Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah

8/19/2019 Contoh Soal Analisa Matriks (Portal Hal.186) Sudut Diubah

1/345


2/345

() 1.2 = 0 = 0

() 2.2 = 12.EI/L*3 = 5+400

() 3.2 = +.EI / L*2 = ,0500

Akibat disla!ement arah 3 ""# $3 %r&tasi arah sb l&kal 3'

() 1.3 = 0 = 0

() 2.3 = +.EI / L*2 = ,0500

() 3.3 = 4 EI / L = 11,500

Akibat disla!ement arah 4 ""# $4 %translasi arah sb l&kal 4'

() 1.4 = " E.A / L = "1410000

() 2.4 = 0 = 0

() 3.4 = 0 = 0


() 1.5 = 0 = 0

() 2.5 = "12.EI/L*3 = "5+400

() 3.5 = "+.EI / L*2 = ",0500

Akibat disla!ement arah + ""# $+ %r&tasi arah sb l&kal +'

() 1.+ = 0 = 0

() 2.+ = +.EI / L*2 = ,0500

() 3.+ = 2 EI / L = 5-,50

(snan matriks kekakan batang 1 %()1' :

()11 ()12 ()13

()21 ()22 ()23

()1 = ()31 ()32 ()33

()41 ()42 ()43

()51 ()52 ()53

()+1 ()+2 ()+3

(dt batang 1 : =

)atriks trans&rmasi r&tasi :

α1


3/345

0

= 0

0 0 1

0 0 0

0 0 0

0 0 0

rans&se matrik &tasi

1.00 0 0

= 0 1.00 0

0 0 1

0 0 0

0 0 0

0 0 0

)atriks kekakan strktr menadi :

1.00 0.00 0.00

0.00 1.00 0.00

0.00 0.00 1.00

()( 1 = 0.00 0.00 0.00

0.00 0.00 0.000.00 0.00 0.00

1410000 0 0

0 5+400 ,0500

0 ,0500 11,500

"1410000 0 0

0 "5+400 ",0500

0 ,0500 5-,50

Hitung matriks kekakuan batang 2 (SM2)


() 1.1 = E.A / L = ,05000

() 2.1 = 0 = 0

() 3.1 = 0 = 0


!&s α1

sin α1

" sin α1

!&s α1

()( = . () .


4/345

() 1.2 = 0 = 0

() 2.2 = 12.EI/L*3 = ,050

() 3.2 = +.EI / L*2 = 1,+25


() 1.3 = 0 = 0

() 2.3 = +.EI / L*2 = 1,+25

() 3.3 = 4 EI / L = 5-,50


() 1.4 = " E.A / L = ",05000

() 2.4 = 0 = 0

() 3.4 = 0 = 0


() 1.5 = 0 = 0

() 2.5 = "12.EI/L*3 = ",050

() 3.5 = "+.EI / L*2 = "1,+25


() 1.+ = 0 = 0

() 2.+ = +.EI / L*2 = 1,+25

() 3.+ = 2 EI / L = 23,5


()11 ()12 ()13

()21 ()22 ()23

()2 = ()31 ()32 ()33

()41 ()42 ()43

()51 ()52 ()53

()+1 ()+2 ()+3

(dt batang 2 : =

ata =

)atriks trans&rmasi r&tasi :

α2

α2


5/345

0

= 0

0 0 1

0 0 0

0 0 0

0 0 0


0.80 -0.6 0

= 0.6 0.80 0

0 0 1

0 0 0

0 0 0

0 0 0


0.-0 "0.+0 0.00

0.+0 0.-0 0.00

0.00 0.00 1.00

()( 2 = 0.00 0.00 0.00

0.00 0.00 0.000.00 0.00 0.00

5+4000 "4230 "105,5

423000 5+40 14100

0 1,+25 5-,50

"5+4000 4230 105,5

"423000 "5+40 "14100

0 1,+25 23,5

Hitung matriks kekakuan batang 3 (SM3)


() 1.1 = E.A / L = 1410000

() 2.1 = 0 = 0

() 3.1 = 0 = 0


() 1.2 = 0 = 0

!&s α1

sin α1

" sin α1

!&s α1

()( = . () .


6/345

() 2.2 = 12.EI/L*3 = 5+400

() 3.2 = +.EI / L*2 = ,0500


() 1.3 = 0 = 0

() 2.3 = +.EI / L*2 = ,0500

() 3.3 = 4 EI / L = 11,500


() 1.4 = " E.A / L = "1410000

() 2.4 = 0 = 0

() 3.4 = 0 = 0


() 1.5 = 0 = 0

() 2.5 = "12.EI/L*3 = "5+400

() 3.5 = "+.EI / L*2 = ",0500


() 1.+ = 0 = 0

() 2.+ = +.EI / L*2 = ,0500

() 3.+ = 2 EI / L = 5-,50


()11 ()12 ()13

()21 ()22 ()23

()3 = ()31 ()32 ()33

()41 ()42 ()43

()51 ()52 ()53

()+1 ()+2 ()+3

(dt batang 3 : =

ata =)atriks trans&rmasi r&tasi :

α3

α3


7/345

0

= 0

0 0 1

0 0 0

0 0 0

0 0 0


1.00 0 0

= 0 1.00 0

0 0 1

0 0 0

0 0 0

0 0 0


1.00 0.00 0.00

0.00 1.00 0.00

0.00 0.00 1.00

()( 3 = 0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

1410000 0 0

0 5+400 ,0500

0 ,0500 11,500

"1410000 0 0

0 "5+400 ",0500

0 ,0500 5-,50

Susun MAT!"S "#"A"$AN ST$"T$

0 0 0

1 2 3

164106000 0 0

0 5+6400 ,06500

()( 1 = 0 ,06500 11,6500

"164106000 0 0

0 "5+6400 ",06500

0 ,06500 5-6,50

$1 0 $2

4 5 +

!&s α1

sin α1

" sin α1

!&s α1

()( = . () .


8/345

4536,3- 335601+ "1065,5

335601+ 25-6312 146100

()( 2 = "1065,5 146100 5-6,50

"4536,3- "335601+ 1065,5

"335601+ "25-6312 "146100

"1065,5 146100 263,5

$3 0 $4

, -

164106000 0 0

0 5+6400 ,06500

()( 3 = 0 ,06500 11,6500

"164106000 0 0

0 "5+6400 ",06500

0 ,06500 5-6,50

MAT!"S "#"A"$AN ST$"T$

$1 $2 $3

4 + ,

16-+36,3- "1065,5 "4536,3-

()( = "1065,5 1,+6250 1065,5

"4536,3- 1065,5 16-+36,3-

"1065,5 263,5 1065,5

Batang 1

Gbr AM 1 =

Batang 2

Gbr AM 2 =

Hitung rekasi di ujung batang / freebody (AML) ---> Beban dimasukkan kecuai beban di joi


9/345

Batang !

Gbr AM 3 =

"ransformasi dari sumbu oka ke sumbu goba struktur

Batang 1

0 1 1

30 2 2

AM 1 = 12.5 3 3

0 4 4

30 5 5

-12.5 6 6

SB LOKAL SB GLOBAL

1.00 0.00 0.00

0.00 1.00 0.00

= 0.00 0.00 1.00

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0 1 1

30 2 2

= 12.53

3

0 4 4

30 5 5

-12.5 + 6

SB LOKAL SB GLOBAL

Batang 2

22.5 1

25.3125 2

AM 2 = 35.15625 3

37.5 4

RT

AMS

1


10/345

54.6875 5

-58.59375 6

SB LOKAL

0.80 -0.60 0.000.60 0.80 0.00

= 0.00 0.00 1.00

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

2.8125 4

33.75 5

= 35.15625 6

-2.8125 7

66.25 8

-58.59375 9

SB GLOBAL

Batang !

0 1

60 2AM 3 = 25 3

0 4

60 5

-25 6

SB LOKAL

1.00 0.00 0.00

0.00 1.00 0.00

= 0.00 0.00 1.00

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0 7

60 8

= 25 9

0 10

60 11

-25 12

RT

AMS 2

RT

AMS 3


11/345


12/345

10 0 0

11 0 "+0

12 0 25

$1 "2.-125

$2 "22.+5+25

$3 2.-125

$4 33.53,5

#$%&'MA "'*+"*'

9itng erindahan

5.,05+5E"00, 2.22125E"00- 1.3-+5524+4-E"00,

= 2.22125E"00- 5.-3-15E"00+ "2.22124-1+3-E"00-

1.3-+55E"00, "2.22125E"00- 5.,05+4+11++,E"00,

2.22125E"00- ".,03+0E"00, "2.22124-1+3-E"00-

,AA-,AA #ALAM *.*, $L$M$

Batang 1

"(r#) *r*r +# #r# SUMBU GLOBAL &) b#*#$, 1 bb

0 1 0

0 2 0

0 0 3 0

-0.000001 4 1

0.000000 5 0

-0.000165 6 2

"(r#) *r*r +# #r# SUMBU LOKAL &) b#*#$, 1 bb

1 0 0

0 1 0

0 0 0 1

0 0 0

0 0 0

0 0 0

G## '$, b#*#$,

B"b#$ '()$* #$, "+#r# O: A:;

!

A%

0

: = S

::-1.A

:;S

::-1 = SMS -1

:

#M 1

∆M 1 = R . MS 1

M 1


13/345

0 1410000

30 0

AM 1 0 12.5 0

0 -141000030 0

-12.5 0

Batang 2

"(r#) *r*r +# #r# SUMBU GLOBAL &) b#*#$, 2 bb

-9.7180E-07 4 1

0 5 0

0 -1.6499E-04 6 29.7180E-07 7 3

0 8 0

2.1799E-04 9 4


0.8 0.6 0-0.6 0.8 0

0 0 0 1

0 0 0

0 0 0

0 0 0

G## '$, b#*#$,

22.5 705000

25.3125 0

AM 2 0 35.15625 0

37.5 -705000

54.6875 0

-58.59375 0

Batang !"(r#) *r*r +# #r# SUMBU GLOBAL &) b#*#$, 3 bb

AM 1 = AML 1 SM 1 . ∆M 1

#M 2

∆M 2 = R . MS 2

M 2

AM 2 = AML 2 SM 2 . ∆M 2


14/345

9.7180E-07 7 3

0 8 0

0 2.1799E-04 9 4

0 10 0

0 11 0

0 12 0


1.0 0.0 0.0

0.0 1.0 0.0

0 0.0 0.0 1.0

0.0 0.0 0.00.0 0.0 0.0

0.0 0.0 0.0

G## '$, b#*#$,

0 1410000

60 0

AM 3 0 25 0

0 -1410000

60 0

-25 0

#M !

