DISEÑO DE UNA ZAPATA AISLADA Diseñar la zapata mostrada en la fig: Si la Columna de 70 x 50 lleva 10 fierros de 1" y transmite las cargas PD = 180 tn y PL = 100 tn . La capacidad portante admisible del suelo es qa = 2.5 kg/cm2 ; ademas fy = 4200kg/cm2 , fy = 280 kg/cm2 en la columna y fc = 210 kg/cm2 en la zapata
DATOS: Zapata 210 kg/cm² Columna f ' c = 280 kg/cm² b= 50 cm t= 70 cm f'c=
S/C = PD = PL =
Otros 550 kg/m² 180 Tn 100 Tn
Df = 2 = qa = db = Lv =
Acero f y = 4200 kg/cm²
Suelo 1.4 1700 2.50 2.54 150
m kg/m³ kg/cm² cm cm
MD,ML
1.- DIMENSIONAMIENTO DE LA ZAPATA
PD, PL
Cálculo del peralte de la zapata (hc )
Ld=
0 . 08 .
d .F b
y
Reemplazo los valores que tenemos: Ld = 58.89 cm ht
√ f'c
Tomar
Ld = 58.89 cm
Df
Lv
(Del problema se emplean varillas de Ø1") Øb ( 1") = 2.54 cm r.e. = 7.50 cm (recubrimiento) hc = 68.93 cm Tomar hc = 70.00 cm hc = Ld + r.e + Øb ht = Df - hc ht = 70.00 cm
hc T
b
Cálculo de la presión neta del suelo ( qm ) qm = 2.16 kg/cm²
qm=qa−g ht−g chc-s/c
t t
T
Cálculo del área de la zapata ( Az )
P qm ( t1-t2) T= √ Az+ 2 (t1-t2 ) S= √ Az− 2 Azap=
Azap = 129,629.63 cm² T = 370.00 cm B = 350.00 cm
Donde: P = Carga de servicio Lv = Volados iguales sin excentricidad
2.- DETERMINACIÓN DE LA REACCIÓN AMPLIFICADA ( qmu )
Pu Wnu= Azap
=
1.4 x 180000 + 1.7 x 100000 350 x 370
=
3.26
kg/cm2
Donde: Pu = Carga Ultima
3.- VERIFICACION POR CORTE ( Ø = 0.85 ) Por Flexión:
T −t Lv= 2 Vdu=( WnuxB)(Lv-d) Vc=0 .53 √ f'c bd ØVc³ Vdu
Lv = r.e = Øb ( 3/4") = d= Vdu = Ø=
150.00 7.50 1.91 60.59 101,975.73 0.85
cm cm cm cm kg
Vc = 162,875.03 kg
(Suponiendo varillas Ø3/4") ( d = hc - Øb - r.e. ) (Coef. De reduccion por corte)
B
ØVc = 138,443.78 kg ØVc > Vdu OK! Por Punzonamiento:
[ β]
Vc=0 . 27 2+
Vu=Pu-Wnu x mn kg
c
β
2m +2n
(perimetro de los planos de falla) * f 'c^.5 * bo * d = 1.06 * f 'c^.5 * bo * d
Vc = 0.27 * 2 + 4 c Vc = 555,426.41 kg Vc= ØVc = 472,112.45 kg ØVc= ØVc > Vdu OK! c = lado mayor columna ( t ) c = 1.4 lado menor columna ( b ) m=t+d n=t+b bo = 2*m + 2*n Vu = Øvc OK !
