Platea

DISEÑO DE PLATEA DE CIMENTACION CONCRETO ARMADO II

DATOS 1.20 kg/cm2 210 kg/cm2 5000 Tn/m3 fy= 4200 kg/cm2

NPT = + 0.25 m 1.50 mS/C sobre el piso = 400 kg/m2 2.00 Tn/m3

Columnas : 8.1 T/m2

COLUMNA

20.80 11.34 4.25 2.98 4.97 3.48 10.63 12.43 5.94 6.9346.32 25.27 3.85 2.70 4.57 3.20 9.63 11.43 13.23 15.4449.19 26.81 3.75 2.63 4.47 3.13 9.38 11.18 14.05 16.4024.58 13.41 4.15 2.91 4.87 3.41 10.38 12.18 7.02 8.1945.38 24.75 3.25 2.28 3.97 2.78 8.13 9.93 12.97 15.13

101.06 55.13 3.25 2.28 3.97 2.78 8.13 9.93 28.87 33.69107.25 58.50 3.45 2.42 4.17 2.92 8.63 10.43 30.64 35.7551.56 28.13 3.10 2.17 3.82 2.67 7.75 9.55 14.73 17.1947.27 25.78 3.15 2.21 3.87 2.71 7.88 9.68 13.51 15.76

105.27 57.42 3.50 2.45 4.22 2.95 8.75 10.55 30.08 35.09111.72 60.94 3.20 2.24 3.92 2.74 8.00 9.80 3.35 3.9153.71 29.30 3.50 2.45 4.22 2.95 8.75 10.55 15.35 17.9050.10 27.33 3.45 2.42 4.17 2.92 8.63 10.43 14.31 16.70

111.59 60.87 3.85 2.70 4.57 3.20 9.63 11.43 31.88 37.20118.42 64.59 3.98 2.79 4.70 3.29 9.95 11.75 33.83 39.4756.93 31.05 3.65 2.56 4.37 3.06 9.13 10.93 16.27 18.9827.41 14.95 4.85 3.40 5.57 3.90 12.13 13.93 7.83 9.14

61.06 33.30 3.75 2.63 4.47 3.13 9.38 11.18 17.45 20.35

64.80 35.34 3.95 2.77 4.67 3.27 9.88 11.68 18.51 21.60

σt= f,c= K0=

hf=γp=

50*50 cm2 σN=

PD PL MDX MLX MDY MLY MSX MSY PSX PSY

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5,50 m 6,75 m 6,25 m

5,50 m

6,50 m

6,00 m

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32.40 17.67 4.95 3.47 5.67 3.97 12.38 14.18 9.26 10.80C20


PRESIONES CONSIDERANDO CARGAS DE SERVICIO

carga muerta = 1286.820 Tn.carga viva = 701.880 Tn.

carga de servicio= 1988.700 Tn.

Carga amplificada = 1.4*1186.820 +1.7*701.880

Carga amplificada = 2994.744 Tn.

DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/1227033.61 m4

25.75*19^3/1214718.27 m4

• ∑My=0

1988.700X' = 18554.185 X'= 9.330 m

9.33-9.25 0.080 m

• ∑Mx=0

1988.700Y' = 25253.943 Y' = 12.699 m

12.699-12.625 0.07 m

5º Momentos causados por la excentricidad

• Mx= 2994.744 Tn. * 0.07 mMx= 220.770 Tn-m

• My= 2994.744 Tn. * 0.08 mMy= 238.998 Tn-m

A.- CONSIDERANDO CARGAS DE GRAVEDAD

1º Carga de servicio

2º Carga amplificada

3º Momentos de inercia de la cimentacion

• IX=IX=

• IY=IY=

4º Calculo de la excentricidad

eX= eX=

eY= eY=


6º Calculo de presiones

q= 4.0647931± 0.016X ± 0.008Y

Elaboro la siguiente tabla de presiones

Punto Q/A (Tn/m2) X (m) 0.016X ± Y (m) ±0.008Y q (Tn/m2)4.065 -9.250 -0.150 12.630 0.103 4.0184.065 -3.750 -0.061 12.630 0.103 4.1074.065 3.000 0.049 12.630 0.103 4.2174.065 9.250 0.150 12.630 0.103 4.3184.065 -9.250 -0.150 7.130 0.058 3.9734.065 -3.750 -0.061 7.130 0.058 4.0624.065 3.000 0.049 7.130 0.058 4.1724.065 9.250 0.150 7.130 0.058 4.2734.065 -9.250 -0.150 0.630 0.005 3.9204.065 -3.750 -0.061 0.630 0.005 4.0094.065 3.000 0.049 0.630 0.005 4.1194.065 9.250 0.150 0.630 0.005 4.2204.065 -9.250 -0.150 -5.370 -0.044 3.8714.065 -3.750 -0.061 -5.370 -0.044 3.9604.065 3.000 0.049 -5.370 -0.044 4.0704.065 9.250 0.150 -5.370 -0.044 4.1714.065 -9.250 -0.150 -12.630 -0.103 3.8114.065 -3.750 -0.061 -12.630 -0.103 3.9014.065 3.000 0.049 -12.630 -0.103 4.0104.065 9.250 0.150 -12.630 -0.103 4.112

A 4.065 -9.500 -0.154 12.875 0.105 4.016B 4.065 -6.500 -0.106 12.875 0.105 4.064C 4.065 -0.380 -0.006 12.875 0.105 4.164D 4.065 6.130 0.100 12.875 0.105 4.269E 4.065 9.500 0.154 12.875 0.105 4.324F 4.065 -9.500 -0.154 9.875 0.081 3.991G 4.065 9.500 0.154 9.875 0.081 4.300H 4.065 -9.500 -0.154 3.875 0.032 3.942I 4.065 9.500 0.154 3.875 0.032 4.251J 4.065 -9.500 -0.154 -2.375 -0.019 3.891K 4.065 9.500 0.154 -2.375 -0.019 4.200L 4.065 -9.500 -0.154 -9.000 -0.073 3.837M 4.065 9.500 0.154 -9.000 -0.073 4.146N 4.065 -9.500 -0.154 -12.875 -0.105 3.805O 4.065 -6.500 -0.106 -12.875 -0.105 3.854P 4.065 -0.380 -0.006 -12.875 -0.105 3.953Q 4.065 6.130 0.100 -12.875 -0.105 4.059R 4.065 9.500 0.154 -12.875 -0.105 4.114

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4.318


carga de sismo= 339.080 Tn.


Carga amplificada = 1.25*1186.820 +1.25*701.880+1*339.08


DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/12 25.75*19^3/1227033.61 m4 14718.27 m4

• ∑My=0

2327.780X' = 21797.950 X'= 9.364 m

9.364-9.25 0.11 m

• ∑Mx=0

2327.780Y' = 29515.845 Y' = 12.680 m

12.68-12.625 0.05 m


• Mx= 2824.955 Tn. * 0.05 mMx= 154.881 Tn-m

• My= 2824.955 Tn. * 0.11 mMy= 322.795 Tn-m

B.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO LONGITUDINAL HORARIO



3º Calculo de inercia de la cimentacion

• IX= • IY=IX= IY=


eX= eX=

eY= eY=


q= 4.75785386± 0.022X ± 0.006Y




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Carga amplificada = 1.25*1186.820 +1.25*701.880-1*339.08


DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/12 25.75*19^3/1227033.61 m4 14718.27 m4

• ∑My=0

1649.620X' = 15310.420 X'= 9.281 m

9.285-9.25 0.03 m

• ∑Mx=0

1649.620Y' = 20992.040 Y' = 12.725 m

13.338-12.625 0.10 m


• Mx= 2146.795 Tn. * 0.10 mMx= 215.494 Tn-m

• My= 2146.795 Tn. * 0.03 mMy= 66.937 Tn-m

C.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO LONGITUDINAL ANTIHORARIO






eX= eX=

eY= eY=



q= 3.37173224± 0.005X ± 0.0080Y


Punto Q/A (Tn/m2) X (m) 0.005X ± Y (m) ±0.008Y q (Tn/m2)3.372 -9.250 -0.042 12.630 0.101 3.4303.372 -3.750 -0.017 12.630 0.101 3.4553.372 3.000 0.014 12.630 0.101 3.4863.372 9.250 0.042 12.630 0.101 3.5143.372 -9.250 -0.042 7.130 0.057 3.3863.372 -3.750 -0.017 7.130 0.057 3.4123.372 3.000 0.014 7.130 0.057 3.4423.372 9.250 0.042 7.130 0.057 3.4713.372 -9.250 -0.042 0.630 0.005 3.3353.372 -3.750 -0.017 0.630 0.005 3.3603.372 3.000 0.014 0.630 0.005 3.3903.372 9.250 0.042 0.630 0.005 3.4193.372 -9.250 -0.042 -5.370 -0.043 3.287

3.372 -3.750 -0.017 -5.370 -0.043 3.3123.372 3.000 0.014 -5.370 -0.043 3.3433.372 9.250 0.042 -5.370 -0.043 3.3713.372 -9.250 -0.042 -12.630 -0.101 3.2293.372 -3.750 -0.017 -12.630 -0.101 3.2543.372 3.000 0.014 -12.630 -0.101 3.2853.372 9.250 0.042 -12.630 -0.101 3.313

A 3.372 -9.500 -0.043 12.875 0.103 3.431B 3.372 -6.500 -0.030 12.875 0.103 3.445C 3.372 -0.380 -0.002 12.875 0.103 3.473D 3.372 6.130 0.028 12.875 0.103 3.502E 3.372 9.500 0.043 12.875 0.103 3.518F 3.372 -9.500 -0.043 9.875 0.079 3.407G 3.372 9.500 0.043 9.875 0.079 3.494H 3.372 -9.500 -0.043 3.875 0.031 3.359I 3.372 9.500 0.043 3.875 0.031 3.446J 3.372 -9.500 -0.043 -2.375 -0.019 3.310K 3.372 9.500 0.043 -2.375 -0.019 3.396L 3.372 -9.500 -0.043 -9.000 -0.072 3.257M 3.372 9.500 0.043 -9.000 3.415N 3.372 -9.500 -0.043 -12.875 -0.103 3.226O 3.372 -6.500 -0.030 -12.875 -0.103 3.240P 3.372 -0.380 -0.002 -12.875 -0.103 3.267Q 3.372 6.130 0.028 -12.875 -0.103 3.297R 3.372 9.500 0.043 -12.875 -0.103 3.312

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DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/12 25.75*19^3/1227033.61 m4 14718.27 m4

