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Analisa Truss Dengan Mengunakan Metode Elemen Hingga
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Analisa Truss Dengan Mengunakan Metode Elemen Hingga
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Author:
Irbar Alwi
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Kelompok 2
MATRIKS KEKAKUAN STRUKTUR
F1
ka11 + kb11
ka12
kb12
0
0
0
0
0
d1
F2
Ka21
ka22 + kc11 + kd11 + ke11
kc12
kd12
ke12
0
0
0
d2
F3
kb21
kc21
kb22 + kc22 + kf11
0
kf12
0
0
0
d3
F4
0
kd21
0
kd22 + kg11 + kh11
kg12
kh12
0
0
d4
F5
0
ke21
kf21
kg21
ke22 + kf22 + kg22 + ki11 + kj11
ki12
kj12
0
d5
F6
0
0
0
kh21
k i2 1
k h2 2 + k i2 2 + k k1 k1 1 + k l1 1
kk12
kl12
d6
F7
0
0
0
0
kj21
kk21
kj22 + kk22 + km11
km12
d7
F8
0
0
0
0
0
kl21
km21
kl22 + km22
d8
=
dikarenakan [Ka] = [Kd] = [Ki], maka
[K]
=
5 36 36 44 44 . 21 21 3
2 68 68 22 22 .0 .0 46 46
- 53 53 64 64 4. 4. 21 21 3
- 26 26 8 22 22 .0 .0 46 46
2 68 68 22 22 . 04 04 6
1 34 34 10 10 .9 .9 93 93
- 26 26 82 82 2. 2. 04 04 6
- 13 13 4 10 10 .9 .9 93 93
- 53 53 64 64 4. 4. 21 21 3
- 26 26 8 22 22 .0 .0 46 46
5 36 36 44 44 . 21 21 3
2 68 68 22 22 .0 .0 46 46
- 26 26 82 82 2. 2. 04 04 6
- 13 13 4 10 10 .9 .9 93 93
2 68 68 22 22 . 04 04 6
1 34 34 10 10 .9 .9 93 93
Kx11
Kx12
Kx21
Kx22
Kx11
Kx12
Kx21
Kx22
dikarenakan [Kb] = [Kf] = [Kj] = [Km], maka
[K]
=
74970. 00 000
0.000
-74970.000
0.000
0. 000
0.000
0. 000
0.000
-74970.000
0.000
74970. 00 000
0.000
0. 000
0.000
0. 000
0.000
TUGAS METODE ELEMENT HINGGA
Kelompok 2
dikarenakan [Ke] = [Kh] = [Kl] , maka
[K]
=
5 36 36 44 44 . 21 21 3
- 26 26 8 22 22 .0 .0 46 46
- 53 53 64 64 4. 4. 21 21 3
2 68 68 22 22 .0 .0 46 46
- 26 26 82 82 2. 2. 04 04 6
1 34 34 10 10 .9 .9 93 93
2 68 68 22 22 . 04 04 6
- 13 13 4 10 10 .9 .9 93 93
- 53 53 64 64 4. 4. 21 21 3
2 68 68 22 22 .0 .0 46 46
5 36 36 44 44 . 21 21 3
- 26 26 8 22 22 .0 .0 46 46
2 68 68 22 22 . 04 04 6
- 13 13 4 10 10 .9 .9 93 93
- 26 26 82 82 2. 2. 04 04 6
1 34 34 10 10 .9 .9 93 93
Kx11
Kx12
Kx21
Kx22
Kx11
Kx12
Kx21
Kx22
Kx11
Kx12
Kx21
Kx22
dikarenakan [Kc] = [Kk] , maka
[K]
=
0. 000
0.000
0. 000
0.000
0 .0 .0 00 00
1 49 49 94 94 0. 0. 00 00 0
0 .0 .0 00 00
- 14 14 99 99 40 40 .0 .0 00 00
0. 000
0.000
0. 000
0.000
0 .0 .0 00 00
- 14 14 99 99 40 40 .0 .0 00 00
0 .0 .0 00 00
1 49 49 94 94 0. 0. 00 00 0
