lec 12 (stress transformations)

8/16/2019 Lec 12 (Stress Transformations)

1/59

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 %


2/59


3/59


4/59

'( 13 ecture 12

(tress

ransfor!ation


5/59

(tate of (tress

eneral (tate of

(tress

5lane (tate of (tr

2 nor!al 1 shea


6/59

'a!ples of 5lane (tate of (tress

hin 5lates (urface of (h


7/59


8/59

(tress ransfor!ation


9/59



10/59

(tress ransfor!ation Aial(tresses4

,ro! tri


11/59


*f we use (to determine )


12/59



13/59



14/59

(tress ransfor!ation (hear(tress4

A


15/59



16/59

'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.


17/59

'a!ple # 12.1

>

>

>


18/59

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

@


19/59


20/59

)ai!u! Nor!al (tress

)ai!ized if$


21/59


he e?uation has two roots

he roots are 19@ apart

2514 and 2524 are 19@ apart


22/59



23/59



24/59



25/59


Principal

Stresses


26/59

5rincipal (tresses

*f


27/59

5rincipal (tresses


28/59

'a!ple # 12.2

Represent thefollowin< state ofstress in ter!s ofthe principal

stresses.


29/59

'a!ple # 12.2

Alon< what directionB


30/59

'a!ple # 12.2

NotNecess

y!


31/59

'a!ple # 12.2

Chen

Chen


32/59

)ai!u! (hear (tress *n 5lane4

)ai!ized if$


33/59


N'A*D' R'*5R+A of theepression for 25

25 and 2s are :@ apart


34/59

)ai!u! Nor!al and (hear(tress


35/59



36/59



37/59



38/59


l ( h (h (


39/59

Nor!al (tress when (hear (tress*n 5lane4 is )ai!u!

Chen

' l # 12 2


40/59

'a!ple # 12.2

"eter!ine the

!ai!u! in-planeshear stress andavera


41/59

'a!ple # 12.2

' l # 12 2


42/59

'a!ple # 12.2

' l # 12 2


43/59

'a!ple # 12.2

Q i # 12 3


44/59

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


45/59



46/59




47/59


akin< the s?uare of &oth sides of the

e?uation



48/59


akin< the su! of the e?uations

CIRCLE!

)ohrEs ircle


49/59

)ohr s ircle

enter at Fave 4

Radius >

)ohrEs ircle (i


50/59

)ohr s ircle (i


51/59

'a!ple # 12.3

"eter!ine the

principal stress the!ai!u! in-planeshear stress andavera


52/59

'a!ple # 12./

"eter!ine the

stress co!ponentseerted on theele!ent o&tained&= rotatin< the


53/59

(tate of (tress

eneral (tate of(tress

5lane (tate of (tr2 nor!al 1 shea

eneral (tate of (tress


54/59

eneral (tate of (tress

eneral (tate of(tress

3 nor!al 3 shear4

riaial (tate of (tre3 nor!al4

5lanar (tate of (tress


55/59

5lanar (tate of (tress

GH 5lane

GI 5lane HI


56/59

5lanar (tate of (tress (opposite


57/59

5lanar (tate of (tress (oppositesign)

%'

F1 and F2 have opposite

si


58/59

'a!ple # 12.0

"eter!ine theprincipalstresses and thea&solute

!ai!u! shearstress.

Quiz # 12./


59/59

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

lec 12 (stress transformations)

Documents