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 answer is "effective stress at point B is 7382 ksi "

Step-by-step explanation:

Calculating the value of Compressive Axial Stress:

`\to \sigma y =(F)/(A) = (4 F)/(( p d ^2 )) = ((4 x ( - 40000 \ lbf)))/([ p * (1 \ in)^2 ]) = - 50.9 \ ksi \\`

Calculating Shear Transverse:

`\to (4v)/( 3 A) = (4 (75 \ lbf + 25 \ lbf))/( (3 ( lni)^2)/(4))`

`= (4 (100 \ lbf))/( (3 ( lni)^2)/(4)) \\\\ = (400 \ lbf))/( (3 ( lni)^2)/(4)) \\\\= 0.17 \ ksi`

`= R * 200 \ in - P * 100 \ in = 12500 \ lbf *\ in`

`\to \sigma' =[ s y^2 +3( t * y^2 + t yz^2 )] * (1)/(2)\\\\`

`= [ (-50.9)^2 +3((63.7)^2 +(0.17)^2 )] * (1)/(2)\\\\=[2590.81+ 3(4057.69)+0.0289]* (1)/(2)\\\\=[2590.81+12,173.07+0.0289] * (1)/(2)\\\\=14763.9089* (1)/(2)\\\\ = 7381.95445 \ ksi\\\\ = 7382 \ ksi`