Seismic parameters
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Transcript of Seismic parameters
Seismic EngineeringGroup 25
3 -Story Building
Basic project parameters:
kN
m2Ec 34 10
6
ρc 2.4t
m3
ρg 2.6t
m3
ts 0.18 m tg 0.01 m
H 3.5 mW 12.5 mL 4 m
Column geometry: Beam geometry:
w12 0.3 m hb 0.3 m
w3 0.2 m tb 0.3 m
dc 0.3 m
Structural damping:
ζin 0.05 ζel 0.03
Loads on the structure:t
m2
gd 0.4t
m2gr 0.25
Computation on X direction:Geometrical property of section:
Ic12x
dc w123
12 Ic12x 0.000675
m4
Ic3x
dc w33
12 Ic3x 0.0002 m
4
Ibx
hb3
tb
12
Ibx 0.000675 m4
Local stiffness matrix of elements:
For columns at first and second storey:m
kc12x11 12
Ec Ic12x
H3
kc12x12 12Ec Ic12x
H3
kc12x13 6
Ec Ic12x
H2
kc12x14 6
Ec Ic12x
H2
kc12x21 12Ec Ic12x
H3
kc12x22 12
Ec Ic12x
H3
kc12x23 6Ec Ic12x
H2
kc12x24 6Ec Ic12x
H2
kc12x31 6
Ec Ic12x
H2
kc12x32 6Ec Ic12x
H2
kc12x33 4
Ec Ic12x
H kc12x34 2
Ec Ic12x
H
kc12x41 6
Ec Ic12x
H2
kc12x42 6Ec Ic12x
H2
kc12x43 2
Ec Ic12x
H kc12x44 4
Ec Ic12x
H
Klocalc12x
kc12x11
kc12x21
kc12x31
kc12x41
kc12x12
kc12x22
kc12x32
kc12x42
kc12x13
kc12x23
kc12x33
kc12x43
kc12x14
kc12x24
kc12x34
kc12x44
Klocalc12x
6423.32362
6423.32362
11240.81633
11240.81633
6423.32362
6423.32362
11240.81633
11240.81633
11240.81633
11240.81633
26228.57143
13114.28571
11240.81633
11240.81633
13114.28571
26228.57143
For columns at third storey:
kc3x11 12
Ec Ic3x
H3
kc3x12 12Ec Ic3x
H3
kc3x13 6
Ec Ic3x
H2
kc3x14 6
Ec Ic3x
H2
kc3x21 12Ec Ic3x
H3
kc3x22 12
Ec Ic3x
H3
kc3x23 6Ec Ic3x
H2
kc3x24 6Ec Ic3x
H2
kc3x31 6
Ec Ic3x
H2
kc3x32 6Ec Ic3x
H2
kc3x33 4
Ec Ic3x
H kc3x34 2
Ec Ic3x
H
kc3x41 6
Ec Ic3x
H2
kc3x42 6Ec Ic3x
H2
kc3x43 2
Ec Ic3x
H kc3x44 4
Ec Ic3x
H
Klocalc3x
kc3x11
kc3x21
kc3x31
kc3x41
kc3x12
kc3x22
kc3x32
kc3x42
kc3x13
kc3x23
kc3x33
kc3x43
kc3x14
kc3x24
kc3x34
kc3x44
Klocalc3x
1903.207
1903.207
3330.61224
3330.61224
1903.207
1903.207
3330.61224
3330.61224
3330.61224
3330.61224
7771.42857
3885.71429
3330.61224
3330.61224
3885.71429
7771.42857
For beams:
kbx11 12
Ec Ibx
W3
kbx12 12Ec Ibx
W3
kbx13 6
Ec Ibx
W2
kbx14 6
Ec Ibx
W2
kbx21 12Ec Ibx
W3
kbx22 12
Ec Ibx
W3
kbx23 6Ec Ibx
W2
kbx24 6Ec Ibx
W2
kbx31 6
Ec Ibx
W2
kbx32 6Ec Ibx
W2
kbx33 4
Ec Ibx
W kbx34 2
Ec Ibx
W
kbx41 6
Ec Ibx
W2
kbx42 6Ec Ibx
W2
kbx43 2
Ec Ibx
W kbx44 4
Ec Ibx
W
Klocalbx
kbx11
kbx21
kbx31
kbx41
kbx12
kbx22
kbx32
kbx42
kbx13
kbx23
kbx33
kbx43
kbx14
kbx24
kbx34
kbx44
Klocalbx
141
141
881.28
881.28
141
141
881.28
881.28
881.28
881.28
7344
3672
881.28
881.28
3672
7344
General stiffness matrix of the structure on X direction:1 2 5 6 2 5
Kx11 kc12x11 kc12x22 kc12x22 kc12x11 Kx12 kc12x21 kc12x21
5 2 2 3 5 4
Kx21 kc12x12 kc12x12 Kx22 kc12x11 kc3x22 kc12x11 kc3x22
3 4
Kx31 0 Kx32 kc3x12 kc3x12
1 2 2
Kx41 kc12x31 kc12x42 Kx42 kc12x41
5 6 5
Kx51 kc12x42 kc12x31 Kx52 kc12x41
2 2 3
Kx61 kc12x32 Kx62 kc12x31 kc3x42
5 4 5
Kx71 kc12x32 Kx72 kc3x42 kc12x31
3
Kx81 0 Kx82 kc3x32
4
Kx91 0 Kx92 kc3x32
1 2
Kx13 0 Kx14 kc12x13 kc12x24
3 4 2
Kx23 kc3x21 kc3x21 Kx24 kc12x14
3 4
Kx33 kc3x11 kc3x11 Kx34 0
1 2 7
Kx43 0 Kx44 kc12x33 kc12x44 kbx44
7
Kx53 0 Kx54 kbx34
3 2
Kx63 kc3x41 Kx64 kc12x34
4
Kx73 kc3x41 Kx74 0
3
Kx83 kc3x31 Kx84 0
4
Kx93 kc3x31 Kx94 0
5 6 2
Kx15 kc12x24 kc12x13 Kx16 kc12x23
5 2 3
Kx25 kc12x14 Kx26 kc12x13 kc3x24
3
Kx35 0 Kx36 kc3x14
7 2
Kx45 kbx43 Kx46 kc12x43
5 6 7
Kx55 kc12x44 kc12x33 kbx33 Kx56 0
2 3 8
Kx65 0 Kx66 kc12x33 kc3x44 kbx44
5 8
Kx75 kc12x34 Kx76 kbx34
3
Kx85 0 Kx86 kc3x34
Kx95 0 Kx96 0
5
Kx17 kc12x23 Kx18 0 Kx19 0
4 5 3 4
Kx27 kc3x24 kc12x13 Kx28 kc3x23 Kx29 kc3x23
4 3 4
Kx37 kc3x14 Kx38 kc3x13 Kx39 kc3x13
Kx47 0 Kx48 0 Kx49 0
5
Kx57 kc12x43 Kx58 0 Kx59 0
8 3
Kx67 kbx43 Kx68 kc3x43 Kx69 0
4 5 8 4
Kx77 kc3x44 kc12x33 kbx33 Kx78 0 Kx79 kc3x43
3 9 9
Kx87 0 Kx88 kc3x33 kbx44 Kx89 kbx43
4 9 4 9
Kx97 kc3x34 Kx98 kbx34 Kx99 kc3x33 kbx33
Kx
Kx11
Kx21
Kx31
Kx41
Kx51
Kx61
Kx71
Kx81
Kx91
Kx12
Kx22
Kx32
Kx42
Kx52
Kx62
Kx72
Kx82
Kx92
Kx13
Kx23
Kx33
Kx43
Kx53
Kx63
Kx73
Kx83
Kx93
Kx14
Kx24
Kx34
Kx44
Kx54
Kx64
Kx74
Kx84
Kx94
Kx15
Kx25
Kx35
Kx45
Kx55
Kx65
Kx75
Kx85
Kx95
Kx16
Kx26
Kx36
Kx46
Kx56
Kx66
Kx76
Kx86
Kx96
Kx17
Kx27
Kx37
Kx47
Kx57
Kx67
Kx77
Kx87
Kx97
Kx18
Kx28
Kx38
Kx48
Kx58
Kx68
Kx78
Kx88
Kx98
Kx19
Kx29
Kx39
Kx49
Kx59
Kx69
Kx79
Kx89
Kx99
Kx
25693.294
12846.647
0
0
0
11240.816
11240.816
0
0
12846.647
16653.061
3806.414
11240.816
11240.816
7910.204
7910.204
3330.612
3330.612
0
3806.414
3806.414
0
0
3330.612
3330.612
3330.612
3330.612
0
11240.816
0
59801.143
3672
13114.286
0
0
0
0
11240.816
0
3672
59801.143
0
13114.286
0
0
11240.816
7910.204
3330.612
13114.286
0
41344
3672
3885.714
0
11240.816
7910.204
3330.612
0
13114.286
3672
41344
0
3885.714
0
3330.612
3330.612
0
0
3885.714
0
15115.429
3672
0
3330.612
3330.612
0
0
0
3885.714
3672
15115.429
Mass matrix x direction:Msx
L W2
ts ρc gdL W2
Msx 20.8 t
MsrxL W2
ts ρc grL W2
Msrx 17 t
Mbx W hb tb ρc 1.5 W H tg ρg Mbx 4.406 t
Mbrx W hb tb ρc Mbrx 2.7 t
Mc1 w12 dc ρc H 0.756 t Mc2 w12 dc ρc H 0.756 t Mc3 w3 dc ρc H 0.504 t
Mtot Mbx 2 Mbrx Mc1 2 Mc2 2 Mc3 2 2 Msx Msrx 74.194 t
mbx
Mbx
W
Msx
W mbx 2.016
t
m
mbrx
Mbrx
W
Msrx
W mbrx 1.58
t
m
mc12x w12 dc ρc mc12x 0.216t
m
mc3x w3 dc ρc mc3x 0.144t
m
Local mass matrix on x direction:For columns at first and second storey:
mc12x11
156 mc12x H
420 mc12x12
54 mc12x H
420 mc12x13
22 mc12x H2
420 mc12x14
13 mc12x H2
420
mc12x21
54 mc12x H
420 mc12x22
156 mc12x H
420 mc12x23
13 mc12x H2
420 mc12x24
22 mc12x H2
420
mc12x31
22 mc12x H2
420 mc12x32
13 mc12x H2
420 mc12x33
4 mc12x H3
420 mc12x34
3 mc12x H3
420
mc12x41
13 mc12x H2
420 mc12x42
22 mc12x H2
420 mc12x43
3 mc12x H3
420 mc12x44
4 mc12x H3
420
