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
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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:
Hacemos Sumatoria de Momentos en A Hacemos Sumatoria de Fuerzas en Y
Err:502 RC2+RD=2041.7
Err:502 Err:502
Err:502
X= Err:502
X= Err:502
M+= Err:502
M+= Err:502
CALCULO DEL EMPOTRAMIENTO PERFECTO:
TRAMO AB:MB= -QL^2/8 -480.4x4.55^2/8 MB= -1243.19TRAMO BC:MB= QL^2/12 344.4x5.75^2/12 MB= 948.89MC= -QL^2/12 -344.4x5.75^2/12 MC= -948.89TRAMO CD:MD= QL^2/8 480.4x4.25^2/8 MC= 1084.65
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
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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
CALCULO DE LA REACCIONES:
TRAMO AB:
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=1980.3
Err:502 Err:502
Err:502
X= Err:502
X= Err:502
M+= Err:502
M+= Err:502
TRAMO C2 D:
Hacemos Sumatoria de Momentos en A Hacemos Sumatoria de Fuerzas en Y
Err:502 RC2+RD=2041.7
Err:502 Err:502
Err:502
X= Err:502
X= Err:502
M+= Err:502
M+= Err:502
CALCULO DEL EMPOTRAMIENTO PERFECTO:
TRAMO AB:MB= -QL^2/8 -344.4x4.55^2/8 MB= -891.24TRAMO 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^2/8 344.4x4.25^2/8 MC= 777.59
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
CALCULO DE LA REACCIONES:
TRAMO AB:
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:
Hacemos Sumatoria de Momentos en A Hacemos Sumatoria de Fuerzas en Y
Err:502 RC2+RD=2041.7
Err:502 Err:502
Err:502
X= Err:502
X= Err:502
M+= Err:502
M+= Err:502
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^2/8 344.4x4.25^2/8 MC= 777.59
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
CALCULO DE LA REACCIONES:
TRAMO AB:
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:
Hacemos Sumatoria de Momentos en A Hacemos Sumatoria de Fuerzas en Y
Err:502 RC2+RD=2041.7
Err:502 Err:502
Err:502
X= Err:502
X= Err:502
M+= Err:502
M+= Err:502
CALCULO DEL EMPOTRAMIENTO PERFECTO:
TRAMO AB:MB= -QL^2/8 -344.4x4.55^2/8 MB= -891.24TRAMO 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 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
CALCULO DE LA REACCIONES:
TRAMO AB:
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:
Hacemos Sumatoria de Momentos en A Hacemos Sumatoria de Fuerzas en Y
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
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+2.425mATP = 3.565m
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
Para la Viga Principal A Tenemos Que:
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
Para la Viga Principal D Tenemos Que:
h = 0.5 mb = 0.2 m
PREDIMENCIONAMIENTO DE LA VIGA PRINCIPAL A
a = Peso del muro / el Peso de la losah = 1.2
Calculo 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
ATP = a+AtATP = 0.47m+2.625mATP = 3.095m
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
Para la Viga Principal A Tenemos Que:
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
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 = 405 Kg/m / 861Kg/m2a = 0.47m
ATP = a+AtATP = 0.47m+2.425mATP = 2.895m
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
Para la Viga Principal D Tenemos Que:
h = 0.45b = 0.2
Para la Viga Principal A Tenemos Que:
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
Para la Viga Principal D Tenemos Que:
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
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.85mInf. Losa =4175.85Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = hxbx&cºAP.P. Viga = 0.5mx0.3mx2400Kg/m3P.P. Viga = 360Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Viga = 360Kg/mx1.4P.P. Viga = 504Kg/m
Hallamos el Peso Propio del Muro
