ujian khusus arifin

7/21/2019 Ujian Khusus Arifin

http://slidepdf.com/reader/full/ujian-khusus-arifin 1/44

5

c d

b 4

3 6

a

1

1.5 28

A= 0.008336 m2

I = 0.000152 m4E= 210000000 kN/m2

Batang EA/L 4EI/L 2EI/L

a 233408 17024 8512 3404.8 907.94666667

b 1110057.0704 80963.8554217 40481.9277108 77010.6424429 97667.270061

c 118923.91304 8673.91304348 4336.95652174 883.890595463 120.09383091

d 118923.91304 8673.91304348 4336.95652174 883.890595463 120.09383091

e 1110057.0704 80963.8554217 40481.9277108 77010.6424429 97667.270061

f 233408 17024 8512 3404.8 907.94666667

Batang a

0 1 0 0 0

1 0 0 0 0

!"#a= 0 0 1 0 0

0 0 0 0 1

0 0 0 1 00 0 0 0 0

233408 0 0 233408 0

0 908 3405 0 908

!k#a= 0 3405 17024 0 3405

233408 0 0 233408 0

0 908 3405 0 908

0 3405 8512 0 3405

6EI/L2 12EI/L3



1 2 3 10 11

907.94666667 0 3404.8 907.94666667 0

0 233408 0 0 233408

!$#a= 3404.8 0 17024 3404.8 0907.94666667 0 3404.8 907.946666667 0

0 233408 0 0 233408

3404.8 0 8512 3404.8 0

Batang b

1 0.3090169944 0 0 0

0.3090169944 1 0 0 0

!"#b= 0 0 1 0 0

0 0 0 1 0.30901699440 0 0 0.3090169944 1

0 0 0 0 0

1110057.0704 0 0 1110057.0704 0

0 97667 77011 0 97667

!k#b= 0 77011 80964 0 77011

1110057.0704 0 0 1110057.07039 0

0 97667 77011 0 97667

0 77011 40482 0 77011

7 8 9 10 11

1013382.4469 297534 23797.597263 1013382.4469 297534

297534 194341.893526 73241 297534 194341.89353

!$#b= 23797.597263 73241 80963.8554217 23797.5972626 73241

1013382.4469 297534 23797.5972626 1013382.44692 297534

297534 194341.89353 73241 297534 194341.89353

23797.597263 73241 40481.9277108 23797.5972626 73241

Batang c

1 0.3090169944 0 0 0

0.3090169944 1 0 0 0

!"#c= 0 0 1 0 0

0 0 0 1 0.3090169944

0 0 0 0.3090169944 1

0 0 0 0 0

!$#=!"# "!k#!"#

!$#=!"# "!k#!"#



118923.91304 0 0 118923.91304 0

0 120 884 0 120

!k#c= 0 884 8674 0 884

118923.91304 0 0 118923.913043 0

0 120 884 0 120

0 884 4337 0 884

10 11 12 13 14

107579.15781 34916 273.13721517 107579.15781 34916

34916 11464.8490674 841 34916 11464.849067

!$#c= 273.13721517 841 8673.91304348 273.137215166 841

107579.15781 34916 273.137215166 107579.157807 34916

34916 11464.849067 841 34916 11464.849067

273.13721517 841 4336.95652174 273.137215166 841

Batang d

1 0.3090169944 0 0 0

0.3090169944 1 0 0 0

!"#d= 0 0 1 0 0

0 0 0 1 0.3090169944

0 0 0 0.3090169944 1

0 0 0 0 0

118923.91304 0 0 118923.91304 0

0 120 884 0 120!k#d=

0 884 8674 0 884

118923.91304 0 0 118923.913043 0

0 120 884 0 120

0 884 4337 0 884

13 14 15 16 17

107579.15781 34916 273.137215166 107579.15781 34916

34916 11464.8490674 841 34916 11464.849067

!$#d= 273.13721517 841 8673.91304348 273.13721517 841107579.15781 34916 273.13721517 107579.157807 34916

34916 11464.849067 841 34916 11464.849067

273.13721517 841 4336.95652174 273.13721517 841

Batang e

1 0.3090169944 0 0 0

0.3090169944 1 0 0 0

!$#=!"# "!k#!"#

!$#=!"# "!k#!"#



!"#e= 0 0 1 0 0

0 0 0 1 0.3090169944

0 0 0 0.3090169944 1

0 0 0 0 0

1110057.0704 0 0 1110057.0704 0

0 97667 77011 0 97667

!k#e= 0 77011 80964 0 77011

1110057.0704 0 0 1110057.07039 0

0 97667 77011 0 97667

0 77011 40482 0 77011

16 17 18 19 20

1013382.4469 297534 23797.5972626 1013382.4469 297534

297534 194341.893526 73241 297534 194341.89353

!$#e= 23797.597263 73241 80963.8554217 23797.597263 732411013382.4469 297534 23797.597263 1013382.44692 297534

