Transcript
Page 1: Examen de Analisis BRUNO

ALEGRE HUAMANCHUMO ROBERTO

unidades de longitud = munidades de fuerza = kg

b (cm) = 0.3h(cm) = 0.6 f`c= 3 klb/pulg2

Io = 0.0054 E= 218819.788867I= 0.0108L= 6

MEPi= -42MEPj= 42

20kg

2 IoA

6mK1 = 2EI/L

matriz de rigidez2K1 K1K1 2(K1 + K2) K2

K2 2(K2 + K3)K3

matriz de rigidez### 787.751240 0### ### 443.110072

0 443.110072 3249.473864680 0 1181.626860

0 0 0

RESOLVIENDO EL SISTEMA DE ECUACIONES CON METODOS ITERATIVOS - METODOS DE SOBRERELAJACIONϐ = 1.09

Page 2: Examen de Analisis BRUNO

K θA ΘB0 0 0

1 0.029057 0.023156

2 0.013822 0.028947

3 0.012037 0.034003

4 0.009443 0.037985

5 0.007506 0.038334

6 0.007490 0.038315

7 0.007501 0.038311

8 0.007503 0.038311

9 0.007503 0.038311

10 0.007503 0.038311

Page 3: Examen de Analisis BRUNO

EXAMEN DE ANALISIS ESCTRUTURAL II 201013024

210 f`c= 3 klb/pulg2 f`c= 3 klb/pulg2E= 218819.788867 E= 218819.788867I= 0.0081 I= 0.0135L= 8 L= 5

MEPi= -117.187500 MEPi= -41.666666666667MEPj= 70.312500 MEPj= 41.6666666666667

3m 5m 20kg

100 kg

1.5 Io 2.5 IoB C

8m 5mK2 = 2EI/L K3= 2EI/L

Giros 2º Miembro θA -(MEPAB)θB -(MEPBA + MEPBC)

K3 θC -(MEPCB + MEPCD)2(K3 + K4) K4 θD -(MEPDC + MEPDE)

K4 2K4 θE -(MEPED)

Giros 2º Miembro0 0 θA 420 0 θB 75.187500

### 0 θC -28.645833### 708.976116 θD 208.3333333333

708.976116 ### θE -250

RESOLVIENDO EL SISTEMA DE ECUACIONES CON METODOS ITERATIVOS - METODOS DE SOBRERELAJACION

Page 4: Examen de Analisis BRUNO

ΘC Θd Θe Giros0 0 0 θA 0.007503

- 0.013051 0.064501 -0.227332 θB 0.038311

- 0.038303 0.113759 -0.233717 θC -0.056497

- 0.056305 0.116762 -0.234780 θD 0.116756

- 0.056468 0.116765 -0.234685 θE -0.234689

- 0.056506 0.116758 -0.234690

- 0.056497 0.116757 -0.234689

- 0.056497 0.116756 -0.234689 matriz de momento ( debido a giros)- 0.056497 0.116756 -0.234689 1575.502480 787.751240- 0.056497 0.116756 -0.234689 787.7512399 1575.502480- 0.056497 0.116756 -0.234689 0 886.220144913215

0 443.1100724566080 0.0000000 00 00 0

Page 5: Examen de Analisis BRUNO

f`c= 3 klb/pulg2E= 218819.788867I= 0.0162L= 10

MEPi= -250MEPj= 250

5m 5m

200 kg

3 IoD E

10mK4 = 2EI/L

M EC. PEND. DEFLEX. 2EI/L MEP

AB 2EI/L(2 θA + θB - 3Ψ) + MEP 787.7512399 -42

BA 2EI/L( θA + 2θB - 3Ψ) + MEP 787.7512399 42

BC 2EI/L(2 θB + θC - 3Ψ) + MEP 443.1100725 -117.1875

CB 2EI/L( θB + 2θC - 3Ψ) + MEP 443.1100725 70.3125

CD 2EI/L( 2θC+ θD - 3Ψ) + MEP 1181.62686 -41.66666667

DC 2EI/L( θC+ 2θD - 3Ψ) + MEP 1181.62686 41.66666667

DE 2EI/L( 2θD+ θE - 3Ψ) + MEP 708.9761159 -250

ED 2EI/L( θD+ 2θE - 3Ψ) + MEP 708.9761159 250

Page 6: Examen de Analisis BRUNO

matriz de momento ( debido a giros) M finales0 0 0 0.000000 AB0 0 0 108.269567 BA

