Diseño de Losa
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Transcript of Diseño de Losa
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ANALISIS Y DISEO DE LOSAS ALIGERADAS
TIPO DE ALIGERADO : TIPO 1
e losa
h lad. h
0.10 m 0.30 m bw l. lad. bw l. lad.
Determinacin del Espesor de la Losa
luz = 5 m _ h = ###
Se toma = 0.20 m esp. Losa = 0.05 mh ladrillo = 0.15 m
Determinacin de la Carga UltimaCarga Viva: Sobrecarga, segn Norma E-020 es 200 kg/m
Peso propio de la losaP. Losa = 120 kg/m2 Peso muertoP. Vigueta = 90 kg/m2 P.P. = 300 kg/m2 Carga de tabiquera equivalenteP. Ladrillo = 90 kg/m2 Sobrecarga
Wcm = 840 kg/m2 Wcv = 340 kg/m2
Wcu = 1180 kg/m2
Vigas = 0.25 x 0.35Columnas = 0.25 x 0.30
El Metrado de Cargas, se va realizar en un
metro de ancho: 2,5 viguetas; 2,5 ladrillos y con un ancho tributario
de 40 cm.
hluz21
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2.52 m 2.65 m 2.2 m
Verificaremos si es que es aplicable los coeficientes del ACI:1. Nmero de tramos = 3 OK2. Diferencia de longitud = Tramo 1 - Tramo 2 = 0.05 OK Es aplicable los coeficientes
Tramo 2 - Tramo 3 = -0.17 OK pero vamos a disear con el segundo 3. Relacin Carga Viva / Carga Muerta = 0.33 OK mtodo (hallar momentos por el mtodo
jardy croos)
Hallando los Momentos de Empotramiento Perfecto:
= -0.624456
ANALISIS
I. Carga Ultima = 0.624456
1.18 Tn/m2
G 2.52 m F 2.65 m E 2.2 m D
21
12U
AB
W xLM
21
12U
BA
W xLM
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1.000 0.513 0.487 0.454 0.546 1.000-0.624 0.624 -0.691 0.691 -0.476 0.4760.017 0.034 0.032 0.0160.608 0.304 -0.052 -0.105 -0.126 -0.063
-0.129 -0.123 -0.4130.000 0.833 -0.833 0.602 -0.602 0.000
### ###
### ### ###
II. Combinacin de Carga N 01
1.18 Tn/m2 1.18 Tn/m20.84 Tn/m2
G F E D
2.52 m 2.65 m 2.2 m
1.000 0.513 0.487 0.454 0.546 1.000-0.624 0.624 -0.492 0.492 -0.476 0.476-0.034 -0.068 -0.065 -0.0320.659 0.329 0.004 0.008 0.009 0.005
-0.171 -0.162 -0.4810.000 0.715 -0.715 0.467 -0.467 0.000
### ###
G F E D
-
### ### ###
III. Combinacin de Carga N 02
1.18 Tn/m20.84 Tn/m2 0.84 Tn/m2
2.52 m 2.65 m 2.2 m
1.000 0.513 0.487 0.454 0.546 1.000-0.445 0.445 -0.691 0.691 -0.339 0.3390.063 0.126 0.120 0.0600.381 0.191 -0.093 -0.187 -0.225 -0.112
-0.050 -0.047 -0.2260.000 0.711 -0.711 0.564 -0.564 0.000
0.71 Tn-m/m 0.56 Tn-m/m
### ### ###
IV. Combinacin de Carga N 031.18 Tn/m2
0.84 Tn/m2
2.52 m 2.65 m 2.2 m
1.000 0.513 0.487 0.454 0.546 1.000
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-0.624 0.624 -0.691 0.691 -0.339 0.3390.017 0.034 0.032 0.0160.608 0.304 -0.083 -0.167 -0.201 -0.100
-0.113 -0.107 -0.2380.000 0.849 -0.849 0.540 -0.540 0.000
0.85 Tn-m/m 0.54 Tn-m/m
0.51 Tn-m/m 0.34 Tn-m/m0.24 Tn-m/m
V. Combinacin de Carga N 04
1.18 Tn/m20.84 Tn/m2
2.52 m 2.65 m 2.2 m
1.000 0.513 0.487 0.454 0.546 1.000-0.445 0.445 -0.492 0.492 -0.476 0.4760.012 0.024 0.023 0.0110.432 0.216 -0.006 -0.012 -0.015 -0.007
-0.108 -0.102 -0.4690.000 0.577 -0.577 0.491 -0.491 0.000
0.58 Tn-m/m 0.49 Tn-m/m
D4E3FG
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0.38 Tn-m/m 0.20 Tn-m/m 0.47 Tn-m/m
Envolvente:### ###
### ###
0.58 Tn-m/m 0.40 Tn-m/m 0.48 Tn-m/m
DISEO DEL REFUERZO DE LA LOSA
A. Para Momentos Positivos:Mu = ### f'c = 210 kg/cm2
b fy = 4200 kg/cm2 b = 100 cmrec. = 2 cm h = 20 cm
5 cm = 1/2 '' A = 1.27 cm2
_ d = 17.37 cm
15 cm
Posicin del eje neutro: asumir que: c = hf = 5 cm a = 4.25 cm
As = 1.01 cm2/m1
A cada vigueta le corresponde (As/2.5) = 0.40 cm2 As =
Area de acero en un metro de aligerado: As = 3.175 cm2/m
a = 0.75 cm c = 0.88 cm
c = 0.88 cm < hf = 5 cm
G D4E3F
A s=M u
0 .9f y(da /2)
a=A sf y
0.85f c'b
wl2
24wl2
24
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El eje neutro est en el ala y se analiza como viga rectangular.