P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx2.9mx1350Kg/m3P.P. Muro = 978.75Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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/m2x4.85mInf. Losa =1649Kg/m
CV = =1649Kg/m
METRADO DE CARGAS
Para la viga Principal C
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.65mInf. Losa =4003.65Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = hxbx&cºAP.P. Viga = 0.5mx0.3mx2400Kg/m3P.P. Viga = 360Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Viga = 360Kg/mx1.4P.P. Viga = 504Kg/m
Hallamos el Peso Propio del Muro
P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx2.9mx1350Kg/m3P.P. Muro = 978.75Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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/m2x4.65mInf. Losa =1581Kg/m
CV = =1581Kg/m
METRADO DE CARGAS
Para la viga Principal D
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x2.425mInf. Losa =2087.93Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = hxbx&cºAP.P. Viga = 0.5mx0.2mx2400Kg/m3P.P. Viga = 240Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Viga = 360Kg/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
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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/m2x2.425mInf. Losa =824.5Kg/m
CV = =824.5Kg/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/m
Inf. Losa 861x2.625mInf. Losa =2260.13Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.5mx0.2mx2400Kg/m3
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 = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/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
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.85mInf. Losa =4175.85Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = hxbx&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 = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/m
Calculamos la Carga Viva
Para la Carga Viva Tomamos La Influencia en la Losa Aligerada de la Carga Viva
Inf. Losa =340Kg/m2x4.85mInf. Losa =1649Kg/m
CV = =1649Kg/m
METRADO DE CARGAS
Para la viga Principal C
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.65mInf. Losa =4003.65Kg/mInf. Losa 4003.65
Hallamos el Peso Propio de la Viga
P.P. Viga = hxbx&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 = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/m
Calculamos la Carga Viva
Para la Carga Viva Tomamos La Influencia en la Losa Aligerada de la Carga Viva
Inf. Losa =340Kg/m2x4.65mInf. Losa =1581Kg/m
CV = =1581Kg/m
METRADO DE CARGAS
Para la viga Principal D
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x2.425mInf. Losa =2087.93Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = hxbx&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 = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/m
Calculamos la Carga Viva
Para la Carga Viva Tomamos La Influencia en la Losa Aligerada de la Carga Viva
Inf. Losa =340Kg/m2x2.425mInf. Losa =824.5Kg/m
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
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 = 5/11h = 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
Para la Viga Principal A Tenemos Que:
h =0.5mb =0.2m
PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 2
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
PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 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
PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 4
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+2.425mATP = 3.565m
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
Para la Viga Principal D Tenemos Que:
h = 0.5
b = 0.2
Para la Viga Secunadaria 1 Tenemos Que:
h = 0.5 mb = 0.2 m
