• Author / Uploaded
• Roger Elmer Flores Cruz

Citation preview

DISEÑO DE LOSAS ALIGERADAS EN DOS DIRECCIONES - METODO COEFICIENTES DEL ACI

1. APLICACIÓN DEL METODO - VIGAS RIGIDAS Se debe determinar si la viga de apoyo es rígida o no para saber si utilizamos el método.Para esto utilizamos el coeficien

Viga 3

Viga 2

Viga 1 4.25

6.00 Losa

Asumiendo Espesor de Losa Ecb = Ecs Viga 1 27.00 40.00 Viga 2 27.00 40.00 Viga 3 27.00 40.00 Viga 4 27.00 40.00 Ib1 = Ib2 = Ib3 = Ib4 =

144000.00 144000.00 144000.00 144000.00

cm cm cm cm

cm4 cm4 cm4 cm4

Viga 4

𝛼=

𝐸𝑐𝑏 . 𝐼𝑏 𝐸𝑐𝑠 . 𝐼𝑠

α1 = α2 = α3 = α4 = αprom =

0.72 1.02 0.51 0.72 0.74 Ok, se puede considerar que la viga es muy rígida con respecto a la losa y que

2. VERIFICACION DEL ESPESOR DE LA LOSA

αprom = 0.74

fy = fy =

Formula 9.6.3.3 NTE E.060 h = Espesor minimo: h = 16.49 Ok No debe ser menor que 12.5 cm

4200.0 411.76

COEFICIENTES DEL ACI

ara esto utilizamos el coeficiente

α 20.00

cm

B= B= B= B=

3.00 2.13 4.25 3.00

m m m m

Is1 = Is2 = Is3 = Is4 =

200000.00 141666.67 283333.33 200000.00

cm4 cm4 cm4 cm4

a con respecto a la losa y que no se deforma al aplicar la carga Kg/cm2 Mpa

ANALISIS Y DISEÑO DE LOSA ALIGERADA EN DOS DIRECCIONES

DATOS Sobrecarga (S/C) = 300 Kg/m2 Recubrimiento = 2.50 cm Tab. Repartida = 0 Kg/m2 f'c = 210 Kg/cm2 fy = 4200 Kg/cm2 Alig. En dos direc = 360 Kg/m2 Peso especifico C° 2400 Kg/m3

4.250 m

6.000 m 1. DETERMINACION DEL ESPESOR DE LA LOSA.

h=

20.00 m

2. METRADO DE CARGAS CARGA MUERTA (Cm) Peso de Alig. 20 360 Kg/m2 Peso Muerto = 180 Kg/m2 Peso Tab. Equiv. = 0 Kg/m2 Cm = 540 Kg/m2

CARGA ULTIMAS

CARGA VIVA (Cv) Sobrecarga (S/C) = 300 Kg/m2 Cv = 300 Kg/m2 3. ANALISIS Restricciones de los apoyos Libre ,

,

756 Kg/m2

Wu cv  1.7 * Cv

Wu cv =

510 Kg/m2

Wu 1.4 * Cm 1.7 * Cv

Wu =

1266 Kg/m2

Para b = 1 m

Wu =

1266 Kg/m

CASO 1

, , , , , ,

,

Wu cm =

CASO :

, , Libre , , , ,

Wu cm  1.4 * Cm

m  Libre

A B

A= B= m=

, Libre

cm 3.1 Determinacion de los Momentos Negativos cv De la Tabla 13.1 de la NORMA E.060: Coeficientes del ACI:

Ca =

Cb =

0.70 0.708 0.75

Ver Tabla #VALUE! Ver Tabla

0.70 0.708 0.75

Ver Tabla #VALUE! Ver Tabla

297 Kg/m2 297.0885324

Ma neg  Ca wu A 2

Ma (-) =

#VALUE!

Mb neg  Cb wu B 2 Mb (-) =

#VALUE!

3.2 Determinacion de los Momentos Positivos De la Tabla 13.2 y 13.3 de la NORMA E.060: Coeficientes del ACI: COEFICIENTES POR CARGA MUERTA

Ca =

0.70 0.708 0.75

0.068 0.067 0.061

Ma posd  Ca wud A2

Ma Pos =

913 Kg-m

0.70 0.708 0.75

Cb =

Mb posd  Cb wud B2

0.016 0.017 0.019

Mb Pos =

449 Kg-m

COEFICIENTES POR CARGA VIVA

Ca =

Cb =

0.70 0.708 0.75

0.068 0.067 0.061

0.70 0.708 0.75

0.016 0.017 0.019

Ma pos l  Ca wul A2

Ma Pos =

616 Kg-m

Mb pos l  Cb wul B2

Mb Pos =

303 Kg-m

Momentos Positivos Ma  Ma pos d  Ma posl

Ma (+) =

1528 Kg-m

Mb  Mb pos d  Mb pos l

Mb (+) =

752 Kg-m

FORMA DE GRAFICAR MOMENTOS EN LOSAS MB (-)