β
448,939.43 Kg 381,598.52
Kg
d/2 d/2
m = 130.59 n = 110.59 Vu = 1.1 x f'c x bo x d Vu = 448,939.43 kg Øvc = 381,598.52 kg
t
B
bo = 2 x ( t + d ) + 2 x ( b + d ) = bo = 482.36 cm
Dmayor c= Dmenor , c≤2→Vc=1. 06 √ f ' c bo d Vu≤ØVc; Ø=0 . 85
n = b+d
374,938.21
√ f ' c bo d
b
Vu =
4
m = t+d T
4.- CALCULO DEL REFUERZO LONGITUDINAL ( Ø = 0.90 ) Dirección Mayor:
( Wnu x B) Lv2 2 Mu As= a ØFy ( d- ) 2 As . Fy a= 0 . 85f'cb Mu=
Lv = 150.00 Mu = 12,831,081.08 B= d= a= As = a=
As mín = 0.0018 * B * d As > As mín OK !! Aøb # Varilla ( n ) = As Aøb Espaciam = B - 2*r.e - Øb n -1
cm ree = 7.50 kg-cm Øb ( 3/4") = 1.91
cm cm2 2 (Valor Asumido) cm 2 Aøb ( 3/4" ) = cm² # Varilla ( n ) = cm 2 Espaciam = As = 57.88 cm2 20 Ø 3/4" @
2.85 20 17.53 17.53 cm
Aøb ( 3/4" ) = # Varilla ( n ) = Espaciam = 15 Ø 3/4" @
2.85 15 23.79 23.79 cm
350.00
60.59 3.89 57.88 3.89
As mín = 44.1
cm2
As
>
As mín
T= B= d= a=
370 350 60.59 5.01
cm 2cm2 cm
OK !!
Dirección Menor: As tranv = As * T B As mín = 0.0018 * B * d As > As mín OK !!
As transv = 61.19 cm2
(Valor Asumido) Aøb ( 3/4" ) = # Varilla ( n ) = Espaciam = 21 Ø 3/4" @
2.85 cm2 21 17.65 17.65 cm
Asmin = 46.62 cm2
Aøb ( 3/4" ) = # Varilla ( n ) = Espaciam = 16 Ø 3/4" @
2.85 16 23.54 23.54 cm
Aøb # Varilla ( n ) = As Aøb
2
Espaciam = B - 2*r.e - Øb n -1
As transv Longitud de desarrollo en Traccion ( Ld ) ld = Øb * fy *
<
ree = 7.50 cm 1.91 2cm
Øb ( 3/4") =
Lv1
>
As mín
OK !!
3.54 * f 'c^.5 * C + Kr Øb Lv1 = Lv - r.e.e
La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv ( + 1 ) = Lado mayor Zapata Lado menor Zapata Aøb # Varilla ( n ) = As Aøb Espaciam = B - 2*r.e.e - Øb n -1
= = = =
1.00 0.80 1.00 1.00
Øb (3/4") = r.e.e = fy = f'c =
1.91 7.50 4200 210
C = 8.50 ktr = 0 2.5
Longitud de desarrollo en tracción Lv1 = 142.50 cm Ld = 50.04 cm Ld < Lv1
q = ( C+kt r )/ Øb q= 10.41 q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!
OK !!
Espaciamiento del Refuerzo Asc = 61.19 cm2
45 cm 3xh
210 cm
> 17.65 OK !!
5.- VERIFICACION DE LA CONEXIÓN COLUMNA - ZAPATA ( Ø = 0.70 ) Para la sección A colum = 70*50 = 3500 cm² ( COLUMNA ) Ø * 0.85 * f 'c * As1 A colum = b *t Pu < ( Ø * 0.85 * f 'c * A1) Aøb As mín = 0.005 * A1 # Varilla = As1 Aøb As col. > As mín OK !!
Pu = 422000 kg A1 = 3500 cm2 Ø * 0.85 * f 'c * A1 = 583100 kg Pu < Ø * 0.85 * f 'c * A1
# Varilla ( n ) =
6
OK !!
As mín = 17.50 cm2 Aøb ( 3/4" ) = 2.85 cm2 USAR As1 = 17.50 cm2 OK !! As col > As min
Para la sección A zapata = 350*370 = 129500 cm² ( ZAPATA ) Pu < Ø x 0.85 x f 'c x A2/A1 x A1
Ø x 0.85 x f 'c x A2/A1 x A1 =
Pu = 422000 kg A1 = 3500 cm2 A2 = 129500 cm2 874650 kg
OK !!
