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Izquierda Derecha

Viga A - B 2.690 Tn-m -4.020 Tn-m 2.000 Tn-m

Viga B - C 4.508 Tn-m -3.230 Tn-m 2.470 Tn-m

Viga A - B 3.194 Tn-m -3.747 Tn-m 1.840 Tn-m

Viga B - C 4.181 Tn-m -3.834 Tn-m 2.370 Tn-m

Viga A - B 2.274 Tn-m -3.811 Tn-m 2.080 Tn-m

Viga B - C 3.869 Tn-m -2.389 Tn-m 2.060 Tn-m

b = 25.00 cm

h = 35.00 cm Asumo : 3/4" 1.91 cm

f'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 29.10 cm

Recub = 4.00 cm

As min = Pmin.b.dPmin = 0 0024

PROYECTO VIVIENDA UNIFAM ILIAR - 3 PISOS - DISEO DE VIGAS PORTANTES

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

2. DETERMINACION DEL ACERO MINIMO

VIGAS PORTANTES EJE 1-1

PISO VIGAS M Max. Negativos M Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

TERCER PISO

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Viga A - B 2.000 Tn-m 2 1/2'' 2.580 cm

Viga B - C 2.470 Tn-m 3 1/2 '' 3.870 cmViga A - B 1.840 Tn-m 2 5/8 3.960 cm

Viga B - C 2.370 Tn-m 4 1/2 '' 5.160 cm

Viga A - B 2.080 Tn-m

Viga B - C 2.060 Tn-m

Mmax (+) 2.000 Tn-m Mmax (+) 2.470 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 1.914 cm a =1.80 cm REPETIR As = 2.364 cm a =2.23 cm REPETIR

As = 1.877 cm a =1.77 cm REPETIR As = 2.335 cm a =2.20 cm REPETIR

As = 1.875 cm a =1.77 cm OK As = 2.334 cm a =2.20 cm OK

As = 1.875 cm As = 2.334 cm

Usar 2 1/2'' As =2.580 cm Usar 2 1/2'' As =2.580 cm

Mmax (+) -1.840 Tn-m Mmax (+) 2.370 Tn-mb = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -1.761 cm -a =1.66 cm REPETIR As = 2.268 cm a =2.13 cm REPETIR

As = -1.627 cm -a =1.53 cm REPETIR As = 2.237 cm a =2.11 cm REPETIR

As = -1.630 cm -a =1.53 cm OK As = 2.236 cm a =2.10 cm OK

PRIMER PISO (TRAMO B-C)PRIMER PISO (TRAMO A - B )

SEGUNDO PISO (TRAMO A - B ) SEGUNDO PISO (TRAMO B-C)

PRIMER PISO

SEGUNDO PISO

TERCER PISO

4. DETERMINACION DEL REFUERZO EN LA VIGA

A. ACEROS POSITIVOS FRMULAS

)2/.(. adfy

Mu

As

bcf

fyAsa

.'.85.0

.

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As = 1.953 cm As = 1.934 cm

Usar 2 1/2'' As =2.580 cm Usar 2 1/2'' As =2.580 cm

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Area b min Area b min1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min

8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm

11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm23 3/8 0 95 0 559 0 71

2 1 + 1 3/4

2 1+ 2 3/4

1 1 + 1 5/8

2 3/4''

2 1

1 1/2'' + 2 3/4''

2 1+ 1 5/8

3 3/4''

2 1/2'' + 2 3/4''

3 1

1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

3 3/8'' 2 1/2 + 1 5/8

4 3/8'' 3 5/8

3 1/2 ''

2 5/8

1 1/2 + 2 5/8

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

4 3/4''

2 1/2''

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"2 3/8'' 1 1/2 + 1 5/8

1 1/2'' + 1 3/8''

3/4 - 1"

1 3/4 + 1 1

1 1 + 2 3/4

1/2 - 3/4"

4 1/2 ''

1 1/2'' + 1 3/4''

2 1/2'' + 1 3/4''

ACEROS COMERCIALES

DIMETRO

2 1+ 2 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

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M ( - )

A -2.690 Tn-m

B -4.508 Tn-m

C -3.230 Tn-mA -3.194 Tn-m

B -4.181 Tn-m

C -3.834 Tn-m

A -2.274 Tn-m

B -3.869 Tn-m

C -2.389 Tn-m

Mmax (-) -2.690 Tn-m Mmax (-) -4.508 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.575 cm -a =2.42 cm REPETIR As = -4.314 cm -a =4.06 cm REPETIR

As = -2.348 cm -a =2.21 cm REPETIR As = -3.831 cm -a =3.61 cm REPETIR

As = -2.357 cm -a =2.22 cm OK As = -3.860 cm -a =3.63 cm REPETIR

As = -3.858 cm -a =3.63 cm OK

As = -2.356 cm As = -3.858 cm

Usar 2 1/2'' As =2.580 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -3.230 Tn-m Mmax (-) -3.194 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.092 cm -a =2.91 cm REPETIR As = -3.057 cm -a =2.88 cm REPETIR

As = -2.797 cm -a =2.63 cm REPETIR As = -2.767 cm -a =2.60 cm REPETIR

As = -2.810 cm -a =2.64 cm REPETIR As = -2.780 cm -a =2.62 cm REPETIR

PRIMER PISO (APOYO B)

PRIMER PISO (APOYO C) SEGUNDO PISO (APOYO A)

PRIMER PISO (APOYO A)

PRIMER PISO

SEGUNDO PISO

TERCER PISO

FRMULASB. ACEROS NEGATIVOS

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

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As = -3.593 cm -a =3.38 cm OK As = -3.309 cm -a =3.11 cm OK

As = -3.593 cm As = -3.309 cm

Usar 3 1/2 '' As =3.870 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -2.274 Tn-m Mmax (-) -3.869 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.176 cm -a =2.05 cm REPETIR As = -3.704 cm -a =3.49 cm REPETIR

As = -1.997 cm -a =1.88 cm REPETIR As = -3.320 cm -a =3.12 cm REPETIR

As = -2.003 cm -a =1.89 cm OK As = -3.339 cm -a =3.14 cm REPETIR

As = -3.338 cm -a =3.14 cm OK

As = -2.003 cm As = -3.338 cm

Usar 2 1/2'' As =2.580 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -2.389 Tn-m

b = 25.00 cm

d = 29.10 cm

= 0.9

Asumir: a = 0.10.d a =2.91 cm

As = -2.286 cm -a =2.15 cm REPETIR

As = -2.095 cm -a =1.97 cm REPETIR

As = -2.101 cm -a =1.98 cm OK

As = -2.101 cm

Usar 2 1/2'' As =2.580 cm

TERCER PISO (APOYO C)

TERCER PISO (APOYO A) TERCER PISO (APOYO B)

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Izquierda Derecha

Viga A - B 4.192 Tn-m -5.855 Tn-m 3.070 Tn-m

Viga B - C 5.443 Tn-m -3.648 Tn-m 2.690 Tn-m

Viga A - B 0.826 Tn-m -5.592 Tn-m 2.830 Tn-m

Viga B - C 4.940 Tn-m -4.312 Tn-m 2.620 Tn-m

Viga A - B 3.794 Tn-m -5.782 Tn-m 3.330 Tn-m

Viga B - C 4.932 Tn-m -2.730 Tn-m 2.220 Tn-m

b = 25.00 cm

h = 35.00 cm Asumo : 3/4" 1.91 cmf'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 29.10 cm

Recub = 4.00 cm

As min = Pmin.b.dPmin = 0 0024

VIGAS PORTANTES EJE 2-2

PISO VIGAS M Max. Negativos M Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

TERCER PISO

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

2. DETERMINACION DEL ACERO MINIMO

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Viga A - B 3.070 Tn-m

Viga B - C 2.690 Tn-mViga A - B 2.830 Tn-m

Viga B - C 2.620 Tn-m

Viga A - B 3.330 Tn-m

Viga B - C 2.220 Tn-m

Mmax (+) 3.070 Tn-m Mmax (+) 2.690 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 2.938 cm a =2.77 cm REPETIR As = 2.575 cm a =2.42 cm REPETIRAs = 2.931 cm a =2.76 cm OK As = 2.552 cm a =2.40 cm REPETIR

As = 2.930 cm a =2.76 cm OK As = 2.551 cm a =2.40 cm OK

As = 2.930 cm As = 2.551 cm

Usar 3 1/2 '' As =3.870 cm Usar 2 1/2'' As =2.580 cm

Mmax (+) -2.830 Tn-m Mmax (+) 2.620 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.709 cm -a =2.55 cm REPETIR As = 2.508 cm a =2.36 cm REPETIR

As = -2.465 cm -a =2.32 cm REPETIR As = 2.483 cm a =2.34 cm REPETIR

As = -2.475 cm -a =2.33 cm OK As = 2.482 cm a =2.34 cm OK

A. ACEROS POSITIVOS FRMULAS

PRIMER PISO

SEGUNDO PISO

TERCER PISO

PRIMER PISO (TRAMO A - B ) PRIMER PISO (TRAMO B-C)

4. DETERMINACION DEL REFUERZO EN LA VIGA

SEGUNDO PISO (TRAMO A - B ) SEGUNDO PISO (TRAMO B-C)

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

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As = 3.193 cm As = 2.089 cm

Usar 3 1/2 '' As =3.870 cm Usar 2 1/2'' As =2.580 cm

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Area b min Area b min1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min

8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm23 3/8 0 95 0 559 0 71

3 3/4'' 1 3/4 + 1 1

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

2 3/4'' 3 1

3 1/2'' + 1 3/8'' 5/8 - 1"

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

1/2 - 3/8" 1/2 - 5/8"2 3/8'' 1 1/2 + 1 5/8

COMBINACIONES RECOMENDADAS DE ACERO

1 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

ACEROS COMERCIALES

DIMETRO

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

4 3/8'' 3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 '' 1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

4 3/4'' 2 1 + 1 3/4

2 1+ 2 3/4

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

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M ( - )

A -4.192 Tn-m

B -5.855 Tn-m

C -3.648 Tn-mA -0.826 Tn-m

B -5.592 Tn-m

C -4.312 Tn-m

A -3.794 Tn-m

B -5.782 Tn-m

C -2.730 Tn-m

Mmax (-) -4.192 Tn-m Mmax (-) -5.855 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -4.012 cm -a =3.78 cm REPETIR As = -5.604 cm -a =5.27 cm REPETIRAs = -3.579 cm -a =3.37 cm REPETIR As = -4.881 cm -a =4.59 cm REPETIR