Mlocalc12x
mc12x11
mc12x21
mc12x31
mc12x41
mc12x12
mc12x22
mc12x32
mc12x42
mc12x13
mc12x23
mc12x33
mc12x43
mc12x14
mc12x24
mc12x34
mc12x44
Mlocalc12x
0.281
0.097
0.139
0.082
0.097
0.281
0.082
0.139
0.139
0.082
0.088
0.066
0.082
0.139
0.066
0.088
For columns at third storey:
mc3x11
156 mc3x H
420 mc3x12
54 mc3x H
420 mc3x13
22 mc3x H2
420 mc3x14
13 mc3x H2
420
mc3x21
54 mc3x H
420 mc3x22
156 mc3x H
420 mc3x23
13 mc3x H2
420 mc3x24
22 mc3x H2
420
mc3x31
22 mc3x H2
420 mc3x32
13 mc3x H2
420 mc3x33
4 mc3x H3
420 mc3x34
3 mc3x H3
420
mc3x41
13 mc3x H2
420 mc3x42
22 mc3x H2
420 mc3x43
3 mc3x H3
420 mc3x44
4 mc3x H3
420
Mlocalc3x
mc3x11
mc3x21
mc3x31
mc3x41
mc3x12
mc3x22
mc3x32
mc3x42
mc3x13
mc3x23
mc3x33
mc3x43
mc3x14
mc3x24
mc3x34
mc3x44
Mlocalc3x
0.187
0.065
0.092
0.055
0.065
0.187
0.055
0.092
0.092
0.055
0.059
0.044
0.055
0.092
0.044
0.059
For beams at first and second storey:
mbx11
156 mbx W
420 mbx12
54 mbx W
420 mbx13
22 mbx W2
420 mbx14
13 mbx W2
420
mbx21
54 mbx W
420 mbx22
156 mbx W
420 mbx23
13 mbx W2
420 mbx24
22 mbx W2
420
mbx31
22 mbx W2
420 mbx32
13 mbx W2
420 mbx33
4 mbx W3
420 mbx34
3 mbx W3
420
mbx41
13 mbx W2
420 mbx42
22 mbx W2
420 mbx43
3 mbx W3
420 mbx44
4 mbx W3
420
Mlocalbx
mbx11
mbx21
mbx31
mbx41
mbx12
mbx22
mbx32
mbx42
mbx13
mbx23
mbx33
mbx43
mbx14
mbx24
mbx34
mbx44
Mlocalbx
9.362
3.241
16.504
9.752
3.241
9.362
9.752
16.504
16.504
9.752
37.509
28.132
9.752
16.504
28.132
37.509
For beams at roof level
mbrx11
156 mbrx W
420 mbrx12
54 mbrx W
420 mbrx13
22 mbrx W2
420 mbrx14
13 mbrx W2
420
mbrx21
54 mbrx W
420 mbrx22
156 mbrx W
420 mbrx23
13 mbrx W2
420 mbrx24
22 mbrx W2
420
mbrx31
22 mbrx W2
420 mbrx32
13 mbrx W2
420 mbrx33
4 mbrx W3
420 mbrx34
3 mbrx W3
420
mbrx41
13 mbrx W2
420 mbrx42
22 mbrx W2
420 mbrx43
3 mbrx W3
420 mbrx44
4 mbrx W3
420
Mlocalbrx
mbrx11
mbrx21
mbrx31
mbrx41
mbrx12
mbrx22
mbrx32
mbrx42
mbrx13
mbrx23
mbrx33
mbrx43
mbrx14
mbrx24
mbrx34
mbrx44
Mlocalbrx
7.336
2.539
12.932
7.641
2.539
7.336
7.641
12.932
12.932
7.641
29.39
22.042
7.641
12.932
22.042
29.39
General mass matrix of the structure on X direction
1 2 5 6 2 5
Mx11 mc12x11 mc12x22 mc12x22 mc12x11 Mbx Msx Mx12 mc12x21 mc12x21
5 22 3 4 5
Mx21 mc12x12 mc12x12Mx22 mc12x11 mc3x22 mc12x11 mc3x22 Mbx Msx
3 4
Mx31 0 Mx32 mc3x12 mc3x12
1 2 2
Mx41 mc12x31 mc12x42 Mx42 mc12x41
5 6 5
Mx51 mc12x42 mc12x31 Mx52 mc12x41
2 2 3
Mx61 mc12x32 Mx62 mc12x31 mc3x42
5 4 5
Mx71 mc12x32 Mx72 mc3x42 mc12x31
3
Mx81 0 Mx82 mc3x32
4
Mx91 0 Mx92 mc3x32
1 2Mx13 0
Mx14 mc12x13 mc12x243 4
2Mx23 mc3x21 mc3x21
Mx24 mc12x14
3 4
Mx33 mc3x11 mc3x11 Mbrx MsrxMx34 0
1 2 7Mx43 0
Mx44 mc12x33 mc12x44 mbx44
7Mx53 0
Mx54 mbx343
2Mx63 mc3x41
Mx64 mc12x344
Mx73 mc3x41Mx74 0
3
Mx83 mc3x31Mx84 0
4
Mx93 mc3x31Mx94 0
25 6
Mx16 mc12x23Mx15 mc12x24 mc12x13
2 35
Mx26 mc12x13 mc3x24Mx25 mc12x14
3
Mx36 mc3x14Mx35 0
27
Mx46 mc12x43Mx45 mbx43
5 6 7Mx56 0
Mx55 mc12x44 mc12x33 mbx332 3 8
Mx66 mc12x33 mc3x44 mbx44Mx65 0
85
Mx76 mbx34Mx75 mc12x34
3
Mx86 mc3x34Mx85 0
Mx96 0Mx95 0
5Mx19 0
Mx17 mc12x23 Mx18 04
4 5 3Mx29 mc3x23
Mx27 mc3x24 mc12x13 Mx28 mc3x234
4 3Mx39 mc3x13
Mx37 mc3x14 Mx38 mc3x13
Mx49 0Mx47 0 Mx48 0
5Mx59 0
Mx57 mc12x43 Mx58 0
8 3Mx69 0
Mx67 mbx43 Mx68 mc3x434
4 5 8Mx79 mc3x43
Mx77 mc3x44 mc12x33 mbx33 Mx78 0
93 9
Mx89 mbrx43Mx87 0 Mx88 mc3x33 mbrx44
4 94 9
Mx99 mc3x33 mbrx33Mx97 mc3x34 Mx98 mbrx34
Mx
Mx11
Mx21
Mx31
Mx41
Mx51
Mx61
Mx71
Mx81
Mx91
Mx12
Mx22
Mx32
Mx42
Mx52
Mx62
Mx72
Mx82
Mx92
Mx13
Mx23
Mx33
Mx43
Mx53
Mx63
Mx73
Mx83
Mx93
Mx14
Mx24
Mx34
Mx44
Mx54
Mx64
Mx74
Mx84
Mx94
Mx15
Mx25
Mx35
Mx45
Mx55
Mx65
Mx75
Mx85
Mx95
Mx16
Mx26
Mx36
Mx46
Mx56
Mx66
Mx76
Mx86
Mx96
Mx17
Mx27
Mx37
Mx47
Mx57
Mx67
Mx77
Mx87
Mx97
Mx18
Mx28
Mx38
Mx48
Mx58
Mx68
Mx78
Mx88
Mx98
Mx19
Mx29
Mx39
Mx49
Mx59
Mx69
Mx79
Mx89
Mx99
Mx
26.329
0.194
0
0
0
0.082
0.082
0
0
0.194
26.142
0.13
0.082
0.082
0.046
0.046
0.055
0.055
0
0.13
20.124
0
0
0.055
0.055
0.092
0.092
0
0.082
0
37.686
28.132
0.066
0
0
0
0
0.082
0
28.132
37.686
0
0.066
0
0
0.082
0.046
0.055
0.066
0
37.656
28.132
0.044
0
0.082
0.046
0.055
0
0.066
28.132
37.656
0
0.044
0
0.055
0.092
0
0
0.044
0
29.449
22.042
0
0.055
0.092
0
0
0
0.044
22.042
29.449
Eigenfrequencies and eigenmodes x direction:ωx genvals Kx Mx
angular frequency:
ωx
87.719
66.033
50.938
29.741
14.487
4.767
30.959
21.96
14.404
sort ωx
4.767
14.404
14.487
21.96
29.741
30.959
50.938
66.033
87.719
fx ωx2
7694.648
4360.358
2594.688
884.554
209.863
22.723
958.438
482.245
207.484
Eigenmode:
ϕx genvecs Kx Mx
ϕx
0.092
0.181
0.025
1
1
0.579
0.579
0.048
0.048
0.263
0.018
0.106
0.624
0.624
1
1
0.32
0.32
0.132
0.178
0.123
0.101
0.101
0.142
0.142
1
1
1
0.602
0.216
0.015
0.015
0.453
0.453
0.369
0.369
0.737
0.926
1
0.197
0.197
0.13
0.13
0.343
0.343
0.239
0.633
1
0.093
0.093
0.095
0.095
0.046
0.046
0
0
0
1
1
0.528
0.528
0.055
0.055
0
0
0
0.539
0.539
1
1
0.292
0.292
0
0
0
0.06
0.06
0.195
0.195
1
1
Vx ϕx
sortf
s fxi
fxifxj
fxjs
fxifxj
if
j i 1( ) 8for
i 0 7for
fxjs
fx
Vx
z fxi
fxifxj
fxjz
zz Vxi
Vxi Vx
j
Vxj zz
fxifxj
if
j i 1( ) 8for
i 0 7for
Vxj zz
Vx
Vx
0.239
0.633
1
0.093
0.093
0.095
0.095
0.046
0.046
0
0
0
0.06
0.06
0.195
0.195
1
1
0.737
0.926
1
0.197
0.197
0.13
0.13
0.343
0.343
0
0
0
0.539
0.539
1
1
0.292
0.292
1
0.602
0.216
0.015
0.015
0.453
0.453
0.369
0.369
0
0
0
1
1
0.528
0.528
0.055
0.055
0.132
0.178
0.123
0.101
0.101
0.142
0.142
1
1
0.263
0.018
0.106
0.624
0.624
1
1
0.32
0.32
0.092
0.181
0.025
1
1
0.579
0.579
0.048
0.048
Tx2π
sort ωx fx
1
Tx
Tx
1.318
0.436
0.434
0.286
0.211
0.203
0.123
0.095
0.072
fx
0.759
2.293
2.306
3.495
4.733
4.927
8.107
10.509
13.961
ϕx1 Vx0 ϕx6 Vx
5
ϕx2 Vx1 ϕx7 Vx
6
ϕx3 Vx2 ϕx8 Vx
7
ϕx4 Vx3 ϕx9 Vx