A2/A1 =
###
Página 4 de 19
DISEÑO DE ZAPATA COMBINADA Diseñar la zapata combinada que soportara las columnas mostradas en la figura. La capacidad portante del suelo es qa = 2 kg/cm2Considere fy = 4200 kg/cm2 y f'c = 210 kg/cm2 para la cimentacion . F'c = 280 kg/cm2 en las columnas. COL: C1 C2
SECCION 50 X 50 40 X 50 b x t
REF. 9 Ø 3/4" 9 Ø 3/4" Acero
PD 20 40 tn
PL 15 24 tn
1
PL1
PL2 S/C = 500 kg/m²
2
t1
hc = 54.00
t2 4.55
Df = 1.60 m = 1800 qa = 2.00
h t = 101.00
b2
b1
m
m
1.40
m Otros kg/m3 S/C = 500 kg/m² kg/cm2 d(eje-eje)= 4.3 m
Columna f ' c = ### kg/cm²
f'c= fy =
Zapata 175 kg/cm² 4200 kg/cm²
1.- DIMENSIONAMIENTO DE LA ZAPATA ( Az = S*T ) Cálculo del peralte de la zapata (hc ) ld = 0.08 * Øb * Fy raiz(f 'c)
Øb ( 3/4" ) = 0.08 x Øb x fy / f ´c =
1.91 49
cm cm
32
cm
ld =
49
cm
r.e = hc= ht=
7.50 59.00 101.00
cm cm cm
ht =
101.00
cm
qm =
1.63
.004*øb*fy =
OK !!
ld >= 0.004 * øb * fy Tomar hc = ld + r.e + Øb hm = Df - hc
Tomar
Longitud de desarrollo en compresión
Cálculo de la presión neta del suelo ( qm ) qm = qa - m*hm -γc*hc - s/c
kg/cm²
Cálculo del área de la zapata ( Az ) P1s =
Ps1 = P1D + P1L Ps2 = P2D + P2L Rs = P1s + P2s 20
+Mo = 0
35
Tn
P2s = 64 Tn
20
30
0
Rs * Xo = P1s* t1/2 + P2s * 455 Xo = ??
Xo 455.00 Rs =
Lz / 2 e = Lz / 2 - Xo Lz / 6 e < Lz/6 q1,2 = Rs * 1 ± 6 * e Lz Lz
30
P1s = P2s = Rs = Xo =
35 64 99 301.21
Tn Tn Tn cm
Lz = Lz / 2 = e= Lz / 6=
625.00 312.50 11.29 104
cm cm cm cm
170.00 99
Tn
cm
Página 5 de 19
L = 2 x Xo B =(P1s +P2s) qn x L
L= 602 cm B= 101 cm tomamos B = 85 cm
Como S/C = 500 kg/cm², Verificamos las presiones del suelo - ADICIONAL ( q 1,2 ) Ps1 = P1D + 50%P1L Ps2 = P2D + P2L R1s = P1s + P2s
P1s =
+Mo = 0
20
R1s * Xo = P1s* t1/2 + P2s * 455 Xo = ??
27.5 Tn
P2s =
20
30
30
0 Xo 455.00
e = Xo1 - Xo q = Ps + Mc = Ps + Ps x e Az I Az I
64 Tn
P1s = P2s = R1s = Xo1 =
27.5 64 91.5 324.26
Tn Tn Tn cm
170.00
R1s = 91.5
e=
23.05
cm
Tn I = ( B x L^3 )/12 I = 1454767.9167 cm4
cm
AUMENTAMOS EL ANCHO B q= 44.56 kg/cm2 q < qm cumple " OK " q > qm no cumple "AUMENTAMOS EL ANCHO B"
150 cm Aumentamos el Ancho hc = Un nuevo calculo Ps = 91500 kg q = 1.41 kg/cm2 e = 23.05 cm B = 265 cm I = 74531250 cm4
OK !!
