| 1

Part 1 midas Civil

1 ........................................................................................................... 3

2 ........................................................................................................... 4

3 ........................................................................................................... 5

3.1 ............................................................................................................................ 5

3.1.1 .................................................................................................................. 5

3.1.2 ....................................................................................... 5

3.1.3 .......................................................................................................... 6

3.1.4 ...................................................................................................... 6

3.2 ........................................................................................................................ 8

3.2.1 .................................................................................................................. 8

3.2.2 ....................................................................................... 8

3.2.3 .......................................................................................................... 8

3.2.4 ...................................................................................................... 8

3.3 ................................................................................................................................ 8

3.3.1 .................................................................................................................. 8

3.3.2 .......................................................................................................... 9

3.3.3 .................................................................................................................. 9

3.4 ...................................................................................................................... 12

3.4.1 ................................................................................................................ 12

3.4.2 ..................................................................................... 12

3.4.3 ................................................................................................................ 12

3.4.4 .................................................................................................... 13

3.5 .............................................................................................................................. 13

3.5.1 ................................................................................................................ 13

3.5.2 ..................................................................................... 13

3.5.3 ................................................................................................................ 13

3.5.4 ........................................................................................................ 14

3.6 .................................................................................................................. 15

3.6.1 ................................................................................................................ 15

3.6.2 ..................................................................................... 16

3.6.3 ................................................................................................................ 17

3.6.4 ............................................................................................................ 17

2 |

3.6.5 ........................................................................................................ 19

3.6.6 .................................................................................................... 20

3.7 .................................................................................................................. 23

3.7.1 ................................................................................................................ 23

3.7.2 ..................................................................................... 23

3.7.3 ................................................................................................................ 25

3.7.4 ............................................................................................................ 25

3.7.5 ........................................................................................................ 27

3.7.6 .................................................................................................... 28

3.8 ...................................................................................................................... 30

3.8.1 ................................................................................................................ 30

3.8.2 ..................................................................................... 31

3.8.3 ................................................................................................................ 32

3.8.4 .................................................................................................... 32

3.9 .............................................................................................................................. 34

3.9.1 ................................................................................................................ 34

3.9.2 ..................................................................................... 35

3.9.3 ........................................................................................................ 35

3.9.4 ............................................................................................................ 36

3.9.5 ........................................................................................................ 37

3.9.6 .................................................................................................... 38

3.10 ........................................................................................................................ 42

3.10.1 .............................................................................................................. 42

3.10.2 ............................................................... 42

3.10.3 ...................................................................................................... 43

3.10.4 .......................................................................................................... 44

3.10.5 ...................................................................................................... 46

3.10.6 .................................................................................................. 48

4 ......................................................................................... 52

4.1 .................................................................................. 54

4.2 .............................................................................................................................. 56

4.3 .................................................................................................................. 58

4.4 .................................................................................................................. 59

4.5 ...................................................................................................................... 59

4.6 .............................................................................................................................. 59

4.7 .......................................................................................................................... 60

4.8 .................................................................................................................. 61

5 ..................................................................................................... 62

5.1 .......................................................................................................................... 63

| 3

5.2 .................................................................................................................. 63

5.3 ...................................................................................................................... 64

5.4 ...................................................................................................................... 70

5.5 ...................................................................................................................... 71

5.6 .......................................................................................................................... 72

5.7 ...................................................................................................... 73

6 ................................................................................................................ 74

6.1 .......................................................................................................................... 74

6.2 .................................................................................................................. 74

6.3 .................................................................................................................. 76

6.4 ...................................................................................... 78

6.5 .................................................................................................................. 80

6.6 .................................................................................................................. 81

6.7 .................................................................................................................. 86

6.8 .................................................................................................................. 87

6.8.1 ............................................................................................. 87

6.8.2 ............................................................................................. 94

6.9 .......................................................................................................... 95

6.10 .......................................................................................................... 101

Part 2 midas Civil

1 ....................................................................................................... 105

2 .............................................................................................................. 106

2.1 ................................................................................................................................ 106

2.2 ........................................................................................ 106

3 ....................................................................................................... 108

3.1 .................................................................................................................... 108

3.2 .................................................................................................................... 112

3.3 ................................................................................................................ 115

3.4 ........................................................................................................................ 116

3.5 ........................................................................................................................ 117

3.5.1 .............................................................................................................. 117

3.5.2 ................................................................................... 117

3.5.3 ......................................................................................... 119

4 ...................................................................................................................... 120

4.1 ................................................................................................................................ 120

4 |

4.2 ........................................................................................................................ 121

4.3 ........................................................................................................................ 123

4.3.1 ........................................... 124

4.3.2 ................................................................... 125

4.4 ........................................................................................ 125

4.4.1 ...................................................................................................................... 125

4.4.2 ................................................... 127

4.5 ........................................................................................................................ 128

4.6 ................................................................................................................ 129

4.7 ............................................................................ 129

4.8 ........................................................................................ 129

5 .......................................................................................................... 131

6 ................................................................................................... 135

6.1 .................................................................................................................... 135

6.2 .................................................................................................................... 137

6.3 ................................................................................................................ 139

7 .............................................................................................................. 141

8 .......................................................................................................... 144

8.1 ................................................................................................................................ 144

8.2 ............................................................................................................ 145

8.2.1 - ..................................................................................................... 146

8.2.2 .................................................................................................................. 147

8.3 P-DELTA ................................................................................................................... 149

8.4 .................................................................................................................... 151

8.4.1 ...................................................................................................................... 151

8.4.2 .............................................................................................. 151

8.5 .................................................................................................... 152

8.5.1 .............................................................................................................. 152

8.5.2 ................................................................................... 153

8.5.3 ........................................................... 154

8.5.4 ........................................................... 157

8.5.5 .............................................................................................................. 158

8.5.6 ....................................................................................... 159

8.5.7 ...................................................................................................... 159

8.5.8 ...................................................................................................................... 164

8.5.9 .......................................................................................................................... 164

8.5.10 ............................................................................................................ 165

8.5.11 .................................................................................................... 167

| 5

8.5.12 ................................................................................................ 168

8.5.13 - ....................................................................................................... 170

8.5.14 - ....................................................................................................... 171

8.5.15 ........................................................................................................ 172

8.6 ............................................................................................................ 172

8.6.1 .............................................................................................................. 172

8.6.2 .............................................................................................................. 175

8.6.3 .............................................................................................................. 175

8.6.4 .............................................................................................. 179

8.6.5 .............................................................................................................. 181

8.6.6 ........................................................... 183

8.7 ............................................................................................................ 186

8.7.1 ...................................................................................................................... 186

8.7.2 .............................................................................................................. 187

8.7.3 ........................................................................................... 188

8.7.4 .......................................................................................................... 192

8.7.5 .......................................................................................................... 196

8.7.6 .............................................................................................................. 196

8.7.7 ............................................................... 197

8.7.8 ...................................................................................................... 210

8.7.9 Pushover .......................................................... 214

8.7.10 ............................................................................................ 218

8.7.11 ............................................................................. 220

8.7.12 Pushover ............................................................................................ 221

9 ................................................................................................... 222

9.1 ................................................................................................................................ 222

