A steel cantilever member as shown in fig. is subjected to a transverse load at its end that varies from 50 N to 150 N down and the axial load varies from 150 N compression to 500 N in tension.

Determine the required diameter at the change of section for the infinite life using FOS=2.

For the material of cantilever $S_u=560 MPa$ and $S_y=480 MPa.$

FOS=2

$\sigma _u=560MPa=5600kgF/cm^2$

$\sigma _y=480 MPa$

$\sigma _{max}=\sigma _a+\sigma _b$

$=\frac{W}{A}+\frac{M}{Z}$

$\sigma _{max}=\frac{500}{\frac{\pi}{4}d^2}+\frac{150\times 125}{\frac{\pi}{32}d^3}$

$\sigma _{min}=-\sigma _a-\sigma _b$

$\sigma _{min}=\frac{-150}{\frac{\pi}{4}d^2}+\frac{-50\times 125}{\frac{\pi}{32}d^3}$

$\sigma _m=\frac{\sigma _{max}+\sigma _{min}}{2}$

$K_a=0.88$..........From graph(PSG 7.17)

Assume machined condition

Assume, d<50, from table,

$K_b=0.85$