Analisis Estructural II Rigideces

EJERCICIOS PROPUESTOS

CASO1:a.) calcular el nmero de grados de libertad.b.) dibujar una deformada lo mas general posibleEJERCICIO 1:

DEFORMADA GENERALIZADA

D1= desplazamiento horizontal del nudo AD3= desplazamiento horizontal del nudo B y C1= giro del nudo A2=giro del nudo DEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 4

EJERCICIO 2:


D1=D2= desplazamiento horizontal del nudo A Y C1= giro del nudo D

EN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 2

EJERCICIO 3

D1= desplazamiento vertical del nudo B D2= desplazamiento horizontal del nudo B D3= desplazamiento horizontal del nudo c1= giro del nudo A2= giro del nudo3= giro del nudo CEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 6

Ejercicio 4

Deformada generalizada

D1= desplazamiento horizontal del nudo B Y C D3= desplazamiento vertical del nudo C1= giro del nudo CEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 3Ejercicio 5

Deformada generalizada

D1= desplazamiento horizontal del nudo BD2= desplazamiento vertical del nudo BD3= desplazamiento horizontal del nudo CD4= desplazamiento vertical del nudo C1= giro del nudo B3= giro del nudo C2= giro del nudo D1= giro del nudo EEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 8

EJERCICIO 6

DEFORMADA GENERALIZADA.

X1= desplazamiento horizontal del nudo BY1= desplazamiento vertical del nudo BY2= desplazamiento vertical del nudo C1= giro del nudo B2= giro del nudo CEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 6

EJERCICIO 8:


X1= desplazamiento horizontal del nudo CY1= desplazamiento vertical del nudo C1= giro del nudo C2= giro del nudo BEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 4

EJERCICIO 9.


X1= desplazamiento horizontal del nudo CY1= desplazamiento vertical del nudo C2= giro del nudo CX2= desplazamiento horizontal del nudo B3= giro del nudo B1= giro del nudo DEN TOTAL EL NUMEORO DE GRADOS DE LIBERTAD SERA: 6

EJERCICIO 10.


X1= desplazamiento horizontal del nudo C Y DX2= desplazamiento horizontal del nudo E Y FX3= desplazamiento horizontal del nudo G Y HEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 3

EJERCICIO 11:


X1= desplazamiento horizontal del nudo C Y DX2= desplazamiento horizontal del nudo E Y F1= giro del nudo C2= giro del nudo D3= giro del nudo E4= giro del nudo FEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 6

EJERCICIO 12


X1= desplazamiento horizontal del nudo C X2= desplazamiento horizontal del nudoBY1= desplazamiento vertical del nudo C 1= giro del nudo B Y CEN TOTAL EL NUMERO DE GRADOS DE LIBERTAD SERA: 4

CASO 2Resolver las estructuras mostradas por el mtodo de las rigideces.EJERCICIO 1:

Prtico con las reacciones numeradas:

Matrices de fijacin en coordenadas locales:

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLOESCUELA PROFESIONAL D INGENIERIA CIVIL

ANALISIS ESTRUCTURAL II

Matrices de fijacin en coordenadas globales:

Calculo de las matrices de rigideces en coordenadas locales

Clculo de las matrices de rigidez globales.

Clculo de las matrices ensambladas:Matriz de fijacin ensamblada en coordenadas globales:

Usando la frmula elemental del Mtodo de las rigideces:

Resolviendo, se obtiene:

Reacciones en losa poyos

Diagrama de cortante:

Diagrama de momento flector:

EJERCICIO 2

Diagrama con los nudos numerados y las reacciones numeradas:

Calculo de la matriz de fijaciones en coordenadas locales:

Clculo de la matriz de fijaciones en coordenadas globales:

Clculo de las matrices de rigideces en coordenadas locales:

Clculo de las matrices de rigideces en coordenadas globales:

Clculo de las matrices ensambladas en coordenadas globalesClculo de la matriz de fijacin ensamblada:

Clculo de la matriz de rigideces ensamblada:

=

Sin embargo, esta matriz resulta poco prctica a la hora de operar, por que se proceder a agrupar las filas y columnas con valores ceros, esto mediante el intercambio de la columna 2 con la columna 6, lo mismo con las filas respectivas.

=

Resolviendo:

Diagrama de cortante:

Diagrama de momento flector:

EJERCICIO 3

Ev = Ec = EIc = IoIv = 1.5 IoMienbroSen Cos AE/LEI2 EI/L4 EI/L6 EI/L212 EI/L3

1 290100.1910.3810.7620.2180.083

2 331.7590.5260.850.1621.50.4860.9720.2360.076

3 4328.241-0.5260.850.1621.50.4860.9720.2360.076

4 5270-100.1910.3810.7620.2180.083

Para la barra 1-2, como no hay fuerzas externas en la barra, los momentos de empotramiento son cero. Para la barra 2-3:

Y23 = Y32 = 10*5.25/2 = 26.25 tM23 = -M32 = 10*5.252/12 = 22.969 t-m

Para la barra 3-4:

Y34 = Y43 = 10*5.25/2 = 26.25 tM34 = - M43 = 10*5.252/12 = 22.969 t-m

Para la barra 4-5:

X45 = -13.504 tX54 = -6.496 tM45 = -15.329 t-mM54 = 9.433 t-m

Calculo de las matrices de rigidez para las barras de la estructura:

BARRA I (1-2)

