The hydraulic cylinder is required to support a force of p = 100 kN . If the cylinder has an inner diameter of 100 mm and is made from a material having an allowable normal stress of \tau_{allow}= 150 \mathrm{MPa} , determine the required minimum thickness t of the wall of the cylinder.
Question 8.80: The hydraulic cylinder is required to support a force of p ...
Equation of Equilibrium: The absolute pressure developed in the hydraulic cylinder can be determined by considering the equilibrium of the free-body diagram of the piston shown in Fig. a. The resultant force of the pressure on the piston is
F=p A=p\left[\frac{\pi}{4}\left(0.1^{2}\right)\right]=0.0025 \pi p . \text { Thus, }
\Sigma F_{x^{\prime}}=0 ; \quad 0.0025 \pi p-100\left(10^{3}\right)=0
p=12.732\left(10^{6}\right) \mathrm{Pa}
Normal Stress: For the cylinder, the hoop stress is twice as large as the longitudinal stress,
\sigma_{\text {allow }}=\frac{p r}{t} ; \quad 150\left(10^{6}\right)=\frac{12.732\left(10^{6}\right)(50)}{t}
t=4.24 \mathrm{mm}
Since \frac{r}{t}=\frac{50}{4.24}=11.78>10 , thin -wall analysis is valid.
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