Trabajo Análisis I

Predimencionamiento de 3*3 Luces

Ingrese los Sguientes Datos :Peso del Ladrillo: 9 Vigas Principales Vigas SecundariasAltura del 2do Nivel 2.9 L1: 4.3 L1: 5Peso del Concreto: 2400 L2: 5.5 L2: 4.2Peso Manposteria: 1350 L3: 4 L3: 4.6S/C : 200Ancho del Ladrillo: 0.25Peso de la Tabiqueria: 100Peso del Cielo Razo: 110Peso del Falso piso: 120F.S.C.V. 1.7F.S.C.M. 1.4

Ejes Principales0.25

4.3 5.5 4

0.25

5 5

0.25 0.25

4.2 4.2

0.25 0.25

4.6 4.6

0.25 0.25

4.3 5.5 4

Lado Mayor de Los Ejes Principales : 550Lado Mayor de Los Ejes Secundarios : 500 V

P

VPVSVP

Realizamos El Predimensionamiento de la losa

h=l/25h=550/25h=22h=20cm

A

0.10 0.30 0.10 0.30 0.10 0.30 0.10

Hacemos el Metrado de Cargas0.40

0.05

20.00

0.15

0.10 0.30 0.10 0.30 0.10

Determinamos el Numero de Viguetas en un Metro

Nro: 1.00/40Nro: 2.5 Viguetas por metro

Realizamos el metrado de cargas

CM=

Hallamos el Peso Propio de la Loza

Hallamos el Peso de Las Viguetas

P.P.Viguetas= 0.1x0.15x2400x1P.P.Viguetas= 36Kg/m

Metramos la Losa Superior

L.S.: 0.4x0.05x2400x1L.S.: 48Kg/m

Peso Propio de la Losa + Peso Propio de la Tabiqueria + Cielo Razo + Falso Piso

A

Hallamos el Peso Propio del Ladrillo Para 1m

P.L.= 100/30x9P.L.= 30Kg/m

Entonces Hacemos la Sumatoria

P.P.Losa= 36Kg/m+48Kg/m+30Kg/mP.P.Losa= 114Kg/m

Lo Multiplicamos por el Numero de Viguetas Que Existen en un Metro

=2.5x114=285Kg/m2

Hacemos La Sumatoria Para la Carga Muerta

CM =285Kg/m2+110+120+100CM =615Kg/m2

Considerando la C.V. Como la Sobre Carga

w =615Kg/m2+200Kg/m2w =815Kg/m2

Multiplicamos a la Carga Muerta y Carga Viva por sus Factores de seguridad

wu= 615Kg/m2x1.4+200Kg/m2x1.7wu= 861Kg/m2+340Kg/m2

Convertimos Las Cargas de K/m2 a Kg/m lo dividimos por el numero de viguetas en un metro

wu= (861Kg/m2+340Kg/m2)/2.5wu= 344.4Kg/m+136Kg/m

Convertimos Las Cargas de K/m2 a Kg/m lo dividimos por el numero de viguetas en un metro

CARGA VIVA: 136.00CARGA MUERTA: 344.40DISTANCIA AB: 4.55DISTANCIA BC: 5.75DISTANCIA CD: 4.25

I: 2.00

CALCULO DE LA RIGIDEZ

K1= 3*I/4LK1= 3x2/4.55x4K1= 0.33

K2= I/LK2= 2/5.75K2= 0.35

K3= 3*I/4LK3= 3x2/4.25x4K3= 0.35

CALCULO DE LOS COEF. DE DISTRIBUCION

APOYO BD1=K1/(K1+K2) 0.33/(0.33+0.35)

D1= 0.49D2=K2/(K1+K2) 0.35/(0.33+0.35)

D2= 0.51APOYO CD2=K2/(K2+K3) 0.35/(0.35+0.35)

D2= 0.50D3=K3/(K2+K3) 0.35/(0.35+0.35)

D3= 0.50

CALCULO DEL EMPOTRAMIENTO PERFECTO:

TRAMO AB:MB= -QL^2/8 -480.4x4.55^2/8 MB= -1243.19TRAMO BC:MB= QL^2/12 480.4x5.75^2/8 MB= 1323.60MC= -QL^2/12 -480.4x5.75^2/8 MC= -1323.60TRAMO CD:MD= QL^2/8 480.4x4.25^2/8 MC= 1084.65

1

CV=136

CM=344.4

A 4.55 B 5.75 C 4.25 D

0.49 0.51 0.50 0.50

-1243.19 1323.60 -1323.6 1084.65

-39.02 -41.39 -20.70

Err:502 129.83 129.83

Err:502 Err:502 Err:502

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CM=136 CM=136 CM=136

CM=344.4 CM=344.4 CM=344.4

A 4.55 B1 B2 5.75 C1 C2 4.25 D

CALCULO DE LA REACCIONES:

TRAMO A B1:

Hacemos Sumatoria de Momentos en A Hacemos Sumatoria de Fuerzas en Y

Err:502 RA+RB1=2185.82

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO B1C1:

Hacemos Sumatoria de Momentos en B2 Hacemos Sumatoria de Fuerzas en Y

Err:502 RB2+RC1=2762.3

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO C2 D:


Err:502 RC2+RD=2041.7

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502



2

CV=136 CV=136

CM=344.4

A 4.55 B 5.75 C 4.25 D

0.49 0.51 0.50 0.50

-1243.19 948.89 -948.9 1084.65

143.20 151.10 75.55

Err:502 -104.87 -106.44

Err:502 Err:502 Err:502

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CM=136 CM=136

CM=344.4 CM=344.4 CM=344.4

A 4.55 B1 B2 5.75 C1 C2 4.25 D


TRAMO AB:


Err:502 RA+RB1=2185.82

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO B1C1:


Err:502 RB2+RC1=1980.3

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO C2 D:


Err:502 RC2+RD=2041.7

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502



3

CV=136

CM=344.4

A 4.55 B 5.75 C 4.25 D

0.49 0.51 0.50 0.50

-891.24 1323.60 -1323.6 777.59

-210.37 -221.99 -111.00

Err:502 326.07 330.94

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CM=136

CM=344.4 CM=344.4 CM=344.4

A 4.55 B1 B2 5.75 C1 C2 4.25 D


TRAMO AB:


Err:502 RA+RB1=2185.82

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO B1C1:


Err:502 RB2+RC1=2762.3

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO C2 D:


Err:502 RC2+RD=2041.7

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502



1

CV=136

CM=344.4

A 4.55 B 5.75 C 4.25 D

0.49 0.51 0.50 0.50

-1243.19 1323.60 -1323.6 777.59

-39.12 -41.29 -20.65

Err:502 281.23 285.43

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CM=136 CM=136

CM=344.4 CM=344.4 CM=344.4

A 4.55 B1 B2 5.75 C1 C2 4.25 D


TRAMO AB:


Err:502 RA+RB1=2185.82

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO B1C1:


Err:502 RB2+RC1=2762.3

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO C2 D:


Err:502 RC2+RD=2041.7

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502



1

CV=136 kg/m

CM=344.4 kg/m

A 4.55 B 5.75 C 4.25 D

0.49 0.51 0.50 0.50

-891.24 1323.60 -1323.6 1084.65

-210.37 -221.99 -111.00

Err:502 173.68 176.27

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CM=136 CM=136

CM=344.4 CM=344.4 CM=344.4

A 4.55 B1 B2 5.75 C1 C2 4.25 D


TRAMO AB:


Err:502 RA+RB1=2185.82

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO B1C1:


Err:502 RB2+RC1=2762.3

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

TRAMO C2 D:


Err:502 RC2+RD=2041.7

Err:502 Err:502

Err:502

X= Err:502

X= Err:502

M+= Err:502

M+= Err:502

Predimencionamiento de la viga principal

a

2.625

2.625

2.225

2.225

2.425

2.425

a

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL A

a = Peso del muro / el Peso de la losa

Calculo del Peso del Muro:

P.M = 0.25mx1350Kg/m3x2.9mP.M = 978.75 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 978.75 Kg/m / 861Kg/m2a = 1.14m

ATP = a+AtATP = 1.14m+2.625mATP = 3.765m

Calculamos h:

h = L / 11h = 5.5/11h = 0.5mh = 0.5 h =0.5m

Calculamos b:

b = ATP/20b = 3.765 / 20b = 0.19m b =0.2mb = 0.2

Para la Viga Principal A Tenemos Que:

h =0.5mb =0.2m

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL B

AT = 2.625m+2.225mAT = 4.85m

h = L / 11h = 5.5/11h = 0.5mh = 0.5 h =0.5m

b = 4.85m/20b = 0.24m b =0.3mb = 0.3

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL C

AT = 2.225m+2.225mAT = 4.45mAT = 4.45

h = L / 11h = 5.5/11h = 0.5mh = 0.5 h =0.5m

b = 4.45/20b = 0.22m b =0.3mb = 0.3

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL D



P.M = 0.25mx1350Kg/m3x2.9mP.M = 978.75 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 978.75 Kg/m / 861Kg/m2a = 1.14m


Calculamos h:

h = L / 11h = 5.5/11h = 0.5mh = 0.5 h =0.5m

Calculamos b:

b = ATP/20b = 3.565 / 20b = 0.18m b =0.2mb = 0.2

Para la Viga Principal D Tenemos Que:

h = 0.5b = 0.2


h = 0.5 mb = 0.2 m

Para la Viga Principal B Tenemos Que:

h = 0.5 mb = 0.3 m

Para la Viga Principal C Tenemos Que:

h = 0.5 mb = 0.3 m


h = 0.5 mb = 0.2 m

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL A

a = Peso del muro / el Peso de la losah = 1.2


P.M = 0.25mx1350Kg/m3x1.2mP.M = 405 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 405 Kg/m / 861Kg/m2a = 0.47m


Calculamos h:

h = L / 11h = 5.5/11h = 0.5mh = 0.45 h =0.45m

Calculamos b:

b = ATP/20b = 3.095 / 20b = 0.15m b =0.2mb = 0.2


h =0.45mb =0.2m

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL B

AT = 2.625m+2.225mAT = 4.85m

h = L / 11h = 5.5/11h = 0.5mh = 0.45 h =0.45m

b = 4.85m/20b = 0.24m b =0.3mb = 0.3

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL C

AT = 2.225m+2.225mAT = 4.45m

h = L / 11h = 5.5/11h = 0.5mh = 0.45 h =0.45m

b = 4.45/20b = 0.22m b =0.3mb = 0.3

PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL D



P.M = 0.25mx1350Kg/m3x2.9mP.M = 978.75 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 405 Kg/m / 861Kg/m2a = 0.47m


Calculamos h:

h = L / 11h = 5.5/11h = 0.5mh = 0.45 h =0.45m

Calculamos b:

b = ATP/20b = 3.095 / 20b = 0.15m b =0.2mb = 0.2


h = 0.45b = 0.2


h = 0.45 mb = 0.2 m

Para la Viga Principal B Tenemos Que:

h = 0.45 mb = 0.3 m

Para la Viga Principal C Tenemos Que:

h = 0.45 mb = 0.3 m


h = 0.45 mb = 0.2 m

METRADO DE CARGAS

Para la viga Principal A

CM=Inf. Losa+P.P.Viga+P.P.Losa

Inf. Losa = P. P. de la Losa x At

P.P. de la Losa =861Kg/mP.P. de la L. 861

Inf. Losa 861x2.625mInf. Losa =2260.13Kg/mInf. Losa 2260.13

Hallamos el Peso Propio de la Viga

P.P. Viga = bxhx&cºAP.P. Viga = 0.5mx0.2mx2400Kg/m3P.P. Viga = 240Kg/m

Lo Multiplicamos por su Factor de Seguridad de Carga Muerta

P.P. Viga = 240Kg/mx1.4P.P. Viga = 336Kg/m

Hallamos el Peso Propio del Muro

P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx2.9mx1350Kg/m3P.P. Muro = 978.75Kg/m


P.P. Muro = 978.75Kg/mx1.4P.P. Muro = 1370.25Kg/m

Entonces Tenemos Que:

C.M. =2260.13Kg/m+336Kg/m+1370.25Kg/mC.M. =3966.38Kg/m

Calculamos la Carga Viva

Para la Carga Viva Tomamos La Influencia en la Losa Aligerada de la Carga Viva

Inf. Losa =340Kg/m2x2.625mInf. Losa =892.5Kg/m

CV = =892.5Kg/m

METRADO DE CARGAS

Para la viga Principal B



P.P. de la Losa =861Kg/m

Inf. Losa 861x4.85mInf. Losa =4175.85Kg/m


P.P. Viga = hxbx&cºAP.P. Viga = 0.5mx0.3mx2400Kg/m3P.P. Viga = 360Kg/m











Inf. Losa =340Kg/m2x4.85mInf. Losa =1649Kg/m

CV = =1649Kg/m

METRADO DE CARGAS

Para la viga Principal C


















CV = =1581Kg/m

METRADO DE CARGAS

Para la viga Principal D


















CV = =824.5Kg/m

METRADO DE CARGAS

Para la viga Principal A






P.P. Viga = bxhx&cºAP.P. Viga = 0.5mx0.2mx2400Kg/m3




P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m


P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m


C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/m




CV = =892.5Kg/m

METRADO DE CARGAS

Para la viga Principal B


















CV = =1649Kg/m

METRADO DE CARGAS

Para la viga Principal C




Inf. Losa 861x4.65mInf. Losa =4003.65Kg/mInf. Losa 4003.65














CV = =1581Kg/m

METRADO DE CARGAS

Para la viga Principal D


















CV = =824.5Kg/m

Predimencionamiento de las Vigas Secundaria

a 2.625 2.625 2.225 2.225 2.425 2.425 a

PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 1



P.M = 0.25mx1350Kg/m3x2.9mP.M = 978.75 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 978.75 Kg/m / 861Kg/m2a = 1.14m


Calculamos h:

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5mh = 0.5

Calculamos b:

b = ATP/20b = 3.765 / 20b = 0.19m b =0.2mb = 0.2b = 0.2


h =0.5mb =0.2m


AT = 2.625m+2.225mAT = 4.85m

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5m

b = 4.85m/20b = 0.24m b =0.3mb = 0.3


AT = 2.225m+2.425mAT = 4.65m

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5m

b = 4.65/20b = 0.23m b =0.2mb = 0.2




P.M = 0.25mx1350Kg/m3x2.9mP.M = 978.75 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 978.75 Kg/m / 861Kg/m2a = 1.14m


Calculamos h:

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5m

Calculamos b:

b = ATP/20b = 3.565 / 20b = 0.18m b =0.2mb = 0.2


h = 0.5

b = 0.2

Para la Viga Secunadaria 1 Tenemos Que:

h = 0.5 mb = 0.2 m


h = 0.5 mb = 0.3 m


h = 0.5 mb = 0.2 m


h = 0.5 mb = 0.2 m


a = Peso del muro / el Peso de la losah = 1.2Calculo del Peso del Muro:

P.M = 0.25mx1350Kg/m3x1.2mP.M = 405 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 405 Kg/m / 861Kg/m2a = 0.47m


Calculamos h:

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5m

Calculamos b:

b = ATP/20b = 3.095 / 20b = 0.15m b =0.2mb = 0.2


h =0.5mb =0.2m


AT = 2.625m+2.225mAT = 4.85m

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5m

b = 4.85m/20b = 0.24m b =0.3mb = 0.3


AT = 2.225m+2.425mAT = 4.65m

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5m

b = 4.65/20b = 0.23m b =0.25mb = 0.25




P.M = 0.25mx1350Kg/m3x1.2mP.M = 405 Kg/m

Peso de la Losa :

P.L. : 861Kg/m2

a = 405 / 861a = 0.47m


Calculamos h:

h = L / 11h = 5/11h = 0.45mh = 0.5 h =0.5m

Calculamos b:

b = ATP/20b = 2.895 / 20b = 0.14m b =0.2mb = 0.2


h = 0.5b = 0.2


h = 0.5 mb = 0.2 m


h = 0.5 mb = 0.3 m


h = 0.5 mb = 0.25 m


h = 0.5 mb = 0.2 m

METRADO DE CARGAS

Para la viga Secundaria 1






P.P. Viga = bxhx&cºAP.P. Viga = 0.2x0.5x2400P.P. Viga = 240Kg/m












CV = =892.5Kg/m

METRADO DE CARGAS



















CV = =894.73Kg/m

METRADO DE CARGAS



















CV = =1581Kg/m

METRADO DE CARGAS










P.P. Viga = 336Kg/m









CV = =824.5Kg/m

METRADO DE CARGAS












405








CV = =892.5Kg/m

METRADO DE CARGAS



















CV = =894.73Kg/m

METRADO DE CARGAS



















CV = =1581Kg/m

METRADO DE CARGAS










P.P. Viga = 336Kg/m









CV = =824.5Kg/m

2.625

2.625

2.225

2.225

2.425

2.425

2.275 2.275 2.875 2.875 2.125 2.125

Columna Tipo I-A

Columna Tipo I-B

Columna Tipo I-C

Columna Tipo I-D

Columna Tipo III-A

Columna Tipo II-A

Columna Tipo II-B

Columna Tipo III-B

Columna Tipo II-D

Columna Tipo II-F

Columna Tipo III-D

Columna Tipo II-H

Columna Tipo II-G

Columna Tipo III-C

Columna Tipo II-C

Columna Tipo II-E

PREDIMENCIONAMIENTO DE COLUMNAS

Para la columna I - A

Hallamos el Area Tributaria:

At = 2.625+2.225x2.275+2.875At = 24.9775m2At = 24.9775

a) Para el AntePenultimo Piso

Ata = 24.9775m2x3Ata = 74.9325m2Ata = 74.9325

K = 0.0014

Ag = 0.0014x74.9325m2Ag = 0.1049m2Ag = 0.1049

Le Sacamos la Raiz a Ag:

L = √0.1049m2L = 0.323882694814033mL = 0.3 L=0.3mL = 0.3x0.3

b) Para el Segundo Piso

At = 24.9775m2

Ata = 24.9775m2x2Ata = 49.955m2Ata = 49.955

K = 0.001125

Ag = 49.955x0.001125Ag = 0.0562m2Ag = 0.0562


L = √0.0562m2L = 0.24mL = L = 0.24mx0.24m

c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo

L = 0.24mx0.24m

Para la columna I - B


At = 2.875+2.125x2.625+2.225At = 24.25m2


Ata = 24.25m2x3Ata = 72.75m2

K = 0.0014

Ag = 72.75x0.0014Ag = 0.1019m2


L = √0.1019m2L = 0.32mL = 0.3 L=0.3mL = 0.3x0.3


At = 24.25m2

Ata = 24.25x2Ata = 48.5m2

K = 0.001125

Ag = 48.5m2x0.001125Ag = 0.0546m2


L = √0.0546m2L = 0.23mL = 0.25 L=0.25mL = 0.25x0.25


L = 0.25x0.25

Para la columna I - C


At = 2.275+2.875x2.225+2.425At = 23.948m2


Ata = 23.948m2x3Ata = 71.844m2

K = 0.0014

Ag = 71.844x0.0014Ag = 0.1006m2


L = √0.1006m2L = 0.32mL = 0.3 L=0.3mL = 0.3x0.3


At = 23.948m2

Ata = 23.948m2x2Ata = 47.896m2

K = 0.001125

Ag = 47.896m2x0.001125Ag = 0.0539m2


L = √0.0539m2L = 0.23mL = 0.25 L=0.25mL = 0.25x0.25


L = 0.25x0.25

Para la columna I - D


At = 2.875+2.125x2.225+2.425At = 23.25m2


Ata = 23.25m2x3Ata = 69.75m2

K = 0.0014

Ag = 69.75x0.0014Ag = 0.0977m2


L = √0.0977m2L = 0.31mL = 0.3 L=0.3mL = 0.3x0.3


At = 23.25m2

Ata = 23.25m2x2Ata = 46.5m2

K = 0.001125

Ag = 46.5m2x0.001125Ag = 0.0523m2


L = √0.0523m2L = 0.23mL = 0.25 L=0.25mL = 0.25x0.25


L = 0.25x0.25

Para la columna II - A


At = 2.275+2.875x2.625At = 13.519m2


Ata = 13.519m2x3Ata = 40.557m2

K = 0.00248

Ag = 40.557x0.00248Ag = 0.1006m2


L = √0.1006m2L = 0.32mL = 0.3 L=0.3mL = 0.3x0.3


At = 13.519m2

Ata = 13.519m2x2Ata = 27.038m2

K = 0.0014

Ag = 27.038m2x0.0014Ag = 0.0379m2


L = √0.0379m2L = 0.19mL = L = 0.19mx0.19m


L = 0.19mx0.19m

Para la columna II - B


At = 2.875+2.125x2.625At = 13.125m2


Ata = 13.125m2x3Ata = 39.375m2

K = 0.00248

Ag = 39.375x0.00248Ag = 0.0977m2


L = √0.0977m2L = 0.31mL = 0.3 L=0.3mL = 0.3x0.3


At = 13.125m2

Ata = 13.125m2x2Ata = 26.25m2

K = 0.0014

Ag = 26.25m2x0.0014Ag = 0.0368m2


L = √0.0368m2L = 0.19mL = 0.25 L=0.25mL = 0.25x0.25


L = 0.25x0.25

Para la columna II - C


At = 2.625+2.225x2.275At = 11.034m2


Ata = 11.034m2x3Ata = 33.102m2

K = 0.00248

Ag = 33.102x0.00248Ag = 0.0821m2


L = √0.0821m2L = 0.29mL = 0.3 L=0.3mL = 0.3x0.3


At = 11.034m2

Ata = 11.034m2x2Ata = 22.068m2

K = 0.0014

Ag = 22.068m2x0.0014Ag = 0.0309m2


L = √0.0309m2L = 0.18mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna II - D


At = 2.625+2.225x2.125At = 10.306m2


Ata = 10.306m2x3Ata = 30.918m2

K = 0.00248

Ag = 30.918x0.00248Ag = 0.0767m2


L = √0.0767m2L = 0.28mL = 0.3 L=0.3mL = 0.3x0.3


At = 10.306m2

Ata = 10.306m2x2Ata = 20.612m2

K = 0.0014

Ag = 20.612m2x0.0014Ag = 0.0289m2


L = √0.0289m2L = 0.17mL = 0.25 L=0.25mL = 0.25x0.25


L = 0.25x0.25

Para la columna II - E


At = 2.225+2.425x2.275At = 10.579m2


Ata = 10.579m2x3Ata = 31.737m2

K = 0.00248

Ag = 31.737x0.00248Ag = 0.0787m2


L = √0.0787m2L = 0.28mL = 0.3 L=0.3mL = 0.3x0.3


At = 10.579m2

Ata = 10.579m2x2Ata = 21.158m2

K = 0.0014

Ag = 21.158m2x0.0014Ag = 0.0296m2


L = √0.0296m2L = 0.17mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna II - F


At = 2.225+2.425x2.125At = 9.881m2


Ata = 9.881m2x3Ata = 29.643m2

K = 0.00248

Ag = 29.643x0.00248Ag = 0.0735m2


L = √0.0735m2L = 0.27mL = 0.3 L=0.3mL = 0.3x0.3


At = 9.881m2

Ata = 9.881m2x2Ata = 19.762m2

K = 0.0014

Ag = 19.762m2x0.0014Ag = 0.0277m2


L = √0.0277m2L = 0.17mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna II - G


At = 2.275+2.875x2.425At = 12.489m2


Ata = 12.489m2x3Ata = 37.467m2

K = 0.00248

Ag = 37.467x0.00248Ag = 0.0929m2


L = √0.0929m2L = 0.3mL = 0.3 L=0.3mL = 0.3x0.3


At = 12.489m2

Ata = 12.489m2x2Ata = 24.978m2

K = 0.0014

Ag = 24.978m2x0.0014Ag = 0.035m2


L = √0.035m2L = 0.19mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna II - H


At = 2.875+2.125x2.425At = 12.125m2


Ata = 12.125m2x3Ata = 36.375m2

K = 0.00248

Ag = 36.375x0.00248Ag = 0.0902m2


L = √0.0902m2L = 0.3mL = 0.3 L=0.3mL = 0.3x0.3


At = 12.125m2

Ata = 12.125m2x2Ata = 24.25m2

K = 0.0014

Ag = 24.25m2x0.0014Ag = 0.034m2


L = √0.034m2L = 0.18mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna III - A


At = 2.625x2.275At = 5.972m2


Ata = 5.972m2x3Ata = 17.916m2

K = 0.0037

Ag = 17.916x0.0037Ag = 0.0663m2


L = √0.0663m2L = 0.26mL = 0.3 L=0.3mL = 0.3x0.3


At = 5.972m2

Ata = 5.972m2x2Ata = 11.944m2

K = 0.00195

Ag = 11.944m2x0.00195Ag = 0.0233m2


L = √0.0233m2L = 0.15mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna III - B


At = 2.625x2.125At = 5.578m2


Ata = 5.578m2x3Ata = 16.734m2

K = 0.0037

Ag = 16.734x0.0037Ag = 0.0619m2


L = √0.0619m2L = 0.25mL = 0.3 L=0.3mL = 0.3x0.3


At = 5.578m2

Ata = 5.578m2x2Ata = 11.156m2

K = 0.00195

Ag = 11.156m2x0.00195Ag = 0.0218m2


L = √0.0218m2L = 0.15mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna III - C


At = 2.425x2.275At = 5.517m2


Ata = 5.517m2x3Ata = 16.551m2

K = 0.0037

Ag = 16.551x0.0037Ag = 0.0612m2


L = √0.0612m2L = 0.25mL = 0.2 L=0.2mL = 0.2x0.2


At = 5.517m2

Ata = 5.517m2x2Ata = 11.034m2

K = 0.00195

Ag = 11.034m2x0.00195Ag = 0.0215m2


L = √0.0215m2L = 0.15mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para la columna III - D


At = 2.425x2.125At = 5.153m2


Ata = 5.153m2x3Ata = 15.459m2

K = 0.0037

Ag = 15.459x0.0037Ag = 0.0572m2


L = √0.0572m2L = 0.24mL = 0.2 L=0.2mL = 0.2x0.2


At = 5.153m2

Ata = 5.153m2x2Ata = 10.306m2

K = 0.00195

Ag = 10.306m2x0.00195Ag = 0.0201m2


L = √0.0201m2L = 0.14mL = 0.2 L=0.2mL = 0.2x0.2


L = 0.2x0.2

Para las Columnas del Tipo I

Para el Primer Nivel

L = 0.3 x 0.3

Para el Segundo Nivel y Azotea

L = 0.24 x 0.24

Para Las Columnas del Tipo II


L= 0.3 x 0.3


L= 0.19 * 0.19

Para Las Columnas del Tipo III


L= 0.3 x 0.3


L= 0.2 * 0.2

Sétimo Ciclo de giro

M1 = 20.925 + (( -0.175 * ( 11.2 + -1.64 )) + (-0.325 * -8.24 )) = 21.930M2 = -3.332 + (( -0.184 * 21.93 ) + ( -0.099 * ( -3.81 + -1.64 )) + ( -0.217 * 6.52 )) = -8.240M3 = 1.55+ ( ( -0.211 * -8.24 ) + ( -0.096 * ( 2.96 + -1.64 ) ) + ( -0.193 * -17.39 ) ) = 6.520M4 = 13.151 + ( ( -0.11 * ( 8.18 + -0.96 ) ) + ( -0.281 * -3.81 ) + ( -0.11 * ( 21.93 + -1.64 ) ) ) = -17.390M5 = -2.228 + ( ( -0.169 * 11.2 ) + ( -0.066 * ( -2.76 + -0.96 ) ) + ( -0.199 * 2.96 ) + ( -0.066 * ( -8.24 + -1.64) ) ) = 11.200

M6 = 1.039 + ( ( -0.194 * -3.81 ) + ( -0.064 * ( 2.1 + -0.96 ) ) + ( -0.178 * -8.8 ) + ( -0.064 * ( 6.52 + -1.64 ) ) ) = -3.810M7 = -10.727 + ( ( -0.29 * 2.96 ) + ( -0.105 * ( -6.51 + -0.96 ) ) + ( -0.105 * ( -17.39 + -1.64 ) ) ) = 2.960M8 = 8.374 + ( ( -0.202 * -0.38 ) + ( -0.214 * -2.76 ) + ( -0.084 * ( 11.2 + -0.96 ) ) ) = -8.800M9 = -1.567 + ( ( -0.142 * 8.18 ) + ( -0.134 * -0.38 ) + ( -0.168 * 2.1 ) + ( -0.056 * ( -3.81 + -0.96 ) ) ) = 8.180M10 = 0.734 + ( ( -0.164 * -2.76 ) + ( -0.131 * -0.38 ) + ( -0.15 * -6.51 ) + ( -0.054 * ( 2.96 + -0.96 ) ) ) = -2.760M11 = -6.903 + ( ( -0.224 * 2.1 ) + ( -0.195 * -0.38 ) + ( -0.081 * ( -8.8 + -0.96 ) ) ) = 2.100M12 = -6.903 + ( ( -0.224 * 2.1 ) + ( -0.195 * -0.38 ) + ( -0.081 * ( + -0.96 ) ) ) = -6.510

M°I 0 + ( ( -0.375 * ( 21.93 + 11.2 ) ) + ( -0.375 * ( -8.24 + -3.81 ) ) + (-0.375 * ( 6.52 + 2.96) ) + ( -0.375 * ( -17= -0.960M°II 0 + ( ( -0.375 * ( 11.2 + 8.18 ) ) + ( -0.375 * ( -3.81 + -2.76 ) ) + ( -0.375 * ( 2.96 + 2.1 ) ) + ( -0.375 * ( -8.8 = -0.380M°III 0 + ( ( -0.375 * 8.18 ) + ( -0.375 * -2.76 ) + ( -0.375 * 2.1 ) + ( -0.375 * -6.51 ) ) = -0.380

Momentos finalesMik = Mik + Kik (2mi + mk + mr)

Nudo 01 Correccion Nudo 07 CorrecciónM1-2 = -4939.455 -4935.603 M7-3 = 790.444 790.161M1-5 = 4933.528 4935.603 M7-6 = 7954.872 7954.012

-5.927 0.000 M7-8 = -9066.168 -9066.957M7-11 = 323.067 322.784

Nudo 02 2.216 0.000

M2-1 = 11427.539 11427.347

M2-3 = -9156.234 -9156.461 Nudo 08

M2-6 = -2270.782 -2270.886 M8-7 = 4836.786 4832.4170.523 0.000 M8-4 = -2991.399 -2992.981

M8-12 = -1837.853 -1839.415Nudo 03 M8-V = 0 0M3-2 = 8032.020 8034.370 7.534 0.020

M3-4 = -9631.51 -9629.363

M3-7 = 1593.923 1594.993 Nudo 09

-5.570 0.000 M9-5 = 2272.644 2272.671M9-10 = -6124.802 -6124.734

Nudo 04 M9-13 = 3852.000 3852.064M4-3 = 4186.547 4185.500 -0.158 0.000

M4-8 = -4184.980 -4185.500

M4-V = 0 0 Nudo 10

1.567 0.000 M10-9 = 9446.227 9444.173M10-6 = -937.547 -938.357

Nudo 05 M10-11 = -6570.947 -6573.377M5-1 = 3478.328 3479.907 M10-14 = -1930.500 -1932.438M5-6 = -5665.044 -5661.012 7.233 0.000

M5-9 = 2179.541 2181.120

-7.175 0.015 Nudo 11

M11-10 = 5972.632 5975.387Nudo 06 M11-7 = 595.8592 596.766M6-2 = -1349.994 -1349.429 M11-12 = -8016.890 -8014.371M6-5 = 10465.040 10466.485 M11-15 = 1440.000 1442.200M6-7 = -8467.602 -8465.900 -8.399 -0.017

M6-10 = -651.721 -651.156

-4.277 0.000 Nudo 12

M12-11 = 5194.725 5194.713M12-8 = -1941.198 -1941.202M12-16 = -3253.500 -3253.511M12-V = 0 0

0.027 0.000


Nudo 01 Correccion Nudo 07 CorrecciónM1-2 = -4106.227 -4103.556 M7-3 = 1042.754 1042.672M1-5 = 4102.118 4103.556 M7-6 = 7663.331 7663.085

-4.109 0.000 M7-8 = -9575.963 -9576.189M7-11 = 870.513 870.513

Nudo 02 0.634 0.081

M2-1 = 10557.861 10556.445

M2-3 = -9113.710 -9115.380 Nudo 08

M2-6 = -1440.303 -1441.065 M8-7 = 5594.004 5594.3263.847 0.000 M8-4 = -3211.122 -3211.006

M8-12 = -2383.437 -2383.318Nudo 03 M8-V = 0 0M3-2 = 8315.088 8315.513 -0.555 0.002

M3-4 = -9154.02 -9153.633

M3-7 = 837.927 838.120 Nudo 09

-1.007 0.000 M9-5 = 2169.300 2169.403M9-10 = -4703.412 -4703.150

Nudo 04 M9-13 = 2533.500 2533.747M4-3 = 3466.682 3466.377 -0.612 0.000

M4-8 = -3466.225 -3466.377

M4-V = 0 0 Nudo 10

0.457 0.000 M10-9 = 8260.551 8259.560M10-6 = -782.996 -783.387

Nudo 05 M10-11 = -7046.567 -7047.739M5-1 = 3747.396 3747.623 M10-14 = -427.500 -428.435M5-6 = -6555.483 -6554.903 3.488 0.000

M5-9 = 2807.055 2807.279

-1.032 -0.001 Nudo 11

M11-10 = 6658.926 6659.508Nudo 06 M11-7 = 441.3082 441.500M6-2 = -1614.406 -1613.548 M11-12 = -7187.508 -7186.976M6-5 = 11348.335 11350.533 M11-15 = 85.500 85.965M6-7 = -8480.747 -8478.159 -1.773 -0.004

M6-10 = -1259.684 -1258.825

-6.502 0.000 Nudo 12

M12-11 = 3963.280 3961.807M12-8 = -1862.991 -1863.524M12-16 = -2097.000 -2098.283M12-V = 0 0

3.289 0.000

VIGA PRINCIPAL A

JUEGO DE DAMERO - MOMENTOS MAXIMOS NEGATIVOS

C.V. =892.5Kg/mC.M.=3163.13kg/m

C.V. =892.5Kg/mC.M.=3966.38kg/m

C.V. =892.5Kg/mC.M.=3966.38kg/m

Descripción Base AlturaColumnas 30 30 cm

Vigas 20 50 cmViga Azotea 20 45 cm

Luces 1-2 5.25 m 2-3 4.45 m 3-4 4.85 m

Volado4-V 0 m8-V 0 m12-V 0 m

Alturas 0 1-2 2.9 m

2-3 2.9 m

3-4 1.2 m

Rigidez relativa Takabeya

VigasK1-2 173.571K2-3 204.775K3-4 187.887K5-6 238.095K6-7 280.899K7-8 257.732K9-10 238.095

K10-11 280.899K11-12 257.732

ColumnasK1-5 93.103K2-6 93.103K3-7 93.103

Kik = h3/l

K4-8 93.103

K5-9 93.103K6-10 93.103K7-11 93.103K8-12 93.103K9-13 225.000K10-14 225.000K11-15 225.000K12-16 225.000

Factores de Giro

Nudo 01 Nudo 07 Calculo de los factores de corrimiento

-(K1-2)/(2(K1-2+K1-5) -(K7-3)/(2(K7-3+K7-6+K7-8+K7-11)

&1-2 = -0.325 &7-3 = -0.064 Nivel I

-(K1-5)/(2(K1-2+K1-5) -(K7-6)/(2(K7-3+K7-6+K7-8+K7-11) -3/2(K1-5/(K1-5+K2-6+K3-7+K4-8)

&1-5 = -0.175 &7-6 = -0.194 V1-5 =

-(K7-8)/(2(K7-3+K7-6+K7-8+K7-11) -3/2(K2-6/(K1-5+K2-6+K3-7+K4-8)

Nudo 02 &7-8 = -0.178 V2-6 =

-(K2-1)/(2(K2-1+K2-3+K2-6) -(K7-11)/(2(K7-3+K7-6+K7-8+K7-11) -3/2(K3-7/(K1-5+K2-6+K3-7+K4-8)

&2-1 = -0.184 &7-11 = -0.064 V3-7 =

-(K2-3)/(2(K2-1+K2-3+K2-6) -3/2(K4-8/(K1-5+K2-6+K3-7+K4-8)

&2-3 = -0.217 Nudo 08 V4-8 =

-(K2-6)/(2(K2-1+K2-3+K2-6) -(K8-7)/(2(K8-7+K8-4+K8-12)

&2-6 = -0.099 &8-7 = -0.290 Nivel II

-(K8-4)/(2(K8-7+K8-4+K8-12) -3/2(K5-9/(K5-9+K6-10+K7-11+K8-12)

Nudo 03 &8-4 = -0.105 V5-9 =

-(K3-2)/(2(K3-2+K3-4+K3-7) -(K8-12)/(2(K8-7+K8-4+K8-12) -3/2(K6-10/(K5-9+K6-10+K7-11+K8-12)

&3-2 = -0.211 &8-12 = -0.105 V6-10 =

-(K3-4)/(2(K3-2+K3-4+K3-7) -3/2(K7-11/(K5-9+K6-10+K7-11+K8-12)

&3-2 = -0.193 Nudo 09 V7-11 =

-(K3-7)/(2(K3-2+K3-4+K3-7) -(K9-5)/(2(K9-5+K9-10+K9-13) -3/2(K8-12/(K5-9+K6-10+K7-11+K8-12)

&3-7 = -0.096 &9-5 = -0.084 V8-12 =

-(K9-10)/(2(K9-5+K9-10+K9-13)

Nudo 04 &9-10 = -0.214 Nivel III

-(K4-3)/(2(K4-3+K4-8) -(K9-13)/(2(K9-5+K9-10+K9-13) -3/2(K9-13/(K9-13+K10-14+K11-15+K12-16)

