215r_74 Fatique loading.pdf

8/18/2019 215r_74 Fatique loading.pdf

1/24

ACI 215R-74(Revised 1992/Reapproved 19

Considerations for Design of Concrete Structures

Subjected to Fatigue LoadingReported by ACI Committee 215

John M. HansonChairman

Paul W. AbelesJohn D. AntrimEarl I. Brown, IIJohn N. CernicaCarl E. Ekberg, Jr.*

Neil M. Hawkins

Hubert K. Hiisdorf

Craig A. Ballinger Secretary

Cornie L. HulsbosDon A. Linger Edmund P. Segner, Jr.Surendra P. ShahLaurence E. SvabWilliam 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. JohnstonChairman

M. ArockiasamyP.N. BalaguruMark D. BowmanJohn N. CernicaLuis F. Estenssoro

John M. Hanson Neil M. HawkinsThomas T.C. Hsu

Craig A. Ballinger Secretary

Ti HuangLambit KaldMichael E. Kreger Basile G. RabbatRaymond S. Rollings

Surendra P. ShahLuc R. TaerweWilliam 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 theChapter 2-Fatigue properties of component materials,

increase in the allowable stress range for prestressing steel from 0.04pu

to 215R-2

0.06 I; . 2.1-Plain concrete

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 matsconcrete; 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-3.1-Beams

3.2-Pavements

Chapter l-Introduction, pg. 215R-2

AC I Committee Reports, Guides, Standard Practices, andCommentaries are intended for guidance in designing, plan-

ning, executing, or inspecting construction and in preparingspecifications. 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 Documents theyshould be phrased in mandatory language and incorporatedinto the Project Documents.

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.

Al l rights reserved including rights of reproduction and use in any form or by anmeans, including the making of copies by any photo process, or by any electronic o

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.


2/24

215R-2

ACI COMMITTEE REPORT

CHAPTER l-INTRODUCTION

In recent years, considerable interest has developed in thefatigue 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 isconcern 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 docu

ment are listed below with their serial designation, includinyear of adoption or revision. These standards are the lates

effort at the time this document was revised. Since some othe standards are revised frequently, although generally onlin minor details, the user of this document may wish to checdirectly with the committee if it is correct to refer to th

members or systems, such as prestressed concrete railroad latest revision.ties and continuously reinforced concrete pavements. Theseuses 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 notcause a fatigue failure. Repeated loading may lead to inclined ASTM A 416-90cracking 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 421-90acteristics.

l.l-Objective and scope ASTM A 615-90This report is intended to provide information that will

serve as a guide for design for concrete structures subjected

to fatigue loading. ASTM 722-90However, 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.4-79concrete and reinforcing materials. This information has beenobtained from reviews of experimental investigations reportedin 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 arerecommended.

An Appendix to this report contains extracts from currentspecifications 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 referredto as static strength.

Dynamic loading varies with time in any arbitrary manner.

Fatigue and impact loadings are special cases of dynamicloading. A fatigue loading consists of a sequence of loadrepetitions 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 100cycles. These failures are sometimes referred to as low-cycle

Specifications for Structural Concrete fo

BuildingsBuilding Code Requirements for Reinforced ConcreteStandard Specification for Uncoated SeveWire Stress Relieved Steel Strand for Pre

stressed ConcreteStandard Specification for Uncoated StresRelieved Steel Wire for Prestressed ConcreteStandard Specification for Deformed anPlain Billet Steel Bars for Concrete Reinforcement

Standard Specification for Uncoated HigStrength Steel Bar for Prestressing ConcreteStructuralWelding Code-Reinforcing St

CHAPTER 2-FATIGUE PROPERTIES

OF COMPONENT MATERIALS

The fatigue properties of concrete, reinforcing bars, an prestressing tendons are described in this section. Much o

this information is presented in the form of diagrams and algebraic relationships that can be utilized for design. Howeveit is emphasized that this information is based on the resultof tests conducted on different types of specimens subjecte

to various loading conditions. Therefore, caution should bexercised in applying the information presented in this repor

2.1-Plain concrete*

2.1.1 General -Plain concrete, when subjected to repeateloads, may exhibit excessive cracking and may eventually faafter a sufficient number of load repetitions, even if the maximum load is less than the static strength of a similar specmen. The fatigue strength of concrete is defined as a fractioof the static strength that it can support repeatedly for

given number of cycles. Fatigue strength is influenced brange of loading, rate of loading, eccentricity of loading, loahistory, material properties, and environmental conditions.

* Dr. Surendra P. Shah

section of the report.

was the chairman of the subcommittee that prepared th


3/24

FATIGUE LOADING DESIGN CONSIDERATIONS 215R-3

1.0

I

icGs it_g

w

Smax

P=5~~~.

f

r Probobi i ty I

0.4 of Foilure

0’

I I

I I

I

I

0 IO 102 103 IO’ IO IO’ IO’

Cycles to Failure, N

Fig. l-Fatigue strength of plain concrete beams

Fatigue is a process of progressive permanent internal

structural change in a material subjected to repetitivestresses. These changes may be damaging and result in pro-gressive growth of cracks and complete fracture if the stressrepetitions are sufficiently large.1,2 Fatigue fracture of concrete is characterized by considerably larger strains andmicrocracking as compared to fracture of concrete under static loading.3,44Fatigue strength of concrete for a life of tenmillion 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 referredto 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 (34.5MPa) 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,Smax

to the static strength. In this case, Smax is the computedflexural tensile stress, and the static strength is the modulusof rupture stress, f The abscissa is the number of cycles tofailure, 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 beobserved that the S-N curves for concrete are approximatelylinear between 102 and 107 cycles. This indicates that con-crete does not exhibit an endurance limit up to 10 millioncycles. 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 fromtests with loads ranging between a maximum and a minimumwhich was equal to 75 and 15 percent of the maximum, re-spectively. It is evident that a decrease of the range betweenmaximum and minimum load results in increased fatigue

strength for a given number of cycles. When the minimumand maximum loads are equal, the strength of the specimen

corresponds to the static strength of concrete determineunder otherwise similar conditions.

The results of fatigue tests usually exhibit substantialllarger scatter than static tests. This inherent statistical naturof fatigue test results can best be accounted for by applyin probabilistic procedures: for a given maximum load, minimumload, and number of cycles, the probability of failure can b

estimated from the test results. By repeating this for severanumbers of cycles, a relationship between probability of failure and number of cycles until failure at a given level omaximum load can be obtained. From such relationships, S-Ncurves for various probabilities of failure can be plottedCurves a and c in Fig. 1 are averages representing 50 percen

probability of failure. Curve d represents 5 percent probabi

ity of failure, while Curve b corresponds to an 80 percenchance of failure.

The usual fatigue curve is that shown for a probability ofailure of 50 percent. However, design may be based on

lower probability of failure.

Design for fatigue may be facilitated by use of a modifieGoodman diagram, as illustrated in Fig. 2. This diagram based on the observation that the fatigue strength of plaiconcrete is essentially the same whether the mode of loadinis tension, compression, or flexure. The diagram alsincorporates the influence of range of loading. For a zerminimum stress level, the maximum stress level the concretcan support for one million cycles without failure is takeconservatively as 50 percent of the static strength. As thminimum stress level is increased, the stress range that thconcrete can support decreases. The linear decrease of stres

range with increasing minimum stress has been observed, least approximately, by many investigators.

