Analisa Dinamika Struktur
SOAL 1 q
H
L
L
DIKETAHUI :
Struktur pada gambar di atas dengan data sebagai berikut : Penampang persegi q
= 2 ton / m2
L
= 15 m
H
=7m
DIMINTA :
Kekakuan kolom di hitung dengan prinsip shear building, tentukan : a.
Simp Simpan anga gan n Dina Dinami mik k Stru Strukt ktur ur
b.
Dynamic Magnification Factor atau Dynamic Load Factor ( DLF )
Struktur rasio tersebut dengan rasio frekuensi masing – masing untuk : r
= 0,10 ; 0,25 ; 0,60 ; 0,90 ; 1,25 ; 1,75
Rasio Rasio Redam Redaman an ( ε ) = 5 % , 10% , 20% , 40% 40% , 70% 70%
1
Analisa Dinamika Struktur
PENYELESAIAN : I =
I =
1
bh
3
12 1 12
×30 ×30
3
I = 67500 cm4
Dengan prinsip shear building akan didapat kekakuan kolom : K =
K =
K
m
12 EI 3
H
12 × 2,1×10
5
700
×
67500
3
= 495, 95,918 kg / cm
=
ω =
ω =
2000 × 30 980
=
( 3kol kolom = 1487,7 7,755 kg/ kg/cm )
2
61, 225kgdt / cm
k m 495,918 61, 225
ω = 2,84 2,846 6 rad rad / deti detik k
2
Analisa Dinamika Struktur
Plot Simpangan Struktur ( Yt ) •
Untuk maka Ω
r = 0,1 → t = 1 detik =r.ω = 0,1 x 2,846 = 0,2846 rad / detik
Yt =
5000 1487,755
×
1 2
1 − 0,1
[sin( Ω×t ) − r sin (ω ×t )]
= 6,789 x 10-6 rad . cm / kg detik
•
Untuk r = 0,25 → t = 1 detik maka Ω
=r.ω = 0,25 x 2,846 = 0,7115 rad / detik
Yt =
5000 1487,755
×
1 1 − 0,25
2
[sin( Ω×t ) − r sin(ω ×t )]
= 0 rad . cm / kg detik
•
Untuk r = 0,6 → t = 1 detik maka Ω
=r.ω = 0,6 x 2,846 = 1,708 rad / detik
Yt =
5000 1487,755
×
1 1 − 0,6
2
[sin( Ω×t ) − r sin(ω ×t )]
= 0 rad . cm / kg detik
3
Analisa Dinamika Struktur
•
Untuk r = 1,25 → t = 1 detik maka Ω
=r.ω = 1,25 x 2,846 = 3,5575 rad / detik
Yt =
5000 1487,755
×
1 1 −1,25
2
[sin ( Ω×t ) − r sin (ω ×t )]
= 8,58 x 10-5 rad . cm / kg detik
Dynamic Load Factor ( DLF ) 1
DLF =
(1
Untuk
r 2 )
2
+
( 2 ×ξ × r ) 2
r = 0,1 dan ξ = 50 % maka DLF nya adalah : 1
DLF =
DLF
−
(1
−
)
2 2
0,1
+
( 2 × 50% × 0,1) 2
1,010
=
Untuk perhitungan selanjutnya dapat dilihat pada tabel berikut ini : R
ξ
ξ
ξ
ξ
ξ
DLF (ξ=5%)
DLF ( ξ =10 % )
DLF ( ξ = 20 % )
DLF ( ξ = 40 % )
DLF ( ξ = 70 % )
0,1
5%
10%
20%
40%
70%
1,0202
1,0199
1,0186
1,0137
1,0003
0,25
5%
10%
20%
40%
70%
1,1370
1,1346
1,1250
1,0883
0,9986
0,6
5%
10%
20%
40%
70%
2,4201
2,3585
2,1404
1,5625
0,8967
0,9
5%
10%
20%
40%
70%
22,6244
14,5985
6,0350
1,8034
0,6159
1,25
5%
10%
20%
40%
70%
3,0118
2,6392
1,7655
0,7596
0,2960
1,75
5%
10%
20%
40%
70%
0,2334
0,2285
0,2108
0,1609
0,0975
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Analisa Dinamika Struktur
DLF = [1 − cos(ω × t ) ]
Dimana : ω
= frekuensi natural
t
= waktu = 1 detik
k m
= 2,846
untuk t diambil selang waktu 0,1 detik
Berikut ini adalah contoh perhitungan untuk t = 0,1 detik : DLF = [1 − cos( 2,846 × 0,1) ]
DLF
= [ 1 – cos 0,2846 ]
DLF
= 0,04023
Untuk perhitungan selanjutnya dapat dilihat pada tabel berikut : Rasio frekuensi ( r )
Rasio peredaman (ξ ) 5% 1,0202 1,1370 2,4201 22,6244 3,0118 0,2334