∆M 3 = R . MS 3

M !

AM 3 = AML 3 SM 3 . ∆M 3


15/345

%ata beban

= 100 kN

;1 = 24 kN/m

;2 = 4- kN/m

#&emen 'a&am matriks kekakuan batang

Batang EA / L 4.EI / L 2.EI / L +.EI / L*2

1 1410000 11,500 5-,50 ,0500

2 ,05000 5-,50 23,5 1,+25

3 1410000 11,500 5-,50 ,0500

9bngan antar batang

N(. B#*#$, U'$, ) U'$, '

1 1 2

2 2 3

3 3 4

(AL $AN (


16/345

() 4.2 = 0 =

() 5.2 = "12.EI/L*3 =

() +.2 = +.EI / L*2 =

() 4.3 = 0 =

() 5.3 = "+.EI / L*2 =

() +.3 = 2 EI / L =

() 4.4 = E.A / L =

() 5.4 = 0 =

() +.4 = 0 =

() 4.5 = 0 =

() 5.5 = 12.EI/L*3 =

() +.5 = "+.EI / L*2 =

() 4.+ = 0 =

() 5.+ = "+.EI / L*2 =

() +.+ = 4 EI / L =

""# !atatan matriks kekakan batang dalam arah smb l&kal %smb l&kal ata

1 2

()14 ()15 ()1+ 1410000 0

()24 ()25 ()2+ 0 5+400

()34 ()35 ()3+ = 0 ,0500

()44 ()45 ()4+ "1410000 0

()54 ()55 ()5+ 0 "5+400

()+4 ()+5 ()++ 0 ,0500

0deg


17/345

0 0 0

0 0 0 =

0 0 0

0

0

0 0 1

0 0 0

0 0 0

0 0 0

1.00 0 0

0 1.00 0

0 0 1

0.00 0.00 0.00 1410000 0

0.00 0.00 0.00 0 5+400

0.00 0.00 0.00 ? 0 ,0500

1.00 0.00 0.00 "1410000 0

0.00 1.00 0.00 0 "5+4000.00 0.00 1.00 0 ,0500

"1410000 0 0 1 0

0 "5+400 ,0500 0 1

0 ",0500 5-,50 ? 0 0

1410000 0 0 0 0

0 5+400 ",0500 0 0

0 ",0500 11,500 0 0

(AL $AN (


18/345

() 4.2 = 0 =

() 5.2 = "12.EI/L*3 =

() +.2 = +.EI / L*2 =

() 4.3 = 0 =

() 5.3 = "+.EI / L*2 =

() +.3 = 2 EI / L =

() 4.4 = E.A / L =

() 5.4 = 0 =

() +.4 = 0 =

() 4.5 = 0 =

() 5.5 = 12.EI/L*3 =

() +.5 = "+.EI / L*2 =

() 4.+ = 0 =

() 5.+ = "+.EI / L*2 =

() +.+ = 4 EI / L =


1 2

()14 ()15 ()1+ ,05000 0

()24 ()25 ()2+ 0 ,050

()34 ()35 ()3+ = 0 1,+25

()44 ()45 ()4+ ",05000 0

()54 ()55 ()5+ 0 ",050

()+4 ()+5 ()++ 0 1,+25

3+.-+-,+4+ deg 0.-

3+.-+-,+4+ deg 0.+


19/345

0 0 0

0 0 0 =

0 0 0

0

0

0 0 1

0 0 0

0 0 0

0 0 0

0.80 -0.6 0

0.6 0.80 0

0 0 1

0.00 0.00 0.00 ,05000 0

0.00 0.00 0.00 0 ,050

0.00 0.00 0.00 ? 0 1,+25

0.-0 "0.+0 0.00 ",05000 0

0.+0 0.-0 0.00 0 ",0500.00 0.00 1.00 0 1,+25

"5+4000 4230 "105,5 1 1

"423000 "5+40 14100 "1 1

0 "1,+25 23,5 ? 0 0

5+4000 "4230 105,5 0 0

423000 5+40 "14100 0 0

0 "1,+25 5-,50 0 0

(AL $AN (


20/345

() 5.2 = "12.EI/L*3 =

() +.2 = +.EI / L*2 =

() 4.3 = 0 =

() 5.3 = "+.EI / L*2 =

() +.3 = 2 EI / L =

() 4.4 = E.A / L =

() 5.4 = 0 =

() +.4 = 0 =

() 4.5 = 0 =

() 5.5 = 12.EI/L*3 =

() +.5 = "+.EI / L*2 =

() 4.+ = 0 =

() 5.+ = "+.EI / L*2 =

() +.+ = 4 EI / L =


1 2

()14 ()15 ()1+ 1410000 0

()24 ()25 ()2+ 0 5+400

()34 ()35 ()3+ = 0 ,0500

()44 ()45 ()4+ "1410000 0

()54 ()55 ()5+ 0 "5+400

()+4 ()+5 ()++ 0 ,0500

0 deg 1

0 deg 0


21/345

0 0 0

0 0 0 =

0 0 0

0

0

0 0 1

0 0 0

0 0 0

0 0 0

1.00 0 0

0 1.00 0

0 0 1

0.00 0.00 0.00 1410000 0

0.00 0.00 0.00 0 5+400

0.00 0.00 0.00 ? 0 ,0500

1.00 0.00 0.00 "1410000 0

0.00 1.00 0.00 0 "5+400

0.00 0.00 1.00 0 ,0500

"1410000 0 0 1 0

0 "5+400 ,0500 0 1

0 ",0500 5-,50 ? 0 0

1410000 0 0 0 0

0 5+400 ",0500 0 0

0 ",0500 11,500 0 0

$1 0 $2

4 5 + ==# EN)AN (B 7LBAL

"164106000 0 0 1 0

0 "5+6400 ,06500 2 0

0 ",06500 5-6,50 3 0

164106000 0 0 4 $1

0 5+6400 ",06500 5 0

0 ",06500 11,6500 + $2

$3 0 $4

, - ==# EN)AN (B 7LBAL

!&s α1

sin α1

" sin α1

!&s α1


22/345

"4536,3- "335601+ "1065,5 4 $1

"335601+ "25-6312 146100 5 0

1065,5 "146100 263,5 + $2

4536,3- 335601+ 1065,5 , $3

335601+ 25-6312 "146100 - 0

1065,5 "146100 5-6,50 $4

0 0 0

10 11 12 ==# EN)AN (B 7LBAL

"164106000 0 0 , $3

0 "5+6400 ,06500 - 0

0 ",06500 5-6,50 $4

164106000 0 0 10 0

0 5+6400 ",06500 11 0

0 ",06500 11,6500 12 0

$4

"1065,5 4 $1

263,5 + $2 =

1065,5 , $3

1,+6250 $4

0 1

30 2 kN

= 12.5 3 kN.m

0 4

30 5 kN

"12.5 + kN.m

SB LOKAL

22.5 1

25.3125 2

= 35.15+25 3

3,.5 4 a =

54.+-,5 5 b =

"5-.53,5 + L =

()("1

t

AML 1

AML 2

AML 3

AML 4

AML 5

AML 6

AML 1 .!&s α =

AML 2 .sin α =

AML 3

AML 4

AML 5

AML 6


23/345

SB LOKAL

0 1

+0 2 kN

= 25 3 kN.m

0 4

+0 5 kN

"25 + kN.m

SB LOKAL

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

1.00 0.00 0.00

0.00 1.00 0.00

0.00 0.00 1.00

0

0

0

1

0

2


24/345

0.00 0.00 0.000.00 0.00 0.00

0.00 0.00 0.00

0.80 -0.60 0.00

0.60 0.80 0.00

0.00 0.00 1.00

1

0

2

3

0

4

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

1.00 0.00 0.00

0.00 1.00 0.00

0.00 0.00 1.00

3

0

4

0

0

0

AMS 2 = R

T

. AML 2

AMS 2

AMS 3 = RT . AM

L 3

AMS 3


25/345

B7 2 B7 3

0 0 0

0 0 30

0 0 12.5

2.-125 0 2.-125

33.,5 0 = +3.,5

35.15+25 8 0 22.+5+25

"2.-125 0 "2.-125

++.25 +0 12+.25

"5-.53,5 25 "33.53,5

0 0 0

0 +0 +0

0 "25 "25

0 0

"30 0

"12.5 0

"2.-125 $1

= "+3.,5 0

"22.+5+25 $2

2.-125 $3"12+.25 0

33.53,5 $4


26/345


27/345

0 0 -1410000 0 0

56400 70500 0 -56400 70500

70500 117500 0 -70500 58750 3

0 0 1410000 0 0

-56400 -70500 0 56400 -70500

70500 58750 0 -70500 117500

0 0 0 -9.7179607165E-0070 0 0 0

0 0 0 3 -0.0001649936 0

0.8 0.6 0 9.7179607165E-007

-0.6 0.8 0 0

0 0 1 0.0002179852

0 0 -705000 0 0

7050 17625 0 -7050 17625

17625 58750 0 -17625 29375 3

0 0 705000 0 0

-7050 -17625 0 7050 -17625

17625 29375 0 -17625 58750


28/345

0.0 0.0 0.0 9.7179607165E-007

0.0 0.0 0.0 0

0.0 0.0 0.0 3 0.0002179852 0

1.0 0.0 0.0 00.0 1.0 0.0 0

0.0 0.0 1.0 0

0 0 -1410000 0 0

56400 70500 0 -56400 70500

70500 117500 0 -70500 58750 3

0 0 1410000 0 0

-56400 -70500 0 56400 -70500

70500 58750 0 -70500 117500


29/345

12.EI / L*3

5+400

,050

5+400

N $AN AN$A %8' %"'

