8-ProjCobMadParte4.pdf
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Transcript of 8-ProjCobMadParte4.pdf
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5.4-Dimensionamento da trelia:
a) Carregamento total:
Peso prprio da trelia (estimado): , . , .
g = 1,54.(1 + 0,33.16)g 9,67 kgf/m2
Carga total: p = 126,51 kgf/m2 + 9,67 kgf/m2
p = 136,18 kgf/m2
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b) rea de influncia:
9
11
1315
P2P2
P3
P3
P3P3
P3
P3P3
P3P3
P3P3
AP1
AP2
AP3
rea de influncia da trelia: 300 cm = 3 m (afastamento entre trelias)rea de influncia de P1: 100/2 cm = 50 cm = 0,5 mrea de influncia de P2: (100+133,3)/2 cm = 116,67 cm = 1,1667 m
rea de influncia de P3: 133,33 cm = 1,3333 m
100 cm133,3
1 2 4 6 8 10 12 14
3
5
1 1
133,3 133,3 133,3 133,3 133,3
V1 V2
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c) Cargas concentradas:
P1 = p . AT . AP1 = 136,18 . 3 . 0,5 = 204,27 kgfP2 = p . AT . AP2 = 136,18 . 3 . 1,1667 = 476,63 kgfP3 = p . AT . AP3 = 136,18 . 3 . 1,3333 = 544,72 kgf
d) Clculo das reaes:
V1 = V2 = (2 . P1 + 2 . P2 + 11 . P3) / 2V
1= V
2= (2 . 204,27 + 2 . 476,63 + 11 . 544,72) / 2
V1 = V2 = 3676,86 kgf
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f) Clculo dos esforos normais:
N 1:x
y
P1 N13
N12
Fy = 0Fy = 0N13 . sen P1 = 0N13 . sen 11,31 204,27 = 0N13 = 1041,57 kgf (T)
Fx = 0Fx = 0
N12 + N13 . cos = 0N12 + 1041,57 . cos 11,31 = 0
N12 = 1021,34 kgf (C)
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N 2:
F = 0F = 0
x
y
N12
N23
V1
N24
N23 + V1 = 0N23 + 3676,86 = 0N23 = 3676,86 kgf (C)
Fx = 0Fx = 0N24 N12 = 0N24 (1021,34) = 0N24 = 1021,34 kgf (C)
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N 3:
F = 0F = 0
P2
N23
N34
+
(N23 + P2) . cos N34 . sen ( + ) = 0(3676,86 + 476,63) . cos 11,31 N34 . sen (11,31 + 8,53) = 0N34 = 9246,12 kgf (T)
Fx = 0Fx = 0N35 N13 (N23 + P2) . sen + N34 . cos ( + ) = 0N35 1041,57 (3676,86 + 476,63) . sen 11,31 + 9246,12 .cos (11,31 + 8,53) = 0
N35 = 8283,35 kgf (C)
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N 4:
F = 0F = 0
x
y
N45N34
N46
N24
N45 + N34 . sen = 0N45 + 9246,12 . sen 8,53 = 0N45 = 1371,45 kgf (C)
Fx = 0Fx = 0
N46 N24 N34 . cos = 0N46 (1021,34) 9246,12 . cos 8,53 = 0N46 = 8122,50 kgf (T)
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N 5:
F = 0F = 0
P3
N45
N56
+
Fx = 0Fx = 0N57 N35 (N45 + P3) . sen + N56 . cos ( + ) = 0N57 + 8283,35 (1371,45 + 544,72) . sen 11,31 + 1592,55 .cos (11,31 + 19,29) = 0
N57 = 9816,27 kgf (C)
(N45 + P3) . cos N56 . sen ( + ) = 0(1371,45 + 544,72) . cos 11,31 N56 . sen (11,31 + 19,29) = 0N56 = 1592,55 kgf (T)
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N 6:
F = 0F = 0
x
y
N67N56
N68
N46
