Anstruk II 2.xlsx

8/17/2019 Anstruk II 2.xlsx

1/84

No. 2

► Derajat Ketidaktentuan Kinematis = 10

► Perhitungan Momen Primer

Mef = 1/12 . 1.4 . 4 2 Mij = 5/96 . 1.6 . 4

= 1.867 = 1.333


2/84

Mfe = -Mef Mji = -Mij

= -1.867 = -1.333

Mfg = 4 . 2.5 . 2.5 2 / 5 2 Mjk = 6 . 2.5 . 2.5

= 2.500 = 3.750

Mgf = -Mfg Mkj = -Mij

= -2.500 = -3.750

Mgh = 12-Jan . 1.4 . 4 2 Mkl = 5/96 . 1.6 . 4

= 1.867 = 1.333

Mhg = -Mgh Mlk = -Mij

= -1.867 = -1.333


3/84

► Gaya luar yang ekivalen dititik yang koresponding dengan lendutan

Q1 = 1.87

[ Q ] =

1.9

Q2 = 0.633 0.6

Q3 = -0.63 -0.63

Q4 = -1.867 -1.867

Q5 = 1.333 1.333

Q6 = 2.417 2.417

Q7 = -2.417 -2.417

Q8 = -1.333 -1.333

►

2 = 1

9 = 1

15 = 1

►

4 = 1

10 = 11 = 1

17 = 1

Dierikan D1 ! 1 satuan

Dierikan D2! 1 satuan


4/84

►

6 = 1

12 = 13 = 1

19 = 1

Dierikan D"! 1 satuan


5/84

►

8 = 1

14 = 1

21 = 1

►

16 = 1

23 = 1

►

18 = 1

24 = 1

25 = 1

►

20 = 1

26 = 27 = 1

►

Dierikan D#! 1 satuan

Dierikan D$! 1 satuan

Dierikan D%! 1 satuan

Dierikan D&! 1 satuan

Dierikan D'! 1 satuan


6/84

22 = 1

28 = 1


7/84

► Momen (khir

M1 = 0.3034 M11 = -2.66006179 M21

M2 = 0.6068 M12 = 2.151089342 M22

M" = 0.01371 M1" = -2.55083807 M2"

M# = 0.02742 M1# = -0.6961434 M2#

M$ = -0.2561 M1$ = 0.716912924 M2$

M% = -0.5122 M1% = 0.523618544 M2%

M& = -0.2698 M1& = 0.476512516 M2&

M' = -0.5395 M1' = 0.911900648 M2'

M) = -1.3237 M1) = -0.11824092

M10 = 2.15613 M20 = -0.23648183

► Kontrol Momen *entang

! "i#ik $

M2 % M9 % M15 = 0 ! "i#ik J

0.6068 % -1.3237 % 0.71691 = 0 M18 %

0 = 0 +ke , 0.911901 %

! "i#ik &

M4 % M10 % M11 % M17 = 0 ! "i#ik '

0.02742 % 2.15613 % -2.6601 % 0.476512516 = 0 M20 %

0 = 0 +ke , -0.236482 %

! "i#ik (

M6 % M12 % M13 % M19 = 0 ! "i#ik )

-0.5122 % 2.15109 % -2.5508 % -0.118240916 = 0 M28 %

-1 = 0 -K 0.453 %

! "i#ik *

M8 % M14 = M21 = 0

-0.5395 % -0.6961 = -0.631 = 0

-2 = 0 -K

! "i#ik +

M16 % M23 = 0

0.52362 % -0.524 = 0

0 = 0 +ke ,

► Menghitung /eaksi Perletakan ,,

! ,en#ang +-J

= 0

M23 M24 ij . 4 - Q

*ij *ji 4 ij - 0

i j 4 ij = 4.2598892738

M j


8/84

ij ji ij = 1.0649723185

= 0

-ji . 4 % Q

-4 ji % 0

4 ji = 8.5401

ji = 2.1350276815

! ,en#ang '-)

