solucion de exmen final parilla
DESCRIPTION
para todosTRANSCRIPT
PROBLEMADATOS SECCION VIGA
E = 2.50E+07 KN/m2G = 8.00E+06 KN/m2 0.6u = 0
0.35
Ixx = 0.0063 m4 Ixx = 0.00312 m4J = 0.005454 m4 J = m4C = 0.2120 C =G = 12500000.00 KN/m2 G = KN/m2
VECTOR FUERZA DE EMP. VECTOR FUERZA EXTERNAMx1F 0 Mx1 0My1F 0 My1 0Z1F 100 Z1 0
Mx2F 0 Mx2 Mx2 My2F 41.67 My2 My2 Z2F 50 Z2 Z2
Mx3F 0 Mx3 Mx3 My3F -41.67 My3 My3 Z3F 50 Z3 Z3 Mx4 0 Mx4 Mx4 My4 0 My4 My4 Z4 0 Z4 Z4
Mx5 0 Mx5 Mx5 My5 0 My5 My5
Z5 0 Z5 Z5 Mx6 Mx6 My6 My6 Z6 Z6
)1(2 UE
G
12
* 3HBI
3** BHCJ
4121
31 1**21.0 H
BHBC
*KFF F
MATRICES DE RIGIDEZ DE LOS ELEMENTOSElemento 1-2
E 2.50E+07G 8000000I 0.0063000J 0.0054541L 5.000ø 0.000
sen ø 0.00cos ø 1.00GJ/L 8726.55EI/L 31500.00
6300.00
1260.00
θx1 θy1 w1 θx2 θy2 w28726.55 0.00 0.00 -8726.55 0.00 0.00
0.00 126000.00 -37800.00 0.00 63000.00 37800.00K 1-2= 0.00 -37800.00 15120.00 0.00 -37800.00 -15120.00
-8726.55 0.00 0.00 8726.55 0.00 0.000.00 63000.00 -37800.00 0.00 126000.00 37800.000.00 37800.00 -15120.00 0.00 37800.00 15120.00
METODO DE RIGIDEZ
VECTOR FUERZA VECTOR FUERZA DE EMP. MATRIZ DE RIGIDEZθx1 θy1
0
=
0
+
269453.103 0.0000 0 0.000 269453.1030 100.00 0.000 0.000
Mx2 0 -8726.552 0.000My2 41.67 0.000 63000.000Z2 50 0.000 37800.000
Mx3 0 63000.000 0.000My3 -41.67 0.000 -8726.552Z3 50.00 -37800.000 0.000
Mx4 0 -8726.552 0.000My4 0 0.000 63000.000Z4 0 0.000 -37800.000
Mx5 0 63000.00 0.00My5 0 0.00 -8726.55Z5 0 37800.00 0.000 00 00 0
Módulo de Elastcidad (KN/m2, lb/pulg2)Módulo de Elasticidad al Cortante (KN/m2, lb/pulg2)Momento de Inercia (m4, pulg4)Momento Polar de Inercia (m4, pulg4)Longitud (m, pulg)Angulo (radianes)
EI/L2
EI/L3
θx1 =
269453.103 0.000 0.000Xθy1 0.000 269453.103 0.000
w1 0.000 0.000 60480.000
Mx2
=
0
+
-8726.552 0.000My2 41.67 0.000 63000.000Z2 50 0.000 37800.000
Mx3 0 63000.000 0.000My3 -41.67 0.000 -8726.552Z3 50.00 -37800.000 0.000
Mx4 0 -8726.552 0.000My4 0 0.000 63000.000Z4 0 0.000 -37800.000
Mx5 0 63000.000 0.000My5 0 0.000 -8726.552Z5 0 37800.000 0.000
SECCION VIGA T
0.5
0.15
0.35
0.2
VECTOR DESPLAZAMIENTOθx1 θx1 θy1 θy1 w1 w1 θx2 0θy2 0w2 0θx3 0θy3 0w3 0θx4 0θy4 0w4 0θx5 0θy5 0w5 0θx6 θy6 w6
Elemento 1-3E 2.50E+07G 8000000I 0.0063000J 0.0054541L 5.000ø 1.571
sen ø 1.00cos ø 0.00GJ/L 8726.55EI/L 31500.00
6300.00
1260.00
θx1 θy1 w1 θx3 θy3θx1 126000.00 0.00 37800.00 63000.00 0.00θy1 0.00 8726.55 0.00 0.00 -8726.55w1 K1-3 = 37800.00 0.00 15120.00 37800.00 0.00θx2 63000.00 0.00 37800.00 126000.00 0.00θy2 0.00 -8726.55 0.00 0.00 8726.55w2 -37800.00 0.00 -15120.00 -37800.00 0.00
MATRIZ DE RIGIDEZw1 θx2 θy2 w2 θx3 θy3 w3
0.0000.000
60480.0000.000
-37800.000-15120.00037800.000
0.000-15120.000
0.00037800.000-15120.000-37800.00
0.00-15120.00
