Tabela para o Dimensionamento de Lajes em Concreto Armado

Prévia do material em texto

5.0 6.3 8.0 10.0 12.5
2.86 4.50 7.14 11.43 17.86
2.67 4.20 6.67 10.67 16.67
2.50 3.94 6.25 10.00 15.63
2.35 3.71 5.88 9.41 14.71
2.22 3.50 5.56 8.89 13.89
2.11 3.32 5.26 8.42 13.16
2.00 3.15 5.00 8.00 12.50
1.82 2.86 4.55 7.27 11.36
1.67 2.62 4.17 6.67 10.42
1.60 2.52 4.00 6.40 10.00
1.54 2.42 3.85 6.15 9.62
1.43 2.25 3.57 5.71 8.93
1.33 2.10 3.33 5.33 8.33
1.25 1.97 3.13 5.00 7.81
1.18 1.85 2.94 4.71 7.35
1.14 1.80 2.86 4.57 7.14
1.11 1.75 2.78 4.44 6.94
1.05 1.66 2.63 4.21 6.58
1.00 1.58 2.50 4.00 6.25
0.95 1.50 2.38 3.81 5.95
0.91 1.43 2.27 3.64 5.68
0.87 1.37 2.17 3.48 5.43
0.83 1.31 2.08 3.33 5.21
0.80 1.26 2.00 3.20 5.00
0.77 1.21 1.92 3.08 4.81
0.74 1.17 1.85 2.96 4.63
0.71 1.12 1.79 2.86 4.46
0.69 1.09 1.72 2.76 4.31
0.67 1.05 1.67 2.67 4.17
ÁREA DE ARMADURAS PARA LAJES E PAREDES (cm²/m) 
25.0
26.0
27.0
28.0
14.0
15.0
16.0
17.0
17.5
18.0
9.5
10.0
11.0
12.0
12.5
13.0
29.0
30.0
19.0
20.0
21.0
22.0
23.0
24.0
8.5
9.0
ESPAÇAMENTO
cm
7.0
7.5
8.0
Lx
Ly
ly / lx mx my kx ly / lx mx my kx
1.00 27.4 27.4 0.500 1.50 13.9 31.3 0.835
1.01 27.0 27.4 0.509 1.51 13.8 31.4 0.838
1.02 26.5 27.4 0.519 1.52 13.7 31.6 0.842
1.03 26.0 27.4 0.528 1.53 13.6 31.8 0.845
1.04 25.6 27.5 0.538 1.54 13.5 31.9 0.848
1.05 25.1 27.5 0.547 1.55 13.4 31.1 0.851
1.06 24.6 27.5 0.556 1.56 13.3 32.3 0.855
1.07 24.2 27.5 0.566 1.57 13.2 32.4 0.858
1.08 23.7 27.5 0.575 1.58 13.1 32.6 0.861
1.09 23.2 27.6 0.585 1.59 13.0 32.8 0.865
1.10 22.8 27.6 0.594 1.60 12.9 33.0 0.868
1.11 22.4 27.6 0.602 1.61 12.8 33.2 0.870
1.12 22.1 27.7 0.610 1.62 12.7 33.4 0.873
1.13 21.8 27.7 0.618 1.63 12.6 33.6 0.875
1.14 21.4 27.8 0.626 1.64 12.5 33.8 0.878
1.15 21.1 27.8 0.634 1.65 12.4 34.0 0.880
1.16 20.8 27.8 0.643 1.66 12.4 34.2 0.883
1.17 20.4 27.9 0.651 1.67 12.3 34.4 0.885
1.18 20.1 27.9 0.659 1.68 12.2 34.6 0.888
1.19 19.8 27.9 0.667 1.69 12.1 34.8 0.890
1.20 19.4 28.0 0.675 1.70 12.0 35.0 0.893
1.21 19.2 28.1 0.682 1.71 12.0 35.2 0.895
1.22 19.0 28.2 0.668 1.72 11.8 35.5 0.897
1.23 18.7 28.3 0.695 1.73 11.8 35.7 0.899
1.24 18.5 28.4 0.701 1.74 11.7 35.9 0.901
1.25 18.2 28.4 0.708 1.75 11.7 36.2 0.903
1.26 18.0 28.5 0.715 1.76 11.6 36.4 0.905
1.27 17.7 28.6 0.721 1.77 11.5 36.7 0.907
1.28 17.5 28.7 0.728 1.78 11.5 36.9 0.909
1.29 17.2 28.8 0.734 1.79 11.4 37.1 0.911
