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Tabelas de Marcus
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3
Tabela de Marcus
TABELA 3
Cálculo das lajes em cruz - Marcus ly qx
=
Mx
q .lx 2
2 My q.lx my
=
=
mx
Xx
q.lx 2
− =
Xy
nx
− =
q .lx 2 ny
K x .q
lx ly/lx
kx
mx
nx
my
ny
ly/lx
kx
mx
nx
my
ny
1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.0! 1.0 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.1! 1.1 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.2! 1.2 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.3! 1.3 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.4! 1.4 1.50
0.500 0.510 0.520 0.52 0.53 0.54 0.55! 0.567 0.576 0.5!5 0.54 0.603 0.611 0.620 0.62! 0.636 0.644 0.652 0.660 0.667 0.674 0.6!2 0.60 0.66 0.703 0.70 0.716 0.722 0.72 0.735 0.741 0.746 0.752 0.75! 0.763 0.76 0.774 0.77 0.7!4 0.7! 0.73 0.7! 0.!03 0.!07 0.!11 0.!15 0.!20 0.!24 0.!27 0.!31 0.!35
37.14 36.42 35.72 35.05 34.42 33.!1 33.21 32.65 32.11 31.5 31.0 30.61 30.14 2.70 2.27 2!.!5 2!.46 2!.0! 27.71 27.35 27.00 26.6! 26.36 26.05 25.75 25.46 25.1! 24.2 24.66 24.40 24.16 23.3 23.70 23.4! 23.26 23.06 22.!6 22.66 22.4! 22.2 22.12 21.5 21.7! 21.62 21.46 21.31 21.16 21.02 20.!! 20.75 20.61
16.00 15.6 15.3 15.11 14.!4 14.5! 14.34 14.10 13.!! 13.67 13.46 13.27 13.0! 12.1 12.74 12.57 12.42 12.27 12.13 11. 11.!5 11.73 11.61 11.4 11.3! 11.2! 11.17 11.07 10.! 10.! 10.!0 10.72 10.63 10.56 10.4! 10.41 10.34 10.27 10.21 1014 10.0! 10.02 .7 .1 .!6 .!1 .76 .71 .67 .62 .3!
37.14 37.15 37.16 37.1 37.22 37.27 27.32 37.3! 37.45 37.53 37.61 37.71 37.!1 37.2 3!.04 3!.16 3!.2 3!.43 3!.5! 3!.73 3!.! 3.06 3.23 3.41 3.5 3.7! 3.! 40.1 40.40 40.61 40.!3 41.06 41.2 41.53 41.77 42.02 42.2! 42.54 42.!0 43.07 43.35 43.63 43.2 44.21 44.50 44.!0 45.11 45.42 45.74 46.06 46.3!
16.00 16.00 16.01 16.03 16.05 16.0! 16.11 16.15 16.1 16.24 16.2 16.35 16.41 16.4! 16.55 16.63 16.71 16.7 16.!! 16.! 17.07 17.1! 17.2! 17.3 17.50 17.62 17.74 17.!6 17. 1!.12 1!.25 1!.3 1!.53 1!.67 1!.!2 1!.7 1.12 1.2! 1.43 1.60 1.76 1.3 20.10 20.27 20.45 20.62 20.!0 20. 21.17 21.36 21.55
1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.5! 1.5 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.6! 1.6 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.7! 1.7 1.!0 1.!1 1.!2 1.!3 1.!4 1.!5 1.!6 1.!7 1.!! 1.! 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.! 1. 2.00
0.!35 0.!3 0.!42 0.!46 0.!4 0.!52 0.!55 0.!5 0.!62 0.!65 0.!6! 0.!70 0.!73 0.!76 0.!7! 0.!!1 0.!!4 0.!!6 0.!!! 0.!1 0.!3 0.!5 0.!7 0.! 0.02 0.04 0.06 0.07 0.0 0.11 0.13 0.15 0.16 0.1! 0.20 0.21 0.23 0.24 0.26 0.27 0.2 0.30 0.31 0.33 0.34 0.35 0.36 0.3! 0.3 0.40 0.41
20.61 20.4 20.36 20.24 20.12 20.01 1.0 1.7 1.6 1.5! 1.4! 1.3 1.2 1.20 1.11 1.02 1!.4 1!.!6 1!.77 1!.70 1!.62 1!.54 1!.47 1!.40 1!.33 1!.26 1!.1! 1!.13 1!.07 1!.00 17.4 17.!! 17.!3 17.77 17.72 17.66 17.61 17.56 17.51 17.46 17.41 17.36 17.32 17.27 17.23 17.1! 17.14 17.10 17.06 17.02 16.3