matriks kekakuan untuk batang [Kg] , ialah
[K]
=
0. 000
0.000
0. 000
0.000
0. 00 000
74970.000
0. 00 000
-749 70 70.000
0. 000
0.000
0. 000
0.000
0. 00 000
-749 70 70.000
0. 00 000
74970.000
TUGAS METODE ELEMENT HINGGA
Kelompok 2
H1
128614. 213
2 6822. 046 26
-53644.213
-26822. 046
-74970.000 -7
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0.000
0.000
0.000
0.000
V1
26822.046
13410. 993 13
-26822.046
-13410. 993
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0.000
0.000
0.000
0.000
0 0
0
-53644 -53 644.21 .213 3
-26822 -26 822.04 .046 6
160932. 638
26822. 046
0.000
0. 000
- 53 53644.213
- 26 26822.046
- 53 53644.213
26822.046
0. 000
0.000
0.000
0.000
0.000
0.000
U2
-3000
-26822 -26 822.04 .046 6
-13410 -13 410.99 .993 3
26822.046
19 190172.980
0.000
-149940.000
-26822.046
-13410.993
26822.046
-13410.993
0. 000
0.000
0.000
0.000
0.000
0.000
V2
H3
- 74 74 97 97 0. 0. 00 00 0
0 .0 .0 00 00
0. 000
0.000
149940.000
0. 000
0. 000
0. 000
-74970.000
0. 000
0. 000
0.000
0.000
0.000
0.000
0.000
U3
V3
0. 000
0.000
0. 000
-149940.000
0.000
149940.000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0.000
0.000
0.000
0.000
V3
0
0. 000
0.000
-53644.213
-2 -26822. 046
0.000
0. 000
10 107288.425
0. 000
0. 000
0. 000
- 53 53644.213
26822. 046
0.000
0.000
0.000
0.000
U4
-3000
0. 000
0.000
-26822.046
- 13 13410. 993
0.000
0. 000
0. 000
10 101791.987
0. 000
-74970.000
26822.046
- 13410. 993
0.000
0.000
0.000
0.000
V4
H5
0. 000
0.000
-53644.213
26822. 046
-74970.000
0. 00 000
0. 00 000
0. 00 000
2 57 57228.425
0. 00 000
-53644.213
- 26 26822. 04 046
- 74 74970. 00 000
0.000
0.000
0.000
U5
V5
0. 000
0.000
26822.046
- 13 13410. 993
0.000
0. 000
0. 000
-74970.000
0. 000
10 101791. 987
-26822.046
- 13410. 993
0.000
0.000
0.000
0.000
V5
0
0. 000
0.000
0. 00 000
0.000
0.000
0. 00 000
-53644.213
26822.046
-53644.213
-26822.046
16 160932. 63 638
- 26 26822. 04 046
0.000
0.000
-53644 -53 644.213 .213
26822.0 268 22.046
U6
-3000
0. 000
0.000
0. 00 000
0.000
0.000
0. 00 000
26822.046
-13410.993
-26822.046
-13410.993
-26822.046
190172. 98 980
0.000
- 14 149940. 00 000
26822.0 268 22.046 46
-13410 -13 410.99 .993 3
V6
H7
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
-74970.000
0. 000
0. 000
0.000
149940. 000
0.000
- 74 74 97 97 0. 0. 00 00 0
0 .0 .0 00 00
U7
V7
