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da viga da direc¸a\u2dco longitudinal. A aplicac¸a\u2dco destas u´ltimas equac¸o\u2dces segue enta\u2dco um procedimento bastante parecido com o exposto no item anterior. Deve-se ter bastante atenc¸a\u2dco no ca´lculo do momento esta´tico, identificando corretamente qual a a´rea a ser considerada no seu ca´lculo. Obvia- mente a aplicac¸a\u2dco destas equac¸o\u2dces podem ser extendidas a vigas de um so´ elemento. Observa-se que das equac¸o\u2dces 3.106 e 3.107 que o fluxo de cisalhamento e´ uma grandeza vetorial e define a direc¸a\u2dco das tenso\u2dces as tenso\u2dces Observa-se tambe´m que na aba do perfil o fluxo de cisalhamento na direc¸a\u2dco vertical provoca tenso\u2dces \u3c4xy de baixa magnitude pois a espessura t e´ relativamente grande. Por um outro lado o fluxo de cisalhamento na direc¸a\u2dco horizontal provoca tenso\u2dces de cisalhamento \u3c4xz de altas magnitudes pois a espessura e e´ relativamente pequena. Assim sendo, e´ comum analisarmos o fluxo de cisalhamento somente nas direc¸o\u2dces paralelas aos lados da sec¸a\u2dco: direc¸a\u2dco horizontal na(s) aba(s) e direc¸a\u2dco vertical na alma. O sentido do fluxo de cisalhamento e, consequ¨entemente das tenso\u2dces cisalhantes, nas abas sa\u2dco mostrados na figura 3.130 e sa\u2dco obtidos pela simetria do tensor de tenso\u2dces (equac¸o\u2dces de equil´\u131brio). Ja´ na alma a direc¸a\u2dco do fluxo e´ a mesma direc¸a\u2dco do cortante atuante na sec¸a\u2dco. 110 M \u3c4zx \u3c4xz \u3c4zx \u3c4xz \u3c4zx \u3c4xz dx dF F + dF F \u3c4xz \u3c4zx dx t e M + dMx y z F dx F + dF dF F dx dF F + dF dx F + dF F dF Figura 3.130: Fluxo de cisalhamento num perfil I A figura 3.131 resume as direc¸o\u2dces de fluxo de cisalhamento considerados na ana´lise de uma viga I, bem como suas intensidades. Estas u´ltimas sera\u2dco discutidas logo a seguir. f max aba f max aba f max alma max aba2f Figura 3.131: Fluxo de cisalhamento num perfil I No que se refere a` intensidade do fluxo de cisalhamento tem-se para uma viga I, tem-se: \u2022 Para as abas do perfil: (ver figura 3.132) y z d/2 e b/2 x Q dz Figura 3.132: Fluxo de cisalhamento nas abas de um perfil I 111 f = QMs I = Qd 2 ( b 2 \u2212 z)e I = Qed 2I ( b 2 \u2212 z ) (3.109) Verifica-se que o fluxo de cisalhamento varia linearmente com z conforme mostra figura 3.131. A forc¸a total desenvolvida em cada trecho das abas pode ser obtida pela integrac¸a\u2dco que segue e as resultantes sa\u2dco mostradas na figura 3.133 Faba = \u222b dF = \u222b fdz = \u222b 0 b/2 Qed 2I ( b 2 \u2212 z ) dz = Qedb2 16I (3.110) Faba Faba FabaFaba Falma = Q Figura 3.133: Resultantes do fluxo de cisalhamento num perfil I Observa-se facilmente que a resultante de forc¸as na horizontal e´ nula, como era de se esperar ja´ que para o caso analisado so´ existe cortante na direc¸a\u2dco y. \u2022 Para a alma do perfil: (ver figura 3.134) Similarmente, observando figura 3.134 faz-se a ana´lise da alma. y z e Q b t dy y e d/2 Figura 3.134: Fluxo de cisalhamento na alma de um perfil I Pode-se escrever para o ca´lculo do momento esta´tico na alma: Ms = bed/2 + t(d/2\u2212 e/2\u2212 y)(d/2\u2212 e/2\u2212 y)1/2 (3.111) Considerando que d/2 À e/2 (paredes