.5! .54 .50 .46 .42 .3 .35 .32 .2! .25 .22 .1 .16 .13 .11 .0! .05 .03 .00 !.! !.6 !.3 !.1 !.! !.!7 !.!5 !.!3 !.!1 !.!0 !.7! !.76 !.74 !.73 !.71 !.70 !.6! !.67 !.65 !.64 !.63 !.61 !.60 !.5 !.5! !.56 !.55 !.54 !.53 !.52 !.51 !.50
46.3! 46.71 47.05 47.3! 47.73 4!.07 4!.43 4!.7! 4.14 4.51 4.!! 50.25 52.63 51.01 51.40 51.7 52.1 52.5! 52. 53.3 53.!1 54.22 54.64 55.07 55.4 55.2 56.36 56.!0 57.24 57.6! 5!.14 5!.5 5.05 5.51 5.7 60.44 60.2 61.3 61.!! 62.36 62.!5 63.34 63.!3 64.33 64.!3 65.34 65.!4 66.36 66.!! 67.3 67.2
21.55 21.75 21.4 22.14 22.34 22.55 22.76 22.6 23.17 23.0 23.60 23.!2 24.04 24.26 24.4 24.72 24.5 25.1! 25.41 25.65 25.! 26.13 26.37 26.61 26.!6 27.11 27.36 27.61 27.!7 2!.13 2!.3 2!.65 2!.1 2.1! 2.44 2.72 2. 30.26 30.54 30.!1 31.0 31.3! 31.66 31.4 32.23 32.52 32.!1 33.10 33.40 33.70 34.00
4 Tabela de Marcus
TABELA 4
Cálculo das lajes em cruz - Marcus ly
Mx
q .lx 2 =
2 My q.lx m y
Xx
=
m x
−
q .lx
=
2 q x
n x
K x . q
=
lx ly/lx
kx
mx
nx
my
ly/lx
kx
mx
nx
my
0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.5! 0.5 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.6! 0.6 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.7! 0.7 0.!0 0.!1 0.!2 0.!3 0.!4 0.!5 0.!6 0.!7 0.!! 0.! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.! 0. 1.00
0.23! 0.253 0.26! 0.2!3 0.2! 0.314 0.330 0.345 0.361 0.377 3.3 0.40 0.425 0.441 0.456 0.472 0.4!7 0.502 0.517 0.531 0.545 0.55 0.573 0.5!7 0.600 0.613 0.625 0.637 0.64 0.661 0.672 0.6!3 0.63 0.703 0.713 0.723 0.732 0.741 0.750 0.75! 0.766 0.774 0.7!2 0.7! 0.76 0.!03 0.!0 0.!16 0.!22 0.!2! 0.!33
137.06 130.06 123.66 117.7 112.3 107.42 102.!3 !.5 4.67 1.02 !7.62 !4.46 !1.51 7!.76 76.1! 73.76 71.4 6.36 67.36 65.47 63.6 62.01 60.42 5!.2 57.51 56.16 54.! 53.6 52.54 51.46 50.42 4.44 4!.51 47.62 46.7! 45.7 45.21 44.4! 43.7! 43.12 42.4! 41.!7 41.30 40.74 40.21 3.70 3.22 3!.75 3!.31 37.!! 37.47
50.40 47.4! 44.!3 42.42 40.23 3!.23 36.40 34.74 33.21 31.!1 30.52 2.33 2!.24 27.24 26.30 25.45 24.65 23.1 23.22 22.5 22.00 21.44 20.3 20.45 20.00 1.3! 1.1 1!.!3 1!.4! 1!.16 17.!6 17.57 17.31 17.06 16.!2 16.60 16.3 16.1 16.00 15.!2 15.66 15.50 15.35 15.21 15.07 14.5 14.!2 14.72 14.60 14.50 14.40
4.2 4.11 4!.3! 47.72 47.13 46.60 46.13 45.72 45.35 45.04 44.77 44.54 44.35 44.21 44.10 44.02 43.! 47.7 43.! 44.03 44.11 44.21 44.34 44.4 44.66 44.!6 45.0! 45.33 45.5 45.!7 46.17 46.30 46.!4 47.20 47.57 47.7 4!.3! 4!.!1 4.25 4.71 50.1 50.6! 51.1! 51.50 52.24 52.7! 53.35 53.2 54.52 55.12 55.74
1.00 1.02 1.04 1.06 1.0! 1.10 1.12 1.14 1.16 1.1! 1.20 1.22 1.24 1.26 1.2! 1.30 1.32 1.34 1.36 1.3! 1.40 1.42 1.44 1.46 1.4! 1.50 1.52 1.54 1.56 1.5! 1.60 1.62 1.64 1.66 1.6! 1.70 1.72 1.74 1.76 1.7! 1.!0 1.!2 1.!4 1.!6 1.!! 1.0 1.2 1.4 1.6 1.! 2.00
0.!33 0.!44 0.!54 0.!63 0.!72 0.!!0 0.!!7 0.!4 0.00 0.06 0.12 0.17 0.22 0.26 0.31 0.34 0.3! 0.42 0.45 0.4! 0.50 0.53 0.55 0.5! 0.60 0.62 0.64 0.66 0.67 0.6 0.70 0.72 0.73 0.74 0.75 0.77 0.7! 0.7 0.!0 0.!0 0.!1 0.!2 0.!3 0.!3 0.!4 0.!5 0.!5 0.!6 0.!7 0.!7 0.!!