As = -3.603 cm -a =3.39 cm REPETIR As = -4.934 cm -a =4.64 cm REPETIR

As = -4.930 cm -a =4.64 cm OK

As = -3.602 cm As = -4.930 cm

Usar 3 1/2 '' As =3.870 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) -3.648 Tn-m Mmax (-) -0.826 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.492 cm -a =3.29 cm REPETIR As = -0.790 cm -a =0.74 cm REPETIR

As = -3.140 cm -a =2.96 cm REPETIR As = -0.741 cm -a =0.70 cm REPETIR

As = -3.157 cm -a =2.97 cm REPETIR As = -0.742 cm -a =0.70 cm OK

PRIMER PISO

SEGUNDO PISO

TERCER PISO

PRIMER PISO (APOYO A)

B. ACEROS NEGATIVOS FRMULAS

PRIMER PISO (APOYO B)

PRIMER PISO (APOYO C) SEGUNDO PISO (APOYO A)

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

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As = -4.723 cm -a =4.45 cm OK As = -3.700 cm -a =3.48 cm OK

As = -4.723 cm As = -3.700 cm

Usar 4 1/2 '' As =5.160 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -3.794 Tn-m Mmax (-) -5.782 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.631 cm -a =3.42 cm REPETIR As = -5.534 cm -a =5.21 cm REPETIR

As = -3.258 cm -a =3.07 cm REPETIR As = -4.825 cm -a =4.54 cm REPETIR

As = -3.277 cm -a =3.08 cm REPETIR As = -4.877 cm -a =4.59 cm REPETIR

As = -3.276 cm -a =3.08 cm OK As = -4.873 cm -a =4.59 cm OK

As = -3.276 cm As = -4.873 cm

Usar 3 1/2 '' As =3.870 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) -2.730 Tn-m

b = 25.00 cmd = 29.10 cm

= 0.9

Asumir: a = 0.10.d a =2.91 cm

As = -2.613 cm -a =2.46 cm REPETIR

As = -2.382 cm -a =2.24 cm REPETIR

As = -2.390 cm -a =2.25 cm OK

As = -2.390 cm

Usar 2 1/2'' As =2.580 cm

TERCER PISO (APOYO A) TERCER PISO (APOYO B)

TERCER PISO (APOYO C)

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Izquierda Derecha

Viga A - B 4.119 Tn-m -5.696 Tn-m 3.120 Tn-m

Viga B - C 4.549 Tn-m -2.835 Tn-m 1.970 Tn-m

Viga A - B 4.721 Tn-m -5.561 Tn-m 2.840 Tn-m

Viga B - C 4.004 Tn-m -3.396 Tn-m 1.990 Tn-m

Viga A - B 3.769 Tn-m -5.488 Tn-m 3.400 Tn-m

Viga B - C 3.707 Tn-m -1.652 Tn-m 1.270 Tn-m

b = 25.00 cm

h = 35.00 cm Asumo : 3/4" 1.91 cmf'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 29.10 cm

Recub = 4.00 cm

As min = Pmin.b.dPmin = 0 0024

h - Recub - estrib - asumo/2

2. DETERMINACION DEL ACERO MINIMO

TERCER PISO

PISO VIGAS M Max. Negativos M Max. Posiitivo

VIGAS PORTANTES EJE 3-3

SEGUNDO PISO

PRIMER PISO

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

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Viga A - B 3.120 Tn-m

Viga B - C 1.970 Tn-m

Viga A - B 2.840 Tn-m

Viga B - C 1.990 Tn-m

Viga A - B 3.400 Tn-m

Viga B - C 1.270 Tn-m

Mmax (+) 3.120 Tn-m Mmax (+) 1.970 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 2.986 cm a =2.81 cm REPETIR As = 1.886 cm a =1.77 cm REPETIRAs = 2.981 cm a =2.81 cm OK As = 1.848 cm a =1.74 cm REPETIR

As = 2.981 cm a =2.81 cm OK As = 1.846 cm a =1.74 cm OK

As = 2.981 cm As = 1.846 cm

Usar 3 1/2 '' As =3.870 cm Usar 2 1/2'' As =2.580 cm

Mmax (+) -2.840 Tn-m Mmax (+) 1.990 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.718 cm -a =2.56 cm REPETIR As = 1.905 cm a =1.79 cm REPETIR

As = -2.474 cm -a =2.33 cm REPETIR As = 1.867 cm a =1.76 cm REPETIR

As = -2.483 cm -a =2.34 cm OK As = 1.866 cm a =1.76 cm OK

SEGUNDO PISO

TERCER PISO

4. DETERMINACION DEL REFUERZO EN LA VIGA

A. ACEROS POSITIVOS FRMULAS

PRIMER PISO

PRIMER PISO (TRAMO A - B ) PRIMER PISO (TRAMO B-C)

SEGUNDO PISO (TRAMO A - B ) SEGUNDO PISO (TRAMO B-C)

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

5/24/2018 Dise o de Vigas Kelly

15/99

As = 3.264 cm As = 1.177 cm

Usar 3 1/2 '' As =3.870 cm Usar 2 1/2'' As =2.580 cm

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Area b min Area b min1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min

8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0 95 0 559 0 71

2 3/4'' 3 1

4 3/8'' 3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 '' 1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

2 1+ 2 3/4

ACEROS COMERCIALES

DIMETRO

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"2 3/8'' 1 1/2 + 1 5/8

1 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

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

3 3/4'' 1 3/4 + 1 1

2 1/2'' + 2 3/4'' 1 1 + 2 3/44 3/4'' 2 1 + 1 3/4

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M ( - )

A -4.119 Tn-m

B -5.696 Tn-m

C -2.835 Tn-m

A -4.721 Tn-m

B -5.561 Tn-m

C -3.396 Tn-m

A -3.769 Tn-m

B -5.488 Tn-m

C -1.652 Tn-m

Mmax (-) -4.119 Tn-m Mmax (-) -5.696 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.942 cm -a =3.71 cm REPETIR As = -5.452 cm -a =5.13 cm REPETIRAs = -3.521 cm -a =3.31 cm REPETIR As = -4.760 cm -a =4.48 cm REPETIR

As = -3.543 cm -a =3.33 cm REPETIR As = -4.809 cm -a =4.53 cm REPETIR

As = -3.542 cm -a =3.33 cm OK As = -4.806 cm -a =4.52 cm OK

As = -3.542 cm As = -4.806 cm

Usar 3 1/2 '' As =3.870 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) -2.835 Tn-m Mmax (-) -4.721 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.713 cm -a =2.55 cm REPETIR As = -4.519 cm -a =4.25 cm REPETIR

As = -2.469 cm -a =2.32 cm REPETIR As = -4.001 cm -a =3.77 cm REPETIR

As = -2.478 cm -a =2.33 cm OK As = -4.032 cm -a =3.79 cm REPETIR

SEGUNDO PISO

TERCER PISO

FRMULASB. ACEROS NEGATIVOS

PRIMER PISO

PRIMER PISO (APOYO A) PRIMER PISO (APOYO B)

PRIMER PISO (APOYO C) SEGUNDO PISO (APOYO A)

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

5/24/2018 Dise o de Vigas Kelly

18/99

As = -4.699 cm -a =4.42 cm OK As = -2.947 cm -a =2.77 cm OK

As = -4.699 cm As = -2.947 cm

Usar 4 1/2 '' As =5.160 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -3.769 Tn-m Mmax (-) -5.488 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.607 cm -a =3.39 cm REPETIR As = -5.252 cm -a =4.94 cm REPETIR

As = -3.238 cm -a =3.05 cm REPETIR As = -4.599 cm -a =4.33 cm REPETIR

As = -3.256 cm -a =3.06 cm REPETIR As = -4.644 cm -a =4.37 cm REPETIR

As = -3.255 cm -a =3.06 cm OK As = -4.641 cm -a =4.37 cm OK

As = -3.255 cm As = -4.641 cm

Usar 3 1/2 '' As =3.870 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) -1.652 Tn-m

b = 25.00 cmd = 29.10 cm

= 0.9

Asumir: a = 0.10.d a =2.91 cm

As = -1.581 cm -a =1.49 cm REPETIR

As = -1.465 cm -a =1.38 cm REPETIR

As = -1.467 cm -a =1.38 cm OK

As = -1.467 cmUsar 2 1/2'' As =2.580 cm

TERCER PISO (APOYO C)

TERCER PISO (APOYO A) TERCER PISO (APOYO B)

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Izquierda Derecha

Viga A - B 4.583 Tn-m -6.076 Tn-m 3.420 Tn-m

Viga B - C 4.105 Tn-m -2.383 Tn-m 1.630 Tn-m

Viga A - B 5.146 Tn-m -5.931 Tn-m 3.170 Tn-m

Viga B - C 3.636 Tn-m -2.896 Tn-m 1.630 Tn-m

Viga A - B 3.229 Tn-m -4.740 Tn-m 2.850 Tn-m

Viga B - C 3.289 Tn-m -1.616 Tn-m 1.270 Tn-m

b = 25.00 cm

h = 35.00 cm Asumo : 3/4" 1.91 cmf'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 29.10 cm

Recub = 4.00 cm

As min = Pmin.b.d

Pmin = 0 0024

VIGAS PORTANTES EJE 4-4

PISO VIGASM Max. Negativos

M Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

TERCER PISO

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

2. DETERMINACION DEL ACERO MINIMO

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Viga A - B 3.420 Tn-m

Viga B - C 1.630 Tn-m

Viga A - B 3.170 Tn-m

Viga B - C 1.630 Tn-m

Viga A - B 2.850 Tn-m

Viga B - C 1.270 Tn-m

Mmax (+) 3.420 Tn-m Mmax (+) 1.630 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 3.273 cm a =3.08 cm REPETIR As = 1.560 cm a =1.47 cm REPETIRAs = 3.284 cm a =3.09 cm OK As = 1.520 cm a =1.43 cm REPETIR

As = 1.519 cm a =1.43 cm OK

As = 3.284 cm As = 1.519 cm

Usar 3 1/2 '' As =3.870 cm Usar 2 1/2'' As =2.580 cm

Mmax (+) -3.170 Tn-m Mmax (+) 1.630 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.034 cm -a =2.86 cm REPETIR As = 1.560 cm a =1.47 cm REPETIR

