losa alivianada con plastoformo en dos direcciones(2)

LOSA ALIVIANADA CON PLASTOFORMO ARMADA EN DOS DIRECCIONES

vista de corteVIGAS 25 X 45 [cm]COLUMNAS 45 X 45 [cm]fc' 280 [kgf/cm2]fy 4200 [kgf/cm2]CASETON 40 X 40 [cm]h DE LOSA 20 [cm]CARGA VIVA 180 [kgf/m2]μ 0.2

2400 [kg/m3] bw= 0.102200 [kg/m3]1150 [kg/m3]

10 [kg/m3]A. Analisis 0.5 X 0.5 [m]P.ceramico 10 [kgf/m2] acero longitudinal =contrapiso 0.03 [m] acero transversal =Recubrimi. 2 [cm]

0.003252671

2038902 [kgf/cm2]1. EJE NEUTRO

Seccion b h A y A*y I1 0.10 0.15 0.015 0.075 0.001125 2.81E-052 0.50 0.05 0.025 0.175 0.004 5.21E-06

∑= 0.04 ∑= 0.006 3.33E-05

yp = 0.137 [m]

1.27E-04 [m4]

2. ALTURA DE LA LOSA EQUIVALENTE

hp = 0.145 [m]

3. PESO EQUIVALENTE

gcgsimple

gyeso

gplastoformo

ξ c

E cE s

Ip =

A

yAy p

*

3*12

cw

pp bb

Ih

)( yyAII pp

Elemento b h lnervio 0.10 0.15 0.90 2400 32.40losa compr. 0.50 0.05 0.50 2400 30.00caseton 0.40 0.15 0.40 10 0.24

∑= 62.64

1727.74 [kgf/m3]

4. MASA POR UNIDAD DE VOLUMEN

ρe = 176.12 [kgf s2/m4]

5. MODULO DE ELASTICIDAD

Ec = 252671 [kgf/cm2]

6. MODULO DE CORTE

Gc = 105280 [kgf/cm2]

7.ESPESOR DE LOSA

Eje Condicionlong. Transversal viga losa

izq. [m] der. [m] b [m] h [m ]3 si 0.00 5.00 0.25 0.45 2.625B no 5.00 5.00 0.25 0.45 5.0002 no 4.50 5.00 0.25 0.45 4.750A si 0.00 5.00 0.25 0.45 2.625

2.19

losa = 5 [m]= 5 [m]

4.55columna = 0.45 [m]

= 0.45 [m]

gc W=gcbhl

ge =

l 2 [m]

αfm =

l c

l l

l n =C 1

C 2

pcwcwe hbbb

W

))(( g

ge

e

g

cc fE '15100

)1(2 c

c

EG

44321

fm

2,0fm

β = 1

8. CARGAS

losa a compresion = 120 [kg/m2]viguetas in situ = 129.6 [kg/m2]piso ceramico = 10 [kg/m2]contrapiso = 66 [kg/m2]cielo raso de yeso = 23 [kg/m2]plastoformo = 0.96 [kg/m2]

∑ = 349.56 [kg/m2]

= 349.56 [kg/m2]= 180 [kg/m2]= 707 [kg/m2]

9. AREA DE ACERO MINIMO

d = 17 [cm]

valor mayor de :0.0032

0.00330.0033

0.56 [cm2] 2f8

Mu = 0.61 [t.m]

10. AREA DE ACERO MAXIMA

WD

WL

WU

ρmin =

Asmin =

2

1

c

c

c

2,0fm

22.0 fm

2fm

2l

t

ddrhd

y

c

f

f '8.0

yf

14min

dbA ws **minmin

)'85,0*2

(bf

fAdfAM

c

ysysu f

0.0286

zonas sismicas fuertes

zonas sismicas moderadas

usamos zona moderada

= 0.021

3.62 [cm2]

