proyecto 1 va que quiere

Calculo del momento para el tercer piso (departamento)

1.- Características de diseño de la losa No 1

SL=3m4m

= 0.75 Como SL>0.50

Se deberá diseñar como losa bidireccional

2.- Determinación del espesor de la losa

Para fy=4200 kg

cm2h= ln33

h=400cm33

=12.2cm

h=Perímetro180

=1400180

=7.7m

Cuando αm>¿ 2 la norma establece que el espesor mínimo deberá cumplir:

h≥ ln (800+0.071 f y )

36000+5000 β (1+βs )≥9cm

h≥ 385 (800+0.071∗4200 )

36000+5000∗1.333 (1+0.5 )≥9cm

h=9.2cm

βs=longitud de los bordes continuos

perímetrototal de lalosa = 0.5 β= luz librelarga

luz libre corta =1.333

Adoptamos h = 15 cm

3.- Verificamos el espesor de la losa asumida (hf=15cm)

Hallamos αm

Para el eje X

Tramo interno

bo=bw+2∗hb hb≤4∗hfbo=20+2∗40 hb≤4∗15bo=100cm 40≤60

Hallamos k mediante ábaco usando los siguientes parámetros

hfh

=15 cm55 cm

=0,272 bobw

=100cm20cm

=5k=1,8

* VIGA. * LOSA .

Ib= k∗bw∗h3

12Is= franja dediseño∗hf 3

12

Ib=1,8∗30∗553

12Is=450∗15

3

12

Ib=499125 cm4 Is=126562.5 cm4

α 1=( Ecb ) (I b)

( Ecs ) (I s)=

(I b)(I s)

= 499125cm4

126562.5cm4 α1=3,94

Tramo Externo o de Borde

bo=bw+hb bo=40+20

bo=60cm


hfh

=15 cm55 cm

=0,272 bobw

=60cm20cm

=3k=1,6

* VIGA .

Ib= k∗bw∗h3

12

Ib=1,6∗40∗553

12

Ib=443666,67 cm4

* LOSA .

Is= franja deborde∗hf 3

12

Is=450∗153

12

Is=132187.5cm4

α 2=( Ecb )(I b)

( Ecs ) (I s)=

(I b)(I s)

= 443666,67cm4

132187.5cm4 α2=¿3.356

Para el eje Y

Tramo interno

bo=bw+2∗hb hb≤4∗hf

bo=20+2∗40 hb≤4∗15bo=100cm 40≤60


hfh

=15 cm55 cm

=0,272 bobw

=100cm20cm

=5k=1,8

* VIGA. * LOSA .

Ib=1,8∗20∗553

12Is=550∗15

3

12

Ib=499125 cm4 Is=154687.5 cm4

α 3=( I b)(I s)

= 499125 cm4

154687.5 cm4 α3=3,227

Tramo Externo o de Borde

bo=bw+hb bo=20+40 bo=60cm


hfh

=15 cm55 cm

=0,272 bobw

=60cm20cm

=3k=1,6

* VIGA .

Ib= k∗bw∗h3

12Ib=1,6∗20∗55

3

12Ib=443666.6667cm4

* LOSA .

Is= franja deborde∗hf 3

12

Is=550∗153

12

Is=160312.5cm4

α 4=( Ecb )(I b)

( Ecs )(I s)=

( I b)( I s)

=443666.6667cm4

160312.5cm4 α 4=2,767

αm de un tablero I

αm=α 1+α2+α 3+α 4

4=3.36+3.23+3,94+2.77

4αm=3.32

Tablero α1 α2 α3 α4 αm1 3.36 3.23 3.94 2.77 3.322 2.78 3.01 3.94 2.94 3.063 3.01 2.94 2.77 3.23 2.984 2.94 3.01 2.94 2.77 2.915 2.36 2.78 3.01 3.22 2.696 2.75 2.98 3.22 2.94 2.977 3.94 3.23 3.36 2.77 3.32

8 2.94 3.01 2.94 2.77 2.919 3.01 2.94 2.77 3.23 2.98

Con el αm mas critico confirmamos nuestra h, y verificamos nuestra h = 15cm

3.- Determinación de las cargas de diseño

Carga Muerta:

Peso propio losa (0.15 m) (2,500 kg/m3) = 375 kg/m2

Peso de piso cerámico = = 60 kg/m2

Peso de cielo raso + instalaciones= = 60 kg/m2

Peso propio muro = (3m*0.15m*4.5m*1800 kg/m3 )/12m = 303.75 kg/m2

Carga Muerta = 800 kg/m2

Carga Viva= 250 kg/m2

Mayoración de cargas Qu = 1.2 CM + 1.6 CV

Qu = 1.2 (800 kg/m2) + 1.6 (250 kg/m2) => Qu = 1360 kg/m2

4.- Cálculo de los Momentos Flectores

En las tablas se utiliza la losa No 1(caso No 6)

Lx/Ly = 3m/4m = 0.75

My - = 0.0001 (1360kg/m2) (953.5) (3m)2 = - 1167.084 Kg m

My + = 0.0001 (1360 kg/m2) (471.5) (3m)2 = + 577.12 Kg m

Mx - = 0.0001 (1360 kg/m2) (775) (3m)2 = - 948.6 Kg m

Mx + = 0.0001 (1360 kg/m2) (306) (3m)2 = + 374.74 Kg m

Mx - = - 948.6 Kg m

Ly = 4 m

Lx = 3 m

Mx + = + 374.74 Kg m


SL=3m5m

= 0.6 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:




Peso propio muro = (3m*0.15m*3m*1800 kg/m3 )/15m = 162 kg/m2




Qu = 1.2 (660 kg/m2) + 1.6 (250 kg/m2) => Qu = 1188,4 kg/m2



Lx/Ly = 3m/5m = 0.6

My - = 0.0001 (1189kg/m2) (1030) (3m)2 = - 1102.03 Kg m

My + = 0.0001 (1189 kg/m2) (532) (3m)2 = + 5692.9 Kg m

Mx - = 0.0001 (1189 kg/m2) (788) (3m)2 = - 8432.39 Kg m

Ly = 5 m

Lx = 3 m

Mx - = - 8432,39 Kg m

Mx + = 3071,19

Mx + = 0.0001 (1189 kg/m2) (287) (3m)2 = + 3071.19 Kg m

My + = + 11022,03 Kg m


SL=3m6m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:




Peso propio muro = (3m*0.15m*7.5m*1800 kg/m3 )/18m = 340 kg/m2




My + = + 5692,9 Kg m

Qu = 1.2 (835 kg/m2) + 1.6 (250 kg/m2) => Qu = 1402 kg/m2



Lx/Ly = 3m/6m = 0.5

My - = 0.0001 (1402kg/m2) (1180) (3m)2 = - 1488,9 Kg m

My + = 0.0001 (1402 kg/m2) (641) (3m)2 = + 808,8 Kg m

Mx - = 0.0001 (1402 kg/m2) (797) (3m)2 = - 1005,65 Kg m

Mx + = 0.0001 (1402 kg/m2) (306) (3m)2 = + 386,1 Kg m

Mx - = - 1005,65Kg m

Mx + = + 386,1 Kg m

My- = - 1488,9 kg m


SL= 4m8m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Lx = 3 m

Ly = 6 m

My + = + 808,8 Kg m

Carga Muerta:








Qu = 1.2 (925 kg/m2) + 1.6 (250 kg/m2) => Qu = 1510 kg/m2



Lx/Ly = 4m/8m = 0.5

My - = 0.0001 (1510kg/m2) (1150) (4m)2 = - 2778,4 Kg m

My + = 0.0001 (1510 kg/m2) (613) (4m)2 = + 1481,01 Kg m

Mx - = 0.0001 (1510 kg/m2) (795) (4m)2 = - 1920,72 Kg m

Mx + = 0.0001 (1510 kg/m2) (287) (4m)2 = + 693,4 Kg m

Mx + = - 1920,72 Kg m

My - = - 2778,4 Kg m

My - = + 1481,01 Kg m

Ly = 8 m

Lx = 4 m

Mx + = + 693,4 Kg m

Mx + = - 1920,72 Kg m


SL=5m8m

= 0.625 Como SL>0.625



Adoptamos h = 15cm


Carga Muerta:








Qu = 1.2 (820 kg/m2) + 1.6 (250 kg/m2) => Qu = 1384 kg/m2



Lx/Ly = 5m/8m = 0.625

My - = 0.0001 (1384kg/m2) (779,5) (5m)2 = - 2697,07 Kg m

My + = 0.0001 (1384 kg/m2) (376,25) (5m)2 = + 1301,8 Kg m

Mx - = 0.0001 (1384 kg/m2) (563) (5m)2 = - 1947,9 Kg m

Ly = 8 m

Lx = 4 m

Mx + = 0.0001 (1384 kg/m2) (214) (5m)2 = + 740,44 Kg m

Mx + = - 1947,9 Kg m

My - = - 2697,07 Kg m

My - = + 1301,8 Kg m

Mx + = - 1947,9 Kg m


SL=6m8m

= 0.75 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:




Mx + = + 740,44 Kg m

Peso propio muro = (3m*0.15m*24,5m*1800 kg/m3 )/48m = 413,4 kg/m2

Carga Muerta = 908,4 kg/m2



Qu = 1.2 (908,4 kg/m2) + 1.6 (250 kg/m2) => Qu = 1490,1 kg/m2



Lx/Ly = 6m/8m = 0.75

My - = 0.0001 (1490,1kg/m2) (837,5) (6m)2 = - 4492,65 Kg m

My + = 0.0001 (1490,1 kg/m2) (401) (6m)2 = + 2151,1 Kg m

Mx - = 0.0001 (1490,1 kg/m2) (741,5) (6m)2 = - 3977,7 Kg m

Mx + = 0.0001 (1490,1 kg/m2) (287) (6m)2 = + 1539,6 Kg m

Mx + = - 3977,7 Kg m

My - = - 4492,65 Kg m

My - = + 2151,1 Kg m

Mx + = - 3977,7 Kg m


SL=3m4m

= 0.75 Como SL>0.5


Ly = 8 m

Lx = 6 m

Mx + = + 1539,6 Kg m


Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (595 kg/m2) + 1.6 (250 kg/m2) => Qu = 1114 kg/m2



Lx/Ly = 3m/4m = 0.75

My - = 0.0001 (994kg/m2) (700) (3m)2 = - 781.82 Kg m

My + = 0.0001 (994 kg/m2) (325) (3m)2 = + 325.84 Kg m

Mx - = 0.0001 (994 kg/m2) (559) (3m)2 = - 560,45 Kg m

Mx + = 0.0001 (994 kg/m2) (214) (3m)2 = + 214,56 Kg m

My + = - 781.82 Kg m

Mx - = - 560,45 Kg m

Lx = 3 m

Ly = 4 m

My + = +325.84Kg m

Mx - = + 214.56 Kg m

Mx + = - 781.82 Kg m


SL=3m5m

= 0.6 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:








Qu = 1.2 (660 kg/m2) + 1.6 (250 kg/m2) => Qu = 1188,4 kg/m2



Lx/Ly = 3m/5m = 0.6

My - = 0.0001 (1189kg/m2) (1030) (3m)2 = - 1102.03 Kg m

My + = 0.0001 (1189 kg/m2) (532) (3m)2 = + 569.29 Kg m

Ly = 5 m

Lx = 3 m

Mx - = - 843,23 Kg m

Mx + = 307,19

Mx - = 0.0001 (1189 kg/m2) (788) (3m)2 = - 843.23 Kg m

Mx + = 0.0001 (1189 kg/m2) (287) (3m)2 = + 307.19 Kg m

My + = + 1102,03 Kg m


SL=3m6m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







My + = + 569,29 Kg m


Qu = 1.2 (835 kg/m2) + 1.6 (250 kg/m2) => Qu = 1156 kg/m2



Lx/Ly = 3m/6m = 0.5

My - = 0.0001 (1156kg/m2) (1180) (3m)2 = - 1227,67 Kg m

My + = 0.0001 (1156 kg/m2) (641) (3m)2 = + 666,9 Kg m

Mx - = 0.0001 (1156 kg/m2) (797) (3m)2 = - 829,3 Kg m

Mx + = 0.0001 (1156 kg/m2) (306) (3m)2 = + 318,4 Kg m

My- = - 1227,67 kg m

Mx - = - 829,2 Kg m

Mx + = + 318,4 Kg m

Lx = 3 m

Ly = 6 m

My + = + 666,9 Kg m

ARMADURA EN LAS LOSAS PARA EL PISO 3 (DEPARTAMENTO)

