Bahan Ajar Mekanika Teknik Statis Tak Tentu Program d4 18 Sept 2013

PROGRAM DIPLOMA 4 TEKNIK 201 SIPIL 1 FTSP ITS BAHAN AJAR MEKAN MEKANIK IKA A REKA REKAYASA 3 PROGRAM DIPLOMA 3 TEKNIK SIPIL

MEKANIKA MEKANIKA TEKNIK TEKNIK STATIS TAK TENTU BAHAN AJAR

2014 BOEDI WIBOWO

BOEDI WIBOWO KAMPUS DIPLOMA TEKNIK SIPIL – JLN . MENUR 127 SURABAYA

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KATA PENGANTAR

Dengan mengucap !u"u# "epa$a A%%a& SWT ' "a#ena $engan #ac&ma( NYA "am) *)a men!e%ea)"an BAHAN AJAR MEKANIKA MEKANI KA TEKNIK TEKNI K STA STATIS TAK TENT+ , Ba&an a-a# )n) $)&a#ap"an $apa( mem*an(u p#.e *e%a-a# menga-a# $) P#.g#am D)p%.ma 4 Te"n)" S)p)% ' e%a)n $)"(a( !ang u$a& a$a , Ma(a "u%)a& Me"an)"a Te"n)" S(a() Ta" Ten(u )n) me#upa"an )%mu )% mu $aa# "ea&%)an !ang &a#u $)pa&am) ma&a)/a m a&a)/a Te"n)" Te"n)" S)p)% ' $)mana pa$a *a&an a-a# )n) $)*e#)"an ca#a pe#&)(ungan (a()"a un(u" K.n(#u") S(a() Ta" Ten(u , O%e& "a#ena )(u ma&a)/a &a#u mema&am) eca#a *ena# ' e&)ngga $)pe#%u"an mem*ua( a-)an ma(e#) $a%am *en(u" *a&an a-a# , Ba&an a-a# )n) $)*ua( $a%am *en(u" !ang



























MATERI ,PENGERTIAN PENGERTIAN DEFORMASI , PERHIT+NGAN DEFORMASI BALOK DAN PORTAL DENGAN 0ARA +NIT LOAD, , PERHIT+NGAN PEN+R+NAN TITIK SIMP+L PADA KONSTR+KSI ONSTR+KSI RANGKA BATANG , , PERHIT PERHIT+NGA +NGAN N STA STATIKA DENGAN 0ARA



























, PERHIT PERHIT+NGA +NGAN N STA STATIKA DENGAN 0ARA

0ROSS,

, PERHIT PERHIT+NG +NGAN AN STA STATIKA DENGAN 0ARA MATRI1 2 METHODE KEKAK+AN  , GARIS PENGAR+H BALOK BALOK MENER+S , REN0ANA PEMBELAJARAN SEMESTER PROGRAM D4 TEKNIK SIPIL FAK+LTAS TEKNIK SIPIL DAN PEREN0ANAAN  ITS MATA K+LIAH

KODE

Rumpun MK

BOBOT 2"

MEKANIKA TEKNIK STATIS TAK TENT+

R0 647363

ILM+ DASAR

T8 3

OTORISASI

K..#$)na(.# MK TTG

0apa)an Pem*e%a-a #an MK

P89

SEM EST ER III

D)#e5))

6: J+LI ;964

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P#.g#a m S(u$) Mam! m"m#"$%&a' #"$#a(a% a)*"$'a*%+ "',")"-a%a' ma-a)a *"&'%& -%%) *"$aa' ,a'( /%a/a% Mam! /%#"$%&a' *a'((!'( aa# -"#a(a% %m%'a' /a)am &")m&',a M"m%)%&% -%&a !!$ Ma(a



























)%'*a'( a/a &'-*$!&-% #a)&  $*a) -*a*%- *a& *"'*! /"'(a' a$a '-%-*"'* /"+$ma*%'  $-- /a' m"*/" m" */" &"&a&!a' .

D)"#)p) Ba&an Ka-)an < T.p)" Ba&aan

Pu(a"a

Ba&an Ka-)an D"+$ma-% #a)&  $*a) ma!!' *%*%& -%m!) a/a KRB  m"'(%*!'( /a' m"'((am#a$ #%/a'( mm"'  '$ma) /a' )%'*a'( a/a &'-*$!&-% -*a*%- *a& *"'*! . Ga$%- "'(a$! #a)& -*a*%- *a& *"'*!