1.30 17.0 28.8 0.741 1.80 11.4 37.4 0.913
1.31 16.8 28.9 0.746 1.81 11.4 37.6 0.915
1.32 16.7 29.0 0.752 1.82 11.3 37.8 0.916
1.33 16.5 29.1 0.757 1.83 11.3 38.1 0.918
1.34 16.3 29.2 0.762 1.84 11.2 38.3 0.919
1.35 16.1 29.3 0.767 1.85 11.2 38.5 0.921
1.36 16.0 29.5 0.773 1.86 11.1 38.8 0.923
1.37 15.8 29.6 0.778 1.87 11.1 39.0 0.924
1.38 15.6 29.7 0.783 1.88 11.0 39.2 0.925
1.39 15.4 29.8 0.789 1.89 11.0 39.5 0.927
1.40 15.2 29.9 0.794 1.90 11.0 39.7 0.929
1.41 15.1 30.0 0.798 1.91 10.9 40.0 0.930
1.42 14.9 30.2 0.802 1.92 10.9 40.2 0.932
1.43 14.8 30.3 0.806 1.93 10.8 40.5 0.933
1.44 14.7 30.5 0.810 1.94 10.8 40.8 0.934
1.45 14.5 30.6 0.814 1.95 10.8 41.0 0.935
1.46 14.4 30.7 0.819 1.96 10.7 41.3 0.936
1.47 14.3 30.9 0.823 1.97 10.7 41.6 0.937
1.48 14.1 31.0 0.827 1.98 10.6 42.8 0.939
1.49 14.0 31.2 0.831 1.99 10.6 42.1 0.940
1.50 13.9 31.3 0.835 2.00 10.6 42.3 0.941
CASO 1
Neste caso não há engastes. A direção Y é a direção em que Ly > Lx
Ly
Lx
ly / lx mx my nx kx ly / lx mx my nx kx
0.50 140.9 45.1 59.2 0.135 1.00 29.9 36.7 11.2 0.714
0.51 134.2 44.3 55.2 0.145 1.02 29.1 37.2 11.0 0.728
0.52 127.5 43.4 51.6 0.155 1.04 28.3 37.7 10.8 0.742
0.53 120.8 42.6 48.2 0.166 1.06 27.5 38.2 10.6 0.756
0.54 114.1 41.8 45.5 0.176 1.08 26.7 38.7 10.4 0.770
0.55 107.4 40.9 43.0 0.186 1.10 26.0 39.3 10.2 0.785
0.56 103.0 40.4 40.4 0.198 1.12 25.5 39.9 10.1 0.795
0.57 98.5 39.8 38.1 0.210 1.14 25.0 40.5 9.9 0.806
0.58 94.1 39.3 36.2 0.221 1.16 24.4 41.2 9.8 0.817
0.59 89.7 38.7 34.5 0.232 1.18 23.8 41.8 9.6 0.827
0.60 85.3 38.1 32.7 0.245 1.20 23.4 42.6 9.5 0.838
0.61 82.8 37.7 31.1 0.257 1.22 23.0 43.3 9.4 0.847
0.62 79.4 37.3 29.6 0.270 1.24 22.6 44.1 9.3 0.853
0.63 76.4 36.9 28.3 0.283 1.26 22.2 44.9 9.3 0.861
0.64 73.5 36.5 27.1 0.296 1.28 21.8 45.7 9.2 0.869
0.65 70.6 36.1 25.9 0.309 1.30 21.4 46.6 9.1 0.877
0.66 68.3 35.9 24.8 0.322 1.32 21.1 47.6 9.1 0.883
0.67 66.0 35.7 23.9 0.335 1.34 20.8 48.5 9.0 0.889
0.68 63.8 35.5 23.0 0.348 1.36 20.5 49.5 8.9 0.895
0.69 61.6 35.3 22.1 0.362 1.38 20.2 50.4 8.9 0.901
0.70 59.3 35.1 21.3 0.375 1.40 20.0 51.2 8.8 0.906
0.71 57.6 34.9 20.6 0.388 1.42 19.8 52.2 8.8 0.910
0.72 56.0 34.8 20.0 0.401 1.44 19.6 53.2 8.8 0.914
0.73 54.3 34.7 19.3 0.415 1.46 19.4 54.2 8.7 0.918
0.74 52.6 34.6 18.7 0.428 1.48 19.2 55.2 8.7 0.922