37.47 36.71 36.00 35.34 34.74 34.1! 33.66 33.1! 32.74 32.32 31.3 31.57 31.23 30.2 30.62 30.34 30.0! 2.!3 2.60 2.3 2.1! 2!. 2!.!0 2!.63 2!.47 2!.31 2!.16 2!.02 27.! 27.76 27.64 27.53 27.42 27.31 27.21 27.12 27.03 26.4 26.!6 26.7! 26.70 26.63 26.56 26.4 26.43 26.37 26.31 26.25 26.1 26.14 26.0
14.40 14.22 14.05 13.0 13.76 13.64 13.52 13.42 13.32 13.24 13.16 13.0! 13.01 12.5 12.! 12.!4 12.7 12.74 12.70 12.66 12.62 12.5 12.56 12.53 12.50 12.47 12.45 12.43 12.40 12.3! 12.37 12.35 12.33 12.32 12.30 12.2 12.27 12.26 12.25 12.24 12.23 12.22 12.21 12.20 12.1 12.1! 12.1! 12.17 12.16 12.16 12.15
55.74 57.01 5!.33 5.70 61.12 62.5 64.10 65.66 67.26 6!.1 70.60 72.33 74.11 75.2 77.7! 7.66 !1.60 !3.5! !5.5! !7.63 !.72 1.!4 4.01 6.20 !.45 100.72 103.02 105.3! 107.76 110.16 112.61 115.12 117.62 120.17 122.76 125.41 12!.04 130.75 133.50 136.24 13.05 141.!5 144.7! 147.65 150.60 153.54 156.53 15.56 162.60 165.75 16!.!
5
TABELA 5
Cálculo das lajes em cruz - Marcus ly q x
Mx
q .lx 2 =
2 My q .lx m y =
m x
Xx
− =
q .lx 2
Xy
− =
n x
q .lx 2 n y
K x . q
=
lx ly/lx
kx
0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.5! 0.5 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.6! 0.6 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.7! 0.7 0.!0 0.!1 0.!2 0.!3 0.!4 0.!5 0.!6 0.!7 0.!! 0.! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.! 0. 1.00
0.111 0.11 0.127 0.136 0.145 0.155 0.164 0.174 0.1!4 0.15 0.206 0.217 0.22! 0.23 0.251 0.263 0.275 0.2!7 0.2 0.312 0.324 0.337 0.34 0.362 0.375 0.3!7 0.400 0.413 0.425 0.43! 0.450 0.463 0.475 0.4!7 0.4 0.511 0.522 0.543 0.545 0.55! 0.567 0.57! 0.5! 0.5 0.610 0.620 0.62 0.63 0.64! 0.65! 0.667
mx
nx
my
246.52 10!.00 71.43 230.76 100.70 6.53 216.51 5.07 67.77 203.52 !!.05 66.13 11.66 !2.56 64.60 1!0.!3 77.57 63.1! 170.1 73.01 61.!6 161.7 6!.!4 60.63 153.42 65.02 5.4 145.72 61.52 5!.42 13!.61 5!.30 57.43 132.05 55.34 56.52 125.! 52.61 55.67 120.36 50.0 54.!! 115.15 47.76 54.15 110.30 45.61 53.4! 105.!1 43.62 52.!5 101.61 41.77 52.2! 7.70 40.06 51.76 4.06 3!.47 51.2! 0.65 36. 50.!4 !7.46 35.61 50.45 !4.4! 34.33 50.0 !1.6! 33.13 4.77 !2.05 32.4! 4.05 76.5! 30.6 4.23 74.26 2.! 4.00 72.0! 2.07 4!.!1 70.02 2!.21 4!.65 6!.0! 27.40 4!.51 66.24 26.65 4!.40 64.51 25.4 4!.32 62.!! 25.27 4!.26 61.33 24.64 4!.22 5.!6 24.05 4!.21 5!.47 23.4 4!.22 57.15 22.7 4!.25 55.0 22.47 4!.30 54.71 22.00 4!.37 53.5! 21.56 4!.46 52.51 21.14 4!.57 51.4 20.75 4!.6 50.51 20.37 4!.!3 4.5 20.02 4!. 4!.70 1.6! 4.17 47.!6 1.37 4.06 47.06 1.06 4.57 46.2 1!.7! 4.!0 45.55 1!.50 50.04 44.!5 1!.25 50.2 44.1! 1!.00 50.56
