Plantilla C°A° I

FACULTAD DE INGENIERIAS

ESCUELA PROFESIONAL DE INGENIERÍA CIVIL

PREDIMENSIONAMIENTO DE ELMENTOS ESTRUCTURALES

Predimensionamiento de la losa aligerada

Luz libre del portico L = 5.00 m0.20 m

Espesor de losa h = 0.20 m

Espesor de losa def. h def. = 0.20 m 5.00 m

Predimensionamiento de la viga principal

0.60 m

Luz libre del portico principal L = 5.60 m

Luz libre del portico segundario B = 5.00 m

Peralte de viga h = 0.51 m

Peralte de viga definitivo h def. = 0.60 m

Base de la viga b = 0.25 m

Base de la viga definitivo b def. = 30.00 m 30.00 m

Predimensionamiento de la viga segundaria

Luz libre del portico principal L = 5.00 m

0.50 m






Predimensionamiento de la viga en voladizo en el de 2.00m.

Luz libre del portico principal Lv = 2.00 m

0.60 m






Predimensionamiento de la viga en voladizo en el de 2.50m.

Luz libre del portico principal Lv = 2.30 m

0.60 m






Por lo tanto si:

n = P

F'c * b * T

n > 1

Fuerza cortante 3

Deficiencia de anclaje del acero en las vigas

Deficiencia en los empalmes del acero en las columnas

Por aplastamiento n <

1

Segun ensayos experimentales en Japon se obtuvo que : 3

UNIVERSIDAD JOSE CARLOS MARIATEGUI

PARA LOSA ALIGERADA (Segun R.N.E. en la norma E - 060 Art. 10.4.1.1)

PARA LAS VIGAS (Segun R.N.E. en la norma E - 060 Art. 10.4.1.3 y el ingeniero Antonio Blanco Blasco recomiendan usar peraltes)

PARA COLUMNAS (Segun el ingeniero antonio blanco blasco recomienda (Ac=Pservicio/0.45*F'c) y (Ac=Pservicio/0.35*F'c) esto en el caso de tener placas o

muros cortantes

PARA COLUMNAS Pero el ICG lo determina con (bT=P/nF'c) y n estara en funcion de que tipo de columna sea tipo 1=0.3; tipo 2y3=0.25 y tipo 4=0.2

Segun la discusion de algunos resultados de investigaciones en Japon debido al sismo de TOKACHI 1968 donde colapsaron muchas columnas por:

Falla fragil por aplastamiento debido a cargas axiales execivas

h ≥ L/25

h ≥ L/16 ; L/10 a L/12 ; b=B/20

A10

elmering: en losas aligeradas continuas conformadas por viguetas de 10 cm de ancho bloques de ladrillos de 30 cm de ancho y losa superior de 5cm coon sobrecargas menores a 300 kg/cm2 y luces menores de 7.50 m cuando se cumple que: h>= L/25

D41

elmerin: h=1.4*(2*Lv/13) donde: Lv: es la distancia del voladizo hasta la cara de la columna

D49

elmerin: h=1.4*(2*Lv/13) donde: Lv: es la distancia del voladizo hasta la cara de la columna

Falla ductil

se recomineda usar: hn

>= 4 T

C - 2

datos P0 = 0.00 Tn

Carga muerta = 2.90 tn/m P1 = 7.00 Tn

Carga viva = 1.90 tn/m P2 = 12.00 Tn

F'c = 210 kg/cm2 Wp = 0.86 tn/m2

F'y = 4200 kg/cm2 Wd = 0.96 tn/m2

Predimensionamiento de columnas

L = 4.40 m Tipo de Col: 2

B = 5.00 m n = 0.25

--- 0.25 ---

At = 22.00 m2 Wu = 1.82 Tn/m2

f'c = 210 kg/cm2 # de Pisos = 3.0

bd = 2865.71 cm2 Pg = 120.360 Tn

b = d = 53.53 cm P = 150.450 Tn

--- 150.45 ---

seccion de columna def.

50.00 cm 60.00 cm

3000.00 cm2

Par este caso tenos un hn = 4.00 m

T = 0.60 m

6.6667 >= 4

FALLA DUCTIL

C - 1

datos P5/2 = 4.50 Tn



F'c = 210 kg/cm2 Wp = 0.98 tn/m2

F'y = 4200 kg/cm2 Wd = 0.96 tn/m2



B = 5.00 m n = 0.30

--- --- 0.30

At = 26.00 m2 Wu = 1.94 Tn/m2

f'c = 210 kg/cm2 # de Pisos = 3.0

bd = 2643.14 cm2 Pg = 151.380 Tn

b = d = 51.41 cm P = 166.518 Tn

--- --- 166.52


50.00 cm 55.00 cm

2750.00 cm2


T = 0.55 m

7.2727 >= 4

FALLA DUCTIL

C - 1




F'c = 210 kg/cm2 Wp = 0.84 tn/m2

F'y = 4200 kg/cm2 Wd = 0.96 tn/m2



B = 5.00 m n = 0.30

--- --- 0.30

si cumple la seccion


T

sismo

D81

elmering: tipo 1: Céntrica Tipo 2: Externa Tipo 3: Esquina

D108


D135


At = 28.00 m2 Wu = 1.80 Tn/m2

f'c = 210 kg/cm2 # de Pisos = 3.0

bd = 2638.95 cm2 Pg = 151.140 Tn

b = d = 51.37 cm P = 166.254 Tn

--- --- 166.25


50.00 cm 55.00 cm

2750.00 cm2


T = 0.55 m

2.7273 >= 4

FALLA FRAGIL

C - 1




F'c = 210 kg/cm2 Wp = 0.84 tn/m2

F'y = 4200 kg/cm2 Wd = 0.96 tn/m2



B = 5.00 m n = 0.30

--- --- 0.30

At = 28.00 m2 Wu = 1.80 Tn/m2

f'c = 210 kg/cm2 # de Pisos = 3.0

bd = 2638.95 cm2 Pg = 151.140 Tn

b = d = 51.37 cm P = 166.254 Tn

--- --- 166.25


50.00 cm 55.00 cm

2750.00 cm2


T = 0.55 m

7.2727 >= 4

FALLA DUCTIL

C - 2

datos P0 = 0.00 Tn



F'c = 210 kg/cm2 Wp = 0.64 tn/m2

F'y = 4200 kg/cm2 Wd = 0.96 tn/m2



B = 5.00 m n = 0.25

--- 0.25 ---

At = 26.50 m2 Wu = 1.60 Tn/m2

f'c = 210 kg/cm2 # de Pisos = 3.0

bd = 3031.43 cm2 Pg = 127.320 Tn

b = d = 55.06 cm P = 159.150 Tn

--- 159.15 ---


50.00 cm 60.00 cm

3000.00 cm2


T = 0.60 m

4.1667 >= 4

FALLA DUCTIL



no cumple la seccion

D162


D189


PREDIMENSIONAMIENTO DE LOSAS

ALIGERADOS

EN FUNCION DE LAS LUCES

Para losas unidireccionales

LUZ (m) h (cm)

€ 7.00 otro

€ 7.00 otro € 20.00

€ 7.00 € 25.00 otro

€ 7.00 € 30.00 € 25.00

Dimensionamiento valido para aligerados armados en una direccion

con sobrecargas maximas de 300 - 350 kg/m2

El dimensionamineto tambien se hace teniendo en cuenta la flecha maxima

(deflexion) según la norma E-060

Para losas bidireccionales

LUZ (m) h (cm)

€ 7.00 € 25.00 € 25.00

€ 7.00 otro € 30.00

Los aligerados armados en 2 direcciones se usan gralment cuando se tienen

paños mas o menos cuadrados y luces mayores a los 6m

Para luces mayores no es usual considerar ninguno de estos aligerados pues

no resultan livianos ni economicos en comparacion con las losas nervadas

LOSAS NERVADAS

suponiendo una distancia de ejes entre viguetas de 70cm se considera el sgte

dimensionamiento para viguetas en una direccion

PERALTE LUZ

Ancho variable de 10@15cm € 35.00 < 7.5



LOSAS MACIZAS

h Luces (m) comentario

€ 2.00 12 o 13

€ 2.00 € 15.00

A231

Romina dice: Cuando el concreto ocupa todo el espesor de la losa se la llama Losa Maciza, y cuando parte del volumen de la losa es ocupado por materiales más livianos o espacios vacíos se la llama Losa Alivianada o Losa Aligerada.

C240

Romina dice: "h" expresa la altura total de la losa alig. incluyendo los 5cm de la losa sup y el espesor del ladrillo de techo, estos ladrillos seran de 12,15,20 y 25 cm

B246

Romina dice: Si existen, tabiques de ladrillo paralelos a la direccion de la vigueta, se puede colocar una viga chata o doble vigueta para reforzar. Si el tabique esta perpendicular a la direccion del aligerado no sirve viga chata, es mejor aunmentar el espesor del techo. Blanco Blasco/Cap 3/ Pg36.

C254


A265

Romina dice: Las losas nervadas se usan en paños de luces grandes > a 6m. Las viguetas se hacen en forma trapezoidal o rectangular. La losa superior puede ser de 5 cm dependiendo de la separac. de la viguetas. Las distancias usuales entre nervaduras son de 50 a 75 cm con secciones de vigueta de ancho variable entre 10 y 15 cm y el peralte depende de la luz del paño q varia entre 35 y 60 cm. BLANCO BLASCO/ Cap3/ Pg37-38

A276

Romina dice: Las losas macizas pueden ser dimensionadas considerando espesores menores en 5cm a los indicados para losas aligeradas. Como se muestra a continuacion. Blanco Blasco/ Cap3/ Pg38

C278


E278

Romina dice: La resistencia y rigidez de una losa armada en dos direcciones es muy buena. Se requieren peraltes reducidos q pueden ser el cuarentavo de la luz igual al perimetro del paño (suma de 4 lados) dividido entre 180. Blanco Blasco/Cap3/ Pg39. En la norma peruana se dan ecuaciones para obtener el espesor requerido de losas mazisas q satisfagan condiciones de deflexiones. Blanco Blasco/Cap3/ Pg39.

C279

Romina dice: luces menores o iguales a 4 m

C280

Romina dice: luces menores o iguales a 5.5 m

€ 2.00 € 20.00

€ 2.00 € 25.00

Las losas pueden estar soportadas perimetral e interiormente por vigas

monolíticas de mayor peralte, por vigas de otros materiales independientes

o integradas a la losa; o soportadas por muros de concreto , muros de

mampostería o muros de otro material. Diseño de losas macizas/html

PREDIMENSIONAMIENTO DE VIGAS

DIMENSIONES USUALES DE LAS VIGAS

LUZ DIMENSIONES comentario

€ 6.00 otro

€ 6.00 25X60 / 30X60 / 40X60

€ 6.00 25X70 / 30X70 / 40X70 / 40X70

€ 6.00 30X75 / 40X75 / 30X80 / 40X80

€ 6.00 30X85 / 30X90 / 40X85 / 40X90

C281

Romina dice: luces menores o iguales a 6.5m

C282

Romina dice: luces menores o iguales a 7.5 m

A290

Romina dice: Las vigas se dimensionan considerando un peralte del orden de 1/10 a 1/12 de la luz libre; esta altura incluye el espesor de la losa de techo o piso. El ancho puede variar entre 0.3 a 0.5 de la altura. La NP de CºAº indica q las vigas deben tener una ancho minimo de 25 cm si estas forman parte de elemetos sismoresistentes o porticos d cº aº; si no forman porticos, pueden ser de 15-20cm. Conforme se tengan luces mas grandes puede disminuirse el peralte obtenido con la recomendacion del 1/10 o 1/12 de la luz y 1/14 de la uz disponiendo de anchos del orden de 0.5 de la altura. Blanco Blasco/Cap3/ Pg40

E295

Romina dice: En la NP en los requerimientos de control de deflexiones indica perales menores pero solo consirera deflexiones a diferencia del libro q considera otros factores como son rigidez lateral y diseño sismo resitente Blanco Blasco/Cap3/ Pg40.

C296

LUZ MENOR IGUAL 5.5

C297

LUZ MENOR IGUAL 6.5

C298

LUZ MENOR IGUAL 7.5

C299

LUZ MENOR IGUAL 8.5

C300

LUZ MENOR IGUAL 9.5

P1 P2 P3 P4 P5 P6

7.00 Tn 12.00 Tn 12.00 Tn 9.00 Tn 9.00 Tn 9.00 Tn

P7 P8 P9

10.00 Tn 10.00 Tn 7.00 Tn

C-1

Carg V. 1.90 tn/m

Carga M. 2.90 tn/m

4.00 m C-2 C-1 C-1 C-2

2.50 m

2.00 m 1.60 m 1.60 m 1.60 m 1.40 m 1.40 m 1.40 m 1.40 m 1.80 m 1.80 m 2.00 m 2.50 m

2.00 m 4.80 m 5.60 m 5.60 m 2.50 m

L

B

P1 P2 P3 P4 P5 P6

7.00 Tn 12.00 Tn 12.00 Tn 9.00 Tn 9.00 Tn 9.00 Tn

P7 P8 P9

10.00 Tn 10.00 Tn 7.00 Tn

C-1

Carga viva 1.90 tn/m

Carg muerta 2.90 tn/m

4.00 m C-2 C-1 C-1 C-2

2.50 m

2.00 m 1.60 m 1.60 m 1.60 m 1.40 m 1.40 m 1.40 m 1.40 m 1.80 m 1.80 m 2.00 m 2.50 m

2.00 m 4.80 m 5.60 m 5.60 m 2.50 m

T

b

T

sismo

hnh de eje a eje

50.00 cm

55.00 cm

50.00 cm 50.00 cm 50.00 cm 50.00 cm

60.00 cm 55.00 cm 55.00 cm 60.00 cm

PREDIMENSIONAMIENTO DE COLUMNAS

1º CASO

Para edificios q tengan muros de corte en las dos direcciones, tal q la rigidez lateral

y la resitencia van a estar principalmente controladas por los muros, las columnas

se pueden dimensionar suponiendo un area igual a:

P (servicio) € 50.00 AREA DE COLUMNA € 0.53

f'c € 210.00

2º CASO

Para el mismo tipo de edificio , el dimensionamiento d las columnas con menos

carga axial (caso de exteriores o esquineras, se hara un area igual a:

P (servicio) € 50.00 AREA DE COLUMNA € 0.68

f'c € 210.00

3º CASO

Para edificios aporticados integramente (se recomienda no exeder de 3 o 4 pisos

las columnas deberan dimensionarse mediante alguna estimacion del momento de sismo

del mº de sismo, se pueden requerir columnas con areas entre 1000 y 2000 cm2, salvo q tengan

vigas conluces mayores a 7m

Para este tipo de edificios se dispondran columnas de 35x35, 40x40, 25x50, 30x60, 30x40 30x50,

o circulares de 40 o 50 cm de diametro. Estas altenativas se escogeran según las dimensiones

cuadradas o rectangulares de los paños Blanco Blasco /Cap3/Pg41-42

4º CASO

Para edificios con luces mayores a 7 u 8 m debe tenerse especial cuidado con las columnas

exteriores pudiendo dimensionarse el peralte de la columna en un 70 u 80% del peralte de la

viga principal

AREAcolumna=P (servicio)0 .45 f ' c

AREAcolumna=P (servicio)0.35 f ' c

K237

Romina dice: Las columnas como son sometidas a carga axial y mº flector tienen q ser dimensionadas considerando los dos efectos tratando de evaluar cual de los dos gobierna en forma mas influyente el dimensionamiento. Para edificaciones con un buen nº de pisos dnd la carga axial es mas importante q el mº flector, se puede dimensionar buscando una seccion total d modo q la carga axial en servicio produzca un esfuerzo de compresion de 0.45f'c Para edificaciones con pocos pisos y de luces importantes los mº pueden producir exentricidades importantes y hay q buscar una seccion con mas peralte para la direccion dnd el mº es critico. Para edificios aporticados los mº de sismo son mayores a los de cargas de gravedad exepto el caso de vigas con luces mayores a 7 u 8 m Blanco Blasco/Cap3/ Pg41

PREDIMENSIONAMIENTO DE PLACAS O MUROS DE CONCRETO

Las placas pueden hacerse minimo de 10 cm de espesor

Pero gnralmente se consideran de 15cm de espesor en casos de edificios de pocos pisos.

Tambien de 20, 25, 30 cm conforme aunmentemos el nº de pisos.

En el Peru se han proyectado una serie de edificaciones de hasta 20 pisos considerando placas d

espesor de 25 cm las cuales tb tenian longitudes apreciables; Si existieran pocas placas en una

direccion probalemente se necesitaran espesores mayores como 40, 50 o 60 cm

Para realizar la evaluacion final se debera hacer un analisis sismico .

L282

Romina dice: Es dificil poder fijar un dimensionamiento para las placas xq como su principal funcion es Absorver las Fuerzas de Sismo (…) se puede prescindir de ellas. Pero no se pueden consideran edificaciones solamente con porticos pues hace q existan deformaciones laterales muy importamntes. Lo ideal es combinar porticos con placas para obtener un balance adecuado en la distribucuion de esfuerzos y controlar la flexibilidad de la edificacion. Blanco Blasco/Cap3/ Pg43

PREDIMENSIONAMIENTO DE VIGAS

Ln 6.00 m

B 5.50 m

Coondicion

h = Ln h = 54.55 cm

€ 11.00 h = 60.00 cm

Condicion Condicion

b = B b = 27.50 cm b = 18.00 cm

€ 20.00 b = 30.00 cm h b = 30.00 cm

PREDIMENSIONAMIENTO DE COLUMNAS

Tipo de columna € 1.00

n = € 0.45

€ 0.45

---

P (servicio) 25000 kg

f'c = 210 kg/cm2

b*d = P b * d = 264.55 cm2

n*f'c b = d = 16.27 cm

b = 20.00 cm

0.30 ≤ b ≤ 0.5

L

B

AN18

USER: calculado con el minimo que es 0.30

AN19

USER: calculado con el maximo que es 0.50

AL37

USER: Tipo 1 Col. centrica Tipo 2 Col. esquinera o externa

7.00 Tn 12.00 Tn 12.00 Tn 9.00 Tn 9.00 Tn 9.00 Tn

10.00 Tn 10.00 Tn 7.00 Tn

4.00 m

2.50 m

2.00 m 1.60 m 1.60 m 1.60 m 1.40 m 1.40 m 1.40 m 1.40 m 1.80 m 1.80 m 2.00 m 2.50 m

2.00 m 4.80 m 5.60 m 5.60 m 2.50 m

datos

Carga muerta = 2.90 tn/m

Carga viva = 1.90 tn/m

F'c = 210 kg/cm2

F'y = 4200 kg/cm2

DISEÑO DE ACERO PARA VIGAS DOBLEMENTE REFORZADAS

DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa 02 capas

Mu = 3654000 kg.cm 3654000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02

Ku = Mu Ku = 49.53 49.53

b*d^2

As = P*b*d 26.24 cm2 24.79 cm2

Ku*b*d^2 4332893.15 kg.cm 3864833.70 kg.cm

Mr = Mr = -678893.15 kg.cm -210833.70 kg.cm

A's = Mu A's = -3.67 cm2 -1.21 cm2

Ø*F'y*(d-d')

As = Total As = ------ ------

Total A's = -3.67 cm2 -1.21 cm2


a = 0.59 0.59

b = -1.00 -1.00

c = 0.22 0.25

w 1 = 0.261 0.301

w 2 = 1.434 1.394

P = 0.0131 0.0151

chequeo de P = SIMPLEM. REFORZADA SIMPLEM. REFORZADA

As = 21.16 cm2 23.05 cm2

ANALISIS O VERIFICACION DE UNA SECCION DOBLEMENTE REFORZADA

As = ------ ------

A's = -3.67 cm2 -1.21 cm2

P = #VALUE! #VALUE!

P' = -0.0023 -0.0008

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

D16

USER: OJO SI CAMBIA MAS DE 280 Kg/cm2 HAY QUE CAMBIAR EL O/

D20

USER: Para la cuantia maxima el Ku sera de 49.5301

E20


P - P' = #VALUE! #VALUE!

VERF. = 0.01115 0.01181

#VALUE! #VALUE!


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 2931000 kg.cm 2931000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2

Pmax = 0.0162 0.0162

Ku = Mu Ku = 49.53 49.53

b*d^2

As = P*b*d 26.24 cm2 24.79 cm2

Ku*b*d^2 4332893.15 kg.cm 3864833.70 kg.cm

Mr = Mr = -1401893.15 kg.cm -933833.70 kg.cm

A's = Mu A's = -7.57 cm2 -5.37 cm2

Ø*F'y*(d-d')

As = Total As = ------ ------

Total A's = -7.57 cm2 -5.37 cm2


a = 0.59 0.59

b = -1.00 -1.00

c = 0.18 0.20

w 1 = 0.201 0.230

w 2 = 1.494 1.465

P = 0.0101 0.0115

chequeo de P = SIMPLEM. REFORZADA SIMPLEM. REFORZADA

As = 16.29 cm2 17.59 cm2


As = ------ ------

A's = -7.57 cm2 -5.37 cm2

P = #VALUE! #VALUE!

P' = -0.0047 -0.0035

P - P' = #VALUE! #VALUE!

VERF. = 0.01115 0.01181

#VALUE! #VALUE!

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

D118


D122


E122


DISEÑO DE ACERO PARA VIGAS DOBLEMENTE REFORZADAS DISEÑO DE ACERO PARA VIGAS DOBLEMENTE REFORZADAS

DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

03 capas DATOS 01 capa

3654000 kg.cm Mu = 4842000 kg.cm

210 kg/cm2 f'c = 210 kg/cm2

4200 kg/cm2 f'y = 4200 kg/cm2

0.02 Pmax = 0.02

49.53 Ku =

Mu Ku = 49.53

b*d^2

23.81 cm2 As = P*b*d 26.24 cm2

3567653.10 kg.cm Ku*b*d^2 4332893.15 kg.cm

86346.90 kg.cm Mr = Mr = 509106.85 kg.cm

0.52 cm2 A's =

Mu A's = 2.75 cm2

Ø*F'y*(d-d')

24.33 cm2 As = Total As = 28.99 cm2

0.52 cm2 Total A's = 2.75 cm2


0.59 a = 0.59

-1.00 b = -1.00

0.27 c = 0.29

0.334 w 1 = 0.376

1.361 w 2 = 1.318

0.0167 P = 0.0188

DOB.REFORZADA chequeo de P = DOB.REFORZADA

----- As = -----

ANALISIS O VERIFICACION DE UNA SECCION DOBLEMENTE REFORZADA ANALISIS O VERIFICACION DE UNA SECCION DOBLEMENTE REFORZADA

24.33 cm2 As = 28.99 cm2

0.52 cm2 A's = 2.75 cm2

0.0166 P = 0.0179

0.0004 P' = 0.0017

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

F20


K20


0.0162 P - P' = 0.0162

0.01229 VERF. =

0.01115

SI FLUYE SI FLUYE


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


2931000 kg.cm Mu = 3783000 kg.cm

210 kg/cm2 f'c = 210 kg/cm2

4200 kg/cm2 f'y = 4200 kg/cm2

0.0162 Pmax = 0.0162

49.53 Ku =

Mu Ku = 49.53

b*d^2

23.81 cm2 As = P*b*d 26.24 cm2

3567653.10 kg.cm Ku*b*d^2 4332893.15 kg.cm

-636653.10 kg.cm Mr = Mr = -549893.15 kg.cm

-3.83 cm2 A's =

Mu A's = -2.97 cm2

Ø*F'y*(d-d')

------ As = Total As = ------

-3.83 cm2 Total A's = -2.97 cm2


0.59 a = 0.59

-1.00 b = -1.00

0.22 c = 0.23

0.253 w 1 = 0.273

1.442 w 2 = 1.422

0.0127 P = 0.0136

SIMPLEM. REFORZADA chequeo de P = SIMPLEM. REFORZADA

18.60 cm2 As = 22.09 cm2


------ As = ------

-3.83 cm2 A's = -2.97 cm2

#VALUE! P = #VALUE!

-0.0026 P' = -0.0018

#VALUE! P - P' = #VALUE!

0.01229 VERF. =

0.01115

#VALUE! #VALUE!

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

F122


K122



DATOS

β =

Ø =

viga

r =

d' =

d =

02 capas 03 capas DATOS

4842000 kg.cm 4842000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

977166.30 kg.cm 1274346.90 kg.cm Mr =

5.62 cm2 7.66 cm2 A's =

Mu

Ø*F'y*(d-d')

30.41 cm2 31.48 cm2 As =

5.62 cm2 7.66 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.33 0.36 c =

0.445 0.508 w 1 =

1.250 1.187 w 2 =

0.0223 0.0254 P =

DOB.REFORZADA DOB.REFORZADA chequeo de P =

----- ----- As =


30.41 cm2 31.48 cm2

5.62 cm2 7.66 cm2

0.0199 0.0214

0.0037 0.0052

Mu1 =

Mu-Mu1

As1 + A's

L20


M20


0.0162 0.0162

0.01181 0.01229

SI FLUYE SI FLUYE


DATOS

β =

Ø =

viga

r =

d' =

d =


3783000 kg.cm 3783000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.0162 0.0162 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

-81833.70 kg.cm 215346.90 kg.cm Mr =

-0.47 cm2 1.29 cm2 A's =

Mu

Ø*F'y*(d-d')

------ 25.11 cm2 As =

-0.47 cm2 1.29 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.26 0.28 c =

0.315 0.350 w 1 =

1.380 1.345 w 2 =

0.0158 0.0175 P =

SIMPLEM. REFORZADA DOB.REFORZADA chequeo de P =

24.10 cm2 ----- As =


------ 25.11 cm2

-0.47 cm2 1.29 cm2

#VALUE! 0.0171

-0.0003 0.0009

#VALUE! 0.0162

0.01181 0.01229

#VALUE! SI FLUYE

Mu1 =

Mu-Mu1

As1 + A's

L122


M122


4 Ø 1"

2 Ø 3/4"


DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa 02 capas 03 capas

Mu = 2057000 kg.cm 2057000 kg.cm 2057000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -2275893.15 kg.cm -1807833.70 kg.cm -1510653.10 kg.cm

A's = -12.29 cm2 -10.40 cm2 -9.08 cm2

Total As = ------ ------ ------

Total A's = -12.29 cm2 -10.40 cm2 -9.08 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.12 0.14 0.15

w 1 = 0.135 0.153 0.168

w 2 = 1.560 1.542 1.527

P = 0.0068 0.0077 0.0084

chequeo de P = SIMPLEM. REFORZADA SIMPLEM. REFORZADA SIMPLEM. REFORZADA

As = 10.95 cm2 11.73 cm2 12.33 cm2


As = ------ ------ ------

A's = -12.29 cm2 -10.40 cm2 -9.08 cm2

P = #VALUE! #VALUE! #VALUE!

P' = -0.0076 -0.0068 -0.0062

As1 =

Mu1 =

R20


S20


T20


P - P' = #VALUE! #VALUE! #VALUE!

VERF. = 0.01115 0.01181 0.01229

#VALUE! #VALUE! #VALUE!


DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 2057000 kg.cm 2057000 kg.cm 2057000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -2275893.15 kg.cm -1807833.70 kg.cm -1510653.10 kg.cm

A's = -12.29 cm2 -10.40 cm2 -9.08 cm2

Total As = ------ ------ ------

Total A's = -12.29 cm2 -10.40 cm2 -9.08 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.12 0.14 0.15

w 1 = 0.135 0.153 0.168

w 2 = 1.560 1.542 1.527

P = 0.0068 0.0077 0.0084


As = 10.95 cm2 11.73 cm2 12.33 cm2


As = ------ ------ ------

A's = -12.29 cm2 -10.40 cm2 -9.08 cm2


P' = -0.0076 -0.0068 -0.0062


VERF. = 0.01115 0.01181 0.01229


As1 =

Mu1 =

R122


S122


T122


2 Ø 1"

1 Ø 3/4"


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 4591000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = 258106.85 kg.cm

A's = Mu A's = 1.39 cm2

Ø*F'y*(d-d')

As = Total As = 27.64 cm2

Total A's = 1.39 cm2

DATOS 01 capa

a = 0.59

b = -1.00

c = 0.28

w 1 = 0.350

w 2 = 1.345

P = 0.0175

chequeo de P = DOB.REFORZADA

As = -----


As = 27.64 cm2

A's = 1.39 cm2

P = 0.0171

P' = 0.0009

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

Y16


Y20


P - P' = 0.0162

VERF. = 0.01115

SI FLUYE


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 3583000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = -749893.15 kg.cm

A's = Mu A's = -4.05 cm2

Ø*F'y*(d-d')

As = Total As = ------

Total A's = -4.05 cm2

DATOS 01 capa

a = 0.59

b = -1.00

c = 0.22

w 1 = 0.255

w 2 = 1.440

P = 0.0128

chequeo de P = SIMPLEM. REFORZADA

As = 20.66 cm2


As = ------

A's = -4.05 cm2

P = #VALUE!

P' = -0.0025

P - P' = #VALUE!

VERF. = 0.01115

#VALUE!

