fc' = 14.1 MPa fc = 6.345 MPa Es = 200000 MPafy = 240 MPa fs = 120 MPa Ec = 14620 MPa

ρMínimo = 0.00391 φ = 0.90 m = 20.025031ρbalanceado = 0.04994 ρMáx = 0.02996

K (kN/m2)213.8373423.3492628.5357811.7860829.39671025.93241218.14271406.02751589.58701768.82101943.72972114.31292280.57072442.50312600.11012753.39172902.34793046.97873187.28413323.26413454.91863582.24783705.25163823.92993938.28294048.31044154.01254255.38924352.44064445.16654530.3300

0.01100.01000.00900.00800.0070

0.02000.01900.01800.01700.0160

0.01400.01300.0120

0.0351183.25030.96080.07830.003911

0.6000 0.7000 85.1635 0.01490.029963

0.5006 0.7497 110.0275 0.01570.5207 0.7397 105.7021 0.01550.0260

0.0250

0.4606 0.7697 118.6783 0.01620.4806 0.7597 114.3529 0.01590.0240

0.0230

0.5807 0.7096 92.7259 0.0150

0.5407 0.7297 101.3767 0.01530.5607 0.7196 97.0513 0.01520.0280

0.0270

0.0173

0.01810.0186

0.40050.3805

0.34040.3204

0.2603

0.79970.8098

0.82980.8398

0.8698

0.02200.0210

0.3004 0.8498 0.0191

0.3605 0.8198 0.0177

153.28160.0150

0.4205 0.7897 0.01670.4406 0.7797 0.0164123.0038

127.3292131.6546135.9800140.3054144.6308148.9562

0.0170

0.02090.87980.2403

0.2804 0.8598 0.0196157.6070161.9324166.2578

0.0202

0.0217174.90860.2003 0.8999 0.0227179.23400.1802 0.9099 0.0238

0.0251

0.0290

0.03120.02870.0267

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 2000 p.s.i. = 14,1 Mpa)

187.8849

0.04860.0684

k2

0.0399

0.034717.6107196.5357192.2103

0.94990.93990.92990.1402

j0.9900

170.58320.2203 0.8899

ΔK

209.5119205.1865

a/d0.02000.0401

183.55940.1602 0.9199

0.00200.0010

ρ

0.00600.00500.0040

0.00300.98000.9700

0.95990.08010.10010.1202

0.0601

fc' = 14.1 MPa fc = 6.345 MPa Es = 200000 MPafy = 420 MPa fs = 210 MPa Ec = 14620 MPa

ρMínimo = 0.00224 φ = 0.90 m = 35.0438048ρbalanceado = 0.02854 ρMáx = 0.02079

K (kN/m2)371.3767729.5069811.78601074.39051406.02751724.41802029.56202321.45932600.11012865.51443117.67213356.58323582.24783794.66583993.83734179.76224352.44064511.87234658.05764790.99624910.68844995.91060.020790 0.7286 0.6357 85.2222 0.0141

0.0200 0.7009 0.6496 119.6921 0.0143

0.0180 0.6308 0.6846 146.1852 0.01470.0190 0.6658 0.6671 132.9387 0.0144

0.0160 0.5607 0.7196 172.6783 0.01520.0170 0.5957 0.7021 159.4318 0.0149

0.0140 0.4906 0.7547 199.1715 0.01580.0150 0.5257 0.7372 185.9249 0.0155

0.0120 0.4205 0.7897 225.6646 0.01670.0130 0.4556 0.7722 212.4180 0.0162

0.0100 0.3504 0.8248 252.1577 0.01790.0110 0.3855 0.8073 238.9111 0.0173

0.0080 0.2804 0.8598 278.6508 0.01960.0090 0.3154 0.8423 265.4043 0.0187

0.0060 0.2103 0.8949 305.1439 0.02220.0070 0.2453 0.8773 291.8974 0.0208

0.0040 0.1402 0.9299 331.6370 0.02670.0050 0.1752 0.9124 318.3905 0.0241

0.0020 0.0701 0.9650 358.1302 0.0370

0.0030 0.1051 0.9474 262.6045 0.03050.002235 0.0783 0.9608 82.2791 0.0351

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 2000 p.s.i. = 14,1 Mpa)ρ a/d j ΔK k2

0.0010 0.0350 0.9825 0.0519

fc' = 17.6 MPa fc = 7.92 MPa Es = 200000 MPafy = 240 MPa fs = 120 MPa Ec = 16380 MPa

ρMínimo = 0.00437 φ = 0.90 m = 16.042781ρbalanceado = 0.06233 ρMáx = 0.03740

K (kN/m2)214.2674425.0695632.4064836.2781910.83971036.68451233.62571427.10161617.11231803.65781986.73802166.35292342.50272515.18722684.40642850.16043012.44923171.27273326.63103478.52413626.95193771.91443913.41184051.44394186.01074317.11234444.74874568.91984689.62574806.86634920.64175030.95195137.79685241.17655341.09095437.54015530.52415620.04285654.8800

