Calculo de Estructura de Tipo Cercha Por El Metodo Matricial
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Transcript of Calculo de Estructura de Tipo Cercha Por El Metodo Matricial
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SIN TOMAR E
DATOS :
E:
A:P.U. =
Barra
1
2
3
4
5
6
7
Barra 1
Dx1 Dy1 Dx2 Dy2
0.20! 0.44!432 "0.20! "0.44!432 Dx1
#1"2= 0.44!432 0.71!10112 "0.44!432 "0.71!10112Dy1
"0.20! "0.44!432 0.20! 0.44!432 Dx2
"0.44!432 "0.71!10112 0.44!432 0.71!10112 Dy2
Barra 2
Dx1 Dy1 Dx3 Dy3
1 0 "1 0 Dx1
#1"3= 0 0 0 0 Dy1
"1 0 1 0 Dx3
0 0 0 0 Dy3
Barra 3
Dx2 Dy2 Dx3 Dy3
0.20! "0.44!432 "0.20! 0.44!432 Dx2#2"3= "0.44!432 0.71!10112 0.44!432 "0.71!10112Dy2
"0.20! 0.44!432 0.20! "0.44!432 Dx3
0.44!432 "0.71!10112 "0.44!432 0.71!10112 Dy3
Barra 4
Dx2 Dy2 Dx4 Dy4
1 0 "1 0 Dx2
1 3
24
5
1
2
3
4
5
6
7
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#2"4= 0 0 0 0 Dy2
"1 0 1 0 Dx4
0 0 0 0 Dy4
Barra 5
Dx3 Dy3 Dx4 Dy40.20! 0.44!432 "0.20! "0.44!432 Dx3
#3"4= 0.44!432 0.71!10112 "0.44!432 "0.71!10112Dy3
"0.20! "0.44!432 0.20! 0.44!432 Dx4
"0.44!432 "0.71!10112 0.44!432 0.71!10112 Dy4
Barra 6
Dx3 Dy3 Dx5 Dy5
1 0 "1 0 Dx3
#3"5= 0 0 0 0 Dy3
"1 0 1 0 Dx50 0 0 0 Dy5
Barra 7
Dx4 Dy4 Dx5 Dy5
0.20! "0.44!432 "0.20! 0.44!432 Dx4
#4"5= "0.44!432 0.71!10112 0.44!432 "0.71!10112Dy4
"0.20! 0.44!432 0.20! "0.44!432 Dx5
0.44!432 "0.71!10112 "0.44!432 0.71!10112 Dy5
MATRI$ ENSAMBLADA
Dx1 Dy1 Dx2 Dy2 Dx3
476534.613 174!35.3 "10!334.613 "174!35.3 "367200
174!35.3 27!!6.60! "174!35.3 "27!!6.60! 0
"10!334.613 "174!35.3 556!.226 0 "10!334.613
"174!35.3 "27!!6.60! 0 55!7!3.217 174!35.3
#= "367200 0 "10!334.613 174!35.3 !5306!.226
0 0 174!35.3 "27!!6.60! 0
0 0 "367200 0 "10!334.613
0 0 0 0 "174!35.30 0 0 0 "367200
0 0 0 0 0
D%&%r'()a)&% 0.00
MATRI$ REDUCIDA
Dx2 Dy2 Dx4 Dy4
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556!.226 0 "367200 0 Dx2
#r%*= 0 55!7!3.217 0 0 Dy2
"367200 0 556!.226 0 Dx4
0 0 0 55!7!3.217 Dy4
MATRI$ REEDUCIDA IN+ERTIDA , DESPLA$AMIENTOS
Dx2 Dy2 Dx4 Dy4
2.1E"06 0.00E-00 1.76E"06 0.00E-00 Dx2
#r%* ()= 0.00E-00 1.7!E"06 0.00E-00 0.00E-00 Dy2
1.76E"06 0.00E-00 2.1E"06 0.00E-00 Dx4
0.00E-00 0.00E-00 0.00E-00 1.7!E"06 Dy4
%/%r/ %) arra/
.0!7E"006
1"2= 3!231.222 0.52!!!!4 0.47!!3 0 =
0
1"3= 367200 1 0 0 =
".10E"006
2"3= 3!231.222 0.52!!!!4 "0.47!!3 0 =
5.2462E"006
2"4= 367200 1 0 0 =
1.4056E"005
3"4= 3!231.222 0.52!!!!4 0.47!!3 0 =
0
3"5= 367200 1 0 0 =
"1.406E"005
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4"5= 3!231.222 0.52!!!!4 "0.47!!3 0 =
TOMANDO EN CUENTA EL PESO PROPIO CARA LIN. 0.7074!