From Fig. 2, the maximum stress in tension, compressionor flexure that concrete can withstand for one million repe

titions and for a given minimum stress can be determinedFor example, consider a structural element to be designed foone million repetitions. If the minimum stress is 15 percenof the static ultimate strength, then the maximum load thawill cause fatigue failure is about 57 percent of static ultimatload.

oo “

Fig. 2-Fatigue sionor flexure

5

80 t

E

i -

80

strength of plain concrete intension, compres-


4/24

215R-4 ACI COMMITTEE REPORT

aen-

0.6-

O

I I I I I I I I I

IO’

IO

IO6

4.10S

Cycles to Failure,N

Fig. 3 -I nf lu en ce 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 available

6showing the effect of random

loading on fatigue behavior of concrete. Effects of differentvalues of maximum stress can be approximately, although notalways conservatively, estimated from constant stress fatiguetests 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 thenumber 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 sustainedloading between repeated load cycles tends to increase thefatigue strength of concrete.5 In these tests, the specimenswere subjected to relatively low levels of sustained stress. If

the sustained stress level is above about 75 percent of thestatic strength, then sustained loading may have detrimentaleffects on fatigue life.3 This contradictory effect of creeploading 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 increasedmicrocracking and failure in some cases.

2.1.4 Rate of loading-Several investigations indicate thatvariations of the frequency of loading between 70 and 900cycles per minute have little effect on fatigue strength pro-vided the maximum stress level is less than about 75 percentof the static strength.8 For higher stress levels, a significantinfluence of rate of loading has been observed.9 Under suchconditions, creep effects become more important, leading to

a reduction in fatigue strength with decreasing rate of loading.

2 5 Material properties-The fatigue strength for a life of 10 million cycles of load and a probability of failure of 50

percent, regardless of whether the specimen is loaded in com pression, tension, or flexure, is approximately 55 percent othe static ultimate strength. Furthermore, the fatigue strengtof mortar and concrete are about the same when expressedas a percentage of their corresponding ultimate stati

strength.

10

’

Many variables such as cement content, watercement ratio, curing conditions, age at loading, amount oentrained air, and type of aggregates that affect statiultimate strength also influence fatigue strength in a simila

proportionate manner.ll

2.1.6 Stress gradient -Stress gradient has been shown to in-fluence the fatigue strength of concrete. Results of test12 on4 x 6 x 12 in. (102 x 152 x 305 mm) concrete prisms under re

peated compressive stresses and three different straigradients are shown in Fig. 3. The prisms had a compressivstrength of about 6000 psi (41.4 MPa). They were tested ata rate of 500 cpm at ages varying between 47 and 77 days.

For one case, marked e = 0, the load was applied concentrically, producing uniform strain throughout the cross section. To simulate the compression zone of a beam, load waapplied eccentrically in the other two cases, marked e =

%

in

(8.5 mm) and e = 1 in. (25.4 mm). The loads were appliesuch that during the first cycle of fatigue loading the maximum strain at the extreme fiber was the same for all thre

sets of specimens. For the two eccentrically loaded cases, thminimum strain was zero and half the maximum strain, respectively. The stress level, S , was defined as the ratio of theextreme fiber stress to the static compressive strength f,‘. Thextreme fiber stress in eccentrically loaded specimens was determined from static stress strain relationships and the maxmum strain at the extreme fiber as observed during the firscycle of fatigue loading.

From the mean S-N curves shown in Fig. 3, it can be seenthat the fatigue strength of eccentric specimens is 15 to 1

percent higher than that for uniformly stressed specimens fo

a fatigue life of 40,000 to l,OOO,OOO cycles. These results arin accord with the results of static tests where it was show

that the strain gradient retards internal microcrack growth.1

For the purpose of design of flexural members limited bconcrete fatigue in compression, it is safe to assume tha

fatigue strength of concrete with a stress gradient is the samas 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 concrete1-4,14-17

Researchers have measured surface strainschanges in pulse velocity, internal microcracking and surfaccracking to understand the phenomenon of fracture. It ha

been observed that fatigue failure is due to progressive internal microcracking. As a result, large increase in both the longitudinal and transverse strains and decrease in pulse velocithave been reported preceding fatigue failure. External surfaccracking has been observed on test specimens long beforactual failure.

Progressive damage under fatigue loading is also indicated

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


5/24

FATIGUE LOADING DESIGN CONSIDERATIONS

21 5R-5

S t r a i n x 106

4-Effect of r epeated load on concrete strain

5-Fatigue fracture of a reinforcing bar

al microcracking, fatigue loading is also likely to causenges in the pore structure of the hardened cement paste.ep effects must also be considered. They become more

nificant as the rate of loading decreases..1.8 Concrete strain-Similar to the behavior of concreteer sustained loads, the strain of concrete during repeated

ding increases substantially beyond the value observedr the first load application,2 as shown in Fig. 4. The strain

atigue failure is likely to be higher if the maximum stressower.

Reinforcing bars*.2.1 General -Fatigue of steel reinforcing bars has notn a significant factor in their application as reinforcementoncrete structures. However, the trend in concrete struc-s toward use of ultimate strength design procedures and

her yield strength reinforcement makes fatigue of rein-ing bars of more concern to designers. It is noteworthy,

ugh, that the lowest stress range known to have caused ague failure of a straight hot-rolled deformed bar em-ded in a concrete beam is 21 ksi (145 MPa). This failureurred after 1,250,000 cycles of loading on a beam con-

ing a #ll, Grade 60 test bar, when the minimum stressl was 17.5 ksi (121 MPa).26

A ty pical 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 repeated loads until the bar failed. In this figure, the orien-tation of the bar is the same as it was in the beam; the

bottom of the bar was adjacent to the extreme tensile fibersin the beam. The smoother zone, with the dull, rubbed ap-

pearance, is the fatigue crack. The remaining zone of more jagged surface texture is the part that finally fractured intension after the growing fatigue crack weakened the bar. It

is noteworthy that the fatigue crack did not start from the bottom 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 reyears from the United States,18-26 Canada, ?

orted in recent

and Japan.35-397;28 Europe,29-34

In most of these investigations, the relation-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.There is contradiction in the technical literature as to

whether a bar has the same fatigue strength when tested inair or embedded in a concrete beam. In an investigation31 of hot-rolled cold-twisted bars, it was found that bars embeddedin beams had a greater fatigue strength than when tested in

air. 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 per minute 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 concrete beams containing straight deformed bars made in NorthAmerica18,21,24-28 are shown in Fig. 6. These curves are for bars varying in size from #5 to #ll, with minimum stresslevels ranging from -0.10 to 0.43 of the tensile yield strengthof the bars.

Although only about one-third of the total number of S,-N

curves reported in the indicated references are shown in Fig.

* Dr. John M. Hanson was the chairman of the subcommittee that prepared this sectionof the report.


6/24


7/24


In another investigation26,411where both bar size and typeof 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, andll-made by a major United States manufacturer. These barswere embedded in rectangular or T-shaped concrete beamshaving 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) imposedon 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 0.85times the life of the #8 bars, respectively. This trend is thesame 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 filletsat 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 manyreinforcing bar lugs may have stress concentration factors of 1.5 to 2.0.

Tests on bars having a base radius varying from about 0.1to 10 times the height of the deformation have been re-

ported.25,26,28,36 These tests indicate that when the base radiusis increased from 0.1 to about 1 to 2 times the height of thedeformation, fatigue strength is increased appreciably. Anincrease in base radius beyond 1 to 2 times the height of thedeformation does not show much effect on fatigue strength.However, Japanese tests366have shown that lugs with radiilarger than 2 to 5 times the height of the deformation havereduced bond capacity.

Tests have indicated30,31,39 that decreasing the angle of in-clination of the sides of the deformations with respect to thelongitudinal axis increases the fatigue strength of a rein-

forcing bar. This increase occurs for bars with lugs havinabrupt changes in slope at their bases. It has been Qnoted4that the base radius should be determined in a plane throughthe 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 ina 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 littleffect on fatigue strength. However, a conflicting opinion ha

been ex‘:

ressed in Reference 32.Tests 2also show a substantial effect on the fatigue resi

tance of reinforcing bars due to brand marks. The branmarks cover the identification of the bar as to size, type osteel (billet, rail, or axle), mill that rolled the steel, and yiel

strength (Grade 40, 60, or 75).44 The stress concentration aa bar mark is similar to that caused by bar deformations.