N67 + N56 . sen = 0N67 + 1592,55 . sen 19,29 = 0N67 = 526,10 kgf (C)
Fx = 0Fx = 0
N68 N46 N56 . cos = 0N68 8122,50 1592,55 . cos 19,29 = 0N68 = 9625,64 kgf (T)
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N 7:
F = 0F = 0
P3
N67
N78
+
(N67 + P3) . cos N78 . sen ( + ) = 0(526,10 + 544,72) . cos 11,31 N78 . sen (11,31 + 28,81) = 0N78 = 28,33 kgf (C)
Fx = 0Fx = 0N79 N57 (N67 + P3) . sen + N78 . cos ( + ) = 0N79 + 9816,27 (526,10 + 544,72) . sen 11,31 28,33 .cos (11,31 + 28,81) = 0
N79 = 9790,95 kgf (C)
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N 8:
F = 0F = 0
x
y
N89N78
N810
N68
N89 + N78 . sen = 0N89 28,33 . sen 28,81 = 0N89 = 13,65 kgf (T)
Fx = 0Fx = 0N810 N68 N78 . cos = 0N810 9625,64 + 28,33 . cos 28,81 = 0N810 = 9600,81 kgf (T)
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N 9:
F = 0F = 0
P3
N89
N910
+
(N89 + P3) . cos N910 . sen ( + ) = 0(13,65 + 544,72) . cos 11,31 N910 . sen (11,31 + 36,87) = 0N910 = 734,70 kgf (C)
Fx = 0Fx = 0N911 N79 (N89 P3) . sen + N910 . cos ( + ) = 0N911 + 9790,95 (13,65 + 544,72) . sen 11,31 734,70 .cos (11,31 + 36,87) = 0
N911 = 9191,55 kgf (C)
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N 10:
F = 0F = 0
x
y
N1011N910N1012
N810
N1011 + N910 . sen = 0N1011 734,70 . sen 36,87 = 0N1011 = 440,82 kgf (T)
Fx = 0Fx = 0N1012 N810 N910 . cos = 0N1012 9600,81 + 734,70 . cos 36,87 = 0N1012 = 9013,05 kgf (T)
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N 11:
F = 0F = 0
P3
N1011
N1112 +
(N1011 + P3) . cos N1112 . sen ( + ) = 0(440,82 + 544,72) . cos 11,31 N1112 . sen (11,31 + 43,53) = 0N1112 = 1182,08 kgf (C)
Fx = 0Fx = 0N1113 N911 (N1011 + P3) . sen + N1112 . cos ( + ) = 0N1113 + 9191,55 (440,82 + 544,72) . sen 11,31 1182,08 .cos (11,31 + 43,53) = 0
N1113 = 8317,56 kgf (C)
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N 12:
F = 0F = 0
x
y
N1213N1112N1214
N1012
N1213 + N1112 . sen = 0N1213 1182,08 . sen 43,53 = 0N1213 = 814,14 kgf (T)
Fx = 0Fx = 0N1214 N1012 N1112 . cos = 0N1214 9013,05 + 1182,08 . cos 43,53 = 0N1214 = 8156,03 kgf (T)
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N 13:
F = 0F = 0
P3
N1213
N1314 +
(N1213 + P3) . cos N1314 . sen ( + ) = 0(814,14 + 544,72) . cos 11,31 N1314 . sen (11,31 + 48,99) = 0N1314 = 1533,99 kgf (C)
Fx = 0Fx = 0N1315 N1113 (N1213 + P3) . sen + N1314 . cos ( + ) = 0N1315 + 8317,56 (814,14 + 544,72) . sen 11,31 1533,99 .cos (11,31 + 48,99) = 0
N1315 = 7291,03 kgf (C)
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N 15:
F = 0F = 0
x
y
N1517 = N1315N1415
P3
N1315
N1415 2 . N1315 . sen P3 = 0N1415 2 . (7291,03) . sen 11,31 544,72 = 0N1415 = 2315,08 kgf (T)
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Esforos normais nas barras da trelia:
