diseño de losa(NTC)
56
Tableros Interior Todos los bordes continuos De borde Un lado corto discontinuo De borde Un lado largo discontinuo De esquina Dos lado adyacentes discontinuo Extremo Tres bordes discontinuo un lado largo conti
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Transcript of diseño de losa(NTC)
Tablero
Interior Todos los
bordes continuos
De borde Un lado
corto discontinuo
De borde Un lado
largo discontinuo
De esquina Dos lado
adyacentes discontinuo
Extremo Tres bordes discontinuo
un lado largo
continuo
Extremo Tres bordes discontinuo
un lado corto
continuo
Aislado Cuatro lado discontinuo
Tableros fotos
Interior Todos los bordes continuos
De borde Un lado corto discontinuo
De borde Un lado largo discontinuo
De esquina Dos lado adyacentes discontinuo
Extremo Tres bordes discontinuo un lado largo continuo
Extremo Tres bordes discontinuo un lado corto continuo
Aislado Cuatro lado discontinuo
Aislado Cuatro lado discontinuo
Interior Todos los bordes continuosDe borde Un lado corto discontinuoDe borde Un lado largo discontinuoDe esquina Dos lado adyacentes discontinuoExtremo Tres bordes discontinuo un lado largo continuoExtremo Tres bordes discontinuo un lado corto continuoAislado Cuatro lado discontinuo
% 1.51 20.042 22.393 22.74 25.055 27.46 27.717 30.06
Tablero
Interior Todos los
bordes continuos
De borde Un lado
corto discontinuo
De borde Un lado
largo discontinuo
De esquina Dos lado
adyacentes discontinuo
Extremo Tres bordes discontinuo
un lado largo
continuo
Extremo Tres bordes discontinuo
un lado corto
continuo
Aislado Cuatro lado discontinuo
Tabla 6.1 Coeficientes de momentos flexionantes para tableros rectangulares, franjas centrales1
Momento ClaroRelación de lados cortos a largos, m=a1/a2
0 0.5 0.6 0.7 0.8I II I II I II I II
corto 998 1018 553 565 489 498 432 438 381 387largo 516 544 409 431 391 412 371 388 347 361
Positivocorto 630 668 312 322 268 276 228 236 192 199largo 175 181 139 144 134 139 130 135 128 133
corto 998 1018 568 594 506 533 451 478 403 431largo 516 544 409 431 391 412 372 392 350 369
Neg. En bordes dis. largo 326 0 258 0 248 0 236 0 222 0
Positivocorto 630 668 329 356 292 306 240 261 202 219largo 179 187 142 149 137 143 133 140 131 137
corto 1060 1143 583 624 514 548 453 481 397 420largo 587 687 465 545 442 513 411 470 379 426
Neg. En bordes dis. corto 651 0 362 0 321 0 283 0 250 0
Positivocorto 751 912 334 366 285 312 241 263 202 218largo 185 200 147 158 142 153 138 149 135 146
corto 1060 1143 598 653 530 582 471 520 419 464largo 600 713 475 564 455 541 429 506 394 457corto 651 0 362 0 321 0 277 0 250 0largo 326 0 258 0 248 0 236 0 222 0
Positivocorto 751 912 358 416 306 354 259 298 216 247largo 191 212 152 168 146 163 142 158 140 156
Neg. En borde cont. corto 1060 1143 970 1070 890 1010 810 940 730 870corto 651 0 370 0 340 0 310 0 280 0largo 220 0 220 0 220 0 220 0 220 0
Positivocorto 751 912 730 800 670 760 610 710 550 650largo 185 200 430 520 430 520 430 520 430 520
Neg. En borde cont. largo 570 710 570 710 570 710 570 710 570 710corto 570 0 480 0 420 0 370 0 310 0 largo 330 0 220 0 220 0 220 0 220 0
Positivocorto 1100 1670 960 1060 840 950 730 850 620 740largo 200 250 430 540 430 540 430 540 430 540
corto 570 0 550 0 530 0 470 0 430 0largo 330 0 330 0 330 0 330 0 330 0
I² II³Neg. En bordes
interiores
Neg. En bordes interiores
Neg. En bordes interiores
Neg. En bordes interiores
Neg. En bordes discontunuos
Neg. En borde discontinuos
Neg. En borde discontinuos
Neg. En bodes discontinuos
Positivocorto 1100 1670 830 1380 800 1330 720 1190 640 1070largo 200 250 500 830 500 830 500 830 500 830
a1= 4.7a2= 5.32
ii0.8 0.81 0.82 0.83
464 458.8 453.6 448.4
Losa MonoliticaLosa no Monolitica y otros casos
(SI(Diseño!A2="Losa Monolitica",1.25,SI(Diseño!A2="Losa no Monolitica y otros casos",1.5)))
Momento Claro 0.88 Mucorto 347.8 554 FALSElargo 336.2 535
0 0
Positivocorto 171 272largo 131.4 209
0corto 396.6 632 FALSElargo 346.6 552
Neg. En bordes dis. largo 0 0
Positivocorto 188.6 300largo 136.2 217
0corto 375.2 598 FALSElargo 392.4 625
Neg. En bordes dis. corto 0 0
Positivocorto 183.6 292largo 145.2 231
0corto 422.4 673 673largo 419.4 668corto 0 0largo 0 0 No. Øpulg. Ømm. Kg/m.
