DISEO DE UNA ZAPATA AISLADADisear 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/cm Columna f ' c = 280 kg/cm 50 cm b= 70 cm t= f'c=S/C = PD = PL =

Otros 550 kg/m 180 Tn 100 Tn

Acero f y = 4200 kg/cm

Df = K2 = qa = db = Lv =

Suelo 1.4 1700 2.50 2.54 150

m kg/m kg/cm cm cm

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

MD,ML PD, PL

Ld =

0.08.db.F y f'c

Reemplazo los valores que tenemos: Ld = 58.89 cm ht Tomar Ld = 58.89 cm DfLv

(Del problema se emplean varillas de 1") b ( 1") = 2.54 cm (recubrimiento) r.e. = 7.50 cm hc = 68.93 cm hc = 70.00 cm hc = Ld + r.e + b Tomar ht = Df - hc ht = 70.00 cm Clculo de la presin neta del suelo ( qm )

hc T

B

qm ! qa Kht Kchc-s/cClculo del rea de la zapata ( Az )

qm = 2.16 kg/cm

t T

P qm (t1-t2) T= Az 2 (t1-t2) S! Az 2 Azap !

Azap = 129,629.63 cm 370.00 T = cm 350.00 B = cm

Donde: P = Carga de servicio Lv = Volados iguales sin excentricidad

2.- DETERMINACIN DE LA REACCIN AMPLIFICADA ( qmu )Donde: Pu = Carga Ultima

Pu Wnu ! Azap

=

1.4 x 180000 + 1.7 x 100000 350 x 370

=

3.26

kg/cm2

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

Lv !

Tt 2 Vdu=(WnuxB)(L v-d)

Vc=0.53 f'cbd Vc u VduPor Punzonamiento :

Lv = 150.00 r.e = 7.50 b ( 3/4") = 1.91 d = 60.59 Vdu = 101,975.73 = 0.85

cm cm cm cm kg

(Suponiendo varillas 3/4") ( d = hc - b - r.e. ) (Coef. De reduccion por corte)

Vc = 162,875.03 kg Vc = 138,443.78 kg Vc > Vdu OK!

Vu=Pu-Wnu x mnVu = 374,938.21 kg bo = 2 x ( t + d ) + 2 x ( b + d )= bo = 482.36 cm 2m +2n (perimetro de los planos de falla) * f 'c^.5 * bo * d = 1.06 * f 'c^.5 * bo * d

4 Vc=0.272+ f ' cbo d F c Dmayor , F e 2 p Vc=1.06 f ' c bo d c Dmenor Vue Vc; =0.85

F

!

c

n = b+d

Vc = 0.27 * 2 + 4 F c Vc = 555,426.41 kg Vc= 472,112.45 kg Vc = Vc= Vc > Vdu OK! Fc = lado mayor columna ( t ) Fc = 1.4 lado menor columna ( b ) m=t+d n=t+b bo = 2*m + 2*n Vu = vc OK !

448,939.43381,598.52

Kg Kg

d/2 b d/2 t m = t+d T

b m = 130.59 n = 110.59 Vu = 1.1 x f'c x b x d o Vu = 448,939.43 kg vc = 381,598.52 kg

4.- CALCULO DEL REFUERZO LONGITUDINAL ( = 0.90 )Direccin Mayor: (Wnu x B)L v 2 Mu= 2 Mu As= a Fy(d- ) 2 As.Fy a! 0.85f'c b As mn = 0.0018 * B * d As > As mn OK !! Lv = Mu = B= d= a= As = a= 150.0012,831,081.08 350.00

cm ree = 7.50 kg-cm b ( 3/4") = 1.91

cm (Valor Asumido) Ab ( 3/4" ) = 2.85 # Varilla ( n ) = 20 Espaciam = 17.53

60.59 3.89 57.88 3.89

cm2 cm cm cm2

B

As = 57.88 cm2 Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1

20 3/4" @ 17.53 cm Ab ( 3/4" ) = 2.85 # Varilla ( n ) = 15 Espaciam = 23.79 15 3/4" @ 23.79 cmOK !!

