calculo de losa aligerada 25.02.2015 ok. ok. ok ok

DIMENSIONES DEL ACERO PARA REFUERZO DEL CONCRETOδ conc. =

ACERO GRADO 60 F'y = 4200 Kgs. / Cm2.NORMA ASTM A - 615

BARRA DIAMETRO AREA PESO AREA ( Cm2. )N° Pulg. Cms. ( Cm2. ) Kgs. / Mts. 1 2 3 4 5 6 7

2 1/4 0.64 0.32 0.26 0.32 0.63 0.95 1.27 1.58 1.90 2.223 3/8 0.95 0.71 0.58 0.71 1.43 2.14 2.85 3.56 4.28 4.994 1/2 1.27 1.27 1.03 1.27 2.53 3.80 5.07 6.33 7.60 8.875 5/8 1.59 1.98 1.61 1.98 3.96 5.94 7.92 9.90 11.88 13.866 3/4 1.91 2.85 2.32 2.85 5.70 8.55 11.40 14.25 17.10 19.958 1 2.54 5.07 4.12 5.07 10.13 15.20 20.27 25.34 30.40 35.479 1 1/8 2.86 6.41 5.22 6.41 12.83 19.24 25.65 32.07 38.48 44.89

10 1 1/4 3.18 7.92 6.44 7.92 15.83 23.75 31.67 39.59 47.50 55.42

### Kg / ( Mts * Cm2 )

8 9 10

2.53 2.85 3.175.70 6.41 7.13

10.13 11.40 12.6715.83 17.81 19.7922.80 25.65 28.5040.54 45.60 50.6751.30 57.72 64.1363.34 71.26 79.17

f'c = 280 Kg/cm² f'c = 210 Kg/cm²

fy = 4200 Kg/cm² fy = 4200 Kg/cm²

ρb = 0.0289 ρb = 0.0289

ρ Ku ρ Ku ρ

0.0106 36.3093 0.0052 18.4500

0.0104 35.6938 0.0050 17.7847

0.0102 35.0756 0.0048 17.1164

0.0100 34.4548 0.0046 16.4442

0.0098 33.8340 0.0044 15.7695

0.0096 33.2132 0.0042 15.0872

0.0094 32.5924 0.0040 14.4064

0.0092 31.9716 0.0038 13.7200

0.0090 31.3508 0.0036 13.0300

0.0088 30.7300 0.0034 12.3364

0.0086 30.1092 0.0032 11.6393

0.0084 29.4884 0.0030 10.9386

0.0082 28.8676 0.0028 10.2343

0.0080 28.2468 0.0026 9.5265

0.0078 27.6260 0.0024 8.8151

0.0076 26.7958 0.0022 8.1002

0.0074 26.1400 0.0020 7.3816

0.0072 25.4819 0.0018 6.6575

0.0070 24.8209 0.0016 5.9339

0.0068 24.1572 0.0014 5.2016

0.0066 23.4909 0.0012 4.4718

0.0064 22.8218 0.0010 3.7354

0.0062 22.1501 0.0008 2.9855

0.0060 21.4758 0.0006 2.2520

0.0058 20.7987 0.0004 1.5047

0.0056 20.1190 0.0002 0.7543

0.0054 19.4366 0.0000 0.0000

0.0052 18.7515

0.0050 18.0637

0.0048 17.3733

0.0046 16.6802

0.0044 15.9844

0.0042 15.4332

0.0040 14.7053

0.0038 13.9774

0.0036 13.2495

0.0034 12.5216

0.0032 11.7937

0.0030 11.0658

TABLA Ku vs ρ

0.0028 10.3379

0.0026 9.6100

0.0024 8.8821

0.0022 8.1542

0.0020 7.4263

0.0018 6.6957

0.0016 5.9624

0.0014 5.2265

0.0012 4.4879

0.0010 3.7166

0.0008 3.0027

f'c = 175 Kg/cm²

fy = 4200 Kg/cm²

ρb = 0.0289

ρ Ku

0.0024 8.7637 f'c = 210 Kg/cm²

0.0022 8.0570 Para fy = 4200 Kg/cm²

0.0020 7.3457 Ku = 18.4500

0.0018 6.6306 usar = 0.0052

0.0016 5.9110

0.0014 5.1871

0.0012 4.4587

0.0010 3.7265

0.0008 2.9598

0.0006 2.2497

0.0004 1.5350

0.0002 0.7539

0.0000 0.0000

p

0.0000

TABLA: 1.0 VALORES TIPICOS DE CARGA VIVA PARA EL DISEÑO DE EDIFICACIONESTIPO DE EDIFICACION CARGA VIVA KG/M2

1.0 VIVIENDAS

1.1 VIVIENDAS 200

2.0 OFICINAS

2.1 EXCEPTUANDO SALAS DE ARCHIVO Y COMPUTACION 250

SALAS DE ARCHIVO 500

SALAS DE COMPUTACION 350

CORREDORES Y ESCALERAS 400

3.0 CENTROS EDUCATIVOS

3.1 AULAS 200

3.2 TALLERES 350

3.3 AUDITORIOS Y GIMNASIOS 300

3.4 LABORATORIOS 300

3.5 CORREDORES Y ESCALERAS 400

4.0 HOSPITALES

4.1 SALSA DE OPERACIÓN, LABORATORIO Y AREAS DE SERVICIO 300

4.2 CUARTOS 200


3.0 BIBLIOTECAS

3.1 SALAS DE LECTURA 300

3.2 SALAS DE ALMACENAJE 750


Fuente REGLAMENTO NACIONAL DE CONSTRUCCIONES, CAPECO, LIMA 1994,10a Edicion.

D2

usuario: SEGÚN REGLAMENTO NACIONAL DE CONSTRUCCIONES, CAPECO, LIMA 1994,10a Edicion.

MOM. RESIST. - f'c = 175 kg/cm2

ALIGERADOS DE 17 cms. Fierro As M+ M-1(3/8) 0.713 0.397 0.3771(1/2) 1.267 0.697 0.6322(3/8) 1.425 0.781 0.699

3/8+1/2 1.979 1.070 0.9131(5/8) 1.979 1.070 0.9132(1/2) 2.534 1.351 1.093

1/2+5/8 3.246 1.700 1.2772(5/8) 3.959 2.035 1.406

Vu LUZ Mu

V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

Peso propio = 0.27 Tn/m2Piso + acab. = 0.10 Tn/m2

A.- AZOTEASSobrecarga 0.150 Tn/m2

Wu = 0.330 Tn/m2(No inc. 0,1 Tn/m2 de albañileria)Vu LUZ Mu

V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.379 0.330 2.00 0.165 0.147 0.132 0.120 0.110 0.094 0.083 0.0550.417 0.363 2.20 0.200 0.177 0.160 0.145 0.133 0.114 0.100 0.0670.455 0.396 2.40 0.238 0.211 0.190 0.173 0.158 0.136 0.119 0.0790.493 0.429 2.60 0.279 0.248 0.223 0.203 0.186 0.159 0.139 0.0930.531 0.462 2.80 0.323 0.287 0.259 0.235 0.216 0.185 0.162 0.1080.569 0.495 3.00 0.371 0.330 0.297 0.270 0.248 0.212 0.186 0.1240.607 0.528 3.20 0.422 0.375 0.338 0.307 0.282 0.241 0.211 0.1410.645 0.561 3.40 0.477 0.424 0.381 0.347 0.318 0.272 0.238 0.1590.683 0.594 3.60 0.535 0.475 0.428 0.389 0.356 0.305 0.267 0.1780.721 0.627 3.80 0.596 0.529 0.477 0.433 0.397 0.340 0.298 0.1990.759 0.660 4.00 0.660 0.587 0.528 0.480 0.440 0.377 0.330 0.2200.797 0.693 4.20 0.728 0.647 0.582 0.529 0.485 0.416 0.364 0.2430.835 0.726 4.40 0.799 0.710 0.639 0.581 0.532 0.456 0.399 0.2660.873 0.759 4.60 0.873 0.776 0.698 0.635 0.582 0.499 0.436 0.2910.911 0.792 4.80 0.950 0.845 0.760 0.691 0.634 0.543 0.475 0.3170.949 0.825 5.00 1.031 0.917 0.825 0.750 0.688 0.589 0.516 0.3440.987 0.858 5.20 1.115 0.991 0.892 0.811 0.744 0.637 0.558 0.3721.025 0.891 5.40 1.203 1.069 0.962 0.875 0.802 0.687 0.601 0.4011.063 0.924 5.60 1.294 1.150 1.035 0.941 0.862 0.739 0.647 0.4311.101 0.957 5.80 1.388 1.233 1.110 1.009 0.925 0.793 0.694 0.4631.138 0.990 6.00 1.485 1.320 1.188 1.080 0.990 0.849 0.743 0.4951.176 1.023 6.20 1.586 1.409 1.269 1.153 1.057 0.906 0.793 0.5291.214 1.056 6.40 1.690 1.502 1.352 1.229 1.126 0.965 0.845 0.5631.252 1.089 6.60 1.797 1.597 1.437 1.307 1.198 1.027 0.898 0.5991.290 1.122 6.80 1.907 1.695 1.526 1.387 1.272 1.090 0.954 0.636

1.328 1.155 7.00 2.021 1.797 1.617 1.470 1.348 1.155 1.011 0.674

B.- VIVIENDASSobrecarga 0.200 Tn/m2

Wu = 0.426 Tn/m2(Inc. 0,1 Tn/m2 de albañileria)Vu LUZ Mu

V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

V1 = 1,15 x Wu x L/2 V2 = Wu x L/2 Mu = C x Wu x L2

0.490 0.426 2.00 0.213 0.189 0.170 0.155 0.142 0.122 0.107 0.0710.539 0.469 2.20 0.258 0.229 0.206 0.187 0.172 0.147 0.129 0.0860.588 0.511 2.40 0.307 0.273 0.245 0.223 0.204 0.175 0.153 0.1020.637 0.554 2.60 0.360 0.320 0.288 0.262 0.240 0.206 0.180 0.1200.686 0.596 2.80 0.417 0.371 0.334 0.304 0.278 0.239 0.209 0.1390.735 0.639 3.00 0.479 0.426 0.383 0.349 0.320 0.274 0.240 0.1600.784 0.682 3.20 0.545 0.485 0.436 0.397 0.364 0.312 0.273 0.1820.833 0.724 3.40 0.616 0.547 0.492 0.448 0.410 0.352 0.308 0.2050.882 0.767 3.60 0.690 0.613 0.552 0.502 0.460 0.394 0.345 0.2300.931 0.809 3.80 0.769 0.683 0.615 0.559 0.513 0.439 0.384 0.2560.980 0.852 4.00 0.852 0.757 0.682 0.620 0.568 0.487 0.426 0.2841.029 0.895 4.20 0.939 0.835 0.751 0.683 0.626 0.537 0.470 0.3131.078 0.937 4.40 1.031 0.916 0.825 0.750 0.687 0.589 0.515 0.3441.127 0.980 4.60 1.127 1.002 0.901 0.819 0.751 0.644 0.563 0.3761.176 1.022 4.80 1.227 1.091 0.982 0.892 0.818 0.701 0.613 0.4091.225 1.065 5.00 1.331 1.183 1.065 0.968 0.888 0.761 0.666 0.4441.274 1.108 5.20 1.440 1.280 1.152 1.047 0.960 0.823 0.720 0.4801.323 1.150 5.40 1.553 1.380 1.242 1.129 1.035 0.887 0.776 0.5181.372 1.193 5.60 1.670 1.484 1.336 1.214 1.113 0.954 0.835 0.5571.421 1.235 5.80 1.791 1.592 1.433 1.303 1.194 1.024 0.896 0.5971.470 1.278 6.00 1.917 1.704 1.534 1.394 1.278 1.095 0.959 0.6391.519 1.321 6.20 2.047 1.819 1.638 1.489 1.365 1.170 1.023 0.6821.568 1.363 6.40 2.181 1.939 1.745 1.586 1.454 1.246 1.091 0.7271.617 1.406 6.60 2.320 2.062 1.856 1.687 1.546 1.325 1.160 0.7731.666 1.448 6.80 2.462 2.189 1.970 1.791 1.642 1.407 1.231 0.821

1.715 1.491 7.00 2.609 2.319 2.087 1.898 1.739 1.491 1.305 0.870

C.- VARIOSSobrecarga 0.300 Tn/m2


V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.504 0.438 2.00 0.219 0.195 0.175 0.159 0.146 0.125 0.110 0.0730.554 0.482 2.20 0.265 0.236 0.212 0.193 0.177 0.151 0.132 0.0880.604 0.526 2.40 0.315 0.280 0.252 0.229 0.210 0.180 0.158 0.1050.655 0.569 2.60 0.370 0.329 0.296 0.269 0.247 0.211 0.185 0.1230.705 0.613 2.80 0.429 0.382 0.343 0.312 0.286 0.245 0.215 0.1430.756 0.657 3.00 0.493 0.438 0.394 0.358 0.329 0.282 0.246 0.1640.806 0.701 3.20 0.561 0.498 0.449 0.408 0.374 0.320 0.280 0.1870.856 0.745 3.40 0.633 0.563 0.506 0.460 0.422 0.362 0.316 0.2110.907 0.788 3.60 0.710 0.631 0.568 0.516 0.473 0.405 0.355 0.2370.957 0.832 3.80 0.791 0.703 0.632 0.575 0.527 0.452 0.395 0.2641.007 0.876 4.00 0.876 0.779 0.701 0.637 0.584 0.501 0.438 0.2921.058 0.920 4.20 0.966 0.858 0.773 0.702 0.644 0.552 0.483 0.3221.108 0.964 4.40 1.060 0.942 0.848 0.771 0.707 0.606 0.530 0.3531.159 1.007 4.60 1.159 1.030 0.927 0.843 0.772 0.662 0.579 0.3861.209 1.051 4.80 1.261 1.121 1.009 0.917 0.841 0.721 0.631 0.4201.259 1.095 5.00 1.369 1.217 1.095 0.995 0.913 0.782 0.684 0.4561.310 1.139 5.20 1.480 1.316 1.184 1.077 0.987 0.846 0.740 0.4931.360 1.183 5.40 1.597 1.419 1.277 1.161 1.064 0.912 0.798 0.5321.410 1.226 5.60 1.717 1.526 1.374 1.249 1.145 0.981 0.858 0.5721.461 1.270 5.80 1.842 1.637 1.473 1.339 1.228 1.052 0.921 0.6141.511 1.314 6.00 1.971 1.752 1.577 1.433 1.314 1.126 0.986 0.6571.561 1.358 6.20 2.105 1.871 1.684 1.531 1.403 1.203 1.052 0.702

1.612 1.402 6.40 2.243 1.993 1.794 1.631 1.495 1.281 1.121 0.7481.662 1.445 6.60 2.385 2.120 1.908 1.734 1.590 1.363 1.192 0.7951.713 1.489 6.80 2.532 2.250 2.025 1.841 1.688 1.447 1.266 0.844

1.763 1.533 7.00 2.683 2.385 2.146 1.951 1.789 1.533 1.341 0.894

D.- VARIOSSobrecarga 0.400 Tn/m2


V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.586 0.510 2.00 0.255 0.227 0.204 0.185 0.170 0.146 0.128 0.0850.645 0.561 2.20 0.309 0.274 0.247 0.224 0.206 0.176 0.154 0.1030.704 0.612 2.40 0.367 0.326 0.294 0.267 0.245 0.210 0.184 0.1220.762 0.663 2.60 0.431 0.383 0.345 0.313 0.287 0.246 0.215 0.1440.821 0.714 2.80 0.500 0.444 0.400 0.363 0.333 0.286 0.250 0.1670.880 0.765 3.00 0.574 0.510 0.459 0.417 0.383 0.328 0.287 0.1910.938 0.816 3.20 0.653 0.580 0.522 0.475 0.435 0.373 0.326 0.2180.997 0.867 3.40 0.737 0.655 0.590 0.536 0.491 0.421 0.368 0.2461.056 0.918 3.60 0.826 0.734 0.661 0.601 0.551 0.472 0.413 0.2751.114 0.969 3.80 0.921 0.818 0.736 0.669 0.614 0.526 0.460 0.3071.173 1.020 4.00 1.020 0.907 0.816 0.742 0.680 0.583 0.510 0.3401.232 1.071 4.20 1.125 1.000 0.900 0.818 0.750 0.643 0.562 0.3751.290 1.122 4.40 1.234 1.097 0.987 0.898 0.823 0.705 0.617 0.4111.349 1.173 4.60 1.349 1.199 1.079 0.981 0.899 0.771 0.674 0.4501.408 1.224 4.80 1.469 1.306 1.175 1.068 0.979 0.839 0.734 0.4901.466 1.275 5.00 1.594 1.417 1.275 1.159 1.063 0.911 0.797 0.5311.525 1.326 5.20 1.724 1.532 1.379 1.254 1.149 0.985 0.862 0.5751.584 1.377 5.40 1.859 1.652 1.487 1.352 1.239 1.062 0.929 0.6201.642 1.428 5.60 1.999 1.777 1.599 1.454 1.333 1.142 1.000 0.6661.701 1.479 5.80 2.145 1.906 1.716 1.560 1.430 1.225 1.072 0.7151.759 1.530 6.00 2.295 2.040 1.836 1.669 1.530 1.311 1.148 0.7651.818 1.581 6.20 2.451 2.178 1.960 1.782 1.634 1.400 1.225 0.8171.877 1.632 6.40 2.611 2.321 2.089 1.899 1.741 1.492 1.306 0.8701.935 1.683 6.60 2.777 2.468 2.222 2.020 1.851 1.587 1.388 0.9261.994 1.734 6.80 2.948 2.620 2.358 2.144 1.965 1.684 1.474 0.983

2.053 1.785 7.00 3.124 2.777 2.499 2.272 2.083 1.785 1.562 1.041

E.- VARIOSSobrecarga 0.500 Tn/m2


V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.669 0.582 2.00 0.291 0.259 0.233 0.212 0.194 0.166 0.146 0.0970.736 0.640 2.20 0.352 0.313 0.282 0.256 0.235 0.201 0.176 0.1170.803 0.698 2.40 0.419 0.372 0.335 0.305 0.279 0.239 0.210 0.1400.870 0.757 2.60 0.492 0.437 0.393 0.358 0.328 0.281 0.246 0.1640.937 0.815 2.80 0.570 0.507 0.456 0.415 0.380 0.326 0.285 0.1901.004 0.873 3.00 0.655 0.582 0.524 0.476 0.437 0.374 0.327 0.2181.071 0.931 3.20 0.745 0.662 0.596 0.542 0.497 0.426 0.372 0.2481.138 0.989 3.40 0.841 0.748 0.673 0.612 0.561 0.481 0.420 0.2801.205 1.048 3.60 0.943 0.838 0.754 0.686 0.629 0.539 0.471 0.3141.272 1.106 3.80 1.051 0.934 0.840 0.764 0.700 0.600 0.525 0.3501.339 1.164 4.00 1.164 1.035 0.931 0.847 0.776 0.665 0.582 0.3881.406 1.222 4.20 1.283 1.141 1.027 0.933 0.856 0.733 0.642 0.4281.472 1.280 4.40 1.408 1.252 1.127 1.024 0.939 0.805 0.704 0.469

1.539 1.339 4.60 1.539 1.368 1.232 1.120 1.026 0.880 0.770 0.5131.606 1.397 4.80 1.676 1.490 1.341 1.219 1.117 0.958 0.838 0.5591.673 1.455 5.00 1.819 1.617 1.455 1.323 1.213 1.039 0.909 0.6061.740 1.513 5.20 1.967 1.749 1.574 1.431 1.311 1.124 0.984 0.6561.807 1.571 5.40 2.121 1.886 1.697 1.543 1.414 1.212 1.061 0.7071.874 1.630 5.60 2.281 2.028 1.825 1.659 1.521 1.304 1.141 0.7601.941 1.688 5.80 2.447 2.175 1.958 1.780 1.632 1.398 1.224 0.8162.008 1.746 6.00 2.619 2.328 2.095 1.905 1.746 1.497 1.310 0.8732.075 1.804 6.20 2.797 2.486 2.237 2.034 1.864 1.598 1.398 0.9322.142 1.862 6.40 2.980 2.649 2.384 2.167 1.987 1.703 1.490 0.9932.209 1.921 6.60 3.169 2.817 2.535 2.305 2.113 1.811 1.584 1.0562.276 1.979 6.80 3.364 2.990 2.691 2.447 2.243 1.922 1.682 1.121

2.343 2.037 7.00 3.565 3.169 2.852 2.593 2.377 2.037 1.782 1.188

ALIGERADOS DE 17 cms.

Vu LUZ Mu

V1 V2 (L) 1/8 1/9

Peso propio = 0.27 Tn/m2Piso + acab. = 0.10 Tn/m2


Wu = 0.330 Tn/m2 (No inc. 0,1 Tn/m2 de albañileria)Vu LUZ

V1 Verif V2 Verif (L) 1/8 Verif 1/9 Verif

0.379 0.000 0.330 0.000 2.00 0.165 0.000 0.147 0.0000.417 0.000 0.363 0.000 2.20 0.200 0.000 0.177 0.0000.455 0.000 0.396 0.000 2.40 0.238 0.000 0.211 0.0000.493 0.000 0.429 0.000 2.60 0.279 0.000 0.248 0.0000.531 0.000 0.462 0.000 2.80 0.323 0.000 0.287 0.0000.569 0.000 0.495 0.000 3.00 0.371 0.000 0.330 0.0000.607 0.000 0.528 0.000 3.20 0.422 0.000 0.375 0.0000.645 0.000 0.561 0.000 3.40 0.477 0.000 0.424 0.0000.683 0.000 0.594 0.000 3.60 0.535 0.000 0.475 0.0000.721 0.000 0.627 0.000 3.80 0.596 0.000 0.529 0.0000.759 0.000 0.660 0.000 4.00 0.660 0.000 0.587 0.0000.797 0.000 0.693 0.000 4.20 0.728 0.000 0.647 0.0000.835 0.000 0.726 0.000 4.40 0.799 0.000 0.710 0.0000.873 0.000 0.759 0.000 4.60 0.873 0.000 0.776 0.0000.911 0.000 0.792 0.000 4.80 0.950 0.000 0.845 0.0000.949 0.000 0.825 0.000 5.00 1.031 0.000 0.917 0.0000.987 0.000 0.858 0.000 5.20 1.115 0.000 0.991 0.0001.025 0.000 0.891 0.000 5.40 1.203 0.000 1.069 0.0001.063 0.000 0.924 0.000 5.60 1.294 0.000 1.150 0.0001.101 0.000 0.957 0.000 5.80 1.388 0.000 1.233 0.0001.138 0.000 0.990 0.000 6.00 1.485 0.000 1.320 0.0001.176 0.000 1.023 0.000 6.20 1.586 0.000 1.409 0.0001.214 0.000 1.056 0.000 6.40 1.690 0.000 1.502 0.0001.252 0.000 1.089 0.000 6.60 1.797 0.000 1.597 0.0001.290 0.000 1.122 0.000 6.80 1.907 0.000 1.695 0.000

1.328 0.000 1.155 0.000 7.00 2.021 0.000 1.797 0.000




Nota.- Cuando las columnas V1 y V2 se presentan azul, significa que se necesita ensanche por corte exterior o interiormente


0.490 0.000 0.426 0.000 2.00 0.213 0.000 0.189 0.0000.539 0.000 0.469 0.000 2.20 0.258 0.000 0.229 0.0000.588 0.000 0.511 0.000 2.40 0.307 0.000 0.273 0.0000.637 0.000 0.554 0.000 2.60 0.360 0.000 0.320 0.0000.686 0.000 0.596 0.000 2.80 0.417 0.000 0.371 0.0000.735 0.000 0.639 0.000 3.00 0.479 0.000 0.426 0.0000.784 0.000 0.682 0.000 3.20 0.545 0.000 0.485 0.0000.833 0.000 0.724 0.000 3.40 0.616 0.000 0.547 0.0000.882 0.000 0.767 0.000 3.60 0.690 0.000 0.613 0.0000.931 0.000 0.809 0.000 3.80 0.769 0.000 0.683 0.0000.980 0.000 0.852 0.000 4.00 0.852 0.000 0.757 0.0001.029 0.000 0.895 0.000 4.20 0.939 0.000 0.835 0.0001.078 0.000 0.937 0.000 4.40 1.031 0.000 0.916 0.0001.127 0.000 0.980 0.000 4.60 1.127 0.000 1.002 0.0001.176 0.000 1.022 0.000 4.80 1.227 0.000 1.091 0.0001.225 0.000 1.065 0.000 5.00 1.331 0.000 1.183 0.0001.274 0.000 1.108 0.000 5.20 1.440 0.000 1.280 0.0001.323 0.000 1.150 0.000 5.40 1.553 0.000 1.380 0.0001.372 0.000 1.193 0.000 5.60 1.670 0.000 1.484 0.0001.421 0.000 1.235 0.000 5.80 1.791 0.000 1.592 0.0001.470 0.000 1.278 0.000 6.00 1.917 0.000 1.704 0.0001.519 0.000 1.321 0.000 6.20 2.047 0.000 1.819 0.0001.568 0.000 1.363 0.000 6.40 2.181 0.000 1.939 0.0001.617 0.000 1.406 0.000 6.60 2.320 0.000 2.062 0.0001.666 0.000 1.448 0.000 6.80 2.462 0.000 2.189 0.000

1.715 0.000 1.491 0.000 7.00 2.609 0.000 2.319 0.000




0.504 0.000 0.438 0.000 2.00 0.219 0.000 0.195 0.0000.554 0.000 0.482 0.000 2.20 0.265 0.000 0.236 0.0000.604 0.000 0.526 0.000 2.40 0.315 0.000 0.280 0.0000.655 0.000 0.569 0.000 2.60 0.370 0.000 0.329 0.0000.705 0.000 0.613 0.000 2.80 0.429 0.000 0.382 0.0000.756 0.000 0.657 0.000 3.00 0.493 0.000 0.438 0.0000.806 0.000 0.701 0.000 3.20 0.561 0.000 0.498 0.0000.856 0.000 0.745 0.000 3.40 0.633 0.000 0.563 0.0000.907 0.000 0.788 0.000 3.60 0.710 0.000 0.631 0.0000.957 0.000 0.832 0.000 3.80 0.791 0.000 0.703 0.0001.007 0.000 0.876 0.000 4.00 0.876 0.000 0.779 0.0001.058 0.000 0.920 0.000 4.20 0.966 0.000 0.858 0.0001.108 0.000 0.964 0.000 4.40 1.060 0.000 0.942 0.0001.159 0.000 1.007 0.000 4.60 1.159 0.000 1.030 0.0001.209 0.000 1.051 0.000 4.80 1.261 0.000 1.121 0.0001.259 0.000 1.095 0.000 5.00 1.369 0.000 1.217 0.0001.310 0.000 1.139 0.000 5.20 1.480 0.000 1.316 0.0001.360 0.000 1.183 0.000 5.40 1.597 0.000 1.419 0.0001.410 0.000 1.226 0.000 5.60 1.717 0.000 1.526 0.0001.461 0.000 1.270 0.000 5.80 1.842 0.000 1.637 0.0001.511 0.000 1.314 0.000 6.00 1.971 0.000 1.752 0.0001.561 0.000 1.358 0.000 6.20 2.105 0.000 1.871 0.000