BARRA 1 D1 D,1 D2 D,2
0.20! 0.44!432 "0.20! "0.44!432 D1
#1"2= 0.44!432 0.71!10112 "0.44!432 "0.71!10112D,1
"0.20! "0.44!432 0.20! 0.44!432 D2
"0.44!432 "0.71!10112 0.44!432 0.71!10112 D,2
BARRA 2
D1 D,1 D3 D,3
1 0 "1 0 D1
#1"3= 0 0 0 0 D,1
"1 0 1 0 D30 0 0 0 D,3
BARRA 3
D2 D,2 D3 D,3
0.20! "0.44!432 "0.20! 0.44!432 D2
#2"3= "0.44!432 0.71!10112 0.44!432 "0.71!10112D,2
"0.20! 0.44!432 0.20! "0.44!432 D3
0.44!432 "0.71!10112 "0.44!432 0.71!10112D,3
BARRA 4
D2 D,2 D4 D,4
1 0 "1 0 D2
#2"4= 0 0 0 0 D,2
"1 0 1 0 D4
0 0 0 0 D,4
BARRA 5
D3 D,3 D4 D,4
0.20! 0.44!432 "0.20! "0.44!432 D3
#3"4= 0.44!432 0.71!10112 "0.44!432 "0.71!10112D,3
"0.20! "0.44!432 0.20! 0.44!432 D4"0.44!432 "0.71!10112 0.44!432 0.71!10112 D,4
BARRA 6
D3 D,3 D5 D,5
1 0 "1 0 D3
#3"5= 0 0 0 0 D,3
"1 0 1 0 D5
0 0 0 0 D,5
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BARRA 7
D4 D,4 D5 D,5
0.20! "0.44!432 "0.20! 0.44!432 D4
#4"5= "0.44!432 0.71!10112 0.44!432 "0.71!10112D,4
"0.20! 0.44!432 0.20! "0.44!432 D5
0.44!432 "0.71!10112 "0.44!432 0.71!10112D,5MATRI$ ENSAMBLADA
D1 D,1 D2 D,2 D3
476534.613 174!35.3 "10!334.613 "174!35.3 "367200
174!35.3 27!!6.60! "174!35.3 "27!!6.60! 0
"10!334.613 "174!35.3 556!.226 0 "10!334.613
"174!35.3 "27!!6.60! 0 55!7!3.217 174!35.3
"367200 0 "10!334.613 174!35.3 !5306!.226
#= 0 0 174!35.3 "27!!6.60! 0
0 0 "367200 0 "10!334.613
0 0 0 0 "174!35.30 0 0 0 "367200
0 0 0 0 0
DETERM. 0.00
MATRI$ REDUCIDA
Dx2 Dy2 Dx4 Dy4
556!.226 0 "367200 0 Dx2
0 55!7!3.217 0 0 Dy2
# r%*8 "367200 0 556!.226 0 Dx4
0 0 0 55!7!3.217 Dy4
MATRI$ IN+ERTIDA
Dx2 Dy2 Dx4 Dy4
2.112E"006 0 1.761!E"006 0 Dx2
# () 0 1.764E"006 0 0 Dy2
1.761!E"006 0 2.112E"006 0 Dx4
0 0 0 1.764E"006 Dy4
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N CUENTA EL PESO PROPIO
20400000 T9M2
0.0! M27.61 T9'3
Nudos Nudo (i) Nudo (j)
Xi Yi Xj Yj L1"2 0 0 2.5 4 4.716!!057
1"3 0 0 5 0 5
2"3 2.5 4 5 0 4.716!!057
2"4 2.5 4 7.5 4 5
3"4 5 0 7.5 4 4.716!!057
3"5 5 0 10 0 5
4"5 7.5 4 10 0 4.716!!057
Dx1 Dy1 Dx2 Dy2
10!334.612 174!35.3 "10!334.612 "174!35.3
#1"2= 174!35.305 27!!6.60! "174!35.305 "27!!6.60!
