Question

A 20 mm diameter rod made of ductile material with a yield strength of 350 MN/m2 is subjected to a torque of 100 N.m, and a bending moment of 150 N.m. An axial tensile force is then gradually applied. What is the value of the axial force when yielding of the rod occurs using: a. The maximum-shear-stress theory b. The maximum-distortional-energy theory.

Answer 1

Answer:

a) 42.422 KN

b) 44.356 KN

Explanation:

Given data :

Diameter = 20 mm

yield strength = 350 MN/m^2

Torque ( T )  = 100 N.m

Bending moment = 150 N.m

Determine the value of the applied axial tensile force when yielding of rod occurs

first we will calculate the shear stress and normal stress

shear stress ( г ) = Tr / J = [( 100 * 10^3)  * 10 ]  /  $\pi /32$ * ( 20)^4  

                                       = 63.662 MPa

Normal stress(  Гb + Гa )  = MY/ I  +  P/A

= [( 150 * 10^3)  * 10 ]  /  $\pi /32$ * ( 20)^4   + 4P / $\pi * 20^2$

= 190.9859 + 4P / $\pi * 20^2$  MPa

a) Using MSS theory

value of axial force = 42.422 KN

solution attached below

b) Using MDE  theory

value of axial force = 44.356 KN

solution attached below