METODO DE FLEXIBILIDADES PARA ARMADURAS 6 4 6 8 8 8 8 8 PRIMER ESTADO CONSIDERANDO FUERZAS 6 4 " F " FUERZAS UNITARIAS EN DIRECCION 1 " U1 " r1 = 1 " U1 " FUERZAS UNITARIAS EN DIRECCION 2 " U2" r2=1 r2=1 1 2 3 4 9 8 7 10 6 5 11 14 15 16 12 13 18 17
Nov 11, 2014
METODO DE FLEXIBILIDADES PARA ARMADURAS
6
4
6
8 8 8 8 8
PRIMER ESTADO CONSIDERANDO FUERZAS6
4
" F "
FUERZAS UNITARIAS EN DIRECCION 1 " U1 "
r1 = 1
" U1 "
FUERZAS UNITARIAS EN DIRECCION 2 " U2"
r2=1
r2=1
1
2 3 4
9 8 710
6
511 1
4
15 1612 13
18
17
BARRA E A L F U1 U2
1 2.10E+07 1 5.00 14 1
2 2.10E+07 1 5.00 14 -0.7071 1
3 2.10E+07 1 5.00 12 1
4 2.10E+07 1 7.07 -16.9706
5 2.10E+07 1 5.00 -12 -0.7071
6 2.10E+07 1 7.07 -11.3137
7 2.10E+07 1 5.00 -0.7071
8 2.10E+07 1 7.07 1 9 2.10E+07 1 7.07 -2.8284 1
10 2.10E+07 1 5.00 2 -0.7071
11 2.10E+07 112 2.10E+07 1 6 1 1 113 2.10E+07 114 2.10E+07 115 2.10E+07 116 2.10E+07 117 2.10E+07 118 2.10E+07 1
-1.3399E-06 1.4352E-06
9.8095E-06 0.000001
1.1736E-07
-1
{ R } = -1.4352E-06 1.1736E-07
*1.1736E-07 0.000001
{ R } = -703503.883 82561.205782561.2057 -1009689.15
{ R } = 1.75254
-10.0151970
" U2 "
∑total=
ΔL1 = F11 =
ΔL2 = F22 =
F12 =
{ R } =- [ F ]-1 * { ΔL }
R1
R2
METODO DE FLEXIBILIDADES PARA ARMADURAS
Grado de indeterminacion :
m = 18r = 4n = 10
ECUACIONES ESTATICAS = 3Redundandes a eliminar EN TOTAL : 2
Redundandes a eliminar EXTERNO : 1
Redundandes a eliminar INTERNO : 1
(F*U1*L)/(E*A) (F*U2*L)/(E*A) (U1^2*L)/(E*A) (U2^2*L)/(E*A) (U1*U2*L)/(E*A)
0 3.333333333E-06 0 2.380952381E-07 0-0.000002357 3.333333333E-06 1.190453357E-07 2.380952381E-07 -1.68357143E-07
0 2.857142857E-06 0 2.380952381E-07 00 0 0 0 0
2.020285714E-06 0 1.190453357E-07 0 00 0 0 0 00 0 1.190453357E-07 0 00 0 3.366666667E-07 0 0
-0.000000952228 0 3.366666667E-07 0 0-3.36714286E-07 0 1.190453357E-07 0 0
0 0 0 0 02.857142857E-07 2.857142857E-07 2.857142857E-07 2.857142857E-07 2.857142857E-07
0 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0
-1.33994229E-06 9.80952381E-06 1.435228962E-06 0.000001 1.173571429E-07
0.7071067811865
-1.33994229E-069.80952381E-06
-1.33994229E-069.80952381E-06
ΔL1 = ΔL2 = F11 = F22 = F12 =
METODO DE FLEXIBILIDADES PARA ARMADURAS
6
4
6
ECUACIONES ESTATICAS =
8 8 8 8 8
PRIMER ESTADO CONSIDERANDO FUERZAS6
4
" F "
FUERZAS UNITARIAS EN DIRECCION 1 " U1 "
r1=1
" U1 "
FUERZAS UNITARIAS EN DIRECCION 2 " U2"
r2=1
r2=1
" U2 "
1
2 3 4
9 8 710
6
511 1
4
15 1612 13
18
17
19
BARRA E A L F U1 U2
1 1 1 10 -1 0 02 1 1 8 -4.8 0 03 1 1 8 -5.6 0 -0.84 1 1 8 -6.4 0 05 1 1 10 -9 0 06 1 1 8 7.2 1 17 1 1 8 7.2 1 18 1 1 8 6.4 1 0.29 1 1 8 5.6 1 1
