Rangka Batang
27
Data Batang Batang i j α E (t/cm2) A (cm2) L (cm) EA/L Degrees Radians 1 1 2 60 1.047 200 100 400 50 2 2 3 0 0.000 200 100 400 50 3 3 5 300 5.236 200 100 400 50 4 1 4 0 0.000 200 100 400 50 5 4 5 0 0.000 200 100 400 50 6 2 4 300 5.236 200 100 400 50 7 3 4 240 4.189 200 100 400 50
-
Upload
muhamadhilmanpermana -
Category
Documents
-
view
35 -
download
0
description
Analisis Struktur Rangka Batang Menggunakan Matriks
Transcript of Rangka Batang
Data Batang
Batang i jα
E (t/cm2) A (cm2) L (cm) EA/LDegrees Radians
1 1 2 60 1.047 200 100 400 502 2 3 0 0.000 200 100 400 503 3 5 300 5.236 200 100 400 504 1 4 0 0.000 200 100 400 505 4 5 0 0.000 200 100 400 506 2 4 300 5.236 200 100 400 507 3 4 240 4.189 200 100 400 50
Matriks Kekakuan BatangElemen 1
1 0 -1 0 50 0 -50 0
[kl(1)] = EA/L0 0 0 0
=0 0 0 0
-1 0 1 0 -50 0 50 00 0 0 0 0 0 0 0
0.500 0.866 0 0
[T(1)] =-0.866 0.500 0 0
0 0 0.500 0.8660 0 -0.866 0.500
0.500 -0.866 0 0 50 0 -50 0 0.500 0.866 0.000 0.000
[kg(1)] =0.866 0.500 0 0
x0 0 0 0
x-0.866 0.500 0.000 0.000
0 0 0.500 -0.866 -50 0 50 0 0.000 0.000 0.500 0.8660 0 0.866 0.500 0 0 0 0 0.000 0.000 -0.866 0.500
25.00 0.00 -25.00 0.00 0.500 0.866 0.000 0.000
=43.30 0.00 -43.30 0.00
x-0.866 0.500 0.000 0.000
-25.00 0.00 25.00 0.00 0.000 0.000 0.500 0.866-43.30 0.00 43.30 0.00 0.000 0.000 -0.866 0.500
12.50 21.65 -12.50 -21.65 1
=21.65 37.50 -21.65 -37.50 2-12.50 -21.65 12.50 21.65 3-21.65 -37.50 21.65 37.50 4
1 2 3 4
Elemen 2
1 0 -1 0 50 0 -50 0
[kl(2)] = EA/L0 0 0 0
=0 0 0 0
-1 0 1 0 -50 0 50 00 0 0 0 0 0 0 0
1.000 0.000 0 0
[T(2)] =0.000 1.000 0 0
0 0 1.000 0.0000 0 0.000 1.000
1.000 0.000 0 0 50 0 -50 0 1.000 0.000 0.000 0.000
[kg(2)] =0.000 1.000 0 0
x0 0 0 0
x0.000 1.000 0.000 0.000
0 0 1.000 0.000 -50 0 50 0 0.000 0.000 1.000 0.0000 0 0.000 1.000 0 0 0 0 0.000 0.000 0.000 1.000
50.00 0.00 -50.00 0.00 1.000 0.000 0.000 0.000
=0.00 0.00 0.00 0.00
x0.000 1.000 0.000 0.000
-50.00 0.00 50.00 0.00 0.000 0.000 1.000 0.0000.00 0.00 0.00 0.00 0.000 0.000 0.000 1.000
50.00 0.00 -50.00 0.00 3
=0.00 0.00 0.00 0.00 4
-50.00 0.00 50.00 0.00 50.00 0.00 0.00 0.00 6
3 4 5 6
Elemen 3
1 0 -1 0 50 0 -50 0
[kl(3)] = EA/L0 0 0 0
=0 0 0 0
-1 0 1 0 -50 0 50 00 0 0 0 0 0 0 0
0.500 -0.866 0 0
[T(3)] =0.866 0.500 0 0