443.110072 0 0 -119.105685 BC886.220144913 0 0 37.220103 CB2363.25371977 1181.626860 0 -37.220103 CD

1181.626860 2363.253720 0.000000 250.833731 DC0 1417.95223186 708.976115931 -250.833731 DE0 708.976116 1417.952232 -0.000000 ED

Page 7: Examen de Analisis BRUNO
Page 8: Examen de Analisis BRUNO
Page 9: Examen de Analisis BRUNO

METODO DE CROSS20kg 3m

2 IoA B

6mK1 = 2EI/L K2 = 2EI/L

CALCULO DEL FACTOR DE DISTRIBUCION:TRAMO I LAB 0.0108 6mBC 0.0081 8m

BC 0.0081 8mCD 0.0135 5m

CD 0.0135 5mDE 0.0162 10m

CALCULOS DE LOS MEP:TRAMO W PAB 20BA 20

BC 100CB 100

CD 20DC 20

DE 200ED 200

0.64 0.36 0.273-42.00 42.00 -117.19 70.31

75.19 -28.6548.12 27.0675 -7.8125

24.06 -3.90625 13.53375

20kg 3m 5m 20kg 5m 5m

100 kg 200 kg

2 Io 1.5 Io 2.5 Io 3 IoA B C D E

6m 8mK1 = 2EI/L K2 = 2EI/L K3= 2EI/L K4 = 2EI/L

5m 10m

Page 10: Examen de Analisis BRUNO

2.5 1.40625 -21.4467045454551.25 -10.72335227273 0.703125

6.8629454545 3.8604068181818 -1.07954545454553.4314727273 -0.539772727273 1.9302034090909

0.3454545455 0.1943181818182 -2.96354462809920.1727272727 -1.48177231405 0.0971590909091

0.948334281 0.5334380330579 -0.1491735537190.4741671405 -0.07458677686 0.2667190165289

0.0477355372 0.0268512396694 -0.40950798497370.0238677686 -0.204753992487 0.0134256198347

0.1310425552 0.0737114372953 -0.02061307287750.0655212776 -0.010306536439 0.0368557186476

0.0065961833 0.003710353118 -0.05658655792360.0032980917 -0.028293278962 0.001855176559

0.0181076985 0.0101855804263 -0.00284835188850.0090538493 -0.001424175944 0.0050927902131

0.0009114726 0.0005127033399 -0.00781923345850.0004557363 -0.003909616729 0.00025635167

0.0025021547 0.0014074620225 -0.00039359044280.0012510774 -0.000196795221 0.0007037310113

