DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 9.56 (tn) MDX = 8.64 (tn.m) MDY = 0.001 (tn.m) Columna ZapataPL = 7.53 (tn) MLX = 12.59 (tn.m) MLY = 0.001 (tn.m) f'c = 210 (kg/cm2) f'c =

fy = 4200 (kg/cm2) fy =a = 50 (cm) conc =b = 50 (cm) c =

Hf = 2.50 (m) N bar = 7 f =Df = 1.90 (m) bar = 2.22 (cm) vc =

apl = 0.65 temp =Suelo c =

ad = 10 (tn/m2) rec =u = 30 (tn/m2) vcp1 =

terr = 1800 (kg/m3) vcp2 =int = 30

1)Obtencin de las cargas de servicioPserv = 17.09 (tn) Mxserv = 21.23 (tn.m) Myserv = 0.002 (tn.m) MXY = 21.23 (tn.m) exy =

ex = 1.24 (m) ey = 0.00 (m) No Cumple2) Predimensionado de la ZapataPlanta y Longitud: a = 10.00 p = -1.71 j =

Lcalc = 2.58 (m) x1 = 2.58 b = 0.00 q = -12.74 k =Lad = 2.60 (m) x2 = Err:502 c = -17.09 u = 2.33 l =

LdLmin = 44.81 (cm) x3 = Err:502 d = -127.39 v = 0.24Altura de la Zapata: z1 = 2.58ldb = 51 (cm) LdL = 95 (cm) Cumple z2 = Err:502

37 (cm) z3 = Err:502hc = 61 (cm) had = 60 (cm) def = 50.0 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3 cv =Relleno = 23.12 (tn) Pu = 71.49 (tn) Mxu = 38.56 (tn.m) Muy =Zapata = 9.73 (tn)Cmtotal = 42.41 (tn)

4) Esfuerzos ltimos sobre el terreno rea = 6.76 (m2) Inercia = 3.8081333333 (m4) X =Y =

1 = 23.74 (tn/m2) 2 = 23.74 (tn/m2) 3 = -2.59 (tn/m2) 4 = -2.59 (tn/m2)

()

ldb

5) Revisin por Cortante d = 50 (cm) xc = 75 (cm)5 = 18.17 (tn/m2) 6 = 18.17 (tn/m2) =

Vu = 30.0 (tn) vu = 2.31 (kg/cm2) vs = 2.71 (kg/cm2) Cumple

5) Revisin por Punzonamiento d = 50 (cm) xc = 50 (cm)7 = 15.64 (tn/m2) 8 = 15.64 (tn/m2) 9 = 5.51 (tn/m2) 10 = 5.51 (tn/m2)

Vu = 60.91 (tn) bo = 4.00 (m) vu = 3.05 (kg/cm2) vs = 3.58 (kg/cm2) Cumple

7) Diseo a Flexin d = 50 (cm) xc = 25 (cm)12 = 13.11 (tn/m2) 11 = 13.11 (tn/m2) Punto de Aplicacin:

X11-2 = 0.58 (m) X12-1 = 0.58 (m)Vu = 50.30 (tn) Xcgp = 0.58 (m)

Mu = 28.95 (tn.m) K = 4.45 m = 23.53 0.00119

As = 15.53 (cm2) = 1/2 = 1.27 (cm) Aunit = 1.27 (cm2)Asmin = 28.08 (cm2) #barr = 22.17 S = 16.00 (cm)

#barrad = 16 Sad = 10 (cm)

=

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETRO210 (kg/cm2) (pulg) cm cm2 cm4200 (kg/cm2)2400 (kg/m3) LISO 6 mm 0.6 0.28 1.880.75 LISO 1/4" 0.635 0.32 1.990.9 8 mm 0.8 0.50 2.51

7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.990.0018 12 mm 1.2 1.13 3.77

1 4 1/2" 1.27 1.27 3.9910 (cm) 5 5/8" 1.588 2.00 4.99

23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.9815.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

1.24 8 1" 2.54 5.10 7.98No Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.990.00 11 1 3/8" 3.58 10.06 11.25-1.71

-12.74

1.670.00 (tn.m)

1.30 (m)

Cumple

0.85

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 39.93 (tn) MDX = 0.74 (tn.m) MDY = 15.36 (tn.m) Columna ZapataPL = 13.44 (tn) MLX = 25.45 (tn.m) MLY = 1.06 (tn.m) f'c = 210 (kg/cm2) f'c =

fy = 4200 (kg/cm2) fy =a = 150 (cm) conc =b = 45 (cm) c =

Hf = 1.55 (m) N bar = 6 f =Df = 0.95 (m) bar = 1.91 (cm) vc =

apl = 0.65 temp =Suelo c =

ad = 10 (tn/m2) rec =u = 30 (tn/m2) vcp1 =

terr = 1800 (kg/m3) vcp2 =int = 30

1)Obtencin de las cargas de servicioPserv = 53.37 (tn) Mxserv = 26.19 (tn.m) Myserv = 16.42 (tn.m) MXY = 30.91 (tn.m) exy =

ex = 0.49 (m) ey = 0.31 (m) Cumple2) Predimensionado de la ZapataPlanta y Longitud: a = 10.00 p = -5.34 j =

Lcalc = 3.54 (m) x1 = 3.54 b = 0.00 q = -25.57 k =Lad = 3.60 (m) x2 = Err:502 c = -53.37 u = 2.94 l =

LdLmin = 56.01 (cm) x3 = Err:502 d = -255.66 v = 0.61Altura de la Zapata: z1 = 3.54ldb = 44 (cm) LdL = 95 (cm) Cumple z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 51 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3 cv =Relleno = 22.16 (tn) Pu = 134.16 (tn) Mxu = 56.21 (tn.m) Muy =Zapata = 18.66 (tn)Cmtotal = 80.75 (tn)

4) Esfuerzos ltimos sobre el terreno rea = 12.96 (m2) Inercia = 13.9968 (m4) X =Y =

1 = 20.44 (tn/m2) 2 = 14.72 (tn/m2) 3 = 0.26 (tn/m2) 4 = 5.99 (tn/m2)

()

ldb

5) Revisin por Cortante d = 51 (cm) xc = 126 (cm)5 = 18.28 (tn/m2) 6 = 12.55 (tn/m2) =

Vu = 32.1 (tn) vu = 1.75 (kg/cm2) vs = 2.05 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 51 (cm) xc = 100.5 (cm)7 = 15.99 (tn/m2) 8 = 12.79 (tn/m2) 9 = 4.72 (tn/m2) 10 = 7.91 (tn/m2)

Vu = 92.34 (tn) bo = 5.94 (m) vu = 3.05 (kg/cm2) vs = 3.59 (kg/cm2) Cumple7) Diseo a FlexinArmadura lado Y d = 51 (cm) xc = 75 (cm)

12 = 16.23 (tn/m2) 11 = 10.50 (tn/m2) Punto de Aplicacin:X11-2 = 0.55 (m) X12-1 = 0.55 (m)

Vu = 58.49 (tn) Xcgp = 0.55 (m)

Mu = 32.15 (tn.m) K = 3.43 m = 23.53 0.00092

As = 16.86 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 33.05 (cm2) #barr = 16.70 S = 20.00 (cm)

#barrad = 18 Sad = 18 (cm)

=

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETRO210 (kg/cm2) (pulg) cm cm2 cm4200 (kg/cm2)2400 (kg/m3) LISO 6 mm 0.6 0.28 1.880.75 LISO 1/4" 0.635 0.32 1.990.9 8 mm 0.8 0.50 2.51

7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.990.0018 12 mm 1.2 1.13 3.77

1 4 1/2" 1.27 1.27 3.9910 (cm) 5 5/8" 1.588 2.00 4.99

23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.9815.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

0.58 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.990.00 11 1 3/8" 3.58 10.06 11.25-5.34

-25.57

1.6722.27 (tn.m)

1.80 (m)

Cumple

0.85

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 39.93 (tn) MDX = 0.74 (tn.m) MDY = 15.36 (tn.m) Columna ZapataPL = 13.44 (tn) MLX = 25.45 (tn.m) MLY = 1.06 (tn.m) f'c = 210 (kg/cm2) f'c =

fy = 4200 (kg/cm2) fy =a = 45 (cm) conc =b = 150 (cm) c =

Hf = 1.55 (m) N bar = 6 f =Df = 0.95 (m) bar = 1.91 (cm) vc =

apl = 0.65 temp =Suelo c =

ad = 10 (tn/m2) rec =u = 30 (tn/m2) vcp1 =

terr = 1800 (kg/m3) vcp2 =int = 30

1)Obtencin de las cargas de servicioPserv = 53.37 (tn) Mxserv = 26.19 (tn.m) Myserv = 16.42 (tn.m) MXY = 30.91 (tn.m) exy =

ex = 0.49 (m) ey = 0.31 (m) Cumple2) Predimensionado de la ZapataPlanta y Longitud: a = 10.00 p = -5.34 j =

Lcalc = 3.54 (m) x1 = 3.54 b = 0.00 q = -25.57 k =Lad = 3.60 (m) x2 = Err:502 c = -53.37 u = 2.94 l =

x3 = Err:502 d = -255.66 v = 0.61Altura de la Zapata: z1 = 3.54ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 51 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3 cv =Relleno = 22.16 (tn) Pu = 134.16 (tn) Mxu = 56.21 (tn.m) Muy =Zapata = 18.66 (tn)Cmtotal = 80.75 (tn)