"1410000

0

0


30/345


31/345

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

0 "1410000 0 0 1

,0500 0 "5+400 ,0500 0

11,500 0 ",0500 5-,50 ? 0

0 1410000 0 0 0

",0500 0 5+400 ",0500 05-,50 0 ",0500 11,500 0

1

0 0 0 0 164106000

0 0 0 0 0

1 0 0 0 = 0

0 1 0 0 "164106000

0 0 1 0 0

0 0 0 1 0

N $AN AN$A %8' %"'

",05000

0

0


32/345

0

",050

1,+25

0

"1,+25

23,5

,05000

0

0

0

,050

"1,+25

0

"1,+25

5-,50

gl&bal menentkan en&m&ran dan tanda %8' %"'

3 4 5 + sb l&kal

0 ",05000 0 0 1

1,+25 0 ",050 1,+25 2

5-,50 0 "1,+25 23,5 3

0 ,05000 0 0 4

"1,+25 0 ,050 "1,+25 5

23,5 0 "1,+25 5-,50 +

sb l&kal


33/345

0.8 0.6 0 0 0 0

-0.6 0.8 0 0 0 0

0 0 1 0 0 0

0 0 0 0.8 0.6 0

0 0 0 -0.6 0.8 0

0 0 0 0 0 1

0 ",05000 0 0 0.-0

1,+25 0 ",050 1,+25 "0.+0

5-,50 0 "1,+25 23,5 ? 0.00

0 ,05000 0 0 0.00

"1,+25 0 ,050 "1,+25 0.0023,5 0 "1,+25 5-,50 0.00

4

0 0 0 0 4536,3-

0 0 0 0 335601+

1 0 0 0 = "1065,5

0 1 1 0 "4536,3-

0 "1 1 0 "335601+

0 0 0 1 "1065,5

N $AN AN$A %8' %"'

"1410000

0

0

0


34/345

"5+400

,0500

0

",0500

5-,50

1410000

0

0

0

5+400

",0500

0

",0500

11,500

gl&bal menentkan en&m&ran dan tanda %8' %"'

3 4 5 + sb l&kal

0 "1410000 0 0 1

,0500 0 "5+400 ,0500 2

11,500 0 ",0500 5-,50 3

0 1410000 0 0 4

",0500 0 5+400 ",0500 5

5-,50 0 ",0500 11,500 +

sb l&kal


35/345

1.0 0.0 0 0 0 0

0.0 1.0 0 0 0 0

0 0 1 0 0 0

0 0 0 1.0 0.0 0

0 0 0 0.0 1.0 0

0 0 0 0 0 1

0 "1410000 0 0 1

,0500 0 "5+400 ,0500 0

11,500 0 ",0500 5-,50 ? 0

0 1410000 0 0 0

",0500 0 5+400 ",0500 0

5-,50 0 ",0500 11,500 0

,

0 0 0 0 164106000

0 0 0 0 0

1 0 0 0 = 0

0 1 0 0 "164106000

0 0 1 0 0

0 0 0 1 0


36/345

5.,05+E"00, 2.22124-1+E"00- 1.3-++E"00, 2.2212E"00-

2.2212E"00- 5.-3-150,E"00+ "2.221E"00- ".,04E"00,

1.3-++E"00, "2.22124-2E"00- 5.,05+E"00, "2.221E"00-

2.2212E"00- ".,035++E"00, "2.221E"00- 5.-3-2E"00+

-0 kN = b/L =

+0 kN =

=

3.125 m = a/L =

1.-,5 m =

5 m =

AML 1

AML 2 b2%3a8b'/L3 =

AML 3 ab2/L2 =

AML 4

AML 5 a2%a83b'/L3 =

AML 6 "a2b/L2 =


37/345

1.00 0.00 0.00 0.00 0.00

0.00 1.00 0.00 0.00 0.00

0.00 0.00 1.00 0.00 0.00

= 0.00 0.00 0.00 1.00 0.00

0.00 0.00 0.00 0.00 1.00

0.00 0.00 0.00 0.00 0.00


38/345

0.80 -0.60 0.00 0.00 0.000.60 0.80 0.00 0.00 0.00

0.00 0.00 1.00 0.00 0.00

= 0.00 0.00 0.00 0.80 -0.60

0.00 0.00 0.00 0.60 0.80

0.00 0.00 0.00 0.00 0.00

1.00 0.00 0.00 0.00 0.00

0.00 1.00 0.00 0.00 0.00

0.00 0.00 1.00 0.00 0.00

= 0.00 0.00 0.00 1.00 0.00

0.00 0.00 0.00 0.00 1.00

0.00 0.00 0.00 0.00 0.00


39/345

0

"30

"12.5

"2.-125

AE = "+3.,5

"22.+5+25

2.-125

"12+.25

33.53,5

0

"+0

25


40/345

-9.71796E-07

-1.64994E-04

9.71796E-07

2.17985E-04

0 1

0 2

0 3

-9.717961E-007 4

0 5

-0.0001649936 6


41/345

0 0 1.370

0 30 -11.632

0 0 12.5 -9.693 0

-9.717961E-007 0 -1.3700 30 11.632

-0.0001649936 -12.5 -19.387

-7.774369E-007 4 15.830776E-007 5 0

-0.0001649936 6 2

7.774369E-007 7 3

-5.830776E-007 8 0

0.0002179852 9 4

-7.774369E-007 22.5 -1.096

5.830776E-007 25.3125 0.942

0.000 0 35.15625 -3.270 0

0.000 37.5 1.096

0.000 54.6875 -0.942

0.000 -58.59375 7.980


42/345

9.717961E-007 7 3

0 8 0

0.0002179852 9 4

0 10 00 11 0

0 12 0

9.717961E-007 0 1.370

0 60 15.368

0.0002179852 0 25 25.613 0

0 0 -1.370

0 60 -15.368

0 -25 12.807


43/345


44/345


45/345

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0

0 0 0 1 00 0 0 0 1

2 3 4 5 + sb gl&bal

0 0 "164106000 0 0 1

5+6400 ,06500 0 "5+6400 ,06500 2

,06500 11,6500 0 ",06500 5-6,50 3

0 0 164106000 0 0 4

"5+6400 ",06500 0 5+6400 ",06500 5

,06500 5-6,50 0 ",06500 11,6500 +

sb gl&bal


46/345


47/345

0.+0 0.00 0.00 0.00 0.00

0.-0 0.00 0.00 0.00 0.00

0.00 1.00 0.00 0.00 0.00

0.00 0.00 0.-0 0.+0 0.00

0.00 0.00 "0.+0 0.-0 0.000.00 0.00 0.00 0.00 1.00

5 + , - sb gl&bal

335601+ "1065,5 "4536,3- "335601+ "1065,5 4

25-6312 146100 "335601+ "25-6312 146100 5

146100 5-6,50 1065,5 "146100 263,5 +

"335601+ 1065,5 4536,3- 335601+ 1065,5 ,

"25-6312 "146100 335601+ 25-6312 "146100 -

146100 263,5 1065,5 "146100 5-6,50

sb gl&bal


48/345


49/345

0 0 0 0 0

1 0 0 0 0

0 1 0 0 0

0 0 1 0 0

0 0 0 1 0

0 0 0 0 1

- 10 11 12 sb gl&bal

0 0 "164106000 0 0 ,

5+6400 ,06500 0 "5+6400 ,06500 -

,06500 11,6500 0 ",06500 5-6,50

0 0 164106000 0 0 10

"5+6400 ",06500 0 5+6400 ",06500 11

,06500 5-6,50 0 ",06500 11,6500 12

sb gl&bal


50/345

30

22.5 kN

25.3125kN

35.15+25kN.m

3,.5 kN

54.+-,5kN

"5-.53,5 kN.m


51/345

0.00 0

0.00 30

0.00 > 12.5

0.00 0

0.00 30

1.00 -12.5


52/345

0.00 22.50.00 25.3125

0.00 > 35.15625

0.00 37.5

0.00 54.6875

1.00 -58.59375

0.00 0

0.00 60

0.00 > 25

0.00 0

0.00 60

1.00 -25


53/345


54/345


55/345

1.37 1 1.3,02kN

18.37 2 1-.3+-0kN

2.81 3 2.-0++ kN.m

-1.37 4 "1.3,02 kN41.63 5 41.+320kN

-31.89 6 "31.--+,kN.m

21.40 1 1 21.403-kN

26.25 2 0 2+.254,kN

31.89 3 2 31.--+,kN.m

38.60 4 3 3-.5+2kN

53.75 5 0 53.,453kN

-50.61 6 4 "50.+133kN.m


56/345

1.37 1 3 1.3,02kN

75.37 2 0 ,5.3+-0kN

50.61 3 4 50.+133kN.m

-1.37 4 0 "1.3,02 kN

44.63 5 0 44.+320kN

-12.19 6 0 "12.134kN.m


57/345


58/345


59/345

0

0

0

$1

0

$2

@E>


60/345


61/345

$1

0

$2

$3

0

$4

@E>


62/345


63/345

$3

0

$4

0

0

0

@E>


64/345


65/345


66/345


67/345


68/345


69/345


70/345


71/345

Beban ekialen

&int (b 7l&bal Element 1 Element 2 Element 3

1 1 0 0 0

1 2 30 0 0

1 3 12.5 0 0

"Ae = 2 4 0 2.-125 0

2 5 30 33.,5 0

2 + "12.5 8 35.15+25 8 0 =

3 , 0 "2.-125 0

3 - 0 ++.25 +0

3 0 "5-.53,5 254 10 0 0 0

4 11 0 0 +0

4 12 0 0 "25

eban *oint akibat beban &uar 'i *oint

&int (b 7l&bal $C

1 1 0

1 2 0

A = 1 3 0

2 4 0 d1

2 5 0

2 + 0 d2

3 , 0 d3

3 - 0

3 0 d4

4 10 0

4 11 0

4 12 0

eban kombinasi atau gabungan (Ae + A*)