• ∑My=0

2384.320X' = 22120.373 X'= 9.277 m

9.277-9.25 0.03 m

• ∑Mx=0

2384.320Y' = 30449.875 Y' = 12.771 m

12.771-12.625 0.15 m


• Mx= 2881.495 Tn. * 0.15 mMx= 420.365 Tn-m

• My= 2881.495 Tn. * 0.03 mMy= 79.052 Tn-m

D.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO TRANSVERSAL HORARIO






eX= eX=

eY= eY=



q= 4.87341850± 0.005X ± 0.0155Y




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DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/12 25.75*19^3/1227033.61 m4 14718.27 m4

• ∑My=0

1593.080X' = 14987.997 X'= 9.408 m

9.408-9.25 0.16 m

• ∑Mx=0

1593.080Y' = 20058.010 Y' = 12.591

12.591-12.625 -0.03 m


• Mx= 2090.255 Tn. * -0.03 mMx= 71.673 Tn-m

• Mx= 2090.255 Tn. * 0.16 mMx= 330.655 Tn-m

E.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO TRANSVERSAL ANTIHORARIO






eX= eX=

eY= eY=



q= 3.2562± 0.02247X ± 0.003Y


Punto Q/A (Tn/m2) X (m) 0.022X ± Y (m) ±0.003Y q (Tn/m2)3.256 -9.250 -0.208 12.630 0.033 3.0823.256 -3.750 -0.084 12.630 0.033 3.2053.256 3.000 0.067 12.630 0.033 3.3573.256 9.250 0.208 12.630 0.033 3.4973.256 -9.250 -0.208 7.130 0.019 3.0673.256 -3.750 -0.084 7.130 0.019 3.1913.256 3.000 0.067 7.130 0.019 3.3423.256 9.250 0.208 7.130 0.019 3.4833.256 -9.250 -0.208 0.630 0.002 3.0503.256 -3.750 -0.084 0.630 0.002 3.1743.256 3.000 0.067 0.630 0.002 3.3253.256 9.250 0.208 0.630 0.002 3.4663.256 -9.250 -0.208 -5.370 -0.014 3.034

3.256 -3.750 -0.084 -5.370 -0.014 3.1583.256 3.000 0.067 -5.370 -0.014 3.3093.256 9.250 0.208 -5.370 -0.014 3.4503.256 -9.250 -0.208 -12.630 -0.033 3.0153.256 -3.750 -0.084 -12.630 -0.033 3.1383.256 3.000 0.067 -12.630 -0.033 3.2903.256 9.250 0.208 -12.630 -0.033 3.430


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PRESIONES CONSIDERANDO CARGAS AMPLIFICADAS


carga de servicio = 1988.700 Tn.

Carga amplificada = 1.4*1286.820 +1.7*701.880


DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/1227033.61 m4

25.75*19^3/1214718.27 m4

• ∑My=0

2994.744X' = 27942.650 X'= 9.331 m

9.33-9.25 0.081 m

• ∑Mx=0

2994.744Y' = 38032.093 Y' = 12.700 m

12.699-12.625 0.07 m


• Mx= 2994.744 Tn. * 0.07 mMx= 220.770 Tn-m

• My= 2994.744 Tn. * 0.08 mMy= 238.998 Tn-m

A.- CONSIDERANDO CARGAS DE GRAVEDAD




• IX=IX=

• IY=IY=


eX= eX=

eY= eY=


PU Mux Muy1 48.4 11 12.92 108 9.98 11.83 114 9.72 11.64 57.2 10.8 12.65 106 8.43 10.36 235 8.43 10.37 250 8.94 10.88 120 8.03 9.899 110 8.17 10

10 245 9.07 10.911 260 8.29 10.112 125 9.07 10.913 117 8.94 10.814 260 9.98 11.815 276 10.3 12.216 132 9.46 11.317 63.8 12.6 14.418 142 9.72 11.619 151 10.2 12.120 75.4 12.8 14.7

2994.744



q= 6.1210915± 0.016X ± 0.008Y


Punto Q/A (Tn/m2) X (m) 0.016X ± Y (m) ±0.008Y q (Tn/m2)6.121 -9.250 -0.150 12.630 0.103 6.0746.121 -3.750 -0.061 12.630 0.103 6.1636.121 3.000 0.049 12.630 0.103 6.273

6.121 9.250 0.150 12.630 0.103 6.3746.121 -9.250 -0.150 7.130 0.058 6.0296.121 -3.750 -0.061 7.130 0.058 6.1186.121 3.000 0.049 7.130 0.058 6.2286.121 9.250 0.150 7.130 0.058 6.3306.121 -9.250 -0.150 0.630 0.005 5.9766.121 -3.750 -0.061 0.630 0.005 6.0656.121 3.000 0.049 0.630 0.005 6.1756.121 9.250 0.150 0.630 0.005 6.2766.121 -9.250 -0.150 -5.370 -0.044 5.9276.121 -3.750 -0.061 -5.370 -0.044 6.0166.121 3.000 0.049 -5.370 -0.044 6.1266.121 9.250 0.150 -5.370 -0.044 6.2276.121 -9.250 -0.150 -12.630 -0.103 5.8686.121 -3.750 -0.061 -12.630 -0.103 5.9576.121 3.000 0.049 -12.630 -0.103 6.0676.121 9.250 0.150 -12.630 -0.103 6.168


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carga muerta = 1286.820 Tn.carga viva = 701.880 Tn.carga sismo = 339.080 Tn.




DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/1227033.61 m4

25.75*19^3/1214718.27 m4

• ∑My=0

2824.955X' = 26436.496 X'= 9.358 m

9.33-9.25 0.108 m

• ∑Mx=0

2824.955Y' = 35829.331 Y' = 12.683 m

12.699-12.625 0.06 m


• Mx= 2994.744 Tn. * 0.07 mMx= 220.770 Tn-m

• My= 2994.744 Tn. * 0.08 mMy= 238.998 Tn-m

B.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO LONGITUDINAL HORARIO




• IX=IX=

• IY=IY=


eX= eX=

eY= eY=


PU Mux Muy1 46.1 19.67 10.62 103 17.82 9.713 109 17.36 9.54 54.5 19.21 10.45 101 15 8.446 224 15 8.447 238 16 8.868 114 14.34 8.119 105 14.58 8.23

10 233 16.19 8.9611 219 14.8 8.3312 119 16.19 8.9613 111 16 8.8614 247 17.82 9.7115 263 18.41 9.9916 126 16.89 9.2917 60.8 22.44 11.818 135 17.36 9.519 144 18.28 9.9320 71.8 22.91 12.1

2824.955



q= 5.7740521± 0.016X ± 0.008Y




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DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/1227033.61 m4

25.75*19^3/1214718.27 m4

• ∑My=0

2146.795X' = 19948.966 X'= 9.292 m

9.33-9.25 0.042 m

• ∑Mx=0

2146.795Y' = 27305.526 Y' = 12.719 m

12.699-12.625 0.094 m


• Mx= 2994.744 Tn. * 0.07 mMx= 220.770 Tn-m

• My= 2994.744 Tn. * 0.08 mMy= 238.998 Tn-m

C.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO LONGITUDINAL ANTIHORARIO




• IX=IX=

• IY=IY=


eX= eX=

eY= eY=


PU Mux Muy1 34.2 -1.59 10.62 76.3 -1.44 9.713 81 -1.41 9.54 40.5 -1.56 10.45 74.7 -1.22 8.446 166 -1.22 8.447 177 -1.29 8.868 84.9 -1.16 8.119 77.8 -1.18 8.23

10 173 -1.31 8.9611 212 -1.2 8.3312 88.4 -1.31 8.9613 82.5 -1.29 8.8614 184 -1.44 9.7115 195 -1.49 9.9916 93.7 -1.37 9.2917 45.1 -1.82 11.818 101 -1.41 9.519 107 -1.48 9.9320 53.3 -1.86 12.1

2146.795



q= 4.3879305± 0.016X ± 0.008Y




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DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/1227033.61 m4

25.75*19^3/1214718.27 m4

• ∑My=0

2881.495X' = 26758.919 X'= 9.286 m

9.33-9.25 0.036 m

• ∑Mx=0

2881.495Y' = 36763.361 Y' = 12.758 m

12.699-12.625 0.13 m


• Mx= 2994.744 Tn. * 0.07 mMx= 220.770 Tn-m

• My= 2994.744 Tn. * 0.08 mMy= 238.998 Tn-m

D.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO TRANSVERSAL HORARIO




• IX=IX=

• IY=IY=


eX= eX=

eY= eY=


PU Mux Muy1 47.1 9.038 232 105 8.188 21.13 111 7.975 20.74 55.7 8.825 22.55 103 6.913 18.46 229 6.913 18.47 243 7.338 19.38 117 6.588 17.79 107 6.7 17.9

10 238 7.438 19.511 220 6.8 18.112 122 7.438 19.513 113 7.338 19.314 253 8.188 21.115 268 8.462 21.716 129 7.763 20.217 62.1 10.31 25.818 138 7.975 20.719 147 8.4 21.620 73.4 10.53 26.2

2881.495



q= 5.8896168± 0.016X ± 0.008Y




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DatosL= 25.75 mB= 19.00 m

19 *25.75 ^3/1227033.61 m4

25.75*19^3/1214718.27 m4

• ∑My=0

2090.255X' = 19626.544 X'= 9.390 m

9.33-9.25 0.140 m

• ∑Mx=0

2090.255Y' = 26371.496 Y' = 12.616 m

12.699-12.625 -0.01 m


• Mx= 2994.744 Tn. * 0.07 mMx= 220.770 Tn-m

• My= 2994.744 Tn. * 0.08 mMy= 238.998 Tn-m

E.- CONSIDERANDO CARGAS DE GRAVEDAD MAS SISMO TRANSVERSAL ANTIHORARIO




• IX=IX=

• IY=IY=


eX= eX=

eY= eY=


PU Mux Muy1 33.2 9.04 -1.872 74 8.19 -1.723 78.6 7.98 -1.684 39.3 8.83 -1.835 72.5 6.91 -1.496 162 6.91 -1.497 171 7.34 -1.578 82.4 6.59 -1.449 75.6 6.7 -1.45

10 168 7.44 -1.5911 212 6.8 -1.4712 85.9 7.44 -1.5913 80.1 7.34 -1.5714 178 8.19 -1.7215 189 8.46 -1.7616 91 7.76 -1.6417 43.8 10.3 -2.0918 97.6 7.98 -1.6819 104 8.4 -1.7520 51.8 10.5 -2.13

