Análise de Fadiga Segundo o Método Tensão – Vida (S-N) – Módulo 2.1 FADIGA DOS MATERIAIS...

Anaacutelise de Fadiga Segundo o Meacutetodo Tensatildeo ndash Vida (S-N) ndash Moacutedulo 21

FADIGA DOS MATERIAIS

Prof

esso

res bull Jorge Luiz Almeida Ferreira


Filosofia utilizada quando a monitoraccedilatildeo da trinca eacute difiacutecil ou antieconocircmica e para componentes criacuteticos quanto a seguranccedila e funcionamento

Determinaccedilatildeo da Resistecircncia a Fadiga e

Previsatildeo da iniciaccedilatildeo de trincas de fadiga nas vidas longas sob tensotildees que satildeo macroscopicamente elaacutesticas

AplicaccedilatildeoProjeto para Vida Segura


Inuacutemeras Fontes de Informaccedilotildees Teacutecnicas Por trabalhar no regime linear elaacutestico admite o uso do princiacutepio da superposiccedilatildeo Facilidades Computacionais Robusto ndash Em geral prevecirc falha antes dela ocorrer

Vantagens na Utilizaccedilatildeo do Meacutetodo


O material eacute modelado como contiacutenuo homogecircneo isotroacutepico linear e elaacutestico

A Maacutexima Tensatildeo Equivalente do ponto analisado deve ser menor do que a resistecircncia ao escoamento material

Baseia-se na correlaccedilatildeo entre o iniacutecio do trincamento de qualquer peccedila com a vida de iniciaccedilatildeo e propagaccedilatildeo de trincas em corpos de prova padronizados

Hipoacuteteses Baacutesicas


Origem do Estudo de Fadiga1829 - Wilhelm August Julius Albert Observou estudou e publicou resultados de testes realizados em correntes de ferro submetidas a carregamentos ciacuteclicos Wilhelm construiu uma maacutequina que carregava repetidamente uma corrente A sua descoberta foi que a falha natildeo era associada a sobrecargas acidentais mas sim dependente da carga e do nuacutemero de repeticcedilotildees dos ciclos de carga

(1787 dagger ndash 1846 )


Origem do Estudo de Fadiga1830 - 1860 - Falhas em Eixos ferroviaacuteriosSem motivo aparente eixos ferroviaacuterios fraturavam apoacutes apenas algumas centenas de quilocircmetros de serviccedilo Embora projetados de acordo com criteacuterios de resistecircncia estaacutetica as fraturas ocorriam sob condiccedilotildees de carregamento normal Apesar de ensaios de traccedilatildeo realizados no material antes da entrada em serviccedilo revelarem adequada ductilidade a ruptura em serviccedilo natildeo apresentava sinais de deformaccedilatildeo plaacutestica Ainda estes mesmos ensaios realizados no material apoacutes a fratura apresentavam as caracteriacutesticas de ductilidade iniciais


Origem do Estudo de Fadiga1860 - August Woumlhler Engenheiro alematildeo que estudou de forma sistemaacutetica o comportamento de falha em eixos ferroviaacuterios Dentre as suas contribuiccedilotildees podem ser citadas (1819 dagger ndash 1914 ) - Ajudou a melhorar os procedimentos de testes de eixos (aumentando a vida uacutetil do eixo)-Desenvolveu o teste de fadiga rotativa de flexatildeo -Introduziu o conceito de limite de fadiga-Iniciou o desenvolvimento de estrateacutegias de projeto contra fadiga e identificou o efeito das tensotildees alternadas e meacutedias e da presenccedila de descontinuidades

sobre o processo de falha


Origem do Estudo de FadigaAbordagem de Woumlhler


M = P ∙ l

P

PP

P

a

a

z z

y

y

l Mz




z z

y

y

Mz

d2

SindI

Mp z 2

p

y

z

xxx (p)

Sindy 2

zz




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

= = ∙t

64

4dI zz




z z

y

y

Mz

d2

3

32dM z

alt

p Sindy 2

0 60 120 180 240 300 360

alt


Origem do Estudo de FadigaAbordagem de Woumlhler Uma das primeiras maacutequinas usadas foi desenvolvida pelo Eng August Woumlhler (22061819 ndash 21031914) e serviu para testar Corpos de Prova em balanccedilo sob flexatildeo rotativa


Origem do Estudo de Fadiga1910 ndash O H Basquin Utilizando dados obtidos por Woumlhler desenvolveu e publicou leis empiacutericas caracterizando a relaccedilatildeo entre a tensatildeo alternada aplicada sobre um componente mecacircnico e a sua vida - curvas S-N (ou de Woumlhler) Ele mostrou uma relaccedilatildeo linear em um graacutefico log-log da tensatildeo com o nuacutemero de ciclos ateacute a falha


Filosofia do Meacutetodo S-NConstruccedilatildeo de relaccedilotildees empiacutericas entre a tensatildeo aplicada no ponto criacutetico de um corpo de prova padronizado e o tempo de vida necessaacuterio para rompecirc-lo