Positivocorto 208.6 332largo 154.4 246 1/4 2 (1/4") 6.4 0.284
Neg. En bordes interiores
Neg. En bordes interiores
Neg. En bordes interiores
Neg. En bordes interiores
Neg. En bordes discontunuos
1/3 2.5 (5/16") 7.9 0.3880 3/8 3 (3/8") 9.5 0.559
Neg. En borde cont. corto 806 1284 FALSE 4 (1/2") 12.7 0.993corto 0 0 5 (5/8") 15.9 1.552largo 0 0 6 (3/4") 19.1 2.235
Positivocorto 610 972 7 (7/8") 22.2 3.042largo 520 828 8 1 25.4 3.973
0 9 (1 1/8") 28.6 5.028Neg. En borde cont. largo 710 1131 FALSE 10 (1 1/4") 31.8 6.207
corto 0 0 11 (1 3/8") 34.9 7.511 largo 0 0 12 (1 1/2") 38.1 8.938
Positivocorto 676 1077largo 540 860
0corto 0 0 FALSElargo 0 0 0 526
0 0 2.66 -796
Positivocorto 974 1551 5.32 526largo 830 1322
dmin= 11cm
Neg. En borde discontinuos
Neg. En borde discontinuos
Neg. En bodes discontinuos
Tabla 6.1 Coeficientes de momentos flexionantes para tableros rectangulares, franjas centrales1Relación de lados cortos a largos, m=a1/a2
0.9 1 iI II I II 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08333 338 288 292 998 989.1 980.2 971.3 962.4 953.5 944.6 935.7 926.8320 330 288 292 516 513.9 511.7 509.6 507.4 505.3 503.2 501 498.9
0 0 0 0 0 0 0 0158 164 126 130 630 623.6 617.3 610.9 604.6 598.2 591.8 585.5 579.1127 131 126 130 175 174.3 173.6 172.8 172.1 171.4 170.7 170 169.2
0 0 0 0 0 0 0 0357 388 315 346 998 989.4 980.8 972.2 963.6 955 946.4 937.8 929.2326 341 297 311 516 513.9 511.7 509.6 507.4 505.3 503.2 501 498.9206 0 190 0 326 324.6 323.3 321.9 320.6 319.2 317.8 316.5 315.1167 181 133 144 630 624 618 611.9 605.9 599.9 593.9 587.9 581.8129 136 129 135 179 178.3 177.5 176.8 176 175.3 174.6 173.8 173.1
0 0 0 0 0 0 0 0346 364 297 311 1060 1050 1041 1031 1022 1012 1003 993.2 983.7347 384 315 346 587 584.6 582.1 579.7 577.2 574.8 572.4 569.9 567.5219 0 190 651 645.2 639.4 633.7 627.9 622.1 616.3 610.5 604.8164 175 129 135 751 742.7 734.3 726 717.6 709.3 701 692.6 684.3134 145 133 144 185 184.2 183.5 182.7 182 181.2 180.4 179.7 178.9
0 0 0 0 0 0 0 0371 412 324 364 1060 1051 1042 1032 1023 1014 1005 995.3 986.1360 410 324 364 600 597.5 595 592.5 590 587.5 585 582.5 580219 0 190 0 651 645.2 639.4 633.7 627.9 622.1 616.3 610.5 604.8206 0 190 0 326 324.6 323.3 321.9 320.6 319.2 317.8 316.5 315.1176 199 137 153 751 743.1 735.3 727.4 719.6 711.7 703.8 696 688.1138 154 137 153 191 190.2 189.4 188.7 187.9 187.1 186.3 185.5 184.8
0 0 0 0 0 0 0 0
650 790 570 710 1060 1058 1056 1055 1053 1051 1049 1047 1046
250 0 220 0 651 645.4 639.8 634.1 628.5 622.9 617.3 611.7 606
220 0 220 0 220 220 220 220 220 220 220 220 220
490 600 430 540 751 750.6 750.2 749.7 749.3 748.9 748.5 748.1 747.6
430 520 430 520 185 189.9 194.8 199.7 204.6 209.5 214.4 219.3 224.2
0 0 0 0 0 0 0 0
570 710 570 710 570 570 570 570 570 570 570 570 570
270 0 220 0 570 568.2 566.4 564.6 562.8 561 559.2 557.4 555.6
220 0 220 0 330 327.8 325.6 323.4 321.2 319 316.8 314.6 312.4
540 660 430 520 1100 1097 1094 1092 1089 1086 1083 1080 1078
430 540 430 540 200 204.6 209.2 213.8 218.4 223 227.6 232.2 236.8
0 0 0 0 0 0 0 0380 0 330 0 570 569.6 569.2 568.8 568.4 568 567.6 567.2 566.8330 0 330 0 330 330 330 330 330 330 330 330 330
0 0 0 0 0 0 0 0
570 950 500 830 1100 1095 1089 1084 1078 1073 1068 1062 1057500 830 500 830 200 206 212 218 224 230 236 242 248
ii0.84 0.85 0.86 0.87
443.2 438 432.8 427.6
No. Øpulg. Ømm. Kg/m.
0.32 0.05 7 (7/8") 22.2 3.042 3.88 0.6
mm.2 pulg.2 mm.2 pulg.2
0.49 0.08 8 1 25.4 3.973 5.07 0.790.71 0.11 9 (1 1/8") 28.6 5.028 6.41 11.27 0.2 10 (1 1/4") 31.8 6.207 7.92 1.231.98 0.31 11 (1 3/8") 34.9 7.511 9.58 1.482.85 0.44 12 (1 1/2") 38.1 8.938 11.4 1.773.88 0.65.07 0.796.41 17.92 1.239.58 1.4811.4 1.77
Tabla 6.1 Coeficientes de momentos flexionantes para tableros rectangulares, franjas centrales1
i0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23917.9 909 900.1 891.2 882.3 873.4 864.5 855.6 846.7 837.8 828.9 820 811.1 802.2 793.3496.7 494.6 492.5 490.3 488.2 486 483.9 481.8 479.6 477.5 475.3 473.2 471.1 468.9 466.8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0572.8 566.4 560 553.7 547.3 541 534.6 528.2 521.9 515.5 509.2 502.8 496.4 490.1 483.7168.5 167.8 167.1 166.4 165.6 164.9 164.2 163.5 162.8 162 161.3 160.6 159.9 159.2 158.4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0920.6 912 903.4 894.8 886.2 877.6 869 860.4 851.8 843.2 834.6 826 817.4 808.8 800.2496.7 494.6 492.5 490.3 488.2 486 483.9 481.8 479.6 477.5 475.3 473.2 471.1 468.9 466.8313.8 312.4 311 309.7 308.3 307 305.6 304.2 302.9 301.5 300.2 298.8 297.4 296.1 294.7575.8 569.8 563.8 557.8 551.7 545.7 539.7 533.7 527.7 521.6 515.6 509.6 503.6 497.6 491.5172.3 171.6 170.9 170.1 169.4 168.6 167.9 167.2 166.4 165.7 164.9 164.2 163.5 162.7 162
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0974.1 964.6 955.1 945.5 936 926.4 916.9 907.4 897.8 888.3 878.7 869.2 859.7 850.1 840.6
565 562.6 560.2 557.7 555.3 552.8 550.4 548 545.5 543.1 540.6 538.2 535.8 533.3 530.9599 593.2 587.4 581.6 575.9 570.1 564.3 558.5 552.7 547 541.2 535.4 529.6 523.8 518.1
675.9 667.6 659.3 650.9 642.6 634.2 625.9 617.6 609.2 600.9 592.5 584.2 575.9 567.5 559.2178.2 177.4 176.6 175.9 175.1 174.4 173.6 172.8 172.1 171.3 170.6 169.8 169 168.3 167.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0976.8 967.6 958.4 949.1 939.9 930.6 921.4 912.2 902.9 893.7 884.4 875.2 866 856.7 847.5577.5 575 572.5 570 567.5 565 562.5 560 557.5 555 552.5 550 547.5 545 542.5
599 593.2 587.4 581.6 575.9 570.1 564.3 558.5 552.7 547 541.2 535.4 529.6 523.8 518.1313.8 312.4 311 309.7 308.3 307 305.6 304.2 302.9 301.5 300.2 298.8 297.4 296.1 294.7680.3 672.4 664.5 656.7 648.8 641 633.1 625.2 617.4 609.5 601.7 593.8 585.9 578.1 570.2
184 183.2 182.4 181.6 180.9 180.1 179.3 178.5 177.7 177 176.2 175.4 174.6 173.8 173.10 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1044 1042 1040 1038 1037 1035 1033 1031 1029 1028 1026 1024 1022 1020 1019