0.0370 0.5936 0.7032 89.5187 0.0133

0.5615 0.7193 96.4492 0.01360.0360 0.5775 0.7112 92.9840 0.01340.0350

0.5294 0.7353 103.3797 0.01380.0340 0.5455 0.7273 99.9144 0.01370.0330

0.4973 0.7513 110.3102 0.01410.0320 0.5134 0.7433 106.8449 0.01400.0310

0.4652 0.7674 117.2406 0.01440.0300 0.4813 0.7594 113.7754 0.01430.0290

0.4332 0.7834 124.1711 0.01480.0280 0.4492 0.7754 120.7059 0.01460.0270

0.4011 0.7995 131.1016 0.01520.0260 0.4171 0.7914 127.6364 0.01500.0250

0.3690 0.8155 138.0321 0.01570.0240 0.3850 0.8075 134.5668 0.01550.0230

0.3369 0.8316 144.9626 0.01630.0220 0.3529 0.8235 141.4973 0.01600.0210

0.3048 0.8476 151.8930 0.01700.0200 0.3209 0.8396 148.4278 0.01660.0190

0.0150

0.2727 0.8636 158.8235 0.01780.0180 0.2888 0.8556 155.3583 0.01730.0170

0.01200.01100.0100

0.02150.1925 0.9037 176.1497 0.02070.1765 0.9118 179.61500.1604

0.0133

0.2086 0.8957 172.6845 0.0199

0.6000 0.7000 34.83720.037400

0.0193169.21930.88770.22460.01400.0130

0.2406 0.8797 165.7540 0.01870.0160 0.2567 0.8717 162.2888 0.0182

0.9198 183.0802 0.02240.1444 0.9278 186.54550.0090

193.4759 0.02650.1283 0.9358 190.0107 0.02490.1123 0.9439

0.00800.0070

0.0235

0.00300.0020

0.0802 0.9599 125.8448 0.03110.00500.0963 0.9519 196.9412 0.02850.0060

0.033174.56170.96490.07010.004370

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 2500 p.s.i. = 17,6 Mpa)a/d j ΔK k2ρ

0.0642 0.9679 203.8717 0.03460.0040

0.0160 0.9920 0.06830.0010

0.0481 0.9759 207.3369 0.03980.0321 0.9840 210.8021 0.0485

fc' = 17.6 MPa fc = 7.92 MPa Es = 200000 MPafy = 420 MPa fs = 210 MPa Ec = 16380 MPa

ρMínimo = 0.00250 φ = 0.90 m = 28.074866ρbalanceado = 0.03562 ρMáx = 0.02595

K (kN/m2)372.6939734.7754910.83971086.24471427.10161757.34632076.97862385.99872684.40642972.20193249.38503515.95593771.91444017.26074251.99474476.11634689.62574892.52275084.80755266.47995437.54015597.98805747.82355887.04686015.65786133.65646236.03020.025951 0.7286 0.6357 102.3738 0.0127

0.0240 0.6738 0.6631 128.6110 0.01290.0250 0.7019 0.6491 117.9987 0.0128

0.0220 0.6176 0.6912 149.8356 0.01320.0230 0.6457 0.6771 139.2233 0.0130

0.0200 0.5615 0.7193 171.0602 0.01360.0210 0.5896 0.7052 160.4479 0.0134

0.0180 0.5053 0.7473 192.2848 0.01400.0190 0.5334 0.7333 181.6725 0.0138

0.0160 0.4492 0.7754 213.5094 0.01460.0170 0.4773 0.7614 202.8971 0.0143

0.0140 0.3930 0.8035 234.7340 0.01530.0150 0.4211 0.7894 224.1217 0.0149

0.0120 0.3369 0.8316 255.9586 0.01630.0130 0.3650 0.8175 245.3463 0.0158

0.0100 0.2807 0.8596 277.1832 0.01750.0110 0.3088 0.8456 266.5709 0.0169

0.0080 0.2246 0.8877 298.4078 0.01930.0090 0.2527 0.8737 287.7955 0.0183

0.0060 0.1684 0.9158 319.6324 0.02190.0070 0.1965 0.9017 309.0201 0.0205

0.0050 0.1404 0.9298 330.2447 0.0239

0.0030 0.0842 0.9579 175.4049 0.03030.0040 0.1123 0.9439 340.8570 0.0265

0.0020 0.0561 0.9719 362.0816 0.03690.002497 0.0701 0.9649 176.0643 0.0331

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 2500 p.s.i. = 17,6 Mpa)ρ a/d j ΔK k2

0.0010 0.0281 0.9860 0.0518

fc' = 21.1 MPa fc = 9.495 MPa Es = 200000 MPafy = 240 MPa fs = 120 MPa Ec = 17900 MPa

ρMínimo = 0.00478 φ = 0.90 m = 13.381656ρbalanceado = 0.07473 ρMáx = 0.04484

K (kN/m2)214.5548426.2191634.9930840.87651000.44331043.86951243.97211441.18431635.50601826.93732015.47812201.12852383.88852563.75802740.73712914.82583086.02403254.33183419.74913582.27603741.91253898.65854052.51414203.47924351.55394496.73824639.03214778.43554914.94845048.57105179.30305307.14475432.09595554.15675673.32705789.60695902.99646013.49546121.10406225.82216327.64986426.58716522.63406615.79046706.05636779.4300

0.5620 0.7190 96.0468 0.0124

0.6000 0.7000 73.3737 0.0121

0.0430 0.5754 0.7123 93.1564 0.01230.0440 0.5888 0.7056 90.2660 0.0122

0.5353 0.7324 101.8277 0.01260.0410 0.5486 0.7257 98.9373 0.0125

0.5085 0.7457 107.6086 0.01280.0390 0.5219 0.7391 104.7181 0.0127

0.4817 0.7591 113.3895 0.01300.0370 0.4951 0.7524 110.4990 0.0129

0.4550 0.7725 119.1703 0.01330.0350 0.4684 0.7658 116.2799 0.0131

0.4282 0.7859 124.9512 0.01360.0330 0.4416 0.7792 122.0608 0.0134

0.4014 0.7993 130.7321 0.01390.0310 0.4148 0.7926 127.8417 0.0137

0.3747 0.8127 136.5130 0.01430.0290 0.3881 0.8060 133.6225 0.0141

0.3479 0.8260 142.2938 0.01470.0270 0.3613 0.8193 139.4034 0.0145

0.3212 0.8394 148.0747 0.01520.0250 0.3345 0.8327 145.1843 0.0149

0.2944 0.8528 153.8556 0.01570.0230 0.3078 0.8461 150.9652 0.0154

0.2676 0.8662 159.6365 0.01630.0210 0.2810 0.8595 156.7460 0.0160

0.01000.00900.00800.00700.00600.0050

0.9680

0.0167162.52690.87290.25430.0190

0.044838

0.01800.01700.01600.01500.01400.01300.01200.0110

0.0200

0.0220

0.0240

0.0260

0.0280

0.0300

0.0320

0.0340

0.0360

0.0380

0.0400

0.0420

0.1873 0.9063 176.9791 0.01910.2007 174.0887

171.1982168.3078165.4173

0.01850.01800.01750.0171

0.21410.22750.2409

0.89960.89290.88630.8796

0.1606 0.9197 182.7600 0.02050.1740 0.9130 179.8695 0.0197

0.1338 0.9331 188.5408 0.02230.1472 0.9264 185.6504 0.0213

0.1204 0.9398 191.4313 0.0234

0.0803 0.9599 200.1026 0.02840.0937 0.9532 197.2122 0.0263

0.0669 0.9665 43.4262 0.03100.0316159.56680.0640

0.1071 0.9465 194.3217 0.0247

0.0047850.0040

0.0268 0.9866 211.6643 0.04840.0401 0.9799 208.7739 0.03970.0030

0.0020

0.0535 0.9732 205.8835 0.0345

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 3000 p.s.i. = 21,1 Mpa)a/d j ΔK k2