As = -2.748 cm -a =2.59 cm REPETIR As = 1.520 cm a =1.43 cm REPETIR

As = -2.760 cm -a =2.60 cm REPETIR As = 1.519 cm a =1.43 cm OK

4. DETERMINACION DEL REFUERZO EN LA VIGA

PRIMER PISO (TRAMO A - B )

A. ACEROS POSITIVOS FRMULAS

PRIMER PISO

SEGUNDO PISO

TERCER PISO

SEGUNDO PISO (TRAMO A - B ) SEGUNDO PISO (TRAMO B-C)

PRIMER PISO (TRAMO B-C)

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

5/24/2018 Dise o de Vigas Kelly

21/99

As = 2.710 cm As = 1.177 cm

Usar 3 1/2 '' As =3.870 cm Usar 2 1/2'' As =2.580 cm

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Area b min Area b min

1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min

8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0 95 0 559 0 71

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"

2 3/8'' 1 1/2 + 1 5/8

1 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

4 3/8'' 3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 '' 1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

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

3 3/4'' 1 3/4 + 1 1

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

3 1/2'' + 1 3/8'' 5/8 - 1"

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

4 3/4''

ACEROS COMERCIALES

DIMETRO

2 1 + 1 3/4

2 1+ 2 3/4

2 3/4'' 3 1

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M ( - )

A -4.583 Tn-m

B -6.076 Tn-m

C -2.383 Tn-m

A -5.146 Tn-m

B -5.931 Tn-m

C -2.896 Tn-m

A -3.229 Tn-m

B -4.740 Tn-m

C -1.616 Tn-m

Mmax (-) -4.583 Tn-m Mmax (-) -6.076 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -4.386 cm -a =4.13 cm REPETIR As = -5.816 cm -a =5.47 cm REPETIRAs = -3.891 cm -a =3.66 cm REPETIR As = -5.050 cm -a =4.75 cm REPETIR

As = -3.920 cm -a =3.69 cm REPETIR As = -5.108 cm -a =4.81 cm REPETIR

As = -3.918 cm -a =3.69 cm OK As = -5.103 cm -a =4.80 cm OK

As = -3.918 cm As = -5.104 cm

Usar 2 5/8 As =3.960 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) -2.383 Tn-m Mmax (-) -5.146 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.281 cm -a =2.15 cm REPETIR As = -4.926 cm -a =4.64 cm REPETIR

As = -2.090 cm -a =1.97 cm REPETIR As = -4.334 cm -a =4.08 cm REPETIR

As = -2.096 cm -a =1.97 cm OK As = -4.373 cm -a =4.12 cm REPETIR

B. ACEROS NEGATIVOS

PRIMER PISO

SEGUNDO PISO

TERCER PISO

PRIMER PISO (APOYO B)

PRIMER PISO (APOYO C) SEGUNDO PISO (APOYO A)

PRIMER PISO (APOYO A)

FRMULAS

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

5/24/2018 Dise o de Vigas Kelly

24/99

As = -4.989 cm -a =4.70 cm OK

As = -4.990 cm As = -2.529 cm

Usar 4 1/2 '' As =5.160 cm Usar 2 1/2'' As =2.580 cm

Mmax (-) -3.229 Tn-m Mmax (-) -4.740 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.091 cm -a =2.91 cm REPETIR As = -4.537 cm -a =4.27 cm REPETIR

As = -2.797 cm -a =2.63 cm REPETIR As = -4.015 cm -a =3.78 cm REPETIR

As = -2.809 cm -a =2.64 cm REPETIR As = -4.047 cm -a =3.81 cm REPETIR

As = -2.809 cm -a =2.64 cm OK As = -4.045 cm -a =3.81 cm OK

As = -2.809 cm As = -4.045 cm

Usar 3 1/2 '' As =3.870 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) -1.616 Tn-m

b = 25.00 cmd = 29.10 cm

= 0.9

Asumir: a = 0.10.d a =2.91 cm

As = -1.546 cm -a =1.46 cm REPETIR

As = -1.433 cm -a =1.35 cm REPETIR

As = -1.436 cm -a =1.35 cm OK

As = -1.436 cmUsar 2 1/2'' As =2.580 cm

TERCER PISO (APOYO A) TERCER PISO (APOYO B)

TERCER PISO (APOYO C)

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Izquierda Derecha

Viga A - B 3.124 Tn-m -3.657 Tn-m 2.420 Tn-m

Viga B - C 3.657 Tn-m -0.036 Tn-m 1.810 Tn-m

Viga A - B 3.677 Tn-m -4.434 Tn-m 2.380 Tn-m

Viga B - C 3.441 Tn-m -3.001 Tn-m 1.700 Tn-m

Viga A - B 2.307 Tn-m -3.894 Tn-m 2.030 Tn-m

Viga B - C 3.887 Tn-m -2.491 Tn-m 2.170 Tn-m

b = 25.00 cm

h = 35.00 cm Asumo : 3/4" 1.91 cm

f'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 29.10 cm

Recub = 4.00 cm

As min = Pmin.b.d

Pmin = 0 0024

VIGAS PORTANTES EJE 5-5

PISO VIGASM Max. Negativos

M Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

TERCER PISO

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

2. DETERMINACION DEL ACERO MINIMO

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Viga A - B 2.420 Tn-m

Viga B - C 1.810 Tn-m

Viga A - B 2.380 Tn-m

Viga B - C 1.700 Tn-m

Viga A - B 2.030 Tn-m

Viga B - C 2.170 Tn-m

Mmax (+) 2.420 Tn-m Mmax (+) 1.810 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 2.316 cm a =2.18 cm REPETIR As = 1.732 cm a =1.63 cm REPETIR

As = 2.286 cm a =2.15 cm REPETIR As = 1.693 cm a =1.59 cm REPETIR

As = 2.285 cm a =2.15 cm OK As = 1.692 cm a =1.59 cm OK

As = 2.285 cm As = 1.692 cm

Usar 2 1/2'' As =2.580 cm Usar 2 1/2'' As =2.580 cm

Mmax (+) -2.380 Tn-m Mmax (+) 1.700 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.278 cm -a =2.14 cm REPETIR As = 1.627 cm a =1.53 cm REPETIR

As = -2.087 cm -a =1.96 cm REPETIR As = 1.588 cm a =1.49 cm REPETIR

As = -2.093 cm -a =1.97 cm OK As = 1.586 cm a =1.49 cm OK

4. DETERMINACION DEL REFUERZO EN LA VIGA

PRIMER PISO (TRAMO A - B ) PRIMER PISO (TRAMO B-C)

SEGUNDO PISO (TRAMO A - B ) SEGUNDO PISO (TRAMO B-C)

A. ACEROS POSITIVOS FRMULAS

PRIMER PISO

SEGUNDO PISO

TERCER PISO

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

5/24/2018 Dise o de Vigas Kelly

27/99

As = 1.904 cm As = 2.040 cm

Usar 2 1/2'' As =2.580 cm Usar 2 1/2'' As =2.580 cm

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Area b min Area b min

1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min

8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm

11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0 95 0 559 0 71

4 3/4'' 2 1 + 1 3/4

2 1+ 2 3/4

4 1/2 '' 1 1 + 1 5/8

2 3/4'' 3 1

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

3 3/4'' 1 3/4 + 1 1

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

4 3/8'' 3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 '' 1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

1 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"

2 3/8'' 1 1/2 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

1 1/2'' + 2 3/8''

ACEROS COMERCIALES

DIMETRO

3 1/2 + 1 5/8

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M ( - )

A -3.124 Tn-m

B -3.657 Tn-m

C -0.036 Tn-m

A -3.677 Tn-m

B -4.434 Tn-m

C -3.001 Tn-m

A -2.307 Tn-m

B -3.894 Tn-m

C -2.491 Tn-m

Mmax (-) -3.124 Tn-m Mmax (-) -3.657 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.990 cm -a =2.81 cm REPETIR As = -3.500 cm -a =3.29 cm REPETIR

As = -2.709 cm -a =2.55 cm REPETIR As = -3.147 cm -a =2.96 cm REPETIR

As = -2.721 cm -a =2.56 cm REPETIR As = -3.164 cm -a =2.98 cm REPETIR

As = -2.721 cm -a =2.56 cm OK As = -3.163 cm -a =2.98 cm OK

As = -2.721 cm As = -3.163 cm

Usar 3 1/2 '' As =3.870 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -0.036 Tn-m Mmax (-) -3.677 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -0.035 cm -a =0.03 cm REPETIR As = -3.519 cm -a =3.31 cm REPETIR

As = -0.033 cm -a =0.03 cm OK As = -3.163 cm -a =2.98 cm REPETIR

As = -3.180 cm -a =2.99 cm REPETIR

PRIMER PISO (APOYO A) PRIMER PISO (APOYO B)

PRIMER PISO (APOYO C) SEGUNDO PISO (APOYO A)

PRIMER PISO

SEGUNDO PISO

TERCER PISO

B. ACEROS NEGATIVOS FRMULAS

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

5/24/2018 Dise o de Vigas Kelly

30/99

As = -3.798 cm -a =3.58 cm OK As = -2.618 cm -a =2.46 cm OK

As = -3.799 cm As = -2.618 cm

Usar 3 1/2 '' As =3.870 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -2.307 Tn-m Mmax (-) -3.894 Tn-mb = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.208 cm -a =2.08 cm REPETIR As = -3.727 cm -a =3.51 cm REPETIR

As = -2.025 cm -a =1.91 cm REPETIR As = -3.340 cm -a =3.14 cm REPETIRAs = -2.031 cm -a =1.91 cm OK As = -3.360 cm -a =3.16 cm REPETIR

As = -3.359 cm -a =3.16 cm OK

As = -2.031 cm As = -3.359 cm

Usar 2 1/2'' As =2.580 cm Usar 3 1/2 '' As =3.870 cm

Mmax (-) -2.491 Tn-m

b = 25.00 cm

d = 29.10 cm

= 0.9

Asumir: a = 0.10.d a =2.91 cm

As = -2.384 cm -a =2.24 cm REPETIR

As = -2.181 cm -a =2.05 cm REPETIR

As = -2.188 cm -a =2.06 cm OK

As = -2.187 cmUsar 2 1/2'' As =2.580 cm

TERCER PISO (APOYO A) TERCER PISO (APOYO B)