8
ϕx5 Vx4
ϕx1
0.239
0.633
1
0.093
0.093
0.095
0.095
0.046
0.046
ϕx3
0.737
0.926
1
0.197
0.197
0.13
0.13
0.343
0.343
ϕx4
0
0
0
0.539
0.539
1
1
0.292
0.292
ϕx2
1.189 1015
1.55 1015
1.723 1015
0.06
0.06
0.195
0.195
1
1
ϕx5
1
0.602
0.216
0.015
0.015
0.453
0.453
0.369
0.369
ϕx6
0
0
0
1
1
0.528
0.528
0.055
0.055
ϕx7
0.132
0.178
0.123
0.101
0.101
0.142
0.142
1
1
ϕx8
0.263
0.018
0.106
0.624
0.624
1
1
0.32
0.32
ϕx9
0.092
0.181
0.025
1
1
0.579
0.579
0.048
0.048
ϕx Vx
0.239
0.633
1
0.093
0.093
0.095
0.095
0.046
0.046
0
0
0
0.06
0.06
0.195
0.195
1
1
0.737
0.926
1
0.197
0.197
0.13
0.13
0.343
0.343
0
0
0
0.539
0.539
1
1
0.292
0.292
1
0.602
0.216
0.015
0.015
0.453
0.453
0.369
0.369
0
0
0
1
1
0.528
0.528
0.055
0.055
0.132
0.178
0.123
0.101
0.101
0.142
0.142
1
1
0.263
0.018
0.106
0.624
0.624
1
1
0.32
0.32
0.092
0.181
0.025
1
1
0.579
0.579
0.048
0.048
Kmodx ϕxT Kx ϕx
Kmodx
743.1
0
0
0
0
0
0
0
0
0
22513.3
0
0
0
0
0
0
0
0
0
12538.4
0
0
0
0
0
0
0
0
0
86169.6
0
0
0
0
0
0
0
0
0
37625.6
0
0
0
0
0
0
0
0
0
161429.1
0
0
0
0
0
0
0
0
0
44125.8
0
0
0
0
0
0
0
0
0
131198.9
0
0
0
0
0
0
0
0
0
203190.5
Mmodx ϕxT Mx ϕx
Mmodx
32.7
0
0
0
0
0
0
0
0
0
108.506
0
0
0
0
0
0
0
0
0
59.745
0
0
0
0
0
0
0
0
0
178.684
0
0
0
0
0
0
0
0
0
42.536
0
0
0
0
0
0
0
0
0
168.429
0
0
0
0
0
0
0
0
0
17.006
0
0
0
0
0
0
0
0
0
30.089
0
0
0
0
0
0
0
0
0
26.407
Shape function of elementsColumn : Beam :
ψcx.1 x( ) 1 3x
H
2
2x
H
3
ψbx.1 x( ) 1 3x
W
2
2x
W
3
ψcx.2 x( ) 3x
H
2
2x
H
3
ψbx.2 x( ) 3x
W
2
2x
W
3
ψcx.3 x( ) x 1x
H
2
ψbx.3 x( ) x 1x
W
2
ψcx.4 x( )x2
H
x
H1
ψbx.4 x( )x2
W
x
W1
Mode 1:
xc 0 0.01 H
xb 0 0.01 W
ux1.1 xc ψcx.1 xc Vx0 0
ψcx.3 xc Vx6 0
ux2.1 xc ψcx.1 xc Vx1 0
ψcx.2 xc Vx0 0
ψcx.3 xc Vx5 0
ψcx.4 xc Vx3 0
ux3.1 xc ψcx.1 xc Vx2 0
ψcx.2 xc Vx1 0
ψcx.3 xc Vx7 0
ψcx.4 xc Vx5 0
ux4.1 xc ψcx.1 xc Vx2 0
ψcx.2 xc Vx1 0
ψcx.3 xc Vx8 0
ψcx.4 xc Vx6 0
ux5.1 xc ψcx.1 xc Vx1 0
ψcx.2 xc Vx0 0
ψcx.3 xc Vx6 0
ψcx.4 xc Vx4 0
ux6.1 xc ψcx.1 xc Vx0 0
ψcx.3 xc Vx4 0
ux7.1 xb ψbx.3 xb Vx4 0
ψbx.4 xb Vx3 0
ux8.1 xb ψbx.3 xb Vx6 0
ψbx.4 xb Vx5 0
ux9.1 xb ψbx.3 xb Vx8 0
ψbx.4 xb Vx7 0
Yx1.1 xc H xc Xx1.1 xc 4 ux1.1 xc
Yx2.1 xc 2H xc Xx2.1 xc 4 ux2.1 xc
Yx3.1 xc 3H xc Xx3.1 xc 4 ux3.1 xc
Yx4.1 xc 3H xc Xx4.1 xc 4 W ux4.1 xc
Yx5.1 xc 2H xc Xx5.1 xc 4 W ux5.1 xc
Yx6.1 xc H xc Xx6.1 xc 4 W ux6.1 xc
Yx7.1 xb H ux7.1 xb Xx7.1 xb Xx1.1 0( ) W xb
Yx8.1 xb 2H ux8.1 xb Xx8.1 xb Xx2.1 0( ) W xb
Yx9.1 xb 3H ux9.1 xb Xx9.1 xb Xx3.1 0( ) W xb
2 3.455 4.909 6.364 7.818 9.273 10.727 12.182 13.636 15.091 16.545 180
5
10
Mode 1 on X
Yx1.1 xc Yx2.1 xc Yx3.1 xc Yx4.1 xc Yx5.1 xc Yx6.1 xc Yx7.1 xb Yx8.1 xb Yx9.1 xb
Xx1.1 xc Xx2.1 xc Xx3.1 xc Xx4.1 xc Xx5.1 xc Xx6.1 xc Xx7.1 xb Xx8.1 xb Xx9.1 xb
Mode 2:
xc 0 0.01 H
xb 0 0.01 W
ux1.2 xc ψcx.1 xc Vx0 1
ψcx.3 xc Vx3 1
ux2.2 xc ψcx.1 xc Vx1 1
ψcx.2 xc Vx0 1
ψcx.3 xc Vx5 1
ψcx.4 xc Vx3 1
ux3.2 xc ψcx.1 xc Vx2 1
ψcx.2 xc Vx1 1
ψcx.3 xc Vx7 1
ψcx.4 xc Vx5 1
ux4.2 xc ψcx.1 xc Vx2 1
ψcx.2 xc Vx1 1
ψcx.3 xc Vx8 1
ψcx.4 xc Vx6 1
ux5.2 xc ψcx.1 xc Vx1 1
ψcx.2 xc Vx0 1
ψcx.3 xc Vx6 1
ψcx.4 xc Vx4 1
ux6.2 xc ψcx.1 xc Vx0 1
ψcx.3 xc Vx4 1
ux7.2 xb ψbx.3 xb Vx4 1
ψbx.4 xb Vx3 1
ux8.2 xb ψbx.3 xb Vx6 1
ψbx.4 xb Vx5 1
ux9.2 xb ψbx.3 xb Vx8 1
ψbx.4 xb Vx7 1
Yx1.2 xc H xc Xx1.2 xc 4 ux1.2 xc
Yx2.2 xc 2H xc Xx2.2 xc 4 ux2.2 xc
Yx3.2 xc 3H xc Xx3.2 xc 4 ux3.2 xc
Yx4.2 xc 3H xc Xx4.2 xc 4 W ux4.2 xc
Yx5.2 xc 2H xc Xx5.2 xc 4 W ux5.2 xc
Yx6.2 xc H xc Xx6.2 xc 4 W ux6.2 xc
Yx7.2 xb H ux7.2 xb Xx7.2 xb Xx1.2 0( ) W xb
Yx8.2 xb 2H ux8.2 xb Xx8.2 xb Xx2.2 0( ) W xb
Yx9.2 xb 3H ux9.2 xb Xx9.2 xb Xx3.2 0( ) W xb
2 3.455 4.909 6.364 7.818 9.273 10.727 12.182 13.636 15.091 16.545 180
5
10
Mode 2 on X
Yx1.2 xc Yx2.2 xc Yx3.2 xc Yx4.2 xc Yx5.2 xc Yx6.2 xc Yx7.2 xb Yx8.2 xb Yx9.2 xb
Xx1.2 xc Xx2.2 xc Xx3.2 xc Xx4.2 xc Xx5.2 xc Xx6.2 xc Xx7.2 xb Xx8.2 xb Xx9.2 xb
Mode 3:xc 0 0.01 H
xb 0 0.01 W
ux1.3 xc ψcx.1 xc Vx0 2
ψcx.3 xc Vx3 2
ux2.3 xc ψcx.1 xc Vx1 2
ψcx.2 xc Vx0 2
ψcx.3 xc Vx5 2
ψcx.4 xc Vx3 2
ux3.3 xc ψcx.1 xc Vx2 2
ψcx.2 xc Vx1 2
ψcx.3 xc Vx7 2
ψcx.4 xc Vx5 2
ux4.3 xc ψcx.1 xc Vx2 2
ψcx.2 xc Vx1 2
ψcx.3 xc Vx8 2
ψcx.4 xc Vx6 2
ux5.3 xc ψcx.1 xc Vx1 2
ψcx.2 xc Vx0 2
ψcx.3 xc Vx6 2
ψcx.4 xc Vx4 2
ux6.3 xc ψcx.1 xc Vx0 2
ψcx.3 xc Vx4 2
ux7.3 xb ψbx.3 xb Vx4 2
ψbx.4 xb Vx3 2
ux8.3 xb ψbx.3 xb Vx6 2
ψbx.4 xb Vx5 2
ux9.3 xb ψbx.3 xb Vx8 2
ψbx.4 xb Vx7 2
Yx1.3 xc H xc Xx1.3 xc 4 ux1.3 xc
Yx2.3 xc 2H xc Xx2.3 xc 4 ux2.3 xc
Yx3.3 xc 3H xc Xx3.3 xc 4 ux3.3 xc
Yx4.3 xc 3H xc Xx4.3 xc 4 W ux4.3 xc
Yx5.3 xc 2H xc Xx5.3 xc 4 W ux5.3 xc
Yx6.3 xc H xc Xx6.3 xc 4 W ux6.3 xc
Yx7.3 xb H ux7.3 xb Xx7.3 xb Xx1.3 0( ) W xb
Yx8.3 xb 2H ux8.3 xb Xx8.3 xb Xx2.3 0( ) W xb
Yx9.3 xb 3H ux9.3 xb Xx9.3 xb Xx3.3 0( ) W xb
5 10 150
5
10
Mode 3 on X
Yx1.3 xc Yx2.3 xc Yx3.3 xc Yx4.3 xc Yx5.3 xc Yx6.3 xc Yx7.3 xb Yx8.3 xb Yx9.3 xb
Xx1.3 xc Xx2.3 xc Xx3.3 xc Xx4.3 xc Xx5.3 xc Xx6.3 xc Xx7.3 xb Xx8.3 xb Xx9.3 xb
Mode 4:xc 0 0.01 H
xb 0 0.01 W
ux1.4 xc ψcx.1 xc Vx0 3
ψcx.3 xc Vx3 3
ux2.4 xc ψcx.1 xc Vx1 3
ψcx.2 xc Vx0 3
ψcx.3 xc Vx5 3
ψcx.4 xc Vx3 3
ux3.4 xc ψcx.1 xc Vx2 3
ψcx.2 xc Vx1 3
ψcx.3 xc Vx7 3
ψcx.4 xc Vx5 3
ux4.4 xc ψcx.1 xc Vx2 3
ψcx.2 xc Vx1 3
ψcx.3 xc Vx8 3
ψcx.4 xc Vx6 3
ux5.4 xc ψcx.1 xc Vx1 3
ψcx.2 xc Vx0 3
ψcx.3 xc Vx6 3
ψcx.4 xc Vx4 3
ux6.4 xc ψcx.1 xc Vx0 3
ψcx.3 xc Vx4 3
ux7.4 xb ψbx.3 xb Vx4 3
ψbx.4 xb Vx3 3
ux8.4 xb ψbx.3 xb Vx6 3
ψbx.4 xb Vx5 3
ux9.4 xb ψbx.3 xb Vx8 3
ψbx.4 xb Vx7 3
Yx1.4 xc H xc Xx1.4 xc 4 ux1.4 xc
Yx2.4 xc 2H xc Xx2.4 xc 4 ux2.4 xc
Yx3.4 xc 3H xc Xx3.4 xc 4 ux3.4 xc
Yx4.4 xc 3H xc Xx4.4 xc 4 W ux4.4 xc
Yx5.4 xc 2H xc Xx5.4 xc 4 W ux5.4 xc
Yx6.4 xc H xc Xx6.4 xc 4 W ux6.4 xc
Yx7.4 xb H ux7.4 xb Xx7.4 xb Xx1.4 0( ) W xb