9.1.1 ............................................................................... 222

9.1.2 .................................................................................................................. 224

9.1.3 ...................................................................................................... 225

9.1.4 ....................................................................................... 226

9.1.5 - ..................................................................................................... 226

9.2 .................................................................................................................... 227

9.2.1 ...................................................................................................... 227

9.2.2 ........................................................................................... 231

9.2.3 .................................................................................................. 232

9.3 .................................................................................................... 232

9.3.1 ...................................................................................................... 232

9.3.2 .............................................................................................. 234

9.4 ................................................................................................................ 235

6 |

9.4.1 ....................................................................................... 236

9.4.2 ........................................................................................... 237

9.4.3 ........................................................................................... 238

9.4.4 ....................................................................................... 239

9.4.5 .............................................................................................. 240

9.4.6 ....................................................................................... 241

9.4.7 ....................................................................................... 242

9.4.8 ....................................................................................... 245

9.4.9 ............................................................................... 246

9.4.10 ............................................................................. 248

9.4.11 ..................................................................................... 249

9.4.12 ..................................................................................... 249

9.4.13 ..................................................................................... 250

9.4.14 ..................................................................................... 252

9.4.15 ..................................................................................... 253

9.4.16 - ............................................................................... 254

9.4.17 - ................................................................................... 255

9.5 .................................................................................................................... 256

9.5.1 ...................................................................................................... 257

9.5.2 P-M P-M-M ..................................................................................... 258

9.5.3 .......................................................................................................... 259

9.6 ........................................................................................................................ 261

9.6.1 .............................................................................................. 265

9.6.2 ........................................................................................... 267

10 ..................................................................................................... 274

10.1 .............................................................................................................................. 274

10.2 .............................................................................................................. 274

10.2.1 ........................................................................................................ 275

10.2.2 ................................................................................................ 278

10.2.3 ........................................................................................................ 280

10.2.4 ..................................................................................... 280

10.3 .............................................................................................. 281

10.4 .................................................................................................. 283

10.4.1 .................................................................................................... 283

10.4.2 .................................................................................................... 284

10.5 .................................................................................................. 284

10.5.1 () ...................................... 285

10.5.2 ............................................................................................ 285

10.5.3 ................................................................................................ 287

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10.5.4 ......................................................... 287

10.5.5 () .................................................. 288

11 ........................................................................................................ 290

11.1 .................................................................................................................. 290

11.1.1 .................................................................................................................... 290

11.1.2 .................................................................................................................... 291

11.1.3 .................................................................................................................... 291

11.1.4 .................................................................................................................... 292

11.1.5 ............................................................................................................ 292

11.1.6 ............................................................................................................ 292

11.1.7 ............................................................................................................ 292

11.2 .................................................................................................................. 293

11.2.1 ......................................................................................... 293

11.2.2 ......................................... 295

11.2.3 ............................................................................. 296

11.2.4 ................................................................................................ 296

11.2.5 ................................................................................................ 296

11.3 .......................................................................................................... 296

12 PSC ...................................................................................................... 299

12.1 ...................................................................................................... 299

12.2 .............................................................................................................. 300

12.2.1 l1 .................................... 300

12.2.2 l2 ................................ 301

12.2.3 l4 ............................................................ 302

12.2.4 l5 ................................................ 303

12.2.5 l6 .................................................... 306

12.3 .................................................................................................................. 306

13 ..................................................................................................... 308

13.1 .............................................................................................................. 309

13.1.1 .................................................................................................................... 309

13.1.2 ................................................................................................................ 310

13.2 .............................................................................................. 311

13.3 .......................................................................................................... 317

13.4 .......................................................................................................... 318

13.5 .......................................................................................... 318

13.6 ...................................................................................................................... 318

14 ..................................................................................................... 319

8 |

15 ......................................................................................... 320

16 ...................................................................... 321

Part3 midas Civil

1 RC ......................................................................................... 327

1.1 RC ................................................................................................. 327

1.1.1 - ............................................................................. 327

1.1.2 - ............................................................................. 329

1.1.3 -.................................................................. 331

1.1.4 - ................................................................................. 332

1.1.5 - ......................................................................................... 335

1.1.6 - ......................................................................................... 336

1.1.7 - ............................................................................. 337

1.1.8 - ............................................................................. 341

1.1.9 - ......................................................................................... 345

1.1.10 - ............................................................................... 350

1.1.11 - ....................................................................................... 354

1.1.12 -/ .......................................... 355

1.1.13 -/ .......................................... 358

1.2 RC ......................................................................................................... 360

1.3 RC ................................................................................................. 364

2 PSC ........................................................... 370

2.1 PSC ................................................................................................ 370

2.1.1 ................................................................................... 370

2.1.2 ................................................................................... 372

2.1.3 ................................................................................... 374

2.1.4 ................................................................................... 376

2.1.5 ............................................................................... 377

2.1.6 ........................................................................... 378

2.1.7 ....................................................................................... 379

2.1.8 ...................................................................................................... 381

2.1.9 .............................................................................................. 382

2.1.10 ................................................................................. 383

2.1.11 ................................................................................ 385

2.1.12 ............................................................................................ 388

2.1.13 ............................................................................................ 390

2.2 PSC ........................................................................................................ 393

| 9

2.3 PSC ................................................................................................. 396

3 ............................................................................................... 400

3.1 ........................................................................................ 400

3.1.1 ...................................................................................................... 400

3.1.2 ...................................................................................................... 402

3.1.3 ...................................................................................................... 403

3.1.4 .............................................................................................. 404

3.1.5 .............................................................................................. 406

3.1.6 .............................................................................................. 408

3.1.7 .............................................................................................. 410

3.1.8 ................................................................................... 411

3.1.9 ....................................................................... 412

3.1.10 ......................................................... 414

3.1.11 ............................................................. 416

3.1.12 ................................................................. 418

3.1.13 ..................................................................... 419

3.1.14 ............................................................................................ 420

3.2 ................................................................................................ 421

3.3 ........................................................................................ 427

4 RC ........................................................................ 434

4.1 RC ................................................................................................. 434

4.1.1 - ......................................................................................... 434

4.1.2 - ..................................................................................... 436

4.1.3 - ............................................................................................. 437

4.1.4 - ................................................................................................. 438

4.1.5 - ......................................................................................... 440

4.1.6 - ......................................................................................... 441

4.1.7 - ......................................................................................... 442

4.1.8 - ..................................................................................... 444

4.1.9 - ............................................................................................. 445

4.1.10 - ........................................................................................... 446

4.1.11 - ............................................................................................... 447

4.1.12 - ................................................................................................... 449

4.2 RC ......................................................................................................... 450

4.3 RC ................................................................................................. 453

5 PSC ...................................................................... 458

5.1 PSC ........................................................................................ 458

5.1.1 - ................................................................................................. 458

10 |

5.1.2 - ............................................................................................. 460

5.1.3 - ............................................................................................. 462

5.1.4 - ..................................................................... 464

5.1.5 - ..................................................................... 466

5.1.6 -.................................................................. 468

5.1.7 -.............................................................. 469

5.1.8 - .......................................................... 471

5.1.9 -.................................................................. 473

5.1.10 - ....................................................................... 474

