Effect of Loading Frecuency and Stress Revesal on Fatige Life of Plain Concrete

7/25/2019 Effect of Loading Frecuency and Stress Revesal on Fatige Life of Plain Concrete

1/15

Magazine of Concrete Research, 1996, 48, No. 177, Dec., 361-375

Effects of loading frequency and

on fatigue life of plain concrete

B. Zhang ,* t D.

V.

Phillips*

and K. Wu?

Universit-v of Glasgow

stress reversal

The effects of loading frequency and stress reversal

on

the fatigue properties of concrete were investigated by

conducting ,flexu ral ,fatigue ests on plain concrete beams. A new fati gue equation based on the classical Aas -

Jakobsen S-N equation is proposed which contains heaboveeffects. This equationagrees well with previous

experimental results and proves to be suitable f o r some other oading states other han bending.

Introduction

Researchnheatigueropertiesfoncrete

materialseganthendfhe last century,'32

because in many oncrete tructures, he ailurewas

often caused by the fatigue rupture of concrete. Since

then, arious atigue quations ave een roposed.

Oneof he betterknown s heclassicalS-Nequa-

tion,.e.tress-fatigue life relationsh ip,utor-

ward by Aas-Jakobsen' in 1970 as ollow s:

S,

.fc

__ = 1 - 1

R)/?logN (1)

where , f c is theelevanttatictrength; N is the

fatigue life; p isamaterialparameter = 0.0685; R is

the stress ratio

= S,,,,,,/S,,,;

and

S,i,

and S,,, are the

minimum and maxim um stresses, respectively. S,,,/ f c

plottedagainst og N is known as the Wohler-curve.

Equation

( 1 )

is conveniento send as een

accepted by both heoretical esearchersandpractical

engineeringdesigners.How ever, it hassome practical

limitations in that

i t

neglectshe ffectsof oading

frequency nd s uitableonlywhen R b 0 i .e.no

stress reversals). Although other researchers have since

modifiedhis equation: the ffects foadingre-

quencyndtresseversal

( R

0) haveetoe

*

Department o f Civil Engineering. University o f Glasgow, Glasgow

GI2

ELT.

Scotland

U.K.

t Department of Materialsciencendngineering, Tongji

University. Shanghai200092,The Peoples Republic of China

Paper received

7

December 1995:

last

revised

I S

March 1996;

accepted 2April 1996.

completelyesolvedndroperlyeflected in the

fatigueequation.

Gra f and Bret~n en ~ first studied the effect of load-

ing frequency .f on hefatigue life of conc rete. They

found hat

.f

= 4.5-7.5 Hz had ittle effect on he

fatigue life, bu t when ,f decreased below 0.16 Hz, he

fatigue life decreased.Hanson

et al.

andMurdock8

suggested hatwhen

S,,,

was ess han

75%

of

f c ,

frequenciesbetween

I

and

15 Hz

had little influence.

Sparks et showed that for

S,,,

between 75 and

100% of f c ,

f

greatly affected

N ,

but when

S,,,

was

smallerhanheong-termtrength,requencies

between 0.1 and100Hzhadno effect on N. None

ofheseesultswere atisfactorily escribed in the

fatiguequation.urtak, owever,onsideredhe

effect foading requency nd roposed atigue

equationcontaininga requency nfluencecoefficient

C, as follows:

S,,,

. f c

C N - A ( 1

+

B log N ) C f

(2)

where

C f

=

1

f a( 1 bR)

o g f ; A ,

B , C, a and b are

materialparameterswhichcanbedetermined hrough

experiments. This equation is cumb ersome and implies

a om plicated nterdependencebetween

N , f

and

R

which is difficult ounravel.Amoredirectextension

ofequation 1) is preferable so that he nfluenceof

loading requencysmoreransparent.This will be

discussed in moredetail in Section 2.