297534 194341.89353 73241 297534 194341.89353

23797.597263 73241 40481.9277108 23797.597263 73241

Batang f

0 1 0 0 0

1 0 0 0 0

!"#f= 0 0 1 0 0

0 0 0 0 10 0 0 1 0

0 0 0 0 0

233408 0 0 233408 0

0 908 3405 0 908

!k#f= 0 3405 17024 0 3405

233408 0 0 233408 0

0 908 3405 0 908

0 3405 8512 0 3405

4 5 6 16 17

907.94666667 0 3404.8 907.94666667 0

0 233408 0 0 233408

!$#f= 3404.8 0 17024 3404.8 0

907.94666667 0 3404.8 907.946666667 0

0 233408 0 0 233408

3404.8 0 8512 3404.8 0

!$#=!"# "!k#!"#

!$#=!"# "!k#!"#



1 2 3 4 5

908 0 3405 0 0

0 233408 0 0 0

3405 0 17024 0 00 0 0 908 0

0 0 0 0 233408

0 0 0 3405 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

908 0 3405 0 0

0 233408 0 0 0

3405 0 8512 0 0

0 0 0 0 00 0 0 0 0

0 0 0 0 0

0 0 0 908 0

0 0 0 0 233408

0 0 0 3405 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

Matriks Kekakuan Struktur

3 6 7 8 9

!$# =

17024 0 0 0 0

0 17024 0 0 0

0 0 1013382 297534 23798

0 0 297534 194342 73241

0 0 23798 73241 80964

3405 0 1013382 297534 23798

0 0 297534 194342 73241

8512 0 23798 73241 40482

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 3405 0 0 0

0 0 0 0 0

0 8512 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0



%EA% L&A% = 47.945 kg/m = 0.47945 kN/m

Gaya jepit ujung batang b

'(1 = 0 0

'(2 = 0.378046325 0.378046325

'(3 = 0.0993631758 0.0993631758

'(4 = 0 0'(5 = 0.378046325 0.378046325

'(6 = 0.0993631758 0.0993631758

Beban titik ekivalen batang b

1 0.3090169944 0 0 0

0.3090169944 1 0 0 00 0 1 0 0

0 0 0 1 0.3090169944

0 0 0 0.3090169944 1

0 0 0 0 0

Gaya jepit ujung batang c

'(1 = 0 0

'(2 = 3.528752 3.528752

'(3 = 8.6572049067 8.6572049067

'(4 = 0 0

'(5 = 3.528752 3.528752

'(6 = 8.6572049067 8.6572049067

Beban titik ekivalen batang c

1 0.3090169944 0 0 0

0.3090169944 1 0 0 0

0 0 1 0 0

0 0 0 1 0.3090169944

0 0 0 0.3090169944 1

0 0 0 0 0

Gaya jepit ujung batang d

'(1 = 0 0

'(2 = 3.528752 3.528752

)'(*b=

)+(*b=!"# "