Log Vida (Ciclos)104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita

Limite de Resistecircncia a FadigaVida Infinita

N

S


Anaacutelise da Resistecircncia agrave FadigaA resistecircncia agrave fadiga do material eacute uma propriedade mecacircnica medida por meio de ensaios mecacircnicos realizados sob condiccedilotildees de carregamento simplesValer ressaltar entretanto que a resistecircncia do corpo de prova depende fortemente dos detalhes geomeacutetricos Log Vida (Ciclos)

104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S


Evoluccedilatildeo dos Ensaios S-NCPs de Fadiga Satildeo Testados em Muitos Tipos de Maacutequinas

Na maacutequina de ensaio proposta por R R Moore o efeito da presenccedila de esforccedilos cortante eacute anulado utilizando o conceito de flexatildeo em 4 pontos

-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo



Nas maacutequinas de ensaio modernas o controle de carga e facilidades de intrumentaccedilatildeo permitem a realizaccedilatildeo de investigaccedilotildees mais completas e complexas aleacutem de permitir a obtenccedilatildeo de resultados mais confiaacuteveis




-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo


Caracterizaccedilatildeo dos Esforccedilos Geradores do Processo de FadigaProcesso de Fadiga eacute Causado

Primariamente pela Aplicaccedilatildeo de Forma Repetida de Esforccedilos (Tensotildees e Deformaccedilotildees) sobre o(s) Ponto(s) Criacuteticos de Estruturas Para Caracterizar os Esforccedilos satildeo Utilizados os Seguintes Paracircmetros

mi nmax

2

minmax a

Gama de Tensatildeo

Tensatildeo Alternada a

Tensatildeo Meacutedia m

2

minmax m

Razatildeo de Carregamento R Min

Max

R


Anaacutelise da Curva de Resistecircncia agrave Fadiga

Conforme pode-se observar do graacutefico ao lado a vida do corpo de prova N depende fortemente do niacutevel de tensatildeo que eacute aplicado na seccedilatildeo criacutetica do corpo de prova

Log Vida (Ciclos)103 104 105 106 Ne

S-N Curve

Vida Finita


N

Sf

Se


Anaacutelise da Curva de Resistecircncia agrave FadigaTiacutepicamente satildeo adotadas as relaccedilotildees

para descrever a dependecircncia entre a resistecircncia a fadiga Sf e a vida N Log Vida (Ciclos)

103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se

Limite de Validade 103 lt N lt Ne

onde Ne rarr Vida Infinita

Se rarr Limite de Resistecircncia a Fadiga

fSbANL og

Atividade Relatoacuterio sobre a Norma ASTM 739


Anaacutelise da Curva de Resistecircncia agrave FadigaO Limite de Resistecircncia a Fadiga foi observado por Woumlhler quando analisava resultados de seus ensaios de fadiga em accedilo

Para accedilos considera-se vida infinita Ne vidas entre os seguintes limites 106 e 107 ciclosOutros materiais podem ou natildeo apresentar um limite de fadiga bem definido


S-N Curve

Vida Finita


N

Sf

Se


Equacionamento da Relaccedilatildeo S-NConforme descrito anteriormente a relaccedilatildeo entre S e N eacute expressa porb

f NAS

NL o gbAL o gSL o g f

103 lt N lt Ne Log(

S)

Log(N)Log(103) Log(Ne)

Assim com base em dados experimentais eacute possiacutevel utilizando-se teacutecnicas de regressatildeo linear obter os valores de A e de b


Equacionamento da Relaccedilatildeo S-NConforme descrito anteriormente a relaccedilatildeo entre S e N eacute expressa por

2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6

Vida (Num de C ic los)

3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes

Pontos Experim enta is Am ostra A

Pontos Experim enta is Am ostra B

C urva S-N - Tendecircncia Am ostra A

C urva S-N - Tendecircncia Am ostra B

L im ites do In terva lo de C onfianccedila

bf NAS


103 lt N lt Ne

Estudo com o Accedilo ASTM A743 CA6NM mostrou que o seu Limite de Resistecircncia a Fadiga eacute 384 MPa

09401406 NS


Equacionamento da Relaccedilatildeo S-N

bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)

Na ausecircncia de informaccedilotildees experimentais confiaacuteveis ainda eacute possiacutevel estimar a curva S-N utilizando-se a seguinte receita

bNALogSLog

SSNN

ee

efe

log


Equacionamento da Relaccedilatildeo S-NResolvendo o Sistema

3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)

Log(103) ee NbSA loglog10



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)

Para Accedilos admite-se que os valores de S103 e Se podem ser estimados por meio das seguintes relaccedilotildees

S103 = 09Srt

Se = 05Srt Srt le 1400MPa ou

= 700MPa Srt gt1400MPa

Ne = 106


Equacionamento da Relaccedilatildeo S-NPara outros materiais o valor de Se pode ser estimado pelas relaccedilotildeesFerros fundidos Sf(106) = 04 Srt

ligas de Alumiacutenio pode-se assumir um limite de resistecircncia agrave fadiga em 5108 ciclos estimado por