Para la Viga Secunadaria 2 Tenemos Que:
h = 0.5 mb = 0.3 m
Para la Viga Secunadaria 3 Tenemos Que:
h = 0.5 mb = 0.2 m
Para la Viga Secunadaria 4 Tenemos Que:
h = 0.5 mb = 0.2 m
PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 1
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
ATP = a+AtATP = 0.47m+2.625mATP = 3.095m
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
Para la Viga Principal A Tenemos Que:
h =0.5mb =0.2m
PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 2
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
PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 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
PREDIMENCIONAMIENTO DE LA VIGA SECUNDARIA 4
a = Peso del muro / el Peso de la losa
Calculo del Peso del Muro:
P.M = 0.25mx1350Kg/m3x1.2mP.M = 405 Kg/m
Peso de la Losa :
P.L. : 861Kg/m2
a = 405 / 861a = 0.47m
ATP = a+AtATP = 0.47m+2.425mATP = 2.895m
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
Para la Viga Principal D Tenemos Que:
h = 0.5b = 0.2
Para la Viga Secunadaria 1 Tenemos Que:
h = 0.5 mb = 0.2 m
Para la Viga Secunadaria 2 Tenemos Que:
h = 0.5 mb = 0.3 m
Para la Viga Secunadaria 3 Tenemos Que:
h = 0.5 mb = 0.25 m
Para la Viga Secunadaria 4 Tenemos Que:
h = 0.5 mb = 0.2 m
METRADO DE CARGAS
Para la viga Secundaria 1
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x2.625mInf. Losa =2260.13Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.2x0.5x2400P.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
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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 Secundaria 2
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.85mInf. Losa =2262.35Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.5x0.3x2400P.P. Viga = 360Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Viga = 360Kg/mx1.4P.P. Viga = 504Kg/m
Hallamos el Peso Propio del Muro
P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx2.9mx1350Kg/m3P.P. Muro = 978.75Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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/m2x4.85mInf. Losa =894.73Kg/m
CV = =894.73Kg/m
METRADO DE CARGAS
Para la viga Secundaria 3
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.65mInf. Losa =4003.65Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.5x0.2x2400P.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
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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/m2x4.65mInf. Losa =1581Kg/m
CV = =1581Kg/m
METRADO DE CARGAS
Para la viga Secundaria 4
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x2.425mInf. Losa =2087.93Kg/m
Hallamos el Peso Propio de la Viga
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.5x0.2x2400P.P. Viga = 240Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Viga = 336Kg/m
P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx2.9mx1350Kg/m3P.P. Muro = 978.75Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
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/m2x2.425mInf. Losa =824.5Kg/m
CV = =824.5Kg/m
METRADO DE CARGAS
Para la viga Secundaria 1
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x2.625mInf. Losa =2260.13Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.2x0.5x2400P.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 = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
405
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/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 Secundaria 2
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.85mInf. Losa =2262.35Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.5x0.3x2400P.P. Viga = 360Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Viga = 360Kg/mx1.4P.P. Viga = 504Kg/m
