plane truss
TRANSCRIPT
PLANE TRUSS
Diketahui:p1 = 23000 kgp2 = 32000 kg
L1 = 8m = 800 cmL2 = 8m = 800 cmH = 8m = 800 cm
Profil WF 200 x 200 x 12 x 12
E = 2,1 x 10⁶ = 2100000 kg/cm²A = 71,53cm²I = 4980 cm⁴
PENYELESAIAN
Titik KoordinatX Y
1 800 8002 800 03 0 04 1600 0
E = 2100000 Kg/cm²A = 71,53 cm²I = 4980 cm⁴
Structure Stiffnes M atrix
M EM BER 1
x (cm) y (cm)3 0 02 800 01 800 1 0 187766,25
Cos Sin EA/LM ember Titik Koordinat L (cm)
1 0 -1 0K = 0 0 0 0
-1 0 1 00 0 0 0
1 0 -1 0K = 0 0 0 0 X 187766.25 -1 0 1 0 0 0 0 0
7 8 1 2
187766.25 0 -187766.25 0 7K = 0 0 0 0 8
-187766.25 0 187766.25 0 10 0 0 0 2
M EM BER 2
x (cm) y (cm)4 1600 02 800 0
L (cm) Cos Sin EA/L
2 800 -1 0 187766,25
M ember Titik Koordinat
1 0 -1 0K = 0 0 0 0
-1 0 1 00 0 0 0
1 0 -1 0K = 0 0 0 0 X 187766,25
-1 0 1 00 0 0 05 6 1 2
187766,25 0 -187766,25 0 5
K = 0 0 0 0 6-187766,25 0 187766,25 0 1
0 0 0 0 2
M EM BER 3
x (cm) y (cm)3 0 01 800 800
M ember Titik Koordinat L (cm) Cos Sin EA/L
3 1131,37085 0,71 0,71 132770,7887
0,5 0,5 -0,5 -0,5K = 0,5 0,5 -0,5 -0,5 -0,5 -0,5 0,5 0,5 -0,5 -0,5 0,5 0,5 0,5 0,5 -0,5 -0,5K = 0,5 0,5 -0,5 -0,5 X 132770,7887 -0,5 -0,5 0,5 0,5
-0,5 -0,5 0,5 0,57 8 3 4
66385,39433 66385,39433 -66385,39433 -66385,39433 7K = 66385,39433 66385,39433 -66385,39433 -66385,39433 8
-66385,39433 -66385,39433 66385,39433 66385,39433 3-66385,39433 -66385,39433 66385,39433 66385,39433 4
M ember 4
x (cm) y (cm)2 800 01 800 800
M ember Titik Koordinat L (cm) Cos Sin EA/L
4 800 0 1 187766,25
0 0 0 0K = 0 1 0 -1 0 0 0 0 0 -1 0 1
0 0 0 0K = 0 1 0 -1 X 187766,25
0 0 0 0 0 -1 0 1 1 2 3 4
0 0 0 0 1K = 0 187766,25 0 -187766,25 2
0 0 0 0 30 -187766,25 0 187766,25 4
M ember 5
x (cm) y (cm)4 1600 01 800 800
M ember Titik Koordinat L (cm) Cos Sin EA/L
5 1131,37085 -0,71 0,71 132770,7887
0,5 -0,5 -0,5 0,5K = -0,5 0,5 0,5 -0,5 -0,5 0,5 0,5 -0,5 0,5 -0,5 -0,5 0,5 0,5 -0,5 -0,5 0,5
K = -0,5 0,5 0,5 -0,5 X 132770,7887 -0,5 0,5 0,5 -0,5 0,5 -0,5 -0,5 0,5 5 6 3 4
66385,39433 -66385,39433 -66385,39433 66385,39433 5K = -66385,39433 0 66385,39433 -66385,39433 6
-66385,39433 0 66385,39433 -66385,39433 366385,39433 0 -66385,39433 66385,39433 4
M atriks Kekakuan Dalam Sistem Koordinat Global
M EM BER 1
1 0 0 0[T] = 0 1 0 0
0 0 1 00 0 0 1
1 0 0 0[TT] = 0 1 0 0
0 0 1 0
0 0 0 1
187766,25 0 -187766,25 0K = 0 0 0 0
-187766,25 0 187766,25 00 0 0 0
[K]= ( [T]T.[k] ). [T]
7 8 1 2[K] = 187766,25 0 -187766,25 0 187766,25 0 -187766,25 0 7
0 0 0 0 × [T] =====► [K] = 0 0 0 0 8-187766,25 0 187766,25 0 -187766,25 0 187766,25 0 1
0 0 0 0 0 0 0 0 2
-1 0 0 0[TT] = 0 -1 0 0
0 0 -1 00 0 0 -1
187766,25 0 -187766,25 0K = 0 0 0 0