0,1 0,25 0,6 0,9 1,25 1,75
No
t
10 % 1,0199 1,1346 2,3585 14,5985 2,6392 0,2285
20% 1,0186 1,1250 2,1404 6,0350 1,7655 0,2108
40% 1,0137 1,0883 1,5625 1,8034 0,7596 0,1609
70% 1,0003 0,9986 0,8967 0,6159 0,2960 0,0975
DLF
ω
1
0
0
0
2
0,1
2,846
0,04023
3
0,2
2,846
0,15767
4
0,3
2,846
0,34288
5
0,4
2,846
0,58095
6
0,5
2,846
0,85274
7
0,6
2,846
1,13638
8
0,7
2,846
1,40904
5
Analisa Dinamika Struktur
9
0,8
2,846
1,6488
10
0,9
2,846
1,83636
11
1
2,846
1,95663
12
1,1
2,846
1,99994
13
1,2
2,846
1,9628
14
1,3
2,846
1,84821
15
1,4
2,846
1,66537
16
1,5
2,846
1,429
17
1,6
2,846
1,15812
18
1,7
2,846
0,87452
19
1,8
2,846
0,60101
20
1,9
2,846
0,35961
21
2
2,846
0,16972
22
2,1
2,846
0,04663
23
2,2
2,846
0,00024
24
2,3
2,846
0,03429
25
2,4
2,846
0,14602
26
2,5
2,846
0,32646
27
2,6
2,846
0,56109
28
2,7
2,846
0,83103
29
2,8
2,846
1,11457
30
2,9
2,846
1,38888
31
3
2,846
1,63191
32
3,1
2,846
1,8241
33
3,2
2,846
1,94999
34
3,3
2,846
1,99946
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Analisa Dinamika Struktur
35
3,4
2,846
1,96851
36
3,5
2,846
1,85964
37
3,6
2,846
1,68162
38
3,7
2,846
1,44876
39
3,8
2,846
1,17979
40
3,9
2,846
0,89636
41
4
2,846
0,62127
42
4,1
2,846
0,37665
43
4,2
2,846
0,18217
44
4,3
2,846
0,0535
45
4,4
2,846
0,00097
46
4,5
2,846
0,02881
47
4,6
2,846
0,13479
48
4,7
2,846
0,31038
49
4,8
2,846
0,54145
50
4,9
2,846
0,80941
51
5
2,846
1,0927
52
5,1
2,846
1,36854
53
5,2
2,846
1,61472
54
5,3
2,846
1,81145
55
5,4
2,846
1,9429
56
5,5
2,846
1,99849
57
5,6
2,846
1,97375
58
5,7
2,846
1,87067
59
5,8
2,846
1,69754
60
5,9
2,846
1,46829
7
Analisa Dinamika Struktur
61
6
2,846
1,20137
62
6,1
2,846
0,91825
63
6,2
2,846
0,64171
64
6,3
2,846
0,39399
65
6,4
2,846
0,19502
66
6,5
2,846
0,06082
67
6,6
2,846
0,00217
68
6,7
2,846
0,02381
69
6,8
2,846
0,12398
70
6,9
2,846
0,29462
71
7
2,846
0,52202
72
7,1
2,846
0,78787
73
7,2
2,846
1,07079
74
7,3
2,846
1,34801
75
7,4
2,846
1,59723
76
7,5
2,846
1,79841
77
7,6
2,846
1,93535
78
7,7
2,846
1,99704
79
7,8
2,846
1,97852
80
7,9
2,846
1,88127
81
8
2,846
1,71312
82
8,1
2,846
1,48761
83
8,2
2,846
1,22286
84
8,3
2,846
0,94018
85
8,4
2,846
0,66232
86
8,5
2,846
0,41162
8
Analisa Dinamika Struktur
87
8,6
2,846
0,20826
88
8,7
2,846
0,06859
89
8,8
2,846
0,00386
90
8,9
2,846
0,01928
91
9
2,846
0,11359
92
9,1
2,846
0,27921
93
9,2
2,846
0,50283
94
9,3
2,846
0,76644
95
9,4
2,846
1,04884
96
9,5
2,846
1,32732
97
9,6
2,846
1,57946
98
9,7
2,846
1,78498
99
9,8
2,846
1,92735
100
9,9
2,846
1,99511
9
Analisa Dinamika Struktur
>> %**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<====================== DINAMIC LOAD FACTOR ====================>>>% gravitasi=980; E=2.1e5; Q=2000; L1=1500; L2=1500; H=700; b1=30; b2=30; h1=30; h2=30; beban=Q*(L1+L2); I1=1/12*b1*(h1^3); I2=1/12*b2*(h2^3); K1=(12*E*I1); K2=(12*E*I2); k=(2*K1)+K2; m=beban/gravitasi; Po=5000; w=(k/m)^0,5; t=linspace(0,30*pi); Y=(Po/k*(1-cos(w*t))); DLF=1-(cos(w*t)); plot(t,Y,'G',t,DLF,'R') legend('DLF','Y(t)') grid on
