DISEO DE UNA ZAPATA AISLADA

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 Otros Suelo

f ' c = 210 kg/cm S/C = 550 kg/m Df = 1.4 m

Columna PD = 180 Tn g 2 = 1700 kg/m

f ' c = 280 kg/cm PL = 100 Tn qa = 2.50 kg/cm

b = 50 cm db = 2.54 cm

t = 70 cm Acero Lv = 150 cm

f y = 4200 kg/cm

1.- DIMENSIONAMIENTO DE LA ZAPATA Clculo del peralte de la zapata (hc )

Ld = 58.89 cm

Tomar Ld = 58.89 cm Df

(Del problema se emplean varillas de 1") b ( 1") = 2.54 cm

r.e. = 7.50 cm (recubrimiento)

hc = 68.93 cm

Tomar hc = 70.00 cm hc = Ld + r.e + b T

ht = Df - hc

ht = 70.00 cm

Clculo de la presin neta del suelo ( qm )

qm = 2.16 kg/cm

T

Clculo del rea de la zapata ( Az )

Azap = cm Donde:

T = cm P = Carga de servicio

B = cm Lv = Volados iguales sin

excentricidad

2.- DETERMINACIN DE LA REACCIN AMPLIFICADA ( qmu )

Donde:

kg/cm2 Pu = Carga Ultima3.26

129,629.63

370.00

350.00

Disear la zapata mostrada en la fig: Si la Columna de 70 x 50 lleva 10 fierros de 1" y transmite

3.- VERIFICACION POR CORTE ( = 0.85 )Por Flexin:

Lv = cm

r.e = 7.50 cm

b ( 3/4") = 1.91 cm (Suponiendo varillas 3/4")

d = cm ( d = hc - b - r.e. )

Vdu = kg

= 0.85 (Coef. De reduccion por corte)

Vc = kg

Vc = kg

Vc > Vdu OK!

Por Punzonamiento :

Vu = kg

= 2m +2n

bo =

Vc = 0.27 * 2 + 4 * f 'c^.5 * bo * d = 1.06 * f 'c^.5 * bo * d

b c

Vc = kg Vc= Kg

Vc = kg Vc= Kg

Vc > Vdu OK!

b c = lado mayor columna ( t ) 1.4

lado menor columna ( b )

m = t + d m =

n = t + b n =

bo = 2*m + 2*n

Vu = vc OK ! Vu =

vc =

4.- CALCULO DEL REFUERZO LONGITUDINAL ( = 0.90 )Direccin Mayor:

Lv = cm ree =

Mu = kg-cm b ( 3/4") = 1.91

B =

d =

a = 3.89 (Valor Asumido)

As = Ab ( 3/4" ) =

As mn = 0.0018 * B * d a = 3.89 20

As > As mn OK !! Espaciam =

As = 20 3/4" @

Ab

# Varilla ( n ) = As Ab ( 3/4" ) =

Ab 15

Espaciam = B - 2*r.e - b Espaciam =

138,443.78

162,875.03

60.59

101,975.73

150.00

2.85

2.85

17.53

17.53

374,938.21

bo = 2 x ( t + d ) + 2 x ( b + d )

482.36

555,426.41472,112.45

7.50150.00

448,939.43

Vu = 1.1 x f'c x bo x d

130.59

110.59

381,598.52

# Varilla ( n ) =

# Varilla ( n ) =

(perimetro de los planos de falla)

448,939.43381,598.52

350.00

12,831,081.08

60.59

57.88

57.88

23.79

n -1 As mn = 15 3/4" @

As > As mn OK !!

Direccin Menor:

As tranv = As * T

B T = 370 ree =

As mn = 0.0018 * B * d B = 350 b ( 3/4") = 1.91

As > As mn OK !! d =

a = 5.01 (Valor Asumido)

Ab Ab ( 3/4" ) =

# Varilla ( n ) = As 21

Ab Espaciam =

As transv = 21 3/4" @

Espaciam = B - 2*r.e - b

n -1 Ab ( 3/4" ) =

16

Espaciam =

Asmin = 16 3/4" @

As transv > As mn OK !!

Longitud de desarrollo en Traccion ( Ld )

ld = b * fy * a * b * g * l < Lv1

3.54 * f 'c^.5 * C + Kr

b

Lv1 = Lv - r.e.e

La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera:

Asc = 2 * Astrv

( b + 1 ) b = 1.00 b (3/4") = 1.91 C =

g = 0.80 r.e.e = 7.50 ktr = 0

b = Lado mayor Zapata l = 1.00 fy = 4200

Lado menor Zapata a = 1.00 f'c = 210 2.5 q = ( C+kt r )/ b

Ab

# Varilla ( n ) = As Longitud de desarrollo en traccin q=

AbEspaciam = B - 2*r.e.e - b Lv1 = 142.50 q >= 2.5 ,PONER 2.5 !!

n -1 Ld = 50.04

Ld < Lv1

Espaciamiento del Refuerzo

Asc = 61.19

45 cm

17.65 OK !!

3 x h 210 cm

5.- VERIFICACION DE LA CONEXIN COLUMNA - ZAPATA ( = 0.70 )

Para la seccin A colum = 70*50 = 3500 cm ( COLUMNA )

* 0.85 * f 'c * As1 Pu = # Varilla ( n ) = 6

A colum = b *t A1 =

422000

3500

q < 2.5 ,PONER q !!

23.54

OK !!

8.50

46.62

# Varilla ( n ) =

61.19

44.1

17.65

2.85

2.85

# Varilla ( n ) =

60.59

23.54

23.79

17.65

7.50

Pu < ( * 0.85 * f 'c * A1) * 0.85 * f 'c * A1 =

Ab

As mn = 0.005 * A1

# Varilla = As1

Ab As mn =

As col. > As mn OK !! Ab ( 3/4" ) =

USAR : As1 =

As col > As min

Para la seccin A zapata = 350*370 = 129500 cm ( ZAPATA )

Pu =

A1 =

A2 =

x 0.85 x f 'c x A2/A1 x A1 =

17.50

2.85

Pu < * 0.85 * f 'c * A1 OK !!

583100

422000

3500

Pu < x 0.85 x f 'c x A2/A1 x A1

129500

874650 OK !!

17.50

OK !!

las cargas PD = 180 tn y PL = 100 tn . La capacidad portante admisible del suelo es qa = 2.5 kg/cm2

MD,ML

PD, PL

ht

Lv

hc

B

Carga de servicio

Volados iguales sin

excentricidad

Carga Ultima

Disear la zapata mostrada en la fig: Si la Columna de 70 x 50 lleva 10 fierros de 1" y transmite

(Suponiendo varillas 3/4")

( d = hc - b - r.e. )

(Coef. De reduccion por corte)

2.85

2.85

17.53

17.53

7.50

23.79

La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera:

q = ( C+kt r )/ b

10.41

q >= 2.5 ,PONER 2.5 !!

q < 2.5 ,PONER q !!

23.54

8.50

17.65

2.85

2.85

23.54

23.79

17.65

7.50

A2/A1 = 2