Sf(5108) = 04S Srt Srt lt 325 MPa ou

Sf(5108) = 130MPa Srt gt 325MPa

ligas de Magneacutesio Sf(108) = 035 Srt

ligas de Cobre Sf(108) = 025 a 050 Srt

ligas de Niacutequel Sf(108) = 035 a 05 Srt

ligas de Titacircnio Sf(106 a 107) = 045 a 065 Srt


Equacionamento da Relaccedilatildeo S-NExemplo Estimar a Curva de Resistecircncia a Fadiga do Accedilo ASTM A743 CA6NM

6

Log(9182)

Log(09918)

3

A 1 8901 9192 917

Meacutedia 918Desvio Padratildeo 16

B

Tensatildeo de Resistecircncia [MPa]

Amostra Ensaio


Equacionamento da Relaccedilatildeo S-NSubstituindo os valores teremos

08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)

3 MPaA b 147510610log200log

09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)

Outra metodologia utilizada consiste em acoplar agrave relaccedilatildeo S-N a equaccedilatildeo de Basquin ou seja

ksiSrtf 50

bff NS 2

bf NAS Relaccedilatildeo S-N

Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)

Recorrendo a equaccedilatildeo de Basquina estimativa da constante A e do expoente b eacute realizada segundo a seguinte expressatildeo

bf

e

f

e

A

N

S

b

2

2log

log


Equacionamento da Relaccedilatildeo S-NExemplo Estimar a Resistecircncia a Fadiga do Accedilo ASTM A743 CA6NM

6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio


Equacionamento da Relaccedilatildeo S-NSrt = 918 MPa

Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)

1o Meacutetodo 2o Meacutetodo


Resistecircncia agrave Fadiga de Componentes Estruturais

A resistecircncia agrave fadiga do material eacute medida em pequenos CPs padronizados com diacircmetro especiacutefico d 8mm sem entalhes ou tensotildees residuais acabamento polido testados em flexatildeo rotativa de 4 pontos temperatura e atmosfera controladas


Resistecircncia agrave Fadiga de Componentes EstruturaisEm Condiccedilotildees Reais de Uso

diversos fatores influenciam significativamente a vida agrave fadiga de peccedilas reais os fatores que alteram as tensotildees macroscoacutepicas devem ser tratados nas solicitaccedilotildees mas quando a escala dimensional do efeito do fator eacute pequena eacute melhor consideraacute-lo como modificador da resistecircncia agrave fadiga do material


Resistecircncia agrave Fadiga de Componentes EstruturaisUma forma de estimar a resistecircncia a fadiga de um componente estrutural Se consiste no uso dos fatores de Marin

ecbae SKKKS

Ka = Fator de Acabamento SuperficialKb = Fator de TamanhoKc = Fator de CarregamentoKd = Fator de TemperaturaKe = Fator de Entalhe = Limite de Resistecircncia a Fadiga do Material

eS


Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Acabamento Superficial -

KaProcura caracterizar o efeito sobre a resistecircncia agrave fadiga do tipo de acabamento que a superfiacutecie da peccedila possui

Para o Accedilo ASTM A743 CA6NM

Ka = 073 (Acabamento Usinado)Ka = 035 (Corroiacutedo em Aacutegua Doce)Ka = 024 (Corroiacutedo em Aacutegua Salgada)



KaAlgumas Relaccedilotildees Empiacutericas

polida ka = 1

retificada ka = 158Srt-0085

laminada a frio ou usinado ka = 451Srt-0265

laminada a quente ka = 577Srt-0718

forjada ka = 272 Srt-0995

[ Srt ] = MPa


Resistecircncia agrave Fadiga de Componentes EstruturaisProjeto contra fadiga - Exemplo

Um eixo deve ser projetado para que seja suportado por mancais de rolos A geometria baacutesica eacute mostrada na figura Para um fator de projeto de 128 estime o diacircmetro do eixo de forma que ele suporte uma carga de 35 kN a 100 mm do mancal esquerdo

Accedilo AISI 1025 Lam a FrioMechanical Properties Metric

Hardness Brinell 121Tensile Strength Ultimate 415 MPa

Tensile Strength Yield 310 MPa

Elongation at Break 20

Reduction of Area 45 Modulus of Elasticity 200 GPaPoissons Ratio 029Shear Modulus 800 GPa




kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN

14 kNMmax = 210 kNxmm


Resistecircncia agrave Fadiga de Componentes Estruturais kNRR 53411221

21kN

14 kN

Mmax = 210 kNxmm

Projeto contra fadiga - ExemploIdentificaccedilatildeo da Seccedilatildeo Critica

z z

y

y

Mz = 210 kNxmm



Dimensionamento Estaacutetico

z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm



Dimensionamento a Fadiga

FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm

eae SKS Srt = 415 MPa

Ka = 08

MPaSe 1664155080


Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Tamanho - Kb

Traccedilatildeo-Compressatildeo

Flexatildeo

Menor diacircmetro

Maior diacircmetro

O gradiente de tensatildeo parece ser o responsaacutevel por ambos os efeitos


No caso de flexatildeo rotativa ou de torccedilatildeo de peccedilas circularesKb = (d 762)-01133 (20 lt d lt 80mm)

