6-Derste Cozulen Problemler

8/18/2019 6-Derste Cozulen Problemler

1/23


2/23

PROBLEM 1: TERMAL STRES

• İki ade 1!"" ## $%&'(da $ak)* +'$'k e,(e#e- iki$ %k a*a,)(da /e $a0 a*)(da( ka&(ak edi #i0 d'*'#da$' '(#ak ad)*.

• Bak)* +'$'k a* a*a,)(da i,e $i* ade a '#i#&'# +'$'k$' '('&%*.

• A '#i(&'# +'$' '( $i* '2' i e $ %k a*a,)(da 1 ##$%0 'k $' '(#ak ad)*.

• Bak)* +'$'k a*)( 3 Ke,i a a() AB45!" ## 5 3 Te*#a '-a#a ka ,a&),) K B 41671" 86 91 ";< 3 EB415" GPa415"="""N ## 5

• A '#i#&'# +'$' '( 3 Ke,i a a() A A 4>"" ## 5

3 Te*#a '-a#a ka ,a&),) K A 45>71"86

91"

;< 3 E A4?" GPa• Ba0 a(@)+da ,)2ak ) ) 1""; % a( ,i, e#

1 ! "; &e kada* ),) ) )&%*.• Si, e# ),) ) d)k a( ,%(*a a '#i(&'# /e $ak)*

+'$'k a*da % '0a( @e*i i# e*i $' '('-.


3/23


4/23


5/23

PROBLEM 5

• 1""71""71"" ##e$ad)(da k 0ek i(de $i*#a -e#e 11=5""N $i*k'//e i e iki a*aJ)(da($%& a#a,)(a,)k)0 )*) #ak ad)*.

• B' #a -e#e(i( e(i 71" 8## a* #)0 % d' '(a @ *e

$' k ( #a -e#e,i (edi*.• Ma -e#e(i( e a, ik #%d

E416=""" N ## 5


6/23

• E( e#e,i(e a* )0)( $i i(#e,i $i-e e(i(e @e*i(i#i /e*i*.• L4 71"8 ##.• L4 1"" ##

• E( e#e,i(e @e*i(i#

• B%& a#a,)(a @e*i i#

• P%i,,%( %*a()

5en

3

en

10X3

10010X3

LL

−

−

=ε⇒

=∆

=ε

5 boy

boy

22

10X7

000,1612.1

mm/ N12.1mm100X100

N200,11

A

F

−−=ε

−=ε⇒

−=σ⇒−

==σ

E boyσ

=ε

43.0

10X710X3

5

5

boy

en

= ν⇒

−−=

ε

ε−= ν

−

−

P%i,,%( %*a()()( ".> % #a,) #a -e#e(i(k'*0'( % d' '(' @ , e*#ek edi*


7/23

PROBLEM

• a(da @ * (e(

k%#$i(e #a -e#e e*eek,e(e % a*ak " kNk'//e e ki edi&%*.

a< B' + #a -e#e(i(

$%&' (e kada* '-a()*$< Ü+ #a -e#e(i(Ce*Ca(@i $i*i(de

a, ik deJ%*#a,&%(

% '*#'


8/23

• Ö(2e *eak,i&%( k'//e i$' '('*

• F4" "8R81"81"4" R46" kN

• S%(*a /e*i a$ %,' &a ) )*


9/23

E*AL*F

L Σ=∆

100*1601000*80

200*40080*60

120*300300*60

L ++=∆⇒

mm56.5L =∆⇒

2Ba!"a mm/ N200300

000,60==σ⇒

AF=σ

2#e$ ! mm/ N150400

000,60==σ⇒

2y%m&an' mm/ N500160

000,80 ==σ⇒

& Bak)* 4?" N ## 5 P a, ik deJ%*#a,&%

& Çe ik 45"" N ##5 E a, ik deJ%*#a,&%(

& Ti a( 4 "" N ##5 E a, ik deJ%*#a,&%(


10/23


11/23

Bi* e,i, de #e *e $%&'(da &a(&a(a di-i #i0 ade BE 16" ki*i0 e(% '0a( $i* a J%*# &a ) a2ak )*. B' a J%*# , (de" kN # &a&) ) & k /e A (%k a,)(da( #e *e #e,aJede 5"" kN (%k a,a

& k $' '(#ak ad)*. B' & k e* ki*i0e e( e#e,i(e da ) #)0 % a*ak$' '(#ak ad)*.

Ki*i0 #a -e#e,i SAE1">" % ' & k ki*i0 e*e Q ek,e(i(e dik k%('#dae ki e #ek edi*.

a. Ki*i0 e* -e*i(deki #ak,i#'# #%#e( i( $ & k ( .$. Ki*i0 e* -e*i(de % '0a( #ak,i#'# +ek#e @e*i i#i(i= e#(i&e ka ,a&),)()

/e $' ki*i0 e*de a, ik deJ%*#a,&%( % ' % #ad) )()2. Ki*i0 e*i( e( Ja- a (e*ede /e (e kada* ,e i# &a ) )() $' '('-.