As mn = 44.1 As >

cm2 As mn

Direccin Menor: As tranv = As * T B As mn = 0.0018 * B * d As > As mn OK !! Ab # Varilla ( n ) = As Ab As transv = 61.19 cm2 Espaciam = B - 2*r.e - b n -1

T= B= d= a=

370 350 cm 60.59 cm2 5.01 cm

b ( 3/4")

ree = 7.50 cm2 = 1.91 cm

(Valor Asumido) Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 21 Espaciam = 17.65 21 3/4" @ 17.65 cm Ab ( 3/4" ) = 2.85 # Varilla ( n ) = 16 Espaciam = 23.54 16 3/4" @ 23.54 cm As mnOK !!

Asmin = 46.62 cm2 As transv Longitud de desarrollo en Traccion ( Ld ) ld = b * fy * EFKP 3.54 * f 'c^.5 * C + Kr b Lv1 = Lv - r.e.e < Lv1 >

La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv (F + 1 ) F = Lado mayor Zapata Lado menor Zapata Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e.e - b n -1 Espaciamiento del Refuerzo Asc = 61.19 cm2 45 cm > 17.65 3xh 210 cmOK !!

F= K= P= E=

1.00 0.80 1.00 1.00

b (3/4") = 1.91 r.e.e = 7.50 fy = 4200 f'c = 210

C = 8.50 ktr = 02.5

q = ( C+kt r )/ b q= 10.41q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!

Longitud de desarrollo en traccin Lv1 = 142.50 cm Ld = 50.04 cm Ld < Lv1

OK !!

5.- VERIFICACION DE LA CONEXIN COLUMNA - ZAPATA ( = 0.70 )Para la seccin A colum = 70*50 = 3500 cm ( COLUMNA ) * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) Ab As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! cm2 # Varilla ( n ) = 6

Pu = 422000 kg A1 = 3500 cm2 * 0.85 * f 'c * A1 = 583100 kg Pu < * 0.85 * f 'c * A1 As mn = 17.50 cm2 Ab ( 3/4" ) = 2.85 cm2 USAR : As1 = 17.50 cm2 OK !! As col > As min

OK !!

Para la seccin A zapata = 350*370 = 129500 cm ( ZAPATA ) Pu < x 0.85 x f 'c x A2/A1 x A1 Pu = 422000 kg A1 = 3500 cm2 A2 = 129500 cm2 874650 kgOK !!

A2/A1 =

2

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

Pgina 1 de 5

DISEO DE ZAPATA COMBINADADisear 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 3/4" 9 3/4" Acero PD 20 40 tn PL 15 24 tn 2 b1 b2

PL1 S/C = 500 kg/m

PL2

1

Km

h t = 101.00

t1

t2

hc = 54.00

4.55

m

1.40

Df = 1.60 Km = 1800 qa = 2.00

m Otros kg/m3 S/C = 500 kg/m kg/cm2 d(eje-eje)= 4.3 m

Columna f ' c = 210 kg/cm

f'c= fy =

Zapata 175 kg/cm 4200 kg/cm

Clculo del peralte de la zapata (hc ) ld = 0.08 * b * Fy raiz(f 'c) ld >= 0.004 * b * fy

1.- DIMENSIONAMIENTO DE LA ZAPATA ( Az = S*T )b ( 3/4" ) = 0.08 x b x fy / f c = .004*b*fy = Tomar ld = r.e = hc= ht= Tomar ht = 1.91 49 32 49 7.50 59.00 101.00 101.00 cm cm cm cm cm cm cm cm

OK !! Longitud de desarrollo en compresin

hc = ld + r.e + b hm = Df - hc

Clculo de la presin neta del suelo ( qm ) qm = qa - Km*hm - c*hc - s/c

qm =

1.63

kg/cm

Clculo del rea de la zapata ( Az ) Ps1 = P1D + P1L Ps2 = P2D + P2L Rs = P1s + P2s 20 +IMo = 0 Rs * Xo = P1s* t1/2 + P2s * 455 Xo = ?? 0 Xo 455.00 Rs = Lz / 2 e = Lz / 2 - Xo Lz / 6 e < Lz/6 q1,2 = Rs * 1 6 * e Lz Lz P1s = P2s = Rs = Xo = Lz = Lz / 2 = e= Lz / 6= 35 64 99 301.21 625.00 312.50 11.29 104 Tn Tn Tn cm cm cm cm cm 99 Tn 170.00 cm P1s = 35 Tn P2s = 64 Tn

