7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
1/70
CONTOH 4.2
Properties penampang
Batang 1 (KOLOM) :
b1 = 0.35 m
h1 = 0.35 m
A1 = 0.1225 m2
I1 = 0.0012505208 m4
L1 = 3.5 m
Batang 2 (BALOK) :
b2 = 0.20 m
h2 = 0.45 m
A2 = 0.09 m2
I2 = 0.00151875 m4
L2 = 5 mBahan / mate!a" :
# = 21000000 $%/m2
&!t'ng mat!$ $e$a$'an batang 1 (M1)
A$!bat *!+"a,ement aah 1 -- 1 (tan"a! aah b "$a" 1)
M 1.1 = #.A / L = 735000
M 2.1 = 0 = 0
M 3.1 = 0 = 0
A$!bat *!+"a,ement aah 2 -- 2 (tan"a! aah b "$a" 2)
M 1.2 = 0 = 0
M 2.2 = 12.#I/L3 = 7350
M 3.2 = .#I / L2 = 1282.5
A$!bat *!+"a,ement aah 3 -- 3 (ta! aah b "$a" 3)
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
2/70
M 1.3 = 0 = 0
M 2.3 = .#I / L2 = 1282.5
M 3.3 = 4 #I / L = 30012.5
A$!bat *!+"a,ement aah 4 -- 4 (tan"a! aah b "$a" 4)
M 1.4 = - #.A / L = -735000
M 2.4 = 0 = 0
M 3.4 = 0 = 0
A$!bat *!+"a,ement aah 5 -- 5 (tan"a! aah b "$a" 5)
M 1.5 = 0 = 0
M 2.5 = -12.#I/L3 = -7350
M 3.5 = -.#I / L2 = -1282.5
A$!bat *!+"a,ement aah -- (ta! aah b "$a" )
M 1. = 0 = 0
M 2. = .#I / L2 = 1282.5
M 3. = 2 #I / L = 1500.25
''nan mat!$ $e$a$'an batang 1 (M1) :
M11 M12 M13 M14
M21 M22 M23 M24
M1 = M31 M32 M33 M34
M41 M42 M43 M44
M51 M52 M53 M54
M1 M2 M3 M4
'*'t batang 1 : = 90
Mat!$ tanma! ta! :
0 0
= 0 0
0 0 1 0
0 0 0
0 0 0
0 0 0 0
1
, 1
!n 1
- !n 1
, 1
, 1
- !n 1
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
3/70
an+e mat!$ ta! 6
0.00 -1 0 0
= 1 0.00 0 0
0 0 1 0
0 0 0 0.000 0 0 1
0 0 0 0
Mat!$ $e$a$'an t'$t' mena*! :
0.00 -1.00 0.00 0.00
1.00 0.00 0.00 0.00
0.00 0.00 1.00 0.00M 1 = 0.00 0.00 0.00 0.00
0.00 0.00 0.00 1.00
0.00 0.00 0.00 0.00
4.50242#-011 -7350 -1282.5 -4.502#-011
735000 4.502#-013 7.8792#-013 -735000
0 1282.5 30012.5 0
-4.5024#-011 7350 1282.5 4.502#-011
-735000 -4.502#-013 -7.879#-013 735000
0 1282.5 1500.25 0
&!t'ng mat!$ $e$a$'an batang 2 (M2)
A$!bat *!+"a,ement aah 1 -- 1 (tan"a! aah b "$a" 1)
M 1.1 = #.A / L = 378000
M 2.1 = 0 = 0
M 3.1 = 0 = 0
A$!bat *!+"a,ement aah 2 -- 2 (tan"a! aah b "$a" 2)
M 1.2 = 0 = 0
M 2.2 = 12.#I/L3 = 301.8
M 3.2 = .#I / L2 = 754.5
A$!bat *!+"a,ement aah 3 -- 3 (ta! aah b "$a" 3)
M 1.3 = 0 = 0
M = . M .
