proyecto_hormigon_i.pdf

P Pr ro oy ye ec ct to o d de e H Ho or rm mi ig g n n I I P Po or r: :: : C Ce elly yn ne et th h G Go on nz z lle ez z C C. .

N000

1.50m

VS VSVS

PROYECTO DE HORMIGN II Semestre de 2004.

E ED DI IF FI IC CI IO O D DE E 3 3 P PL LA AN NT TA AS S D DE E H HO OR RM MI IG G N N A AR RM MA AD DO O

N200

N100

N300

Escalera

5.00m

5.00m

5.00m

2.00m

2.00m

5.00m 5.50m4.00m


DIMENSIONES ENTRE NIVELES DE PISO: N 000 a N 100 4.50 m N 100 a N 300 3.20 m

TIPO DE USO: N 100 Para oficinas N 200 Tipo apartamentos de dos Recmaras ms un estudio. N 300 Techo.

ESPECIFICACIONES: Losa repellada por debajo y el piso ser de cermica. Anlisis lateral del edificio. Cumplir con deflexiones, agrietamiento, largo de desarrollo y espaciamientos de barras. Capacidad del suelo Qa = 10 ton / m 2. Todo concreto ser de:

Fc = 4000 lbs/pulg 2 en vigas y columnas Fc = 3000 lbs/pulg 2 en losas

Acero de refuerzo G60 y estribos G40.

DISEE: Columnas (tres de cada nivel una de esquina, una de borde y otra del interior). Vigas principales (vigas continuas de cada nivel una lateral y otra del interior). Vigas de amarres (vigas continuas de cada nivel una lateral y otra del interior). Losa slida 1D en el N 300 Losa de viguetas con bloques de arcilla N 200 Losa de viguetas con bloques de concreto N100 Viga ssmica (vigas continuas una lateral y otra del interior) Escalera Zapatas aisladas con carga axial (una de esquina, una de borde y otra del interior).

CUMPLIR CON: El cdigo ACI Vigente y REP 94 Utilizar un criterio razonable


DIRECCIN DE LAS VIGAS PRINCIPALES Y LOSAS ASUMIDAS EN EL EDIFICIO

Ancho de banda a utilizar para el diseo de Losa en cada zona.

1.00m

Zona1

Zona2

Zona3

Escalera


Especificaciones: Valores Asumidos: Bloques de arcilla Cols = 30 x 30 cm Fy= 60,000 lb/plg 2 barras 6/8 1.91 cm Fc= 3,000 lb/plg 2 C.V. = 150 kg/m 2

mLn

t 186.02820.5

28 = = = mt 20.0 =

Peso de la Losa por m 2 = 2400 kg/m 3 * 0.20 m = 480 kg/m 2

A AN N L LI IS SI IS S D DE E C CA AR RG GA AS S: :

C Ca ar rg ga a M Mu ue er rt ta a: :

Losa = 480 kg/m 2 Repello Inferior = 30 kg/m 2 Otros = 25 kg/m 2

C C. . M M. . = 535 kg/m 2 *1.4 = 749.00 kg/m 2 C. V. = 150 kg/m 2 *1.7 = 255.00 kg/m 2

C C. . S S. . = = 6 68 85 5. .0 00 0 k kg g/ /m m 2 2 C C. .u u. . = = 1 10 00 04 4. .0 00 0 k kg g/ /m m 2 2

00.1533.0/00.1004

/00.535...

2

2

= =mkgmkg

MCR O OK K

466.1466.1/00.685

/00.1004..

2

2

= =mkgmkg

CF O OK K

P Pa ar ra a u un na a b ba an nd da a d de e 1 1m m d de e a an nc ch ho o: : qu = 1004 kg/m

1.00 m

0.20 m

S SE EC CC CI I N N D DE E L LO OS SA A

Ln = 5.20 m


Vud = 2761.0 kg (0.15 + 0.17) *1004kg/m

Vud = 2439.720 kg.

D D DI I IS S SE E E O O O P P PO O OR R R F F FL L LE E EX X X I I I N N N: : :

Mu (+) = 3796.375 kg.m 379637.500 kg.cm rmn = 0.0033 As (+) = 6.55 cm 2 rmax = 0.0160

00385.0)17)(100(

55.6 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

3796.375kg.m

2760.99kg

2760.99kg

2.75m

Qu=1004kg/m

4.00 m

0160.00038.00033.0


Cantidad de Barras: Espaciado entre Barras:

mLinealbarrascmcm

deBarras /31.284.2

55.6#

2

2

= = mmmLB

m40.043.0

/3.21

=

Para As (+) Usar barras 6/8 @ 0.40 m C/C A/D. Para Asmn 0.0033 (17)(100) = 5.61cm 2 Usar barras 5/8 @ 0.35m C/C

V VE ER RI IF FI IC CA AC CI I N N D DE EL L C CO OR RT TA AN NT TE E: :

2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/688.1)17)(100(85.0

72.2439cmkg

kgbd

VudVud = = =

f f

OK

A AC CE ER RO O P PO OR R T TE EM MP PE ER RA AT TU UR RA A: :

Ast = 0.0018 (bt) Utilizando barras 3/8 = 0.71 cm 2 = 0.0018 (100) (20) = 3.60 cm 2


mLinealbarrascmcm

deBarras /07.571.0

60.3#

2

2

= = mmmLB

m20.019.0

/07.51

=

Para As(t) Usar barras 3/8 @ 0.20 m C/C Para Temperatura perpendicular a las barras de flexin.

VcVud f


Vud = 3037.10 kg (0.15 + 0.17) *1004kg/m

Vud = 2715.820 kg.

