Question

The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a 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 Young's modulus is 200 GPa. The factor of safety for the piston rod is

• A. 2.75
• B. 6.32
• C. 11.0
• D. 0.68

Answer 1

The correct option is B 6.32

Assuming guided end to be fixed and other end given as hinged. The crippling load according to Euler's equation.
$P_{cr}=\frac{2{\pi }^{2}EI}{L^2}$
$I=\frac{\pi }{64}(20{)}^4=7853.9m{m}^4$
$E=200\times {10}^{9}N/m^2=200\times {10}^{3}N/m{m}^2$
$=\frac{2{\pi }^2\times 200\times {10}^3\times 7853.9}{(700{)}^2}=63.27kN$

Factor of safety

$=\frac{Cripplingload}{Workingload}=\frac{63.27}{10}=6.32$