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,σx and σy as shown in Fig. 1.32. Determine the magnitude of σx and σy if modulus of elasticity is 200 GPa and Poisson's ratio is 0.3.

Question

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,[latex]\sigma _x[/latex] and [latex]\sigma _y[/latex] as shown in Fig. 1.32. Determine the magnitude of [latex]\sigma _x[/latex] and [latex]\sigma _y[/latex] if modulus of elasticity is 200 GPa and Poisson's ratio is 0.3.

Accepted Answer

It is plane stress problem where,

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

[latex]\varepsilon_y=\frac{0.01}{50}=0.0002 mm / mm [/latex]

Substituting in Eq. (1.231),

[latex]\sigma_x =\frac{E}{1-\mu^2}\left(\varepsilon_x+\mu \varepsilon_y ight) [/latex]

[latex]=\frac{200000}{1-0.3^2}(0.0005+0.3 imes 0.0002) [/latex] =123.07 MPa
[latex]\sigma_y =\frac{E}{1-\mu^2}\left(\varepsilon_y+\mu \varepsilon_x ight) [/latex]

[latex]=\frac{200000}{1-0.3^2}(0.0002+03 imes 0.0005)[/latex] =76.92 MPa

Q. 1.22

Chapter 1

Q. 1.22

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