A! = Ae 8 A

$C

1 0 0 1 0

A! = 2 "30 0 1 "30

3 "12.5 0 hi1 "12.5

4 "2.-125 0 2 "2.-125 d1

5 "+3.,5 0 2 "+3.,5+ "22.+5+25 8 0 = hi2 "22.+5+25 d2

, 2.-125 0 3 2.-125 d3

- "12+.25 0 3 "12+.25

33.53,5 0 hi3 33.53,5 d4

10 0 0 4 0

11 "+0 0 4 "+0

12 25 0 hi4 25


72/345

+0

sin 0.-++0254 +0

cos 0.5 +0

1.,32050-1 +0

tan theta 0.,5 3+.-+-,+

0.,5


73/345

M#"AN!"A #"A,ASA -

%ata beban

= 100 kN

;1 = 24 kN/m

;2 = 4- kN/m

versi lengka


74/345

ST#P 1 %is/reti0e an' &oba& %egrees o ree'om (%O)


75/345

P#N,##SA!AN

Properties penampang

Bahan / material :

E = 2.35E80, kN/m2

Batang 1 :

b = 0.30 m

h = 0.50 m

0.15 m2E = 2.35E80, kN/m2

3.13E"03m4

2.5m

Batang 3 :

b = 0.30 m

h = 0.50 m

0.15 m2

E = 2.35E80, kN/m2

3.13E"03m4

2.5m

ekap #&emen 'a&am Matriks "ekakuan atang

Batang EA ? L 4.EI ? L 2.EI ? L 6.EI ? L@2 12.EI ? L@3 S&* &",! D?

1 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 0 1

2 ,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803 3+.-+-,+4+ 0.-

3 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 0 1

4 $I@/0F $I@/0F $I@/0F $I@/0F $I@/0F 0 1

5 ECF ECF ECF ECF ECF ECF

%O sesuai sumbu g&oba& struktur 'an tentukan eban atau Momen pa'a Titik 5oint Struktur 'a&am Ara6 Sumbu &oba&7Su

A1 =

I1 =

L1 =

A3 =

I3 =

L3 =


76/345

DOF

1

1 1 0

2 2 0

3 3 0

2

4 d1 0

5 5 0

+ d2 0

3

, d3 0

- - 0

d4 0

410 10 011 11 0

12 12 0

Nomor *oint untuk setiap e&ement

#&ement (i)5oint

* k

1 1 22 2 3

3 3 4

%isp&a/ement titik sumbu g&oba& struktur pa'a tiap e&ement

#&ement * k

1 1 2 3 4 5 + ==> Global axis

2 4 5 + , - ==> Global axis

3 , - 10 11 12 ==> Global axis

No.titik!oint"

Dis.GlobalAxis

B#ban $%on


77/345

==> Global axis

==> Global axis

Meng6itung a8a 'an Momen $*ung (Akibat beban &uar 'i sepan*ang bentang 'engan u*ung 'ikekang7'i*epit) (%AAM AA

a8a 'an Momen $*ung pa'a #&ement 91

'a = 0 kN 'b = 0 kN

(a = 30 kN (b = 30 kN

%a = 12.5 kN.& %b = "12.5 kN.&

a8a 'an Momen $*ung pa'a #&ement 92'a = 22.5 kN 'b = 3,.5 kN

(a = 25.3125kN (b = 54.+-,5 kN

%a = 35.15+25 kN.& %b = "5-.53,5kN.&

a8a 'an Momen $*ung pa'a #&ement 93

'a = 0 kN 'b = 0 kN

(a = +0 kN (b = +0 kN

%a = 25 kN.& %b = "25 kN.&

ekap a8a $*ung atang (Sumbu oka&)

No. Btg)*+ng ki,i *" )*+ng kanan k"

B"b#$ :'! B"b#$ :'! B"b#$ MC'! B"b#$ :! B"b#$ :! B"b#$ MC!

1 0 30 12.5 0 30 "12.5

2 22.5 25.3125 35.15+25 3,.5 54.+-,5 "5-.53,5

3 0 +0 25 0 +0 "25

4 ECF ECF ECF ECF ECF ECF

5

Tentukan parameter 8ang 'ibutu6kan

a. (mb gl&bal strktr ada tia element

b. $C sesai smb gl&bal strktr


78/345

!. -#s#s+aian sb lokal #l#nt d#ngan DOF a,a global

d.

!.

Local Axis 1 2 3 4 5

/l#nt k# 1 1 2 3 d1 d2

/l#nt k# 2 &1.;>;&2;>; &1.;>;&2;>; d3 4 5

/l#nt k# 3 d1 d2 d3 , -

/l#nt 01

Local axis 1 2 3 4 5 +

Global axis 1 1 2 3 4 5

DOF 0 0 0 d1 0 d2

/l#nt 02

Local axis 1 2 3 4 5 +

Global axis 4 5 + , -

DOF d1 0 d2 0

d.

#&ement 1

0 0 0 0

0 0 0 0

= 0 0 1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0 1

)atriks rans&rmasi dan tia element

-#s#s+aian S O"A #l#nt d#ngan S OA 'an %O ara6 g&oba&

)atriks rans&rmasi dan tia element

!&s α1

sin α1

" sin α1

!&s α1

!&s α1

sin α1

" sin α1

!&s α1


79/345

#&ement 2

0 0 0 0

0 0 0 0

= 0 0 1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0 1

#&ement 3

0 0 0 0

0 0 0 0

= 0 0 1 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0 0 1

!&s α1

sin α1

" sin α1

!&s α1

!&s α1

sin α1

" sin α1

!&s α1

!&s α1

sin α1

" sin α1

!&s α1

!&s α1

sin α1

" sin α1

!&s α1


80/345

:::; %AAM S$M$ O"A

Batang = 1

/l#n dala& &at,iks k#kak+an batang :

EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3

1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804

D? = !&s theta = 1

DG = sin theta = 0

L&!al a?is 1 2 3 4 5 +

1 1410000 0 0 "1410000 0 0

2 0 5+400 ,0500 0 "5+400 ,0500

3 0 ,0500 11,500 0 ",0500 5-,50

4 "1410000 0 0 1410000 0 0

5 0 "5+400 ",0500 0 5+400 ",0500

+ 0 ,0500 5-,50 0 ",0500 11,500

:::; %AAM S$M$ O"A

Batang = 2


EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803

D? = !&s theta = 0.-

DG = sin theta = 0.+

L&!al a?is 1 2 3 4 5 +

1 ,05000 0 0 ",05000 0 0

2 0 ,050 1,+25 0 ",050 1,+25

3 0 1,+25 5-,50 0 "1,+25 23,5

4 ",05000 0 0 ,05000 0 0

Hitung matriks kekakuan batang 1


81/345

5 0 ",050 "1,+25 0 ,050 "1,+25

+ 0 1,+25 23,5 0 "1,+25 5-,50

:::; %AAM S$M$ O"A

Batang = 3



1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804

D? = !&s theta = 1DG = sin theta = 0

L&!al a?is 1 2 3 4 5 +

1 1410000 0 0 "1410000 0 0

2 0 5+400 ,0500 0 "5+400 ,0500

3 0 ,0500 11,500 0 ",0500 5-,50

4 "1410000 0 0 1410000 0 0

5 0 "5+400 ",0500 0 5+400 ",0500

+ 0 ,0500 5-,50 0 ",0500 11,500


82/345

, "453,3- 105,5 1-+3,3- 105,5 0 0

"105,5 23,5 105,5 1,+250 0 0

1 "1410000 0 0 0 1410000 0

2 0 ,0500 0 0 0 5+400

3 0 5-,50 0 0 0 ,0500

5 33501+ "5+400 "33501+ 14100 0 "5+400

- "33501+ "14100 33501+ 5+400 0 0

10 0 0 "1410000 0 0 0

11 0 0 0 ",0500 0 0

12 0 0 0 5-,50 0 0

0 0 0 0 0 0

0 0 0 0 0 00 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

Hitung Matriks eban 5oint7 No'a&

No'a& or/es

a. Akibat beban 'i sepan*ang bentang (ke'ua u*ung 'ikekang)

#&ement 1 rans&rmasi sb l&k

L&!al a?is

0 1

30 2

= 12.5 3

0 4

30 5

"12.5 +

()( =

A)L1

A)(1

A)(1


83/345


L&!al a?is

22.5 1

25.3125 2

= 35.15+25 3

3,.5 4

54.+-,5 5

"5-.53,5 +


L&!al a?is

0 1

+0 2

= 25 3

0 4

+0 5

"25 +

A)L2

A)(2

A)(2

A%L3

A%(3

A%(3


84/345

Susun matriks beban eki>a&en

&int (b 7l&bal Element 1 Element 2

1 1 0 0

1 2 30 01 3 12.5 0

2 4 0 2.-125

"Ae = 2 5 30 8 33.,5 8

2 + "12.5 35.15+25

3 , 0 "2.-125

3 - 0 ++.25

3 0 "5-.53,5

4 10 0 0

4 11 0 0

4 12 0 0

5 13 0 0

5 14 0 0

5 15 0 0

+ 1+ 0 0

+ 1, 0 0+ 1- 0 0

b. Akibat eban 'i *oint (ke'ua u*ung 'ikekang)

&int (b 7l&bal $C

1 1 0 1

1 2 0 2

1 3 0 3

2 4 0 d1

A = 2 5 0 5


85/345

2 + 0 d2

3 , 0 d3

3 - 0 -

3 0 d4

4 10 0 10

4 11 0 11

4 12 0 12

5 13 N/A N/A

5 14 N/A N/A

5 15 N/A N/A

+ 1+ N/A N/A

+ 1, N/A N/A

+ 1- N/A N/A

/. eban kombinasi atau gabungan (Ae + A*)