20

30

30

Pgina 2 de 5

L = 2 x Xo B =(P1s +P2s) qn x L

602 L= cm B= 101 cm tomamos B = 85 cm

Como S/C = 500 kg/cm, Verificamos las presiones del suelo - ADICIONAL ( q 1,2 ) Ps1 = P1D + 50%P1L Ps2 = P2D + P2L R1s = P1s + P2s +IMo = 0 R1s * Xo = P1s* t1/2 + P2s * 455 Xo = ?? 0 Xo 455.00 e = Xo1 - Xo q = Ps + Mc = Ps + Ps x e Az I Az I P1s = P2s = R1s = Xo1 = 27.5 64 91.5 324.26 Tn Tn Tn cm R1s = 91.5 Tn I = ( B x L^3 )/12 I= 1454767.917 cm4 170.00 cm 20

P1s =

27.5 Tn

P2s =

64 Tn

20

30

30

e=

23.05

cm

AUMENTAMOS EL ANCHO B q= 44.56 kg/cm2 q < qm cumple " OK " q > qm no cumple "AUMENTAMOS EL ANCHO B" Aumentamos el Ancho hc = 150 cm 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 +IMo = 0 R2s * Xo = P1s* t1/2 + P2s * 455 Xo = ?? 0 20

P1s =

35 Tn

P2s =

52 Tn

20

30

30

Xo 470.00 1.40 87 Tn m

Lz / 2 e2 = Lz / 2 - Xo Lz / 6 e2 < Lz/6 q1,2 = R2s * 1 6 * e2 L B L

P1s = P2s = R2s = Xo =

35 52 87 288.97

Tn Tn Tn cm e=

R2s =

12.24

cm

I = ( B x L^3 )/12 I= 74531250

cm4

q > qm no cumple "AUMENTAMOS EL ANCHO B" q < qm cumple " OK "

q=

1.62

kg/cm2

OK !!

2.- DISEO EN SENTIDO LONGITUDINALClculo de la presin neta por unidad de longitud( qm )

P1s =

35 Tn

P2s =

64 Tn

cm3 qm qn = P1s + P2s Az qn = 6205.729 kg/m Por unidad de Longitud qm = qm1*B 0.2 ( No amplificada ) qm = 6205.73 kg/m m 4.50 m 140.00 m

Por Unidad de LONGITUD

Pgina 3 de 5

V 1241.15 kg

55311.98 kg

+ -

+

1.6297

m

+ -8688.022 kg

-33758.85 kg kg - m -27385.1

M

+

+124.12 kg - m

+6081.62 kg - m

Encontramos el diagrama de fuerzas cortantes verificamos el corte por Flexion: 67050.27 d = -ree + hc 1.50 x Vu = 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 = 222678.8 kg Aumentamos el Peralte a h = 150 cm. 44700.18 kg 261975.02 kg OK !! d= h- ree d= 141 cm

kg

ya que : F = ( 1.4 x D + 1.7 x L )/( D + L ) F= 1.5

Vu < 0 x Vc

Cumple !!

Vu = Vmax - qn x ( b2/2 + d ) = Aporte del Concreto :

Vc = 0.53 x f ' c x b x d = 0.85 x Vc = 222678.8 kg

261975.02 kg Vu < 0 x Vc Cumple !! Vu < O x Vc CUMPLE !!