Hallamos el Peso Propio del Muro
P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/m
Calculamos la Carga Viva
Para la Carga Viva Tomamos La Influencia en la Losa Aligerada de la Carga Viva
Inf. Losa =340Kg/m2x4.85mInf. Losa =894.73Kg/m
CV = =894.73Kg/m
METRADO DE CARGAS
Para la viga Secundaria 3
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x4.65mInf. Losa =4003.65Kg/m
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.5x0.2x2400P.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 = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/m
Calculamos la Carga Viva
Para la Carga Viva Tomamos La Influencia en la Losa Aligerada de la Carga Viva
Inf. Losa =340Kg/m2x4.65mInf. Losa =1581Kg/m
CV = =1581Kg/m
METRADO DE CARGAS
Para la viga Secundaria 4
CM=Inf. Losa+P.P.Viga+P.P.Losa
Inf. Losa = P. P. de la Losa x At
P.P. de la Losa =861Kg/m
Inf. Losa 861x2.425mInf. Losa =2087.93Kg/m
Hallamos el Peso Propio de la Viga
Hallamos el Peso Propio de la Viga
P.P. Viga = bxhx&cºAP.P. Viga = 0.5x0.2x2400P.P. Viga = 240Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Viga = 336Kg/m
P.P. Muro = bxhxP. ManposteriaP.P. Muro = 0.25mx1.2mx1350Kg/m3P.P. Muro = 405Kg/m
Lo Multiplicamos por su Factor de Seguridad de Carga Muerta
P.P. Muro = 405Kg/mx1.4P.P. Muro = 567Kg/m
Entonces Tenemos Que:
C.M. =2260.13Kg/m+336Kg/m+567Kg/mC.M. =3163.13Kg/m
Calculamos la Carga Viva
Para la Carga Viva Tomamos La Influencia en la Losa Aligerada de la Carga Viva
Inf. Losa =340Kg/m2x2.425mInf. Losa =824.5Kg/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
Le Sacamos la Raiz a Ag:
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
Hallamos el Area Tributaria:
At = 2.875+2.125x2.625+2.225At = 24.25m2
a) Para el AntePenultimo Piso
Ata = 24.25m2x3Ata = 72.75m2
K = 0.0014
Ag = 72.75x0.0014Ag = 0.1019m2
Le Sacamos la Raiz a Ag:
L = √0.1019m2L = 0.32mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 24.25m2
Ata = 24.25x2Ata = 48.5m2
K = 0.001125
Ag = 48.5m2x0.001125Ag = 0.0546m2
Le Sacamos la Raiz a Ag:
L = √0.0546m2L = 0.23mL = 0.25 L=0.25mL = 0.25x0.25
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.25x0.25
Para la columna I - C
Hallamos el Area Tributaria:
At = 2.275+2.875x2.225+2.425At = 23.948m2
a) Para el AntePenultimo Piso
Ata = 23.948m2x3Ata = 71.844m2
K = 0.0014
Ag = 71.844x0.0014Ag = 0.1006m2
Le Sacamos la Raiz a Ag:
L = √0.1006m2L = 0.32mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 23.948m2
Ata = 23.948m2x2Ata = 47.896m2
K = 0.001125
Ag = 47.896m2x0.001125Ag = 0.0539m2
Le Sacamos la Raiz a Ag:
L = √0.0539m2L = 0.23mL = 0.25 L=0.25mL = 0.25x0.25
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.25x0.25
Para la columna I - D
Hallamos el Area Tributaria:
At = 2.875+2.125x2.225+2.425At = 23.25m2
a) Para el AntePenultimo Piso
Ata = 23.25m2x3Ata = 69.75m2
K = 0.0014
Ag = 69.75x0.0014Ag = 0.0977m2
Le Sacamos la Raiz a Ag:
L = √0.0977m2L = 0.31mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 23.25m2
Ata = 23.25m2x2Ata = 46.5m2
K = 0.001125
Ag = 46.5m2x0.001125Ag = 0.0523m2
Le Sacamos la Raiz a Ag:
L = √0.0523m2L = 0.23mL = 0.25 L=0.25mL = 0.25x0.25
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.25x0.25
Para la columna II - A
Hallamos el Area Tributaria:
At = 2.275+2.875x2.625At = 13.519m2
a) Para el AntePenultimo Piso
Ata = 13.519m2x3Ata = 40.557m2
K = 0.00248
Ag = 40.557x0.00248Ag = 0.1006m2
Le Sacamos la Raiz a Ag:
L = √0.1006m2L = 0.32mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 13.519m2
Ata = 13.519m2x2Ata = 27.038m2
K = 0.0014
Ag = 27.038m2x0.0014Ag = 0.0379m2
Le Sacamos la Raiz a Ag:
L = √0.0379m2L = 0.19mL = L = 0.19mx0.19m
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.19mx0.19m