T.p)" Ba&aa n Da)am Ma*a&!)%a %'% maa-%-a a&a' m"m")aa$% && #aa-a'5 && #aa-a' -"#a(a% #"$%&!*6 DEORMASI 6 m"'(%*!'( /"+$ma-% #a)&  $*a) -*a*%- *"$*"'*!  m"'(%*!'( "'!$!'a' *%*%& -%m!) a/a KRB KONSTRUKSI STATIS TAK TENTU 6 "'("$*%a' /a-a$  "$%*!'(a' -*a*%&a /"'(a' a$a 8 9ONSISTENT DEORMATION DEORMATION /a' 8 9ROSS 8 ma!!' 8 ANALISA STRUKTUR METHODE MATRI: 8 GARIS PENGARUH 6 m"'(%*!'( /a' m"'((am#a$ (a$%- "'(a$! #a)& m"'"$!- . +(ama = 1. Baa' aa$ M"&a'%&a T"&'%& T"&'%& S*a*%- Ta& Ta& T"'*! T"'*! D4 T"&'%& T"&'%& S%%)  BOEDI WIBOWO 2. Struktur Struktur Statis Statis Tak Tak Tentu, Tentu, Chu Chu Kia Wong Wong Ph.D, Ph.D, Ir. Ir. Herman Herman Widodo S Pen$u"u ng = 1.. Analisa Struktur Lanutan !ilid 1 , Chu Kia Wong PH, D, Kusuma Wira"an # $ul%adi &ata Pra"ira

Me$)a Pem*e%a-a #an

KULIAH  LATIHAN SOAL KULIAH  LATIHAN SOAL TUGAS

Team ESTUTIE MAULANIE  RIDHO BA BAYUAJI YUAJI  IBNU PUDJI PUD JI RAHARDJO  BOEDI Teac&)ng WIBOWO Aeme T!(a T!(a- /a' !%a' n( Ma(a"u%)a M"&a'%&a T"&'%& S*a*%- T"$*"'*! "$*"' *! /a' M"&a'%&a T"&'%& T"(a'(a' "(a'(a ' & S!a#a( Mg Su* Ma(e#) Me(.$e > Aemen(



























26

Maa-%-a mam! m"'(%*!'( /"+$ma-% a/a #a)&

M"'(%*!'( /"+$ma-% #a)& -*a*%- *"$*"'*! /"'(a' a$a !'%* )a/

Wa"(u@ K!)%a  )a*%a' -a) ?TM= 3C9@

NO 6 Ha%aman 7  63

K"*"a*a' m"'(%*! '( /"<"&-% /a' $*a-% a/a #a)&

NO ; Ha%aman ;6  ;3 2;

Maa-%-a mam! m"'(%*!'( /"+$ma-% a/a $*a)

M"'(%*!'( /"+$ma-% $*a) -*a*%- *"$*"'*! /"'(a' a$a !'%* )a/

K!)%a  )a*%a' -a) *!(a?TM= 3C9@

K"*"a*a' T!(a T!(am"'(%*! m"'(%*! '( '( /"+$ma-% "'!$!'a a/a ' #a)& "$("-"$a ma!!' ' /a' $*a) $*a-% a/a $*a)

K!)%a  )a*%a' -a) ?TM= 3C9@

K"*"a*a' m"'(%*! '( "'!$!'a ' *%*%& -%m!) a/a KRB

NO 6 Ha%aman 7  63 NO ; Ha%aman 3C  4; 23

Maa-%-a mam! m"'(%*!'( "'!$!'a' *%*%& -%m!) a/a &'-*$!&-% $a'(&a #a*a'(

24

2C

M"'(%*!'( "'!$!'a' *%*%& -%m!) /"'(a' a$a > &"+%-%"'

NO 6 Ha%aman ;6  ;: NO ; Ha%aman 7C  C

EAL+ASI KE 6 Maa-%-a mam! m"'(5 %/"'*%?&a-% "$#"/aa' &'-*$!&-% -*a*%-

;=

P"'("$*%a' &'-*$!&-% -*a*%*a& *"'*! #"-"$*a a)%&a-%',a . M"'(%*!'( /a' m"'((am#a$ #%/a'( M  N  D

+JIAN K!)%a  )a*%a' -a) ?TM= 3C9@

K"*"a*a' m"'(%*! '( /a' m"'((am #a$ #%/a'( MND

;9 





























*"'*! /a' !(a mam! m"'(%*!'( -*a*%&a &'-*$!&-% -*a*%- *a& *"'*!

