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1 I s a r u O t u L t r s U E s T a Í d P i a r A o e C T
Teoria das Estruturas I Prof. Eng. Civil Henrique S Pimenta
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Ementa • Class Classific ificaçã ação o das estrut estrutura uras; s; • Grau Grauss de libe liberd rdad ade; e;
1 I s a r u O t u L t r s U E T s
• Esfor Esforços ços simple simples; s; • Di Diag agra rama mass de esfo esforç rços os;; • Vi Vigas gas isostá isostátic ticas; as; • Pórticos Pórticos isostático isostáticos; s;
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Bibliografia 1 I s a r u O t u L t r s U E T s
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Bibliografia 1 I s a r u O t u L t r s U E T s
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Introdução 1 I s a r u O t u L t r s U E T s
O projeto e a construção de estruturas compõem uma área da engenharia civil na qual muitos engenheiros civis se especializam. Estes são os chamados engenhei engenheiros ros estrutu estruturais rais ou calculistas. A engenharia estrutural trata-se do: Planejamento; • Análise; • Projeto; •
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Introdução 1 I s a r u O t u L t r s U E T s
Um estrutura pode ser concebida como um empreendimento por si próprio, como no caso de pontes e estádios esportivos, ou pode ser utilizada como o esqueleto de outro empreendimento; por exemplo, edifícios e teatros. Uma
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Ações
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Equilíbrio Definição: Uma estr strutur tura está stá em equ equilíb ilíbrrio está stático tico quando ndo as gran randezas zas exte xterna rnas possu ssuem o 1 I s a mesmo módulo das grandezas internas, onde a soma de todas deformações dos esforços r u O t inte intern rnos os gera gera o desl desloc ocam amen ento to das das açõe açõess ativ ativas as e reat reativ ivas as na estr estrut utur ura. a. u L t r s U E O equilíbrio estático de um sistemas de forças coplanares deve preencher as s T a Í ndiçõ ndiçõ da três três çõ da táti táti
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Equilíbrio • A A resultante das das forças horizontais horizontais igual a zero ( S FH=0 )
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Equilíbrio Deve-se aplicar, aplicar, ainda, a terceira equação, a que se refere ao giro, convencionando-se que se a força tender a fazer a viga girar no sentido horário, em relação a um ponto qualquer escolhido, ela será positiva, caso contrário negativa.
1 I s a Para tomar o resultado mais rápido, recomenda-se que o ponto escolhido (também r u O t denominado polo de momento) para considerar os momentos das forças, seja um dos apoios. u L t r s U E • A resultante resultante dos dos momentos das das forças e dos dos momentos aplicados é igual igual a zero ( S M=0 ) s T a Í
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Diagramas Diagrama de Força Cortante:
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Diagramas DMF Diagrama de Momento fletor:
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Quando carregadas por uma ou mais forças, as vigas isostáticas deformam-se de maneira que suas seções, antes paralelas, giram umas em relação às outras, de forma que se afastam em uma das faces e se aproximam em outra.
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Obtenção dos Diagramas EXEMPLO PRÁTICO DE OBTENÇAÕ DE VALORES - DMF •
1 I s a r u O t u L t r s U E s T a Í
E por fim temos: A Va
B C
Vb
