1.1 Verificar a estaticidade

Figura 1 – Treliça Plana – Descrição dos nós e barras.

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1.2 Verificar o Equilíbrio Global

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Figura 2 - Equilíbrio global

1.3 Determinar os esforços normais em todas as barras

1.3.1 – Cortes

Figura 3 - Cortes

1.3.2 – Corte 1-1

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Figura 4 – N1 representa o esforço normal na barra 2, N2 representa o esforço normal na barra 3, N3 representa o esforço normal na barra 4.

1.3.3 – Corte 2-2

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1.3.4 – Cálculo do nó 2

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1.3.5 – Cálculo do nó 5

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Figura 5 – N1 representa o esforço normal na barra 6, N2 representa o esforço normal na barra 7, N3 representa o esforço normal na barra 8.

Figura 6 - N1 representa o esforço normal na barra 1.

Figura 7 - N1 representa o esforço normal na barra 9.

1.3.6 – Cálculo do nó 3

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1.4 – Construir uma tabela de esforços internos indicando o tipo de esforço (compressão ou tração)

Barra Nós Esforço Tipo1 1_2 0 Nulo2 1_3 112,5 kN Compressão3 1_4 375 kN Compressão4 2_4 337,5 kN Tração5 3_4 300 kN Tração6 3_5 0 Nulo7 3_6 187,5 kN Compressão8 4_6 112,5 kN Tração9 5_6 150 kN Tração

Figura 8 - N1 representa o esforço normal na barra 5.

1.5– Encontrar as barras, diagonal e banzo, mais solicitadas.

Tabela 1 - Esforços Internos

Figura 9 - Definição das barras.

Barra 3 é a diagonal mais solicitada, com 375 kN.

Barra 9 é o banzo mais solicitado, com 150 kN.

2.0– Para as duas barras críticas acima encontradas, sigam as etapas abaixo:

Estilo BarrasBanzo 1 e 9Diagonal 3 e 7Montante 2,4,5,6 e 8

2.1 – Adote as características do aço ASTM – A36.

Propriedades mecânicas;

Limite de escoamento: 250 MPa

Limite de resistência: 400MPa a 550 MPa

Alongamento mín. Lo = 50mm: 23%

2.2 – Com base na tensão de ruptura desse aço, determine o coeficiente de segurança adequado para que os elementos trabalhem no limite máximo do regime elástico.

Limite máximo do regime elástico: 250MPa

Tensão de ruptura: 400MPa

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2.3 – Com a tensão admissível determinada, calcule a área necessária para suportar os esforços determinados na parte 1 do trabalho.

___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2.4 – Adote o perfil mais econômico que atenda ao cálculo feito no item 3. Usar cantoneiras de abas iguais para as diagonais e montantes, e perfil U para os banzos. Usar tabela fornecida fazendo o devido cálculo da seção transversal do perfil mais econômico.

Equação 1 - Tensão Admissível

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2.5 – Calcule o peso total da estrutura.

Equação 2 - Área da cantoneira de abas iguais. Equação 3 - Área do Perfil U

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2.6 – Pode-se esboçar o gráfico tensão x deformação numa escala aceitável com todos os dados reunidos até agora.

Barras Estilo L (m) Peso (kg/m)

Peso real (kg)

1 Banzo 3,6 6,1 21,962 Montante 2,7 12,2 32,943 Diagonal 4,5 12,2 54,94 Montante 2,7 12,2 32,945 Montante 3,6 12,2 43,926 Montante 2,7 12,2 32,947 Diagonal 4,5 12,2 54,98 Montante 2,7 12,2 32,949 Banzo 3,6 6,1 21,96

Peso Total 329,4 KG

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2.7 – Considere um módulo de eslasticidade igual a 205GPa e determine qual a máxima deformação que os elementos mais solicitados estarão sujeitos. Indique se é encurtamento ou alongamento.

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________