Analisa Struktur Sebelum Uas_wjs.xlsx
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Analisa Struktur Sebelum Uas_wjs.xlsx as PDF for free.
More details
- Words: 4,135
- Pages: 6
1. Merakit matriks Kekakuan elemen Lokas [S] m
3. Menghitung Matriks kekakuan elemen [K]m Terhadap sumbu Struktur [T]m dan [T]mT
Elemen 1 lebar penampang (B)
=
300 mm
0.3 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
120000 mm2
Inersia (I)
= 1600000000 mm4
elastisitas beton ( E ) ɣ
= =
20000 Mpa 90 ° 1 65753.42466
1 0
0 0
0 0
0 0
0 0
0 0
0 0
1 0
0 0
0 1
0 0
0.120 m2
0
0
0
-1
0
0
-65753
0.0016 m4
0
0
0
0
0
1
0
0 0
0 0
0 1 789.683 0.000
(Tm )1 =
(Tm )1T X (Sm )1 =
0 65753
-790 0
-1441 0
0 -65753
790 0
-1441 0
0 0
1441 790
3507 1441
0 0
-1441 -790
1753 1441
0
0
65753
0
0
1441
1753
0
-1441
3507
0 2 0.000 65753.425
0 3 -1441.171 0.000
1 4 -789.683 0.000
2000000 Ton/m2
3 0
4 -65753.42
5 0
6 0
1
-789.6827 1441.17095
2
0 1441.171 3506.8493 0 -1441.171 1753.42466 -65753.42466 0 0 65753.42 0 0 0 -789.6827 -1441.171 0 789.6827 -1441.171 0 1441.171 1753.4247 0 -1441.171 3506.84932
3
0 (Sm )1 =
2 0
0 -1
789.6827 1441.171
0
(Tm )1 T =
4 5 6
2 3 5 6 0.000 -1441.171 -65753.425 0.000
1 2
0 0
1753.425
3
0
0.000 1441.171 65753.425 0.000 0.000 3506.849
4
1
5 6
2 3
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
-1441.171
0.000
3506.849
1441.171
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
-789.683 0.000 -1441.171
0.000 -65753.425 0.000
1441.171 0.000 1753.425
789.683 0.000 1441.171
1 0
0 1
0 0
0 0
0 0
0 0
37500 0
0 211
0 844
-37500 0
0 -211
0 844
0 0
0 0
1 0
0 1
0 0
0 0
0 -37500
844 0
4500 0
0 37500
-844 0
2250 0
(km )1 =
0.000
Elemen 2 lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
600 mm 8000 mm
0.6 m 8m
Luas Penampang (A)
=
150000 mm2
0.150 m2
0
0
0
0
1
0
0
-211
-844
0
211
-844
Inersia (I)
= 4500000000 mm4
0.0045 m4
0
0
0
0
0
1
0
844
2250
0
-844
4500
elastisitas beton ( E ) ɣ
= =
1 1 37500.000 0.000
2 2 0.000 210.938
3 3 0.000 843.750
4 4 -37500.000 0.000
5 5 0.000 -210.938
6 6 0.000 843.750
1 2
1 2
(Sm )2 =
20000 Mpa 0°
(Tm )2 =
2000000 Ton/m2
1 37500
2 0
3 0
4 -37500
5 0
6 0
1
0
210.9375
843.75
0
-210.9375
843.75
2
0 37500 0 0
-843.75 0 210.9375 -843.75
2250 0 -843.75 4500
3 4 5 6
0 -37500 0 0
(Tm )2T X (Sm )2 =
843.75 4500 0 0 -210.9375 -843.75 843.75 2250
(Tm )2T =
1 0
0 1
0 0
0 0
0 0
0 0
0
0
1
0
0
0
0.000
843.750
4500.000
0.000
-843.750
2250.000
3
3
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
-37500.000 0.000 0.000
0.000 -210.938 843.750
0.000 -843.750 2250.000
37500.000 0.000 0.000
0.000 210.938 -843.750
0.000 -843.750 4500.000
4 5 6
4 5 6
0 -1
1 0
0 0
0 0
0 0
0 0
0 65753
-790 0
-1441 0
0 -65753
790 0
-1441 0
0 0
0 0
1 0
0 0
0 1
0 0
0 0
1441 790
3507 1441
0 0
-1441 -790
1753 1441
1 2
0 0
1753.425
3
0
0.000 1441.171 65753.425 0.000 0.000 3506.849
4 5 6
4 5 6
1 2
1 2
(km )2 =
Elemen 3 lebar penampang (B)
=
300 mm
0.3 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
120000 mm2
0.120 m2
0
0
0
-1
0
0
-65753
0
0
65753
0
0
Inersia (I)
= 1600000000 mm4
0.0016 m4
0
0
0
0
0
1
0
1441
1753
0
-1441
3507
elastisitas beton ( E ) ɣ
= =
0 0
0 0
0 1 789.683 0.000
0 2 0.000 65753.425
0 3 -1441.171 0.000
4 4 -789.683 0.000
20000 Mpa 90 ° 1 65753.42466
(Tm )3T X (Sm )3 =
2000000 Ton/m2
3 0
4 -65753.42
5 0
6 0
1
-789.6827 1441.17095
2
0 1441.171 3506.8493 0 -1441.171 1753.42466 -65753.42466 0 0 65753.42 0 0 0 -789.6827 -1441.171 0 789.6827 -1441.171 0 1441.171 1753.4247 0 -1441.171 3506.84932
3 4 5 6
0 (Sm )3 =
2 0
(Tm )3 =
789.6827 1441.171
0
(Tm )3T =
5 6 5 6 0.000 -1441.171 -65753.425 0.000
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
-1441.171
0.000
3506.849
1441.171
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
-789.683 0.000 -1441.171
0.000 -65753.425 0.000
1441.171 0.000 1753.425
789.683 0.000 1441.171
0 -1
1 0
0 0
0 0
0 0
0 0
0 54795
-658 0
-1201 0
0 -54795
658 0
-1201 0
0 0
0 0
1 0
0 0
0 1
0 0
0 0
1201 658
2922 1201
0 0
-1201 -658
1461 1201
(km )3 =
0.000
Elemen 4 lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
100000 mm2
0.100 m2
0
0
0
-1
0
0
-54795
0
0
54795
0
0
Inersia (I)
= 1333333333 mm4
0.0013 m4
0
0
0
0
0
1
0
1201
1461
0
-1201
2922
elastisitas beton ( E ) ɣ
= =
0 0
0 0
1 1 658.069 0.000
2 2 0.000 54794.521
3 3 -1200.976 0.000
10 4 -658.069 0.000
20000 Mpa 90 ° 1 54794.52055
Elemen 5
(Tm )4T X (Sm )4 =
2000000 Ton/m2
3 0
4 -54794.52
5 0
6 0
1
-658.0689 1200.97579
2
0 1200.976 2922.3744 0 -1200.976 1461.18721 -54794.52055 0 0 54794.52 0 0 0 -658.0689 -1200.976 0 658.0689 -1200.9758 0 1200.976 1461.1872 0 -1200.976 2922.37443
3 4 5 6
0 (Sm )4 =
2 0
(Tm )4 =
658.0689 1200.9758
0
(Tm )4 T =
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
-1200.976
0.000
2922.374
1200.976
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