27

Mam! m"'(%*!'( -*a*%&a &'-*$!&-% -*a*%- *a& *"'*!

DEORMATION

NO 6 Ha%aman ;  37

M"'(%*!'( /a' m"'((am#a$ #%/a'( M  N  D a/a $*a) -*a*%*a& *"'*! /"'(a' a$a 9ONSISTENT DEORMATION

K!)%a  )a*%a' -a) ?TM= 3C9@

K"*"a*a' m"'(%*! '( /a' m"'((am #a$ #%/a'( MND a/a $*a) -*a*%- *a& *"'*!

K!)%a  )a*%a' -a)  *!(a?TM= ;23C9 @

K"*"a*a' T!(a T!(am"'(%*! m"'(%* !'( /a' '( /a' m"'((am m"'((a m#a$ #a$ #%/a'( M #%/a'( ND MND a/a a/a #a)& $*a) -*a*%- *a& -*a*%- *a& *"'*! *"'*!

NO 6 Ha%aman 3  4;

2':

Mam! m"'(%*!'( -*a*%&a &'-*$!&-% -*a*%- *a& *"'*!

M"'(%*!'( /a' m"'((am#a$ #%/a'( M  N  D a/a #a)&/a' $*a) *"*a -*a*%*a& *"'*! /"'(a' a$a 9ROSS

NO 6 Ha%aman 43 79

2

EAL+ASI KE ;

+JIAN

C

;9 





























76 6

26;

Mam! m"'(%*!'( -*a*%&a &'-*$!&-% -*a*%- *a& *"'*!

M"'(%*!'( /a' m"'((am#a$ #%/a'( M  N  D a/a #a)& -*a*%*a& *"'*! /"'(a' a$a METHODE KEKAKUAN

K!)%a  )a*%a' -a) ?TM= 3C9@

NO 3 Ha%aman ; :C

263

264

K"*"a*a' m"'(%*! '( /a' m"'((am #a$ #%/a'( MND a/a #a)& -*a*%- *a& *"'*!

EAL+ASI KE 3 Mam! m"'(%*!'( -*a*%&a &'-*$!&-% -*a*%- *a& *"'*!

M"'(%*!'( /a' m"'((am#a$ #%/a'( M  N  D a/a $*a) *"*a -*a*%- *a& *"'*! /"'(a' a$a METHODE KEKAKUAN

+JIAN K!)%a  )a*%a' -a) ?TM= 3C9@

K"*"a*a' m"'(%*! '( /a' m"'((am #a$ #%/a'( MND a/a $*a) *"*a -*a*%- *a& *"'*!

;=

K!)%a  )a*%a' -a)  *!(a?TM= ;23C9 @

K"*"a*a' T!(a T!(am"'(%*! m"'(%*! '( /a' '( /a' m"'((am m"'((am #a$ (a$%#a$ (a$%"'(a$! "'(a$!

;=

NO 3 Ha%aman :7:

Mam! 26C'6 Mam! m"'(%*!'( m"'(%*!'( /a' 7 /a' m"'((am# a$ (a$%"'(a$!

m"'((am#a$ (a$%"'(a$! $"a&-%  D /a' M

;9 





























PROGRAM DIPLOMA TEKNIK SIPIL TEKNIK SIPIL AKULTAS TEKNIK SIPIL TEKNIK SIPIL DAN PEREN9ANAAN INSTITUT TEKNOLOGI SEPULUH NOPEMBER

MEKANIKA TEKNIK STATIS TAK TENT+ ,

DOSEN

1.

KOD E MK6

R9 0041 SKS

2.

K ONTRAK K ULIAH ONTRAK K ULIAH  MATERI PEMBELAJARAN 1

MINGGU KE

KOMPETENSI

1 53

Mam! m"'(%*!'( /"+$ma-% a/a &'-*$!&-% -*a*%*"$*"'*! #a%& #a)& ma!!' $*a)  mam! m"'(%*!'( "'!$!'a' *%*%& -%m!) a/a K'-*$!&-% Ra'(&a Ba*a'( .

4 ;5

MATA KULIAH DAN K ELAS ELAS 6

MATERI PEMBELAJARAN M"'(%*!'( /"+$ma-% a/a #a)& /"'(a' a$a UNIT LOAD

PENGAMPU 2

1 

M"'(%*!'( /"+$ma-% a/a a/a $*a) /"'(a' a$a UNIT LOAD



M"'(%*!'( "'!$!'a' *%*%& -%m!) /"'(a' a$a > K"+%-%"'



P"'("$*%a' &'-*$!&-% -*a*%- *a& *"'*! /a' a)%&a-% /% )aa'(a' .