= 0

M27 M28 kl . 4.00 - Q

*kl *kl 4.00 kl - 0

k l 4 kl = 8.8016215025

kl kl kl = 2.2004053756

= 0

-lk . 4.00 % Q

-4.00 lk % 0

4.00 lk = 3.9983

lk = 0.9995946244

Mi

M j

Mi


9/84

! ,en#ang +-$

Mi = 0

*ie i - *ei . 3.5 % M16 % M15 = 0

M16 -3.5 *ei % 0.523618544 % 0.71691292 = 0

-3.5 *ei % 1.24053147 = 0

*ei = 0.3544

Me = 0

*ei M15 *ie . 3.5 % M16 % M15 = 0

e 3.5 *ie % 0.523618544 % 0.71691292 = 0

3.5 *ie % 1.24053147 = 0

*ie = -0.3544

! ,en#ang J-&

Mj = 0

*jf j - *fj . 3.5 % M18 % M17 = 0

M18 -3.5 *fj % 0.911900648 % 0.47651252 = 0

-3.5 *fj % 1.38841316 = 0

*fj = 0.3966

Mf = 0

*fj M17 *jf . 3.5 % M18 % M17 = 0

f 3.5 *jf f 0.911900648 % 0.47651252 = 0

3.5 *jf % 1.38841316 = 0

*jf = -0.3966

! ,en#ang '-(

Me = 0

*kg k - *gk . 3.5 % M20 % M19 = 0

M20 -3.5 *gk % -0.23648183 % -0.1182409 = 0

-3.5 *gk % -0.3547227 = 0

*gk = -0.1013

Ma = 0

*gk M19 *kg . 3.5 % M20 % M19 = 0

g 3.5 *kg % -0.23648183 % -0.1182409 = 0

3.5 *kg % -0.3547227 = 0

*kg = 0.1013

! ,en#ang )-*

Mf = 0

*lh f - *hl . 3.5 % M22 % M21 = 0

M22 -3.5 *hl % -0.453 % -0.631 = 0

-3.5 *hl % -1.0837456 = 0

*hl = -0.3096

M = 0

*hl M21 *lh . 3.5 % M22 % M21 = 0

3.5 *lh % -0.45273883 % -0.6310068 = 0


10/84

3.5 *lh % -1.0837456 = 0

*lh = 0.3096

! ,en#ang $-

Mg = 0 0

*ea e - *ae . 3.50 % M2 % M1 = 0

M2 -3.5 *ae % 0.60680487 % 0.30340243 = 0

-3.5 *ae % 0.9102073 = 0

*ae = 0.2600

M = 0

*ae M1 *ea . 3.50 % M2 % M1 = 0

a 3.5 *ea % 0.60680487 % 0.30340243 = 0

3.5 *ea % 0.9102073 = 0

*ea = -0.2600


11/84

! ,en#ang &-,

Mh = 0

*f f - *f . 3.50 % M4 % M3 = 0

M4 -3.50 *f % 0.027416256 % 0.01370813 = 0

-3.50 *f % 0.04112438 = 0

*f = 0.0117

M = 0

*f M3 *f . 3.50 % M4 % M3 = 0

3.5 *f % 0.027416256 % 0.01370813 = 0

3.5 *f % 0.04112438 = 0

*f = -0.0117

! ,en#ang (-

Mh = 0

*g g - *g . 3.50 % M6 % M5 = 0

M6 -3.50 *g % -0.51215192 % -0.256076 = 0

-3.50 *g % -0.7682279 = 0

*g = -0.2194

M = 0

*g M5 *g . 3.5 % M6 % M5 = 0

3.5 *g % -0.51215192 % -0.256076 = 0

3.5 *g % -0.7682279 = 0

*g = 0.2194

! ,en#ang *-

Mh = 0

*h h - *h . 3.50 % M8 % M7 = 0

M8 -3.50 *h % -0.53951649 % -0.2697582 = 0

-3.50 *h % -0.8092747 = 0

*h = -0.2312

M = 0

*h M7 *h . 3.5 % M8 % M7 = 0

3.5 *h % -0.53951649 % -0.2697582 = 0

3.5 *h % -0.8092747 = 0

*h = 0.2312

! ,en#ang $-&

Me = 0

Q1 - fe . 4 % Q 1/2 .

-4 fe % 0.7 .

*ef *fe -4 fe = -12.0324152279

M9 e f M10 fe = 3.01 #

ef fe Mf = 0

ef . 4 - Q 1/2 .

4 ef - 0.7 .


12/84

4 ef = 10.3675847721

ef = 2.59 #

! ,en#ang (-*

Mf = 0

Q1 - gh . 4.00 % Q 1/2 .

-4.00 gh % 0.7 .

*hg *gh 4.00 gh = 12.6888488635

M13 g h M14 gh = 3.17221222 #

hg gh Mg = 0

hg . 4.00 - Q 1/2 .

4.00 hg - 0.7 .

4.00 hg = 22.3111511365

hg = 5.57778778 #

! ,en#ang J-'

Mf = 0

- kj . 4 % 2 1/2 .

2 -4 kj % 3 .

*jk *kj 4 kj = 11.7516940764

M25 j k M26 kj = 2.94 #

jk kj Mg = 0

jk . 4 - 2 1/2 .

4 jk - 3 .

4 jk = 12.2483059236

jk = 3.06 #


13/84

! ,en#ang &-(

Mf = 0

- gf . 4.00 % 1 1/2 .

1 -4.00 gf % 2 .

*fg *gf 4.00 gf = 7.4910275482

M11 f g M12 gf = 1.87 #

fg gf Mg = 0

fg . 4.00 - 1 1/2 .

4.00 fg - 2 .