It has also been demonstrated24 that the fatigue strength

of a reinforcing bar may be influenced by the orientation othe longitudinal ribs. In that study, an increased fatigue lifwas obtained when the longitudinal ribs were oriented in horizontal position rather than a vertical position. This phenomenon is apparently associated with the location at whicthe fatigue crack initiates. In other words, if there is

particular location on the surface of a bar which is morcritical for fatigue than other locations, then the positioninof that location in the beam will influence the fatigu

strength.2.2.5 Yield and tensile strength- In three investiga-tions 21,27,289 the fatigue strength of different grades44 of barmade by the same North American manufacturer were com

pared. The results of these comparisons, all of which are ithe long life region of fatigue life, are shown by the bagraphs in Fig. 7. It was concluded in References 21 and 2that the fatigue strength of the bars was relatively insensitivto their yield or tensile strength. References 21 and 28 include 157 and 72 tests, respectively. Reference 27, whicincludes 19 tests, indicated that fatigue strength may be predicted for grade of steel as a function of the stress range.

4 0

Sr 20 N = 2 on

ksi cycles

0Grade 4060 75 406075 40 75 40 75

Smln 0 Ify 0 fy 0 Ify 0 fy

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

0Grade 40 6075

Smm

5fy

b) Data from Reference 27, No. 5 Bars

‘r 20ksi

0

N = 5 millioncycles

Grade 40 60 75 4060 75 40 6075 40 60 75

Smi n 0fy

0 4fy 0 Ify 0 fy

Size No8 No 8 No 5 No 10

c) Data from Reference 28

Fig. 7-Effect of grade of bar


8/24


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 rangeof 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 thesame 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 andmade 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 between30 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 outon both straight and bent #8 deformed bars embedded inconcrete beams. The bends were through an angle of 45 degaround a pin of 6 in. (152 mm) diameter. The fatiguestrength 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 18ksi (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 stresswere 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 havinga 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 andGrade 60 reinforcement with the same deformation pattern,it was found that the fatigue strength of bars with stirrupsattached by tack welding was about one-third less than barswith stirrups attached by wire ties. The results of the tests onthe Grade 60 reinforcement are shown in Fig. 8. For bothgrades 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 evaluatethe behavior of butt-welded reinforcing bars in reinforced

8 0

6 0

St ressRange

Sr , ks i

4 0

2 0

0

\Tack-WeldedS t i r r u p s

I

4 0.1

I

1.0Cyc les to Failure,N, m i l l i o n s

Stress

Range

S, MPa

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

concrete beams. In tests conducted at a minimum stress levof 2 ksi (13.8 MPa) tension, the least stress range that pro-

duced a fatigue failure was 24 ksi (165 MPa). It was observ

that minimum stress level in the butt-welded joint was not significant factor affecting the fatigue strength of the beam

2.3Welded wire fabric and bar mats*

Welded wire fabric may consist of smooth or deformewires while bar mats usually consist of deformed bars. Oftefabric and bar mats are not used in structures subject to significant repeated loads because of concern that the weldeintersections will create significant stress concentrations. Thfeeling has been heightened by experience from abroad45 athe relatively poor performance of smooth wire fabric in con

tinuously reinforced concrete pavements.46,47,48 In some ca

pavements reinforced with this fabric performed adequatein service for 3 to 5 years. Then several wide cracks occurrenecessitating extensive repairs. While most of this crackinwas caused b

Y

inadequate detailing of splices, field studies Connecticut

4have revealed failures at the welds in a signif

cant number of instances.Any assessment of welded wire fabric or bar mats base

primarily on their performance in pavements is unrealistic. any given length of pavement, wide variations are possible ithe stress spectrum for the reinforcement. The average strelevel in the reinforcement is strongly dependent on the pavement’s age, its thermal and moisture history, and the longtudinal restraint offered by the subgrade. The stress range the reinforcement caused by the traffic depends on the sup

port offered by the subgrade as well as the magnitude of thloading.

Several recent investigations have examined the fatigucharacteristics of fabric and bar mats in air.45,48,49 For smowire fabric45,499the disturbance due to the welded intersect

dominated over all other influences, so that failures werconfined to the heat affected zone of the weld. For bar matthe disturbance due to the welded intersection dominateonly if the stress concentration caused by the intersection wa

greater than the concentration caused by the deformationThe available evidence does not indicate that these effec

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


9/24


StressRangeSr ,ksi

- 276Stress

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) smoothwire fabric, and in the other investigation48 22 “cross-weld”tests and 30 between weld tests were made on #5 Grade 60deformed bars with #3 deformed bars welded to them.

The University of Washington49 investigation was intendedto provide a statistically analyzable set of test data for threestress ranges. It was observed that when the penetrationacross the weld was less than one-tenth of the diameter of

the wire, there was incomplete fusion of the wires and theformation of a cold joint. For a greater penetration, themolten metal squirted into the intersection between the wirescausing a marked stress concentration so that the fatigue lifefor a hot joint was about half that for a cold joint. The resultshown in Fig. 9 is the median fatigue life value for the pene-tration considered as a random variable. In those tests thefatigue life values for a given stress range and a 95 percent

probability of survival exceeded the life values obtained intests on high yield deformed bars.25 In the tests48 on the bar mats it was found that the welded intersection reduced thefatigue life for a given range by about 50 percent throughoutthe short life stress range.

Tests on slabs reinforced with smooth wire mats have beenreported in References 49 and 50. The results are summar-ized in Fig. 10, where it is apparent that there is reasonablecorrelation 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 wireswelded 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 x2-6 x 6 fabric as that tested in air. In the slab tests, it wasobserved 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

60t‘ .

\

414

‘v..

Lower Bound forReference 50) Data

\ J

\

276

a\

Stress

‘

Range

S, MPa0

138

Refe rence Symbo l W i re Spac ing

in

(49) A 6

(50)

l 6

(50)

0 12

I

0 1

IO

Cycles to Failure,N,millions

IO

IO 0

Fig.IO A’ N

curves for slabs containing mats

the results for the wire tested in air and a deterministiassessment of the appropriate probability based on the num

ber of approximately equally stressed welds in the slab. Thappropriate probability level for these slabs was about 9

percent, indicating a need for a design approach for weldereinforcing mats based on a probability of survival greatethan the 95 percent commonly accepted for reinforcing barand concrete.

The fatigue life values for collapse were about doublthose for fracture of the first wire. The values for collapscould 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 predicumulative damage effects.

A comparison of the S-N curves for wire fabric and bamats with those for deformed bars indicates that an endurance limit may not be reached for the fabric and mats untabout 5 x 106 c cles, whereas a limit is reached for the barat about 1 x 10Jcycles. However, the total amount of data ithe long life range for fabric and mats is extremely limiteand insufficient for reliable comparison.

2.4-Prestressing tendons*

2.4.1 General - If the precompression in a prestressed con-

crete member is sufficient to &sure an u&racked sectiothroughout the service life of the member, the fatigue characteristics of the prestressing steel and anchorages are nolikely to be critical design factors. Further, in a properly

designed unbonded member, it is almost impossible tachieve a condition for which fatigue characteristics arimportant.

51 Consequently, fatigue considerations have no been a major factor in either the specification of steel for prestressed concrete52 or the development of anchoragesystems.

No structural problems attributable to fatigue failures o

of

Dr. Neil M.

the report.

Hawkins was chairman of the subcommittee that prepared this secti


10/24


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 structuressubject to frequent repeated loads which may involvehigh impact loadings or significant overloads.