0.0134 0.9933 0.0683ρ

0.0010

fc' = 21.1 MPa fc = 9.495 MPa Es = 200000 MPafy = 420 MPa fs = 210 MPa Ec = 17900 MPa

ρMínimo = 0.00273 φ = 0.90 m = 23.417898ρbalanceado = 0.04270 ρMáx = 0.03111

K (kN/m2)373.5740738.2961

1000.44331094.16621441.18431779.35042108.66462429.12682740.73713043.49543337.40173622.45613898.65854166.00894424.50744674.15394914.94845146.89105369.98165584.22025789.60695986.14166173.82446352.65516522.63406683.76086836.03576979.45867114.02967239.74857356.61567464.63067476.14980.031112 0.7286 0.6357 11.5192 0.0116

0.0300 0.7025 0.6487 116.8670 0.01170.0310 0.7260 0.6370 108.0151 0.0116

0.0280 0.6557 0.6721 134.5710 0.01190.0290 0.6791 0.6604 125.7190 0.0118

0.0260 0.6089 0.6956 152.2749 0.01210.0270 0.6323 0.6839 143.4229 0.0120

0.0240 0.5620 0.7190 169.9788 0.01240.0250 0.5854 0.7073 161.1268 0.0122

0.0220 0.5152 0.7424 187.6827 0.01270.0230 0.5386 0.7307 178.8308 0.0125

0.0200 0.4684 0.7658 205.3867 0.01310.0210 0.4918 0.7541 196.5347 0.0129

0.0180 0.4215 0.7892 223.0906 0.01360.0190 0.4449 0.7775 214.2386 0.0134

0.0160 0.3747 0.8127 240.7945 0.01430.0170 0.3981 0.8009 231.9426 0.0139

0.0140 0.3279 0.8361 258.4985 0.01500.0150 0.3513 0.8244 249.6465 0.0146

0.0120 0.2810 0.8595 276.2024 0.01600.0130 0.3044 0.8478 267.3504 0.0155

0.0100 0.2342 0.8829 293.9063 0.01730.0110 0.2576 0.8712 285.0544 0.0166

0.0080 0.1873 0.9063 311.6103 0.01910.0090 0.2108 0.8946 302.7583 0.0181

0.0060 0.1405 0.9297 329.3142 0.02180.0070 0.1639 0.9180 320.4622 0.0203

0.0050 0.1171 0.9415 338.1662 0.0237

0.0030 0.0703 0.9649 93.7228 0.03020.0040 0.0937 0.9532 347.0181 0.0263

0.0020 0.0468 0.9766 364.7221 0.03680.002734 0.0640 0.9680 262.1473 0.0316

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 3000 p.s.i. = 21,1 Mpa)ρ a/d j ΔK k2

0.0010 0.0234 0.9883 0.0517

fc' = 24.6 MPa fc = 11.07 MPa Es = 200000 MPafy = 240 MPa fs = 120 MPa Ec = 19340 MPa

ρMínimo = 0.00517 φ = 0.90 m = 11.477762ρbalanceado = 0.08713 ρMáx = 0.05228

K (kN/m2)214.7604427.0416636.8436844.1664

1049.01001082.87551251.37451451.25971648.66571843.59252036.04022226.00862413.49782598.50792781.03872961.09043138.66283313.75613486.37023656.50503824.16073989.33724152.03444312.25254469.99144625.25114778.03164928.33295076.15495221.49785364.36155504.74615642.65145778.07755911.02446041.49216169.48066294.99006418.02016538.57106656.64286772.23536885.34866995.98287104.13777209.81357313.01007413.72747511.96567607.72457701.00437791.80497880.12637903.9800

0.0520 0.5968 0.7016 88.3214 0.0113

0.0500 0.5739 0.7131 93.2798 0.01140.0510 0.5854 0.7073 90.8006 0.0113

0.0480 0.5509 0.7245 98.2382 0.01150.0490 0.5624 0.7188 95.7590 0.0115

0.0460 0.5280 0.7360 103.1966 0.01170.0470 0.5395 0.7303 100.7174 0.0116

0.0440 0.5050 0.7475 108.1549 0.01190.0450 0.5165 0.7418 105.6758 0.0118

0.0420 0.4821 0.7590 113.1133 0.01210.0430 0.4935 0.7532 110.6341 0.0120

0.0400 0.4591 0.7704 118.0717 0.01230.0410 0.4706 0.7647 115.5925 0.0122

0.0380 0.4362 0.7819 123.0301 0.01250.0390 0.4476 0.7762 120.5509 0.0124

0.0360 0.4132 0.7934 127.9885 0.01270.0370 0.4247 0.7877 125.5093 0.0126

0.0340 0.3902 0.8049 132.9469 0.01300.0350 0.4017 0.7991 130.4677 0.0129

0.0320 0.3673 0.8164 137.9053 0.01330.0330 0.3788 0.8106 135.4261 0.0132

0.0300 0.3443 0.8278 142.8637 0.01370.0310 0.3558 0.8221 140.3845 0.0135

0.0280 0.3214 0.8393 147.8221 0.01400.0290 0.3329 0.8336 145.3429 0.0138

0.01470.0260 0.2984 0.8508 152.7805 0.01450.0270 0.3099 0.8451 150.3013 0.0142

0.0051660.00600.00700.00800.0090

0.0918 0.9541 197.4060 0.02460.1033 0.9484 194.9268 0.0233

0.0689 0.9656 168.4990 0.02830.0803 0.9598 199.8852

0.2296 0.8852 167.6557 0.01620.2410 0.8795 165.1765 0.0158

0.02000.0210

0.6000 0.7000 23.8537 0.0112

0.2525 0.8737 162.6973 0.01550.02200.0230

0.052275

0.2640 0.8680 160.2181 0.01520.0240 0.2755 0.8623 157.7389 0.01500.0250 0.2869 0.8565 155.2597