0.75 50.9 34.5 18.1 0.442 1.50 19.0 56.3 8.6 0.926
0.76 49.7 34.5 17.6 0.455 1.52 18.8 57.2 8.6 0.929
0.77 48.4 34.5 17.1 0.468 1.54 18.7 58.3 8.6 0.932
0.78 47.2 34.4 16.6 0.481 1.56 18.6 59.4 8.6 0.935
0.79 45.9 34.4 16.2 0.494 1.58 18.5 60.6 8.5 0.938
0.80 44.6 34.3 15.8 0.506 1.60 18.3 61.9 8.5 0.943
0.81 43.6 34.3 15.4 0.518 1.62 18.2 63.1 8.5 0.945
0.82 42.6 34.4 15.1 0.530 1.64 18.0 64.3 8.4 0.947
0.83 41.7 34.4 14.8 0.542 1.66 17.8 65.6 8.4 0.949
0.84 40.7 34.5 14.4 0.554 1.68 17.7 66.9 8.4 0.952
0.85 39.7 34.5 14.1 0.566 1.70 17.6 68.1 8.4 0.954
0.86 38.9 34.6 13.9 0.577 1.72 17.5 69.3 8.4 0.956
0.87 38.1 34.7 13.6 0.588 1.74 17.4 70.5 8.4 0.958
0.88 37.3 34.8 13.4 0.599 1.76 17.3 71.7 8.3 0.959
0.89 36.5 34.9 13.1 0.610 1.78 17.2 72.8 8.3 0.961
0.90 35.7 35.0 12.9 0.621 1.80 17.0 74.0 8.3 0.963
0.91 35.1 35.1 12.7 0.631 1.82 16.9 75.5 8.3 0.964
0.92 34.5 35.3 12.5 0.641 1.84 16.8 77.0 8.3 0.966
0.93 33.9 35.5 12.3 0.651 1.86 16.8 78.5 8.3 0.967
0.94 33.3 35.6 12.1 0.661 1.88 16.7 80.1 8.2 0.968
0.95 32.7 35.8 11.9 0.671 1.90 16.6 81.7 8.2 0.970
0.96 32.2 36.0 11.8 0.680 1.92 16.6 83.2 8.2 0.971
0.97 31.6 36.2 11.6 0.688 1.94 16.6 84.7 8.2 0.972
0.98 31.0 36.3 11.5 0.697 1.96 16.5 86.2 8.2 0.973
0.99 30.4 36.5 11.3 0.706 1.98 16.5 87.7 8.2 0.974
1.00 29.9 36.7 11.2 0.714 2.00 16.5 89.2 8.2 0.976
CASO 2
Neste caso a direção X é obrigatoriamente a direção do maior número de engastes. 
Ly
Lx
ly / lx mx my nx ny kx ly / lx mx my nx ny kx
1.00 37.1 37.1 16.0 16.0 0.500 1.50 20.6 46.4 9.6 21.6 0.835
1.01 36.5 37.2 15.7 16.0 0.509 1.51 20.5 46.8 9.5 21.8 0.838
1.02 35.9 37.2 15.4 16.0 0.519 1.52 20.4 47.1 9.5 22.0 0.842
1.03 35.3 37.3 15.1 16.1 0.528 1.53 20.3 47.5 9.4 22.2 0.845
1.04 34.7 37.3 14.9 16.1 0.538 1.54 20.2 47.8 9.4 22.4 0.848
1.05 34.1 37.4 14.6 16.1 0.547 1.55 20.0 48.2 9.4 22.6 0.851
1.06 33.5 37.4 14.4 16.2 0.556 1.56 19.9 48.5 9.3 22.8 0.855
1.07 32.9 37.5 14.1 16.2 0.566 1.57 19.8 48.9 9.3 23.0 0.858
1.08 32.3 37.5 13.9 16.2 0.575 1.58 19.7 49.2 9.2 23.2 0.861
1.09 31.7 37.6 13.7 16.3 0.585 1.59 19.6 49.6 9.2 23.4 0.865
1.10 31.1 37.6 13.5 16.3 0.594 1.60 19.5 49.9 9.2 23.7 0.868
1.11 30.6 37.7 13.3 16.3 0.602 1.61 109.4 50.3 9.2 23.9 0.870
1.12 30.2 37.8 13.1 16.4 0.610 1.62 19.3 50.7 9.1 24.1 0.873
1.13 29.8 38.0 12.9 16.5 0.618 1.63 19.2 51.0 9.1 24.3 0.875
