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7/26/2019 Ejercico de Armadura 1
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[ ]'
EA EA
L LkEA EA
L L
=
[ ]T =
[ ] ['k =
[
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0 0
0 0
os Sen
Cos Sen
] [ ] [ ]'T
T k T [ ] [ ] [ ]'u T u=
1] [ ] [ ]K F
= [F'] [k'][u']=
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RESOLVER LA ARMADURA
A=7.5cm2
E=200tn/cm2
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Solucin
1. ENUMERACIN DE LAS DEFORMACIONES
Def 1 2 3 4 5
ux 0 4 7 10 13uy 0 5 8 11 0
! 0 0 0 0 0
2. VECTOR DEFORMACIN DEL SISTEMA
u2x 4
u2y 5
u3x 7
"U# = u3y 8
u4x 10u4y 11
u5x 13
u$x 1$
u$y 17
3. VECTOR FUERZAS DE NUDOS COORDENADAS GLOBALES
00
2
"%# = 0
0
&2
0
0
&3
2. MATRICES DE RIGIDECES LOCALES
BARRA 1
A= 7.5 cm2
E= 200 'n/cm2 "()1# = 4.1$025147 &4.1$025147
L= 3$0.555128 cm2 &4.1$025147 4.1$025147
*= 0.588002$ +,-
u-
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De 1 , 2
"'1# = 0.8320502 0.5547002
0 0
0.8320502 0
"(1# = 0.5547002 00 0.8320502
0 0.5547002
BARRA 2
A= 7.5 cm2
E= 200 'n/cm2 "()1# = 5 &5
L= 300 cm2 &5 5
*= 0 +,-
De 2 , 3
"'1# = 1 0
0 0
1 0
"(1# = 0 0
0 1
0 0
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BARRA 3
A= 7.5 cm2
E= 200 'n/cm2 "()1# = 4.1$025147 &4.1$025147
L= 3$0.555128 cm2 &4.1$025147 4.1$025147
*= &0.588002$ +,-
De 3 , 4
"'1# = 0.8320502 &0.55470020 0
0.8320502 0
"(1# = &0.5547002 0
0 0.8320502
0 &0.5547002
BARRA 4
A= 7.5 cm2
E= 200 'n/cm2 "()1# = 5 &5
L= 300 cm2 &5 5
*= 0 +,-
De 1 , $
"'1# = 1 0
0 0
1 0
"(1# = 0 0
0 1
0 0
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BARRA 5A= 7.5 cm2
E= 200 'n/cm2 "()1# = 5 &5
L= 300 cm2 &5 5
*= 0 +,-
De $ , 5
"'1# = 1 0
0 0
1 0"(1# = 0 0
0 1
0 0
BARRA 6
A= 7.5 cm2
E= 200 'n/cm2 "()1# = 5 &5
L= 300 cm2 &5 5
*= 0 +,-
De 5 , 4
"'1# = 1 0
0 0
1 0
"(1# = 0 0
0 1
0 0
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BARRA 7
A= 7.5 cm2
E= 200 'n/cm2 "()1# = 7.5 &7.5
L= 200 cm2 &7.5 7.5
*= 1.5707$33 +,-
De $ , 2
"'1# = 0 10 0
0 0
"(1# = 1 0
0 0
0 1
BARRA 8
A= 7.5 cm2
E= 200 'n/cm2 "()1# = 4.1$025147 &4.1$025147
L= 3$0.555128 cm2 &4.1$025147 4.1$025147
*= 0.588002$ +,-
De $ , 3
"'1# = 0.8320502 0.5547002
0 0
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0.8320502 0
"(1# = 0.5547002 0
0 0.8320502
0 0.5547002
BARRA 9
A= 7.5 cm2E= 200 'n/cm2 "()1# = 7.5 &7.5
L= 200 cm2 &7.5 7.5
*= 1.5707$33 +,-
De 5 , 3
"'1# = 0 1
0 0
0 0
"(1# = 1 0
0 0
0 1
3. MATRIZ DEL SISTEMA EN COORDENADAS GLOBALES
4 5 7 8 10
7.8801741 1.2011$0$ &5 0 0
1.2011$0$ 8.78007738 0 0 0
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&5 0 10.7$03482 0 &2.8801741
"# = 0 0 0 10.0$01548 1.2011$0$
0 0 &2.8801741 1.2011$0$ 7.8801741
0 0 1.2011$0$ &1.28007738 &1.2011$0$
0 0 0 0 &5
0 0 &2.8801741 &1.2011$0$ 0
0 &7.5 &1.2011$0$ &1.28007738 0
3. DESPLAZAMIENTOS GLOBALES
0.30323025 &0.1444444 0.20323025 &0.04444444 0.1
&0.1444444 0.$822$805 &0.04444444 0.0$$$$$$7 &0.15
