Guia Para El P2 de Estructuras 2 (2)

ESTRUCTURAS II PROBLEMA RESUELTO METODO DISTRIBUCION DE MOMENTOS SOBRE LA CONFIGURACION GEOMETRIA

PROF: ING. MARIO CENCI

NOVIEMBRE, 2014

JUNTA MIEMBRO KIJ

BA 0,25

B BC 0,5

0,20

-8775 -1260

E

F

BE 0,5

EB 0,5

0,40

0,40

0,56 0,44 0,50 PROBLEMA PRIMARIO

-10125 -2520 -718 355 -89 63 -14 10 -2 2

10125 -1260 -1435 177 -178 31 -27 5 -4

1

25200 -2520 -169 355 -68 63 -12 10 -2 2

∑Mom Prim

-9820

22858

-13038

M. Comp.

-1000

∑KI FDIJ Mom. Vol. Mom. Prim.

31 5

-1

-83 -433 83 -39 7 -3

-1238 -1,2377

-468 -0,4676

-217 -19

∑M.C*Eiα/1000

MBA MBC MBE MEB MEF MFE MFG MCB MCD MGF

CD 0,15

G GF 0,4

0,23

0,00

-25200 -1260 -338 177 -136 31 -24 5 -4

18900

-3000 -656

-26749

18749

CB 0,5

0,50

0,77

5625 -1313 -574 287 -71 36 -11 5 -2 1

-3000 -1313

7434 -7434 3983 PROBLEMA COMPLEMENTARIO 3000 -1667 -1333 -667 -217 167 333 28 22 11 -19 11 9 4 -1 -4 -8 3 2

-3983

1137 1,1373

326 0,3256

0,9

0,65

0,8

8000

177

∑M.Com

FE 0,4

C FG 0,4

1,25

EF 0,4

-9820 22858 -13038 7434 -7434 3983 -3983 -26749 18749 -3492

-1,2377 -0,4676 1,7052 1,1373 -1,1373 -0,3256 0,3256 -0,2207 0,2207 0,1628

ECUACION DE TRABAJO VIRTUAL MBA -9820 -1,2377 .-MBE 13038 -1,7052 .-MEB -7434 -1,1373 .-0,36MCD -6750 -0,0794 125250 114285 -4,1596

3000 -833 -433 14 -39 -3

1705 1,7052 27474,9442 27474,9442 27474,9442 27474,9442 27474,9442 27474,9442 27474,9442 27474,9442 27474,9442 27474,9442

-5625 -656 -1148 144 -143 18 -22 3 -4

-1137 -1,1373

-43824,93 m*kgf 10011,61 m*kgf 33813,32 m*kgf 38679,60 m*kgf -38679,60 m*kgf -4962,74 m*kgf 4962,74 m*kgf -32811,54 m*kgf 24811,54 m*kgf 980,93 m*kgf

Eiα=

27474,9442

-326 -0,3256

27000 40500 10000

287 36 5

-102 144 -41 18 -7 3 -1

1

-166 -217 167 -19 15

333

-3492

216 -50 167 50 4

-8

-4

1,5 1,5 2,4

-221 -0,2207

40500 60750 24000 125250

221 0,2207

163 0,1628

JUNTA MIEMBRO RIGIDEZ ∑R FD

B BA 0.15

HG 0.3

0.71

0.32

0.525 0.29

H HI 0.375 0.925 0.41

K HK 0.25

KH 0.25

0.27

0.33

-2500 2,229

-20000 5,405 -2,784 752 -63 17

20000 2,703 -5,568 376 -125 8 -3

-271

KL 0.5 0.75

-8000

MOMENTO APLICADO

MOMENTOS PRIMARIO

BC 0.375

0.67

L LK 0.5 ∞ 0

J JH 0.3

JI 0.3

0.23

0.23

8,271

6,486

8,108

903

1,129

20

25

7,410

9,262

-16,672

17,392

JL 0.4

0.23

0.31

1.3

-6000 2700 5,571

JK 0.3

L LJ 0.4 ∞ 0

5616 0 -11,135

-5,568

-251

-125

-1,296

-1,296

-1,296

-1,728

-1,296

-1,296

-1,296

-1,728

-6

-11,392

-5,693

0

RESOLUCION: Problema Complementario No. 01 Nodo C Miembro CB CD Rigidez 0.3 0.5 ΣR 0.8 FD 0.375 0.625 Mom Junta Mprima.