Earlytresseversalests erearriedut by

Hatt 'andCrepps13whoconcluded hatstress ever-

sal hadnoeffecton he fati ue life ofconcrete,and

by Clemmer14ndClifford'whohought

it

had

small nfluence.TepfersI6studiedstressreversalusing

361

B

wnloaded by [ Universidad de Costa Rica] on [16/12/15]. Copyright ICE Publishing, all rights reserved.


2/15

Zhang et al.

two loading com bination s: constan t com pression in the

horizontalirection and variableplitting in the

vertical direction; nd onstant plitting in thehori-

zontal direction and variableompression in the

vertical direction. He observed that the stress reversal

did affect the atigue life b ut thought hat heeffect

was oo small todescribe in the fatigueequation. He

actuallyttributed it to the low precision ofhe

applied loads in theesting mac hine. HsuI7 system -

atically studiedheatiguef plain concre te. In

considering stresseversal, however, he applied the

fatigueequation ntended for

R 3 0

to stress eversal

( R

< 0) withou t sufficient experimental supp ort, ead-

ingoonservative results.ornelissen and col-

leagueslso realized theetrimen tal effect of

stresseversal on theatigueife of oncrete nd

carried outwoeries of lternating stresseversal

tests: irect oncentricension-compressionests on

concreteylinders withariedections;ndhree-

point flexural ests on concre te beam s by using a pre-

stressingechnique.hey proposedheollowing

fatigueequations:

I n

for direct tests, log N = 9.36 .93 .59-

I,,,

S,,

.f

i

. f c

(3a)

and for flexure, log N = 9.91 7.45 .93

m a xm i n

. f r . / c

(3b)

where ,h,

, f r

and

fS

arehe tensiletrength, the

modulusof rupture nd he ompressive trength of

concrete, respectively. Fairly large scatters were ob-

tained, probably due to difficulties in applying conce n-

tric oads in direct ension-comp ression ests nd in

ensuring he correct prestressing load in flexure. They

also did not makeallowancefor loading requency in

theroposedatiguequations, evenhoughhey

noticed he existenc eofsuc h an effect.

The purpose of this paper is to examine loading fre-

quencyand stress eversaleffectsusing he esults of

flexural fatigue tests on plain concretebeams. Based

on Aas-Jakobsen's approach,

a

new fatigue quation

which includes these effects is proposed and dis-

cussed.The resultswillbe com pared with other re-

sults by previous researchers.

Loading

frequency effects

Aas-Jakobson 'S fatigue equation

According to Aas-Jakobson'sriginaldea, when

the tatic oading is applied there is only onecycle

and the max imum stress is equal to the static strength,

i.e.

N = 1

and Sm,,/fc

= 1.

In actualact, under

static oadingconditions, S,,, is not thesameas

j c ,

because f c is amaterial constan t etermin ed at a

standard loading rate, whereas S,,, will vary with the

loading rate. In gen eral, the loading rate influences the

fatigue ife of concre te to acertaindegree,especially

for low-cycle fatigue

N < lo3).

For practical concrete

structures, if the pplied yclicoadingate is less

than he tandard oading ate, heprediction of the

fatigue life by equation ( 1 ) tends

to

be unsafe.There-

fore, his equatio n should be modified to account for

this.

I t follows that theerm Sma,.,f; in equation ( 1 )

representsnominal tress level, and not the ctual

stressevel. To ach ieve the latter,

,fc

should be re-

placed by the real strength

fe r

measured at the same

loading rate applied to S,,,. Thus, equation (1) can

thenbewritten

Letting

,fcf

= Cf.,fc, where

C,

is aoading rate

coefficient,equation

(4)

can be rewritten as

~

= Cf[l - 1

R)[jlog

NI

m

. f c

( 5 )

Loading

j-eqzrency coqfficient

Staticoading is actually l imi t case of cyclic

loading. If

a

static oadingpathcovershalfa ingle

cycle and akes ime

T

(in second s), then the oading

frequency

,/

is related to theoadingime by

f =

1

/2T, in hertz. Also since T is related

to

the

loading ate then Cf couldbe nterpretedaseither a

loading requencycoefficient or a oading ate coef-

ficient.The orm er is more relevant here.

