Diseño de Cimentaciones.. - Copia

DISEÑO DE UNA ZAPATA AISLADA Diseñar la zapata mostrada en la fig: Si la Columna de 70 x 50 lleva 8 fierros de 3/4" 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 Otros Suelof ' c = 210 kg/cm² S/C = 550 kg/m² Df = 1.4 m

Columna PD = 45 Tn 1700 kg/m³f ' c = 210 kg/cm² PL = 53 Tn qa = 1.00 kg/cm²

b = 40 cm db = 2.54 cmt = 40 cm Acero Lv = 150 cm

f y = 4200 kg/cm²

MD,ML

PD, PL

Ld = 58.89 cmht

Tomar Ld = 58.89 cm Df Lv

(Del problema se emplean varillas de Ø1") Øb ( 1") = 2.54 cmr.e. = 7.50 cm (recubrimiento) hchc = 68.93 cm

Tomar hc = 70.00 cm hc = Ld + r.e + Øb Tht = Df - hc

ht = 70.00 cm

Bqm = 0.66 kg/cm²

T

Azap = 148,484.85 cm² Donde:T = 385.00 cm P = Carga de servicioB = 385.00 cm Lv = Volados iguales sin

excentricidad

2.- DETERMINACIÓN DE LA REACCIÓN AMPLIFICADA ( qmu )

Donde:1.03 kg/cm2 Pu = Carga Ultima

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

Lv = 172.50 cmr.e = 7.50 cm

Øb ( 3/4") = 1.91 cm (Suponiendo varillas Ø3/4")d = 60.59 cm ( d = hc - Øb - r.e. )

Vdu = 44,502.39 kgØ = 0.85 (Coef. De reduccion por corte)

Vc = 179,162.54 kg

g 2 =

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

Cálculo de la presión neta del suelo ( qm )

Cálculo del área de la zapata ( Az )b

tt

Reemplazo los valores que tenemos:

= 1.4 x 180000 + 1.7 x 100000 350 x 370

=

Ld= 0 .08 .db .F y

√f'c

Azap=Pqm

T=√Az+( t1-t2 )2

S=√Az−( t1-t2)2

qm=qa−ght−gchc-s/c

Wnu=PuAzap

Lv=T−t2

Vdu=(WnuxB)(Lv-d )Vc=0. 53√f'c bdØVc ³ Vdu

ØVc = 152,288.16 kgØVc > Vdu OK!

Vu = 142,648.87 kg

= 2m +2nbo = 402.36

Vc = 572,321.96 kg Vc= 374,482.27 KgØVc = 486,473.67 kg ØVc= 318,309.93 Kg

ØVc > Vdu OK!1

lado menor columna ( b )

m = t + d m = 100.59n = t + b n = 100.59bo = 2*m + 2*nVu = Øvc OK ! Vu = 374,482.27

Øvc = 318,309.93

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

Lv = 172.50 cm ree = 7.50

Mu = 5,916,469.97 kg-cm 1.91

B = 385.00

d = 60.59a = 3.89 (Valor Asumido)

As = 26.69 2.85As mín = 0.0018 * B * d a = 1.63 # Varilla ( n ) = 9As > As mín OK !! 46.01

As = 26.18 9 Ø 3/4" @ 46.01Aøb

2.85 Aøb # Varilla ( n ) = 10

40.90 n -1 As mín = 27.72 10 Ø 3/4" @ 40.90

As > As mínASUMIR As mín !!

Dirección Menor:

B T = 385 ree = 7.50

As mín = 0.0018 * B * d B = 385 1.91

As > As mín OK !! d = 60.59a = 5.01 (Valor Asumido)

Aøb 2.85# Varilla ( n ) = 9

Aøb 46.01As transv = 26.18 9 Ø 3/4" @ 46.01

n -1 2.85# Varilla ( n ) = 17

23.01Asmin = 48.51 17 Ø 3/4" @ 23.01

As transv > As mínASUMIR As mín !!