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
- 149940. 000
0.000
149940. 000
0.000
0.000
V7
H8
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
- 53644.213 -5
26822. 046
- 74970. 000 -7
0.000
128614.213
- 26822. 046 -2
0
V8
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
26822.046
-13410. 993 -1
0.000
0.000
-26822. 046 -2
13410. 993
0
SYARAT BATAS U1
=
0
U2
=
Berpindah
U3
=
Berpindah
U4
=
B erpindah
U5
=
Berpindah
V1
=
0
V2
=
Berpindah
V3
=
Berpindah
V4
=
B erpindah
V5
=
Berpindah
U6
=
Berpindah
U7
=
B erpindah
U8
=
0
V6
=
Berpindah
V7
=
Be B erpindah
V8
=
0
TUGAS METODE ELEMENT HINGGA
Kelompok 2
Maka Matriks menjadi 0 -3000 H3
U2
160932. 638
26822. 046
0. 000
0.000
-5 -53644.213
-2 -26822.046
-5 -53644.213
26822.046
0. 000
0. 000
0. 000
0.000
26822.046
19 190172.980
0. 000
-149940.000
-26822.046
-13410.993
26822.046
-13410.993
0. 000
0. 000
0. 000
0.000
V2
0. 000
0.000
149940. 000
0.000
0.000
0. 000
-74970.000
0. 000
0. 000
0. 000
0. 000
0.000
U3
0. 000
-149940.000
0. 000
149940.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
V3
-53644.213
-26822. 046
0. 000
0.000
107288.425
0. 000
0. 000
0. 000
-5 -53644.213
26822.046
0. 000
0.000
U4
-3000
-26822.046
-1 -13410. 993
0. 000
0.000
0.000
101791.987
0. 000
-7 -74970.000
26822.046
-1 -13410.993
0. 000
0.000
V4
H5
-53644.213
26822. 046
- 74 74970.000
0.000
0.000
0. 000
25 257228.425
0. 000
- 53 53644.213
-26822.046
-74970.000
0.000
U5
V5
26822.046
-1 -13410. 993
0. 000
0.000
0.000
-7 - 74970.000
0. 000
10 101791.987
- 26 26822.046
- 13 13410.993
0. 000
0.000
V5
0. 000
0.000
0. 000
0.000
-5 - 53644.213
26822.046
-5 - 53644.213
-2 - 26822.046
16 160932.638
-2 - 26822.046
0. 000
0.000
U6
V3 0
0 -3000
0. 000
0.000
0. 000
0.000
26822.046
-13410.993
-26822.046
-13410.993
-26822.046
1 90 90172. 980
0. 000
- 149940. 000
V6
H7
0. 000
0.000
0. 000
0.000
0.000
0. 000
-74970.000
0. 000
0. 000
0. 000
149940. 000
0.000
U7
V7
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
-149940. 000
0. 000
149940. 000
V7
Invers Matriks kekakuan struktur menjadi : U2
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0
V2
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
-3000
U3
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0
V3
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0
U4
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0