Outra receita eacute dada por d lt 8 mm Kb = 1 8 lt d lt 50mm Kb = 090 50 lt d lt 80mm Kb = 080

d gt 80mm Kb = 075 a 060 No caso de traccedilatildeo pura usar kb = 1Este valor de kb = 1 em traccedilatildeo estaacute associado ao fato do ser o gradiente de tensotildees a causa do efeito de tamanho





FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM


Para peccedilas natildeo-circulares ou de carregamento por flexatildeo alternada eacute comum usar um deq para obter kb

igualando as regiotildees das peccedilas e dos CPs com (digamos) S gt 095Smax por exemplo



Carregamentos Torcionais ATENCcedilAtildeO ndash VER EXEMPLO

No caso de carregamentos axiais puros usar

Kc = 092 quando Srt lt 1520MPa ou

Kc = 1 se Srt gt 1520MPa

(uma provaacutevel causa para o uso desses valores sob condiccedilotildees de carregamentos axiais puros estaacute relacionada a falta de controle da excentricidade nos testes axiais de traccedilatildeo-compressatildeo onde eacute muito difiacutecil alinhar as garras da maacutequina e eliminar os fletores indesejaacuteveis)

Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Carregamento - Kc


Am b ientea Tem p era tur

T ra b a lhod e a T em p era tur

rt

rtd S

SK

0 200 400 600 800Tem peratura [C els ius]

0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd

Accedilo Meacutedio Carbono

Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Temperatura - Kd


Entalhes satildeo pontos preferenciais de iniciaccedilatildeo de trincas

Tipicamente as tensotildees maacuteximas observadas nesses pontos podem ser estimadas utilizando-se o conceito de fator de concentraccedilatildeo de tensotildees Kt ou seja N o mtM a x SKS

Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Entalhe - Ke


bullEntrento a iniciaccedilatildeo de uma trinca eacute fortemente dependente da presenccedila de gradiente das tensotildees atuantes no ponto criacuteticobull Como consequumlecircncia o efeito real dos entalhes pequenos em fadiga eacute menor do que o valor teoacuterico previsto por Kt

bull Assim Para quantificar o efeito da presenccedila do entalhe sobre a fadiga introduz-se os conceitos do fator de reduccedilatildeo da resistecircncia agrave fadiga Kf e da sensibilidade ao entalhe q



O Fator de Reduccedilatildeo da Resistecircncia agrave Fadiga eacute definido pela seguinte relaccedilatildeo

E nta lhe) C o m (C P

E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K

SS E nta lhe) Sem (C P

(E nta lhe)

Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Reduccedilatildeo de Resistecircncia a Fadiga

- Kf

Assim de forma semelhante ao Fator de Concentraccedilatildeo Teoacuterico o Fator de Reduccedilatildeo da Resistecircncia agrave fadiga pode ser usado para estimar a tensatildeo maacutexima atuante no ponto mais solicitado do entalhe devido a aplicaccedilatildeo de uma tensatildeo nominal de intensidade igual a Snom ou seja


O Fator de Concentraccedilatildeo de Tensotildees Kt e o Fator de Reduccedilatildeo da

Resistecircncia agrave Fadiga Kf relacionam-se da seguinte Forma

11 tf KqK

tf KK 1IMPORTANTE

Resistecircncia agrave Fadiga de Componentes EstruturaisRelaccedilatildeo entre Kt Kf e o Material

onde q representa a Sensibilidade do material a presenccedila do entalhe


O Fator de Sensibilidade ao Entalhe q eacute um Paracircmetro que Procura Quantificar o Efeito do Material e das Dimensotildees do Entalhe sobre a Intensidade do Gradiente de Tensotildees

x

Sx

Tamanho Meacutedio dos

Gratildeos

x


Gratildeos

Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Sensibilidade a Presenccedila de Entalhes - q



Relaccedilotildees Mais Usadas

0 400 800 1200 1600 2000Limite de Resistencia a Traccedilatildeo rt [MPa]

0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]

Ligas Al RecozidasLigas Al EndurecidasAccedilos Baixa Liga (sob flexatildeo)Curva de TendecircnciaLineScatter Plot 3

07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq

Valores Tiacutepicos para a satildeo os que seguem

ap = 051mm (ligas de Al)

ap = 0185(700Srt) mm (accedilos Srtlt 700MPa) ou

ap = 0025(2000Srt)19 mm (accedilos Srt gt700MPa)

Peterson (1959)



0 400 800 1200 1600 2000

Limite de Resistencia a Traccedilatildeo rt [MPa]