Longitud de desarrollo en Traccion ( Ld )

< Lv1

Por Punzonamiento:

bo = 2 x ( t + d ) + 2 x ( b + d ) (perimetro de los planos de falla)

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

b c = lado mayor columna ( t )

Vu = 1.1 x f'c x bo x d

Øb ( 3/4") =

Aøb ( 3/4" ) =

Espaciam =

# Varilla ( n ) = As Aøb ( 3/4" ) =

Espaciam = B - 2*r.e - Øb Espaciam =

As tranv = As * T

Øb ( 3/4") =

Aøb ( 3/4" ) =# Varilla ( n ) = As

Espaciam =

Espaciam = B - 2*r.e - ØbAøb ( 3/4" ) =

Espaciam =

ld = Øb * fy * a * b * g * l

d/2

d/2

m = t+d

n =

b+

d

t

b

T

B

bc =

cm

kgkg

cm

cm

cm2

cm2

cm2

cm2

cm2

cm2

cm²

cm

cm

cm2

cm2

cm2

cm2

cm2

cm2

cm2

cm

Vu=Pu-Wnu x mnVc=0. 27[2+

4

βc]√ f ' c bo d

β c=DmayorDmenor ,β c≤2→Vc=1. 06√ f ' c bo d

Vu≤ØVc; Ø=0 . 85

Mu=(Wnu x B )Lv2

2

As=Mu

ØFy (d-a2)

a=As. Fy0 . 85f'cb

ØbLv1 = Lv - r.e.e

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

1.00 Øb (3/4") = 1.91 8.500.80 r.e.e = 7.50 ktr = 01.00 fy = 4200

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

Longitud de desarrollo en tracción q= 10.41 Aøb

Lv1 = 142.50 q >= 2.5 ,PONER 2.5 !!

n -1 Ld = 50.04 q < 2.5 ,PONER q !!

Ld < Lv1 OK !!

Espaciamiento del RefuerzoAsc = 26.18

46.01 OK !!

3 x h 210 cm

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 Pu = 153100 # Varilla ( n ) = 3A colum = b *t A1 = 1600Pu < ( Ø * 0.85 * f 'c * A1) Ø * 0.85 * f 'c * A1 = 199920AøbAs mín = 0.005 * A1 Pu < Ø * 0.85 * f 'c * A1 OK !!

Aøb As mín = 8.00As col. > As mín OK !! Aøb ( 3/4" ) = 2.85

USAR As1 = 8.00As col > As min OK !!

Para la sección A zapata = 350*370 = 129500 cm² ( ZAPATA )

Pu < Ø x 0.85 x f 'c x A2/A1 x A1 Pu = 153100A1 = 1600 A2/A1 = ###A2 = 148225

Ø x 0.85 x f 'c x A2/A1 x A1 = 399840 OK !!

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

Asc = 2 * Astrv ( b + 1 ) b = C =

g =b = Lado mayor Zapata l =

a =

# Varilla ( n ) = As

Espaciam = B - 2*r.e.e - Øb

45 cm

# Varilla = As1

cm

cm

cm2

>

kg

kgcm2

cm2cm2

cm2

kg

kg

cm2cm2

de 23

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: SECCION REF. PD PLC1 40 40 6 Ø 3/4" 20 12 PL1 PL2C2 40 60 8 Ø 3/4" 38 18

b x t Acero tn tn S/C = 500 kg/m²

h t = 66.00

hc = 54.00

4.70 m 1.40

Df = 1.20 Otros Columna Zapata1800 S/C = 500 kg/m² f ' c = ### kg/cm² f ' c = 210 kg/cm²

qa = 2.00 f y = 4200 kg/cm²

1.- DIMENSIONAMIENTO DE LA ZAPATA ( Az = S*T )

Øb ( 3/4" ) = 1.91 cm raiz(f 'c) 0.08 x Øb x fy / f ´c = 44 cm

.004*øb*fy = 32 cm OK !!ld >= 0.004 * øb * fy

Tomar ld = 44 cm Longitud de desarrollo en compresión

hc = ld + r.e + Øb r.e = 7.50 cmhm = Df - hc h c = 54.00 cm

h t = 66.00 cm

Tomar ht = 66.00 cm

qm = 1.70 kg/cm²

Cálculo del área de la zapata ( Az )

Ps1 = P1D + P1L P1s = 32 Tn P2s = 56 TnPs2 = P2D + P2LRs = P1s + P2s

20 20 30 30

Rs * Xo = P1s* t1/2 + P2s * 455Xo = ??