1.612 0.000 1.402 0.000 6.40 2.243 0.000 1.993 0.0001.662 0.000 1.445 0.000 6.60 2.385 0.000 2.120 0.0001.713 0.000 1.489 0.000 6.80 2.532 0.000 2.250 0.000

1.763 0.000 1.533 0.000 7.00 2.683 0.000 2.385 0.000




0.586 0.000 0.510 0.000 2.00 0.255 0.000 0.227 0.0000.645 0.000 0.561 0.000 2.20 0.309 0.000 0.274 0.0000.704 0.000 0.612 0.000 2.40 0.367 0.000 0.326 0.0000.762 0.000 0.663 0.000 2.60 0.431 0.000 0.383 0.0000.821 0.000 0.714 0.000 2.80 0.500 0.000 0.444 0.0000.880 0.000 0.765 0.000 3.00 0.574 0.000 0.510 0.0000.938 0.000 0.816 0.000 3.20 0.653 0.000 0.580 0.0000.997 0.000 0.867 0.000 3.40 0.737 0.000 0.655 0.0001.056 0.000 0.918 0.000 3.60 0.826 0.000 0.734 0.0001.114 0.000 0.969 0.000 3.80 0.921 0.000 0.818 0.0001.173 0.000 1.020 0.000 4.00 1.020 0.000 0.907 0.0001.232 0.000 1.071 0.000 4.20 1.125 0.000 1.000 0.0001.290 0.000 1.122 0.000 4.40 1.234 0.000 1.097 0.0001.349 0.000 1.173 0.000 4.60 1.349 0.000 1.199 0.0001.408 0.000 1.224 0.000 4.80 1.469 0.000 1.306 0.0001.466 0.000 1.275 0.000 5.00 1.594 0.000 1.417 0.0001.525 0.000 1.326 0.000 5.20 1.724 0.000 1.532 0.0001.584 0.000 1.377 0.000 5.40 1.859 0.000 1.652 0.0001.642 0.000 1.428 0.000 5.60 1.999 0.000 1.777 0.0001.701 0.000 1.479 0.000 5.80 2.145 0.000 1.906 0.0001.759 0.000 1.530 0.000 6.00 2.295 0.000 2.040 0.0001.818 0.000 1.581 0.000 6.20 2.451 0.000 2.178 0.0001.877 0.000 1.632 0.000 6.40 2.611 0.000 2.321 0.0001.935 0.000 1.683 0.000 6.60 2.777 0.000 2.468 0.0001.994 0.000 1.734 0.000 6.80 2.948 0.000 2.620 0.000

2.053 0.000 1.785 0.000 7.00 3.124 0.000 2.777 0.000




0.669 0.000 0.582 0.000 2.00 0.291 0.000 0.259 0.0000.736 0.000 0.640 0.000 2.20 0.352 0.000 0.313 0.0000.803 0.000 0.698 0.000 2.40 0.419 0.000 0.372 0.0000.870 0.000 0.757 0.000 2.60 0.492 0.000 0.437 0.0000.937 0.000 0.815 0.000 2.80 0.570 0.000 0.507 0.0001.004 0.000 0.873 0.000 3.00 0.655 0.000 0.582 0.0001.071 0.000 0.931 0.000 3.20 0.745 0.000 0.662 0.0001.138 0.000 0.989 0.000 3.40 0.841 0.000 0.748 0.0001.205 0.000 1.048 0.000 3.60 0.943 0.000 0.838 0.0001.272 0.000 1.106 0.000 3.80 1.051 0.000 0.934 0.0001.339 0.000 1.164 0.000 4.00 1.164 0.000 1.035 0.0001.406 0.000 1.222 0.000 4.20 1.283 0.000 1.141 0.0001.472 0.000 1.280 0.000 4.40 1.408 0.000 1.252 0.000

1.539 0.000 1.339 0.000 4.60 1.539 0.000 1.368 0.0001.606 0.000 1.397 0.000 4.80 1.676 0.000 1.490 0.0001.673 0.000 1.455 0.000 5.00 1.819 0.000 1.617 0.0001.740 0.000 1.513 0.000 5.20 1.967 0.000 1.749 0.0001.807 0.000 1.571 0.000 5.40 2.121 0.000 1.886 0.0001.874 0.000 1.630 0.000 5.60 2.281 0.000 2.028 0.0001.941 0.000 1.688 0.000 5.80 2.447 0.000 2.175 0.0002.008 0.000 1.746 0.000 6.00 2.619 0.000 2.328 0.0002.075 0.000 1.804 0.000 6.20 2.797 0.000 2.486 0.0002.142 0.000 1.862 0.000 6.40 2.980 0.000 2.649 0.0002.209 0.000 1.921 0.000 6.60 3.169 0.000 2.817 0.0002.276 0.000 1.979 0.000 6.80 3.364 0.000 2.990 0.000

2.343 0.000 2.037 0.000 7.00 3.565 0.000 3.169 0.000

MOM. RESIST. f'c = 175 kg/cm2

Fierro As M+ M-1(3/8) 0.713 #N/A #N/A1(1/2) 1.267 #N/A 0.632 Kg-m2(3/8) 1.425 #N/A 0.699 Kg-m

3/8+1/2 1.979 #N/A 0.913 Kg-m1(5/8) 1.979 #N/A 0.913 Kg-m2(1/2) 2.534 #N/A 1.093 Kg-m

1/2+5/8 3.246 #N/A 1.277 Kg-m2(5/8) 3.959 #N/A 1.406 Kg-m

Mu

1/10 1/11 1/12 1/14 1/16 1/24

(No inc. 0,1 Tn/m2 de albañileria)Mu

1/10 Verif 1/11 Verif 1/12 Verif 1/14 Verif 1/16 Verif 1/24 Verif

0.132 0.000 0.120 0.000 0.110 0.000 0.094 0.000 0.082 0.000 0.055 0.0000.160 0.000 0.145 0.000 0.133 0.000 0.114 0.000 0.100 0.000 0.067 0.0000.190 0.000 0.173 0.000 0.158 0.000 0.136 0.000 0.119 0.000 0.079 0.0000.223 0.000 0.203 0.000 0.186 0.000 0.159 0.000 0.139 0.000 0.093 0.0000.259 0.000 0.235 0.000 0.216 0.000 0.185 0.000 0.162 0.000 0.108 0.0000.297 0.000 0.270 0.000 0.247 0.000 0.212 0.000 0.186 0.000 0.124 0.0000.338 0.000 0.307 0.000 0.282 0.000 0.241 0.000 0.211 0.000 0.141 0.0000.381 0.000 0.347 0.000 0.318 0.000 0.272 0.000 0.238 0.000 0.159 0.0000.428 0.000 0.389 0.000 0.356 0.000 0.305 0.000 0.267 0.000 0.178 0.0000.477 0.000 0.433 0.000 0.397 0.000 0.340 0.000 0.298 0.000 0.199 0.0000.528 0.000 0.480 0.000 0.440 0.000 0.377 0.000 0.330 0.000 0.220 0.0000.582 0.000 0.529 0.000 0.485 0.000 0.416 0.000 0.364 0.000 0.243 0.0000.639 0.000 0.581 0.000 0.532 0.000 0.456 0.000 0.399 0.000 0.266 0.0000.698 0.000 0.635 0.000 0.582 0.000 0.499 0.000 0.436 0.000 0.291 0.0000.760 0.000 0.691 0.000 0.634 0.000 0.543 0.000 0.475 0.000 0.317 0.0000.825 0.000 0.750 0.000 0.688 0.000 0.589 0.000 0.516 0.000 0.344 0.0000.892 0.000 0.811 0.000 0.744 0.000 0.637 0.000 0.558 0.000 0.372 0.0000.962 0.000 0.875 0.000 0.802 0.000 0.687 0.000 0.601 0.000 0.401 0.0001.035 0.000 0.941 0.000 0.862 0.000 0.739 0.000 0.647 0.000 0.431 0.0001.110 0.000 1.009 0.000 0.925 0.000 0.793 0.000 0.694 0.000 0.463 0.0001.188 0.000 1.080 0.000 0.990 0.000 0.849 0.000 0.742 0.000 0.495 0.0001.269 0.000 1.153 0.000 1.057 0.000 0.906 0.000 0.793 0.000 0.529 0.0001.352 0.000 1.229 0.000 1.126 0.000 0.965 0.000 0.845 0.000 0.563 0.0001.437 0.000 1.307 0.000 1.198 0.000 1.027 0.000 0.898 0.000 0.599 0.0001.526 0.000 1.387 0.000 1.272 0.000 1.090 0.000 0.954 0.000 0.636 0.000

1.617 0.000 1.470 0.000 1.348 0.000 1.155 0.000 1.011 0.000 0.674 0.000




0.170 0.000 0.155 0.000 0.142 0.000 0.122 0.000 0.107 0.000 0.071 0.0000.206 0.000 0.187 0.000 0.172 0.000 0.147 0.000 0.129 0.000 0.086 0.0000.245 0.000 0.223 0.000 0.204 0.000 0.175 0.000 0.153 0.000 0.102 0.0000.288 0.000 0.262 0.000 0.240 0.000 0.206 0.000 0.180 0.000 0.120 0.0000.334 0.000 0.304 0.000 0.278 0.000 0.239 0.000 0.209 0.000 0.139 0.0000.383 0.000 0.349 0.000 0.320 0.000 0.274 0.000 0.240 0.000 0.160 0.0000.436 0.000 0.397 0.000 0.364 0.000 0.312 0.000 0.273 0.000 0.182 0.0000.492 0.000 0.448 0.000 0.410 0.000 0.352 0.000 0.308 0.000 0.205 0.0000.552 0.000 0.502 0.000 0.460 0.000 0.394 0.000 0.345 0.000 0.230 0.0000.615 0.000 0.559 0.000 0.513 0.000 0.439 0.000 0.384 0.000 0.256 0.0000.682 0.000 0.620 0.000 0.568 0.000 0.487 0.000 0.426 0.000 0.284 0.0000.751 0.000 0.683 0.000 0.626 0.000 0.537 0.000 0.470 0.000 0.313 0.0000.825 0.000 0.750 0.000 0.687 0.000 0.589 0.000 0.515 0.000 0.344 0.0000.901 0.000 0.819 0.000 0.751 0.000 0.644 0.000 0.563 0.000 0.376 0.0000.982 0.000 0.892 0.000 0.818 0.000 0.701 0.000 0.613 0.000 0.409 0.0001.065 0.000 0.968 0.000 0.887 0.000 0.761 0.000 0.666 0.000 0.444 0.0001.152 0.000 1.047 0.000 0.960 0.000 0.823 0.000 0.720 0.000 0.480 0.0001.242 0.000 1.129 0.000 1.035 0.000 0.887 0.000 0.776 0.000 0.518 0.0001.336 0.000 1.214 0.000 1.113 0.000 0.954 0.000 0.835 0.000 0.557 0.0001.433 0.000 1.303 0.000 1.194 0.000 1.024 0.000 0.896 0.000 0.597 0.0001.534 0.000 1.394 0.000 1.278 0.000 1.095 0.000 0.959 0.000 0.639 0.0001.638 0.000 1.489 0.000 1.365 0.000 1.170 0.000 1.023 0.000 0.682 0.0001.745 0.000 1.586 0.000 1.454 0.000 1.246 0.000 1.091 0.000 0.727 0.0001.856 0.000 1.687 0.000 1.546 0.000 1.325 0.000 1.160 0.000 0.773 0.0001.970 0.000 1.791 0.000 1.642 0.000 1.407 0.000 1.231 0.000 0.821 0.000

2.087 0.000 1.898 0.000 1.739 0.000 1.491 0.000 1.305 0.000 0.870 0.000



0.175 0.000 0.159 0.000 0.146 0.000 0.125 0.000 0.110 0.000 0.073 0.0000.212 0.000 0.193 0.000 0.177 0.000 0.151 0.000 0.132 0.000 0.088 0.0000.252 0.000 0.229 0.000 0.210 0.000 0.180 0.000 0.158 0.000 0.105 0.0000.296 0.000 0.269 0.000 0.247 0.000 0.211 0.000 0.185 0.000 0.123 0.0000.343 0.000 0.312 0.000 0.286 0.000 0.245 0.000 0.215 0.000 0.143 0.0000.394 0.000 0.358 0.000 0.329 0.000 0.282 0.000 0.246 0.000 0.164 0.0000.449 0.000 0.408 0.000 0.374 0.000 0.320 0.000 0.280 0.000 0.187 0.0000.506 0.000 0.460 0.000 0.422 0.000 0.362 0.000 0.316 0.000 0.211 0.0000.568 0.000 0.516 0.000 0.473 0.000 0.405 0.000 0.355 0.000 0.237 0.0000.632 0.000 0.575 0.000 0.527 0.000 0.452 0.000 0.395 0.000 0.264 0.0000.701 0.000 0.637 0.000 0.584 0.000 0.501 0.000 0.438 0.000 0.292 0.0000.773 0.000 0.702 0.000 0.644 0.000 0.552 0.000 0.483 0.000 0.322 0.0000.848 0.000 0.771 0.000 0.707 0.000 0.606 0.000 0.530 0.000 0.353 0.0000.927 0.000 0.843 0.000 0.772 0.000 0.662 0.000 0.579 0.000 0.386 0.0001.009 0.000 0.917 0.000 0.841 0.000 0.721 0.000 0.631 0.000 0.420 0.0001.095 0.000 0.995 0.000 0.913 0.000 0.782 0.000 0.684 0.000 0.456 0.0001.184 0.000 1.077 0.000 0.987 0.000 0.846 0.000 0.740 0.000 0.493 0.0001.277 0.000 1.161 0.000 1.064 0.000 0.912 0.000 0.798 0.000 0.532 0.0001.374 0.000 1.249 0.000 1.145 0.000 0.981 0.000 0.858 0.000 0.572 0.0001.473 0.000 1.339 0.000 1.228 0.000 1.052 0.000 0.921 0.000 0.614 0.0001.577 0.000 1.433 0.000 1.314 0.000 1.126 0.000 0.986 0.000 0.657 0.0001.684 0.000 1.531 0.000 1.403 0.000 1.203 0.000 1.052 0.000 0.702 0.000

1.794 0.000 1.631 0.000 1.495 0.000 1.281 0.000 1.121 0.000 0.748 0.0001.908 0.000 1.734 0.000 1.590 0.000 1.363 0.000 1.192 0.000 0.795 0.0002.025 0.000 1.841 0.000 1.688 0.000 1.447 0.000 1.266 0.000 0.844 0.000

2.146 0.000 1.951 0.000 1.789 0.000 1.533 0.000 1.341 0.000 0.894 0.000



0.204 0.000 0.185 0.000 0.170 0.000 0.146 0.000 0.128 0.000 0.085 0.0000.247 0.000 0.224 0.000 0.206 0.000 0.176 0.000 0.154 0.000 0.103 0.0000.294 0.000 0.267 0.000 0.245 0.000 0.210 0.000 0.184 0.000 0.122 0.0000.345 0.000 0.313 0.000 0.287 0.000 0.246 0.000 0.215 0.000 0.144 0.0000.400 0.000 0.363 0.000 0.333 0.000 0.286 0.000 0.250 0.000 0.167 0.0000.459 0.000 0.417 0.000 0.383 0.000 0.328 0.000 0.287 0.000 0.191 0.0000.522 0.000 0.475 0.000 0.435 0.000 0.373 0.000 0.326 0.000 0.218 0.0000.590 0.000 0.536 0.000 0.491 0.000 0.421 0.000 0.368 0.000 0.246 0.0000.661 0.000 0.601 0.000 0.551 0.000 0.472 0.000 0.413 0.000 0.275 0.0000.736 0.000 0.669 0.000 0.614 0.000 0.526 0.000 0.460 0.000 0.307 0.0000.816 0.000 0.742 0.000 0.680 0.000 0.583 0.000 0.510 0.000 0.340 0.0000.900 0.000 0.818 0.000 0.750 0.000 0.643 0.000 0.562 0.000 0.375 0.0000.987 0.000 0.898 0.000 0.823 0.000 0.705 0.000 0.617 0.000 0.411 0.0001.079 0.000 0.981 0.000 0.899 0.000 0.771 0.000 0.674 0.000 0.450 0.0001.175 0.000 1.068 0.000 0.979 0.000 0.839 0.000 0.734 0.000 0.490 0.0001.275 0.000 1.159 0.000 1.063 0.000 0.911 0.000 0.797 0.000 0.531 0.0001.379 0.000 1.254 0.000 1.149 0.000 0.985 0.000 0.862 0.000 0.575 0.0001.487 0.000 1.352 0.000 1.239 0.000 1.062 0.000 0.929 0.000 0.620 0.0001.599 0.000 1.454 0.000 1.333 0.000 1.142 0.000 1.000 0.000 0.666 0.0001.716 0.000 1.560 0.000 1.430 0.000 1.225 0.000 1.072 0.000 0.715 0.0001.836 0.000 1.669 0.000 1.530 0.000 1.311 0.000 1.148 0.000 0.765 0.0001.960 0.000 1.782 0.000 1.634 0.000 1.400 0.000 1.225 0.000 0.817 0.0002.089 0.000 1.899 0.000 1.741 0.000 1.492 0.000 1.306 0.000 0.870 0.0002.222 0.000 2.020 0.000 1.851 0.000 1.587 0.000 1.388 0.000 0.926 0.0002.358 0.000 2.144 0.000 1.965 0.000 1.684 0.000 1.474 0.000 0.983 0.000

2.499 0.000 2.272 0.000 2.083 0.000 1.785 0.000 1.562 0.000 1.041 0.000



0.233 0.000 0.212 0.000 0.194 0.000 0.166 0.000 0.146 0.000 0.097 0.0000.282 0.000 0.256 0.000 0.235 0.000 0.201 0.000 0.176 0.000 0.117 0.0000.335 0.000 0.305 0.000 0.279 0.000 0.239 0.000 0.210 0.000 0.140 0.0000.393 0.000 0.358 0.000 0.328 0.000 0.281 0.000 0.246 0.000 0.164 0.0000.456 0.000 0.415 0.000 0.380 0.000 0.326 0.000 0.285 0.000 0.190 0.0000.524 0.000 0.476 0.000 0.437 0.000 0.374 0.000 0.327 0.000 0.218 0.0000.596 0.000 0.542 0.000 0.497 0.000 0.426 0.000 0.372 0.000 0.248 0.0000.673 0.000 0.612 0.000 0.561 0.000 0.481 0.000 0.420 0.000 0.280 0.0000.754 0.000 0.686 0.000 0.629 0.000 0.539 0.000 0.471 0.000 0.314 0.0000.840 0.000 0.764 0.000 0.700 0.000 0.600 0.000 0.525 0.000 0.350 0.0000.931 0.000 0.847 0.000 0.776 0.000 0.665 0.000 0.582 0.000 0.388 0.0001.027 0.000 0.933 0.000 0.856 0.000 0.733 0.000 0.642 0.000 0.428 0.0001.127 0.000 1.024 0.000 0.939 0.000 0.805 0.000 0.704 0.000 0.469 0.000

1.232 0.000 1.120 0.000 1.026 0.000 0.880 0.000 0.770 0.000 0.513 0.0001.341 0.000 1.219 0.000 1.117 0.000 0.958 0.000 0.838 0.000 0.559 0.0001.455 0.000 1.323 0.000 1.213 0.000 1.039 0.000 0.909 0.000 0.606 0.0001.574 0.000 1.431 0.000 1.311 0.000 1.124 0.000 0.984 0.000 0.656 0.0001.697 0.000 1.543 0.000 1.414 0.000 1.212 0.000 1.061 0.000 0.707 0.0001.825 0.000 1.659 0.000 1.521 0.000 1.304 0.000 1.141 0.000 0.760 0.0001.958 0.000 1.780 0.000 1.632 0.000 1.398 0.000 1.224 0.000 0.816 0.0002.095 0.000 1.905 0.000 1.746 0.000 1.497 0.000 1.310 0.000 0.873 0.0002.237 0.000 2.034 0.000 1.864 0.000 1.598 0.000 1.398 0.000 0.932 0.0002.384 0.000 2.167 0.000 1.987 0.000 1.703 0.000 1.490 0.000 0.993 0.0002.535 0.000 2.305 0.000 2.113 0.000 1.811 0.000 1.584 0.000 1.056 0.0002.691 0.000 2.447 0.000 2.243 0.000 1.922 0.000 1.682 0.000 1.121 0.000

2.852 0.000 2.593 0.000 2.377 0.000 2.037 0.000 1.782 0.000 1.188 0.000

Sección transversal de vigueta :bf

PROP:ELEMENTO:NIVEL: tf

hGEOMETRIA DE SECCION

h = 0.17 m. bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. twd = #N/A

MATERIAL DE LA SECCIONf'c = 210 Kg/cm2 fy = 4200 Kg/cm2

Fuerzas y Momentos Resistentes :Verificacion de la Seccion

0.0212 - 0.0159 - 0.0024 -

OK

Momentos Maximos Resistentes:

7.225 cm2 -

Mu max ( + ) = #N/A = #N/A #N/A

-

#N/A #N/A

Mu max ( - ) = #N/A = #N/A #N/A

-

-

-

-

#N/A #N/A

Mu min ( + ) = #N/A #N/A #N/A

-

#N/A #N/A

Mu min ( - ) = #N/A #N/A #N/A

-

-

Fuerza Cortante Maxima Resistente : -

7.18 Kg/cm2 -

Vu resistente #N/A #N/A

OK

HOJA DE VIGUETAS DE ALIGERADOS

VIGUETA DE SECCION CUALQUIERA

rb =rmax =rmin =

Momentos Maximos :As max =

As max =

Momentos Minimos :As min =

As min =

nu max =

Ø (pulg)PESO PROPIO DE LAS LOSAS ALIGERADAS 1/4"HLosa Alig. Peso Propio Según el RNC 3/8"

Cm KG/M2 Kg/cm2 12mm17.00 247.00 280.00 1/2"20.00 284.00 300.00 5/8"25.00 345.00 350.00 3/4"

7/8"PESO DE LOSA ALIGERADA 1"Para nuestra losa aligerada

según luz h = 10.00 cm 3.1HLosa Aligerada = h = 17.00 cm

Peso de Losa Aligerada = 280.00 Kg/cm2

Numero de Viguetas por Mts = 2.50 Vig. / Mts.

Recubrimiento = 2.50 cm. 0.025 M

Acero principal a usar = 1/2"

Diámetro acero principal - a usar = #N/A Cm. #N/A M

d = #N/A Cm. #N/A M

AT7

usuario: CONSIDERAR HASTA LUCES DE 5.00M

AT8

usuario: CONSIDERAR EN LUCES MAYORES DE 5.50M

AT18

Spacheco: cuando el area de acero es inferior al minimo arroja falso en distribucion de acero en viguetas de luces mayores

Ø (cm) As (cm²)0.64 0.310.95 0.710.80 1.131.27 1.271.59 1.981.91 2.852.22 3.882.54 5.07

3.1 3.1 3.1

MOM. RESIST. - f'c = 175 kg/cm2

ALIGERADOS DE 20 cms. Fierro As M+ M-1(3/8) 0.713 0.478 0.4571(1/2) 1.267 0.840 0.7762(3/8) 1.425 0.942 0.860

3/8+1/2 1.979 1.294 1.1361(5/8) 1.979 1.294 1.1362(1/2) 2.534 1.637 1.379

1/2+5/8 3.246 2.066 1.6442(5/8) 3.959 2.482 1.853

Vu LUZ Mu

V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

Peso propio = 0.30 Tn/m2Piso + acab. = 0.10 Tn/m2Tabiqueria. = 0.12 Tn/m2


Wu = 0.348 Tn/m2 (No inc. 0,1 Tn/m2 de albañileria)Vu LUZ Mu

V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.400 0.348 2.00 0.174 0.155 0.139 0.127 0.116 0.099 0.087 0.0580.440 0.383 2.20 0.211 0.187 0.168 0.153 0.140 0.120 0.105 0.0700.480 0.418 2.40 0.251 0.223 0.200 0.182 0.167 0.143 0.125 0.0840.520 0.452 2.60 0.294 0.261 0.235 0.214 0.196 0.168 0.147 0.0980.560 0.487 2.80 0.341 0.303 0.273 0.248 0.227 0.195 0.171 0.1140.600 0.522 3.00 0.392 0.348 0.313 0.285 0.261 0.224 0.196 0.1310.640 0.557 3.20 0.445 0.396 0.356 0.324 0.297 0.255 0.223 0.1480.680 0.592 3.40 0.503 0.447 0.402 0.366 0.335 0.287 0.251 0.1680.720 0.626 3.60 0.564 0.501 0.451 0.410 0.376 0.322 0.282 0.1880.760 0.661 3.80 0.628 0.558 0.503 0.457 0.419 0.359 0.314 0.2090.800 0.696 4.00 0.696 0.619 0.557 0.506 0.464 0.398 0.348 0.2320.840 0.731 4.20 0.767 0.682 0.614 0.558 0.512 0.438 0.384 0.2560.880 0.766 4.40 0.842 0.749 0.674 0.612 0.561 0.481 0.421 0.2810.920 0.800 4.60 0.920 0.818 0.736 0.669 0.614 0.526 0.460 0.3070.960 0.835 4.80 1.002 0.891 0.802 0.729 0.668 0.573 0.501 0.3341.001 0.870 5.00 1.088 0.967 0.870 0.791 0.725 0.621 0.544 0.3631.041 0.905 5.20 1.176 1.046 0.941 0.855 0.784 0.672 0.588 0.3921.081 0.940 5.40 1.268 1.128 1.015 0.923 0.846 0.725 0.634 0.4231.121 0.974 5.60 1.364 1.213 1.091 0.992 0.909 0.780 0.682 0.4551.161 1.009 5.80 1.463 1.301 1.171 1.064 0.976 0.836 0.732 0.4881.201 1.044 6.00 1.566 1.392 1.253 1.139 1.044 0.895 0.783 0.5221.241 1.079 6.20 1.672 1.486 1.338 1.216 1.115 0.956 0.836 0.5571.281 1.114 6.40 1.782 1.584 1.425 1.296 1.188 1.018 0.891 0.5941.321 1.148 6.60 1.895 1.684 1.516 1.378 1.263 1.083 0.947 0.6321.361 1.183 6.80 2.011 1.788 1.609 1.463 1.341 1.149 1.006 0.670