ny
ly/lx
kx
mx
nx
my
ny
36.00 34.2 33.1 32.7 32.10 31.2 30.53 2.!2 2.16 2!.55 27.! 27.45 26.6 26.51 26.0! 25.6 25.33 25.00 24.70 24.42 24.17 23.3 23.73 23.54 23.37 23.22 23.0 22.! 22.!! 22.!0 22.74 22.6 22.65 22.63 22.63 22.63 22.65 22.6! 22.72 22.77 22.!4 22.1 22. 23.0 23.1 13.30 23.42 23.56 23.70 23.!4 24.00
1.00 1.02 1.04 1.06 1.0! 1.10 1.12 1.14 1.16 1.1! 1.20 1.22 1.24 1.26 1.2! 1.30 1.32 1.34 1.36 1.3! 1.40 1.42 1.44 1.46 1.4! 1.50 1.52 1.54 1.56 1.5! 1.60 1.62 1.64 1.66 1.6! 1.70 1.72 1.74 1.76 1.7! 1.!0 1.!2 1.!4 1.!6 1.!! 1.0 1.2 1.4 1.6 1.! 2.00
0.667 0.6!4 0.700 0.716 0.731 0.745 0.75 0.772 0.7!4 0.75 0.!06 0.!16 0.!25 0.!34 0.!43 0.!51 0.!5 0.!66 0.!72 0.!7 0.!!5 0.!0 0.!6 0.01 0.06 0.10 0.14 01! 0.22 0.26 0.2 0.32 0.35 0.3! 0.41 0.43 0.46 0.4! 0.50 0.52 0.54 0.56 0.5! 0.60 0.61 0.63 0.64 0.66 0.67 0.6! 0.70
44.1! 42.2 41.77 40.71 3.74 3!.!4 3!.01 37.25 36.54 35.!! 35.27 34.70 34.17 33.6! 33.22 32.7 32.3! 32.01 31.65 31.02 31.01 30.72 30.44 30.1! 2.4 2.71 2.4 2.2! 2.0 2!.0 2!.73 2!.56 2!.40 2!.25 2!.11 27.7 27.!4 27.72 27.60 27.4 27.3! 27.2! 27.1! 27.0 27.00 26.1 26.!3 26.75 26.6! 26.61 26.54
1!.00 17.54 17.13 16.75 16.41 16.10 15.!1 15.55 15.31 15.0 14.! 14.71 14.54 14.3! 14.23 14.10 13.! 13.!6 13.75 13.65 13.56 13.47 13.3 13.32 13.25 13.1! 13.12 1307 1301 12.6 12.1 12.!7 12.!3 12.7 12.75 12.72 12.6! 12.65 12.62 12.60 12.57 12.55 12.52 12.50 12.4! 12.46 12.44 12.42 12.41 12.3 12.37
50.56 51.14 51.76 52.44 53.1! 53.5 54.7! 55.64 56.55 57.50 5!.50 5.53 60.60 61.71 62.!5 64.03 65.25 66.50 66.7! 6.10 70.45 71.!3 73.24 74.6 76.17 77.67 7.20 !0.77 !2.36 !3.! !5.64 !7.31 !.02 0.77 2.52 4.32 6.13 7.! .!6 101.75 103.6! 105.63 107.62 10.63 111.65 110.71 115.7 117.! 120.04 122.1 124.35
24.00 24.33 24.70 25.10 25.52 25.7 26.45 26.5 27.47 2!.02 2!.5 2.1 2.!0 30.44 31.10 31.77 32.47 33.1! 33.2 34.67 35.44 36.23 37.03 37.!6 3!.70 3.55 40.43 41.32 12.22 43.14 44.0! 45.03 46.00 46. 47.! 4.00 50.03 51.0! 52.14 53.21 54.30 55.41 56.63 57.67 5!.!1 5.7 61.15 62.33 63.55 64.76 65.!