EAL+ASI 6 Mam! m"'( %/"'*%?&a-% "$#"/aa' a'*a$a K'-*$!&-% K'-*$!&-% -*a*%*a& *"'*! /"'(a' K'-*$!&-% K'-*$!&-% -*a*%-

3



M"'(%*!'( /a' m"'((am#a$ #%/a'( mm"'   '$ma) '$ma) /a' /a' )%'*a'( )%'*a'( a/a a/a #a)& #a)& /"'(a' /"'(a' a$a 9ONSISTENT DEORMATION M"'(%*!'( /a' m"'((am#a$ #%/a'( mm"' 



2

3





























*a& *"'*! .

M"'(%*!'( /a /a' m" m"'((am#a$ #% #%/a'( m mm"'   '$m '$ma) a) /a' /a' )%'* )%'*a' a'( ( a/a a/a $* $*a) a) #"$( #"$(, ,a' a'( ( /"'(a' a$a 9ROSS M"'(%*!'( /a' m"'((am#a$ #%/a'( mm"'   '$ma) '$ma) /a' )%'*a' )%'*a'( ( a/a a/a #a) #a)& & /"'(a' /"'(a' a$a a$a ANALISA STRUKTUR METODE MATRI:  METHODE KEKAKUAN   EAL+ASI 3

Mam! m"'(%*!'( -*a*%&a &'-*$!&-% -*a*%*a& *"'*! /a' m"'((am#a$ (a$%"'(a$! #a)& m"'"$!- .

M"'(%*!'( /a' m"'((am#a$ #%/a'( mm"'   '$ma) '$ma) /a' )%'*a'( )%'*a'( a/a $*a) $*a) *"*a /"'(a' /"'(a' a$a a$a ANAL ANALIS ISA A STRU STRUK KTUR TUR METO METODE DE MATR MATRI: I:  METHODE KEKAKUAN  M"'(%*!'( M"'(%*!'( /a' m"'((am#a$ m"'((am#a$ (a$%- "'(a$!  $"a&-% "$)"*a&a' a/a #a)& -*a*%- *a& *"'*!

13

1451@

1751

M"'(%*!'( /a' m"'((am#a$ (a$%- "'(a$! M /a' D a/a #a)& -*a*%- *a& *"'*!



EAL+ASI 4



Ta'/a Ta'/a Ta'(a' Ta'(a' D-"' P"'(am! D-"' 1 K$/%'a*$ PERNYATAAN6 D"'(a' %'% -a,a m"',a*a&a' #"$-"/%a m"m#"$%&a' ma*"$% -"-!a% &"-"a&a*a' ,a'( *")a /%*"*a&a' /% #$a'( %'%.

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DEFORMASI

DEFORMASI 2 PER+BAHAN BENT+K 

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EI

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3'C6C

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6 ;:

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D1 89

Mma 8 ;'4:C, ;'4:C  6,;'4:C ,6>; , ;'4:C 3'C;,6':7  ;,6':7,6>;,6':7 ;

M ma8

8 3'9:: TM '93  3'C6  ; 8 6'C; TM

8

ME 8 ;';; ,;  3'9 8 6'4C4 TM

3'C6C

M ; ;'

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EI KONSTANT E

CT ;m n8;,4  2 ;,6  ;,6 6  3  8 9

F

p.#(a% (e(ap

3m

4m

4m

[ BA = [ BD = [ BF 8

[ BA 8

9'44

[ BD 8

[ BF 8

MF BA 8  6>: , 6 , 3 ; 8  6'6;C TM MF BD 8  6>: ,C , : 8  C TM MF BF 8  3>67 , C , 4 8  3'C TM

MF DB 8  C TM



























TITIK

B

D BATANG FAKTOR DIST MF MD MI MD MOMEN AKHIR

BA  9'44

BF  9'34

BD  9';;

DB 

 6'6;C  3'3CC

 3'C  ;'C;C

9

9

C  6'7C 9 9

C 9  9':3:C 9

 4'4:

 6'67

 3'3;

 C':4

V MB 8 9 2 OK 

8 6(>m

CT

A D

;'

B ;'

4'4:

C'66C

9'99

0

3'3;

;'3

C':4

;'6:C

;':6C 6'67

;'

*a%."

FB

V MB 8 9

HF MISAL

E 89

CT

 HF,4 HF,4  C,;  6'67

HF 8 ;';6 T HB 8 C  ;' ;68 ;'

T *a%."