600.4 594.8 589.2 583.6 577.9 572.3 566.7 561.1 555.5 549.8 544.2 538.6 533 527.4 521.7
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
747.2 746.8 746.4 746 745.5 745.1 744.7 744.3 743.9 743.4 743 742.6 742.2 741.8 741.3
229.1 234 238.9 243.8 248.7 253.6 258.5 263.4 268.3 273.2 278.1 283 287.9 292.8 297.7
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
570 570 570 570 570 570 570 570 570 570 570 570 570 570 570
553.8 552 550.2 548.4 546.6 544.8 543 541.2 539.4 537.6 535.8 534 532.2 530.4 528.6
310.2 308 305.8 303.6 301.4 299.2 297 294.8 292.6 290.4 288.2 286 283.8 281.6 279.4
1075 1072 1069 1066 1064 1061 1058 1055 1052 1050 1047 1044 1041 1038 1036
241.4 246 250.6 255.2 259.8 264.4 269 273.6 278.2 282.8 287.4 292 296.6 301.2 305.8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0566.4 566 565.6 565.2 564.8 564.4 564 563.6 563.2 562.8 562.4 562 561.6 561.2 560.8
330 330 330 330 330 330 330 330 330 330 330 330 330 330 3300 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1051 1046 1041 1035 1030 1024 1019 1014 1008 1003 997.4 992 986.6 981.2 975.8254 260 266 272 278 284 290 296 302 308 314 320 326 332 338
ii
Tabla 6.1 Coeficientes de momentos flexionantes para tableros rectangulares, franjas centrales1
i0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38784.4 775.5 766.6 757.7 748.8 739.9 731 722.1 713.2 704.3 695.4 686.5 677.6 668.7 659.8464.6 462.5 460.4 458.2 456.1 453.9 451.8 449.7 447.5 445.4 443.2 441.1 439 436.8 434.7
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0477.4 471 464.6 458.3 451.9 445.6 439.2 432.8 426.5 420.1 413.8 407.4 401 394.7 388.3157.7 157 156.3 155.6 154.8 154.1 153.4 152.7 152 151.2 150.5 149.8 149.1 148.4 147.6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0791.6 783 774.4 765.8 757.2 748.6 740 731.4 722.8 714.2 705.6 697 688.4 679.8 671.2464.6 462.5 460.4 458.2 456.1 453.9 451.8 449.7 447.5 445.4 443.2 441.1 439 436.8 434.7293.4 292 290.6 289.3 287.9 286.6 285.2 283.8 282.5 281.1 279.8 278.4 277 275.7 274.3485.5 479.5 473.5 467.5 461.4 455.4 449.4 443.4 437.4 431.3 425.3 419.3 413.3 407.3 401.2161.2 160.5 159.8 159 158.3 157.5 156.8 156.1 155.3 154.6 153.8 153.1 152.4 151.6 150.9
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0831 821.5 812 802.4 792.9 783.3 773.8 764.3 754.7 745.2 735.6 726.1 716.6 707 697.5
528.4 526 523.6 521.1 518.7 516.2 513.8 511.4 508.9 506.5 504 501.6 499.2 496.7 494.3512.3 506.5 500.7 494.9 489.2 483.4 477.6 471.8 466 460.3 454.5 448.7 442.9 437.1 431.4550.8 542.5 534.2 525.8 517.5 509.1 500.8 492.5 484.1 475.8 467.4 459.1 450.8 442.4 434.1166.8 166 165.2 164.5 163.7 163 162.2 161.4 160.7 159.9 159.2 158.4 157.6 156.9 156.1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0838.2 829 819.8 810.5 801.3 792 782.8 773.6 764.3 755.1 745.8 736.6 727.4 718.1 708.9
540 537.5 535 532.5 530 527.5 525 522.5 520 517.5 515 512.5 510 507.5 505512.3 506.5 500.7 494.9 489.2 483.4 477.6 471.8 466 460.3 454.5 448.7 442.9 437.1 431.4293.4 292 290.6 289.3 287.9 286.6 285.2 283.8 282.5 281.1 279.8 278.4 277 275.7 274.3562.4 554.5 546.6 538.8 530.9 523.1 515.2 507.3 499.5 491.6 483.8 475.9 468 460.2 452.3172.3 171.5 170.7 169.9 169.2 168.4 167.6 166.8 166 165.3 164.5 163.7 162.9 162.1 161.4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1017 1015 1013 1011 1010 1008 1006 1004 1002 1001 998.8 997 995.2 993.4 991.6
516.1 510.5 504.9 499.3 493.6 488 482.4 476.8 471.2 465.5 459.9 454.3 448.7 443.1 437.4
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
740.9 740.5 740.1 739.7 739.2 738.8 738.4 738 737.6 737.1 736.7 736.3 735.9 735.5 735
302.6 307.5 312.4 317.3 322.2 327.1 332 336.9 341.8 346.7 351.6 356.5 361.4 366.3 371.2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
570 570 570 570 570 570 570 570 570 570 570 570 570 570 570
526.8 525 523.2 521.4 519.6 517.8 516 514.2 512.4 510.6 508.8 507 505.2 503.4 501.6
277.2 275 272.8 270.6 268.4 266.2 264 261.8 259.6 257.4 255.2 253 250.8 248.6 246.4
1033 1030 1027 1024 1022 1019 1016 1013 1010 1008 1005 1002 999.2 996.4 993.6
310.4 315 319.6 324.2 328.8 333.4 338 342.6 347.2 351.8 356.4 361 365.6 370.2 374.8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0560.4 560 559.6 559.2 558.8 558.4 558 557.6 557.2 556.8 556.4 556 555.6 555.2 554.8
330 330 330 330 330 330 330 330 330 330 330 330 330 330 3300 0 0 0 0 0 0 0 0 0 0 0 0 0 0
970.4 965 959.6 954.2 948.8 943.4 938 932.6 927.2 921.8 916.4 911 905.6 900.2 894.8344 350 356 362 368 374 380 386 392 398 404 410 416 422 428
ii0.88 0.89 0.9
422.4 417.2 412
i0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53650.9 642 633.1 624.2 615.3 606.4 597.5 588.6 579.7 570.8 561.9 553 546.6 540.2 533.8432.5 430.4 428.3 426.1 424 421.8 419.7 417.6 415.4 413.3 411.1 409 407.2 405.4 403.6
0 0 0 0 0 0 0 0 0 0 0382 375.6 369.2 362.9 356.5 350.2 343.8 337.4 331.1 324.7 318.4 312 307.6 303.2 298.8
146.9 146.2 145.5 144.8 144 143.3 142.6 141.9 141.2 140.4 139.7 139 138.5 138 137.50 0 0 0 0 0 0 0 0 0 0
662.6 654 645.4 636.8 628.2 619.6 611 602.4 593.8 585.2 576.6 568 561.8 555.6 549.4432.5 430.4 428.3 426.1 424 421.8 419.7 417.6 415.4 413.3 411.1 409 407.2 405.4 403.6
273 271.6 270.2 268.9 267.5 266.2 264.8 263.4 262.1 260.7 259.4 258 257 256 255395.2 389.2 383.2 377.2 371.1 365.1 359.1 353.1 347.1 341 335 329 325.3 321.6 317.9150.1 149.4 148.7 147.9 147.2 146.4 145.7 145 144.2 143.5 142.7 142 141.5 141 140.5
0 0 0 0 0 0 0 0 0 0 0687.9 678.4 668.9 659.3 649.8 640.2 630.7 621.2 611.6 602.1 592.5 583 576.1 569.2 562.3491.8 489.4 487 484.5 482.1 479.6 477.2 474.8 472.3 469.9 467.4 465 462.7 460.4 458.1425.6 419.8 414 408.2 402.5 396.7 390.9 385.1 379.3 373.6 367.8 362 357.9 353.8 349.7425.7 417.4 409.1 400.7 392.4 384 375.7 367.4 359 350.7 342.3 334 329.1 324.2 319.3155.4 154.6 153.8 153.1 152.3 151.6 150.8 150 149.3 148.5 147.8 147 146.5 146 145.5
