estructuras 2 a

DATOS

Col.b h d'

tm tm t cm cm cm MPa cm G/LC4 1.23 0.65 8.39 30 26 4 20 500 0.63

límite EItm tm tm² t tm

64.1026 40 1.23 0.19129 0.4 190.844 75.3421 1 1.23

ObservacionesInfluyen:

cm² La esbeltez, lo que incluye el tipo de vínculos y posibilidad de desplazamiento.3.9 El valor de la carga mayorada respecto a la crítica.

La curvatura o forma de la deformada debida a los momentos de los nudos.La fluencia lenta del Hº.

Armadura simétrica para secciones rectangulares de columnas indesplazables.

Mu1 Mu2 Pu f'c ℓu βd

k ℓu /r Mumáx M2mím Cm Pc δns Mc

As = A's

b ≥ 20 cm

h ≥

20

cm

As

A’s

Ing. Alberto Elicabe

M1 y M2 son positivos si son horarios.Pu positiva si es de compresión.EI calculado para una cuantía total del 1%.

Observaciones

CALCULAR CON Mc

La esbeltez, lo que incluye el tipo de vínculos y posibilidad de desplazamiento.El valor de la carga mayorada respecto a la crítica.La curvatura o forma de la deformada debida a los momentos de los nudos.La fluencia lenta del Hº.

0.054 OBSERVACIONES:

Mu Pu b h d' f'c β1 As=A's Φ = 0.9 ξt = 0.0223

KNm KN mm mm mm MPa mm² elegir elegir ξt lím sup ξt lím inf

12.3 83.9 300 260 40 20 0.85 26.6028 E S 0.0221957 0.0226

1er ciclo As mínima: 390 ρ= 0.01 2º cicloξt lím ξt Φ fs ξ' f's β1 · c As P elegir ξt Φ

0.004 MPa MPa mm mm² KN-0.003 0.65 -420 -420 260 N

ξt máx -0.00209 0.65 -418 -0.0028 -420 260 1E+05 58125 N 0.0221957 0.90.025 -0.00195 0.65 -390 -0.0028 -420 260 6925 4506.52 N 0.0221997 0.9

-0.00181 0.65 -361 -0.0028 -420 260 3581 2680.27 N 0.0222037 0.9-0.00166 0.65 -333 -0.0028 -420 260 2415 2043.56 N 0.0222077 0.9-0.00152 0.65 -305 -0.0027 -420 260 1821 1719.69 N 0.0222117 0.9-0.00138 0.65 -276.2 -0.0027 -420 260 1462 1523.56 N 0.0222157 0.9-0.00124 0.65 -248 -0.0027 -420 260 1221 1392.05 N 0.0222197 0.9

-0.0011 0.65 -219 -0.0027 -420 260 1049 1297.74 N 0.0222237 0.9-0.00096 0.65 -191 -0.0026 -420 260 918.63 1226.81 N 0.0222277 0.9-0.00081 0.65 -163 -0.0026 -420 256.6 721.53 1124 N 0.0222317 0.9-0.00067 0.65 -134.4 -0.0026 -420 241 281.47 900.278 N 0.0222357 0.9-0.00053 0.65 -106 -0.0026 -420 227.1 0 752.982 N 0.0222397 0.9-0.00039 0.65 -77.68 -0.0025 -420 214.8 0 712.098 N 0.0222437 0.9-0.00025 0.65 -49.32 -0.0025 -420 203.7 0 675.425 N 0.0222477 0.9

-0.0001 0.65 -21 -0.0025 -420 193.8 0 642.344 N 0.0222517 0.93.7E-05 0.65 7.4 -0.0024 -420 184.7 0 612.353 N 0.0222557 0.9

0.000179 0.65 35.76 -0.0024 -420 176.5 0 585.037 N 0.0222597 0.90.000321 0.65 64.12 -0.0024 -420 168.9 0 560.054 N 0.0222637 0.90.000462 0.65 92.48 -0.0024 -420 162 0 537.117 N 0.0222677 0.90.000604 0.65 120.8 -0.0023 -420 155.7 0 515.986 N 0.0222717 0.90.000746 0.65 149.2 -0.0023 -420 149.8 0 496.454 N 0.0222757 0.90.000888 0.65 177.6 -0.0023 -420 144.3 0 478.346 N 0.0222797 0.9

0.00103 0.65 205.9 -0.0023 -420 139.2 0 461.514 N 0.0222837 0.90.001171 0.65 234.3 -0.0022 -420 134.5 0 445.825 N 0.0222877 0.90.001313 0.65 262.6 -0.0022 -420 130.1 0 431.168 N 0.0222917 0.90.001455 0.65 291 -0.0022 -420 125.9 0 417.444 N 0.0222957 0.90.001597 0.65 319.4 -0.0022 -420 122 0 404.567 N 0.0222997 0.90.001739 0.65 347.7 -0.0021 -420 118.4 0 392.461 N 0.0223037 0.9

0.00188 0.65 376.1 -0.0021 -420 114.9 0 381.058 N 0.0223077 0.90.002022 0.652 404.4 -0.0021 -417 111.7 0 371.353 N 0.0223117 0.90.002164 0.664 420 -0.0021 -412 108.6 0 367.703 N 0.0223157 0.90.002306 0.675 420 -0.002 -407 105.7 0 364.248 N 0.0223197 0.90.002448 0.687 420 -0.002 -402 103 0 360.973 N 0.0223237 0.90.002589 0.699 420 -0.002 -397 100.4 0 357.864 N 0.0223277 0.90.002731 0.711 420 -0.002 -392 97.89 0 354.908 N 0.0223317 0.90.002873 0.723 420 -0.0019 -386 95.52 0 352.096 N 0.0223357 0.90.003015 0.735 420 -0.0019 -381 93.27 0 349.416 N 0.0223397 0.90.003157 0.746 420 -0.0019 -376 91.12 0 346.86 N 0.0223437 0.90.003298 0.758 420 -0.0019 -371 89.07 0 344.419 N 0.0223477 0.9

0.00344 0.77 420 -0.0018 -366 87.11 0 342.085 N 0.0223517 0.90.003582 0.782 420 -0.0018 -361 85.23 0 339.852 N 0.0223557 0.90.003724 0.794 420 -0.0018 -355 83.43 0 337.713 N 0.0223597 0.90.003866 0.805 420 -0.0018 -350 81.71 0 335.662 N 0.0223637 0.90.004007 0.817 420 -0.0017 -345 80.06 0 333.694 N 0.0223677 0.90.004149 0.829 420 -0.0017 -340 78.47 0 331.805 N 0.0223717 0.90.004291 0.841 420 -0.0017 -335 76.94 0 329.989 N 0.0223757 0.9

0.004433 0.853 420 -0.0016 -330 75.48 0 328.242 N 0.0223797 0.90.004575 0.865 420 -0.0016 -325 74.06 0 326.56 N 0.0223837 0.90.004716 0.876 420 -0.0016 -319 72.7 0 324.941 N 0.0223877 0.90.004858 0.888 420 -0.0016 -314 71.39 0 323.38 N 0.0223917 0.9

0.005 0.9 420 -0.0015 -309 70.13 0 321.874 N 0.0223957 0.90.0054 0.9 420 -0.0015 -295 66.79 0 306.55 N 0.0223996 0.90.0058 0.9 420 -0.0014 -280 63.75 0 292.619 N 0.0224036 0.90.0062 0.9 420 -0.0013 -265 60.98 0 279.899 N 0.0224076 0.90.0066 0.9 420 -0.0013 -251 58.44 0 268.239 N 0.0224116 0.9

0.007 0.9 420 -0.0012 -236 56.1 0 257.512 N 0.0224156 0.90.007399 0.9 420 -0.0011 -222 53.95 0 247.609 N 0.0224196 0.90.007799 0.9 420 -0.001 -207 51.95 0 238.44 N 0.0224236 0.90.008199 0.9 420 -0.001 -193 50.09 0 229.926 N 0.0224276 0.90.008599 0.9 420 -0.0009 -178 48.37 0 222 N 0.0224316 0.90.008999 0.9 420 -0.0008 -164 46.75 0 214.6 N 0.0224356 0.90.009399 0.9 420 -0.0007 -149 45.25 0 207.679 N 0.0224396 0.90.009799 0.9 420 -0.0007 -135 43.83 0 201.19 N 0.0224436 0.90.010199 0.9 420 -0.0006 -120 42.5 0 195.094 N 0.0224476 0.90.010599 0.9 420 -0.0005 -106 41.25 0 189.357 N 0.0224516 0.90.010999 0.9 420 -0.0005 -91 40.08 0 183.948 N 0.0224556 0.90.011398 0.9 420 -0.0004 -76.42 38.96 0 178.839 N 0.0224596 0.90.011798 0.9 420 -0.0003 -61.88 37.91 0 174.006 N 0.0224636 0.90.012198 0.9 420 -0.0002 -47.34 36.91 0 169.427 N 0.0224676 0.90.012598 0.9 420 -0.0002 -32.8 35.97 0 165.084 N 0.0224716 0.90.012998 0.9 420 -9E-05 -18.25 35.07 0 160.957 N 0.0224756 0.90.013398 0.9 420 -2E-05 -3.713 34.21 0 157.032 N 0.0224796 0.90.013798 0.9 420 5.4E-05 10.83 33.4 0 153.293 N 0.0224836 0.90.014198 0.9 420 0.00013 25.37 32.62 0 149.729 N 0.0224876 0.90.014598 0.9 420 0.0002 39.91 31.88 0 146.326 N 0.0224916 0.90.014997 0.9 420 0.00027 54.45 31.17 0 143.075 N 0.0224956 0.90.015397 0.9 420 0.00034 69 30.49 0 139.965 N 0.0224996 0.90.015797 0.9 420 0.00042 83.54 29.84 0 136.987 N 0.0225036 0.90.016197 0.9 420 0.00049 98.08 29.22 0 134.134 N 0.0225076 0.90.016597 0.9 420 0.00056 112.6 28.63 0 131.396 N 0.0225116 0.90.016997 0.9 420 0.00064 127.2 28.05 0 128.769 N 0.0225156 0.90.017397 0.9 420 0.00071 141.7 27.5 0 126.244 N 0.0225196 0.90.017797 0.9 420 0.00078 156.2 26.98 0 123.817 N 0.0225236 0.90.018197 0.9 420 0.00085 170.8 26.47 0 121.481 N 0.0225276 0.90.018597 0.9 420 0.00093 185.3 25.98 0 119.231 N 0.0225316 0.90.018997 0.9 420 0.001 199.9 25.5 0 117.064 N 0.0225356 0.90.019396 0.9 420 0.00107 214.4 25.05 0 114.973 N 0.0225396 0.90.019796 0.9 420 0.00114 229 24.61 0 112.956 N 0.0225436 0.90.020196 0.9 420 0.00122 243.5 24.18 0 111.009 N 0.0225476 0.90.020596 0.9 420 0.00129 258 23.78 0 109.128 N 0.0225516 0.90.020996 0.9 420 0.00136 272.6 23.38 0 107.309 N 0.0225556 0.90.021396 0.9 420 0.00144 287.1 23 0 105.55 N 0.0225596 0.90.021796 0.9 420 0.00151 301.7 22.62 0 103.848 N 0.0225636 0.90.022196 0.9 420 0.00158 316.2 22.27 18.059 90.2338 E 0.0225676 0.90.022596 0.9 420 0.00165 330.7 21.92 44.835 70.3088 S 0.0225716 0.90.022996 0.9 420 0.00173 345.3 21.58 81.247 43.0955 N 0.0225756 0.90.023395 0.9 420 0.0018 359.8 21.25 134.32 3.28247 N 0.0225796 0.90.023795 0.9 420 0.00187 374.4 20.94 220 -61.212 N 0.0225836 0.90.024195 0.9 420 0.00194 388.9 20.63 384.27 -185.07 N 0.0225876 0.90.024595 0.9 420 0.00202 403.5 20.33 834.24 -524.95 N 0.0225916 0.9

