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1/18
180 210 250 280 350 420 490 560
13 0.005000 0.005000 0.005000 0.005000
1 4 0 .0 05 25 2 0 .0 05 21 3 0 .0 05 17 7 0 .0 05 15 6 0.005345
1 5 0 .0 05 64 9 0 .0 05 60 3 0 .0 05 56 1 0 .0 05 53 8 0 .0 05 49 9
1 6 0 .0 06 04 9 0 .0 05 99 6 0 .0 05 94 7 0 .0 05 92 0 0 .0 05 87 7 0.005855
1 7 0 .0 06 45 2 0 .0 06 39 2 0 .0 06 33 6 0 .0 06 30 5 0 .0 06 25 6 0 .0 06 22 3 0.006325
1 8 0 .0 06 85 9 0 .0 06 79 0 0 .0 06 72 7 0 .0 06 69 2 0 .0 06 63 6 0 .0 06 59 9 0 .0 06 57 4 0.006761
1 9 0 .0 0 72 6 9 0 .0 0 71 9 1 0 .0 07 1 20 0 .0 07 0 81 0 .0 0 70 1 7 0 .0 0 69 7 7 0 .0 0 69 4 8 0 .0 0 69 2 7
2 0 0 .0 0 76 8 3 0 .0 0 75 9 5 0 .0 07 5 15 0 .0 07 4 71 0 .0 0 74 0 1 0 .0 0 73 5 5 0 .0 0 73 2 3 0 .0 0 73 0 0
2 1 0 .0 0 81 0 0 0 .0 0 80 0 2 0 .0 07 9 12 0 .0 07 8 64 0 .0 0 77 8 5 0 .0 0 77 3 5 0 .0 0 76 9 9 0 .0 0 76 7 3
2 2 0 .0 0 85 2 2 0 .0 0 84 1 2 0 .0 08 3 12 0 .0 08 2 58 0 .0 0 81 7 1 0 .0 0 81 1 5 0 .0 0 80 7 6 0 .0 0 80 4 8
2 3 0 .0 0 89 4 7 0 .0 0 88 2 5 0 .0 08 7 15 0 .0 08 6 55 0 .0 0 85 5 9 0 .0 0 84 9 7 0 .0 0 84 5 5 0 .0 0 84 2 3
2 4 0 .0 0 93 7 6 0 .0 0 92 4 1 0 .0 09 1 19 0 .0 09 0 54 0 .0 0 89 4 8 0 .0 0 88 8 1 0 .0 0 88 3 4 0 .0 0 87 9 92 5 0 .0 0 98 0 9 0 .0 0 96 6 1 0 .0 09 5 26 0 .0 09 4 54 0 .0 0 93 3 9 0 .0 0 92 6 5 0 .0 0 92 1 4 0 .0 0 91 7 6
2 6 0 .0 1 02 4 6 0 .0 1 00 8 3 0 .0 09 9 36 0 .0 09 8 57 0 .0 0 97 3 1 0 .0 0 96 5 1 0 .0 0 95 9 5 0 .0 0 95 5 4
2 7 0 .0 1 06 8 8 0 .0 1 05 0 9 0 .0 10 3 48 0 .0 10 2 62 0 .0 1 01 2 5 0 .0 1 00 3 8 0 .0 0 99 7 7 0 .0 0 99 3 3
2 8 0 .0 1 11 3 4 0 .0 1 09 3 8 0 .0 10 7 63 0 .0 10 6 70 0 .0 1 05 2 1 0 .0 1 04 2 6 0 .0 1 03 6 1 0 .0 1 03 1 3
2 9 0 .0 1 15 8 5 0 .0 1 13 7 1 0 .0 11 1 81 0 .0 11 0 79 0 .0 1 09 1 8 0 .0 1 08 1 6 0 .0 1 07 4 5 0 .0 1 06 9 3
3 0 0 .0 1 20 4 1 0 .0 1 18 0 8 0 .0 11 6 01 0 .0 11 4 91 0 .0 1 13 1 7 0 .0 1 12 0 7 0 .0 1 11 3 1 0 .0 1 10 7 5
3 1 0 .0 1 25 0 2 0 .0 1 22 4 8 0 .0 12 0 24 0 .0 11 9 05 0 .0 1 17 1 8 0 .0 1 15 9 9 0 .0 1 15 1 7 0 .0 1 14 5 8
3 2 0 .0 1 29 6 7 0 .0 1 26 9 2 0 .0 12 4 50 0 .0 12 3 22 0 .0 1 21 2 0 0 .0 1 19 9 3 0 .0 1 19 0 5 0 .0 1 18 4 1
3 3 0 .0 1 34 3 8 0 .0 1 31 4 0 0 .0 12 8 78 0 .0 12 7 41 0 .0 1 25 2 4 0 .0 1 23 8 7 0 .0 1 22 9 4 0 .0 1 22 2 5
3 4 0 .0 1 39 1 4 0 .0 1 35 9 2 0 .0 13 3 10 0 .0 13 1 62 0 .0 1 29 3 0 0 .0 1 27 8 4 0 .0 1 26 8 4 0 .0 1 26 1 1
3 5 0 .0 1 43 9 6 0 .0 1 40 4 8 0 .0 13 7 45 0 .0 13 5 86 0 .0 1 33 3 7 0 .0 1 31 8 1 0 .0 1 30 7 5 0 .0 1 29 9 7
3 6 0 .0 1 48 8 4 0 .0 1 45 0 8 0 .0 14 1 82 0 .0 14 0 12 0 .0 1 37 4 6 0 .0 1 35 8 0 0 .0 1 34 6 7 0 .0 1 33 8 4
3 7 0 .0 1 53 7 8 0 .0 1 49 7 3 0 .0 14 6 23 0 .0 14 4 41 0 .0 1 41 5 8 0 .0 1 39 8 1 0 .0 1 38 6 0 0 .0 1 37 7 2
3 8 0 .0 1 58 7 8 0 .0 1 54 4 2 0 .0 15 0 67 0 .0 14 8 73 0 .0 1 45 7 0 0 .0 1 43 8 3 0 .0 1 42 5 4 0 .0 1 41 6 1
3 9 0 .0 1 63 8 5 0 .0 1 59 1 5 0 .0 15 5 14 0 .0 15 3 07 0 .0 1 49 8 5 0 .0 1 47 8 6 0 .0 1 46 5 0 0 .0 1 45 5 1
4 0 0 .0 1 68 9 9 0 .0 1 63 9 4 0 .0 15 9 65 0 .0 15 7 44 0 .0 1 54 0 2 0 .0 1 51 9 1 0 .0 1 50 4 7 0 .0 1 49 4 2
41 0.017417 0 .0 1 6 87 7 0 .0 1 6 41 9 0 .0 1 6 18 3 0 .0 1 5 82 1 0 .0 1 5 59 7 0 .0 1 5 44 5 0 .0 1 5 33 4
42 0.017365 0.016876 0.016626 0.016241 0.016004 0.015844 0.015728
43 0.017859 0.017337 0.017071 0.016664 0.016414 0.016244 0.016122
44 0.018357 0.017802 0.017520 0.017088 0.016824 0.016646 0.016517
45 0.018862 0.018271 0.017971 0.017515 0.017237 0.017048 0.016913
46 0.019372 0.018743 0.018426 0.017944 0.017650 0.017452 0.017310
47 0.019888 0.019219 0.018883 0.018375 0.018066 0.017858 0.017708
48 0.020320 0 .0 1 9 70 0 0 .0 1 9 34 4 0 .0 1 8 80 7 0 .0 1 8 48 2 0 .0 1 8 26 4 0 .0 1 8 10 7
49 0.020184 0.019808 0.019242 0.018901 0.018672 0.018507
50 0.020673 0.020275 0.019680 0.019321 0.019081 0.018909
51 0.021166 0.020746 0.020119 0.019743 0.019491 0.019311
52 0.021663 0.021220 0.020561 0.020166 0.019903 0.019715
53 0.022165 0.021698 0.021005 0.020591 0.020316 0.020119
54 0.022672 0.022179 0.021451 0.021018 0.020730 0.020525
55 0.023184 0.022665 0.021900 0.021447 0.021146 0.020931
56 0.023701 0.023153 0.022351 0.021877 0.021563 0.021339
57 0.024191 0 .0 2 3 64 6 0 .0 2 2 80 4 0 .0 2 2 30 9 0 .0 2 1 98 1 0 .0 2 1 74 8
58 0.024143 0.023260 0.022743 0.022401 0.022158
59 0.024644 0.023719 0.023178 0.022822 0.022570
60 0.025149 0.024180 0.023616 0.023245 0.022982
61 0.025658 0.024644 0.024055 0.023669 0.023396
62 0.026172 0.025110 0.024496 0.024094 0.023810
63 0.026690 0.025579 0.024939 0.024521 0.024226
64 0.027094 0 .0 2 6 05 1 0 .0 2 5 38 4 0 .0 2 4 95 0 0 .0 2 4 64 3
65 0.026525 0.025831 0.025379 0.025062
66 0.027003 0.026280 0.025811 0.025481
67 0.027483 0.026731 0.026244 0.025902
68 0.027966 0.027184 0.026678 0.026324
69 0.028452 0.027638 0.027114 0.026747
70 0.028942 0.028096 0.027552 0.027171
71 0.029434 0.028555 0.027991 0.027597
72 0.029930 0.029016 0.028431 0.028024