V4
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
-3000
U5
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0
V5
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0
U6
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
0
V6
0. 000
0.000
0. 000
0.000
0.000
0. 000
0. 000
0. 000
0. 000
0. 000
0. 000
0.000
-3000
U7
0.000
0. 000
0.000
0. 000
0. 000
0.00 0
0.000
0.000
0.000
0.000
0.000
0.000
0
V7
0.000
0. 000
0.000
0. 000
0. 000
0.00 0
0.000
0.000
0.000
0.000
0.000
0.000
0
TUGAS METODE ELEMENT HINGGA
Kelompok 2
PERPINDAHAN TITIK U2
=
0. 094
V2
=
-0.523
Cm Cm
U3
=
0. 000
Cm
V3
=
-0.523
Cm
U4
=
0. 000
Cm
V4
=
-0.559
Cm
U5
=
0. 000
Cm
V5
=
-0.599
Cm
U6
=
-0.094
Cm
V6
=
-0.523
Cm
U7
=
0. 000
Cm
V7
=
-0.523
Cm
MATRIKS REAKSI TUMPUAN S X1
=
128614.2 126
26822.0464
-53644.21258
-26822. 0464
-74970
0
0
0
0
0
0
0
0
0
0
0
0
S Y1
=
26822. 0464
13410.99325
- 26822.0464
-13410 .99325
0
0
0
0
0
0
0
0
0
0
0
0
0
S X2
=
-53644.21258
-26822. 0464
160932.6 377
26822.0464
-5.0 6381E-27
-2.75 548E-11
- 53644.21258
-26822.0464
-5 3644.21258
26822.0464
0
0
0
0
0
0
0.094
S Y2
=
- 26822.0464
-13410 .99325
26822. 0464
190172.9798
-2.7 5548E-11
-149940
-26822.0464
- 13410.99325
26822.0464
-13 410.99325
0
0
0
0
0
0
-0.523
S X3
=
-7 -74970
0
-5.06381E -27
-2. 75548E-1 1
149940
2. 75548E-1 1
0
0
-74970
0
0
0
0
0
0
0
0.000
S Y3
=
0
0
-2.75548E -11
- 149940
2 .75548E- 11
149940
0
0
0
0
0
0
0
0
0
0
-0.523
SX 4
=
0
0
-53644.21258
- 26822. 0464
0
0
107288. 4252
-2. 91038E -11
-2. 53191E -27
-1. 37774E -11
- 53644. 21258
26822.0464
0
0
0
0
0. 000
SY4
=
0
0
-26822.0464
- 13410. 99325
0
0
-2. 91038E-11
101791. 9865
-1. 37774E -11
-74970
26822.0464
- 13410. 99325
0
0
0
0
-0. 559
SX 5
=
0
0
-53644.21258
26822.0464
- 74970
0
-2. 53191E-27
-1. 37774E -11
257228. 4252
-2. 91038E -11
- 53644. 21258
-26822.0464
-74970
0
0
0
0. 000
SY5
=
0
0
26822. 0464
- 13410. 99325
0
0
-1. 37774E-11
-74970
-2. 91038E -11
101791.9865
-26822.0464
- 13410. 99325
0
0
0
0
-0. 599
SX 6
=
0
0
0
0
0
0
-53644.21258
26822. 0464
-53644.21258
-26822.0464
160932.6377
-26822.0464
-5.06381E- 27
-2.75548E- 11
-53644. 21258
26822. 0464
-0. 094
SY6
=
0
0
0
0
0
0
26822. 0464
-13410.99325
-26822.0464
-13410.99325
-26822.0464
190172.9798
-2.75548E- 11
- 149940
26822.0464
-13410.99325
-0. 523
SX 7
=
0
0
0
0
0