LOSA 1 LUZ LARGA L = 4M

d = h – recubrimiento – Ф/2

Ф = 1,2cm

d = 11,9 cm

Para el momento negativo

a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,626

As= Mu

φ . f y(d−a2 )

As = 2,66 cm2 Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m

Para el momento positivo

a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,205

As= Mu

φ . f y(d−a2 )

As = 0,87cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m

LOSA 1 LUZ CORTA Lx = 3m


Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,506

As= Mu

φ . f y(d−a2 )

As = 2,15 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,253

As= Mu

φ . f y(d−a2 )

As = 1,07cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m

Cuantías límites por flexión ρb = cuantía balanceada

ρmax=0 .75 ρb=0.75[0 .85 β1f ' c

f y

×60906090+ f y

]=0.75[0 .85(0 .85) (210 )(4200 )

×60906090+4200 ]

ρb = 0.0214 ρmax= 0.016

ρmin = 0.79√ f c

f y > 14f y

ρmin = 0.79√2104200 = 0.002726 >

144200= 0.0033

Armadura máxima y mínima a flexión

As max = ρmax (b) (d) = (0.016) (100 cm) (11,9 cm) Asmax = 19,08 cm2/m

As min = ρmin (b) (d) = (0.0033) (100 cm) (11,9 cm) Asmin = 3,24 cm2/m

Armadura mínima por contracción y temperatura

As min = (0.0018) (b) (h) = (0.0018) (100 cm) (15 cm) Asmin = 2,14 cm2/m

LOSA 2 LUZ LARGA L = 5m


Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,591

As= Mu

φ . f y(d−a2 )

As = 2,51 cm2

rmin< r < rmax

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,301

As= Mu

φ . f y(d−a2 )

As = 1,281cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,449

As= Mu

φ . f y(d−a2 )

As = 1,91 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,162

As= Mu

φ . f y(d−a2 )

As = 0,69 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,806

As= Mu

φ . f y(d−a2 )

As = 3,42 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,431

As= Mu

φ . f y(d−a2 )

As = 1,83cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,538

As= Mu

φ . f y(d−a2 )

As = 2,29 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,2037

As= Mu

φ . f y(d−a2 )

As = 0,87 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,555

As= Mu

φ . f y(d−a2 )

As = 6,61 cm2

Usar ∅ = 16 mm c/30 cm As = 6.70 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,802

As= Mu

φ . f y(d−a2 )

As = 3,41cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,051

As= Mu

φ . f y(d−a2 )

As = 4,47 cm2

Usar ∅ = 12 mm c/25 cm As = 4.52 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,368

As= Mu

φ . f y(d−a2 )

As = 1,57 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,505

As= Mu

φ . f y(d−a2 )

As = 6,39 cm2

Usar ∅ = 16 mm c/30 cm As = 6.70 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,701

As= Mu

φ . f y(d−a2 )

As = 2,98cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,066

As= Mu

φ . f y(d−a2 )

As = 4,52 cm2

Usar ∅ = 12 mm c/25 cm As = 4.52 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,393

As= Mu

φ . f y(d−a2 )

As = 1,67 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 2,6437

As= Mu

φ . f y(d−a2 )

As = 11,24 cm2

Usar ∅ = 12 mm c/10 cm As = 11.3 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,1841

As= Mu

φ . f y(d−a2 )

As = 5,03cm2

Usar ∅ = 12 mm c/20 cm As = 5.65 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 2,3036

As= Mu

φ . f y(d−a2 )

As = 9,79 cm2

Usar ∅ = 16 mm c/20 cm As = 10.05 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,8346

As= Mu

φ . f y(d−a2 )

As = 3,55 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,373

As= Mu

φ . f y(d−a2 )

As = 1,58 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,172

As= Mu

φ . f y(d−a2 )

As = 0,73cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,2969

As= Mu

φ . f y(d−a2 )

As = 1,26 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,11276

As= Mu

φ . f y(d−a2 )

As = 0,49 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,591

As= Mu

φ . f y(d−a2 )

As = 1,58 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,301

As= Mu

φ . f y(d−a2 )

As = 0,73cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4493

As= Mu

φ . f y(d−a2 )

As = 1,91 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1617

As= Mu

φ . f y(d−a2 )

As = 0,69 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6605

As= Mu

φ . f y(d−a2 )

As = 2,8 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3541

As= Mu

φ . f y(d−a2 )

As = 1,5 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4419

As= Mu

φ . f y(d−a2 )

As = 1,88 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1677

As= Mu

φ . f y(d−a2 )

As = 0,71 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m

Calculo del momento para el segundo piso (salón de evento)


SL=3m4m

= 0.75 Como SL>0.50



Para fy=4200 kg

cm2h= ln33

h=400cm33

=12.2cm

h=Perímetro180

=1400180

=7.7m


h≥ ln (800+0.071 f y )

36000+5000 β (1+βs )≥9cm

h≥ 385 (800+0.071∗4200 )