73 0.030429 0.029479 0.028874 0.028452
74 0.030931 0.029945 0.029318 0.028882
75 0.031436 0.030413 0.029763 0.029313
76 0.031875 0 .0 3 0 88 3 0 .0 3 0 21 1 0 .0 2 9 74 5
77 0.031356 0.030660 0.030179
78 0.031830 0.031110 0.030614
79 0.032308 0.031563 0.031050
80 0.032787 0.032017 0.031487
81 0.033269 0.032473 0.031927
82 0.033754 0.032931 0.032367
83 0.034241 0.033391 0.032809
84 0.034730 0.033852 0.033252
85 0.035222 0.034315 0.033697
86 0.035717 0.034780 0.034143
87 0.035859 0.035248 0.034591
88 0.035717 0.035040
89 0.036188 0.035490
90 0.036660 0.035942
91 0.037135 0.036396
92 0.037612 0.036851
93 0.038091 0.037308
94 0.038573 0.037766
95 0.039047 0.03822696 0.038688
97 0.039151
98 0.039616
99 0.040082
100 0.040551
101 0.041020
102 0.041438
b 0.03188 0.0372 0.04428 0.04959 0.05835 0.06564 0.07148 0.07585
f'c [kg/cm2] fy=2800 kg/cm2Rn
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180 210 250 280 350 420 490 560
13 0.003333 0.003333 0.003333 0.003333
1 4 0 .0 03 50 2 0 .0 03 47 5 0 .0 03 45 1 0 .0 03 43 8 0.003563
1 5 0 .0 03 76 6 0 .0 03 73 6 0 .0 03 70 7 0 .0 03 69 2 0 .0 03 66 6
1 6 0 .0 04 03 3 0 .0 03 99 8 0 .0 03 96 5 0 .0 03 94 7 0 .0 03 91 8 0.003904
1 7 0 .0 04 30 2 0 .0 04 26 1 0 .0 04 22 4 0 .0 04 20 4 0 .0 04 17 0 0 .0 04 14 9 0.004216
1 8 0 .0 04 57 3 0 .0 04 52 7 0 .0 04 48 4 0 .0 04 46 1 0 .0 04 42 4 0 .0 04 40 0 0 .0 04 38 3 0.004507
1 9 0 .0 0 48 4 6 0 .0 0 47 9 4 0 .0 0 47 4 6 0 .0 0 47 2 0 0 .0 0 46 7 8 0 .0 0 46 5 1 0 .0 0 46 3 2 0 .0 0 46 1 8
2 0 0 .0 0 51 2 2 0 .0 0 50 6 4 0 .0 0 50 1 0 0 .0 0 49 8 1 0 .0 0 49 3 4 0 .0 0 49 0 3 0 .0 0 48 8 2 0 .0 0 48 6 6
2 1 0 .0 0 54 0 0 0 .0 0 53 3 5 0 .0 0 52 7 5 0 .0 0 52 4 3 0 .0 0 51 9 0 0 .0 0 51 5 6 0 .0 0 51 3 3 0 .0 0 51 1 5
2 2 0 .0 0 56 8 1 0 .0 0 56 0 8 0 .0 0 55 4 2 0 .0 0 55 0 6 0 .0 0 54 4 8 0 .0 0 54 1 0 0 .0 0 53 8 4 0 .0 0 53 6 5
2 3 0 .0 0 59 6 4 0 .0 0 58 8 3 0 .0 0 58 1 0 0 .0 0 57 7 0 0 .0 0 57 0 6 0 .0 0 56 6 5 0 .0 0 56 3 6 0 .0 0 56 1 5
2 4 0 .0 0 62 5 1 0 .0 0 61 6 1 0 .0 0 60 8 0 0 .0 0 60 3 6 0 .0 0 59 6 5 0 .0 0 59 2 0 0 .0 0 58 8 9 0 .0 0 58 6 6
2 5 0 .0 0 65 3 9 0 .0 0 64 4 0 0 .0 0 63 5 1 0 .0 0 63 0 3 0 .0 0 62 2 6 0 .0 0 61 7 7 0 .0 0 61 4 3 0 .0 0 61 1 7
2 6 0 .0 0 68 3 1 0 .0 0 67 2 2 0 .0 0 66 2 4 0 .0 0 65 7 2 0 .0 0 64 8 8 0 .0 0 64 3 4 0 .0 0 63 9 7 0 .0 0 63 6 9
2 7 0 .0 0 71 2 5 0 .0 0 70 0 6 0 .0 0 68 9 9 0 .0 0 68 4 2 0 .0 0 67 5 0 0 .0 0 66 9 2 0 .0 0 66 5 2 0 .0 0 66 2 2
2 8 0 .0 0 74 2 3 0 .0 0 72 9 2 0 .0 0 71 7 5 0 .0 0 71 1 3 0 .0 0 70 1 4 0 .0 0 69 5 1 0 .0 0 69 0 7 0 .0 0 68 7 5
2 9 0 .0 0 77 2 4 0 .0 0 75 8 1 0 .0 0 74 5 4 0 .0 0 73 8 6 0 .0 0 72 7 9 0 .0 0 72 1 1 0 .0 0 71 6 3 0 .0 0 71 2 9
3 0 0 .0 0 80 2 7 0 .0 0 78 7 2 0 .0 0 77 3 4 0 .0 0 76 6 1 0 .0 0 75 4 5 0 .0 0 74 7 1 0 .0 0 74 2 0 0 .0 0 73 8 3
3 1 0 .0 0 83 3 4 0 .0 0 81 6 5 0 .0 0 80 1 6 0 .0 0 79 3 7 0 .0 0 78 1 2 0 .0 0 77 3 3 0 .0 0 76 7 8 0 .0 0 76 3 8
3 2 0 .0 0 86 4 5 0 .0 0 84 6 1 0 .0 0 83 0 0 0 .0 0 82 1 4 0 .0 0 80 8 0 0 .0 0 79 9 5 0 .0 0 79 3 7 0 .0 0 78 9 4
3 3 0 .0 0 89 5 9 0 .0 0 87 6 0 0 .0 0 85 8 6 0 .0 0 84 9 4 0 .0 0 83 4 9 0 .0 0 82 5 8 0 .0 0 81 9 6 0 .0 0 81 5 0
3 4 0 .0 0 92 7 6 0 .0 0 90 6 1 0 .0 0 88 7 3 0 .0 0 87 7 5 0 .0 0 86 2 0 0 .0 0 85 2 2 0 .0 0 84 5 6 0 .0 0 84 0 7
3 5 0 .0 0 95 9 8 0 .0 0 93 6 5 0 .0 0 91 6 3 0 .0 0 90 5 7 0 .0 0 88 9 1 0 .0 0 87 8 8 0 .0 0 87 1 6 0 .0 0 86 6 5
3 6 0 .0 0 99 2 3 0 .0 0 96 7 2 0 .0 0 94 5 5 0 .0 0 93 4 1 0 .0 0 91 6 4 0 .0 0 90 5 4 0 .0 0 89 7 8 0 .0 0 89 2 3
3 7 0 .0 1 02 5 2 0 .0 0 99 8 2 0 .0 0 97 4 9 0 .0 0 96 2 7 0 .0 0 94 3 8 0 .0 0 93 2 1 0 .0 0 92 4 0 0 .0 0 91 8 1
3 8 0 .0 1 05 8 6 0 .0 1 02 9 4 0 .0 1 00 4 5 0 .0 0 99 1 5 0 .0 0 97 1 4 0 .0 0 95 8 8 0 .0 0 95 0 3 0 .0 0 94 4 1
3 9 0 .0 1 09 2 3 0 .0 1 06 1 0 0 .0 1 03 4 3 0 .0 1 02 0 5 0 .0 0 99 9 0 0 .0 0 98 5 7 0 .0 0 97 6 7 0 .0 0 97 0 1
4 0 0 .0 1 12 6 6 0 .0 1 09 2 9 0 .0 1 06 4 3 0 .0 1 04 9 6 0 .0 1 02 6 8 0 .0 1 01 2 7 0 .0 1 00 3 1 0 .0 0 99 6 2
41 0.011612 0 .0 1 1 25 1 0 .0 1 0 94 6 0 .0 1 0 78 9 0 .0 1 0 54 7 0 .0 1 0 39 8 0 .0 1 0 29 6 0 .0 1 0 22 3
42 0.011577 0.011251 0.011084 0.010828 0.010670 0.010563 0.01048543 0.011906 0.011558 0.011381 0.011109 0.010942 0.010829 0.010748
44 0.012238 0.011868 0.011680 0.011392 0.011216 0.011097 0.011011
45 0.012574 0.012180 0.011981 0.011677 0.011491 0.011366 0.011275
46 0.012915 0.012495 0.012284 0.011963 0.011767 0.011635 0.011540
47 0.013259 0.012813 0.012589 0.012250 0.012044 0.011905 0.011805
48 0.013547 0 .0 1 3 13 3 0 .0 1 2 89 6 0 .0 1 2 53 8 0 .0 1 2 32 2 0 .0 1 2 17 6 0 .0 1 2 07 1
49 0.013456 0.013205 0.012828 0.012601 0.012448 0.012338
50 0.013782 0.013517 0.013120 0.012881 0.012721 0.012606
51 0.014110 0.013831 0.013413 0.013162 0.012994 0.012874
52 0.014442 0.014147 0.013707 0.013444 0.013269 0.013143
53 0.014777 0.014465 0.014003 0.013728 0.013544 0.013413
54 0.015115 0.014786 0.014301 0.014012 0.013820 0.013683