MB(+)/3

MB (+)

B

MA (-)

A

MA (+)

LOSA EN DOS DIRECCIONES

MA(+)/3

4. DISEÑO DE REFUERZO POR FLEXION Diseño para un ancho b = 100.0 cm 4.1 REFUERZO NEGATIVO Datos bw = f'c = fy = d=

25.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm

Para Mu-: a= As = As Vigueta =

#VALUE! #VALUE! #VALUE! #VALUE! 1 Φ 1/2 + 1 Φ 3/8

4.2 REFUERZO POSITIVO Datos

Peralte Efectivo d = hn - Rec.- (3/8")/2 d= 17.02 cm

As . fy a  0 . 85 . f ' c .b

2.00 cm²

Mu As  . fy.(d  a / 2)

#VALUE!

Longitud de desarrollo 1.427 2.02

bw = f'c = fy = d=

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm As 

Para Mu+: a= As = As Vigueta =

Datos bw = f'c = fy = d= Para Mu+: a= As = As Vigueta =

1528 Kg-m 0.57 cm 2.42 cm² 0.97 cm² 1 Φ 1/2

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

Para Mu+/3: a= As = As Vigueta =

509 Kg-m 0.19 cm 0.80 cm² 0.32 cm² 1 Φ 3/8

Para Mu+/3: a= As = As Vigueta =

251 Kg-m 0.09 cm 0.39 cm² 0.16 cm² 1 Φ 3/8

Ok

1.29 cm²

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm 752 Kg-m 0.28 cm 1.18 cm² 0.47 cm² 1 Φ 3/8

As  a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.0024

As min   min .b .d

0.71 cm²

Ok

5. ACERO MAXIMO Y MINIMO 5.1 ACERO MINIMO Cuantia Minima: As min = As min/vig =

1.028 cm2 0.411 cm2 1 Φ 3/8

5.1 ACERO MAXIMO Cuantia Maxima As max = As max/vig =

6.923 cm2 2.769 cm2 2 Φ 1/2

0.75*ρb

= ρb =

0.0162675 0.02169

As max   max .b .d

2.58 cm²

As Insuficiente

Continuo Libre

4.250 6.000 0.708

CASO Coef. CASO 1 1.00 Ca Ver Tabla Cb Ver Tabla 0.95 Ca Ver Tabla Cb Ver Tabla 0.90 Ca Ver Tabla Cb Ver Tabla 0.85 Ca Ver Tabla Cb Ver Tabla 0.80 Ca Ver Tabla Cb Ver Tabla 0.75 Ca Ver Tabla Cb Ver Tabla 0.70 Ca Ver Tabla Cb Ver Tabla 0.65 Ca Ver Tabla Cb Ver Tabla 0.60 Ca Ver Tabla Cb Ver Tabla 0.55 Ca Ver Tabla Cb Ver Tabla 0.50 Ca Ver Tabla Cb Ver Tabla

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 1 0.036 0.036 0.040 0.033 0.045 0.029 0.050 0.026 0.056 0.023 0.061 0.019 0.068 0.016 0.074 0.013 0.081 0.010 0.088 0.008 0.095 0.006

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 1 0.036 0.036 0.040 0.033 0.045 0.029 0.050 0.026 0.056 0.023 0.061 0.019 0.068 0.016 0.074 0.013 0.081 0.010 0.088 0.008 0.095 0.006

Longitud de desarrollo

As 

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.71 cm²

Ok

ANALISIS Y DISEÑO DE LOSA ALIGERADA EN DOS DIRECCIONES

DATOS Sobrecarga (S/C) = 300 Kg/m2 Recubrimiento = 2.50 cm Tab. Repartida = 0 Kg/m2 f'c = 210 Kg/cm2 fy = 4200 Kg/cm2 Alig. En dos direc = 360 Kg/m2 Peso especifico C° 2400 Kg/m3

4.250 m

6.000 m 1. DETERMINACION DEL ESPESOR DE LA LOSA.

h=

20.00 m

2. METRADO DE CARGAS CARGA MUERTA (Cm) Peso de Alig. 20 360 Kg/m2 Peso Muerto = 180 Kg/m2 Peso Tab. Equiv. = 0 Kg/m2 Cm = 540 Kg/m2

CARGA ULTIMAS

CARGA VIVA (Cv) Sobrecarga (S/C) = 300 Kg/m2 Cv = 200 Kg/m2 3. ANALISIS Restricciones de los apoyos Continuo .

.