2
TABELA 2
Cálculo das lajes em cruz - Marcus ly
Mx
q .lx 2 =
2 My q .lx m y
Xx
=
m x
− =
q .lx
2 q x
n x
K x . q
=
lx
ly/lx
kx
mx
nx
my
ly/lx
kx
mx
nx
my
0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.5! 0.5 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.6! 0.6 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.7! 0.7 0.!0 0.!1 0.!2 0.!3 0.!4 0.!5 0.!6 0.!7 0.!! 0.! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.! 0. 1.00
0.135 0.145 0.154 0.165 0.175 0.1!6 0.17 0.20 0.220 0.232 0.245 0.257 0.270 0.2!2 0.25 0.30! 0.322 0.335 0.34! 0.362 0.375 0.3!! 0.402 0.415 0.42! 0.442 0.455 0.46! 0.4!1 0.43 0.506 0.51! 0.531 0.543 0.554 0.566 0.57! 0.5! 0.600 0.611 0.621 0.632 0.642 0.652 0.661 0.671 0.6!0 0.6! 0.67 0.706 0.714
140.3 132.5 125.6! 11.03 112.4 107.35 102.20 7.46 3.0! !.03 !5.2! !1.7 7!.55 75.53 72.71 70.07 67.60 65.2! 63.10 61.05 5.12 57.30 55.5! 53.5 52.41 50.4 4.56 4!.24 46.! 45.7 44.65 43.56 42.53 41.54 40.60 3.6 3!.!3 3!.01 7.22 6.46 5.73 35.04 34.37 33.73 33.12 32.53 31.7 31.43 30.1 30.41 2.3
5.20 55.31 51.77 4!.56 45.64 42.7 40.54 3!.32 36.2! 34.41 32.6 31.11 2.66 2!.31 27.07 25.3 24.!6 23.!! 22.7 22.12 21.33 20.5 1.1 1.27 1!.67 1!.11 17.5 17.10 16.64 16.21 15.!1 15.43 15.0! 14.74 14.43 14.13 13.!5 13.5 13.34 13.10 12.!! 12.67 12.47 12.2! 12.10 11.3 11.77 11.61 11.47 11.33 11.20
45.13 44.11 43.22 42.3! 41.60 40.!! 40.21 3.60 3.03 3!.51 3!.04 37.60 37.20 36.!3 36.4 36.1 35.2 35.67 35.44 35.25 35.07 34.2 34.7! 34.67 34.57 34.50 34.44 34.3 34.36 34.35 34.35 34.36 34.3 34.42 34.4! 34.54 34.62 34.70 34.!0 34.1 35.03 35.16 35.2 35.44 35.60 35.77 35.5 36.13 36.33 36.53 36.74
1.00 1.02 1.04 1.06 1.0! 1.10 1.12 1.14 1.16 1.1! 1.20 1.22 1.24 1.26 1.2! 1.30 1.32 1.34 1.36 1.3! 1.40 1.42 1.44 1.46 1.4! 1.50 1.52 1.54 1.56 1.5! 1.60 1.62 1.64 1.66 1.6! 1.70 1.72 1.74 1.76 1.7! 1.!0 1.!2 1.!4 1.!6 1.!! 1.0 1.2 1.4 1.6 1.! 2.00
0.714 0.730 0.745 0.75 0.773 0.7!5 0.77 0.!0! 0.!1 0.!2 0.!3! 0.!47 0.!55 0.!63 0.!70 0.!77 0.!!4 0.!! 0.!5 0.01 0.06 0.10 0.15 0.1 0.23 0.27 0.30 0.34 0.37 0.40 0.42 0.45 0.4! 0.50 0.52 0.54 0.56 0.5! 0.60 0.62 0.63 0.65 0.66 0.6! 0.6 0.70 0.71 0.72 0.74 0.75 0.76
2.3 2.02 2!.1! 27.41 26.6 26.02 25.40 24.!3 24.2 23.7 23.33 22.! 22.4 22.11 21.75 21.42 21.11 20.!2 20.54 20.2! 20.04 1.!1 1.5 1.3 1.20 1.01 1!.!4 1!.6! 1!.52 1!.37 1!.23 1!.10 17.7 17.!5 17.74 17.63 17.52 17.42 17.33 17.25 17.15 17.07 16. 16.1 16.!4 16.77 16.70 16.64 16.57 16.51 16.46
11.20 10.6 10.73 10.53 10.35 10.1! 10.03 .! .77 .65 .45 .44 .35 .27 .1 .12 .05 !. !.3 !.!! !.!3 !.7 !.74 !.70 !.67 !.63 !.60 !.57 !.54 !.51 !.4 !.46 !.44 !.42 !.40 !.3! !.36 !.35 !.33 !.32 !.30 !.2 !.2! !.27 !.26 !.24 !.23 !.23 !.22 !.21 !.20