1.14 29.4 38.1 12.8 16.6 0.626 1.64 19.1 51.4 9.1 24.5 0.878
1.15 29.0 38.2 12.6 16.7 0.634 1.65 19.0 51.8 9.1 24.9 0.880
1.16 28.6 38.4 12.4 16.7 0.643 1.66 19.0 52.2 9.0 25.0 0.883
1.17 28.2 38.5 12.3 16.8 0.651 1.67 18.9 52.6 9.0 25.2 0.885
1.18 27.8 38.6 12.2 16.9 0.659 1.68 18.8 53.0 9.0 25.4 0.888
1.19 27.4 38.8 12.0 17.0 0.667 1.69 18.7 53.4 9.0 25.6 0.890
1.20 27.0 38.9 11.9 17.1 0.675 1.70 18.6 53.8 8.9 25.9 0.893
1.21 26.7 39.1 11.8 17.2 0.682 1.71 18.5 54.2 8.9 26.1 0.895
1.22 26.4 39.3 11.6 17.3 0.688 1.72 18.4 54.7 8.9 26.4 0.897
1.23 26.1 39.511.5 17.4 0.695 1.73 18.4 55.1 8.9 26.6 0.899
1.24 25.9 39.7 11.4 17.6 0.701 1.74 18.3 55.6 8.9 26.9 0.901
1.25 25.7 39.9 11.3 17.7 0.708 1.75 18.2 56.0 8.8 27.1 0.903
1.26 25.4 40.0 11.2 17.8 0.715 1.76 18.2 56.5 8.8 27.4 0.905
1.27 25.1 40.2 11.1 17.9 0.721 1.77 18.1 56.9 8.8 27.6 0.907
1.28 24.8 40.4 11.0 18.0 0.728 1.78 18.0 57.4 8.8 27.9 0.909
1.29 24.5 40.6 10.9 18.1 0.734 1.79 18.0 57.8 8.8 28.1 0.911
1.30 24.2 40.8 10.8 18.3 0.741 1.80 17.9 58.2 8.8 28.4 0.913
1.31 24.0 41.0 10.7 18.4 0.746 1.81 17.8 58.7 8.8 28.6 0.915
1.32 23.8 41.3 10.6 18.6 0.752 1.82 17.8 59.2 8.7 28.9 0.916
1.33 23.6 41.5 10.6 18.7 0.757 1.83 17.7 59.6 8.7 29.2 0.918
1.34 23.4 41.8 10.5 18.9 0.762 1.84 17.7 60.1 8.7 29.5 0.919
1.35 23.2 42.0 10.4 19.0 0.767 1.85 17.6 60.6 8.7 29.7 0.921
1.36 23.0 42.3 10.4 19.2 0.773 1.86 17.6 61.0 8.7 30.0 0.923
1.37 22.8 42.5 10.3 19.3 0.776 1.87 17.5 61.5 8.7 30.3 0.924
1.38 22.6 42.8 10.2 19.5 0.783 1.88 17.5 62.0 8.6 30.6 0.926
1.39 22.3 43.0 10.1 19.6 0.789 1.89 17.4 62.4 8.6 30.9 0.924
1.40 22.1 43.3 10.1 19.8 0.794 1.90 17.4 62.9 8.6 31.2 0.929
1.41 22.0 43.8 10.0 19.9 0.796 1.91 17.3 63.4 8.6 31.4 0.930
1.42 21.8 43.9 10.0 20.1 0.802 1.92 17.3 63.9 8.6 31.7 0.932
1.43 21.7 44.2 9.9 20.3 0.806 1.93 17.3 64.4 8.6 32.0 0.933
1.44 21.5 44.5 9.9 20.5 0.810 1.94 17.2 64.9 8.6 32.2 0.934
1.45 21.4 44.8 9.8 20.6 0.814 1.95 17.2 65.4 8.6 32.5 0.935
1.46 21.2 45.1 9.8 20.8 0.819 1.96 17.1 65.9 8.5 32.8 0.936
1.47 21.1 45.4 9.7 21.0 0.823 1.97 17.1 66.4 8.5 33.0 0.937
1.48 20.9 45.7 9.7 21.2 0.827 1.98 17.0 66.9 8.5 33.3 0.939
1.49 20.8 46.0 9.6 21.4 0.831 1.99 17.0 67.4 8.5 33.6 0.940
1.50 20.6 46.4 9.6 21.6 0.835 2.00 17.0 67.9 8.5 33.9 0.941
CASO 3
Neste caso o número de engastes em qualquer direção é igual, utilizar sempre ly maior ou igual a lx. 