11. AREA DE ACEROS Ø = 0.9

Num. Losa Lx/Ly d

1 707 6 5 5 1 406

2 707 3 5 5 1 265

3 707 6 5 5 1 406

4 707 6 4.5 5 0.9 489

5 707 3 4.5 5 0.9 297

6 707 6 4.5 5 0.9 489

12. VERIFICACION A CORTANTE Ø = 0.85

β1 =

ρb =

ρmax

Asmax =

q [kg/m2]

losa tipo

Lx[m]

Ly [m]

]/[560'280 2cmkgf c

]/[560' 2cmkgf c

]/[280' 2cmkgf c 85,01

70

280'05,085,01

cf

65,01

yss

sc

y

cb fE

E

f

f

*'85,0 1

b 5,0max

b 75,0max

dbA ws maxmax

Vc = 1273.97 [kgf]

4.551489.94 [kgf]

6Av = 0.28 [cm2]

S = 83.81 [cm]

13. AREAS DE ACEROS POR TEMPERATURA EN LOSA DE COMPRESION

0.9

14. LONGITUD ACERO A FLEXIONAncho de la viga b 0.25 m

14.1 Para longitud corta Lx = 4.5 m

Ln= 4.25 m

borde al medio|

bm= 1.06 m

borde exterior

be= 1.185 m

14.2. Para logitud larga Ly= 5 m

ln= 4.75 m

Borde al medio

bm= 1.17 m

Borde externo

l n =Vud =

acero Ø =

Asmin =

𝑙_𝑛=𝑙_𝑥-𝑏

𝑏_𝑚=0,22𝑙_𝑛+𝑏/2

𝑏_𝑒=〖 0,22𝑙〗 _𝑛+𝑏𝑙_𝑛=𝑙_𝑦−𝑏𝑏_𝑚=0,22𝑙_𝑛+𝑏/2

dbfV wcc '*53.0 f

dWW

V unu

ud 2

cud

ytv

VV

dfAS

ff

bhAs 0018,0min

be= 1.295 m𝑏_𝑒=0,22𝑙_𝑛+b

LOSA ALIVIANADA CON PLASTOFORMO ARMADA EN DOS DIRECCIONES

hf= 0.05

hb= 0.15

[m] 0.10 bc= 0.40 0.10 [m]lc = 0.40

vista plantaacero longitudinal = 8 [mm]acero transversal = 6 [mm] 0.10

0.40

A(yp-y)^2 0.10 0.405.86E-053.52E-05

9.37E-05

losahp [m]0.145 2.8450.145 1.4940.145 1.5720.145 2.845

∑= 8.757

[m]

tabla 9.5

3

2

))((*

*

pscs

bcbf h

hb

IE

IE

cm

f

hfm

yn

5.12)2.0(536

140008.0

h = 0.111 [m]

1.01 (cm2)Asr =

cm

f

hfm

yn

5.12)2.0(536

140008.0

cm

f

h

yn

5.12936

140008.0

0.85

my (-) my (+) mx(-) mx(+)

839 428 839 428 1484 757 1484 757

718 354 597 269 1270 626 1056 476

839 428 839 428 1484 757 1484 757

980 525 857 409 1404 752 1228 586

790 401 586 240 1132 574 840 344

980 525 857 409 1404 752 1228 586

Muy(-) [kg.m]/m

Muy(+) [kg.m]/m

Mux(-) [kg.m]/m

Mux(+) [kg.m]/m

colocar estribos

0.57usar45cm

6 c/ 31acero Ø =

LOSA ALIVIANADA CON PLASTOFORMO ARMADA EN DOS DIRECCIONES

[m]

[m]

2.70 1.27 2.70 1.27 0.231f10 1f16 1f8 1f10 1f10 1f16 1f8 1f10

2.25 1.04 1.83 0.78 0.152f12 1f8 1f10 1f10 1f12 2f8

2.70 1.27 2.70 1.27 0.231f10 1f16 1f8 1f10 1f10 1f16 1f8 1f10

2.53 1.26 2.17 0.97 0.181f10 1f16 1f8 1f10 2f12 2f8

1.98 0.95 1.42 0.55 0.112f12 2f8 2f10 2f8

2.53 1.26 2.17 0.97 0.181f10 1f16 1f8 1f10 2f12 2f8

Asy (-)[cm2]/m

Asy (+)[cm2]/m

Asx (-)[cm2]/m

Asx (+)[cm2]/m

Δ[cm]