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

Y118


Y122



DATOS

β =

Ø =

viga

r =

d' =

d =


4591000 kg.cm 4591000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

726166.30 kg.cm 1023346.90 kg.cm Mr =

4.18 cm2 6.15 cm2 A's =

Mu

Ø*F'y*(d-d')

28.96 cm2 29.97 cm2 As =

4.18 cm2 6.15 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.31 0.34 c =

0.411 0.465 w 1 =

1.284 1.230 w 2 =

0.0205 0.0232 P =


----- ----- As =


28.96 cm2 29.97 cm2

4.18 cm2 6.15 cm2

0.0189 0.0204

0.0027 0.0042

Mu1 =

Mu-Mu1

As1 + A's

Z20


AA20


0.0162 0.0162

0.01181 0.01229

SI FLUYE SI FLUYE


DATOS

β =

Ø =

viga

r =

d' =

d =


3583000 kg.cm 3583000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

-281833.70 kg.cm 15346.90 kg.cm Mr =

-1.62 cm2 0.09 cm2 A's =

Mu

Ø*F'y*(d-d')

------ 23.91 cm2 As =

-1.62 cm2 0.09 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.24 0.26 c =

0.294 0.326 w 1 =

1.401 1.369 w 2 =

0.0147 0.0163 P =

SIMPLEM. REFORZADA DOB.REFORZADA chequeo de P =

22.49 cm2 ----- As =


------ 23.91 cm2

-1.62 cm2 0.09 cm2

#VALUE! 0.0163

-0.0011 0.0001

#VALUE! 0.0162

0.01181 0.01229

#VALUE! SI FLUYE

Mu1 =

Mu-Mu1

As1 + A's

Z122


AA122



DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 5104000 kg.cm 5104000 kg.cm 5104000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = 771106.85 kg.cm 1239166.30 kg.cm 1536346.90 kg.cm

A's = 4.16 cm2 7.13 cm2 9.24 cm2

Total As = 30.41 cm2 31.91 cm2 33.05 cm2

Total A's = 4.16 cm2 7.13 cm2 9.24 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.31 0.35 0.37

w 1 = 0.406 0.485 0.560

w 2 = 1.289 1.210 1.135

P = 0.0203 0.0242 0.0280

chequeo de P = DOB.REFORZADA DOB.REFORZADA DOB.REFORZADA

As = ----- ----- -----


As = 30.41 cm2 31.91 cm2 33.05 cm2

A's = 4.16 cm2 7.13 cm2 9.24 cm2

P = 0.0188 0.0209 0.0225

P' = 0.0026 0.0047 0.0063

As1 =

Mu1 =

AF20


AG20


AH20


P - P' = 0.0162 0.0162 0.0162

VERF. = 0.01115 0.01181 0.01229

SI FLUYE SI FLUYE SI FLUYE


DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 3990000 kg.cm 3990000 kg.cm 3990000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -342893.15 kg.cm 125166.30 kg.cm 422346.90 kg.cm

A's = -1.85 cm2 0.72 cm2 2.54 cm2

Total As = ------ 25.51 cm2 26.35 cm2

Total A's = -1.85 cm2 0.72 cm2 2.54 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.24 0.27 0.29

w 1 = 0.291 0.338 0.377

w 2 = 1.403 1.357 1.318

P = 0.0146 0.0169 0.0188

chequeo de P = SIMPLEM. REFORZADA DOB.REFORZADA DOB.REFORZADA

As = 23.61 cm2 ----- -----


As = ------ 25.51 cm2 26.35 cm2

A's = -1.85 cm2 0.72 cm2 2.54 cm2

P = #VALUE! 0.0167 0.0179

P' = -0.0011 0.0005 0.0017

P - P' = #VALUE! 0.0162 0.0162

VERF. = 0.01115 0.01181 0.01229

#VALUE! SI FLUYE SI FLUYE

As1 =

Mu1 =

AF122


AG122


AH122


4 Ø 1"

2 Ø 3/4"

2 Ø 1"


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 2991000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = -1341893.15 kg.cm

A's = Mu A's = -7.24 cm2

Ø*F'y*(d-d')



DATOS 01 capa

a = 0.59

b = -1.00

c = 0.18

w 1 = 0.206

w 2 = 1.489

P = 0.0103


As = 16.68 cm2


As = ------

A's = -7.24 cm2

P = #VALUE!

P' = -0.0045

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

AM16


AM20


P - P' = #VALUE!

VERF. = 0.01115

#VALUE!


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 2991000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = -1341893.15 kg.cm

A's = Mu A's = -7.24 cm2

Ø*F'y*(d-d')



DATOS 01 capa

a = 0.59

b = -1.00

c = 0.18

w 1 = 0.206

w 2 = 1.489

P = 0.0103


As = 16.68 cm2


As = ------

A's = -7.24 cm2

P = #VALUE!

P' = -0.0045

P - P' = #VALUE!

VERF. = 0.01115

#VALUE!

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

AM118


AM122



DATOS

β =

Ø =

viga

r =

d' =

d =


2991000 kg.cm 2991000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

-873833.70 kg.cm -576653.10 kg.cm Mr =

-5.03 cm2 -3.47 cm2 A's =

Mu

Ø*F'y*(d-d')

------ ------ As =

-5.03 cm2 -3.47 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.20 0.22 c =

0.236 0.259 w 1 =

1.459 1.436 w 2 =

0.0118 0.0130 P =

SIMPLEM. REFORZADA SIMPLEM. REFORZADA chequeo de P =

18.02 cm2 19.07 cm2 As =


------ ------

-5.03 cm2 -3.47 cm2

#VALUE! #VALUE!

-0.0033 -0.0024

Mu1 =

Mu-Mu1

As1 + A's

AN20


AO20


#VALUE! #VALUE!

0.01181 0.01229

#VALUE! #VALUE!


DATOS

β =

Ø =

viga

r =

d' =

d =


2991000 kg.cm 2991000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

-873833.70 kg.cm -576653.10 kg.cm Mr =

-5.03 cm2 -3.47 cm2 A's =

Mu

Ø*F'y*(d-d')

------ ------ As =

-5.03 cm2 -3.47 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.20 0.22 c =

0.236 0.259 w 1 =

1.459 1.436 w 2 =

0.0118 0.0130 P =


18.02 cm2 19.07 cm2 As =


------ ------

-5.03 cm2 -3.47 cm2

#VALUE! #VALUE!

-0.0033 -0.0024

#VALUE! #VALUE!

0.01181 0.01229

#VALUE! #VALUE!

Mu1 =

Mu-Mu1

As1 + A's

AN122


AO122


2 Ø 3/4"

3 Ø 1"


DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 4280000 kg.cm 4280000 kg.cm 4280000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -52893.15 kg.cm 415166.30 kg.cm 712346.90 kg.cm

A's = -0.29 cm2 2.39 cm2 4.28 cm2

Total As = ------ 27.17 cm2 28.10 cm2

Total A's = -0.29 cm2 2.39 cm2 4.28 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.26 0.29 0.31

w 1 = 0.319 0.372 0.417

w 2 = 1.376 1.323 1.278

P = 0.0159 0.0186 0.0208


As = 25.83 cm2 ----- -----


As = ------ 27.17 cm2 28.10 cm2

A's = -0.29 cm2 2.39 cm2 4.28 cm2

P = #VALUE! 0.0178 0.0191

P' = -0.0002 0.0016 0.0029

As1 =

Mu1 =

AT20


AU20


AV20


P - P' = #VALUE! 0.0162 0.0162

VERF. = 0.01115 0.01181 0.01229



DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 4 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 3304000 kg.cm 3304000 kg.cm 3304000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -1028893.15 kg.cm -560833.70 kg.cm -263653.10 kg.cm

A's = -5.55 cm2 -3.23 cm2 -1.59 cm2

Total As = ------ ------ ------

Total A's = -5.55 cm2 -3.23 cm2 -1.59 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.20 0.22 0.24

w 1 = 0.231 0.266 0.294

w 2 = 1.463 1.429 1.401

P = 0.0116 0.0133 0.0147


As = 18.75 cm2 20.32 cm2 21.57 cm2


As = ------ ------ ------

A's = -5.55 cm2 -3.23 cm2 -1.59 cm2


P' = -0.0034 -0.0021 -0.0011


VERF. = 0.01115 0.01181 0.01229


As1 =

Mu1 =

AT122


AU122


AV122


3 Ø 1"

2 Ø 3/4"

2 Ø 1"


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 4408000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = 75106.85 kg.cm

A's = Mu A's = 0.41 cm2

Ø*F'y*(d-d')



DATOS 01 capa

a = 0.59

b = -1.00

c = 0.27

w 1 = 0.331

w 2 = 1.364

P = 0.0166


As = -----


As = 26.65 cm2

A's = 0.41 cm2

P = 0.0165

P' = 0.0003

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

BA16


BA20


P - P' = 0.0162

VERF. = 0.01115

SI FLUYE


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 3516000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = -816893.15 kg.cm

A's = Mu A's = -4.41 cm2

Ø*F'y*(d-d')



DATOS 01 capa

a = 0.59

b = -1.00

c = 0.21

w 1 = 0.249

w 2 = 1.446

P = 0.0125


As = 20.20 cm2


As = ------

A's = -4.41 cm2

P = #VALUE!

P' = -0.0027

P - P' = #VALUE!

VERF. = 0.01115

#VALUE!

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

BA118


BA122



DATOS

β =

Ø =

viga

r =

d' =

d =


4408000 kg.cm 4408000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

543166.30 kg.cm 840346.90 kg.cm Mr =

3.12 cm2 5.05 cm2 A's =

Mu

Ø*F'y*(d-d')

27.91 cm2 28.87 cm2 As =

3.12 cm2 5.05 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.30 0.32 c =

0.387 0.436 w 1 =

1.307 1.259 w 2 =

0.0194 0.0218 P =


----- ----- As =


27.91 cm2 28.87 cm2

3.12 cm2 5.05 cm2

0.0182 0.0196

0.0020 0.0034

Mu1 =

Mu-Mu1

As1 + A's

BB20


BC20


0.0162 0.0162

0.01181 0.01229

SI FLUYE SI FLUYE


DATOS

β =

Ø =

viga

r =

d' =

d =


3516000 kg.cm 3516000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

-348833.70 kg.cm -51653.10 kg.cm Mr =

-2.01 cm2 -0.31 cm2 A's =

Mu

Ø*F'y*(d-d')

------ ------ As =

-2.01 cm2 -0.31 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.24 0.26 c =

0.287 0.318 w 1 =

1.408 1.377 w 2 =

0.0144 0.0159 P =


21.96 cm2 23.37 cm2 As =


------ ------

-2.01 cm2 -0.31 cm2

#VALUE! #VALUE!

-0.0013 -0.0002

#VALUE! #VALUE!

0.01181 0.01229

#VALUE! #VALUE!

Mu1 =

Mu-Mu1

As1 + A's

BB122


BC122


4 Ø 1"

2 Ø 3/4"


DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 2283000 kg.cm 2283000 kg.cm 2283000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -2049893.15 kg.cm -1581833.70 kg.cm -1284653.10 kg.cm

A's = -11.07 cm2 -9.10 cm2 -7.72 cm2

Total As = ------ ------ ------

Total A's = -11.07 cm2 -9.10 cm2 -7.72 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.14 0.15 0.17

w 1 = 0.152 0.172 0.189

w 2 = 1.543 1.523 1.506

P = 0.0076 0.0086 0.0094


As = 12.28 cm2 13.18 cm2 13.87 cm2


As = ------ ------ ------

A's = -11.07 cm2 -9.10 cm2 -7.72 cm2


P' = -0.0068 -0.0059 -0.0053

As1 =

Mu1 =

BH16


BH20


BI20


BJ20



VERF. = 0.01115 0.01181 0.01229



DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 2283000 kg.cm 2283000 kg.cm 2283000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -2049893.15 kg.cm -1581833.70 kg.cm -1284653.10 kg.cm

A's = -11.07 cm2 -9.10 cm2 -7.72 cm2

Total As = ------ ------ ------

Total A's = -11.07 cm2 -9.10 cm2 -7.72 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.14 0.15 0.17

w 1 = 0.152 0.172 0.189

w 2 = 1.543 1.523 1.506

P = 0.0076 0.0086 0.0094


As = 12.28 cm2 13.18 cm2 13.87 cm2


As = ------ ------ ------

A's = -11.07 cm2 -9.10 cm2 -7.72 cm2


P' = -0.0068 -0.0059 -0.0053


VERF. = 0.01115 0.01181 0.01229


As1 =

Mu1 =

BH118


BH122


BI122


BJ122


3 Ø 1"


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 5339000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = 1006106.85 kg.cm

A's = Mu A's = 5.43 cm2

Ø*F'y*(d-d')



DATOS 01 capa

a = 0.59

b = -1.00

c = 0.32

w 1 = 0.434

w 2 = 1.261

P = 0.0217


As = -----


As = 31.68 cm2

A's = 5.43 cm2

P = 0.0196

P' = 0.0034

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

BO16


BO20


P - P' = 0.0162

VERF. = 0.01115

SI FLUYE


DATOS

β = 0.85

Ø = 0.90

viga b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

d =

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm

DATOS 01 capa

Mu = 4173000 kg.cm

f'c = 210 kg/cm2

f'y = 4200 kg/cm2

Pmax = 0.02

Ku = Mu Ku = 49.53

b*d^2

As = P*b*d 26.24 cm2

Ku*b*d^2 4332893.15 kg.cm

Mr = Mr = -159893.15 kg.cm

A's = Mu A's = -0.86 cm2

Ø*F'y*(d-d')



DATOS 01 capa

a = 0.59

b = -1.00

c = 0.25

w 1 = 0.309

w 2 = 1.386

P = 0.0154


As = 24.99 cm2


As = ------

A's = -0.86 cm2

P = #VALUE!

P' = -0.0005

P - P' = #VALUE!

VERF. = 0.01115

#VALUE!

As1 =

Mu1 = Mu1 =

Mu-Mu1

As1 + A's

BO118


BO122



DATOS

β =

Ø =

viga

r =

d' =

d =


5339000 kg.cm 5339000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

1474166.30 kg.cm 1771346.90 kg.cm Mr =

8.48 cm2 10.65 cm2 A's =

Mu

Ø*F'y*(d-d')

33.26 cm2 34.46 cm2 As =

8.48 cm2 10.65 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.36 0.39 c =

0.524 0.616 w 1 =

1.171 1.079 w 2 =

0.0262 0.0308 P =


----- ----- As =


33.26 cm2 34.46 cm2

8.48 cm2 10.65 cm2

0.0217 0.0234

0.0055 0.0072

Mu1 =

Mu-Mu1

As1 + A's

BP20


BQ20


0.0162 0.0162

0.01181 0.01229

SI FLUYE SI FLUYE


DATOS

β =

Ø =

viga

r =

d' =

d =


4173000 kg.cm 4173000 kg.cm Mu =

210 kg/cm2 210 kg/cm2 f'c =

4200 kg/cm2 4200 kg/cm2 f'y =

0.02 0.02 Pmax =

49.53 49.53 Ku =

Mu

b*d^2

24.79 cm2 23.81 cm2 As = P*b*d

3864833.70 kg.cm 3567653.10 kg.cm Ku*b*d^2

308166.30 kg.cm 605346.90 kg.cm Mr =

1.77 cm2 3.64 cm2 A's =

Mu

Ø*F'y*(d-d')

26.56 cm2 27.45 cm2 As =

1.77 cm2 3.64 cm2


0.59 0.59 a =

-1.00 -1.00 b =

0.28 0.31 c =

0.359 0.402 w 1 =

1.336 1.293 w 2 =

0.0179 0.0201 P =


----- ----- As =


26.56 cm2 27.45 cm2

1.77 cm2 3.64 cm2

0.0174 0.0187

0.0012 0.0025

0.0162 0.0162

0.01181 0.01229

SI FLUYE SI FLUYE

Mu1 =

Mu-Mu1

As1 + A's

BP122


BQ122


4 Ø 1"

2 Ø 3/4"

2 Ø 3/4"

2 Ø 1"


DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 5053000 kg.cm 5053000 kg.cm 5053000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = 720106.85 kg.cm 1188166.30 kg.cm 1485346.90 kg.cm

A's = 3.89 cm2 6.83 cm2 8.93 cm2

Total As = 30.13 cm2 31.62 cm2 32.74 cm2

Total A's = 3.89 cm2 6.83 cm2 8.93 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.31 0.34 0.37

w 1 = 0.400 0.477 0.549

w 2 = 1.295 1.218 1.146

P = 0.0200 0.0238 0.0274

chequeo de P = DOB.REFORZADA DOB.REFORZADA DOB.REFORZADA

As = ----- ----- -----


As = 30.13 cm2 31.62 cm2 32.74 cm2

A's = 3.89 cm2 6.83 cm2 8.93 cm2

P = 0.0186 0.0207 0.0223

P' = 0.0024 0.0045 0.0061

As1 =

Mu1 =

BV16


BV20


BW20


BX20


P - P' = 0.0162 0.0162 0.0162

VERF. = 0.01115 0.01181 0.01229

SI FLUYE SI FLUYE SI FLUYE


DATOS

β = 0.85

Ø = 0.90

b = 30 cm

h = 60 cm

r = 5 cm

d' = 5 cm

01 capa 54 cm

02 capas 51 cm

03 capas 49 cm


Mu = 4144000 kg.cm 4144000 kg.cm 4144000 kg.cm

f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2

f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = 0.02 0.02 0.02

Ku = 49.53 49.53 49.53

26.24 cm2 24.79 cm2 23.81 cm2

4332893.15 kg.cm 3864833.70 kg.cm 3567653.10 kg.cm

Mr = -188893.15 kg.cm 279166.30 kg.cm 576346.90 kg.cm

A's = -1.02 cm2 1.61 cm2 3.47 cm2

Total As = ------ 26.39 cm2 27.28 cm2

Total A's = -1.02 cm2 1.61 cm2 3.47 cm2


a = 0.59 0.59 0.59

b = -1.00 -1.00 -1.00

c = 0.25 0.28 0.30

w 1 = 0.306 0.356 0.398

w 2 = 1.389 1.339 1.297

P = 0.0153 0.0178 0.0199


As = 24.77 cm2 ----- -----


As = ------ 26.39 cm2 27.28 cm2

A's = -1.02 cm2 1.61 cm2 3.47 cm2

P = #VALUE! 0.0172 0.0186

P' = -0.0006 0.0010 0.0024

P - P' = #VALUE! 0.0162 0.0162

VERF. = 0.01115 0.01181 0.01229


As1 =

Mu1 =

BV118


BV122


BW122


BX122


DISEÑO POR CORTANTE

F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b) 60 cm (h)

Av = 0.71 cm2 β = 0.85 Ø = 0.85

distancia = 84 cm 81 cm19746.30 kg

b = 30 cm h = 60 cm r = 5 cm

01 capa 02 capas d = 54 cm 51 cm

Vc = 12442.30 kg 11751.06 kg

Necesita Refuerzo Necesita Refuerzo Vs = 10788.65 kg 11479.88 kg S = 29.85 cm 26.50 cm

d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm

1ra Cond. = Vs=<2.1*b*d*F'c^0.5 Si Cumple Si Cumple

S max = 27.00 cm 25.50 cm

2da Cond. = Vs=>1.1*b*d*F'c^0.5 No Cumple No Cumple

S max = 0.00 cm 0.00 cm d = 54 cm 51 cm

0.49 m 0.46 m2.80 Und. 1.84 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 2 0.25 6

Avance @ = 0.75 m 0.55 m

1.59 m 1.36 m

Vu1 =

Cortante Vu2 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2 β = 0.85 Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 13.21 cm 12.13 cm

2da Cond. = Vs=>1.1*b*d*F'c^0.5 No Cumple Si Cumple

S max = 0.00 cm 12.13 cm d = 54 cm 51 cm

0.49 m 0.46 m2.80 Und. 4.60 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 5 0.10 6

Avance @ = 0.75 m 0.55 m

1.59 m 1.36 m

Vu1 =

Cortante Vu2 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2 β = 0.85 Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 12.14 cm 11.17 cm

2da Cond. = Vs=>1.1*b*d*F'c^0.5 Si Cumple Si Cumple

Vu1 =

2da Cond. = S max = 12.14 cm 11.17 cm

d = 54 cm 51 cm0.49 m 0.46 m

2.80 Und. 4.60 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 5 0.10 6

Avance @ = 0.75 m 0.55 m

1.57 m 1.34 m


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2 β = 0.85 Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm

Cortante Vu2 =

Vu1 =


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 9.64 cm 8.92 cm


S max = 9.64 cm 8.92 cm d = 54 cm 51 cm

0.49 m 0.46 m2.80 Und. 6.13 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 7 0.075 6

Avance @ = 0.75 m 0.58 m

1.57 m 1.36 mCortante Vu2 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2 β = 0.85 Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 12.34 cm 11.35 cm


S max = 12.34 cm 11.35 cm d = 54 cm 51 cm

0.49 m 0.46 m2.80 Und. 4.60 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 5 0.100 6

Avance @ = 0.75 m 0.55 m

1.57 m 1.34 m

Vu1 =

Cortante Vu2 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2 β = 0.85 Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 14.84 cm 13.58 cm


S max = 0.00 cm 0.00 cm d = 54 cm 51 cm

0.49 m 0.46 m2.80 Und. 3.68 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 4 0.125 6

Avance @ = 0.75 m 0.55 m

1.57 m 1.34 m

Vu1 =

Cortante Vu2 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2 β = 0.85 Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

Vu1 =

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 12.35 cm 11.37 cm


S max = 12.35 cm 11.37 cm d = 54 cm 51 cm

0.49 m 0.46 m2.80 Und. 3.68 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 4 0.125 5

Avance @ = 0.75 m 0.55 m

1.62 m 1.39 m


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2 β = 0.85 Ø = 0.85

distancia = 87 cm 84 cm

Cortante Vu2 =

23553.60 kg b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 21.09 cm 19.06 cm


S max = 0.00 cm 0.00 cm d = 54 cm 51 cm

0.49 m 0.46 m2.80 Und. 3.68 Und.

Estribos @ =1 0.05 1 0.05 14 0.18 4 0.125 3

Avance @ = 0.75 m 0.55 m

1.62 m 1.39 m

Vu1 =

Cortante Vu2 =

DISEÑO POR CORTANTE DISEÑO POR CORTANTE

F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85

79 cm distancia = 1.59 m15472.80 kg

b = 30 cm h = 60 cm r = 5 cm

03 capas 01 capa 49 cm d = 54 cm

11290.23 kg Vc =

12442.30 kg Necesita Refuerzo Necesita Refuerzo

11940.71 kg Vs = 5761.00 kg24.47 cm S = 55.90 cm24.50 cm d/2 = 27.00 cm60.00 cm o = 60.00 cm12.25 cm d/4 = 13.50 cm30.00 cm o = 30.00 cm

Si Cumple 1ra Cond. =

Vs=<2.1*b*d*F'c^0.5 Si Cumple 24.47 cm S max = 27.00 cm

No Cumple 2da Cond. =

Vs=>1.1*b*d*F'c^0.5 No Cumple 0.00 cm S max = 0.00 cm49 cm d = 54 cm0.44 m 0.54 m

1.76 Und. 1.69 Und.0.05

Estribos @ =0 0.00 0

0.25 2 0.32 21.55 m Avance @ = 0.640 m

2.34 m 2.23 m

Vu2 =

Cortante Vu3 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


11290.23 kg Vc =





Si Cumple 2da Cond. =

Vs=>1.1*b*d*F'c^0.5 No Cumple 11.44 cm S max = 0.00 cm

49 cm d = 54 cm0.44 m 0.54 m

1.76 Und. 1.69 Und.0.05


0.25 2 0.320 21.55 m Avance @ = 0.640 m

2.34 m 2.23 m

Vu2 =

Cortante Vu3 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


11290.23 kg Vc =






Vs=>1.1*b*d*F'c^0.5 No Cumple

Vu2 =

10.55 cm 2da Cond. =

S max = 0.00 cm49 cm d = 54 cm0.44 m 0.54 m

1.76 Und. 1.69 Und.0.05


0.25 2 0.320 21.55 m Avance @ = 0.640 m

2.32 m 2.21 m


F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm

Cortante Vu3 =

Vu2 =


11290.23 kg Vc =


34560.36 kg Vs = 28197.82 kg8.46 cm S = 11.42 cm

24.50 cm d/2 = 27.00 cm60.00 cm o = 60.00 cm12.25 cm d/4 = 13.50 cm30.00 cm o = 30.00 cm




Vs=>1.1*b*d*F'c^0.5 Si Cumple 8.46 cm S max = 11.42 cm49 cm d = 54 cm0.44 m 0.54 m

1.76 Und. 1.69 Und.0.05


0.25 2 0.320 51.55 m Avance @ = 0.640 m



F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


11290.23 kg Vc =







49 cm d = 54 cm0.44 m 0.54 m

1.76 Und. 1.69 Und.0.05


0.25 2 0.320 41.55 m Avance @ = 0.640 m

2.32 m 2.21 m

Vu2 =

Cortante Vu3 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


11290.23 kg Vc =







1.76 Und. 1.69 Und.0.05


0.25 2 0.320 31.55 m Avance @ = 0.640 m

2.32 m 2.21 m

Vu2 =

Cortante Vu3 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85


b = 30 cm h = 60 cm r = 5 cm


11290.23 kg Vc =


27223.06 kg Vs = 21864.65 kg10.73 cm S = 14.73 cm24.50 cm d/2 = 27.00 cm60.00 cm o = 60.00 cm

Vu2 =

12.25 cm d/4 = 13.50 cm30.00 cm o = 30.00 cm





49 cm d = 54 cm0.44 m 0.54 m

4.40 Und. 1.69 Und.0.05


0.10 2 0.320 40.55 m Avance @ = 0.640 m

1.37 m 2.26 m


F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85

82 cm distancia = 1.62 m

Cortante Vu3 =

19668.60 kg b = 30 cm h = 60 cm r = 5 cm


11290.23 kg Vc =







2.93 Und. 1.69 Und.0.05


0.15 2 0.320 40.50 m Avance @ = 0.640 m

1.32 m 2.26 m

Vu2 =

Cortante Vu3 =


210 kg/cm2 F'c = 4200 kg/cm2 F'y =

60 cm (h) COLUMNA= 0.71 cm2 Av =

0.85 β =0.85 Ø =

1.36 m 2.34 m distancia = 15472.80 kg

30 cm b = 60 cm h = 5 cm r =

02 capas 03 capas 51 cm 49 cm d =

11751.06 kg 11290.23 kg Vc =

Necesita Refuerzo Necesita Refuerzo 6452.24 kg 6913.06 kg Vs = 47.14 cm 42.27 cm S = 25.50 cm 24.50 cm d/2 = 60.00 cm 60.00 cm o = 12.75 cm 12.25 cm d/4 = 30.00 cm 30.00 cm o =

Si Cumple Si Cumple 1ra Cond. =

Vs=<2.1*b*d*F'c^0.5 25.50 cm 24.50 cm S max =

No Cumple No Cumple 2da Cond. =

Vs=>1.1*b*d*F'c^0.5 0.00 cm 0.00 cm S max = 51 cm 49 cm d = 0.51 m 0.49 m

2.04 Und. 6.53 Und.0.00 0 0.00

Estribos @ =1

0.25 6 0.08 30.50 m 0.45 m Avance @ =

1.86 m 2.79 m

Vu3 =

Cortante Vu4 =


210 kg/cm2 F'c = 4200 kg/cm2 F'y =


0.85 β =0.85 Ø =

1.36 m 2.34 m distancia = 28003.00 kg

30 cm b = 60 cm h = 5 cm r =


11751.06 kg 11290.23 kg Vc =



Vs=<2.1*b*d*F'c^0.5 14.35 cm 13.50 cm S max =



4.08 Und. 6.53 Und.0.00 0 0.00

Estribos @ =1

0.125 6 0.075 30.25 m 0.45 m Avance @ =

1.61 m 2.79 m

Vu3 =

Cortante Vu4 =


210 kg/cm2 F'c = 4200 kg/cm2 F'y =


0.85 β =0.85 Ø =

1.34 m 2.32 m distancia = 29834.40 kg

30 cm b = 60 cm h = 5 cm r =


11751.06 kg 11290.23 kg Vc =



Vs=<2.1*b*d*F'c^0.5 13.03 cm 12.27 cm S max =

No Cumple Si Cumple 2da Cond. =

Vs=>1.1*b*d*F'c^0.5

Vu3 =

0.00 cm 12.27 cm 2da Cond. =

S max = 51 cm 49 cm d = 0.51 m 0.49 m

4.08 Und. 6.53 Und.0.00 0 0.00

Estribos @ =1

0.125 6 0.075 30.25 m 0.45 m Avance @ =

1.59 m 2.77 m


210 kg/cm2 F'c = 4200 kg/cm2 F'y =


0.85 β =0.85 Ø =

1.36 m 2.32 m distancia = 34544.10 kg

30 cm b = 60 cm h = 5 cm r =

Cortante Vu4 =

Vu3 =


11751.06 kg 11290.23 kg Vc =



Vs=<2.1*b*d*F'c^0.5 10.53 cm 9.96 cm S max =

Si Cumple Si Cumple 2da Cond. =

Vs=>1.1*b*d*F'c^0.5 10.53 cm 9.96 cm S max =

51 cm 49 cm d = 0.51 m 0.49 m

5.10 Und. 6.53 Und.0.00 0 0.00

Estribos @ =1

0.100 6 0.075 30.50 m 0.45 m Avance @ =

1.86 m 2.77 m Cortante Vu4 =


210 kg/cm2 F'c = 4200 kg/cm2 F'y =


0.85 β =0.85 Ø =

1.34 m 2.32 m distancia = 28904.30 kg

30 cm b = 60 cm h = 5 cm r =


11751.06 kg 11290.23 kg Vc =



Vs=<2.1*b*d*F'c^0.5 13.67 cm 12.87 cm S max =



4.08 Und. 6.53 Und.0.00 0 0.00

Estribos @ =1

0.125 6 0.075 30.50 m 0.45 m Avance @ =

1.84 m 2.77 m

Vu3 =

Cortante Vu4 =


210 kg/cm2 F'c = 4200 kg/cm2 F'y =


0.85 β =0.85 Ø =

1.34 m 2.32 m distancia = 25721.40 kg

30 cm b = 60 cm h = 5 cm r =


11751.06 kg 11290.23 kg Vc =



Vs=<2.1*b*d*F'c^0.5 16.43 cm 15.40 cm S max =



3.40 Und. 6.53 Und.0.00 0 0.00

Estribos @ =1

0.150 6 0.075 30.45 m 0.45 m Avance @ =

1.79 m 2.77 m

Vu3 =

Cortante Vu4 =


210 kg/cm2 F'c = 4200 kg/cm2 F'y =


0.85 β =0.85 Ø =

1.39 m 1.37 m distancia = 29160.90 kg

30 cm b = 60 cm h = 5 cm r =


11751.06 kg 11290.23 kg Vc =

Necesita Refuerzo Necesita Refuerzo 22555.88 kg 23016.71 kg Vs = 13.48 cm 12.70 cm S = 25.50 cm 24.50 cm d/2 = 60.00 cm 60.00 cm o =

Vu3 =

12.75 cm 12.25 cm d/4 = 30.00 cm 30.00 cm o =


Vs=<2.1*b*d*F'c^0.5 13.48 cm 12.70 cm S max =



3.40 Und. 3.92 Und.0.00 0 0.00

Estribos @ =1

0.150 4 0.125 30.60 m 0.50 m Avance @ =

1.98 m 1.87 m


210 kg/cm2 F'c = 4200 kg/cm2 F'y =


0.85 β =0.85 Ø =

1.39 m 1.32 m distancia =

Cortante Vu4 =

19668.60 kg30 cm b = 60 cm h = 5 cm r =


11751.06 kg 11290.23 kg Vc =



Vs=<2.1*b*d*F'c^0.5 25.50 cm 24.50 cm S max =



3.40 Und. 2.18 Und.0.00 0 0.00

Estribos @ =1

0.150 2 0.225 30.60 m 0.45 m Avance @ =

1.98 m 1.77 m

Vu3 =

Cortante Vu4 =


210 kg/cm24200 kg/cm2

50 cm (b) 60 cm (h)

0.71 cm20.850.85

2.23 m 1.86 m 2.79 m11587.80 kg

30 cm60 cm5 cm

01 capa 02 capas 03 capas 54 cm 51 cm 49 cm

12442.30 kg 11751.06 kg 11290.23 kg Refuerzo Minimo Refuerzo Minimo Necesita Refuerzo

1190.41 kg 1881.65 kg 2342.47 kg270.54 cm 161.65 cm 124.76 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm

Si Cumple Si Cumple Si Cumple 27.00 cm 25.50 cm 24.50 cm

No Cumple No Cumple No Cumple 0.00 cm 0.00 cm 0.00 cm54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