Mr = 2039.23 kg-m/m
Tramo 1 - 2 : 579.24 kg-m/m = As As = ###2039.23 kg-m/m 3.175 cm2/m
1 1/2 ''A cada vigueta le corresponde (As/2.5) = 0.36 cm2 As = 1.27 cm2
Tramo 2 - 3 : 398.21 kg-m/m = As As = ###2039.23 kg-m/m 3.175 cm2/m
1 1/2 ''A cada vigueta le corresponde (As/2.5) = 0.25 cm2 As = 1.27 cm2
B. Para Momentos Negativos:
5 cm Mu = ### f'c = 210 kg/cm2fy = 4200 kg/cm2 bw = 25 cmrec. = 2 cm h = 20 cm = 3/8 '' A = 0.71 cm2
15 cm_ d = 17.52 cm
bw
Asumir: a = 0.15d a = 2.63 cm
As = 1.39 cm2/m a = 1.30 cmAs = 1.33 cm2/m a = 1.25 cmAs = 1.33 cm2/m a = 1.25 cm
2 3/8 ''A cada vigueta le corresponde (As/2.5) = 0.53 cm2 As = 1.42 cm2
Apoyo 1: 312.23 kg-m/m = As As = ###849.16 kg-m/m ###
Mr=Asfy(da2 )
A s=M u
0 .9f y(da /2)a=
A sf y0.85f c
'b
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1 3/8 ''A cada vigueta le corresponde (As/2.5) = 0.20 cm2 As = 0.71 cm2
Apoyo 2 : 849.16 kg-m/m = As As = ###849.16 kg-m/m ###
2 3/8 ''A cada vigueta le corresponde (As/2.5) = 0.53 cm2 As = 1.42 cm2
Apoyo 4 : 237.97 kg-m/m = As As = ###849.16 kg-m/m ###
1 3/8 ''A cada vigueta le corresponde (As/2.5) = 0.15 cm2 As = 0.71 cm2
C. Acero por temperatura: Astemp = 0.0018*b*hf = 1/4 '' A = 0.32 cm2
Astemp = 0.90 cm2 s = 35.56 cm
_ Usar: 1/4 '' @ 36 cm
D. Distribucin del refuerzo:
0.38 m 0.63 m 0.66 m 0.66 m 0.55 m 0.33 m
1 3/8 '' 2 3/8 '' 2 3/8 '' 1 3/8 ''
1 1/2 '' 1 1/2 '' 1 1/2 ''
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VERIFICACION POR CORTANTE
V1 V'' 2 V'' 3
V' 2 V' 3 V4
A. Determinacin de los momentos nominales:
As/vig = 1 3/8 '' (Ao =0.71 cm2) As = 1.775 cm2Mn1 :
a = 1.67 cm Mn1 = 1119.71 kg-m/m
As/vig = 2 3/8 '' (Ao =0.71 cm2) As = 3.55 cm2Mn2 :
a = 3.34 cm Mn2 = 2127.34 kg-m/m
As/vig = 2 3/8 '' (Ao =0.71 cm2) As = 3.55 cm2Mn3 :
a = 3.34 cm Mn3 = 2127.34 kg-m/m
As/vig = 1 3/8 '' (Ao =0.71 cm2) As = 1.775 cm2Mn4 :
a = 1.67 cm Mn4 = 1119.71 kg-m/m
B. Determinacin del cortante:
V1 = 1886.65 kgV' 2 = 1086.95 kgV'' 2 = 1563.50 kgV' 3 = 1563.50 kg
Vi=WuiLi2
(Mi+MjLi )
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V'' 3 = 839.99 kgV4 = 1756.01 kg
Cortante a una distancia "d":
Vud = 1679.87 kg
Corte que toma el Concreto:
Vc = 3364.75 kg 2860.04 kg
Verificar que Vc > Vud : CORRECTO
_Vc =
d
Vi=WuiLi2
(Mi+MjLi )
Vc=0 .53 f ' cbd
-
ANALISIS Y DISEO DE LOSAS ALIGERADAS
100 kg/m2200 kg/m2200 kg/m2
El Metrado de Cargas, se va realizar en un
metro de ancho: 2,5 viguetas; 2,5 ladrillos y con un ancho tributario
de 40 cm.