0 0 0.500 -0.8660 0 0.866 0.500
0.500 0.866 0 0 50 0 -50 0 0.500 -0.866 0.000 0.000
[kg(3)] =-0.866 0.500 0 0
x0 0 0 0
x0.866 0.500 0.000 0.000
0 0 0.500 0.866 -50 0 50 0 0.000 0.000 0.500 -0.8660 0 -0.866 0.500 0 0 0 0 0.000 0.000 0.866 0.500
25.00 0.00 -25.00 0.00 0.500 -0.866 0.000 0.000
=-43.30 0.00 43.30 0.00
x0.866 0.500 0.000 0.000
-25.00 0.00 25.00 0.00 0.000 0.000 0.500 -0.86643.30 0.00 -43.30 0.00 0.000 0.000 0.866 0.500
12.50 -21.65 -12.50 21.65 5
=-21.65 37.50 21.65 -37.50 6-12.50 21.65 12.50 -21.65 921.65 -37.50 -21.65 37.50 10
5 6 9 10
Elemen 4
1 0 -1 0 50 0 -50 0
[kl(4)] = EA/L0 0 0 0
=0 0 0 0
-1 0 1 0 -50 0 50 00 0 0 0 0 0 0 0
1.000 0.000 0 0
[T(4)] =0.000 1.000 0 0
0 0 1.000 0.0000 0 0.000 1.000
1.000 0.000 0 0 50 0 -50 0 1.000 0.000 0.000 0.000
[kg(4)] =0.000 1.000 0 0
x0 0 0 0
x0.000 1.000 0.000 0.000
0 0 1.000 0.000 -50 0 50 0 0.000 0.000 1.000 0.0000 0 0.000 1.000 0 0 0 0 0.000 0.000 0.000 1.000
50.00 0.00 -50.00 0.00 1.000 0.000 0.000 0.000
=0.00 0.00 0.00 0.00
x0.000 1.000 0.000 0.000
-50.00 0.00 50.00 0.00 0.000 0.000 1.000 0.0000.00 0.00 0.00 0.00 0.000 0.000 0.000 1.000
50.00 0.00 -50.00 0.00 1
=0.00 0.00 0.00 0.00 2
-50.00 0.00 50.00 0.00 70.00 0.00 0.00 0.00 8
1 2 7 8
Elemen 5
1 0 -1 0 50 0 -50 0
[kl(5)] = EA/L0 0 0 0
=0 0 0 0
-1 0 1 0 -50 0 50 00 0 0 0 0 0 0 0
1.000 0.000 0 0
[T(5)] =0.000 1.000 0 0
0 0 1.000 0.0000 0 0.000 1.000
1.000 0.000 0 0 50 0 -50 0 1.000 0.000 0.000 0.000
[kg(5)] =0.000 1.000 0 0
x0 0 0 0
x0.000 1.000 0.000 0.000
0 0 1.000 0.000 -50 0 50 0 0.000 0.000 1.000 0.0000 0 0.000 1.000 0 0 0 0 0.000 0.000 0.000 1.000
50.00 0.00 -50.00 0.00 1.000 0.000 0.000 0.000
=0.00 0.00 0.00 0.00
x0.000 1.000 0.000 0.000
-50.00 0.00 50.00 0.00 0.000 0.000 1.000 0.0000.00 0.00 0.00 0.00 0.000 0.000 0.000 1.000
50.00 0.00 -50.00 0.00 7
=0.00 0.00 0.00 0.00 8
-50.00 0.00 50.00 0.00 90.00 0.00 0.00 0.00 10
7 8 9 10
Elemen 6
1 0 -1 0 50 0 -50 0
[kl(6)] = EA/L0 0 0 0
=0 0 0 0
-1 0 1 0 -50 0 50 00 0 0 0 0 0 0 0
0.500 -0.866 0 0
[T(6)] =0.866 0.500 0 0
0 0 0.500 -0.8660 0 0.866 0.500
0.500 0.866 0 0 50 0 -50 0 0.500 -0.866 0.000 0.000
[kg(6)] =-0.866 0.500 0 0
x0 0 0 0
x0.866 0.500 0.000 0.000
0 0 0.500 0.866 -50 0 50 0 0.000 0.000 0.500 -0.8660 0 -0.866 0.500 0 0 0 0 0.000 0.000 0.866 0.500