0 0 0 0 0 0 0 0 0 0 0699.6 690.4 681.2 671.9 662.7 653.4 644.2 635 625.7 616.5 607.2 598 591.2 584.4 577.6502.5 500 497.5 495 492.5 490 487.5 485 482.5 480 477.5 475 473 471 469425.6 419.8 414 408.2 402.5 396.7 390.9 385.1 379.3 373.6 367.8 362 357.9 353.8 349.7
273 271.6 270.2 268.9 267.5 266.2 264.8 263.4 262.1 260.7 259.4 258 257 256 255444.5 436.6 428.7 420.9 413 405.2 397.3 389.4 381.6 373.7 365.9 358 352.8 347.6 342.4160.6 159.8 159 158.2 157.5 156.7 155.9 155.1 154.3 153.6 152.8 152 151.4 150.8 150.2
0 0 0 0 0 0 0 0 0 0 0
989.8 988 986.2 984.4 982.6 980.8 979 977.2 975.4 973.6 971.8 970 962 954 946
431.8 426.2 420.6 415 409.3 403.7 398.1 392.5 386.9 381.2 375.6 370 367 364 361
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
734.6 734.2 733.8 733.4 732.9 732.5 732.1 731.7 731.3 730.8 730.4 730 724 718 712
376.1 381 385.9 390.8 395.7 400.6 405.5 410.4 415.3 420.2 425.1 430 430 430 430
0 0 0 0 0 0 0 0 0 0 0
570 570 570 570 570 570 570 570 570 570 570 570 570 570 570
499.8 498 496.2 494.4 492.6 490.8 489 487.2 485.4 483.6 481.8 480 474 468 462
244.2 242 239.8 237.6 235.4 233.2 231 228.8 226.6 224.4 222.2 220 220 220 220
990.8 988 985.2 982.4 979.6 976.8 974 971.2 968.4 965.6 962.8 960 948 936 924
379.4 384 388.6 393.2 397.8 402.4 407 411.6 416.2 420.8 425.4 430 430 430 430
0 0 0 0 0 0 0 0 0 0 0554.4 554 553.6 553.2 552.8 552.4 552 551.6 551.2 550.8 550.4 550 548 546 544
330 330 330 330 330 330 330 330 330 330 330 330 330 330 3300 0 0 0 0 0 0 0 0 0 0
889.4 884 878.6 873.2 867.8 862.4 857 851.6 846.2 840.8 835.4 830 827 824 821434 440 446 452 458 464 470 476 482 488 494 500 500 500 500
0.5 0.51 0.52565431
0 322
144
594
431
0
356
149
624545
0.88 0ii 366
0.88 158
653564
00
416168
107000
800520
71000
1060540
00
1380830
i0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68
527.4 521 514.6 508.2 501.8 495.4 489 483.3 477.6 471.9 466.2 460.5 454.8 449.1 443.4401.8 400 398.2 396.4 394.6 392.8 391 389 387 385 383 381 379 377 375
294.4 290 285.6 281.2 276.8 272.4 268 264 260 256 252 248 244 240 236137 136.5 136 135.5 135 134.5 134 133.6 133.2 132.8 132.4 132 131.6 131.2 130.8
543.2 537 530.8 524.6 518.4 512.2 506 500.5 495 489.5 484 478.5 473 467.5 462401.8 400 398.2 396.4 394.6 392.8 391 389.1 387.2 385.3 383.4 381.5 379.6 377.7 375.8
254 253 252 251 250 249 248 246.8 245.6 244.4 243.2 242 240.8 239.6 238.4314.2 310.5 306.8 303.1 299.4 295.7 292 286.8 281.6 276.4 271.2 266 260.8 255.6 250.4
140 139.5 139 138.5 138 137.5 137 136.6 136.2 135.8 135.4 135 134.6 134.2 133.8
555.4 548.5 541.6 534.7 527.8 520.9 514 507.9 501.8 495.7 489.6 483.5 477.4 471.3 465.2455.8 453.5 451.2 448.9 446.6 444.3 442 438.9 435.8 432.7 429.6 426.5 423.4 420.3 417.2345.6 341.5 337.4 333.3 329.2 325.1 321 317.2 313.4 309.6 305.8 302 298.2 294.4 290.6314.4 309.5 304.6 299.7 294.8 289.9 285 280.6 276.2 271.8 267.4 263 258.6 254.2 249.8
145 144.5 144 143.5 143 142.5 142 141.6 141.2 140.8 140.4 140 139.6 139.2 138.8
570.8 564 557.2 550.4 543.6 536.8 530 524.1 518.2 512.3 506.4 500.5 494.6 488.7 482.8467 465 463 461 459 457 455 452.4 449.8 447.2 444.6 442 439.4 436.8 434.2
345.6 341.5 337.4 333.3 329.2 325.1 321 316.6 312.2 307.8 303.4 299 294.6 290.2 285.8254 253 252 251 250 249 248 246.8 245.6 244.4 243.2 242 240.8 239.6 238.4
337.2 332 326.8 321.6 316.4 311.2 306 301.3 296.6 291.9 287.2 282.5 277.8 273.1 268.4149.6 149 148.4 147.8 147.2 146.6 146 145.6 145.2 144.8 144.4 144 143.6 143.2 142.8
938 930 922 914 906 898 890 882 874 866 858 850 842 834 826
358 355 352 349 346 343 340 337 334 331 328 325 322 319 316
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
706 700 694 688 682 676 670 664 658 652 646 640 634 628 622
430 430 430 430 430 430 430 430 430 430 430 430 430 430 430
570 570 570 570 570 570 570 570 570 570 570 570 570 570 570
456 450 444 438 432 426 420 415 410 405 400 395 390 385 380
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
912 900 888 876 864 852 840 829 818 807 796 785 774 763 752
430 430 430 430 430 430 430 430 430 430 430 430 430 430 430
542 540 538 536 534 532 530 524 518 512 506 500 494 488 482330 330 330 330 330 330 330 330 330 330 330 330 330 330 330
818 815 812 809 806 803 800 792 784 776 768 760 752 744 736500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6498412
276
139
533
412
0
306
143
548513
0312153
582541
00
354163
101000
760520
71000
950540
00
1330830
i0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83
437.7 432 426.9 421.8 416.7 411.6 406.5 401.4 396.3 391.2 386.1 381 376.2 371.4 366.6373 371 368.6 366.2 363.8 361.4 359 356.6 354.2 351.8 349.4 347 344.3 341.6 338.9
232 228 224.4 220.8 217.2 213.6 210 206.4 202.8 199.2 195.6 192 188.6 185.2 181.8130.4 130 129.8 129.6 129.4 129.2 129 128.8 128.6 128.4 128.2 128 127.9 127.8 127.7
456.5 451 446.2 441.4 436.6 431.8 427 422.2 417.4 412.6 407.8 403 398.4 393.8 389.2373.9 372 369.8 367.6 365.4 363.2 361 358.8 356.6 354.4 352.2 350 347.6 345.2 342.8237.2 236 234.6 233.2 231.8 230.4 229 227.6 226.2 224.8 223.4 222 220.4 218.8 217.2245.2 240 236.2 232.4 228.6 224.8 221 217.2 213.4 209.6 205.8 202 198.5 195 191.5133.4 133 132.8 132.6 132.4 132.2 132 131.8 131.6 131.4 131.2 131 130.8 130.6 130.4
459.1 453 447.4 441.8 436.2 430.6 425 419.4 413.8 408.2 402.6 397 391.9 386.8 381.7414.1 411 407.8 404.6 401.4 398.2 395 391.8 388.6 385.4 382.2 379 375.8 372.6 369.4286.8 283 279.7 276.4 273.1 269.8 266.5 263.2 259.9 256.6 253.3 250 246.9 243.8 240.7245.4 241 237.1 233.2 229.3 225.4 221.5 217.6 213.7 209.8 205.9 202 198.2 194.4 190.6138.4 138 137.7 137.4 137.1 136.8 136.5 136.2 135.9 135.6 135.3 135 134.9 134.8 134.7