470.00 170.00 cm

Rs 88 TnP1s = 32 Tn

Lz / 2 P2s = 56 Tne = Lz / 2 - Xo Rs = 88 TnLz / 6 Xo = 306.36 cme < Lz/6

Lz = 640.00 cm Lz Lz / 2 = 320.00 cm

e = 13.64 cm

g m

g m =

Cálculo del peralte de la zapata (hc )

ld = 0.08 * Øb * Fy


qm = qa - gm*hm - gc*hc - s/c

e Mo = 0

q1,2 = Rs * 1 ± 6 * e

1 2

t1 t2

b1 b2

0Xo

+

X

X

de 23

L = 613 cm

B = 84 cmB =(P1s +P2s) tomamos B = 85 cm

qn x L

Como S/C = 500 kg/cm², Verificamos las presiones del suelo - ADICIONAL ( q 1,2 )

Ps1 = P1D + 50%P1LPs2 = P2D + P2L P1s = 26 Tn P2s = 56 TnR1s = P1s + P2s

20 20 30 30

R1s * Xo = P1s* t1/2 + P2s * 455Xo = ??

470.00 170.00 cm

e = Xo1 - Xo P1s = 26 Tn R1s 82 TnP2s = 56 Tn

q = Ps + Mc = Ps + Ps x e R1s = 82 TnXo1 = 327.32 cm e = 20.96 cm 1631620312 cm3

q = 1.90 kg/cm2 AUMENTAMOS EL ANCHO Bq < qm cumple " OK "q > qm no cumple "AUMENTAMOS EL ANCHO B"

Aumentamos el Ancho B = 100 cmUn nuevo calculo

Ps = 82000 tn q = 1.61 OK !!e = 20.96 cmB = 100 cm

1919553308.3333

Ps1 = P1D + P1LPs2 = P2D + 50%P2L P1s = 32 Tn P2s = 47 TnR2s = P1s + P2s

20 20 30 30

R2s * Xo = P1s* t1/2 + P2s * 455Xo = ??

470.00 1.40 cmLz / 2e2 = Lz / 2 - Xo P1s = 32 Tn R2s = 79 TnLz / 6 P2s = 47 Tne2 < Lz/6 R2s = 79 Tn

Xo = 287.72 cm B e = 18.64 cm 1919553308 cm3

q > qm no cumple "AUMENTAMOS EL ANCHO B" q = 1.52 kg/cm2 OK !!q < qm cumple " OK "

2.- DISEÑO EN SENTIDO LONGITUDINAL P1s = 32 Tn P2s = 56 Tn

qmqn = P1s + P2s 0.2 m 4.50 m 140.00 m

Azqn = 14355.628 kg/m² ( No amplificada )

Por unidad de Longitudqm = qm1*B Por Unidad de LONGITUD qm = 14355.63 kg/m

L = 2 x Xo

e Mo = 0

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

I =

e Mo = 0

q1,2 = R2s * 1 ± 6 * e2 I = ( B x L^3 )/12I =

Cálculo de la presión neta por unidad de longitud ( qm )

+

0Xo

+

0Xo

kg/cm2

cm3

cm3

de 23

V 35902.118 kg2871.13

+ 1.593 m-

-20097.88 kg-29128.87

kg - m-22914.03

M

-+

287.11 kg - m

14068.52 kg - m

Encontramos el diagrama de fuerzas cortantes verificamos el corte por Flexion: d = -ree + hc 1.50 x Vu = 37703.09 kg ya que : F = ( 1.4 x D + 1.7 x L )/( D + L )

d = 45.00 cmVu = Vmax - qn x ( b2/2 + d ) = 25135.396 kg F = 1.5

Aporte del Concreto : Vc = 0.53 x f ' c x b x d = 34561.93 kg Vu < 0 x Vc Cumple !!

0.85 x Vc = 29377.64 kg Vu > O x Vc , NO CUMPLE Aumentamos el Peralte a h = 65 cm. d = h- ree

d = 56 cmVu = Vmax - qn x ( b2/2 + d ) = 23556.276 kg

Aporte del Concreto : Vc = 0.53 x f ' c x b x d = 43010.41 kg Vu < 0 x Vc Cumple !!

0.85 x Vc = 36558.849 kg Vu < O x Vc CUMPLE !!

VERIFICACION POR CORTE ( Ø = 0.85 )

COLUMNA EXTERIOR : COLUMNA INTERIOR :Vu = 1.50 x ( Pu - qnu x m x n ) = 33942.969 kg Vu = 1.50 x ( Pu - qnu x m x n ) = 60020.36 kgVu = 33942.969 kg Vu = 60020.36 kg

El aporte del Concreto : 1 El aporte del Concreto : 1.5

232 cm 308 cm

Vc = 352184.3409 kg Vc = 363653.95 kgØVc = 299356.69 kg ØVc = 309105.9 kg

Vc = 1.10 x f 'c x bo x d = 239137.52 kg Vc = 1.10 x f 'c x bo x d = 317476 kg

Vc = 239137.52 kg Vc = 317475.7 kgØVc = 203266.89 kg ØVc = 269854.3 kg

Vu < ØVc CUMPLE !! Vu < ØVc CUMPLE !!