0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1

Resistecircncia agrave Fadiga de Componentes EstruturaisFator de Entalhe Ke

Se = KaKbKcKdKeSe

Limite de Resistecircncia a Fadiga do Componente

Se1

Se2

Se3Cada Ponto Material do Componente Teraacute a Sua Resistecircncia a Fadiga


Resistecircncia agrave Fadiga de Componentes EstruturaisCurva de Resistecircncia a Fadiga Corrigida em Funccedilatildeo dos Fatores de

Marin

1E+3 1E+4 1E+5 1E+6 1E+7Nuacutemero de Ciclos

S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn


Resistecircncia agrave Fadiga de Componentes EstruturaisExemplo Determinar a Resistecircncia a Fadiga da Peccedila abaixo

considerando que a mesma eacute fabricado por usinagem em accedilo ASTM A743 CA6NMH2 = 200 mm

V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm

Srt = 918 MPaSrsquoe = 417 MPa (Flexatildeo Rotativa)

Pontos Criacuteticos



considerando que a mesma eacute fabricada em accedilo ASTM A743 CA6NM

A ndash Determinaccedilatildeo do Fator de acabamento ka

Acabamento Usinado ka = 451Srt-0265

O Dois Pontos Criacuteticos possuem Fator de Acabamento Iguais a 075




B ndash Determinaccedilatildeo do Fator de Tamanho kb

Carga de Traccedilatildeo kb = 1

O Dois Pontos Criacuteticos possuem Fator de Tamanho Iguais a 1




C ndash Determinaccedilatildeo do Fator de Carregamento kc

Carga de Traccedilatildeo kc = 092 (Srt lt 1520 MPa)

O Dois Pontos Criacuteticos possuem Fator de Carregamento Iguais a 092




D ndash Determinaccedilatildeo do Fator de Temperatura kd

Temperatura Ambiente kd = 1





E ndash Determinaccedilatildeo do Fator de Entalhe ke

E1 ndash Fator de Concentraccedilatildeo de Tensotildees Kt

Furo Kt = 254

Pescoccedilo Kt = 242Forma de Obtenccedilatildeo Elementos Finitos





E1 ndash Fator de Sensibilidade ao Entalhe q Furo = 25 mmPesc = 125 mm

11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919





E2 ndash Fator de Reduccedilatildeo de Resistencia a Fadiga Kf

KtFuro = 254 qFuro = 0958

KtPesc = 242 qPesc = 0919

11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa


Resistecircncia agrave Fadiga de Componentes EstruturaisTeacutecnicas para Minimizar o efeito dos Concentradores de Tensatildeo

sobre a FadigaSuavizar o Fluxo dos Esforccedilos retirando material se necessaacuterio

Projeto Eficiente

Projeto Pobre



sobre a FadigaReverter o fluxo das linhas de forccedila diminui o Kt

Projeto EficienteProjeto Pobre



sobre a Fadiga

No Parafuso as Linhas de Forccedila satildeo Melhor Distribuiacutedas se a Fecircmea da

Uniatildeo Roscada tambeacutem trabalhar agrave traccedilatildeo

Projeto Pobre Projeto Pobre

Projeto Eficiente



sobre a FadigaCantos Vivos tecircm Kt Grande e Devem ser Evitados

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente



sobre a Fadiga Projetos Eficientes

Retirar material para diminuir a rigidez do engaste gera um Kt menor e aumenta a sua resistecircncia final



sobre a Fadiga

Outros Projetos Eficientes


A vida em fadiga eacute fortemente influenciada pela presenccedila de tensotildees normais meacutedias

Stre

ss S

Cycles (Log N)

Tensatildeo normal de Traccedilatildeo aumenta

2 3 4 5 6 7 8 91E +5 1E +6Life [N um ber o f C ycle ]

2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Diagrama de Haig

Vida Especificada N

N


Melhor Ajuste para os Pontos Experimentais

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Modelos de Previsatildeo


rt

mara S

S 1

aresistecircnci de limite 0 para fadiga de limite

meacutedia normal tensatildeo de presenccedila na fadiga de limite

rt

mar

m

ma

SS

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Equaccedilatildeo de Goodman

(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Equaccedilatildeo de Gerber

(1874)


TensotildeesdeRazatildeoRaFadiga parLimite de S

mal MeacutediaTensatildeo Norepresenccedila dFadiga naLimite de

mar

m

ma

0

ara SR

12

2araam S

aram SR

21

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Smith-Watson-Topper

(1970)


MaterialdoParacircmetroTensotildeesdeRazatildeoR

aFadiga parLimite de Smal MeacutediaTensatildeo Nor

epresenccedila dFadiga naLimite de

mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Walker (1970)


0

tan

1

1

mar

R

f

m

ma

aFadiga parLimite de SCiclosdeNumeroN

MaterialdoParacircmetroBasquindeExpoenteb

BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Kwofie (2001)


