viga de cimentacion eje 11

7/28/2019 Viga de Cimentacion Eje 11

1/22

DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II

DISE O DE VIGA DE CIMENTACION: EJE 1-1

P1 P2 P3 P4

DATOS

t = a 1.50m de profundidad fc =

Ko = fy = e piso =

DF = Es = Co = peso volumetrico del concreto armado

NPT= Cs = peso volumetrico del concreto simple

s/c = s = peso volumetrico del suelo

Columna 01 Columna 02 Columna 03 Columna 04

Cargas Cargas Cargas Cargas

PD = PD = PD = PD =

PL = PL = PL = PL =

Momentos Longitudinales Momentos Longitudinales Momentos Longitudinales Momentos Longitudinales

MD = (Horario) MD = MD = MD =

ML = (Horario) ML = ML = ML =

Msx = Msx = Msx = Msx =

Psx = Psx = Psx = Psx =

Momentos Transversales Momentos Transversales Momentos Transversales Momentos Transversales

MD = MD = (Horario) MD = (Horario) MD = (Horario)

ML = ML = (Horario) ML = (Horario) ML = (Horario)

Msy = Msy = Msy = Msy =

Psy = Psy = Psy = Psy =

11.500 m B

hf

H

bw

4.400 m 3.683 m 2.017 m

-0.25Tn-m

5.25Tn-m

20.22Tn-m

-0.04Tn-m

40.18 Tn

rec.=

2.4 Tn/m3

0.075 m

0.150 m

2.0 Tn/m3

1.7 Tn/m3

2.10E+06 Kg/cm2

0.3 m0.5 m

210 Kg/cm

4200 Tn/m

1.5 Kg/cm

5000 Tn/m

1.5 m

0.3 m

200 Kg/m2

0.4 m

74.98 Tn

14.36 Tn

-0.42Tn-m

-0.06Tn-m

12.47Tn-m

1.79Tn-m

0.6 m

5.99 Tn

0.47Tn-m

0.07Tn-m

11.18Tn-m

13.52Tn-m

0.3 m 0.3 m

10.01 Tn

1.54 Tn

-0.19Tn-m

-0.03Tn-m

3.91Tn-m

4.86Tn-m

-0.25Tn-m

0.4 m 0.3 m

38.61 Tn

7.29 Tn

-0.24Tn-m

-0.04Tn-m

3.41Tn-m

16.59Tn-m

0.00Tn-m

0.00Tn-m

0.00Tn-m

0.00Tn-m

-0.07Tn-m

7.76Tn-m

14.07Tn-m

-1.02Tn-m

-0.28Tn-m

16.56Tn-m

30.02Tn-m

JUAN MANUEL CHERO DAMIAN


2/22

DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMAD

DIAGRAMA DE CARGAS

ML1= ML2= ML3= ML4=P1= P2= P3 = P4 =

1. DETERMINACION DE LA PRESION NETA

h = asumido

n =

n = para el caso de sismo

2. DIMENSIONAMIENTO EN PLANTA

A. SIN CONSIDERAR EFECTOS DE SISMO

A.1. POSICION DE LA RESULTANTE CONSIDERANDO ATERNANCIA DE LA CARGA:

1

2

3

4

5

6

0.47 +40.18 +

0.075.99

-0.42 + -0.0674.98 + 14.36

-0.24 + -0.0438.61 + 7.29

-0.19 + -0.0310.01 + 1.54

4.950 m 4.183 m 2.367 m

15.0 - 1.2 -

0.500 m

0.2 -

17.63 Tn/m2

4.95 100 %50 %50 %50 %

0.3 - 0.2 = 13.130 Tn/m2

19.5 - 1.2 - 0.2 - 0.3 - 0.2 =

ALTERNANCIA

x 82.16 + 9.13 x 42.26 + 11.50 x 11.55 + 924.992

179.140== 5.164 m

50 % 100 % 50 %5.216 m

182.015 182.015

50 %x 10.78 + ( 0.54 + -0.48 + -0.28 + -0.22 )=Xg =

4.95

= 5.129 m50 %

Xg =( 0.54 + -0.48 + -0.28 + -0.22 )