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
4/70
M 2.3 = .#I / L2 = 754.5
M 3.3 = 4 #I / L = 25515
A$!bat *!+"a,ement aah 4 -- 4 (tan"a! aah b "$a" 4)
M 1.4 = - #.A / L = -378000
M 2.4 = 0 = 0
M 3.4 = 0 = 0
A$!bat *!+"a,ement aah 5 -- 5 (tan"a! aah b "$a" 5)
M 1.5 = 0 = 0
M 2.5 = -12.#I/L3 = -301.8
M 3.5 = -.#I / L2 = -754.5
A$!bat *!+"a,ement aah -- (ta! aah b "$a" )
M 1. = 0 = 0
M 2. = .#I / L2 = 754.5
M 3. = 2 #I / L = 12757.5
''nan mat!$ $e$a$'an batang 2 (M2) :
M11 M12 M13 M14
M21 M22 M23 M24
M2 = M31 M32 M33 M34
M41 M42 M43 M44
M51 M52 M53 M54
M1 M2 M3 M4
'*'t batang 2 : = 0
Mat!$ tanma! ta! :
0 0
= 0 0
0 0 1 0
0 0 0
0 0 00 0 0 0
2
, 1
!n 1
- !n 1
, 1
, 1
- !n
1
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
5/70
an+e mat!$ ta! 6
1.00 0 0 0
= 0 1.00 0 0
0 0 1 0
0 0 0 1.00
0 0 0 0
0 0 0 0
Mat!$ $e$a$'an t'$t' mena*! :
1.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00
0.00 0.00 1.00 0.00
M 2 = 0.00 0.00 0.00 1.000.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
378000 0 0 -378000
0 301.8 754.5 0
0 754.5 25515 0
-378000 0 0 378000
0 -301.8 -754.5 0
0 754.5 12757.5 0
Susun MATRIKS KEKAKUAN STRUKTUR
1
1 2 3 7
7350 0 -1283 -7350
0 735000 0 0
M 1 = -1283 0 30013 1283
-7350 0 1283 7350
0 -735000 0 0
-1283 0 1500 1283
1 2 3
7 8 9 4
378000 0 0 -378000
0 302 755 0
M 2 = 0 755 25515 0
-378000 0 0 378000
0 -302 -755 0
0 755 12758 0
MATRIKS KEKAKUAN STRUKTUR
M = . M .
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
6/70
1 2 3
7 8 9
385350 0 1283 7
M = 0 73802 755 8
1283 755 55528 9
Batang 1
Gbr AM 1 =
Batang 2
Gbr AM 2 =
Transformasi dari sumbu lokal ke sumbu global struktur
Batang 1
0 1
0 2
AM 1 = 0 3
0 4
0 5
0 6
SB LOKAL
0.00 -1.00 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
Hitung rekasi di ujung batang / freebody (AML) --- Beban dimasukkan ke!uali beban di joint
AML1
AML2
AML3
AML4
AML5
AML6
AML1
AML2
AML3
AML4
AML5AM
L6
RT
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
7/70
0.00 0.00 0.00 1.00
0.00 0.00 0.00 0.00
0 2 1
0 1 2
= 0 3 30 5 7 D1
0 4 8 D2
0 9 D3
SB GLOBAL
Batang 2
0 1 7
150 2 8AM 2 = 125 3 9
0 4 4
150 5 5
-125 6
SB LOKAL
1.00 0.00 0.00 0.00
0.00 1.00 0.00 0.00= 0.00 0.00 1.00 0.00
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 1 7 D1
150 2 8 D2
= 125 3 9 D3
0 4 4150 5 5
-125 6
SB GLOBAL
BEBAN EKIVALEN GABNGAN !AE"
B 1 B 2
1 0 0
2 0 0
3 0 0
4 0 0
5 0 150
AMS1
RT
AMS2
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
8/70
-A# = 0 ; -125
1 7 0 0
2 8 0 150
3 9 0 125
SB GLOBAL
B#b$% &$'$ ()*%+ ,$%/% !A("
1 0
2 0
3 0
4 0
A = 5 0
0
1 7 40
2 8 03 9 0
SB GLOBAL
BEBAN OINT GABNGAN !A"
A = A( AE
1 0 0
2 0 0
3 0 04 0 0
A, = 5 0 ; -150 =
0 125
7 40 0
8 0 -150
9 0 -125
1 402 -150
3 -125
"#$%&MA' 'T&*T&
&!t'ng +e+!n*ahan
2.1529#-00 .292#-009 -.07#-007
= .29192#-009 1.357#-00 -1.885#-007 'at!n:
ea,t!n A++"!e*
40 ; 0
0 ; -1500 ; -125
&1 ; 0 =
E1 ; 0
M1 ; 0
&3 ; 0
E3 ; -150
M3 ; 125
an*a (;) (-) *!tent'$an "eh aa
THEOR10
1
2
1=
2=
eF!te 1: $G*1=1-$G*2
*1=!nee($)G(1-$G*2)
