4 Defleksi.ppsx

8/18/2019 4 Defleksi.ppsx

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RA + RC

= PA B C

RA RC

L1 L

2

L

P

PRA

RC

RA =

RC =

ΔL1

ΔL2

A1 E1 A2 E2

A1 E1 L1

A2 E2 L2

L! = L +ΔL = LΔL1 + ΔL2 =ΔL = "

ΔL ="ΔL1 + ΔL2 = "

ΔL2 =−ΔL1

=P1 L1

A1 E1

P2 L2

A2 E2 =

RA L1

A1 E1

RC L2

A2 E2

=RC

A2 E2

L2

RA L1

A1

E1

=

A2 E2 L1

A1

E1

L2

RA

RA + RC

= P

RA =P

A2 E2 L1

A1 E1

L2

+

RA RA =P

A2 E2 L1

A1 E1

L2

1+

#

RA PA1 E1 L2

A1 E1 L2 + A2 E2 L1

=

RC PA2 E2 L1

A1 E1 L2 + A2 E2 L1

=



A B C

RA RC

1""$% &"$%

L

'"()

'"2"

*"

A1 E1 A2 E2

RA PA1 E1 L2

A1

E1

L2

+ A2

E2 L1

=

A1 = A2 = 1 $%2E1 = E2 = 2"" ()/%%2

L2

L=

P = 2"

()

RC PA2 E2 L1

A1 E1 L2 + A2

E2 L1

=

L1

L=

P = *"()

P1 L1

A1 E1 ΔL1

=

RA L1

A1 E1 = = 1

%%

P2 L2

A2 E2 ΔL2

=

RC L2

A2 E2 = = −1

%%



A B C

RA RC

1""$% &"$%

L

1'"()

1'"2

12,

A1 E1 A2 E2

RA PA

1

E1

L2

A1 E1 L2 + A2

E2 L1

=

A1 = 1 $%2 E1 = 2"" ()/%%2

= 2()

RC PA2 E2 L1

A1 E1 L2 + A2

E2 L1

=

= 12,()

P1 L1

A1 E1 ΔL1 =

RA L1

A1 E1 = = 1-'%%

P2 L2

A2 E2 ΔL2

=

RC L2

A2 E2 = = −1-'

%%

A2 = 2 $%2 E2 = 2"" ()/%%2



A B D

RA RDA

1 E1 A EA2 E2

11"()

C

1""$% ,"$%

RA1 11

"

12"

22"

=

= '"()

A1 = A2 = A = 1 $%2E1 = E2 = E = 2"" ()/%

*"$%A B

C

RA RD

L

1'&()A1 E1 A EA2 E2

11"()

D

11"'"

&"

1'&'"1"&

A B C

RA RD

1'&()A1 E1 A EA2 E2

D

RD1 11

"

1""

22"

=

= &"()

RA2 1'

&

,"

22"

=

= '"()

RD2 1'

&

1*"

22"

=

= 1"&()

1'&11"

&&

RA = RA1 + RA

2 = '" −

'" = " ()RD = RD

1 + RD2 = &" −

1"& = && ()P1 L1

A1 E1

ΔL1

=

RA L1

A1 E1

= = "

%%

P2 L2

A2 E2

ΔL2

=

= 2-2

%%

RD L

A E

ΔL

=

= −2-2

%%



1""$% ,"$%

A1 = 2 $%2

*"$%A B C

RA RD

L

1'&()A1 E1 A EA2 E2

11"()

DE1 = E2 = E = 2"" ()/%%2

A2 = 1 $%2 A = 1-& $%2

P1 A E L2 P2 + A2

E2 L

P

A2 E2 A E

=

P1 L1

A1 E1

P2 L2

A2 E2 =

P L

A E +

ΔL = ΔLAB + ΔLBC + ΔLCD = "

ΔLAB = ΔLBC + ΔLCD

A1 E1

L1

RA

1

A E L2 RD1 + A2 E2

L RD1A2 E2 A

E

=

A1 E1

L1

RA

1

A E L2 + A2

E LA2

E

A E

=

RD

1

A1 E

L1

A L2 +

A2 LA2

A

= RD

1

A1

L1

A

B C

RA RD

LA1 E1 A EA2 E2

11"()