-658.069 0.000 -1200.976
0.000 -54794.521 0.000
1200.976 0.000 1461.187
658.069 0.000 1200.976
1
0
0
0
0
0
33333
0
0
-33333
(km )4 =
11 12 5 6 0.000 -1200.976 -54794.521 0.000 1461.187
3
3
0.000 1200.976 54794.521 0.000 0.000 2922.374
4 5 6
10 11 12
0.000
0
0
lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
800 mm 12000 mm
0.8 m 12 m
Luas Penampang (A)
=
200000 mm2
Inersia (I)
= 10666666667 mm4
elastisitas beton ( E ) ɣ
= =
20000 Mpa 0° 1 33333.33333
1
0
0
0
0
0 0
0 0
1 0
0 1
0 0
0 0
0.200 m2
0
0
0
0
1
0.0107 m4
0
0
0
0
0
0
148
889
0
-148
889
0 -33333
889 0
7111 0
0 33333
-889 0
3556 0
0
0
-148
-889
0
148
-889
1
0
889
3556
0
-889
7111
10 1 33333.333 0.000
11 2 0.000 148.148
12 3 0.000 888.889
7 4 -33333.333 0.000
8 5 0.000 -148.148
9 6 0.000 888.889
1 2
10 11
(Tm )5T X (Sm )5 =
2000000 Ton/m2
3 0
4 -33333.33
5 0
6 0
1
-148.1481 888.888889
2
0 888.8889 7111.1111 0 -888.8889 3555.55556 -33333.33333 0 0 33333.33 0 0 0 -148.1481 -888.8889 0 148.1481 -888.88889 0 888.8889 3555.5556 0 -888.8889 7111.11111
3 4 5 6
0 (Sm )5 =
2 0
0 (Tm )5 =
148.1481 888.88889
0
(Tm )5T =
1 0
0 1
0 0
0 0
0 0
0 0
0
0
1
0
0
0
0.000
888.889
7111.111
0.000
-888.889
3555.556
3
12
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
-33333.333 0.000 0.000
0.000 -148.148 888.889
0.000 -888.889 3555.556
33333.333 0.000 0.000
0.000 148.148 -888.889
0.000 -888.889 7111.111
4 5 6
7 8 9
0 -1
1 0
0 0
0 0
0 0
0 0
0 54795
-658 0
-1201 0
0 -54795
658 0
-1201 0
0 0
0 0
1 0
0 0
0 1
0 0
0 0
1201 658
2922 1201
0 0
-1201 -658
1461 1201
1 2
4 5
1461.187
3
6
0.000 1200.976 54794.521 0.000 0.000 2922.374
4 5 6
7 8 9
(km )5 =
Elemen 6 lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
100000 mm2
0.100 m2
0
0
0
-1
0
0
-54795
0
0
54795
0
0
Inersia (I)
= 1333333333 mm4
0.0013 m4
0
0
0
0
0
1
0
1201
1461
0
-1201
2922
elastisitas beton ( E ) ɣ
= =
0 0
0 0
4 1 658.069 0.000
5 2 0.000 54794.521
6 3 -1200.976 0.000
7 4 -658.069 0.000
-1200.976
0.000
2922.374
1200.976
-658.069 0.000 -1200.976
0.000 -54794.521 0.000
1200.976 0.000 1461.187
658.069 0.000 1200.976
20000 Mpa 90 ° 1 54794.52055
(Tm )6T X (Sm )6 =
2000000 Ton/m2
3 0
4 -54794.52
5 0
6 0
1
-658.0689 1200.97579
2
0 1200.976 2922.3744 0 -1200.976 1461.18721 -54794.52055 0 0 54794.52 0 0 0 -658.0689 -1200.976 0 658.0689 -1200.9758 0 1200.976 1461.1872 0 -1200.976 2922.37443
3 4 5 6
0 (Sm )6 =
2 0
(Tm )6 =
658.0689 1200.9758
0
(Tm )6 T =
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
(km )6 =
3. Merakit Unsur elemen matrik [K]s dari Ʃ[K]m pada masing - masing DOF Struktur
kS =
1 38947.8 0.0 240.2 -37500.0 0.0 0.0 0.0 0.0 0.0 -658.1 0.0 -1201.0
2 0.0 120758.9 843.8 0.0 -210.9 843.8 0.0 0.0 0.0 0.0 -54794.5 0.0
3 240.2 843.8 10929.2 0.0 -843.8 2250.0 0.0 0.0 0.0 1201.0 0.0 1461.2
4 5 6 -37500.0 0.0 0.0 0.0 -210.9 843.8 0.0 -843.8 2250.0 38947.8 0.0 240.2 0.0 120758.9 -843.8 240.2 -843.8 10929.2 -658.1 0.0 1201.0 0.0 -54794.5 0.0 -1201.0 0.0 1461.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
7 0.0 0.0 0.0 -658.1 0.0 1201.0 33991.4 0.0 1201.0 -33333.3 0.0 0.0
8 0.0 0.0 0.0 0.0 -54794.5 0.0 0.0 54942.7 -888.9 0.0 -148.1 -888.9
9 0.0 0.0 0.0 -1201.0 0.0 1461.2 1201.0 -888.9 10033.5 0.0 888.9 3555.6
10 -658.1 0.0 1201.0 0.0 0.0 0.0 -33333.3 0.0 0.0 33991.4 0.0 1201.0
11 0.0 -54794.5 0.0 0.0 0.0 0.0 0.0 -148.1 888.9 0.0 54942.7 888.9
12 -1201.0 0.0 1461.2 0.0 0.0 0.0 0.0 -888.9 3555.6 1201.0 888.9 10033.5
1 2 3 4 5 6 7 8 9 10 11 12
+
1
qLL
4. Merakit Vektor Beban Ekivalen titik Kumpul {P} s dengan menghitung {FEM}m dari tabel dan merubah {FEF}m ke {PEF}m dengan matrik Transpose [T]mT Elemen 1 Panajang Penampang ( L) Beban Mati (qDL1)
=
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.36
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.657
FEN1
0.657
0.000
0
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.657
0
1
0
0
0
0
0
FEM3
=
0.000
0.000
0
0
0
1
0
0
0
FEN4
=
0.657
FEN4
0.657
0.000
1
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.657
2
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
3
0
0
0
0
0
1
=
3650 2.5 x A
mm =
3.65 0.3
m
mutu beton =
2.5
Ton/m
kombinasi =
1.2
=
0
Ton/m
ɣ
=
0.36
Ton/m
FE1
=
FEM3
=
=
0.000
90
Ton/m qDL °
P1 = (Tm)1Tx(-FE1)
=
(Tm )1 T =
8 9 5 6 0.000 -1200.976 -54794.521 0.000 0.000
Elemen 2 Panajang Penampang ( L) Beban Mati (qDL1)
=
8000
=
2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0
Ton/m
qUy1
=
0.45
Ton/m
FEN1
=
0.000
FEN1
0.000
0.000
1
1
0
0
0
0
0
FEV2
=
1.800
FEV2
1.800
-1.800
2
0
1
0
0
0
0
FEM3
=
2.400
-2.400
3
0
0
1
0
0
0
FEN4
=
0.000
FEN4
0.000
0.000
4
0
0
0
1
0
0
FEV5
=
1.800
FEV5
1.800
-1.800
5
0
0
0
0
1
0
FEM6
=
-2.400
FEM6
-2.400
2.400
6
0
0
0
0
0
1
Elemen 3 Panajang Penampang ( L) Beban Mati (qDL1)
=