"10!334.613 "174!35.3 10!334.6127! 174!35.3
"174!35.3 "27!!6.60! 174!35.3047 27!!6.60!
Dx1 Dy1 Dx3 Dy3
367200 0 "367200 0
#1"3= 0 0 0 0
"367200 0 367200 0
0 0 0 0
Dx2 Dy2 Dx3 Dy3
10!334.612 "174!35.3 "10!334.612 174!35.3#2"3= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!
"10!334.613 174!35.3 10!334.6127! "174!35.3
174!35.305 "27!!6.60! "174!35.305 27!!6.60!
Dx2 Dy2 Dx4 Dy4
367200 0 "367200 0
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#2"4= 0 0 0 0
"367200 0 367200 0
0 0 0 0
Dx3 Dy3 Dx4 Dy410!334.612 174!35.3 "10!334.612 "174!35.3
#3"4= 174!35.305 27!!6.60! "174!35.305 "27!!6.60!
"10!334.613 "174!35.3 10!334.6127! 174!35.3
"174!35.3 "27!!6.60! 174!35.3047 27!!6.60!
Dx3 Dy3 Dx5 Dy5
367200 0 "367200 0
#3"5= 0 0 0 0
"367200 0 367200 00 0 0 0
Dx4 Dy4 Dx5 Dy5
10!334.612 "174!35.3 "10!334.612 174!35.3
#4"5= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!
"10!334.613 174!35.3 10!334.6127! "174!35.3
174!35.305 "27!!6.60! "174!35.305 27!!6.60!
Dy3 Dx4 Dy4 Dx5 Dy5
0 0 0 0 0 Dx1
0 0 0 0 0 Dy1
174!35.3 "367200 0 0 0 Dx2
"27!!6.60! 0 0 0 0 Dy2
0 "10!334.613 "174!35.3 "367200 0 Dx3
55!7!3.217 "174!35.3 "27!!6.60! 0 0 Dy3
"174!35.3 556!.226 0 "10!334.613 174!35.3047 Dx4
"27!!6.60! 0 55!7!3.2175 174!35.3 "27!!6.607 Dy40 "10!334.613 174!35.305 476534.613 "174!35.305Dx5
0 174!35.3 "27!!6.60! "174!35.3 27!!6.6075 Dy5
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%ra/ D%/;
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"7.450E"006 = "2.!0 T COMPRESION
T9'
D1 D,1 D2 D,2
10!334.612 174!35.3 "10!334.612 "174!35.3
#1"2= 174!35.305 27!!6.60! "174!35.305 "27!!6.60!
"10!334.613 "174!35.3 10!334.6127! 174!35.3
"174!35.3 "27!!6.60! 174!35.3047 27!!6.60!
D1 D,1 D3 D,3
367200 0 "367200 0
#1"3= 0 0 0 0
"367200 0 367200 00 0 0 0
D2 D,2 D3 D,3
10!334.612 "174!35.3 "10!334.612 174!35.3
#2"3= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!
"10!334.613 174!35.3 10!334.6127! "174!35.3
174!35.305 "27!!6.60! "174!35.305 27!!6.60!
