hw ads 1.made oka
TRANSCRIPT
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Home Work. 01
MATA KULIAH
ANALISA DINAMIKA STRUKTUR
Dosen : Dr. Ir. Bambang Supriyadi, CES,DEA.
DIKERJAKAN OLEH
GUSTI MADE OKA
18695/I-1/1859/02
JURUSAN TEKNIK SIPIL
0
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PROGRAM PASCA SARJANA
UNIVERSITAS GADJAH MADA
2003
1). Detahui struktur seperti pada gambar dibawah ini :
Diminta : entukan kekakuan matrik struktur !
x
v
v
v
∂
∂=→
= θ
θ
θ δ
2
2
1
1
3
4
2
321 xa xa xaav x +++=
2
432 32 xa xaa x ++=θ
"ondisi batas :
110 av x =→= . . . . . . . . . . . . . . . .
. . # 1 )
21 a=→ θ . . . . . . . . . . . . . . . .
. # $ )
3
4
2
3112
3
4
2
3212
La La Lvv
La La Laav L x
+++=+++=→=
θ
La L L
v
L
va 4
1
2
1
2
2
3 −−−= θ
. . . . . . . . . . . .
.# % )
2
4322 32 La Laa L x ++=→= θ
2
4312 32 La La ++= θ θ
1
L I E S ,,,, ρ
1v2v
2θ
1θ
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L
a
L La
3
2
33
3
2
1
2
2
4 −−= θ θ
. . . . . . . . . . . .
. .# & )
"oe'sien 4a dimasukkan keda(am persamaan # % )
dipero(eh :
L L L L
v
L
va
a
L L L L
v
L
va
L
a
L L L
L L
v
L
va
333
3
2
33
3
2
33
121
2
1
2
23
3121
2
1
2
2
3
3
2
1
2
21
2
1
2
2
3
θ θ θ
θ θ θ
θ θ θ
+−−−=
++−−−=
−−−−−=
L L L L
v
L
va
333
121
2
1
2
23 θ θ θ +−−−=
L L L L
v
L
va
121
2
1
2
2
3
333 θ θ θ +−−−=
L L L
v
L
va
21
2
1
2
2
3
233 θ θ −−−= . . . . . . . . . . . .
. . . # )"oe'sien 3a dimasukkan ke persamaan #&) akan dipero(eh
:
L
a
L La
3
2
33
3
2
1
2
2
4 −−= θ θ
−−−−−=
L L L
v
L
v
L L La
21
2
1
2
2
2
1
2
2
4
233
3
2
33
θ θ θ θ
2
2
2
1
3
1
3
2
2
1
2
2
43
2
3
422
33 L L L
v
L
v
L La
θ θ θ θ +++−−=
3
1
3
2
2
1
2
2
4
22
L
v
L
v
L La +−+=
θ θ . . . . . . . . . . . . . . .
. . .# * )
+aka persamaan xv menadi :
3
4
2
321 xa xa xaav x +++=
2
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+−−+−+−
+−
−
+−
+−
= 232232
2
32
2
32
62;126;64;126
62
126
64
126
L
x
L L
x
L L
x
L L
x
L
L
x
L
L
x
L
L
x
L
L
x
L
B BT
[ ] ∫ = L
T dx B B EI K
0
3
333333
6
3
5
2
4
0
6
3
5
2
4
0
6
2
54
0
6
2
554
32
0
3211
12
487236
3
144
2
14436
3
144
2
14436
3
144
2
14436
14414436144727236
126126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−
=
∫ ∫
∫
2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
2
0
3212
6
244224
3
72
2
8424
3
72
2
8424
3
72
2
8424
72842472483624
64126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−
=
∫ ∫
∫
4
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3
333333
6
3
5
2
4
0
6
3
5
2
4
0
6
2
54
0
6
2
554
32
0
3213
6
487236
3
144
2
14436
3
144
2
14436
3
144
2
14436
14414436144727236
126126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx
L
x
L
x
L
dx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
−=
−+−=
−+−=
−+−=
−+−=
−+−=
−++−=
−
+−
=
∫ ∫
∫
2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
2
0
3214
6
243012
3
72
2
6012
3
72
2
6012
3
72
2
6012
72601272243612
62126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−=
∫ ∫
∫
2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
32
0
221
6
244224
3
72
2
8424
3
72
2
8424
3
72
2
8424
72842472364824
12664
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−
=
∫ ∫
∫
5
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2
4
3
3
2
2
0
4
3
3
2
2
0
4
2