-250 -37 -5

E EE´ 0 0.6875 0.727 0.000 PROBLEMA PRIMARIO

DE 0.5

1423 -5108 668 -417 98 -61 14 -9

2846 -2554 1335 -209 196 -31 29 -5 4

854

1

-6545 2846 -517 1335 -243 196 -36 29 -5 4

401 59 9

-3393

1613

1323

-2936

CB 900

CD 6250

DC 6250

DF -600

-873 -3923 357 -223 53 -33 8 -5

-1745 -1962 715 -112 105 -16 15 -2 2

-524

1

DE -3000 1364 -1745 317 715 -130 105 -19 15 -3 2

3250 3.2505

-872 -0.8722

-2378 -2.3783

-134 -20 -3

-1611 -1.6107

3392.55 -3392.55 1612.77 1323.20 -2935.97 -12490.04 35200.00 -22709.96

1611 1.6107

-1.6107 1.6107 3.2505 -0.8722 -2.3783 -0.3968 0.0000 0.3968

214 32 5

-14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56

G

ED 0.5

0.435

3393

-2354

MCB MCD MDC MDF MDE MED MEE MEF

0.435

D DF 0.15 1.15 0.130

6750

-3065

Miembro Mcomplem.

DC 0.5

-13091 1423 -1035 668 -486 98 -71 14 -10

-12490

EF 0.1875

GF 0.5

0.273

35200 0

HG 0.25

0.667

0.333

0.400

0.600

-17200 -4909

12075 -8450

-388

-452

0

-182

-15

-2400 -2113 1355 -113 45 -4 2

1125

0

600 -4225 678 -226 23 -8

0

-27

0

-4

35200

-22710

3,158.28

-3,158.28

-3,227.51

3,227.51

EF -750 1023

GF

GH

HG

HA

0.75

PROBLEMA COMPLEMENTARIO ED EE´ -3000 0 2727 0 -873 635 0 357 -260 0 53 -38 0 8 -6 0

-397 -0.3968

0 0.0000

26,421.75 -26,421.75 -44,860.86 13,793.32 31,067.55 -6,817.37 35,200.00 -28,382.63

-97 -14 -2

397 0.3968

TRABAJO VIRTUAL 26,200.00 34,400.00 7,000.00 6,500.00

-4.00 -2.00 2.25 3.00

-104,800.00 -68,800.00 15,750.00 19,500.00 -138,350.00

-2544 7068 -3360 1323 -2936 -12490 -22710 -138350

1.2080 -3.3556 -6.7718 -0.8722 -2.3783 -0.3968 0.3968

-173999.3227

-12.1699

MCB MCD MDC MDF MDE MED MEE MEF

Eiψ=

23,029.20 -23,029.20 -46,473.64 12,470.12 34,003.52 5,672.66 0.00 -5,672.66

-14,297.56

ψ=

-0.00047659

radianes

HA 0.375 0.625

238

Ecuaciones de trabajo virtual .-0,75*MCB .-25/12*MCD .-25/12*MDC MDF MDE MED MEF

H GH 0.25

-0.02730627

grados

2033 68 2

RESOLUCION: Problema Complementario No. 02 Nodo C Miembro CB CD Rigidez 0.3 0.5 ΣR 0.8 FD 0.375 0.625 Mom Junta Mprima.