D

RA1

RA1 + RD

1 = P

1&"*"" +1"",""

1""1&"

= RD1

2""

1"""= 1-,''' RD

1

11071,6

38,4

1-,''' RD1

+ RD1 = 11"

RD1

= ,-2"0 ()RA1

= 1-'201 ()



1""$% ,"$%*"$%A B C

RA RD

L

1'&()A1 E1 A EA2 E2

11"()

D

A B C

RA RD

LA1 E1 A EA2 E2

11"()

D

RD1

= ,-2"0 ()RA1

= 1-'201 ()

A B C

RA RD

L

1'&()A1 E1 A EA2 E2

D

P A2 E2 L1 P1 + A1 E1 L2 P2A1 E1 A2

E2

=

P L

A E

P1 L1

A1 E1 =

P2 L2

A2 E2 +

RD

2

A2 E2 L1 RA2 + A1 E1

L2 RA2A1 E1 A2

E2

=

A E

L

A E

L

RD

2 =

A2 L1 +

A1 L2A1

A2

RA

2

A

L

A1 = 2 $%2

E1 = E2 = E = 2"" ()/%%2

A2 = 1 $%2 A = 1-& $%2

= 1-',& RA2

RA2 + RD

2 = P RA2 + 1-',& RA

2 = 1'&

RA2 = '1-0&& ()RD

2 = 1"-'"*'& ()

11071,6

38,4



1""$% ,"$%*"$%A B C

RA RD

L

1'&()A1 E1 A EA2 E2

11"()

D

A B C

RA RD

LA1 E1 A EA2 E2

11"()

D

11071,6

38,4

RD1

= ,-2"0 ()RA1

= 1-'201 ()

A B C

RA RD

L

1'&()A1 E1 A EA2 E2

D

A1 = 2 $%2

E1 = E2 = E = 2"" ()/%%2

A2 = 1 $%2 A = 1-& $%2

RA2

= '1-0&& ()RD2

= 1"-'"*'& ()

16561,4

103,6

RA = 1"-22&' ()

RD = '&-22&' ()

11010,2

65,2

165P1 = PAB = 1"-2 ()

(tekan)P2 = PBC = 00-, () (tarik )

P = PCD = '&-2 () (tekan)

∆L1 =

"-2&'%% (−)∆L2 =

1-00'%% (+)

∆L =1-*"%% (−)



IV.

DEFLECTI

N!

A

B

C

D

E

12 ()

LAB

LBC

LBD LDE

" ()

Baan AB3 LAB

= '" "mAAB

= 1&" mm2

Baan BC3 LBC = 0" "mABC = 1"" mm2

Baan BDE3 LBD = LDEABD = ADE

M4d5657 86a797 :a;an3 21" GPa

H95n <8<9nda;an 99( C >δC#- ?9(a3PERPI)DAHA)@I@IK

9(a P d9 C 8a< 12 ()- :8a<a P d9 E aa 99( C

8a< d9 8%<ana

9(a P d9 E 8a< " ()- :8a<a P d9 C aa 99( C 8a< d9 8%<ana



IV.

DEFLECTI

N!

A

C

E

12 ()

LAB

LBC

LBD LDE

" ()

PERPI)DAHA)@I@IK

RD

RB

PB

∑MD = " RB LBD + " LDE = "

RB = " LDE / LDE = " ()

PB = RB = " ()

PBC = PC = 12 ()

PAB = PB PC = " 12 = 1, ()

a# P8<9nda;an 99( C3

PAB LAB

AAB EAB

PBC LBC

ABC EBC = +C = ∆LAB + ∆LBC

(desak )

(tarik )

(desak )



IV.

DEFLECTI

N!

