7/27/2019 T. Autos. - ACI318-02 R2

1/11

CLIENTE :

DEPTO.: INGENIE

ELABORO: ING. JR

Revisin de Esfuerzos en el Terreno

a ) Materiales

Acero de ref fy: 4200 kg/cm2

Concreto f`c: 250 kg/cm

gc: 2.40 ton/mTerreno gr: 1.60 ton/m

qa: 5.00 ton/m

10.00

b ) Dimensiones de zapata

Zapata Lx: 19.00 m

Lz: 19.00 m

Dist. entre Dadosx1: 5.435 m Z1: 5.980 m

x2: 9.500 m Z2: 7.041 m

Fvx = 6.40 Lo: 8.130 m Z3: 5.980 m

Fvz = 2 o.k

ok Prof de desplante hf: 2.00 m

qo = 4.50 Peralte de Losa h: 0.70 m

ok. Altura de relleno hr: 1.30 m

OK OK Dados bx: 0.80 m

OK O.K bz: 0.80 m

255.772 Altura de dado f: 0.30 m

ht = 1.60 m

Elementos Mecnicos sin factorizar Elementos Mecnicos factorizados

ACI318-02

1) CM + CV + C Viento 4) (1.2 CM + 1.0 CV + 1.3 CViento)

viento Puro

-138.57 11.23 P1 = -127.34 Ton P1 = -166.69 Ton

-12.84 Vx1 = -11.91 Ton Vx1 = -15.58 Ton

-9.87 Vz1 = -9.34 Ton Vz1 = -12.19 Ton

-138.57 11.23 P2 = -127.34 Ton P2 = -166.69 Ton

12.74 Vx2 = 11.81 Ton Vx2 = 15.45 Ton

-10.04 Vz2 = -9.51 Ton Vz2 = -12.41 Ton

277.14 11.11 P3 = 288.25 Ton P3 = 373.6 Ton

0.1 Vx3 = 0.1 Ton Vx3 = 0.13 Ton

-32.08 Vz3 = -33.14 Ton Vz3 = -42.98 Ton

-51.99

0.00 33.57 c ) Peso de cimentacin

Dado Ad = bx bz = 0.80 x 0.80 = 0.640 m

Pd = 3(Pds) = 3.000 x 2.46

Pd = 7.37 ton

Losa Az = Lz Lx = 19.00 x 19.00 = 361.000 m

Pz = Az h gc = 361.000 x 1.68

Pz = 606.48 ton

Terreno arenoso

72m-120mph-NORMAL

Torre Autosoportada de 72 m

Lo

Lx

X2

Lo

PLANTA

Lz

X1 X1

Lo

X2

Z3

Z2

Z1

Lz Lx

h

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CLIENTE :

DEPTO.: INGENIE

ELABORO: ING. JR

Terreno arenoso

72m-120mph-NORMAL

Torre Autosoportada de 72 m

Relleno Ar = Az - 3*Ad = 361.000 - 1.920 = 359.080 m

Pr = Ar (Prs) = 359.080 x 2.08

Pr = 746.89 ton

Pcim = Pd+Pz+Pr = 7.37 + 606.48 + 746.89 = 1,360.74 ton

Po = P1+P2+P3 = 33.57 ton

Paso de la resultante de las fuerzas incluyendo peso de cimentacin

z=bz/2 = 9.50m

x=bx/2 = 9.50m

Momento resistente

Mx = Rt* z = 13245.94 ton-m

Mz = Rt* x = 13245.94 ton-m

Momento Volteo

Mxo = = 1951.28 ton-m

Mzo = = 0.0000 ton-m

f d ) Revisin por Volteo (Alrededor del eje X)

Volteo alrededor eje x P t = 33.57 + 1360.74 = 1394.3

P Mvx = Mxo + ( SVz) * ht = 1951.28 + 119.58 = 2,070.8Vz Mrx = = 1394.31 * 9.50 = 13245.

Fvx = Mrx = 13245.94 = 6.40 > 2 o.k

hf Mvx 2,070.86

Volteo alrededor eje z

Mvz = = 0.0000 + 0.0000 = 0.000

Mrz = = 1394.31 * 9.50 = 13245.

P cim Fvz = Mrz = 13245.94 = 1324593740 > 2 o.k

ht=hf +f Mvz 0.0000

Pt = P + Pcim

e ) Distribucion uniforme de presiones en el terreno.

ex = Mvx / Pt = 1,592.41 / 1394.31 = 1.14 m

ez = Mvz / Pt = 318.92 / 1394.31 = 0.23 m

Lx - 2 ex = 19.00 - 2 x 1.14 = 16.72 m

Lz - 2 ez = 19.00 - 2 x 0.23 = 18.54 m

q0 = ---------------------------------- = 4.50 ton/m

( 16.72 ) * ( 18.54 )

Mzo + (S Vx) * htR t * x

R t *z

P3*X2 + P2*(X1+Lo) + P1*X1

P3*Z3 + (P1+P2)*(Z3+Z2)

1394.31

P

Lx

Lz

qo

(Lx-2ex)

(Lz-2ez)

Mx

Mz

X

Z

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CLIENTE :

DEPTO.: INGENIE

ELABORO: ING. JR

Terreno arenoso

72m-120mph-NORMAL

Torre Autosoportada de 72 m

f ) Distribucin Uniforme de Presiones para Diseo.