D2 D,2 D4 D,4
367200 0 "367200 0
#2"4= 0 0 0 0
"367200 0 367200 0
0 0 0 0
D3 D,3 D4 D,4
103146.0674 165033.70 "103146.0674 "165033.70
#3"4= 165033.707! 264053.!33 "165033.707! "264053.!33
"103146.067 "165033.70 103146.06742 165033.70"165033.70 "264053.!33 165033.7077 264053.!33
D3 D,3 D5 D,5
3!231.2215 0 "3!231.2215 0
#3"5= 0 0 0 0
"3!231.222 0 3!231.22154 0
0 0 0 0
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D4 D,4 D5 D,5
10!334.612 "174!35.3 "10!334.612 174!35.3
#4"5= "174!35.3 27!!6.60! 174!35.3047 "27!!6.60!
"10!334.613 174!35.3 10!334.6127! "174!35.3
174!35.305 "27!!6.60! "174!35.305 27!!6.60!
+E
D,3 D4 D,4 D5 D,5
0 0 0 0 0 D1
0 0 0 0 0 D,1
174!35.3 "367200 0 0 0 D2
"27!!6.60! 0 0 0 0 D,2
0 "10!334.613 "174!35.3 "367200 0 D3
55!7!3.217 "174!35.3 "27!!6.60! 0 0 D,3
"174!35.3 556!.226 0 "10!334.613 174!35.3047 D4
"27!!6.60! 0 55!7!3.2175 174!35.3 "27!!6.607 D,40 "10!334.613 174!35.305 476534.613 "174!35.305D5
0 174!35.3 "27!!6.60! "174!35.3 27!!6.6075 D,5
DE$PLA$AMIENTOS
"MEP D
0 Dx2 .0!7E"006 Dx2 '
"5.105!4! Dy2 "!.1211E"006 Dy2 '
5 Dx4 1.4056E"005 Dx4 '
"!.22!3! Dy4 "1.7547E"005 Dy4 '
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l mE A E*A/L os s!"
20400000 0.0! 3!231.221533 0.52!!!!4 0.47!!3
20400000 0.0! 367200 1 0
20400000 0.0! 3!231.221533 0.52!!!!4 "0.47!!3
20400000 0.0! 367200 1 0
20400000 0.0! 3!231.221533 0.52!!!!4 0.47!!3
20400000 0.0! 367200 1 0
20400000 0.0! 3!231.221533 0.52!!!!4 "0.47!!3
Dx1
Dy1
Dx2
Dy2
Dx1
Dy1
Dx3
Dy3
Dx2Dy2
Dx3
Dy3
Dx2
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Dy2
Dx4
Dy4
Dx3
Dy3
Dx4
Dy4
Dx3
Dy3
Dx5Dy5
Dx4
Dy4
Dx5
Dy5
%ra/ DESPLA$AMIENTOS REACCIONES
D =#D
0 Dx1 0 Dx1 "0.!6 T Dx1
0 Dy1 0 Dy1 "1.54 T Dy1
0 Dx2 .0!67E"006 Dx2 0.00 T Dx2
0 Dy2 0 Dy2 0.00 T Dy2
0 Dx3 0 Dx3 "2.50 T Dx3
0 Dy3 0 Dy3 "0.!2 T Dy3
5 Dx4 1.4055!7E"005 Dx4 5.00 T Dx4
0 Dy4 0 Dy4 0.00 T Dy40 Dx5 0 Dx5 "1.54 T Dx5
0 Dy5 0 Dy5 2.46 T Dy5
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EP D
D1 0.00 D1 0 D1 0
D,1 0.00 D,1 1.66612 D,1 0
D2 0.00 D2 0 D2 .0!7E"006
D,2 0.00 D,2 1.66612 D,2 "!.121E"006
EP D
D1 0.00 D1 0 D1 .0!7E"006
D,1 0.00 D,1 6.76725 D,1 "!.121E"006
D3 0.00 D3 0 D3 0D,3 0.00 D,3 6.76725 D,3 0