3.09 Und. 2.04 Und. 3.27 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 r 0.25 4 0.15

0.52 m #VALUE! 0.60 mEstribos @ =

2.755 m #VALUE! 3.390 m


210 kg/cm24200 kg/cm2

50 cm (b) 60 cm (h)

0.71 cm20.850.85

2.23 m 1.60 m 2.79 m26532.80 kg

30 cm60 cm5 cm


12442.30 kg 11751.06 kg 11290.23 kg Necesita Refuerzo Necesita Refuerzo Necesita Refuerzo


Si Cumple Si Cumple Si Cumple 1ra Cond. =

17.16 cm 15.63 cm 14.67 cm No Cumple No Cumple No Cumple

2da Cond. = 0.00 cm 0.00 cm 0.00 cm54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

3.09 Und. 3.40 Und. 3.27 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 4 0.15 4 0.15

0.52 m 0.60 m 0.60 m

2.76 m 2.20 m 3.39 m


210 kg/cm24200 kg/cm2

50 cm (b) 55 cm (h)

0.71 cm20.850.85

2.21 m 1.60 m 2.77 m28275.00 kg

30 cm60 cm5 cm






2da Cond. =

0.00 cm 0.00 cm 0.00 cm 2da Cond. =

54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

3.09 Und. 4.08 Und. 3.27 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 4 0.125 4 0.15

0.52 m 0.50 m 0.60 m

2.73 m 2.10 m 3.37 m


210 kg/cm24200 kg/cm2

50 cm (b) 55 cm (h)

0.71 cm20.850.85

2.21 m 1.86 m 2.77 m19503.50 kg

30 cm60 cm5 cm







3.09 Und. 2.04 Und. 3.27 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 2 0.250 4 0.15

0.52 m 0.50 m 0.60 m

2.73 m 2.36 m 3.37 m


210 kg/cm24200 kg/cm2

50 cm (b) 55 cm (h)

0.71 cm20.850.85

2.21 m 1.84 m 2.77 m14609.40 kg

30 cm60 cm5 cm







3.09 Und. 2.04 Und. 3.27 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 2 0.250 4 0.15

0.52 m 0.50 m 0.60 m

2.73 m 2.34 m 3.37 m


210 kg/cm24200 kg/cm2

50 cm (b) 55 cm (h)

0.71 cm20.850.85

2.21 m 1.80 m 2.77 m22961.40 kg

30 cm60 cm5 cm







3.09 Und. 2.91 Und. 3.27 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 3 0.175 4 0.15

0.52 m 0.52 m 0.60 m

2.73 m 2.33 m 3.37 m


210 kg/cm24200 kg/cm2

50 cm (b) 65 cm (h)

0.71 cm20.850.85

2.26 m 1.98 m 1.87 m26160.90 kg

30 cm60 cm5 cm



18335.23 kg 19026.47 kg 19487.30 kg17.56 cm 15.99 cm 15.00 cm27.00 cm 25.50 cm 24.50 cm60.00 cm 60.00 cm 60.00 cm

13.50 cm 12.75 cm 12.25 cm30.00 cm 30.00 cm 30.00 cm




3.09 Und. 2.91 Und. 3.27 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 3 0.175 4 0.15

0.52 m 0.52 m 0.60 m

2.78 m 2.51 m 2.47 m


210 kg/cm24200 kg/cm2

50 cm (b) 65 cm (h)

0.71 cm20.850.85

2.26 m 1.98 m 1.77 m

16172.10 kg30 cm60 cm5 cm







3.09 Und. 2.91 Und. 2.18 Und.0.00 1 0.00 1 0.00

Estribos @ =0.18 3 0.175 2 0.225

0.52 m 0.52 m 0.45 m

2.78 m 2.51 m 2.22 m

1 @ 0.05; 2 @ 0.25; 2 @ 0.25; Rsto. @ 0.25

1 @ 0.05; 2 @ 0.075; 3 @ 0.10; 3 @ 0.15; 2 @ 0.20; Rsto. @ 0.25


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 2.76 m 2.20 m 3.39 m8128.40 kg

b = 30 cm h = 60 cm r = 5 cm

01 capa 02 capas 03 capas d = 54 cm 51 cm 49 cm

Vc = 12442.30 kg 11751.06 kg 11290.23 kg

Refuerzo Minimo Refuerzo Minimo Refuerzo Minimo Vs = -2879.47 kg -2188.23 kg -1727.41 kg S = -111.85 cm -139.00 cm -169.18 cm

d/2 = 27.00 cm 25.50 cm 24.50 cm o = 60.00 cm 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm 12.25 cm o = 30.00 cm 30.00 cm 30.00 cm

Vs=<2.1*b*d*F'c^0.5 Si Cumple Si Cumple Si Cumple S max = -111.85 cm -139.00 cm -169.18 cm

Vs=>1.1*b*d*F'c^0.5 No Cumple No Cumple No Cumple S max = 0.00 cm 0.00 cm 0.00 cm

d = 54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

2.16 Und. 2.04 Und. 3.27 Und.1 0.00 1 0.00 1 0.002 0.25 r 0.25 4 0.15

Avance @ = 0.50 m #VALUE! 0.60 m

3.26 m #VALUE! 3.99 m

Vu3 =

Cortante Vu4 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 2.73 m 2.10 m 3.37 m10274.40 kg

b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg 11290.23 kg

Refuerzo Minimo Refuerzo Minimo Refuerzo Minimo Vs = -354.77 kg 336.47 kg 797.30 kg S = -907.80 cm 903.98 cm 366.53 cm

d/2 = 27.00 cm 25.50 cm 24.50 cm o = 60.00 cm 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm 12.25 cm o = 30.00 cm 30.00 cm 30.00 cm

Vs=<2.1*b*d*F'c^0.5 Si Cumple Si Cumple Si Cumple S max = -907.80 cm 25.50 cm 24.50 cm

Vs=>1.1*b*d*F'c^0.5 No Cumple No Cumple No Cumple

Vu3 =

S max = 0.00 cm 0.00 cm 0.00 cm d = 54 cm 51 cm 49 cm

0.54 m 0.51 m 0.49 m2.16 Und. 2.04 Und. 3.27 Und.

1 0.00 1 0.00 1 0.002 0.25 r 0.25 4 0.15


3.23 m #VALUE! 3.97 m


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 2.73 m 2.36 m 3.37 m16503.50 kg

b = 30 cm h = 60 cm r = 5 cm

Cortante Vu4 =

Vu3 =


Vc = 12442.30 kg 11751.06 kg 11290.23 kg

Necesita Refuerzo Necesita Refuerzo Necesita Refuerzo Vs = 6973.59 kg 7664.82 kg 8125.65 kg S = 46.18 cm 39.68 cm 35.96 cm

d/2 = 27.00 cm 25.50 cm 24.50 cm o = 60.00 cm 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm 12.25 cm o = 30.00 cm 30.00 cm 30.00 cm

Vs=<2.1*b*d*F'c^0.5 Si Cumple Si Cumple Si Cumple S max = 27.00 cm 25.50 cm 24.50 cm


d = 54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

2.16 Und. 2.04 Und. 3.27 Und.1 0.00 1 0.00 1 0.002 0.25 2 0.25 4 0.15

Avance @ = 0.50 m 0.50 m 0.60 m

3.23 m 2.86 m 3.97 mCortante Vu4 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 2.73 m 2.34 m 3.37 m11609.40 kg

b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg 11290.23 kg

Refuerzo Minimo Refuerzo Minimo Necesita Refuerzo Vs = 1215.82 kg 1907.06 kg 2367.89 kg S = 264.89 cm 159.49 cm 123.42 cm

d/2 = 27.00 cm 25.50 cm 24.50 cm o = 60.00 cm 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm 12.25 cm o = 30.00 cm 30.00 cm 30.00 cm



d = 54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

2.16 Und. 2.04 Und. 3.27 Und.1 0.00 1 0.00 1 0.002 0.25 r 0.25 4 0.15


3.23 m #VALUE! 3.97 m

Vu3 =

Cortante Vu4 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 2.73 m 2.33 m 3.37 m7366.20 kg

b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg 11290.23 kg

Refuerzo Minimo Refuerzo Minimo Refuerzo Minimo Vs = -3776.18 kg -3084.94 kg -2624.11 kg S = -85.29 cm -98.60 cm -111.37 cm

d/2 = 27.00 cm 25.50 cm 24.50 cm o = 60.00 cm 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm 12.25 cm o = 30.00 cm 30.00 cm 30.00 cm

Vs=<2.1*b*d*F'c^0.5 Si Cumple Si Cumple Si Cumple S max = -85.29 cm -98.60 cm -111.37 cm


d = 54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

2.16 Und. 2.04 Und. 3.27 Und.1 0.00 1 0.00 1 0.002 0.25 r 0.25 4 0.15


3.23 m #VALUE! 3.97 m

Vu3 =

Cortante Vu4 =


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 2.78 m 2.51 m 2.00 m25381.50 kg

b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg 11290.23 kg


d/2 = 27.00 cm 25.50 cm 24.50 cm o = 60.00 cm 60.00 cm 60.00 cm

Vu3 =

d/4 = 13.50 cm 12.75 cm 12.25 cm o = 30.00 cm 30.00 cm 30.00 cm



d = 54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

2.16 Und. 2.04 Und. 3.27 Und.1 0.00 1 0.00 1 0.002 0.25 1 0.25 3 0.15

Avance @ = 0.50 m 0.25 m 0.45 m

3.28 m 2.76 m 2.45 m


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 2.78 m 2.51 m 2.22 m

Cortante Vu4 =

12675.60 kg b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg 11290.23 kg


d/2 = 27.00 cm 25.50 cm 24.50 cm o = 60.00 cm 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm 12.25 cm o = 30.00 cm 30.00 cm 30.00 cm



d = 54 cm 51 cm 49 cm0.54 m 0.51 m 0.49 m

2.16 Und. 2.04 Und. 2.18 Und.1 0.00 1 0.00 1 0.002 0.25 1 0.25 r 0.225

Avance @ = 0.50 m 0.25 m #VALUE!

3.28 m 2.76 m #VALUE!

Vu3 =

Cortante Vu4 =

Estribos @ = 1 @ 0.05; 5 @ 0.10; 2 @ 0.125; 4 @ 0.15; Rsto. @ 0.25

Estribos @ = 1 @ 0.05; 5 @ 0.10; 2 @ 0.125; 2 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

Estribos @ = 1 @ 0.05; 5 @ 0.10; 2 @ 0.125; 4 @ 0.125; Rsto. @ 0.25

Estribos @ = 1 @ 0.05; 5 @ 0.10; 6 @ 0.125; 2 @ 0.15; 2 @ 0.20; Rsto. @ 0.25


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 3.23 m 2.80 m13863.50 kg

b = 30 cm h = 60 cm r = 5 cm

Vu3 =


Vc = 12442.30 kg 11751.06 kg


d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = 27.00 cm 25.50 cm


S max = 0.00 cm 0.00 cm d = 54 cm 51 cm

0.54 m 0.51 m2.16 Und. 2.04 Und.

Estribos @ =1 0.00 1 0.00 11 0.25 1 0.25 4

Avance @ = 0.25 m 0.25 m


Estribos @ = 1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 2 @ 0.25; Rsto. @ 0.25

Estribos @ = 1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 2 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

Estribos @ = 1 @ 0.05; 3 @ 0.125; 4 @ 0.15; 3 @ 0.175; Rsto. @ 0.25

Estribos @ = 1 @ 0.05; 4 @ 0.10; 4 @ 0.15; 3 @ 0.175; 2 @ 0.20; Rsto. @ 0.25


F'c = 210 kg/cm2 F'y = 4200 kg/cm2


Av = 0.71 cm2β = 0.85Ø = 0.85

distancia = 3.28 m 2.80 m10180.90 kg

b = 30 cm h = 60 cm r = 5 cm


Vc = 12442.30 kg 11751.06 kg

Refuerzo Minimo Refuerzo Minimo Vs = -464.77 kg 226.47 kg S = -692.94 cm 1343.05 cm

d/2 = 27.00 cm 25.50 cm o = 60.00 cm 60.00 cm

Vu3 =

d/4 = 13.50 cm 12.75 cm o = 30.00 cm 30.00 cm


S max = -692.94 cm 25.50 cm


S max = 0.00 cm 0.00 cm d = 54 cm 51 cm

0.54 m 0.51 m2.16 Und. 2.04 Und.

Estribos @ =1 0.00 1 0.00 11 0.25 1 0.25 r

Avance @ = 0.25 m 0.25 m


Estribos @ = 1 @ 0.05; 3 @ 0.15; 2 @ 0.225; 2 @ 0.225; Rsto @ 0.225.

Estribos @ = 1 @ 0.05; 2 @ 0.10; 2 @ 0.15; 3 @ 0.175 2 @ 0.20; Rsto. @ 0.225

1 @ 0.05; 5 @ 0.10; 2 @ 0.125; 4 @ 0.15; Rsto. @ 0.25

1 @ 0.05; 5 @ 0.10; 2 @ 0.125; 2 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

1 @ 0.05; 5 @ 0.10; 2 @ 0.125; 4 @ 0.125; Rsto. @ 0.25

1 @ 0.05; 5 @ 0.10; 6 @ 0.125; 2 @ 0.15; 2 @ 0.20; Rsto. @ 0.25


F'c = 210 kg/cm2 F'y = 4200 kg/cm2

COLUMNA= 50 cm (b)

Av = 0.71 cm2β = 0.85Ø = 0.85

3.97 m distancia = 3.48 m2543.60 kg

b = 30 cm h = 60 cm r = 5 cm

Vu3 =


11290.23 kg Vc =

12442.30 kg Necesita Refuerzo Refuerzo Minimo

5019.77 kg Vs = -9449.83 kg58.22 cm S = -34.08 cm24.50 cm d/2 = 27.00 cm60.00 cm o = 60.00 cm12.25 cm d/4 = 13.50 cm30.00 cm o = 30.00 cm


Vs=<2.1*b*d*F'c^0.5 Si Cumple 24.50 cm S max = -34.08 cm



3.27 Und. 2.16 Und.0.00


0.15 1 0.25 r0.60 m Avance @ = 0.25 m


1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 2 @ 0.25; Rsto. @ 0.25

1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 2 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

1 @ 0.05; 3 @ 0.125; 4 @ 0.15; 3 @ 0.175; Rsto. @ 0.25

1 @ 0.05; 4 @ 0.10; 4 @ 0.15; 3 @ 0.175; 2 @ 0.20; Rsto. @ 0.25


2.45 m

03 capas 49 cm

11290.23 kg Refuerzo Minimo

687.30 kg425.20 cm24.50 cm60.00 cm

12.25 cm30.00 cm

Si Cumple 24.50 cm

No Cumple 0.00 cm49 cm0.49 m

3.27 Und.0.00

Estribos @ = 1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 4 @ 0.15; 3 @ 0.15; Rsto. @ 0.250.15

#VALUE!Estribos @ = 1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 7 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

#VALUE!

1 @ 0.05; 3 @ 0.15; 2 @ 0.225; 2 @ 0.225; Rsto @ 0.225.

1 @ 0.05; 2 @ 0.10; 2 @ 0.15; 3 @ 0.175 2 @ 0.20; Rsto. @ 0.225


210 kg/cm24200 kg/cm2

55 cm (h)

0.71 cm20.850.85

3.05 m 4.57 m2543.60 kg

30 cm60 cm5 cm

02 capas 03 capas 51 cm 49 cm

11751.06 kg 11290.23 kg Refuerzo Minimo Refuerzo Minimo

-8758.59 kg -8297.76 kg-34.73 cm -35.22 cm25.50 cm 24.50 cm60.00 cm 60.00 cm12.75 cm 12.25 cm30.00 cm 30.00 cm

Si Cumple Si Cumple -34.73 cm -35.22 cm

No Cumple No Cumple 0.00 cm 0.00 cm51 cm 49 cm0.51 m 0.49 m

2.04 Und. 3.27 Und.0.00 1 0.00

Estribos @ = 1 @ 0.05; 7 @ 0.075; 5 @ 0.10; 2 @ 0.25; 2 @ 0.25; Rsto. @ 0.250.25 4 0.15

#VALUE! 0.60 mEstribos @ = 1 @ 0.05; 7 @ 0.075; 5 @ 0.10; 4 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

#VALUE! 5.17 m

1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 4 @ 0.15; 3 @ 0.15; Rsto. @ 0.25

1 @ 0.05; 5 @ 0.10; 4 @ 0.125; 7 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

1 @ 0.05; 7 @ 0.075; 5 @ 0.10; 2 @ 0.25; 2 @ 0.25; Rsto. @ 0.25

1 @ 0.05; 7 @ 0.075; 5 @ 0.10; 4 @ 0.15; 2 @ 0.20; Rsto. @ 0.25

VERIFICACION DE UNA VIGA DOBLEMENTE REFORZADAF'c = 210.00Fy = 4200.00F's = ?β = 0.85ø = 0.90

As = 20.40A`s = 5.18 a b c

r (d') = 6.00 fs^2 fsEs = 2000000.00 5.18 -116760.00 350217000.00b = 30.00h = 55.00 fs 3562.51fs = 3562.51 fs 18978.03

NO FLUYE capasC 14.77 d1 49.00a 12.55 d2 46.00

d3 44.00

Tomando momentos en el punto del area en traccion tenemos01 capa 02 capas 03 capas

Mu 31.16 28.97 27.52

CV = 0.25 0.25 0.25CM = 1.00 1.00 1.00Mu = 1.8*CV+1.5*CM 1.8*CV+1.5*CM 1.8*CV+1.5*CMCM = 15.98 14.86 14.11CV = 3.99 3.71 3.53

B8

Area de acero en traccion

B9

Area de acero en compresion

B14

Trabajamos con el menor

B16

El eje neutro

B17

Altura del rectangulo de withney el rectangulo comprimido

VERIFICACION DE UNA VIGA DOBLEMENTE REFORZADA VERIFICACION DE UNA VIGA DOBLEMENTE REFORZADAF'c = 210.00 F'c =Fy = 4200.00 Fy =F's = ? F's =β = 0.85 β =ø = 0.90 ø =

As = 20.40 As =A`s = 5.18 a b c A`s =

r (d') = 6.00 fs^2 fs r (d') =Es = 2000000.00 5.18 -116760.00 350217000.00 Es =b = 30.00 b =h = 55.00 fs 3562.51 h =fs = 3562.51 fs 18978.03 fs =

NO FLUYE capas NO FLUYEC 14.77 d1 49.00 Ca 12.55 d2 46.00 a

d3 44.00

Tomando momentos en el punto del area en traccion tenemos Tomando momentos en el punto del area en traccion tenemos01 capa 02 capas 03 capas

Mu 31.16 28.97 27.52 Mu

CV = 0.25 0.25 0.25 CV =CM = 1.00 1.00 1.00 CM =Mu = 1.8*CV+1.5*CM 1.8*CV+1.5*CM 1.8*CV+1.5*CM Mu =CM = 15.98 14.86 14.11 CM =CV = 3.99 3.71 3.53 CV =

I8


P8


I9


P9


I14


P14


I16

El eje neutro

P16

El eje neutro

I17


P17


VERIFICACION DE UNA VIGA DOBLEMENTE REFORZADA VERIFICACION DE UNA VIGA DOBLEMENTE REFORZADA210.00 F'c = 210.00

4200.00 Fy = 4200.00? F's = ?

0.85 β = 0.850.90 ø = 0.90

20.40 As = 20.405.18 a b c A`s = 5.186.00 fs^2 fs r (d') = 6.00

2000000.00 5.18 -116760.00 350217000.00 Es = 2000000.0030.00 b = 30.0055.00 fs 3562.51 h = 55.00

3562.51 fs 18978.03 fs = 3562.51NO FLUYE capas NO FLUYE

14.77 d1 49.00 C 14.7712.55 d2 46.00 a 12.55

d3 44.00

Tomando momentos en el punto del area en traccion tenemos Tomando momentos en el punto del area en traccion tenemos01 capa 02 capas 03 capas 01 capa31.16 28.97 27.52 Mu 31.16

0.25 0.25 0.25 CV = 0.251.00 1.00 1.00 CM = 1.00

1.8*CV+1.5*CM 1.8*CV+1.5*CM 1.8*CV+1.5*CM Mu = 1.8*CV+1.5*CM15.98 14.86 14.11 CM = 15.983.99 3.71 3.53 CV = 3.99

W8


W9


W14


W16

El eje neutro

W17


VERIFICACION DE UNA VIGA DOBLEMENTE REFORZADA

a b cfs^2 fs5.18 -116760.00 350217000.00

fs 3562.51fs 18978.03

capasd1 49.00d2 46.00d3 44.00

Tomando momentos en el punto del area en traccion tenemos02 capas 03 capas

28.97 27.52

0.25 0.251.00 1.00

1.8*CV+1.5*CM 1.8*CV+1.5*CM14.86 14.113.71 3.53

PREDIMENSIONAMIENTO VIGA L: LOSA Y VIGA PERIMETRAL VIGA T AISLADA

1ra Condición Si Cumple 1ra Condición Si Cumple 1ra Condición No Cumple

2da Condición Si Cumple 2da Condición Si Cumple 2da Condición Si Cumple

3ra Condición Si Cumple 3ra Condición Si Cumple


DATOS β = € 0.85 Ø = € 0.90

viga b = 40 cm h = 70 cm

r = 4 cm d' = 5 cm

d = 01 capa 02 capas 03 capas

64 cm 61 cm 59 cm

Mu = 5365000 kg.cm 5365000 kg.cm 5365000 kg.cm f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2 f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2

Pmax = € 0.02 € 0.02 € 0.02

DATOS 01 capa 02 capas 03 capas a = € 0.59 € 0.59 € 0.59 b = € -1.00 € -1.00 € -1.00 c = 0.17 0.19 0.20

w 1 = 0.196 0.219 0.237 w 2 = 1.499 1.476 1.458

P = 0.0098 0.0110 0.0119 chequeo de P = SIMP. REFORZADA SIMP. REFORZADA SIMP. REFORZADA

As = 25.07 cm2 26.72 cm2 28.91 cm2

Ku = € 49.53 € 49.53 € 49.53 41.47 cm2 39.53 cm2 38.23 cm2

8115011.58 kg.cm 7372060.08 kg.cm 6896571.12 kg.cm

Mr = -2750011.58 kg.cm -2007060.08 kg.cm -1531571.12 kg.cm A's = -12.33 cm2 -9.48 cm2 -7.50 cm2

Total As = 29.14 cm2 30.05 cm2 30.73 cm2 Total A's = -12.33 cm2 -9.48 cm2 -7.50 cm2

VIGA T: LOSA Y VIGA INTERIOR

As1 =

Mu1 =

B3

USER: b=<bw+16hf

D3

USER: b=<bw+6*hf

F3

USER: hf>=bw/2

B4

USER: b=<bw+((si-1+si)/2)

D4

USER: b=<bw+s/2

F4

USER: b<=4*bw

B5

USER: b=<ln/4

D5

USER: b=<bw+ln/12

E21


D35

USER: ku=Mu/b*d^2

E35


F35


G35


D36

USER: As=P*b*d

D37

USER: Mu1=Ku*b*d^2

D39

USER: Mr=Mu-Mu1

D40

USER: A's=Mu/Ø*F'y*(d-d')

D42

USER: As=As1+A's

DISEÑO DE VIGA T Y L DISEÑO DE ACERO PARA VIGAS DOBLEMENTE REFORZADAS β = € 0.85

Ø = 0.90 Ln = 6.60 m DATOS

viga

b = 80 cm r = 4 cm β = 40 cm d' = 5 cm Ø =

h = 70 cm F'c = 280 kg/cm2 viga

hf = 10 cm F'y = 4200 kg/cm2120 cm F's = 4200 kg/cm2 r = 120 cm Mu = 5261000 kg.cm d' =


d = 64 cm 61 cm 59 cm

Ku = 16.06 17.67 18.89 Mu = P = 0.00442 0.00552 0.00508 f'c =

As = 22.63 cm2 26.94 cm2 23.98 cm2 f'y =

a = 4.99 cm 5.94 cm 5.29 cm Pmax =

VIGA RECT. VIGA RECT. VIGA RECT. DATOS

a = b = c =

w 1 = 22.67 cm2 22.67 cm2 22.67 cm2 w 2 =

5055120 kg.cm 4798080 kg.cm 4626720 kg.cm P = 205880 kg.cm 462920 kg.cm 634280 kg.cm chequeo de P =

As = Ku = 1.26 3.11 4.56 P = € 0.00 € 0.01 € 0.00

0.84 cm2 26.84 cm2 0.87 cm2 As total = 23.51 cm2 49.51 cm2 23.54 cm2

bw =

sj =sj-1 =

As1 =

Mu1 =Mu2 =

As2 =

As2As1

b

bw

h

hf

J34

USER: Ku=Mu2/bw*d^2

DISEÑO DE ACERO PARA VIGAS DOBLEMENTE REFORZADAS DISEÑO DE VIGA T Y L

β =

DATOS Ø = β = € 0.85

viga

b = Ø = € 0.90

b = 40 cm h = h = 70 cm hf =

r = 5 cm d' = 5 cm


d = 64 cm 61 cm 59 cm

Mu = 9076000 kg.cm 9076000 kg.cm 9076000 kg.cm Ku = f'c = 210 kg/cm2 210 kg/cm2 210 kg/cm2 P = f'y = 4200 kg/cm2 4200 kg/cm2 4200 kg/cm2 As =

Pmax = € 0.02 € 0.02 € 0.02 a =

DATOS 01 capa 02 capas 03 capas a = € 0.59 € 0.59 € 0.59 b = € -1.00 € -1.00 € -1.00 c = 0.29 0.32 0.34

w 1 = 0.377 0.434 0.482 w 2 = 1.318 1.261 1.213

P = 0.0188 0.0217 0.0241 chequeo de P = DOB.REFORZADA DOB.REFORZADA DOB.REFORZADA

As = 48.25 cm2 52.89 cm2 58.79 cm2 Ku =

Ku = € 49.53 € 49.53 € 49.53 P = 41.47 cm2 39.53 cm2 38.23 cm2

8115011.58 kg.cm 7372060.08 kg.cm 6896571.12 kg.cm As total =

Mr = 960988.42 kg.cm 1703939.92 kg.cm 2179428.88 kg.cm A's = 4.31 cm2 8.05 cm2 10.68 cm2

Total As = 45.78 cm2 47.58 cm2 48.91 cm2 Total A's = 4.31 cm2 8.05 cm2 10.68 cm2

bw =

sj =sj-1 =

As1 =

Mu1 =Mu2 =

As1 = As2 =

Mu1 =

R21


Q35

USER: ku=Mu/b*d^2

R35


S35


T35


Q36

USER: As=P*b*d

Q37

USER: Mu1=Ku*b*d^2

Q39

USER: Mr=Mu-Mu1

Q40


Q42

USER: As=As1+A's

DISEÑO DE VIGA T Y L DISEÑO DE ACERO PARA VIGAS DOBLEMENTE REFORZADAS € 0.85

0.90 Ln = 5.60 m DATOS 80 cm r = 5 cm β = 40 cm d' = 5 cm Ø = 70 cm F'c = 210 kg/cm2

viga b =

10 cm F'y = 4200 kg/cm2 h = 120 cm F's = 4200 kg/cm2 r = 120 cm Mu = 2492000 kg.cm d' =

01 capa 02 capas 03 capas d =

64 cm 61 cm 59 cm

7.60 8.37 8.95 Mu = 0.00205 0.00552 0.00233 f'c =

10.50 cm2 26.94 cm2 11.00 cm2 f'y =

3.09 cm 7.92 cm 3.23 cm Pmax =

VIGA RECT. VIGA RECT. VIGA RECT. DATOS

a = b = c =

w 1 = 17.00 cm2 17.00 cm2 17.00 cm2 w 2 =

3791340 kg.cm 3598560 kg.cm 3470040 kg.cm P = -1299340 kg.cm -1106560 kg.cm -978040 kg.cm chequeo de P =

As = ---- ---- ----

€ 0.01 € 0.01 € 0.01 Ku =

28.16 cm2 26.84 cm2 25.96 cm245.16 cm2 43.84 cm2 42.96 cm2

Mr = A's =

Total As = Total A's =

As1 =

Mu1 =

AD35

USER: ku=Mu/b*d^2

AD36

USER: As=P*b*d

AD37

USER: Mu1=Ku*b*d^2

AD39

USER: Mr=Mu-Mu1

AD40


AD42

USER: As=As1+A's


β =

DATOS Ø = € 0.85

viga

b = € 0.90

40 cm h = 70 cm hf = 5 cm5 cm


64 cm 61 cm 59 cm

6049000 kg.cm 6049000 kg.cm 6049000 kg.cm Ku = 210 kg/cm2 210 kg/cm2 210 kg/cm2 P =

4200 kg/cm2 4200 kg/cm2 4200 kg/cm2 As =

€ 0.02 € 0.02 € 0.02 a =

01 capa 02 capas 03 capas € 0.59 € 0.59 € 0.59 € -1.00 € -1.00 € -1.00

0.20 0.22 0.23 0.225 0.253 0.2741.470 1.442 1.421

0.0113 0.0126 0.0137SIMPLEM. REFORZADASIMPLEM. REFORZADASIMPLEM. REFORZADA

28.84 cm2 30.83 cm2 33.46 cm2 Ku =

€ 49.53 € 49.53 € 49.53 P = 41.47 cm2 39.53 cm2 38.23 cm2


-2066011.58 kg.cm -1323060.08 kg.cm -847571.12 kg.cm-9.26 cm2 -6.25 cm2 -4.15 cm2

32.21 cm2 33.28 cm2 34.08 cm2-9.26 cm2 -6.25 cm2 -4.15 cm2

bw =

sj =sj-1 =

As1 =

Mu1 =Mu2 =

As2 =

AE21


AE35


AF35


AG35


DISEÑO DE VIGA T Y L DISEÑO DE ACERO PARA VIGAS DOBLEMENTE REFORZADAS € 0.85

0.90 Ln = 6.00 m DATOS 80 cm r = 5 cm β = 40 cm d' = 5 cm Ø = 70 cm F'c = 210 kg/cm2

viga b =

10 cm F'y = 4200 kg/cm2 h = 120 cm F's = 4200 kg/cm2 r = 120 cm Mu = 5069000 kg.cm d' =


64 cm 61 cm 59 cm

15.47 17.03 18.20 Mu = 0.00488 0.00552 0.01524 f'c =

24.99 cm2 26.94 cm2 71.93 cm2 f'y =

7.35 cm 7.92 cm 21.16 cm Pmax =

VIGA RECT. VIGA RECT. a > hf == VIGA T DATOS

a = b = c =

w 1 = 17.00 cm2 17.00 cm2 17.00 cm2 w 2 =

3791340 kg.cm 3598560 kg.cm 3470040 kg.cm P = 1277660 kg.cm 1470440 kg.cm 1598960 kg.cm chequeo de P =

As = 7.80 9.88 11.48

€ 0.01 € 0.01 € 0.01 Ku =

28.16 cm2 26.84 cm2 25.96 cm245.16 cm2 43.84 cm2 42.96 cm2

Mr = A's =

Total As = Total A's =

As1 =

Mu1 =

AQ35

USER: ku=Mu/b*d^2

AQ36

USER: As=P*b*d

AQ37

USER: Mu1=Ku*b*d^2

AQ39

USER: Mr=Mu-Mu1

AQ40


AQ42

USER: As=As1+A's


β =

DATOS Ø = € 0.85

viga

b = € 0.90

40 cm h = 70 cm hf = 5 cm5 cm


64 cm 61 cm 59 cm

9076000 kg.cm 9076000 kg.cm 9076000 kg.cm Ku = 210 kg/cm2 210 kg/cm2 210 kg/cm2 P =

4200 kg/cm2 4200 kg/cm2 4200 kg/cm2 As =

€ 0.02 € 0.02 € 0.02 a =

01 capa 02 capas 03 capas € 0.59 € 0.59 € 0.59 € -1.00 € -1.00 € -1.00

0.29 0.32 0.34 0.377 0.434 0.4821.318 1.261 1.213

0.0188 0.0217 0.0241DOB.REFORZADA DOB.REFORZADA DOB.REFORZADA

48.25 cm2 52.89 cm2 58.79 cm2 Ku =

€ 49.53 € 49.53 € 49.53 P = 41.47 cm2 39.53 cm2 38.23 cm2


960988.42 kg.cm 1703939.92 kg.cm 2179428.88 kg.cm4.31 cm2 8.05 cm2 10.68 cm2

45.78 cm2 47.58 cm2 48.91 cm24.31 cm2 8.05 cm2 10.68 cm2

bw =

sj =sj-1 =

As1 =

Mu1 =Mu2 =

As2 =

AR21


AR35


AS35


AT35


DISEÑO DE VIGA T Y L

€ 0.85

0.90 Ln = 6.00 m80 cm r = 5 cm40 cm d' = 5 cm70 cm F'c = 210 kg/cm210 cm F'y = 4200 kg/cm2

120 cm F's = 4200 kg/cm2120 cm Mu = 5069000 kg.cm


15.47 17.03 18.200.00488 0.00552 0.01524

24.99 cm2 26.94 cm2 71.93 cm2

7.35 cm 7.92 cm 21.16 cm

VIGA RECT. VIGA RECT. a > hf == VIGA T

17.00 cm2 17.00 cm2 17.00 cm23791340 kg.cm 3598560 kg.cm 3470040 kg.cm1277660 kg.cm 1470440 kg.cm 1598960 kg.cm

7.80 9.88 11.48 € 0.01 € 0.01 € 0.01

28.16 cm2 26.84 cm2 25.96 cm245.16 cm2 43.84 cm2 42.96 cm2

DISEÑO DE VIGA POR TORSION

DATOS 45 cm F'c = 210 kg/cm2 15 cm F'y = 4200 kg/cm2 Ø = € 0.85

area Ø 3/8" = 0.71 cm2 60 cm 45 cm d 1 74 cm

Mu = 1132000 kg-cm Vu = 10460.40 kg 10460.40 kg 40 cm Tu = 949440 kg-cm 949440 kg-cm

Columna = 40 cm 40 cm Viga = 60 cm 40 cm

d = 54 cm

T = 15 cm COND. X < Y X = Y =

El. 01 = 40 cm 60 cm El. 02 = 15 cm 45 cm

€ 106,125.00

Tu = 169938 kg-cm

Ct = 0.02035 Tc = 300613.45 kg-cm Vc = 3510.71 kg

αt = € 1.30 <= 1.50

Ts = 816,374.79 Vs = 8,795.64 X1 € 27.00 Y1 € 52.00

X1 * Y1 € 1,404.00

Av/S = 0.0388 At/S = 0.1069

S = 5.62. cm

Cumple 5.62

Cumple5.62

Estribos @ 8.71

€ 1.00 € 0.05 € 6.00 € 0.08

AVANCE @: 0.50 m

Tu2 y Vu2 @: 1.04 m 0.50 m

ACERO LONGITUDINAL TRAMO I1

∑ X2 * Y =

Diseño por torsion transversal y longitudinal

1ra condicion S<=(X1+Y1)/4

2da condicion S<=30cm.