476.9 471 465.8 460.6 455.4 450.2 445 439.8 434.6 429.4 424.2 419 414.2 409.4 404.6431.6 429 425.5 422 418.5 415 411.5 408 404.5 401 397.5 394 390.6 387.2 383.8281.4 277 274.3 271.6 268.9 266.2 263.5 260.8 258.1 255.4 252.7 250 246.9 243.8 240.7237.2 236 234.6 233.2 231.8 230.4 229 227.6 226.2 224.8 223.4 222 220.4 218.8 217.2263.7 259 254.7 250.4 246.1 241.8 237.5 233.2 228.9 224.6 220.3 216 212 208 204142.4 142 141.8 141.6 141.4 141.2 141 140.8 140.6 140.4 140.2 140 139.8 139.6 139.4
818 810 802 794 786 778 770 762 754 746 738 730 722 714 706
313 310 307 304 301 298 295 292 289 286 283 280 277 274 271
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
616 610 604 598 592 586 580 574 568 562 556 550 544 538 532
430 430 430 430 430 430 430 430 430 430 430 430 430 430 430
570 570 570 570 570 570 570 570 570 570 570 570 570 570 570
375 370 364 358 352 346 340 334 328 322 316 310 306 302 298
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
741 730 719 708 697 686 675 664 653 642 631 620 612 604 596
430 430 430 430 430 430 430 430 430 430 430 430 430 430 430
476 470 466 462 458 454 450 446 442 438 434 430 425 420 415330 330 330 330 330 330 330 330 330 330 330 330 330 330 330
728 720 712 704 696 688 680 672 664 656 648 640 633 626 619500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
i0.84 0.85 0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
361.8 357 352.2 347.4 342.6 337.8 333 328.5 324 319.5 315 310.5 306 301.5 297336.2 333.5 330.8 328.1 325.4 322.7 320 316.8 313.6 310.4 307.2 304 300.8 297.6 294.4
178.4 175 171.6 168.2 164.8 161.4 158 154.8 151.6 148.4 145.2 142 138.8 135.6 132.4127.6 127.5 127.4 127.3 127.2 127.1 127 126.9 126.8 126.7 126.6 126.5 126.4 126.3 126.2
384.6 380 375.4 370.8 366.2 361.6 357 352.8 348.6 344.4 340.2 336 331.8 327.6 323.4340.4 338 335.6 333.2 330.8 328.4 326 323.1 320.2 317.3 314.4 311.5 308.6 305.7 302.8215.6 214 212.4 210.8 209.2 207.6 206 204.4 202.8 201.2 199.6 198 196.4 194.8 193.2
188 184.5 181 177.5 174 170.5 167 163.6 160.2 156.8 153.4 150 146.6 143.2 139.8130.2 130 129.8 129.6 129.4 129.2 129 129 129 129 129 129 129 129 129
376.6 371.5 366.4 361.3 356.2 351.1 346 341.1 336.2 331.3 326.4 321.5 316.6 311.7 306.8366.2 363 359.8 356.6 353.4 350.2 347 343.8 340.6 337.4 334.2 331 327.8 324.6 321.4237.6 234.5 231.4 228.3 225.2 222.1 219 216.1 213.2 210.3 207.4 204.5 201.6 198.7 195.8186.8 183 179.2 175.4 171.6 167.8 164 160.5 157 153.5 150 146.5 143 139.5 136134.6 134.5 134.4 134.3 134.2 134.1 134 133.9 133.8 133.7 133.6 133.5 133.4 133.3 133.2
399.8 395 390.2 385.4 380.6 375.8 371 366.3 361.6 356.9 352.2 347.5 342.8 338.1 333.4380.4 377 373.6 370.2 366.8 363.4 360 356.4 352.8 349.2 345.6 342 338.4 334.8 331.2237.6 234.5 231.4 228.3 225.2 222.1 219 216.1 213.2 210.3 207.4 204.5 201.6 198.7 195.8215.6 214 212.4 210.8 209.2 207.6 206 204.4 202.8 201.2 199.6 198 196.4 194.8 193.2
200 196 192 188 184 180 176 172.1 168.2 164.3 160.4 156.5 152.6 148.7 144.8139.2 139 138.8 138.6 138.4 138.2 138 137.9 137.8 137.7 137.6 137.5 137.4 137.3 137.2
698 690 682 674 666 658 650 642 634 626 618 610 602 594 586
268 265 262 259 256 253 250 247 244 241 238 235 232 229 226
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
526 520 514 508 502 496 490 484 478 472 466 460 454 448 442
430 430 430 430 430 430 430 430 430 430 430 430 430 430 430
570 570 570 570 570 570 570 570 570 570 570 570 570 570 570
294 290 286 282 278 274 270 265 260 255 250 245 240 235 230
220 220 220 220 220 220 220 220 220 220 220 220 220 220 220
588 580 572 564 556 548 540 529 518 507 496 485 474 463 452
430 430 430 430 430 430 430 430 430 430 430 430 430 430 430
410 405 400 395 390 385 380 375 370 365 360 355 350 345 340330 330 330 330 330 330 330 330 330 330 330 330 330 330 330
612 605 598 591 584 577 570 563 556 549 542 535 528 521 514500 500 500 500 500 500 500 500 500 500 500 500 500 500 500
i ii0.99 1 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
292.5 288 1018 1008.94 999.88 990.8 981.8 972.7 963.6 954.6 945.5 936.5 927.4291.2 288 544 541.74 539.48 537.2 535 532.7 530.4 528.2 525.9 523.7 521.4
0 0 0 0 0 0 0 0 0 0129.2 126 668 661.08 654.16 647.2 640.3 633.4 626.5 619.6 612.6 605.7 598.8126.1 126 181 180.26 179.52 178.8 178 177.3 176.6 175.8 175.1 174.3 173.6
0 0 0 0 0 0 0 0 0 0319.2 315 1018 1009.52 1001 992.6 984.1 975.6 967.1 958.6 950.2 941.7 933.2299.9 297 544 541.74 539.48 537.2 535 532.7 530.4 528.2 525.9 523.7 521.4191.6 190 0 0 0 0 0 0 0 0 0 0 0136.4 133 668 661.76 655.52 649.3 643 636.8 630.6 624.3 618.1 611.8 605.6
129 129 187 186.24 185.48 184.7 184 183.2 182.4 181.7 180.9 180.2 179.40 0 0 0 0 0 0 0 0 0
301.9 297 1143 1132.62 1122.2 1112 1101 1091 1081 1070 1060 1050 1039318.2 315 687 684.16 681.32 678.5 675.6 672.8 670 667.1 664.3 661.4 658.6192.9 190 0 0 0 0 0 0 0 0 0 0 0132.5 129 912 901.08 890.16 879.2 868.3 857.4 846.5 835.6 824.6 813.7 802.8133.1 133 200 199.16 198.32 197.5 196.6 195.8 195 194.1 193.3 192.4 191.6
0 0 0 0 0 0 0 0 0 0328.7 324 1143 1133.2 1123.4 1114 1104 1094 1084 1074 1065 1055 1045327.6 324 713 710.02 707.04 704.1 701.1 698.1 695.1 692.1 689.2 686.2 683.2192.9 190 0 0 0 0 0 0 0 0 0 0 0191.6 190 0 0 0 0 0 0 0 0 0 0 0140.9 137 912 902.08 892.16 882.2 872.3 862.4 852.5 842.6 832.6 822.7 812.8137.1 137 212 211.12 210.24 209.4 208.5 207.6 206.7 205.8 205 204.1 203.2
0 0 0 0 0 0 0 0 0 0
578 570 1143 1141.54 1140.1 1139 1137 1136 1134 1133 1131 1130 1128
223 220 0 0 0 0 0 0 0 0 0 0 0
220 220 0 0 0 0 0 0 0 0 0 0 0
436 430 912 909.76 907.52 905.3 903 900.8 898.6 896.3 894.1 891.8 889.6
430 430 200 206.4 212.8 219.2 225.6 232 238.4 244.8 251.2 257.6 264
0 0 0 0 0 0 0 0 0 0
570 570 710 710 710 710 710 710 710 710 710 710 710
225 220 0 0 0 0 0 0 0 0 0 0 0
220 220 0 0 0 0 0 0 0 0 0 0 0
