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
7/28/2019 Viga de Cimentacion Eje 11
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
= /
7/28/2019 Viga de Cimentacion Eje 11
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
=
7/28/2019 Viga de Cimentacion Eje 11
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DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
5/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
6/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
7/28/2019 Viga de Cimentacion Eje 11
7/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
8/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
7/28/2019 Viga de Cimentacion Eje 11
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DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
10/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
7/28/2019 Viga de Cimentacion Eje 11
11/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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 +
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
12/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
7/28/2019 Viga de Cimentacion Eje 11
13/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
14/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
15/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
PRESIONES APROXIMADAS: SEGUNDA ITERACION
P1 P1 P1 P1
DIAGRAMA DE CORTANTES
DIAGRAMAS DE MOMENTOS FLECTORES
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
16/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
PRESIONES APROXIMADAS: TERCERA ITERACION
P1 P1 P1 P1
DIAGRAMA DE CORTANTES
DIAGRAMAS DE MOMENTOS FLECTORES
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
17/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
PRESIONES APROXIMADAS: CUARTA ITERACION
P1 P1 P1 P1
DIAGRAMA DE CORTANTES
DIAGRAMAS DE MOMENTOS FLECTORES
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
JUAN MANUEL CHERO DAMIAN
7/28/2019 Viga de Cimentacion Eje 11
18/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
DISEO DE VIGA DE CIMENTACION EJE 1 1
7/28/2019 Viga de Cimentacion Eje 11
19/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
DISEO DE VIGA DE CIMENTACION EJE 1 1
7/28/2019 Viga de Cimentacion Eje 11
20/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
e) DETERMINACION DEL REFUERZO
DIAGRAMA DE CORTANTES
DIAGRAMAS DE MOMENTOS FLECTORES
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
JUAN MANUEL CHERO DAMIAN
DISEO DE VIGA DE CIMENTACION EJE 1 1 UNPRG ING CIVIL CONCRETO ARMADO II
7/28/2019 Viga de Cimentacion Eje 11
21/22
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
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
JUAN MANUEL CHERO DAMIAN
DISEO DE VIGA DE CIMENTACION EJE 1-1 UNPRG - ING CIVIL CONCRETO ARMADO II
7/28/2019 Viga de Cimentacion Eje 11
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
JUAN MANUEL CHERO DAMIAN
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