D DI IS SE E O O P PO OR R F FL LE EX XI I N N: :


0019.0)17)(100(

30.3 2)()( = = = +

+ cmbdAs

s r

1349.12 kg Vud = 2715.82 kg

3037.10 kg

2666.87 kg 1982.89 kg

906.44 kg

1958.11 kg

2635.50 kg

qu = 1004 kg/m

4.00m 5.00m


Se utiliza el valor de rmn para calcular el valor de As(+): As(+) = 0.0033(100)(17) As(+) = 5.610 cm 2


mLinealbarrascmcm

deBarras /805.200.2

61.5#

2

2

= = mmLB

m35.0

/805.21

=

Mu () = 2635.50 kg.m 263550.0 kg.cm As () = 4.48 cm 2

0026.0)17)(100(

48.4 2)()( = = = -

- cmbdAs

s r

Se utiliza el valor de rmn para calcular el valor de As():

As() = 0.0033(100)(17) As() = 5.610 cm 2


mLinealbarrascmcm

deBarras /805.200.2

61.5#

2

2

= = mmLB

m35.0

/805.21

=

As(+) Usar barras 5/8 @ 0.35 m C/C As real = 5.97 cm 2 As() Usar barras 5/8 @ 0.35 m C/C As real = 5.97 cm 2


2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/879.1)17)(100(85.0

820.2715cmkg

kgbd

VudVud = = =

f f

OK VcVud f





mLinealbarrascmcm

deBarras /07.571.0

60.3#

2

2

= = mmmLB

m20.019.0

/07.51

=



Vud = 3016.88 kg (0.15 + 0.17) *1004kg/m

Vud = 2995.60 kg.


0024.0)17)(100(

11.4 2)()( = = = +

+ cmbdAs

s r

2210.00 kg

2764.22 kg.m

3316.88 kg

2454.56 kg

3057.33 kg.m

2421.59 kg.m

747.89 kg.m 1214.19 kg.m

1786.24 kg.m 2571.09 kg.m Mn()= 2653.99 kg.m

Vu = 2995.59 kg

Mn(+) = 2267.71 kg.m

qu = 1004.00 kg/m

1561.44 kg

2205.12 kg


Se utiliza el valor de rmn para calcular el valor de As(+): As(+) = 0.0033(100)(17) As(+) = 5.610 cm 2


mLinealbarrascmcm

deBarras /805.200.2

61.5#

2

2

= = mmLB

m35.0

/805.21

=

Mu () = 3057.33 kg.m 305733.0 kg.cm As () = 5.226 cm 2

00307.0)17)(100(

226.5 2)()( = = = -

- cmbdAs

s r

Se utiliza el valor de rmn para calcular el valor de As():

As() = 0.0033(100)(17) As() = 5.610 cm 2


mLinealbarrascmcm

deBarras /805.200.2

61.5#

2

2

= = mmLB

m35.0

/805.21

=

As(+) Usar barras 5/8 @ 0.35 m C/C As real = 5.97 cm 2 As() Usar barras 5/8 @ 0.35 m C/C As real = 5.97 cm 2


2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/073.2)17)(100(85.0

578.2995cmkg

kgbd

VudVud = = =

f f

OK VcVud f





mLinealbarrascmcm

deBarras /07.571.0

60.3#

2

2

= = mmmLB

m20.019.0

/07.51

=



Yc

Yt

100 cm

2858.42)1( cmAsn = -

Anlisis de Deflexin para Losa slida N 300

4

3

3

667.66666

)20)(100(121121

cmIg

Ig

bhIg

=

=

=

Valor de du: Clculo de r:

du = 0.390 cm a 12.30m2

`

/983.28

2102

2

cmkgfr

fr

ffr c

=

=

=

Deformacin de las Cargas de Servicio dc.s.

cm

cmCFu

sc

sc

266.0

466.13905.0

..

..

..

=

= =

d

d d

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

Clculo de Mcr (En el centro de la Luz):

2)(

2)(

678.5

)2(/85.2

cmAs

cmmLBAs

=

= +

+

du

12.30 m

2

5.13

5.1

/337.238536

)21014.0()/2400(

)`14.0(

cmkgE

mkgE

cfWE

c

c

cc

=

=

=


Clculo de Yc:

cmYc

cmcm

AsnAsdn

bh

bh

Yc

147.10

)678.5)(1548.8()20)(100(

)17)(678.5)(1548.8(2

)20)(100(

)1()1(2

222

=

- +

- + =

- + - +

=

YchYt - = = 2010.147

Yt = 9.853 cm

223

)()1()2

(12

YcdAsnh

Ycbhbh

Igt - - + - + =

223 )147.1017)(678.5)(1548.8()220

147.10)(20)(100()20)(100(121

- - + - + =Igt

4630.68722 cmIgt =

433 667.66666)20)(100)(12/1(121

cmbhIg = = =

cmkgcm

cmcmkgYtIgtfr

MCR .410.202150)853.9()630.68722)(/983.28(* 42

= = =

MCR= 2021.504 kg.m

Evaluando Iem para Mn = Ma

mkgmkg

CFMn

Ma .720.1819466.1

.71.2267..

)(

= = = +

cgemCR II

mkgmkg

MaM

= \ = = 00.1246.1.720.1819.71.2267

Iem = 66666.67 cm 4


Clculo de Mcr (para el punto Ie1 del 1 er extremo continuo):

As () = 2.85 (5/8) (2cm 2 ) = 5.678 cm 2

cmYc

cmcm

AsnAsdn

bh

bh

Yc

147.10

)678.5)(1548.8()20)(100(

)17)(678.5)(1548.8(2

)20)(100(

)1()1(2

222

=

- +

- + =

- + - +

=

YchYt - = = 2010.147

Yt = 9.853 cm

223 )147.1017)(678.5)(1548.8()220

147.10)(20)(100()20)(100(121

- - + - + =Igt

4630.68722 cmIgt =

cmkgcm

cmcmkgYtIgtfr

MCR .410.202150)853.9()630.68722)(/983.28(* 42

= = =

MCR= 2021.504 kg.m

mkgmkg

CFMn

Ma .362.1810466.1

.99.2653..