4) Esfuerzos ltimos sobre el terreno rea = 12.96 (m2) Inercia = 13.9968 (m4) X =Y =

1 = 20.44 (tn/m2) 2 = 14.72 (tn/m2) 3 = 0.26 (tn/m2) 4 = 5.99 (tn/m2)

()

ldb

5) Revisin por Cortante d = 51 (cm) xc = 73.5 (cm)5 = 16.17 (tn/m2) 6 = 10.44 (tn/m2) =

Vu = 59.2 (tn) vu = 3.22 (kg/cm2) vs = 3.79 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 51 (cm) xc = 48 (cm)7 = 13.04 (tn/m2) 8 = 11.52 (tn/m2) 9 = 7.66 (tn/m2) 10 = 9.19 (tn/m2)

Vu = 124.62 (tn) bo = 5.94 (m) vu = 4.11 (kg/cm2) vs = 4.84 (kg/cm2) Cumple7) Diseo a FlexinArmadura lado Y d = 51 (cm) xc = 22.5 (cm)

12 = 14.12 (tn/m2) 11 = 8.39 (tn/m2) Punto de Aplicacin:X11-2 = 0.86 (m) X12-1 = 0.84 (m)

Vu = 81.75 (tn) Xcgp = 0.85 (m)

Mu = 69.28 (tn.m) K = 7.40 m = 23.53 0.00200

As = 36.81 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 33.05 (cm2) #barr = 18.59 S = 18.89 (cm)

#barrad = 19 Sad = 18 (cm)

=

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETRO210 (kg/cm2) (pulg) cm cm2 cm4200 (kg/cm2)2400 (kg/m3) LISO 6 mm 0.6 0.28 1.880.75 LISO 1/4" 0.635 0.32 1.990.9 8 mm 0.8 0.50 2.51

7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.990.0018 12 mm 1.2 1.13 3.77

1 4 1/2" 1.27 1.27 3.9910 (cm) 5 5/8" 1.588 2.00 4.99

23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.9815.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

0.58 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.990.00 11 1 3/8" 3.58 10.06 11.25-5.34

-25.57

1.6722.27 (tn.m)

1.80 (m)

Cumple

0.85

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 39.93 (tn) MDX = 0.74 (tn.m) MDY = 15.36 (tn.m) ColumnaPL = 13.44 (tn) MLX = 25.45 (tn.m) MLY = 1.06 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 150 (cm)b = 45 (cm)

Hf = 2.50 (m) N bar = 6Df = 1.90 (m) bar = 1.91 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 53.37 (tn) Mxserv = 26.19 (tn.m) Myserv = 16.42 (tn.m) MXY = 30.91 (tn.m)

ex = 0.49 (m) ey = 0.31 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -5.34

Lcalc = 3.54 (m) x1 = 3.54 b = 0.00 q = -25.57Lad = 3.60 (m) x2 = Err:502 c = -53.37 u = 2.94

x3 = Err:502 d = -255.66 v = 0.61Altura de la Zapata: z1 = 3.54ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 47.88 (tn) Pu = 169.54 (tn) Mxu = 56.21 (tn.m)Zapata = 20.16 (tn)Cmtotal = 107.97 (tn) Li = 4.00 (m) S1 = 3.18 (m)

S2 = -1.23 (m)ZAPATA RECTANGULAR LdL = 115 (cm) CumpleScalc = 3.22 (m) LdL min= 69 (cm)Sad = 3.50 (m) rearect = 14.00 (m2)

()

ldb

Ixx = 18.67 (m4) Iyy = 14.29 (m4) X = 2.00 (m)LdS = 142.5 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 20.86 (tn/m2) 2 = 15.41 (tn/m2) 3 = 3.36 (tn/m2) 4 = 8.81 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 125 (cm)

5 = 18.60 (tn/m2) 6 = 13.15 (tn/m2)

Vu = 51.0 (tn) vu = 2.55 (kg/cm2) vs = 3.00 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 100 (cm)7 = 16.68 (tn/m2) 8 = 13.56 (tn/m2) 9 = 7.54 (tn/m2) 10 = 10.66 (tn/m2)

Vu = 121.10 (tn) bo = 5.90 (m) vu = 4.11 (kg/cm2) vs = 4.83 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 72.5 (cm)

11 = 19.26 (tn/m2) 12 = 17.00 (tn/m2)

Vu = 59.1 (tn) vu = 3.38 (kg/cm2) vs = 3.98 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 47.5 (cm)13 = 15.86 (tn/m2) 14 = 14.38 (tn/m2) 15 = 8.36 (tn/m2) 16 = 9.84 (tn/m2)

Vu = 158.61 (tn) bo = 5.90 (m) vu = 5.38 (kg/cm2) vs = 6.33 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 75 (cm)

18 = 11.64 (tn/m2) 17 = 17.10 (tn/m2) Punto de Aplicacin:X11-2 = 0.52 (m) X12-1 = 0.57 (m)

Vu = 61.43 (tn) Xcgp = 0.55 (m)

Mu = 33.49 (tn.m) K = 3.83 m = 23.53 0.00103 =

As = 17.94 (cm2) = 3/4 = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 37.80 (cm2) #barr = 13.26 S = 25.38 (cm)

#barrad = 14 Sad = 25.0 (cm) Astot = 39.90 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 22.5 (cm)20 = 6.44 (tn/m2) 19 = 18.48 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.78 (m) Y20-4 = 0.80 (m)Vu = 72.85 (tn) Xcgp = 0.79 (m)

Mu = 57.55 (tn.m) K = 6.39 m = 23.53 0.00173

As = 31.08 (cm2) = 3/4 = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 43.20 (cm2) #barr = 15.16 S = 25.33 (cm)

#barrad = 16 Sad = 25.0 (cm) Astot = 45.60 (cm2)

Grficos de TensionesPunto X Y3 0 0 -3.362 4.00 0 -15.411 4.00 3.50 -20.864 0.00 3.50 -8.81

=

(tn/m2)

0 1 1 2 2 3 3 4 4 5

-3.36-15.41

Tensin 3 - 20 1 1 2 2 3 3 4 4 5

-20.86-8.81Tensin 1 - 4

0 1 1 2 2 3 3 4 4-15.41 -20.86

Tensin 2 - 10 1 1 2 2 3 3 4 4

-3.36-8.81

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 1.14 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 21.52 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 0.58 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -5.34l = -25.57

cv = 1.67Muy = 22.27 (tn.m)

A = 160B = -312.00C = -628.56

Y = 1.75 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

Armadura de Retraccin y Temperatur0.0018

Ast = 37.8 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)

#barr = 13.26 S = 25.38 (cm)#barrad = 14 Sad = 23 (cm) Astot = 39.90 (cm2)

temp =

Armadura de Retraccin y Temperatur0.0018

Ast = 43.2 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)

#barr = 15.16 S = 25.33 (cm)#barrad = 16 Sad = 25 (cm) Astot = 45.60 (cm2)

temp =

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 39.93 (tn) MDX = 0.74 (tn.m) MDY = 15.36 (tn.m) ColumnaPL = 13.44 (tn) MLX = 25.45 (tn.m) MLY = 1.06 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 150 (cm)b = 45 (cm)

Hf = 2.50 (m) N bar = 6Df = 1.90 (m) bar = 1.91 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 53.37 (tn) Mxserv = 26.19 (tn.m) Myserv = 16.42 (tn.m) MXY = 30.91 (tn.m)

ex = 0.49 (m) ey = 0.31 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -5.34

Lcalc = 3.54 (m) x1 = 3.54 b = 0.00 q = -25.57Lad = 3.60 (m) x2 = Err:502 c = -53.37 u = 2.94

x3 = Err:502 d = -255.66 v = 0.61Altura de la Zapata: z1 = 3.54ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 43.78 (tn) Pu = 161.96 (tn) Mxu = 56.21 (tn.m)Zapata = 18.43 (tn)Cmtotal = 102.14 (tn) Li = 4.00 (m) S1 = 3.18 (m)

S2 = -1.23 (m)ZAPATA RECTANGULAR LdL = 115 (cm) CumpleScalc = 3.18 (m) LdL min= 56 (cm)Sad = 3.20 (m) rearect = 12.80 (m2)

()

ldb

Ixx = 17.07 (m4) Iyy = 10.92 (m4) X = 2.00 (m)LdS = 127.5 (cm) CumpleLdSmin = 56 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 22.50 (tn/m2) 2 = 15.98 (tn/m2) 3 = 2.80 (tn/m2) 4 = 9.33 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 125 (cm)

5 = 20.03 (tn/m2) 6 = 13.51 (tn/m2)

Vu = 54.0 (tn) vu = 2.70 (kg/cm2) vs = 3.18 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 100 (cm)7 = 17.99 (tn/m2) 8 = 13.91 (tn/m2) 9 = 7.32 (tn/m2) 10 = 11.40 (tn/m2)

Vu = 111.35 (tn) bo = 5.90 (m) vu = 3.77 (kg/cm2) vs = 4.44 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 72.5 (cm)

11 = 20.72 (tn/m2) 12 = 17.76 (tn/m2)

Vu = 49.2 (tn) vu = 3.08 (kg/cm2) vs = 3.62 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 47.5 (cm)13 = 16.92 (tn/m2) 14 = 14.98 (tn/m2) 15 = 8.39 (tn/m2) 16 = 10.33 (tn/m2)

Vu = 150.54 (tn) bo = 5.90 (m) vu = 5.10 (kg/cm2) vs = 6.00 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 75 (cm)