5.1.11 - .................................................... 476

5.1.12 - .................................................... 476

5.1.13 - ............................................................................................... 479

5.1.14 - ................................................................................... 480

5.1.15 - ................................................................................... 483

5.1.16 - ................................................................... 485

5.1.17 - ............................................................... 487

5.1.18 - ........................................................... 488

5.1.19 - ............................................................... 489

5.1.20 - .................................................... 490

5.1.21 - .................................................... 491

5.2 PSC ........................................................................................................ 492

5.3 PSC ................................................................................................ 495

6 ............................................................................................... 501

6.1 ........................................................................................ 501

6.1.1 ....................................................................................... 501

6.1.2 ........................................................................................... 503

6.1.3 ........................................................................................... 504

6.1.4 .................................................................................................. 505

6.1.5 .................................................................................................. 506

6.1.6 ........................................................................... 507

6.2 ................................................................................................ 508

6.3 ........................................................................................ 512

Part1 midas Civil

| 1

Part 1 midas Civil

2 |

1

| 3

1

Finite Element

4 |

2

midas Civil

1 (Global Coordinate System)

2 (Element Coordinate System)

3 (Node local Coordinate System)

XYZ

(Conventional Cartesian Coordinate System) XYZ

midas Civil

X=0Y=0Z=0

Z

Z

xyz

xyz

xyz

xyz

1.2.1

(Xi, Yi, Zi)

3

| 5

3

midas Civil

1

2

3

4

5/

6

7

8

9

10

3.1

3.1.1

2

(Space Truss)(Diagonal Brace)

3.1.2

x

x yz

6 |

midas Civil yz

x N1 N2

1.3.1 x Z X

z x

x Z

Z x-z

XN1X YN1Y ZN1Z

GCS -

a x Z

GCS-

b x Z

1.3.1

3.1.3

3.1.4

3

| 7

1.3.2 +

y

Axial Force

z

x

Axial Force

1.3.2

1.3.3

Civil

8 |

3.2

3.2.1

2

=0

>0

a (b)

1.3.4

3.2.2

3.2.3

3.2.4

3.3

3.3.1

2

3

| 9

1.3.5

3.3.2

(sag)

1

1/ 1/comb

sag elastic

KK K

1.3.1

2 2

31

12

comb

EAK

L EAL

T

1.3.2

elastic

EAK

L

3

2 3

12sag

TK

L 1.3.3

E

A

L

w

T

3.3.3

midas Civil

1.3.6 i 123, j 45

6 F01F02F

03F

04F

05F

06 F1F2F3F4F5F6

4 1F F 1.3.4

10 |

5 2F F 1.3.5

6 3 0 0F F w l w0=w 1.3.6

0 1 4 1 2 3( , , )x xl l D D f F F F 1.3.7

0 2 5 1 2 3( , , )y yl l g F F F 1.3.8

0 3 6 1 2 3( , , )z zl l D D h F F F 1.3.9

1.3.6

([F])

([K])

x 1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

1 2 3

= d + d + d

y

z

f f fdl F F F

F F F

g g gdl dF dF dF

F F F

h h hdl dF dF dF

F F F

1.3.10

3

| 11

1

2

3

x

y

z

dl dF

dl F dF

dl dF

1 2 3

11 12 13

21 22 23

1 2 3

31 32 33

1 2 3

f f f

F F Ff f f

g g gF f f f

F F Ff f f

h h h

F F F

1.3.11

1

2

3

x

y

z

dF dl

dF K dl

dF dl

(K=F-1) 1.3.12

2

0 111 3 0 3 2 2

1 0 3 0 3

1 1 1ln ln

L Fff F wL B F A

F EA w w B F wL B A F A

1.3.13

1 2

12 2 2

2 3 0 3

1 1F Fff

F w B F wL B A F A

1.3.14

3 0 31

13 2 2

3 3 0 3

F wL B F AFff

F w B F wL B A F A

1.3.15

21 12

1

gf f

F

1.3.16

2

0 222 3 0 3 2 2

2 0 3 0 3

1 1 1ln ln

L Fgf F wL B F A

F EA w w B F wL B A F A

1.3.17

223 13

3 1

Fgf f

F F

1.3.18

131

1

1 1Fhf

F w B A

1.3.19

232 31

2 1

Fhf f

F F

1.3.20

12 |

0 3 0 333

3 0

1L F wL Fhf

F EA w B A

1.3.21

1/21/2 22 2 2 2 2

1 2 3 1 2 3 0,A F F F B F F F wL ) 1.3.22

TdF K d 1.3.23

1 1 1 1 1 1

1 2 3 4 5 6

2 2 2 2 2 2

1 2 3 4 5 6

3 3 3 3 3 3

1 2 3 4 5 6

1 1 1 1 1 1

1 2 3 4 5 6

1 2 2 2 2 2

1 2 3 4 5 6

1

T

F F F F F F

F F F F F F

F F F F F F

F F F F F F

F F F F F F

F

K

3 3 3 3 3

1 2 3 4 5 6

ii ij

ii ij

F F F F F

F F

F F 1.3.24

3.4

3.4.1

2

(Cap Distance)

3.4.2

3.4.3

3

| 13

3.4.4

=0

>0

a b)

1.3.7

3.5

3.5.1

2

midas Civil

x (Linear Variation) x 1

2 3

3.5.2

6

3.5.3

14 |

3.5.4

1.3.8 +

x

y

z

Axial Force

Axial Force

Sheary

Sheary

Shearz

Shearz

Momentz

Momentz

Momenty

Momenty

Torque

Torque

1/4

2/4

3/4

* +

1.3.8

3

| 15

1.3.9

3.6

3.6.1

3 4

Isoparametric Plan Stress

Formulation with Incompatible Modes)

(Poisson Effects)

16 |

3.6.2

xy

xyz

1.3.10

N1N2N3N4

z N1 N4

N2 N3 x

x y

N1N2 x

yz

z

(N1N2N3N4)

x (N1 N2)

yx

a

(N1N2N3)

z

yx

x(N1 N2)

b

1.3.10

3

| 17

3.6.3

1

N4 N3

N1 N2

24

3

P2P2

P2

P2

1.3.11

3.6.4

1. 3

1/31/3

x

y

N1

N2

N3

P

1 1,

3 3P

1.3.12 3

1 1N 2N 3N

18 |

1

,N N

p i i p i i

i i

x N x y N y

1.3.25

1/3 1/3

3

1 2 3 1 2 3

1

1 1 1 1 11

3 3 3 3 3p i i

i

x N x x x x x x x

1.3.26

1 2 31

3py y y y 1.3.27

2. 4

4 Pi

x

y

1

3

1

3

1

3

1

3

N1

N2

N3

N4

P4P3

P1P2

1

2

3

4

1 1,

3 3

1 1,

3 3

1 1,

3 3

1 1,

3 3

P

P

P

P

1.3.13 4

1 2 3 41 1 1 1

1 1 , 1 1 , 1 1 , 1 14 4 4 4

N N N N

1.3.28

Pi

P1 x

4

1 1 2 3 4

1

12 3 2 3

6p i i

i

x N x x x x x

1.3.29

3

| 19

1

2

3

4

2 3 1 2 3 1

2 3 1 2 31

6 2 3 1

2 3

p

x

xx

x

xsymmetry

1.3.30

1

2

3

4

2 3 1 2 3 1

2 3 1 2 31

6 2 3 1

2 3

p

y

yy

y

ysymmetry

1.3.31

3.6.5

3

1s 1s

1t

1t

1

1

1

1 1

1

1

1

1.3.14 4

4

3 , 3s t 1.3.32

20 |

1, 2, 3, 4N i iN i 1.3.33

1

4

1 1 2

1

3 4

1 2 3 4

11 3 1 3 1 3 1 3

4

1 3 1 3 1 3 1 3

14 2 3 2 4 2 3 2

4

N i i

i

N

1.3.34

1 1

2 2

3 3

4 4

2 3 1 2 3 1

2 3 1 2 31

2 2 3 1

2 3

N

N

N

N

1.3.35

3.6.6

(Gauss Point)