3650 2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.36
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.657
FEN1
0.657
0.000
0
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.657
0
1
0
0
0
0
0
FEM3
=
0.000
0.000
0
0
0
1
0
0
0
FEN4
=
0.657
FEN4
0.657
0.000
4
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.657
5
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
6
0
0
0
0
0
1
Elemen 4 Panajang Penampang ( L) Beban Mati (qDL1)
=
3650 2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.3
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.548
FEN1
0.548
0.000
1
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.548
2
1
0
0
0
0
0
FEM3
=
0.000
0.000
3
0
0
1
0
0
0
FEN4
=
0.548
FEN4
0.548
0.000
10
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.548
11
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
12
0
0
0
0
0
1
Elemen 5 Panajang Penampang ( L) Beban Mati (qDL1)
=
12000 2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0
Ton/m
qUy1
=
0.60
Ton/m
FEN1
=
0.000
FEN1
0.000
0.000
10
1
0
0
0
0
0
FEV2
=
3.600
FEV2
3.600
-3.600
11
0
1
0
0
0
0
FEM3
=
7.200
-7.200
12
0
0
1
0
0
0
FEN4
=
0.000
FEN4
0.000
0.000
7
0
0
0
1
0
0
FEV5
=
3.600
FEV5
3.600
-3.600
8
0
0
0
0
1
0
FEM6
=
-7.200
FEM6
-7.200
7.200
9
0
0
0
0
0
1
=
=
=
mm
m
mutu beton =
2.5
=
0.375
8
Ton/m
kombinasi =
1.2
=
0
Ton/m
ɣ
=
0.45
Ton/m
FE2
mm =
3.65 0.3
= =
=
2.5
kombinasi =
1.2
0
Ton/m
ɣ
0.36
Ton/m
3.65 0.25
= =
FEM3
=
=
90
mutu beton =
2.5
Ton/m
kombinasi =
1.2
0
Ton/m
ɣ
0.3
Ton/m
FE4
=
12 0.5
= =
=
FEM3
=
90
mutu beton =
2.5
kombinasi =
1.2
0
Ton/m
ɣ
0.6
Ton/m
=
FEM3
=
=
7.200
+
0
=
(Tm )2T =
1
qLL
=
(Tm )3T =
Ton/m qDL
+
1
qLL
°
P1 = (Tm)1Tx(-FE1)
Ton/m
FE5
qDL
0.000
m
qLL
°
P1 = (Tm)1Tx(-FE1)
m
1
Ton/m
0.000
=
+
P1 = (Tm)1Tx(-FE1)
mutu beton =
=
qDL °
2.400
Ton/m
=
mm
=
0
m
FE3
mm
FEM3
=
Ton/m
=
(Tm )4 T =
Ton/m qDL
+
1
qLL
°
P1 = (Tm)1Tx(-FE1)
=
(Tm )5T =
Elemen 6 Panajang Penampang ( L) Beban Mati (qDL1)
=
3650
=
2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.3
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.548
FEN1
0.548
0.000
4
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.548
5
1
0
0
0
0
0
FEM3
=
0.000
0.000
6
0
0
1
0
0
0
FEN4
=
0.548
FEN4
0.548
0.000
7
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.548
8
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
9
0
0
0
0
0
1
0.000 -3.005 -2.400 0.000 -3.005 2.400
0 0 0 0 0 0
=
0.000 -3.005 -2.400 0.000 -3.005 2.400
0 0 0 0 -1 0
0 0 0 1 0 0
0 0 0 0 0 1
Sehingga
FEF
=
mm
3.65
m
mutu beton =
2.5
=
0.25
Ton/m
kombinasi =
1.2
=
0
Ton/m
ɣ
=
0.3
Ton/m
FE6
PE
=
=
0.000 -4.148 7.200 0.000 -4.148 -7.200
FEM3
=
=
90
Ton/m qDL
+
P1 = (Tm)1Tx(-FE1)
0.000
1
qLL
°
=
Ps
Maka {Ps}= {FEF} + {PE}
0 0 0 0 0 0
(Tm )6 T =
0.000 -4.148 7.200 0.000 -4.148 -7.200
1 2 3 4 5 6 7 8 9 10 11 12
5. Menyusun Persamaan Linear simultan [K]s {x}s = {Ps} dengan metode dekomposisi LU
Xs
=
0.00000 -0.00253 -0.00202 0.00000 -0.00253 0.00202
1 2 3 4 5 6
0.00000 -0.00349 0.00606 0.00000 -0.00349 -0.00606
7 8 9 10 11 12
Xs-1=
0.000841
kS =
38947.75 0.00 240.20 -37500.00 0.00
0.00 240.20 120758.88 843.75 843.75 10929.22 0.00 0.00 -210.94 -843.75
-37500.00 0.00 0.00 -210.94 0.00 -843.75 38947.75 0.00 0.00 120758.88
0.00 843.75 2250.00 240.20 -843.75
0.00 0.00 0.00 -658.07 0.00
0.00 0.00 0.00 0.00 -54794.52
0.00 0.00 0.00 -1200.98 0.00
-658.07 0.00 1200.98 0.00 0.00
0.00 -54794.52 0.00 0.00 0.00
-1200.98 0.00 1461.19 0.00 0.00
0.00 0.00 0.00 0.00 -658.07 0.00 -1200.98
843.75 0.00 0.00 0.00 0.00 -54794.52 0.00
240.20 -658.07 0.00 -1200.98 0.00 0.00 0.00
10929.22 1200.98 0.00 1461.19 0.00 0.00 0.00
1200.98 33991.40 0.00 1200.98 -33333.33 0.00 0.00
0.00 0.00 54942.67 -888.89 0.00 -148.15 -888.89
1461.19 1200.98 -888.89 10033.49 0.00 888.89 3555.56
0.00 -33333.33 0.00 0.00 33991.40 0.00 1200.98
0.00 0.00 -148.15 888.89 0.00 54942.67 888.89
0.00 0.00 -888.89 3555.56 1200.98 888.89 10033.49
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
2250.00 0.00 0.00 0.00 1200.98 0.00 1461.19
-843.75 0.00 -54794.52 0.00 0.00 0.00 0.00
6. Menggambar Garis Elastis Sistem Struktur dari {Xs}
7. Menghitung gaya-gaya dalam ujung elemen untuk menggambar diagaram gaya gaya dalam struktur dimana : {Fm} = [Sm] [Tm]{Xm} + {FEFm} Elemen1
X1
=
0 0 0 0.00000 -0.00253 -0.00202
0 0 0 1 2 3
(Sm )1 =
65753.4247 0 0 -65753.425 0 0
0 0 -65753.425 0 0 789.68271 1441.17095 0 -789.68271 1441.1709514 1441.171 3506.84932 0 -1441.171 1753.4246575 0 0 65753.4247 0 0 -789.68271 -1441.171 0 789.68271 -1441.170951 1441.171 1753.42466 0 -1441.171 3506.8493151
(Tm )1 =
FE1
0.657 0.000 0.000 0.657 0.000 0.000
{F1} = [S1] [T1]{X1} + {FE1}
F1
=
166.863 -2.910 -3.540 -165.549 2.910 -7.081
(Sm)1 x ( Tm )1=
0.00 -789.68
65753.42 0.00
0.00 1441.17
0.00 789.68
-65753.42 0.00