25.00 0.00 -25.00 0.00 0.500 -0.866 0.000 0.000
=-43.30 0.00 43.30 0.00
x0.866 0.500 0.000 0.000
-25.00 0.00 25.00 0.00 0.000 0.000 0.500 -0.86643.30 0.00 -43.30 0.00 0.000 0.000 0.866 0.500
12.50 -21.65 -12.50 21.65 3
=-21.65 37.50 21.65 -37.50 4-12.50 21.65 12.50 -21.65 721.65 -37.50 -21.65 37.50 8
3 4 7 8
Elemen 7
1 0 -1 0 50 0 -50 0
[kl(7)] = EA/L0 0 0 0
=0 0 0 0
-1 0 1 0 -50 0 50 00 0 0 0 0 0 0 0
-0.500 -0.866 0 0
[T(7)] =0.866 -0.500 0 0
0 0 -0.500 -0.8660 0 0.866 -0.500
-0.500 0.866 0 0 50 0 -50 0 -0.500 -0.866 0.000 0.000
[kg(7)] =-0.866 -0.500 0 0
x0 0 0 0
x0.866 -0.500 0.000 0.000
0 0 -0.500 0.866 -50 0 50 0 0.000 0.000 -0.500 -0.8660 0 -0.866 -0.500 0 0 0 0 0.000 0.000 0.866 -0.500
-25.00 0.00 25.00 0.00 -0.500 -0.866 0.000 0.000
=-43.30 0.00 43.30 0.00
x0.866 -0.500 0.000 0.000
25.00 0.00 -25.00 0.00 0.000 0.000 -0.500 -0.86643.30 0.00 -43.30 0.00 0.000 0.000 0.866 -0.500
12.50 21.65 -12.50 -21.65 5
=21.65 37.50 -21.65 -37.50 6-12.50 -21.65 12.50 21.65 7-21.65 -37.50 21.65 37.50 8
5 6 7 8
Matriks Kekauan Struktur
1 2 3 4 5 6 7 8 9 10F1 62.50 21.65 -12.50 -21.65 0 0 -50.00 0.00 0 0 1 u1G1 21.65 37.50 -21.65 -37.50 0 0 0.00 0.00 0 0 2 v1F2 -12.50 -21.65 75.00 0.00 -50.0 0.00 -12.50 21.65 0 0 3 u2G2 -21.65 -37.50 0.00 75.00 0.00 0.00 21.65 -37.50 0 0 4 v2
F3=
0 0 -50.00 0.0075.0
00.00 -12.50 -21.65 -12.50 21.65 5
xu3
G3 0 0 0.00 0.00 0.00 75.00 -21.65 -37.50 21.65 -37.5 6 v3F4 -50.00 0.00 -12.50 21.65 -12.5 -21.65 125.00 0.00 -50.00 0.00 7 u4G4 0.00 0.00 21.65 -37.50 -21.6 -37.50 0.00 75.00 0.00 0.00 8 v4F5 0 0 0 0 -12.5 21.65 -50.00 0.00 62.50 -21.6 9 u5
G5 0 0 0 021.6
5-37.50 0.00 0.00 -21.65 37.50 10 v5
Penyusunan Kembali3 4 5 6 7 8 9 1 2 10
0 75.00 0.00 -50.00 0.00 -12.50 21.65 0 -12.50 -21.65 0 3 u20 0.00 75.00 0.00 0.00 21.65 -37.50 0 -21.65 -37.50 0 4 v2
-5.43 -50.00 0.00 75.00 0.00 -12.50 -21.65 -12.50 0 0 21.65 5 u3
0 0.00 0.00 0.00 75.00 -21.65 -37.50 21.65 0 0-
37.506 v3
0=
-12.50 21.65 -12.50 0.00125.0
00.00 -50.00 -50.00 0.00 0.00 7
xu4
-7.43 21.65 -37.50 -21.65 0.00 0.00 75.00 0.00 0.00 0.00 0.00 8 v4
0 0 0 -12.50 21.65 -50.00 0.00 62.50 0 0-
21.659 u5
F1 -12.50 -21.65 0 0 -50.00 0.00 0 62.50 21.65 0 1 0G1 -21.65 -37.50 0 0 0.00 0.00 0 21.65 37.50 0 2 0G5 0 0 21.65 -37.50 0.00 0.00 -21.65 0 0 37.50 10 0