1.401 1.218 7.00 2.132 1.895 1.705 1.550 1.421 1.218 1.066 0.711


Wu = 0.444 Tn/m2 (Inc. 0,1 Tn/m2 de albañileria)Vu LUZ Mu

V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24


0.511 0.444 2.00 0.222 0.197 0.178 0.161 0.148 0.127 0.111 0.0740.562 0.488 2.20 0.269 0.239 0.215 0.195 0.179 0.153 0.134 0.0900.613 0.533 2.40 0.320 0.284 0.256 0.232 0.213 0.183 0.160 0.1070.664 0.577 2.60 0.375 0.333 0.300 0.273 0.250 0.214 0.188 0.1250.715 0.622 2.80 0.435 0.387 0.348 0.316 0.290 0.249 0.218 0.1450.766 0.666 3.00 0.500 0.444 0.400 0.363 0.333 0.285 0.250 0.1670.817 0.710 3.20 0.568 0.505 0.455 0.413 0.379 0.325 0.284 0.1890.868 0.755 3.40 0.642 0.570 0.513 0.467 0.428 0.367 0.321 0.2140.919 0.799 3.60 0.719 0.639 0.575 0.523 0.480 0.411 0.360 0.2400.970 0.844 3.80 0.801 0.712 0.641 0.583 0.534 0.458 0.401 0.2671.021 0.888 4.00 0.888 0.789 0.710 0.646 0.592 0.507 0.444 0.2961.072 0.932 4.20 0.979 0.870 0.783 0.712 0.653 0.559 0.490 0.3261.123 0.977 4.40 1.074 0.955 0.860 0.781 0.716 0.614 0.537 0.3581.174 1.021 4.60 1.174 1.044 0.940 0.854 0.783 0.671 0.587 0.3911.225 1.066 4.80 1.279 1.137 1.023 0.930 0.852 0.731 0.639 0.4261.277 1.110 5.00 1.388 1.233 1.110 1.009 0.925 0.793 0.694 0.4631.328 1.154 5.20 1.501 1.334 1.201 1.091 1.000 0.858 0.750 0.5001.379 1.199 5.40 1.618 1.439 1.295 1.177 1.079 0.925 0.809 0.5391.430 1.243 5.60 1.740 1.547 1.392 1.266 1.160 0.995 0.870 0.5801.481 1.288 5.80 1.867 1.660 1.494 1.358 1.245 1.067 0.934 0.6221.532 1.332 6.00 1.998 1.776 1.598 1.453 1.332 1.142 0.999 0.6661.583 1.376 6.20 2.133 1.896 1.707 1.552 1.422 1.219 1.067 0.7111.634 1.421 6.40 2.273 2.021 1.819 1.653 1.516 1.299 1.137 0.7581.685 1.465 6.60 2.418 2.149 1.934 1.758 1.612 1.381 1.209 0.8061.736 1.510 6.80 2.566 2.281 2.053 1.866 1.711 1.466 1.283 0.855

1.787 1.554 7.00 2.720 2.417 2.176 1.978 1.813 1.554 1.360 0.907



V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.524 0.456 2.00 0.228 0.203 0.182 0.166 0.152 0.130 0.114 0.0760.577 0.502 2.20 0.276 0.245 0.221 0.201 0.184 0.158 0.138 0.0920.629 0.547 2.40 0.328 0.292 0.263 0.239 0.219 0.188 0.164 0.1090.682 0.593 2.60 0.385 0.343 0.308 0.280 0.257 0.220 0.193 0.1280.734 0.638 2.80 0.447 0.397 0.358 0.325 0.298 0.255 0.223 0.1490.787 0.684 3.00 0.513 0.456 0.410 0.373 0.342 0.293 0.257 0.1710.839 0.730 3.20 0.584 0.519 0.467 0.424 0.389 0.334 0.292 0.1950.891 0.775 3.40 0.659 0.586 0.527 0.479 0.439 0.377 0.329 0.2200.944 0.821 3.60 0.739 0.657 0.591 0.537 0.492 0.422 0.369 0.2460.996 0.866 3.80 0.823 0.732 0.658 0.599 0.549 0.470 0.412 0.2741.049 0.912 4.00 0.912 0.811 0.730 0.663 0.608 0.521 0.456 0.3041.101 0.958 4.20 1.005 0.894 0.804 0.731 0.670 0.575 0.503 0.3351.154 1.003 4.40 1.104 0.981 0.883 0.803 0.736 0.631 0.552 0.3681.206 1.049 4.60 1.206 1.072 0.965 0.877 0.804 0.689 0.603 0.4021.259 1.094 4.80 1.313 1.167 1.051 0.955 0.876 0.750 0.657 0.4381.311 1.140 5.00 1.425 1.267 1.140 1.036 0.950 0.814 0.713 0.4751.363 1.186 5.20 1.541 1.370 1.233 1.121 1.028 0.881 0.771 0.5141.416 1.231 5.40 1.662 1.477 1.330 1.209 1.108 0.950 0.831 0.5541.468 1.277 5.60 1.788 1.589 1.430 1.300 1.192 1.021 0.894 0.5961.521 1.322 5.80 1.917 1.704 1.534 1.395 1.278 1.096 0.959 0.6391.573 1.368 6.00 2.052 1.824 1.642 1.492 1.368 1.173 1.026 0.6841.626 1.414 6.20 2.191 1.948 1.753 1.594 1.461 1.252 1.096 0.730

1.678 1.459 6.40 2.335 2.075 1.868 1.698 1.556 1.334 1.167 0.7781.731 1.505 6.60 2.483 2.207 1.986 1.806 1.655 1.419 1.241 0.8281.783 1.550 6.80 2.636 2.343 2.109 1.917 1.757 1.506 1.318 0.879

1.835 1.596 7.00 2.793 2.483 2.234 2.031 1.862 1.596 1.397 0.931



V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.607 0.528 2.00 0.264 0.235 0.211 0.192 0.176 0.151 0.132 0.0880.668 0.581 2.20 0.319 0.284 0.256 0.232 0.213 0.183 0.160 0.1060.729 0.634 2.40 0.380 0.338 0.304 0.276 0.253 0.217 0.190 0.1270.789 0.686 2.60 0.446 0.397 0.357 0.324 0.297 0.255 0.223 0.1490.850 0.739 2.80 0.517 0.460 0.414 0.376 0.345 0.296 0.259 0.1720.911 0.792 3.00 0.594 0.528 0.475 0.432 0.396 0.339 0.297 0.1980.972 0.845 3.20 0.676 0.601 0.541 0.492 0.451 0.386 0.338 0.2251.032 0.898 3.40 0.763 0.678 0.610 0.555 0.509 0.436 0.381 0.2541.093 0.950 3.60 0.855 0.760 0.684 0.622 0.570 0.489 0.428 0.2851.154 1.003 3.80 0.953 0.847 0.762 0.693 0.635 0.545 0.477 0.3181.214 1.056 4.00 1.056 0.939 0.845 0.768 0.704 0.603 0.528 0.3521.275 1.109 4.20 1.164 1.035 0.931 0.847 0.776 0.665 0.582 0.3881.336 1.162 4.40 1.278 1.136 1.022 0.929 0.852 0.730 0.639 0.4261.397 1.214 4.60 1.397 1.241 1.117 1.016 0.931 0.798 0.698 0.4661.457 1.267 4.80 1.521 1.352 1.217 1.106 1.014 0.869 0.760 0.5071.518 1.320 5.00 1.650 1.467 1.320 1.200 1.100 0.943 0.825 0.5501.579 1.373 5.20 1.785 1.586 1.428 1.298 1.190 1.020 0.892 0.5951.639 1.426 5.40 1.925 1.711 1.540 1.400 1.283 1.100 0.962 0.6421.700 1.478 5.60 2.070 1.840 1.656 1.505 1.380 1.183 1.035 0.6901.761 1.531 5.80 2.220 1.974 1.776 1.615 1.480 1.269 1.110 0.7401.822 1.584 6.00 2.376 2.112 1.901 1.728 1.584 1.358 1.188 0.7921.882 1.637 6.20 2.537 2.255 2.030 1.845 1.691 1.450 1.269 0.8461.943 1.690 6.40 2.703 2.403 2.163 1.966 1.802 1.545 1.352 0.9012.004 1.742 6.60 2.875 2.556 2.300 2.091 1.917 1.643 1.437 0.9582.064 1.795 6.80 3.052 2.713 2.441 2.220 2.035 1.744 1.526 1.017

2.125 1.848 7.00 3.234 2.875 2.587 2.352 2.156 1.848 1.617 1.078



V1 V2 (L) 1/8 1/9 1/10 1/11 1/12 1/14 1/16 1/24

0.690 0.600 2.00 0.300 0.267 0.240 0.218 0.200 0.171 0.150 0.1000.759 0.660 2.20 0.363 0.323 0.290 0.264 0.242 0.207 0.182 0.1210.828 0.720 2.40 0.432 0.384 0.346 0.314 0.288 0.247 0.216 0.1440.897 0.780 2.60 0.507 0.451 0.406 0.369 0.338 0.290 0.254 0.1690.966 0.840 2.80 0.588 0.523 0.470 0.428 0.392 0.336 0.294 0.1961.035 0.900 3.00 0.675 0.600 0.540 0.491 0.450 0.386 0.338 0.2251.104 0.960 3.20 0.768 0.683 0.614 0.559 0.512 0.439 0.384 0.2561.173 1.020 3.40 0.867 0.771 0.694 0.631 0.578 0.495 0.434 0.2891.242 1.080 3.60 0.972 0.864 0.778 0.707 0.648 0.555 0.486 0.3241.311 1.140 3.80 1.083 0.963 0.866 0.788 0.722 0.619 0.542 0.3611.380 1.200 4.00 1.200 1.067 0.960 0.873 0.800 0.686 0.600 0.4001.449 1.260 4.20 1.323 1.176 1.058 0.962 0.882 0.756 0.662 0.4411.518 1.320 4.40 1.452 1.291 1.162 1.056 0.968 0.830 0.726 0.484

1.587 1.380 4.60 1.587 1.411 1.270 1.154 1.058 0.907 0.793 0.5291.656 1.440 4.80 1.728 1.536 1.382 1.257 1.152 0.987 0.864 0.5761.725 1.500 5.00 1.875 1.667 1.500 1.364 1.250 1.071 0.938 0.6251.794 1.560 5.20 2.028 1.803 1.622 1.475 1.352 1.159 1.014 0.6761.863 1.620 5.40 2.187 1.944 1.750 1.591 1.458 1.250 1.094 0.7291.932 1.680 5.60 2.352 2.091 1.882 1.711 1.568 1.344 1.176 0.7842.001 1.740 5.80 2.523 2.243 2.018 1.835 1.682 1.442 1.262 0.8412.070 1.800 6.00 2.700 2.400 2.160 1.964 1.800 1.543 1.350 0.9002.139 1.860 6.20 2.883 2.563 2.306 2.097 1.922 1.647 1.442 0.9612.208 1.920 6.40 3.072 2.731 2.458 2.234 2.048 1.755 1.536 1.0242.277 1.980 6.60 3.267 2.904 2.614 2.376 2.178 1.867 1.633 1.0892.346 2.040 6.80 3.468 3.083 2.774 2.522 2.312 1.982 1.734 1.156

2.415 2.100 7.00 3.675 3.267 2.940 2.673 2.450 2.100 1.838 1.225

ALIGERADOS DE 20 cms.

Vu LUZ Mu

V1 V2 (L) 1/8 1/9

ojoPeso propio = 0.30 Tn/m2Piso + acab. = 0.10 Tn/m2




0.400 0.000 0.348 0.000 2.00 0.174 0.000 0.155 0.0000.440 0.000 0.383 0.000 2.20 0.211 0.000 0.187 0.0000.480 0.000 0.418 0.000 2.40 0.251 0.000 0.223 0.0000.520 0.000 0.452 0.000 2.60 0.294 0.000 0.261 0.0000.560 0.000 0.487 0.000 2.80 0.341 0.000 0.303 0.0000.600 0.000 0.522 0.000 3.00 0.392 0.000 0.348 0.0000.640 0.000 0.557 0.000 3.20 0.445 0.000 0.396 0.0000.680 0.000 0.592 0.000 3.40 0.503 0.000 0.447 0.0000.720 0.000 0.626 0.000 3.60 0.564 0.000 0.501 0.0000.760 0.000 0.661 0.000 3.80 0.628 0.000 0.558 0.0000.800 0.000 0.696 0.000 4.00 0.696 0.000 0.619 0.0000.840 0.000 0.731 0.000 4.20 0.767 0.000 0.682 0.0000.880 0.000 0.766 0.000 4.40 0.842 0.000 0.749 0.0000.920 0.000 0.800 0.000 4.60 0.920 0.000 0.818 0.0000.960 0.000 0.835 0.000 4.80 1.002 0.000 0.891 0.0001.001 0.000 0.870 0.000 5.00 1.088 0.000 0.967 0.0001.041 0.000 0.905 0.000 5.20 1.176 0.000 1.046 0.0001.081 0.000 0.940 0.000 5.40 1.268 0.000 1.128 0.0001.121 0.000 0.974 0.000 5.60 1.364 0.000 1.213 0.0001.161 0.000 1.009 0.000 5.80 1.463 0.000 1.301 0.0001.201 0.000 1.044 0.000 6.00 1.566 0.000 1.392 0.0001.241 0.000 1.079 0.000 6.20 1.672 0.000 1.486 0.0001.281 0.000 1.114 0.000 6.40 1.782 0.000 1.584 0.0001.321 0.000 1.148 0.000 6.60 1.895 0.000 1.684 0.0001.361 0.000 1.183 0.000 6.80 2.011 0.000 1.788 0.000

1.401 0.000 1.218 0.000 7.00 2.132 0.000 1.895 0.000






0.511 0.000 0.444 0.000 2.00 0.222 0.000 0.197 0.0000.562 0.000 0.488 0.000 2.20 0.269 0.000 0.239 0.0000.613 0.000 0.533 0.000 2.40 0.320 0.000 0.284 0.0000.664 0.000 0.577 0.000 2.60 0.375 0.000 0.333 0.0000.715 0.000 0.622 0.000 2.80 0.435 0.000 0.387 0.0000.766 0.000 0.666 0.000 3.00 0.500 0.000 0.444 0.0000.817 0.000 0.710 0.000 3.20 0.568 0.000 0.505 0.0000.868 0.000 0.755 0.000 3.40 0.642 0.000 0.570 0.0000.919 0.000 0.799 0.000 3.60 0.719 0.000 0.639 0.0000.970 0.000 0.844 0.000 3.80 0.801 0.000 0.712 0.0001.021 0.000 0.888 0.000 4.00 0.888 0.000 0.789 0.0001.072 0.000 0.932 0.000 4.20 0.979 0.000 0.870 0.0001.123 0.000 0.977 0.000 4.40 1.074 0.000 0.955 0.0001.174 0.000 1.021 0.000 4.60 1.174 0.000 1.044 0.0001.225 0.000 1.066 0.000 4.80 1.279 0.000 1.137 0.0001.277 0.000 1.110 0.000 5.00 1.388 0.000 1.233 0.0001.328 0.000 1.154 0.000 5.20 1.501 0.000 1.334 0.0001.379 0.000 1.199 0.000 5.40 1.618 0.000 1.439 0.0001.430 0.000 1.243 0.000 5.60 1.740 0.000 1.547 0.0001.481 0.000 1.288 0.000 5.80 1.867 0.000 1.660 0.0001.532 0.000 1.332 0.000 6.00 1.998 0.000 1.776 0.0001.583 0.000 1.376 0.000 6.20 2.133 0.000 1.896 0.0001.634 0.000 1.421 0.000 6.40 2.273 0.000 2.021 0.0001.685 0.000 1.465 0.000 6.60 2.418 0.000 2.149 0.0001.736 0.000 1.510 0.000 6.80 2.566 0.000 2.281 0.000

1.787 0.000 1.554 0.000 7.00 2.720 0.000 2.417 0.000




0.524 0.000 0.456 0.000 2.00 0.228 0.000 0.203 0.0000.577 0.000 0.502 0.000 2.20 0.276 0.000 0.245 0.0000.629 0.000 0.547 0.000 2.40 0.328 0.000 0.292 0.0000.682 0.000 0.593 0.000 2.60 0.385 0.000 0.343 0.0000.734 0.000 0.638 0.000 2.80 0.447 0.000 0.397 0.0000.787 0.000 0.684 0.000 3.00 0.513 0.000 0.456 0.0000.839 0.000 0.730 0.000 3.20 0.584 0.000 0.519 0.0000.891 0.000 0.775 0.000 3.40 0.659 0.000 0.586 0.0000.944 0.000 0.821 0.000 3.60 0.739 0.000 0.657 0.0000.996 0.000 0.866 0.000 3.80 0.823 0.000 0.732 0.0001.049 0.000 0.912 0.000 4.00 0.912 0.000 0.811 0.0001.101 0.000 0.958 0.000 4.20 1.005 0.000 0.894 0.0001.154 0.000 1.003 0.000 4.40 1.104 0.000 0.981 0.0001.206 0.000 1.049 0.000 4.60 1.206 0.000 1.072 0.0001.259 0.000 1.094 0.000 4.80 1.313 0.000 1.167 0.0001.311 0.000 1.140 0.000 5.00 1.425 0.000 1.267 0.0001.363 0.000 1.186 0.000 5.20 1.541 0.000 1.370 0.0001.416 0.000 1.231 0.000 5.40 1.662 0.000 1.477 0.0001.468 0.000 1.277 0.000 5.60 1.788 0.000 1.589 0.0001.521 0.000 1.322 0.000 5.80 1.917 0.000 1.704 0.0001.573 0.000 1.368 0.000 6.00 2.052 0.000 1.824 0.0001.626 0.000 1.414 0.000 6.20 2.191 0.000 1.948 0.000

1.678 0.000 1.459 0.000 6.40 2.335 0.000 2.075 0.0001.731 0.000 1.505 0.000 6.60 2.483 0.000 2.207 0.0001.783 0.000 1.550 0.000 6.80 2.636 0.000 2.343 0.000

1.835 0.000 1.596 0.000 7.00 2.793 0.000 2.483 0.000




0.607 0.000 0.528 0.000 2.00 0.264 0.000 0.235 0.0000.668 0.000 0.581 0.000 2.20 0.319 0.000 0.284 0.0000.729 0.000 0.634 0.000 2.40 0.380 0.000 0.338 0.0000.789 0.000 0.686 0.000 2.60 0.446 0.000 0.397 0.0000.850 0.000 0.739 0.000 2.80 0.517 0.000 0.460 0.0000.911 0.000 0.792 0.000 3.00 0.594 0.000 0.528 0.0000.972 0.000 0.845 0.000 3.20 0.676 0.000 0.601 0.0001.032 0.000 0.898 0.000 3.40 0.763 0.000 0.678 0.0001.093 0.000 0.950 0.000 3.60 0.855 0.000 0.760 0.0001.154 0.000 1.003 0.000 3.80 0.953 0.000 0.847 0.0001.214 0.000 1.056 0.000 4.00 1.056 0.000 0.939 0.0001.275 0.000 1.109 0.000 4.20 1.164 0.000 1.035 0.0001.336 0.000 1.162 0.000 4.40 1.278 0.000 1.136 0.0001.397 0.000 1.214 0.000 4.60 1.397 0.000 1.241 0.0001.457 0.000 1.267 0.000 4.80 1.521 0.000 1.352 0.0001.518 0.000 1.320 0.000 5.00 1.650 0.000 1.467 0.0001.579 0.000 1.373 0.000 5.20 1.785 0.000 1.586 0.0001.639 0.000 1.426 0.000 5.40 1.925 0.000 1.711 0.0001.700 0.000 1.478 0.000 5.60 2.070 0.000 1.840 0.0001.761 0.000 1.531 0.000 5.80 2.220 0.000 1.974 0.0001.822 0.000 1.584 0.000 6.00 2.376 0.000 2.112 0.0001.882 0.000 1.637 0.000 6.20 2.537 0.000 2.255 0.0001.943 0.000 1.690 0.000 6.40 2.703 0.000 2.403 0.0002.004 0.000 1.742 0.000 6.60 2.875 0.000 2.556 0.0002.064 0.000 1.795 0.000 6.80 3.052 0.000 2.713 0.000

2.125 0.000 1.848 0.000 7.00 3.234 0.000 2.875 0.000




0.690 0.000 0.600 0.000 2.00 0.300 0.000 0.267 0.0000.759 0.000 0.660 0.000 2.20 0.363 0.000 0.323 0.0000.828 0.000 0.720 0.000 2.40 0.432 0.000 0.384 0.0000.897 0.000 0.780 0.000 2.60 0.507 0.000 0.451 0.0000.966 0.000 0.840 0.000 2.80 0.588 0.000 0.523 0.0001.035 0.000 0.900 0.000 3.00 0.675 0.000 0.600 0.0001.104 0.000 0.960 0.000 3.20 0.768 0.000 0.683 0.0001.173 0.000 1.020 0.000 3.40 0.867 0.000 0.771 0.0001.242 0.000 1.080 0.000 3.60 0.972 0.000 0.864 0.0001.311 0.000 1.140 0.000 3.80 1.083 0.000 0.963 0.0001.380 0.000 1.200 0.000 4.00 1.200 0.000 1.067 0.0001.449 0.000 1.260 0.000 4.20 1.323 0.000 1.176 0.0001.518 0.000 1.320 0.000 4.40 1.452 0.000 1.291 0.000

1.587 0.000 1.380 0.000 4.60 1.587 0.000 1.411 0.0001.656 0.000 1.440 0.000 4.80 1.728 0.000 1.536 0.0001.725 0.000 1.500 0.000 5.00 1.875 0.000 1.667 0.0001.794 0.000 1.560 0.000 5.20 2.028 0.000 1.803 0.0001.863 0.000 1.620 0.000 5.40 2.187 0.000 1.944 0.0001.932 0.000 1.680 0.000 5.60 2.352 0.000 2.091 0.0002.001 0.000 1.740 0.000 5.80 2.523 0.000 2.243 0.0002.070 0.000 1.800 0.000 6.00 2.700 0.000 2.400 0.0002.139 0.000 1.860 0.000 6.20 2.883 0.000 2.563 0.0002.208 0.000 1.920 0.000 6.40 3.072 0.000 2.731 0.0002.277 0.000 1.980 0.000 6.60 3.267 0.000 2.904 0.0002.346 0.000 2.040 0.000 6.80 3.468 0.000 3.083 0.000

2.415 0.000 2.100 0.000 7.00 3.675 0.000 3.267 0.000

MOM. RESIST. f'c = 175 kg/cm2

Fierro As M+ M-1(3/8) 0.713 #N/A #N/A1(1/2) 1.267 #N/A 0.632 Kg-m2(3/8) 1.425 #N/A 0.699 Kg-m

3/8+1/2 1.979 #N/A 0.913 Kg-m1(5/8) 1.979 #N/A 0.913 Kg-m2(1/2) 2.534 #N/A 1.093 Kg-m

1/2+5/8 3.246 #N/A 1.277 Kg-m2(5/8) 3.959 #N/A 1.406 Kg-m

Mu

1/10 1/11 1/12 1/14 1/16 1/24

con factores amplif 1.400 1.500

no incl tabiqueria



0.139 0.000 0.127 0.000 0.116 0.000 0.099 0.000 0.087 0.000 0.058 0.0000.168 0.000 0.153 0.000 0.140 0.000 0.120 0.000 0.105 0.000 0.070 0.0000.200 0.000 0.182 0.000 0.167 0.000 0.143 0.000 0.125 0.000 0.084 0.0000.235 0.000 0.214 0.000 0.196 0.000 0.168 0.000 0.147 0.000 0.098 0.0000.273 0.000 0.248 0.000 0.227 0.000 0.195 0.000 0.171 0.000 0.114 0.0000.313 0.000 0.285 0.000 0.261 0.000 0.224 0.000 0.196 0.000 0.131 0.0000.356 0.000 0.324 0.000 0.297 0.000 0.255 0.000 0.223 0.000 0.148 0.0000.402 0.000 0.366 0.000 0.335 0.000 0.287 0.000 0.251 0.000 0.168 0.0000.451 0.000 0.410 0.000 0.376 0.000 0.322 0.000 0.282 0.000 0.188 0.0000.503 0.000 0.457 0.000 0.419 0.000 0.359 0.000 0.314 0.000 0.209 0.0000.557 0.000 0.506 0.000 0.464 0.000 0.398 0.000 0.348 0.000 0.232 0.0000.614 0.000 0.558 0.000 0.512 0.000 0.438 0.000 0.384 0.000 0.256 0.0000.674 0.000 0.612 0.000 0.561 0.000 0.481 0.000 0.421 0.000 0.281 0.0000.736 0.000 0.669 0.000 0.614 0.000 0.526 0.000 0.460 0.000 0.307 0.0000.802 0.000 0.729 0.000 0.668 0.000 0.573 0.000 0.501 0.000 0.334 0.0000.870 0.000 0.791 0.000 0.725 0.000 0.621 0.000 0.544 0.000 0.363 0.0000.941 0.000 0.855 0.000 0.784 0.000 0.672 0.000 0.588 0.000 0.392 0.0001.015 0.000 0.923 0.000 0.846 0.000 0.725 0.000 0.634 0.000 0.423 0.0001.091 0.000 0.992 0.000 0.909 0.000 0.780 0.000 0.682 0.000 0.455 0.0001.171 0.000 1.064 0.000 0.976 0.000 0.836 0.000 0.732 0.000 0.488 0.0001.253 0.000 1.139 0.000 1.044 0.000 0.895 0.000 0.783 0.000 0.522 0.0001.338 0.000 1.216 0.000 1.115 0.000 0.956 0.000 0.836 0.000 0.557 0.0001.425 0.000 1.296 0.000 1.188 0.000 1.018 0.000 0.891 0.000 0.594 0.0001.516 0.000 1.378 0.000 1.263 0.000 1.083 0.000 0.947 0.000 0.632 0.0001.609 0.000 1.463 0.000 1.341 0.000 1.149 0.000 1.006 0.000 0.670 0.000