VERIFICACION POR CORTE ( = 0.85 )COLUMNA EXTERIOR : 31075.81 kg Vu = 1.50 x ( Pu - qnu x m x n ) = Vu = 31075.8055 kg El aporte del Concreto : Fc = 1 bo = ( b + ,5*d ) + 2x( t + d ) = 422 cm COLUMNA INTERIOR : Vu = 1.50 x ( Pu - qnu x m x n ) = Vu = 75697.49 kg El aporte del Concreto : Fc = 75697.49 1.25 kg

bo = ( b + 0,5*d ) + 2x( t + d ) = 493 cm

Vc = 0.27 x 2 + 4 x f 'c x bo x d Fc Vc = 1396870.76 kg Vc = 1187340.14 kg Vc = 1.10 x f 'c x bo x d = Vc = 948492.49 kg Vc = 806218.62 kg CUMPLE !! Vu < Vc 948492.5 kg

Vc = 0.27 x 2 + 4 x f 'c x bo x d Fc Vc = 1412870 kg Vc = 1200939 kg Vc = 1.10 x f 'c x bo x d = Vc = 1106949 kg Vc = 940906.8 kg CUMPLE !! Vu < Vc 1E+06 kg

Pgina 4 de 5

4.- CALCULO DEL REFUERZO EN EL TRAMO CENTRALX x qn - P1 = 0 X= P1 qn Calculo de As : X = 5.64 mMu =

qn x X^2 2

_

P1 x X

Mu = -91699.11

kg - m

Mu =

91699.11 r .e .e = 8 cm

kg - m db = 1.91c

As = Mu / ( * fy * ( d - a/2 )) a = As * fy / ( 0.85 * f 'c * B )

As mn = 0.0018 * B * d As > As mn OK !! Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1

B= d= a= As = a=

265 cm2 141 cm2 2.77 cm 26.06 cm2 2.78 cm

As = 26.06 cm2

(Valor Asumido) Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 9 Espaciam = 31 cm 9 3/4" @ 31 cm Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 24 Espaciam = 11 cm 24 3/4" @ 11 cm

As mn = 67.26 cm2 As >

As mn

5.- CALCULO DEL REFUERZO POR DEBAJO DE LA COLUMNA INTERIORqn x ( L )^2 2

Mu =

Mu =

6081.61 1.91 m

kg - m 1.4 6081.61 r .e .e = 8 cmc

L= Calculo de As :

14 5/8"@ 22cm kg - m db = 1.91

Mu =

As = Mu / ( * fy * ( d - a/2 )) a = As * fy / ( 0.85 * f 'c * B )

As mn = 0.0018 * B * d As > As mn OK !! Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1

B= d= a= As = a=

265 141 0.18 1.71 0.18

cm2 cm2 cm2 cm2 cm

As = 1.71 cm2

(Valor Asumido) Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 1 Espaciam = #DIV/0! cm 1 3/4" @ #DIV/0! cm Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 25 Espaciam = 10 cm 25 3/4" @ 10 cmASUMIR As mn !!

As mn = 71.55 cm2 As >

As mn

Disear en sentido transversal a cada columna le corresponde una porcion de Zapata

d/2

d/2

d/2

1.205

1.91

ZAPATA EXTERIOR

ZAPATA INTERIOR

Pgina 5 de 5

qn =

Pu Az

qn =

1.68

kg/cm2

qn =

Pu Az qnu x B x (L^2) 2 191 141 0.64 4.34 0.64 cm cm2 cm cm2 cm cm2

qn = 1.91 kg/cm2

Mu = B= d= a= As = a=

qnu x B x (L^2) 2

Mu = 1169724 1.59 cm2

Mu = B= d= a= As = a=

Mu = 2E+06 r .e .e = 8 cm (Valor Asumido) db = 1.59 cm2

120.5 cm2 r .e .e = 8 cm db = 141 cm2 0.52 (Valor Asumido) cm 2.20 cm2 0.52 cm cm2

As = 2.2

As mn = 32.54 cm2

Ab ( 3/4" ) = 2.85 cm2 # Varilla ( n ) = 11 Espaciam = 10.00 cm 11 3/4" @ 10 cm

As = 4.34

As mn = 51.57

cm2

Ab ( 3/4" ) = # Varilla ( n ) = Espaciam = 18 3/4" @

2.85 cm2 18 10.00 cm 10 cm

6.- VERIFICACION DE LA CONEXIN ZAPATA - COLUMNA( = 0.70 )Para la seccin A columna = 50*50 = 2500 cm ( COLUMNA ) c * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! Pu = 53500 kg A1 = 2500 cm2 * 0.85 * f 'c * A1 = 312375 kg Pu < * 0.85 * f 'c * A1CUMPLE !!