Now since Cf = c f / , f c , it can be seen that Cf

expresses theelative con crete strength at different

loading requencies.

C,

will increase with increasing

f : Also

when J'approa ches zero (i.e. the loading ime

nearsnfinity),

Cf

approaches the relativeong-term

strength under static oading.

A

suitable expression for

C, embracing theseproperties is given by

Cf

= f

+ c (6 )

where

U , h

and

c

are materialarameters to be

determined throughexperiments and

0 h

< 1. When

concretendertaticoading. When

, /

equalshe

standardoadingrequency ,fi for a iven trength,

then C , =

I ,

i.e. Jcf = c Finally by substituting

equation (6) into equation (5) we obtain

f

0,

Cf

c,

theelativeong-term trength of

&,ax

. f c

__

+ C ) [ I 1 - R)[j log NI (7 )

Tests jar determination

o f C,

To

determine

Cf.

both flexural staticndyclic

tests were conducted on

500 X

100

X

100 mm con-

crete beams with an effective span of 450 mm . The

beamsereested in a 250 kN Instron servo-

controlledesting mac hine using a triangular wave-

Maguzinr

of

Concrete

Reseurch.

1996, 48, No.

ll

62



3/15

Loading freq uenc y and stress reversal effects

on

concrete fatigue

formortaticoadingndinusoidalwaveor

cyclicoading.pecialpparatusorpplyinghe

loads, ncluding eversal,wasdesign ed (Fig. 1).

The oncrete was maderommix f ement:

water:sand:gravel

=

1: 0.45: 1.18:2.74sing525

ordinaryortlandement,atural river sandnd

gravelwith article sizerom

2.5

to 5 mm .The

specimenshadbeencured in thecuring oom or

28

days, at 2 0 2C ndelative umidity f 0%,

beforeheyweremoved utdoors.At 28 days,he

compressivetrength

j:

was0.7MPa,ndhe

modulus f upture,

f r ,

was .19MPa.The eams

wereestedmonthsater,ecauseyhenhe

strengthsndlasticonstantsfoncrete ould

changevery ittlewith urther geing.

At

this ime,

f h

was 57.4MPaand fr was7.88MPa. Theelastic

constantsweremeasured obe: E = 41. I GPaand

Poissons ratio

v

= 0.17.

Eleven groups of staticndyclicestsere

employed, ach group ontaining six identical peci-

mens.The irst ivegroups were estedunder tatic

loading (i.e. R = 0, S,,,/.fc =

1 )

with loading times T

of00,20,0, I O andeconds,hichre

equivalentooadingrequenciesf 4.1 167

X

I O p 2 ,

5

X

and

I O -

Hz, respectively. The

latter six group s were tested under cyclic loading, with

loading requenciesof0.5, I , 5, 10, 20 nd

30

Hz.

The tress ratio

R

and he tress level S,,,/ f r were

keptonstantt.2nd.80,espectively,nd

represented ypicalconditions.

Discussion

of

results

Full esultsarepresented in Append ix

1.

Figure2

illustrates he elationshipobtainedbetween

C,

and

,f:

I t is clearly een hat Cf increaseswith log f, or in

other words,he igherheoadingrequency,he

longerheatigueife. For exam ple,or

R =

0.2,

S,,,a,/,fc = 0.8,

when

.f =

0.5Hz, Cf

=

1,038and

N

N

3900,whereaswhen

, f

= 30 Hz,

Cf

= 1.077

and N

O

400. This behaviour indicates less damage

is caused o heconcrete at high oading requencies

and is related to the well-know n observation that static

strength ncreaseswith ateof oading.

Using hevariable terativeoptimizationmethod,

thematerialparameters a, h, c and

p

in equation (7)

werenon-linearlyestimatedas

ir = 0.249, b = 0.920, i = 0.796, a = 0.0804

Theineepresentinghese alues as eenuper-

imposedon Fig. 2 whe re it canbe een hat a very

good it is obtained imultaneously hroughboth he

static ests

( R

= 0,

S,,,,,/,fc

=

1 )

and hecyclic ests

( R = 0.2, S,,,,/,fc =

0.8).Thisugge sts that the

fatigue quation (7 ) may have eneral pplicability.