18 = 11.86 (tn/m2) 17 = 18.39 (tn/m2) Punto de Aplicacin:X11-2 = 0.51 (m) X12-1 = 0.58 (m)

Vu = 64.95 (tn) Xcgp = 0.55 (m)

Mu = 35.46 (tn.m) K = 4.43 m = 23.53 0.00119 =

As = 19.03 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 34.56 (cm2) #barr = 17.46 S = 17.65 (cm)

#barrad = 18 Sad = 17.5 (cm) Astot = 35.63 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 22.5 (cm)20 = 6.52 (tn/m2) 19 = 19.70 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.70 (m) Y20-4 = 0.73 (m)Vu = 63.86 (tn) Xcgp = 0.72 (m)

Mu = 45.68 (tn.m) K = 5.08 m = 23.53 0.00136

As = 24.57 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 43.20 (cm2) #barr = 21.83 S = 18.10 (cm)

#barrad = 22 Sad = 18.0 (cm) Astot = 43.55 (cm2)

Grficos de TensionesPunto X Y3 0 0 -2.802 4.00 0 -15.981 4.00 3.20 -22.504 0.00 3.20 -9.33

=

(tn/m2)

0 1 1 2 2 3 3 4 4 5

-2.80-15.98

Tensin 3 - 20 1 1 2 2 3 3 4 4 5

-22.50-9.33Tensin 1 - 4

0 1 1 2 2 3 3 4-15.98 -22.50

Tensin 2 - 10 1 1 2 2 3 3 4

-2.80-9.33

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 1.25 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 20.35 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 0.58 8 1" 2.54 5.10 7.98No Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -5.34l = -25.57

cv = 1.67Muy = 22.27 (tn.m)

A = 160B = -312.00C = -628.56

Y = 1.60 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 4.22 (tn) MDX = 0.81 (tn.m) MDY = 0.03 (tn.m) Columna ZapataPL = 0.60 (tn) MLX = 0.65 (tn.m) MLY = 0.02 (tn.m) f'c = 210 (kg/cm2) f'c =

fy = 4200 (kg/cm2) fy =a = 75 (cm) conc =b = 75 (cm) c =

Hf = 2.50 (m) N bar = 6 f =Df = 1.90 (m) bar = 1.91 (cm) vc =

apl = 0.65 temp =Suelo c =

ad = 10 (tn/m2) rec =u = 30 (tn/m2) vcp1 =

terr = 1800 (kg/m3) vcp2 =int = 30

1)Obtencin de las cargas de servicioPserv = 4.812 (tn) Mxserv = 1.46 (tn.m) Myserv = 0.05 (tn.m) MXY = 1.46 (tn.m) exy =

ex = 0.30 (m) ey = 0.01 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -0.48 j =

Lcalc = 1.13 (m) x1 = 1.13 b = 0.00 q = -0.91 k =Lad = 1.60 (m) x2 = Err:502 c = -4.81 u = 0.97 l =

x3 = Err:502 d = -9.06 v = 0.17Altura de la Zapata: z1 = 1.13ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3 cv =Relleno = 19.70 (tn) Pu = 43.17 (tn) Mxu = 2.46 (tn.m) Muy =Zapata = 8.29 (tn)Cmtotal = 32.21 (tn) Li = 2.40 (m) S1 = 0.72 (m) A =

S2 = -0.51 (m) B =ZAPATA RECTANGULAR LdL = 72.5 (cm) Cumple C =Scalc = 2.40 (m) LdL min= 69 (cm)Sad = 2.40 (m) rearect = 5.76 (m2)

()

ldb

Ixx = 2.76 (m4) Iyy = 2.76 (m4) X = 1.20 (m) Y =LdS = 72.5 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 8.60 (tn/m2) 2 = 8.53 (tn/m2) 3 = 6.39 (tn/m2) 4 = 6.46 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 87.5 (cm)

5 = 8.31 (tn/m2) 6 = 8.24 (tn/m2) =

Vu = 6.6 (tn) vu = 0.55 (kg/cm2) vs = 0.64 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 62.5 (cm)7 = 8.07 (tn/m2) 8 = 8.03 (tn/m2) 9 = 6.92 (tn/m2) 10 = 6.96 (tn/m2)

Vu = 31.46 (tn) bo = 5.00 (m) vu = 1.26 (kg/cm2) vs = 1.48 (kg/cm2) Cumple

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 87.5 (cm)

11 = 8.59 (tn/m2) 12 = 8.54 (tn/m2) =

Vu = 6.3 (tn) vu = 0.52 (kg/cm2) vs = 0.62 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 62.5 (cm)13 = 8.07 (tn/m2) 14 = 8.03 (tn/m2) 15 = 6.92 (tn/m2) 16 = 6.96 (tn/m2)

Vu = 31.46 (tn) bo = 5.00 (m) vu = 1.26 (kg/cm2) vs = 1.48 (kg/cm2) Cumple

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 37.5 (cm) Armadura de Retraccin y Tempera

18 = 7.79 (tn/m2) 17 = 7.86 (tn/m2) Punto de Aplicacin:X11-2 = 0.22 (m) X12-1 = 0.22 (m) Ast =

Vu = 5.57 (tn) Xcgp = 0.22 (m) =#barr =

Mu = 1.20 (tn.m) K = 0.20 m = 23.53 0.00005 #barrad =

temp =

=

As = 0.64 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 25.92 (cm2) #barr = 9.09 S = 24.44 (cm)

#barrad = 10 Sad = 24.5 (cm) Astot = 28.50 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 37.5 (cm) Armadura de Retraccin y Tempera20 = 6.44 (tn/m2) 19 = 8.58 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.41 (m) Y20-4 = 0.41 (m) Ast =Vu = 14.89 (tn) Xcgp = 0.41 (m) =

#barr =Mu = 6.14 (tn.m) K = 1.54 m = 23.53 0.00041 #barrad =

As = 3.27 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 25.92 (cm2) #barr = 9.09 S = 24.44 (cm)

#barrad = 10 Sad = 24.5 (cm) Astot = 28.50 (cm2)

Grficos de TensionesPunto X Y3 0 0 -6.392 2.40 0 -8.531 2.40 2.40 -8.604 0.00 2.40 -6.46

temp =

=

(tn/m2)

0 1 1 2 2 3 3-6.39 -8.53

Tensin 3 - 20 1 1 2 2 3 3

-8.60-6.46

Tensin 1 - 4

0 1 1 2 2 3 3-8.53 -8.60

Tensin 2 - 10 1 1 2 2 3 3

-6.39 -6.46

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETRO210 (kg/cm2) (pulg) cm cm2 cm4200 (kg/cm2)2400 (kg/m3) LISO 6 mm 0.6 0.28 1.880.75 LISO 1/4" 0.635 0.32 1.990.9 8 mm 0.8 0.50 2.51

7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.990.0018 12 mm 1.2 1.13 3.77

1 4 1/2" 1.27 1.27 3.9910 (cm) 5 5/8" 1.588 2.00 4.99

23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.9815.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

0.30 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.990.00 11 1 3/8" 3.58 10.06 11.25-0.48-0.91

1.670.08 (tn.m)

57.6-11.85-21.02

1.20 (m)

Cumple

0.85

0.85

Armadura de Retraccin y Tempera0.001825.92 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

20.46 S = 11.58 (cm)20 Sad = 10 (cm) Astot = 25.34 (cm2)

Armadura de Retraccin y Tempera0.001825.92 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

20.46 S = 11.58 (cm)20 Sad = 10 (cm) Astot = 25.34 (cm2)

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 4.70 (tn) MDX = 0.59 (tn.m) MDY = 0.80 (tn.m) ColumnaPL = 2.29 (tn) MLX = 0.42 (tn.m) MLY = 0.58 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 60 (cm)b = 60 (cm)

Hf = 2.00 (m) N bar = 6Df = 1.40 (m) bar = 1.91 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 6.99 (tn) Mxserv = 1.01 (tn.m) Myserv = 1.38 (tn.m) MXY = 1.71 (tn.m)

ex = 0.14 (m) ey = 0.20 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -0.70

Lcalc = 1.33 (m) x1 = 1.33 b = 0.00 q = -1.43Lad = 1.40 (m) x2 = Err:502 c = -6.99 u = 1.13

x3 = Err:502 d = -14.34 v = 0.21Altura de la Zapata: z1 = 1.33ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 12.20 (tn) Pu = 36.00 (tn) Mxu = 1.68 (tn.m)Zapata = 6.97 (tn)Cmtotal = 23.87 (tn) Li = 2.20 (m) S1 = 0.82 (m)

S2 = -0.33 (m)ZAPATA RECTANGULAR LdL = 70 (cm) CumpleScalc = 2.20 (m) LdL min= 69 (cm)Sad = 2.20 (m) rearect = 4.84 (m2)

()

ldb

Ixx = 1.95 (m4) Iyy = 1.95 (m4) X = 1.10 (m)LdS = 70 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 9.68 (tn/m2) 2 = 7.09 (tn/m2) 3 = 5.20 (tn/m2) 4 = 7.79 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 80 (cm)

5 = 9.42 (tn/m2) 6 = 6.83 (tn/m2)

Vu = 5.4 (tn) vu = 0.50 (kg/cm2) vs = 0.58 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 55 (cm)7 = 8.56 (tn/m2) 8 = 7.26 (tn/m2) 9 = 6.32 (tn/m2) 10 = 7.61 (tn/m2)

Vu = 27.00 (tn) bo = 4.40 (m) vu = 1.23 (kg/cm2) vs = 1.44 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 80 (cm)