0.2066 0.8967 172.6141 0.01690.2181 0.8910 170.1349 0.0165

0.01800.0190

0.1836 0.9082 177.5725 0.01780.1951 0.9024 175.0933 0.0174

0.01600.0170

0.1607 0.9197 182.5308 0.01900.1722 0.9139 180.0516 0.0184

0.01400.0150

0.1377 0.9311 187.4892 0.02040.1492 0.9254 185.0100 0.0196

0.01200.0130

0.1148 0.9426 192.4476 0.02220.1263 0.9369 189.9684 0.0212

0.01000.0110

0.0262

0.0459 0.9770 207.3228 0.03440.0574 0.9713 204.8436 0.0309

0.030433.86540.97040.0593

0.00400.0050

0.0230 0.9885 212.2812 0.04840.0344 0.9828 209.8020 0.0396

0.00200.0030

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 3500 p.s.i. = 24,6 Mpa)a/d j ΔK k2

0.0115 0.9943 0.0682ρ

0.0010

fc' = 24.6 MPa fc = 11.07 MPa Es = 200000 MPafy = 420 MPa fs = 210 MPa Ec = 19340 MPa

ρMínimo = 0.00295 φ = 0.90 m = 20.086083ρbalanceado = 0.04979 ρMáx = 0.03627

K (kN/m2)374.2037740.81491082.87551099.83361451.25971795.09332131.33432459.98282781.03873094.50223400.37303698.65143989.33724272.43044547.93114815.83935076.15495328.87805574.00865811.54666041.49216263.84516478.60556685.77336885.34867077.33147261.72177438.51947607.72457769.33727923.35728069.78488208.61988339.86238463.51228579.56968688.03448716.26950.036272 0.7286 0.6357 28.2351 0.0107

0.0360 0.7231 0.6385 108.4648 0.0107

0.0340 0.6829 0.6585 123.6499 0.01090.0350 0.7030 0.6485 116.0574 0.0108

0.0320 0.6428 0.6786 138.8350 0.01100.0330 0.6628 0.6686 131.2425 0.0110

0.0300 0.6026 0.6987 154.0201 0.01120.0310 0.6227 0.6887 146.4275 0.0111

0.0280 0.5624 0.7188 169.2052 0.01150.0290 0.5825 0.7088 161.6126 0.0113

0.0260 0.5222 0.7389 184.3902 0.01170.0270 0.5423 0.7288 176.7977 0.0116

0.0240 0.4821 0.7590 199.5753 0.01210.0250 0.5022 0.7489 191.9828 0.0119

0.0220 0.4419 0.7791 214.7604 0.01240.0230 0.4620 0.7690 207.1679 0.0122

0.0200 0.4017 0.7991 229.9455 0.01290.0210 0.4218 0.7891 222.3529 0.0126

0.0180 0.3615 0.8192 245.1306 0.01340.0190 0.3816 0.8092 237.5380 0.0131

0.0160 0.3214 0.8393 260.3156 0.01400.0170 0.3415 0.8293 252.7231 0.0137

0.0140 0.2812 0.8594 275.5007 0.01480.0150 0.3013 0.8494 267.9082 0.0144

0.0120 0.2410 0.8795 290.6858 0.01580.0130 0.2611 0.8694 283.0933 0.0153

0.0100 0.2009 0.8996 305.8709 0.01710.0110 0.2209 0.8895 298.2783 0.0164

0.0080 0.1607 0.9197 321.0560 0.01900.0090 0.1808 0.9096 313.4634 0.0180

0.0262

0.0060 0.1205 0.9397 336.2410 0.02170.0070 0.1406 0.9297 328.6485 0.0202

0.0020 0.0402 0.9799 366.6112 0.0367

0.0050 0.1004 0.9498 343.8336 0.0236

0.002952 0.0593 0.9704 342.0606 0.03040.0030 0.0603 0.9699 16.9581 0.03020.0040 0.0803 0.9598 351.4261

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 3500 p.s.i. = 24,6 Mpa)ρ a/d j ΔK k2

0.0010 0.0201 0.9900 0.0517

fc' = 28.1 MPa fc = 12.645 MPa Es = 200000 MPafy = 240 MPa fs = 120 MPa Ec = 20670 MPa

ρMínimo = 0.00552 φ = 0.90 m = 10.048147ρbalanceado = 0.09952 ρMáx = 0.05971

K (kN/m2)214.9148427.6592638.2332846.6368

1052.87001159.62401256.93281458.82521658.54721856.09882051.48002244.69082435.73122624.60122811.30082995.83003178.18883358.37723536.39523712.24283885.92004057.42684226.76324393.92924558.92484721.75014882.40495040.88935197.20335351.34695503.32015653.12295800.75535946.21736089.50896230.63016369.58096506.36136640.97136773.41096903.68017031.77897157.70737281.46547403.05307522.47027639.71707754.79347867.69947978.43508087.00028193.39508297.61948399.67348499.55708597.27038692.81318786.18558877.38758966.41919028.5300