TERCER PISO (APOYO C)

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Izquierda Derecha

Viga A - B -2.544 Tn-m -4.904 Tn-m 0.290 Tn-m

Viga B - C 3.675 Tn-m -2.702 Tn-m 0.100 Tn-m

Viga A - B 3.085 Tn-m -5.068 Tn-m 0.300 Tn-m

Viga B - C 3.986 Tn-m -2.321 Tn-m 0.100 Tn-m

b = 25.00 cm

h = 35.00 cm Asumo : 3/4" 1.91 cm

f'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 29.10 cm

Recub = 4.00 cm

As min = Pmin.b.d

Pmin = 0 0024

VIGAS PORTANTES EJE 6-6

PISO VIGAS

M Max. Negativos

M Max. Posiitivo

PRIMER PISO

SEGUNDO PISO

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

2. DETERMINACION DEL ACERO MINIMO

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Viga A - B 0.290 Tn-m

Viga B - C 0.100 Tn-m

Viga A - B 0.300 Tn-m

Viga B - C 0.100 Tn-m

Mmax (+) 0.290 Tn-m Mmax (+) 0.100 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 0.278 cm a =0.26 cm REPETIR As = 0.096 cm a =0.09 cm REPETIR

As = 0.265 cm a =0.25 cm REPETIR As = 0.091 cm a =0.09 cm OK

As = 0.265 cm a =0.25 cm OK

As = 0.265 cm As = 0.091 cm

Usar 2 1/2'' As =2.580 cm Usar 2 1/2'' As =2.580 cm

Mmax (+) -0.300 Tn-m Mmax (+) 0.100 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -0.287 cm -a =0.27 cm REPETIR As = 0.096 cm a =0.09 cm REPETIR

As = -0.272 cm -a =0.26 cm REPETIR As = 0.091 cm a =0.09 cm OK

As = -0.272 cm -a =0.26 cm OK

A. ACEROS POSITIVOS FRMULAS

PRIMER PISO

SEGUNDO PISO (TRAMO A - B ) SEGUNDO PISO (TRAMO B-C)

SEGUNDO PISO

PRIMER PISO (TRAMO A - B ) PRIMER PISO (TRAMO B-C)

4. DETERMINACION DEL REFUERZO EN LA VIGA

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Area b min Area b min

1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min

8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm

11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0 95 0 559 0 71

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"

2 3/8'' 1 1/2 + 1 5/8

1 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

4 3/8'' 3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 '' 1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

2 3/4'' 3 1

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

3 3/4'' 1 3/4 + 1 1

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

4 3/4'' 2 1 + 1 3/4

2 1+ 2 3/4

ACEROS COMERCIALES

DIMETRO

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M ( - )

A 2.544 Tn-m

B -4.904 Tn-m

C -2.702 Tn-m

A -3.085 Tn-m

B -5.068 Tn-m

C -2.321 Tn-m

Mmax (-) 2.544 Tn-m Mmax (-) -4.904 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 2.435 cm a =2.29 cm REPETIR As = -4.694 cm -a =4.42 cm REPETIR

As = 2.408 cm a =2.27 cm REPETIR As = -4.145 cm -a =3.90 cm REPETIR

As = 2.407 cm a =2.27 cm OK As = -4.179 cm -a =3.93 cm REPETIR

As = -4.177 cm -a =3.93 cm OK

As = 2.407 cm As = -4.177 cm

Usar 2 1/2'' As =2.580 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) -2.702 Tn-m Mmax (-) -3.085 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -2.586 cm -a =2.43 cm REPETIR As = -2.953 cm -a =2.78 cm REPETIR

As = -2.358 cm -a =2.22 cm REPETIR As = -2.678 cm -a =2.52 cm REPETIR

As = -2.367 cm -a =2.23 cmOK

As = -2.689 cm -a =2.53 cmREPETIR

PRIMER PISO

PRIMER PISO (APOYO C) SEGUNDO PISO (APOYO A)

SEGUNDO PISO

PRIMER PISO (APOYO A) PRIMER PISO (APOYO B)

B. ACEROS NEGATIVOS FRMULAS

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As = -4.308 cm -a =4.05 cm OK

As = -4.308 cm As = -2.043 cm

Usar 4 1/2 '' As =5.160 cm Usar 2 1/2'' As =2.580 cm

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Izquierda Derecha

Viga A - B 3.603 Tn-m -5.273 Tn-m 0.290 Tn-m

Viga B - C 2.903 Tn-m 0.000 Tn-m 0.100 Tn-m

Viga A - B 3.069 Tn-m -5.293 Tn-m 0.300 Tn-m

Viga B - C 2.983 Tn-m 0.000 Tn-m 0.100 Tn-m

b = 25.00 cm

h = 35.00 cm Asumo : 3/4" 1.91 cm

f'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 29.10 cm

Recub = 4.00 cm

As min = Pmin.b.d

Pmin = 0 0024

PRIMER PISO

SEGUNDO PISO

VIGAS PORTANTES EJE 7-7

PISO VIGAS

M Max. Negativos

M Max. Posiitivo

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

2. DETERMINACION DEL ACERO MINIMO

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Viga A - B 0.290 Tn-m

Viga B - C 0.100 Tn-m

Viga A - B 0.300 Tn-m

Viga B - C 0.100 Tn-m

Mmax (+) 0.290 Tn-m Mmax (+) 0.100 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 0.278 cm a =0.26 cm REPETIR As = 0.096 cm a =0.09 cm REPETIR

As = 0.265 cm a =0.25 cm REPETIR As = 0.091 cm a =0.09 cm OK

As = 0.265 cm a =0.25 cm OK

As = 0.265 cm As = 0.091 cm

Usar 2 1/2'' As =2.580 cm Usar 2 1/2'' As =2.580 cm

Mmax (+) -0.300 Tn-m Mmax (+) 0.100 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -0.287 cm -a =0.27 cm REPETIR As = 0.096 cm a =0.09 cm REPETIR

As = -0.272 cm -a =0.26 cm REPETIR As = 0.091 cm a =0.09 cm OK

As = -0.272 cm -a =0.26 cm OK

4. DETERMINACION DEL REFUERZO EN LA VIGA

A. ACEROS POSITIVOS FRMULAS

PRIMER PISO

SEGUNDO PISO

PRIMER PISO (TRAMO A - B ) PRIMER PISO (TRAMO B-C)

SEGUNDO PISO (TRAMO A - B ) SEGUNDO PISO (TRAMO B-C)

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Area b min Area b min

1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min

8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm

11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0 95 0 559 0 71

4 3/8'' 3 5/8

1 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"

2 3/8'' 1 1/2 + 1 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 '' 1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

2 3/4'' 3 1

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

3 3/4'' 1 3/4 + 1 1

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

4 3/4'' 2 1 + 1 3/4

2 1+ 2 3/4

ACEROS COMERCIALES

DIMETRO

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M ( - )

A -3.603 Tn-m

B -5.273 Tn-m

C 0.000 Tn-m

A -3.069 Tn-m

B -5.293 Tn-m

C 0.000 Tn-m

Mmax (-) -3.603 Tn-m Mmax (-) -5.273 Tn-m

b = 25.00 cm b = 25.00 cm

d = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = -3.448 cm -a =3.25 cm REPETIR As = -5.047 cm -a =4.75 cm REPETIR

As = -3.103 cm -a =2.92 cm REPETIR As = -4.432 cm -a =4.17 cm REPETIR

As = -3.119 cm -a =2.94 cm REPETIR As = -4.474 cm -a =4.21 cm REPETIR

As = -3.119 cm -a =2.94 cm OK As = -4.471 cm -a =4.21 cm OK

As = -3.119 cm As = -4.471 cm

Usar 3 1/2 '' As =3.870 cm Usar 4 1/2 '' As =5.160 cm

Mmax (-) 0.000 Tn-m Mmax (-) -3.069 Tn-m

b = 25.00 cm b = 25.00 cmd = 29.10 cm d = 29.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =2.91 cm Asumir: a = 0.10.d a =2.91 cm

As = 0.000 cm a =0.00 cm REPETIR As = -2.937 cm -a =2.76 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = -2.664 cm -a =2.51 cm REPETIR

As = -2.675 cm -a =2.52 cm REPETIR

B. ACEROS NEGATIVOS FRMULAS

PRIMER PISO

SEGUNDO PISO

PRIMER PISO (APOYO A) PRIMER PISO (APOYO B)

PRIMER PISO (APOYO C) SEGUNDO PISO (APOYO A)

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As = -4.487 cm -a =4.22 cm OK

As = -4.487 cm As = 0.000 cm

Usar 4 1/2 '' As =5.160 cm Usar 2 1/2'' As =2.580 cm

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Izquierda Derecha

Viga 1 - 2 0.620 Tn-m -0.930 Tn-m 0.410 Tn-m

Viga 2 - 3 0.930 Tn-m -1.502 Tn-m 0.880 Tn-m

Viga 3 - 4 1.502 Tn-m 0.974 Tn-m 0.320 Tn-m

Viga 4 - 5 0.974 Tn-m -0.752 Tn-m 0.460 Tn-m

Viga 5 - 6 0.752 Tn-m -0.332 Tn-m 0.000 Tn-m

Viga 6 - 7 0.332 Tn-m -0.910 Tn-m 0.690 Tn-m

Viga 7 - 8 -0.910 Tn-m 0.000 Tn-m 0.000 Tn-mViga 1 - 2 0.861 Tn-m -0.716 Tn-m 0.400 Tn-m