Hipoacuteteses Equaccedilatildeo Resultante Modelo

= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1

Sy controla o efeito da tensatildeo meacutedia 1

y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt

21 RSara Walker Eq (29)

Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Particularizaccedilatildeo do Modelo de

Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie


Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Anaacutelise do Accedilo ASTM A743 CA6NM

09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie

10E+3 10E+4 10E+5 10E+6 10E +7Num ber o f Cycle (N )

2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3

T rend Line - K w ofie E q

Basqu in Eq Based on Experim enta l D ata

C on fidence Interva l L im its - Basquin E q

C onfidence Interval L im its - Kw o fie Eq

10E+3 10 E+4 1 0E+5 10E+6 10E +7N um ber of Cycle (N )

2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23

Trend L ine - W alker E q

Basquin Eq Based on Experim ental D ata

C onfide nce In terva l L im its - B asquin E q

Con fidence In terva l L im its - W alker Eq

Goodman

Gerber


Resistecircncia agrave Fadiga de Componentes EstruturaisEfeito da Presenccedila de Tensatildeo Meacutedia ndash Exemplo de Aplicaccedilatildeo

Uma liga de accedilo de alta resistecircncia tem um limite de fadiga de 500 MPa e um limite de resistecircncia de 1000 MPa

O material falharaacute se a tensatildeo ciacuteclica variar entre 0 and 400 MPa Um processo de soldagem introduziu tensotildees residuais de traccedilatildeo da ordem de 500 MPa Que efeito isto traraacute


Tens

atildeo A

ltern

ada

Sa

Tensatildeo Meacutedia Sm

Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1

Natildeo Falha por Escoamento nem por FadigaNatildeo Falha por Fadiga mas Falha por Escoamento

Natildeo Falha por Escoamento mas Falha por Fadiga

Falha por Escoamento e por Fadiga

Resistecircncia agrave Fadiga de Componentes EstruturaisVerificaccedilatildeo da Condiccedilatildeo de Falha


o meacutetodo SN correlaciona o tempo de iniciaccedilatildeo de uma trinca de fadiga nos pontos criacuteticos (geralmente as raizes de entalhes) de qualquer peccedila com a vida de pequenos CPs que tenham a mesma resistecircncia daquele ponto e que sejam submetidos agrave mesma histoacuteria de tensotildees s em serviccediloP

Sy

SMax=KfSNom

Resistecircncia agrave Fadiga de Componentes EstruturaisProjeto Estrutural usando o Meacutetodo Tensatildeo-Vida


P

Sy

SMax= KfSNom

Rotina Baacutesica de projeto 1 avaliar a resistecircncia agrave fadiga do ponto criacutetico da peccedila (incluindo o efeito dos detalhes que afetam a resistecircncia agrave fadiga) 2 calcular a histoacuteria de tensotildees S(t) nele induzida pelo carregamento real

3 quantificar o dano acumulado pelos diversos eventos do carregamento


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Filosofia utilizada quando a monitoraccedilatildeo da trinca eacute difiacutecil ou antieconocircmica e para componentes criacuteticos quanto a seguranccedila e funcionamento

Determinaccedilatildeo da Resistecircncia a Fadiga e

Previsatildeo da iniciaccedilatildeo de trincas de fadiga nas vidas longas sob tensotildees que satildeo macroscopicamente elaacutesticas

AplicaccedilatildeoProjeto para Vida Segura




















M = P ∙ l

P

PP

P

a

a

z z

y

y

l Mz




z z

y

y

Mz

d2

SindI

Mp z 2

p

y

z

xxx (p)

Sindy 2

zz




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

= = ∙t

64

4dI zz




z z

y

y

Mz

d2

3

32dM z

alt

p Sindy 2

0 60 120 180 240 300 360

alt







Log Vida (Ciclos)104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S



104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




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M = P ∙ l

P

PP

P

a

a

z z

y

y

l Mz




z z

y

y

Mz

d2

SindI

Mp z 2

p

y

z

xxx (p)

Sindy 2

zz




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

= = ∙t

64

4dI zz




z z

y

y

Mz

d2

3

32dM z

alt

p Sindy 2

0 60 120 180 240 300 360

alt







Log Vida (Ciclos)104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S



104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

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Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




z z

y

y

Mz

d2

SindI

Mp z 2

p

y

z

xxx (p)

Sindy 2

zz




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

= = ∙t

64

4dI zz




z z

y

y

Mz

d2

3

32dM z

alt

p Sindy 2

0 60 120 180 240 300 360

alt







Log Vida (Ciclos)104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S



104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

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Slide 89

Slide 91

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Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

= = ∙t

64

4dI zz




z z

y

y

Mz

d2

3

32dM z

alt

p Sindy 2

0 60 120 180 240 300 360

alt







Log Vida (Ciclos)104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S



104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

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Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




z z

y

y

Mz

d2

3

32dM z

alt

p Sindy 2

0 60 120 180 240 300 360

alt







Log Vida (Ciclos)104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S



104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

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Slide 96

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Slide 98







Log Vida (Ciclos)104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S



104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

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Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