55 0.015456 0.015110 0.014600 0.014298 0.014097 0.013954
56 0.015801 0.015436 0.014901 0.014585 0.014375 0.014226
57 0.016127 0 .0 1 5 76 4 0 .0 1 5 20 3 0 .0 1 4 87 3 0 .0 1 4 65 4 0 .0 1 4 49 9
58 0.016095 0.015507 0.015162 0.014934 0.014772
59 0.016429 0.015813 0.015452 0.015215 0.015046
60 0.016766 0.016120 0.015744 0.015497 0.015321
61 0.017106 0.016429 0.016037 0.015779 0.015597
62 0.017448 0.016740 0.016331 0.016063 0.015874
63 0.017794 0.017053 0.016626 0.016347 0.016151
64 0.018063 0 .0 1 7 36 7 0 .0 1 6 92 3 0 .0 1 6 63 3 0 .0 1 6 42 9
65 0.017684 0.017221 0.016920 0.016708
66 0.018002 0.017520 0.017207 0.016987
67 0.018322 0.017820 0.017496 0.017268
68 0.018644 0.018122 0.017785 0.017549
69 0.018968 0.018426 0.018076 0.017831
70 0.019295 0.018730 0.018368 0.018114
71 0.019623 0.019036 0.018660 0.018398
72 0.019953 0.019344 0.018954 0.018683
73 0.020286 0.019653 0.019249 0.018968
74 0.020620 0.019963 0.019545 0.019255
75 0.020957 0.020275 0.019842 0.019542
76 0.021250 0 .0 2 0 58 9 0 .0 2 0 14 0 0 .0 1 9 83 0
77 0.020904 0.020440 0.020119
78 0.021220 0.020740 0.020409
79 0.021538 0.021042 0.020700
80 0.021858 0.021345 0.020992
81 0.022179 0.021649 0.021284
82 0.022502 0.021954 0.021578
83 0.022827 0.022260 0.021873
84 0.023153 0.022568 0.022168
85 0.023482 0.022877 0.022465
86 0.023811 0.023187 0.022762
87 0.023906 0.023498 0.023060
88 0.023811 0.023360
89 0.024125 0.023660
90 0.024440 0.023962
91 0.024757 0.024264
92 0.025075 0.024568
93 0.025394 0.024872
94 0.025715 0.025178
95 0.026031 0.025484
96 0.025792
97 0.026101
98 0.026411
99 0.026722
100 0.027034
101 0.027347
102 0.027625
b 0.01837 0.02144 0.02552 0.02858 0.03363 0.03783 0.04119 0.04371
Rnf'c [kg/cm2] fy=4200 kg/cm2
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3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 114 76 57 45 38 32 28 25 23
0.70 114 76 57 45 38 32 28 25 23
0.80 110 73 55 44 37 31 27 24 22
0.90 80 53 40 32 27 23 20 18 16
1.00 63 42 32 25 21 18 16 14 13
1.10 52 35 26 21 17 15 13 12 10
1.20 44 29 22 18 15 13 11 10 9
1.30 38 26 19 15 13 11 10 9 8
1.40 34 23 17 14 11 10 9 8 7
1.50 31 20 15 12 10 9 8 7 6
1.60 28 18 14 11 9 8 7 6 6
1.63 27 18 13 11 9 8 7 6 5
1.70 25 17 13 10 8 7 6 6 5
1.80 23 16 12 9 8 7 6 5 5
1.90 22 14 11 9 7 6 5 5 4
2.00 20 13 10 8 7 6 5 4 4
2.10 19 13 9 8 6 5 5 4 4
2.20 18 12 9 7 6 5 4 4 4
2.30 17 11 8 7 6 5 4 4 3
2.40 16 11 8 6 5 5 4 4 3
2.50 15 10 8 6 5 4 4 3 3
2.60 14 10 7 6 5 4 4 3 3
2.70 14 9 7 5 5 4 3 3 3
2.73 13 9 7 5 4 4 3 3 3
Smax 114 76 57 45 38 32 28 25 23 Smax
SEPARACION S [cm]
bw [cm] f'c=180 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 114 76 57 45 38 32 28 25 23
0.70 114 76 57 45 38 32 28 25 23
0.80 102 68 51 44 34 29 25 23 20
0.90 74 49 37 32 25 21 19 16 15
1.00 58 39 29 25 19 17 15 13 12
1.10 48 32 24 21 16 14 12 11 10
1.20 41 27 20 18 14 12 10 9 8
1.30 36 24 18 15 12 10 9 8 7
1.40 32 21 16 14 11 9 8 7 6
1.50 28 19 14 12 9 8 7 6 6
1.60 26 17 13 11 9 7 6 6 5
1.63 25 17 12 11 8 7 6 6 5
1.70 23 16 12 10 8 7 6 5 5
1.80 22 14 11 9 7 6 5 5 4
1.90 20 13 10 9 7 6 5 4 4
2.00 19 12 9 8 6 5 5 4 4
2.10 17 12 9 8 6 5 4 4 3
2.20 16 11 8 7 5 5 4 4 3
2.30 16 10 8 7 5 4 4 3 3
2.40 15 10 7 6 5 4 4 3 3
2.50 14 9 7 6 5 4 3 3 3
2.60 13 9 7 6 4 4 3 3 3
2.70 13 8 6 5 4 4 3 3 3
2.73 12 8 6 5 4 4 3 3 2
Smax 114 76 57 45 38 32 28 25 23 Smax
SEPARACION S [cm]
bw [cm] f'c=210 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
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3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 114 76 57 45 38 32 28 25 23
0.70 114 76 57 45 38 32 28 25 23
0.80 93 62 47 44 31 27 23 21 19
0.90 68 45 34 32 23 19 17 15 14
1.00 54 36 27 25 18 15 13 12 11
1.10 44 29 22 21 15 13 11 10 9
1.20 38 25 19 18 13 11 9 8 8
1.30 33 22 16 15 11 9 8 7 7
1.40 29 19 14 14 10 8 7 6 6
1.50 26 17 13 12 9 7 6 6 5
1.60 24 16 12 11 8 7 6 5 5
1.63 23 15 11 11 8 7 6 5 5
1.70 21 14 11 10 7 6 5 5 4
1.80 20 13 10 9 7 6 5 4 4
1.90 18 12 9 9 6 5 5 4 4
2.00 17 11 9 8 6 5 4 4 3
2.10 16 11 8 8 5 5 4 4 3
2.20 15 10 8 7 5 4 4 3 3
2.30 14 9 7 7 5 4 4 3 3
2.40 13 9 7 6 4 4 3 3 3
2.50 13 9 6 6 4 4 3 3 3
2.60 12 8 6 6 4 3 3 3 2
2.70 12 8 6 5 4 3 3 3 2
2.73 11 8 6 5 4 3 3 3 2
Smax 114 76 57 45 38 32 28 25 23 Smax
SEPARACION S [cm]
bw [cm] f'c=250 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 114 76 57 45 38 32 28 25 23
0.70 114 76 57 45 38 32 28 25 23
0.80 88 59 44 44 29 25 22 20 18
0.90 64 43 32 32 21 18 16 14 13
1.00 51 34 25 25 17 14 13 11 10
1.10 42 28 21 21 14 12 10 9 8
1.20 35 24 18 18 12 10 9 8 7
1.30 31 21 15 15 10 9 8 7 6
1.40 27 18 14 14 9 8 7 6 5
1.50 24 16 12 12 8 7 6 5 5
1.60 22 15 11 11 7 6 6 5 4
1.63 22 14 11 11 7 6 5 5 4
1.70 20 14 10 10 7 6 5 5 4
1.80 19 12 9 9 6 5 5 4 4
1.90 17 12 9 9 6 5 4 4 3
2.00 16 11 8 8 5 5 4 4 3
2.10 15 10 8 8 5 4 4 3 3
2.20 14 9 7 7 5 4 4 3 3
2.30 13 9 7 7 4 4 3 3 3
2.40 13 8 6 6 4 4 3 3 3
2.50 12 8 6 6 4 3 3 3 2