-
Es aplicable los coeficientespero vamos a disear con el segundo mtodo (hallar momentos por el mtodo
-
1/2 ''1.27 cm2
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ANALISIS Y DISEO DE LOSAS ALIGERADAS
TIPO DE ALIGERADO : TIPO 1
e losa
h lad. h
0.10 m 0.30 m bw l. lad. bw l. lad.
Determinacin del Espesor de la Losa
luz = 5.46 m _ h = 0.2184 m
Se toma = 0.20 m esp. Losa = 0.05 mh ladrillo = 0.15 m
Determinacin de la Carga Ultima
Peso propio de la losaP. Losa = 120 kg/m2 Peso muerto 100 kg/m2P. Vigueta = 90 kg/m2 P.P. = 300 kg/m2 Carga de tabiquera equivalente 200 kg/m2P. Ladrillo = 90 kg/m2 Sobrecarga 200 kg/m2
Wcm = 840 kg/m2 Wcv = 340 kg/m2
Wcu = 1180 kg/m2
Vigas = 0.25 x 0.35Columnas = 0.25 x 0.30
hluz25
DO
RM
1.
SH.
SALA
CLO
SET
V 5
P6
P1
P1
V 3
V 10
910
1112
1314
1516
21
322
2123
24
P3P3
5.46
-
3.24 m 3.54 m 2.2 m 5.46 m
2.98 m 3.7 m
Verificaremos si es que es aplicable los coeficientes del ACI:1. Nmero de tramos = 4 OK2. Diferencia de longitud = Tramo 1 - Tramo 2 = 0.09 OK No es aplicable los coeficientes
Tramo 2 - Tramo 3 = -0.38 OKTramo 3 - Tramo 4 = 1.48
3. Relacin Carga Viva / Carga Muerta = 0.33 OK
ANALISIS
I. Carga Ultima
1.18 Tn/m2
3.24 m 3.54 m 2.2 m 5.46 m
1.000 0.522 0.478 0.383 0.617 0.713 0.287-1.032 1.032 -1.232 1.232 -0.476 0.476 -2.9310.052 0.104 0.096 -0.290 -0.466 -0.2330.980 0.490 -0.089 -0.179 -0.288 1.917 0.772
DO
RM
1.
SH.
SALA
CLO
SET
V 5
P6
P1
P1
V 3
V 10
910
1112
1314
1516
21
322
2123
24
P3P3
5.46
-
-0.209 -0.191 0.179 0.2880.000 1.418 -1.418 0.942 -0.942 2.159 -2.159
### ### ### ### ###
### ### ### ###
DISEO DEL REFUERZO DE LA LOSA
A. Para Momentos Positivos:Mu = ### f'c = 210 kg/cm2
b fy = ### b = 100 cmrec. = 2 cm h = 20 cm
5 cm = 1/2 '' A = 1.29 cm2
_ d = 17.37 cm
15 cm
Posicin del eje neutro: asumir que: c = hf = 5 cm a = 4.25 cm
As = 5.76 cm2/m2 1/2 ''
A cada vigueta le corresponde (As/2.5) = 2.30 cm2 As = 2.58 cm2
Area de acero en un metro de aligerado: As = 6.45 cm2/m
a = 1.52 cm c = 1.79 cm
c = 1.79 cm < hf = 5 cm
El eje neutro est en el ala y se analiza como viga rectangular.