As mn = 12.50 cm2 As col > As minOK !!

Para la seccin B columna = 40*50 = 2000 cm ( COLUMNA ) * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! Pu = 96800 kg A1 = 2000 cm2 c * 0.85 * f 'c * A1 = 249900 kg Pu < * 0.85 * f 'c * A1CUMPLE !!

As mn = 10.00 cm2 As col > As minOK !!

Detalle de refuerzos en la Zapata Combinada verificamos primero el espaciamiento maximo Espaciamiento del Refuerzo > 45 cm OK !! 450 3xh= 450 cm

d/2 24 3/4"@ 11cm

d/2

d/2

18 3/4"@ 10cm

11 3/4"@ 10cm Longitud de desarrollo en Traccion ( Ld ) ld = b * fy * EFKP < 3.54 * f 'c^.5 * C + Kr b Lv1 = Lv - r.e.e Lv1 Ld = 71 cm

25 3/4"@ 10cm

Ld1 = 46 cm

La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv (F + 1 ) F = Lado mayor Zapata Lado menor Zapata # Varilla ( n ) = As Ab Espaciam = B - 2*r.e.e - b n -1 Calculo del refuerzo minimo : As mn = 71.55 cm2 Ab ( 3/4" ) = # Varilla ( n ) = Espaciam = 25 3/4" @ 2.85 cm2 25 10.00 cm 10 cm b (3/4") = 1.91 F = 1.00 b (5/8") = 1.59 K = 0.80 r.e.e = 7.50 P = 1.00 fy = 4200 E = 1.30 f'c = 175 E = 1.00 Longitud de desarrollo en traccin

C = 6.50 ktr = 0

2.5

q=

q = ( C+kt r )/ b 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 3/8" para refuerzo principal =< 3/4" 1/2" para refuerzo principal > 3/4" con espaciamiento maximo de 45 cm.

OK !!

0.2

Pgina 1 de 4

DISEO DE ZAPATA CONECTADA

Disear 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/cm Columna f ' c = 210 kg/cm b1 = 50 cm t1 = 50 cm b2 = 40 cm t2 = 50 cm COL 1 2 fy= Df = Km = Kc = qa = db = Acero 4200 Suelo 1.60 1800 2400 2.00 1.91 PD (tn) 50 40 kg/cm m kg/m kg/m kg/cm cm PL (tn) 30 24 S/C = 500 kg/m

Lc = 550 cm db = 1.91 cm

SECCION REFUERZO 50 X 50 9 3/4" 40 X 50 9 3/4"

1.- DIMENSIONAMIENTO DE LA ZAPATA Y VIGA DE CIMENTACIONZAPATA EXTERIOR:

Ld =

0.08xdbxfy

f 'c

Ld = 0.08x1,91x4200/(175^(1/2)) = Ld = 49 cm

48.5

cm

hc = Ld + r.ee + b hm = Df - hc

ld >= 0.004 * b * fy

Ld >= 0.004x1.91x4200 = Ld = 32 cm

32.09 cm

Clculo del peralte de la zapata (hc ) hc = 59 cm hc = Ld + 10 = ht = Df - hc = ht = 101 cm

Clculo de la presin neta del suelo ( qm ) qn = qa - Km*hm - gc*hc - s/c qn = 2.4-(1800xE^-06)x(101)-(2400xE^06)x(59)-(500xE^04) = qn = CALCULO DE P'2 : Tanteo 1.63 kg/cm2

e =

57 cm

P'2 = P'2 = Az = Ps qn

P1xe 9249.49 kg

=

( PD + PL ) x

e

Lc - eAz =

=

( 50 + 30 ) x 1000 x 57 550 - 57

= =

9249.49

P1 + P' 2 qn b = 166

= 54868.437 cm P'1 = P'2 =

cm2

A = 2 x( b )^2 = nuevo e = + b -t 2 2

54868.44 e = 58

=

A = 2 x( b )^2 = 54980

9431 54980 b = 166 b= 165 t= 330

0 tomamos

+

t=2b

Tomamos b = 165 cm

-----> A = 165 x 330

e = 57 cm

Pgina 2 de 4

ZAPATA EXTERIOR:

Ld =

0.08xdbxfy

f 'c

Ld = 0.08x1.91x4200/(175^(1/2)) = Ld = 49 cm

49 cm

hc = Ld + r.ee + b hm = Df - hc

ld >= 0.004 * b * fy

Ld >= 0.004x1.91x4200 = Ld = 32 cm

32 cm

Clculo del peralte de la zapata (hc ) hc = 60 cm hc = Ld + 10 = ht = Df - hc = ht = 100 cm

Clculo de la presin neta del suelo ( qm ) qn = qa - Km*hm - gc*hc - s/c qn = 2.4-(1700xE^-06)x(120)-(2400xE-06)x(60)-(500xE-04) = qn = CALCULO DE P'2 : Tanteo 2.00 kg/cm2

e =

71 cm

P'2 = P'2 = Az = Ps qn

P1xe 9486.00 kg

=

( PD + PL ) x

e

Lc - eAz =

=

( 40 + 24 ) x 1000 x 50 550 - 50

=

= 9486

P2 + P' 2 qn b = 192

=

36743 usamos b = 2 P'1 = P'2 =

cm2 155 cm

A = ( b )^2 = nuevo e = + b -t 2 2

36743.00 e = 71

=

A = 2 x( b )^2 = 44743

9486 44743 b = 150

0

b= 150 + VIGAS DE CIMENTACION h= b= Lc 7 = P1 31 x Lc 550 7

A2 = ( 150 x 150 ) =

0

+

h = 79 cm b = 47 cm

SECCION 50 x 80

DISEO DE LA VIGA DE CONEXIN Wv = b x h x Kc = 9.6 kg/m Mu = P' 2 x L + Wv x ( L^2 )/2= 7250000 Mu = 7250000 kg-cm b ( 3/4") = 1.91 ree = 7.50 B = 50 cm d = 79.00 cm2 a = 5.00 cm2 (Valor Asumido) Ab ( 1" ) = 2.54 cm2 As = 25.07 cm2 a = 14.16 cm # Varilla ( n ) = 11 Espaciam = 3 cm As = 26.67 cm2 11 1" @ 3 cm

As = Mu / ( * fy * ( d - a/2 )) a = As x fy / ( 0.85 x f 'c x b ) As mn = 0.8 x (f ' c ^0.5) x B * d/ fy As > As mn OK !! # Varilla ( n ) = As Ab Espaciam = B - 2*r.e - b n -1

As mn = 9.95

cm2 As > Asmin

11

1" @OK !!

3 cm

Pgina 3 de 4

VERIFICACION POR CORTE Vu = P' 2 + Wv x L L Vu = 21982 KG Vu < Vc

APORTE DEL CONCRETO Vc = 0.53 x (f ' c ^0.5) x b x d =OK !!

23540 kg

DISEO DE LA ZAPATA EXTERIOR

ZAPATA EXTERIOR qn = Pu Az qnu x B x (L^2) 2 150 cm2 41 cm2 5.00 #DIV/0! #DIV/0! qn = #DIV/0! kg/cm2

ZAPATA INTERIOR qn = Pu Az #DIV/0!

Mu = B= d= a= As = a=

Mu =

#DIV/0!

Mu = L= B= d= a= As = a=

cm2 cm2 cm

r .e .e = 7.5 cm db = 1.59 cm2 (Valor Asumido)

qnu x B x (L^2) #DIV/0! kg 2 100 cm r .e .e = 8 cm 250 cm2 51 5 cm ( Valor Asumido ) #DIV/0! 2 cm cm #DIV/0!

