Lec 13 (Theories of Failure)

8/16/2019 Lec 13 (Theories of Failure)

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Review Quiz # 13.1Determine

a) Normal and shearingstresses on the horizontal and vertical planes.

b) The orientation φ

(0≤φ≤60°), with re!e"t tothe iven tate o$ tre, o$the !%ane where the norma%tre i e&ua% to zero. 'hati the "orre!onin

hearin tre on that


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*+ 13 4e"ture 13

Theorie o$

ai%ure


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ateria% ai%ure

Du"ti%e ateria%($ai%ure ue to hear

tree)

8ritt%e ateria%($ai%ure ue to norm

tree)


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Theorie o$ ai%ureDu"ti%e ateria%

a9imum +hear +tre Theor: ;

Tre"a ai%ure -riterion

a9imum Ditortion *ner:

Theor:

8ritt%e ateria%

a9imum orma% +tre Theor:


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a9imum +hear +tre Theor: ; Tre"a ai%ure -riterion

tate that :ie%in o$ the materia% beinwhen the abo%ute ma9imum hear trethe materia% rea"he the hear tre that

"aue the ame materia% to :ie% when itub>e"te only to a9ia% tenion


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$ @1 an @5 have the ame in,


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$ @1 an @5 have o!!oite in,


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$ @1 an @5 have o!!oite in,

$ @1 an @5 have ame in,


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*9am!%e # 13.1/ a reu%t o$ evera%

teni%e tet, it ha been$oun that the teni%e:ie% trenth i @Y C 570

a $or the rae o$ tee%

ue.Determine the $a"tor o$a$et: with re!e"t to:ie%, uin the

ma9imumEhearin


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a9imum Ditortion *ner: Theor:

tate that :ie%in in a u"ti%e materia%o""ur when the itortion ener: !er univo%ume o$ the materia% e&ua% or e9"ee

itortion ener: !er unit vo%ume o$ theame materia% when it i ub>e"te to:ie%in in a im!%e tenion tet.


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+train *ner: Denit:

ener: tore uner e9terna% %oain !er

unit vo%ume o$ materia%

'ithin the e%ati" rane,


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+train *ner: Denit:

C FGo%ume -hane +ha!e

D+T


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Ditortion *ner: Denit:

When , ,

or !%anar "ae (),


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Ditortion *ner: Denit:

or !%anar "ae (),

or unia9ia% "ae (),


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a9imum Ditortion *ner: Theor:

von Mises stress:


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Theorie o$ ai%ure $or Du"ti%eateria%

D*T i, at mot, 17I more

a""urate than ++T (ure hear)


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a9imum orma% +tre Theor:

tate that a britt%e materia% wi%% $ai% when

the ma9imum norma% tre in the materirea"he a va%ue e&ua% to the u%timate nortre the materia% "an utain when it iub>e"te to im!%e tenion.


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ohr


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ohr


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*9am!%e # 13.5Liven that the materia%

ha a :ie% tre o$ 570a, @:C0.7@9 an

M9:C0.57@9 , etermine

ma9 @9 uin

a) the ma9imum hearintre theor:

b) the ma9imum

itortion ener:


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Theorie o$ ai%ure $or Du"ti%eateria%


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Quiz # 13.5

Nnowin that $or the a%uminum a%%o: u@OT C ?0 a an @O- C 500 a an u

ohr

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Lec 13 (Theories of Failure)