&4-3 = -0.334 &9-13 = -0.202 V9-13 =

-(K4-8)/(2(K4-3+K4-8) -3/2(K10-14/(K9-13+K10-14+K11-15+K12-16)

&4-8 = -0.166 Nudo 10 V10-14 =

-(K10-9)/(2(K10-9+K10-6+K10-11+K10-14) -3/2(K11-15/(K9-13+K10-14+K11-15+K12-16)

Nudo 05 &10-9 = -0.142 V11-15 =

-(K5-1)/(2(K5-1+K5-6+K5-9) -(K10-6)/(2(K10-9+K10-6+K10-11+K10-14) -3/2(K12-16/(K9-13+K10-14+K11-15+K12-16)

&5-1 = -0.110 &10-6 = -0.056 V12-16 =

-(K5-6)/(2(K5-1+K5-6+K5-9) -(K10-11)/(2(K10-9+K10-6+K10-11+K10-14)

&5-6 = -0.281 &10-11 = -0.168

-(K5-9)/(2(K5-1+K5-6+K5-9) -(K10-14)/(2(K10-9+K10-6+K10-11+K10-14)

&5-9 = -0.110 &10-14 = -0.134

Nudo 06

-(K6-2)/(2(K6-2+K6-5+K6-7+K6-10) Nudo 11

&6-2 = -0.066 -(K11-10)/(2(K11-10+K11-7+K11-12+K11-15)

-(K6-5)/(2(K6-2+K6-5+K6-7+K6-10) &11-10 = -0.164

&6-5 = -0.169 -(K11-7)/(2(K11-10+K11-7+K11-12+K11-15)

-(K6-7)/(2(K6-2+K6-5+K6-7+K6-10) &11-7 = -0.054

&6-7 = -0.199 -(K11-12)/(2(K11-10+K11-7+K11-12+K11-15)

-(K6-10)/(2(K6-2+K6-5+K6-7+K6-10) &11-12 = -0.150

&6-10 = -0.066 -(K11-15)/(2(K11-10+K11-7+K11-12+K11-15)

&11-15 = -0.131

Nudo 12

-(K12-11)/(2(K12-11+K12-8+K12-16)

&12-11 = -0.224

-(K12-8)/(2(K12-11+K12-8+K12-16)

&12-8 = -0.081

-(K12-16)/(2(K12-11+K12-8+K12-16)

&12-16 = -0.195

Calculo de los factores de corrimiento Momentos de empotramiento perfecto

-3/2(K1-5/(K1-5+K2-6+K3-7+K4-8)

-0.375

-3/2(K2-6/(K1-5+K2-6+K3-7+K4-8) Nivel I Nivel II-0.375 M1-2 M5-6

-3/2(K3-7/(K1-5+K2-6+K3-7+K4-8) Carga = 4858.88 Carga = 3966.38

-0.375 -11160.240 -9110.279 -3/2(K4-8/(K1-5+K2-6+K3-7+K4-8)

-0.375 M2-1 M6-5Carga = 4858.88 Carga = 3966.38 +ql2/12 11160.24 +ql2/12 9110.279

-3/2(K5-9/(K5-9+K6-10+K7-11+K8-12)

-0.375 M2-3 M6-7

-ql2/12 -ql2/12


-0.375 -8018.164 -8018.164 -3/2(K7-11/(K5-9+K6-10+K7-11+K8-12)

-0.375 M3-2 M7-6 -3/2(K8-12/(K5-9+K6-10+K7-11+K8-12) Carga = 4858.88 Carga = 4858.88

-0.375 +ql2/12 8018.164 +ql2/12 8018.164

M3-4 M7-8 -3/2(K9-13/(K9-13+K10-14+K11-15+K12-16) Carga = 3966.38 Carga = 4858.88

-0.375 -7774.931 -9524.417 -3/2(K10-14/(K9-13+K10-14+K11-15+K12-16)

-0.375 M4-3 M8-7 -3/2(K11-15/(K9-13+K10-14+K11-15+K12-16) Carga = 3966.38 Carga = 4858.88

-0.375 +ql2/12 7774.931 +ql2/12 9524.417 -3/2(K12-16/(K9-13+K10-14+K11-15+K12-16)

-0.375 M4-V M8-VCarga = 0 Carga = 0 -ql2/2 0 -ql2/2 0

-ql2/12 -ql2/12

-ql2/12 -ql2/12

Calculo de Momentos de Sujeción

Nudo 01 Nudo 07

M1= M1-2 -11160.24 M7= M7-6+M7-8

Nivel III Nudo 02 Nudo 08M9-10 M2= M2-1+M2-3 3142.076 M8= M8-7+M8-V

Carga = 4055.63

-9315.275 Nudo 03 Nudo 09

M3 = M3-2 + M3-4 243.233 M9= M9-10M10-9Carga = 4055.63 Nudo 04 Nudo 10 +ql2/12 9315.275 M4 = M4-3 +M4-V 7774.931 M10= M10-9+M10-11

M10-11 Nudo 05 Nudo 11

-ql2/12

Carga = 4055.63 M5 = M5-6 -9110.279 M11= M11-10+M11-12

-6692.634Nudo 06 Nudo 12

M11-10 M6 = M6-5 + M6-7 1092.115 M12= M12-11+M12-VCarga = 4055.63 +ql2/12 6692.634

M11-12Carga = 3163.13

-6200.394

M12-11Carga = 3163.13 +ql2/12 6200.394

M12-VCarga = 0 -ql2/2 0

-ql2/12

-ql2/12

Cálculo de los momentos en los nudos

Nudo 01 Nudo 07

-1506.253 M°1= -1/2(M1)/(K1-2+K1-5) -1/2(M7)/(K7-3+K7-6+K7-8+K7-11)

M°1= 20.925 M°7 = 1.039

9524.417 Nudo 02 Nudo 08

-1/2(M2)/(K2-1)/(K2-1+K2-3+K2-6) -1/2(M8)/(K8-7+K8-4+K8-12)

M°2 = -3.332 M°8 = -10.727

-9315.275

Nudo 03 Nudo 09

-1/2(M3)/(K3-2+K3-4+K3-7) -1/2(M9)/(K9-5+K9-10+K9-13)

2622.641 M°3 = -0.25 M°9 = 8.374

Nudo 04 Nudo 10

492.24 -1/2(M4)/(K4-3+K4-8) -1/2(M10)/(K10-9+K10-6+K10-11+K10-14)

M°4 = -13.835 M°10 = -1.567

6200.394 Nudo 05 Nudo 11

-1/2(M5)/(K5-1+K5-6+K5-9) -1/2(M11)/(K11-10+K11-7+K11-12+K11-15)

M°5 = 10.736 M°11 = -0.287

Nudo 06 Nudo 12

-1/2(M6)/(K6-2+K6-5+K6-7+K6-10) -1/2(M12)/(K12-11+K12-8+K12-16)

M°6 = -0.774 M°12 = -5.384

Cálculo de los momentos por piso

Nivel Im°I = 0

Nivel IIm°II = 0

Nivel IIIm°III = 0

GIROS TAKABEYA

-0.325 -0.184 -0.217 -0.211 -0.193

M° I -0.1

75

-0.0

99

-0.0

96

0 M1 20.925 M2 -3.332 M3 -0.25-0.930 20.130 -7.350 2.490-1.670 22.110 -7.890 3.600

-1.810

-0.3

75 22.350

-0.3

75 -7.920

-0.3

75 3.830

-1.820 22.390 -7.930 3.870-1.820 22.390 -7.930 3.870-1.820 22.400 -7.930 3.870-1.820 22.400 -7.930 3.870

-0.1

10

-0.0

66

-0.0

64

-0.281 -0.169 -0.199 -0.194 -0.18

M° II -0.1

10

-0.0

66

-0.0

64

0 M5 10.736 M6 -0.774 M7 1.039-0.180 7.820 -2.250 2.810-0.550 8.170 -2.020 3.040

-0.650

-0.3

75

8.170

-0.3

75

-1.900

-0.3

75

2.980

-0.660 8.150 -1.880 2.950

-0.670 8.140 -1.870 2.950

-0.670 8.140 -1.870 2.940-0.680 8.140 -1.870 2.940

-0.0

84

-0.0

56

-0.0

54

-0.214 -0.142 -0.168 -0.164 -0.15

M° III -0.2

02

-0.1

34

-0.1

31

0 M9 8.374 M10 -1.567 M11 -0.287-0.490 8.050 -2.770 0.600-0.690 8.390 -2.690 0.780

-0.740

-0.3

75 8.450

-0.3

75 -2.660

-0.3

75 0.800

-0.750 8.460 -2.660 0.810-0.760 8.470 -2.660 0.810-0.760 8.470 -2.660 0.820-0.760 8.470 -2.660 0.820

Iteraciones

M1 = 20.925 M7 =M2 = -3.332 M8 =M3 = -0.25 M9 =M4 = -13.835 M10 =M5 = 10.736 M11 =M6 = -0.774 M12 =

M°I 0M°II 0M°III 0

Primer ciclo de giro

M1 = 20.925 + (( -0.175 * ( 10.736 + 0 )) + (-0.325 * -3.332 ))M2 = -3.332 + (( -0.184 * 20.13 ) + ( -0.099 * ( -2.25 + 0 )) + ( -0.217 * 2.49 ))M3 = -0.25+ ( ( -0.211 * -3.332 ) + ( -0.096 * ( 2.81 + 0 ) ) + ( -0.193 * -11.97 ) )M4 = -13.835 + ( ( -0.334 * -0.25 ) + ( -0.166 * ( -10.727 + 0 ) ) )M5 = 10.736 + ( ( -0.11 * ( 8.374 + 0 ) ) + ( -0.281 * -0.774 ) + ( -0.11 * ( 20.13 + 0 ) ) )

M6 = -0.774 + ( ( -0.169 * 7.82 ) + ( -0.066 * ( -2.77 + 0 ) ) + ( -0.199 * 2.81 ) + ( -0.066 * ( -3.332 + 0) ) ) M7 = 1.039 + ( ( -0.194 * -0.774 ) + ( -0.064 * ( 0.6 + 0 ) ) + ( -0.178 * -9.21 ) + ( -0.064 * ( -0.25 + 0 ) ) )M8 = -10.727 + ( ( -0.29 * 1.039 ) + ( -0.105 * ( -5.384 + 0 ) ) + ( -0.105 * ( -11.97 + 0 ) ) )M9 = 8.374 + ( ( -0.202 * 0 ) + ( -0.214 * -1.567 ) + ( -0.084 * ( 7.82 + 0 ) ) )M10 = -1.567 + ( ( -0.142 * 8.05 ) + ( -0.134 * 0 ) + ( -0.168 * 0.6 ) + ( -0.056 * ( -0.774 + 0 ) ) ) M11 = -0.287 + ( ( -0.164 * -1.567 ) + ( -0.131 * 0 ) + ( -0.15 * -4.57 ) + ( -0.054 * ( 1.039 + 0 ) ) )M12 = -5.384 + ( ( -0.224 * -0.287 ) + ( -0.195 * 0 ) + ( -0.081 * ( -9.21 + 0 ) ) )

M°I = 0 + ( ( -0.375 * ( 20.13 + 7.82 ) ) + ( -0.375 * ( -7.35 + -2.25 ) ) + (-0.375 * ( 2.49 + 2.81) ) + ( -0.375 * ( -11.97 + -9.2M°II = 0 + ( ( -0.375 * ( 7.82 + 8.05 ) ) + ( -0.375 * ( -2.25 + -2.77 ) ) + ( -0.375 * ( 2.81 + 0.6 ) ) + ( -0.375 * ( -9.21 + -4.57 )M°III = 0 + ( ( -0.375 * 8.05 ) + ( -0.375 * -2.77 ) + ( -0.375 * 0.6 ) + ( -0.375 * -4.57 ) )

Segundo Ciclo de giro

M1 = 20.925 + (( -0.175 * ( 7.82 + -0.93 )) + (-0.325 * -7.35 ))M2 = -3.332 + (( -0.184 * 22.11 ) + ( -0.099 * ( -2.02 + -0.93 )) + ( -0.217 * 3.6 ))M3 = -0.25+ ( ( -0.211 * -7.35 ) + ( -0.096 * ( 3.04 + -0.93 ) ) + ( -0.193 * -12.98 ) )M4 = -13.835 + ( ( -0.334 * 2.49 ) + ( -0.166 * ( -10.727 + -0.93 ) ) )M5 = 10.736 + ( ( -0.11 * ( 8.05 + -0.18 ) ) + ( -0.281 * -2.25 ) + ( -0.11 * ( 22.11 + -0.93 ) ) ) M6 = -0.774 + ( ( -0.169 * 8.17 ) + ( -0.066 * ( -2.69 + -0.18 ) ) + ( -0.199 * 3.04 ) + ( -0.066 * ( -7.35 + -0.93) ) ) M7 = 1.039 + ( ( -0.194 * -2.25 ) + ( -0.064 * ( 0.78 + -0.18 ) ) + ( -0.178 * -9.58 ) + ( -0.064 * ( 2.49 + -0.93 ) ) )M8 = -10.727 + ( ( -0.29 * 2.81 ) + ( -0.105 * ( -4.57 + -0.18 ) ) + ( -0.105 * ( -12.98 + -0.93 ) ) )M9 = 8.374 + ( ( -0.202 * -0.49 ) + ( -0.214 * -2.77 ) + ( -0.084 * ( 8.17 + -0.18 ) ) )M10 = -1.567 + ( ( -0.142 * 8.39 ) + ( -0.134 * -0.49 ) + ( -0.168 * 0.78 ) + ( -0.056 * ( -2.25 + -0.18 ) ) ) M11 = -0.287 + ( ( -0.164 * -2.77 ) + ( -0.131 * -0.49 ) + ( -0.15 * -4.63 ) + ( -0.054 * ( 2.81 + -0.18 ) ) )M12 = -5.384 + ( ( -0.224 * 0.6 ) + ( -0.195 * -0.49 ) + ( -0.081 * ( -9.58 + -0.18 ) ) )

M°I = 0 + ( ( -0.375 * ( 22.11 + 8.17 ) ) + ( -0.375 * ( -7.89 + -2.02 ) ) + (-0.375 * ( 3.6 + 3.04) ) + ( -0.375 * ( -12.98 + -9.58M°II = 0 + ( ( -0.375 * ( 8.17 + 8.39 ) ) + ( -0.375 * ( -2.02 + -2.69 ) ) + ( -0.375 * ( 3.04 + 0.78 ) ) + ( -0.375 * ( -9.58 + -4.63M°III = 0 + ( ( -0.375 * 8.39 ) + ( -0.375 * -2.69 ) + ( -0.375 * 0.78 ) + ( -0.375 * -4.63 ) )

GIROS TAKABEYA

-0.334

-0.1

66

M4 -13.835-11.970-12.980

-0.3

75 -13.170

-13.240-13.260-13.260-13.260

-0.1

05

-0.290

-0.1

05

M8 -10.727-9.210-9.580

-0.3

75

-9.510

-9.460

-9.450

-9.450-9.440

-0.0

81

-0.224

-0.1

95

M12 -5.384-4.570-4.630

-0.3

75 -4.610

-4.600-4.600-4.600-4.600

1.039-10.727

8.374-1.567-0.287-5.384

20.925 + (( -0.175 * ( 10.736 + 0 )) + (-0.325 * -3.332 )) = 20.130-3.332 + (( -0.184 * 20.13 ) + ( -0.099 * ( -2.25 + 0 )) + ( -0.217 * 2.49 )) = -7.350-0.25+ ( ( -0.211 * -3.332 ) + ( -0.096 * ( 2.81 + 0 ) ) + ( -0.193 * -11.97 ) ) = 2.490-13.835 + ( ( -0.334 * -0.25 ) + ( -0.166 * ( -10.727 + 0 ) ) ) = -11.97010.736 + ( ( -0.11 * ( 8.374 + 0 ) ) + ( -0.281 * -0.774 ) + ( -0.11 * ( 20.13 + 0 ) ) ) = 7.820

-0.774 + ( ( -0.169 * 7.82 ) + ( -0.066 * ( -2.77 + 0 ) ) + ( -0.199 * 2.81 ) + ( -0.066 * ( -3.332 + 0) ) ) = -2.2501.039 + ( ( -0.194 * -0.774 ) + ( -0.064 * ( 0.6 + 0 ) ) + ( -0.178 * -9.21 ) + ( -0.064 * ( -0.25 + 0 ) ) ) = 2.810-10.727 + ( ( -0.29 * 1.039 ) + ( -0.105 * ( -5.384 + 0 ) ) + ( -0.105 * ( -11.97 + 0 ) ) ) = -9.2108.374 + ( ( -0.202 * 0 ) + ( -0.214 * -1.567 ) + ( -0.084 * ( 7.82 + 0 ) ) ) = 8.050-1.567 + ( ( -0.142 * 8.05 ) + ( -0.134 * 0 ) + ( -0.168 * 0.6 ) + ( -0.056 * ( -0.774 + 0 ) ) ) = -2.770-0.287 + ( ( -0.164 * -1.567 ) + ( -0.131 * 0 ) + ( -0.15 * -4.57 ) + ( -0.054 * ( 1.039 + 0 ) ) ) = 0.600-5.384 + ( ( -0.224 * -0.287 ) + ( -0.195 * 0 ) + ( -0.081 * ( -9.21 + 0 ) ) ) = -4.570

0 + ( ( -0.375 * ( 20.13 + 7.82 ) ) + ( -0.375 * ( -7.35 + -2.25 ) ) + (-0.375 * ( 2.49 + 2.81) ) + ( -0.375 * ( -11.97 + -9.2= -0.9300 + ( ( -0.375 * ( 7.82 + 8.05 ) ) + ( -0.375 * ( -2.25 + -2.77 ) ) + ( -0.375 * ( 2.81 + 0.6 ) ) + ( -0.375 * ( -9.21 + -4.57 )= -0.1800 + ( ( -0.375 * 8.05 ) + ( -0.375 * -2.77 ) + ( -0.375 * 0.6 ) + ( -0.375 * -4.57 ) ) = -0.490