Ly
Lx
ly / lx mx my nx kx ly / lx mx my nx kx
0.50 136.1 49.9 50.4 0.238 1.00 37.5 55.7 14.4 0.833
0.51 130.4 49.3 47.4 0.253 1.02 36.8 57.0 14.2 0.843
0.52 124.6 48.6 44.7 0.268 1.04 36.2 58.3 14.1 0.852
0.53 118.9 48.0 42.4 0.283 1.06 35.5 59.6 14.0 0.861
0.54 113.1 47.3 40.3 0.298 1.08 34.8 60.9 13.8 0.871
0.55 107.4 46.6 38.2 0.314 1.10 34.2 62.2 13.6 0.880
0.56 103.4 46.3 36.3 0.330 1.12 33.7 63.9 13.5 0.886
0.57 99.5 45.9 34.8 0.345 1.14 33.2 65.6 13.5 0.892
0.58 95.5 45.6 33.2 0.361 1.16 32.8 67.2 13.4 0.899
0.59 91.6 45.2 31.8 0.377 1.18 32.3 68.9 13.3 0.906
0.60 87.6 44.8 30.5 0.393 1.20 31.9 70.6 13.2 0.912
0.61 84.8 44.6 29.4 0.409 1.22 31.6 72.4 13.1 0.916
0.62 82.0 44.5 28.2 0.425 1.24 31.3 74.3 13.0 0.921
0.63 79.3 44.3 27.3 0.440 1.26 31.0 76.0 13.0 0.926
0.64 76.6 44.2 26.3 0.456 1.28 30.7 77.8 12.9 0.930
0.65 73.8 44.0 25.4 0.472 1.30 30.3 79.7 12.9 0.935
0.66 71.8 44.0 24.7 0.487 1.32 30.1 81.7 12.8 0.938
0.67 69.8 44.0 23.9 0.502 1.34 29.9 83.7 12.8 0.941
0.68 67.7 44.1 23.2 0.517 1.36 29.7 85.7 12.7 0.944
0.69 65.7 44.1 22.6 0.532 1.38 29.5 87.7 12.6 0.947
0.70 63.7 44.1 22.0 0.546 1.40 29.2 89.7 12.6 0.950
0.71 62.2 44.3 21.4 0.560 1.42 29.1 91.9 12.6 0.952
0.72 60.7 44.4 21.0 0.573 1.44 28.9 94.1 12.6 0.954
0.73 59.2 44.6 20.4 0.587 1.46 28.7 96.3 12.5 0.957
0.74 57.7 44.7 20.0 0.600 1.48 28.5 98.5 12.5 0.959
0.75 56.2 44.9 19.6 0.613 1.50 28.3 100.7 12.5 0.962
0.76 55.0 45.1 19.2 0.625 1.52 28.1 103.1 12.5 0.964
0.77 53.8 45.4 18.9 0.636 1.54 28.0 105.5 12.4 0.966
0.78 52.6 45.6 18.5 0.646 1.56 27.9 107.9 12.4 0.967
0.79 51.5 45.9 18.2 0.659 1.58 27.7 110.3 12.4 0.969
0.80 50.4 46.2 17.9 0.671 1.60 27.6 112.6 12.4 0.970
0.81 40.5 46.5 17.6 0.681 1.62 27.5 115.2 12.4 0.972
0.82 46.6 46.9 17.3 0.692 1.64 27.4 117.8 12.3 0.973
0.83 47.8 47.2 17.1 0.702 1.66 27.3 120.4 12.3 0.975
0.84 45.9 47.6 16.8 0.713 1.68 27.2 122.9 12.3 0.976
0.85 46.0 48.0 16.6 0.723 1.70 27.1 125.4 12.3 0.977
0.86 45.3 48.4 16.4 0.731 1.72 27.0 128.1 12.3 0.978
0.87 44.6 48.9 16.2 0.740 1.74 27.0 130.8 12.3 0.979
0.88 43.9 49.3 16.0 0.748 1.76 26.9 133.5 12.3 0.980
0.89 43.2 49.8 15.9 0.757 1.78 26.8 136.3 12.3 0.980
0.90 42.5 50.2 15.7 0.766 1.80 26.7 139.1 12.2 0.981
0.91 42.0 50.7 15.5 0.773 1.82 26.6 143.0 12.2 0.982
0.92 41.4 51.2 15.4 0.780 1.84 26.5 145.9 12.2 0.983
0.93 40.9 51.7 15.2 0.788 1.86 26.5 148.8 12.2 0.983
0.94 40.3 52.2 15.1 0.795 1.88 26.4 151.7 12.2 0.984
0.95 39.7 52.8 14.9 0.803 1.90 26.4 153.6 12.2 0.985
0.96 39.2 53.3 14.8 0.809 1.92 26.3 156.7 12.2 0.986
0.97 38.8 53.9 14.7 0.815 1.94 26.3 159.7 12.2 0.986
0.98 38.3 54.6 14.6 0.821 1.96 26.2 162.8 12.2 0.987
0.99 37.9 55.1 14.5 0.827 1.98 26.1 165.8 12.2 0.988
1.00 37.5 55.7 14.4 0.833 2.00 26.1 168.9 12.1 0.988
CASO 4
Neste caso a direção X é obrigatoriamente a direção do maior número de engastes. 