&int (b 7l&bal $C

1 1 1 0 0

1 2 2 "30 0

1 3 3 "12.5 0

2 4 d1 "2.-125 0

A! = 2 5 5 "+3.,5 8 0

2 + d2 "22.+5+25 0

3 , d3 2.-125 0

3 - - "12+.25 0

3 d4 33.53,5 0

4 10 10 0 04 11 11 "+0 0

4 12 12 25 0

5 13 N/A 0 N/A

5 14 N/A 0 N/A

5 15 N/A 0 N/A

+ 1+ N/A 0 N/A

+ 1, N/A 0 N/A

+ 1- N/A 0 N/A

$isla!ement / $e&rmasi (trktr


86/345

d1 = ".,1,+0,1+E"00,

d2 = "0.0001+43+

d3 = .,1,+0,1+5E"00,

d4 = 0.00021,-52

=

=

=

=

=

=

=

=

=

ea!ti&ns:

7AHA"7AHA $ALA)


87/345

0 1410000 0 0 "1410000

30 0 5+400 ,0500 0

12.5 8 0 ,0500 11,500 0

0 "1410000 0 0 1410000

30 0 "5+400 ",0500 0

"12.5 0 ,0500 5-,50 0

atang 2

$e&rmasi strktr dalam arah (


88/345

10 10 0

11 11 0

12 12 0

7aGa ng batang

0 1410000 0 0 "1410000

+0 0 5+400 ,0500 0

25 8 0 ,0500 11,500 0

0 "1410000 0 0 1410000

+0 0 "5+400 ",0500 0

"25 0 ,0500 5-,50 0

S##SA!

AM ! 0 AML ! M ! 4 M !

A%3 =


89/345


90/345

Defined DOF

after boundary conditions


91/345

Batang 2 :

b = 0.30 m

h = 0.50 m

0.15 m2E = 2.35E80, kN/m2

3.13E"03m4

5 m

DG

0

0.+

0

0

mbu Struktur

A2 =

I2 =

L2 =


92/345


93/345

H S$M$ O"A)


94/345

+

d3 6=== DOF s#s+ai sb global

+ 6=== DOF s#s+ai sb global

6=== DOF s#s+ai sb global

),aian sb global :

),aian sb 4 = 1.7x 8 2.79

),aian sb = 1.79 8 2.7x

),aian sb ; = 4.7x 8 .79

),aian sb < = 4.79 8 .7x

1 0 0 0 0 0

0 1 0 0 0 0

= 0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 0


95/345

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

0.- 0.+ 0 0 0 0

"0.+ 0.- 0 0 0 0

= 0 0 1 0 0 0

0 0 0 0.- 0.+ 0

0 0 0 "0.+ 0.- 00 0 0 0 0 1

0.- "0.+ 0 0 0 0

0.+ 0.- 0 0 0 0

0 0 1 0 0 0

0 0 0 0.- "0.+ 0

0 0 0 0.+ 0.- 0

0 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 0

= 0 0 1 0 0 00 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

=

=

=


96/345

1 2 3 d1 5 d2

7l&bal a?is 1 2 3 4 5 +

1 1410000 0 0 "1410000 0 0 "

2 0 5+400 ,0500 0 "5+400 ,0500 "

3 0 ,0500 11,500 0 ",0500 5-,50 "

4 "1410000 0 0 1410000 0 0 "

5 0 "5+400 ",0500 0 5+400 ",0500 "

+ 0 ,0500 5-,50 0 ",0500 11,500 "

d1 5 d2 d3 - d4

7l&bal a?is 4 5 + , -

4 453,3- 33501+ "105,5 "453,3- "33501+ "105,5 "

5 33501+ 25-312 14100 "33501+ "25-312 14100 "

+ "105,5 14100 5-,50 105,5 "14100 23,5 "

, "453,3- "33501+ 105,5 453,3- 33501+ 105,5 "

()(1

=

()(2

=


97/345

- "33501+ "25-312 "14100 33501+ 25-312 "14100 "

"105,5 14100 23,5 105,5 "14100 5-,50 "

d3 - d4 10 11 12

7l&bal a?is , - 10 11 12

, 1410000 0 0 "1410000 0 0 "

- 0 5+400 ,0500 0 "5+400 ,0500 "

0 ,0500 11,500 0 ",0500 5-,50 "

10 "1410000 0 0 1410000 0 0 "

11 0 "5+400 ",0500 0 5+400 ",0500 "

12 0 ,0500 5-,50 0 ",0500 11,500 "

d3 - d4 10 11 12

, - 10 11 12

3 5 - 10 11 12 0 0 0 0 0

3 5 - 10 11 12

0 33501+ "33501+ 0 0 0 0 0 0 0 0

5-,50 "5+400 "14100 0 0 0 0 0 0 0 0

%(3

=


98/345


99/345

al ke gl&bal ==#

0.- "0.+ 0 0 0 0 22.5

0.+ 0.- 0 0 0 0 25.3125

= 0 0 1 0 0 0 ? 35.15+25

0 0 0 0.- "0.+ 0 3,.5

0 0 0 0.+ 0.- 0 54.+-,5

0 0 0 0 0 1 "5-.53,5

7l&bal a?is !ek

4 2.-125 "

5 33.,5 "

= + 35.15+25 "

, "2.-125 "

- ++.25 "

"5-.53,5 "

al ke gl&bal ==#

1 0 0 0 0 0 0

0 1 0 0 0 0 +0

= 0 0 1 0 0 0 ? 25

0 0 0 1 0 0 0

0 0 0 0 1 0 +0

0 0 0 0 0 1 "25

7l&bal a?is !ek

, 0 "

- +0 "

= 25 "

10 0 "

11 +0 "

AMS 2 = RT . AM

L 2

AMS 3 = RT . AM

L 3


100/345

12 "25 "

/l#nt 3 /l#nt 4 /l#nt

0 0 0 0 0 1

0 0 0 30 "30 20 0 0 12.5 "12.5 3

0 0 0 2.-125 "2.-125 4

0 8 0 8 0 = +3.,5 Ae = "+3.,5 5

0 0 0 22.+5+25 "22.+5+25 +

0 0 0 "2.-125 2.-125 ,

+0 0 0 12+.25 "12+.25 -

25 0 0 "33.53,5 33.53,5

0 0 0 0 0 10

+0 0 0 +0 "+0 11

"25 0 0 "25 25 12

0 0 0 0 0 13

0 0 0 0 0 14

0 0 0 0 0 15

0 0 0 0 0 1+

0 0 0 0 0 1,0 0 0 0 0 1-


101/345

ata lang A! :

0 d1 "2.-125 "

"30 d2 "22.+5+25 "

"12.5 d3 2.-125 "

"2.-125 d4 33.53,5 "

= "+3.,5 A! = 1 0 "

"22.+5+25 2 "30 "

2.-125 3 "12.5 "

"12+.25 5 "+3.,5 "

33.53,5 - "12+.25 "

0 10 0 ""+0 11 "+0 "

25 12 25 "

N/A 0 N/A

N/A 0 N/A

N/A 0 N/A

N/A 0 N/A

N/A 0 N/A

N/A 0 N/A


102/345

7#k: O-

"

"

"

"

$e&rmasi strktr dalam arah (AL di batang 16 sbb :

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 ? 0 = 0

0 0 0 1 0 0 ".,1-E"00, ".,1-E"00,

0 0 0 0 1 0 0 0

0 0 0 0 0 1 "0.0001+4 "0.0001+4

sb l&kal

M 1 0 ' 4 #M 1

∆M 1 =


103/345

0 0 0 0 1.3,02324+1 1.3,02324+1 1

"5+400 ,0500 0 30 "11.+3204+1 1-.3+,530 2

",0500 5-,50 ? 0 = 12.5 8 ".+33,2425 = 2.-0++2,5,52 3

0 0 ".,1-E"00, 0 "1.3,02324+1 "1.3,02324+1 4

5+400 ",0500 0 30 11.+3204+1 41.+3204+1 5

",0500 11,500 "0.0001+4 "12.5 "1.3-+,44-5 "31.--+,44-5 +

$e&rmasi strktr dalam arah (AL di batang 26 sbb :

0.- 0.+ 0 0 0 0 ".,1-E"00, ",.,,4E"00,

"0.+ 0.- 0 0 0 0 0 5.-31E"00,

0 0 1 0 0 0 ? "0.0001+4 = "0.0001+4

0 0 0 0.- 0.+ 0 .,1-E"00, ,.,,4E"00,

0 0 0 "0.+ 0.- 0 0 "5.-31E"00,

0 0 0 0 0 1 0.00021, 0.00021,

sb l&kal

0 0 ",.,,4E"00, 22.5 "1.0+1-5+ 21.403-14031 1

",050 1,+25 5.-31E"00, 25.3125 0.421,3 2+.254+,4 2

"1,+25 23,5 ? "0.0001+4 = 35.15+25 8 "3.2+50515 = 31.--+,44-5 3

0 0 ,.,,4E"00, 3,.5 1.0+1-5+-- 3-.5+1-5+ 4

,050 "1,+25 "5.-31E"00, 54.+-,5 "0.421,4 53.,453020+ 5

"1,+25 5-,50 0.00021, "5-.53,5 ,.-044-4, "50.+1325515 +

D#o,&asi st,+kt+, dala& a,a )%B) LO-AL di batang 35 sbb :

1 0 0 0 0 0 .,1-E"00, .,1-E"00,

0 1 0 0 0 0 0 0

0 0 1 0 0 0 ? 0.00021, = 0.00021,

M 2 0 ' 4 #M 2

∆M 2 =

M ! 0 ' 4 #M !