2.60 11 8 6 6 4 3 3 3 2
2.70 11 7 5 5 4 3 3 2 2
2.73 11 7 5 5 4 3 3 2 2
Smax 114 76 57 45 38 32 28 25 23 Smax
SEPARACION S [cm]
bw [cm] f'c=280 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
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3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 106 71 53 43 35 30 27 24 21
0.70 106 71 53 43 35 30 27 24 21
0.80 79 52 39 43 26 22 20 17 16
0.90 57 38 29 32 19 16 14 13 11
1.00 45 30 23 25 15 13 11 10 9
1.10 37 25 19 21 12 11 9 8 7
1.20 32 21 16 18 11 9 8 7 6
1.30 28 18 14 15 9 8 7 6 6
1.40 24 16 12 14 8 7 6 5 5
1.50 22 15 11 12 7 6 5 5 4
1.60 20 13 10 11 7 6 5 4 4
1.63 19 13 10 11 6 6 5 4 4
1.70 18 12 9 10 6 5 5 4 4
1.80 17 11 8 9 6 5 4 4 3
1.90 16 10 8 9 5 4 4 3 3
2.00 14 10 7 8 5 4 4 3 3
2.10 14 9 7 8 5 4 3 3 3
2.20 13 8 6 7 4 4 3 3 3
2.30 12 8 6 7 4 3 3 3 2
2.40 11 8 6 6 4 3 3 3 2
2.50 11 7 5 6 4 3 3 2 2
2.60 10 7 5 6 3 3 3 2 2
2.70 10 7 5 5 3 3 2 2 2
2.73 10 6 5 5 3 3 2 2 2
Smax 106 71 53 43 35 30 27 24 21 Smax
SEPARACION S [cm]
bw [cm] f'c=350 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 97 65 49 39 32 28 24 22 19
0.70 97 65 49 39 32 28 24 22 19
0.80 72 48 36 39 24 21 18 16 14
0.90 52 35 26 32 17 15 13 12 10
1.00 41 28 21 25 14 12 10 9 8
1.10 34 23 17 21 11 10 9 8 7
1.20 29 19 14 18 10 8 7 6 6
1.30 25 17 13 15 8 7 6 6 5
1.40 22 15 11 14 7 6 6 5 4
1.50 20 13 10 12 7 6 5 4 4
1.60 18 12 9 11 6 5 5 4 4
1.63 18 12 9 11 6 5 4 4 4
1.70 17 11 8 10 6 5 4 4 3
1.80 15 10 8 9 5 4 4 3 3
1.90 14 9 7 9 5 4 4 3 3
2.00 13 9 7 8 4 4 3 3 3
2.10 12 8 6 8 4 4 3 3 2
2.20 12 8 6 7 4 3 3 3 2
2.30 11 7 5 7 4 3 3 2 2
2.40 10 7 5 6 3 3 3 2 2
2.50 10 7 5 6 3 3 2 2 2
2.60 9 6 5 6 3 3 2 2 2
2.70 9 6 4 5 3 3 2 2 2
2.73 9 6 4 5 3 3 2 2 2
Smax 97 65 49 39 32 28 24 22 19 Smax
SEPARACION S [cm]
bw [cm] f'c=420 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
6/18
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 90 60 45 36 30 26 22 20 18
0.70 90 60 45 36 30 26 22 20 18
0.80 67 44 33 36 22 19 17 15 13
0.90 49 32 24 32 16 14 12 11 10
1.00 38 25 19 25 13 11 10 8 8
1.10 32 21 16 21 11 9 8 7 6
1.20 27 18 13 18 9 8 7 6 5
1.30 23 16 12 15 8 7 6 5 5
1.40 21 14 10 14 7 6 5 5 4
1.50 19 12 9 12 6 5 5 4 4
1.60 17 11 8 11 6 5 4 4 3
1.63 16 11 8 11 5 5 4 4 3
1.70 15 10 8 10 5 4 4 3 3
1.80 14 9 7 9 5 4 4 3 3
1.90 13 9 7 9 4 4 3 3 3
2.00 12 8 6 8 4 3 3 3 2
2.10 11 8 6 8 4 3 3 3 2
2.20 11 7 5 7 4 3 3 2 2
2.30 10 7 5 7 3 3 3 2 2
2.40 10 6 5 6 3 3 2 2 2
2.50 9 6 5 6 3 3 2 2 2
2.60 9 6 4 6 3 2 2 2 2
2.70 8 6 4 5 3 2 2 2 2
2.73 8 5 4 5 3 2 2 2 2
Smax 90 60 45 36 30 26 22 20 18 Smax
SEPARACION S [cm]
bw [cm] f'c=490 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 84 56 42 34 28 24 21 19 17
0.70 84 56 42 34 28 24 21 19 17
0.80 62 41 31 34 21 18 16 14 12
0.90 45 30 23 32 15 13 11 10 9
1.00 36 24 18 25 12 10 9 8 7
1.10 29 20 15 21 10 8 7 7 6
1.20 25 17 13 18 8 7 6 6 5
1.30 22 15 11 15 7 6 5 5 4
1.40 19 13 10 14 6 6 5 4 4
1.50 17 12 9 12 6 5 4 4 3
1.60 16 10 8 11 5 4 4 3 3
1.63 15 10 8 11 5 4 4 3 3
1.70 14 10 7 10 5 4 4 3 3
1.80 13 9 7 9 4 4 3 3 3
1.90 12 8 6 9 4 4 3 3 2
2.00 11 8 6 8 4 3 3 3 2
2.10 11 7 5 8 4 3 3 2 2
2.20 10 7 5 7 3 3 3 2 2
2.30 9 6 5 7 3 3 2 2 2
2.40 9 6 4 6 3 3 2 2 2
2.50 9 6 4 6 3 2 2 2 2
2.60 8 5 4 6 3 2 2 2 2
2.70 8 5 4 5 3 2 2 2 2
2.73 8 5 4 5 3 2 2 2 2
Smax 84 56 42 34 28 24 21 19 17 Smax
SEPARACION S [cm]
bw [cm] f'c=560 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
7/18
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 170 114 85 68 57 49 43 38 34
0.70 170 114 85 68 57 49 43 38 34
0.80 165 110 82 44 55 47 41 37 33
0.90 120 80 60 32 40 34 30 27 24
1.00 95 63 47 25 32 27 24 21 19
1.10 78 52 39 21 26 22 19 17 16
1.20 66 44 33 18 22 19 17 15 13
1.30 58 38 29 15 19 16 14 13 12
1.40 51 34 26 14 17 15 13 11 10
1.50 46 31 23 12 15 13 11 10 9
1.60 42 28 21 11 14 12 10 9 8
1.63 40 27 20 11 13 12 10 9 8
1.70 38 25 19 10 13 11 9 8 8
1.80 35 23 18 9 12 10 9 8 7
1.90 32 22 16 9 11 9 8 7 6
2.00 30 20 15 8 10 9 8 7 6
2.10 28 19 14 8 9 8 7 6 6
2.20 27 18 13 7 9 8 7 6 5
2.30 25 17 13 7 8 7 6 6 5
2.40 24 16 12 6 8 7 6 5 5
2.50 23 15 11 6 8 6 6 5 5
2.60 21 14 11 6 7 6 5 5 4
2.70 20 14 10 5 7 6 5 5 4
2.73 20 13 10 5 7 6 5 4 4
Smax 170 114 85 68 57 49 43 38 34 Smax
SEPARACION S [cm]
bw [cm] f'c=180 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 170 114 85 68 57 49 43 38 34
0.70 170 114 85 68 57 49 43 38 34
0.80 152 102 76 44 51 44 38 34 30
0.90 111 74 56 32 37 32 28 25 22
1.00 88 58 44 25 29 25 22 19 18
1.10 72 48 36 21 24 21 18 16 14
1.20 61 41 31 18 20 18 15 14 12
1.30 53 36 27 15 18 15 13 12 11
1.40 47 32 24 14 16 14 12 11 9
1.50 42 28 21 12 14 12 11 9 8
1.60 38 26 19 11 13 11 10 9 8
1.63 37 25 19 11 12 11 9 8 7
1.70 35 23 18 10 12 10 9 8 7
1.80 32 22 16 9 11 9 8 7 6
1.90 30 20 15 9 10 9 8 7 6
2.00 28 19 14 8 9 8 7 6 6
2.10 26 17 13 8 9 7 7 6 5
2.20 25 16 12 7 8 7 6 5 5
2.30 23 16 12 7 8 7 6 5 5
2.40 22 15 11 6 7 6 6 5 4