Lx
Ly
ly / lx mx my nx ny kx ly / lx mx my nx ny kx
0.50 246.4 71.5 108.1 35.6 0.110 1.00 44.2 50.6 18.0 24.0 0.667
0.51 234.5 69.8 100.8 34.7 0.119 1.02 43.1 51.3 17.6 24.3 0.683
0.52 222.6 68.1 94.4 33.8 0.127 1.04 42.0 52.0 17.2 24.7 0.699
0.53 210.7 66.4 88.2 32.9 0.136 1.06 40.9 52.7 16.8 25.1 0.714
0.54 198.8 64.7 82.7 32.1 0.145 1.08 39.9 53.4 16.4 25.5 0.730
0.55 187.0 63.0 77.3 31.3 0.155 1.10 38.9 54.0 16.1 25.9 0.745
0.56 177.3 61.8 72.6 30.6 0.165 1.12 38.1 54.9 15.9 26.4 0.757
0.57 167.6 60.6 68.5 29.9 0.175 1.14 37.4 55.8 15.6 26.9 0.770
0.58 157.9 59.4 64.8 29.2 0.185 1.16 36.7 56.7 15.4 27.4 0.782
0.59 148.2 58.2 61.5 28.6 0.195 1.18 36.0 57.6 15.1 28.0 0.794
0.60 138.6 57.1 58.2 28.0 0.206 1.20 35.3 58.5 14.9 28.6 0.806
0.61 132.9 56.4 55.3 27.5 0.217 1.22 34.8 59.7 14.7 29.2 0.815
0.62 127.2 55.8 52.3 27.0 0.229 1.24 34.3 60.8 14.5 29.8 0.824
0.63 121.5 55.1 49.9 26.5 0.240 1.26 33.8 61.9 14.4 30.4 0.833
0.64 115.9 54.3 47.6 26.1 0.252 1.28 33.3 63.1 14.3 31.0 0.842
0.65 110.3 53.5 45.6 25.7 0.263 1.30 32.8 64.2 14.1 31.8 0.851
0.66 103.3 52.9 43.6 25.3 0.275 1.32 32.4 65.4 14.0 32.5 0.858
0.67 102.3 52.4 41.7 25.0 0.287 1.34 32.0 66.7 13.9 33.2 0.865
0.68 96.4 52.0 40.0 24.7 0.300 1.36 31.6 68.0 13.8 34.0 0.872
0.69 94.5 51.4 38.5 24.4 0.312 1.38 31.3 69.3 13.7 34.7 0.879
0.70 90.6 50.9 37.0 24.1 0.324 1.40 31.0 70.5 13.6 35.5 0.885
0.71 87.8 50.6 35.7 23.0 0.336 1.42 30.7 71.9 13.5 36.3 0.890
0.72 85.0 50.2 34.4 23.7 0.349 1.44 30.4 73.3 13.4 37.1 0.895
0.73 82.2 49.9 33.2 23.5 0.361 1.46 30.1 74.8 13.3 37.9 0.900
0.74 79.4 49.5 32.0 23.3 0.375 1.48 29.0 76.2 13.3 38.7 0.905
0.75 76.6 49.2 30.9 23.2 0.388 1.50 29.7 77.7 13.2 39.5 0.910
0.76 74.5 49.1 30.0 23.1 0.400 1.52 29.5 79.3 13.1 40.4 0.914
0.77 72.4 48.9 29.0 23.0 0.413 1.54 29.3 80.9 13.1 41.3 0.918
0.78 70.3 48.8 28.2 22.9 0.425 1.56 29.1 82.5 13.0 42.2 0.921
0.79 68.2 48.6 27.4 22.8 0.438 1.58 28.9 84.1 13.0 43.1 0.925
0.80 66.2 48.4 26.7 22.7 0.450 1.60 28.7 85.7 12.9 44.0 0.929
0.81 64.6 48.4 26.0 22.6 0.462 1.62 28.5 87.4 12.9 44.9 0.932
0.82 63.0 48.3 25.3 22.6 0.474 1.64 28.3 89.1 12.8 45.8 0.935
0.83 61.5 48.3 24.7 22.6 0.486 1.66 28.2 90.8 12.8 46.7 0.938
0.84 60.0 48.2 24.0 22.6 0.496 1.68 28.1 92.5 12.8 47.6 0.940