(a)

BARRA II (2-3)

(b)

BARRA 3-4

(c)

BARRA III (4-5)

(d)

Matriz de rigidez de la estructura:

Dando forma a la ecuacin matricial, tenemos:

(e)

Resolviendo, la ecuacin (e), obtenemos las deformaciones, y las reacciones:

DEFORMACIONES REACCIONESu2=37.945mX1=12.972 tv2=-267.943 mY1=51.037 t2=-74.047 radM1=-19.948 t-mu3=124.531 mX5=-32.972 tv3=-690.249 mY5=53.963 t3=3.33 radM5=69.584 t-mu4=190.419 mv4=-283.307 m4=49.085rad

Reemplazando los valores encontrados, en las ecuaciones (a), (b), (c) y (d), obtenemos las fuerzas en las barras:

BARRA I (1-2)X12 =12.972 tY12=51.037tM12=-19.948 t-mX21=-12.972 tY21=-51.037 tM21=-48.159 t-mBARRA II (2-3)X23 = 12.868 t Y23 = 50.976 t M23 = 48.159 t-m X32 = -12.868 t Y32 = 1.524 t M32 = 39.901 t-mBARRA III (3-4)X34 = 12.871 t Y34 = -1.405 t M34 = -39.901 t-m X43 = -12.871 t Y43 = 53.905 t M43 = -63.605 t-mBARRA IV (4-5)X45 = 12.972 t Y45 = -53.963 t M45 = 63.605 t-m X54 = -32.972 t Y54 = 53.963 t M54 = 69.584 t-m

DIAGRAMA DE CORTANTE

DIAGRAMA DE MOMENTO FLECTOR

EJERCICIO 4

MienbroSen Cos AE/LEI2 EI/L4 EI/L6 EI/L212 EI/L3

1 20100.26710.5331.0670.4270.228

2 30100.30810.6151.2310.5680.350

3 40100.26710.5331.0670.4270.228

2 5270-100.23510.4710.9410.3320.156

3 6270-100.23510.4710.9410.3320.156

Para la barra 2-5 Y 3-6, como no hay fuerzas externas en la barra, los momentos de empotramiento son cero. Barra I (1-2):

Y12 = 10.56 tM12 = 10.8 t-mY21 = 19.44 tM21 = -16.20 t-m

Barra II (2-3):

Y23 = 5.85 tM23 = 4.225 t-mY32 = 13.65 tM32 = -6.338 t-m

Barra III (3-4):

Y34 = 19.44 tM34 = 16.20 t-mY43 = 10.56 tM43 = -10.80 t-m

Matriz de rigidez, para las barras de la estructura:

Barra I (1-2)

(a)

Barra II (2-3)

(b)

Barra III (3-4)

(c)

Barra IV (2-5)

(d)

Barra V (3-6)

(e)

Matriz de rigidez de la estructura:

(f)

Resolviendo la ecuacin (f), obtenemos las reacciones, y las deformaciones:

DEFORMACIONESREACCIONESu1=3.995Y1=11.5351=-52.543X4=-0.114u2=3.995Y4=12.629v2=-112.525X5=1.0982=-5.184Y5=26.477u3=0.428M5=-1.113v3=-122.651X6=-0.9833=2.759Y6=28.8594=57.806M6=1.441

Reemplazando los valores encontrados, en las ecuaciones (a), (b), (c), (d) y (e), obtenemos las fuerzas en las barras:

BARRA I (1-2)X12 = 0 t Y12 = 11.566 t M12 = 0 t-m X21 = 0 t Y21 = 18.434 t M21 = -1.689 t-mBARRA II (2-3)X23 = 1.099 t Y23 = 8.017 t M23 = 5.292 t-m X32 = -1.099 t Y32 = 11.483 t M32 = -0.378 t-mBARRA III (3-4)X34 = 0.114 t Y34 = 17.337 t M34 = -2.418 t-m X43 = -0.114 t Y43 = 12.663 t M43 = -0 t-mBARRA IV (2-5)X25 = -1.098 t Y25 = -26.443 t M25 = -3.552 t-m X52 = 1.098 t Y52 = 26.443 tM52 = -1.115 t-m

BARRA V (3-6)X36 = 0.983 t Y36 = -28.823 t M36 = 2.738 t-m X63 = -0.983 t Y63 = 28.823 t M63 = 1.442 t-m

DIAGRAMA DE CORTANTES

DIAGRAMA DE MOMENTOS FLECTORES

EJERCICIO 5

Solucin

Asumimos valores para:A=1 E=1 I=Io=1N BARRAcossenEA/L(12EI/L3)(6EI/L2)(4EI/L)(2EI/L)

10.0001.0000.3080.6991.1362.4621.231

20.9190.3940.1750.0640.1840.7000.350

30.509-0.8610.1570.0460.1470.6260.313

Hallando las fuerzas externas:Para la barra 1-2

Y12=18.308 TnY21=8.308 TnM12=4.5 Tn-mM21= 4.5 Tn -m Para la barra 2-3

Y23 = Y32 = 10*5.25/2 = 26.25 tM23 = -M32 = 10*5.252/12 = 22.969 t-mPara la barra 3-4

X34=15.031 TnX43= 10.405 TnY34= 27.331 TnX43= 15.715 TnM34= 39.28 Tn-mM43= -27.189 Tn-m

1.- Hallamos los k' (k raya) matriz de rigideces de cada elemento.BARRA I(1-2)