b)'(*

b

)+(*b=

)'(*c=

)+(*c=



'(3 = 8.6572049067 8.6572049067

'(4 = 0 0

'(5 = 3.528752 3.528752

'(6 = 8.6572049067 8.6572049067

Beban titik ekivalen batang d

1 0.3090169944 0 0 0

0.3090169944 1 0 0 0

0 0 1 0 0

0 0 0 1 0.3090169944

0 0 0 0.3090169944 1

0 0 0 0 0

Gaya jepit ujung batang e

'(1 = 0 0

'(2 = 0.378046325 0.378046325

'(3 = 0.0993631758 0.0993631758

'(4 = 0 0

'(5 = 0.378046325 0.378046325

'(6 = 0.0993631758 0.0993631758

Beban titik ekivalen batang e

1 0.3090169944 0 0 0

0.3090169944 1 0 0 0

0 0 1 0 0

0 0 0 1 0.3090169944

0 0 0 0.3090169944 1

0 0 0 0 0

Vektor beban

!+# =

0.1168227391

0.3595434209

0.0993631758

1.207267076

3.7155860048

8.5578417309

0

6.712085168

0

)'(*d=

)+(*d=

)'(*e=

)+(*e=



1.207267076

3.7155860048

8.5578417309

0.1168227391

0.3595434209

0.0993631758

Perpindahan

!$# ),* = )+*

3 6 7 8 9

17024 0 0 0 0

0 17024 0 0 0

0 0 1013382.44692 297533.897101 23797.597263

0 0 297533.897101 194341.893526 73241.473319

0 0 23797.597263 73241.4733194 80963.855422

3404.8 0 1013382.4469 297533.8971 23797.5972632.08569E013 0 297533.8971 194341.89353 73241.473319

8512 0 23797.597263 73241.4733194 40481.927711

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 3404.8 0 0 0

0 2.08569E013 0 0 0

0 8512 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

,3

=

0.00024772 0.00014099 0.00106753 0.00009155

,6 0.00014099 0.00024772 0.00089173 0.00013934

,7 0.00106753 0.00089173 0.00636579 0.00075193

,8 0.00009155 0.00013934 0.00075193 0.00026963

,9 0.00006094 0.00009280 0.00049644 0.00018906

,10 0.00109723 0.00093696 0.00660886 0.00083778

,11 0.00000015 0.00000015 0.00000107 0.00000451

,12 0.00006094 0.00009280 0.00050848 0.00015201

,13 0.00101724 0.00101724 0.00624689 0.00086677

,14 0.00024522 0.00024522 0.00110775 0.00008603

,15 0.00003842 0.00003842 0.00026940 0.00005746

,16 0.00093696 0.00109723 0.00588285 0.00089392

,17 0.00000015 0.00000015 0.00000107 0.00000023

,18 0.00009280 0.00006094 0.00056967 0.00007889

,19 0.00089173 0.00106753 0.00560524 0.00085548

,20 0.00013934 0.00009155 0.00085548 0.00011855



,21 0.00009280 0.00006094 0.00056967 0.00007889

,3

=

0.0016905

,6 0.0016905

,7 0.0069637

,8 0.0010640

,9 0.0007282,10 0.0066076

,11 0.0000318

,12 0.0007380

,13 0.0000000

,14 0.0205019

,15 0.0000000

,16 0.0066076

,17 0.0000318

,18 0.0007380

,19 0.0069637,20 0.0010640

,21 0.0007282

Deformasi Gaya Batang

Batang a

),* =

0 -1 0 1

0 -2 1 0

0.0016905 -3 0 0

0.0066076 -10 0 0

0.0000318 -11 0 0

0.0007380 -12 0 0

1 233408 0

2 0 907.94666667

3 0 3404.8

10 233408 0

11 0 907.94666667

12 0 3404.8

Batang b

),* =

0.0069637 -7 0.9510565163 0.3090169944

0.0010640 -8 0.3090169944 0.9510565163

0.0007282 -9 0 0

0.0066076 -10 0 0

0.0000318 -11 0 0

0.0007380 -12 0 0



7 1110057.07039 0

8 0 97667.270061

9 0 77010.642443

10 1110057.0704 0

11 0 97667.270061

12 0 77010.642443

Batang c

),* =

0.0066076 -10 0.9510565163 0.3090169944

0.0000318 -11 0.3090169944 0.9510565163

0.0007380 -12 0 0

0.0000000 -13 0 0

0.0205019 -14 0 0

0.0000000 -15 0 0

10 118923.913043 0

11 0 120.0938309112 0 883.89059546

13 118923.91304 0

14 0 120.09383091

15 0 883.89059546

Batang d

),* =

0 -13 0.9510565163 0.3090169944

0.0205019 -14 0.3090169944 0.9510565163

0.0000000 -15 0 0

0.0066076 -16 0 0

0.0000318 -17 0 0

0.0007380 -18 0 0

13 118923.913043 0

14 0 120.09383091

15 0 883.89059546

16 118923.91304 0

17 0 120.09383091