0.000126 0.000071 -0.0010800.000063 -0.000540 0.000035

0.0003457523 0.0001944856613 -0.0000540.000173 -0.000027 0.000097

0.000017 0.000010 -0.0001490.000009 -0.000075 0.000005

0.000048 0.000027 -0.0000080.000024 -0.000004 0.000013

0.000002 0.000001 -0.0000210.000001 -0.000010 0.000001

0.000007 0.000004 -0.0000010.000003 -0.000001 0.000002

0.000000 0.000000 -0.000003-12.51 100.98 -100.98 52.95

Page 11: Examen de Analisis BRUNO

5m 20kg 5m

100 kg

1.5 Io 2.5 IoC D

8m 5m 10mK2 = 2EI/L K3= 2EI/L K4 = 2EI/L

K=I/L FD0.001800 0.640.001013 0.36

0.001013 0.2730.002700 0.727

0.002700 0.6250.001620 0.375

a b L MEP6 -42.006 42.00

3 5 8 -117.193 5 8 70.31

5 -41.675 41.67

5 5 10 -250.005 5 10 250.00

0.727 0.625 0.375-41.67 41.67 -250.00 250.00

-28.65 208.33-20.833333 130.208333 78.12565.104167 -10.416667 39.0625

20kg 3m 5m 20kg 5m 5m

100 kg 200 kg

2 Io 1.5 Io 2.5 Io 3 IoA B C D E

6m 8mK1 = 2EI/L K2 = 2EI/L K3= 2EI/L K4 = 2EI/L

5m 10m

Page 12: Examen de Analisis BRUNO

-57.191212121 6.5104166667 3.906253.2552083333 -28.595606061 1.953125-2.8787878788 17.872253788 10.7233522738.9361268939 -1.4393939394 5.3616761364-7.9027856749 0.8996212121 0.53977272730.4498106061 -3.9513928375 0.2698863636-0.3977961433 2.4696205234 1.4817723141.2348102617 -0.1988980716 0.740886157-1.0920212933 0.1243112948 0.07458677690.0621556474 -0.5460106466 0.0372933884-0.0549681943 0.3412566541 0.20475399250.1706283271 -0.0274840972 0.1023769962-0.1508974878 0.0171775607 0.01030653640.0085887804 -0.0754487439 0.0051532682-0.007595605 0.0471554649 0.0282932790.0235777325 -0.0037978025 0.0141466395-0.0208512892 0.0023736266 0.00142417590.0011868133 -0.0104256446 0.000712088-0.0010495745 0.0065160279 0.00390961670.0032580139 -0.0005247873 0.0019548084-0.002881 0.000328 0.0001970.000164 -0.001441 0.000098-0.000145 0.000900 0.0005400.000450 -0.000073 0.000270-0.000398 0.000045 0.0000270.000023 -0.000199 0.000014-0.000020 0.000124 0.0000750.000062 -0.000010 0.000037-0.000055 0.000006 0.0000040.000003 -0.000028 0.000002-0.000003 0.000017 0.0000100.000009 -0.000001 0.000005-0.000008 0.000001 0.000001-52.95 154.90 -154.90 297.55