4.00 fg = 7.4910275482

fg = 1.87 #

► D(G/(M / *+D

Q1

M23 M24 2

*ij *ji *jk

i j M25 j

ij ji jk

ie jf

*ie i *jf j

M16 M18

*ei M15 *fj M17

e f

ei fj

Q1

1

*ef *fe *fg

M9 e f M10 M11 f

ef fe fg

ea f

*ea e *f f

M2 M4


14/84

*ae M1 *f M3

a

ae f

! i:;l J

j = 0

ji % jk - jf = 0

2.13503 % 3.06 - jf = 0

jf = 5.197104162 # <

fj - jf = 0

fj = 5.1971 #

*j = 0

*jf - *ji % *jk = 0

-0.4 - 0.35444 % *jk = 0

*jk = 0.75113


15/84

! i:;l $

*e = 0 e =

*ea - *ei - *ef = 0 ef

-0.2601 - 0.35444 - *ef = 0 2.591896193

*ef = -0.614497 #

*fe % *ef = 0 ae

*fe % -0.6145 = 0

*fe = 0.6144968 # >

! i:;l &

*f = 0

*f % *fj - *fe - *fg = 0 *fg

-0.0117 % 0.39669 - 0.6145 - *fg = 0 -0.229557141

*fg = -0.2295571 #

f = 0

fe % fj % fg - f = 0 f

3.0081 % 2.13503 % 1.87 - f = 0 f

f = 7.0158884 # <

! i:;l (

*g = 0

*gk - *gf % *g % *gh = 0 *gh

-0.1013 % -0.2296 % 0.21949 % *gh = 0 0.3477014663

*gh = 0.3477015 #

g = 0

gh % gf % gk - g = 0 g

3.17221 % 1.87 % 5.13833 - g = 0 10.183297998

g = 10.183298 # <

! i:;l *

g = 0 hl

hl % hg - h = 0 h

2.20 % 1.06497 - h = 0 h

h = 3.27 # <

*h = 0

*f = 0

*hl % *h - *hg = 0

-0.3096 % 0.23122 - *hg = 0

= -0.07842 #


16/84

► MNN34K(N G(( D(5(M

! ,en#ang -$ 0 ? @ ? 3.5 @ M@ @

0 0.303402435 -0.260059 3.6568

e 1 0.043343205 -0.260059 3.6568

M@ = M1 - *ae @ 2 -0.21671602 -0.260059 3.6568

= 0.3034024 - 0.260059 @ 3 -0.47677525 -0.260059 3.6568

@ = -0.260059 3.5 -0.60680487 -0.260059 3.6568

*ae a A@ = -ae

= 3.6568685

ae

! ,en#ang ,-& 0 ? @ ? 3.5 @ M@ @

0 0.013708128 -0.01175 7.0158

f 1 0.001958304 -0.01175 7.0158

M@ = M3 - *f @ 2 -0.00979152 -0.01175 7.0158

= 0.0137081 - 0.01175 @ 3 -0.02154134 -0.01175 7.0158

@ = -0.01175 3.5 -0.02741626 -0.01175 7.0158

*f A@ = -f

= 7.0158884

f

! ,en#ang -( 0 ? @ ? 3.5 @ M@ @

0 -0.25607596 0.219494 10.183

g 1 -0.03658228 0.219494 10.183

M@ = M5 - *g @ 2 0.182911402 0.219494 10.183

= -0.256076 - -0.219494 @ 3 0.402405084 0.219494 10.183

@ = 0.2194937 3.5 0.512151925 0.219494 10.183

*g A@ = -g 4.5 0.731645607 0.219494 10.183

= 10.183298

g

! ,en#ang *- 0 ? @ ? 3.5 @ M@ @

0 -0.26975824 0.231221 3.2653

h 1 -0.03853689 0.231221 3.2653

M@ = M7 - *h @ 2 0.192684461 0.231221 3.2653

= -0.269758 - -0.231221 @ 3 0.423905813 0.231221 3.2653

@ = 0.2312214 3.5 0.53951649 0.231221 3.2653

*h A@ = -h

= 3.27

h

! ,en#ang $-+ 0 ? @ ? 3.5 @ M@ @


17/84

0 0.716912924 -0.354438 1.0649

i 1 0.362475362 -0.354438 1.0649

M@ = M15 - *ei @ 2 0.0080378 -0.354438 1.0649

= 0.7169129 - 0.354438 @ 3 -0.34639976 -0.354438 1.0649

@ = -0.354438 3.5 -0.52361854 -0.354438 1.0649

*ei e A@ = -ei

= 1.0649723

ei


18/84

! ,en#ang (-J 0 ? @ ? 3.5 @ M@ @

0 0.476512516 -0.396689 2.1350

j 1 0.079823041 -0.396689 2.1350

M@ = M17 - *fj @ 2 -0.31686643 -0.396689 2.1350

= 0.4765125 - 0.396689 @ 3 -0.71355591 -0.396689 2.1350

@ = -0.396689 3.5 -0.91190065 -0.396689 2.1350

*fj f A@ = fj

= 2.1350277

fj

! ,en#ang &-+ 0 ? @ ? 3.5 @ M@ @

0 -0.11824092 0.101349 5.1383

k 1 -0.01689156 0.101349 5.1383

M@ = M19 - *gk @ 2 0.084457797 0.101349 5.1383

= -0.118241 - -0.101349 @ 3 0.185807154 0.101349 5.1383

@ = 0.1013494 3.5 0.236481832 0.101349 5.1383

*gk g A@ = gk

= 5.1383289

gk

! ,en#ang (-J 0 ? @ ? 3.5 @ M@ @

0 -0.63100678 0.309642 2.2004

l 1 -0.32136518 0.309642 2.2004

M@ = M21 - *hl @ 2 -0.01172358 0.309642 2.2004

= -0.631 - -0.309642 @ 3 0.297918026 0.309642 2.2004

M21 @ = 0.3096416 3.5 0.452738828 0.309642 2.2004

*hl h A@ = hl

= 2.2004054

hl

! ,en#ang $-& 0 ? @ ? 4

M9 Q1 M@ = M9 % ef @ - Q1

*ef = -1.323718 % 2.59 @ - 1.40 @

e f = -1.323718 % 2.591896193 @ - 0.7 @ 2

ef @ = 2.591896 - 1.4 @

A@ = *ef

= -0.614497

! ,en#ang &- ( 0 ? @ ? 5

1 M@ = M11 % fg @ -

1 @


19/84

*fg = -2.660062 % 1.87 @ -

4 @

M11 f g = -2.660062 % -2.13 @

fg @ = -2.13

A@ = *fg

= -0.229557

! ,en#ang (-* 0 ? @ ? 4

M13 Q1 M@ = M13 % gh @ - Q1

*gh = -2.550838 % 3.172212216 @ - 1.40 @

g h = -2.550838 % 3.172212216 @ - 0.7 @ 2

gh @ = 3.172212 - 1.4 @

A@ = *gh

= 0.347701

! ,en#ang +-J 0 ? @ ? 5.5

Q1 M@ = M23 % ij @ - Q 1/4

M23 = -0.524 % 1.064972318 @ - 0.2

*ij = -0.523619 % 1.064972318 @ - 0.05 @

i @ = 1.064972 - 0.15 @ 2

ij A@ = *ij

= 0

! ,en#ang (-* 0 ? @ ? 5

2 M@ = M25 % jk @ -

2 @

*jk = -3.339 % 3.06 @ -

4 @

M25 j k = -3.339148 % -0.94 @

jk @ = -0.94

A@ = *jk

= 3.06

! ,en#ang +-J 0 ? @ ? 4

Q1 M@ = M27 % kl @ - Q1 1/4

M27 = -2.854 % 2.200405376 @ - 0.2

*kl = -2.85436 % 2.200405376 @ - 0.05 @

i @ = 2.200405 - 0.15 @ 2

kl A@ = *kl

= -0.852

@2 .

@2 .