Ps1 = P1D + P1L Ps2 = P2D + 50%P2L R2s = P1s + P2s
P1s =
+Mo = 0
20
R2s * Xo = P1s* t1/2 + P2s * 455 Xo = ??
35 Tn
P2s =
20
30
30
0 Xo 470.00
Lz / 2 e2 = Lz / 2 - Xo Lz / 6 e2 < Lz/6 q1,2 = R2s * 1 ± 6 * e2 B
52 Tn
P1s = P2s = R2s = Xo =
35 52 87 288.97
Tn Tn Tn cm
1.40
R2s =
q > qm no cumple "AUMENTAMOS EL ANCHO B" q < qm cumple " OK "
87 Tn
e=
12.24
cm
q=
1.62
kg/cm2
2.- DISEÑO EN SENTIDO LONGITUDINAL
m
P1s =
I = ( B x L^3 )/12 I= 74531250
cm4
OK !!
35 Tn
P2s =
64 Tn
Cálculo de la presión neta por unidad de longitud ( qm ) qm 0.2
qn = P1s + P2s Az qn = 6205.7293 kg/m² Por unidad de Longitud qm = qm1*B
m
4.50
( No amplificada )
Por Unidad de LONGITUD
qm =
6205.73
kg/m
m
140.00 m
cm3
Página 6 de 19
55311.978 kg
V 1241.15 kg
+ -
+
1.6297
+
m
-
-
-8688.022 kg -33758.85 kg kg - m -27385.1 M
+
+
+ 124.12
kg - m kg - m
6081.62 Encontramos el diagrama de fuerzas cortantes verificamos el corte por Flexion: d = -ree + hc 1.50 x Vu = 67050.27 d = 141.00 cm Vu = Vmax - qn x ( b2/2 + d ) = 44700.18 kg Aporte del Concreto :
Vc = 0.53 x f ' c x b x d =
0.85 x Vc = 222678.77 kg Aumentamos el Peralte a h = 150 cm. Vu = Vmax - qn x ( b2/2 + d ) = Aporte del Concreto :
261975.02 kg OK !! d= h- ree d= ### cm
kg
ya que : F = ( 1.4 x D + 1.7 x L )/( D + L ) F=
Vu < 0 x Vc
1.5
Cumple !!
44700.18 kg
Vc = 0.53 x f ' c x b x d = 0.85 x Vc = 222678.77 kg
261975.02 kg Vu < 0 x Vc Cumple !! Vu < O x Vc CUMPLE !!
VERIFICACION POR CORTE ( Ø = 0.85 ) COLUMNA EXTERIOR : Vu = 1.50 x ( Pu - qnu x m x n ) = 31075.805 kg Vu = 31075.80549 kg c = El aporte del Concreto : 1 bo = ( b + ,5*d ) + 2x( t + d ) =
Vc = 0.27 x 2 +
422 cm
4 x f 'c x bo x d c
Vc = 1396870.757 kg ØVc = 1187340.143 kg Vc = 1.10 x f 'c x bo x d = Vc = 948492.49 kg ØVc = 806218.62 kg CUMPLE !! Vu < ØVc
COLUMNA INTERIOR : Vu = 1.50 x ( Pu - qnu x m x n ) = Vu = 75697.49 kg c = 1.25 El aporte del Concreto :
75697.49
bo = ( b + 0,5*d ) + 2x( t + d ) = 493 cm
Vc = 0.27 x 2 +
4 x f 'c x bo x d c
Vc = 1412870 kg ØVc = 1200939 kg 948492.49 kg
Vc = 1.10 x f 'c x bo x d = Vc = 1106949 kg ØVc = 940906.79 kg CUMPLE !! Vu < ØVc
###
kg
kg
Página 7 de 19
4.- CALCULO DEL REFUERZO EN EL TRAMO CENTRAL X x qn - P1 = 0 X=
P1 qn Calculo de As :
X = 5.64 m m m
As = Mu / ( Ø * fy * ( d - a/2 )) a = As * fy / ( 0.85 * f 'c * B )
As mín = 0.0018 * B * d As > As mín OK !! Aøb # Varilla ( n ) = As Aøb Espaciam = B - 2*r.e - Øb n -1
Mu =
Mu =
B= d= a= As = a=
>
P1 x X
91699.11
Mu = -91699.11 kg - m
kg - m 8cm
db =1.91 c
(Valor Asumido) m Aøb ( 3/4" ) = 2.85 2 cm2 # Varilla ( n ) = 9 Espaciam =31 cm 9 Ø 3/4" @ 31 cm
As = 26.06 cm2
As
_
r .e .e =
265 cm2 141 cm2 2.77 cm 26.06 cm2 2.78 cm
As mín = 67.26 cm2
qn x X^2 2
Aøb ( 3/4" ) = 2.85 cm2 Varilla ( n ) = 24 Espaciam =11 cm 24 Ø 3/4" @ 11 cm
As mín ASUMIR As mín !!