!+"a,ement: '2 = 0.0001795029
2 = -0.000179714
+h!2 = -0.002279435
ea,t!n: &1 = 0
E1 = 0
M1 = 0
&3 = 0
E3 = 150M3 = -125
ata' 27.852077784
132.089777923
-31.724472274
-7.852077785
17.910222077
-155.3089103
ata' 27.852077784
132.089777923
-31.724472274
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
44/70
-7.852077785
17.910222077
-155.3089103
ata' 27.852077784
132.089777923
-31.724472274-7.852077785
17.910222077
-155.3089103
Ata'
Bent'$ mat!$ A, *ah'"' : 1
2
A/ A3 Ae A = 3
4
5
7
8
9
b g"ba"
0.0001795029m
*! = -0.000179714 m
-0.002279435 a*
0 27.852077784
0 132.089777923
0 ; -31.724472274 =
ea,t = 0 -7.852077785
150 17.910222077
-125 -30.308910357
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
45/70
@atatan a = %/m2
Batang 2 :
0.20
0.45
9.00#-02
# = 2.10#;07
1.52#-03
5
0
E!emen "a!am matri#s #e#a#uan atang
12.EI L>3 EA L 4.EI L
7.35#;03 3.78#;05 2.55#;04
.#I / L2 12.#I / L3 theta
1.29#;04 7.35#;03 90 *eg7.5#;03 3.0#;03 0 *eg
AM SUM$U STRUKTUR)*(O$A(
12.#I / L3
7.35#;03
b2=
h2=
A2=
I2=
L2=
theta2=
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
46/70
'2 2 +h!2 ,e$ :
-7350 -4.45739#-011 -1282.5 7350
-4.45739#-011 -735000 7.88#-13 0
1.29#;04 -7.87923#-013 1.50#;04 -1283
7.35#;03 4.45739#-011 1.29#;04 -7350
4.45739#-011 7.35#;05 -7.87924#-013 01.29#;04 -7.87923#-013 3.00#;04 -1283
AM SUM$U STRUKTUR)*(O$A(
12.#I / L3
3.0#;03
'3 3 +h!3 ,e$ :
-378000 0 0 378000
0 -301.8 7.5#;03 0
0.00#;00 -754.5 1.28#;04 0
3.78#;05 0 0.00#;00 -378000
0 3.0#;03 -754.5 0
0.00#;00 -754.5 2.55#;04 0
0 0 0 0 0 0
'1 1 +h!1 '3 3 +h!3
-7350 -4.45739#-011 1282.5 -378000 0 0
-4.45739#-011 -735000 -7.87924#-013 0 -301.8 754.5
-1282.5 7.87923#-013 1500.25 0 -754.5 12757.5
7350 4.45739#-011 -1282.5 0 0 0
4.45739#-011 735000 7.87923#-013 0 0 0
-1282.5 7.87923#-013 30012.5 0 0 00 0 0 378000 0 0
0 0 0 0 301.8 -754.5
0 0 0 0 -754.5 25515
6K < C*D
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
47/70
H,e ! a,t!ng *FnFa*
'2 2 +h!2 '1 1
'2 385350 4.45739#-011 1282.5 -7350 -4.45739#-011
2 4.45739#-011 73801.8 754.5 -4.45739#-011 -735000+h!2 1282.5 754.5 55527.5 -1282.5 7.87923#-013
'1 -7350 -4.45740#-011 -1282.5 7350 4.45739#-011
1 -4.45739#-011 -735000 7.879#-013 4.45739#-011 735000
+h!1 1282.5 -7.87924#-013 1500.25 -1282.5 7.87923#-013
'3 -378000 0 0 0 0
3 0 -301.8 -754.5 0 0
+h!3 0 754.5 12757.5 0 0
b g"ba"
= $ $ G *1
$ $ *2
$G*1;$G*2
$G*1;$G*2
m
m
a*
; 27.852077784 = 27.8520778 $%
; 132.089777923 = 132.089778 $%
; -31.724472274 = -31.7244723 $%.m
; -7.852077785 = -7.8520778 $%
; 17.910222077 = 17.910222 $%; -30.308910357 = -155.30891 $%.m
-
-
-
-
-
-
-
-
-
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
48/70
-
-
-
-
-
--
-
-
0 1 0
0 2 0
0 -Ae = 3 0
40 4 0
0 5 150
0 125
0 7 0
0 8 150
0 9 -125
b g"ba"
@e$:
-
-
-
@e$:
27.852077784 $% &1 -
132.089777923 $% E1 -
-31.724472274 $%.m M1 -
-7.852077785 $% &3 -
17.910222077 $% E3 -
-155.3089103 $%.m M3 -
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
49/70
m
m
m2
$%/m2