11 = 9.33 (tn/m2) 12 = 7.44 (tn/m2)

Vu = 5.6 (tn) vu = 0.51 (kg/cm2) vs = 0.60 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 55 (cm)13 = 8.56 (tn/m2) 14 = 7.26 (tn/m2) 15 = 6.32 (tn/m2) 16 = 7.61 (tn/m2)

Vu = 27.00 (tn) bo = 4.40 (m) vu = 1.23 (kg/cm2) vs = 1.44 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 30 (cm)

18 = 6.40 (tn/m2) 17 = 8.99 (tn/m2) Punto de Aplicacin:X11-2 = 0.19 (m) X12-1 = 0.21 (m)

Vu = 4.50 (tn) Xcgp = 0.20 (m)

Mu = 0.91 (tn.m) K = 0.17 m = 23.53 0.00004 =

As = 0.48 (cm2) = 3/4 = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 23.76 (cm2) #barr = 8.34 S = 25.00 (cm)

#barrad = 9 Sad = 25.0 (cm) Astot = 25.65 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 30 (cm)20 = 6.84 (tn/m2) 19 = 8.74 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.41 (m) Y20-4 = 0.41 (m)Vu = 14.54 (tn) Xcgp = 0.41 (m)

Mu = 5.93 (tn.m) K = 1.69 m = 23.53 0.00045

As = 3.15 (cm2) = 3/4 = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 23.76 (cm2) #barr = 8.34 S = 25.00 (cm)

#barrad = 9 Sad = 25.0 (cm) Astot = 25.65 (cm2)

Grficos de TensionesPunto X Y3 0 0 -5.202 2.20 0 -7.091 2.20 2.20 -9.684 0.00 2.20 -7.79

=

(tn/m2)

0 1 1 2 2 3-5.20 -7.09

Tensin 3 - 20 1 1 2 2 3

-9.68-7.79Tensin 1 - 4

0 1 1 2 2 3-7.09 -9.68

Tensin 2 - 10 1 1 2 2 3

-5.20 -7.79

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 1 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 0.24 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -0.70l = -1.43

cv = 1.67Muy = 2.30 (tn.m)

A = 48.4B = -23.66C = -13.33

Y = 1.10 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

Armadura de Retraccin y Temperatur0.0018

Ast = 23.76 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 18.76 S = 10.53 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

Armadura de Retraccin y Temperatur0.0018

Ast = 23.76 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 18.76 S = 10.53 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 4.9 (tn) MDX = 0.07 (tn.m) MDY = 0.30 (tn.m) ColumnaPL = 0.76 (tn) MLX = 0.04 (tn.m) MLY = 0.22 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 75 (cm)b = 75 (cm)

Hf = 2.00 (m) N bar = 6Df = 1.40 (m) bar = 1.91 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 5.66 (tn) Mxserv = 0.11 (tn.m) Myserv = 0.52 (tn.m) MXY = 0.53 (tn.m)

ex = 0.02 (m) ey = 0.09 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -0.57

Lcalc = 0.98 (m) x1 = 0.98 b = 0.00 q = -0.38Lad = 3.60 (m) x2 = Err:502 c = -5.66 u = 0.71

x3 = Err:502 d = -3.78 v = 0.27Altura de la Zapata: z1 = 0.98ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 14.52 (tn) Pu = 37.67 (tn) Mxu = 0.18 (tn.m)Zapata = 8.29 (tn)Cmtotal = 27.71 (tn) Li = 2.40 (m) S1 = 0.37 (m)

S2 = -0.08 (m)ZAPATA RECTANGULAR LdL = 72.5 (cm) CumpleScalc = 2.40 (m) LdL min= 69 (cm)Sad = 2.40 (m) rearect = 5.76 (m2)

()

ldb

Ixx = 2.76 (m4) Iyy = 2.76 (m4) X = 1.20 (m)LdS = 72.5 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 6.99 (tn/m2) 2 = 6.24 (tn/m2) 3 = 6.09 (tn/m2) 4 = 6.84 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 87.5 (cm)

5 = 6.97 (tn/m2) 6 = 6.22 (tn/m2)

Vu = 5.2 (tn) vu = 0.43 (kg/cm2) vs = 0.51 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 62.5 (cm)7 = 6.78 (tn/m2) 8 = 6.38 (tn/m2) 9 = 6.30 (tn/m2) 10 = 6.70 (tn/m2)

Vu = 27.45 (tn) bo = 5.00 (m) vu = 1.10 (kg/cm2) vs = 1.29 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 87.5 (cm)

11 = 6.89 (tn/m2) 12 = 6.34 (tn/m2)

Vu = 5.3 (tn) vu = 0.44 (kg/cm2) vs = 0.52 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 62.5 (cm)13 = 6.78 (tn/m2) 14 = 6.38 (tn/m2) 15 = 6.30 (tn/m2) 16 = 6.70 (tn/m2)

Vu = 27.45 (tn) bo = 5.00 (m) vu = 1.10 (kg/cm2) vs = 1.29 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 37.5 (cm)

18 = 6.19 (tn/m2) 17 = 6.94 (tn/m2) Punto de Aplicacin:X11-2 = 0.70 (m) X12-1 = 0.73 (m)

Vu = 33.81 (tn) Xcgp = 0.71 (m)

Mu = 24.12 (tn.m) K = 4.02 m = 23.53 0.00108 =

As = 12.93 (cm2) = 3/4 = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 25.92 (cm2) #barr = 9.09 S = 24.44 (cm)

#barrad = 10 Sad = 24.5 (cm) Astot = 28.50 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 37.5 (cm)20 = 6.58 (tn/m2) 19 = 6.74 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.42 (m) Y20-4 = 0.42 (m)Vu = 13.44 (tn) Xcgp = 0.42 (m)

Mu = 5.58 (tn.m) K = 0.62 m = 23.53 0.00016

As = 2.96 (cm2) = 3/4 = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 25.92 (cm2) #barr = 9.09 S = 24.44 (cm)

#barrad = 10 Sad = 24.5 (cm) Astot = 28.50 (cm2)

Grficos de TensionesPunto X Y3 0 0 -6.092 2.40 0 -6.241 2.40 2.40 -6.994 0.00 2.40 -6.84

=

(tn/m2)

0 1 1 2 2 3 3-6.09 -6.24

Tensin 3 - 20 1 1 2 2 3 3

-6.99-6.84Tensin 1 - 4

0 1 1 2 2 3 3-6.24 -6.99

Tensin 2 - 10 1 1 2 2 3 3

-6.09 -6.84

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 1 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 0.09 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -0.57l = -0.38

cv = 1.67Muy = 0.87 (tn.m)

A = 57.6B = -16.70C = -1.58

Y = 1.20 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

Armadura de Retraccin y Temperatur0.0018

Ast = 25.92 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 20.46 S = 11.58 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

Armadura de Retraccin y Temperatur0.0018

Ast = 25.92 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 20.46 S = 11.58 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 3.57 (tn) MDX = 0.52 (tn.m) MDY = 0.11 (tn.m) ColumnaPL = 0.36 (tn) MLX = 0.36 (tn.m) MLY = 0.08 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 40 (cm)b = 40 (cm)

Hf = 2.00 (m) N bar = 6Df = 1.40 (m) bar = 1.91 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 3.93 (tn) Mxserv = 0.88 (tn.m) Myserv = 0.19 (tn.m) MXY = 0.90 (tn.m)

ex = 0.22 (m) ey = 0.05 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -0.39

Lcalc = 1.01 (m) x1 = 1.01 b = 0.00 q = -0.64Lad = 1.10 (m) x2 = Err:502 c = -3.93 u = 0.86

x3 = Err:502 d = -6.42 v = 0.15Altura de la Zapata: z1 = 1.01ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 10.08 (tn) Pu = 26.01 (tn) Mxu = 1.46 (tn.m)Zapata = 5.76 (tn)Cmtotal = 19.41 (tn) Li = 2.00 (m) S1 = 0.64 (m)

S2 = -0.41 (m)ZAPATA RECTANGULAR LdL = 70 (cm) CumpleScalc = 2.00 (m) LdL min= 56 (cm)Sad = 2.00 (m) rearect = 4.00 (m2)

()

ldb

Ixx = 1.33 (m4) Iyy = 1.33 (m4) X = 1.00 (m)LdS = 70 (cm) CumpleLdSmin = 56 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 7.83 (tn/m2) 2 = 7.36 (tn/m2) 3 = 5.17 (tn/m2) 4 = 5.65 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 70 (cm)

5 = 7.51 (tn/m2) 6 = 7.03 (tn/m2)

Vu = 4.5 (tn) vu = 0.45 (kg/cm2) vs = 0.52 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 45 (cm)7 = 7.10 (tn/m2) 8 = 6.89 (tn/m2) 9 = 5.90 (tn/m2) 10 = 6.12 (tn/m2)

Vu = 20.75 (tn) bo = 3.60 (m) vu = 1.15 (kg/cm2) vs = 1.36 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 70 (cm)

11 = 7.76 (tn/m2) 12 = 7.43 (tn/m2)

Vu = 4.3 (tn) vu = 0.43 (kg/cm2) vs = 0.51 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 45 (cm)13 = 7.10 (tn/m2) 14 = 6.89 (tn/m2) 15 = 5.90 (tn/m2) 16 = 6.12 (tn/m2)

Vu = 20.75 (tn) bo = 3.60 (m) vu = 1.15 (kg/cm2) vs = 1.36 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 20 (cm)