-187766,25 0 187766,25 00 0 0 0
[K]= ( [T]T.[k] ). [T]
5 6 1 2-187766,25 0 187766,25 0 187766,25 0 -187766,25 0 5
[K] = 0 0 0 0 × [T] =====► [K] = 0 0 0 0 6187766,25 0 -187766,25 0 -187766,25 0 187766,25 0 1
0 0 0 0 0 0 0 0 2
[T] = -0,71 0,71 0,00 0,000,00 0,00 0,71 0,710,00 0,00 -0,71 0,71
0,71 -0,71 0,00 0,00[TT] = 0,71 0,71 0,00 0,00
0,00 0,00 0,71 -0,710,00 0,00 0,71 0,71
66385,39433 66385,39433 -66385,39433 -66385,39433K = 66385,39433 66385,39433 -66385,39433 -66385,39433
-66385,39433 -66385,39433 66385,39433 66385,39433-66385,39433 -66385,39433 66385,39433 66385,39433
[K]= ( [T]T.[k] ). [T]
7 8 3 42,18279E-11 0 0 0 1,54346E-11 1,54346E-11 0 0 7
[K] = 93883,125 93883,125 -93883,125 -93883,125 × [T] =====► [K] = 1,45519E-11 132770,7887 0 -132770,79 80 0 0 0 0 0 0 0 3
-93883,125 -93883,125 93883,125 93883,125 0 -132770,7887 0 132770,79 4
0 1 0 0[T] = -1 0 0 0
0 0 0 10 0 -1 0
0 -1 0 0[TT] = 1 0 0 0
0 0 0 -10 0 1 0
0 0 0 0K = 0 187766,25 0 -187766,25
0 0 0 00 -187766,25 0 187766,25
[K]= ( [T]T.[k] ). [T]
1 2 3 40 -187766,25 0 187766,25 187766,25 0 -187766,25 0 1
[K] = 0 0 0 0 × [T] =====► [K] = 0 0 0 0 20 187766,25 0 -187766,25 -187766,25 0 187766,25 0 30 0 0 0 0 0 0 0 4
M ember 5
-0,71 0,71 0,00 0,00[T] = -0,71 -0,71 0,00 0,00
0,00 0,00 -0,71 0,710,00 0,00 -0,71 -0,71
-0,71 -0,71 0,00 0,00[TT] = 0,71 -0,71 0,00 0,00
0,00 0,00 -0,71 -0,710,00 0,00 0,71 -0,71
66385,39433 -66385,39433 -66385,39433 66385,39433K = -66385,39433 0 66385,39433 -66385,39433
-66385,39433 0 66385,39433 -66385,3943366385,39433 0 -66385,39433 66385,39433
[K]= ( [T]T.[k] ). [T]
5 6 3 40 46941,5625 0 0 -33192,6972 -33192,69716 0 0 5
[K] = 93883,125 -46941,5625 -93883,125 93883,125 × [T] =====► [K] = -33192,6972 99578,09149 0 -132770,79 60 0 0 0 0 0 0 0 3
-93883,125 0 93883,125 -93883,125 66385,39433 -66385,39433 0 132770,79 4
Joint Load vector
Gaya Yang Bekerja Terhadap Kontruksi
0 1[P] = 0 2
32000 3-23000 4
M atriks Kekakuan Struktur Dari M asing-M asing M ember
[S1] = 187766,25 0 0 0 10 0 0 0 20 0 0 0 30 0 0 0 4
187766,25 0 0 0 1[S2] = 0 0 0 0 2
0 0 0 0 30 0 0 0 4
0 0 0 0 1[S3] = 0 0 0 0 2
0 0 66385,39433 66385,39433 3
0 0 66385,39433 66385,39 4
0 0 0 0 1[S4] = 0 187766,25 0 -187766,25 2
0 0 0 0 30 -187766,25 0 187766,25 4
0 0 0 0 1[S5] = 0 0 0 0 2
0 0 66385,39433 -66385,39433 30 0 -66385,39433 66385,39 4
M atriks Kekakuan Struktur Secara Keseluruhan
375532,5 0 0 0 1[S] = 0 187766,25 0 -187766,25 2
0 0 132770,7887 0 30 -187766,25 0 320537,04 4
Invers M atriks Struktur Secara Keseluruhan
0,000002663 0,000000000 0,000000000 0,000000000[S-1] = 0,000000000 0,000012858 0,000000000 0,000007532