0.3080.0000.000-0.3080.0000.000

0.0000.6991.1360.000-0.6991.136

K'1 =0.0001.1362.4620.000-1.1361.231

-0.3080.0000.0000.3080.0000.000

0.000-0.699-1.1360.0000.699-1.136

0.0001.1361.2310.000-1.1362.462

123456

0.6990.000-1.136-0.6990.000-1.1361

0.0000.3080.0000.000-0.3080.0002

K1 =-1.1360.0002.4621.1360.0001.2313

-0.6990.0001.1360.6990.0001.1364

0.000-0.3080.0000.0000.3080.0005

-1.1360.0001.2311.1360.0002.4626

BARRA II(2-3)

0.1750.0000.000-0.1750.0000.000

0.0000.0640.1840.000-0.0640.184

K'2 =0.0000.1840.7000.000-0.1840.350

-0.1750.0000.0000.1750.0000.000

0.000-0.064-0.1840.0000.064-0.184

0.0000.1840.3500.000-0.1840.700

4

56789

0.1580.040-0.072-0.158-0.040-0.0724

0.0400.0820.169-0.040-0.0820.1695

K2 =-0.0720.1690.7000.072-0.1690.3506

-0.158-0.0400.0720.1580.0400.0727

-0.040-0.082-0.1690.0400.082-0.1698

-0.0720.1690.3500.072-0.1690.7009

BARRA III(3-4)

0.160.000.00-0.160.000.00

0.000.050.150.00-0.050.15

K'3 =0.000.150.630.00-0.150.31

-0.160.000.000.160.000.00

0.00-0.05-0.150.000.05-0.15

0.000.150.310.00-0.150.63

789101112

0.075

-0.0480.127-0.0750.0480.1277

-0.0480.1280.0750.048-0.1280.0758

K3 =0.1270.0750.626-0.127-0.0750.3139

-0.0750.048-0.1270.075-0.048-0.12710

0.048-0.128-0.075-0.0480.128-0.07511

0.1270.0750.313-0.127-0.0750.62612

Ahora toca hacer el ensamblaje de una matriz de rigideces en coordenadas globales para toda la estructura, para lo cual debemos tomar en cuenta lo siguiente:

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLOESCUELA PROFESIONAL D INGENIERIA CIVIL

ANALISIS ESTRUCTURAL II

Para hallar cada elemento en la matriz ensamblada solo tenemos que ubicar el lugar del elemento y buscarlo en las matrices de rigideces de cada barra, en caso de que cada elemento se reptase en ms de una matriz de rigideces solo se har una suma algebraica de cada uno de estos.Definimos la matriz de rigideces en coordenadas globales ensamblada:

123456789101112

0.6990.000-1.136-0.6990.000-1.1360.0000.0000.0000.0000.0001.1361

0.0000.3080.0000.000-0.3080.0000.0000.0000.0000.0000.0000.0002

-1.1360.0002.4621.1360.0001.2310.0000.0000.0000.0000.0001.2313

-0.6990.0001.1360.8570.0401.064-0.158-0.040-0.0720.0000.0000.0004

0.000-0.3080.0000.0400.3890.169-0.040-0.0820.1690.0000.0000.0005

[K] =-1.1360.0001.2311.0640.1693.1620.072-0.1690.3500.0000.0000.0006

0.0000.0000.000-0.158-0.0400.0720.233-0.0080.199-0.0750.0480.1277

0.0000.0000.000-0.040-0.082-0.169-0.0080.210-0.0940.048-0.1280.0758

0.0000.0000.000-0.0720.1690.3500.199-0.0941.326-0.127-0.0750.3139

0.0000.0000.0000.0000.0000.000-0.0750.048-0.1270.075-0.048-0.12710

0.0000.0000.0000.0000.0000.0000.048-0.128-0.075-0.0480.128-0.07511

0.0000.0000.0000.0000.0000.0000.1270.0750.313-0.127-0.0750.62612

Dando forma a la ecuacin matricial, tenemos: (e)

123456789101112

X1

0.6990.000-1.136-0.6990.000-1.1360.0000.0000.0000.0000.0000.000u1=00

Y10.0000.3080.0000.000-0.3080.0000.0000.0000.0000.0000.0000.000v2=08.308

M1-1.1360.0002.4621.1360.0001.2310.0000.0000.0000.0000.0000.0003=04.5

X2=0-0.6990.0001.1360.8570.0401.064-0.158-0.040-0.0720.0000.0000.000u40

Y2=00.000-0.3080.0000.0400.3890.169-0.040-0.0820.1690.0000.0000.000v5 34.56

M2=0-1.1360.0001.2311.0640.1693.1620.072-0.1690.3500.0000.0000.000627.47

X3=0=0.0000.0000.000-0.158-0.0400.0720.233-0.0080.199-0.0750.0480.127u7+15.031

Y3=00.0000.0000.000-0.040-0.082-0.169-0.0080.210-0.0940.048-0.1280.075v853.54

M3=00.0000.0000.000-0.0720.1690.3500.199-0.0941.326-0.127-0.0750.313916.32

X40.0000.0000.0000.0000.0000.000-0.0750.048-0.1270.075-0.048-0.127u10=010.405

Y40.0000.0000.0000.0000.0000.0000.048-0.128-0.075-0.0480.128-0.075v11=015.715

M40.0000.0000.0000.0000.0000.0000.1270.0750.313-0.127-0.0750.62612=0-27.189

Resolviendo, la ecuacin (e), obtenemos las deformaciones, y las reacciones:

DEFORMACIONES REACCIONESu2=59.888mX1= -10.340tv2= 97.955mY1= 30.140t2= -38.11radM1= 25.334t-mu3= 55.795mX4=60.340 tv3= 168.849mY4= 22.361t3=25.942radM4= -20.87t-m

Reemplazando los valores encontrados, en las ecuaciones (a), (b), (c) y (d), obtenemos las fuerzas en las barras:

BARRA I (1-2)X12 =30.14 tY12=-6.881tM12=25.674 t-mX21=-30.14 tY21=6.88 tM21=-21.27 t-mBARRA II (2-3)X23 = 5.548 t Y23 = -30.414 t M23 = 21.270 t-m X32 = -5.548 t Y32 = -26.706 t M32 = -10.677 t-mBARRA III (3-4)X34 = 27.198 t Y34 = -2.071 t M34 = 10.677 t-m X43 = -27.198 t Y43 = 2.071 t M43 = -20.87 t-m

Diagrama de cortante

Diagrama de momento

ejercicio 30.1900-0.190000.0830.2180-0.0830.218K'1 =00.2180.7620-0.2180.381-0.19000.19000-0.083-0.21800.083-0.21800.2180.3810-0.2180.7620.0830-0.218-0.0830-0.218X120.6990-1.136-0.6990-1.136u100.0830-0.218-0.0830-0.21800000000000.1900-0.190Y1200.30800-0.3080v18.3080.1900-0.190000000000K1 =-0.21800.7620.21800.381M12=-1.13602.4621.13601.2311+4.50.7620.21800.381000000000-0.08300.2180.08300.218X21-0.69901.1360.69901.136u200.2210.0380.093-0.138-0.038-0.1240000000-0.19000.190Y210-0.308000.3080v28.3080.2910.201-0.038-0.10.201000000-0.21800.3810.21800.762M21-1.13601.2311.13602.46224.51.7340.124-0.2010.4860000000.27700.249-0.1380.0380.124000X120.0830-0.218-0.0830-0.2180012.993K =0.200.038-0.10.2010000.16200-0.16200Y1200.1900-0.1900050.9091.943-0.124-0.2010.48600000.0760.2360-0.0760.236M12=-0.21800.7620.21800.3810+0=-19.9400.221-0.0380.093-0.08300.218K'2 =00.2360.9720-0.2360.486X21-0.08300.2180.08300.21837.9450-12.9930.291-0.2010-0.190-0.162000.16200Y210-0.19000.190-267.9430-50.9091.734-0.21800.3810-0.076-0.23600.076-0.236M21-0.21800.3810.21800.762-74.0470-48.1520.0830-0.21800.2360.4860-0.2360.9720.1900.7620.1380.038-0.124-0.138-0.038-0.124X230.1380.038-0.124-0.138-0.038-0.124u200.0380.10.201-0.038-0.10.201Y230.0380.10.201-0.038-0.10.201v226.25K2 =-0.1240.2010.9720.124-0.2010.486M23=-0.1240.2010.9720.124-0.2010.4862+22.969-0.138-0.0380.1240.1380.0380.124X32-0.138-0.0380.1240.1380.0380.124u30X10.0830-0.218-0.0830-0.218000000000u1=00-0.038-0.1-0.2010.0380.1-0.201Y32-0.038-0.1-0.2010.0380.1-0.201v326.25Y10.1900-0.190000000000v1=00-0.1240.2010.4860.124-0.2010.972M32-0.1240.2010.4860.124-0.2010.9723-22.969M10.7620.21800.3810000000001=00X2=00.2210.0380.093-0.138-0.038-0.124000000u20X230.1380.038-0.124-0.138-0.038-0.12437.945012.868Y2=00.2910.201-0.038-0.10.201000000v226.250.16200-0.16200Y230.0380.10.201-0.038-0.10.201-267.94326.2550.976M2=01.7340.124-0.2010.486000000222.96900.0760.2360-0.0760.236M23=-0.1240.2010.9720.124-0.2010.486-74.047+22.969=48.234X3=00.27700.249-0.1380.0380.124000u30K'3 =00.2360.9720-0.2360.486X32-0.138-0.0380.1240.1380.0380.124124.5310-12.868Y3=0=0.200.038-0.10.201000v3+52.5-0.162000.16200Y32-0.038-0.1-0.2010.0380.1-0.201-690.24926.251.524M3=01.943-0.124-0.2010.486000300-0.076-0.23600.076-0.236M32-0.1240.2010.4860.124-0.2010.9723.33-22.96939.901X4=00.221-0.0380.093-0.08300.218u4-13.50400.2360.4860-0.2360.972Y4=00.291-0.2010-0.190v426.25M4=01.734-0.21800.3814-38.2980.138-0.0380.124-0.1380.0380.124X340.138-0.0380.124-0.1380.0380.124u30X50.0830-0.218u5=0-6.496-0.0380.10.2010.038-0.10.201Y34-0.0380.10.2010.038-0.10.201v326.25Y50.190v5=00K3 =0.1240.2010.972-0.124-0.2010.486M34=0.1240.2010.972-0.124-0.2010.4863+22.969M50.7625=09.433-0.1380.038-0.1240.138-0.038-0.124X43-0.1380.038-0.1240.138-0.038-0.124u400.038-0.1-0.201-0.0380.1-0.201Y430.038-0.1-0.201-0.0380.1-0.201v426.250.1240.2010.486-0.124-0.2010.972M430.1240.2010.486-0.124-0.2010.9724-22.969RESOLVIENDO, TENEMOS:X340.138-0.0380.124-0.1380.0380.124124.531012.8710.1900-0.1900Y34-0.0380.10.2010.038-0.10.201-690.24926.25-1.405u2=37.945X1=12.97200.0830.2180-0.0830.218M34=0.1240.2010.972-0.124-0.2010.4863.33+22.969=-39.904v2=-267.943Y1=51.037K'4 =00.2180.7620-0.2180.381X43-0.1380.038-0.1240.138-0.038-0.124190.4190-12.8712=-74.047M1=-19.948-0.19000.1900Y430.038-0.1-0.201-0.0380.1-0.201-283.30726.2553.905u3=124.531X5=-32.9720-0.083-0.21800.083-0.218M430.1240.2010.486-0.124-0.2010.97249.085-22.969-63.605v3=-690.249Y5=53.96300.2180.3810-0.2180.7623=3.33M5=69.584u4=190.4190.08300.218-0.08300.218X450.08300.218-0.08300.218u4-13.504v4=-283.30700.1900-0.190Y4500.1900-0.190v404=49.085K4 =0.21800.762-0.21800.381M45=0.21800.762-0.21800.3814+-15.329-0.0830-0.2180.0830-0.218X54-0.0830-0.2180.0830-0.218u5-6.4960-0.19000.190Y540-0.19000.190v500.21800.381-0.21800.762M540.21800.381-0.21800.76259.433