179.140

Xg =4.95 x 82.16 + 9.13 x 42.26 + 11.50 x 10.78 + ( 0.54 +

Xg =4.95 x 89.34 + 9.13 x 42.26 + 11.50 x 10.78 +

949.427=

x 82.16 + 9.13 x 45.90 + 11.50

x 45.90 + 11.50

5.051 m100 % 50 % 50 % 50 %

181.365 181.365

-0.48 + -0.28 + -0.22 )=

916.137=

100 %

100 % 50 % 50 %( 0.54 + -0.48 + -0.28 + -0.22 )=

951.678

185.550 185.550

182.785 182.785

Xg =4.95 x 89.34 + 9.13 x 45.90 + 11.50 x 10.78 +

958.282= 5.243 m

50 % 50 % 100 %x 11.55 + ( 0.54 + -0.48 + -0.28 + -0.22 )=Xg =

4.95

189.195 189.195= 5.206 m

50 % 100 % 100 %

x 82.16 + 9.13

50 %( 0.54 + -0.48 + -0.28 + -0.22 )=

984.968

= /


3/22

DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARM

7

8

9

10

11

12

13

EL MAYOR: Xg = EL MENOR: Xg =

EXCENTRICIDAD

e1 < L/6 = e1 < L/6 =

A.2 DETERMINACION DEL ANCHO "B" P = cargas de servicio aplicadas al 100%

aumentamos en por accion de los momentos

Az =

adoptamos B=

L =

= 5.047 m 100 % 100 % 50 % 50 %Xg = 4.95 x 89.34 + 9.13 x 42.26 + 11.50188.545

951.678x 10.78 + ( 0.54 + -0.48 + -0.28 + -0.22 ) =188.545

ALTERNANCIA

Xg =4.95 x 82.16 + 9.13 x 42.26 + 11.50 x 11.55 + ( 0.54 + -0.48 +

x 89.34 + 9.13 x 42.26 + 11.50

100 % 50 % 50 % 100 %

182.135 182.135

-0.28 + -0.22 )=

924.992= 5.079 m

100 %

186.320 186.320

Xg =4.95 x 82.16 + 9.13 x 45.90 + 11.50 x 10.78 +

960.533= 5.155 m

50 % 100 % 50 %x 11.55 + ( 0.54 + -0.48 + -0.28 + -0.22 )=Xg =

4.95

= 5.132 m100 % 50 % 100 % 50 %( 0.54 + -0.48 + -0.28 + -0.22 )

=949.427

185.010 185.010

Xg =4.95 x 89.34 + 9.13 x 45.90 + 11.50 x 11.55 + ( 0.54 +

5.150 m100 % 100 % 100 % 100 %

192.960 192.960

-0.48 + -0.28 + -0.22 )=

993.823=

-0.28 + -0.22 )=

993.823

50 % 100 % 100 %x 11.55 + ( 0.54 + -0.48 + -0.28 + -0.22 )=

Xg =4.95 x 89.34 + 9.13 x 45.90 + 11.50 x 11.55 +

993.823=Xg =

4.95 x 89.34 + 9.13 x 45.90 + 11.50

192.960 192.960

100 %

189.965 189.9655.232 m

1.983 m O.K

192.960

13.13

- 5.05 = 0.70 m e12=11.5

- 5.24 = 0.51 m2

Az = = 14.70 m210 %

16.17 m

5.24 m 5.05 m

e1 =11.5

2

= 5.150 m100 % 100 % 100 % 100 %( 0.54 + -0.48 +

B =16.17 m

11.9= 1.36 m

1.983 m O.K

2.20 m

11.90 m

=


4/22


A.2 VERIFICACION DE PRESIONES

- considerando solo momentos longitudinales

Ps = carga mas desvavorable para Xg mayor y menor

= < n =

= < n =

= < n =

= < n =

- considerando solo momentos transversales

= < n =

= < n =

= < n =

= < n =

13.13 Tn/m2 O.K

1 =1.00 * 182.785 5.20 Tn/m2 13.13 Tn/m2 O.K

1 =1.00 * 182.785

11.90 *

11.90 * 2.2

2.20

-6.00 * ( - 0.29 + - 1.30 + - 0.32 +

- 0.32 +11.90 * 2.20

+ 6.00 * ( - 0.29 + - 1.30 +

1 =1.00 * 188.545 * 0.70) 9.75 Tn/m2

0.00 ) 7.18 Tn/m2 13.13 Tn/m2 O.K

11.90 * 2.2 11.90 * 2.20

13.13 Tn/m2 O.K0.00 ) 6.78 Tn/m2

0.00 ) 6.78 Tn/m2 13.13 Tn/m2 O.K1 =

1.00 * 182.785+

6.00 * ( - 0.29 +

11.90 * 2.2 11.90 *

1 = 1.00 * 182.78511.90 * 2.2

2 =1.00 * 182.785

2 =1.00 * 182.785

-6.00 * ( - 0.29 + - 1.30 + - 0.32 +

- 1.30 + - 0.32 +

0.00 ) 7.18 Tn/m2 13.13 Tn/m2 O.K

11.90 * 2.2 11.90 * 2.20

2.20

+

-

6.00 * ( 182.785 * 0.51)

2.20 * 11.90

8.77 Tn/m2

6.00 * ( 182.785 * 0.51)

2.20 * 11.90

+6.00 * ( 13.13 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90

1 =1.00 * 188.545

-6.00 * ( 188.545 * 0.70) 4.65 Tn/m2 13.13 Tn/m2 O.K

11.90 * 2.2 2.20 * 11.90

188.545

=

6

=

6



5/22


B. CONSIDERANDO EFECTOS DE SISMO EN DIRECCION LONGITUDINAL X-X

B.1 Caso de Momentos Ssmicos horarios

P1 = = P3 = =

ML1 = = ML3 = =

MT1 = = MT3 = =

P2 = = P4 = =

ML2 = = ML4 = =

MT2 = = MT4 = =

P1 = P2 = P3 = P4 =

ML1 = ML2 = ML3 = ML4 =

MT1 = MT2 = MT3 = MT4 =

B.1.1 POSICION DE LA RESULTANTE CONSIDERANDO ATERNANCIA DE LA CARGA:

1

2

EXCENTRICIDAD

e1 < L/6 = e1 < L/6 =

-0.28 +

-0.06 +

14.36 +

-0.04 +

0.07 +

5.99 +40.18 +

0.47 +

-0.25 +

74.98 +

-0.42 +

-1.02 +

12.47

0

59.69 Tn

11.72 Tn-m

-0.29 Tn-m

11.99 Tn-m

-1.30 Tn-m

13.52

11.18

0

1.79 91.13 Tn

38.61 + 7.29 + 4.86 50.76 Tn

-0.24 + -0.04 + 3.91 3.63 Tn-m

-0.25 +

-0.19 + -0.03 + 3.41 3.19 Tn-m

0.00 + 0.00 + 0 0.00 Tn-m

-0.07 + 0 -0.32 Tn-m

10.01 + 1.54 + 16.59 28.14 Tn

3.19 Tn-m

0.00 Tn-m

4.95 m 4.183 m 2.367 m

59.69 Tn

11.72 Tn-m

-0.29 Tn-m

91.13 Tn

11.99 Tn-m

-1.30 Tn-m

ALTERNANCIA

Xg =4.95 x 83.95 + 9 .13 x 50.76 + 11.50 x 28.14 + ( 11.72 + 11.99 + 100 %

219.545 219.545

3.63 + 3.19 )=

1233.284

Xg =4.95 x 91.13 + 9 .13 x 47.12 + 11.50

50 % 50 % 100 %

e1 =11.5

- 5.62 = 0.13 m e12=11.5

- 5.44 =

1226.680=

x 27.37 + ( 11.72 + 11.99 + 3.63 + 3.19 )=

0.31 m2 2

1.983 m O.K 1.983 m O.K

50 %

225.305 225.3055.44 m

100 % 100 % 50 %

= 5.62 m

50.76 Tn

3.63 Tn-m

-0.32 Tn-m

28.14 Tn



6/22


B.1.2 VERIFICACION DE PRESIONES

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

O.K

O.K

O.K

O.K

O.K

O.K

O.K

O.K- 0.29 + - 1.30 + - 0.32 + 0.00 ) 7.48 Tn/m2 17.63 Tn/m2

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

- 0.29 + - 1.30 + - 0.32 + 0.00 ) 10.13 Tn/m2 17.63 Tn/m2

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

4 =1.00 * 225.305

-6.00 * 225.305 0.31

-6.00 * (

- 0.29 + - 1.30 + - 0.32 + 0.00 ) 7.08 Tn/m2 17.63 Tn/m2

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 3 =

1.00 * 225.305-

6.00 * 225.305 0.31+

6.00 * (

2 =1.00 * 225.305

+6.00 * 225.305 0.31

-6.00 * (

- 0.29 + - 1.30 + - 0.32 + 0.00 ) 9.73 Tn/m2 17.63 Tn/m2

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 1 =

1.00 * 225.305+

6.00 * 225.305 0.31+

6.00 * (

- 0.29 + - 1.30 + - 0.32 + 0.00 ) 8.02 Tn/m2 17.63 Tn/m2

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 4 =

1.00 * 219.545-

6.00 * 219.545 * 0.13-

6.00 * (

0.00 ) 7.63 Tn/m2 17.63 Tn/m211.90 * 2.20 2.20 * 11.90 11.90 * 2.20

2.20 2.20 * 11.90 11.90 * 2.20

3 = 1.00 * 219.545 - 6.00 * 219.545 * 0.13 + 6.00 * ( - 0.29 + - 1.30 + - 0.32 +

- 0.32 + 0.00 )

11.90 * 2.20

8.75 Tn/m2 17.63 Tn/m2

2 =1.00 * 219.545

+6.00 * 219.545 * 0.13

-6.00 * ( - 0.29 + - 1.30 + - 0.32 + 0.00 ) 9.15 Tn/m2 17.63 Tn/m2

11.90 *

1 =1.00 * 219.545

+11.90 * 2.20

6.00 * 219.545 * 0.13

2.20 * 11.90 +

6.00 * ( - 0.29 + - 1.30 +

=

6

6


7/22


B.2 Caso de Momentos Ssmicos anti-horarios

P1 = = P3 = =

ML1 = = ML3 = =

MT1 = = MT3 = =

P2 = = P4 = =

ML2 = = ML4 = =

MT2 = = MT4 = =

P1 = P2 = P3 = P4 =

ML1 = ML2 = ML3 = ML4 =MT1 = MT2 = MT3 = MT4 =

B.2.1 POSICION DE LA RESULTANTE CONSIDERANDO ATERNANCIA DE LA CARGA:

1

2

EXCENTRICIDAD

e1 < L/6 = e1 < L/6 =

11.5

50 %

151.785 151.785

676.676

ALTERNANCIA

2 2

1.983 m O.K 1.983 m O.K

e1 = - 4.68 = 1.07 m e12= - 4.46 = 1.29 m11.5

Xg =4.95 x 87.55 + 9.13 x 37.40 + 11.50 -x 5.81 + -( 10.64 + -12.95 + -4.19 + -3.63 )

= = 4.46 m100 % 100 % 50 %

-0.29 Tn-m -1.30 Tn-m -0.32 Tn-m 0.00 Tn-m

4.95 m 4.183 m 2.367 m

ALTERNANCIA

Xg = 4.95 x 80.37 + 9.13 x 41.04 + 11.50 -x 5.04 + -( 10.64 + -12.95 + -4.19 + -3.63 ) = = 4.68 m 50 % 50 %683.280 100 % 100 %

146.025 146.025

32.65 Tn 87.55 Tn 41.04 Tn -5.04 Tn

-10.64 Tn-m -12.95 Tn-m -4.19 Tn-m -3.63 Tn-m

-0.42 + -0.06 - 12.47 -12.95 Tn-m -0.19 + -0.03 - 3.41 -3.63 Tn-m

-1.02 + -0.28 - 0 -1.30 Tn-m 0.00 + 0.00 - 0 0.00 Tn-m

-0.25 + -0.04 - 0 -0.29 Tn-m -0.25 + -0.07 - 0 -0.32 Tn-m

74.98 + 14.36 - 1.79 87.55 Tn 10.01 + 1.54 - 16.59 -5.04 Tn

40.18 + 5.99 - 13.52 32.65 Tn 38.61 + 7.29 - 4.86 41.04 Tn

0.47 + 0.07 - 11.18 -10.64 Tn-m -0.24 + -0.04 - 3.91 -4.19 Tn-m



8/22


B.2.2 VERIFICACION DE PRESIONES

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =0.00 ) 2.22 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

0.00 ) 1.82 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

1.00 * 151.785-

6.00 * 151.785 1.29-

6.00 * ( - 0.29 + - 1.30 + - 0.32 +

9.77 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

0.00 ) 9.38 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

1.00 * 151.785+

6.00 * 151.785 1.29+

6.00 * ( - 0.29 + - 1.30 + - 0.32 +

11.90 * 2.20

3 =1.00 * 146.025

-6.00 * 146.025 * 1.07

+6.00 * (

11.90 * 2.20 2.20 *

0.00 )

1 =

0.00 )

11.90

17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

2 =1.00 * 146.025

+6.00 * 146.025 * 1.07

-6.00 * ( - 0.29 + - 1.30 + - 0.32 + 0.00 ) 8.79 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20

1 =1.00 * 146.025

+6.00 * 146.025 * 1.07

+6.00 * ( - 0.29 + - 1.30 + - 0.32 + 0.00 ) 8.39 Tn/m2

4 =

1.00 * 151.785-

6.00 * 151.785 1.29+

6.00 * ( - 0.29 + - 1.30 + - 0.32 +3 =

1.00 * 151.785

+6.00 * 151.785 1.29

-6.00 * ( - 0.29 + - 1.30 + - 0.32 +

2 =

2.77 Tn/m2 17.63 Tn/m2 O.K

- 0.29 + - 1.30 + - 0.32 + 0.00 ) 2.37 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

4 =1.00 * 146.025

-6.00 * 146.025 * 1.07

-6.00 * ( - 0.29 + - 1.30 + - 0.32 +

11.90 * 2.20 2.20 * 11.90

=

6

6


9/22


C. CONSIDERANDO EFECTOS DE SISMO EN DIRECCION TRANSVERSAL Y-Y

C.1 Caso de Momentos Ssmicos horarios

P1 = = P3 = =

ML1 = = ML3 = =

MT1 = = MT3 = =

P2 = = P4 = =

ML2 = = ML4 = =

MT2 = = MT4 = =

P1 = P2 = P3 = P4 =

ML1 = ML2 = ML3 = ML4 =

MT1 = MT2 = MT3 = MT4 =

C.1.1 POSICION DE LA RESULTANTE CONSIDERANDO ATERNANCIA DE LA CARGA:

1

2

EXCENTRICIDAD

e1 < L/6 = e1 < L/6 =1.983 m O.K 1.983 m O.K

4.86 m100 % 100 % 50 % 50 %

252.855 252.855

e1 =11.5

- 5.00 = 0.75 m e12=11.5

- 4.86 = 0.89 m2 2

Xg =4.95 x 119.36 + 9.13 x 56.33 + 11.50 x 10.78 + ( 0.54 + -0.48 + -0.28 + -0.22 )