(Extrapolation)

1.3.15 +

1.3.16 +

3

| 21

Fx1

Fy1

Fy2

Fy3

a

b

1.3.15

* +

y

y

x x

2

2

1

1

xy

xy

xy

xy

a b

x x

y y

xy x-y

22 |

1.3.16

1.3.17

:

:

:

:

:

:

:

:

x

y

xy

2

x y x y 2

1 xy

2

x y x y 2

2 xy

2

x y 2

max xy

eff von-Mises St

x

y

x-y

+ = + +

2 2

+ = +

2 2

= +

2

x

( )2 21 1 2 2ress = +

3

| 23

3.7

3.7.1

(Dam)(Tunnel)

(Isoparametric Plane Strain Formulation with Incompatible Models)

midas Civil x-z 1.0()

1.3.18

(Poisson Effects)

1.0

1.3.18

3.7.2

XZ

xyz

1.3.19

N1N2N3N4

z N1 N4

N2 N3 x

x y

24 |

N1N2

x yz

* +

yx

(N1N2N3N4)

x

z

a

yx

(N1N2N3)

z

xN1N2

b

1.3.19

3

| 25

3.7.3

1.3.20

1

N4 N3

N1 N2

24

3

P2P2

P2

P2

1.3.20

3.7.4

13

1/31/3

x

z

N1

N2

N3

P

1 1,

3 3P

1.3.21 3

26 |

1 1N 2N 3N

1

,N N

p i i p i i

i i

x N x z N z

1.3.36

1/3 1/3

3

1 2 3 1 2 3

1

1 1 1 1 11

3 3 3 3 3p i i

i

x N x x x x x x x

1.3.37

1 2 31

3pz z z z 1.3.38

24

4 Pi

x

z

1

3

1

3

1

3

1

3

N1

N2

N3

N4

P4P3

P1P2

1

2

3

4

1 1,

3 3

1 1,

3 3

1 1,

3 3

1 1,

3 3

P

P

P

P

1.3.22 4

1 21 1

1 1 , 1 14 4

N N

3 41 1

1 1 , 1 14 4

N N 1.3.39

Pi

P1 x

3

| 27

4

1 1 2 3 4

1

12 3 2 3

6p i i

i

x N x x x x x

1.3.40

1

2

3

4

2 3 1 2 3 1

2 3 1 2 31

6 2 3 1

2 3

p

x

xx

x

xsymmetry

1.3.41

3.7.5

3

1s 1s

1t

1t

1

1

1

1 1

1

1

1

1.3.23 4

4

3 , 3s t 1.3.42

4

1

N i i

i

N

1.3.43

1

28 |

4

1 1 2

1

3 4

1 2 3 4

11 3 1 3 1 3 1 3

4

1 3 1 3 1 3 1 3

14 2 3 2 4 2 3 2

4

N i i

i

N

1.3.44

1 1

2 2

3 3

4 4

2 3 1 2 3 1

2 3 1 2 31

2 2 3 1

2 3

N

N

N

N

1.3.45

3.7.6

1.3.24 Segment

(Gauss Point)

(Extrapolation)

1.3.19 +

1.3.24 +

xx

xy

zz

zz

xx

xy

yy

yx

yx

yy

x

y

z

1

x

y

z

23

2

3

1

1

23

a b

3

| 29

:

:

:

:

:1 2 3

xx

yy

zz

xy yx

1, 2, 3

3 2

1 2 3

1 xx yy zz

xx xy yxx xz

2

xy yy xz zz

x

y

z

x-y

- I - I - I = 0

I =

I =

,

2 2 2

, 0

: , ,

1: ( ) ( ) ( )

2

:

y yz

yz zz

xx xy xz

3 xy yy yz xz zy

xz yz zz

1

2 3 3 11 2

max

eff 1 2 2 3 3 1

oct

= max

von-Mises Stress

Oct

I

: x-y x

2 2 2

2 2 2

1( )

3

1: ( ) ( ) ( )

9

1 2 3

oct 1 2 2 3 3 1

ahedral Normal Stress

Octahedral Shear Stress

+ +

1.3.24

30 |

1.3.25

3.8

3.8.1

(

)(Isoparametric

Formulation)

3 2

midas Civil Z

X-Z Z X

X (X0)

1 1.3.25

(XY, YZ) (XY, YZ)

Z

1.0

1.3.26

3

| 31

3.8.2

XZ

xyz

1.3.26

N1N2N3N4

z N1 N4

N2 N3 x

x y

N1N2 x

y z

* +

yx

(N1N2N3N4)

x

z

FX1FX2

FX4

FX3

FZ1FZ2

FZ3

FZ4

a

yx

(N1N2N3)

z

xN1N2

FZ1

FZ2

FZ3

FX1

FX2

FX3

b

1.3.27

32 |

3.8.3

1.3.28

1

N4 N3

N1 N2

24

3

P2P2

P2

P2

1.3.28

3.8.4

1.3.29 Segment

(Gauss Point)

(Extrapolation)

1.3.27 +

1.3.29 + * +

3

| 33

xx

xy

zz

zz

xx

xy

yy

yx

yx

yy

x

y

z

1

x

y

z

23

2

3

1

1

23

a b

:

:

:

:

:1 2 3

xx

yy

zz

xy yx

1, 2, 3

3 2

1 2 3

1 xx yy zz

xx xy yxx xz

2

xy yy xz zz

x

y

z

x-y

- I - I - I = 0

I =

I =

,

2 2 2

, 0

: , ,

1: ( ) ( ) ( )

2

:

y yz

yz zz

xx xy xz

3 xy yy yz yz zx

xz yz zz

1

2 3 3 11 2

max

eff 1 2 2 3 3 1

oct

= max

von-Mises Stress

Oct

I

: x-y x

2 2 2

2 2 2

1( )

3

1: ( ) ( ) ( )

9

1 2 3

oct 1 2 2 3 3 1

ahedral Normal Stress

Octahedral Shear Stress

+ +

1.3.29

34 |

1.3.30

3.9

3.9.1

3 4 Plate Element)

midas Civil DKT/DKQ(Discrete Kichhoff Element)

DKMT/DKMQ(Discrete Kirchhoff-Mindlin Element)

