Influence of Phase Transformations on the Residual Stress ...
Lec 12 (Stress Transformations)
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Transcript of Lec 12 (Stress Transformations)
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Review Quiz # 12.1
A 13-kN force isapplied as shown tothe 6-!!dia!eter cast-iron
post ABD."eter!ine the stateof stress at point H.
lue$ draw point %
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'( 13 ecture 12
(tress
ransfor!ation
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(tate of (tress
eneral (tate of
(tress
5lane (tate of (tr
2 nor!al 1 shea
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'a!ples of 5lane (tate of (tress
hin 5lates (urface of (h
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(tress ransfor!ation
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(tress ransfor!ation
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(tress ransfor!ation Aial(tresses4
,ro! tri
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(tress ransfor!ation Aial(tresses4
*f we use (to determine )
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(tress ransfor!ation Aial(tresses4
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(tress ransfor!ation
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(tress ransfor!ation (hear(tress4
A
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(tress ransfor!ation
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'a!ple # 12.1
he state of plane
stress at a point isrepresented &= theele!ent shown."eter!ine the state of
stress at the point onanother ele!entoriented 30° clockwisefro! the positionshown.
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'a!ple # 12.1
>
>
>
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Quiz # 12.2
a.4 "eter!ine the state of stress at poinA
&.4 "eter!ine an e?uivalent state ofstress of an ele!ent at point A rotated
@
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)ai!u! Nor!al (tress
)ai!ized if$
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)ai!u! Nor!al (tress
he e?uation has two roots
he roots are 19@ apart
2514 and 2524 are 19@ apart
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)ai!u! Nor!al (tress
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)ai!u! Nor!al (tress
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)ai!u! Nor!al (tress
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)ai!u! Nor!al (tress
Principal
Stresses
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5rincipal (tresses
*f
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5rincipal (tresses
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'a!ple # 12.2
Represent thefollowin< state ofstress in ter!s ofthe principal
stresses.
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'a!ple # 12.2
Alon< what directionB
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'a!ple # 12.2
NotNecess
y!
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'a!ple # 12.2
Chen
Chen
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)ai!u! (hear (tress *n 5lane4
)ai!ized if$
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)ai!u! (hear (tress *n 5lane4
N'A*D' R'*5R+A of theepression for 25
25 and 2s are :@ apart
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)ai!u! Nor!al and (hear(tress
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)ai!u! (hear (tress *n 5lane4
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)ai!u! (hear (tress *n 5lane4
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)ai!u! (hear (tress *n 5lane4
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)ai!u! (hear (tress *n 5lane4
l ( h (h (
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Nor!al (tress when (hear (tress*n 5lane4 is )ai!u!
Chen
' l # 12 2
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'a!ple # 12.2
"eter!ine the
!ai!u! in-planeshear stress andavera
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'a!ple # 12.2
' l # 12 2
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'a!ple # 12.2
' l # 12 2
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'a!ple # 12.2
Q i # 12 3
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Quiz # 12.3
,or the loadin<
showndeter!ine theprincipal stressand !ai!u! in-
plane shearstress at point A."raw the state ofstress at each
case
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(tress ransfor!ation
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(tress ransfor!ation
(tress ransfor!ation
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(tress ransfor!ation
akin< the s?uare of &oth sides of the
e?uation
(tress ransfor!ation
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(tress ransfor!ation
akin< the su! of the e?uations
CIRCLE!
)ohrEs ircle
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)ohr s ircle
enter at Fave 4
Radius >
)ohrEs ircle (i
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)ohr s ircle (i
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'a!ple # 12.3
"eter!ine the
principal stress the!ai!u! in-planeshear stress andavera
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'a!ple # 12./
"eter!ine the
stress co!ponentseerted on theele!ent o&tained&= rotatin< the
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(tate of (tress
eneral (tate of(tress
5lane (tate of (tr2 nor!al 1 shea
eneral (tate of (tress
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eneral (tate of (tress
eneral (tate of(tress
3 nor!al 3 shear4
riaial (tate of (tre3 nor!al4
5lanar (tate of (tress
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5lanar (tate of (tress
GH 5lane
GI 5lane HI
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5lanar (tate of (tress (opposite
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5lanar (tate of (tress (oppositesign)
%'
F1 and F2 have opposite
si
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'a!ple # 12.0
"eter!ine theprincipalstresses and thea&solute
!ai!u! shearstress.
Quiz # 12./
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Quiz # 12./
"eter!ine
a4 the value of τ=for which the in-planeshearin< stressparallel to the weld is
zero
&4 the correspondin<principal stresses
c4 the a&solute !a