0
0
0
-74970
0
-5.06381E -27
-2.75548E- 11
149940
2.75548E -11
-74970
0
0. 000
SY7
=
0
0
0
0
0
0
0
0
0
0
-2.75548E -11
-149940
2. 75548E -11
149940
0
0
-0. 523
SX 8
=
0
0
0
0
0
0
0
0
0
0
- 53644. 21258
26822.0464
-7 -74970
0
128614.2126
-26822. 0464
0
SY8
=
0
0
0
0
0
0
0
0
0
0
26822.0464
- 13410. 99325
0
0
- 26822. 0464
13410.99325
0
TUGAS METODE ELEMENT HINGGA
Kelompok 2
REAKSI PADA SETIAP TITIK SIMPUL SX 1
=
9000.020
Kg
SY1
=
4500.000
Kg
SX 2
=
0.000
Kg
SY2
=
-3000.000
Kg
SX 3
=
0.000
Kg
SY3
=
0.000
Kg
SX 4
=
0.000
Kg
SY4
=
-3000.000
Kg
SX 5
=
0.000
Kg
SY5
=
0.000
Kg
SX 6
=
0.000
Kg
SY6
=
-3000.000
Kg
SX 7
=
0.000
Kg
SY7
=
0.000
Kg
SX 8
=
-9000.020
Kg
SY8
=
4500.000
Kg
∑SX ∑SY
= =
0.000 0.000
TUGAS METODE ELEMENT HINGGA
Kelompok 2
GAYA BATANG Batang a U1 V1 U2 V2 U1 V1 U2 V2 U1 V1 U2
=
=
=
S C 0 0
0 0 C -S -S
0 0 S C
x
0.894 -0.447
0.447 0.894
0.000 0.000
0.000 0.000
0.000 0.000
0.000 0.000
0.894 -0.447
0.447 0.894
1 -1
-1 -1 1
U1 U2
1
-1
0. 0.00000
-1
1
-0.15006
x
U1 V1 U2 V2 0.000000 0.000000 0.093890 -0.523326
0.00000 0.00000 -0.15006 -0.51007
V2 SX1 SX2
C -S 0 0
=
EA La
V8 SX1
SX1 SX2
=
67055.20 .206
→ 1
SX1 SX2
=
SX1 SX2
=
67055.20 .206
(-)
0 SX2 ←
a
2
0.1501 -0.1501
10062.324 Kg -10062.324 Kg
Batang b U1 V1 U3 V3
=
C -S 0 0
=
SX1 SX3
=
0 0 S C
x
0.000 1.000
0.000 0.000
0.000 0.000
0.000 0.000
0.000 0.000
1.000 0.000
0.000 1.000
EA
1
-1 -1
Lb
-1
1
U1 U3
1
-1
0. 0.00000
-1
1
0.00000
=
U1 V1 U3 V3
0 0 C -S -S
1.000 0.000
U1 V1 U3 V3
S C 0 0
x
U1 V1 U3 V3 0.000000 0.000000 0.000000 -0.523326
0.00000 0.00000 0.00000 -0.52333 V8 SX1
SX1 SX3
=
74970.00 .000
1 SX1 SX3
=
SX1 SX3
=
74970.00 .000
0 SX3
b
3
0.0000 0.0000
0.000 Kg 0.000 Kg
TUGAS METODE ELEMEN HINGGA
Kelompok 2
Batang c U2 V2 U3 V3
=
C -S
S C
0 0
0 0
0 0
0 0
C -S -S
S C
0.000 1.000 0.000 0.000
U2 V2 U3 V3
=
x
-1.000 0.000 0.000 0.000
0.000 0.000 0.000 1.000
0.000 0.000 -1.000 0.000
1 -1
-1 -1 1
U2 U3
1
-1
0. 0.52333
-1
1
0.52333
x
U2 V2 U3 V3 0.093890 -0.523326 0.000000 -0.523326
0.52333
U2 V2 U3 V3
=
SX2 SX3
=
0.09389 0.52333 0.00000 EA Lc
V8 SX2
SX2 SX3
=
1499 149940 40.0 .000 00
2 SX2 SX3 SX2 SX3
=
1499 149940 40.0 .000 00
0 SX3
c
3
0.0000 0.0000
0.000 Kg 0.000 Kg
=
Batang d U2 V2 U4
=
V4 U2 V2 U4 V4
=
U2 V2 U4 V4 SX2 SX4
C -S 0 0
=
=
S C 0 0
0 0 C -S -S
0 0 S C
x
U2 V2 U4 V4
0.894
0.447
0.000
0.000