-250 -37 -5

E EE´ 0 0.6875 0.727 0.000 PROBLEMA PRIMARIO

DE 0.5

1423 -5108 668 -417 98 -61 14 -9

2846 -2554 1335 -209 196 -31 29 -5 4

854

1

-6545 2846 -517 1335 -243 196 -36 29 -5 4

401 59 9

-3393

1613

1323

-2936

CB 900

CD 6250

DC 6250

DF -600

-873 -3923 357 -223 53 -33 8 -5

-1745 -1962 715 -112 105 -16 15 -2 2

-524

1

DE -3000 1364 -1745 317 715 -130 105 -19 15 -3 2

3250 3.2505

-872 -0.8722

-2378 -2.3783

-134 -20 -3

-1611 -1.6107

3392.55 -3392.55 1612.77 1323.20 -2935.97 -12490.04 35200.00 -22709.96

1611 1.6107

-1.6107 1.6107 3.2505 -0.8722 -2.3783 -0.3968 0.0000 0.3968

214 32 5

-14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56 -14,297.56

-13091 1423 -1035 668 -486 98 -71 14 -10

-12490

EF 0.1875

GF 0.5

0.273

35200 0

26,421.75 -26,421.75 -44,860.86 13,793.32 31,067.55 -6,817.37 35,200.00 -28,382.63

-397 -0.3968

H GH 0.25

HG 0.25

0.667

0.333

0.400

0.600

-17200 -4909

12075 -8450

-388

-452

0

-182

-15

-2400 -2113 1355 -113 45 -4 2

1125

0

600 -4225 678 -226 23 -8

0

-27

0

-4

35200

-22710

3,158.28

-3,158.28

-3,227.51

3,227.51

EF -750 1023

GF

GH

HG

HA

0.75

PROBLEMA COMPLEMENTARIO ED EE´ -3000 0 2727 0 -873 635 0 357 -260 0 53 -38 0 8 -6 0

Ecuaciones de trabajo virtual MCB .25/9*MCD .25/9*MDC .-4/3*MDF .-4/3*MDE .-4/3*MED .-4/3*MEF

G

ED 0.5

0.435

3393

-2354

MCB MCD MDC MDF MDE MED MEE MEF

0.435

D DF 0.15 1.15 0.130

6750

-3065

Miembro Mcomplem.

DC 0.5

0 0.0000

0.625

238 -97 -14 -2

397 0.3968

TRABAJO VIRTUAL 26,200.00 34,400.00 7,000.00 6,500.00

5.33 2.67 -3.00 -4.00

139,733.33 91,733.33 -21,000.00 -26,000.00 184,466.67

3393 -9424 4480 -1764 3915 16653 30280 184466.6667

-1.6107 4.4742 9.0291 1.1629 3.1710 0.5290 -0.5290

231999.0969

16.2265

MCB MCD MDC MDF MDE MED MEE MEF

Eiα=

23,029.20 -23,029.20 -46,473.64 12,470.12 34,003.52 5,672.66 0.00 -5,672.66

-14,297.56

HA 0.375

2033 68 2

ESTRUCTURAS II PROBLEMARIO

PROF: ING. MARIO CENCI NOVIEMBRE 2014

JUNTA MIEMBRO KIJ

A AB 0,4

BA 0,4

B BC 0,15

0,42

-3150

∑KI

DB 0,4

0,16

0,42

0,80

-5175

6600

-6600

0,95

FIJ Mom. Vol. Mom. Prim.

D BD 0,4

-1459

-2917

-1094

-163

-327

-122

-17

-35

-13

-4

-1

-6432

-6406

Mo m. Co mp .

AB -2,40EIα -2400

BA -2,40EIα -2400

BC 0,60EIα 600

106

211

79

14

28

11

3

1

-2280 -2,2802

-2157 -2,1574

1511 -6432 -6406 12838 10802 -2802 -12744 6744

-2,2802 -2,1574 0,6910 1,4665 0,1676 -0,1676 -0,0522 0,0522

MAB MBA MBC MBD MDB MDE MED MEC

0,20

0,44

Ecuacion de Trabajo Virtual MAB 1511 MBA -6432 .-MBC 6406 .-MBD -12838 .-MDB -10802 .-MDE 2802 .-MED 12744 .-MEC -6744 -11400 -24754

8653 -2917 776 -327 83 -35 9 -4

17307 -1459 1551 -163 165 -17 18

12838 0 BD 2,40EIα 2400

10802 DB 2,40EIα 2400

-1102 211 -67 28 -7 3

-2204 106 -134 14 -14

691 0,6910

1466 1,4665 0

168 0,1676

-3753 -3753 -3753 -3753 -3753 -3753 -3753 -3753

10069,23 1665,38 -8999,32 7333,94 10172,64 -2172,64 -12548,31 6548,31

EC 0,125 0,225

-8000 3150

1511

∑Mo. Com.