The esultsalso how hat he ong-term trengthof

concreteunder lexural oading is about

80

of the

static strength,hich is similar to thealue

o f

Maguzine

qf

ConcreteResearch, 1996.

48

No.

177

1-

1 -

lnstron servo-controlled

2 -

Special loading apparatus

3

-

Load

cell

4 -

Displacement transducer

5

-

Specimen

testing machine

J

Fig.

1.

General arrangement of static and cyclic oading

apparatus

75-80%ftatictrengthbtained by other re-

s e a r c h e r ~ . ~ ~ ~

Stress reversal effects

New definition

of

stress ratio R

The conventional stress ratio

R = S,,,/S,,,

defines

the range of applied stress. Typically S,,, might repre-

sent hedead oadstressand S,,, thedead oadplus

live loadstress, (S,,,

S,,,)

being hestress ange.

In general, the larger this range, the shorter the fatigue

life

N

of conc rete. It is also well establish ed that N is

veryensitiveo this rangeoriven S,,,. In

practice N isoftenobtained romamodifiedGood-

man diagram which is essentially designed for stresses

of he samesign, .e.

R 3 0.

Under tress eversals, .e.

R

0, he oncretewill

beubjected to alternateensionndompression.

Since hebehaviourofconcrete,andparticularly its

strength, is significantlyifferentnderhese two

stress states, it would be preferable to define the stress

ratio to reflect this. T his anbe chievedby sso-

ciatinghemaximumtress

S,,,

withhe static

strength fc,,, which will dominate he failure process,

a = 0-249 = 0.920

c

=

0.796

Loading frequency

:

Hz

Fig 2.

Relationship between loading fpeqerenq,coeficient

and loading ,fi.equency

363



4/15

Zhang et

a1

and by associating heminimum tress Sminwith he

staticstrength f c m l n , whichplays a secondary ole.

A suitable re-definition of the stress ratio for R < 0

is thenprovided by

subject o hecondition that

R = R for R 0

(9)

Replacing

R

by

R

in equation (71, afatigueequation

which ncorporatesboth oading requencyand tress

reversal is ob tained, .e.

J c

For lexural tress eversals, ensionwillbedomi-

nant nd om pression econdary.Hence

, fcmax = f r ,

the static modulus of rupture and ,fcmin =

f:,

he static

compressive trength.Thusheatio f

. fcmax/.fcmi,,

becomesheension-compressiontrength ratio

. f t c = r / f

Experimental ests

In order oevaluate thenew atiqueequation (10)

andassess he nfluenceofstress eversals,a total of

171eams ereestedsingheamematerials

andoadingmethodescribedboveorhee-

terminationf

Cf.

Bothositiveepeatedoading

( R 3

)andreversible oading

( R

0.75), the effect of sustained loading should

be considered.

Stress eversalcauses atigue ife

of

concrete

to

decrease, but not as much as that for R

0.

This

effectalsocanbeexpre ssed in the atigueequa-

tlon.

A new atigueequationcontaining heeffectsof

loading frequency and stress reversal on the fatigue

properties of concrete

is

proposed. It agrees well

with previo us test results for -1

< R 0.75,

and

is suitable for many different oading states.

Finally, the effects of other param eters whic h nflu-

ence the fatigue properties of concrete, such as water-

cementatio, ggregateype ndoadingequence,

aswell ashe racticalpplication fheatigue

equation ( l o ) , willeiscussed in subsequent

papers.

Magazine of Concrete Research,

1996, 48,

No.

177

References

I .

2.

3 .

4.

5 .

6.

7.

8 .

DE

JOLY.

La resistancet'elasticitt esiments ortland.