1.705 0.000 1.550 0.000 1.421 0.000 1.218 0.000 1.066 0.000 0.711 0.000




0.178 0.000 0.161 0.000 0.148 0.000 0.127 0.000 0.111 0.000 0.074 0.0000.215 0.000 0.195 0.000 0.179 0.000 0.153 0.000 0.134 0.000 0.090 0.0000.256 0.000 0.232 0.000 0.213 0.000 0.183 0.000 0.160 0.000 0.107 0.0000.300 0.000 0.273 0.000 0.250 0.000 0.214 0.000 0.188 0.000 0.125 0.0000.348 0.000 0.316 0.000 0.290 0.000 0.249 0.000 0.218 0.000 0.145 0.0000.400 0.000 0.363 0.000 0.333 0.000 0.285 0.000 0.250 0.000 0.167 0.0000.455 0.000 0.413 0.000 0.379 0.000 0.325 0.000 0.284 0.000 0.189 0.0000.513 0.000 0.467 0.000 0.428 0.000 0.367 0.000 0.321 0.000 0.214 0.0000.575 0.000 0.523 0.000 0.480 0.000 0.411 0.000 0.360 0.000 0.240 0.0000.641 0.000 0.583 0.000 0.534 0.000 0.458 0.000 0.401 0.000 0.267 0.0000.710 0.000 0.646 0.000 0.592 0.000 0.507 0.000 0.444 0.000 0.296 0.0000.783 0.000 0.712 0.000 0.653 0.000 0.559 0.000 0.490 0.000 0.326 0.0000.860 0.000 0.781 0.000 0.716 0.000 0.614 0.000 0.537 0.000 0.358 0.0000.940 0.000 0.854 0.000 0.783 0.000 0.671 0.000 0.587 0.000 0.391 0.0001.023 0.000 0.930 0.000 0.852 0.000 0.731 0.000 0.639 0.000 0.426 0.0001.110 0.000 1.009 0.000 0.925 0.000 0.793 0.000 0.694 0.000 0.463 0.0001.201 0.000 1.091 0.000 1.000 0.000 0.858 0.000 0.750 0.000 0.500 0.0001.295 0.000 1.177 0.000 1.079 0.000 0.925 0.000 0.809 0.000 0.539 0.0001.392 0.000 1.266 0.000 1.160 0.000 0.995 0.000 0.870 0.000 0.580 0.0001.494 0.000 1.358 0.000 1.245 0.000 1.067 0.000 0.934 0.000 0.622 0.0001.598 0.000 1.453 0.000 1.332 0.000 1.142 0.000 0.999 0.000 0.666 0.0001.707 0.000 1.552 0.000 1.422 0.000 1.219 0.000 1.067 0.000 0.711 0.0001.819 0.000 1.653 0.000 1.516 0.000 1.299 0.000 1.137 0.000 0.758 0.0001.934 0.000 1.758 0.000 1.612 0.000 1.381 0.000 1.209 0.000 0.806 0.0002.053 0.000 1.866 0.000 1.711 0.000 1.466 0.000 1.283 0.000 0.855 0.000

2.176 0.000 1.978 0.000 1.813 0.000 1.554 0.000 1.360 0.000 0.907 0.000



0.182 0.000 0.166 0.000 0.152 0.000 0.130 0.000 0.114 0.000 0.076 0.0000.221 0.000 0.201 0.000 0.184 0.000 0.158 0.000 0.138 0.000 0.092 0.0000.263 0.000 0.239 0.000 0.219 0.000 0.188 0.000 0.164 0.000 0.109 0.0000.308 0.000 0.280 0.000 0.257 0.000 0.220 0.000 0.193 0.000 0.128 0.0000.358 0.000 0.325 0.000 0.298 0.000 0.255 0.000 0.223 0.000 0.149 0.0000.410 0.000 0.373 0.000 0.342 0.000 0.293 0.000 0.257 0.000 0.171 0.0000.467 0.000 0.424 0.000 0.389 0.000 0.334 0.000 0.292 0.000 0.195 0.0000.527 0.000 0.479 0.000 0.439 0.000 0.377 0.000 0.329 0.000 0.220 0.0000.591 0.000 0.537 0.000 0.492 0.000 0.422 0.000 0.369 0.000 0.246 0.0000.658 0.000 0.599 0.000 0.549 0.000 0.470 0.000 0.412 0.000 0.274 0.0000.730 0.000 0.663 0.000 0.608 0.000 0.521 0.000 0.456 0.000 0.304 0.0000.804 0.000 0.731 0.000 0.670 0.000 0.575 0.000 0.503 0.000 0.335 0.0000.883 0.000 0.803 0.000 0.736 0.000 0.631 0.000 0.552 0.000 0.368 0.0000.965 0.000 0.877 0.000 0.804 0.000 0.689 0.000 0.603 0.000 0.402 0.0001.051 0.000 0.955 0.000 0.876 0.000 0.750 0.000 0.657 0.000 0.438 0.0001.140 0.000 1.036 0.000 0.950 0.000 0.814 0.000 0.713 0.000 0.475 0.0001.233 0.000 1.121 0.000 1.028 0.000 0.881 0.000 0.771 0.000 0.514 0.0001.330 0.000 1.209 0.000 1.108 0.000 0.950 0.000 0.831 0.000 0.554 0.0001.430 0.000 1.300 0.000 1.192 0.000 1.021 0.000 0.894 0.000 0.596 0.0001.534 0.000 1.395 0.000 1.278 0.000 1.096 0.000 0.959 0.000 0.639 0.0001.642 0.000 1.492 0.000 1.368 0.000 1.173 0.000 1.026 0.000 0.684 0.0001.753 0.000 1.594 0.000 1.461 0.000 1.252 0.000 1.096 0.000 0.730 0.000

1.868 0.000 1.698 0.000 1.556 0.000 1.334 0.000 1.167 0.000 0.778 0.0001.986 0.000 1.806 0.000 1.655 0.000 1.419 0.000 1.241 0.000 0.828 0.0002.109 0.000 1.917 0.000 1.757 0.000 1.506 0.000 1.318 0.000 0.879 0.000

2.234 0.000 2.031 0.000 1.862 0.000 1.596 0.000 1.397 0.000 0.931 0.000



0.211 0.000 0.192 0.000 0.176 0.000 0.151 0.000 0.132 0.000 0.088 0.0000.256 0.000 0.232 0.000 0.213 0.000 0.183 0.000 0.160 0.000 0.106 0.0000.304 0.000 0.276 0.000 0.253 0.000 0.217 0.000 0.190 0.000 0.127 0.0000.357 0.000 0.324 0.000 0.297 0.000 0.255 0.000 0.223 0.000 0.149 0.0000.414 0.000 0.376 0.000 0.345 0.000 0.296 0.000 0.259 0.000 0.172 0.0000.475 0.000 0.432 0.000 0.396 0.000 0.339 0.000 0.297 0.000 0.198 0.0000.541 0.000 0.492 0.000 0.451 0.000 0.386 0.000 0.338 0.000 0.225 0.0000.610 0.000 0.555 0.000 0.509 0.000 0.436 0.000 0.381 0.000 0.254 0.0000.684 0.000 0.622 0.000 0.570 0.000 0.489 0.000 0.428 0.000 0.285 0.0000.762 0.000 0.693 0.000 0.635 0.000 0.545 0.000 0.477 0.000 0.318 0.0000.845 0.000 0.768 0.000 0.704 0.000 0.603 0.000 0.528 0.000 0.352 0.0000.931 0.000 0.847 0.000 0.776 0.000 0.665 0.000 0.582 0.000 0.388 0.0001.022 0.000 0.929 0.000 0.852 0.000 0.730 0.000 0.639 0.000 0.426 0.0001.117 0.000 1.016 0.000 0.931 0.000 0.798 0.000 0.698 0.000 0.466 0.0001.217 0.000 1.106 0.000 1.014 0.000 0.869 0.000 0.760 0.000 0.507 0.0001.320 0.000 1.200 0.000 1.100 0.000 0.943 0.000 0.825 0.000 0.550 0.0001.428 0.000 1.298 0.000 1.190 0.000 1.020 0.000 0.892 0.000 0.595 0.0001.540 0.000 1.400 0.000 1.283 0.000 1.100 0.000 0.962 0.000 0.642 0.0001.656 0.000 1.505 0.000 1.380 0.000 1.183 0.000 1.035 0.000 0.690 0.0001.776 0.000 1.615 0.000 1.480 0.000 1.269 0.000 1.110 0.000 0.740 0.0001.901 0.000 1.728 0.000 1.584 0.000 1.358 0.000 1.188 0.000 0.792 0.0002.030 0.000 1.845 0.000 1.691 0.000 1.450 0.000 1.269 0.000 0.846 0.0002.163 0.000 1.966 0.000 1.802 0.000 1.545 0.000 1.352 0.000 0.901 0.0002.300 0.000 2.091 0.000 1.917 0.000 1.643 0.000 1.437 0.000 0.958 0.0002.441 0.000 2.220 0.000 2.035 0.000 1.744 0.000 1.526 0.000 1.017 0.000

2.587 0.000 2.352 0.000 2.156 0.000 1.848 0.000 1.617 0.000 1.078 0.000



0.240 0.000 0.218 0.000 0.200 0.000 0.171 0.000 0.150 0.000 0.100 0.0000.290 0.000 0.264 0.000 0.242 0.000 0.207 0.000 0.182 0.000 0.121 0.0000.346 0.000 0.314 0.000 0.288 0.000 0.247 0.000 0.216 0.000 0.144 0.0000.406 0.000 0.369 0.000 0.338 0.000 0.290 0.000 0.254 0.000 0.169 0.0000.470 0.000 0.428 0.000 0.392 0.000 0.336 0.000 0.294 0.000 0.196 0.0000.540 0.000 0.491 0.000 0.450 0.000 0.386 0.000 0.337 0.000 0.225 0.0000.614 0.000 0.559 0.000 0.512 0.000 0.439 0.000 0.384 0.000 0.256 0.0000.694 0.000 0.631 0.000 0.578 0.000 0.495 0.000 0.434 0.000 0.289 0.0000.778 0.000 0.707 0.000 0.648 0.000 0.555 0.000 0.486 0.000 0.324 0.0000.866 0.000 0.788 0.000 0.722 0.000 0.619 0.000 0.542 0.000 0.361 0.0000.960 0.000 0.873 0.000 0.800 0.000 0.686 0.000 0.600 0.000 0.400 0.0001.058 0.000 0.962 0.000 0.882 0.000 0.756 0.000 0.662 0.000 0.441 0.0001.162 0.000 1.056 0.000 0.968 0.000 0.830 0.000 0.726 0.000 0.484 0.000

1.270 0.000 1.154 0.000 1.058 0.000 0.907 0.000 0.793 0.000 0.529 0.0001.382 0.000 1.257 0.000 1.152 0.000 0.987 0.000 0.864 0.000 0.576 0.0001.500 0.000 1.364 0.000 1.250 0.000 1.071 0.000 0.938 0.000 0.625 0.0001.622 0.000 1.475 0.000 1.352 0.000 1.159 0.000 1.014 0.000 0.676 0.0001.750 0.000 1.591 0.000 1.458 0.000 1.250 0.000 1.094 0.000 0.729 0.0001.882 0.000 1.711 0.000 1.568 0.000 1.344 0.000 1.176 0.000 0.784 0.0002.018 0.000 1.835 0.000 1.682 0.000 1.442 0.000 1.262 0.000 0.841 0.0002.160 0.000 1.964 0.000 1.800 0.000 1.543 0.000 1.350 0.000 0.900 0.0002.306 0.000 2.097 0.000 1.922 0.000 1.647 0.000 1.442 0.000 0.961 0.0002.458 0.000 2.234 0.000 2.048 0.000 1.755 0.000 1.536 0.000 1.024 0.0002.614 0.000 2.376 0.000 2.178 0.000 1.867 0.000 1.633 0.000 1.089 0.0002.774 0.000 2.522 0.000 2.312 0.000 1.982 0.000 1.734 0.000 1.156 0.000

2.940 0.000 2.673 0.000 2.450 0.000 2.100 0.000 1.838 0.000 1.225 0.000

Sección transversal de vigueta :bf

PROP:ELEMENTO:NIVEL: tf

hGEOMETRIA DE SECCION

h = 0.20 m. bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. twd = #N/A



0.0212 - 0.0159 - 0.0024 -

OK -

-

Momentos Maximos Resistentes: -

-

7.225 cm2 -

Mu max ( + ) = #N/A = #N/A #N/A

-

#N/A #N/A

Mu max ( - ) = #N/A = #N/A #N/A

-

-

-

-

#N/A #N/A

Mu min ( + ) = #N/A #N/A #N/A

-

#N/A #N/A

Mu min ( - ) = #N/A #N/A #N/A

-

-


7.18 Kg/cm2 -

Vu resistente #N/A #N/A

OK



rb =rmax =rmin =


As max =


As min =

nu max =

Ø (pulg) Ø (cm)PESO PROPIO DE LAS LOSAS ALIGERADAS 1/4" 0.64HLosa Alig. Peso Propio Según el RNC 3/8" 0.95

Cm KG/M2 Kg/cm2 12mm 0.8017.00 247.00 280.00 1/2" 1.2720.00 284.00 300.00 5/8" 1.5925.00 345.00 350.00 3/4" 1.91

7/8" 2.22PESO DE LOSA ALIGERADA 1" 2.54Para nuestra losa aligerada

según luz h = 20.00 cm 4 4HLosa Aligerada h = 20.00 cm

Peso de Losa Aligerada = 300.00 Kg/cm2

Numero de Viguetas por Mts = 2.50 Vig. / Mts.

Recubrimiento = 2.50 cm. 0.025 M


Diámetro acero principal - a usar = #N/A Cm. #N/A M

d = #N/A Cm. #N/A M

AT7


AT8


AT18


As (cm²)0.310.711.131.271.982.853.885.07

4 4

METRADO DE CARGASPESO DE LOSAS ALIGERADAS

PARA LOSA ALIGERADA DE PESO DE LOSAS ALIGERADAS

H=Ladrillo Peso Propio RNC

(H - 0.05) KG/M2

0.17 247.00 280.00

0.20 284.00 300.00

0.25 345.00 350.00

para losa de H = 0.25 mpeso de ladrillo = 10.50 kgh de ladrillo = 0.20

peso de losa aligerada/m2peso concreto parte superior = 0.05 x 1.00 x 1.00 x 2,400.00 = 120 kg/m2peso concreto viguetas(2.5unid) = 0.20 x 0.10 x 1.00 x 2,400.00 = 120 kg/m2peso ladrillo hueco = 4 x 2.5 x 10.50 = 105 kg/m2peso de losa aligerada/m2 345 kg/m2


peso de losa aligerada/m2peso concreto parte superior = 0.05 x 1.00 x 1.00 x 2,400.00 = 120 kg/m2peso concreto viguetas(2.5unid) = 0.15 x 0.10 x 1.00 x 2,400.00 = 90 kg/m2peso ladrillo hueco = 4 x 2.5 x 7.40 = 74 kg/m2peso de losa aligerada/m2 284 kg/m2


peso de losa aligerada/m2peso concreto parte superior = 0.05 x 1.00 x 1.00 x 2,400.00 = 120 kg/m2peso concreto viguetas(2.5unid) = 0.12 x 0.10 x 1.00 x 2,400.00 = 72 kg/m2

E28


E29


peso ladrillo hueco = 4 x 2.5 x 5.50 = 55 kg/m2peso de losa aligerada/m2 247 kg/m2

DISEÑO DE LOSA ALIGERADA:

DATOS:0.072 : Momento actuante positivo.0.042 : Momento actuante negativo.1.223 : Cortante máximo actuante en la sección.

Zona Sísmica = Si : Sismicidad de la zona.210 : Resistencia del concreto a la compresion.4200 : Esfuerzo de fluencia del acero.1.27 : Diámetro del acero principal positivo a usar.1.27 : Diámetro del acero principal negativo a usar.0.31 : Area del refuerzo por temperatura a usar.20 : Altura de la losa aligerada.5 : Altura de la losa de reparticion.2 : Recubrimiento.4010300 : Peso propio del aligerado.100 : Peso de acabados.120 : Peso de tabiqueria.250 : Sobrecarga.1.4 : Factor de amplificación para carga muerta.1.7 : Factor de amplificación para carga viva.0.90 : Factor de reducción por flexión.0.85 : Factor de reducción por cortante.

SOLUCION:

a) MAXIMOS MOMENTOS ADMISIBLES EN LA SECCION:

0.85 : Factor.17.37 : Peralte efectivo refuerzo positivo.17.37 : Peralte efectivo refuerzo negativo.0.208 : Carga muerta por vigueta0.100 : Carga viva por vigueta0.461 : Carga última por vigueta.

0.20735 : Cuantia mecánica.0.10368 : Cuantia mecánica máxima. analizar caso sismo 0.1036752.220 : Momento positivo máximo resistente.

0.02125 : Cuantía balanceada.0.01063 : Cuantía máxima. analizar caso sismo 0.0106250.21260 : Cuantia mecánica máxima.1.060 : Momento negativo máximo resistente.

b) VERIFICACION DE MOMENTOS EN LA SECCION:

2.220 : Momento positivo máximo resistente.0.072 : Momento actuante positivo.

==> CONFORME

1.060 : Momento negativo máximo resistente.0.042 : Momento actuante negativo.

==> CONFORME

CONCLUSION:

M+ (ton-m) =M- (ton-m) =

Vu (ton) =

f'c (kg/cm²) =f y (kg/cm²) =

Øp+ (cm) =Øp- (cm) =Ast (cm²) =

h (cm) =e (cm) =r (cm) =b (cm) = : Ancho del alma de la vigueta [Mto (+)].b (cm) = : Ancho del alma de la vigueta [Mto (- )].

Propio (kg/m²) =Acaba. (kg/m²) =Tabiq. (kg/m²) =

S/C (kg/m²) =fD =fL =Ø =Ø =

ß1 =d+ (cm) =d- (cm) =

WD (ton/m) =WL (ton/m) =Wu (ton/m) =

a.1) Momento Máximo Admisible Positivo:

w =wmax =

M (Ton-m) =

a.2) Momento Máximo Admisible Negativo:

pb =pmax =wmax =

M (Ton-m) =

b.1) Momento Positivo:

M+(ton-m) =M+(ton-m) =

b.2) Momento Negativo:

M-(ton-m) =M-(ton-m) =

C18

1) h.losa = 0.17m: P.P = 270kg/m² 2) h.losa = 0.20m: P.P = 300kg/m² 3) h.lLosa = 0.25m: P.P = 350kg/m² 4) h.losa = 0.30m: P.P = 420kg/m²

C22

R.N.C = 1.5 A.C.I = 1.4

C23

R.N.C = 1.8 A.C.I = 1.7

C43

El profesor vargas, toma "w", yo estoy tomando "wmax" para el calculo del momento. VERIFICAR

SIENDO EL MOMENTO RESISTENTE MAYOR QUE EL MOMENTO ACTUANTE,MANTENEMOS LA ALTURA Y CALIDAD DE LOS MATERIALES DE LA LOSAALIGERADA (CONFORME).

c) DISEÑO POR MOMENTO EN FLEXION DE LA SECCION:

0.42 : Area de acero mínimo en la sección.

0.42 : Area de acero positivo.

0.42 : Area de acero negativo.

d) VERIFICACION POR CORTANTE EN LA SECCION:Según Norma, la fuerza cortante que toma el concreto no debe exceder de:

1.247 : Cortante que toma el concreto.1.143 : Cortante a la distancia "d" de la cara de apoyo (cortante de diseño).

==> CONFORME

CONCLUSION:SIENDO EL CORTANTE QUE TOMA EL CONCRETO MAYOR QUE EL

CORTANTE DE DISEÑO, ENTONCES NO SERA NECESARIO HACER

ENSANCHAMIENTO DE VIGUETAS.

e) DISEÑO DEL REFUERZO POR CONTRACCION Y TEMPERATURA:

0.90

Espaciamiento (tomar menor o igual que el menor valor):34.44 : Espaciamiento resistente.25 : Espaciamiento debido a 5*e.45 : Espaciamiento debido a <= 45cm

Finalmente Usar:Ø 1/4pulg @ 0.20m

FIN

c.1) Area de acero mínimo:

Asmin (cm²) =

c.2) Area de acero positivo:

As+ (cm²) =

c.3) Area de acero negativo:

As- (cm²) =

Vcn = Ø*1.1*0.53*RAIZ(f'c)*bw*d ; Ø=0.85 ; Entonces:

Vcn (ton) =Vud (ton) =

Ast (cm²/m) =

s (cm) =s (cm) <=s (cm) <=

G73

EL DISEÑO SE EFECTUARA SIEMPRE Y CUANDO LA VERIFICACION DE MOMENTO EN LA SECCION SEA "CONFORME".

DISEÑO DE LOSA ALIGERADA

DISEÑO DEL MÓDULO N° 1

Datos de Entrada

Resistencia del concreto f'c = 210

Resistencia a fluencia del acero fy = 4200

Peralte Efectivo d= 17.03 cm

Ancho de Vigueta b= 40 cm

Ancho de Alma bw= 10 cm

Carga Muerta

1. Peso del Aligerado según espesor = 300

2. Acabados de piso = 100

3. Tabiquería = 120

520

Carga Viva

4. Sobrecarga 250

Carga Última de rotura: Según Normas Peruana:

Coeficiente de Carga Muerta 1.40

Coeficiente de Carga Viva 1.70

Wu = 1.40 + 1.70

Wu = 1153

Carga Repartida por vigueta:

461 Kg/m

0.461 T/m

Kg/cm2

Kg/cm2

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

WD WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

E9

Spacheco: Ancho del alma de la vigueta [Mto (+)].

E10

Spacheco: Ancho del alma de la vigueta [Mto (- )].

F22

Spacheco: Factor de amplificación para carga muerta.

F23

Spacheco: Factor de amplificación para carga viva.

Sección Apoyo 1 Tramo 1 Apoyo 2 Tramo 2 Apoyo 3 Tramo 3 Apoyo 4

α =-1/24 1/14 -1/10 1/16 -1/10 1/16 -1/11

-0.04 0.07 -0.10 0.06 -0.10 0.06 -0.09

ℓ (m) 1.48 1.48 2.33 3.17 4.00 4.83 4.41

-4.2E+03 7.2E+03 -2.5E+04 2.9E+04 -7.4E+04 6.7E+04 -8.2E+04

0.6220 2.4969 5.7966

1.4514 8.5962 25.4437 28.1154

0.0004 0.0002 0.0023 0.0007 0.0074 0.0016 0.0082

0.14 0.48 1.09

0.07 0.39 1.26 1.40

As mín =

0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm²

0.41Cm² 0.41Cm² 0.41Cm² 0.48Cm² 1.26Cm² 1.09Cm² 1.40Cm²

Baston Acero Principal Balancin Acero Principal Balancin Acero Principal Baston

1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 3/8" 3/8" 3/8" 1/2" 12mm 5/8"

0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm² 1.27Cm² 1.13Cm² 1.98Cm²

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2

Tramo 4 Apoyo 5 Tramo 5 Apoyo 6 Tramo 6 Apoyo 7 Tramo 7 Apoyo 8

1/16 -1/11 1/16 -1/10 1/16 -1/10 1/14 -1/24

0.06 -0.09 0.06 -0.10 0.06 -0.10 0.07 -0.04

3.99 3.50 3.00 4.05 5.10 4.35 3.60 3.60

4.6E+04 -5.1E+04 2.6E+04 -7.6E+04 7.5E+04 -8.7E+04 4.3E+04 -2.5E+04

3.9557 2.2363 6.4628 3.6802

17.6588 26.0838 30.0911 8.5872

0.0011 0.0050 0.0006 0.0076 0.0017 0.0089 0.0010 0.0023

0.75 0.41 1.16 0.68

0.85 1.29 1.52 0.39

0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm²


Acero Principal Balancin Acero Principal Balancin Acero Principal BastonAcero PrincipalBaston

1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

12mm 12mm 3/8" 5/8" 1/2" 5/8" 3/8" 3/8"


Acero por Temperatura: Ast = 0.0018.b.t

1.00 m. = 100 cm (ancho de análisis)

5 cm (Espesor de losa superior)

Ast = 0.90

Av Ø1/4"= 0.32

Espaciamiento de las varillas:

Usando Ø1/4"

S = 36 cm Tomando el menor: S = 25

S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

Ø 1/4pulg @ 0.20m

cm2

cm2

VERIFICACION POR CORTANTE EN LA SECCION:

Según Norma, la fuerza cortante que toma el concreto no debe exceder de:


1.223 : Cortante máximo actuante en la sección.

1.223 : Cortante que toma el concreto.

1.144 : Cortante a la distancia "d" de la cara de apoyo (cortante de diseño).

==> CONFORME

CONCLUSION:

SIENDO EL CORTANTE QUE TOMA EL CONCRETO MAYOR QUE EL



DISEÑO DEL REFUERZO POR CONTRACCION Y TEMPERATURA:

0.31 : Area del refuerzo por temperatura a usar.

0.90

Espaciamiento (tomar menor o igual que el menor valor):

34.44 : Espaciamiento resistente.

25 : Espaciamiento debido a 5*e.

45 : Espaciamiento debido a <= 45cm

Finalmente Usar:

Ø 1/4pulg @ 0.20m

Vu (ton) =

Vcn (ton) =

Vud (ton) =

Ast (cm²) =

Ast (cm²/m) =

s (cm) =

s (cm) <=

s (cm) <=

EJE NEUTRO

Se verificará la posición del eje neutro para el momento positivo máximo de todos los tramos:

Mmax= 7.5E+04 kg-cm 749.73825 kg-m 0.74973825 ton-m

Mmax= 0.6724555425 ton-m

0.031

c= 0.74 cm < 5 cm, el eje neutro se encuentra en el ala

w =

DISEÑO LOSA ALIGERADA EN UNA DIRECCION

DATOS DE ENTRADA:

Longitud de tramo de Viga 1-2 1.48 m



Longitud de tramo de Viga 4-5 3.99


Agregado Longitud de tramo de Viga 6-7 5.10


Dimension del Ancho del Ladrillo 0.30 m

Dimension del Alto del Ladrillo 0.15 m

Peso del Ladrillo 8.00 Kg/piez

Ancho de Alma 0.10 m

agregado Ancho de la Vigueta 0.40 m

Espesor del concreto de la Losa Aligerada 0.05 m

d = 16.87 cm.

210.00

Peso especifico del concreto 2400.00 Kg/m3

4200.00

Recubrimiento = 2.50 cm.

Diámetro acero principal - a usar = 1.27 Cm.

Factor de reducción por cortante. 0.85

Peso Propio por Vigueta (una vigueta + un ladrillo hueco = 0.10 + 0.30 = 0.40)

se supondra un espesor de :

h = 20.00 cm.

h = 20.00 cm.

- Concreto :

Vol. Losa 0.40x0.05x1.00 = 0.020 m3

Vol. Vigueta 0.10x0.15x1.00 = 0.015 m3

0.035 m3 x 2400 Kg/m3 = 84.00 Kg

- Ladrillo Hueco Rex (8 kg/pieza) 1.000 x 8 = 27.00 Kg

0.300 111.00 Kg

- Peso po m2 : 2.5 Viguetas/m2 x 111.00 Kg = 277.50 Kg/m2

Introdusca el valor redondeado de peso/m2

300.00 Kg/m2

1. CARGA SOBRE EL ALIGERADO (SERVICIO)

CARGA MUERTA

N° DESCRIPCION P. UNIT. UNID.