As = #DIV/0!cm2

Ab ( 5/8" ) = 1.98 cm2 # Varilla ( n ) = #DIV/0! Espaciam = #DIV/0! cm cm2 #DIV/0! cm

As mn = 13.5 ####

As = #DIV/0! 2 cm #Varilla n = 14 Espaciam. = 17.88 Asmin = 27 cm2 14 5/8" @ 18 cm

5/8" @

6.- VERIFICACION DE LA CONEXIN ZAPATA - COLUMNA( = 0.70 )Columna Exterior Para la seccin A columna = 50 x 50 = 2500 cm ( COLUMNA ) * 0.85 * f 'c * As1 A colum = b *t Pu < ( * 0.85 * f 'c * A1) As mn = 0.005 * A1 # Varilla = As1 Ab As col. > As mn OK !! c # Varilla ( n ) = 4

Pu = 121000 kg A1 = 2500 cm2 * 0.85 * f 'c * A1 = 312375 kg Pu < * 0.85 * f 'c * A1

OK !!

As mn = 12.50 cm2 Ab ( 3/4" ) = 2.85 cm2 USAR : As1 = 12.50 cm2 OK !! As col > As min Columna Interior Para la seccin B columna = 50 x 50 = 2500 cm ( COLUMNA ) Pu = 96800 c kg * 0.85 * f 'c * As1 A1 = 2000 cm2 A colum = b *t * 0.85 * f 'c * A1 = 249900 kg # Varilla ( n ) = 4 cm2 Pu < ( * 0.85 * f 'c * A1) Ab ( 3/4" ) = 2.85 Pu < * 0.85 * f 'c * A1 As mn = 0.005 * A1 USAR : As1 = 10.00 cm2 # Varilla = As1 OK !! Ab As mn = 10.00 cm2 OK !! As col. > As mn OK !! As col > As min

Longitud de desarrollo en Traccion ( Ld ) ld = b * fy * EFKP 3.54 * f 'c^.5 * C + Kr b Lv1 = Lv - r.e.e < Lv1

Pgina 4 de 4

La Zapata es rectangular se debe compartir el Refuerzo adecuadamente de la siguiente manera: Asc = 2 * Astrv (F + 1 ) F = Lado mayor Zapata Lado menor Zapata Ab # Varilla ( n ) = As Ab Espaciam = B - 2*r.e.e - b n -1 Espaciamiento del Refuerzo 45 cm As1 = > 3xh 0 cmOK !!

F= K= P= E=

1.00 0.80 1.00 1.00

b (5/8") = 1.59 r.e.e = 7.50 fy = 4200 f'c = 175

C = 8.50 ktr = 02.5

q = ( C+kt r )/ b q= 10.09

Longitud de desarrollo en traccin Lv1 = 38.13 cm Ld = 46 cm AUMENTAR EL T !! Ld < Lv1

q >= 2.5 ,PONER 2.5 !! q < 2.5 ,PONER q !!

6 1"@ 7cm

d/2 d/2

14 5/8"@ 22cm 12 5/8"@ 12cm

14 5/8"@ 18cm

DISEO DE LOSA DE CIMENTACIONS/C= 450

Km1=

1700

KS 0.9

Y' A 1 B 2 C 3 D 0.2

E Y 9.8 4 5 X G 6

F

4.5

H 4.5

7 I O 0.2 J 5.4 11.6 DATOSCOLUMNA

8

9 L K 5.4 0.6 0.6 X'

PD (ton) 45 60 60 60 100 70 60 70 60 585

PL (ton) 25 30 30 30 40 30 30 30 30 275

Pu 70 90 90 90 140 100 90 100 90 860

1 2 3 4 5 6 7 8 9

F'c = Fy =

210 4200 2400 1.4 1 450 1700

kg/cm kg/cm2

2

Kc=qa = Ks = S/C=

kg/m3 2 kg/cm 3 kg/cm 2 Kg/m kg/m3

Km1=

1.- CALCULO DEL ESPESOR DE LA PLACA METODO DE DISEO ASUMIENDO

t=

50

cm.

P=

4

3Ks Et3 P= 0.003242 m 5.401-1

E=15000*F'c

P= Lc= 5.4 Lc= 4.5

0.003240

m

-1

1.75 P

Se debe cumplir la siguiente condicin: 1.75/P