2090.255



q= 4.2723659± 0.016X ± 0.008Y




C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

X

X

Y

Y

I

YM

I

XM

A

Qq

*±

*±


Espesor de la platea

Efecto de corte por punzonamiento

1.4*118.42 +1.7*64.59

275.591 Tn.

275591-0.81*(50+d)*(50+d)

2*(d/2+50+d/2)+ 2*(d/2+50+d/2)

200 + 4d

Pero:

275591-0.81*(50+d)*(50+d)= 0.85*1.1*(210^0.5)*(200+4d)*dd= 49.576 cm

1.4*32.40 +1.7*17.67

75.399 Tn.

a) Analisis para la columna 15

• PU=

PU=

• VU= PU - σN*A0

VU=

• VC= ø*1.1 (f,c)^0.5 *b0 *d

• b0=

b0=

VU = VC

b) Analisis para la columna 20

• PU=

PU=

• VU= PU - σN*A0

d/2

50 cm

d/2

d/2 50 cm d/2

d/2

50 cm

d/2 50 cm


75399-0.81*(50+d/2)*(50+d/2) VU=


(50+d/2)+ (50+d/2)

100+d

Pero:

75399-0.81*(50+d/2)*(50+d/2)= 0.85*1.1*210^0.5*(100+d)*dd= 38.200cm

1.4*56.93 +1.7*31.05

132.487 Tn.

132487-0.81*(50+d/2)*(50+d)

2*(50+d/2)+ (d/2+50+d/2)

150+2d

Pero:

132487-0.81*(50+d/2)*(50+d)= 0.85*1.1*210^0.5*(150+2d)*dd= 40.633cm

d= 49.576cm

t=49.576+7+2.54/2

t=57.846 cm

• VC= ø*1.1 (f,c)^0.5 *b0 *d

• b0=

b0=

VU = VC

c) Analisis para la columna 16

• PU=

PU=

• VU= PU - σN*A0

VU=

• VC= ø*1.1 (f,c)^0.5 *b0 *d

• b0=

b0=

VU = VCP

t= d+rec. +фLon./2

d/2 50 cm

d/2

50 cm

d/2


t=60 cm


PRESION PROMEDIO POR FRANJA:

Franja

01 19.000 3.000 6.380 48.398 107.807 114.443 57.209 345.773 6.06602 19.000 6.000 6.356 105.607 235.205 249.600 120.005 717.500 6.29403 19.000 6.250 6.307 110.004 244.992 260.006 125.004 744.481 6.26904 19.000 6.625 6.256 116.601 259.705 275.591 132.487 785.926 6.24405 19.000 3.875 6.202 63.789 142.094 150.798 75.399 444.346 6.035

F

18.199 1.055 51.043 113.698 120.697 60.33537.763 1.010 106.660 237.550 252.089 121.20239.183 1.006 110.669 246.474 261.578 125.76041.365 1.002 116.830 260.216 276.133 132.74823.387 1.028 65.600 146.128 155.079 77.539

25.750 3.000 6.121 48.398 105.607 110.004 116.601 63.789 458.611 5.93725.750 6.125 6.220 107.807 235.205 244.992 259.705 142.094 985.412 6.24825.750 6.500 6.326 114.443 249.600 260.006 275.591 150.798 1054.607 6.30125.750 3.375 6.380 57.209 120.005 125.004 132.487 75.399 532.305 6.125

F

17.810 1.032 49.946 108.984 113.522 120.330 65.82938.268 0.996 107.329 234.162 243.905 258.553 141.46440.956 1.004 114.897 250.591 261.038 276.685 151.397

a). Franjas de cimentacion

b). Presion promedio por franjas y cargas corregidas

b (m) b1 (m)

q

(Tn/m2)Q1

(Tn)Q2

(Tn)Q3

(Tn)Q4

(Tn)Qprom.

(Tn) q'

mod.

(Tn/m2)

q'mod.

(Tn/m)Q1

'

(Tn)Q2

'

(Tn)Q3

'

(Tn)Q4

'

(Tn)

b (m)

b1

(m)q

(Tn/m2)

Q1

(Tn)Q2

(Tn)Q3

(Tn)Q4

(Tn)Q5

(Tn)Qprom.

(Tn) q'

mod.

(Tn/m2)

q'mod.

(Tn/m)Q1

'

(Tn)Q2

'

(Tn)Q3

'

(Tn)Q4

'

(Tn)Q5

'

(Tn)

19,000

3,00

06,

000

6,25

06,

625

3,87

5

3,000 6,125 6,500 3,375

25,7

50

Franja 01

Franja 02

Franja 03

Franja 04

Franja 05

Fra

nja

06

Fra

nja

07

Fra

nja

08

Fra

nja

09

DIRECCCION X DIRECCCION Y

A E

N R

F G

H I

J K

L M

A B C E

N O P R

D

Q


20.672 1.044 59.699 125.228 130.444 138.253 78.680


Metodo De Harry Cross:

Datos:

B= 300 cm 0.25 m 6.25 m

H= 60 cm 5.50 m 0.25 m

I= 5400000 cm4 6.75 m q= 18.199 T/m

1º Factores de distribucion

Nudo 1: Nudo 2:

7364 7364 8000∑(K)= 7364 ∑(K)= 15364

1 0.48 0.52Nudo 3: Nudo 4:

8000 6480 6480∑(K)= 14480 ∑(K)= 6480

0.55 0.45 1

2º Momentos de empotramiento

-0.57 T m 0.57 T m

45.88 T m 69.10 T m 59.24 T m

-45.88 T m -69.10 T m -59.24 T m

diferencia: 2º 45.31

3º 23.22

4º -9.86

1º -58.67

1º Analisis de franja 01

L1= L4=

L2= L5=

L3=

KR12= KR

21= K23=

F12= F21= F23=

K32= KR34= KR

43=

F32= F34= F43=

M1A= M4B=

M12= M23= M34=

M21= M32= M43=

51.043 tn 60.335 tn113.698 tn 120.697 tn

0,250 5.500 6,750 6,250 0,250

18.199 tn/m 18.199 tn/m

A1 2 43

B


3º Momentos finales

2º 3º 4º 1º∞ 1 0.48 0.52 0.55 0.45 1 ∞

-0.569 45.876 -45.876 69.098 -69.098 59.240 -59.240 0.569 -45.307 -22.653 29.336 58.671

-0.273 -0.296 -0.148

-5.340 -10.680 -8.650

2.559 2.780 1.390 -0.384 -0.768 -0.622

0.184 0.200 0.100

-0.028 -0.055 -0.045

0.013 0.014 0.007

-0.002 -0.004 -0.003

0.001 0.001 0.001

-0.569 0.569 -66.044 66.044 -79.255 79.255 -0.569 0.569

51.043 T

0.569 T m 46.493 T

18.199 T/m

113.698 T

x -38.141 T

51.747 T

0.569 T m 66.044 T m 0.569 -38.14 X +18.199 X^2/2

∂M/∂x=0 X= 2.096 m

18.199 T/m -39.401 T m

120.697 Tx

-59.463 T

66.044 T m 79.255 T m 57.319 T

66.044 -59.46 X +18.199 X^2/2

R'1=

R'1

R''1=

R'2=

Mx=

Mmax=

R''1 R'2

R''2=

R'3=

Mx=


18.199 T/m ∂M/∂x=0 X= 3.267 m

-31.102 T m

60.335 Tx

-69.460 T

79.255 T m 0.569 T m 16.055 T

79.255 -69.46 X +18.199 X^2/2

18.199 T/m ∂M/∂x=0 X= 3.817 m

-53.303 T m

0.569 T m -4.550 T

18.199 T/m

Reacciones:

8.352 T -7.716 T -12.14 T 11.50 T

Diagrama de momentos :

Mmax=

R''2 R'3

R''3=

R'4=

Mx=

Mmax=

R''3 R'4

R''3=

R''4

R1 R2 R3 R4

0.569 T-m

-39.401 T-m

66.044 T-m

-31.102 T-m

79.225 T-m

-53.303 T-m

0.569 T-m


0 0.0 T0.25 4.5 T0.25 -38.1 T5.75 62.0 T5.75 -59.5 T12.5 63.4 T12.5 -69.5 T

18.75 44.3 T18.75 -4.5 T

19 0.0 T


Acero positivo:calculo para M= 66.044 T m

•

26.563 cm2

•

Datos: ø= 0.9 rec.= 7.0 cm 210 kg/cm2

66.044 T m 1''

4200 kg/cm2 t= 60 cm

b= 300 cm d= 49.190 cm

5 39.466 cm2 a= 3.095 1.98 36.673 cm2 a= 2.876 16.2296 36.589 cm2 a= 2.870 18.4848 36.587 cm2 a= 2.870

36.586 cm2

usar: 19 ø Nº05 @ 0.16 m (As=37.606 cm2)

calculo para M= 79.255 T m


79.255 T m 1''

4200 kg/cm2 t= 60 cm

b= 300 cm d= 49.190 cm5.00

47.360 cm2 a= 3.715 1.97928 44.297 cm2 a= 3.474 13.44 44.185 cm2 a= 3.465 22.3214 44.180 cm2 a= 3.465 44.180 cm2

usar: 23 ø Nº05 @ 0.13 m (As=45.523 cm2)

Asmin.=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US


Acero negativo:calculo para M= 39.40 T m


39.401 T m 1''

4200 kg/cm2 t= 60 cmb= 300 cm d= 51.190 cm

5 22.625 cm2 a= 1.774 1.97928 20.721 cm2 a= 1.625 22.3541 20.691 cm2 a= 1.623 13.4203 20.690 cm2 a= 1.623 20.690 cm2

usar: 14 ø Nº05 @ 0.22 m (As=27.710 cm2)



31.102 T m 1''

4200 kg/cm2 t= 60 cmb= 300 cm d= 51.190 cm

5 17.860 cm2 a= 1.401 1.97928 16.297 cm2 a= 1.278 22.3541 16.277 cm2 a= 1.277 14.2245 16.277 cm2 a= 1.277 16.277 cm2

usar: 15 ø Nº05 @ 0.22 m (As=29.689 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




53.303 T m 1''

4200 kg/cm2 t= 60 cmb= 300 cm d= 51.190 cm

30.608 cm2 a= 2.401 5 28.208 cm2 a= 2.212 1.97928 28.155 cm2 a= 2.208 21.0903 28.154 cm2 a= 2.208 14.2245 28.154 cm2

usar: 15 ø Nº05 @ 0.21 m (As=29.689 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US



