The circular rod is subjected to 700KN tensile to 300KN compressive varying axial load. Find the diameter of the rod using Soderberg criteria and assuming following data. Endurance limit = 280Mpa, tensile yield strength = 350Mpa, factor of safety = 2, correction factor for loading = 0.7, surface factor = 0.8, size factor = 0.85, stress concentration factor = 1.

Subject: Machine Design -I

Topic: Basic properties of Machine design and theories of failure

Difficulty: High

Area =

$A=\frac{\pi}{4}*d^2=0.7854d^2 mm^2$

Mean or average load=

$W_m=\frac{W_max+W_min}{2}=500kN$

Mean stress=

$\sigma_m=\frac{W_m}{A}=\frac{636618.28}{d^2}N/mm^2$

Variable load=

$W_v=\frac{W_max-W_min}{2}=200kN$

Variable stress=

$\sigma_v=\frac{W_v}{A}=\frac{254647.31}{d^2} N/mm^2$

Endurance limit in reverse axial loading=

$\sigma_ea=\sigma_e*K_a=0.5\sigma_u*0.7=0.35\sigma_u$

$0.35*560=196 N/mm^2$

By Sodenberg's formula=

$\frac{1}{FS}=\frac{\sigma_m}{\sigma_y}+\frac{\sigma_v*K_f}{\sigma_ea*K_sur*K_sz}$

$\frac{1}{2}=$ $\frac{636618.28}{d^2*350}+\frac{254647.31*1}{d^2*196*0.8*0.85}=\frac{3729.51}{d^2}$

$d=86.36 \space \space or \space \space 88mm$