b c = b c =

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

Vc = 0.27 x 2 + 4 x f 'c x bo x d Vc = 0.27 x 2 + 4 x f 'c x bo x d b c b c

-

+ +

-

+

kg

kg

-

+

R203

Elaborado por : MARCO ANTONIO PINEDO RUIZ

de 23

4.- CALCULO DEL REFUERZO EN EL TRAMO CENTRAL

X x qn - P1 = 0

X =P1

X = 2.23 Mu =qn x X^2 _ P1 x X

Mu = -29265.45 kg - mqn 2

Calculo de As :Mu = 29265.45 kg - m

As = Mu / ( Ø * fy * ( d - a/2 )) B = 100 r .e .e = 8 db =1.91a = As * fy / ( 0.85 * f 'c * B ) d = 56

a = 5.00 (Valor Asumido)As = 21.71 2.85

As mín = 0.0018 * B * d a = 5.11 Varilla ( n ) = 8As > As mín OK !! 12Aøb As = 21.73 8 Ø 3/4" @ 12

Aøb 1.89 Varilla ( n ) = 5

n -1 21As mín = 10.08 5 Ø 5/8" @ 21

As > As mín OK !!

5.- CALCULO DEL REFUERZO POR DEBAJO DE LA COLUMNA INTERIOR

Mu =qn x ( L )^2

Mu = 9658.47 kg - m2L = 1.16 m

Calculo de As :Mu = 9658.47 kg - m

As = Mu / ( Ø * fy * ( d - a/2 )) B = 100 r .e .e = 8 db =1.91a = As * fy / ( 0.85 * f 'c * B ) d = 56

a = 5.00 (Valor Asumido)As = 7.16 2.85

As mín = 0.0018 * B * d a = 1.68 Varilla ( n ) = 2As > As mín OK !! 82Aøb As = 6.95 2 Ø 3/4" @ 82

Aøb 1.98 Varilla ( n ) = 6

n -1 16As mín = 11.7 6 Ø 5/8" @ 16

As > As mín ASUMIR As mín !!

Diseñar en sentido transverzal a cada columna le corresponde una porcion de Zapata

d/2 d/2 d/2

0.68 1.16

Aøb ( 3/4" ) =

Espaciam =

# Varilla ( n ) = AsAøb ( 5/8" ) =

Espaciam = B - 2*r.e - ØbEspaciam =

Aøb ( 3/4" ) =

Espaciam =

# Varilla ( n ) = AsAøb ( 5/8" ) =

Espaciam = B - 2*r.e - ØbEspaciam =

cm

cm2

cm

cm2

cm2

cm2

cm2cm2

cm

cm2

cm

cmcm

cm

cm2

cm

cm2

cm

cm2

cm2

cm2

cm2cm2

cm2

cm

cmcm

cm

cm2

14 Ø 5/8"@ 22cm

de 23

ZAPATA EXTERIOR ZAPATA INTERIOR

de 23

qn =Pu

qn = 7.12 kg/cm2 qn =Pu

qn = 7.22 kg/cm2Az Az

Mu =qnu x B x (L^2)

Mu = 217872 Mu =qnu x B x (L^2)

Mu = 4E+052 2

B = 68 r .e .e = 8 db = 1.59 B = 68 r .e .e = 8 db = 1.59d = 56 d = 56a = 5.00 (Valor Asumido) a = 5.00 (Valor Asumido)

As = 1.08 As = 1.86a = 0.37 a = 0.64

As = 1.03 1.98 As = 1.79 1.98# Varilla ( n ) = 4 # Varilla ( n ) = 7

17.00 16.00As mín = 7.96 4 Ø 5/8" @ 17 As mín = 13.57 7 Ø 5/8" @ 16

6.- VERIFICACION DE LA CONEXIÓN ZAPATA - COLUMNA( Ø = 0.70 )

Para la sección A columna = 40*40 = 1600 cm² ( COLUMNA )

Ø * 0.85 * f 'c * As1 Pu = 48400A colum = b *t A1 = 1600Pu < ( Ø * 0.85 * f 'c * A1) Ø * 0.85 * f 'c * A1 = 266560 As mín = 8.00As mín = 0.005 * A1

Pu < Ø * 0.85 * f 'c * A1 CUMPLE !! As col > As min OK !!

