Diseño zapata combinada

DISEÑO DE ZAPATAS COMBINADAS

Parametros de diseño:
fc = 210 kg/cm2 fy = 4200kg/cm2
ɣs = 1.6 ton/m3 ɣs = 2.4 ton/m3
r = 10 cm L = 7 m
be = 0.45m te = 0.55m
bi = 0.45m ti = 0.55m

Cargas:
Exterior Interior
PDe =83.706 ton PDi = 173.157 ton
PLe = 32.511 ton PLi = 66.438 ton
PEe = 58.971 ton PEe = 8.787 ton

Diseño de la zapata exterior
Diseño en planta:Calculo del pe:
* Sin sismo:
* Pe = PDe + PLe
Pe = 83.706 + 32.511= 116.217 ton
* Pi = PDi +PLi
Pi = 173.157 + 66.438 = 239.595 ton

* Con sismo:
* Pe = PD + PL + PE
Pe = 83.706 + 32.511 + 58.971=175.188 ton
* Pi = PDi +PLi
Pi = 173.157 + 66.438 + 8.787 = 248.382 ton

Calculo del qe:
ɣ = ɣs∓ ɣc2 = 1.6+2.42 = 2 ton/m3
qe = 2- (200*2000/10^6 + 550/10^4) = 1.545kg/cm2qe* = 1.3*2- (200*2000/10^6 + 550/10^4 = 2.145 kg/cm2

Calculo del Area:
* Az = b*l = Pe+piqe

* Sin sismo:
* Az = Pe+piqe = 355.812x10^31.545 = 230299.029 cm2

* Con sismo:
* Az* = Pe+piqe = 423.57x10^32.145 = 197468.531 cm2

∑Mo = 0
* Lpi = (l/2 - he/2)xR

* R = Pe + Pi
R = 175.188 + 248.382 = 423.57 ton

* l = 2L*Pipe+pi+he
l = 2*7*248.382175.188 +248.382+0.55 = 8.76 m

* b = Az/l
b = 230299.029 / 875.96 = 262.91 cm = 2.63 m

Dimensionamiento en altura:
* Por longitud de desarrollo:
Para fierros de #7:
Ld=0.08xdbxFy/fc = 0.08x2.222x4200/210 = 51.52 cm.
-----> d = 60 cm recubrimiento = 10 cm Peralte = 70 cm

* Corte por punzonamiento: d=60cm

Para Ce:
bo = (55+30)x2 + (45+60) bo = 275 cm
Para ci:
bo =(55+60)x2 + (45+60)x2 bo = 440 cm

* Sin sismo:
Peu = 1.4(83.706) + 1.7(32.511) = 172.457 ton
Piu = 1.4(173.157) + 1.7(66.438) = 355.364 ton

* Con sismo:
Peu = 1.25(83.706 + 32.511) + 58.971 = 204.242 ton
Piu = 1.25(173.157 + 66.438 ) + 8.787 = 308.281 ton
Escogemos las cargas mas criticas:
Peu = 204.242 ton Piu = 355.364 ton
Calculo del qu:
qu= 355.364+204.242263x876*10^3 =2.429 kg/cm2
Para Ce: Para Ci:
a) Vuo = Peu – qu*Ao a) Vuo = Piu – qu*Ao
Vuo = 204242-2.429*8925 Vuo = 355364-2.429*12075
= 182563.175 kg = 326033.825 kg
β =1.22 < 1.93 β =1.22 < 1.93
α = 30 α = 30

b) Vco = 0.27*(αxdbo + 2)xfc*bo*d b) Vco = 0.27*(αxdbo + 2)xfc*bo*d
Vco = 0.27*(30x60275 + 2)x210*275*60 Vco = 0.27*(40x60275 +2)x210*440*60
= 551686.713 kg = 770013.795 kg

Vco = 1.1*fc*bo*d Vco = 1.1*fc*bo*d
Vco = 1.1*210*275*60 Vco = 1.1*210*440*60
= 26318.488 kg = 420829.581 kg
Se escoge el menor valor: Se escoge el menor valor:
ØVc = 0.85*263018.488 kg ØVc = 0.85*263018.488 kg
= 223565.715 kg = 357705.144 kg
Como: Vuo < ØVc (cumple) Como:Vuo < ØVc (cumple)
Seguridad a la flexion:
Se verifica si requiere viga transversal.

Como B grande el refuerzo se calcula considerando el volado “m”, para un ancho de 1m.
qu = 2.429 kg/cm2
Mu = qu*m2*B/2
Mu = 2.429*104^2*263/2 = 3454776.416 kg.cm
Refuerzo para 1 metro de ancho, con d=60cm, b=100cm y:
Mu = 3454.8 t.cm/2.63 = 1313.603 t.cm/m

* Calculo de acero:
d = 60cm 0.9*d =0.9*(60) = 54 cm

As = 1313.603*10^30.9*4200*54 = 6.44 cm2 a = 6.44*42000.85*210*100 = 1.515
As = 1313.603*10^30.9*4200*(60-1.5122) = 5.87 cm2
Asmin = 0.0018*b*d = 0.0018*100*60 = 10.8 cm2
Como: Asmin > As ------> As = 4/3*(5.87) = 7.83 cm2

Distribucion:
Para # 4: (As = 1.29 cm2) Para # 5: (As = 2 cm2)
---> 7.831.29 = 6.01 = 6 7.832 = 3.92 = 4
En un metro: Enun metro:
100/6 = 16.67cm = 0.16m 100/4 = 25.00cm = 0.25m
---> #4@0.16m ---> #5@0.25m

Diseño de Viga:
L = 7m
Peu = 204.242 ton Piu = 355.364 ton
qul = peu+piul
= 204.242 + 355.364700*10^3 = 799.44 kg/cm

* Piu – qul*(a+hi) = 355.364*10^3 – 799.44*(121+55) = 214662.56 kg

* Peu – qul*he = 172457-799.44*55 = 128487.8 kg

* A*qul = 121*799.44 = 96732.24...