756 Kg/m2

Wu cv  1.7 * Cv

Wu cv =

340 Kg/m2

Wu 1.4 * Cm 1.7 * Cv

Wu =

1096 Kg/m2

Para b = 1 m

Wu =

1096 Kg/m

CASO 5

. , , , , ,

.

Wu cm =

CASO :

, , Libre , , , .

Wu cm  1.4 * Cm

m  Libre

A B

m=

. Continuo

3.1 Determinacion de los Momentos Negativos De la Tabla 13.1 de la NORMA E.060: Coeficientes del ACI:

Ca =

Cb =

0.70 0.708 0.75

0.086 0.086 0.085

0.70 0.708 0.75

0 0.000 0

Ma neg  Ca wu A 2

Ma (-) =

1699 Kg-m

Mb neg  Cb wu B 2 Mb (-) =

0 Kg-m

3.2 Determinacion de los Momentos Positivos De la Tabla 13.2 y 13.3 de la NORMA E.060: Coeficientes del ACI: COEFICIENTES POR CARGA MUERTA

Ca =

0.70 0.708 0.75

0.035 0.035 0.033

A= B=

Ma posd  Ca wud A2

Ma Pos =

473 Kg-m

0.70 0.708 0.75

Cb =

Mb posd  Cb wud B2

0.005 0.005 0.007

Mb Pos =

145 Kg-m

COEFICIENTES POR CARGA VIVA

Ca =

Cb =

0.70 0.708 0.75

0.051 0.050 0.047

0.70 0.708 0.75

0.011 0.011 0.013

Ma pos l  Ca wul A2

Ma Pos =

309 Kg-m

Mb pos l  Cb wul B2

Mb Pos =

139 Kg-m

Momentos Positivos Ma  Ma pos d  Ma posl

Ma (+) =

782 Kg-m

Mb  Mb pos d  Mb pos l

Mb (+) =

284 Kg-m

FORMA DE GRAFICAR MOMENTOS EN LOSAS MB (-)

MB(+)/3

MB (+)

B

MA (-)

A

MA (+)

LOSA EN DOS DIRECCIONES

MA(+)/3

4. DISEÑO DE REFUERZO POR FLEXION Diseño para un ancho b = 100.0 cm 4.1 REFUERZO NEGATIVO Datos bw = f'c = fy = d= Para Mu-: a= As = As Vigueta =

25.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm 1699 Kg-m 2.70 cm 2.87 cm² 1.15 cm² 1 Φ 1/2

4.2 REFUERZO POSITIVO Datos

Peralte Efectivo d = hn - Rec.- (3/8")/2 d= 17.02 cm

As . fy a  0 . 85 . f ' c .b

1.29 cm²

Ok

Mu As  . fy.(d  a / 2)

Longitud de desarrollo 1.427 2.02

bw = f'c = fy = d=

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm As 

Para Mu+: a= As = As Vigueta =

Datos bw = f'c = fy = d= Para Mu+: a= As = As Vigueta =

782 Kg-m 0.29 cm 1.23 cm² 0.49 cm² 1 Φ 3/8

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

Para Mu+/3: a= As = As Vigueta =

261 Kg-m 0.10 cm 0.41 cm² 0.16 cm² 1 Φ 3/8

Para Mu+/3: a= As = As Vigueta =

95 Kg-m 0.03 cm 0.15 cm² 0.06 cm² 1 Φ 3/8

Ok

0.71 cm²

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm 284 Kg-m 0.10 cm 0.44 cm² 0.18 cm² 1 Φ 3/8

As  a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.0024

As min   min .b .d

0.71 cm²

Ok

5. ACERO MAXIMO Y MINIMO 5.1 ACERO MINIMO Cuantia Minima: As min = As min/vig =

1.028 cm2 0.411 cm2 1 Φ 3/8

5.1 ACERO MAXIMO Cuantia Maxima As max = As max/vig =

6.923 cm2 2.769 cm2 2 Φ 1/2

0.75*ρb

= ρb =

0.0162675 0.02169

As max   max .b .d

2.58 cm²

As Insuficiente

Continuo Libre

4.250 6.000 0.708

CASO Coef. 1.00 Ca Cb 0.95 Ca Cb 0.90 Ca Cb 0.85 Ca Cb 0.80 Ca Cb 0.75 Ca Cb 0.70 Ca Cb 0.65 Ca Cb 0.60 Ca Cb 0.55 Ca Cb 0.50 Ca Cb

CASO 5 0.075 0.000 0.079 0.000 0.080 0.000 0.082 0.000 0.083 0.000 0.085 0.000 0.086 0.000 0.087 0.000 0.088 0.000 0.089 0.000 0.090 0.000

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 5 0.027 0.018 0.028 0.015 0.029 0.013 0.031 0.011 0.032 0.009 0.033 0.007 0.035 0.005 0.036 0.004 0.037 0.003 0.038 0.002 0.039 0.001