Viga 2 - 3 1.464 Tn-m -1.528 Tn-m 0.870 Tn-m

Viga 3 - 4 0.871 Tn-m -0.851 Tn-m 0.320 Tn-m

Viga 4 - 5 0.612 Tn-m -0.833 Tn-m 0.450 Tn-m

Viga 5 - 6 0.030 Tn-m -0.452 Tn-m 0.000 Tn-m

Viga 6 - 7 1.011 Tn-m -0.763 Tn-m 0.740 Tn-m

Viga 7 -0.763 Tn-m 0.000 Tn-m 0.000 Tn-m

Viga 1 - 2 0.597 Tn-m -0.908 Tn-m 0.430 Tn-m

Viga 2 - 3 1.410 Tn-m -1.496 Tn-m 0.910 Tn-m

Viga 3 - 4 1.072 Tn-m -0.558 Tn-m 0.410 Tn-m

Viga 4 - 5 0.209 Tn-m -0.280 Tn-m 0.060 Tn-m

Viga 5 - 6 #REF! 0.000 Tn-m 0.000 Tn-m

b = 25.00 cm

h = 25.00 cm Asumo : 3/4" 1.91 cm

f'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 19.10 cm

Recub = 4.00 cm

PROYECTO VIVIENDA UNIFAMIL IAR - 3 PISOS - DISEO DE VIGAS NO PORTANTES

VIGAS NO PORTANTES EJE A- A

PISO VIGAS

M Max. Negativos

M Max. Posiitivo

PRIMER PISO

SEGUNDO

PISO

1. DIMENSION Y PROPIEDADES DE LA VIGAPeralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

2 DETERMINACION DEL ACERO MINIMO

TERCER PISO

A ACEROS POSITIVOS S

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Viga 1 - 2 0.410 Tn-m

Viga 2 - 3 0.880 Tn-m

Viga 3 - 4 0.320 Tn-m

Viga 4 - 5 0.460 Tn-mViga 5 - 6 0.000 Tn-m

Viga 6 - 7 0.690 Tn-m

Viga 7 - 8 0.000 Tn-m

Viga 1 - 2 0.400 Tn-m

Viga 2 - 3 0.870 Tn-m

Viga 3 - 4 0.320 Tn-m

Viga 4 - 5 0.450 Tn-m 2 3/8'' 1.420 cm

Viga 5 - 6 0.000 Tn-m 1 1/2'' + 1 3/8'' 2.000 cm

Viga 6 - 7 0.740 Tn-m 3 3/8'' 2.130 cm

Viga 7 - 8 0.000 Tn-m 2 1/2'' 2.580 cm

Viga 1 - 2 0.430 Tn-m

Viga 2 - 3 0.910 Tn-m

Viga 3 - 4 0.410 Tn-m

Viga 4 - 5 0.060 Tn-m

Viga 5 - 6 0.000 Tn-m

Mmax (+) 0.410 Tn-m Mmax (+) 0.880 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.598 cm a =0.56 cm REPETIR As = 1.283 cm a =1.21 cm REPETIR

As = 0.577 cm a =0.54 cm REPETIR As = 1.259 cm a =1.18 cm REPETIR

As = 0.576 cm a =0.54 cm OK As = 1.258 cm a =1.18 cm OK

As = 0.576 cm As = 1.258 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.320 Tn-m Mmax (+) 0.460 Tn-m

A. ACEROS POSITIVOS FRMULAS

PRIMER PISO

SEGUNDO

PISO

TERCER PISO

PRIMER PISO (TRAMO 3 - 4 ) PRIMER PISO (TRAMO 4 - 5)

PRIMER PISO (TRAMO 1 - 2 ) PRIMER PISO (TRAMO 2 - 3 )

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Mmax (+) 0.000 Tn-m Mmax (+) 0.690 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.000 cm a =0.00 cm REPETIR As = 1.006 cm a =0.95 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.980 cm a =0.92 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.980 cm a =0.92 cm OK

As = 0.000 cm As = 0.980 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.000 Tn-m Mmax (+) 0.400 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.000 cm a =0.00 cm REPETIR As = 0.583 cm a =0.55 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.562 cm a =0.53 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.562 cm a =0.53 cm OK

As = 0.000 cm As = 0.562 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.870 Tn-m Mmax (+) 0.320 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 1.269 cm a =1.19 cm REPETIR As = 0.467 cm a =0.44 cm REPETIR

As = 1.244 cm a =1.17 cm REPETIR As = 0.448 cm a =0.42 cm REPETIR

As = 1.243 cm a =1.17 cm OK As = 0.448 cm a =0.42 cm OK

A 1 243 A 0 448

SEGUNDO PISO (TRAMO 2 - 3 ) SEGUNDO PISO (TRAMO 3 - 4)

PRIMER PISO (TRAMO 5 - 6) PRIMER PISO (TRAMO 6 -7)

PRIMER PISO (TRAMO 7-8) SEGUNDO PISO (TRAMO 1 - 2 )

Usar 2 3/8'' As =1 420 cm Usar 2 3/8'' As =1 420 cm

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Usar 2 3/8 As =1.420 cm Usar 2 3/8 As =1.420 cm

SEGUNDO PISO (TRAMO 6 - 7) SEGUNDO PISO (TRAMO 7 - 8)

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Mmax (+) 0.740 Tn-m Mmax (+) 0.000 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 1.079 cm a =1.02 cm REPETIR As = 0.000 cm a =0.00 cm REPETIR

As = 1.053 cm a =0.99 cm REPETIR As = 0.000 cm a =0.00 cm OK

As = 1.053 cm a =0.99 cm OK As = 0.000 cm a =0.00 cm OK

As = 1.053 cm As = 0.000 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.430 Tn-m Mmax (+) 0.910 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.627 cm a =0.59 cm REPETIR As = 1.327 cm a =1.25 cm REPETIR

As = 0.605 cm a =0.57 cm REPETIR As = 1.303 cm a =1.23 cm REPETIR

As = 0.605 cm a =0.57 cm OK As = 1.303 cm a =1.23 cm OK

As = 0.605 cm As = 1.303 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.410 Tn-m Mmax (+) 0.060 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.598 cm a =0.56 cm REPETIR As = 0.088 cm a =0.08 cm REPETIR

As = 0.577 cm a =0.54 cm REPETIR As = 0.083 cm a =0.08 cm OK

As = 0.576 cm a =0.54 cm OK As = 0.083 cm a =0.08 cm OK

As = 0.576 cm As = 0.083 cm

U 2 3/8'' A 1 420 U 2 3/8'' A 1 420

SEGUNDO PISO (TRAMO 6 7) SEGUNDO PISO (TRAMO 7 8)

TERCER PISO (TRAMO 2 - 3 )

TERCER PISO (TRAMO 3 - 4 ) TERCER PISO (TRAMO 4 - 5)

TERCER PISO (TRAMO 1 - 2 )

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Area b min Area b min

1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm

11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0.95 0.559 0.71

4 1/2 1.27 0.993 1.29

5 5/8 1.59 1.552 1.98

6 3/4 1.91 2.235 2.85

8 1 2 54 3 973 5 1

2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

4 3/8'' 3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 ''

1 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"

2 3/8'' 1 1/2 + 1 5/8

1 3/4 + 1 1

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

4 3/4'' 2 1 + 1 3/4

2 1+ 2 3/4

2 3/4'' 3 1

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

1 1/2 + 3 5/8

2 1/2'' + 2 3/8''

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

4 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4"

3 3/4''

ACEROS COMERCIALES

DIMETRO

M ( - ) A.B. ACEROS NEGATIVOS FRMULAS

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( )

Viga 1 - 2 0.620 Tn-m

Viga 2 - 3 -0.930 Tn-m

Viga 3 - 4 -1.502 Tn-m

Viga 4 - 5 0.974 Tn-mViga 5 - 6 -0.752 Tn-m

Viga 6 - 7 -0.332 Tn-m

Viga 7 - 8 -0.910 Tn-m

Viga 1 - 2 0.861 Tn-m

Viga 2 - 3 -0.716 Tn-m

Viga 3 - 4 -1.528 Tn-m

Viga 4 - 5 -0.851 Tn-m

Viga 5 - 6 -0.833 Tn-m

Viga 6 - 7 -0.452 Tn-m

Viga 7 - 8 -0.763 Tn-m

Viga 1 - 2 0.597 Tn-m

Viga 2 - 3 -0.908 Tn-m

Viga 3 - 4 -1.496 Tn-m

Viga 4 - 5 -0.558 Tn-m

Viga 5 - 6 -0.280 Tn-m

Mmax (-) 0.620 Tn-m Mmax (-) -0.930 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cmAs = 0.905 cm a =0.85 cm REPETIR As = -1.357 cm -a =1.28 cm REPETIR

As = 0.879 cm a =0.83 cm REPETIR As = -1.247 cm -a =1.17 cm REPETIR

As = 0.878 cm a =0.83 cm OK As = -1.250 cm -a =1.18 cm OK

As = 0.878 cm As = -1.250 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) -1.502 Tn-m Mmax (-) 0.974 Tn-m

PRIMER PISO (APOYO 1)

PRIMER PISO

SEGUNDO

PISO

TERCER PISO

PRIMER PISO (APOYO 2)

PRIMER PISO (APOYO 3) PRIMER PISO (APOYO 4)

)2/.(. adfy

MuAs

bcf

fyAsa

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.

PRIMER PISO (APOYO 6)PRIMER PISO (APOYO 5)

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Mmax (-) -0.752 Tn-m Mmax (-) -0.332 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -1.096 cm -a =1.03 cm REPETIR As = -0.484 cm -a =0.46 cm REPETIR

As = -1.014 cm -a =0.95 cm REPETIR As = -0.454 cm -a =0.43 cm REPETIR

As = -1.016 cm -a =0.96 cm OK As = -0.455 cm -a =0.43 cm OK

As = -1.016 cm As = -0.455 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) -0.910 Tn-m Mmax (-) 0.861 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -1.327 cm -a =1.25 cm REPETIR As = 1.256 cm a =1.18 cm REPETIR

As = -1.221 cm -a =1.15 cm REPETIR As = 1.231 cm a =1.16 cm REPETIR

As = -1.224 cm -a =1.15 cm OK As = 1.231 cm a =1.16 cm OK

As = -1.224 cm As = 1.231 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) -0.716 Tn-m Mmax (-) -1.528 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm = 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -1.045 cm -a =0.98 cm REPETIR As = -2.228 cm -a =2.10 cm REPETIR

As = -0.968 cm -a =0.91 cm REPETIR As = -2.006 cm -a =1.89 cm REPETIR

As = -0.969 cm -a =0.91 cm OK As = -2.017 cm -a =1.90 cm OK

PRIMER PISO (APOYO 7) SEGUNDO PISO (APOYO 1)

SEGUNDO PISO (APOYO 2) SEGUNDO PISO (APOYO 3)

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

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SEGUNDO PISO (APOYO 6) SEGUNDO PISO (APOYO 7)