In the United States, the growing concern with the fatiguecharacteristics 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 423,54 ACI Committee 301,55 and thePCI Post-Tensioning Committees56 have recommended thattendon assemblies consisting of prestressing steel and

anchorages be able to withstand, without failure, 500,000cycles of stressing varying from 60 to 66 percent of thespecified 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 highimpact, low cycle, repeated loadings during an earthquake.ACI-ASCE Committee 42354 and the PCI Post-TensioningCommittee56 have developed design recommendations for that situation.

Many factors can influence the strength measured in afatigue test on a tendon assembly. The tendon should betested 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 100times the diameter of the prestressing steel, eight times thestrand pitch or 40 in. (1.02 m). Test conditions must notcause 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 treatment3. Anchorage type4. 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 focusedmainly on the fatigue characteristics of seven-wire strand.Recent data on the fatigue characteristics of foreign systemshas been summarized by Baus and Brenneisen.59

2.4.2 Type of prestressing steel -Prestressing steels can beclassified into three basic types: wire, strand, and bars. Wires

are usually drawn steels and strands are manufactured fromwires. Bars are usually hot-rolled alloy steels. Wires are usu-

ally made from a steel whose principal alloying componentare about 0.8 percent carbon, 0.7 percent manganese, an0.25 percent silicon. Hot-rolled alloy steels contain about 0.

percent carbon, 1.0 percent manganese and 1.0 percenchromium. Typically, hot-rolled steels have a tensile strengthof 160 ksi (1100 MPa) while drawn wires have strengthsranging between about 250 and 280 ksi (1720 and 1930 MP

Drawing increases the tensile strength of the wire. It produces a grain structure which inhibits crack nucleation an

provides a smooth surface which reduces stress concentrations. Consequently, the fatigue strengths of wires for a givenumber of cycles are higher than those of rolled steelsHowever, the differences are small for stress ranges expresseas percentages of the ultimate tensile strengths.

Wires-Wires of United States manufacture conform tASTM Designation: A 421,60 “Specifications for UncoatedStress Relieved Wire for Prestressed Concrete.” This specfication covers plain wires only. Ribbed varieties are icommon use abroad. The fatigue characteristics of wires var

greatly with the manufacturing process, the tensile strengtof the wire, and the type of rib. In Fig. 11, fatigue strengthare shown for 2 x 106 cycles for tests performed in GermanyCzechoslovakia, and Belgium,59 and Japan.* The solid circin Fig. 11 is the result of a limited series of tests on 0.25 in(6.3 mm) diameter wires of United States manufacture.These tests showed a fatigue strength at 4 x 106 cycles iexcess of 30 ksi (207 MPa). The squares are results for testson 4 and 5 mm (0.157 and 0.197 in.) diameter wires performed by the Shinko Wire Company.

Also shown in Fig. 11 are likely ranges in stress for bonde beams designed in accordance with the ACI Code. The lowvalue is about the maximum possible when the tensile stres

Stress Range , PercentTensile Strength

05 0 6 0 7 0

Minimum StressTensi le Strength Percent

Germany

- - Czechoslovakia

Belgium

0 Japan (63)

l Japan -4mm

o Japan - 5mm

l U.S.A.

Fig. 11-Fatigue strength at two million cycles for wires

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


11/24

FATIGUE LOADING DESIGN CONSIDERATIONS 21 5R-1 1

Smax

fPU

0.5

II 1 I

o’4 ‘0.06 0.1I I I I I

0.4 1.0 4.0

Cycles to FaiIure,N,miIIions

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

II l

S t r e s s 20

t

”

5 0 6 0 7 0Minimum Stress

Tensi le S trength , Percent

- - - B e l g i u m - W i r eB e lg i u m - S t r a n d

- - * - R u s s i a- - - -U .S.A. -Warn er

.. U.S.A.-Tide 8 Van Horn*U .S .A . - H i lme sBJopan 2Wires

0 Jopcrn-3 Wires

Fig. 13-Fatigue strength at two million cycles for prestressing

strand

in the precompressed zone is limited to m psiOSC

MPa) 1 q kgf/cm2), so that the section is uncracked Theupper 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 characteristicsof wires vary widely, all could probably be justified for usewith 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 within5 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 GermanyRussia,59 andJapan.633These tests have shown that the char

acteristics depend on the height of the rib, its slope and, moof all, the sharpness of the radii at the base of the rib. Wit

a 0.3 mm (0.012 in.) rib height, a 45 deg slope, and no radiat the base of the rib, the theoretical stress concentratiofactor was 2.0, and there was a 57 percent reduction in th

fatigue strength.59g

This reduction decreased with a decreasingstress concentration factor until for the same rib height otained using a circular cut out of 10 mm (0.4 in.) radius, tstress concentration factor was 1.36, and there was no redution in the fatigue strength. Wires crimped62 with a pitch 2 in. (51 mm) and a crimp height of at least 15 percent of twire diameter in the unstressed condition, showed a fatigstrength 20 percent lower than that of the plain wire.

Strand-Strands of United States manufacture up throug0.6 in. (15.24 mm) diameter conform to ASTM A 41664 “Spcifications for Uncoated Seven Wire Stress-Relieved Stra

for Prestressed Concrete.” This specification covers stran

used for prestressing in the United States, and foreign su pliers conform to these requirements. In the United Stateseveral series of tests65-69 have been made on seven-wstrand of either 7/16 or l/2 in. (11.1 or 12.7 mm) diametFatigue data compiled from these studies68 are shown in Fig12. These data are shown along with data obtained from teson Russian,59 Belgian,59 and Japanese63 strand, in Fig. 13.

The Japanese tests633indicated by squares were conducon 3 mm (0.118 in.) diameter plain wires. Tests on similsize strand made from deformed wires showed strengtabout 15 percent lower. Comparison of Fig. 11 and 12 a

the results of the Belgian tests indicate the stress rangavailable with strand are less than those for wire. The UnitStates and Russian tests indicate a decrease in fatigstrength with increasing size for the wires in the stran

Several writers59 have hypothesized that for strands the sucessive lengthening and shortening of the cables produces aternating tensions in the individual wires. Failures initiawhere the neighboring wires rub together under this altenating load.

Bars-Bars of United States manufacture conform to trequirements of the PCI Post-Tensioning Committee. Al-though fatigue tests on such bars have been made (Personcommunication from E. Schechter, Stressteel Corp., WilkBarre, Pa.), most published information is for European baless than 0.7 in. (18 mm) in diameter. Bars manufactured the United States range between % and 13/8 in. (19 and mm) in diameter. Tests on bars ranging between 1 and

1%

(25 and 35 mm) in diameter have shown that the fatigulimits of these bars are in excess of 0.1 times the tensistrength of the bar for 1 x 106 cycles of loading at a minimustress of 0.6 times the tensile strength. As with other potensioning systems, the characteristics of the anchorage annot the prestressing system control the fatigue characterist

of the unbonded tendon.German and Russian tests59 have shown that the fatigue

characteristics for their bars, expressed as a percentage

their ultimate tensile strength, are similar t o those of thstrand. Tests in Russia on bars with tensile strengths of abo


12/24


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

be independent of bar size for bar diameters ranging between0.4 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 ontapered 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’sstatic strength.

2.4.3 Statistical considerations-Reliable design informationrequires the collection of the test data in such a manner thatstatistical 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 survivalsranging from 90 to 10 percent. To establish the finite-life partof 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 thefatigue 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 beendeveloped by Hilmes and Ekberg68 for three discrete proba-

bility levels. As shown in Fig. 14, these levels correspond tosurvival probabilities of 0.1, 0.5, and 0.9, and they weredeveloped from data with minimum stress levels of 0.4, 0.5,and 0.6 times the static tensile strength. For the desiredminimum 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 abroadare not. Czechoslovakian and Russian tests59 have shown thatstress relieving increases the fatigue limit significantly. For applications external to a member, the prestressing steel issometimes protected by hot dip galvanizing. Galvanizing can

Smin

f

Fig. 14-Strength envelopes for strand tested in United States

result in hydrogen embrittlement73 and therefore its use structures where fatigue is a consideration is not recommended. For wires and strand, galvanizing reduces the ulmate and yield strength significantly and therefore also r

duces the fatigue limit. For bars, galvanizing does not altthe static properties, but it does reduce the fatigue limit.