20/84

Momem ma6

! ,en#ang $-& ! ,en#ang &-(

@= 0

@=

@ @

2.5919 - 1.4 @ = 0 -2.13 - BC$&D

@ = 1.851

M@ = -1.3237 % 2.5919 @ - 0.7 @ 2 M@ = BC$&D

= -1.3237 % 2.5919 BBB - 0.7 BBB 2 = BC$&D

= 1.07554 # = BC$&D

! ,en#ang (-* ! ,en#ang +-J

@= 0

@=

@ @

3.17221 - 1.4 @ = 0 2.20040538 - 0.

@ = 2.266

M@ = -2.5508 % 3.17221 @ - 0.7 @ 2 M@ = -2.85436033

= -2.5508 % 3.17221 BBB - 0.7 BBB 2 = -2.85436033

= 1.04307 # = 2.7640979107


21/84

" E )1 = 4

)2 = 5

)3 = 4

*1 = 3.5

*2 = 3.5

1 = 4 #

2 = 6 #

F1 = 1.4 #/

F2 = 1.6 #/

2


22/84

2 / 5 2

2


23/84


24/84


25/84


26/84


27/84

= -0.631

= -0.453

= -0.524

= 2.664

= -3.339

= 3.091

= -2.854

= 0.453

M24 % M25 = 0

2.664 % -3.339 = 0

0 = 0 -K

M26 % M27 = 0

3.091 % -2.854 = 0

0 = 0 +ke ,

M22 = 0

-0.453 = 0

0 = 0 +ke ,

1/4 . 4 % M23 % M24 = 0

.4 . 16 % -0.524 % 2.664 = 0

2


28/84

#

1/4 . 4 % M23 % M24 = 0

.4 . 16 % -0.524 % 2.664 = 0

107262

#

1/4 . 4 % M27 % M28 = 0

.4 . 16 % -2.854 % 0.453 = 0

#

1/4 . 4.00 % M27 % M28 = 0

.4 . 16.0 % -2.854 % 0.453 = 0

784975

#

2

2

2


29/84

375622 # >

375622 #

894754 # >

894754 #

493566 # >

493566 #

416025 # >


30/84

416025 #

592298 # >

592298 #


31/84

98242 # >

498242 #

936821 # >

936821 #

213528 # >

213528 #

4 % M9 % M10 = 0

16 % -1.323718 % 2.15613 = 0

4 % M9 % M10 = 0

16 % -1.323718 % 2.15613 = 0

2

2


32/84

5 % M13 % M14 = 0

25 % -2.660062 % -2.1511 = 0

5 % M13 % M14 = 0

25 % -2.660062 % -2.1511 = 0

4 - M25 % M26 = 0

4 - -3.339 % 3.091 = 0

4 - M25 % M26 = 0

4 - -3.339148 % 3.09084 = 0

2

2


33/84

4.00 - M11 % M12 = 0

4.00 - -2.660 % 2.151 = 0

4 - M11 % M12 = 0

4 - -2.660062 % 2.15109 = 0

Q1

M27 M28 *kl

*kj *kl

k M26 k l

kj kl kl

kg lh

*kg k *lh l

M20 M22

*gk M19 *hl M21

g h

gk hl

Q1

*gf *gh *hg

g M12 M13 g h M14

gf gh hg

g h

*g g *h h

M6 M8


34/84

*g M5 *h M7

g h

! i:;l '

k = 0

kj % kl - kg = 0

2.94 % 2.20041 - kg = 0

kg = 5.13833 # <

gk - kg = 0

gk = 5.13833 #

*j = 0

*kl - *kj % *kg = 0

*kl - -0.751 % 0.101 = 0

*kl = -0.852


35/84

0

- ea % ei = 0 ij = ei = 1.06497

- ea % 1.064972 = 0

ea = 3.656869 # <

- ea = 0

ae = 3.656869 #

- *gf = 0

- *gf = 0

*gf = -0.229557 # >

- f = 0 fj = fe = 2.13503 #

- 7.015888 = 0

f = 7.015888 #

- *hg = 0

- *hg = 0

*hg = 0.347701 # >

- g = 0

- g = 0

g = 10.1833 #

= kl = 2.200405

- h = 0

- 3.27 = 0

h = 3.27


36/84

@

685115

685115

685115

685115

685115

@

883756

883756

883756

883756

883756

@

979976

979976

979976

979976

979976

979976

@

776941

776941

776941

776941

776941

@


37/84

723185

723185

723185

723185

723185


38/84

@

276815

276815

276815

276815

276815

@

288947

288947

288947

288947

288947

@

053756

053756

053756

053756

053756

@ M@ @ A@

0 -1.3237 2.5919 -0.6145

1/2 @ 1 0.56818 1.1919 -0.6145

1/2 @ 2 1.06007 -0.2081 -0.6145

3 0.15197 -1.6081 -0.6145

4 -2.1561 -3.0081 -0.6145

@ M@ @ A@

0 -2.6601 -2.13 -0.2296


39/84

1 -4.7873 -2.13 -0.2296

2 -6.9145 -2.13 -0.2296

3 -9.0418 -2.13 -0.2296

5 -13.296 -2.13 -0.2296

@ M@ @ A@

1/2 @ 0 -2.5508 3.17221 0.3477

1/2 @ 1 -0.0786 1.77221 0.3477

2 0.99359 0.37221 0.3477

3 0.6658 -1.0278 0.3477

4.00 -1.062 -2.4278 0.3477

@ M@ @ A@

. @ 0 -0.5236 1.06497 0

1/4 @ 1 0.49135 0.91497 0

3 2 1.20633 0.46497 0

3 1.3213 -0.285 0

4 0.53627 -1.335 0

@ M@ @ A@

0 -3.3391 -0.94 3.06208

1 -4.7873 -2.13 0

2 -6.9145 -2.13 -0.2296

3 -9.0418 -2.13 -0.2296

5 -13.296 -2.13 -0.2296

@ M@ @ A@

. @ 0 -2.8544 2.20041 -0.8525

1/4 @ 1 -0.704 2.05041 -0.8525

3 2 1.14645 1.60041 -0.8525

3 2.39686 0.85041 -0.8525

4 2.74726 -0.1996 -0.8525


40/84

0

BC$&D = 0

@ = BC$&D

% BC$&D @ - BBB @ 2

% BC$&D BC$&D - BBB BC$&D 2

#

0

15 @ 2 = 0

@ = 3.830

% 2.200405 @ - 0.05 @ 3

% 2.200405 BBB - 0.05 BBB 3

#


41/84

PERHITUNGAN MATRIKS (METODE MATRIKS KEKAKUAN)