5.- CALCULO DEL REFUERZO POR DEBAJO DE LA COLUMNA INTERIOR
Mu =
qn x ( L )^2 2
Mu =
6081.61
L=
1.91
Calculo de As :
As = Mu / ( Ø * fy * ( d - a/2 )) a = As * fy / ( 0.85 * f 'c * B )
As mín = 0.0018 * B * d As > As mín OK !! Aøb # Varilla ( n ) = As Aøb Espaciam = B - 2*r.e - Øb n -1
kg - m m
1.4
Mu =
B= d= a= As = a=
265 141 0.18 1.71 0.18
As
>
kg - m 8cm
db =1.91
c (Valor Asumido) m Aøb ( 3/4" ) = 2.85 2 cm2 # Varilla ( n ) = 1 Espaciam =#DIV/0! cm 1 Ø 3/4" @ #DIV/0! cm
As = 1.71 cm2
As mín = 71.55 cm2
6081.61 r .e .e =
cm2 cm2 cm2 cm2 cm
14 Ø 5/8"@ 22cm
Aøb ( 3/4" ) = 2.85 cm2 Varilla ( n ) = 25 Espaciam =10 cm 25 Ø 3/4" @ 10 cm
As mín
ASUMIR As mín !!
Diseñar en sentido transversal a cada columna le corresponde una porcion de Zapata
d/2
1.205
d/2
d/2
1.91
Página 8 de 19
ZAPATA EXTERIOR
ZAPATA INTERIOR
Página 9 de 19
qn =
Pu Az
Mu =
qnu x B x (L^2) 2
B= d= a= As = a=
120.5 cm2 r .e .e = 8 cm db = 1.59 cm2 141 cm2 0.52 (Valor Asumido) cm 2.20 cm2 0.52 cm
As = 2.2
qn =
cm2
As mín = 32.54 cm2
1.68
kg/cm2
Mu = 1169724
qn =
Pu Az
Mu =
qnu x B x (L^2) 2
B= d= a= As = a=
Aøb ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 11 Espaciam = 10.00 cm 11 Ø 3/4" @ 10 cm
qn = 1.91 kg/cm2
Mu = r .e .e = 8 cm
191 141 0.64 4.34 0.64
cm cm2
As = 4.34
cm2
db =
1.59 cm2
(Valor Asumido)
cm cm2 cm
As mín = 51.57
###
Aøb ( 3/4" ) = # Varilla ( n ) = Espaciam = ### Ø 3/4" @
cm2
6.- VERIFICACION DE LA CONEXIÓN ZAPATA - COLUMNA( Ø = 0.70 ) Para la sección A columna = 50*50 = 2500 cm² ( COLUMNA ) Ø * 0.85 * f 'c * As1 A colum = b *t Pu < ( Ø * 0.85 * f 'c * A1) As mín = 0.005 * A1 # Varilla = As1 Aøb As col. > As mín OK !!