0.85 58.5 48.2 23.5 22.6 0.511 1.70 28.0 94.3 12.7 48.5 0.943
0.86 57.3 48.3 23.0 22.7 0.522 1.72 27.8 96.2 12.7 49.5 0.945
0.87 56.1 48.3 22.5 22.7 0.534 1.74 27.7 98.1 12.7 50.5 0.947
0.88 54.9 48.4 22.0 22.8 0.545 1.76 27.6 100.0 12.7 51.5 0.949
0.89 53.7 48.4 21.6 22.8 0.557 1.78 27.5 101.9 12.6 52.6 0.952
0.90 52.5 48.5 21.1 22.8 0.568 1.80 27.4 103.7 12.6 53.7 0.954
0.91 51.5 48.7 20.7 22.9 0.578 1.82 27.3 105.0 12.5 54.9 0.956
0.92 50.6 48.9 20.4 23.0 0.589 1.84 27.2 107.7 12.5 56.1 0.958
0.93 49.7 49.0 20.0 23.1 0.599 1.86 27.1 109.7 12.5 57.3 0.960
0.94 48.8 49.2 19.7 23.2 0.611 1.88 27.0 111.7 12.5 58.5 0.961
0.95 47.9 49.4 19.4 23.3 0.620 1.90 26.9 113.7 12.5 59.8 0.963
0.96 47.1 49.6 19.1 23.5 0.630 1.92 26.8 115.9 12.4 61.1 0.965
0.97 46.3 49.9 18.8 23.60.639 1.94 26.7 118.1 12.4 62.5 0.966
0.98 45.6 50.1 18.5 23.8 0.649 1.96 26.6 120.2 12.4 63.9 0.967
0.99 44.9 50.4 18.2 23.9 0.658 1.98 26.5 122.3 12.4 65.3 0.969
1.00 44.2 50.6 18.0 24.0 0.667 2.00 26.5 124.4 12.4 66.7 0.970
CASO 5
Neste caso a direção X é obrigatoriamente a direção do maior número de engastes.
Ly
Lx
ly / lx mx my nx ny kx ly / lx mx my nx ny kx
1.00 55.7 55.7 24.0 24.0 0.500 1.50 32.0 72.2 14.4 32.3 0.835
1.01 54.8 55.8 23.6 24.0 0.509 1.51 31.9 72.8 14.3 32.6 0.838
1.02 53.9 55.9 23.1 24.0 0.519 1.52 31.7 73.4 14.3 32.9 0.842
1.03 53.0 56.0 22.7 24.1 0.528 1.53 31.6 74.0 14.2 33.2 0.845
1.04 52.1 56.0 22.8 24.1 0.538 1.54 31.4 74.6 14.2 33.6 0.848
1.05 51.2 56.1 21.9 24.2 0.547 1.55 31.3 75.2 14.1 33.9 0.851
1.06 50.3 56.2 21.7 24.2 0.556 1.56 31.1 75.8 14.0 34.2 0.855
1.07 49.4 56.3 21.2 24.3 0.566 1.57 31.0 76.4 14.0 34.5 0.858
1.08 48.5 56.4 20.9 24.3 0.575 1.58 30.8 77.0 14.0 34.9 0.861
1.09 47.6 56.5 20.5 24.4 0.585 1.59 30.6 77.6 13.9 35.2 0.865
1.10 46.8 56.6 20.2 24.4 0.594 1.60 30.5 78.2 13.8 35.5 0.868
1.11 46.2 56.8 20.0 24.5 0.602 1.61 30.4 78.8 13.8 35.8 0.870
1.12 45.6 57.0 19.7 24.6 0.610 1.62 30.3 79.5 13.7 36.1 0.873
1.13 45.0 57.3 19.4 24.7 0.618 1.63 30.2 80.2 13.7 36.5 0.875
1.14 44.4 57.3 19.2 24.8 0.626 1.64 30.1 80.8 13.7 36.8 0.878
1.15 43.8 57.5 18.9 25.0 0.634 1.65 30.0 81.5 13.6 37.1 0.880
1.16 43.2 57.7 18.7 25.1 0.643 1.66 29.9 82.2 13.6 37.5 0.883