0.00 1441.17
-1441.17 0.00 789.68 -1441.17
0.00 -65753.42 0.00 0.00
3506.85 0.00 -1441.17 1753.42
1441.17 0.00 -789.68 1441.17
0.00 65753.42 0.00 0.00
1753.42 0.00 -1441.17 3506.85
0 843.75
-37500 0
0 -210.9375
0 843.75
166.20604 -2.90993 -3.54042 -166.20604 2.90993 -7.08084
{(Sm)1 x ( Tm )1}x (X1)=
Elemen2 0.00000 -0.00253
1 2
37500 0
0 210.9375
1 0
0 1
0 0
0 0
0 0
0 0
0.000 1.800
X2
=
-0.00202
3
0.00000 -0.00253 0.00202
4 5 6
(Sm )2 =
0
843.75
4500
0
-843.75
2250
-37500 0 0
0 -210.9375 843.75
0 -843.75 2250
37500 0 0
0 210.9375 -843.75
0 -843.75 4500
37500.00 0.00
0.00 210.94
0.00 843.75
-37500.00 0.00
0.00 -210.94
0.00 843.75
0.00 -37500.00 0.00 0.00
843.75 0.00 -210.94 843.75
4500.00 0.00 -843.75 2250.00
0.00 37500.00 0.00 0.00
-843.75 0.00 210.94 -843.75
2250.00 0.00 -843.75 4500.00
(Tm )2 =
0
0
1
0
0
0
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
FE2
2.400 0.000 1.800 -2.400
0.657 0.000 0.000
{F1} = [S1] [T1]{X1} + {FE1} 0.000 1.800 F2
=
-2.143 0.000 1.800 2.143
(Sm)1 x ( Tm )1=
0.00000 0.00000 -4.54308 0.00000 0.00000 4.54308
{(Sm)1 x ( Tm )1}x (X1)=
Elemen3
X3
=
0 0 0
0 0 0
0.00000 -0.00253 0.00202
4 5 6
(Sm )3 =
65753.4247 0 0 -65753.425 0 0 0 789.68271 1441.17095 0 -789.68271 1441.1709514 0 1441.171 3506.84932 0 -1441.171 1753.4246575
(Tm )3 =
-65753.425 0 0 65753.4247 0 0 0 -789.68271 -1441.171 0 789.68271 -1441.170951 0 1441.171 1753.42466 0 -1441.171 3506.8493151
0 -1 0
1 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 -1 0
1 0 0
0 0 1
0.657 0.000 0.000
0 0 0 0 0 1
0.548 0.000 0.000 0.548 0.000 0.000
FE3
{F1} = [S1] [T1]{X1} + {FE1}
F3
=
166.863 2.910 3.540 -165.549 -2.910 7.081
(Sm)1 x ( Tm )1=
0.00 -789.68
65753.42 0.00
0.00 1441.17
0.00 789.68
-65753.42 0.00
0.00 1441.17
-1441.17 0.00 789.68 -1441.17
0.00 -65753.42 0.00 0.00
3506.85 0.00 -1441.17 1753.42
1441.17 0.00 -789.68 1441.17
0.00 65753.42 0.00 0.00
1753.42 0.00 -1441.17 3506.85
166.20604 2.90993 3.54042 -166.20604 -2.90993 7.08084
{(Sm)1 x ( Tm )1}x (X1)=
Elemen4
X4
=
0.00000 -0.00253 -0.00202 0.00000 -0.00349 -0.00606
1 2 3 10 11 12
(Sm )4 =
54794.5205 0 0 -54794.521 0 0
0 0 -54794.521 0 0 658.06893 1200.97579 0 -658.06893 1200.9757928 1200.9758 2922.37443 0 -1200.9758 1461.1872146 0 0 54794.5205 0 0 -658.06893 -1200.9758 0 658.06893 -1200.975793 1200.9758 1461.18721 0 -1200.9758 2922.3744292
(Tm )4 =
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 0
FE4
{F1} = [S1] [T1]{X1} + {FE1}
F4
=
53.239 -9.700 -14.752 -52.144 9.700 -20.652
(Sm)1 x ( Tm )1=
0.00 -658.07
54794.52 0.00
0.00 1200.98
0.00 658.07
-54794.52 0.00
0.00 1200.98
-1200.98 0.00 658.07 -1200.98
0.00 -54794.52 0.00 0.00
2922.37 0.00 -1200.98 1461.19
1200.98 0.00 -658.07 1200.98
0.00 54794.52 0.00 0.00
1461.19 0.00 -1200.98 2922.37
52.69138 -9.69978 -14.75174 -52.69138 9.69978 -20.65244
{(Sm)1 x ( Tm )1}x (X1)=
Elemen5
X5
=
0.00000 -0.00349 -0.00606 0.00000 -0.00349 0.00606
10 11 12 7 8 9
(Sm )5 =
33333.3333 0 0 -33333.333 0 0
0 0 -33333.333 0 0 148.14815 888.888889 0 -148.14815 888.88888889 888.88889 7111.11111 0 -888.88889 3555.5555556 0 0 33333.3333 0 0 -148.14815 -888.88889 0 148.14815 -888.8888889 888.88889 3555.55556 0 -888.88889 7111.1111111
(Tm )5 =
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
FE5
0.000 3.600 7.200 0.000 3.600 -7.200
{F1} = [S1] [T1]{X1} + {FE1}
F5
=
0.000 3.600 -14.338 0.000 3.600 14.338
(Sm)1 x ( Tm )1=
33333.33 0.00
0.00 148.15
0.00 888.89
-33333.33 0.00
0.00 -148.15
0.00 888.89
0.00 -33333.33 0.00 0.00
888.89 0.00 -148.15 888.89
7111.11 0.00 -888.89 3555.56
0.00 33333.33 0.00 0.00
-888.89 0.00 148.15 -888.89
3555.56 0.00 -888.89 7111.11
0.00000 0.00000 -21.53754 0.00000 0.00000 21.53754
{(Sm)1 x ( Tm )1}x (X1)=
Elemen6
X6
=
{F1} = [S1] [T1]{X1} + {FE1}
0.00000 -0.00253 0.00202 0.00000 -0.00349 0.00606
4 5 6 7 8 9
(Sm )6 =
54794.5205 0 0 -54794.521 0 0
0 0 -54794.521 0 0 658.06893 1200.97579 0 -658.06893 1200.9757928 1200.9758 2922.37443 0 -1200.9758 1461.1872146 0 0 54794.5205 0 0 -658.06893 -1200.9758 0 658.06893 -1200.975793 1200.9758 1461.18721 0 -1200.9758 2922.3744292
(Tm )6 =
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 0
0 0 0 0 0 1
FE6
0.548 0.000 0.000 0.548 0.000 0.000
53.239 9.700 F6
=
14.752 -52.144 -9.700 20.652
8. Diagram gaya Normal N, Gaya Lintang L dan Momen M
(Sm)1 x ( Tm )1=
0.00 -658.07
54794.52 0.00
0.00 1200.98
0.00 658.07
-54794.52 0.00
0.00 1200.98
-1200.98 0.00 658.07 -1200.98
0.00 -54794.52 0.00 0.00
2922.37 0.00 -1200.98 1461.19
1200.98 0.00 -658.07 1200.98
0.00 54794.52 0.00 0.00
1461.19 0.00 -1200.98 2922.37
52.69138 9.69978 {(Sm)1 x ( Tm )1}x (X1)=
14.75174 -52.69138 -9.69978 20.65244
3. Menghitung Matriks kekakuan elemen [K]m Terhadap sumbu Struktur [T]m dan [T]mT
Elemen 1 lebar penampang (B)
=
300 mm
