Analisis y Diseño de Losa Aligerada 1º,2º,3º,4º Piso

U.N.P.R.G - FICSA ESCUELA PROFESIONAL DE INGENIERIA CIVIL

A1, A5

1 PREDIMENSIONAMIENTO

L = 2.95 m Promedio Luces

Ln (HG) = 2.5 m

Ln(GF) = 2.95 m

h >= L/18.5 16 cm

h = 20 cm

r = 2 cm

ø N°4 = 1.27 cm

2 METRADO DE CARGAS

- Carga permanente

Peso Unitario ancho trib.

300 kg/m2 0.40 m

100 kg/m2 0.40 m

247 kg/m2 0.40 m

Carga permanente = 258.80 kg/m

- Sobrecarga


200 kg/m2 0.40 m

- Carga Amplificada

Wu = 498.32 kg/m

3 CARGA DE VIGUETA

Wuv = Wu

Wuv = 498.32 Kg/m/vigueta

4 MOMENTOS POSITIVOS

Entre H y G 283.14 kg.m

Entre G y F 394.24 kg.m

5 MOMENTOS NEGATIVOS

Apoyo H 129.77 kg.m

Apoyo G 411.15 kg.m

Apoyo F 180.69 kg.m

6 DISEÑO POR FLEXION

Peralte efectivo (d)

d = 17.37 cm

En los nudos

b = 10 cm

En el centro del claro

b = 40 cm

Elementos Peso/ml

120.00 kg/m

40.00 kg/m

98.80 kg/m

DISEÑO DE LOSA ALIGERADA

ALIGERADO TIPO

Peso propio de losa

Peso piso + cielo raso

Peso tabiquería

ALIGERADO DOS TRAMOS

Peso/mlElementos

2.725 m

Mu = (Wu*Ln^2)/9 =

Mu = (Wu*Ln^2)/24 =

S/C = 80.00 kg/m

Mu = (Wu*Ln^2)/11 =

Mu = (Wu*Ln^2)/11 =

Mu = (Wu*Ln^2)/24 =

Wu = 1.4CM + 1.7CV

d = h-rec -ø/2

CONCRETO ARMADO I DISEÑO DE LOSA ALIGERADA EN UNA DIRECCIÓN


DATOS

Mu = 129.77 kg.m = 12977.08 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.90

Iteramos hasta una igualdad

As a

0.2197 0.517

0.2007 0.472

0.2004 0.472

0.2004 0.472

As = 0.20 cm2

a = 0.47 cm

, b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 180.69 kg.m = 18069.29 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.306 0.720

0.281 0.661

0.281 0.660

0.281 0.660

As = 0.28 cm2

a = 0.66 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2

Viga T con el ala en traccion

Usar 1 ø N° 4 ( As =1.27 cm2)


Usar 1 ø N° 4 ( As =1.27 cm2)

Nudos H

Nudos F



DATOS

Mu = 411.15 kg.m = 41114.86 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.696 1.638

0.657 1.547

0.656 1.543

0.655 1.542

As = 0.66 cm2

a = 1.54 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 283.14 kg.m = 28313.64 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.479 0.282

0.435 0.256

0.435 0.256

0.435 0.256

As = 0.43 cm2

a = 0.26 cm

b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.43 cm2


Usar 1 ø N° 4 ( As =1.27 cm2)

Viga T con ala en compresion

Usar 1 ø N° 3 ( As =0.71 cm2)

Nudo G

Claros HG



DATOS

Mu = 394.24 kg.m = 39423.91 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.667 0.393

0.607 0.357

0.607 0.357

0.607 0.357

As = 0.61 cm2

a = 0.36 cm

b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.61 cm2

Refuerzo considerando: H G F

As (-) 1.27 cm2 1.27 cm2

As (+) 0.71 cm2 0.71 cm2

Refuerzo por contraccion y temperatura (Ast)

pt = 0.0018 b = 100 cm

Ast = pt*b*h h = 5 cm

Ast = 0.90 cm2

St = Ab*b/Ast

St = 34.44 cm

Asumimos St = 25.00 cm

Usar 1 ø N° 3 @ 0.25 cm


Usar 1 ø N° 3 ( As =0.71 cm2)

Claros FG

1.27 cm2



Revision por cortante

cortante actuante (Vu)

Vu = 1.15*Wu*Ln/2

Vu = 845.2753

cortante tomado por el concreto (Vn)