MATRIKS TRANSFORMASI [A]

[A] =

0 0 0 0 0 0 0 0 d1

1 0 0 0 0 0 0 0 d2

0 0 0 0 0 0 0 0 d3

0 1 0 0 0 0 0 0 d4

0 0 0 0 0 0 0 0 d5

0 0 1 0 0 0 0 0 d6

0 0 0 0 0 0 0 0 d7

0 0 0 1 0 0 0 0 d8

1 0 0 0 0 0 0 0 d9

0 1 0 0 0 0 0 0 d10

0 1 0 0 0 0 0 0 d11

0 0 1 0 0 0 0 0 d12

0 0 1 0 0 0 0 0 d13

0 0 0 1 0 0 0 0 d14

1 0 0 0 0 0 0 0 d15

0 0 0 0 1 0 0 0 d16

0 1 0 0 0 0 0 0 d17

0 0 1 0 0 1 0 0 d18

0 0 0 0 0 0 0 0 d19

0 0 0 0 0 1 1 0 d20

0 0 0 1 0 0 0 0 d21

0 0 0 0 0 0 0 1 d22

0 0 0 0 1 0 0 0 d23

0 0 0 0 0 1 0 0 d24

0 0 0 0 0 1 0 0 d25

0 0 0 0 0 0 1 0 d26

0 0 0 0 0 0 1 0 d27

0 0 0 0 0 0 0 1 d28


42/84

D1 D2 D3 D4 D5 D6 D7 D8

0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0

0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1

0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0

0 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 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

MATRIKS KEKAKUAN INTERN ELEMEN [S]

[S] =

H1 1.143 0.571 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H2 0.571 1.143 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H3 0 0 1.143 0.571 0 0 0 0 0 0 0 0 0 0 0 0

H4 0 0 0.571 1.143 0 0 0 0 0 0 0 0 0 0 0 0

H5 0 0 0 0 1.143 0.571 0 0 0 0 0 0 0 0 0 0

H6 0 0 0 0 0.571 1.143 0 0 0 0 0 0 0 0 0 0

H7 0 0 0 0 0 0 1.143 0.571 0 0 0 0 0 0 0 0H8 0 0 0 0 0 0 0.571 1.143 0 0 0 0 0 0 0 0

H9 0 0 0 0 0 0 0 0 1.000 0.500 0 0 0 0 0 0

H10 0 0 0 0 0 0 0 0 0.500 1.000 0 0 0 0 0 0

H11 0 0 0 0 0 0 0 0 0 0 0.8 0.4 0 0 0 0

H12 0 0 0 0 0 0 0 0 0 0 0.4 0.8 0 0 0 0

H13 0 0 0 0 0 0 0 0 0 0 0 0 1.000 0.500 0 0

H14 0 0 0 0 0 0 0 0 0 0 0 0 0.500 1.000 0 0

H15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.14286 0.5714

H16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.57143 1.1428

H17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

MATRIKS A TRANS!OSE [A]T

[A]T =


43/84

H19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H22 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H23 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H24 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

H28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13 d14 d15 d16

MATRIKS KEKAKUAN STRUKTUR [K]

[K] = [A]T [S] [A]

[K] =

3.286 0.500 0 0 0.57143 0 0.000 0

0.500 4.086 0.97143 0 0 0.57143 0 0

0 0.97143 4.086 0.500 0 1.14286 0 0

0 0 0.500 3.286 0 0 0.000 0.57143

0.57143 0 0 0 2.14286 0.5 0 0

0 0.57143 1.14286 0 0.5 4.08571 1.54286 00.000 0 0 0.000 0 1.54286 2.943 0.5

0 0 0 0.57143 0 0 0.5 2.14286

MATRIKS LENDUTAN [D]

[D] = [K]"1 [#]

0.327 "0.044 0.005 "0.001 "0.092 0.020 "0.011 0.003

1.86667

"0.044 0.268 "0.056 0.010 0.019 "0.030 0.017 "0.007 0.63333

0.005 "0.056 0.290 "0.044 0.021 "0.094 0.049 0.000 "0.633

"0.001 0.010 "0.044 0.327 "0.001 0.007 0.012 "0.090 "1.867"1


44/84

"0.092 0.019 0.021 "0.001 0.512 "0.090 0.049 "0.011

1.33

0.020 "0.030 "0.094 0.007 "0.090 0.361 "0.197 0.044 2.417

"0.011 0.017 0.049 0.012 0.049 "0.197 0.462 "0.111 "2.417

0.003 "0.007 0.000 "0.090 "0.011 0.044 "0.111 0.516 "1.333

[S].[A]=

0.571 0 0 0 0 0 0.000 0

1.143 0 0 0 0 0 0.000 0

0 0.571 0 0 0 0 0.000 0

0 1.143 0 0 0 0 0.000 0

0 0 0.571 0 0 0 0.000 0

0 0 1.143 0 0 0 0.000 0

[D] =

0.531 0 0 0 0.571 0 0 0.000 0

0.024 0 0 0 1.143 0 0 0.000 0

"0.448 1.000 0.500 0 0 0 0 0 0

"0.472 0.500 1.000 0 0 0 0 0 0

0.193 0 0.8 0.4 0 0 0 0 0

1.234 0 0.4 0.8 0 0 0 0 0

"1.441 0 0 1.000 0.500 0 0 0 0

"0.16 0 0 0.500 1.000 0 0 0 0

1.14286 0 0 0 0.57143 0 0.000 0.000

0.57143 0 0 0 1.14286 0 0.000 0.0000 1.14286 0.57143 0 0 0.57143 0.000 0.000

0 0.57143 1.14286 0 0 1.14286 0.000 0.000

"