0.3 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
120000 mm2
Inersia (I)
= 1600000000 mm4
elastisitas beton ( E ) ɣ
= =
20000 Mpa 90 ° 1 65753.42466
1 0
0 0
0 0
0 0
0 0
0 0
0 0
1 0
0 0
0 1
0 0
0.120 m2
0
0
0
-1
0
0
-65753
0.0016 m4
0
0
0
0
0
1
0
0 0
0 0
0 1 789.683 0.000
(Tm )1 =
(Tm )1T X (Sm )1 =
0 65753
-790 0
-1441 0
0 -65753
790 0
-1441 0
0 0
1441 790
3507 1441
0 0
-1441 -790
1753 1441
0
0
65753
0
0
1441
1753
0
-1441
3507
0 2 0.000 65753.425
0 3 -1441.171 0.000
1 4 -789.683 0.000
2000000 Ton/m2
3 0
4 -65753.42
5 0
6 0
1
-789.6827 1441.17095
2
0 1441.171 3506.8493 0 -1441.171 1753.42466 -65753.42466 0 0 65753.42 0 0 0 -789.6827 -1441.171 0 789.6827 -1441.171 0 1441.171 1753.4247 0 -1441.171 3506.84932
3
0 (Sm )1 =
2 0
0 -1
789.6827 1441.171
0
(Tm )1 T =
4 5 6
2 3 5 6 0.000 -1441.171 -65753.425 0.000
1 2
0 0
1753.425
3
0
0.000 1441.171 65753.425 0.000 0.000 3506.849
4
1
5 6
2 3
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
-1441.171
0.000
3506.849
1441.171
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
-789.683 0.000 -1441.171
0.000 -65753.425 0.000
1441.171 0.000 1753.425
789.683 0.000 1441.171
1 0
0 1
0 0
0 0
0 0
0 0
37500 0
0 211
0 844
-37500 0
0 -211
0 844
0 0
0 0
1 0
0 1
0 0
0 0
0 -37500
844 0
4500 0
0 37500
-844 0
2250 0
(km )1 =
0.000
Elemen 2 lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
600 mm 8000 mm
0.6 m 8m
Luas Penampang (A)
=
150000 mm2
0.150 m2
0
0
0
0
1
0
0
-211
-844
0
211
-844
Inersia (I)
= 4500000000 mm4
0.0045 m4
0
0
0
0
0
1
0
844
2250
0
-844
4500
elastisitas beton ( E ) ɣ
= =
1 1 37500.000 0.000
2 2 0.000 210.938
3 3 0.000 843.750
4 4 -37500.000 0.000
5 5 0.000 -210.938
6 6 0.000 843.750
1 2
1 2
(Sm )2 =
20000 Mpa 0°
(Tm )2 =
2000000 Ton/m2
1 37500
2 0
3 0
4 -37500
5 0
6 0
1
0
210.9375
843.75
0
-210.9375
843.75
2
0 37500 0 0
-843.75 0 210.9375 -843.75
2250 0 -843.75 4500
3 4 5 6
0 -37500 0 0
(Tm )2T X (Sm )2 =
843.75 4500 0 0 -210.9375 -843.75 843.75 2250
(Tm )2T =
1 0
0 1
0 0
0 0
0 0
0 0
0
0
1
0
0
0
0.000
843.750
4500.000
0.000
-843.750
2250.000
3
3
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
-37500.000 0.000 0.000
0.000 -210.938 843.750
0.000 -843.750 2250.000
37500.000 0.000 0.000
0.000 210.938 -843.750
0.000 -843.750 4500.000
4 5 6
4 5 6
0 -1
1 0
0 0
0 0
0 0
0 0
0 65753
-790 0
-1441 0
0 -65753
790 0
-1441 0
0 0
0 0
1 0
0 0
0 1
0 0
0 0
1441 790
3507 1441
0 0
-1441 -790
1753 1441
1 2
0 0
1753.425
3
0
0.000 1441.171 65753.425 0.000 0.000 3506.849
4 5 6
4 5 6
1 2
1 2
(km )2 =
Elemen 3 lebar penampang (B)
=
300 mm
0.3 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
120000 mm2
0.120 m2
0
0
0
-1
0
0
-65753
0
0
65753
0
0
Inersia (I)
= 1600000000 mm4
0.0016 m4
0
0
0
0
0
1
0
1441
1753
0
-1441
3507
elastisitas beton ( E ) ɣ
= =
0 0
0 0
0 1 789.683 0.000
0 2 0.000 65753.425
0 3 -1441.171 0.000
4 4 -789.683 0.000
20000 Mpa 90 ° 1 65753.42466
(Tm )3T X (Sm )3 =
2000000 Ton/m2
3 0
4 -65753.42
5 0
6 0
1
-789.6827 1441.17095
2
0 1441.171 3506.8493 0 -1441.171 1753.42466 -65753.42466 0 0 65753.42 0 0 0 -789.6827 -1441.171 0 789.6827 -1441.171 0 1441.171 1753.4247 0 -1441.171 3506.84932
3 4 5 6
0 (Sm )3 =
2 0
(Tm )3 =
789.6827 1441.171
0
(Tm )3T =
5 6 5 6 0.000 -1441.171 -65753.425 0.000
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
-1441.171
0.000
3506.849
1441.171
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
-789.683 0.000 -1441.171
0.000 -65753.425 0.000
1441.171 0.000 1753.425
789.683 0.000 1441.171
0 -1
1 0
0 0
0 0
0 0
0 0
0 54795
-658 0
-1201 0
0 -54795
658 0
-1201 0
0 0
0 0
1 0
0 0
0 1
0 0
0 0
1201 658
2922 1201
0 0
-1201 -658
1461 1201
(km )3 =
0.000
Elemen 4 lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
100000 mm2
0.100 m2
0
0
0
-1
0
0
-54795
0
0
54795
0
0
Inersia (I)
= 1333333333 mm4
0.0013 m4
0
0
0
0
0
1
0
1201
1461
0
-1201
2922
elastisitas beton ( E ) ɣ
= =
0 0
0 0
1 1 658.069 0.000
2 2 0.000 54794.521
3 3 -1200.976 0.000
10 4 -658.069 0.000
20000 Mpa 90 ° 1 54794.52055
Elemen 5
(Tm )4T X (Sm )4 =
2000000 Ton/m2
3 0
4 -54794.52
5 0
6 0
1
-658.0689 1200.97579
2
0 1200.976 2922.3744 0 -1200.976 1461.18721 -54794.52055 0 0 54794.52 0 0 0 -658.0689 -1200.976 0 658.0689 -1200.9758 0 1200.976 1461.1872 0 -1200.976 2922.37443
3 4 5 6
0 (Sm )4 =
2 0
(Tm )4 =
658.0689 1200.9758
0
(Tm )4 T =
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
-1200.976
0.000
2922.374
1200.976
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
-658.069 0.000 -1200.976
0.000 -54794.521 0.000
1200.976 0.000 1461.187
658.069 0.000 1200.976
1
0
0
0
0
0
33333
0
0
-33333
(km )4 =
11 12 5 6 0.000 -1200.976 -54794.521 0.000 1461.187
3
3
0.000 1200.976 54794.521 0.000 0.000 2922.374
4 5 6
10 11 12
0.000
0
0
lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
800 mm 12000 mm