Perpindahan3 4 5 6 7 8 9
0 75.00 0.00 -50.00 0.00 -12.50 21.65 0 3 u20 0.00 75.00 0.00 0.00 21.65 -37.50 0 4 v2
-5.05 -50.00 0.00 75.00 0.00 -12.50 -21.65 -12.50 5x
u30 = 0.00 0.00 0.00 75.00 -21.65 -37.50 21.65 6 v30 -12.50 21.65 -12.50 0.00 125.00 0.00 -50.00 7 u4
-7.05 21.65 -37.50 -21.65 0.00 0.00 75.00 0.00 8 v40 0 0 -12.50 21.65 -50.00 0.00 62.50 9 u5
u2 0.0370370 -0.0094086 0.0274074 -0.005559 0.0148148 -0.0102640 0.0192592 0v2 -0.0076980 0.022222 -0.003849 0.0022222 -0.007698 0.0133333 -0.007698 0u3 0.0288888 -0.0064150 0.0377777 -0.0064150 0.0155555 -0.0038490 0.0222222 -5.05v3 = -0.0042766 0.0064197 -0.000855 0.0153086 -0.001710 0.0118518 -0.006842 x 0u4 0.0159259 -0.0100501 0.0151851 -0.006201 0.0203703 -0.0083395 0.0214814 0v4 -0.006201 0.0119753 0.0010691 0.0008641 -0.003635 0.0218518 -0.002993 -7.05u5 0.02 -0.011547 0.02 -0.0115470 0.02 -0.0115470 0.04 0
u2 -0.0660461 cmv2 -0.0745625 cmu3 -0.1636423 cmv3 = -0.0792361 cmu4 -0.0178916 cmv4 -0.1594548 cmu5 -0.0195936 cm
Reaksi Tumpuan
-0.06604613 4 5 6 7 8 9 -0.0745625
F1 -12.50 -21.65 0 0 -50.0 0.00 0 1 -0.1636423G1 = -21.65 -37.50 0 0 0.00 0.00 0 2 x -0.0792361G5 0 0 21.65 -37.50 0.00 0.00 -21.65 10 -0.0178916
-0.1594548-0.0195936
F13.33448767
5ton
G1 =4.22603689
1ton
G5 -0.14739139 ton
u1=
0
v1=
0
u2=
-0.0660461
v2=
-0.0745625
u3=
-0.1636423
v3=
-0.0792361
u4=
-0.0178916
v4=
-0.1594548
u5=
-0.0195936
v5=
0
Gaya-Gaya BatangBatang
1[F] = [T] x [k] x [D]
F1 0.500 0.866 0.000 0.000 12.50 21.65 -12.50 -21.6 0G1
=-0.866 0.500 0.000 0.000
x21.65 37.50 -21.65 -37.5
x0
F2 0.000 0.000 0.500 0.866 -12.50 -21.65 12.50 21.65 -0.066046G2 0.000 0.000 -0.866 0.500 -21.65 -37.50 21.65 37.50 -0.074562
25 43.301270 -25 -43.301270 0
=-1.776E-15 0 1.776E-15 0
x0
-25 -43.301270 25 43.301270 -0.06604611.77636E-15 0 -1.776E-15 0 -0.0745625
4.8798 ton
=0.0000 ton
TEKAN-4.8798 ton
0.0000 ton
Batang 2
[F] = [T] x [k] x [D]
F2 1.000 0.000 0.000 0.000 50.00 0.00 -50.00 0.00 -0.0660461G2
=0.000 1.000 0.000 0.000
x0.00 0.00 0.00 0.00
x-0.0745625
F3 0.000 0.000 1.000 0.000 -50.00 0.00 50.00 0.00 -0.1636423G3 0.000 0.000 0.000 1.000 0.00 0.00 0.00 0.00 -0.0792361
50 0 -50 0 -0.0660461
=0 0 0 0
x-0.0745625
-50 0 50 0 -0.16364230 0 0 0 -0.0792361