X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646

ejercicio 40.26700-0.2670000.2280.4270-0.2280.427K'1 =00.4271.0670-0.4270.533-0.267000.267000-0.228-0.42700.228-0.42700.4270.5330-0.4271.0670.26700-0.26700X120.26700-0.26700u100.26700-0.2670000000000000000.2280.4270-0.2280.427Y1200.2280.4270-0.2280.427v110.560.2280.4270-0.2280.427000000000000K1 =00.4271.0670-0.4270.533M12=00.4271.0670-0.4270.5331+10.81.0670-0.4270.533000000000000-0.267000.26700X21-0.267000.26700u200.73100.332-0.30800000-0.15600.3320000-0.228-0.42700.228-0.427Y210-0.228-0.42700.228-0.427v219.440.8120.1410-0.350.5680000-0.235000000.4270.5330-0.4271.067M2100.4270.5330-0.4271.0672-16.23.2390-0.5680.615000-0.33200.4710000.73100.332-0.26700000-0.15600.332X120.26700-0.267003.99500.00.812-0.1510-0.2280.4270000-0.23500.30800-0.30800Y1200.2280.4270-0.2280.427010.5611.566K =3.2390-0.4270.533000-0.33200.47100.350.5680-0.350.568M12=00.4271.0670-0.4270.533-52.543+10.8=0.0220.26700000000K'2 =00.5681.2310-0.5680.615X21-0.267000.267003.99500.00.228-0.427000000-0.308000.30800Y210-0.228-0.42700.228-0.427-112.52519.4418.4341.0670000000-0.35-0.56800.35-0.568M2100.4270.5330-0.4271.067-5.184-16.2-1.6890.1560-0.33200000.5680.6150-0.5681.2310.23500000.9410000.30800-0.30800X230.30800-0.30800u200.1560-0.33200.350.5680-0.350.568Y2300.350.5680-0.350.568v25.850.2350K2 =00.5681.2310-0.5680.615M23=00.5681.2310-0.5680.6152+4.2250.941-0.308000.30800X32-0.308000.30800u300-0.35-0.56800.35-0.568Y320-0.35-0.56800.35-0.568v313.6500.5680.6150-0.5681.231M3200.5680.6150-0.5681.2313-6.338X1=00.26700-0.26700000000000000u10X230.30800-0.308003.99501.099Y10.2280.4270-0.2280.427000000000000v1=010.560.26700-0.26700Y2300.350.5680-0.350.568-112.5255.858.017M1=01.0670-0.4270.533000000000000110.800.2280.4270-0.2280.427M23=00.5681.2310-0.5680.615-5.184+4.225=5.292X2=00.73100.332-0.30800000-0.15600.332000u20K'3 =00.4271.0670-0.4270.533X32-0.308000.308000.4280-1.099Y2=00.8120.1410-0.350.5680000-0.2350000v225.29-0.267000.26700Y320-0.35-0.56800.35-0.568-122.65113.6511.483M2=03.2390-0.5680.615000-0.33200.4710002-11.9750-0.228-0.42700.228-0.427M3200.5680.6150-0.5681.2312.759-6.338-0.378X3=00.73100.332-0.26700000-0.15600.332u3000.4270.5330-0.4271.067Y3=00.812-0.1510-0.2280.4270000-0.2350v3+33.09M3=0=3.2390-0.4270.533000-0.33200.47139.8620.26700-0.26700X340.26700-0.26700u30X40.26700000000u4=0000.2280.4270-0.2280.427Y3400.2280.4270-0.2280.427v319.44Y40.228-0.427000000v4=010.56K3 =00.4271.0670-0.4270.533M34=00.4271.0670-0.4270.5333+16.2M4=01.0670000004-10.8-0.267000.26700X43-0.267000.26700u40X50.1560-0.332000u5=000-0.228-0.42700.228-0.427Y430-0.228-0.42700.228-0.427v410.56Y50.2350000v5=0000.4270.5330-0.4271.067M4300.4270.5330-0.4271.0674-10.8M50.9410005=00X60.1560-0.332u6=00X340.26700-0.267000.42800.114Y60.2350v6=000.23500-0.23500Y3400.2280.4270-0.2280.427-122.65119.4417.337M60.9416=0000.1560.3320-0.1560.332M34=00.4271.0670-0.4270.5332.759+16.2=-2.418K'4 =00.3320.9410-0.3320.471X43-0.267000.2670000-0.114-0.235000.23500Y430-0.228-0.42700.228-0.427010.5612.6630-0.156-0.33200.083-0.332M4300.4270.5330-0.4271.06757.806-10.8-0.022RESOLVIENDO, TENEMOS:00.3320.4710-0.3320.941u1=3.995Y1=11.5350.15600.332-0.15600.332X250.15600.332-0.15600.332u201=-52.543X4=-0.11400.23500-0.2350Y2500.23500-0.2350v20u2=3.995Y4=12.629K4 =0.33200.941-0.33200.471M25=0.33200.941-0.33200.4712+0v2=-112.525X5=1.098-0.1560-0.3320.1560-0.332X52-0.1560-0.3320.1560-0.332u502=-5.184Y5=26.4770-0.235000.2350Y520-0.235000.2350v50u3=0.428M5=-1.1130.33200.471-0.33200.941M520.33200.471-0.33200.94150v3=-122.651X6=-0.9833=2.759Y6=28.859X250.15600.332-0.15600.3323.9950-1.0984=57.806M6=1.4410.23500-0.23500Y2500.23500-0.2350-112.5250-26.44300.1560.3320-0.1560.332M25=0.33200.941-0.33200.471-5.184+0=-3.552K'5 =00.3320.9410-0.3320.471X52-0.1560-0.3320.1560-0.332001.098-0.235000.23500Y520-0.235000.23500026.4430-0.156-0.33200.083-0.332M520.33200.471-0.33200.94100-1.11500.3320.4710-0.3320.9410.15600.332-0.15600.332X360.15600.332-0.15600.332u3000.23500-0.2350Y3600.23500-0.2350v30K5 =0.33200.941-0.33200.471M36=0.33200.941-0.33200.4713+0-0.1560-0.3320.1560-0.332X63-0.1560-0.3320.1560-0.332u600-0.235000.2350Y630-0.235000.2350v600.33200.471-0.33200.941M630.33200.471-0.33200.94160X360.15600.332-0.15600.3320.42800.983Y3600.23500-0.2350-122.6510-28.823M36=0.33200.941-0.33200.4712.759+0=2.738X63-0.1560-0.3320.1560-0.33200-0.983Y630-0.235000.23500028.823M630.33200.471-0.33200.941001.442

