REFUERZOS DE BARRAS A 45º PARA ESFUERZO CORTANTE
___________________________________________________________________________________________________________Vu1 = Esfuerzo cortante de agotamiento por compresion oblicua del hormigon
Vcu = Esfuerzo cortante que absorbe el hormigon At = area de las armaduras de traccion
b = dimension de la pieza (ancho) h = altura d = altura util
___________________________________________________________________________________________________________
At =< (cm2)
_____________________________
10 14 18 22 26 32
____________________ _____________________________
b h d Vu1 Vcu s/d
cm cm m kN kN kN kN kN kN kN
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 30 25.5 383 47 49 53 56 60 63 0.39 0.59 0.78 0.98
30 459 56 60 64 67 71
35 536 66 66 71 75 78
40 612 75 77 82 86
45 689 85 88 93
50 765 94 95 99
55 842 104 106
60 918 113
65 995 122
70 1071 132
75 1148 141
80 1224 151
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 35 30.5 458 54 57 61 65 68 0.33 0.49 0.66 0.82 0.98
30 549 65 69 73 76
35 641 76 76 81 85
40 732 86 88 93
45 824 97 100
50 915 108
55 1007 119
60 1098 130
65 1190 140
70 1281 151
75 1373 162
80 1464 173
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 40 35.5 533 61 61 65 69 72 0.28 0.42 0.56 0.70 0.85 0.99
30 639 73 74 78 82
35 746 85 86 91
40 852 97 99
45 959 109
50 1065 122
55 1172 134
60 1278 146
65 1385 158
70 1491 170
75 1598 182
80 1704 195
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 45 40.5 608 67 69 73 77 0.25 0.37 0.49 0.62 0.74 0.86 0.99
30 729 81 83 87
35 851 94 96
40 972 108
45 1094 121
50 1215 135
55 1337 148
60 1458 162
65 1580 175
70 1701 189
75 1823 202
80 1944 216
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 50 45.5 683 74 77 81 0.22 0.33 0.44 0.55 0.66 0.77 0.88 0.99
30 819 89 92
35 956 104
40 1092 118
45 1229 133
50 1365 148
55 1502 163
60 1638 178
65 1775 193
70 1911 207
75 2048 222
80 2184 237
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 55 50.5 758 81 81 85 0.30 0.40 0.50 0.59 0.69 0.79 0.89 0.99
30 909 97
35 1061 113
40 1212 129
45 1364 145
50 1515 161
55 1667 177
60 1818 193
65 1970 209
70 2121 225
75 2273 242
80 2424 258
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 60 55.5 832 87 89 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90
30 999 104
35 1165 122
40 1332 139
45 1498 156
50 1665 174
55 1832 191
60 1998 209
65 2164 226
70 2331 243
75 2497 261
80 2664 278
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 65 60.5 908 93 0.25 0.33 0.41 0.50 0.58 0.66 0.74 0.83
30 1089 112
35 1271 131
40 1452 149
45 1634 168
50 1815 187
55 1997 205
60 2178 224
65 2360 242
70 2541 261
75 2723 280
80 2904 298
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 70 65.5 982 100 0.23 0.31 0.38 0.46 0.53 0.61 0.69 0.76
30 1179 119
35 1375 139
40 1572 159
45 1768 179
50 1965 199
55 2162 219
60 2358 239
65 2554 259
70 2751 279
75 2947 299
80 3144 318
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 75 70.5 1058 106 0.21 0.28 0.35 0.43 0.50 0.57 0.64 0.71
30 1269 127
35 1481 148
40 1692 169
45 1904 190
50 2115 212
55 2327 233
60 2538 254
65 2750 275
70 2961 296
75 3173 317
80 3384 338
____________________ _____________________________ s= 10 15 20 25 30 35 40 45 50 cm
25 x 80 75.5 1133 112 0.26 0.33 0.40 0.46 0.53 0.60 0.66
30 1359 134
35 1586 157
40 1812 179
45 2039 201
50 2265 224
55 2492 246
60 2718 269
65 2945 291
70 3171 313
75 3398 336
80 3624 358
TABLA 2
Vsu = Esfu.cort. que deben absorver las barras a 45º y 90º = esf.cort de servicio - Vcu (tabla 1)