0,000000000 0,000000000 0,000007532 0,0000000000,000000000 0,000007532 0,000000000 0,000007532
Perpindahan Struktur yang Timbul
[d] = [S-1]*[P]
0 1[d] = -0,173230876 2
0,241016871 3-0,173230876 4
CEK
375532,5 0 0 0 0 0P = Sd = 0 187766,25 0 -187766,25 x -0,173230876 P = 0
0 0 132770,7887 0 0,241016871 320000 -187766,25 0 320537,0387 -0,173230876 -23000
M ember End Displacement and End Forces
M EM BER 1
0 7[v1] = 0 8
0 1-0,173230876 2
u = T v
1 0 0 0[T] = 0 1 0 0
0 0 1 00 0 0 1
0 7[u1] = 0 8
0 1-0,173230876 2
Q = ku
187766,25 0 -187766,25 0 0 7k = 0 0 0 0 [Q1] = 0 8
-187766,25 0 187766,25 0 0 10 0 0 0 0 2
F = TT Q
1 0 0 0 0 7[TT] = 0 1 0 0 [F1] = 0 8
0 0 1 0 0 10 0 0 1 0 2
M EM BER 2
0 5[v2] = 0 6
0 1 -0,173230876 2
u = T v
-1 0 0 0[T] = 0 -1 0 0
0 0 -1 00 0 0 -1
0 5[u2] = 0 6
0 10,173230876 2
Q = ku
187766,25 0 -187766,25 0 0 5k = 0 0 0 0 [Q2] = 0 6
-187766,25 0 187766,25 0 0 10 0 0 0 0 2
F = TT Q
-1 0 0 0 0 5[TT] = 0 -1 0 0 [F2] = 0 6
0 0 -1 0 0 10 0 0 -1 0 2
M EM BER 3
0 7[v3] = 0 8
0,241016871 3-0,173230876 4
u = T v
0,707106781 0,707106781 0 0[T] = -0,707106781 0,707106781 0 0
0 0 0,707106781 0,7071067810 0 -0,707106781 0,707106781
0 7[u3] = 0 8
0,047931937 3-0,292917391 4
Q = ku
132770,7887 0 -132770,7887 0 -6363,961031 7k = 0 0 0 0 [Q3] = 0 8
-132770,7887 0 132770,7887 0 6363,961031 30 0 0 0 0 4
F = TT Q
0,707106781 -0,707106781 0 0[TT] = 0,707106781 0,707106781 0 0 -4500 7
0 0 0,707106781 -0,707106781 [F3] = -4500 80 0 0,707106781 0,707106781 4500 3
4500 4
M ember 4
0 1[v4] = -0,173230876 2
0,241016871 3-0,173230876 4
u = T v
0 1 0 0[T] = -1 0 0 0
0 0 0 10 0 -1 0
-0,173230876 1[u4] = 0 2
-0,173230876 3-0,241016871 4
Q = ku
187766,25 0 -187766,25 0 0 1k = 0 0 0 0 [Q4] = 0 2
-187766,25 0 187766,25 0 0 30 0 0 0 0 4
F = TT Q
0 -1 0 0 0 1[TT] = 1 0 0 0 [F4] = 0 2
0 0 0 -1 0 30 0 1 0 0 4
M ember 5
0 5[v5] = 0 6
0,241016871 3-0,173230876 4
u = T v
-0,707106781 0,707106781 0 0[T] = -0,707106781 -0,707106781 0 0
0 0 -0,707106781 0,7071067810 0 -0,707106781 -0,707106781
0,0000000 5[u5] = 0,0000000 6
-0,2929174 3-0,0479319 4
Q = ku
132770,7887 0 -132770,7887 0 38891 5k = 0 0 0 0 [Q5] = 0 6
-132770,7887 0 132770,7887 0 -38891 30 0 0 0 0 4
F = TT Q
-0,707106781 -0,707106781 0 0 -27500 5[TT] = 0,707106781 -0,707106781 0 0 [F5] = 27500 6
0 0 -0,707106781 -0,707106781 27500 30 0 0,707106781 -0,707106781 -27500 4
Equilibrium Check
Titik MemberΣ1 2 3 4 5
1 0 0 0 0 0 02 0 0 0 0 0 03 0 0 4500 0 27500 320004 0 0 4500 0 -27500 -230005 0 0 0 0 -27500 -275006 0 0 0 0 27500 275007 0 0 -4500 0 0 -45008 0 0 -4500 0 0 -4500ΣF 0 0 0 0 0 0
→ Fx = 0∑↑ Fy = 0∑
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