finas), pode-se simplificar a equac¸a\u2dco 3.111 por: Ms ' bed/2 + t(d/2\u2212 y)(d/2\u2212 y)1/2 = bed/2 + t/2(d2/4\u2212 y2) (3.112) Resultando para o fluxo de cisalhamento, para o caso de t = e: 112 f = QMs I = Qt I [ db 2 + 1 2 ( d2 4 \u2212 y2 )] (3.113) Neste caso, conforme mostrado na figura 3.131 o fluxo de cisalhamento varia de modo parabo´lico, de f = 2fabamax = Qtdb/(2I) em y = d/2 ao ma´ximo de f = falmamax = (Qtd/I)(b/2 + d/8) em y = 0. A forc¸a total desenvolvida na alma pode ser obtida pela integrac¸a\u2dco que segue e a resultante e´ mostrada na figura 3.133 Falma = \u222b dF = \u222b fdy (3.114) Desenvolvendo a integral da equac¸a\u2dco 3.114, sendo o valor do fluxo de cisalhamento dado por 3.113, pode-se mostrar que: Falma = \u222b dF = \u222b d/2 \u2212d/2 fdy = Q (3.115) ou seja, que a resultante vertical e´ igual ao cortante que atua na sec¸a\u2dco, conforme era esperado. (ver figura 3.133) 3.4.6 Exerc´\u131cios 1. Um esforc¸o cortante vertical de 18 kN atua na sec¸a\u2dco transversal de uma viga con- stitu´\u131da de quatro pec¸as de madeira 50 mm × 200 mm (veja figura 3.135 Determinar: (a) a tensa\u2dco tangencial horizontal ma´xima, indicando onde ela ocorre na sec¸a\u2dco transversal. (b) a tensa\u2dco tangencial vertical a 80 mm abaixo do topo. Resposta: 821,7 kPa e 706,7 kPa \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd Figura 3.135: Figura do exerc´\u131cio 1 2. Uma viga caixa e´ formada por quatro ta´buas de madeira 25 mm × 150 mm, unidas com parafusos. O esforc¸o cortante de 4 kN e´ constante ao longo do comprimento. Calcular o espac¸amento entre os parafusos, no comprimento, se cada um suporta uma forc¸a de cisalhamento de 1 kN. Resposta: 110 mm, no ma´ximo. 113 \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd Figura 3.136: Figura do exerc´\u131cio 2 3. Uma viga caixa\u2dco de madeira sec¸a\u2dco quadrada 250mm × 250 mm externamente, espessura de 50 mm, e´ formada por quatro pec¸as de madeira pregadas de uma das tre\u2c6s formas indicadas. O esforc¸o cortante de 3,02 kN ao longo do comprimento e cada prego resiste a uma forc¸a cortante de 240 N. escolher a soluc¸a\u2dco que exige menor nu´mero de pregos e calcular o espac¸amento entre os pregos para esta soluc¸a\u2dco. Resposta: (b) 60 mm (para (a) 36 mm e para (c) 45 mm) \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd \ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd (a) (b) (c) Figura 3.137: Figura do exerc´\u131cio 3 4. A sec¸a\u2dco transversal AB da viga da figura 3.138, e´ constitu´\u131da por va´rias pec¸as de madeira (dimenso\u2dces em mm), conforme a figura 3.138. O momento de ine´rcia em relac¸a\u2dco a` LN e´ igual a 2360×106 mm4. Cada parafuso representado e´ capaz de resistir a uma forc¸a de cisalhamento longitudinal de 2 kN. Pede-se o espac¸amento, ao longo do comprimento, dos parafusos necessa´rios a` ligac¸a\u2dco: (a) nos trechos AC e DB. (b) no trecho CD. Resposta: 120 mm e 240mm 3.4.7 Centro de cisalhamento Seja uma sec¸a\u2dco com perfil U como a mostrada na figura 3.139. que esta´ em balanc¸o em um apoio fixo e submetida a` forc¸a P. Se a forc¸a for aplicada ao longo do eixo vertical assime´trico que passa pelo centro´ide C da a´rea da sec¸a\u2dco transversal,