A

C

E

PC

LAB

LBC

LBD LDE

" ()

PERPI)DAHA)@I@IK

RD

PB

∑MD = " RB LBD + " LDE = "

RB = " LDE / LDE = " ()

PB = RB = " ()

PBC = PC

PAB = PB PC = " PC

:# 9(a P d9 E 8a< " ()- :8a<a P d9 C aa 99( C 8a< d9 8%<ana

PAB LAB

AAB EAB

PBC LBC

ABC EBC = +C = ∆LAB + ∆LBC

(desak )

= "



IV.

DEFLECTI

N!

A

C

E

12 ()

LAB

LBC

LBD LDE

PE

PERPI)DAHA)@I@IK

RD

PB

∑MD = " RB LBD + PE LDE = "

RB = PE LDE / LDE = PE

PB = RB = PE

PBC = PC = 12 ()

PAB = PB PC = PE 12

$# 9(a P d9 C 8a< 12 ()- :8a<a P d9 E aa 99( C 8a< d9 8%<ana

PAB LAB

AAB EAB

PBC LBC

ABC EBC = +C = ∆LAB + ∆LBC = "



1()

"

1()

"

1 / 7 9 n

" F

1/an"

IV.

DEFLECTI

N!

A =

0 " " %

% 2

A =2'""%%2

L =2-*%

A

BC

H95n <8<9nda;an 99( Baa; 89(a6 >B# dan ;494na6>B;#.

P A B = +

2 ' - " "

" ( )

PBC

=

22-&1''()ΔLAB

=

PAB LAB

AAB EAB

E ="G<a

=1-1**%%

ΔLBC

=

PBC LBC

ABC EBC ="-20%%

B

PERPI)DAHA)@I@IK



1()

"

IV.

DEFLECTI

N!

A =

0 " " %

% 2

A =2'""%%2

L =2-*%

A

BC

P A B = +

2 ' - " "

" ( )

PBC

=

22-&1''()

E ="G<a

ΔLAB =

1-1**%%

ΔLBC =

"-20%%

"

A

BC

CB

BB

A

BB

C

B!

B;

B

#B$ = − 0,2%7 &' 301,144 + 0,2%7 *" 30

* 30= 2,803mm (ke bawah)

#B- = 0,2%7mm (ke kanan)

PERPI)DAHA)@I@IK



2()

"

IV.

DEFLECTI

N!

A =0"%%2

A

B

C

*&

L =

+ " " $ %

L = 1 , " $ %

H95n <8<9nda;an 99( Baa; 89(a6 >B# dan ;494na6>B;#.

E =

21"GPa

2()

"

*&

B

PBC $47 " =

P B

C

P B

A

PBA $47 *&

PBC $47 "

P B A 7

9 n

* & F P B C

7 9 n

+ " F

PBC =PBA $47 *&

$47 "

PBA 79n *&+ PBC 79n "= 2PBA 79n *& +PBA $47 *&

$47 "79n " = 2

PBA = 2*-01& () >tarik #PBC = 2"-* () >tekan#

PERPI)DAHA)@I@IK

IV



2()

"

IV.

DEFLECTI

N!

A =0"%%2

A

B

C

*&

L =

+ " " $ %

L = 1 , " $ %

E =

21"GPa

P B A =

2 * - 0 1

& ( )

P B C = 2 " - + * + ( )

ΔLBA =

PBA LBA

ABA EBA ="-01%%

ΔLBC

=

PBC LBC

ABC EBC ="-**%%

"

A

B

C

*&

ΔLBA

=

"-01%% ΔLBC = − "-**%%

PERPI)DAHA)@I@IK

IV



"

IV.

DEFLECTI

N! A

B

C

*&

ΔLBA

=

"-01%% ΔLBC = − "-**%%

B!

B

C

APERPI)DAHA)@I@IK

IV



IV.

DEFLECTI

N!ΔLBA

=

"-01%% ΔLBC = − "-**%%

*& "1"&

&

"

A

B

C

*&

B

B!

PERPI)DAHA)@I@IK

IV



IV.

DEFLECTI

N!ΔLBA

=

"-01%% ΔLBC = − "-**%%

1"&

&

B

B!