Para la columna II - B
Hallamos el Area Tributaria:
At = 2.875+2.125x2.625At = 13.125m2
a) Para el AntePenultimo Piso
Ata = 13.125m2x3Ata = 39.375m2
K = 0.00248
Ag = 39.375x0.00248Ag = 0.0977m2
Le Sacamos la Raiz a Ag:
L = √0.0977m2L = 0.31mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 13.125m2
Ata = 13.125m2x2Ata = 26.25m2
K = 0.0014
Ag = 26.25m2x0.0014Ag = 0.0368m2
Le Sacamos la Raiz a Ag:
L = √0.0368m2L = 0.19mL = 0.25 L=0.25mL = 0.25x0.25
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.25x0.25
Para la columna II - C
Hallamos el Area Tributaria:
At = 2.625+2.225x2.275At = 11.034m2
a) Para el AntePenultimo Piso
Ata = 11.034m2x3Ata = 33.102m2
K = 0.00248
Ag = 33.102x0.00248Ag = 0.0821m2
Le Sacamos la Raiz a Ag:
L = √0.0821m2L = 0.29mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 11.034m2
Ata = 11.034m2x2Ata = 22.068m2
K = 0.0014
Ag = 22.068m2x0.0014Ag = 0.0309m2
Le Sacamos la Raiz a Ag:
L = √0.0309m2L = 0.18mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna II - D
Hallamos el Area Tributaria:
At = 2.625+2.225x2.125At = 10.306m2
a) Para el AntePenultimo Piso
Ata = 10.306m2x3Ata = 30.918m2
K = 0.00248
Ag = 30.918x0.00248Ag = 0.0767m2
Le Sacamos la Raiz a Ag:
L = √0.0767m2L = 0.28mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 10.306m2
Ata = 10.306m2x2Ata = 20.612m2
K = 0.0014
Ag = 20.612m2x0.0014Ag = 0.0289m2
Le Sacamos la Raiz a Ag:
L = √0.0289m2L = 0.17mL = 0.25 L=0.25mL = 0.25x0.25
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.25x0.25
Para la columna II - E
Hallamos el Area Tributaria:
At = 2.225+2.425x2.275At = 10.579m2
a) Para el AntePenultimo Piso
Ata = 10.579m2x3Ata = 31.737m2
K = 0.00248
Ag = 31.737x0.00248Ag = 0.0787m2
Le Sacamos la Raiz a Ag:
L = √0.0787m2L = 0.28mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 10.579m2
Ata = 10.579m2x2Ata = 21.158m2
K = 0.0014
Ag = 21.158m2x0.0014Ag = 0.0296m2
Le Sacamos la Raiz a Ag:
L = √0.0296m2L = 0.17mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna II - F
Hallamos el Area Tributaria:
At = 2.225+2.425x2.125At = 9.881m2
a) Para el AntePenultimo Piso
Ata = 9.881m2x3Ata = 29.643m2
K = 0.00248
Ag = 29.643x0.00248Ag = 0.0735m2
Le Sacamos la Raiz a Ag:
L = √0.0735m2L = 0.27mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 9.881m2
Ata = 9.881m2x2Ata = 19.762m2
K = 0.0014
Ag = 19.762m2x0.0014Ag = 0.0277m2
Le Sacamos la Raiz a Ag:
L = √0.0277m2L = 0.17mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna II - G
Hallamos el Area Tributaria:
At = 2.275+2.875x2.425At = 12.489m2
a) Para el AntePenultimo Piso
Ata = 12.489m2x3Ata = 37.467m2
K = 0.00248
Ag = 37.467x0.00248Ag = 0.0929m2
Le Sacamos la Raiz a Ag:
L = √0.0929m2L = 0.3mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 12.489m2
Ata = 12.489m2x2Ata = 24.978m2
K = 0.0014
Ag = 24.978m2x0.0014Ag = 0.035m2
Le Sacamos la Raiz a Ag:
L = √0.035m2L = 0.19mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna II - H
Hallamos el Area Tributaria:
At = 2.875+2.125x2.425At = 12.125m2
a) Para el AntePenultimo Piso
Ata = 12.125m2x3Ata = 36.375m2
K = 0.00248
Ag = 36.375x0.00248Ag = 0.0902m2
Le Sacamos la Raiz a Ag:
L = √0.0902m2L = 0.3mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 12.125m2
Ata = 12.125m2x2Ata = 24.25m2
K = 0.0014
Ag = 24.25m2x0.0014Ag = 0.034m2
Le Sacamos la Raiz a Ag:
L = √0.034m2L = 0.18mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna III - A
Hallamos el Area Tributaria:
At = 2.625x2.275At = 5.972m2
a) Para el AntePenultimo Piso
Ata = 5.972m2x3Ata = 17.916m2
K = 0.0037
Ag = 17.916x0.0037Ag = 0.0663m2
Le Sacamos la Raiz a Ag:
L = √0.0663m2L = 0.26mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 5.972m2
Ata = 5.972m2x2Ata = 11.944m2