1 Peso propio 300 Kg/m2

2 Piso + Cielo Raso 100 Kg/m2

3 Tabiqueria 120 Kg/m2

TOTAL CM 520 Kg/m2

CARGA VIVA


1 oficinas 250 Kg/m2

TOTAL CV 250 Kg/m2

2. CARGA DE ROTURA DE DISEÑO Wu

Carga Última deSegún Normas Peruana:



Wu = 1.40 + 1.70

Wu 1,153.00

3. CARGA POR VIGUETA W1

1,153.00 = W1 461.20 Kg/ml

2.5

4. MOMENTOS FLECTORES (POR COEFICIENTES DEL ACI)

Apoyos (Momentos Negativos)

Apoyo l M1 0.042 T-m 4209.21867 kg-cm 42.092187 kg-m 0.0421 ton-m

Apoyo 2 M2 0.249 T-m 24930.7425 kg-cm 249.30743 kg-m 0.2493 ton-m

Apoyo 3 M3 0.738 T-m 73792 kg-cm 737.92 kg-m 0.7379 ton-m



Resistencia del concreto f'c Kg/cm2

Resistencia del acero fy Kg/cm2

WD WL

Kg/m2

h=L

25

M 1=1

24∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 2=1

11∗W 1∗L

2

M 2=1

11∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 2=1

10∗W 1∗L

2

DISEÑO LOSA ALIGERADA EN UNA DIRECCIONApoyo 6 M4 0.756 T-m 75648.33 kg-cm 756.4833 kg-m 0.7565 ton-mM 2=

110

∗W 1∗L2

M 2=1

10∗W 1∗L

2

DISEÑO LOSA ALIGERADA EN UNA DIRECCIONApoyo 7 M4 0.873 T-m 87270.57 kg-cm 872.7057 kg-m 0.8727 ton-m


Tramos (Momentos Positivos)

Tramo 1 M1-2 0.07 T-m 7215.80343 kg-cm 72.158034 kg-m 0.0722 ton-m







5. MOMENTOS MAXIMO QUE PUEDE TOMAR LA VIGUETA

Se calculará para las regiones vecinas a los apoyos donde el ancho de la seccion rectangular es 10 cm., ya que

el momento es negativo

………………..(1)

…………………(2)

A. CUANTIA BALANCEADA :

donde: 210.00 su factor : ß1 = 0.85

0.85 para resistencias de concreto

de hasta f'c=280 Kg/cm2

ρb 0.0213

B. CUANTIA MAXIMA EN ELEMENTOS SUJETOS A FLEXION :

ρmax 0.016 ………(3) falta caso sismicidad de la zona

Reemplazando (3) en (2)

a = 6.326 cm. ………(4)


Mu max = 154,782.92 Kg/cm.

Mu max = 1.55 Tn-m > Mmay alig = 0.82 Tn-m Ok! Cumple

6. AREAS DE ACERO

6.1 VERIFICACION DEL ACERO MINIMO :

As min = 0.41 cm2

6.2 CALCULO DE LAS AREAS DE ACERO :

Apoyo 1 : M1 0.04 T-m

Iterando

As = 0.066 cm2 para el primer tanteo a=0

a = 0.16 cm

As = 0.07 cm2

a = 0.10 cm

0.07 As = 0.07 cm2 Introdusca el valor redondeado de As

a = 0.09904 cm As = 0.71 cm2

1.00 f 3/8"

Resistencia del concreto a la comprension f'c = Kg/cm2

M 3=1

24∗W 1∗L

2

M 12=1

14∗W 1∗L

2

M 23=1

14∗W 1∗L

2

ρb=0 .85∗β1∗f ' c

f yx

60006000+ fy

β1=

ρmax .=0 .75 ρb

MUmax=0. 85∗b '∗a∗f c' (d− a2 )

a=ρmax∗fy∗d0.85∗f ' c

AS=M u

φ∗fy∗(d−a/2)a=

As∗fy0 .85∗f ' c∗b

Asmin=0 . 70∗√ f ' c

fy∗b∗d

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 23=1

16∗W 1∗L

2


Apoyo 2 :

M2 0.25 T-m

Iterando


a = 0.92 cm

As = 0.40 cm2

a = 0.59 cm


a = 0.586606 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 3 :

M3 0.74 T-m

Iterando


a = 2.72 cm

As = 1.26 cm2

a = 1.74 cm


a = 1.736282 cm As = 1.27 cm2

1.00 f 1/2"

Apoyo 4 :

M3 0.82 T-m

Iterando


a = 3.01 cm

As = 1.40 cm2

a = 1.92 cm


a = 1.918602 cm As = 1.98 cm2

1.00 f 5/8"

Apoyo 5 :

M3 0.51 T-m

Iterando


a = 1.89 cm

As = 0.85 cm2

a = 1.21 cm


a = 1.205042 cm As = 1.13 cm2

1.00 f 12mm

Apoyo 6 :

M3 0.76 T-m

Iterando


a = 2.79 cm

As = 1.29 cm2

a = 1.78 cm


a = 1.779961 cm As = 1.27 cm2

1.00 f 1/2"

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

DISEÑO LOSA ALIGERADA EN UNA DIRECCIONApoyo 7 :

M3 0.87 T-m

Iterando


a = 3.22 cm

As = 1.51 cm2

a = 2.05 cm

p As = 1.46 cm2 Introdusca el valor redondeado de As

a = 2.053425 cm As = 1.98 cm2

1.00 f 5/8"

Apoyo 8 :

M5 0.25 T-m

Iterando


a = 0.92 cm

As = 0.40 cm2

a = 0.94 cm


a = 0.94541 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 1-2: M12 0.07 T-m

Iterando


a = 0.27 cm

As = 0.11 cm2

a = 0.27 cm


a = 0.268384 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 2-3: M23 0.29 T-m

Iterando


a = 1.07 cm

As = 0.47 cm2

a = 1.10 cm


a = 1.104935 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 3-4: M23 0.67 T-m

Iterando


a = 2.48 cm

As = 1.14 cm2

a = 2.68 cm


a = 2.695169 cm As = 1.27 cm2

1.00 f 1/2"

Tramo 4-5: M23 0.46 T-m

Iterando


a = 1.69 cm

As = 0.76 cm2

a = 1.78 cm


AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

DISEÑO LOSA ALIGERADA EN UNA DIRECCIONa = 1.787699 cm As = 1.13 cm2

1.00 f 12mm

Tramo 5-6: M23 0.26 T-m

Iterando


a = 0.96 cm

As = 0.42 cm2

a = 0.99 cm


a = 0.98602 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 5-6: M23 0.75 T-m

Iterando


a = 2.77 cm

As = 1.28 cm2

a = 0.26 cm


a = 2.788183 cm As = 1.27 cm2

1.00 f 1/2"

Tramo 6-7: M23 0.43 T-m

Iterando


a = 1.58 cm

As = 0.70 cm2

a = 1.65 cm


a = 1.656454 cm As = 0.71 cm2

1.00 f 3/8"

7. VERIFICACION POR CORTANTE EN LA SECCION:



1.296 : Cortante máxima que toma el concreto.

1.211 : Cortante max que toma el concreto en losa alig


==> CONFORME

CONCLUSION:




8- EJE NEUTRO


Mmax= 6.7E-01 ton-m

Mmax= 0.67 ton-m

0.0319

c = 0.75 cm < 5 cm, el eje neutro se encuentra en el ala

Vc (ton) =Vcn (ton) =

Vud (ton) =

w =

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

HOJA DE VIGUETAS DE ALIGERADOS Sección transversal de vigueta :

PROP:

ELEMENTO:NIVEL:

VIGUETA DE SECCION CUALQUIERA h

GEOMETRIA DE SECCIONh = 0.20 m.

bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. d = 0.1703

MATERIAL DE LA SECCIONf'c = 210 Kg/cm2 Calculo del acero de Refuerzo : Ingrese como dato de Valor del Momento Actuante ( Mu )fy = 4200 Kg/cm2 Diseño Estructural :

Calculo de momentos Positivos Mu + :Fuerzas y Momentos Resistentes : Calculo del refuerzo :Verificacion de la Seccion As +

0.0212 Mu + =0.01590.0024 a =

As =a =

Momentos Maximos Resistentes: As =a =

7.225 cm2 As +=Mu max ( + ) = 4070.63 Kg-m = 4.07 Ton-m

2.714 cm2 Mu max ( - ) = 1419.60 Kg-m = 1.42 Ton-m

(cm2)

Calculo de momentos Negativos Mu - :0.411 cm2 Calculo del refuerzo :

Mu min ( + ) = 262.90 Kg-m 0.26 Ton-m As -Mu - =

0.411 cm2 Mu min ( - ) = 257.25 Kg-m 0.26 Ton-m a =

As- =a =

Fuerza Cortante Maxima Resistente : As =7.18 Kg/cm2 a =

Vu resistente = 1222.96 Kg As- =

(cm2)

rb =rmax =rmin =


As max = ρ (Tablas)


As min =

nu max =

ρ (Tablas)

Sección transversal de vigueta :

bf


GEOMETRIA DE SECCION tf h =

bf =

tw =tf =d =

MATERIAL DE LA SECCION tw f'c =

fy =

Calculo del acero de Refuerzo : Ingrese como dato de Valor del Momento Actuante ( Mu )Diseño Estructural :

Calculo de momentos Positivos Mu + :Calculo del refuerzo : Calculo del refuerzo : Calculo del refuerzo :

As + As +7215.80 kg-cm Mu + = 28965.95 kg-m Mu + =

3.406 cm. a = 3.406 cm. a =0.12 cm2 As = 0.50 cm2 As =0.073 cm. a = 0.294 cm. a =0.11 cm2 As = 0.45 cm2 As =0.066 cm. a = 0.267 cm. a =0.11 cm2 As += 0.45 cm2 As +=

0.6220 2.4969

0.0002 0.0007

0.14 0.48(cm2) (cm2)82.44% 95.11%

Calculo de momentos Negativos Mu - :Calculo del refuerzo : Calculo del refuerzo : Calculo del refuerzo :

As - As --4209.22 kg-cm Mu - = -24930.74 kg-m Mu - =

3.406 cm. a = 3.406 cm. a =0.07 cm2 As = 0.43 cm2 As =0.342 cm. a = 2.025 cm. a =0.07 cm2 As = 0.41 cm2 As =0.311 cm. a = 1.938 cm. a =0.07 cm2 As- = 0.41 cm2 As- =

2.9027 17.1924

0.0008 0.0048

0.07 0.41(cm2) (cm2)96.87% 100.47%

ρ (Tablas) ρ (Tablas)



GEOMETRIA DE SECCION20.00 cm. 40.00 cm.

10.00 cm. 5.00 cm.

17.03 cm. MATERIAL DE LA SECCION

210 Kg/cm2 4200 Kg/cm2

Calculo del refuerzo : Calculo del refuerzo :As +

67245.55 kg-m Mu + = 45889.69 kg-m

3.406 cm. a = 3.406 cm.1.16 cm2 As = 0.79 cm20.683 cm. a = 0.466 cm.1.07 cm2 As = 0.72 cm20.627 cm. a = 0.425 cm.1.06 cm2 As += 0.72 cm2

5.7966 3.9557

0.0016 0.0011

1.09 0.75(cm2)97.64% 96.34%

Calculo del refuerzo : Calculo del refuerzo :As -

-73792.00 kg-m Mu - = -81540.58 kg-m

3.406 cm. a = 3.406 cm.1.27 cm2 As = 1.41 cm25.994 cm. a = 6.623 cm.1.39 cm2 As = 1.57 cm26.546 cm. a = 7.400 cm.1.42 cm2 As- = 1.62 cm2

50.8874 56.2308

0.0168 0.0192

1.43 1.63(cm2)99.20% 98.98%

ρ (Tablas)

ρ (Tablas)

)2/(** adfy

MA uS f

bcf

fyAsa

*'*85.0

*

Calculo del refuerzo : Calculo del refuerzo :As + As +

Mu + = 25942.50 kg-m Mu + = 74973.83 kg-m

a = 3.406 cm. a = 3.406 cm.As = 0.45 cm2 As = 1.29 cm2

a = 0.263 cm. a = 0.761 cm.As = 0.41 cm2 As = 1.19 cm2

a = 0.239 cm. a = 0.701 cm.As += 0.41 cm2 As += 1.19 cm2

2.2363 6.4628

0.0006 0.0017

0.41 1.16(cm2) (cm2)99.30% 102.69%

Calculo del refuerzo : Calculo del refuerzo :As - As -

Mu - = -51214.27 kg-m Mu - = -75648.33 kg-m

a = 3.406 cm. a = 3.406 cm.As = 0.88 cm2 As = 1.31 cm2

a = 4.160 cm. a = 6.145 cm.As = 0.91 cm2 As = 1.43 cm2

a = 4.265 cm. a = 6.747 cm.As- = 0.91 cm2 As- = 1.47 cm2

35.3176 52.1675

0.0107 0.0174

0.91 1.48(cm2) (cm2)99.82% 98.91%




Mu + = 42693.94 kg-m Mu + = 0.00 kg-m

a = 3.406 cm. a = 3.406 cm.As = 0.74 cm2 As = 0.00 cm2

a = 0.433 cm. a = 0.000 cm.As = 0.67 cm2 As = 0.00 cm2

a = 0.395 cm. a = 0.000 cm.As += 0.67 cm2 As += 0.00 cm2

3.6802 0.0000

0.0010 0.0000

0.68 0.00(cm2) (cm2)98.50% #DIV/0!


Mu - = -87270.57 kg-m Mu - = -24904.80 kg-m

a = 3.406 cm. a = 3.406 cm.As = 1.51 cm2 As = 0.43 cm2

a = 7.089 cm. a = 2.023 cm.As = 1.71 cm2 As = 0.41 cm2

a = 8.056 cm. a = 1.936 cm.As- = 1.78 cm2 As- = 0.41 cm2

60.1823 17.1745

0.0212 0.0048

1.81 0.41(cm2) (cm2)98.37% 100.36%





Datos de Entrada






Carga Muerta




520

Carga Viva

4. Sobrecarga 250




Wu = 1.40 + 1.70

Wu = 1153


461 Kg/m

0.461 T/m

Kg/cm2

Kg/cm2

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

WD WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

Sección Apoyo 1 Tramo 1 Apoyo 2 Tramo 2 Apoyo 3 Tramo 3 Apoyo 4 Tramo 4 Apoyo 5

α -1/24 1/14 -1/10 1/16 -1/11 1/16 -1/10 1/14 -1/24

-0.04 0.07 -0.10 0.06 -0.09 0.06 -0.10 0.07 -0.04

ℓ (m) 1.48 1.48 2.30 3.11 4.26 5.41 4.94 4.47 4.47

-4.2E+03 7.2E+03 -2.4E+04 2.8E+04 -7.6E+04 8.4E+04 -1.1E+05 6.6E+04 -3.8E+04

0.6220 2.4033 7.2723 5.6740

1.4514 8.3758 26.2353 38.8073 13.2393

0.0004 0.0002 0.0023 0.0006 0.0076 0.0020 0.0120 0.0015 0.0037

0.14 0.41 1.36 1.02

0.07 0.39 1.29 2.04 0.63

As mín =

0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm²


Baston Acero Principal Balancin Acero Principal Balancin Acero Principal Balancin Acero Principal Baston

1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 3/8" 3/8" 3/8" 5/8" 5/8" 3/4" 12mm 3/8"


Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

Ø 1/4pulg @ 0.20m

cm2

cm2







==> CONFORME

CONCLUSION:






0.90





Finalmente Usar:

Ø 3/8pulg @ 0.25m

Vu (ton) =

Vcn (ton) =

Vud (ton) =

Ast (cm²) =

Ast (cm²/m) =

s (cm) =

s (cm) <=

s (cm) <=

EJE NEUTRO



Mmax= 0.8436529825 ton-m

0.039


w =


DATOS DE ENTRADA:








Ancho del alma 0.10 m

Ancho de la Vigueta 0.40 m


d = 17.03 cm.

210.00


4200.00






h = 20.00 cm.

h = 20.00 cm.

- Concreto :

Vol. Losa 0.40x0.05x1.00 = 0.020 m3

Vol. Vigueta 0.10x0.15x1.00 = 0.015 m3

0.035 m3 x 2400 Kg/m3 = 84.00 Kg


0.300 111.00 Kg



300.00 Kg/m2


CARGA MUERTA





TOTAL CM 520 Kg/m2

CARGA VIVA



TOTAL CV 250 Kg/m2





Wu = 1.40 + 1.70

Wu 1,153.00


1,153.00 = W1 461.20 Kg/ml

2.5









WD WL

Kg/m2

h=L

25

M 1=1

24∗W 1∗L

2

M2=1

10∗W1∗L

2

M 2=1

11∗W 1∗L

2

M 3=1

10∗W 1∗L

2


Apoyo 5 M5 0.384 T-m 38396.6295 kg-cm 383.96629 kg-m 0.384 ton-mM 3=1

24∗W 1∗L

2

M 3=1

10∗W 1∗L

2










………………..(1)

…………………(2)





ρb 0.0213


ρmax 0.016 ………(3)


a = 6.386 cm. ………(4)


Mu max = 157,732.85 Kg/cm.


6. AREAS DE ACERO


As min = 0.41 cm2


Apoyo 1 : M1 0.04 T-m

Iterando


a = 0.15 cm

As = 0.07 cm2

a = 0.10 cm


a = 0.09904 cm As = 0.71 cm2

1.00 f 3/8"


M 12=1

14∗W 1∗L

2

M 23=1

14∗W 1∗L

2

ρb=0 . 85∗β1∗f ' c

f yx

60006000+ fy

β1=

ρmax .=0 .75 ρb

MUmax=0. 85∗b '∗a∗f c' (d−a2 )


AS=M u


As∗fy0 .85∗f ' c∗b

Asmin=0 .70∗√ f ' c

fy∗b∗d

M23=1

16∗W 1∗L

2

M23=1

16∗W 1∗L

2


Apoyo 2 :

M2 0.24 T-m

Iterando


a = 0.89 cm

As = 0.39 cm2

a = 0.57 cm


a = 0.571565 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 3 :

M3 0.76 T-m

Iterando


a = 2.78 cm

As = 1.29 cm2

a = 1.79 cm


a = 1.790304 cm As = 1.27 cm2

1.00 f 1/2"

Apoyo 4 :

M3 1.13 T-m

Iterando


a = 4.11 cm

As = 1.99 cm2

a = 2.65 cm


a = 2.648221 cm As = 1.98 cm2

1.00 f 5/8"

Apoyo 5 :

M5 0.38 T-m

Iterando


a = 1.40 cm

As = 0.62 cm2

a = 1.46 cm


a = 1.466476 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 1-2: M12 0.07 T-m

Iterando


a = 0.26 cm

As = 0.11 cm2

a = 0.27 cm

As = 0.11 cm2 Introdusca el valor redondeado de As

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b


1.00 f 3/8"


Tramo 2-3: M23 0.28 T-m

Iterando


a = 1.02 cm

As = 0.45 cm2

a = 1.05 cm


a = 1.051478 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 3-4: M23 0.84 T-m

Iterando


a = 3.08 cm

As = 1.44 cm2

a = 3.39 cm


a = 3.42459 cm As = 1.98 cm2

1.00 f 5/8"

Tramo 4-5: M23 0.66 T-m

Iterando


a = 2.41 cm

As = 1.10 cm2

a = 2.59 cm


a = 2.603827 cm As = 1.13 cm2

1.00 f 12mm

FALTA VERIFICAR POR CORTANTE







==> CONFORME

CONCLUSION:




8- EJE NEUTRO


Mmax= 8.4E-01 ton-m

Mmax= 8.4E-01 ton-m

0.0394



Vud (ton) =

w =

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b


PROP:

ELEMENTO:NIVEL:



bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. d = 0.17 m.



0.0212 Mu + =0.01590.0024 a =

As =a =



2.714 cm2 Mu max ( - ) = 1419.60 Kg-m = 1.42 Ton-m

(cm2)




As- =a =



(cm2)

rb =rmax =rmin =




As min =

nu max =

ρ (Tablas)


bf



bf =

tw =tf =d =


fy =





0.6220 2.4033

0.0002 0.0006

0.14 0.41(cm2) (cm2)82.44% 106.77%




2.9027 16.7516

0.0008 0.0047

0.07 0.40(cm2) (cm2)96.87% 99.81%





10.00 cm. 5.00 cm.


210 Kg/cm2 4200 Kg/cm2


84365.30 kg-m Mu + = 65822.79 kg-m


7.2723 5.6740

0.0020 0.0015

1.36 1.02(cm2)98.48% 101.91%


-76087.94 kg-m Mu - = -112549.40 kg-m


52.4707 77.6147

0.0175 0.0349

1.49 2.97(cm2)99.09% 87.84%

ρ (Tablas)

ρ (Tablas)

)2/(** adfy

MA uS f

bcf

fyAsa

*'*85.0

*


Mu + = 0.00 kg-m Mu + = 0.00 kg-m

a = 3.406 cm. a = 3.406 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As += 0.00 cm2 As += 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!


Mu - = -38396.63 kg-m Mu - = 0.00 kg-m

a = 3.406 cm. a = 3.406 cm.As = 0.66 cm2 As = 0.00 cm2

a = 3.119 cm. a = 0.000 cm.As = 0.66 cm2 As = 0.00 cm2

a = 3.090 cm. a = 0.000 cm.As- = 0.66 cm2 As- = 0.00 cm2

26.4785 0.0000

0.0077 0.0000

0.66 0.00(cm2) (cm2)100.05% #DIV/0!




Mu + = 0.00 kg-m Mu + = 0.00 kg-m

a = 3.406 cm. a = 3.406 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As += 0.00 cm2 As += 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!


Mu - = 0.00 kg-m Mu - = 0.00 kg-m

a = 3.406 cm. a = 3.406 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As- = 0.00 cm2 As- = 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!



MOMENTOS RESISTENTES EN ALIGERADOS

Mu = K *As*fy*d*(1-0,59*p*fy/f´c) d = h-2 b(+)=40 b(-)=10 p = As/(bd)

h

10 17

Fierro As M+ M- M+ M- 1(3/8) 0.713 0.209 0.188 0.397 0.377 1(1/2) 1.267 0.362 0.297 0.697 0.632 2(3/8) 1.425 0.404 0.322 0.781 0.699 1(3/8)+1(1/2) 1.979 0.546 0.389 1.070 0.913 1(5/8) 1.979 0.546 0.389 1.070 0.913 2(1/2) 2.534 0.680 0.423 1.351 1.093 1(1/2)+1(5/8) 3.246 0.841 0.418 1.700 1.277 2(5/8) 3.959 0.987 0.358 2.035 1.406

MOM. RESIST. - f'c = 175 kg/cm2 17 Fierro As M+ M- M+ M- 1(3/8) 0.713 0.397 0.377 0.397 0.377 1(1/2) 1.267 0.697 0.632 0.697 0.632 2(3/8) 1.425 0.781 0.699 0.781 0.699

3/8+1/2 1.979 1.070 0.913 1.070 0.913 1(5/8) 1.979 1.070 0.913 1.070 0.913 2(1/2) 2.534 1.351 1.093 1.351 1.093

1/2+5/8 3.246 1.700 1.277 1.700 1.277 2(5/8) 3.959 2.035 1.406 2.035 1.406

MOM. RESIST. - f'c = 175 kg/cm2 20 Fierro As M+ M- M+ M- 1(3/8) 0.713 0.478 0.457 0.478 0.457 1(1/2) 1.267 0.840 0.776 0.840 0.776 2(3/8) 1.425 0.942 0.860 0.942 0.860

3/8+1/2 1.979 1.294 1.136 1.294 1.136 1(5/8) 1.979 1.294 1.136 1.294 1.136 2(1/2) 2.534 1.637 1.379 1.637 1.379

1/2+5/8 3.246 2.066 1.644 2.066 1.644 2(5/8) 3.959 2.482 1.853 2.482 1.853

MOMENTOS RESISTENTES EN ALIGERADOS HOJA DE CALCULO DE VIGUETAS DE LOSA ALIGERADA

f´c = 175 kg/cm2 ELEMENTO:

fy = 4,200 kg/cm² NIVEL:

M → Tn-m

(cm.) VIGUETA DE SECCION CUALQUIERA

20 25 GEOMETRIA DE SECCION

M+ M- M+ M- h =

0.478 0.457 0.613 0.593 bf =

0.840 0.776 1.081 1.016 tf =

0.942 0.860 1.213 1.131 tw =

1.294 1.136 1.670 1.512 d =

1.294 1.136 1.670 1.512 1.637 1.379 2.118 1.860 MATERIAL DE LA SECCION

2.066 1.644 2.683 2.260 f'c =

2.482 1.853 3.234 2.605 fy =

Fuerzas y Momentos Resistentes :

Verificacion de la Seccion


Mu max ( + ) =

Mu max ( - ) =

Mu min ( + ) =

Mu min ( - ) =

Fuerza Cortante Maxima Resistente :

rb =

rmax =

rmin =

Momentos Maximos :

As max =

As max =

Momentos Minimos :

As min =

As min =

Vu resistente =

nu max =

HOJA DE CALCULO DE VIGUETAS DE LOSA ALIGERADA

bf

PESO PROPIO DE LAS LOSAS ALIGERADAS

HLosa Alig. Peso Propio Según el RNC

tf Cm KG/M2 Kg/cm2

17.00 247.00 280.00

VIGUETA DE SECCION CUALQUIERA h 20.00 284.00 300.00

GEOMETRIA DE SECCION 25.00 345.00 350.00

0.17 m.

0.40 m. PESO DE LOSA ALIGERADA

0.05 m. Para nuestra losa aligerada

0.10 m. tw según luz h = 10.00

#N/A Sección transversal de vigueta : HLosa Aligerada h = 17.00

Peso de Losa Aligerada = 280.00

MATERIAL DE LA SECCION Numero de Viguetas por Mts = 2.50

210 Kg/cm2

4200 Kg/cm2 Recubrimiento = 2.50


Diámetro acero principal - a usar #N/A

Fuerzas y Momentos Resistentes : d = #N/A

0.0212 -

0.0159 -

0.0024 -


7.225 cm2 -

#N/A = #N/A #N/A

-

#N/A #N/A

#N/A = #N/A #N/A

-

-

-

-

#N/A #N/A

#N/A #N/A #N/A

-

#N/A #N/A

#N/A #N/A #N/A

-

-


U7


U8


U18


7.18 Kg/cm2 -

#N/A #N/A

Ø (pulg) Ø (cm) As (cm²)

1/4" 0.64 0.31

3/8" 0.95 0.71

12mm 0.80 1.13

1/2" 1.27 1.27

5/8" 1.59 1.98

3/4" 1.91 2.85

7/8" 2.22 3.88

1" 2.54 5.07

cm 3.47 3 1.35 3.5

cm

Kg/cm2

Vig. / Mts.

cm. 0.025 M

Cm. #N/A M

Cm. #N/A M



f'c = 280

Carga Muerta fy = 4200

1. Peso del Aligerado (e=0.20m 300 d= 17

2. Acabados de piso = 100 b= 40

3. Tabiquería = 120 bw= 10

520

Carga Viva

4. Sobrecarga 250

Carga Última de rotura: Wu =

Wu = 1230


492 Kg/m

0.49 T/m

Sección Apoyo Tramo Apoyo Tramo Apoyo

α -1/24 1/14 -1/10 1/16 -1/11

-0.04 0.07 -0.10 0.07 -0.09 ℓ (m) 1.48 1.48 2.30 3.11 4.26

-4.5E+03 7.7E+03 -2.6E+04 3.4E+04 -8.1E+04

0.6659 2.9404

1.5537 8.9667 28.0863

0.0006 0.0002 0.0026 0.0008 0.0084

0.14 0.54

0.10 0.44 1.43

As mín =

0.47 0.47 0.47 0.47 0.47

0.47 0.47 0.47 0.54 1.43

1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø5/8"

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

1.5WD + 1.8WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2(0.71cm2) (0.71cm2) (0.71cm2) (0.71cm2) (1.98cm2)




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

cm2

cm2


cm

cm

cm

Tramo Apoyo Tramo Apoyo

1/16 -1/10 1/14 -1/24

0.07 -0.10 0.07 -0.045.41 4.94 4.47 4.47

1.0E+05 -1.2E+05 7.0E+04 -4.1E+04

8.8976 6.0743

41.5452 14.1733

0.0026 0.013 0.0020 0.0042 0.0002 0.0000

1.77 1.36

2.21 0.71

0.47 0.47 0.47 0.47

1.77 2.21 1.36 0.71

1Ø5/8" 1Ø3/4" 1Ø5/8" 1Ø3/8"

Kg/cm2

Kg/cm2

(1.98cm2) (2.85cm2) (1.98cm2) (0.71cm2)

cm (ancho de análisis)

Ø1/4" @ 0.25m.