1.17 42.6 58.0 18.4 25.2 0.651 1.67 29.8 82.8 13.6 37.8 0.885
1.18 42.0 58.2 18.2 25.3 0.659 1.68 29.7 83.5 13.5 38.1 0.888
1.19 41.4 58.4 18.0 25.4 0.667 1.69 29.6 84.2 13.5 38.5 0.890
1.20 40.9 58.7 17.8 25.6 0.675 1.70 29.4 84.9 13.5 38.8 0.893
1.21 40.5 58.9 17.6 25.7 0.682 1.71 29.3 85.6 13.4 39.1 0.895
1.22 40.1 59.2 17.4 25.9 0.688 1.72 29.2 86.4 13.4 39.5 0.897
1.23 39.7 59.6 17.3 26.0 0.695 1.73 29.1 87.1 13.4 39.9 0.899
1.24 39.3 59.9 17.1 26.2 0.701 1.74 29.0 87.9 13.3 40.2 0.901
1.25 38.9 60.3 16.9 26.4 0.708 1.75 29.0 88.6 13.3 40.6 0.903
1.26 38.5 60.6 16.8 26.6 0.715 1.76 28.9 89.4 13.3 41.0 0.905
1.27 38.1 61.0 16.6 26.8 0.721 1.77 28.8 90.1 13.2 41.3 0.907
1.28 37.7 61.3 16.5 27.0 0.728 1.78 28.7 90.9 13.2 41.7 0.909
1.29 37.8 61.7 16.4 27.2 0.734 1.79 28.5 91.6 13.2 42.1 0.911
1.30 36.9 62.0 16.2 27.4 0.741 1.80 28.5 92.5 13.1 42.5 0.913
1.31 36.6 62.4 16.1 27.6 0.746 1.81 28.4 93.2 13.1 42.9 0.915
1.32 36.3 62.8 16.0 27.8 0.752 1.82 28.3 94.0 13.1 43.3 0.916
1.33 36.0 63.3 15.9 28.0 0.757 1.83 28.2 94.7 13.1 43.8 0.918
1.34 35.7 63.7 15.8 28.3 0.762 1.84 28.1 95.5 13.0 44.2 0.919
1.35 35.5 64.2 15.6 28.5 0.767 1.85 28.0 96.2 13.0 44.6 0.921
1.36 35.2 64.8 15.5 28.7 0.773 1.86 28.0 97.0 13.0 45.1 0.923
1.37 34.9 65.5 15.4 29.0 0.778 1.87 27.9 97.7 13.0 45.6 0.924
1.38 34.6 65.9 15.3 29.3 0.783 1.88 27.8 98.5 13.0 45.9 0.926
1.39 34.3 66.4 15.2 29.5 0.789 1.89 27.7 99.2 12.9 46.4 0.927
1.40 34.4 65.8 15.1 29.7 0.797 1.90 27.7 100.0 12.9 46.8 0.929
1.41 33.9 67.3 15.0 30.0 0.798 1.91 27.6 100.9 12.9 47.2 0.930
1.42 33.7 67.9 15.0 30.2 0.802 1.92 27.6 101.8 12.9 47.6 0.932
1.43 33.5 68.4 14.9 30.5 0.806 1.93 27.5 102.7 12.9 48.0 0.933
1.44 33.3 69.0 14.8 30.7 0.810 1.94 27.5 103.6 12.8 48.4 0.934
1.45 33.1 69.5 14.8 31.0 0.814 1.95 27.5 104.5 12.8 48.8 0.935
1.46 32.9 70.0 14.7 31.3 0.819 1.96 27.4 105.4 12.8 49.2 0.936
1.47 32.7 70.6 14.6 31.5 0.823 1.97 27.4 106.3 12.8 49.6 0.937
1.48 32.5 71.1 14.5 31.8 0.827 1.98 27.3 107.3 12.8 50.0 0.939
1.49 32.0 71.7 14.5 32.0 0.831 1.99 27.3 108.1 12.8 50.4 0.940
1.50 32.0 72.2 14.4 32.3 0.835 2.00 27.3 109.1 12.7 50.8 0.941
CASO 6
Neste caso o número de engastes em qualquer direção é igual. Utilizar sempre ly maior ou igual a lx.