18 0 883.89059546

Batang e

),* =

0 -16 0.9510565163 0.3090169944

0.0000318 -17 0.3090169944 0.9510565163

0.0007380 -18 0 0

0.0069637 -19 0 0

0.0010640 -20 0 0

0.0007282 -21 0 0



16 1110057.07039 0

17 0 97667.270061

18 0 77010.642443

19 1110057.0704 0

20 0 97667.270061

21 0 77010.642443

Batang f

),* =

0 -4 0 1

0 -5 1 6.125742E017

0.0016905 -6 0 0

0.0066076 -16 0 0

0.0000318 -17 0 0

0.0007380 -18 0 0

4 233408 0

5 0 907.946666676 0 3404.8

16 233408 0

17 0 907.94666667

18 0 3404.8



e

7

f 7.5

2

1.5

adan L

90 1.5707963268 0 1 7.5

18 0.3141592654 0.9510565163 0.3090169944 1.577

18 0.3141592654 0.9510565163 0.3090169944 14.72

342 5.9690260418 0.9510565163 0.3090169944 14.72

342 5.9690260418 0.9510565163 0.3090169944 1.577

90 1.5707963268 0 1 7.5

0 0 1

0 1 0

0 0 0

0 0 0

0 0 01 0 0

0

3405

8512

0

3405

17024

c( n

!"# "=



12

3404.8 1

0 2

8512 33404.810

0 11

1702412

0 1 0.309016994

0 0.30901699 1

0 0 0

0 0 00 0 0

1 0 0

0

77011

40482

0

77011

80964

12

23797.5972637

732418

40481.92771089

23797.597262610

73241 11

80963.855421712

0 1 0.309016994

0 0.30901699 1

0 0 0

0 0 0

0 0 0

1 0 0

!"# "=

!"# "=



0

884

4337

0

884

8674

15

273.1372151710

841 11

4336.9565217412

273.13721516613

841 14

8673.9130434815

0 1 0.309016994

0 0.30901699 1

0 0 0

0 0 0

0 0 0

1 0 0

0

8844337

0

884

8674

18

273.13721516613

841 14

4336.9565217415273.1372151716

841 17

8673.9130434818

0 1 0.309016994

0 0.30901699 1

!"# "=



0 0 0

0 0 0

0 0 0

1 0 0

0

7701140482

0

77011

80964

21

23797.597262616

7324117

40481.92771081823797.59726319

73241 20

80963.855421721

0 0 1

0 1 0

0 0 0

0 0 00 0 0

1 0 0

0

3405

8512

0

3405

17024

18

3404.8 4

0 5

8512 6

3404.816

0 17

1702418

!"# "=

!"# "=



6 7 8 9 10

0 0 0 0 908

0 0 0 0 0

0 0 0 0 34053405 0 0 0 0

0 0 0 0 0

17024 0 0 0 0

0 1013382 297534 23798 1013382

0 297534 194342 73241 297534

0 23798 73241 80964 23798

0 1013382 297534 23798 1121870

0 297534 194342 73241 332449

0 23798 73241 40482 26929

0 0 0 0 1075790 0 0 0 34916

0 0 0 0 273

3405 0 0 0 0

0 0 0 0 0

8512 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

10 11 12 13 14

3405 0 8512 0 0

0 0 0 0 0

1013382 297534 23798 0 0

297534 194342 73241 0 0

23798 73241 40482 0 0

1121870 332449 26929 107579 34916

332449 439215 72401 34916 11465

26929 72401 106662 273 841

107579 34916 273 215158 0

34916 11465 841 0 22930

273 841 4337 546 0

0 0 0 107579 34916

0 0 0 34916 11465

0 0 0 273 841

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0



0 0 0.116822739

0 0.378046325 0.3595434210 0.0993631758

= 0.099363176

0 0 0.116822739

0 0.378046325 0.359543421

1 0.0993631758 0.099363176

0 0 1.090444337

0 3.528752 3.356042584

0 8.6572049067

=

8.657204907

0 0 1.090444337

0 3.528752 3.356042584

1 8.6572049067 8.657204907



0 0 1.090444337

0 3.528752 3.356042584

0 8.6572049067=

8.657204907

0 0 1.090444337

0 3.528752 3.356042584

1 8.6572049067 8.657204907

0 0 0.116822739

0 0.378046325 0.359543421

0 0.0993631758=

0.099363176

0 0 0.116822739

0 0.378046325 0.359543421

1 0.0993631758 0.099363176



10 11 12 13 14

3404.8 2.085693E013 8512 0 0

0 0 0 0 0

1013382.4469 297533.8971 23797.597263 0 0

297533.8971 194341.89353 73241.473319 0 0

23797.5972626 73241.473319 40481.927711 0 0

1121869.5514 332449.463526 26929.260047 107579.15781 34915.56642332449.463526 439214.742593 72400.843409 34915.566425 11464.84907