11

22

TS=At∗αt∗X1∗Y 1∗fy / S TS=At∗αt∗X1∗Y 1∗fy / S

B32

elmering: (Tu/Ø)-Tc

B33

elmering: (Vu/Ø)-Vc

D49

PENTIUM 4: Este valor tiene que ser >=d que es la distancia en la que se van a coloccar los estribos.

01 CAPA 02 CAPAS

16.88

Smáx 20 cm

As

1RA CONDICIÓN Al=2*At*(x1+y1)/s

AtAt<=2*Av

2da CONDICIÓN s<=(X1+y1)/5

DISEÑO DE VIGA POR TORSION

DATOS 45 cm F'c = 210 kg/cm2 F'y = 4200 kg/cm2 Ø = € 0.85

area Ø 3/8" = 0.71 cm2 60 cm 45 cm d 1 89 cm

Mu = 1263000 kg-cm Vu = 8018.35 kg 8018.35 kg 35 cm Tu = 665385 kg-cm 665385 kg-cm

Columna = 35 cm 40 cm Viga = 60 cm 35 cm

d = 54 cm

T = 15 cm COND. X < Y X = Y =

El. 01 = 35 cm 60 cm El. 02 = 15 cm 45 cm

€ 83,625.00

Tu = 133908 kg-cm

Ct = 0.02260 Tc = 237037.11 kg-cm Vc = 3027.85 kg

αt = € 1.16 <= 1.50

Ts = 545,768.77 Vs = 6,405.50 X1 € 30.00 Y1 € 45.00

X1 * Y1 € 1,350.00

Av/S = 0.0282 At/S = 0.0833

S = 7.29. cm

Cumple 7.29

Cumple7.29

Estribos @ 6.73

€ 1.00 € 0.05 € 9.00 € 0.05

AVANCE @: 0.50 m

Tu2 y Vu2 @: 1.04 m 0.50 m

ACERO LONGITUDINAL TRAMO I1

∑ X2 * Y =

Diseño por torsion transversal y longitudinal

1ra condicion S<=(X1+Y1)/4

2da condicion S<=30cm.

11

22

TS=At∗αt∗X1∗Y 1∗fy / S

L32

elmering: (Tu/Ø)-Tc

L33

elmering: (Vu/Ø)-Vc

N49

PENTIUM 4: Este valor tiene que ser >=d que es la distancia en la que se van a coloccar los estribos.

01 CAPA 02 CAPAS

12.501RA CONDICIÓN Al=2*At*(x1+y1)/s

DISEÑO DE MUROS DISEÑO DE MUROS

DATOS DATOS F'c = 210 kg/cm2 ALT. MURO = 300.00 cm F'c = F'y = 4200 kg/cm2 ESPESOR = 12.00 cm F'y = Ø = € 0.70 Ø = K = € 0.80 K = K = 1.0 K = K = 2.0 ESPESOR = 25.00 cm K = Lc = 300.00 cm SOLO UNA CAPA Lc = b = 100.00 cm b =

Pu = 78.00. Tn Pu =

TANTEANDO PARA UN ESPESOR DE MURO TANTEANDO PARA UN ESPESOR DE MURO T = 14.00 cm T =

Ag = 1400.00 cm2 Ag =

ØPnw = 80705.63 kg ØPnw = ØPnw = 80.71 tn ØPnw =

PU < ØPnw SI PASA PU < ØPnw

LUEGO DISEÑAMOS LOS ACEROS LUEGO DISEÑAMOS LOS ACEROS ACERO VERTICAL DISTRIBUCION DEL ACERO ACERO VERTICAL

N DE FILAS = S = 0.71 cm2 2.37 42.26 cm1.29 cm2 1.30 76.79 cm

P = € 0.00 Ø 3/8" @ = 40.00 cm P = As = 1.68 cm2 Ø 1/2" @ = 75.00 cm As =

LUEGO DISEÑAMOS LOS ACEROS LUEGO DISEÑAMOS LOS ACEROS ACERO HORIZONTAL DISTRIBUCION DEL ACERO ACERO HORIZONTAL

N DE FILAS = S = 0.71 cm2 3.94 25.36 cm1.29 cm2 2.17 46.07 cm

P = € 0.00 Ø 3/8" @ = 25.00 cm P = As = 2.80 cm2 Ø 1/2" @ = 45.00 cm As =

Cuando el espesor sea mayor a 25 cm debera ponerse refuerzo en las

dos caras

area Ø 3/8" = area Ø 3/8" =area Ø 1/2" = area Ø 1/2" =


F5

elmering dice: que nunca debera ser menor de 10cm.

B7

elmering dice: muros arriostrados arriba y abajo con rotacion restringida en uno de los dos apoyos

H7


B8

elmering dice: muros arriostrados arriba y abajosin rotacion restringida en los apoyos

H8


B9

elmering dice: muros sin arriostre lateral

H9


C27

elmering dice: para barras <= a 5/8" se utiliza una cuantia 0.0012 y para mayores a 5/8" 0.0015

C35


DISEÑO DE MUROS DISEÑO DE MUROS

DATOS DATOS 210 kg/cm2 ALT. MURO = 300.00 cm F'c = 210 kg/cm2

4200 kg/cm2 ESPESOR = 12.00 cm F'y = 4200 kg/cm2 € 0.70 Ø = € 0.70 € 0.80 K = € 0.80

1.0 K = 1.02.0 ESPESOR = 25.00 cm K = 2.0

300.00 cm ACERO A DOS CAPAS Lc = 300.00 cm100.00 cm b = 100.00 cm200.00. Tn Pu = 78.00. Tn

TANTEANDO PARA UN ESPESOR DE MURO TANTEANDO PARA UN ESPESOR DE MURO 27.00 cm T = 14.00 cm

2700.00 cm2 Ag = 1400.00 cm2

201451.25 kg ØPnw = 80705.63 kg201.45 tn ØPnw = 80.71 tn

SI PASA PU < ØPnw SI PASA

LUEGO DISEÑAMOS LOS ACEROS LUEGO DISEÑAMOS LOS ACEROS ACERO VERTICAL DISTRIBUCION DEL ACERO ACERO VERTICAL DISTRIBUCION DEL ACERO

N DE FILAS = S = 0.71 cm2 2.28 43.83 cm 0.71 cm21.29 cm2 1.26 79.63 cm 1.29 cm2

€ 0.00 Ø 3/8" @ = 40.00 cm P = € 0.00 Ø 3/8" @ = 1.62 cm2 Ø 1/2" @ = 75.00 cm As = 1.68 cm2 Ø 1/2" @ =

LUEGO DISEÑAMOS LOS ACEROS LUEGO DISEÑAMOS LOS ACEROS ACERO HORIZONTAL DISTRIBUCION DEL ACERO ACERO HORIZONTAL DISTRIBUCION DEL ACERO

N DE FILAS = S = 0.71 cm2 3.80 26.30 cm 0.71 cm21.29 cm2 2.09 47.78 cm 1.29 cm2

€ 0.00 Ø 3/8" @ = 25.00 cm P = € 0.00 Ø 3/8" @ = 2.70 cm2 Ø 1/2" @ = 45.00 cm As = 2.80 cm2 Ø 1/2" @ =


dos caras



L5


N7


N8


N9


I27


O27


I35


O35


DISEÑO DE MUROS

ALT. MURO = 300.00 cm ESPESOR = 12.00 cm

ESPESOR = 25.00 cm SOLO UNA CAPA

TANTEANDO PARA UN ESPESOR DE MURO

LUEGO DISEÑAMOS LOS ACEROS DISTRIBUCION DEL ACERO

N DE FILAS = S = 2.37 42.26 cm1.30 76.79 cm

Ø 3/8" @ = 40.00 cm Ø 1/2" @ = 75.00 cm

LUEGO DISEÑAMOS LOS ACEROS DISTRIBUCION DEL ACERO

N DE FILAS = S = 3.94 25.36 cm2.17 46.07 cm

Ø 3/8" @ = 25.00 cm Ø 1/2" @ = 45.00 cm


dos caras

R5


FISURACIONES POR FLEXION

DATOSEXTERIOR Z = 26000.00INTERIOR Z = 31000.00

Caso = 1Condicion = EXTERIOR

f'y = 4200.00h = 60.00b = 30.00r = 5.00

Ø 1 fila = 2.54Ø 2 fila = 1.91Ø de 3/8" 0.95

N de barras 6X1 = 4.73

PARA DOS CAPASdc = 7.22

2dc = 14.44y=dc = 7.22

A = 95.82Fs = 2520.00

Z = 22288.07

22288.07SI PASA

------NO PASA

CALCULO DE ANCHO DE GRIETA

EXTERIORWmax = 0.31

0.20SI PASA

INTERIORWmax = 0.37

0.20SI PASA

4 Ø 1"

2 Ø 3/4"

CONDICION EXTERIOR

CONDICION INTERIOR

Wmax 1ra condicion =

Wmax 2da condicion =

B4

elmering dice: Z < 26000 kg/cm2 para condiciones de exposicion exterior

B5

elmering dice: Z < 31000 kg/cm2 para condiciones de exposicion interior

C6

elmering dice: caso 1 : exterior caso 2 : interior

C11

elmering dice: para barras 5/8" y menores 4.00cm. para barras 3/4" y mayores 5.00cm.

C12

elmering dice: # ESTRIBO AREA DIAMETRO 3 3/8 0.71 CM2 0.95 CM. 4 1/2 1.27 1.27 5 5/8 1.98 1.59 6 3/4 2.85 1.91 7 1 5.07 2.54

C29

elmering dice: en el caso que no pase debera optarse por otras opciones como cambiar el diametro de acero longitudinal o la base de la viga

C31


FISURACIONES POR FLEXION FISURACIONES POR FLEXION

DATOS DATOSEXTERIOR Z = 26000.00 EXTERIOR Z = 26000.00INTERIOR Z = 31000.00 INTERIOR Z = 31000.00

Caso = 2 Caso = 1Condicion = INTERIOR Condicion = EXTERIOR

f'y = 4200.00 f'y = 4200.00h = 60.00 h = 60.00b = 30.00 b = 30.00r = 5.00 r = 5.00

Ø 1 fila = 2.54 Ø = 2.54Ø 2 fila = 1.91 Ø de 3/8" 0.95Ø de 3/8" 0.95 N de barras 3.00


PARA DOS CAPAS PARA UNA CAPAdc = 7.22 dc = 7.22

2dc = 14.44 2dc = 14.44y=dc = 7.22

A = 95.82 A = 144.40Fs = 2520.00 Fs = 2520.00

Z = 22288.07 Z = 25552.61

------ 25552.61NO PASA SI PASA22288.07 ------SI PASA NO PASA

CALCULO DE ANCHO DE GRIETA CALCULO DE ANCHO DE GRIETA

EXTERIORWmax = 0.31

EXTERIORWmax = 0.31

0.20 0.23SI PASA SI PASA

INTERIORWmax = 0.37

INTERIORWmax = 0.37


CONDICION EXTERIOR

CONDICION EXTERIOR

CONDICION INTERIOR

CONDICION INTERIOR





H4


L4


H5


L5


I6


M6


I11


M11


I12


M12


I29


M29


I31


M31




Caso = 2Condicion = INTERIOR

f'y = 4200.00h = 60.00b = 30.00r = 5.00Ø = 2.54

Ø de 3/8" 0.95N de barras 3.00

PARA UNA CAPAdc = 7.22

2dc = 14.44

A = 144.40Fs = 2520.00

Z = 25552.61

------NO PASA25552.61SI PASA


EXTERIORWmax = 0.31

0.23SI PASA

INTERIORWmax = 0.37

0.23SI PASA

2 Ø 1"

1 Ø 3/4"

CONDICION EXTERIOR

CONDICION INTERIOR



R4


R5


S6


S11


S12


S29


S31





f'y = 4200.00h = 60.00b = 30.00r = 5.00

Ø 1 fila = 2.54Ø 2 fila = 1.91Ø de 3/8" 0.95



2dc = 14.44y=dc = 7.22

A = 95.82Fs = 2520.00

Z = 22288.07

22288.07SI PASA

------NO PASA


EXTERIORWmax = 0.31

0.20SI PASA

INTERIORWmax = 0.37

0.20SI PASA

CONDICION EXTERIOR

CONDICION INTERIOR



V4


V5


W6


W11


W12


W29


W31



DATOS DATOSEXTERIOR Z = 26000.00 EXTERIOR Z =INTERIOR Z = 31000.00 INTERIOR Z =

Caso = 2 Caso =Condicion = INTERIOR Condicion =

f'y = 4200.00 f'y =h = 60.00 h =b = 30.00 b =r = 5.00 r =

Ø 1 fila = 2.54 Ø 1 fila =Ø 2 fila = 1.91 Ø 2 fila =Ø de 3/8" 0.95 Ø de 3/8"

N de barras 6 N de barrasX1 = 4.73 X1 =

PARA DOS CAPAS PARA DOS CAPASdc = 7.22 dc =

2dc = 14.44 2dc =y=dc = 7.22 y=dc =

A = 95.82 A =Fs = 2520.00 Fs =

Z = 22288.07 Z =



EXTERIORWmax = 0.31

EXTERIORWmax =

0.20SI PASA

INTERIORWmax = 0.37

INTERIORWmax =

0.20SI PASA

4 Ø 1"

2 Ø 3/4"

2 Ø 1"

CONDICION EXTERIOR

CONDICION EXTERIOR

CONDICION INTERIOR

CONDICION INTERIOR





AB4


AF4


AB5


AF5


AC6


AC11


AC12


AC29


AC31



DATOS DATOS26000.00 EXTERIOR Z =31000.00 INTERIOR Z =

1 Caso =EXTERIOR Condicion =4200.00 f'y =

60.00 h =30.00 b =5.00 r =2.54 Ø 1 fila =1.91 Ø 2 fila =0.95 Ø de 3/8"

5 N de barras4.73 X1 =

PARA DOS CAPAS PARA DOS CAPAS7.22 dc =

14.44 2dc =7.22 y=dc =

114.99 A =2520.00 Fs =

23684.61 Z =

23684.61SI PASA

------NO PASA

CALCULO DE ANCHO DE GRIETA CALCULO DE ANCHO DE GRIETA0.31

EXTERIORWmax =

0.21SI PASA

0.37INTERIOR

Wmax =

0.21SI PASA

2 Ø 3/4"

3 Ø 1"

CONDICION EXTERIOR

CONDICION INTERIOR



AL4


AL5


AG6


AG11


AG12


AG29


AG31



DATOS DATOS26000.00 EXTERIOR Z = 26000.0031000.00 INTERIOR Z = 31000.00

2 Caso = 1INTERIOR Condicion = EXTERIOR4200.00 f'y = 4200.00

60.00 h = 60.0030.00 b = 30.005.00 r = 5.002.54 Ø 1 fila = 2.541.91 Ø 2 fila = 1.910.95 Ø de 3/8" 0.95

5 N de barras 64.73 X1 = 4.73

PARA DOS CAPAS PARA DOS CAPAS7.22 dc = 7.22

14.44 2dc = 14.447.22 y=dc = 7.22

114.99 A = 95.822520.00 Fs = 2520.00

23684.61 Z = 22288.07


CALCULO DE ANCHO DE GRIETA CALCULO DE ANCHO DE GRIETA0.31

EXTERIORWmax = 0.31


0.37INTERIOR

Wmax = 0.370.21 0.20

SI PASA SI PASA

CONDICION EXTERIOR

CONDICION INTERIOR



AP4


AP5


AM6


AQ6


AM11


AQ11


AM12


AQ12


AM29


AQ29


AM31


AQ31





f'y = 4200.00h = 60.00b = 30.00r = 5.00

Ø 1 fila = 2.54Ø 2 fila = 1.91Ø de 3/8" 0.95



2dc = 14.44y=dc = 7.22

A = 95.82Fs = 2520.00

Z = 22288.07

22288.07SI PASA

------NO PASA


EXTERIORWmax = 0.31

0.20SI PASA

INTERIORWmax = 0.37

0.20SI PASA

4 Ø 1"

2 Ø 3/4"

CONDICION EXTERIOR

CONDICION INTERIOR



AV4


AV5


AW6


AW11


AW12


AW29


AW31





f'y = 4200.00h = 60.00b = 30.00r = 5.00Ø = 2.54


PARA UNA CAPAdc = 7.22

2dc = 14.44

A = 144.40Fs = 2520.00

Z = 25552.61

25552.61SI PASA

------NO PASA


EXTERIORWmax = 0.31

0.23SI PASA

INTERIORWmax = 0.37

0.23SI PASA

3 Ø 1"

CONDICION EXTERIOR

CONDICION INTERIOR



AZ4


AZ5


BA6


BA11


BA12


BA29


BA31



DATOS DATOSEXTERIOR Z = 26000.00 EXTERIOR Z = 26000.00INTERIOR Z = 31000.00 INTERIOR Z = 31000.00

Caso = 2 Caso = 1Condicion = INTERIOR Condicion = EXTERIOR

f'y = 4200.00 f'y = 4200.00h = 60.00 h = 50.00b = 30.00 b = 30.00r = 5.00 r = 4.00Ø = 2.54 Ø 1 fila = 2.54

Ø de 3/8" 0.95 Ø 2 fila = 2.54N de barras 3.00 Ø 3 fila = 2.54


PARA UNA CAPA PARA TRES CAPASdc = 7.22 dc = 6.22

2dc = 14.44 2dc = 12.44y=dc = 6.22

A = 144.40 A = 84.45Fs = 2520.00 Fs = 2520.00

Z = 25552.61 Z = 20332.80



EXTERIORWmax = 0.31

EXTERIORWmax = 0.31


INTERIORWmax = 0.37

INTERIORWmax = 0.37


CONDICION EXTERIOR

CONDICION EXTERIOR

CONDICION INTERIOR

CONDICION INTERIOR





BF4


BJ4


BF5


BJ5


BG6


BK6


BG11


BK11


BG12


BK12


BG29


BK29


BG31


BK31




Caso = 2Condicion = INTERIOR

f'y = 4200.00h = 50.00b = 30.00r = 4.00

Ø 1 fila = 2.54Ø 2 fila = 2.54Ø 3 fila = 2.54


PARA TRES CAPASdc = 6.22

2dc = 12.44y=dc = 6.22

A = 84.45Fs = 2520.00

Z = 20332.80



EXTERIORWmax = 0.31

0.20SI PASA

INTERIORWmax = 0.37

0.20SI PASA

4 Ø 1"

2 Ø 3/4"

2 Ø 3/4"

2 Ø 1"

CONDICION EXTERIOR

CONDICION INTERIOR



BP4


BP5


BQ6


BQ11


BQ12


BQ29


BQ31



DATOSEXTERIOR Z =INTERIOR Z =

Caso =Condicion =

f'y =h =b =r =Ø =

Ø de 3/8"N de barras

PARA UNA CAPAdc =

2dc =

A =Fs =

Z =

CALCULO DE ANCHE DE GRIETA

EXTERIORWmax =

INTERIORWmax =

CONDICION EXTERIOR

CONDICION INTERIOR



CF4


CF5


FISURACIONES POR FLEXION FISURACIONES POR FLEXION FISURACIONES POR FLEXION

DATOS DATOS DATOS26000.00 EXTERIOR Z = 26000.00 EXTERIOR Z =31000.00 INTERIOR Z = 31000.00 INTERIOR Z =

2.00 Caso = 1.00 Caso =INTERIOR Condicion = EXTERIOR Condicion =4200.00 f'y = 4200.00 f'y =

50.00 h = 50.00 h =30.00 b = 30.00 b =5.00 r = 5.00 r =1.59 Ø 1 fila = 2.54 Ø 1 fila =0.95 Ø 2 fila = 1.91 Ø 2 fila =2.00 Ø de 3/8" 0.95 Ø 3 fila =

N de barras 4.00 Ø de 3/8"X1 = 4.73 N de barras

PARA UNA CAPA PARA DOS CAPAS PARA TRES CAPAS6.75 dc = 7.22 dc =

13.49 2dc = 14.44 2dc =y=dc = 7.22 y=dc =

202.35 A = 143.74 A =2520.00 Fs = 2520.00 Fs =

27953.03 Z = 25513.48 Z =


CALCULO DE ANCHE DE GRIETA CALCULO DE ANCHE DE GRIETA CALCULO DE ANCHE DE GRIETA0.31

EXTERIORWmax = 0.31

EXTERIORWmax =


0.37INTERIOR

Wmax = 0.37INTERIOR

Wmax =


CONDICION EXTERIOR

CONDICION EXTERIOR

CONDICION INTERIOR

CONDICION INTERIOR





CJ4


CN4


CJ5


CN5


CG6


CK6


CG11


CK11


CG12


CK12


CG29


CK29


CG31


CK31



DATOS26000.0031000.00

1.00EXTERIOR4200.00

50.0030.004.002.542.542.54

0.956.00

PARA TRES CAPAS6.22

12.446.22

112.602520.00

22379.14

22379.14SI PASA

------NO PASA

CALCULO DE ANCHE DE GRIETA0.310.21

SI PASA0.370.21

SI PASA

CO6


CO11


CO12


CO29


CO31


DIAGRAMA DE INTERACCION

DATOSF'c = 210.00 r = 4.00 5.10 3 1F'y = 4200.00 Ø = 0.95 2.54(Ø) = 0.85 d' = 6.22As1 = 15.30 5.10 2 1As2 = 10.20 2.54As3 = 15.30

5.10 3 1SECCION DE COLUMNA 2.54

30.00 40.00

CALCULO DE CENTROIDE PLASTICOFuerza (kg) x Momento (kg-m)

Cc. = 214200.00 20.00 4284000.00AsI = 61528.95 35.00 2153513.25AsII = 41019.30 20.00 820386.00

AsIII = 61528.95 5.00 307644.75CP

378277.20 7565544.00CP = 20.00

PUNTO N 01 d = 40.00Calculo de las deformaciones unitarias

2000000.00 0.00 Є1 0.00Є1 = 0.00 F's1 = 4200.00 0.00 40.00 40.00

Є2 = 0.00 F's2 = 4200.00 0.00 Є2 0.000.00 40.00 40.00

Є3 = 0.00 F's3 = 4200.000.00 Є3 0.00

Calculamos la contribucion del concreto Dist. al CP 0.00 40.00 40.00Cc. = 214200.00 0.00

Calculamos la contribucion del acero Calculando la carga axial nominalP1 = 64260.00 15.00P2 = 42840.00 0.00

Pn1 = 385560.00P3 = 64260.00 -15.00

Calculando el momento con respecto al CP.Mcc = 0.00M1 = 963900.00

Mn1 = 0.00M2 = 0.00M3 = -963900.00

PUNTO N 03 d = 30.00Calculo de las deformaciones unitarias a = 25.50

2000000.00 0.00 Є1 0.00

F4


F7


F10


B17

Elmering dice: Cc=0.85*F'c*b*d

B18

Elmering dice: AsI=As1*(F'y-(0.85*F'c))

B19

Elmering dice: AsII=As1*(F'y-(0.85*F'c))

B20

Elmering dice: AsIII=As1*(F'y-(0.85*F'c))

B34


Є1 = 0.00 F's1 = 4200.00 0.00 25.00 30.00

Є2 = 0.00 F's2 = 2000.00 0.00 Є2 0.000.00 10.00 30.00

Є3 = 0.00 F's3 = 1000.000.00 Є3 0.00



Pn3 = 205912.50P3 = -15300.00 -15.00


Mn3 = 2183405.63M2 = 0.00M3 = 229500.00

PUNTO N 05 d = 35.00Calculos de las deformaciones unitarias a = 29.75

2000000.00 0.00 Є1 0.00Є1 = 0.00 F's1 = 4200.00 0.00 30.00 35.00

Є2 = 0.00 F's2 = 2571.43 0.00 Є2 0.000.00 15.00 35.00

Є3 = 0.00 F's3 = 857.140.00 Є3 0.00



Pn5 = 236685.54P3 = -13114.29 -15.00


Mn5 = 1976287.89M2 = 0.00M3 = 196714.29

CUADRO DE RESUMEN DISTANCIAPn1 = 385560.00 Mn1 = 0.00 40.00Pn2 = 288405.00 Mn2 = 1337985.00 40.00Pn3 = 205912.50 Mn3 = 2183405.63 30.00Pn4 = 91035.00 Mn4 = 2974702.50 20.00Pn5 = 236685.54 Mn5 = 1976287.89 35.00

B57


B80


Pn6 = 85616.25 Mn6 = 2811822.53 15.00

0.00 385560.001337985.00 288405.001976287.89 236685.542183405.63 205912.502974702.50 91035.002811822.53 85616.25

6.22

40.00

30.00

Є F'c PUNTO N 02Calculo de las deformaciones unitarias

Є1 P1 Є1 =

Є2 P2Є2 =

Є3 =

Є3 P3 Calculamos la contribucion del concretoCc. =

Calculamos la contribucion del aceroP1 =P2 =P3 =

Calculando el momento con respecto al CP.Mcc =M1 =M2 =M3 =


Є1 P1

Q34


Є125.50

P112.75

Є1 =

Є2 P2Є2 =

Є3 =





Є1 P129.75 14.88

Є1 =

Є2 P2Є2 =

Є3 =




0.00 500000.00 1000000.001500000.002000000.002500000.003000000.003500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C

Q57


Q80


0.00 500000.00 1000000.001500000.002000000.002500000.003000000.003500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C


2000000.00 0.00 Є1 0.000.00 F's1 = 4200.00 0.00 35.00 40.00

0.00 F's2 = 3000.00 0.00 Є2 0.000.00 20.00 40.00

0.00 F's3 = 750.000.00 Є3 0.00

Calculamos la contribucion del concreto Dist. al CP 0.00 5.00 40.00182070.00 3.00

Calculamos la contribucion del acero Calculando la carga axial nominal64260.00 15.0030600.00 0.00

Pn2 = 288405.0011475.00 -15.00

Calculando el momento con respecto al CP.546210.00963900.00

Mn2 = 1337985.000.00

-172125.00


2000000.00 0.00 Є1 0.00

0.00 F's1 = 4200.00 0.00 15.00 20.00

0.00 F's2 = 0.00 0.00 Є2 0.000.00 0.00 20.00

0.00 F's3 = 4200.000.00 Є3 0.00


Calculamos la contribucion del acero Calculando la carga axial nominal64260.00 15.00

0.00 0.00Pn4 = 91035.00

-64260.00 -15.00


Mn4 = 2974702.500.00

963900.00


2000000.00 0.00 Є1 0.000.00 F's1 = 4000.00 0.00 10.00 15.00

0.00 F's2 = 2000.00 0.00 Є2 0.000.00 5.00 15.00

0.00 F's3 = 4200.000.00 Є3 0.00


Calculamos la contribucion del acero Calculando la carga axial nominal61200.00 15.0020400.00 0.00

Pn6 = 85616.25-64260.00 -15.00


Mn6 = 2811822.530.00

963900.00

0.00 500000.00 1000000.001500000.002000000.002500000.003000000.003500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C

0.00 500000.00 1000000.001500000.002000000.002500000.003000000.003500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C


DATOSF'c = 210.00F'y = 4200.00(Ø) = 0.85As1 = 7.62As2 = 5.08As3 = 7.62

SECCION DE COLUMNA40.00 40.00

CALCULO DE CENTROIDE PLASTICOFuerza (kg)

Cc. = 285600.00AsI = 30643.83AsII = 20429.22

AsIII = 30643.83

367316.88CP = 20.00


Є1 P1 17.00 Є1 = 0.00

34.00Є2 P2

Є2 = 0.00

Є3 = 0.00

Є3 P3 Calculamos la contribucion del concretoCc. = 285600.00

Calculamos la contribucion del aceroP1 = 32004.00P2 = 21336.00P3 = 32004.00

Calculando el momento con respecto al CP.Mcc = 0.00M1 = 448056.00M2 = 0.00M3 = -448056.00


Є1 P18.50

AG17


AG18


AG19


AG20


AG34


Є117.00 P1 Є1 = 0.00

Є2 P2Є2 = 0.00

Є3 = 0.00


Calculamos la contribucion del aceroP1 = 32004.00P2 = 10668.00P3 = -6400.80

Calculando el momento con respecto al CP.Mcc = 1320007.50M1 = 448056.00M2 = 0.00M3 = 89611.20

Є F'c PUNTO N 05Calculos de las deformaciones unitarias

Є1 P16.38

12.75 Є1 = 0.00

Є2 P2Є2 = 0.00

Є3 = 0.00


Calculamos la contribucion del aceroP1 = 8764.04P2 = 21336.00P3 = -32004.00

Calculando el momento con respecto al CP.Mcc = 751944.24M1 = 131460.57M2 = 0.00M3 = 480060.00

CUADRO DE RESUMENPn1 = 370944.00Pn2 = 297966.90Pn3 = 218341.20Pn4 = 121380.00Pn5 = 42642.50

AG57


AG80


Pn6 = 101703.00

0.00 370944.001075523.40 297966.901363464.82 42642.501857674.70 218341.202291982.00 121380.002200016.70 101703.00


2.54 3 1

7.62 2.54 2 140.00

5.087.62

2.54 3 1

40.00

CALCULO DE CENTROIDE PLASTICOx Momento (kg-m)

20.00 5712000.0035.00 1072534.0520.00 408584.40

5.00 153219.15CP

7346337.60

d = 40.00 Є

2100000.00 0.00 Є1 0.00Є1F's1 = 4200.00 0.00 40.00 40.00

F's2 = 4200.00 0.00 Є2 0.00Є2

0.00 40.00 40.00F's3 = 4200.00

0.00 Є3 0.00Є3Dist. al CP 0.00 40.00 40.00

0.00

Calculamos la contribucion del acero Calculando la carga axial nominal14.000.00

Pn1 = 370944.00-14.00

Calculando el momento con respecto al CP.