2.4.5 Anchorage type- For unbonded construction, stres

changes in the prestressing steel are transmitted directly the anchorage. Although most anchorages can develop tstatic strength of the prestressing steel, they are unlikely develop its fatigue strength. Further, bending at an anchoracan cause higher local stresses than those calculated from ttensile pull in the prestressing steel. Bending is likely whethe prestressing steel is connected to the member at a felocations only throughout its length or where there is ang

larity of the prestressing steel at the anchorage. Fatigcharacteristics based on tests of single wire or strand anchoages are likely to overestimate the strength of multi-wire

multistrand anchorages.

Tests on single wire anchorages have been conducted the United States,611Great Britain (Test reports supplied A.H. Stubbs, Western Concrete Structures, Inc., Los AngelCA), Japan and Switzerland.599The types of anchorages teand the results are shown in Fig. 15. In each case the ratio the minimum stress to the nominal tensile strength of thwire was about 0.6. The broken line indicates the fatigucharacteristics of the wire used in the Japanese tests,

estimated from the results of rotating beam tests. It coresponds also to the fatigue characteristics of the weakewire in Fig. 11.

All anchorages shown in Fig. 15 developed the f

strength of the wire for static loading. However, moresulted in a fatigue strength for the tendon of less than 5 percent of the fatigue strength of the wire. The exceptio

are the conical anchorages for the Swiss, British, an

American wires. If failures did not occur due to the fatigloading, the static strength was not impaired. In the case the American wire, five specimens out of seven took mothan 107 cycles of the stress range shown without failure. Tlowest life was 3.5 x 106 cycles for a specimen which failed the button head fillets.

For the Swiss and British wires, ranges are shown on t bar charts in Fig. 15 to indicate the variation in results fdifferent characteristics for the button head. The characteistics of a button head are influenced by the wire cutmethod, the type of heading equipment, the geometric ch

acteristics of the head, the properties of the seating blocand the type of wire. Successive improvements have led

button heads showing no failures even after 107 cycles ostress range equal to 0.13 times the tensile strength at average of 0.6 times this strength. British tests on 0.276 in. mm) diameter button-headed wires have shown that defecin the button head have little effect on the fatigue strengtFor a wire with an ultimate tensile strength of 244 ksi (168

MPa) tested at an average stress of 0.6 times that strength,the stress range for 2 x 106 cycles dropped from 0.15 timethe tensile strength for a defect free head to a minimum

0.12 times that strength for a diagonal split in the head.


13/24


Amer ic lCount ry

An ch or age

Type

Japon

But ton Head H a m m e r H e a d

ConicaBut tonHead

Nut

76

9

Series?M a r k B8 T5 T7A T7B T7C

0 .3 15 0 , 19 7 0 . 2 7 6 0 . 2 7 6 0 . 2 7 6

0 . 2 8 0 0 0 . 4 9 0 . 8 9

W i r e

Diameter,in.0.250

Rodius, R

D i a m e t e r 0 . 2 5

L o we r L im i t o f Wi re T e s t Re su l t s( B e l g i a n a n d J a p a n ese)

2c

?I

fpuIC

percent5.7

I

I2 5

c

I

II.8

L

6.4

IL

5.7

IL

Fig. 15-Fatigue strength of anchorages at two million cycles

contrast a soft steel seating block for a defect free headresulted in a marked decrease in the fatigue life. The life

dropped to 2 x 105 cycles for a stress range of 0.15 times thetensile strength, and the failure was due to fretting betweenthe tendon and the soft steel.

The Japanese investigation showed that, to a limited ex-tent, the strength increased as the ratio of the radius at the

base of the head to the wire diameter increased. In thesetests the fatigue crack usually developed where the shoulder for the head and the wire met. Clearly, the reduced fatiguecapacity of the anchorage is due to the stress concentrationcaused by the change in section. The conically shaped anchor-age forces the fatigue crack to develop at a section 50 to 80

percent larger in diameter than the wire.Results for the

States,* and Japan74fatigue tests conducted in the United

on anchorages for bars are shown in Fig.16. Arrows indicate specimens for which failures did notoccur. The dotted line is a lower bound to the test results.The ratio of the minimum stress to the tensile strength of the bar was about 0.6 for all tests. It is apparent that the stressrange was insensitive to bar diameter or country of origin,and that all anchorages comply with the requirements of Sec-tion 7.2 of Reference 56. The reduction in the fatiguestrength of the system for cut threads with couplers is lessthan for cut threads with nuts, and the reduction for boththese systems is markedly more than for bars with grip n u t s

or wedges. In the American tests on grip nuts and wedges, astress range of 0.1 times the tensile strength at a minimum

stress of about 0.6 times that strength did not cause failureeven after 3 x 106 cycles of loading.

Tests on single strand anchorages have been reported byseveral organizations.*j- For % in. (12.7 mm) seven-wirestrand anchored in S7 and S9 C. C. L. spiral units,? cast insmall concrete blocks, failure did not occur within 1 x 106

cycles of a loading varying between 0.6 and 0.65 times thetensile strength of the strand. For

%

in. (12.7 mm), sevcn-wire strand anchored by 5% x 2 in. (140 x 51 mm) cast steelanchors,S failures have not occurred within 0.5 x106 cycles of loadings varying between 0.6 and 0.65, and between 0.56 and0.64 times the tensile strength of the strand. Ten tests* onStressteel S-H % in. (12.7 mm) Monostrand wedges have

shown that for a 10 or 7 deg angle, this system can takewithout failure at least 5 x 105 cycles of a load varying be-tween 0.6 and 0.66 times the strength of a 270 ksi (1.860MPa) seven-wire strand. For a load varying between 0.5 and0.7 times the strength of the strand, failures occurred in thegrips when one wire of the strand ruptured. Average fatigue

* personal communication from E. Schechter, Stress steell Corp.,Wilkes-Barre, Pa.t Test reports supplied by L. Gerber, The Prescon Corp.,Corpus Christi Tex.

Test reports supplied by K. B. Bondy, Atlas Prestressing Corp., Panorama City,

Calif.


14/24


15/24


16/24


17/24

FATIGUE LOADING DESIGN CONSIDERATIONS 21 5R-1 7

A 416,64 A 421,60 and A 722,81 respectively.Whereas the determination of critical flexural stresses in

nonprestressed members is relatively straightforward, the de-termination of critical flexural stresses in the concrete andtendons of prestressed members is quite complex. The reasonis that flexural cracking must have occurred before fatigue of reinforcement can be critical. Hence an analysis which con-siders cracking must be employed.

Stress computations should be made using the basic as-sumptions of equilibrium and compatibility given in the ACICode,53 although this procedure is len thy.method of analysis has been 9 presented,8

A simplified,83 but the results

may be too conservative to be useful. Other design alterna-tives have also been presented.84,85,86

As far as the fatigue strength of the concrete is concerned,the first criterion previously given in Section 3.1.1 is appli-cable. However, criteria for the fatigue strength of the pre-stressing steel and the anchorages are not as easy to establish.

Most of the information included in Section 2.3 is basedon fatigue tests of prestressing tendons in air. Concern has

been expressed87 over the applicability of the information to

full sized members. Where comparisons67,78 have been made,it was found that the observed life of test beams could besubstantially less than that expected from S-N curves of thetendons alone. Differences were attributed to the difficulty of accurately determining stress in a tendon in a beam, and alsoto the local effects in the vicinity of a crack.

In addition, the probability of a wire fracture in a tendondue to fatiuge may be greater in a large beam than in a smallspecimen tested in air.