PROBLEM !


12/23


13/23

5. A AMA: a&) ) & k /e N%k a,a & k k'//e di&a@*a# a*)()( % a# di&a@*a#)

$


14/23

. A AMA. T% a# k'//e di&a@*a#)(da $%& ek,e(i( , (de ka a( k'//e a a()$' '('*ak M%#e( di&a@*a#) +i-i i*

• AT4A1 A5 AT4A1 A5• A1 415H> 5 3 A!

• A1 415"H> 581! A145>"81!455!• A5415!H A 4 ?!

• AT4 ?! 55! AT46""E e* $%& ek,e(i(i( a )(daki a a() Ce,a a,a&d)k a&() ,%('2' $' '*d'k

30-)34(

-

4

120=⇒

−= A! 4 "H1 5 A! 41!


15/23

>. A AMA: k' a() a2ak #a -e#e e*i( a a e #%#e( i(i /e #a -e#e da&a()#)()$' #ak )*.B' *%$ e#de Ca-)* *%Ji e* k' a() a2a ) i+i( a a e #%#e( i(i Ji*#aka a %@ a*)(da(= #a -e#e da&a()#)() i,e a$ % a*da( e de ede*i-

Ka a %@da( EB 16" *%Ji i i+i(Q77 45>I" K@J 2#> O a*ak $' '('*.Se i# ## 2i(,i(de( i, e(di i /e M%#e( N8#

% d' ' i+i( $i*i# e* $i*$i*i(e '&@'( d'*'#a@e i*i i*.

44

44

XX mm000,00,24m)mm10(*m24 0 ==

;4C 5416"## 5 ;4 "##M46"" kN8#4 6""="""=""" N8##

M46""71" 6 N8##

M=σ

k ( ki*i0e e0i da ) d) )() ka$'ede*,ek T% a# a a e #%#e( i

QT 4 H5>.I"71" 6 QT 41II.571" 6 ## >

26

6

mm/ N24010X2.1

80*10X600==σ


16/23

!.A AMA: P*%Ji #a -e#e,i(i( $' '(a( @e*i i#e da&a() da&a(a#a&a2a )Ce,a a()*. Ma -e#e SAE1">" % a*ak /e*i #i0= i @i i a$ % a*da( #a -e#e ak#da&a()#) $' '('*

&45I!" K@J 2#5&45I" N ## 5

Ki*i0i( e a, ik $ @ede(+)k#ada( ,e i#

&a a$i #e,i i+i(&X #a % #a )d)*.

5I"X5>"N ## 5Ki*i0 ,e i#i e a, ik$ @ede ka )*.

E#(i&e ka ,a&),) N4 #a #i( N45I" 5>" N41=5


17/23

6. A AMA: Mak,i#'# ,e i# (e*ede /e (e kada* % '*

• Mak,i#'# ,e i# #ak,i#'# #%#e( i( % d' ' &e*de %* a&a +)ka*.• B'(' $' #ak i+i( e( $a,i &% eki ik #e %d'('( '&@' a#a,)d)*.• T% a#da #ak,i#'# #%#e( #e *ede % '0 ' ' i+i( $' (%k adaki ,e i# e* a&*) a&*)

Ce,a a() % a(#a )d)*.• a&) ) & k ( A (%k a,)(da( #e *e '-ak a &a ) ) ,e i#i i @i i J%*# a,&%(da( $' a

&a&).)4 ! ##

• N%k a,a & k """ ## de e ki(di* /e J%*# de(9a4 """=$4!"""=L4 """##= F45""="""N<

TOPLAM 4 & N4 ! >!4I" TOPLAM 4 " ##

W 4 " kN # 4 " N ##4 """ ##

E451"="""N ## 5Q41II71" 6 ## >

)3000)3000*8000*2(8000(10X1*000,210*24

3000*30y 3236 +−=∆

L**E3 b*a*F 22

N =∆ mm45

8000*10X1*000,210*35000*3000*000,200

N6

22

N =∆⇒=∆


18/23

PROBLEM 6 : RESQDUAL STRESS

• Ke,i a a( a*) 1!" /e 6" ## 5 % a( 1 #e *e $%&'(daki iki #e a+'$'k $a0 a*)(da( e,(e#e&e2ekiki $ %k a*a,)(a $a a(#)0$' '(#ak ad)*.

• U $ %k a* ?! kN $ & k (de$i* k'//e i e @e*di*i dik e( ,%(*a'&@' a(a( k'//eka d)*) #ak ad)*.