0.2211 0.8895 169.3364 0.01540.2311 0.8844 167.1660 0.0151

0.02200.0230

0.2412 0.8794 164.9956 0.01480.2512 0.8744 162.8252 0.0146

0.02400.0250

0.2613 0.8694 160.6548 0.0143

0.6000 0.7000 62.1109 0.0105

0.02600.01410.86440.27130.0270

0.059713

0.0280 0.2813 0.8593 0.01390.0290 0.2914 0.8543 0.0137

0.2010 0.8995 173.6772 0.01600.2110 0.8945 171.5068 0.0157

0.02000.0210

0.1809 0.9096 178.0180 0.01680.1909 0.9045 175.8476 0.0164

0.01800.0190

0.1608 0.9196 182.3588 0.01770.1708 0.9146 180.1884 0.0173

0.01600.0170

0.1407 0.9297 186.6996 0.01890.1507 0.9246 184.5292 0.0183

0.01400.0150

0.01000.0110

0.1206 0.9397 191.0404 0.02030.1306 0.9347 188.8700 0.0195

0.01200.0130

0.02320.1005 0.9498 195.3812 0.02210.1105 0.9447 193.2108 0.0211

0.0402 0.9799 208.4036 0.03440.0502 0.9749 206.2332 0.0308

0.00400.0050

0.0020 0.0201 0.9900 212.7444 0.04840.0301 0.9849 210.5740 0.03960.0030

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 4000 p.s.i. = 28,1 Mpa)a/d j ΔK k2

0.0100 0.9950 0.0682ρ

0.0010

0.0294106.75400.97230.05550.0055220.00600.00700.00800.0090

0.0603 0.9699 97.3088 0.02820.0703 0.9648 201.8924 0.02620.0804 0.9598 199.7220 0.02460.0904 0.9548 197.5516

0.0300 0.3014 0.8493 0.01350.0310 0.3115 0.8443 0.01330.0320 0.3215 0.8392 0.0131147.6324

149.8028151.9732

0.0330 0.3316 0.8342 0.01300.0340 0.3416 0.8292 0.01280.0350 0.3517 0.8242 0.0127141.1212

143.2916145.4620

0.0360 0.3617 0.8191 0.01250.0370 0.3718 0.8141 0.01240.0380 0.3818 0.8091 0.0123134.6100

136.7804138.9508

0.0390 0.3919 0.8041 0.01220.0400 0.4019 0.7990 0.01200.0410 0.4120 0.7940 0.0119128.0988

130.2692132.4396

0.0420 0.4220 0.7890 0.01180.0430 0.4321 0.7840 0.01170.0440 0.4421 0.7789 0.0116121.5876

123.7580125.9284

0.0450 0.4522 0.7739 0.01150.0460 0.4622 0.7689 0.01140.0470 0.4723 0.7639 0.0114115.0764

117.2468119.4172

104.2244106.3948

0.0480 0.4823 0.7588 0.01130.0490 0.4924 0.7538 0.01120.0500 0.5024 0.7488 0.0111108.5652

110.7356112.9060

0.0590 0.5928 0.7036 0.010689.031691.202093.3724

0.0540 0.5426 0.7287 0.01080.0550 0.5526 0.7237 0.01080.0560 0.5627 0.7187 0.010795.5428

97.713299.8836

154.1436156.3140158.4844

0.0570 0.5727 0.7136 0.01070.0580 0.5828 0.7086 0.0106

0.0510 0.5125 0.7438 0.01100.0520 0.5225 0.7387 0.01100.0530 0.5326 0.7337 0.0109102.0540

fc' = 28.1 MPa fc = 12.645 MPa Es = 200000 MPafy = 420 MPa fs = 210 MPa Ec = 20670 MPa

ρMínimo = 0.00316 φ = 0.90 m = 17.584258ρbalanceado = 0.05687 ρMáx = 0.04143

K (kN/m2)374.6766742.70631104.08921159.62401458.82521806.91442148.35672483.15222811.30083132.80263447.65753755.86564057.42684352.34124640.60884922.22945197.20335465.53025727.21045982.24376230.63016472.36976707.46246935.90837157.70737372.85957581.36497783.22347978.43508166.99988348.91778524.18888692.81318854.79059010.12109158.80479300.84159436.23159564.97479687.07109802.52049911.32309956.3891

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 4000 p.s.i. = 28,1 Mpa)ρ a/d j ΔK k2

0.0010 0.0176 0.9912 0.05170.0020 0.0352 0.9824 368.0297 0.03670.0030 0.0528 0.9736 361.3829 0.0301

0.0040 0.0703 0.9648 299.2012 0.02620.0050 0.0879 0.9560 348.0892 0.0235

0.003155 0.0555 0.9723 55.5348 0.0294

0.0060 0.1055 0.9472 341.4423 0.02160.0070 0.1231 0.9385 334.7955 0.02010.0080 0.1407 0.9297 328.1486 0.01890.0090 0.1583 0.9209 321.5018 0.01790.0100 0.1758 0.9121 314.8549 0.01700.0110 0.1934 0.9033 308.2081 0.01630.0120 0.2110 0.8945 301.5612 0.01570.0130 0.2286 0.8857 294.9144 0.01520.0140 0.2462 0.8769 288.2675 0.01470.0150 0.2638 0.8681 281.6207 0.01430.0160 0.2813 0.8593 274.9738 0.01390.0170 0.2989 0.8505 268.3270 0.01350.0180 0.3165 0.8417 261.6801 0.01320.0190 0.3341 0.8329 255.0333 0.01290.0200 0.3517 0.8242 248.3864 0.01270.0210 0.3693 0.8154 241.7396 0.01240.0220 0.3869 0.8066 235.0927 0.01220.0230 0.4044 0.7978 228.4459 0.01200.0240 0.4220 0.7890 221.7990 0.01180.0250 0.4396 0.7802 215.1522 0.01160.0260 0.4572 0.7714 208.5053 0.01150.0270 0.4748 0.7626 201.8585 0.01130.0280 0.4924 0.7538 195.2116 0.01120.0290 0.5099 0.7450 188.5648 0.01110.0300 0.5275 0.7362 181.9179 0.01090.0310 0.5451 0.7274 175.2711 0.01080.0320 0.5627 0.7187 168.6242 0.01070.0330 0.5803 0.7099 161.9774 0.01060.0340 0.5979 0.7011 155.3305 0.01050.0350 0.6154 0.6923 148.6837 0.01040.0360 0.6330 0.6835 142.0368 0.01040.0370 0.6506 0.6747 135.3900 0.01030.0380 0.6682 0.6659 128.7431 0.01020.0390 0.6858 0.6571 122.0963 0.0102