2.50 21 14 10 6 7 6 5 5 4
2.60 20 13 10 6 7 6 5 4 4
2.70 19 13 9 5 6 5 5 4 4
2.73 19 12 9 5 6 5 5 4 4
Smax 170 114 85 68 57 49 43 38 34 Smax
SEPARACION S [cm]
bw [cm] f'c=210 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
8/18
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 170 114 85 68 57 49 43 38 34
0.70 170 114 85 68 57 49 43 38 34
0.80 140 93 70 44 47 40 35 31 28
0.90 102 68 51 32 34 29 25 23 20
1.00 80 54 40 25 27 23 20 18 16
1.10 66 44 33 21 22 19 17 15 13
1.20 56 38 28 18 19 16 14 13 11
1.30 49 33 24 15 16 14 12 11 10
1.40 43 29 22 14 14 12 11 10 9
1.50 39 26 19 12 13 11 10 9 8
1.60 35 24 18 11 12 10 9 8 7
1.63 34 23 17 11 11 10 9 8 7
1.70 32 21 16 10 11 9 8 7 6
1.80 30 20 15 9 10 8 7 7 6
1.90 28 18 14 9 9 8 7 6 6
2.00 26 17 13 8 9 7 6 6 5
2.10 24 16 12 8 8 7 6 5 5
2.20 23 15 11 7 8 6 6 5 5
2.30 21 14 11 7 7 6 5 5 4
2.40 20 13 10 6 7 6 5 4 4
2.50 19 13 10 6 6 5 5 4 4
2.60 18 12 9 6 6 5 5 4 4
2.70 17 12 9 5 6 5 4 4 3
2.73 17 11 9 5 6 5 4 4 3
Smax 170 114 85 68 57 49 43 38 34 Smax
SEPARACION S [cm]
bw [cm] f'c=250 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 170 114 85 68 57 49 43 38 34
0.70 170 114 85 68 57 49 43 38 34
0.80 132 88 66 44 44 38 33 29 26
0.90 96 64 48 32 32 28 24 21 19
1.00 76 51 38 25 25 22 19 17 15
1.10 63 42 31 21 21 18 16 14 13
1.20 53 35 27 18 18 15 13 12 11
1.30 46 31 23 15 15 13 12 10 9
1.40 41 27 20 14 14 12 10 9 8
1.50 37 24 18 12 12 10 9 8 7
1.60 33 22 17 11 11 10 8 7 7
1.63 32 22 16 11 11 9 8 7 6
1.70 30 20 15 10 10 9 8 7 6
1.80 28 19 14 9 9 8 7 6 6
1.90 26 17 13 9 9 7 7 6 5
2.00 24 16 12 8 8 7 6 5 5
2.10 23 15 11 8 8 6 6 5 5
2.20 21 14 11 7 7 6 5 5 4
2.30 20 13 10 7 7 6 5 4 4
2.40 19 13 10 6 6 5 5 4 4
2.50 18 12 9 6 6 5 5 4 4
2.60 17 11 9 6 6 5 4 4 3
2.70 16 11 8 5 5 5 4 4 3
2.73 16 11 8 5 5 5 4 4 3
Smax 170 114 85 68 57 49 43 38 34 Smax
SEPARACION S [cm]
bw [cm] f'c=280 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
9/18
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 159 106 80 64 53 46 40 35 32
0.70 159 106 80 64 53 46 40 35 32
0.80 118 79 59 44 39 34 30 26 24
0.90 86 57 43 32 29 25 22 19 17
1.00 68 45 34 25 23 19 17 15 14
1.10 56 37 28 21 19 16 14 12 11
1.20 48 32 24 18 16 14 12 11 10
1.30 41 28 21 15 14 12 10 9 8
1.40 37 24 18 14 12 10 9 8 7
1.50 33 22 16 12 11 9 8 7 7
1.60 30 20 15 11 10 9 7 7 6
1.63 29 19 14 11 10 8 7 6 6
1.70 27 18 14 10 9 8 7 6 5
1.80 25 17 13 9 8 7 6 6 5
1.90 23 16 12 9 8 7 6 5 5
2.00 22 14 11 8 7 6 5 5 4
2.10 20 14 10 8 7 6 5 5 4
2.20 19 13 10 7 6 5 5 4 4
2.30 18 12 9 7 6 5 5 4 4
2.40 17 11 9 6 6 5 4 4 3
2.50 16 11 8 6 5 5 4 4 3
2.60 15 10 8 6 5 4 4 3 3
2.70 15 10 7 5 5 4 4 3 3
2.73 14 10 7 5 5 4 4 3 3
Smax 159 106 80 64 53 46 40 35 32 Smax
SEPARACION S [cm]
bw [cm] f'c=350 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 146 97 73 58 49 42 36 32 29
0.70 146 97 73 58 49 42 36 32 29
0.80 108 72 54 44 36 31 27 24 22
0.90 79 52 39 32 26 22 20 17 16
1.00 62 41 31 25 21 18 15 14 12
1.10 51 34 26 21 17 15 13 11 10
1.20 43 29 22 18 14 12 11 10 9
1.30 38 25 19 15 13 11 9 8 8
1.40 33 22 17 14 11 10 8 7 7
1.50 30 20 15 12 10 9 8 7 6
1.60 27 18 14 11 9 8 7 6 5
1.63 26 18 13 11 9 8 7 6 5
1.70 25 17 12 10 8 7 6 6 5
1.80 23 15 11 9 8 7 6 5 5
1.90 21 14 11 9 7 6 5 5 4
2.00 20 13 10 8 7 6 5 4 4
2.10 19 12 9 8 6 5 5 4 4
2.20 17 12 9 7 6 5 4 4 3
2.30 16 11 8 7 5 5 4 4 3
2.40 16 10 8 6 5 4 4 3 3
2.50 15 10 7 6 5 4 4 3 3
2.60 14 9 7 6 5 4 4 3 3
2.70 13 9 7 5 4 4 3 3 3
2.73 13 9 7 5 4 4 3 3 3
Smax 146 97 73 58 49 42 36 32 29 Smax
SEPARACION S [cm]
bw [cm] f'c=420 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
10/18
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 135 90 67 54 45 38 34 30 27
0.70 135 90 67 54 45 38 34 30 27
0.80 100 67 50 44 33 29 25 22 20
0.90 73 49 36 32 24 21 18 16 15
1.00 57 38 29 25 19 16 14 13 11
1.10 47 32 24 21 16 14 12 11 9
1.20 40 27 20 18 13 11 10 9 8
1.30 35 23 17 15 12 10 9 8 7
1.40 31 21 15 14 10 9 8 7 6
1.50 28 19 14 12 9 8 7 6 6
1.60 25 17 13 11 8 7 6 6 5
1.63 24 16 12 11 8 7 6 5 5
1.70 23 15 12 10 8 7 6 5 5
1.80 21 14 11 9 7 6 5 5 4
1.90 20 13 10 9 7 6 5 4 4
2.00 18 12 9 8 6 5 5 4 4
2.10 17 11 9 8 6 5 4 4 3
2.20 16 11 8 7 5 5 4 4 3
2.30 15 10 8 7 5 4 4 3 3
2.40 14 10 7 6 5 4 4 3 3
2.50 14 9 7 6 5 4 3 3 3
2.60 13 9 7 6 4 4 3 3 3
2.70 12 8 6 5 4 4 3 3 2
2.73 12 8 6 5 4 3 3 3 2
Smax 135 90 67 54 45 38 34 30 27 Smax
SEPARACION S [cm]
bw [cm] f'c=490 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
3/8''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 126 84 63 50 42 36 32 28 25
0.70 126 84 63 50 42 36 32 28 25
0.80 93 62 47 44 31 27 23 21 19
0.90 68 45 34 32 23 19 17 15 14
1.00 54 36 27 25 18 15 13 12 11
1.10 44 29 22 21 15 13 11 10 9
1.20 38 25 19 18 13 11 9 8 8
1.30 33 22 16 15 11 9 8 7 7
1.40 29 19 14 14 10 8 7 6 6
1.50 26 17 13 12 9 7 6 6 5
1.60 24 16 12 11 8 7 6 5 5
1.63 23 15 11 11 8 7 6 5 5
1.70 22 14 11 10 7 6 5 5 4