20.925 + (( -0.175 * ( 7.82 + -0.93 )) + (-0.325 * -7.35 )) = 22.110-3.332 + (( -0.184 * 22.11 ) + ( -0.099 * ( -2.02 + -0.93 )) + ( -0.217 * 3.6 )) = -7.890-0.25+ ( ( -0.211 * -7.35 ) + ( -0.096 * ( 3.04 + -0.93 ) ) + ( -0.193 * -12.98 ) ) = 3.600-13.835 + ( ( -0.334 * 2.49 ) + ( -0.166 * ( -10.727 + -0.93 ) ) ) = -12.98010.736 + ( ( -0.11 * ( 8.05 + -0.18 ) ) + ( -0.281 * -2.25 ) + ( -0.11 * ( 22.11 + -0.93 ) ) ) = 8.170-0.774 + ( ( -0.169 * 8.17 ) + ( -0.066 * ( -2.69 + -0.18 ) ) + ( -0.199 * 3.04 ) + ( -0.066 * ( -7.35 + -0.93) ) ) = -2.0201.039 + ( ( -0.194 * -2.25 ) + ( -0.064 * ( 0.78 + -0.18 ) ) + ( -0.178 * -9.58 ) + ( -0.064 * ( 2.49 + -0.93 ) ) ) = 3.040-10.727 + ( ( -0.29 * 2.81 ) + ( -0.105 * ( -4.57 + -0.18 ) ) + ( -0.105 * ( -12.98 + -0.93 ) ) ) = -9.5808.374 + ( ( -0.202 * -0.49 ) + ( -0.214 * -2.77 ) + ( -0.084 * ( 8.17 + -0.18 ) ) ) = 8.390-1.567 + ( ( -0.142 * 8.39 ) + ( -0.134 * -0.49 ) + ( -0.168 * 0.78 ) + ( -0.056 * ( -2.25 + -0.18 ) ) ) = -2.690-0.287 + ( ( -0.164 * -2.77 ) + ( -0.131 * -0.49 ) + ( -0.15 * -4.63 ) + ( -0.054 * ( 2.81 + -0.18 ) ) ) = 0.780-5.384 + ( ( -0.224 * 0.6 ) + ( -0.195 * -0.49 ) + ( -0.081 * ( -9.58 + -0.18 ) ) ) = -4.630

0 + ( ( -0.375 * ( 22.11 + 8.17 ) ) + ( -0.375 * ( -7.89 + -2.02 ) ) + (-0.375 * ( 3.6 + 3.04) ) + ( -0.375 * ( -12.98 + -9.58= -1.6700 + ( ( -0.375 * ( 8.17 + 8.39 ) ) + ( -0.375 * ( -2.02 + -2.69 ) ) + ( -0.375 * ( 3.04 + 0.78 ) ) + ( -0.375 * ( -9.58 + -4.63= -0.5500 + ( ( -0.375 * 8.39 ) + ( -0.375 * -2.69 ) + ( -0.375 * 0.78 ) + ( -0.375 * -4.63 ) ) = -0.670

Tercer Ciclo de giro

M1 = 20.925 + (( -0.175 * ( 8.17 + -1.67 )) + (-0.325 * -7.89 ))M2 = -3.332 + (( -0.184 * 22.35 ) + ( -0.099 * ( -1.9 + -1.67 )) + ( -0.217 * 3.83 ))M3 = -0.25+ ( ( -0.211 * -7.89 ) + ( -0.096 * ( 2.98 + -1.67 ) ) + ( -0.193 * -13.17 ) )M4 = -13.835 + ( ( -0.334 * 3.6 ) + ( -0.166 * ( -10.727 + -1.67 ) ) )M5 = 10.736 + ( ( -0.11 * ( 8.39 + -0.55 ) ) + ( -0.281 * -2.02 ) + ( -0.11 * ( 22.35 + -1.67 ) ) )

M6 = -0.774 + ( ( -0.169 * 8.17 ) + ( -0.066 * ( -2.66 + -0.55 ) ) + ( -0.199 * 2.98 ) + ( -0.066 * ( -7.89 + -1.67) ) ) M7 = 1.039 + ( ( -0.194 * -2.02 ) + ( -0.064 * ( 0.8 + -0.55 ) ) + ( -0.178 * -9.51 ) + ( -0.064 * ( 3.6 + -1.67 ) ) )M8 = -10.727 + ( ( -0.29 * 3.04 ) + ( -0.105 * ( -4.63 + -0.55 ) ) + ( -0.105 * ( -13.17 + -1.67 ) ) )M9 = 8.374 + ( ( -0.202 * -0.69 ) + ( -0.214 * -2.69 ) + ( -0.084 * ( 8.17 + -0.55 ) ) )M10 = -1.567 + ( ( -0.142 * 8.45 ) + ( -0.134 * -0.69 ) + ( -0.168 * 0.8 ) + ( -0.056 * ( -2.02 + -0.55 ) ) ) M11 = -0.287 + ( ( -0.164 * -2.69 ) + ( -0.131 * -0.69 ) + ( -0.15 * -4.61 ) + ( -0.054 * ( 3.04 + -0.55 ) ) )M12 = -5.384 + ( ( -0.224 * 0.78 ) + ( -0.195 * -0.69 ) + ( -0.081 * ( -9.51 + -0.55 ) ) )

M°I = 0 + ( ( -0.375 * ( 22.35 + 8.17 ) ) + ( -0.375 * ( -7.92 + -1.9 ) ) + (-0.375 * ( 3.83 + 2.98) ) + ( -0.375 * ( -13.17 + -9.51M°II = 0 + ( ( -0.375 * ( 8.17 + 8.45 ) ) + ( -0.375 * ( -1.9 + -2.66 ) ) + ( -0.375 * ( 2.98 + 0.8 ) ) + ( -0.375 * ( -9.51 + -4.61 ) M°III = 0 + ( ( -0.375 * 8.45 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.8 ) + ( -0.375 * -4.61 ) )

Cuarto Ciclo de giro

M1 = 20.925 + (( -0.175 * ( 8.17 + -1.81 )) + (-0.325 * -7.92 ))M2 = -3.332 + (( -0.184 * 22.39 ) + ( -0.099 * ( -1.88 + -1.81 )) + ( -0.217 * 3.87 ))M3 = -0.25+ ( ( -0.211 * -7.92 ) + ( -0.096 * ( 2.95 + -1.81 ) ) + ( -0.193 * -13.24 ) )M4 = -13.835 + ( ( -0.334 * 3.83 ) + ( -0.166 * ( -10.727 + -1.81 ) ) )M5 = 10.736 + ( ( -0.11 * ( 8.45 + -0.65 ) ) + ( -0.281 * -1.9 ) + ( -0.11 * ( 22.39 + -1.81 ) ) ) M6 = -0.774 + ( ( -0.169 * 8.15 ) + ( -0.066 * ( -2.66 + -0.65 ) ) + ( -0.199 * 2.95 ) + ( -0.066 * ( -7.92 + -1.81) ) ) M7 = 1.039 + ( ( -0.194 * -1.9 ) + ( -0.064 * ( 0.81 + -0.65 ) ) + ( -0.178 * -9.46 ) + ( -0.064 * ( 3.83 + -1.81 ) ) )M8 = -10.727 + ( ( -0.29 * 2.98 ) + ( -0.105 * ( -4.61 + -0.65 ) ) + ( -0.105 * ( -13.24 + -1.81 ) ) )M9 = 8.374 + ( ( -0.202 * -0.74 ) + ( -0.214 * -2.66 ) + ( -0.084 * ( 8.15 + -0.65 ) ) )M10 = -1.567 + ( ( -0.142 * 8.46 ) + ( -0.134 * -0.74 ) + ( -0.168 * 0.81 ) + ( -0.056 * ( -1.9 + -0.65 ) ) ) M11 = -0.287 + ( ( -0.164 * -2.66 ) + ( -0.131 * -0.74 ) + ( -0.15 * -4.6 ) + ( -0.054 * ( 2.98 + -0.65 ) ) )M12 = -5.384 + ( ( -0.224 * 0.8 ) + ( -0.195 * -0.74 ) + ( -0.081 * ( -9.46 + -0.65 ) ) )

M°I = 0 + ( ( -0.375 * ( 22.39 + 8.15 ) ) + ( -0.375 * ( -7.93 + -1.88 ) ) + (-0.375 * ( 3.87 + 2.95) ) + ( -0.375 * ( -13.24 + -9.4M°II = 0 + ( ( -0.375 * ( 8.15 + 8.46 ) ) + ( -0.375 * ( -1.88 + -2.66 ) ) + ( -0.375 * ( 2.95 + 0.81 ) ) + ( -0.375 * ( -9.46 + -4.6 )M°III = 0 + ( ( -0.375 * 8.46 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.81 ) + ( -0.375 * -4.6 ) )

20.925 + (( -0.175 * ( 8.17 + -1.67 )) + (-0.325 * -7.89 )) = 22.350-3.332 + (( -0.184 * 22.35 ) + ( -0.099 * ( -1.9 + -1.67 )) + ( -0.217 * 3.83 )) = -7.920-0.25+ ( ( -0.211 * -7.89 ) + ( -0.096 * ( 2.98 + -1.67 ) ) + ( -0.193 * -13.17 ) ) = 3.830-13.835 + ( ( -0.334 * 3.6 ) + ( -0.166 * ( -10.727 + -1.67 ) ) ) = -13.17010.736 + ( ( -0.11 * ( 8.39 + -0.55 ) ) + ( -0.281 * -2.02 ) + ( -0.11 * ( 22.35 + -1.67 ) ) ) = 8.170

-0.774 + ( ( -0.169 * 8.17 ) + ( -0.066 * ( -2.66 + -0.55 ) ) + ( -0.199 * 2.98 ) + ( -0.066 * ( -7.89 + -1.67) ) ) = -1.9001.039 + ( ( -0.194 * -2.02 ) + ( -0.064 * ( 0.8 + -0.55 ) ) + ( -0.178 * -9.51 ) + ( -0.064 * ( 3.6 + -1.67 ) ) ) = 2.980-10.727 + ( ( -0.29 * 3.04 ) + ( -0.105 * ( -4.63 + -0.55 ) ) + ( -0.105 * ( -13.17 + -1.67 ) ) ) = -9.5108.374 + ( ( -0.202 * -0.69 ) + ( -0.214 * -2.69 ) + ( -0.084 * ( 8.17 + -0.55 ) ) ) = 8.450-1.567 + ( ( -0.142 * 8.45 ) + ( -0.134 * -0.69 ) + ( -0.168 * 0.8 ) + ( -0.056 * ( -2.02 + -0.55 ) ) ) = -2.660-0.287 + ( ( -0.164 * -2.69 ) + ( -0.131 * -0.69 ) + ( -0.15 * -4.61 ) + ( -0.054 * ( 3.04 + -0.55 ) ) ) = 0.800-5.384 + ( ( -0.224 * 0.78 ) + ( -0.195 * -0.69 ) + ( -0.081 * ( -9.51 + -0.55 ) ) ) = -4.610

0 + ( ( -0.375 * ( 22.35 + 8.17 ) ) + ( -0.375 * ( -7.92 + -1.9 ) ) + (-0.375 * ( 3.83 + 2.98) ) + ( -0.375 * ( -13.17 + -9.51= -1.8100 + ( ( -0.375 * ( 8.17 + 8.45 ) ) + ( -0.375 * ( -1.9 + -2.66 ) ) + ( -0.375 * ( 2.98 + 0.8 ) ) + ( -0.375 * ( -9.51 + -4.61 ) = -0.6500 + ( ( -0.375 * 8.45 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.8 ) + ( -0.375 * -4.61 ) ) = -0.740

20.925 + (( -0.175 * ( 8.17 + -1.81 )) + (-0.325 * -7.92 )) = 22.390-3.332 + (( -0.184 * 22.39 ) + ( -0.099 * ( -1.88 + -1.81 )) + ( -0.217 * 3.87 )) = -7.930-0.25+ ( ( -0.211 * -7.92 ) + ( -0.096 * ( 2.95 + -1.81 ) ) + ( -0.193 * -13.24 ) ) = 3.870-13.835 + ( ( -0.334 * 3.83 ) + ( -0.166 * ( -10.727 + -1.81 ) ) ) = -13.24010.736 + ( ( -0.11 * ( 8.45 + -0.65 ) ) + ( -0.281 * -1.9 ) + ( -0.11 * ( 22.39 + -1.81 ) ) ) = 8.150-0.774 + ( ( -0.169 * 8.15 ) + ( -0.066 * ( -2.66 + -0.65 ) ) + ( -0.199 * 2.95 ) + ( -0.066 * ( -7.92 + -1.81) ) ) = -1.8801.039 + ( ( -0.194 * -1.9 ) + ( -0.064 * ( 0.81 + -0.65 ) ) + ( -0.178 * -9.46 ) + ( -0.064 * ( 3.83 + -1.81 ) ) ) = 2.950-10.727 + ( ( -0.29 * 2.98 ) + ( -0.105 * ( -4.61 + -0.65 ) ) + ( -0.105 * ( -13.24 + -1.81 ) ) ) = -9.4608.374 + ( ( -0.202 * -0.74 ) + ( -0.214 * -2.66 ) + ( -0.084 * ( 8.15 + -0.65 ) ) ) = 8.460-1.567 + ( ( -0.142 * 8.46 ) + ( -0.134 * -0.74 ) + ( -0.168 * 0.81 ) + ( -0.056 * ( -1.9 + -0.65 ) ) ) = -2.660-0.287 + ( ( -0.164 * -2.66 ) + ( -0.131 * -0.74 ) + ( -0.15 * -4.6 ) + ( -0.054 * ( 2.98 + -0.65 ) ) ) = 0.810-5.384 + ( ( -0.224 * 0.8 ) + ( -0.195 * -0.74 ) + ( -0.081 * ( -9.46 + -0.65 ) ) ) = -4.600

0 + ( ( -0.375 * ( 22.39 + 8.15 ) ) + ( -0.375 * ( -7.93 + -1.88 ) ) + (-0.375 * ( 3.87 + 2.95) ) + ( -0.375 * ( -13.24 + -9.4= -1.8200 + ( ( -0.375 * ( 8.15 + 8.46 ) ) + ( -0.375 * ( -1.88 + -2.66 ) ) + ( -0.375 * ( 2.95 + 0.81 ) ) + ( -0.375 * ( -9.46 + -4.6 )= -0.6600 + ( ( -0.375 * 8.46 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.81 ) + ( -0.375 * -4.6 ) ) = -0.750

Quinto Ciclo de giro

M1 = 20.925 + (( -0.175 * ( 8.15 + -1.82 )) + (-0.325 * -7.93 ))M2 = -3.332 + (( -0.184 * 22.39 ) + ( -0.099 * ( -1.87 + -1.82 )) + ( -0.217 * 3.87 ))M3 = -0.25+ ( ( -0.211 * -7.93 ) + ( -0.096 * ( 2.95 + -1.82 ) ) + ( -0.193 * -13.26 ) )M4 = -13.835 + ( ( -0.334 * 3.87 ) + ( -0.166 * ( -10.727 + -1.82 ) ) )M5 = 10.736 + ( ( -0.11 * ( 8.46 + -0.66 ) ) + ( -0.281 * -1.88 ) + ( -0.11 * ( 22.39 + -1.82 ) ) )

M6 = -0.774 + ( ( -0.169 * 8.14 ) + ( -0.066 * ( -2.66 + -0.66 ) ) + ( -0.199 * 2.95 ) + ( -0.066 * ( -7.93 + -1.82) ) ) M7 = 1.039 + ( ( -0.194 * -1.88 ) + ( -0.064 * ( 0.81 + -0.66 ) ) + ( -0.178 * -9.45 ) + ( -0.064 * ( 3.87 + -1.82 ) ) )M8 = -10.727 + ( ( -0.29 * 2.95 ) + ( -0.105 * ( -4.6 + -0.66 ) ) + ( -0.105 * ( -13.26 + -1.82 ) ) )M9 = 8.374 + ( ( -0.202 * -0.75 ) + ( -0.214 * -2.66 ) + ( -0.084 * ( 8.14 + -0.66 ) ) )M10 = -1.567 + ( ( -0.142 * 8.47 ) + ( -0.134 * -0.75 ) + ( -0.168 * 0.81 ) + ( -0.056 * ( -1.88 + -0.66 ) ) ) M11 = -0.287 + ( ( -0.164 * -2.66 ) + ( -0.131 * -0.75 ) + ( -0.15 * -4.6 ) + ( -0.054 * ( 2.95 + -0.66 ) ) )M12 = -5.384 + ( ( -0.224 * 0.81 ) + ( -0.195 * -0.75 ) + ( -0.081 * ( -9.45 + -0.66 ) ) )

M°I = 0 + ( ( -0.375 * ( 22.39 + 8.14 ) ) + ( -0.375 * ( -7.93 + -1.87 ) ) + (-0.375 * ( 3.87 + 2.95) ) + ( -0.375 * ( -13.26 + M°II = 0 + ( ( -0.375 * ( 8.14 + 8.47 ) ) + ( -0.375 * ( -1.87 + -2.66 ) ) + ( -0.375 * ( 2.95 + 0.81 ) ) + ( -0.375 * ( -9.45 + -M°III = 0 + ( ( -0.375 * 8.47 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.81 ) + ( -0.375 * -4.6 ) )

Sexto Ciclo de giro

M1 = 20.925 + (( -0.175 * ( 8.14 + -1.82 )) + (-0.325 * -7.93 ))M2 = -3.332 + (( -0.184 * 22.4 ) + ( -0.099 * ( -1.87 + -1.82 )) + ( -0.217 * 3.87 ))M3 = -0.25+ ( ( -0.211 * -7.93 ) + ( -0.096 * ( 2.94 + -1.82 ) ) + ( -0.193 * -13.26 ) )M4 = -13.835 + ( ( -0.334 * 3.87 ) + ( -0.166 * ( -10.727 + -1.82 ) ) )M5 = 10.736 + ( ( -0.11 * ( 8.47 + -0.67 ) ) + ( -0.281 * -1.87 ) + ( -0.11 * ( 22.4 + -1.82 ) ) ) M6 = -0.774 + ( ( -0.169 * 8.14 ) + ( -0.066 * ( -2.66 + -0.67 ) ) + ( -0.199 * 2.94 ) + ( -0.066 * ( -7.93 + -1.82) ) ) M7 = 1.039 + ( ( -0.194 * -1.87 ) + ( -0.064 * ( 0.82 + -0.67 ) ) + ( -0.178 * -9.45 ) + ( -0.064 * ( 3.87 + -1.82 ) ) )M8 = -10.727 + ( ( -0.29 * 2.95 ) + ( -0.105 * ( -4.6 + -0.67 ) ) + ( -0.105 * ( -13.26 + -1.82 ) ) )M9 = 8.374 + ( ( -0.202 * -0.76 ) + ( -0.214 * -2.66 ) + ( -0.084 * ( 8.14 + -0.67 ) ) )M10 = -1.567 + ( ( -0.142 * 8.47 ) + ( -0.134 * -0.76 ) + ( -0.168 * 0.82 ) + ( -0.056 * ( -1.87 + -0.67 ) ) ) M11 = -0.287 + ( ( -0.164 * -2.66 ) + ( -0.131 * -0.76 ) + ( -0.15 * -4.6 ) + ( -0.054 * ( 2.95 + -0.67 ) ) )M12 = -5.384 + ( ( -0.224 * 0.81 ) + ( -0.195 * -0.76 ) + ( -0.081 * ( -9.45 + -0.67 ) ) )

M°I = 0 + ( ( -0.375 * ( 22.4 + 8.14 ) ) + ( -0.375 * ( -7.93 + -1.87 ) ) + (-0.375 * ( 3.87 + 2.94) ) + ( -0.375 * ( -13.26 + -M°II = 0 + ( ( -0.375 * ( 8.14 + 8.47 ) ) + ( -0.375 * ( -1.87 + -2.66 ) ) + ( -0.375 * ( 2.94 + 0.82 ) ) + ( -0.375 * ( -9.45 + -M°III = 0 + ( ( -0.375 * 8.47 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.82 ) + ( -0.375 * -4.6 ) )