Momento Volteo

Mux = = 2106.76 + 155.43 = ########

Muz = = 382.0900 + 0.00 = 382.09 To

Pu = = 1673.1070

ex = Mux / Pu = 2,262.19 / 1673.11 = 1.35 m

ez = Muz / Pu = 382.09 / 1673.11 = 0.23 m

Lx - 2 ex = 19.00 - 2 x 1.35 = 16.30 m

Lz - 2 ez = 19.00 - 2 x 0.23 = 18.54 m

q0 = ---------------------------------- = 5.54 ton/m

( 16.30 ) * ( 18.54 )

qmax = 5.54 ton/m

Elementos Pu = 1673.11 ton

Mec de diseo Mux = 2106.76 ton-mMuz = 382.09 ton-m

d = 0.62

Planta

L1x = (Lx-bx/2) - d/2 = ( 9.10 - 0.312 ) = 8.79

L1x = 8.788 m

L1z = (Lo-bz) - d = ( 7.33 - 0.62 ) = 6.71

L1z = 6.706 m

P3*X2 + P2*(X1+Lo) + P1*X1+(SVx)*ht

P1+P2+P3+Pcim

1673.11

P3*Z3 + (P1+P2)*(Z3+Z2)+(SVz)*ht

Lo

Lx

X2

Lo

PLANTA

Lz

X1 X1

Lo

X2

Z3

Z2

Z1

SECCION A - A'

ALZADO

DADO

Lo1

bx

X1

bx

h

CORTANTE MOMENTO

d

P

Lx

Lz

qo

(Lx-2ex)

(Lz-2ez)

Mx

Mz

X

Z

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CLIENTE :

DEPTO.: INGENIE

ELABORO: ING. JR

Terreno arenoso

72m-120mph-NORMAL

Torre Autosoportada de 72 m

g ) Flexinr : 7.60 cm

d = 70.00 - 7.60 = 62.40 cmCuanta de acero

b1 = 0.85 f"c 6000 b1 170 5100

rb = --------------- x ---------------- = --------------- x ----------------fy 6000 + fy 4200 10200

rb = 0.02024rmx = 0.75 rb = 0.75 x 0.0202 = 0.0152r min = 0.8(fc)^(1/2) = 12.65 = 0.00301

fy 4200

Direccin x

Tomando una franja de 1.00 m de ancho

qu = qmax -q cim

qo qcim. = 3.76 ton/m

Lx

qu = 1.78 ton/m

Mu = qu Lx / 2

Mu = 1.78 x ( 9.10 ) / 2 = 73.570 ton-m

Mu = 7,356,981 kg-cm

F f 'c b d = 0.90 x 250.00 x 100.00 x 62.40 F f 'c b d = 87609600

Mr = F f 'c b d * w( 1 - 0.59w )

w = 0.088711543

250r = w f 'c / fy = 0.0887 x ---------------- = 0.0052804,200

como r > r mn< r mx OK

Usar r = 0.00528 Rige p CalculadoAs = r b d = 0.00528 x 100.00 x 62.40As = 32.95 cm

Proponiendo varillas # 8 ( as = 5.07 cm )

Cantidad requerida = 32.95 / 5.07 = 6.50 vars.

Separacin necesaria = 100.00 / 6.50 = 15.38 cm

Usar var. # 8 @ 15 cm

Direccin z

Tomando una franja de 1.0 m de ancho

1.00 Lo. = 7.33

Lz

Mcent = qu Lz / 24 = 3.98 ton-m

Mu = qu Lz / 12

Mu = 1.78 x ( 7.33 ) / 12 = 7.956 ton-m

Mu = 795,561 kg-cm

F f 'c b d = 0.90 x 250.00 x 100.00 x ( 62.40 )F f 'c b d = 87609600

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CLIENTE :

DEPTO.: INGENIE

ELABORO: ING. JR

Terreno arenoso

72m-120mph-NORMAL

Torre Autosoportada de 72 m

Mr = F f 'c b d * w( 1 - 0.59w ) Acero positivoq = 0.0046

w = 0.009231416 p = 0.0003

250r = w f 'c / fy = 0.0092 x ---------------- = 0.000549

4200

como r < r mn< r mx OK

Usar r = 0.00073 Rige 1.33 p Calculado

As = r b d = 0.00073 x 100.00 x 62.40As = 4.56 cm

Proponiendo varillas # 8 ( as = 5.07 cm )

Cantidad requerida = 4.56 / 5.07 = 0.90 vars.