∆M 3 =


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0 0 0 1 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 1 0 0

sb l&kal

0 0 .,1-E"00, 0 1.3,02324+1 1.3,02324+1 1

"5+400 ,0500 0 +0 15.3+,530 ,5.3+,530 2

",0500 5-,50 ? 0.00021, = 25 8 25.+1325515 = 50.+1325515 3

0 0 0 0 "1.3,02324+1 "1.3,02324+1 4

5+400 ",0500 0 +0 "15.3+,530 44.+3204+1 5

",0500 11,500 0 "25 12.-0++2,5,5 "12.133,2425 +


105/345


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111/345


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" " "

" " "

" " "

" " "

" " "

" " "

" " "

" " "

" " "

" " "


113/345

" " "

" " "

" " "

" " "

" " "

" " "

" " "

" " "

0 === $itata

0 4 d1

0 + d2


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0 , d3

0 d4

0 1 1

0 2 2

0 3 3

0 5 5

0 - -

0 10 10

0 11 11

0 12 12

0 0 0

0 0 00 0 0

0 0 0

0 0 0

0 0 0


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1

23

d1

5

d2

d3

-

d4

10

11

12

N/A

N/A

N/A

N/A

N/AN/A


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"

"

"

"


118/345

sb l&kal DOF

1 1

2 2

3 3

4 d1

5 d2

+ d3

$C / sb gl&bal


119/345

1

2

3

d1

d2

d3

sb l&kal DOF

1 .D?DG8d2D?DG

2 .D?DG8d2D?DG

3 d3

4 4

5 5

+ +

$C / sb gl&bal

.D?DG8d2D?DG

.D?DG8d2D?DG

d3

4

5

+

sb l&kal DOF

1 d1

2 d2

3 d3


120/345

4 ,

5 -

+

$C / sb gl&bal

d1

d2

d3

,

-


121/345


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125/345


126/345


127/345


128/345

%

" " 1 0 0 0 0 0 1410000 0

" " 0 1 0 0 0 0 0 5+400

" " 0 0 1 0 0 0 0 ,0500

" " 0 0 0 1 0 0 "1410000 0

" " 0 0 0 0 1 0 0 "5+400

" " 0 0 0 0 0 1 0 ,0500

" " %

" " 0.- "0.+ 0 0 0 0 ,05000 0

" " 0.+ 0.- 0 0 0 0 0 ,050

" " 0 0 1 0 0 0 0 1,+25


129/345


130/345

@ @ @ @

@ @ @ @


131/345


132/345


133/345


134/345

Dek


135/345

"

"

"

"

"

"

Dek

"

"

"

"

"

"


136/345

Dek

"

"

"

"

"

"


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144/345

?

0 "1410000 0 0 1 0 0 0 0 0

,0500 0 "5+400 ,0500 0 1 0 0 0 0

11,500 0 ",0500 5-,50 0 0 1 0 0 0 =

0 1410000 0 0 0 0 0 1 0 0

",0500 0 5+400 ",0500 0 0 0 0 1 0

5-,50 0 ",0500 11,500 0 0 0 0 0 1

?

0 ",05000 0 0 1 1 0 0 0 0

1,+25 0 ",050 1,+25 "1 1 0 0 0 0

5-,50 0 "1,+25 23,5 0 0 1 0 0 0 =


145/345

0 ,05000 0 0 0 0 0 1 1 0

"1,+25 0 ,050 "1,+25 0 0 0 "1 1 0

23,5 0 "1,+25 5-,50 0 0 0 0 0 1

?

0 "1410000 0 0 1 0 0 0 0 0

,0500 0 "5+400 ,0500 0 1 0 0 0 0

11,500 0 ",0500 5-,50 0 0 1 0 0 0 =

0 1410000 0 0 0 0 0 1 0 0

",0500 0 5+400 ",0500 0 0 0 0 1 0

5-,50 0 ",0500 11,500 0 0 0 0 0 1


146/345


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1410000 0 0 "1410000 0 0 1 0 0 0 0

0 5+400 ,0500 0 "5+400 ,0500 0 1 0 0 0

0 ,0500 11,500 0 ",0500 5-,50 0 0 1 0 0

"1410000 0 0 1410000 0 0 0 0 0 1 0

0 "5+400 ",0500 0 5+400 ",0500 0 0 0 0 1

0 ,0500 5-,50 0 ",0500 11,500 0 0 0 0 0

5+4000 "4230 "105,5 "5+4000 4230 "105,5 0.- 0.+ 0 0 0

423000 5+40 14100 "423000 "5+40 14100 "0.+ 0.- 0 0 0

0 1,+25 5-,50 0 "1,+25 23,5 0 0 1 0 0


161/345

"5+4000 4230 105,5 5+4000 "4230 105,5 0 0 0 0.- 0.+

"423000 "5+40 "14100 423000 5+40 "14100 0 0 0 "0.+ 0.-

0 1,+25 23,5 0 "1,+25 5-,50 0 0 0 0 0

1410000 0 0 "1410000 0 0 1 0 0 0 0

0 5+400 ,0500 0 "5+400 ,0500 0 1 0 0 0

0 ,0500 11,500 0 ",0500 5-,50 0 0 1 0 0

"1410000 0 0 1410000 0 0 0 0 0 1 0

0 "5+400 ",0500 0 5+400 ",0500 0 0 0 0 1

0 ,0500 5-,50 0 ",0500 11,500 0 0 0 0 0


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176/345

DE>

0 1410000 0 0 "1410000 0 0 " " "

0 0 5+400 ,0500 0 "5+400 ,0500 " " "

0 = 0 ,0500 11,500 0 ",0500 5-,50 " " "

0 "1410000 0 0 1410000 0 0 " " "

0 0 "5+400 ",0500 0 5+400 ",0500 " " "

1 0 ,0500 5-,50 0 ",0500 11,500 " " "

DE>

0 453,3- 33501+ "105,5 "453,3- "33501+ "105,5 " " "

0 33501+ 25-312 14100 "33501+ "25-312 14100 " " "

0 = "105,5 14100 5-,50 105,5 "14100 23,5 " " "


177/345

0 "453,3- "33501+ 105,5 453,3- 33501+ 105,5 " " "

0 "33501+ "25-312 "14100 33501+ 25-312 "14100 " " "

1 "105,5 14100 23,5 105,5 "14100 5-,50 " " "

DE>

0 1410000 0 0 "1410000 0 0 " " "

0 0 5+400 ,0500 0 "5+400 ,0500 " " "

0 = 0 ,0500 11,500 0 ",0500 5-,50 " " "

0 "1410000 0 0 1410000 0 0 " " "

0 0 "5+400 ",0500 0 5+400 ",0500 " " "

1 0 ,0500 5-,50 0 ",0500 11,500 " " "


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192/345

" " "

" " "

" " "

" " "

" " "

" " "

" " "

" " "

" " "


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201/345

M#"AN!"A #"A,ASA -

%ata beban

= 100 kN

;1 = 24 kN/m

;2 = 4- kN/m

versi lengkap


202/345

ST#P 1 %is/reti0e an' &oba& %egrees o ree'om (%O)

Defined DOF

after boundary

1

2

12


203/345

P#N,##SA!AN

Properties penampang

Bahan / material :

E = 2.35E80, kN/m2

Batang 1 : Batang 2 :

b = 0.30 m b =

h = 0.50 m h =

0.15 m2E = 2.35E80, kN/m2 E =

3.13E"03m4

2.5m

Batang 3 :

b = 0.30 m

h = 0.50 m

0.15 m2

E = 2.35E80, kN/m2

3.13E"03m4

2.5m

ekap #&emen 'a&am Matriks "ekakuan atang

Batang EA ? L 4.EI ? L 2.EI ? L 6.EI ? L@2 12.EI ? L@3 S&* &",! D? DG

1 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 1-0 "1 1.22515E"01+

2 ,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803 21+.-+-,+5 "0.- "0.+

3 1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804 1-0 "1 1.22515E"01+

4 $I@/0F $I@/0F $I@/0F $I@/0F $I@/0F 1 0

5 ECF ECF ECF ECF ECF 1 0

%O sesuai sumbu g&oba& struktur 'an tentukan eban atau Momen pa'a Titik 5oint Struktur 'a&am Ara6 Sumbu &oba&7Sumbu Struktur

A1 = A2 =

I1 = I

2 =

L1 = L

2 =

A3 =

I3 =

L3 =

3


204/345


205/345


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208/345

:::; %AAM S$M$ O"A

Batang = 1



1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804

D? = !&s theta = "1DG = sin theta = 1.22515E"01+

L&!al a?is 1 2 3 4 5 +

1 1410000 0 0 "1410000 0 0

2 0 5+400 ,0500 0 "5+400 ,0500

3 0 ,0500 11,500 0 ",0500 5-,50

4 "1410000 0 0 1410000 0 0

5 0 "5+400 ",0500 0 5+400 ",0500

+ 0 ,0500 5-,50 0 ",0500 11,500

:::; %AAM S$M$ O"A

Batang = 2

/l#n dala& &at,iks k#kak+an batang :EA / L 4.EI / L 2.EI / L +.EI / L*2 12.EI / L*3