The effect of cyclic creep112,113 and other factors such asdifferential shrinkage between girder and deck, determinationof losses, and temperature effects also complicates assessmentof results from laboratory tests of members. Under the highfrequency of loading typical in laboratory tests, creep of concrete, in compression and tension, gradually leads to anincrease in the steel stress range and beam deflection. For most practical applications, the comparatively low frequencyencountered in service would not normally result in cyclicload induced creep.

Although no in-service fatigue failures of members have been reported, failures have been induced in laboratory testsof precracked full size members with pretensioned strand. Inone study110’reporting failures as early as 3 million cyclesunder a nominal tensile stress of m psi OSC , the initialstress range was as low as 8.5 to 12.3 ksi (58 to 85 MPa)

(0.031 to 0.045 f pu ]; however, by 2.5 million cycles, the stressrange had increased to 18 to 20 ksi (124 to 138 MPA) [0.066to 0.074 f pu and was higher by the time of failure. The in-crease in stress range can probably be attributed to cycliccreep and other factors. In another study,111 a failure wasreported at 9.4 million cycles where the stress range was typi-cally maintained at 11.7 ksi (80.7 MPa) [0.043 f pu]; however;the beam was subjected to periodic overloads increasing thestress range to 16 ksi (110 MPa) [0.059 f pu ]. In each study,the investigators conservatively assumed that all prestresslosses had occurred at the start of the test. However, addi-tional losses occurring during the test would have increased

the stress range.Thus the Committee recommends that the following

criteria be used for the fatigue design of beams with prestressed reinforcement:

The stress range in prestressed reinforcement that may be imposed on minimum stress levels up to 60 percentof the tensile strength shall not exceed 0.06 f pu based on

cracked section analysis if the nominal tensile stress inthe precompressed tensile zone exceeds 3e psi (0.25 MPa) under a realistic estimate of serviceloadings. *In prestressed members containing unbonded reinfor-cement, special attention shall be given to the possibilityof fatigue in the anchorages or couplers. Unbonded re-inforcement is particularly vulnerable to fatigue if corrosive action occurs. Where information based ontests is not available, the fatigue strength of wire, strand,or bar at anchorage shall not be taken greater than one-half of the fatigue strength (maximum stress range) of the prestressing steel. Lesser values should be used at

anchorages with multiple elements.

Tests have shown that fretting fatigue114-117 can cause fail-ures of bonded post-tensioning wires and strands in curvedregions of plastic and metal ducts. The lower bound on mostof these data appears to be a stress range of 0.054 f pu.

The need for statistical considerations in evaluating fatiguelife of prestressed beams has also been cited.67,88 Other information on the flexural fatigue behavior of large members89-91

and bridges92 is available.Regarding the shear fatigue strength of prestr essed con-

crete members, the discussion in Section 3.1.1 f or nonpre-

stressed members is also applicable to prestressed members.The mode of shear fatigue failure has been documented inreseach,78,93

3

which demonstrated that prestressed beamshave a remarkably high shear fatigue strength under verysevere loading conditions.

3 2 Pavements?

Portland cement concrete pavements for airports and high-ways are subjected to repetitive loadings caused by traffic andcyclic environmental conditions. Although the resultingstresses may eventually cause cracking, localized distress doesnot necessarily terminate the pavement’s useful life. Pave-ments normally are serviceable as long as load transfer across

cracks and joints is effective, and the subgrade continues tosupport the slabs without excessive deflection. It is thereforenecessary to design pavements to resist the expected repeti-tive traffic and environmental stresses for the predeterminedservice life.

* In its 1974 report, the Committee recommended stress ranges of 0.10 f pu

for strand

and bars, and 0.12 f pu

for wires. The lower stress range recommended in the 1986

revision is based on results of recent tests performed at the Portland Cement

Association110 and the University of Texas at Austin111 on prestressed concrete girders

that failed under repetitive loading slightly in excess of 3 million cycles and under a

nominal tensile stress of6fl

psi(OSJT;

MPa).

t

Mr. Craig A. Ballinger was the chairman of the subcommittee that prepared thii

section of the report.


18/24

215R-18


Currently three types of concrete pavements are used inthe United States: a) plain pavements, with frequent jointsand no reinforcement (with and without dowels); b) rein-forced concrete pavements, consisting of lontributed reinforcing and doweled joints;94V9 B

slabs with dis-and c) contin-

uously reinforced pavements (CRCP), consisting of very longslabs with more reinforcement than a reinforced concrete

pavement and no transverse joints.95Prestressed pavements may eventually be a fourth type.

However, they are presently in a developmental stage. Themajority of highway pavements are either of the plain or thereinforced concrete type. Hence, the following discussion willdeal mainly with these types of pavements, although some of the comments will apply to the others.

Highway pavements are commonly designed by usingeither the Portland Cement Association (PCA) method,97 or variations of the American Association of State HighwayOfficials (AASHO) method.

98

The PCA method is based ona modification of the Westergaard theory, and the AASHO

method is based on the results of a comprehensive field studyat the AASHO Road Test. For airports, the U.S. Corps of Engineers procedure is based on pavement performance andfull-scale test track studies.99

The following is a brief description of some of the factorswhich affect the service life of concrete pavements.

1. Traffic-The volume and axle weights of the expectedtraffic must be predicted. For highways, these are

predicted from highway department truck weightstudies, and for airports they are based on aircraftmanufacturers’ data on the loads and configurations of existing and projected future aircraft.

2. Environment -Nonuniform stress gradients are createdin pavement slabs because of restraint to slab movementinduced by changes in temperature and moisture condi-tions. Temperature and moisture gradients also affectthe performance of the slabs because they change theshape of the slabs and hence alter the degree of sub-grade support.100-102

3. Boundary conditions-The stress state in the pavementis affected by subgrade friction, the type and efficiencyof load transfer at joints, and the position of loads with

respect to the joints and pavement edges.4. Support conditions-Several phenomena may affect the

underlying subgrade, and reduce the support which it provides to the concrete slab. These include loss of material by pumping, densification, and displacement of the subgrade, as well as soil volume changes due tomoisture changes and frost.

In the following section, the PCA, AASHO, and Corps of

Engineers methods are briefly reviewed. Other designmethods are not specific in their evaluation of repeated loads.It is expected that the PCA, AASHO, and Corps of Engineers approaches will continue to be the basic modelsfor design. Refinements in design methods are expected as

more sophisticated analvsis and computer techniques are

3.2.1 PCA design method -The PCA design procedure fhighways is based on an extension of the Westergaatheory lo4 which permits stress computations for multip

wheeled vehicles and relates support, axle load, and slthickness to the stress created in the concrete. Only the heaaxle loads which stress the concrete to greater than

percent of its modulus of rupture are considered; i.e., t

effects of passenger cars and light trucks are not considersignificant. The criteria for the fatigue life of the pavemeis the appearance of the first structural crack in the slab.

The basic tool of the designer using this method is a set flexural design stress charts for highway vehicles and for acraft. The charts are the result of analysis of exact wheel cofigurations involving influence charts105 or computer programs. 1066 Computed stresses are normalized by dividingthe design flexural strength of the concrete, and comparedagainst a “standard” S-N curve to determine the allowabnumber of repetitions of load at each level. A perce

damage is obtained by dividing the predicted number of loa

by the number indicated to cause failure. These values athen accumulated in accordance with the Miner hypothesto determine whether the design life is satisfactory. The PCmethod for airport pavement design107 is similar to the higway design method.

3.2.2 AASHO design method -The philosophy associatwith the AASHO design procedure is different than that the PCA method, in that failure is considered to occur whe

pavement has deteriorated to a minimum tolerance level serviceability.1088Serviceability is a unique concept whichdirectly related to the pleasantness of ride experienced by tdriver traveling over the roadway. The serviceability index a pavement is affected by cracking, joint faulting, etc., onlythe extent that it affects rider comfort. The serviceabilindex scale is linear from 5.0 down to 0.0. New pavemengenerally have an index between 4.2 and 4.6, and pavemenare ready for resurfacing when the index drops to a value 2.0 or 2.5 depending on the facility.