0.024995 0.9 420 0.00209 418 20.04 7803 -5793.4 N 0.0225956 0.9

Solución para fuera de rango (fuerza de compresión) Solución para toda la sección traccionadaΔAs ΔA's As f'smm² mm² mm² MPa-7774.22 7811 M N 291.75485 181.82

As A's KNm KNmm² mm² 12.3 83.929.26803 -7.929

► Ver solución al pié

Si ξt lím sup = -0,003 ► ξt lím As P M

Si M = 0 ► As -0.003 -1175 83.9 12.3

-1425 mm²fs ξ' f's β1 · c As N ρtot elegir AsMPa Mpa mm mm² KN mm²

26.6028420 0.00158104 316.2 22.27 18.06 90.23382 0 N Φ420 0.00158176 316.4 22.26 18.29 90.06052 0 N 0.9420 0.00158249 316.5 22.26 18.53 89.88677 0 N ξt420 0.00158322 316.6 22.26 18.76 89.71256 0 N 0.022332420 0.00158394 316.8 22.25 19 89.5379 0 N420 0.00158467 316.9 22.25 19.23 89.36278 0 N420 0.0015854 317.1 22.24 19.47 89.18721 0 N420 0.00158613 317.2 22.24 19.71 89.01117 0.001 N420 0.00158685 317.4 22.24 19.94 88.83466 0.001 N420 0.00158758 317.5 22.23 20.18 88.6577 0.001 N420 0.00158831 317.7 22.23 20.42 88.48026 0.001 N420 0.00158903 317.8 22.23 20.66 88.30236 0.001 N420 0.00158976 318 22.22 20.9 88.12398 0.001 N420 0.00159049 318.1 22.22 21.14 87.94514 0.001 N420 0.00159122 318.2 22.22 21.38 87.76581 0.001 N420 0.00159194 318.4 22.21 21.62 87.58601 0.001 N420 0.00159267 318.5 22.21 21.87 87.40573 0.001 N420 0.0015934 318.7 22.21 22.11 87.22497 0.001 N420 0.00159412 318.8 22.2 22.35 87.04372 0.001 N420 0.00159485 319 22.2 22.6 86.86199 0.001 N420 0.00159558 319.1 22.2 22.84 86.67977 0.001 N420 0.00159631 319.3 22.19 23.09 86.49707 0.001 N420 0.00159703 319.4 22.19 23.34 86.31386 0.001 N420 0.00159776 319.6 22.18 23.58 86.13017 0.001 N420 0.00159849 319.7 22.18 23.83 85.94598 0.001 N420 0.00159921 319.8 22.18 24.08 85.76129 0.001 N420 0.00159994 320 22.17 24.33 85.5761 0.001 N420 0.00160067 320.1 22.17 24.58 85.3904 0.001 N420 0.00160139 320.3 22.17 24.83 85.2042 0.001 N420 0.00160212 320.4 22.16 25.08 85.0175 0.001 N420 0.00160285 320.6 22.16 25.33 84.83028 0.001 N420 0.00160358 320.7 22.16 25.59 84.64255 0.001 N420 0.0016043 320.9 22.15 25.84 84.45431 0.001 N420 0.00160503 321 22.15 26.09 84.26555 0.001 N420 0.00160576 321.2 22.15 26.35 84.07627 0.001 E420 0.00160648 321.3 22.14 26.6 83.88647 0.001 S420 0.00160721 321.4 22.14 26.86 83.69615 0.001 N420 0.00160794 321.6 22.14 27.12 83.5053 0.001 N420 0.00160867 321.7 22.13 27.37 83.31392 0.001 N420 0.00160939 321.9 22.13 27.63 83.12202 0.001 N420 0.00161012 322 22.13 27.89 82.92958 0.001 N420 0.00161085 322.2 22.12 28.15 82.7366 0.001 N420 0.00161157 322.3 22.12 28.41 82.54309 0.001 N420 0.0016123 322.5 22.11 28.67 82.34904 0.001 N420 0.00161303 322.6 22.11 28.93 82.15444 0.001 N420 0.00161376 322.8 22.11 29.19 81.9593 0.001 N

Si ξt lím sup = ξt máx

420 0.00161448 322.9 22.1 29.46 81.76361 0.001 N420 0.00161521 323 22.1 29.72 81.56738 0.001 N420 0.00161594 323.2 22.1 29.99 81.37059 0.001 N420 0.00161666 323.3 22.09 30.25 81.17324 0.001 N420 0.00161739 323.5 22.09 30.52 80.97534 0.001 N420 0.00161812 323.6 22.09 30.78 80.77687 0.001 N420 0.00161885 323.8 22.08 31.05 80.57785 0.001 N420 0.00161957 323.9 22.08 31.32 80.37826 0.001 N420 0.0016203 324.1 22.08 31.59 80.1781 0.001 N420 0.00162103 324.2 22.07 31.86 79.97737 0.001 N420 0.00162175 324.4 22.07 32.13 79.77607 0.001 N420 0.00162248 324.5 22.07 32.4 79.57419 0.001 N420 0.00162321 324.6 22.06 32.67 79.37174 0.001 N420 0.00162393 324.8 22.06 32.94 79.1687 0.001 N420 0.00162466 324.9 22.06 33.22 78.96508 0.001 N420 0.00162539 325.1 22.05 33.49 78.76088 0.001 N420 0.00162612 325.2 22.05 33.77 78.55608 0.001 N420 0.00162684 325.4 22.05 34.04 78.35069 0.001 N420 0.00162757 325.5 22.04 34.32 78.14471 0.001 N420 0.0016283 325.7 22.04 34.6 77.93813 0.001 N420 0.00162902 325.8 22.03 34.88 77.73096 0.001 N420 0.00162975 326 22.03 35.15 77.52317 0.001 N420 0.00163048 326.1 22.03 35.43 77.31479 0.001 N420 0.00163121 326.2 22.02 35.71 77.10579 0.001 N420 0.00163193 326.4 22.02 36 76.89618 0.001 N420 0.00163266 326.5 22.02 36.28 76.68596 0.001 N420 0.00163339 326.7 22.01 36.56 76.47513 0.001 N420 0.00163411 326.8 22.01 36.85 76.26367 0.001 N420 0.00163484 327 22.01 37.13 76.05159 0.001 N420 0.00163557 327.1 22 37.42 75.83888 0.001 N420 0.0016363 327.3 22 37.7 75.62554 0.001 N420 0.00163702 327.4 22 37.99 75.41157 0.001 N420 0.00163775 327.5 21.99 38.28 75.19697 0.001 N420 0.00163848 327.7 21.99 38.57 74.98173 0.001 N420 0.0016392 327.8 21.99 38.86 74.76585 0.001 N420 0.00163993 328 21.98 39.15 74.54932 0.001 N420 0.00164066 328.1 21.98 39.44 74.33215 0.001 N420 0.00164138 328.3 21.98 39.73 74.11433 0.001 N420 0.00164211 328.4 21.97 40.02 73.89585 0.001 N420 0.00164284 328.6 21.97 40.32 73.67672 0.001 N420 0.00164357 328.7 21.97 40.61 73.45693 0.001 N420 0.00164429 328.9 21.96 40.91 73.23647 0.001 N420 0.00164502 329 21.96 41.21 73.01535 0.001 N420 0.00164575 329.1 21.96 41.5 72.79356 0.001 N420 0.00164647 329.3 21.95 41.8 72.5711 0.001 N420 0.0016472 329.4 21.95 42.1 72.34796 0.001 N420 0.00164793 329.6 21.95 42.4 72.12415 0.001 N420 0.00164866 329.7 21.94 42.7 71.89965 0.001 N420 0.00164938 329.9 21.94 43 71.67446 0.001 N420 0.00165011 330 21.93 43.31 71.44859 0.001 N420 0.00165084 330.2 21.93 43.61 71.22203 0.001 N420 0.00165156 330.3 21.93 43.92 70.99476 0.001 N420 0.00165229 330.5 21.92 44.22 70.7668 0.001 N420 0.00165302 330.6 21.92 44.53 70.53814 0.001 N

420 0.00165375 330.7 21.92 44.84 70.30877 0.001 N

Solución para toda la sección traccionadaAsmm²NA

Mu N b h d' f'c β1 As1KNm KN mm mm mm Mpa mm²

300 30 200 500 25 30 0.85 3750

ξt lím ξt Φ fs ξ' f's β1 · c Mred Nred Nredlím0.004 Mpa Mpa mm

-0.003 0.65 -420 -420 500 0 1.235 0.955 0 0.826ξt máx -0.00209 0.65 -418 -0.00295 -420 500 0.001 1.233 0.955 0 0.825

0.05 -0.00195 0.65 -389.6 -0.00294 -420 500 0.011 1.21 0.955 0.004 0.816-0.00181 0.65 -361.3 -0.00294 -420 500 0.021 1.187 0.955 0.009 0.806-0.00166 0.65 -332.9 -0.00293 -420 500 0.032 1.164 0.955 0.013 0.797-0.00152 0.65 -304.6 -0.00292 -420 500 0.042 1.141 0.955 0.017 0.788-0.00138 0.65 -276.2 -0.00291 -420 500 0.053 1.118 0.955 0.021 0.779-0.00124 0.65 -247.8 -0.00291 -420 500 0.063 1.095 0.955 0.025 0.77

-0.0011 0.65 -219.5 -0.0029 -420 500 0.073 1.072 0.955 0.029 0.76-0.00096 0.65 -191.1 -0.00289 -420 500 0.084 1.049 0.955 0.033 0.751-0.00081 0.65 -162.8 -0.00288 -420 500 0.094 1.026 0.955 0.038 0.742-0.00067 0.65 -134.4 -0.00288 -420 500 0.104 1.003 0.955 0.042 0.733-0.00053 0.65 -106 -0.00287 -420 490 0.12 0.969 0.955 0.051 0.713-0.00039 0.65 -77.68 -0.00286 -420 464 0.144 0.917 0.917 0.069 0.674-0.00025 0.65 -49.32 -0.00286 -420 440 0.165 0.867 0.867 0.083 0.639

-0.0001 0.65 -20.96 -0.00285 -420 418 0.184 0.821 0.821 0.096 0.6063.7E-05 0.65 7.4 -0.00284 -420 399 0.201 0.776 0.776 0.107 0.5750.00018 0.65 35.76 -0.00283 -420 381 0.217 0.733 0.733 0.117 0.5460.00032 0.65 64.12 -0.00283 -420 365 0.232 0.692 0.692 0.125 0.5190.00046 0.65 92.48 -0.00282 -420 350 0.245 0.653 0.653 0.133 0.493