)(

= = = -

cgeCR II

mkgmkg

MaM

= \ = = 100.1117.1.362.1810.504.2021

Ie1 = 66666.67 cm 4

Yc

Yt

Fibra superior en tensin (n1) As ( )


Clculo de Momento de Inercia Efectivo Ie:

4

1

67.66666

)67.66666(15.0)67.66666(85.0

15.085.0

cmI

I

III

e

e

eeme

=

+ =

+ =

Entonces la Deformacin Real Instantnea es:

cm

cmIeIg

instreal

screal

266.0

)67.6666667.66666

(266.0)(.

=

= =

d

d d


Evaluacin de Deflexin Adicional a largo Plazo (dLP) del Concreto en la Losa Slida N 300.

CONSIDERANDO: r = 0 en medio del claro es = 2.00 (factor para 5 aos o ms)

00.2)0(501

00.2)'(501

= +

= +

= r

e l s

dtotal = dreal inst (1+l) = 0.266cm (1+2) = 0.798 cm

Comprobando segn tabla 9.5 (b) A.C.I.480/L d

OK Se acepta el diseo

de la Losa

Clculos de Ancho de Grieta para Losa Slida N 300 (Zona en Traccin)

mkgMa

mkgMa

CFMu

Ma

.835.1651466.1

.59.2421..

)(

=

=

= +

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

d= 0.17m 6.69 b= 39.37 As = 5.678 cm 2 0.88 plg 2 # Barras= 2.85 por banda

1 m = 39.37

d

cmcm 083.1480/520798.0 =


Calculando Icr:02/2 = - + nAsdnAscbc

0)69.6)(88.0(548.8)88.0(548.8237.39 2

= - + cc

0324.50522.7685.19 2 = - + cc"419.1 = \c

4lg519.246 pIcr = lg945.143372 plbMa - =

ncdIcrMa

fs )( - =

ksifyksifs

plbfs

pplb

fs

366.0207.26

lg/490.26207

)548.8)(419.169.6(lg519.246

lg.323.143072

2

4

= =

=

- =

OK

2lg601.3285.2

)37.39)(18.1(2#

))(2(p

barrasbarrasbdc

A = = =

33max )60.32)(18.1()207.26)(225.1(076.0076.0 = = dcAfsW b

236.8max =W milsimas de pulgada"120.0lg00824.0max = pW OK

La separacin entre barras es correcta y no permiten mayor agrietamiento.

225.1419.169.6419.1874.7 =

- - =

- - =cdch b


Clculos de Ancho de Grieta para Losa Slida N 300 (Zona en Tensin)

mkgMa

mkgMa

CFMu

Ma

.491.2085466.1

.33.3057..

)(

=

=

= +

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n


0)69.6)(88.0(548.8)88.0(548.8237.39 2

= - + cc

0324.50522.7685.19 2 = - + cc"419.1 = \c

4lg519.246 pIcr = lg079.180633 plbMa - =

ncdIcrMa

fs )( - =

ksifyksifs

plbfs

pplb

fs

366.0014.33

lg/477.33014

)548.8)(419.169.6(lg519.246

lg.079.180633

2

4

= =

=

- =

OK

2lg601.3285.2

)37.39)(18.1(2#

))(2(p

barrasbarrasbdc

A = = =

33max )60.32)(18.1()014.33)(225.1(076.0076.0 = = dcAfsW b


La separacin entre barras es correcta y no permiten agrietamiento mayor.

1 m = 39.37

d

225.1419.169.6419.1874.7

= - -

= - -

=cdch b


Especificaciones: Valores Asumidos: Bloques de arcilla Cols = 30 x 30 cm Fy= 60,000 lb/plg 2 barras 6/8 1.91 cm Fc= 3,000 lb/plg 2 C.V. = 300 kg/m 2

mmLn

t 30.028.05.1820.5

5.18 = = =

P Pe es so o d de e V Vi ig gu ue et ta a: : = =m00.1*50.0

))20.0*20.0()50.0*10.0((*2400*1 +

P P. .V V. . = = 4 43 32 2. .0 00 0 k kg g/ /m m 2 2

P Pe es so o d de e B Bl lo oq qu ue e = = 2/64.90)1)(50.0(

61.13*33.3mkg

mmkg

=

A AN N L LI IS SI IS S D DE E C CA AR RG GA AS S: : C Ca ar rg ga as s M Mu ue er rt ta as s: :

Vigueta = 432.00 kg/m 2 Bloques = 90.64 Kg/m 2 Baldosas = 145 kg/m 2 Paredes = 160 kg/m 2 Repello Inferior = 35 kg/m 2 Otros = 30 kg/m 2

C C. . M M. . = 892.64 kg/m 2 *1.4 = 1249.69 kg/m 2 C. V. = 300 kg/m 2 *1.7 = 510.00 kg/m 2

C C. . S S. . = = 1 11 19 92 2. .6 64 4 k kg g/ /m m 2 2 C C. .u u. . = = 1 17 75 59 9. .6 69 9 k kg g/ /m m 2 2

0.30 m

t

0.20 m

0.30 m

0.50 m

0.10 m

Bloques de Arcilla de 8

0.30 m


20 cm

d

00.1507.0/69.1759/64.892

... 22

= =mkgmkg

MCR O OK K

00.1475.1/64.1192/69.1759

.. 22

= =mkgmkg

CF O OK K

q qu u = = ( (1 17 75 59 9. .6 69 9 k kg g/ /m m 2 2 ) ) ( (0 0. .5 50 0m m) ) = = 8 87 79 9. .8 84 4 k kg g/ /m m


