Question 23.3: A cylinder made of steel (σult = 580 MPa) is subjected to in......
A cylinder made of steel (σ_{ult} = 580 MPa) is subjected to internal pressure 10 MPa. The inner diameter and thickness of the vessel are 200 mm and 80 mm respectively. Calculate the maximum shear stress.
Step-by-Step
Given p_i=10 \mathrm{MPa}, t=80 \mathrm{~mm}, d_i=200 \mathrm{~mm}, r_i=100 \mathrm{~mm}, d_o=200 \mathrm{~mm}+2 \times 80
=200+160=360 \mathrm{~mm} \text {, and } r_o=180 \mathrm{~mm}\sigma_{r r}=-p_i=-10 ~\mathrm{MPa}
\sigma_{\theta \theta}=p \frac{r_o^2+r_i^2}{r_o^2-r_i^2}=10 \times \frac{180^2+100^2}{180^2-100^2}=18.93 ~\mathrm{MPa}
\tau_{\max }=\frac{1}{2}(18.92+10)=14.46 ~\mathrm{MPa}
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