METODO ARBITRARIAMENTE ORIENTADO1.xlsx
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Transcript of METODO ARBITRARIAMENTE ORIENTADO1.xlsx
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PROBLEMA 1:
Resuelva por analisis matricial el siguiente portico.
DATOS:
SECCION (mm)
COLUMNA 300 400
VIGA 300 300
ELASTICIDAD 19 KN/mm2
SOLUCION:
PASO 1):
Sa!"#$%
Angulo = 0.93
20 1&'
'&00
! = "0 M1
1 = "0 M3
*1
*3
M1 #$1.%%&
M2 $1.%%&
*1 30+1 #$0
*2 30
+2 #$0
PASO 2):
ELEMENTO 1 , COLUMNA
A 0.1! m!
E 19000000 '(m!
I 0.001% m$
L ".00 m- $.0%*9 ra+
."# - #0.*0
%. - #0.%0
AE/L $"%000.00
EI/L %0*0.00
1!1%.00
!$3.!0
EI/L2
EI/L3
M
M
M
Y
Y
Y
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U1 V1 1 U2 V2
1%%0!&.&&% !1&$&9.1%* "*3%.*00 #1%%0!&.&&% #!1&$&9.1%*
!1&$&9.1%* !9!*90.%!$ #$3&&.%00 #!1&$&9.1%* #!9!*90.%!$
,-1#! = "*3%.*00 #$3&&.%00 !$3!0.000 #"*3%.*00 $3&&.%00
#1%%0!&.&&% #!1&$&9.1%* #"*3%.*00 1%%0!&.&&% !1&$&9.1%*
#!1&$&9.1%* #!9!*90.%!$ $3&&.%00 !1&$&9.1%* !9!*90.%!$"*3%.*00 #$3&&.%00 1!1%0.000 #"*3%.*00 $3&&.%00
PASO 3):
U1
100
=
#$0
/
&3%0!&.&&%
0 90 !1&$&9.1%*
0 3.333 "*3%.*00! #$0 #1%%0!&.&&%
! 30 #!1&$&9.1%*
! $1.%%& "*3%.*00
3 0 #"&0000.000
3 %0 0.000
3 #$" 0.000
atri2 inversa
1
=
&3%0!&.&&% !1&$&9.1%* "*3%.*00
41 !1&$&9.1%* !9*"90.%!$ $1&!.$00
51 "*3%.*00 $1&!.$00 $1$!0.000
!
=
#$0
/
#1%%0!&.&&%
! 30 #!1&$&9.1%*
! $1.%%& "*3%.*00
3 0 #"&0000.000
3 %0 0.000
3 #$" 0.000
[ ] [ ] [ ] [ ]*KFF F +=
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120
100
204
'&00
3 1&' 1&'
120
VECTOR UERA DE EMP&
1 = #$0
1 = 901&' 1 = 3.333
6 ! = #$0
,6= ! = 30
$" ! = $1.%%&
#$" 3 = 0
%0 3 = %0
%0 3 = #$"
ELEMENTO 1 , COLUMNA
A 0.09 m!
E 19000000 '(m!
I 0.000%&" m$
L 3.00 m- 0.0000 ra+
."# - 0.00
%. - 1.00
AE/L "&0000.00
EI/L $!&".00
1$!".00
$&".00
EI/L2
EI/L3
3
3
M3
Y3
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2 U1 V1 1
"*3%.*00 U1 "&0000.000 0.000 0.000
#$3&&.%00 V1 0.000 "&00.000 *""0.000
1!1%0.000 1 ,-1#3 = 0.000 *""0.000 1&100.000
#"*3%.*00 U2 #"&0000.000 0.000 0.000
$3&&.%00 V2 0.000 #"&00.000 #*""0.000!$3!0.000 2 0.000 *""0.000 *""0.000
V1 1 U2 V2 2 U3
!1&$&9.1%* "*3%.*00 #1%%0!&.&&% #!1&$&9.1%* "*3%.*00 #"&0000.000
!9*"90.%!$ $1&!.$00 #!1&$&9.1%* #!9!*90.%!$ #$3&&.%00 0.000
$1&!.$00 $1$!0.000 #"*3%.*00 $3&&.%00 1!1%0.000 0.000#!1&$&9.1%* #"*3%.*00 1%%0!&.&&% !1&$&9.1%* #"*3%.*00
#!9!*90.%!$ $3&&.%00 !1&$&9.1%* !9!*90.%!$ $3&&.%00
#$3&&.%00 1!1%0.000 #"*3%.*00 $3&&.%00 !$3!0.000
0.000 0.000 "&0000.000
#"&00.000 #*""0.000 0.000
*""0.000 *""0.000 0.000
1$0
=
0.0003"%!1"% m
#90 #0.000""9*!*" m
#3.333 #&.$!&9&7#00" ra+
#!1&$&9.1%* #"*3%.*00
0.0003"%!1"%
=
!3.0$
#!9!*90.%!$ $3&&.%00 #0.000""9*!*" 11%.1&
#$3&&.%00 1!1%0.000 #&.$!&9&7#00" $".!9
0.000 0.000 #!03.0$
#"&00.000 #*""0.000 %3.*3
*""0.000 *""0.000 #"0.$!
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VECTOR UERA E+TERNA VECTOR DESPLAAMIENTO
1 = 100 1 = 1
1 = 0 41 = 411 = 0 51 = 51
! = ! ! = 0
! = ! 4! = 0
! = ! 5! = 0
3 = 3 3 = 0
3 = 3 43 = 0
3 = 3 53 = 0
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U3 V3 3
#"&0000.000 0.000 0.000 U1
0.000 #"&00.000 *""0.000 V1
0.000 #*""0.000 *""0.000 1
"&0000.000 0.000 0.000 U3
0.000 "&00.000 #*""0.000 V30.000 #*""0.000 1&100.000 3
V3 3
0.000 0.000 U1
1
#"&00.000 *""0.000 V1 41
#*""0.000 *""0.000 1 51U2 0
V2 0
2 0
0.000 0.000 U3 0
"&00.000 #*""0.000 V3 0
#*""0.000 1&100.000 3 0
