Ejercico de Armadura 1

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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35/40


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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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Ejercico de Armadura 1