Page 13: Examen de Analisis BRUNO

5m

200 kg

3 IoE

10mK4 = 2EI/L

Page 14: Examen de Analisis BRUNO

METODO DE CROSS20kg 3m

2 IoA B

6mK1 = 2EI/L K2 = 2EI/L

CALCULO DEL FACTOR DE DISTRIBUCION:TRAMO I LAB 0.0108 6mBC 0.0081 8m

BC 0.0081 8mCD 0.0135 5m

CD 0.0135 5mDE 0.0162 10m

CALCULOS DE LOS MEP:TRAMO W PAB 20BA 20

BC 100CB 100

CD 20DC 20

DE 200ED 200

0.64 0.36 0.273-42.00 42.00 -117.19 70.3142.00 21.00

54.19 -28.65-34.68 -19.5075 -7.8125

20kg 3m 5m 20kg 5m 5m

100 kg 200 kg

2 Io 1.5 Io 2.5 Io 3 IoA B C D E

6m 8mK1 = 2EI/L K2 = 2EI/L K3= 2EI/L K4 = 2EI/L

5m 10m

Page 15: Examen de Analisis BRUNO

-3.90625 -9.753752.5 1.40625 -25.748977272727

-12.87448863636 0.7031258.2396727273 4.6348159090909 -1.0795454545455

-0.539772727273 2.31740795454550.3454545455 0.1943181818182 -3.5580404958678

-1.779020247934 0.09715909090911.1385729587 0.6404472892562 -0.149173553719

-0.07458677686 0.32022364462810.0477355372 0.0268512396694 -0.4916565048835

-0.245828252442 0.01342561983470.1573300816 0.088498170879 -0.0206130728775

-0.010306536439 0.04424908543950.0065961833 0.003710353118 -0.0679379897657

-0.033968994883 0.0018551765590.0217401567 0.0122288381578 -0.0028483518885

-0.001424175944 0.00611441907890.0009114726 0.0005127033399 -0.0093877949494

-0.004693897475 0.000256351670.0030040944 0.0016898030909 -0.0003935904428

-0.000196795221 0.00084490154550.000126 0.000071 -0.001297

-0.000649 0.0000350.0004151112 0.0002335000635 -0.000054

-0.000027 0.0001170.000017 0.000010 -0.000179

-0.000090 0.0000050.000057 0.000032 -0.000008

-0.000004 0.0000160.000002 0.000001 -0.000025

-0.000012 0.0000010.000008 0.000004 -0.000001

-0.000001 0.0000020.000000 0.000000 -0.000003

MOMENTOS FLECTORES FINALES 0.00 94.97 -149.16 25.12

CALCULOS DE LOS CORTANTES:TRAMO W P a b

AB 20BA 20

BC 100 3 5CB 100 3 5

CD 20DC 20

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DE 200 5 5ED 200 5 5

CALCULO DE LAS REACCIONES:94.97 -124.04

6 8-15.828191 15.828190708 15.504461895247 -15.504461895247

27.00 27.00 68.36 31.6411.171809 42.828191 83.863837 16.136163

CORTANTES FINALES 11.171809 -42.828191 83.863837 -16.136163

REACCIONES 11.171809 126.692028 25.054614

Page 17: Examen de Analisis BRUNO

5m 20kg 5m

100 kg

1.5 Io 2.5 IoC D

8m 5m 10mK2 = 2EI/L K3= 2EI/L K4 = 2EI/L

K=I/L FD0.001800 0.640.001013 0.36

0.001013 0.2730.002700 0.727

0.002700 0.6250.001620 0.375

a b L MEP6 -42.006 42.00

3 5 8 -117.193 5 8 70.31

5 -41.675 41.67

5 5 10 -250.005 5 10 250.00

-333.33

0.727 0.625 0.375-41.67 41.67 -250.00 250.00

-125.00 -250.00-28.65 333.33

-20.833333 208.333333 125

20kg 3m 5m 20kg 5m 5m

100 kg 200 kg

2 Io 1.5 Io 2.5 Io 3 IoA B C D E

6m 8mK1 = 2EI/L K2 = 2EI/L K3= 2EI/L K4 = 2EI/L

5m 10m

Page 18: Examen de Analisis BRUNO

104.166667 -10.416667-68.663939394 6.5104166667 3.906253.2552083333 -34.331969697-2.8787878788 21.457481061 12.87448863610.72874053 -1.4393939394-9.488107989 0.8996212121 0.53977272730.4498106061 -4.7440539945-0.3977961433 2.9650337466 1.77902024791.4825168733 -0.1988980716-1.311084013 0.1243112948 0.07458677690.0621556474 -0.6555420065-0.0549681943 0.4097137541 0.24582825240.204856877 -0.0274840972-0.1811679727 0.0171775607 0.01030653640.0085887804 -0.0905839864-0.007595605 0.0566149915 0.03396899490.0283074957 -0.0037978025-0.0250341199 0.0023736266 0.00142417590.0011868133 -0.0125170599-0.0010495745 0.0078231625 0.00469389750.0039115812 -0.0005247873-0.003459 0.000328 0.0001970.000164 -0.001730-0.000145 0.001081 0.0006490.000541 -0.000073-0.000478 0.000045 0.0000270.000023 -0.000239-0.000020 0.000149 0.0000900.000075 -0.000010-0.000066 0.000006 0.0000040.000003 -0.000033-0.000003 0.000021 0.0000120.000010 -0.000001-0.000009 0.000001 0.000001-25.12 230.53 -230.53 0.00

L V6 27.006 27.00

8 68.368 31.64

5 50.005 50.00

Page 19: Examen de Analisis BRUNO

10 100.0010 100.00

205.41 -230.535 10

-41.081548693 41.081548693 2305.2868139 -23.05286813950.00 50.00 100.00 100.00

8.918451 91.081549 2405.286814 76.9471328.918451 -91.081549 2405.286814 -76.947132

25.054614 2496.368363 -76.947132

Page 20: Examen de Analisis BRUNO

5m

200 kg

3 IoE

10mK4 = 2EI/L


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