0.0003 0.0002 0.0008 0.0006 0.0010 0.0005 0.0005



Datos de Entrada






Carga Muerta




500

Carga Viva

4. Sobrecarga 250




Wu = 1.40 + 1.70

Wu = 1125


450 Kg/m

0.45 T/m

Kg/cm2

Kg/cm2

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

WD WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =


α -1/24 1/14 -1/10 1/16 -1/11 1/16 -1/10

-0.04 0.07 -0.10 0.06 -0.09 0.06 -0.10

ℓ (m) 3.47 3.47 3.24 3 2.18 1.35 2.43

-2.3E+04 3.9E+04 -4.7E+04 2.5E+04 -1.9E+04 5.1E+03 -2.6E+04

5.0296 3.2894 0.6661

11.7357 24.4798 10.0597 13.7557

0.0032 0.0014 0.0071 0.0009 0.0028 0.0002 0.0038

0.78 0.50 0.11

0.44 0.98 0.39 0.53

As mín =

0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm²

0.44Cm² 0.78Cm² 0.98Cm² 0.50Cm² 0.39Cm² 0.33Cm² 0.53Cm²

Baston Acero Principal Balancin Acero Principal Balancin Acero Principal Balancin

1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 12mm 12mm 3/8" 3/8" 3/8" 3/8"

0.71Cm² 1.13Cm² 1.13Cm² 0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm²

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2

Tramo 4 Apoyo 5

1/14 -1/24

0.07 -0.04

3.5 3.50

3.9E+04 -2.3E+04

5.1169

11.9395

0.0014 0.0033

0.78

0.46

0.33Cm² 0.33Cm²

0.78Cm² 0.46Cm²

Acero Principal Baston

1 Ø 1 Ø

12mm 3/8"

1.13Cm² 0.71Cm²




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

cm2

cm2

COEFICIENTES DEL ACI

TRAMO 1 2 3 4

1/24 1/10 1/11 1/10 1/24

1/14 1/16 1/16 1/14

LONGITUD 3 1.35 3.5 3.5

∆ ∆ ∆ ∆ ∆

WL 24²8 WL 10²8 WL 11²8 WL 10²8 WL 24²8

WL 14²8 WL 16²8 WL 16²8 WL 14²8







==> CONFORME

CONCLUSION:






0.90





Finalmente Usar:

Ø 1/4pulg @ 0.20m

Vu (ton) =

Vcn (ton) =

Vud (ton) =

Ast (cm²) =

Ast (cm²/m) =

s (cm) =

s (cm) <=

s (cm) <=

EJE NEUTRO



Mmax= 0.39375 ton-m

0.028


w =


DATOS DE ENTRADA:









Ancho de la Vigueta 0.40 m


d = 13.87 cm.

210.00


4200.00






h = 10.00 cm.

h = 17.00 cm.

- Concreto :

Vol. Losa 0.40x0.05x1.00 = 0.020 m3

Vol. Vigueta 0.10x0.15x1.00 = 0.012 m3

0.032 m3 x 2400 Kg/m3 = 76.80 Kg


0.300 103.80 Kg



280.00 Kg/m2


CARGA MUERTA





TOTAL CM 500 Kg/m2

CARGA VIVA



TOTAL CV 250 Kg/m2





Wu = 1.40 + 1.70

Wu 1,125.00


1,125.00 = W1 450.00 Kg/ml

2.5









WD WL

Kg/m2

h=L

25

M 1=1

24∗W 1∗L

2

M2=1

10∗W1∗L

2

M 2=1

11∗W 1∗L

2

M 3=1

10∗W 1∗L

2



24∗W 1∗L

2

M 3=1

10∗W 1∗L

2






Tramo 4 M3-4 0.39 T-m 39375 kg-cm 393.75 kg-m 0.3937 ton-m




………………..(1)

…………………(2)





ρb 0.0213


ρmax 0.016 ………(3)


a = 5.201 cm. ………(4)


Mu max = 104,627.48 Kg/cm.


6. AREAS DE ACERO


As min = 0.33 cm2


Apoyo 1 : M1 0.23 T-m

Iterando


a = 1.01 cm

As = 0.45 cm2

a = 0.53 cm


a = 0.531216 cm As = 0.71 cm2

1.00 f 3/8"


M 12=1

14∗W 1∗L

2

M 23=1

14∗W 1∗L

2

ρb=0 . 85∗β1∗f ' c

f yx

60006000+ fy

β1=

ρmax .=0 .75 ρb

MUmax=0. 85∗b '∗a∗f c' (d−a2 )


AS=M u


As∗fy0 .85∗f ' c∗b

Asmin=0 .70∗√ f ' c

fy∗b∗d

M23=1

16∗W 1∗L

2

M23=1

16∗W 1∗L

2


Apoyo 2 :

M2 0.47 T-m

Iterando


a = 2.11 cm

As = 0.97 cm2

a = 1.11 cm


a = 1.108083 cm As = 1.13 cm2

1.00 f 12mm

Apoyo 3 :

M3 0.19 T-m

Iterando


a = 0.87 cm

As = 0.38 cm2

a = 0.46 cm


a = 0.455354 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 4 :

M3 0.26 T-m

Iterando


a = 1.19 cm

As = 0.53 cm2

a = 0.62 cm


a = 0.622654 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 5 :

M5 0.23 T-m

Iterando


a = 1.03 cm

As = 0.46 cm2

a = 1.07 cm


a = 1.072194 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 1-2: M12 0.39 T-m

Iterando


a = 1.74 cm

As = 0.79 cm2

a = 1.85 cm


a = 1.861275 cm As = 1.13 cm2

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

DISEÑO LOSA ALIGERADA EN UNA DIRECCION1.00 f 12mm


Tramo 2-3: M23 0.25 T-m

Iterando


a = 1.14 cm

As = 0.50 cm2

a = 1.18 cm


a = 1.18667 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 3-4: M23 0.05 T-m

Iterando


a = 0.23 cm

As = 0.10 cm2

a = 0.23 cm


a = 0.23198 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 4-5: M23 0.39 T-m

Iterando


a = 1.77 cm

As = 0.80 cm2

a = 1.89 cm


a = 1.896114 cm As = 1.13 cm2

1.00 f 12mm








==> CONFORME

CONCLUSION:




8- EJE NEUTRO


Mmax= 3.9E-01 ton-m

Mmax= 3.9E-01 ton-m

0.0275



Vud (ton) =

w =

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b


PROP:

ELEMENTO:NIVEL:



bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. d = 0.14 m.



0.02120.01590.0024


7.225 cm2 Mu max ( + ) = 3207.62 Kg-m = 3.21 Ton-m

2.211 cm2 Mu max ( - ) = 941.65 Kg-m = 0.94 Ton-m

0.335 cm2 Mu min ( + ) = 174.38 Kg-m 0.17 Ton-m

0.335 cm2 Mu min ( - ) = 170.64 Kg-m 0.17 Ton-m

Fuerza Cortante Maxima Resistente :7.18 Kg/cm2

Vu resistente = 996.03 Kg

rb =rmax =rmin =


As max =


As min =

nu max =


bf

tf

h

tw


Calculo de momentos Positivos Mu + :Calculo del refuerzo : Calculo del refuerzo :As + As +

Mu + = 38702.89 kg-cm Mu + = 25312.50 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.82 cm2 As = 0.54 cm2

a = 0.482 cm. a = 0.316 cm.As = 0.75 cm2 As = 0.49 cm2

a = 0.442 cm. a = 0.287 cm.As += 0.75 cm2 As += 0.49 cm2

5.0296 3.2894

0.0014 0.0009

0.78 0.50(cm2) (cm2)96.58% 97.70%

Calculo de momentos Negativos Mu - :Calculo del refuerzo : Calculo del refuerzo :As - As -

Mu - = -22576.69 kg-cm Mu - = -47093.51 kg-m

a = 2.774 cm. a = 2.774 cm.As- = 0.48 cm2 As = 1.00 cm2

a = 2.252 cm. a = 4.697 cm.As = 0.47 cm2 As = 1.08 cm2

a = 2.205 cm. a = 5.089 cm.As- = 0.47 cm2 As- = 1.10 cm2

23.4713 48.9596

0.0067 0.0160

0.46 1.11(cm2) (cm2)100.68% 99.14%




GEOMETRIA DE SECCIONh = 17.00 cm.

bf = 40.00 cm.

tw = 10.00 cm. tf = 5.00 cm. d = 13.87 cm.



Mu + = 5125.78 kg-m Mu + = 39375.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.11 cm2 As = 0.83 cm2

a = 0.064 cm. a = 0.491 cm.As = 0.10 cm2 As = 0.76 cm2

a = 0.058 cm. a = 0.450 cm.As += 0.10 cm2 As += 0.76 cm2

0.6661 5.1169

0.0002 0.0014

0.11 0.78(cm2) (cm2)88.29% 98.28%


Mu - = -19352.56 kg-m Mu - = -26462.81 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.41 cm2 As = 0.56 cm2

a = 1.930 cm. a = 2.639 cm.As = 0.40 cm2 As = 0.56 cm2

a = 1.867 cm. a = 2.625 cm.As- = 0.40 cm2 As- = 0.56 cm2

20.1194 27.5114

0.0057 0.0080

0.40 0.55(cm2) (cm2)100.12% 100.49%



)2/(** adfy

MA uS f

bcf

fyAsa

*'*85.0

*


Mu + = 0.00 kg-m Mu + = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As += 0.00 cm2 As += 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!


Mu - = -22968.75 kg-m Mu - = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.49 cm2 As = 0.00 cm2

a = 2.291 cm. a = 0.000 cm.As = 0.48 cm2 As = 0.00 cm2

a = 2.247 cm. a = 0.000 cm.As- = 0.48 cm2 As- = 0.00 cm2

23.8789 0.0000

0.0069 0.0000

0.48 0.00(cm2) (cm2)99.62% #DIV/0!



HOJA DE CALCULO DE MOMENTOS RESISTENTES Y/O AREAS DE ACERO NECESARIASPARA UN ELEMENTO CUYA SECCION ESTA SOMETIDA A FLEXION PURA VIGUETAS DE SECCION TEE PARA MOMENTO NEGATIVODatos generales

Simbolo Und DENOMINACION:

b = 10.00 cm base de la seccion

h = 17.00 cm Peralte de la seccion

d = 13.87 cm Peralte efectivo de la seccion

r = 2.50 cm Recubrimiento al eje del refuerzo longitudinal - traccion

d'= 2.50 cm Recubrimiento al eje del refuerzo longitudinal - compr.

f'c = 210.00 kg/cm2 Resistencia del concreto a la compresion

fy = 4200.00 kg/cm2 Resistencia del acero a la traccion

Resultados…Viga simplemente Armada

As min = 0.46 cm2 Area de acero minima en traccion

B1 = 0.85 Factor de la zona de compresion del concreto

Pb = 0.0213 Cuantia balanceada de viga simplemente armada

Zona= Asismica

75% Pb 0.0159 Cuantia maxima permitida por el RNC

As máx = 2.21 cm2 Area de acero maxima segun la seccion

DISENO DEL REFUERZO LONGITUDINAL POR FLEXION

PARA VIGA SIMPLEMENTE ARMADA

Mu = 0.23 Tn.m Ast = 0.43 cm2

a = 1.05 cm.

a_max= 5.20 cm.

Recomendación: Usar el Area de Acero minima


PARA VIGA DOBLEMENTE ARMADA

Calculo del Area de Acero en Compresion Omitir este cuadro

Fuerza de compresion maxima C= 9.28 Tn

Momento maximo Mu1 resistente como viga simple Muc= 0.94 Tn.m

Momento remanente M2 que tomara el acero en compresion Mus= 0.00 Tn.m

Eje neutro maximo c_máx= 6.12 cm

Esfuerzo en el acero en compresion No fluye f's= 3548.67 kg/cm2

Area de acero total en compresion A's= 0.00 cm2

Area de acero maxima como viga simple As1= 0.43 cm2

Area de acero en traccion adicional al acero de viga simple As2= 0.00 cm2

Area de acero total en traccion As= 0.43 cm2

Cuantia de acero en compresion P's = 0.0000

Cuantia de acero en traccion Ps = 0.0031

Resultados…Viga doblemente Armada



Pb = 0.0213 Cuantia balanceada de viga doblemente armada


As max = 2.21 cm2 Area de acero maxima segun la seccion

HOJA DE CALCULO DE MOMENTOS RESISTENTES Y/O AREAS DE ACERO NECESARIASPARA UN ELEMENTO CUYA SECCION ESTA SOMETIDA A FLEXION PURA

Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento

Resistencia del concreto

Resistencia a fluencia del acero

Calculo de Areas

Obtener un Ast > o = 0.71 cm2

Cant de Varillas Tipo 1 01

Numero ACI de Varilla 3 /8"



As = 0.71 cm2

RESISTENCIA 0.71Cm²PARA VIGA SIMPLEMENTE ARMADA Mu =

Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm

Si es simple Falla: Ductil-Subreforzada 0.0051

Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-22576.69 Kg - cm

0.23 Tn.m

< 0.0213 Ductil-Subreforzada

HOJA DE CALCULO DE MOMENTOS RESISTENTES Y/O AREAS DE ACERO NECESARIASPARA UN ELEMENTO CUYA SECCION ESTA SOMETIDA A FLEXION PURA VIGUETAS DE SECCION TEE PARA MOMENTO POSITIVODatos generales



bw= 10.00 cm ancho de la nervadura

t= 5.00 cm Espesor de losita





f'c = 210 kg/cm2 Resistencia del concreto a la compresion

fy = 4200 kg/cm2 Resistencia del acero a la traccion





Zona= Asismica





Mu = 0.39 Tn.m Ast = 0.72 cm2

a = 0.44 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.

Recomendación: Ok Usar Ast






















Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA

PARA VIGA SIMPLEMENTE ARMADA Mu =

Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales


40.00 cm b = 40 cm base de la seccion

10.00 cm bw= 10 cm ancho de la nervadura

5.00 cm t= 5 cm Espesor de losita

17.00 cm h = 17 cm Peralte de la seccion

13.87 cm d = 14.5 cm Peralte efectivo de la seccion

2.50 cm r = 2.5 cm Recubrimiento al eje del refuerzo longitudinal - traccion

2.50 cm d'= 2.5 cm Recubrimiento al eje del refuerzo longitudinal - compr.

210 kg/cm2 f'c = 210 kg/cm2 Resistencia del concreto a la compresion

4200 kg/cm2 fy = 4200 kg/cm2 Resistencia del acero a la traccion

38702.89 Kg - cm

0.39 Tn.m


DENOMINACION:

base de la seccion

ancho de la nervadura

Espesor de losita

Peralte de la seccion

Peralte efectivo de la seccion

Recubrimiento al eje del refuerzo longitudinal - traccion

Recubrimiento al eje del refuerzo longitudinal - compr.

Resistencia del concreto a la compresion

Resistencia del acero a la traccion














Zona= Asismica





Mu = 0.47 Tn.m Ast = 0.93 cm2

a = 2.31 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.62 Tn.m 0.69

a = 2.99 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-47093.51 Kg - cm

0.47 Tn.m

















Zona= Asismica





Mu = 0.25 Tn.m Ast = 0.47 cm2

a = 0.29 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.38 Tn.m 0.43

a = 0.42 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











25312.50 Kg - cm

0.25 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.19 Tn.m Ast = 0.36 cm2

a = 0.90 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-19352.56 Kg - cm

0.19 Tn.m

















Zona= Asismica





Mu = 0.05 Tn.m Ast = 0.09 cm2

a = 0.06 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.38 Tn.m 0.43

a = 0.42 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











5125.78 Kg - cm

0.05 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.39 Tn.m Ast = 0.77 cm2

a = 1.90 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.62 Tn.m 0.69

a = 2.99 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

39375.00 Kg - cm

0.39 Tn.m

















Zona= Asismica





Mu = 0.39 Tn.m Ast = 0.73 cm2

a = 0.45 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











39375.00 Kg - cm

0.39 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.23 Tn.m Ast = 0.44 cm2

a = 1.07 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-22968.75 Kg - cm

0.23 Tn.m


DISEÑO LOSA ALIGERADA EN UNA SOLA DIRECCION

PROYECTO : MEJORAMIENTO INFRAESTRUCTURA I.E. No 501258 CORONEL FRANCISCO BOLOGNESI CERVANTES

DATOS :F'c= 210.00 Kg/cm2

d= 17.53 Cm.b= 40.00 Cm.

bw= 10.00 Cm.Fy= 4,200.00 Kg/cm2

h Losa alig = 20.00 Cm.Recubrimiento = 2.00 Cm.

Diámetro acero principal + a usar = 0.95 Cm.


CARGA MUERTAPESO PROPIO LOSA ALIGERADA 300.00 Kg/m2PISO + CIELO RASO 100.00 Kg/m2TABIQUERIA 50.00 Kg/m2

WD= 450.00 Kg/m2

CARGA VIVAWL= 350.00 Kg/m2

WU= 1.5WD+1.8WLWU= 1.5 WD + 1.8WU= 1,305.00 Kg/m2

CARGA POR VIGUETA 522.00 Kg/ml


TRAMO 1 2 3 4

1/24 1/10 1/11 1/10 1/24

1/14 1/16 1/16 1/14

LONGITUD 4.75 4.75 4.75 4.75

MOMENTOS (ton-m)

0.49 1.18 1.07 1.18 0.49

0.84 0.74 0.74 0.84

ACERO (cm²) ACERO MINIMO= 0.42 Cm2

0.78 2.06 1.84 2.06 0.78

1.30 1.13 1.13 1.30

EJE NEUTROSe verificará la posición del eje neutro para el momento positivo máximo de todos los tramos:

Mmax= 0.84 ton-m

C18


0.037c= 0.90 cm < 5 cm, el eje neutro se encuentra en el ala w =


MEJORAMIENTO INFRAESTRUCTURA I.E. No 501258 CORONEL FRANCISCO BOLOGNESI CERVANTES

Ø (pulg) Ø (cm) As (cm²)1/4" 0.64 0.313/8" 0.95 0.711/2" 1.27 1.275/8" 1.59 1.983/4" 1.91 2.857/8" 2.22 3.881" 2.54 5.07

17.53 : Peralte efectivo refuerzo positivo.

17.53 : Peralte efectivo refuerzo negativo.

WL

d+ (cm) =

d- (cm) =

: Peralte efectivo refuerzo positivo.

: Peralte efectivo refuerzo negativo.



f'c = 280





520

Carga Viva

4. Sobrecarga 250


Wu = 1230


492 Kg/m

0.49 T/m


α -1/24 1/14 -1/10 1/16 -1/11

-0.04 0.07 -0.10 0.07 -0.09 ℓ (m) 3.47 3.47 3.24 3 2.18

-2.5E+04 4.2E+04 -5.1E+04 3.2E+04 -2.1E+04

3.6605 2.7360

8.5411 17.8162 7.3214

0.0024 0.0012 0.0052 0.0008 0.0022

0.82 0.54

0.41 0.88 0.37

As mín =

0.47 0.47 0.47 0.47 0.47

0.47 0.82 0.88 0.54 0.47

1Ø3/8" 1Ø1/2" 1Ø1/2" 1Ø3/8" 1Ø3/8"

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

1.5WD + 1.8WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2(0.71cm2) (1.27cm2) (1.27cm2) (0.71cm2) (0.71cm2)




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

cm2

cm2


cm

cm

cm

Tramo Apoyo Tramo Apoyo

1/16 -1/10 1/14 -1/24

0.07 -0.10 0.07 -0.041.35 2.43 3.5 3.50

6.4E+03 -2.9E+04 4.3E+04 -2.5E+04

0.5540 3.7240

10.0113 8.6894

0.0002 0.003 0.0012 0.0024

0.14 0.82

0.51 0.41

0.47 0.47 0.47 0.47

0.47 0.51 0.82 0.47

1Ø3/8" 1Ø3/8" 1Ø1/2" 1Ø3/8"

Kg/cm2

Kg/cm2

(0.71cm2) (0.71cm2) (1.27cm2) (0.71cm2)


Ø1/4" @ 0.25m.



Datos de Entrada






Carga Muerta




500

Carga Viva

4. Sobrecarga 250




Wu = 1.40 + 1.70

Wu = 1125


450 Kg/m

0.45 T/m

Kg/cm2

Kg/cm2

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

WD WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =


α -1/24 1/14 -1/10 1/16 -1/10 1/14 -1/24

-0.04 0.07 -0.10 0.07 -0.10 0.07 -0.04

ℓ (m) 3 3 2.18 1.35 2.43 3.5 3.50

-1.7E+04 2.9E+04 -2.1E+04 5.9E+03 -2.6E+04 3.9E+04 -2.3E+04

3.7594 0.7613 5.1169

8.7718 11.0657 13.7557 11.9395

0.0024 0.0010 0.0030 0.0002 0.0038 0.0014 0.0033

0.55 0.11 0.78

0.33 0.42 0.53 0.46

As mín =

0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm²

0.33Cm² 0.55Cm² 0.42Cm² 0.33Cm² 0.53Cm² 0.78Cm² 0.46Cm²


1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 3/8" 3/8" 3/8" 3/8" 12mm 3/8"

0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm² 1.13Cm² 0.71Cm²

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

Ø 1/4pulg @ 0.20m

cm2

cm2


TRAMO 1 2 3

1/24 1/10 1/10 1/24

1/14 1/16 1/14

LONGITUD 3 1.35 3.5

∆ ∆ ∆ ∆

WL 24²8 WL 10²8 WL 10²8 WL 24²8

WL 14²8 WL 16²8 WL 14²8







==> CONFORME

CONCLUSION:






0.90





Finalmente Usar:

Ø 1/4pulg @ 0.20m

Vu (ton) =

Vcn (ton) =

Vud (ton) =

Ast (cm²) =

Ast (cm²/m) =

s (cm) =

s (cm) <=

s (cm) <=

EJE NEUTRO



Mmax= 0.39375 ton-m

0.028


w =


DATOS DE ENTRADA:










d = 13.87 cm.

210.00


4200.00






h = 10.00 cm.

h = 17.00 cm.

- Concreto :

Vol. Losa 0.40x0.05x1.00 = 0.020 m3

Vol. Vigueta 0.10x0.15x1.00 = 0.012 m3

0.032 m3 x 2400 Kg/m3 = 76.80 Kg


0.300 103.80 Kg



280.00 Kg/m2


CARGA MUERTA





TOTAL CM 500 Kg/m2

CARGA VIVA



TOTAL CV 250 Kg/m2





Wu = 1.40 + 1.70

Wu 1,125.00


1,125.00 = W1 450.00 Kg/ml

2.5



Apoyo l M1 0.169 T-m 16875 kg-cm 168.75 kg-m 0.1688 ton-m





WD WL

Kg/m2

h=L

25

M 1=1

24∗W 1∗L

2

M 3=1

24∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 2=1

10∗W 1∗L

2

DISEÑO LOSA ALIGERADA EN UNA DIRECCIONApoyo 4 M3 0.230 T-m 22968.75 kg-cm 229.6875 kg-m 0.2297 ton-mM 3=

124

∗W 1∗L2





Tramo 3 M3-4 0.39 T-m 39375 kg-cm 393.75 kg-m 0.3937 ton-m




………………..(1)

…………………(2)





ρb 0.0213


ρmax 0.016 ………(3)


a = 5.201 cm. ………(4)


Mu max = 104,627.48 Kg/cm.


6. AREAS DE ACERO


As min = 0.33 cm2


Apoyo 1 : M1 0.17 T-m

Iterando


a = 0.76 cm

As = 0.33 cm2

a = 0.40 cm


a = 0.397059 cm As = 0.71 cm2

1.00 f 3/8"


M 12=1

14∗W 1∗L

2

M 23=1

14∗W1∗L

2

ρb=0 .85∗β1∗f ' c

f yx

60006000+ fy

β1=

ρmax .=0 .75 ρb

MUmax=0.85∗b '∗a∗f c' (d−a2 )


AS=M u


As∗fy0 .85∗f ' c∗b

Asmin=0 . 70∗√ f ' c

fy∗b∗d

M 23=1

14∗W1∗L

2


Apoyo 2 :

M2 0.21 T-m

Iterando


a = 0.96 cm

As = 0.42 cm2

a = 0.50 cm


a = 0.50089 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 3 :

M3 0.26 T-m

Iterando


a = 1.19 cm

As = 0.53 cm2

a = 0.62 cm


a = 0.622654 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 4 :

M4 0.23 T-m

Iterando


a = 1.03 cm

As = 0.46 cm2

a = 1.07 cm


a = 1.072194 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 1-2: M12 0.29 T-m

Iterando


a = 1.30 cm

As = 0.58 cm2

a = 1.36 cm


a = 1.365321 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 2-3: M23 0.06 T-m

Iterando


a = 0.26 cm

As = 0.11 cm2

a = 0.27 cm


a = 0.265442 cm As = 0.71 cm2

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

DISEÑO LOSA ALIGERADA EN UNA DIRECCION1.00 f 3/8"


Tramo 3-4: M23 0.39 T-m

Iterando


a = 1.77 cm

As = 0.80 cm2

a = 1.89 cm


a = 1.896114 cm As = 1.13 cm2

1.00 f 12mm








==> CONFORME

CONCLUSION:




8- EJE NEUTRO


Mmax= 3.9E-01 ton-m

Mmax= 3.9E-01 ton-m

0.0275



Vud (ton) =

w =

AS=M u


As∗fy0 .85∗f ' c∗b


PROP:

ELEMENTO:NIVEL:



bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. d = 0.14 m.



0.0212 Mu + =0.01590.0024 a =

As =a =



2.211 cm2 Mu max ( - ) = 941.65 Kg-m = 0.94 Ton-m

(cm2)




As- =a =



(cm2)

rb =rmax =rmin =




As min =

nu max =

ρ (Tablas)


bf



bf =

tw =tf =d =


fy =





3.7594 0.7613

0.0010 0.0002

0.55 0.11(cm2) (cm2)100.65% 100.94%




17.5437 22.1314

0.0049 0.0063

0.34 0.44(cm2) (cm2)100.56% 100.42%





10.00 cm. 5.00 cm.