BD

VMD89

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F C':4 8 9

;';6

B,: 3'3;  C,4 



























Ba%."

AB

V MB8 9

A MISAL

A,3  3,6'C  4'4: 8 9

A 8 9'99 T

;'

N C'66C C'66C 9'99

;'6:C ;' ;'3

;':6C

Ba( AB

D1 89

9'996189

D

;' 18 9'99 m

DARI A

;';6 C':4 4'4: 3'3; 6'67



























Mma 8 9

C'4;

189'99 m

M

4'4;

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9'99,9'99 6,9'99,6>;,9'99 Mma 8 9 ME 8 ;';6 , ; 8 4 '4; TM

; (>m 7T E G

F

D

0

;m H

4T

4m

4m ;m

m

A

7m

n 8 ;,7  2 ;,;  ;,6  6  C  8 9

p.#(a% (e(ap

[ E0 = [ EF = [ EA 8 [ E0 8 9'36

[ EF 8 9';:

[ EA 8 9'46

[ FE = [ FB = [ FD 8 [ FE 8 9';: MOMEN PRIMAIR

[ FB 8 9'46

[ FD 8 9'36

B

;





























MF FD 8  3>67 , 7 , 4 8  4'C TM MF EA 8  MF AE 8 6>: , 4 , 4 8  ; TM T TK BATA NG FD MF MD MI MD

E0

E EA

9'36 4 6';4

 9'97C 6

MI

MD

MAKH IR

EF

A AE

FE

9'46 ; 6'74

9';: 7 6'6;

 ; 9

9';: 7 9'4;

9  9'9:7 6 9

9';6  9'9C: : 9'9 :4

 9':; 9

9'C7 9'6C 7:

 9'9439 C 9

 9'9; 4 9'99: ;3

9'99 66

9'96; 9C

9

;':7

7

C'6C

9':C

9'4;

   9'9;4 9'93; 9'9;6 3 6  C'33 9';4 C'9

6 (>m

F FD

FB

9'36  4'C 9'47 C

9'46 9 9'76 C

9'6 37

C'6C

C'33

9'39C 9

7T 9'3;F

D

66'6:

0

9';9 7

 9 9

9'664 :

6(>m 6'77C E 9'3;

B BF

69'44 C'9

7





























;'7CC 9'3;

A

B 66'6:

69'44

9'3;

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N

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7 C'33 C'9

9';4

9':C

3'C7

3'4;

;'4C

M

6;'9; ;':7

9'4;

 8 6(>m 6m

A

F 6m

E

B

0 4T

3m





























[ 0B = [ 0D 8 [ 0B 8 9'4C

[ 0D 8 9'CC MF AB 8  MF BA 8  6>6; , 6 , 3 ; 8  9'C TM MF B0 8 MF 0D 8  6>6; , 6 , 7 ; 8  3 TM MF BE 8  3>67 , 4 , ; 8  6'C TM

TITIK BATAN G FD MF MD

MI MD

MI

MD

M AKHIR

A

B

D

AB

BA

B0

BE

  9'C 9

 9'3:  9'C  6'4;C

 9'6 3  9'6;C

 9'43  6'C  6'76; C

 9'6;C 9

 9'6;:; C 9

 9'9

 9'7C  9';C7C

9'6;:;C

 9';9; C

0 0B

0D

D0

 9'4C 3  6'3C

 9'CC 9  6'7C

 9 9

 9'3C7;C 9'6793 6;C

 9'9394 7

 9'9:96C7 ;  9'96C;; 

 9'9344 7

 9'9746; C  9'9;::C 7

;'4C

 ;'9

 9'4C

 6'::

FREE BODY DIAGRAM

 9'6C3 

 9':;C 9

 9'9  9'93C; 7

 6'::

 9';





























4T

9';

E ;';;C C'44

BE V MB 8 9 6'C T

4'6

 HE,;  4,6  9'4C 8 9

HE 8 ;';;C T

HB 8

D

0D V MD 8 9 4'6 T

 HD,3 9'; 6'::  ;':3,4 89

3M

HD 8 4'6 T

;':3

H0 8

CM

X

X

D

X

4M

SIN X 8 3>C

4'6 SIN X

;':3 0OS X X

0OS X 8 4>C

;':3

4'6 4'6 0OS X ;' :3 SIN X

N D0 8  4'6 0OS X  ;':3 SIN X 8  3'7:  6'7: 8  C'477 T D D0 8  4'6 SIN X  ;':3 0OS X 8 ;':;7  ;';74 8  9'C7; T D1 8 3'6  61 8 9

