Cálculo de zapatas
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SEGÚN LA TABLA DE SAFEN° calibre area diametros
#2 1/4 0.32 0.635 0.635#3 3/8 0.71 0.953 0.953#4 1/2 1.29 1.27 1.270#5 5/8 2 1.588 1.588#6 3/4 2.84 1.905 1.905#7 7/8 3.87 2.223 2.223#8 1 5.1 2.54 2.540#9 1 1/8 6.45 2.865 1 11/86 2.858
#10 1 1/4 8.19 3.2258 1 17/63 3.175#11 1 2/5 10.06 3.5814 1 2/5 3.556#14 1 2/3 14.52 4.3 1 5/7 4.233#18 2 1/4 25.81 5.733 2 1/4 5.715
UNIVERSIDAD PERUANA UNIÓN FACULTAD DE INGENIERIA CIVIL
CONCRETO ARMADO II DISEÑO COMPLETO DE EDIFICACION 4 PISOS
DISEÑO DE ZAPATA AISLADA (JAIR CHILENO)DATOS:
γm= 1.8 Tn/m3 σt= 1.0 kg/cm2 fy= 4200 kg/cm2 σn= 7.73 tn/m2
S/C= 200 kg/m2 f'c(zap)= 210 kg/cm2 f'c(col)= 210 kg/cm2 hf= 1.15 m
COLUMNA C-1
PD= 7.62 Tn
PL= 4.74 Tn
t1= 0.3 m
t2= 0.3 m
Az= 1.60 m2
S'= 1.3 m
T'= 1.3 m
S= 1.30 m
T= 1.30 m0.5
Lv1= 0.50 Condición:
Lv2= 0.50 GO!!! 1.30
A Zap= 1.69 m2 8 Ø 1/2 @ 0.15
Pu= 18.73 Tn
1.3
Wnu= 11.08 tn/m2
h= 50 cm
dprom= 40.59 cm
Vdu= 1.36 Tn Vn=Vdu/Ø
Vn= 1.81 Tn Condición:
Vc= 40.53 Tn GO!!! 1.30
Mu= 1.80 Tn-m 8 Ø 1/2 @ 0.15
As= 1.18 cm2
Asmin= 9.50 cm2 Pn= 28.81 Tn Condicion:
USAR Asmin Pnb= 160.65 Tn CONFORME!
Asdiseño= 9.50 cm2 X0= 1.300
Ø= 1/2 A2= 1.69 m2
As= 1.29 cm2 A1= 0.09 m2
Diam= 1.27 cm [raiz(A2/A1)]>2 4.33
ACERO LONGITUDINAL: A0= 0.18 Condicion:
USAR: 8 Ø 1/2 @ 0.17 m Pnb= 321.30 Tn CONFORME!
Longitud de desarrollo
Disp= 42.50 cm
Ld1= 22.432651 cm
Ld2= 30.40 cm
Ld3= 30 cm
Ld = 24.32 cm
ESTA CONFORME!!!
ACERO TRANSVERSAL
Ast= 9.50 cm2
n= 8 Ø 1/2 @ 0.17 m
DISEÑO DE ZAPATAS AISLADAS PRE - COLUMNA (JAIR CHILENO)DATOS:
γm= 2.1 Tn/m3 σt= 3.5 kg/cm2 fy= 4200 kg/cm2 σn= 30.3 tn/m2
S/C= 500 kg/m2 f'c(zap)= 210 kg/cm2 Df= 1.7 NPT= 0.3 hf= 2.00 m
COLUMNA C-1
PD= 180 Tn Datos para Dimensionar Columna
PL= 65 Tn n= 0.25 USAR:
Ps= 1.25 P b.D= 4375.00 cm2 b= 66.144 t1=
f'c(col)= 280 kg/cm2 D= 66.144 t2=
NTP: +0.3
2.00
NTN:0+0 0.30
1.70
AREA DE ZAPATA
A= 245 = A= 8.09 m2 B= 2.85 m30.3 L= 2.85 m
Para q cumpla la condicion
para la cual podemos demostrar q:
T= 2.975 m
S= 2.725 m
Usar=3.00 x 2.75 m2 REVISAR EL REGLAMNTO
RNE = 1.4WD+1.7WL1.1 = 1.1 CONFORME ACI = 1.2WD+1.6WL
REACCION NETA DEL TERRENO
Pu= 320 TN Wnu= 38.79 Tn/m2
Azap= 8.25 m2
0.8 + d
DIMENSIONAMIENTO DEL Hz DE LA ZAPATA
2.75
POR PUNZONAMIENTO d/2 d/2
Condiciones de diseño d/2
b=(b
ase)
t=(lado) d/2
Vu= cortante x punzonamiento actuante
0.55
d
+
d/2 0.80 d/2 0.55
m= 0.8 + d d/2 d/2
n= 0.55 + d
3.00
1.45 <2 CUMPLE CONDICION
Donde: bo= ( 1.6 + 2d ) + ( 1.1 + 2d)
βc=
𝑏.𝐷=𝑃𝑠/(𝑛.𝑓^′ 𝑐)
𝜎𝑛=𝜎𝑡−𝛾_𝑝𝑟𝑜𝑚.ℎ𝑓−𝑆 /𝐶
𝐴=𝑃/𝜎𝑛〖𝐿𝑣〗_1=〖𝐿𝑣〗_2𝑇=√(𝐴_𝑧 )+((𝑡_1−𝑡_2 ))/2𝑆=√(𝐴_𝑧 )−((𝑡_1−𝑡_2 ))/2〖𝐿𝑣〗_1=〖𝐿𝑣〗_2𝑊𝑛𝑢=𝑃𝑢/𝐴𝑧𝑎𝑝
𝑉𝑢/∅=𝑉𝑐𝑉𝑢=𝑃𝑢−𝑊𝑛𝑢(𝑚.𝑛) (1)
𝛽_𝑐=𝐷𝑚𝑎𝑦𝑜𝑟/𝐷𝑚𝑒𝑛𝑜𝑟𝑉𝑐=0.27(2+4/𝛽) √(𝑓^′ 𝑐) .𝑏_0.𝑑≤1.06√(𝑓^′ 𝑐) .𝑏_0.𝑑 → 𝑉_𝑐=1.06√(𝑓^′ 𝑐)
𝑉_𝑐=1.06√(𝑓^′ 𝑐) . 𝑏_0.𝑑 (2) 𝑏_0=2(𝑚)+2(𝑛)
Resolvemos?