0.0006 0.65 120.84 -0.00281 -420 336 0.259 0.614 0.614 0.14 0.4690.00075 0.65 149.2 -0.0028 -420 323 0.271 0.577 0.577 0.146 0.4450.00089 0.65 177.56 -0.0028 -420 312 0.283 0.541 0.541 0.152 0.4230.00103 0.65 205.92 -0.00279 -420 301 0.295 0.506 0.506 0.158 0.4020.00117 0.65 234.28 -0.00278 -420 290 0.306 0.472 0.472 0.163 0.3810.00131 0.65 262.64 -0.00277 -420 281 0.318 0.438 0.438 0.168 0.3610.00146 0.65 291 -0.00277 -420 272 0.328 0.405 0.405 0.173 0.342

0.0016 0.65 319.36 -0.00276 -420 263 0.339 0.373 0.373 0.177 0.3240.00174 0.65 347.72 -0.00275 -420 256 0.35 0.341 0.341 0.181 0.3060.00188 0.65 376.08 -0.00274 -420 248 0.36 0.31 0.31 0.185 0.2890.00202 0.652 404.44 -0.00274 -420 241 0.371 0.28 0.28 XX 0.19 0.2720.00216 0.664 420 -0.00273 -420 235 0.384 0.265 0.265 0.196 0.2650.00231 0.675 420 -0.00272 -420 228 0.39 0.262 0.262 0.199 0.2620.00245 0.687 420 -0.00271 -420 222 0.397 0.26 0.26 0.202 0.260.00259 0.699 420 -0.00271 -420 217 0.403 0.258 0.258 0.205 0.2580.00273 0.711 420 -0.0027 -420 211 0.41 0.255 0.255 0.208 0.2550.00287 0.723 420 -0.00269 -420 206 0.416 0.253 0.253 0.211 0.2530.00301 0.735 420 -0.00268 -420 201 0.422 0.251 0.251 0.214 0.2510.00316 0.746 420 -0.00268 -420 197 0.428 0.25 0.25 0.217 0.25

0.0033 0.758 420 -0.00267 -420 192 0.435 0.248 0.248 0.22 0.2480.00344 0.77 420 -0.00266 -420 188 0.441 0.246 0.246 0.222 0.2460.00358 0.782 420 -0.00265 -420 184 0.447 0.245 0.245 0.225 0.2450.00372 0.794 420 -0.00265 -420 180 0.453 0.243 0.243 0.228 0.2430.00387 0.805 420 -0.00264 -420 176 0.459 0.242 0.242 0.23 0.2420.00401 0.817 420 -0.00263 -420 173 0.465 0.24 0.24 0.233 0.240.00415 0.829 420 -0.00262 -420 169 0.471 0.239 0.239 0.236 0.2390.00429 0.841 420 -0.00262 -420 166 0.477 0.237 0.237 0.238 0.237

0.00443 0.853 420 -0.00261 -420 163 0.483 0.236 0.236 0.241 0.2360.00457 0.865 420 -0.0026 -420 160 0.488 0.235 0.235 0.243 0.2350.00472 0.876 420 -0.00259 -420 157 0.494 0.234 0.234 0.246 0.2340.00486 0.888 420 -0.00259 -420 154 0.5 0.233 0.233 0.248 0.233

0.005 0.9 420 -0.00258 -420 151 0.506 0.232 0.232 XX 0.251 0.2320.0059 0.9 420 -0.00253 -420 136 0.501 0.208 0.208 0.246 0.2080.0068 0.9 420 -0.00248 -420 124 0.496 0.189 0.189 0.241 0.1890.0077 0.9 420 -0.00244 -420 113 0.492 0.173 0.173 0.237 0.1730.0086 0.9 420 -0.00239 -420 104 0.488 0.16 0.16 0.233 0.160.0095 0.9 420 -0.00234 -420 96.9 0.485 0.148 0.148 0.23 0.1480.0104 0.9 420 -0.00229 -420 90.39 0.482 0.138 0.138 0.227 0.1380.0113 0.9 420 -0.00225 -420 84.7 0.479 0.13 0.13 0.224 0.130.0122 0.9 420 -0.0022 -420 79.69 0.476 0.122 0.122 0.221 0.1220.0131 0.9 420 -0.00215 -420 75.23 0.474 0.115 0.115 0.219 0.115

0.014 0.9 420 -0.00211 -420 71.25 0.472 0.109 0.109 0.217 0.1090.0149 0.9 420 -0.00206 -411.6 67.67 0.466 0.094 0.094 0.213 0.10.0158 0.9 420 -0.00201 -402.1 64.43 0.459 0.078 0.078 0.209 0.0910.0167 0.9 420 -0.00196 -392.6 61.48 0.453 0.063 0.063 0.206 0.0820.0176 0.9 420 -0.00192 -383.2 58.8 0.446 0.049 0.049 0.202 0.0730.0185 0.9 420 -0.00187 -373.7 56.34 0.44 0.034 0.034 0.199 0.0650.0194 0.9 420 -0.00182 -364.2 54.07 0.434 0.02 0.02 0.196 0.0580.0203 0.9 420 -0.00177 -354.7 52 0.428 0.006 0.006 0.193 0.050.0212 0.9 420 -0.00173 -345.3 50.05 0.422 -0.007 -0.007 0.189 0.0430.0221 0.9 420 -0.00168 -335.8 48.26 0.416 -0.021 -0.021 0.186 0.036

0.023 0.9 420 -0.00163 -326.3 46.59 0.41 -0.034 -0.034 0.183 0.0290.0239 0.9 420 -0.00158 -316.8 45 0.404 -0.047 -0.047 0.181 0.0220.0248 0.9 420 -0.00154 -307.4 43.57 0.399 -0.06 -0.06 0.178 0.0160.0257 0.9 420 -0.00149 -297.9 42.2 0.393 -0.073 -0.073 0.175 0.010.0266 0.9 420 -0.00144 -288.4 40.92 0.387 -0.085 -0.085 0.172 0.0030.0275 0.9 420 -0.00139 -278.9 39.71 0.382 -0.098 -0.098 0.17 00.0284 0.9 420 -0.00135 -269.5 38.57 0.376 -0.11 -0.11 0.167 -0.0090.0293 0.9 420 -0.0013 -260 37.5 0.371 -0.123 -0.123 0.164 -0.0150.0302 0.9 420 -0.00125 -250.5 36.48 0.365 -0.135 -0.135 0.162 -0.020.0311 0.9 420 -0.00121 -241.1 35.52 0.36 -0.147 -0.147 0.159 -0.026

0.032 0.9 420 -0.00116 -231.6 34.61 0.355 -0.159 -0.159 0.157 -0.0320.0329 0.9 420 -0.00111 -222.1 33.74 0.349 -0.171 -0.171 0.154 -0.0370.0338 0.9 420 -0.00106 -212.6 32.91 0.344 -0.183 -0.183 0.152 -0.0430.0347 0.9 420 -0.00102 -203.2 32.13 0.338 -0.195 -0.195 0.149 -0.0480.0356 0.9 420 -0.00097 -193.7 31.38 0.333 -0.207 -0.207 0.147 -0.0540.0365 0.9 420 -0.00092 -184.2 30.66 0.328 -0.218 -0.218 0.144 -0.0590.0374 0.9 420 -0.00087 -174.7 30 0.323 -0.23 -0.23 0.142 -0.0640.0383 0.9 420 -0.00083 -165.3 29.33 0.317 -0.242 -0.242 0.14 -0.070.0392 0.9 420 -0.00078 -155.8 28.7 0.312 -0.253 -0.253 0.137 -0.0750.0401 0.9 420 -0.00073 -146.3 28.1 0.307 -0.265 -0.265 0.135 -0.08

0.041 0.9 420 -0.00068 -136.8 27.53 0.302 -0.276 -0.276 0.133 -0.0850.0419 0.9 420 -0.00064 -127.4 27 0.297 -0.288 -0.288 0.13 -0.090.0428 0.9 420 -0.00059 -117.9 26.45 0.291 -0.299 -0.299 0.128 -0.0950.0437 0.9 420 -0.00054 -108.4 25.94 0.286 -0.311 -0.311 0.126 -0.1010.0446 0.9 420 -0.00049 -98.95 25.45 0.281 -0.322 -0.322 0.124 -0.1060.0455 0.9 420 -0.00045 -89.47 25 0.276 -0.334 -0.334 0.121 -0.1110.0464 0.9 420 -0.0004 -80 24.52 0.271 -0.345 -0.345 0.119 -0.1150.0473 0.9 420 -0.00035 -70.53 24.08 0.266 -0.356 -0.356 0.117 -0.120.0482 0.9 420 -0.00031 -61.05 23.66 0.261 -0.368 -0.368 0.115 -0.1250.0491 0.9 420 -0.00026 -51.58 23.25 0.256 -0.379 -0.379 0.112 -0.13

0.05 0.9 420 -0.00021 -42.11 22.85 0.251 -0.39 -0.39 0.11 -0.135

375.9 -1170

As2mm²

1500

0.6470.6470.6470.6470.6470.6470.6470.6470.6470.6470.6470.6470.6470.6470.6390.6060.5750.5460.5190.4930.4690.4450.4230.4020.3810.3610.3420.3240.3060.2890.2720.2650.262

0.260.2580.2550.2530.251

0.250.2480.2460.2450.2430.242

0.240.2390.237

0 0.1 0.2 0.3 0.4 0.5 0.6

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Gráfico de interacción

M/(b · h · f'c)

N/ (b · h · f'c)

0 0.05 0.1 0.15 0.2 0.25 0.3

-0.2

0

0.2

0.4

0.6

0.8

1

Interacción

M/(b · h · f'c)

N/ (b · h · f'c)

0.2360.2350.2340.2330.2320.2080.1890.173

0.160.1480.138

0.130.1220.1150.109

0.10.0910.0820.0730.0650.058

0.050.0430.0360.0290.0220.016

0.010.003

0-0.009-0.015

-0.02-0.026-0.032-0.037-0.043-0.048-0.054-0.059-0.064

-0.07-0.075

-0.08-0.085

-0.09-0.095-0.101-0.106-0.111-0.115

-0.12-0.125

-0.13

-0.135

0 0.1 0.2 0.3 0.4 0.5 0.6

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Gráfico de interacción

M/(b · h · f'c)

N/ (b · h · f'c)

0 0.05 0.1 0.15 0.2 0.25 0.3

-0.2

0

0.2

0.4

0.6

0.8

1

Interacción

M/(b · h · f'c)

N/ (b · h · f'c)

Mu N b h d' f'c β1KNm KN mm mm mm Mpa Flexión pura

400 0 200 500 25 20 0.85 Para rec. Relativos grandes o chicos no hay solución.

Caso 1: Si el recubrimiento es muy chico no hay forma de eliminar la fuerza de compresión ξt Φ fs ξ' f's β1 · c As N en el Hº, puede aumentarse la armadura traccionada y disminuírse la comprimida.

Mpa Mpa mm mm² N0.004 0.8167 420 -0.0026 -420 173.04 2082.6 480462 N

ξt máx 0.0049 0.8933 420 -0.0026 -420 152.94 1891.7 464516 N Si es muy grande está toda la armadura traccionada 0.05 0.0058 0.9 420 -0.0025 -420 137.02 1904.2 419279 N y no hay compresiones suficientes para anularla, se debe redimensionar.