= 22.390 M1 = 20.925 + (( -0.175 * ( 8.14 + -1.82 )) + (-0.325 * -7.93 ))= -7.930 M2 = -3.332 + (( -0.184 * 22.4 ) + ( -0.099 * ( -1.87 + -1.82 )) + ( -0.217 * 3.87 ))= 3.870 M3 = -0.25+ ( ( -0.211 * -7.93 ) + ( -0.096 * ( 2.94 + -1.82 ) ) + ( -0.193 * -13.26 ) )= -13.260 M4 = 10.736 + ( ( -0.11 * ( 8.47 + -0.67 ) ) + ( -0.281 * -1.87 ) + ( -0.11 * ( 22.4 + -1.82 ) ) ) = 8.140 M5 = -0.774 + ( ( -0.169 * 8.14 ) + ( -0.066 * ( -2.66 + -0.67 ) ) + ( -0.199 * 2.94 ) + ( -0.066 * ( -7.93 + -1.82) ) )

-0.774 + ( ( -0.169 * 8.14 ) + ( -0.066 * ( -2.66 + -0.66 ) ) + ( -0.199 * 2.95 ) + ( -0.066 * ( -7.93 + -1.82) ) ) = -1.870 M6 = 1.039 + ( ( -0.194 * -1.87 ) + ( -0.064 * ( 0.82 + -0.67 ) ) + ( -0.178 * -9.44 ) + ( -0.064 * ( 3.87 + -1.82 ) ) )1.039 + ( ( -0.194 * -1.88 ) + ( -0.064 * ( 0.81 + -0.66 ) ) + ( -0.178 * -9.45 ) + ( -0.064 * ( 3.87 + -1.82 ) ) ) = 2.950 M7 = -10.727 + ( ( -0.29 * 2.94 ) + ( -0.105 * ( -4.6 + -0.67 ) ) + ( -0.105 * ( -13.26 + -1.82 ) ) )

= -9.450 M8 = 8.374 + ( ( -0.202 * -0.76 ) + ( -0.214 * -2.66 ) + ( -0.084 * ( 8.14 + -0.67 ) ) )= 8.470 M9 = -1.567 + ( ( -0.142 * 8.47 ) + ( -0.134 * -0.76 ) + ( -0.168 * 0.82 ) + ( -0.056 * ( -1.87 + -0.67 ) ) ) = -2.660 M10 = -0.287 + ( ( -0.164 * -2.66 ) + ( -0.131 * -0.76 ) + ( -0.15 * -4.6 ) + ( -0.054 * ( 2.94 + -0.67 ) ) )= 0.810 M11 = -5.384 + ( ( -0.224 * 0.82 ) + ( -0.195 * -0.76 ) + ( -0.081 * ( -9.44 + -0.67 ) ) )= -4.600 M12 = -5.384 + ( ( -0.224 * 0.82 ) + ( -0.195 * -0.76 ) + ( -0.081 * ( + -0.68 ) ) )

0 + ( ( -0.375 * ( 22.39 + 8.14 ) ) + ( -0.375 * ( -7.93 + -1.87 ) ) + (-0.375 * ( 3.87 + 2.95) ) + ( -0.375 * ( -13.26 + = -1.820 M°I = 0 + ( ( -0.375 * ( 22.4 + 8.14 ) ) + ( -0.375 * ( -7.93 + -1.87 ) ) + (-0.375 * ( 3.87 + 2.94) ) + ( -0.375 * ( -13.26 + -0 + ( ( -0.375 * ( 8.14 + 8.47 ) ) + ( -0.375 * ( -1.87 + -2.66 ) ) + ( -0.375 * ( 2.95 + 0.81 ) ) + ( -0.375 * ( -9.45 + - = -0.670 M°II = 0 + ( ( -0.375 * ( 8.14 + 8.47 ) ) + ( -0.375 * ( -1.87 + -2.66 ) ) + ( -0.375 * ( 2.94 + 0.82 ) ) + ( -0.375 * ( -9.44 + -

= -0.760 M°III = 0 + ( ( -0.375 * 8.47 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.82 ) + ( -0.375 * -4.6 ) )

= 22.400= -7.930= 3.870= -13.260= 8.140

-0.774 + ( ( -0.169 * 8.14 ) + ( -0.066 * ( -2.66 + -0.67 ) ) + ( -0.199 * 2.94 ) + ( -0.066 * ( -7.93 + -1.82) ) ) = -1.8701.039 + ( ( -0.194 * -1.87 ) + ( -0.064 * ( 0.82 + -0.67 ) ) + ( -0.178 * -9.45 ) + ( -0.064 * ( 3.87 + -1.82 ) ) ) = 2.940

= -9.450= 8.470= -2.660= 0.820= -4.600

0 + ( ( -0.375 * ( 22.4 + 8.14 ) ) + ( -0.375 * ( -7.93 + -1.87 ) ) + (-0.375 * ( 3.87 + 2.94) ) + ( -0.375 * ( -13.26 + -= -1.8200 + ( ( -0.375 * ( 8.14 + 8.47 ) ) + ( -0.375 * ( -1.87 + -2.66 ) ) + ( -0.375 * ( 2.94 + 0.82 ) ) + ( -0.375 * ( -9.45 + - = -0.670

= -0.760

20.925 + (( -0.175 * ( 8.14 + -1.82 )) + (-0.325 * -7.93 )) = 22.400-3.332 + (( -0.184 * 22.4 ) + ( -0.099 * ( -1.87 + -1.82 )) + ( -0.217 * 3.87 )) = -7.930-0.25+ ( ( -0.211 * -7.93 ) + ( -0.096 * ( 2.94 + -1.82 ) ) + ( -0.193 * -13.26 ) ) = 3.87010.736 + ( ( -0.11 * ( 8.47 + -0.67 ) ) + ( -0.281 * -1.87 ) + ( -0.11 * ( 22.4 + -1.82 ) ) ) = -13.260-0.774 + ( ( -0.169 * 8.14 ) + ( -0.066 * ( -2.66 + -0.67 ) ) + ( -0.199 * 2.94 ) + ( -0.066 * ( -7.93 + -1.82) ) ) = 8.140

1.039 + ( ( -0.194 * -1.87 ) + ( -0.064 * ( 0.82 + -0.67 ) ) + ( -0.178 * -9.44 ) + ( -0.064 * ( 3.87 + -1.82 ) ) ) = -1.870-10.727 + ( ( -0.29 * 2.94 ) + ( -0.105 * ( -4.6 + -0.67 ) ) + ( -0.105 * ( -13.26 + -1.82 ) ) ) = 2.9408.374 + ( ( -0.202 * -0.76 ) + ( -0.214 * -2.66 ) + ( -0.084 * ( 8.14 + -0.67 ) ) ) = -9.440-1.567 + ( ( -0.142 * 8.47 ) + ( -0.134 * -0.76 ) + ( -0.168 * 0.82 ) + ( -0.056 * ( -1.87 + -0.67 ) ) ) = 8.470-0.287 + ( ( -0.164 * -2.66 ) + ( -0.131 * -0.76 ) + ( -0.15 * -4.6 ) + ( -0.054 * ( 2.94 + -0.67 ) ) ) = -2.660-5.384 + ( ( -0.224 * 0.82 ) + ( -0.195 * -0.76 ) + ( -0.081 * ( -9.44 + -0.67 ) ) ) = 0.820-5.384 + ( ( -0.224 * 0.82 ) + ( -0.195 * -0.76 ) + ( -0.081 * ( + -0.68 ) ) ) = -4.600

0 + ( ( -0.375 * ( 22.4 + 8.14 ) ) + ( -0.375 * ( -7.93 + -1.87 ) ) + (-0.375 * ( 3.87 + 2.94) ) + ( -0.375 * ( -13.26 + -= -0.6800 + ( ( -0.375 * ( 8.14 + 8.47 ) ) + ( -0.375 * ( -1.87 + -2.66 ) ) + ( -0.375 * ( 2.94 + 0.82 ) ) + ( -0.375 * ( -9.44 + - = -0.7600 + ( ( -0.375 * 8.47 ) + ( -0.375 * -2.66 ) + ( -0.375 * 0.82 ) + ( -0.375 * -4.6 ) ) = -0.760


Nudo 01 Correccion Nudo 07

M1-2 = -4760.677 -4759.864 M7-3 =

M1-5 = 4759.425 4759.864 M7-6 =

-1.252 0.000 M7-8 =

M7-11 =

Nudo 02

M2-1 = 12295.394 12294.727

M2-3 = -10473.416 -10474.204 Nudo 08

M2-6 = -1820.164 -1820.523 M8-7 =

1.814 0.000 M8-4 =

M8-12 =

Nudo 03 M8-V =

M3-2 = 7979.257 7982.598

M3-4 = -8812.07 -8809.011

M3-7 = 824.893 826.413 Nudo 09

-7.918 0.000 M9-5 =

M9-10 =

Nudo 04 M9-13 =

M4-3 = 3519.290 3518.049

M4-8 = -3517.431 -3518.049

M4-V = 0 0 Nudo 10

1.859 0.000 M10-9 =

M10-6 =

Nudo 05 M10-11 =

M5-1 = 3431.777 3433.221 M10-14 =

M5-6 = -5679.330 -5675.641

M5-9 = 2240.989 2242.433

-6.564 0.013 Nudo 11

M11-10 =

Nudo 06 M11-7 =

M6-2 = -1255.959 -1255.944 M11-12 =

M6-5 = 10157.897 10157.936 M11-15 =

M6-7 = -8242.883 -8242.837

M6-10 = -659.169 -659.156

-0.115 -0.002 Nudo 12

M12-11 =

M12-8 =

M12-16 =

M12-V =

Corrección738.307 738.126

9144.569 9144.021-10441.943 -10442.446

560.480 560.289

1.413 -0.010

5416.169 5413.256-3161.778 -3162.833-2249.368 -2250.423

0 0

5.023 0.000

2271.713 2272.228-5915.278 -5913.9663640.500 3641.738

-3.065 0.000

10065.274 10063.038-732.721 -733.603

-7956.680 -7959.325-1368.000 -1370.121

7.874 -0.011

6406.117 6404.825363.1017 362.676

-6963.281 -6964.462198.000 196.964

3.938 0.004

4040.600 4040.219-1798.750 -1798.888-2241.000 -2241.331

0 00.850 0.000

VIGA PRINCIPAL A

C.V. =892.5Kg/mC.M.=3163.13kg/m

C.V.=892.5kg/mC.M.=3966.38kg/m

C.V.=892.5kg/mC.M.=3966.38kg/m

Descripción Base AlturaColumnas 30 30 cm

Vigas 20 50 cmViga Azotea 20 45 cm

Luces 1-2 5.25 m 2-3 4.45 m 3-4 4.85 m

Volado4-V 0 m8-V 0 m12-V 0 m

Alturas 1-2 2.9 m 2-3 2.9 m

3-4 1.2 m

Rigidez relativa Takabeya Factores de Giro

Vigas Nudo 01

K1-2 173.571 -(K1-2)/(2(K1-2+K1-5)K2-3 204.775 &1-2 =K3-4 187.887 -(K1-5)/(2(K1-2+K1-5)K5-6 238.095 &1-5 =

K6-7 280.899K7-8 257.732 Nudo 02K9-10 238.095 -(K2-1)/(2(K2-1+K2-3+K2-6)

K10-11 280.899 &2-1 =K11-12 257.732 -(K2-3)/(2(K2-1+K2-3+K2-6)

&2-3 =Columnas -(K2-6)/(2(K2-1+K2-3+K2-6)

K1-5 93.103 &2-6 =K2-6 93.103K3-7 93.103 Nudo 03

K4-8 93.103 -(K3-2)/(2(K3-2+K3-4+K3-7)

K5-9 93.103 &3-2 =K6-10 93.103 -(K3-4)/(2(K3-2+K3-4+K3-7)K7-11 93.103 &3-2 =

K8-12 93.103 -(K3-7)/(2(K3-2+K3-4+K3-7)K9-13 225.000 &3-7 =K10-14 225.000

Kik = h3/l

K11-15 225.000 Nudo 04

K12-16 225.000 -(K4-3)/(2(K4-3+K4-8)

&4-3 =

-(K4-8)/(2(K4-3+K4-8)

&4-8 =

Nudo 05

-(K5-1)/(2(K5-1+K5-6+K5-9)

&5-1 =

-(K5-6)/(2(K5-1+K5-6+K5-9)

&5-6 =

-(K5-9)/(2(K5-1+K5-6+K5-9)

&5-9 =

Nudo 06

-(K6-2)/(2(K6-2+K6-5+K6-7+K6-10)

&6-2 =

-(K6-5)/(2(K6-2+K6-5+K6-7+K6-10)

&6-5 =

-(K6-7)/(2(K6-2+K6-5+K6-7+K6-10)

&6-7 =

-(K6-10)/(2(K6-2+K6-5+K6-7+K6-10)

&6-10 =

Factores de Giro

Nudo 07 Calculo de los factores de corrimiento

-(K1-2)/(2(K1-2+K1-5) -(K7-3)/(2(K7-3+K7-6+K7-8+K7-11)

-0.325 &7-3 = -0.064 Nivel I

-(K1-5)/(2(K1-2+K1-5) -(K7-6)/(2(K7-3+K7-6+K7-8+K7-11) -3/2(K1-5/(K1-5+K2-6+K3-7+K4-8)

-0.175 &7-6 = -0.194 V1-5 = -0.375

-(K7-8)/(2(K7-3+K7-6+K7-8+K7-11) -3/2(K2-6/(K1-5+K2-6+K3-7+K4-8)

&7-8 = -0.178 V2-6 = -0.375

-(K2-1)/(2(K2-1+K2-3+K2-6) -(K7-11)/(2(K7-3+K7-6+K7-8+K7-11) -3/2(K3-7/(K1-5+K2-6+K3-7+K4-8)

-0.184 &7-11 = -0.064 V3-7 = -0.375

-(K2-3)/(2(K2-1+K2-3+K2-6) -3/2(K4-8/(K1-5+K2-6+K3-7+K4-8)

-0.217 Nudo 08 V4-8 = -0.375

-(K2-6)/(2(K2-1+K2-3+K2-6) -(K8-7)/(2(K8-7+K8-4+K8-12)

-0.099 &8-7 = -0.290 Nivel II

-(K8-4)/(2(K8-7+K8-4+K8-12) -3/2(K5-9/(K5-9+K6-10+K7-11+K8-12)

&8-4 = -0.105 V5-9 = -0.375

-(K3-2)/(2(K3-2+K3-4+K3-7) -(K8-12)/(2(K8-7+K8-4+K8-12) -3/2(K6-10/(K5-9+K6-10+K7-11+K8-12)

-0.211 &8-12 = -0.105 V6-10 = -0.375

-(K3-4)/(2(K3-2+K3-4+K3-7) -3/2(K7-11/(K5-9+K6-10+K7-11+K8-12)

-0.193 Nudo 09 V7-11 = -0.375

-(K3-7)/(2(K3-2+K3-4+K3-7) -(K9-5)/(2(K9-5+K9-10+K9-13) -3/2(K8-12/(K5-9+K6-10+K7-11+K8-12)

-0.096 &9-5 = -0.084 V8-12 = -0.375

-(K9-10)/(2(K9-5+K9-10+K9-13)

&9-10 = -0.214 Nivel III

-(K4-3)/(2(K4-3+K4-8) -(K9-13)/(2(K9-5+K9-10+K9-13) -3/2(K9-13/(K9-13+K10-14+K11-15+K12-16)

-0.334 &9-13 = -0.202 V9-13 = -0.375

-(K4-8)/(2(K4-3+K4-8) -3/2(K10-14/(K9-13+K10-14+K11-15+K12-16)

-0.166 Nudo 10 V10-14 = -0.375

-(K10-9)/(2(K10-9+K10-6+K10-11+K10-14) -3/2(K11-15/(K9-13+K10-14+K11-15+K12-16)

&10-9 = -0.142 V11-15 = -0.375

-(K5-1)/(2(K5-1+K5-6+K5-9) -(K10-6)/(2(K10-9+K10-6+K10-11+K10-14) -3/2(K12-16/(K9-13+K10-14+K11-15+K12-16)

-0.110 &10-6 = -0.056 V12-16 = -0.375

-(K5-6)/(2(K5-1+K5-6+K5-9) -(K10-11)/(2(K10-9+K10-6+K10-11+K10-14)

-0.281 &10-11 = -0.168

-(K5-9)/(2(K5-1+K5-6+K5-9) -(K10-14)/(2(K10-9+K10-6+K10-11+K10-14)

-0.110 &10-14 = -0.134

-(K6-2)/(2(K6-2+K6-5+K6-7+K6-10) Nudo 11

-0.066 -(K11-10)/(2(K11-10+K11-7+K11-12+K11-15)

-(K6-5)/(2(K6-2+K6-5+K6-7+K6-10) &11-10 = -0.164

-0.169 -(K11-7)/(2(K11-10+K11-7+K11-12+K11-15)

-(K6-7)/(2(K6-2+K6-5+K6-7+K6-10) &11-7 = -0.054

-0.199 -(K11-12)/(2(K11-10+K11-7+K11-12+K11-15)

-(K6-10)/(2(K6-2+K6-5+K6-7+K6-10) &11-12 = -0.150

-0.066 -(K11-15)/(2(K11-10+K11-7+K11-12+K11-15)

&11-15 = -0.131

Nudo 12

-(K12-11)/(2(K12-11+K12-8+K12-16)

&12-11 = -0.224

-(K12-8)/(2(K12-11+K12-8+K12-16)

&12-8 = -0.081

-(K12-16)/(2(K12-11+K12-8+K12-16)

&12-16 = -0.195

Calculo de los factores de corrimiento Momentos de empotramiento perfecto

-3/2(K1-5/(K1-5+K2-6+K3-7+K4-8)

-3/2(K2-6/(K1-5+K2-6+K3-7+K4-8) Nivel I Nivel IIM1-2 M5-6


-9110.279 -11160.24 -3/2(K4-8/(K1-5+K2-6+K3-7+K4-8)

M2-1 M6-5Carga = 3966.38 Carga = 4858.88 +ql2/12 9110.279 +ql2/12 11160.24

-3/2(K5-9/(K5-9+K6-10+K7-11+K8-12)M2-3 M6-7


-8018.164 -8018.164 -3/2(K7-11/(K5-9+K6-10+K7-11+K8-12)


+ql2/12 8018.164 +ql2/12 8018.164

-ql2/12 -ql2/12

-ql2/12 -ql2/12


-9524.417 -7774.931 -3/2(K10-14/(K9-13+K10-14+K11-15+K12-16)


+ql2/12 9524.417 +ql2/12 7774.931 -3/2(K12-16/(K9-13+K10-14+K11-15+K12-16)

