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HORMIGÓN ARMADO II TEMA LOSAS M kg-f /cm 48468
b
d
-129839
10C
13
=
M . b.d2.fcd 48468 .= 0.022 < 0.319 100cm .132.133 kg-f/cm 129838 = 0.058< 0.319 100cm .132.133 kg-f/cm 107320 = 0.048 < 0.319 100cm .132.133 kg-f/cm
107320
fcd = 133 kg-f cm fyd = 3565 kg-f cm
d =13 As r =2
-1298.38
-
-
48460
1073.20
C
C
T
T
As
As
< 0.319
(+)
M
As´
Si
< 0.319
Armadura de compresión
As ω=
(1 +
)
0.022 (1 + 0.022 ) =0.022 0.022 (1 + 0.022 ) =0.061 0.022 (1 + 0.022 ) =0.050
As = ω. b . d . fcd fyd 0.022 x 100 x 13 x 133 = 1.07 cm2 3565 0.061 x 100 x 13 x 133 = 2.96 cm2 3565 0.050 x 100 x 13 x 133 = 2.42 cm2 3565
As cuantia
= As b.d As cuantia
min = 2 x 100 cm x 13 cm = 2.6 cm 1000
Ascuantia
Asmax As cargas As cuantia
2.6
2.6 cm2
2.6
2.96 cm2
2.6
2.6 cm2
Separación As = 2.6 cm – b x 100 cm AƟ12 = π x 1.2 cm2 2 = 1.13 cm2
S = AƟ12 . b As S = 1.13 cm2 . 100cm 2.6 cm S = 13.46 cm2 Smax = 30 cm
M kg-f /cm 48468
As Requerida 2.6 cm2
Ɵ
-129839
2.96 cm2
10
107320
2.6 cm2
S = AƟ12 . b As 0.78 cm2 x 100cm x 30 cm = 30 cm 2.6 cm 0.78 cm2 x 100cm = 26.35 cm => adoptamos 25 2.96 cm 0.78cm2 x 100cm = 30 cm 2.6 cm
AƟ12 = π x 10 cm2 = 0.78 cm2 4 Ascd = A1Ɵ . b S 0.78 cm2 x 100cm 30 cm 2 0.78 cm x 100cm 25 cm 0.78cm2 x 100cm 30 cm
≥ Asrequerida = 2.6 cm2 ≥ 2.6 cm2 (ok) = 3.12 cm2 ≥ 2.6 cm2 (ok) = 2.6 cm2 ≥ 2.6 cm2 (ok)
Verificando cuantía del trabajo Cuantia de trabajo c = As . b.d 2.6 cm2 = 0.002 100cm x 13 cm 3.12 cm2 = 0.002 100cm x 13 cm 2.6 cm2 = 0.002 100cm x 13 cm
min ≥ 0.0020 √ (ok) ≥ 0.0020 √ (ok) ≥ 0.0020 √ (ok) ω=
M 143820
143820 kg-f/cm2 100cm x 132cm x 138 kg-f/cm2 = 0.064 ≤ 0.319
(1 +
)
0.064 (1+0.069) =0.068
Ascuantia
Asmax As cargas As cuantia
S = AƟ12 . b As
2.6 cm2
3.30 cm2
0.78cm2 x 100cm 3.30 cm2 = 23.63 cm2 => adoptamos S =20 cm
As = ω. b . d . fcd fyd 0.068 x 100 x 13 x 133 3565 =3.30 cm2 Ascolocada Ascd = A1Ɵ . b ≥ Asrequerida S 0.78cm2 x 100cm 75 cm2 = 3.9 cm2 ≥ 3.3 cm (ok)
Trabajo T= As . ≥ b.d
min
3.9 = 0.003 ≥ 0.002 √ (ok) 100 x 13
M kg-f/cm
Ɵ
Ly
48460
10 c / 30
8m
-124838
10 c / 25
8m
107320
10 c / 30
8m
14320
10 c / 20
8m
N piezas Np = L S 8 + 0.30 m 8 + 0.25 m 8 + 0.30 m 8 + 0.20 m