As = Area de las barras a 45º necesarias
s = separacion horizontal entre barras de 45º o cercos a 90º
___________________________________________________________________________________________________________Vsu As (cm2)
kN ____________________________________________________________________________________________________
1.00 0.83 0.71 0.63 0.56 0.50 0.45 0.42 0.38 0.36 0.33 0.31 0.29 0.28 0.26 0.25 0.24 s/d
___________________________________________________________________________________________________________
100 1.96 1.64 1.40 1.23 1.09 0.98 0.89 0.82 0.76 0.70 0.65 0.61 0.58 0.55 0.52 0.49 0.4745º
2.78 2.31 1.98 1.74 1.54 1.39 1.26 1.16 1.07 0.99 0.93 0.87 0.82 0.77 0.73 0.69 0.6690º
150 2.95 2.46 2.10 1.84 1.64 1.47 1.34 1.23 1.13 1.05 0.98 0.92 0.87 0.82 0.78 0.74 0.70
4.17 3.47 2.98 2.60 2.31 2.08 1.89 1.74 1.60 1.49 1.39 1.30 1.23 1.16 1.10 1.04 0.99
200 3.93 3.27 2.81 2.46 2.18 1.96 1.79 1.64 1.51 1.40 1.31 1.23 1.16 1.09 1.03 0.98 0.94
5.56 4.63 3.97 3.47 3.09 2.78 2.53 2.31 2.14 1.98 1.85 1.74 1.63 1.54 1.46 1.39 1.32
250 4.91 4.09 3.51 3.07 2.73 2.46 2.23 2.05 1.89 1.75 1.64 1.53 1.44 1.36 1.29 1.23 1.17
6.94 5.79 4.96 4.34 3.86 3.47 3.16 2.89 2.67 2.48 2.31 2.17 2.04 1.93 1.83 1.74 1.65
300 5.89 4.91 4.21 3.68 3.27 2.95 2.68 2.46 2.27 2.10 1.96 1.84 1.73 1.64 1.55 1.47 1.40
8.33 6.94 5.95 5.21 4.63 4.17 3.79 3.47 3.21 2.98 2.78 2.60 2.45 2.31 2.19 2.08 1.98
350 6.87 5.73 4.91 4.30 3.82 3.44 3.12 2.86 2.64 2.46 2.29 2.15 2.02 1.91 1.81 1.72 1.64
9.72 8.10 6.94 6.08 5.40 4.86 4.42 4.05 3.74 3.47 3.24 3.04 2.86 2.70 2.56 2.43 2.31
400 7.86 6.55 5.61 4.91 4.36 3.93 3.57 3.27 3.02 2.81 2.62 2.46 2.31 2.18 2.07 1.96 1.87
11.11 9.26 7.94 6.94 6.17 5.56 5.05 4.63 4.27 3.97 3.70 3.47 3.27 3.09 2.92 2.78 2.65
450 8.84 7.37 6.31 5.52 4.91 4.42 4.02 3.68 3.40 3.16 2.95 2.76 2.60 2.46 2.33 2.21 2.10
12.50 10.42 8.93 7.81 6.94 6.25 5.68 5.21 4.81 4.46 4.17 3.91 3.68 3.47 3.29 3.12 2.98
500 9.82 8.18 7.01 6.14 5.46 4.91 4.46 4.09 3.78 3.51 3.27 3.07 2.89 2.73 2.58 2.46 2.34
13.89 11.57 9.92 8.68 7.72 6.94 6.31 5.79 5.34 4.96 4.63 4.34 4.08 3.86 3.65 3.47 3.31
550 10.80 9.00 7.72 6.75 6.00 5.40 4.91 4.50 4.16 3.86 3.60 3.38 3.18 3.00 2.84 2.70 2.57
15.28 12.73 10.91 9.55 8.49 7.64 6.94 6.37 5.88 5.46 5.09 4.77 4.49 4.24 4.02 3.82 3.64
600 11.79 9.82 8.42 7.37 6.55 5.89 5.36 4.91 4.53 4.21 3.93 3.68 3.47 3.27 3.10 2.95 2.81
16.67 13.89 11.90 10.42 9.26 8.33 7.58 6.94 6.41 5.95 5.56 5.21 4.90 4.63 4.39 4.17 3.97
650 12.77 10.64 9.12 7.98 7.09 6.38 5.80 5.32 4.91 4.56 4.26 3.99 3.76 3.55 3.36 3.19 3.04
18.06 15.05 12.90 11.28 10.03 9.03 8.21 7.52 6.94 6.45 6.02 5.64 5.31 5.02 4.75 4.51 4.30
700 13.75 11.46 9.82 8.59 7.64 6.87 6.25 5.73 5.29 4.91 4.58 4.30 4.04 3.82 3.62 3.44 3.27
19.44 16.20 13.89 12.15 10.80 9.72 8.84 8.10 7.48 6.94 6.48 6.08 5.72 5.40 5.12 4.86 4.63
750 14.73 12.28 10.52 9.21 8.18 7.37 6.70 6.14 5.67 5.26 4.91 4.60 4.33 4.09 3.88 3.68 3.51
20.83 17.36 14.88 13.02 11.57 10.42 9.47 8.68 8.01 7.44 6.94 6.51 6.13 5.79 5.48 5.21 4.96
800 15.71 13.09 11.22 9.82 8.73 7.86 7.14 6.55 6.04 5.61 5.24 4.91 4.62 4.36 4.14 3.93 3.74
22.22 18.52 15.87 13.89 12.35 11.11 10.10 9.26 8.55 7.94 7.41 6.94 6.54 6.17 5.85 5.56 5.29
850 16.70 13.91 11.93 10.43 9.28 8.35 7.59 6.96 6.42 5.96 5.57 5.22 4.91 4.64 4.39 4.17 3.98
23.61 19.68 16.87 14.76 13.12 11.81 10.73 9.84 9.08 8.43 7.87 7.38 6.94 6.56 6.21 5.90 5.62
900 17.68 14.73 12.63 11.05 9.82 8.84 8.04 7.37 6.80 6.31 5.89 5.52 5.20 4.91 4.65 4.42 4.21