Yx8.4 xb 2H ux8.4 xb Xx8.4 xb Xx2.4 0( ) W xb
Yx9.4 xb 3H ux9.4 xb Xx9.4 xb Xx3.4 0( ) W xb
2 3.455 4.909 6.364 7.818 9.273 10.727 12.182 13.636 15.091 16.545 180
5
10
Mode 4 on X
Yx1.4 xc Yx2.4 xc Yx3.4 xc Yx4.4 xc Yx5.4 xc Yx6.4 xc Yx7.4 xb Yx8.4 xb Yx9.4 xb
Xx1.4 xc Xx2.4 xc Xx3.4 xc Xx4.4 xc Xx5.4 xc Xx6.4 xc Xx7.4 xb Xx8.4 xb Xx9.4 xb
Mode 5:
xc 0 0.01 H
xb 0 0.01 W
ux1.5 xc ψcx.1 xc Vx0 4
ψcx.3 xc Vx3 4
ux2.5 xc ψcx.1 xc Vx1 4
ψcx.2 xc Vx0 4
ψcx.3 xc Vx5 4
ψcx.4 xc Vx3 4
ux3.5 xc ψcx.1 xc Vx2 4
ψcx.2 xc Vx1 4
ψcx.3 xc Vx7 4
ψcx.4 xc Vx5 4
ux4.5 xc ψcx.1 xc Vx2 4
ψcx.2 xc Vx1 4
ψcx.3 xc Vx8 4
ψcx.4 xc Vx6 4
ux5.5 xc ψcx.1 xc Vx1 4
ψcx.2 xc Vx0 4
ψcx.3 xc Vx6 4
ψcx.4 xc Vx4 4
ux6.5 xc ψcx.1 xc Vx0 4
ψcx.3 xc Vx4 4
ux7.5 xb ψbx.3 xb Vx4 4
ψbx.4 xb Vx3 4
ux8.5 xb ψbx.3 xb Vx6 4
ψbx.4 xb Vx5 4
ux9.5 xb ψbx.3 xb Vx8 4
ψbx.4 xb Vx7 4
Yx1.5 xc H xc Xx1.5 xc 4 ux1.5 xc
Yx2.5 xc 2H xc Xx2.5 xc 4 ux2.5 xc
Yx3.5 xc 3H xc Xx3.5 xc 4 ux3.5 xc
Yx4.5 xc 3H xc Xx4.5 xc 4 W ux4.5 xc
Yx5.5 xc 2H xc Xx5.5 xc 4 W ux5.5 xc
Yx6.5 xc H xc Xx6.5 xc 4 W ux6.5 xc
Yx7.5 xb H ux7.5 xb Xx7.5 xb Xx1.5 0( ) W xb
Yx8.5 xb 2H ux8.5 xb Xx8.5 xb Xx2.5 0( ) W xb
Yx9.5 xb 3H ux9.5 xb Xx9.5 xb Xx3.5 0( ) W xb
2 3.455 4.909 6.364 7.818 9.273 10.727 12.182 13.636 15.091 16.545 180
5
10
Mode 5 on X
Yx1.5 xc Yx2.5 xc Yx3.5 xc Yx4.5 xc Yx5.5 xc Yx6.5 xc Yx7.5 xb Yx8.5 xb Yx9.5 xb
Xx1.5 xc Xx2.5 xc Xx3.5 xc Xx4.5 xc Xx5.5 xc Xx6.5 xc Xx7.5 xb Xx8.5 xb Xx9.5 xb
Mode 6:
xc 0 0.01 H
xb 0 0.01 W
ux1.6 xc ψcx.1 xc Vx0 5
ψcx.3 xc Vx3 5
ux2.6 xc ψcx.1 xc Vx1 5
ψcx.2 xc Vx0 5
ψcx.3 xc Vx5 5
ψcx.4 xc Vx3 5
ux3.6 xc ψcx.1 xc Vx2 5
ψcx.2 xc Vx1 5
ψcx.3 xc Vx7 5
ψcx.4 xc Vx5 5
ux4.6 xc ψcx.1 xc Vx2 5
ψcx.2 xc Vx1 5
ψcx.3 xc Vx8 5
ψcx.4 xc Vx6 5
ux5.6 xc ψcx.1 xc Vx1 5
ψcx.2 xc Vx0 5
ψcx.3 xc Vx6 5
ψcx.4 xc Vx4 5
ux6.6 xc ψcx.1 xc Vx0 5
ψcx.3 xc Vx4 5
ux7.6 xb ψbx.3 xb Vx4 5
ψbx.4 xb Vx3 5
ux8.6 xb ψbx.3 xb Vx6 5
ψbx.4 xb Vx5 5
ux9.6 xb ψbx.3 xb Vx8 5
ψbx.4 xb Vx7 5
Yx1.6 xc H xc Xx1.6 xc 4 ux1.6 xc
Yx2.6 xc 2H xc Xx2.6 xc 4 ux2.6 xc
Yx3.6 xc 3H xc Xx3.6 xc 4 ux3.6 xc
Yx4.6 xc 3H xc Xx4.6 xc 4 W ux4.6 xc
Yx5.6 xc 2H xc Xx5.6 xc 4 W ux5.6 xc
Yx6.6 xc H xc Xx6.6 xc 4 W ux6.6 xc
Yx7.6 xb H ux7.6 xb Xx7.6 xb Xx1.6 0( ) W xb
Yx8.6 xb 2H ux8.6 xb Xx8.6 xb Xx2.6 0( ) W xb
Yx9.6 xb 3H ux9.6 xb Xx9.6 xb Xx3.6 0( ) W xb
3 4.273 5.545 6.818 8.091 9.364 10.636 11.909 13.182 14.455 15.727 170
5
10
Mode 6 on X
Yx1.6 xc Yx2.6 xc Yx3.6 xc Yx4.6 xc Yx5.6 xc Yx6.6 xc Yx7.6 xb Yx8.6 xb Yx9.6 xb
Xx1.6 xc Xx2.6 xc Xx3.6 xc Xx4.6 xc Xx5.6 xc Xx6.6 xc Xx7.6 xb Xx8.6 xb Xx9.6 xb
Mode 7:xc 0 0.01 H
xb 0 0.01 W
ux1.7 xc ψcx.1 xc Vx0 6
ψcx.3 xc Vx3 6
ux2.7 xc ψcx.1 xc Vx1 6
ψcx.2 xc Vx0 6
ψcx.3 xc Vx5 6
ψcx.4 xc Vx3 6
ux3.7 xc ψcx.1 xc Vx2 6
ψcx.2 xc Vx1 6
ψcx.3 xc Vx7 6
ψcx.4 xc Vx5 6
ux4.7 xc ψcx.1 xc Vx2 6
ψcx.2 xc Vx1 6
ψcx.3 xc Vx8 6
ψcx.4 xc Vx6 6
ux5.7 xc ψcx.1 xc Vx1 6
ψcx.2 xc Vx0 6
ψcx.3 xc Vx6 6
ψcx.4 xc Vx4 6
ux6.7 xc ψcx.1 xc Vx0 6
ψcx.3 xc Vx4 6
ux7.7 xb ψbx.3 xb Vx4 6
ψbx.4 xb Vx3 6
ux8.7 xb ψbx.3 xb Vx6 6
ψbx.4 xb Vx5 6
ux9.7 xb ψbx.3 xb Vx8 6
ψbx.4 xb Vx7 6
Yx1.7 xc H xc Xx1.7 xc 4 ux1.7 xc
Yx2.7 xc 2H xc Xx2.7 xc 4 ux2.7 xc
Yx3.7 xc 3H xc Xx3.7 xc 4 ux3.7 xc
Yx4.7 xc 3H xc Xx4.7 xc 4 W ux4.7 xc
Yx5.7 xc 2H xc Xx5.7 xc 4 W ux5.7 xc
Yx6.7 xc H xc Xx6.7 xc 4 W ux6.7 xc
Yx7.7 xb H ux7.7 xb Xx7.7 xb Xx1.7 0( ) W xb
Yx8.7 xb 2H ux8.7 xb Xx8.7 xb Xx2.7 0( ) W xb
Yx9.7 xb 3H ux9.7 xb Xx9.7 xb Xx3.7 0( ) W xb
3 4.364 5.727 7.091 8.455 9.818 11.182 12.545 13.909 15.273 16.636 180
5
10
Mode 7 on X
Yx1.7 xc Yx2.7 xc Yx3.7 xc Yx4.7 xc Yx5.7 xc Yx6.7 xc Yx7.7 xb Yx8.7 xb Yx9.7 xb
Xx1.7 xc Xx2.7 xc Xx3.7 xc Xx4.7 xc Xx5.7 xc Xx6.7 xc Xx7.7 xb Xx8.7 xb Xx9.7 xb
Mode 8:xc 0 0.01 H
xb 0 0.01 W
ux1.8 xc ψcx.1 xc Vx0 7
ψcx.3 xc Vx3 7
ux2.8 xc ψcx.1 xc Vx1 7
ψcx.2 xc Vx0 7
ψcx.3 xc Vx5 7
ψcx.4 xc Vx3 7
ux3.8 xc ψcx.1 xc Vx2 7
ψcx.2 xc Vx1 7
ψcx.3 xc Vx7 7
ψcx.4 xc Vx5 7
ux4.8 xc ψcx.1 xc Vx2 7
ψcx.2 xc Vx1 7
ψcx.3 xc Vx8 7
ψcx.4 xc Vx6 7
ux5.8 xc ψcx.1 xc Vx1 7
ψcx.2 xc Vx0 7
ψcx.3 xc Vx6 7
ψcx.4 xc Vx4 7
ux6.8 xc ψcx.1 xc Vx0 7
ψcx.3 xc Vx4 7
ux7.8 xb ψbx.3 xb Vx4 7
ψbx.4 xb Vx3 7
ux8.8 xb ψbx.3 xb Vx6 7
ψbx.4 xb Vx5 7
ux9.8 xb ψbx.3 xb Vx8 7
ψbx.4 xb Vx7 7
Yx1.8 xc H xc Xx1.8 xc 4 ux1.8 xc
Yx2.8 xc 2H xc Xx2.8 xc 4 ux2.8 xc
Yx3.8 xc 3H xc Xx3.8 xc 4 ux3.8 xc
Yx4.8 xc 3H xc Xx4.8 xc 4 W ux4.8 xc
Yx5.8 xc 2H xc Xx5.8 xc 4 W ux5.8 xc
Yx6.8 xc H xc Xx6.8 xc 4 W ux6.8 xc
Yx7.8 xb H ux7.8 xb Xx7.8 xb Xx1.8 0( ) W xb
Yx8.8 xb 2H ux8.8 xb Xx8.8 xb Xx2.8 0( ) W xb
Yx9.8 xb 3H ux9.8 xb Xx9.8 xb Xx3.8 0( ) W xb
3 4.364 5.727 7.091 8.455 9.818 11.182 12.545 13.909 15.273 16.636 180
5
10
Mode 8 on X
Yx1.8 xc Yx2.8 xc Yx3.8 xc Yx4.8 xc Yx5.8 xc Yx6.8 xc Yx7.8 xb Yx8.8 xb Yx9.8 xb
Xx1.8 xc Xx2.8 xc Xx3.8 xc Xx4.8 xc Xx5.8 xc Xx6.8 xc Xx7.8 xb Xx8.8 xb Xx9.8 xb
Mode 9:
xc 0 0.01 H
xb 0 0.01 W
ux1.9 xc ψcx.1 xc Vx0 8
ψcx.3 xc Vx3 8
ux2.9 xc ψcx.1 xc Vx1 8
ψcx.2 xc Vx0 8
ψcx.3 xc Vx5 8
ψcx.4 xc Vx3 8
ux3.9 xc ψcx.1 xc Vx2 8
ψcx.2 xc Vx1 8
ψcx.3 xc Vx7 8
ψcx.4 xc Vx5 8
ux4.9 xc ψcx.1 xc Vx2 8
ψcx.2 xc Vx1 8
ψcx.3 xc Vx8 8
ψcx.4 xc Vx6 8
ux5.9 xc ψcx.1 xc Vx1 8
ψcx.2 xc Vx0 8
ψcx.3 xc Vx6 8
ψcx.4 xc Vx4 8
ux6.9 xc ψcx.1 xc Vx0 8
ψcx.3 xc Vx4 8
ux7.9 xb ψbx.3 xb Vx4 8
ψbx.4 xb Vx3 8
ux8.9 xb ψbx.3 xb Vx6 8
ψbx.4 xb Vx5 8
ux9.9 xb ψbx.3 xb Vx8 8
ψbx.4 xb Vx7 8
Yx1.9 xc H xc Xx1.9 xc 4 ux1.9 xc
Yx2.9 xc 2H xc Xx2.9 xc 4 ux2.9 xc
Yx3.9 xc 3H xc Xx3.9 xc 4 ux3.9 xc
Yx4.9 xc 3H xc Xx4.9 xc 4 W ux4.9 xc
Yx5.9 xc 2H xc Xx5.9 xc 4 W ux5.9 xc
Yx6.9 xc H xc Xx6.9 xc 4 W ux6.9 xc
Yx7.9 xb H ux7.9 xb Xx7.9 xb Xx1.9 0( ) W xb
Yx8.9 xb 2H ux8.9 xb Xx8.9 xb Xx2.9 0( ) W xb