2/45.4)04.27)(20(85.0

03.2050cmkg

kgbd

VudVud = = =

f f

OK

L La a v vi ig gu ue et ta a c cu um mp pl le e p po or r s si i s so ol la a p pa ar ra a n no o l ll le ev va ar r e es st tr ri ib bo os s

3326.89 kg.m

2419.56 kg

2419.56 kg

Vu= 2050.03 kg

2.75 m

Qu = 879.84 kg/m

VcVud f

2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =




0065.0)04.27)(20(

53.3 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

Asmn = rmn bd = 0.0033(20)(27.04) = 1.78 cm 2

Para As (+) Usar barras 1/2 @ 0.30 m C/C Para Asmn Usar barras 5/8 @ 1.00 m C/C




mLinealbarrascmcm

deBarras /66.627.0

80.1#

2

2

= = mmLB

m15.0

/66.61

=

Para As(t) Usar barras 1/4 @ 0.15 m C/C A/D Para Temperatura perpendicular a las barras de flexin.

0160.00065.00033.0


20 cm

d


2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/98.4)04.27)(20(85.0

98.2291cmkg

kgbd

VudVud = = =

f f

OK




0032.0)04.27)(20(

74.1 2)()( = = = +

+ cmbdAs

s r

2309.58 kg.m

794.09 kg.m

1715.96 kg.m

1182.28 kg 2661.52 kg

2337.07 kg 1737.68 kg

qu = 746.0 kg

Vu= 2291.98 kg

VcVud f


Se utiliza el rmn: As (+) = 0.0033(20)(27.04) = 1.78 cm 2

Mu () = 2309.58 kg.m 230958.00 kg.cm rmn = 0.0033 As () = 2.38 cm 2 rmax = 0.0160

0044.0)04.27)(20(

38.2 2)()( = = = -

- cmbdAs

s r

mxmn r r r -)(

OK

As(+) Usar barras 5/8 C/C @ 1.00 m As real = 1.99 cm 2 As() Usar barras 1/2 C/C @ 0.50 m As real = 2.58 cm 2




mLinealbarrascmcm

deBarras /66.627.0

80.1#

2

2

= = mmLB

m15.0

/66.61

=


0160.00044.00033.0


20 cm


2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/51.5)04.27)(20(85.0

16.2537cmkg

kgbd

VudVud = = =

f f

OK


qu = 760.91 kg/m

2679.24 kg.m

2122.12 kg.m

655.41 kg.m

1565.34 kg.m

1064.03 kg.m

2151.02 kg

1940 kg 1368.34 kg

2422.38 kg

2906.69 kg

4.00 m 5.00 m 5.50 m

Vud =2537.16 kg

1.56 m

Mn ( + )=1987.27 kg.m

Mn () = 1536.03kg.m Mn () = 1739.45 kg.m

1932.42kg

VcVud f




0040.0)04.27)(20(

18.2 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

dreal = 30 cm (2 cm+0.64 cm) = 27.36 cm

rreal = 0047.0)21.27)(20(

58.2 =

cm

Mu real = 251230.4 kg.cm 2512.30 kg.m


0052.0)04.27)(20(

79.2 2)()( = = = -

- cmbdAs

s r

mxmn r r r -)(

OK

dreal = 30 cm (2 cm+0.64 cm) = 27.36 cm

rreal = 0070.0)36.27)(20(

87.3 =

cm

Mu real = 363421.6 kg.cm 3634.21 kg.m




0160.00040.00033.0

0160.00052.00033.0


0.25 m

0.50 m

0.20 m

0.15 m

0.20 m

0.10 m


mLinealbarrascmcm

deBarras /66.627.0

80.1#

2

2

= = mmLB

m15.0

/66.61

=



cmx 2590022500

= =

cmy 33.18900

16500 = =

Fig Area (m 2 ) x (m) y (m) XA (m 2 ) YA (m 2 ) 1 500 25 25 12500 12500 2 400 25 10 10000 4000

900 22500 16500

du

12.05 m

2

5.13

5.1

/337.238536

)21014.0()/2400(

)`14.0(

cmkgE

mkgE

cfWE

c

c

cc

=

=

=


Yc

Yt

100 cm

2858.42)1( cmAsn = -

I1x = (1/12)(50)(10) 3 +500(2518.33) 2 = 26411.12 cm 4

I2x = (1/12)(20)(20) 3 +400(18.3310) 2 = 41088.89 cm 4

Ig = I1x + I2x = 26411.12 cm 4 + 41088.89 cm 4

= 67500 cm 4 6.75 x 10 4 m 4

du = 0.0034 m @ 12.05 m


cm

cmCFu

sc

sc

23.0

475.134.0

..

..

..

=

= =

d

d d

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

Clculo de r:


cmYc

Yc

46.8

)58.2)(155.8()20()10)(50(

)36.27)(58.2)(155.8()15()20()2/10)(50(2

22

= - + + - + +

=

2

`

/983.28

2102

2

cmkgfr

fr

ffr c

=

=

=

248.19)1(

)58.2)(155.8()1(

cmAsn

Asn

= -

- = -


YchYt - = = 308.46

Yt = 21.54 cm

4

24

17.76751

)46.836.27(48.19)46.833.18(90067500

cmIgt

cmcmcmcmIgt

=

- + - + =

54.21)17.76751)(98.28(*

= =YtIgtfr

Mcr

Mcr = 103261.32 kg.cm = 1032.61 kg.m


mkgmkg

CFMn

Ma .28.1179475.1

.45.1739..