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 5 0.032 0.027 0.034 0.024 0.037 0.021 0.041 0.019 0.044 0.010 0.047 0.013 0.051 0.011 0.055 0.009 0.059 0.007 0.063 0.005 0.067 0.004

Longitud de desarrollo

As 

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.71 cm²

Ok

ANALISIS Y DISEÑO DE LOSA ALIGERADA EN DOS DIRECCIONES

DATOS Sobrecarga (S/C) = 250 Kg/m2 Recubrimiento = 2.50 cm Tab. Repartida = 0 Kg/m2 f'c = 210 Kg/cm2 fy = 4200 Kg/cm2 Alig. En dos direc = 360 Kg/m2 Peso especifico C° 2400 Kg/m3

4.250 m

6.000 m 1. DETERMINACION DEL ESPESOR DE LA LOSA.

h=

20.00 m

2. METRADO DE CARGAS CARGA MUERTA (Cm) Peso de Alig. 20 360 Kg/m2 Peso Muerto = 180 Kg/m2 Peso Tab. Equiv. = 0 Kg/m2 Cm = 540 Kg/m2

CARGA ULTIMAS

CARGA VIVA (Cv) Sobrecarga (S/C) = 250 Kg/m2 Cv = 200 Kg/m2 3. ANALISIS Restricciones de los apoyos Continuo .

.

756 Kg/m2

Wu cv  1.7 * Cv

Wu cv =

340 Kg/m2

Wu 1.4 * Cm 1.7 * Cv

Wu =

1096 Kg/m2

Para b = 1 m

Wu =

1096 Kg/m

CASO 6

. , , , , ,

,

Wu cm =

CASO :

, , Libre , , , ,

Wu cm  1.4 * Cm

m  Libre

A B

m=

, Libre

3.1 Determinacion de los Momentos Negativos De la Tabla 13.1 de la NORMA E.060: Coeficientes del ACI:

Ca =

Cb =

0.70 0.708 0.75

0.091 0.091 0.088

0.70 0.708 0.75

0 0.000 0

Ma neg  Ca wu A 2

Ma (-) =

1792 Kg-m

Mb neg  Cb wu B 2 Mb (-) =

0 Kg-m

3.2 Determinacion de los Momentos Positivos De la Tabla 13.2 y 13.3 de la NORMA E.060: Coeficientes del ACI: COEFICIENTES POR CARGA MUERTA

Ca =

0.70 0.708 0.75

0.051 0.051 0.048

A= B=

Ma posd  Ca wud A2

Ma Pos =

690 Kg-m

0.70 0.708 0.75

Cb =

Mb posd  Cb wud B2

0.009 0.010 0.012

Mb Pos =

259 Kg-m

COEFICIENTES POR CARGA VIVA

Ca =

Cb =

0.70 0.708 0.75

0.06 0.059 0.055

0.70 0.708 0.75

0.013 0.014 0.016

Ma pos l  Ca wul A2

Ma Pos =

363 Kg-m

Mb pos l  Cb wul B2

Mb Pos =

165 Kg-m

Momentos Positivos Ma  Ma pos d  Ma posl

Ma (+) =

1053 Kg-m

Mb  Mb pos d  Mb pos l

Mb (+) =

424 Kg-m

FORMA DE GRAFICAR MOMENTOS EN LOSAS MB (-)

MB(+)/3

MB (+)

B

MA (-)

A

MA (+)

LOSA EN DOS DIRECCIONES

MA(+)/3

4. DISEÑO DE REFUERZO POR FLEXION Diseño para un ancho b = 100.0 cm 4.1 REFUERZO NEGATIVO Datos bw = f'c = fy = d= Para Mu-: a= As = As Vigueta =

25.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm 1792 Kg-m 2.86 cm 3.04 cm² 1.22 cm² 1 Φ 1/2

4.2 REFUERZO POSITIVO Datos

Peralte Efectivo d = hn - Rec.- (3/8")/2 d= 17.02 cm

As . fy a  0 . 85 . f ' c .b

1.29 cm²

Ok

Mu As  . fy.(d  a / 2)

Longitud de desarrollo 1.427 2.02

bw = f'c = fy = d=

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm As 

Para Mu+: a= As = As Vigueta =

Datos bw = f'c = fy = d= Para Mu+: a= As = As Vigueta =

1053 Kg-m 0.39 cm 1.66 cm² 0.66 cm² 1 Φ 3/8

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

Para Mu+/3: a= As = As Vigueta =

351 Kg-m 0.13 cm 0.55 cm² 0.22 cm² 1 Φ 3/8

Para Mu+/3: a= As = As Vigueta =

141 Kg-m 0.05 cm 0.22 cm² 0.09 cm² 1 Φ 3/8

Ok

0.71 cm²

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm 424 Kg-m 0.16 cm 0.66 cm² 0.26 cm² 1 Φ 3/8