0.8 m 12 m
Luas Penampang (A)
=
200000 mm2
Inersia (I)
= 10666666667 mm4
elastisitas beton ( E ) ɣ
= =
20000 Mpa 0° 1 33333.33333
1
0
0
0
0
0 0
0 0
1 0
0 1
0 0
0 0
0.200 m2
0
0
0
0
1
0.0107 m4
0
0
0
0
0
0
148
889
0
-148
889
0 -33333
889 0
7111 0
0 33333
-889 0
3556 0
0
0
-148
-889
0
148
-889
1
0
889
3556
0
-889
7111
10 1 33333.333 0.000
11 2 0.000 148.148
12 3 0.000 888.889
7 4 -33333.333 0.000
8 5 0.000 -148.148
9 6 0.000 888.889
1 2
10 11
(Tm )5T X (Sm )5 =
2000000 Ton/m2
3 0
4 -33333.33
5 0
6 0
1
-148.1481 888.888889
2
0 888.8889 7111.1111 0 -888.8889 3555.55556 -33333.33333 0 0 33333.33 0 0 0 -148.1481 -888.8889 0 148.1481 -888.88889 0 888.8889 3555.5556 0 -888.8889 7111.11111
3 4 5 6
0 (Sm )5 =
2 0
0 (Tm )5 =
148.1481 888.88889
0
(Tm )5T =
1 0
0 1
0 0
0 0
0 0
0 0
0
0
1
0
0
0
0.000
888.889
7111.111
0.000
-888.889
3555.556
3
12
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
-33333.333 0.000 0.000
0.000 -148.148 888.889
0.000 -888.889 3555.556
33333.333 0.000 0.000
0.000 148.148 -888.889
0.000 -888.889 7111.111
4 5 6
7 8 9
0 -1
1 0
0 0
0 0
0 0
0 0
0 54795
-658 0
-1201 0
0 -54795
658 0
-1201 0
0 0
0 0
1 0
0 0
0 1
0 0
0 0
1201 658
2922 1201
0 0
-1201 -658
1461 1201
1 2
4 5
1461.187
3
6
0.000 1200.976 54794.521 0.000 0.000 2922.374
4 5 6
7 8 9
(km )5 =
Elemen 6 lebar penampang (B)
=
250 mm
0.25 m
Tinggi Penampang (H) Panajang Penampang ( L)
= =
400 mm 3650 mm
0.4 m 3.65 m
Luas Penampang (A)
=
100000 mm2
0.100 m2
0
0
0
-1
0
0
-54795
0
0
54795
0
0
Inersia (I)
= 1333333333 mm4
0.0013 m4
0
0
0
0
0
1
0
1201
1461
0
-1201
2922
elastisitas beton ( E ) ɣ
= =
0 0
0 0
4 1 658.069 0.000
5 2 0.000 54794.521
6 3 -1200.976 0.000
7 4 -658.069 0.000
-1200.976
0.000
2922.374
1200.976
-658.069 0.000 -1200.976
0.000 -54794.521 0.000
1200.976 0.000 1461.187
658.069 0.000 1200.976
20000 Mpa 90 ° 1 54794.52055
(Tm )6T X (Sm )6 =
2000000 Ton/m2
3 0
4 -54794.52
5 0
6 0
1
-658.0689 1200.97579
2
0 1200.976 2922.3744 0 -1200.976 1461.18721 -54794.52055 0 0 54794.52 0 0 0 -658.0689 -1200.976 0 658.0689 -1200.9758 0 1200.976 1461.1872 0 -1200.976 2922.37443
3 4 5 6
0 (Sm )6 =
2 0
(Tm )6 =
658.0689 1200.9758
0
(Tm )6 T =
0 1
-1 0
0 0
0 0
0
0
1
0
0
0
0 0 0
0 0 0
0 0 0
0 1 0
-1 0 0
0 0 1
(km )6 =
3. Merakit Unsur elemen matrik [K]s dari Ʃ[K]m pada masing - masing DOF Struktur
kS =
1 38947.8 0.0 240.2 -37500.0 0.0 0.0 0.0 0.0 0.0 -658.1 0.0 -1201.0
2 0.0 120758.9 843.8 0.0 -210.9 843.8 0.0 0.0 0.0 0.0 -54794.5 0.0
3 240.2 843.8 10929.2 0.0 -843.8 2250.0 0.0 0.0 0.0 1201.0 0.0 1461.2
4 5 6 -37500.0 0.0 0.0 0.0 -210.9 843.8 0.0 -843.8 2250.0 38947.8 0.0 240.2 0.0 120758.9 -843.8 240.2 -843.8 10929.2 -658.1 0.0 1201.0 0.0 -54794.5 0.0 -1201.0 0.0 1461.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
7 0.0 0.0 0.0 -658.1 0.0 1201.0 33991.4 0.0 1201.0 -33333.3 0.0 0.0
8 0.0 0.0 0.0 0.0 -54794.5 0.0 0.0 54942.7 -888.9 0.0 -148.1 -888.9
9 0.0 0.0 0.0 -1201.0 0.0 1461.2 1201.0 -888.9 10033.5 0.0 888.9 3555.6
10 -658.1 0.0 1201.0 0.0 0.0 0.0 -33333.3 0.0 0.0 33991.4 0.0 1201.0
11 0.0 -54794.5 0.0 0.0 0.0 0.0 0.0 -148.1 888.9 0.0 54942.7 888.9
12 -1201.0 0.0 1461.2 0.0 0.0 0.0 0.0 -888.9 3555.6 1201.0 888.9 10033.5
1 2 3 4 5 6 7 8 9 10 11 12
+
1
qLL
4. Merakit Vektor Beban Ekivalen titik Kumpul {P} s dengan menghitung {FEM}m dari tabel dan merubah {FEF}m ke {PEF}m dengan matrik Transpose [T]mT Elemen 1 Panajang Penampang ( L) Beban Mati (qDL1)
=
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.36
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.657
FEN1
0.657
0.000
0
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.657
0
1
0
0
0
0
0
FEM3
=
0.000
0.000
0
0
0
1
0
0
0
FEN4
=
0.657
FEN4
0.657
0.000
1
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.657
2
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
3
0
0
0
0
0
1
=
3650 2.5 x A
mm =
3.65 0.3
m
mutu beton =
2.5
Ton/m
kombinasi =
1.2
=
0
Ton/m
ɣ
=
0.36
Ton/m
FE1
=
FEM3
=
=
0.000
90
Ton/m qDL °
P1 = (Tm)1Tx(-FE1)
=
(Tm )1 T =
8 9 5 6 0.000 -1200.976 -54794.521 0.000 0.000
Elemen 2 Panajang Penampang ( L) Beban Mati (qDL1)
=
8000
=
2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0
Ton/m
qUy1
=
0.45
Ton/m
FEN1
=
0.000
FEN1
0.000
0.000
1
1
0
0
0
0
0
FEV2
=
1.800
FEV2
1.800
-1.800
2
0
1
0
0
0
0
FEM3
=
2.400
-2.400
3
0
0
1
0
0
0
FEN4
=
0.000
FEN4
0.000
0.000
4
0
0
0
1
0
0
FEV5
=
1.800
FEV5
1.800
-1.800
5
0
0
0
0
1
0
FEM6
=
-2.400
FEM6
-2.400
2.400
6
0
0
0
0
0
1
Elemen 3 Panajang Penampang ( L) Beban Mati (qDL1)
=
3650 2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.36
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.657
FEN1
0.657
0.000
0
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.657
0
1
0
0
0
0
0
FEM3
=
0.000
0.000
0
0
0
1
0
0
0
FEN4
=
0.657
FEN4
0.657
0.000
4
