Design a footing for a column with a section of 30 × 70 cm, with a load of 1,000 kN, for an allowable soil stress of \sigma_{adm}=0.450 MPa.



Answer to a math question Design a footing for a column with a section of 30 × 70 cm, with a load of 1,000 kN, for an allowable soil stress of \sigma_{adm}=0.450 MPa.

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Para dimensionar a sapata, primeiro precisamos determinar a área de contato da sapata com o solo. A carga atuando sobre a sapata é de 1000 kN e a tensão admissível do solo é de 0,450 MPa.

Sabendo que a pressão atuante sobre o solo é dada por:

p = \dfrac{F}{A}

onde p é a pressão, F é a força e A é a área de contato.

A área de contato da sapata com o solo pode ser calculada como:

A = \dfrac{F}{\sigma_{adm}}

Substituindo os valores na fórmula, temos:

A = \dfrac{1000 kN}{0,450 MPa}

Convertendo 1000 kN para N e 0,450 MPa para N/m², temos:

A = \dfrac{1000 \times 1000 N}{0,450 \times 10^6 N/m²}

A = \dfrac{1000000 N}{450000 N/m²}

A = 2,2222 m²

Portanto, a área de contato da sapata com o solo é de 2,2222 m² . Como a seção da sapata é retangular, podemos determinar as dimensões necessárias para a sapata sabendo que a largura é de 30 cm e a área de contato é de 2,2222 m² .

Calculamos o comprimento necessário da sapata:

30 \times comprimento = 2,2222

comprimento = \dfrac{2,2222}{30}

comprimento = 0,0741 m

Portanto, a sapata deve ter as dimensões de 30 cm x 74,1 cm para suportar a carga de 1000 kN considerando uma tensão admissível do solo de \sigma_{adm}=0,450 MPa .

\textbf{Resposta:} A sapata deve ter dimensões de 30 cm x 74,1 cm.

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