As  a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.0024

As min   min .b .d

0.71 cm²

Ok

5. ACERO MAXIMO Y MINIMO 5.1 ACERO MINIMO Cuantia Minima: As min = As min/vig =

1.028 cm2 0.411 cm2 1 Φ 3/8

5.1 ACERO MAXIMO Cuantia Maxima As max = As max/vig =

6.923 cm2 2.769 cm2 2 Φ 1/2

0.75*ρb

= ρb =

0.0162675 0.02169

As max   max .b .d

2.58 cm²

As Insuficiente

Continuo Libre

4.250 6.000 0.708

CASO Coef. 1.00 Ca Cb 0.95 Ca Cb 0.90 Ca Cb 0.85 Ca Cb 0.80 Ca Cb 0.75 Ca Cb 0.70 Ca Cb 0.65 Ca Cb 0.60 Ca Cb 0.55 Ca Cb 0.50 Ca Cb

CASO 6 0.071 0.000 0.075 0.000 0.079 0.000 0.083 0.000 0.086 0.000 0.088 0.000 0.091 0.000 0.093 0.000 0.095 0.000 0.096 0.000 0.097 0.000

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 6 0.033 0.027 0.036 0.024 0.039 0.021 0.042 0.017 0.045 0.015 0.048 0.012 0.051 0.009 0.054 0.007 0.056 0.006 0.058 0.004 0.061 0.003

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 6 0.035 0.032 0.038 0.029 0.042 0.025 0.046 0.022 0.051 0.019 0.055 0.016 0.060 0.013 0.064 0.010 0.068 0.008 0.073 0.006 0.078 0.005

Longitud de desarrollo

As 

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.71 cm²

Ok

ANALISIS Y DISEÑO DE LOSA ALIGERADA EN DOS DIRECCIONES

DATOS Sobrecarga (S/C) = 100 Kg/m2 Recubrimiento = 2.50 cm Tab. Repartida = 0 Kg/m2 f'c = 210 Kg/cm2 fy = 4200 Kg/cm2 Alig. En dos direc = 360 Kg/m2 Peso especifico C° 2400 Kg/m3

4.250 m

6.000 m 1. DETERMINACION DEL ESPESOR DE LA LOSA.

h=

20.00 m

2. METRADO DE CARGAS CARGA MUERTA (Cm) Peso de Alig. 20 360 Kg/m2 Peso Muerto = 180 Kg/m2 Peso Tab. Equiv. = 0 Kg/m2 Cm = 540 Kg/m2

CARGA ULTIMAS

CARGA VIVA (Cv) Sobrecarga (S/C) = 100 Kg/m2 Cv = 200 Kg/m2 3. ANALISIS Restricciones de los apoyos Libre ,

,

756 Kg/m2

Wu cv  1.7 * Cv

Wu cv =

340 Kg/m2

Wu 1.4 * Cm 1.7 * Cv

Wu =

1096 Kg/m2

Para b = 1 m

Wu =

1096 Kg/m

CASO 1

, , , , , ,

,

Wu cm =

CASO :

, , Libre , , , ,

Wu cm  1.4 * Cm

m  Libre

A B

m=

, Libre

3.1 Determinacion de los Momentos Negativos De la Tabla 13.1 de la NORMA E.060: Coeficientes del ACI:

Ca =

Cb =

0.70 0.708 0.75

Ver Tabla 0.000 Ver Tabla

0.70 0.708 0.75

Ver Tabla 0.000 Ver Tabla

Ma neg  Ca wu A 2

Ma (-) =

0 Kg-m

Mb neg  Cb wu B 2 Mb (-) =

0 Kg-m

3.2 Determinacion de los Momentos Positivos De la Tabla 13.2 y 13.3 de la NORMA E.060: Coeficientes del ACI: COEFICIENTES POR CARGA MUERTA

Ca =

0.70 0.708 0.75

0.068 0.067 0.061

A= B=

Ma posd  Ca wud A2

Ma Pos =

913 Kg-m

0.70 0.708 0.75

Cb =

Mb posd  Cb wud B2

0.016 0.017 0.019

Mb Pos =

449 Kg-m

COEFICIENTES POR CARGA VIVA

Ca =

Cb =

0.70 0.708 0.75

0.068 0.067 0.061

0.70 0.708 0.75

0.016 0.017 0.019

Ma pos l  Ca wul A2

Ma Pos =

410 Kg-m

Mb pos l  Cb wul B2

Mb Pos =

202 Kg-m

Momentos Positivos Ma  Ma pos d  Ma posl

Ma (+) =

1323 Kg-m

Mb  Mb pos d  Mb pos l

Mb (+) =

651 Kg-m

FORMA DE GRAFICAR MOMENTOS EN LOSAS MB (-)