441 430 1670 1657.8 1645.6 1633 1621 1609 1597 1585 1572 1560 1548
430 430 250 255.8 261.6 267.4 273.2 279 284.8 290.6 296.4 302.2 308
0 0 0 0 0 0 0 0 0 0335 330 0 0 0 0 0 0 0 0 0 0 0330 330 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
507 500 1670 1664.2 1658.4 1653 1647 1641 1635 1629 1624 1618 1612500 500 250 261.6 273.2 284.8 296.4 308 319.6 331.2 342.8 354.4 366
ii0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25918.3 909.3 900.2 891.2 882.1 873 864 854.9 845.9 836.8 827.7 818.7 809.6 800.6 791.5519.1 516.9 514.6 512.4 510.1 507.8 505.6 503.3 501.1 498.8 496.5 494.3 492 489.8 487.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0591.9 585 578 571.1 564.2 557.3 550.4 543.4 536.5 529.6 522.7 515.8 508.8 501.9 495172.9 172.1 171.4 170.6 169.9 169.2 168.4 167.7 166.9 166.2 165.5 164.7 164 163.2 162.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0924.7 916.2 907.8 899.3 890.8 882.3 873.8 865.4 856.9 848.4 839.9 831.4 823 814.5 806519.1 516.9 514.6 512.4 510.1 507.8 505.6 503.3 501.1 498.8 496.5 494.3 492 489.8 487.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0599.4 593.1 586.9 580.6 574.4 568.2 561.9 555.7 549.4 543.2 537 530.7 524.5 518.2 512178.6 177.9 177.1 176.4 175.6 174.8 174.1 173.3 172.6 171.8 171 170.3 169.5 168.8 168
0 0 0 0 0 0 0 0 0 0 0 0 0 0 01029 1018 1008 997.7 987.3 976.9 966.5 956.2 945.8 935.4 925 914.6 904.3 893.9 883.5
655.8 652.9 650.1 647.2 644.4 641.6 638.7 635.9 633 630.2 627.4 624.5 621.7 618.8 6160 0 0 0 0 0 0 0 0 0 0 0 0 0 0
791.9 781 770 759.1 748.2 737.3 726.4 715.4 704.5 693.6 682.7 671.8 660.8 649.9 639190.8 189.9 189.1 188.2 187.4 186.6 185.7 184.9 184 183.2 182.4 181.5 180.7 179.8 179
0 0 0 0 0 0 0 0 0 0 0 0 0 0 01035 1025 1016 1006 996 986.2 976.4 966.6 956.8 947 937.2 927.4 917.6 907.8 898
680.2 677.2 674.3 671.3 668.3 665.3 662.3 659.4 656.4 653.4 650.4 647.4 644.5 641.5 638.50 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
802.9 793 783 773.1 763.2 753.3 743.4 733.4 723.5 713.6 703.7 693.8 683.8 673.9 664202.3 201.4 200.6 199.7 198.8 197.9 197 196.2 195.3 194.4 193.5 192.6 191.8 190.9 190
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1127 1125 1124 1123 1121 1120 1118 1117 1115 1114 1112 1111 1109 1108 1106
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
887.4 885.1 882.9 880.6 878.4 876.2 873.9 871.7 869.4 867.2 865 862.7 860.5 858.2 856
270.4 276.8 283.2 289.6 296 302.4 308.8 315.2 321.6 328 334.4 340.8 347.2 353.6 360
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
710 710 710 710 710 710 710 710 710 710 710 710 710 710 710
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1536 1524 1511 1499 1487 1475 1463 1450 1438 1426 1414 1402 1389 1377 1365
313.8 319.6 325.4 331.2 337 342.8 348.6 354.4 360.2 366 371.8 377.6 383.4 389.2 395
0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1606 1600 1595 1589 1583 1577 1571 1566 1560 1554 1548 1542 1537 1531 1525377.6 389.2 400.8 412.4 424 435.6 447.2 458.8 470.4 482 493.6 505.2 516.8 528.4 540
ii0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4782.4 773.4 764.3 755.3 746.2 737.1 728.1 719 710 700.9 691.8 682.8 673.7 664.7 655.6485.2 483 480.7 478.5 476.2 473.9 471.7 469.4 467.2 464.9 462.6 460.4 458.1 455.9 453.6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0488.1 481.2 474.2 467.3 460.4 453.5 446.6 439.6 432.7 425.8 418.9 412 405 398.1 391.2161.8 161 160.3 159.5 158.8 158.1 157.3 156.6 155.8 155.1 154.4 153.6 152.9 152.1 151.4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0797.5 789 780.6 772.1 763.6 755.1 746.6 738.2 729.7 721.2 712.7 704.2 695.8 687.3 678.8485.2 483 480.7 478.5 476.2 473.9 471.7 469.4 467.2 464.9 462.6 460.4 458.1 455.9 453.6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0505.8 499.5 493.3 487 480.8 474.6 468.3 462.1 455.8 449.6 443.4 437.1 430.9 424.6 418.4167.2 166.5 165.7 165 164.2 163.4 162.7 161.9 161.2 160.4 159.6 158.9 158.1 157.4 156.6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0873.1 862.7 852.4 842 831.6 821.2 810.8 800.5 790.1 779.7 769.3 758.9 748.6 738.2 727.8613.2 610.3 607.5 604.6 601.8 599 596.1 593.3 590.4 587.6 584.8 581.9 579.1 576.2 573.4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0628.1 617.2 606.2 595.3 584.4 573.5 562.6 551.6 540.7 529.8 518.9 508 497 486.1 475.2178.2 177.3 176.5 175.6 174.8 174 173.1 172.3 171.4 170.6 169.8 168.9 168.1 167.2 166.4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0888.2 878.4 868.6 858.8 849 839.2 829.4 819.6 809.8 800 790.2 780.4 770.6 760.8 751635.5 632.5 629.6 626.6 623.6 620.6 617.6 614.7 611.7 608.7 605.7 602.7 599.8 596.8 593.8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
654.1 644.2 634.2 624.3 614.4 604.5 594.6 584.6 574.7 564.8 554.9 545 535 525.1 515.2189.1 188.2 187.4 186.5 185.6 184.7 183.8 183 182.1 181.2 180.3 179.4 178.6 177.7 176.8
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1105 1104 1102 1101 1099 1098 1096 1095 1093 1092 1090 1089 1088 1086 1085
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
853.8 851.5 849.3 847 844.8 842.6 840.3 838.1 835.8 833.6 831.4 829.1 826.9 824.6 822.4
366.4 372.8 379.2 385.6 392 398.4 404.8 411.2 417.6 424 430.4 436.8 443.2 449.6 456
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
710 710 710 710 710 710 710 710 710 710 710 710 710 710 710
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1353 1341 1328 1316 1304 1292 1280 1267 1255 1243 1231 1219 1206 1194 1182
400.8 406.6 412.4 418.2 424 429.8 435.6 441.4 447.2 453 458.8 464.6 470.4 476.2 482
