire fabric and bar

mats with those for deformed bars indicates that an ance limit may not be reached for the fabric and mats untilabout 5 x 106 c cles, whereas a limit is reached for the bars

endur-at about 1 x 10Jcycles However, the total amount of dendur-ata inthe long life range for fabric and mats is extremely limitedand insufficient for reliable comparison

2.4-Prestressing tendons*

2.4.1 General -If the precompression in a prestressed crete member is sufficient to &sure an u&racked sectionthroughout the service life of the member, the fatigue char-acteristics of the prestressing steel and anchorages are notlikely to be critical design factors Further, in a properlydesigned unbonded member, it is almost impossible toachieve a condition for which fatigue characteristics areimportant.51 Consequently, fatigue considerations have notbeen a major factor in either the specification of steel forprestressed concrete52 2 or the development of anchoragesystems

con-No structural problems attributable to fatigue failures of

ACI COMMITTEE REPORT

the prestressing steel or anchorages have been reported in

North America However, in the near future fatigue

consider-ations may merit closer scrutiny due to:

1 The acceptance of designs53 which can result in a

con-crete section cracked in tension under loads, and

2 The increasing use of prestressing in marine

environ-ments, railroad bridges, machinery components, nuclear

reactor vessels, railroad crossties, and other structures

subject to frequent repeated loads which may involve

high impact loadings or significant overloads

In the United States, the growing concern with the fatigue

characteristics of the prestressing system is reflected in

sev-eral design recommendations developed recently As a

mini-mal requirement appropriate for unbonded construction,

ACI-ASCE Committee 423,54ACI Committee 301,55 and the

PCI Post-Tensioning Committees56 have recommended that

tendon assemblies consisting of prestressing steel and

anchorages be able to withstand, without failure, 500,000

cycles of stressing varying from 60 to 66 percent of the

specified ultimate strength of the assembly Abroad,

stan-dards specifying fatigue characteristics for the tendons have

been published in German57 and Japan.58

This report does not consider conditions where unbonded

prestressing steels and their anchorages are subjected to high

impact, low cycle, repeated loadings during an earthquake

ACI-ASCE Committee 42354 and the PCI Post-Tensioning

Committee56 have developed design recommendations for

that situation

Many factors can influence the strength measured in a

fatigue test on a tendon assembly The tendon should be

tested in the “as delivered” condition and the ambient

tem-perature for a test series maintained with t 3 F (_’ 1.7 C)

The length between anchorages should be not less than 100

times the diameter of the prestressing steel, eight times the

strand pitch or 40 in (1.02 m) Test conditions must not

cause heating of the specimen, especially at the anchorages,

so that a frequency of 200 to 600 cpm is desirable.59

Many variables affect the fatigue characteristics of the

pre-stressing system Within commercially available limits, the

de-signer can specify the following:

1 Type of prestressing steel (wire, strand, or bar)

2 Steel treatment

3 Anchorage type

4 Degree of bond

Seven-wire strand was developed in the United States,

while most other prestressing systems are of European origin

Therefore, in the United States, attention has been focused

mainly on the fatigue characteristics of seven-wire strand

Recent data on the fatigue characteristics of foreign systems

has been summarized by Baus and Brenneisen.59

2.4.2 Type of prestressing steel-Prestressing steels can be

classified into three basic types: wire, strand, and bars Wires

are usually drawn steels and strands are manufactured from

wires Bars are usually hot-rolled alloy steels Wires are

usu-ally made from a steel whose principal alloying componentsare about 0.8 percent carbon, 0.7 percent manganese, and0.25 percent silicon Hot-rolled alloy steels contain about 0.6percent carbon, 1.0 percent manganese and 1.0 percentchromium Typically, hot-rolled steels have a tensile strength

of 160 ksi (1100 MPa) while drawn wires have strengthsranging between about 250 and 280 ksi (1720 and 1930 MPa).Drawing increases the tensile strength of the wire It pro-duces a grain structure which inhibits crack nucleation andprovides a smooth surface which reduces stress concentra-tions Consequently, the fatigue strengths of wires for a givennumber of cycles are higher than those of rolled steels.However, the differences are small for stress ranges expressed

as percentages of the ultimate tensile strengths

Wires-Wires of United States manufacture conform to

ASTM Designation: A 421,60 “Specifications for UncoatedStress Relieved Wire for Prestressed Concrete.” This speci-fication covers plain wires only Ribbed varieties are incommon use abroad The fatigue characteristics of wires varygreatly with the manufacturing process, the tensile strength

of the wire, and the type of rib In Fig 11, fatigue strengthsare shown for 2 x 106 cycles for tests performed in Germany,Czechoslovakia, and Belgium,59 and Japan.* The solid circle

in Fig 11 is the result of a limited series of tests on 0.25 in.(6.3 mm) diameter wires of United States manufacture.61