,.05E805 5.--E804 2.4E804 1.,+E804 ,.05E803

D? = !&s theta = "0.-

DG = sin theta = "0.+

L&!al a?is 1 2 3 4 5 +

1 ,05000 0 0 ",05000 0 0

2 0 ,050 1,+25 0 ",050 1,+25

3 0 1,+25 5-,50 0 "1,+25 23,5

Hitung matriks kekakuan batang 1


209/345

4 ",05000 0 0 ,05000 0 0

5 0 ",050 "1,+25 0 ,050 "1,+25

+ 0 1,+25 23,5 0 "1,+25 5-,50

:::; %AAM S$M$ O"A

Batang = 3



1.41E80+ 1.1-E805 5.--E804 ,.05E804 5.+4E804

D? = !&s theta = "1

DG = sin theta = 1.22515E"01+

L&!al a?is 1 2 3 4 5 +

1 1410000 0 0 "1410000 0 0

2 0 5+400 ,0500 0 "5+400 ,0500

3 0 ,0500 11,500 0 ",0500 5-,50

4 "1410000 0 0 1410000 0 0

5 0 "5+400 ",0500 0 5+400 ",0500

+ 0 ,0500 5-,50 0 ",0500 11,500


210/345

+ 105,5 1,+250 "105,5 23,5 "-.+3,3E"012 ",0500 5-,50 5+400

, "453,3- "105,5 1-+3,3- "105,5 0 0 0 "33501+

105,5 23,5 "105,5 1,+250 0 0 0 "14100

1 "1410000 "-.+3,3E"012 0 0 1410000 "1.+5-3+05E"010 "-.+3,3E"012 1.+5-E"010

2 1.+5-3+E"010 ",0500 0 0 "1.+5-4E"010 5+400 ",0500 "5+400

3 -.+3,30E"012 5-,50 0 0 "-.+3,3E"012 ",0500 11,500 ,0500

5 33501+ 5+400 "33501+ "14100 1.+5-3+E"010 "5+400 ,0500 314,12

- "33501+ 14100 33501+ "5+400 0 0 0 "25-312

10 0 0 "1410000 -.+3,2++0,1E"012 0 0 0 0

11 0 0 1.+5-3+E"010 ,0500 0 0 0 0

12 0 0 "-.+3,3E"012 5-,50 0 0 0 0

0 0 0 0 0 0 0 00 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

Hitung Matriks eban 5oint7 No'a&

No'a& or/es

a. Akibat beban 'i sepan*ang bentang (ke'ua u*ung 'ikekang)

#&ement 1 rans&rmasi sb l&kal ke gl&bal ==#

L&!al a?is

0 1 "1

"+0 2 1.225E"01+

= "25 3 = 0

0 4 0

"+0 5 0

25 + 0

7l&bal a?is

1

2

= 3

4

5

()( =

A)L1

A)(1

A)(1


211/345

+


L&!al a?is

"3,.5 1 "0.-

"54.+-,5 2 "0.+

= "5-.53,5 3 = 0

"22.5 4 0

"25.3125 5 0

35.15+25 + 0

7l&bal a?is

4

5

= +

,

-


L&!al a?is

0 1 "1"30 2 1.225E"01+

= "12.5 3 = 0

0 4 0

"30 5 0

12.5 + 0

7l&bal a?is

,

-

=

10

A)L2

A)(2

A)(2

A%L3

A%(3

A%(3


212/345


213/345

A = 2 5 0 5

2 + 0 d2

3 , 0 d3

3 - 0 -

3 0 d4

4 10 0 10

4 11 0 11

4 12 0 12

5 13 N/A N/A

5 14 N/A N/A

5 15 N/A N/A

+ 1+ N/A N/A

+ 1, N/A N/A

+ 1- N/A N/A

/. eban kombinasi atau gabungan (Ae + A*)

&int (b 7l&bal $C

1 1 1 ",.350-0,2E"015 0 ",.351E"015

1 2 2 "+0 0 "+0

1 3 3 25 0 25

2 4 d1 2.-125 0 2.-125

A! = 2 5 5 "12+.25 8 0 = "12+.25

2 + d2 33.53,5 0 33.53,5

3 , d3 "2.-125 0 "2.-125

3 - - "+3.,5 0 "+3.,5

3 d4 "22.+5+25 0 "22.+5+254 10 10 "3.+,54453+5E"015 0 "3.+,5E"015

4 11 11 "30 0 "30

4 12 12 "12.5 0 "12.5

5 13 N/A 0 N/A N/A

5 14 N/A 0 N/A N/A

5 15 N/A 0 N/A N/A

+ 1+ N/A 0 N/A N/A

+ 1, N/A 0 N/A N/A

+ 1- N/A 0 N/A N/A


214/345

$isla!ement / $e&rmasi (trktr

d1 = .,1,+0,1+5E"00,

d2 = 0.00021,-52

d3 = ".,1,+0,1+E"00,

d4 = "0.0001+43+

=

=

=

=

=

=

=

=

=

ea!ti&ns:

7AHA"7AHA $ALA)


215/345

0 1410000 0 0 "1410000 0 0

"+0 0 5+400 ,0500 0 "5+400 ,0500

"25 8 0 ,0500 11,500 0 ",0500 5-,50

0 "1410000 0 0 1410000 0 0

"+0 0 "5+400 ",0500 0 5+400 ",0500

25 0 ,0500 5-,50 0 ",0500 11,500

atang 2 $e&rmasi strktr dalam ar

$e&rmasi strktr dalam arah (


216/345

d4 "0.0001+44 0

10 10 0 0

11 11 0 0

12 12 0 0

7aGa ng batang

0 1410000 0 0 "1410000 0 0

"30 0 5+400 ,0500 0 "5+400 ,0500

"12.5 8 0 ,0500 11,500 0 ",0500 5-,50

0 "1410000 0 0 1410000 0 0

"30 0 "5+400 ",0500 0 5+400 ",0500

12.5 0 ,0500 5-,50 0 ",0500 11,500

S##SA!

D%(3 = ∆M 3 =

AM ! 0 AML ! M ! 4 M !

A%3 =


217/345


218/345

3

3

4

3

1 2

3 4

1

2

4

;

<

12

1

11

C#,indaan titik st,+kt+, dislac#nt titik"

J

H

gl&bal a?is

2

;

<

4

02

;

<

12

03


219/345

0.30 m

0.50 m

0.15 m22.35E80,kN/m2

3.13E"03m4

5 m

1

4

01

C#,indaan titik tia ,##bod9

12

3

4

d1

d2

d4 d3

DOF = 4 b+a


220/345


221/345

a/L = 3,.5

54.+-,5

"5-.53,5

b/L = 22.5

25.3125

35.15+25

a2%a83b'/L3 =

"a2b/L2 =

b2%3a8b'/L3 =

ab2/L2 =


222/345

s#s+ai sb global

s#s+ai sb global

s#s+ai sb global

lobal :

= 1.7x 8 2.79

= 1.79 8 2.7x

= 4.7x 8 .79

= 4.79 8 .7x

"1 1.225E"01+ 0 0 0 0

"1.2251E"01+ "1 0 0 0 0

0 0 1 0 0 0

0 0 0 "1 1.225E"01+ 0

0 0 0 "1.22514-455E"01+ "1 0

0 0 0 0 0 1

"1 "1.225E"01+ 0 0 0 0


223/345

1.22515E"01+ "1 0 0 0 0

0 0 1 0 0 0

0 0 0 "1 "1.225E"01+ 0

0 0 0 1.22514-454E"01+ "1 0

0 0 0 0 0 1

"0.- "0.+ 0 0 0 0

0.+ "0.- 0 0 0 0

0 0 1 0 0 0

0 0 0 "0.- "0.+ 00 0 0 0.+ "0.- 0

0 0 0 0 0 1

"0.- 0.+ 0 0 0 0

"0.+ "0.- 0 0 0 0

0 0 1 0 0 0

0 0 0 "0.- 0.+ 0

0 0 0 "0.+ "0.- 0

0 0 0 0 0 1

"1 1.225E"01+ 0 0 0 0

"1.2251E"01+ "1 0 0 0 0

0 0 1 0 0 0

0 0 0 "1 1.225E"01+ 0

0 0 0 "1.22514-455E"01+ "1 0

0 0 0 0 0 1

"1 "1.225E"01+ 0 0 0 0

1.22515E"01+ "1 0 0 0 0

0 0 1 0 0 0

0 0 0 "1 "1.225E"01+ 0

0 0 0 1.22514-454E"01+ "1 0


224/345


225/345

, "453,3- "33501+ "105,5 453,3- 33501+ "105,5 " "

- "33501+ "25-312 14100 33501+ 25-312 14100 " "

105,5 "14100 23,5 "105,5 14100 5-,50 216150.00 %2-6200.00'

d3 - d4 10 11 12

7l&bal a?is , - 10 11 12

, 1410000 "1.+5-4E"010 "-.+3,2++0,E"012 "1410000 1.+5-3+E"010 "-.+3,E"012 " %0.00'

- "1.+5-E"010 5+400 ",0500 1.+5-E"010 "5+400 ",0500 %0.00' "

"-.+3,E"012 ",0500 11,500 -.+3,E"012 ,0500 5-,50 %0.00'

10 "1410000 1.+5-4E"010 -.+3,2++0,1E"012 1410000 "1.+5-4E"010 -.+3,E"012 " 0.00

11 1.+5-E"010 "5+400 ,0500 "1.+5-E"010 5+400 ,0500 0.00 "

12 "-.+3,E"012 ",0500 5-,50 -.+3,E"012 ,0500 11,500 %0.00'

d4 10 11 12

10 11 12

- 10 11 12 0 0 0 0 0 0

- 10 11 12

"33501+ 0 0 0 0 0 0 0 0 0


226/345

14100 0 0 0 0 0 0 0 0 0

33501+ "1410000 1.+5-4E"010 "-.+3,2++0,E"012 0 0 0 0 0 0

"5+400 -.+3,E"012 ,0500 5-,50 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

"25-312 0 0 0 0 0 0 0 0 0

314,12 1.+5-E"010 "5+400 ",0500 0 0 0 0 0 0

1.+5-3+E"010 1410000 "1.+5-4E"010 -.+3,2++0,1E"012 0 0 0 0 0 0

"5+400 "1.+5-E"010 5+400 ,0500 0 0 0 0 0 0

",0500 -.+3,E"012 ,0500 11,500 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