0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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ii0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55646.5 637.5 628.4 619.4 610.3 601.2 592.2 583.1 574.1 565 558.3 551.6 544.9 538.2 531.5451.3 449.1 446.8 444.6 442.3 440 437.8 435.5 433.3 431 429.1 427.2 425.3 423.4 421.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0384.3 377.4 370.4 363.5 356.6 349.7 342.8 335.8 328.9 322 317.4 312.8 308.2 303.6 299150.7 149.9 149.2 148.4 147.7 147 146.2 145.5 144.7 144 143.5 143 142.5 142 141.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0670.3 661.8 653.4 644.9 636.4 627.9 619.4 611 602.5 594 587.9 581.8 575.7 569.6 563.5451.3 449.1 446.8 444.6 442.3 440 437.8 435.5 433.3 431 429.1 427.2 425.3 423.4 421.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0412.2 405.9 399.7 393.4 387.2 381 374.7 368.5 362.2 356 351 346 341 336 331155.8 155.1 154.3 153.6 152.8 152 151.3 150.5 149.8 149 148.4 147.8 147.2 146.6 146
0 0 0 0 0 0 0 0 0 0 0 0 0 0717.4 707 696.7 686.3 675.9 665.5 655.1 644.8 634.4 624 616.4 608.8 601.2 593.6 586570.6 567.7 564.9 562 559.2 556.4 553.5 550.7 547.8 545 541.8 538.6 535.4 532.2 529
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0464.3 453.4 442.4 431.5 420.6 409.7 398.8 387.8 376.9 366 360.6 355.2 349.8 344.4 339165.6 164.7 163.9 163 162.2 161.4 160.5 159.7 158.8 158 157.5 157 156.5 156 155.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0741.2 731.4 721.6 711.8 702 692.2 682.4 672.6 662.8 653 645.9 638.8 631.7 624.6 617.5590.8 587.8 584.9 581.9 578.9 575.9 572.9 570 567 564 561.7 559.4 557.1 554.8 552.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
505.3 495.4 485.4 475.5 465.6 455.7 445.8 435.8 425.9 416 409.8 403.6 397.4 391.2 385175.9 175 174.2 173.3 172.4 171.5 170.6 169.8 168.9 168 167.5 167 166.5 166 165.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1083 1082 1080 1079 1077 1076 1074 1073 1071 1070 1064 1058 1052 1046 1040
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
820.2 817.9 815.7 813.4 811.2 809 806.7 804.5 802.2 800 796 792 788 784 780
462.4 468.8 475.2 481.6 488 494.4 500.8 507.2 513.6 520 520 520 520 520 520
0 0 0 0 0 0 0 0 0 0 0 0 0 0
710 710 710 710 710 710 710 710 710 710 710 710 710 710 710
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1170 1158 1145 1133 1121 1109 1097 1084 1072 1060 1049 1038 1027 1016 1005
487.8 493.6 499.4 505.2 511 516.8 522.6 528.4 534.2 540 540 540 540 540 540
0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0
1432 1426 1421 1415 1409 1403 1397 1392 1386 1380 1375 1370 1365 1360 1355725.6 737.2 748.8 760.4 772 783.6 795.2 806.8 818.4 830 830 830 830 830 830
ii0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7
524.8 518.1 511.4 504.7 498 492 486 480 474 468 462 456 450 444 438419.6 417.7 415.8 413.9 412 409.6 407.2 404.8 402.4 400 397.6 395.2 392.8 390.4 388
0 0 0 0 0 0 0 0 0 0 0 0 0294.4 289.8 285.2 280.6 276 272 268 264 260 256 252 248 244 240 236
141 140.5 140 139.5 139 138.6 138.2 137.8 137.4 137 136.6 136.2 135.8 135.4 1350 0 0 0 0 0 0 0 0 0 0 0 0
557.4 551.3 545.2 539.1 533 527.5 522 516.5 511 505.5 500 494.5 489 483.5 478419.6 417.7 415.8 413.9 412 410 408 406 404 402 400 398 396 394 392
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0326 321 316 311 306 301.5 297 292.5 288 283.5 279 274.5 270 265.5 261
145.4 144.8 144.2 143.6 143 142.7 142.4 142.1 141.8 141.5 141.2 140.9 140.6 140.3 1400 0 0 0 0 0 0 0 0 0 0 0 0
578.4 570.8 563.2 555.6 548 541.3 534.6 527.9 521.2 514.5 507.8 501.1 494.4 487.7 481525.8 522.6 519.4 516.2 513 508.7 504.4 500.1 495.8 491.5 487.2 482.9 478.6 474.3 470
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0333.6 328.2 322.8 317.4 312 307.1 302.2 297.3 292.4 287.5 282.6 277.7 272.8 267.9 263
155 154.5 154 153.5 153 152.6 152.2 151.8 151.4 151 150.6 150.2 149.8 149.4 1490 0 0 0 0 0 0 0 0 0 0 0 0
610.4 603.3 596.2 589.1 582 575.8 569.6 563.4 557.2 551 544.8 538.6 532.4 526.2 520550.2 547.9 545.6 543.3 541 537.5 534 530.5 527 523.5 520 516.5 513 509.5 506
0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
378.8 372.6 366.4 360.2 354 348.4 342.8 337.2 331.6 326 320.4 314.8 309.2 303.6 298165 164.5 164 163.5 163 162.5 162 161.5 161 160.5 160 159.5 159 158.5 158
0 0 0 0 0 0 0 0 0 0 0 0 0
1034 1028 1022 1016 1010 1003 996 989 982 975 968 961 954 947 940
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
776 772 768 764 760 755 750 745 740 735 730 725 720 715 710
520 520 520 520 520 520 520 520 520 520 520 520 520 520 520
0 0 0 0 0 0 0 0 0 0 0 0 0
710 710 710 710 710 710 710 710 710 710 710 710 710 710 710
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
994 983 972 961 950 940 930 920 910 900 890 880 870 860 850
540 540 540 540 540 540 540 540 540 540 540 540 540 540 540
0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0
1350 1345 1340 1335 1330 1316 1302 1288 1274 1260 1246 1232 1218 1204 1190830 830 830 830 830 830 830 830 830 830 830 830 830 830 830
ii0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85
432.9 427.8 422.7 417.6 412.5 407.4 402.3 397.2 392.1 387 382.1 377.2 372.3 367.4 362.5385.3 382.6 379.9 377.2 374.5 371.8 369.1 366.4 363.7 361 357.9 354.8 351.7 348.6 345.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0232.3 228.6 224.9 221.2 217.5 213.8 210.1 206.4 202.7 199 195.5 192 188.5 185 181.5134.8 134.6 134.4 134.2 134 133.8 133.6 133.4 133.2 133 132.8 132.6 132.4 132.2 132
0 0 0 0 0 0 0 0 0 0 0 0 0 0473.3 468.6 463.9 459.2 454.5 449.8 445.1 440.4 435.7 431 426.7 422.4 418.1 413.8 409.5389.7 387.4 385.1 382.8 380.5 378.2 375.9 373.6 371.3 369 366.2 363.4 360.6 357.8 355
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0256.8 252.6 248.4 244.2 240 235.8 231.6 227.4 223.2 219 215.2 211.4 207.6 203.8 200139.7 139.4 139.1 138.8 138.5 138.2 137.9 137.6 137.3 137 136.9 136.8 136.7 136.6 136.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0474.9 468.8 462.7 456.6 450.5 444.4 438.3 432.2 426.1 420 414.4 408.8 403.2 397.6 392465.6 461.2 456.8 452.4 448 443.6 439.2 434.8 430.4 426 421.8 417.6 413.4 409.2 405