To apply this design method, all levels of axle loading aconverted to equivalent 18 kip (80 kN) single axle loads, busing a table of equivalency factors derived from the RoTest. As an example, the effect of one passage of an 18 kaxle load equates to 5000 repetitions of a 2 kip (8.9 kN) ax

load. The thickness of the required pavement is determindirectly by using a nomograph relating the thickness to t

predicted number of equivalent axle loads to reach the minmum serviceability, the underlying subgrade support, and allowable working stress in the concrete.

3.2.3 Corps of Engineers method -For this design proce-dure99 load stresses are computed for the aircraft that areexpected to use the pavement. Design charts indicate rquired pavement thicknesses for specific aircraft dependinon concrete flexural strength, subgrade support and aircragear loads. The thickness so determined is for a fixed amouof traffic-5000 coverages of the design aircraft. The ter“coverage” is used to convert the number of traffic operatioto the number of full stress repetitions; i.e., a coverage occu

when each point of the pavement surface has been subjectto one maximum stress by the operating aircraft. An equati


19/24


to convert operations to coverages considers the wheel con-figuration and transverse wander width of the aircraft passes

on taxiways and runways. To recognize levels of traffic other than the fixed 5000 coverage level, the following increases in

pavement thickness are specified; an increase of 5 percent for 10,000 coverages and up to 12 percent for 30,000 coverages.

NOTATION

f ’

= compressive strength of concrete

fu

=

ultimate strength of prestressing steel

r

= modulus of rupture of concrete

%

= number of cycles applied at a particular stress con-dition

N = fatigue life, i.e., number of cycles at which SO percentof a group of specimens would be expected to havefailed, or the number of cycles causing failure in a

given specimenNr

= number of cycles which will cause fatigue failure atthe same stress condition as rz,

P = probability of failureS = the stress calculated on the net section by simple

theory such as S = P/A, MC/I, or Tc/J without takinginto account the variation in stress conditions caused

by geometrical discontinuitiesS max = the stress having the highest algebraic value in the

stress cycle, tensile stress being considered positiveand compressive stress negative

S mi n

= the stress having the lowest algebraic value in the

stress cycle, tensile stress being considered positiveand compressive stress negative

s,

= stress range, i.e., the algebraic difference between themaximum and minimum stress in one cycle,

S

-

Smi n

REFERENCES

1. Shah, Surendra P., and Chandra, S. “Fracture of Concrete Subjected to Cyclic Loading” ACI JOURNAL,

Proceedings V. 67, No. 10, Oct. 1970, pp. 816824.2. Raju, N.K., “Small Concrete Specimens Under Repeated

Compressive Loads by Pulse Velocity Technique,” Journal of Materials, V. 5, No. 2, June 1970, pp. 262-272.

3. Shah, Surendra P., and Chandra, S., “MechanicalBehavior of Concrete Examined by Ultrasonic Measure-ments,” Journal of Materials, V. 5, No. 3, Sept. 1970, pp.550-563.

4. Beres, L., “Relationship of Deformational Processes andStructure Changes in Concrete,” Proceedings, InternationalConference on Structures, Solid Mechanics and EngineeringDesign in Civil Engineering Materials, University of South-ampton, Apr. 1969.

5. Hilsdorf, Hubert K., and Kesler, Clyde E., “FatigueStrength of Concrete Under Varying Flexural Stresses,” ACI

JOURNAL, Proceedings V. 63, No. 10, Oct. 1966, pp. 1059

1076.6. Kesler, Clyde E., “Fatigue and Fracture of Concrete

Lecture No. 8, Stanton Walker Lecture Series on the Matials Sciences, National Sand and Gravel Association/NationReady Mixed Concrete Association, Silver Spring, Marylan

Nov. 1970, 19 pp.

7. Miner, M.A., “Cumulative Damage in Fatigue,” Transactions, ASME, V. 67, 1945.

8. Murdock, John W., “A Critical Review of Research o

Fatigue of Plain Concrete,” Bulletin No. 475, EngineeringExperiment Station, University of Illinois, Urbana, 1965, 2

pp.9. Awad, M.E., and Hilsdorf, H.K., “Strength and Defor

mation Characteristics of Plain Concrete Subjected to HigRepeated and Sustained Loads,” Structural Research Serie

No. 373, Department of Civil Engineering, University Illinois, Urbana, Feb. 1971.

10. Raju, N.K., “Comparative Study of the Fatigue B

havior of Concrete, Mortar, and Paste in Uniaxial Compresion,” ACI JOURNAL, Proceedings V. 67, No. 6, June 1970,

461-463.11. Nordby, Gene M., “Fatigue of Concrete-A Review

Research,” ACI JOURNAL, Proceedings V. 55, No. 2, Aug.1958, pp. 191-220.

12. Ople, F.S., and Hulsbos, C.L., “Probable Fatigue Lifof Plain Concrete with Stress Gradient,” ACI JOURNAL, Proceedings V. 63, No. 1, Jan. 1966, pp. 59-82.

13. Sturman, Gerald M.; Shah, Surendra P.; and WinteGeorge, “Effects of Flexural Strain Gradients on Micro-

cracking and Stress-Strain Behavior of Concrete,” ACI

JOURNAL, Proceedings V. 62, No. 7, July 1965, pp. 805-8214. Shah, Surendra P., and Winter, George, “Response Concrete to Repeated Loading,” Proceedings, RILEM Intenational Symposium on Effects of Repeated Loading Materials and Structures (Mexico City, Sept. 1966), Institude Ingenieria, Mexico City, 1967, V. 3, 23 pp.

15. Gaede, V.K., “Experiments on the Strength and Defo

mation Characteristics of Concrete Subjected to RepeateCompressive Stresses (Versuche tiber die Festigkeit und d

Verformung von Beton bei Druck-Schwellbeanspruchung) Bulletin No. 144, Deutscher Ausschuss fur Stahlbeton, Ber1962, pp. l-48.

16. Glucklich, Joseph, “Fracture of Plain Concrete,” Proceedings, ASCE, V. 89, EM6, Dec. 1963, pp. 127-138.

17. Diaz, S.I., and Hilsdorf, H.K., “Fracture Mechanism Concrete Under Static, Sustained and Repeated CompressiLoads,” Structural Research Series No. 383, Department oCivil Engineering, University of Illinois, Urbana, 1972.

18. Fisher, J.W., and Viest, I.M., “Fatigue Tests of BridMaterials of the AASHO Road Test,” Special Report No. 6Highway Research Board, 1961, pp. 132-147.

19. Sanders, W.W.; Hoadley, P.G.; and Munse, W.H“Fatigue Behavior of Welded Joints in Reinforcing Bars fConcrete,” The Welding Journal, Research Supplement, V

No. 12, 1961, pp. 529-s to 535-s.20. “The AASHO Road Test, Report 4, Bridge Research

Special Report No. 61D, Highway Research Board,Washin


20/24


21/24

FATIGUE LOADING DESIGN CONSIDERATIONS 21 5R-21

Record, Highway Research Board. No. 5, 1963, pp. 99-119.47. Sternberg, F., “Performance of Continuously Rein-

forced Concrete Pavement, I-84 Southington,” ConnecticutState Highway Department, June 1969.

48. Pasko, T.J., “Final Report on Effect of Welding onFatigue Life of High Strength Reinforcing Steel Used inContinuously Reinforced Concrete Pavements,” Pavement

Systems Group, Federal Highway Administration, Washing-ton, D.C., Nov. 1971.

49. Hawkins, N.M., and Heaton, L.W., “The Fatigue Char-acteristics of Welded Wire Fabric,” Report No. SM 71-3,Department of Civil Engineering, University of Washington,Seattle, Sept. 1971.