1

d my (-) my (+) mx(-)1 200 564 258 564

0.9 241 659 319 5770.8 281 752 378 5740.7 315 830 428 5590.6 336 878 459 5380.5 339 887 464 520

2

d my (-) my (+) mx(-)1 265 597 269 718

0.9 347 736 362 7790.8 443 899 473 8190.7 545 1071 590 8290.6 635 1222 694 8080.5 691 1317 759 773

3

d my (-) my (+) mx(-)1 265 718 354 597

0.9 297 790 401 5860.8 322 850 439 5680.7 339 888 464 5480.6 345 902 473 5320.5 339 888 464 520

4

d my (-) my (+) mx(-)1 323 0 231 853

0.9 456 0 340 9850.8 644 0 496 11190.7 894 0 705 12320.6 1191 0 952 12880.5 1479 0 1191 1268

5

d my (-) my (+) mx(-)1 323 853 440 0

0.9 340 891 465 00.8 351 914 481 00.7 354 921 485 00.6 348 909 477 00.5 335 878 458 0

6

d my (-) my (+) mx(-)1 406 839 428 839

0.9 489 980 525 8570.8 572 1120 621 8520.7 644 1240 704 8270.6 693 1323 761 7930.5 712 1353 782 764

7

d my (-) my (+) mx(-)1 569 1118 616 0

70.9 630 1220 687 00.8 681 1303 746 00.7 715 1360 785 00.6 729 1382 802 00.5 718 1364 790 0

8

d my (-) my (+) mx(-)1 569 0 433 1118

0.9 754 0 587 12250.8 979 0 775 13040.7 1230 0 984 13340.6 1469 0 1183 13080.5 1644 0 1329 1246

9

d my (-) my (+) mx(-)1 969 0 765 0

0.9 1170 0 932 00.8 1371 0 1101 00.7 1550 0 1250 00.6 1684 0 1361 00.5 1749 0 1416 0

mx(+)258242208157126123

mx(+)354368359318239179

mx(+)269240205185167177

mx(+)440498547566525400

mx(+)231199183174165178

mx(+)428409369310271238

mx(+)433

375311269252238

mx(+)616654659615527434

mx(+)765737665547439397

0 1.01

1.01 1.29

1.29 1.57

1.57 1.63

1.63 1.92

1.92 2.26

2.26 2.80

2.80 3.14

3.14 4.02

4.02 4.27

4.27 5.15

5.15 6.28

6.28 6.92

6.92 8.05

8.05 9.82

9.82

SECCIÓN TRANSVERSAL DE BARRAS CIRCULARES PARA ARMADURA (Norma DIN 488)

NÚMERO DE BARRAS

1 2 3 4

0.222 1/4 6 0.28 0.57 0.85 1.13

0.395 5/16 8 0.50 1.01 1.51 2.01

0.617 # 3 3/8 10 0.79 1.57 2.36 3.14

0.888 # 4 1/2 12 1.13 2.26 3.39 4.52

1.58 # 5 5/8 16 2.01 4.02 6.03 8.04

2.47 # 6 3/4 20 3.14 6.28 9.42 12.57

3.85 # 8 1 25 4.91 9.82 14.73 19.63

ÁREAS PARA 1 m DE ANCHO

SEPARACIÓN (cm)

5 6 7 8 9

1/4 6 5.65 4.71 4.04 3.53 3.14

5/16 8 10.05 8.38 7.18 6.28 5.59

# 3 3/8 10 15.71 13.09 11.22 9.82 8.73

# 4 1/2 12 22.62 18.85 16.16 14.14 12.57

# 5 5/8 16 40.21 33.51 28.72 25.13 22.34

# 6 3/4 20 62.83 52.36 44.88 39.27 34.91

2f8 2f8

1f8 + 1f10 1f8 + 1f10

2f10 2f10

1f8 + 1f12 1f8 + 1f12

1f10 + 1f12 1f10 + 1f12

2f12 2f12

1f10 + 1f16 1f10 + 1f16

1f12 + 1f16 1f12 + 1f16

2f16 2f16

1f12 + 1f20 1f12 + 1f20

1f16 + 1f20 1f16 + 1f20

2f20 2f20

1f16 + 1f25 1f16 + 1f25

1f20 + 1f25 1f20 + 1f25

2f25 2f25

2f25

Peso

(kgf/m)