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Mmax (-) -0.452 Tn-m Mmax (-) -0.763 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -0.659 cm -a =0.62 cm REPETIR As = -1.113 cm -a =1.05 cm REPETIR

As = -0.616 cm -a =0.58 cm REPETIR As = -1.029 cm -a =0.97 cm REPETIR

As = -0.617 cm -a =0.58 cm OK As = -1.031 cm -a =0.97 cm OK

As = -0.617 cm As = -1.031 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) 0.597 Tn-m Mmax (-) -0.908 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.870 cm a =0.82 cm REPETIR As = -1.325 cm -a =1.25 cm REPETIR

As = 0.845 cm a =0.80 cm REPETIR As = -1.219 cm -a =1.15 cm REPETIR

As = 0.844 cm a =0.79 cm OK As = -1.222 cm -a =1.15 cm OK

As = 0.844 cm As = -1.222 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) -1.496 Tn-m Mmax (-) -0.558 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm = 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -2.181 cm -a =2.05 cm REPETIR As = -0.814 cm -a =0.77 cm REPETIR

As = -1.966 cm -a =1.85 cm REPETIR As = -0.758 cm -a =0.71 cm REPETIR

As = -1.976 cm -a =1.86 cm OK As = -0.759 cm -a =0.71 cm OK

As = -1.976 cm As = -0.759 cm

A 2 000 A 1 420

TERCER PISO (APOYO 1) TERCER PISO (APOYO 2)

TERCER PISO (APOYO 3) TERCER PISO (APOYO 4)

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Izquierda Derecha

Viga 1 - 2 0.832 Tn-m -0.816 Tn-m 0.460 Tn-m

Viga 2 - 3 1.204 Tn-m -1.167 Tn-m 0.720 Tn-m

Viga 3 - 4 0.418 Tn-m -0.166 Tn-m 0.000 Tn-m

Viga 4 - 5 0.537 Tn-m -0.558 Tn-m 0.370 Tn-m

Viga 5 - 6 0.222 Tn-m -0.386 Tn-m 0.090 Tn-m

Viga 6 - 7 0.316 Tn-m -0.166 Tn-m 0.160 Tn-m

Viga 7 - 8 0.166 Tn-m 0.000 Tn-m 0.000 Tn-m

Viga 1-vol 0.000 Tn-m -0.367 Tn-m 0.000 Tn-m

Viga 1 - 2 0.991 Tn-m -0.717 Tn-m 0.430 Tn-m

Viga 2 - 3 1.119 Tn-m -1.247 Tn-m 0.720 Tn-m

Viga 3 - 4 0.357 Tn-m -0.203 Tn-m 0.000 Tn-m

Viga 4 - 5 0.506 Tn-m -0.610 Tn-m 0.350 Tn-m

Viga 5 - 6 0.082 Tn-m -0.474 Tn-m 0.140 Tn-m

Viga 6 - 7 0.393 Tn-m -0.083 Tn-m 0.170 Tn-m

Viga 7 0.083 Tn-m 0.000 Tn-m 0.000 Tn-m

Viga 1-vol 0.000 Tn-m -0.099 Tn-m 0.000 Tn-m

Viga 1 - 2 0.643 Tn-m -0.411 Tn-m 0.510 Tn-m

Viga 2 - 3 0.308 Tn-m -0.458 Tn-m 0.180 Tn-m

Viga 3 - 4 0.154 Tn-m -0.211 Tn-m 0.390 Tn-m

Viga 4 - 5 0.206 Tn-m -0.182 Tn-m 0.110 Tn-m

Viga 5 - 6 0.182 Tn-m 0.000 Tn-m 0.000 Tn-m

b = 25.00 cm

h = 20.00 cm Asumo : 3/4" 1.91 cm

f'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 14.10 cm

Recub = 4.00 cm

VIGAS NO PORTANTES EJE B-B

PISO VIGASM Max. Negativos

M Max. Posiitivo

PRIMER PISO

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

SEGUNDO

PISO

TERCER PISO

1. DIMENSION Y PROPIEDADES DE LA VIGA

CEROS POSITIVOS

Vi 1 2 0 460 T

FRMULAS

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Viga 1 - 2 0.460 Tn-m

Viga 2 - 3 0.720 Tn-m

Viga 3 - 4 0.000 Tn-m

Viga 4 - 5 0.370 Tn-mViga 5 - 6 0.090 Tn-m

Viga 6 - 7 0.160 Tn-m

Viga 7 - 8 0.000 Tn-m

Viga 1 - 2 0.430 Tn-m

Viga 2 - 3 0.720 Tn-m

Viga 3 - 4 0.000 Tn-m

Viga 4 - 5 0.350 Tn-m

Viga 5 - 6 0.140 Tn-m

Viga 6 - 7 0.170 Tn-m

Viga 7 - 8 0.000 Tn-m

Viga 1 - 2 0.510 Tn-m

Viga 2 - 3 0.180 Tn-m

Viga 3 - 4 0.390 Tn-m

Viga 4 - 5 0.110 Tn-m

Viga 5 - 6 0.000 Tn-m

Mmax (+) 0.460 Tn-m Mmax (+) 0.720 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cmAs = 0.909 cm a =0.86 cm REPETIR As = 1.422 cm a =1.34 cm REPETIR

As = 0.890 cm a =0.84 cm REPETIR As = 1.419 cm a =1.34 cm OK

As = 0.890 cm a =0.84 cm OK As = 1.419 cm a =1.34 cm OK

As = 0.890 cm As = 1.419 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.000 Tn-m Mmax (+) 0.370 Tn-m

TERCER PISO

PRIMER PISO (TRAMO 1 - 2 ) PRIMER PISO (TRAMO 2 - 3 )

PRIMER PISO (TRAMO 3 - 4 ) PRIMER PISO (TRAMO 4 - 5)

PRIMER PISO

SEGUNDO

PISO

)2/.(. adfy

MuAs

bcf

fyAsa

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.

Mma (+) 0 090 Tn m Mma (+) 0 160 Tn m

PRIMER PISO (TRAMO 5 - 6) PRIMER PISO (TRAMO 6 -7)

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Mmax (+) 0.090 Tn-m Mmax (+) 0.160 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = 0.178 cm a =0.17 cm REPETIR As = 0.316 cm a =0.30 cm REPETIR

As = 0.170 cm a =0.16 cm OK As = 0.304 cm a =0.29 cm REPETIR

As = 0.170 cm a =0.16 cm OK As = 0.303 cm a =0.29 cm OK

As = 0.170 cm As = 0.303 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.000 Tn-m Mmax (+) 0.430 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = 0.000 cm a =0.00 cm REPETIR As = 0.850 cm a =0.80 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.831 cm a =0.78 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.830 cm a =0.78 cm OK

As = 0.000 cm As = 0.830 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.720 Tn-m Mmax (+) 0.000 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm = 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = 1.422 cm a =1.34 cm REPETIR As = 0.000 cm a =0.00 cm REPETIR

As = 1.419 cm a =1.34 cm OK As = 0.000 cm a =0.00 cm OK

As = 1.419 cm a =1.34 cm OK As = 0.000 cm a =0.00 cm OK

PRIMER PISO (TRAMO 7-8) SEGUNDO PISO (TRAMO 1 - 2 )

SEGUNDO PISO (TRAMO 2 - 3 ) SEGUNDO PISO (TRAMO 3 - 4)

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

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Mmax (+) 0 170 Tn-m Mmax (+) 0 000 Tn-m

SEGUNDO PISO (TRAMO 6 - 7) SEGUNDO PISO (TRAMO 7 - 8)

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Mmax (+) 0.170 Tn-m Mmax (+) 0.000 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = 0.336 cm a =0.32 cm REPETIR As = 0.000 cm a =0.00 cm REPETIR

As = 0.323 cm a =0.30 cm REPETIR As = 0.000 cm a =0.00 cm OK

As = 0.323 cm a =0.30 cm OK As = 0.000 cm a =0.00 cm OK

As = 0.323 cm As = 0.000 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.510 Tn-m Mmax (+) 0.180 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = 1.008 cm a =0.95 cm REPETIR As = 0.356 cm a =0.33 cm REPETIR

As = 0.991 cm a =0.93 cm REPETIR As = 0.342 cm a =0.32 cm REPETIR

As = 0.990 cm a =0.93 cm OK As = 0.342 cm a =0.32 cm OK

As = 0.990 cm As = 0.342 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.390 Tn-m Mmax (+) 0.110 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm = 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = 0.771 cm a =0.73 cm REPETIR As = 0.217 cm a =0.20 cm REPETIR

As = 0.751 cm a =0.71 cm REPETIR As = 0.208 cm a =0.20 cm OK

As = 0.751 cm a =0.71 cm OK As = 0.208 cm a =0.20 cm OK

As = 0.751 cm As = 0.208 cm

TERCER PISO (TRAMO 3 - 4 ) TERCER PISO (TRAMO 4 - 5)

TERCER PISO (TRAMO 1 - 2 ) TERCER PISO (TRAMO 2 - 3 )

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Area b min Area b min

1.420 cm 14.34 cm 3.270 cm 15.30 cm

2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm

11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0.95 0.559 0.71

4 1/2 1.27 0.993 1.29

5 5/8 1.59 1.552 1.98

6 3/4 1.91 2.235 2.85

3 1/2 '' 1 1/2 + 3 5/8

4 3/8''

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

2 3/4'' 3 1

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"

1 1/2 + 1 5/81 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

1 1/2'' + 2 3/8''

3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 + 1 5/8

2 3/8''

2 1/2'' + 2 3/8'' 4 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

ACEROS COMERCIALES

DIMETRO

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

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

4 3/4'' 2 1 + 1 3/4

2 1+ 2 3/4

Viga 1 - 2 0.832 Tn-m

Viga 2 - 3 -0.816 Tn-m Mu

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g

Viga 3 - 4 -1.167 Tn-m

Viga 4 - 5 -0.166 Tn-m

Viga 5 - 6 -0.558 Tn-m

Viga 6 - 7 -0.386 Tn-m

Viga 7 - 8 -0.166 Tn-m

Viga 1 - voladizo -0.367 Tn-m

Viga 1 - 2 0.991 Tn-m

Viga 2 - 3 -0.717 Tn-m

Viga 3 - 4 -1.247 Tn-m

Viga 4 - 5 -0.203 Tn-m

Viga 5 - 6 -0.610 Tn-m

Viga 6 - 7 -0.474 Tn-m

Viga 7 - 8 -0.083 Tn-m

Viga 1 - voladizo -0.099 Tn-m

Viga 1 - 2 0.643 Tn-m

Viga 2 - 3 -0.411 Tn-m

Viga 3 - 4 -0.458 Tn-m

Viga 4 - 5 -0.211 Tn-m

Viga 5 - 6 -0.182 Tn-m

Mmax (-) 0.832 Tn-m Mmax (-) -0.816 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cmAs = 1.643 cm a =1.55 cm REPETIR As = -1.613 cm -a =1.52 cm REPETIR

As = 1.652 cm a =1.55 cm OK As = -1.454 cm -a =1.37 cm REPETIR

As = 1.652 cm a =1.56 cm OK As = -1.461 cm -a =1.38 cm OK

As = 1.652 cm As = -1.461 cm

Usar 1/2'' + 1 3/8'' As =2.000 cm Usar 1 1/2'' + 1 3/8'' As =2.000 cm

Mmax (-) -1.167 Tn-m Mmax (-) -0.166 Tn-m

PRIMER PISO (APOYO 4)

PRIMER PISO (APOYO 1) PRIMER PISO (APOYO 2)

SEGUNDO

PISO

TERCER PISO

PRIMER PISO (APOYO 3)

PRIMER PISO )2/.(. adfy

MuAs

bcf

fyAsa

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.