ED 0,1

0,5

∑Mo. Prim.

Mo m. Co mp .

E DE 0,1

0,56 6000

-7033 4327 -481 388 -43 41 -5 4

-2802 8000 DE 0,60EIα 600 -244 -551 61 -33 4 -4

-168 -0,1676 0

-14067 2163 -961 194 -86 21 -9 2 -1

-12744 ED 0,60EIα 600 -489 -276 122 -17 7 -2 1

Eiα=

-1202 -108 -11 -1

6744 -6000 EC 0,50EIα 500 -611 153 9 1

-52 -0,0522

52 0,0522 0

13800 10000 13800 -27600

1,5 3 1,5 3

-2,2802 -2,1574 -0,6910 -1,4665 -0,1676 0,1676 0,0522 -0,0522 -6,5951

25650 -17583

-3753,3946

20700 30000 20700 -82800 -11400

METODO DE LOS DESPLAZAMIENTO. CROSS Nodo A Miembro AB BA Rigidez 0.28 ΣR CB 0 0.26 Mom Junta Mprima.

-5467

5467

-2587.5

-1,019

-2,037

-2,183

-60

-120

-129

-4

-7

-8

-6549

Miembro Mcomplem.

3302

-4907

BD 0.50 0.46

1800 3,178 -3,638 464 -215 27 -13

1604

AB -1680 1,091

BA -1680 2,181

BC 1600 2,337

-127

-253

-271

-7

-15

-16

-1

-1

BD -8333 3,895 976 -452 58 -27 3 -2

232 0.2323

3649 3.6489

-3881 -3.8812

-723 -0.7234

MAB MBA MBC MBD MDB MDE MDG MEC MEF

B BC 0.30 1.08 0.28

-6,549.27 3,302.45 -4,906.66 1,604.20 -3,590.47 1,294.29 2,296.18 516.00 -516.00

-0.7234 0.2323 3.6489 -3.8812 -4.5509 2.8443 1.7066 -1.9980 1.9980

1,502.6388 1,502.6388 1,502.6388 1,502.6388 1,502.6388 1,502.6388 1,502.6388 1,502.6388 1,502.6388

D DE 0.30 0.98 0.510 0.306 PROBLEMA PRIMARIO DB 0.50

E DG 0.18

EC 0.30

EF 0.45 0.75

0.184

0.400

0.600

860 -344

-516

-9000 6,356 -1,819 928 -107 55 -6 3

-3111 3,814

-347 2,288

557

334

33

20

2

1

-3590

1294

2296

516

-516

DG 960

EC -3330 1,332

1,998

-1998 -1.9980

1998 1.9980

PROBLEMA COMPLEMENTARIO DB DE -8,333 1600 1,947 1,952 1,171 -226 115 69 -13 4 7

-4551 -4.5509

2844 2.8443

EF

703 41 2

1707 1.7066

-7636.29 3651.54 576.33 -4227.87 -10428.86 5568.29 4860.57 -2486.27 2486.27

TRABAJO VIRTUAL 18,200.00 -12,600.00 6,900.00 7,000.00 6,500.00 4,600.00

2.00 1.17 2.00 1.33 1.33 2.78

Ecuaciones de trabajo virtual MAB MBA .-4/3MBC 25/9MBD 25/9MDB .-4/3MDE .-4/3MDG 25/9MEC