4.8798 ton
=0.0000 ton
TEKAN-4.8798 ton0.0000 ton
Batang 3
[F] = [T] x [k] x [D]
F3 0.500 -0.866 0.000 0.000 12.50 -21.65 -12.50 21.65 -0.1636423G3
=0.866 0.500 0.000 0.000
x-21.65 37.50 21.65 -37.50
x-0.0792361
F5 0.000 0.000 0.500 -0.866 -12.50 21.65 12.50 -21.65 -0.0195936G5 0.000 0.000 0.866 0.500 21.65 -37.50 -21.65 37.50 0
25 -43.3012701 -2543.3012701
9-0.1636423
=1.776E-15 0 -1.776E-15 0
x-0.079236
-2543.3012701
925 -43.3012701 -0.0195936
-1.776E-15 0 1.776E-15 0 0
-0.1702 ton
=0.0000 ton
TARIK0.1702 ton0.0000 ton
Batang 4
[F] = [T] x [k] x [D]
F1 1.000 0.000 0.000 0.000 50.00 0.00 -50.00 0.00 0G1
=0.000 1.000 0.000 0.000
x0.00 0.00 0.00 0.00
x0
F4 0.000 0.000 1.000 0.000 -50.00 0.00 50.00 0.00 -0.0178916G4 0.000 0.000 0.000 1.000 0.00 0.00 0.00 0.00 -0.159454
50 0 -50 0 0
=0 0 0 0
x0
-50 0 50 0 -0.01789160 0 0 0 -0.159454
0.8946 ton
=0.0000 ton
TEKAN-0.8946 ton0.0000 ton
Batang 5
[F] = [T] x [k] x [D]
F4 1.000 0.000 0.000 0.000 50.00 0.00 -50.00 0.00 -0.0178916G4
=0.000 1.000 0.000 0.000
x0.00 0.00 0.00 0.00
x-0.1594548
F5 0.000 0.000 1.000 0.000 -50.00 0.00 50.00 0.00 -0.0195936G5 0.000 0.000 0.000 1.000 0.00 0.00 0.00 0.00 0
50 0 -50 0 -0.0178916
=0 0 0 0
x-0.1594548
-50 0 50 0 -0.01959360 0 0 0 0
0.0851 ton
=0.0000 ton
TEKAN-0.0851 ton0.0000 ton
Batang 6
[F] = [T] x [k] x [D]
F2 0.500 -0.866 0.000 0.000 12.50 -21.65 -12.50 21.65 -0.0660461G2
=0.866 0.500 0.000 0.000
x-21.65 37.50 21.65 -37.50
x-0.0745625
F4 0.000 0.000 0.500 -0.866 -12.50 21.65 12.50 -21.65 -0.0178916G4 0.000 0.000 0.866 0.500 21.65 -37.50 -21.65 37.50 -0.159454
25 -43.301270 -2543.3012701
9-0.0660461
=1.776E-15 0 -1.776E-15 0
x-0.0745625
-2543.3012701
925 -43.301270 -0.0178916
-1.776E-15 0 1.776E-15 0 -0.159454
-4.8798 ton
=0.0000 ton
TARIK4.8798 ton0.0000 ton
Batang 7
[F] = [T] x [k] x [D]
F3 -0.500 -0.866 0.000 0.000 12.50 21.65 -12.50 -21.65 -0.1636423G3
=0.866 -0.500 0.000 0.000
x21.65 37.50 -21.65 -37.50
x-0.0792361
F4 0.000 0.000 -0.500 -0.866 -12.50 -21.65 12.50 21.65 -0.01789G4 0.000 0.000 0.866 -0.500 -21.65 -37.50 21.65 37.50 -0.159454
-25 -43.3012 25 43.30127 -0.163642
=1.77E-15 0 -1.77E-15 0
x-0.07923
2543.3012701
9-25 -43.3012 -0.017891
-1.77E-15 0 1.77E-15 0 -0.15945
0.1702 ton
=0.0000 ton
TEKAN-0.1702 ton0.0000 ton