)(

= = = +

00.187.0.28.1179.61.1032

= =mkgmkg

MaMCR OK

C C l lc cu ul lo o d de e I Ic cr r P Pa ar ra a S Se ec cc ci i n n A Ag gr ri ie et ta ad da a: :

Para primer momento de Area:

)36.27)(58.2(55.8)5)(10)(20()5)(10)(50( cccc - = - - + -

c = 6.11 cm

c

d c

2)(

)(

48.19)1(

)58.2)(155.8()1(

cmAsn

Asn

= -

- = - +

+


Yc

Yt

100 cm

Momento de Inercia Icr:

4

23

67.13762

)11.636.27)(58.2)(55.8()11.6)(50)(3/1(

cmIcr

Icr

=

- + =

44

4434

00.6750086.49148

)67.1376267500()87.0(67.13762

cmcmI

IgcmcmcmI

em

em

=

- + = OK

Clculo de Mcr (en Ie1)

cmYc

Yc

62.18

)87.3)(155.8()10)(50()20)(20(

)36.27)(87.3)(155.8()25)(10)(50()20)(10)(20(

= - + + - + +

=

YchYt - = =3018.62 cm

Yt = 11.38 cm

4

24

38.68016

)62.1836.27(22.29)33.1862.18(90067500

cmIgt

cmcmcmcmIgt

=

- + - + =

38.11)38.68016)(98.28(*

= =YtIgtfr

Mcr

Mcr = 173208.67 kg.cm = 1732.08 kg.m

mkgmkg

CFMn

Ma .28.1179475.1

.45.1739..

)(

= = = -

2

)(

22.29)1(

)87.3)(155.8()1(

cmAsn

Asn

= -

- = - -


IgIemkgmkg

MaMCR = \ = = 100.146.1.28.1179

.08.1732

Ie1= 67500 cm 4


4

1

53.51901

)67500(15.0)86.49148(85.0

15.085.0

cmI

I

III

e

e

eeme

=

+ =

+ =


cm

cmIeIg

instreal

screal

29.0

)53.51901

67500(23.0)(.

=

= =

d

d d



00.2)0(501

00.2)'(501

= +

= +

= r

e l s


C Co om mp pr ro ob ba an nd do o s se eg g n n t ta ab bl la a 9 9. .5 5 ( (b b) ) C C d di ig go o A A. .C C. .I I. .

480/L dcmcm 08.187.0 OK


Clculos de Ancho de Grieta para Losa Nervada N 200 (Zona N1)

mkgMa

mkgMa

CFMu

Ma

.48.2255475.1

.84.3326..

)(

=

=

= +

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

Calculando Icr:

02/2 = - + nAsdnAscbc

0)65.10)(59.0(548.8)59.0(548.8287.7 2

= - + cc

0518.54121.5937.3 2 = - + cc"13.3 = \ c

4lg18.370 pIcr =

ncdIcrMa

fs )( - =

O OK K ksifyksifs

plbfs

pplb

fs

366.0.34.135

lg/34135.62.

)548.8)(.3.13.10.65(lg.370.18

lg..195798.251

2

4

= =

=

- =


2lg12.60.3

)87.7)(17.1(2#

))(2(p

barrasbarrasbdc

A = = =

33max )12.6)(17.1()135.34)(16.1(076.0076.0 = = dcAfsW b


L La a s se ep pa ar ra ac ci i n n e en nt tr re e b ba ar rr ra as s e es s c co or rr re ec ct ta a y y n no o p pe er rm mi it te en n a ag gr ri ie et ta am mi ie en nt to o m ma ay yo or r. .

Clculos de Ancho de Grieta para Losa Nervada N 200 (Zona N 2) Mu (+)

mkgMa

mkgMa

CFMu

Ma

.36.1169475.1

.96.1715..

)(

=

=

= +

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n


0)78.10)(31.0(548.8)31.0(548.8287.7 2

= - + cc

0559.28651.2937.3 2 = - + cc"37.2 = \ c

4lg41.219 pIcr =

16.113.365.1013.381.11

= - -

= - -

=cdch b


ncdIcrMa

fs )( - =

OK

2lg29.171

)87.7)(09.1(2#

))(2(p

barrabarrasbdc

A = = =

33max )29.17)(09.1()970.32)(13.1(076.0076.0 = = dcAfsW b



ksifyksifs

plbfs

pplb

fs

366.0.32.970

lg/32970.59.

)548.8)(.2.37.10.78(lg.219.41

lg..101495.958

2

4

= =

=

=

13.137.278.1037.281.11

= - -

= - -

=cdch b


Clculos de Ancho de Grieta para Losa Nervada N 200 (Zona N2) Mu ()

mkgMa

mkgMa

CFMu

Ma

.82.1565475.1

.58.2309..

)(

=

=

= +

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

Calculando Icr:


0)78.10)(40.0(548.8)40.0(548.8287.7 2

= - + cc

0868.36420.3937.3 2 = - + cc"66.2 = \ c

4lg59.274 pIcr = ncdIcrMa

fs )( - =

2lg15.82

)87.7)(04.1(2#

))(2(p

barrabarrasbdc

A = = =

ksifyksifs

plbfs

pplb

fs

366.0.34.512

lg/34512.42.

)548.8)(.2.65.10.78(lg.274.59

lg..135907.164

2

4

= =

=

=

13.137.278.1037.281.11

= - -

= - -

=cdch b


33max )15.8)(04.1()512.34)(127.1(076.0076.0 = = dcAfsW b

023.6max =W milsimas de pulgada

"120.0lg00602.0max = pW OK


Clculos de Ancho de Grieta para Losa Nervada N 200 (Zona N3) Mu (+)

mkgMa

mkgMa

CFMu

Ma

.78.1438475.1

.20.2122..