0.041433 0.7286 0.6357 45.0661 0.0100

0.0400 0.7034 0.6483 115.4494 0.01010.0410 0.7210 0.6395 108.8026 0.0100

fc' = 31.6 MPa fc = 14.22 MPa Es = 200000 MPafy = 240 MPa fs = 120 MPa Ec = 21920 MPa

ρMínimo = 0.00586 φ = 0.90 m = 8.93521966ρbalanceado = 0.11192 ρMáx = 0.06715

K (kN/m2)215.0350428.1400639.3150848.55991055.87491231.72401261.25991464.71481666.23981865.83472063.49962259.23452453.03952644.91442834.85933022.87423208.95903393.11393575.33883755.63373933.99854110.43344284.93824457.51304628.15794796.87274963.65755128.51235291.43715452.43195611.49665768.63145923.83626077.11096228.45576377.87046525.35526670.90996814.53466956.22937095.99407233.82877369.73347503.70817635.75287765.86757894.05218020.30688144.63148267.02618387.49078506.02538622.62998737.30458850.04918960.86379069.74839176.70299281.72759384.82209485.98669585.22119682.52579777.90029871.34489962.859310052.443810140.098310153.0800

0.0179 0.9911 213.1050 0.04830.0268 0.9866 211.1750 0.0395

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 4500 p.s.i. = 31,6 Mpa)a/d j ΔK k2

0.0089 0.9955 0.0682

0.0261

0.0357 0.9821 209.2450 0.03430.0447 0.9777 207.3150 0.0308

0.1072 0.9464 193.8049 0.02020.1162 0.9419 191.8749 0.0194

0.0894 0.9553 197.6649 0.02200.0983 0.9509 195.7349 0.0210

0.1430 0.9285 186.0849 0.01770.1519 0.9241 184.1549 0.0172

0.1251 0.9375 189.9449 0.01880.1340 0.9330 188.0149 0.0182

0.1787 0.9106 178.3649 0.01590.1876 0.9062 176.4348 0.0156

0.1608 0.9196 182.2249 0.01670.1698 0.9151 180.2949 0.0163

174.5048 0.0153

0.2234 0.8883 168.7148 0.0144

0.2055 0.8972 172.5748 0.01500.2144 0.8928 170.6448 0.0147

0.0300

0.2323 0.8838 166.7848 0.0142

0.0133159.06480.86600.2681

0.2413 0.8794 164.8548 0.0140

0.2591 0.8704 160.9948

0.0190

0.01350.2502 0.8749 162.9248 0.0137

ρ

0.00100.00200.00300.00400.0050

0.02000.02100.02200.02300.02400.02500.02600.02700.02800.0290

0.1966 0.9017

0.01000.01100.01200.01300.01400.01500.01600.01700.0180

0.0285175.84910.97380.05230.0058560.00600.00700.00800.0090

0.0715 0.9643 201.5249 0.02450.0804 0.9598 199.5949 0.0232

0.0536 0.9732 29.5359 0.02820.0625 0.9687 203.4550

0.03100.0320 0.2859 0.8570 155.2048 0.01300.0330 0.2949 0.8526 153.2748 0.0128

0.2770 0.8615 157.1348 0.0132

0.0340 0.3038 0.8481 151.3448 0.01270.0350 0.3127 0.8436 149.4147 0.01250.0360 0.3217 0.8392 147.4847 0.01240.0370 0.3306 0.8347 145.5547 0.01220.0380 0.3395 0.8302 143.6247 0.01210.0390 0.3485 0.8258 141.6947 0.01200.0400 0.3574 0.8213 139.7647 0.01190.0410 0.3663 0.8168 137.8347 0.01180.0420 0.3753 0.8124 135.9047 0.01160.0430 0.3842 0.8079 133.9747 0.01150.0440 0.3931 0.8034 132.0447 0.01140.0450 0.4021 0.7990 130.1147 0.01130.0460 0.4110 0.7945 128.1847 0.01130.0470 0.4200 0.7900 126.2547 0.01120.0480 0.4289 0.7856 124.3246 0.01110.0490 0.4378 0.7811 122.3946 0.01100.0500 0.4468 0.7766 120.4646 0.01090.0510 0.4557 0.7722 118.5346 0.01080.0520 0.4646 0.7677 116.6046 0.01080.0530 0.4736 0.7632 114.6746 0.01070.0540 0.4825 0.7587 112.7446 0.01060.0550 0.4914 0.7543 110.8146 0.01060.0560 0.5004 0.7498 108.8846 0.01050.0570 0.5093 0.7453 106.9546 0.01040.0580 0.5182 0.7409 105.0246 0.01040.0590 0.5272 0.7364 103.0946 0.01030.0600 0.5361 0.7319 101.1646 0.01030.0610 0.5450 0.7275 99.2345 0.01020.0620 0.5540 0.7230 97.3045 0.01020.0630 0.5629 0.7185 95.3745 0.01010.0640 0.5719 0.7141 93.4445 0.01010.0650 0.5808 0.7096 91.5145 0.0100

0.6000 0.7000 12.9817 0.0099

0.0660 0.5897 0.7051 89.5845 0.01000.0670 0.5987 0.7007 87.6545 0.0099

0.067150

fc' = 31.6 MPa fc = 14.22 MPa Es = 200000 MPafy = 420 MPa fs = 210 MPa Ec = 21920 MPa

ρMínimo = 0.00335 φ = 0.90 m = 15.636634ρbalanceado = 0.06395 ρMáx = 0.04659

K (kN/m2)375.0447744.17871107.40211231.72401464.71481816.11692161.60832501.18912834.85933162.61883484.46763800.40584110.43344414.55034712.75655005.05215291.43715571.91145846.47516115.12816377.87046634.70226885.62327130.63377369.73347602.92267830.20108051.56898267.02618476.57268680.20858877.93379069.74839255.65239435.64569609.72829777.90029940.161610096.512310246.952310391.481810530.100510662.808610789.606110910.492911025.469111134.534611196.5088

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 4500 p.s.i. = 31,6 Mpa)ρ a/d j ΔK k2

0.0010 0.0156 0.9922 0.05160.0020 0.0313 0.9844 369.1340 0.03670.0030 0.0469 0.9765 363.2234 0.0301