0.093890
-0.447 0.000 0.000
0.894 0.000 0.000
0.000 0.894 -0.447
0.000 0.447 0.894
-0.523326 0.000000 -0.559243
1 -1
-1 -1 1
U2 U4
1
-1
-0.15006
-1
1
-0.25010
x
-0.15006 -0.51007 -0.25010 -0.50020 EA Ld
V8 SX2
SX2 SX4
=
67055.20 .206
→ 2
SX2 SX4
=
SX2 SX4
=
67055.20 .206
(-)
0 SX4 ←
d
4
0.1000 -0.1000
6708.216 Kg -6708.216 Kg
TUGAS METODE ELEMEN HINGGA
Kelompok 2
Batang e U2 V2 U5 V5 U2 V2 U5 V5
=
C -S
S C
0 0
0 0
0 0
0 0
C -S -S
S C
=
U2 V2 U5 V5
=
SX2 SX5
=
x
0.894 0.447 0.000
-0.447 0.894 0.000
0.000 0.000 0.894
0.000 0.000 -0.447
0.000
0.000
0.447
0.894
1 -1
-1 -1 1
U2 U5
1
-1
0. 0.31802
-1
1
0.26800
x
U2 V2 U5 V5 0.093890 -0.523326 0.000000 -0.599259
0.31802 -0.42609 0.26800 -0.53599 EA Le
V8 SX2
SX2 SX5
=
67055.20 .206
→ 2
SX2 SX5 SX2 SX5
=
67055.20 .206
(-)
0 SX5 ←
e
5
0.0500 -0.0500
=
3354.108 Kg -3354.108 Kg
U3
C
S
0
0
V3 U5 V5
=
-S 0
C 0
0 C
0 S
0
0
-S -S
C
Batang f
V5
1.000 0.000 0.000 0.000
U3 V3 U5 V5
-0.52333 0.00000 -0.59926
U3 V3 U5
SX3 SX5
=
U3 x
V3 U5 V5
0.000 1.000 0.000 0.000
0.000 0.000 1.000 0.000
0.000 0.000 0.000 1.000
1 -1
-1 -1 1
U3
1
-1
0. 0.00000
-1
1
0.00000
x
0.000000 -0.523326 0.000000 -0.599259
0.00000 =
=
EA Lf
V8
U5 SX3
SX3 SX5
=
74970.00 .000
3 SX3 SX5
=
SX3 SX5
=
74970.00 .000
0 SX5
f
5
0.0000 0.0000
0.000 Kg 0.000 Kg
TUGAS METODE ELEMEN HINGGA
Kelompok 2
Batang g U4 V4 U5 V5
=
C -S 0 0
S C 0 0
0 0 C -S -S
0 0 S C
x
U4 V4 U5 V5
U4
0.000
-1.000
0.000
0.000
0.000000
V4 U5 V5
1.000 0.000 0.000
0.000 0.000 0.000
0.000 0.000 1.000
0.000 -1.000 0.000
-0.559243 0.000000 -0.599259
1 -1
-1 -1 1
U4 U5
1
-1
0. 0.55924
-1
1
0.59926
U4 V4 U5 V5 SX4 SX5
=
0.55924 0.00000 0.59926 0.00000
=
=
x
EA Lg
V8 SX4
SX4 SX5
=
74970.00 .000
← 4
SX4 SX5
=
SX4 SX5
=
74970.00 .000
(+)
0 SX5 →
g
5
-0.0400 0.0400
-3000.000 Kg 3000.000 Kg
Batang h U4 V4 U6 V6 U4 V4 U6 V6
=
C -S 0 0
=
U4 V4 U6 V6
=
SX4 SX6
=
S C 0 0
0 0 C -S -S
0 0 S C
x
U4 V4 U6 V6
0.894
-0.447
0.000
0.000
0.000000
0.447 0.000 0.000
0.894 0.000 0.000
0.000 0.894 0.447
0.000 -0.447 0.894
-0.559243 -0.093890 -0.523326
1 -1
-1 -1 1
U4 U6
x
0.25010 -0.50020 0.15006 -0.51007 EA Lh
V8 SX4
SX4 SX6
=
67055.20 .206
1
-1
0. 0.25010
-1
1
0.15006
→ 4
SX4 SX6 SX4 SX6
=
=
67055.20 .206
(-)
0 SX6 ←
h
6
0.1000 -0.1000
6708.216 Kg -6708.216 Kg
TUGAS METODE ELEMEN HINGGA
Kelompok 2
Batang i U5 V5 U6 V6
=
C -S 0 0