Pu = 53500 kg A1 = 2500 cm2 Ø * 0.85 * f 'c * A1 = 312375 kg
As mín = 12.50cm2
Pu < Ø * 0.85 * f 'c * A1
As col > As min
CUMPLE !!
OK !!
Para la sección B columna = 40*50 = 2000 cm² ( COLUMNA ) Ø * 0.85 * f 'c * As1 A colum = b *t Pu < ( Ø * 0.85 * f 'c * A1) As mín = 0.005 * A1 # Varilla = As1 Aøb As col. > As mín OK !!
Pu = 96800 kg A1 = 2000 cm2 Ø * 0.85 * f 'c * A1 = 249900 kg Pu < Ø * 0.85 * f 'c * A1
As mín = 10.00cm2 As col > As min
CUMPLE !!
OK !!
Detalle de refuerzos en la Zapata Combinada verificamos primero el espaciamiento maximo Espaciamiento del Refuerzo 45 cm 3xh= 450 cm
> 450
d/2
OK !!
d/2
d/2
24 Ø3/4"@ 11cm
18 Ø 3/4"@ 10cm 11 Ø 3/4"@ 10cm
25 Ø 3/4"@ 10cm
Longitud de desarrollo en Traccion ( Ld ) ld = Øb * fy * < 3.54 * f 'c^.5 * C + Kr Øb Lv1 = Lv - r.e.e
Lv1 Ld =
71 cm
Ld1 = 46 cm
La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv ( + 1 ) = Lado mayor Zapata Lado menor Zapata # Varilla ( n ) = As Aøb Espaciam = B - 2*r.e.e - Øb n -1 Calculo del refuerzo minimo : As mín = 71.55 cm2 Aøb ( 3/4" ) = # Varilla ( n ) = Espaciam = 25 Ø 3/4" @
2.85 cm2 25 10.00 cm 10 cm
Øb (3/4") = 1.91 = 1.00 Øb (5/8") = 1.59 = 0.80 r.e.e = 7.50 = 1.00 fy = 4200 = 1.30 f'c = ### = 1.00 Longitud de desarrollo en tracción
C = 6.50 ktr = 0
2.5
q=
q = ( C+kt r )/ Øb 8.41
q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!
Lv1 = 132.50 Ld < Lv1 Ld = 71.26 cm Refuerzo montaje en forma de Garrido
OK !!
Ø 3/8" para refuerzo principal Ø =< 3/4" Ø 1/2" para refuerzo principal Ø > 3/4" con espaciamiento maximo de 45 cm. 0.2
2.85 cm2 18 10.00 cm 10 cm
Página 10 de 19
DISEÑO DE ZAPATA CONECTADA Diseñar la zapata conectada que soportara las columnas mostradas en la figura . La capacidad portante admisible del suelo es qa = 2.0 kg/cm2 . Considere Fy = 4200 kg/cm2 , f'c = 175 kg/cm2 para la cimentacion
DATOS: Zapata f ' c = 175 kg/cm² Columna f ' c = 210 kg/cm² b1 = 50 cm t1 = 50 cm b2 = 40 cm t2 = 50 cm COL 1 2
fy= Df = m = c = qa = db =
SECCION REFUERZO 50 X 50 9 Ø 3/4" 40 X 50 9 Ø 3/4"
Acero 4200 Suelo 1.60 1800 2400 2.00 1.91 PD (tn) 50 40
kg/cm²
S/C = 500 kg/m²
m kg/m³ kg/m³ kg/cm² cm
Lc = 550 cm db = 1.91 cm
PL (tn) 30 24
1.- DIMENSIONAMIENTO DE LA ZAPATA Y VIGA DE CIMENTACION ZAPATA EXTERIOR:
Ld =
Ld = 0.08x1,91x4200/(175^(1/2)) = Ld = 49 cm
0.08xdbxfy
f 'c
ld >= 0.004 * øb * fy