18 = 6.48 (tn/m2) 17 = 6.96 (tn/m2) Punto de Aplicacin:X11-2 = 0.18 (m) X12-1 = 0.18 (m)

Vu = 2.76 (tn) Xcgp = 0.18 (m)

Mu = 0.49 (tn.m) K = 0.10 m = 23.53 0.00003 =

As = 0.26 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 21.60 (cm2) #barr = 10.91 S = 16.36 (cm)

#barrad = 12 Sad = 16.0 (cm) Astot = 23.75 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 20 (cm)20 = 5.46 (tn/m2) 19 = 7.64 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.40 (m) Y20-4 = 0.40 (m)Vu = 10.63 (tn) Xcgp = 0.40 (m)

Mu = 4.27 (tn.m) K = 1.55 m = 23.53 0.00041

As = 2.27 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 21.60 (cm2) #barr = 10.91 S = 16.36 (cm)

#barrad = 12 Sad = 16.0 (cm) Astot = 23.75 (cm2)

Grficos de TensionesPunto X Y3 0 0 -5.172 2.00 0 -7.361 2.00 2.00 -7.834 0.00 2.00 -5.65

=

(tn/m2)

0 1 1 2 2 3-5.17 -7.36

Tensin 3 - 20 1 1 2 2 3

-7.83-5.65Tensin 1 - 4

0 1 1 2 2 3-7.36

-7.83

Tensin 2 - 10 1 1 2 2 3

-5.17 -5.65

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 1 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 0.23 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -0.39l = -0.64

cv = 1.67Muy = 0.32 (tn.m)

A = 40B = -9.00C = -10.56

Y = 1.00 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

Armadura de Retraccin y Temperatur0.0018

Ast = 21.6 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 17.05 S = 9.47 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

Armadura de Retraccin y Temperatur0.0018

Ast = 21.6 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 17.05 S = 9.47 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 0.51 (tn) MDX = 0.00 (tn.m) MDY = 0.00 (tn.m) ColumnaPL = 0.89 (tn) MLX = 0.00 (tn.m) MLY = 0.00 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 120 (cm)b = 40 (cm)

Hf = 0.80 (m) N bar = 4Df = 0.30 (m) bar = 1.27 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 1.4 (tn) Mxserv = 0.002 (tn.m) Myserv = 0.002 (tn.m) MXY = 0.00 (tn.m)

ex = 0.00 (m) ey = 0.00 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -0.14

Lcalc = Err:502 (m) x1 = Err:502 b = 0.00 q = 0.00Lad = 3.60 (m) x2 = Err:502 c = -1.40 u = Err:502

x3 = Err:502 d = -0.02 v = Err:502Altura de la Zapata: z1 = Err:502ldb = 29 (cm) z2 = Err:502

21 (cm) z3 = Err:502hc = 39 (cm) had = 50 (cm) def = 40 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 0.45 (tn) Pu = 4.50 (tn) Mxu = 0.00 (tn.m)Zapata = 1.01 (tn)Cmtotal = 1.97 (tn) Li = 1.40 (m) S1 = 0.11 (m)

S2 = -0.01 (m)ZAPATA RECTANGULAR LdL = 0 (cm)Scalc = 0.52 (m) LdL min= 45 (cm)Sad = 0.60 (m) rearect = 0.84 (m2)

()

ldb

Ixx = 0.14 (m4) Iyy = 0.03 (m4) X = 0.70 (m)LdS = 0 (cm)LdSmin = 45 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 5.41 (tn/m2) 2 = 5.33 (tn/m2) 3 = 5.29 (tn/m2) 4 = 5.38 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 40 (cm) xc = 100 (cm)

5 = 5.42 (tn/m2) 6 = 5.34 (tn/m2)

Vu = -2.3 (tn) vu = -0.40 (kg/cm2) vs = -0.47 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 40 (cm) xc = 80 (cm)7 = 5.48 (tn/m2) 8 = 5.26 (tn/m2) 9 = 5.22 (tn/m2) 10 = 5.44 (tn/m2)

Vu = -9.20 (tn) bo = 4.80 (m) vu = -0.48 (kg/cm2) vs = -0.56 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 40 (cm) yc = 60 (cm)

11 = 5.45 (tn/m2) 12 = 5.29 (tn/m2)

Vu = -1.0 (tn) vu = -0.40 (kg/cm2) vs = -0.47 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 40 (cm) yc = 40 (cm)13 = 5.43 (tn/m2) 14 = 5.32 (tn/m2) 15 = 5.28 (tn/m2) 16 = 5.39 (tn/m2)

Vu = 1.07 (tn) bo = 4.80 (m) vu = 0.06 (kg/cm2) vs = 0.07 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 40 (cm) xc = 60 (cm)

18 = 5.33 (tn/m2) 17 = 5.41 (tn/m2) Punto de Aplicacin:X11-2 = 0.60 (m) X12-1 = 0.60 (m)

Vu = 23.19 (tn) Xcgp = 0.60 (m)

Mu = 13.91 (tn.m) K = 14.49 m = 23.53 0.00403 =

As = 9.66 (cm2) = 1/2 = 1.27 (cm) Aunit = 1.27 (cm2)Asmin = 5.40 (cm2) #barr = 7.63 S = 2.35 (cm)

#barrad = 18 Sad = 17.5 (cm) Astot = 22.80 (cm2)

Armadura en la Direccin X - X d = 40 (cm) yc = 20 (cm)20 = 5.36 (tn/m2) 19 = 5.40 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.05 (m) Y20-4 = 0.05 (m)Vu = 0.32 (tn) Xcgp = 0.05 (m)

Mu = 0.02 (tn.m) K = 0.00 m = 23.53 0.00000

As = 0.01 (cm2) = 1/2 = 1.27 (cm) Aunit = 1.27 (cm2)Asmin = 12.60 (cm2) #barr = 9.95 S = 5.71 (cm)

#barrad = 22 Sad = 18.0 (cm) Astot = 27.87 (cm2)

Grficos de TensionesPunto X Y3 0 0 -5.292 1.40 0 -5.331 1.40 0.60 -5.414 0.00 0.60 -5.38

=

(tn/m2)

0 0 0 1 1 1 1 1 2-5.29 -5.33

Tensin 3 - 20 0 0 1 1 1 1 1 2

-5.41-5.38Tensin 1 - 4

0 0 0 0 0 1 1 1-5.33 -5.41

Tensin 2 - 10 0 0 0 0 1 1 1

-5.29 -5.38

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 2.33 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 14.53 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 0.00 8 1" 2.54 5.10 7.98Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -0.14l = 0.00

cv = 1.67Muy = 0.00 (tn.m)

A = 19.6B = -1.97C = -0.02

Y = 0.30 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

Armadura de Retraccin y Temperatur0.0018

Ast = 5.4 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 4.26 S = 2.11 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

Armadura de Retraccin y Temperatur0.0018

Ast = 12.6 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 9.95 S = 6.32 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 39.93 (tn) MDX = 0.74 (tn.m) MDY = 15.36 (tn.m) ColumnaPL = 13.44 (tn) MLX = 25.45 (tn.m) MLY = 1.06 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 150 (cm)b = 45 (cm)

Hf = 2.50 (m) N bar = 6Df = 1.90 (m) bar = 1.91 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 53.37 (tn) Mxserv = 26.19 (tn.m) Myserv = 16.42 (tn.m) MXY = 30.91 (tn.m)

ex = 0.49 (m) ey = 0.31 (m) Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -5.34

Lcalc = 3.54 (m) x1 = 3.54 b = 0.00 q = -25.57Lad = 3.60 (m) x2 = Err:502 c = -53.37 u = 2.94

x3 = Err:502 d = -255.66 v = 0.61Altura de la Zapata: z1 = 3.54ldb = 44 (cm) z2 = Err:502

32 (cm) z3 = Err:502hc = 54 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 43.78 (tn) Pu = 161.96 (tn) Mxu = 56.21 (tn.m)Zapata = 18.43 (tn)Cmtotal = 102.14 (tn) Li = 4.00 (m) S1 = 3.18 (m)

S2 = -1.23 (m)ZAPATA RECTANGULAR LdL = 115 (cm) CumpleScalc = 3.18 (m) LdL min= 56 (cm)Sad = 3.20 (m) rearect = 12.80 (m2)

()

ldb

Ixx = 17.07 (m4) Iyy = 10.92 (m4) X = 2.00 (m)LdS = 127.5 (cm) CumpleLdSmin = 56 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 22.50 (tn/m2) 2 = 15.98 (tn/m2) 3 = 2.80 (tn/m2) 4 = 9.33 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 125 (cm)

5 = 20.03 (tn/m2) 6 = 13.51 (tn/m2)

Vu = 54.0 (tn) vu = 2.70 (kg/cm2) vs = 3.18 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 100 (cm)7 = 17.99 (tn/m2) 8 = 13.91 (tn/m2) 9 = 7.32 (tn/m2) 10 = 11.40 (tn/m2)

Vu = 111.35 (tn) bo = 5.90 (m) vu = 3.77 (kg/cm2) vs = 4.44 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 72.5 (cm)

11 = 20.72 (tn/m2) 12 = 17.76 (tn/m2)

Vu = 49.2 (tn) vu = 3.08 (kg/cm2) vs = 3.62 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 47.5 (cm)13 = 16.92 (tn/m2) 14 = 14.98 (tn/m2) 15 = 8.39 (tn/m2) 16 = 10.33 (tn/m2)

Vu = 150.54 (tn) bo = 5.90 (m) vu = 5.10 (kg/cm2) vs = 6.00 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 75 (cm)

