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TUGAS ANALISIS STRUKTUR
SOAL
b (ton)
a (ton)
460.98
300
BEBANa = 4 tonb = 5 ton
BATANG 1 A = 45 cmL = 300 cm BATANG 3
A = 40 cmL = 350 cm
BATANG 2 A = 50 cmL = 461 cm
E = 2100 t/cm
1 = 90 0
350300
3 = 0 0
= 319.3987 0
350
2 = 360-(90-arc tg
2
13
1 2
3
2
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8/10/2019 perhitungan anstruk metode matriks
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PENYELESAIAN
Matriks Kekakuan Elemen
Elemen 1 (dipilih nodal i = 1, dan j = 2)
315 0 -315 00 0 0 0
-315 0 315 00 0 0 0
0 1 0 0 0 -1 0 0-1 6E-17 0 0 1 0 0 00 0 6.1E-17 1 0 0 0 -10 0 -1
6E-17 0 0 1 0
0 -1 0 0 315 0 -315 0 0 1 0 01 6E-17 0 0 0 0 0 0 -1 0 0 00 0 0
-1 -315 0 315 0 0 0 0 10 0 1 6E-17 0 0 0 0 0 0 -1 0
0 -1 0 0 0 315 -0 -3151 6E-17 0 0 0 0 0 00 0 0 -1 -0 -315 0 315
00 0 1 6E-17 0 0 0 01 2 3 4
1E-30 1.9E-14 -1E-30 -2E-14 1 0 0 -0 -02E-14 315 -2E-14 -315 2 0
315 -0 -315
-0 -1.9E-14 1E-30 1.9E-14 3 -0 -0 0 0-0 -315 2E-14 315 4 -0 -315
0 315
Elemen 2 (dipilih nodal i = 2, dan j = 3)
228 0 -227.766 00 0 0 0
-228 0 227.766 00 0 0 0
0.76 -0.65 0 0 0.76 0.65 0 00.65 0.759 0 0 -0.7 0.76 0 0
0 0 0.75926 -0.651 0 0 0.76 0.650 0 0.65079 0.759 0 0 -0.7
0.76
0.759 0.65079 0 0 228 0 -228 0 0.76 -0.7 0 0-0.65 0.75926 0 0 0
0 0 0 0.65 0.76 0 0
0 0 0.759 0.65079 -228 0 228 0 0 0 0.76 -0.70 0 -0.651 0.75926 0
0 0 0 0 0 0.65 0.76
0.759 0.65079 0 0 173 -148 -173 148-0.65 0.75926 0 0 0 0 0 0
0 0 0.759 0.65079 -173 148 173 -1480 0 -0.651 0.75926 0 0 0 03 4
5 6
131.3 -112.543 -131.3 112.543 3-113 96.4655 112.5 -96.465 4-131
112.543 131.3 -112.54 5
112.5 -96.4655 -112.5 96.4655 6
[T(2)]T=
[kl (2)]=
[T(2)]=
[kg(2)]=[T(2)]T[kl (2)][T(2)]=
=
[kl (1)]=
[T(1)]=
=
[kg(1)]=[T(1)]T[kl (1)][T(1)]=
[T(1)]T=
=
=
SIKLUS
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Elemen 3 (dipilih nodal i = 1, dan j = 3)
240 0 -240 00 0 0 0
-240 0 240 00 0 0 0
1 0 0 0 1 0 00 1 0 0 0 1 0
0 0 1 0 0 0 10 0 0 1 0 0 0
1 0 0 0 240 0 -240 0 1 00 1 0 0 0 0 0 0 0 10 0 1 0 -240 0 240 0
0 00 0 0 1 0 0 0 0 0 0
1 0 0 0 240 0 -240 00 1 0 0 0 0 0 00 0 1 0 -240 0 240 00 0 0 1 0
0 0 01 2 5 6
240 0 -240 0 1
0 0 0 0 2-240 0 240 0 5
0 0 0 0 6
OVERALL STIFFNESS MATRIKS1 2 3 4 5 6
F1 240 0 0 -0 -240 0 U1 1G1 0 315 0 -315 0 0 V1 2F2 0 -2E-14
131.3 -113 -131.3 112.54 U2 3G2 0 -315 -112.543 411 112.543 -96.465
V2 4F3 -240 0 -131.3 113 371.3 -112.54 U3 5G3 0 0 112.543 -96
-112.54 96.465 V3 6
menjadiF1 240 0 0 -0 -240 0 0G1 0 315 0 -315 0 0 0
5 0 -2E-14 131.3 -113 -131.3 112.54 U2-4 0 -315 -112.543 411
112.543 -96.465 V20 -240 0 -131.3 113 371.3 -112.54 U3
G3 0 0 112.543 -96 -112.54 96.465 0
UNKNOW DISPLACEMENTS AND REACTIONS
5 131.3 -112.5 -131.3 U2-4 = -112.54 411.5 112.543 V20 -131.3
112.5 371.3 U3
U2 0.0141 0.003 0.00417 5V2 = 0.0027 0.003 0 -4U3 0.0042 -2E-19
0.00417 0
U2 0.0597V2 = 0U3 0.0208
[kl (3) ]=
[T(3)]= [T (3)]T=
=
=
=
=
SIKLUS
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F1 0 -0 -263 0.06G1 0 -280 0 0G3 90.72 -68 -90.7 0.02
-5.47= -0.25
0 3.4630
0MEMBER FORCES
1 Elemen 1 ( nodal i = 1, dan j = 2)
f10 0 g10 0 f21 0 g20 1
0 1 0 0 0 0 0 0 0-1 0 0 0 0 315 0 -315 00 0 0 1 0 0 0 0 0.059690
0 -1 0 0 -315 0 315 0.00091
2E-14 315 -0 -315 00 0 0 0 0
-0 -315 2E-14 315 0.060 0 0 0 9E-04
-0.290
0.2860
Elemen 2 ( nodal i = 2, dan j = 3)
f2g2f3
g3
0.759 -0.65 0 0 131 -113 -131 113 0.059690.651 0.76 0 0 -113
96.47 113 -96 0
0 0 0.759 -0.7 -131 112.5 131 -113 0.020830 0 0.651 0.76 113
-96.5 -113 96.5 0
172.9 -148 -173 148 0.06
1E-14 0 -0 0 0-173 148 172.9 -148 0.021
-0 0 1E-14 0 0
6.5850
-6.590
[T(2)
][kg(2)
][U(2)
]
=
=
=
=
[T(1)][kg (1)]{U(1)}=
=
=
=
=
SIKLUS
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Elemen 3 ( nodal i = 1, dan j = 3)
f1g1f3
g3
1 0 0 0 240 0 -240 0 00 1 0 0 0 0 0 0 0
0 0 1 0 -240 0 240 0 0.02080 0 0 1 0 0 0 0 0
240 0 -240 0 00 0 0 0 0
-240 0 240 0 0.0210 0 0 0 0
-5050
Hasil Analisa-5 ton
4 ton
6.5854
-5.5 ton
-0.3 ton 3.46 ton
* Elemen 1 = TekanElemen 2 = TekanElemen 3 = Tarik
= [T(3)][kg(3)][U(3)]
=
=
=
-0.3
5
SIKLUS
(2011-21-028)