0.0068 0.9 420 -0.0025 -420 124.1 1932 379757 N0.0077 0.9 420 -0.0024 -420 113.41 1957.2 347044 N0.0086 0.9 420 -0.0024 -420 104.42 1980 319519 N Solución caso 10.0095 0.9 420 -0.0023 -420 96.745 2000.6 296040 N ΔAs+As0.0104 0.9 420 -0.0023 -420 90.123 2019.3 275776 N 2345.98 21555.680.0114 0.9 420 -0.0022 -420 84.349 2036.2 258108 N M N0.0123 0.9 420 -0.0022 -420 79.27 2051.6 242567 N 400 -7.9E-110.0132 0.9 420 -0.0021 -420 74.769 2065.6 228792 N0.0141 0.9 420 -0.0021 -419.79 70.751 2078.9 216103 N

0.015 0.9 420 -0.0021 -410.11 67.142 2115.1 186621 N0.016 0.9 420 -0.002 -400.42 63.884 2151.1 157582 N

0.0169 0.9 420 -0.002 -390.74 60.928 2187.1 128838 N0.0178 0.9 420 -0.0019 -381.05 58.233 2223.2 100263 N0.0187 0.9 420 -0.0019 -371.37 55.767 2259.5 71749 N0.0196 0.9 420 -0.0018 -361.68 53.5 2296.1 43203 N0.0206 0.9 420 -0.0018 -352 51.411 2333 14540 E0.0215 0.9 420 -0.0017 -342.32 49.479 2370.3 -14312 N0.0224 0.9 420 -0.0017 -332.63 47.687 2408 -43423 N0.0233 0.9 420 -0.0016 -322.95 46.02 2446.3 -72854 N0.0242 0.9 420 -0.0016 -313.26 44.466 2485.1 -1E+05 N0.0252 0.9 420 -0.0015 -303.58 43.013 2524.7 -1E+05 N0.0261 0.9 420 -0.0015 -293.89 41.652 2564.9 -2E+05 N

0.027 0.9 420 -0.0014 -284.21 40.375 2605.9 -2E+05 N0.0279 0.9 420 -0.0014 -274.53 39.174 2647.7 -2E+05 N0.0288 0.9 420 -0.0013 -264.84 38.042 2690.4 -3E+05 N0.0298 0.9 420 -0.0013 -255.16 36.973 2734.1 -3E+05 N0.0307 0.9 420 -0.0012 -245.47 35.963 2778.8 -3E+05 N0.0316 0.9 420 -0.0012 -235.79 35.007 2824.6 -4E+05 N0.0325 0.9 420 -0.0011 -226.11 34.101 2871.5 -4E+05 N0.0334 0.9 420 -0.0011 -216.42 33.24 2919.6 -4E+05 N0.0344 0.9 420 -0.001 -206.74 32.421 2969 -5E+05 N0.0353 0.9 420 -0.001 -197.05 31.642 3019.7 -5E+05 N0.0362 0.9 420 -0.0009 -187.37 30.899 3071.9 -5E+05 N0.0371 0.9 420 -0.0009 -177.68 30.191 3125.6 -6E+05 N

0.038 0.9 420 -0.0008 -168 29.514 3180.9 -6E+05 N0.039 0.9 420 -0.0008 -158.32 28.867 3237.9 -7E+05 N

0.0399 0.9 420 -0.0007 -148.63 28.247 3296.7 -7E+05 N0.0408 0.9 420 -0.0007 -138.95 27.654 3357.4 -8E+05 N0.0417 0.9 420 -0.0006 -129.26 27.085 3420.1 -8E+05 N0.0426 0.9 420 -0.0006 -119.58 26.539 3484.9 -9E+05 N0.0436 0.9 420 -0.0005 -109.89 26.015 3551.9 -9E+05 N0.0445 0.9 420 -0.0005 -100.21 25.511 3621.3 -1E+06 N0.0454 0.9 420 0 -90.526 25.026 3693.2 -1E+06 N0.0463 0.9 420 0 -80.842 24.559 3767.8 -1E+06 N

A`s-ΔA's

0.0472 0.9 420 0 -71.158 24.109 3845.2 -1E+06 N0.0482 0.9 420 0 -61.474 23.676 3925.7 -1E+06 N0.0491 0.9 420 0 -51.789 23.257 4009.3 -1E+06 N

0.05 0.9 420 0 -42.105 22.854 4096.3 -1E+06 N

Para rec. Relativos grandes o chicos no hay solución.

Caso 1: Si el recubrimiento es muy chico no hay forma de eliminar la fuerza de compresión en el Hº, puede aumentarse la armadura traccionada y disminuírse la comprimida.

Si es muy grande está toda la armadura traccionada y no hay compresiones suficientes para anularla, se debe redimensionar.

1ra zona: ξt<= -0,0021 ; fs = f's = -420 Mpa ; β1 · c = h ; Φ= 0,65 2da zona: β1· 0,003 · (1 - d'/h) - 0,003 >= ξt > -0,021 ; fs = ξt · E ; f's = -420 MPa ; β1 · c = h ; Φ = 0,65 3ra zona: 0,002 >= ξt > β1· 0,003 · (1 - d'/h) - 0,003 ; fs = ξt · E ; f's = -420 MPa ; β1 · c = β1 · 0,003 · (h - d') / (0,003 + ξt) ; Φ = 0,65 4ta zona: varían fs, β1 · c y Φ, por su complejidad se la evita5ta zona: (-0,0021+ 0,003) · (h-d') / d' - 0,003 >= ξt >=0,0021 ; fs = 420 Mpa ; f's = -420 Mpa ; β1 · c = variable ; Φ = 0,48 + 83 · ξt6ta zona: 0,005 > ξt > (-0,0021+ 0,003) · (h-d') / d' - 0,003 ; fs = 420 Mpa ; f's = E · [(0,003 + ξt) · d' / (h - d') - 0,003] ; β1 · c = variable ; Φ = 0,48 + 83 · ξt7ma zona: (-0,0021+ 0,003) · (h/d' - 1) - 0,003 >= ξt >= 0,005 ; fs = 420 Mpa ; f's = -420MPa ; β1 · c = variable ; Φ = 0,98va zona: ξt > (-0,0021+ 0,003) · (h/d' - 1) - 0,003 ; fs = 420 Mpa ; f's = E · [(0,003 + ξt) · d' / (h - d') - 0,003] ; β1 · c = variable ; Φ = 0,9

η = N/(bhf'c)m = M/(bh^2f'c)ρtot = 2 · As · fy / (b · h · f'c) La zona 5 tiene validez para 0,15 > d'/h > 0,1012f'c = 30 Se obvia el caso 5β1 = 0.85 ρtot =

d'/h = 0.05 ρtot = 0.21β1 = 0.85 ξtlímsup 0.21 0.42 0.63 0.84 1.05 η caso ξt2

ηlím1: -0.0021 0.689 0.8255 0.962 1.0985 1.235 0.9558 0ηlím2: -0.000577 0.63952 0.72654 0.8136 0.9006 0.9876 0.9462 0ηlím3: 0.002 0.27094 0.27419 0.2774 0.2807 0.2839 0.9367 0ηlím4: 0.0021 0.2658 0.2658 0.2658 0.2658 0.2658 0.9271 0ηlím5: 0.0141 0.10837 0.10837 0.1084 0.1084 0.1084 0.9176 0ηlím6: 0.005 0.23165 0.23165 0.2317 0.2317 0.2317 0.908 0ηlím7: 0.0141 0.10837 0.10837 0.1084 0.1084 0.1084 0.8985 0ηlím8: 0.8889 0

0.8793 0Φpnmáx= 0.54457 0.64714 0.7497 0.8523 0.9549 0.8698 0

0.8602 00.8507 00.8411 00.8316 0

0.822 00.8124 00.8029 00.7933 00.7838 00.7742 00.7646 00.7551 00.7455 0

0.736 00.7264 00.7169 00.7073 00.6977 00.6882 2 00.6786 2 00.6691 2 00.6595 2 00.6499 2 00.6404 2 00.6308 30.6213 30.6117 3

0.6022 30.5926 3

0.583 30.5735 30.5639 30.5544 30.5448 30.5353 30.5257 30.5161 30.5066 3

0.497 30.4875 30.4779 30.4683 30.4588 30.4492 30.4397 30.4301 30.4206 3

0.411 30.4014 30.3919 30.3823 30.3728 30.3632 30.3536 30.3441 30.3345 3

0.325 30.3154 30.3059 30.2963 30.2867 30.2772 30.2676 40.2581 60.2485 6

0.239 60.2294 70.2198 70.2103 70.2007 70.1912 70.1816 7

0.172 70.1625 70.1529 70.1434 70.1338 70.1243 70.1147 70.1051 80.0956 8

0.086 80.0765 80.0669 80.0573 80.0478 80.0382 80.0287 80.0191 80.0096 82E-15 8

2da zona: β1· 0,003 · (1 - d'/h) - 0,003 >= ξt > -0,021 ; fs = ξt · E ; f's = -420 MPa ; β1 · c = h ; Φ = 0,65 3ra zona: 0,002 >= ξt > β1· 0,003 · (1 - d'/h) - 0,003 ; fs = ξt · E ; f's = -420 MPa ; β1 · c = β1 · 0,003 · (h - d') / (0,003 + ξt) ; Φ = 0,65

5ta zona: (-0,0021+ 0,003) · (h-d') / d' - 0,003 >= ξt >=0,0021 ; fs = 420 Mpa ; f's = -420 Mpa ; β1 · c = variable ; Φ = 0,48 + 83 · ξt6ta zona: 0,005 > ξt > (-0,0021+ 0,003) · (h-d') / d' - 0,003 ; fs = 420 Mpa ; f's = E · [(0,003 + ξt) · d' / (h - d') - 0,003] ; β1 · c = variable ; Φ = 0,48 + 83 · ξt7ma zona: (-0,0021+ 0,003) · (h/d' - 1) - 0,003 >= ξt >= 0,005 ; fs = 420 Mpa ; f's = -420MPa ; β1 · c = variable ; Φ = 0,98va zona: ξt > (-0,0021+ 0,003) · (h/d' - 1) - 0,003 ; fs = 420 Mpa ; f's = E · [(0,003 + ξt) · d' / (h - d') - 0,003] ; β1 · c = variable ; Φ = 0,9

La zona 5 tiene validez para 0,15 > d'/h > 0,1012Se obvia el caso 5

b c ξt3 b c ξt4 ξt6 ξt7 b c ξt8 ξt fs f's Φ00000000000000000000000000000 -415 -420 0.650 -356 -420 0.650 -297 -420 0.650 -238 -420 0.650 -180 -420 0.650 -121 -420 0.65

0.02 1E-05 0 0 -109 -420 0.650.02 1E-05 0 0 -101 -420 0.650.02 9E-06 0 0 -93.31 -420 0.65

0.019 8E-06 0 0 -85.27 -420 0.650.019 7E-06 0 0 -77 -420 0.650.019 6E-06 0 0 -68.52 -420 0.650.019 5E-06 0 0 -59.78 -420 0.650.018 5E-06 0 0 -50.81 -420 0.650.018 4E-06 0 0 -41.58 -420 0.650.018 3E-06 0 0 -32.08 -420 0.650.017 2E-06 0 0 -22.31 -420 0.650.017 1E-06 -6E-05 -6E-05 -12.26 -420 0.650.017 2E-07 -1E-05 -1E-05 -1.916 -420 0.650.016 -7E-07 4E-05 4E-05 8.73 -420 0.650.016 -2E-06 1E-04 1E-04 19.69 -420 0.650.016 -2E-06 0 0 30.97 -420 0.650.016 -3E-06 0 0 42.59 -420 0.650.015 -4E-06 0 0 54.55 -420 0.650.015 -5E-06 0 0 66.88 -420 0.650.015 -6E-06 0 0 79.57 -420 0.650.014 -7E-06 0 0 92.64 -420 0.650.014 -8E-06 0.001 0.001 106.1 -420 0.650.014 -9E-06 0.001 0.001 120 -420 0.650.014 -1E-05 0.001 0.001 134.3 -420 0.650.013 -1E-05 0.001 0.001 149 -420 0.650.013 -1E-05 0.001 0.001 164.2 -420 0.650.013 -1E-05 0.001 0.001 179.8 -420 0.650.012 -1E-05 0.001 0.001 195.9 -420 0.650.012 -1E-05 0.001 0.001 212.5 -420 0.650.012 -1E-05 0.001 0.001 229.5 -420 0.650.011 -2E-05 0.001 0.001 247.1 -420 0.650.011 -2E-05 0.001 0.001 265.2 -420 0.650.011 -2E-05 0.001 0.001 283.9 -420 0.650.011 -2E-05 0.002 0.002 303.1 -420 0.65