S C 0 0
0 0 C -S -S
0 0 S C
x
U5 V5 U6 V6
U5
0.894
0.447
0.000
0.000
0.000000
V5 U6 V6
-0.447 0.000 0.000
0.894 0.000 0.000
0.000 0.894 -0.447
0.000 0.447 0.894
-0.599259 -0.093890 -0.523326
1 -1
-1 -1 1
U5 U6
1
-1
-0.26800
-1
1
-0.31802
U5 V5 U6 V6 SX5 SX6
=
=
=
x
-0.26800 -0.53599 -0.31802 -0.42609 EA Li
V8 SX5
SX5 SX6
=
67055.20 .206
→ 5
SX5 SX6
=
SX5 SX6
=
67055.20 .206
(-)
0 SX6 ←
i
6
0.0500 -0.0500
3354.108 Kg -3354.108 Kg
Batang j U5 V5 U7 V7 U5 V5 U7 V7
=
C -S 0 0
=
U5 V5 U7 V7
=
SX5 SX7
=
S C 0 0
0 0 C -S -S
0 0 S C
x
U5 V5 U7 V7
1.000
0.000
0.000
0.000
0.000000
0.000 0.000 0.000
1.000 0.000 0.000
0.000 1.000 0.000
0.000 0.000 1.000
-0.599259 0.000000 -0.523326
1 -1
-1 -1 1
U5 U7
x
0.00000 -0.59926 0.00000 -0.52333 EA Lj
V8 SX5
SX5 SX7
=
74970.00 .000
1
-1
0. 0.00000
-1
1
0.00000 5
SX5 SX7 SX5 SX7
=
=
74970.00 .000
0 SX7
j
7
0.0000 0.0000
0.000 Kg 0.000 Kg
TUGAS METODE ELEMEN HINGGA
Kelompok 2
Batang k U6 V6 U7 V7
=
C -S 0 0
S C 0 0
0 0 C -S -S
0 0 S C
x
U6 V6 U7 V7
U6
0.000
-1.000
0.000
0.000
-0.093890
V6 U7 V7
1.000 0.000 0.000
0.000 0.000 0.000
0.000 0.000 1.000
0.000 -1.000 0.000
-0.523326 0.000000 -0.523326
1 -1
-1 -1 1
U6 U7
1
-1
0. 0.52333
-1
1
0.52333
U6 V6 U7 V7 SX6 SX7
=
=
=
x
0.52333 -0.09389 0.52333 0.00000 EA Lk
V8 SX6
SX6 SX7
=
1499 149940 40.0 .000 00
6 SX6 SX7
=
SX6 SX7
=
1499 149940 40.0 .000 00
0 SX7
k
7
0.0000 0.0000
0.000 Kg 0.000 Kg
Batang l U6 V6 U8 V8 U6 V6 U8 V8
=
C -S 0 0
=
U6 V6 U8 V8
=
SX6 SX8
=
S C 0 0
0 0 C -S -S
0 0 S C
x
U6 V6 U8 V8
0.894
-0.447
0.000
0.000
-0.093890
0.447 0.000 0.000
0.894 0.000 0.000
0.000 0.894 0.447
0.000 -0.447 0.894
-0.523326 0.000000 0.000000
1 -1
-1 -1 1
U6 U8
x
0.15006 -0.51007 0.00000 0.00000 EA Ll
V8 SX6
SX6 SX8
=
67055.20 .206
1
-1
0. 0.15006
-1
1
0.00000
→ 6
SX6 SX8 SX6 SX8
=
=
67055.20 .206
(-)
0 SX8 ←
l
8
0.1501 -0.1501
10062.324 Kg -10062.324 Kg
TUGAS METODE ELEMEN HINGGA
Kelompok 2
Batang m U7 V7 U8 V8
=
C -S 0 0
S C 0 0
0 0 C -S -S
0 0 S C
U7 V7 U8 V8
x
U7
1.000
0.000
0.000
0.000
0.000000
V7 U8 V8
0.000 0.000 0.000
1.000 0.000 0.000
0.000 1.000 0.000
0.000 0.000 1.000
-0.523326 0.000000 0.000000
1 -1
-1 -1 1
U7 U8
1
-1
0. 0.00000
-1
1
0.00000
U7 V7 U8 V8 SX7 SX8
=
=
=
x
0.00000 -0.52333 0.00000 0.00000 EA Lm
V8 SX7
SX7 SX8
=
74970.00 .000
7 SX7 SX8
=
SX7 SX8
=
74970.00 .000
0 SX8
m
8
0.0000 0.0000