45/84

0 0 0 0 0 0.57143 0.57143 0

0 0 0 0 0 1.14286 1.14286 0

0 0 0 1.14286 0 0 0 0.57143

0 0 0 0.57143 0 0 0 1.14286

0 0 0 0 1 0.5 0 0

0 0 0 0 0.5 1 0 0

0 0 0 0 0 0.8 0.4 0

0 0 0 0 0 0.4 0.8 0

0 0 0 0 0 0 1 0.5

0 0 0 0 0 0 0.5 1

[H] =

0.303 H1

0.607 H2

0.014 H3

0.027 H4

"0.256 H5

"0.512 H6

"0.270 H7

MATRIKS $A%A DALAM [H] "0.540 H8

[H] = [S] [A] [D] 0.543 H9

0.289 H10

"0.160 H11

"0.349 H12

"0.684 H13

"0.696 H14

0.717 H15

0.524 H16

0.477 H17

0.912 H18

"0.118 H19

"0.236 H20

"0.631 H21


46/84

"0.453 H22

0.810 H23

1.330 H24

0.411 H25

"0.659 H26

"1.521 H27

"0.881 H28

► Momen Akhir = [ H ] - Momen Primer

M1 = 0.303 " 0 = 0.303 !""#

M$ = 0.607 " 0 = 0.607 !%%&

M" = 0.014 " 0 = 0.014 !1"'

M# = 0.027 " 0 = 0.027 !$'#

M = "0.256 " 0 = "0.256 -!$%1M% = "0.512 " 0 = "0.512 -!1$$

M' = "0.270 " 0 = "0.270 -!$%&

M& = "0.540 " 0 = "0.540 -!"

M = 0.543 " 1.86667 = "1.324 -1!"$"'

M1 = 0.289 " "1.8667 = 2.156 $!1%1

M11 = "0.160 " 2.5 = "2.660 -$!%%1

M1$ = "0.349 " "2.5 = 2.151 $!111

M1" = "0.684 " 1.86667 = "2.551 -$!&

M1# = "0.696 " 0 = "0.696 -!%%1

M1 = 0.717 " 0 = 0.717 !'1%

M1% = 0.524 " 0 = 0.524 !$"%

M1' = 0.477 " 0 = 0.477 !#'%


47/84

M1& = 0.912 " 0 = 0.912 !11

M1 = "0.118 " 0 = "0.118 -!11&$

M$ = "0.236 " 0 = "0.236 -!$"%

M$1 = "0.631 " 0 = "0.631

M$$ = "0.453 " 0 = "0.453

M$" = 0.810 " 1.33 = "0.524

M$# = 1.330 " "1.33 = 2.664

M$ = 0.411 " 3.75 = "3.339

M$% = "0.659 " "3.75 = 3.091

M$' = "1.521 " 1.33 = "2.854

M$& = "0.881 " "1.33 = 0.453


48/84


49/84

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 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0

0 1 0 0 0 1 1 0 0 0

0 1 0 0 0 0 0 1 1 0

0 0 0 1 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 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 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 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0.57143 1.14286 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0.57143 1.142

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

0.57143 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1.14286 0 0 0 0 0 0 0 0 0 0 0 0 0 0

[A]T.[S] =


50/84

0 1.14286 0.571429 0 0 0 0 0 0 0 0 0 0 0 0

0 0.57143 1.142857 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1.14286 0.57143 0 0 0 0 0 0

0 0 0 0.57143 1.14286 0 0 0 0 0 0

0 0 0 0 0 1.000 0.500 0 0 0 0

0 0 0 0 0 0.500 1.000 0 0 0 0

0 0 0 0 0 0 0 0.8 0.4 0 0

0 0 0 0 0 0 0 0.4 0.8 0 0

0 0 0 0 0 0 0 0 0 1.000 0.500

0 0 0 0 0 0 0 0 0 0.500 1.000

d18 d19 d20 d21 d22 d23 d24 d25 d26 d27 d28


51/84


52/84


53/84


54/84


55/84


56/84

0 0 0 1 0.5 0 0 0 0 1.14286 0.57143 0 0 0 0 0 0 0

0 0 0 0.5 1 0.8 0.4 0 0 0 0 1.14286 0.57143 0 0 0 0 0

1.14286 0 0 0 0 0.4 0.8 1 0.5 0 0 0.57143 1.14286 0 0 0 0 0

0 0.57143 1.14286 0 0 0 0 0.5 1 0 0 0 0 0 0 1.14286 0.57143 0

0 0 0 0 0 0 0 0 0 0.57143 1.14286 0 0 0 0 0 0 1

0 0 0 0 0 0 0 0 0 0 0 0.57143 1.14286 0.57143 1.14286 0 0 0.5


57/84

0 0 0 0 0 0 0 0 0 0 0 0 0 0.57143 1.14286 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.57143 1.14286 0


58/84


59/84


60/84


61/84


62/84


63/84

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0.8 0.4 0 0


64/84

0.4 0.8 1 0.5

0 0 0.5 1


65/84


66/84


67/84


68/84


69/84

No. "

1.6 #/

6

i j

3.51.4 #/

4

e f g h

3.5

a

4 5 4

► Derajat Ketidaktentuan Kinematis = '

