Lec 13 (Theories of Failure)
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Transcript of 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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a9imum +hear +tre Theor: ; Tre"a ai%ure -riterion
$ @1 an @5 have the ame in,
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a9imum +hear +tre Theor: ; Tre"a ai%ure -riterion
$ @1 an @5 have o!!oite in,
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a9imum +hear +tre Theor: ; Tre"a ai%ure -riterion
$ @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