0.000 Kg 0.000 Kg
Tabel : Rekapitulasi Gaya pada Masing-masing Batang NAMA BATANG
GAYA BATANG
KETERANGAN
Batang a
-10062.3239
Batang b
0.0000
-
Batang c
0.0000
-
Batang d
-6708.2159
Tekan
Batang e
-3354.1080
Tekan
Batang f
0.0000
Batang g
3000.0000
Tarik
Batang h
-6708.2159
Tekan
Batang i
-3354.1080
Tekan
Batang j
0.0000
-
Batang k
0.0000
-
Batang l
-10062.3239
Batang m
0.0000
Tekan
-
Tekan -
TUGAS METODE ELEMEN HINGGA
Kelompok 2
TABLE: Joint Displacements Joint
OutputCase
Text 1 2 3 4 5 6 7 8
Text DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD
CaseType
Text LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic
U cm 0.000 0.093 0.001 0.000 0.000 -0.093 -0.001 0.000
V cm
0.000 -0.524 -0.523 -0.561 -0.600 -0.524 -0.523 0.000
TABLE: Element Forces Forces - Frames Frames Frame
Station
Text A A A B B B C C C D D D E E E F F F G G G H H H I I I J J J K K K L L L M M M
cm
Perhitungan Versi SAP2000
0 279.508 559.017 0 250 500 0 125 250 0 279.508 559.017 0 279.508 559.017 0 250 500 0 250 500 0 279.508 559.017 0 279.508 559.017 0 250 500 0 125 250 0 279.508 559.017 0 250 500
OutputCase
CaseType
Text
Text
DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD DEAD
LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic LinStatic
P
Kgf -9818.720 -9818.720 -9818.720 45.860 45.860 45.860 -57.210 -57.210 -57.210 -6500.360 -6500.360 -6500.360 -3186.970 -3186.970 -3186.970 -45.860 -45.860 -45.860 2812.800 2812.800 2812.800 -6500.360 -6500.360 -6500.360 -3186.970 -3186.970 -3186.970 -45.860 -45.860 -45.860 -57.210 -57.210 -57.210 -9818.720 -9818.720 -9818.720 45.860 45.860 45.860
V
M
Kgf -46.850 -46.850 -46.850 67.040 67.040 67.040 91.730 91.730 91.730 0.730 0.730 0.730 -10.090 -10.090 -10.090 9.830 9.830 9.830 0.000 0.000 0.000 -0.730 -0.730 -0.730 10.090 10.090 10.090 -9.830 -9.830 -9.830 -91.730 -91.730 -91.730 46.850 46.850 46.850 -67.040 -67.040 -67.040
Kgf-cm -13093.610 0.000 13093.610 16758.750 0.000 -16758.750 11466.240 0.000 -11466.240 203.330 0.000 -203.330 -2820.550 0.000 2820.550 2457.270 0.000 -2457.270 0.000 0.000 0.000 -203.330 0.000 203.330 2820.550 0.000 -2820.550 -2457.270 0.000 2457.270 -11466.240 0.000 11466.240 13093.610 0.000 -13093.610 -16758.750 0.000 16758.750
TUGAS METODE ELEMEN HINGGA
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