Kirchhoff Plate Theory Mindlin-Reissner Plate Theory

LST(Linear Strain Triangle)

(Isoparametric Plane Stress

Formulation with Incompatible Modes)

(Isoparametric Plane Stress Formulation

with Incompatible Modes)

Allman

(In-plane Stiffness)

(Out-of-Plane-Stiffness)

3

| 35

3.9.2

xyz

xy

xyz

1.3.31

3.9.3

z

(N1N2N3N4)

x (N1 N2)

yx

a

(N1N2N3)

z

yx

x(N1 N2)

b

1.3.31

36 |

3.9.4

13

1/31/3

x

z

N1

N2

N3

P

1 1,

3 3P

1.3.32 3

1 1N 2N 3N

1

,N N

p i i p i i

i i

x N x y N y

1.3.46

1/3 1/3

3

1 2 3 1 2 3

1

1 1 1 1 11

3 3 3 3 3p i i

i

x N x x x x x x x

1.3.47

1 2 31

3py y y y 1.3.48

24

4 Pi

x

z

1

3

1

3

1

3

1

3

N1

N2

N3

N4

P4P3

P1P2

1

2

3

4

1 1,

3 3

1 1,

3 3

1 1,

3 3

1 1,

3 3

P

P

P

P

1.3.33 4

3

| 37

1 2 3 41 1 1 1

1 1 , 1 1 , 1 1 , 1 14 4 4 4

N N N N 1.3.49

Pi

P1 x

4

1 1 2 3 4

1

12 3 2 3

6p i i

i

x N x x x x x

1.3.50

1

2

3

4

2 3 1 2 3 1

2 3 1 2 31

6 2 3 1

2 3

p

x

xx

x

xsymmetry

1.3.51

1

2

3

4

2 3 1 2 3 1

2 3 1 2 31

6 2 3 1

2 3

p

y

yy

y

ysymmetry

1.3.52

3.9.5

3

1s 1s

1t

1t

1

1

1

1 1

1

1

1

1.3.34 4

4

38 |

3 , 3s t 1.3.53

1, 2, 3, 4N i iN i 1.3.54

1

4

1 1 2

1

3 4

1 2 3 4

11 3 1 3 1 3 1 3

4

1 3 1 3 1 3 1 3

14 2 3 2 4 2 3 2

4

N i i

i

N

1.3.55

1 1

2 2

3 3

4 4

2 3 1 2 3 1

2 3 1 2 31

2 2 3 1

2 3

N

N

N

N

1.3.56

3.9.6

(Gauss Point)

(Extrapolation)

1.3.35 +

3

| 39

1.3.36

+

(Top Surface)

(Bottom Surface) 1.3.37 +

* +

Fz4

Fz1

Fz2

Fz3

Fx4

Fx1

Fx2

Fx3

Fy4

Fy1

Fy2

Fy3

N1

N2

N3

N4

x

y

z

My4Mx4

Mx3

Mx2

Mx1My3

Mx2

My1

(a)

Fz1

Fx1

Fy1

N1

Mx1

My1

Fz2

Fx2Fy2

N2My2

Mx2

Fz3Fy3

N3

My3Mx3

x

yz

Fx3

(b)

1.3.35

* +

N1

N2

N3

N4

x

y

z

N1

N2

N3

x

y

z

a

40 |

b

c

1.3.36

* +

/

a

y

y

x x

2

2

1

1

xy

xy

xy

xy

b

3

| 41

:

:

:

:

:

:

:

:

x

y

xy

2

x y x y 2

1 xy

2

x y x y 2

2 xy

2

x y 2

max xy

effvon-Mises St

x

y

x-y

+ = + +

2 2

+ = +

2 2

= +

2

x

( )2 2

1 1 2 2ress = +

1.3.37

1.3.38

42 |

3.10

3.10.1

4 6 8 (Solid

Element)(Solid Structure)(Thick

Shell)

(Isoparametric Formulation with Incompatible

Modes)

3.10.2

1

5

4

3

6

a8 Hexahedron

1N1N2N3

2(N4N5N6)