Mn1 = 0.00

d = 30.00 Єa = 25.50

2100000.00 0.00 Є1 0.00Є1

AK4


AK7


AK10


F's1 = 4200.00 0.00 24.00 30.00 Є125.50

F's2 = 2100.00 0.00 Є2 0.00Є2

0.00 10.00 30.00F's3 = 840.00

0.00 Є3 0.00Є3Dist. al CP 0.00 4.00 30.00

7.25


Pn3 = 218341.20-14.00


Mn3 = 1857674.70

d = 7.34 Єa = 6.24

2100000.00 0.00 Є1 0.00Є1F's1 = 1150.14 0.00 1.34 7.34

6.24

F's2 = 4200.00 0.01 Є2 0.00Є2

0.00 12.66 7.34F's3 = 4200.00

0.01 Є3 0.00Є3Dist. al CP 0.00 26.66 7.34

16.88


Pn5 = 42642.50-15.00


Mn5 = 1363464.82

CUADRO DE RESUMEN DISTANCIAMn1 = 0.00 40.00Mn2 = 1075523.40 40.00Mn3 = 1857674.70 30.00Mn4 = 2291982.00 20.00Mn5 = 1363464.82 7.34

0.00

500000.00

1000000.00

1500000.00

2000000.00

2500000.00

3000000.00

3500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C

Mn6 = 2200016.70 15.00

0.00

500000.00

1000000.00

1500000.00

2000000.00

2500000.00

3000000.00

3500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C

F'c PUNTO N 02 d = 40.00Calculo de las deformaciones unitarias a = 34.00

P12100000.00 0.00

Є1 = 0.00 F's1 = 4200.00 0.00

P2Є2 = 0.00 F's2 = 3150.00 0.00

0.00Є3 = 0.00 F's3 = 945.00

P3 0.00Calculamos la contribucion del concreto Dist. al CP 0.00

Cc. = 242760.00 3.00


Pn2 = 297966.90P3 = 7200.90 -14.00


Mn2 = 1075523.40M2 = 0.00M3 = -100812.60


P12100000.00 0.00

AV34


P112.75

Є1 = 0.00 F's1 = 4200.00 0.00

P2Є2 = 0.00 F's2 = 0.00 0.00

0.00Є3 = 0.00 F's3 = 4200.00


Cc. = 121380.00 11.50


Pn4 = 121380.00P3 = -32004.00 -14.00


Mn4 = 2291982.00M2 = 0.00M3 = 448056.00


P12100000.00 0.00

3.12Є1 = 0.00 F's1 = 4200.00 0.00

P2Є2 = 0.00 F's2 = 2100.00 0.00

0.00Є3 = 0.00 F's3 = 4200.00


Cc. = 91035.00 13.62


Pn6 = 101703.00P3 = -32004.00 -15.00


Mn6 = 2200016.70M2 = 0.00M3 = 480060.00

0.00

500000.00

1000000.00

1500000.00

2000000.00

2500000.00

3000000.00

3500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C

AV57


AV80


0.00

500000.00

1000000.00

1500000.00

2000000.00

2500000.00

3000000.00

3500000.000.00

50000.00

100000.00

150000.00

200000.00

250000.00

300000.00

350000.00

400000.00

450000.00

Column C

Є F'c

Є1 0.00Є1 P1### 40.00 17.00

34.00Є2 0.00Є2 P2### 40.00

Є3 0.00Є3 P36.00 40.00

Calculando la carga axial nominal

297966.90

1075523.40

Є F'c

Є1 0.00Є1 P1

8.50

### 20.00 Є117.00 P1

Є2 0.00Є2 P20.00 20.00

Є3 0.00Є3 P3### 20.00


121380.00

2291982.00

Є F'c

Є1 0.00Є1 P1

6.38### 15.00 12.75

Є2 0.00Є2 P25.00 15.00

Є3 0.00Є3 P3### 15.00


101703.00

2200016.70

ACEROS DIAMETRO DE BARRA SECCION PERIMETRO PESO F'c = 350.00

pulgadas cm. cm kg/m F'y = 4200.003/8" 0.95 0.71 2.99 0.56 pb = 0.031/2" 1.27 1.29 3.99 0.995/8" 1.59 1.99 4.99 1.553/4" 1.91 2.84 5.98 2.24

1" 2.54 5.10 7.98 3.971 3/8" 3.49 10.06 11.25 7.91

r = 4.00e = 2.50

(cm2)

F'c = 280.00 F'c = 210.00 F'c = 175.00

F'y = 4200.00 F'y = 4200.00 F'y = 4200.00pb = 0.03 pb = 0.03 pb = 0.03

P Ku P Ku P Ku0.02 66.04 0.02 49.53 0.01 41.040.02 65.37 0.02 49.06 0.01 40.570.02 65.10 0.02 48.59 0.01 40.090.02 64.63 0.02 48.11 0.01 39.610.02 64.15 0.02 47.63 0.01 39.130.02 63.67 0.02 47.15 0.01 38.640.02 63.19 0.02 46.66 0.01 38.150.02 62.71 0.01 46.17 0.01 37.640.02 62.22 0.01 45.68 0.01 37.150.02 61.73 0.01 45.18 0.01 36.650.02 61.24 0.01 44.68 0.01 36.140.02 60.74 0.01 44.18 0.01 35.620.02 60.24 0.01 43.67 0.01 35.100.02 59.74 0.01 43.16 0.01 34.580.02 59.24 0.01 42.64 0.01 34.050.02 58.73 0.01 42.12 0.01 33.520.02 58.23 0.01 41.60 0.01 32.990.02 57.72 0.01 41.08 0.01 32.450.02 57.20 0.01 40.55 0.01 31.900.02 56.68 0.01 40.01 0.01 31.360.02 56.17 0.01 39.48 0.01 30.800.02 55.64 0.01 38.94 0.01 30.250.02 55.12 0.01 38.39 0.01 29.680.02 54.59 0.01 37.85 0.01 29.120.02 54.06 0.01 37.29 0.01 28.550.02 53.53 0.01 36.24 0.01 27.980.02 52.99 0.01 36.18 0.01 27.400.02 52.46 0.01 35.62 0.01 26.810.02 51.92 0.01 35.06 0.01 26.230.02 51.37 0.01 34.49 0.01 25.640.02 50.83 0.01 33.92 0.01 25.040.02 50.28 0.01 33.34 0.01 24.440.02 49.73 0.01 32.76 0.01 23.840.02 49.17 0.01 32.18 0.01 23.230.01 48.62 0.01 31.39 0.01 22.620.01 48.06 0.01 31.00 0.01 22.000.01 47.50 0.01 30.41 0.01 21.380.01 46.93 0.01 29.81 0.01 20.750.01 46.36 0.01 29.21 0.01 20.120.01 45.79 0.01 28.60 0.01 19.490.01 45.22 0.01 28.00 0.01 18.850.01 44.65 0.01 27.39 0.01 18.210.01 44.07 0.01 26.77 0.01 17.560.01 43.49 0.01 26.15 0.00 16.910.01 42.90 0.01 25.53 0.00 16.260.01 42.32 0.01 24.90 0.00 15.600.01 41.73 0.01 24.27 0.00 14.930.01 41.14 0.01 23.64 0.00 14.26

0.01 40.54 0.01 23.01 0.00 13.590.01 39.95 0.01 22.37 0.00 12.910.01 39.35 0.01 21.72 0.00 12.230.01 38.74 0.01 21.07 0.00 11.550.01 38.14 0.01 20.42 0.00 10.860.01 37.53 0.01 19.77 0.00 10.160.01 36.92 0.01 19.11 0.00 9.470.01 36.31 0.01 18.45 0.00 8.760.01 35.69 0.01 17.78 0.00 8.060.01 35.08 0.00 17.12 0.00 7.350.01 34.45 0.00 16.44 0.00 6.630.01 33.83 0.00 15.77 0.00 5.910.01 33.21 0.00 15.09 0.00 5.190.01 32.58 0.00 14.41 0.00 4.460.01 31.94 0.00 13.72 0.00 3.730.01 31.31 0.00 13.03 0.00 2.990.01 30.67 0.00 12.34 0.00 2.250.01 30.03 0.00 11.64 0.00 1.500.01 29.39 0.00 10.94 0.00 0.750.01 28.75 0.00 10.23 0.00 0.000.01 28.10 0.00 9.530.01 27.45 0.00 8.820.01 26.80 0.00 8.100.01 26.14 0.00 7.380.01 25.48 0.00 6.660.01 24.82 0.00 5.930.01 24.16 0.00 5.200.01 23.49 0.00 4.470.01 22.82 0.00 3.740.01 22.15 0.00 3.000.01 21.48 0.00 2.250.01 20.80 0.00 1.500.01 20.12 0.00 0.750.01 19.44 0.00 0.000.01 18.750.01 18.060.00 17.370.00 16.680.00 15.980.00 15.290.00 14.580.00 13.880.00 13.170.00 12.470.00 11.750.00 11.040.00 10.320.00 9.600.00 8.880.00 8.150.00 7.430.00 6.700.00 5.960.00 5.230.00 4.490.00 3.750.00 3.00

0.00 2.260.00 1.510.00 0.750.00 0.00

INTERPOLANDOP Ku

d = 0.02 a = 47.63x = 0.02 b = 47.28e = 0.02 c = 47.15

x = 0.02

T12

USER: x=e+(((b-c)/(a-c))*(d-e))

TABLA Ku VS ρ

f'c 280.00 f'c 210.00 f'cfy 4200.00 fy 4200.00 fypb 0.03 pb 0.02 pb

ρ Ku ρ Ku ρ

0.02 66.04 0.02 49.53 0.010.02 65.57 0.02 49.06 0.010.02 65.10 0.02 48.59 0.010.02 64.63 0.02 48.11 0.010.02 64.15 0.02 47.63 0.010.02 63.67 0.02 47.15 0.010.02 63.19 0.02 46.66 0.010.02 62.71 0.01 46.17 0.010.02 62.22 0.01 45.68 0.010.02 61.73 0.01 45.18 0.010.02 61.24 0.01 44.68 0.010.02 60.74 0.01 44.18 0.010.02 60.24 0.01 43.67 0.010.02 59.74 0.01 43.16 0.010.02 59.24 0.01 42.64 0.010.02 58.73 0.01 42.12 0.010.02 58.23 0.01 41.60 0.010.02 57.72 0.01 41.08 0.010.02 57.20 0.01 40.55 0.010.02 56.68 0.01 40.01 0.010.02 56.17 0.01 37.48 0.010.02 55.64 0.01 38.94 0.010.02 55.12 0.01 38.39 0.010.02 54.59 0.01 37.85 0.010.02 54.06 0.01 37.29 0.010.02 53.33 0.01 36.74 0.010.02 52.98 0.01 36.18 0.010.02 52.46 0.01 35.62 0.010.02 51.92 0.01 35.06 0.010.02 51.37 0.01 34.49 0.010.02 50.83 0.01 33.92 0.010.02 50.28 0.01 33.34 0.010.02 49.73 0.01 32.76 0.010.01 49.17 0.01 32.18 0.010.01 48.62 0.01 31.57 0.010.01 48.06 0.01 31.00 0.010.01 47.50 0.01 30.41 0.010.01 46.93 0.01 29.81 0.010.01 46.36 0.01 29.21 0.010.01 45.79 0.01 28.60 0.010.01 45.22 0.01 28.00 0.010.01 44.65 0.01 27.39 0.010.01 44.07 0.01 26.77 0.000.01 43.49 0.01 26.15 0.000.01 42.90 0.01 25.53 0.000.01 42.32 0.01 24.80 0.000.01 41.73 0.01 24.27 0.00

0.01 41.14 0.01 23.64 0.000.01 40.54 0.01 23.01 0.000.01 37.92 0.01 22.37 0.000.01 38.35 0.01 21.72 0.000.01 38.74 0.01 21.07 0.000.01 38.14 0.01 20.42 0.000.01 37.33 0.01 19.77 0.000.01 36.92 0.01 19.11 0.000.01 36.31 0.01 18.45 0.000.01 35.69 0.01 17.78 0.000.01 35.08 0.00 17.12 0.000.01 34.45 0.00 16.44 0.000.01 33.83 0.00 15.77 0.000.01 33.21 0.00 15.09 0.000.01 32.58 0.00 14.40 0.000.01 31.94 0.00 13.72 0.000.01 31.31 0.00 13.03 0.000.01 30.67 0.00 12.34 0.000.01 30.03 0.00 11.64 0.000.01 29.39 0.00 10.94 0.000.01 28.75 0.00 10.23 0.000.01 28.10 0.00 9.530.01 27.45 0.00 8.820.01 26.80 0.00 8.100.01 26.14 0.00 7.380.01 25.48 0.00 6.660.01 24.82 0.00 5.930.01 24.16 0.00 5.200.01 23.49 0.00 4.470.01 22.82 0.00 3.740.01 22.15 0.00 3.000.01 21.48 0.00 2.250.01 20.80 0.00 1.500.01 20.12 0.00 0.750.01 19.44 0.00 0.000.01 18.750.00 18.060.00 17.370.00 16.680.00 15.980.00 15.290.00 14.580.00 13.880.00 13.170.00 12.470.00 11.750.00 11.040.00 10.320.00 9.600.00 8.880.00 8.150.00 7.430.00 6.700.00 5.960.00 5.230.00 4.490.00 3.72

0.00 3.000.00 2.260.00 1.510.00 0.750.00 0.00

TABLA Ku VS ρ

175.004200.00

0.02

KuKu Ku

41.04 0.01 49.00 0.02 49.00 0.0240.57 0.01 49.00 0.02 49.00 0.0240.09 0.01 49.00 0.02 49.00 0.0239.61 0.01 49.00 0.02 49.00 0.0239.13 0.01 49.00 0.02 47.25 0.0238.64 0.01 49.00 0.02 49.00 0.0238.15 0.01 49.00 0.01 46.50 0.0237.65 0.01 49.00 0.02 49.00 0.0237.15 0.01 49.00 0.02 49.00 0.0236.65 0.01 49.00 0.02 49.00 0.0236.14 0.01 49.00 0.01 44.46 0.0235.62 0.01 49.00 0.02 49.00 0.0235.10 0.01 49.00 0.01 43.62 0.0234.58 0.01 49.00 0.02 49.00 0.0234.05 0.01 49.00 0.02 49.00 0.0233.52 0.01 49.00 0.01 42.00 0.0232.99 0.01 49.00 0.02 49.00 0.0232.45 0.01 49.00 0.02 49.00 0.0231.90 0.01 49.00 0.02 49.00 0.0231.36 0.01 49.00 0.01 49.00 0.0230.80 0.01 49.00 0.01 49.00 0.0230.24 0.01 49.00 0.01 38.91 0.0229.68 0.01 49.00 0.02 49.00 0.0229.12 0.01 49.00 0.01 37.40 0.0228.55 0.02 49.00 0.02 49.00 0.0227.98 0.01 49.00 0.02 49.00 0.0227.40 0.01 49.00 0.02 49.00 0.0226.81 0.01 49.00 0.02 49.00 0.0226.23 0.01 49.00 0.01 34.58 0.0225.64 0.01 49.00 0.02 49.00 0.0225.04 0.01 49.00 0.02 49.00 0.0224.44 0.01 49.00 0.02 49.00 0.0223.84 0.01 49.00 0.02 49.00 0.0223.23 0.01 49.00 0.02 49.00 0.0222.62 0.01 49.00 0.01 31.12 0.0222.00 0.01 49.00 0.02 49.00 0.0221.38 0.01 49.00 0.02 49.00 0.0220.75 0.01 49.00 0.01 29.54 0.0120.12 0.01 49.00 0.01 28.90 0.0119.49 0.01 49.00 0.02 49.00 0.0118.85 0.01 49.00 0.01 27.84 0.0118.21 0.01 49.00 0.02 49.00 0.0117.56 0.01 49.00 0.01 49.00 0.0116.91 0.01 49.00 0.01 25.77 0.0116.26 0.01 49.00 0.01 24.83 0.0115.60 0.01 49.00 0.02 49.00 0.0114.93 0.01 49.00 0.01 49.00 0.01

x = ρ x = ρ x = ρ

14.26 0.01 49.00 0.01 49.00 0.0113.59 0.01 49.00 0.01 49.00 0.0112.91 0.01 49.00 0.01 21.73 0.0112.23 0.01 49.00 0.01 49.00 0.0111.55 0.01 49.00 0.01 49.00 0.0110.86 0.01 49.00 0.01 49.00 0.0110.16 0.02 49.00 0.01 19.49 0.019.47 0.01 49.00 0.01 49.00 0.018.76 0.01 49.00 0.01 18.04 0.018.06 0.01 49.00 0.00 17.38 0.017.35 0.01 49.00 0.01 49.00 0.016.63 0.01 49.00 0.01 49.00 0.015.91 0.01 49.00 0.00 15.11 0.015.19 0.01 49.00 0.01 49.00 0.014.46 0.01 49.00 0.01 49.00 0.013.73 0.01 49.00 0.01 49.00 0.012.99 0.01 49.00 0.01 49.00 0.012.25 0.01 49.00 0.01 49.00 0.011.50 0.01 49.00 0.01 49.00 0.010.75 0.01 49.00 0.01 49.00 0.010.00 0.01 49.00 0.01 49.00 #DIV/0!

0.01 49.00 0.01 49.000.01 49.00 0.00 8.550.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.01 49.000.01 49.00 0.00 1.410.01 49.00 0.01 49.000.01 49.00 #DIV/0! 49.000.01 49.000.01 49.000.01 49.000.00 16.060.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.00 7.600.01 49.000.01 49.000.01 49.000.01 49.000.01 49.000.01 49.00

0.01 49.000.01 49.000.00 1.260.01 49.000.00 49.00

Ku49.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.00

49.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.0049.00

CALCULO DE CENTRO PLASTICO r = 6.25 area Cant. Acero area Cant. Acero

DATOS As1 = 20.40 d1' = 63.75 5.10 4 1 5.10 0

F'c = 280.00 kg/cm2 As2 = 10.20 d2' = 55.54 5.10 2 1 5.10 0

F'y = 4200.00 kg/cm2 As3 = 10.20 d3 = 47.32 5.10 2 1 5.10 0

(Ø) = 0.85 As4 = 10.20 d4' = 39.11 5.10 2 1 5.10 0

SECCION DE COLUMNA As5 = 10.20 d5' = 30.89 5.10 2 1 5.10 0

60.00 70.00 As6 = 10.20 d6' = 22.68 5.10 2 1 5.10 0

1

N. de capas de acero 4-11 As7 = 10.20 d7' = 14.46 5.10 2 1 5.10 0

8.00 As8 = 10.20 d8' = 0.00 5.10 2 1 5.10 0

19.17 11.50 As9 = 10.20 d9' = 0.00 5.10 2 1 5.10 0

8.21 6.39 As10 = 10.20 d10' = 0.00 5.10 2 1 5.10 0

0.00 0.00 As11 = 20.40 d11' = 6.25 5.10 4 1 5.10 0

0.00 0.00

8.21 0.00

0.00 0.00

8.21 CALCULO DE CENTROIDE PLASTICO

Fuerza (kg) x Momento (kg-m)

Cc1. = 999600.00 35.00 34986000.00

AsI = 80824.80 63.75 5152581.00

AsII = 40412.40 55.54 2244331.50

AsIII = 40412.40 47.32 1912372.50

AsIV = 40412.40 39.11 1580413.50

AsV = 40412.40 30.89 1248454.50

AsVI = 40412.40 22.68 916495.50

AsVII = 40412.40 14.46 584536.50

AsVIII = 0.00 0.00 0.00

AsIX = 0.00 0.00 0.00

AsX = 0.00 0.00 0.00

AsXI = 80824.80 6.25 505155.00

1403724.00 49130340.00

CP = 35.00

PUNTO N 01 d = 70.00 SECCION DE COLUMNA

F'c = 280.00 kg/cm2 D = 70.00 60 cm 70 cm

F'y = 4200.00 kg/cm2 a = 70.00 d' = 0.0. cm % de h = 100.00 %

CP = 35.00 Calculo de las deformaciones unitarias 2000000.00 Є1 0.003

DIAGRAMA DEINTERACCION DE UNA COLUMNA RECTANGULARDIAGRAMA DEINTERACCION DE UNA COLUMNA RECTANGULAR

ITERACIONES PARA EL DIAGRAMAITERACIONES PARA EL DIAGRAMA

AM6


AP6


F7


U7


AM7


AP7


AM8


AP8


U9


AM9


AP9


F10


AM10


AP10


U11


F13


U13


Q19


B20


Q20


B21


Q21


B22


Q22


AJ22


B23


Q23


AJ23


AJ24


AJ25


AJ26


AJ27


B41


Q43


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0030 70.00

As2 = 10.20 d2' = 55.54 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 70.00

As3 = 10.20 d3 = 47.32 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 70.00

As4 = 10.20 d4' = 39.11 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 70.00

As5 = 10.20 d5' = 30.89 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0030 70.00

As6 = 10.20 d6' = 22.68 Є6 = 0.0021 F's6 = 4200.00 0.0021 0.0030 70.00

As7 = 10.20 d7' = 14.46 Є7 = 0.0021 F's7 = 4200.00 0.0021 0.0030 70.00

As8 = 10.20 d8' = 0.00 Є8 = 0.0021 F's8 = 4200.00 0.0021 0.0030 70.00

As9 = 10.20 d9' = 0.00 Є9 = 0.0021 F's9 = 4200.00 0.0021 0.0030 70.00

As10 = 10.20 d10' = 0.00 Є10 = 0.0021 F's10 = 4200.00 0.0021 0.0030 70.00

As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.0021 0.0030 70.00

Calculamos la contribucion del concreto Dist. al CP

Cc1. = 999600.00 0.00 Mcc = 0.00

Calculamos la contribucion del acero Carga Nominal Momento con respecto al CP. M. Nominal

P1 85680.00 28.75

1556520.00 kg

M1 2463300.00

-4498200.00 kg.cm

P2 42840.00 20.54 M2 879750.00

P3 42840.00 12.32 M3 527850.00

P4 42840.00 4.11 M4 175950.00

P5 42840.00 -4.11 M5 -175950.00

P6 42840.00 -12.32 M6 -527850.00

P7 42840.00 -20.54 M7 -879750.00

P8 42840.00 -35.00 M8 -1499400.00

P9 42840.00 -35.00 M9 -1499400.00

P10 42840.00 -35.00 M10 -1499400.00

P11 85680.00 -28.75 M11 -2463300.00


F'c = 280.00 kg/cm2 D = 70.00 60 cm 70 cm

F'y = 4200.00 kg/cm2 a = 59.50 d' = 0.0. cm % de h = 100.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0027 63.75

As2 = 10.20 d2' = 55.54 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 70.00

As3 = 10.20 d3 = 47.32 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 70.00

As4 = 10.20 d4' = 39.11 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 70.00

As5 = 10.20 d5' = 30.89 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0024 55.54

As6 = 10.20 d6' = 22.68 Є6 = 0.0021 F's6 = 4200.00 0.0021 0.0020 47.32

As7 = 10.20 d7' = 14.46 Є7 = 0.0017 F's7 = 3352.04 0.0017 0.0017 39.11

As8 = 10.20 d8' = 0.00 Є8 = 0.0013 F's8 = 2647.96 0.0013 0.0013 30.89

As9 = 10.20 d9' = 0.00 Є9 = 0.0010 F's9 = 1943.88 0.0010 0.0010 22.68

As10 = 10.20 d10' = 0.00 Є10 = 0.0006 F's10 = 1239.80 0.0006 0.0006 14.46

As11 = 20.40 d11' = 6.25 Є11 = 0.0003 F's4 = 535.71 0.0003 0.0003 6.25


Cc. = 849660.00 5.25 Mcc = 4460715.00


AG58


B72


Q74


AG90


P1 85680.00 28.75

1135176.73 kg

M1 2463300.00

4705542.88 kg.cm

P2 42840.00 20.54 M2 879750.00P3 42840.00 12.32 M3 527850.00

P4 42840.00 4.11 M4 175950.00

P5 42840.00 -4.11 M5 -175950.00

P6 42840.00 -12.32 M6 -527850.00

P7 34190.82 -20.54 M7 -702132.84

P8 -27009.18 -35.00 M8 -945321.43

P9 -19827.55 -35.00 M9 -693964.29

P10 -12645.92 -35.00 M10 -442607.14

P11 10928.57 -28.75 M11 -314196.43


F'c = 280.00 kg/cm2 D = 70.00 60 cm 70 cm

F'y = 4200.00 kg/cm2 a = 47.60 d' = 14.0. cm % de h = 80.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0027 49.75

As2 = 10.20 d2' = 55.54 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 56.00

As3 = 10.20 d3 = 47.32 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 56.00

As4 = 10.20 d4' = 39.11 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 56.00

As5 = 10.20 d5' = 30.89 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0022 41.54

As6 = 10.20 d6' = 22.68 Є6 = 0.0018 F's6 = 3570.15 0.0018 0.0018 33.32

As7 = 10.20 d7' = 14.46 Є7 = 0.0013 F's7 = 2690.05 0.0013 0.0013 25.11

As8 = 10.20 d8' = 0.00 Є8 = 0.0009 F's8 = 1809.95 0.0009 0.0009 16.89

As9 = 10.20 d9' = 0.00 Є9 = 0.0005 F's9 = 929.85 0.0005 0.0005 8.68

As10 = 10.20 d10' = 0.00 Є10 = 0.0000 F's10 = 49.74 0.0000 0.0000 0.46

As11 = 20.40 d11' = 6.25 Є11 = 0.0004 F's4 = 830.36 0.0004 0.0004 7.75


Cc. = 679728.00 11.20 Mcc = 7612953.60


P1 85680.00 28.75

955229.48 kg

M1 2463300.00

8988821.71 kg.cm

P2 42840.00 20.54 M2 879750.00

P3 42840.00 12.32 M3 527850.00

P4 42840.00 4.11 M4 175950.00

P5 42840.00 -4.11 M5 -175950.00

P6 36415.56 -12.32 M6 -448691.74

P7 27438.52 -20.54 M7 -563469.62

P8 -18461.48 -35.00 M8 -646151.79

P9 -9484.44 -35.00 M9 -331955.36

P10 -507.40 -35.00 M10 -17758.93

P11 -16939.29 -28.75 M11 -487004.46


B101


Q103


AG122


B130


Q132


F'c = 280.00 kg/cm2 D = 70.00 60 cm 70 cm

F'y = 4200.00 kg/cm2 a = 35.70 d' = 28 cm % de h = 60.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0026 35.75

As2 = 10.20 d2' = 55.54 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 42.00

As3 = 10.20 d3 = 47.32 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 42.00

As4 = 10.20 d4' = 39.11 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 42.00

As5 = 10.20 d5' = 30.89 Є5 = 0.0020 F's5 = 3933.67 0.0020 0.0020 27.54

As6 = 10.20 d6' = 22.68 Є6 = 0.0014 F's6 = 2760.20 0.0014 0.0014 19.32

As7 = 10.20 d7' = 14.46 Є7 = 0.0008 F's7 = 1586.73 0.0008 0.0008 11.11

As8 = 10.20 d8' = 0.00 Є8 = 0.0002 F's8 = 413.27 0.0002 0.0002 2.89

As9 = 10.20 d9' = 0.00 Є9 = 0.0004 F's9 = 760.20 0.0004 0.0004 5.32

As10 = 10.20 d10' = 0.00 Є10 = 0.0010 F's10 = 1933.67 0.0010 0.0010 13.54As11 = 20.40 d11' = 6.25 Є11 = 0.0016 F's4 = 3107.14 0.0016 0.0016 21.75


Cc. = 509796.00 17.15 Mcc = 8743001.40


P1 85680.00 28.75

624702.12 kg

M1 2463300.00

9014206.54 kg.cm

P2 42840.00 20.54 M2 879750.00

P3 42840.00 12.32 M3 527850.00

P4 42840.00 4.11 M4 175950.00

P5 40123.47 -4.11 M5 -164792.82

P6 -28154.08 -12.32 M6 -346898.51

P7 -16184.69 -20.54 M7 -332364.25

P8 -4215.31 -35.00 M8 -147535.71

P9 -7754.08 -35.00 M9 -271392.86

P10 -19723.47 -35.00 M10 -690321.43

P11 -63385.71 -28.75 M11 -1822339.29


F'c = 280.00 kg/cm2 D = 70.00 60 cm 70 cm

F'y = 4200.00 kg/cm2 a = 23.80 d' = 42 cm % de h = 40.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0023 21.75