0.01 -2E-05 0.002 0.002 322.8 -420 0.650.01 -2E-05 0.002 0.002 343.2 -420 0.650.01 -2E-05 0.002 0.002 364.1 -420 0.65

0.009 -2E-05 0.002 0.002 385.6 -420 0.650.009 -2E-05 0.002 0.002 407.7 -420 0.653

0.003 0.003 420 -420 0.6960.003 0.003 420 -420 0.7540.004 0.004 420 -420 0.828

0.005 0.005 420 -420 0.90.005 0.005 420 -420 0.90.006 0.006 420 -420 0.90.006 0.006 420 -420 0.90.007 0.007 420 -420 0.90.007 0.007 420 -420 0.90.008 0.008 420 -420 0.90.008 0.008 420 -420 0.90.009 0.009 420 -420 0.9

0.01 0.01 420 -420 0.90.011 0.011 420 -420 0.90.012 0.012 420 -420 0.90.013 0.013 420 -420 0.9

0.033 0 0.014 0.014 420 -416 0.90.029 0 0.016 0.016 420 -404 0.9

0.025 0 0.017 0.017 420 -390 0.90.021 0 0.018 0.018 420 -375 0.90.017 0 0.02 0.02 420 -358 0.90.013 0 0.022 0.022 420 -341 0.90.009 0 0.023 0.023 420 -321 0.90.005 0 0.025 0.025 420 -300 0.90.001 0 0.028 0.028 420 -278 0.9

0 0 0.03 0.03 420 -254 0.9-0.007 0 0.032 0.032 420 -229 0.9-0.011 0 0.035 0.035 420 -202 0.9

ρtot =0.42

m η caso ξt2 b c ξt3 b c ξt4 ξt6 ξt7 b0 0.9558 00 0.94625 00 0.93669 00 0.92713 00 0.91757 00 0.90801 00 0.89846 00 0.8889 00 0.87934 00 0.86978 00 0.86022 00 0.85067 00 0.84111 00 0.83155 00 0.82199 2 00 0.81243 2 00 0.80288 2 00 0.79332 2 00 0.78376 2 00 0.7742 2 00 0.76464 2 00 0.75509 2 00 0.74553 2 00 0.73597 2 00 0.72641 3 0.012 7E-06 00 0.71685 3 0.012 6E-06 00 0.7073 3 0.012 6E-06 00 0.69774 3 0.012 5E-06 0

1 0 0.68818 3 0.011 5E-06 01 0 0.67862 3 0.011 4E-06 01 0 0.66906 3 0.011 4E-06 01 0 0.65951 3 0.011 4E-06 01 0 0.64995 3 0.011 3E-06 01 0 0.64039 3 0.011 3E-06 0

0.986 0 0.63083 3 0.011 2E-06 00.971 0 0.62127 3 0.01 2E-06 00.956 0 0.61172 3 0.01 1E-06 0

β1 · c

0.941 0 0.60216 3 0.01 9E-07 -9E-050.926 0 0.5926 3 0.01 5E-07 -5E-050.912 0 0.58304 3 0.01 2E-08 -2E-060.897 0 0.57348 3 0.01 -4E-07 4E-050.882 0 0.56392 3 0.01 -9E-07 9E-050.868 0 0.55437 3 0.009 -1E-06 00.853 0 0.54481 3 0.009 -2E-06 00.839 0.061 0.53525 3 0.009 -2E-06 00.824 0.064 0.52569 3 0.009 -3E-06 0

0.81 0.067 0.51613 3 0.009 -3E-06 00.796 0.069 0.50658 3 0.009 -4E-06 00.782 0.072 0.49702 3 0.009 -4E-06 00.768 0.075 0.48746 3 0.008 -4E-06 00.754 0.077 0.4779 3 0.008 -5E-06 0.001

0.74 0.08 0.46834 3 0.008 -5E-06 0.0010.727 0.082 0.45879 3 0.008 -6E-06 0.0010.713 0.085 0.44923 3 0.008 -6E-06 0.001

0.7 0.087 0.43967 3 0.008 -7E-06 0.0010.686 0.089 0.43011 3 0.008 -7E-06 0.0010.673 0.091 0.42055 3 0.007 -7E-06 0.001

0.66 0.093 0.411 3 0.007 -8E-06 0.0010.647 0.095 0.40144 3 0.007 -8E-06 0.0010.634 0.097 0.39188 3 0.007 -9E-06 0.0010.621 0.099 0.38232 3 0.007 -9E-06 0.0010.609 0.101 0.37276 3 0.007 -1E-05 0.0010.596 0.103 0.36321 3 0.006 -1E-05 0.0010.584 0.105 0.35365 3 0.006 -1E-05 0.0010.572 0.106 0.34409 3 0.006 -1E-05 0.001

0.56 0.108 0.33453 3 0.006 -1E-05 0.0020.548 0.11 0.32497 3 0.006 -1E-05 0.0020.536 0.111 0.31542 3 0.006 -1E-05 0.0020.525 0.113 0.30586 3 0.006 -1E-05 0.0020.514 0.114 0.2963 3 0.005 -1E-05 0.0020.503 0.116 0.28674 3 0.005 -1E-05 0.0020.492 0.118 0.27718 3 0.005 -1E-05 0.0020.481 0.12 0.26763 4 0.005 -1E-05 0.0020.436 0.128 0.25807 6 0.002560.388 0.136 0.24851 6 0.00325

0.34 0.145 0.23895 6 0.004130.3 0.153 0.22939 7 0.005

0.287 0.152 0.21984 7 0.0050.275 0.15 0.21028 7 0.0060.262 0.148 0.20072 7 0.006

0.25 0.146 0.19116 7 0.0070.237 0.144 0.1816 7 0.0070.225 0.142 0.17204 7 0.0080.212 0.139 0.16249 7 0.008

0.2 0.137 0.15293 7 0.0090.187 0.135 0.14337 7 0.010.175 0.132 0.13381 7 0.0110.162 0.129 0.12425 7 0.012

0.15 0.126 0.1147 7 0.0130.139 0.123 0.10514 8 0.011

0.13 0.12 0.09558 8 0.009

0.121 0.117 0.08602 8 0.0070.113 0.113 0.07646 8 0.0050.106 0.11 0.06691 8 0.0030.098 0.106 0.05735 8 0.0010.091 0.102 0.04779 8 00.085 0.098 0.03823 8 00.079 0.094 0.02867 8 -0.0050.074 0.09 0.01912 8 -0.0070.069 0.087 0.00956 8 -0.0090.064 0.082 2E-15 8 -0.011

ρtot =0.63

c ξt8 ξt fs f's Φ m η caso ξt2 b c ξt3 b0 0 0.9558 2 00 0 0.94625 2 00 0 0.93669 2 00 0 0.92713 2 00 0 0.91757 2 00 0 0.90801 2 00 0 0.89846 2 00 0 0.8889 2 00 0 0.87934 2 00 0 0.86978 2 00 0 0.86022 2 00 0 0.85067 2 00 0 0.84111 2 00 0 0.83155 2 00 -409 -420 0.65 1 0 0.82199 2 00 -380 -420 0.65 1 0 0.81243 3 0.009 5E-06 -0.0010 -350 -420 0.65 1 0 0.80288 3 0.009 5E-06 -0.0010 -321 -420 0.65 1 0 0.79332 3 0.009 4E-06 -0.0010 -292 -420 0.65 1 0 0.78376 3 0.009 4E-06 00 -262 -420 0.65 1 0 0.7742 3 0.009 4E-06 00 -233 -420 0.65 1 0 0.76464 3 0.009 4E-06 00 -203 -420 0.65 1 0 0.75509 3 0.009 3E-06 00 -174 -420 0.65 1 0 0.74553 3 0.009 3E-06 00 -145 -420 0.65 1 0 0.73597 3 0.008 3E-06 00 -115 -420 0.65 1 0 0.72641 3 0.008 2E-06 00 -109 -420 0.65 0.986 0 0.71685 3 0.008 2E-06 00 -102 -420 0.65 0.973 0 0.7073 3 0.008 2E-06 00 -95.21 -420 0.65 0.96 0 0.69774 3 0.008 1E-06 00 -88.19 -420 0.65 0.947 0 0.68818 3 0.008 1E-06 00 -81 -420 0.65 0.934 0 0.67862 3 0.008 9E-07 00 -73.69 -420 0.65 0.921 0 0.66906 3 0.008 6E-07 -7E-050 -66.21 -420 0.65 0.908 0 0.65951 3 0.008 3E-07 -3E-050 -58.57 -420 0.65 0.895 0 0.64995 3 0.008 -3E-08 4E-060 -50.77 -420 0.65 0.882 0.078 0.64039 3 0.007 -3E-07 4E-050 -42.81 -420 0.65 0.87 0.082 0.63083 3 0.007 -6E-07 8E-050 -34.67 -420 0.65 0.857 0.085 0.62127 3 0.007 -9E-07 0.00010 -26.36 -420 0.65 0.845 0.088 0.61172 3 0.007 -1E-06 0.0002

β1 · c

-9E-05 -17.88 -420 0.65 0.832 0.092 0.60216 3 0.007 -1E-06 0.0002-5E-05 -9.216 -420 0.65 0.82 0.095 0.5926 3 0.007 -2E-06 0.0002-2E-06 -0.372 -420 0.65 0.808 0.098 0.58304 3 0.007 -2E-06 0.00034E-05 8.659 -420 0.65 0.796 0.101 0.57348 3 0.007 -2E-06 0.00039E-05 17.88 -420 0.65 0.784 0.104 0.56392 3 0.007 -3E-06 0.0004

0 27.29 -420 0.65 0.772 0.107 0.55437 3 0.007 -3E-06 0.00040 36.89 -420 0.65 0.761 0.11 0.54481 3 0.006 -3E-06 0.00050 46.7 -420 0.65 0.749 0.112 0.53525 3 0.006 -4E-06 0.00050 56.7 -420 0.65 0.738 0.115 0.52569 3 0.006 -4E-06 0.00060 66.91 -420 0.65 0.726 0.118 0.51613 3 0.006 -4E-06 0.00060 77.33 -420 0.65 0.715 0.121 0.50658 3 0.006 -4E-06 0.00070 87.96 -420 0.65 0.704 0.123 0.49702 3 0.006 -5E-06 0.00070 98.79 -420 0.65 0.693 0.126 0.48746 3 0.006 -5E-06 0.0008