MB(+)/3

MB (+)

B

MA (-)

A

MA (+)

LOSA EN DOS DIRECCIONES

MA(+)/3

4. DISEÑO DE REFUERZO POR FLEXION Diseño para un ancho b = 100.0 cm 4.1 REFUERZO NEGATIVO Datos bw = f'c = fy = d= Para Mu-: a= As = As Vigueta =

25.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm 0 Kg-m 0.00 cm 0.00 cm² 0.00 cm² 1 Φ 3/8

4.2 REFUERZO POSITIVO Datos

Peralte Efectivo d = hn - Rec.- (3/8")/2 d= 17.02 cm

As . fy a  0 . 85 . f ' c .b

0.71 cm²

Ok

Mu As  . fy.(d  a / 2)

Longitud de desarrollo 1.427 2.02

bw = f'c = fy = d=

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm As 

Para Mu+: a= As = As Vigueta =

Datos bw = f'c = fy = d= Para Mu+: a= As = As Vigueta =

1323 Kg-m 0.49 cm 2.09 cm² 0.83 cm² 1 Φ 1/2

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

Para Mu+/3: a= As = As Vigueta =

441 Kg-m 0.16 cm 0.69 cm² 0.28 cm² 1 Φ 3/8

Para Mu+/3: a= As = As Vigueta =

217 Kg-m 0.08 cm 0.34 cm² 0.14 cm² 1 Φ 3/8

Ok

1.29 cm²

100.00 cm 210 Kg/cm2 4200 Kg/cm2 17.02 cm 651 Kg-m 0.24 cm 1.02 cm² 0.41 cm² 1 Φ 3/8

As  a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.0024

As min   min .b .d

0.71 cm²

Ok

5. ACERO MAXIMO Y MINIMO 5.1 ACERO MINIMO Cuantia Minima: As min = As min/vig =

1.028 cm2 0.411 cm2 1 Φ 3/8

5.1 ACERO MAXIMO Cuantia Maxima As max = As max/vig =

6.923 cm2 2.769 cm2 2 Φ 1/2

0.75*ρb

= ρb =

0.0162675 0.02169

As max   max .b .d

2.58 cm²

As Insuficiente

Continuo Libre

4.250 6.000 0.708

CASO Coef. CASO 1 1.00 Ca Ver Tabla Cb Ver Tabla 0.95 Ca Ver Tabla Cb Ver Tabla 0.90 Ca Ver Tabla Cb Ver Tabla 0.85 Ca Ver Tabla Cb Ver Tabla 0.80 Ca Ver Tabla Cb Ver Tabla 0.75 Ca Ver Tabla Cb Ver Tabla 0.70 Ca Ver Tabla Cb Ver Tabla 0.65 Ca Ver Tabla Cb Ver Tabla 0.60 Ca Ver Tabla Cb Ver Tabla 0.55 Ca Ver Tabla Cb Ver Tabla 0.50 Ca Ver Tabla Cb Ver Tabla

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 1 0.036 0.036 0.040 0.033 0.045 0.029 0.050 0.026 0.056 0.023 0.061 0.019 0.068 0.016 0.074 0.013 0.081 0.010 0.088 0.008 0.095 0.006

CASO 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

Coef. Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

CASO 1 0.036 0.036 0.040 0.033 0.045 0.029 0.050 0.026 0.056 0.023 0.061 0.019 0.068 0.016 0.074 0.013 0.081 0.010 0.088 0.008 0.095 0.006

Longitud de desarrollo

As 

a 

Mu

. fy.(d  a / 2) As . fy 0 . 85 . f ' c .b

0.71 cm²

Ok

0.71 cm²

Ok

TABLA 13.1 COEFICIENTES PARA MOMENTOS NEGATIVOS Ma neg  Ca wu A2

B

Wu = Carga amplificada total A

Mb neg  Cb wu B 2

Relacion m

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

CASO 1

CASO 2

CASO 3

CASO 4 CASO 5

CASO 6

CASO 7

CASO 8

CASO 9

0.033 0.061 0.038 0.056 0.043 0.052 0.049 0.046 0.055 0.041 0.061 0.036 0.068 0.029 0.074 0.024 0.080 0.018 0.085 0.014 0.089 0.010

0.061 0.033 0.065 0.029 0.068 0.025 0.072 0.021 0.075 0.017 0.078 0.014 0.081 0.011 0.083 0.008 0.085 0.006 0.086 0.005 0.088 0.003

A B

Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

0.045 0.045 0.050 0.041 0.055 0.037 0.060 0.031 0.065 0.027 0.069 0.022 0.074 0.017 0.077 0.014 0.081 0.010 0.084 0.007 0.086 0.006

