resmat2007a
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resmat2007a


DisciplinaResistência dos Materiais II6.408 materiais138.920 seguidores
Pré-visualização27 páginas
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300
M
C D
A B
400
600
P
Figura 3.42: Figura do exerc´\u131cio 6
9. Comparar as tenso\u2dces de cisalhamento e os a\u2c6ngulos de torc¸a\u2dco em dois tubos de paredes
delgadas, um de parede delgadas,um de sec¸a\u2dco cirular e outro de sec¸a\u2dco quadrada, mas
de mesmo comprimento, mesma a´rea de sec¸a\u2dco e mesma espessura, sujeitos ao mesmo
torque.
Resposta \u3c4circular
\u3c4quadrada
= 0, 7854 e \u3b8circular
\u3b8quadrada
= 0, 617
10. Uma chapa de ac¸o de 500mm de largura e 3mm de espessurae´ usada para fazer um
tubo, curvando-se a chapa em 3600 e soltando-se as bordas juntas longitudinalmente
(topo a topo). As formas a considerar sa\u2dco
(a) circular,
(b) quadrada
(c) reta\u2c6ngular 150× 100mm
.Admita um comprimento me´dio de 500mm (nenhum esforc¸o na placa devido ao
encurvamento e cantos retos para sec¸o\u2dces, na\u2dco circulares). calcular o momento torque
ma´ximo admissivel e o correspondente a\u2c6ngulo de torc¸a\u2dco para 2m de comprimento,
em cada caso, dados G = 80Gpa e \u3c4 = 70Mpa.
Resposta 8, 04kNm e 0, 0224rd; 6, 25kNm e 0, 0287rd; 5, 99kNm e 0, 0299rd
11. A figura 3.43 representa a sec¸a\u2dco tansversal da fuselagem de um avia\u2dco feito de liga
de alum\u131´nio (G = 27 GPa). As espessuras das placas sa\u2dco 1,5 mm em AB e CD;
1,2 mm em BC e 1,0 mm em DA. Dados \u3c4 = 85 MPa, calcular o momento torsor
admiss´\u131vel e o correspondente a\u2c6ngulo de torc¸a\u2dco.
Resposta 124,59 kN e 0,00575 rad.
66
B C
DA
700 mm
35
0 
m
m
50
0 
m
m
35
0 
m
m
Figura 3.43: Figura do exerc´\u131cio 11
67
3.3 Solicitac¸a\u2dco por momento fletor
3.3.1 Introduc¸a\u2dco
Uma barra de eixo reto e cargas transversais esta´ sujeita a momentos fletores e esforc¸os
cortantes, geralmente. A barra e´ designada por viga e o efeito do momento fletor e´ a
flexa\u2dco.
1. Tipos de Flexa\u2dco ( de acordo com os esforc¸os simples atuantes)
PURA : somente momento fletor, constante (esforc¸o cortante nulo);
SIMPLES : momento fletor e esforc¸o cortante;
COMPOSTA : momento fletor e esforc¸o normal.
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~Ex. 1) Flexao Pura
DMF constante
DEC nulo
+
A B
BA
DMF
M0
P P
A B
a L a
P.a
DMF
A B DC
DECP
P
DC A B
Ex. 2) Flexao pura no vao AB
Flexao simples nos balancos
~ ~
~
~
Figura 3.44: Tipos de Flexa\u2dco
2. Tipos de Flexa\u2dco (de acordo com os mom. fletores atuantes)
Os eixos locais y e z sa\u2dco os eixos principais de ine´rcia da sec¸a\u2dco.
O eixo de solicitac¸a\u2dco (ES) e´ a intersec¸a\u2dco do plano de solicitac¸a\u2dco (que conte´m as
cargas e reac¸o\u2dces) com a sec¸a\u2dco transversal.
1. Flexa\u2dco Normal ou Reta:
\u2022 ES \u2261 eixo -y \u2192My = 0 e Mf =Mz (ex.3 e 4)
\u2022 ES \u2261 eixo -z \u2192Mz = 0 e Mf =My
2. Flexa\u2dco obl´\u131qua:
ES na\u2dco coincide com nenhum dos eixos principais de ine´rcia:
\u2212\u2192
M f =
\u2212\u2192
My +
\u2212\u2192
M z (ex. 5 e 6)
68
Observac¸o\u2dces:
1. Mf =M e´ normal ao plano de solicitac¸a\u2dco, portanto M \u22a5 ES
2. Res Mat.I \u2192 Flexa\u2dco Reta, Pura e Simples
Res Mat.II \u2192 Flexa\u2dco obl´\u131qua e flexa\u2dco composta
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My
Mz
M
E.S. E.S.
z
z
y = E.S. y = E.S. y
z
z
y
Ex.3) Ex. 4) Ex. 5) Ex. 6)
Mz
M=Mz
G
My
G
M=Mz
G
Figura 3.45: Direc¸o\u2dces de Momentos Fletores e de eixos de solicitac¸o\u2dces
3.3.2 Ca´lculo das Tenso\u2dces Normais
1. Flexa\u2dco Pura e Reta
Para vigas horizontais ou com pequena inclinac¸a\u2dco, admitindo-se pequenas deformac¸o\u2dces
ela´sticas e proporcionais, sendo va´lida portanto a Lei de Hooke: \u3c3x = E²x
Seja a viga AB do ex.1 anterior, fazendo M0 =M(M > 0)
L
A B
A B
comp < L
comp > L
M M
Figura 3.46: Configurac¸o\u2dces inicial e deformada de uma viga bi-apoias sob flexa\u2dco pura.
- Linhas longitudinais (fibras longitudinais ao eixo) assumem o aspecto curvo. O
eixo deformado a` flexa\u2dco e´ a linha ela´stica .
- Linhas transversais (sec¸o\u2dces transversais) permanecem retas (planas) e \u22a5s ao eixo
deformado. Sofrem um rotac¸a\u2dco em torno do eixo-z local.
- Uma camada de fibras situadas em um plano horizontal na configurac¸a\u2dco inicial
mante´m o comprimento L ( ²x = 0\u2192 \u3c3x = 0). E´ designada por superf´\u131cie neutra e
sua intersec¸a\u2dco