As2 = 10.20 d2' = 55.54 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 28.00

As3 = 10.20 d3 = 47.32 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 28.00

As4 = 10.20 d4' = 39.11 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 28.00

As5 = 10.20 d5' = 30.89 Є5 = 0.0015 F's5 = 2900.51 0.0015 0.0015 13.54

As6 = 10.20 d6' = 22.68 Є6 = 0.0006 F's6 = 1140.31 0.0006 0.0006 5.32

As7 = 10.20 d7' = 14.46 Є7 = 0.0003 F's7 = 619.90 0.0003 0.0003 2.89

As8 = 10.20 d8' = 0.00 Є8 = 0.0012 F's8 = 2380.10 0.0012 0.0012 11.11

As9 = 10.20 d9' = 0.00 Є9 = 0.0021 F's9 = 4200.00 0.0021 0.0021 19.32

As10 = 10.20 d10' = 0.00 Є10 = 0.0021 F's10 = 4200.00 0.0021 0.0030 27.54

AG154


B159


Q161


As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.0021 0.0038 35.75


Cc. = 339864.00 23.10 Mcc = 7850858.40


P1 85680.00 28.75

225207.67 kg

M1 2463300.00

5191242.78 kg.cm

P2 42840.00 20.54 M2 879750.00

P3 42840.00 12.32 M3 527850.00

P4 -42840.00 4.11 M4 175950.00

P5 -29585.20 -4.11 M5 -121510.66

P6 -11631.12 -12.32 M6 -143312.04

P7 -6322.96 -20.54 M7 -129846.48

P8 -24277.04 -35.00 M8 -849696.43

P9 -42840.00 -35.00 M9 -1499400.00

P10 -42840.00 -35.00 M10 -1499400.00

P11 -85680.00 -28.75 M11 -2463300.00


F'c = 280.00 kg/cm2 D = 70.00 60 cm 70 cm

F'y = 4200.00 kg/cm2 a = 11.90 d' = 56 cm % de h = 20.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0017 F's1 = 3321.43 0.0017 0.0017 7.75

As2 = 10.20 d2' = 55.54 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 14.00

As3 = 10.20 d3 = 47.32 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 14.00

As4 = 10.20 d4' = 39.11 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 14.00

As5 = 10.20 d5' = 30.89 Є5 = 0.0001 F's5 = 198.98 0.0001 0.0001 0.46

As6 = 10.20 d6' = 22.68 Є6 = 0.0019 F's6 = 3719.39 0.0019 0.0019 8.68

As7 = 10.20 d7' = 14.46 Є7 = 0.0021 F's7 = 4200.00 0.0021 0.0036 16.89

As8 = 10.20 d8' = 0.00 Є8 = 0.0021 F's8 = 4200.00 0.0021 0.0054 25.11

As9 = 10.20 d9' = 0.00 Є9 = 0.0021 F's9 = 4200.00 0.0021 0.0071 33.32

As10 = 10.20 d10' = 0.00 Є10 = 0.0021 F's10 = 4200.00 0.0021 0.0089 41.54

As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.0021 0.0107 49.75


Cc. = 169932.00 29.05 Mcc = 4936524.60


P1 67757.14 28.75

-187838.20 kg

M1 1948017.86

151059.29 kg.cm

P2 -42840.00 20.54 M2 879750.00

P3 -42840.00 12.32 M3 527850.00

P4 -42840.00 4.11 M4 175950.00

P5 -2029.59 -4.11 M5 -8335.82

P6 -37937.76 -12.32 M6 -467447.34

P7 -42840.00 -20.54 M7 -879750.00

P8 -42840.00 -35.00 M8 -1499400.00

P9 -42840.00 -35.00 M9 -1499400.00

AG186


Q190


AG218


Q219


P10 -42840.00 -35.00

-187838.20 kg

M10 -1499400.00

151059.29 kg.cm

P11 -85680.00 -28.75 M11 -2463300.00


F'c = 280.00 kg/cm2 D = 70.00 60 cm 70 cm

F'y = 4200.00 kg/cm2 a = 0.00 d' = 70.0. cm % de h = 0.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.00 26785.71 6.25

As2 = 10.20 d2' = 55.54 Є2 = 0.0021 F's2 = 4200.00 0.00 0.00 0.00

As3 = 10.20 d3 = 47.32 Є3 = 0.0021 F's3 = 4200.00 0.00 0.00 0.00

As4 = 10.20 d4' = 39.11 Є4 = 0.0021 F's4 = 4200.00 0.00 0.00 0.00

As5 = 10.20 d5' = 30.89 Є5 = 0.0021 F's5 = 4200.00 0.00 61989.79 14.46

As6 = 10.20 d6' = 22.68 Є6 = 0.0021 F's6 = 4200.00 0.00 97193.87 22.68

As7 = 10.20 d7' = 14.46 Є7 = 0.0021 F's7 = 4200.00 0.00 132397.96 30.89

As8 = 10.20 d8' = 0.00 Є8 = 0.0021 F's8 = 4200.00 0.00 167602.04 39.11

As9 = 10.20 d9' = 0.00 Є9 = 0.0021 F's9 = 4200.00 0.00 202806.12 47.32

As10 = 10.20 d10' = 0.00 Є10 = 0.0021 F's10 = 4200.00 0.00 238010.20 55.54

As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.00 273214.28 63.75


Cc. = 0.01 35.00 Mcc = 0.30


P1 -85680.00 28.75

-556919.99 kg

M1 2463300.00

-4498199.70 kg.cm

P2 -42840.00 20.54 M2 879750.00

P3 -42840.00 12.32 M3 527850.00

P4 -42840.00 4.11 M4 175950.00

P5 -42840.00 -4.11 M5 -175950.00

P6 -42840.00 -12.32 M6 -527850.00

P7 -42840.00 -20.54 M7 -879750.00

P8 -42840.00 -35.00 M8 -1499400.00

P9 -42840.00 -35.00 M9 -1499400.00

P10 -42840.00 -35.00 M10 -1499400.00

P11 -85680.00 -28.75 M11 -2463300.00

Con carga nominal del 100% Afectada por el Fi del 0.70

CUADRO DE RESUMEN DISTANCIA CUADRO DE RESUMEN DISTANCIA

Tn-m Tn cm Tn-m Tn cm

Mn1 = -4498200.00 1556520.00 Pn1 = 70.00 Mn1 = -3148740.00 1089564.00 Pn1 = 70.00

Mn2 = 4705542.88 1135176.73 Pn2 = 70.00 Mn2 = 3293880.02 794623.71 Pn2 = 70.00

Mn3 = 8988821.71 955229.48 Pn3 = 56.00 Mn3 = 6292175.20 668660.64 Pn3 = 56.00

Mn4 = 9014206.54 624702.12 Pn4 = 42.00 Mn4 = 6309944.58 437291.49 Pn4 = 42.00

Mn5 = 5191242.78 225207.67 Pn5 = 28.00 Mn5 = 3633869.95 157645.37 Pn5 = 28.00

Mn6 = 151059.29 -187838.20 Pn6 = 14.00 Mn6 = 105741.51 -131486.74 Pn6 = 14.00

Mn7 = -4498199.70 -556919.99 Pn7 = 0.00 Mn7 = -3148739.79 -389843.99 Pn7 = 0.00

AG250


0.00 1000000.00 2000000.00 3000000.00 4000000.00 5000000.00 6000000.00 7000000.00 8000000.00 9000000.00

-800000.00

-600000.00

-400000.00

-200000.00

0.00

200000.00

400000.00

600000.00

800000.00

1000000.00

1200000.00

Carga nominalLinear (Carga nominal)Afectado por 0.70Linear (Afectado por 0.70)

Momentos (Tn-m)

Carg

as P

untu

ale

s (

Tn)

0.00 1000000.00 2000000.00 3000000.00 4000000.00 5000000.00 6000000.00 7000000.00 8000000.00 9000000.00

-800000.00

-600000.00

-400000.00

-200000.00

0.00

200000.00

400000.00

600000.00

800000.00

1000000.00

1200000.00

Carga nominal

Afectado por 0.70

Momentos (Tn-m)

Carg

as P

untu

ale

s (

Tn)


CENTRO PLASTICO COLUMNA TIPO "ELE"Cant. Acero CALCULO DE CENTRO PLASTICO

1

70.00

DATOS

1 F'c =

1 F'y =

1 (Ø) =

1 SECCION DE COLUMNA

1 30 cm

1 100 cm

1

1

2 o 3 capas

1 0

1 50.00

1 ---

60.00

2

2 o 3 capas

2

20.00

20.00

CP 35.00

PUNTO N 01

F'c =

F'y =

Є


ITERACIONES PARA EL DIAGRAMAITERACIONES PARA EL DIAGRAMA

70.000

70.00 cm 70.00 cm

P1 +1

35.00 cm

As1 =

70.000 P2 +1 As2 =

70.000 P3 +1 As3 =

70.000 P4 +1 As4 =

70.000 P5 +1 As5 =

70.000 P6 +1 As6 =

70.000 P7 +1 As7 =

70.000 P8 -1 As8 =

70.000 P9 -1 As9 =

70.000 P10 -1 As10 =

70.000 P11 +1

Calculamos la contribucion del concreto

Cc1. =

Calculamos la contribucion del acero

P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

PUNTO N 02

F'c =

F'y =

Є

70.000

70.00 cm 59.50 cm

P1 +1

29.75 cm

As1 =

70.000 P2 +1 As2 =

70.000 P3 +1 As3 =

70.000 P4 +1 As4 =

70.000 P5 +1 As5 =

70.000 P6 +1 As6 =

70.000 P7 +1 As7 =

70.000 P8 -1 As8 =

70.000 P9 -1 As9 =

70.000 P10 -1 As10 =

70.000 P11 +1


Cc. =


BF58


BF90


P1

P2P3

P4

P5

P6

P7

P8

P9

P10

PUNTO N 03F'c =

F'y =

Є

56.000

56.00 cm 47.60 cm

P1 +1

23.80 cm

As1 =

56.000 P2 +1 As2 =

56.000 P3 +1 As3 =

56.000 P4 +1 As4 =

56.000 P5 +1 As5 =

56.000 P6 +1 As6 =

56.000 P7 +1 As7 =

56.000 P8 -1 As8 =

56.000 P9 -1 As9 =

56.00014.00 cm

P10 -1 As10 =

56.000 P11 -1


Cc. =


P1

P2

P3

P4

P5

P6

P7

P8

P9

P10

BF122


Є

42.000

42.00 cm 35.70 cm

P1 +1

17.85 cm

42.000 P2 +1

42.000 P3 +1

42.000 P4 +1

42.000 P5 +1

42.000 P6 -1

42.000 P7 -1

42.000 P8 -1

42.000 P9 -1

42.00028.00 cm

P10 -142.000 P11 -1

Є

28.000

28.00 cm 23.80 cm

P1 +1

11.90 cm

28.000 P2 +1

28.000 P3 +1

28.000 P4 -1

28.000 P5 -1

28.000 P6 -1

28.000 P7 -1

28.000 P8 -1

28.000 P9 -1

28.00042.00 cm

P10 -1

28.00042.00 cm

P11 -1

Є

14.000

14.00 cm 11.90 cm

P1 +1

5.95 cm

14.000 P2 -1

14.000 P3 -1

14.000 P4 -1

14.000 P5 -1

14.000 P6 -1

14.000 P7 -1

14.000 P8 -1

14.000 P9 -1

14.00056.00 cm

P10 -1

14.000 P11 -1

Є

0.000

0.00 cm 0.00 cm

P1 -1

0.00 cm

0.000 P2 -1

0.000 P3 -1

0.000 P4 -1

0.000 P5 -1

0.000 P6 -1

0.000 P7 -1

0.000 P8 -1

0.000 P9 -1

0.00070.00 cm

P10 -1

0.000 P11 -1

0.00 1000000.00 2000000.00 3000000.00 4000000.00 5000000.00 6000000.00 7000000.00 8000000.00 9000000.00

-800000.00

-600000.00

-400000.00

-200000.00

0.00

200000.00

400000.00

600000.00

800000.00

1000000.00

1200000.00


Momentos (Tn-m)

Carg

as P

untu

ale

s (

Tn)


CENTRO PLASTICO COLUMNA TIPO "ELE"CALCULO DE CENTRO PLASTICO r = 5.00 Area Cant. Acero area Cant. Acero

DATOS As1 = 4.00 d1' = 125.00 2.00 2 1.00 5.10 0 1

100.00

210.00 As2 = 4.00 d2' = 105.00 2.00 2 1.00 5.10 0 1

4200.00 As3 = 4.00 d3 = 85.00 2.00 2 1.00 5.10 0 1

0.85 As4 = 4.00 d4' = 65.00 2.00 2 1.00 5.10 0 1

SECCION DE COLUMNA As5 = 4.00 d5' = 45.00 2.00 2 1.00 5.10 0 1

85 cm As6 = 12.00 d6' = 25.00 2.00 6 1.00 5.10 0 1

25 cm As7 = 0.00 d7' = 0.00 0.00 0 1.00 5.10 0 1

4 o 5 capas As8 = 0.00 d8' = 0.00 0.00 0 1.00 5.10 0 1

30.005 As9 = 0.00 d9' = 0.00 0.00 0 1.00 5.10 0 1

20.00 As10 = 12.00 d10' = 5.00 2.00 6 1.00 5.10 0 1

20.00

4 o 5 capas

0

6.67

--- CALCULO DE CENTROIDE PLASTICO


Cc2. = 455175.00 15.00 6827625.00

Cc1. = 446250.00 80.00 35700000.00

AsI = 16086.00 125.00 2010750.00

AsII = 16086.00 105.00 1689030.00

AsIII = 16086.00 85.00 1367310.00

AsIV = 16086.00 65.00 1045590.00

CP 47.12AsV = 16086.00 45.00 723870.00

AsVI = 48258.00 25.00 1206450.00

AsVII = 0.00 0.00 0.00

AsVIII = 0.00 0.00 0.00

AsIX = 0.00 0.00 0.00

AsX = 48258.00 5.00 241290.00

1078371.00 50811915.00

CP = 47.12


210.00 kg/cm2 D = 130.00 85 cm 130 cm

4200.00 kg/cm2 a = 130.00 d' = 0.0. cm % de h = 100.00 %


BL6

elmering dice: # ESTRIBO AREA DIAMETRO 3 3/8" 0.71 CM2 0.95 CM. 4 1/2" 1.27 1.27 5 5/8" 1.98 1.59 6 3/4" 2.85 1.91 7 1 " 5.07 2.54

BO6


BL7


BO7


BL8


BO8


BL9


BO9


BL10


BO10


BI22


BI23


BI24


BI25


BI26


BI27


BI28


4.00 d1' = 125.00 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0030 130.00 130.000

4.00 d2' = 105.00 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 130.00 130.000

4.00 d3 = 85.00 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 130.00 130.000

4.00 d4' = 65.00 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 130.00 130.000

4.00 d5' = 45.00 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0030 130.00 130.000

12.00 d6' = 25.00 Є6 = 0.0021 F's6 = 4200.00 0.0021 0.0030 130.00 130.000

0.00 d7' = 0.00 Є7 = 0.0021 F's7 = 4200.00 0.0021 0.0030 130.00 130.000

0.00 d8' = 0.00 Є8 = 0.0021 F's8 = 4200.00 0.0021 0.0030 130.00 130.000

0.00 d9' = 0.00 Є9 = 0.0021 F's9 = 4200.00 0.0021 0.0030 130.00 130.000

12.00 d10' = 5.00 Є10 = 0.0021 F's10 = 4200.00 0.0021 0.0030 130.00 130.000


1972425.00 -17.88 Mcc = -35268653.68


16800.00 77.88

2157225.00 kg

M1 1308398.43

-35324270.90 kg.cm

16800.00 57.88 M2 972398.43

16800.00 37.88 M3 636398.43

16800.00 17.88 M4 300398.43

16800.00 -2.12 M5 -35601.57

50400.00 -22.12 M6 -1114804.70

0.00 -47.12 M7 0.00

0.00 -47.12 M8 0.00

0.00 -47.12 M9 0.00

50400.00 -42.12 M10 -2122804.70


210.00 kg/cm2 D = 130.00 85 cm 130 cm

4200.00 kg/cm2 a = 110.50 d' = 0.0. cm % de h = 100.00 %


4.00 d1' = 125.00 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0029 125.00 130.000

4.00 d2' = 105.00 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 130.00 130.000

4.00 d3 = 85.00 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 130.00 130.000

4.00 d4' = 65.00 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 130.00 130.000

4.00 d5' = 45.00 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0024 105.00 130.000

12.00 d6' = 25.00 Є6 = 0.0020 F's6 = 3923.08 0.0020 0.0020 85.00 130.000

0.00 d7' = 0.00 Є7 = 0.0015 F's7 = 3000.00 0.0015 0.0015 65.00 130.000

0.00 d8' = 0.00 Є8 = 0.0010 F's8 = 2076.92 0.0010 0.0010 45.00 130.000

0.00 d9' = 0.00 Є9 = 0.0006 F's9 = 1153.85 0.0006 0.0006 25.00 130.000

12.00 d10' = 5.00 Є10 = 0.0001 F's10 = 230.77 0.0001 0.0001 5.00 130.000


1676561.25 -8.13 Mcc = -13631883.44


16800.00 77.88

1810407.40 kg

M1 1308398.43

-11607829.98 kg.cm

16800.00 57.88 M2 972398.4316800.00 37.88 M3 636398.43

16800.00 17.88 M4 300398.43

16800.00 -2.12 M5 -35601.57

47076.92 -22.12 M6 -1041301.09

0.00 -47.12 M7 0.00

0.00 -47.12 M8 0.00

0.00 -47.12 M9 0.00

2769.23 -42.12 M10 -116637.62


210.00 kg/cm2 D = 130.00 85 cm 130 cm

4200.00 kg/cm2 a = 88.40 d' = 26.0. cm % de h = 80.00 %


4.00 d1' = 125.00 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0029 99.00 104.000

4.00 d2' = 105.00 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 104.00 104.000

4.00 d3 = 85.00 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 104.00 104.000

4.00 d4' = 65.00 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 104.00 104.000

4.00 d5' = 45.00 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0023 79.00 104.000

12.00 d6' = 25.00 Є6 = 0.0017 F's6 = 3403.85 0.0017 0.0017 59.00 104.000

0.00 d7' = 0.00 Є7 = 0.0011 F's7 = 2250.00 0.0011 0.0011 39.00 104.000

0.00 d8' = 0.00 Є8 = 0.0005 F's8 = 1096.15 0.0005 0.0005 19.00 104.000

0.00 d9' = 0.00 Є9 = 0.0000 F's9 = 57.69 0.0000 0.0000 1.00 104.000

12.00 d10' = 5.00 Є10 = 0.0006 F's10 = 1211.54 0.0006 0.0006 21.00 104.000


1341249.00 2.92 Mcc = 3915294.70


16800.00 77.88

1369864.38 kg

M1 1308398.43

5581457.53 kg.cm

16800.00 57.88 M2 972398.43

16800.00 37.88 M3 636398.43

16800.00 17.88 M4 300398.43

16800.00 -2.12 M5 -35601.57

-40846.15 -22.12 M6 -903481.83

0.00 -47.12 M7 0.00

0.00 -47.12 M8 0.00

0.00 -47.12 M9 0.00

-14538.46 -42.12 M10 -612347.51

CENTRO PLASTICO COLUMNA TIPO "ELE" CENTRO PLASTICO COLUMNA TIPO "TEE"105.00 25.00

130.00

1

21

85.00

2

Є

130.00 cm 130.00 cm

P1 +1

65.00 cm

P2 +1

P3 +1

P4 +1

P5 +1

P6 +1

P7 -1

P8 -1

P9 -1

P10 +1

Є

130.00 cm 110.50 cm

P1 +1

55.25 cmP2 +1

P3 +1

P4 +1

P5 +1

P6 +1

P7 -1

P8 -1

P9 -1

P10 +1

Є

104.00 cm 88.40 cm

P1 +1

44.20 cm

P2 +1

P3 +1

P4 +1

P5 +1

P6 -1

P7 -1

P8 -1

P9 -1

P10 -1

CENTRO PLASTICO COLUMNA TIPO "TEE"CALCULO DE CENTRO PLASTICO r = 6.25 area Ø area Ø

DATOS As1 = 10.20 d1' = 73.75 5.10 2.00 1 5.10 0.00 1

80.00

F'c = 210.00 As2 = 10.20 d2' = 65.75 5.10 2.00 1 5.10 0.00 1

F'y = 4200.00 As3 = 10.20 d3 = 57.75 5.10 2.00 1 5.10 0.00 1

(Ø) = 0.85 As4 = 10.20 d4' = 49.75 5.10 2.00 1 5.10 0.00 1

SECCION DE COLUMNA As5 = 10.20 d5' = 41.75 5.10 2.00 1 5.10 0.00 1

40.00 80.00 As6 = 20.40 d6' = 33.75 5.10 4.00 1 5.10 0.00 1

40.00 30.00 As7 = 10.20 d7' = 39.38 5.10 2.00 1 5.10 0.00 1

2 o 3 capas 4 o 5 capas As8 = 10.20 d8' = 20.00 5.10 2.00 1 5.10 0.00 1

0.00 5.00 As9 = 10.20 d9' = 13.13 5.10 2.00 2 5.10 0.00 1

20.00 8.00 As10 = 20.40 d10' = 6.25 5.10 4.00 3 5.10 0.00 1

--- 8.00

2 o 3 capas 4 o 5 capas

0.00 5.00

27.50 6.88

--- 6.88 CALCULO DE CENTROIDE PLASTICO


Cc1. = 571200.00 20.00 11424000.00

Cc2. = 214200.00 60.00 12852000.00

AsI = 41019.30 73.75 3025173.37

AsII = 41019.30 65.75 2697018.97

AsIII = 41019.30 57.75 2368864.57

AsIV = 41019.30 49.75 2040710.17

CP 33.17AsV = 41019.30 41.75 1712555.78

AsVI = 82038.60 33.75 2768802.75

AsVII = 41019.30 39.38 1615134.94

AsVIII = 41019.30 20.00 820386.00

AsIX = 41019.30 13.13 538378.31

AsX = 82038.60 6.25 512741.25

1277631.60 42375766.13

CP = 33.17

CQ6


CT6


CQ7


CT7


CQ8


CT8


CQ9


CT9


CQ10


CT10


CN22


CN23


CN24


CN25


CN26


CN27


CN28


CENTRO PLASTICO COLUMNA TIPO "TEE" CENTRO PLASTICO COLUMNA TIPO "U"25.00 30.00 25.00 CALCULO DE CENTRO PLASTICO r = 6.25 area

40.00 1

DATOS As1 = 20.40 d1' = 73.75 5.10

F'c = 210.00 As2 = 20.40 d2' = 63.75 5.10

F'y = 4200.00 As3 = 20.40 d3 = 53.75 5.10

(Ø) = 0.85 As4 = 20.40 d4' = 43.75 5.10

SECCION DE COLUMNA As5 = 20.40 d5' = 33.75 5.10

30.00 120.00 As6 = 10.20 d6' = 23.75 5.10

50.00 30.00 As7 = 10.20 d7' = 31.88 5.10

40.00 21

2 o 3 capas 4 o 5 capas As8 = 10.20 d8' = 15.00 5.10

0.00 5.00 As9 = 20.40 d9' = 10.63 5.10

25.00 10.00 As10 = 15.30 d10' = 6.25 5.10

80.00 --- 10.00

2


0.00 5.00

17.50 4.38 CALCULO DE CENTROIDE PLASTICO

--- 4.38 Fuerza (kg) x Momento (kg-m)

Cc1. = 642600.00 15.00 9639000.00

Cc2. = 267750.00 55.00 14726250.00

Cc3. = 267750.00 55.00 14726250.00

AsI = 82038.60 73.75 6050346.75

AsII = 82038.60 63.75 4409574.75

AsIII = 82038.60 53.75 5229960.75

AsIV = 82038.60 43.75 3589188.75

AsV = 82038.60 33.75 2768802.75

AsVI = 41019.30 23.75 974208.37

AsVII = 41019.30 31.88 1307490.19

AsVIII = 41019.30 15.00 615289.50

AsIX = 82038.60 10.63 871660.12

AsX = 61528.95 6.25 384555.94

1854918.45 65292577.87

CP = 35.20

DK6


DK7


DK8


DK9


DK10


DK11


DK12


DK13


DK14


DK15


DH21


DH22


DH23


DH24


DH25


DH26


DH27


DH28


CENTRO PLASTICO COLUMNA TIPO "U"Ø area Ø 30.00 60.00 30.00

4.00 1 5.10 0.00 1

80.00

50.00 1

4.00 1 5.10 0.00 3/8

4.00 1 5.10 0.00 1

4.00 1 5.10 0.00 1

4.00 1 5.10 0.00 1

2.00 1 5.10 0.00 1

2.00 1 5.10 0.00 1

2.00 1 5.10 0.00 1

30.00 24.00 1 5.10 0.00 1

3.00 1 5.10 0.00 1

120.00

CP 35.20

DN6


DN7


DN8


DN9


DN10


DN11


DN12


DN13


DN14


DN15


DIAGRAMA DE INTERACCIONCALCULO DE CENTRO PLASTICO

DATOS

F'c = 210.00 r = 5.00 5.10 3 1 35.00 d1' =

F'y = 4200.00 Ø = 0.95 2.54

(Ø) = 0.85 d1' = 35.00

As1 = 15.30 d2' = 20.00 5.10 2 140.00

As2 = 10.20 d3' = 5.00 2.54

As3 = 15.30

5.10 3 1

SECCION DE COLUMNA 2.54 35.00 d3' =

30.00 40.00

30.00

CALCULO DE CENTROIDE PLASTICO


Cc. = 214200.00 20.00 4284000.00

AsI = 61528.95 35.00 2153513.25

AsII = 41019.30 20.00 820386.00

AsIII = 61528.95 5.00 307644.75CP 20.00

378277.20 7565544.00

CP = 20.00

PUNTO N 01 d = 40.00 d1' = 35.00

F'c = 210.00 a = 40.00 d3' = 20.00

F'y = 4200.00 CP = 20.00 d2' = 5.00

As1 = 15.30 SECCION DE COLUMNA

As2 = 10.20 30.00 40.00

As3 = 15.30 Є F'cCalculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00

Є1 P1Є1 = 0.00 F's1 = 4200.00 0.00 40.00 40.00 20.00

Є2 = 0.00 F's2 = 4200.00 0.00 Є2 0.00Є2 40.00 P2

0.00 40.00 40.00

Є3 = 0.00 F's3 = 4200.00

0.00 Є3 0.00Є3 P3 1.00

Calculamos la contribucion del concreto Dist. al CP 0.00 40.00 40.00

Cc. = 214200.00 0.00

Calculamos la contribucion del acero Calculando la carga axial nominal

P1 = 64260.00 15.00

Pn1 = 385560.00P2 = 42840.00 0.00

P3 = 64260.00 -15.00

Calculando el momento con respecto al CP. Calculando el momento con respecto al CP.