Númerode

barra a

Diámetro a

(in)

DiámetroNominal

(mm)

SECCIONES NOMINALES (cm2)

Númerode

barra a

Diámetro a

(in)

DiámetroNominal

(mm)

SECCIONES TRANSVERSALES (cm2)

# 8 1 25 98.17 81.81 70.12 61.36 54.54

SECCIÓN TRANSVERSAL DE BARRAS CIRCULARES PARA ARMADURA (Norma DIN 488)

NÚMERO DE BARRAS

5 6 7 8 9 10 11 12

1.41 1.70 1.98 2.26 2.54 2.83 3.11 3.39

2.51 3.02 3.52 4.02 4.52 5.03 5.53 6.03

3.93 4.71 5.50 6.28 7.07 7.85 8.64 9.42

5.65 6.79 7.92 9.05 10.18 11.31 12.44 13.57

10.05 12.06 14.07 16.08 18.10 20.11 22.12 24.13

15.71 18.85 21.99 25.13 28.27 31.42 34.56 37.70

24.54 29.45 34.36 39.27 44.18 49.09 54.00 58.90

ÁREAS PARA 1 m DE ANCHO

SEPARACIÓN (cm)

10 11 12 13 14 15 16 17

2.83 2.57 2.36 2.17 2.02 1.88 1.77 1.66

5.03 4.57 4.19 3.87 3.59 3.35 3.14 2.96

7.85 7.14 6.54 6.04 5.61 5.24 4.91 4.62

11.31 10.28 9.42 8.70 8.08 7.54 7.07 6.65

20.11 18.28 16.76 15.47 14.36 13.40 12.57 11.83

31.42 28.56 26.18 24.17 22.44 20.94 19.63 18.48

SECCIONES NOMINALES (cm2)

SECCIONES TRANSVERSALES (cm2)

49.09 44.62 40.91 37.76 35.06 32.72 30.68 28.87

SECCIÓN TRANSVERSAL DE BARRAS CIRCULARES PARA ARMADURA (Norma DIN 488)

NÚMERO DE BARRAS

13 14 15 16 17 18 19 20

3.68 3.96 4.24 4.52 4.81 5.09 5.37 5.65

6.53 7.04 7.54 8.04 8.55 9.05 9.55 10.05

10.21 11.00 11.78 12.57 13.35 14.14 14.92 15.71

14.70 15.83 16.96 18.10 19.23 20.36 21.49 22.62

26.14 28.15 30.16 32.17 34.18 36.19 38.20 40.21

40.84 43.98 47.12 50.27 53.41 56.55 59.69 62.83

63.81 68.72 73.63 78.54 83.45 88.36 93.27 98.17

ÁREAS PARA 1 m DE ANCHO

SEPARACIÓN (cm)

18 19 20 21 22 23 24 25

1.57 1.49 1.41 1.35 1.29 1.23 1.18 1.13

2.79 2.65 2.51 2.39 2.28 2.19 2.09 2.01

4.36 4.13 3.93 3.74 3.57 3.41 3.27 3.14

6.28 5.95 5.65 5.39 5.14 4.92 4.71 4.52

11.17 10.58 10.05 9.57 9.14 8.74 8.38 8.04

17.45 16.53 15.71 14.96 14.28 13.66 13.09 12.57

SECCIONES NOMINALES (cm2)

SECCIONES TRANSVERSALES (cm2)

27.27 25.84 24.54 23.37 22.31 21.34 20.45 19.63

SECCIÓN TRANSVERSAL DE BARRAS CIRCULARES PARA ARMADURA (Norma DIN 488)