Vn = 0.53*f¨c^1/2 *b*d

Vn = 1333.71 kg

ø*Vn = 1133.65 kg

Vu ˂ ø*Vn ok



A2, A3, A6, A7


L = 2.95 m Promedio Luces

Ln (HG) = 2.5 m

Ln(GF) = 2.95 m

Ln(FE) = 2.65 m

h >= L/21 14.05 m

h = 20 cm

r = 2 cm

ø N°4 = 1.27 cm

2 METRADO DE CARGAS

- Carga permanente


300 kg/m2 0.40 m

100 kg/m2 0.40 m

247 kg/m2 0.40 m

Carga permanente = 258.8 kg/m

- Sobrecarga


200 kg/m2 0.40 m

- carga amplificada

Wu = 498.32 kg/m

3 CARGA DE VIGUETA

Wuv = Wu





Entre F y E 249.96 kg.m


Apoyo H 129.77 kg.m

Apoyo G 370.03 kg.m

Apoyo F 390.68 kg.m

Apoyo E 145.81 kg.m



d = 17 cm

En los nudos

b = 10 cm


b = 40 cm


ALIGERADO TIPO

Peso propio de losa


Peso tabiquería

Mu = (Wu*Ln^2)/24 =

ALIGERADO TRES TRAMOS

2.725 m

Elementos Peso/ml

2.800 m

Elementos Peso/ml

S/C = 80.00 kg/m

Wu = 1.4CM + 1.7CV

d = h-rec -ø/2

Mu = (Wu*Ln^2)/14 =

Mu = (Wu*Ln^2)/16 =

Mu = (Wu*Ln^2)/24 =

Mu = (Wu*Ln^2)/10 =

Mu = (Wu*Ln^2)/10 =

Mu = (Wu*Ln^2)/14 =

120.00 kg/m

40.00 kg/m

98.80 kg/m



DATOS

Mu = 129.77 kg.m = 12977.08 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.2197 0.517

0.2007 0.472

0.2004 0.472

0.2004 0.472

As = 0.20 cm2

a = 0.47 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 145.81 kg.m = 14581.05 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.2468 0.581

0.2259 0.532

0.2256 0.531

0.2256 0.531

As = 0.23 cm2

a = 0.53 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2

Nudos H

Nudos E


Usar 1 ø N° 4 ( As =1.27 cm2)


Usar 1 ø N° 4 ( As =1.27 cm2)



DATOS

Mu = 370.03 kg.m = 37003.37 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.6264 1.474

0.5887 1.385

0.5872 1.382

0.5871 1.381

As = 0.59 cm2

a = 1.38 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 390.68 kg.m = 39068.29 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.6613 1.556

0.6231 1.466

0.5886 1.385

0.5871 1.382

As = 0.59 cm2

a = 1.38 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2



Nudo G

Nudo F

Usar 1 ø N° 4 ( As =1.27 cm2)

Usar 1 ø N° 4 ( As =1.27 cm2)



DATOS

Mu = 222.46 kg.m = 22246.43 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.3766 0.222

0.3411 0.201

0.3409 0.201

0.3409 0.201

As = 0.34 cm2

a = 0.20 cm

b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.42 cm2

DATOS

Mu = 271.04 kg.m = 27103.94 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.4588 0.270

0.4162 0.245

0.4159 0.245

0.4158 0.245

As = 0.42 cm2

a = 0.24 cm

b = bw = 10 cm

Asmin = 0.42 cm2

As requerido As = 0.42 cm2

Claros HG

Claros FG


Usar 1 ø N° 3 ( As =0.71 cm2)

Usar 1 ø N° 3 ( As =0.71 cm2)




DATOS

Mu = 249.96 kg.m = 24996.09 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.4231 0.249

0.3836 0.226

0.3833 0.225

0.3833 0.225

As = 0.38 cm2

a = 0.23 cm

b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.42 cm2

Refuerzo considerando:

H G F E

As (-) 1.27 cm2 1.27 cm2 1.27 cm2 1.27 cm2

As (+) 0.71 cm2 0.71 cm2 0.71 cm2


pt = 0.0018 b = 100.00 cm

Ast = pt*b*h h = 5.00 cm

Ast = 0.90 cm

St = Ab*b/Ast

St = 78.89 cm

Asumimos, St = 25.00 cm

Claros FE

Usar 1 ø N° 3 @ 0.25 cm


Usar 1 ø N° 3 ( As =0.71 cm2)