18 = 11.86 (tn/m2) 17 = 18.39 (tn/m2) Punto de Aplicacin:X11-2 = 0.51 (m) X12-1 = 0.58 (m)

Vu = 64.95 (tn) Xcgp = 0.55 (m)

Mu = 35.46 (tn.m) K = 4.43 m = 23.53 0.00119 =

As = 19.03 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 34.56 (cm2) #barr = 17.46 S = 17.65 (cm)

#barrad = 18 Sad = 17.5 (cm) Astot = 35.63 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 22.5 (cm)20 = 6.52 (tn/m2) 19 = 19.70 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.70 (m) Y20-4 = 0.73 (m)Vu = 63.86 (tn) Xcgp = 0.72 (m)

Mu = 45.68 (tn.m) K = 5.08 m = 23.53 0.00136

As = 24.57 (cm2) = 5/8 = 1.59 (cm) Aunit = 1.98 (cm2)Asmin = 43.20 (cm2) #barr = 21.83 S = 18.10 (cm)

#barrad = 22 Sad = 18.0 (cm) Astot = 43.55 (cm2)

Grficos de TensionesPunto X Y3 0 0 -2.802 4.00 0 -15.981 4.00 3.20 -22.504 0.00 3.20 -9.33

=

(tn/m2)

0 1 1 2 2 3 3 4 4 5

-2.80-15.98

Tensin 3 - 20 1 1 2 2 3 3 4 4 5

-22.50-9.33Tensin 1 - 4

0 1 1 2 2 3 3 4-15.98 -22.50

Tensin 2 - 10 1 1 2 2 3 3 4

-2.80-9.33

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 1.25 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 20.35 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 0.58 8 1" 2.54 5.10 7.98No Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -5.34l = -25.57

cv = 1.67Muy = 22.27 (tn.m)

A = 160B = -312.00C = -628.56

Y = 1.60 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

Armadura de Retraccin y Temperatur0.0018

Ast = 34.56 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 27.28 S = 15.79 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

Armadura de Retraccin y Temperatur0.0018

Ast = 43.2 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 34.10 S = 20.00 (cm)#barrad = 20 Sad = 10 (cm) Astot = 25.34 (cm2)

temp =

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 9.56 (tn) MDX = 8.64 (tn.m) MDY = 0.001 (tn.m) ColumnaPL = 7.53 (tn) MLX = 12.59 (tn.m) MLY = 0.001 (tn.m) f'c = 210 (kg/cm2)

fy = 4200 (kg/cm2)a = 90 (cm)b = 90 (cm)

Hf = 2.50 (m) N bar = 7Df = 1.90 (m) bar = 2.22 (cm)

apl = 0.65Suelo

ad = 10 (tn/m2)u = 30 (tn/m2)

terr = 1800 (kg/m3)int = 30

1)Obtencin de las cargas de servicioPserv = 17.09 (tn) Mxserv = 21.23 (tn.m) Myserv = 0.002 (tn.m) MXY = 21.23 (tn.m)

ex = 1.24 (m) ey = 0.00 (m) No Cumple2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -1.71

Lcalc = 2.58 (m) x1 = 2.58 b = 0.00 q = -12.74Lad = 2.60 (m) x2 = Err:502 c = -17.09 u = 2.33

x3 = Err:502 d = -127.39 v = 0.24Altura de la Zapata: z1 = 2.58ldb = 51 (cm) z2 = Err:502

37 (cm) z3 = Err:502hc = 61 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3Relleno = 30.47 (tn) Pu = 85.07 (tn) Mxu = 38.56 (tn.m)Zapata = 12.83 (tn)Cmtotal = 52.86 (tn) Li = 3.30 (m) S1 = 2.24 (m)

S2 = -1.72 (m)ZAPATA RECTANGULAR LdL = 110 (cm) CumpleScalc = 2.98 (m) LdL min= 69 (cm)Sad = 2.70 (m) rearect = 8.91 (m2)

()

ldb

Ixx = 8.09 (m4) Iyy = 5.41 (m4) X = 1.65 (m)LdS = 80 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 17.42 (tn/m2) 2 = 17.42 (tn/m2) 3 = 1.68 (tn/m2) 4 = 1.68 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 95 (cm)

5 = 14.08 (tn/m2) 6 = 14.08 (tn/m2)

Vu = 36.4 (tn) vu = 2.20 (kg/cm2) vs = 2.59 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 70 (cm)7 = 12.89 (tn/m2) 8 = 12.89 (tn/m2) 9 = 6.21 (tn/m2) 10 = 6.21 (tn/m2)

Vu = 66.36 (tn) bo = 5.60 (m) vu = 2.37 (kg/cm2) vs = 2.79 (kg/cm2)

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 95 (cm)

11 = 17.42 (tn/m2) 12 = 17.42 (tn/m2)

Vu = 14.6 (tn) vu = 1.08 (kg/cm2) vs = 1.27 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 70 (cm)13 = 12.89 (tn/m2) 14 = 12.89 (tn/m2) 15 = 6.21 (tn/m2) 16 = 6.21 (tn/m2)

Vu = 66.36 (tn) bo = 5.60 (m) vu = 2.37 (kg/cm2) vs = 2.79 (kg/cm2)

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 45 (cm)

18 = 11.69 (tn/m2) 17 = 11.69 (tn/m2) Punto de Aplicacin:X11-2 = 0.45 (m) X12-1 = 0.45 (m)

Vu = 32.17 (tn) Xcgp = 0.45 (m)

Mu = 14.57 (tn.m) K = 2.16 m = 23.53 0.00057 =

As = 7.76 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 29.16 (cm2) #barr = 10.23 S = 25.00 (cm)

#barrad = 11 Sad = 25.0 (cm) Astot = 31.35 (cm2)

Armadura en la Direccin X - X d = 50 (cm) yc = 45 (cm)20 = 1.68 (tn/m2) 19 = 17.42 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.45 (m) Y20-4 = 0.45 (m)Vu = 23.20 (tn) Xcgp = 0.45 (m)

Mu = 10.44 (tn.m) K = 1.61 m = 23.53 0.00043

As = 5.55 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 35.64 (cm2) #barr = 12.50 S = 25.83 (cm)

#barrad = 13 Sad = 26.0 (cm) Astot = 37.05 (cm2)

Grficos de TensionesPunto X Y3 0 0 -1.682 3.30 0 -17.421 3.30 2.70 -17.424 0.00 2.70 -1.68

=

(tn/m2)

0 1 1 2 2 3 3 4

-1.68-17.42

Tensin 3 - 20 1 1 2 2 3 3 4

-17.42-1.68

Tensin 1 - 4

0 1 1 2 2 3 3-17.42 -17.42

Tensin 2 - 10 1 1 2 2 3 3

-1.68 -1.68

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETROf'c = 210 (kg/cm2) (pulg) cm cm2 cmfy = 4200 (kg/cm2)

conc = 2400 (kg/m3) LISO 6 mm 0.6 0.28 1.88c = 0.75 LISO 1/4" 0.635 0.32 1.99f = 0.9 8 mm 0.8 0.50 2.51vc = 7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.99

temp = 0.0018 12 mm 1.2 1.13 3.77c = 1.2222222222 4 1/2" 1.27 1.27 3.99rec = 10 (cm) 5 5/8" 1.588 2.00 4.99

vcp1 = 20.63 (kg/cm2) 6 3/4" 1.905 2.84 5.98vcp2 = 15.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

exy = 1.24 8 1" 2.54 5.10 7.98No Cumple 9 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.99j = 0.00 11 1 3/8" 3.58 10.06 11.25k = -1.71l = -12.74

ex = 1.242246928 (m)ey = 0.0001170275 (m)

m = 0.4219753086

cv = 1.67Muy = 0.00 (tn.m)

A = 108.9B = -56.41C = -420.35

Y = 1.35 (m)

Cumple

= 0.85

Cumple

= 0.85

Cumple

Armadura de Retraccin y Temperatura en la Direccin Y - Y0.0018

Ast = 29.16 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 23.02 S = 11.36 (cm)#barrad = 23 Sad = 11 (cm) Astot = 29.14 (cm2)

temp =

Cumple

Armadura de Retraccin y Temperatura en la Direccin X - X0.0018

Ast = 35.64 (cm2) = 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

#barr = 28.13 S = 11.48 (cm)#barrad = 28 Sad = 11.5 (cm) Astot = 35.47 (cm2)

Cumple

temp =

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 23.73 (tn) MDX = 15.09 (tn.m) MDY = 0.001 (tn.m) Columna ZapataPL = 15.40 (tn) MLX = 12.33 (tn.m) MLY = 0.001 (tn.m) f'c = 210 (kg/cm2) f'c =

fy = 4200 (kg/cm2) fy =a = 90 (cm) conc =b = 90 (cm) c =

Hf = 2.50 (m) N bar = 7 f =Df = 1.90 (m) bar = 2.22 (cm) vc =

apl = 0.65 temp =Suelo c =

ad = 10 (tn/m2) rec =u = 30 (tn/m2) vcp1 =

terr = 1800 (kg/m3) vcp2 =int = 30

1)Obtencin de las cargas de servicioPserv = 39.13 (tn) Mxserv = 27.42 (tn.m) Myserv = 0.002 (tn.m) MXY = 27.42 (tn.m) exy =

ex = 0.70 (m) ey = 0.00 (m)2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -3.91 j =