Datos:

B= 600 cm 0.250 T 6.250 T

H= 60 cm 5.500 T 0.250 T

I= 10800000 cm4 6.750 T q= 37.76 T/m


Nudo 1: Nudo 2:

14727 14727 16000∑(K)= 14727 ∑(K)= 30727

1 0.48 0.52Nudo 3: Nudo 4:

16000 12960 12960∑(K)= 28960 ∑(K)= 12960

0.55 0.45 1


-1.18 T m 1.18 T m

95.19 T m 143.38 T m 122.93 T m

-95.19 T m -143.38 T m -122.93 T m


3º 48.19

4º -20.46

1º -121.75


L1= L4=

L2= L5=

L3=

KR12= KR

21= K23=

F12= F21= F23=

K32= KR34= KR

43=

F32= F34= F43=

M1A= M4B=

M12= M23= M34=

M21= M32= M43=

106.660 tn 121.202 tn237.550 tn 252.089 tn

0,250 6,750 6,250 0,250

37.763 tn/m 37.763 tn/m

5,500

A1 2 43

B


2º 3º 4º 1º∞ 1 0.48 0.52 0.55 0.45 1 ∞

-1.180 95.195 -95.195 143.38 -143.382 122.927 -122.927 1.180 -94.015 -47.007 60.873 121.747

-0.566 -0.614 -0.307 -11.080 -22.161 -17.950

5.311 5.770 2.885

-0.797 -1.594 -1.291

0.382 0.415 0.207 -0.057 -0.115 -0.093

0.027 0.030 0.015

-0.004 -0.008 -0.007

0.002 0.002 0.001

0.000 -0.001 0.000

-1.180 1.180 -137.045 137.05 -164.459 164.459 -1.180 1.180

106.660 T

1.180 T m 97.219 T

37.763 T/m

237.550 T

x -79.146 T

108.999 T

1.180 T m 137.045 T m 1.180 -79.15 X +37.763 X^2/2

∂M/∂x=0 X= 2.096 m

37.763 T/m -81.759 T m

252.089 T

x

-123.389 T

137.045 T m 164.459 T m 120.577 T

137.05 -123.4 X +37.763 X^2/237.763 T/m ∂M/∂x=0 X= 3.267 m

R'1=

R'1

R''1=

R'2=

Mx=

Mmax=

R''1 R'2

R''2=

R'3=

Mx=


-64.539 T m

121.202 T

x

-144.135 T

164.459 T m 1.180 T m 29.316 T

164.46 -144.1 X +37.763 X^2/2

37.763 T/m ∂M/∂x=0 X= 3.817 m

-110.607 T m

1.180 T m -9.441 T

37.763 T/m

Reacciones:

18.07 T -14.39 T -23.6 T 19.9 T

Diagrama de momentos :

Mmax=

R''2 R'3

R''3=

R'4=

Mx=

Mmax=

R''3 R'4

R''3=

R''4

R1 R2 R3 R4

1.180 T-m

137.05 T-m164.459 T-m

1.180 T-m

-81.759 T-m

-64.539 T-m

-110.607 T-m


19 0

0 0.0 T0.25 9.4 T0.25 -79.1 T5.75 128.6 T5.75 -123.4 T12.5 131.5 T12.5 -144.1 T

18.75 91.9 T18.75 -9.4 T

19 0.0 T


Acero positivo:


•

53.125 cm2

•


137.045 T m 1''

4200 kg/cm2 t= 60 cm

b= 600 cm d= 49.190 cm

5 81.894 cm2 a= 3.212 1.97928 76.192 cm2 a= 2.988 15.6243 76.013 cm2 a= 2.981 38.4017 76.008 cm2 a= 2.981

76.008 cm2

usar: 39 ø Nº05 @ 0.16 m (As=77.192 cm2)



164.459 T m 1''

4200 kg/cm2 t= 60 cm

b= 600 cm d= 49.190 cm5

98.276 cm2 a= 3.854 1.97928 92.054 cm2 a= 3.610 12.9353 91.817 cm2 a= 3.601 45.3847 91.808 cm2 a= 3.600 91.808 cm2

usar: 46 ø Nº05 @ 0.13 m (As=91.047 cm2)

Asmin.=

f'c=

Mu= øvarilla=

fy=

As=

As=

As=As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US


Acero negativo:



81.759 T m 1''

4200 kg/cm2 t= 60 cmb= 600.0 cm d= 51.190 cm

5 46.948 cm2 a= 1.841 1.97928 43.027 cm2 a= 1.687 22.3541 42.961 cm2 a= 1.685 26.8407 42.960 cm2 a= 1.685 42.960 cm2

usar: 27 ø Nº05 @ 0.22 m (As=53.441 cm2)



64.539 T m 1''

4200 kg/cm2 t= 60 cm

b= 600 cm d= 51.190 cm

5 37.060 cm2 a= 1.453 1.97928 33.834 cm2 a= 1.327 22.3541 33.792 cm2 a= 1.325 26.8407 33.791 cm2 a= 1.325 33.791 cm2

usar: 27 ø Nº05 @ 0.22 m (As=53.441 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




110.607 T m 1''

4200 kg/cm2 t= 60 cm

b= 600 cm d= 51.190 cm5

63.513 cm2 a= 2.491 1.97928 58.587 cm2 a= 2.298 20.3101 58.474 cm2 a= 2.293 29.5419 58.472 cm2 a= 2.293 58.472 cm2

usar: 30 ø Nº05 @ 0.20 m (As=59.378 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US



Datos:

B= 625 cm 0.25 m 6.25 m

H= 60 cm 5.50 m 0.25 m

I= 11250000 cm4 6.75 m q= 39.18 T/m


Nudo 1: Nudo 2:

15341 15341 16667∑(K)= 15341 ∑(K)= 32008

1 0.48 0.52Nudo 3: Nudo 4:

16667 13500 13500∑(K)= 30167 ∑(K)= 13500

0.55 0.45 1


-1.22 T m 1.22 T m

98.77 T m 148.77 T m 127.55 T m

-98.77 T m -148.77 T m -127.55 T m


3º 50.00

4º -21.22

1º -126.33


L1= L4=

L2= L5=

L3=

KR12= KR

21= K23=

F12= F21= F23=

K32= KR34= KR

43=

F32= F34= F43=

M1A= M4B=

M12= M23= M34=

M21= M32= M43=

110.669 tn 125.760 tn246.474 tn 261.578 tn

0,250 6,750 6,250 0,250

39.183 tn/m 39.183 tn/m

5,500

A1 2 43

B


2º 3º 4º 1º∞ 1 0.48 0.52 0.55 0.45 1 ∞

-1.224 98.774 -98.774 148.774 -148.774 127.550 -127.550 1.224 -97.550 -48.775 63.163 126.325

-0.587 -0.638 -0.319 -11.497 -22.994 -18.625

5.510 5.987 2.993

-0.827 -1.654 -1.340

0.396 0.431 0.215

-0.059 -0.119 -0.096 0.029 0.031 0.015

-0.004 -0.009 -0.007

0.002 0.002 0.001

0.000 -0.001 0.000

-1.224 1.224 -142.199 142.199 -170.643 170.643 -1.224 1.224

110.669 T

1.224 T m 100.873 T

39.183 T/m

246.474 T

x -82.122 T

113.088 T

1.224 T m 142.199 T m 1.224 -82.12 X +39.183 X^2/2∂M/∂x=0 X= 2.096 m

39.183 T/m -84.833 T m

261.578 T

x

-128.029 T

142.199 T m 170.643 T m 125.121 T

142.199 -128.0 X +39.183 X^2/239.183 T/m ∂M/∂x=0 X= 3.267 m

R'1=

R'1

R''1=

R'2=

Mx=

Mmax=

R''1 R'2

R''2=

R'3=

Mx=


-66.966 T m

125.760 T

x

-149.555 T

170.643 T m 1.224 T m 30.419 T

170.643 -149.6 X +39.183 X^2/2

39.183 T/m ∂M/∂x=0 X= 3.817 m

-114.767 T m

1.224 T m -9.796 T

39.183 T/m

Reacciones:

18.75 T -14.94 T -24.4 T 20.62 T

Diagrama de momentos:

x y

Mmax=

R''2 R'3

R''3=

R'4=

Mx=

Mmax=

R''3 R'4

R''3=

R''4

R1 R2 R3 R4

1.224 T-m

142.199 T-m170.643 T-m

1.224 T-m

-84.833 T-m

--66.966 T-m

-114.767 T-m


18.7519.0 T 0

0 0.0 T0.25 9.8 T0.25 -82.1 T5.75 133.4 T5.75 -128.0 T12.5 136.5 T12.5 -149.6 T

18.75 95.3 T18.75 -9.8 T

19 0.0 T


Acero positivo:


•

55.339 cm2

•


142.199 T m 1''

4200 kg/cm2 t= 60 cm

b= 625 cm d= 49.190 cm

5 84.974 cm2 a= 3.199 1.98 79.047 cm2 a= 2.976 15.69 78.862 cm2 a= 2.969 39.84 78.856 cm2 a= 2.969

78.856 cm2

usar: 40 ø Nº05 @ 0.16 m (As=79.171 cm2)



170.643 T m 1''

4200 kg/cm2 t= 60 cm

b= 625 cm d= 49.190 cm5

101.971 cm2 a= 3.839 1.98 95.501 cm2 a= 3.595 12.99 95.255 cm2 a= 3.586 48.12 95.246 cm2 a= 3.586 95.246 cm2

usar: 48 ø Nº05 @ 0.13 m (As=95.005 cm2)

Asmin.=

f'c=

Mu= øvarilla=

fy=

As=

As=

As=As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US


Acero negativo:



84.833 T m 1''

4200 kg/cm2 t= 60 cmb= 625.0 cm d= 51.190 cm

5 48.713 cm2 a= 1.834 1.98 44.642 cm2 a= 1.681 22.35 44.574 cm2 a= 1.678 27.96 44.573 cm2 a= 1.678 44.572 cm2

usar: 28 ø Nº05 @ 0.22 m (As=55.420 cm2)



66.966 T m 1''

4200 kg/cm2 t= 60 cm

b= 625 cm d= 51.190 cm5

38.454 cm2 a= 1.448 1.98 35.105 cm2 a= 1.322 22.35 35.061 cm2 a= 1.320 27.96 35.060 cm2 a= 1.320 35.060 cm2

usar: 28 ø Nº05 @ 0.22 m (As=55.420 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