-6549 3302 6542 4456 -9974 -1726 -3062 1433 66,277.78

-0.7234 0.2323 -4.8652 -10.7812 -12.6414 -3.7924 -2.2755 -5.5500

60,701.79

-40.40

Eiψ=

1,502.64

ψ=

5.0088E-05

radianes

36,400.00 -14,700.00 13,800.00 9,333.33 8,666.67 12,777.78 66,277.78

0.00286982

JUNTA MIEMBRO RIGIDEZ ?R FD

C CD 0.4 ? 0.00

D DC 0.4

E DE 0.5

ED 0.5

EF 0.3

0.44

0.56

0.625

0.375

4,500

-4,500 -1,135

-49

-99

-4

-9

15,300 23,109 -710 444 -62 39 -5 3

-52,275 13,866

-568

-4,500 11,555 -1,419 222 -123 19 -11

0.8

0.9

MOMENTO APLICADO

MOMENTOS PRIMARIOS

MOMENTOS COMPLEMENTARIOS CASO No. 1 Eiψ = 1000

?(MOM. COMPLEM. No.1) ?(MOM. COMPLEM. No.1)/1000

23 2

3,879

-5,743

5,743

38,118

-38,118

-2.40Eiψ -2,400

-2.40Eiψ -2,400 -1,702

-74

-148

-6

-13

8.33Eiψ 8,333 -4,208 -1,064 665 -92 58 -8 5

-1.60Eiψ -1,600 -2,525

-851

-1

8.33Eiψ 8,333 -2,104 -2,127 332 -185 29 -16 3 -1

-4,264 -4.2635

4,264 4.2635

3,688 3.6885

-3,688 -3.6885

-3.00Eiα -3,000 1,313 651 -407 57 -35 5 -3

0.90Eiψ 900 788

1

-3.00Eiα -3,000 656 1,302 -203 113 -18 10 -2 1

1,141 1.1406

-1,141 -1.1406

-1,420 -1.4203

1,420 1.4203

-3,331 -3.3312

CASO No. 2 Eiα = 1000

?(MOM. COMPLEM. No.2) ?(MOM. COMPLEM. No.2)/1000

266

521

1,042

45

90

4

8

570 0.5700

399 35 3

-244 -21 -2

MCD MDC MDE MED MEF

TRABAJO VIRTUAL No.1 MCD MDC .-(25/9)*MDE .-(25/9)*MED .4/3*MEF

TRABAJO VIRTUAL No.2 MDE MED .-3/4*MEF

0.5700 1.1406 -1.1406 -1.4203 1.4203

65214.3115 65214.3115 65214.3115 65214.3115 65214.3115

3,879 -5,743 5,743 38,118 -38,118

-3.3312 -4.2635 4.2635 3.6885 -3.6885

3,878.73 -5,742.53 -15,951.48 -105,883.77 -50,824.21 -179,000.00 -353,523.26

-3.3312 -4.2635 -11.8431 -10.2458 -4.9180

0.5700 1.1406 3.1684 3.9454 1.8938

-34.60

10.72

5,742.53 38,118 28,589 111600 184,049.31

4.2635 3.6885 2.7664

-1.1406 -1.4203 -1.0652

10.72

-3.63

243517.68 -74565.8051 243517.68 -6023.93643 243517.68 6023.93643 243517.68 -67213.678 243517.68 67213.678

-34.601658 10.718392 125.472250 -114.880779 10.591471 Eiψ = 370.87 -370.87 0.00 Eiα =

CASO No. 2-1 Eiα = 1000

TRABAJO VIRTUAL No.1 MCD MDC .-MDE .-MED

TRABAJO VIRTUAL No.2 MDE MED .-3/4*MEF

DC -2.40Eiα -2,400 -267

197

394

17

34

-2,319 -2.3195

?(MOM. COMPLEM. No.2) ?(MOM. COMPLEM. No.2)/1000

MCD MDC MDE MED MEF

CD -2.40Eiα -2,400 -133

-114.88 125.47 10.59 243517.684

ED 3.00Eiα 3,000 -167 -1,771 246 -154 21 -13

-1,063

3

-2,236 -2.2360

2,236 2.2360

1,163 1.1627

-1,163 -1.1627

0.5700 1.1406 -1.1406 -1.4203 1.4203

3,879 -5,743 -5,743 -38,118 19400 -26,324.49

0.5700 1.1406 1.1406 1.4203

-2.3195 -2.2360 -2.2360 -1.1627

4.27

-7.95

5,742.53 38,118.16 28,588.62 111600 184,049.31

-1.1406 -1.4203 -1.0652

2.2360 1.1627 0.8721

-3.63

4.27

-2.3195 -2.2360 2.2360 1.1627 -1.1627

353523.255203 -184049.306420

-38.865882 -1281943.139173 38.865882 1972658.621936 0.000000 690715.482763 65214.3115