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Pons

et

Chaussees, Memoires,

1898, Vol. 16,

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CONSIDERE.nfluenceesrmaturesmetalliquesur

les

proprietesdesmortiers tbetons.

Compte Rendu de L Aca-

demic

des

Sciences, 1899,

127,

992-995.

AAS-JAKOBSEN

.

Fatigue f oncrete eams nd olumns.

Bulletin No. 70-1, NTH InstituttorBetongkonstruksjoner,

Trondheim,Sept.1970.

TEPFERS and

KUTTI T.

Fatigue trength of plain,ordinary

and ightweightconcrete.

ACI

1

979,

76,

No.

5, May, 635-

652.

CRAF 0 . and BREN NER . Versuche

zur

Ermittlunger

Widerstandsfihigkeit von Betonegenftmalswiederholte

Druckbelastung (Experiments for investigating the resistance

of

concrete under often repeated compression oads). Bulletin

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76,DeutscherAusschuss

fur

Eisenbeton,1934.

CRAP0. and BRENNER . Versucheurrmittlung der

Widerstandsfahigkeit von Betonegenftmalswiederholte

Druckbelastung (Experiments for investigating the resistance

of

concretenderftenepeatedompressionoads). 2.eil,

Bulletin No.

83,

DeutscherAusschuss

fur

Eisenbeton, 1936.

HANSON

.

M. t al. Considerationsor esign f oncrete

structuresubjectedoatigueoading.eport byCI

Committee215.

ACI

1

974,

71,

No.

3, March,97-120.

MUDOCK,.

W.

A

critical review of research on fatigue of plain

concrete.Bulletin No. 475,EngineeringExperimentStation,

Universityof llinois,Urbara,25,1965.

369



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Zhang

et

al.

9.

10.

11 .

12.

13.

14.

15.

16.

17.

18.

19.

20.

SPARKS

R.

and MENZIES.B. Theeffect of rate of loading

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No.

83. June,73-

80.

FURTAK. EinVerfahren zur Berechnung der Betonfestigkeit

UnterSchwellendenBelastungen. C m .

Concr.

Res., 1984.

14,

No. 6,855-865.

HATTW. K. Fatigue of concrete. Proc.4th

Annua l Meeting.

Highwu.v Reseurch Board. 1924, Dec., 47-60.

HATT

W. K.

Report on experiments on extensibility of

concrete. Proc. 5th Annuul Meeting. Highwy Re.seurch Board.

1925,Dec.112-118.

CREPPS

.

B. Fatigue of mortar. Pmc.

ASTILI,

1923.

23

Part 11

CLEMMER. F. Fatigue of concrete. Proc. A S T M , 1922, 12.

Part

I t

1188-1222.

CLIFFORD Highway research in Illinois. Funs. ASCE. 1924,

87 329-340.

TEPFERS . Fatigue of plainoncreteubjected to stress

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SpecialPublication,1982, 75,No. 9. 195-

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Hsu T.T. C. Fatigue of plain concrete.

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W.

Fatigue failure of concrete

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.

andSAMUELSSON. Concretesubjected

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Appendix

1.

Experimental results

.for

determination

of C,

Test

number

I

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

370

T :

5

00

120

50

10

5

21.

22.

23.

24.

25.

26.

27.

wave form. NordiskBetong, 4, Stockholm,1973,27-36.

ANTRIM. C . and MCLALJGHLIN

.

F. Fatigue study f ir-

entrained concrete. A C I J , 1959, 55. No.

1

I . May,1173-1182.

AWADM. E. and HILSDORF. K. Strength nd deformation

characteristlcs of plain concrete subjected o high repeated and

sustamed oads. Civil EngineeringStudies,Structural Research

Series N. 372,Department of CivilEngineering.University of

Illinois,Urbara.Feb.1971.

BENNETT

.

W. and M LIR S. E. St. J. Some fatigueests of

high-strengthconcrete in axial compression.

Mug. Concr:

Res.,

1967, 19. No. 59.June. 113-

I

17.