36.74 37.1 37.6! 3!.1 3!.74 3.31 3.2 40.55 41.21 41.0 42.62 43.36 44.13 44.3 45.75 46.5 47.46 4!.34 4.26 50.20 51.15 52.14 53.14 54.16 55.21 56.2! 57.36 5!.47 5.60 60.74 61.1 63.11 64.31 65.53 66.7! 6!.04 6.33 70.63 71.6 73.30 74.65 76.03 77.42 7!.!5 !0.27 !1.73 !3.1! !4.67 !6.1 !7.70 !.22
61
TABELA 1
Cálculo das lajes em cruz - Marcus ly
Mx
q .lx 2 =
2 My q .lx m y =
m x
q x
K x . q
=
lx ly/lx
kx
mx
my
ly/lx
kx
mx
my
ly/lx
kx
mx
my
0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.5! 0.5 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.6! 0.6 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.7! 0.7 0.!0 0.!1 0.!2 0.!3 0.!4 0.!5 0.!6 0.!7 0.!! 0.! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.! 0. 1.00
0.05 0.063 0.06! 0.073 0.07! 0.0!4 0.0! 0.05 0.102 0.10! 0.115 0.122 0.12 0.136 0.144 0.151 0.15 0.16! 0.176 0.1!5 0.14 0.203 0.212 0.221 0.231 0.240 0.250 0.260 0.270 0.2!0 0.20 0.301 0.311 0.322 0.332 0.343 0.354 0.364 0.375 0.3!5 0.36 0.407 0.417 0.42! 0.43! 0.44 0.45 0.46 0.4!0 0.40 0.500
16.1! 15!.42 14!.64 13.70 131.55 124.10 117.25 110.6 105.1 .!6 4.4 0.40 !6.20 !2.30 7!.6! 75.32 72.1 6.27 66.54 63. 61.60 5.37 57.27 55.2 53.44 51.6 50.04 4!.4! 47.01 45.61 44.2 43.03 41.!4 40.70 3.62 3!.5 37.61 36.67 35.77 34.1 34.0 33.30 32.54 31.!1 31.11 30.44 2.7 2.17 2!.57 27. 27.43
42.2 41.20 40.1 3.24 3!.36 37.53 36.77 36.05 35.3! 34.76 34.1! 33.64 33.13 32.66 32.23 31.!2 31.44 31.0 30. 30.46 30.1! 2.3 2.6 2.47 2.26 2.07 2!.0 2!.74 2!.60 2!.46 2!.34 2!.23 2!.13 2!.04 27.6 27.!! 27.!1 27.75 27.70 27.65 27.61 27.57 27.54 27.51 27.4 27.47 27.45 27.44 27.43 27.43 27.43
1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.0! 1.0 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.1! 1.1 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.2! 1.2 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.3! 1.3 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.4! 1.4 1.50
0.500 0.510 0.520 0.52 0.53 0.54 0.55! 0.567 0.576 0.5!5 0.54 0.603 0.611 0.620 0.62! 0.636 0.644 0.652 0.660 0.667 0.675 0.6!2 0.6! 0.66 0.703 0.70 0.716 0.722 0.72 0.735 0.741 0.746 0.752 0.75! 0.763 0.76 0.774 0.77 0.7!4 0.7! 0.73 0.7! 0.!03 0.!07 0.!11 0.!15 0.!20 0.!24 0.!27 0.!31 0.!35
27.43 26.! 26.37 25.!7 25.3! 24.1 24.46 24.02 23.60 23.1 22.7 22.41 22.03 21.67 21.32 20. 20.66 20.34 20.04 1.74 1.45 1.17 1!.0 1!.64 1!.3 1!.14 17.0 17.67 17.44 17.23 17.01 16.!1 16.61 16.42 16.23 16.05 15.!7 15.70 15.53 15.37 15.21 15.06 14.1 14.77 14.63 14.4 14.36 14.23 14.11 13. 13.!7