8

5 6

7

1 2 3 4

► Perhitungan Momen Primer

Mij Mji

Mef Mhg

Mfe Mfg Mgf Mgh

Mef = -1/12 . 1.4 . 4 2 Mij = -5/96 . 1.6 . 5 2

= -1.867 = -2.083

Mfe = -Mef Mji = -Mij


70/84

= 1.867 = 2.083

Mfg = -1/12 . 1.4 . 5 2

= -2.917

Mgf = -Mfg

= 2.917

Mgh = -1/12 . 1.4 . 4 2= -1.867

Mhg = -Mgh

= 1.867


71/84

► Gaya luar yang ekivalen dititik yang koresponding dengan lendutan

Q8

Q5 Q6

Q7

Q1 Q2 Q3 Q4

Q1 = -1.867

[ Q ] =

-1.9

Q2 = -1.050 -1.1

Q3 = 1.050 1.050

Q4 = 1.867 1.867

Q5 = -2.083 -2.083

Q6 = 2.083 2.083

Q7 = 4.000 4.000

Q8 = 6.000 6.000

► Diuat statis tertentu dengan 12 gaya redundant

+ J

$ & ( *

,

► Menentukan matriks statis tertentu akiat gaya luar 7Po8

! kia# ekeGjanHa Q1 = 1 Ia#;an

19 20

16 18

Q1 *1 = 1

9 10 15 17 13 14 *2 = -1


72/84

2 4 11 12 6 8

1 1 3 5 7


73/84


19 20

16 18

Q2 *3 = 1

9 10 15 17 13 14

*4 = -12 4 11 12 6 8

1 1 3 5 7


19 20

16 18

Q3 *5 = 1

9 10 15 17 13 14 *6 = -1

2 4 11 12 6 8

1 3 1 5 7


19 20

16 18

Q4 *7 = 1

9 10 15 17 13 14 *8 = -1

2 4 11 12 6 8

1 3 5 1 7


Q5 19 20

16 18

*3 = 1

9 10 15 17 13 14 *4 = -1

2 4 11 12 6 8 *15 = 1


74/84

*16 = -1

1 1 3 5 7


75/84


19 Q6 20

16 18

*5 = 1

9 10 15 17 13 14

*6 = -12 4 11 12 6 8 *17 = 1

*18 = -1

1 3 1 5 7


19 20

16 18

*1 = -3.5

Q7 9 10 15 17 13 14 *2 = 0

2 4 11 12 6 8

1 3 5 7


Q8 19 20

16 18

*3 = -7

9 10 15 17 13 14 *4 = 3.5

2 4 11 12 6 8 *15 = -3.5

*16 = 0

1 3 5 7

►

! kia# ekeGjanHa C1 = 1 Ia#;an

19 20

16 C1 18 *3 = -7

*4 = 3.5

Menentukan matriks statis akiat gaya redundant 7P18


76/84

*5 = 7

9 10 15 17 13 14 *6 = -3.5

2 4 11 12 6 8 *15 = -3.5

*16 = 0

*17 = 3.5

*18 = 01 3 5 7


77/84


19 20 *3 = -2.5

16 18 *4 = 2.5

C2 *5 = -2.5

*6 = 2.59 10 15 17 13 14 *15 = -2.5

2 4 11 12 6 8 *16 = 2.5

*17 = -2.5

*18 = 2.5

*19 = -2.5

1 3 5 7 *20 = -2.5


C3

19 20 *3 = 1

16 18 *4 = -1

*5 = -1

*6 = 1

9 10 15 17 13 14 *15 = 1

2 4 11 12 6 8 *16 = -1

*17 = -1

*18 = 1

*19 = 1

1 3 5 7 *20 = -1


19 20

16 18

9 10 15 17 13 14 *1 = -3.5

2 C4 4 11 12 6 8 *3 = 3.5

*2 = *4 = 0

1 3 5 7


19 20

16 18


78/84

C5 *1 = -2

9 10 15 17 13 14 *2 = 2

2 4 11 12 6 8 *3 = -2

*4 = 2

*9 = -2*10 = -2

1 3 5 7


19 20

16 18

*1 = 1

9 10 15 17 13 14 *2 = -1

2 4 11 12 6 8 *3 = -1

C6 *4 = 1

*9 = 1

*10 = -1

1 3 5 7


19 20

16 18

9 10 15 17 13 14 *3 = -3.5

2 4 11 C7 12 6 8 *5 = 3.5

*4 = *6 = 0

1 3 5 7


19 20

16 18

*3 = -2.5

9 10 15 17 13 14 *4 = 2.5

2 4 11 12 6 8 *5 = -2.5


79/84

C8 *6 = 2.5

*11 = -2.5

*12 = -2.5

1 3 5 7


19 20

16 18

*3 = 1

9 10 15 17 13 14 *4 = -1

2 4 11 12 6 8 *5 = -1

C9 *6 = 1

*11 = 1

*12 = -1

1 3 5 7


19 20

16 18

9 10 15 17 13 14 *5 = -3.5

2 4 11 12 6 C10 8 *7 = 3.5

*6 = *8 = 0

1 3 5 7


19 20

16 18

C11 *5 = -2

9 10 15 17 13 14 *6 = 2

2 4 11 12 6 8 *7 = -2

*8 = 2

*13 = -2

*14 = -2

1 3 5 7


80/84


19 20

16 18

*5 = 1

9 10 15 17 13 14 *6 = -1

2 4 11 12 6 8 *7 = -1

C12 *8 = 1

*13 = 1

*14 = -1

1 3 5 7


81/84

0.04803 0 0.05669 0.00525 "0.0132 "0.0142 "0.0653 0 0.01837 0.00525 0.0132

0 0.01711 0 0.00375 "0.0053 "0.0038 0 "0.0071 0 "0.0037 "0.0053

0.05669 0 0.14488 0.00252 "0.0063 "0.0068 "0.065 0 0.00883 0.00252 0.00634

0.00525 0.00375 0.00252 0.12414 "0.0502 0.06225 0.08511 0.01949 "0.0068 0.0399 0.02577

"0.0132 "0.0053 "0.0063 "0.0502 0.08081 0.02112 "0.0457 "0.0274 0.01713 "0.0258 "0.0164