AøbAs col. > As mín OK !!

Para la sección B columna = 40*60 = 2400 cm² ( COLUMNA )

Ø * 0.85 * f 'c * As1 Pu = 83800A colum = b *t A1 = 2400Pu < ( Ø * 0.85 * f 'c * A1) Ø * 0.85 * f 'c * A1 = 399840 As mín = 12.00As mín = 0.005 * A1

Pu < Ø * 0.85 * f 'c * A1 CUMPLE !! As col > As min OK !!

AøbAs col. > As mín OK !! Detalle de refuerzos en la Zapata Combinada verificamos primero el espaciamiento maximo

Espaciamiento del Refuerzo

45 cm195 OK !!

3 x h = 0 cm

d/2 d/2 d/2


< Lv1

Øb Ld = 65 Ld1 = 42Lv1 = Lv - r.e.e


Øb (3/4") = 1.911.00 Øb (5/8") = 1.59 6.50 2.5 q = ( C+kt r )/ Øb0.80 r.e.e = 7.50 ktr = 0 q= 8.41

Lado menor Zapata 1.00 fy = 42001.30 f'c = ### q >= 2.5 ,PONER 2.5 !!

Aøb 1.00 q < 2.5 ,PONER q !!

Longitud de desarrollo en tracción n -1

Lv1 = -7.50 Ld < Lv1 AUMENTAR EL T !!

Calculo del refuerzo minimo : Ld = 65.05As mín = 11.70 Refuerzo montaje en forma de Garrido

1.98 Ø 3/8" para refuerzo principal Ø =< 3/4"# Varilla ( n ) = 6 Ø 1/2" para refuerzo principal Ø > 3/4"

17.00 con espaciamiento maximo de 45 cm.6 Ø 5/8" @ 17 0.2

Aøb ( 5/8" ) = Aøb ( 5/8" ) =

Espaciam = Espaciam =

# Varilla = As1

# Varilla = As1

ld = Øb * fy * a * b * g * l 3.54 * f 'c^.5 * C + Kr

Asc = 2 * Astrv ( b + 1 ) b = C =b = Lado mayor Zapata g =

l =# Varilla ( n ) = As a =

a1 =Espaciam = B - 2*r.e.e - Øb

Aøb ( 5/8" ) =

Espaciam =

cm

cm2 cm2

cm

cm2

cm2

cm2

cm2

cm2

cm2

cm

cmcm

cm2

cm2 cm2

cm

cm2

cmcm2

cm

cm

cm2cm2

kg

kgcm2

cm2

kg

kgcm2

cm2

cm

cm

>

cm

cm2

cmcm

cm2

4 Ø 5/8"@ 19.5cm 6 Ø 5/8"@ 17cm

8 Ø 3/4"@ 12.10cm

7 Ø 5/8"@ 19cm

DISEÑO DE UNA VIGA SOMETIDO A TORSIONDiseñar la viga mostrada, asumir empotramiento en los extremos. Usar la norma nacional

S/C= 3 Ton/m2

ɣ= 1900 kg/m3

L= 10

ELEVACION

s/c= 0.3 ton/m2.

0.15

0.750.6

0.4 1.6

2

CORTE A-A

DATOS:

f´c= 210 kg/cm2.fy= 4200 kg/cm2.

Wlosa=Wviga=

1.- DETERMINACION DE CARGAS ULTIMAS:

Wcm=

Wlosa=Wviga=Wcv=

Wuvol= 1.4 CM+1.7 CV Wuvol=Wutotal= 1.4 Cvtotal+1.7CVtotal Wutotal=

a) momentos torsionantes en caras de los apoyos de la viga

T= 1.728*1.6^2/2*L/2

T = 10.38336 Txm

d=

b) momentos torsionantes en la seccion critica de la viga

T= 6.376672 Txm

c) momentos flectores en la viga

Apoyos: 23.62 Txm

CentroLuz : 11.81 Txm

c) Fuerz cortante

Apoyos: 14.172 Ton

Sección critica. 12.1879 Ton

3.- DETERMINACIóN SI SE TOMA EN CUENTA O N OLA TORSION EN EL DISEÑO

T=

T= 5296290.258976

2.- ACCIONES INTERNAS:

Vu = 0.00 kg

=bo = 0

Vc = #DIV/0! kg Vc= 0.00ØVc = #DIV/0! kg ØVc 0.00

ØVc > Vdu OK!###

lado menor columna ( b )

m = t + d m = 0.00n = t + b n = 0.00bo = 2*m + 2*nVu = Øvc OK ! Vu = 0.00

Øvc = 0.00

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

Lv = 0.00Mu = 0.00

B = 0.00

d = 0.00a = 3.89

As = #DIV/0!As mín = 0.0018 * B * d a = ###As > As mín OK !!