=1228.778

4.95 m 4.183 m 2.367 m

=

ALTERNANCIA

Xg =4.95 x 112.18 + 9.13 x 59.97 + 11.50 x 11.55 + ( 0.54 + -0.48 + -0.28 + -0.22 )

=1235.382

= 5.00 m50 % 50 % 100 % 100 %

247.095 247.095

66.39 Tn 119.36 Tn 59.97 Tn 11.55 Tn

0.54 Tn-m -0.48 Tn-m -0.28 Tn-m -0.22 Tn-m

4.96 Tn-m 15.26 Tn-m 7.44 Tn-m 0.00 Tn-m

-0.42 + -0.06 + 0 -0.48 Tn-m -0.19 + -0.03 + 0 -0.22 Tn-m

-1.02 + -0.28 + 16.56 15.26 Tn-m 0.00 + 0.00 + 0 0.00 Tn-m

-0.25 + -0.04 + 5.25 4.96 Tn-m -0.25 + -0.07 + 7.76 7.44 Tn-m

74.98 + 14.36 + 30.02 119.36 Tn 10.01 + 1.54 + 0 11.55 Tn

40.18 + 5.99 + 20.22 66.39 Tn 38.61 + 7.29 + 14.07 59.97 Tn

0.47 + 0.07 + 0 0.54 Tn-m -0.24 + -0.04 + 0 -0.28 Tn-m



10/22


C.1.2 VERIFICACION DE PRESIONES

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =4.96 + 15.26 + 7.44 + 0.00 ) 3.89 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 4 =

1.15 * 252.855-

6.00 * 252.855 0.89-

6.00 * (

4.96 + 15.26 + 7.44 + 0.00 ) 9.65 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 3 =

1.15 * 252.855-

6.00 * 252.855 0.89+

6.00 * (

4.96 + 15.26 + 7.44 + 0.00 ) 11.11 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 2 =1.00 * 252.855

+6.00 * 252.855 0.89

-6.00 * (

4.96 + 15.26 + 7.44 + 0.00 ) 16.88 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 1 =

1.00 * 252.855+

6.00 * 252.855 0.89+

6.00 * (

4.96 + 15.26 + 7.44 + 0.00 ) 2.99 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 4 =

1.00 * 247.095-

6.00 * 247.095 * 0.75-

6.00 * (

0.00 ) 8.75 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

3 =1.00 * 247.095

-6.00 * 247.095 * 0.75

+6.00 * ( 4.96 + 15.26 + 7.44 +

17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

2 =1.00 * 247.095

+6.00 * 247.095 * 0.75

-6.00 * ( 4.96 + 15.26 + 7.44 + 0.00 ) 10.13 Tn/m2 17.63 Tn/m2 O.K

1 =1.00 * 247.095

+6.00 * 247.095 * 0.75

+6.00 * ( 4.96 + 15.26 + 7.44 + 0.00 ) 15.89 Tn/m2

=

6

6


11/22


C.2 Caso de Momentos Ssmicos anti-horarios

P1 = = P3 = =

ML1 = = ML3 = =

MT1 = = MT3 = =

P2 = = P4 = =

ML2 = = ML4 = =

MT2 = = MT4 = =

P1 = P2 = P3 = P4 =

ML1 = ML2 = ML3 = ML4 =

MT1 = MT2 = MT3 = MT4 =

C.2.1 POSICION DE LA RESULTANTE CONSIDERANDO ATERNANCIA DE LA CARGA:

1

2

EXCENTRICIDAD

e1 < L/6 = e1 < L/6 =1.983 m O.K 1.983 m O.K

100 % 100 % 50 %Xg =

4.95 50 %

124.235 124.235

e1 =11.5

- 5.75 = 0.00 m e12=11.5

- 5.43 = 0.32 m2

x 10.78 + ( 0.54 + -0.48 + -0.28 + -0.22 )=

674.578= 5.43 m

2

x 59.32 + 9.13 x 28.19 + 11.50

=681.181

= 5.75 m50 % 50 % 100 % 100 %

118.475 118.475Xg =

4.95 x 52.14 + 9 .13 x 31.83 + 11.50 x 11.55 + ( 0.54 + -0.48 +

25.95 Tn 59.32 Tn 31.83 Tn 11.55 Tn

0.54 Tn-m -0.48 Tn-m -0.28 Tn-m -0.22 Tn-m

-5.54 Tn-m -17.86 Tn-m -8.08 Tn-m 0.00 Tn-m

-0.42 + -0.06 + 0 -0.48 Tn-m -0.19 + -0.03 + 0 -0.22 Tn-m

-1.02 + -0.28 + 16.56 -17.86 Tn-m 0.00 + 0.00 + 0 0.00 Tn-m

1.54 + 0 11.55 Tn

40.18 + 5.99 + -20.22 25.95 Tn 38.61 + 7.29 + -14.07 31.83 Tn

0.47 + 0.07 + 0 0.54 Tn-m -0.24 + -0.04 + 0 -0.28 Tn-m

4.95 m 4.183 m 2.367 m

ALTERNANCIA

-0.28 + -0.22 )