25.00 20.83 17.86 15.63 13.89 12.50 11.36 10.42 9.62 8.93 8.33 7.81 7.35 6.94 6.58 6.25 5.95
950 18.66 15.55 13.33 11.66 10.37 9.33 8.48 7.77 7.18 6.66 6.22 5.83 5.49 5.18 4.91 4.66 4.44
26.39 21.99 18.85 16.49 14.66 13.19 11.99 11.00 10.15 9.42 8.80 8.25 7.76 7.33 6.94 6.60 6.28
1000 19.64 16.37 14.03 12.28 10.91 9.82 8.93 8.18 7.55 7.01 6.55 6.14 5.78 5.46 5.17 4.91 4.68
27.78 23.15 19.84 17.36 15.43 13.89 12.63 11.57 10.68 9.92 9.26 8.68 8.17 7.72 7.31 6.94 6.61
TABLA 3
Con el resultado de la tabla 2 se ve aqui la combinacion de redondos mas conveniente
________________________________________________________________________________________________Areas (cm2)
1 2 3 4 5 6 7 8 9 10
_______________________________________________________________________________________________
6 0.283 0.565 0.848 1.131 1.414 1.696 1.979 2.262 2.545 2.827
_______________________________________________________________________________________________
8 0.503 1.005 1.508 2.011 2.513 3.016 3.519 4.021 4.524 5.027
_______________________________________________________________________________________________
10 0.785 1.571 2.356 3.142 3.927 4.712 5.498 6.283 7.069 7.854
_______________________________________________________________________________________________
12 1.131 2.262 3.393 4.524 5.655 6.786 7.917 9.048 10.179 11.310
_______________________________________________________________________________________________
14 1.539 3.079 4.618 6.158 7.697 9.236 10.776 12.315 13.854 15.394
_______________________________________________________________________________________________
16 2.011 4.021 6.032 8.042 10.053 12.064 14.074 16.085 18.096 20.106
_______________________________________________________________________________________________
20 3.142 6.283 9.425 12.566 15.708 18.850 21.991 25.133 28.274 31.416
_______________________________________________________________________________________________
25 4.909 9.817 14.726 19.635 24.544 29.452 34.361 39.270 44.179 49.087
_______________________________________________________________________________________________
32 8.042 16.085 24.127 32.170 40.212 48.255 56.297 64.340 72.382 80.425
_______________________________________________________________________________________________
40 12.566 25.133 37.699 50.265 62.832 75.398 87.965 100.531 113.097 125.664
_______________________________________________________________________________________________
Ejemplo: Tenemos que absorver un esfuerzo cortante de 400 kN (ya mayorado con su coeficiente de seguridad correspondiente) en una viga de 30x50 (ancho x alto)
Tabla 1: buscamos el esfuerzo cortante que absorve el hormigón de esa viga: 89 kN y comprobamos que 400<819 (si no fuese así tendriamos que aumentar la escuadría). Tomamos s/d=0.44 (s=20 cm). Si después vieramos que no es apropiada esta separación probaríamos otra menor o mayor.
Tabla 2: entramos con 400-89 = 311 kN en la columna de la izquierda en las lineas de 300 y 350 kN y a la derecha en la columna de s/d=0.45 vemos que necesitamos 2.68 y 3.12 cm2 en barras a 45º o bien 3.79 y 4.42 cm2 en estribos a 90º. Si interpolamos para mayor precisión, aunque no es complétamente necesario, tendremos (3.12-2.68)*11/50=0.1 y (4.42-3.79)*11/50=0.14. Asi que tendremos 3.12+0.1=3.13 cm2 en barras a 45 y 3.79+0.14=3.93 cm2 en estribos.
Tabla 3: elegimos las barras a utilizar, pueden ser 2 de 16 a 45º o en forma de estribo o bien 3 de d=12 a 45º.
No hay comentarios:
Publicar un comentario