210 Kg/cm2 4200 Kg/cm2


39375.00 kg-m Mu + = 0.00 kg-m


5.1169 0.0000

0.0014 0.0000

0.78 0.00(cm2)98.28% #DIV/0!


-26462.81 kg-m Mu - = -22968.75 kg-m


27.5114 23.8789

0.0080 0.0069

0.55 0.48(cm2)100.49% 99.62%

ρ (Tablas)

ρ (Tablas)

)2/(** adfy

MA uS f

bcf

fyAsa

*'*85.0

*


Mu + = 0.00 kg-m Mu + = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As += 0.00 cm2 As += 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!


Mu - = 0.00 kg-m Mu - = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As- = 0.00 cm2 As- = 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!
















Zona= Asismica





Mu = 0.17 Tn.m Ast = 0.32 cm2

a = 0.74 cm.

a_max= 5.44 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.37 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-16875.00 Kg - cm

0.17 Tn.m

















Zona= Asismica





Mu = 0.29 Tn.m Ast = 0.53 cm2

a = 0.31 cm.

a_max= 5.44 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.38 Tn.m 0.43

a = 0.42 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.38 Tn.m

Datos generales











28928.57 Kg - cm

0.29 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.21 Tn.m Ast = 0.40 cm2

a = 0.94 cm.

a_max= 5.44 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales









-21287.81 Kg - cm

0.21 Tn.m

















Zona= Asismica





Mu = 0.06 Tn.m Ast = 0.11 cm2

a = 0.06 cm.

a_max= 5.44 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.38 Tn.m 0.43

a = 0.42 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.38 Tn.m

Datos generales











5858.04 Kg - cm

0.06 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.26 Tn.m Ast = 0.50 cm2

a = 1.18 cm.

a_max= 5.44 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales









-26462.81 Kg - cm

0.26 Tn.m

















Zona= Asismica





Mu = 0.39 Tn.m Ast = 0.73 cm2

a = 0.43 cm.

a_max= 5.44 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

OJO PERALTE EFECTIVO Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.38 Tn.m

Datos generales











39375.00 Kg - cm

0.39 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.23 Tn.m Ast = 0.43 cm2

a = 1.02 cm.

a_max= 5.44 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales









-22968.75 Kg - cm

0.23 Tn.m




f'c = 280





520

Carga Viva

4. Sobrecarga 250


Wu = 1230


492 Kg/m

0.49 T/m


α -1/24 1/14 -1/10 1/16 -1/10

-0.04 0.07 -0.10 0.07 -0.10 ℓ (m) 3 3 2.18 1.35 2.43

-1.8E+04 3.2E+04 -2.3E+04 6.4E+03 -2.9E+04

2.7360 0.5540

6.3841 8.0535 10.0113

0.0018 0.0008 0.0024 0.0002 0.0028

0.54 0.14

0.31 0.41 0.48

As mín =

0.47 0.47 0.47 0.47 0.47

0.47 0.54 0.47 0.47 0.48

1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø3/8"

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

1.5WD + 1.8WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2(0.71cm2) (0.71cm2) (0.71cm2) (0.71cm2) (0.71cm2)




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

cm2

cm2


cm

cm

cm

Tramo Apoyo

1/14 -1/24

0.07 -0.043.5 3.50

4.3E+04 -2.5E+04

3.7240

8.6894

0.0012 0.0024

0.82

0.41

0.47 0.47

0.82 0.47

1Ø1/2" 1Ø3/8"

Kg/cm2

Kg/cm2

(1.27cm2) (0.71cm2)


Ø1/4" @ 0.25m.



Datos de Entrada






Carga Muerta




500

Carga Viva

4. Sobrecarga 250




Wu = 1.40 + 1.70

Wu = 1125


450 Kg/m

0.45 T/m

Kg/cm2

Kg/cm2

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

WD WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =


α -1/24 1/14 -1/10 1/16 -1/11 1/16 -1/11

-0.04 0.07 -0.10 0.06 -0.09 0.06 -0.09

ℓ (m) 3.47 3.47 3.24 3 2.18 1.35 2.43

-2.3E+04 3.9E+04 -4.7E+04 2.5E+04 -1.9E+04 5.1E+03 -2.4E+04

5.0296 3.2894 0.6661

11.7357 24.4798 10.0597 12.5052

0.0032 0.0014 0.0071 0.0009 0.0028 0.0002 0.0035

0.78 0.50 0.11

0.44 0.98 0.39 0.49

As mín =

0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm²

0.44Cm² 0.78Cm² 0.98Cm² 0.50Cm² 0.39Cm² 0.33Cm² 0.49Cm²


1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 12mm 12mm 3/8" 3/8" 3/8" 3/8"

0.71Cm² 1.13Cm² 1.13Cm² 0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm²

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2

Tramo 4 Apoyo 5 Tramo 5 Apoyo 6

1/16 -1/10 1/14 -1/24

0.06 -0.10 0.07 -0.04

3.5 3.55 3.6 3.60

3.4E+04 -5.7E+04 4.2E+04 -2.4E+04

4.4773 5.4135

29.4792 12.6315

0.0012 0.0087 0.0015 0.0035

0.67 0.83

1.21 0.49

0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm²

0.67Cm² 1.21Cm² 0.83Cm² 0.49Cm²

Acero Principal Balancin Acero Principal Baston

1 Ø 1 Ø 1 Ø 1 Ø

3/8" 1/2" 12mm 3/8"

0.71Cm² 1.27Cm² 1.13Cm² 0.71Cm²




Ast = 0.90

Av Ø1/4"= 0.31


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

Ø 1/4pulg @ 0.20m

cm2

cm2


TRAMO 1 2 3 4 5

1/24 1/10 1/11 1/11 1/10 1/24

1/14 1/16 1/16 1/16 1/14

LONGITUD 3 1.35 3.5 3.5 3.5

∆ ∆ ∆ ∆ ∆ ∆

WL 24²8 WL 10²8 WL 11²8 WL 11²8 WL 10²8 WL 24²8

WL 14²8 WL 16²8 WL 16²8 WL 16²8 WL 14²8







==> CONFORME

CONCLUSION:






0.90





Finalmente Usar:

Ø 3/8pulg @ 0.25m

Vu (ton) =

Vcn (ton) =

Vud (ton) =

Ast (cm²) =

Ast (cm²/m) =

s (cm) =

s (cm) <=

s (cm) <=

EJE NEUTRO



Mmax= 0.4165714285714 ton-m

0.029


w =


DATOS DE ENTRADA:












d = 13.87 cm.

210.00


4200.00






h = 10.00 cm.

h = 17.00 cm.

- Concreto :

Vol. Losa 0.40x0.05x1.00 = 0.020 m3

Vol. Vigueta 0.10x0.15x1.00 = 0.012 m3

0.032 m3 x 2400 Kg/m3 = 76.80 Kg


0.300 103.80 Kg



280.00 Kg/m2


CARGA MUERTA





TOTAL CM 500 Kg/m2

CARGA VIVA



TOTAL CV 250 Kg/m2





Wu = 1.40 + 1.70

Wu 1,125.00


1,125.00 = W1 450.00 Kg/ml

2.5









WD WL

Kg/m2

h=L

25

M 1=1

24∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 2=1

11∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 2=1

11∗W 1∗L

2

DISEÑO LOSA ALIGERADA EN UNA DIRECCIONApoyo 5 M4 0.567 T-m 56711.25 kg-cm 567.1125 kg-m 0.5671 ton-m

Apoyo 6 M5 0.243 T-m 24300 kg-cm 243 kg-m 0.243 ton-mM 3=1

24∗W 1∗L

2

M 2=1

10∗W 1∗L

2











………………..(1)

…………………(2)





ρb 0.0213




a = 5.201 cm. ………(4)


Mu max = 104,627.48 Kg/cm.


6. AREAS DE ACERO


As min = 0.33 cm2


Apoyo 1 : M1 0.23 T-m

Iterando


a = 1.01 cm

As = 0.45 cm2

a = 0.53 cm


a = 0.531216 cm As = 0.71 cm2

1.00 f 3/8"


M 12=1

14∗W1∗L

2

M 23=1

14∗W 1∗L

2

ρb=0 . 85∗β1∗f ' c

f yx

60006000+ fy

β1=

ρmax .=0 .75 ρb

MUmax=0. 85∗b '∗a∗f c' (d−a2 )


AS=M u


As∗fy0 .85∗f ' c∗b

Asmin=0 .70∗√ f ' c

fy∗b∗d

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2


Apoyo 2 :

M2 0.47 T-m

Iterando


a = 2.11 cm

As = 0.97 cm2

a = 1.11 cm


a = 1.108083 cm As = 1.13 cm2

1.00 f 12mm

Apoyo 3 :

M3 0.19 T-m

Iterando


a = 0.87 cm

As = 0.38 cm2

a = 0.46 cm


a = 0.455354 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 4 :

M3 0.24 T-m

Iterando


a = 1.08 cm

As = 0.48 cm2

a = 0.57 cm


a = 0.566049 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 5 :

M3 0.57 T-m

Iterando


a = 2.55 cm

As = 1.19 cm2

a = 1.33 cm


a = 1.334382 cm As = 1.27 cm2

1.00 f 1/2"

Apoyo 6 :

M5 0.24 T-m

Iterando


a = 1.09 cm

As = 0.48 cm2

a = 1.14 cm


AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b


1.00 f 3/8"


Tramo 1-2: M12 0.39 T-m

Iterando


a = 1.74 cm

As = 0.79 cm2

a = 1.85 cm


a = 1.861275 cm As = 1.13 cm2

1.00 f 12mm

Tramo 2-3: M23 0.25 T-m

Iterando


a = 1.14 cm

As = 0.50 cm2

a = 1.18 cm


a = 1.18667 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 3-4: M23 0.05 T-m

Iterando


a = 0.23 cm

As = 0.10 cm2

a = 0.23 cm


a = 0.23198 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 4-5: M23 0.34 T-m

Iterando


a = 1.55 cm

As = 0.70 cm2

a = 1.64 cm


a = 1.64322 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 5-6: M23 0.42 T-m

Iterando


a = 1.87 cm

As = 0.85 cm2

a = 2.00 cm


a = 2.015154 cm As = 1.13 cm2

1.00 f 12mm




1.065 : Cortante máxima que toma el concreto.Vc (ton) =

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

DISEÑO LOSA ALIGERADA EN UNA DIRECCION0.996 : Cortante max que toma el concreto en losa alig


==> CONFORME

CONCLUSION:




8- EJE NEUTRO


Mmax= 4.2E-01 ton-m

Mmax= 0.42 ton-m

0.0291


Vcn (ton) =

Vud (ton) =

w =


PROP:

ELEMENTO:NIVEL:



bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. d = 0.14 m.



0.0212 Mu + =0.01590.0024 a =

As =a =



2.211 cm2 Mu max ( - ) = 941.65 Kg-m = 0.94 Ton-m

(cm2)




As- =a =



(cm2)

rb =rmax =rmin =




As min =

nu max =

ρ (Tablas)


bf



bf =

tw =tf =d =


fy =





5.0296 3.2894

0.0014 0.0009

0.78 0.50(cm2) (cm2)96.58% 97.70%




11.7357 24.4798

0.0032 0.0071

0.44 0.98(cm2) (cm2)100.86% 99.49%





5.00 cm. 10.00 cm. 13.87 cm.

MATERIAL DE LA SECCION210 Kg/cm2

4200 Kg/cm2


5125.78 kg-m Mu + = 34453.13 kg-m


0.6661 4.4773

0.0002 0.0012

0.11 0.67(cm2)88.29% 100.12%


-19352.56 kg-m Mu - = -24057.10 kg-m


10.0597 12.5052

0.0028 0.0035

0.39 0.49(cm2)98.23% 98.53%

ρ (Tablas)

ρ (Tablas)

)2/(** adfy

MA uS f

bcf

fyAsa

*'*85.0

*


Mu + = 41657.14 kg-m Mu + = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.88 cm2 As = 0.00 cm2

a = 0.519 cm. a = 0.000 cm.As = 0.81 cm2 As = 0.00 cm2

a = 0.476 cm. a = 0.000 cm.As += 0.81 cm2 As += 0.00 cm2

5.4135 0.0000

0.0015 0.0000

0.83 0.00(cm2) (cm2)97.14% #DIV/0!


Mu - = -56711.25 kg-m Mu - = -24300.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 1.20 cm2 As = 0.51 cm2

a = 2.828 cm. a = 1.212 cm.As = 1.20 cm2 As = 0.48 cm2

a = 2.834 cm. a = 1.140 cm.As- = 1.20 cm2 As- = 0.48 cm2

29.4792 12.6315

0.0087 0.0035

1.21 0.49(cm2) (cm2)99.84% 99.57%




Mu + = 0.00 kg-m Mu + = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As += 0.00 cm2 As += 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!


Mu - = 0.00 kg-m Mu - = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As- = 0.00 cm2 As- = 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!
















Zona= Asismica





Mu = 0.23 Tn.m Ast = 0.43 cm2

a = 1.05 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-22576.69 Kg - cm

0.23 Tn.m

















Zona= Asismica





Mu = 0.39 Tn.m Ast = 0.72 cm2

a = 0.44 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











38702.89 Kg - cm

0.39 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.47 Tn.m Ast = 0.93 cm2

a = 2.31 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.62 Tn.m 0.69

a = 2.99 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-47093.51 Kg - cm

0.47 Tn.m

















Zona= Asismica





Mu = 0.25 Tn.m Ast = 0.47 cm2

a = 0.29 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











25312.50 Kg - cm

0.25 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.19 Tn.m Ast = 0.36 cm2

a = 0.90 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-19352.56 Kg - cm

0.19 Tn.m

















Zona= Asismica





Mu = 0.05 Tn.m Ast = 0.09 cm2

a = 0.06 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











5125.78 Kg - cm

0.05 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.24 Tn.m Ast = 0.46 cm2

a = 1.13 cm.

a_max= 5.20 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-24057.10 Kg - cm

0.24 Tn.m

















Zona= Asismica





Mu = 0.34 Tn.m Ast = 0.64 cm2

a = 0.39 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











34453.13 Kg - cm

0.34 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.57 Tn.m Ast = 1.15 cm2

a = 2.83 cm.

a_max= 5.20 cm.























Calculo de Areas






As = 1.27 cm2

RESISTENCIA 0.71Cm²PARA VIGA SIMPLEMENTE ARMADA

Ast = 1.27 cm2 OK !!

Fi_Mn= 0.62 Tn.m 0.69

a = 2.99 cm

Si es simple Falla: Ductil-Subreforzada

Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

Ancho de Alma 10.00 cm

H Losa Aligerada 17.00 cm

Peralte Efectivo 13.87 cm

Recubrimiento 2.50 cm


Resistencia del concreto 210 kg/cm2

Resistencia a fluencia del acero 4200 kg/cm2

Mu = -56711.25 Kg - cm

Mu = 0.57 Tn.m

0.0092 < 0.0213 Ductil-Subreforzada
















Zona= Asismica





Mu = 0.42 Tn.m Ast = 0.77 cm2

a = 0.48 cm.

a_max= 5.20 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 1.27 cm2

RESISTENCIA


Ast = 1.27 cm2 OK !! Mu =

Fi_Mn= 0.68 Tn.m 0.75

a = 0.75 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.37 Tn.m

Datos generales











41657.14 Kg - cm

0.42 Tn.m


DENOMINACION:

base de la seccion


Espesor de losita




















Zona= Asismica





Mu = 0.24 Tn.m Ast = 0.46 cm2

a = 1.14 cm.

a_max= 5.20 cm.























Calculo de Areas






As = 1.27 cm2

RESISTENCIA 0.71Cm²PARA VIGA SIMPLEMENTE ARMADA

Ast = 1.27 cm2 OK !!

Fi_Mn= 0.62 Tn.m 0.69

a = 2.99 cm

Si es simple Falla: Ductil-Subreforzada

Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.35 Tn.m

Ancho de Alma 10.00 cm

H Losa Aligerada 17.00 cm

Peralte Efectivo 13.87 cm



Resistencia del concreto 210 kg/cm2

Resistencia a fluencia del acero 4200 kg/cm2

Mu = -24300.00 Kg - cm

Mu = 0.24 Tn.m

0.0092 < 0.0213 Ductil-Subreforzada



f'c = 280





520

Carga Viva

4. Sobrecarga 250


Wu = 1230


492 Kg/m

0.49 T/m


α -1/24 1/14 -1/10 1/16 -1/11

-0.04 0.07 -0.10 0.07 -0.09 ℓ (m) 3.47 3.47 3.24 3 2.18

-2.5E+04 4.2E+04 -5.1E+04 3.2E+04 -2.1E+04

3.6605 2.7360

8.5411 17.8162 7.3214

0.0024 0.0012 0.0052 0.0008 0.0020

0.82 0.54

0.41 0.88 0.34

As mín =

0.47 0.47 0.47 0.47 0.47

0.47 0.82 0.88 0.54 0.47

1Ø3/8" 1Ø1/2" 1Ø1/2" 1Ø3/8" 1Ø3/8"

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

1.5WD + 1.8WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2(0.71cm2) (1.27cm2) (1.27cm2) (0.71cm2) (0.71cm2)




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

cm2

cm2


cm

cm

cm

Tramo Apoyo Tramo Apoyo Tramo Apoyo

1/16 -1/10 1/16 -1/10 1/14 -1/24

0.07 -0.10 0.07 -0.10 0.07 -0.041.35 2.43 3.5 3.55 3.6 3.60

6.4E+03 -2.9E+04 4.3E+04 -6.2E+04 4.6E+04 -2.7E+04

0.5540 3.7240 3.9399

10.0113 21.4548 9.1931

0.0002 0.0028 0.0010 0.0062 0.0012 0.0026

0.14 0.68 0.82

0.48 1.05 0.44

0.47 0.47 0.47 0.47 0.47 0.47

0.47 0.48 0.68 1.05 0.82 0.47

1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø1/2" 1Ø3/8"

Kg/cm2

Kg/cm2

(0.71cm2) (0.71cm2) (0.71cm2) (0.71cm2) (1.27cm2) (0.71cm2)


Ø1/4" @ 0.25m.



Datos de Entrada






Carga Muerta




500

Carga Viva

4. Sobrecarga 250




Wu = 1.40 + 1.70

Wu = 1125


450 Kg/m

0.45 T/m

Kg/cm2

Kg/cm2

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

WD WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

Sección Apoyo 1 Tramo 1 Apoyo 2 Tramo 2 Apoyo 3 Tramo Apoyo

α -1/24 1/14 -1/9 1/14 -1/24 1/16 -1/10

-0.04 0.07 -0.11 0.07 -0.04 0.07 -0.10

ℓ (m) 1.48 1.48 1.83 2.17 2.17 0 0.00

-4.1E+03 7.0E+03 -1.7E+04 1.5E+04 -8.8E+03 0.0E+00 -0.0E+00

0.9149 1.9669 0.0000

2.1349 8.6565 4.5895 0.0000

0.0006 0.0002 0.0024 0.0005 0.0012 0.0000 0.0000

0.11 0.28 0.00

0.08 0.33 0.17 0.00

As mín =

0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm²

0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm² 0.33Cm²


1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 3/8" 3/8" 3/8" 3/8" 3/8" 3/8"

0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm² 0.71Cm²

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2


TRAMO 1 2

1/24 1/10 1/24

1/14 1/14

LONGITUD 3 1.35

∆ ∆ ∆

WL 24²8 WL 10²8 WL 24²8

WL 14²8 WL 16²8




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

Ø 1/4pulg @ 0.20m

cm2

cm2







==> CONFORME

CONCLUSION:






0.90





Finalmente Usar:

Ø 1/4pulg @ 0.20m

Vu (ton) =

Vcn (ton) =

Vud (ton) =

Ast (cm²) =

Ast (cm²/m) =

s (cm) =

s (cm) <=

s (cm) <=

EJE NEUTRO



Mmax= 0.1513575 ton-m

0.010


w =


DATOS DE ENTRADA:









d = 13.87 cm.

210.00


4200.00






h = 10.00 cm.

h = 17.00 cm.

- Concreto :

Vol. Losa 0.40x0.05x1.00 = 0.020 m3

Vol. Vigueta 0.10x0.15x1.00 = 0.012 m3

0.032 m3 x 2400 Kg/m3 = 76.80 Kg


0.300 103.80 Kg



280.00 Kg/m2


CARGA MUERTA





TOTAL CM 500 Kg/m2

CARGA VIVA



TOTAL CV 250 Kg/m2





Wu = 1.40 + 1.70

Wu 1,125.00


1,125.00 = W1 450.00 Kg/ml

2.5



M1 0.041 T-m 4107 kg-cm 41.07 kg-m 0.0411 ton-m

M2 0.167 T-m 16653.125 kg-cm 166.53125 kg-m 0.1665 ton-m



WD WL

Kg/m2

h=L

25

M 1=1

24∗W 1∗L

2

M 3=1

24∗W 1∗L

2

M 2=19∗W 1∗L

2

DISEÑO LOSA ALIGERADA EN UNA DIRECCIONM3 0.088 T-m 8829.1875 kg-cm 88.291875 kg-m 0.0883 ton-mM 3=

124

∗W 1∗L2



M1-2 0.07 T-m 7040.57143 kg-cm 70.405714 kg-m 0.0704 ton-m

M2-3 0.15 T-m 15135.75 kg-cm 151.3575 kg-m 0.1514 ton-m




………………..(1)

…………………(2)


donde: 210.00 su factor ß1 = 0.85



ρb 0.0213


ρmax 0.016 ………(3)


a = 5.201 cm. ………(4)


Mu max = 104,627.48 Kg/cm.


6. AREAS DE ACERO


As min = 0.33 cm2


Apoyo 1 : M1 0.04 T-m

Iterando


a = 0.18 cm

As = 0.08 cm2

a = 0.10 cm


a = 0.096635 cm As = 0.71 cm2

1.00 f 3/8"


M12=1

14∗W1∗L

2

M 23=1

14∗W1∗L

2

ρb=0 . 85∗β1∗f ' c

f yx

60006000+ fy

β1=

ρmax .=0 .75 ρb

MUmax=0. 85∗b '∗a∗f c' (d−a2 )


AS=M u


As∗fy0 .85∗f ' c∗b

Asmin=0 . 70∗√ f ' c

fy∗b∗d


Apoyo 2 :

M2 0.17 T-m

Iterando


a = 0.75 cm

As = 0.33 cm2

a = 0.39 cm


a = 0.391838 cm As = 0.71 cm2

1.00 f 3/8"

Apoyo 3 :

M3 0.09 T-m

Iterando


a = 0.40 cm

As = 0.17 cm2

a = 0.40 cm


a = 0.402071 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 1-2: M12 0.07 T-m

Iterando


a = 0.32 cm

As = 0.14 cm2

a = 0.32 cm


a = 0.319657 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 2-3: M23 0.15 T-m

Iterando


a = 0.68 cm

As = 0.30 cm2

a = 0.70 cm


a = 0.696767 cm As = 0.71 cm2

1.00 f 3/8"

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b







0.996 : Cortante max que toma el concreto en losa alig Fuerza Cortante Maxima Resistente


==> CONFORME

CONCLUSION:




8- EJE NEUTRO


Mmax= 1.5E-01 ton-m

Mmax= 0.15 ton-m

0.0105



Vud (ton) =

w =


PROP:

ELEMENTO:NIVEL:



bf = 0.40 m. tf = 0.05 m.

tw = 0.10 m. d = 0.14 m.



0.0212 Mu + =0.01590.0024 a =

As =a =



2.211 cm2 Mu max ( - ) = 941.65 Kg-m = 0.94 Ton-m

(cm2)




As- =a =



(cm2)

rb =rmax =rmin =




As min =

nu max =

ρ (Tablas)


bf



bf =

tw =tf =d =


fy =





0.9149 1.9669

0.0002 0.0005

0.11 0.28(cm2) (cm2)121.37% 104.72%




4.2697 17.3130

0.0011 0.0049

0.08 0.34(cm2) (cm2)104.09% 99.16%





10.00 cm. 5.00 cm.


210 Kg/cm2 4200 Kg/cm2


0.00 kg-m Mu + = 0.00 kg-m


0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2)#DIV/0! #DIV/0!


-8829.19 kg-m Mu - = 0.00 kg-m


9.1791 0.0000

0.0025 0.0000

0.17 0.00(cm2)100.09% #DIV/0!

ρ (Tablas)

ρ (Tablas)

)2/(** adfy

MA uS f

bcf

fyAsa

*'*85.0

*


Mu + = 0.00 kg-m Mu + = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As += 0.00 cm2 As += 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!


Mu - = 0.00 kg-m Mu - = 0.00 kg-m

a = 2.774 cm. a = 2.774 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As = 0.00 cm2 As = 0.00 cm2

a = 0.000 cm. a = 0.000 cm.As- = 0.00 cm2 As- = 0.00 cm2

0.0000 0.0000

0.0000 0.0000

0.00 0.00(cm2) (cm2)#DIV/0! #DIV/0!
















Zona= Asismica





Mu = 0.04 Tn.m Ast = 0.08 cm2

a = 0.18 cm.

a_max= 5.44 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.37 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-4107.00 Kg - cm

0.04 Tn.m

















Zona= Asismica





Mu = 0.07 Tn.m Ast = 0.13 cm2

a = 0.08 cm.

a_max= 5.44 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.38 Tn.m 0.43

a = 0.42 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.38 Tn.m

40.00 cm

10.00 cm

5.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

7040.57 Kg - cm

0.07 Tn.m















Zona= Asismica





Mu = 0.17 Tn.m Ast = 0.31 cm2

a = 0.73 cm.

a_max= 5.44 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas






As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.37 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

-16653.13 Kg - cm

0.17 Tn.m

















Zona= Asismica





Mu = 0.15 Tn.m Ast = 0.28 cm2

a = 0.16 cm.

a_max= 5.44 cm.

a_max= 5.00 cm.























Ancho de Vigueta

Ancho de Alma

Espesor de losita

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.38 Tn.m 0.43

a = 0.42 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 0.42 cm

c= 0.49 cm

f`s= -24,528.17 kg/cm2

Fi_Mn= 0.38 Tn.m

40.00 cm

10.00 cm

5.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210 kg/cm2

4200 kg/cm2

15135.75 Kg - cm

0.15 Tn.m















Zona= Asismica





Mu = 0.09 Tn.m Ast = 0.16 cm2

a = 0.38 cm.

a_max= 5.44 cm.