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Analisa Dinamika Struktur
%**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<====================== DINAMIC LOAD FACTOR ====================>>>% gravitasi=980; E=2.1e5; Q=2000; L1=1500; L2=1500; H=700; b1=30; b2=30; h1=30; h2=30; beban=Q*(L1+L2); I1=1/12*b1*(h1^3); I2=1/12*b2*(h2^3); K1=(12*E*I1); K2=(12*E*I2); k=(2*K1)+K2; m=beban/gravitasi; Po=5000; O=1.75; w=(k/m)^0.5; t=linspace(0,30*pi); TotalRespons=(Po/m*((w^2)-(O^2)))*(sin(O*t)-(O/w)*sin(w*t)); SteadyStatateRespons=(Po/m*((w^2)-(O^2)))*sin(O*t); TransientRespons=(Po/m*((w^2)-(O^2)))*(O/w)*sin(w*t); plot(t,TotalRespons,'k',t,SteadyStatateRespons,'b',t,TransientRespons,'g') legend('TotalRespons','SteadyStatateRespons','TransientRespons') grid on
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Analisa Dinamika Struktur
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Analisa Dinamika Struktur
%**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<====================== DINAMIC LOAD FACTOR ====================>>>% gravitasi=980; E=2.1e5; Q=2000; L1=1500; L2=1500; H=700; b1=30; b2=30; h1=30; h2=30; beban=Q*(L1+L2); I1=1/12*b1*(h1^3); I2=1/12*b2*(h2^3); K1=(12*E*I1); K2=(12*E*I2); k=(2*K1)+K2; m=beban/gravitasi; Po=5000; O=1.25; w=(k/m)^0.5; t=linspace(0,30*pi); TotalRespons=(Po/m*((w^2)-(O^2)))*(sin(O*t)-(O/w)*sin(w*t)); SteadyStatateRespons=(Po/m*((w^2)-(O^2)))*sin(O*t); TransientRespons=(Po/m*((w^2)-(O^2)))*(O/w)*sin(w*t); plot(t,TotalRespons,'k',t,SteadyStatateRespons,'b',t,TransientRespons,'g') legend('TotalRespons','SteadyStatateRespons','TransientRespons') grid on
13
Analisa Dinamika Struktur
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Analisa Dinamika Struktur
%**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<====================== DINAMIC LOAD FACTOR ====================>>>% gravitasi=980; E=2.1e5; Q=2000; L1=1500; L2=1500; H=700; b1=30; b2=30; h1=30; h2=30; beban=Q*(L1+L2); I1=1/12*b1*(h1^3); I2=1/12*b2*(h2^3); K1=(12*E*I1); K2=(12*E*I2); k=(2*K1)+K2; m=beban/gravitasi; Po=5000; O=0.90; w=(k/m)^0.5; t=linspace(0,30*pi); TotalRespons=(Po/m*((w^2)-(O^2)))*(sin(O*t)-(O/w)*sin(w*t)); SteadyStatateRespons=(Po/m*((w^2)-(O^2)))*sin(O*t); TransientRespons=(Po/m*((w^2)-(O^2)))*(O/w)*sin(w*t); plot(t,TotalRespons,'k',t,SteadyStatateRespons,'b',t,TransientRespons,'g') legend('TotalRespons','SteadyStatateRespons','TransientRespons') grid on
15
Analisa Dinamika Struktur
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Analisa Dinamika Struktur