1.80 20 13 10 9 7 6 5 4 4
1.90 18 12 9 9 6 5 5 4 4
2.00 17 11 9 8 6 5 4 4 3
2.10 16 11 8 8 5 5 4 4 3
2.20 15 10 8 7 5 4 4 3 3
2.30 14 9 7 7 5 4 4 3 3
2.40 13 9 7 6 4 4 3 3 3
2.50 13 9 6 6 4 4 3 3 3
2.60 12 8 6 6 4 3 3 3 2
2.70 12 8 6 5 4 3 3 3 2
2.73 11 8 6 5 4 3 3 3 2
Smax 126 84 63 50 42 36 32 28 25 Smax
SEPARACION S [cm]
bw [cm] f'c=560 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
11/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 305 203 152 122 102 87 76 68 61
0.70 305 203 152 122 102 87 76 68 61
0.80 294 196 147 79 98 84 74 65 59
0.90 215 143 107 57 72 61 54 48 43
1.00 169 113 85 45 56 48 42 38 34
1.10 139 93 70 37 46 40 35 31 28
1.20 119 79 59 32 40 34 30 26 24
1.30 103 69 52 28 34 30 26 23 21
1.40 91 61 46 24 30 26 23 20 18
1.50 82 55 41 22 27 23 20 18 16
1.60 74 50 37 20 25 21 19 17 15
1.63 72 48 36 19 24 21 18 16 14
1.70 68 45 34 18 23 19 17 15 14
1.80 63 42 31 17 21 18 16 14 13
1.90 58 39 29 15 19 17 15 13 12
2.00 54 36 27 14 18 15 14 12 11
2.10 51 34 25 14 17 14 13 11 10
2.20 48 32 24 13 16 14 12 11 10
2.30 45 30 22 12 15 13 11 10 9
2.40 43 28 21 11 14 12 11 9 9
2.50 40 27 20 11 13 12 10 9 8
2.60 38 26 19 10 13 11 10 9 8
2.70 37 24 18 10 12 10 9 8 7
2.73 36 24 18 10 12 10 9 8 7
Smax 305 203 152 122 102 87 76 68 61 Smax
SEPARACION S [cm]
bw [cm] f'c=180 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 305 203 152 122 102 87 76 68 61
0.70 305 203 152 122 102 87 76 68 61
0.80 273 182 136 79 91 78 68 61 55
0.90 199 133 99 57 66 57 50 44 40
1.00 157 104 78 45 52 45 39 35 31
1.10 129 86 65 37 43 37 32 29 26
1.20 110 73 55 32 37 31 27 24 22
1.30 96 64 48 28 32 27 24 21 19
1.40 85 56 42 24 28 24 21 19 17
1.50 76 51 38 22 25 22 19 17 15
1.60 69 46 34 20 23 20 17 15 14
1.63 67 45 33 19 22 19 17 15 13
1.70 63 42 31 18 21 18 16 14 13
1.80 58 39 29 17 19 17 14 13 12
1.90 54 36 27 15 18 15 13 12 11
2.00 50 33 25 14 17 14 13 11 10
2.10 47 31 23 14 16 13 12 10 9
2.20 44 29 22 13 15 13 11 10 9
2.30 42 28 21 12 14 12 10 9 8
2.40 39 26 20 11 13 11 10 9 8
2.50 37 25 19 11 12 11 9 8 7
2.60 36 24 18 10 12 10 9 8 7
2.70 34 23 17 10 11 10 8 8 7
2.73 33 22 17 10 11 10 8 7 7
Smax 305 203 152 122 102 87 76 68 61 Smax
SEPARACION S [cm]
bw [cm] f'c=210 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
12/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 305 203 152 122 102 87 76 68 61
0.70 305 203 152 122 102 87 76 68 61
0.80 250 167 125 79 83 71 62 56 50
0.90 182 122 91 57 61 52 46 41 36
1.00 144 96 72 45 48 41 36 32 29
1.10 118 79 59 37 39 34 30 26 24
1.20 101 67 50 32 34 29 25 22 20
1.30 88 58 44 28 29 25 22 19 18
1.40 78 52 39 24 26 22 19 17 16
1.50 70 46 35 22 23 20 17 15 14
1.60 63 42 32 20 21 18 16 14 13
1.63 61 41 31 19 20 18 15 14 12
1.70 58 38 29 18 19 16 14 13 12
1.80 53 35 27 17 18 15 13 12 11
1.90 49 33 25 15 16 14 12 11 10
2.00 46 31 23 14 15 13 11 10 9
2.10 43 29 21 14 14 12 11 10 9
2.20 40 27 20 13 13 12 10 9 8
2.30 38 25 19 12 13 11 10 8 8
2.40 36 24 18 11 12 10 9 8 7
2.50 34 23 17 11 11 10 9 8 7
2.60 33 22 16 10 11 9 8 7 7
2.70 31 21 16 10 10 9 8 7 6
2.73 31 20 15 10 10 9 8 7 6
Smax 305 203 152 122 102 87 76 68 61 Smax
SEPARACION S [cm]
bw [cm] f'c=250 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 305 203 152 122 102 87 76 68 61
0.70 305 203 152 122 102 87 76 68 61
0.80 236 157 118 79 79 67 59 52 47
0.90 172 115 86 57 57 49 43 38 34
1.00 136 90 68 45 45 39 34 30 27
1.10 112 75 56 37 37 32 28 25 22
1.20 95 63 48 32 32 27 24 21 19
1.30 83 55 41 28 28 24 21 18 17
1.40 73 49 37 24 24 21 18 16 15
1.50 66 44 33 22 22 19 16 15 13
1.60 60 40 30 20 20 17 15 13 12
1.63 58 39 29 19 19 17 14 13 12
1.70 54 36 27 18 18 16 14 12 11
1.80 50 33 25 17 17 14 13 11 10
1.90 47 31 23 15 16 13 12 10 9
2.00 43 29 22 14 14 12 11 10 9
2.10 41 27 20 14 14 12 10 9 8
2.20 38 25 19 13 13 11 10 8 8
2.30 36 24 18 12 12 10 9 8 7
2.40 34 23 17 11 11 10 9 8 7
2.50 32 22 16 11 11 9 8 7 6
2.60 31 21 15 10 10 9 8 7 6
2.70 29 20 15 10 10 8 7 7 6
2.73 29 19 14 10 10 8 7 6 6
Smax 305 203 152 122 102 87 76 68 61 Smax
SEPARACION S [cm]
bw [cm] f'c=280 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
13/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 285 190 143 114 95 81 71 63 57
0.70 285 190 143 114 95 81 71 63 57
0.80 211 141 106 79 70 60 53 47 42
0.90 154 103 77 57 51 44 39 34 31
1.00 121 81 61 45 40 35 30 27 24
1.10 100 67 50 37 33 29 25 22 20
1.20 85 57 43 32 28 24 21 19 17
1.30 74 49 37 28 25 21 19 16 15
1.40 66 44 33 24 22 19 16 15 13
1.50 59 39 29 22 20 17 15 13 12
1.60 53 36 27 20 18 15 13 12 11
1.63 52 35 26 19 17 15 13 12 10
1.70 49 32 24 18 16 14 12 11 10
1.80 45 30 22 17 15 13 11 10 9
1.90 42 28 21 15 14 12 10 9 8
2.00 39 26 19 14 13 11 10 9 8
2.10 36 24 18 14 12 10 9 8 7
2.20 34 23 17 13 11 10 9 8 7
2.30 32 21 16 12 11 9 8 7 6
2.40 30 20 15 11 10 9 8 7 6
2.50 29 19 14 11 10 8 7 6 6
2.60 28 18 14 10 9 8 7 6 6
2.70 26 18 13 10 9 8 7 6 5
2.73 26 17 13 10 9 7 6 6 5