Ld >= 0.004x1.91x4200 = Ld = 32 cm
48.51 cm
hc = Ld + r.ee + Øb hm = Df - hc
32.09 cm
Cálculo del peralte de la zapata (hc ) hc = 59 cm hc = Ld + 10 = ht = 101 cm
ht = Df - hc =
Cálculo de la presión neta del suelo ( qm ) qn = qa - m*hm - gc*hc - s/c
qn = 2.4-(1800xE^-06)x(101)-(2400xE^06)x(59)-(500xE^04) = 1.63 kg/cm2 qn =
CALCULO DE P'2 : Tanteo e =
P'2 =
P1xe
=
L
( PD + PL ) x e
P'2 = 9249.49kg Ps Az = qn A = 2 x( b )^2 = nuevo e =
57 cm
Lc - e Az =
( 50 + 30 ) x 1000 x 57 550 - 57
P1 + P' 2 qn
54868.44 b -t 2 2
=
= 54868.437
b = 166
A = 2 x( b )^2 = 54980
t=2b
Tomamos b = 165 cm
cm2
9431 54980 b = 166 b= 165 t= 330
----->
A = 165 x 330
e = 57 cm
9249.49
cm P'1 = P'2 =
e = 58
== =
tomamos
Página 11 de 19
ZAPATA EXTERIOR:
Ld =
49
Ld = 0.08x1.91x4200/(175^(1/2)) = Ld = 49 cm
0.08xdbxfy
f 'c
ld >= 0.004 * øb * fy
hc = Ld + r.ee + Øb hm = Df - hc
cm
32 cm
Ld >= 0.004x1.91x4200 = Ld = 32 cm
Cálculo del peralte de la zapata (hc ) hc = 60 cm hc = Ld + 10 = ht = 100 cm
ht = Df - hc =
Cálculo de la presión neta del suelo ( qm ) qn = qa - m*hm - gc*hc - s/c
qn = 2.4-(1700xE^-06)x(120)-(2400xE-06)x(60)-(500xE-04) = qn =
CALCULO DE P'2 : Tanteo e =
P'2 =
P1xe
=
L
A = ( b )^2 =
71 cm
( PD + PL ) x e
P'2 = 9486.00kg Ps Az = qn
Lc - e Az =
=
( 40 + 24 ) x 1000 x 50 550 - 50
P2 + P' 2 qn
36743.00
=
b = 192
b -t 2 2
nuevo e =
2.00 kg/cm2
36743
P'1 = P'2 =
A = 2 x( b )^2 = 44743
b=
150
cm2
usamos b =
e = 71
= 9486
=
155 cm
9486 44743 b = 150
A2 = ( 150 x 150 )
VIGAS DE CIMENTACION h= b=
Lc 7
=
550 7
P1 31 x Lc
h = 79 cm
SECCION 50 x 80
b = 47 cm
DISEÑO DE LA VIGA DE CONEXIÓN Wv = b x h x c =
9.6
As = Mu / ( Ø * fy * ( d - a/2 )) a = As x fy / ( 0.85 x f 'c x b ) As mín = 0.8 x (f ' c ^0.5) x B * d/ fy As > As mín OK !! # Varilla ( n ) = As Aøb Espaciam = B - 2*r.e - Øb n -1
kg/m
Mu = P' 2 x L + Wv x ( L^2 )/2= 7250000 Mu = 7250000 kg-cm Øb ( 3/4") = ree = 7.50 1.91 B = 50 cm d = 79.00 2cm2 a = 5.00 cm2(Valor Asumido) As = 25.07 Aøb ( 1" ) = cm2 a = 14.16 cm # Varilla ( n ) = Espaciam = As = 26.67 cm2 11 Ø 1" @
2.54 cm2 11 3 cm 3 cm
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As mín = 9.95
cm2
As > Asmin
11
Ø 1" @ OK !!
3
cm
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VERIFICACION POR CORTE Vu = P' 2 + Wv x L L
APORTE DEL CONCRETO Vu =
21982 KG Vu < Ø Vc
23540
Vc = 0.53 x (f ' c ^0.5) x b x d = OK !!