Ancho de Alma

H Losa Aligerada

Peralte Efectivo

Recubrimiento

Recubrimiento



Calculo de Areas






As = 0.71 cm2

RESISTENCIA


Ast = 0.71 cm2 OK !! Mu =

Fi_Mn= 0.37 Tn.m 0.41

a = 1.67 cm


Si cumple As min

Calculo de Areas





As = 0.71 cm2

RESISTENCIA


A's= 0 cm2

As = 0.71 cm2

As>As_:máx: No

A's: No fluye

a= 1.67 cm

c= 1.97 cm

f`s= -1,632.04 kg/cm2

Fi_Mn= 0.37 Tn.m

10.00 cm

17.00 cm

13.87 cm

2.50 cm

2.50 cm

210.00 kg/cm2

4200.00 kg/cm2

-8,829.19 Kg - cm

0.09 Tn.m




f'c = 280





520

Carga Viva

4. Sobrecarga 250


Wu = 1230


492 Kg/m

0.49 T/m


α -1/24 1/14 -1/9 1/14 -1/24

-0.04 0.07 -0.11 0.07 -0.04 ℓ (m) 1.48 1.48 1.83 2.17 2.17

-4.5E+03 7.7E+03 -1.8E+04 1.7E+04 -9.7E+03

0.6659 1.4315

1.5537 6.3001 3.3402

0.0006 0.0002 0.0018 0.0004 0.0010

0.14 0.27

0.10 0.31 0.17

As mín =

0.47 0.47 0.47 0.47 0.47

0.47 0.47 0.47 0.47 0.47

1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø3/8" 1Ø3/8"

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

1.5WD + 1.8WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2(0.71cm2) (0.71cm2) (0.71cm2) (0.71cm2) (0.71cm2)




Ast = 0.90

Av Ø1/4"= 0.32


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

cm2

cm2


cm

cm

cm

Kg/cm2

Kg/cm2


Ø1/4" @ 0.25m.



Datos de Entrada






Carga Muerta




520

Carga Viva

4. Sobrecarga 250




Wu = 1.40 + 1.70

Wu = 1153


461 Kg/m

0.46 T/m

Kg/cm2

Kg/cm2

Kg/m2

Kg/m2

Kg/m2

WD = Kg/m2

WL = Kg/m2

WD WL

Kg/m2

WU = Wu x 0.40m

WU =

WU =


α -1/24 1/14 -1/10 1/16 -1/11 1/16 -1/11

-0.04 0.07 -0.10 0.06 -0.09 0.06 -0.09

ℓ (m) 3.75 3.75 3.63 3.5 3.50 3.5 3.50

-2.7E+04 4.6E+04 -6.1E+04 3.5E+04 -5.1E+04 3.5E+04 -5.1E+04

4.0694 3.1018 3.1018

9.4953 21.2949 18.0469 18.0469

0.0026 0.0011 0.0061 0.0008 0.0051 0.0008 0.0051

0.74 0.54 0.54

0.44 1.03 0.86 0.86

As mín =

0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm²

0.44Cm² 0.74Cm² 1.03Cm² 0.54Cm² 0.86Cm² 0.54Cm² 0.86Cm²


1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 12mm 12mm 3/8" 12mm 3/8" 12mm

0.71Cm² 1.13Cm² 1.13Cm² 0.71Cm² 1.13Cm² 0.71Cm² 1.13Cm²

Mu = a.w.ℓ2

(Kg.cm)

ρ (Tablas)

(cm2)

(cm2)

(cm2)

As (Definitiva)

cm2

Tramo 4 Apoyo 5 Tramo 5 Apoyo 6 Tramo 6 Apoyo 6

1/16 -1/11 1/16 -1/10 1/14 -1/24

0.06 -0.09 0.06 -0.10 0.07 -0.04

3.5 3.50 3.5 3.63 3.75 3.75

3.5E+04 -5.1E+04 3.5E+04 -6.1E+04 4.6E+04 -2.7E+04

3.1018 3.1018 4.0694

18.0469 21.2949 9.4953

0.0008 0.0051 0.0008 0.0061 0.0011 0.0026

0.54 0.54 0.74

0.86 1.03 0.44

0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm² 0.41Cm²

0.54Cm² 0.86Cm² 0.54Cm² 1.03Cm² 0.74Cm² 0.44Cm²

Acero Principal Balancin Acero Principal Balancin Acero Principal Baston

1 Ø 1 Ø 1 Ø 1 Ø 1 Ø 1 Ø

3/8" 12mm 3/8" 12mm 12mm 3/8"

0.71Cm² 1.13Cm² 0.71Cm² 1.13Cm² 1.13Cm² 0.71Cm²




Ast = 0.90

Av Ø1/4"= 0.31


Usando Ø1/4"


S = 5t → S = 25 cm

S = 45 cm Usar : Ø1/4" @ 0.25m.

Ø 1/4pulg @ 0.20m

cm2

cm2


TRAMO 1 2 3 4 5 6

1/24 1/10 1/11 1/11 1/11 1/10 1/24

1/14 1/16 1/16 1/16 1/16 1/14

LONGITUD 3 1.35 3.5 3.5 3.5 3.5

∆ ∆ ∆ ∆ ∆ ∆ ∆

WL 24²8 WL 10²8 WL 11²8 WL 11²8 WL 11²8 WL 10²8 WL 24²8

WL 14²8 WL 16²8 WL 16²8 WL 16²8 WL 16²8 WL 14²8







==> CONFORME

CONCLUSION:






0.90





Finalmente Usar:

Ø 3/8pulg @ 0.25m

Vu (ton) =

Vcn (ton) =

Vud (ton) =

Ast (cm²) =

Ast (cm²/m) =

s (cm) =

s (cm) <=

s (cm) <=

EJE NEUTRO



Mmax= 0.4632589285714 ton-m

0.022


w =


DATOS DE ENTRADA:













d = 16.87 cm.

210.00


4200.00






h = 20.00 cm.

h = 20.00 cm.

- Concreto :

Vol. Losa 0.40x0.05x1.00 = 0.020 m3

Vol. Vigueta 0.10x0.15x1.00 = 0.015 m3

0.035 m3 x 2400 Kg/m3 = 84.00 Kg


0.300 111.00 Kg



300.00 Kg/m2


CARGA MUERTA





TOTAL CM 520 Kg/m2

CARGA VIVA



TOTAL CV 250 Kg/m2





Wu = 1.40 + 1.70

Wu 1,153.00


1,153.00 = W1 461.20 Kg/ml

2.5











WD WL

Kg/m2

h=L

25

M 1=1

24∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 2=1

11∗W 1∗L

2

M 2=1

10∗W 1∗L

2

M 2=1

11∗W 1∗L

2

M 2=1

10∗W 1∗L

2



24∗W 1∗L

2

M 2=1

10∗W 1∗L

2












………………..(1)

…………………(2)





ρb 0.0213




a = 6.326 cm. ………(4)


Mu max = 154,782.92 Kg/cm.


6. AREAS DE ACERO


As min = 0.41 cm2


Apoyo 1 : M1 0.27 T-m

Iterando


a = 1.00 cm

As = 0.44 cm2

a = 0.64 cm


a = 0.635846 cm As = 0.71 cm2

1.00 f 3/8"


M 12=1

14∗W 1∗L

2

M 23=1

14∗W 1∗L

2

ρb=0 .85∗β1∗f ' c

f yx

60006000+ fy

β1=

ρmax .=0 .75 ρb

MUmax=0. 85∗b '∗a∗f c' (d− a2 )


AS=M u


As∗fy0 .85∗f ' c∗b

Asmin=0 .70∗√ f ' c

fy∗b∗d

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2

M 23=1

16∗W 1∗L

2


Apoyo 2 :

M2 0.61 T-m

Iterando


a = 2.24 cm

As = 1.02 cm2

a = 1.43 cm


a = 1.42599 cm As = 1.13 cm2

1.00 f 12mm

Apoyo 3 :

M3 0.51 T-m

Iterando


a = 1.90 cm

As = 0.85 cm2

a = 1.21 cm


a = 1.208492 cm As = 1.13 cm2

1.00 f 12mm

Apoyo 4 :

M3 0.51 T-m

Iterando


a = 1.90 cm

As = 0.85 cm2

a = 1.21 cm


a = 1.208492 cm As = 1.13 cm2

2.00 f 12mm

Apoyo 5 :

M3 0.56 T-m

Iterando


a = 2.08 cm

As = 0.94 cm2

a = 1.33 cm


a = 1.329341 cm As = 1.13 cm2

1.00 f 12mm

Apoyo 6 :

M3 0.61 T-m

Iterando


a = 2.24 cm

As = 1.02 cm2

a = 1.43 cm


a = 1.42599 cm As = 1.13 cm2

1.00 f 12mm

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b


Apoyo 7 :

M5 0.27 T-m

Iterando


a = 1.00 cm

As = 0.44 cm2

a = 1.03 cm


a = 1.028433 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 1-2: M12 0.46 T-m

Iterando


a = 1.71 cm

As = 0.77 cm2

a = 1.80 cm


a = 1.805701 cm As = 1.13 cm2

1.00 f 12mm

Tramo 2-3: M23 0.35 T-m

Iterando


a = 1.30 cm

As = 0.58 cm2

a = 1.36 cm


a = 1.357419 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 3-4: M23 0.35 T-m

Iterando


a = 1.30 cm

As = 0.58 cm2

a = 1.36 cm


a = 1.357419 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 4-5: M23 0.35 T-m

Iterando


a = 1.30 cm

As = 0.58 cm2

a = 1.36 cm


a = 1.357419 cm As = 0.71 cm2

1.00 f 3/8"

Tramo 5-6: M23 0.35 T-m

Iterando


a = 1.30 cm

As = 0.58 cm2

a = 1.36 cm


AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b

AS=M u


As∗fy0 .85∗f ' c∗b


1.00 f 3/8"

Tramo 5-6: M23 0.46 T-m

Iterando


a = 1.71 cm

As = 0.77 cm2

a = 1.80 cm


a = 1.805701 cm As = 1.13 cm2

1.00 f 12mm







==> CONFORME

CONCLUSION:




8- EJE NEUTRO


Mmax= 4.6E-01 ton-m

Mmax= 0.46 ton-m

0.0218



Vud (ton) =

w =

AS=M u


As∗fy0 .85∗f ' c∗b


PROYECTO :

DATOS :

F'c= 210.00 Kg/cm2d= 17.53 Cm.

b= 40.00 Cm.

bw= 10.00 Cm.

Fy= 4,200.00 Kg/cm2h Losa alig = 20.00 Cm.

Recubrimiento = 2.00 Cm.Diámetro acero principal + a usar = 0.95 Cm.


CARGA MUERTAPESO PROPIO LOSA ALIGERADA 300.00 Kg/m2PISO + CIELO RASO 100.00 Kg/m2TABIQUERIA Kg/m2

WD= 400.00 Kg/m2

CARGA VIVAWL= 150.00 Kg/m2

WU= 1.5WD+1.8WLWU= 1.5 WD + 1.8WU= 870.00 Kg/m2

CARGA POR VIGUETA 348.00 Kg/ml


TRAMO 1 2 3 4 5

1/24 1/10 1/11 1/11 1/11

1/14 1/16 1/16 1/16 1/16

LONGITUD 4.20 4.63 4.63 4.63 4.63

MOMENTOS (TON-M)

0.26 0.75 0.68 0.68 0.68

0.44 0.47 0.47 0.47 0.47

ACERO (cm2) ACERO MINIMO= 0.42 Cm2

0.397 1.227 1.106 1.106 1.106

0.67 0.71 0.71 0.71 0.71

EJE NEUTRO

MEJORAMIENTO INFRAESTRUCTURA I.E. No 501258 CORONEL FRANCISCO BOLOGNESI CERVANTES

C18



Mmax= 0.53 ton-m

0.023c= 0.57 cm < 5 cm, el eje neutro se encuentra en el ala w =


Ø (pulg) Ø (cm) As (cm²)1/4" 0.64 0.313/8" 0.95 0.711/2" 1.27 1.275/8" 1.59 1.98

3/4" 1.91 2.85

7/8" 2.22 3.88

1" 2.54 5.07

17.53 : Peralte efectivo refuerzo positivo.

17.53 : Peralte efectivo refuerzo negativo.

Diámetro acero principal + a usar =Diámetro acero principal - a usar =

WL

REVISAR


Acero principal a usar = 12mm

Diámetro acero principal a usar = 0.64 Cm.

6 d = 17.18 Cm.

1/10 1/24

1/14 Losa Aligerada = 20 cm

4.63

0.75 0.31

0.53

1.227 0.485

0.82

MEJORAMIENTO INFRAESTRUCTURA I.E. No 501258 CORONEL FRANCISCO BOLOGNESI

d+ (cm) =

d- (cm) =

Øp+ (cm) =Øp- (cm) =

Se les denomina losas aligeradas a un tipo de losas en la que parte del concreto se

reemplaza por otros materiales como cajones de madera, poliestireno, esferas, etc, y

en el caso de viviendas de uno y dos pisos se reemplaza por ladrillos o bloques. De

esta forma se disminuye el peso de la losa y se pueden cubrir mayores luces de

manera mas económica

K32


: Peralte efectivo refuerzo positivo.

: Peralte efectivo refuerzo negativo.

Diámetro acero principal + a usar =Diámetro acero principal - a usar =

Ø (pulg) Ø (cm) As (cm²)

0.025 M 1/4" 0.64 0.31

3/8" 0.95 0.71

0.0064 M 12mm 0.80 1.13

0.18 M 1/2" 1.27 1.27

5/8" 1.59 1.98

3/4" 1.91 2.85

7/8" 2.22 3.88

1" 2.54 5.07

Se les denomina losas aligeradas a un tipo de losas en la que parte del concreto se

reemplaza por otros materiales como cajones de madera, poliestireno, esferas, etc, y

en el caso de viviendas de uno y dos pisos se reemplaza por ladrillos o bloques. De

esta forma se disminuye el peso de la losa y se pueden cubrir mayores luces de

Ø (pulg) Ø (cm)

Recubrimiento = 2.50 cm. ### M 1/4" 0.64

Acero principal a usar = 3/8" 3/8" 0.95

Diámetro acero principal - a usar = 0.71 Cm. 0 M 12mm 0.80

d = 17.15 Cm. 0.2 M 1/2" 1.27

5/8" 1.59

3/4" 1.91

Losa Aligerada = 20 cm 7/8" 2.22

1" 2.54

K32


As (cm²)

0.31

0.71

1.13

1.27

1.98

2.85

3.88

5.07

HOJA DE CALCULO DE VIGAS PROP: Sección de la viga :ELEMENTO:NIVEL: h

VIGA CUALQUIERA Fuerzas y Momentos Resistentes :GEOMETRIA DE SECCION Verificacion de la Seccion

h = 0.20 m. 0.0212 bb= 0.25 m. 0.0159

d = 0.14 m. 0.0024MATERIAL DE LA SECCION Momentos Maximos Resistentes:

f'c = 210 Kg/cm2 fy = 4200 Kg/cm2 5.578 cm2

0.01594 Mu max ( + ) = 2396.794 Kg-m0.31875

0.0024 0.845 cm2 0.04830 Mu min ( + ) = 434.599 Kg-m

Fuerza Cortante Maxima toma el concreto :

Vc = 2688.15 Kg

2284.93 Kg


Calculo de momentos Positivos Mu + : Calculo de momentos Negativos - :Calculo del refuerzo : Calculo del refuerzo :As + As -

Mu + = 11100 kg-m Mu - = 16500 kg-m

a = 0.028 cm. a = 0.028 cm.As = 23.31 cm2 As = 34.64 cm2

a = 0.219 cm. a = 0.326 cm.As = 96.83 cm2 As = -189.55 cm2

a = 0.911 cm. a = -1.784 cm.As + = -9.30 cm2 As- = 4.23 cm2

rb =rmax =rmin =


rmax =wmax = Momentos Minimos :rmin = As min =wmin =

FVc =

DISEÑO DE VIGAS

VP-101 (eje A-A) entre eje 2-3

DATOS

RESISTENCIA DEL CONCRETO 210.00

LÍMITE DE INFLUENCIA 4200.00

LUZ LIBRE 3.10AREA TRIBUTARIA 1.37

PREDIMENSIONAMIENTO (h) 0.22

(b) (h)0.25 0.30

METRADO DE CARGAS

a) CARGAS MUERTAS

PESO PROPIO 180.00 kg/mlP. ALIGERADO 479.50 kg/mlP. ACABADOS 137.00 kg/ml

WD 796.50 kg/ml

b) CARGAS VIVAS

SOBRE CARGA S/C 200.00

WL 274.00 kg/ml

CARGA ÚLTIMA DE ROTURA

WU 1687.95 kg/ml

ANÁLISIS ESTRUCTURAL

WU = 1687.95 kg/ml

L = 3.10 m

1,013.82 kg-m 1,013.82 kg-m

kg/cm2

kg/cm2

kg/cm2

kg/m2

1,622.12 kg-mDIAGRAMA DE MOMENTO FLECTOR

2,616.32 kg

2,616.32 kg

DIAGRAMA DE FUERZA CORTANTE

a) MOMENTO POSITIVO

1,622.12 kg-m

b) MOMENTO NEGATIVO

1,013.82 kg-m

c) FUERZA CORTANTE

Vu = (Wu x L)/2 2,616.32 kg

DISEÑO POR FLEXIÓN

a) CÁLCULO DE CUANTÍAS

β1 = 0.85

ρb =0.85 β1 (f´c/fy) (6000/(6000+fy)) = 0.02125

ρ máx = 0.0159

ρ mín = 0.002760.00333

ρ mín = 0.00333

b) CÁLCULO DE ÁREAS DE ACERO

ACERO POSITIVO

1,622.12 kg-m

SECCIÓN = (b x h) = 25.00 x 30

M+ a-b (máx) =(1/10) x Wu x L2

M- a = M-

b = (1/16) x Wu x L2

M+ a-b (máx) =(1/10) x Wu x L2

d = 24 cm

Se tiene :

14,400.00

Du = 11.26

Observamos que aproximadamente es: ρ 0.0091

As = 5.46 USAR:

As mín = 2.00

ACERO NEGATIVO

1,013.82

SECCIÓN = (b x h) = 25.00 x 30

d = 24 cm

Se tiene :

14,400.00

Du = 7.04


As = 3.30 USAR:

As mín = 2.00

VERIFICACIÓN POR CORTE

a) CORTE ACTUANTE

Vu = 2,616.32 kg

b) CORTE ADMISIBLE (Vc)

Vc = 4,608.26 kg

Vu > Vc/2

2,616.32 > 2,304.13

bd 2 = cm3

cm2 (3Φ5/8")

cm2

M- a = M-

b = (1/16) x Wu x L2

bd 2 = cm3

cm2 (3Φ1/2")cm2

0.30

0.25 (3Φ1/2")X

0.30

X(3Φ5/8")

0.25 3.10 0.25

VP-102 (eje B-B) entre eje 1 - 3

DATOS





(b) (h)0.25 0.40

METRADO DE CARGAS

a) CARGAS MUERTAS


WD 1402.80 kg/ml

b) CARGAS VIVAS


WL 612.00 kg/ml


WU 3205.80 kg/ml

Φ 3/8"; [email protected], [email protected], [email protected], rto 0.20 c/ext

kg/cm2

kg/cm2

kg/cm2

kg/m2


WU = 3205.80 kg/ml

L = 3.80 m

2,893.23 kg-m 2,893.23 kg-m


6,091.02 kg

6,091.02 kg


a) MOMENTO POSITIVO

4,629.18 kg-m

b) MOMENTO NEGATIVO

2,893.23 kg-m

c) FUERZA CORTANTE

Vu = (Wu x L)/2 6,091.02 kg



β1 = 0.85

ρb =0.85 β1 (f´c/fy) (6000/(6000+fy)) = 0.02125

M+ a-b (máx) =(1/10) x Wu x L2

M- a = M-

b = (1/16) x Wu x L2

ρ máx = 0.0159

ρ mín = 0.002760.00333

ρ mín = 0.00333


ACERO POSITIVO

4,629.18 kg-m

SECCIÓN = (b x h) = 25.00 x 40.00

d = 34.00 cm

Se tiene :

28,900.00

Du = 16.02


As = 4.16 USAR:

As mín = 2.83

ACERO NEGATIVO

2,893.23

SECCIÓN = (b x h) = 25.00 x 40.00

d = 34.00 cm

Se tiene :

28,900.00

Du = 10.01


As = 2.63

As mín = 2.83


M+ a-b (máx) =(1/10) x Wu x L2

bd 2 = cm3

cm2 (1Φ1/2"+2Φ3/8")

cm2

M- a = M-

b = (1/16) x Wu x L2

bd 2 = cm3

cm2 USAR: (3Φ1/2")

cm2

a) CORTE ACTUANTE

Vu = 6,091.02 kg


Vc = 6,528.37 kg

Vu > Vc/2

6,091.02 > 3,264.18

0.40

0.25 USAR: (3Φ1/2")X

0.40

X(1Φ1/2"+2Φ3/8")

0.25 3.80 0.25

VP-103 (eje 4-4 entre C-C)


DATOS





(b) (h)0.25 0.40

METRADO DE CARGAS

a) CARGAS MUERTAS


WD 1691.60 kg/ml

b) CARGAS VIVAS


WL 764.00 kg/ml


WU 3912.60 kg/ml


WU = 3912.60 kg/ml

L = 3.80 m

3,531.12 kg-m 3,531.12 kg-m

5,649.79 kg-m

kg/cm2

kg/cm2

kg/cm2

kg/m2

DIAGRAMA DE MOMENTO FLECTOR

7,433.94 kg

7,433.94 kg


a) MOMENTO POSITIVO

5,649.79 kg-m

b) MOMENTO NEGATIVO

3,531.12 kg-m

c) FUERZA CORTANTE

Vu = (Wu x L)/2 7,433.94 kg



β1 = 0.85

ρb =0.85 β1 (f´c/fy) (6000/(6000+fy)) = 0.02125

ρ máx = 0.0159

ρ mín = 0.002760.00333

ρ mín = 0.00333


ACERO POSITIVO

5,649.79 kg-m

SECCIÓN = (b x h) = 25.00 x 40.00

d = 34.00 cm

M+ a-b (máx) =(1/10) x Wu x L2

M- a = M-

b = (1/16) x Wu x L2

M+ a-b (máx) =(1/10) x Wu x L2

Se tiene :

28,900.00

Du = 19.55


As = 5.52 USAR:

As mín = 2.83

ACERO NEGATIVO

3,531.12

SECCIÓN = (b x h) = 25.00 x 40.00

d = 34.00 cm

Se tiene :

28,900.00

Du = 12.22


As = 3.31 USAR:

As mín = 2.83


a) CORTE ACTUANTE

Vu = 7,433.94 kg


Vc = 6,528.37 kg

Vu > Vc/2

7,433.94 > 3,264.18

0.40

bd 2 = cm3

cm2 (3Φ5/8")

cm2

M- a = M-

b = (1/16) x Wu x L2

bd 2 = cm3

cm2 (3Φ1/2")

cm2

0.25 (3Φ1/2")X

0.40

X(3Φ5/8")

0.25 3.80 0.25

VP-104 (eje 4-4 entre E-G)

DATOS





(b) (h)0.25 0.30

METRADO DE CARGAS

a) CARGAS MUERTAS


WD 1643.00 kg/ml

b) CARGAS VIVAS


WL 770.00 kg/ml


WU 3850.50 kg/ml



kg/cm2

kg/cm2

kg/cm2

kg/m2

WU = 3850.50 kg/ml

L = 3.63 m

3,171.10 kg-m 3,171.10 kg-m


6,988.66 kg

6,988.66 kg


a) MOMENTO POSITIVO

5,073.77 kg-m

b) MOMENTO NEGATIVO

3,171.10 kg-m

c) FUERZA CORTANTE

Vu = (Wu x L)/2 6,988.66 kg



β1 = 0.85

ρb =0.85 β1 (f´c/fy) (6000/(6000+fy)) = 0.02125

ρ máx = 0.0159

M+ a-b (máx) =(1/10) x Wu x L2

M- a = M-

b = (1/16) x Wu x L2

ρ mín = 0.002760.00333

ρ mín = 0.00333


ACERO POSITIVO

5,073.77 kg-m

SECCIÓN = (b x h) = 25.00 x 30.00

d = 24.00 cm

Se tiene :

14,400.00

Du = 35.23


As = 6.42 USAR:

As mín = 2.00

ACERO NEGATIVO

3,171.10

SECCIÓN = (b x h) = 25.00 x 30.00

d = 24.00 cm

Se tiene :

14,400.00

Du = 22.02


As = 3.78 USAR:

As mín = 2.00


a) CORTE ACTUANTE

M+ a-b (máx) =(1/10) x Wu x L2

bd 2 = cm3

cm2 (2Φ1/2"+2Φ5/8")

cm2

M- a = M-

b = (1/16) x Wu x L2

bd 2 = cm3

cm2 (2Φ5/8")

cm2

Vu = 6,988.66 kg


Vc = 4,608.26 kg

Vu > Vc/2

6,988.66 > 2,304.13

0.30

0.25 (2Φ5/8")X

0.30

X(2Φ1/2"+2Φ5/8")

0.25 3.63 0.25

VP-103 (eje 3-3 entre E-G)

DATOS





(b) (h)0.25 0.30

METRADO DE CARGAS

a) CARGAS MUERTAS



kg/cm2

kg/cm2

kg/cm2

WD 1339.00 kg/ml

b) CARGAS VIVAS


WL 610.00 kg/ml


WU 3106.50 kg/ml


WU = 3106.50 kg/ml

L = 3.63 m

2,558.38 kg-m 2,558.38 kg-m


5,638.30 kg

5,638.30 kg


a) MOMENTO POSITIVO

4,093.40 kg-m

b) MOMENTO NEGATIVO

kg/m2

M+ a-b (máx) =(1/10) x Wu x L2

2,558.38 kg-m

c) FUERZA CORTANTE

Vu = (Wu x L)/2 5,638.30 kg



β1 = 0.85

ρb =0.85 β1 (f´c/fy) (6000/(6000+fy)) = 0.02125

ρ máx = 0.0159

ρ mín = 0.002760.00333

ρ mín = 0.00333


ACERO POSITIVO

4,093.40 kg-m

SECCIÓN = (b x h) = 25.00 x 30.00

d = 24.00 cm

Se tiene :

14,400.00

Du = 28.43


As = 5.10 USAR:

As mín = 2.00

ACERO NEGATIVO

2,558.38

SECCIÓN = (b x h) = 25.00 x 30.00

d = 24.00 cm

Se tiene :

M- a = M-

b = (1/16) x Wu x L2

M+ a-b (máx) =(1/10) x Wu x L2

bd 2 = cm3

cm2 (1Φ1/2"+2Φ5/8")

cm2

M- a = M-

b = (1/16) x Wu x L2

14,400.00

Du = 17.77


As = 3.06 USAR:

As mín = 2.00


a) CORTE ACTUANTE

Vu = 5,638.30 kg


Vc = 4,608.26 kg

Vu > Vc/2

5,638.30 > 2,304.13

0.30

0.25 (1Φ1/2"+1Φ5/8")X

0.30

X(1Φ1/2"+2Φ5/8")

0.25 3.63 0.25

bd 2 = cm3

cm2 (1Φ1/2"+1Φ5/8")

cm2


calculo de losa aligerada 25.02.2015 ok. ok. ok ok

Documents