Smax 285 190 143 114 95 81 71 63 57 Smax
SEPARACION S [cm]
bw [cm] f'c=350 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 260 174 130 104 87 74 65 58 52
0.70 260 174 130 104 87 74 65 58 52
0.80 193 129 96 79 64 55 48 43 39
0.90 141 94 70 57 47 40 35 31 28
1.00 111 74 55 45 37 32 28 25 22
1.10 91 61 46 37 30 26 23 20 18
1.20 78 52 39 32 26 22 19 17 16
1.30 68 45 34 28 23 19 17 15 14
1.40 60 40 30 24 20 17 15 13 12
1.50 54 36 27 22 18 15 13 12 11
1.60 49 32 24 20 16 14 12 11 10
1.63 47 32 24 19 16 14 12 11 9
1.70 44 30 22 18 15 13 11 10 9
1.80 41 27 20 17 14 12 10 9 8
1.90 38 25 19 15 13 11 9 8 8
2.00 35 24 18 14 12 10 9 8 7
2.10 33 22 17 14 11 9 8 7 7
2.20 31 21 16 13 10 9 8 7 6
2.30 29 20 15 12 10 8 7 7 6
2.40 28 19 14 11 9 8 7 6 6
2.50 26 18 13 11 9 8 7 6 5
2.60 25 17 13 10 8 7 6 6 5
2.70 24 16 12 10 8 7 6 5 5
2.73 24 16 12 10 8 7 6 5 5
Smax 260 174 130 104 87 74 65 58 52 Smax
SEPARACION S [cm]
bw [cm] f'c=420 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
14/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 241 161 120 96 80 69 60 54 48
0.70 241 161 120 96 80 69 60 54 48
0.80 178 119 89 79 59 51 45 40 36
0.90 130 87 65 57 43 37 33 29 26
1.00 103 68 51 45 34 29 26 23 21
1.10 85 56 42 37 28 24 21 19 17
1.20 72 48 36 32 24 21 18 16 14
1.30 63 42 31 28 21 18 16 14 13
1.40 55 37 28 24 18 16 14 12 11
1.50 50 33 25 22 17 14 12 11 10
1.60 45 30 23 20 15 13 11 10 9
1.63 44 29 22 19 15 13 11 10 9
1.70 41 27 21 18 14 12 10 9 8
1.80 38 25 19 17 13 11 9 8 8
1.90 35 23 18 15 12 10 9 8 7
2.00 33 22 16 14 11 9 8 7 7
2.10 31 20 15 14 10 9 8 7 6
2.20 29 19 14 13 10 8 7 6 6
2.30 27 18 14 12 9 8 7 6 5
2.40 26 17 13 11 9 7 6 6 5
2.50 24 16 12 11 8 7 6 5 5
2.60 23 16 12 10 8 7 6 5 5
2.70 22 15 11 10 7 6 6 5 4
2.73 22 15 11 10 7 6 5 5 4
Smax 241 161 120 96 80 69 60 54 48 Smax
SEPARACION S [cm]
bw [cm] f'c=490 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 225 150 113 90 75 64 56 50 45
0.70 225 150 113 90 75 64 56 50 45
0.80 167 111 83 79 56 48 42 37 33
0.90 122 81 61 57 41 35 30 27 24
1.00 96 64 48 45 32 27 24 21 19
1.10 79 53 40 37 26 23 20 18 16
1.20 67 45 34 32 22 19 17 15 13
1.30 59 39 29 28 20 17 15 13 12
1.40 52 35 26 24 17 15 13 12 10
1.50 46 31 23 22 15 13 12 10 9
1.60 42 28 21 20 14 12 11 9 8
1.63 41 27 20 19 14 12 10 9 8
1.70 39 26 19 18 13 11 10 9 8
1.80 35 24 18 17 12 10 9 8 7
1.90 33 22 16 15 11 9 8 7 7
2.00 31 20 15 14 10 9 8 7 6
2.10 29 19 14 14 10 8 7 6 6
2.20 27 18 13 13 9 8 7 6 5
2.30 25 17 13 12 8 7 6 6 5
2.40 24 16 12 11 8 7 6 5 5
2.50 23 15 11 11 8 7 6 5 5
2.60 22 15 11 10 7 6 5 5 4
2.70 21 14 10 10 7 6 5 5 4
2.73 20 14 10 10 7 6 5 5 4
Smax 225 150 113 90 75 64 56 50 45 Smax
SEPARACION S [cm]
bw [cm] f'c=560 kg/cm2 fy=4200 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
15/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 203 135 102 81 68 58 51 45 41
0.70 203 135 102 81 68 58 51 45 41
0.80 196 131 98 79 65 56 49 44 39
0.90 143 96 72 57 48 41 36 32 29
1.00 113 75 56 45 38 32 28 25 23
1.10 93 62 46 37 31 27 23 21 19
1.20 79 53 40 32 26 23 20 18 16
1.30 69 46 34 28 23 20 17 15 14
1.40 61 41 30 24 20 17 15 14 12
1.50 55 36 27 22 18 16 14 12 11
1.60 50 33 25 20 17 14 12 11 10
1.63 48 32 24 19 16 14 12 11 10
1.70 45 30 23 18 15 13 11 10 9
1.80 42 28 21 17 14 12 10 9 8
1.90 39 26 19 15 13 11 10 9 8
2.00 36 24 18 14 12 10 9 8 7
2.10 34 23 17 14 11 10 8 8 7
2.20 32 21 16 13 11 9 8 7 6
2.30 30 20 15 12 10 9 7 7 6
2.40 28 19 14 11 9 8 7 6 6
2.50 27 18 13 11 9 8 7 6 5
2.60 26 17 13 10 9 7 6 6 5
2.70 24 16 12 10 8 7 6 5 5
2.73 24 16 12 10 8 7 6 5 5
Smax 203 135 102 81 68 58 51 45 41 Smax
SEPARACION S [cm]
bw [cm] f'c=180 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 203 135 102 81 68 58 51 45 41
0.70 203 135 102 81 68 58 51 45 41
0.80 182 121 91 79 61 52 45 40 36
0.90 133 88 66 57 44 38 33 29 27
1.00 104 70 52 45 35 30 26 23 21
1.10 86 57 43 37 29 25 22 19 17
1.20 73 49 37 32 24 21 18 16 15
1.30 64 42 32 28 21 18 16 14 13
1.40 56 38 28 24 19 16 14 13 11
1.50 51 34 25 22 17 14 13 11 10
1.60 46 31 23 20 15 13 11 10 9
1.63 45 30 22 19 15 13 11 10 9
1.70 42 28 21 18 14 12 10 9 8
1.80 39 26 19 17 13 11 10 9 8
1.90 36 24 18 15 12 10 9 8 7
2.00 33 22 17 14 11 10 8 7 7
2.10 31 21 16 14 10 9 8 7 6
2.20 29 20 15 13 10 8 7 7 6
2.30 28 18 14 12 9 8 7 6 6
2.40 26 17 13 11 9 7 7 6 5
2.50 25 17 12 11 8 7 6 6 5
2.60 24 16 12 10 8 7 6 5 5
2.70 23 15 11 10 8 6 6 5 5
2.73 22 15 11 10 7 6 6 5 4
Smax 203 135 102 81 68 58 51 45 41 Smax
SEPARACION S [cm]
bw [cm] f'c=210 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
16/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 203 135 102 81 68 58 51 45 41
0.70 203 135 102 81 68 58 51 45 41
0.80 167 111 83 79 56 48 42 37 33
0.90 122 81 61 57 41 35 30 27 24
1.00 96 64 48 45 32 27 24 21 19
1.10 79 53 39 37 26 23 20 18 16
1.20 67 45 34 32 22 19 17 15 13
1.30 58 39 29 28 19 17 15 13 12
1.40 52 34 26 24 17 15 13 11 10