0.076 0.072 0.070 0.065 0.061 0.056 0.050 0.043 0.035 0.028 0.022

0.050 0.050 0.055 0.045 0.060 0.040 0.066 0.034 0.071 0.029 0.076 0.024 0.081 0.019 0.085 0.015 0.089 0.011 0.092 0.008 0.094 0.006

0.075

0.071 0.071

0.079

0.075

0.080

0.079

0.082

0.083

0.083

0.086

0.085

0.088

0.086

0.091

0.087

0.093

0.088

0.095

0.089

0.096

0.090

0.097

0.067 0.062 0.057 0.051 0.044 0.038 0.031 0.024 0.019 0.014

TABLA 13.2 COEFICIENTES PARA MOMENTOS POSITIVOS DEBIDO A LA CARGA MUERTA

Ma pos d  Ca wud A2

B

Wud = Carga muerta amplificada A

Mb pos d  Cb wud B 2 Relacion m

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

CASO 1

CASO 2

0.036 0.036 0.040 0.033 0.045 0.029 0.050 0.026 0.056 0.023 0.061 0.019 0.068 0.016 0.074 0.013 0.081 0.010 0.088 0.008 0.095 0.006

0.018 0.018 0.020 0.016 0.022 0.014 0.024 0.012 0.026 0.011 0.028 0.009 0.030 0.007 0.032 0.006 0.034 0.004 0.035 0.003 0.080 0.007

CASO 3 CASO 4 CASO 5 CASO 6 CASO 7 CASO 8

A B

Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

0.018 0.027 0.021 0.025 0.025 0.024 0.029 0.022 0.034 0.020 0.040 0.018 0.046 0.016 0.054 0.014 0.062 0.011 0.071 0.009 0.080 0.007

0.027 0.027 0.030 0.024 0.033 0.022 0.036 0.019 0.039 0.016 0.043 0.013 0.046 0.011 0.050 0.009 0.053 0.007 0.056 0.005 0.059 0.004

0.027 0.018 0.028 0.015 0.029 0.013 0.031 0.011 0.032 0.009 0.033 0.007 0.035 0.005 0.036 0.004 0.037 0.003 0.038 0.002 0.039 0.001

0.033 0.027 0.036 0.024 0.039 0.021 0.042 0.017 0.045 0.015 0.048 0.012 0.051 0.009 0.054 0.007 0.056 0.006 0.058 0.004 0.061 0.003

0.027 0.033 0.031 0.031 0.035 0.028 0.040 0.025 0.045 0.022 0.051 0.020 0.058 0.017 0.065 0.014 0.073 0.012 0.081 0.009 0.089 0.007

0.020 0.023 0.022 0.021 0.025 0.019 0.029 0.017 0.032 0.015 0.036 0.013 0.040 0.011 0.044 0.009 0.048 0.007 0.052 0.005 0.056 0.004

TABLA 13.3 COEFICIENTES PARA MOMENTOS POSITIVOS DEBIDO A LA CARGA VIVA

Ma pos l  Ca wul A 2

A

Mb pos l  Cb wul B 2 CASO 9

Relacion

m 0.023 0.020 0.024 0.017 0.026 0.015 0.028 0.013 0.029 0.010 0.031 0.007 0.033 0.006 0.034 0.005 0.036 0.004 0.037 0.003 0.038 0.002

1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50

B

Wul = Carga viva amplificada

CASO 1

CASO 2

CASO 3

CASO 4

CASO 5

CASO 6

CASO 7

0.036 0.036 0.040 0.033 0.045 0.029 0.050 0.026 0.056 0.023 0.061 0.019 0.068 0.016 0.074 0.013 0.081 0.010 0.088 0.008 0.095 0.006

0.027 0.027 0.030 0.025 0.034 0.022 0.037 0.019 0.041 0.017 0.045 0.014 0.049 0.012 0.053 0.010 0.058 0.007 0.062 0.006 0.066 0.004

0.027 0.032 0.031 0.029 0.035 0.027 0.040 0.024 0.045 0.022 0.051 0.019 0.057 0.016 0.064 0.014 0.071 0.011 0.080 0.009 0.088 0.007

0.032 0.032 0.035 0.029 0.039 0.026 0.043 0.023 0.048 0.020 0.052 0.016 0.057 0.014 0.062 0.011 0.067 0.009 0.072 0.007 0.077 0.005

0.032 0.027 0.034 0.024 0.037 0.021 0.041 0.019 0.044 0.010 0.047 0.013 0.051 0.011 0.055 0.009 0.059 0.007 0.063 0.005 0.067 0.004

0.035 0.032 0.038 0.029 0.042 0.025 0.046 0.022 0.051 0.019 0.055 0.016 0.060 0.013 0.064 0.010 0.068 0.008 0.073 0.006 0.078 0.005