A s=M u
0 .9f y(da /2)
a=A sf y
0.85f c'b
-
Mr = 4048.75 kg-m/m
Tramo 1 - 2 : 839.63 kg-m/m = As As = ###4048.75 kg-m/m 6.45 cm2/m
1 1/2 ''A cada vigueta le corresponde (As/2.5) = 0.54 cm2 As = 1.29 cm2
Tramo 2 - 3 : 668.45 kg-m/m = As As = ###4048.75 kg-m/m 6.45 cm2/m
1 1/2 ''A cada vigueta le corresponde (As/2.5) = 0.43 cm2 As = 1.29 cm2
Tramo 2 - 3 : 242.71 kg-m/m = As As = ###4048.75 kg-m/m 6.45 cm2/m
1 1/2 ''A cada vigueta le corresponde (As/2.5) = 0.15 cm2 As = 1.29 cm2
B. Para Momentos Negativos:
5 cm Mu = ### f'c = 210 kg/cm2fy = ### bw = 25 cmrec. = 2 cm h = 20 cm = 3/8 '' A = 0.71 cm2
15 cm_ d = 17.52 cm
bw
Asumir: a = 0.15d a = 2.63 cm
As = 5.41 cm2/m a = 5.10 cmAs = 5.86 cm2/m a = 5.52 cmAs = 5.94 cm2/m a = 5.59 cm
4 3/8 ''
Mr=Asfy(da2 )
A s=M u
0 .9f y(da /2)a=
A sf y0.85f c
'b
-
A cada vigueta le corresponde (As/2.5) = 2.38 cm2 As = 2.84 cm2
Apoyo 1: 516.13 kg-m/m = As As = ###3317.59 kg-m/m ###
1 3/8 ''A cada vigueta le corresponde (As/2.5) = 0.37 cm2 As = 0.71 cm2
Apoyo 2 : 1417.54 kg-m/m = As As = ###3317.59 kg-m/m ###
2 3/8 ''A cada vigueta le corresponde (As/2.5) = 1.02 cm2 As = 1.42 cm2
Apoyo 5 : 1465.74 kg-m/m = As As = ###3317.59 kg-m/m ###
2 3/8 ''A cada vigueta le corresponde (As/2.5) = 1.05 cm2 As = 1.42 cm2
C. Acero por temperatura: Astemp = 0.0018*b*hf = 1/4 '' A = 0.32 cm2
Astemp = 0.90 cm2 s = 35.56 cm
_ Usar: 1/4 '' @ 36 cm
D. Distribucin del refuerzo:
0.45 m 0.75 m 0.93 m 0.93 m 0.00 m 0.00 m
1 3/8 '' 2 3/8 '' 4 3/8 '' 2 3/8 ''
1 1/2 '' 1 1/2 '' 2 1/2 ''
-
VERIFICACION POR CORTANTE
V1 V'' 2 V'' 3
V' 2 V' 3 V4
A. Determinacin de los momentos nominales:
As/vig = 1 3/8 '' (Ao =0.71 cm2) As = 1.775 cm2Mr1 :
a = 1.67 cm Mr1 = 1119.71 kg-m/m
As/vig = 2 3/8 '' (Ao =0.71 cm2) As = 3.55 cm2Mr2 :
a = 3.34 cm Mr2 = 2127.34 kg-m/m
As/vig = 4 3/8 '' (Ao =0.71 cm2) As = 7.1 cm2Mr3 :
a = 6.68 cm Mr3 = 3806.32 kg-m/m
As/vig = 2 3/8 '' (Ao =0.71 cm2) As = 3.55 cm2Mr4 :
a = 3.34 cm Mr4 = 2127.34 kg-m/m
B. Determinacin del cortante:
-
V1 = 2222.60 kgV' 2 = 1600.60 kgV'' 2 = 2562.89 kgV' 3 = 1614.31 kgV'' 3 = 534.83 kgV4 = 2061.17 kg
Cortante a una distancia "d":
Vud = 2356.11 kg
Corte que toma el Concreto:
Vc = 3364.75 kg 2860.04 kg
Verificar que Vc > Vud : CORRECTO
_Vc =
d
Vi=WuiLi2
(Mi+MjLi )
Vc=0 .53 f ' cbd
-
1.0002.931
0.386
-
-3.3180.000
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RON .2NO TOCAR