F4


F7


F10


B17


B18


B19


B20


B38


Mcc = 0.00

Mn1 = 0.00M1 = 963900.00

M2 = 0.00

M3 = -963900.00

PUNTO N 02 d = 40.00 d1' = 35.00

F'c = 210.00 a = 34.00 d2' = 20.00

F'y = 4200.00 CP = 20.00 d3' = 5.00


As2 = 10.20 30.00 40.00

As3 = 15.30 Є F'c

Calculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00Є1 P1

Є1 = 0.00 F's1 = 4200.00 0.00 35.00 40.00 17.00

34.00Є2 = 0.00 F's2 = 3000.00 0.00 Є2 0.00Є2 P2

0.00 20.00 40.00

Є3 = 0.00 F's3 = 750.00

0.00 Є3 0.00Є3 P3 1.00

Calculamos la contribucion del concretoDist. al CP 0.00 5.00 40.00

Cc. = 182070.00 3.00


P1 = 64260.00 15.00

Pn2 = 288405.00P2 = 30600.00 0.00

P3 = 11475.00 -15.00


Mcc = 546210.00

Mn2 = 1337985.00M1 = 963900.00

M2 = 0.00

M3 = -172125.00

PUNTO N 03 d = 10.00 d1' = 35.00

F'c = 210.00 D = 30.00 d2' = 20.00

F'y = 4200.00 a = 25.50 d3' = 5.00 35.00

As1 = 15.30 CP = 20.00


As3 = 15.30 30.00 40.00 Є F'cCalculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00

Є1 P1Є1 = 0.00 F's1 = 4200.00 0.00 25.00 30.00

25.5012.75

B69


25.50

Є2 = 0.00 F's2 = 2000.00 0.00 Є2 0.00Є2 P2

0.00 10.00 30.00

Є3 = 0.00 F's3 = 1000.00

0.00 Є3 0.00Є3 P3 -1.00


Cc. = 136552.50 7.25


P1 = 64260.00 15.00

Pn3 = 205912.50P2 = 20400.00 0.00

P3 = 15300.00 -15.00


Mcc = 990005.63

Mn3 = 2183405.63M1 = 963900.00

M2 = 0.00

M3 = 229500.00

PUNTO N 04 d = 20.00 d1' = 35.00

F'c = 210.00 D = 20.00 d2' = 20.00

F'y = 4200.00 a = 17.00 d3' = 5.00

As1 = 15.30 CP = 20.00


As3 = 15.30 30.00 40.00 Є F'c

Calculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00Є1 P1 8.50

Є1 = 0.00 F's1 = 4200.00 0.00 15.00 20.00 17.00

Є2 = 0.00 F's2 = 0.00 0.00 Є2 0.00Є2 P2 -1.00

0.00 0.00 20.00

Є3 = 0.00 F's3 = 4200.00

0.00 Є3 0.00Є3 P3 -1.00


Cc. = 91035.00 11.50


P1 = 64260.00 15.00

Pn4 = 91035.00P2 = 0.00 0.00

P3 = 64260.00 -15.00


Mcc = 1046902.50

Mn4 = 2974702.50M1 = 963900.00

M2 = 0.00

B98


B127


M3 = 963900.00

PUNTO N 05 d = 30.00 d1' = 35.00

F'c = 210.00 D = 10.00 d2' = 20.00

F'y = 4200.00 a = 8.50 d3' = 5.00 35.00

As1 = 15.30 CP = 20.00


As3 = 15.30 30.00 40.00 Є F'cCalculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00

Є1 8.50 P1 4.25Є1 = 0.00 F's1 = 3000.00 0.00 5.00 10.00

Є2 = 0.00 F's2 = 4200.00 0.00 Є2 0.00Є2 P2 -1.00

0.00 10.00 10.00

Є3 = 0.00 F's3 = 4200.00

0.01 Є3 0.00Є3 P3 -1.00


Cc. = 45517.50 15.75


P1 = 45900.00 15.00

Pn5 = 69997.50P2 = 42840.00 0.00

P3 = 64260.00 -15.00


Mcc = 716900.63

Mn5 = 2369300.63M1 = 688500.00

M2 = 0.00

M3 = 963900.00

CUADRO DE RESUMEN DISTANCIA

Tn-m Tn cm

Mn1 = 0.00 385.56 Pn1 = 40.00

Mn2 = 133798.50 288.41 Pn2 = 40.00

Mn3 = 218340.56 205.91 Pn3 = 10.00

Mn4 = 297470.25 91.04 Pn4 = 20.00

Mn5 = 236930.06 70.00 Pn5 = 30.00

0.00 50000.00 100000.00 150000.00 200000.00 250000.00 300000.00 350000.000.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

450.00DIAGRAMA DE ITERACION

Column D

MOMENTOS (Tn-m)

CARG

AS

PUN

TUA

LES

(Tn)

B156


0.00 50000.00 100000.00 150000.00 200000.00 250000.00 300000.00 350000.000.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00


Column D

MOMENTOS (Tn-m)

CARG

AS

PUN

TUA

LES

(Tn)

DIAGRAMA DE INTERACCION CENTRO PLASTICO COLUMNA TIPO "RECTANGULAR"CALCULO DE CENTRO PLASTICO

DATOS

F'c = 210.00 r = 5.00 5.10 3 1 55.00 d1' =

F'y = 4200.00 Ø = 0.95 2.54

(Ø) = 0.85 d1' = 55.00 5.10 2 1

As1 = 15.30 d2' = 38.33 2.5460.00

As2 = 10.20 d3 = 21.67 5.10 2 1

As3 = 10.20 d4' = 5.00 2.54

1As4 = 15.30 5.10 3 1

SECCION DE COLUMNA 2.54 55.00 d4' =

30.00 60.00

30.00



Cc. = 321300.00 30.00 9639000.00

AsI = 61528.95 55.00 3384092.25

AsII = 41019.30 38.33 1572406.50

AsIII = 41019.30 21.67 888751.50

CP 30.00AsIV = 61528.95 5.00 307644.75

526396.50 15791895.00

CP = 30.00

PUNTO N 01 d = 60.00 d1' = 55.00

F'c = 210.00 a = 60.00 d2' = 38.33

F'y = 4200.00 CP = 30.00 d3 = 21.67

As1 = 15.30 SECCION DE COLUMNA d4' = 5.00

As2 = 10.20 30.00 60.00

As3 = 10.20 Calculo de las deformaciones unitarias Є F'cAs4 = 15.30

2000000.00 0.00 Є1 0.003 Є1 P1

Є1 = 0.00 F's1 = 4200.00 0.0021 60.00 60.00 30.00

0.00 Є2 0.003 Є260.00

P2Є2 = 0.00 F's2 = 4200.00 0.0021 60.00 60.00

0.00 Є3 0.003

Є3 = 0.00 F's3 = 4200.00 0.0021 60.00 60.00 Є3 P3 1.000.00 Є3 0.003

Є4 = 0.00 F's4 = 4200.00 0.0021 60.00 60.00 Є4 P4 1.00


Cc. = 321300.00 0.00


P1 = 64260.00 25.00

Pn1 = 535500.00P2 = 42840.00 8.33

P3 = 42840.00 -8.33

P4 = 64260.00 -25.00

U4


U6


U8


U10


Q16


Q17


Q18


Q19


Q20


Q40



Mcc = 0.00

Mn1 = 0.00M1 = 1606500.00

M2 = 357000.00

M3 = -357000.00

M4 = -1606500.00

PUNTO N 02 d = 60.00 d1' = 55.00

F'c = 210.00 a = 51.00 d2' = 38.33

F'y = 4200.00 CP = 30.00 d3 = 21.67

As1 = 15.30 SECCION DE COLUMNA d4' = 5.00

As2 = 10.20 30.00 60.00

As3 = 10.20 Є F'c

As4 = 15.30

Calculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00 Є1 P125.50

Є1 = 0.00 F's1 = 4200.00 0.00 55.00 60.00

51.000.00 Є2 0.00 Є2 P2

Є2 = 0.00 F's2 = 3833.33 0.00 38.33 60.00

0.00 Є3 0.00

Є3 = 0.00 F's3 = 2166.67 0.00 21.67 60.00 Є3 P3 1.00

0.00 Є3 0.00

Є3 = 0.00 F's3 = 500.00 0.00 5.00 60.00 Є5 P4 -1.00


Cc. = 273105.00 4.50


P1 = 64260.00 25.00

Pn2 = 354365.00P2 = 39100.00 8.33

P3 = 22100.00 -8.33

P4 = 7650.00 -25.00


Mcc = 1228972.50

Mn2 = 2977139.17M1 = 1606500.00

M2 = 325833.33

M3 = -184166.67

M4 = 191250.00

PUNTO N 03 d = 10.00 d1' = 55.00

F'c = 210.00 D = 50.00 d2' = 38.33

F'y = 4200.00 a = 42.50 d3 = 21.67

As1 = 15.30 CP = 30.00 d4' = 5.00


As3 = 10.20 30.00 60.00 Є F'cAs4 = 15.30

Calculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00 Є1 P1 21.25

Q71


Є1 = 0.00 F's1 = 4200.00 0.00 45.00 50.0042.50

0.00 Є2 0.00 Є2 P2Є2 = 0.00 F's2 = 3400.00 0.00 28.33 50.00

0.00 Є3 0.00

Є3 = 0.00 F's3 = 1400.00 0.00 11.67 50.00 Є3 P3 1.000.00 Є3 0.00

Є3 = 0.00 F's3 = 600.00 0.00 5.00 50.00 Є4 P4 -1.00


Cc. = 227587.50 8.75


P1 = 64260.00 25.00

Pn3 = 312247.50P2 = 34680.00 8.33

P3 = 14280.00 -8.33

P3 = 9180.00 -25.00


Mcc = 1991390.63

Mn3 = 3767890.63M1 = 1606500.00

M2 = 289000.00

M3 = -119000.00

M4 = 229500.00

PUNTO N 04 d = 20.00 d1' = 55.00

F'c = 210.00 D = 40.00 d2' = 38.33

F'y = 4200.00 a = 34.00 d3 = 21.67

As1 = 15.30 CP = 30.00 d4' = 5.00


As3 = 10.20 30.00 60.00 Є F'c

As4 = 15.30Є1

P1

Calculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00 17.00

Є1 = 0.00 F's1 = 4200.00 0.00 35.00 40.00 34.00

0.00 Є2 0.00 Є2 P2

Є2 = 0.00 F's2 = 2750.00 0.00 18.33 40.00

0.00 Є3 0.00

Є3 = 0.00 F's3 = 250.00 0.00 1.67 40.00 Є3 P3 -1.00

0.00 Є3 0.00

Є3 = 0.00 F's3 = 2250.00 0.00 15.00 40.00 Є4 P4 -1.00


Cc. = 182070.00 13.00


P1 = 64260.00 25.00

Pn4 = 271830.00P2 = 28050.00 8.33

P3 = 2550.00 -8.33

P4 = 34425.00 -25.00


Mcc = 2366910.00

Mn4 = 4228410.00M1 = 1606500.00

Q100


Q129


M2 = 233750.00

Mn4 = 4228410.00

M3 = 21250.00

M4 = 860625.00

PUNTO N 05 d = 30.00 d1' = 55.00

F'c = 210.00 D = 30.00 d2' = 38.33

F'y = 4200.00 a = 25.50 d3 = 21.67

As1 = 15.30 CP = 30.00 d4' = 5.00


As3 = 10.20 30.00 60.00 Є F'cAs4 = 15.30 P1

12.75Calculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00 Є1

25.50Є1 = 0.00 F's1 = 4200.00 0.00 25.00 30.00

0.00 Є2 0.00 Є2 P2Є2 = 0.00 F's2 = 1666.67 0.00 8.33 30.00

0.00 Є3 0.00 Є3 P3 -1.00Є3 = 0.00 F's3 = 1666.67 0.00 8.33 30.00

0.00 Є3 0.00 Є4 P4 -1.00

Є3 = 0.00 F's3 = 4200.00 0.00 25.00 30.00


Cc. = 136552.50 17.25


P1 = 64260.00 25.00

Pn5 = 200812.50P2 = 17000.00 8.33

P3 = 17000.00 -8.33

P4 = 64260.00 -25.00


Mcc = 2355530.63

Mn5 = 4245363.96M1 = 1606500.00

M2 = 141666.67

M3 = 141666.67

M4 = 1606500.00

PUNTO N 06 d = 40.00 d1' = 55.00

F'c = 210.00 D = 20.00 d2' = 38.33

F'y = 4200.00 a = 17.00 d3 = 21.67

As1 = 15.30 CP = 30.00 d4' = 5.00


As3 = 10.20 30.00 60.00 Є F'c

As4 = 15.3017.00

P18.50

Calculo de las deformaciones unitarias 2000000.00 0.00 Є1 0.00 Є1

Є1 = 0.00 F's1 = 4200.00 0.00 15.00 20.00

0.00 Є2 0.00 Є2 P2 -1.00

Є2 = 0.00 F's2 = 500.00 0.00 1.67 20.00

0.00 Є3 0.00 Є3 P3 -1.00

Є3 = 0.00 F's3 = 4200.00 0.00 18.33 20.00

Q158


0.01 Є3 0.00 Є4 P4 -1.00

Є3 = 0.00 F's3 = 4200.00 0.00 35.00 20.00


Cc. = 91035.00 21.50


P1 = 64260.00 25.00

Pn5 = 117555.00P2 = 5100.00 8.33

P3 = 42840.00 -8.33

P4 = 64260.00 -25.00


Mcc = 1957252.50

Mn5 = 3878252.50M1 = 1606500.00

M2 = -42500.00

M3 = 357000.00

M4 = 1606500.00

PUNTO N 07 d = 50.00 d1' = 55.00

F'c = 210.00 D = 10.00 d2' = 38.33

F'y = 4200.00 a = 8.50 d3 = 21.67

As1 = 15.30 CP = 30.00 d4' = 5.00


As3 = 10.20 30.00 60.00 Є F'c

As4 = 15.30Є1

8.50 P1 4.25

Calculo de las deformaciones unitarias 2000000.00 0.002 Є1 0.00 1.00

Є1 = 0.00 F's1 = 3000.00 0.002 5.00 10.00

0.003 Є2 0.00 Є2 P2 -1.00

Є2 = 0.00 F's2 = 4200.00 0.002 11.67 10.00

0.008 Є3 0.00 Є3 P3 -1.00

Є3 = 0.00 F's3 = 4200.00 0.002 28.33 10.00

0.014 Є3 0.00 Є4 P4 -1.00

Є3 = 0.00 F's3 = 4200.00 0.002 45.00 10.00


Cc. = 45517.50 25.75


P1 = 45900.00 25.00

Pn5 = 91417.50P2 = 42840.00 8.33

P3 = 42840.00 -8.33

P4 = 64260.00 -25.00


Mcc = 1172075.63

Mn5 = 2319575.63M1 = 1147500.00

M2 = -357000.00

M3 = 357000.00

M4 = 1606500.00

Q187


Q216


CUADRO DE RESUMEN DISTANCIA

Tn-m Tn cm

Mn1 = 0.00 535.50 Pn1 = 60.00

Mn2 = 297713.92 354.37 Pn2 = 60.00

Mn3 = 376789.06 312.25 Pn3 = 10.00

Mn4 = 422841.00 271.83 Pn4 = 20.00

Mn5 = 424536.40 200.81 Pn5 = 30.00

Mn6 = 387825.25 117.56 Pn6 = 40.00

Mn7 = 231957.56 91.42 Pn7 = 50.00

0.00 50000.00 100000.00 150000.00 200000.00 250000.00 300000.00 350000.00 400000.00 450000.000.00

100.00

200.00

300.00

400.00

500.00


Column S

MOMENTOS (Tn-m)

CA

RG

AS

PU

NTU

ALES

(Tn)


0.00 1000000.00 2000000.00 3000000.00 4000000.00 5000000.00 6000000.00 7000000.00 8000000.00 9000000.00

-800000.00

-600000.00

-400000.00

-200000.00

0.00

200000.00

400000.00

600000.00

800000.00

1000000.00

1200000.00

Carga nominal

Afectado por 0.70

Momentos (Tn-m)

Carg

as P

untu

ale

s (

Tn)


CENTRO PLASTICO COLUMNA TIPO "RECTANGULAR"CALCULO DE CENTRO PLASTICO r = 6.25 area Cant. Acero area Cant. Acero

DATOS As1 = 20.40 d1' = 63.75 5.10 4 1 5.10 0 1

F'c = 210.00 kg/cm2 As2 = 10.20 d2' = 58.00 5.10 2 1 5.10 0 1

F'y = ### As3 = 10.20 d3 = 52.25 5.10 2 1 5.10 0 1

(Ø) = 0.85 As4 = 10.20 d4' = 46.50 5.10 2 1 5.10 0 1

SECCION DE COLUMNA As5 = 10.20 d5' = 40.75 5.10 2 1 5.10 0 1

40.00 70.00 As6 = 10.20 d6' = 35.00 5.10 2 1 5.10 0 1

N. de capas de acero 4-11 As7 = 10.20 d7' = 29.25 5.10 2 1 5.10 0 1

11.00 As8 = 10.20 d8' = 23.50 5.10 2 1 5.10 0 1

19.17 11.50 As9 = 10.20 d9' = 17.75 5.10 2 1 5.10 0 1

8.21 5.75 As10 = 10.20 d10' = 12.00 5.10 2 1 5.10 0 1

0.00 0.00 As11 = 20.40 d11' = 6.25 5.10 4 1 5.10 0 1

0.00 0.00

0.00 0.00

0.00 5.75

5.75 CALCULO DE CENTROIDE PLASTICO


Cc1. = 499800.00 35.00 17493000.00

AsI = 82038.60 63.75 5229960.75

AsII = 41019.30 58.00 2379119.40

CP

AsIII = 41019.30 52.25 2143258.43

AsIV = 41019.30 46.50 1907397.45

AsV = 41019.30 40.75 1671536.47

AsVI = 41019.30 35.00 1435675.50

AsVII = 41019.30 29.25 1199814.53

AsVIII = 41019.30 23.50 963953.55

AsIX = 41019.30 17.75 728092.58

AsX = 41019.30 12.00 492231.60

AsXI = 82038.60 6.25 512741.25

1033050.90 36156781.50

CP = 35.00

DIAGRAMA DE INTERACION


F'c = 210.00 kg/cm2 D = 70.00 40 cm 70 cm

F'y = ### a = 70.00 d' = 0.0. cm


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0030 70.00 70.000

As2 = 10.20 d2' = 58.00 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0030 70.00 70.000

As3 = 10.20 d3 = 52.25 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0030 70.00 70.000

AM3


AP3


AM4


AP4


AM5


AP5


AM6


AP6


AM7


AP7


AJ19


AJ20


AJ21


AJ22


AJ23


AJ24


As4 = 10.20 d4' = 46.50 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0030 70.00 70.000

As5 = 10.20 d5' = 40.75 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0030 70.00 70.000

As6 = 10.20 d6' = 35.00 Є6 = 0.0021 F's6 = 4200.00 0.0021 0.0030 70.00 70.000

As7 = 10.20 d7' = 29.25 Є7 = 0.0021 F's7 = 4200.00 0.0021 0.0030 70.00 70.000

As8 = 10.20 d8' = 23.50 Є8 = 0.0021 F's8 = 4200.00 0.0021 0.0030 70.00 70.000

As9 = 10.20 d9' = 17.75 Є9 = 0.0021 F's9 = 4200.00 0.0021 0.0030 70.00 70.000

As10 = 10.20 d10' = 12.00 Є10 = 0.0021 F's10 = 4200.00 0.0021 0.0030 70.00 70.000

As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.0021 0.0030 70.00 70.000


Cc. = 499800.00 0.00 Mcc = 0.00


P1 85680.00 28.75

1056720.00 kg

M1 2463300.00

0.00 kg.cm

P2 42840.00 23.00 M2 985320.00

P3 42840.00 17.25 M3 738990.00

P4 42840.00 11.50 M4 492660.00

P5 42840.00 5.75 M5 246330.00

P6 42840.00 0.00 M6 0.00

P7 42840.00 -5.75 M7 -246330.00

P8 42840.00 -11.50 M8 -492660.00

P9 42840.00 -17.25 M9 -738990.00

P10 42840.00 -23.00 M10 -985320.00

P11 85680.00 -28.75 M11 -2463300.00


F'c = 210.00 kg/cm2 D = 70.00 40 cm 70 cm

F'y = ### a = 59.50 d' = 0.0. cm


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0027 63.75 70.000

As2 = 10.20 d2' = 58.00 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0025 58.00 70.000

As3 = 10.20 d3 = 52.25 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0022 52.25 70.000

As4 = 10.20 d4' = 46.50 Є4 = 0.0020 F's4 = 3985.71 0.0020 0.0020 46.50 70.000

As5 = 10.20 d5' = 40.75 Є5 = 0.0017 F's5 = 3492.86 0.0017 0.0017 40.75 70.000

As6 = 10.20 d6' = 35.00 Є6 = 0.0015 F's6 = 3000.00 0.0015 0.0015 35.00 70.000

As7 = 10.20 d7' = 29.25 Є7 = 0.0013 F's7 = 2507.14 0.0013 0.0013 29.25 70.000

As8 = 10.20 d8' = 23.50 Є8 = 0.0010 F's8 = 2014.29 0.0010 0.0010 23.50 70.000

As9 = 10.20 d9' = 17.75 Є9 = 0.0008 F's9 = 1521.43 0.0008 0.0008 17.75 70.000

As10 = 10.20 d10' = 12.00 Є10 = 0.0005 F's10 = 1028.57 0.0005 0.0005 12.00 70.000

As11 = 20.40 d11' = 6.25 Є11 = 0.0003 F's4 = 535.71 0.0003 0.0003 6.25 70.000


Cc. = 424830.00 5.25 Mcc = 2230357.50


P1 85680.00 28.75

786128.57 kg

M1 2463300.00

5883833.57 kg.cm

P2 42840.00 23.00 M2 985320.00P3 42840.00 17.25 M3 738990.00

AG55


AG87


P4 40654.29 11.50

786128.57 kg

M4 467524.29

5883833.57 kg.cm

P5 35627.14 5.75 M5 204856.07

P6 30600.00 0.00 M6 0.00

P7 25572.86 -5.75 M7 -147043.93

P8 20545.71 -11.50 M8 -236275.71

P9 15518.57 -17.25 M9 -267695.36

P10 10491.43 -23.00 M10 -241302.86

P11 10928.57 -28.75 M11 -314196.43


F'c = 210.00 kg/cm2 D = 70.00 40 cm 70 cm

F'y = ### a = 47.60 d' = 14.0. cm % de h = 80.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0027 49.75 56.000

As2 = 10.20 d2' = 58.00 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0024 44.00 56.000

As3 = 10.20 d3 = 52.25 Є3 = 0.0021 F's3 = 4200.00 0.0021 0.0020 38.25 56.000

As4 = 10.20 d4' = 46.50 Є4 = 0.0017 F's4 = 3482.14 0.0017 0.0017 32.50 56.000

As5 = 10.20 d5' = 40.75 Є5 = 0.0014 F's5 = 2866.07 0.0014 0.0014 26.75 56.000

As6 = 10.20 d6' = 35.00 Є6 = 0.0011 F's6 = 2250.00 0.0011 0.0011 21.00 56.000

As7 = 10.20 d7' = 29.25 Є7 = 0.0008 F's7 = 1633.93 0.0008 0.0008 15.25 56.000

As8 = 10.20 d8' = 23.50 Є8 = 0.0005 F's8 = 1017.86 0.0005 0.0005 9.50 56.000

As9 = 10.20 d9' = 17.75 Є9 = 0.0002 F's9 = 401.79 0.0002 0.0002 3.75 56.000

As10 = 10.20 d10' = 12.00 Є10 = 0.0001 F's10 = 214.29 0.0001 0.0001 2.00 56.000

As11 = 20.40 d11' = 6.25 Є11 = 0.0004 F's4 = 830.36 0.0004 0.0004 7.75 56.000


Cc. = 339864.00 11.20 Mcc = 3806476.80


P1 85680.00 28.75

610947.21 kg

M1 2463300.00

7747442.60 kg.cm

P2 42840.00 23.00 M2 985320.00

P3 42840.00 17.25 M3 738990.00

P4 35517.86 11.50 M4 408455.36

P5 29233.93 5.75 M5 168095.09

P6 22950.00 0.00 M6 0.00

P7 16666.07 -5.75 M7 -95829.91

P8 10382.14 -11.50 M8 -119394.64

P9 4098.21 -17.25 M9 -70694.20

P10 -2185.71 -23.00 M10 -50271.43

P11 -16939.29 -28.75 M11 -487004.46


F'c = 210.00 kg/cm2 D = 70.00 40 cm 70 cm

F'y = ### a = 35.70 d' = 28 cm % de h = 60.00 %


AG119


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0026 35.75 42.000

As2 = 10.20 d2' = 58.00 Є2 = 0.0021 F's2 = 4200.00 0.0021 0.0021 30.00 42.000

As3 = 10.20 d3 = 52.25 Є3 = 0.0017 F's3 = 3464.29 0.0017 0.0017 24.25 42.000

As4 = 10.20 d4' = 46.50 Є4 = 0.0013 F's4 = 2642.86 0.0013 0.0013 18.50 42.000

As5 = 10.20 d5' = 40.75 Є5 = 0.0009 F's5 = 1821.43 0.0009 0.0009 12.75 42.000

As6 = 10.20 d6' = 35.00 Є6 = 0.0005 F's6 = 1000.00 0.0005 0.0005 7.00 42.000

As7 = 10.20 d7' = 29.25 Є7 = 0.0001 F's7 = 178.57 0.0001 0.0001 1.25 42.000

As8 = 10.20 d8' = 23.50 Є8 = 0.0003 F's8 = 642.86 0.0003 0.0003 4.50 42.000

As9 = 10.20 d9' = 17.75 Є9 = 0.0007 F's9 = 1464.29 0.0007 0.0007 10.25 42.000

As10 = 10.20 d10' = 12.00 Є10 = 0.0011 F's10 = 2285.71 0.0011 0.0011 16.00 42.000As11 = 20.40 d11' = 6.25 Є11 = 0.0016 F's4 = 3107.14 0.0016 0.0016 21.75 42.000


Cc. = 254898.00 17.15 Mcc = 4371500.70


P1 85680.00 28.75

368118.00 kg

M1 2463300.00

6144406.41 kg.cm

P2 42840.00 23.00 M2 985320.00

P3 35335.71 17.25 M3 609541.07

P4 26957.14 11.50 M4 310007.14

P5 18578.57 5.75 M5 106826.79

P6 10200.00 0.00 M6 0.00

P7 1821.43 -5.75 M7 -10473.21

P8 -6557.14 -11.50 M8 -75407.14

P9 -14935.71 -17.25 M9 -257641.07

P10 -23314.29 -23.00 M10 -536228.57

P11 -63385.71 -28.75 M11 -1822339.29


F'c = 210.00 kg/cm2 D = 70.00 40 cm 70 cm

F'y = ### a = 23.80 d' = 42 cm % de h = 40.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.0021 0.0023 21.75 28.000

As2 = 10.20 d2' = 58.00 Є2 = 0.0017 F's2 = 3428.57 0.0017 0.0017 16.00 28.000

As3 = 10.20 d3 = 52.25 Є3 = 0.0011 F's3 = 2196.43 0.0011 0.0011 10.25 28.000

As4 = 10.20 d4' = 46.50 Є4 = 0.0005 F's4 = 964.29 0.0005 0.0005 4.50 28.000

As5 = 10.20 d5' = 40.75 Є5 = 0.0001 F's5 = 267.86 0.0001 0.0001 1.25 28.000

As6 = 10.20 d6' = 35.00 Є6 = 0.0008 F's6 = 1500.00 0.0008 0.0008 7.00 28.000

As7 = 10.20 d7' = 29.25 Є7 = 0.0014 F's7 = 2732.14 0.0014 0.0014 12.75 28.000

As8 = 10.20 d8' = 23.50 Є8 = 0.0020 F's8 = 3964.29 0.0020 0.0020 18.50 28.000

As9 = 10.20 d9' = 17.75 Є9 = 0.0021 F's9 = 4200.00 0.0021 0.0026 24.25 28.000

As10 = 10.20 d10' = 12.00 Є10 = 0.0021 F's10 = 4200.00 0.0021 0.0032 30.00 28.000

As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.0021 0.0038 35.75 28.000


Cc. = 169932.00 23.10 Mcc = 3925429.20

AG151


AG183



P1 85680.00 28.75

65127.00 kg

M1 2463300.00

2895493.31 kg.cm

P2 34971.43 23.00 M2 804342.86

P3 22403.57 17.25 M3 386461.61

P4 9835.71 11.50 M4 113110.71

P5 -2732.14 5.75 M5 15709.82

P6 -15300.00 0.00 M6 0.00

P7 -27867.86 -5.75 M7 -160240.18

P8 -40435.71 -11.50 M8 -465010.71

P9 -42840.00 -17.25 M9 -738990.00

P10 -42840.00 -23.00 M10 -985320.00

P11 -85680.00 -28.75 M11 -2463300.00


F'c = 210.00 kg/cm2 D = 70.00 40 cm 70 cm

F'y = ### a = 11.90 d' = 56 cm % de h = 20.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0017 F's1 = 3321.43 0.0017 0.0017 7.75 14.000

As2 = 10.20 d2' = 58.00 Є2 = 0.0004 F's2 = 857.14 0.0004 0.0004 2.00 14.000

As3 = 10.20 d3 = 52.25 Є3 = 0.0008 F's3 = 1607.14 0.0008 0.0008 3.75 14.000

As4 = 10.20 d4' = 46.50 Є4 = 0.0021 F's4 = 4200.00 0.0021 0.0020 9.50 14.000

As5 = 10.20 d5' = 40.75 Є5 = 0.0021 F's5 = 4200.00 0.0021 0.0033 15.25 14.000

As6 = 10.20 d6' = 35.00 Є6 = 0.0021 F's6 = 4200.00 0.0021 0.0045 21.00 14.000

As7 = 10.20 d7' = 29.25 Є7 = 0.0021 F's7 = 4200.00 0.0021 0.0057 26.75 14.000

As8 = 10.20 d8' = 23.50 Є8 = 0.0021 F's8 = 4200.00 0.0021 0.0070 32.50 14.000

As9 = 10.20 d9' = 17.75 Є9 = 0.0021 F's9 = 4200.00 0.0021 0.0082 38.25 14.000

As10 = 10.20 d10' = 12.00 Є10 = 0.0021 F's10 = 4200.00 0.0021 0.0094 44.00 14.000

As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.0021 0.0107 49.75 14.000


Cc. = 84966.00 29.05 Mcc = 2468262.30


P1 67757.14 28.75

-240486.86 kg

M1 1948017.86

712532.66 kg.cm

P2 8742.86 23.00 M2 201085.71

P3 -16392.86 17.25 M3 282776.79

P4 -42840.00 11.50 M4 492660.00

P5 -42840.00 5.75 M5 246330.00

P6 -42840.00 0.00 M6 0.00

P7 -42840.00 -5.75 M7 -246330.00

P8 -42840.00 -11.50 M8 -492660.00

P9 -42840.00 -17.25 M9 -738990.00

P10 -42840.00 -23.00 M10 -985320.00

P11 -85680.00 -28.75 M11 -2463300.00

AG215



F'c = 210.00 kg/cm2 D = 70.00 40 cm 70 cm

F'y = ### a = 0.00 d' = 70.0. cm % de h = 0.00 %


As1 = 20.40 d1' = 63.75 Є1 = 0.0021 F's1 = 4200.00 0.00 26785.71 6.25 0.000

As2 = 10.20 d2' = 58.00 Є2 = 0.0021 F's2 = 4200.00 0.00 51428.57 12.00 0.000

As3 = 10.20 d3 = 52.25 Є3 = 0.0021 F's3 = 4200.00 0.00 76071.43 17.75 0.000

As4 = 10.20 d4' = 46.50 Є4 = 0.0021 F's4 = 4200.00 0.00 100714.28 23.50 0.000

As5 = 10.20 d5' = 40.75 Є5 = 0.0021 F's5 = 4200.00 0.00 125357.14 29.25 0.000

As6 = 10.20 d6' = 35.00 Є6 = 0.0021 F's6 = 4200.00 0.00 150000.00 35.00 0.000

As7 = 10.20 d7' = 29.25 Є7 = 0.0021 F's7 = 4200.00 0.00 174642.85 40.75 0.000

As8 = 10.20 d8' = 23.50 Є8 = 0.0021 F's8 = 4200.00 0.00 199285.71 46.50 0.000

As9 = 10.20 d9' = 17.75 Є9 = 0.0021 F's9 = 4200.00 0.00 223928.57 52.25 0.000

As10 = 10.20 d10' = 12.00 Є10 = 0.0021 F's10 = 4200.00 0.00 248571.43 58.00 0.000

As11 = 20.40 d11' = 6.25 Є11 = 0.0021 F's4 = 4200.00 0.00 273214.28 63.75 0.000


Cc. = 0.00 35.00 Mcc = 0.15


P1 -85680.00 28.75

-556920.00 kg

M1 2463300.00

0.15 kg.cm

P2 -42840.00 23.00 M2 985320.00

P3 -42840.00 17.25 M3 738990.00

P4 -42840.00 11.50 M4 492660.00

P5 -42840.00 5.75 M5 246330.00

P6 -42840.00 0.00 M6 0.00

P7 -42840.00 -5.75 M7 -246330.00

P8 -42840.00 -11.50 M8 -492660.00

P9 -42840.00 -17.25 M9 -738990.00

P10 -42840.00 -23.00 M10 -985320.00

P11 -85680.00 -28.75 M11 -2463300.00

Con carga nominal del 100% Afectada por el Fi del 0.70

CUADRO DE RESUMEN DISTANCIA CUADRO DE RESUMEN DISTANCIA

Tn-m Tn cm Tn-m Tn cm

Mn1 = 0.00 1056720.00 Pn1 = 70.00 Mn1 = 0.00 739704.00 Pn1 = 70.00

Mn2 = 5883833.57 786128.57 Pn2 = 70.00 Mn2 = 4118683.50 550290.00 Pn2 = 70.00

Mn3 = 7747442.60 610947.21 Pn3 = 56.00 Mn3 = 5423209.82 427663.05 Pn3 = 56.00

Mn4 = 6144406.41 368118.00 Pn4 = 42.00 Mn4 = 4301084.49 257682.60 Pn4 = 42.00

Mn5 = 2895493.31 65127.00 Pn5 = 28.00 Mn5 = 2026845.32 45588.90 Pn5 = 28.00

Mn6 = 712532.66 -240486.86 Pn6 = 14.00 Mn6 = 498772.86 -168340.80 Pn6 = 14.00

Mn7 = 0.15 -556920.00 Pn7 = 0.00 Mn7 = 0.10 -389844.00 Pn7 = 0.00


AG247


0.00 1000000.00 2000000.00 3000000.00 4000000.00 5000000.00 6000000.00 7000000.00 8000000.00 9000000.00

