Matriz
10
BARRA Nº 1 E= 2.10E+07 Tn/m2 #Nudo A= 0.06 m2 Izquierdo 1 I= 0.00045 m4 Derecho 2 L= 6 cm α= 0º EA/L = 210000 1575 525 4EI/L = 6300 1 2 3 4 1 210000 0 0 -210000 2 0 525 1575 0 3 0 1575 6300 0 4 -210000 0 0 210000 5 0 -525 -1575 0 6 0 1575 3150 0 1 2 3 4 {G} 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 210000 0 0 -210000 0 525 1575 0 0 1575 6300 0 -210000 0 0 210000 0 -525 -1575 0 0 1575 3150 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 6EI/L 2 = 12EI/L 3 = {K L } {G} X {K L } {G T }
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Transcript of Matriz
BARRA Nº 1E= 2.10E+07Tn/m2 #Nudo
A= 0.06m2 Izquierdo 1
I= 0.00045m4 Derecho 2
L= 6cm
α= 0º
EA/L = 210000 1575
525 4EI/L = 6300
1 2 3 4
1 210000 0 0 -210000
2 0 525 1575 0
3 0 1575 6300 0
4 -210000 0 0 210000
5 0 -525 -1575 0
6 0 1575 3150 01 2 3 4
{G}
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
210000 0 0 -210000
0 525 1575 0
0 1575 6300 0
-210000 0 0 210000
0 -525 -1575 0
0 1575 3150 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
6EI/L2 =
12EI/L3 =
{KL}
{G} X {KL}
{GT}
{KG} = {G} X {KL} X {GT} - BARRA Nº11 2 3 4
1 210000 0 0 -210000
2 0 525 1575 0
3 0 1575 6300 0
4 -210000 0 0 210000
5 0 -525 -1575 0
6 0 1575 3150 01 2 3 4
BARRA Nº11 0
2 -2.5
3 2.08
4 0
5 -2.5
6 -2.08
1 0
2 0
3 0
4 0.0005079365
5 Err:509
6 Err:509
1 Err:509
2 Err:509
3 Err:509
4 Err:509
5 Err:509 BARRA Nº16 Err:509
Fuerzas Locales [PL]
[PG] = [L] X [PL] ==>
Des.Global { DG }
[DL] = [LT] X [DG] ==>
Fza.Local { FL } = { KL } X { DL }
Fza Local Fin { F } = { FL } - { PL }
BARRA NºX (cm) Y (cm) E= 2.10E+07Tn/m2
0 0 A= 0.06m2
6 0 I= 0.00045m4
6 0 L= 4cm
0 α= 0º
2EI/L = 3150 EA/L = 315000
1771.875
5 6 4 5
0 0 1 4 315000 0
-525 1575 2 5 0 1771.875
-1575 3150 3 6 0 3543.75
0 0 4 7 -315000 0
525 -1575 5 8 0 -1771.875
-1575 6300 6 9 0 3543.755 6 4 5
{G} {G}
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 315000 0
-525 1575 0 1771.875
-1575 3150 0 3543.75
0 0 -315000 0
525 -1575 0 -1771.875
-1575 6300 0 3543.75
0 0 1 0
0 0 0 1
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
12EI/L3 =
{KL}
{G} X {KL}
{LT}
{KG} = {G} X {KL} X {GT} - BARRA Nº1 {KG} = {L} X {KL} X {LT} - BARRA Nº25 6 4 5
0 0 1 4 315000 0
-525 1575 2 5 0 1771.875
-1575 3150 3 6 0 3543.75
0 0 4 7 -315000 0
525 -1575 5 8 0 -1771.875
-1575 6300 6 9 0 3543.755 6 4 5
BARRA Nº20 1 4 0
-2.5 2 5 10
2.08 3 6 10
0 4 7 0
-2.5 5 8 10
-2.08 6 9 -10
Err:509 1 4 0
Err:509 2 5 0
Err:509 3 6 0
Err:509 4 7 0
Err:509 5 8 Err:509
Err:509 6 9 Err:509