High speed fatlgue ests on small specimens of plain concrete.

J

Prestressed

Concr:

Inst.. 1959. 4, No. 2. Sept ., 53-70.

GAELE

K.

Versuche uberdie Festigkeitund die Verformung

vonetonei Druck-Schwellbeanspruchung (Strengthf

deformationharacteristicsfoncrete whenubjected to

repeatedompressivetress). Bulletin

No.

144,eutscher

Ausschuss

fur

Stahlbeton, Berlin,1962.1-48.

M ~ J R I ) O C K. W. and KF SL ~ R . E. Effect of range of stress on

fatigue strength of plain concrete beams.

ACI

J . 1958. 55. No.

12,Aug., 221-231.

MCCALLl.

T

Probability of fatigue ailure of plain concrete.

ACI

1.

1958,

SS.

No.

2,Aug., 233-244.

ASSIMACOPOULOS. M, , W A R h t R R. F., and EKR~RG. E.

Discussion contributions on this pape r should reach the editor by

27 June 1997.

(0.001)

0.967

0.97

0.981

0.982

0.995

1 .001

(4.17 X IO- )

0.984

0.99

I

.006

1.008

1.014

I .023

(0.01)

(0.05)

0,979

0.985

1.007

1.015

1,023

1.037

0.987

I .00

1.005

1.017

1.035

1.048

0.995

1.018

1.031

I .035

1,045

1.046

R

N:

cycles

CI.

0.967

0.971

0.98

0.982

0.995

1 .00

0.984

0.99

1.006

1.008

1.014

1,023

0.979

0.985

1.007

1.015

1.023

I .037

0.987

1.001

1.005

1.017

1.035

1.048

0.995

1.018

I .03

1.035

1.045

1.046

Magazine of Concrete Research, 1996, 48,

No. 177



11/15

Loading freq uenc y and stress reversal effects

on

concrete fatigue

T :

f: z

R

Cf

est

number

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

h0

61

62

63

64

65

66

N

cycles

I707

2592

3628

3847

566

1

7900

1846

I952

4588

4936

5267

7900

3430

5026

7840

8223

9454

1 1 455

2790

4142

4700

9550

1 1

710

14732

4088

6946

7723

9110

13413

l7 322

3736

6210

10696

12718

22 260

22416

1.010

1.025

1.038

1.040

1.055

1.068

0.5

1.013

1.015

1.047

1.049

1.052

1.068

1.036

1.050

1.067

1.069

1.075

1.083

5

0.8

0.2

~

1.028

1.043

1.047

1.075

1.084

1.093

1.042

1,063

1.067

1,073

1.089

1.100

1.039

1.058

1.080

1,087

1 1 1 1

1 1 1 1

(0.05) I O

(0.025)

20

~ ~

(0.0 167)

30

Appendi-w 2. Futigw test twu1t.s

Test

.

r

number

~S,,,

I

2

3

0.975

4

5

6

0.9

5

7

9

0.925

0.5

I O

I I

13

12

0.9

Maguzine of

Concrete Rrsearch

1996,

48, No.

177

f : Hz

N :

cycles

P

50

66

69

0.0784

0.0732

0.0725

84

170

229

0.094

0.081

2

0.0768

0.0860

0.0824

0.08 12

459

603

660

4950

5490

6300

41 760

0.0815

0.0805

0.0792

0.065 1

5

371



12/15

Zhang et al.

Test

number

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

R

0.5

0.2

0,875

0.85

0.95

0.9

0.85

0.8

0.75

. f :