-0.25 + -0.04 + -5.25 -5.54 Tn-m -0.25 + -0.07 + -7.76 -8.08 Tn-m

74.98 + 14.36 + -30.02 59.32 Tn 10.01 +



12/22


C.2.2 VERIFICACION DE PRESIONES

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =

= < n =- 5.54 + - 17.86 + - 8.08 + 0.00 ) 7.26 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20 4 =

1.00 * 124.235-

6.00 * 124.235 0.32-

6.00 * (

0.00 ) 0.70 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

3 =1.00 * 124.235

-6.00 * 124.235 0.32

+6.00 * ( - 5.54 + - 17.86 + - 8.08 +

17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

2 =1.00 * 124.235

+6.00 * 124.235 0.32

-6.00 * ( - 5.54 + - 17.86 + - 8.08 + 0.00 ) 8.79 Tn/m2 17.63 Tn/m2 O.K

+6.00 * 124.235 0.32

+6.00 * ( - 5.54 + - 17.86 +

17.63 Tn/m2 O.K11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

- 8.08 + 0.00 ) 2.23 Tn/m2

0.00 ) 1.25 Tn/m2

- 8.08 + 0.00 ) 7.80 Tn/m2 17.63 Tn/m2 O.K

17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

2 =1.00 * 118.475

+6.00 * 118.475 * 0.00

-6.00 * ( - 5.54 + - 17.86 + - 8.08 + 0.00 ) 7.81 Tn/m2 17.63 Tn/m2 O.K

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

1 =1.00 * 118.475

+6.00 * 118.475 * 0.00

+6.00 * ( - 5.54 + - 17.86 + - 8.08 + 0.00 ) 1.25 Tn/m2

1 =1.00 * 124.235

11.90 * 2.20 2.20 * 11.90 11.90 * 2.20

- 6.00 * 118.475 * 0.00 + 6.00 * ( - 5.54 + - 17.86 + - 8.08 +3 = 1.00 * 118.475

4 =1.00 * 118.475

-6.00 * 118.475 * 0.00

-6.00 * ( - 5.54 + - 17.86 +

=

6

6


13/22


CARGAS DE SERVICIO

RESUMEN DE PRESIONES- CARGAS DE GRAVEDAD - CARGAS DE GRAVEDAD + SISMO LONGITUDINAL HORARIO

1 = W1 = 1 = W1 =

'1 = W'1 = '1 = W'1 =

- CARGAS DE GRAVEDAD + SISMO LONGITUDINAL ANTI-HORARIO - CARGAS DE GRAVEDAD + SISMO TRANSVERSAL HORARIO

1 = W1 = 1 = W1 =

'1 = W'1 = '1 = W'1 =

- CARGAS DE GRAVEDAD + SISMO TRANSVERSAL ANTI-HORARIO

1 = W1 =

'1 = W'1 =

PRESIONES Y CARGAS ADOPTADAS

1 = W1 =

2 = W2 =

ENVOLVENTE DE PRESIONES

8.79 Tn/m2 19.34 Tn/m

8.77 Tn/m2

9.75 Tn/m2

19.29 Tn/m

21.46 Tn/m

9.15 Tn/m2 20.12 Tn/m

8.79 Tn/m2 19.33 Tn/m

8.79 Tn/m2 19.33 Tn/m 15.89 Tn/m2 34.96 Tn/m

15.89 Tn/m2 34.96 Tn/m

16.88 Tn/m2 37.13 Tn/m

11.90 m

46.17 Tn 89.34 Tn 45.90 Tn 11.55 Tn

34.96 Tn/m

37.13 Tn/m

4.950 m 4.1830 m 2.3670 m

9.77 Tn/m2 21.50 Tn/m 16.88 Tn/m2 37.13 Tn/m

7.81 Tn/m2 17.17 Tn/m



14/22


PRESIONES APROXIMADAS: PRIMERA ITERACION

P1 P1 P1 P1

DIAGRAMA DE CORTANTES

DIAGRAMAS DE MOMENTOS FLECTORES

W1 = W1 =

W2 = W1 =

W3 = W1 =

W4 = W1 =

11.55 Tn

-10.73 Tn/m

108.121 60.458

54.72289.52472.727

28.845

71.747

89.592

21.127

30.353

11.849

-23.72 Tn/m

-21.15 Tn/m

35.11 Tn/m

2.4750 m 4.5665 m 3.2750 m 1.1835 m

36.86 Tn/m

36.21 Tn/m 35.50 Tn/m

46.17 Tn 89.34 Tn 45.90 Tn

-14.61 Tn/m

26.13 Tn/m

12.50 Tn/m

14.35 Tn/m

20.49 Tn/m



15/22


PRESIONES APROXIMADAS: SEGUNDA ITERACION

