Tabela PTV

Prévia do material em texto

TABELA PARA O CÁLCULO DE ∫ MM. 
 
 
abL 
2
1 abL 
2
1 abL 
2
1 b(a+d)L 
2
1 abL 
3
2 abL 
3
1 abL 
3
1 abL 
2
1 b(a+d)L 
3
2 abL 
3
2 abL 
 
3
1 abL 
6
1 abL 
6
1 b(2d+a)L 
6
1 ab(L+L1) 
3
1
abL 4
1 abL 
12
1
abL 6
1 b(a+2d)L 
12
5 abL 
4
1 abL 
 
 
3
1 abL 
6
1 b(2a+d)L 
6
1 ab(L+L2) 3
1 abL 
12
1 abL 
4
1 abL 
6
1
b(2a+d)L 
4
1 abL 
12
5 abL 
 
 6
1 [a(2b+c)+ 
d(b+2c)]L 6
1 a[b(L+L2)+c(L+L1)] 3
1 a(c+b)L 
12
1 a(b+3c)L 
12
1 a(c+3b)L 6
1 [b(2a+d)+ 
c(a+2d)]L 12
1 a(3b+5c)L 
12
1 a(5b+3c) L 
 
 6
1 ab[2-
32
2
31
LL
LL )( − ]L 
(*) 
3
1 ab(L+
L
LL 43 ) 
12
1 ab(3L3+ L
L 24 ) 
12
1 ab(3L4+ L
L 23 ) 6
1 b[a(L+L4)+ 
d(L+L3)] 
12
1 ab(5L-L4-
L42) 
12
1 ab(5L-L3-
L32) 
 
 
15
8 abL 
5
1 abL 
5
1 abL 
3
1 b(a+d)L 
15
7 abL 
15
7 abL 
 
 
5
1 abL 
30
1 abL 
12
1 b(a+3d)L 
10
3 abL 
15
2 abL 
 
 
5
1 abL 
12
1 b(3a+d)L 
15
2 abL 
10
3 abL 
 
 6
1 [a(2b+c)+ 
d(b+2c)]L 
12
1 a(3b-5c)L 
12
1 a(5b-3c)L 
 
 
15
8 abL 
30
11 abL 
 
 
15
8 abL 
(*) para L3 ≥ L1 
L 
a 
L 
a 
L 
a 
L
d a a 
L 
2ºgrau 
a 
L 
2ºgrau 
L 
2ºgrau 
a a 
L 
2ºgrau 
a 
L 
2ºgrau 
L 
d 
a 
L 
L1 L2 
a 
L 
b 
L 
b 
L 
b 
L 
c b 
L 
L3 L4 
b 
b 
L 
2ºgrau 
b 
L 
2ºgrau 
L 
2ºgrau 
b 
L 
c 
b 
b 
L 
2ºgrau 
b 
L 
2ºgrau 
M 
M