Separacin necesaria = 100.00 / 0.90 = 111.11 cm

Usar var. # 8 @ 110 cmh ) Cortante en x

Vu = qu*L1x

Vu = 15.61 Ton Vu d / Mu = 0.12

Mu = 80.18 Ton m

Vc = F (0.5(f'c)^0.5 + 175 r Vu d / Mu ) b dVc = 0.75(0.5(250)^0.5 + 175 (0.00528) x 0.12 ) x 100 x 62.4

Vcr = 37,524.20 kg

Vcr = 37.52 ton

Como vu < vcr OK

i ) Cortante en z

Vu = qu*L1z/2

Vu = 5.96 ton Vu d / Mu = 0.47

Mu = 7.96 Ton m

Vc = F (0.5(f'c)^0.5 + 175 r Vu d / Mu ) b dVc = 0.75(0.5(250)^0.5 + 175 (0.00528) x 0.47 ) x 100 x 62.4

Vcr = 35,298.77 kg

Vcr = 35.30 ton

Como vu < vcr OK

j ) Revisin por Penetracin

d/2 d/2

Cx

Cz d h

r

qo

z Cx

Cz

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CLIENTE :

DEPTO.: INGENIE

ELABORO: ING. JR

Terreno arenoso

72m-120mph-NORMAL

Torre Autosoportada de 72 m

Cx = bx + d = 0.80 + 0.62 = 1.42 m

Cz = bz + d = 0.80 + 0.62 = 1.42 m

bo = 2 (Cx + Cz) = 2 ( 1.42 + 1.42 )

bo = 5.70 m = 569.60 cm

Ac = bo d = 569.60 x 62.40 = 35,543.04 cm

Cortante actuante

Vu = Pu - qo( Cx Cz )

Vu = 373.60 - 1.78 ( 1.42 x 1.42 )

Vu = 369.997 ton = 369,997 kg

Mu = Vz3 ht

Mu = 42.980 * 1.60 = 68.77 Ton m

Transmisin de momento direccin x

Fraccin de momento transmitido

1

gvx = 1 - ---------------------------------------------------------- = 0.401 + ( 2/3 ) ( 1.42 / 1.42 )

Momento polar de inercia

d Cx = 62.40 x ( 142.40 ) = cm4

Cx d = 142.40 x ( 62.40 ) = 34,599,017 cm4

d Cz Cx = 62.40 x 142.40 x ( 142.40 ) = 180,183,309 cm4

Jcx = 30,030,551 + 5,766,503 + 90,091,654 = 125,888,709 cm

4

Cxx = Cx / 2 = 142.40 / 2 = 71.20 cm

Transmisin de momento direccin z

Fraccin de momento transmitido

1

gvz = 1 - ---------------------------------------------------------- = 0.401 + ( 2/3 ) ( 142.40 / 142.40 )

Momento polar de inercia

d Cz = 62.40 x ( 142.40 ) = 180,183,309 cm4

Cz d = 142.40 x ( 62.40 ) = 34,599,017 cm4

d Cx Cz = 62.40 x 142.40 x ( 142.40 ) = 180,183,309 cm4

Jcz = 30,030,551 + 5,766,503 + 90,091,654 = 125,888,709 cm4

Czz = Cz / 2 = 142.40 / 2 = 71.20 cm

Esfuerzo actuante

Vu gvx Mzu Cxx gvz Mxu Czz

vu = --------------- + --------------- + ---------------

Ac Jcx Jcz

Vu = 10.41 + 0.00 + 1.20 = 11.61 kg/cm

180,183,309

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CLIENTE :

DEPTO.: INGENIE

ELABORO: ING. JR

Terreno arenoso

72m-120mph-NORMAL

Torre Autosoportada de 72 m

Esfuerzo resistente

Vc = 0.27 F ( 2+ 4/ bc ) f 'c^0.5bc = bx / bz = 0.80 / 0.80 = 1.00Vc = 0.27 ( 0.75) x (2+4/ 1.00) x ( 250 )^0.5

Vc = 19.21083679

Vc = 0.27 F ( 2+ 40 d / b ) f 'c^0.5

Vc = 0.27 ( 0.75) x (2 + 40x62.40 / 569.60 ) ( 250 )^0.5

vcr= 20.43399868 kg/cm

Vc = 1.1 F f 'c^0.5

Vc = 1.1 ( 0.75) x ( 250 )^0.5

Vc = 13.04439535

Rige Vc = 13.04

Como vu < vcr OK

k ) Refuerzo por temperatura

as =0.0018 b d

as 11.23 separacin = @ 25 cm

COLOCAR VARILLA # 6 @ 25 cm

l ) Armado de Dado

p= 0.005 As = 30.48 cm.

p= 0.018 As = 114.38 cm.

COLOCAR :

28 VARILLAS # 8 141.88 cm

VARILLAS # 0.00 cm

141.88 cm O.K

Est # 4 @ 20

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Varillas "A"= 8 @ 15 cm cin al 90% Proctor en cap

Varillas "B"= 6 @ 25 cm de espesor.

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5.00 t/m2

e la excava-

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s de 15 cm