0.001 109.8 -420 0.65 0.683 0.128 0.4779 3 0.006 -5E-06 0.00080.001 121.1 -420 0.65 0.672 0.131 0.46834 3 0.006 -6E-06 0.00090.001 132.6 -420 0.65 0.661 0.133 0.45879 3 0.006 -6E-06 0.00090.001 144.3 -420 0.65 0.651 0.136 0.44923 3 0.006 -6E-06 0.0010.001 156.3 -420 0.65 0.641 0.138 0.43967 3 0.005 -6E-06 0.0010.001 168.4 -420 0.65 0.631 0.141 0.43011 3 0.005 -7E-06 0.00110.001 180.8 -420 0.65 0.62 0.143 0.42055 3 0.005 -7E-06 0.00110.001 193.5 -420 0.65 0.611 0.146 0.411 3 0.005 -7E-06 0.00120.001 206.3 -420 0.65 0.601 0.148 0.40144 3 0.005 -8E-06 0.00120.001 219.4 -420 0.65 0.591 0.15 0.39188 3 0.005 -8E-06 0.00130.001 232.7 -420 0.65 0.582 0.153 0.38232 3 0.005 -8E-06 0.00130.001 246.3 -420 0.65 0.573 0.155 0.37276 3 0.005 -9E-06 0.00140.001 260.1 -420 0.65 0.563 0.157 0.36321 3 0.005 -9E-06 0.00150.001 274.1 -420 0.65 0.554 0.16 0.35365 3 0.005 -9E-06 0.00150.001 288.4 -420 0.65 0.545 0.162 0.34409 3 0.004 -9E-06 0.00160.002 302.9 -420 0.65 0.537 0.164 0.33453 3 0.004 -1E-05 0.00160.002 317.6 -420 0.65 0.528 0.166 0.32497 3 0.004 -1E-05 0.00170.002 332.6 -420 0.65 0.519 0.169 0.31542 3 0.004 -1E-05 0.00180.002 347.9 -420 0.65 0.511 0.171 0.30586 3 0.004 -1E-05 0.00180.002 363.3 -420 0.65 0.503 0.173 0.2963 3 0.004 -1E-05 0.00190.002 379 -420 0.65 0.495 0.176 0.28674 3 0.004 -1E-05 0.00190.002 395 -420 0.65 0.487 0.178 0.27718 4 0.0040.002 411.1 -420 0.655 0.479 0.181 0.26763 4 0.0040.003 420 -420 0.696 0.436 0.193 0.25807 60.003 420 -420 0.754 0.388 0.207 0.24851 60.004 420 -420 0.828 0.34 0.224 0.23895 60.005 420 -420 0.9 0.3 0.238 0.22939 70.005 420 -420 0.9 0.287 0.237 0.21984 70.006 420 -420 0.9 0.275 0.235 0.21028 70.006 420 -420 0.9 0.262 0.233 0.20072 70.007 420 -420 0.9 0.25 0.231 0.19116 70.007 420 -420 0.9 0.237 0.229 0.1816 70.008 420 -420 0.9 0.225 0.227 0.17204 70.008 420 -420 0.9 0.212 0.224 0.16249 70.009 420 -420 0.9 0.2 0.222 0.15293 7

0.01 420 -420 0.9 0.187 0.22 0.14337 70.011 420 -420 0.9 0.175 0.217 0.13381 70.012 420 -420 0.9 0.162 0.214 0.12425 70.013 420 -420 0.9 0.15 0.212 0.1147 7

0 0.014 0.014 420 -417 0.9 0.139 0.208 0.10514 80 0.015 0.015 420 -407 0.9 0.132 0.205 0.09558 8

0 0.016 0.016 420 -397 0.9 0.126 0.201 0.08602 80 0.017 0.017 420 -387 0.9 0.12 0.198 0.07646 80 0.018 0.018 420 -376 0.9 0.114 0.194 0.06691 80 0.019 0.019 420 -364 0.9 0.108 0.19 0.05735 80 0.021 0.021 420 -352 0.9 0.103 0.186 0.04779 80 0.022 0.022 420 -339 0.9 0.098 0.182 0.03823 80 0.023 0.023 420 -326 0.9 0.093 0.178 0.02867 80 0.024 0.024 420 -312 0.9 0.089 0.174 0.01912 80 0.026 0.026 420 -298 0.9 0.084 0.17 0.00956 80 0.027 0.027 420 -283 0.9 0.08 0.166 2E-15 8

ρtot =0.84

c ξt4 ξt6 ξt7 b c ξt8 ξt fs f's Φ m η caso0 -407 -420 0.65 1 0 0.956 20 -388 -420 0.65 1 0 0.946 20 -368 -420 0.65 1 0 0.937 20 -348 -420 0.65 1 0 0.927 20 -329 -420 0.65 1 0 0.918 20 -309 -420 0.65 1 0 0.908 20 -290 -420 0.65 1 0 0.898 30 -270 -420 0.65 1 0 0.889 30 -250 -420 0.65 1 0 0.879 30 -231 -420 0.65 1 0 0.87 30 -211 -420 0.65 1 0 0.86 30 -192 -420 0.65 1 0 0.851 30 -172 -420 0.65 1 0 0.841 30 -152 -420 0.65 1 0 0.832 30 -133 -420 0.65 1 0 0.822 30 -115 -420 0.65 0.999 0 0.812 30 -109 -420 0.65 0.987 0 0.803 30 -103 -420 0.65 0.975 0 0.793 30 -96.7 -420 0.65 0.963 0 0.784 30 -90.46 -420 0.65 0.951 0 0.774 30 -84.12 -420 0.65 0.939 0 0.765 30 -77.66 -420 0.65 0.928 0 0.755 30 -71.1 -420 0.65 0.916 0.095 0.746 30 -64.43 -420 0.65 0.905 0.098 0.736 30 -57.64 -420 0.65 0.893 0.102 0.726 30 -50.75 -420 0.65 0.882 0.105 0.717 30 -43.74 -420 0.65 0.871 0.109 0.707 30 -36.61 -420 0.65 0.86 0.112 0.698 30 -29.37 -420 0.65 0.849 0.116 0.688 30 -22 -420 0.65 0.838 0.119 0.679 3

-7E-05 -14.54 -420 0.65 0.828 0.122 0.669 3-3E-05 -6.946 -420 0.65 0.817 0.126 0.66 34E-06 0.769 -420 0.65 0.806 0.129 0.65 34E-05 8.606 -420 0.65 0.796 0.132 0.64 38E-05 16.57 -420 0.65 0.786 0.135 0.631 3

0 24.65 -420 0.65 0.776 0.138 0.621 30 32.86 -420 0.65 0.766 0.141 0.612 3

β1 · c

0 41.19 -420 0.65 0.756 0.145 0.602 30 49.64 -420 0.65 0.746 0.148 0.593 30 58.23 -420 0.65 0.736 0.151 0.583 30 66.94 -420 0.65 0.726 0.153 0.573 30 75.78 -420 0.65 0.717 0.156 0.564 30 84.74 -420 0.65 0.708 0.159 0.554 30 93.84 -420 0.65 0.698 0.162 0.545 3

0.001 103.1 -420 0.65 0.689 0.165 0.535 30.001 112.4 -420 0.65 0.68 0.168 0.526 30.001 121.9 -420 0.65 0.671 0.171 0.516 30.001 131.5 -420 0.65 0.662 0.174 0.507 30.001 141.3 -420 0.65 0.654 0.176 0.497 30.001 151.1 -420 0.65 0.645 0.179 0.487 30.001 161.1 -420 0.65 0.637 0.182 0.478 30.001 171.3 -420 0.65 0.628 0.185 0.468 30.001 181.5 -420 0.65 0.62 0.187 0.459 30.001 191.9 -420 0.65 0.612 0.19 0.449 30.001 202.4 -420 0.65 0.604 0.193 0.44 30.001 213.1 -420 0.65 0.596 0.195 0.43 30.001 223.8 -420 0.65 0.588 0.198 0.421 30.001 234.7 -420 0.65 0.58 0.201 0.411 30.001 245.8 -420 0.65 0.573 0.204 0.401 30.001 256.9 -420 0.65 0.565 0.206 0.392 30.001 268.2 -420 0.65 0.558 0.209 0.382 30.001 279.6 -420 0.65 0.551 0.212 0.373 30.001 291.1 -420 0.65 0.544 0.214 0.363 30.002 302.8 -420 0.65 0.537 0.217 0.354 30.002 314.6 -420 0.65 0.53 0.22 0.344 30.002 326.5 -420 0.65 0.523 0.222 0.335 30.002 338.5 -420 0.65 0.516 0.225 0.325 30.002 350.6 -420 0.65 0.51 0.228 0.315 30.002 362.9 -420 0.65 0.503 0.23 0.306 30.002 375.2 -420 0.65 0.497 0.233 0.296 30.002 387.7 -420 0.65 0.491 0.236 0.287 3

-1E-05 0.002 0.002 400.3 -420 0.65 0.484 0.239 0.277 4-1E-05 0.0021 0.002 413.1 -420 0.655 0.478 0.243 0.268 4

0.003 0.003 420 -420 0.696 0.436 0.259 0.258 60.003 0.003 420 -420 0.754 0.388 0.278 0.249 60.004 0.004 420 -420 0.828 0.34 0.302 0.239 6

0.005 0.005 420 -420 0.9 0.3 0.323 0.229 70.005 0.005 420 -420 0.9 0.287 0.322 0.22 70.006 0.006 420 -420 0.9 0.275 0.32 0.21 70.006 0.006 420 -420 0.9 0.262 0.318 0.201 70.007 0.007 420 -420 0.9 0.25 0.316 0.191 70.007 0.007 420 -420 0.9 0.237 0.314 0.182 70.008 0.008 420 -420 0.9 0.225 0.312 0.172 70.008 0.008 420 -420 0.9 0.212 0.31 0.162 70.009 0.009 420 -420 0.9 0.2 0.307 0.153 7

0.01 0.01 420 -420 0.9 0.187 0.305 0.143 70.011 0.011 420 -420 0.9 0.175 0.302 0.134 70.012 0.012 420 -420 0.9 0.162 0.299 0.124 70.013 0.013 420 -420 0.9 0.15 0.297 0.115 7

0.004 0 0.014 0.014 420 -417 0.9 0.14 0.293 0.105 80.002 0 0.015 0.015 420 -410 0.9 0.134 0.29 0.096 8

0.001 0 0.016 0.016 420 -402 0.9 0.129 0.286 0.086 80 0 0.017 0.017 420 -393 0.9 0.123 0.282 0.076 80 0 0.017 0.017 420 -385 0.9 0.119 0.278 0.067 80 0 0.018 0.018 420 -376 0.9 0.114 0.275 0.057 80 0 0.019 0.019 420 -367 0.9 0.109 0.271 0.048 8

-0.006 0 0.02 0.02 420 -357 0.9 0.105 0.267 0.038 8-0.007 0 0.021 0.021 420 -348 0.9 0.101 0.263 0.029 8-0.008 0 0.022 0.022 420 -338 0.9 0.097 0.259 0.019 8

-0.01 0 0.023 0.023 420 -328 0.9 0.094 0.255 0.01 8-0.011 0 0.024 0.024 420 -318 0.9 0.09 0.251 2E-15 8

ξt2 b c ξt3 b c ξt4 ξt6 ξt7 b c ξt8 ξt fs f's0 0 -200 -4200 0 -186 -4200 0 -171 -4200 0 -156 -4200 0 -142 -4200 0 -127 -420