As = #DIV/0!Aøb

Aøb

n -1 As mín = 0

As >Dirección Menor:

B T = 0As mín = 0.0018 * B * d B = 0As > As mín OK !! d = 0.00

a = 5.01Aøb

Por Punzonamiento:

bo = 2 x ( t + d ) + 2 x ( b + d ) (perimetro de los planos de falla)

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

b c = lado mayor columna ( t )

Vu = 1.1 x f'c x bo x d


Espaciam = B - 2*r.e - Øb

As tranv = As * T

bc =

cm

kgkg

Vu=Pu-Wnu x mn

Mu=(Wnu x B )Lv2

2

As=Mu

ØFy(d-a2)

a=As.Fy0 .85f'cb

AøbAs transv = #DIV/0!

n -1

Asmin = 0

As transvLongitud de desarrollo en Traccion ( Ld )

< Lv1

ØbLv1 = Lv - r.e.e


1.00 Øb (3/4") =0.801.00

Lado menor Zapata 1.00Aøb

Longitud de desarrollo en tracción Aøb

Lv1 = n -1 Ld =

Ld < Lv1Espaciamiento del Refuerzo

Asc =

#DIV/0!OK !!

3 x h 0 cm

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 Pu = 0A colum = b *t A1 = 0Pu < ( Ø * 0.85 * f 'c * A1) Ø * 0.85 * f 'c * A1 = 0AøbAs mín = 0.005 * A1 Pu < Ø * 0.85 * f 'c * A1

Aøb As mín = 0.00As col. > As mín OK !! Aøb ( 3/4" ) = 2.85

USA As1 = 0.00As col > As minAUMENTAR EL T !!

Para la sección A zapata = 350*370 = 129500 cm² ( ZAPATA )


Espaciam = B - 2*r.e - Øb


Asc = 2 * Astrv ( b + 1 ) b =


a =



45 cm

# Varilla = As1

>

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 = 0

Diseñar la viga mostrada, asumir empotramiento en los extremos. Usar la norma nacional

0.576 ton/m0.72 ton/m

1.296 ton/m

0.48 ton/m0.12 ton/m

0.6 ton/m

1.6224 ton/m2.8344 ton/m

d= 0.7

3.- DETERMINACIóN SI SE TOMA EN CUENTA O N OLA TORSION EN EL DISEÑO

KgKg

0.00 cm ree = 0.00

0.00 kg-cm 1.91

0.00

0.00(Valor Asumido)

#DIV/0! 2.85# Varilla ( n ) = #DIV/0!

#DIV/0!#DIV/0! #DIV/0! Ø 3/4" @ #DIV/0!

2.85# Varilla ( n ) = 0

1.910 0 Ø 3/4" @ 1.91

As mín #DIV/0!

ree = 7.50

1.91

0.00(Valor Asumido)

2.85

Øb ( 3/4") =

Aøb ( 3/4" ) =

Espaciam =

Aøb ( 3/4" ) =

Espaciam =

Øb ( 3/4") =

Aøb ( 3/4" ) =

d/2

d/2

m = t+d

n =

b+

d

t

b

T

B

cm

cm

cm2

cm2

cm2

cm2

cm2

cm2

cm²

cm

cm2

cm2

cm2

cm2

cm2

# Varilla ( n ) = #DIV/0!#DIV/0!

#DIV/0! #DIV/0! Ø 3/4" @ #DIV/0!

2.85# Varilla ( n ) = 0

16.910 0 Ø 3/4" @ 16.91

> As mín #DIV/0!


Øb (3/4") = 1.91 8.50r.e.e = 7.50 ktr = 0

fy = 0f'c = 0 2.5 q = ( C+kt r )/ Øb

Longitud de desarrollo en tracción q= 10.41

-7.50 q >= 2.5 ,PONER 2.5 !!

#DIV/0! q < 2.5 ,PONER q !!

Ld < Lv1 #DIV/0!

#DIV/0!

0 # Varilla ( n ) = 000

Pu < Ø * 0.85 * f 'c * A1 AUMENTAR EL T !!

0.002.850.00AUMENTAR EL T !!