0.0040 0.0625 0.9687 232.9908 0.02610.0050 0.0782 0.9609 351.4021 0.0235

0.003346 0.0523 0.9738 124.3219 0.0285

0.0060 0.0938 0.9531 345.4914 0.02150.0070 0.1095 0.9453 339.5808 0.02000.0080 0.1251 0.9375 333.6701 0.01880.0090 0.1407 0.9296 327.7595 0.01780.0100 0.1564 0.9218 321.8488 0.01690.0110 0.1720 0.9140 315.9382 0.01620.0120 0.1876 0.9062 310.0276 0.01560.0130 0.2033 0.8984 304.1169 0.01510.0140 0.2189 0.8905 298.2063 0.01460.0150 0.2345 0.8827 292.2956 0.01410.0160 0.2502 0.8749 286.3850 0.01370.0170 0.2658 0.8671 280.4743 0.01340.0180 0.2815 0.8593 274.5637 0.01310.0190 0.2971 0.8515 268.6530 0.01280.0200 0.3127 0.8436 262.7424 0.01250.0210 0.3284 0.8358 256.8317 0.01230.0220 0.3440 0.8280 250.9211 0.01210.0230 0.3596 0.8202 245.0104 0.01180.0240 0.3753 0.8124 239.0998 0.01160.0250 0.3909 0.8045 233.1891 0.01150.0260 0.4066 0.7967 227.2785 0.01130.0270 0.4222 0.7889 221.3678 0.01110.0280 0.4378 0.7811 215.4572 0.01100.0290 0.4535 0.7733 209.5465 0.01090.0300 0.4691 0.7655 203.6359 0.01070.0310 0.4847 0.7576 197.7252 0.01060.0320 0.5004 0.7498 191.8146 0.01050.0330 0.5160 0.7420 185.9039 0.01040.0340 0.5316 0.7342 179.9933 0.01030.0350 0.5473 0.7264 174.0827 0.01020.0360 0.5629 0.7185 168.1720 0.01010.0370 0.5786 0.7107 162.2614 0.01000.0380 0.5942 0.7029 156.3507 0.01000.0390 0.6098 0.6951 150.4401 0.00990.0400 0.6255 0.6873 144.5294 0.00980.0410 0.6411 0.6794 138.6188 0.00970.0420 0.6567 0.6716 132.7081 0.00970.0430 0.6724 0.6638 126.7975 0.00960.0440 0.6880 0.6560 120.8868 0.00960.0450 0.7036 0.6482 114.9762 0.0095

0.046594 0.7286 0.6357 61.9742 0.00950.0460 0.7193 0.6404 109.0655 0.0095

fc' = 35.2 MPa fc = 15.84 MPa Es = 200000 MPafy = 420 MPa fs = 210 MPa Ec = 23130 MPa

ρMínimo = 0.00353 φ = 0.90 m = 14.037433ρbalanceado = 0.07124 ρMáx = 0.05190

K (kN/m2)375.3469745.38771110.12231301.82751469.55081823.67312172.48932515.99932854.20323187.10093514.69253836.97794153.95724465.63034771.99735073.05825368.81285659.26145944.40376224.24006498.77016767.99407031.91187290.52347543.82897791.82828034.52148271.90848503.98938730.76408952.23269168.39519379.25139584.80159785.04559979.983310169.615010353.940510532.959910706.673110875.080211038.181111195.975911348.464611495.647111637.523411774.093611905.357612031.315512151.967212267.312812377.352312472.0604

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 5000 p.s.i. = 35,2 Mpa)a/d j ΔK k2

0.0140 0.9930 0.0516

0.0561 0.9719 167.7233 0.02610.0702 0.9649 354.1223 0.0234

0.0281 0.9860 370.0408 0.03660.0421 0.9789 364.7346 0.0300

0.00900.0080

0.0842 0.9579 348.8162 0.02150.0983 0.9509 343.5100 0.01990.0070

0.1404 0.9298 327.5916 0.01690.1544 0.9228 322.2854 0.0161

0.1123 0.9439 338.2039 0.01870.1263 0.9368 332.8977 0.0177

0.1965 0.9017 306.3670 0.01450.2106 0.8947 301.0608 0.0140

0.1684 0.9158 316.9793 0.01550.1825 0.9088 311.6731 0.0150

0.2527 0.8737 285.1424 0.01300.2667 0.8666 279.8362 0.0127

0.2246 0.8877 295.7547 0.01360.2386 0.8807 290.4485 0.0133

0.2807 0.8596 274.5301 0.01240.2948 0.8526 269.2239 0.01220.02100.3088 0.8456 263.9178 0.01190.3229 0.8386 258.6116 0.01170.0230

0.0220

0.3369 0.8316 253.3055 0.01150.3509 0.8245 247.9993 0.01130.0250

0.0240

0.3930 0.8035 232.0809 0.01080.4071 0.7965 226.7747 0.0107

0.3650 0.8175 242.6932 0.01120.3790 0.8105 237.3870 0.0110

0.4913 0.7543 194.9378 0.0100

0.051902

0.0380 0.5334 0.7333 179.0194 0.0097

0.03500.0360 0.5053 0.7473 189.6317 0.00990.0370 0.5194

0.4773 0.7614 200.2440 0.0101

0.4211 0.7894 221.4686 0.01060.4352 0.7824 216.1624 0.01040.4492 0.7754 210.8563 0.01030.4632 0.7684 205.5501 0.0102

ρ

0.0010

0.0277191.70520.97520.04960.003532

0.00600.00500.0040

0.00300.0020

0.02000.01900.01800.01700.01600.01500.01400.01300.01200.01100.0100

0.03400.03300.03200.03100.03000.02900.02800.02700.0260

0.7403 184.3255 0.0098

0.0390 0.5475 0.7263 173.7132 0.00970.0400 0.5615 0.7193 168.4071 0.00960.0410 0.5755 0.7122 163.1009 0.00950.0420 0.5896 0.7052 157.7948 0.00950.0430 0.6036 0.6982 152.4886 0.00940.0440 0.6176 0.6912 147.1825 0.00930.0450 0.6317 0.6842 141.8763 0.00930.0460 0.6457 0.6771 136.5702 0.00920.0470 0.6598 0.6701 131.2640 0.00920.0480 0.6738 0.6631 125.9579 0.00910.0490 0.6878 0.6561 120.6517 0.00910.0500 0.7019 0.6491 115.3456 0.0090