Yx9.9 xb 3H ux9.9 xb Xx9.9 xb Xx3.9 0( ) W xb
0 2 4 6 8 10 12 14 16 18 20 220
5
10
Mode 9 on X
Yx1.9 xc Yx2.9 xc Yx3.9 xc Yx4.9 xc Yx5.9 xc Yx6.9 xc Yx7.9 xb Yx8.9 xb Yx9.9 xb
Xx1.9 xc Xx2.9 xc Xx3.9 xc Xx4.9 xc Xx5.9 xc Xx6.9 xc Xx7.9 xb Xx8.9 xb Xx9.9 xb
Stiffness matrix Y direction:
Ic12y
dc3
w12
12 Ic12y 0.000675 m
4
Ic3y
dc3
w3
12 Ic3y 0.00045 m
4
Iby
hb3
tb
12 Iby 0.000675 m
4
Local stiffness matrix: For columns at first and second storey:
kc12y11 12
Ec Ic12y
H3
kc12y12 12Ec Ic12y
H3
kc12y13 6
Ec Ic12y
H2
kc12y14 6
Ec Ic12y
H2
kc12y21 12Ec Ic12y
H3
kc12y22 12
Ec Ic12y
H3
kc12y23 6Ec Ic12y
H2
kc12y24 6Ec Ic12y
H2
kc12y31 6
Ec Ic12y
H2
kc12y32 6Ec Ic12y
H2
kc12y33 4
Ec Ic12y
H kc12y34 2
Ec Ic12y
H
kc12y41 6
Ec Ic12y
H2
kc12y42 6Ec Ic12y
H2
kc12y43 2
Ec Ic12y
H kc12y44 4
Ec Ic12y
H
Klocal12cy
kc12y11
kc12y21
kc12y31
kc12y41
kc12y12
kc12y22
kc12y32
kc12y42
kc12y13
kc12y23
kc12y33
kc12y43
kc12y14
kc12y24
kc12y34
kc12y44
Klocal12cy
6423.32362
6423.32362
11240.81633
11240.81633
6423.32362
6423.32362
11240.81633
11240.81633
11240.81633
11240.81633
26228.57143
13114.28571
11240.81633
11240.81633
13114.28571
26228.57143
For columns at third storey:
kc3y11 12
Ec Ic3y
H3
kc3y12 12Ec Ic3y
H3
kc3y13 6
Ec Ic3y
H2
kc3y14 6
Ec Ic3y
H2
kc3y21 12Ec Ic3y
H3
kc3y22 12
Ec Ic3y
H3
kc3y23 6Ec Ic3y
H2
kc3y24 6Ec Ic3y
H2
kc3y31 6
Ec Ic3y
H2
kc3y32 6Ec Ic3y
H2
kc3y33 4
Ec Ic3y
H kc3y34 2
Ec Ic3y
H
kc3y41 6
Ec Ic3y
H2
kc3y42 6Ec Ic3y
H2
kc3y43 2
Ec Ic3y
H kc3y44 4
Ec Ic3y
H
Klocalc3y
kc3y11
kc3y21
kc3y31
kc3y41
kc3y12
kc3y22
kc3y32
kc3y42
kc3y13
kc3y23
kc3y33
kc3y43
kc3y14
kc3y24
kc3y34
kc3y44
Klocalc3y
4282.22
4282.22
7493.88
7493.88
4282.22
4282.22
7493.88
7493.88
7493.88
7493.88
17485.71
8742.86
7493.88
7493.88
8742.86
17485.71
For beams at first and second storey:
kby11 12
Ec Iby
L3
kby12 12Ec Iby
L3
kby13 6
Ec Iby
L2
kby14 6
Ec Iby
L2
kby21 12Ec Iby
L3
kby22 12
Ec Iby
L3
kby23 6Ec Iby
L2
kby24 6Ec Iby
L2
kby31 6
Ec Iby
L2
kby32 6Ec Iby
L2
kby33 4
Ec Iby
L kby34 2
Ec Iby
L
kby41 6
Ec Iby
L kby42 6
Ec Iby
L2
kby43 2
Ec Iby
L kby44 4
Ec Iby
L
Klocalby
kby11
kby21
kby31
kby41
kby12
kby22
kby32
kby42
kby13
kby23
kby33
kby43
kby14
kby24
kby34
kby44
Klocalby
4303.12
4303.12
8606.25
34425
4303.12
4303.12
8606.25
8606.25
8606.25
8606.25
22950
11475
8606.25
8606.25
11475
22950
Genereal stiffness matrix of the structure on Y direction1 2 5 6 2 5
Ky11 kc12y11 kc12y22 kc12y22 kc12y11 Ky12 kc12y21 kc12y21
5 2 2 3 5 4
Ky21 kc12y12 kc12y12 Ky22 kc12y11 kc3y22 kc12y11 kc3y22
3 4
Ky31 0 Ky32 kc3y12 kc3y12
1 2 2
Ky41 kc12y31 kc12y42 Ky42 kc12y41
5 6 5
Ky51 kc12y42 kc12y31 Ky52 kc12y41
2 2 3
Ky61 kc12y32 Ky62 kc12y31 kc3y42
5 4 5
Ky71 kc12y32 Ky72 kc3y42 kc12y31
3
Ky81 0 Ky82 kc3y32
4
Ky91 0 Ky92 kc3y32
1 2
Ky13 0 Ky14 kc12y13 kc12y24
3 4 2
Ky23 kc3y21 kc3y21 Ky24 kc12y14
3 4
Ky33 kc3y11 kc3y11 Ky34 0
1 2 7
Ky43 0 Ky44 kc12y33 kc12y44 kby44
7
Ky53 0 Ky54 kby34
3 2
Ky63 kc3y41 Ky64 kc12y34
4
Ky73 kc3y41 Ky74 0
3
Ky83 kc3y31 Ky84 0
4
Ky93 kc3y31 Ky94 0
5 6 2
Ky15 kc12y24 kc12y13 Ky16 kc12y23
5 2 3
Ky25 kc12y14 Ky26 kc12y13 kc3y24
3
Ky35 0 Ky36 kc3y14
7 2
Ky45 kby43 Ky46 kc12y43
5 6 7
Ky55 kc12y44 kc12y33 kby33 Ky56 0
2 3 8
Ky65 0 Ky66 kc12y33 kc3y44 kby44
5 8
Ky75 kc12y34 Ky76 kby34
3
Ky85 0 Ky86 kc3y34
Ky95 0 Ky96 0
5
Ky17 kc12y23 Ky18 0 Ky19 0
4 5 3 4
Ky27 kc3y24 kc12y13 Ky28 kc3y23 Ky29 kc3y23
4 3 4
Ky37 kc3y14 Ky38 kc3y13 Ky39 kc3y13
Ky47 0 Ky48 0 Ky49 0
5
Ky57 kc12y43 Ky58 0 Ky59 0
8 3
Ky67 kby43 Ky68 kc3y43 Ky69 0
4 5 8 4
Ky77 kc3y44 kc12y33 kby33 Ky78 0 Ky79 kc3y43
3 9 9
Ky87 0 Ky88 kc3y33 kby44 Ky89 kby43
4 9 4 9
Ky97 kc3y34 Ky98 kby34 Ky99 kc3y33 kby33
Ky
Ky11
Ky21
Ky31
Ky41
Ky51
Ky61
Ky71
Ky81
Ky91
Ky12
Ky22
Ky32
Ky42
Ky52
Ky62
Ky72
Ky82
Ky92
Ky13
Ky23
Ky33
Ky43
Ky53
Ky63
Ky73
Ky83
Ky93
Ky14
Ky24
Ky34
Ky44
Ky54
Ky64
Ky74
Ky84
Ky94
Ky15
Ky25
Ky35
Ky45
Ky55
Ky65
Ky75
Ky85
Ky95
Ky16
Ky26
Ky36
Ky46
Ky56
Ky66
Ky76
Ky86
Ky96
Ky17
Ky27
Ky37
Ky47
Ky57
Ky67
Ky77
Ky87
Ky97
Ky18
Ky28
Ky38
Ky48
Ky58
Ky68
Ky78
Ky88
Ky98
Ky19
Ky29
Ky39
Ky49
Ky59
Ky69
Ky79
Ky89
Ky99
Ky
25693.294
12846.647
0
0
0
11240.816
11240.816
0
0
12846.647
21411.079
8564.431
11240.816
11240.816
3746.939
3746.939
7493.878
7493.878
0
8564.431
8564.431
0
0
7493.878
7493.878
7493.878
7493.878
0
11240.816
0
75407.143
11475
13114.286
0
0
0
0
11240.816
0
11475
75407.143
0
13114.286
0
0
11240.816
3746.939
7493.878
13114.286
0
66664.286
11475
8742.857
0
11240.816
3746.939
7493.878
0
13114.286
11475
66664.286
0
8742.857
0
7493.878
7493.878
0
0
8742.857
0
40435.714
11475
0
7493.878
7493.878
0
0
0
8742.857
11475
40435.714
Mass matrix Y direction:Msy
L W2
ts ρc gdL W2
Msy 20.8 t
MsryL W2
ts ρc grL W2
Msry 17 t
Mby L hb tb ρc 1.5 L H tg ρg Mby 1.41 t
Mbry L hb tb ρc Mbry 0.864 t
Mcy1 w12 dc ρc H 0.756 t Mcy2 w12 dc ρc H 0.756 t Mcy3 w3 dc ρc H 0.504 t
Mtoty Mby 2 Mbry Mcy1 2 Mcy2 2 Mcy3 2 Msy Msry 45.566 t
mby
Mby
L
Msy
L mby 5.552
t
m
mbry
Mbry
L
Msry
L mbry 4.478
t
m
mc12y w12 dc ρc mc12y 0.216t
m
mc3y w3 dc ρc mc3y 0.144t
m
Local mass matrix on y direction:For columns at first and second storey:
mc12y11
156 mc12y H
420 mc12y12
54 mc12y H
420 mc12y13
22 mc12y H2
420 mc12y14
13 mc12y H2
420
mc12y21
54 mc12y H
420 mc12y22
156 mc12y H
420 mc12y23
13 mc12y H2
420 mc12y24
22 mc12y H2
420
mc12y31
22 mc12y H2
420 mc12y32
13 mc12y H2
420 mc12y33
4 mc12y H3
420 mc12y34
3 mc12y H3
420
mc12y41
13 mc12y H2
420 mc12y42
22 mc12y H2
420 mc12y43
3 mc12y H3
420 mc12y44
4 mc12y H3
420
Mlocalc12y
mc12y11
mc12y21
mc12y31
mc12y41
mc12y12
mc12y22
mc12y32
mc12y42
mc12y13
mc12y23
mc12y33
mc12y43
mc12y14
mc12y24
mc12y34
mc12y44
Mlocalc12y
