Tudo
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Integral do Produto de duas Funções :TABELA DE KURT BEYER s s i i1 s i2 s i i i i k
∫ f (x ).g (x ).dx s 0
s
s
k
k1
s
k2 s
k
s
k
s
k
α.s
k
β .s
s.i.k
1 .s.i.k 2 1 .s.i.k 2
1 .s.i.k 2 1 .s.i.k 3 1 .s.i.k 6
1 .s.i.(k 1 + k 2 ) 2 1 .s.i.(k 1 + 2 .k 2 ) 6 1 .s.i.(2 .k 1 + k 2 ) 6
1 .s.[2.i1.k1 + i1.k2 + i2.k1 + 2.i2.k2 ] 6
2 .s.i.k 3 1 .s.i.k 3 1 .s.i.k 3
2 .s.i.k 3 5 .s.i.k 12 1 .s.i.k 4
1 .s.i.k 3 1 .s.i.k 4 1 .s.i.k 12
1 .s.i.k 2 1 .s.i.k .(1 + α ) 6 1 .s.i.k .(1 + β ) 6
1 1 .s.k .(i1 + i 2 ) .s.k .(i1 + 2.i2 ) 2 6 2 .s.i.k 3 2 .s.i.k 3 2 .s.i.k 3 1 .s.i.k 3 1 .s.i.k 3 1 .s.i.k 2 1 .s.i.k 3 5 .s.i.k 12 1 .s.i.k 4 1 .s.i.k 4 1 .s.i.k 12 1 .s.i.k .(1 + α ) 6
1 1 1 1 .s.k .(i1 + i 2 ) .s.k .(3 .i1 + 5 .i 2 ) .s.k .(.i1 + 3.i2 ) .s.k.[(1 + β ).i1 + (1 + α ).i2 ] 6 3 12 12
s
1 .s.i.(k 1 + k 2 ) 3 1 .s.i.(3 .k1 + 5 .k 2 ) 12 1 .s.i.(5 .k1 + 3 .k 2 ) 12 1 .s.i.(k1 + 3 .k 2 ) 12 1 .s.i.(3 .k1 + k 2 ) 12
s i s
8 .s.i.k 15 7 .s.i.k 15 7 .s.i.k 15 1 .s.i.k 5 1 .s.i.k 5
7 .s.i.k 15 8 .s.i.k 15 11 .s.i.k 30 3 .s.i.k 10 2 .s.i.k 15
1 .s.i.k 5 3 .s.i.k 10 2 .s.i.k 15 1 .s.i.k 5 1 .s.i.k 30
1 .s.i.k .(1 + α .β ) 3
1 .s.i.k 5 − β − β 2 12
(
)
i s i s
α.s
1 .s.i.k 5 − α − α 2 12 1 .s.i.k 1 + α + α 2 12
(
) )
(
1 .s.i.k 1 + β + β 2 12
(
)
i
β .s
1 1 1 .s.i[(1 + β ).k1 + (1 + α ).k 2 ] .s.i.k .(1 + α .β ) .s.i.k 5 − β − β 2 6 3 12
(
)
1 .s.i.k 1 + α + α 2 12
(
)
1 .s.i.k 3
1/3
ESTÁTICA DAS ESTRUTURAS I - PROF. IBERÊ
Cálculo de Reações e Diagramas de Momento para vigas bi-apoiadas isostáticas simples : q B C A B
F A C B A
F
F 2
F 2
F.b
F .a
q. 2
q. 2
/2
F 2
/2
F.b
a
b
q. 2
V
+ –
+
V
–
F 2
+ –
+
V
–
F.a
+ –
+ –
2
q. 2
M
– +
F. 4
M
– +
F .a.b
M
– +
q. 2 8
* sendo : (a + b) = ESTÁTICA DAS ESTRUTURAS I - PROF. IBERÊ 2 /3