1.50 46 31 23 22 15 13 12 10 9
1.60 42 28 21 20 14 12 11 9 8
1.63 41 27 20 19 14 12 10 9 8
1.70 38 26 19 18 13 11 10 9 8
1.80 35 24 18 17 12 10 9 8 7
1.90 33 22 16 15 11 9 8 7 7
2.00 31 20 15 14 10 9 8 7 6
2.10 29 19 14 14 10 8 7 6 6
2.20 27 18 13 13 9 8 7 6 5
2.30 25 17 13 12 8 7 6 6 5
2.40 24 16 12 11 8 7 6 5 5
2.50 23 15 11 11 8 7 6 5 5
2.60 22 14 11 10 7 6 5 5 4
2.70 21 14 10 10 7 6 5 5 4
2.73 20 14 10 10 7 6 5 5 4
Smax 203 135 102 81 68 58 51 45 41 Smax
SEPARACION S [cm]
bw [cm] f'c=250 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 203 135 102 81 68 58 51 45 41
0.70 203 135 102 81 68 58 51 45 41
0.80 157 105 79 79 52 45 39 35 31
0.90 115 77 57 57 38 33 29 26 23
1.00 90 60 45 45 30 26 23 20 18
1.10 75 50 37 37 25 21 19 17 15
1.20 63 42 32 32 21 18 16 14 13
1.30 55 37 28 28 18 16 14 12 11
1.40 49 33 24 24 16 14 12 11 10
1.50 44 29 22 22 15 13 11 10 9
1.60 40 26 20 20 13 11 10 9 8
1.63 39 26 19 19 13 11 10 9 8
1.70 36 24 18 18 12 10 9 8 7
1.80 33 22 17 17 11 10 8 7 7
1.90 31 21 16 15 10 9 8 7 6
2.00 29 19 14 14 10 8 7 6 6
2.10 27 18 14 14 9 8 7 6 5
2.20 25 17 13 13 8 7 6 6 5
2.30 24 16 12 12 8 7 6 5 5
2.40 23 15 11 11 8 6 6 5 5
2.50 22 14 11 11 7 6 5 5 4
2.60 21 14 10 10 7 6 5 5 4
2.70 20 13 10 10 7 6 5 4 4
2.73 19 13 10 10 6 6 5 4 4
Smax 203 135 102 81 68 58 51 45 41 Smax
SEPARACION S [cm]
bw [cm] f'c=280 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
17/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 190 127 95 76 63 54 48 42 38
0.70 190 127 95 76 63 54 48 42 38
0.80 141 94 70 76 47 40 35 31 28
0.90 103 68 51 57 34 29 26 23 21
1.00 81 54 40 45 27 23 20 18 16
1.10 67 44 33 37 22 19 17 15 13
1.20 57 38 28 32 19 16 14 13 11
1.30 49 33 25 28 16 14 12 11 10
1.40 44 29 22 24 15 12 11 10 9
1.50 39 26 20 22 13 11 10 9 8
1.60 36 24 18 20 12 10 9 8 7
1.63 35 23 17 19 12 10 9 8 7
1.70 32 22 16 18 11 9 8 7 6
1.80 30 20 15 17 10 9 7 7 6
1.90 28 18 14 15 9 8 7 6 6
2.00 26 17 13 14 9 7 6 6 5
2.10 24 16 12 14 8 7 6 5 5
2.20 23 15 11 13 8 7 6 5 5
2.30 21 14 11 12 7 6 5 5 4
2.40 20 14 10 11 7 6 5 5 4
2.50 19 13 10 11 6 6 5 4 4
2.60 18 12 9 10 6 5 5 4 4
2.70 18 12 9 10 6 5 4 4 4
2.73 17 12 9 10 6 5 4 4 3
Smax 190 127 95 76 63 54 48 42 38 Smax
SEPARACION S [cm]
bw [cm] f'c=350 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 174 116 87 69 58 50 43 39 35
0.70 174 116 87 69 58 50 43 39 35
0.80 129 86 64 69 43 37 32 29 26
0.90 94 63 47 57 31 27 23 21 19
1.00 74 49 37 45 25 21 18 16 15
1.10 61 41 30 37 20 17 15 14 12
1.20 52 35 26 32 17 15 13 12 10
1.30 45 30 23 28 15 13 11 10 9
1.40 40 27 20 24 13 11 10 9 8
1.50 36 24 18 22 12 10 9 8 7
1.60 32 22 16 20 11 9 8 7 6
1.63 32 21 16 19 11 9 8 7 6
1.70 30 20 15 18 10 8 7 7 6
1.80 27 18 14 17 9 8 7 6 5
1.90 25 17 13 15 8 7 6 6 5
2.00 24 16 12 14 8 7 6 5 5
2.10 22 15 11 14 7 6 6 5 4
2.20 21 14 10 13 7 6 5 5 4
2.30 20 13 10 12 7 6 5 4 4
2.40 19 12 9 11 6 5 5 4 4
2.50 18 12 9 11 6 5 4 4 4
2.60 17 11 8 10 6 5 4 4 3
2.70 16 11 8 10 5 5 4 4 3
2.73 16 11 8 10 5 5 4 4 3
Smax 174 116 87 69 58 50 43 39 35 Smax
SEPARACION S [cm]
bw [cm] f'c=420 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
7/25/2019 ayudas de diseno.pdf
18/18
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 161 107 80 64 54 46 40 36 32
0.70 161 107 80 64 54 46 40 36 32
0.80 119 79 59 64 40 34 30 26 24
0.90 87 58 43 57 29 25 22 19 17
1.00 68 46 34 45 23 20 17 15 14
1.10 56 38 28 37 19 16 14 13 11
1.20 48 32 24 32 16 14 12 11 10
1.30 42 28 21 28 14 12 10 9 8
1.40 37 25 18 24 12 11 9 8 7
1.50 33 22 17 22 11 9 8 7 7
1.60 30 20 15 20 10 9 8 7 6
1.63 29 19 15 19 10 8 7 6 6
1.70 27 18 14 18 9 8 7 6 5
1.80 25 17 13 17 8 7 6 6 5
1.90 23 16 12 15 8 7 6 5 5
2.00 22 15 11 14 7 6 5 5 4
2.10 20 14 10 14 7 6 5 5 4
2.20 19 13 10 13 6 5 5 4 4
2.30 18 12 9 12 6 5 5 4 4
2.40 17 11 9 11 6 5 4 4 3
2.50 16 11 8 11 5 5 4 4 3
2.60 16 10 8 10 5 4 4 3 3
2.70 15 10 7 10 5 4 4 3 3
2.73 15 10 7 10 5 4 4 3 3
Smax 161 107 80 64 54 46 40 36 32 Smax
SEPARACION S [cm]
bw [cm] f'c=490 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm
1/2''
10 15 20 25 30 35 40 45 50 Smax
0.50
0.60 150 100 75 60 50 43 38 33 30
0.70 150 100 75 60 50 43 38 33 30
0.80 111 74 56 60 37 32 28 25 22
0.90 81 54 41 57 27 23 20 18 16
1.00 64 43 32 45 21 18 16 14 13
1.10 53 35 26 37 18 15 13 12 11
1.20 45 30 22 32 15 13 11 10 9
1.30 39 26 20 28 13 11 10 9 8
1.40 35 23 17 24 12 10 9 8 7
1.50 31 21 15 22 10 9 8 7 6
1.60 28 19 14 20 9 8 7 6 6
1.63 27 18 14 19 9 8 7 6 5
1.70 26 17 13 18 9 7 6 6 5
1.80 24 16 12 17 8 7 6 5 5
1.90 22 15 11 15 7 6 5 5 4
2.00 20 14 10 14 7 6 5 5 4
2.10 19 13 10 14 6 5 5 4 4
2.20 18 12 9 13 6 5 4 4 4
2.30 17 11 8 12 6 5 4 4 3
2.40 16 11 8 11 5 5 4 4 3
2.50 15 10 8 11 5 4 4 3 3
2.60 15 10 7 10 5 4 4 3 3
2.70 14 9 7 10 5 4 3 3 3
2.73 14 9 7 10 5 4 3 3 3
Smax 150 100 75 60 50 43 38 33 30 Smax
SEPARACION S [cm]
bw [cm] f'c=560 kg/cm2 fy=2800 kg/cm2
d/4, 30 cm
Vu/f'cbwd
d/2, 60 cm