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)2/(* adf

MA

Y

US

bf

fAa

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**85.0

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MA

Y

US




114.767 T m 1''

4200 kg/cm2 t= 60 cm

b= 625 cm d= 51.190 cm5

65.902 cm2 a= 2.481 1.98 60.785 cm2 a= 2.288 20.39 60.668 cm2 a= 2.284 30.65 60.665 cm2 a= 2.284 60.665 cm2

usar: 31 ø Nº05 @ 0.20 m (As=61.358 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

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**85.0

*'

)*9.0(* df

MA

Y

US



Datos:

B= 663 cm 0.25 m 6.25 m

H= 60 cm 5.50 m 0.25 m

I= 11925000 cm4 6.75 m q= 41.36 T/m


Nudo 1: Nudo 2:

16261 16261 17667∑(K)= 16261 ∑(K)= 33928

1 0.48 0.52Nudo 3: Nudo 4:

17667 14310 14310∑(K)= 31977 ∑(K)= 14310

0.55 0.45 1


-1.29 T m 1.29 T m

104.27 T m 157.06 T m 134.65 T m

-104.27 T m -157.06 T m -134.65 T m


3º 52.78

4º -22.41

1º -133.36


L1= L4=

L2= L5=

L3=

KR12= KR

21= K23=

F12= F21= F23=

K32= KR34= KR

43=

F32= F34= F43=

M1A= M4B=

M12= M23= M34=

M21= M32= M43=

116.830 tn 132.748 tn260.216 tn 276.133 tn

0,250 6,750 6,250 0,250

41.365 tn/m 41.365 tn/m

5,500

A1 2 43

B


2º 3º 4º 1º∞ 1 0.48 0.52 0.55 0.45 1 ∞

-1.293 104.273 -104.273 157.056 -157.056 134.650 -134.650 1.293 -102.980 -51.490 66.679 133.358

-0.620 -0.673 -0.337 -12.137 -24.274 -19.662

5.817 6.320 3.160

-0.873 -1.746 -1.414

0.418 0.455 0.227

-0.063 -0.126 -0.102 0.030 0.033 0.016

-0.005 -0.009 -0.007

0.002 0.002 0.001

0.000 -0.001 -0.001

-1.293 1.293 -150.115 150.115 -180.143 180.143 -1.293 1.293

116.830 T

1.293 T m 106.489 T

41.365 T/m

260.216 T

x -86.694 T

119.405 T

1.293 T m 150.115 T m 1.293 -86.69 X +41.365 X^2/2∂M/∂x=0 X= 2.096 m

41.365 T/m -89.556 T m

276.133 Tx

-135.157 T

150.115 T m 180.143 T m 132.079 T

150.115 -135.2 X +41.365 X^2/241.365 T/m ∂M/∂x=0 X= 3.267 m

-70.694 T m

R'1=

R'1

R''1=

R'2=

Mx=

Mmax=

R''1 R'2

R''2=

R'3=

Mx=

Mmax=


132.748 Tx

-157.880 T

180.143 T m 1.293 T m 32.099 T

180.143 -157.9 X +41.365 X^2/2

41.365 T/m ∂M/∂x=0 X= 3.817 m

-121.156 T m

1.293 T m -10.341 T

41.365 T/m

Reacciones:

19.80 T -15.75 T -25.8 T 21.8 T


x y

R''2 R'3

R''3=

R'4=

Mx=

Mmax=

R''3 R'4

R''3=

R''4

R1 R2 R3 R4

1.293 T-m

150.115 T-m

180.143 T-m

1.293 T-m

-89.556 T-m

-70.694 T-m

-121.156 T-m


19 0

0 00.25 10.3410.25 -86.6945.75 140.815.75 -135.1612.5 144.0512.5 -157.88

18.75 100.6518.75 -10.341

19 0


Acero positivo:


•

58.659 cm2

•


150.115 T m 1''

4200 kg/cm2 t= 60 cm

b= 663 cm d= 49.190 cm

5 89.704 cm2 a= 3.186 1.98 83.436 cm2 a= 2.963 15.75 83.241 cm2 a= 2.956 42.05 83.235 cm2 a= 2.956

83.235 cm2

usar: 43 ø Nº05 @ 0.16 m (As=85.109 cm2)



180.143 T m 1''

4200 kg/cm2 t= 60 cm

b= 663 cm d= 49.190 cm5

107.648 cm2 a= 3.823 1.98 100.801 cm2 a= 3.580 13.04 100.542 cm2 a= 3.571 50.79 100.532 cm2 a= 3.571 100.532 cm2

usar: 51 ø Nº05 @ 0.13 m (As=100.94 cm2)

Asmin.=

f'c=

Mu= øvarilla=

fy=

As=

As=

As=As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US


Acero negativo:



89.556 T m 1''

4200 kg/cm2 t= 60 cmb= 663 cm d= 51.190 cm

5 51.425 cm2 a= 1.826 1.98 47.123 cm2 a= 1.674 22.35 47.052 cm2 a= 1.671 29.64 47.051 cm2 a= 1.671 47.051 cm2

usar: 30 ø Nº05 @ 0.22 m (As=59.38 cm2)



70.694 T m 1''

4200 kg/cm2 t= 60 cm

b= 663 cm d= 51.190 cm5

40.594 cm2 a= 1.442 1.98 37.057 cm2 a= 1.316 22.35 37.011 cm2 a= 1.314 29.64 37.010 cm2 a= 1.314 37.010 cm2

usar: 30 ø Nº05 @ 0.22 m (As=59.38 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




121.156 T m 1''

4200 kg/cm2 t= 60 cmb= 663 cm d= 51.190 cm

5 69.570 cm2 a= 2.471 1.98 64.162 cm2 a= 2.279 20.48 64.039 cm2 a= 2.274 32.35 64.036 cm2 a= 2.274 64.036 cm2

usar: 33 ø Nº05 @ 0.20 m (As=65.32 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US



Datos:

B= 388 cm 0.25 m 6.25 m

H= 60 cm 5.50 m 0.25 m

I= 6975000 cm4 6.75 m q= 23.39 T/m


Nudo 1: Nudo 2:

9511 9511 10333∑(K)= 9511 ∑(K)= 19845

1 0.48 0.52Nudo 3: Nudo 4:

10333 8370 8370∑(K)= 18703 ∑(K)= 8370

0.55 0.45 1


-0.73 T m 0.73 T m

58.95 T m 88.80 T m 76.13 T m

-58.95 T m -88.80 T m -76.13 T m


3º 29.84

4º -12.67

1º -75.40


L1= L4=

L2= L5=

L3=

KR12= KR

21= K23=

F12= F21= F23=

K32= KR34= KR

43=

F32= F34= F43=

M1A= M4B=

M12= M23= M34=

M21= M32= M43=

65.600 tn 77.539 tn146.128 tn 155.079 tn

0,250 6,750 6,250 0,250

23.387 tn/m 23.387 tn/m

5,500

A1 2 43

B


2º 3º 4º 1º∞ 1 0.48 0.52 0.55 0.45 1 ∞

-0.731 58.954 -58.954 88.796 -88.796 76.128 -76.128 0.731 -58.223 -29.111 37.699 75.397

-0.350 -0.381 -0.190 -6.862 -13.724 -11.117

3.289 3.573 1.787

-0.494 -0.987 -0.800

0.237 0.257 0.128 -0.035 -0.071 -0.058

0.017 0.018 0.009

-0.003 -0.005 -0.004

0.001 0.001 0.001

-0.731 0.731 -84.872 84.872 -101.849 101.849 -0.731 0.731

65.600 T

0.731 T m 59.753 T

23.387 T/m 5.847 T

146.128 T

x -49.015 T

66.516 T

0.731 T m 84.872 T m 0.731 -49.01 X +23.387 X^2/2

∂M/∂x=0 X= 2.096 m

23.387 T/m -50.633 T m

155.079 Tx

-76.415 T

84.872 T m 101.849 T m 73.634 T

84.872 -76.41 X +23.387 X^2/223.387 T/m ∂M/∂x=0 X= 3.267 m

R'1=

R'1

R''1=

R'2=

Mx=

Mmax=

R''1 R'2

R''2=

R'3=

Mx=


-39.969 T m

77.539 Tx

-89.262 T

101.849 T m 0.731 T m 20.635 T

101.849 -89.26 X +23.387 X^2/2

23.387 T/m ∂M/∂x=0 X= 3.817 m

-68.499 T m

0.731 T m -5.847 T

23.387 T/m

Reacciones:

10.74 T -9.90 T -15.6 T 14.789 T


x y0 0

Mmax=

R''2 R'3

R''3=

R'4=

Mx=

Mmax=

R''3 R'4

R''3=

R''4

R1 R2 R3 R4

0.731 T-m

84.872 T-m

101.849 T-m

0.731 T-m

-50.663 T-m

-39.969 T-m

-68.499 T-m


18.75 #REF!19 0

0 00.25 5.846660.25 -49.01485.75 79.61165.75 -76.414812.5 81.444912.5 -89.2622

18.75 56.904218.75 -5.84666

19 0


Acero positivo:


•

34.310 cm2

•


84.872 T m 1''

4200 kg/cm2 t= 60 cm

b= 388 cm d= 49.190 cm

5 50.717 cm2 a= 3.080 1.98 47.120 cm2 a= 2.861 23.75 47.012 cm2 a= 2.855 16.32 47.009 cm2 a= 2.854

47.009 cm2

usar: 24 ø Nº05 @ 0.16 m (As=47.50 cm2)



101.849 T m 1''

4200 kg/cm2 t= 60 cm

b= 387.5 cm d= 49.190 cm5

60.862 cm2 a= 3.696 1.98 56.914 cm2 a= 3.456 13.51 56.770 cm2 a= 3.447 28.68 56.765 cm2 a= 3.447 56.765 cm2

usar: 29 ø Nº05 @ 0.14 m (As=57.40 cm2)

Asmin.=

f'c=

Mu= øvarilla=

fy=

As=

As=

As=As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US


Acero negativo:



50.633 T m 1''

4200 kg/cm2 t= 60 cmb= 387.5 cm d= 51.190 cm

5 29.075 cm2 a= 1.765 1.98 26.626 cm2 a= 1.617 22.35 26.587 cm2 a= 1.614 17.33 26.586 cm2 a= 1.614 26.586 cm2

usar: 18 ø Nº05 @ 0.22 m (As=35.63 cm2)