0.032 0.035 0.036 0.032 0.040 0.029 0.045 0.026 0.051 0.023 0.056 0.020 0.063 0.017 0.070 0.014 0.077 0.011 0.085 0.009 0.092 0.007

A B Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb Ca Cb

DEBIDO A LA CARGA VIVA

CASO 8 CASO 9

0.028 0.030 0.031 0.027 0.035 0.024 0.040 0.022 0.044 0.019 0.049 0.016 0.054 0.014 0.059 0.011 0.065 0.009 0.070 0.007 0.076 0.005

0.030 0.028 0.032 0.025 0.036 0.022 0.039 0.020 0.042 0.017 0.046 0.013 0.050 0.011 0.054 0.009 0.059 0.007 0.063 0.006 0.067 0.004

COMBINACIONES DE ACEROS COMERCIALES ACEROS COMERCIALES DIAMETRO BARRA Peso N° pulg cm Kg/m 3 1 Φ 3/8 0.95 0.559 4 1 Φ 1/2 1.27 0.993 5 1 Φ 5/8 1.59 1.552 6 1 Φ 3/4 1.91 2.235 7 1 Φ 7/8 2.22 3.042 8 1Φ1 2.54 3.973 9 1 Φ 1 1/8 2.86 5.028 10 1 Φ 1 1/4 3.18 6.207 11 1 Φ 1 3/8 3.49 7.511 12 1 Φ 1 1/2 3.81 8.938

Area cm2 0.71 1.29 1.98 2.85 3.88 5.1 6.45 8.19 9.58 11.4

COMBINACIONES RECOMENDADAS 1/2 - 3/8"

1/2 - 5/8"

1/2 - 3/4"

5/8 - 3/4"

5/8 - 1"

5/8 - 3/4"

3/4 - 1" 1 Φ 3/4 + 1 Φ 1 1 Φ 1 + 2 Φ 3/4 2 Φ 1 + 1 Φ 3/4 2 Φ 1+ 2 Φ 3/4

Evitando tener diametros excesivamente diferentes

Area (cm2) b min (cm) 7.950 16.89 10.800 21.34 13.050 21.97 15.900 26.42

1/2 - 3/8" 2 Φ 3/8 1 Φ 1/2 + 1 Φ 3/8 3 Φ 3/8 2 Φ 1/2 1 Φ 1/2 + 2 Φ 3/8 4 Φ 3/8 2 Φ 1/2 + 1 Φ 3/8 3 Φ 1/2 2 Φ 1/2 + 2 Φ 3/8 3 Φ 1/2 + 1 Φ 3/8 4 Φ 1/2

Area (cm2) b min (cm) 1.420 14.34 2.000 14.66 2.130 17.83 2.580 14.98 2.710 18.15 2.840 21.32 3.290 18.47 3.870 18.79 4.000 21.96 4.580 22.28 5.160 22.60

11.64 1/2 - 5/8" 1 Φ 1/2 + 1 Φ 5/8 2 Φ 5/8 2 Φ 1/2 + 1 Φ 5/8 1 Φ 1/2 + 2 Φ 5/8 3 Φ 1/2 + 1 Φ 5/8 3 Φ 5/8 2 Φ 1/2 + 2 Φ 5/8 1 Φ 1/2 + 3 Φ 5/8 4 Φ 5/8

Area (cm2) b min (cm) 3.270 15.30 3.960 15.62 4.560 19.11 5.250 19.43 5.850 22.92 5.940 19.75 6.540 23.24 7.230 23.56 7.920 23.88

1/2 - 3/4" 1 Φ 1/2 + 1 Φ 3/4 2 Φ 1/2 + 1 Φ 3/4 2 Φ 3/4 1 Φ 1/2 + 2 Φ 3/4 3 Φ 3/4 2 Φ 1/2 + 2 Φ 3/4 4 Φ 3/4

Area (cm2) b min (cm) 4.140 15.62 5.430 19.43 5.700 16.26 6.990 20.07 8.550 20.71 6.456 23.88 11.400 25.16

5/8 - 3/4" 1 Φ 5/8 + 1 Φ 3/4 2 Φ 5/8 + 1 Φ 3/4 1 Φ 5/8 + 2 Φ 3/4 3 Φ 5/8 + 1 Φ 3/4 2 Φ 5/8 + 2 Φ 3/4 1 Φ 5/8 + 3 Φ 3/4

Area (cm2) b min (cm) 4.830 15.94 6.810 20.07 7.680 20.39 8.790 24.200 9.660 24.520 10.530 24.840

5/8 - 1" 1 Φ 1 + 1 Φ 5/8 2Φ1 2 Φ 1+ 1 Φ 5/8 2 Φ 1+ 2 Φ 5/8 3Φ1

Area (cm2) b min (cm) 7.080 16.57 10.200 17.52 12.180 21.65 14.160 25.78 15.300 22.60