m4
m
*egee
2.EI L 6.EI L>2 12.EI L>3
1.28#;04 7.5#;03 3.0#;03
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
50/70
0 -1283 -7350 0 -1283
735000 0 0 -735000 0
0 30013 1283 0 1500
0 1283 7350 0 1283
-735000 0 0 735000 00 1500 1283 0 30013
0 0 -378000 0 0
302 755 0 -302 755
755 25515 0 -755 12758
0 0 378000 0 0
-302 -755 0 302 -755
755 12758 0 -755 25515
,e$ :
*1 385350 4.45740#-011 1282.5
*2 4.45739#-011 73801.8 754.5
*3 1282.5 754.5 55527.5
0
0
00
0
0
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
51/70
+h!1 '3 3 +h!3
1282.5 -378000 0 0 '2
-7.87923#-013 0 -301.8 754.5 21500.25 0 -754.5 12757.5 +h!2
-1282.5 0 0 0 < 0
7.87923#-013 0 0 0 0
30012.5 0 0 0 0
0 378000 0 0 0
0 0 301.8 -754.5 0
0 0 -754.5 25515 0
,e$:
0.000179503
-0.000179714
-0.00227944
,e$:
132.09
-27.85
-31.72
-7.85
17.91-155.31
b "$a"
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
52/70
0 0 1
0 0 2
Ae = 0 A, = 0 3
0 40 4
-150 -150 5
-125 -125
0 0 7
-150 -150 8
125 125 9
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
53/70
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
54/70
- - - - - -
- - - - - -
- - - - - -
- - - - - -
- - - - - -- - - - - -
- - - - - -
- - - - - -
- - - - - -
- - - - - -
- - - - - -
- - - - - -
385350 0 1283 - - -
0 73802 755 - - -
1283 755 55528 - - -
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
55/70
-
-
-
27.8520778 -
132.09 -
-31.72 -
-7.85 -
17.91 --155.31 -
b g"ba"
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
56/70
40 *1 4
-150 *2 5
A, = -125 *3
*1 0 1
*2 0 2
*3 0 3
0 7
-150 8
125 9
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
57/70
Properties penampang
Bahan / mate!a" :
# = 2.10#;07 $%/m2
Batang 1 :
0.35m
0.35m
1.23#-01 m2
# = 2.10#;07 $%/m2
1.25#-03 m4
3.5m
90 *egee
E!emen "a!am matri#s #e#a#uan atang
EA L 4.EI L 2.EI L 6.EI L>2
7.35#;05 3.00#;04 1.50#;04 1.29#;04
Re#ap E!emen "a!am Matri#s Ke#a#uan $atangBatang #A / L 4.#I / L 2.#I / L
1 7.35#;05 3.00#;04 1.50#;04
2 3.78#;05 2.55#;04 1.28#;04
%%%& su"a' DA(
u1 v1 phi1
u1 7350 0 -12862.5
v1 0 735000 0
phi1 -12862.5 0 30012.5
u2 -7350 0 12862.5
b1=
h1=
A1=
I1=
L1=
theta1=
Hitung matri#s #e#a#uan atang + ,SM+-
6M1 =
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
58/70
v2 0 -735000 0
phi2 -12862.5 0 15006.25
%%%& su"a' DA(
u2 v2 phi2
u2 378000 0 0
v2 0 3061.8 7654.5
phi2 0 7654.5 25515
u3 -378000 0 0
v3 0 -3061.8 -7654.5
phi3 0 7654.5 12757.5
u2 v2 phi2u2 385350 0 12862.5
v2 0 738061.8 7654.5
phi2 12862.5 7654.5 55527.5
u1 -7350 0 -12862.5
v1 0 -735000 0
phi1 12862.5 0 15006.25
u3 -378000 0 0
v3 0 -3061.8 -7654.5
phi3 0 7654.5 12757.5
Hitung matri#s #e#a#uan atang 2 ,SM2-
6M2 =
MATRIKS KEKAKUAN STRUKTUR ,SMS-
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
59/70
@atatan a = %/m2
Batang 2 :
# =
E!emen "a!am matri#s #e#a#ua
12.EI L>3 EA L
7.35#;03 3.78#;05
.#I / L2 12.#I / L3 theta
1.29#;04 7.35#;03 90 *eg
7.5#;03 3.0#;03 0 *eg
M SUM$U STRUKTUR)*(O$A(
u2 v2 phi2
-7350 0 -12862.5 7350
0 -735000 0 4.45740E-011