0.281
0.097
0.139
0.082
0.097
0.281
0.082
0.139
0.139
0.082
0.088
0.066
0.082
0.139
0.066
0.088
For columns at third storey:
mc3y11
156 mc3y H
420 mc3y12
54 mc3y H
420 mc3y13
22 mc3y H2
420 mc3y14
13 mc3y H2
420
mc3y21
54 mc3y H
420 mc3y22
156 mc3y H
420 mc3y23
13 mc3y H2
420 mc3y24
22 mc3y H2
420
mc3y31
22 mc3y H2
420 mc3y32
13 mc3y H2
420 mc3y33
4 mc3y H3
420 mc3y34
3 mc3y H3
420
mc3y41
13 mc3y H2
420 mc3y42
22 mc3y H2
420 mc3y43
3 mc3y H3
420 mc3y44
4 mc3y H3
420
Mlocalc3y
mc3y11
mc3y21
mc3y31
mc3y41
mc3y12
mc3y22
mc3y32
mc3y42
mc3y13
mc3y23
mc3y33
mc3y43
mc3y14
mc3y24
mc3y34
mc3y44
Mlocalc3y
0.187
0.065
0.092
0.055
0.065
0.187
0.055
0.092
0.092
0.055
0.059
0.044
0.055
0.092
0.044
0.059
For beams at first and second storey:
mby11
156 mby L
420 mby12
54 mby L
420 mby13
22 mby L2
420 mby14
13 mby L2
420
mby21
54 mby L
420 mby22
156 mby L
420 mby23
13 mby L2
420 mby24
22 mby L2
420
mby31
22 mby L2
420 mby32
13 mby L2
420 mby33
4 mby L3
420 mby34
3 mby L3
420
mby41
13 mby L2
420 mby42
22 mby L2
420 mby43
3 mby L3
420 mby44
4 mby L3
420
Mlocalby
mby11
mby21
mby31
mby41
mby12
mby22
mby32
mby42
mby13
mby23
mby33
mby43
mby14
mby24
mby34
mby44
Mlocalby
8.249
2.856
4.654
2.75
2.856
8.249
2.75
4.654
4.654
2.75
3.384
2.538
2.75
4.654
2.538
3.384
For roof beam:
mbry11
156 mbry L
420 mbry12
54 mbry L
420 mbry13
22 mbry L2
420 mbry14
13 mbry L2
420
mbry21
54 mbry L
420 mbry22
156 mbry L
420 mbry23
13 mbry L2
420 mbry24
22 mbry L2
420
mbry31
22 mbry L2
420 mbry32
13 mbry L2
420 mbry33
4 mbry L3
420 mbry34
3 mbry L3
420
mbry41
13 mbry L2
420 mbry42
22 mbry L2
420 mbry43
3 mbry L3
420 mbry44
4 mbry L3
420
Mlocalbry
mbry11
mbry21
mbry31
mbry41
mbry12
mbry22
mbry32
mbry42
mbry13
mbry23
mbry33
mbry43
mbry14
mbry24
mbry34
mbry44
Mlocalbry
6.654
2.303
3.753
2.218
2.303
6.654
2.218
3.753
3.753
2.218
2.73
2.047
2.218
3.753
2.047
2.73
Genereal mass matrix of the structure on Y direction:1 2 5 6 2 5
My11 mc12y11 mc12y22 mc12y22 mc12y11 Mby Msy My12 mc12y21 mc12y21
5 2 2 3 4 5
My21 mc12y12 mc12y12 My22 mc12y11 mc3y22 mc12y11 mc3y22 Mby Msy
3 4
My31 0 My32 mc3y12 mc3y12
1 2 2
My41 mc12y31 mc12y42 My42 mc12y41
5 6 5
My51 mc12y42 mc12y31 My52 mc12y41
2 2 3
My61 mc12y32 My62 mc12y31 mc3y42
5 4 5
My71 mc12y32 My72 mc3y42 mc12y31
3
My81 0 My82 mc3y32
4
My91 0 My92 mc3y32
1 2
My13 0 My14 mc12y13 mc12y24
3 4 2
My23 mc3y21 mc3y21 My24 mc12y14
3 4
My33 mc3y11 mc3y11 Mbry Msry My34 0
1 2 7
My43 0 My44 mc12y33 mc12y44 mby44
7
My53 0 My54 mby34
3 2
My63 mc3y41 My64 mc12y34
4
My73 mc3y41 My74 0
3
My83 mc3y31 My84 0
4
My93 mc3y31 My94 0
5 6 2
My15 mc12y24 mc12y13 My16 mc12y23
5 2 3
My25 mc12y14 My26 mc12y13 mc3y24
3
My35 0 My36 mc3y14
7 2
My45 mby43 My46 mc12y43
5 6 7
My55 mc12y44 mc12y33 mby33 My56 0
2 3 8
My65 0 My66 mc12y33 mc3y44 mby44
5 8
My75 mc12y34 My76 mby34
3
My85 0 My86 mc3y34
My95 0 My96 0
5
My17 mc12y23 My18 0 My19 0
4 5 3 4
My27 mc3y24 mc12y13 My28 mc3y23 My29 mc3y23
4 3 4
My37 mc3y14 My38 mc3y13 My39 mc3y13
My47 0 My48 0 My49 0
5
My57 mc12y43 My58 0 My59 0
8 3
My67 mby43 My68 mc3y43 My69 0
4 5 8 4
My77 mc3y44 mc12y33 mby33 My78 0 My79 mc3y43
3 9 9
My87 0 My88 mc3y33 mbry44 My89 mbry43
4 9 4 9
My97 mc3y34 My98 mbry34 My99 mc3y33 mbry33
My
My11
My21
My31
My41
My51
My61
My71
My81
My91
My12
My22
My32
My42
My52
My62
My72
My82
My92
My13
My23
My33
My43
My53
My63
My73
My83
My93
My14
My24
My34
My44
My54
My64
My74
My84
My94
My15
My25
My35
My45
My55
My65
My75
My85
My95
My16
My26
My36
My46
My56
My66
My76
My86
My96
My17
My27
My37
My47
My57
My67
My77
My87
My97
My18
My28
My38
My48
My58
My68
My78
My88
My98
My19
My29
My39
My49
My59
My69
My79
My89
My99
My
23.333
0.194
0
0
0
0.082
0.082
0
0
0.194
23.146
0.13
0.082
0.082
0.046
0.046
0.055
0.055
0
0.13
18.288
0
0
0.055
0.055
0.092
0.092
0
0.082
0
3.561
2.538
0.066
0
0
0
0
0.082
0
2.538
3.561
0
0.066
0
0
0.082
0.046
0.055
0.066
0
3.531
2.538
0.044
0
0.082
0.046
0.055
0
0.066
2.538
3.531
0
0.044
0
0.055
0.092
0
0
0.044
0
2.789
2.047
0
0.055
0.092
0
0
0
0.044
2.047
2.789
Eigenfrequencies and eigenmodes y direction:ωy genvals Ky My
angular frequency:
ωy
324.817
276.616
237.896
37.822
21.564
7.158
111.151
90.472
71.417
sort ωy
7.158
21.564
37.822
71.417
90.472
111.151
237.896
276.616
324.817
fy ωy2
105505.835
76516.245
56594.372
1430.507
465.024
51.239
12354.563
8185.216
5100.342
Eigenmode:
ϕy genvecs Ky My
ϕy
0.016
0.01
0.013
0.966
0.966
1
1
0.504
0.504
0.007
0.028
0.007
0.721
0.721
0.37
0.37
1
1
0.022
0.005
0.014
0.519
0.519
0.889
0.889
1
1
1
0.862
0.389
0.09
0.09
0.16
0.16
0.212
0.212
0.889
0.69
1
0.119
0.119
0.189
0.189
0.213
0.213
0.316
0.721
1
0.083
0.083
0.068
0.068
0.029
0.029
0
0
0
1
1
0.82
0.82
0.247
0.247
0
0
0
0.975
0.975
1
1
0.857
0.857
0
0
0
0.196
0.196
0.479
0.479
1
1
Vy ϕy
sortf
s fyi
fyifyj
fyjs
fyifyj
if
j i 1( ) 8for
i 0 7for
fyjs
fy
Vy
z fyi
fyifyj
fyjz
zz Vyi
Vyi Vy
j
Vyj zz
fyifyj
if
j i 1( ) 8for
i 0 7for
Vyj zz
Vy
Vy
0.316
0.721
1
0.083
0.083
0.068
0.068
0.029
0.029
0.889
0.69
1
0.119
0.119
0.189
0.189
0.213
0.213
1
0.862
0.389
0.09
0.09
0.16
0.16
0.212
0.212
0
0
0
0.196
0.196
0.479
0.479
1
1
0
0
0
0.975
0.975
1
1
0.857
0.857
0
0
0
1
1
0.82
0.82
0.247
0.247
0.022
0.005
0.014
0.519
0.519
0.889
0.889
1
1
0.007
0.028
0.007
0.721
0.721
0.37
0.37
1
1
0.016
0.01
0.013
0.966
0.966
1
1
0.504
0.504
Ty2π
sort ωy fy
1
Ty Ty
T0.878 0.291 0.166 0.088 0.069 0.057 0.026 0.023 0.019( )
ϕy1 Vy0 ϕy6 Vy
5
ϕy2 Vy1 ϕy7 Vy
6
Ty
0.878
0.291
0.166
0.088
0.069
0.057
0.026
0.023
0.019
fy
1.139
3.432
6.02
11.366
14.399
17.69
37.862
44.025
51.696
ϕy3 Vy2 ϕy8 Vy
7
ϕy4 Vy3 ϕy9 Vy
8
ϕy5 Vy4
ϕy1
0.316
0.721
1
0.083
0.083
0.068
0.068
0.029
0.029
ϕy2