1"&−

0 ,4 4 7

0 , % 1 3

BB! =

ΔLBA

$47

ΔLBC

$47 >1"&−#=

ΔLBA

ΔLBC

$47

$47 >1"&−#= = 2-"*

$47

$47 >$47 1"& + 79n 1"& an #= 2-"*

1

$47 1"&+

79n 1"& an = 2-"*

1

"-2&0 + "-0'' an = 2-"*

an = "-& = -'

BB! =ΔLBA

$47

"-01ΔLBA

$47 $47 -'= 1-1&&%%

*&

D B G

B = 1-1&& $47 >*&#= 1-1*'%%

B;

B; = 1-1&& 79n >*&#= "-1*&%%

PERPI)DAHA)@I@IK



1""$% ,"$%*"$%A B C

RA RD

L

1'&()A1 E1 A EA2 E2

11"()

D

A B C

RA RDLA1 E1 A EA2 E2

11"()

D

11071,6

38,4

RD1

= ,-2"0 ()RA1

= 1-'201 ()

A B C

RA RD

L

1'&()A1 E1 A EA2 E2

D

A1 = 2 $%2

E1 = E2 = E = 2"" ()/%%2

A2 = 1 $%2 A = 1-& $%2

RA2

= '1-0&& ()RD2

= 1"-'"*'& ()

1'&'1-*1"-'

RA = 1"-22&' ()

RD = '&-22&' ()

11010,2

65,2

165 P1 = PAB = 1"-2 ()

(tekan)P2 = PBC = 00-, () (tarik )

P = PCD = '&-2 () (tekan)

P1 L1

A1 E1

P2 L2

A2 E2 =

P L

A E +

∆L1 =

"-2&&%% (−)∆L2 =

1-00'%% (+)∆L =

−

IV



"

IV.

DEFLECTI

N! A

B

C

P8<9nda;an@99(.

*&

ΔLBA

=

"-01%% ΔLBC = − "-**%%

" - 0 1 + %

%

" - * * / % % 1"&

&

1"&−

" - 0 1 + %

%

"-01%%

= 2-"* >"-2&0 + "-0'' an #

= 1-0* >"-2', + an #

an = "-& = -'

BB! =ΔLBA

$47

ΔLBC

$47 >1"&−#=

BB! = 1-1&&B = 1-1&& $47 >*&# = 1-1*'

B; = 1-1&& 79n >*&# = "-1*&%%

B = 1-1&& $47 >1"&'"# = 1-1*'

B;

IV



"

IV.

DEFLECTI

N! A

B

C

P8<9nda;an@99(.

*&

ΔLBA

=

"-01%% ΔLBC = − "-**%%

" - 0 1 + %

%

" - * * / % %

*& "

1"&

&

IV



IV.

DEFLECTI

N!P8<9nda;an@99(.

ΔLBA

=

"-01%% ΔLBC = − "-**%%

"

A

B

C

*&

IV



IV.

DEFLECTI

N!P8<9nda;an@99(.

ΔLBA

=

"-01%% ΔLBC = − "-**%%

0 ,4 4 7 1"&

&

1"&− 0

, % 1 3

BB! =

ΔLBA

$47

ΔLBC

$47 >1"&−#=

ΔLBA

ΔLBC

$47

$47 >1"&−#= = 2-"*

B!

$47

$47 >$47 1"& + 79n 1"& an #= 2-"*

1

$47 1"&+

79n 1"& an = 2-"*

1

"-2&0 + "-0'' an = 2-"*

an = "-& = -'

IV



"

IV.

DEFLECTI

N! A

B

C

P8<9nda;an@99(.

*&

ΔLBA

=

"-01%% ΔLBC = − "-**%%

" - 0 1 + %

%

" - * * / % % 1"&

&

1"&−

" - 0 1 + %

%

"-01%%

$47

$47 >1"&−#= 2-"*

$47

$47 1"& $47 + 79n 1"& 79n

$47

$47 >$47 1"& + 79n 1"& an #

1

$47 1"& + 79n 1"& an

1

"-2&0 + "-0'' an

1 = 2-"* >"-2&0 + "-0'' an #

1 = 1-0* >"-2', + an #

an = "-& = -'

IV



IV.

