Seismic parameters

49
Seismic Engineering Group 25 3 -Story Building Basic project parameters: kN m 2 E c 34 10 6 ρ c 2.4 t m 3 ρ g 2.6 t m 3 t s 0.18 m t g 0.01 m H 3.5 m W 12.5 m L 4 m Column geometry: Beam geometry: w 12 0.3 m h b 0.3 m w 3 0.2 m t b 0.3 m d c 0.3 m Structural damping: ζ in 0.05 ζ el 0.03 Loads on the structure: t m 2 g d 0.4 t m 2 g r 0.25 Computation on X direction: Geometrical property of section: I c12x d c w 12 3 12 I c12x 0.000675 m 4 I c3x d c w 3 3 12 I c3x 0.0002 m 4 I bx h b 3 t b 12 I bx 0.000675 m 4

description

Seismic parameters for a 3 storey building

Transcript of Seismic parameters

Page 1: 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

Page 2: Seismic parameters

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

Page 3: Seismic parameters

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

Page 4: Seismic parameters

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

Page 5: Seismic parameters

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

Page 6: Seismic parameters

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

Page 7: Seismic parameters

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

Page 8: Seismic parameters

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

Page 9: Seismic parameters

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

Page 10: Seismic parameters

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

Page 11: Seismic parameters

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

Page 12: Seismic parameters

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

Page 13: Seismic parameters

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

Page 14: Seismic parameters

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

Page 15: Seismic parameters

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

Page 16: Seismic parameters

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

Page 17: Seismic parameters

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

Page 18: Seismic parameters

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

Page 19: Seismic parameters

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

Page 20: Seismic parameters

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

Page 21: Seismic parameters

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

Page 22: Seismic parameters

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

Page 23: Seismic parameters

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

Page 24: Seismic parameters

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

Page 25: Seismic parameters

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

Page 26: Seismic parameters

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

Page 27: Seismic parameters

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

Page 28: Seismic parameters

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

Page 29: Seismic parameters

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

Page 30: Seismic parameters

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

Page 31: Seismic parameters

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

Page 32: Seismic parameters

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

Page 33: Seismic parameters

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

Page 34: Seismic parameters

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

Page 35: Seismic parameters

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( )

Page 36: Seismic parameters

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

Page 37: Seismic parameters

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

Page 38: Seismic parameters

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

Page 39: Seismic parameters

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

Page 40: Seismic parameters

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

Page 41: Seismic parameters

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

Page 42: Seismic parameters

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

Page 43: Seismic parameters

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

Page 44: Seismic parameters

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

Page 45: Seismic parameters

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

Page 46: Seismic parameters

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

Page 47: Seismic parameters

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

Page 48: Seismic parameters

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

Page 49: Seismic parameters

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