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Chapter 1

Q. 1.22

A thin rectangular steel plate 100 mm by 50 mm undergoes deformations 0.05 mm and 0.01 mm in x and y directions due to stresses a,\sigma _x and \sigma _y as shown in Fig. 1.32. Determine the magnitude of \sigma _x and \sigma _y if modulus of elasticity is 200 GPa and Poisson’s ratio is 0.3.

Screenshot 2022-10-07 122704

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Verified Solution

It is plane stress problem where,

\varepsilon_x=\frac{0.05}{100}=0.005  mm / mm , and

\varepsilon_y=\frac{0.01}{50}=0.0002  mm / mm

Substituting in Eq. (1.231),

\sigma_x =\frac{E}{1-\mu^2}\left(\varepsilon_x+\mu \varepsilon_y\right)

=\frac{200000}{1-0.3^2}(0.0005+0.3 \times 0.0002) =123.07  MPa
\sigma_y =\frac{E}{1-\mu^2}\left(\varepsilon_y+\mu \varepsilon_x\right)

=\frac{200000}{1-0.3^2}(0.0002+03 \times 0.0005) =76.92  MPa