DEFLECTI

N!P8<9nda;an@99(.

ΔLBA

=

"-01%% ΔLBC = − "-**%%

1"&

&

B

B!

1"&−

0 ,4 4 7

0 , % 1 3

BB! =

ΔLBA

$47

ΔLBC

$47 >1"&−#=

ΔLBA

ΔLBC

$47

$47 >1"&−#= = 2-"*

$47

$47 >$47 1"& + 79n 1"& an #= 2-"*

1

$47 1"&+

79n 1"& an = 2-"*

1

"-2&0 + "-0'' an = 2-"*

an = "-& = -'

BB! =ΔLBA

$47

"-01ΔLBA

$47 $47 -'= 1-1&&%% B = 1-1&& $47 >*&#= 1-1*'%%

D B

G

IV



1()

"

IV.

DEFLECTI

N!

A =

0 " " % %

2

A =2'""%%2

A =2-*%

A

BC

P A B = +

2 ' - " "

" ( )

PBC =

22-&1''()

E ="G<a

P8<9nda;an@99(.

ΔLAB =

1-1**%%

ΔLBC =

"-20%%

IV



"

IV.

DEFLECTI

N!A

BC

P8<9nda;an@99(.

ΔLAB =

1-1**%%

ΔLBC =

"-20%%

CB

BB

A

BB

C

B!

B;

B

#B$ = − 0,2%7 &' 301,144 + 0,2%7 "*" 30

* 30= 2,803mm (ke bawah)

#B- = 0,2%7mm (ke kanan)

IV.



∆L

IV.

DEFLECTI

N!

/B. DEFA!I A!IAL ' AA E =σξ

P/AΔL/L

=P L

ΔL A= ΔL =

LE A

P

A1 E1 L1 A2 E2 L2

L

P PΔL =

∑

LE A

P

Ø =100 mm1000 kN

Ø =65 mmA B C

L = 1,0 m L = 0,8 m

ΔL = ΔLAB

+ ΔLBC

=L1 P1

E1 A1

+L2 P2

E2 A2

= 0,606 + 1,148 = 1,754 mm

Ø =100 mm500 kN

Ø =65 mmA B C

L = 1,0 m L = 0,8 m

ΔL = ΔLAB + ΔLBC

= 0,606 + 0,574 = 1,180 mm

500 kN

Ø =100 mm1500 kN

Ø =65 mmA B C

L = 1,0 m L = 0,8 m

ΔL = ΔLAB + ΔLBC

= 0,606 + 0,574 = 1,180 mm

500 kN

IV.



IV.

DEFLECTI

N!


P/AΔL/L

=P L

ΔL A= ΔL =

LE A

P

A1 E1 L1 A2 E2 L2

IV.



IV.

DEFLECTI

N!


P/AΔL/L

=P L

ΔL A= ΔL =

LE A

P

A1 E1 L1 A2 E2 L2 ΔL =L

E AP

IV.



DEFLECTI

N!


P/AΔL/L

=P L

ΔL A= ΔL =

LE A

P

A1 E1 L1 A2 E2 L2 ΔL =L

E AP

P l a n e T r u s



=

0

0

0

0

0

0

AE

L

AE L

−

0

0

AE

L

−

AE L

0

0

0

0

P l a n e T r u s

s

kl

e AE

L=

0

0

1

-1

0

0

0

0

0

0

-1

1

0

0

0

0

P l a n e T r u s



=

0

0

0

0

0

0

AE

L

AE L

−

0

0

AE

L

−

AE L

0

0

0

0

P l a n e T r u s

s

kl

e AE

L=

0

0

1

-1

0

0

0

0

0

0

-1

1

0

0

0

0

IV.



"

DEFLECTI

N!A

BC

P8<9nda;an@99(.

ΔLAB =

1-1**%%

ΔLBC =

"-20%%

CB

BB

A

BB

C

B

B;

B

4 Defleksi.ppsx

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Transcript of 4 Defleksi.ppsx