"1.2251E"01+ 0 0 0 0 0

"1 0 0 0 0 "+0

0 1 0 0 0 ? "25

0 0 "1 "1.22514-455E"01+ 0 0

0 0 1.2251E"01+ "1 0 "+0

0 0 0 0 1 25

,.350-E"015

+0

"25

,.350-E"015

+0

AMS 1 = RT . AM

L 1


227/345


228/345

30

12.5

/l#nt 4 /l#nt

0 0 ,.351E"015 ",.350-0,2E"015 1 10 0 +0 "+0 2 2

0 0 "25 25 3 3

0 0 "2.-125 2.-125 4 d1

0 8 0 = 12+.25 Ae = "12+.25 5 5

0 0 "33.53,5 33.53,5 + d2

0 0 2.-125 "2.-125 , d3

0 0 +3.,5 "+3.,5 - -

0 0 22.+5+25 "22.+5+25 d4

0 0 3.+,5E"015 "3.+,54453+5E"015 10 10

0 0 30 "30 11 11

0 0 12.5 "12.5 12 12

0 0 0 0 13 N/A

0 0 0 0 14 N/A

0 0 0 0 15 N/A

0 0 0 0 1+ N/A0 0 0 0 1, N/A

0 0 0 0 1- N/A


229/345

ata lang A! :

d1 2.-125 "2.-125

d2 33.53,5 "22.+5+25

d3 "2.-125 2.-125

d4 "22.+5+25 33.53,5

A! = 1 ",.350E"015 0

2 "+0 "30

3 25 "12.5

5 "12+.25 "+3.,5

- "+3.,5 "12+.2510 "3.+,54E"015 0

11 "30 "+0

12 "12.5 25

0 N/A

0 N/A

0 N/A

0 N/A

0 N/A

0 N/A


230/345

7#k: O-

".,1,+0,1+E"00, "+.352,4,104E"021

"0.0001+43+ 0.0003-2,-,

.,1,+0,1+5E"00, "1.4352143E"00+

0.00021,-52 "0.0003-2,-,

ah (AL di batang 16 sbb :

sb l&kal

1.22515E"01+ 0 0 0 0 0 0 1

"1 0 0 0 0 0 0 2

0 1 0 0 0 ? 0 = 0 3

0 0 "1 1.22514-454E"01+ 0 .,1-E"00, ".,1-E"00, 4

0 0 "1.2251E"01+ "1 0 0 "1.11E"022 5

0 0 0 0 1 0.00021, 0.00021, +


231/345

sb l&kal $C / sb gl&

0 0 1.3,02324+1 1.3,02324+1 1 1

0 "+0 15.3+,530 "44.+3204+0- 2 2

? 0 = "25 8 12.-0++2,5,5 = "12.133,2424- 3 3

".,1-E"00, 0 "1.3,02324+1 "1.3,02324+1 4 d1

"1.11E"022 "+0 "15.3+,530 ",5.3+,53002 5 d2

0.00021, 25 25.+1325515 50.+132551503 + d3

ah (AL di batang 26 sbb :

sb l&kal"0.+ 0 0 0 0 .,1-E"00, ",.,,4E"00, 1

"0.- 0 0 0 0 0 5.-31E"00, 2

0 1 0 0 0 ? 0.00021, = 0.00021, 3

0 0 "0.- "0.+ 0 ".,1-E"00, ,.,,4E"00, 4

0 0 0.+ "0.- 0 0 "5.-31E"00, 5

0 0 0 0 1 "0.0001+4 "0.0001+4 +


",.,,4E"00, "3,.5 "1.0+1-5+ "3-.5+1-5+-- 1 .D?DG8d2D?

5.-31E"00, "54.+-,5 0.421,3 "53.,453020+01 2 .D?DG8d2D?

? 0.00021, = "5-.53,5 8 ,.-044-4, = "50.+132551503 3 d3

,.,,4E"00, "22.5 1.0+1-5+-- "21.403-140312 4 .D?DG8d2D?

"5.-31E"00, "25.3125 "0.421,4 "2+.254+,3 5 .D?DG8d2D?

"0.0001+4 35.15+25 "3.2+50515 31.--+,44-4, + +

a,a )%B) LO-AL di batang 35 sbb :

sb l&kal

1.22515E"01+ 0 0 0 0 ".,1-E"00, .,1-E"00, 1

"1 0 0 0 0 0 1.11E"022 2


232/345

0 1 0 0 0 ? "0.0001+4 = "0.0001+4 3

0 0 "1 1.22514-454E"01+ 0 0 0 4

0 0 "1.2251E"01+ "1 0 0 0 5

0 0 0 0 1 0 0 +


.,1-E"00, 0 1.3,02324+1 1.3,02324+1 1 d1

1.11E"022 "30 "11.+3204+1 "41.+3204+0- 2 d2

? "0.0001+4 = "12.5 8 "1.3-+,44-5 = "31.--+,44-4, 3 d3

0 0 "1.3,02324+1 "1.3,02324+1 4 ,

0 "30 11.+3204+1 "1-.3+,53002 5 -

0 12.5 ".+33,2425 2.-0++2,5,52 +


233/345


234/345

1

1


235/345


236/345


237/345


238/345


239/345


240/345

%0.00' "

0.00

" 0.00

0.00 "

1416000.00 %0.00'

" 0.00

216150.00 "

%2-6200.00' "

" %216150.00'


241/345

%216150.00' "

2-6200.00 "

" %216150.00'

%0.00' "

0.00

" 0.00

0.00 "

1416000.00 %0.00'

" 0.00

=== $itata

4 d1


242/345

+ d2

, d3

d4

1 1

2 2

3 3

5 5

- -

10 10

11 11

12 12

0 00 0

0 0

0 0

0 0

0 0


243/345


244/345


245/345


246/345

DOF1

2

3

d1

d2

d3


247/345

al

"1.3,02324+

44.+3204+

"12.133,24

1.3,02324+

,5.3+,531

50.+132552

DOF

.D?DG8d2D?DG

.D?DG8d2D?DG

d3

.D?DG8d2D?DG

.D?DG8d2D?DG

+

al

G 3-.5+1-+

G 53.,453021

"50.+132552

G 21.403-14

G 2+.254+,

31.--+,44-

DOF

d1

d2


248/345


249/345


250/345


251/345


252/345


253/345


254/345


255/345


256/345

%

0.00 %0.00' "1 "1.225E"01+ 0 0 0 0 1410000

" 1.22514-4540E"01+ "1 0 0 0 0 0

1416000.00 " 0 0 1 0 0 0 0

%0.00' 0.00 0 0 0 "1 "1.225E"01+ 0 "1410000

" 1416000.00 0 0 0 1.225E"01+ "1 0 0

1416000.00 " 0 0 0 0 0 1 0

" 216150.00 %

" %2-6200.00' "0.- 0.+ 0 0 0 0 ,05000

2-6200.00 " "0.+ "0.- 0 0 0 0 0


257/345

" %216150.00' 0 0 1 0 0 0 0

" 2-6200.00 0 0 0 "0.- 0.+ 0 ",05000

2-6200.00 " 0 0 0 "0.+ "0.- 0 0

0 0 0 0 0 1 0

0.00 %0.00' %

" "1 "1.225E"01+ 0 0 0 0 1410000

1416000.00 " 1.22514-4540E"01+ "1 0 0 0 0 0

%0.00' 0.00 0 0 1 0 0 0 0

" 1416000.00 0 0 0 "1 "1.225E"01+ 0 "1410000

1416000.00 " 0 0 0 1.225E"01+ "1 0 0

0 0 0 0 0 1 0

7#k:

lang manal

@ 000 @ 000


258/345


259/345


260/345


261/345


262/345


263/345

Dek

%0.00' ?.43@B4B?@1#D1

"

"

0.00 ?.43@B4B?@11#D1

"

"

Dek

"

"

"

"

"

"


264/345

Dek

0.00 .11112312#D1

"

"

%0.00' .11112313#D1

"

"


265/345


266/345


267/345


268/345


269/345


270/345


271/345


272/345

?

0 0 "1410000 0 0 "1 0 0 0 0 0

5+400 ,0500 0 "5+400 ,0500 0 "1 0 0 0 0

,0500 11,500 0 ",0500 5-,50 0 0 1 0 0 0

0 0 1410000 0 0 0 0 0 "1 0 0

"5+400 ",0500 0 5+400 ",0500 0 0 0 0 "1 0

,0500 5-,50 0 ",0500 11,500 0 0 0 0 0 1

?

0 0 ",05000 0 0 "1 "1 0 0 0 0

,050 1,+25 0 ",050 1,+25 1 "1 0 0 0 0


273/345

1,+25 5-,50 0 "1,+25 23,5 0 0 1 0 0 0

0 0 ,05000 0 0 0 0 0 "1 "1 0

",050 "1,+25 0 ,050 "1,+25 0 0 0 1 "1 0

1,+25 23,5 0 "1,+25 5-,50 0 0 0 0 0 1

?

0 0 "1410000 0 0 "1 0 0 0 0 0

5+400 ,0500 0 "5+400 ,0500 0 "1 0 0 0 0

,0500 11,500 0 ",0500 5-,50 0 0 1 0 0 0

0 0 1410000 0 0 0 0 0 "1 0 0

"5+400 ",0500 0 5+400 ",0500 0 0 0 0 "1 0

,0500 5-,50 0 ",0500 11,500 0 0 0 0 0 1


274/345


275/345


276/345


277/345


278/345


279/345


280/345


281/345


282/345


283/345


284/345


285/345


286/345


287/345


288/345

"1410000 "+.10E"012 "-.+3,E"012 1410000 +.10E"012 "-.+3,E"012 "1 1.225E"01+ 0 0

1.,2,E"010 "5+400 ",0500 "1.,2,E"010 5+400 ",0500 "1.225E"01+ "1 0 0

= 0 ,0500 11,500 0 ",0500 5-,50 0 0 1 0

1410000 +.10E"012 -.+3,E"012 "1410000 "+.10E"012 -.+3,E"012 0 0 0 "1

"1.,2,E"010 5+400 ,0500 1.,2,E"010 "5+400 ,0500 0 0 0 "1.225E"01+

0 ,0500 5-,50 0 ",0500 11,500 0 0 0 0

"5+4000 4230 105,5 5+4000 "4230 105,5 "0.- "0.+ 0 0

"423000 "5+40 "14100 423000 5+40 "14100 0.+ "0.- 0 0


289/345

= 0 1,+25 5-,50 0 "1,+25 23,5 0 0 1 0

5+4000 "4230 "105,5 "5+4000 4230 "105,5 0 0 0 "0.-

423000 5+40 14100 "423000 "5+40

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