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