These tests showed a fatigue strength at 4 x 106 cycles inexcess of 30 ksi (207 MPa) The squares are results for tests

on 4 and 5 mm (0.157 and 0.197 in.) diameter wires formed by the Shinko Wire Company

per-Also shown in Fig 11 are likely ranges in stress for bondedbeams designed in accordance with the ACI Code The lowervalue is about the maximum possible when the tensile stress

Stress Range , Percent

Tensile Strength

0

5 0 6 0 7 0 Minimum Stress

Tensile Strength * Percent

Fig 11-Fatigue strength at two million cycles for wires

* Personal communication from Dr A Doi, Shinko Wire Co., Ltd Amagasaki, Hyogo,

Japan

FATIGUE LOADING DESIGN CONSIDERATIONS 21 5R-1 1

Fig 12-Data for United States made seven-wire strand

II -l

Stress 20 t

”

5 0 6 0 7 0 Minimum Stress

Tensile Strength , Percent

- - - B e l g i u m - W i r e

Belgium -Strand

- * - * - R u s s i a -*** ***-U.S.A.-Warner -** - U.S.A.-Tide 8 Van Horn

*U.S.A.-Hilmes

0 Jopcrn-3 Wires

Fig 13-Fatigue strength at two million cycles for prestressing

strand

in the precompressed zone is limited to m psi (OSC

MPa) (1.q kgf/cm2), so that the section is uncracked The

upper value is about the maximum possible when the tensile

stress is limited to 12fl psi (l.Oc MPa) (3.18fl kgf/cm2)

so that the section may contain a crack as wide as 0.005 in

(0.125 mm) It can be seen that although the characteristics

of wires vary widely, all could probably be justified for use

with a limiting stress of 12c psi (l.Oc MPa)

In Czechoslovakia, tests on plain wires of 3,4.5, and 7 mm

(0.076, 0.114, and 0.127 in.) diameter have shown that within

5 percent, the fatigue characteristics of these wires were

inde-pendent of the wire diameter

The effects of ribbing and indentations on fatigue

charac-teristics have been studied in Great Britain,62 Germany59

Russia,59 and Japan.633These tests have shown that the acteristics depend on the height of the rib, its slope and, most

char-of all, the sharpness char-of the radii at the base char-of the rib With

a 0.3 mm (0.012 in.) rib height, a 45 deg slope, and no radius

at the base of the rib, the theoretical stress concentrationfactor was 2.0, and there was a 57 percent reduction in thefatigue strength.59gThis reduction decreased with a decreasingstress concentration factor until for the same rib height ob-tained using a circular cut out of 10 mm (0.4 in.) radius, thestress concentration factor was 1.36, and there was no reduc-tion in the fatigue strength Wires crimped62 with a pitch of

2 in (51 mm) and a crimp height of at least 15 percent of thewire diameter in the unstressed condition, showed a fatiguestrength 20 percent lower than that of the plain wire

Strand-Strands of United States manufacture up through0.6 in (15.24 mm) diameter conform to ASTM A 41664 “Spe-cifications for Uncoated Seven Wire Stress-Relieved Strandfor Prestressed Concrete.” This specification covers strandused for prestressing in the United States, and foreign sup-pliers conform to these requirements In the United States,several series of tests65-69 have been made on seven-wirestrand of either 7/16 or l/2 in (11.1 or 12.7 mm) diameter.Fatigue data compiled from these studies68 are shown in Fig

12 These data are shown along with data obtained from tests

on Russian,59 Belgian,59 and Japanese63 strand, in Fig 13.The Japanese tests633indicated by squares were conducted

on 3 mm (0.118 in.) diameter plain wires Tests on similarsize strand made from deformed wires showed strengthsabout 15 percent lower Comparison of Fig 11 and 12 andthe results of the Belgian tests indicate the stress rangesavailable with strand are less than those for wire The UnitedStates and Russian tests indicate a decrease in fatiguestrength with increasing size for the wires in the strand.Several writers59 have hypothesized that for strands the suc-cessive lengthening and shortening of the cables produces al-ternating tensions in the individual wires Failures initiatewhere the neighboring wires rub together under this alter-nating load

Bars-Bars of United States manufacture conform to therequirements of the PCI Post-Tensioning Committee Al-though fatigue tests on such bars have been made (Personalcommunication from E Schechter, Stressteel Corp., Wilkes-Barre, Pa.), most published information is for European barsless than 0.7 in (18 mm) in diameter Bars manufactured inthe United States range between % and 13/8 in (19 and 35mm) in diameter Tests on bars ranging between 1 and 1% in.(25 and 35 mm) in diameter have shown that the fatiguelimits of these bars are in excess of 0.1 times the tensilestrength of the bar for 1 x 106 cycles of loading at a minimumstress of 0.6 times the tensile strength As with other post-tensioning systems, the characteristics of the anchorage andnot the prestressing system control the fatigue characteristics

of the unbonded tendon

German and Russian tests59 have shown that the fatiguecharacteristics for their bars, expressed as a percentage oftheir ultimate tensile strength, are similar t o those of theirstrand Tests in Russia on bars with tensile strengths of about