36000+5000∗1.333 (1+0.5 )≥9cm

h=9.2cm




Adoptamos h = 15 cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234 kg/m2



Lx/Ly = 3m/4m = 0.75

My - = 0.0001 (1234kg/m2) (953.5) (3m)2 = - 1058,96 Kg m

My + = 0.0001 (1234 kg/m2) (471.5) (3m)2 = + 523,65 Kg m

Mx - = 0.0001 (1234 kg/m2) (775) (3m)2 = - 860,72 Kg m

Mx + = 0.0001 (1234 kg/m2) (306) (3m)2 = + 339,84 Kg m

My - = - 1058,96 Kg m

My - = 523,65 Kg m

Mx + = -860,72 Kg m

Ly = 4 m

Lx = 3 m

Mx + = + 339,84 Kg m


SL=3m5m

= 0.6 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234kg/m2



Lx/Ly = 3m/5m = 0.6

My - = 0.0001 (1234kg/m2) (1030) (3m)2 = - 1143,92 Kg m

My + = 0.0001 (1234 kg/m2) (532) (3m)2 = + 590,84 Kg m

Mx - = 0.0001 (1234 kg/m2) (788) (3m)2 = - 875,15 Kg m

Mx + = 0.0001 (1234 kg/m2) (287) (3m)2 = + 318,74 Kg m

Ly = 5 m

Lx = 3 m

Mx - = - 875,15 Kg m

Mx + = 318,74

My + = + 1143,92 Kg m


SL=3m6m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234 kg/m2



Lx/Ly = 3m/6m = 0.5

My + = + 590,84 Kg m

Lx = 3 m

Ly = 6 m

My - = 0.0001 (1234kg/m2) (1180) (3m)2 = - 1310,51 Kg m

My + = 0.0001 (1234 kg/m2) (641) (3m)2 = + 711,89 Kg m

Mx - = 0.0001 (1234 kg/m2) (797) (3m)2 = - 885,15 Kg m

Mx + = 0.0001 (1234 kg/m2) (306) (3m)2 = + 339,84 Kg m

Mx - = - 885,15Kg m

Mx + = + 339,84Kg m

My- = - 1310,51kg m


SL= 4m8m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:

My + = + 711,89 Kg m







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234 kg/m2



Lx/Ly = 4m/8m = 0.5

My - = 0.0001 (1234kg/m2) (1150) (4m)2 = - 2270,56Kg m

My + = 0.0001 (1234 kg/m2) (613) (4m)2 = + 1210,31 Kg m

Mx - = 0.0001 (1234 kg/m2) (795) (4m)2 = - 1569,65 Kg m

Mx + = 0.0001 (1234 kg/m2) (287) (4m)2 = + 566,65 Kg m

Mx + = - 1569,65 Kg m

My - = - 2270,56 Kg m

My - = + 1210,31 Kg m

Mx + = - 1569,65 Kg m

Ly = 8 m

Lx = 4 m

Mx + = + 566,65 Kg m


SL=5m8m

= 0.625 Como SL>0.625



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234 kg/m2



Lx/Ly = 5m/8m = 0.625

My - = 0.0001 (1234kg/m2) (779,5) (5m)2 = - 2404,76 Kg m

My + = 0.0001 (1234 kg/m2) (376,25) (5m)2 = + 1160,73 Kg m

Mx - = 0.0001 (1234 kg/m2) (563) (5m)2 = - 1736,86 Kg m

Mx + = 0.0001 (1234 kg/m2) (214) (5m)2 = + 660,19 Kg m

Mx + = - 1736,86 Kg m

Ly = 8 m

Lx = 4 m

Mx + = + 660,19 Kg m

My - = - 2404,76 Kg m

My - = + 1160,73 Kg m

Mx + = - 1736,86 Kg m


SL=6m8m

= 0.75 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234 kg/m2



Lx/Ly = 6m/8m = 0.75

My - = 0.0001 (1234,1kg/m2) (837,5) (6m)2 = - 3720,51 Kg m

Mx + = + 660,19 Kg m

Ly = 8 m

Lx = 6 m

My + = 0.0001 (1234 kg/m2) (401) (6m)2 = + 1781,4Kg m

Mx - = 0.0001 (1234 kg/m2) (741,5) (6m)2 = - 3294,04Kg m

Mx + = 0.0001 (1234 kg/m2) (287) (6m)2 = + 1274,97 Kg m

Mx + = - 3294,04Kg m

My - = - 3720,51 Kg m

My - = + 1781,4 Kg m

Mx + = - 3294,04 Kg m


SL=3m4m

= 0.75 Como SL>0.5



Adoptamos h = 15cm


Carga Muerta:

Mx + = + 1274,97 Kg m







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234 kg/m2



Lx/Ly = 3m/4m = 0.75

My - = 0.0001 (1234kg/m2) (700) (3m)2 = - 777,42 Kg m

My + = 0.0001 (1234 kg/m2) (325) (3m)2 = + 360,95 Kg m

Mx - = 0.0001 (1234 kg/m2) (559) (3m)2 = - 621,38 Kg m

Mx + = 0.0001 (1234 kg/m2) (214) (3m)2 = + 237,67 Kg m

My + = - 777,42 Kg m

Mx - = - 621,38Kg m

Mx - = + 237,67 Kg m

Mx + = - 777,42 Kg m

Lx = 3 m

Ly = 4 m

My + = +360,95 Kg m


SL=3m5m

= 0.6 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234kg/m2



Lx/Ly = 3m/5m = 0.6

My - = 0.0001 (1234kg/m2) (1030) (3m)2 = - 1143,92 Kg m

My + = 0.0001 (1234 kg/m2) (532) (3m)2 = + 590,84 Kg m

Mx - = 0.0001 (1234 kg/m2) (788) (3m)2 = - 875,15 Kg m

Mx + = 0.0001 (1234 kg/m2) (287) (3m)2 = + 318,74 Kg m

Ly = 5 m

Lx = 3 m

Mx - = - 875,15 Kg m

Mx + = 318,74

My + = + 1143,92 Kg m


SL=3m6m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (400 kg/m2) => Qu = 1234 kg/m2

My + = + 590,84 Kg m



Lx/Ly = 3m/6m = 0.5

My - = 0.0001 (1234kg/m2) (1180) (3m)2 = - 1310,51 Kg m

My + = 0.0001 (1234 kg/m2) (641) (3m)2 = + 711,89 Kg m

Mx - = 0.0001 (1234 kg/m2) (797) (3m)2 = - 885,15 Kg m

Mx + = 0.0001 (1234 kg/m2) (306) (3m)2 = + 339,84 Kg m

My- = - 1310,51 kg m

Mx - = - 885,15 Kg m

Mx + = + 339,84 Kg m

ARMADURA EN LAS LOSAS PARA EL PISO 2 (salón de evento)



Ф = 1,2cm

d = 11,9 cm

Lx = 3 m

Ly = 6 m

My + = + 711,89 Kg m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,5674

As= Mu

φ . f y(d−a2 )

As = 2,41 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,2771

As= Mu

φ . f y(d−a2 )

As = 1,18cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4591

As= Mu

φ . f y(d−a2 )

As = 1,95 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1791

As= Mu

φ . f y(d−a2 )

As = 0,76 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


ρmax=0 .75 ρb=0.75[0 .85 β1f ' c

f y

×60906090+ f y

]=0.75[0 .85(0 .85) (210 )(4200 )