0.20323025 &0.04444444 0.30323025 &0.04444444 0.1
"U# = &0.04444444 0.0$$$$$$7 &0.04444444 0.13333333 &5.74E&017
0.1 &0.15 0.1 &2.170E&018 0.$
&0.12881 &0.01$$$$7 &0.342881 0.2 0.75
0.1 &0.15 0.1 1.1$$3E&018 0.4
0.1 &0.15 0.1 4.$358E&018 0.2
&0.15 0.$15$013 5.$810E&017 0.0$$$$$$7 &0.15
1.25504012 4
&1.7523572 5
1.30504012 7
"U# = &0.$888888 8
&0.85 10
&5.483854$2 11
&0.25 13
0.35 1$
&1.7301375 17
3. PROCESO DE RETORNO
BARRA DEFORMACIONES L
1 "u)1# = 0.8320502 0.5547002 0
1[ ] [ ] [ ]U K F=
[ ] [ ] ['u T=
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0 0 0.8320502
2 "u)2# = 1 0 0
0 0 1
3 "u)3# = 0.8320502 &0.5547002 0
0 0 0.8320502
4 "u)4# = 1 0 0
0 0 1
5 "u)5# = 1 0 0
0 0 1
$ "u)$# = 1 0 0
0 0 1
7 "u)7# = 0 1 0
0 0 0
8 "u)8# = 0.8320502 0.5547002 0
0 0 0.8320502
"u)# = 0 1 0
0 0 0
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3. REACCIONES EN LOS APOOS
R1x = 0.30043/460.51.75 R1y =
R1x = 1.843074 R1y =
!.3
1.75
1.89
!.12
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$
1$17
0
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0 0
0.8320502 0.5547002
x 4.1$025147 &4.1$025147 x 0.8320502 0.5547002&4.1$025147 4.1$025147 0 0
3.4$15384$ &3.4$15384$ x 0.8320502 0.5547002 0
2.307$231 &2.307$231 0 0 0.8320502
&3.4$15384$ 3.4$15384$
&2.307$231 2.307$231
0 0
2.8801741 1.2011$0$
"(1# = 1.2011$0$ 1.28007738&2.8801741 &1.2011$0$
&1.2011$0$ &1.28007738
0 0
1 0
x 5 &5 x 1 0
&5 5 0 0
5 &5 x 1 0 0
0 0 0 0 1
&5 5
0 0
4 5
5 0
"(2# = 0 0
&5 0
0 0
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0 00.8320502 &0.5547002
x 4.1$025147 &4.1$025147 x 0.8320502 &0.5547002
&4.1$025147 4.1$025147 0 0
3.4$15384$ &3.4$15384$ x 0.8320502 &0.5547002 0
&2.307$231 2.307$231 0 0 0.8320502&3.4$15384$ 3.4$15384$
2.307$231 &2.307$231
7 8
2.8801741 &1.2011$0$
"(3# = &1.2011$0$ 1.28007738
&2.8801741 1.2011$0$
1.2011$0$ &1.28007738
0 0
1 0
x 5 &5 x 1 0
&5 5 0 0
5 &5 x 1 0 0
0 0 0 0 1
&5 5
0 0
0 0
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5 0
"(4# = 0 0
&5 0
0 0
0 0
1 0
x 5 &5 x 1 0
&5 5 0 0
5 &5 x 1 0 0
0 0 0 0 1
&5 5
0 0
1$ 17
5 0
"(5# = 0 0
&5 0
0 0
0 0
1 0
x 5 &5 x 1 0
&5 5 0 0
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5 &5 x 1 0 0
0 0 0 0 1
&5 5
0 0
13 0
5 0
"($# = 0 0&5 0
0 0
0 00 1
x 7.5 &7.5 x 0 1
&7.5 7.5 0 0
0 0 x 0 1 0
7.5 &7.5 0 0 0
0 0
&7.5 7.5
1$ 17
0 0
"(7# = 0 7.5
0 0
0 &7.5
0 0
0.8320502 0.5547002
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x 4.1$025147 &4.1$025147 x 0.8320502 0.5547002
&4.1$025147 4.1$025147 0 0
3.4$15384$ &3.4$15384$ x 0.8320502 0.5547002 0
2.307$231 &2.307$231 0 0 0.8320502&3.4$15384$ 3.4$15384$
&2.307$231 2.307$231
1$ 17
2.8801741 1.2011$0$
"(8# = 1.2011$0$ 1.28007738
&2.8801741 &1.2011$0$
&1.2011$0$ &1.28007738
0 0
0 1
x 7.5 &7.5 x 0 1
&7.5 7.5 0 0
0 0 x 0 1 0
7.5 &7.5 0 0 0
0 0
&7.5 7.5
13 0
"(1# = 0 0
0 7.5
0 0
0 &7.5
11 13 1$ 17
0 0 0 0 4
0 0 0 &7.5 5
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1.2011$0$ 0 &2.8801741 &1.2011$0$ 7
