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
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
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
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
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
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
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
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
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
-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
5m
200 kg
3 IoE
10mK4 = 2EI/L
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
-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
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
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
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
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
5m
200 kg
3 IoE
10mK4 = 2EI/L
Recommended