27.43 27.43 27.43 27.44 27.45 27.47 27.4! 27.50 27.52 27.55 27.57 27.61 27.64 27.67 27.71 27.76 27.!0 27.!5 27.0 27.5 2!.01 2!.07 2!.13 2!.20 2!.27 2!.34 2!.42 2!.50 2!.5! 2!.67 2!.76 2!.!5 2!.4 2.04 2.14 2.25 2.36 2.47 2.5! 2.70 2.!2 2.5 30.07 30.20 30.34 30.47 30.61 30.76 30.0 31.05 31.21
1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.5! 1.5 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.6! 1.6 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.7! 1.7 1.!0 1.!1 1.!2 1.!3 1.!4 1.!5 1.!6 1.!7 1.!! 1.! 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.! 1. 2.00
0.!35 0.!3 0.!42 0.!46 0.!4 0.!52 0.!55 0.!5 0.!62 0.!65 0.!6! 0.!70 0.!73 0.!76 0.!7! 0.!!1 0.!!4 0.!!6 0.!!! 0.!1 0.!3 0.!5 0.!7 0.! 0.02 0.04 0.06 0.07 0.0 0.11 0.13 0.15 0.16 0.1! 0.20 0.21 0.23 0.24 0.26 0.27 0.2 0.30 0.31 0.33 0.34 0.35 0.36 0.3! 0.3 0.40 0.41
13.!7 13.75 13.64 13.53 13.43 13.32 13.22 13.13 13.03 12.4 12.!5 12.76 12.6! 12.5 12.51 12.43 12.35 12.2! 12.21 12.13 12.06 12.00 11.3 11.!6 11.!0 11.74 11.6! 11.62 11.56 11.51 11.45 11.40 11.34 11.2 11.24 11.1 11.15 11.10 11.05 11.01 10.6 10.2 10.!! 10.!4 10.!0 10.76 10.72 10.6! 10.64 10.60 10.57
31.21 31.36 31.52 31.6! 31.!5 32.01 32.1! 32.36 32.53 32.71 32.!0 33.0! 33.27 33.46 33.65 33.!5 34.04 34.24 34.45 34.65 34.!7 35.0! 35.2 35.51 35.73 35.5 36.17 36.40 36.63 36.!6 37.10 37.33 37.5! 37.!2 3!.06 3!.31 3!.56 3!.!1 3.07 3.32 3.5! 3.!4 40.10 40.37 40.63 40.1 41.1! 41.45 41.73 42.01 42.2
66
TABELA 6
Cálculo das lajes em cruz - Marcus ly q x
Mx
q .lx 2 =
2 My q .lx m y =
m x
Xx
− =
q .lx 2
Xy
− =
n x
q .lx 2 n y
K x . q
=
lx ly/lx
kx
mx
nx
my
ny
ly/lx
kx
mx
nx
my
ny
1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.0! 1.0 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.1! 1.1 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.2! 1.2 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.3! 1.3 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.4! 1.4 1.50
0.500 0.510 0.520 0.52 0.53 0.54 0.55! 0.567 0.576 0.5!5 0.54 0.603 0.611 0.620 0.62! 0.636 0.644 0.652 0.660 0.667 0.675 0.6!2 0.6! 0.66 0.703 0.70 0.716 0.722 0.72 0.735 0.741 0.746 0.752 0.75! 0.763 0.76 0.774 0.77 0.7!4 0.7! 0.73 0.7! 0.!03 0.!07 0.!11 0.!15 0.!20 0.!24 0.!27 0.!31 0.!35
55.74 54.65 53.61 52.62 51.76 50.76 4.! 4.06 4!.27 47.50 46.77 46.07 45.40 44.75 44.13 43.54 42.7 42.42 41.! 41.3! 40.0 40.42 3.7 3.54 3.12 3!.71 3!.32 37.5 37.5! 37.23 36.! 36.57 36.25 35.5 35.65 35.37 35.0 34.!3 34.57 34.32 34.0! 33.!5 33.62 33.40 33.1 32.! 32.7! 32.5 32.40 32.22 32.04