EP D
D2 0.00 D2 0 D2 .0!7E"006
D,2 0.00 D,2 1.66612 D,2 "!.121E"006
D3 0.00 D3 0 D3 0
D,3 0.00 D,3 1.66612 D,3 0
EP D
D2 0.00 D2 0 D2 .0!7E"006
D,2 0.00 D,2 1.76725 D,2 "!.121E"006
D4 5.00 D4 0 D4 1.4056E"005
D,4 0.00 D,4 1.76725 D,4 "1.755E"005
EP D
D3 5.00 D3 0 D3 0
D,3 0.00 D,3 6.35602 D,3 0
D4 0.00 D4 0 D4 1.4056E"005D,4 0.00 D,4 6.35602 D,4 "1.755E"005
EP D
D3 0.00 D3 0 D3 0
D,3 0.00 D,3 1.76725 D,3 0
D5 0.00 D5 0 D5 0
D,5 0.00 D,5 1.76725 D,5 0
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EP D
D4 0.00 D4 0 D4 1.4056E"005
D,4 0.00 D,4 1.66612 D,4 "1.755E"005
D5 0.00 D5 0 D5 0
D,5 0.00 D,5 1.66612 D,5 0
CTOR UER$AS EMPOTRAMIENTO PERECTO
MEP "MEP
0 D1 0 D1 0 D1
0 D,1 .44 D,1 ".437337 D,1
0 D2 0 D2 0 D2
0 D,2 5.105!4! D,2 "5.105!4! D,2
0 D3 0 D3 0 D3
0 D,3 16.5!1664 D,3 "16.5!1664 D,3
5 D4 0 D4 5 D4
0 D,4 !.22!3! D,4 "!.22!3! D,40 D5 0 D5 0 D5
0 D,5 3.437337 D,5 "3.437337 D,5
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#D =#D-MEP
D1 0.63 D1 0.63 T D1
D,1 1.01 D,1 2.6 T D,1
D2 "0.63 D2 "0.63 T D2
D,2 "1.01 D,2 0.66 T D,2
#D =#D-MEP
D1 3.23 D1 3.23 T D1
D,1 0.00 D,1 6.77 T D,1
D3 "3.23 D3 "3.23 T D3D,3 0.00 D,3 6.77 T D,3
#D =#D-MEP
D2 2.56 D2 2.56 T D2
D,2 "4.0! D,2 "2.43 T D,2
D3 "2.56 D3 "2.56 T D3
D,3 4.0! D,3 5.76 T D,3
#D =#D-MEP
D2 "1.!3 D2 "1.!3 T D2
D,2 0.00 D,2 1.77 T D,2
D4 1.!3 D4 1.!3 T D4
D,4 0.00 D,4 1.77 T D,4
#D =#D-MEP
D3 1.45 D3 1.45 T D3
D,3 2.31 D,3 .70 T D,3
D4 "1.45 D4 "1.45 T D4D,4 "2.31 D,4 4.07 T D,4
#D =#D-MEP
D3 0.00 D3 0.00 T D3
D,3 0.00 D,3 1.77 T D,3
D5 0.00 D5 0.00 T D5
D,5 0.00 D,5 1.77 T D,5
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#D =#D-MEP
D4 4.61 D4 4.61 T D4
D,4 "7.37 D,4 "5.70 T D,4
D5 "4.61 D5 "4.61 T D5
D,5 7.37 D,5 !.04 T D,5
DE$PLA$AMIENTOS REACCIONES
D #D =#D-MEP
0 D1 0.63240516 D1 0.632 D1
0 D,1 1.011425 D,1 !.44! D,1
.0!7E"006 D2 0 D2 0.000 D2
"!.1211E"006 D,2 "5.105!4! D,2 0.000 D,2
0 D3 "1.025!4063 D3 "1.026 D3
0 D,3 6.5466!65 D,3 23.13 D,3
1.4056E"005 D4 5 D4 5.000 D4
"1.7547E"005 D,4 "!.22!3! D,4 0.000 D,40 D5 "4.60646453 D5 "4.606 D5
0 D,5 7.37034325 D,5 10.0 D,5
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T
T
T
T
T
T
T
TT
T