Lcalc = 3.05 (m) x1 = 3.05 b = 0.00 q = -16.45 k =Lad = 3.10 (m) x2 = Err:502 c = -39.13 u = 2.54 l =

x3 = Err:502 d = -164.53 v = 0.51Altura de la Zapata: z1 = 3.05ldb = 51 (cm) z2 = Err:502

37 (cm) z3 = Err:502hc = 61 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3 cv =Relleno = 32.87 (tn) Pu = 125.00 (tn) Mxu = 46.39 (tn.m) Muy =Zapata = 13.84 (tn)Cmtotal = 70.43 (tn) Li = 3.10 (m) S1 = 3.02 (m) A =

S2 = -1.76 (m) B =ZAPATA RECTANGULAR LdL = 100 (cm) Cumple C =Scalc = 3.10 (m) LdL min= 69 (cm)Sad = 3.10 (m) rearect = 9.61 (m2)

()

ldb

Ixx = 7.70 (m4) Iyy = 7.70 (m4) X = 1.55 (m) Y =LdS = 100 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 22.35 (tn/m2) 2 = 22.35 (tn/m2) 3 = 3.66 (tn/m2) 4 = 3.67 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 95 (cm)

5 = 18.73 (tn/m2) 6 = 18.73 (tn/m2) =

Vu = 38.2 (tn) vu = 2.46 (kg/cm2) vs = 2.90 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 70 (cm)7 = 17.23 (tn/m2) 8 = 17.23 (tn/m2) 9 = 8.79 (tn/m2) 10 = 8.79 (tn/m2)

Vu = 99.50 (tn) bo = 5.60 (m) vu = 3.55 (kg/cm2) vs = 4.18 (kg/cm2) Cumple

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 95 (cm)

11 = 22.35 (tn/m2) 12 = 22.35 (tn/m2) =

Vu = 32.9 (tn) vu = 2.12 (kg/cm2) vs = 2.50 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 70 (cm)13 = 17.23 (tn/m2) 14 = 17.23 (tn/m2) 15 = 8.79 (tn/m2) 16 = 8.79 (tn/m2)

Vu = 99.50 (tn) bo = 5.60 (m) vu = 3.55 (kg/cm2) vs = 4.18 (kg/cm2) Cumple

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 45 (cm) Armadura de Retraccin y Temperatura en la Direccin Y - Y

18 = 15.72 (tn/m2) 17 = 15.72 (tn/m2) Punto de Aplicacin:X11-2 = 0.58 (m) X12-1 = 0.58 (m) Ast =

Vu = 64.91 (tn) Xcgp = 0.58 (m) =#barr =

Mu = 37.77 (tn.m) K = 4.87 m = 23.53 0.00131 #barrad =

temp =

=

As = 20.30 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 33.48 (cm2) #barr = 11.75 S = 26.36 (cm)

#barrad = 12 Sad = 26.0 (cm) Astot = 34.20 (cm2) Cumple

Armadura en la Direccin X - X d = 50 (cm) yc = 45 (cm) Armadura de Retraccin y Temperatura en la Direccin X - X20 = 3.67 (tn/m2) 19 = 22.35 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.55 (m) Y20-4 = 0.55 (m) Ast =Vu = 44.36 (tn) Xcgp = 0.55 (m) =

#barr =Mu = 24.40 (tn.m) K = 3.15 m = 23.53 0.00084 #barrad =

As = 13.04 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 33.48 (cm2) #barr = 11.75 S = 26.36 (cm)

#barrad = 12 Sad = 26.0 (cm) Astot = 34.20 (cm2) Cumple

Grficos de TensionesPunto X Y3 0 0 -3.662 3.10 0 -22.351 3.10 3.10 -22.354 0.00 3.10 -3.67

temp =

=

(tn/m2)

0 1 1 2 2 3 3 4

-3.66 -22.35Tensin 3 - 2

0 1 1 2 2 3 3 4-22.35-3.67

Tensin 1 - 4

0 1 1 2 2 3 3 4-22.35 -22.35

Tensin 2 - 10 1 1 2 2 3 3 4

-3.66 -3.67

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETRO210 (kg/cm2) (pulg) cm cm2 cm4200 (kg/cm2)2400 (kg/m3) LISO 6 mm 0.6 0.28 1.880.75 LISO 1/4" 0.635 0.32 1.990.9 8 mm 0.8 0.50 2.51

7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.990.0018 12 mm 1.2 1.13 3.77

1 4 1/2" 1.27 1.27 3.9910 (cm) 5 5/8" 1.588 2.00 4.99

23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.9815.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

0.70 8 1" 2.54 5.10 7.989 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.990.00 11 1 3/8" 3.58 10.06 11.25-3.91

-16.45

1.670.00 (tn.m)

96.1-121.32-510.01

1.55 (m)

Cumple

0.85

0.85

Armadura de Retraccin y Temperatura en la Direccin Y - Y0.001833.48 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

26.43 S = 11.15 (cm)27 Sad = 11 (cm) Astot = 34.20 (cm2)

Armadura de Retraccin y Temperatura en la Direccin X - X0.001833.48 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

26.43 S = 11.15 (cm)27 Sad = 11 (cm) Astot = 34.20 (cm2)

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 28.48 (tn) MDX = 16.25 (tn.m) MDY = 0.001 (tn.m) Columna ZapataPL = 16.80 (tn) MLX = 13.35 (tn.m) MLY = 0.001 (tn.m) f'c = 210 (kg/cm2) f'c =

fy = 4200 (kg/cm2) fy =a = 90 (cm) conc =b = 90 (cm) c =

Hf = 2.50 (m) N bar = 7 f =Df = 1.90 (m) bar = 2.22 (cm) vc =

apl = 0.65 temp =Suelo c =

ad = 10 (tn/m2) rec =u = 30 (tn/m2) vcp1 =

terr = 1800 (kg/m3) vcp2 =int = 30

1)Obtencin de las cargas de servicioPserv = 45.28 (tn) Mxserv = 29.6 (tn.m) Myserv = 0.002 (tn.m) MXY = 29.60 (tn.m) exy =

ex = 0.65 (m) ey = 0.00 (m)2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -4.53 j =

Lcalc = 3.18 (m) x1 = 3.18 b = 0.00 q = -17.76 k =Lad = 3.20 (m) x2 = Err:502 c = -45.28 u = 2.60 l =

x3 = Err:502 d = -177.61 v = 0.58Altura de la Zapata: z1 = 3.18ldb = 51 (cm) z2 = Err:502

37 (cm) z3 = Err:502hc = 61 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3 cv =Relleno = 37.24 (tn) Pu = 142.30 (tn) Mxu = 50.11 (tn.m) Muy =Zapata = 15.68 (tn)Cmtotal = 81.41 (tn) Li = 3.30 (m) S1 = 3.11 (m) A =

S2 = -1.73 (m) B =ZAPATA RECTANGULAR LdL = 110 (cm) Cumple C =Scalc = 3.30 (m) LdL min= 69 (cm)Sad = 3.30 (m) rearect = 10.89 (m2)

()

ldb

Ixx = 9.88 (m4) Iyy = 9.88 (m4) X = 1.65 (m) Y =LdS = 110 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 21.43 (tn/m2) 2 = 21.43 (tn/m2) 3 = 4.70 (tn/m2) 4 = 4.70 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 95 (cm)

5 = 17.88 (tn/m2) 6 = 17.88 (tn/m2) =

Vu = 45.4 (tn) vu = 2.75 (kg/cm2) vs = 3.24 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 70 (cm)7 = 16.62 (tn/m2) 8 = 16.62 (tn/m2) 9 = 9.52 (tn/m2) 10 = 9.52 (tn/m2)

Vu = 116.69 (tn) bo = 5.60 (m) vu = 4.17 (kg/cm2) vs = 4.90 (kg/cm2) Cumple

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 95 (cm)

11 = 21.43 (tn/m2) 12 = 21.43 (tn/m2) =

Vu = 39.8 (tn) vu = 2.42 (kg/cm2) vs = 2.84 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 70 (cm)13 = 16.62 (tn/m2) 14 = 16.62 (tn/m2) 15 = 9.52 (tn/m2) 16 = 9.52 (tn/m2)

Vu = 116.69 (tn) bo = 5.60 (m) vu = 4.17 (kg/cm2) vs = 4.90 (kg/cm2) Cumple

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 45 (cm) Armadura de Retraccin y Temperatura en la Direccin Y - Y

18 = 15.35 (tn/m2) 17 = 15.35 (tn/m2) Punto de Aplicacin:X11-2 = 0.61 (m) X12-1 = 0.61 (m) Ast =

Vu = 67.68 (tn) Xcgp = 0.61 (m) =#barr =

Mu = 41.06 (tn.m) K = 4.98 m = 23.53 0.00134 #barrad =

temp =

=

As = 22.07 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 35.64 (cm2) #barr = 12.50 S = 25.83 (cm)

#barrad = 13 Sad = 26.0 (cm) Astot = 37.05 (cm2) Cumple

Armadura en la Direccin X - X d = 50 (cm) yc = 45 (cm) Armadura de Retraccin y Temperatura en la Direccin X - X20 = 4.70 (tn/m2) 19 = 21.43 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.60 (m) Y20-4 = 0.60 (m) Ast =Vu = 51.75 (tn) Xcgp = 0.60 (m) =

#barr =Mu = 31.05 (tn.m) K = 3.88 m = 23.53 0.00104 #barrad =

As = 16.63 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 35.64 (cm2) #barr = 12.50 S = 25.83 (cm)