)(

=

=

= +

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

Calculando Icr:


0)78.10)(40.0(548.8)40.0(548.8287.7 2

= - + cc

0868.36420.3937.3 2 = - + cc"66.2 = \ c

4lg59.274 pIcr = ncdIcrMa

fs )( - =

ksifyksifs

plbfs

pplb

fs

366.0.31.712

lg/31712.37.

)548.8)(.2.65.10.78(lg.274.59

lg..124880.579

2

4

= =

=

=


2lg15.82

)87.7)(04.1(2#

))(2(p

barrabarrasbdc

A = = =

33max )15.8)(04.1()712.31)(127.1(076.0076.0 = = dcAfsW b


"120.0lg00553.0max = pW OK


Clculos de Ancho de Grieta para Losa Nervada N 200 (Zona N3) Mu ()

mkgMa

mkgMa

CFMu

Ma

.43.1816475.1

.24.2679..

)(

=

=

= +

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

Calculando Icr:


0)78.10)(60.0(548.8)60.0(548.8287.7 2

= - + cc

030.5513.5937.3 2 = - + cc

"15.3 = \ c

13.137.278.1037.281.11

= - -

= - -

=cdch b


4lg27.380 pIcr =

ncdIcrMa

fs )( - =

2lg43.53

)87.7)(04.1(2#

))(2(p

barrabarrasbdc

A = = =

33max )43.5)(04.1()026.27)(136.1(076.0076.0 = = dcAfsW b


"120.0lg00602.0max = pW OK


ksifyksifs

plbfs

pplb

fs

366.0.27.026

lg/27026.06.

)548.8)(.3.15.10.78(lg.380.27

lg..157659.149

2

4

= =

=

=

136.137.278.1037.281.11

= - -

= - -

=cdch b


Especificaciones: Valores Asumidos: Bloques de concreto Cols = 35 x 35 cm Fy= 60,000 lb/plg 2 barras 6/8 1.91 cm Fc= 3,000 lb/plg 2 C.V. = 250 kg/m 2

Bloques de Concreto 8

mmLn

t 30.028.05.1820.5

5.18 = = =

P Pe es so o d de e V Vi ig gu ue et ta a: : = =m00.1*60.0

))20.0*20.0()60.0*10.0((*2400*1 +

P P. .V V. . = = 4 40 00 0 k kg g/ /m m 2 2

P Pe es so o d de e B Bl lo oq qu ue e = = 2/67.166)1)(60.0(

20*00.5mkg

mmkg

=

0.60 m

0.30 m

0.20 m

0.10 m

0.40 m

0.20 m

0.20 m



Vigueta = 400.00 kg/m 2 Bloques = 166.67 Kg/m 2 Baldosas = 145 kg/m 2 Paredes = 180 kg/m 2 Repello Inferior = 30 kg/m 2 Otros = 30 kg/m 2

C C. . M M. . = 951.67 kg/m 2 *1.4 = 1332.34 kg/m 2 C. V. = 250 kg/m 2 *1.7 = 425 kg/m 2


00.154.0/34.1757/67.951

... 22

= =mkgmkg

MCR O OK K

00.146.1/67.1201/34.1757

.. 22

= =mkgmkg

CF O OK K

q qu u = = ( (1 17 75 57 7. .3 34 4 k kg g/ /m m 2 2 ) ) ( (0 0. .6 60 0m m) ) = = 1 10 05 54 4. .4 40 0 k kg g/ /m m


