Baixe Cap 4 - Ligações com Solda e outras Manuais, Projetos, Pesquisas em PDF para Engenharia Civil, somente na Docsity!
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Solução Como a espessura da cantoneira é 12,7 mm (1/
ļ) e a da chapa também, a dimensão mínima da perna do filete é
b^ = 5 mm (<
bmáx
= 12,5 − 1,5 = 11
mm), que vamos adotar neste problema.
Os esforços desenvolvidos nas soldas devem ter resultante passando por
G^ (centro de gravidade do perfil L) para que não haja efeitos de flexão na
ligação soldada e no perfil. As propriedades da cantoneira estão na Tabela A6.4, Anexo A. Os comprimentos das soldas são
ℓ^1 e^ ℓ
A equação de equilíbrio de momentos em relação a um ponto no filete inferior fornece:
F× 12,7 − 150 × 3,63 = 0^1 F=^1
= 42,8 kN
F^2 = 150 − 42,8 = 107,2 kN
O comprimento
ℓ^1 pode ser determinado com a solicitação de cálculo 1,3 × 42,8 kN, e a resistência de cálculo dada por:
R^ d^ = 0,7 × 0,
ℓ^1 × 0,6 × 48,5/1,35 = 7,
ℓ^1
A resistência ao cisalhamento das peças ligadas na vizinhança da solda é dada por [ver Eq. (3.7)]
R^ = 1,20d^
ℓ^ × 0,6 × 25/1,1 = 16,
ℓ^ > 7,
ℓ
Igualando a resistência à solicitação, tem-se:
7,
ℓ^1 = 1,3 × 42,
䴞
ℓ^1 = 7,38 cm ≈ 80 mm < 100
b
ℓ=^2
ℓ= 18,5 cm ≈ 190 mm < 100^1
b
Os comprimentos dos filetes podem ser reduzidos utilizando-se solda de maior lado. Adotando-se, por exemplo,
b^ = 8 mm, tem-se:
ℓ= 4,61 cm ≈ 50 mm^1 ℓ= 11,5 cm ≈ 120 mm^2
A verificação da cantoneira à tração deve ser feita com as Eqs. (2.
a) e (2.
b), sendo a área líquida efetiva [ver Eq. (2.5)] calculada com o coeficiente
das Eqs. (2.
a) e (2.
b).
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Solução Neste problema, o esforço solicitante (150 kN) é equilibrado pelos esforços resistentes de três cordões de solda (
F,^1
F^2 e^ F ).^3
Admitindo-se filete de solda com perna
b^ = 5 mm, têm-se as seguintes resistências de projeto (determinadas pelo metal de solda, Eq. (4.
a)):
F^3 d = 0,7 × 0,5 × 12,7 × 0,6 × 48,5/1,35 = 95,8 kN F^1 d
= 0,7 × 0,
ℓ^ × 0,6 × 48,5/1,35 = 7,
ℓ^1
Fd^2 = 7,
ℓ^2
Os valores de
F^1 d^ e^ Fd^2 são determinados com as duas equações de equilíbrio:
Fd^1
+^ F
d^ + 2
F^3 d^ = 1,3 × 150
Fd^1 × 12,7 +
Fd^3
× 6,35 − 1,3 × 150 × 3,63 = 0
7,54 (
ℓ^1 +
ℓ^2 ) + 95,8 = 195
䴞
ℓ^1 +^ ℓ^2 = 13,16 cm
95,
ℓ^1
- 608,3 − 707,9 = 0^ ℓ^1 = 1,04 cm ℓ= 12,1 cm 2
Adotam-se então
ℓ^1 = 20 mm e
ℓ^2
= 130 mm, a serem executados em um único passe com
ℓ^3.
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Solução A carga vertical de 60 kN pode ser transportada para o centro de gravidade
G^ dos cordões de solda (Fig. Probl. 4.6.
b). Com isso, são aplicados uma carga
de 60 kN e um momento
M^ = 60(40 −
x).g
Determinação de
xg
Calculando o momento estático dos cordões de solda em relação ao eixo vertical passando por
G, temos:
2 × 20(10 −
x) − 30g
x= 0g^
x= 5,71 cmg^
Esforço solicitante por unidade de comprimento devido ao cortante
V^ = 60 kN
Consultando a Tabela 4.2, tomaremos como primeira tentativa
b^ = 6 mm <
bmáx
= 19 − 1,5 = 17,5 mm
Esforço solicitante por unidade de comprimento devido ao momento
M
M^ = 60(40 −
xg) = 60(40 − 5,71) = 2057,4 kN · cm
I^ = 0,7 × 0,6 × 20 × 15x
2 × 2 +
= 4725 cm
4
I^ y^ = 0,7 × 0,6 × 30 × 5,
2 + 2 × 0,7 × 0,6 × 20
3 /12 + 2 × 0,7 × 0,6 × 20 (10 − 5,71)
2 = 1280 cm
(^4)
I^ =p^
I^ x^ +^ I^ = 6005 cmy^
4
Alternativamente pode-se usar a Tabela A11.2, Anexo A, para calcular e verificar que
I^ 䴯p^
t^ I^ p
(t^ = 1) = 0,7 × 0,6 × 14.297 = 6004 cm
4
Os pontos mais solicitados serão os mais afastados de
G. Nas extremidades livres dos filetes horizontais, obtemos:
Esforço combinadoSomando os efeitos do momento e do cortante no ponto considerado, teremos^ Esforço solicitante de cálculo
p= 1,4 × 3,63 = 5,07 kN/cmd^
e) f) a) b) c)
Esforço resistente de projeto [Eq. (4.
b)]
- Metal-base adjacente à ligação
pd^ res
=1,9 × 0,6 × 25/1,10 = 25,9 kN/cm
pd^ res
=0,7 × 0,6 × 0,6 × 41,5/1,35 = 7,75 kN/cm
Conclusão: Como
pdres
^ p, o dimensionamento está satisfatório.d
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Solução
Tensão de cisalhamento atuante na garganta da solda [Eq. (4.13)]
S^ = 25 × 0,95 × 24,525 = 582,5 cm
3
Tensão resistente de projeto, referida à garganta da solda— Metal da solda
τdres
= 0,6 × 415/1,35 = 184 MPa >
τd
Para a verificação do perfil, as tensões cisalhantes junto à solda não são determinantes, uma vez que são menores do que as tensões cisalhantes na altura da linha neutra da seção.Combinação de tensões normais e de cisalhamento na soldaDe acordo com a NBR 8800, nas soldas de ligação de mesas e almas de perfis soldados, o dimensionamento da solda pode ser feito com as tensões de cisalhamento, sem considerar as tensões normais de tração ou compressão, paralelas ao eixo da solda.
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Resistência ao cisalhamento da chapa gusset na região dos filetes de solda
2 × 0,5 × 12 × 0,6 × 25/1,10 = 164 kN > 122 kN
A resistência da ligação é maior que a solicitação.Solda de entalhe ligando a alma ao gussetTrata-se de solda de entalhe com penetração total, sujeita a um esforço de tração normal ao eixo da solda.Esforço de cálculo transmitido pela alma
1,4 × 120 − 122 = 46 kN
Esforço resistente da solda
(7,6 − 2 × 0,66) 0,432 × 25/1,10 = 62 kN
A solda de entalhe satisfaz.
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