×60906090+4200 ]

ρb = 0.0214 ρmax= 0.016

ρmin = 0.79√ f c

f y > 14f y

ρmin = 0.79√2104200 = 0.002726 >

144200= 0.0033



rmin< r < rmax






Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6142

As= Mu

φ . f y(d−a2 )

As = 2,61 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3131

As= Mu

φ . f y(d−a2 )

As = 1,33cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4669

As= Mu

φ . f y(d−a2 )

As = 1,98cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1679

As= Mu

φ . f y(d−a2 )

As = 0,71 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,7065

As= Mu

φ . f y(d−a2 )

As = 3 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3784

As= Mu

φ . f y(d−a2 )

As = 1,6 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4724

As= Mu

φ . f y(d−a2 )

As = 2,01 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1791

As= Mu

φ . f y(d−a2 )

As = 0,76 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,2537

As= Mu

φ . f y(d−a2 )

As = 5,33 cm2

Usar ∅ = 12 mm c/20 cm As = 5.65 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6509

As= Mu

φ . f y(d−a2 )

As = 2,77 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,8515

As= Mu

φ . f y(d−a2 )

As = 3,62 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3002

As= Mu

φ . f y(d−a2 )

As = 1,27 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,33

As= Mu

φ . f y(d−a2 )

As = 5,65 cm2

Usar ∅ = 12 mm c/20 cm As = 5.65 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6235

As= Mu

φ . f y(d−a2 )

As = 2,65cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,9461

As= Mu

φ . f y(d−a2 )

As = 4,02 cm2

Usar ∅ = 12 mm c/25 cm As = 4.52 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3505

As= Mu

φ . f y(d−a2 )

As = 1,49 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 2,1382

As= Mu

φ . f y(d−a2 )

As = 9,1 cm2

Usar ∅ = 16 mm c/20 cm As = 10.05 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,9715

As= Mu

φ . f y(d−a2 )

As = 4,13 cm2

Usar ∅ = 12 mm c/25 cm As = 4.52 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,8699

As= Mu

φ . f y(d−a2 )

As = 7,95 cm2

Usar ∅ = 16 mm c/25 cm As = 8.04 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6867

As= Mu

φ . f y(d−a2 )

As = 2,91 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4138

As= Mu

φ . f y(d−a2 )

As = 1,76 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1903

As= Mu

φ . f y(d−a2 )

As = 0,81 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3296

As= Mu

φ . f y(d−a2 )

As = 1,4 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1248

As= Mu

φ . f y(d−a2 )

As = 0,53 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6142

As= Mu

φ . f y(d−a2 )

As = 2,61 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3131

As= Mu

φ . f y(d−a2 )

As = 1,33cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4669

As= Mu

φ . f y(d−a2 )

As = 1,98cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1679

As= Mu

φ . f y(d−a2 )

As = 0,71 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,7065

As= Mu

φ . f y(d−a2 )

As = 3 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3784

As= Mu

φ . f y(d−a2 )

As = 1,61 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4724

As= Mu

φ . f y(d−a2 )

As = 2 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1791

As= Mu

φ . f y(d−a2 )

As = 0,76 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m

Calculo del momento para el primer piso (restaurant)


SL=3m4m

= 0.75 Como SL>0.50



Para fy=4200 kg

cm2h= ln33

h=400cm33

=12.2cm

h=Perímetro180

=1400180

=7.7m


h≥ ln (800+0.071 f y )

36000+5000 β (1+βs )≥9cm

h≥ 385 (800+0.071∗4200 )

36000+5000∗1.333 (1+0.5 )≥9cm

h=9.2cm




Adoptamos h = 15 cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2



Lx/Ly = 3m/4m = 0.75

My - = 0.0001 (1154kg/m2) (953.5) (3m)2 = - 990,31 Kg m

My + = 0.0001 (1154 kg/m2) (471.5) (3m)2 = + 489,7 Kg m

Mx - = 0.0001 (1154 kg/m2) (775) (3m)2 = - 804,92 Kg m

Mx + = 0.0001 (1154 kg/m2) (306) (3m)2 = + 317,81 Kg m

Ly = 4 m

Lx = 3 m

My - = - 990,31 Kg m

My - = 489,7 Kg m

Mx + = -804,92 Kg m


SL=3m5m

= 0.6 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2

4.- Cálculo de los Momentos FlectoresLx = 3 m

Mx - = - 818,42 Kg m

Mx + = 298,08


Lx/Ly = 3m/5m = 0.6

My - = 0.0001 (1154kg/m2) (1030) (3m)2 = - 1069,76 Kg m

My + = 0.0001 (1154 kg/m2) (532) (3m)2 = + 552,53 Kg m

Mx - = 0.0001 (1154 kg/m2) (788) (3m)2 = - 818,42 Kg m

Mx + = 0.0001 (1154 kg/m2) (287) (3m)2 = + 298,08 Kg m

My + = + 1069,76 Kg m


SL=3m6m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:



Ly = 5 m

My + = + 552,53 Kg m





Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2



Lx/Ly = 3m/6m = 0.5

My - = 0.0001 (1154kg/m2) (1180) (3m)2 = - 1225,55 Kg m

My + = 0.0001 (1154 kg/m2) (641) (3m)2 = + 665,74 Kg m

Mx - = 0.0001 (1154 kg/m2) (797) (3m)2 = - 827,76 Kg m

Mx + = 0.0001 (1154 kg/m2) (306) (3m)2 = + 317,81 Kg m

Mx - = - 827,76Kg m

Mx + = + 317,81Kg m

Lx = 3 m

Ly = 6 m

My + = + 665,74 Kg m

My- = - 1225,55 kg m


SL= 4m8m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2



Lx/Ly = 4m/8m = 0.5

My - = 0.0001 (1154kg/m2) (1150) (4m)2 = - 2123,36Kg m

My + = 0.0001 (1154 kg/m2) (613) (4m)2 = + 1131,84 Kg m

Mx - = 0.0001 (1154 kg/m2) (795) (4m)2 = - 1467,89 Kg m

Mx + = 0.0001 (1154 kg/m2) (287) (4m)2 = + 529,92 Kg m

Mx + = - 1467,89 Kg m

Ly = 8 m

Lx = 4 m

My - = - 2123,36 Kg m

My - = + 1131,84 Kg m

Mx + = - 1467,89 Kg m


SL=5m8m

= 0.625 Como SL>0.625



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2



Lx/Ly = 5m/8m = 0.625

My - = 0.0001 (1154kg/m2) (779,5) (5m)2 = - 2248,86 Kg m

My + = 0.0001 (1154 kg/m2) (376,25) (5m)2 = + 1085 Kg m

Mx - = 0.0001 (1154 kg/m2) (563) (5m)2 = - 1624,26 Kg m

Mx + = 0.0001 (1154 kg/m2) (214) (5m)2 = + 617,39 Kg m

Mx + = - 1624,26 Kg m

My - = - 2248,86 Kg m

My - = + 1085 Kg m

Mx + = - 1624,26 Kg m


SL=6m8m

= 0.75 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:

Ly = 8 m

Lx = 4 m

Mx + = + 617,39 Kg m







Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2



Lx/Ly = 6m/8m = 0.75

My - = 0.0001 (1154,1kg/m2) (837,5) (6m)2 = - 3479,31 Kg m

My + = 0.0001 (1154 kg/m2) (401) (6m)2 = + 1665,9 Kg m

Mx - = 0.0001 (1154 kg/m2) (741,5) (6m)2 = - 3080,49 Kg m

Mx + = 0.0001 (1154 kg/m2) (287) (6m)2 = + 1192,31 Kg m

Mx + = - 3080,49 Kg m

My - = - 3479,31 Kg m

Ly = 8 m

Lx = 6 m

Mx + = + 1192,31 Kg m

My - = + 1665,9 Kg m

Mx + = - 3080,49 Kg m


SL=3m4m

= 0.75 Como SL>0.5



Adoptamos h = 15cm


Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2



Lx/Ly = 3m/4m = 0.75

My - = 0.0001 (1154kg/m2) (700) (3m)2 = - 727,02 Kg m

Lx = 3 m

Ly = 4 m

My + = 0.0001 (1154 kg/m2) (325) (3m)2 = + 307,54 Kg m

Mx - = 0.0001 (1154 kg/m2) (559) (3m)2 = - 581,1 Kg m

Mx + = 0.0001 (1154 kg/m2) (214) (3m)2 = + 222,26 Kg m

My + = - 727,02 Kg m

Mx - = - 581,1Kg m

Mx - = + 222,26 Kg m

Mx + = - 727,02 Kg m


SL=3m5m

= 0.6 Como SL>0.50



Adoptamos h = 15cm


Carga Muerta:





My + = +307,54Kg m

Mx - = - 818,42 Kg m

Mx + = 298,1



Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154kg/m2



Lx/Ly = 3m/5m = 0.6

My - = 0.0001 (1154kg/m2) (1030) (3m)2 = - 1069,76 Kg m

My + = 0.0001 (1154 kg/m2) (532) (3m)2 = + 552,53 Kg m

Mx - = 0.0001 (1154 kg/m2) (788) (3m)2 = - 818,42 Kg m

Mx + = 0.0001 (1154 kg/m2) (287) (3m)2 = + 298,1 Kg m

My + = + 1069,76 Kg m


SL=3m6m

= 0.5 Como SL>0.50



Adoptamos h = 15cm


Ly = 5 m

Lx = 3 m

My + = + 552,53Kg m

Carga Muerta:







Qu = 1.2 (495 kg/m2) + 1.6 (350 kg/m2) => Qu = 1154 kg/m2



Lx/Ly = 3m/6m = 0.5

My - = 0.0001 (1154kg/m2) (1180) (3m)2 = - 1225,55 Kg m

My + = 0.0001 (1154 kg/m2) (641) (3m)2 = + 665,74 Kg m

Mx - = 0.0001 (1154 kg/m2) (797) (3m)2 = - 827,76 Kg m

Mx + = 0.0001 (1154 kg/m2) (306) (3m)2 = + 317,81 Kg m

My- = - 1225,55kg m

Mx - = - 827,74 Kg m

Lx = 3 m

Ly = 6 m

My + = + 665,74 Kg m

Mx + = + 317,81 Kg m

ARMADURA EN LAS LOSAS PARA EL PISO 1 (restaurant)

LOSA 1 LUZ LARGA L = 4M


Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,5298

As= Mu

φ . f y(d−a2 )

As = 2,25 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,25897

As= Mu

φ . f y(d−a2 )

As = 1,1cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4288

As= Mu

φ . f y(d−a2 )

As = 1,82 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1674

As= Mu

φ . f y(d−a2 )

As = 0,71cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


ρmax=0 .75 ρb=0.75[0 .85 β1f ' c

f y

×60906090+ f y

]=0.75[0 .85(0 .85) (210 )(4200 )

×60906090+4200 ]

ρb = 0.0214 ρmax= 0.016

ρmin = 0.79√ f c

f y > 14f y

ρmin = 0.79√2104200 = 0.002726 >

144200= 0.0033








Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,5734

rmin< r < rmax

As= Mu

φ . f y(d−a2 )

As = 2,44 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,2926

As= Mu

φ . f y(d−a2 )

As = 1,24cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4361

As= Mu

φ . f y(d−a2 )

As = 1,85cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1569

As= Mu

φ . f y(d−a2 )

As = 0,67 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6593

As= Mu

φ . f y(d−a2 )

As = 2,8 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3535

As= Mu

φ . f y(d−a2 )

As = 1,5 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4412

As= Mu

φ . f y(d−a2 )

As = 1,87 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1674

As= Mu

φ . f y(d−a2 )

As = 0,71 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,168

As= Mu

φ . f y(d−a2 )

As = 4,96 cm2

Usar ∅ = 16 mm c/40 cm As = 5.06 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6075

As= Mu

φ . f y(d−a2 )

As = 2,58 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,7943

As= Mu

φ . f y(d−a2 )

As = 3,37 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,2805

As= Mu

φ . f y(d−a2 )

As = 1,19 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,241

As= Mu

φ . f y(d−a2 )

As = 4,27 cm2

Usar ∅ = 12 mm c/25 cm As = 4.52 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,58203

As= Mu

φ . f y(d−a2 )

As = 2,47cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,8823

As= Mu

φ . f y(d−a2 )

As = 3,75 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3274

As= Mu

φ . f y(d−a2 )