20 cm


2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/56.3)04.27)(20(85.0

32.1634cmkg

kgbd

VudVud = = =

f f

OK


qu = 1054.40 kg

2108.80 kg.m

2108.80 kg

2108.80 kg

1634.32 kg

2.00 m

VcVud f



Mu (+) = 2180.8 kg.m 218080 kg.cm rmn = 0.0033 As (+) = 2.24 cm 2 rmax = 0.0160

0041.0)04.27)(20(

24.2 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

dreal = 30 cm (2cm+0.64 cm) = 27.36 cm

rreal = 0047.0)36.27)(20(

58.2 =

cm

Mu real = 251230.40 kg.cm 2512.30 kg.m

Asmn = rmn bd = 0.0033(20)(27.36) = 1.81 cm 2

Para As (+) Usar barras 1/2 @ 0.50 m C/C Para Asmn Usar barras 1/2 @ 0.50 m C/C




mLinealbarrascmcm

deBarras /66.627.0

80.1#

2

2

= = mmLB

m15.0

/66.61

=


0160.00041.00033.0


20 cm


2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/91.5)04.27)(20(85.0

08.2715cmkg

kgbd

VudVud = = =

f f

OK


951.25 kg.m

2767.8 kg.m

2056.41 kg.m 2800.75 kg.m

1416.85 kg.m

3189.56 kg.m

2082.44 kg.m

2715.08 kg.m

4.00 m 5.00 m

qu = 1054.4 kg/m

VcVud f




0039.0)04.27)(20(

11.2 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

Asreal = 2.58 cm 2

dreal = 30 cm (2cm+0.64 cm) = 27.36 cm

rreal = 0047.0)36.27)(20(

58.2 =

cm

Mu real = 251230.40 kg.cm 2512.30 kg.m


0053.0)04.27)(20(

89.2 2)()( = = = -

- cmbdAs

s r

mxmn r r r -)(

OK

Asreal = 3.87 cm 2

dreal = 30 cm (2 cm+0.64 cm) = 27.36 cm

0160.00039.00033.0

0160.00053.00033.0


rreal = 0070.0)36.27)(20(

87.3 =

cm

Mu real = 363421.62 kg.cm 3634.21 kg.m





mLinealbarrascmcm

deBarras /66.627.0

80.1#

2

2

= = mmLB

m15.0

/66.61

=



20 cm


2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/54.6)04.27)(20(85.0

9.3008cmkg

kgbd

VudVud = = =

f f

OK


2315.82kg

qu = 953.60 kg/m

3210.80 kg.m

2543.15 kg.m

785.44 kg.m

1875.91 kg.m

1275.13 kg.m

2577.78 kg

2320 kg 1639.82 kg

2902.98 kg

3483.38 kg

4.00 m 5.00 m 5.50 m

Vud =3008.90 kg

1.67 m

Mn ( + )=2381.55 kg.m

Mn () = 1750.04kg.m Mn () = 2011.22 kg.m

VcVud f




0048.0)04.27)(20(

64.2 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

Asreal = 3.87 cm 2

dreal = 30 cm (2cm+0.64 cm) = 27.36 cm

rreal = 0070.0)36.27)(20(

87.3 =

cm

Mu real = 363421.62 kg.cm 3634.21 kg.m

Mu () = 3210.80 kg.m 321080 kg.cm rmn = 0.0033 As () = 3.39 cm 2 rmax = 0.0160

0063.0)04.27)(20(

39.3 2)()( = = = -

- cmbdAs

s r

mxmn r r r -)(

OK

Asreal = 3.87 cm 2

dreal = 30 cm (2 cm+0.64 cm) = 27.36 cm

0160.00048.00033.0

0160.00063.00033.0


rreal = 0070.0)36.27)(20(

87.3 =

cm

Mu real = 363421.62 kg.cm 3634.21 kg.m

As(+) Usar barras de 1/2 @ 0.30m C/C As real = 3.87 cm 2 As() Usar barras de 1/2 @ 0.30 m C/C As real = 3.87 cm 2




mLinealbarrascmcm

deBarras /66.627.0

80.1#

2

2

= = mmLB

m15.0

/66.61

=



du

12.05 m

2

5.13

5.1

/337.238536

)21014.0()/2400(

)`14.0(

cmkgE

mkgE

cfWE

c

c

cc

=

=

=


0.30 m

0.50 m

0.20 m

0.20 m

0.20 m

0.10 m

0.20 m

cmx 3070021000

= =

cmy 19100019000

= =

I1x = (1/12) (60)(10) 3 +600(2519) 2 = 26600 cm 4

I2x = (1/12) (20)(20) 3 +400(1910) 2 = 45733.33 cm 4

Ig = I1x + I2x = 26600 cm 4 + 47533.33 cm 4 = 72333.33 cm 4 7.23 x 10 4 m 4

du = 0.0038 m @ 12.05 m


cm

cmCFu

sc

sc

26.0

46.138.0

..

..

..

=

= =

d

d d

548.8

/337.238536

/20390002

2

=

= =

n

cmkgcmkg

EcEs

n

Clculo de r:

Fig Area (cm 2 ) x (cm) y (cm) XA (cm 2 ) YA (cm 2 ) 1 600 30 25 18000 15000 2 400 30 10 12000 4000

1000 30000 19000

0.60 m

2

`

/983.28

2102

2

cmkgfr

fr

ffr c

=

=

=


Yc

Yt

100 cm

d

2858.42)1( cmAsn = -


cmYc

Yc

46.11

)22.29()20()10)(60(

)36.27)(22.29()20()20()5)(10)(60(2

22

= + + + +

=

YchYt - = = 3011.46

Yt = 18.54 cm

4

24

93.80337

)46.1136.27(22.29)46.1119(100033.72333

cmIgt

cmcmcmcmcmcmIgt

=

- + - + =

54.18)93.80337)(98.28(*

= =YtIgtfr

Mcr

Mcr = 125576.76 kg.cm = 1255.76 kg.m


mkgmkg

CFMn

Ma .20.163146.1

.55.2381..

)(

= = = +

00.176.0.20.1631.76.1255

= =mkgmkg

MaMCR OK

222.29)1(

)87.3)(155.8()1(

cmAsn

Asn

= -

- = -


Yc

Yt

100 cm

C C l lc cu ul lo o d de e I Ic cr r P Pa ar ra a S Se ec cc ci i n n A Ag gr ri ie et ta ad da a: :

Para primer momento de Area:

)36.27)(22.29()5)(10)(20()5)(10)(60( cccc - = - - + -

c = 6.18 cm

Momento de Inercia Icr:

4

23

50.19564

)18.636.27)(09.33()18.6)(60)(3/1(

cmIcr

Icr

=

- + =

44

4434

93.8033759.65361

)5.1956493.80337()91.0(50.19564

cmcmI

IgcmcmcmI

em

em

=

- + = OK

Clculo de Mcr (en Ie1)

cmYc

Yc

24.19

)22.29()10)(60()20)(20(

)36.27)(22.29()25)(10)(60()20)(10)(20(

= + + + +

=

c

d c

2)(

)(

22.29)1(

)58.2)(155.8()1(

cmAsn

Asn

= -

- = - +

+

2

)(

22.29)1(

)87.3)(155.8()1(

cmAsn

Asn

= -

- = - -


YchYt - = =3019.24

Yt = 10.76 cm

4

24

59.72810

)24.1936.27(22.29)1924.19(100033.72333

cmIgt

cmcmcmcmIgt

=

- + - + =

76.10)59.72810)(98.28(*

= =YtIgtfr

Mcr

Mcr = 196101.38 kg.cm = 1961.01 kg.m

mkgmkg

CFMn

Ma .55.137746.1

.22.2011..

)(

= = = -

41 33.7233300.142.1.55.1377

.01.1961cmIgIe

mkgmkg

MaMCR = = \ = =


4

1

35.66407

)33.72333(15.0)59.65361(85.0

15.085.0

cmI

I

III

e

e

eeme

=

+ =

+ =


cm

cmIeIg

instreal

screal

28.0

)35.66407

33.72333(26.0)(.