0.889
0.69
1
0.119
0.119
0.189
0.189
0.213
0.213
ϕy3
1
0.862
0.389
0.09
0.09
0.16
0.16
0.212
0.212
ϕy4
0
0
0
0.196
0.196
0.479
0.479
1
1
ϕy5
0
0
0
0.975
0.975
1
1
0.857
0.857
ϕy6
0
0
0
1
1
0.82
0.82
0.247
0.247
ϕy7
0.022
0.005
0.014
0.519
0.519
0.889
0.889
1
1
ϕy8
6.922 103
0.028
7.183 103
0.721
0.721
0.37
0.37
1
1
ϕy9
0.016
9.534 103
0.013
0.966
0.966
1
1
0.504
0.504
ϕy Vy
0.316
0.721
1
0.083
0.083
0.068
0.068
0.029
0.029
0.889
0.69
1
0.119
0.119
0.189
0.189
0.213
0.213
1
0.862
0.389
0.09
0.09
0.16
0.16
0.212
0.212
0
0
0
0.196
0.196
0.479
0.479
1
1
0
0
0
0.975
0.975
1
1
0.857
0.857
0
0
0
1
1
0.82
0.82
0.247
0.247
0.022
0.005
0.014
0.519
0.519
0.889
0.889
1
1
0.007
0.028
0.007
0.721
0.721
0.37
0.37
1
1
0.016
0.01
0.013
0.966
0.966
1
1
0.504
0.504
Kmody ϕyT Ky ϕy
Kmody
1688.3
0
0
0
0
0
0
0
0
0
22357.4
0
0
0
0
0
0
0
0
0
61615.9
0
0
0
0
0
0
0
0
0
66494.5
0
0
0
0
0
0
0
0
0
253249.6
0
0
0
0
0
0
0
0
0
255649.7
0
0
0
0
0
0
0
0
0
219752.9
0
0
0
0
0
0
0
0
0
216550.7
0
0
0
0
0
0
0
0
0
414766.3
Mmody ϕyT My ϕy
Mmody
32.949
0
0
0
0
0
0
0
0
0
48.078
0
0
0
0
0
0
0
0
0
43.073
0
0
0
0
0
0
0
0
0
13.037
0
0
0
0
0
0
0
0
0
30.94
0
0
0
0
0
0
0
0
0
20.693
0
0
0
0
0
0
0
0
0
3.883
0
0
0
0
0
0
0
0
0
2.83
0
0
0
0
0
0
0
0
0
3.931
Shape function for elements:
ψcy.1 y( ) 1 3y
H
2
2y
H
3
ψbq.1 y( ) 1 3y
L
2
2y
L
3
ψcy.2 y( ) 3y
H
2
2y
H
3
ψby.2 y( ) 3y
L
2
2y
L
3
ψcy.3 y( ) y 1y
H
2
ψby.3 y( ) y 1y
L
2
ψcy.4 y( )y2
H
y
H1
ψby.4 y( )y2
L
y
L1
Mode 1:
yc 0 0.01 H
yb 0 0.01 L
uy1.1 yc ψcy.1 yc Vy0 0
ψcy.3 yc Vy3 0
uy2.1 yc ψcy.1 yc Vy1 0
ψcy.2 yc Vy0 0
ψcy.3 yc Vy5 0
ψcy.4 yc Vy3 0
uy3.1 yc ψcy.1 yc Vy2 0
ψcy.2 yc Vy1 0
ψcy.3 yc Vy7 0
ψcy.4 yc Vy5 0
uy4.1 yc ψcy.1 yc Vy2 0
ψcy.2 yc Vy1 0
ψcy.3 yc Vy8 0
ψcy.4 yc Vy6 0
uy5.1 yc ψcy.1 yc Vy1 0
ψcy.2 yc Vy0 0
ψcy.3 yc Vy6 0
ψcy.4 yc Vy4 0
uy6.1 yc ψcy.1 yc Vy0 0
ψcy.3 yc Vy4 0
uy7.1 yb ψby.3 yb Vy4 0
ψby.4 yb Vy3 0
uy8.1 yb ψby.3 yb Vy6 0
ψby.4 yb Vy5 0
uy9.1 yb ψby.3 yb Vy8 0
ψby.4 yb Vy7 0
Yy1.1 yc H yc Xy1.1 yc 3 uy1.1 yc
Yy2.1 yc 2H yc Xy2.1 yc 3 uy2.1 yc
Yy3.1 yc 3H yc Xy3.1 yc 3 uy3.1 yc
Yy4.1 yc 3H yc Xy4.1 yc 3 L uy4.1 yc
Yy5.1 yc 2H yc Xy5.1 yc 3 L uy5.1 yc
Yy6.1 yc H yc Xy6.1 yc 3 L uy6.1 yc
Yy7.1 yb H uy7.1 yb Xy7.1 yb Xy1.1 0( ) L yb
Yy8.1 yb 2H uy8.1 yb Xy8.1 yb Xy2.1 0( ) L yb
Yy9.1 yb 3H uy9.1 yb Xy9.1 yb Xy3.1 0( ) L yb
2 2.636 3.273 3.909 4.545 5.182 5.818 6.455 7.091 7.727 8.364 90
5
10
Mode 1 on Y
Yy1.1 yc Yy2.1 yc Yy3.1 yc Yy4.1 yc Yy5.1 yc Yy6.1 yc Yy7.1 yb Yy8.1 yb Yy9.1 yb
Xy1.1 yc Xy2.1 yc Xy3.1 yc Xy4.1 yc Xy5.1 yc Xy6.1 yc Xy7.1 yb Xy8.1 yb Xy9.1 yb
Mode 2:
yc 0 0.01 H
yb 0 0.01 L
uy1.2 yc ψcy.1 yc Vy0 1
ψcy.3 yc Vy3 1
uy2.2 yc ψcy.1 yc Vy1 1
ψcy.2 yc Vy0 1
ψcy.3 yc Vy5 1
ψcy.4 yc Vy3 1
uy3.2 yc ψcy.1 yc Vy2 1
ψcy.2 yc Vy1 1
ψcy.3 yc Vy7 1
ψcy.4 yc Vy5 1
uy4.2 yc ψcy.1 yc Vy2 1
ψcy.2 yc Vy1 1
ψcy.3 yc Vy8 1
ψcy.4 yc Vy6 1
uy5.2 yc ψcy.1 yc Vy1 1
ψcy.2 yc Vy0 1
ψcy.3 yc Vy6 1
ψcy.4 yc Vy4 1
uy6.2 yc ψcy.1 yc Vy0 1
ψcy.3 yc Vy4 1
uy7.2 yb ψby.3 yb Vy4 1
ψby.4 yb Vy3 1
uy8.2 yb ψby.3 yb Vy6 1
ψby.4 yb Vy5 1
uy9.2 yb ψby.3 yb Vy8 1
ψby.4 yb Vy7 1
Yy1.2 yc H yc Xy1.2 yc 3 uy1.2 yc
Yy2.2 yc 2H yc Xy2.2 yc 3 uy2.2 yc
Yy3.2 yc 3H yc Xy3.2 yc 3 uy3.2 yc
Yy4.2 yc 3H yc Xy4.2 yc 3 L uy4.2 yc
Yy5.2 yc 2H yc Xy5.2 yc 3 L uy5.2 yc
Yy6.2 yc H yc Xy6.2 yc 3 L uy6.2 yc
Yy7.2 yb H uy7.2 yb Xy7.2 yb Xy1.2 0( ) L yb
Yy8.2 yb 2H uy8.2 yb Xy8.2 yb Xy2.2 0( ) L yb
Yy9.2 yb 3H uy9.2 yb Xy9.2 yb Xy3.2 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 2 on Y
Yy1.2 yc Yy2.2 yc Yy3.2 yc Yy4.2 yc Yy5.2 yc Yy6.2 yc Yy7.2 yb Yy8.2 yb Yy9.2 yb
Xy1.2 yc Xy2.2 yc Xy3.2 yc Xy4.2 yc Xy5.2 yc Xy6.2 yc Xy7.2 yb Xy8.2 yb Xy9.2 yb
Mode 3:
yc 0 0.01 H
yb 0 0.01 L
uy1.3 yc ψcy.1 yc Vy0 2
ψcy.3 yc Vy3 2
uy2.3 yc ψcy.1 yc Vy1 2
ψcy.2 yc Vy0 2
ψcy.3 yc Vy5 2
ψcy.4 yc Vy3 2
uy3.3 yc ψcy.1 yc Vy2 2
ψcy.2 yc Vy1 2
ψcy.3 yc Vy7 2
ψcy.4 yc Vy5 2
uy4.3 yc ψcy.1 yc Vy2 2
ψcy.2 yc Vy1 2
ψcy.3 yc Vy8 2
ψcy.4 yc Vy6 2
uy5.3 yc ψcy.1 yc Vy1 2
ψcy.2 yc Vy0 2
ψcy.3 yc Vy6 2
ψcy.4 yc Vy4 2
uy6.3 yc ψcy.1 yc Vy0 2
ψcy.3 yc Vy4 2
uy7.3 yb ψby.3 yb Vy4 2
ψby.4 yb Vy3 2
uy8.3 yb ψby.3 yb Vy6 2
ψby.4 yb Vy5 2
uy9.3 yb ψby.3 yb Vy8 2
ψby.4 yb Vy7 2
Yy1.3 yc H yc Xy1.3 yc 3 uy1.3 yc
Yy2.3 yc 2H yc Xy2.3 yc 3 uy2.3 yc
Yy3.3 yc 3H yc Xy3.3 yc 3 uy3.3 yc
Yy4.3 yc 3H yc Xy4.3 yc 3 L uy4.3 yc
Yy5.3 yc 2H yc Xy5.3 yc 3 L uy5.3 yc
Yy6.3 yc H yc Xy6.3 yc 3 L uy6.3 yc
Yy7.3 yb H uy7.3 yb Xy7.3 yb Xy1.3 0( ) L yb
Yy8.3 yb 2H uy8.3 yb Xy8.3 yb Xy2.3 0( ) L yb
Yy9.3 yb 3H uy9.3 yb Xy9.3 yb Xy3.3 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 3 on Y
Yy1.3 yc Yy2.3 yc Yy3.3 yc Yy4.3 yc Yy5.3 yc Yy6.3 yc Yy7.3 yb Yy8.3 yb Yy9.3 yb
Xy1.3 yc Xy2.3 yc Xy3.3 yc Xy4.3 yc Xy5.3 yc Xy6.3 yc Xy7.3 yb Xy8.3 yb Xy9.3 yb
Mode 4:yc 0 0.01 H
yb 0 0.01 L
uy1.4 yc ψcy.1 yc Vy0 3
ψcy.3 yc Vy3 3
uy2.4 yc ψcy.1 yc Vy1 3
ψcy.2 yc Vy0 3
ψcy.3 yc Vy5 3
ψcy.4 yc Vy3 3
uy3.4 yc ψcy.1 yc Vy2 3
ψcy.2 yc Vy1 3
ψcy.3 yc Vy7 3
ψcy.4 yc Vy5 3
uy4.4 yc ψcy.1 yc Vy2 3
ψcy.2 yc Vy1 3
ψcy.3 yc Vy8 3
ψcy.4 yc Vy6 3
uy5.4 yc ψcy.1 yc Vy1 3
ψcy.2 yc Vy0 3
ψcy.3 yc Vy6 3
ψcy.4 yc Vy4 3
uy6.4 yc ψcy.1 yc Vy0 3
ψcy.3 yc Vy4 3
uy7.4 yb ψby.3 yb Vy4 3
ψby.4 yb Vy3 3
uy8.4 yb ψby.3 yb Vy6 3
ψby.4 yb Vy5 3
uy9.4 yb ψby.3 yb Vy8 3
ψby.4 yb Vy7 3
Yy1.4 yc H yc Xy1.4 yc 3 uy1.4 yc
Yy2.4 yc 2H yc Xy2.4 yc 3 uy2.4 yc
Yy3.4 yc 3H yc Xy3.4 yc 3 uy3.4 yc
Yy4.4 yc 3H yc Xy4.4 yc 3 L uy4.4 yc
Yy5.4 yc 2H yc Xy5.4 yc 3 L uy5.4 yc
Yy6.4 yc H yc Xy6.4 yc 3 L uy6.4 yc
Yy7.4 yb H uy7.4 yb Xy7.4 yb Xy1.4 0( ) L yb
Yy8.4 yb 2H uy8.4 yb Xy8.4 yb Xy2.4 0( ) L yb
Yy9.4 yb 3H uy9.4 yb Xy9.4 yb Xy3.4 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 4 on Y