320 - 38.79 * ( 0.44 + 1.35 d + d^2 ) = 0.75 1.06 14.4914 10 * ( 2.7 d
320 - 17.0676 - 52.37 d - 38.79 d^2 = 115.21 * ( 2.7 d + 4 d^2 )
302.9324 - 52.37 d - 38.79 d^2 = 311.06 d + 460.83 d^2
499.62 d^2 + 363.42 d - 302.9324 = 0
a= 499.61578
b= 363.4239 xo= 0.50 m
c= -302.9324
USAR: h= 60 cm
dprom= 50.59 cm
VERIFICACION DE LA CORTANTE
Vdu=(Wu*S)(Lv-d) Wu= 38.79 Tn/m2
Vdu= 62.94 tn S= 2.75 m
Lv= 1.1 m
d= 0.51 m
Vn= 83.92 Tn ø=0.75
Vc=0.53*210^0.5*b*d
Vc= 107718.03 Kg S= 275 d= 51.00
Vc= 107.71803 Tn >Vn SI CUMPLE!!!
d= 50.59 cm
DISEÑO X FLEXION b= 275.00 cm
Mu= (Wu*S)*(Lv^2)/2 Wu= 38.79 Tn/m2 Mu= 64.540 Tn-m
Mu= 64.54 Tn-m S= 2.75 m Ø= 0.9
T= 3.00 m fy= 4200 kg/cm2
As2= 34.77 cm2 Lv= 1.1 m f'c= 210 kg/cm2
Asmin= 0.0018*b*d a= 2.98 cm
Asmin= 25.042 cm2 <As req SI CUMPLE!!!
USAR Asreq
Asdiseño= 34.77 cm2
Ø= 3/4
As= 2.84 cm2
Diam= 1.905 cm
ACERO LONGITUDINAL:
USAR: 13 Ø 3/4 @ 0.22 m
ACERO TRANSVERSAL:
Ast= 37.933498 cm^2
USAR: 14 Ø 3/4 @ 0.22 m
13 Ø 3/4 @ 0.20
2.75
60
3.00
3.00
14 Ø 3/4 @ 0.20
Vn=Vdu/ø
𝑉_𝑐=1.06√(𝑓^′ 𝑐) . 𝑏_0.𝑑 (2) 𝑏_0=2(𝑚)+2(𝑛)
𝐴𝑠1,𝐴𝑠2=(∅𝑓𝑦𝑑±√(∅^2 〖 〗𝑓𝑦 ^2 𝑑^2−4∗(∅〖 〗𝑓𝑦 ^2)/(1.7𝑓^′ 𝑐𝑏)∗𝑀𝑢))/(2∗(∅〖 〗𝑓𝑦 ^2)/(1.7𝑓^′ 𝑐𝑏))
DISEÑO DE ZAPATAS AISLADAS PRE - COLUMNA (JAIR CHILENO)
80 cm
55 cm
REVISAR EL REGLAMNTO
𝜎𝑛=𝜎𝑡−𝛾_𝑝𝑟𝑜𝑚.ℎ𝑓−𝑆 /𝐶
+ 4 d^2 )
DISEÑO DE ZAPATAS COMBINADA T-1 (JAIR CHILENO)DATOS:
γm= 2.1 Tn/m3 σt= 1.5 kg/cm2 fy= 4200 kg/cm2 σn= 12.08 tn/m2
S/C= 400 kg/m2 f'c(zap)= 175 kg/cm2 f'c(col)= 210 kg/cm2 hf= 1.20 m
COLUMNA C-1 COLUMNA C-2
PD= 30 Tn PD= 45 Tn
PL= 12 Tn PL= 18 Tn
t1= 35 cm t1= 40 cm
t2= 35 cm t2= 40 cm
c1 c2 42 63
1.20
7.00 0.175 0.2
6.80
AREA DE ZAPATA
Azap= B*Lz
R.Xo= 42 * 0.175 + 63 * 6.80
Xo= 435.75 Xo= 4.15 m
105
CHEKEAR EXCENTRICIDAD e=Xo-Lz/2
e= 4.15 - 7.00 e= 0.65 m <Lz/6 GO!! 1° CASO
2
q1,2= P ± 6P.e = 105 ± 6 105 0.65 =
Lz Lz^2 7.00 7.00 * 7.00
q1= 23.36 Tn/m
q2= 6.64 Tn/m
q1=σn*B B=q1/σn
B= 23.36 >>> B= 1.93 USAR B= 2.00 m
12.08
DISEÑO POR FLEXION EN SENTIDO LONGITUDINAL