-800000.00

-600000.00

-400000.00

-200000.00

0.00

200000.00

400000.00

600000.00

800000.00

1000000.00

1200000.00


Momentos (Tn-m)

Carg

as P

untu

ale

s (

Tn)

0.00 1000000.00 2000000.00 3000000.00 4000000.00 5000000.00 6000000.00 7000000.00 8000000.00 9000000.00

-800000.00

-600000.00

-400000.00

-200000.00

0.00

200000.00

400000.00

600000.00

800000.00

1000000.00

1200000.00

Carga nominal

Afectado por 0.70

Momentos (Tn-m)

Carg

as P

untu

ale

s (

Tn)


CENTRO PLASTICO COLUMNA TIPO "RECTANGULAR" CENTRO PLASTICO COLUMNA TIPO "ELE"CALCULO DE CENTRO PLASTICO

70.00

DATOS

F'c =

F'y =

(Ø) =

SECCION DE COLUMNA

30.00

100.00

1

2 o 3 capas

0

50.00

---

40.00

2

2 o 3 capas

2

20.00

20.00

35.00

DIAGRAMA DE INTERACION

Є

70.00 cm 70.00 cm

P1 +1

35.00 cm

P2 +1

P3 +1

70.00 cm 70.00 cm

P4 +1

35.00 cm

P5 +1

P6 +1

P7 +1

P8 +1

P9 +1

P10 +1

P11 +1

Є

70.00 cm 59.50 cm

P1 +1

29.75 cmP2 +1

P3 +1

P4 +1

P5 +1

P6 +1

P7 +1

P8 +1

P9 +1

P10 +1

P11 +1

Є

56.00 cm 47.60 cm

P1 +1

23.80 cm

P2 +1

P3 +1

P4 +1

P5 +1

P6 +1

P7 +1

P8 +1

P9 +1

14.00 cmP10 -1

P11 -1

Є

42.00 cm 35.70 cm

P1 +1

17.85 cm

P2 +1

P3 +1

P4 +1

P5 +1

P6 +1

P7 +1

P8 -1

P9 -1

28.00 cmP10 -1P11 -1

Є

28.00 cm 23.80 cm

P1 +1

11.90 cm

P2 +1

P3 +1

P4 +1

P5 -1

P6 -1

P7 -1

P8 -1

P9 -1

42.00 cmP10 -1

P11 -1

Є

14.00 cm 11.90 cm

P1 +1

5.95 cm

P2 +1

P3 -1

P4 -1

P5 -1

P6 -1

P7 -1

P8 -1

P9 -1

56.00 cmP10 -1

P11 -1

Є

0.00 cm 0.00 cm

P1 -1

0.00 cm

P2 -1

P3 -1

P4 -1

P5 -1

P6 -1

P7 -1

P8 -1

P9 -1

70.00 cmP10 -1

P11 -1


0.00 1000000.00 2000000.00 3000000.00 4000000.00 5000000.00 6000000.00 7000000.00 8000000.00 9000000.00

-800000.00

-600000.00

-400000.00

-200000.00

0.00

200000.00

400000.00

600000.00

800000.00

1000000.00

1200000.00


Momentos (Tn-m)

Carg

as P

untu

ale

s (

Tn)


CENTRO PLASTICO COLUMNA TIPO "ELE"CALCULO DE CENTRO PLASTICO r = 5.00 Area Cant. Acero area Cant. Acero 105.00

DATOS As1 = 4.00 d1' = 125.00 2.00 2 1.00 5.10 0 1

100.00

210.00 As2 = 4.00 d2' = 105.00 2.00 2 1.00 5.10 0 1

4200.00 As3 = 4.00 d3 = 85.00 2.00 2 1.00 5.10 0 1

0.85 As4 = 4.00 d4' = 65.00 2.00 2 1.00 5.10 0 1

SECCION DE COLUMNA As5 = 4.00 d5' = 45.00 2.00 2 1.00 5.10 0 1

85.00 As6 = 12.00 d6' = 25.00 2.00 6 1.00 5.10 0 1

25.00 As7 = 0.00 d7' = 0.00 2.00 0 1.00 5.10 0 1

4 o 5 capas As8 = 0.00 d8' = 0.00 2.00 0 1.00 5.10 0 1

30.005 As9 = 0.00 d9' = 0.00 2.00 0 1.00 5.10 0 1

20.00 As10 = 12.00 d10' = 5.00 2.00 6 1.00 5.10 0 1

20.00 85.00

4 o 5 capas

0

6.67

--- CALCULO DE CENTROIDE PLASTICO


Cc2. = 455175.00 15.00 6827625.00

Cc1. = 446250.00 80.00 35700000.00

AsI = 16086.00 125.00 2010750.00

AsII = 16086.00 105.00 1689030.00

AsIII = 16086.00 85.00 1367310.00

AsIV = 16086.00 65.00 1045590.00

CP 47.12AsV = 16086.00 45.00 723870.00

AsVI = 48258.00 25.00 1206450.00

AsVII = 0.00 0.00 0.00

AsVIII = 0.00 0.00 0.00

AsIX = 0.00 0.00 0.00

AsX = 48258.00 5.00 241290.00

1078371.00 50811915.00

CP = 47.12

BL3

elmering dice: # ESTRIBO AREA DIAMETRO 3 3/8" 0.71 CM2 0.95 CM. 4 1/2" 1.27 1.27 5 5/8" 1.98 1.59 6 3/4" 2.85 1.91 7 1 " 5.07 2.54

BO3


BL4


BO4


BL5


BO5


BL6


BO6


BL7


BO7


BI19


BI20


BI21


BI22


BI23


BI24


BI25


CENTRO PLASTICO COLUMNA TIPO "ELE" CENTRO PLASTICO COLUMNA TIPO "TEE"105.00 25.00 CALCULO DE CENTRO PLASTICO r = 6.25 area Ø

130.00

1

DATOS As1 = 10.20 d1' = 73.75 5.10 2.00

F'c = 210.00 As2 = 10.20 d2' = 65.75 5.10 2.00

F'y = 4200.00 As3 = 10.20 d3 = 57.75 5.10 2.00

(Ø) = 0.85 As4 = 10.20 d4' = 49.75 5.10 2.00

SECCION DE COLUMNA As5 = 10.20 d5' = 41.75 5.10 2.00

40.00 80.00 As6 = 20.40 d6' = 33.75 5.10 4.00

40.00 30.00 As7 = 10.20 d7' = 39.38 5.10 2.00

21

2 o 3 capas 4 o 5 capas As8 = 10.20 d8' = 20.00 5.10 2.00

0.00 5.00 As9 = 10.20 d9' = 13.13 5.10 2.00

20.00 8.00 As10 = 20.40 d10' = 6.25 5.10 4.00

85.00 --- 8.00

2


0.00 5.00

27.50 6.88

--- 6.88 CALCULO DE CENTROIDE PLASTICO


Cc1. = 571200.00 20.00 11424000.00

Cc2. = 214200.00 60.00 12852000.00

AsI = 41019.30 73.75 3025173.37

AsII = 41019.30 65.75 2697018.97

AsIII = 41019.30 57.75 2368864.57

AsIV = 41019.30 49.75 2040710.17

AsV = 41019.30 41.75 1712555.78

AsVI = 82038.60 33.75 2768802.75

AsVII = 41019.30 39.38 1615134.94

AsVIII = 41019.30 20.00 820386.00

AsIX = 41019.30 13.13 538378.31

AsX = 82038.60 6.25 512741.25

1277631.60 42375766.13

CP = 33.17

CF3


CF4


CF5


CF6


CF7


CC19


CC20


CC21


CC22


CC23


CC24


CC25


CENTRO PLASTICO COLUMNA TIPO "TEE" CENTRO PLASTICO COLUMNA TIPO "U"area Ø 25.00 30.00 25.00 CALCULO DE CENTRO PLASTICO

1 5.10 0.00 1

80.00

40.00 1

DATOS As1 =

1 5.10 0.00 1 F'c = 210.00 As2 =

1 5.10 0.00 1 F'y = 4200.00 As3 =

1 5.10 0.00 1 (Ø) = 0.85 As4 =

1 5.10 0.00 1 SECCION DE COLUMNA As5 =

1 5.10 0.00 1 30.00 120.00 As6 =

1 5.10 0.00 1 50.00 30.00 As7 =

1 5.10 0.00 1

40.00 21

2 o 3 capas 4 o 5 capas As8 =

2 5.10 0.00 1 0.00 5.00 As9 =

3 5.10 0.00 1 25.00 10.00 As10 =

80.00 --- 10.00

2


0.00 5.00

17.50 4.38

--- 4.38

CP 33.17

CI3


CI4


CI5


CI6


CI7


CENTRO PLASTICO COLUMNA TIPO "U"r = 6.25 area Ø area Ø 30.00 60.00 30.00

20.40 d1' = 73.75 5.10 4.00 1 5.10 0.00 1

80.00

20.40 d2' = 63.75 5.10 4.00 1 5.10 0.00 3/8

20.40 d3 = 53.75 5.10 4.00 1 5.10 0.00 1

20.40 d4' = 43.75 5.10 4.00 1 5.10 0.00 1

20.40 d5' = 33.75 5.10 4.00 1 5.10 0.00 1

10.20 d6' = 23.75 5.10 2.00 1 5.10 0.00 1

10.20 d7' = 31.88 5.10 2.00 1 5.10 0.00 1

10.20 d8' = 15.00 5.10 2.00 1 5.10 0.00 1

20.40 d9' = 10.63 5.10 4.00 1 5.10 0.00 1

15.30 d10' = 6.25 5.10 3.00 1 5.10 0.00 1

120.00



Cc1. = 642600.00 15.00 9639000.00

Cc2. = 267750.00 55.00 14726250.00

Cc3. = 267750.00 55.00 14726250.00

AsI = 82038.60 73.75 6050346.75

AsII = 82038.60 63.75 4409574.75

AsIII = 82038.60 53.75 5229960.75

AsIV = 82038.60 43.75 3589188.75

AsV = 82038.60 33.75 2768802.75

CP 35.20AsVI = 41019.30 23.75 974208.37

AsVII = 41019.30 31.88 1307490.19

AsVIII = 41019.30 15.00 615289.50

AsIX = 82038.60 10.63 871660.12

AsX = 61528.95 6.25 384555.94

1854918.45 65292577.87

CP = 35.20

CZ3


DC3


CZ4


DC4


CZ5


DC5


CZ6


DC6


CZ7


DC7


CZ8


DC8


CZ9


DC9


CZ10


DC10


CZ11


DC11


CZ12


DC12


CW18


CW19


CW20


CW21


CW22


CW23


CW24


CW25


CENTRO PLASTICO COLUMNA TIPO "U"

50.00 1

30.00 2

DISEÑO DE COLUMNAS 1 2 3 4 5

1.5CM + 1.8CV ----- ----- ----- -----

HIPOTESIS

DIS

EÑ

O D

E C

OLU

MN

A 0

1

Aceros

DATOS 1 2.54 cm

F'c = 280.00 kg/cm2 4 ksi Estribos

F'y = 4200.00 kg/cm2 60 ksi 0.95 cm

COLUMNA 01

40.00 cm (b) num. de columnas

60.00 cm (h) 1

ln = 390.00 cm

recubrim. = 5.00 cm

r = 18.00

COLUMNA 02


60.00 cm (h) 1

ln = 390.00 cm

recubrim. = 5.00 cm

r = 18.00

VIGA P

40.00 cm (b) num. de vigas

60.00 cm (h) 1

ln = 500.00 cm

recubrim. = 5.00 cm

r = 18.00

VIGA S


60.00 cm (h) 1

ln = 300.00 cm

recubrim. = 5.00 cm

r = 18.00

DATOS

Pu = 339130.00 kg 339.13

Mus = 21032.00 kg.cm

Muv = 1138000.00 11.38

M1 = 380000.00 3.80

M2 = -1138000.00 -11.38

Ln/r 34-12*(M1/M2)

21.67 38.01

∆l definitivo = 1.00

∆l = 1.00

∆l = 0.520

DATOSEc = 250998.01. kg/cm2

Ig = 720000.00 cm4

Bd = 0.00

SECCION DE COLUMNA 01


SECCION DE VIGA P.

SECCION DE VIGA S.

Para efectos locales se pueden despreciar si Ln/r < 34-12*M1/M2

Si cumple, y ya no es necesario calcular ∆l = 1

D8

elmering si es: 1 primera hipotesis 2 segunda hipotesis 3 tercera hipotesis 4 cuarta hipotesis 5 quinta hipotesis

C15

elmering: el radio de giro es. r = √raiz(I/A) o tambien si es rectangular se puede usar r = 0.3*h que (h) es el peralte

C20


D24

elmering: la longitud de la viga es la total entre dos para casos desiguales y para casos iguales la mitad de la loongitud

C26


D29


C31


C36

elmering: M1 = siempre sera el momento flector menor

C37

elmering: M2 = siempre sara el momento flector mayor

C48

elmering: modulo de elasticidad del concreto Ec =15000*raiz(F'c)

C49

elmering: inercia de la seccion bruta del concreto en la seccioin analizada

C50

elmering: relacion entre el momento maximo debido a carga muerta y el momento maximo debido a la carga total. ( momento de carga sostenida sobre momento total)

DIS

EÑ

O D

E C

OLU

MN

A 0

1Cm = 0.466 0.40

Pu = 339130.00 kg

Ø = 0.70

Pc =(pi^2*EI)/Ln^2 Pc = 4690652.86

EI =(Ec*Ig)/(2.5(1+Bd)) EI = 72287426292.54

kLn/r < 22.00

29.00 < 22.00

∆g definitivo = 1.02

∆g = 1.00

∆g = 1.02

Calculo de "k" k = 1.34

Ψm = 0.98

ΨA = 1

ΨB = 0.96

COLUMNAS

Inercia Col 1 = 720000.00 cm4


Kc1 = 1846.15

Kc2 = 1846.15

Kc = 3692.31

VIGAS

Inercia Viga P = 720000.00 cm4

Inercia Viga S = 720000.00 cm4

KvP = 1440.00

KvS = 2400.00

Kv = 3840.00

∆g = 1.02

Ø = 0.70

N. de col. total = 12 col

328600.00 kg 328.60

Pc =(pi^2*EI)/(k*Ln^2) 31423514.35

EI =(Ec*Ig)/(2.5) EI = 72287426292.54

Ec = 250998.01. kg/cm2

Ig = 720000.00 cm4

Calculo del McMc = 1159350.96

g = 0.76

En el eje Y K =Pu/(F'c*b*t)

donde K = 0.50

En el eje X e =Mc/Pu

e = 3.36

donde K*e/t = 0.03

1.50

Calculo de ∆I=Cm/(1-Pu/ ØPc)>=1

Para efectos globales se pueden despreciar si kLn/r < 22

No cumple, si es necesario calc. ∆g = ?

∆g =1 / (1-(∑Pu/Ø∑Pc))

∑Pu =

∑Pc =

Esto es para ir al cuadro de abacos de un diagrama de iteracion de columna

Ṗ =

As = (b*h* Ṗ)/100

D52

elmering: Cm: tiene que ser mayor o igual a 0.4

C53

elmering: Carga amplificada actuante sobre sobre la columna (del SAP)

C54

elmering: Factor de reduccion de resistencia a = 0.70 para columnas estribadas ; y a = 0.75 para columnas con espirales

C55

elmering; Carga critica de pandeo (Formula de Euler)

C71

elmering: ΨB = ∑Kc/∑Kv

C74

elmering: Kc = I/L

C76

elmering: Kc = I/L

C79

elmering: Kc = I/L

C81

elmering: Kc = I/L

C84


C86

elmering; Sumatoria de cargas axiales de diseño amplificadas y acumuladas desde el extremo superior del edificio hasta el entrepiso considerado.

D86

elmering: dato sacado de la sumatoria de los Pu de todas las columnas del SAP.

C87


D87

elmering: se multiplicara por el numero de columnas si todas son del mismo area

C89


C90


B92

elmering: Se calcula segun Mc = ∆I*Muv + ∆g*Mus

C92

elmering: Mc=(∆l*Muv)+(∆g*Mus)

C93

elmering: el "g" dependera mucho en la direccion en el cual se estara diseñando la columna (peralte)

C98

elmering: K = Pu/(F'c*b*t)

C100

elmering: e = Mc/Pu pero ambos casos en (Tn y cm)

B101

elmering: K*e/t = (Pu*e)/(F'c*b*t^2)

C102

elmering: esta cuantia sale segun el cuadro de abacos en porcentajes con los datos obtenidos de los calculos para cada eje (X y Y)

D102

elmering: Segun el RNC la cuantia minima es de 1% y la maxima es de 6% pero se recomienda usar 4% como maxima

DIS

EÑ

O D

E C

OLU

MN

A 0

1As = 36.00 cm2

c

vs

vp

DISEÑO DE COLUMNAS 1 2 3 4

1.5CM + 1.8CV ----- ----- -----

HIPOTESIS

DIS

EÑ

O D

E C

OLU

MN

A 0

1DATOS 1

F'c = 210.00 kg/cm2 3 ksi

F'y = 4200.00 kg/cm2 60 ksi

COLUMNA 01

40.00 cm (b)

40.00 cm (h)

ln = 300.00 cm

recubrim. = 4.00 cm

r = 12.00

COLUMNA 02

40.00 cm (b)

40.00 cm (h)

ln = 300.00 cm

recubrim. = 4.00 cm

r = 12.00

VIGA P

30.00 cm (b)

60.00 cm (h)

ln = 300.00 cm

recubrim. = 4.00 cm

r = 18.00

VIGA S

30.00 cm (b)

60.00 cm (h)

ln = 275.00 cm

recubrim. = 4.00 cm

r = 18.00

DATOS

Pu = 261050.00 kg

Mus = 0.00 kg.cm

Muv = 70844.00

M1 = 34150.00

M2 = -70844.00

Ln/r 34-12*(M1/M2)

25.00 39.78


∆l = 1.00

∆l = 0.499

DATOSEc = 217370.65. kg/cm2

Ig = 213333.33 cm4

Bd = 0.00



SECCION DE VIGA P.

SECCION DE VIGA S.



J8


I15


I20


J24


I26


J29


I31


I36


I37


I48


I49


I50


DIS

EÑ

O D

E C

OLU

MN

A 0

1

Cm = 0.41

Pu = 261050.00 kg

Ø = 0.70

Pc =(pi^2*EI)/Ln^2 Pc = 2034121.33

EI =(Ec*Ig)/(2.5(1+Bd)) EI = 18548962235.12

kLn/r < 22.00

30.63 < 22.00


∆g = 1.00

∆g = 1.29

Calculo de "k" k = 1.23

Ψm = 0.59

ΨA = 1

ΨB = 0.19

COLUMNAS



Kc1 = 711.11

Kc2 = 711.11

Kc = 1422.22

VIGAS



KvP = 3600.00

KvS = 3927.27

Kv = 7527.27

∆g = 1.29

Ø = 0.70

N. de col. total = 12

2550712.30 kg

Pc =(pi^2*EI)/(k*Ln^2) 16261119.03

EI =(Ec*Ig)/(2.5) EI = 18548962235.12

Ec = 217370.65. kg/cm2

Ig = 213333.33 cm4

Calculo del McMc = 70844.00

g = 0.69


donde K = 0.78


e = 0.27

donde K*e/t = 0.00527

1.50




∆g =1 / (1-(∑Pu/Ø∑Pc))

∑Pu =

∑Pc =


Ṗ =

As = (b*h* Ṗ)/100

J52


I53


I54


I55


I71


I74

elmering: Kc = I/L

I76

elmering: Kc = I/L

I79

elmering: Kc = I/L

I81

elmering: Kc = I/L

I84


I86


J86


I87


J87


I89


I90


H92


I92


I93


I98


I100


H101


I102


J102


DIS

EÑ

O D

E C

OLU

MN

A 0

1

As = 24.00 cm2

30.00 50.00

25.00 50.00

30.00 50.00

DISEÑO DE COLUMNAS DISEÑO DE COLUMNAS 5 1 2 3

----- ----- 1.25(CM+CV+CS) -----

HIPOTESIS HIPOTESIS Aceros

DIS

EÑ

O D

E C

OLU

MN

A 0

1

2.54 cm DATOS

Estribos F'c = 210.00 kg/cm2

0.95 cm F'y = 4200.00 kg/cm2

num. de columnas

COLUMNA 011

ln =

recubrim. =

r =

num. de columnas

COLUMNA 02

1

ln =

recubrim. =

r =

num. de vigas

VIGA P2

ln =

recubrim. =

r =

num. de vigas

VIGA S2

ln =

recubrim. =

r =

DATOS

Pu =

Mus =

Muv =

M1 =

M2 =

Ln/r

25.00

∆l definitivo =

∆l =

∆l =

DATOSEc =

Ig =

Bd =



SECCION DE VIGA P.

SECCION DE VIGA S.



O15


O20


O26


O31


O36


O37


O48


O49


O50


0.40

DIS

EÑ

O D

E C

OLU

MN

A 0

1

Cm =

Pu =

Ø =

Pc =(pi^2*EI)/Ln^2 Pc =

EI =(Ec*Ig)/(2.5(1+Bd)) EI =

kLn/r <

30.63 <

∆g definitivo =

∆g =

∆g =

Calculo de "k" k =

Ψm =

ΨA =

ΨB =

COLUMNAS

Inercia Col 1 =

Inercia Col 2 =

Kc1 =

Kc2 =

Kc =

VIGAS

Inercia Viga P =

Inercia Viga S =

KvP =

KvS =

Kv =

∆g =

Ø =

N. de col. total =

Pc =(pi^2*EI)/(k*Ln^2)

EI =(Ec*Ig)/(2.5) EI =

Ec =

Ig =

Calculo del McMc =

g =


donde K =


e =

donde K*e/t =




∆g =1 / (1-(∑Pu/Ø∑Pc))

∑Pu =

∑Pc =


Ṗ =

As = (b*h* Ṗ)/100

O53


O54


O55


O71


O74

elmering: Kc = I/L

O76

elmering: Kc = I/L

O79

elmering: Kc = I/L

O81

elmering: Kc = I/L

O84


O86


O87


O89


O90


N92


O92


O93


O98


O100


N101


O102


DIS

EÑ

O D

E C

OLU

MN

A 0

1

As =

DISEÑO DE COLUMNAS DISEÑO DE COLUMNAS 4 5 1 2

----- ----- ----- -----

HIPOTESIS HIPOTESIS Aceros

DIS

EÑ

O D

E C

OLU

MN

A 0

1

2 2.54 cm DATOS

3 ksi Estribos F'c =

60 ksi 0.95 cm F'y =


COLUMNA 0140.00 cm (h) 1

300.00 cm

4.00 cm

12.00


COLUMNA 02

40.00 cm (h) 1

300.00 cm

4.00 cm

12.00


VIGA P60.00 cm (h) 2

300.00 cm

4.00 cm

18.00


VIGA S60.00 cm (h) 2

275.00 cm

4.00 cm

18.00

217610.00 kg

DATOS0.00 kg.cm

42860.00 kg.cm

34950.00

-42860.00

34-12*(M1/M2)

43.79

1.00

1.00

0.472

217370.65. kg/cm2

DATOS213333.33 cm4

0.00



P8


P24


P29


0.27 0.40

DIS

EÑ

O D

E C

OLU

MN

A 0

1

217610.00 kg

0.70

2034121.33 Pc =(pi^2*EI)/Ln^2

18548962235.12 EI =(Ec*Ig)/(2.5(1+Bd))

22.00

22.00

1.29

1.00

1.29

1.23 Calculo de "k"

0.59

1

0.19

213333.33 cm4

COLUMNAS213333.33 cm4

711.11

711.11

1422.22

540000.00 cm4

VIGAS540000.00 cm4

3600.00

3927.27

7527.27

1.29

0.70

12

2550712.30 kg

16261119.03 Pc =(pi^2*EI)/(k*Ln^2)

18548962235.12 EI =(Ec*Ig)/(2.5)

217370.65. kg/cm2

213333.33 cm4

42860.00Calculo del Mc

0.69

K =Pu/(F'c*b*t) En el eje Y

0.65

e =Mc/Pu En el eje X

0.20

0.00319 donde

1.50




∆g =1 / (1-(∑Pu/Ø∑Pc))



As = (b*h* Ṗ)/100

P52


P86


P87


T92


T101


P102


24.00 cm2

DIS

EÑ

O D

E C

OLU

MN

A 0

1

DISEÑO DE COLUMNAS 3 4 5

1.25(CM+CV-CS) ----- -----

HIPOTESIS Aceros

DATOS 3 2.54 cm

210.00 kg/cm2 3 ksi Estribos

4200.00 kg/cm2 60 ksi 0.95 cm


40.00 cm (h) 1

ln = 300.00 cm

recubrim. = 4.00 cm

r = 12.00


40.00 cm (h) 1

ln = 300.00 cm

recubrim. = 4.00 cm

r = 12.00


60.00 cm (h) 2

ln = 300.00 cm

recubrim. = 4.00 cm

r = 18.00


60.00 cm (h) 2

ln = 275.00 cm

recubrim. = 4.00 cm

r = 18.00

Pu = 190280.00 kg

Mus = 0.00 kg.cm

Muv = 42332.10 kg.cm

M1 = 33844.50

M2 = -42332.10

Ln/r 34-12*(M1/M2)

25.00 43.59


∆l = 1.00

∆l = 0.46

Ec = 217370.65. kg/cm2

Ig = 213333.33 cm4

Bd = 0.00



SECCION DE VIGA P.

SECCION DE VIGA S.



V8


U15


U20


V24


U26


V29


U31


U36


U37


U48


U49


U50


Cm = 0.28 0.40

Pu = 190280.00 kg

Ø = 0.70

Pc = 2034121.33

EI = 18548962235.12

kLn/r < 22.00

30.63 < 22.00


∆g = 1.00

∆g = 1.29

k = 1.23

Ψm = 0.59

ΨA = 1

ΨB = 0.19



Kc1 = 711.11

Kc2 = 711.11

Kc = 1422.22



KvP = 3600.00

KvS = 3927.27

Kv = 7527.27

∆g = 1.29

Ø = 0.70

N. de col. total = 12

2550712.30 kg

16261119.03

EI = 18548962235.12

Ec = 217370.65. kg/cm2

Ig = 213333.33 cm4

Mc = 42332.10

g = 0.69

K =Pu/(F'c*b*t)

donde K = 0.57

e =Mc/Pu

e = 0.22

K*e/t = 0.00315

1.50



∑Pu =

∑Pc =


Ṗ =

As = (b*h* Ṗ)/100

V52


U53


U54


U55


U71


U74

elmering: Kc = I/L

U76

elmering: Kc = I/L

U79

elmering: Kc = I/L

U81

elmering: Kc = I/L

U84


U86


V86


U87


V87


U89


U90


U92


U93


U98


U100


U102


V102


As = 24.00 cm2

DATOS SECCION DE COLUMNA

F'c = 210.00 kg/cm2 40.00 cm (b) 40.00 cm (h)

Pu = 217.61 Tn ln = 300.00 cm

Mu = 42.86 recubrim. = 4.00 cm

M1 = 34.95 r = 12.00

M2 = -42.86


Ln/r 34-12*(M1/M2)

25.00 < 43.79

∆l = 1.00

Calculo del Mc

Mc = 42.86

g = 0.80 SECCION DE VIGA secundaria

2

30.00 cm (b) 60.00 cm (h)

Ln de viga = 275.00

I = 540000.00

Kv = 3927.27

Se necesita calcular Kc y Kv

SECCION DE COLUMNA SECCION DE VIGA principal

2 2

40.00 cm (b) 40.00 cm (h) 30.00 cm (b) 60.00 cm (h)

ln = 300.00 cm Ln de viga = 300.00 cm

I = 213333.33 I = 540000.00

Kc = 1422.22 Kv = 3600.00

∑Kc = 1422.22 ∑Kv = 7527.27

ΨA = 1.00

ΨB = 0.19

Ψm = 0.59 K = 1.23

Para efectos globales se pueden despreciar si K*Ln/r < 22

(K*Ln/r) < 22

30.63 < 22.00

DISEÑO DE COLUMNAS 2da HIPOTESIS "(1.25*CM+1.25*CV+1.25*CS)"



AA10


AC10

elmering: r = √(I/A) o tambien si es rectangular se puede usar r = 0.3*h que (h) es el peralte

AA11


AA18

elmering: tambien se puede despreciar si cumple la siguiente relacion ln/r < 34-12*(M1/M2)

AA19

elmering: Mc=∆l*Muv+∆g*Mus

AC25

elmering: Kv = I/L

AA32

elmering: Kc = I/L

AC32

elmering: Kv = I/L

AA35


Mc = ∆l*Muv + ∆g*Mus

DATOS SECCION DE COLUMNA

F'c = 210.00 kg/cm2 40.00 cm (b) 40.00 cm (h)

Pu = 190.28 Tn ln = 300.00 cm

Mu = 42.86 recubrim. = 4.00 cm

M1 = 34.95 r = 12.00

M2 = -42.86


Ln/r 34-12*(M1/M2)

25.00 < 43.79

∆l = 1.00

Calculo del Mc

Mc = 42.86

g = 0.80 SECCION DE VIGA secundaria

2

30.00 cm (b) 60.00 cm (h)

Ln de viga = 550.00

I = 540000.00

Kv = 1963.64

Se necesita calcular Kc y Kv

SECCION DE COLUMNA SECCION DE VIGA principal

2 2

40.00 cm (b) 40.00 cm (h) 30.00 cm (b) 60.00 cm (h)

ln = 300.00 cm Ln de viga = 600.00 cm

I = 213333.33 I = 540000.00

Kc = 1422.22 Kv = 1800.00

∑Kc = 1422.22 ∑Kv = 3763.64

ΨA = 1.00

ΨB = 0.38

Ψm = 0.69 K = 1.25

Para efectos globales se pueden despreciar si K*Ln/r < 22

(K*Ln/r) < 22

31.37 < 22.00

DISEÑO DE COLUMNAS 2da HIPOTESIS "(1.25*CM+1.25*CV+1.25*CS)"



Mc = ∆l*Muv + ∆g*Mus

AG10


AI10

elmering: r = √(I/A) o tambien si es rectangular se puede usar r = 0.3*h que (h) es el peralte

AG11


AG18

elmering: tambien se puede despreciar si cumple la siguiente relacion ln/r < 34-12*(M1/M2)

AG19

elmering: Mc=∆l*Muv+∆g*Mus

AI25

elmering: Kv = I/L

AG32

elmering: Kc = I/L

AI32

elmering: Kv = I/L

AG35


Plantilla C°A° I

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