Hz

20

I

20

N:

cycles

40810

57310

57 800

34 800

59 850

I7 6870

14

16

20

24

26

27

27

28

41

76

69

91

95

103

I l l

146

I63

204

462

600

277

410

43

693

744

9x7

1052

I390

I948

2192

2330

2640

3310

41 70

50 O

7460

I0 050

l 3

230

l6980

24 330

20 550

22 030

28 1 I O

3 200

34 250

54 630

62 430

62610

152 490

I52 740

io

0.0800

0.0775

0,0775

0.0915

0.0870

0.0792

0.0988

0.0940

0.0870

0.0820

0.0800

0.079

0.079

0.0782

0.0702

0.0602

0,094

0.0883

0.0875

0.0860

0.0846

0,0800

0.0782

0.0749

0.0649

0.0623

0.0953

0.089

0.0884

0.0820

0.08

I

0.077x

0.077

0.074

1

0.0708

0.0697

0.0909

0.0895

0.0870

0.0846

0.0827

0.0790

0.0765

0.0743

0.0724

0.0698

04872

0.0866

0.0846

0.0837

04830

0.0794

0.0785

04784

0.0726

0.0726

3 72

Muguzine of

Concrete

Research, 1996. 48, No. 1l1



13/15

Loading f requency and stress reversal effects on concrete fat igue

R f

Hz

P

0.0883

0.0870

0.0846

0.083

1

0.08 17

0.08 13

0.0778

0.0774

0.0766

0.0707

0.0870

0.0837

0.0833

0.0745

0.0702

0.0894

0,0837

0.0831

0.0727

0,0835

0.0832

0,0790

0.0750

0.0846

0.0804

0.0799

0.0844

0.08 15

0.0721

0.0811

0,0806

0.0799

0.0932

0.0828

0.0757

0.0842

0.0775

0.0711

0.0937

0.08 I7

0.0796

0.0749

0.0833

0.0787

0,0773

0.0864

0,0826

0.0794

0.081 3

0.0803

0.0776

373

N :

cycles

82

890

99 220

137 150

168 100

208 750

219710

387 100

409610

467 990

1

407 700

39

45

46

72

94

121

168

175

3 64

637

655

923

1327

2830

4280

4530

13 150

18 320

66 360

72 880

77 800

86 360

88

155

249

508

875

1600

853

2298

2816

4626

9220

15630

l8 670

27420

44 160

67 960

188 220

220 960

336 330

Test

number

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

8 5

86

87

88

89

90

91

92

93

94

95

96

97

98

99

I U0

101

IO2

103

I04

105

I06

107

I08

109

110

I l l

112

I

l3

I l4

I l5

116

I

l 7

1 l8

1 l9

I20

0.2 0.7

20

0.9

0.85 1

0 0.8

5

.75

0.7

20

0.65

0.85

0.8

0.75

-0.2

0.7 5

0.65

20

0.6

Magazine of Concrete Research, 1996,

48,

No. 177



14/15

Zhang et al

Test

number

121

122

123

124

125

126

127

I28

I29

130

131

I32

133

134

I35

136

137

138

139

I40

141

142

I43

I44

145

l46

147

148

I49

150

151

I52

1

53

54

155

156

I57

158

159

l60

161

162

I63

I

64

165

166

374

R

-0.2

-0.5

-0.8

I

S,,,,

~

P

:

f :

Hz

r

cycles

398 380

0.0784116880

0.08031180

0

.55

0.0847

0.9

0.0748

4

0.0853

3

0.85

0.8

I

l

0.084

0.0834

0.0887

0.0798

I

0.0896

0.0822

3235.0752

8860 0.0804

l5 470.0758

0.65

20

5 0

520

IO4 300

0.0784

0.0735

0.6

0.0809

25 770

0.081417350

0.85

0.0807

20

0.0861

1

0.0853

364 0.0X24

0.75

0.0839069

0.0842046

0.7

0.07482 230

0.08

I5

650

0 5

20

1

0.7

5



15/15

Test

number

167

I68

169

170

171

R

- 1

Loading frequ ency and stress reversal effects

on

concrete fat igue

N :

cycles

P

0.65

0.6

20 500

58 070

204 590

93 860

I58 240

0.0804

0,0728

0.0931

0.0779

0.0745

Effect of Loading Frecuency and Stress Revesal on Fatige Life of Plain Concrete

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Transcript of Effect of Loading Frecuency and Stress Revesal on Fatige Life of Plain Concrete