24.00 32.53 32.0 22.66 22.26 21.!7 21.50 21.15 20.!2 20.50 20.20 1.0 1.63 1.36 1.10 1!.!6 1!.63 1!.40 1!.1 17.! 17.7 17.60 17.42 17.24 17.07 16.1 16.76 16.61 16.47 16.33 16.20 16.07 15.5 15.!3 15.72 15.61 15.51 15.41 15.31 15.21 15.12 15.04 14.5 14.!7 14.7 14.71 14.64 14.57 14.50 14.43 14.37
55.74 55.75 55.7! 55.!2 55.!! 556 56.06 56.17 56.30 56.44 56.5 56.76 56.5 57.14 57.36 57.5! 57.!2 5!.07 5!.33 5!.60 5!.! 5.1 5.4 5.!1 60.15 60.4 60.!4 61.20 61.57 61.6 62.05 62.75 63.16 63.5 64.02 64.46 64.1 65.36 65.!3 66.31 66.7 67.2 67.7 6!.30 6!.!2 6.34 6.!! 70.42 70.7 71.53 72.10
24.00 24.00 24.02 24.04 24.07 24.11 24.16 24.22 24.2! 24.36 24.44 24.52 24.62 24.72 24.!3 24.4 25.06 25.1 25.33 25.47 25.61 25.76 25.2 26.0 26.25 26.43 26.61 26.7 26.! 27.1! 27.3! 27.5! 27.7 2!.01 2!.23 2!.45 2!.6! 2!.1 2.15 2.3 2.64 2.! 30.15 30.40 30.67 30.4 31.21 31.4! 31.76 32.04 32.33
1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.5! 1.5 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.6! 1.6 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.7! 1.7 1.!0 1.!1 1.!2 1.!3 1.!4 1.!5 1.!6 1.!7 1.!! 1.! 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.! 1. 2.00
0.!35 0.!3 0.!42 0.!46 0.!4 0.!52 0.!55 0.!5 0.!62 0.!65 0.!6! 0.!70 0.!73 0.!76 0.!7! 0.!!1 0.!!4 0.!!6 0.!!! 0.!1 0.!3 0.!5 0.!7 0.! 0.02 0.04 0.06 0.07 0.0 0.11 0.13 0.15 0.16 0.1! 0.20 0.21 0.23 0.24 0.26 0.27 0.2 0.30 0.31 0.33 0.34 0.35 0.36 0.3! 0.3 0.40 0.41
32.04 31.!7 31.71 31.54 31.3 31.24 31.0 30.4 30.!0 30.67 30.54 30.41 30.2! 30.16 30.04 2.3 2.!2 2.71 2.60 2.50 2.40 2.30 2.20 2.11 2.02 2!.3 2!.!4 2!.76 2!.6! 2!.60 2!.52 2!.44 2!.37 2!.2 2!.22 2!.15 2!.0 2!.02 27.5 27.! 27.!3 27.77 27.71 27.65 27.60 27.54 27.4 27.43 27.3! 27.33 27.2!
14.37 14.31 14.25 14.1 14.13 14.0! 14.03 13.7 13.2 13.!! 13.!3 13.7 13.74 13.70 13.66 13.62 13.5! 13.54 13.51 13.47 13.44 13.40 13.37 13.34 13.31 13.2! 13.25 13.22 13.1 13.17 13.14 13.12 13.0 1307 13.05 13.02 13.00 12.! 12.6 12.4 12.2 12.0 12.!! 12.!6 12.!5 12.!3 12.!1 12.!0 12.7! 12.76 12.75
72.10 72.67 73.25 73.!4 74.44 75.04 75.65 76.27 76.0 77.52 7!.17 7!.!1 7.47 !0.13 !0.!0 !1.4! !2.16 !2.!4 !3.54 !4.24 !4.5 !5.67 !6.3! !7.12 !7.!5 !!.60 !.34 0.0 0.!6 1.61 2.3 3.17 3.6 4.75 5.54 6.35 7.16 7.! !.!0 .62 100.46 101.30 102.14 103.00 103.!5 104.72 105.5! 106.45 107.35 10!.23 10.12
32.33 32.62 32.2 33.22 33.52 33.!2 34.13 34.45 34.7 35.0! 35.41 35.73 36.06 36.40 36.74 37.0! 37.42 37.77 3!.12 3!.47 3!.!3 3.1 3.55 3.2 40.2 40.67 41.04 41.42 41.!1 42.1 42.5! 42.7 43.37 43.77 44.17 44.57 44.! 45.0 45.!1 46.22 46.64 47.06 47.4 47.2 4!.35 4!.7! 4.21 4.65 50.10 50.55 50.
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