39.969 T m 1''

4200 kg/cm2 t= 60 cm

b= 388 cm d= 51.190 cm

5 22.951 cm2 a= 1.394 1.98 20.941 cm2 a= 1.272 22.35 20.916 cm2 a= 1.270 17.33 20.916 cm2 a= 1.270 20.916 cm2

usar: 18 ø Nº05 @ 0.22 m (As=35.63 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




68.499 T m 1''

4200 kg/cm2 t= 60 cm

b= 388 cm d= 51.190 cm5

39.334 cm2 a= 2.388 1.98 36.246 cm2 a= 2.201 21.2008 36.178 cm2 a= 2.197 18.2776 36.176 cm2 a= 2.197 36.176 cm2

usar: 19 ø Nº05 @ 0.21 m (As=37.61 cm2)

f'c=

Mu= øvarilla=

fy=

• As=

As=

As=

As=

As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US



Datos:B= 300 cm 0.25 m 6.00 mH= 60 cm 5.50 m 7.25 m q= 17.81 T/mI= 5400000 cm4 6.50 m 0.25 m


Nudo 1: Nudo 2:7364 7364 8308

∑(K)= 7364 ∑(K)= 156711 0.47 0.53

Nudo 3: Nudo 4:8308 9000 9000 5586

∑(K)= 17308 ∑(K)= 145860.48 0.52 0.62 0.38

Nudo 5:5586

∑(K)= 55861


-0.56 T m 53.43 T m44.90 T m -53.43 T m-44.90 T m 78.01 T m62.71 T m -78.01 T m-62.71 T m 0.56 T m

diferencia: 2º 44.340 4º 17.810 5º -9.276 3º 24.582 1º -77.456


L1= L4=L2= L5=L3= L6=

KR12= KR

21= K23=

F12= F21= F23=

K32= K34= K43= KR45=

F32= F34= F43= F45=

KR54=

F54=

M1A= M34=M12= M43=M21= M45=M23= M54=M32= M4B=

49.946 tn 108.984 tn 113.522 tn 120.330 tn 65.829 tn

17.810 tn/m 17.810 tn/m

5,500 6,500 6,000 7,2500,250 0,250

A B1 2 3 4 5


2º 4º 5º 3º 1º∞ 1 0.47 0.53 0.48 0.52 0.62 0.38 1 ∞

-0.56 44.90 -44.90 62.71 -62.71 53.43 -53.43 78.01 -78.01 0.56-44.34 -22.17 38.73 77.46

2.05 2.31 1.16 -19.53 -39.06 -24.256.64 13.27 14.38 7.19

-3.12 -3.52 -1.76 -2.22 -4.44 -2.750.95 1.91 2.07 1.03

-0.45 -0.51 -0.25 -0.32 -0.64 -0.400.14 0.27 0.30 0.15

-0.06 -0.07 -0.04 -0.05 -0.09 -0.060.02 0.04 0.04 0.02

-0.01 -0.01 -0.01 -0.01 -0.01 -0.010.00284 0.0057 0.0062 0.0031

-0.001 -0.002 -0.001 -0.001 -0.002 -0.0010.000 0.001 0.001 0.000

-0.56 0.56 -68.66 68.66 -48.10 48.10 -89.28 89.28 -0.56 0.56

49.946 T

0.557 T m 45.493 T

17.810 T/m

108.984 Tx -36.595 T

47.624 T

0.557 T m 68.660 T m 0.557 -36.6 X +17.81 X^2/2M/∂x=0 X= 2.055 m

17.810 T/m -37.041 T m

113.522 Tx

-61.046 T

68.660 T m 48.103 T m 58.802 T68.660 -61.0 X +17.810 X^2/2

17.810 T/m ∂M/∂x=0 X= 3.428 m-35.959 T m

R'1=

R'1

R''1=R'2=Mx=

Mmax=

R''1 R'2

R''2=R'3=Mx=

Mmax=R''2 R'3


120.330 Tx

-46.568 T

48.103 T m 89.277 T m 60.037 T48.103 -46.6 X +17.810 X^2/2

17.810 T/m ∂M/∂x=0 X= 2.615 m-12.778 T m

65.829 Tx

-76.799 T

89.278 T m 0.557 T m 13.505 T89.278 -76.8 X +17.810 X^2/2

17.810 T/m ∂M/∂x=0 X= 4.312 m-76.305 T m

0.557 T m -4.453 T

17.810 T/m

Reacciones:

8.90 T -13.4 T 12.2 T -17 T 9.1 T


19 0

R''3=R'4=Mx=

Mmax=R''3 R'4

R''4=R'5=Mx=

Mmax=R''4 R'5

R''5=

R''5

R1 R2 R3 R4 R5

0.56 T-m

-37.041 T-m

68.66 T-m

-35.959T-m

48.1 T-m

-12.778T-m

89.28 T-m

-76.305 T-m

0.56 T-m


0 00.25 4.45250.25 -36.65.75 61.365.75 -61.05

12.25 54.7212.25 -46.5718.25 60.29318.25 -76.8

25.5 52.32425.5 -4.453

25.75 0


Acero positivo:


•

26.563 cm2

•

Datos: ø= 0.9 rec.= 7.0 cm 210 kg/cm268.660 T m 1'' 4200 kg/cm2 t= 60 cm

b= 300 cm d= 49.190 cm5

41.029 cm2 a= 3.218 1.98 38.175 cm2 a= 2.994 16 38.085 cm2 a= 2.987 19.24 38.083 cm2 a= 2.987 38.083 cm2

usar: 20 ø Nº05 @ 0.16 m (As=39.59 cm2)


Datos: ø= 0.9 rec.= 7.0 cm 210 kg/cm248.103 T m 1''

4200 kg/cm2 t= 60 cmb= 300 cm d= 49.190 cm

5 28.745 cm2 a= 2.254 1.98 26.477 cm2 a= 2.077 22 26.428 cm2 a= 2.073 13.42 26.427 cm2 a= 2.073 26.427 cm2

usar: 14 ø Nº05 @ 0.22 m (As=27.71 cm2)

Asmin.=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 300 cm d= 49.190 cm5

53.350 cm2 a= 4.184 1.98 50.148 cm2 a= 3.933 11.874 50.014 cm2 a= 3.923 25.266 50.009 cm2 a= 3.922 50.009 cm2

usar: 26 ø Nº05 @ 0.12 m (As=51.46 cm2)

Acero negativo:



b= 300 cm d= 51.190 cm5

21.270 cm2 a= 1.668 1.98 19.460 cm2 a= 1.526 22.354 19.432 cm2 a= 1.524 13.42 19.432 cm2 a= 1.524 19.432 cm2

usar: 14 ø Nº05 @ 0.22 m (As=27.71 cm2)

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 300 cm d= 51.190 cm5

20.649 cm2 a= 1.619 1.98 18.882 cm2 a= 1.481 22.354 18.856 cm2 a= 1.479 13.42 18.856 cm2 a= 1.479 18.856 cm2

usar: 14 ø Nº05 @ 0.22 m (As=27.71 cm2)



b= 300 cm d= 51.190 cm5

7.337 cm2 a= 0.575 1.98 6.641 cm2 a= 0.521 22.354 6.637 cm2 a= 0.521 13.42 6.637 cm2 a= 0.521 6.637 cm2

usar: 14 ø Nº05 @ 0.22 m (As=27.71 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 300 cm d= 51.190 cm5

43.816 cm2 a= 3.437 1.98 40.804 cm2 a= 3.200 14.588 40.707 cm2 a= 3.193 20.565 40.704 cm2 a= 3.192 40.704 cm2

usar: 21 ø Nº05 @ 0.15 m (As=41.56 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US





Nudo 1: Nudo 2:15034 15034 16962

∑(K)= 15034 ∑(K)= 319961 0.47 0.53

Nudo 3: Nudo 4:16962 18375 18375 11405

∑(K)= 35337 ∑(K)= 297800.48 0.52 0.62 0.38

Nudo 5:11405

∑(K)= 114051





L1= L4=L2= L5=L3= L6=

KR12= KR

21= K23=

F12= F21= F23=

K32= K34= K43= KR45=

F32= F34= F43= F45=

KR54=

F54=

M1A= M34=M12= M43=M21= M45=M23= M54=M32= M4B=

107.329 tn 234.162 tn 243.905 tn 258.553 tn 141.464 tn

38.268 tn/m 38.268 tn/m

5,500 6,500 6,000 7,2500,250 0,250

A B1 2 3 4 5


2º 4º 5º 3º 1º∞ 1 0.47 0.53 0.48 0.52 0.62 0.38 1 ∞

-1.20 96.47 -96.47 134.74 -134.74 114.81 -114.81 167.62 -167.62 1.20-95.27 -47.64 83.21 166.43

4.40 4.97 2.48 -41.97 -83.93 -52.1014.26 28.52 30.90 15.45

-6.70 -7.56 -3.78 -4.77 -9.53 -5.922.05 4.10 4.44 2.22

-0.96 -1.09 -0.54 -0.69 -1.37 -0.850.29 0.59 0.64 0.32

-0.14 -0.16 -0.08 -0.10 -0.20 -0.120.04 0.08 0.09 0.05

-0.02 -0.02 -0.01 -0.01 -0.03 -0.020.0061 0.0122 0.0132 0.00661

-0.003 -0.003 -0.002 -0.002 -0.004 -0.0030.001 0.002 0.002 0.001

-1.20 1.20 -147.53 147.53 -103.36 103.36 -191.83 191.83 -1.20 1.20

107.329 T

1.196 T m 97.762 T

38.268 T/m

234.162 Tx

-78.632 T

1.196 T m 147.528 T m 102.317 T1.196 -78.63 X +38.268 X^2/2

38.268 T/m ∂M/∂x=0 X= 2.055 m-79.589 T m

243.905 Tx

-131.168 T

147.529 T m 103.358 T m 126.328 T147.53 -131.2 X +38.268 X^2/2

38.268 T/m ∂M/∂x=0 X= 3.428 m-77.265 T m

R'1=

R'1

R''1=R'2=Mx=

Mmax=R''1 R'2

R''2=R'3=Mx=

Mmax=R''2 R'3


258.553 Tx

-100.060 T

103.358 T m 191.829 T m 129.002 T103.36 -100.1 X +38.268 X^2/2

38.268 T/m ∂M/∂x=0 X= 2.615 m-27.455 T m

141.464 Tx

-165.017 T

191.830 T m 1.196 T m 29.035 T191.83 -165.0 X +38.268 X^2/2

38.268 T/m ∂M/∂x=0 X= 4.312 m-163.956 T m

1.196 T m -9.567 T

38.268 T/m

Reacciones:

19.13 T -29 T 26 T -36 T 19.5 T


19 0

R''3=R'4=Mx=

Mmax=R''3 R'4

R''4=R'5=Mx=

Mmax=R''4 R'5

R''5=

R''5

R1 R2 R3 R4 R5

1.20T-m

-79.589 T-m

147.53 T-m

-77.265 T-m

103.36 T-m

-27.455 T-m

191.83 T-m

-163.956 T-m

1.20 T-m


0 00.25 9.56710.25 -78.635.75 131.845.75 -131.2

12.25 117.5812.25 -100.118.25 129.5518.25 -165

25.5 112.4325.5 -9.567

25.75 0


Acero positivo:


•

54.232 cm2

•


b= 613 cm d= 49.190 cm5

88.159 cm2 a= 3.387 1.98 82.172 cm2 a= 3.157 14.7903 81.973 cm2 a= 3.149 41.4124 81.967 cm2 a= 3.149 81.967 cm2

usar: 42 ø Nº05 @ 0.15 m (As=83.13 cm2)



4200 kg/cm2 t= 60 cmb= 613 cm d= 49.190 cm

5 61.764 cm2 a= 2.373 1.98 56.961 cm2 a= 2.19 21.325 56.852 cm2 a= 2.184 28.7222 56.849 cm2 a= 2.184 56.849 cm2

usar: 29 ø Nº05 @ 0.21 m (As=57.40 cm2)

Asmin.=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 613 cm d= 49.190 cm5

114.632 cm2 a= 4.404 1.98 108.003 cm2 a= 4.149 11.2565 107.711 cm2 a= 4.138 54.4128 107.699 cm2 a= 4.137 107.698 cm2

usar: 55 ø Nº05 @ 0.11 m (As=108.86 cm2)

Acero negativo:



b= 613 cm d= 51.190 cm5

45.702 cm2 a= 1.756 1.98 41.849 cm2 a= 1.608 22.3541 41.788 cm2 a= 1.605 27.3999 41.787 cm2 a= 1.605 41.787 cm2

usar: 28 ø Nº05 @ 0.22 m (As=55.42 cm2)

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 613 cm d= 51.190 cm5

44.367 cm2 a= 1.704 1.98 40.607 cm2 a= 1.560 22.3541 40.548 cm2 a= 1.558 27.3999 40.548 cm2 a= 1.558 40.548 cm2

usar: 28 ø Nº05 @ 0.22 m (As=55.42 cm2)



b= 613 cm d= 51.190 cm5

15.765 cm2 a= 0.606 1.98 14.273 cm2 a= 0.548 22.3541 14.265 cm2 a= 0.548 27.3999 14.265 cm2 a= 0.548 14.265 cm2

usar: 28 ø Nº05 @ 0.22 m (As=55.42 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 613 cm d= 51.190 cm5

94.147 cm2 a= 3.617 1.98 87.835 cm2 a= 3.374 13.8371 87.620 cm2 a= 3.366 44.265 87.613 cm2 a= 3.366 87.613 cm2

usar: 45 ø Nº05 @ 0.14 m (As=89.07 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US





Nudo 1: Nudo 2:15955 15955 18000

∑(K)= 15955 ∑(K)= 339551 0.47 0.53

Nudo 3: Nudo 4:18000 19500 19500 12103

∑(K)= 37500 ∑(K)= 316030.48 0.52 0.62 0.38

Nudo 5:12103

∑(K)= 121031





L1= L4=L2= L5=L3= L6=

KR12= KR

21= K23=

F12= F21= F23=

K32= K34= K43= KR45=

F32= F34= F43= F45=

KR54=

F54=

M1A= M34=M12= M43=M21= M45=M23= M54=M32= M4B=

114.897tn 250.591 tn 261.038 tn 276.685 tn 151.397 tn

40.956 tn/m 40.956 tn/m

5,500 6,500 6,000 7,2500,250 0,250

A B1 2 3 4 5


2º 4º 5º 3º 1º∞ 1 0.47 0.53 0.48 0.52 0.62 0.38 1 ∞

-1.28 103.24 -103.24 144.20 -144.20 122.87 -122.87 179.39 -179.39 1.28-101.96 -50.98 89.06 178.11

4.71 5.31 2.66 -44.91 -89.83 -55.7615.26 30.52 33.07 16.53

-7.17 -8.09 -4.05 -5.10 -10.20 -6.332.19 4.39 4.76 2.38

-1.03 -1.16 -0.58 -0.73 -1.47 -0.910.32 0.63 0.68 0.34

-0.15 -0.17 -0.08 -0.11 -0.21 -0.130.05 0.09 0.10 0.05

-0.02 -0.02 -0.01 -0.02 -0.03 -0.020.0065 0.01306 0.0141 0.00707

-0.003 -0.003 -0.002 -0.002 -0.004 -0.0030.001 0.002 0.002 0.001

-1.28 1.28 -157.89 157.89 -110.62 110.62 -205.30 205.30 -1.28 1.28

114.897 T

1.280 T m 104.658 T

40.956 T/m

250.591 Tx -84.154 T

109.489 T

1.280 T m 157.888 T m 1.280 -84.15 X +40.96 X^2/2∂M/∂x=0 X= 2.055 m

40.956 T/m -85.178 T m

261.038 Tx

-140.379 T

157.889 T m 110.616 T m 135.205 T157.89 -140.4 X +40.956 X^2/2

40.956 T/m ∂M/∂x=0 X= 3.428 m-82.691 T m

R'1=

R'1

R''1=R'2=Mx=

Mmax=

R''1 R'2

R''2=R'3=Mx=

Mmax=R''2 R'3


276.685 Tx

-107.086 T

110.616 T m 205.300 T m 138.037 T110.62 -107.1 X +40.956 X^2/2

40.956 T/m ∂M/∂x=0 X= 2.615 m-29.383 T m

151.397 Tx

-176.605 T

205.301 T m 1.280 T m 31.073 T205.30 -176.6 X +40.956 X^2/2

40.956 T/m ∂M/∂x=0 X= 4.312 m-175.469 T m

1.280 T m -10.239 T

40.956 T/m

Reacciones:

20.50 T -31 T 28 T -39 T 20.8 T


19 0

R''3=R'4=Mx=

Mmax=R''3 R'4

R''4=R'5=Mx=

Mmax=R''4 R'5

R''5=

R''5

R1 R2 R3 R4 R5

1.28T-m

-85.178 T-m

157.89 T-m

-82.691 T-m

110.62 T-m

-29.383 T-m

205.3 T-m

-175.469 T-m

1.28 T-m


0 00.25 10.2390.25 -84.155.75 141.15.75 -140.4

12.25 125.8312.25 -107.118.25 138.6518.25 -176.6

25.5 120.3225.5 -10.24

25.75 0


Acero positivo:


•

57.552 cm2

•


b= 650 cm d= 49.190 cm

94.350 cm2 a= 3.415 14.6617 87.968 cm2 a= 3.184 44.3332 87.755 cm2 a= 3.177 2 87.748 cm2 a= 3.176 5.00 87.748 cm2

usar: 45 ø Nº05 @ 0.15 m (As=89.07 cm2)



4200 kg/cm2 t= 60 cmb= 650 cm d= 49.190 cm

5 66.101 cm2 a= 2.393 1.98 60.973 cm2 a= 2.21 21.1416 60.856 cm2 a= 2.203 30.7451 60.853 cm2 a= 2.203 60.853 cm2

usar: 31 ø Nº05 @ 0.21 m (As=61.36 cm2)

Asmin.=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 650 cm d= 49.190 cm5

122.682 cm2 a= 4.441 1.98 115.633 cm2 a= 4.186 11.1576 115.320 cm2 a= 4.174 58.2563 115.306 cm2 a= 4.174 115.305 cm2

usar: 59 ø Nº05 @ 0.11 m (As=116.78 cm2)

Acero negativo:



b= 650 cm d= 51.190 cm5

48.911 cm2 a= 1.771 1.98 44.795 cm2 a= 1.622 22.3541 44.728 cm2 a= 1.619 29.0774 44.727 cm2 a= 1.619 44.727 cm2

usar: 30 ø Nº05 @ 0.22 m (As=59.38 cm2)

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 650 cm d= 51.190 cm5

47.483 cm2 a= 1.719 1.98 43.464 cm2 a= 1.573 22.3541 43.402 cm2 a= 1.571 29.0774 43.401 cm2 a= 1.571 43.401 cm2

usar: 30 ø Nº05 @ 0.22 m (As=59.38 cm2)



b= 650 cm d= 51.190 cm5

16.872 cm2 a= 0.611 1.98 15.276 cm2 a= 0.553 22.3541 15.268 cm2 a= 0.553 29.0774 15.268 cm2 a= 0.553 15.268 cm2

usar: 30 ø Nº05 @ 0.22 m (As=59.38 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 650 cm d= 51.190 cm5

100.758 cm2 a= 3.647 1.98 94.032 cm2 a= 3.404 13.7167 93.801 cm2 a= 3.396 47.3874 93.793 cm2 a= 3.395 93.793 cm2

usar: 48 ø Nº05 @ 0.14 m (As=95.01 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US





Nudo 1: Nudo 2:8284 8284 9346

∑(K)= 8284 ∑(K)= 176301 0.47 0.53

Nudo 3: Nudo 4:9346 10125 10125 6284

∑(K)= 19471 ∑(K)= 164090.48 0.52 0.62 0.38

Nudo 5:6284

∑(K)= 62841





L1= L4=L2= L5=L3= L6=

KR12= KR

21= K23=

F12= F21= F23=

K32= K34= K43= KR45=

F32= F34= F43= F45=

KR54=

F54=

M1A= M34=M12= M43=M21= M45=M23= M54=M32= M4B=

59.699 tn 125.228 tn 130.444 tn 138.253 tn 78.680 tn

20.672 tn/m 20.672 tn/m

5,500 6,500 6,000 7,2500,250 0,250

A B1 2 3 4 5


2º 4º 5º 3º 1º∞ 1 0.47 0.53 0.48 0.52 0.62 0.38 1 ∞

-0.65 52.11 -52.11 72.78 -72.78 62.02 -62.02 90.55 -90.55 0.65-51.46 -25.73 44.95 89.90