Mmax (-) -0.558 Tn-m Mmax (-) -0.386 Tn-m

PRIMER PISO (APOYO 5) PRIMER PISO (APOYO 6)

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b = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = -1.102 cm -a =1.04 cm REPETIR As = -0.762 cm -a =0.72 cm REPETIR

As = -1.010 cm -a =0.95 cm REPETIR As = -0.706 cm -a =0.66 cm REPETIR

As = -1.013 cm -a =0.95 cm OK As = -0.707 cm -a =0.67 cm OK

As = -1.013 cm As = -0.707 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) -0.166 Tn-m Mmax (-) 0.991 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = -0.327 cm -a =0.31 cm REPETIR As = 1.958 cm a =1.84 cm REPETIR

As = -0.307 cm -a =0.29 cm REPETIR As = 1.990 cm a =1.87 cm REPETIR

As = -0.308 cm -a =0.29 cm OK As = 1.993 cm a =1.88 cm OK

As = -0.308 cm As = 1.993 cm

Usar 2 3/8'' As =1.420 cm Usar 1 1/2'' + 1 3/8'' As =2.000 cm

Mmax (-) -0.717 Tn-m Mmax (-) -1.247 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm = 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = -1.418 cm -a =1.33 cm REPETIR As = -2.464 cm -a =2.32 cm REPETIR

As = -1.286 cm -a =1.21 cm REPETIR As = -2.163 cm -a =2.04 cm REPETIR

As = -1.291 cm -a =1.22 cm OK As = -2.183 cm -a =2.05 cm REPETIR

As = -2.182 cm -a =2.05 cm OK

SEGUNDO PISO (APOYO 3)

PRIMER PISO (APOYO 7) SEGUNDO PISO (APOYO 1)

SEGUNDO PISO (APOYO 2)

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

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Mmax (-) -0.474 Tn-m Mmax (-) -0.083 Tn-m

SEGUNDO PISO (APOYO 6) SEGUNDO PISO (APOYO 7)

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b = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = -0.936 cm -a =0.88 cm REPETIR As = -0.165 cm -a =0.15 cm REPETIR

As = -0.863 cm -a =0.81 cm REPETIR As = -0.155 cm -a =0.15 cm OK

As = -0.865 cm -a =0.81 cm OK As = -0.155 cm -a =0.15 cm OK

As = -0.865 cm As = -0.155 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) 0.643 Tn-m Mmax (-) -0.411 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = 1.270 cm a =1.20 cm REPETIR As = -0.811 cm -a =0.76 cm REPETIR

As = 1.260 cm a =1.19 cm OK As = -0.750 cm -a =0.71 cm REPETIR

As = 1.259 cm a =1.19 cm OK As = -0.752 cm -a =0.71 cm OK

As = 1.259 cm As = -0.752 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) -0.458 Tn-m Mmax (-) -0.211 Tn-mb = 25.00 cm b = 25.00 cm

d = 14.10 cm d = 14.10 cm = 0.9 = 0.9

Asumir: a = 0.10.d a =1.41 cm Asumir: a = 0.10.d a =1.41 cm

As = -0.905 cm -a =0.85 cm REPETIR As = -0.417 cm -a =0.39 cm REPETIR

As = -0.834 cm -a =0.79 cm REPETIR As = -0.391 cm -a =0.37 cm REPETIR

As = -0.836 cm -a =0.79 cm OK As = -0.391 cm -a =0.37 cm OK

As = -0.836 cm As = -0.391 cm

TERCER PISO (APOYO 2)

TERCER PISO (APOYO 3) TERCER PISO (APOYO 4)

TERCER PISO (APOYO 1)

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Izquierda DerechaViga 1 - 2 1.053355 -1.307294 0.410 Tn-m

Viga 2 - 3 1.573198 -1.458748 0.880 Tn-m

Viga 3 - 4 1.044184 -0.727946 0.320 Tn-m

Viga 4 - 5 0.863615 -0.012636 0.460 Tn-m

Viga 5 - 6 -0.678232 -0.628797 0.000 Tn-m

Viga 6 - 7 0.629 Tn-m 0.000 Tn-m 0.690 Tn-m

Viga 1 - 2 1.248724 -1.201479 0.400 Tn-m

Viga 2 - 3 1.469133 -1.576467 0.870 Tn-m

Viga 3 - 4 0.927875 -0.793864 0.320 Tn-m

Viga 4 - 5 0.835273 -0.751936 0.450 Tn-m

Viga 5 - 6 0.637150 -0.603549 0.000 Tn-m

Viga 6 - 7 0.604 Tn-m 0.000 Tn-m 0.740 Tn-m

Viga 1 - 2 0.867703 -1.373056 0.430 Tn-mViga 2 - 3 1.481510 -1.515017 0.910 Tn-m

Viga 3 - 4 0.985624 -0.857317 0.410 Tn-m

Viga 4 - 5 0.903491 -0.440950 0.060 Tn-m

Viga 5 - 6 0.441 Tn-m 0.000 Tn-m 0.000 Tn-m

b = 25.00 cm

h = 25.00 cm Asumo : 3/4" 1.91 cm

f'c = 210 Kg/cm Estribos : 3/8" 0.95 cm

fy = 4200 Kg/cm d:

= 0.85 d: 19.10 cm

Recub = 4.00 cm

1. DIMENSION Y PROPIEDADES DE LA VIGA

Peralte Efectivo de la seccion:

h - Recub - estrib - asumo/2

TERCER PISO

VIGAS NO PORTANTES EJE C- C

PISO VIGASM Max. Negativos

M Max. Posiitivo

SEGUNDO

PISO

PRIMER PISO

Viga 1 - 2 0.410 Tn-m

Vi 2 3 0 880 T

A. ACEROS POSITIVOS FRMULAS

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Viga 2 - 3 0.880 Tn-m

Viga 3 - 4 0.320 Tn-m

Viga 4 - 5 0.460 Tn-m

Viga 5 - 6 0.000 Tn-m

Viga 6 - 7 0.690 Tn-m

Viga 7 - 8 0.000 Tn-m

Viga 1 - 2 0.400 Tn-m

Viga 2 - 3 0.870 Tn-m

Viga 3 - 4 0.320 Tn-m

Viga 4 - 5 0.450 Tn-m

Viga 5 - 6 0.000 Tn-mViga 6 - 7 0.740 Tn-m

Viga 7 - 8 0.000 Tn-m

Viga 1 - 2 0.430 Tn-m

Viga 2 - 3 0.910 Tn-m

Viga 3 - 4 0.410 Tn-m

Viga 4 - 5 0.060 Tn-m

Viga 5 - 6 0.000 Tn-m

Mmax (+) 0.410 Tn-m Mmax (+) 0.880 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cmAs = 0.598 cm a =0.56 cm REPETIR As = 1.283 cm a =1.21 cm REPETIR

As = 0.577 cm a =0.54 cm REPETIR As = 1.259 cm a =1.18 cm REPETIR

As = 0.576 cm a =0.54 cm OK As = 1.258 cm a =1.18 cm OK

As = 0.576 cm As = 1.258 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.320 Tn-m Mmax (+) 0.460 Tn-m

PRIMER PISO (TRAMO 3 - 4 ) PRIMER PISO (TRAMO 4 - 5)

PRIMER PISO

SEGUNDO

PISO

TERCER PISO

PRIMER PISO (TRAMO 1 - 2 ) PRIMER PISO (TRAMO 2 - 3 )

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

Mmax (+) 0.000 Tn-m Mmax (+) 0.690 Tn-mb 25 00 b 25 00

PRIMER PISO (TRAMO 5 - 6) PRIMER PISO (TRAMO 6 -7)

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b = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.000 cm a =0.00 cm REPETIR As = 1.006 cm a =0.95 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.980 cm a =0.92 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.980 cm a =0.92 cm OK

As = 0.000 cm As = 0.980 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.000 Tn-m Mmax (+) 0.400 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.000 cm a =0.00 cm REPETIR As = 0.583 cm a =0.55 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.562 cm a =0.53 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = 0.562 cm a =0.53 cm OK

As = 0.000 cm As = 0.562 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.870 Tn-m Mmax (+) 0.320 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 1.269 cm a =1.19 cm REPETIR As = 0.467 cm a =0.44 cm REPETIR

As = 1.244 cm a =1.17 cm REPETIR As = 0.448 cm a =0.42 cm REPETIR

As = 1.243 cm a =1.17 cm OK As = 0.448 cm a =0.42 cm OK

SEGUNDO PISO (TRAMO 2 - 3 ) SEGUNDO PISO (TRAMO 3 - 4)

PRIMER PISO (TRAMO 7-8) SEGUNDO PISO (TRAMO 1 - 2 )

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

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SEGUNDO PISO (TRAMO 6 - 7) SEGUNDO PISO (TRAMO 7 - 8)

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b 25.00 cm b 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 1.079 cm a =1.02 cm REPETIR As = 0.000 cm a =0.00 cm REPETIR