NÚMERO DE BARRAS

21 22 23 24 25 26 27 28

5.94 6.22 6.50 6.79 7.07 7.35 7.63 7.92

10.56 11.06 11.56 12.06 12.57 13.07 13.57 14.07

16.49 17.28 18.06 18.85 19.63 20.42 21.21 21.99

23.75 24.88 26.01 27.14 28.27 29.41 30.54 31.67

42.22 44.23 46.24 48.25 50.27 52.28 54.29 56.30

65.97 69.12 72.26 75.40 78.54 81.68 84.82 87.96

103.08 107.99 112.90 117.81 122.72 127.63 132.54 137.44

ÁREAS PARA 1 m DE ANCHO

SEPARACIÓN (cm)

26 27 28 29 30 31 32 33

1.09 1.05 1.01 0.97 0.94 0.91 0.88 0.86

1.93 1.86 1.80 1.73 1.68 1.62 1.57 1.52

3.02 2.91 2.80 2.71 2.62 2.53 2.45 2.38

4.35 4.19 4.04 3.90 3.77 3.65 3.53 3.43

7.73 7.45 7.18 6.93 6.70 6.49 6.28 6.09

12.08 11.64 11.22 10.83 10.47 10.13 9.82 9.52

SECCIONES NOMINALES (cm2)

SECCIONES TRANSVERSALES (cm2)

18.88 18.18 17.53 16.93 16.36 15.83 15.34 14.87

SECCIÓN TRANSVERSAL DE BARRAS CIRCULARES PARA ARMADURA (Norma DIN 488)

NÚMERO DE BARRAS

29 30 31 32 33 34 35 36

8.20 8.48 8.77 9.05 9.33 9.61 9.90 10.18

14.58 15.08 15.58 16.08 16.59 17.09 17.59 18.10

22.78 23.56 24.35 25.13 25.92 26.70 27.49 28.27

32.80 33.93 35.06 36.19 37.32 38.45 39.58 40.72

58.31 60.32 62.33 64.34 66.35 68.36 70.37 72.38

91.11 94.25 97.39 100.53 103.67 106.81 109.96 113.10

142.35 147.26 152.17 157.08 161.99 166.90 171.81 176.71

ÁREAS PARA 1 m DE ANCHO

SEPARACIÓN (cm)

34 35 36 37 38 39 40 41

0.83 0.81 0.79 0.76 0.74 0.72 0.71 0.69

1.48 1.44 1.40 1.36 1.32 1.29 1.26 1.23

2.31 2.24 2.18 2.12 2.07 2.01 1.96 1.92

3.33 3.23 3.14 3.06 2.98 2.90 2.83 2.76

5.91 5.74 5.59 5.43 5.29 5.16 5.03 4.90

9.24 8.98 8.73 8.49 8.27 8.06 7.85 7.66

14.44 14.02 13.64 13.27 12.92 12.59 12.27 11.97

SECCIÓN TRANSVERSAL DE BARRAS CIRCULARES PARA ARMADURA (Norma DIN 488)Ing. Vladimir Aliendre

NÚMERO DE BARRAS

37 38 39 40

10.46 10.74 11.03 11.31

18.60 19.10 19.60 20.11

29.06 29.85 30.63 31.42

41.85 42.98 44.11 45.24

74.39 76.40 78.41 80.42

116.24 119.38 122.52 125.66

181.62 186.53 191.44 196.35

ÁREAS PARA 1 m DE ANCHO

SEPARACIÓN (cm)