1 = 27.66 1 = 33 1 = 27.66 1 = 41
b
d
-129839
10C
13
=
M . b.d2.fcd 48468 .= 0.022 < 0.319 100cm .132.133 kg-f/cm 129838 = 0.058< 0.319 100cm .132.133 kg-f/cm 107320 = 0.048 < 0.319 100cm .132.133 kg-f/cm
107320
fcd = 133 kg-f cm fyd = 3565 kg-f cm
d =13 As r =2
-1298.38
-
-
48460
1073.20
C
C
T
T
As
As
< 0.319
(+)
M
As´
Si
< 0.319
Armadura de compresión
As ω=
(1 +
)
0.022 (1 + 0.022 ) =0.022 0.022 (1 + 0.022 ) =0.061 0.022 (1 + 0.022 ) =0.050
As = ω. b . d . fcd fyd 0.022 x 100 x 13 x 133 = 1.07 cm2 3565 0.061 x 100 x 13 x 133 = 2.96 cm2 3565 0.050 x 100 x 13 x 133 = 2.42 cm2 3565
As cuantia
= As b.d As cuantia
min = 2 x 100 cm x 13 cm = 2.6 cm 1000
Ascuantia
Asmax As cargas As cuantia
2.6
2.6 cm2
2.6
2.96 cm2
2.6
2.6 cm2
Separación As = 2.6 cm – b x 100 cm AƟ12 = π x 1.2 cm2 2 = 1.13 cm2
S = AƟ12 . b As S = 1.13 cm2 . 100cm 2.6 cm S = 13.46 cm2 Smax = 30 cm
M kg-f /cm 48468
As Requerida 2.6 cm2
Ɵ
-129839
2.96 cm2
10
107320
2.6 cm2
S = AƟ12 . b As 0.78 cm2 x 100cm x 30 cm = 30 cm 2.6 cm 0.78 cm2 x 100cm = 26.35 cm => adoptamos 25 2.96 cm 0.78cm2 x 100cm = 30 cm 2.6 cm
AƟ12 = π x 10 cm2 = 0.78 cm2 4 Ascd = A1Ɵ . b S 0.78 cm2 x 100cm 30 cm 2 0.78 cm x 100cm 25 cm 0.78cm2 x 100cm 30 cm
≥ Asrequerida = 2.6 cm2 ≥ 2.6 cm2 (ok) = 3.12 cm2 ≥ 2.6 cm2 (ok) = 2.6 cm2 ≥ 2.6 cm2 (ok)
Verificando cuantía del trabajo Cuantia de trabajo c = As . b.d 2.6 cm2 = 0.002 100cm x 13 cm 3.12 cm2 = 0.002 100cm x 13 cm 2.6 cm2 = 0.002 100cm x 13 cm
min ≥ 0.0020 √ (ok) ≥ 0.0020 √ (ok) ≥ 0.0020 √ (ok) ω=
M 143820
143820 kg-f/cm2 100cm x 132cm x 138 kg-f/cm2 = 0.064 ≤ 0.319
(1 +
)
0.064 (1+0.069) =0.068
Ascuantia
Asmax As cargas As cuantia
S = AƟ12 . b As
2.6 cm2
3.30 cm2
0.78cm2 x 100cm 3.30 cm2 = 23.63 cm2 => adoptamos S =20 cm
As = ω. b . d . fcd fyd 0.068 x 100 x 13 x 133 3565 =3.30 cm2 Ascolocada Ascd = A1Ɵ . b ≥ Asrequerida S 0.78cm2 x 100cm 75 cm2 = 3.9 cm2 ≥ 3.3 cm (ok)
Trabajo T= As . ≥ b.d
min
3.9 = 0.003 ≥ 0.002 √ (ok) 100 x 13
M kg-f/cm
Ɵ
Ly
48460
10 c / 30
8m
-124838
10 c / 25
8m
107320
10 c / 30
8m
14320
10 c / 20
8m
N piezas Np = L S 8 + 0.30 m 8 + 0.25 m 8 + 0.30 m 8 + 0.20 m
1 = 27.66 1 = 33 1 = 27.66 1 = 41