10 1 1 8 4.8 1 111 1 1 6 0.6 0 012 1 1 6 0.6 0 -0.613 1 1 6 0.6 0 -0.614 1 1 6 0 0 015 1 1 10 -1 0 016 1 1 10 -1 0 017 1 1 10 -1 0 018 1 1 10 0 0 019 1 1 8
249.6 40
240.16 41.76
38.04 12.06
33.6
10.4
5.56
FUERZAS UNITARIAS EN DIRECCION 3 " U3"
r3=1 r3=1
" U3 "
ΔL1 = F11 =
ΔL2 = F22 =
ΔL3 = F33 =
F12 =
F13 =
F23 =
{ R } =- [ F ]-1 * { ΔL }
{ R } = -40 33.6 10.4
33.6 41.76 5.5610.4 5.56 12.06
{ R } = -0.101392 0.074512 0.0530840.074512 -0.080271 -0.0272490.053084 -0.027249 -0.116133
{ R } =
-5.39330
-1.71614
2.28789
R1
R2
R3
METODO DE FLEXIBILIDADES PARA ARMADURAS
Grado de indeterminacion :
m = 19r = 4n = 10
ECUACIONES ESTATICAS = 3Redundandes a eliminar EN TOTAL : 3
Redundandes a eliminar EXTERNO : 1
Redundandes a eliminar INTERNO : 2
U3
0 0 0 0 0 0 00.2 0 0 -7.68 0 0 0.320.6 0 35.84 -26.88 0 5.12 2.880 0 0 0 0 0 00 0 0 0 0 0 01 57.6 57.6 57.6 8 8 8
0.2 57.6 57.6 11.52 8 8 0.320.1 51.2 10.24 5.12 8 0.32 0.080 44.8 44.8 0 8 8 00 38.4 38.4 0 8 8 00 0 0 0 0 0 00 0 -2.16 0 0 2.16 0
0.1 0 -2.16 0.36 0 2.16 0.060 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0
0.2 0 0 -2 0 0 0.40 0 0 0 0 0 00
249.6 240.16 38.04 40 41.76 12.06
(F*U1*L) / (E*A)
(F*U2*L) / (E*A)
(F*U3*L) / (E*A)
(U1^2*L) / (E*A)
(U2^2*L) / (E*A)
(U3^2*L) / (E*A)
∑total=
249.6* 240.16
38.04
249.6* 240.16
38.04
0 0 00 0 00 0 -3.840 0 00 0 08 8 88 1.6 1.6
1.6 0.8 0.168 0 08 0 00 0 00 0 00 0 -0.360 0 00 0 00 0 00 0 00 0 00 0 0
33.6 10.4 5.56
(U1*U2*L) / (E*A)
(U1*U3*L) / (E*A)
(U2*U3*L) / (E*A)
METODO DE FLEXIBILIDADES PARA ARMADURAS
62
1
3
ECUACIONES ESTATICAS =
4 4 4 4 4
PRIMER ESTADO CONSIDERANDO FUERZAS
2 61
" F "
FUERZAS UNITARIAS EN DIRECCION 1 " U1 "
r1=1
" U1 "
FUERZAS UNITARIAS EN DIRECCION 2 " U2"
r2=1
r2=1
" U2 "
1
2 3 4
9 8 710
6
511 1
4
15
16
12 1318
17
19
r3=1
r3=1
BARRA E A L F U1 U2
1 1 1 5 -4.4167 0 02 1 1 4 -4.5333 0 03 1 1 4 -5.4 0 -0.84 1 1 4 -6.2667 0 05 1 1 5 -8.9167 0 06 1 1 4 7.1333 1 07 1 1 4 7.1333 1 08 1 1 4 6.2667 1 -0.89 1 1 4 5.4 1 0
10 1 1 4 4.5333 1 011 1 1 3 0.65 0 012 1 1 3 0.65 0 -0.613 1 1 3 0.65 0 -0.614 1 1 3 0 0 015 1 1 5 -1.0833 0 016 1 1 5 -1.0833 0 117 1 1 5 -1.0833 0 018 1 1 5 0 0 019 1 1 5 0 0
121.8664 20
-10.52994 12.28
-10.52994 12.28
-3.2
-3.2
1.08
FUERZAS UNITARIAS EN DIRECCION 3 " U3"
" U3 "
ΔL1 = F11 =
ΔL2 = F22 =
ΔL3 = F33 =
F12 =
F13 =
F23 =
{ R } =- [ F ]-1 * { ΔL }
{ R } = -20 -3.2 -3.2
-3.2 12.28 1.08-3.2 1.08 12.28
{ R } = -0.054150 -0.012970 -0.012970-0.012970 -0.085175 0.004111-0.012970 0.004111 -0.085175
{ R } =
-6.32597
-0.72703
-0.72703
R1
R2
R3
METODO DE FLEXIBILIDADES PARA ARMADURAS
Grado de indeterminacion :
m = 19 numero de barras
r = 4 numero de reacciones
n = 10 numero de nudos
ECUACIONES ESTATICAS = 3Redundandes a eliminar EN TOTAL : 3
