Question

The piston rod of diameter 20 mm and length 700 mm in hydraulic cylinder is subjected to compressive force of 10 kn due to the internal pressure. The end conditions for the rod may be assumed as guided at the piston end and hinged at the other end. The youngs modulus is 200 gpa. The factor of safety for the piston rod is

Answer 1

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Answer 2

Answer:

The factor of safety is 3.16

Explanation:

Given,

Diameter of the piston rod = 20mm

Length of the piston rod = 700 mm

Compressive force = 10 kn

Young's modulus = 200 gpa

$P_{c r}=\frac{\pi^{2} E I}{L^{2}}$

$I=\frac{\pi}{64} \times 20^{4}=7853.98 \mathrm{mm}^{4} \\\\ E=200 \times 10^{3} \mathrm{N} / \mathrm{m}^{2} \\\\ P_{c r}=\frac{\pi^{2} \times 200 \times 10^{3} \times 7853.98}{700^{2}}=31.64 \mathrm{KN}$

Factor of safety = $\frac{31.64}{10}=3.16$

The rod is subjected to a compressive force which causes shortening of the length. We have to check how much load the road can carry before buckling of yielding hence why we calculated the critical load. The critical load is the maximum load a member can carry before it deforms.

When comparing the applied load of 10KN with the critical load, we can conclude that the rod will safely carry the load without deforming. The factor of safety is also since it is higher than 1 also shows that the material of the rod is sufficient for the load subjected.