=

= =

d

d d




00.2)0(501

00.2)'(501

= +

= +

= r

e l s


Comprobando segn tabla 9.5 (b) A.C.I.480/L d

cmcm 08.184.0 OK


A AR RE EA A T TR RI IB BU UT TA AR RI IA A D DE E L LA AS S C CO OL LU UM MN NA AS S P PO OR R N NI IV VE EL L

N N 3 30 00 0 N N 1 10 00 0

Nota: Las columnas entre los niveles N300 N200 N200 N100

poseen dimensiones asumidas de 30 x 30 cm.

La dimensin de la escalera entre estos niveles es de:

3.90 m 2

2.50 m

9.67 m 2 20.25 m 2 23.62 m 2 13.05 m 2

10.75 m 2 22.5 m 2 23.19 m 2 8.39 m 2

5.69 m 2 11.92 m 2 20.73 m 2 14.5 m 2

7.68 m 2 7.68 m 2


N 100 N 000

Nota: Las columnas entre los niveles N300 N200 N200 N100

poseen dimensiones asumidas de 35 x 35 cm.

La dimensin de la escalera entre estos niveles es de:

5.10 m 2

2.50 m

9.67 m 2 20.25 m 2 23.62 m 2 13.05 m 2

10.75 m 2 22.5 m 2 20.37 m 2 7.59 m 2

5.69 m 2 11.92 m 2 20.35 m 2 14.11 m 2

7.68 m 2 7.68 m 2


N NI IV VE EL L N N0 00 00 0 N N1 10 00 0 Especificaciones: Valores Asumidos:

Fy = 60000 lb/plg 2 Huella = 0.30 m F`c = 3000 lb/plg 2 Contrahuella = 0.17m C.V. = 500 Kg/m 2 # de escalones = 13

D Di is se e o o d de e l lo os s E Es sc ca a l lo on ne es s

0.30 m

0.17 m

3.90 m 1.20 m

2.25 m


mmLn

t 20.0272.02171.5

21 = = =

P Pe es so o d de e L Lo os sa a s s l li id da a = = )20.0(/2400 3 mmkgP P. .L L. . = = 4 48 80 0 k kg g/ /m m 2 2

P Pe es so o d de e E Es sc ca al lo on ne es s = = 232

/267.180)2)(5.4(

)2)(/2400(0026.0*0.13mkg

mmkgm

=


Peso de Losa = 480.00 kg/m 2 Peso Escalones = 166.67 Kg/m 2 Baldosas = 145 kg/m 2 Repello Inferior = 36 kg/m 2 Otros = 30 kg/m 2

C C. . M M. . = 871.26 kg/m 2 *1.4 = 1219.77 kg/m 2 C. V. = 500 kg/m 2 *1.7 = 850 kg/m 2


00.142.0/77.2069/26.871

... 22

= =mkgmkg

MCR O OK K

00.1106.1/26.1871/77.2069

.. 22

= =mkgmkg

CF O OK K

q qu u = = ( (2 20 06 69 9. .7 77 7 k kg g/ /m m 2 2 ) ) ( (1 1m m) ) = = 2 20 06 69 9. .7 77 7 k kg g/ /m m



2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/839.3)17)(100(85.0

99.5546cmkg

kgbd

VudVud = = =

f f

OK



0085.0)17)(100(

55.14 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

qu = 2069.77 kg/m

5898.86 kg

5898.86 kg

Vud =5898.86 kg

8405.86 kg.m

VcVud f

0160.00085.00033.0


Asreal = 17.04 cm 2

dreal = dasum

rreal = 0100.0)17)(100(

04.17 =

cm

Mu real = 926447.76 kg.cm 9264.47 kg.m


mLinealbarrascmcm

deBarras /12.584.2

55.14#

2

2

= = mmmLB

m20.019.0

/3.21

=

Asmn = (0.0033)(100)(17) = 5.66 cm 2

Para As (+) Usar barras 6/8 @ 0.20 m C/C A/D. Para Asmn Usar barras 1/2 @ 0.25m C/C




mLinealbarrascmcm

deBarras /07.571.0

60.3#

2

2

= = mmmLB

m20.019.0

/07.51

=



N NI IV VE EL L N N1 10 00 0 N N3 30 00 0 Especificaciones: Valores Asumidos:

Fy = 60000 lb/plg 2 Huella = 0.30 m F`c = 3000 lb/plg 2 Contrahuella = 0.17m C.V. = 500 Kg/m 2 # de escalones = 9

D Di is se e o o d de e l lo os s E Es sc ca a l lo on ne es s

0.30 m

0.17 m

2.70 m 1.20 m

1.60 m



2/45.8)21053.0(1.1)'53.0(1.1 cmkgcfVc = = =

2/62.2)17)(100(85.0

96.4472cmkg

kgbd

VudVud = = =

f f

OK



00431.0)17)(100(

33.7 2)()( = = = +

+ cmbdAs

s r

mxmn r r r +)(

OK

4122.54 kg

4122.54 kg

Vud =3799.58 kg

4472.96 kg.m

VcVud f

0160.00043.00033.0

qu = 1899.79 kg/m


Asreal = 8.00 cm 2

dreal > dasum ( (c cu um mp pl le e) )

rreal = 0046.0)17)(100(

00.8 2 =

cm

Mu real = 491770.44 kg.cm 4917.70 kg.m


mLinealbarrascmcm

deBarras /67.300.2

33.7#

2

2

= = mmmLB

m30.027.0

/67.31

=

Asmn = (0.0033)(100)(17.21) = 5.73 cm 2

Para As (+) Usar barras 5/8 @ 0.20 m C/C A/D. Para Asmn Usar barras 1/2 @ 0.25m C/C




mLinealbarrascmcm

deBarras /07.571.0

60.3#

2

2

= = mmmLB

m20.019.0

/07.51

=


proyecto_hormigon_i.pdf

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