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.657
5
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
6
0
0
0
0
0
1
Elemen 4 Panajang Penampang ( L) Beban Mati (qDL1)
=
3650 2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.3
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.548
FEN1
0.548
0.000
1
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.548
2
1
0
0
0
0
0
FEM3
=
0.000
0.000
3
0
0
1
0
0
0
FEN4
=
0.548
FEN4
0.548
0.000
10
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.548
11
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
12
0
0
0
0
0
1
Elemen 5 Panajang Penampang ( L) Beban Mati (qDL1)
=
12000 2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0
Ton/m
qUy1
=
0.60
Ton/m
FEN1
=
0.000
FEN1
0.000
0.000
10
1
0
0
0
0
0
FEV2
=
3.600
FEV2
3.600
-3.600
11
0
1
0
0
0
0
FEM3
=
7.200
-7.200
12
0
0
1
0
0
0
FEN4
=
0.000
FEN4
0.000
0.000
7
0
0
0
1
0
0
FEV5
=
3.600
FEV5
3.600
-3.600
8
0
0
0
0
1
0
FEM6
=
-7.200
FEM6
-7.200
7.200
9
0
0
0
0
0
1
=
=
=
mm
m
mutu beton =
2.5
=
0.375
8
Ton/m
kombinasi =
1.2
=
0
Ton/m
ɣ
=
0.45
Ton/m
FE2
mm =
3.65 0.3
= =
=
2.5
kombinasi =
1.2
0
Ton/m
ɣ
0.36
Ton/m
3.65 0.25
= =
FEM3
=
=
90
mutu beton =
2.5
Ton/m
kombinasi =
1.2
0
Ton/m
ɣ
0.3
Ton/m
FE4
=
12 0.5
= =
=
FEM3
=
90
mutu beton =
2.5
kombinasi =
1.2
0
Ton/m
ɣ
0.6
Ton/m
=
FEM3
=
=
7.200
+
0
=
(Tm )2T =
1
qLL
=
(Tm )3T =
Ton/m qDL
+
1
qLL
°
P1 = (Tm)1Tx(-FE1)
Ton/m
FE5
qDL
0.000
m
qLL
°
P1 = (Tm)1Tx(-FE1)
m
1
Ton/m
0.000
=
+
P1 = (Tm)1Tx(-FE1)
mutu beton =
=
qDL °
2.400
Ton/m
=
mm
=
0
m
FE3
mm
FEM3
=
Ton/m
=
(Tm )4 T =
Ton/m qDL
+
1
qLL
°
P1 = (Tm)1Tx(-FE1)
=
(Tm )5T =
Elemen 6 Panajang Penampang ( L) Beban Mati (qDL1)
=
3650
=
2.5 x A
Beban Hidup (qLL1)
=
qU1
=
1.2qDL+1LL
qUx1
=
0.3
Ton/m
qUy1
=
0.00
Ton/m
FEN1
=
0.548
FEN1
0.548
0.000
4
0
-1
0
0
0
0
FEV2
=
0.000
FEV2
0.000
-0.548
5
1
0
0
0
0
0
FEM3
=
0.000
0.000
6
0
0
1
0
0
0
FEN4
=
0.548
FEN4
0.548
0.000
7
0
0
0
0
-1
0
FEV5
=
0.000
FEV5
0.000
-0.548
8
0
0
0
1
0
0
FEM6
=
0.000
FEM6
0.000
0.000
9
0
0
0
0
0
1
0.000 -3.005 -2.400 0.000 -3.005 2.400
0 0 0 0 0 0
=
0.000 -3.005 -2.400 0.000 -3.005 2.400
0 0 0 0 -1 0
0 0 0 1 0 0
0 0 0 0 0 1
Sehingga
FEF
=
mm
3.65
m
mutu beton =
2.5
=
0.25
Ton/m
kombinasi =
1.2
=
0
Ton/m
ɣ
=
0.3
Ton/m
FE6
PE
=
=
0.000 -4.148 7.200 0.000 -4.148 -7.200
FEM3
=
=
90
Ton/m qDL
+
P1 = (Tm)1Tx(-FE1)
0.000
1
qLL
°
=
Ps
Maka {Ps}= {FEF} + {PE}
0 0 0 0 0 0
(Tm )6 T =
0.000 -4.148 7.200 0.000 -4.148 -7.200
1 2 3 4 5 6 7 8 9 10 11 12
5. Menyusun Persamaan Linear simultan [K]s {x}s = {Ps} dengan metode dekomposisi LU
Xs
=
0.00000 -0.00253 -0.00202 0.00000 -0.00253 0.00202
1 2 3 4 5 6
0.00000 -0.00349 0.00606 0.00000 -0.00349 -0.00606
7 8 9 10 11 12
Xs-1=
0.000841
kS =
38947.75 0.00 240.20 -37500.00 0.00
0.00 240.20 120758.88 843.75 843.75 10929.22 0.00 0.00 -210.94 -843.75
-37500.00 0.00 0.00 -210.94 0.00 -843.75 38947.75 0.00 0.00 120758.88
0.00 843.75 2250.00 240.20 -843.75
0.00 0.00 0.00 -658.07 0.00
0.00 0.00 0.00 0.00 -54794.52
0.00 0.00 0.00 -1200.98 0.00
-658.07 0.00 1200.98 0.00 0.00
0.00 -54794.52 0.00 0.00 0.00
-1200.98 0.00 1461.19 0.00 0.00
0.00 0.00 0.00 0.00 -658.07 0.00 -1200.98
843.75 0.00 0.00 0.00 0.00 -54794.52 0.00
240.20 -658.07 0.00 -1200.98 0.00 0.00 0.00
10929.22 1200.98 0.00 1461.19 0.00 0.00 0.00
1200.98 33991.40 0.00 1200.98 -33333.33 0.00 0.00
0.00 0.00 54942.67 -888.89 0.00 -148.15 -888.89
1461.19 1200.98 -888.89 10033.49 0.00 888.89 3555.56
0.00 -33333.33 0.00 0.00 33991.40 0.00 1200.98
0.00 0.00 -148.15 888.89 0.00 54942.67 888.89
0.00 0.00 -888.89 3555.56 1200.98 888.89 10033.49
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
2250.00 0.00 0.00 0.00 1200.98 0.00 1461.19
-843.75 0.00 -54794.52 0.00 0.00 0.00 0.00
6. Menggambar Garis Elastis Sistem Struktur dari {Xs}
7. Menghitung gaya-gaya dalam ujung elemen untuk menggambar diagaram gaya gaya dalam struktur dimana : {Fm} = [Sm] [Tm]{Xm} + {FEFm} Elemen1
X1
=
0 0 0 0.00000 -0.00253 -0.00202
0 0 0 1 2 3
(Sm )1 =
65753.4247 0 0 -65753.425 0 0
0 0 -65753.425 0 0 789.68271 1441.17095 0 -789.68271 1441.1709514 1441.171 3506.84932 0 -1441.171 1753.4246575 0 0 65753.4247 0 0 -789.68271 -1441.171 0 789.68271 -1441.170951 1441.171 1753.42466 0 -1441.171 3506.8493151
(Tm )1 =
FE1
0.657 0.000 0.000 0.657 0.000 0.000
{F1} = [S1] [T1]{X1} + {FE1}
F1
=
166.863 -2.910 -3.540 -165.549 2.910 -7.081
(Sm)1 x ( Tm )1=
0.00 -789.68
65753.42 0.00
0.00 1441.17
0.00 789.68
-65753.42 0.00
0.00 1441.17
-1441.17 0.00 789.68 -1441.17
0.00 -65753.42 0.00 0.00
3506.85 0.00 -1441.17 1753.42
1441.17 0.00 -789.68 1441.17
0.00 65753.42 0.00 0.00
1753.42 0.00 -1441.17 3506.85
0 843.75
-37500 0
0 -210.9375
0 843.75
166.20604 -2.90993 -3.54042 -166.20604 2.90993 -7.08084
{(Sm)1 x ( Tm )1}x (X1)=
Elemen2 0.00000 -0.00253