104 105 106 107 108

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

S




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

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Slide 12

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Slide 98




-15

-10

-5

0

5

10

15

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

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Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98







-40

-30

-20

-10

0

10

20

30

40

0 5 10 15 20 25 30 35 40

Tempo

Tens

atildeo




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 36

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Slide 49

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Slide 51

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Slide 54

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Slide 56

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Slide 60

Slide 61

Slide 62

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Slide 64

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Slide 67

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Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

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Slide 80

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Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




mi nmax

2

minmax a

Gama de Tensatildeo



2

minmax m


Max

R





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

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Slide 6

Slide 7

Slide 8

Slide 9

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Slide 13

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Slide 28

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Slide 31

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Slide 33

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Slide 36

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Slide 39

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Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98





S-N Curve

Vida Finita


N

Sf

Se




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




103 104 105 106 Ne

Tens

atildeo (M

Pa)

S-N Curve

Vida Finita


N

Sf

bf NAS

Se




fSbANL og






S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

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Slide 98





S-N Curve

Vida Finita


N

Sf

Se



f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

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Slide 3

Slide 4

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f NAS


103 lt N lt Ne Log(

S)





2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

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Slide 6

Slide 7

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Slide 91

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Slide 93

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Slide 97

Slide 98



2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 31E+5 1E+6


3

4

5

6

Ten

satildeo

Alte

rnad

a (x

10 P

a)8

Lotes






bf NAS


103 lt N lt Ne


09401406 NS



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

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Slide 7

Slide 8

Slide 9

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Slide 12

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Slide 44

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Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

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Slide 60

Slide 61

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Slide 77

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Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



bALogSLog

SSN f

3

10

3

3

10

103

Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bNALogSLog

SSNN

ee

efe

log



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 36

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Slide 49

Slide 50

Slide 51

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Slide 84

Slide 86

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Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



3

10

10log

log3

e

e

NSS

b

Log(Ne)

Log(Se)

Log(S103)




Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

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Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


S103 = 09Srt



Ne = 106












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

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Slide 24

Slide 25

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Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98












6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

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Slide 25

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Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



08390

1010log

8267462log

3

6

b

6

Log(4627)

Log(826)


09401406 NS



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


ksiSrtf 50

bff NS 2


Eq de Basquin

MPaSrtf 345



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



Log(Ne)

Log(Se)

Log(S103)

Log(103)

Log(

S)

Log(N)


bf

e

f

e

A

N

S

b

2

2log

log



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 33

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Slide 36

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Slide 39

Slide 40

Slide 41

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Slide 43

Slide 44

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Slide 46

Slide 47

Slide 48

Slide 49

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Slide 51

Slide 52

Slide 53

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Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



6

Log(9182)

Log(09918)

3

A 1 8901 9192 917


B


Amostra Ensaio



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



Sf = Srt + 345 = 1263 MPa

MPaA

b

bf 1192212632

0690102log

12636462log

0690

6

100

1000

1000 10000 100000 1000000

Vida (N)

Tens

atildeo (M

Pa)










ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98









ecbae SKKKS


eS









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 28

Slide 29

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Slide 31

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Slide 33

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Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98









polida ka = 1





[ Srt ] = MPa












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

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Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98












kNRa 1225015053 kNRb 41

25010053

kNRR 53411221

21kN




21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



21kN

14 kN

Mmax = 210 kNxmm


z z

y

y

Mz = 210 kNxmm




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

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Slide 19

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Slide 21

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Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




z z

y

y

Mz

d2

tSindMp z

3

32

p

y

z

xxx (p)

Sindy 2

64

4dI zz

FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




FSS

p yMax

31

3

3232

y

zy

z

SFSMdS

dM

mmMPa

mmNd 67120310

2811021032 31

3

d ge 2067mm




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

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Slide 20

Slide 21

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Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




FSSp e

alt

31

3

3232

e

ze

z

SFSMdS

dM

mmMPa

mmNd 4525166

2811021032 31

3

d ge 2545mm


Ka = 08

MPaSe 1664155080




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

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Slide 16

Slide 17

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Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




Flexatildeo

Menor diacircmetro

Maior diacircmetro










FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98









FSSp e

alt

31

32

eba

z

SKKFSMd

mmMPa

mmNd 36269149

2811021032 31

3

d ge 2636mm

ebae SKKS

rarr Kb

MPaSe 9149415509080




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




FSSp e

alt

415508062732 11330

88672

zMd

mmMPa

mmNd 68926166

6272811021032 1133031

113303

d ge 2669mm

ebae SKKS

Kb = (d 762)-01133 (20 lt d lt 80mm) 11330

3 6278032

eez SdS

dM















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

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Slide 12

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Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98















rt

rtd S

SK


0

200

400

600

800

Lim

ite d

e R

esis

tenc

ia a

Tra

ccedilatildeo

[MP

a]


000

020

040

060

080

100

Kd














E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 33

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Slide 35

Slide 36

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Slide 39

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Slide 41

Slide 42

Slide 43

Slide 44

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Slide 46

Slide 47

Slide 48

Slide 49

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Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