Espaciam =

Aøb ( 3/4" ) =

Espaciam =

C =

cm

cm2

cm2

cm

cm

cm

cm2

kg

kgcm2

cm2cm2

cm2

Pu = 0A1 = 0 A2/A1 = ###A2 = 0

0 AUMENTAR EL T !!

kg

kg

cm2cm2

de 23

DISEÑO DE ZAPATA CONECTADA

Diseñar la zapata conectada que soportara las columnas mostradas en la figura . La capacidad portante admisible del suelo es qa = 2.4 kg/cm2 . Considere Fy = 4200 kg/cm2 , f'c = 175 kg/cm2 para la cimentacion

DATOS:Zapata Acero

f ' c = 175 kg/cm f y = 4200 kg/cm² S/C = 500 kg/cm²Columna Suelo

f ' c = 210 kg/cm Df = 1.80 m Lc = 600 cmb1 = 50 cm 1700 kg/m³ db = 1.91 cmt1 = 50 cm 2400 kg/m³b2 = 50 cm qa = 2.40 kg/cm²t2 = 50 cm db = 1.59 cm

COL SECCION REFUERZO PD (tn) PL (tn)1 50 50 8 Ø 5/8" 50 302 50 50 8 Ø 3/4" 80 50

1.- DIMENSIONAMIENTO DE LA ZAPATA Y VIGA DE CIMENTACION

40.38 cm hc = Ld + r.ee + ØbLd = 40 hm = Df - hc

ld >= 0.004 * øb * fy 26.71 cmLd = 27

Cálculo del peralte de la zapata (hc )hc = 50

ht = 130


2.01

40

5714.29

5714.29

Az =Ps

Az =P1 + P' 2

= 42665.007 cm2qn qn

A = 2 x( b )^2 = 42665.01 b = 146

nuevo e =b - t

e = 48P'1 = 6957

2 2 P'2 = 43284A = 2 x( b )^2 = 43284 b = 147

150 300

g m =g c =

ZAPATA EXTERIOR:

qn = qa - gm*hm - gc*hc - s/c

CALCULO DE P'2 : Tanteo e =

Tomamos b = 150 cm -----> A = 150 x 300 e = 50 cm

X

Ld0.08xdbxfy f 'c=

Ld = 0.08x1.59x4200/(175^(1/2)) =

Ld >= 0.004x1.59x4200 =

cm

cm

cm

qn = 2.4-(1700xE^-06)x(130)-(2400xE-06)x(50)-(500xE-04) =

qn =

cmhc = Ld + 10 =

ht = Df - hc =

kg/cm2

( PD + PL ) x e Lc - e

P'2 = =P1xe L=

( 50 + 30 ) x 1000 x 40 600 - 40=

X

=

kg

cm

P'2 =

de 23

49 hc = Ld + r.ee + ØbLd = 49 cm hm = Df - hc

ld >= 0.004 * øb * fy 32 cmLd = 32

Cálculo del peralte de la zapata (hc )hc = 60

ht = 120


2.00

50

7273

7273.00

Az =Ps

Az =P2 + P' 2

= 61364 cm2qn qn

A = ( b )^2 = 61364.00 b = 248 usamos b = 250 cm

b = 250 A2 = ( 250 x 250 ) 250 250

VIGAS DE CIMENTACION

h =Lc

=600

86 SECCION

7 7 45 85

b = P1

b = 4331 x Lc

DISEÑO DE LA VIGA DE CONEXIÓN

9.18 Mu = P' 2 x L + Wv x ( L^2 )/2 7438475Mu = 7438475 kg-cm

1.91 ree = 7.50

As = Mu / ( Ø * fy * ( d - a/2 )) B = 45a = As x fy / ( 0.85 x f 'c x b ) d = 79.00As mín = 0.8 x (f ' c ^0.5) x B * d/ fy a = 5.00 (Valor Asumido)As > As mín OK !! As = 25.72 2.54

a = 16.14 # Varilla ( n ) = 11 Aøb 3

As = 27.74 11 Ø 1" @ 3 n -1

As mín = 8.96 11 Ø 1" @ 3

As > Asmin OK !!