DE 3.00Eiα 3,000 -333 -885 492 -77 43 -7 4

3,879 -5,743 5,743 38,118 -38,118

127495.22 127495.22 127495.22 127495.22 127495.22

10.718099 -3.626192

EF

-92 -8

65156.8704 -74583.9126 65156.8704 -6011.26117 65156.8704 6011.26117 65156.8704 -67206.435 67206.435 65156.8704

4.271535 -3.626192 18.242930 -28.843738 -10.600808 Eiψ = 15.49 -15.49 0.00 Eiα =

-7.954278 4.270813

26324.488234 -184049.306420

-33.971235 112426.970853 33.971235 -1463979.341395 0.000000 -1351552.370542 127495.22 -28.84 18.24 -10.60 65156.8704

95,457.64 -786,173.13 -690,715.48

-3,789,200.70 6,368,411.17 2,579,210.47

JUNTA MIEMBRO RIGIDEZ ∑R FD

B BA 0.15

HG 0.3

0.71

0.32

0.525 0.29

H HI 0.375 0.925 0.41

K HK 0.25

KH 0.25

0.27

0.33

-2500 2,229

-20000 5,405 -2,784 752 -63 17

20000 2,703 -5,568 376 -125 8 -3

-271

KL 0.5 0.75

-8000

MOMENTO APLICADO

MOMENTOS PRIMARIO

BC 0.375

0.67

L LK 0.5 ∞ 0

J JH 0.3

JI 0.3

0.23

0.23

8,271

6,486

8,108

903

1,129

20

25

7,410

9,262

-16,672

17,392

JL 0.4

0.23

0.31

1.3

-6000 2700 5,571

JK 0.3

L LJ 0.4 ∞ 0

5616 0 -11,135

-5,568

-251

-125

-1,296

-1,296

-1,296

-1,728

-1,296

-1,296

-1,296

-1,728

-6

-11,392

-5,693

0

JUNTA MIEMBRO RIGIDEZ

A AB

B BA 0.40

ΣMPrimarios MIEMBRO MCOMPLEM

ΣMComplemen

MIEMBRO MCOMPLEM

EB

0.40 0.60 0.67

Maplicado Mprimario

E BE

EF

0.20 0.33

0.20 0.65 0.31

0.45 0.69

5000

-826

-1,652

-21

-42

-1

-1

-847 -1,695 PROBLEMA COMPLEMENTARIO 1 AB BA -2400 -2400 402 804 73

145

2

4

-1,924 -1,447 -1.9236 -1.4471 PROBLEMA COMPLEMENTARIO 2 AB BA 402

804

-145

-291

-4

-7

-3000 465 -813 63 -21 2 -1

3000 930 -407 126 -10 3

-6000 2,070

-3,305

3,642

-3,642

BE

EB

281 7

EF

1200 396 -217 72 -6 2

1200 198 -433 36 -11

-965

1,447 1.4471

989 0.9893

-989 -0.9893

BE -1,200 396 434 -143 11 -4

EB -1200 198 869 -72 22 -2 1

-25

EF -1800 1933 49 1

ΣMComplemen

253 0.2528

506 0.5056

-506 -0.5056

-184 -0.1841

184 0.1841

MAB MBA MBE MEB MEF

-847 -1,695 -3,305 3,642 -3,642

-1.9236 -1.4471 1.4471 0.9893 -0.9893

29,019.43 29,019.43 29,019.43 29,019.43 29,019.43

0.2528 0.5056 -0.5056 -0.1841 0.1841

242,674.52 242,674.52 242,674.52 242,674.52 242,674.52

TRABAJO VIRTUAL No.1 MAB -847 MBA -1,695 .-MBE 3,305 .-MEB -3,642 -180,000 -182,879.35 TRABAJOVIRTUAL No.2 MBE MEB MEF

-3,305 3,642 -3,642 84,000 80,694.87

-182,879.3540 80,694.8686

-1.9236 -1.4471 -1.4471 -0.9893

0.2528 0.5056 0.5056 0.1841

-5.8071

1.4480

1.4471 0.9893 -0.9893

-0.5056 -0.1841 0.1841

1.4471

-0.5056

-5.8071 Eiα 1.4471 Eiα

-92458.36794 -2.93587287 116847.5016 2.09543143 24389.13362 -0.84044143 -182,879 80,695