As = 1,39 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,9843

As= Mu

φ . f y(d−a2 )

As = 8,43 cm2

Usar ∅ = 16 mm c/20 cm As = 10.05 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,9059

As= Mu

φ . f y(d−a2 )

As = 3,85cm2

Usar ∅ = 12 mm c/25 cm As = 4.52 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 1,7383

As= Mu

φ . f y(d−a2 )

As = 7,39 cm2

Usar ∅ = 16 mm c/25 cm As = 8.04 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6409

As= Mu

φ . f y(d−a2 )

As = 2,72 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3866

As= Mu

φ . f y(d−a2 )

As = 1,64 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1779

As= Mu

φ . f y(d−a2 )

As = 0,76cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3079

As= Mu

φ . f y(d−a2 )

As = 1,31 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1168

As= Mu

φ . f y(d−a2 )

As = 0,5cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4361

As= Mu

φ . f y(d−a2 )

As = 1,85cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1569

As= Mu

φ . f y(d−a2 )

As = 0,67 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,6593

As= Mu

φ . f y(d−a2 )

As = 2,8 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,3535

As= Mu

φ . f y(d−a2 )

As = 1,5 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m



Ф = 1,2cm

d = 11,9 cm


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,4412

As= Mu

φ . f y(d−a2 )

As = 1,87 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m


a=d−√d2−2(Mu )

φ(0 .85 )( f 'c )(b )

a = 0,1674

As= Mu

φ . f y(d−a2 )

As = 0,71 cm2

Usar ∅ = 12 mm c/30 cm As = 3.77 cm2/m

CALCULO DE VIGAS

Portico en la direccion corta L = 14m

1,5m 2m 1,5m 1,5m 3m 1,5m

Tramo 1=3m

Tramo 2=8m

Tramo 3=3m

Para la dirección corta L=14m

Para la azotea

Tramo 1

Carga Viva = 150kg/m2 * 1,6 = 240kg/m2

CV =

240Kgm 2

∗3m∗1,5m

23m

CV=180Kg/m * 2 = 360Kg/m

Carga Muerta = 495kg/m2 * 1,2= 594kg/m2

PPlosa=

594 Kgm2

∗3m∗1,5m

23m

PP losa = 445.5kg/m * 2= 891kg/m

PP viga = 2500kg/m3 *0,2m*0,4m = 200kg/m * 1,2= 240kg/m

PP muro = 1800kg/m3 *0,15m*3m = 810kg/m * 1,2= 972kg/m

CM total =2103 kg/m

Tramo 2


C V =

240Kgm2

∗3m∗(8m+2m)

28m

CV=450Kg/m * 2 = 900Kg/m


PPlosa=

594 Kgm2

∗3m∗(8m+2m)

28m

PP losa = 1113,75kg/m * 2= 2227,5kg/m



CM total =3439,5 kg/m

Tramo 3


CV =

240Kgm 2

∗3m∗1,5m

23m

CV=180Kg/m * 2 = 360Kg/m


PPlosa=

594 Kgm2

∗3m∗1,5m

23m

PP losa = 445.5kg/m * 2= 891kg/m



CM total =2103 kg/m

Para el tercer piso departamento

Tramo 1


CV =

400Kgm 2

∗3m∗1,5m

23m

CV=300Kg/m * 2 = 600Kg/m

Carga Muerta = 657kg/m2 * 1,2= 788,4kg/m2

PPlosa=

788,4 Kgm2

∗3m∗1,5m

23m

PP losa = 607,5/m * 2= 1215kg/m



CM total =2427 kg/m

Tramo 2


CV =

400Kgm 2

∗3m∗(8m+2m)

28m

CV=750Kg/m * 2 = 1500Kg/m


PPlosa=

788,4 Kgm2

∗3m∗(8m+2m)

28m

PP losa = 1113,75kg/m * 2= 3888,9kg/m




Tramo 3


CV =

400Kgm 2

∗3m∗1,5m

23m

CV=300Kg/m * 2 = 600Kg/m

Carga Muerta = 657kg/m2 * 1,2= 788,4kg/m2

PPlosa=

788,4 Kgm2

∗3m∗1,5m

23m

PP losa = 607,5/m * 2= 1215kg/m



CM total =2427 kg/m

Para el segundo piso salón de evento

Tramo 1


CV =

640Kgm 2

∗3m∗1,5m

23m

CV=480Kg/m * 2 = 960Kg/m


PPlosa=

594 Kgm2

∗3m∗1,5m

23m

PP losa = 607,5/m * 2= 891,5kg/m



CM total =2103 kg/m

Tramo 2


CV =

640Kgm 2

∗3m∗(8m+2m)

28m

CV=1200Kg/m * 2 = 2400Kg/m


PPlosa=

594 Kgm2

∗3m∗(8m+2m)

28m

PP losa = 1113,75kg/m * 2= 2227,5kg/m




Tramo 3


CV=

640Kgm 2

∗3m∗1,5m

23m

CV=480Kg/m * 2 = 960Kg/m


PPlosa=

594 Kgm2

∗3m∗1,5m

23m

PP losa = 607,5/m * 2= 891,5kg/m



CM total =2103 kg/m

Para el primer piso restaurant

Tramo 1


CV=

560Kgm 2

∗3m∗1,5m

23m

CV=420Kg/m * 2 = 840Kg/m


PPlosa=

594 Kgm2

∗3m∗1,5m

23m

PP losa = 607,5/m * 2= 891,5kg/m



CM total =2103 kg/m

Tramo 2


CV=

560Kgm 2

∗3m∗(8m+2m)

28m

CV=1050Kg/m * 2 = 2100Kg/m


PPlosa=

594 Kgm2

∗3m∗(8m+2m)