0.008 4E-06 0 0 -114 -4200.008 4E-06 0 0 -109 -4200.008 4E-06 0 0 -103 -4200.008 3E-06 0 0 -97.91 -4200.008 3E-06 0 0 -92.29 -4200.007 3E-06 0 0 -86.59 -4200.007 3E-06 0 0 -80.81 -4200.007 3E-06 0 0 -75 -4200.007 2E-06 0 0 -69 -4200.007 2E-06 0 0 -63 -4200.007 2E-06 0 0 -56.9 -4200.007 2E-06 0 0 -50.73 -4200.007 1E-06 0 0 -44.47 -4200.007 1E-06 0 0 -38.13 -4200.007 1E-06 0 0 -31.71 -4200.007 8E-07 0 0 -25.2 -4200.007 6E-07 -9E-05 -9E-05 -18.61 -4200.007 4E-07 -6E-05 -6E-05 -11.94 -4200.006 2E-07 -3E-05 -3E-05 -5.191 -4200.006 -5E-08 8E-06 8E-06 1.646 -4200.006 -3E-07 4E-05 4E-05 8.566 -4200.006 -5E-07 8E-05 8E-05 15.57 -4200.006 -7E-07 0 0 22.66 -4200.006 -9E-07 0 0 29.83 -4200.006 -1E-06 0 0 37.09 -4200.006 -1E-06 0 0 44.43 -4200.006 -2E-06 0 0 51.86 -4200.006 -2E-06 0 0 59.36 -4200.006 -2E-06 0 0 66.96 -4200.006 -2E-06 0 0 74.64 -4200.006 -2E-06 0 0 82.4 -420

0.006 -3E-06 0 0 90.24 -4200.005 -3E-06 0 0 98.17 -4200.005 -3E-06 0.001 0.001 106.2 -4200.005 -3E-06 0.001 0.001 114.3 -4200.005 -4E-06 0.001 0.001 122.5 -4200.005 -4E-06 0.001 0.001 130.7 -4200.005 -4E-06 0.001 0.001 139.1 -4200.005 -4E-06 0.001 0.001 147.5 -4200.005 -4E-06 0.001 0.001 156 -4200.005 -5E-06 0.001 0.001 164.6 -4200.005 -5E-06 0.001 0.001 173.2 -4200.005 -5E-06 0.001 0.001 182 -4200.005 -5E-06 0.001 0.001 190.8 -4200.005 -6E-06 0.001 0.001 199.7 -4200.005 -6E-06 0.001 0.001 208.7 -4200.004 -6E-06 0.001 0.001 217.8 -4200.004 -6E-06 0.001 0.001 226.9 -4200.004 -6E-06 0.001 0.001 236.1 -4200.004 -7E-06 0.001 0.001 245.4 -4200.004 -7E-06 0.001 0.001 254.8 -4200.004 -7E-06 0.001 0.001 264.2 -4200.004 -7E-06 0.001 0.001 273.7 -4200.004 -8E-06 0.001 0.001 283.3 -4200.004 -8E-06 0.001 0.001 293 -4200.004 -8E-06 0.002 0.002 302.7 -4200.004 -8E-06 0.002 0.002 312.5 -4200.004 -8E-06 0.002 0.002 322.4 -4200.004 -9E-06 0.002 0.002 332.3 -4200.003 -9E-06 0.002 0.002 342.4 -4200.003 -9E-06 0.002 0.002 352.4 -4200.003 -9E-06 0.002 0.002 362.6 -4200.003 -1E-05 0.002 0.002 372.8 -4200.003 -1E-05 0.002 0.002 383.1 -4200.003 -1E-05 0.002 0.002 393.4 -420

0.003 -1E-05 0.002 0.002 403.8 -4200.003 -1E-05 0.002 0.002 414.3 -420

0.003 0.003 420 -4200.003 0.003 420 -4200.004 0.004 420 -420

0.005 0.005 420 -4200.005 0.005 420 -4200.006 0.006 420 -4200.006 0.006 420 -4200.007 0.007 420 -4200.007 0.007 420 -4200.008 0.008 420 -4200.008 0.008 420 -4200.009 0.009 420 -420

0.01 0.01 420 -4200.011 0.011 420 -4200.012 0.012 420 -4200.013 0.013 420 -420

-2E-06 0 0.014 0.014 420 -4180 0 0.015 0.015 420 -411

0 0 0.016 0.016 420 -4050 0 0.016 0.016 420 -3980 0 0.017 0.017 420 -391

-0.005 0 0.018 0.018 420 -384-0.006 0 0.018 0.018 420 -376-0.007 0 0.019 0.019 420 -369-0.008 0 0.02 0.02 420 -361-0.009 0 0.02 0.02 420 -353

-0.01 0 0.021 0.021 420 -345-0.011 0 0.022 0.022 420 -337

ρtot =1.05

Φ m η caso ξt2 b c ξt3 b c ξt4 ξt6 ξt7 b0.65 1 0 0.956 3 0.007 3E-06 00.65 1 0 0.946 3 0.007 3E-06 00.65 1 0 0.937 3 0.007 3E-06 00.65 1 0 0.927 3 0.007 3E-06 00.65 1 0 0.918 3 0.007 2E-06 00.65 1 0 0.908 3 0.006 2E-06 00.65 0.998 0 0.898 3 0.006 2E-06 00.65 0.987 0 0.889 3 0.006 2E-06 00.65 0.976 0 0.879 3 0.006 2E-06 00.65 0.965 0 0.87 3 0.006 2E-06 00.65 0.954 0 0.86 3 0.006 1E-06 00.65 0.944 0.11 0.851 3 0.006 1E-06 00.65 0.933 0.114 0.841 3 0.006 1E-06 00.65 0.923 0.118 0.832 3 0.006 8E-07 00.65 0.912 0.121 0.822 3 0.006 6E-07 00.65 0.902 0.125 0.812 3 0.006 5E-07 -8E-050.65 0.892 0.129 0.803 3 0.006 3E-07 -5E-050.65 0.882 0.132 0.793 3 0.006 1E-07 -2E-050.65 0.872 0.136 0.784 3 0.006 -7E-08 1E-050.65 0.862 0.14 0.774 3 0.006 -2E-07 4E-050.65 0.853 0.143 0.765 3 0.006 -4E-07 7E-050.65 0.843 0.147 0.755 3 0.006 -6E-07 00.65 0.833 0.15 0.746 3 0.005 -8E-07 00.65 0.824 0.153 0.736 3 0.005 -9E-07 00.65 0.815 0.157 0.726 3 0.005 -1E-06 00.65 0.805 0.16 0.717 3 0.005 -1E-06 00.65 0.796 0.163 0.707 3 0.005 -1E-06 00.65 0.787 0.167 0.698 3 0.005 -2E-06 00.65 0.778 0.17 0.688 3 0.005 -2E-06 00.65 0.769 0.173 0.679 3 0.005 -2E-06 00.65 0.76 0.176 0.669 3 0.005 -2E-06 00.65 0.752 0.18 0.66 3 0.005 -2E-06 00.65 0.743 0.183 0.65 3 0.005 -3E-06 00.65 0.735 0.186 0.64 3 0.005 -3E-06 0.0010.65 0.726 0.189 0.631 3 0.005 -3E-06 0.0010.65 0.718 0.192 0.621 3 0.005 -3E-06 0.0010.65 0.71 0.195 0.612 3 0.005 -3E-06 0.001

β1 · c

0.65 0.702 0.198 0.602 3 0.005 -3E-06 0.0010.65 0.694 0.201 0.593 3 0.005 -4E-06 0.0010.65 0.686 0.204 0.583 3 0.004 -4E-06 0.0010.65 0.678 0.208 0.573 3 0.004 -4E-06 0.0010.65 0.671 0.211 0.564 3 0.004 -4E-06 0.0010.65 0.663 0.214 0.554 3 0.004 -4E-06 0.0010.65 0.656 0.217 0.545 3 0.004 -4E-06 0.0010.65 0.648 0.22 0.535 3 0.004 -5E-06 0.0010.65 0.641 0.223 0.526 3 0.004 -5E-06 0.0010.65 0.634 0.225 0.516 3 0.004 -5E-06 0.0010.65 0.627 0.228 0.507 3 0.004 -5E-06 0.0010.65 0.62 0.231 0.497 3 0.004 -5E-06 0.0010.65 0.613 0.234 0.487 3 0.004 -6E-06 0.0010.65 0.606 0.237 0.478 3 0.004 -6E-06 0.0010.65 0.599 0.24 0.468 3 0.004 -6E-06 0.0010.65 0.592 0.243 0.459 3 0.004 -6E-06 0.0010.65 0.586 0.246 0.449 3 0.004 -6E-06 0.0010.65 0.579 0.249 0.44 3 0.004 -6E-06 0.0010.65 0.573 0.252 0.43 3 0.004 -7E-06 0.0010.65 0.567 0.255 0.421 3 0.003 -7E-06 0.0010.65 0.561 0.258 0.411 3 0.003 -7E-06 0.0010.65 0.555 0.261 0.401 3 0.003 -7E-06 0.0010.65 0.548 0.264 0.392 3 0.003 -7E-06 0.0020.65 0.543 0.267 0.382 3 0.003 -7E-06 0.0020.65 0.537 0.27 0.373 3 0.003 -8E-06 0.0020.65 0.531 0.273 0.363 3 0.003 -8E-06 0.0020.65 0.525 0.276 0.354 3 0.003 -8E-06 0.0020.65 0.52 0.279 0.344 3 0.003 -8E-06 0.0020.65 0.514 0.282 0.335 3 0.003 -8E-06 0.0020.65 0.509 0.285 0.325 3 0.003 -9E-06 0.0020.65 0.503 0.288 0.315 3 0.003 -9E-06 0.0020.65 0.498 0.291 0.306 3 0.003 -9E-06 0.0020.65 0.493 0.294 0.296 3 0.003 -9E-06 0.0020.65 0.488 0.297 0.287 3 0.003 -9E-06 0.002

0.652 0.483 0.3 0.277 4 0.003 -9E-06 0.0020.656 0.478 0.305 0.268 4 0.003 -1E-05 0.0020.696 0.436 0.325 0.258 6 0.0030.754 0.388 0.35 0.249 6 0.0030.828 0.34 0.38 0.239 6 0.004

0.9 0.3 0.408 0.229 7 0.0050.9 0.287 0.407 0.22 7 0.0050.9 0.275 0.405 0.21 7 0.0060.9 0.262 0.403 0.201 7 0.0060.9 0.25 0.401 0.191 7 0.0070.9 0.237 0.399 0.182 7 0.0070.9 0.225 0.397 0.172 7 0.0080.9 0.212 0.395 0.162 7 0.0080.9 0.2 0.392 0.153 7 0.0090.9 0.187 0.39 0.143 7 0.010.9 0.175 0.387 0.134 7 0.0110.9 0.162 0.384 0.124 7 0.0120.9 0.15 0.382 0.115 7 0.0130.9 0.14 0.378 0.105 8 00.9 0.135 0.375 0.096 8 0

0.9 0.131 0.371 0.086 8 00.9 0.126 0.367 0.076 8 00.9 0.122 0.363 0.067 8 -0.0050.9 0.118 0.359 0.057 8 -0.0060.9 0.114 0.355 0.048 8 -0.0070.9 0.11 0.351 0.038 8 -0.0080.9 0.107 0.347 0.029 8 -0.0090.9 0.103 0.343 0.019 8 -0.0090.9 0.1 0.339 0.01 8 -0.010.9 0.097 0.335 2E-15 8 -0.011