Yy1.4 yc Yy2.4 yc Yy3.4 yc Yy4.4 yc Yy5.4 yc Yy6.4 yc Yy7.4 yb Yy8.4 yb Yy9.4 yb
Xy1.4 yc Xy2.4 yc Xy3.4 yc Xy4.4 yc Xy5.4 yc Xy6.4 yc Xy7.4 yb Xy8.4 yb Xy9.4 yb
Mode 5:
yc 0 0.01 H
yb 0 0.01 L
uy1.5 yc ψcy.1 yc Vy0 4
ψcy.3 yc Vy3 4
uy2.5 yc ψcy.1 yc Vy1 4
ψcy.2 yc Vy0 4
ψcy.3 yc Vy5 4
ψcy.4 yc Vy3 4
uy3.5 yc ψcy.1 yc Vy2 4
ψcy.2 yc Vy1 4
ψcy.3 yc Vy7 4
ψcy.4 yc Vy5 4
uy4.5 yc ψcy.1 yc Vy2 4
ψcy.2 yc Vy1 4
ψcy.3 yc Vy8 4
ψcy.4 yc Vy6 4
uy5.5 yc ψcy.1 yc Vy1 4
ψcy.2 yc Vy0 4
ψcy.3 yc Vy6 4
ψcy.4 yc Vy4 4
uy6.5 yc ψcy.1 yc Vy0 4
ψcy.3 yc Vy4 4
uy7.5 yb ψby.3 yb Vy4 4
ψby.4 yb Vy3 4
uy8.5 yb ψby.3 yb Vy6 4
ψby.4 yb Vy5 4
uy9.5 yb ψby.3 yb Vy8 4
ψby.4 yb Vy7 4
Yy1.5 yc H yc Xy1.5 yc 3 uy1.5 yc
Yy2.5 yc 2H yc Xy2.5 yc 3 uy2.5 yc
Yy3.5 yc 3H yc Xy3.5 yc 3 uy3.5 yc
Yy4.5 yc 3H yc Xy4.5 yc 3 L uy4.5 yc
Yy5.5 yc 2H yc Xy5.5 yc 3 L uy5.5 yc
Yy6.5 yc H yc Xy6.5 yc 3 L uy6.5 yc
Yy7.5 yb H uy7.5 yb Xy7.5 yb Xy1.5 0( ) L yb
Yy8.5 yb 2H uy8.5 yb Xy8.5 yb Xy2.5 0( ) L yb
Yy9.5 yb 3H uy9.5 yb Xy9.5 yb Xy3.5 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 5 on Y
Yy1.5 yc Yy2.5 yc Yy3.5 yc Yy4.5 yc Yy5.5 yc Yy6.5 yc Yy7.5 yb Yy8.5 yb Yy9.5 yb
Xy1.5 yc Xy2.5 yc Xy3.5 yc Xy4.5 yc Xy5.5 yc Xy6.5 yc Xy7.5 yb Xy8.5 yb Xy9.5 yb
Mode 6:yc 0 0.01 H
yb 0 0.01 L
uy1.6 yc ψcy.1 yc Vy0 5
ψcy.3 yc Vy3 5
uy2.6 yc ψcy.1 yc Vy1 5
ψcy.2 yc Vy0 5
ψcy.3 yc Vy5 5
ψcy.4 yc Vy3 5
uy3.6 yc ψcy.1 yc Vy2 5
ψcy.2 yc Vy1 5
ψcy.3 yc Vy7 5
ψcy.4 yc Vy5 5
uy4.6 yc ψcy.1 yc Vy2 5
ψcy.2 yc Vy1 5
ψcy.3 yc Vy8 5
ψcy.4 yc Vy6 5
uy5.6 yc ψcy.1 yc Vy1 5
ψcy.2 yc Vy0 5
ψcy.3 yc Vy6 5
ψcy.4 yc Vy4 5
uy6.6 yc ψcy.1 yc Vy0 5
ψcy.3 yc Vy4 5
uy7.6 yb ψby.3 yb Vy4 5
ψby.4 yb Vy3 5
uy8.6 yb ψby.3 yb Vy6 5
ψby.4 yb Vy5 5
uy9.6 yb ψby.3 yb Vy8 5
ψby.4 yb Vy7 5
Yy1.6 yc H yc Xy1.6 yc 3 uy1.6 yc
Yy2.6 yc 2H yc Xy2.6 yc 3 uy2.6 yc
Yy3.6 yc 3H yc Xy3.6 yc 3 uy3.6 yc
Yy4.6 yc 3H yc Xy4.6 yc 3 L uy4.6 yc
Yy5.6 yc 2H yc Xy5.6 yc 3 L uy5.6 yc
Yy6.6 yc H yc Xy6.6 yc 3 L uy6.6 yc
Yy7.6 yb H uy7.6 yb Xy7.6 yb Xy1.6 0( ) L yb
Yy8.6 yb 2H uy8.6 yb Xy8.6 yb Xy2.6 0( ) L yb
Yy9.6 yb 3H uy9.6 yb Xy9.6 yb Xy3.6 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 6 on Y
Yy1.6 yc Yy2.6 yc Yy3.6 yc Yy4.6 yc Yy5.6 yc Yy6.6 yc Yy7.6 yb Yy8.6 yb Yy9.6 yb
Xy1.6 yc Xy2.6 yc Xy3.6 yc Xy4.6 yc Xy5.6 yc Xy6.6 yc Xy7.6 yb Xy8.6 yb Xy9.6 yb
Mode 7:
yc 0 0.01 H
yb 0 0.01 L
uy1.7 yc ψcy.1 yc Vy0 6
ψcy.3 yc Vy3 6
uy2.7 yc ψcy.1 yc Vy1 6
ψcy.2 yc Vy0 6
ψcy.3 yc Vy5 6
ψcy.4 yc Vy3 6
uy3.7 yc ψcy.1 yc Vy2 6
ψcy.2 yc Vy1 6
ψcy.3 yc Vy7 6
ψcy.4 yc Vy5 6
uy4.7 yc ψcy.1 yc Vy2 6
ψcy.2 yc Vy1 6
ψcy.3 yc Vy8 6
ψcy.4 yc Vy6 6
uy5.7 yc ψcy.1 yc Vy1 6
ψcy.2 yc Vy0 6
ψcy.3 yc Vy6 6
ψcy.4 yc Vy4 6
uy6.7 yc ψcy.1 yc Vy0 6
ψcy.3 yc Vy4 6
uy7.7 yb ψby.3 yb Vy4 6
ψby.4 yb Vy3 6
uy8.7 yb ψby.3 yb Vy6 6
ψby.4 yb Vy5 6
uy9.7 yb ψby.3 yb Vy8 6
ψby.4 yb Vy7 6
Yy1.7 yc H yc Xy1.7 yc 3 uy1.7 yc
Yy2.7 yc 2H yc Xy2.7 yc 3 uy2.7 yc
Yy3.7 yc 3H yc Xy3.7 yc 3 uy3.7 yc
Yy4.7 yc 3H yc Xy4.7 yc 3 L uy4.7 yc
Yy5.7 yc 2H yc Xy5.7 yc 3 L uy5.7 yc
Yy6.7 yc H yc Xy6.7 yc 3 L uy6.7 yc
Yy7.7 yb H uy7.7 yb Xy7.7 yb Xy1.7 0( ) L yb
Yy8.7 yb 2H uy8.7 yb Xy8.7 yb Xy2.7 0( ) L yb
Yy9.7 yb 3H uy9.7 yb Xy9.7 yb Xy3.7 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 7 on Y
Yy1.7 yc Yy2.7 yc Yy3.7 yc Yy4.7 yc Yy5.7 yc Yy6.7 yc Yy7.7 yb Yy8.7 yb Yy9.7 yb
Xy1.7 yc Xy2.7 yc Xy3.7 yc Xy4.7 yc Xy5.7 yc Xy6.7 yc Xy7.7 yb Xy8.7 yb Xy9.7 yb
Mode 8:
yc 0 0.01 H
yb 0 0.01 L
uy1.8 yc ψcy.1 yc Vy0 7
ψcy.3 yc Vy3 7
uy2.8 yc ψcy.1 yc Vy1 7
ψcy.2 yc Vy0 7
ψcy.3 yc Vy5 7
ψcy.4 yc Vy3 7
uy3.8 yc ψcy.1 yc Vy2 7
ψcy.2 yc Vy1 7
ψcy.3 yc Vy7 7
ψcy.4 yc Vy5 7
uy4.8 yc ψcy.1 yc Vy2 7
ψcy.2 yc Vy1 7
ψcy.3 yc Vy8 7
ψcy.4 yc Vy6 7
uy5.8 yc ψcy.1 yc Vy1 7
ψcy.2 yc Vy0 7
ψcy.3 yc Vy6 7
ψcy.4 yc Vy4 7
uy6.8 yc ψcy.1 yc Vy0 7
ψcy.3 yc Vy4 7
uy7.8 yb ψby.3 yb Vy4 7
ψby.4 yb Vy3 7
uy8.8 yb ψby.3 yb Vy6 7
ψby.4 yb Vy5 7
uy9.8 yb ψby.3 yb Vy8 7
ψby.4 yb Vy7 7
Yy1.8 yc H yc Xy1.8 yc 3 uy1.8 yc
Yy2.8 yc 2H yc Xy2.8 yc 3 uy2.8 yc
Yy3.8 yc 3H yc Xy3.8 yc 3 uy3.8 yc
Yy4.8 yc 3H yc Xy4.8 yc 3 L uy4.8 yc
Yy5.8 yc 2H yc Xy5.8 yc 3 L uy5.8 yc
Yy6.8 yc H yc Xy6.8 yc 3 L uy6.8 yc
Yy7.8 yb H uy7.8 yb Xy7.8 yb Xy1.8 0( ) L yb
Yy8.8 yb 2H uy8.8 yb Xy8.8 yb Xy2.8 0( ) L yb
Yy9.8 yb 3H uy9.8 yb Xy9.8 yb Xy3.8 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 8 on Y
Yy1.8 yc Yy2.8 yc Yy3.8 yc Yy4.8 yc Yy5.8 yc Yy6.8 yc Yy7.8 yb Yy8.8 yb Yy9.8 yb
Xy1.8 yc Xy2.8 yc Xy3.8 yc Xy4.8 yc Xy5.8 yc Xy6.8 yc Xy7.8 yb Xy8.8 yb Xy9.8 yb
Mode 9:
yc 0 0.01 H
yb 0 0.01 L
uy1.9 yc ψcy.1 yc Vy0 8
ψcy.3 yc Vy3 8
uy2.9 yc ψcy.1 yc Vy1 8
ψcy.2 yc Vy0 8
ψcy.3 yc Vy5 8
ψcy.4 yc Vy3 8
uy3.9 yc ψcy.1 yc Vy2 8
ψcy.2 yc Vy1 8
ψcy.3 yc Vy7 8
ψcy.4 yc Vy5 8
uy4.9 yc ψcy.1 yc Vy2 8
ψcy.2 yc Vy1 8
ψcy.3 yc Vy8 8
ψcy.4 yc Vy6 8
uy5.9 yc ψcy.1 yc Vy1 8
ψcy.2 yc Vy0 8
ψcy.3 yc Vy6 8
ψcy.4 yc Vy4 8
uy6.9 yc ψcy.1 yc Vy0 8
ψcy.3 yc Vy4 8
uy7.9 yb ψby.3 yb Vy4 8
ψby.4 yb Vy3 8
uy8.9 yb ψby.3 yb Vy6 8
ψby.4 yb Vy5 8
uy9.9 yb ψby.3 yb Vy8 8
ψby.4 yb Vy7 8
Yy1.9 yc H yc Xy1.9 yc 3 uy1.9 yc
Yy2.9 yc 2H yc Xy2.9 yc 3 uy2.9 yc
Yy3.9 yc 3H yc Xy3.9 yc 3 uy3.9 yc
Yy4.9 yc 3H yc Xy4.9 yc 3 L uy4.9 yc
Yy5.9 yc 2H yc Xy5.9 yc 3 L uy5.9 yc
Yy6.9 yc H yc Xy6.9 yc 3 L uy6.9 yc
Yy7.9 yb H uy7.9 yb Xy7.9 yb Xy1.9 0( ) L yb
Yy8.9 yb 2H uy8.9 yb Xy8.9 yb Xy2.9 0( ) L yb
Yy9.9 yb 3H uy9.9 yb Xy9.9 yb Xy3.9 0( ) L yb
2 2.545 3.091 3.636 4.182 4.727 5.273 5.818 6.364 6.909 7.455 80
5
10
Mode 9 on Y
Yy1.9 yc Yy2.9 yc Yy3.9 yc Yy4.9 yc Yy5.9 yc Yy6.9 yc Yy7.9 yb Yy8.9 yb Yy9.9 yb
Xy1.9 yc Xy2.9 yc Xy3.9 yc Xy4.9 yc Xy5.9 yc Xy6.9 yc Xy7.9 yb Xy8.9 yb Xy9.9 yb