215R-12 ACI COMMITTEE REPORT

150 ksi (1030 MPa) have shown the fatigue characteristics to

be independent of bar size for bar diameters ranging between

0.4 and 0.7 in (10 and 18 mm) In Great Britain tests70 have

been made on bonded and unbonded beams post-tensioned

with l/2 in (12.7 mm) diameter bars anchored by nuts on

tapered threads There were no fatigue failures of either the

bar or the anchorage for 2 x 106 cycles of a loading for which

the stress range in the bonded bar was about 12 ksi (83 MPa)

at a minimum stress equal to at least 60 percent of the bar’s

static strength

2.4.3 Statistical considerations-Reliable design information

requires the collection of the test data in such a manner that

statistical methods can be used to define the properties of the

material and to investigate the effects of differing

parame-ters 71,72 At least six and preferably 12 tests are necessary at

each stress level to establish fatigue strengths for survivals

ranging from 90 to 10 percent To establish the finite-life part

of the S-N diagram for a constant minimum stress, tests

should be made-at a minimum of three stress levels, one near

the static strength, one near the fatigue limit, and one in

between Special techniques are needed to establish the

fatigue limit

The overall scatter of fatigue data is of paramount

impor-tance in defining the quality of the prestressing steel For

United States strand, a modified Goodman diagram has been

developed by Hilmes and Ekberg68 for three discrete

proba-bility levels As shown in Fig 14, these levels correspond to

survival probabilities of 0.1, 0.5, and 0.9, and they were

developed from data with minimum stress levels of 0.4, 0.5,

and 0.6 times the static tensile strength For the desired

minimum stress and probability level, vertical intercepts

within Fig 14 define permissible stress ranges for failure for

strands tested in the United States at 5 x 106, 1 x 106, 5 x 106,

2 x 105, 1 x 105, and 5 x 104 cycles

2.4.4 Steel treatment-While all United States prestressing

steels are stress-relieved, some of those manufactured abroad

are not Czechoslovakian and Russian tests59 have shown that

stress relieving increases the fatigue limit significantly For

applications external to a member, the prestressing steel is

sometimes protected by hot dip galvanizing Galvanizing can

Smin

f PU

Fig 14-Strength envelopes for strand tested in United States

result in hydrogen embrittlement73 and therefore its use instructures where fatigue is a consideration is not recom-mended For wires and strand, galvanizing reduces the ulti-mate and yield strength significantly and therefore also re-duces the fatigue limit For bars, galvanizing does not alterthe static properties, but it does reduce the fatigue limit

2.4.5 Anchorage type -For unbonded construction, stresschanges in the prestressing steel are transmitted directly tothe anchorage Although most anchorages can develop thestatic strength of the prestressing steel, they are unlikely todevelop its fatigue strength Further, bending at an anchoragecan cause higher local stresses than those calculated from thetensile pull in the prestressing steel Bending is likely wherethe prestressing steel is connected to the member at a fewlocations only throughout its length or where there is angu-larity of the prestressing steel at the anchorage Fatiguecharacteristics based on tests of single wire or strand anchor-ages are likely to overestimate the strength of multi-wire ormultistrand anchorages

Tests on single wire anchorages have been conducted inthe United States,611Great Britain (Test reports supplied byA.H Stubbs, Western Concrete Structures, Inc., Los Angeles,CA), Japan and Switzerland.599The types of anchorages testedand the results are shown in Fig 15 In each case the ratio ofthe minimum stress to the nominal tensile strength of thewire was about 0.6 The broken line indicates the fatiguecharacteristics of the wire used in the Japanese tests, asestimated from the results of rotating beam tests It cor-responds also to the fatigue characteristics of the weakestwire in Fig 11

All anchorages shown in Fig 15 developed the fullstrength of the wire for static loading However, mostresulted in a fatigue strength for the tendon of less than 50percent of the fatigue strength of the wire The exceptionsare the conical anchorages for the Swiss, British, andAmerican wires If failures did not occur due to the fatigueloading, the static strength was not impaired In the case ofthe American wire, five specimens out of seven took morethan 107 cycles of the stress range shown without failure Thelowest life was 3.5 x 106 cycles for a specimen which failed atthe button head fillets

For the Swiss and British wires, ranges are shown on thebar charts in Fig 15 to indicate the variation in results fordifferent characteristics for the button head The character-istics of a button head are influenced by the wire cutoffmethod, the type of heading equipment, the geometric char-acteristics of the head, the properties of the seating block,and the type of wire Successive improvements have led tobutton heads showing no failures even after 107 cycles of astress range equal to 0.13 times the tensile strength at anaverage of 0.6 times this strength British tests on 0.276 in (7mm) diameter button-headed wires have shown that defects

in the button head have little effect on the fatigue strength.For a wire with an ultimate tensile strength of 244 ksi (1680MPa) tested at an average stress of 0.6 times that strength,the stress range for 2 x 106 cycles dropped from 0.15 timesthe tensile strength for a defect free head to a minimum of0.12 times that strength for a diagonal split in the head In