ZAPATA EXTERIOR:

qn = qa - gm*hm - gc*hc - s/c

CALCULO DE P'2 : Tanteo e =

Wv = b x h x g c =

Øb ( 3/4") =

Aøb ( 1" ) =# Varilla ( n ) = As

Espaciam =Espaciam = B - 2*r.e - Øb

Ld0.08xdbxfy f 'c=

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

Ld >= 0.004x1.91x4200 =

cm

cm

cm

qn = 2.4-(1700xE^-06)x(120)-(2400xE-06)x(60)-(500xE-04) =

qn =

cmhc = Ld + 10 =

ht = Df - hc =

kg/cm2

( PD + PL ) x e Lc - e

P'2 = =P1xe L=

( 50 + 30 ) x 1000 x 50 600 - 50= =

kg

cm

P'2 =

cm

cm

h =x

cm

cm2

cm2

cm

cm2

cm2

cm2

cm2

cm2

cm

cm

de 23

VERIFICACION POR CORTE APORTE DEL CONCRETO

Vu = P' 2 + Wv x L Vu = 16049 KG Vc = 0.53 x (f ' c ^0.5) x b x d = 21186 kg L Vu < Ø Vc OK !!

DISEÑO DE LA ZAPATA EXTERIOR

ZAPATA EXTERIOR ZAPATA INTERIOR

qn =Pu

qn = 2.93 kg/cm2 qn =Pu

2.98Az Az

Mu =qnu x B x (L^2)

Mu = 3689455 Mu =qnu x B x (L^2) 3720000

2 2L = 100 r .e .e = 8

B = 150 r .e .e = 7.5 B = 250d = 41 db = 1.59 d = 51a = 5.00 (Valor Asumido) a = 5 ( Valor Asumido )

As = 25.35 As = 19.3a = 4.77 a = 2.18

As = 25.28 1.98 As = 19.72# Varilla ( n ) = 13 #Varilla n = 14

11 Espaciam. = 17.88As mín = 13.5 Asmin = 27

13 Ø 5/8" @ 11 14 Ø 5/8" @ 18

6.- VERIFICACION DE LA CONEXIÓN ZAPATA - COLUMNA( Ø = 0.70 )

Columna ExteriorPara la sección A columna = 50 x 50 = 2500 cm² ( COLUMNA )

Ø * 0.85 * f 'c * As1 Pu = 121000 # Varilla ( n ) = 4A colum = b *t A1 = 2500Pu < ( Ø * 0.85 * f 'c * A1) Ø * 0.85 * f 'c * A1 = 312375As mín = 0.005 * A1

Pu < Ø * 0.85 * f 'c * A1 OK !!

AøbAs col. > As mín OK !! As mín = 12.50

Aøb ( 3/4" ) = 2.85USAR : As1 = 12.50

Columna Interior As col > As min OK !!

Para la sección B columna = 50 x 50 = 2500 cm² ( COLUMNA )Pu = 197000

Ø * 0.85 * f 'c * As1 A1 = 2500A colum = b *t Ø * 0.85 * f 'c * A1 = 312375 # Varilla ( n ) = 4Pu < ( Ø * 0.85 * f 'c * A1) Aøb ( 3/4" ) = 2.85As mín = 0.005 * A1 Pu < Ø * 0.85 * f 'c * A1 USAR : As1 = 12.50

OK !!

Aøb As mín = 12.50As col. > As mín OK !! As col > As min OK !!


< Lv1

ØbLv1 = Lv - r.e.e

Aøb ( 5/8" ) =

Espaciam =

# Varilla = As1

# Varilla = As1


cm2

cm2

cm

cm2

cm2

cm2

cm

cm2

cm2

cm

cm

cm

cm2

cm2

cm2

cm

cm2

cm

cmcm2

kg

cm

kg

kgcm2

cm2cm2

cm2

kg

kgcm2

cm2

cm2

cm2

de 23


1.00 Øb (5/8") = 1.59 8.500.80 r.e.e = 7.50 ktr = 01.00 fy = 4200

Lado menor Zapata 1.00 f'c = 175 2.5 q = ( C+kt r )/ ØbAøb

Longitud de desarrollo en tracción q= 10.09 Aøb

Lv1 = 38.13 q >= 2.5 ,PONER 2.5 !!

n -1 Ld = 46 q < 2.5 ,PONER q !!

Ld < Lv1 AUMENTAR EL T !!

Espaciamiento del Refuerzo

45 cmAs1 = OK !!

3 x h 0 cm

d/2d/2

Asc = 2 * Astrv ( b + 1 ) b = C =


a =



cm

cm

>

12 Ø 5/8"@ 12cm

14 Ø 5/8"@ 22cm

6 Ø 1"@ 7cm

14 Ø 5/8"@ 18cm

Diseño de Cimentaciones.. - Copia

Documents

Transcript of Diseño de Cimentaciones.. - Copia