M4-V M8-VCarga = 0 Carga = 0 -ql2/2 0 -ql2/2 0

-ql2/12 -ql2/12

Calculo de Momentos de Sujeción

Nudo 01 Nudo 07

M1= M1-2 -9110.279 M7= M7-6+M7-8 243.233

Nivel III Nudo 02 Nudo 08M9-10 M2= M2-1+M2-3 1092.115 M8= M8-7+M8-V 7774.931Carga = 3163.13

-7265.314 Nudo 03 Nudo 09

M3 = M3-2 + M3-4 -1506.253 M9= M9-10 -7265.314M10-9Carga = 3163.13 Nudo 04 Nudo 10

+ql2/12 7265.314 M4 = M4-3 +M4-V 9524.417 M10= M10-9+M10-11 572.68

M10-11 Nudo 05 Nudo 11

Carga = 4055.63 M5 = M5-6 -11160.24 M11= M11-10+M11-12 -1257.246

-6692.634Nudo 06 Nudo 12

M11-10 M6 = M6-5 + M6-7 3142.076 M12= M12-11+M12-V 7949.88

Carga = 4055.63 +ql2/12 6692.634

-ql2/12

-ql2/12

M11-12Carga = 4055.63

-7949.88

M12-11Carga = 4055.63 +ql2/12 7949.88

M12-VCarga = 0 -ql2/2 0

-ql2/12

Cálculo de los momentos en los nudos Cálculo de los momentos por piso

Nudo 01 Nudo 07 Nivel IM°1= -1/2(M1)/(K1-2+K1-5) -1/2(M7)/(K7-3+K7-6+K7-8+K7-11) m°I =M°1= 17.081 M°7 = -0.168

Nivel IINudo 02 Nudo 08 m°II = -1/2(M2)/(K2-1)/(K2-1+K2-3+K2-6) -1/2(M8)/(K8-7+K8-4+K8-12)

M°2 = -1.158 M°8 = -8.757 Nivel IIIm°III =

Nudo 03 Nudo 09

-1/2(M3)/(K3-2+K3-4+K3-7) -1/2(M9)/(K9-5+K9-10+K9-13)

M°3 = 1.55 M°9 = 6.531

Nudo 04 Nudo 10

-1/2(M4)/(K4-3+K4-8) -1/2(M10)/(K10-9+K10-6+K10-11+K10-14)

M°4 = -16.948 M°10 = -0.342

Nudo 05 Nudo 11

-1/2(M5)/(K5-1+K5-6+K5-9) -1/2(M11)/(K11-10+K11-7+K11-12+K11-15)

M°5 = 13.151 M°11 = 0.734

Nudo 06 Nudo 12

-1/2(M6)/(K6-2+K6-5+K6-7+K6-10) -1/2(M12)/(K12-11+K12-8+K12-16)

M°6 = -2.228 M°12 = -6.903

Cálculo de los momentos por piso

0

0

0

GIROS TAKABEYA

M° I0

-0.530-1.100

-1.190

-1.190-1.190-1.190-1.190

M° II0

-0.600-0.990

-1.070

-1.090

-1.080

-1.080-1.080

M° III0

0.1700.100

0.080

0.0700.0700.0700.070

GIROS TAKABEYA

-0.325 -0.184 -0.217 -0.211 -0.193 -0.334

-0.1

75

-0.0

99

-0.0

96

-0.1

66

M1 17.081 M2 -1.158 M3 1.5515.160 -4.560 4.77016.660 -5.020 5.780

-0.3

75 16.800

-0.3

75 -5.040

-0.3

75 5.980

-0.3

75

-0.3

75

16.820 -0.3

75

-5.050 -0.3

75

6.010 -0.3

75

16.830 -5.050 6.01016.830 -5.050 6.01016.830 -5.050 6.010

-0.1

10

-0.0

66

-0.0

64

-0.1

05

-0.281 -0.169 -0.199 -0.194 -0.18 -0.290

-0.1

10

-0.0

66

-0.0

64

-0.1

05

M5 13.151 M6 -2.228 M7 -0.16811.390 -4.220 1.17012.010 -4.090 1.450

-0.3

75

12.040

-0.3

75

-3.990

-0.3

75

1.410

-0.3

75

12.030 -3.970 1.380

12.020 -3.970 1.370

12.020 -3.970 1.37012.020 -3.970 1.370

-0.0

84

-0.0

56

-0.0

54

-0.0

81

-0.214 -0.142 -0.168 -0.164 -0.15 -0.224

-0.2

02

-0.1

34

-0.1

31

-0.1

95

M9 6.531 M10 -0.342 M11 0.7345.650 -1.320 1.7805.820 -1.240 1.910

-0.3

75 5.850

-0.3

75 -1.220

-0.3

75 1.910

-0.3

75

5.860 -1.220 1.9205.860 -1.220 1.9205.860 -1.220 1.9205.860 -1.220 1.920

Iteraciones

M1 = 17.081 M7 = -0.168M2 = -1.158 M8 = -8.757M3 = 1.55 M9 = 6.531M4 = -16.948 M10 = -0.342M5 = 13.151 M11 = 0.734M6 = -2.228 M12 = -6.903

M°I 0M°II 0M°III 0

Primer ciclo de giro

M1 = 17.081 + (( -0.175 * ( 13.151 + 0 )) + (-0.325 * -1.158 ))M2 = -1.158 + (( -0.184 * 15.16 ) + ( -0.099 * ( -4.22 + 0 )) + ( -0.217 * 4.77 ))M3 = 1.55+ ( ( -0.211 * -1.158 ) + ( -0.096 * ( 1.17 + 0 ) ) + ( -0.193 * -16.01 ) )

M4 = -16.948 + ( ( -0.334 * 1.55 ) + ( -0.166 * ( -8.757 + 0 ) ) )M5 = 13.151 + ( ( -0.11 * ( 6.531 + 0 ) ) + ( -0.281 * -2.228 ) + ( -0.11 * ( 15.16 + 0 ) ) )

M6 = -2.228 + ( ( -0.169 * 11.39 ) + ( -0.066 * ( -1.32 + 0 ) ) + ( -0.199 * 1.17 ) + ( -0.066 * ( -1.158 + 0) ) ) M7 = -0.168 + ( ( -0.194 * -2.228 ) + ( -0.064 * ( 1.78 + 0 ) ) + ( -0.178 * -6.3 ) + ( -0.064 * ( 1.55 + 0 ) ) )M8 = -8.757 + ( ( -0.29 * -0.168 ) + ( -0.105 * ( -6.903 + 0 ) ) + ( -0.105 * ( -16.01 + 0 ) ) )M9 = 6.531 + ( ( -0.202 * 0 ) + ( -0.214 * -0.342 ) + ( -0.084 * ( 11.39 + 0 ) ) )M10 = -0.342 + ( ( -0.142 * 5.65 ) + ( -0.134 * 0 ) + ( -0.168 * 1.78 ) + ( -0.056 * ( -2.228 + 0 ) ) ) M11 = 0.734 + ( ( -0.164 * -0.342 ) + ( -0.131 * 0 ) + ( -0.15 * -6.56 ) + ( -0.054 * ( -0.168 + 0 ) ) )M12 = -6.903 + ( ( -0.224 * 0.734 ) + ( -0.195 * 0 ) + ( -0.081 * ( -6.3 + 0 ) ) )

M°I = 0 + ( ( -0.375 * ( 15.16 + 11.39 ) ) + ( -0.375 * ( -4.56 + -4.22 ) ) + (-0.375 * ( 4.77 + 1.17) ) + ( -0.375 * ( -16.01 + -6.M°II = 0 + ( ( -0.375 * ( 11.39 + 5.65 ) ) + ( -0.375 * ( -4.22 + -1.32 ) ) + ( -0.375 * ( 1.17 + 1.78 ) ) + ( -0.375 * ( -6.3 + -6.56M°III = 0 + ( ( -0.375 * 5.65 ) + ( -0.375 * -1.32 ) + ( -0.375 * 1.78 ) + ( -0.375 * -6.56 ) )

Segundo Ciclo de giro

M1 = 17.081 + (( -0.175 * ( 11.39 + -0.53 )) + (-0.325 * -4.56 ))M2 = -1.158 + (( -0.184 * 16.66 ) + ( -0.099 * ( -4.09 + -0.53 )) + ( -0.217 * 5.78 ))M3 = 1.55+ ( ( -0.211 * -4.56 ) + ( -0.096 * ( 1.45 + -0.53 ) ) + ( -0.193 * -17.41 ) )M4 = -16.948 + ( ( -0.334 * 4.77 ) + ( -0.166 * ( -8.757 + -0.53 ) ) )M5 = 13.151 + ( ( -0.11 * ( 5.65 + -0.6 ) ) + ( -0.281 * -4.22 ) + ( -0.11 * ( 16.66 + -0.53 ) ) ) M6 = -2.228 + ( ( -0.169 * 12.01 ) + ( -0.066 * ( -1.24 + -0.6 ) ) + ( -0.199 * 1.45 ) + ( -0.066 * ( -4.56 + -0.53) ) ) M7 = -0.168 + ( ( -0.194 * -4.22 ) + ( -0.064 * ( 1.91 + -0.6 ) ) + ( -0.178 * -6.46 ) + ( -0.064 * ( 4.77 + -0.53 ) ) )M8 = -8.757 + ( ( -0.29 * 1.17 ) + ( -0.105 * ( -6.56 + -0.6 ) ) + ( -0.105 * ( -17.41 + -0.53 ) ) )M9 = 6.531 + ( ( -0.202 * 0.17 ) + ( -0.214 * -1.32 ) + ( -0.084 * ( 12.01 + -0.6 ) ) )M10 = -0.342 + ( ( -0.142 * 5.82 ) + ( -0.134 * 0.17 ) + ( -0.168 * 1.91 ) + ( -0.056 * ( -4.22 + -0.6 ) ) ) M11 = 0.734 + ( ( -0.164 * -1.32 ) + ( -0.131 * 0.17 ) + ( -0.15 * -6.76 ) + ( -0.054 * ( 1.17 + -0.6 ) ) )M12 = -6.903 + ( ( -0.224 * 1.78 ) + ( -0.195 * 0.17 ) + ( -0.081 * ( -6.46 + -0.6 ) ) )

M°I = 0 + ( ( -0.375 * ( 16.66 + 12.01 ) ) + ( -0.375 * ( -5.02 + -4.09 ) ) + (-0.375 * ( 5.78 + 1.45) ) + ( -0.375 * ( -17.41 + -6M°II = 0 + ( ( -0.375 * ( 12.01 + 5.82 ) ) + ( -0.375 * ( -4.09 + -1.24 ) ) + ( -0.375 * ( 1.45 + 1.91 ) ) + ( -0.375 * ( -6.46 + -6.7M°III = 0 + ( ( -0.375 * 5.82 ) + ( -0.375 * -1.24 ) + ( -0.375 * 1.91 ) + ( -0.375 * -6.76 ) )

GIROS TAKABEYA

M4 -16.948-16.010-17.410

-17.620

-17.690-17.700-17.700-17.700

M8 -8.757-6.300-6.460

-6.400

-6.360

-6.350

-6.350-6.350

M12 -6.903-6.560-6.760

-6.750

-6.740-6.740-6.740-6.740


M1 =M2 =M3 =M4 =M5 =

M6 =M7 =M8 =M9 =M10 =M11 =M12 =

M°I =M°II =

= 15.160 M°III =-1.158 + (( -0.184 * 15.16 ) + ( -0.099 * ( -4.22 + 0 )) + ( -0.217 * 4.77 )) = -4.5601.55+ ( ( -0.211 * -1.158 ) + ( -0.096 * ( 1.17 + 0 ) ) + ( -0.193 * -16.01 ) ) = 4.770

= -16.010 Cuarto Ciclo de giro13.151 + ( ( -0.11 * ( 6.531 + 0 ) ) + ( -0.281 * -2.228 ) + ( -0.11 * ( 15.16 + 0 ) ) ) = 11.390

-2.228 + ( ( -0.169 * 11.39 ) + ( -0.066 * ( -1.32 + 0 ) ) + ( -0.199 * 1.17 ) + ( -0.066 * ( -1.158 + 0) ) ) = -4.220 M1 =-0.168 + ( ( -0.194 * -2.228 ) + ( -0.064 * ( 1.78 + 0 ) ) + ( -0.178 * -6.3 ) + ( -0.064 * ( 1.55 + 0 ) ) ) = 1.170 M2 =-8.757 + ( ( -0.29 * -0.168 ) + ( -0.105 * ( -6.903 + 0 ) ) + ( -0.105 * ( -16.01 + 0 ) ) ) = -6.300 M3 =6.531 + ( ( -0.202 * 0 ) + ( -0.214 * -0.342 ) + ( -0.084 * ( 11.39 + 0 ) ) ) = 5.650 M4 =-0.342 + ( ( -0.142 * 5.65 ) + ( -0.134 * 0 ) + ( -0.168 * 1.78 ) + ( -0.056 * ( -2.228 + 0 ) ) ) = -1.320 M5 =0.734 + ( ( -0.164 * -0.342 ) + ( -0.131 * 0 ) + ( -0.15 * -6.56 ) + ( -0.054 * ( -0.168 + 0 ) ) ) = 1.780 M6 =-6.903 + ( ( -0.224 * 0.734 ) + ( -0.195 * 0 ) + ( -0.081 * ( -6.3 + 0 ) ) ) = -6.560 M7 =

M8 =M9 =M10 =

0 + ( ( -0.375 * ( 15.16 + 11.39 ) ) + ( -0.375 * ( -4.56 + -4.22 ) ) + (-0.375 * ( 4.77 + 1.17) ) + ( -0.375 * ( -16.01 + -6.= -0.530 M11 =0 + ( ( -0.375 * ( 11.39 + 5.65 ) ) + ( -0.375 * ( -4.22 + -1.32 ) ) + ( -0.375 * ( 1.17 + 1.78 ) ) + ( -0.375 * ( -6.3 + -6.56= -0.600 M12 =0 + ( ( -0.375 * 5.65 ) + ( -0.375 * -1.32 ) + ( -0.375 * 1.78 ) + ( -0.375 * -6.56 ) ) = 0.170

M°I == 16.660 M°II =

-1.158 + (( -0.184 * 16.66 ) + ( -0.099 * ( -4.09 + -0.53 )) + ( -0.217 * 5.78 )) = -5.020 M°III =1.55+ ( ( -0.211 * -4.56 ) + ( -0.096 * ( 1.45 + -0.53 ) ) + ( -0.193 * -17.41 ) ) = 5.780-16.948 + ( ( -0.334 * 4.77 ) + ( -0.166 * ( -8.757 + -0.53 ) ) ) = -17.41013.151 + ( ( -0.11 * ( 5.65 + -0.6 ) ) + ( -0.281 * -4.22 ) + ( -0.11 * ( 16.66 + -0.53 ) ) ) = 12.010-2.228 + ( ( -0.169 * 12.01 ) + ( -0.066 * ( -1.24 + -0.6 ) ) + ( -0.199 * 1.45 ) + ( -0.066 * ( -4.56 + -0.53) ) ) = -4.090-0.168 + ( ( -0.194 * -4.22 ) + ( -0.064 * ( 1.91 + -0.6 ) ) + ( -0.178 * -6.46 ) + ( -0.064 * ( 4.77 + -0.53 ) ) ) = 1.450-8.757 + ( ( -0.29 * 1.17 ) + ( -0.105 * ( -6.56 + -0.6 ) ) + ( -0.105 * ( -17.41 + -0.53 ) ) ) = -6.4606.531 + ( ( -0.202 * 0.17 ) + ( -0.214 * -1.32 ) + ( -0.084 * ( 12.01 + -0.6 ) ) ) = 5.820-0.342 + ( ( -0.142 * 5.82 ) + ( -0.134 * 0.17 ) + ( -0.168 * 1.91 ) + ( -0.056 * ( -4.22 + -0.6 ) ) ) = -1.2400.734 + ( ( -0.164 * -1.32 ) + ( -0.131 * 0.17 ) + ( -0.15 * -6.76 ) + ( -0.054 * ( 1.17 + -0.6 ) ) ) = 1.910-6.903 + ( ( -0.224 * 1.78 ) + ( -0.195 * 0.17 ) + ( -0.081 * ( -6.46 + -0.6 ) ) ) = -6.760

0 + ( ( -0.375 * ( 16.66 + 12.01 ) ) + ( -0.375 * ( -5.02 + -4.09 ) ) + (-0.375 * ( 5.78 + 1.45) ) + ( -0.375 * ( -17.41 + -6= -1.1000 + ( ( -0.375 * ( 12.01 + 5.82 ) ) + ( -0.375 * ( -4.09 + -1.24 ) ) + ( -0.375 * ( 1.45 + 1.91 ) ) + ( -0.375 * ( -6.46 + -6.7= -0.9900 + ( ( -0.375 * 5.82 ) + ( -0.375 * -1.24 ) + ( -0.375 * 1.91 ) + ( -0.375 * -6.76 ) ) = -1.080


17.081 + (( -0.175 * ( 12.01 + -1.1 )) + (-0.325 * -5.02 ))-1.158 + (( -0.184 * 16.8 ) + ( -0.099 * ( -3.99 + -1.1 )) + ( -0.217 * 5.98 ))1.55+ ( ( -0.211 * -5.02 ) + ( -0.096 * ( 1.41 + -1.1 ) ) + ( -0.193 * -17.62 ) )-16.948 + ( ( -0.334 * 5.78 ) + ( -0.166 * ( -8.757 + -1.1 ) ) )13.151 + ( ( -0.11 * ( 5.82 + -0.99 ) ) + ( -0.281 * -4.09 ) + ( -0.11 * ( 16.8 + -1.1 ) ) )

-2.228 + ( ( -0.169 * 12.04 ) + ( -0.066 * ( -1.22 + -0.99 ) ) + ( -0.199 * 1.41 ) + ( -0.066 * ( -5.02 + -1.1) ) ) -0.168 + ( ( -0.194 * -4.09 ) + ( -0.064 * ( 1.91 + -0.99 ) ) + ( -0.178 * -6.4 ) + ( -0.064 * ( 5.78 + -1.1 ) ) )-8.757 + ( ( -0.29 * 1.45 ) + ( -0.105 * ( -6.76 + -0.99 ) ) + ( -0.105 * ( -17.62 + -1.1 ) ) )6.531 + ( ( -0.202 * 0.1 ) + ( -0.214 * -1.24 ) + ( -0.084 * ( 12.04 + -0.99 ) ) )-0.342 + ( ( -0.142 * 5.85 ) + ( -0.134 * 0.1 ) + ( -0.168 * 1.91 ) + ( -0.056 * ( -4.09 + -0.99 ) ) ) 0.734 + ( ( -0.164 * -1.24 ) + ( -0.131 * 0.1 ) + ( -0.15 * -6.75 ) + ( -0.054 * ( 1.45 + -0.99 ) ) )-6.903 + ( ( -0.224 * 1.91 ) + ( -0.195 * 0.1 ) + ( -0.081 * ( -6.4 + -0.99 ) ) )