Fuerzas Local FinErr:509 Kgf 1 4 Err:509
Err:509 Kgf 2 5 Err:509
Err:509 Kgf 3 6 Err:509
Kgf 4 7 Err:509
Err:509 Kgf 5 8 Err:509 BARRA Nº2Err:509 Kgf 6 9 Err:509
Fuerzas Globales [PG] Fuerzas Locales [PL]
L] ==> [PG] = [L] X [PL] ==>
Des.Local { DL } Des.Global { DG }
G] ==> [DL] = [LT] X [DG] ==>
Fza.Local { FL } = { KL } X { DL }
Fza Local Fin { F } = { FL } - { PL }
2#Nudo X (cm) Y (cm)
Izquierdo 2 6 0
Derecho 3 10 0
4 0
0
3543.75 2EI/L = 4725
4EI/L = 9450
6 7 8 9
0 -315000 0 0 4
3543.75 0 -1771.875 3543.75 5
9450 0 -3543.75 4725 6
0 315000 0 0 7
-3543.75 0 1771.875 -3543.75 8
4725 0 -3543.75 9450 9
6 7 8 9
{G}
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 -315000 0 0
3543.75 0 -1771.875 3543.75
9450 0 -3543.75 4725
0 315000 0 0
-3543.75 0 1771.875 -3543.75
4725 0 -3543.75 9450
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
6EI/L2 =
{KL}
{G} X {KL}
{LT}
{KG} = {L} X {KL} X {LT} - BARRA Nº26 7 8 9
0 -315000 0 0 4
3543.75 0 -1771.875 3543.75 5
9450 0 -3543.75 4725 6
0 315000 0 0 7
-3543.75 0 1771.875 -3543.75 8
4725 0 -3543.75 9450 9
6 7 8 9
BARRA Nº2 0 4
10 5
10 6
0 7
10 8
-10 9
Err:509 4
Err:509 5
Err:509 6
Err:509 7
Err:509 8
Err:509 9
Fuerzas Local FinErr:509 Kgf 4
Err:509 Kgf 5
Err:509 Kgf 6
Kgf 7
BARRA Nº2 Err:509 Kgf 8
Err:509 Kgf 9
Fuerzas Globales [PG]
[PG] = [L] X [PL] ==>
Des.Local { DL }
[DL] = [LT] X [DG] ==>
Fza Local Fin { F } = { FL } - { PL }
Matriz Ensamblada Reducida[1] [2] [3] [6]
[1] 77150.6208 28142.7603 158.481318 158.481318[2] 28142.7603 56421.4612 62.509341 -79.240659[3] 158.481318 62.509341 1000.77106 264.13553[6] 158.481318 -79.240659 264.13553 528.27106
Matriz Inversa[1] [2] [3] [6]
[1] 1.5863E-005 -0.00000792 -5.159E-007 -5.689E-006[2] -0.00000792 2.1685E-005 -1.827E-006 6.5423E-006[3] -5.159E-007 -1.827E-006 0.0011514 -0.00057582[6] -5.689E-006 6.5423E-006 -0.00057582 0.00218357
MATRIZ GLOBAL DE FUERZASNudo Exteriores
[1] 0 [1] 0[2] -10 [2] -10[3] 0 [3] 0[4] 0 [6] 0[5] 0[6] 0[7] 0[8] 0[9] 0
MATRIZ ENSAMBLADA GLOBAL (sin restricciones)6
6 15750
MATRIZ INVERSA (sin restricciones)6
6 6.349206E-005
6 8
DESPLAZAMIENTOS GLOBALES6 0.0005079365
+EA/L 0 0 -EA/L 0 0
0 0
0 +6/(EIL2) +4/(EIL) 0 +2/(EIL)L
-EA/L 0 0 +EA/L 0 00 -12/(EIL3) -6/(EIL2) 0 +12/(EIL3) -6/(EIL2)0 +6/(EIL2) +2/(EIL) 0 -6/(EIL2) +4/(EIL)
+12/(EIL3) +6/(EIL2) -12/(EIL3) +6/(EIL2)
KL
-6/(EIL2)
KG = L · KL · LT
LT
Cos -Sen 0 0 0 0
Sen Cos 0 0 0 0
0 0 1 0 0 0
0 0 0 Cos -Sen 00 0 0 Sen Cos 00 0 0 0 0 1
Cos Sen 0 0 0 0-Sen Cos 0 0 0 0
0 0 1 0 0 00 0 0 Cos Sen 00 0 0 -Sen Cos 00 0 0 0 0 1