26929.2600474 72400.843409 106661.76847 273.137215166 840.6299105

107579.15781 34915.566425 273.13721517 215158.315614 0

34915.566425 11464.849067 840.62991051 0 22929.69813

273.13721517 840.629910507 4336.9565217 546.274430333 0

0 0 0 107579.15781 34915.56642

0 0 0 34915.5664246 11464.84907

0 0 0 273.137215166 840.6299105

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0.00006094 0.00109723 0.00000015 0.00006094 0.00101724

0.00009280 0.00093696 0.00000015 0.00009280 0.00101724

0.00049644 0.00660886 0.00000107 0.00050848 0.00624689

0.00018906 0.00083778 0.00000451 0.00015201 0.00086677

0.00015065 0.00055782 0.00000015 0.00010125 0.00057669

0.00055782 0.00688069 0.00000115 0.00055782 0.00652792

0.00000015 0.00000115 0.00000428 0.00000015 0.00000184

0.00010125 0.00055782 0.00000015 0.00010125 0.00057669

0.00057669 0.00652792 0.00000184 0.00057669 0.00653389

0.00005879 0.00107910 0.00000214 0.00005879 0.00000000

0.00003842 0.00028812 0.00000015 0.00003842 0.00028798

0.00059526 0.00617293 0.00000115 0.00059526 0.00652792

0.00000015 0.00000115 0.00000000 0.00000015 0.00000184

0.00005250 0.00059526 0.00000015 0.00005250 0.00057669

0.00056967 0.00588285 0.00000107 0.00056967 0.00624689

0.00007889 0.00089392 0.00000023 0.00007889 0.00086677



0.00005250 0.00059526 0.00000015 0.00005250 0.00057669

0 0 0 0 0

0 0 0 0 0

1 0 0 0 0.001690541

0 0 1 0 0.006607639

0 1 0 0 3.1838E005

0 0 0 1 0.000738027

0 233408 0 0 0

3404.8 0 907.94666667 3404.8 0

17024 0 3404.8 8512 0.001690541

0 233408 0 0 3.1838E005

3404.8 0 907.94666667 3404.8 0.006607639

8512 0 3404.8 17024 0.000738027

0 0 0 0 0.006963706

0 0 0 0 0.001064022

1 0 0 0 0.000728208

0 0.9510565163 0.3090169944 0 0.006607639

0 0.3090169944 0.9510565163 0 3.1838E005

0 0 0 1 0.000738027



0 1110057.0704 0 0 0.006294077

77010.6424429 0 97667.270061 77010.6424429 0.003163849

80963.8554217 0 77010.642443 40481.9277108 0.000728208

0 1110057.07039 0 0 0.006294077

77010.642443 0 97667.270061 77010.642443 0.002011593

40481.9277108 0 77010.642443 80963.8554217 0.000738027

0 0 0 0 0.006607639

0 0 0 0 3.1838E005

1 0 0 0 0.000738027

0 0.9510565163 0.3090169944 0 2.7555E015

0 0.3090169944 0.9510565163 0 0.020501877

0 0 0 1 1.2168E016

0 118923.91304 0 0 0.006294077

883.890595463 0 120.09383091 883.890595463 0.0020115938673.91304348 0 883.89059546 4336.95652174 0.000738027

0 118923.913043 0 0 0.006335428

883.89059546 0 120.09383091 883.89059546 0.019498443

4336.95652174 0 883.89059546 8673.91304348 1.2168E016

0 0 0 0 2.7555E015

0 0 0 0 0.020501877

1 0 0 0 1.2168E016

0 0.9510565163 0.3090169944 0 0.006607639

0 0.3090169944 0.9510565163 0 3.1838E005

0 0 0 1 0.000738027

0 118923.91304 0 0 0.006335428

883.890595463 0 120.09383091 883.890595463 0.019498443

8673.91304348 0 883.89059546 4336.95652174 1.2168E016

0 118923.913043 0 0 0.006294077

883.89059546 0 120.09383091 883.89059546 0.002011593

4336.95652174 0 883.89059546 8673.91304348 0.000738027

0 0 0 0 0.006607639

0 0 0 0 3.1838E005

1 0 0 0 0.000738027

0 0.9510565163 0.3090169944 0 0.006963706

0 0.3090169944 0.9510565163 0 0.001064022

0 0 0 1 0.000728208



0 1110057.0704 0 0 0.006294077

77010.6424429 0 97667.270061 77010.6424429 0.002011593

80963.8554217 0 77010.642443 40481.9277108 0.000738027

0 1110057.07039 0 0 0.006294077

77010.642443 0 97667.270061 77010.642443 0.003163849

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