Redundandes a eliminar EXTERNO : 1
Redundandes a eliminar INTERNO : 2
U3
0 0 0 0 0 0 0-0.8 0 0 14.50656 0 0 2.56
0 0 17.28 0 0 2.56 00 0 0 0 0 0 00 0 0 0 0 0 00 28.5332 0 0 4 0 00 28.5332 0 0 4 0 00 25.0668 -20.05344 0 4 2.56 0
-0.8 21.6 0 -17.28 4 0 2.560 18.1332 0 0 4 0 0
-0.6 0 0 -1.17 0 0 1.08-0.6 0 -1.17 -1.17 0 1.08 1.08
0 0 -1.17 0 0 1.08 00 0 0 0 0 0 01 0 0 -5.4165 0 0 50 0 -5.4165 0 0 5 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0
121.8664 -10.52994 -10.52994 20 12.28 12.28
(F*U1*L) / (E*A)
(F*U2*L) / (E*A)
(F*U3*L) / (E*A)
(U1^2*L) / (E*A)
(U2^2*L) / (E*A)
(U3^2*L) / (E*A)
∑total=
121.8664* -10.52994
-10.52994
121.8664* -10.52994
-10.52994
0 0 00 0 00 0 00 0 00 0 00 0 00 0 0
-3.2 0 00 -3.2 00 0 00 0 00 0 1.080 0 00 0 00 0 00 0 00 0 00 0 00 0 0
-3.2 -3.2 1.08
(U1*U2*L) / (E*A)
(U1*U3*L) / (E*A)
(U2*U3*L) / (E*A)
METODO DE FLEXIBILIDADES PARA ARMADURAS
5
4.5
10
3.5 4.5 5
PRIMER ESTADO CONSIDERANDO FUERZAS
5
10" F "
FUERZAS UNITARIAS EN DIRECCION 1 " U1 "
r1 = 1
r1 = 1
" U1 "
FUERZAS UNITARIAS EN DIRECCION 2 " U2"
r2 = 1
Tn
Tn
1
2 3
4
9
8
7
10
6 5
11
1213
Tn
Tn
BARRA E A L F U1 U21 21000000 0.0005 4.5 -1.1538 -0.78942 21000000 0.0005 3.5 2.9915 -0.6143 21000000 0.0005 4.5 6.8376 -0.70714 21000000 0.0005 6.72681202 9.19915 21000000 0.0005 5 -6.83766 21000000 0.0005 4.5 -2.99157 21000000 0.0005 3.5 0 -0.6139 -0.70718 21000000 0.0005 5.70087713 09 21000000 0.0005 5.70087713 -4.8725 1
10 21000000 0.0005 4.5 3.8462 -0.7894 -0.707111 21000000 0.0005 6.36396103 012 21000000 0.0005 6.36396103 -5.4393 113 21000000 0.0005 4.5 -6.1538 -0.7071
-0.00416862 0.00132836
-0.0046695 0.0014156
0.00038392
-1
{ R } = -0.00132836 0.000383918
*0.00038392 0.0014156
{ R } = -816.833089 221.529515221.529515 -766.4943291
{ R } = 2.37063
2.65567
r2 = 1
" U2 "
∑total=
ΔL1 = F11 =
ΔL2 = F22 =
F12 =
{ R } =- [ F ]-1 * { ΔL }
R1
R2
METODO DE FLEXIBILIDADES PARA ARMADURAS
Grado de indeterminacion :
m = 13r = 3n = 7
ECUACIONES ESTATICAS = 3Redundandes a eliminar EN TOTAL : 2
Redundandes a eliminar EXTERNO : 0
Redundandes a eliminar INTERNO : 2
E= 2100000 kg/cm2 21000000 Tn/m2A= 5 cm2 0.0005 m2
(F*U1*L)/(E*A) (F*U2*L)/(E*A(U1^2*L)/(E (U2^2*L)/(E*A) (U1*U2*L)/(E*A)
0.00039034702 0 0.00027 0 0-0.00061226033 0 0.00013 0 0
0 -0.002072 0 0.00021428 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0.00013 0.00016666 0.00014470 0 0 0 0
-0.00264547846 0 0.00054 0 0-0.00130122441 -0.001166 0.00027 0.00021428 0.00023922
0 0 0 0 00 -0.003297 0 0.00060609 00 0.001865 0 0.00021428 0
-0.00416861617 -0.004669 0.00133 0.0014156 0.00038392
-0.00416861617-0.00466949778
-0.00416861617-0.00466949778