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Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98












E nta lhe) Sem (C P

n

nf S

SK

N o mfM a x SKS

f

nn K


(E nta lhe)


- Kf





11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

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Slide 20

Slide 21

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Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

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Slide 77

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Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




11 tf KqK

tf KK 1IMPORTANTE





x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



x

Sx


Gratildeos

x


Gratildeos






0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98





0

05

1

15

2

25

3

025

075

125

175

225

275

Con

stan

te d

e N

eube

r a

[mm

]


07688394 rta

11233532 rta 31919101215 rta e

Na

q

1

1

Neuber (1958)




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




Na

q

1

1

Neuber (1958)


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98


11

paq





Peterson (1959)



0 400 800 1200 1600 2000


0

01

02

03

04

05

a p [m

m]


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98


11

paq





Peterson (1959)




fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98


fe K

K 1


Se = KaKbKcKdKeSe


Se1

Se2




Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



Marin


S

Sn

09 Srt

Se

Ne

a

09Srt

Sn = KaKbKcKdKeSn

Sn




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




V1 = 200 mm

V4 = 150 mm

V7 = 25 mm

d11 = 5 mm

H10 = 10 mm

V9 = 10 mm
































Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98






























Furo Kt = 254







11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98






11

paq

Peterson (1959)



ap = 01098

qFuro = 0958

qPesc = 0919








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98








11 tf KqK

KfFuro = 247

KfPesc = 230




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




Sn = 075109210405417=116

Sn = 075109210435417=125 MPa




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




Projeto Eficiente

Projeto Pobre







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98







sobre a Fadiga




Projeto Eficiente




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente

Projeto Pobre

Projeto Eficiente







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98







sobre a Fadiga




Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



Stre

ss S

Cycles (Log N)



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim en tal Data

R = -1

R = 0

R = 13

R = 23

Trend Line




2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



2

3

4

5

6

7

8

9

100

1000

Sa

MP

a

Experim enta l Data

R = -1

R = 0

R = 13

R = 23

Trend L ine


Vida Especificada N

N





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98





rt

mara S

S 1



rt

mar

m

ma

SS


(1899)


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98


2

1ty

mara S

S



rt

mar

m

ma

SS


(1874)




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98




mar

m

ma

0

ara SR

12

2araam S

aram SR

21


(1970)





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98





mar

m

ma

0

ara SR

1

12

araam S 1

aram SR

2

1



0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98


0

tan

1

1

mar

R

f

m

ma



BasquindeteConsS


R

0940

1

NeS rt

m

R

Sfa

rt

m

Sara eS




= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

Slide 61

Slide 62

Slide 63

Slide 64

Slide 65

Slide 66

Slide 67

Slide 68

Slide 69

Slide 70

Slide 71

Slide 72

Slide 73

Slide 74

Slide 75

Slide 76

Slide 77

Slide 78

Slide 79

Slide 80

Slide 81

Slide 82

Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

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Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



= 1 1rt

m

ar

a

SS

Goodman Eq (24)

= 1


y

m

ar

a

SS

Soderberg Eq (26)

rt

m

rt

m

SSf

1

2

y

m

ar

a

SS

Gerber Eq (23)

f

m

f

m

SSf

1

2

f

m

ar

a

SS

Morrow Eq (27)

2

12

RLnS

SRfm

rtmrt

21

21

RSara Smith-Watson-

Topper Eq (28)

2

1 RLnS

SRfm

rtmrt



Kwofie



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

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Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



09409184531

1406

Nem

a

094040701

14061

2

N

Ra

Modelo de Walker

Modelo de Kwofie


2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 1 3

R = 2 3






2

3

4

5

6

7

8

9

100

1000

Sar [

MPa

]

R = -1

R = 0

R = 13

R = 23





Goodman

Gerber






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

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Slide 23

Slide 24

Slide 25

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Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

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Slide 57

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Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98






Tens

atildeo A

ltern

ada

Sa


Sa

Sm Syt

Syt

Se

Srt

rte

e

yt

m

SS

SS

S 11

1







Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

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Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98



Sy

SMax=KfSNom



P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 42

Slide 43

Slide 44

Slide 45

Slide 46

Slide 47

Slide 48

Slide 49

Slide 50

Slide 51

Slide 52

Slide 53

Slide 54

Slide 55

Slide 56

Slide 57

Slide 58

Slide 59

Slide 60

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Slide 83

Slide 84

Slide 86

Slide 87

Slide 89

Slide 91

Slide 92

Slide 93

Slide 94

Slide 96

Slide 97

Slide 98


P

Sy

SMax= KfSNom




Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Análise de Fadiga Segundo o Método Tensão – Vida (S-N) – Módulo 2.1 FADIGA DOS MATERIAIS...

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Transcript of Análise de Fadiga Segundo o Método Tensão – Vida (S-N) – Módulo 2.1 FADIGA DOS MATERIAIS...