Hoja3

ejercicio 30.1900-0.190000.0830.2180-0.0830.218K'1 =00.2180.7620-0.2180.381-0.19000.19000-0.083-0.21800.083-0.21800.2180.3810-0.2180.7620.0830-0.218-0.0830-0.218X120.0830-0.218-0.0830-0.218u100.0830-0.218-0.0830-0.21800000000000.1900-0.190Y1200.1900-0.190v100.1900-0.190000000000K1 =-0.21800.7620.21800.381M12=-0.21800.7620.21800.3811+00.7620.21800.381000000000-0.08300.2180.08300.218X21-0.08300.2180.08300.218u200.2210.0380.093-0.138-0.038-0.1240000000-0.19000.190Y210-0.19000.190v200.2910.201-0.038-0.10.201000000-0.21800.3810.21800.762M21-0.21800.3810.21800.762201.7340.124-0.2010.4860000000.27700.249-0.1380.0380.124000X120.0830-0.218-0.0830-0.2180012.993K =0.200.038-0.10.2010000.16200-0.16200Y1200.1900-0.1900050.9091.943-0.124-0.2010.48600000.0760.2360-0.0760.236M12=-0.21800.7620.21800.3810+0=-19.9400.221-0.0380.093-0.08300.218K'2 =00.2360.9720-0.2360.486X21-0.08300.2180.08300.21837.9450-12.9930.291-0.2010-0.190-0.162000.16200Y210-0.19000.190-267.9430-50.9091.734-0.21800.3810-0.076-0.23600.076-0.236M21-0.21800.3810.21800.762-74.0470-48.1520.0830-0.21800.2360.4860-0.2360.9720.1900.7620.1380.038-0.124-0.138-0.038-0.124X230.1580.04-0.072-0.158-0.04-0.072u200.0380.10.201-0.038-0.10.201Y230.040.0820.169-0.04-0.0820.169v226.25K2 =-0.1240.2010.9720.124-0.2010.486M23=-0.0720.1690.70.072-0.1690.352+22.969-0.138-0.0380.1240.1380.0380.124X32-0.158-0.040.0720.1580.040.072u30X10.0830-0.218-0.0830-0.218000000000u1=00-0.038-0.1-0.2010.0380.1-0.201Y32-0.04-0.082-0.1690.040.082-0.169v326.25Y10.1900-0.190000000000v1=00-0.1240.2010.4860.124-0.2010.972M32-0.0720.1690.350.072-0.1690.73-22.969M10.7620.21800.3810000000001=00X2=00.2210.0380.093-0.138-0.038-0.124000000u20X230.1380.038-0.124-0.138-0.038-0.12437.945012.868Y2=00.2910.201-0.038-0.10.201000000v226.250.16200-0.16200Y230.0380.10.201-0.038-0.10.201-267.94326.2550.976M2=01.7340.124-0.2010.486000000222.96900.0760.2360-0.0760.236M23=-0.1240.2010.9720.124-0.2010.486-74.047+22.969=48.234X3=00.27700.249-0.1380.0380.124000u30K'3 =00.2360.9720-0.2360.486X32-0.138-0.0380.1240.1380.0380.124124.5310-12.868Y3=0=0.200.038-0.10.201000v3+52.5-0.162000.16200Y32-0.038-0.1-0.2010.0380.1-0.201-690.24926.251.524M3=01.943-0.124-0.2010.486000300-0.076-0.23600.076-0.236M32-0.1240.2010.4860.124-0.2010.9723.33-22.96939.901X4=00.221-0.0380.093-0.08300.218u4-13.50400.2360.4860-0.2360.972Y4=00.291-0.2010-0.190v426.25M4=01.734-0.21800.3814-38.2980.138-0.0380.124-0.1380.0380.124X340.138-0.0380.124-0.1380.0380.124u30X50.0830-0.218u5=0-6.496-0.0380.10.2010.038-0.10.201Y34-0.0380.10.2010.038-0.10.201v326.25Y50.190v5=00K3 =0.1240.2010.972-0.124-0.2010.486M34=0.1240.2010.972-0.124-0.2010.4863+22.969M50.7625=09.433-0.1380.038-0.1240.138-0.038-0.124X43-0.1380.038-0.1240.138-0.038-0.124u400.038-0.1-0.201-0.0380.1-0.201Y430.038-0.1-0.201-0.0380.1-0.201v426.250.1240.2010.486-0.124-0.2010.972M430.1240.2010.486-0.124-0.2010.9724-22.969RESOLVIENDO, TENEMOS:X340.138-0.0380.124-0.1380.0380.124124.531012.8710.1900-0.1900Y34-0.0380.10.2010.038-0.10.201-690.24926.25-1.405u2=37.945X1=12.97200.0830.2180-0.0830.218M34=0.1240.2010.972-0.124-0.2010.4863.33+22.969=-39.904v2=-267.943Y1=51.037K'4 =00.2180.7620-0.2180.381X43-0.1380.038-0.1240.138-0.038-0.124190.4190-12.8712=-74.047M1=-19.948-0.19000.1900Y430.038-0.1-0.201-0.0380.1-0.201-283.30726.2553.905u3=124.531X5=-32.9720-0.083-0.21800.083-0.218M430.1240.2010.486-0.124-0.2010.97249.085-22.969-63.605v3=-690.249Y5=53.96300.2180.3810-0.2180.7623=3.33M5=69.584u4=190.4190.08300.218-0.08300.218X450.08300.218-0.08300.218u4-13.504v4=-283.30700.1900-0.190Y4500.1900-0.190v404=49.085K4 =0.21800.762-0.21800.381M45=0.21800.762-0.21800.3814+-15.329-0.0830-0.2180.0830-0.218X54-0.0830-0.2180.0830-0.218u5-6.4960-0.19000.190Y540-0.19000.190v500.21800.381-0.21800.762M540.21800.381-0.21800.76259.433