32
0
4
2
332
2
0
222
4
364816
3
36
2
4816
3
36
2
4816
3
36
2
4816
36481636242416
6464
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx
L
x
L
x
L
dx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−
=
∫ ∫
∫
2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
320
223
6
244224
3
72
2
8424
3
72
2
8424
3
72
2
8424
72842472364824
12664
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx
L
x
L L
x
L
K
L
L L
L
−=
−+−=
−+−=
−+−=
−+−=
−+−=
−++
−=
−
+−
=
∫ ∫ ∫
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
2
12188
3
36
2
368
3
36
2
368
3
36
2
368
363683612248
6264
4
3
3
2
2
0
4
3
3
2
2
0
4
2
32
0
4
2
332
2
0
224
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−
=
∫ ∫
∫
6
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3
333333
6
3
5
2
4
0
6
3
5
2
4
0
6
2
54
0
6
2
554
32
0
3231
12
487236
3
144
2
14436
3
144
2
14436
3
144
2
14436
14414436144727236
126126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx
L
x
L
x
L
dx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
−=
−+−=
−+−=
−+−=
−+−=
−+−=
−++−=
+−
−=
∫ ∫
∫
2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
20
3232
6
244224
3
72
2
8424
3
72
2
8424
3
72
2
8424
72842472483624
64126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx
L
x
L L
x
L
K
L
L L
L
−=
−+−=
−+−=
−+−=
−+−=
−+−=
−++−=
+−
−=
∫ ∫ ∫
3
333333
6
3
5
2
4
0
6
3
5
2
4
0
6
2
54
0
6
2
554
32
0
3233
12
487236
3
144
2
14436
3
144
2
14436
3
144
2
14436
14414436144727236
126126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
=
+−=
+−=
+−=
+−=
+−=
+−−=
−
−=
∫ ∫
∫
7
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2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
2
0
3234
6
243012
3
72
2
6012
3
72
2
6012
3
72
2
6012
72601272243612
62126
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx
L
x
L
x
L
dx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
−=
−+−=
−+−=
−+−=
−+−=
−+−=
−++−=
+−
−=
∫ ∫
∫
2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
320
241
6
243012
3
72
2
6012
3
72
2
6012
3
72
2
6012
72601272362412
12662
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx
L
x
L L
x
L
K
L
L L
L
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−=
∫ ∫ ∫
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
2
12188
3
36
2
368
3
36
2
368
3
36
2
368
363683624128
6462
4
3
3
2
2
0
4
3
3
2
2
0
3
2
32
0
4
2
332
2
0
242
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−=
∫ ∫
∫
8
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2
222222
5
3
4
2
3
0
5
3
4
2
3
0
5
2
43
0
5
2
443
32
0
243
6
243012
3
72
2
6012
3
72
2
6012
3
72
2
6012
72601272362412
12662
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx
L
x
L
x
L
dx
L
x
L
x
L
x
L
dx L
x
L L
x
L K
L
L L
L
−=
−+−=
−+−=
−+−=
−+−=
−+−=
−++−=
−
+−=
∫ ∫
∫
L
L L L L L L
L
L
L
L
L
L
L
x
L
x
L
x
dx L
x
L
x
Ldx
L
x
L
x
L
x
L
dx
L
x
L L
x
L
K
L
L L
L
4
12124
3
36
2
244
3
36
2
244
3
36
2
244
362443612124
6262
4
3
3
2
2
0
4
3
3
2
2
0
4
2
32
0
4
2
332
20
244
=
+−=
+−=
+−=
+−=
+−=
+−−=
+−
+−=
∫ ∫ ∫
adi kekakuan matrik struktur :
[ ]
−
−−−
−
−
=
L L L L
L L L L
L L L L
L L L L
EI K
4626
612612
2646
612612
22
2323
22
2323
[ ]
−−−−
−−
=
22
22
3
4626
612612
2646
612612
L L L L
L L
L L L L
L L
L
EI K
9