Question

A force Fof 40000 lbf is applied to rod AC
the negative Y-direction. The rod is 1000
inches tall. A Force P of 25 lbf is applied in the
negative Z- direction at point E, and a force R
of 75 ibf is applied in the negative Z-direction
at point F. Rod AC has a diameter of 1 inch
from A to ca diameter of 15 inches from 3
tic, and all fillet radii are 0.25 in. The rod is
made of 1020 CD steel, and has a Sy of 135
ksi, a Sur of 150 ksi, and an ef = 0.15.
Determine the effective stress at point B​

Answer 1

The effective stress at point B is 121.5 ksi

Explanation:

Axial Compressive stress

σ y  = F/A = 4 F/( p d ^2 ) = (4 x ( - 40000 lbf))/[ p  x (1 in) 2 ]

= - 50.9 ksi

Transverse shear = 4 v / 3 A = 4 (75 lbf + 25 lbf) / 3 ( lni)^2 / 4 = 0.17 ksi

= R x 200 in - P x 100 in = 12500 lbf x in

σ’ =[ s y2  +3( t xy2 + t yz2 )] 1/2

σ’ = [ (-50.9) 2 +3((63.7) 2 +(0.17) 2 )] 1/2

= 121.5 ksi