Vu = 1.15*Wu*Ln/2

Vu = 845.2753


Vn = 0.53*f¨c^1/2 *b*d

Vn = 1333.71 kg

ø*Vn = 1133.65 kg

Vu ˂ ø*Vn ok



A4


L = 2.95 m promedio luces

Ln (HG) = 2.5 m

Ln(GF) = 2.95 m

Ln(FE) = 2.65 m 2.80

Ln(ED) = 2.4 m 2.53

Ln(DC) = 2.65 m 2.53

Ln(CB) = 2.95 m 2.80

Ln(BA) = 2.5 m 2.73

h >= L/21 14.05 m

h = 20.00 cm

r = 2 cm

ø N°4 = 1.27 cm

2 METRADO DE CARGAS

- Carga permanente


300 kg/m2 0.40 m

100 kg/m2 0.40 m

330 kg/m2 0.40 m

Carga permanente = 292 kg/m

- Sobrecarga


100 kg/m2 0.40 m

- carga amplificada

Wu = 476.8 kg/m

3 CARGA DE VIGUETA

Wuv = Wu





Entre F y E 209.27 kg.m

Entre E y D 171.65 kg.m

Entre D y C 209.27 kg.m

Entre C y B 259.33 kg.m

Entre B y A 212.86 kg.m


Apoyo H 124.17 kg.m

Apoyo G 354.05 kg.m

Apoyo F 339.83 kg.m

Apoyo E 276.35 kg.m

Apoyo D 276.35 kg.m

Apoyo C 339.83 kg.m

Apoyo B 354.05 kg.m

Apoyo A 124.17 kg.m

Wu = 1.4CM + 1.7CV

S/C =

132.00 kg/m

Elementos Peso/ml


Peso tabiquería

2.725 m

Elementos Peso/ml

120.00 kg/m

40.00 kg/m


ALIGERADO TIPO

Peso propio de losa

Mu = (Wu*Ln^2)/14 =

Mu = (Wu*Ln^2)/16 =

Mu = (Wu*Ln^2)/16 =

Mu = (Wu*Ln^2)/24 =

Mu = (Wu*Ln^2)/10 =

Mu = (Wu*Ln^2)/10 =

Mu = (Wu*Ln^2)/16 =

Mu = (Wu*Ln^2)/16 =

Mu = (Wu*Ln^2)/16 =

40.00 kg/m

ALIGERADO SIETE TRAMOS

Mu = (Wu*Ln^2)/14 =

Mu = (Wu*Ln^2)/24 =

Mu = (Wu*Ln^2)/11 =

Mu = (Wu*Ln^2)/11 =

Mu = (Wu*Ln^2)/11 =

Mu = (Wu*Ln^2)/11 =





d = 17 cm

En los nudos

b = 10 cm


b = 40 cm

DATOS

Mu = 124.17 kg.m = 12416.67 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.210 0.495

0.192 0.452

0.192 0.451

0.192 0.451

As = 0.19 cm2

a = 0.45 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 276.35 kg.m = 27635.44 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.468 1.101

0.435 1.023

0.434 1.021

0.434 1.021

As = 0.43 cm2

a = 1.02 cm

Nudos H y A

Nudos E y D


d = h-rec -ø/2


Usar 1 ø N° 4 ( As =1.27 cm2)



b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 354.05 kg.m = 35405.38 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.599 1.410

0.562 1.323

0.561 1.319

0.561 1.319

As = 0.56 cm2

a = 1.32 cm

b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 339.83 kg.m = 33982.84 kg.cm

d = 17.37 cm

b = 10 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.575 1.354

0.539 1.268

0.560 1.317

0.561 1.319

As = 0.56 cm2

a = 1.32 cm

Nudo G y B

Nudo F y C

Usar 1 ø N° 4 ( As =1.27 cm2)


Usar 1 ø N° 4 ( As =1.27 cm2)




b = 2bw = 20 cm

Asmin = 0.84 cm2

DATOS

Mu = 212.86 kg.m = 21285.71 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.360 0.212

0.326 0.192

0.326 0.192

0.326 0.192

As = 0.33 cm2

a = 0.19 cm

b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.42 cm2

DATOS

Mu = 259.33 kg.m = 25933.45 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.439 0.258

0.398 0.234

0.398 0.234

0.398 0.234

As = 0.40 cm2

a = 0.23 cm

Claros HG y AB

Claros FG y BC

Usar 1 ø N° 4 ( As =1.27 cm2)


Usar 1 ø N° 3 ( As =0.71 cm2)




b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.42 cm2

DATOS

Mu = 209.27 kg.m = 20927.05 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.354 0.208

0.321 0.189

0.321 0.189

0.321 0.189

As = 0.32 cm2

a = 0.19 cm

b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.42 cm2

DATOS

Mu = 171.65 kg.m = 17164.80 kg.cm

d = 17.37 cm

b = 40 cm

f¨c = 210 kg/cm2

f¨y = 4200 kg/cm2

ø = 0.9


As a

0.291 0.171

0.263 0.155

0.263 0.155

0.263 0.155

As = 0.26 cm2

a = 0.15 cm

Claros ED

Claros FE y DC


Usar 1 ø N° 3 ( As =0.71 cm2)


Usar 1 ø N° 3 ( As =0.71 cm2)



b = bw = 10 cm

Asmin = 0.42 cm2

As = 0.42 cm2

Refuerzo considerando:

H G F E D C B A

As (-) 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27

As (+) 0.71 0.71 0.71 0.71 0.71 0.71 0.71


pt = 0.0018 b = 100.00 cm

Ast = pt*b*h h = 5.00 cm

Ast = 0.90 cm

St = Ab*b/Ast

St = 78.89 cm

Asumimos, St = 25.00 cm



Vu = 1.15*Wu*Ln/2

Vu = 808.772


Vn = 0.53*f¨c^1/2 *b*d

Vn = 1333.71 kg

ø*Vn = 1133.65 kg

Vu ˂ ø*Vn ok

Usar 1 ø N° 3 @ 0.25 cm

Usar 1 ø N° 3 ( As =0.71 cm2)


Analisis y Diseño de Losa Aligerada 1º,2º,3º,4º Piso

Documents

Transcript of Analisis y Diseño de Losa Aligerada 1º,2º,3º,4º Piso