"0.0142 "0.0038 "0.0068 0.06225 0.02112 0.19224 0.02549 "0.0199 0.01837 0.00539 0.00378

"0.0653 0 "0.065 0.08511 "0.0457 0.02549 0.28543 0 0 0.08511 0.04573

0 "0.0071 0 0.01949 "0.0274 "0.0199 0 0.05934 0 "0.0195 "0.0274

0.01837 0 0.00883 "0.0068 0.01713 0.01837 0 0 0.17617 "0.0068 "0.0171

0.00525 "0.0037 0.00252 0.0399 "0.0258 0.00539 0.08511 "0.0195 "0.0068 0.12414 0.05016

0.0132 "0.0053 0.00634 0.02577 "0.0164 0.00378 0.04573 "0.0274 "0.0171 0.05016 0.08081

"0.0142 0.00383 "0.0068 0.00539 "0.0038 0.00028 0.02549 0.01989 0.01837 0.06225 "0.0211

"0.006 "0.006 "0.003 "0.272 0.035 "0.068 "0.181 "0.033 0.008 "0.083 "0.054

"0.012 "0.007 "0.006 "0.163 0.140 "0.150 "0.117 "0.035 0.016 "0.057 "0.037

0.026 0.002 0.013 0.076 "0.013 0.064 "0.239 0.012 "0.034 "0.095 "0.062

0.052 0.011 0.025 0.043 0.044 0.114 "0.233 0.056 "0.068 "0.082 "0.054

"0.026 0.002 "0.013 0.095 "0.062 0.012 0.239 0.012 0.034 "0.076 "0.013

"0.052 0.011 "0.025 0.082 "0.054 0.009 0.233 0.056 0.068 "0.043 0.044

0.006 "0.006 0.003 0.083 "0.054 0.011 0.181 "0.033 "0.008 0.272 0.035

0.012 "0.007 0.006 0.057 "0.037 0.008 0.117 "0.035 "0.016 0.163 0.140

0.012 0.007 0.006 0.163 "0.140 0.150 0.117 0.035 "0.016 0.057 0.037

0.041 0.014 0.019 0.038 "0.183 "0.234 0.066 0.075 "0.053 0.046 0.029

0.018 0.018 0.009 "0.056 0.086 0.068 0.004 "0.148 0.176 0.042 0.051

"0.018 0.018 "0.009 "0.042 0.051 0.031 "0.004 "0.148 "0.176 0.056 0.086

"0.041 0.014 "0.019 "0.046 0.029 "0.007 "0.066 0.075 0.053 "0.038 "0.183

"0.012 0.007 "0.006 "0.057 0.037 "0.008 "0.117 0.035 0.016 "0.163 "0.140"0.111 "0.043 "0.054 "0.025 0.053 0.052 0.164 0.018 "0.055 "0.006 "0.027

"0.057 0.043 "0.145 0.007 "0.007 "0.003 0.065 "0.018 "0.009 "0.012 "0.020

0.111 "0.043 0.054 0.006 "0.027 "0.033 "0.164 0.018 0.055 0.025 0.053

0.057 0.043 0.145 0.012 "0.020 "0.016 "0.065 "0.018 0.009 "0.007 "0.007

0.057 "0.043 0.145 "0.007 0.007 0.003 "0.065 0.018 0.009 0.012 0.020

"0.057 "0.043 "0.145 "0.012 0.020 0.016 0.065 0.018 "0.009 0.007 0.007

[F1]"1=

[!1][F1]"1


82/84

[!] =

"0.183 0.089 0.049 0.093 0.006 0.021 "0.459 "0.603

"0.487 0.113 0.033 0.065 "0.001 0.029 "0.316 "0.469

0.146 "0.111 0.060 0.106 0.027 "0.036 "0.525 "0.472

0.170 "0.287 0.054 0.090 0.041 "0.085 "0.449 "0.206

0.106 0.060 "0.111 0.146 "0.036 0.027 "0.525 "0.472

0.090 0.054 "0.287 0.170 "0.085 0.041 "0.449 "0.206

0.093 0.049 0.089 "0.183 0.021 0.006 "0.459 "0.603

0.065 0.033 0.113 "0.487 0.029 "0.001 "0.316 "0.469

"0.513 "0.113 "0.033 "0.065 0.001 "0.029 0.316 0.469

"0.225 "0.287 "0.024 "0.053 0.019 "0.079 0.258 0.583

0.022 "0.251 "0.131 "0.006 "0.015 "0.059 0.160 0.559

"0.006 "0.131 "0.251 0.022 "0.059 "0.015 0.160 0.559

"0.053 "0.024 "0.287 "0.225 "0.079 0.019 0.258 0.583

"0.065 "0.033 "0.113 "0.513 "0.029 0.001 0.316 0.469

0.034 "0.175 0.102 "0.031 "0.045 0.223 0.031 "0.9360.004 0.015 0.059 "0.007 "0.451 0.273 "0.031 "0.814

"0.031 0.102 "0.175 0.034 0.223 "0.045 0.031 "0.936

"0.007 0.059 0.015 0.004 0.273 "0.451 "0.031 "0.814

"0.004 "0.015 "0.059 0.007 "0.549 "0.273 0.031 0.814

0.007 "0.059 "0.015 "0.004 "0.273 "0.549 0.031 0.814

MATRIKS STATIS [!] = [!0] " [!1].[F1]"1.[F0]


83/84

"0.0142

0.00383

"0.0068

0.00539

"0.0038

0.00028

0.02549

0.01989

0.01837

0.06225

"0.0211

0.19224

"0.011

"0.008

"0.012

"0.009

"0.064

"0.114

0.068

0.150

0.008

0.007

"0.031

"0.068

0.234

"0.1500.033

0.016

"0.052

0.003

"0.016

"0.003


84/84

Documents

Anstruk II 2.xlsx