&1.28007738 0 &1.2011$0$ &1.28007738 8
&1.2011$0$ &5 0 0 10
1.28007738 0 0 0 11
0 10 &5 0 13
0 &5 12.8801741 1.2011$0$ 1$
0 0 1.2011$0$ 8.78007738 17
&0.12881 0.1 0.1 &0.15 0
&0.01$$$$7 &0.15 &0.15 0.$15$013 0
&0.342881 0.1 0.1 &1.48E&017 2
0.2 &1.37E&017 &8.277E&018 0.0$$$$$$7 0
0.75 0.4 0.2 &0.15 0
2.$301375 0.45 0.15 &0.15833333 &2
0.45 0.4 0.2 &0.15 0
0.15 0.2 0.2 &0.15 0
&0.15833333 &0.15 &0.15 0.$822$805 &3
CALES
0
0 x 0 = 0
]
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0.5547002 1.25504012 0.07222222
&1.7523572
1.25504012
0 x &1.7523572 = 1.25504012
0 1.30504012 1.30504012
&0.$888888
1.30504012
0 x &0.$888888 = 1.4$78582
&0.5547002 &0.85 2.334$524
&5.483854$2
0
0 x 0 = 0
0 0.35 0.35
&1.7301375
0.35
0 x &1.7301375 = 0.35
0 &0.25 &0.25
0
&0.25
0 x 0 = &0.25
0 &0.85 &0.85
&5.483854$2
0.35
0 x &1.7301375 = &1.7301375
1 1.25504012 &1.7523572
&1.7523572
0.35
0 x &1.7301375 = &0.$$84001
0.5547002 1.30504012 0.70373222
&0.$888888
&0.25
0 x 0 = 0
1 1.30504012 &0.$888888
&0.$888888
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0.32/460.5
0.117$$$8
5.17
33
5.17
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0 00.8320502 0.5547002
0
0.5547002
4 5
&2.8801741 &1.2011$0$ 0
&1.2011$0$ &1.28007738 02.8801741 1.2011$0$ 4
1.2011$0$ 1.28007738 5
0 0
1 0
0
0
7 8
&5 0 4
0 0 5
5 0 7
0 0 8
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0 0
0.8320502 &0.5547002
0
&0.5547002
10 11
&2.8801741 1.2011$0$ 7
1.2011$0$ &1.28007738 8
2.8801741 &1.2011$0$ 10
&1.2011$0$ 1.28007738 11
0 0
1 0
0
0
1$ 17
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&5 0 0
0 0 0
5 0 1$
0 0 17
0 0
1 0
0
0
13 0
&5 0 1$
0 0 17
5 0 13
0 0 0
0 0
1 0
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0
0
10 11
&5 0 13
0 0 05 0 10
0 0 11
0 0
0 1
0
1
4 5
0 0 1$
0 &7.5 17
0 0 4
0 7.5 5
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0 0
0.8320502 0.5547002
0
0.5547002
7 8
&2.8801741 &1.2011$0$ 1$
&1.2011$0$ &1.28007738 17
2.8801741 1.2011$0$ 7
1.2011$0$ 1.28007738 8
0 0
0 1
0
1
7 8
0 0 13
0 &7.5 0
0 0 7
0 7.5 8
4 5
7 8
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ESFUERZOS LOCALES
"%)1# = 4.1$025147 &4.1$025147 x 0
13 01$ 17
[F'1] [k'1][u'1]=
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&4.1$025147 4.1$025147 0.07222222
"%)2# = 5 &5 x 1.25504012
&5 5 1.30504012
"%)3# = 4.1$025147 &4.1$025147 x 1.4$78582
&4.1$025147 4.1$025147 2.334$524
"%)4# = 5 &5 x 0
&5 5 0.35
"%)5# = 5 &5 x 0.35
&5 5 &0.25
"%)$# = 5 &5 x &0.25
&5 5 &0.85
"%)7# = 7.5 &7.5 x &1.7301375
&7.5 7.5 &1.7523572
"%)8# = 4.1$025147 &4.1$025147 x &0.$$84001
&4.1$025147 4.1$025147 0.70373222
"%)# = 7.5 &7.5 x 0
&7.5 7.5 &0.$888888
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= &0.3004$2$1
10 11
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0.3004$2$1
= &0.25
0.25
= &3.$0555128
3.$0555128
= &1.75
1.75
= 3
&3
= 3
&3
= 0.1$$$$$$7
&0.1$$$$$$7
= &5.7087852
5.7087852
= 5.1$$$$$$7
&5.1$$$$$$7
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