54

3

1

4

3

b6 Wedge b4 Tetrahedron

1.3.39

3

| 43

XYZ

xyz

1

1.3.39 4 6

8

3.10.3

1.3.40

* +

6

2

5

4

3

1

1.3.40

44 |

3.10.4

14

1/41/41/4

xy

N1

N4

P

N3

N2

z1 1 1

, ,4 4 4

P

1

2

3

4

1N

N

N

N

1.3.41 4

P

4

1 2 3 4 1 2 3 4

1

1 1 1 1 1 1 11

4 4 4 4 4 4 4p i i

i

x N x x x x x x x x x

1.3.57

4

1 2 3 4

1

1

4p i i

i

y N y y y y y

1.3.58

26

6 Pi

x y

N4

N5

N6

P1

N1

N2

1

3

1

3

P2P3

P4

P5P6

z

1

2

3

4

5

1 1 1, ,

6 6 3

2 1 1, ,

3 6 3

1 2 1, ,

6 3 3

1 1 1, ,

6 6 3

2 1 1, ,

3 6 3

P

P

P

P

P

1.3.42 6

1

3

| 45

1 (1 )2

N

2 ( 1 )2

N

3 ( 1 )2

N

1.3.59

4 (1 )2

N

5 ( 1 )2

N

6 ( 1 )2

N

P1

6

1 1 2 3

1

4 5 6

112 4 3 3 3 3 3

36

12 4 3 3 3 3 3

p i i

i

x N x x x x

x x x

1.3.60

1

2

3

4

5

6

12 4 3 3 3 3 3 12 4 3 3 3 3 3

12 4 3 3 3 3 3 12 4 3 3 3

12 4 3 3 3 3 3 12 4 31

36 12 4 3 3 3 3 3

12 4 3 3 3

12 4 3

p

x

x

xx

x

x

xsymmetry

1.3.61

38

8 Pi

x

y

N8

N5

N6

N2

N3

1

3

1

3

P1

P6

z

N1

N7

1

3

1

3

1

3

1

3

N4

P2

P3P4

P5

P7P8

1

2

3

4

5

6

7

8

1 1 1, ,

3 3 3

1 1 1, ,

3 3 3

1 1 1, ,

3 3 3

1 1 1, ,

3 3 3

1 1 1, ,

3 3 3

1 1 1, ,

3 3 3

1 1 1, ,

3 3 3

1 1 1, ,

3 3 3

P

P

P

P

P

P

P

P

1.3.43 8

46 |

1 2

3 4

5 6

7 8

1 11 1 1 1 1 1

8 8

1 11 1 1 1 1 1

8 8

1 11 1 1 1 1 1

8 8

1 11 1 1 1 1 1

8 8

N N

N N

N N

N N

1.3.62

P1

8

1 1 2 3 4

1

5 6 7 8

19 5 3 3 3 3 3 3 3

36

3 3 3 3 9 5 3 3 3

p i i

i

x N x x x x x

x x x x

1.3.63

1

2

3

4

5

6

7

8

9 5 3 3 3 3 3 3 3 3 3 3 3 9 5 3 3 3

9 5 3 3 3 3 3 3 3 3 3 3 3 9 5 3

9 5 3 3 3 9 5 3 3 3 3 3 3 3

9 5 3 3 3 9 5 3 3 3 3 31

36 9 5 3 3 3 3 3 3 3

9 5 3 3 3 3 3

9 5 3 3 3

9 5 3

p

x

x

x

xx

x

x

x

xsymmetry

1.3.64

3.10.5

4

3

| 47

P1

P2

P3

t

s

1

3

u

1.3.44 6

6

1 1 12 1 , 2 , 2 , 3

6 6 6s t u

1.3.65

6

1

N i i

i

N

1.3.66

1

6

1 1 2 3

1

4 5 6

15 1 3 1 3 1 3

6

5 1 3 1 3 1 3

N i ii

N

1.3.67

1 1

2 2

3 3

4 4

5 5

6 6

5 5 3 1 3 1 3 5 5 3 1 3 1 3

5 5 3 1 3 1 3 5 5 3 1 3

5 5 3 1 3 1 3 5 5 31

6 5 5 3 1 3 1 3

5 5 3 1 3

5 5 3

N

N

N

N

N

N

1.3.68

8

48 |

1s 1s

1t

1t

1

1

1

1 1

1

1

1

1.3.45 8

3 , 3 , 3s t u 1.3.69

1

8

1 1 2

1

3 4

5 6

7 8

1 2 3 4

5 6 7 8

11 3 1 3 1 3 1 3 1 3 1 3

8

1 3 1 3 1 3 1 3 1 3 1 3

1 3 1 3 1 3 1 3 1 3 1 3

1 3 1 3 1 3 1 3 1 3 1 3

110 6 3 2 2 3 2 2 3 2 2 3

8

2 2 3 2 2 3 10 6 3 2 2 3

N i i

i

N

1.3.70

1

2

3

4

5

6

7

8

5 3 3 1 3 1 3 1 3 1 3 1 3 5 3 3 1 3

5 3 3 1 3 1 3 1 3 1 3 1 3 5 3 3

5 3 3 1 3 5 3 3 1 3 1 3 1 3

5 3 3 1 3 5 3 3 1 3 1 31

4 5 3 3 1 3 1 3 1 3

5 3 3 1 3 1 3

5 3 3 1 3

5 3 3

N

N

N

N

N

N

N

N

1

2

3

4

5

6

7

8

1.3.71

3.10.6

3

| 49

(Gauss Point)

(Extrapolation )

1.3.46 +

1.3.47 +

* +

1.3.46

50 |

:

:

:

:

:

:

:

xx

yy

zz

xz zx

xy yx

yz zy

1, 2, 3

3 2

1 2 3

1 xx yy

x

x-z

x-y

-z

1 2 3

- I - I - I = 0

I =

,

y

z

y

zz

xx xy yy yzxx xz

2

xy yy yz zzxz zz

xx xy xz

3 xy yy yz

xz yz zz

I =

I

2 2 2

2 2 2

: , ,

1: ( ) ( ) ( )

2

1: ( )

3

1: ( ) ( ) ( )

9

2 3 3 11 2

max

eff 1 2 2 3 3 1

oct 1 2 3

oct 1 2 2 3 3 1

= max

von-Mises Stress

Octahedral Normal Stress

Octahedral Shear Stress

2 2 2

+ +

1.3.47

3

| 51

1.3.48

52 |

4

(Local Mode)

(Preliminary Design Phase)

)

(Contour)

4

| 53

(Logarithmic Configuration)

1/2

4 8

11 14

110

90

60

45 135

30 150

1/100

54 |

4.1

(Sagging)(Wind

Bracing)

(Contact Element)

(Pretension Loads)

(Singular Error)midas Civil

1.4.1

1.4.1a

1.4.1b 1.4.1c

a X-Z b Y-Z c Y-Z

X X X

1.4.1

4

| 55

a b

1.4.2

1.4.2(a)

0 1.4.2(b)

0

a

b

1.4.3

1.4.3a

1.4.3b

56 |

midas Civil

1/100~1/1000 1/1000

P-Delta Pushover

4.2

(Tapered Member)

6

Timoshenko Beam Theory

1/5

(Torsional Resistance)(Polar Moment of Inertia)

(Panel Zone)

(Pin Connection)(Slot Hole)

(Beam End Release)

(Singular Error)

4

| 57

a(Pin Connection) b(Slot Hole)

c(Pin Connection)

d

1.4.4 (Beam End Release)

(Rigid Beam)

105~108

1.4.4

()

58 |

(Pin Connection)

(Singular Error)

(Beam End Release)

4.3

1.4.5

1.4.5

midas Civil

Aspect Ratio

1

90

4

| 59

4.4

(Dam)(Tunnel)

(Poisson Effect)

1

4.5

1

4.6

midas Civil

DKTDKQ(Discrete Kichhoff Element) DKMTDKMQ(Discrete Kirchhoff-

Mindlin Element) Euler-Bernoulli Beam

Timoshenko Beam

60 |

LST(Linear Strain Triangle)

(Isoparametric Plane Stress

Formulation with Incompatible Modes)

(In-plane Stiffness)

(Out-of-Plane-Stiffness)

1.4.6

4

10 23

2%

10

4.7

XYZ

4

| 61

midas Civil

Aspect Ratio

1

90

4.8

1

2

x

xy

xyz

3

, ,xy yx yz zyxz zx

x y x z y zE E E E E E

1.4.1

1 xy

2 xy

62 |

5

>>>>

1.5.1

midas Civil

1

2

3

midas Civil

5

| 63

5.1

1 2 3

(300 15) (573 10) (320 12)

14070

Area dA A A A

1.5.1

5.2

y z

MIDAT/Civil

1.5.2

Asy y

Asz z

64 |

1.5.2

1. L

5

6

5

6

sy f

sz w

A B t

A H t

2.

5(2 )

6sy f

sz w

A B t

A H t

3. I

5(2 )

6sy f

sz w

A B t

A H t

4. T

5( )

6sy f

sz w

A B t

A H t

5.

2

2

sy f

sz w

A B t

A H t

6.

sy w

sz w

A r t

A r t

7.

2

2

0.9

0.9

sy

sz

A r

A r

8.

5

6

5

6

sy

sz

A BH

A BH

5.3

(1.5.1)

xx

TGI

1.5.1

5

| 65

G

Ixx

T

(Polar Moment of Inertia)

(Open Section)(Close Section)

(1.5.2)

xx xxI i

43

4

163.36 1

3 12xx

b bi ab

a a

ab 1.5.2

ixx

2a

2b

(Tube)(1.5.3)( 1.5.2)

24

/xx

s

AI

d t

1.5.3

A

ds

t

66 |

: 24

/xx

s s

AI

d t

: 2

Ts

T

At

st

1.5.2

(Tube)

(1.5.1)(1.5.3)

1.5.3 (Solid Section)

1.

21

2xxI r

2.

42.25xxI a

3.

43

4

163.36

3 12xx

b bI ab I

a a

(where, a b )

5

| 67

1.5.4

1.

22( )xx

f w

b hI

b h

t t

2.