0 + ( ( -0.375 * ( 16.8 + 12.04 ) ) + ( -0.375 * ( -5.04 + -3.99 ) ) + (-0.375 * ( 5.98 + 1.41) ) + ( -0.375 * ( -17.62 + -6.40 + ( ( -0.375 * ( 12.04 + 5.85 ) ) + ( -0.375 * ( -3.99 + -1.22 ) ) + ( -0.375 * ( 1.41 + 1.91 ) ) + ( -0.375 * ( -6.4 + -6.750 + ( ( -0.375 * 5.85 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.91 ) + ( -0.375 * -6.75 ) )

Cuarto Ciclo de giro

17.081 + (( -0.175 * ( 12.04 + -1.19 )) + (-0.325 * -5.04 ))-1.158 + (( -0.184 * 16.82 ) + ( -0.099 * ( -3.97 + -1.19 )) + ( -0.217 * 6.01 ))1.55+ ( ( -0.211 * -5.04 ) + ( -0.096 * ( 1.38 + -1.19 ) ) + ( -0.193 * -17.69 ) )-16.948 + ( ( -0.334 * 5.98 ) + ( -0.166 * ( -8.757 + -1.19 ) ) )13.151 + ( ( -0.11 * ( 5.85 + -1.07 ) ) + ( -0.281 * -3.99 ) + ( -0.11 * ( 16.82 + -1.19 ) ) ) -2.228 + ( ( -0.169 * 12.03 ) + ( -0.066 * ( -1.22 + -1.07 ) ) + ( -0.199 * 1.38 ) + ( -0.066 * ( -5.04 + -1.19) ) ) -0.168 + ( ( -0.194 * -3.99 ) + ( -0.064 * ( 1.92 + -1.07 ) ) + ( -0.178 * -6.36 ) + ( -0.064 * ( 5.98 + -1.19 ) ) )-8.757 + ( ( -0.29 * 1.41 ) + ( -0.105 * ( -6.75 + -1.07 ) ) + ( -0.105 * ( -17.69 + -1.19 ) ) )6.531 + ( ( -0.202 * 0.08 ) + ( -0.214 * -1.22 ) + ( -0.084 * ( 12.03 + -1.07 ) ) )-0.342 + ( ( -0.142 * 5.86 ) + ( -0.134 * 0.08 ) + ( -0.168 * 1.92 ) + ( -0.056 * ( -3.99 + -1.07 ) ) ) 0.734 + ( ( -0.164 * -1.22 ) + ( -0.131 * 0.08 ) + ( -0.15 * -6.74 ) + ( -0.054 * ( 1.41 + -1.07 ) ) )-6.903 + ( ( -0.224 * 1.91 ) + ( -0.195 * 0.08 ) + ( -0.081 * ( -6.36 + -1.07 ) ) )

0 + ( ( -0.375 * ( 16.82 + 12.03 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.38) ) + ( -0.375 * ( -17.69 + -6.0 + ( ( -0.375 * ( 12.03 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.38 + 1.92 ) ) + ( -0.375 * ( -6.36 + -6.70 + ( ( -0.375 * 5.86 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.92 ) + ( -0.375 * -6.74 ) )

17.081 + (( -0.175 * ( 12.01 + -1.1 )) + (-0.325 * -5.02 )) = 16.800-1.158 + (( -0.184 * 16.8 ) + ( -0.099 * ( -3.99 + -1.1 )) + ( -0.217 * 5.98 )) = -5.0401.55+ ( ( -0.211 * -5.02 ) + ( -0.096 * ( 1.41 + -1.1 ) ) + ( -0.193 * -17.62 ) ) = 5.980-16.948 + ( ( -0.334 * 5.78 ) + ( -0.166 * ( -8.757 + -1.1 ) ) ) = -17.62013.151 + ( ( -0.11 * ( 5.82 + -0.99 ) ) + ( -0.281 * -4.09 ) + ( -0.11 * ( 16.8 + -1.1 ) ) ) = 12.040

-2.228 + ( ( -0.169 * 12.04 ) + ( -0.066 * ( -1.22 + -0.99 ) ) + ( -0.199 * 1.41 ) + ( -0.066 * ( -5.02 + -1.1) ) ) = -3.990-0.168 + ( ( -0.194 * -4.09 ) + ( -0.064 * ( 1.91 + -0.99 ) ) + ( -0.178 * -6.4 ) + ( -0.064 * ( 5.78 + -1.1 ) ) ) = 1.410-8.757 + ( ( -0.29 * 1.45 ) + ( -0.105 * ( -6.76 + -0.99 ) ) + ( -0.105 * ( -17.62 + -1.1 ) ) ) = -6.4006.531 + ( ( -0.202 * 0.1 ) + ( -0.214 * -1.24 ) + ( -0.084 * ( 12.04 + -0.99 ) ) ) = 5.850-0.342 + ( ( -0.142 * 5.85 ) + ( -0.134 * 0.1 ) + ( -0.168 * 1.91 ) + ( -0.056 * ( -4.09 + -0.99 ) ) ) = -1.2200.734 + ( ( -0.164 * -1.24 ) + ( -0.131 * 0.1 ) + ( -0.15 * -6.75 ) + ( -0.054 * ( 1.45 + -0.99 ) ) ) = 1.910-6.903 + ( ( -0.224 * 1.91 ) + ( -0.195 * 0.1 ) + ( -0.081 * ( -6.4 + -0.99 ) ) ) = -6.750

0 + ( ( -0.375 * ( 16.8 + 12.04 ) ) + ( -0.375 * ( -5.04 + -3.99 ) ) + (-0.375 * ( 5.98 + 1.41) ) + ( -0.375 * ( -17.62 + -6.4= -1.1900 + ( ( -0.375 * ( 12.04 + 5.85 ) ) + ( -0.375 * ( -3.99 + -1.22 ) ) + ( -0.375 * ( 1.41 + 1.91 ) ) + ( -0.375 * ( -6.4 + -6.75= -1.0700 + ( ( -0.375 * 5.85 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.91 ) + ( -0.375 * -6.75 ) ) = 0.080

17.081 + (( -0.175 * ( 12.04 + -1.19 )) + (-0.325 * -5.04 )) = 16.820-1.158 + (( -0.184 * 16.82 ) + ( -0.099 * ( -3.97 + -1.19 )) + ( -0.217 * 6.01 )) = -5.0501.55+ ( ( -0.211 * -5.04 ) + ( -0.096 * ( 1.38 + -1.19 ) ) + ( -0.193 * -17.69 ) ) = 6.010-16.948 + ( ( -0.334 * 5.98 ) + ( -0.166 * ( -8.757 + -1.19 ) ) ) = -17.69013.151 + ( ( -0.11 * ( 5.85 + -1.07 ) ) + ( -0.281 * -3.99 ) + ( -0.11 * ( 16.82 + -1.19 ) ) ) = 12.030-2.228 + ( ( -0.169 * 12.03 ) + ( -0.066 * ( -1.22 + -1.07 ) ) + ( -0.199 * 1.38 ) + ( -0.066 * ( -5.04 + -1.19) ) ) = -3.970-0.168 + ( ( -0.194 * -3.99 ) + ( -0.064 * ( 1.92 + -1.07 ) ) + ( -0.178 * -6.36 ) + ( -0.064 * ( 5.98 + -1.19 ) ) ) = 1.380-8.757 + ( ( -0.29 * 1.41 ) + ( -0.105 * ( -6.75 + -1.07 ) ) + ( -0.105 * ( -17.69 + -1.19 ) ) ) = -6.3606.531 + ( ( -0.202 * 0.08 ) + ( -0.214 * -1.22 ) + ( -0.084 * ( 12.03 + -1.07 ) ) ) = 5.860-0.342 + ( ( -0.142 * 5.86 ) + ( -0.134 * 0.08 ) + ( -0.168 * 1.92 ) + ( -0.056 * ( -3.99 + -1.07 ) ) ) = -1.2200.734 + ( ( -0.164 * -1.22 ) + ( -0.131 * 0.08 ) + ( -0.15 * -6.74 ) + ( -0.054 * ( 1.41 + -1.07 ) ) ) = 1.920-6.903 + ( ( -0.224 * 1.91 ) + ( -0.195 * 0.08 ) + ( -0.081 * ( -6.36 + -1.07 ) ) ) = -6.740

0 + ( ( -0.375 * ( 16.82 + 12.03 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.38) ) + ( -0.375 * ( -17.69 + -6.= -1.1900 + ( ( -0.375 * ( 12.03 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.38 + 1.92 ) ) + ( -0.375 * ( -6.36 + -6.7= -1.0900 + ( ( -0.375 * 5.86 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.92 ) + ( -0.375 * -6.74 ) ) = 0.070

Quinto Ciclo de giro

M1 = 17.081 + (( -0.175 * ( 12.03 + -1.19 )) + (-0.325 * -5.05 ))M2 = -1.158 + (( -0.184 * 16.83 ) + ( -0.099 * ( -3.97 + -1.19 )) + ( -0.217 * 6.01 ))M3 = 1.55+ ( ( -0.211 * -5.05 ) + ( -0.096 * ( 1.37 + -1.19 ) ) + ( -0.193 * -17.7 ) )M4 = -16.948 + ( ( -0.334 * 6.01 ) + ( -0.166 * ( -8.757 + -1.19 ) ) )M5 = 13.151 + ( ( -0.11 * ( 5.86 + -1.09 ) ) + ( -0.281 * -3.97 ) + ( -0.11 * ( 16.83 + -1.19 ) ) )

M6 = -2.228 + ( ( -0.169 * 12.02 ) + ( -0.066 * ( -1.22 + -1.09 ) ) + ( -0.199 * 1.37 ) + ( -0.066 * ( -5.05 + -1.19) ) ) M7 = -0.168 + ( ( -0.194 * -3.97 ) + ( -0.064 * ( 1.92 + -1.09 ) ) + ( -0.178 * -6.35 ) + ( -0.064 * ( 6.01 + -1.19 ) ) )M8 = -8.757 + ( ( -0.29 * 1.38 ) + ( -0.105 * ( -6.74 + -1.09 ) ) + ( -0.105 * ( -17.7 + -1.19 ) ) )M9 = 6.531 + ( ( -0.202 * 0.07 ) + ( -0.214 * -1.22 ) + ( -0.084 * ( 12.02 + -1.09 ) ) )M10 = -0.342 + ( ( -0.142 * 5.86 ) + ( -0.134 * 0.07 ) + ( -0.168 * 1.92 ) + ( -0.056 * ( -3.97 + -1.09 ) ) ) M11 = 0.734 + ( ( -0.164 * -1.22 ) + ( -0.131 * 0.07 ) + ( -0.15 * -6.74 ) + ( -0.054 * ( 1.38 + -1.09 ) ) )M12 = -6.903 + ( ( -0.224 * 1.92 ) + ( -0.195 * 0.07 ) + ( -0.081 * ( -6.35 + -1.09 ) ) )

M°I = 0 + ( ( -0.375 * ( 16.83 + 12.02 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.37) ) + ( -0.375 * ( -17.7 + M°II = 0 + ( ( -0.375 * ( 12.02 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.37 + 1.92 ) ) + ( -0.375 * ( -6.35 + M°III = 0 + ( ( -0.375 * 5.86 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.92 ) + ( -0.375 * -6.74 ) )

Sexto Ciclo de giro

M1 = 17.081 + (( -0.175 * ( 12.02 + -1.19 )) + (-0.325 * -5.05 ))M2 = -1.158 + (( -0.184 * 16.83 ) + ( -0.099 * ( -3.97 + -1.19 )) + ( -0.217 * 6.01 ))M3 = 1.55+ ( ( -0.211 * -5.05 ) + ( -0.096 * ( 1.37 + -1.19 ) ) + ( -0.193 * -17.7 ) )M4 = -16.948 + ( ( -0.334 * 6.01 ) + ( -0.166 * ( -8.757 + -1.19 ) ) )M5 = 13.151 + ( ( -0.11 * ( 5.86 + -1.08 ) ) + ( -0.281 * -3.97 ) + ( -0.11 * ( 16.83 + -1.19 ) ) ) M6 = -2.228 + ( ( -0.169 * 12.02 ) + ( -0.066 * ( -1.22 + -1.08 ) ) + ( -0.199 * 1.37 ) + ( -0.066 * ( -5.05 + -1.19) ) ) M7 = -0.168 + ( ( -0.194 * -3.97 ) + ( -0.064 * ( 1.92 + -1.08 ) ) + ( -0.178 * -6.35 ) + ( -0.064 * ( 6.01 + -1.19 ) ) )M8 = -8.757 + ( ( -0.29 * 1.37 ) + ( -0.105 * ( -6.74 + -1.08 ) ) + ( -0.105 * ( -17.7 + -1.19 ) ) )M9 = 6.531 + ( ( -0.202 * 0.07 ) + ( -0.214 * -1.22 ) + ( -0.084 * ( 12.02 + -1.08 ) ) )M10 = -0.342 + ( ( -0.142 * 5.86 ) + ( -0.134 * 0.07 ) + ( -0.168 * 1.92 ) + ( -0.056 * ( -3.97 + -1.08 ) ) ) M11 = 0.734 + ( ( -0.164 * -1.22 ) + ( -0.131 * 0.07 ) + ( -0.15 * -6.74 ) + ( -0.054 * ( 1.37 + -1.08 ) ) )M12 = -6.903 + ( ( -0.224 * 1.92 ) + ( -0.195 * 0.07 ) + ( -0.081 * ( -6.35 + -1.08 ) ) )

M°I = 0 + ( ( -0.375 * ( 16.83 + 12.02 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.37) ) + ( -0.375 * ( -17.7 + M°II = 0 + ( ( -0.375 * ( 12.02 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.37 + 1.92 ) ) + ( -0.375 * ( -6.35 + M°III = 0 + ( ( -0.375 * 5.86 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.92 ) + ( -0.375 * -6.74 ) )


= 16.830 M1 = 17.081 + (( -0.175 * ( 12.02 + -1.19 )) + (-0.325 * -5.05 ))= -5.050 M2 = -1.158 + (( -0.184 * 16.83 ) + ( -0.099 * ( -3.97 + -1.19 )) + ( -0.217 * 6.01 ))= 6.010 M3 = 1.55+ ( ( -0.211 * -5.05 ) + ( -0.096 * ( 1.37 + -1.19 ) ) + ( -0.193 * -17.7 ) )= -17.700 M4 = 13.151 + ( ( -0.11 * ( 5.86 + -1.08 ) ) + ( -0.281 * -3.97 ) + ( -0.11 * ( 16.83 + -1.19 ) ) ) = 12.020 M5 = -2.228 + ( ( -0.169 * 12.02 ) + ( -0.066 * ( -1.22 + -1.08 ) ) + ( -0.199 * 1.37 ) + ( -0.066 * ( -5.05 + -1.19) ) )

-2.228 + ( ( -0.169 * 12.02 ) + ( -0.066 * ( -1.22 + -1.09 ) ) + ( -0.199 * 1.37 ) + ( -0.066 * ( -5.05 + -1.19) ) ) = -3.970 M6 = -0.168 + ( ( -0.194 * -3.97 ) + ( -0.064 * ( 1.92 + -1.08 ) ) + ( -0.178 * -6.35 ) + ( -0.064 * ( 6.01 + -1.19 ) ) )-0.168 + ( ( -0.194 * -3.97 ) + ( -0.064 * ( 1.92 + -1.09 ) ) + ( -0.178 * -6.35 ) + ( -0.064 * ( 6.01 + -1.19 ) ) ) = 1.370 M7 = -8.757 + ( ( -0.29 * 1.37 ) + ( -0.105 * ( -6.74 + -1.08 ) ) + ( -0.105 * ( -17.7 + -1.19 ) ) )

= -6.350 M8 = 6.531 + ( ( -0.202 * 0.07 ) + ( -0.214 * -1.22 ) + ( -0.084 * ( 12.02 + -1.08 ) ) )= 5.860 M9 = -0.342 + ( ( -0.142 * 5.86 ) + ( -0.134 * 0.07 ) + ( -0.168 * 1.92 ) + ( -0.056 * ( -3.97 + -1.08 ) ) ) = -1.220 M10 = 0.734 + ( ( -0.164 * -1.22 ) + ( -0.131 * 0.07 ) + ( -0.15 * -6.74 ) + ( -0.054 * ( 1.37 + -1.08 ) ) )= 1.920 M11 = -6.903 + ( ( -0.224 * 1.92 ) + ( -0.195 * 0.07 ) + ( -0.081 * ( -6.35 + -1.08 ) ) )= -6.740 M12 = -6.903 + ( ( -0.224 * 1.92 ) + ( -0.195 * 0.07 ) + ( -0.081 * ( + -1.08 ) ) )

0 + ( ( -0.375 * ( 16.83 + 12.02 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.37) ) + ( -0.375 * ( -17.7 + = -1.190 M°I = 0 + ( ( -0.375 * ( 16.83 + 12.02 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.37) ) + ( -0.375 * ( -17.7 + 0 + ( ( -0.375 * ( 12.02 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.37 + 1.92 ) ) + ( -0.375 * ( -6.35 + = -1.080 M°II = 0 + ( ( -0.375 * ( 12.02 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.37 + 1.92 ) ) + ( -0.375 * ( -6.35 +

= 0.070 M°III = 0 + ( ( -0.375 * 5.86 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.92 ) + ( -0.375 * -6.74 ) )

= 16.830= -5.050= 6.010= -17.700= 12.020

-2.228 + ( ( -0.169 * 12.02 ) + ( -0.066 * ( -1.22 + -1.08 ) ) + ( -0.199 * 1.37 ) + ( -0.066 * ( -5.05 + -1.19) ) ) = -3.970-0.168 + ( ( -0.194 * -3.97 ) + ( -0.064 * ( 1.92 + -1.08 ) ) + ( -0.178 * -6.35 ) + ( -0.064 * ( 6.01 + -1.19 ) ) ) = 1.370

= -6.350= 5.860= -1.220= 1.920= -6.740

0 + ( ( -0.375 * ( 16.83 + 12.02 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.37) ) + ( -0.375 * ( -17.7 + = -1.1900 + ( ( -0.375 * ( 12.02 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.37 + 1.92 ) ) + ( -0.375 * ( -6.35 + = -1.080

= 0.070

17.081 + (( -0.175 * ( 12.02 + -1.19 )) + (-0.325 * -5.05 )) = 16.830-1.158 + (( -0.184 * 16.83 ) + ( -0.099 * ( -3.97 + -1.19 )) + ( -0.217 * 6.01 )) = -5.0501.55+ ( ( -0.211 * -5.05 ) + ( -0.096 * ( 1.37 + -1.19 ) ) + ( -0.193 * -17.7 ) ) = 6.01013.151 + ( ( -0.11 * ( 5.86 + -1.08 ) ) + ( -0.281 * -3.97 ) + ( -0.11 * ( 16.83 + -1.19 ) ) ) = -17.700-2.228 + ( ( -0.169 * 12.02 ) + ( -0.066 * ( -1.22 + -1.08 ) ) + ( -0.199 * 1.37 ) + ( -0.066 * ( -5.05 + -1.19) ) ) = 12.020