1 2
37500 0
0 210.9375
1 0
0 1
0 0
0 0
0 0
0 0
0.000 1.800
X2
=
-0.00202
3
0.00000 -0.00253 0.00202
4 5 6
(Sm )2 =
0
843.75
4500
0
-843.75
2250
-37500 0 0
0 -210.9375 843.75
0 -843.75 2250
37500 0 0
0 210.9375 -843.75
0 -843.75 4500
37500.00 0.00
0.00 210.94
0.00 843.75
-37500.00 0.00
0.00 -210.94
0.00 843.75
0.00 -37500.00 0.00 0.00
843.75 0.00 -210.94 843.75
4500.00 0.00 -843.75 2250.00
0.00 37500.00 0.00 0.00
-843.75 0.00 210.94 -843.75
2250.00 0.00 -843.75 4500.00
(Tm )2 =
0
0
1
0
0
0
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
FE2
2.400 0.000 1.800 -2.400
0.657 0.000 0.000
{F1} = [S1] [T1]{X1} + {FE1} 0.000 1.800 F2
=
-2.143 0.000 1.800 2.143
(Sm)1 x ( Tm )1=
0.00000 0.00000 -4.54308 0.00000 0.00000 4.54308
{(Sm)1 x ( Tm )1}x (X1)=
Elemen3
X3
=
0 0 0
0 0 0
0.00000 -0.00253 0.00202
4 5 6
(Sm )3 =
65753.4247 0 0 -65753.425 0 0 0 789.68271 1441.17095 0 -789.68271 1441.1709514 0 1441.171 3506.84932 0 -1441.171 1753.4246575
(Tm )3 =
-65753.425 0 0 65753.4247 0 0 0 -789.68271 -1441.171 0 789.68271 -1441.170951 0 1441.171 1753.42466 0 -1441.171 3506.8493151
0 -1 0
1 0 0
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 -1 0
1 0 0
0 0 1
0.657 0.000 0.000
0 0 0 0 0 1
0.548 0.000 0.000 0.548 0.000 0.000
FE3
{F1} = [S1] [T1]{X1} + {FE1}
F3
=
166.863 2.910 3.540 -165.549 -2.910 7.081
(Sm)1 x ( Tm )1=
0.00 -789.68
65753.42 0.00
0.00 1441.17
0.00 789.68
-65753.42 0.00
0.00 1441.17
-1441.17 0.00 789.68 -1441.17
0.00 -65753.42 0.00 0.00
3506.85 0.00 -1441.17 1753.42
1441.17 0.00 -789.68 1441.17
0.00 65753.42 0.00 0.00
1753.42 0.00 -1441.17 3506.85
166.20604 2.90993 3.54042 -166.20604 -2.90993 7.08084
{(Sm)1 x ( Tm )1}x (X1)=
Elemen4
X4
=
0.00000 -0.00253 -0.00202 0.00000 -0.00349 -0.00606
1 2 3 10 11 12
(Sm )4 =
54794.5205 0 0 -54794.521 0 0
0 0 -54794.521 0 0 658.06893 1200.97579 0 -658.06893 1200.9757928 1200.9758 2922.37443 0 -1200.9758 1461.1872146 0 0 54794.5205 0 0 -658.06893 -1200.9758 0 658.06893 -1200.975793 1200.9758 1461.18721 0 -1200.9758 2922.3744292
(Tm )4 =
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 0
FE4
{F1} = [S1] [T1]{X1} + {FE1}
F4
=
53.239 -9.700 -14.752 -52.144 9.700 -20.652
(Sm)1 x ( Tm )1=
0.00 -658.07
54794.52 0.00
0.00 1200.98
0.00 658.07
-54794.52 0.00
0.00 1200.98
-1200.98 0.00 658.07 -1200.98
0.00 -54794.52 0.00 0.00
2922.37 0.00 -1200.98 1461.19
1200.98 0.00 -658.07 1200.98
0.00 54794.52 0.00 0.00
1461.19 0.00 -1200.98 2922.37
52.69138 -9.69978 -14.75174 -52.69138 9.69978 -20.65244
{(Sm)1 x ( Tm )1}x (X1)=
Elemen5
X5
=
0.00000 -0.00349 -0.00606 0.00000 -0.00349 0.00606
10 11 12 7 8 9
(Sm )5 =
33333.3333 0 0 -33333.333 0 0
0 0 -33333.333 0 0 148.14815 888.888889 0 -148.14815 888.88888889 888.88889 7111.11111 0 -888.88889 3555.5555556 0 0 33333.3333 0 0 -148.14815 -888.88889 0 148.14815 -888.8888889 888.88889 3555.55556 0 -888.88889 7111.1111111
(Tm )5 =
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
FE5
0.000 3.600 7.200 0.000 3.600 -7.200
{F1} = [S1] [T1]{X1} + {FE1}
F5
=
0.000 3.600 -14.338 0.000 3.600 14.338
(Sm)1 x ( Tm )1=
33333.33 0.00
0.00 148.15
0.00 888.89
-33333.33 0.00
0.00 -148.15
0.00 888.89
0.00 -33333.33 0.00 0.00
888.89 0.00 -148.15 888.89
7111.11 0.00 -888.89 3555.56
0.00 33333.33 0.00 0.00
-888.89 0.00 148.15 -888.89
3555.56 0.00 -888.89 7111.11
0.00000 0.00000 -21.53754 0.00000 0.00000 21.53754
{(Sm)1 x ( Tm )1}x (X1)=
Elemen6
X6
=
{F1} = [S1] [T1]{X1} + {FE1}
0.00000 -0.00253 0.00202 0.00000 -0.00349 0.00606
4 5 6 7 8 9
(Sm )6 =
54794.5205 0 0 -54794.521 0 0
0 0 -54794.521 0 0 658.06893 1200.97579 0 -658.06893 1200.9757928 1200.9758 2922.37443 0 -1200.9758 1461.1872146 0 0 54794.5205 0 0 -658.06893 -1200.9758 0 658.06893 -1200.975793 1200.9758 1461.18721 0 -1200.9758 2922.3744292
(Tm )6 =
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 0
0 0 0 0 0 1
FE6
0.548 0.000 0.000 0.548 0.000 0.000
53.239 9.700 F6
=
14.752 -52.144 -9.700 20.652
8. Diagram gaya Normal N, Gaya Lintang L dan Momen M
(Sm)1 x ( Tm )1=
0.00 -658.07
54794.52 0.00
0.00 1200.98
0.00 658.07
-54794.52 0.00
0.00 1200.98
-1200.98 0.00 658.07 -1200.98
0.00 -54794.52 0.00 0.00
2922.37 0.00 -1200.98 1461.19
1200.98 0.00 -658.07 1200.98
0.00 54794.52 0.00 0.00
1461.19 0.00 -1200.98 2922.37
52.69138 9.69978 {(Sm)1 x ( Tm )1}x (X1)=
14.75174 -52.69138 -9.69978 20.65244
Related Documents
Analisa Struktur Sebelum Uas_wjs.xlsx
April 2020 20
Analisa Struktur 1
May 2020 18
Rangkuman Analisa Struktur Clear.pdf
June 2020 18
Analisa Struktur Dengan Matriks.pdf
April 2020 22
Analisa Struktur Metode Matriks.pdf
May 2020 24
Analisa Struktur Dome.docx
August 2019 41More Documents from "Awilliambuth Balthasar Lewikinta"
1. Cover.docx
April 2020 8
3 Ka.pdf
April 2020 6
Angkutan_berbasis_rel.doc
April 2020 8