%**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<====================== DINAMIC LOAD FACTOR ====================>>>% gravitasi=980; E=2.1e5; Q=2000; L1=1500; L2=1500; H=700; b1=30; b2=30; h1=30; h2=30; beban=Q*(L1+L2); I1=1/12*b1*(h1^3); I2=1/12*b2*(h2^3); K1=(12*E*I1); K2=(12*E*I2); k=(2*K1)+K2; m=beban/gravitasi; Po=5000; O=0.60; w=(k/m)^0.5; t=linspace(0,30*pi); TotalRespons=(Po/m*((w^2)-(O^2)))*(sin(O*t)-(O/w)*sin(w*t)); SteadyStatateRespons=(Po/m*((w^2)-(O^2)))*sin(O*t); TransientRespons=(Po/m*((w^2)-(O^2)))*(O/w)*sin(w*t); plot(t,TotalRespons,'k',t,SteadyStatateRespons,'b',t,TransientRespons,'g') legend('TotalRespons','SteadyStatateRespons','TransientRespons') grid on
17
Analisa Dinamika Struktur
18
Analisa Dinamika Struktur
%**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<====================== DINAMIC LOAD FACTOR ====================>>>% gravitasi=980; E=2.1e5; Q=2000; L1=1500; L2=1500; H=700; b1=30; b2=30; h1=30; h2=30; beban=Q*(L1+L2); I1=1/12*b1*(h1^3); I2=1/12*b2*(h2^3); K1=(12*E*I1); K2=(12*E*I2); k=(2*K1)+K2; m=beban/gravitasi; Po=5000; O=0.25; w=(k/m)^0.5; t=linspace(0,30*pi); TotalRespons=(Po/m*((w^2)-(O^2)))*(sin(O*t)-(O/w)*sin(w*t)); SteadyStatateRespons=(Po/m*((w^2)-(O^2)))*sin(O*t); TransientRespons=(Po/m*((w^2)-(O^2)))*(O/w)*sin(w*t); plot(t,TotalRespons,'k',t,SteadyStatateRespons,'b',t,TransientRespons,'g') legend('TotalRespons','SteadyStatateRespons','TransientRespons') grid on
19
Analisa Dinamika Struktur
20
Analisa Dinamika Struktur
%**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<====================== DINAMIC LOAD FACTOR ====================>>>% gravitasi=980; E=2.1e5; Q=2000; L1=1500; L2=1500; H=700; b1=30; b2=30; h1=30; h2=30; beban=Q*(L1+L2); I1=1/12*b1*(h1^3); I2=1/12*b2*(h2^3); K1=(12*E*I1); K2=(12*E*I2); k=(2*K1)+K2; m=beban/gravitasi; Po=5000; O=0.1; w=(k/m)^0.5; t=linspace(0,30*pi); TotalRespons=(Po/m*((w^2)-(O^2)))*(sin(O*t)-(O/w)*sin(w*t)); SteadyStatateRespons=(Po/m*((w^2)-(O^2)))*sin(O*t); TransientRespons=(Po/m*((w^2)-(O^2)))*(O/w)*sin(w*t); plot(t,TotalRespons,'k',t,SteadyStatateRespons,'b',t,TransientRespons,'g') legend('TotalRespons','SteadyStatateRespons','TransientRespons') grid on
21
Analisa Dinamika Struktur
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Analisa Dinamika Struktur
%**** ANALISA DINAMIKA STRUKTUR ************** %**** dikerjakan oleh ===>>> PRALAMBANG GALIH WICAKSONO ( 02 208 2965 ) %**** f=w/(2*pi) %**** T=1/f %**** w=(k/m)^0.5 %<<<==================== DYNAMIC LOAD FACTOR MAGNITUDO ===============>>>% clear ks=5/100; ks2=10/100; ks3=20/100; ks4=40/100; ks5=70/100; r=linspace(0,5); DLF=(((1-(r.^2))).^2+((2*ks.*r).^2)).^(-0.5); DLF2=(((1-(r.^2))).^2+((2*ks2.*r).^2)).^(-0.5); DLF3=(((1-(r.^2))).^2+((2*ks3.*r).^2)).^(-0.5); DLF4=(((1-(r.^2))).^2+((2*ks4.*r).^2)).^(-0.5); DLF5=(((1-(r.^2))).^2+((2*ks5.*r).^2)).^(-0.5); plot(r,DLF,'r',r,DLF2,'y',r,DLF3,'g',r,DLF4,'b',r,DLF5,'m') legend('DLF ks=5/100','DLF2 ks=10/100','DLF ks=20/100','DLF ks=40/100','DLF ks=70/100') grid on
23
