losa aligerda

1. LOSA ALIGERAD
Datos :
Acabados : 152 kg/m2
Tabiqueria : 100 kg/m2
Sobrecarga : 350 kg/m2 0.05
f ´c = 210 kg/cm2
f y = 4200 kg/cm2
φ = 0.9
L = 5.050 m. 0.1 0.1 0.3 0.1
Ancho de Viga = 0.25 m
DIMENSIONAMIENTO
h = L h = L 0.202 , 0.2525 USAR h = 0.20
25 20
asumimos ø 1/2" = 0.0127 r = 0.02 d = h - r - ø/2 d = 0.17
METRADO DE CARGAS ( para piso tipico )
CARGA MUERTA
PESO PROPIO
Losa = 0.75 x 0.05 x 1.00 x 2400 = 90.00 kg/m2
Vigueta = 2.50 0.10 x 0.20 x 1.00 x 2400 = 120.00 kg/m2
Ladrillo = 8.33 lad/m2 8.20 kg/lad = 68.31 kg/m2
278.31 kg/m2
Piso+Cielo raso (acabados) = 152.00 kg/m2
Tabiqueria = 100.00 kg/m2
WD = 530.31 kg/m2
CARGA VIVA
Sobrecarga = WL = 350.00 kg/m2
METRADO DE LOSA ALIGERADA
0.20
0.15
0.3

2. Sobre carga de diseño (Wu)
Wu = 1.4 WD + 1.7 WL
Wu = 742.43 kg/m2 + 595 kg/m2 = kg/m2
Carga Ultima : ( por vigueta ) Wu = 534.97 kg/ml
WD = kg/ml WL = kg/ml
ANALISIS DE MOMENTOS CON EL SAP 2000
RESULTADOS DEL SAP2000 SE TIENE :
T1 = 4.35 m M B = 1431.98 kg-m M AB = 973.18 kg-m V A = 1021.07 kg
T2 = 5.05 m M C = 1377.19 kg-m M BC = 841.84 kg-m V B = 1526.20 kg 1541.73 kg
T3 = 5.05 m M D = 1431.98 kg-m M CD = 841.84 kg-m V C = 1488.59 kg 1488.59 kg
T4 = 4.35 m M DE = 973.18 kg-m V D = 1541.73 kg 1526.20 kg
V E = 1021.07 kg
534.97 kg/m
4.35 5.05 5.05 4.35
421.79 1431.98 1377.19 1431.98 421.79 M (-)
A B C D E
973.18 841.84 841.84 973.18 M (+)
296.97 238.00
1337.43
Nº DE TRAMOS
NEGATIVOS POSITIVOS NEGATIVOS POSITIVOS

3. 1021.07 1526.20 1488.59 1541.73 V (-)
1541.73 1488.59 1526.20 1021.07 V (+)
El momentos en los extremos se asume un valor minimo
Entonces
b = 10 cm d = 17.37 cm
MOMENTO MAXIMO QUE PUEDE TOMAR LA VIGUETA
Como simplemente reforzada
0.20 d= 0.175 m
Para momentos Negativos
ρmax=
0.4
0.015940
22
2
)(
Mub'8.6
)(
d)b'(89.2
2
1
2
db'7.1
fy
cf
fy
cf
fy
cf
As
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)
'
**59.0
1(***** max2
max
cf
fy
fydbwMrest
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fyfy
cf
b
6000
6000
*
1*'*85.0
*75.0*75.0max



4. M resist = kg-m
Para momentos Positivos
C ≤ 5 cm Trabaja como viga rectangular
a=B1*C = 4.25 cm
b= 40.00 cm
As = 7.23 cm2
M resist = kg-m
PARA LOSA ALIGERADA TENEMOS :
MOMENTOS NEGATIVOS
M (-) A = kg - ml
M (-) B = kg - ml
M (-) C = kg - ml M max (-) = kg-ml
M (-) D = kg - ml
M (-) E = kg - ml M max (-) < M resist (-) CUMPLE
MOMENTOS POSITIVOS
M (+) AB = kg - ml
M (+) BC = kg - ml kg-ml
M (+) CD = kg - ml
M (+) DE = kg - ml M max (+) < M resist (+) CUMPLE
1498.18
4198.99
421.79
1431.98
1377.19 1431.98
1431.98
421.79
973.18
841.84 M max (+) = 973.18
841.84
973.18
fy
abcf
As
**'*85.0