42 43 44 45

0.67 0.66 0.64 0.63

1.20 1.17 1.14 1.12

1.87 1.83 1.78 1.75

2.69 2.63 2.57 2.51

4.79 4.68 4.57 4.47

7.48 7.31 7.14 6.98

11.69 11.42 11.16 10.91

Ing. Vladimir Aliendre

6 8 100 45 0 45 0

0.63 44 1.12 44 15.71

0.64 43 1.14 43 13.09

0.66 42 1.17 42 11.22

0.67 41 1.20 41 9.82

0.69 40 1.23 40 8.73

0.71 39 1.26 39 7.85

0.72 38 1.29 38 7.14

0.74 37 1.32 37 6.54

0.76 36 1.36 36 6.04

0.79 35 1.40 35 5.61

0.81 34 1.44 34 5.24

0.83 33 1.48 33 4.91

0.86 32 1.52 32 4.62

0.88 31 1.57 31 4.36

0.91 30 1.62 30 4.13

0.94 29 1.68 29 3.93

0.97 28 1.73 28 3.74

1.01 27 1.80 27 3.57

1.05 26 1.86 26 3.41

1.09 25 1.93 25 3.27

1.13 24 2.01 24 3.14

1.18 23 2.09 23 3.02

1.23 22 2.19 22 2.91

1.29 21 2.28 21 2.80

1.35 20 2.39 20 2.71

1.41 19 2.51 19 2.62

1.49 18 2.65 18 2.53

1.57 17 2.79 17 2.45

1.66 16 2.96 16 2.38

1.77 15 3.14 15 2.31

1.88 14 3.35 14 2.24

2.02 13 3.59 13 2.18

2.17 12 3.87 12 2.12

2.36 11 4.19 11 2.07

2.57 10 4.57 10 2.01

2.83 9 5.03 9 1.96

3.14 8 5.59 8 1.92

3.53 7 6.28 7 1.87

4.04 6 7.18 6 1.83

4.71 5 8.38 5 1.78

5.65 45 10.05 45 1.75

12 165 0 5 0 56 22.62 6 40.21 67 18.85 7 33.51 78 16.16 8 28.72 89 14.14 9 25.13 9

10 12.57 10 22.34 1011 11.31 11 20.11 1112 10.28 12 18.28 1213 9.42 13 16.76 1314 8.70 14 15.47 1415 8.08 15 14.36 1516 7.54 16 13.40 1617 7.07 17 12.57 1718 6.65 18 11.83 1819 6.28 19 11.17 1920 5.95 20 10.58 2021 5.65 21 10.05 2122 5.39 22 9.57 2223 5.14 23 9.14 2324 4.92 24 8.74 2425 4.71 25 8.38 2526 4.52 26 8.04 2627 4.35 27 7.73 2728 4.19 28 7.45 2829 4.04 29 7.18 2930 3.90 30 6.93 3031 3.77 31 6.70 3132 3.65 32 6.49 3233 3.53 33 6.28 3334 3.43 34 6.09 3435 3.33 35 5.91 3536 3.23 36 5.74 3637 3.14 37 5.59 3738 3.06 38 5.43 3839 2.98 39 5.29 3940 2.90 40 5.16 4041 2.83 41 5.03 4142 2.76 42 4.90 4243 2.69 43 4.79 43

44 2.63 44 4.68 4445 2.57 45 4.57 4545 2.51 45 4.47 45

20 250 5 0 5

62.83 6 98.17 652.36 7 81.81 744.88 8 70.12 839.27 9 61.36 934.91 10 54.54 1031.42 11 49.09 1128.56 12 44.62 1226.18 13 40.91 1324.17 14 37.76 1422.44 15 35.06 1520.94 16 32.72 1619.63 17 30.68 1718.48 18 28.87 1817.45 19 27.27 1916.53 20 25.84 2015.71 21 24.54 2114.96 22 23.37 2214.28 23 22.31 2313.66 24 21.34 2413.09 25 20.45 2512.57 26 19.63 2612.08 27 18.88 2711.64 28 18.18 2811.22 29 17.53 2910.83 30 16.93 3010.47 31 16.36 3110.13 32 15.83 329.82 33 15.34 339.52 34 14.87 349.24 35 14.44 358.98 36 14.02 368.73 37 13.64 378.49 38 13.27 388.27 39 12.92 398.06 40 12.59 407.85 41 12.27 417.66 42 11.97 427.48 43 11.69 43

7.31 44 11.42 447.14 45 11.16 456.98 45 10.91 45