K = 0.00195
Ag = 11.944m2x0.00195Ag = 0.0233m2
Le Sacamos la Raiz a Ag:
L = √0.0233m2L = 0.15mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna III - B
Hallamos el Area Tributaria:
At = 2.625x2.125At = 5.578m2
a) Para el AntePenultimo Piso
Ata = 5.578m2x3Ata = 16.734m2
K = 0.0037
Ag = 16.734x0.0037Ag = 0.0619m2
Le Sacamos la Raiz a Ag:
L = √0.0619m2L = 0.25mL = 0.3 L=0.3mL = 0.3x0.3
b) Para el Segundo Piso
At = 5.578m2
Ata = 5.578m2x2Ata = 11.156m2
K = 0.00195
Ag = 11.156m2x0.00195Ag = 0.0218m2
Le Sacamos la Raiz a Ag:
L = √0.0218m2L = 0.15mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna III - C
Hallamos el Area Tributaria:
At = 2.425x2.275At = 5.517m2
a) Para el AntePenultimo Piso
Ata = 5.517m2x3Ata = 16.551m2
K = 0.0037
Ag = 16.551x0.0037Ag = 0.0612m2
Le Sacamos la Raiz a Ag:
L = √0.0612m2L = 0.25mL = 0.2 L=0.2mL = 0.2x0.2
b) Para el Segundo Piso
At = 5.517m2
Ata = 5.517m2x2Ata = 11.034m2
K = 0.00195
Ag = 11.034m2x0.00195Ag = 0.0215m2
Le Sacamos la Raiz a Ag:
L = √0.0215m2L = 0.15mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
L = 0.2x0.2
Para la columna III - D
Hallamos el Area Tributaria:
At = 2.425x2.125At = 5.153m2
a) Para el AntePenultimo Piso
Ata = 5.153m2x3Ata = 15.459m2
K = 0.0037
Ag = 15.459x0.0037Ag = 0.0572m2
Le Sacamos la Raiz a Ag:
L = √0.0572m2L = 0.24mL = 0.2 L=0.2mL = 0.2x0.2
b) Para el Segundo Piso
At = 5.153m2
Ata = 5.153m2x2Ata = 10.306m2
K = 0.00195
Ag = 10.306m2x0.00195Ag = 0.0201m2
Le Sacamos la Raiz a Ag:
L = √0.0201m2L = 0.14mL = 0.2 L=0.2mL = 0.2x0.2
c) Para el Tercer Nivel Usaremos el mismo Predimencionamiento que del Segundo
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
Para el Primer Nivel
L= 0.3 x 0.3
Para el Segundo Nivel y Azotea
L= 0.19 * 0.19
Para Las Columnas del Tipo III
Para el Primer Nivel
L= 0.3 x 0.3
Para el Segundo Nivel y Azotea
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
Momentos finalesMik = Mik + Kik (2mi + mk + mr)
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
-3/2(K6-10/(K5-9+K6-10+K7-11+K8-12) Carga = 4858.88 Carga = 4858.88
-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 ) )
Sétimo Ciclo de giro
= 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
Momentos finalesMik = Mik + Kik (2mi + mk + mr)
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
-3/2(K3-7/(K1-5+K2-6+K3-7+K4-8) Carga = 3966.38 Carga = 4858.88
-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
-3/2(K6-10/(K5-9+K6-10+K7-11+K8-12) Carga = 4858.88 Carga = 4858.88
-8018.164 -8018.164 -3/2(K7-11/(K5-9+K6-10+K7-11+K8-12)
M3-2 M7-6 -3/2(K8-12/(K5-9+K6-10+K7-11+K8-12) Carga = 4858.88 Carga = 4858.88
+ql2/12 8018.164 +ql2/12 8018.164
-ql2/12 -ql2/12
-ql2/12 -ql2/12
M3-4 M7-8 -3/2(K9-13/(K9-13+K10-14+K11-15+K12-16) Carga = 4858.88 Carga = 3966.38
-9524.417 -7774.931 -3/2(K10-14/(K9-13+K10-14+K11-15+K12-16)
M4-3 M8-7 -3/2(K11-15/(K9-13+K10-14+K11-15+K12-16) Carga = 4858.88 Carga = 3966.38
+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
Tercer Ciclo de giro
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
Tercer Ciclo de giro
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 ) )
Sétimo Ciclo de giro
= 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
Momentos finalesMik = Mik + Kik (2mi + mk + mr)
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
CARACTERISTICAS DE LAS BARRAS
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
CARACTERISTICAS DE LAS BARRAS
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
Calculo del diseño de acero
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 %
Calculo del diseño de acero
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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