4 41

2 2 2

o ixx

D DI

1.5.5

1. L

4

1 2

43

1 4

43

2 4

10.21 1

3 12

10.105 1

3 192

0.07 0.076

2 3 2 2 2

xxI I I D

b bI ab

a a

d dI cd

c c

d r

b b

D d b r r b r d

(where, b < 2(d + r))

2. T

IF bd : t=d, t1=b

4

1 2

43

1 4

43

2 4

1

22

10.21 1

3 12

10.105 1

3 192

0.15 0.10

4

2

xxI I I D

b bI ab

a a

d dI cd

c c

t r

t b

db r rd

Dr b

(where, d < 2(b + r))

3.

(Angle)(Angle)

4. I-

IF bd : t=d, t1=b

4

1 2

43

1 4

3

2

1

22

2 2

10.21 1

3 12

1

3

0.15 0.10

4

2

xxI I I D

b bI ab

a a

I cd

t r

t b

db r rd

Dr b

(where, d < 2(b + r))

Angle 1

Angle 2 Angle2

Tee1

Tee2

68 |

1.5.6

1. L

3 31

3xx w fI h t b t

2.

3 31

23

xx w fI h t b t

3. I

3 31

23

xx w fI h t b t

4. T

3 31

3xx w fI h t b t

5.

3 33 1 1 2 213

xx w f fI h t b t b t

2 1

H (Double H-Section) 1.5.3(a)

()

5

| 69

2

1 1

1 1

2( )C

f w

b hI

b h

t t

1.5.4

()

311

2 23

O w wI b b t t

1.5.5

xx C OI I I 1.5.6

H 2 (Flat Bar) 1.5.3(b)

H (Flat Bar)

()(1.5.7)

2

1 1

1 1

2( )xx

f w

b hI

b h

t t

1.5.7

a

70 |

b2

1.5.3

5.4

y

2

yyI z dA 1.5.8

z

2

zzI y dA 1.5.9

1.5.4

b h Ai iz Qyi iy Qzi

10 4 40 2 80 5 200

2 10 20 9 180 5 100

8 3 24 15.5 372 5 120

- - 84 - 632 - 420

5

| 71

Ai

iz z

yi y

Qyi y

QZi z

( Z , Y )

6327.5238

84

yzdA Q

ZArea Area

4205.0000

84

zydA Q

ZArea Area

(Iyy, Izz )

Ai iZ z Iy1 Iy2 Iyy iY y Iz1 Iz2 Izz

40 5.5328 1224.5 53.3 1277.8 0 0 333.3 333.3

20 1.4672 43.1 166.7 209.8 0 0 6.7 6.7

24 7.9762 1526.9 18.0 1544.9 0 0 128.0 128.0

2794.5 238.0 3032.5 0 468.0 468.0

2

1 ( )y i iI A Z z 3

212

y

bhI 1 2yy y yI I I

2

1 ( )z i iI A Y y , 3

212

z

hbI ,

1 2zz z zI I I

5.5

yQ zdA 1.5.10

zQ ydA 1.5.11

y z

72 |

y z

y

zz z

V Q

I b

1.5.12

z y

z

yy y

V Q

I b

1.5.13

:

Vy y

Vz z

Iyy y

Izz z

by z

bz y

5.6

y z y yz

y zb

zz z zz z zz

V Q V VQQ

I b I b I

z

zb

z

QQ

b 1.5.14

z y yz z

z yb

yy y yy y yy

V Q QV VQ

I b I b I

y

yb

y

QQ

b 1.5.15

z y zz yb

yy y yy

V Q VQ

I b I 1.5.16

1.5.5

tw

5

| 73

( )y fQ zdA B t z 1.5.17

y wb t 1.5.18

{( ) }/yb f wQ B t z t 1.5.19

5.7

midas Civil -(SRC)

(Equivalent Sectional Properties)

1 1

0.80.8

c con

eq st con st

s

E AArea A A A

E REN 1.5.20

1 1

0.80.8

c con

eq st con st

s

E AsAs As As As

E REN 1.5.21

1 1

0.80.8

c con

eq st con st

s

E II I I I

E REN 1.5.22

Astl

Acon

Asstl

Ascon

Istl

Icon

REN (Es/Ec)

0.8

1.0

74 |

6

6.1

midas Civil

Constraint

(Spring support)

(Elastic Link)

Element end release

(Beam End Offset)

Rigid link

6.2

(Constraint)

(Singular Error)

1.6.1

1.6.1

6

| 75

X-Z

>> Y

X Z

N1 XZ ()

Y

N3 Z

N5 X

z

1.6.2

a

b H

1.6.2

1.6.2(a)

X

76 |

1.6.2b H

Y

6.3

(Singular Error)

(Modulus of Subgrade Reaction)(Tributary Area)

midas Civil (Surface

Spring Supports)>>

a

6

| 77

K=

b

1.6.3

1.6.1

EA/H E

A H

EI/H

I H

(Coupled)

1.6.1

(KN/m3)

12000 ~ 24000

24000 ~ 48000

48000~ 112000

4800 ~ 16000

9600 ~ 80000

24000 ~ 48000

48000 ~ 96000

32000 ~ 80000

64000 ~ 130000

80000~ 190000

80000~ 190000

78 |

(Singular Error)

0.00010.001

midas Civil

6.4

(Winkler) midas Civil >

>

1

2

Winkler

1q2q

x

y

vk v

L

1 2

1.6.4

[ ] [ ] [ ] [ ]T vU dV v k v dV 1.6.1

U

6

| 79

V v kv ()

[ ] [ ] [ ][ ] [ ] [ ]T T Tvq f k f q dV q P 1.6.2

[ ] [ ] [ ] [ ]Tvk f f dV q P 1.6.3

[ ] [ ] [ ]rK q P 1.6.4

[ ] [ ] [ ]Tr vK k f f dV 1.6.5

P f q

Kr

L Winkler

2 2

2 2

156 22 54 13

22 4 13 3[ ]

54 13 156 22420

13 3 22 4

vr

L L

L L L Lk LK

L L

L L L L

1.6.6

x q

3 2 3 3 2 2 3

1 1

3 3 2 3 2 2

2 2

2 3 21( )

2 3 ( )

x Lx L q Lx L x L xv y x

L x Lx q Lx L x

1.6.7

Winkler

Winkler

80 |

0

2 34 3 3 4 3 2

1 1

3 24 3 4 3

2 2

( ) ( )

1 2

2 4 3 2

1

2 4 3

x

v

v

V x k y x dx

L L Lx Lx L x q x x x

k

L L Lx Lx q x x

1.6.8

0 0 0

2 35 4 3 2 5 4 3

1 1

3 25 4 5 4

2 2

35 4 2 5

1

3

( ) ( )( ) ( ) ( )

1 2

2 4 3 2

1

2 4 3

2 3 2

5 4 2 5

x x x

v v v

v

v

M x k y x x x dx k x y x dx k y x x dx

L L Lx Lx L x q x x x

k

L L Lx Lx q x x

L L L Lx x x q x

k

L

2 34 3

1

25 4 5 4

2 2

4 3

2 3

5 4 5 4

Lx x

L L Lx x q x x

1.6.9

6.5

(Radian)