1 8 3'6 M

M1 8 3'6,1  6,1,6>;,1  ;'9 18 3'6 M MA1 8 3'6,3'6  6,3'6 ,  , 3'6  ;'9 8 ;'6; TM































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M MA1 8;'6;































DARI GAMBAR DISAMPING ' Pen$e% DIHIT+NG MOMEN AKHIR NYA J+GA REAKSI PENDEL PENDEL NYA, NYA,

DAN

;, PORTAL PORTAL DIBIARKAN BERGOYANG BERGOYANG , 2 PHASE SAT+ SAT+  HIT+NG MOMEN AKHIR DAN J+GA REAKSI PENDEL NYA , B\



B JEPIT  JEPIT































DIMANA

RP9  RP6 8 9

1 DAPA DAPAT DITEM+KAN

SEHINGGA MOMEN AKHIR DAPA DAPAT DIHIT+NG DARI MOMEN AKHIR PHASE NOL DITAMBAH MOMEN AKHIR PHASE SAT+ ,

4, DARI HASIL MOMEN AKHIR AK HIR YANG DIDAPA DIDAPAT DIA DI ATAS ' MAKA DAPAT DILANJ+TKAN DENGAN MENGHIT+NG DAN MENGGAMBAR BIDANG MOMEN ' NORMAL DAN LINTANG ,































B

;EI

0

;EI

D

;EI

E

EI 4m p.#(a% *e#g.!ang

6m

n8 ;,3  2 ;,6  ;,9  6  ;  8 6  9

A

7m

;m

;T

6T

B

6(>m ;EI

0

;EI

E $)anggap $u%u ()$a" *e#g.!ang 4m memaang pen$e% ,

6m

A

D

;EI p.#(a%

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7m

;m

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9

9

;'C

 ;'C

4

4

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0

D

;'C

;'C

4

4

V M0 8 9

HA MISAL

 HA , 4  9 8 9

HA 8 9 T

RP9 8 9 T A

PHASE SAT+ SAT+

PORTAL PORTAL DIBIARKAN BERGOYANG BERGOYANG 

B

;EI

0

 06

;EI

D

;EI

E

































MI MD MOMEN AKHIR

B D

;C1 9 C1

9 9 C91

0

9 9 C91

9 9

 9 9

9 9

C91 E

36';C1 36';C1 36';C1

36';C1

































;'C TM ;T 3T

89

3T

T

4T 4 TM

;'C TM

BAT BATANG 0D D8 ;T

0 8 4T

D1 8 9

4 TM

V MD89

D1 8 4  61 8 9

0,7;'C46,7,3 0,7;'C46, 7,3

1 8 4M

(e#-a$)

M ma M1 8 41  6,1,6>;,1  ;'C A ;'C 8 C'C TM

T

18 4

M ma 8 4,4  6,4,6>;,4 

































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M

C'C TM

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3m

































MF 0D 8  6,; 8  ;TM

TITIK BATANG FD MF MD MI MD MI MD M AKHIR

A AB  9 9 9 9 9'36;C 9 9'36;C

B BA 9'7;C 9 9 9 9'7;C 9 9 9'7;C

B0 9'3C 9 9 6 9'3C 9 9 9'7;C

0 0B 6 9 ;

0D 9 ; 9

9

9

9 ;

9 ;

































PHASE SA SAT+ T+ ' PORT PORTAL AL DIBIARKAN DI BIARKAN BERGOY BE RGOYANG ANG 3

C

)nX83>C 4

B

B\

(gX83>4

B



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B\

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6C7';C1

A

B ;93'6;C1 :':43C1

:':43C1

6C7';C1 :':43C1

0



































4T

4'34TM

A

B C';6;TM

;'496CT

4'34TM



































9'C6T

;'496CT

;'496CT



































MATRI: MATRI: YANG YANG DIJUMLAH HARUS MEMPUNYAI JUMLAH BARIS DAN DAN KOLOM KOLOM YANG YANG SAMA.

4

53

2

;



54



@



54

2

3

@



10

;

7

11

52

2



































A



A

A

9





































3

@

2

3

@

 1.3.7  ;.2.2  4.@  –



































TAHAPAN PENYELESAIAN KONSTR+KSI







































































































MENENT+KAN MATRI1 MATRI1

A

+NT+K



























































































































































































































































































































































































































































































































































Bahan Ajar Mekanika Teknik Statis Tak Tentu Program d4 18 Sept 2013

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