P1 P1 P1 P1



W1 = W1 =

W2 = W1 =

W3 = W1 =

W4 = W1 =

46.17 Tn 89.34 Tn 45.90 Tn 11.55 Tn

20.49 Tn/m

12.50 Tn/m 14.35 Tn/m

26.13 Tn/m

2.4750 m 4.5665 m 3.2750 m 1.1835 m

47.811 34.715 22.984

18.248

47.798 21.442

43.741 6.113 8.126

41.713 9.905

-0.66 Tn/m 25.46 Tn/m

1.50 Tn/m 13.99 Tn/m

0.45 Tn/m 14.80 Tn/m

-5.66 Tn/m 14.84 Tn/m



16/22


PRESIONES APROXIMADAS: TERCERA ITERACION

P1 P1 P1 P1



W1 = W1 =

W2 = W1 =

W3 = W1 =

W4 = W1 =

46.17 Tn 89.34 Tn 45.90 Tn 11.55 Tn

14.84 Tn/m

13.99 Tn/m 14.80 Tn/m

25.46 Tn/m

2.4750 m 4.5665 m 3.2750 m 1.1835 m

47.101 37.726 21.7497

13.329

50.537 22.489

43.569 7.091 5.986

43.634 9.995

-0.38 Tn/m 25.09 Tn/m

0.24 Tn/m 14.23 Tn/m

0.51 Tn/m 15.30 Tn/m

-1.50 Tn/m 13.33 Tn/m



17/22


PRESIONES APROXIMADAS: CUARTA ITERACION

P1 P1 P1 P1



W1 = W1 =

W2 = W1 = ESTOS RESULTADOS SON ACEPTABLES PARA LOS CALCULOS Y ESTOS SERIAN LOS

W3 = W1 = DIAGRAMAS FINALES

W4 = W1 =

11.979

50.799 23.434

43.123 7.579 5.383

46.17 Tn 89.34 Tn 45.90 Tn 11.55 Tn

13.33 Tn/m

14.23 Tn/m 15.30 Tn/m

25.09 Tn/m

2.4750 m 4.5665 m 3.2750 m 1.1835 m

46.518 38.327 21.904

43.859 10.366

-0.14 Tn/m 24.95 Tn/m

0.05 Tn/m 14.27 Tn/m

0.17 Tn/m 15.48 Tn/m

-0.36 Tn/m 12.97 Tn/m



18/22


DISE O DE LA VIGA DE CIMENTACION

a) Mayoracion de las cargas

FACTOR DE MAYORACION

FPM = + =

Presion ultima: =

Carga ultima: =

b) Determinacion de la seccion tranversal por rigidez

- ancho de columna L = adoptado

entonces bw = Ko =

B = f'c =

hf = (asumida) Ec =

Lm = H = VALOR DE "H" ASUMIDO

determinacion de la inercia de la seccion y verificacion de la rigidez

yt = posicion del eje centroidal (teorema de steiner)

Ig =

= L =

1.2

0.45

valor de H correcto u optimizar H

0.45

2.2

0.40 m

0.45 m

2.20 m

0.45 m

4.95 m 1.20 m

5000.0 Tn/m3

210.0 Kg/cm

2173706.51 Tn/m

1.40 *( 40.18 + 74.98 + 38.61 + 10.01 ) 1.70 *( 5.99 + 14.36 + 7.29 + 1.54 ) 1.445

16.88 Tn/m2 * 1.445 24.39 Tn/m2

24.39 Tn/m2 * 2.2 53.66 Tn/m

40.18 + 74.98 + 38.61 + 10.01 + 5.99 + 14.36 + 7.29 + 1.54

0.38 m

0.12314 m4

1.60

0.3184 1.576 =

4


DISEO DE VIGA DE CIMENTACION EJE 1 1


19/22


c) VERIFICACION POR CORTANTE

Se toma el mayor valor del cortante actuante ds = diametro del estribo

Vu = dbL = diametro longitudinal asumidob =

col =

d =

Wu =

cortante ultimo Vud Vud= - =

cortante tomado por el concreto Vc = Vc Vud

d) VERIFICACION POR PUNZONAMINENTO

dbT= diametro transversal asumido

se analiza la zona donde se aplica la mayor carga

dl =

dt =

columna 2 columna 1

m = m =

n = n =

bo = bo =

Ao = Ao =

Pu = Pu =

Vup = Vup =

Vcp1 = Vcp1 =

Vcp2 = Vcp2 =

Vup < Vcp : Vup < Vcp :

2.20 m

0.60 m

35.754 cm

53.66 Tn/m

73.42 Tn 35.28 Tn 38.14 Tn

51.35 Tn O.K VALOR DE hf CORRECTO

0.6

0.4

0.5

0.3

5/8 ''

73.42 Tn

3/8 ''

5/8 ''