As = 1.053 cm a =0.99 cm REPETIR As = 0.000 cm a =0.00 cm OK

As = 1.053 cm a =0.99 cm OK As = 0.000 cm a =0.00 cm OK

As = 1.053 cm As = 0.000 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.430 Tn-m Mmax (+) 0.910 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.627 cm a =0.59 cm REPETIR As = 1.327 cm a =1.25 cm REPETIR

As = 0.605 cm a =0.57 cm REPETIR As = 1.303 cm a =1.23 cm REPETIR

As = 0.605 cm a =0.57 cm OK As = 1.303 cm a =1.23 cm OK

As = 0.605 cm As = 1.303 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (+) 0.410 Tn-m Mmax (+) 0.060 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.598 cm a =0.56 cm REPETIR As = 0.088 cm a =0.08 cm REPETIR

As = 0.577 cm a =0.54 cm REPETIR As = 0.083 cm a =0.08 cm OK

As = 0.576 cm a =0.54 cm OK As = 0.083 cm a =0.08 cm OK

As = 0.576 cm As = 0.083 cm

TERCER PISO (TRAMO 3 - 4 ) TERCER PISO (TRAMO 4 - 5)

TERCER PISO (TRAMO 1 - 2 ) TERCER PISO (TRAMO 2 - 3 )

COMBINACIONES RECOMENDADAS DE ACERO

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Area b min Area b min

1.420 cm 14.34 cm 3.270 cm 15.30 cm2.000 cm 14.66 cm 3.960 cm 15.62 cm

2.130 cm 17.83 cm 4.560 cm 19.11 cm

2.580 cm 14.98 cm 5.250 cm 19.43 cm

2.710 cm 18.15 cm 5.850 cm 22.92 cm

2.840 cm 21.32 cm 5.940 cm 19.75 cm

3.290 cm 18.47 cm 6.540 cm 23.24 cm

3.870 cm 18.79 cm 7.230 cm 23.56 cm

4.000 cm 21.96 cm 7.920 cm 23.88 cm

4.580 cm 22.28 cm Area b min

5.160 cm 22.60 cm 7.080 cm 16.57 cm

Area b min 10.200 cm 17.52 cm

4.140 cm 15.62 cm 12.180 cm 21.65 cm

5.430 cm 19.43 cm 14.160 cm 25.78 cm

5.700 cm 15.62 cm 15.300 cm 22.60 cm

6.990 cm 20.07 cm Area b min8.550 cm 20.71 cm 7.950 cm 16.89 cm

8.280 cm 23.88 cm 10.800 cm 21.34 cm

11.400 cm 25.16 cm 13.050 cm 21.97 cm

15.900 cm 26.42 cm

BARRA Peso rea

Nmero pulg cm Kg/m cm2

3 3/8 0.95 0.559 0.71

4 1/2 1.27 0.993 1.29

5 5/8 1.59 1.552 1.98

6 3/4 1.91 2.235 2.85

ACEROS COMERCIALES

DIMETRO

COMBINACIONES RECOMENDADAS DE ACERO

1/2 - 3/8" 1/2 - 5/8"

2 3/8'' 1 1/2 + 1 5/81 1/2'' + 1 3/8'' 2 5/8

3 3/8'' 2 1/2 + 1 5/8

2 1/2'' 1 1/2 + 2 5/8

1 1/2'' + 2 3/8'' 3 1/2 + 1 5/8

4 3/8'' 3 5/8

2 1/2'' + 1 3/8'' 2 1/2 + 2 5/8

3 1/2 '' 1 1/2 + 3 5/8

2 1/2'' + 2 3/8'' 4 5/8

3 1/2'' + 1 3/8'' 5/8 - 1"

4 1/2 '' 1 1 + 1 5/8

1/2 - 3/4" 2 1

1 1/2'' + 1 3/4'' 2 1+ 1 5/8

2 1/2'' + 1 3/4'' 2 1+ 2 5/8

2 3/4'' 3 1

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

2 1/2'' + 2 3/4'' 1 1 + 2 3/4

4 3/4'' 2 1 + 1 3/4

2 1+ 2 3/4

M ( - )

Viga 1 - 2 -1.053 Tn-m

Viga 2 - 3 -1.307 Tn-m

B. ACEROS NEGATIVOS FRMULAS

Mu

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g

Viga 3 - 4 -1.459 Tn-m

Viga 4 - 5 -0.728 Tn-m

Viga 5 - 6 -0.013 Tn-m

Viga 6 - 7 -0.629 Tn-m

Viga 7 - 8 0.000 Tn-m

Viga 1 - 2 -1.249 Tn-m

Viga 2 - 3 -1.201 Tn-m

Viga 3 - 4 -1.576 Tn-m

Viga 4 - 5 -0.794 Tn-m

Viga 5 - 6 -0.752 Tn-mViga 6 - 7 -0.604 Tn-m

Viga 7 - 8 0.000 Tn-m

Viga 1 - 2 -0.868 Tn-m

Viga 2 - 3 -1.373 Tn-m

Viga 3 - 4 -1.515 Tn-m

Viga 4 - 5 -0.857 Tn-m

Viga 5 - 6 -0.441 Tn-m

Mmax (-) -1.053 Tn-m Mmax (-) -1.307 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -1.536 cm -a =1.45 cm REPETIR As = -1.907 cm -a =1.79 cm REPETIR

As = -1.406 cm -a =1.32 cm REPETIR As = -1.730 cm -a =1.63 cm REPETIR

As = -1.410 cm -a =1.33 cm OK As = -1.737 cm -a =1.63 cm OK

As = -1.410 cm As = -1.737 cm

Usar 2 3/8'' As =1.420 cm Usar 1 1/2'' + 1 3/8'' As =2.000 cm

Mmax (-) -1.459 Tn-m Mmax (-) -0.728 Tn-m

PRIMER PISO (APOYO 3) PRIMER PISO (APOYO 4)

PRIMER PISO

SEGUNDO

PISO

TERCER PISO

PRIMER PISO (APOYO 1) PRIMER PISO (APOYO 2)

)2/.(. adfy

MuAs

bcf

fyAsa

.'.85.0

.

Mmax (-) -0.013 Tn-m Mmax (-) -0.629 Tn-mb = 25.00 cm b = 25.00 cm

PRIMER PISO (APOYO 5) PRIMER PISO (APOYO 6)

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d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -0.018 cm -a =0.02 cm REPETIR As = -0.917 cm -a =0.86 cm REPETIR

As = -0.017 cm -a =0.02 cm OK As = -0.852 cm -a =0.80 cm REPETIR

As = -0.017 cm -a =0.02 cm OK As = -0.853 cm -a =0.80 cm OK

As = -0.017 cm As = -0.853 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) 0.000 Tn-m Mmax (-) -1.249 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = 0.000 cm a =0.00 cm REPETIR As = -1.821 cm -a =1.71 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = -1.656 cm -a =1.56 cm REPETIR

As = 0.000 cm a =0.00 cm OK As = -1.662 cm -a =1.56 cm OK

As = 0.000 cm As = -1.662 cm

Usar 2 3/8'' As =1.420 cm Usar 1 1/2'' + 1 3/8'' As =2.000 cm

Mmax (-) -1.201 Tn-m Mmax (-) -1.576 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -1.752 cm -a =1.65 cm REPETIR As = -2.299 cm -a =2.16 cm REPETIR

As = -1.596 cm -a =1.50 cm REPETIR As = -2.067 cm -a =1.95 cm REPETIR

As = -1.602 cm -a =1.51 cm OK As = -2.078 cm -a =1.96 cm REPETIR

As = -2.078 cm -a =1.96 cm OK

PRIMER PISO (APOYO 7) SEGUNDO PISO (APOYO 1)

SEGUNDO PISO (APOYO 2) SEGUNDO PISO (APOYO 3)

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

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71/99Mmax (-) -0.604 Tn-m Mmax (-) 0.000 Tn-mb = 25.00 cm b = 25.00 cm

SEGUNDO PISO (APOYO 6) SEGUNDO PISO (APOYO 7)

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d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -0.880 cm -a =0.83 cm REPETIR As = 0.000 cm a =0.00 cm REPETIR

As = -0.818 cm -a =0.77 cm REPETIR As = 0.000 cm a =0.00 cm OK

As = -0.820 cm -a =0.77 cm OK As = 0.000 cm a =0.00 cm OK

As = -0.820 cm As = 0.000 cm

Usar 2 3/8'' As =1.420 cm Usar 2 3/8'' As =1.420 cm

Mmax (-) -0.868 Tn-m Mmax (-) -1.373 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -1.265 cm -a =1.19 cm REPETIR As = -2.002 cm -a =1.88 cm REPETIR

As = -1.166 cm -a =1.10 cm REPETIR As = -1.813 cm -a =1.71 cm REPETIR

As = -1.169 cm -a =1.10 cm OK As = -1.821 cm -a =1.71 cm OK

As = -1.169 cm As = -1.821 cm

Usar 2 3/8'' As =1.420 cm Usar 1 1/2'' + 1 3/8'' As =2.000 cm

Mmax (-) -1.515 Tn-m Mmax (-) -0.857 Tn-mb = 25.00 cm b = 25.00 cm

d = 19.10 cm d = 19.10 cm

= 0.9 = 0.9

Asumir: a = 0.10.d a =1.91 cm Asumir: a = 0.10.d a =1.91 cm

As = -2.209 cm -a =2.08 cm REPETIR As = -1.250 cm -a =1.18 cm REPETIR

As = -1.991 cm -a =1.87 cm REPETIR As = -1.152 cm -a =1.08 cm REPETIR

As = -2.001 cm -a =1.88 cm OK As = -1.155 cm -a =1.09 cm OK

As = -2.000 cm As = -1.155 cm

TERCER PISO (APOYO 3) TERCER PISO (APOYO 4)

TERCER PISO (APOYO 1) TERCER PISO (APOYO 2)

PROYECTO 3 PISOS - RESUMEN DE ACERO EN VIGAS

VIGAS PORTANTESACERO POSITIVOS

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PRTICO TRAMO A-B TRAMO B - C

1 - 1 2 1/2'' 2 1/2''

2- 2 3 1/2 '' 2 1/2''

3- 3 3 1/2 '' 2 1/2''

4 - 4 3