1.6.5

x

6

| 81

1.6.5

6.6

joint i

x

z

y

local coordinate axis

L

joint j

kx

yk

zk

xk

ky

kz

yiL yjL

ziL zjL

1.6.6

/

1.6.6

1.0

yi yi zi zi

yj yj zj zj

yi yj zi zj

L c L L c L

L c L L c L

c c c c

82 |

>>

6

()()

1

2

3

4

1.6.10

M C

Ceff Ks

u u u p

5

1.6.2

eff SMu Cu C u K u p

6

| 83

1.6.2

+

- - -

1) 1) 1)

1) 1) 1)

2) 2) 2)

1) 1) () 1)

2) 2) () 2)

1)

2)

3)

()()

2effC K

1.6.11

Ceff K

SF K u

u

a

84 |

eff SF C u K u

u

b

1.6.7

1.6.3

- SF K u SF K u

SF K u SF K u

()

SF K u

SF K u SF K u

eff SF C u K u

()

SF K u

SF K u

eff SF C u K u

SF K u

eff SF C u K u

1.6.7 1.6.3

>

6

| 85

yiL yjL ij y

ziL zjL ij z

1.6.8

1

2

1.6.9

zk

yL

yiL yjL

ziyi ziL

zjyj zjL

yk

z zj zi

yiq yjq

zimzjm

V

M

Shear force

diagram

Bending momentdiagram

zm

yq

x

y

z

i

jv

iv

v

j

i j

location of shear spring

in direction 2

location of shear spring

in direction 3

x

y

z(-)

(-)

(-)(-)

(-)

(-)Axial

Momentx

Momenty

Momentz

Sheary

Shearzx

y

z(+)

(+)

(+)(+)

(+)

(+)Axial

Momentx

Momenty

Momentz

Sheary

Shearz

L

yiL yjL

ziL zjL

86 |

j yj zj i yi zi

j i yj zj yi zi

v v L v L

v v L L

y y

y j i yj zj yi zi

yj yi

q k v

k v v L L

q q

( )

( )

z z z

z zj zi

zj yj zj

zi yi zi

m k

k

m L q

m L q

z j z i

yi

zj zi

yj

m mq

L

m mq

L

zi z yi yi

zj z yj yj

m m L q

m m L q

1.6.9

6.7

1.6.10 ()

6

| 87

4 Fx, My

4 My

b c

1.6.10

6.8

()

midas Civil

1.6.11

1(Panel Zone)

2(Panel Zone)

midas Civil ()(Panel Zone)

6.8.1

1 ( )i jL L R R 1.6.12

L Ri Rj (Rigid End Offset Length)

L1 (Rigid Zone

Deformation)

midas Civil (Offset Factor)

1 ( )F i jL L Z R R 1.6.13

ZF

34 Fx, My

34 My

88 |

01

() L

a

Y

X

Z

b c

1.6.11 ()

midas Civil >>

Z XY

(ZF (Ri +Rj))

6

| 89

(

)

1.0

0.0

(L1 = L - ZF (Ri +Rj))( 1.6.12)

(Rigid End Offset Length)( L1 = L - (Ri +Rj))( 1.66)

( L1 = L - (Ri +Rj))(L1 = L - ZF (Ri +Rj))

1.0

(Beam End Release Condition)

( 1.6.12)

1.6.15

y z

1.6.16

RCy=BDcos2 RCz=BDsin

2

90 |

RCy y () RCz z () BD

z

( Z )

a

b

1.00 1.00 ( )L A B

0.75 0.75 ( )L A B

0.50 0.50 ( )L A B

0.25 0.25 ( )L A B

0.00 0.00 ( )L A B

c ( B=0)

1.6.12 /

6

| 91

Li = 1.0 Ri () Li=ZF Ri ()

Lj = 1.0 Rj () Lj=ZF Rj ()

Ri : i Rj : j

ZF : Offset Factor

V1, V2 :

M1, M2 :

V3, V4 :

1.6.13

92 |

LR = 1.0 R LR = ZF R

R

V1V2 :

M1M2:

V3

1.6.14

y

z

Z

1

2

a

y

2

1

z

b

1.6.15

6

| 93

1

z

y

2

3

: 250 0 250 0 0.0 0 250.0

: 200 40 200 40 82.6 200 0 117.4

: 150 90 150 90 150 150 90 0.0

2 2

z y

2 2

z y

2 2

z y

1 BD RC sin RC cos

2 BD RC sin RC cos

3 BD RC sin RC cos

MAX(250.0,117.4,0.0) 250.0 MAX(0.0,82.6,150.0) 150.0y zRC RC

BD

RCz

RCy

1.6.16

-( 1.6.17)

2 2cos sin

2 2

Depth WidthRB

(1.6.14)

Depth z

Width y z

94 |

3

1

2

Z

y

x

2

3

1

1.6.17

j

z

x

i

150, 100 40

150 0 100 075.0

2 2

150 40 100 4064.7

2 2

2 2

2 2

cos sin

cos sin

= = , =

i =

j =

1.6.18

6.8.2

1 XYZ

2 x

6

| 95

( 1.6.11(b)(c))

1.0

6.9

(>>)

1

2

3

4

Xs Xm Ym Zm

Ys Ym Zm Xm

Zs Zm Xm Ym

U U R Z R Y

U U R X R Z

R R R Y R X

(1.6.15)

Xs Xm

Ys Ym

Zs Zm

R R

R R

R R

(1.6.16)

, X = Xm - Xs, Y = Ym - Ys, Z = Zm - Zs

ms UxUyUz

XYZ RxRyRz XYZ

XmYmZm XsYsZs

96 |

X-Y Y-Z Z-X

X-Y

Xs Xm Zm

Ys Ym Zm

Zs Zm

U U R Y

U U R X

R R

(1.6.17)

Y-Z

Ys Ym Xm

Zs Zm Xm

Xs Xm

U U R Z

U U R Y

R R

(1.6.18)

Z-X

Zs Zm Ym

Xs Xm Ym

Ys Ym

U U R X

U U R Z

R R

(1.6.19)

XYZ

X

Xs XmU U (1.6.20)

Y

Ys YmU U (1.6.21)

Z

Zs ZmU U (1.6.22)

XYZ

6

| 97

X

Xs XmR R (1.6.23)

Y

Ys YmR R (1.6.24)

Z

Zs ZmR R (1.6.25)

(

)(Rigid Diaphragm

Action)

1 2

1 2

1.6.19

1.6.19

1 2

98 |

1 2 3 4 5

1.6.20

1.6.20 (123

4)

1.6.21 24 (

6 ) 15

Ux Uy Uz Rx Ry Rz Ux Uy Uz Rx Ry Rz

Ux Uy Uz Rx Ry RzUx Uy Uz Rx Ry Rz

UxUyRz

Uz Rx Ry Uz Rx Ry

Uz Rx RyUz Rx Ry

6

| 99

UX : X RX : X

UY : Y RY : Y

UZ : Z RZ : Z

1.6.21

UXm : X UYm : Y

RZm : Z UXs : X

UYs : Y RZs : Z

1.6.22

Xs Xm Zm

Ys Ym Zm

Zs Zm

U U R Y

U U R X

R R

(1.6.26)

3

1.6.23

100 |

1.6.23a

1.6.23