ρtot =0.21 0.42 0.63 0.84 1.05

c ξt8 ξt fs f's Φ m η m0 -98.9 -420 0.65 0.967 0 0.956 0 0 0 0 00 -93.78 -420 0.65 0.957 0.129 0.946 0 0 0 0 0.1290 -88.61 -420 0.65 0.947 0.133 0.937 0 0 0 0 0.1330 -83.37 -420 0.65 0.938 0.137 0.927 0 0 0 0 0.1370 -78.08 -420 0.65 0.928 0.141 0.918 0 0 0 0 0.1410 -72.72 -420 0.65 0.919 0.144 0.908 0 0 0 0 0.1440 -67.31 -420 0.65 0.91 0.148 0.898 0 0 0 0 0.1480 -61.84 -420 0.65 0.9 0.152 0.889 0 0 0 0 0.1520 -56.3 -420 0.65 0.891 0.156 0.879 0 0 0 0 0.1560 -50.71 -420 0.65 0.882 0.159 0.87 0 0 0 0 0.1590 -45.06 -420 0.65 0.873 0.163 0.86 0 0 0 0 0.1630 -39.34 -420 0.65 0.864 0.167 0.851 0 0 0 0.11 0.1670 -33.57 -420 0.65 0.855 0.17 0.841 0 0 0 0.114 0.170 -27.73 -420 0.65 0.847 0.174 0.832 0 0 0 0.118 0.1740 -21.84 -420 0.65 0.838 0.177 0.822 0 0 0 0.121 0.177

-8E-05 -15.89 -420 0.65 0.829 0.181 0.812 0 0 0 0.125 0.181-5E-05 -9.871 -420 0.65 0.821 0.184 0.803 0 0 0 0.129 0.184-2E-05 -3.796 -420 0.65 0.813 0.188 0.793 0 0 0 0.132 0.1881E-05 2.34 -420 0.65 0.804 0.191 0.784 0 0 0 0.136 0.1914E-05 8.535 -420 0.65 0.796 0.195 0.774 0 0 0 0.14 0.1957E-05 14.79 -420 0.65 0.788 0.198 0.765 0 0 0 0.143 0.198

0 21.11 -420 0.65 0.78 0.202 0.755 0 0 0 0.147 0.2020 27.48 -420 0.65 0.772 0.205 0.746 0 0 0.095 0.15 0.2050 33.91 -420 0.65 0.764 0.208 0.736 0 0 0.098 0.153 0.2080 40.41 -420 0.65 0.757 0.212 0.726 0 0 0.102 0.157 0.2120 46.96 -420 0.65 0.749 0.215 0.717 0 0 0.105 0.16 0.2150 53.57 -420 0.65 0.741 0.218 0.707 0 0 0.109 0.163 0.2180 60.24 -420 0.65 0.734 0.221 0.698 0 0 0.112 0.167 0.2210 66.97 -420 0.65 0.726 0.225 0.688 0 0 0.116 0.17 0.2250 73.76 -420 0.65 0.719 0.228 0.679 0 0 0.119 0.173 0.2280 80.61 -420 0.65 0.712 0.231 0.669 0 0 0.122 0.176 0.2310 87.51 -420 0.65 0.705 0.234 0.66 0 0 0.126 0.18 0.2340 94.47 -420 0.65 0.698 0.238 0.65 0 0 0.129 0.183 0.238

0.001 101.5 -420 0.65 0.691 0.241 0.64 0 0.078 0.132 0.186 0.2410.001 108.6 -420 0.65 0.684 0.244 0.631 0 0.082 0.135 0.189 0.2440.001 115.7 -420 0.65 0.677 0.247 0.621 0 0.085 0.138 0.192 0.2470.001 122.9 -420 0.65 0.67 0.25 0.612 0 0.088 0.141 0.195 0.25

β1 · c

0.001 130.1 -420 0.65 0.664 0.254 0.602 0 0.092 0.145 0.198 0.2540.001 137.4 -420 0.65 0.657 0.257 0.593 0 0.095 0.148 0.201 0.2570.001 144.8 -420 0.65 0.651 0.26 0.583 0 0.098 0.151 0.204 0.260.001 152.2 -420 0.65 0.644 0.263 0.573 0 0.101 0.153 0.208 0.2630.001 159.6 -420 0.65 0.638 0.266 0.564 0 0.104 0.156 0.211 0.2660.001 167.2 -420 0.65 0.632 0.269 0.554 0 0.107 0.159 0.214 0.2690.001 174.7 -420 0.65 0.625 0.272 0.545 0 0.11 0.162 0.217 0.2720.001 182.3 -420 0.65 0.619 0.276 0.535 0.061 0.112 0.165 0.22 0.2760.001 190 -420 0.65 0.613 0.279 0.526 0.064 0.115 0.168 0.223 0.2790.001 197.7 -420 0.65 0.607 0.282 0.516 0.067 0.118 0.171 0.225 0.2820.001 205.5 -420 0.65 0.601 0.285 0.507 0.069 0.121 0.174 0.228 0.2850.001 213.4 -420 0.65 0.596 0.288 0.497 0.072 0.123 0.176 0.231 0.2880.001 221.2 -420 0.65 0.59 0.291 0.487 0.075 0.126 0.179 0.234 0.2910.001 229.2 -420 0.65 0.584 0.294 0.478 0.077 0.128 0.182 0.237 0.2940.001 237.1 -420 0.65 0.579 0.298 0.468 0.08 0.131 0.185 0.24 0.2980.001 245.2 -420 0.65 0.573 0.301 0.459 0.082 0.133 0.187 0.243 0.3010.001 253.2 -420 0.65 0.568 0.304 0.449 0.085 0.136 0.19 0.246 0.3040.001 261.4 -420 0.65 0.562 0.307 0.44 0.087 0.138 0.193 0.249 0.3070.001 269.5 -420 0.65 0.557 0.31 0.43 0.089 0.141 0.195 0.252 0.310.001 277.7 -420 0.65 0.552 0.313 0.421 0.091 0.143 0.198 0.255 0.3130.001 286 -420 0.65 0.547 0.316 0.411 0.093 0.146 0.201 0.258 0.3160.001 294.3 -420 0.65 0.542 0.319 0.401 0.095 0.148 0.204 0.261 0.3190.002 302.7 -420 0.65 0.537 0.323 0.392 0.097 0.15 0.206 0.264 0.3230.002 311.1 -420 0.65 0.532 0.326 0.382 0.099 0.153 0.209 0.267 0.3260.002 319.5 -420 0.65 0.527 0.329 0.373 0.101 0.155 0.212 0.27 0.3290.002 328 -420 0.65 0.522 0.332 0.363 0.103 0.157 0.214 0.273 0.3320.002 336.5 -420 0.65 0.517 0.335 0.354 0.105 0.16 0.217 0.276 0.3350.002 345.1 -420 0.65 0.513 0.338 0.344 0.106 0.162 0.22 0.279 0.3380.002 353.7 -420 0.65 0.508 0.342 0.335 0.108 0.164 0.222 0.282 0.3420.002 362.4 -420 0.65 0.503 0.345 0.325 0.11 0.166 0.225 0.285 0.3450.002 371.1 -420 0.65 0.499 0.348 0.315 0.111 0.169 0.228 0.288 0.3480.002 379.8 -420 0.65 0.494 0.351 0.306 0.113 0.171 0.23 0.291 0.3510.002 388.6 -420 0.65 0.49 0.354 0.296 0.114 0.173 0.233 0.294 0.3540.002 397.4 -420 0.65 0.486 0.358 0.287 0.116 0.176 0.236 0.297 0.3580.002 406.3 -420 0.653 0.481 0.362 0.277 0.118 0.178 0.239 0.3 0.3620.002 415.2 -420 0.656 0.477 0.367 0.268 0.12 0.181 0.243 0.305 0.3670.003 420 -420 0.696 0.436 0.391 0.258 0.128 0.193 0.259 0.325 0.3910.003 420 -420 0.754 0.388 0.421 0.249 0.136 0.207 0.278 0.35 0.4210.004 420 -420 0.828 0.34 0.458 0.239 0.145 0.224 0.302 0.38 0.4580.005 420 -420 0.9 0.3 0.494 0.229 0.153 0.238 0.323 0.408 0.4940.005 420 -420 0.9 0.287 0.492 0.22 0.152 0.237 0.322 0.407 0.4920.006 420 -420 0.9 0.275 0.49 0.21 0.15 0.235 0.32 0.405 0.490.006 420 -420 0.9 0.262 0.488 0.201 0.148 0.233 0.318 0.403 0.4880.007 420 -420 0.9 0.25 0.486 0.191 0.146 0.231 0.316 0.401 0.4860.007 420 -420 0.9 0.237 0.484 0.182 0.144 0.229 0.314 0.399 0.4840.008 420 -420 0.9 0.225 0.482 0.172 0.142 0.227 0.312 0.397 0.4820.008 420 -420 0.9 0.212 0.48 0.162 0.139 0.224 0.31 0.395 0.480.009 420 -420 0.9 0.2 0.477 0.153 0.137 0.222 0.307 0.392 0.477

0.01 420 -420 0.9 0.187 0.475 0.143 0.135 0.22 0.305 0.39 0.4750.011 420 -420 0.9 0.175 0.472 0.134 0.132 0.217 0.302 0.387 0.4720.012 420 -420 0.9 0.162 0.469 0.124 0.129 0.214 0.299 0.384 0.4690.013 420 -420 0.9 0.15 0.467 0.115 0.126 0.212 0.297 0.382 0.467

0 0.014 0.014 420 -418 0.9 0.14 0.463 0.105 0.123 0.208 0.293 0.378 0.4630 0.015 0.015 420 -412 0.9 0.136 0.46 0.096 0.12 0.205 0.29 0.375 0.46

0 0.015 0.015 420 -407 0.9 0.132 0.456 0.086 0.117 0.201 0.286 0.371 0.4560 0.016 0.016 420 -401 0.9 0.128 0.452 0.076 0.113 0.198 0.282 0.367 0.4520 0.016 0.016 420 -395 0.9 0.124 0.448 0.067 0.11 0.194 0.278 0.363 0.4480 0.017 0.017 420 -389 0.9 0.121 0.444 0.057 0.106 0.19 0.275 0.359 0.4440 0.018 0.018 420 -383 0.9 0.117 0.44 0.048 0.102 0.186 0.271 0.355 0.440 0.018 0.018 420 -376 0.9 0.114 0.436 0.038 0.098 0.182 0.267 0.351 0.4360 0.019 0.019 420 -370 0.9 0.111 0.432 0.029 0.094 0.178 0.263 0.347 0.4320 0.019 0.019 420 -364 0.9 0.108 0.428 0.019 0.09 0.174 0.259 0.343 0.4280 0.02 0.02 420 -357 0.9 0.105 0.424 0.01 0.087 0.17 0.255 0.339 0.4240 0.021 0.021 420 -351 0.9 0.102 0.42 2E-15 0.082 0.166 0.251 0.335 0.42

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

00

.10

.20

.30

.40

.50

.6

Inte

rac

ció

n (

B1

= 0

,85

)

0,21 0.42 0.63 0.84 1.05

n =

N/(

b·h

·f'c

)

m=

M/(

b·h

^2·

f'c)