28m

PP losa = 1113,75kg/m * 2= 2227,5kg/m




Tramo 3


CV =

560Kgm 2

∗3m∗1,5m

23m

CV=420Kg/m * 2 = 840Kg/m


PPl osa=

594Kgm 2

∗3m∗1,5m

23m

PP losa = 607,5/m * 2= 891,5kg/m



CM total =2103 kg/m

Para la dirección larga L=16,5m

Para la azotea

Tramo 2


CVtra=

240Kgm2

∗1m∗6m

23m

CVtri=

240Kgm 2

∗1m∗4m

23m

CVtra=240Kg/m

CVtri=160Kg/m

CVT= 400kg/m


PPtra=

594 Kgm2

∗1m∗6m

23m

PPtri=

240Kgm 2

∗1m∗4m

23m

PPtra=594kg/m

PPtri =396kg/m

PP losa = 990kg/m



CM total =2202 kg/m

Tramo 3


CVtra=

240Kgm2

∗1,5m∗7m

23m

CVtri=

240Kgm 2

∗1,25m∗5m

23m

CVtra=420Kg/m

CVtri=250Kg/m

CVT= 625kg/m


PPtra=

594 Kgm2

∗1,5m∗7m

23m

PPtri=

594Kgm2

∗1,25m∗5m

23m

PPtra=1039,5kg/m

PPtri =618,75kg/m

PP losa = 1658,25kg/m




Tramo 4


CVtra=

240Kgm2

∗1,5m∗9m

23m

CVtri=

240Kgm 2

∗1,5m∗6m

23m

CVtra=540Kg/m

CVtri=360Kg/m

CVT= 900kg/m


PPtra=

594 Kgm2

∗1,5m∗9m

23m

PPtri=

594Kgm2

∗1,5m∗6m

23m

PPtra=1336,5kg/m

PPtri =891kg/m





Para el tercer piso (departamento)

Tramo 1


CV =

400Kgm 2

∗1,5m∗0,75m

23m

CVT= 400kg/m


PPlosa=

594 Kgm2

∗1,5m∗0,75m

23m





Tramo 2


CVtra=

400Kgm2

∗1m∗6m

23m

CVtri=

400Kgm2

∗1m∗4m

23m

CVtra=400Kg/m

CVtri=266,67Kg/m

CVT= 666,7kg/m


PPtra=

594 Kgm2

∗1m∗6m

23m

PPtri=

240Kgm 2

∗1m∗4m

23m

PPtra=594kg/m

PPtri =396kg/m

PP losa = 990kg/m



CM total =2202 kg/m

Tramo 3


CVtra=

400Kgm2

∗1,5m∗7m

23m

CVtri=

400Kgm2

∗1,25m∗5m

23m

CVtra=700Kg/m

CVtri=416,67Kg/m

CVT= 1116,67kg/m


PPtra=

660Kgm2

∗1,5m∗7m

23m

PPtri=

660Kgm 2

∗1,25m∗5m

23m

PPtra=1155kg/m

PPtri =687,5kg/m





Tramo 4


CVtra=

400Kgm2

∗1,5m∗9m

23m

CVtri=

400Kgm2

∗1,5m∗6m

23m

CVtra=900Kg/m

CVtri=600Kg/m

CVT= 1500kg/m


PPtra=

630Kgm2

∗1,5m∗9m

23m

PPtri=

630Kgm 2

∗1,5m∗6m

23m

PPtra=1417,5kg/m

PPtri =945kg/m





Para el segundo piso (salón de evento)

Tramo 1


CV =

600Kgm 2

∗1,5m∗0,75m

23m

CVT= 120kg/m


PPlosa=

594 Kgm2

∗1,5m∗0,75m

23m





Tramo 2


CVtra=

640Kgm2

∗1m∗6m

23m

CVtri=

640Kgm 2

∗1m∗4m

23m

CVtra=640Kg/m

CVtri=426,67 Kg/m

CVT= 1066,67kg/m


PPtra=

594 Kgm2

∗1m∗6m

23m

PPtri=

594Kgm2

∗1m∗4m

23m

PPtra=594kg/m

PPtri =396kg/m

PP losa = 990kg/m



CM total =2202 kg/m

Tramo 3


CVtra=

640Kgm2

∗1,5m∗7m

23m

CVtri=

640Kgm 2

∗1,25m∗5m

23m

CVtra=1120Kg/m

CVtri=666,67Kg/m

CVT= 1666,67kg/m


PPtra=

660Kgm2

∗1,5m∗7m

23m

PPtri=

660Kgm 2

∗1,25m∗5m

23m

PPtra=1039,5kg/m

PPtri =618,75kg/m

PP losa = 1645kg/m




Tramo 4


CVtra=

640Kgm2

∗1,5m∗9m

23m

CVtri=

640Kgm 2

∗1,5m∗6m

23m

CVtra=1440Kg/m

CVtri=960Kg/m

CVT= 2400kg/m


PPtra=

594 Kgm2

∗1,5m∗9m

23m

PPtri=

594Kgm2

∗1,5m∗6m

23m

PPtra=1336,5 kg/m

PPtri =891 kg/m





Para el primer piso (restaurant)

Tramo 1


CV=

560Kgm 2

∗1,5m∗0,75m

23m

CVT= 105kg/m


PPlosa=

594 Kgm2

∗1,5m∗0,75m

23m





Tramo 2


CVtra=

560Kgm2

∗1m∗6m

23m

CVtri=

560Kgm 2

∗1m∗4m

23m

CVtra=560Kg/m

CVtri=373,33 Kg/m

CVT= 933,33kg/m


PPtra=

594 Kgm2

∗1m∗6m

23m

PPtri=

594Kgm2

∗1m∗4m

23m

PPtra=594kg/m

PPtri =396kg/m

PP losa = 990kg/m



CM total =2202 kg/m

Tramo 3


CVtra=

560Kgm2

∗1,5m∗7m

23m

CVtri=

560Kgm 2

∗1,25m∗5m

23m

CVtra=980Kg/m

CVtri=583,33Kg/m

CVT= 1563,33kg/m


PPtra=

660Kgm2

∗1,5m∗7m

23m

PPtri=

660Kgm 2

∗1,25m∗5m

23m

PPtra=1039,5kg/m

PPtri =618,75kg/m

PP losa = 1645kg/m




Tramo 4


CVtra=

560Kgm2

∗1,5m∗9m

23m

CVtri=

560Kgm 2

∗1,5m∗6m

23m

CVtra=1260Kg/m

CVtri=840Kg/m

CVT= 2100kg/m


PPtr a=

594Kgm2

∗1,5m∗9m

23m

PPtri=

594Kgm2

∗1,5m∗6m

23m

PPtra=1336,5 kg/m

PPtri =891 kg/m





proyecto 1 va que quiere

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