2.38 2.68 1.34 -22.67 -45.34 -28.147.70 15.41 16.69 8.34

-3.62 -4.08 -2.04 -2.57 -5.15 -3.201.11 2.22 2.40 1.20

-0.52 -0.59 -0.29 -0.37 -0.74 -0.460.16 0.32 0.35 0.17

-0.07 -0.08 -0.04 -0.05 -0.11 -0.070.02 0.05 0.05 0.02

-0.01 -0.01 -0.01 -0.01 -0.02 -0.010.0033 0.00659 0.0071 0.00357

-0.002 -0.002 -0.001 -0.001 -0.002 -0.0010.000 0.001 0.001 0.001

-0.65 0.65 -79.69 79.69 -55.83 55.83 -103.62 103.62 -0.65 0.65

59.699 T

0.646 T m 54.531 T

20.672 T/m

125.228 Tx -42.476 T

54.008 T

0.646 T m 79.693 T m 0.646 -42.5 X +20.67 X^2/2∂M/∂x=0 X= 2.055 m

20.672 T/m -42.993 T m

130.444 Tx

-70.855 T

79.693 T m 55.832 T m 66.931 T79.69 -70.9 X +20.672 X^2/2

20.672 T/m ∂M/∂x=0 X= 3.428 m-41.737 T m

R'1=

R'1

R''1=R'2=Mx=

Mmax=

R''1 R'2

R''2=R'3=Mx=

Mmax=R''2 R'3


138.253 Tx

-54.051 T

55.832 T m 103.623 T m 68.272 T55.83 -54.1 X +20.672 X^2/2

20.672 T/m ∂M/∂x=0 X= 2.615 m-14.831 T m

78.680 Tx

-89.140 T

103.624 T m 0.646 T m 17.948 T103.62 -89.1 X +20.672 X^2/2

20.672 T/m ∂M/∂x=0 X= 4.312 m-88.566 T m

0.646 T m -5.168 T

20.672 T/m

Reacciones:

12.05 T -17 T 13 T -21 T 12.8 T


19 0

R''3=R'4=Mx=

Mmax=R''3 R'4

R''4=R'5=Mx=

Mmax=R''4 R'5

R''5=

R''5

R1 R2 R3 R4 R5

0.65T-m

-42.993 T-m

79.69 T-m

-41.737 T-m

55.83 T-m

-14.831 T-m

103.62 T-m

-88.566 T-m

0.65 T-m


0 00.3 5.168010.3 -42.4765.8 71.22025.8 -70.85512 63.513212 -54.05118 69.981218 -89.1426 60.732226 -5.16826 0


Acero positivo:


•

29.883 cm2

•


b= 338 cm d= 49.190 cm15

47.622 cm2 a= 3.320 22.36 44.357 cm2 a= 3.092 2 44.251 cm2 a= 3.085 5.00 44.247 cm2 a= 3.085 44.247 cm2

usar: 23 ø Nº05 @ 0.15 m (As=45.52 cm2)



4200 kg/cm2 t= 60 cmb= 338 cm d= 49.190 cm

5 33.364 cm2 a= 2.326 1.98 30.754 cm2 a= 2.1 22 30.696 cm2 a= 2.140 15.51 30.695 cm2 a= 2.140 30.695 cm2

usar: 16 ø Nº05 @ 0.22 m (As=31.67 cm2)

Asmin.=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

bdAS 0018.0min

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 338 cm d= 49.190 cm5

61.923 cm2 a= 4.317 1.98 58.288 cm2 a= 4.064 11 58.131 cm2 a= 4.053 29.37 58.125 cm2 a= 4.052 58.124 cm2

usar: 30 ø Nº05 @ 0.11 m (As=59.38 cm2)

Acero negativo:



b= 338 cm d= 51.190 cm5

24.687 cm2 a= 1.721 1.98 22.599 cm2 a= 1.576 22 22.566 cm2 a= 1.573 15.10 22.565 cm2 a= 1.573 22.565 cm2

usar: 16 ø Nº05 @ 0.22 m (As=31.67 cm2)

f'c=Mu= øvarilla=

fy=

As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 338 cm d= 51.190 cm5

23.967 cm2 a= 1.671 1.98 21.928 cm2 a= 1.529 22 21.897 cm2 a= 1.527 15.10 21.896 cm2 a= 1.527 21.896 cm2

usar: 16 ø Nº05 @ 0.22 m (As=31.67 cm2)



b= 338 cm d= 51.190 cm4

8.516 cm2 a= 0.594 1.27 7.709 cm2 a= 0.537 14 7.705 cm2 a= 0.537 23.59 7.705 cm2 a= 0.537 7.705 cm2

usar: 24 ø Nº04 @ 0.14 m (As=30.40 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US




b= 338 cm d= 51.190 cm5

50.857 cm2 a= 3.546 1.98 47.413 cm2 a= 3.305 14 47.298 cm2 a= 3.297 23.89 47.294 cm2 a= 3.297 47.294 cm2

usar: 24 ø Nº05 @ 0.14 m (As=47.50 cm2)

f'c=Mu= øvarilla=

fy=

• As=As=As=As=As=

)2/(* adf

MA

Y

US

bf

fAa

C

yS

**85.0

*'

)*9.0(* df

MA

Y

US


Franja ø Nº Varillas S (m)

01 18.19856 3.000 19.00

66.044 49.190 Nº05 19 37.606 0.1679.255 49.190 Nº05 23 45.523 0.13-39.401 51.190 Nº05 14 27.710 0.22-31.102 51.190 Nº05 15 29.689 0.22-53.303 51.190 Nº05 15 29.689 0.21

02 37.76318 6.000 19.00

137.045 49.190 Nº05 39 77.192 0.16164.459 49.190 Nº05 46 91.047 0.13-81.759 51.190 Nº05 27 53.441 0.22-64.539 51.190 Nº05 27 53.441 0.22

-110.607 51.190 Nº05 30 59.378 0.20

03 39.18322 6.250 19.00

142.199 49.190 Nº05 40 79.171 0.16170.643 49.190 Nº05 48 95.005 0.13-84.833 51.190 Nº05 28 55.420 0.22-66.966 51.190 Nº05 28 55.420 0.22

-114.767 51.190 Nº05 31 61.358 0.20

04 41.36455 6.625 19.00

150.115 49.190 Nº05 43 85.109 0.16180.143 49.190 Nº05 51 100.943 0.13-89.556 51.190 Nº05 30 59.378 0.22-70.694 51.190 Nº05 30 59.378 0.22

-121.156 51.190 Nº05 33 65.316 0.20

05 23.38662 3.875 19.00

84.872 49.190 Nº05 24 47.503 0.16101.849 49.190 Nº05 29 57.399 0.14-50.633 51.190 Nº05 18 35.627 0.22-39.969 51.190 Nº05 18 35.627 0.22-68.499 51.190 Nº05 19 37.606 0.21

06 17.810 3.000 25.75

68.660 49.190 Nº05 20 39.586 0.1648.103 49.190 Nº05 14 27.710 0.2289.278 49.190 Nº05 26 51.461 0.12-37.041 51.190 Nº05 14 27.710 0.22-35.959 51.190 Nº05 14 27.710 0.22-12.778 51.190 Nº05 14 27.710 0.22-76.305 51.190 Nº05 21 41.565 0.15

07 38.268 6.125 25.75

147.529 49.190 Nº05 42 83.130 0.15103.358 49.190 Nº05 29 57.399 0.21191.830 49.190 Nº05 55 108.860 0.11-79.589 51.190 Nº05 28 55.420 0.22-77.265 51.190 Nº05 28 55.420 0.22-27.455 51.190 Nº05 28 55.420 0.22

-163.956 51.190 Nº05 45 89.068 0.14

08 40.956 6.500 25.75

157.889 49.190 Nº05 45 89.068 0.15110.616 49.190 Nº05 31 61.358 0.21205.301 49.190 Nº05 59 116.777 0.11-85.178 51.190 Nº05 30 59.378 0.22-82.691 51.190 Nº05 30 59.378 0.22-29.383 51.190 Nº05 30 59.378 0.22

-175.469 51.190 Nº05 48 95.005 0.14

09 20.672 3.375 25.75

79.693 49.190 Nº05 23 45.523 0.1555.832 49.190 Nº05 16 31.668 0.22

103.624 49.190 Nº05 30 59.378 0.11-42.993 51.190 Nº05 16 31.668 0.22-41.737 51.190 Nº05 16 31.668 0.22-14.831 51.190 Nº04 24 30.402 0.14-88.566 51.190 Nº05 24 47.503 0.14

q'mod.

(Tn/m)b'

(m)L

(m)M

(T-m)d

(cm)As (cm2)


Verificacion por cortante:

Franja d (cm) ф

01 18.19856 3.000 49.190 0.85 210 13.79633 96.34 ok18.19856 3.000 51.190 0.85 210 13.43236 100.26 ok

02 37.76318 6.000 49.190 0.85 210 85.27304 192.68 ok37.76318 6.000 51.190 0.85 210 84.51777 200.51 ok

03 39.18322 6.250 49.190 0.85 210 93.37752 200.71 ok39.18322 6.250 51.190 0.85 210 92.59386 208.87 ok

04 41.36455 6.625 49.190 0.85 210 106.3317 212.75 ok41.36455 6.625 51.190 0.85 210 105.5044 221.40 ok

05 23.38662 3.875 49.190 0.85 210 27.96105 124.44 ok23.38662 3.88 51.190 0.85 210 27.49331 129.50 ok

06 17.810 3.00 49.190 0.85 210 13.50186 96.34 ok17.810 3.00 51.190 0.85 210 13.14566 100.26 ok

07 38.268 6.125 49.190 0.85 210 88.8057 196.69 ok38.268 6.125 51.190 0.85 210 88.04033 204.69 ok

08 40.956 6.500 49.190 0.85 210 102.7208 208.73 ok40.956 6.500 51.190 0.85 210 101.9017 217.22 ok

09 20.672 3.375 49.190 0.85 210 19.54746 108.38 ok20.672 3.375 51.190 0.85 210 19.13402 112.79 ok

A continuacion se detallara la distribucion de acero que se ejecutara en obra:

MALLA SUPERIOR:

Usar recubrimiento :7.5 cm

Direccion X: usar: 197 ø Nº05 @ 0.13 m

Direccion Y: usar: 171 ø Nº05 @ 0.11 m

MALLA INFERIOR:

Usar recubrimiento :7.5 cm

Direccion X: usar: 128 ø Nº05 @ 0.20 m

Direccion Y: usar: 135 ø Nº05 @ 0.14 m

q'mod.

(Tn/m)b'

(m) f'c (kg/cm2) Vu (T)

ф Vc (T)

DETALLE DE DISTRIBUCION DE ACERO

DIRECCION Y

5 cm

7 cm

60 cm


94.25

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