DISEÑO DE LA ZAPATA EXTERIOR
ZAPATA EXTERIOR
ZAPATA INTERIOR
qn =
Pu Az
Mu =
qnu x B x (L^2) 2
B= d= a= As = a=
qn =
150 cm2 41 cm2 5.00 #DIV/0! #DIV/0!
cm2 cm2 cm
###
Mu =
kg/cm2
#DIV/0!
r .e .e = 7.5 cm db = 1.59 cm2 (Valor Asumido)
Aøb ( 5/8" ) = 1.98 cm2 # Varilla ( n ) = #DIV/0! Espaciam = #DIV/0! cm
As = #DIV/0!cm2 As mín = 13.5
#DIV/0!
cm2
Ø 5/8" @
Pu Az
qn =
Mu = L= B= d= a= As = a=
#DIV/0!
qnu x B x (L^2) 2 100 cm r .e .e = 250 cm2 51 5 cm ( Valor Asumido ) #DIV/0!cm2 #DIV/0! cm
As = #DIV/0!cm2 #Varilla n = 14 Espaciam. = 17.88 Asmin = 27 cm2
#DIV/0! cm
14
Ø 5/8" @
6.- VERIFICACION DE LA CONEXIÓN ZAPATA - COLUMNA( Ø = 0.70 ) Columna Exterior Para la sección A columna = 50 x 50 = 2500 cm² ( COLUMNA ) Ø * 0.85 * f 'c * As1 A colum = b *t Pu < ( Ø * 0.85 * f 'c * A1) As mín = 0.005 * A1 # Varilla = As1 Aøb As col. > As mín OK !!
Pu = 121000 kg A1 = 2500 cm2 Ø * 0.85 * f 'c * A1 = 312375 kg Pu < Ø * 0.85 * f 'c * A1
# Varilla ( n ) =
OK !!
As mín = 12.50 cm2 Aøb ( 3/4" ) = 2.85 cm2 USAR : As1 = 12.50 cm2 OK !! Columna Interior As col > As min Para la sección B columna = 50 x 50 = 2500 cm² ( COLUMNA ) Pu = 96800 kg Ø * 0.85 * f 'c * As1 A1 = 2000 cm2 A colum = b *t Ø * 0.85 * f 'c * A1 = 249900 kg # Varilla ( n ) = Pu < ( Ø * 0.85 * f 'c * A1) Aøb ( 3/4" ) = As mín = 0.005 * A1 Pu < Ø * 0.85 * f 'c * A1 USAR : As1 = OK !! # Varilla = As1 Aøb As mín = 10.00 cm2 OK !! As col. > As mín OK !! As col > As min
Longitud de desarrollo en Traccion ( Ld ) ld = Øb * fy * 3.54 * f 'c^.5 * C + Kr Øb Lv1 = Lv - r.e.e
<
Lv1
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La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv ( + 1 ) = Lado mayor Zapata Lado menor Zapata Aøb # Varilla ( n ) = As Aøb Espaciam = B - 2*r.e.e - Øb n -1
= = = =
1.00 0.80 1.00 1.00
Øb (5/8") = r.e.e = fy = f'c =
1.59 7.50 4200 175
C = 8.50 ktr = 0 2.5
Longitud de desarrollo en tracción Lv1 = 38.13 cm Ld = 46 cm AUMENTAR EL T !! Ld < Lv1
q = ( C+kt r )/ Øb q= q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!
Espaciamiento del Refuerzo 45 cm 3xh
0 cm
As1 = >
OK !!
6 Ø 1"@ 7cm
14 Ø 5/8"@ 22cm 12 Ø 5/8"@ 12cm
d/2 d/2
14 Ø 5/8"@ 18cm
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cm2
3 3
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kg
#DIV/0! kg 8 cm ( Valor Asumido )
18 cm
4
4 2.85 cm2 10.00 cm2
OK !!
Página 19 de 19
8.50
q = ( C+kt r )/ Øb 10.09 q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!