• Çe ik +'$'k a*da( Ca(@i,i(dea, ik deJ%*#a,&%( /e ka )2)

9*e,id'a < , *e, % '0'* Ye*i a$ %,'


19/23

1.A AMA Ç'$'k a* $i*$i* e*i(de( $a )#,)-

% a*ak a, ik deJ%*#a,&%(a' *a#ada( $%& a*) #ak,i#'# (ekada* '-a(a$i i*.

Çe ik +'$'k

Ti a(&'# +'$'k

!N45150*300A*F ==σ=

mm3000,200*150

1000*000.45E*AL*F

L ===∆

!N4860*800A*F ''' ==σ=

mm8000,100*60

1000*000.48E*AL*F

L''

'''

===∆


20/23

İKİN;İ A AMA• Ü+@e( J%*# e*i k' a() a*ak +e ik

#a -e#e(i( e a, ik $ @edeki #a'-a#a,)()()( i a(&'##a -e#ede (e kada* k'//e% '0 '*d' ' $' '(a*ak $a )#,)-k'//e di&a@*a# a*)()( % a#)/e*e( k%#$i(e #a -e#e k'//edi&a@*a#) Ca-)* a()*.

• K%#$i(e #a -e#e&e '&@' a(a(#ak,i#'# k'//e i( (e kada*'-a#a &a ) ) $' '('*.

Ma U-a#a4 LK4! ##

18y3y

848

=⇒=

2--

)6375(5

30=⇒

−=


21/23

ÜÇÜN;Ü A AMAK%#$i(e #a -e#ede 2 (%k a,)(da

% '0a( ! ## ik '-a#a +e ik +'$'k aa (%k a,)(a de(k @e #ek edi*. B'(ede( e '-a#a()( +e ik +'$'k a

a, ik deJ%*#a,&%(a ,e$e$ % d' '%* a&a +)k#ak ad)*.

Ma '-a#a()( i a(&'# #a -e#ek'//e di&a@*a#)(da $ (%k a,)(ade(k @e #i0 % #a,) i,e '-a#a()(

i a(&'# +'$'k a e a, ik $ @e&ed 0#ek e % d' '(da( '-a#a()e a, ik % d' ' a( a0) #ak ad)*.


22/23

DÖRDÜNCÜ AŞAMA• K%#$i(e #a -e#e -e*i(e '&@' a(a(

& k ka d)*) d)k a( ,%(*a +e ik /ei a(&'# #a -e#ede ka a( *e,id'a

, *e,, e*i $' #ak i+i( e a, ik $ @ee *i,ie (%k a,)(a ka&d)*) )*.

• O* a&a +)ka( &e(i di&a@*a# k%#$i(e#a -e#e(i( ak#a e *i,i(i@ , e*#ek edi* /e $' e *i(i( e i#i

a, ik deJ%*#a,&%(da( (2eki e *i(i(e i#i(e e0i i*.

• K%#$i(e #a -e#edeki &e(i e a, ik$ @e e *i,i(i( (e kada* a, ikdeJ%*#a,&%(da( ,%(*a $a0 ad) ) &i(e

+@e( e%*e#i(de( $' '('*.

mm5.1L

5L

5.3

63

3

75

E + AL

E + AL

=∆⇒

−=∆⇒

=⇒=


23/23

BEŞİNCİ AŞAMA• K%#$i(e #a -e#ede % '0a( a, ik '-a#a #ik a*)

$e i* e(dik e( ,%(*a +e ik /e i a(&'# +'$' '( %*i i(ak'//e e *i e*i #ak,i#'# '-a#a (%k a,)(da $a0 a&a2ak/e *e,id'a '-a#a $ @e,i(de ,%(a e*e2ek 0eki de ke(di%*i i(a e i# e*i #'CaJa-a edi e*ek &e(ide( % '0 '*' '*.

• P a, ik '-a#a()( $i #i0 % d' ' e (%k a,)()( k'//eek,e(i(de Ca(@i de e*e ka*0) )k @e di i &i(e +@e(e%*i,i(de( $' '('*.

!N5.7F5.3F45

345

−=⇒+

=

!NF5.18

F48

8

48'

' =⇒

−

−=

Ti a(&'# +'$'k Re,id'a k'//e 4F RT4 IkN

Ti a(&'# +'$'k aki *e,id'a , *e,4F RT AT

RT4 I=""" 6"4 1!"M a

Ti a(&'# $%*'daki %-i iJ @e*i i# $%*'daki *e,id'a , *e,i(+ek#e @e*i i#i 9Te(,i%(< % d' '(' $e i* #ek edi*

Çe ik +'$'k Re,id'a k'//e 4F R; 4 8?.! kN

Çe ik +'$'k aki *e,id'a , *e,4FR; A2

R; 4 8?=!"" 1!"4 8!"M a

Çe ik +'$'k aki (e@a iJ @e*i i# *e,id'a , *e,i( $a,#a@e*i i#i 9;%# *e,i%(

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6-Derste Cozulen Problemler