-0.168 + ( ( -0.194 * -3.97 ) + ( -0.064 * ( 1.92 + -1.08 ) ) + ( -0.178 * -6.35 ) + ( -0.064 * ( 6.01 + -1.19 ) ) ) = -3.970-8.757 + ( ( -0.29 * 1.37 ) + ( -0.105 * ( -6.74 + -1.08 ) ) + ( -0.105 * ( -17.7 + -1.19 ) ) ) = 1.3706.531 + ( ( -0.202 * 0.07 ) + ( -0.214 * -1.22 ) + ( -0.084 * ( 12.02 + -1.08 ) ) ) = -6.350-0.342 + ( ( -0.142 * 5.86 ) + ( -0.134 * 0.07 ) + ( -0.168 * 1.92 ) + ( -0.056 * ( -3.97 + -1.08 ) ) ) = 5.8600.734 + ( ( -0.164 * -1.22 ) + ( -0.131 * 0.07 ) + ( -0.15 * -6.74 ) + ( -0.054 * ( 1.37 + -1.08 ) ) ) = -1.220-6.903 + ( ( -0.224 * 1.92 ) + ( -0.195 * 0.07 ) + ( -0.081 * ( -6.35 + -1.08 ) ) ) = 1.920-6.903 + ( ( -0.224 * 1.92 ) + ( -0.195 * 0.07 ) + ( -0.081 * ( + -1.08 ) ) ) = -6.740

0 + ( ( -0.375 * ( 16.83 + 12.02 ) ) + ( -0.375 * ( -5.05 + -3.97 ) ) + (-0.375 * ( 6.01 + 1.37) ) + ( -0.375 * ( -17.7 + = -1.0800 + ( ( -0.375 * ( 12.02 + 5.86 ) ) + ( -0.375 * ( -3.97 + -1.22 ) ) + ( -0.375 * ( 1.37 + 1.92 ) ) + ( -0.375 * ( -6.35 + = 0.0700 + ( ( -0.375 * 5.86 ) + ( -0.375 * -1.22 ) + ( -0.375 * 1.92 ) + ( -0.375 * -6.74 ) ) = 0.070


Nudo 01 Correccion Nudo 07

M1-2 = -4144.413 -4142.944 M7-3 =

M1-5 = 4142.152 4142.944 M7-6 =

-2.260 0.000 M7-8 =

M7-11 =

Nudo 02

M2-1 = 10278.412 10277.688

M2-3 = -8855.694 -8856.547 Nudo 08

M2-6 = -1420.752 -1421.141 M8-7 =

1.966 0.000 M8-4 =

M8-12 =

Nudo 03 M8-V =

M3-2 = 9445.446 9449.798

M3-4 = -10591.62 -10587.634

M3-7 = 1135.857 1137.837 Nudo 09

-10.313 0.000 M9-5 =

M9-10 =

Nudo 04 M9-13 =

M4-3 = 4002.418 3999.362

M4-8 = -3997.843 -3999.362

M4-V = 0 0 Nudo 10

4.575 0.000 M10-9 =

M10-6 =

Nudo 05 M10-11 =

M5-1 = 3694.327 3695.233 M10-14 =

M5-6 = -6381.673 -6379.359

M5-9 = 2683.228 2684.134

-4.118 0.008 Nudo 11

M11-10 =

Nudo 06 M11-7 =

M6-2 = -1320.201 -1319.464 M11-12 =

M6-5 = 12131.668 12133.553 M11-15 =

M6-7 = -9863.670 -9861.450

M6-10 = -953.375 -952.628

-5.578 0.010 Nudo 12

M12-11 =

M12-8 =

M12-16 =

M12-V =

Corrección703.859 703.285

7672.658 7670.919-8705.344 -8706.939

333.309 332.737

4.482 0.002

4854.827 4852.954-2941.124 -2941.802-1910.474 -1911.152

0 03.230 0.000

2109.714 2110.193-4765.317 -4764.0962652.750 2653.902

-2.853 0.000

8079.599 8076.672-697.341 -698.496

-6838.701 -6842.164-533.250 -536.008

10.306 0.004

7428.589 7430.048384.5154 384.996

-8697.303 -8695.968879.750 880.926

-4.448 0.002

4970.498 4967.602-1946.784 -1947.831-3017.250 -3019.771

0 06.464 0.000

DISEÑO DE LOSAS ALIGERADAS

* Asumiendo la carga muerta del predimencionamiento anterior

Datos:

CM= 344.4 Kg/m

L1 = 4.3 h = 20.00 Ø = 0.9 f'c= 210L2 = 5.5 recu = 2 fy= 4200 ß= 0.85L3 = 4 base= 10

L1 + L2 = 4.9 L2 + L3 = 4.75 2 2

10 10

24 24

- -- -

+ + +

4.3 m 5.5 m 4 m

Calculo de los momento negativos

MA = WL1² ==> 344.4( 4.3 )² = 265.332 Kg - m24 24

MB = WLm² ==> 344.4( 4.9 )² = 826.904 Kg - m10 10

MC = WLm² ==> 344.4( 4.75 )² = 777.053 Kg - m10 10

MD = WL3² ==> 344.4( 4 )² = 229.6 Kg - m24 24

Calculo de los momento positivos

TRAMO AB

= WL² ==> 344.4( 4.3 )² = 454.854 Kg - m14 14

TRAMO BC

= WL² ==> 344.4( 5.5 )² = 651.131 Kg - m16 16

TRAMO CD

= WL² ==> 344.4( 4 )² = 393.6 Kg - m14 14

WLm = WLm =

WL m² WL m²

WL 1² WL 3²

MA-B

MB-C

MC-D

826.9 777.0525

265.33 229.6

-+

454.85 651.13125 393.6

0.5WuLn 0.5WuLn 0.575WuLn

a b c

b a a

0.575WuLn 0.5WuLn 0.5WuLn

Cortante Actuante

= 0.5 (344.4 ) (4.3) = 740.46 Kg

= 0.575 (344.4 ) (4.9) = 970.35 Kg

= 0.5 (344.4 ) (4.9) = 843.78 Kg

= 0.5 (344.4 ) (4.75) = 817.95 Kg

= 0.575 (344.4 ) (4.7 = 940.64 Kg

= 0.5 (344.4 ) (4) = 688.80 Kg

740.46 Kg 843.78 Kg 940.6425 Kg

a b c

b a a

970.347 Kg 817.95 Kg 688.8 Kg

Ø 3/8

RECUBRIMIENTO DE LOSA ALIGERADA : r = 2cm (mínimo)

aA

bB1

aB2

aC1

bC2

aD

d = h - (r + Ø/2) ==> d = 20 - ( 2 + 0.953/2 ) = 17.5235 cm = 0.18 m

Calculando el área del acero negativo

A)As = Mu = 0.41 cm2

Ø fy (d-a/2)

a = As fy = 0.97 cm0.85 f'c ß

As(-) = 0.41 cm2 ==> 1 Ø 3/8 0.71

Total 0.71 cm2

B)As = Mu = 1.38 cm2

Ø fy (d-a/2)

a = As fy = 3.24 cm0.85 f'c ß

As(-) = 1.38 cm2 ==> 1 Ø 1/2 1.29

Total 1.29 cm2

C)As = Mu = 1.28 cm2

Ø fy (d-a/2)

a = As fy = 3.02 cm0.85 f'c ß

As(-) = 1.28 cm2 ==> 1 Ø 1/2 1.29

Total 1.29 cm2

D)As = Mu = 0.36

Ø fy (d-a/2)

a = As fy = 0.840.85 f'c ß

As(-) = 0.36 cm2 ==> 1 Ø 3/8 0.71

Total 0.71 cm2

Calculando el área del acero positivo

A) Tramo ABAs = Mu = 0.72 cm2

Ø fy (d-a/2)

a = As fy = 1.70 cm0.85 f'c ß

As(+) = 0.72 cm2 ==> 1 Ø 1/2 1.293/8

Total 1.29 cm2

B) Tramo BCAs = Mu = 1.06 cm2

Ø fy (d-a/2)

a = As fy = 2.49 cm0.85 f'c ß

As(+) = 1.06 cm2 ==> 1 Ø 1/2 1.29

Total 1.29 cm2

C) Tramo CDAs = Mu = 0.62 cm2

Ø fy (d-a/2)

a = As fy = 1.46 cm0.85 f'c ß

As(-) = 0.62 cm2 ==> 1 Ø 1/2 1.29

Total 1.29 cm2

0.05

0.15

0.1 0.3 0.1

A Ø 1/4 = 0.32 cm2

Ast. = 0.0025 x 25 x b x d

b = 100d = 5

Ast = 0.0025 x 100 x 5= 1.25 cm2

S = A Ø x 100Ast

S = 0.32 x 100 = 25.6 cm = 0.26 m1.25

En el interior se colocará acero de temperatura

As Temp. Ø 1/4 @ 0.25 m

CARACTERISTICAS DE LAS BARRAS

DIAMETRO PERI. PESO AREA EN CENTIMETROS CUADRADOS SEGÚN EL NUMERO DE BARRASPULG. Cms. Cms. Kg/ml. 1 2 3 4 5 6 7 8

# 8 1 2.54 8 4.04 5.1 10.2 15.3 20.4 25.5 30.6 35.7 40.8# 11 1 1/8 3.581 11.2 7.95 10.06 20.12 30.18 40.24 50.3 60.36 70.42 80.48# 4 1/2 1.27 4 1.02 1.29 2.58 3.87 5.16 6.45 7.74 9.03 10.32

# 2 1/4 0.635 2 0.25 0.32 0.64 0.96 1.28 1.6 1.92 2.24 2.56# 6 3/4 1.905 6 3.26 2.84 5.68 8.52 11.36 14.2 17.04 19.88 22.72# 3 3/8 0.953 3 0.58 0.71 1.42 2.13 2.84 3.55 4.26 4.97 5.68

# 5 5/8 1.587 5 1.6 2 4 6 8 10 12 14 16

NOTA:Las dimencviones, diametros, areas, perimetros y pesos son tomados del Reglamento Nacional de Construcciones (801).

Tanteo de acero

AREA EN CENTIMETROS CUADRADOS SEGÚN EL NUMERO DE BARRAS Carga Ø fy d f'c ß9 10 11 12 MA 26533.15 0.9 4200 17.52 210 0.85

45.9 51 56.1 61.2 MB 82690.4490.54 100.6 110.66 120.72 MC 77705.2511.61 12.9 14.19 15.48 MD 22960.00

2.88 3.2 3.52 3.84 Tramo AB 45485.425.56 28.4 31.24 34.08 Tramo BC 65113.1256.39 7.1 7.81 8.82 Tramo CD 39360

18 20 22 24

Las dimencviones, diametros, areas, perimetros y pesos son tomados del Reglamento Nacional de Construcciones (801).

MOMENTOS NEGATIVOS MOMENTOS POSITIVOSM A MB MC MD Tramo AB

b a As a As a As a As a As10 3.5047 0.45 3.50 1.39 3.50 1.30 3.50 0.39 3.50 0.76

1.05 0.41 3.26 1.38 3.07 1.29 0.91 0.36 1.80 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.72

0.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.72

0.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.72

0.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.720.97 0.41 3.24 1.38 3.02 1.28 0.84 0.36 1.70 0.72

MOMENTOS POSITIVOSTramo BC Tramo CD

a As a As3.50 1.09 3.50 0.662.57 1.06 1.55 0.622.50 1.06 1.46 0.622.49 1.06 1.46 0.62

2.49 1.06 1.46 0.622.49 1.06 1.46 0.622.49 1.06 1.46 0.62

2.49 1.06 1.46 0.622.49 1.06 1.46 0.62

2.49 1.06 1.46 0.622.49 1.06 1.46 0.622.49 1.06 1.46 0.622.49 1.06 1.46 0.622.49 1.06 1.46 0.622.49 1.06 1.46 0.622.49 1.06 1.46 0.62

DISEÑO DE ACEROS

As Temp. Ø1/[email protected]

L/5 L/50.86 L/3 L/3 L/3 L/3 0.80

1.43 1.83 1.83 1.331Ø3/8 1Ø1/2 1Ø1/2 1Ø3/8

1Ø1/2

1Ø1/2 1Ø1/2

A

DISEÑO DE ACERO EN VIGAS PRINCIPALES

VIGA PRINCIPAL - A 3er PISO

L = 5.5 mlado 1 = 20 cmlado 2 = 45 cm

Wd= 3163.13 kg/mWl= 892.5 kg/m

f'c = 210 kg/cm2

Cálculo de la carga amplificada

Wu = 1.2D + 1.6LWu = 1.2 (3163.13 ) + 1.6 (892.5 )Wu = 5223.756 Kg/m

5223.756 Kg/m

5.5 m

Calculo del diseño de acero

45 cm

20 cm

Cálculo del peralte efectivo de la viga

d = 0.45 - 0.04 = 0.41 m

Cálculo del momento último

Mu = = 5223.756 x (5.5) 28 8

Mu = 19752.33 Kg-m

Hallando parámetro Ru

Ru = Mu = 19752.33 x 100

20 x (41)2

Ru = 58.751725

Hallamos cuantía del acero þ(%)

10.94 0.3 Para concreto de 21058.752 X

X = 1.611 %

Cálculo del área de acero

þ = As ==> As = þxbxdbxd

As = 0.01611 x 20 x 41

As = 13.2102

Verificación de cuantías

Hallamos þb

þb = 0,85x ß x f'c (6000 / 6000+fy)fy

þb = 0,85 x 0,85 x 210 (6000 / 6000 +4200)4200

þb = 0.02125 = 2.125 %

Cuantía Máxima (þ Max)

þMax = 0,75 x þb

þMax = 0,75 x 0.02125

þMax = 0.0159375 = 1.59 %

WL2

bd2

Kg/cm2

Cm2

Cuantía Mínima (þ Min)

þMin = 14/4200 = 0.003333 = 0.33 %

þMin < þ < þMax 0.33 < 1.611 < 1.59 MAL

DISEÑO DE ACEROS

As = 13.21 ==> 2 Ø 1 10.21 Ø 1/2 1.29

3 Total 11.49 cm2

0.41 cm 45 cm

O O O

20 cm

1Ø1/2 2Ø1

cm2

DISEÑO DE ACERO EN VIGAS PRINCIPALES


DIAMETRO PERI. PESO AREA EN CENTIMETROS CUADRADOS SEGÚN EL NUMERO DE BARRASPULG. Cms. Cms. Kg/ml. 1 2 3 4

# 8 1 2.54 8 4.04 5.1 10.2 15.3 20.4# 11 1 1/8 3.581 11.2 7.95 10.06 20.12 30 40.24# 4 1/2 1.27 4 1.02 1.29 2.58 3.87 5.16# 2 1/4 0.635 2 0.25 0.32 0.64 0.96 1.28

NOTA:Las dimencviones, diametros, areas, perimetros y pesos son tomados del Reglamento Nacional de Construcciones (801).

CANTIDAD

1 O2 O O3 O O O4 O O O O5 O O O O O

1 O

2O O3O O O4O O O O5O O O O O


AREA EN CENTIMETROS CUADRADOS SEGÚN EL NUMERO DE BARRAS5 6 7 8 9 10 11 12

25.5 30.6 35.7 40.8 45.9 51 56.1 61.250.3 60.36 70.42 80.48 90.54 100.6 110.7 1216.45 7.74 9.03 10.32 11.61 12.9 14.19 15.51.6 1.92 2.24 2.56 2.88 3.2 3.52 3.84

Las dimencviones, diametros, areas, perimetros y pesos son tomados del Reglamento Nacional de Construcciones (801).

DISEÑO DE ACERO EN VIGAS SECUNDARIAS

VIGA SECUNDARIA 1 3er PISO

L = 5 mlado 1 = 20 cmlado 2 = 50 cm

Wd= 3966.38 kg/mWl= 892.5 kg/m

f'c = 210 kg/cm2

Cálculo de la carga amplificada

Wu = 1.2D + 1.6LWu = 1.2 (3966.38 ) + 1.6 (892.5 )Wu = 6187.656 Kg/m

6187.656 Kg/m

5 m


50 cm

20 cm

Cálculo del peralte efectivo de la viga

d = 0.5 - 0.04 = 0.46 m

Cálculo del momento último

Mu = = 6187.656 x (5) 28 8

Mu = 19336.43 Kg-m

Hallando parámetro Ru

Ru = Mu = 19336.43 x 100

20 x (46)2

Ru = 45.690997

Hallamos cuantía del acero þ(%)

10.94 0.3 Para concreto de 21045.691 X

X = 1.253 %

Cálculo del área de acero

þ = As ==> As = þxbxdbxd

As = 0.01253 x 20 x 46

As = 11.5276

Verificación de cuantías

Hallamos þb

þb = 0,85x ß x f'c (6000 / 6000+fy)fy

þb = 0,85 x 0,85 x 210 (6000 / 6000 +4200)4200

þb = 0.02125 = 2.125 %

Cuantía Máxima (þ Max)

þMax = 0,75 x þb

þMax = 0,75 x 0.02125

þMax = 0.0159375 = 1.59 %

WL2

bd2

Kg/cm2

Cm2

Cuantía Mínima (þ Min)

þMin = 14/4200 = 0.003333 = 0.33 %

þMin < þ < þMax 0.33 < 1.253 < 1.59 OK..

DISEÑO DE ACEROS

As = 11.53 ==> 2 Ø 1 10.21 Ø 3/4 2.84

3 Total 13.04 cm2

0.46 cm 50 cm

O O O

20 cm

1Ø3/4 2Ø1

cm2

DISEÑO DE ACERO EN COLUMNAS

ACERO EN COLUMNAS TIPO I, II, III y IV

lado 1 = 25 cm Seccion minima = 25 x 25lado 2 = 25 cm Seccion minima = 625 cm

= 1.5 %


25 cm

25 cm

Calculo del acero mninmo.

Asmin = min * b * d

Asmin =

Asmin = 25 X 25X þ

Asmin = 9.375 cm

As = 9.38 cm2 ==> 4 Ø 3/4 11.362 Ø 1/2 2.58

Total 13.94 cm2

4Ø3/4

O O O

2Ø1/2

O O O

* Calculo de estribos

* Primer psio

h = 2.9 cm

Donde:

6 Dimension mayor de la columna

0.483 0.5

0.05 1 @ 0.05

0.5 5 @ 0.10

2.9 cm Rto @ 0.25

Rto @ 0.25

0.5 5 @ 0.10

0.05 1 @ 0.05

L0 > L

N

LN

=

L0 >

* Calculo de estribos

* Segundo piso

h = 2.9 cmh = 2.9 cm

Donde:

6 Dimension mayor de la columna

1er piso 0.483 0.5

2do piso 0.483 5

0.05 1 @ 0.05

0.5 5 @ 0.10

2.9 cm Rto @ 0.25

Rto @ 0.25

0.5 5 @ 0.10

0.05 1 @ 0.05

0.05 1 @ 0.05

5 5 @ 0.10

Rto @ 0.25

2.9 cm

Rto @ 0.25

5 5 @ 0.10

0.05 5 @ 0.10

0.05 1 @ 0.05

L0 > L

N

LN

=

L0 >

L0 >

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Trabajo Análisis I