35.754 cm

34.166 cm

95.754 cm

74.166 cm

339.840 cm

7101.697 cm2

129.13 Tn

111.81 Tn

189.08 Tn

164.63 Tn

O.K

67.877 cm

64.166 cm

199.920 cm

4355.405 cm2

66.73 Tn

56.11 Tn

104.77 Tn

96.85 Tn

O.K

= 0.85 0.53

d/2

d/2d/2

d/2 d/2

d/2

d/2

C-1C-2

1 = 0.53 +1.1

2 = 1.1


DISEO DE VIGA DE CIMENTACION EJE 1 1


20/22


e) DETERMINACION DEL REFUERZO



DETERMINACION DEL ACERO MINIMO POSITIVO

yt = posicion del eje centroidal (teorema de steiner)

Ig =

Mag = d =

Asmin1=

Asmin2=

entonces el acero minimo sera:

Asmin=

3 + 2 =

1.20 m

0.45 m

1.80 m

0.80 m

0.11525 m4

41831.54 kg.m

12.622 cm2

110.754 cm

12.037 cm2

12.622 cm2

3/4 '' 5/8 '' 12.509 cm2

67.24 Tn 55.40 Tn 31.66 Tn

73.42 Tn 33.87 Tn

17.31 Tn

62.33 Tn.m

63.39 Tn.m

10.95 Tn.m 7.78 Tn.m

14.98 Tn.m

distribuir en una capa

As positivo

bw=

b < 4bw =

As negativo

. 2 = 0.7

. 1 =1.2

0.9 (0.95 )

=

2


DISEO DE VIGA DE CIMENTACION EJE 1 1 UNPRG ING CIVIL CONCRETO ARMADO II


21/22


DETERMINACION DEL ACERO MINIMO NEGATIVO momentos resistentes del acero negativo

- Para acero minimo positivo

a=yb = posicion del eje centroidal (teorema de steiner) Mur =

Ig =

Mag = d = se colocara bastones donde falte cubrir por el acero minimo

Asmin1=

Asmin2= - Para momento negativo

a=

entonces el acero minimo sera: Mur =

Asmin= db = se observa que es suficiente colocar el acero minimo

S = adoptamos 1 @

As =

calculo de los bastones para el momento positivo Mu =

a=

As =

as =As-Asmin =

Se adicionara 1 =

CALCULO DEL ACERO TRANSVERSAL COLUMNA 2: se toma para 1 metro

COLUMNA 1: se toma para 1 metro acero minimo L= t + d=

L= t + d= Asmin= 0.0018*100*d Wu = u*1 =

Wu = u*1 = Asmin = x =

x = tomando db = Mu =

Mu = S = d =

d = adoptamos 1 @ a =

a = As = As =

As = tomando db =

tomando db = S =

S = adoptamos 1 @

adoptamos 1 @ As =

As =

1 '' 0.150 m

33.780 cm2

1.28 m

24.39 Tn/m

1.80 m

39.51 Tn-m

34.166 cm

8.178 cm

34.76 cm

6.15 cm

1/2 ''

20.60 cm

1/2 '' 0.200 m

6.334 cm2

1 ''

14.58 cm

2.51 cm

5/8 '' 1.98 cm

0.84 m

24.39 Tn/m

1.90 m

44.03 Tn-m

34.166 cm

9.282 cm

39.45 cm

1 ''

12.84 cm

1 '' 0.125 m

40.537 cm2

62.33 Tn.m

1.964 cm

15.021 cm2

18.45895833

25.652 cm2

0.40 m

0.11525 m4

83203.39 kg.m 110.754 cm

25.104 cm2

24.075 cm2

25.104 cm2 3/4 ''

0.20 m 3/4 '' 0.200 m

1.635 cm51.98 Tn.m

13.413 cm

100.89 Tn.m

. 2 = 0.7

2

. 1 =1.2

0.9 (0.95 )

= 2




22/22

DISEO DE VIGA DE CIMENTACION EJE 1 1 UNPRG ING CIVIL CONCRETO ARMADO II

COLUMNA 3: se toma para 1 metro COLUMNA 4: se toma para 1 metro

L= t + d= L= t + d=

Wu = u*1 = Wu = u*1 =

x = x =

Mu = Mu =

d = d =

a = a =

As = As =

tomando db = tomando db =

S = S =

adoptamos 1 @ adoptamos 1 @

As = As =

VERIFICACION POR APLASTAMIENTO

Pu =

Pn =

f.aplast =

Ac/Az =

fu.apalast =

ACERO POR TEMPERATURA

s = 30 cm

s = d/6 = adoptamos 1 3/8" a 0.20 m18.459 cm

129.38 Tn

299.88 Tn O.K

0.05 Tn/m2

0.085

0.15 Tn/m2 O.K

1.08 m

24.39 Tn/m

1.90 m

44.03 Tn-m

34.166 cm

9.282 cm

39.45 cm

1 ''

12.84 cm

1 '' 0.125 m

40.537 cm2

0.64 m

24.39 Tn/m

1.90 m

44.03 Tn-m

34.166 cm

9.282 cm

39.45 cm

1 ''

12.84 cm

1 '' 0.125 m

40.537 cm2

= 0.7 0.95 1


viga de cimentacion eje 11

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