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0258.5 254 249.5 245 240.5 236 231.5 227 222.5 218 213.7 209.4 205.1 200.8 196.5148.7 148.4 148.1 147.8 147.5 147.2 146.9 146.6 146.3 146 145.9 145.8 145.7 145.6 145.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0514.4 508.8 503.2 497.6 492 486.4 480.8 475.2 469.6 464 458.8 453.6 448.4 443.2 438501.1 496.2 491.3 486.4 481.5 476.6 471.7 466.8 461.9 457 452.3 447.6 442.9 438.2 433.5
0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
292.9 287.8 282.7 277.6 272.5 267.4 262.3 257.2 252.1 247 242.2 237.4 232.6 227.8 223157.8 157.6 157.4 157.2 157 156.8 156.6 156.4 156.2 156 155.8 155.6 155.4 155.2 155
0 0 0 0 0 0 0 0 0 0 0 0 0 0
933 926 919 912 905 898 891 884 877 870 862 854 846 838 830
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
704 698 692 686 680 674 668 662 656 650 645 640 635 630 625
520 520 520 520 520 520 520 520 520 520 520 520 520 520 520
0 0 0 0 0 0 0 0 0 0 0 0 0 0
710 710 710 710 710 710 710 710 710 710 710 710 710 710 710
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
839 828 817 806 795 784 773 762 751 740 732 724 716 708 700
540 540 540 540 540 540 540 540 540 540 540 540 540 540 540
0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0
1178 1166 1154 1142 1130 1118 1106 1094 1082 1070 1058 1046 1034 1022 1010830 830 830 830 830 830 830 830 830 830 830 830 830 830 830
ii0.86 0.87 0.88 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1
357.6 352.7 347.8 342.9 338 333.4 328.8 324.2 319.6 315 310.4 305.8 301.2 296.6 292342.4 339.3 336.2 333.1 330 326.2 322.4 318.6 314.8 311 307.2 303.4 299.6 295.8 292
0 0 0 0 0 0 0 0 0 0 0 0 0178 174.5 171 167.5 164 160.6 157.2 153.8 150.4 147 143.6 140.2 136.8 133.4 130
131.8 131.6 131.4 131.2 131 130.9 130.8 130.7 130.6 130.5 130.4 130.3 130.2 130.1 1300 0 0 0 0 0 0 0 0 0 0 0 0
405.2 400.9 396.6 392.3 388 383.8 379.6 375.4 371.2 367 362.8 358.6 354.4 350.2 346352.2 349.4 346.6 343.8 341 338 335 332 329 326 323 320 317 314 311
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0196.2 192.4 188.6 184.8 181 177.3 173.6 169.9 166.2 162.5 158.8 155.1 151.4 147.7 144136.4 136.3 136.2 136.1 136 135.9 135.8 135.7 135.6 135.5 135.4 135.3 135.2 135.1 135
0 0 0 0 0 0 0 0 0 0 0 0 0386.4 380.8 375.2 369.6 364 358.7 353.4 348.1 342.8 337.5 332.2 326.9 321.6 316.3 311400.8 396.6 392.4 388.2 384 380.2 376.4 372.6 368.8 365 361.2 357.4 353.6 349.8 346
0 0 0 0 0 0 0 0 0 0 0 0 0 0192.2 187.9 183.6 179.3 175 171 167 163 159 155 151 147 143 139 135145.4 145.3 145.2 145.1 145 144.9 144.8 144.7 144.6 144.5 144.4 144.3 144.2 144.1 144
0 0 0 0 0 0 0 0 0 0 0 0 0432.8 427.6 422.4 417.2 412 407.2 402.4 397.6 392.8 388 383.2 378.4 373.6 368.8 364428.8 424.1 419.4 414.7 410 405.4 400.8 396.2 391.6 387 382.4 377.8 373.2 368.6 364
0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0
218.2 213.4 208.6 203.8 199 194.4 189.8 185.2 180.6 176 171.4 166.8 162.2 157.6 153154.8 154.6 154.4 154.2 154 153.9 153.8 153.7 153.6 153.5 153.4 153.3 153.2 153.1 153
0 0 0 0 0 0 0 0 0 0 0 0 0
822 814 806 798 790 782 774 766 758 750 742 734 726 718 710
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
620 615 610 605 600 594 588 582 576 570 564 558 552 546 540
520 520 520 520 520 520 520 520 520 520 520 520 520 520 520
0 0 0 0 0 0 0 0 0 0 0 0 0
710 710 710 710 710 710 710 710 710 710 710 710 710 710 710
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
692 684 676 668 660 646 632 618 604 590 576 562 548 534 520
540 540 540 540 540 540 540 540 540 540 540 540 540 540 540
0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0
998 986 974 962 950 938 926 914 902 890 878 866 854 842 830830 830 830 830 830 830 830 830 830 830 830 830 830 830 830
Losa no Monolitica y otros casos Concreto Clase 1
De esquina Dos lado adyacentes discontinuo CV= 40 Determinacion de Peralte Minimo
CM= 435 Perimetro =
W= 515 Fcorreccion=F´c= 250 Pcorregido =
a1 Fy= 4200 dmin =4.7 a1= 4.7 m Hefectiva =
a2= 5.32 mm= 0.88 Revisión por cortante
a2 Fs= 2520
5.32 Wu= 721 F*c=Vcr=V=
Vu=
Diseño por FlexionMu=
As=Acero minimo por temperatura
barra # As=3 S=
Kg/m2
Kg/m2
Kg/m2
Kg/cm2
Kg/cm2
Kg/m2 FR =
Kg/m2
G11
ver NTC 1.7 factor de resistencia
D12
Wu=1.4(C.V+C.M)
G13
cortante resistente Vcr=0.5FRbd√f*c
G18
Mu=(Cof)(10-4*W*a12
Interior Todos los bordes continuosDe borde Un lado corto discontinuo
Determinacion de Peralte Minimo De borde Un lado largo discontinuo25.05m De esquina Dos lado adyacentes discontinuo
1.08 Extremo Tres bordes discontinuo un lado largo continuo27.054m Extremo Tres bordes discontinuo un lado corto continuo
11cm Aislado Cuatro lado discontinuo13cm CONCATENAR(REDONDEAR(SI(F8="m",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/170))*100,SI(F8="cm",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/170))*1)),0),"cm")
Revisión por cortante0.8
200Kg/cm26222.54Kg
821Kg944Kg pasa
Diseño por Flexion673 Kg-cm
2.02Acero minimo por temperatura
35 cm
cm2
De esquina Dos lado adyacentes discontinuo
Extremo Tres bordes discontinuo un lado largo continuoExtremo Tres bordes discontinuo un lado corto continuo
CONCATENAR(REDONDEAR(SI(F8="m",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/170))*100,SI(F8="cm",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/170))*1)),0),"cm")
CONCATENAR(REDONDEAR(SI(F8="m",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/170))*100,SI(F8="cm",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/170))*1)),0),"cm")
CONCATENAR(REDONDEAR(SI(F8="m",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-1)))/170))*100,SI(F8="cm",SI(D2="Concreto Clase 1",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/250,SI(D2="Concreto Clase 2",(VALOR(IZQUIERDA(H6,LARGO(H6)-2)))/170))*1)),0),"cm")