#barrad = 13 Sad = 26.0 (cm) Astot = 37.05 (cm2) Cumple

Grficos de TensionesPunto X Y3 0 0 -4.702 3.30 0 -21.431 3.30 3.30 -21.434 0.00 3.30 -4.70

temp =

=

(tn/m2)

0 1 1 2 2 3 3 4

-4.70 -21.43Tensin 3 - 2

0 1 1 2 2 3 3 4-21.43-4.70

Tensin 1 - 4

0 1 1 2 2 3 3 4-21.43 -21.43

Tensin 2 - 10 1 1 2 2 3 3 4

-4.70 -4.70

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETRO210 (kg/cm2) (pulg) cm cm2 cm4200 (kg/cm2)2400 (kg/m3) LISO 6 mm 0.6 0.28 1.880.75 LISO 1/4" 0.635 0.32 1.990.9 8 mm 0.8 0.50 2.51

7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.990.0018 12 mm 1.2 1.13 3.77

1 4 1/2" 1.27 1.27 3.9910 (cm) 5 5/8" 1.588 2.00 4.99

23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.9815.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

0.65 8 1" 2.54 5.10 7.989 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.990.00 11 1 3/8" 3.58 10.06 11.25-4.53

-17.76

1.670.00 (tn.m)

108.9-149.44-586.08

1.65 (m)

Cumple

0.85

0.85

Armadura de Retraccin y Temperatura en la Direccin Y - Y0.001835.64 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

28.13 S = 11.07 (cm)29 Sad = 11 (cm) Astot = 36.74 (cm2)

Armadura de Retraccin y Temperatura en la Direccin X - X0.001835.64 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

28.13 S = 11.07 (cm)29 Sad = 11 (cm) Astot = 36.74 (cm2)

DISEO DE ZAPATA SOMETIDA A FLEXIN BIAXIALCARGAS DE SERVICIO: MATERIALES:

PD = 28.92 (tn) MDX = 16.69 (tn.m) MDY = 0.001 (tn.m) Columna ZapataPL = 17.38 (tn) MLX = 13.65 (tn.m) MLY = 0.001 (tn.m) f'c = 210 (kg/cm2) f'c =

fy = 4200 (kg/cm2) fy =a = 90 (cm) conc =b = 90 (cm) c =

Hf = 2.50 (m) N bar = 7 f =Df = 1.90 (m) bar = 2.22 (cm) vc =

apl = 0.65 temp =Suelo c =

ad = 10 (tn/m2) rec =u = 30 (tn/m2) vcp1 =

terr = 1800 (kg/m3) vcp2 =int = 30

1)Obtencin de las cargas de servicioPserv = 46.3 (tn) Mxserv = 30.34 (tn.m) Myserv = 0.002 (tn.m) MXY = 30.34 (tn.m) exy =

ex = 0.66 (m) ey = 0.00 (m)2) Predimensionado de la ZapataZAPATA CUADRADAPlanta y Longitud: a = 10.00 p = -4.63 j =

Lcalc = 3.21 (m) x1 = 3.21 b = 0.00 q = -18.21 k =Lad = 3.00 (m) x2 = Err:502 c = -46.30 u = 2.62 l =

x3 = Err:502 d = -182.05 v = 0.59Altura de la Zapata: z1 = 3.21ldb = 51 (cm) z2 = Err:502

37 (cm) z3 = Err:502hc = 61 (cm) had = 60 (cm) def = 50 (cm)

3) Obtencin de Cargas Mayoradas Cargas - Resistencia ltima cm = 1.3 cv =Relleno = 37.24 (tn) Pu = 144.13 (tn) Mxu = 51.33 (tn.m) Muy =Zapata = 15.68 (tn)Cmtotal = 81.85 (tn) Li = 3.30 (m) S1 = 3.15 (m) A =

S2 = -1.75 (m) B =ZAPATA RECTANGULAR LdL = 110 (cm) Cumple C =Scalc = 3.30 (m) LdL min= 69 (cm)Sad = 3.30 (m) rearect = 10.89 (m2)

()

ldb

Ixx = 9.88 (m4) Iyy = 9.88 (m4) X = 1.65 (m) Y =LdS = 110 (cm) CumpleLdSmin = 69 (cm)4) Esfuerzos ltimos sobre el terreno

1 = 21.81 (tn/m2) 2 = 21.80 (tn/m2) 3 = 4.66 (tn/m2) 4 = 4.67 (tn/m2)Cumple Cumple Cumple Cumple

En la Direccin X - X5) Revisin por Cortante d = 50 (cm) xc = 95 (cm)

5 = 18.17 (tn/m2) 6 = 18.17 (tn/m2) =

Vu = 46.2 (tn) vu = 2.80 (kg/cm2) vs = 3.29 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) xc = 70 (cm)7 = 16.87 (tn/m2) 8 = 16.87 (tn/m2) 9 = 9.60 (tn/m2) 10 = 9.60 (tn/m2)

Vu = 118.19 (tn) bo = 5.60 (m) vu = 4.22 (kg/cm2) vs = 4.97 (kg/cm2) Cumple

En la Direccin Y - Y5) Revisin por Cortante d = 50 (cm) yc = 95 (cm)

11 = 21.81 (tn/m2) 12 = 21.81 (tn/m2) =

Vu = 40.5 (tn) vu = 2.45 (kg/cm2) vs = 2.89 (kg/cm2) Cumple

6) Revisin por Punzonamiento d = 50 (cm) yc = 70 (cm)13 = 16.87 (tn/m2) 14 = 16.87 (tn/m2) 15 = 9.60 (tn/m2) 16 = 9.60 (tn/m2)

Vu = 118.19 (tn) bo = 5.60 (m) vu = 4.22 (kg/cm2) vs = 4.97 (kg/cm2) Cumple

7) Diseo a FlexinArmadura en la Direccin Y - Y d = 50 (cm) xc = 45 (cm) Armadura de Retraccin y Temperatura en la Direccin Y - Y

18 = 15.57 (tn/m2) 17 = 15.57 (tn/m2) Punto de Aplicacin:X11-2 = 0.55 (m) X12-1 = 0.55 (m) Ast =

Vu = 58.87 (tn) Xcgp = 0.55 (m) =#barr =

Mu = 32.62 (tn.m) K = 3.95 m = 23.53 0.00106 #barrad =

temp =

=

As = 17.48 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 35.64 (cm2) #barr = 12.50 S = 25.83 (cm)

#barrad = 13 Sad = 26.0 (cm) Astot = 37.05 (cm2) Cumple

Armadura en la Direccin X - X d = 50 (cm) yc = 45 (cm) Armadura de Retraccin y Temperatura en la Direccin X - X20 = 4.67 (tn/m2) 19 = 21.81 (tn/m2) Punto de Aplicacin:

Y19-1 = 0.60 (m) Y20-4 = 0.60 (m) Ast =Vu = 52.41 (tn) Xcgp = 0.60 (m) =

#barr =Mu = 31.45 (tn.m) K = 4.19 m = 23.53 0.00112 #barrad =

As = 16.86 (cm2) = 3/4 (plg) = 1.91 (cm) Aunit = 2.85 (cm2)Asmin = 35.64 (cm2) #barr = 12.50 S = 25.83 (cm)

#barrad = 13 Sad = 26.0 (cm) Astot = 37.05 (cm2) Cumple

Grficos de TensionesPunto X Y3 0 0 -4.662 3.30 0 -21.801 3.30 3.30 -21.814 0.00 3.30 -4.67

temp =

=

(tn/m2)

0 1 1 2 2 3 3 4

-4.66 -21.80Tensin 3 - 2

0 1 1 2 2 3 3 4-21.81-4.67

Tensin 1 - 4

0 1 1 2 2 3 3 4-21.80 -21.81

Tensin 2 - 10 1 1 2 2 3 3 4

-4.66 -4.67

Tensin 3 - 4

ELECCION DEL TIPO DE ACERO A UTILIZARMATERIALES: ACEROS DISPONIBLES EN cm

Zapata No DIAMETRO DIAMETRO AREA PERMETRO210 (kg/cm2) (pulg) cm cm2 cm4200 (kg/cm2)2400 (kg/m3) LISO 6 mm 0.6 0.28 1.880.75 LISO 1/4" 0.635 0.32 1.990.9 8 mm 0.8 0.50 2.51

7.68 (kg/cm2) 3 3/8" 0.952 0.71 2.990.0018 12 mm 1.2 1.13 3.77

1 4 1/2" 1.27 1.27 3.9910 (cm) 5 5/8" 1.588 2.00 4.99

23.48 (kg/cm2) 6 3/4" 1.905 2.84 5.9815.94 (kg/cm2) 7 7/8" 2.22 3.88 6.97

0.66 8 1" 2.54 5.10 7.989 1 1/8" 2.86 6.41 8.98

10 1 1/4" 3.18 7.92 9.990.00 11 1 3/8" 3.58 10.06 11.25-4.63

-18.21

1.670.00 (tn.m)

108.9-152.80-600.73

1.65 (m)

Cumple

0.85

0.85

Armadura de Retraccin y Temperatura en la Direccin Y - Y0.001835.64 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

28.13 S = 11.07 (cm)29 Sad = 11 (cm) Astot = 36.74 (cm2)

Armadura de Retraccin y Temperatura en la Direccin X - X0.001835.64 (cm2) 1/2 (plg) = 1.27 (cm) Aunit = 1.27 (cm2)

28.13 S = 11.07 (cm)29 Sad = 11 (cm) Astot = 36.74 (cm2)

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