R.Xo= Pu1 * 0.175 + Pu2 * 6.80
R.Xo= 55.2 * 0.175 + 82.8 * 6.80
Xo= 572.7 Xo= 4.15 m
138 e= 0.65
q1,2= 138 ± 6 138 0.65
7.00 7.00 * 7.00
q1= 30.70 Tn/m
q2= 8.73 Tn/m
qu2= 8.730612 q' qu1=
Xo 30.698
SECCION DE MOMENTO MAXIMO Vx=0
Vx= -55.2 + 8.73 Xo + q'. Xo = 0
2
q' = qu1-qu2
Xo Lz
q'= 30.69796 - 8.730612 * Xo
7.00
q'= 3.14 Xo
Vx= -55.2 + 8.730612 Xo + 3.14 Xo . Xo
2
Vx= -55.2 + 8.730612 Xo + 1.569096 Xo^2
Vx= -35.1795 + 5.564103 Xo + 1 Xo^2 Vascara= - b+-Raiz(b^2-4ac)/2a
Para Vascara=
a= 1
b= 5.564103 xo= 3.77 m
c= -35.1795
CALCULO DEL MOMENTO MAXIMO
Mmáx= -55.2 ( Xo - 0.175 ) + 8.73 Xo^2 + 3.14 Xo (Xo)^2
2 2 3
Mmáx= -55.2 ( 3.77 - 0.175 ) + 8.73 * 14.21 + 3.14 53.54984
2 6
Mmáx= -108.375 Tn-m
Por tanto-> 108.3749 x10^5 = 0.9 * 175 *b*d^2*w(1-0.59w)
si= ρ= 0.004 w= ρ*fy/f'c w= 0.10
B= 200 cm
hallamos "d"
108.3749 x10^5 = 2852.721 d^2
d = 61.63604 USAR= d= 70 cm
d= 70 - 5 - 1.91/2
d= 64.05 cm d= 64.05 cm
As= 47.22 cm2 b= 200 cm
Asmin= 0.0018*b*d Mu= 10837491 kg-cm
Asmin= 23.056 cm2 <As req GO!!! Ø= 0.9
Usar Asreq fy= 4200 kg/cm2
Asdiseño= 47.22 cm2 f'c= 175 kg/cm2
Ø= 1
As= 5.1 cm2
Diam= 2.54 cm
Asumir varilla de 3/4"
USAR: 10 Ø 1 @ 0.21 m
10 Ø 1 @ 0.20
Asmin
𝐴𝑠1,𝐴𝑠2=(∅𝑓𝑦𝑑±√(∅^2 〖 〗𝑓𝑦 ^2 𝑑^2−4∗(∅〖 〗𝑓𝑦 ^2)/(1.7𝑓^′ 𝑐𝑏)∗𝑀𝑢))/(2∗(∅〖 〗𝑓𝑦 ^2)/(1.7𝑓^′ 𝑐𝑏))
DISEÑO DE ZAPATAS COMBINADA T-2 (JAIR CHILENO)DATOS:
γm= 2.1 Tn/m3 σt= 1.3 kg/cm2 fy= 2800 kg/cm2 σn=
S/C= 400 kg/m2 f'c(zap)= 175 kg/cm2 hf=
COLUMNA C-1 COLUMNA C-2
PD= 85 Tn PD= 95 Tn
PL= 15 Tn PL= 25 Tn
t1= 45 cm t1= 50 cm
t2= 50 cm t2= 55 cm
C-1 C-2
100 120 126 T 154 T
0.5 6.00 0.55 0.25 6.525 0.825
7.6
b= Az/lz
b= 2.76 m
Wnu= 36.84 T/m 3.17Vu= -126 + 36.84 Xo= 0
Vu= 3.42 m
Mumáx= 36.84 * 11.6964 -126 3.17
2
Mumáx= -183.96 T-m
DIMENSIONAMIENTO DE LA ALTURA (h2)=
0.006 Ø= 3/4
ω= 0.096 As= 2.84 cm2
d= 68.40 cm Diam= 1.905 cm
h= 75.30 Rec= 5 cm
USAR= 75.5 m
Mu=Øf'cb.d^2*ω(1-0.59ω)ρ=
DISEÑO DE ZAPATAS COMBINADA T-2 (JAIR CHILENO)
10.5 tn/m2
1.00 m