0.7286 0.6357 94.7081 0.00900.0510 0.7159 0.6420 110.0394 0.0090

fc' = 35.2 MPa fc = 15.84 MPa Es = 200000 MPafy = 240 MPa fs = 120 MPa Ec = 23130 MPa

ρMínimo = 0.00618 φ = 0.90 m = 8.0213904ρbalanceado = 0.12467 ρMáx = 0.07480

K (kN/m2)215.1337428.5348640.2032850.13901058.34221264.81281301.82751469.55081672.55611873.82892073.36902271.17652467.25132661.59362854.20323045.08023234.22463421.63643607.31553791.26203973.47594153.95724332.70594509.72194685.00534858.55615030.37435200.45995368.81285535.43325700.32095863.47596024.89846184.58826342.54556498.77016653.26206806.02146957.04817106.34227253.90377399.73267543.82897686.19257826.82357965.72198102.88778238.32098372.02148503.98938634.22468762.72738889.49739014.53489137.83969259.41189379.25139497.35839613.73269728.37439841.28349952.4599

10061.903710169.615010275.593610379.839610482.352910583.133710682.181810779.497310875.080210968.930511061.048111151.433211240.085611309.7600

TABLAS PARA DISEÑO METODO DE LA ROTURA (fc' = 5000 p.s.i. = 35,2 Mpa)ρ a/d j ΔK k2

0.0010 0.0080 0.9960 0.06820.0020 0.0160 0.9920 213.4011 0.04830.0030 0.0241 0.9880 211.6684 0.03950.0040 0.0321 0.9840 209.9358 0.03430.0050 0.0401 0.9799 208.2032 0.03070.0060 0.0481 0.9759 206.4706 0.0281

0.006180 0.0496 0.9752 37.0147 0.02770.0070 0.0561 0.9719 167.7233 0.02610.0080 0.0642 0.9679 203.0053 0.02450.0090 0.0722 0.9639 201.2727 0.02310.0100 0.0802 0.9599 199.5401 0.02200.0110 0.0882 0.9559 197.8075 0.02100.0120 0.0963 0.9519 196.0749 0.02010.0130 0.1043 0.9479 194.3422 0.01940.0140 0.1123 0.9439 192.6096 0.01870.0150 0.1203 0.9398 190.8770 0.01810.0160 0.1283 0.9358 189.1444 0.01760.0170 0.1364 0.9318 187.4118 0.01710.0180 0.1444 0.9278 185.6791 0.01660.0190 0.1524 0.9238 183.9465 0.01620.0200 0.1604 0.9198 182.2139 0.01590.0210 0.1684 0.9158 180.4813 0.01550.0220 0.1765 0.9118 178.7487 0.01520.0230 0.1845 0.9078 177.0160 0.01490.0240 0.1925 0.9037 175.2834 0.01460.0250 0.2005 0.8997 173.5508 0.01430.0260 0.2086 0.8957 171.8182 0.01410.0270 0.2166 0.8917 170.0856 0.01390.0280 0.2246 0.8877 168.3529 0.01360.0290 0.2326 0.8837 166.6203 0.01340.0300 0.2406 0.8797 164.8877 0.01320.0310 0.2487 0.8757 163.1551 0.01310.0320 0.2567 0.8717 161.4225 0.01290.0330 0.2647 0.8676 159.6898 0.01270.0340 0.2727 0.8636 157.9572 0.01260.0350 0.2807 0.8596 156.2246 0.01240.0360 0.2888 0.8556 154.4920 0.01230.0370 0.2968 0.8516 152.7594 0.01210.0380 0.3048 0.8476 151.0267 0.01200.0390 0.3128 0.8436 149.2941 0.01190.0400 0.3209 0.8396 147.5615 0.01170.0410 0.3289 0.8356 145.8289 0.01160.0420 0.3369 0.8316 144.0963 0.01150.0430 0.3449 0.8275 142.3636 0.01140.0440 0.3529 0.8235 140.6310 0.01130.0450 0.3610 0.8195 138.8984 0.01120.0460 0.3690 0.8155 137.1658 0.01110.0470 0.3770 0.8115 135.4332 0.01100.0480 0.3850 0.8075 133.7005 0.01090.0490 0.3930 0.8035 131.9679 0.01080.0500 0.4011 0.7995 130.2353 0.01080.0510 0.4091 0.7955 128.5027 0.01070.0520 0.4171 0.7914 126.7701 0.01060.0530 0.4251 0.7874 125.0374 0.01050.0540 0.4332 0.7834 123.3048 0.01050.0550 0.4412 0.7794 121.5722 0.01040.0560 0.4492 0.7754 119.8396 0.01030.0570 0.4572 0.7714 118.1070 0.01030.0580 0.4652 0.7674 116.3743 0.01020.0590 0.4733 0.7634 114.6417 0.01010.0600 0.4813 0.7594 112.9091 0.01010.0610 0.4893 0.7553 111.1765 0.01000.0620 0.4973 0.7513 109.4439 0.01000.0630 0.5053 0.7473 107.7112 0.00990.0640 0.5134 0.7433 105.9786 0.00990.0650 0.5214 0.7393 104.2460 0.00980.0660 0.5294 0.7353 102.5134 0.00980.0670 0.5374 0.7313 100.7807 0.00970.0680 0.5455 0.7273 99.0481 0.00970.0690 0.5535 0.7233 97.3155 0.00960.0700 0.5615 0.7193 95.5829 0.00960.0710 0.5695 0.7152 93.8503 0.00950.0720 0.5775 0.7112 92.1176 0.00950.0730 0.5856 0.7072 90.3850 0.00950.0740 0.5936 0.7032 88.6524 0.0094

0.074800 0.6000 0.7000 69.6744 0.0094