)
2
(***
a
dfyAsM resist  

5. Acero minimo
As min = 0.42 cm2
As max = 2.77 cm2
CALCULO DE REFUERZO : ( As )
MOMENTOS NEGATIVOS
Debe cumplir As min < As < As max
a a As min As max
M (-) A = 1.58 0.67 cm2 1.58 Cumple Cumple
M (-) B = 6.26 2.66 cm2 6.26 Cumple Cumple
M (-) C = 5.96 2.53 cm2 5.96 Cumple Cumple
M (-) D = 6.26 2.66 cm2 6.26 Cumple Cumple
M (-) E = 1.58 0.67 cm2 1.58 Cumple Cumple
MOMENTOS POSITIVOS Debe cumplir As min < As < As max
a a As min As max
M (+) AB = 0.90 1.52 cm2 0.90 Cumple Cumple
M (+) BC = 0.77 1.31 cm2 0.77 Cumple Cumple
M (+) CD = 0.77 1.31 cm2 0.77 Cumple Cumple DIM AREA CANT SUB
M (+) DE = 0.90 1.52 cm2 0.90 Cumple Cumple cm2 n TOTAL
6 0.28 0
8 0.5 0
ACEROS NEGATIVOS 3/8" 0.71 1 0.71
12 1.13 0
A = 0.67 cm2 Usar : 1 Ø 3/8 " 1/2" 1.29 1 1.29
B = 2.66 cm2 Usar : 1 Ø 5/8 " + 1 Ø 12 mm 5/8" 1.99 0
C = 2.53 cm2 Usar : 1 Ø 5/8 " + 1 Ø 12 mm 3/4" 2.84 0
D = 2.66 cm2 Usar : 1 Ø 5/8 " + 1 Ø 12 mm 1" 5.1 0
E = 0.67 cm2 Usar : 1 Ø 3/8 " 1 3/8" 10.06 0
suma 2
As
As
dbw
fy
cf
As
'
7.0min 
bcf
fyAs
a
*'85.0
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
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a
dfy
Mu
As

dbwAs **maxmax 
Diametro Seccion Peso Longitud
mm pulg cm cm2 kg/m m
6 0.60 0.28 0.220
8 0.80 0.50 0.395
3 3/8" 0.95 0.71 0.560
12 1.20 1.13 0.888
4 1/2" 1.27 1.29 0.994
5 5/8" 1.59 1.99 1.552
6 3/4" 1.91 2.84 2.235
8 1" 2.54 5.10 3.973
11 1 3/8" 3.49 10.06 7.907 12
9
ASTM A615 ‐ GRADO 60 / NTP 341.031 ‐ GRADO 60
N°
Diametro barra

6. ACEROS POSITIVOS
AB = 1.52 cm2 Usar : 1 Ø 1/2 " + 1 Ø 3/8
BC = 1.31 cm2 Usar : 1 Ø 1/2 "
CD = 1.31 cm2 Usar : 1 Ø 1/2 "
DE = 1.52 cm2 Usar : 1 Ø 1/2 " + 1 Ø 3/8
DISEÑO CORTANTES
d
v resit = kg Vact = kg
Vresit = kg Vd = Kg
Vd
V A = kg
V B = kg Vresist > Vd
V C = kg
V D = kg
V E = kg
x' = 0.25 m
x = 0.4 m
b' = 0.11 m
x b'
0 0
0.8 0.1 VIGUETA b'
0 0
0 0 x
0 0
0 0
1247.02
1541.73
1021.07
1381.96
1021.07
1541.73 Ensanche de Vigueta
1488.59
1541.73
7.1812
cfresistv '*53.0**10.1  d*bw*resistvVresist
∗

7. CALCULO DEL REFUERZO POR TEMPERATURA
Area de acero minimo : As minimo = 0.0020 * b * t Ver R.N.E. 9.7.2
b = 100.00 cm.
t = 5.00 cm.
As minimo = 1.00 cm² / m.
Para Ø 6 As = 0.28 cm²
Por lo tanto : S = As S = Separacion
Asmin As = Area de acero
S = 0.28 m.
Según el R.N.E. en ningun caso las separación del Ast sera 5 veces el espesor de la losa sin exceder 40 cm
Ast = 5 x 5 = 25 cm
USAR : Ø 6 mm @ 0.25 m