## Mechanics of Materials, 7th Edition

Published by McGraw-Hill Education

# Chapter 1 - Problems: 1.21

#### Answer

$\sigma_{FTG} = 3.33\space MPa$ $b = 52.5\space cm$

#### Work Step by Step

1) Bearing Stress on the Footing, $\sigma_{FTG}$ : $\sigma_{FTG} = \frac{P}{A_{POST}} = \frac{40 * 10^3\space N}{120 * 100\space m^2}$ $\sigma_{FTG} = \boxed{3.33\space MPa}\space\space\leftarrow\space ANS1$ 2)Footing Dimensions: $\space\space\bullet$Bearing stress on Soil: $\sigma_{SOIL} =\frac{P}{A_{FTG}} = \frac{40 * 10^3\space N}{b^2\space m^2} = 145 * 10^3 \space Pa$ Solving for the unknown quantity, b : $b = \sqrt{\frac{40*10^3}{145*10^3}} = 0.525 \space m = \boxed{52.5 cm^2}\space\space\leftarrow ANS2$

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