X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3

ejercicio 30.1900-0.190000.0830.2180-0.0830.218K'1 =00.2180.7620-0.2180.381-0.19000.19000-0.083-0.21800.083-0.21800.2180.3810-0.2180.7620.0830-0.218-0.0830-0.218X120.0830-0.218-0.0830-0.218u100.0830-0.218-0.0830-0.21800000000000.1900-0.190Y1200.1900-0.190v100.1900-0.190000000000K1 =-0.21800.7620.21800.381M12=-0.21800.7620.21800.3811+00.7620.21800.381000000000-0.08300.2180.08300.218X21-0.08300.2180.08300.218u200.2210.0380.093-0.138-0.038-0.1240000000-0.19000.190Y210-0.19000.190v200.2910.201-0.038-0.10.201000000-0.21800.3810.21800.762M21-0.21800.3810.21800.762201.7340.124-0.2010.4860000000.27700.249-0.1380.0380.124000X120.0830-0.218-0.0830-0.2180012.993K =0.200.038-0.10.2010000.16200-0.16200Y1200.1900-0.1900050.9091.943-0.124-0.2010.48600000.0760.2360-0.0760.236M12=-0.21800.7620.21800.3810+0=-19.9400.221-0.0380.093-0.08300.218K'2 =00.2360.9720-0.2360.486X21-0.08300.2180.08300.21837.9450-12.9930.291-0.2010-0.190-0.162000.16200Y210-0.19000.190-267.9430-50.9091.734-0.21800.3810-0.076-0.23600.076-0.236M21-0.21800.3810.21800.762-74.0470-48.1520.0830-0.21800.2360.4860-0.2360.9720.1900.7620.1380.038-0.124-0.138-0.038-0.124X230.1380.038-0.124-0.138-0.038-0.124u200.0380.10.201-0.038-0.10.201Y230.0380.10.201-0.038-0.10.201v226.25K2 =-0.1240.2010.9720.124-0.2010.486M23=-0.1240.2010.9720.124-0.2010.4862+22.969-0.138-0.0380.1240.1380.0380.124X32-0.138-0.0380.1240.1380.0380.124u30X10.0830-0.218-0.0830-0.218000000000u1=00-0.038-0.1-0.2010.0380.1-0.201Y32-0.038-0.1-0.2010.0380.1-0.201v326.25Y10.1900-0.190000000000v1=00-0.1240.2010.4860.124-0.2010.972M32-0.1240.2010.4860.124-0.2010.9723-22.969M10.7620.21800.3810000000001=00X2=00.2210.0380.093-0.138-0.038-0.124000000u20X230.1380.038-0.124-0.138-0.038-0.12437.945012.868Y2=00.2910.201-0.038-0.10.201000000v226.250.16200-0.16200Y230.0380.10.201-0.038-0.10.201-267.94326.2550.976M2=01.7340.124-0.2010.486000000222.96900.0760.2360-0.0760.236M23=-0.1240.2010.9720.124-0.2010.486-74.047+22.969=48.234X3=00.27700.249-0.1380.0380.124000u30K'3 =00.2360.9720-0.2360.486X32-0.138-0.0380.1240.1380.0380.124124.5310-12.868Y3=0=0.200.038-0.10.201000v3+52.5-0.162000.16200Y32-0.038-0.1-0.2010.0380.1-0.201-690.24926.251.524M3=01.943-0.124-0.2010.486000300-0.076-0.23600.076-0.236M32-0.1240.2010.4860.124-0.2010.9723.33-22.96939.901X4=00.221-0.0380.093-0.08300.218u4-13.50400.2360.4860-0.2360.972Y4=00.291-0.2010-0.190v426.25M4=01.734-0.21800.3814-38.2980.138-0.0380.124-0.1380.0380.124X340.075-0.0480.127-0.0750.0480.127u315.031X50.0830-0.218u5=0-6.496-0.0380.10.2010.038-0.10.201Y34-0.0480.1280.0750.048-0.1280.075v327.331Y50.190v5=00K3 =0.1240.2010.972-0.124-0.2010.486M34=0.1270.0750.626-0.127-0.0750.3133+39.28M50.7625=09.433-0.1380.038-0.1240.138-0.038-0.124X43-0.0750.048-0.1270.075-0.048-0.127u410.4050.038-0.1-0.201-0.0380.1-0.201Y430.048-0.128-0.075-0.0480.128-0.075v415.7150.1240.2010.486-0.124-0.2010.972M430.1270.0750.313-0.127-0.0750.6264-22.969RESOLVIENDO, TENEMOS:X340.138-0.0380.124-0.1380.0380.124124.531012.8710.1900-0.1900Y34-0.0380.10.2010.038-0.10.201-690.24926.25-1.405u2=37.945X1=12.97200.0830.2180-0.0830.218M34=0.1240.2010.972-0.124-0.2010.4863.33+22.969=-39.904v2=-267.943Y1=51.037K'4 =00.2180.7620-0.2180.381X43-0.1380.038-0.1240.138-0.038-0.124190.4190-12.8712=-74.047M1=-19.948-0.19000.1900Y430.038-0.1-0.201-0.0380.1-0.201-283.30726.2553.905u3=124.531X5=-32.9720-0.083-0.21800.083-0.218M430.1240.2010.486-0.124-0.2010.97249.085-22.969-63.605v3=-690.249Y5=53.96300.2180.3810-0.2180.7623=3.33M5=69.584u4=190.4190.08300.218-0.08300.218X450.08300.218-0.08300.218u4-13.504v4=-283.30700.1900-0.190Y4500.1900-0.190v404=49.085K4 =0.21800.762-0.21800.381M45=0.21800.762-0.21800.3814+-15.329-0.0830-0.2180.0830-0.218X54-0.0830-0.2180.0830-0.218u5-6.4960-0.19000.190Y540-0.19000.190v500.21800.381-0.21800.762M540.21800.381-0.21800.76259.433

X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3


X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3


X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3


X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3


X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3


X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3


X450.08300.218-0.08300.218190.419-13.50413.001Y4500.1900-0.190-283.3070-53.828M45=0.21800.762-0.21800.38149.085+-15.329=63.585X54-0.0830-0.2180.0830-0.2180-6.496-33.001Y540-0.19000.1900053.828M540.21800.381-0.21800.76209.43369.646


Hoja3

ejercicio 30.1900-0.190000.0830.2180-0.0830.218K'1 =00.2180.7620-0.2180.381-0.19000.19000-0.083-0.21800.083-0.21800.2180.3810-0.2180.7620.0830-0.218-0.0830-0.218X120.0830-0.218-0.0830-0.218u100.0830-0.218-0.0830-0.21800000000000.1900-0.190Y1200.1900-0.190v100.1900-0.190000000000K1 =-0.21800.7620.21800.381M12=-0.21800.7620.21800.3811+00.7620.21800.381000000000-0.08300.2180.08300.218X21-0.08300.2180.08300.218u200.2210.0380.093-0.138-0.038-0.1240000000-0.19000.190Y210-0.19000.190v200.2910.201-0.038-0.10.201000000-0.21800.3810.21800.762M21-0.21800.3810.21800.762201.7340.124-0.2010.4860000000.277

Analisis Estructural II Rigideces

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