50. Bianchini, Albert C., and Kesler, Clyde E., “InterimReport on Studies of Welded Wire Fabric for ReinforcedConcrete,” T& AM Report No. 593, Department of Theoreti-cal and Applied Mechanics, University of Illinois, Urbana,Nov. 1960.

51. Bondy, K.B., “Realistic Requirements for Unbonded

Post-Tensioning Tendons,” Journal, Prestressed ConcreteInstitute, V. 15, No. 2, Feb. 1970, pp. 50-59.52. “Les Armatures Speciales de Beton Arme et les Arma-

tures de Precontrainte," Proceedings, RILEM Symposium(Liege, July 1958), RILEM, Paris, 1958.

53. ACI Committee 318, “Building Code Requirements for Reinforced Concrete,” (ACI 318), American Concrete Insti-tute, Detroit. See Section 1.3 for current reference.

54. ACI-ASCE Committee 423, “Tentative Recommenda-tions for Concrete Members Prestressed with UnbondedTendons,” ACI JOURNAL, Proceedings V. 66, No. 2, Feb.1969, p. 85.

55. ACI Committee 301, “Specifications for StructuralConcrete for Buildings,” (AC1 301), American Concrete Insti-tute, Detroit. See Section 1.3 for current reference.

56. PCI Committee on Post-Tensioning, “Tentative Speci-

fication for Post-Tensioning Materials,” Journal , PrestressedConcrete Institute, V. 16, No. 1, Jan.-Feb. 1971, pp. 14-20.

57. “Tentative Specifications for Testing of PrestressingSteel According to DIN 4227 for Their Acceptance, Manufac-turing and Supervision (Vorlaufige Richtlinien fur die Prti-fung bei Zulassung, Herstellung und Uberwachung vonSpannstahlen fur Spannbeton nach DIN 4227),” Departmentof Transportation, Federal Republic of Germany, Dec. 1965.

58. “Design and Engineering Code for Prestressed Con-

crete Railway Bridges,” Japanese National Railway.59. Baus, R., and Brenneisen, A., “The Fatigue Strength of

Prestressing Steel,” Steel for Prestressing, FIP Symposium (Ma-drid, June 1968), Cement and Concrete Association, London,1969, pp. 95-117.

60. “Standard Specification for Uncoated Stress-RelievedWire for Prestressed Concrete,” (A 421), American Societyfor Testing and Materials, Philadelphia. See Section 1.3 for current reference.

61. Ball, C.G., “Tensile Properties of Fatigue-Cycled USSHigh-Tensile-Strength, Stress-Relieved, Button-Anchoring-Quality 0.250-in. Diameter Wire,” Report, Project No. 57.019-

901 (ll), Applied Research Laboratory, U.S. Steel Corpora-tion, Mar. 1963, 18 pp. Also, Part II, Western Concrete

Structures, Technical Report No. 6, “Investigation of Button-Head Efficiency,” July 1968.

62. Bennett, E.W., and Boga, R.K., “Some Fatigue Tests of Large Diameter Deformed Hard Drawn Wire,” Civil En-

gineering and Public Works Review (London), V. 62, No. 726Jan. 1967, pp. 59-61.

63. Iwasaki, I., and Asanuma, H., “Quality Tests of De-

formed Prestressing Wires for Prestressed Concrete RailroadTies,” Report No. 7, Japanese National Railways ResearchLaboratories, 1969, p. 346. Also, Structural Research Labor-atory Report No. 42, Technical Research Institute for Rail-roads, Feb. 1969, 20 pp.

64. “Standard Specification for Uncoated Seven-WireStress-Relieved Strand for Prestressed Concrete,” (A 416),American Society for Testing and Materials, Philadelphia.See Section 1.3 for current reference.

65. Lane, R.E., and Ekberg, C.E. Jr., “Repeated LoadTests on 7-Wire Prestressing Strands,” Progress Report No.223.21, Fritz Engineering Laboratory, Lehigh University,

Bethlehem, Pennsylvania, 1959.66. Fisher, J.W., and Viest, I.M., “Fatigue Tests of BridgeMaterials of the AASHO Road Test,” Special Report No. 66,Highway Research Board, Washington, D.C., 1961, pp. 132-147.

67. Warner, R.F., and Hulsbos, C.L., “Probable FatigueLife of Prestressed Concrete Beams,” Journal, PrestressedConcrete Institute, V. 11, No. 2, Apr. 1966, p. 16-39.

68. Hilmes, J.B., and Ekberg, C.E. Jr., “Statistical Analysisof the Fatigue Characteristics of Under-Reinforced Pre-stressed Concrete Flexural Members,” Iowa Engineering Ex-

periment Station, Iowa State University, Ames, 1965.69. Tide, R.H.R., and Van Horn, D.A., “A Statistical Study

of the Static and Fatigue Properties of High Strength Pre-stressing Strand,” Report No. 309.2, Fritz Engineering Lab-oratory, Lehigh University, Bethlehem, Pennsylvania, 1966.

70. Eastwood, W., and Rao, R.M., “Fatigue Tests on Lee-McCall Prestressed Concrete Beams,” Civil Engineering and

Public Works Review (London), V. 52, No. 613, July 1957, pp786-787.

71. 1958 Tentative Guide for Fatigue Testing and the Statitical Analysis of Fatigue Data, STP-91A, 2nd Edition, American Society for Testing and Materials, Philadelphia, 1963.

72. Brenneisen, A., and Baus, R., “Statistics and Probabil-ities,” Steel for Prestressing, FIP Symposium (Madrid, June

1968), Cement and Concrete Association, London, 1969, pp.119-138.

73. Moore, D.G.; Klodt, D.T.; and Hensen, R.J., “Protec-tion of Steel in Prestressed Concrete Bridges,” NCHRP Repo No. 90, Highway Research Board, Washington, D.C., 1970,8

pp.74. Research Group for Steel for Prestressed Concrete,

“Tests of Prestressing Steel,” Prestressed Concrete (Japan), V3, No. 3, June 1961, pp. 46-53.

75. Mamada, K.; Naito, K.; and Mogami, T., “Tests onAnchorages for VSL Tendons,” Prestressed Concrete (JapanV. 13, No. 4, Aug. 1971, pp. 42-48.

76. Leonhardt, Fritz, Prestressed Concrete-Design and Construction translated by V. Amerongen, 2nd Edition, Wil-


22/24


helm Ernst and Sons, Berlin, 1964, pp. 136-141.77. Seki, M.; Yamamoto, S.; Shimbo, E.; and Toyokawa,

T., “Pulsating Tension Fatigue Strength of PC Steel Strand,”Journal, Japan Society for Materials Science (Kyoto), V. 18,

No. 190, July 1969, pp. 12-16.78. Hanson, John M.; Hulsbos, Cornie L.; and Van Horn,

David A., “Fatigue Tests of Prestressed Concrete I-Beams,”

Proceedings, ASCE, V. 96, ST11, Nov. 1970, pp. 2443-2464.79. Shah, Surendra P., and McGarry, Fred J., “Griffith

Fracture Criteria and Concrete,” Proceedings, ASCE, V. 97,

EM6, Dec. 1971, pp. 1663-1676.80. Chang, Tien S., and Kesler, Clyde E., “Fatigue Be-

havior of Reinforced Concrete Beams,” ACI JOURNAL, Pro-ceedings V. 55, No. 2, Aug. 1958, pp. 245-254.

81. “Standard Specification for Uncoated High-Strength

Steel Bar for Prestressing Concrete,” (A 722), AmericanSociety for Testing and Materials, Philadelphia. See Section1.3 for current reference.

82. Ekberg, C.E. Jr.;

215r_74 Fatique loading.pdf

Documents

Transcript of 215r_74 Fatique loading.pdf