Question

For a solid cylinder under uniaxial normal stress along $x_2$, $\sigma_{22} = \sigma$ a) Find the shear stress $\sigma_{\alpha\beta}$ for orthonormal ($\alpha, \beta, x_3$) and $\alpha, \beta$ rotated by $\theta_3$ about $x_3$ with respect to $x_1, x_2$. b) Find the shear stress $\sigma_{\alpha\beta}$ for a general rotation $\theta$ and show that it is maximum for $\theta = \pi / 4$

          For a solid cylinder under uniaxial normal stress along $x_2$, $\sigma_{22} = \sigma$
a) Find the shear stress $\sigma_{\alpha\beta}$ for orthonormal ($\alpha, \beta, x_3$) and $\alpha, \beta$ rotated by $\theta_3$ about $x_3$ with respect to $x_1, x_2$.
b) Find the shear stress $\sigma_{\alpha\beta}$ for a general rotation $\theta$ and show that it is maximum for $\theta = \pi / 4$

For a solid cylinder under uniaxial normal stress along x2, σ22 = σ
a) Find the shear stress σαβ for orthonormal (α, β, x3) and α, β rotated by θ3 about x3 with respect to x1, x2.
b) Find the shear stress σαβ for a general rotation θ and show that it is maximum for θ = π / 4

Added by Leroy M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Kamlesh Goyal

Step 1

Since σ22 = 0, we know that there is no stress along the x2 axis. Show more…

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For a solid cylinder under uniaxial normal stress along x2, Ïƒ22 = 0. a) Find the shear stress Ïƒ13 for orthonormal (a, B, x3) and a, B rotated by Î¸ about x3 with respect to x1, x2. b) Find the shear stress Ïƒ13 for a general rotation Î¸ and show that it is maximum for Î¸ = Ï€/4.