Módulo de Elastcidad (KN/m2, lb/pulg2)Módulo de Elasticidad al Cortante (KN/m2, lb/pulg2)Momento de Inercia (m4, pulg4)Momento Polar de Inercia (m4, pulg4)Longitud (m, pulg)Angulo (radianes)
EI/L2
EI/L3
0=
2.2729089E-36 rad0 4.2626218E-20 rad
-100.00 -0.0016534392 m
0.000
x
2.2729089E-36
=
-1.983466E-32-37800.000 4.2626218E-20 104.17-15120.000 -0.0016534392 7537800.000 -62.5
0.000 -41.67-15120.000 75
0.000 -7.657178E-1537800.000 -62.5-15120.000 25-37800.000 62.5
0.000 -1.185775E-14-15120.000 25
Elemento 1-4E 2.50E+07G 8000000I 0.0063000J 0.0054541L 5.000ø 3.142
sen ø 0.00cos ø -1.00GJ/L 8726.55EI/L 31500.00
6300.00
1260.00
w3 θx1 θy1 w1 θx4 θy4-37800.00 θx1 8726.55 0.00 0.00 -8726.55 0.00
0.00 θy1 0.00 126000.00 37800.00 0.00 63000.00-15120.00 w1 K 1-4 = 0.00 37800.00 15120.00 0.00 37800.00-37800.00 θx3 -8726.55 0.00 0.00 8726.55 0.00
0.00 θy3 0.00 63000.00 37800.00 0.00 126000.0015120.00 w3 0.00 -37800.00 -15120.00 0.00 -37800.00
MATRIZ DE RIGIDEZ VECTOR DESPLAZAMIENTOθx4 θy4 w4
θx1
X
θx1 θy1 θy1 w1 w1 θx2 0θy2 0w2 0θx3 0θy3 0w3 0θx4 0θy4 0w4 0θx5 0θy5 0w5 0θx6 0θy6 0w6 0
Módulo de Elastcidad (KN/m2, lb/pulg2)Módulo de Elasticidad al Cortante (KN/m2, lb/pulg2)Momento de Inercia (m4, pulg4)Momento Polar de Inercia (m4, pulg4)Longitud (m, pulg)Angulo (radianes)
EI/L2
EI/L3
Elemento 1-5E 2.50E+07G 8000000I 0.0063000J 0.0054541L 5.000ø 4.712
sen ø -1.00cos ø 0.00GJ/L 8726.55EI/L 31500.00
6300.00
1260.00
w4 θx1 θy1 w1 θx5 θy50.00 θx1 126000.00 0.00 -37800.00 63000.00 0.00
-37800.00 θy1 0.00 8726.55 0.00 0.00 -8726.55-15120.00 w1 K1-5 = -37800.00 0.00 15120.00 -37800.00 0.00
0.00 θx4 63000.00 0.00 -37800.00 126000.00 0.00-37800.00 θy4 0.00 -8726.55 0.00 0.00 8726.5515120.00 w4 37800.00 0.00 -15120.00 37800.00 0.00
Módulo de Elastcidad (KN/m2, lb/pulg2)KN/m2, lb/pulg2) Módulo de Elasticidad al Cortante (KN/m2, lb/pulg2)
Momento de Inercia (m4, pulg4)Momento Polar de Inercia (m4, pulg4)Longitud (m, pulg)Angulo (radianes)
EI/L2
EI/L3
Elemento 3E 0.00E+00G 0I 0.0000000J 0.0000000L 5.000ø 3.142
sen ø 0.00cos ø -1.00GJ/L 0.00EI/L 0.00
0.00
0.00
w5 θx2 θy2 w2 θx3 θy337800.00 θx1 0.00 0.00 0.00 0.00 0.00
0.00 θy1 0.00 0.00 0.00 0.00 0.00-15120.00 w1 K 2-3 = 0.00 0.00 0.00 0.00 0.0037800.00 θx5 0.00 0.00 0.00 0.00 0.00
0.00 θy5 0.00 0.00 0.00 0.00 0.0015120.00 w5 0.00 0.00 0.00 0.00 0.00
Módulo de Elastcidad (KN/m2, lb/pulg2)KN/m2, lb/pulg2) Módulo de Elasticidad al Cortante (KN/m2, lb/pulg2)
Momento de Inercia (m4, pulg4)Momento Polar de Inercia (m4, pulg4)Longitud (m, pulg)Angulo (radianes)
EI/L2
EI/L3
w30.00 θx20.00 θy20.00 w20.00 θx30.00 θy30.00 w3
KN/m2, lb/pulg2)
0.5A1
0.15
0.35
A20.2
A Y A*YA1 0.075 0.425 0.031875A2 0.07 0.175 0.01225
∑ = 0.145 ∑ = 0.0441
y = 0.30431034
d2 = 0.12931034d1 = 0.12068966
0.00312 m4Ixx
2^AdII
A
AyY 2^AdII
A
AyY