12862.5 0 15006.25 -12862.5
7350 0 12862.5 -7350
b2=
h2=
A2=
I2=
L2=
theta2=
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
60/70
0 735000 0 -4.4574E-011
12862.5 0 30012.5 -12862.5
M SUM$U STRUKTUR)*(O$A(
u3 v3 phi3 u2
-3.78E+05 0 0 378000
0 -3061.8 7654.5 0
0 -7654.5 12757.5 0
3.78E+05 0 0 -378000
0 3061.8 -7654.5 0
0 -7654.5 25515 0
u1 v1 phi1 u3 v3-7350 0 12862.5 -378000 0
0 -735000 0 0 -3061.8
-12862.5 0 15006.25 0 -7654.5
7350 0 -12862.5 0 0
0 735000 0 0 0
-12862.5 0 30012.5 0 0
0 0 0 378000 0
0 0 0 0 3061.8
0 0 0 0 -7654.5
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
61/70
0.20m
0.45m
9.00#-02m2
2.10#;07$%/m2
1.52#-03m4
5 m
0 *egee
atang
4.EI L 2.EI L 6.EI L>2 12.EI L>3
2.55#;04 1.28#;04 7.5#;03 3.0#;03
4.45740E-011 -12862.5 -7350 -4.4574E-011 -12862.5
735000 7.87924E-013 -4.4574E-011 -735000 7.88E-013
7.87924E-013 30012.5 12862.5 -7.8792E-013 15006.25
-4.4574E-011 12862.5 7350 4.45740E-011 12862.5
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
62/70
-735000 -7.8792E-013 4.45740E-011 735000 -7.9E-013
7.87924E-013 15006.25 12862.5 -7.8792E-013 30012.5
v2 phi2 u3 v3 phi3
0 0 -378000 0 0
3061.8 7654.5 0 -3061.8 7654.5
7654.5 25515 0 -7654.5 12757.5
0 0 378000 0 0
-3061.8 -7654.5 0 3061.8 -7654.5
7654.5 12757.5 0 -7654.5 25515
phi30
7654.5
12757.5
0
0
0
0
-7654.5
25515
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
63/70
- -4.45740E-011 - - 4.46E-011 -
-4.45740E-011 - -7.8792360E-013 4.46E-011 - -7.9E-013
- -7.87924E-013 - - 7.88E-013 -
- 4.457396E-011 - - -4.5E-011 -
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
64/70
4.457396E-011 - 7.8792360E-013 -4.5E-011 - 7.88E-013
- -7.87924E-013 - - 7.88E-013 -
- - - - - -
- - - - - -
- - - - - -
- - - - - -
- - - - - -
- - - - - -
385350 4.457396E-011 12862.5 -7350 -4.5E-011 12862.5
4.457396E-011 738061.8 7654.5 -4.5E-011 -735000 -7.9E-013
12862.5 7654.5 55527.5 -12862.5 7.88E-013 15006.25
-7350 -4.45740E-011 -12862.5 7350 4.46E-011 -12862.5
-4.45740E-011 -735000 7.8792360E-013 4.46E-011 735000 7.88E-013
12862.5 -7.87924E-013 15006.25 -12862.5 7.88E-013 30012.5
-378000 0 0 0 0 0
0 -3061.8 -7654.5 0 0 0
0 7654.5 12757.5 0 0 0
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
65/70
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
66/70
-378000 0 0 - -4.457396E-011
0 -3061.8 7654.5 -4.45740E-011 -
0 -7654.5 12757.5 - -
0 0 0 - 4.4573964E-011
0 0 0 4.457396E-011 -
0 0 0 - 7.8792360E-013
378000 0 0 - -
0 3061.8 -7654.5 - -
0 -7654.5 25515 - -
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
67/70
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
68/70
- - 4.4573964E-011 - -
- 4.457396E-011 - 7.8792360E-013 -
- - -7.8792360E-013 - -
- - -4.4573964E-011 - -
-7.8792360E-013 -4.45740E-011 - -7.8792360E-013 -
- - -7.8792360E-013 - -
- - - - -
- - - - -
- - - - -
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
69/70
7/25/2019 Contoh Soal Analisa Matriks (Portal Hal.172)
70/70
- -
- -
- -
- -
- -
- -
- -
- -
- -
Top Related