-5.8071 Eiα 1.4471 Eiα

-264645.5658 -8.40341176 468599.2832 8.40341176 203953.7174 0

4,676.68 79,000.00 -84,000.00 -12,323.32 12,323.32

1.4480 Eiβ -0.5056 Eiβ 0.732074123 -0.73207412 0

6 8 8

-36000 -48000 -96000 -180000

6000 -8000 6000 12000

2 3 4 6

12000 -24000 24000 72000 84000

0.5056 1.4480

Eiα=

1.4480 Eiβ -0.5056 Eiβ 2.095431434 -2.93587287 -0.84044143

-6000 -6000 -12000

29,019.43 1.4471 5.8071

Eiβ=

242,674.52

ESTRUCTURAS II II EXAMEN PARCIAL METODO DE CROSS 29-05-2015

PROF: ING. MARIO CENCI MAYO 2015

JUNTA MIEMBRO RIGIDEZ

A AB 0.19

D

C CB 0.30

CD 0.30

DC 0.30

0.50

0.69

0.43

0.60 0.50 Maplicados MPrimario

20,400 505 44 4

ΣMPrimarios

0 20,952 PROBLEMA COMPLEMENTARIO 1 MIEMBRO AB CB MCOMPLEM -750 1,200 -600 -52 -5

-750 543 -0.7500 0.5435 PROBLEMA COMPLEMENTARIO 2 MIEMBRO AB CB MCOMPLEM 0 0 ΣMCompleme

496 43 4

ΣMCompleme

DF 0.13

-11,700 -9,709 505 -87 44 -8 4 -20,952 CD

0.31

7,000.00 11,700 -19,418 252 -175 22 -15

-543 -0.5435

-101 -0.1006

CD -1,800 808 496 -86 43 -7 4

DC -1,800 1,616 248 -172 21 -15 2 -1

-543 -0.5427

-101 -0.1007

0 20,952 -20,952 -7,634 634

-0.7500 0.5435 -0.5435 -0.1006 0.1006

41,333.33 41,333.33 41,333.33 41,333.33 41,333.33

0.0000 0.5427 -0.5427 -0.1007 0.1007

TRABAJO VIRTUAL1 MAB 0.00 .-MCB -20,952.10

-0.750000 -0.543478

0.000000 -0.542696

-20,952.10

-1.293478

-0.542696

-0.543478 -0.100609 0.100609

-0.542696 -0.100729 0.100729

-0.543478

-0.542696

-20,952 -51,952

-1.2935 Eiα -0.5435 Eiα

20952.09691 1.293477848 -51,952 -0.5435 -31000 0.75

-20,952 -51,952

-1.2935 Eiβ -0.5435 Eiβ

-11387.00055 -0.70297656 67198.88653 0.702976558 55811.88598 0

634

-300 208 -26 18 -2 2

543 0.5427

TRABAJOVIRTUAL 2 MCD -20,952.10 MDC -7,634.24 MDF 634.24 -24000.000000 -51952.096912

-7

DF

0 0.0000

MAB MCB MCD MDC MDF

-77

-7,634 DC

-600 104 -52 9 -5

9,300 -8,582

92 8 1 101 0.1006 DF -530 714 -76 -7 -1

101 0.1007

-137,122.50 -31000 -137,122.50 -31000 -137,122.50 31000 -137,122.50 2019.44179 -137,122.50 -9019.44179

-0.5427 Eiβ -0.5427 Eiβ 0.542696098 -0.5427 0

Eiα=

41,333.33

Eiβ=

-137,122.50

-0.5427 Eiβ -0.5427 Eiβ -0.29494331 0.701965381 0.407022073